LMFDB - Embedded newform 30.11.b.a.29.6

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			29.6
Root			$1.41421 + 231.440i$ of defining polynomial
Character	$\chi$	$=$	30.29
Dual form			30.11.b.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.6274 q^{2} +(13.7033 + 242.613i) q^{3} +512.000 q^{4} +(-1831.56 + 2532.00i) q^{5} +(-310.070 - 5489.71i) q^{6} -26803.8i q^{7} -11585.2 q^{8} +(-58673.4 + 6649.20i) q^{9} +O(q^{10})$	\(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} +(-639395. - 409664. 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} +(1.44679e7 + 9.26964e6i) 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} +(9.06281e7 - 1.60739e8i) 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} +(-3.27370e8 - 2.09748e8i) 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} +(2.20836e9 - 8.68623e8i) 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} +(-2.05068e9 + 3.63712e9i) 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	$-0.706208\pi$
$7$		−	26803.8i		−	1.59480i	0.603450	−	0.797400i	$-0.293792\pi$
$8$	−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	$-0.921931\pi$
$13$		−	180307.i		−	0.485619i	0.970074	−	0.242810i	$-0.0780691\pi$
$14$			606501.i			1.12769i
$15$	−639395.	−	409664.i	−0.842002	−	0.539475i
$16$	262144.			0.250000
$17$	−1.72450e6			−1.21456			−0.607281	−	0.794487i	$-0.707740\pi$
$17$	−1.72450e6			−1.21456			−0.607281	+	0.794487i	$0.707740\pi$
$18$	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	$-0.226431\pi$
$23$	9.75079e6			1.51496			0.757479	+	0.652859i	$0.226431\pi$
$24$	−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	$-0.169563\pi$
$30$	1.44679e7	+	9.26964e6i	0.595385	+	0.381466i
$31$	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	$-0.930153\pi$
$37$		−	3.01887e7i		−	0.435348i	0.976022	−	0.217674i	$-0.0698469\pi$
$38$	−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	$0.145424\pi$
$43$			1.29701e8i			0.882271i	−0.897441	+	0.441135i	$0.854576\pi$
$44$			3.22857e7i			0.195770i
$45$	9.06281e7	−	1.60739e8i	0.491134	−	0.871084i
$46$	−2.20635e8			−1.07124
$47$	−1.82559e8			−0.796001			−0.398001	−	0.917385i	$-0.630296\pi$
$47$	−1.82559e8			−0.796001			−0.398001	+	0.917385i	$0.630296\pi$
$48$	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	$-0.173346\pi$
$53$	7.15401e8			1.71069			0.855343	+	0.518061i	$0.173346\pi$
$54$	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	$-0.250239\pi$
$60$	−3.27370e8	−	2.09748e8i	−0.421001	−	0.269738i
$61$	−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	$-0.741943\pi$
$67$		−	1.95708e9i		−	1.44955i	0.688984	−	0.724777i	$-0.258057\pi$
$68$	−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	$-0.922916\pi$
$73$		−	9.94272e8i		−	0.479613i	0.970821	−	0.239806i	$-0.0770840\pi$
$74$			6.83093e8i			0.307837i
$75$	2.20836e9	−	8.68623e8i	0.930600	−	0.366037i
$76$	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	$-0.698597\pi$
$83$	−4.60248e9			−1.16843			−0.584213	+	0.811601i	$0.698597\pi$
$84$	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	$0.997161\pi$
$90$	−2.05068e9	+	3.63712e9i	−0.347284	+	0.615949i
$91$	−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	$-0.973970\pi$
$97$		−	1.40290e9i		−	0.163369i	0.996658	−	0.0816843i	$-0.0260299\pi$
$98$	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	$-0.890330\pi$
$103$		−	7.83117e9i		−	0.675524i	0.941232	−	0.337762i	$-0.109670\pi$
$104$			2.08890e9i			0.171692i
$105$	−1.09806e10	+	1.71382e10i	−0.860355	+	1.34282i
$106$	−1.61877e10			−1.20964
$107$	−1.67237e10			−1.19238			−0.596188	−	0.802845i	$-0.703319\pi$
$107$	−1.67237e10			−1.19238			−0.596188	+	0.802845i	$0.703319\pi$
$108$	−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	$-0.488640\pi$
