LMFDB - Embedded newform 177.12.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+10.6976 q^{2} +243.000 q^{3} -1933.56 q^{4} +12608.0 q^{5} +2599.53 q^{6} -75685.5 q^{7} -42593.3 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+10.6976 q^{2} +243.000 q^{3} -1933.56 q^{4} +12608.0 q^{5} +2599.53 q^{6} -75685.5 q^{7} -42593.3 q^{8} +59049.0 q^{9} +134876. q^{10} +77504.2 q^{11} -469855. q^{12} +1.47974e6 q^{13} -809655. q^{14} +3.06375e6 q^{15} +3.50428e6 q^{16} -9.88109e6 q^{17} +631685. q^{18} -5.07206e6 q^{19} -2.43784e7 q^{20} -1.83916e7 q^{21} +829112. q^{22} +4.46983e7 q^{23} -1.03502e7 q^{24} +1.10134e8 q^{25} +1.58297e7 q^{26} +1.43489e7 q^{27} +1.46342e8 q^{28} -8.95326e7 q^{29} +3.27749e7 q^{30} +4.40237e7 q^{31} +1.24719e8 q^{32} +1.88335e7 q^{33} -1.05704e8 q^{34} -9.54244e8 q^{35} -1.14175e8 q^{36} -3.52130e7 q^{37} -5.42590e7 q^{38} +3.59577e8 q^{39} -5.37017e8 q^{40} +5.31218e8 q^{41} -1.96746e8 q^{42} -1.39647e9 q^{43} -1.49859e8 q^{44} +7.44491e8 q^{45} +4.78166e8 q^{46} -2.26305e9 q^{47} +8.51541e8 q^{48} +3.75096e9 q^{49} +1.17817e9 q^{50} -2.40111e9 q^{51} -2.86117e9 q^{52} -5.83333e9 q^{53} +1.53499e8 q^{54} +9.77174e8 q^{55} +3.22369e9 q^{56} -1.23251e9 q^{57} -9.57786e8 q^{58} -7.14924e8 q^{59} -5.92394e9 q^{60} +1.97255e9 q^{61} +4.70950e8 q^{62} -4.46915e9 q^{63} -5.84258e9 q^{64} +1.86566e10 q^{65} +2.01474e8 q^{66} -1.49525e10 q^{67} +1.91057e10 q^{68} +1.08617e10 q^{69} -1.02081e10 q^{70} +1.84247e10 q^{71} -2.51509e9 q^{72} +1.03519e10 q^{73} -3.76695e8 q^{74} +2.67626e10 q^{75} +9.80714e9 q^{76} -5.86594e9 q^{77} +3.84663e9 q^{78} -4.76733e9 q^{79} +4.41821e10 q^{80} +3.48678e9 q^{81} +5.68277e9 q^{82} -6.60401e10 q^{83} +3.55612e10 q^{84} -1.24581e11 q^{85} -1.49389e10 q^{86} -2.17564e10 q^{87} -3.30116e9 q^{88} +6.92452e10 q^{89} +7.96429e9 q^{90} -1.11995e11 q^{91} -8.64268e10 q^{92} +1.06978e10 q^{93} -2.42093e10 q^{94} -6.39486e10 q^{95} +3.03066e10 q^{96} +1.01541e11 q^{97} +4.01264e10 q^{98} +4.57655e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	10.6976	0.236387	0.118193	−	0.992991i	$-0.462290\pi$
$2$	10.6976	0.236387	0.118193	+	0.992991i	$0.462290\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1933.56	−0.944121
$5$	12608.0	1.80431	0.902156	−	0.431409i	$-0.141984\pi$
$5$	12608.0	1.80431	0.902156	+	0.431409i	$0.141984\pi$
$6$	2599.53	0.136478
$7$	−75685.5	−1.70205	−0.851027	−	0.525122i	$-0.824020\pi$
$7$	−75685.5	−1.70205	−0.851027	+	0.525122i	$0.824020\pi$
$8$	−42593.3	−0.459564
$9$	59049.0	0.333333
$10$	134876.	0.426515
$11$	77504.2	0.145099	0.0725497	−	0.997365i	$-0.476886\pi$
$11$	77504.2	0.145099	0.0725497	+	0.997365i	$0.476886\pi$
$12$	−469855.	−0.545089
