LMFDB - Embedded newform 177.14.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

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:	yes
Analytic conductor:	$189.798744245$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-102.312 q^{2} +729.000 q^{3} +2275.81 q^{4} -9860.18 q^{5} -74585.7 q^{6} +439885. q^{7} +605299. q^{8} +531441. q^{9} +O(q^{10})$	\(q-102.312 q^{2} +729.000 q^{3} +2275.81 q^{4} -9860.18 q^{5} -74585.7 q^{6} +439885. q^{7} +605299. q^{8} +531441. q^{9} +1.00882e6 q^{10} -959631. q^{11} +1.65907e6 q^{12} +5.60936e6 q^{13} -4.50057e7 q^{14} -7.18807e6 q^{15} -8.05730e7 q^{16} -1.88295e8 q^{17} -5.43730e7 q^{18} -3.80650e6 q^{19} -2.24399e7 q^{20} +3.20677e8 q^{21} +9.81821e7 q^{22} +1.27095e9 q^{23} +4.41263e8 q^{24} -1.12348e9 q^{25} -5.73907e8 q^{26} +3.87420e8 q^{27} +1.00110e9 q^{28} +4.95175e9 q^{29} +7.35428e8 q^{30} +8.24954e9 q^{31} +3.28500e9 q^{32} -6.99571e8 q^{33} +1.92649e10 q^{34} -4.33735e9 q^{35} +1.20946e9 q^{36} -2.50637e10 q^{37} +3.89452e8 q^{38} +4.08922e9 q^{39} -5.96836e9 q^{40} -3.30388e10 q^{41} -3.28092e10 q^{42} +4.90496e10 q^{43} -2.18394e9 q^{44} -5.24010e9 q^{45} -1.30034e11 q^{46} +8.62871e10 q^{47} -5.87377e10 q^{48} +9.66102e10 q^{49} +1.14946e11 q^{50} -1.37267e11 q^{51} +1.27658e10 q^{52} +2.96825e11 q^{53} -3.96379e10 q^{54} +9.46214e9 q^{55} +2.66262e11 q^{56} -2.77494e9 q^{57} -5.06626e11 q^{58} -4.21805e10 q^{59} -1.63587e10 q^{60} -6.27896e11 q^{61} -8.44029e11 q^{62} +2.33773e11 q^{63} +3.23958e11 q^{64} -5.53093e10 q^{65} +7.15748e10 q^{66} -6.94025e11 q^{67} -4.28524e11 q^{68} +9.26520e11 q^{69} +4.43764e11 q^{70} +1.94174e11 q^{71} +3.21681e11 q^{72} +3.28001e11 q^{73} +2.56433e12 q^{74} -8.19017e11 q^{75} -8.66289e9 q^{76} -4.22128e11 q^{77} -4.18378e11 q^{78} +3.01833e10 q^{79} +7.94464e11 q^{80} +2.82430e11 q^{81} +3.38028e12 q^{82} +5.53645e11 q^{83} +7.29799e11 q^{84} +1.85662e12 q^{85} -5.01838e12 q^{86} +3.60983e12 q^{87} -5.80864e11 q^{88} -2.05690e12 q^{89} +5.36127e11 q^{90} +2.46748e12 q^{91} +2.89244e12 q^{92} +6.01391e12 q^{93} -8.82824e12 q^{94} +3.75328e10 q^{95} +2.39477e12 q^{96} +5.32259e12 q^{97} -9.88442e12 q^{98} -5.09988e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−102.312	−1.13040	−0.565201	−	0.824953i	$-0.691201\pi$
$2$	−102.312	−1.13040	−0.565201	+	0.824953i	$0.691201\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	2275.81	0.277809
$5$	−9860.18	−0.282215	−0.141107	−	0.989994i	$-0.545066\pi$
$5$	−9860.18	−0.282215	−0.141107	+	0.989994i	$0.545066\pi$
$6$	−74585.7	−0.652638
$7$	439885.	1.41320	0.706598	−	0.707615i	$-0.250229\pi$
$7$	439885.	1.41320	0.706598	+	0.707615i	$0.250229\pi$
$8$	605299.	0.816366
$9$	531441.	0.333333
$10$	1.00882e6	0.319016
$11$	−959631.	−0.163325	−0.0816624	−	0.996660i	$-0.526023\pi$
$11$	−959631.	−0.163325	−0.0816624	+	0.996660i	$0.526023\pi$
$12$	1.65907e6	0.160393
$13$	5.60936e6	0.322316	0.161158	−	0.986929i	$-0.448477\pi$
$13$	5.60936e6	0.322316	0.161158	+	0.986929i	$0.448477\pi$
$14$	−4.50057e7	−1.59748
$15$	−7.18807e6	−0.162937
$16$	−8.05730e7	−1.20063
$17$	−1.88295e8	−1.89200	−0.945999	−	0.324169i	$-0.894915\pi$
$17$	−1.88295e8	−1.89200	−0.945999	+	0.324169i	$0.894915\pi$
$18$	−5.43730e7	−0.376801
$19$	−3.80650e6	−0.0185621	−0.00928107	−	0.999957i	$-0.502954\pi$
$19$	−3.80650e6	−0.0185621	−0.00928107	+	0.999957i	$0.502954\pi$
$20$	−2.24399e7	−0.0784018
$21$	3.20677e8	0.815909
$22$	9.81821e7	0.184623
$23$	1.27095e9	1.79018	0.895089	−	0.445887i	$-0.147112\pi$
$23$	1.27095e9	1.79018	0.895089	+	0.445887i	$0.147112\pi$
$24$	4.41263e8	0.471329
$25$	−1.12348e9	−0.920355
$26$	−5.73907e8	−0.364346
$27$	3.87420e8	0.192450
$28$	1.00110e9	0.392599
$29$	4.95175e9	1.54587	0.772934	−	0.634487i	$-0.218789\pi$
$29$	4.95175e9	1.54587	0.772934	+	0.634487i	$0.218789\pi$
$30$	7.35428e8	0.184184
$31$	8.24954e9	1.66947	0.834735	−	0.550652i	$-0.185621\pi$
$31$	8.24954e9	1.66947	0.834735	+	0.550652i	$0.185621\pi$
$32$	3.28500e9	0.540830
$33$	−6.99571e8	−0.0942956
$34$	1.92649e10	2.13872
$35$	−4.33735e9	−0.398825
$36$	1.20946e9	0.0926030
$37$	−2.50637e10	−1.60596	−0.802979	−	0.596008i	$-0.796753\pi$
$37$	−2.50637e10	−1.60596	−0.802979	+	0.596008i	$0.796753\pi$
$38$	3.89452e8	0.0209827
$39$	4.08922e9	0.186089
$40$	−5.96836e9	−0.230391
$41$	−3.30388e10	−1.08625	−0.543124	−	0.839652i	$-0.682759\pi$
$41$	−3.30388e10	−1.08625	−0.543124	+	0.839652i	$0.682759\pi$
$42$	−3.28092e10	−0.922305
$43$	4.90496e10	1.18329	0.591644	−	0.806199i	$-0.298479\pi$
$43$	4.90496e10	1.18329	0.591644	+	0.806199i	$0.298479\pi$
$44$	−2.18394e9	−0.0453731
$45$	−5.24010e9	−0.0940716
$46$	−1.30034e11	−2.02362
$47$	8.62871e10	1.16764	0.583821	−	0.811882i	$-0.301557\pi$
$47$	8.62871e10	1.16764	0.583821	+	0.811882i	$0.301557\pi$
$48$	−5.87377e10	−0.693185
$49$	9.66102e10	0.997122
$50$	1.14946e11	1.04037
$51$	−1.37267e11	−1.09235
$52$	1.27658e10	0.0895422
$53$	2.96825e11	1.83953	0.919767	−	0.392464i	$-0.128377\pi$
$53$	2.96825e11	1.83953	0.919767	+	0.392464i	$0.128377\pi$
$54$	−3.96379e10	−0.217546
$55$	9.46214e9	0.0460927
$56$	2.66262e11	1.15369
$57$	−2.77494e9	−0.0107169
$58$	−5.06626e11	−1.74745
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−1.63587e10	−0.0452653
$61$	−6.27896e11	−1.56043	−0.780214	−	0.625513i	$-0.784890\pi$
$61$	−6.27896e11	−1.56043	−0.780214	+	0.625513i	$0.784890\pi$
$62$	−8.44029e11	−1.88717
$63$	2.33773e11	0.471065
$64$	3.23958e11	0.589276
$65$	−5.53093e10	−0.0909622
$66$	7.15748e10	0.106592
$67$	−6.94025e11	−0.937323	−0.468661	−	0.883378i	$-0.655264\pi$
$67$	−6.94025e11	−0.937323	−0.468661	+	0.883378i	$0.655264\pi$
$68$	−4.28524e11	−0.525614
$69$	9.26520e11	1.03356
$70$	4.43764e11	0.450832
$71$	1.94174e11	0.179892	0.0899460	−	0.995947i	$-0.471331\pi$
$71$	1.94174e11	0.179892	0.0899460	+	0.995947i	$0.471331\pi$
$72$	3.21681e11	0.272122
$73$	3.28001e11	0.253674	0.126837	−	0.991924i	$-0.459517\pi$
$73$	3.28001e11	0.253674	0.126837	+	0.991924i	$0.459517\pi$
$74$	2.56433e12	1.81538
$75$	−8.19017e11	−0.531367
$76$	−8.66289e9	−0.00515673