$113$	1.31475e9			0.0713594			0.0356797	+	0.999363i	$0.488640\pi$
$114$	−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
$120$	7.40754e9	+	4.74605e9i	0.297693	+	0.190733i
$121$	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	$0.0455011\pi$
$127$			9.41327e9i			0.284919i	−0.989801	+	0.142460i	$0.954499\pi$
$128$	−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
$135$	4.02394e10	+	1.97849e10i	0.897394	+	0.441231i
$136$	1.99788e10			0.429412
$137$	−3.32929e10			−0.689841			−0.344920	−	0.938632i	$-0.612094\pi$
$137$	−3.32929e10			−0.689841			−0.344920	+	0.938632i	$0.612094\pi$
$138$	−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	$-0.127920\pi$
$150$	−4.99694e10	+	1.96547e10i	−0.658034	+	0.258827i
$151$	−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	$0.0904508\pi$
$157$			5.34847e10i			0.560701i	−0.959898	+	0.280351i	$0.909549\pi$
$158$	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	$0.168341\pi$
$163$			1.16111e11i			1.00910i	−0.863383	+	0.504549i	$0.831659\pi$
$164$			2.60349e10i			0.219451i
$165$	2.58326e10	−	4.03190e10i	0.211226	−	0.329678i
$166$	1.04142e11			0.826202
$167$	6.14992e10			0.473464			0.236732	−	0.971575i	$-0.423924\pi$
$167$	6.14992e10			0.473464			0.236732	+	0.971575i	$0.423924\pi$
$168$	−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	$-0.570944\pi$
$173$	−6.85054e10			−0.442073			−0.221037	+	0.975266i	$0.570944\pi$
$174$	−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	$-0.161246\pi$
$180$	4.64016e10	−	8.22986e10i	0.245567	−	0.435542i
$181$	−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	$0.320413\pi$
$193$			4.52569e11i			1.69005i	−0.534730	+	0.845023i	$0.679587\pi$
$194$			3.17440e10i			0.115519i
$195$	−7.38653e10	+	1.15287e11i	−0.261980	+	0.408892i
$196$	−2.23216e11			−0.771695
$197$	2.74268e11			0.924367			0.462183	−	0.886784i	$-0.347066\pi$
$197$	2.74268e11			0.924367			0.462183	+	0.886784i	$0.347066\pi$
$198$	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
$210$	2.48462e11	−	3.87794e11i	0.608363	−	0.949521i
$211$	−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	$-0.904064\pi$
$223$		−	3.27409e11i		−	0.593698i	0.954924	−	0.296849i	$-0.0959358\pi$
$224$			1.58991e11i			0.281924i
$225$	2.41001e11	+	5.23874e11i	0.417933	+	0.908478i
$226$	−2.97494e10			−0.0504587
$227$	−6.91626e11			−1.14747			−0.573736	−	0.819041i	$-0.694506\pi$
$227$	−6.91626e11			−1.14747			−0.573736	+	0.819041i	$0.694506\pi$
$228$	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	$-0.383719\pi$
$233$	4.90642e11			0.714472			0.357236	+	0.934014i	$0.383719\pi$
$234$	−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	$0.819725\pi$
$240$	−1.67614e11	−	1.07391e11i	−0.210500	−	0.134869i
$241$	−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
$255$	1.10264e12	+	7.06467e11i	1.02266	+	0.655226i
$256$	6.87195e10			0.0625000
$257$	3.60164e11			0.321243			0.160622	−	0.987016i	$-0.448650\pi$
$257$	3.60164e11			0.321243			0.160622	+	0.987016i	$0.448650\pi$
$258$	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	$-0.705290\pi$
$263$	−1.51283e12			−1.20230			−0.601148	+	0.799137i	$0.705290\pi$
$264$	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	$-0.340302\pi$
$270$	−9.10515e11	−	4.47682e11i	−0.634553	−	0.311997i
$271$	−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	$-0.933891\pi$
$277$		−	6.72531e11i		−	0.412395i	0.978510	−	0.206197i	$-0.0661089\pi$
$278$	−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	$-0.938056\pi$
$283$		−	7.02044e11i		−	0.386752i	0.981125	−	0.193376i	$-0.0619437\pi$
$284$		−	6.43978e11i		−	0.348562i
$285$	−1.57229e12	−	1.00737e12i	−0.836197	−	0.535756i
$286$	−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	$-0.365745\pi$
