LMFDB - Embedded newform 30.11.b.a.29.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,11,Mod(29,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("30.29");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	30.b (of order $2$, degree $1$, 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:	$19.0607175802$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 486208 x^{18} + 102177590160 x^{16} + \cdots + 19\!\cdots\!56 $ x^20 + 486208x^18 + 102177590160x^16 + 12163246978195592x^14 + 901852059051373360190x^12 + 43041684876012377720793120x^10 + 1315208254211691475328581167088x^8 + 24631202994254750968745967947735032x^6 + 255458085186222729465717424009250507841x^4 + 1189499460361456603778873278804378847018016*x^2 + 1960059820713142147560032279654477796001005456
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{68}\cdot 3^{32}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.15
Root			$-1.41421 - 231.440i$ of defining polynomial
Character	$\chi$	$=$	30.29
Dual form			30.11.b.a.29.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274 q^{2} +(-13.7033 - 242.613i) q^{3} +512.000 q^{4} +(1831.56 + 2532.00i) q^{5} +(-310.070 - 5489.71i) q^{6} +26803.8i q^{7} +11585.2 q^{8} +(-58673.4 + 6649.20i) q^{9} +O(q^{10})$	\(q+22.6274 q^{2} +(-13.7033 - 242.613i) q^{3} +512.000 q^{4} +(1831.56 + 2532.00i) q^{5} +(-310.070 - 5489.71i) q^{6} +26803.8i q^{7} +11585.2 q^{8} +(-58673.4 + 6649.20i) q^{9} +(41443.4 + 57292.6i) q^{10} +63058.0i q^{11} +(-7016.08 - 124218. i) q^{12} +180307. i q^{13} +606501. i q^{14} +(589198. - 479057. i) q^{15} +262144. q^{16} +1.72450e6 q^{17} +(-1.32763e6 + 150454. i) q^{18} +2.45903e6 q^{19} +(937758. + 1.29638e6i) q^{20} +(6.50296e6 - 367301. i) q^{21} +1.42684e6i q^{22} -9.75079e6 q^{23} +(-158756. - 2.81073e6i) q^{24} +(-3.05641e6 + 9.27501e6i) q^{25} +4.07988e6i q^{26} +(2.41720e6 + 1.41438e7i) q^{27} +1.37236e7i q^{28} -2.08335e7i q^{29} +(1.33320e7 - 1.08398e7i) q^{30} +4.03517e7 q^{31} +5.93164e6 q^{32} +(1.52987e7 - 864102. i) q^{33} +3.90211e7 q^{34} +(-6.78672e7 + 4.90928e7i) q^{35} +(-3.00408e7 + 3.40439e6i) q^{36} +3.01887e7i q^{37} +5.56414e7 q^{38} +(4.37449e7 - 2.47080e6i) q^{39} +(2.12190e7 + 2.93338e7i) q^{40} +5.08495e7i q^{41} +(1.47145e8 - 8.31106e6i) q^{42} -1.29701e8i q^{43} +3.22857e7i q^{44} +(-1.24300e8 - 1.36383e8i) q^{45} -2.20635e8 q^{46} +1.82559e8 q^{47} +(-3.59224e6 - 6.35996e7i) q^{48} -4.35969e8 q^{49} +(-6.91586e7 + 2.09870e8i) q^{50} +(-2.36314e7 - 4.18388e8i) q^{51} +9.23172e7i q^{52} -7.15401e8 q^{53} +(5.46951e7 + 3.20039e8i) q^{54} +(-1.59663e8 + 1.15494e8i) q^{55} +3.10529e8i q^{56} +(-3.36968e7 - 5.96593e8i) q^{57} -4.71409e8i q^{58} -1.01181e9i q^{59} +(3.01669e8 - 2.45277e8i) q^{60} -1.84851e8 q^{61} +9.13055e8 q^{62} +(-1.78224e8 - 1.57267e9i) q^{63} +1.34218e8 q^{64} +(-4.56537e8 + 3.30243e8i) q^{65} +(3.46170e8 - 1.95524e7i) q^{66} +1.95708e9i q^{67} +8.82946e8 q^{68} +(1.33618e8 + 2.36567e9i) q^{69} +(-1.53566e9 + 1.11084e9i) q^{70} -1.25777e9i q^{71} +(-6.79746e8 + 7.70326e7i) q^{72} +9.94272e8i q^{73} +6.83093e8i q^{74} +(2.29212e9 + 6.14427e8i) q^{75} +1.25902e9 q^{76} -1.69020e9 q^{77} +(9.89834e8 - 5.59078e7i) q^{78} -7.90158e8 q^{79} +(4.80132e8 + 6.63748e8i) q^{80} +(3.39836e9 - 7.80263e8i) q^{81} +1.15059e9i q^{82} +4.60248e9 q^{83} +(3.32952e9 - 1.88058e8i) q^{84} +(3.15853e9 + 4.36644e9i) q^{85} -2.93480e9i q^{86} +(-5.05449e9 + 2.85488e8i) q^{87} +7.30542e8i q^{88} +9.95968e7i q^{89} +(-2.81258e9 - 3.08599e9i) q^{90} -4.83292e9 q^{91} -4.99240e9 q^{92} +(-5.52951e8 - 9.78986e9i) q^{93} +4.13084e9 q^{94} +(4.50385e9 + 6.22626e9i) q^{95} +(-8.12830e7 - 1.43910e9i) q^{96} +1.40290e9i q^{97} -9.86486e9 q^{98} +(-4.19286e8 - 3.69983e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10240 q^{4} + 6080 q^{6} - 65360 q^{9}+O(q^{10}) $ 20 * q + 10240 * q^4 + 6080 * q^6 - 65360 * q^9	$ 20 q + 10240 q^{4} + 6080 q^{6} - 65360 q^{9} - 33536 q^{10} + 2083928 q^{15} + 5242880 q^{16} + 3209040 q^{19} - 654460 q^{21} + 3112960 q^{24} - 7480596 q^{25} + 34614848 q^{30} + 86022560 q^{31} + 81633280 q^{34} - 33464320 q^{36} + 93388800 q^{39} - 17170432 q^{40} + 440775292 q^{45} + 696625280 q^{46} - 1574325300 q^{49} - 2571307840 q^{51} + 681294400 q^{54} - 2158399088 q^{55} + 1066971136 q^{60} + 1300067680 q^{61} + 2684354560 q^{64} - 308783360 q^{66} - 2771050340 q^{69} - 443470976 q^{70} + 2946710128 q^{75} + 1643028480 q^{76} + 9709493760 q^{79} + 7324584140 q^{81} - 335083520 q^{84} + 10789531168 q^{85} - 5101384192 q^{90} - 20875353600 q^{91} + 7266454400 q^{94} + 1593835520 q^{96} - 39571273840 q^{99}+O(q^{100}) $ 20 * q + 10240 * q^4 + 6080 * q^6 - 65360 * q^9 - 33536 * q^10 + 2083928 * q^15 + 5242880 * q^16 + 3209040 * q^19 - 654460 * q^21 + 3112960 * q^24 - 7480596 * q^25 + 34614848 * q^30 + 86022560 * q^31 + 81633280 * q^34 - 33464320 * q^36 + 93388800 * q^39 - 17170432 * q^40 + 440775292 * q^45 + 696625280 * q^46 - 1574325300 * q^49 - 2571307840 * q^51 + 681294400 * q^54 - 2158399088 * q^55 + 1066971136 * q^60 + 1300067680 * q^61 + 2684354560 * q^64 - 308783360 * q^66 - 2771050340 * q^69 - 443470976 * q^70 + 2946710128 * q^75 + 1643028480 * q^76 + 9709493760 * q^79 + 7324584140 * q^81 - 335083520 * q^84 + 10789531168 * q^85 - 5101384192 * q^90 - 20875353600 * q^91 + 7266454400 * q^94 + 1593835520 * q^96 - 39571273840 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	22.6274			0.707107
$2$	22.6274			0.707107
$3$	−13.7033	−	242.613i	−0.0563921	−	0.998409i
$3$	−13.7033	−	242.613i	−0.0563921	−	0.998409i
$4$	512.000			0.500000
$5$	1831.56	+	2532.00i	0.586099	+	0.810240i
$5$	1831.56	+	2532.00i	0.586099	+	0.810240i
$6$	−310.070	−	5489.71i	−0.0398753	−	0.705982i
$7$			26803.8i			1.59480i	0.603450	+	0.797400i	$0.293792\pi$
$7$			26803.8i			1.59480i	−0.603450	+	0.797400i	$0.706208\pi$
$8$	11585.2			0.353553
$9$	−58673.4	+	6649.20i	−0.993640	+	0.112605i
$10$	41443.4	+	57292.6i	0.414434	+	0.572926i
$11$			63058.0i			0.391541i	0.980650	+	0.195770i	$0.0627207\pi$
$11$			63058.0i			0.391541i	−0.980650	+	0.195770i	$0.937279\pi$
$12$	−7016.08	−	124218.i	−0.0281961	−	0.499204i
$13$			180307.i			0.485619i	0.970074	+	0.242810i	$0.0780691\pi$
$13$			180307.i			0.485619i	−0.970074	+	0.242810i	$0.921931\pi$
$14$			606501.i			1.12769i
$15$	589198.	−	479057.i	0.775899	−	0.630857i
$16$	262144.			0.250000
$17$	1.72450e6			1.21456			0.607281	−	0.794487i	$-0.292260\pi$
$17$	1.72450e6			1.21456			0.607281	+	0.794487i	$0.292260\pi$
$18$	−1.32763e6	+	150454.i	−0.702609	+	0.0796236i
$19$	2.45903e6			0.993106			0.496553	−	0.868007i	$-0.334599\pi$
$19$	2.45903e6			0.993106			0.496553	+	0.868007i	$0.334599\pi$
$20$	937758.	+	1.29638e6i	0.293049	+	0.405120i
$21$	6.50296e6	−	367301.i	1.59226	−	0.0899342i
$22$			1.42684e6i			0.276861i
$23$	−9.75079e6			−1.51496			−0.757479	−	0.652859i	$-0.773569\pi$
$23$	−9.75079e6			−1.51496			−0.757479	+	0.652859i	$0.773569\pi$
$24$	−158756.	−	2.81073e6i	−0.0199376	−	0.352991i
$25$	−3.05641e6	+	9.27501e6i	−0.312976	+	0.949761i
$26$			4.07988e6i			0.343385i
$27$	2.41720e6	+	1.41438e7i	0.168459	+	0.985709i
$28$			1.37236e7i			0.797400i
$29$		−	2.08335e7i		−	1.01572i	−0.861441	−	0.507858i	$-0.830437\pi$
$29$		−	2.08335e7i		−	1.01572i	0.861441	−	0.507858i	$-0.169563\pi$
$30$	1.33320e7	−	1.08398e7i	0.548643	−	0.446084i
$31$	4.03517e7			1.40946			0.704731	−	0.709475i	$-0.251068\pi$
$31$	4.03517e7			1.40946			0.704731	+	0.709475i	$0.251068\pi$
$32$	5.93164e6			0.176777
$33$	1.52987e7	−	864102.i	0.390918	−	0.0220798i
$34$	3.90211e7			0.858825
$35$	−6.78672e7	+	4.90928e7i	−1.29217	+	0.934711i
$36$	−3.00408e7	+	3.40439e6i	−0.496820	+	0.0563024i
$37$			3.01887e7i			0.435348i	0.976022	+	0.217674i	$0.0698469\pi$
$37$			3.01887e7i			0.435348i	−0.976022	+	0.217674i	$0.930153\pi$
$38$	5.56414e7			0.702232
$39$	4.37449e7	−	2.47080e6i	0.484847	−	0.0273851i
$40$	2.12190e7	+	2.93338e7i	0.207217	+	0.286463i
$41$			5.08495e7i			0.438902i	0.975624	+	0.219451i	$0.0704266\pi$
$41$			5.08495e7i			0.438902i	−0.975624	+	0.219451i	$0.929573\pi$
$42$	1.47145e8	−	8.31106e6i	1.12590	−	0.0635931i
$43$		−	1.29701e8i		−	0.882271i	−0.897441	−	0.441135i	$-0.854576\pi$
$43$		−	1.29701e8i		−	0.882271i	0.897441	−	0.441135i	$-0.145424\pi$
$44$			3.22857e7i			0.195770i
$45$	−1.24300e8	−	1.36383e8i	−0.673608	−	0.739089i
$46$	−2.20635e8			−1.07124
$47$	1.82559e8			0.796001			0.398001	−	0.917385i	$-0.369704\pi$
$47$	1.82559e8			0.796001			0.398001	+	0.917385i	$0.369704\pi$
$48$	−3.59224e6	−	6.35996e7i	−0.0140980	−	0.249602i
$49$	−4.35969e8			−1.54339
$50$	−6.91586e7	+	2.09870e8i	−0.221308	+	0.671582i
$51$	−2.36314e7	−	4.18388e8i	−0.0684917	−	1.21263i
$52$			9.23172e7i			0.242810i