$13$	1.47974e6	1.10534	0.552672	−	0.833399i	$-0.313608\pi$
$13$	1.47974e6	1.10534	0.552672	+	0.833399i	$0.313608\pi$
$14$	−809655.	−0.402343
$15$	3.06375e6	1.04172
$16$	3.50428e6	0.835487
$17$	−9.88109e6	−1.68786	−0.843929	−	0.536455i	$-0.819763\pi$
$17$	−9.88109e6	−1.68786	−0.843929	+	0.536455i	$0.819763\pi$
$18$	631685.	0.0787955
$19$	−5.07206e6	−0.469937	−0.234968	−	0.972003i	$-0.575499\pi$
$19$	−5.07206e6	−0.469937	−0.234968	+	0.972003i	$0.575499\pi$
$20$	−2.43784e7	−1.70349
$21$	−1.83916e7	−0.982681
$22$	829112.	0.0342995
$23$	4.46983e7	1.44806	0.724032	−	0.689767i	$-0.242287\pi$
$23$	4.46983e7	1.44806	0.724032	+	0.689767i	$0.242287\pi$
$24$	−1.03502e7	−0.265329
$25$	1.10134e8	2.25554
$26$	1.58297e7	0.261288
$27$	1.43489e7	0.192450
$28$	1.46342e8	1.60695
$29$	−8.95326e7	−0.810573	−0.405286	−	0.914190i	$-0.632828\pi$
$29$	−8.95326e7	−0.810573	−0.405286	+	0.914190i	$0.632828\pi$
$30$	3.27749e7	0.246249
$31$	4.40237e7	0.276183	0.138092	−	0.990419i	$-0.455903\pi$
$31$	4.40237e7	0.276183	0.138092	+	0.990419i	$0.455903\pi$
$32$	1.24719e8	0.657062
$33$	1.88335e7	0.0837731
$34$	−1.05704e8	−0.398987
$35$	−9.54244e8	−3.07104
$36$	−1.14175e8	−0.314707
$37$	−3.52130e7	−0.0834821	−0.0417410	−	0.999128i	$-0.513290\pi$
$37$	−3.52130e7	−0.0834821	−0.0417410	+	0.999128i	$0.513290\pi$
$38$	−5.42590e7	−0.111087
$39$	3.59577e8	0.638171
$40$	−5.37017e8	−0.829197
$41$	5.31218e8	0.716079	0.358040	−	0.933706i	$-0.383445\pi$
$41$	5.31218e8	0.716079	0.358040	+	0.933706i	$0.383445\pi$
$42$	−1.96746e8	−0.232293
$43$	−1.39647e9	−1.44862	−0.724311	−	0.689473i	$-0.757842\pi$
$43$	−1.39647e9	−1.44862	−0.724311	+	0.689473i	$0.757842\pi$
$44$	−1.49859e8	−0.136991
$45$	7.44491e8	0.601438
$46$	4.78166e8	0.342303
$47$	−2.26305e9	−1.43932	−0.719659	−	0.694328i	$-0.755702\pi$
$47$	−2.26305e9	−1.43932	−0.719659	+	0.694328i	$0.755702\pi$
$48$	8.51541e8	0.482368
$49$	3.75096e9	1.89699
$50$	1.17817e9	0.533180
$51$	−2.40111e9	−0.974485
$52$	−2.86117e9	−1.04358
$53$	−5.83333e9	−1.91602	−0.958008	−	0.286742i	$-0.907428\pi$
$53$	−5.83333e9	−1.91602	−0.958008	+	0.286742i	$0.907428\pi$
$54$	1.53499e8	0.0454926
$55$	9.77174e8	0.261805
$56$	3.22369e9	0.782203
$57$	−1.23251e9	−0.271318
$58$	−9.57786e8	−0.191608
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−5.92394e9	−0.983510
$61$	1.97255e9	0.299030	0.149515	−	0.988759i	$-0.452229\pi$
$61$	1.97255e9	0.299030	0.149515	+	0.988759i	$0.452229\pi$
$62$	4.70950e8	0.0652860
$63$	−4.46915e9	−0.567351
$64$	−5.84258e9	−0.680166
$65$	1.86566e10	1.99439
$66$	2.01474e8	0.0198028
$67$	−1.49525e10	−1.35302	−0.676509	−	0.736435i	$-0.736508\pi$
$67$	−1.49525e10	−1.35302	−0.676509	+	0.736435i	$0.736508\pi$
$68$	1.91057e10	1.59354
$69$	1.08617e10	0.836040
$70$	−1.02081e10	−0.725952
