LMFDB - Embedded newform 84.9.l.b.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,9,Mod(67,84)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("84.67");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	84.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$34.2198032451$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.5
Character	$\chi$	$=$	84.67
Dual form			84.9.l.b.79.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.8009 + 6.07739i) q^{2} +(40.5000 + 23.3827i) q^{3} +(182.131 - 179.901i) q^{4} +(317.935 + 550.680i) q^{5} +(-741.540 - 99.9494i) q^{6} +(-968.291 + 2197.09i) q^{7} +(-1602.36 + 3769.57i) q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(-14.8009 + 6.07739i) q^{2} +(40.5000 + 23.3827i) q^{3} +(182.131 - 179.901i) q^{4} +(317.935 + 550.680i) q^{5} +(-741.540 - 99.9494i) q^{6} +(-968.291 + 2197.09i) q^{7} +(-1602.36 + 3769.57i) q^{8} +(1093.50 + 1894.00i) q^{9} +(-8052.41 - 6218.32i) q^{10} +(-15973.0 - 9222.04i) q^{11} +(11582.9 - 3027.29i) q^{12} +2631.91 q^{13} +(978.949 - 38403.5i) q^{14} +29736.7i q^{15} +(807.138 - 65531.0i) q^{16} +(-580.579 + 1005.59i) q^{17} +(-27695.3 - 21387.2i) q^{18} +(-43138.0 + 24905.7i) q^{19} +(156974. + 43098.8i) q^{20} +(-90589.7 + 66341.0i) q^{21} +(292461. + 39419.6i) q^{22} +(-426474. + 246225. i) q^{23} +(-153038. + 115200. i) q^{24} +(-6853.06 + 11869.8i) q^{25} +(-38954.5 + 15995.1i) q^{26} +102276. i q^{27} +(218904. + 574354. i) q^{28} +274933. q^{29} +(-180722. - 440129. i) q^{30} +(1.34087e6 + 774150. i) q^{31} +(386311. + 974821. i) q^{32} +(-431272. - 746985. i) q^{33} +(2481.69 - 18412.0i) q^{34} +(-1.51775e6 + 165314. i) q^{35} +(539892. + 148233. i) q^{36} +(-1.45635e6 - 2.52248e6i) q^{37} +(487118. - 630793. i) q^{38} +(106592. + 61541.1i) q^{39} +(-2.58527e6 + 316092. i) q^{40} -1.28629e6 q^{41} +(937625. - 1.53245e6i) q^{42} -1.94938e6i q^{43} +(-4.56823e6 + 1.19395e6i) q^{44} +(-695324. + 1.20434e6i) q^{45} +(4.81577e6 - 6.23618e6i) q^{46} +(-172631. + 99668.5i) q^{47} +(1.56498e6 - 2.63513e6i) q^{48} +(-3.88963e6 - 4.25485e6i) q^{49} +(29293.4 - 217333. i) q^{50} +(-47026.9 + 27151.0i) q^{51} +(479351. - 473484. i) q^{52} +(1.05362e6 - 1.82493e6i) q^{53} +(-621570. - 1.51377e6i) q^{54} -1.17280e7i q^{55} +(-6.73054e6 - 7.17057e6i) q^{56} -2.32945e6 q^{57} +(-4.06924e6 + 1.67087e6i) q^{58} +(-4.94634e6 - 2.85577e6i) q^{59} +(5.34967e6 + 5.41597e6i) q^{60} +(-2.39772e6 - 4.15296e6i) q^{61} +(-2.45508e7 - 3.30911e6i) q^{62} +(-5.22011e6 + 568579. i) q^{63} +(-1.16421e7 - 1.20804e7i) q^{64} +(836777. + 1.44934e6i) q^{65} +(1.09229e7 + 8.43501e6i) q^{66} +(-3.15865e7 - 1.82365e7i) q^{67} +(75166.1 + 287596. i) q^{68} -2.30296e7 q^{69} +(2.14593e7 - 1.16707e7i) q^{70} +3.65484e7i q^{71} +(-8.89174e6 + 1.08716e6i) q^{72} +(1.07300e7 - 1.85849e7i) q^{73} +(3.68854e7 + 2.84840e7i) q^{74} +(-555098. + 320486. i) q^{75} +(-3.37618e6 + 1.22967e7i) q^{76} +(3.57282e7 - 2.61646e7i) q^{77} +(-1.95167e6 - 263058. i) q^{78} +(-4.94567e7 + 2.85538e7i) q^{79} +(3.63432e7 - 2.03901e7i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(1.90382e7 - 7.81730e6i) q^{82} -8.09822e7i q^{83} +(-4.56434e6 + 2.83799e7i) q^{84} -738346. q^{85} +(1.18471e7 + 2.88525e7i) q^{86} +(1.11348e7 + 6.42866e6i) q^{87} +(6.03577e7 - 4.54345e7i) q^{88} +(2.73691e7 + 4.74047e7i) q^{89} +(2.97217e6 - 2.20510e7i) q^{90} +(-2.54845e6 + 5.78255e6i) q^{91} +(-3.33778e7 + 1.21568e8i) q^{92} +(3.62034e7 + 6.27062e7i) q^{93} +(1.94936e6 - 2.52432e6i) q^{94} +(-2.74302e7 - 1.58368e7i) q^{95} +(-7.14831e6 + 4.85132e7i) q^{96} +7.04047e7 q^{97} +(8.34282e7 + 3.93366e7i) q^{98} -4.03372e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 3 q^{2} + 2592 q^{3} - 93 q^{4} + 2256 q^{7} + 4500 q^{8} + 69984 q^{9}+O(q^{10}) $ 64 * q - 3 * q^2 + 2592 * q^3 - 93 * q^4 + 2256 * q^7 + 4500 * q^8 + 69984 * q^9	\( 64 q - 3 q^{2} + 2592 q^{3} - 93 q^{4} + 2256 q^{7} + 4500 q^{8} + 69984 q^{9} - 10335 q^{10} - 17040 q^{11} - 7533 q^{12} - 25696 q^{13} + 177402 q^{14} - 69049 q^{16} + 6561 q^{18} + 43056 q^{19} + 198564 q^{20} + 121824 q^{21} - 609694 q^{22} + 311769 q^{24} - 2659344 q^{25} - 36774 q^{26} - 546649 q^{28} + 2132352 q^{29} + 143289 q^{30} + 372336 q^{31} + 2856627 q^{32} - 460080 q^{33} + 1904308 q^{34} + 4556928 q^{35} - 406782 q^{36} - 1288016 q^{37} - 9363948 q^{38} - 1040688 q^{39} + 5606515 q^{40} + 3397056 q^{41} + 6988275 q^{42} - 26115 q^{44} - 1011480 q^{46} + 4538208 q^{47} - 4733640 q^{48} + 1891264 q^{49} - 6560430 q^{50} + 51739864 q^{52} + 6584736 q^{53} + 531441 q^{54} - 59028579 q^{56} + 2325024 q^{57} + 7804851 q^{58} + 1478544 q^{59} + 7776729 q^{60} + 8242048 q^{61} + 24347610 q^{62} + 4933872 q^{63} + 64036842 q^{64} + 9060000 q^{65} - 38899845 q^{66} + 60524688 q^{67} + 16861008 q^{68} + 163999149 q^{70} + 15411789 q^{72} + 733520 q^{73} + 56169900 q^{74} - 215406864 q^{75} - 57126708 q^{76} - 18996480 q^{77} - 7000830 q^{78} - 65450640 q^{79} + 96711867 q^{80} - 153055008 q^{81} + 27795688 q^{82} + 14330358 q^{84} + 102461312 q^{85} - 245748096 q^{86} + 86360256 q^{87} - 186227585 q^{88} - 31284288 q^{89} + 34209054 q^{90} - 106053648 q^{91} - 300155772 q^{92} + 10053072 q^{93} + 7117734 q^{94} - 116488896 q^{95} + 145538937 q^{96} + 143986208 q^{97} - 275744049 q^{98}+O(q^{100}) \) 64 * q - 3 * q^2 + 2592 * q^3 - 93 * q^4 + 2256 * q^7 + 4500 * q^8 + 69984 * q^9 - 10335 * q^10 - 17040 * q^11 - 7533 * q^12 - 25696 * q^13 + 177402 * q^14 - 69049 * q^16 + 6561 * q^18 + 43056 * q^19 + 198564 * q^20 + 121824 * q^21 - 609694 * q^22 + 311769 * q^24 - 2659344 * q^25 - 36774 * q^26 - 546649 * q^28 + 2132352 * q^29 + 143289 * q^30 + 372336 * q^31 + 2856627 * q^32 - 460080 * q^33 + 1904308 * q^34 + 4556928 * q^35 - 406782 * q^36 - 1288016 * q^37 - 9363948 * q^38 - 1040688 * q^39 + 5606515 * q^40 + 3397056 * q^41 + 6988275 * q^42 - 26115 * q^44 - 1011480 * q^46 + 4538208 * q^47 - 4733640 * q^48 + 1891264 * q^49 - 6560430 * q^50 + 51739864 * q^52 + 6584736 * q^53 + 531441 * q^54 - 59028579 * q^56 + 2325024 * q^57 + 7804851 * q^58 + 1478544 * q^59 + 7776729 * q^60 + 8242048 * q^61 + 24347610 * q^62 + 4933872 * q^63 + 64036842 * q^64 + 9060000 * q^65 - 38899845 * q^66 + 60524688 * q^67 + 16861008 * q^68 + 163999149 * q^70 + 15411789 * q^72 + 733520 * q^73 + 56169900 * q^74 - 215406864 * q^75 - 57126708 * q^76 - 18996480 * q^77 - 7000830 * q^78 - 65450640 * q^79 + 96711867 * q^80 - 153055008 * q^81 + 27795688 * q^82 + 14330358 * q^84 + 102461312 * q^85 - 245748096 * q^86 + 86360256 * q^87 - 186227585 * q^88 - 31284288 * q^89 + 34209054 * q^90 - 106053648 * q^91 - 300155772 * q^92 + 10053072 * q^93 + 7117734 * q^94 - 116488896 * q^95 + 145538937 * q^96 + 143986208 * q^97 - 275744049 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−14.8009	+	6.07739i	−0.925053	+	0.379837i
$2$	−14.8009	+	6.07739i	−0.925053	+	0.379837i
$3$	40.5000	+	23.3827i	0.500000	+	0.288675i
$3$	40.5000	+	23.3827i	0.500000	+	0.288675i
$4$	182.131	−	179.901i	0.711448	−	0.702739i
$5$	317.935	+	550.680i	0.508696	+	0.881088i	0.999949	+	0.0100709i	$0.00320572\pi$
$5$	317.935	+	550.680i	0.508696	+	0.881088i	−0.491253	+	0.871017i	$0.663461\pi$
$6$	−741.540	−	99.9494i	−0.572176	−	0.0771215i
$7$	−968.291	+	2197.09i	−0.403287	+	0.915074i
$7$	−968.291	+	2197.09i	−0.403287	+	0.915074i
$8$	−1602.36	+	3769.57i	−0.391201	+	0.920305i
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	−8052.41	−	6218.32i	−0.805241	−	0.621832i
$11$	−15973.0	−	9222.04i	−1.09098	−	0.629878i	−0.157143	−	0.987576i	$-0.550228\pi$
$11$	−15973.0	−	9222.04i	−1.09098	−	0.629878i	−0.933837	+	0.357698i	$0.883562\pi$
$12$	11582.9	−	3027.29i	0.558587	−	0.145992i
$13$	2631.91			0.0921505			0.0460752	−	0.998938i	$-0.485329\pi$
$13$	2631.91			0.0921505			0.0460752	+	0.998938i	$0.485329\pi$
$14$	978.949	−	38403.5i	0.0254829	−	0.999675i
$15$			29736.7i			0.587392i
$16$	807.138	−	65531.0i	0.0123159	−	0.999924i
$17$	−580.579	+	1005.59i	−0.00695130	+	0.0120400i	−0.869480	−	0.493968i	$-0.835546\pi$
$17$	−580.579	+	1005.59i	−0.00695130	+	0.0120400i	0.862529	+	0.506008i	$0.168879\pi$
$18$	−27695.3	−	21387.2i	−0.263825	−	0.203734i
$19$	−43138.0	+	24905.7i	−0.331014	+	0.191111i	−0.656291	−	0.754508i	$-0.727876\pi$
$19$	−43138.0	+	24905.7i	−0.331014	+	0.191111i	0.325277	+	0.945619i	$0.394542\pi$
$20$	156974.	+	43098.8i	0.981086	+	0.269367i
$21$	−90589.7	+	66341.0i	−0.465802	+	0.341118i
$22$	292461.	+	39419.6i	1.24847	+	0.168276i
$23$	−426474.	+	246225.i	−1.52399	+	0.879874i	−0.524389	+	0.851479i	$0.675706\pi$
$23$	−426474.	+	246225.i	−1.52399	+	0.879874i	−0.999597	+	0.0283947i	$0.990960\pi$
$24$	−153038.	+	115200.i	−0.461270	+	0.347223i
$25$	−6853.06	+	11869.8i	−0.0175438	+	0.0303868i
$26$	−38954.5	+	15995.1i	−0.0852441	+	0.0350022i
$27$			102276.i			0.192450i
$28$	218904.	+	574354.i	0.356141	+	0.934432i
$29$	274933.			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$29$	274933.			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$30$	−180722.	−	440129.i	−0.223113	−	0.543369i
$31$	1.34087e6	+	774150.i	1.45191	+	0.838259i	0.998590	−	0.0530893i	$-0.0169068\pi$
$31$	1.34087e6	+	774150.i	1.45191	+	0.838259i	0.453318	+	0.891349i	$0.350240\pi$
$32$	386311.	+	974821.i	0.368415	+	0.929661i
$33$	−431272.	−	746985.i	−0.363660	−	0.629878i
$34$	2481.69	−	18412.0i	0.00185708	−	0.0137780i
$35$	−1.51775e6	+	165314.i	−1.01141	+	0.110164i
$36$	539892.	+	148233.i	0.321438	+	0.0882541i
$37$	−1.45635e6	−	2.52248e6i	−0.777070	−	1.34593i	−0.933624	−	0.358256i	$-0.883372\pi$
$37$	−1.45635e6	−	2.52248e6i	−0.777070	−	1.34593i	0.156553	−	0.987670i	$-0.449962\pi$
$38$	487118.	−	630793.i	0.233614	−	0.302519i
$39$	106592.	+	61541.1i	0.0460752	+	0.0266015i
$40$	−2.58527e6	+	316092.i	−1.00987	+	0.123473i
$41$	−1.28629e6			−0.455202			−0.227601	−	0.973754i	$-0.573088\pi$
$41$	−1.28629e6			−0.455202			−0.227601	+	0.973754i	$0.573088\pi$
$42$	937625.	−	1.53245e6i	0.301323	−	0.492481i
$43$		−	1.94938e6i		−	0.570194i	−0.958499	−	0.285097i	$-0.907974\pi$
$43$		−	1.94938e6i		−	0.570194i	0.958499	−	0.285097i	$-0.0920258\pi$
$44$	−4.56823e6	+	1.19395e6i	−1.21881	+	0.318549i
$45$	−695324.	+	1.20434e6i	−0.169565	+	0.293696i
$46$	4.81577e6	−	6.23618e6i	1.07556	−	1.39280i
$47$	−172631.	+	99668.5i	−0.0353775	+	0.0204252i	−0.517584	−	0.855632i	$-0.673169\pi$
$47$	−172631.	+	99668.5i	−0.0353775	+	0.0204252i	0.482207	+	0.876057i	$0.339835\pi$