$293$	1.76805e12			0.818760			0.409380	+	0.912364i	$0.365745\pi$
$294$	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
$300$	1.13068e12	−	4.44735e11i	0.465300	−	0.183019i
$301$	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	$-0.897561\pi$
$307$		−	1.72510e12i		−	0.632591i	0.948661	−	0.316296i	$-0.102439\pi$
$308$	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	$-0.998648\pi$
$313$		−	2.55232e10i		−	0.00849599i	0.999991	−	0.00424799i	$-0.00135218\pi$
$314$		−	1.21022e12i		−	0.396476i
$315$	−4.30843e12	−	2.42918e12i	−1.38921	−	0.783261i
$316$	−4.04561e11			−0.128395
$317$	3.37573e12			1.05456			0.527280	−	0.849691i	$-0.323212\pi$
$317$	3.37573e12			1.05456			0.527280	+	0.849691i	$0.323212\pi$
$318$	−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
$330$	−5.84525e11	+	9.12314e11i	−0.149360	+	0.233117i
$331$	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	$-0.935527\pi$
$337$		−	1.74877e12i		−	0.402331i	0.979557	−	0.201166i	$-0.0644729\pi$
$338$	−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
$345$	−6.23461e12	−	3.99455e12i	−1.27560	−	0.817282i
$346$	1.55010e12			0.312593
$347$	7.30493e10			0.0145201			0.00726004	−	0.999974i	$-0.497689\pi$
$347$	7.30493e10			0.0145201			0.00726004	+	0.999974i	$0.497689\pi$
$348$	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	$-0.773886\pi$
$353$	−8.31087e12			−1.51626			−0.758129	+	0.652105i	$0.773886\pi$
$354$	−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	$0.958595\pi$
$360$	−1.04995e12	+	1.86220e12i	−0.173642	+	0.307975i
$361$	−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	$0.136404\pi$
$367$			5.53301e12i			0.831058i	−0.909580	+	0.415529i	$0.863596\pi$
$368$	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	$0.152840\pi$
$373$			6.67025e12i			0.923842i	−0.886921	+	0.461921i	$0.847160\pi$
$374$			2.46059e12i			0.336265i
$375$	−1.84538e12	+	7.18249e12i	−0.248846	+	0.968543i
$376$	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	$-0.374426\pi$
$383$	6.33504e12			0.768698			0.384349	+	0.923188i	$0.374426\pi$
$384$	−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	$0.721077\pi$
$390$	1.67138e12	−	2.60866e12i	0.185248	−	0.289131i
$391$	−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	$-0.720338\pi$
$397$		−	1.51838e13i		−	1.53967i	0.638242	−	0.769836i	$-0.279662\pi$
$398$	−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
$405$	−4.24867e12	+	1.00337e13i	−0.389922	+	0.920848i
$406$	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	$-0.103452\pi$
$420$	−5.62205e12	+	8.77477e12i	−0.430178	+	0.671412i
$421$	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	$-0.642782\pi$
$433$		−	2.74302e13i		−	1.80214i	0.433672	−	0.901071i	$-0.357218\pi$
$434$			2.44733e13i			1.58944i
$435$	−8.53474e12	+	1.33208e13i	−0.547954	+	0.855235i
$436$	−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	$-0.594590\pi$
$443$	−9.99157e12			−0.585619			−0.292809	+	0.956171i	$0.594590\pi$
$444$	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	$-0.0783916\pi$
$450$	−5.45324e12	−	1.18539e13i	−0.295523	−	0.642391i
$451$	−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	$0.0543468\pi$
$457$			6.77365e12i			0.339814i	−0.985460	+	0.169907i	$0.945653\pi$
$458$	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	$0.0511013\pi$
$463$			6.80220e12i			0.319701i	−0.987141	+	0.159851i	$0.948899\pi$
$464$		−	5.46138e12i		−	0.253929i
$465$	−2.58007e13	−	1.65306e13i	−1.18677	−	0.760369i
$466$	−1.11020e13			−0.505208
$467$	3.04905e13			1.37271			0.686357	−	0.727265i	$-0.259209\pi$
$467$	3.04905e13			1.37271			0.686357	+	0.727265i	$0.259209\pi$
$468$	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	$-0.103574\pi$