$77$	−4.22128e11	−0.230810
$78$	−4.18378e11	−0.210355
$79$	3.01833e10	0.0139698	0.00698491	−	0.999976i	$-0.497777\pi$
$79$	3.01833e10	0.0139698	0.00698491	+	0.999976i	$0.497777\pi$
$80$	7.94464e11	0.338836
$81$	2.82430e11	0.111111
$82$	3.38028e12	1.22790
$83$	5.53645e11	0.185876	0.0929382	−	0.995672i	$-0.470374\pi$
$83$	5.53645e11	0.185876	0.0929382	+	0.995672i	$0.470374\pi$
$84$	7.29799e11	0.226667
$85$	1.85662e12	0.533950
$86$	−5.01838e12	−1.33759
$87$	3.60983e12	0.892507
$88$	−5.80864e11	−0.133333
$89$	−2.05690e12	−0.438711	−0.219355	−	0.975645i	$-0.570395\pi$
$89$	−2.05690e12	−0.438711	−0.219355	+	0.975645i	$0.570395\pi$
$90$	5.36127e11	0.106339
$91$	2.46748e12	0.455495
$92$	2.89244e12	0.497328
$93$	6.01391e12	0.963869
$94$	−8.82824e12	−1.31991
$95$	3.75328e10	0.00523851
$96$	2.39477e12	0.312248
$97$	5.32259e12	0.648794	0.324397	−	0.945921i	$-0.394839\pi$
$97$	5.32259e12	0.648794	0.324397	+	0.945921i	$0.394839\pi$
$98$	−9.88442e12	−1.12715
$99$	−5.09988e11	−0.0544416
$100$	−2.55683e12	−0.255683
$101$	4.79471e12	0.449442	0.224721	−	0.974423i	$-0.427853\pi$
$101$	4.79471e12	0.449442	0.224721	+	0.974423i	$0.427853\pi$
$102$	1.40441e13	1.23479
$103$	−1.39519e13	−1.15131	−0.575655	−	0.817693i	$-0.695253\pi$
$103$	−1.39519e13	−1.15131	−0.575655	+	0.817693i	$0.695253\pi$
$104$	3.39534e12	0.263128
$105$	−3.16193e12	−0.230262
$106$	−3.03689e13	−2.07941
$107$	8.69685e12	0.560232	0.280116	−	0.959966i	$-0.409627\pi$
$107$	8.69685e12	0.560232	0.280116	+	0.959966i	$0.409627\pi$
$108$	8.81696e11	0.0534644
$109$	2.50601e13	1.43123	0.715616	−	0.698494i	$-0.246146\pi$
$109$	2.50601e13	1.43123	0.715616	+	0.698494i	$0.246146\pi$
$110$	−9.68093e11	−0.0521032
$111$	−1.82714e13	−0.927200
$112$	−3.54429e13	−1.69673
$113$	−2.11671e13	−0.956424	−0.478212	−	0.878244i	$-0.658715\pi$
$113$	−2.11671e13	−0.956424	−0.478212	+	0.878244i	$0.658715\pi$
$114$	2.83911e11	0.0121144
$115$	−1.25318e13	−0.505215
$116$	1.12693e13	0.429456
$117$	2.98104e12	0.107439
$118$	4.31559e12	0.147166
$119$	−8.28282e13	−2.67376
$120$	−4.35093e12	−0.133016
$121$	−3.36018e13	−0.973325
$122$	6.42415e13	1.76391
$123$	−2.40853e13	−0.627146
$124$	1.87744e13	0.463794
$125$	2.31141e13	0.541952
$126$	−2.39179e13	−0.532493
$127$	−1.50766e13	−0.318846	−0.159423	−	0.987210i	$-0.550963\pi$
$127$	−1.50766e13	−0.318846	−0.159423	+	0.987210i	$0.550963\pi$
$128$	−6.00556e13	−1.20695
$129$	3.57572e13	0.683172
$130$	5.65882e12	0.102824
$131$	−6.12475e13	−1.05883	−0.529413	−	0.848364i	$-0.677588\pi$
$131$	−6.12475e13	−1.05883	−0.529413	+	0.848364i	$0.677588\pi$
$132$	−1.59209e12	−0.0261962
$133$	−1.67443e12	−0.0262319
$134$	7.10073e13	1.05955
$135$	−3.82003e12	−0.0543123
$136$	−1.13975e14	−1.54456
$137$	6.52569e13	0.843224	0.421612	−	0.906776i	$-0.361464\pi$
$137$	6.52569e13	0.843224	0.421612	+	0.906776i	$0.361464\pi$
$138$	−9.47944e13	−1.16834
$139$	7.06004e13	0.830254	0.415127	−	0.909763i	$-0.363737\pi$
$139$	7.06004e13	0.830254	0.415127	+	0.909763i	$0.363737\pi$
$140$	−9.87099e12	−0.110797
$141$	6.29033e13	0.674139
$142$	−1.98664e13	−0.203350
$143$	−5.38292e12	−0.0526421
$144$	−4.28198e13	−0.400210
$145$	−4.88252e13	−0.436267
$146$	−3.35585e13	−0.286754
$147$	7.04288e13	0.575689
$148$	−5.70403e13	−0.446150
$149$	−5.00979e13	−0.375067	−0.187533	−	0.982258i	$-0.560049\pi$
$149$	−5.00979e13	−0.375067	−0.187533	+	0.982258i	$0.560049\pi$
$150$	8.37955e13	0.600659
$151$	−1.38699e14	−0.952191	−0.476096	−	0.879394i	$-0.657948\pi$
$151$	−1.38699e14	−0.952191	−0.476096	+	0.879394i	$0.657948\pi$
$152$	−2.30407e12	−0.0151535
$153$	−1.00068e14	−0.630666
$154$	4.31889e13	0.260908
$155$	−8.13419e13	−0.471149
$156$	9.30630e12	0.0516972
$157$	3.48457e13	0.185696	0.0928479	−	0.995680i	$-0.470403\pi$
$157$	3.48457e13	0.185696	0.0928479	+	0.995680i	$0.470403\pi$
$158$	−3.08813e12	−0.0157915
$159$	2.16386e14	1.06206
$160$	−3.23907e13	−0.152630
$161$	5.59071e14	2.52987
$162$	−2.88960e13	−0.125600
$163$	3.37036e12	0.0140753	0.00703763	−	0.999975i	$-0.497760\pi$
$163$	3.37036e12	0.0140753	0.00703763	+	0.999975i	$0.497760\pi$
$164$	−7.51901e13	−0.301770
$165$	6.89790e12	0.0266116
$166$	−5.66447e13	−0.210115
$167$	9.27764e13	0.330964	0.165482	−	0.986213i	$-0.447082\pi$
$167$	9.27764e13	0.330964	0.165482	+	0.986213i	$0.447082\pi$
$168$	1.94105e14	0.666081
$169$	−2.71410e14	−0.896113
$170$	−1.89955e14	−0.603578
$171$	−2.02293e12	−0.00618738
$172$	1.11628e14	0.328728
$173$	−2.55428e14	−0.724383	−0.362192	−	0.932104i	$-0.617971\pi$
$173$	−2.55428e14	−0.724383	−0.362192	+	0.932104i	$0.617971\pi$
$174$	−3.69330e14	−1.00889
$175$	−4.94203e14	−1.30064
$176$	7.73204e13	0.196093
$177$	−3.07496e13	−0.0751646
$178$	2.10446e14	0.495920
$179$	5.21459e14	1.18488	0.592441	−	0.805613i	$-0.298164\pi$
$179$	5.21459e14	1.18488	0.592441	+	0.805613i	$0.298164\pi$
$180$	−1.19255e13	−0.0261339
$181$	1.91276e14	0.404343	0.202171	−	0.979350i	$-0.435200\pi$
$181$	1.91276e14	0.404343	0.202171	+	0.979350i	$0.435200\pi$
$182$	−2.52453e14	−0.514893
$183$	−4.57736e14	−0.900913
$184$	7.69303e14	1.46144
$185$	2.47133e14	0.453225
$186$	−6.15297e14	−1.08956
$187$	1.80694e14	0.309010
$188$	1.96373e14	0.324382
$189$	1.70421e14	0.271970
$190$	−3.84007e12	−0.00592162
$191$	−3.71672e14	−0.553914	−0.276957	−	0.960882i	$-0.589326\pi$
$191$	−3.71672e14	−0.553914	−0.276957	+	0.960882i	$0.589326\pi$
$192$	2.36165e14	0.340219
$193$	3.74464e14	0.521540	0.260770	−	0.965401i	$-0.416024\pi$
$193$	3.74464e14	0.521540	0.260770	+	0.965401i	$0.416024\pi$
$194$	−5.44567e14	−0.733398
$195$	−4.03205e13	−0.0525171
$196$	2.19867e14	0.277010
$197$	1.03975e15	1.26735	0.633677	−	0.773598i	$-0.281545\pi$
$197$	1.03975e15	1.26735	0.633677	+	0.773598i	$0.281545\pi$
$198$	5.21780e13	0.0615409
$199$	1.58199e15	1.80575	0.902875	−	0.429903i	$-0.141452\pi$
$199$	1.58199e15	1.80575	0.902875	+	0.429903i	$0.141452\pi$
$200$	−6.80041e14	−0.751347
$201$	−5.05944e14	−0.541163
$202$	−4.90558e14	−0.508050
$203$	2.17821e15	2.18461
$204$	−3.12394e14	−0.303464
$205$	3.25768e14	0.306555