$71$	1.84247e10	1.21193	0.605966	−	0.795490i	$-0.292787\pi$
$71$	1.84247e10	1.21193	0.605966	+	0.795490i	$0.292787\pi$
$72$	−2.51509e9	−0.153188
$73$	1.03519e10	0.584447	0.292224	−	0.956350i	$-0.405605\pi$
$73$	1.03519e10	0.584447	0.292224	+	0.956350i	$0.405605\pi$
$74$	−3.76695e8	−0.0197340
$75$	2.67626e10	1.30224
$76$	9.80714e9	0.443678
$77$	−5.86594e9	−0.246967
$78$	3.84663e9	0.150855
$79$	−4.76733e9	−0.174312	−0.0871559	−	0.996195i	$-0.527778\pi$
$79$	−4.76733e9	−0.174312	−0.0871559	+	0.996195i	$0.527778\pi$
$80$	4.41821e10	1.50748
$81$	3.48678e9	0.111111
$82$	5.68277e9	0.169272
$83$	−6.60401e10	−1.84025	−0.920127	−	0.391619i	$-0.871915\pi$
$83$	−6.60401e10	−1.84025	−0.920127	+	0.391619i	$0.871915\pi$
$84$	3.55612e10	0.927770
$85$	−1.24581e11	−3.04542
$86$	−1.49389e10	−0.342435
$87$	−2.17564e10	−0.467984
$88$	−3.30116e9	−0.0666825
$89$	6.92452e10	1.31445	0.657226	−	0.753694i	$-0.271730\pi$
$89$	6.92452e10	1.31445	0.657226	+	0.753694i	$0.271730\pi$
$90$	7.96429e9	0.142172
$91$	−1.11995e11	−1.88136
$92$	−8.64268e10	−1.36715
$93$	1.06978e10	0.159455
$94$	−2.42093e10	−0.340235
$95$	−6.39486e10	−0.847913
$96$	3.03066e10	0.379355
$97$	1.01541e11	1.20059	0.600295	−	0.799778i	$-0.295050\pi$
$97$	1.01541e11	1.20059	0.600295	+	0.799778i	$0.295050\pi$
$98$	4.01264e10	0.448422
$99$	4.57655e9	0.0483664
$100$	−2.12951e11	−2.12951
$101$	1.23150e11	1.16592	0.582958	−	0.812502i	$-0.301895\pi$
$101$	1.23150e11	1.16592	0.582958	+	0.812502i	$0.301895\pi$
$102$	−2.56861e10	−0.230355
$103$	−1.08902e11	−0.925618	−0.462809	−	0.886458i	$-0.653158\pi$
$103$	−1.08902e11	−0.925618	−0.462809	+	0.886458i	$0.653158\pi$
$104$	−6.30271e10	−0.507977
$105$	−2.31881e11	−1.77306
$106$	−6.24028e10	−0.452920
$107$	−7.98634e10	−0.550474	−0.275237	−	0.961376i	$-0.588756\pi$
$107$	−7.98634e10	−0.550474	−0.275237	+	0.961376i	$0.588756\pi$
$108$	−2.77445e10	−0.181696
$109$	−2.02795e11	−1.26244	−0.631222	−	0.775602i	$-0.717446\pi$
$109$	−2.02795e11	−1.26244	−0.631222	+	0.775602i	$0.717446\pi$
$110$	1.04535e10	0.0618871
$111$	−8.55675e9	−0.0481984
$112$	−2.65223e11	−1.42204
$113$	−1.71570e11	−0.876012	−0.438006	−	0.898972i	$-0.644315\pi$
$113$	−1.71570e11	−0.876012	−0.438006	+	0.898972i	$0.644315\pi$
$114$	−1.31849e10	−0.0641360
$115$	5.63556e11	2.61276
$116$	1.73117e11	0.765279
$117$	8.73773e10	0.368448
$118$	−7.64800e9	−0.0307749
$119$	7.47855e11	2.87283
$120$	−1.30495e11	−0.478737
$121$	−2.79305e11	−0.978946
$122$	2.11017e10	0.0706866
$123$	1.29086e11	0.413429
$124$	−8.51226e10	−0.260751
$125$	7.72945e11	2.26539
$126$	−4.78093e10	−0.134114
$127$	−2.24500e11	−0.602971	−0.301485	−	0.953471i	$-0.597482\pi$
$127$	−2.24500e11	−0.602971	−0.301485	+	0.953471i	$0.597482\pi$