$480$	3.79266e12	+	2.42998e12i	0.148846	+	0.0953666i
$481$	−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	$0.205018\pi$
$487$			3.28975e13i			1.20093i	−0.799650	+	0.600466i	$0.794982\pi$
$488$	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
$495$	1.01359e13	+	5.71483e12i	0.341065	+	0.192299i
$496$	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	$-0.726480\pi$
$503$	−4.20502e13			−1.30595			−0.652977	+	0.757378i	$0.726480\pi$
$504$	−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	$-0.0286310\pi$
$510$	−2.49499e13	−	1.59855e13i	−0.723132	−	0.463315i
$511$	−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	$-0.896379\pi$
$523$		−	2.50287e13i		−	0.639630i	0.947480	−	0.319815i	$-0.103621\pi$
$524$		−	3.93164e13i		−	0.995216i
$525$	−2.32824e13	−	5.91924e13i	−0.583757	−	1.48412i
$526$	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
$540$	2.06026e13	+	1.01299e13i	0.448697	+	0.220615i
$541$	−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	$0.177117\pi$
$547$			5.17286e13i			1.05632i	−0.849146	+	0.528158i	$0.822883\pi$
$548$	−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
$555$	−1.23672e13	+	1.93025e13i	−0.234859	+	0.366563i
$556$	4.80901e13			0.905069
$557$	−5.93902e12			−0.110774			−0.0553871	−	0.998465i	$-0.517639\pi$
$557$	−5.93902e12			−0.110774			−0.0553871	+	0.998465i	$0.517639\pi$
$558$	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	$-0.739820\pi$
$563$	−7.73950e13			−1.36827			−0.684134	+	0.729357i	$0.739820\pi$
$564$	−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	$0.933143\pi$
$570$	3.55769e13	+	2.27943e13i	0.591280	+	0.378837i
$571$	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	$0.0605884\pi$
$577$			2.42004e13i			0.378394i	−0.981939	+	0.189197i	$0.939412\pi$
$578$	−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
$585$	−2.89825e13	−	1.63409e13i	−0.423015	−	0.238504i
$586$	−4.00064e13			−0.578951
$587$	2.52767e13			0.362685			0.181343	−	0.983420i	$-0.441956\pi$
$587$	2.52767e13			0.362685			0.181343	+	0.983420i	$0.441956\pi$
$588$	−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	$-0.226718\pi$
$593$	1.11003e14			1.51378			0.756889	+	0.653543i	$0.226718\pi$
$594$	−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	$0.967624\pi$
$600$	−2.55844e13	+	1.00632e13i	−0.329017	+	0.129414i
$601$	−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	$0.108975\pi$
$607$			5.53263e13i			0.671410i	−0.941967	+	0.335705i	$0.891025\pi$
$608$	−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	$-0.768878\pi$
$613$		−	1.14939e14i		−	1.32790i	0.747776	−	0.663952i	$-0.231122\pi$
$614$			3.90346e13i			0.447310i
$615$	2.08312e13	−	3.25129e13i	0.236776	−	0.369556i
$616$	−1.95813e13			−0.220769
$617$	1.71741e14			1.92065			0.960325	−	0.278885i	$-0.0899647\pi$
$617$	1.71741e14			1.92065			0.960325	+	0.278885i	$0.0899647\pi$
$618$	−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
$630$	9.74887e13	+	5.49660e13i	0.982317	+	0.553850i
$631$	−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	$-0.943827\pi$
$643$		−	3.85929e13i		−	0.351118i	0.984469	−	0.175559i	$-0.0561732\pi$
$644$		−	1.33816e14i		−	1.20803i
$645$	5.31339e13	−	8.29303e13i	0.475963	−	0.742873i
$646$	9.59539e13			0.852904
$647$	6.15081e13			0.542514			0.271257	−	0.962507i	$-0.412561\pi$
$647$	6.15081e13			0.542514			0.271257	+	0.962507i	$0.412561\pi$
$648$	−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	$-0.500500\pi$
$653$	−3.73149e11			−0.00314280			−0.00157140	+	0.999999i	$0.500500\pi$
$654$	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	$0.999945\pi$
$660$	1.32263e13	−	2.06433e13i	0.105613	−	0.164839i
$661$	−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	$-0.741545\pi$