$206$	1.42745e15	1.30144
$207$	6.75433e14	0.596726
$208$	−4.51963e14	−0.386982
$209$	3.65284e12	0.00303166
$210$	3.23504e14	0.260288
$211$	−1.04660e15	−0.816481	−0.408241	−	0.912874i	$-0.633858\pi$
$211$	−1.04660e15	−0.816481	−0.408241	+	0.912874i	$0.633858\pi$
$212$	6.75519e14	0.511039
$213$	1.41553e14	0.103861
$214$	−8.89795e14	−0.633287
$215$	−4.83638e14	−0.333941
$216$	2.34505e14	0.157110
$217$	3.62885e15	2.35929
$218$	−2.56395e15	−1.61787
$219$	2.39113e14	0.146459
$220$	2.15340e13	0.0128050
$221$	−1.05621e15	−0.609821
$222$	1.86939e15	1.04811
$223$	−7.62200e14	−0.415037	−0.207519	−	0.978231i	$-0.566539\pi$
$223$	−7.62200e14	−0.415037	−0.207519	+	0.978231i	$0.566539\pi$
$224$	1.44502e15	0.764299
$225$	−5.97063e14	−0.306785
$226$	2.16565e15	1.08114
$227$	2.97374e15	1.44256	0.721282	−	0.692642i	$-0.243553\pi$
$227$	2.97374e15	1.44256	0.721282	+	0.692642i	$0.243553\pi$
$228$	−6.31525e12	−0.00297724
$229$	3.26361e14	0.149544	0.0747719	−	0.997201i	$-0.476177\pi$
$229$	3.26361e14	0.149544	0.0747719	+	0.997201i	$0.476177\pi$
$230$	1.28215e15	0.571096
$231$	−3.07731e14	−0.133258
$232$	2.99729e15	1.26199
$233$	2.53194e15	1.03667	0.518335	−	0.855178i	$-0.326552\pi$
$233$	2.53194e15	1.03667	0.518335	+	0.855178i	$0.326552\pi$
$234$	−3.04997e14	−0.121449
$235$	−8.50807e14	−0.329526
$236$	−9.59950e13	−0.0361677
$237$	2.20036e13	0.00806548
$238$	8.47435e15	3.02243
$239$	1.47267e15	0.511117	0.255558	−	0.966794i	$-0.417741\pi$
$239$	1.47267e15	0.511117	0.255558	+	0.966794i	$0.417741\pi$
$240$	5.79164e14	0.195627
$241$	3.16431e15	1.04032	0.520161	−	0.854068i	$-0.325872\pi$
$241$	3.16431e15	1.04032	0.520161	+	0.854068i	$0.325872\pi$
$242$	3.43788e15	1.10025
$243$	2.05891e14	0.0641500
$244$	−1.42897e15	−0.433501
$245$	−9.52594e14	−0.281403
$246$	2.46422e15	0.708927
$247$	−2.13521e13	−0.00598287
$248$	4.99343e15	1.36290
$249$	4.03607e14	0.107316
$250$	−2.36485e15	−0.612624
$251$	−4.90008e15	−1.23687	−0.618435	−	0.785836i	$-0.712233\pi$
$251$	−4.90008e15	−1.23687	−0.618435	+	0.785836i	$0.712233\pi$
$252$	5.32024e14	0.130866
$253$	−1.21964e15	−0.292381
$254$	1.54253e15	0.360424
$255$	1.35348e15	0.308276
$256$	3.49057e15	0.775062
$257$	2.79467e15	0.605014	0.302507	−	0.953147i	$-0.402176\pi$
$257$	2.79467e15	0.605014	0.302507	+	0.953147i	$0.402176\pi$
$258$	−3.65840e15	−0.772259
$259$	−1.10252e16	−2.26953
$260$	−1.25874e14	−0.0252701
$261$	2.63157e15	0.515289
$262$	6.26637e15	1.19690
$263$	6.06854e15	1.13076	0.565382	−	0.824829i	$-0.308729\pi$
$263$	6.06854e15	1.13076	0.565382	+	0.824829i	$0.308729\pi$
$264$	−4.23450e14	−0.0769797
$265$	−2.92675e15	−0.519144
$266$	1.71314e14	0.0296526
$267$	−1.49948e15	−0.253290
$268$	−1.57947e15	−0.260397
$269$	−1.58413e15	−0.254919	−0.127459	−	0.991844i	$-0.540682\pi$
$269$	−1.58413e15	−0.254919	−0.127459	+	0.991844i	$0.540682\pi$
$270$	3.90837e14	0.0613947
$271$	−6.06086e15	−0.929467	−0.464733	−	0.885451i	$-0.653850\pi$
$271$	−6.06086e15	−0.929467	−0.464733	+	0.885451i	$0.653850\pi$
$272$	1.51715e16	2.27159
$273$	1.79879e15	0.262980
$274$	−6.67659e15	−0.953182
$275$	1.07813e15	0.150317
$276$	2.10859e15	0.287132
$277$	−1.10110e16	−1.46456	−0.732279	−	0.681005i	$-0.761543\pi$
$277$	−1.10110e16	−1.46456	−0.732279	+	0.681005i	$0.761543\pi$
$278$	−7.22329e15	−0.938521
$279$	4.38414e15	0.556490
$280$	−2.62539e15	−0.325587
$281$	8.50276e15	1.03031	0.515156	−	0.857097i	$-0.327734\pi$
$281$	8.50276e15	1.03031	0.515156	+	0.857097i	$0.327734\pi$
$282$	−6.43579e15	−0.762048
$283$	1.83458e15	0.212287	0.106144	−	0.994351i	$-0.466150\pi$
$283$	1.83458e15	0.212287	0.106144	+	0.994351i	$0.466150\pi$
$284$	4.41904e14	0.0499757
$285$	2.73614e13	0.00302445
$286$	5.50739e14	0.0595068
$287$	−1.45333e16	−1.53508
$288$	1.74578e15	0.180277
$289$	2.55504e16	2.57966
$290$	4.99542e15	0.493157
$291$	3.88017e15	0.374581
$292$	7.46468e14	0.0704730
$293$	−7.11647e15	−0.657090	−0.328545	−	0.944488i	$-0.606558\pi$
$293$	−7.11647e15	−0.657090	−0.328545	+	0.944488i	$0.606558\pi$
$294$	−7.20574e15	−0.650760
$295$	4.15908e14	0.0367412
$296$	−1.51710e16	−1.31105
$297$	−3.71781e14	−0.0314319
$298$	5.12563e15	0.423976
$299$	7.12920e15	0.577003
$300$	−1.86393e15	−0.147619
$301$	2.15762e16	1.67222
$302$	1.41906e16	1.07636
$303$	3.49534e15	0.259485
$304$	3.06702e14	0.0222863
$305$	6.19116e15	0.440376
$306$	1.02382e16	0.712906
$307$	3.06811e15	0.209157	0.104578	−	0.994517i	$-0.466651\pi$
$307$	3.06811e15	0.209157	0.104578	+	0.994517i	$0.466651\pi$
$308$	−9.60684e14	−0.0641211
$309$	−1.01709e16	−0.664709
$310$	8.32228e15	0.532588
$311$	2.41527e16	1.51364	0.756821	−	0.653623i	$-0.226752\pi$
$311$	2.41527e16	1.51364	0.756821	+	0.653623i	$0.226752\pi$
$312$	2.47520e15	0.151917
$313$	−1.62698e16	−0.978010	−0.489005	−	0.872281i	$-0.662640\pi$
$313$	−1.62698e16	−0.978010	−0.489005	+	0.872281i	$0.662640\pi$
$314$	−3.56515e15	−0.209911
$315$	−2.30504e15	−0.132942
$316$	6.86916e13	0.00388094
$317$	−1.23819e16	−0.685333	−0.342666	−	0.939457i	$-0.611330\pi$
$317$	−1.23819e16	−0.685333	−0.342666	+	0.939457i	$0.611330\pi$
$318$	−2.21389e16	−1.20055
$319$	−4.75186e15	−0.252478
$320$	−3.19428e15	−0.166302
$321$	6.34001e15	0.323450
$322$	−5.71999e16	−2.85977
$323$	7.16746e14	0.0351195
$324$	6.42757e14	0.0308677
$325$	−6.30200e15	−0.296645
$326$	−3.44829e14	−0.0159107
$327$	1.82688e16	0.826322
$328$	−1.99984e16	−0.886777
$329$	3.79565e16	1.65011
$330$	−7.05740e14	−0.0300818
$331$	2.36825e16	0.989797	0.494898	−	0.868951i	$-0.335205\pi$
$331$	2.36825e16	0.989797	0.494898	+	0.868951i	$0.335205\pi$
$332$	1.25999e15	0.0516381
$333$	−1.33199e16	−0.535319
$334$	−9.49217e15	−0.374122
$335$	6.84321e15	0.264526
$336$	−2.58379e16	−0.979606
$337$	−2.61147e16	−0.971161	−0.485580	−	0.874192i	$-0.661392\pi$
$337$	−2.61147e16	−0.971161	−0.485580	+	0.874192i	$0.661392\pi$
$338$	2.77686e16	1.01297
$339$	−1.54308e16	−0.552192
$340$	4.22532e15	0.148336
$341$	−7.91651e15	−0.272666
$342$	2.06971e14	0.00699423
$343$	−1.22640e14	−0.00406651
$344$	2.96897e16	0.965996
$345$	−9.13565e15	−0.291686
$346$	2.61334e16	0.818844