$53$	−7.15401e8			−1.71069			−0.855343	−	0.518061i	$-0.826654\pi$
$53$	−7.15401e8			−1.71069			−0.855343	+	0.518061i	$0.826654\pi$
$54$	5.46951e7	+	3.20039e8i	0.119119	+	0.697001i
$55$	−1.59663e8	+	1.15494e8i	−0.317242	+	0.229482i
$56$			3.10529e8i			0.563847i
$57$	−3.36968e7	−	5.96593e8i	−0.0560034	−	0.991525i
$58$		−	4.71409e8i		−	0.718220i
$59$		−	1.01181e9i		−	1.41527i	−0.706576	−	0.707637i	$-0.749761\pi$
$59$		−	1.01181e9i		−	1.41527i	0.706576	−	0.707637i	$-0.250239\pi$
$60$	3.01669e8	−	2.45277e8i	0.387949	−	0.315429i
$61$	−1.84851e8			−0.218863			−0.109431	−	0.993994i	$-0.534903\pi$
$61$	−1.84851e8			−0.218863			−0.109431	+	0.993994i	$0.534903\pi$
$62$	9.13055e8			0.996640
$63$	−1.78224e8	−	1.57267e9i	−0.179582	−	1.58466i
$64$	1.34218e8			0.125000
$65$	−4.56537e8	+	3.30243e8i	−0.393468	+	0.284621i
$66$	3.46170e8	−	1.95524e7i	0.276421	−	0.0156128i
$67$			1.95708e9i			1.44955i	0.688984	+	0.724777i	$0.258057\pi$
$67$			1.95708e9i			1.44955i	−0.688984	+	0.724777i	$0.741943\pi$
$68$	8.82946e8			0.607281
$69$	1.33618e8	+	2.36567e9i	0.0854317	+	1.51255i
$70$	−1.53566e9	+	1.11084e9i	−0.913703	+	0.660941i
$71$		−	1.25777e9i		−	0.697123i	−0.937286	−	0.348562i	$-0.886670\pi$
$71$		−	1.25777e9i		−	0.697123i	0.937286	−	0.348562i	$-0.113330\pi$
$72$	−6.79746e8	+	7.70326e7i	−0.351305	+	0.0398118i
$73$			9.94272e8i			0.479613i	0.970821	+	0.239806i	$0.0770840\pi$
$73$			9.94272e8i			0.479613i	−0.970821	+	0.239806i	$0.922916\pi$
$74$			6.83093e8i			0.307837i
$75$	2.29212e9	+	6.14427e8i	0.965899	+	0.258919i
$76$	1.25902e9			0.496553
$77$	−1.69020e9			−0.624430
$78$	9.89834e8	−	5.59078e7i	0.342838	−	0.0193642i
$79$	−7.90158e8			−0.256790			−0.128395	−	0.991723i	$-0.540983\pi$
$79$	−7.90158e8			−0.256790			−0.128395	+	0.991723i	$0.540983\pi$
$80$	4.80132e8	+	6.63748e8i	0.146525	+	0.202560i
$81$	3.39836e9	−	7.80263e8i	0.974640	−	0.223777i
$82$			1.15059e9i			0.310350i
$83$	4.60248e9			1.16843			0.584213	−	0.811601i	$-0.301403\pi$
$83$	4.60248e9			1.16843			0.584213	+	0.811601i	$0.301403\pi$
$84$	3.32952e9	−	1.88058e8i	0.796132	−	0.0449671i
$85$	3.15853e9	+	4.36644e9i	0.711853	+	0.984086i
$86$		−	2.93480e9i		−	0.623860i
$87$	−5.05449e9	+	2.85488e8i	−1.01410	+	0.0572784i
$88$			7.30542e8i			0.138431i
$89$			9.95968e7i			0.0178359i	0.999960	+	0.00891796i	$0.00283871\pi$
$89$			9.95968e7i			0.0178359i	−0.999960	+	0.00891796i	$0.997161\pi$
$90$	−2.81258e9	−	3.08599e9i	−0.476313	−	0.522615i
$91$	−4.83292e9			−0.774466
$92$	−4.99240e9			−0.757479
$93$	−5.52951e8	−	9.78986e9i	−0.0794826	−	1.40722i
$94$	4.13084e9			0.562858
$95$	4.50385e9	+	6.22626e9i	0.582058	+	0.804653i
$96$	−8.12830e7	−	1.43910e9i	−0.00996882	−	0.176495i
$97$			1.40290e9i			0.163369i	0.996658	+	0.0816843i	$0.0260299\pi$
$97$			1.40290e9i			0.163369i	−0.996658	+	0.0816843i	$0.973970\pi$
$98$	−9.86486e9			−1.09134
$99$	−4.19286e8	−	3.69983e9i	−0.0440894	−	0.389050i
$100$	−1.56488e9	+	4.74880e9i	−0.156488	+	0.474880i
$101$		−	1.31695e10i		−	1.25303i	−0.779409	−	0.626515i	$-0.784481\pi$
$101$		−	1.31695e10i		−	1.25303i	0.779409	−	0.626515i	$-0.215519\pi$
$102$	−5.34717e8	−	9.46703e9i	−0.0484310	−	0.857458i
$103$			7.83117e9i			0.675524i	0.941232	+	0.337762i	$0.109670\pi$
$103$			7.83117e9i			0.675524i	−0.941232	+	0.337762i	$0.890330\pi$
$104$			2.08890e9i			0.171692i
$105$	1.28406e10	+	1.57928e10i	1.00609	+	1.23740i
$106$	−1.61877e10			−1.20964
$107$	1.67237e10			1.19238			0.596188	−	0.802845i	$-0.296681\pi$
$107$	1.67237e10			1.19238			0.596188	+	0.802845i	$0.296681\pi$
$108$	1.23761e9	+	7.24165e9i	0.0842296	+	0.492854i
$109$	−2.64533e10			−1.71928			−0.859641	−	0.510899i	$-0.829313\pi$
$109$	−2.64533e10			−1.71928			−0.859641	+	0.510899i	$0.829313\pi$
$110$	−3.61276e9	+	2.61334e9i	−0.224324	+	0.162268i
$111$	7.32419e9	−	4.13685e8i	0.434655	−	0.0245502i
$112$			7.02646e9i			0.398700i
$113$	−1.31475e9			−0.0713594			−0.0356797	−	0.999363i	$-0.511360\pi$
$113$	−1.31475e9			−0.0713594			−0.0356797	+	0.999363i	$0.511360\pi$
$114$	−7.62471e8	−	1.34994e10i	−0.0396004	−	0.701114i
$115$	−1.78591e10	−	2.46890e10i	−0.887915	−	1.22748i
$116$		−	1.06668e10i		−	0.507858i
$117$	−1.19890e9	−	1.05792e10i	−0.0546831	−	0.482531i
$118$		−	2.28947e10i		−	1.00075i
$119$			4.62233e10i			1.93698i
$120$	6.82600e9	−	5.54999e9i	0.274322	−	0.223042i
$121$	2.19611e10			0.846696
$122$	−4.18269e9			−0.154759
$123$	1.23368e10	−	6.96805e8i	0.438203	−	0.0247506i
$124$	2.06601e10			0.704731
$125$	−2.90823e10	+	9.24891e9i	−0.952969	+	0.303068i
$126$	−4.03275e9	−	3.55855e10i	−0.126984	−	1.12052i
$127$		−	9.41327e9i		−	0.284919i	−0.989801	−	0.142460i	$-0.954499\pi$
$127$		−	9.41327e9i		−	0.284919i	0.989801	−	0.142460i	$-0.0455011\pi$
$128$	3.03700e9			0.0883883
$129$	−3.14673e10	+	1.77733e9i	−0.880867	+	0.0497531i
$130$	−1.03303e10	+	7.47255e9i	−0.278224	+	0.201257i
$131$		−	7.67898e10i		−	1.99043i	−0.0977024	−	0.995216i	$-0.531149\pi$
$131$		−	7.67898e10i		−	1.99043i	0.0977024	−	0.995216i	$-0.468851\pi$
$132$	7.83294e9	−	4.42420e8i	0.195459	−	0.0110399i
$133$			6.59113e10i			1.58381i
$134$			4.42836e10i			1.02499i
$135$	−3.13849e10	+	3.20256e10i	−0.699926	+	0.714215i
$136$	1.99788e10			0.429412
$137$	3.32929e10			0.689841			0.344920	−	0.938632i	$-0.387906\pi$
$137$	3.32929e10			0.689841			0.344920	+	0.938632i	$0.387906\pi$
$138$	3.02343e9	+	5.35290e10i	0.0604094	+	1.06953i
$139$	9.39260e10			1.81014			0.905069	−	0.425264i	$-0.139819\pi$
$139$	9.39260e10			1.81014			0.905069	+	0.425264i	$0.139819\pi$
$140$	−3.47480e10	+	2.51355e10i	−0.646085	+	0.467356i
$141$	−2.50166e9	−	4.42912e10i	−0.0448882	−	0.794734i
$142$		−	2.84601e10i		−	0.492940i
$143$	−1.13698e10			−0.190140
$144$	−1.53809e10	+	1.74305e9i	−0.248410	+	0.0281512i
$145$	5.27504e10	−	3.81578e10i	0.822974	−	0.595310i
$146$			2.24978e10i			0.339137i
$147$	5.97422e9	+	1.05772e11i	0.0870351	+	1.54093i
$148$			1.54566e10i			0.217674i
$149$		−	5.74506e10i		−	0.782282i	−0.920331	−	0.391141i	$-0.872080\pi$
$149$		−	5.74506e10i		−	0.782282i	0.920331	−	0.391141i	$-0.127920\pi$
$150$	5.18648e10	+	1.39029e10i	0.682994	+	0.183083i
$151$	−2.05680e10			−0.262004			−0.131002	−	0.991382i	$-0.541819\pi$
$151$	−2.05680e10			−0.262004			−0.131002	+	0.991382i	$0.541819\pi$
$152$	2.84884e10			0.351116
$153$	−1.01183e11	+	1.14666e10i	−1.20684	+	0.136766i
$154$	−3.82448e10			−0.441538
$155$	7.39065e10	+	1.02170e11i	0.826084	+	1.14200i
$156$	2.23974e10	−	1.26505e9i	0.242423	−	0.0136926i
$157$		−	5.34847e10i		−	0.560701i	−0.959898	−	0.280351i	$-0.909549\pi$
$157$		−	5.34847e10i		−	0.560701i	0.959898	−	0.280351i	$-0.0904508\pi$
$158$	−1.78792e10			−0.181578
$159$	9.80335e9	+	1.73566e11i	0.0964693	+	1.70796i
$160$	1.08642e10	+	1.50189e10i	0.103609	+	0.143231i
$161$		−	2.61358e11i		−	2.41606i
$162$	7.68961e10	−	1.76553e10i	0.689175	−	0.158234i
$163$		−	1.16111e11i		−	1.00910i	−0.863383	−	0.504549i	$-0.831659\pi$
$163$		−	1.16111e11i		−	1.00910i	0.863383	−	0.504549i	$-0.168341\pi$
$164$			2.60349e10i			0.219451i
$165$	3.02084e10	+	3.71537e10i	0.247006	+	0.303796i
$166$	1.04142e11			0.826202
$167$	−6.14992e10			−0.473464			−0.236732	−	0.971575i	$-0.576076\pi$
$167$	−6.14992e10			−0.473464			−0.236732	+	0.971575i	$0.576076\pi$
$168$	7.53384e10	−	4.25526e9i	0.562950	−	0.0317966i
$169$	1.05348e11			0.764174
$170$	7.14694e10	+	9.88013e10i	0.503356	+	0.695854i
$171$	−1.44280e11	+	1.63506e10i	−0.986789	+	0.111828i
$172$		−	6.64071e10i		−	0.441135i
$173$	6.85054e10			0.442073			0.221037	−	0.975266i	$-0.429056\pi$
$173$	6.85054e10			0.442073			0.221037	+	0.975266i	$0.429056\pi$
$174$	−1.14370e11	+	6.45985e9i	−0.717077	+	0.0405020i
$175$	−2.48606e11	−	8.19234e10i	−1.51468	−	0.499135i
$176$			1.65303e10i			0.0978852i
$177$	−2.45479e11	+	1.38652e10i	−1.41302	+	0.0798103i
$178$			2.25362e9i			0.0126119i
$179$		−	1.78320e11i		−	0.970363i	−0.874413	−	0.485182i	$-0.838754\pi$
$179$		−	1.78320e11i		−	0.970363i	0.874413	−	0.485182i	$-0.161246\pi$
$180$	−6.36414e10	−	6.98279e10i	−0.336804	−	0.369544i
$181$	−5.06142e10			−0.260543			−0.130271	−	0.991478i	$-0.541585\pi$
$181$	−5.06142e10			−0.260543			−0.130271	+	0.991478i	$0.541585\pi$
$182$	−1.09356e11			−0.547630
$183$	2.53306e9	+	4.48472e10i	0.0123421	+	0.218514i
$184$	−1.12965e11			−0.535619
$185$	−7.64378e10	+	5.52924e10i	−0.352736	+	0.255157i
$186$	−1.25119e10	−	2.21519e11i	−0.0562027	−	0.995054i
$187$			1.08744e11i			0.475550i
$188$	9.34701e10			0.398001
$189$	−3.79109e11	+	6.47903e10i	−1.57201	+	0.268659i
$190$	1.01911e11	+	1.40884e11i	0.411577	+	0.568976i
$191$			3.05334e10i			0.120118i	0.998195	+	0.0600591i	$0.0191289\pi$
$191$			3.05334e10i			0.120118i	−0.998195	+	0.0600591i	$0.980871\pi$
$192$	−1.83922e9	−	3.25630e10i	−0.00704902	−	0.124801i
$193$		−	4.52569e11i		−	1.69005i	−0.534730	−	0.845023i	$-0.679587\pi$