$128$	−3.17925e11	−0.817844
$129$	−3.39342e11	−0.836363
$130$	1.99582e11	0.471446
$131$	1.94886e11	0.441354	0.220677	−	0.975347i	$-0.429173\pi$
$131$	1.94886e11	0.441354	0.220677	+	0.975347i	$0.429173\pi$
$132$	−3.64158e10	−0.0790920
$133$	3.83881e11	0.799858
$134$	−1.59957e11	−0.319835
$135$	1.80911e11	0.347240
$136$	4.20868e11	0.775679
$137$	−2.31749e11	−0.410256	−0.205128	−	0.978735i	$-0.565761\pi$
$137$	−2.31749e11	−0.410256	−0.205128	+	0.978735i	$0.565761\pi$
$138$	1.16194e11	0.197629
$139$	−7.66906e11	−1.25361	−0.626803	−	0.779178i	$-0.715637\pi$
$139$	−7.66906e11	−1.25361	−0.626803	+	0.779178i	$0.715637\pi$
$140$	1.84509e12	2.89943
$141$	−5.49922e11	−0.830990
$142$	1.97100e11	0.286485
$143$	1.14686e11	0.160385
$144$	2.06925e11	0.278496
$145$	−1.12883e12	−1.46253
$146$	1.10741e11	0.138155
$147$	9.11484e11	1.09523
$148$	6.80864e10	0.0788172
$149$	−4.09977e11	−0.457335	−0.228668	−	0.973505i	$-0.573437\pi$
$149$	−4.09977e11	−0.457335	−0.228668	+	0.973505i	$0.573437\pi$
$150$	2.86296e11	0.307832
$151$	−1.09706e12	−1.13726	−0.568628	−	0.822595i	$-0.692525\pi$
$151$	−1.09706e12	−1.13726	−0.568628	+	0.822595i	$0.692525\pi$
$152$	2.16036e11	0.215966
$153$	−5.83469e11	−0.562619
$154$	−6.27517e10	−0.0583797
$155$	5.55052e11	0.498321
$156$	−6.95264e11	−0.602511
$157$	−4.85099e11	−0.405865	−0.202933	−	0.979193i	$-0.565047\pi$
$157$	−4.85099e11	−0.405865	−0.202933	+	0.979193i	$0.565047\pi$
$158$	−5.09992e10	−0.0412049
$159$	−1.41750e12	−1.10621
$160$	1.57245e12	1.18555
$161$	−3.38301e12	−2.46468
$162$	3.73003e10	0.0262652
$163$	2.00016e12	1.36155	0.680774	−	0.732494i	$-0.261644\pi$
$163$	2.00016e12	1.36155	0.680774	+	0.732494i	$0.261644\pi$
$164$	−1.02714e12	−0.676066
$165$	2.37453e11	0.151153
$166$	−7.06472e11	−0.435011
$167$	−2.88974e12	−1.72154	−0.860772	−	0.508991i	$-0.830018\pi$
$167$	−2.88974e12	−1.72154	−0.860772	+	0.508991i	$0.830018\pi$
$168$	7.83357e11	0.451605
$169$	3.97475e11	0.221786
$170$	−1.33272e12	−0.719897
$171$	−2.99500e11	−0.156646
$172$	2.70016e12	1.36768
$173$	−1.64101e12	−0.805114	−0.402557	−	0.915395i	$-0.631878\pi$
$173$	−1.64101e12	−0.805114	−0.402557	+	0.915395i	$0.631878\pi$
$174$	−2.32742e11	−0.110625
$175$	−8.33554e12	−3.83906
$176$	2.71597e11	0.121229
$177$	−1.73727e11	−0.0751646
$178$	7.40760e11	0.310719
$179$	1.52449e12	0.620058	0.310029	−	0.950727i	$-0.399661\pi$
$179$	1.52449e12	0.620058	0.310029	+	0.950727i	$0.399661\pi$
$180$	−1.43952e12	−0.567830
$181$	−3.25654e12	−1.24602	−0.623010	−	0.782214i	$-0.714090\pi$
$181$	−3.25654e12	−1.24602	−0.623010	+	0.782214i	$0.714090\pi$
$182$	−1.19808e12	−0.444727
$183$	4.79330e11	0.172645
$184$	−1.90385e12	−0.665478
$185$	−4.43966e11	−0.150628
$186$	1.14441e11	0.0376929
$187$	−7.65826e11	−0.244907