$347$	1.23055e16	0.378405	0.189202	−	0.981938i	$-0.439410\pi$
$347$	1.23055e16	0.378405	0.189202	+	0.981938i	$0.439410\pi$
$348$	8.21529e15	0.247947
$349$	1.37929e16	0.408591	0.204296	−	0.978909i	$-0.434510\pi$
$349$	1.37929e16	0.408591	0.204296	+	0.978909i	$0.434510\pi$
$350$	5.05630e16	1.47025
$351$	2.17318e15	0.0620297
$352$	−3.15239e15	−0.0883309
$353$	−4.63927e16	−1.27619	−0.638093	−	0.769960i	$-0.720276\pi$
$353$	−4.63927e16	−1.27619	−0.638093	+	0.769960i	$0.720276\pi$
$354$	3.14606e15	0.0849662
$355$	−1.91459e15	−0.0507682
$356$	−4.68112e15	−0.121878
$357$	−6.03818e16	−1.54370
$358$	−5.33517e16	−1.33939
$359$	−1.44346e16	−0.355870	−0.177935	−	0.984042i	$-0.556942\pi$
$359$	−1.44346e16	−0.355870	−0.177935	+	0.984042i	$0.556942\pi$
$360$	−3.17183e15	−0.0767969
$361$	−4.20385e16	−0.999655
$362$	−1.95699e16	−0.457070
$363$	−2.44957e16	−0.561949
$364$	5.61551e15	0.126541
$365$	−3.23415e15	−0.0715906
$366$	4.68320e16	1.01839
$367$	4.45889e16	0.952571	0.476286	−	0.879291i	$-0.341983\pi$
$367$	4.45889e16	0.952571	0.476286	+	0.879291i	$0.341983\pi$
$368$	−1.02404e17	−2.14934
$369$	−1.75582e16	−0.362083
$370$	−2.52847e16	−0.512326
$371$	1.30569e17	2.59962
$372$	1.36865e16	0.267771
$373$	7.97536e16	1.53336	0.766678	−	0.642032i	$-0.221908\pi$
$373$	7.97536e16	1.53336	0.766678	+	0.642032i	$0.221908\pi$
$374$	−1.84872e16	−0.349306
$375$	1.68502e16	0.312896
$376$	5.22295e16	0.953224
$377$	2.77762e16	0.498257
$378$	−1.74361e16	−0.307435
$379$	5.34113e16	0.925717	0.462859	−	0.886432i	$-0.346824\pi$
$379$	5.34113e16	0.925717	0.462859	+	0.886432i	$0.346824\pi$
$380$	8.54176e13	0.00145531
$381$	−1.09909e16	−0.184086
$382$	3.80266e16	0.626146
$383$	2.41068e16	0.390254	0.195127	−	0.980778i	$-0.437488\pi$
$383$	2.41068e16	0.390254	0.195127	+	0.980778i	$0.437488\pi$
$384$	−4.37805e16	−0.696832
$385$	4.16226e15	0.0651380
$386$	−3.83123e16	−0.589550
$387$	2.60670e16	0.394429
$388$	1.21132e16	0.180241
$389$	6.28632e16	0.919865	0.459933	−	0.887954i	$-0.347874\pi$
$389$	6.28632e16	0.919865	0.459933	+	0.887954i	$0.347874\pi$
$390$	4.12528e15	0.0593654
$391$	−2.39313e17	−3.38702
$392$	5.84781e16	0.814017
$393$	−4.46494e16	−0.611314
$394$	−1.06379e17	−1.43262
$395$	−2.97613e14	−0.00394249
$396$	−1.16064e15	−0.0151244
$397$	4.95048e16	0.634613	0.317306	−	0.948323i	$-0.397222\pi$
$397$	4.95048e16	0.634613	0.317306	+	0.948323i	$0.397222\pi$
$398$	−1.61857e17	−2.04122
$399$	−1.22066e15	−0.0151450
$400$	9.05222e16	1.10501
$401$	7.60000e16	0.912799	0.456399	−	0.889775i	$-0.349139\pi$
$401$	7.60000e16	0.912799	0.456399	+	0.889775i	$0.349139\pi$
$402$	5.17644e16	0.611732
$403$	4.62746e16	0.538096
$404$	1.09119e16	0.124859
$405$	−2.78481e15	−0.0313572
$406$	−2.22857e17	−2.46949
$407$	2.40519e16	0.262293
$408$	−8.30876e16	−0.891754
$409$	7.38271e16	0.779855	0.389928	−	0.920845i	$-0.372500\pi$
$409$	7.38271e16	0.779855	0.389928	+	0.920845i	$0.372500\pi$
$410$	−3.33301e16	−0.346531
$411$	4.75723e16	0.486836
$412$	−3.17520e16	−0.319844
$413$	−1.85546e16	−0.183982
$414$	−6.91051e16	−0.674541
$415$	−5.45904e15	−0.0524570
$416$	1.84268e16	0.174318
$417$	5.14677e16	0.479347
$418$	−3.73731e14	−0.00342699
$419$	5.18667e16	0.468271	0.234136	−	0.972204i	$-0.424774\pi$
$419$	5.18667e16	0.468271	0.234136	+	0.972204i	$0.424774\pi$
$420$	−7.19595e15	−0.0639688
$421$	2.46988e16	0.216193	0.108096	−	0.994140i	$-0.465524\pi$
$421$	2.46988e16	0.216193	0.108096	+	0.994140i	$0.465524\pi$
$422$	1.07080e17	0.922952
$423$	4.58565e16	0.389214
$424$	1.79668e17	1.50173
$425$	2.11546e17	1.74131
$426$	−1.44826e16	−0.117404
$427$	−2.76202e17	−2.20519
$428$	1.97924e16	0.155637
$429$	−3.92415e15	−0.0303929
$430$	4.94821e16	0.377488
$431$	2.15093e17	1.61630	0.808152	−	0.588974i	$-0.200468\pi$
$431$	2.15093e17	1.61630	0.808152	+	0.588974i	$0.200468\pi$
$432$	−3.12156e16	−0.231062
$433$	2.35585e17	1.71782	0.858909	−	0.512128i	$-0.171143\pi$
$433$	2.35585e17	1.71782	0.858909	+	0.512128i	$0.171143\pi$
$434$	−3.71276e17	−2.66694
$435$	−3.55936e16	−0.251879
$436$	5.70320e16	0.397609
$437$	−4.83787e15	−0.0332295
$438$	−2.44642e16	−0.165557
$439$	−1.21164e17	−0.807893	−0.403947	−	0.914783i	$-0.632362\pi$
$439$	−1.21164e17	−0.807893	−0.403947	+	0.914783i	$0.632362\pi$
$440$	5.72742e15	0.0376285
$441$	5.13426e16	0.332374
$442$	1.08064e17	0.689343
$443$	−4.75701e16	−0.299026	−0.149513	−	0.988760i	$-0.547771\pi$
$443$	−4.75701e16	−0.299026	−0.149513	+	0.988760i	$0.547771\pi$
$444$	−4.15824e16	−0.257585
$445$	2.02814e16	0.123811
$446$	7.79824e16	0.469159
$447$	−3.65214e16	−0.216545
$448$	1.42504e17	0.832762
$449$	1.21062e17	0.697279	0.348640	−	0.937257i	$-0.386644\pi$
$449$	1.21062e17	0.697279	0.348640	+	0.937257i	$0.386644\pi$
$450$	6.10869e16	0.346790
$451$	3.17051e16	0.177411
$452$	−4.81722e16	−0.265703
$453$	−1.01112e17	−0.549748
$454$	−3.04250e17	−1.63068
$455$	−2.43297e16	−0.128547
$456$	−1.67967e15	−0.00874888
$457$	−2.45726e17	−1.26182	−0.630909	−	0.775857i	$-0.717318\pi$
$457$	−2.45726e17	−1.26182	−0.630909	+	0.775857i	$0.717318\pi$
$458$	−3.33908e16	−0.169045
$459$	−7.29493e16	−0.364115
$460$	−2.85199e16	−0.140353
$461$	3.78798e17	1.83803	0.919013	−	0.394227i	$-0.128988\pi$
$461$	3.78798e17	1.83803	0.919013	+	0.394227i	$0.128988\pi$
$462$	3.14847e16	0.150635
$463$	−2.59238e17	−1.22299	−0.611495	−	0.791248i	$-0.709432\pi$
$463$	−2.59238e17	−1.22299	−0.611495	+	0.791248i	$0.709432\pi$
$464$	−3.98978e17	−1.85602
$465$	−5.92982e16	−0.272018
$466$	−2.59049e17	−1.17185
$467$	6.08852e16	0.271614	0.135807	−	0.990735i	$-0.456637\pi$
$467$	6.08852e16	0.271614	0.135807	+	0.990735i	$0.456637\pi$
$468$	6.78429e15	0.0298474
$469$	−3.05292e17	−1.32462
$470$	8.70480e16	0.372497
$471$	2.54025e16	0.107211
$472$	−2.55318e16	−0.106282
$473$	−4.70695e16	−0.193260
$474$	−2.25124e15	−0.00911724
$475$	4.27653e15	0.0170838
$476$	−1.88501e17	−0.742796
$477$	1.57745e17	0.613178
$478$	−1.50673e17	−0.577767
$479$	3.07859e17	1.16459	0.582293	−	0.812979i	$-0.302156\pi$
$479$	3.07859e17	1.16459	0.582293	+	0.812979i	$0.302156\pi$