$193$		−	4.52569e11i		−	1.69005i	0.534730	−	0.845023i	$-0.320413\pi$
$194$			3.17440e10i			0.115519i
$195$	8.63774e10	+	1.06237e11i	0.306357	+	0.376792i
$196$	−2.23216e11			−0.771695
$197$	−2.74268e11			−0.924367			−0.462183	−	0.886784i	$-0.652934\pi$
$197$	−2.74268e11			−0.924367			−0.462183	+	0.886784i	$0.652934\pi$
$198$	−9.48735e9	−	8.37176e10i	−0.0311759	−	0.275100i
$199$	3.88617e11			1.24525			0.622625	−	0.782520i	$-0.286066\pi$
$199$	3.88617e11			1.24525			0.622625	+	0.782520i	$0.286066\pi$
$200$	−3.54092e10	+	1.07453e11i	−0.110654	+	0.335791i
$201$	4.74813e11	−	2.68184e10i	1.44725	−	0.0817434i
$202$		−	2.97991e11i		−	0.886026i
$203$	5.58418e11			1.61987
$204$	−1.20993e10	−	2.14214e11i	−0.0342459	−	0.606315i
$205$	−1.28751e11	+	9.31338e10i	−0.355615	+	0.257240i
$206$			1.77199e11i			0.477667i
$207$	5.72112e11	−	6.48350e10i	1.50532	−	0.170592i
$208$			4.72664e10i			0.121405i
$209$			1.55061e11i			0.388841i
$210$	2.90549e11	+	3.57349e11i	0.711414	+	0.874977i
$211$	−9.39925e10			−0.224740			−0.112370	−	0.993666i	$-0.535844\pi$
$211$	−9.39925e10			−0.224740			−0.112370	+	0.993666i	$0.535844\pi$
$212$	−3.66286e11			−0.855343
$213$	−3.05152e11	+	1.72356e10i	−0.696014	+	0.0393123i
$214$	3.78414e11			0.843137
$215$	3.28403e11	−	2.37556e11i	0.714851	−	0.517098i
$216$	2.80039e10	+	1.63860e11i	0.0595593	+	0.348501i
$217$			1.08158e12i			2.24781i
$218$	−5.98569e11			−1.21572
$219$	2.41224e11	−	1.36248e10i	0.478850	−	0.0270464i
$220$	−8.17474e10	+	5.91332e10i	−0.158621	+	0.114741i
$221$			3.10940e11i			0.589815i
$222$	1.65727e11	−	9.36062e9i	0.307347	−	0.0173596i
$223$			3.27409e11i			0.593698i	0.954924	+	0.296849i	$0.0959358\pi$
$223$			3.27409e11i			0.593698i	−0.954924	+	0.296849i	$0.904064\pi$
$224$			1.58991e11i			0.281924i
$225$	1.17659e11	−	5.64519e11i	0.204038	−	0.978963i
$226$	−2.97494e10			−0.0504587
$227$	6.91626e11			1.14747			0.573736	−	0.819041i	$-0.305494\pi$
$227$	6.91626e11			1.14747			0.573736	+	0.819041i	$0.305494\pi$
$228$	−1.72527e10	−	3.05456e11i	−0.0280017	−	0.495763i
$229$	−1.12655e11			−0.178885			−0.0894425	−	0.995992i	$-0.528509\pi$
$229$	−1.12655e11			−0.178885			−0.0894425	+	0.995992i	$0.528509\pi$
$230$	−4.04106e11	−	5.58648e11i	−0.627851	−	0.867959i
$231$	2.31612e10	+	4.10064e11i	0.0352129	+	0.623436i
$232$		−	2.41361e11i		−	0.359110i
$233$	−4.90642e11			−0.714472			−0.357236	−	0.934014i	$-0.616281\pi$
$233$	−4.90642e11			−0.714472			−0.357236	+	0.934014i	$0.616281\pi$
$234$	−2.71280e10	−	2.39381e11i	−0.0386668	−	0.341201i
$235$	3.34367e11	+	4.62239e11i	0.466535	+	0.644952i
$236$		−	5.18049e11i		−	0.707637i
$237$	1.08278e10	+	1.91703e11i	0.0144809	+	0.256381i
$238$			1.04591e12i			1.36965i
$239$			8.36824e11i			1.07311i	0.843865	+	0.536556i	$0.180275\pi$
$239$			8.36824e11i			1.07311i	−0.843865	+	0.536556i	$0.819725\pi$
$240$	1.54455e11	−	1.25582e11i	0.193975	−	0.157714i
$241$	−1.63344e11			−0.200918			−0.100459	−	0.994941i	$-0.532031\pi$
$241$	−1.63344e11			−0.200918			−0.100459	+	0.994941i	$0.532031\pi$
$242$	4.96923e11			0.598704
$243$	−2.35871e11	−	8.13795e11i	−0.278383	−	0.960470i
$244$	−9.46435e10			−0.109431
$245$	−7.98504e11	−	1.10387e12i	−0.904579	−	1.25052i
$246$	2.79149e11	−	1.57669e10i	0.309856	−	0.0175013i
$247$			4.43380e11i			0.482271i
$248$	4.67484e11			0.498320
$249$	−6.30691e10	−	1.11662e12i	−0.0658900	−	1.16657i
$250$	−6.58057e11	+	2.09279e11i	−0.673851	+	0.214302i
$251$			1.36090e12i			1.36602i	0.730410	+	0.683009i	$0.239329\pi$
$251$			1.36090e12i			1.36602i	−0.730410	+	0.683009i	$0.760671\pi$
$252$	−9.12507e10	−	8.05208e11i	−0.0897911	−	0.792329i
$253$		−	6.14866e11i		−	0.593168i
$254$		−	2.12998e11i		−	0.201468i
$255$	1.01607e12	−	8.26136e11i	0.942377	−	0.766215i
$256$	6.87195e10			0.0625000
$257$	−3.60164e11			−0.321243			−0.160622	−	0.987016i	$-0.551350\pi$
$257$	−3.60164e11			−0.321243			−0.160622	+	0.987016i	$0.551350\pi$
$258$	−7.12023e11	+	4.02165e10i	−0.622867	+	0.0351808i
$259$	−8.09173e11			−0.694293
$260$	−2.33747e11	+	1.69084e11i	−0.196734	+	0.142311i
$261$	1.38526e11	+	1.22237e12i	0.114375	+	1.00926i
$262$		−	1.73756e12i		−	1.40745i
$263$	1.51283e12			1.20230			0.601148	−	0.799137i	$-0.294710\pi$
$263$	1.51283e12			1.20230			0.601148	+	0.799137i	$0.294710\pi$
$264$	1.77239e11	−	1.00108e10i	0.138210	−	0.00780640i
$265$	−1.31030e12	−	1.81140e12i	−1.00263	−	1.38607i
$266$			1.49140e12i			1.11992i
$267$	2.41635e10	−	1.36480e9i	0.0178075	−	0.00100581i
$268$			1.00202e12i			0.724777i
$269$		−	2.46987e12i		−	1.75353i	−0.480923	−	0.876763i	$-0.659698\pi$
$269$		−	2.46987e12i		−	1.75353i	0.480923	−	0.876763i	$-0.340302\pi$
$270$	−7.10160e11	+	7.24657e11i	−0.494923	+	0.505026i
$271$	−1.92795e12			−1.31902			−0.659508	−	0.751697i	$-0.729235\pi$
$271$	−1.92795e12			−1.31902			−0.659508	+	0.751697i	$0.729235\pi$
$272$	4.52068e11			0.303640
$273$	6.62269e10	+	1.17253e12i	0.0436738	+	0.773234i
$274$	7.53332e11			0.487791
$275$	−5.84864e11	−	1.92731e11i	−0.371870	−	0.122543i
$276$	6.84124e10	+	1.21122e12i	0.0427159	+	0.756274i
$277$			6.72531e11i			0.412395i	0.978510	+	0.206197i	$0.0661089\pi$
$277$			6.72531e11i			0.412395i	−0.978510	+	0.206197i	$0.933891\pi$
$278$	2.12530e12			1.27996
$279$	−2.36757e12	+	2.68307e11i	−1.40050	+	0.158712i
$280$	−7.86258e11	+	5.68751e11i	−0.456851	+	0.330470i
$281$			3.18568e11i			0.181832i	0.995859	+	0.0909159i	$0.0289795\pi$
$281$			3.18568e11i			0.181832i	−0.995859	+	0.0909159i	$0.971021\pi$
$282$	−5.66060e10	−	1.00220e12i	−0.0317408	−	0.561962i
$283$			7.02044e11i			0.386752i	0.981125	+	0.193376i	$0.0619437\pi$
$283$			7.02044e11i			0.386752i	−0.981125	+	0.193376i	$0.938056\pi$
$284$		−	6.43978e11i		−	0.348562i
$285$	1.44885e12	−	1.17802e12i	0.770550	−	0.626508i
$286$	−2.57269e11			−0.134449
$287$	−1.36296e12			−0.699961
$288$	−3.48030e11	+	3.94407e10i	−0.175652	+	0.0199059i
$289$	9.57921e11			0.475161
$290$	1.19361e12	−	8.63413e11i	0.581930	−	0.420948i
$291$	3.40363e11	−	1.92244e10i	0.163109	−	0.00921270i
$292$			5.09067e11i			0.239806i
$293$	−1.76805e12			−0.818760			−0.409380	−	0.912364i	$-0.634255\pi$
$293$	−1.76805e12			−0.818760			−0.409380	+	0.912364i	$0.634255\pi$
$294$	1.35181e11	+	2.39335e12i	0.0615431	+	1.08960i
$295$	2.56191e12	−	1.85320e12i	1.14671	−	0.829490i
$296$			3.49744e11i			0.153919i
$297$	−8.91883e11	+	1.52424e11i	−0.385945	+	0.0659586i
$298$		−	1.29996e12i		−	0.553157i
$299$		−	1.75814e12i		−	0.735693i
$300$	1.17357e12	+	3.14587e11i	0.482950	+	0.129460i
$301$	3.47649e12			1.40705
$302$	−4.65402e11			−0.185265
$303$	−3.19509e12	+	1.80465e11i	−1.25104	+	0.0706611i
$304$	6.44619e11			0.248276
$305$	−3.38565e11	−	4.68042e11i	−0.128275	−	0.177331i
$306$	−2.28950e12	+	2.59459e11i	−0.853363	+	0.0967078i
$307$			1.72510e12i			0.632591i	0.948661	+	0.316296i	$0.102439\pi$
$307$			1.72510e12i			0.632591i	−0.948661	+	0.316296i	$0.897561\pi$
$308$	−8.65380e11			−0.312215
$309$	1.89995e12	−	1.07313e11i	0.674449	−	0.0380942i
$310$	1.67231e12	+	2.31185e12i	0.584130	+	0.807517i
$311$			4.37831e12i			1.50489i	0.658656	+	0.752444i	$0.271125\pi$
$311$			4.37831e12i			1.50489i	−0.658656	+	0.752444i	$0.728875\pi$
$312$	5.06795e11	−	2.86248e10i	0.171419	−	0.00968210i
$313$			2.55232e10i			0.00849599i	0.999991	+	0.00424799i	$0.00135218\pi$
$313$			2.55232e10i			0.00849599i	−0.999991	+	0.00424799i	$0.998648\pi$
$314$		−	1.21022e12i		−	0.396476i
$315$	3.65558e12	−	3.33170e12i	1.17870	−	1.07427i
$316$	−4.04561e11			−0.128395
$317$	−3.37573e12			−1.05456			−0.527280	−	0.849691i	$-0.676788\pi$
$317$	−3.37573e12			−1.05456			−0.527280	+	0.849691i	$0.676788\pi$
$318$	2.21825e11	+	3.92735e12i	0.0682141	+	1.20771i
$319$	1.31372e12			0.397694
$320$	2.45828e11	+	3.39839e11i	0.0732624	+	0.101280i
$321$	−2.29170e11	−	4.05739e12i	−0.0672407	−	1.19048i
$322$		−	5.91387e12i		−	1.70841i
$323$	4.24060e12			1.20619
$324$	1.73996e12	−	3.99495e11i	0.487320	−	0.111889i
$325$	−1.67235e12	−	5.51092e11i	−0.461222	−	0.151987i
$326$		−	2.62728e12i		−	0.713540i
$327$	3.62497e11	+	6.41792e12i	0.0969540	+	1.71655i
$328$			5.89103e11i			0.155175i
$329$			4.89327e12i			1.26946i
$330$	6.83538e11	+	8.40692e11i	0.174660	+	0.214816i
$331$	1.15965e12			0.291868			0.145934	−	0.989294i	$-0.453381\pi$
$331$	1.15965e12			0.291868			0.145934	+	0.989294i	$0.453381\pi$
$332$	2.35647e12			0.584213
$333$	−2.00731e11	−	1.77128e12i	−0.0490222	−	0.432579i
$334$	−1.39157e12			−0.334790
$335$	−4.95532e12	+	3.58451e12i	−1.17449	+	0.849582i
$336$	1.70471e12	−	9.62856e10i	0.398066	−	0.0224836i
$337$			1.74877e12i			0.402331i	0.979557	+	0.201166i	$0.0644729\pi$
$337$			1.74877e12i			0.402331i	−0.979557	+	0.201166i	$0.935527\pi$
$338$	2.38375e12			0.540352
$339$	1.80164e10	+	3.18976e11i	0.00402411	+	0.0712459i