$48$	1.56498e6	−	2.63513e6i	0.294811	−	0.496407i
$49$	−3.88963e6	−	4.25485e6i	−0.674720	−	0.738074i
$50$	29293.4	−	217333.i	0.00468695	−	0.0347732i
$51$	−47026.9	+	27151.0i	−0.00695130	+	0.00401333i
$52$	479351.	−	473484.i	0.0655602	−	0.0647577i
$53$	1.05362e6	−	1.82493e6i	0.133531	−	0.231282i	−0.791504	−	0.611163i	$-0.790702\pi$
$53$	1.05362e6	−	1.82493e6i	0.133531	−	0.231282i	0.925035	+	0.379881i	$0.124035\pi$
$54$	−621570.	−	1.51377e6i	−0.0730997	−	0.178027i
$55$		−	1.17280e7i		−	1.28167i
$56$	−6.73054e6	−	7.17057e6i	−0.684381	−	0.729125i
$57$	−2.32945e6			−0.220676
$58$	−4.06924e6	+	1.67087e6i	−0.359585	+	0.147649i
$59$	−4.94634e6	−	2.85577e6i	−0.408203	−	0.235676i	0.281814	−	0.959469i	$-0.409064\pi$
$59$	−4.94634e6	−	2.85577e6i	−0.408203	−	0.235676i	−0.690017	+	0.723793i	$0.742397\pi$
$60$	5.34967e6	+	5.41597e6i	0.412783	+	0.417899i
$61$	−2.39772e6	−	4.15296e6i	−0.173172	−	0.299943i	0.766355	−	0.642417i	$-0.222068\pi$
$61$	−2.39772e6	−	4.15296e6i	−0.173172	−	0.299943i	−0.939527	+	0.342474i	$0.888735\pi$
$62$	−2.45508e7	−	3.30911e6i	−1.66149	−	0.223947i
$63$	−5.22011e6	+	568579.i	−0.331373	+	0.0360935i
$64$	−1.16421e7	−	1.20804e7i	−0.693923	−	0.720049i
$65$	836777.	+	1.44934e6i	0.0468766	+	0.0811927i
$66$	1.09229e7	+	8.43501e6i	0.575656	+	0.444539i
$67$	−3.15865e7	−	1.82365e7i	−1.56748	−	0.904985i	−0.996462	−	0.0840487i	$-0.973215\pi$
$67$	−3.15865e7	−	1.82365e7i	−1.56748	−	0.904985i	−0.571019	−	0.820937i	$-0.693452\pi$
$68$	75166.1	+	287596.i	0.00351549	+	0.0134508i
$69$	−2.30296e7			−1.01599
$70$	2.14593e7	−	1.16707e7i	0.893765	−	0.486078i
$71$			3.65484e7i			1.43825i	0.694880	+	0.719126i	$0.255458\pi$
$71$			3.65484e7i			1.43825i	−0.694880	+	0.719126i	$0.744542\pi$
$72$	−8.89174e6	+	1.08716e6i	−0.330869	+	0.0404542i
$73$	1.07300e7	−	1.85849e7i	0.377840	−	0.654438i	−0.612908	−	0.790155i	$-0.710000\pi$
$73$	1.07300e7	−	1.85849e7i	0.377840	−	0.654438i	0.990748	+	0.135716i	$0.0433335\pi$
$74$	3.68854e7	+	2.84840e7i	1.23006	+	0.949893i
$75$	−555098.	+	320486.i	−0.0175438	+	0.0101289i
$76$	−3.37618e6	+	1.22967e7i	−0.101198	+	0.368581i
$77$	3.57282e7	−	2.61646e7i	1.01636	−	0.744306i
$78$	−1.95167e6	−	263058.i	−0.0527263	−	0.00710678i
$79$	−4.94567e7	+	2.85538e7i	−1.26975	+	0.733088i	−0.974940	−	0.222470i	$-0.928588\pi$
$79$	−4.94567e7	+	2.85538e7i	−1.26975	+	0.733088i	−0.294805	+	0.955557i	$0.595255\pi$
$80$	3.63432e7	−	2.03901e7i	0.887286	−	0.497806i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	1.90382e7	−	7.81730e6i	0.421086	−	0.172903i
$83$		−	8.09822e7i		−	1.70639i	−0.521595	−	0.853193i	$-0.674663\pi$
$83$		−	8.09822e7i		−	1.70639i	0.521595	−	0.853193i	$-0.325337\pi$
$84$	−4.56434e6	+	2.83799e7i	−0.0916771	+	0.570025i
$85$	−738346.			−0.0141444
$86$	1.18471e7	+	2.88525e7i	0.216581	+	0.527460i
$87$	1.11348e7	+	6.42866e6i	0.194359	+	0.112213i
$88$	6.03577e7	−	4.54345e7i	1.00647	−	0.757626i
$89$	2.73691e7	+	4.74047e7i	0.436215	+	0.755546i	0.997394	−	0.0721481i	$-0.0229854\pi$
$89$	2.73691e7	+	4.74047e7i	0.436215	+	0.755546i	−0.561179	+	0.827694i	$0.689652\pi$
$90$	2.97217e6	−	2.20510e7i	0.0453005	−	0.336092i
$91$	−2.54845e6	+	5.78255e6i	−0.0371630	+	0.0843245i
$92$	−3.33778e7	+	1.21568e8i	−0.465915	+	1.69695i
$93$	3.62034e7	+	6.27062e7i	0.483969	+	0.838259i
$94$	1.94936e6	−	2.52432e6i	0.0249678	−	0.0323321i
$95$	−2.74302e7	−	1.58368e7i	−0.336771	−	0.194435i
$96$	−7.14831e6	+	4.85132e7i	−0.0841625	+	0.571183i
$97$	7.04047e7			0.795270			0.397635	−	0.917544i	$-0.369831\pi$
$97$	7.04047e7			0.795270			0.397635	+	0.917544i	$0.369831\pi$
$98$	8.34282e7	+	3.93366e7i	0.904500	+	0.426474i
$99$		−	4.03372e7i		−	0.419918i
$100$	887247.	+	3.39474e6i	0.00887247	+	0.0339474i
$101$	−6.10125e7	+	1.05677e8i	−0.586319	+	1.01553i	0.408391	+	0.912807i	$0.366090\pi$
$101$	−6.10125e7	+	1.05677e8i	−0.586319	+	1.01553i	−0.994710	+	0.102726i	$0.967243\pi$
$102$	531031.	−	687659.i	0.00490591	−	0.00635291i
$103$	6.69245e7	−	3.86388e7i	0.594615	−	0.343301i	−0.172305	−	0.985044i	$-0.555122\pi$
$103$	6.69245e7	−	3.86388e7i	0.594615	−	0.343301i	0.766920	+	0.641742i	$0.221788\pi$
$104$	−4.21727e6	+	9.92117e6i	−0.0360494	+	0.0848066i
$105$	−6.53343e7	−	2.87938e7i	−0.537507	−	0.236887i
$106$	−4.50371e6	+	3.34138e7i	−0.0356736	+	0.264668i
$107$	−1.14291e8	+	6.59857e7i	−0.871917	+	0.503402i	−0.867985	−	0.496591i	$-0.834585\pi$
$107$	−1.14291e8	+	6.59857e7i	−0.871917	+	0.503402i	−0.00393241	+	0.999992i	$0.501252\pi$
$108$	1.83995e7	+	1.86276e7i	0.135242	+	0.136918i
$109$	−4.63767e7	+	8.03268e7i	−0.328544	+	0.569055i	−0.982223	−	0.187717i	$-0.939891\pi$
$109$	−4.63767e7	+	8.03268e7i	−0.328544	+	0.569055i	0.653679	+	0.756772i	$0.273225\pi$
$110$	7.12759e7	+	1.73585e8i	0.486824	+	1.18561i
$111$		−	1.36214e8i		−	0.897283i
$112$	1.43196e8	+	6.52265e7i	0.910037	+	0.414526i
$113$	−2.27142e8			−1.39311			−0.696553	−	0.717505i	$-0.745284\pi$
$113$	−2.27142e8			−1.39311			−0.696553	+	0.717505i	$0.745284\pi$
$114$	3.44779e7	−	1.41570e7i	0.204137	−	0.0838208i
$115$	−2.71182e8	−	1.56567e8i	−1.55049	−	0.895177i
$116$	5.00737e7	−	4.94607e7i	0.276552	−	0.273167i
$117$	2.87799e6	+	4.98483e6i	0.0153584	+	0.0266015i
$118$	9.05657e7	+	1.22070e7i	0.467128	+	0.0629624i
$119$	−1.64721e6	−	2.24929e6i	−0.00821412	−	0.0112165i
$120$	−1.12095e8	−	4.76489e7i	−0.540580	−	0.229788i
$121$	6.29125e7	+	1.08968e8i	0.293491	+	0.508342i
$122$	6.07274e7	+	4.68956e7i	0.274123	+	0.211686i
$123$	−5.20949e7	−	3.00770e7i	−0.227601	−	0.131406i
$124$	3.83484e8	−	1.00227e8i	1.62203	−	0.423934i
$125$	2.39672e8			0.981695
$126$	7.38067e7	−	4.01401e7i	0.292829	−	0.159256i
$127$		−	3.92645e8i		−	1.50933i	−0.656108	−	0.754667i	$-0.727799\pi$
$127$		−	3.92645e8i		−	1.50933i	0.656108	−	0.754667i	$-0.272201\pi$
$128$	2.45730e8	+	1.08047e8i	0.915417	+	0.402506i
$129$	4.55817e7	−	7.89498e7i	0.164601	−	0.285097i
$130$	−2.11932e7	−	1.63660e7i	−0.0742033	−	0.0573021i
$131$	−2.91234e8	+	1.68144e8i	−0.988911	+	0.570948i	−0.904949	−	0.425521i	$-0.860091\pi$
$131$	−2.91234e8	+	1.68144e8i	−0.988911	+	0.570948i	−0.0839623	+	0.996469i	$0.526758\pi$
$132$	−2.12931e8	−	5.84625e7i	−0.701365	−	0.192567i
$133$	−1.29501e7	−	1.18894e8i	−0.0413871	−	0.379974i
$134$	5.78337e8	+	7.79519e7i	1.79375	+	0.241773i
$135$	−5.63213e7	+	3.25171e7i	−0.169565	+	0.0978986i
$136$	−2.86036e6	−	3.79986e6i	−0.00836112	−	0.0111074i
$137$	−4.80601e7	+	8.32426e7i	−0.136428	+	0.236300i	−0.926142	−	0.377175i	$-0.876895\pi$
$137$	−4.80601e7	+	8.32426e7i	−0.136428	+	0.236300i	0.789714	+	0.613475i	$0.210229\pi$
$138$	3.40857e8	−	1.39960e8i	0.939845	−	0.385911i
$139$		−	1.74146e7i		−	0.0466503i	−0.999728	−	0.0233252i	$-0.992575\pi$
$139$		−	1.74146e7i		−	0.0466503i	0.999728	−	0.0233252i	$-0.00742530\pi$
$140$	−2.46688e8	+	3.03153e8i	−0.642150	+	0.789133i
$141$	−9.32207e6			−0.0235850
$142$	−2.22119e8	−	5.40948e8i	−0.546301	−	1.33046i
$143$	−4.20396e7	−	2.42716e7i	−0.100534	−	0.0580435i
$144$	1.24998e8	−	7.01295e7i	0.290706	−	0.163099i
$145$	8.74108e7	+	1.51400e8i	0.197739	+	0.342494i
$146$	−4.58654e7	+	3.40283e8i	−0.100942	+	0.748908i
$147$	−5.80400e7	−	2.63271e8i	−0.124296	−	0.563812i
$148$	−7.19044e8	−	1.97421e8i	−1.49868	−	0.411478i
$149$	4.61606e7	+	7.99525e7i	0.0936540	+	0.162213i	0.909046	−	0.416696i	$-0.136812\pi$
$149$	4.61606e7	+	7.99525e7i	0.0936540	+	0.162213i	−0.815392	+	0.578909i	$0.803479\pi$
$150$	6.26820e6	−	8.11701e6i	0.0123816	−	0.0160336i
$151$	−1.03805e8	−	5.99320e7i	−0.199669	−	0.115279i	0.396832	−	0.917891i	$-0.370110\pi$
$151$	−1.03805e8	−	5.99320e7i	−0.199669	−	0.115279i	−0.596501	+	0.802612i	$0.703443\pi$
$152$	−2.47613e7	−	2.02520e8i	−0.0463874	−	0.379396i
$153$	−2.53945e6			−0.00463420
$154$	−3.69796e8	+	6.04393e8i	−0.657474	+	1.07457i
$155$			9.84518e8i			1.70568i
$156$	3.04850e7	−	7.96756e6i	0.0514741	−	0.0134532i
$157$	−3.92060e8	+	6.79068e8i	−0.645289	+	1.11767i	0.338946	+	0.940806i	$0.389930\pi$
$157$	−3.92060e8	+	6.79068e8i	−0.645289	+	1.11767i	−0.984235	+	0.176867i	$0.943404\pi$
$158$	5.58468e8	−	7.23189e8i	0.896128	−	1.16044i
$159$	8.53434e7	−	4.92730e7i	0.133531	−	0.0770940i
$160$	−4.13992e8	+	5.22664e8i	−0.631702	+	0.797521i
$161$	−1.28028e8	−	1.17542e9i	−0.190546	−	1.74940i
$162$	1.02224e7	−	7.58417e7i	0.0148420	−	0.110115i
$163$	5.48479e8	−	3.16665e8i	0.776980	−	0.448590i	−0.0583789	−	0.998294i	$-0.518593\pi$
$163$	5.48479e8	−	3.16665e8i	0.776980	−	0.448590i	0.835359	+	0.549705i	$0.185260\pi$
$164$	−2.34273e8	+	2.31406e8i	−0.323853	+	0.319888i
$165$	2.74233e8	−	4.74986e8i	0.369985	−	0.640833i
$166$	4.92161e8	+	1.19861e9i	0.648149	+	1.57850i
$167$			5.18122e8i			0.666141i	0.942902	+	0.333071i	$0.108085\pi$
$167$			5.18122e8i			0.666141i	−0.942902	+	0.333071i	$0.891915\pi$
$168$	−1.04920e8	−	4.47786e8i	−0.131710	−	0.562126i
$169$	−8.08804e8			−0.991508
$170$	1.09282e7	−	4.48722e6i	0.0130843	−	0.00537256i
$171$	−9.43428e7	−	5.44689e7i	−0.110338	−	0.0637036i
$172$	−3.50696e8	−	3.55042e8i	−0.400697	−	0.405663i
$173$	2.51234e8	+	4.35150e8i	0.280475	+	0.485796i	0.971502	−	0.237033i	$-0.0761748\pi$
$173$	2.51234e8	+	4.35150e8i	0.280475	+	0.485796i	−0.691027	+	0.722829i	$0.742841\pi$
$174$	−2.03874e8	−	2.74794e7i	−0.222415	−	0.0299785i
$175$	−1.94434e7	−	2.65503e7i	−0.0207310	−	0.0283085i
$176$	−6.17222e8	+	1.03929e9i	−0.643266	+	1.08314i
$177$	−1.33551e8	−	2.31317e8i	−0.136068	−	0.235676i
$178$	−6.93183e8	−	5.35297e8i	−0.690506	−	0.533230i
$179$	−8.02748e7	−	4.63467e7i	−0.0781928	−	0.0451447i	0.460394	−	0.887715i	$-0.347708\pi$
$179$	−8.02748e7	−	4.63467e7i	−0.0781928	−	0.0451447i	−0.538587	+	0.842570i	$0.681042\pi$
$180$	9.00218e7	+	3.44436e8i	0.0857546	+	0.328110i
$181$	1.62931e9			1.51806			0.759031	−	0.651055i	$-0.225673\pi$
$181$	1.62931e9			1.51806			0.759031	+	0.651055i	$0.225673\pi$
$182$	2.57651e6	−	1.01075e8i	0.00234826	−	0.0921205i
$183$		−	2.24260e8i		−	0.199962i
$184$	−2.44797e8	−	2.00216e9i	−0.213567	−	1.74674i
$185$	9.26053e8	−	1.60397e9i	0.790585	−	1.36933i
$186$	−9.16932e8	−	7.08083e8i	−0.766099	−	0.591605i
$187$	1.85472e7	−	1.07082e7i	0.0151675	−	0.00875693i
$188$	−1.35109e7	+	4.92092e7i	−0.0108157	+	0.0393926i
$189$	−2.24709e8	−	9.90328e7i	−0.176106	−	0.0776125i
$190$	5.02237e8	+	6.76946e7i	0.385384	+	0.0519445i
$191$	3.67907e8	−	2.12411e8i	0.276442	−	0.159604i	−0.355370	−	0.934726i	$-0.615645\pi$
$191$	3.67907e8	−	2.12411e8i	0.276442	−	0.159604i	0.631812	+	0.775122i	$0.282312\pi$
$192$	−1.89033e8	−	7.61480e8i	−0.139102	−	0.560343i