$673$		−	2.00366e14i		−	1.45127i	0.688078	−	0.725637i	$-0.258455\pi$
$674$			3.95702e13i			0.284491i
$675$	−1.23796e14	+	6.56489e13i	−0.883464	+	0.468499i
$676$	5.39381e13			0.382087
$677$	−5.80314e13			−0.408056			−0.204028	−	0.978965i	$-0.565403\pi$
$677$	−5.80314e13			−0.408056			−0.204028	+	0.978965i	$0.565403\pi$
$678$	−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	$-0.519497\pi$
$683$	−1.81960e13			−0.122425			−0.0612127	+	0.998125i	$0.519497\pi$
$684$	−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
$690$	1.41073e14	+	9.03863e13i	0.901983	+	0.577906i
$691$	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
$705$	1.16727e14	+	7.47878e13i	0.670234	+	0.429423i
$706$	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	$0.995060\pi$
$720$	2.37576e13	−	4.21369e13i	0.122784	−	0.217771i
$721$	−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	$0.0652097\pi$
$727$			8.26270e13i			0.406864i	−0.979089	+	0.203432i	$0.934790\pi$
$728$	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	$0.149431\pi$
$733$			1.91457e14i			0.904796i	−0.891816	+	0.452398i	$0.850569\pi$
$734$		−	1.25198e14i		−	0.587647i
$735$	2.78757e14	+	1.78601e14i	1.29954	+	0.832620i
$736$	−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	$-0.392328\pi$
$743$	1.50284e14			0.663696			0.331848	+	0.943333i	$0.392328\pi$
$744$	−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
$750$	4.17563e13	−	1.62521e14i	0.175961	−	0.684863i
$751$	−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	$-0.830709\pi$
$757$		−	2.52129e14i		−	1.01424i	0.861874	−	0.507122i	$-0.169291\pi$
$758$	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
$765$	−1.56289e14	+	2.77196e14i	−0.596513	+	1.05799i
$766$	−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	$-0.708844\pi$
$773$	−3.36730e14			−1.22007			−0.610034	+	0.792376i	$0.708844\pi$
$774$	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
$780$	−3.78190e13	+	5.90272e13i	−0.130990	+	0.204446i
$781$	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	$-0.857592\pi$
$787$		−	2.61217e14i		−	0.865224i	0.901580	−	0.432612i	$-0.142408\pi$
$788$	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
$795$	−4.57424e14	−	2.93074e14i	−1.44040	−	0.922873i
$796$	1.98972e14			0.622625
$797$	1.21825e14			0.378830			0.189415	−	0.981897i	$-0.439341\pi$
$797$	1.21825e14			0.378830			0.189415	+	0.981897i	$0.439341\pi$
$798$	−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	$0.941971\pi$
$810$	9.61365e13	−	2.27038e14i	0.275717	−	0.651138i
$811$	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	$0.211295\pi$
$823$			4.65256e14i			1.23223i	−0.787655	+	0.616117i	$0.788705\pi$
$824$			9.07260e13i			0.238834i
$825$	5.47737e13	+	1.39255e14i	0.143318	+	0.364368i
$826$	6.13666e14			1.59600
$827$	7.57703e13			0.195872			0.0979358	−	0.995193i	$-0.468776\pi$
$827$	7.57703e13			0.195872			0.0979358	+	0.995193i	$0.468776\pi$
$828$	−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	$-0.437181\pi$
$840$	1.27212e14	−	1.98550e14i	0.304182	−	0.474760i
$841$	−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	$-0.846363\pi$
$853$		−	4.19205e14i		−	0.928284i	0.885761	−	0.464142i	$-0.153637\pi$
$854$		−	1.12112e14i		−	0.246810i
$855$	2.22857e14	−	3.95263e14i	0.487748	−	0.865078i
$856$	1.93748e14			0.421569
$857$	1.28827e14			0.278679			0.139339	−	0.990245i	$-0.455502\pi$
$857$	1.28827e14			0.278679			0.139339	+	0.990245i	$0.455502\pi$
$858$	−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	$-0.267154\pi$
$863$	6.39522e14			1.33599			0.667993	+	0.744168i	$0.267154\pi$
$864$	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
$870$	1.93119e14	−	3.01416e14i	0.387462	−	0.604742i
$871$	−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	$0.0969764\pi$