$480$	−2.36128e16	−0.0881211
$481$	−1.40591e17	−0.517625
$482$	−3.23748e17	−1.17598
$483$	4.07563e17	1.46062
$484$	−7.64714e16	−0.270399
$485$	−5.24817e16	−0.183099
$486$	−2.10652e16	−0.0725153
$487$	−1.84377e17	−0.626279	−0.313139	−	0.949707i	$-0.601381\pi$
$487$	−1.84377e17	−0.626279	−0.313139	+	0.949707i	$0.601381\pi$
$488$	−3.80065e17	−1.27388
$489$	2.45699e15	0.00812636
$490$	9.74621e16	0.318098
$491$	2.52379e17	0.812873	0.406437	−	0.913679i	$-0.366771\pi$
$491$	2.52379e17	0.812873	0.406437	+	0.913679i	$0.366771\pi$
$492$	−5.48136e16	−0.174227
$493$	−9.32391e17	−2.92478
$494$	2.18458e15	0.00676305
$495$	5.02857e15	0.0153642
$496$	−6.64690e17	−2.00442
$497$	8.54144e16	0.254223
$498$	−4.12940e16	−0.121310
$499$	−2.98918e17	−0.866760	−0.433380	−	0.901211i	$-0.642679\pi$
$499$	−2.98918e17	−0.866760	−0.433380	+	0.901211i	$0.642679\pi$
$500$	5.26033e16	0.150559
$501$	6.76340e16	0.191082
$502$	5.01338e17	1.39816
$503$	4.01278e17	1.10472	0.552362	−	0.833605i	$-0.313727\pi$
$503$	4.01278e17	1.10472	0.552362	+	0.833605i	$0.313727\pi$
$504$	1.41503e17	0.384562
$505$	−4.72767e16	−0.126839
$506$	1.24784e17	0.330508
$507$	−1.97858e17	−0.517371
$508$	−3.43116e16	−0.0885782
$509$	6.16098e17	1.57030	0.785152	−	0.619303i	$-0.212585\pi$
$509$	6.16098e17	1.57030	0.785152	+	0.619303i	$0.212585\pi$
$510$	−1.38477e17	−0.348476
$511$	1.44283e17	0.358491
$512$	1.34848e17	0.330817
$513$	−1.47472e15	−0.00357229
$514$	−2.85929e17	−0.683909
$515$	1.37568e17	0.324916
$516$	8.13766e16	0.189791
$517$	−8.28039e16	−0.190705
$518$	1.12801e18	2.56548
$519$	−1.86207e17	−0.418223
$520$	−3.34786e16	−0.0742585
$521$	−4.14914e17	−0.908892	−0.454446	−	0.890774i	$-0.650163\pi$
$521$	−4.14914e17	−0.908892	−0.454446	+	0.890774i	$0.650163\pi$
$522$	−2.69242e17	−0.582484
$523$	3.78452e17	0.808630	0.404315	−	0.914620i	$-0.367510\pi$
$523$	3.78452e17	0.808630	0.404315	+	0.914620i	$0.367510\pi$
$524$	−1.39388e17	−0.294152
$525$	−3.60274e17	−0.750926
$526$	−6.20886e17	−1.27822
$527$	−1.55335e18	−3.15863
$528$	5.63666e16	0.113214
$529$	1.11127e18	2.20474
$530$	2.99443e17	0.586841
$531$	−2.24165e16	−0.0433963
$532$	−3.81068e15	−0.00728747
$533$	−1.85327e17	−0.350115
$534$	1.53415e17	0.286319
$535$	−8.57525e16	−0.158106
$536$	−4.20093e17	−0.765198
$537$	3.80144e17	0.684092
$538$	1.62076e17	0.288161
$539$	−9.27102e16	−0.162855
$540$	−8.69368e15	−0.0150884
$541$	1.85708e17	0.318456	0.159228	−	0.987242i	$-0.449100\pi$
$541$	1.85708e17	0.318456	0.159228	+	0.987242i	$0.449100\pi$
$542$	6.20101e17	1.05067
$543$	1.39440e17	0.233447
$544$	−6.18549e17	−1.02325
$545$	−2.47097e17	−0.403915
$546$	−1.84038e17	−0.297273
$547$	−4.62369e17	−0.738026	−0.369013	−	0.929424i	$-0.620304\pi$
$547$	−4.62369e17	−0.738026	−0.369013	+	0.929424i	$0.620304\pi$
$548$	1.48513e17	0.234255
$549$	−3.33690e17	−0.520142
$550$	−1.10306e17	−0.169918
$551$	−1.88489e16	−0.0286946
$552$	5.60822e17	0.843764
$553$	1.32772e16	0.0197421
$554$	1.12656e18	1.65554
$555$	1.80160e17	0.261670
$556$	1.60673e17	0.230652
$557$	−1.03129e18	−1.46327	−0.731633	−	0.681699i	$-0.761242\pi$
$557$	−1.03129e18	−1.46327	−0.731633	+	0.681699i	$0.761242\pi$
$558$	−4.48552e17	−0.629057
$559$	2.75137e17	0.381392
$560$	3.49473e17	0.478841
$561$	1.31726e17	0.178407
$562$	−8.69937e17	−1.16467
$563$	8.59022e17	1.13684	0.568420	−	0.822738i	$-0.307555\pi$
$563$	8.59022e17	1.13684	0.568420	+	0.822738i	$0.307555\pi$
$564$	1.43156e17	0.187282
$565$	2.08711e17	0.269917
$566$	−1.87700e17	−0.239970
$567$	1.24237e17	0.157022
$568$	1.17533e17	0.146858
$569$	5.29538e17	0.654135	0.327068	−	0.945001i	$-0.393939\pi$
$569$	5.29538e17	0.654135	0.327068	+	0.945001i	$0.393939\pi$
$570$	−2.79941e15	−0.00341885
$571$	1.43746e17	0.173565	0.0867825	−	0.996227i	$-0.472341\pi$
$571$	1.43746e17	0.173565	0.0867825	+	0.996227i	$0.472341\pi$
$572$	−1.22505e16	−0.0146245
$573$	−2.70949e17	−0.319803
$574$	1.48693e18	1.73526
$575$	−1.42788e18	−1.64760
$576$	1.72164e17	0.196425
$577$	1.10842e18	1.25044	0.625219	−	0.780450i	$-0.285010\pi$
$577$	1.10842e18	1.25044	0.625219	+	0.780450i	$0.285010\pi$
$578$	−2.61412e18	−2.91605
$579$	2.72984e17	0.301111
$580$	−1.11117e17	−0.121199
$581$	2.43541e17	0.262680
$582$	−3.96989e17	−0.423428
$583$	−2.84843e17	−0.300442
$584$	1.98538e17	0.207091
$585$	−2.93936e16	−0.0303207
$586$	7.28103e17	0.742776
$587$	−1.21677e18	−1.22761	−0.613804	−	0.789458i	$-0.710362\pi$
$587$	−1.21677e18	−1.22761	−0.613804	+	0.789458i	$0.710362\pi$
$588$	1.60283e17	0.159932
$589$	−3.14019e16	−0.0309889
$590$	−4.25525e16	−0.0415324
$591$	7.57977e17	0.731707
$592$	2.01946e18	1.92816
$593$	1.51158e18	1.42750	0.713750	−	0.700401i	$-0.246995\pi$
$593$	1.51158e18	1.42750	0.713750	+	0.700401i	$0.246995\pi$
$594$	3.80378e16	0.0355306
$595$	8.16701e17	0.754576
$596$	−1.14013e17	−0.104197
$597$	1.15327e18	1.04255
$598$	−7.29405e17	−0.652245
$599$	−1.83163e18	−1.62018	−0.810089	−	0.586307i	$-0.800581\pi$
$599$	−1.83163e18	−1.62018	−0.810089	+	0.586307i	$0.800581\pi$
$600$	−4.95750e17	−0.433790
$601$	−1.65935e17	−0.143633	−0.0718164	−	0.997418i	$-0.522880\pi$
$601$	−1.65935e17	−0.143633	−0.0718164	+	0.997418i	$0.522880\pi$
$602$	−2.20751e18	−1.89028
$603$	−3.68833e17	−0.312441
$604$	−3.15654e17	−0.264527
$605$	3.31320e17	0.274687
$606$	−3.57617e17	−0.293323
$607$	−6.74725e17	−0.547520	−0.273760	−	0.961798i	$-0.588267\pi$
$607$	−6.74725e17	−0.547520	−0.273760	+	0.961798i	$0.588267\pi$
$608$	−1.25044e16	−0.0100390
$609$	1.58791e18	1.26129
$610$	−6.33432e17	−0.497802
$611$	4.84015e17	0.376350
$612$	−2.27735e17	−0.175205
$613$	−9.98298e17	−0.759919	−0.379960	−	0.925003i	$-0.624062\pi$
$613$	−9.98298e17	−0.759919	−0.379960	+	0.925003i	$0.624062\pi$
$614$	−3.13906e17	−0.236431
$615$	2.37485e17	0.176990
$616$	−2.55514e17	−0.188425
$617$	−8.96065e17	−0.653862	−0.326931	−	0.945048i	$-0.606014\pi$
$617$	−8.96065e17	−0.653862	−0.326931	+	0.945048i	$0.606014\pi$
$618$	1.04061e18	0.751388
$619$	−1.05232e18	−0.751897	−0.375948	−	0.926641i	$-0.622683\pi$
$619$	−1.05232e18	−0.751897	−0.375948	+	0.926641i	$0.622683\pi$