$340$	1.61717e12	+	2.23562e12i	0.355927	+	0.492043i
$341$			2.54450e12i			0.551862i
$342$	−3.26468e12	+	3.69971e11i	−0.697765	+	0.0790747i
$343$		−	4.11423e12i		−	0.866599i
$344$		−	1.50262e12i		−	0.311930i
$345$	−5.74515e12	+	4.67119e12i	−1.17545	+	0.955723i
$346$	1.55010e12			0.312593
$347$	−7.30493e10			−0.0145201			−0.00726004	−	0.999974i	$-0.502311\pi$
$347$	−7.30493e10			−0.0145201			−0.00726004	+	0.999974i	$0.502311\pi$
$348$	−2.58790e12	+	1.46170e11i	−0.507050	+	0.0286392i
$349$	−9.21465e11			−0.177972			−0.0889860	−	0.996033i	$-0.528363\pi$
$349$	−9.21465e11			−0.177972			−0.0889860	+	0.996033i	$0.528363\pi$
$350$	−5.62530e12	−	1.85372e12i	−1.07104	−	0.352942i
$351$	−2.55024e12	+	4.35839e11i	−0.478679	+	0.0818070i
$352$			3.74038e11i			0.0692153i
$353$	8.31087e12			1.51626			0.758129	−	0.652105i	$-0.226114\pi$
$353$	8.31087e12			1.51626			0.758129	+	0.652105i	$0.226114\pi$
$354$	−5.55457e12	+	3.13733e11i	−0.999157	+	0.0564344i
$355$	3.18467e12	−	2.30368e12i	0.564837	−	0.408583i
$356$			5.09936e10i			0.00891796i
$357$	1.12144e13	−	6.33411e11i	1.93390	−	0.109231i
$358$		−	4.03492e12i		−	0.686150i
$359$			1.54697e12i			0.259424i	0.991552	+	0.129712i	$0.0414052\pi$
$359$			1.54697e12i			0.259424i	−0.991552	+	0.129712i	$0.958595\pi$
$360$	−1.44004e12	−	1.58003e12i	−0.238156	−	0.261307i
$361$	−8.42481e10			−0.0137412
$362$	−1.14527e12			−0.184232
$363$	−3.00939e11	−	5.32806e12i	−0.0477470	−	0.845349i
$364$	−2.47445e12			−0.387233
$365$	−2.51749e12	+	1.82107e12i	−0.388601	+	0.281101i
$366$	5.73167e10	+	1.01478e12i	0.00872721	+	0.154513i
$367$		−	5.53301e12i		−	0.831058i	−0.909580	−	0.415529i	$-0.863596\pi$
$367$		−	5.53301e12i		−	0.831058i	0.909580	−	0.415529i	$-0.136404\pi$
$368$	−2.55611e12			−0.378740
$369$	−3.38108e11	−	2.98351e12i	−0.0494224	−	0.436110i
$370$	−1.72959e12	+	1.25112e12i	−0.249422	+	0.180423i
$371$		−	1.91755e13i		−	2.72820i
$372$	−2.83111e11	−	5.01241e12i	−0.0397413	−	0.703609i
$373$		−	6.67025e12i		−	0.923842i	−0.886921	−	0.461921i	$-0.847160\pi$
$373$		−	6.67025e12i		−	0.923842i	0.886921	−	0.461921i	$-0.152840\pi$
$374$			2.46059e12i			0.336265i
$375$	2.64243e12	+	6.92901e12i	0.356326	+	0.934362i
$376$	2.11499e12			0.281429
$377$	3.75643e12			0.493252
$378$	−8.57826e12	+	1.46604e12i	−1.11158	+	0.189970i
$379$	−6.58776e11			−0.0842445			−0.0421222	−	0.999112i	$-0.513412\pi$
$379$	−6.58776e11			−0.0842445			−0.0421222	+	0.999112i	$0.513412\pi$
$380$	2.30597e12	+	3.18784e12i	0.291029	+	0.402327i
$381$	−2.28378e12	+	1.28993e11i	−0.284466	+	0.0160672i
$382$			6.90893e11i			0.0849364i
$383$	−6.33504e12			−0.768698			−0.384349	−	0.923188i	$-0.625574\pi$
$383$	−6.33504e12			−0.768698			−0.384349	+	0.923188i	$0.625574\pi$
$384$	−4.16169e10	−	7.36817e11i	−0.00498441	−	0.0882477i
$385$	−3.09569e12	−	4.27957e12i	−0.365977	−	0.505937i
$386$		−	1.02405e13i		−	1.19504i
$387$	8.62410e11	+	7.61002e12i	0.0993480	+	0.876660i
$388$			7.18285e11i			0.0816843i
$389$			1.36879e13i			1.53670i	0.640027	+	0.768352i	$0.278923\pi$
$389$			1.36879e13i			1.53670i	−0.640027	+	0.768352i	$0.721077\pi$
$390$	1.95450e12	+	2.40386e12i	0.216627	+	0.266432i
$391$	−1.68153e13			−1.84001
$392$	−5.05081e12			−0.545671
$393$	−1.86302e13	+	1.05227e12i	−1.98726	+	0.112245i
$394$	−6.20598e12			−0.653626
$395$	−1.44722e12	−	2.00068e12i	−0.150504	−	0.208061i
$396$	−2.14674e11	−	1.89431e12i	−0.0220447	−	0.194525i
$397$			1.51838e13i			1.53967i	0.638242	+	0.769836i	$0.279662\pi$
$397$			1.51838e13i			1.53967i	−0.638242	+	0.769836i	$0.720338\pi$
$398$	8.79340e12			0.880525
$399$	1.59910e13	−	9.03202e11i	1.58129	−	0.0893142i
$400$	−8.01219e11	+	2.43139e12i	−0.0782441	+	0.237440i
$401$			4.32442e12i			0.417068i	0.978015	+	0.208534i	$0.0668691\pi$
$401$			4.32442e12i			0.417068i	−0.978015	+	0.208534i	$0.933131\pi$
$402$	1.07438e13	−	6.06832e11i	1.02336	−	0.0578013i
$403$			7.27570e12i			0.684462i
$404$		−	6.74277e12i		−	0.626515i
$405$	8.19992e12	+	7.17555e12i	0.752549	+	0.658537i
$406$	1.26356e13			1.14542
$407$	−1.90364e12			−0.170456
$408$	−2.73775e11	−	4.84712e12i	−0.0242155	−	0.428729i
$409$	−4.49174e12			−0.392462			−0.196231	−	0.980558i	$-0.562870\pi$
$409$	−4.49174e12			−0.392462			−0.196231	+	0.980558i	$0.562870\pi$
$410$	−2.91330e12	+	2.10738e12i	−0.251458	+	0.181896i
$411$	−4.56222e11	−	8.07730e12i	−0.0389016	−	0.688743i
$412$			4.00956e12i			0.337762i
$413$	2.71205e13			2.25708
$414$	1.29454e13	−	1.46705e12i	1.06442	−	0.120626i
$415$	8.42971e12	+	1.16535e13i	0.684813	+	0.946705i
$416$			1.06952e12i			0.0858462i
$417$	−1.28710e12	−	2.27877e13i	−0.102078	−	1.80726i
$418$			3.50864e12i			0.274952i
$419$		−	8.24737e12i		−	0.638625i	−0.947650	−	0.319312i	$-0.896548\pi$
$419$		−	8.24737e12i		−	0.638625i	0.947650	−	0.319312i	$-0.103452\pi$
$420$	6.57437e12	+	8.08589e12i	0.503046	+	0.618702i
$421$	2.28488e13			1.72764			0.863819	−	0.503803i	$-0.168066\pi$
$421$	2.28488e13			1.72764			0.863819	+	0.503803i	$0.168066\pi$
$422$	−2.12681e12			−0.158915
$423$	−1.07114e13	+	1.21387e12i	−0.790938	+	0.0896336i
$424$	−8.28810e12			−0.604819
$425$	−5.27079e12	+	1.59948e13i	−0.380129	+	1.15354i
$426$	−6.90480e12	+	3.89997e11i	−0.492156	+	0.0277980i
$427$		−	4.95470e12i		−	0.349042i
$428$	8.56253e12			0.596188
$429$	1.55804e11	+	2.75847e12i	0.0107224	+	0.189837i
$430$	7.43092e12	−	5.37527e12i	0.505476	−	0.365644i
$431$		−	2.00440e13i		−	1.34771i	−0.738863	−	0.673856i	$-0.764637\pi$
$431$		−	2.00440e13i		−	1.34771i	0.738863	−	0.673856i	$-0.235363\pi$
$432$	6.33656e11	+	3.70772e12i	0.0421148	+	0.246427i
$433$			2.74302e13i			1.80214i	0.433672	+	0.901071i	$0.357218\pi$
$433$			2.74302e13i			1.80214i	−0.433672	+	0.901071i	$0.642782\pi$
$434$			2.44733e13i			1.58944i
$435$	−9.98045e12	−	1.22751e13i	−0.640772	−	0.788093i
$436$	−1.35441e13			−0.859641
$437$	−2.39775e13			−1.50451
$438$	5.45827e12	−	3.08294e11i	0.338598	−	0.0191247i
$439$	8.88880e11			0.0545156			0.0272578	−	0.999628i	$-0.491323\pi$
$439$	8.88880e11			0.0545156			0.0272578	+	0.999628i	$0.491323\pi$
$440$	−1.84973e12	+	1.33803e12i	−0.112162	+	0.0811340i
$441$	2.55798e13	−	2.89885e12i	1.53357	−	0.173793i
$442$			7.03578e12i			0.417062i
$443$	9.99157e12			0.585619			0.292809	−	0.956171i	$-0.405410\pi$
$443$	9.99157e12			0.585619			0.292809	+	0.956171i	$0.405410\pi$
$444$	3.74998e12	−	2.11807e11i	0.217327	−	0.0122751i
$445$	−2.52179e11	+	1.82418e11i	−0.0144514	+	0.0104536i
$446$			7.40841e12i			0.419808i
$447$	−1.39383e13	+	7.87263e11i	−0.781037	+	0.0441146i
$448$			3.59755e12i			0.199350i
$449$		−	8.89779e12i		−	0.487585i	−0.969827	−	0.243793i	$-0.921608\pi$
$449$		−	8.89779e12i		−	0.487585i	0.969827	−	0.243793i	$-0.0783916\pi$
$450$	2.66231e12	−	1.27736e13i	0.144277	−	0.692231i
$451$	−3.20647e12			−0.171848
$452$	−6.73153e11			−0.0356797
$453$	2.81850e11	+	4.99008e12i	0.0147750	+	0.261587i
$454$	1.56497e13			0.811385
$455$	−8.85178e12	−	1.22369e13i	−0.453914	−	0.627503i
$456$	−3.90385e11	−	6.91167e12i	−0.0198002	−	0.350557i
$457$		−	6.77365e12i		−	0.339814i	−0.985460	−	0.169907i	$-0.945653\pi$
$457$		−	6.77365e12i		−	0.339814i	0.985460	−	0.169907i	$-0.0543468\pi$
$458$	−2.54910e12			−0.126491
$459$	4.16848e12	+	2.43911e13i	0.204604	+	1.19720i
$460$	−9.14388e12	−	1.26408e13i	−0.443958	−	0.613740i
$461$		−	2.26439e13i		−	1.08754i	−0.839234	−	0.543771i	$-0.816996\pi$
$461$		−	2.26439e13i		−	1.08754i	0.839234	−	0.543771i	$-0.183004\pi$
$462$	5.24079e11	+	9.27869e12i	0.0248993	+	0.440836i
$463$		−	6.80220e12i		−	0.319701i	−0.987141	−	0.159851i	$-0.948899\pi$
$463$		−	6.80220e12i		−	0.319701i	0.987141	−	0.159851i	$-0.0511013\pi$
$464$		−	5.46138e12i		−	0.253929i
$465$	2.37751e13	−	1.93308e13i	1.09360	−	0.889169i
$466$	−1.11020e13			−0.505208
$467$	−3.04905e13			−1.37271			−0.686357	−	0.727265i	$-0.740791\pi$
$467$	−3.04905e13			−1.37271			−0.686357	+	0.727265i	$0.740791\pi$
$468$	−6.13836e11	−	5.41657e12i	−0.0273415	−	0.241265i
$469$	−5.24572e13			−2.31175
$470$	7.56587e12	+	1.04593e13i	0.329890	+	0.456050i
$471$	−1.29761e13	+	7.32917e11i	−0.559809	+	0.0316192i
$472$		−	1.17221e13i		−	0.500375i
$473$	8.17871e12			0.345445
$474$	2.45004e11	+	4.33774e12i	0.0102396	+	0.181289i
$475$	−7.51579e12	+	2.28075e13i	−0.310818	+	0.943213i
$476$			2.36663e13i			0.968492i
$477$	4.19751e13	−	4.75685e12i	1.69981	−	0.192632i
$478$			1.89352e13i			0.758804i
$479$		−	1.61220e13i		−	0.639352i	−0.947527	−	0.319676i	$-0.896426\pi$
$479$		−	1.61220e13i		−	0.639352i	0.947527	−	0.319676i	$-0.103574\pi$
$480$	3.49491e12	−	2.84160e12i	0.137161	−	0.111521i
$481$	−5.44324e12			−0.211413
$482$	−3.69606e12			−0.142070
$483$	−6.34090e13	+	3.58147e12i	−2.41221	+	0.136247i
$484$	1.12441e13			0.423348
$485$	−3.55214e12	+	2.56950e12i	−0.132368	+	0.0957501i