$193$	4.50563e7	−	7.80397e7i	0.0324733	−	0.0562453i	−0.849332	−	0.527859i	$-0.822995\pi$
$193$	4.50563e7	−	7.80397e7i	0.0324733	−	0.0562453i	0.881805	+	0.471614i	$0.156328\pi$
$194$	−1.04205e9	+	4.27877e8i	−0.735667	+	0.302073i
$195$			7.82643e7i			0.0541284i
$196$	−1.47387e9	−	7.51902e7i	−0.998701	−	0.0509492i
$197$	−1.38684e9			−0.920795			−0.460397	−	0.887713i	$-0.652293\pi$
$197$	−1.38684e9			−0.920795			−0.460397	+	0.887713i	$0.652293\pi$
$198$	2.45145e8	+	5.97025e8i	0.159501	+	0.388447i
$199$	1.62143e9	+	9.36131e8i	1.03392	+	0.596931i	0.918104	−	0.396340i	$-0.129720\pi$
$199$	1.62143e9	+	9.36131e8i	1.03392	+	0.596931i	0.115812	+	0.993271i	$0.463053\pi$
$200$	−3.37632e7	−	4.48529e7i	−0.0211020	−	0.0280330i
$201$	−8.52835e8	−	1.47715e9i	−0.522494	−	0.904985i
$202$	2.60798e8	−	1.93490e9i	0.156639	−	1.16213i
$203$	−2.66215e8	+	6.04052e8i	−0.156765	+	0.355705i
$204$	−3.68055e6	+	1.34052e7i	−0.00212516	+	0.00774022i
$205$	−4.08958e8	−	7.08336e8i	−0.231560	−	0.401073i
$206$	−7.55716e8	+	9.78614e8i	−0.419652	+	0.543429i
$207$	−9.32698e8	−	5.38493e8i	−0.507995	−	0.293291i
$208$	2.12431e6	−	1.72472e8i	0.00113492	−	0.0921435i
$209$	9.18727e8			0.481505
$210$	1.14199e9	+	2.91107e7i	0.587201	+	0.0149684i
$211$			3.15392e9i			1.59119i	0.605832	+	0.795593i	$0.292840\pi$
$211$			3.15392e9i			1.59119i	−0.605832	+	0.795593i	$0.707160\pi$
$212$	−1.36410e8	−	5.21923e8i	−0.0675308	−	0.258382i
$213$	−8.54600e8	+	1.48021e9i	−0.415188	+	0.719126i
$214$	1.29058e9	−	1.67123e9i	0.615360	−	0.796860i
$215$	1.07348e9	−	6.19776e8i	0.502391	−	0.290055i
$216$	−3.85536e8	−	1.63883e8i	−0.177113	−	0.0752867i
$217$	−2.99923e9	+	2.19641e9i	−1.35260	+	0.990544i
$218$	1.98237e8	−	1.47075e9i	0.0877727	−	0.651200i
$219$	8.69130e8	−	5.01792e8i	0.377840	−	0.218146i
$220$	−2.10989e9	−	2.13604e9i	−0.900676	−	0.911838i
$221$	−1.52803e6	+	2.64663e6i	−0.000640565	+	0.00110949i
$222$	8.27825e8	+	2.01608e9i	0.340821	+	0.830035i
$223$		−	3.39098e9i		−	1.37122i	−0.727971	−	0.685608i	$-0.759536\pi$
$223$		−	3.39098e9i		−	1.37122i	0.727971	−	0.685608i	$-0.240464\pi$
$224$	−2.51583e9	−	9.51485e7i	−0.999286	−	0.0377929i
$225$	−2.99753e7			−0.0116959
$226$	3.36190e9	−	1.38043e9i	1.28870	−	0.529153i
$227$	3.99291e9	+	2.30531e9i	1.50379	+	0.868212i	0.999990	+	0.00438983i	$0.00139733\pi$
$227$	3.99291e9	+	2.30531e9i	1.50379	+	0.868212i	0.503797	+	0.863822i	$0.331936\pi$
$228$	−4.24265e8	+	4.19071e8i	−0.156999	+	0.155077i
$229$	1.95437e9	+	3.38507e9i	0.710665	+	1.23091i	0.964608	+	0.263688i	$0.0849390\pi$
$229$	1.95437e9	+	3.38507e9i	0.710665	+	1.23091i	−0.253943	+	0.967219i	$0.581728\pi$
$230$	4.96524e9	+	6.69246e8i	1.77431	+	0.239152i
$231$	2.05879e9	−	2.24245e8i	0.723044	−	0.0787545i
$232$	−4.40541e8	+	1.03638e9i	−0.152067	+	0.357739i
$233$	1.51553e9	+	2.62497e9i	0.514210	+	0.890638i	0.999864	+	0.0164869i	$0.00524817\pi$
$233$	1.51553e9	+	2.62497e9i	0.514210	+	0.890638i	−0.485654	+	0.874151i	$0.661418\pi$
$234$	−7.28915e7	−	5.62891e7i	−0.0243116	−	0.0187742i
$235$	−1.09771e8	−	6.33763e7i	−0.0359928	−	0.0207805i
$236$	−1.41464e9	+	3.69729e8i	−0.456034	+	0.119189i
$237$	−2.67066e9			−0.846497
$238$	3.80500e7	+	2.32807e7i	0.0118590	+	0.00725585i
$239$			5.70835e9i			1.74952i	0.484556	+	0.874760i	$0.338981\pi$
$239$			5.70835e9i			1.74952i	−0.484556	+	0.874760i	$0.661019\pi$
$240$	1.94868e9	+	2.40016e7i	0.587347	+	0.00723429i
$241$	−5.01774e8	+	8.69098e8i	−0.148744	+	0.257633i	−0.930764	−	0.365622i	$-0.880856\pi$
$241$	−5.01774e8	+	8.69098e8i	−0.148744	+	0.257633i	0.782019	+	0.623254i	$0.214190\pi$
$242$	−1.59340e9	−	1.23047e9i	−0.464582	−	0.358765i
$243$	−1.93710e8	+	1.11839e8i	−0.0555556	+	0.0320750i
$244$	−1.18382e9	−	3.25030e8i	−0.333985	−	0.0916990i
$245$	1.10641e9	−	3.49470e9i	0.307080	−	0.969943i
$246$	9.53838e8	+	1.28564e8i	0.260456	+	0.0351059i
$247$	−1.13535e8	+	6.55497e7i	−0.0305031	+	0.0176109i
$248$	−5.06677e9	+	3.81403e9i	−1.33944	+	1.00827i
$249$	1.89358e9	−	3.27978e9i	0.492591	−	0.853193i
$250$	−3.54734e9	+	1.45658e9i	−0.908120	+	0.372884i
$251$		−	3.47424e9i		−	0.875316i	−0.899141	−	0.437658i	$-0.855808\pi$
$251$		−	3.47424e9i		−	0.875316i	0.899141	−	0.437658i	$-0.144192\pi$
$252$	−8.48454e8	+	1.04266e9i	−0.210391	+	0.258548i
$253$	9.08277e9			2.21685
$254$	2.38626e9	+	5.81148e9i	0.573301	+	1.39621i
$255$	−2.99030e7	−	1.72645e7i	−0.00707220	−	0.00408314i
$256$	−4.29366e9	−	1.05785e8i	−0.999697	−	0.0246300i
$257$	−2.78868e8	−	4.83013e8i	−0.0639243	−	0.110720i	0.832292	−	0.554337i	$-0.187028\pi$
$257$	−2.78868e8	−	4.83013e8i	−0.0639243	−	0.110720i	−0.896216	+	0.443617i	$0.853695\pi$
$258$	−1.94839e8	+	1.44554e9i	−0.0439742	+	0.326251i
$259$	6.95230e9	−	7.57250e8i	1.54500	−	0.168283i
$260$	4.13141e8	+	1.13432e8i	0.0904075	+	0.0248223i
$261$	3.00639e8	+	5.20722e8i	0.0647863	+	0.112213i
$262$	3.28864e9	−	4.25862e9i	0.697928	−	0.903782i
$263$	−1.33847e9	−	7.72768e8i	−0.279761	−	0.161520i	0.353554	−	0.935414i	$-0.384973\pi$
$263$	−1.33847e9	−	7.72768e8i	−0.279761	−	0.161520i	−0.633315	+	0.773894i	$0.718306\pi$
$264$	3.50687e9	−	4.28772e8i	0.721944	−	0.0882694i
$265$	1.33993e9			0.271707
$266$	9.14238e8	+	1.68103e9i	0.182614	+	0.335776i
$267$			2.55985e9i			0.503698i
$268$	−9.03363e9	+	2.36103e9i	−1.75115	+	0.457680i
$269$	−2.33450e9	+	4.04346e9i	−0.445845	+	0.772226i	−0.998111	−	0.0614420i	$-0.980430\pi$
$269$	−2.33450e9	+	4.04346e9i	−0.445845	+	0.772226i	0.552266	+	0.833668i	$0.313763\pi$
$270$	6.35984e8	−	8.23567e8i	0.119672	−	0.154969i
$271$	−2.54122e9	+	1.46718e9i	−0.471157	+	0.272023i	−0.716724	−	0.697357i	$-0.754359\pi$
$271$	−2.54122e9	+	1.46718e9i	−0.471157	+	0.272023i	0.245567	+	0.969380i	$0.421026\pi$
$272$	6.54289e7	+	3.88576e7i	0.0119535	+	0.00709905i
$273$	−2.38424e8	+	1.74603e8i	−0.0429239	+	0.0314342i
$274$	2.05433e8	−	1.52414e9i	0.0364476	−	0.270410i
$275$	2.18928e8	−	1.26398e8i	0.0382799	−	0.0221009i
$276$	−4.19439e9	+	4.14305e9i	−0.722824	+	0.713976i
$277$	8.90513e8	−	1.54241e9i	0.151259	−	0.261988i	−0.780432	−	0.625241i	$-0.785001\pi$
$277$	8.90513e8	−	1.54241e9i	0.151259	−	0.261988i	0.931691	+	0.363253i	$0.118334\pi$
$278$	1.05835e8	+	2.57751e8i	0.0177195	+	0.0431540i
$279$			3.38613e9i			0.558840i
$280$	1.80881e9	−	5.98615e9i	0.294281	−	0.973903i
$281$	−3.76968e9			−0.604615			−0.302308	−	0.953210i	$-0.597757\pi$
$281$	−3.76968e9			−0.604615			−0.302308	+	0.953210i	$0.597757\pi$
$282$	1.37975e8	−	5.66539e7i	0.0218174	−	0.00895846i
$283$	−4.98475e8	−	2.87794e8i	−0.0777136	−	0.0448680i	0.460640	−	0.887587i	$-0.347620\pi$
$283$	−4.98475e8	−	2.87794e8i	−0.0777136	−	0.0448680i	−0.538353	+	0.842719i	$0.680953\pi$
$284$	6.57510e9	+	6.65658e9i	1.01072	+	1.02324i
$285$	−7.40615e8	−	1.28278e9i	−0.112257	−	0.194435i
$286$	7.69730e8	+	1.03749e8i	0.115047	+	0.0155067i
$287$	1.24551e9	−	2.82610e9i	0.183577	−	0.416544i
$288$	−1.42388e9	+	1.79764e9i	−0.206968	+	0.261296i
$289$	3.48720e9	+	6.04002e9i	0.499903	+	0.865858i
$290$	−2.21387e9	−	1.70962e9i	−0.313011	−	0.241717i
$291$	2.85139e9	+	1.64625e9i	0.397635	+	0.229575i
$292$	−1.38918e9	−	5.31522e9i	−0.191086	−	0.731122i
$293$	−8.42327e9			−1.14291			−0.571453	−	0.820635i	$-0.693620\pi$
$293$	−8.42327e9			−1.14291			−0.571453	+	0.820635i	$0.693620\pi$
$294$	2.45904e9	+	3.54391e9i	0.329137	+	0.474344i
$295$		−	3.63180e9i		−	0.479550i
$296$	1.18423e10	−	1.44791e9i	1.54265	−	0.188615i
$297$	9.43192e8	−	1.63366e9i	0.121220	−	0.209959i
$298$	−1.16912e9	−	9.02829e8i	−0.148250	−	0.114483i
$299$	−1.12244e9	+	6.48041e8i	−0.140436	+	0.0810808i
$300$	−4.34445e7	+	1.58233e8i	−0.00536352	+	0.0195349i
$301$	4.28296e9	+	1.88757e9i	0.521769	+	0.229951i
$302$	1.90064e9	+	2.56180e8i	0.228492	+	0.0307976i
$303$	−4.94202e9	+	2.85327e9i	−0.586319	+	0.338511i
$304$	1.59728e9	+	2.84698e9i	0.187020	+	0.333342i
$305$	1.52464e9	−	2.64075e9i	0.176184	−	0.305160i
$306$	3.75861e7	−	1.54333e7i	0.00428688	−	0.00176024i
$307$			3.69646e9i			0.416134i	0.978115	+	0.208067i	$0.0667171\pi$
$307$			3.69646e9i			0.416134i	−0.978115	+	0.208067i	$0.933283\pi$
$308$	1.80016e9	−	1.11929e10i	0.200036	−	1.24377i
$309$	3.61392e9			0.396410
$310$	−5.98330e9	−	1.45717e10i	−0.647879	−	1.57784i
$311$	−1.32190e10	−	7.63199e9i	−1.41305	−	0.815823i	−0.417373	−	0.908735i	$-0.637049\pi$
$311$	−1.32190e10	−	7.63199e9i	−1.41305	−	0.815823i	−0.995674	+	0.0929122i	$0.970382\pi$
$312$	−4.02783e8	+	3.03196e8i	−0.0425062	+	0.0319967i
$313$	7.29755e9	+	1.26397e10i	0.760325	+	1.31692i	0.942683	+	0.333690i	$0.108294\pi$
$313$	7.29755e9	+	1.26397e10i	0.760325	+	1.31692i	−0.182357	+	0.983232i	$0.558373\pi$
$314$	1.67586e9	−	1.24335e10i	0.172393	−	1.27901i
$315$	−1.97276e9	−	2.69384e9i	−0.200370	−	0.273609i
$316$	−3.87071e9	+	1.40978e10i	−0.388188	+	1.41385i
$317$	−8.44458e9	−	1.46264e10i	−0.836259	−	1.44844i	−0.893001	−	0.450054i	$-0.851405\pi$
$317$	−8.44458e9	−	1.46264e10i	−0.836259	−	1.44844i	0.0567424	−	0.998389i	$-0.481929\pi$
$318$	−9.63704e8	+	1.24795e9i	−0.0942400	+	0.122036i
$319$	−4.39151e9	−	2.53544e9i	−0.424083	−	0.244845i
$320$	2.95101e9	−	1.02519e10i	0.281430	−	0.977694i
$321$	−6.17169e9			−0.581278
$322$	9.03840e9	+	1.66191e10i	0.840752	+	1.54591i
$323$		−	5.78390e7i		−	0.00531387i
$324$	3.09619e8	+	1.18465e9i	0.0280962	+	0.107500i
$325$	−1.80366e7	+	3.12404e7i	−0.00161667	+	0.00280016i
$326$	−6.19347e9	+	8.02023e9i	−0.548357	+	0.710095i
$327$	−3.75651e9	+	2.16882e9i	−0.328544	+	0.189685i
$328$	2.06110e9	−	4.84877e9i	0.178076	−	0.418925i
$329$	−5.18239e7	−	4.75794e8i	−0.00442330	−	0.0406102i
$330$	−1.17221e9	+	8.69682e9i	−0.0988439	+	0.733339i
$331$	−7.03363e9	+	4.06087e9i	−0.585960	+	0.338304i	−0.763498	−	0.645810i	$-0.776520\pi$
$331$	−7.03363e9	+	4.06087e9i	−0.585960	+	0.338304i	0.177539	+	0.984114i	$0.443187\pi$
$332$	−1.45688e10	−	1.47493e10i	−1.19914	−	1.21400i
$333$	3.18505e9	−	5.51666e9i	0.259023	−	0.448642i
$334$	−3.14883e9	−	7.66865e9i	−0.253025	−	0.616216i
$335$		−	2.31921e10i		−	1.84145i
$336$	4.27427e9	+	5.98998e9i	0.335355	+	0.469968i
$337$	−6.13235e8			−0.0475453			−0.0237726	−	0.999717i	$-0.507568\pi$
$337$	−6.13235e8			−0.0475453			−0.0237726	+	0.999717i	$0.507568\pi$
$338$	1.19710e10	−	4.91542e9i	0.917198	−	0.376611i
$339$	−9.19926e9	−	5.31120e9i	−0.696553	−	0.402155i
$340$	−1.34475e8	+	1.32829e8i	−0.0100630	+	0.00993982i
$341$	−1.42785e10	−	2.47311e10i	−1.05600	−	1.82905i
$342$	1.72738e9	+	2.32827e8i	0.126265	+	0.0170188i
$343$	1.31146e10	−	4.42593e9i	0.947498	−	0.319763i