$620$	−1.85119e17	−0.130889
$621$	4.92391e17	0.344520
$622$	−2.47112e18	−1.71102
$623$	−9.04801e17	−0.619984
$624$	−3.29481e17	−0.223424
$625$	1.14353e18	0.767408
$626$	1.66460e18	1.10554
$627$	2.66292e15	0.00175033
$628$	7.93023e16	0.0515880
$629$	4.71937e18	3.03847
$630$	2.35835e17	0.150277
$631$	2.40986e16	0.0151985	0.00759927	−	0.999971i	$-0.497581\pi$
$631$	2.40986e16	0.0151985	0.00759927	+	0.999971i	$0.497581\pi$
$632$	1.82699e16	0.0114045
$633$	−7.62974e17	−0.471396
$634$	1.26682e18	0.774701
$635$	1.48658e17	0.0899830
$636$	4.92453e17	0.295049
$637$	5.41921e17	0.321388
$638$	4.86174e17	0.285402
$639$	1.03192e17	0.0599640
$640$	5.92159e17	0.340619
$641$	2.96151e17	0.168630	0.0843151	−	0.996439i	$-0.473130\pi$
$641$	2.96151e17	0.168630	0.0843151	+	0.996439i	$0.473130\pi$
$642$	−6.48661e17	−0.365628
$643$	−1.31913e18	−0.736065	−0.368032	−	0.929813i	$-0.619968\pi$
$643$	−1.31913e18	−0.736065	−0.368032	+	0.929813i	$0.619968\pi$
$644$	1.27234e18	0.702822
$645$	−3.52572e17	−0.192801
$646$	−7.33319e16	−0.0396992
$647$	−1.31456e18	−0.704533	−0.352266	−	0.935900i	$-0.614589\pi$
$647$	−1.31456e18	−0.704533	−0.352266	+	0.935900i	$0.614589\pi$
$648$	1.70954e17	0.0907074
$649$	4.04778e16	0.0212631
$650$	6.44773e17	0.335328
$651$	2.64543e18	1.36214
$652$	7.67030e15	0.00391024
$653$	2.65086e18	1.33798	0.668992	−	0.743269i	$-0.266726\pi$
$653$	2.65086e18	1.33798	0.668992	+	0.743269i	$0.266726\pi$
$654$	−1.86912e18	−0.934077
$655$	6.03911e17	0.298817
$656$	2.66204e18	1.30418
$657$	1.74313e17	0.0845580
$658$	−3.88341e18	−1.86529
$659$	2.83726e18	1.34941	0.674706	−	0.738086i	$-0.264270\pi$
$659$	2.83726e18	1.34941	0.674706	+	0.738086i	$0.264270\pi$
$660$	1.56983e16	0.00739295
$661$	−3.49795e18	−1.63119	−0.815594	−	0.578625i	$-0.803589\pi$
$661$	−3.49795e18	−1.63119	−0.815594	+	0.578625i	$0.803589\pi$
$662$	−2.42301e18	−1.11887
$663$	−7.69980e17	−0.352080
$664$	3.35121e17	0.151743
$665$	1.65101e16	0.00740304
$666$	1.36279e18	0.605126
$667$	6.29342e18	2.76738
$668$	2.11142e17	0.0919448
$669$	−5.55644e17	−0.239622
$670$	−7.00145e17	−0.299021
$671$	6.02548e17	0.254856
$672$	1.05342e18	0.441268
$673$	2.56691e18	1.06491	0.532455	−	0.846458i	$-0.321270\pi$
$673$	2.56691e18	1.06491	0.532455	+	0.846458i	$0.321270\pi$
$674$	2.67186e18	1.09780
$675$	−4.35259e17	−0.177122
$676$	−6.17679e17	−0.248948
$677$	2.29224e18	0.915028	0.457514	−	0.889202i	$-0.348740\pi$
$677$	2.29224e18	0.915028	0.457514	+	0.889202i	$0.348740\pi$
$678$	1.57876e18	0.624199
$679$	2.34133e18	0.916873
$680$	1.12381e18	0.435899
$681$	2.16786e18	0.832865
$682$	8.09957e17	0.308222
$683$	−4.35324e18	−1.64088	−0.820442	−	0.571730i	$-0.806273\pi$
$683$	−4.35324e18	−1.64088	−0.820442	+	0.571730i	$0.806273\pi$
$684$	−4.60382e15	−0.00171891
$685$	−6.43445e17	−0.237970
$686$	1.25476e16	0.00459679
$687$	2.37918e17	0.0863391
$688$	−3.95207e18	−1.42069
$689$	1.66500e18	0.592911
$690$	9.34690e17	0.329722
$691$	2.24198e18	0.783475	0.391737	−	0.920077i	$-0.371874\pi$
$691$	2.24198e18	0.783475	0.391737	+	0.920077i	$0.371874\pi$
$692$	−5.81305e17	−0.201240
$693$	−2.24336e17	−0.0769366
$694$	−1.25900e18	−0.427750
$695$	−6.96133e17	−0.234310
$696$	2.18503e18	0.728612
$697$	6.22104e18	2.05518
$698$	−1.41118e18	−0.461873
$699$	1.84579e18	0.598521
$700$	−1.12471e18	−0.361330
$701$	7.33703e17	0.233536	0.116768	−	0.993159i	$-0.462747\pi$
$701$	7.33703e17	0.233536	0.116768	+	0.993159i	$0.462747\pi$
$702$	−2.22343e17	−0.0701185
$703$	9.54051e16	0.0298100
$704$	−3.10880e17	−0.0962433
$705$	−6.20238e17	−0.190252
$706$	4.74654e18	1.44260
$707$	2.10912e18	0.635149
$708$	−6.99803e16	−0.0208814
$709$	−1.88660e18	−0.557802	−0.278901	−	0.960320i	$-0.589970\pi$
$709$	−1.88660e18	−0.557802	−0.278901	+	0.960320i	$0.589970\pi$
$710$	1.95886e17	0.0573885
$711$	1.60407e16	0.00465661
$712$	−1.24504e18	−0.358149
$713$	1.04847e19	2.98865
$714$	6.17780e18	1.74500
$715$	5.30765e16	0.0148564
$716$	1.18674e18	0.329171
$717$	1.07358e18	0.295093
$718$	1.47684e18	0.402277
$719$	−4.39256e18	−1.18571	−0.592857	−	0.805308i	$-0.702000\pi$
$719$	−4.39256e18	−1.18571	−0.592857	+	0.805308i	$0.702000\pi$
$720$	4.22211e17	0.112945
$721$	−6.13725e18	−1.62703
$722$	4.30106e18	1.13001
$723$	2.30678e18	0.600630
$724$	4.35308e17	0.112330
$725$	−5.56320e18	−1.42275
$726$	2.50621e18	0.635229
$727$	−4.05770e18	−1.01931	−0.509655	−	0.860379i	$-0.670227\pi$
$727$	−4.05770e18	−1.01931	−0.509655	+	0.860379i	$0.670227\pi$
$728$	1.49356e18	0.371851
$729$	1.50095e17	0.0370370
$730$	3.30893e17	0.0809261
$731$	−9.23579e18	−2.23878
$732$	−1.04172e18	−0.250282
$733$	−6.78795e17	−0.161645	−0.0808226	−	0.996729i	$-0.525755\pi$
$733$	−6.78795e17	−0.161645	−0.0808226	+	0.996729i	$0.525755\pi$
$734$	−4.56200e18	−1.07679
$735$	−6.94441e17	−0.162468
$736$	4.17506e18	0.968182
$737$	6.66009e17	0.153088
$738$	1.79642e18	0.409299
$739$	3.45469e18	0.780225	0.390113	−	0.920767i	$-0.372436\pi$
$739$	3.45469e18	0.780225	0.390113	+	0.920767i	$0.372436\pi$
$740$	5.62427e17	0.125910
$741$	−1.55656e16	−0.00345421
$742$	−1.33588e19	−2.93862
$743$	−5.30362e18	−1.15650	−0.578249	−	0.815860i	$-0.696264\pi$
$743$	−5.30362e18	−1.15650	−0.578249	+	0.815860i	$0.696264\pi$
$744$	3.64021e18	0.786870
$745$	4.93974e17	0.105849
$746$	−8.15978e18	−1.73331
$747$	2.94230e17	0.0619588
$748$	4.11225e17	0.0858458
$749$	3.82562e18	0.791717
$750$	−1.72398e18	−0.353699
$751$	6.33957e17	0.128944	0.0644719	−	0.997920i	$-0.479464\pi$
$751$	6.33957e17	0.128944	0.0644719	+	0.997920i	$0.479464\pi$
$752$	−6.95241e18	−1.40191
$753$	−3.57216e18	−0.714107
$754$	−2.84184e18	−0.563231
$755$	1.36760e18	0.268722
$756$	3.87845e17	0.0755556
$757$	−3.67271e18	−0.709355	−0.354677	−	0.934989i	$-0.615409\pi$
$757$	−3.67271e18	−0.709355	−0.354677	+	0.934989i	$0.615409\pi$
$758$	−5.46463e18	−1.04643
$759$	−8.89118e17	−0.168806
$760$	2.27186e16	0.00427654
$761$	1.00521e19	1.87611	0.938056	−	0.346485i	$-0.112625\pi$
$761$	1.00521e19	1.87611	0.938056	+	0.346485i	$0.112625\pi$
$762$	1.12450e18	0.208091