$486$	−5.33715e12	−	1.84141e13i	−0.196847	−	0.679155i
$487$		−	3.28975e13i		−	1.20093i	−0.799650	−	0.600466i	$-0.794982\pi$
$487$		−	3.28975e13i		−	1.20093i	0.799650	−	0.600466i	$-0.205018\pi$
$488$	−2.14154e12			−0.0773797
$489$	−2.81700e13	+	1.59110e12i	−1.00749	+	0.0569052i
$490$	−1.80681e13	−	2.49778e13i	−0.639634	−	0.884248i
$491$			4.12828e13i			1.44664i	0.690511	+	0.723322i	$0.257386\pi$
$491$			4.12828e13i			1.44664i	−0.690511	+	0.723322i	$0.742614\pi$
$492$	6.31642e12	−	3.56764e11i	0.219102	−	0.0123753i
$493$		−	3.59275e13i		−	1.23365i
$494$			1.00325e13i			0.341017i
$495$	8.60002e12	−	7.83809e12i	0.289383	−	0.263745i
$496$	1.05780e13			0.352365
$497$	3.37130e13			1.11177
$498$	−1.42709e12	−	2.52663e13i	−0.0465913	−	0.824887i
$499$	2.61076e13			0.843848			0.421924	−	0.906631i	$-0.361355\pi$
$499$	2.61076e13			0.843848			0.421924	+	0.906631i	$0.361355\pi$
$500$	−1.48901e13	+	4.73544e12i	−0.476484	+	0.151534i
$501$	8.42741e11	+	1.49205e13i	0.0266997	+	0.472711i
$502$			3.07936e13i			0.965920i
$503$	4.20502e13			1.30595			0.652977	−	0.757378i	$-0.273520\pi$
$503$	4.20502e13			1.30595			0.652977	+	0.757378i	$0.273520\pi$
$504$	−2.06477e12	−	1.82198e13i	−0.0634919	−	0.560261i
$505$	3.33451e13	−	2.41207e13i	1.01525	−	0.734400i
$506$		−	1.39128e13i		−	0.419433i
$507$	−1.44361e12	−	2.55588e13i	−0.0430934	−	0.762958i
$508$		−	4.81959e12i		−	0.142460i
$509$		−	6.13790e12i		−	0.179651i	−0.995957	−	0.0898257i	$-0.971369\pi$
$509$		−	6.13790e12i		−	0.179651i	0.995957	−	0.0898257i	$-0.0286310\pi$
$510$	2.29911e13	−	1.86933e13i	0.666361	−	0.541796i
$511$	−2.66503e13			−0.764887
$512$	1.55494e12			0.0441942
$513$	5.94397e12	+	3.47801e13i	0.167298	+	0.978913i
$514$	−8.14957e12			−0.227153
$515$	−1.98285e13	+	1.43432e13i	−0.547336	+	0.395924i
$516$	−1.61112e13	+	9.09995e11i	−0.440433	+	0.0248766i
$517$			1.15118e13i			0.311667i
$518$	−1.83095e13			−0.490939
$519$	−9.38749e11	−	1.66203e13i	−0.0249295	−	0.441370i
$520$	−5.28909e12	+	3.82594e12i	−0.139112	+	0.100629i
$521$			5.56655e13i			1.45010i	0.688697	+	0.725049i	$0.258183\pi$
$521$			5.56655e13i			1.45010i	−0.688697	+	0.725049i	$0.741817\pi$
$522$	3.13449e12	+	2.76592e13i	0.0808750	+	0.713652i
$523$			2.50287e13i			0.639630i	0.947480	+	0.319815i	$0.103621\pi$
$523$			2.50287e13i			0.639630i	−0.947480	+	0.319815i	$0.896379\pi$
$524$		−	3.93164e13i		−	0.995216i
$525$	−1.64690e13	+	6.14377e13i	−0.412924	+	1.54042i
$526$	3.42315e13			0.850152
$527$	6.95867e13			1.71188
$528$	4.01047e12	−	2.26519e11i	0.0977294	−	0.00551996i
$529$	5.36514e13			1.29510
$530$	−2.96487e13	−	4.09872e13i	−0.708968	−	0.980097i
$531$	6.72775e12	+	5.93666e13i	0.159367	+	1.40627i
$532$			3.37466e13i			0.791903i
$533$	−9.16852e12			−0.213139
$534$	5.46758e11	−	3.08820e10i	0.0125918	−	0.000711212i
$535$	3.06304e13	+	4.23444e13i	0.698850	+	0.966110i
$536$			2.26732e13i			0.512495i
$537$	−4.32627e13	+	2.44357e12i	−0.968819	+	0.0547209i
$538$		−	5.58867e13i		−	1.23993i
$539$		−	2.74914e13i		−	0.604300i
$540$	−1.60691e13	+	1.63971e13i	−0.349963	+	0.357107i
$541$	−3.96569e13			−0.855721			−0.427861	−	0.903845i	$-0.640733\pi$
$541$	−3.96569e13			−0.855721			−0.427861	+	0.903845i	$0.640733\pi$
$542$	−4.36246e13			−0.932686
$543$	6.93580e11	+	1.22797e13i	0.0146926	+	0.260128i
$544$	1.02291e13			0.214706
$545$	−4.84507e13	−	6.69796e13i	−1.00767	−	1.39303i
$546$	1.49854e12	+	2.65313e13i	0.0308821	+	0.546759i
$547$		−	5.17286e13i		−	1.05632i	−0.849146	−	0.528158i	$-0.822883\pi$
$547$		−	5.17286e13i		−	1.05632i	0.849146	−	0.528158i	$-0.177117\pi$
$548$	1.70460e13			0.344920
$549$	1.08458e13	−	1.22911e12i	0.217471	−	0.0246450i
$550$	−1.32340e13	−	4.36101e12i	−0.262952	−	0.0866509i
$551$		−	5.12302e13i		−	1.00871i
$552$	1.54800e12	+	2.74069e13i	0.0302047	+	0.534766i
$553$		−	2.11792e13i		−	0.409529i
$554$			1.52176e13i			0.291607i
$555$	1.44621e13	+	1.77871e13i	0.274642	+	0.337786i
$556$	4.80901e13			0.905069
$557$	5.93902e12			0.110774			0.0553871	−	0.998465i	$-0.482361\pi$
$557$	5.93902e12			0.110774			0.0553871	+	0.998465i	$0.482361\pi$
$558$	−5.35720e13	+	6.07108e12i	−0.990301	+	0.112226i
$559$	2.33861e13			0.428448
$560$	−1.77910e13	+	1.28694e13i	−0.323043	+	0.233678i
$561$	2.63827e13	−	1.49015e12i	0.474794	−	0.0268173i
$562$			7.20836e12i			0.128575i
$563$	7.73950e13			1.36827			0.684134	−	0.729357i	$-0.260180\pi$
$563$	7.73950e13			1.36827			0.684134	+	0.729357i	$0.260180\pi$
$564$	−1.28085e12	−	2.26771e13i	−0.0224441	−	0.397367i
$565$	−2.40804e12	−	3.32895e12i	−0.0418237	−	0.0578182i
$566$			1.58854e13i			0.273475i
$567$	2.09140e13	+	9.10890e13i	0.356880	+	1.55436i
$568$		−	1.45716e13i		−	0.246470i
$569$			2.48709e13i			0.416994i	0.978023	+	0.208497i	$0.0668572\pi$
$569$			2.48709e13i			0.416994i	−0.978023	+	0.208497i	$0.933143\pi$
$570$	3.27838e13	−	2.66554e13i	0.544861	−	0.443008i
$571$	9.35364e13			1.54099			0.770495	−	0.637446i	$-0.220009\pi$
$571$	9.35364e13			1.54099			0.770495	+	0.637446i	$0.220009\pi$
$572$	−5.82134e12			−0.0950699
$573$	7.40782e12	−	4.18408e11i	0.119927	−	0.00677372i
$574$	−3.08403e13			−0.494947
$575$	2.98024e13	−	9.04387e13i	0.474146	−	1.43885i
$576$	−7.87502e12	+	8.92441e11i	−0.124205	+	0.0140756i
$577$		−	2.42004e13i		−	0.378394i	−0.981939	−	0.189197i	$-0.939412\pi$
$577$		−	2.42004e13i		−	0.378394i	0.981939	−	0.189197i	$-0.0605884\pi$
$578$	2.16753e13			0.335989
$579$	−1.09799e14	+	6.20169e12i	−1.68736	+	0.0953053i
$580$	2.70082e13	−	1.95368e13i	0.411487	−	0.297655i
$581$			1.23364e14i			1.86341i
$582$	7.70152e12	−	4.34998e11i	0.115335	−	0.00651436i
$583$		−	4.51118e13i		−	0.669804i
$584$			1.15189e13i			0.169569i
$585$	2.45908e13	−	2.24121e13i	0.358916	−	0.327117i
$586$	−4.00064e13			−0.578951
$587$	−2.52767e13			−0.362685			−0.181343	−	0.983420i	$-0.558044\pi$
$587$	−2.52767e13			−0.362685			−0.181343	+	0.983420i	$0.558044\pi$
$588$	3.05880e12	+	5.41553e13i	0.0435175	+	0.770467i
$589$	9.92259e13			1.39974
$590$	5.79694e13	−	4.19330e13i	0.810847	−	0.586538i
$591$	3.75838e12	+	6.65411e13i	0.0521270	+	0.922896i
$592$			7.91379e12i			0.108837i
$593$	−1.11003e14			−1.51378			−0.756889	−	0.653543i	$-0.773282\pi$
$593$	−1.11003e14			−1.51378			−0.756889	+	0.653543i	$0.773282\pi$
$594$	−2.01810e13	+	3.44896e12i	−0.272904	+	0.0466398i
$595$	−1.17037e14	+	8.46607e13i	−1.56942	+	1.13526i
$596$		−	2.94147e13i		−	0.391141i
$597$	−5.32533e12	−	9.42837e13i	−0.0702223	−	1.24327i
$598$		−	3.97821e13i		−	0.520214i
$599$			1.56598e13i			0.203072i	0.994832	+	0.101536i	$0.0323758\pi$
$599$			1.56598e13i			0.203072i	−0.994832	+	0.101536i	$0.967624\pi$
$600$	2.65548e13	+	7.11828e12i	0.341497	+	0.0915417i
$601$	−6.15296e13			−0.784715			−0.392357	−	0.919813i	$-0.628340\pi$
$601$	−6.15296e13			−0.784715			−0.392357	+	0.919813i	$0.628340\pi$
$602$	7.86640e13			0.994932
$603$	−1.30130e13	−	1.14829e14i	−0.163227	−	1.44033i
$604$	−1.05308e13			−0.131002
$605$	4.02231e13	+	5.56055e13i	0.496247	+	0.686026i
$606$	−7.22966e13	+	4.08346e12i	−0.884616	+	0.0499649i
$607$		−	5.53263e13i		−	0.671410i	−0.941967	−	0.335705i	$-0.891025\pi$
$607$		−	5.53263e13i		−	0.671410i	0.941967	−	0.335705i	$-0.108975\pi$
$608$	1.45861e13			0.175558
$609$	−7.65216e12	−	1.35480e14i	−0.0913477	−	1.61729i
$610$	−7.66085e12	−	1.05906e13i	−0.0907043	−	0.125392i
$611$			3.29167e13i			0.386554i
$612$	−5.18055e13	+	5.87089e12i	−0.603419	+	0.0683828i
$613$			1.14939e14i			1.32790i	0.747776	+	0.663952i	$0.231122\pi$
$613$			1.14939e14i			1.32790i	−0.747776	+	0.663952i	$0.768878\pi$
$614$			3.90346e13i			0.447310i
$615$	2.43598e13	+	2.99604e13i	0.276884	+	0.340543i
$616$	−1.95813e13			−0.220769
$617$	−1.71741e14			−1.92065			−0.960325	−	0.278885i	$-0.910035\pi$
$617$	−1.71741e14			−1.92065			−0.960325	+	0.278885i	$0.910035\pi$
$618$	4.29909e13	−	2.42821e12i	0.476907	−	0.0269367i
$619$	−3.87020e13			−0.425873			−0.212937	−	0.977066i	$-0.568303\pi$
$619$	−3.87020e13			−0.425873			−0.212937	+	0.977066i	$0.568303\pi$
$620$	3.78401e13	+	5.23113e13i	0.413042	+	0.571001i
$621$	−2.35696e13	−	1.37914e14i	−0.255208	−	1.49331i
$622$			9.90698e13i			1.06412i
$623$	−2.66958e12			−0.0284447
$624$	1.14675e13	−	6.47706e11i	0.121212	−	0.00684628i
$625$	−7.66842e13	−	5.66964e13i	−0.804092	−	0.594505i
$626$			5.77525e11i			0.00600757i
$627$	3.76200e13	−	2.12485e12i	0.388223	−	0.0219276i
$628$		−	2.73842e13i		−	0.280351i
$629$			5.20606e13i			0.528757i
$630$	8.27162e13	−	7.53879e13i	0.833466	−	0.759624i
$631$	−1.88475e14			−1.88411			−0.942057	−	0.335454i	$-0.891110\pi$
$631$	−1.88475e14			−1.88411			−0.942057	+	0.335454i	$0.891110\pi$
$632$	−9.15416e12			−0.0907890
$633$	1.28801e12	+	2.28038e13i	0.0126736	+	0.224383i
$634$	−7.63841e13			−0.745687