$344$	7.34832e9	+	3.12361e9i	0.524752	+	0.223060i
$345$	−7.32191e9	−	1.26819e10i	−0.516831	−	0.895177i
$346$	−6.36305e9	−	4.91374e9i	−0.443978	−	0.342853i
$347$	−1.24787e10	−	7.20457e9i	−0.860698	−	0.496924i	0.00354792	−	0.999994i	$-0.498871\pi$
$347$	−1.24787e10	−	7.20457e9i	−0.860698	−	0.496924i	−0.864246	+	0.503069i	$0.832204\pi$
$348$	3.18451e9	−	8.32302e8i	0.217133	−	0.0567497i
$349$	−2.38225e10			−1.60578			−0.802889	−	0.596129i	$-0.796705\pi$
$349$	−2.38225e10			−1.60578			−0.802889	+	0.596129i	$0.796705\pi$
$350$	4.49135e8	+	2.74802e8i	0.0299299	+	0.0183125i
$351$			2.69181e8i			0.0177344i
$352$	2.81927e9	−	1.91334e10i	0.183639	−	1.24630i
$353$	−2.52553e9	+	4.37435e9i	−0.162650	+	0.281718i	−0.935818	−	0.352483i	$-0.885337\pi$
$353$	−2.52553e9	+	4.37435e9i	−0.162650	+	0.281718i	0.773168	+	0.634201i	$0.218671\pi$
$354$	3.38248e9	+	2.61205e9i	0.215388	+	0.166329i
$355$	−2.01265e10	+	1.16200e10i	−1.26723	+	0.731633i
$356$	1.35129e10	+	3.71011e9i	0.841296	+	0.230987i
$357$	−1.41175e7	−	1.29613e8i	−0.000869131	−	0.00797947i
$358$	1.46980e9	+	1.98109e8i	0.0894802	+	0.0120607i
$359$	1.83423e10	−	1.05899e10i	1.10427	−	0.637552i	0.166932	−	0.985968i	$-0.446614\pi$
$359$	1.83423e10	−	1.05899e10i	1.10427	−	0.637552i	0.937340	+	0.348417i	$0.113281\pi$
$360$	−3.42567e9	−	4.55085e9i	−0.203956	−	0.270946i
$361$	−7.25119e9	+	1.25594e10i	−0.426953	+	0.739505i
$362$	−2.41152e10	+	9.90195e9i	−1.40429	+	0.576616i
$363$			5.88425e9i			0.338895i
$364$	5.76135e8	+	1.51165e9i	0.0328185	+	0.0861084i
$365$	1.36458e10			0.768824
$366$	1.36292e9	+	3.31924e9i	0.0759530	+	0.184976i
$367$	−1.65172e10	−	9.53618e9i	−0.910481	−	0.525666i	−0.0298951	−	0.999553i	$-0.509517\pi$
$367$	−1.65172e10	−	9.53618e9i	−0.910481	−	0.525666i	−0.880586	+	0.473887i	$0.842851\pi$
$368$	1.57911e10	+	2.81460e10i	0.861037	+	1.53471i
$369$	−1.40656e9	−	2.43624e9i	−0.0758670	−	0.131406i
$370$	−3.95842e9	+	2.93681e10i	−0.211210	+	1.56700i
$371$	2.98932e9	+	4.08197e9i	0.157789	+	0.215464i
$372$	1.78747e10	+	4.90768e9i	0.933396	+	0.256274i
$373$	1.28258e10	+	2.22150e10i	0.662597	+	1.14765i	0.979931	+	0.199338i	$0.0638793\pi$
$373$	1.28258e10	+	2.22150e10i	0.662597	+	1.14765i	−0.317333	+	0.948314i	$0.602787\pi$
$374$	−2.09437e8	+	2.71210e8i	−0.0107045	+	0.0138618i
$375$	9.70670e9	+	5.60416e9i	0.490847	+	0.283391i
$376$	−9.90907e7	−	8.10449e8i	−0.00495771	−	0.0405485i
$377$	7.23598e8			0.0358205
$378$	3.92775e9	+	1.00123e8i	0.192388	+	0.00490418i
$379$			1.63650e10i			0.793159i	0.918000	+	0.396579i	$0.129803\pi$
$379$			1.63650e10i			0.793159i	−0.918000	+	0.396579i	$0.870197\pi$
$380$	−7.84494e9	+	2.05035e9i	−0.376232	+	0.0983318i
$381$	9.18110e9	−	1.59021e10i	0.435707	−	0.754667i
$382$	−4.15443e9	+	5.37978e9i	−0.195100	+	0.252645i
$383$	−3.47852e9	+	2.00832e9i	−0.161659	+	0.0933337i	−0.578647	−	0.815578i	$-0.696419\pi$
$383$	−3.47852e9	+	2.00832e9i	−0.161659	+	0.0933337i	0.416988	+	0.908912i	$0.363086\pi$
$384$	7.42566e9	+	1.01217e10i	0.341515	+	0.465511i
$385$	2.57676e10	+	1.13562e10i	1.17282	+	0.516879i
$386$	−1.92593e8	+	1.42888e9i	−0.00867545	+	0.0643645i
$387$	3.69212e9	−	2.13165e9i	0.164601	−	0.0950323i
$388$	1.28229e10	−	1.26659e10i	0.565793	−	0.558867i
$389$	−1.90009e9	+	3.29105e9i	−0.0829805	+	0.143726i	−0.904529	−	0.426412i	$-0.859777\pi$
$389$	−1.90009e9	+	3.29105e9i	−0.0829805	+	0.143726i	0.821548	+	0.570139i	$0.193111\pi$
$390$	−4.75643e8	−	1.15838e9i	−0.0205600	−	0.0500717i
$391$		−	5.71812e8i		−	0.0244651i
$392$	2.22715e10	−	7.84442e9i	0.943204	−	0.332213i
$393$	−1.57266e10			−0.659274
$394$	2.05265e10	−	8.42839e9i	0.851784	−	0.349752i
$395$	−3.14480e10	−	1.81565e10i	−1.29183	−	0.745838i
$396$	−7.25671e9	−	7.34664e9i	−0.295093	−	0.298750i
$397$	9.40632e9	+	1.62922e10i	0.378667	+	0.655871i	0.990869	−	0.134831i	$-0.0430492\pi$
$397$	9.40632e9	+	1.62922e10i	0.378667	+	0.655871i	−0.612201	+	0.790702i	$0.709716\pi$
$398$	−2.96877e10	−	4.00150e9i	−1.18316	−	0.159474i
$399$	2.25559e9	−	5.11802e9i	0.0889955	−	0.201935i
$400$	7.72312e8	+	4.58669e8i	0.0301684	+	0.0179167i
$401$	1.20060e10	+	2.07951e10i	0.464326	+	0.804235i	0.999171	−	0.0407146i	$-0.0129634\pi$
$401$	1.20060e10	+	2.07951e10i	0.464326	+	0.804235i	−0.534845	+	0.844950i	$0.679630\pi$
$402$	2.15999e10	+	1.66801e10i	0.827081	+	0.638698i
$403$	3.52904e9	+	2.03749e9i	0.133794	+	0.0772460i
$404$	7.89913e9	+	3.02232e10i	0.296520	+	1.13453i
$405$	−3.04135e9			−0.113044
$406$	2.69145e8	−	1.05584e10i	0.00990563	−	0.388591i
$407$			5.37222e10i			1.95784i
$408$	−2.69936e7	−	2.20777e8i	−0.000974137	−	0.00796734i
$409$	−1.33362e10	+	2.30990e10i	−0.476583	+	0.825466i	−0.999640	−	0.0268316i	$-0.991458\pi$
$409$	−1.33362e10	+	2.30990e10i	−0.476583	+	0.825466i	0.523057	+	0.852298i	$0.324792\pi$
$410$	1.03578e10	+	7.99858e9i	0.366547	+	0.283059i
$411$	−3.89287e9	+	2.24755e9i	−0.136428	+	0.0787666i
$412$	5.23782e9	−	1.90771e10i	0.181786	−	0.662100i
$413$	1.10639e10	−	8.10235e9i	0.380284	−	0.278491i
$414$	1.70774e10	+	2.30179e9i	0.581326	+	0.0783547i
$415$	4.45953e10	−	2.57471e10i	1.50348	−	0.868032i
$416$	1.01674e9	+	2.56564e9i	0.0339496	+	0.0856687i
$417$	4.07200e8	−	7.05292e8i	0.0134668	−	0.0233252i
$418$	−1.35979e10	+	5.58346e9i	−0.445418	+	0.182894i
$419$		−	1.36118e10i		−	0.441630i	−0.975316	−	0.220815i	$-0.929128\pi$
$419$		−	1.36118e10i		−	0.441630i	0.975316	−	0.220815i	$-0.0708716\pi$
$420$	−1.70794e10	+	6.50948e9i	−0.548878	+	0.209194i
$421$	5.38313e9			0.171359			0.0856794	−	0.996323i	$-0.472694\pi$
$421$	5.38313e9			0.171359			0.0856794	+	0.996323i	$0.472694\pi$
$422$	−1.91676e10	−	4.66807e10i	−0.604391	−	1.47193i
$423$	−3.77544e8	−	2.17975e8i	−0.0117925	−	0.00680840i
$424$	5.19091e9	+	6.89589e9i	0.160613	+	0.213367i
$425$	−7.95749e6	−	1.37828e7i	−0.000243905	−	0.000422456i
$426$	3.65299e9	−	2.71021e10i	0.110920	−	0.822934i
$427$	1.14461e10	−	1.24672e9i	0.344308	−	0.0375023i
$428$	−8.94491e9	+	3.25790e10i	−0.266564	+	0.970874i
$429$	−1.13507e9	−	1.96600e9i	−0.0335114	−	0.0580435i
$430$	−1.21219e10	+	1.56972e10i	−0.354565	+	0.459143i
$431$	−3.07045e10	−	1.77272e10i	−0.889800	−	0.513726i	−0.0159228	−	0.999873i	$-0.505069\pi$
$431$	−3.07045e10	−	1.77272e10i	−0.889800	−	0.513726i	−0.873877	+	0.486147i	$0.838402\pi$
$432$	6.70224e9	+	8.25507e7i	0.192435	+	0.00237020i
$433$	1.30571e10			0.371444			0.185722	−	0.982602i	$-0.440538\pi$
$433$	1.30571e10			0.371444			0.185722	+	0.982602i	$0.440538\pi$
$434$	3.10427e10	−	5.07362e10i	0.874986	−	1.43008i
$435$			8.17559e9i			0.228330i
$436$	6.00427e9	+	2.29732e10i	0.166155	+	0.635734i
$437$	1.22648e10	−	2.12433e10i	0.336307	−	0.582500i
$438$	−9.81427e9	+	1.27090e10i	−0.266662	+	0.345314i
$439$	−2.20705e10	+	1.27424e10i	−0.594229	+	0.343078i	−0.766768	−	0.641925i	$-0.778136\pi$
$439$	−2.20705e10	+	1.27424e10i	−0.594229	+	0.343078i	0.172539	+	0.985003i	$0.444803\pi$
$440$	4.42097e10	+	1.87925e10i	1.17952	+	0.501389i
$441$	3.80537e9	−	1.20196e10i	0.100610	−	0.317787i
$442$	6.53158e6	−	4.84588e7i	0.000171131	−	0.00126965i
$443$	1.08507e10	−	6.26466e9i	0.281737	−	0.162661i	−0.352473	−	0.935822i	$-0.614659\pi$
$443$	1.08507e10	−	6.26466e9i	0.281737	−	0.162661i	0.634209	+	0.773161i	$0.281326\pi$
$444$	−2.45050e10	−	2.48087e10i	−0.630556	−	0.638370i
$445$	−1.74032e10	+	3.01432e10i	−0.443802	+	0.768687i
$446$	2.06083e10	+	5.01894e10i	0.520838	+	1.26845i
$447$			4.31743e9i			0.108142i
$448$	3.78147e10	−	1.38814e10i	0.938748	−	0.344605i
$449$	4.39582e10			1.08157			0.540785	−	0.841161i	$-0.318127\pi$
$449$	4.39582e10			1.08157			0.540785	+	0.841161i	$0.318127\pi$
$450$	4.43660e8	−	1.82172e8i	0.0108193	−	0.00444253i
$451$	2.05460e10	+	1.18622e10i	0.496616	+	0.286722i
$452$	−4.13696e10	+	4.08632e10i	−0.991122	+	0.978990i
$453$	−2.80274e9	−	4.85449e9i	−0.0665565	−	0.115279i
$454$	−7.31088e10	−	9.85406e9i	−1.72086	−	0.231949i
$455$	−3.99458e9	+	4.35093e8i	−0.0932020	+	0.0101516i
$456$	3.73262e9	−	8.78104e9i	0.0863286	−	0.203089i
$457$	−1.07316e10	−	1.85877e10i	−0.246036	−	0.426148i	0.716386	−	0.697704i	$-0.245795\pi$
$457$	−1.07316e10	−	1.85877e10i	−0.246036	−	0.426148i	−0.962422	+	0.271557i	$0.912462\pi$
$458$	−4.94987e10	−	3.82244e10i	−1.12495	−	0.868718i
$459$	−1.02848e8	−	5.93793e7i	−0.00231710	−	0.00133778i
$460$	−7.75571e10	+	2.02703e10i	−1.73217	+	0.452719i
$461$	−3.34964e10			−0.741642			−0.370821	−	0.928704i	$-0.620924\pi$
$461$	−3.34964e10			−0.741642			−0.370821	+	0.928704i	$0.620924\pi$
$462$	−2.91091e10	+	1.58311e10i	−0.638940	+	0.347491i
$463$		−	4.61955e10i		−	1.00525i	−0.864503	−	0.502627i	$-0.832367\pi$
$463$		−	4.61955e10i		−	1.00525i	0.864503	−	0.502627i	$-0.167633\pi$
$464$	2.21909e8	−	1.80166e10i	0.00478743	−	0.388688i
$465$	−2.30207e10	+	3.98730e10i	−0.492387	+	0.852839i
$466$	−3.83841e10	−	2.96414e10i	−0.813969	−	0.628572i
$467$	6.60466e10	−	3.81320e10i	1.38862	−	0.801719i	0.395459	−	0.918484i	$-0.370586\pi$
$467$	6.60466e10	−	3.81320e10i	1.38862	−	0.801719i	0.993160	+	0.116764i	$0.0372522\pi$
$468$	1.42095e9	+	3.90136e8i	0.0296207	+	0.00813266i
$469$	7.06521e10	−	5.17402e10i	1.46027	−	1.06939i
$470$	2.00987e9	+	2.70902e8i	0.0411885	+	0.00555164i
$471$	−3.17569e10	+	1.83348e10i	−0.645289	+	0.372558i
$472$	1.86908e10	−	1.40696e10i	0.376583	−	0.283474i
$473$	−1.79772e10	+	3.11375e10i	−0.359152	+	0.622070i
$474$	3.95281e10	−	1.62306e10i	0.783055	−	0.321531i
$475$		−	6.82722e8i		−	0.0134113i
$476$	−7.04658e8	−	1.13330e8i	−0.0137262	−	0.00220758i
$477$	4.60854e9			0.0890205
$478$	−3.46919e10	−	8.44885e10i	−0.664532	−	1.61840i
$479$	7.92686e10	+	4.57657e10i	1.50577	+	0.869358i	0.999978	+	0.00670332i	$0.00213375\pi$
$479$	7.92686e10	+	4.57657e10i	1.50577	+	0.869358i	0.505794	+	0.862654i	$0.331200\pi$
$480$	−2.89880e10	+	1.14876e10i	−0.546076	+	0.216404i
$481$	−3.83299e9	−	6.63894e9i	−0.0716074	−	0.124028i
$482$	2.14484e9	−	1.59129e10i	0.0397380	−	0.294822i
$483$	2.22993e10	−	5.05981e10i	0.409735	−	0.929706i
$484$	3.10617e10	+	8.52831e9i	0.566036	+	0.155411i
$485$	2.23841e10	+	3.87705e10i	0.404551	+	0.700703i
$486$	2.18739e9	−	2.83256e9i	0.0392086	−	0.0507732i
$487$	2.57998e10	+	1.48955e10i	0.458671	+	0.264814i	0.711485	−	0.702701i	$-0.248023\pi$
$487$	2.57998e10	+	1.48955e10i	0.458671	+	0.264814i	−0.252814	+	0.967515i	$0.581356\pi$
$488$	1.94969e10	−	2.38381e9i	0.343784	−	0.0420333i
$489$	2.96179e10			0.517987
$490$	4.86286e9	+	5.84487e10i	0.0843543	+	1.01389i
$491$			7.84200e10i			1.34928i	0.738149	+	0.674638i	$0.235700\pi$