$188$	4.37575e12	1.35889
$189$	−1.08600e12	−0.327560
$190$	−6.84099e11	−0.200435
$191$	−4.50654e12	−1.28280	−0.641402	−	0.767205i	$-0.721647\pi$
$191$	−4.50654e12	−1.28280	−0.641402	+	0.767205i	$0.721647\pi$
$192$	−1.41975e12	−0.392694
$193$	−4.73174e12	−1.27191	−0.635954	−	0.771727i	$-0.719393\pi$
$193$	−4.73174e12	−1.27191	−0.635954	+	0.771727i	$0.719393\pi$
$194$	1.08624e12	0.283804
$195$	4.53356e12	1.15146
$196$	−7.25272e12	−1.79099
$197$	−6.75309e12	−1.62158	−0.810790	−	0.585338i	$-0.800962\pi$
$197$	−6.75309e12	−1.62158	−0.810790	+	0.585338i	$0.800962\pi$
$198$	4.89582e10	0.0114332
$199$	2.26182e12	0.513767	0.256884	−	0.966442i	$-0.417304\pi$
$199$	2.26182e12	0.513767	0.256884	+	0.966442i	$0.417304\pi$
$200$	−4.69097e12	−1.03657
$201$	−3.63347e12	−0.781165
$202$	1.31742e12	0.275607
$203$	6.77631e12	1.37964
$204$	4.64268e12	0.920032
$205$	6.69760e12	1.29203
$206$	−1.16500e12	−0.218804
$207$	2.63939e12	0.482688
$208$	5.18544e12	0.923500
$209$	−3.93106e11	−0.0681875
$210$	−2.48058e12	−0.419129
$211$	2.16403e12	0.356213	0.178106	−	0.984011i	$-0.443003\pi$
$211$	2.16403e12	0.356213	0.178106	+	0.984011i	$0.443003\pi$
$212$	1.12791e13	1.80895
$213$	4.47719e12	0.699710
$214$	−8.54349e11	−0.130125
$215$	−1.76067e13	−2.61377
$216$	−6.11167e11	−0.0884432
$217$	−3.33196e12	−0.470079
$218$	−2.16943e12	−0.298425
$219$	2.51552e12	0.337431
$220$	−1.88943e12	−0.247175
$221$	−1.46215e13	−1.86566
$222$	−9.15370e10	−0.0113935
$223$	1.44094e12	0.174972	0.0874861	−	0.996166i	$-0.472117\pi$
$223$	1.44094e12	0.174972	0.0874861	+	0.996166i	$0.472117\pi$
$224$	−9.43939e12	−1.11835
$225$	6.50330e12	0.751848
$226$	−1.83539e12	−0.207077
$227$	−8.12350e12	−0.894542	−0.447271	−	0.894398i	$-0.647604\pi$
$227$	−8.12350e12	−0.894542	−0.447271	+	0.894398i	$0.647604\pi$
$228$	2.38313e12	0.256157
$229$	1.36595e13	1.43331	0.716653	−	0.697430i	$-0.245673\pi$
$229$	1.36595e13	1.43331	0.716653	+	0.697430i	$0.245673\pi$
$230$	6.02872e12	0.617621
$231$	−1.42542e12	−0.142586
$232$	3.81348e12	0.372510
$233$	6.34784e12	0.605576	0.302788	−	0.953058i	$-0.402083\pi$
$233$	6.34784e12	0.605576	0.302788	+	0.953058i	$0.402083\pi$
$234$	9.34730e11	0.0870962
$235$	−2.85326e13	−2.59698
$236$	1.38235e12	0.122914
$237$	−1.15846e12	−0.100639
$238$	8.00028e12	0.679097
$239$	9.27269e12	0.769161	0.384580	−	0.923091i	$-0.374346\pi$
$239$	9.27269e12	0.769161	0.384580	+	0.923091i	$0.374346\pi$
$240$	1.07362e13	0.870343
$241$	1.00141e13	0.793446	0.396723	−	0.917938i	$-0.370147\pi$
$241$	1.00141e13	0.793446	0.396723	+	0.917938i	$0.370147\pi$
$242$	−2.98790e12	−0.231410
$243$	8.47289e11	0.0641500
$244$	−3.81405e12	−0.282321
$245$	4.72922e13	3.42276
$246$	1.38091e12	0.0977290
$247$	−7.50534e12	−0.519442