$635$	2.38344e13	−	1.72410e13i	0.230853	−	0.166991i
$636$	5.01932e12	+	8.88658e13i	0.0482346	+	0.853982i
$637$		−	7.86084e13i		−	0.749500i
$638$	2.97261e13			0.281212
$639$	8.36317e12	+	7.37977e13i	0.0784994	+	0.692689i
$640$	5.56245e12	+	7.68968e12i	0.0518043	+	0.0716157i
$641$		−	1.28723e14i		−	1.18951i	−0.803908	−	0.594754i	$-0.797250\pi$
$641$		−	1.28723e14i		−	1.18951i	0.803908	−	0.594754i	$-0.202750\pi$
$642$	−5.18552e12	−	9.18083e13i	−0.0475463	−	0.841796i
$643$			3.85929e13i			0.351118i	0.984469	+	0.175559i	$0.0561732\pi$
$643$			3.85929e13i			0.351118i	−0.984469	+	0.175559i	$0.943827\pi$
$644$		−	1.33816e14i		−	1.20803i
$645$	−6.21343e13	−	7.64198e13i	−0.556587	−	0.684553i
$646$	9.59539e13			0.852904
$647$	−6.15081e13			−0.542514			−0.271257	−	0.962507i	$-0.587439\pi$
$647$	−6.15081e13			−0.542514			−0.271257	+	0.962507i	$0.587439\pi$
$648$	3.93708e13	−	9.03953e12i	0.344587	−	0.0791172i
$649$	6.38030e13			0.554137
$650$	−3.78410e13	−	1.24698e13i	−0.326134	−	0.107471i
$651$	2.62406e14	−	1.48212e13i	2.24423	−	0.126759i
$652$		−	5.94486e13i		−	0.504549i
$653$	3.73149e11			0.00314280			0.00157140	−	0.999999i	$-0.499500\pi$
$653$	3.73149e11			0.00314280			0.00157140	+	0.999999i	$0.499500\pi$
$654$	8.20237e12	+	1.45221e14i	0.0685568	+	1.21378i
$655$	1.94432e14	−	1.40645e14i	1.61273	−	1.16659i
$656$			1.33299e13i			0.109725i
$657$	−6.61111e12	−	5.83373e13i	−0.0540067	−	0.476562i
$658$			1.10722e14i			0.897646i
$659$			4.28552e10i			0.000344807i	1.00000		0.000172404i	$5.48778e-5\pi$
$659$			4.28552e10i			0.000344807i	−1.00000		0.000172404i	$0.999945\pi$
$660$	1.54667e13	+	1.90227e13i	0.123503	+	0.151898i
$661$	−1.10553e14			−0.876117			−0.438059	−	0.898946i	$-0.644334\pi$
$661$	−1.10553e14			−0.876117			−0.438059	+	0.898946i	$0.644334\pi$
$662$	2.62398e13			0.206382
$663$	7.54383e13	−	4.26091e12i	0.588876	−	0.0332609i
$664$	5.33208e13			0.413101
$665$	−1.66887e14	+	1.20721e14i	−1.28326	+	0.928267i
$666$	−4.54202e12	−	4.00794e13i	−0.0346640	−	0.305879i
$667$			2.03143e14i			1.53877i
$668$	−3.14876e13			−0.236732
$669$	7.94337e13	−	4.48657e12i	0.592753	−	0.0334799i
$670$	−1.12126e14	+	8.11081e13i	−0.830487	+	0.600745i
$671$		−	1.16563e13i		−	0.0856937i
$672$	3.85732e13	−	2.17870e12i	0.281475	−	0.0158983i
$673$			2.00366e14i			1.45127i	0.688078	+	0.725637i	$0.258455\pi$
$673$			2.00366e14i			1.45127i	−0.688078	+	0.725637i	$0.741545\pi$
$674$			3.95702e13i			0.284491i
$675$	−1.38572e14	−	2.08098e13i	−0.988911	−	0.148507i
$676$	5.39381e13			0.382087
$677$	5.80314e13			0.408056			0.204028	−	0.978965i	$-0.434597\pi$
$677$	5.80314e13			0.408056			0.204028	+	0.978965i	$0.434597\pi$
$678$	4.07665e11	+	7.21761e12i	0.00284548	+	0.0503784i
$679$	−3.76031e13			−0.260540
$680$	3.65923e13	+	5.05863e13i	0.251678	+	0.347927i
$681$	−9.47755e12	−	1.67798e14i	−0.0647084	−	1.14565i
$682$			5.75754e13i			0.390225i
$683$	1.81960e13			0.122425			0.0612127	−	0.998125i	$-0.480503\pi$
$683$	1.81960e13			0.122425			0.0612127	+	0.998125i	$0.480503\pi$
$684$	−7.38712e13	+	8.37149e12i	−0.493395	+	0.0559142i
$685$	6.09779e13	+	8.42976e13i	0.404315	+	0.558936i
$686$		−	9.30944e13i		−	0.612778i
$687$	1.54375e12	+	2.73317e13i	0.0100877	+	0.178600i
$688$		−	3.40004e13i		−	0.220568i
$689$		−	1.28992e14i		−	0.830743i
$690$	−1.29998e14	+	1.05697e14i	−0.831172	+	0.675798i
$691$	1.73043e14			1.09841			0.549205	−	0.835688i	$-0.314931\pi$
$691$	1.73043e14			1.09841			0.549205	+	0.835688i	$0.314931\pi$
$692$	3.50748e13			0.221037
$693$	9.91696e13	−	1.12385e13i	0.620458	−	0.0703138i
$694$	−1.65292e12			−0.0102672
$695$	1.72031e14	+	2.37820e14i	1.06092	+	1.46665i
$696$	−5.85574e13	+	3.30744e12i	−0.358539	+	0.0202510i
$697$			8.76901e13i			0.533073i
$698$	−2.08504e13			−0.125845
$699$	6.72341e12	+	1.19036e14i	0.0402906	+	0.713335i
$700$	−1.27286e14	−	4.19448e13i	−0.757340	−	0.249567i
$701$			8.19269e13i			0.483990i	0.970277	+	0.241995i	$0.0778018\pi$
$701$			8.19269e13i			0.483990i	−0.970277	+	0.241995i	$0.922198\pi$
$702$	−5.77052e13	+	9.86191e12i	−0.338477	+	0.0578463i
$703$			7.42349e13i			0.432346i
$704$			8.46350e12i			0.0489426i
$705$	1.07563e14	−	8.74562e13i	0.617616	−	0.502163i
$706$	1.88054e14			1.07216
$707$	3.52992e14			1.99833
$708$	−1.25685e14	+	7.09897e12i	−0.706511	+	0.0399052i
$709$	9.73930e13			0.543622			0.271811	−	0.962351i	$-0.412378\pi$
$709$	9.73930e13			0.543622			0.271811	+	0.962351i	$0.412378\pi$
$710$	7.20609e13	−	5.21263e13i	0.399400	−	0.288912i
$711$	4.63613e13	−	5.25392e12i	0.255157	−	0.0289158i
$712$			1.15385e12i			0.00630595i
$713$	−3.93461e14			−2.13528
$714$	2.53753e14	−	1.43325e13i	1.36748	−	0.0772378i
$715$	−2.08245e13	−	2.87883e13i	−0.111441	−	0.154059i
$716$		−	9.12997e13i		−	0.485182i
$717$	2.03025e14	−	1.14672e13i	1.07140	−	0.0605151i
$718$			3.50039e13i			0.183440i
$719$			5.96355e12i			0.0310356i	0.999880	+	0.0155178i	$0.00493967\pi$
$719$			5.96355e12i			0.0310356i	−0.999880	+	0.0155178i	$0.995060\pi$
$720$	−3.25844e13	−	3.57519e13i	−0.168402	−	0.184772i
$721$	−2.09905e14			−1.07733
$722$	−1.90632e12			−0.00971648
$723$	2.23836e12	+	3.96295e13i	0.0113302	+	0.200598i
$724$	−2.59144e13			−0.130271
$725$	1.93231e14	+	6.36757e13i	0.964688	+	0.317895i
$726$	−6.80948e12	−	1.20560e14i	−0.0337622	−	0.597752i
$727$		−	8.26270e13i		−	0.406864i	−0.979089	−	0.203432i	$-0.934790\pi$
$727$		−	8.26270e13i		−	0.406864i	0.979089	−	0.203432i	$-0.0652097\pi$
$728$	−5.59905e13			−0.273815
$729$	−1.94205e14	+	6.83771e13i	−0.943243	+	0.332103i
$730$	−5.69644e13	+	4.12060e13i	−0.274783	+	0.198768i
$731$		−	2.23670e14i		−	1.07157i
$732$	1.29693e12	+	2.29618e13i	0.00617107	+	0.109257i
$733$		−	1.91457e14i		−	0.904796i	−0.891816	−	0.452398i	$-0.850569\pi$
$733$		−	1.91457e14i		−	0.904796i	0.891816	−	0.452398i	$-0.149431\pi$
$734$		−	1.25198e14i		−	0.587647i
$735$	−2.56872e14	+	2.08854e14i	−1.19751	+	0.973659i
$736$	−5.78382e13			−0.267809
$737$	−1.23410e14			−0.567559
$738$	−7.65052e12	−	6.75092e13i	−0.0349469	−	0.308376i
$739$	−2.50313e14			−1.13569			−0.567847	−	0.823134i	$-0.692224\pi$
$739$	−2.50313e14			−1.13569			−0.567847	+	0.823134i	$0.692224\pi$
$740$	−3.91362e13	+	2.83097e13i	−0.176368	+	0.127578i
$741$	1.07570e14	−	6.07577e12i	0.481504	−	0.0271963i
$742$		−	4.33892e14i		−	1.92913i
$743$	−1.50284e14			−0.663696			−0.331848	−	0.943333i	$-0.607672\pi$
$743$	−1.50284e14			−0.663696			−0.331848	+	0.943333i	$0.607672\pi$
$744$	−6.40607e12	−	1.13418e14i	−0.0281013	−	0.497527i
$745$	1.45465e14	−	1.05224e14i	0.633836	−	0.458495i
$746$		−	1.50930e14i		−	0.653255i
$747$	−2.70043e14	+	3.06028e13i	−1.16099	+	0.131570i
$748$			5.56768e13i			0.237775i
$749$			4.48259e14i			1.90160i
$750$	5.97914e13	+	1.56786e14i	0.251960	+	0.660694i
$751$	−1.13593e14			−0.475501			−0.237751	−	0.971326i	$-0.576410\pi$
$751$	−1.13593e14			−0.475501			−0.237751	+	0.971326i	$0.576410\pi$
$752$	4.78567e13			0.199000
$753$	3.30171e14	−	1.86488e13i	1.36384	−	0.0770327i
$754$	8.49983e13			0.348782
$755$	−3.76716e13	−	5.20783e13i	−0.153560	−	0.212286i
$756$	−1.94104e14	+	3.31726e13i	−0.786005	+	0.134329i
$757$			2.52129e14i			1.01424i	0.861874	+	0.507122i	$0.169291\pi$
$757$			2.52129e14i			1.01424i	−0.861874	+	0.507122i	$0.830709\pi$
$758$	−1.49064e13			−0.0595698
$759$	−1.49175e14	+	8.42568e12i	−0.592224	+	0.0334500i
$760$	5.21782e13	+	7.21326e13i	0.205789	+	0.284488i
$761$		−	4.70884e14i		−	1.84498i	−0.386026	−	0.922488i	$-0.626153\pi$
$761$		−	4.70884e14i		−	1.84498i	0.386026	−	0.922488i	$-0.373847\pi$
$762$	−5.16761e13	+	2.91877e12i	−0.201148	+	0.0113612i
$763$		−	7.09049e14i		−	2.74191i
$764$			1.56331e13i			0.0600591i
$765$	−2.14355e14	−	2.35192e14i	−0.818139	−	0.897669i
$766$	−1.43346e14			−0.543551
$767$	1.82437e14			0.687284
$768$	−9.41683e11	−	1.66723e13i	−0.00352451	−	0.0624005i
$769$	−1.13616e14			−0.422482			−0.211241	−	0.977434i	$-0.567750\pi$
$769$	−1.13616e14			−0.422482			−0.211241	+	0.977434i	$0.567750\pi$
$770$	−7.00475e13	−	9.68357e13i	−0.258785	−	0.357752i
$771$	4.93543e12	+	8.73805e13i	0.0181156	+	0.320732i
$772$		−	2.31716e14i		−	0.845023i
$773$	3.36730e14			1.22007			0.610034	−	0.792376i	$-0.291156\pi$
$773$	3.36730e14			1.22007			0.610034	+	0.792376i	$0.291156\pi$
$774$	1.95141e13	+	1.72195e14i	0.0702496	+	0.619892i
$775$	−1.23331e14	+	3.74262e14i	−0.441128	+	1.33865i
$776$			1.62529e13i			0.0577595i
$777$	1.10883e13	+	1.96316e14i	0.0391527	+	0.693188i
$778$			3.09723e14i			1.08661i
$779$			1.25040e14i			0.435876i
$780$	4.42253e13	+	5.43932e13i	0.153178	+	0.188396i
$781$	7.93125e13			0.272952
$782$	−3.80486e14			−1.30108
$783$	2.94666e14	−	5.03589e13i	1.00120	−	0.171107i
$784$	−1.14287e14			−0.385848
$785$	1.35423e14	−	9.79605e13i	0.454302	−	0.328626i
$786$	−4.21554e14	+	2.38102e13i	−1.40521	+	0.0793690i