$491$			7.84200e10i			1.34928i	−0.738149	+	0.674638i	$0.764300\pi$
$492$	−1.48990e10	+	3.89399e9i	−0.254270	+	0.0664560i
$493$	−1.59620e8	+	2.76470e8i	−0.00270209	+	0.00468016i
$494$	1.28205e9	−	1.66019e9i	0.0215277	−	0.0278773i
$495$	2.22129e10	−	1.28246e10i	0.369985	−	0.213611i
$496$	5.18131e10	−	8.72436e10i	0.856078	−	1.44147i
$497$	−8.03002e10	−	3.53895e10i	−1.31611	−	0.580028i
$498$	−8.09413e9	+	6.00516e10i	−0.131599	+	0.976354i
$499$	8.33053e10	−	4.80963e10i	1.34360	−	0.775729i	0.356268	−	0.934384i	$-0.384049\pi$
$499$	8.33053e10	−	4.80963e10i	1.34360	−	0.775729i	0.987334	+	0.158655i	$0.0507158\pi$
$500$	4.36515e10	−	4.31172e10i	0.698424	−	0.689875i
$501$	−1.21151e10	+	2.09839e10i	−0.192298	+	0.333071i
$502$	2.11143e10	+	5.14217e10i	0.332477	+	0.809714i
$503$			1.23672e11i			1.93197i	0.258600	+	0.965985i	$0.416739\pi$
$503$			1.23672e11i			1.93197i	−0.258600	+	0.965985i	$0.583261\pi$
$504$	6.22120e9	−	2.05887e10i	0.0964166	−	0.319085i
$505$	−7.75921e10			−1.19303
$506$	−1.34433e11	+	5.51996e10i	−2.05071	+	0.842042i
$507$	−3.27566e10	−	1.89120e10i	−0.495754	−	0.286224i
$508$	−7.06373e10	−	7.15127e10i	−1.06067	−	1.07381i
$509$	−4.94959e10	−	8.57295e10i	−0.737392	−	1.27720i	−0.953666	−	0.300868i	$-0.902724\pi$
$509$	−4.94959e10	−	8.57295e10i	−0.737392	−	1.27720i	0.216274	−	0.976333i	$-0.430610\pi$
$510$	5.47514e8	+	7.37973e7i	0.00809309	+	0.00109084i
$511$	3.04430e10	+	4.15704e10i	0.446481	+	0.609678i
$512$	6.41928e10	−	2.45286e10i	0.934128	−	0.356938i
$513$	−2.54726e9	−	4.41198e9i	−0.0367793	−	0.0637036i
$514$	7.06294e9	+	5.45422e9i	0.101189	+	0.0781412i
$515$	4.25553e10	+	2.45693e10i	0.604957	+	0.349272i
$516$	−5.90134e9	−	2.25794e10i	−0.0832438	−	0.318503i
$517$	3.67659e9			0.0514615
$518$	−9.82978e10	+	5.34598e10i	−1.36529	+	0.742520i
$519$			2.34981e10i			0.323864i
$520$	−6.80420e9	+	8.31925e8i	−0.0930602	+	0.0113781i
$521$	−2.28617e10	+	3.95976e10i	−0.310283	+	0.537425i	−0.978423	−	0.206609i	$-0.933757\pi$
$521$	−2.28617e10	+	3.95976e10i	−0.310283	+	0.537425i	0.668141	+	0.744035i	$0.267090\pi$
$522$	−7.61434e9	−	5.88003e9i	−0.102553	−	0.0791949i
$523$	−1.22733e11	+	7.08598e10i	−1.64042	+	0.947094i	−0.659730	+	0.751503i	$0.729329\pi$
$523$	−1.22733e11	+	7.08598e10i	−1.64042	+	0.947094i	−0.980685	+	0.195592i	$0.937337\pi$
$524$	−2.27933e10	+	8.30176e10i	−0.302331	+	1.10115i
$525$	−1.66641e8	−	1.52992e9i	−0.00219353	−	0.0201388i
$526$	2.45070e10	+	3.30320e9i	0.320145	+	0.0431511i
$527$	−1.55696e9	+	8.98911e8i	−0.0201853	+	0.0116540i
$528$	−4.92988e10	+	2.76588e10i	−0.634309	+	0.355875i
$529$	8.20977e10	−	1.42197e11i	1.04835	−	1.81580i
$530$	−1.98322e10	+	8.14331e9i	−0.251343	+	0.103204i
$531$		−	1.24911e10i		−	0.157117i
$532$	−2.37478e10	−	1.93245e10i	−0.296467	−	0.241247i
$533$	−3.38541e9			−0.0419471
$534$	−1.55572e10	−	3.78880e10i	−0.191323	−	0.465947i
$535$	−7.26740e10	−	4.19583e10i	−0.887082	−	0.512157i
$536$	1.19357e11	−	8.98461e10i	1.44606	−	1.08853i
$537$	−2.16742e9	−	3.75408e9i	−0.0260643	−	0.0451447i
$538$	9.97881e9	−	7.40344e10i	0.119110	−	0.883699i
$539$	2.28908e10	+	1.03833e11i	0.271210	+	1.23021i
$540$	−4.40796e9	+	1.60546e10i	−0.0518398	+	0.188810i
$541$	4.87715e10	+	8.44748e10i	0.569347	+	0.986138i	0.996631	+	0.0820207i	$0.0261373\pi$
$541$	4.87715e10	+	8.44748e10i	0.569347	+	0.986138i	−0.427283	+	0.904118i	$0.640529\pi$
$542$	2.86957e10	−	3.71595e10i	0.332521	−	0.430599i
$543$	6.59870e10	+	3.80976e10i	0.759031	+	0.438227i
$544$	−1.20456e9	−	1.77489e8i	−0.0137541	−	0.00202663i
$545$	−5.89791e10			−0.668517
$546$	2.46774e9	−	4.03328e9i	0.0277670	−	0.0453824i
$547$			3.01422e9i			0.0336686i	0.999858	+	0.0168343i	$0.00535878\pi$
$547$			3.01422e9i			0.0336686i	−0.999858	+	0.0168343i	$0.994641\pi$
$548$	6.22222e9	+	2.38071e10i	0.0689958	+	0.263988i
$549$	5.24380e9	−	9.08253e9i	0.0577241	−	0.0999810i
$550$	−2.47215e9	+	3.20132e9i	−0.0270162	+	0.0349847i
$551$	−1.18600e10	+	6.84740e9i	−0.128671	+	0.0742881i
$552$	3.69017e10	−	8.68116e10i	0.397457	−	0.935021i
$553$	−1.48469e10	−	1.36309e11i	−0.158758	−	1.45755i
$554$	−3.80650e9	+	2.82410e10i	−0.0404098	+	0.299807i
$555$	7.50103e10	−	4.33072e10i	0.790585	−	0.456445i
$556$	−3.13291e9	−	3.17173e9i	−0.0327830	−	0.0331893i
$557$	7.90127e10	−	1.36854e11i	0.820873	−	1.42179i	−0.0841596	−	0.996452i	$-0.526821\pi$
$557$	7.90127e10	−	1.36854e11i	0.820873	−	1.42179i	0.905033	−	0.425342i	$-0.139846\pi$
$558$	−2.05789e10	−	5.01177e10i	−0.212268	−	0.516957i
$559$		−	5.13059e9i		−	0.0525436i
$560$	9.60819e9	+	9.95930e10i	0.0976989	+	1.01269i
$561$	1.00155e9			0.0101116
$562$	5.57945e10	−	2.29098e10i	0.559301	−	0.229655i
$563$	−1.34076e11	−	7.74087e10i	−1.33450	−	0.770471i	−0.348510	−	0.937305i	$-0.613312\pi$
$563$	−1.34076e11	−	7.74087e10i	−1.33450	−	0.770471i	−0.985985	+	0.166834i	$0.946646\pi$
$564$	−1.69783e9	+	1.67705e9i	−0.0167795	+	0.0165741i
$565$	−7.22165e10	−	1.25083e11i	−0.708668	−	1.22745i
$566$	9.12689e9	+	1.23018e9i	0.0889318	+	0.0119868i
$567$	−6.78508e9	−	9.26514e9i	−0.0656482	−	0.0896437i
$568$	−1.37772e11	−	5.85637e10i	−1.32363	−	0.562646i
$569$	5.16525e10	+	8.94648e10i	0.492768	+	0.853499i	0.999965	−	0.00833088i	$-0.00265183\pi$
$569$	5.16525e10	+	8.94648e10i	0.492768	+	0.853499i	−0.507197	+	0.861830i	$0.669318\pi$
$570$	1.87577e10	+	1.44853e10i	0.177697	+	0.137223i
$571$	1.03131e9	+	5.95428e8i	0.00970165	+	0.00560125i	0.504843	−	0.863211i	$-0.331550\pi$
$571$	1.03131e9	+	5.95428e8i	0.00970165	+	0.00560125i	−0.495141	+	0.868812i	$0.664884\pi$
$572$	−1.20232e10	+	3.14238e9i	−0.112314	+	0.0293544i
$573$	1.98670e10			0.184295
$574$	−1.25922e9	+	4.93982e10i	−0.0115999	+	0.455054i
$575$		−	6.74957e9i		−	0.0617454i
$576$	1.01496e10	−	3.52600e10i	0.0922063	−	0.320327i
$577$	−7.00546e10	+	1.21338e11i	−0.632023	+	1.09470i	0.355114	+	0.934823i	$0.384442\pi$
$577$	−7.00546e10	+	1.21338e11i	−0.632023	+	1.09470i	−0.987137	+	0.159874i	$0.948891\pi$
$578$	−8.83211e10	−	6.82043e10i	−0.791322	−	0.611083i
$579$	3.64956e9	−	2.10707e9i	0.0324733	−	0.0187484i
$580$	4.31572e10	+	1.18493e10i	0.381365	+	0.104708i
$581$	1.77925e11	+	7.84144e10i	1.56147	+	0.688163i
$582$	−5.22079e10	−	7.03691e9i	−0.455035	−	0.0613324i
$583$	−3.36591e10	+	1.94331e10i	−0.291359	+	0.168216i
$584$	5.28638e10	+	7.02272e10i	0.454472	+	0.603745i
$585$	−1.83003e9	+	3.16971e9i	−0.0156255	+	0.0270642i
$586$	1.24672e11	−	5.11915e10i	1.05725	−	0.434118i
$587$		−	7.30161e10i		−	0.614987i	−0.951550	−	0.307494i	$-0.900510\pi$
$587$		−	7.30161e10i		−	0.614987i	0.951550	−	0.307494i	$-0.0994903\pi$
$588$	−5.79337e10	−	3.75083e10i	−0.484643	−	0.313775i
$589$	−7.71231e10			−0.640802
$590$	2.20719e10	+	5.37537e10i	0.182151	+	0.443609i
$591$	−5.61672e10	−	3.24281e10i	−0.460397	−	0.265811i
$592$	−1.66476e11	+	9.34004e10i	−1.35539	+	0.760435i
$593$	9.22851e10	+	1.59843e11i	0.746299	+	1.29263i	0.949585	+	0.313509i	$0.101504\pi$
$593$	9.22851e10	+	1.59843e11i	0.746299	+	1.29263i	−0.203286	+	0.979119i	$0.565162\pi$
$594$	−4.03168e9	+	2.99117e10i	−0.0323847	+	0.240267i
$595$	7.14934e8	−	1.62221e9i	0.00570425	−	0.0129432i
$596$	2.27908e10	+	6.25745e9i	0.180624	+	0.0495921i
$597$	4.37785e10	+	7.58266e10i	0.344638	+	0.596931i
$598$	1.26747e10	−	1.64131e10i	0.0991133	−	0.128347i
$599$	−6.76518e10	−	3.90588e10i	−0.525499	−	0.303397i	0.213683	−	0.976903i	$-0.431454\pi$
$599$	−6.76518e10	−	3.90588e10i	−0.525499	−	0.303397i	−0.739182	+	0.673506i	$0.764787\pi$
$600$	−3.18628e8	−	2.60601e9i	−0.00245855	−	0.0201081i
$601$	−2.18632e11			−1.67578			−0.837888	−	0.545842i	$-0.816210\pi$
$601$	−2.18632e11			−1.67578			−0.837888	+	0.545842i	$0.816210\pi$
$602$	−7.48630e10	−	1.90834e9i	−0.570009	−	0.0145302i
$603$		−	7.97663e10i		−	0.603324i
$604$	−2.96880e10	+	7.75924e9i	−0.223066	+	0.0583004i
$605$	−4.00042e10	+	6.92893e10i	−0.298596	+	0.517184i
$606$	5.58056e10	−	7.22655e10i	0.413797	−	0.535846i
$607$	7.13716e10	−	4.12064e10i	0.525740	−	0.303536i	−0.213540	−	0.976934i	$-0.568499\pi$
$607$	7.13716e10	−	4.12064e10i	0.525740	−	0.303536i	0.739280	+	0.673398i	$0.235166\pi$
$608$	−4.09433e10	−	3.24305e10i	−0.299619	−	0.237322i
$609$	−2.49061e10	+	1.82393e10i	−0.181066	+	0.132599i
$610$	−6.51707e9	+	4.83511e10i	−0.0470688	+	0.349210i
$611$	−4.54349e8	+	2.62319e8i	−0.00326005	+	0.00188219i
$612$	−4.62512e8	+	4.56851e8i	−0.00329699	+	0.00325663i
$613$	5.11522e10	−	8.85983e10i	0.362262	−	0.627456i	−0.626071	−	0.779766i	$-0.715338\pi$
$613$	5.11522e10	−	8.85983e10i	0.362262	−	0.627456i	0.988333	+	0.152310i	$0.0486713\pi$
$614$	−2.24648e10	−	5.47108e10i	−0.158063	−	0.384946i
$615$		−	3.82501e10i		−	0.267382i
$616$	4.13799e10	+	1.76605e11i	0.287387	+	1.22654i
$617$	−3.87988e10			−0.267718			−0.133859	−	0.991000i	$-0.542737\pi$
$617$	−3.87988e10			−0.267718			−0.133859	+	0.991000i	$0.542737\pi$
$618$	−5.34891e10	+	2.19632e10i	−0.366700	+	0.150571i
$619$	1.83290e11	+	1.05823e11i	1.24847	+	0.720802i	0.970803	−	0.239877i	$-0.0771072\pi$
$619$	1.83290e11	+	1.05823e11i	1.24847	+	0.720802i	0.277662	+	0.960679i	$0.410441\pi$
$620$	1.77116e11	+	1.79311e11i	1.19865	+	1.21350i
$621$	−2.51828e10	−	4.36180e10i	−0.169332	−	0.293291i
$622$	2.42035e11	+	3.26230e10i	1.61702	+	0.217953i
$623$	−1.30654e11	+	1.42309e10i	−0.867300	+	0.0944671i
$624$	4.11889e9	−	6.93543e9i	0.0271670	−	0.0457441i
$625$	7.88770e10	+	1.36619e11i	0.516928	+	0.895346i
$626$	−1.84826e11	−	1.42729e11i	−1.20356	−	0.929424i
$627$	3.72084e10	+	2.14823e10i	0.240753	+	0.138999i
$628$	5.07590e10	+	1.94211e11i	0.326343	+	1.24864i
$629$	3.38212e9			0.0216066
$630$	4.55701e10	+	2.78819e10i	0.289280	+	0.176995i
$631$		−	2.45550e11i		−	1.54890i	−0.632637	−	0.774448i	$-0.718027\pi$
$631$		−	2.45550e11i		−	1.54890i	0.632637	−	0.774448i	$-0.281973\pi$
$632$	−2.83883e10	−	2.32184e11i	−0.177939	−	1.45534i
$633$	−7.37471e10	+	1.27734e11i	−0.459336	+	0.795593i
$634$	2.13877e11	+	1.65163e11i	1.32376	+	1.02225i
$635$	2.16222e11	−	1.24836e11i	1.32986	−	0.767792i
$636$	6.67937e9	−	2.43275e10i	0.0408232	−	0.148686i
$637$	−1.02371e10	−	1.11984e10i	−0.0621758	−	0.0680139i
$638$	8.04069e10	+	1.08377e10i	0.485301	+	0.0654118i
$639$	−6.92226e10	+	3.99657e10i	−0.415188	+	0.239709i
$640$	1.86272e10	+	1.69671e11i	0.111026	+	1.01132i
$641$	1.00623e11	−	1.74284e11i	0.596024	−	1.03234i	−0.397378	−	0.917655i	$-0.630080\pi$
$641$	1.00623e11	−	1.74284e11i	0.596024	−	1.03234i	0.993401	−	0.114689i	$-0.0365870\pi$
$642$	9.13463e10	−	3.75078e10i	0.537713	−	0.220791i