$763$	1.10236e19	2.02261
$764$	−8.45855e17	−0.153882
$765$	9.86685e17	0.177983
$766$	−2.46642e18	−0.441144
$767$	−2.36606e17	−0.0419619
$768$	2.54462e18	0.447482
$769$	4.26376e18	0.743485	0.371742	−	0.928336i	$-0.378760\pi$
$769$	4.26376e18	0.743485	0.371742	+	0.928336i	$0.378760\pi$
$770$	−4.25850e17	−0.0736321
$771$	2.03732e18	0.349305
$772$	8.52209e17	0.144888
$773$	6.88616e18	1.16094	0.580471	−	0.814281i	$-0.302869\pi$
$773$	6.88616e18	1.16094	0.580471	+	0.814281i	$0.302869\pi$
$774$	−2.66697e18	−0.445864
$775$	−9.26819e18	−1.53650
$776$	3.22176e18	0.529654
$777$	−8.03734e18	−1.31032
$778$	−6.43168e18	−1.03982
$779$	1.25762e17	0.0201631
$780$	−9.17618e16	−0.0145897
$781$	−1.86336e17	−0.0293808
$782$	2.44847e19	3.82869
$783$	1.91841e18	0.297502
$784$	−7.78417e18	−1.19718
$785$	−3.43585e17	−0.0524061
$786$	4.56819e18	0.691031
$787$	5.53498e18	0.830386	0.415193	−	0.909733i	$-0.363714\pi$
$787$	5.53498e18	0.830386	0.415193	+	0.909733i	$0.363714\pi$
$788$	2.36627e18	0.352083
$789$	4.42397e18	0.652847
$790$	3.04495e16	0.00445660
$791$	−9.31108e18	−1.35161
$792$	−3.08695e17	−0.0444443
$793$	−3.52209e18	−0.502950
$794$	−5.06495e18	−0.717368
$795$	−2.13360e18	−0.299728
$796$	3.60030e18	0.501654
$797$	−4.66478e18	−0.644691	−0.322346	−	0.946622i	$-0.604471\pi$
$797$	−4.66478e18	−0.644691	−0.322346	+	0.946622i	$0.604471\pi$
$798$	1.24888e17	0.0171200
$799$	−1.62474e19	−2.20918
$800$	−3.69063e18	−0.497755
$801$	−1.09312e18	−0.146237
$802$	−7.77574e18	−1.03183
$803$	−3.14760e17	−0.0414313
$804$	−1.15143e18	−0.150340
$805$	−5.51254e18	−0.713968
$806$	−4.73446e18	−0.608265
$807$	−1.15483e18	−0.147177
$808$	2.90223e18	0.366909
$809$	1.15917e19	1.45373	0.726865	−	0.686781i	$-0.240977\pi$
$809$	1.15917e19	1.45373	0.726865	+	0.686781i	$0.240977\pi$
$810$	2.84920e17	0.0354462
$811$	−1.26453e19	−1.56061	−0.780303	−	0.625401i	$-0.784935\pi$
$811$	−1.26453e19	−1.56061	−0.780303	+	0.625401i	$0.784935\pi$
$812$	4.95719e18	0.606905
$813$	−4.41837e18	−0.536628
$814$	−2.46081e18	−0.296496
$815$	−3.32323e16	−0.00397225
$816$	1.10600e19	1.31150
$817$	−1.86708e17	−0.0219644
$818$	−7.55342e18	−0.881550
$819$	1.31132e18	0.151832
$820$	7.41388e17	0.0851639
$821$	5.27633e18	0.601314	0.300657	−	0.953732i	$-0.402794\pi$
$821$	5.27633e18	0.601314	0.300657	+	0.953732i	$0.402794\pi$
$822$	−4.86723e18	−0.550320
$823$	1.62086e19	1.81822	0.909109	−	0.416558i	$-0.136764\pi$
$823$	1.62086e19	1.81822	0.909109	+	0.416558i	$0.136764\pi$
$824$	−8.44508e18	−0.939890
$825$	7.85954e17	0.0867854
$826$	1.89836e18	0.207974
$827$	2.39103e18	0.259895	0.129948	−	0.991521i	$-0.458519\pi$
$827$	2.39103e18	0.259895	0.129948	+	0.991521i	$0.458519\pi$
$828$	1.53716e18	0.165776
$829$	−5.11216e18	−0.547016	−0.273508	−	0.961870i	$-0.588184\pi$
$829$	−5.11216e18	−0.547016	−0.273508	+	0.961870i	$0.588184\pi$
$830$	5.58527e17	0.0592976
$831$	−8.02699e18	−0.845563
$832$	1.81720e18	0.189933
$833$	−1.81912e19	−1.88655
$834$	−5.26578e18	−0.541855
$835$	−9.14792e17	−0.0934029
$836$	8.31318e15	0.000842222 0
$837$	3.19604e18	0.321290
$838$	−5.30661e18	−0.529335
$839$	1.31828e19	1.30484	0.652418	−	0.757859i	$-0.273755\pi$
$839$	1.31828e19	1.30484	0.652418	+	0.757859i	$0.273755\pi$
$840$	−1.91391e18	−0.187978
$841$	1.42592e19	1.38971
$842$	−2.52699e18	−0.244385
$843$	6.19851e18	0.594851
$844$	−2.38187e18	−0.226826
$845$	2.67615e18	0.252896
$846$	−4.69169e18	−0.439969
$847$	−1.47810e19	−1.37550
$848$	−2.39161e19	−2.20860
$849$	1.33741e18	0.122564
$850$	−2.16437e19	−1.96838
$851$	−3.18546e19	−2.87495
$852$	3.22148e17	0.0288535
$853$	−6.75596e18	−0.600507	−0.300253	−	0.953859i	$-0.597071\pi$
$853$	−6.75596e18	−0.600507	−0.300253	+	0.953859i	$0.597071\pi$
$854$	2.82589e19	2.49275
$855$	1.99465e16	0.00174617
$856$	5.26420e18	0.457354
$857$	−1.81595e19	−1.56577	−0.782885	−	0.622167i	$-0.786253\pi$
$857$	−1.81595e19	−1.56577	−0.782885	+	0.622167i	$0.786253\pi$
$858$	4.01489e17	0.0343563
$859$	8.37991e18	0.711678	0.355839	−	0.934547i	$-0.384195\pi$
$859$	8.37991e18	0.711678	0.355839	+	0.934547i	$0.384195\pi$
$860$	−1.10067e18	−0.0927719
$861$	−1.05948e19	−0.886280
$862$	−2.20066e19	−1.82707
$863$	3.86530e18	0.318503	0.159251	−	0.987238i	$-0.449092\pi$
$863$	3.86530e18	0.318503	0.159251	+	0.987238i	$0.449092\pi$
$864$	1.27268e18	0.104083
$865$	2.51856e18	0.204432
$866$	−2.41033e19	−1.94183
$867$	1.86263e19	1.48937
$868$	8.25858e18	0.655431
$869$	−2.89649e16	−0.00228162
$870$	3.64166e18	0.284724
$871$	−3.89304e18	−0.302114
$872$	1.51688e19	1.16841
$873$	2.82864e18	0.216265
$874$	4.94973e17	0.0375628
$875$	1.01675e19	0.765885
$876$	5.44175e17	0.0406876
$877$	6.56613e18	0.487317	0.243659	−	0.969861i	$-0.421652\pi$
$877$	6.56613e18	0.487317	0.243659	+	0.969861i	$0.421652\pi$
$878$	1.23966e19	0.913244
$879$	−5.18791e18	−0.379371
$880$	−7.62393e17	−0.0553403
$881$	−2.31895e19	−1.67089	−0.835446	−	0.549572i	$-0.814791\pi$
$881$	−2.31895e19	−1.67089	−0.835446	+	0.549572i	$0.814791\pi$
$882$	−5.25298e18	−0.375716
$883$	−9.76153e18	−0.693064	−0.346532	−	0.938038i	$-0.612641\pi$
$883$	−9.76153e18	−0.693064	−0.346532	+	0.938038i	$0.612641\pi$
$884$	−2.40374e18	−0.169414
$885$	3.03197e17	0.0212126
$886$	4.86700e18	0.338020
$887$	9.48722e18	0.654087	0.327044	−	0.945009i	$-0.393948\pi$
$887$	9.48722e18	0.654087	0.327044	+	0.945009i	$0.393948\pi$
$888$	−1.10597e19	−0.756935
$889$	−6.63200e18	−0.450591
$890$	−2.07504e18	−0.139956
$891$	−2.71028e17	−0.0181472
$892$	−1.73462e18	−0.115301
$893$	−3.28452e17	−0.0216739
$894$	3.73659e18	0.244783
$895$	−5.14168e18	−0.334391
$896$	−2.64176e19	−1.70565
$897$	5.19718e18	0.333133
$898$	−1.23861e19	−0.788206
$899$	4.08497e19	2.58078
$900$	−1.35880e18	−0.0852277
$901$	−5.58907e19	−3.48040
$902$	−3.24382e18	−0.200546
$903$	1.57291e19	0.965455
$904$	−1.28124e19	−0.780792
$905$	−1.88602e18	−0.114111
$906$	1.03450e19	0.621436
$907$	2.20544e19	1.31537	0.657686	−	0.753293i	$-0.271536\pi$
$907$	2.20544e19	1.31537	0.657686	+	0.753293i	$0.271536\pi$
$908$	6.76768e18	0.400757
$909$	2.54810e18	0.149814