$787$			2.61217e14i			0.865224i	0.901580	+	0.432612i	$0.142408\pi$
$787$			2.61217e14i			0.865224i	−0.901580	+	0.432612i	$0.857592\pi$
$788$	−1.40425e14			−0.462183
$789$	−2.07308e13	−	3.67033e14i	−0.0678001	−	1.20038i
$790$	−3.27469e13	−	4.52702e13i	−0.106423	−	0.147122i
$791$		−	3.52404e13i		−	0.113804i
$792$	−4.85752e12	−	4.28634e13i	−0.0155879	−	0.137550i
$793$		−	3.33299e13i		−	0.106284i
$794$			3.43570e14i			1.08871i
$795$	−4.21513e14	+	3.42718e14i	−1.32732	+	1.07920i
$796$	1.98972e14			0.622625
$797$	−1.21825e14			−0.378830			−0.189415	−	0.981897i	$-0.560659\pi$
$797$	−1.21825e14			−0.378830			−0.189415	+	0.981897i	$0.560659\pi$
$798$	3.61834e14	−	2.04371e13i	1.11814	−	0.0631547i
$799$	3.14824e14			0.966793
$800$	−1.81295e13	+	5.50160e13i	−0.0553269	+	0.167896i
$801$	−6.62240e11	−	5.84369e12i	−0.00200841	−	0.0177225i
$802$			9.78506e13i			0.294911i
$803$	−6.26968e13			−0.187788
$804$	2.43104e14	−	1.37310e13i	0.723623	−	0.0408717i
$805$	6.61759e14	−	4.78693e14i	1.95758	−	1.41605i
$806$			1.64630e14i			0.483988i
$807$	−5.99222e14	+	3.38453e13i	−1.75074	+	0.0988851i
$808$		−	1.52571e14i		−	0.443013i
$809$			1.25650e14i			0.362592i	0.983429	+	0.181296i	$0.0580293\pi$
$809$			1.25650e14i			0.362592i	−0.983429	+	0.181296i	$0.941971\pi$
$810$	1.85543e14	+	1.62364e14i	0.532132	+	0.465656i
$811$	2.80582e14			0.799752			0.399876	−	0.916569i	$-0.369053\pi$
$811$	2.80582e14			0.799752			0.399876	+	0.916569i	$0.369053\pi$
$812$	2.85910e14			0.809933
$813$	2.64193e13	+	4.67747e14i	0.0743822	+	1.31692i
$814$	−4.30745e13			−0.120531
$815$	2.93992e14	−	2.12663e14i	0.817612	−	0.591432i
$816$	−6.19483e12	−	1.09678e14i	−0.0171229	−	0.303157i
$817$		−	3.18939e14i		−	0.876188i
$818$	−1.01636e14			−0.277513
$819$	2.83564e14	−	3.21351e13i	0.769541	−	0.0872086i
$820$	−6.59204e13	+	4.76845e13i	−0.177808	+	0.128620i
$821$			6.21120e14i			1.66517i	0.553894	+	0.832587i	$0.313141\pi$
$821$			6.21120e14i			1.66517i	−0.553894	+	0.832587i	$0.686859\pi$
$822$	−1.03231e13	−	1.82768e14i	−0.0275076	−	0.487015i
$823$		−	4.65256e14i		−	1.23223i	−0.787655	−	0.616117i	$-0.788705\pi$
$823$		−	4.65256e14i		−	1.23223i	0.787655	−	0.616117i	$-0.211295\pi$
$824$			9.07260e13i			0.238834i
$825$	−3.87446e13	+	1.44537e14i	−0.101377	+	0.378189i
$826$	6.13666e14			1.59600
$827$	−7.57703e13			−0.195872			−0.0979358	−	0.995193i	$-0.531224\pi$
$827$	−7.57703e13			−0.195872			−0.0979358	+	0.995193i	$0.531224\pi$
$828$	2.92922e14	−	3.31955e13i	0.752661	−	0.0852958i
$829$	−4.71947e14			−1.20537			−0.602685	−	0.797979i	$-0.705902\pi$
$829$	−4.71947e14			−1.20537			−0.602685	+	0.797979i	$0.705902\pi$
$830$	1.90742e14	+	2.63688e14i	0.484236	+	0.669421i
$831$	1.63165e14	−	9.21588e12i	0.411739	−	0.0232558i
$832$			2.42004e13i			0.0607024i
$833$	−7.51831e14			−1.87454
$834$	−2.91236e13	−	5.15627e14i	−0.0721798	−	1.27792i
$835$	−1.12639e14	−	1.55716e14i	−0.277497	−	0.383619i
$836$			7.93915e13i			0.194421i
$837$	9.75383e13	+	5.70728e14i	0.237437	+	1.38932i
$838$		−	1.86617e14i		−	0.451576i
$839$		−	8.15318e14i		−	1.96118i	−0.196072	−	0.980589i	$-0.562819\pi$
$839$		−	8.15318e14i		−	1.96118i	0.196072	−	0.980589i	$-0.437181\pi$
$840$	1.48761e14	+	1.82963e14i	0.355707	+	0.437488i
$841$	−1.33280e13			−0.0316800
$842$	5.17009e14			1.22162
$843$	7.72887e13	−	4.36542e12i	0.181543	−	0.0102539i
$844$	−4.81241e13			−0.112370
$845$	1.92951e14	+	2.66741e14i	0.447881	+	0.619164i
$846$	−2.42370e14	+	2.74668e13i	−0.559278	+	0.0633805i
$847$			5.88642e14i			1.35031i
$848$	−1.87538e14			−0.427672
$849$	1.70325e14	−	9.62032e12i	0.386136	−	0.0218098i
$850$	−1.19264e14	+	3.61921e14i	−0.268792	+	0.815678i
$851$		−	2.94364e14i		−	0.659533i
$852$	−1.56238e14	+	8.82462e12i	−0.348007	+	0.0196561i
$853$			4.19205e14i			0.928284i	0.885761	+	0.464142i	$0.153637\pi$
$853$			4.19205e14i			0.928284i	−0.885761	+	0.464142i	$0.846363\pi$
$854$		−	1.12112e14i		−	0.246810i
$855$	−3.05656e14	−	3.35369e14i	−0.668964	−	0.733993i
$856$	1.93748e14			0.421569
$857$	−1.28827e14			−0.278679			−0.139339	−	0.990245i	$-0.544498\pi$
$857$	−1.28827e14			−0.278679			−0.139339	+	0.990245i	$0.544498\pi$
$858$	3.52544e12	+	6.24170e13i	0.00758188	+	0.134235i
$859$	7.12085e14			1.52253			0.761265	−	0.648441i	$-0.224579\pi$
$859$	7.12085e14			1.52253			0.761265	+	0.648441i	$0.224579\pi$
$860$	1.68143e14	−	1.21628e14i	0.357425	−	0.258549i
$861$	1.86770e13	+	3.30672e14i	0.0394723	+	0.698847i
$862$		−	4.53543e14i		−	0.952976i
$863$	−6.39522e14			−1.33599			−0.667993	−	0.744168i	$-0.732846\pi$
$863$	−6.39522e14			−1.33599			−0.667993	+	0.744168i	$0.732846\pi$
$864$	1.43380e13	+	8.38962e13i	0.0297796	+	0.174250i
$865$	1.25472e14	+	1.73456e14i	0.259099	+	0.358185i
$866$			6.20674e14i			1.27431i
$867$	−1.31267e13	−	2.32404e14i	−0.0267953	−	0.474404i
$868$			5.53769e14i			1.12391i
$869$		−	4.98258e13i		−	0.100544i
$870$	−2.25832e14	−	2.77753e14i	−0.453094	−	0.557266i
$871$	−3.52875e14			−0.703931
$872$	−3.06467e14			−0.607858
$873$	−9.32817e12	−	8.23130e13i	−0.0183961	−	0.162329i
$874$	−5.42548e14			−1.06385
$875$	−2.47906e14	−	7.79517e14i	−0.483333	−	1.51980i
$876$	1.23506e14	−	6.97589e12i	0.239425	−	0.0135232i
$877$		−	3.11247e14i		−	0.599938i	−0.953949	−	0.299969i	$-0.903024\pi$
$877$		−	3.11247e14i		−	0.599938i	0.953949	−	0.299969i	$-0.0969764\pi$
$878$	2.01131e13			0.0385483
$879$	2.42281e13	+	4.28953e14i	0.0461716	+	0.817457i
$880$	−4.18547e13	+	3.02762e13i	−0.0793104	+	0.0573704i
$881$			5.12092e14i			0.964869i	0.875932	+	0.482434i	$0.160247\pi$
$881$			5.12092e14i			0.964869i	−0.875932	+	0.482434i	$0.839753\pi$
$882$	5.78805e14	−	6.55935e13i	1.08440	−	0.122890i
$883$			5.23468e14i			0.975184i	0.873072	+	0.487592i	$0.162125\pi$
$883$			5.23468e14i			0.975184i	−0.873072	+	0.487592i	$0.837875\pi$
$884$			1.59201e14i			0.294907i
$885$	−4.84717e14	−	5.96159e14i	−0.892836	−	1.09811i
$886$	2.26083e14			0.414095
$887$	2.10107e14			0.382668			0.191334	−	0.981525i	$-0.438719\pi$
$887$	2.10107e14			0.382668			0.191334	+	0.981525i	$0.438719\pi$
$888$	8.48524e13	−	4.79264e12i	0.153674	−	0.00867980i
$889$	2.52312e14			0.454390
$890$	−5.70616e12	+	4.12764e12i	−0.0102187	+	0.00739182i
$891$	4.92018e13	+	2.14294e14i	0.0876179	+	0.381611i
$892$			1.67633e14i			0.296849i
$893$	4.48917e14			0.790513
$894$	−3.15387e14	+	1.78137e13i	−0.552277	+	0.0311937i
$895$	4.51505e14	−	3.26603e14i	0.786227	−	0.568729i
$896$			8.14032e13i			0.140962i
$897$	−4.26547e14	+	2.40923e13i	−0.734522	+	0.0414873i
$898$		−	2.01334e14i		−	0.344775i
$899$		−	8.40667e14i		−	1.43161i
$900$	6.02412e13	−	2.89034e14i	0.102019	−	0.489481i
$901$	−1.23371e15			−2.07773
$902$	−7.25541e13			−0.121515
$903$	−4.76393e13	−	8.43443e14i	−0.0793464	−	1.40481i
$904$	−1.52317e13			−0.0252294
$905$	−9.27028e13	−	1.28155e14i	−0.152704	−	0.211102i
$906$	6.37754e12	+	1.12913e14i	0.0104475	+	0.184970i
$907$			2.52335e14i			0.411094i	0.978647	+	0.205547i	$0.0658973\pi$
$907$			2.52335e14i			0.411094i	−0.978647	+	0.205547i	$0.934103\pi$
$908$	3.54112e14			0.573736
$909$	8.75665e13	+	7.72698e14i	0.141097	+	1.24506i
$910$	−2.00293e14	−	2.76890e14i	−0.320966	−	0.443712i
$911$			2.59070e14i			0.412881i	0.978459	+	0.206440i	$0.0661880\pi$
$911$			2.59070e14i			0.412881i	−0.978459	+	0.206440i	$0.933812\pi$
$912$	−8.83341e12	−	1.56393e14i	−0.0140008	−	0.247881i
$913$			2.90223e14i			0.457486i
$914$		−	1.53270e14i		−	0.240285i
$915$	−1.08914e14	+	8.85540e13i	−0.169815	+	0.138071i
$916$	−5.76795e13			−0.0894425
$917$	2.05826e15			3.17434
$918$	9.43219e13	+	5.51908e14i	0.144677	+	0.846551i
$919$	−4.93667e14			−0.753107			−0.376553	−	0.926395i	$-0.622891\pi$
$919$	−4.93667e14			−0.753107			−0.376553	+	0.926395i	$0.622891\pi$
$920$	−2.06902e14	−	2.86028e14i	−0.313925	−	0.433979i
$921$	4.18533e14	−	2.36396e13i	0.631585	−	0.0356732i
$922$		−	5.12372e14i		−	0.769009i
$923$	2.26785e14			0.338537
$924$	1.18586e13	+	2.09953e14i	0.0176065	+	0.311718i
$925$	−2.80001e14	−	9.22691e13i	−0.413476	−	0.136253i
$926$		−	1.53916e14i		−	0.226063i
$927$	−5.20710e13	−	4.59482e14i	−0.0760672	−	0.671227i
$928$		−	1.23577e14i		−	0.179555i
$929$		−	7.29374e14i		−	1.05408i	−0.849842	−	0.527038i	$-0.823303\pi$
$929$		−	7.29374e14i		−	1.05408i	0.849842	−	0.527038i	$-0.176697\pi$
$930$	5.37970e14	−	4.37405e14i	0.773292	−	0.628738i
$931$	−1.07206e15			−1.53275
$932$	−2.51209e14			−0.357236
$933$	1.06224e15	−	5.99972e13i	1.50249	−	0.0848639i
$934$	−6.89921e14			−0.970655
$935$	−2.75339e14	+	1.99171e14i	−0.385310	+	0.278720i
$936$	−1.38895e13	−	1.22563e14i	−0.0193334	−	0.170600i
$937$		−	5.14506e14i		−	0.712349i	−0.934419	−	0.356174i	$-0.884081\pi$
$937$		−	5.14506e14i		−	0.712349i	0.934419	−	0.356174i	$-0.115919\pi$
$938$	−1.18697e15			−1.63465