$643$		−	9.83121e10i		−	0.575126i	−0.957762	−	0.287563i	$-0.907155\pi$
$643$		−	9.83121e10i		−	0.575126i	0.957762	−	0.287563i	$-0.0928451\pi$
$644$	−2.34777e11	−	1.91048e11i	−1.36494	−	1.11070i
$645$	5.79681e10			0.334927
$646$	3.51510e8	+	8.56067e8i	0.00201840	+	0.00491561i
$647$	−1.21022e10	−	6.98721e9i	−0.0690633	−	0.0398737i	0.465071	−	0.885274i	$-0.346029\pi$
$647$	−1.21022e10	−	6.98721e9i	−0.0690633	−	0.0398737i	−0.534134	+	0.845400i	$0.679362\pi$
$648$	−1.17822e10	−	1.56521e10i	−0.0668230	−	0.0887714i
$649$	5.26720e10	+	9.12307e10i	0.296894	+	0.514235i
$650$	7.70977e7	−	5.72000e8i	0.000431905	−	0.00320437i
$651$	−1.72827e11	+	1.88244e10i	−0.962248	+	0.104809i
$652$	4.29265e10	−	1.56346e11i	0.237539	−	0.865162i
$653$	7.55348e10	+	1.30830e11i	0.415426	+	0.719540i	0.995473	−	0.0950436i	$-0.0302990\pi$
$653$	7.55348e10	+	1.30830e11i	0.415426	+	0.719540i	−0.580047	+	0.814583i	$0.696966\pi$
$654$	4.24188e10	−	5.49302e10i	0.231872	−	0.300262i
$655$	−1.85187e11	−	1.06918e11i	−1.00611	−	0.580878i
$656$	−1.03822e9	+	8.42921e10i	−0.00560625	+	0.455168i
$657$	4.69330e10			0.251893
$658$	3.65863e9	+	6.72721e9i	0.0195171	+	0.0358865i
$659$		−	4.43048e10i		−	0.234914i	−0.993078	−	0.117457i	$-0.962526\pi$
$659$		−	4.43048e10i		−	0.234914i	0.993078	−	0.117457i	$-0.0374742\pi$
$660$	−3.55042e10	−	1.35844e11i	−0.187113	−	0.715922i
$661$	8.88117e10	−	1.53826e11i	0.465227	−	0.805796i	−0.533985	−	0.845494i	$-0.679306\pi$
$661$	8.88117e10	−	1.53826e11i	0.465227	−	0.805796i	0.999212	+	0.0396977i	$0.0126395\pi$
$662$	7.94243e10	−	1.02850e11i	0.413544	−	0.535518i
$663$	−1.23771e8	+	7.14590e7i	−0.000640565	+	0.000369831i
$664$	3.05268e11	+	1.29763e11i	1.57040	+	0.667540i
$665$	6.13554e10	−	4.49320e10i	0.313737	−	0.229757i
$666$	−1.36145e10	+	1.01008e11i	−0.0691998	+	0.513404i
$667$	−1.17252e11	+	6.76952e10i	−0.592400	+	0.342022i
$668$	9.32108e10	+	9.43659e10i	0.468123	+	0.473925i
$669$	7.92902e10	−	1.37335e11i	0.395836	−	0.685608i
$670$	1.40947e11	+	3.43262e11i	0.699451	+	1.70344i
$671$			8.84473e10i			0.436309i
$672$	−9.96664e10	−	6.26804e10i	−0.488733	−	0.307365i
$673$	−2.06382e11			−1.00603			−0.503016	−	0.864277i	$-0.667776\pi$
$673$	−2.06382e11			−1.00603			−0.503016	+	0.864277i	$0.667776\pi$
$674$	9.07640e9	−	3.72687e9i	0.0439819	−	0.0180594i
$675$	−1.21400e9	−	7.00903e8i	−0.00584794	−	0.00337631i
$676$	−1.47308e11	+	1.45505e11i	−0.705406	+	0.696771i
$677$	1.17710e11	+	2.03881e11i	0.560351	+	0.970557i	0.997466	+	0.0711511i	$0.0226672\pi$
$677$	1.17710e11	+	2.03881e11i	0.560351	+	0.970557i	−0.437114	+	0.899406i	$0.643999\pi$
$678$	1.68435e11	+	2.27027e10i	0.797102	+	0.107438i
$679$	−6.81722e10	+	1.54686e11i	−0.320722	+	0.727731i
$680$	1.18310e9	−	2.78325e9i	0.00553330	−	0.0130172i
$681$	1.07809e11	+	1.86730e11i	0.501262	+	0.868212i
$682$	3.61634e11	+	2.79265e11i	1.67160	+	1.29086i
$683$	−1.88820e11	−	1.09015e11i	−0.867691	−	0.500962i	−0.00111075	−	0.999999i	$-0.500354\pi$
$683$	−1.88820e11	−	1.09015e11i	−0.867691	−	0.500962i	−0.866580	+	0.499038i	$0.833687\pi$
$684$	−2.69817e10	+	7.05194e9i	−0.123267	+	0.0322169i
$685$	−6.11200e10			−0.277601
$686$	−1.67209e11	+	1.45210e11i	−0.755028	+	0.655693i
$687$			1.82794e11i			0.820605i
$688$	−1.27745e11	−	1.57342e9i	−0.570151	−	0.00702248i
$689$	2.77304e9	−	4.80304e9i	0.0123049	−	0.0213128i
$690$	1.85444e11	+	1.43205e11i	0.818117	+	0.631775i
$691$	−2.72393e11	+	1.57266e11i	−1.19477	+	0.689800i	−0.959384	−	0.282102i	$-0.908968\pi$
$691$	−2.72393e11	+	1.57266e11i	−1.19477	+	0.689800i	−0.235385	+	0.971902i	$0.575635\pi$
$692$	1.24041e11	+	3.40568e10i	0.540931	+	0.148518i
$693$	8.86245e10	+	3.90581e10i	0.384256	+	0.169347i
$694$	2.28480e11	+	3.07960e10i	0.984942	+	0.132757i
$695$	9.58988e9	−	5.53672e9i	0.0411030	−	0.0237308i
$696$	−4.20752e10	+	3.16723e10i	−0.179304	+	0.134972i
$697$	7.46795e8	−	1.29349e9i	0.00316425	−	0.00548064i
$698$	3.52593e11	−	1.44779e11i	1.48543	−	0.609934i
$699$			1.41749e11i			0.593759i
$700$	−8.31766e9	−	1.33773e9i	−0.0346425	−	0.00557155i
$701$	6.00348e10			0.248617			0.124308	−	0.992244i	$-0.460329\pi$
$701$	6.00348e10			0.248617			0.124308	+	0.992244i	$0.460329\pi$
$702$	−1.63592e9	−	3.98411e9i	−0.00673617	−	0.0164052i
$703$	1.25648e11	+	7.25432e10i	0.514441	+	0.297013i
$704$	7.45537e10	+	3.00325e11i	0.303514	+	1.22265i
$705$	−2.96381e9	−	5.13348e9i	−0.0119976	−	0.0207805i
$706$	1.07954e10	−	8.00928e10i	0.0434530	−	0.322385i
$707$	−1.73104e11	−	2.36376e11i	−0.692834	−	0.946076i
$708$	−6.59380e10	−	1.81040e10i	−0.262424	−	0.0720512i
$709$	−2.15862e11	−	3.73884e11i	−0.854263	−	1.47963i	−0.877327	−	0.479894i	$-0.840675\pi$
$709$	−2.15862e11	−	3.73884e11i	−0.854263	−	1.47963i	0.0230632	−	0.999734i	$-0.492658\pi$
$710$	2.27270e11	−	2.94303e11i	0.894351	−	1.15814i
$711$	−1.08162e11	−	6.24472e10i	−0.423248	−	0.244363i
$712$	−2.22550e11	+	2.72104e10i	−0.865981	+	0.105880i
$713$	−7.62460e11			−2.95025
$714$	9.96657e8	+	1.83258e9i	0.00383489	+	0.00705131i
$715$		−	3.08671e10i		−	0.118106i
$716$	−2.29583e10	+	6.00038e9i	−0.0873550	+	0.0228311i
$717$	−1.33477e11	+	2.31188e11i	−0.505043	+	0.874760i
$718$	−2.07123e11	+	2.68213e11i	−0.779345	+	1.00921i
$719$	1.39391e11	−	8.04775e10i	0.521578	−	0.301133i	−0.216002	−	0.976393i	$-0.569302\pi$
$719$	1.39391e11	−	8.04775e10i	0.521578	−	0.301133i	0.737580	+	0.675260i	$0.235968\pi$
$720$	7.83602e10	+	4.65374e10i	0.291585	+	0.173170i
$721$	2.00908e10	+	1.84453e11i	0.0743456	+	0.682565i
$722$	3.09952e10	−	2.29959e11i	0.114063	−	0.846254i
$723$	−4.06437e10	+	2.34657e10i	−0.148744	+	0.0858775i
$724$	2.96747e11	−	2.93115e11i	1.08002	−	1.06680i
$725$	−1.88413e9	+	3.26341e9i	−0.00681960	+	0.0118119i
$726$	−3.57609e10	−	8.70920e10i	−0.128725	−	0.313496i
$727$			1.58978e11i			0.569114i	0.958659	+	0.284557i	$0.0918465\pi$
$727$			1.58978e11i			0.569114i	−0.958659	+	0.284557i	$0.908154\pi$
$728$	−1.77142e10	−	1.88723e10i	−0.0630660	−	0.0671892i
$729$	−1.04604e10			−0.0370370
$730$	−2.01969e11	+	8.29307e10i	−0.711203	+	0.292028i
$731$	1.96028e9	+	1.13177e9i	0.00686513	+	0.00396359i
$732$	−4.03447e10	−	4.08446e10i	−0.140521	−	0.142263i
$733$	−2.45952e11	−	4.26001e11i	−0.851990	−	1.47569i	−0.879410	−	0.476066i	$-0.842062\pi$
$733$	−2.45952e11	−	4.26001e11i	−0.851990	−	1.47569i	0.0274195	−	0.999624i	$-0.491271\pi$
$734$	3.02423e11	+	4.07625e10i	1.04191	+	0.140435i
$735$	1.26525e11	−	1.15665e11i	0.433539	−	0.396325i
$736$	−4.04777e11	−	3.20616e11i	−1.37944	−	1.09263i
$737$	3.36355e11	+	5.82584e11i	1.14006	+	1.97464i
$738$	3.56243e10	+	2.75101e10i	0.120094	+	0.0927401i
$739$	−2.02337e11	−	1.16819e11i	−0.678417	−	0.391684i	0.120841	−	0.992672i	$-0.461441\pi$
$739$	−2.02337e11	−	1.16819e11i	−0.678417	−	0.391684i	−0.799259	+	0.600987i	$0.794774\pi$
$740$	−1.19894e11	−	4.58730e11i	−0.399824	−	1.52979i
$741$	−6.13091e9			−0.0203354
$742$	−6.90522e10	−	4.22493e10i	−0.227804	−	0.139381i
$743$		−	1.66507e11i		−	0.546359i	−0.961963	−	0.273180i	$-0.911925\pi$
$743$		−	1.66507e11i		−	0.546359i	0.961963	−	0.273180i	$-0.0880753\pi$
$744$	−2.94386e11	+	3.59935e10i	−0.960784	+	0.117472i
$745$	−2.93521e10	+	5.08394e10i	−0.0952828	+	0.165035i
$746$	−3.24842e11	−	2.50853e11i	−1.04886	−	0.809961i
$747$	1.53380e11	−	8.85541e10i	0.492591	−	0.284398i
$748$	1.45159e9	−	5.28697e9i	0.00463701	−	0.0168889i
$749$	−3.43101e10	−	3.15000e11i	−0.109017	−	1.00088i
$750$	−1.77726e11	−	2.39550e10i	−0.561702	−	0.0757097i
$751$	−6.86064e10	+	3.96099e10i	−0.215677	+	0.124521i	−0.603947	−	0.797024i	$-0.706406\pi$
$751$	−6.86064e10	+	3.96099e10i	−0.215677	+	0.124521i	0.388270	+	0.921546i	$0.373073\pi$
$752$	6.39204e9	+	1.13931e10i	0.0199880	+	0.0356264i
$753$	8.12371e10	−	1.40707e11i	0.252682	−	0.437658i
$754$	−1.07099e10	+	4.39759e9i	−0.0331359	+	0.0136060i
$755$		−	7.62180e10i		−	0.234568i
$756$	−5.87426e10	+	2.23886e10i	−0.179832	+	0.0685393i
$757$	1.24185e11			0.378169			0.189084	−	0.981961i	$-0.439448\pi$
$757$	1.24185e11			0.378169			0.189084	+	0.981961i	$0.439448\pi$
$758$	−9.94567e10	−	2.42216e11i	−0.301271	−	0.733714i
$759$	3.67852e11	+	2.12380e11i	1.10843	+	0.639950i
$760$	1.03651e11	−	7.80237e10i	0.310684	−	0.233869i
$761$	−6.38294e10	−	1.10556e11i	−0.190319	−	0.329642i	0.755037	−	0.655682i	$-0.227619\pi$
$761$	−6.38294e10	−	1.10556e11i	−0.190319	−	0.329642i	−0.945356	+	0.326040i	$0.894286\pi$
$762$	−3.92446e10	+	2.91162e11i	−0.116402	+	0.863605i
$763$	−1.31579e11	−	1.79674e11i	−0.388230	−	0.530134i
$764$	2.87941e10	−	1.04873e11i	0.0845142	−	0.307817i
$765$	−8.07382e8	−	1.39843e9i	−0.00235740	−	0.00408314i
$766$	3.92797e10	−	5.08652e10i	0.114091	−	0.147743i
$767$	−1.30183e10	−	7.51613e9i	−0.0376161	−	0.0217176i
$768$	−1.71420e11	−	1.04682e11i	−0.492738	−	0.300903i
$769$	2.95762e10			0.0845740			0.0422870	−	0.999106i	$-0.486536\pi$
$769$	2.95762e10			0.0845740			0.0422870	+	0.999106i	$0.486536\pi$
$770$	−4.50398e11	−	1.14812e10i	−1.28125	−	0.0326605i
$771$		−	2.60827e10i		−	0.0738134i
$772$	−5.83331e9	−	2.23191e10i	−0.0164228	−	0.0628359i
$773$	3.03527e11	−	5.25724e11i	0.850117	−	1.47245i	−0.0309846	−	0.999520i	$-0.509864\pi$
$773$	3.03527e11	−	5.25724e11i	0.850117	−	1.47245i	0.881102	−	0.472926i	$-0.156802\pi$
$774$	−4.16917e10	+	5.39886e10i	−0.116168	+	0.150431i
$775$	−1.83781e10	+	1.06106e10i	−0.0509441	+	0.0294126i
$776$	−1.12814e11	+	2.65395e11i	−0.311111	+	0.731891i
$777$	2.99275e11	+	1.31895e11i	0.821080	+	0.361862i
$778$	8.12195e9	−	6.02580e10i	0.0221688	−	0.164474i
$779$	5.54881e10	−	3.20361e10i	0.150678	−	0.0869940i
$780$	1.40798e10	+	1.42543e10i	0.0380382	+	0.0385096i
$781$	3.37051e11	−	5.83789e11i	0.905923	−	1.56910i
$782$	3.47512e9	+	8.46330e9i	0.00929273	+	0.0226315i
$783$			2.81190e10i			0.0748088i
$784$	−2.81964e11	+	2.51457e11i	−0.746328	+	0.665579i
$785$	−4.98599e11			−1.31302
$786$	2.32768e11	−	9.55770e10i	0.609864	−	0.250417i
$787$	5.56985e11	+	3.21575e11i	1.45193	+	0.838270i	0.998591	−	0.0530706i	$-0.0169008\pi$
$787$	5.56985e11	+	3.21575e11i	1.45193	+	0.838270i	0.453335	+	0.891340i	$0.350234\pi$
$788$	−2.52587e11	+	2.49495e11i	−0.655097	+	0.647078i
$789$	−3.61388e10	−	6.25942e10i	−0.0932536	−	0.161520i
$790$	5.75802e11	+	7.76102e10i	1.47831	+	0.199256i
$791$	2.19940e11	−	4.99052e11i	0.561821	−	1.27479i
$792$	1.52054e11	+	6.46347e10i	0.386453	+	0.164273i
$793$	−6.31057e9	−	1.09302e10i	−0.0159579	−	0.0276399i
$794$	−2.38236e11	−	1.83973e11i	−0.599411	−	0.462884i
$795$	5.42673e10	+	3.13313e10i	0.135853	+	0.0784349i