$877$			3.11247e14i			0.599938i	−0.953949	+	0.299969i	$0.903024\pi$
$878$	−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	$-0.837875\pi$
$883$		−	5.23468e14i		−	0.975184i	0.873072	−	0.487592i	$-0.162125\pi$
$884$			1.59201e14i			0.294907i
$885$	−4.14503e14	+	6.46948e14i	−0.763505	+	1.19166i
$886$	2.26083e14			0.414095
$887$	−2.10107e14			−0.382668			−0.191334	−	0.981525i	$-0.561281\pi$
$887$	−2.10107e14			−0.382668			−0.191334	+	0.981525i	$0.561281\pi$
$888$	−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
$900$	1.23393e14	+	2.68224e14i	0.208967	+	0.454239i
$901$	−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	$-0.934103\pi$
$907$		−	2.52335e14i		−	0.411094i	0.978647	−	0.205547i	$-0.0658973\pi$
$908$	−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
$915$	1.18193e14	+	7.57266e13i	0.184283	+	0.118071i
$916$	−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	$-0.176697\pi$
$930$	5.83802e14	+	3.74045e14i	0.839172	+	0.537662i
$931$	−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	$0.115919\pi$
$937$			5.14506e14i			0.712349i	−0.934419	+	0.356174i	$0.884081\pi$
$938$	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
$945$	5.30312e14	−	1.07857e15i	0.703675	−	1.43116i
$946$	1.85063e14			0.244266
$947$	4.17259e14			0.547842			0.273921	−	0.961752i	$-0.411679\pi$
$947$	4.17259e14			0.547842			0.273921	+	0.961752i	$0.411679\pi$
$948$	−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	$-0.520447\pi$
$953$	−1.00920e14			−0.128385			−0.0641924	+	0.997938i	$0.520447\pi$
$954$	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
$960$	−8.58181e13	−	5.49842e13i	−0.105250	−	0.0674344i
$961$	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	$-0.677976\pi$
$967$		−	1.43355e15i		−	1.69544i	0.530448	−	0.847718i	$-0.322024\pi$
$968$	−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
$975$	−1.56619e14	−	3.98183e14i	−0.177755	−	0.451918i
$976$	−4.84575e13			−0.0547157
$977$	7.18491e14			0.807139			0.403570	−	0.914949i	$-0.367769\pi$
$977$	7.18491e14			0.807139			0.403570	+	0.914949i	$0.367769\pi$
$978$	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	$-0.458661\pi$
$983$	2.37730e14			0.259010			0.129505	+	0.991579i	$0.458661\pi$
$984$	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
$990$	−2.29350e14	−	1.29312e14i	−0.241169	−	0.135976i
$991$	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	$0.227123\pi$
$997$			1.28949e15i			1.30901i	−0.756057	+	0.654505i	$0.772877\pi$
$998$	−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.29.6	yes	20
3.2	odd	2	inner	30.11.b.a.29.16	yes	20
5.2	odd	4		150.11.d.e.101.10		20
5.3	odd	4		150.11.d.e.101.11		20
5.4	even	2	inner	30.11.b.a.29.15	yes	20
15.2	even	4		150.11.d.e.101.20		20
15.8	even	4		150.11.d.e.101.1		20
15.14	odd	2	inner	30.11.b.a.29.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.11.b.a.29.5	✓	20	15.14	odd	2	inner
30.11.b.a.29.6	yes	20	1.1	even	1	trivial
30.11.b.a.29.15	yes	20	5.4	even	2	inner
30.11.b.a.29.16	yes	20	3.2	odd	2	inner
150.11.d.e.101.1		20	15.8	even	4
150.11.d.e.101.10		20	5.2	odd	4
150.11.d.e.101.11		20	5.3	odd	4
150.11.d.e.101.20		20	15.2	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} +(-639395. - 409664. 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} +(1.44679e7 + 9.26964e6i) 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} +(9.06281e7 - 1.60739e8i) 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} +(-3.27370e8 - 2.09748e8i) 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} +(2.20836e9 - 8.68623e8i) 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} +(-2.05068e9 + 3.63712e9i) 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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