$910$	2.48923e18	0.145310
$911$	−9.61120e18	−0.557068	−0.278534	−	0.960426i	$-0.589848\pi$
$911$	−9.61120e18	−0.557068	−0.278534	+	0.960426i	$0.589848\pi$
$912$	2.23585e17	0.0128670
$913$	−5.31296e17	−0.0303582
$914$	2.51408e19	1.42636
$915$	4.51336e18	0.254251
$916$	7.42737e17	0.0415446
$917$	−2.69419e19	−1.49633
$918$	7.46362e18	0.411597
$919$	−4.68978e18	−0.256804	−0.128402	−	0.991722i	$-0.540985\pi$
$919$	−4.68978e18	−0.256804	−0.128402	+	0.991722i	$0.540985\pi$
$920$	−7.58546e18	−0.412440
$921$	2.23665e18	0.120757
$922$	−3.87557e19	−2.07771
$923$	1.08919e18	0.0579820
$924$	−7.00339e17	−0.0370203
$925$	2.81586e19	1.47805
$926$	2.65233e19	1.38247
$927$	−7.41462e18	−0.383770
$928$	1.62665e19	0.836051
$929$	−1.15841e19	−0.591236	−0.295618	−	0.955306i	$-0.595526\pi$
$929$	−1.15841e19	−0.591236	−0.295618	+	0.955306i	$0.595526\pi$
$930$	6.06694e18	0.307490
$931$	−3.67747e17	−0.0185087
$932$	5.76222e18	0.287996
$933$	1.76073e19	0.873901
$934$	−6.22931e18	−0.307033
$935$	−1.78167e18	−0.0872072
$936$	1.80442e18	0.0877092
$937$	9.56007e18	0.461481	0.230741	−	0.973015i	$-0.425885\pi$
$937$	9.56007e18	0.461481	0.230741	+	0.973015i	$0.425885\pi$
$938$	3.12351e19	1.49735
$939$	−1.18607e19	−0.564654
$940$	−1.93628e18	−0.0915453
$941$	9.33756e18	0.438431	0.219215	−	0.975676i	$-0.429650\pi$
$941$	9.33756e18	0.438431	0.219215	+	0.975676i	$0.429650\pi$
$942$	−2.59899e18	−0.121192
$943$	−4.19906e19	−1.94458
$944$	3.39861e18	0.156309
$945$	−1.68038e18	−0.0767539
$946$	4.81579e18	0.218462
$947$	2.92837e19	1.31932	0.659661	−	0.751563i	$-0.270700\pi$
$947$	2.92837e19	1.31932	0.659661	+	0.751563i	$0.270700\pi$
$948$	5.00761e16	0.00224066
$949$	1.83987e18	0.0817631
$950$	−4.37542e17	−0.0193115
$951$	−9.02639e18	−0.395677
$952$	−5.01358e19	−2.18277
$953$	−2.00892e19	−0.868679	−0.434340	−	0.900749i	$-0.643018\pi$
$953$	−2.00892e19	−0.868679	−0.434340	+	0.900749i	$0.643018\pi$
$954$	−1.61393e19	−0.693138
$955$	3.66475e18	0.156323
$956$	3.35153e18	0.141993
$957$	−3.46411e18	−0.145768
$958$	−3.14978e19	−1.31645
$959$	2.87056e19	1.19164
$960$	−2.32863e18	−0.0960147
$961$	4.36373e19	1.78713
$962$	1.43842e19	0.585125
$963$	4.62186e18	0.186744
$964$	7.20137e18	0.289011
$965$	−3.69228e18	−0.147186
$966$	−4.16987e19	−1.65109
$967$	−7.24814e18	−0.285072	−0.142536	−	0.989790i	$-0.545526\pi$
$967$	−7.24814e18	−0.285072	−0.142536	+	0.989790i	$0.545526\pi$
$968$	−2.03391e19	−0.794590
$969$	5.22508e17	0.0202763
$970$	5.36952e18	0.206976
$971$	3.66311e19	1.40257	0.701285	−	0.712881i	$-0.252610\pi$
$971$	3.66311e19	1.40257	0.701285	+	0.712881i	$0.252610\pi$
$972$	4.68570e17	0.0178215
$973$	3.10561e19	1.17331
$974$	1.88640e19	0.707947
$975$	−4.59416e18	−0.171268
$976$	5.05914e19	1.87350
$977$	3.40906e19	1.25407	0.627033	−	0.778993i	$-0.284269\pi$
$977$	3.40906e19	1.25407	0.627033	+	0.778993i	$0.284269\pi$
$978$	−2.51380e17	−0.00918605
$979$	1.97387e18	0.0716523
$980$	−2.16792e18	−0.0781762
$981$	1.33180e19	0.477077
$982$	−2.58214e19	−0.918873
$983$	1.21319e19	0.428874	0.214437	−	0.976738i	$-0.431208\pi$
$983$	1.21319e19	0.428874	0.214437	+	0.976738i	$0.431208\pi$
$984$	−1.45788e19	−0.511981
$985$	−1.02521e19	−0.357666
$986$	9.53950e19	3.30618
$987$	2.76703e19	0.952690
$988$	−4.85933e16	−0.00166210
$989$	6.23394e19	2.11830
$990$	−5.14484e17	−0.0173677
$991$	5.37442e19	1.80241	0.901204	−	0.433395i	$-0.142685\pi$
$991$	5.37442e19	1.80241	0.901204	+	0.433395i	$0.142685\pi$
$992$	2.70997e19	0.902899
$993$	1.72646e19	0.571460
$994$	−8.73894e18	−0.287374
$995$	−1.55987e19	−0.509609
$996$	9.18535e17	0.0298133
$997$	−3.97542e19	−1.28193	−0.640964	−	0.767571i	$-0.721465\pi$
$997$	−3.97542e19	−1.28193	−0.640964	+	0.767571i	$0.721465\pi$
$998$	3.05830e19	0.979788
$999$	−9.71019e18	−0.309067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.8	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.8	✓	31	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-102.312 q^{2} +729.000 q^{3} +2275.81 q^{4} -9860.18 q^{5} -74585.7 q^{6} +439885. q^{7} +605299. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-102.312 q^{2} +729.000 q^{3} +2275.81 q^{4} -9860.18 q^{5} -74585.7 q^{6} +439885. q^{7} +605299. q^{8} +531441. q^{9} +1.00882e6 q^{10} -959631. q^{11} +1.65907e6 q^{12} +5.60936e6 q^{13} -4.50057e7 q^{14} -7.18807e6 q^{15} -8.05730e7 q^{16} -1.88295e8 q^{17} -5.43730e7 q^{18} -3.80650e6 q^{19} -2.24399e7 q^{20} +3.20677e8 q^{21} +9.81821e7 q^{22} +1.27095e9 q^{23} +4.41263e8 q^{24} -1.12348e9 q^{25} -5.73907e8 q^{26} +3.87420e8 q^{27} +1.00110e9 q^{28} +4.95175e9 q^{29} +7.35428e8 q^{30} +8.24954e9 q^{31} +3.28500e9 q^{32} -6.99571e8 q^{33} +1.92649e10 q^{34} -4.33735e9 q^{35} +1.20946e9 q^{36} -2.50637e10 q^{37} +3.89452e8 q^{38} +4.08922e9 q^{39} -5.96836e9 q^{40} -3.30388e10 q^{41} -3.28092e10 q^{42} +4.90496e10 q^{43} -2.18394e9 q^{44} -5.24010e9 q^{45} -1.30034e11 q^{46} +8.62871e10 q^{47} -5.87377e10 q^{48} +9.66102e10 q^{49} +1.14946e11 q^{50} -1.37267e11 q^{51} +1.27658e10 q^{52} +2.96825e11 q^{53} -3.96379e10 q^{54} +9.46214e9 q^{55} +2.66262e11 q^{56} -2.77494e9 q^{57} -5.06626e11 q^{58} -4.21805e10 q^{59} -1.63587e10 q^{60} -6.27896e11 q^{61} -8.44029e11 q^{62} +2.33773e11 q^{63} +3.23958e11 q^{64} -5.53093e10 q^{65} +7.15748e10 q^{66} -6.94025e11 q^{67} -4.28524e11 q^{68} +9.26520e11 q^{69} +4.43764e11 q^{70} +1.94174e11 q^{71} +3.21681e11 q^{72} +3.28001e11 q^{73} +2.56433e12 q^{74} -8.19017e11 q^{75} -8.66289e9 q^{76} -4.22128e11 q^{77} -4.18378e11 q^{78} +3.01833e10 q^{79} +7.94464e11 q^{80} +2.82430e11 q^{81} +3.38028e12 q^{82} +5.53645e11 q^{83} +7.29799e11 q^{84} +1.85662e12 q^{85} -5.01838e12 q^{86} +3.60983e12 q^{87} -5.80864e11 q^{88} -2.05690e12 q^{89} +5.36127e11 q^{90} +2.46748e12 q^{91} +2.89244e12 q^{92} +6.01391e12 q^{93} -8.82824e12 q^{94} +3.75328e10 q^{95} +2.39477e12 q^{96} +5.32259e12 q^{97} -9.88442e12 q^{98} -5.09988e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * q^99

Introduction

L-functions

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