$796$	4.63723e11	−	1.21198e11i	1.15506	−	0.301887i
$797$	−4.94633e11			−1.22589			−0.612943	−	0.790127i	$-0.710014\pi$
$797$	−4.94633e11			−1.22589			−0.612943	+	0.790127i	$0.710014\pi$
$798$	−2.28042e9	+	8.94592e10i	−0.00562345	+	0.220604i
$799$		−	2.31462e8i		−	0.000567927i
$800$	−1.42184e10	−	2.09505e9i	−0.0347129	−	0.00511486i
$801$	−5.98562e10	+	1.03674e11i	−0.145405	+	0.251849i
$802$	−3.04080e11	−	2.34820e11i	−0.735004	−	0.567593i
$803$	−3.42781e11	+	1.97905e11i	−0.824432	+	0.475986i
$804$	−4.21069e11	−	1.15609e11i	−1.00770	−	0.276673i
$805$	6.06575e11	−	4.44209e11i	1.44445	−	1.05780i
$806$	−6.46155e10	−	8.70928e9i	−0.153107	−	0.0206368i
$807$	−1.89094e11	+	1.09174e11i	−0.445845	+	0.257409i
$808$	−3.00592e11	−	3.99323e11i	−0.705232	−	0.936870i
$809$	−1.57193e11	+	2.72267e11i	−0.366978	+	0.635624i	−0.989091	−	0.147303i	$-0.952941\pi$
$809$	−1.57193e11	+	2.72267e11i	−0.366978	+	0.635624i	0.622114	+	0.782927i	$0.286274\pi$
$810$	4.50146e10	−	1.84835e10i	0.104571	−	0.0429381i
$811$		−	3.23021e10i		−	0.0746702i	−0.999303	−	0.0373351i	$-0.988113\pi$
$811$		−	3.23021e10i		−	0.0746702i	0.999303	−	0.0373351i	$-0.0118869\pi$
$812$	6.01838e10	+	1.57909e11i	0.138438	+	0.363230i
$813$	−1.37226e11			−0.314105
$814$	−3.26491e11	−	7.95135e11i	−0.743659	−	1.81110i
$815$	3.48762e11	+	2.01358e11i	0.790494	+	0.456392i
$816$	1.74128e9	+	3.10364e9i	0.00392742	+	0.00700020i
$817$	4.85507e10	+	8.40923e10i	0.108970	+	0.188742i
$818$	5.70056e10	−	4.22934e11i	0.127322	−	0.944624i
$819$	−1.37389e10	+	1.49645e9i	−0.0305362	+	0.00332603i
$820$	−2.01914e11	−	5.54376e10i	−0.446592	−	0.122617i
$821$	2.94799e11	+	5.10606e11i	0.648863	+	1.12386i	0.983395	+	0.181479i	$0.0580883\pi$
$821$	2.94799e11	+	5.10606e11i	0.648863	+	1.12386i	−0.334532	+	0.942384i	$0.608578\pi$
$822$	4.39586e10	−	5.69241e10i	0.0962845	−	0.124684i
$823$	6.95248e11	+	4.01402e11i	1.51545	+	0.874943i	0.999836	+	0.0181191i	$0.00576781\pi$
$823$	6.95248e11	+	4.01402e11i	1.51545	+	0.874943i	0.515610	+	0.856824i	$0.327566\pi$
$824$	3.84148e10	+	3.14190e11i	0.0833278	+	0.681527i
$825$	1.18221e10			0.0255200
$826$	−1.14514e11	+	1.87161e11i	−0.246002	+	0.402064i
$827$		−	5.44519e11i		−	1.16410i	−0.813152	−	0.582051i	$-0.802250\pi$
$827$		−	5.44519e11i		−	1.16410i	0.813152	−	0.582051i	$-0.197750\pi$
$828$	−2.66748e11	+	6.97173e10i	−0.567519	+	0.148327i
$829$	1.13777e11	−	1.97068e11i	0.240900	−	0.417252i	−0.720071	−	0.693901i	$-0.755891\pi$
$829$	1.13777e11	−	1.97068e11i	0.240900	−	0.417252i	0.960971	+	0.276649i	$0.0892239\pi$
$830$	−5.03573e11	+	6.52102e11i	−1.06109	+	1.37405i
$831$	7.21315e10	−	4.16452e10i	0.151259	−	0.0873294i
$832$	−3.06410e10	−	3.17946e10i	−0.0639454	−	0.0663528i
$833$	6.53688e9	−	1.44110e9i	0.0135766	−	0.00299306i
$834$	−1.74058e9	+	1.29136e10i	−0.00359774	+	0.0266922i
$835$	−2.85319e11	+	1.64729e11i	−0.586929	+	0.338864i
$836$	1.67328e11	−	1.65280e11i	0.342566	−	0.338373i
$837$	−7.91769e10	+	1.37138e11i	−0.161323	+	0.279420i
$838$	8.27240e10	+	2.01466e11i	0.167747	+	0.408531i
$839$			6.19807e11i			1.25086i	0.780280	+	0.625430i	$0.215077\pi$
$839$			6.19807e11i			1.25086i	−0.780280	+	0.625430i	$0.784923\pi$
$840$	2.13229e11	−	2.00144e11i	0.428282	−	0.402000i
$841$	−4.24658e11			−0.848899
$842$	−7.96749e10	+	3.27154e10i	−0.158516	+	0.0650884i
$843$	−1.52672e11	−	8.81452e10i	−0.302308	−	0.174537i
$844$	5.67394e11	+	5.74425e11i	1.11819	+	1.13205i
$845$	−2.57147e11	−	4.45392e11i	−0.504377	−	0.873606i
$846$	6.91269e9	+	9.31735e8i	0.0134948	+	0.00181891i
$847$	−3.00330e11	+	3.27122e10i	−0.583532	+	0.0635588i
$848$	−1.18739e11	−	7.05179e10i	−0.229620	−	0.136369i
$849$	−1.34588e10	−	2.33113e10i	−0.0259045	−	0.0448680i
$850$	2.01541e8	+	1.55636e8i	0.000386089	+	0.000298150i
$851$	1.24219e12	+	7.17181e11i	2.36849	+	1.36745i
$852$	1.10643e11	+	4.23335e11i	0.209974	+	0.803389i
$853$	−3.47217e11			−0.655851			−0.327925	−	0.944704i	$-0.606349\pi$
$853$	−3.47217e11			−0.655851			−0.327925	+	0.944704i	$0.606349\pi$
$854$	−1.61836e11	+	8.80152e10i	−0.304259	+	0.165473i
$855$		−	6.92703e10i		−	0.129623i
$856$	−6.56031e10	−	5.36559e11i	−0.122188	−	0.999361i
$857$	−2.31885e11	+	4.01636e11i	−0.429882	+	0.744577i	−0.996862	−	0.0791538i	$-0.974778\pi$
$857$	−2.31885e11	+	4.01636e11i	−0.429882	+	0.744577i	0.566980	+	0.823731i	$0.308111\pi$
$858$	2.87481e10	+	2.22002e10i	0.0530469	+	0.0409645i
$859$	2.25884e11	−	1.30414e11i	0.414871	−	0.239526i	−0.278010	−	0.960578i	$-0.589675\pi$
$859$	2.25884e11	−	1.30414e11i	0.414871	−	0.239526i	0.692880	+	0.721053i	$0.256341\pi$
$860$	8.40158e10	−	3.06001e11i	0.153592	−	0.559409i
$861$	1.16525e11	−	8.53339e10i	0.212034	−	0.155278i
$862$	5.62187e11	+	7.57751e10i	1.01824	+	0.137245i
$863$	−5.01373e11	+	2.89468e11i	−0.903895	+	0.521864i	−0.878462	−	0.477813i	$-0.841430\pi$
$863$	−5.01373e11	+	2.89468e11i	−0.903895	+	0.521864i	−0.0254329	+	0.999677i	$0.508096\pi$
$864$	−9.97006e10	+	3.95103e10i	−0.178913	+	0.0709015i
$865$	−1.59752e11	+	2.76699e11i	−0.285353	+	0.494246i
$866$	−1.93256e11	+	7.93528e10i	−0.343606	+	0.141088i
$867$			3.26161e11i			0.577239i
$868$	−1.51115e11	+	9.39598e11i	−0.266213	+	1.65525i
$869$	1.05330e12			1.84702
$870$	−4.96863e10	−	1.21006e11i	−0.0867280	−	0.211217i
$871$	−8.31328e10	−	4.79967e10i	−0.144444	−	0.0833948i
$872$	−2.28485e11	−	3.03533e11i	−0.395178	−	0.524976i
$873$	7.69875e10	+	1.33346e11i	0.132545	+	0.229575i
$874$	−5.24260e10	+	3.88957e11i	−0.0898465	+	0.666585i
$875$	−2.32072e11	+	5.26580e11i	−0.395904	+	0.898323i
$876$	6.80221e10	−	2.47749e11i	0.115514	−	0.420723i
$877$	2.73671e11	+	4.74012e11i	0.462627	+	0.801293i	0.999091	−	0.0426302i	$-0.0135737\pi$
$877$	2.73671e11	+	4.74012e11i	0.462627	+	0.801293i	−0.536464	+	0.843923i	$0.680240\pi$
$878$	2.49221e11	−	3.22729e11i	0.419379	−	0.543075i
$879$	−3.41142e11	−	1.96959e11i	−0.571453	−	0.329928i
$880$	−7.68551e11	−	9.46615e9i	−1.28157	−	0.0157849i
$881$	5.80017e11			0.962802			0.481401	−	0.876501i	$-0.340128\pi$
$881$	5.80017e11			0.962802			0.481401	+	0.876501i	$0.340128\pi$
$882$	1.67252e10	+	2.01027e11i	0.0276374	+	0.332186i
$883$			1.45083e11i			0.238657i	0.992855	+	0.119329i	$0.0380742\pi$
$883$			1.45083e11i			0.238657i	−0.992855	+	0.119329i	$0.961926\pi$
$884$	1.97830e8	+	7.56927e8i	0.000323954	+	0.00123950i
$885$	8.49212e10	−	1.47088e11i	0.138434	−	0.239775i
$886$	−1.22527e11	+	1.58666e11i	−0.198837	+	0.257484i
$887$	1.38098e11	−	7.97307e10i	0.223096	−	0.128805i	−0.384287	−	0.923214i	$-0.625553\pi$
$887$	1.38098e11	−	7.97307e10i	0.223096	−	0.128805i	0.607383	+	0.794409i	$0.292219\pi$
$888$	5.13468e11	+	2.18264e11i	0.825775	+	0.351018i
$889$	8.62677e11	+	3.80195e11i	1.38115	+	0.608694i
$890$	7.43901e10	−	5.51912e11i	0.118565	−	0.879649i
$891$	7.63985e10	−	4.41087e10i	0.121220	−	0.0699864i
$892$	−6.10041e11	−	6.17601e11i	−0.963607	−	0.975549i
$893$	4.96464e9	−	8.59900e9i	0.00780695	−	0.0135220i
$894$	−2.62387e10	−	6.39017e10i	−0.0410764	−	0.100037i
$895$		−	5.89409e10i		−	0.0918597i
$896$	−4.75327e11	+	4.35272e11i	−0.737498	+	0.675349i
$897$	−6.06118e10			−0.0936240
$898$	−6.50619e11	+	2.67151e11i	−1.00051	+	0.410820i
$899$	3.68648e11	+	2.12839e11i	0.564382	+	0.325846i
$900$	−5.45942e9	+	5.39259e9i	−0.00832101	+	0.00821916i
$901$	1.22342e9	+	2.11903e9i	0.00185642	+	0.00321542i
$902$	−3.76190e11	−	5.07052e10i	−0.568304	−	0.0765996i
$903$	1.29324e11	+	1.76594e11i	0.194503	+	0.265598i
$904$	3.63964e11	−	8.56229e11i	0.544985	−	1.28208i
$905$	5.18015e11	+	8.97228e11i	0.772232	+	1.33755i
$906$	7.09856e10	+	5.48173e10i	0.105356	+	0.0813588i
$907$	8.32002e10	+	4.80356e10i	0.122941	+	0.0709797i	0.560209	−	0.828351i	$-0.310721\pi$
$907$	8.32002e10	+	4.80356e10i	0.122941	+	0.0709797i	−0.437269	+	0.899331i	$0.644054\pi$
$908$	1.14196e12	−	2.98462e11i	1.67999	−	0.439082i
$909$	−2.66869e11			−0.390879
$910$	5.64789e10	−	3.07163e10i	0.0823608	−	0.0447924i
$911$		−	8.55278e11i		−	1.24175i	−0.783910	−	0.620875i	$-0.786778\pi$
$911$		−	8.55278e11i		−	1.24175i	0.783910	−	0.620875i	$-0.213222\pi$
$912$	−1.88019e9	+	1.52651e11i	−0.00271783	+	0.220659i
$913$	−7.46821e11	+	1.29353e12i	−1.07481	+	1.86163i
$914$	2.71801e11	+	2.09893e11i	0.389463	+	0.300756i
$915$	1.23496e11	−	7.13002e10i	0.176184	−	0.101720i
$916$	9.64928e11	+	2.64931e11i	1.37061	+	0.376315i
$917$	−8.74287e10	−	8.02681e11i	−0.123645	−	1.13518i
$918$	1.88311e9	+	2.53817e8i	0.00265158	+	0.000357396i
$919$	6.71149e11	−	3.87488e11i	0.940929	−	0.543246i	0.0506778	−	0.998715i	$-0.483862\pi$
$919$	6.71149e11	−	3.87488e11i	0.940929	−	0.543246i	0.890252	+	0.455469i	$0.150528\pi$
$920$	1.02472e12	−	7.71363e11i	1.43039	−	1.07673i
$921$	−8.64332e10	+	1.49707e11i	−0.120127	+	0.208067i
$922$	4.95775e11	−	2.03571e11i	0.686058	−	0.281703i
$923$			9.61921e10i			0.132536i
$924$	3.34627e11	−	4.11221e11i	0.459064	−	0.564141i
$925$	3.99219e10			0.0545312
$926$	2.80748e11	+	6.83733e11i	0.381833	+	0.929914i
$927$	1.46364e11	+	8.45032e10i	0.198205	+	0.114434i
$928$	1.06210e11	+	2.68010e11i	0.143210	+	0.361376i
$929$	−6.28612e11	−	1.08879e12i	−0.843956	−	1.46178i	−0.886524	−	0.462682i	$-0.846887\pi$
$929$	−6.28612e11	−	1.08879e12i	−0.843956	−	1.46178i	0.0425679	−	0.999094i	$-0.486446\pi$
$930$	9.84020e10	−	7.30060e11i	0.131544	−	0.975948i
$931$	2.73761e11	+	8.66717e10i	0.364395	+	0.115366i
$932$	7.48260e11	+	2.05443e11i	0.991720	+	0.272287i
$933$	−3.56913e11	−	6.18191e11i	−0.471016	−	0.815823i
$934$	−7.45803e11	+	9.65778e11i	−0.980024	+	1.26908i
$935$	1.17936e10	+	6.80906e9i	0.0154313	+	0.00890924i
$936$	−2.34022e10	+	2.86131e9i	−0.0304898	+	0.00372787i
$937$	−9.93326e11			−1.28865			−0.644323	−	0.764754i	$-0.722861\pi$
$937$	−9.93326e11			−1.28865			−0.644323	+	0.764754i	$0.722861\pi$
$938$	−7.31266e11	+	1.19518e12i	−0.944635	+	1.54391i
$939$			6.82545e11i			0.877948i
$940$	−3.13941e10	+	8.20515e9i	−0.0402102	+	0.0105093i
$941$	3.03420e11	−	5.25539e11i	0.386978	−	0.670265i	−0.605064	−	0.796177i	$-0.706852\pi$
$941$	3.03420e11	−	5.25539e11i	0.386978	−	0.670265i	0.992041	+	0.125912i	$0.0401857\pi$
$942$	3.58601e11	−	4.64370e11i	0.455416	−	0.589740i
$943$	5.48570e11	−	3.16717e11i	0.693722	−	0.400520i
$944$	−1.91134e11	+	3.21834e11i	−0.240685	+	0.405269i
$945$	−1.69077e10	−	1.55229e11i	−0.0212010	−	0.194646i
$946$	7.68438e10	−	5.70116e11i	0.0959499	−	0.711867i
$947$	2.50041e11	−	1.44361e11i	0.310893	−	0.179494i	−0.336433	−	0.941707i	$-0.609221\pi$