$939$	6.19228e12	−	3.49752e11i	0.00848247	−	0.000479107i
$940$	1.71196e14	+	2.36666e14i	0.233268	+	0.322476i
$941$			9.69858e14i			1.31450i	0.753673	+	0.657249i	$0.228280\pi$
$941$			9.69858e14i			1.31450i	−0.753673	+	0.657249i	$0.771720\pi$
$942$	−2.93616e14	+	1.65840e13i	−0.395845	+	0.0223581i
$943$		−	4.95823e14i		−	0.664918i
$944$		−	2.65241e14i		−	0.353818i
$945$	−8.58409e14	−	8.41236e14i	−1.13903	−	1.11624i
$946$	1.85063e14			0.244266
$947$	−4.17259e14			−0.547842			−0.273921	−	0.961752i	$-0.588321\pi$
$947$	−4.17259e14			−0.547842			−0.273921	+	0.961752i	$0.588321\pi$
$948$	5.54381e12	+	9.81518e13i	0.00724047	+	0.128191i
$949$	−1.79274e14			−0.232909
$950$	−1.70063e14	+	5.16075e14i	−0.219782	+	0.666952i
$951$	4.62586e13	+	8.18997e14i	0.0594689	+	1.05288i
$952$			5.35508e14i			0.684827i
$953$	1.00920e14			0.128385			0.0641924	−	0.997938i	$-0.479553\pi$
$953$	1.00920e14			0.128385			0.0641924	+	0.997938i	$0.479553\pi$
$954$	9.49787e14	−	1.07635e14i	1.20194	−	0.136211i
$955$	−7.73106e13	+	5.59238e13i	−0.0973245	+	0.0704011i
$956$			4.28454e14i			0.536556i
$957$	−1.80023e13	−	3.18726e14i	−0.0224268	−	0.397062i
$958$		−	3.64798e14i		−	0.452090i
$959$			8.92377e14i			1.10016i
$960$	7.90808e13	−	6.42980e13i	0.0969874	−	0.0788572i
$961$	8.08631e14			0.986582
$962$	−1.23167e14			−0.149492
$963$	−9.81237e14	+	1.11199e14i	−1.18479	+	0.134267i
$964$	−8.36323e13			−0.100459
$965$	1.14590e15	−	8.28907e14i	1.36934	−	0.990534i
$966$	−1.43478e15	+	8.10394e13i	−1.70569	+	0.0963409i
$967$			1.43355e15i			1.69544i	0.530448	+	0.847718i	$0.322024\pi$
$967$			1.43355e15i			1.69544i	−0.530448	+	0.847718i	$0.677976\pi$
$968$	2.54425e14			0.299352
$969$	−5.81102e13	−	1.02883e15i	−0.0680195	−	1.20427i
$970$	−8.03758e13	+	5.81411e13i	−0.0935981	+	0.0677056i
$971$		−	2.69630e14i		−	0.312371i	−0.987728	−	0.156186i	$-0.950080\pi$
$971$		−	2.69630e14i		−	0.312371i	0.987728	−	0.156186i	$-0.0499198\pi$
$972$	−1.20766e14	−	4.16663e14i	−0.139192	−	0.480235i
$973$			2.51758e15i			2.88681i
$974$		−	7.44386e14i		−	0.849187i
$975$	−1.10786e14	+	4.13286e14i	−0.125736	+	0.469059i
$976$	−4.84575e13			−0.0547157
$977$	−7.18491e14			−0.807139			−0.403570	−	0.914949i	$-0.632231\pi$
$977$	−7.18491e14			−0.807139			−0.403570	+	0.914949i	$0.632231\pi$
$978$	−6.37413e14	+	3.60024e13i	−0.712405	+	0.0402381i
$979$	−6.28038e12			−0.00698349
$980$	−4.08834e14	−	5.65184e14i	−0.452290	−	0.625258i
$981$	1.55210e15	−	1.75893e14i	1.70835	−	0.193599i
$982$			9.34123e14i			1.02293i
$983$	−2.37730e14			−0.259010			−0.129505	−	0.991579i	$-0.541339\pi$
$983$	−2.37730e14			−0.259010			−0.129505	+	0.991579i	$0.541339\pi$
$984$	1.42924e14	−	8.07265e12i	0.154928	−	0.00875066i
$985$	−5.02338e14	−	6.94447e14i	−0.541770	−	0.748959i
$986$		−	8.12946e14i		−	0.872323i
$987$	1.18717e15	−	6.70540e13i	1.26744	−	0.0715878i
$988$			2.27011e14i			0.241136i
$989$			1.26469e15i			1.33660i
$990$	1.94596e14	−	1.77356e14i	0.204625	−	0.186496i
$991$	5.78095e14			0.604827			0.302414	−	0.953177i	$-0.402208\pi$
$991$	5.78095e14			0.604827			0.302414	+	0.953177i	$0.402208\pi$
$992$	2.39352e14			0.249160
$993$	−1.58910e13	−	2.81346e14i	−0.0164590	−	0.291403i
$994$	7.62839e14			0.786142
$995$	7.11775e14	+	9.83978e14i	0.729840	+	1.00895i
$996$	−3.22914e13	−	5.71710e14i	−0.0329450	−	0.583283i
$997$		−	1.28949e15i		−	1.30901i	−0.756057	−	0.654505i	$-0.772877\pi$
$997$		−	1.28949e15i		−	1.30901i	0.756057	−	0.654505i	$-0.227123\pi$
$998$	5.90748e14			0.596691
$999$	−4.26985e14	+	7.29723e13i	−0.429126	+	0.0733383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.11.b.a.29.15	yes	20
3.2	odd	2	inner	30.11.b.a.29.5	✓	20
5.2	odd	4		150.11.d.e.101.11		20
5.3	odd	4		150.11.d.e.101.10		20
5.4	even	2	inner	30.11.b.a.29.6	yes	20
15.2	even	4		150.11.d.e.101.1		20
15.8	even	4		150.11.d.e.101.20		20
15.14	odd	2	inner	30.11.b.a.29.16	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.11.b.a.29.5	✓	20	3.2	odd	2	inner
30.11.b.a.29.6	yes	20	5.4	even	2	inner
30.11.b.a.29.15	yes	20	1.1	even	1	trivial
30.11.b.a.29.16	yes	20	15.14	odd	2	inner
150.11.d.e.101.1		20	15.2	even	4
150.11.d.e.101.10		20	5.3	odd	4
150.11.d.e.101.11		20	5.2	odd	4
150.11.d.e.101.20		20	15.8	even	4

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	30.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+22.6274 q^{2} +(-13.7033 - 242.613i) q^{3} +512.000 q^{4} +(1831.56 + 2532.00i) q^{5} +(-310.070 - 5489.71i) q^{6} +26803.8i q^{7} +11585.2 q^{8} +(-58673.4 + 6649.20i) q^{9} +O(q^{10})\)	\(q+22.6274 q^{2} +(-13.7033 - 242.613i) q^{3} +512.000 q^{4} +(1831.56 + 2532.00i) q^{5} +(-310.070 - 5489.71i) q^{6} +26803.8i q^{7} +11585.2 q^{8} +(-58673.4 + 6649.20i) q^{9} +(41443.4 + 57292.6i) q^{10} +63058.0i q^{11} +(-7016.08 - 124218. i) q^{12} +180307. i q^{13} +606501. i q^{14} +(589198. - 479057. i) q^{15} +262144. q^{16} +1.72450e6 q^{17} +(-1.32763e6 + 150454. i) q^{18} +2.45903e6 q^{19} +(937758. + 1.29638e6i) q^{20} +(6.50296e6 - 367301. i) q^{21} +1.42684e6i q^{22} -9.75079e6 q^{23} +(-158756. - 2.81073e6i) q^{24} +(-3.05641e6 + 9.27501e6i) q^{25} +4.07988e6i q^{26} +(2.41720e6 + 1.41438e7i) q^{27} +1.37236e7i q^{28} -2.08335e7i q^{29} +(1.33320e7 - 1.08398e7i) q^{30} +4.03517e7 q^{31} +5.93164e6 q^{32} +(1.52987e7 - 864102. i) q^{33} +3.90211e7 q^{34} +(-6.78672e7 + 4.90928e7i) q^{35} +(-3.00408e7 + 3.40439e6i) q^{36} +3.01887e7i q^{37} +5.56414e7 q^{38} +(4.37449e7 - 2.47080e6i) q^{39} +(2.12190e7 + 2.93338e7i) q^{40} +5.08495e7i q^{41} +(1.47145e8 - 8.31106e6i) q^{42} -1.29701e8i q^{43} +3.22857e7i q^{44} +(-1.24300e8 - 1.36383e8i) q^{45} -2.20635e8 q^{46} +1.82559e8 q^{47} +(-3.59224e6 - 6.35996e7i) q^{48} -4.35969e8 q^{49} +(-6.91586e7 + 2.09870e8i) q^{50} +(-2.36314e7 - 4.18388e8i) q^{51} +9.23172e7i q^{52} -7.15401e8 q^{53} +(5.46951e7 + 3.20039e8i) q^{54} +(-1.59663e8 + 1.15494e8i) q^{55} +3.10529e8i q^{56} +(-3.36968e7 - 5.96593e8i) q^{57} -4.71409e8i q^{58} -1.01181e9i q^{59} +(3.01669e8 - 2.45277e8i) q^{60} -1.84851e8 q^{61} +9.13055e8 q^{62} +(-1.78224e8 - 1.57267e9i) q^{63} +1.34218e8 q^{64} +(-4.56537e8 + 3.30243e8i) q^{65} +(3.46170e8 - 1.95524e7i) q^{66} +1.95708e9i q^{67} +8.82946e8 q^{68} +(1.33618e8 + 2.36567e9i) q^{69} +(-1.53566e9 + 1.11084e9i) q^{70} -1.25777e9i q^{71} +(-6.79746e8 + 7.70326e7i) q^{72} +9.94272e8i q^{73} +6.83093e8i q^{74} +(2.29212e9 + 6.14427e8i) q^{75} +1.25902e9 q^{76} -1.69020e9 q^{77} +(9.89834e8 - 5.59078e7i) q^{78} -7.90158e8 q^{79} +(4.80132e8 + 6.63748e8i) q^{80} +(3.39836e9 - 7.80263e8i) q^{81} +1.15059e9i q^{82} +4.60248e9 q^{83} +(3.32952e9 - 1.88058e8i) q^{84} +(3.15853e9 + 4.36644e9i) q^{85} -2.93480e9i q^{86} +(-5.05449e9 + 2.85488e8i) q^{87} +7.30542e8i q^{88} +9.95968e7i q^{89} +(-2.81258e9 - 3.08599e9i) q^{90} -4.83292e9 q^{91} -4.99240e9 q^{92} +(-5.52951e8 - 9.78986e9i) q^{93} +4.13084e9 q^{94} +(4.50385e9 + 6.22626e9i) q^{95} +(-8.12830e7 - 1.43910e9i) q^{96} +1.40290e9i q^{97} -9.86486e9 q^{98} +(-4.19286e8 - 3.69983e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10240 q^{4} + 6080 q^{6} - 65360 q^{9}+O(q^{10}) \) 20 * q + 10240 * q^4 + 6080 * q^6 - 65360 * q^9	\( 20 q + 10240 q^{4} + 6080 q^{6} - 65360 q^{9} - 33536 q^{10} + 2083928 q^{15} + 5242880 q^{16} + 3209040 q^{19} - 654460 q^{21} + 3112960 q^{24} - 7480596 q^{25} + 34614848 q^{30} + 86022560 q^{31} + 81633280 q^{34} - 33464320 q^{36} + 93388800 q^{39} - 17170432 q^{40} + 440775292 q^{45} + 696625280 q^{46} - 1574325300 q^{49} - 2571307840 q^{51} + 681294400 q^{54} - 2158399088 q^{55} + 1066971136 q^{60} + 1300067680 q^{61} + 2684354560 q^{64} - 308783360 q^{66} - 2771050340 q^{69} - 443470976 q^{70} + 2946710128 q^{75} + 1643028480 q^{76} + 9709493760 q^{79} + 7324584140 q^{81} - 335083520 q^{84} + 10789531168 q^{85} - 5101384192 q^{90} - 20875353600 q^{91} + 7266454400 q^{94} + 1593835520 q^{96} - 39571273840 q^{99}+O(q^{100}) \) 20 * q + 10240 * q^4 + 6080 * q^6 - 65360 * q^9 - 33536 * q^10 + 2083928 * q^15 + 5242880 * q^16 + 3209040 * q^19 - 654460 * q^21 + 3112960 * q^24 - 7480596 * q^25 + 34614848 * q^30 + 86022560 * q^31 + 81633280 * q^34 - 33464320 * q^36 + 93388800 * q^39 - 17170432 * q^40 + 440775292 * q^45 + 696625280 * q^46 - 1574325300 * q^49 - 2571307840 * q^51 + 681294400 * q^54 - 2158399088 * q^55 + 1066971136 * q^60 + 1300067680 * q^61 + 2684354560 * q^64 - 308783360 * q^66 - 2771050340 * q^69 - 443470976 * q^70 + 2946710128 * q^75 + 1643028480 * q^76 + 9709493760 * q^79 + 7324584140 * q^81 - 335083520 * q^84 + 10789531168 * q^85 - 5101384192 * q^90 - 20875353600 * q^91 + 7266454400 * q^94 + 1593835520 * q^96 - 39571273840 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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