$947$	2.50041e11	−	1.44361e11i	0.310893	−	0.179494i	0.647326	+	0.762213i	$0.275887\pi$
$948$	−4.86409e11	+	4.80455e11i	−0.602238	+	0.594866i
$949$	2.82404e10	−	4.89138e10i	0.0348181	−	0.0603068i
$950$	4.14917e9	+	1.01049e10i	0.00509409	+	0.0124061i
$951$		−	7.89827e11i		−	0.965629i
$952$	1.11183e10	−	2.60510e9i	0.0135360	−	0.00317159i
$953$	−2.41602e11			−0.292906			−0.146453	−	0.989218i	$-0.546786\pi$
$953$	−2.41602e11			−0.292906			−0.146453	+	0.989218i	$0.546786\pi$
$954$	−6.82104e10	+	2.80079e10i	−0.0823488	+	0.0338133i
$955$	2.33941e11	+	1.35066e11i	0.281250	+	0.162380i
$956$	1.02694e12	+	1.03967e12i	1.22946	+	1.24469i
$957$	−1.18571e11	−	2.05371e11i	−0.141361	−	0.244845i
$958$	−1.45138e12	−	1.95626e11i	−1.72313	−	0.232255i
$959$	−1.36355e11	−	1.86196e11i	−0.161212	−	0.220138i
$960$	3.59232e11	−	3.46198e11i	0.422951	−	0.407605i
$961$	7.72172e11	+	1.33744e12i	0.905358	+	1.56813i
$962$	9.70790e10	+	7.49674e10i	0.113351	+	0.0875331i
$963$	−2.49953e11	−	1.44311e11i	−0.290639	−	0.167801i
$964$	6.49634e10	+	2.48559e11i	0.0752247	+	0.287820i
$965$	5.72999e10			0.0660761
$966$	−2.25448e10	+	8.84417e11i	−0.0258903	+	1.01566i
$967$		−	8.52879e10i		−	0.0975397i	−0.998810	−	0.0487698i	$-0.984470\pi$
$967$		−	8.52879e10i		−	0.0975397i	0.998810	−	0.0487698i	$-0.0155301\pi$
$968$	−5.11570e11	+	6.25478e10i	−0.582644	+	0.0712378i
$969$	1.35243e9	−	2.34248e9i	0.00153398	−	0.00265694i
$970$	−5.66927e11	−	4.37799e11i	−0.640384	−	0.494524i
$971$	−6.99097e11	+	4.03624e11i	−0.786431	+	0.454046i	−0.838705	−	0.544587i	$-0.816687\pi$
$971$	−6.99097e11	+	4.03624e11i	−0.786431	+	0.454046i	0.0522735	+	0.998633i	$0.483353\pi$
$972$	−1.51607e10	+	5.52179e10i	−0.0169845	+	0.0618608i
$973$	3.82615e10	+	1.68624e10i	0.0426885	+	0.0188134i
$974$	−4.72386e11	−	6.36711e10i	−0.524881	−	0.0707467i
$975$	−1.46097e9	+	8.43490e8i	−0.00161667	+	0.000933386i
$976$	−2.74083e11	+	1.53773e11i	−0.302053	+	0.169465i
$977$	−1.11608e9	+	1.93310e9i	−0.00122494	+	0.00212166i	−0.866637	−	0.498939i	$-0.833723\pi$
$977$	−1.11608e9	+	1.93310e9i	−0.00122494	+	0.00212166i	0.865412	+	0.501060i	$0.167057\pi$
$978$	−4.38370e11	+	1.79999e11i	−0.479165	+	0.196750i
$979$		−	1.00960e12i		−	1.09905i
$980$	−4.27190e11	−	8.35537e11i	−0.463145	−	0.905861i
$981$	−2.02852e11			−0.219029
$982$	−4.76589e11	−	1.16068e12i	−0.512505	−	1.24815i
$983$	−4.68693e11	−	2.70600e11i	−0.501966	−	0.289810i	0.227559	−	0.973764i	$-0.426926\pi$
$983$	−4.68693e11	−	2.70600e11i	−0.501966	−	0.289810i	−0.729525	+	0.683954i	$0.760259\pi$
$984$	1.96852e11	−	1.48181e11i	0.209971	−	0.158057i
$985$	−4.40927e11	−	7.63707e11i	−0.468405	−	0.811301i
$986$	6.82297e8	−	5.06207e9i	0.000721882	−	0.00535575i
$987$	9.02648e9	−	2.04814e10i	0.00951152	−	0.0215820i
$988$	−8.88580e9	+	3.23637e10i	−0.00932543	+	0.0339650i
$989$	4.79985e11	+	8.31359e11i	0.501698	+	0.868967i
$990$	−2.50829e11	+	3.24812e11i	−0.261119	+	0.338135i
$991$	−1.26756e12	−	7.31827e11i	−1.31424	−	0.758776i	−0.331444	−	0.943475i	$-0.607536\pi$
$991$	−1.26756e12	−	7.31827e11i	−1.31424	−	0.758776i	−0.982795	+	0.184699i	$0.940869\pi$
$992$	−2.36665e11	+	1.60617e12i	−0.244392	+	1.65861i
$993$	−3.79816e11			−0.390640
$994$	1.40359e12	+	3.57790e10i	1.43778	+	0.0366508i
$995$			1.19052e12i			1.21463i
$996$	−2.45157e11	−	9.38006e11i	−0.249119	−	0.953165i
$997$	−4.82444e11	+	8.35618e11i	−0.488277	+	0.845721i	−0.999909	−	0.0134840i	$-0.995708\pi$
$997$	−4.82444e11	+	8.35618e11i	−0.488277	+	0.845721i	0.511632	+	0.859205i	$0.329041\pi$
$998$	−9.40690e11	+	1.21815e12i	−0.948253	+	1.22794i
$999$	2.57989e11	−	1.48950e11i	0.259023	−	0.149547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.9.l.b.67.5	yes	64
4.3	odd	2		84.9.l.a.67.25	✓	64
7.2	even	3		84.9.l.a.79.25	yes	64
28.23	odd	6	inner	84.9.l.b.79.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.l.a.67.25	✓	64	4.3	odd	2
84.9.l.a.79.25	yes	64	7.2	even	3
84.9.l.b.67.5	yes	64	1.1	even	1	trivial
84.9.l.b.79.5	yes	64	28.23	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	84.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.8009 + 6.07739i) q^{2} +(40.5000 + 23.3827i) q^{3} +(182.131 - 179.901i) q^{4} +(317.935 + 550.680i) q^{5} +(-741.540 - 99.9494i) q^{6} +(-968.291 + 2197.09i) q^{7} +(-1602.36 + 3769.57i) q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(-14.8009 + 6.07739i) q^{2} +(40.5000 + 23.3827i) q^{3} +(182.131 - 179.901i) q^{4} +(317.935 + 550.680i) q^{5} +(-741.540 - 99.9494i) q^{6} +(-968.291 + 2197.09i) q^{7} +(-1602.36 + 3769.57i) q^{8} +(1093.50 + 1894.00i) q^{9} +(-8052.41 - 6218.32i) q^{10} +(-15973.0 - 9222.04i) q^{11} +(11582.9 - 3027.29i) q^{12} +2631.91 q^{13} +(978.949 - 38403.5i) q^{14} +29736.7i q^{15} +(807.138 - 65531.0i) q^{16} +(-580.579 + 1005.59i) q^{17} +(-27695.3 - 21387.2i) q^{18} +(-43138.0 + 24905.7i) q^{19} +(156974. + 43098.8i) q^{20} +(-90589.7 + 66341.0i) q^{21} +(292461. + 39419.6i) q^{22} +(-426474. + 246225. i) q^{23} +(-153038. + 115200. i) q^{24} +(-6853.06 + 11869.8i) q^{25} +(-38954.5 + 15995.1i) q^{26} +102276. i q^{27} +(218904. + 574354. i) q^{28} +274933. q^{29} +(-180722. - 440129. i) q^{30} +(1.34087e6 + 774150. i) q^{31} +(386311. + 974821. i) q^{32} +(-431272. - 746985. i) q^{33} +(2481.69 - 18412.0i) q^{34} +(-1.51775e6 + 165314. i) q^{35} +(539892. + 148233. i) q^{36} +(-1.45635e6 - 2.52248e6i) q^{37} +(487118. - 630793. i) q^{38} +(106592. + 61541.1i) q^{39} +(-2.58527e6 + 316092. i) q^{40} -1.28629e6 q^{41} +(937625. - 1.53245e6i) q^{42} -1.94938e6i q^{43} +(-4.56823e6 + 1.19395e6i) q^{44} +(-695324. + 1.20434e6i) q^{45} +(4.81577e6 - 6.23618e6i) q^{46} +(-172631. + 99668.5i) q^{47} +(1.56498e6 - 2.63513e6i) q^{48} +(-3.88963e6 - 4.25485e6i) q^{49} +(29293.4 - 217333. i) q^{50} +(-47026.9 + 27151.0i) q^{51} +(479351. - 473484. i) q^{52} +(1.05362e6 - 1.82493e6i) q^{53} +(-621570. - 1.51377e6i) q^{54} -1.17280e7i q^{55} +(-6.73054e6 - 7.17057e6i) q^{56} -2.32945e6 q^{57} +(-4.06924e6 + 1.67087e6i) q^{58} +(-4.94634e6 - 2.85577e6i) q^{59} +(5.34967e6 + 5.41597e6i) q^{60} +(-2.39772e6 - 4.15296e6i) q^{61} +(-2.45508e7 - 3.30911e6i) q^{62} +(-5.22011e6 + 568579. i) q^{63} +(-1.16421e7 - 1.20804e7i) q^{64} +(836777. + 1.44934e6i) q^{65} +(1.09229e7 + 8.43501e6i) q^{66} +(-3.15865e7 - 1.82365e7i) q^{67} +(75166.1 + 287596. i) q^{68} -2.30296e7 q^{69} +(2.14593e7 - 1.16707e7i) q^{70} +3.65484e7i q^{71} +(-8.89174e6 + 1.08716e6i) q^{72} +(1.07300e7 - 1.85849e7i) q^{73} +(3.68854e7 + 2.84840e7i) q^{74} +(-555098. + 320486. i) q^{75} +(-3.37618e6 + 1.22967e7i) q^{76} +(3.57282e7 - 2.61646e7i) q^{77} +(-1.95167e6 - 263058. i) q^{78} +(-4.94567e7 + 2.85538e7i) q^{79} +(3.63432e7 - 2.03901e7i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(1.90382e7 - 7.81730e6i) q^{82} -8.09822e7i q^{83} +(-4.56434e6 + 2.83799e7i) q^{84} -738346. q^{85} +(1.18471e7 + 2.88525e7i) q^{86} +(1.11348e7 + 6.42866e6i) q^{87} +(6.03577e7 - 4.54345e7i) q^{88} +(2.73691e7 + 4.74047e7i) q^{89} +(2.97217e6 - 2.20510e7i) q^{90} +(-2.54845e6 + 5.78255e6i) q^{91} +(-3.33778e7 + 1.21568e8i) q^{92} +(3.62034e7 + 6.27062e7i) q^{93} +(1.94936e6 - 2.52432e6i) q^{94} +(-2.74302e7 - 1.58368e7i) q^{95} +(-7.14831e6 + 4.85132e7i) q^{96} +7.04047e7 q^{97} +(8.34282e7 + 3.93366e7i) q^{98} -4.03372e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 3 q^{2} + 2592 q^{3} - 93 q^{4} + 2256 q^{7} + 4500 q^{8} + 69984 q^{9}+O(q^{10}) \) 64 * q - 3 * q^2 + 2592 * q^3 - 93 * q^4 + 2256 * q^7 + 4500 * q^8 + 69984 * q^9	\( 64 q - 3 q^{2} + 2592 q^{3} - 93 q^{4} + 2256 q^{7} + 4500 q^{8} + 69984 q^{9} - 10335 q^{10} - 17040 q^{11} - 7533 q^{12} - 25696 q^{13} + 177402 q^{14} - 69049 q^{16} + 6561 q^{18} + 43056 q^{19} + 198564 q^{20} + 121824 q^{21} - 609694 q^{22} + 311769 q^{24} - 2659344 q^{25} - 36774 q^{26} - 546649 q^{28} + 2132352 q^{29} + 143289 q^{30} + 372336 q^{31} + 2856627 q^{32} - 460080 q^{33} + 1904308 q^{34} + 4556928 q^{35} - 406782 q^{36} - 1288016 q^{37} - 9363948 q^{38} - 1040688 q^{39} + 5606515 q^{40} + 3397056 q^{41} + 6988275 q^{42} - 26115 q^{44} - 1011480 q^{46} + 4538208 q^{47} - 4733640 q^{48} + 1891264 q^{49} - 6560430 q^{50} + 51739864 q^{52} + 6584736 q^{53} + 531441 q^{54} - 59028579 q^{56} + 2325024 q^{57} + 7804851 q^{58} + 1478544 q^{59} + 7776729 q^{60} + 8242048 q^{61} + 24347610 q^{62} + 4933872 q^{63} + 64036842 q^{64} + 9060000 q^{65} - 38899845 q^{66} + 60524688 q^{67} + 16861008 q^{68} + 163999149 q^{70} + 15411789 q^{72} + 733520 q^{73} + 56169900 q^{74} - 215406864 q^{75} - 57126708 q^{76} - 18996480 q^{77} - 7000830 q^{78} - 65450640 q^{79} + 96711867 q^{80} - 153055008 q^{81} + 27795688 q^{82} + 14330358 q^{84} + 102461312 q^{85} - 245748096 q^{86} + 86360256 q^{87} - 186227585 q^{88} - 31284288 q^{89} + 34209054 q^{90} - 106053648 q^{91} - 300155772 q^{92} + 10053072 q^{93} + 7117734 q^{94} - 116488896 q^{95} + 145538937 q^{96} + 143986208 q^{97} - 275744049 q^{98}+O(q^{100}) \) 64 * q - 3 * q^2 + 2592 * q^3 - 93 * q^4 + 2256 * q^7 + 4500 * q^8 + 69984 * q^9 - 10335 * q^10 - 17040 * q^11 - 7533 * q^12 - 25696 * q^13 + 177402 * q^14 - 69049 * q^16 + 6561 * q^18 + 43056 * q^19 + 198564 * q^20 + 121824 * q^21 - 609694 * q^22 + 311769 * q^24 - 2659344 * q^25 - 36774 * q^26 - 546649 * q^28 + 2132352 * q^29 + 143289 * q^30 + 372336 * q^31 + 2856627 * q^32 - 460080 * q^33 + 1904308 * q^34 + 4556928 * q^35 - 406782 * q^36 - 1288016 * q^37 - 9363948 * q^38 - 1040688 * q^39 + 5606515 * q^40 + 3397056 * q^41 + 6988275 * q^42 - 26115 * q^44 - 1011480 * q^46 + 4538208 * q^47 - 4733640 * q^48 + 1891264 * q^49 - 6560430 * q^50 + 51739864 * q^52 + 6584736 * q^53 + 531441 * q^54 - 59028579 * q^56 + 2325024 * q^57 + 7804851 * q^58 + 1478544 * q^59 + 7776729 * q^60 + 8242048 * q^61 + 24347610 * q^62 + 4933872 * q^63 + 64036842 * q^64 + 9060000 * q^65 - 38899845 * q^66 + 60524688 * q^67 + 16861008 * q^68 + 163999149 * q^70 + 15411789 * q^72 + 733520 * q^73 + 56169900 * q^74 - 215406864 * q^75 - 57126708 * q^76 - 18996480 * q^77 - 7000830 * q^78 - 65450640 * q^79 + 96711867 * q^80 - 153055008 * q^81 + 27795688 * q^82 + 14330358 * q^84 + 102461312 * q^85 - 245748096 * q^86 + 86360256 * q^87 - 186227585 * q^88 - 31284288 * q^89 + 34209054 * q^90 - 106053648 * q^91 - 300155772 * q^92 + 10053072 * q^93 + 7117734 * q^94 - 116488896 * q^95 + 145538937 * q^96 + 143986208 * q^97 - 275744049 * q^98

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