$248$	−1.87512e12	−0.126924
$249$	−1.60477e13	−1.06247
$250$	8.26868e12	0.535508
$251$	−4.68629e12	−0.296909	−0.148455	−	0.988919i	$-0.547430\pi$
$251$	−4.68629e12	−0.296909	−0.148455	+	0.988919i	$0.547430\pi$
$252$	8.64138e12	0.535648
$253$	3.46430e12	0.210113
$254$	−2.40162e12	−0.142534
$255$	−3.02732e13	−1.75828
$256$	8.56456e12	0.486839
$257$	−1.62432e13	−0.903730	−0.451865	−	0.892086i	$-0.649241\pi$
$257$	−1.62432e13	−0.903730	−0.451865	+	0.892086i	$0.649241\pi$
$258$	−3.63016e12	−0.197705
$259$	2.66511e12	0.142091
$260$	−3.60737e13	−1.88294
$261$	−5.28681e12	−0.270191
$262$	2.08481e12	0.104330
$263$	1.75074e13	0.857955	0.428978	−	0.903315i	$-0.358874\pi$
$263$	1.75074e13	0.857955	0.428978	+	0.903315i	$0.358874\pi$
$264$	−8.02181e11	−0.0384991
$265$	−7.35467e13	−3.45709
$266$	4.10662e12	0.189076
$267$	1.68266e13	0.758899
$268$	2.89116e13	1.27741
$269$	2.83159e13	1.22573	0.612863	−	0.790189i	$-0.290018\pi$
$269$	2.83159e13	1.22573	0.612863	+	0.790189i	$0.290018\pi$
$270$	1.93532e12	0.0820829
$271$	3.16183e13	1.31404	0.657019	−	0.753874i	$-0.271817\pi$
$271$	3.16183e13	1.31404	0.657019	+	0.753874i	$0.271817\pi$
$272$	−3.46262e13	−1.41018
$273$	−2.72148e13	−1.08620
$274$	−2.47917e12	−0.0969790
$275$	8.53584e12	0.327278
$276$	−2.10017e13	−0.789323
$277$	−4.49678e13	−1.65677	−0.828387	−	0.560156i	$-0.810741\pi$
$277$	−4.49678e13	−1.65677	−0.828387	+	0.560156i	$0.810741\pi$
$278$	−8.20408e12	−0.296336
$279$	2.59956e12	0.0920611
$280$	4.06444e13	1.41134
$281$	−2.03149e11	−0.00691718	−0.00345859	−	0.999994i	$-0.501101\pi$
$281$	−2.03149e11	−0.00691718	−0.00345859	+	0.999994i	$0.501101\pi$
$282$	−5.88286e12	−0.196435
$283$	−3.83681e13	−1.25645	−0.628225	−	0.778031i	$-0.716218\pi$
$283$	−3.83681e13	−1.25645	−0.628225	+	0.778031i	$0.716218\pi$
$284$	−3.56252e13	−1.14421
$285$	−1.55395e13	−0.489543
$286$	1.22687e12	0.0379128
$287$	−4.02055e13	−1.21881
$288$	7.36451e12	0.219021
$289$	6.33641e13	1.84886
$290$	−1.20758e13	−0.345722
$291$	2.46744e13	0.693162
$292$	−2.00161e13	−0.551789
$293$	4.18480e12	0.113215	0.0566073	−	0.998397i	$-0.481972\pi$
$293$	4.18480e12	0.113215	0.0566073	+	0.998397i	$0.481972\pi$
$294$	9.75072e12	0.258897
$295$	−9.01378e12	−0.234901
$296$	1.49984e12	0.0383654
$297$	1.11210e12	0.0279244
$298$	−4.38578e12	−0.108108
$299$	6.61419e13	1.60061
$300$	−5.17470e13	−1.22947
$301$	1.05693e14	2.46563
$302$	−1.17360e13	−0.268832
$303$	2.99255e13	0.673142
$304$	−1.77739e13	−0.392626
$305$	2.48700e13	0.539543
$306$	−6.24173e12	−0.132996
$307$	−3.13464e13	−0.656033	−0.328017	−	0.944672i	$-0.606380\pi$
$307$	−3.13464e13	−0.656033	−0.328017	+	0.944672i	$0.606380\pi$
$308$	1.13422e13	0.233167
$309$	−2.64632e13	−0.534406
$310$	5.93774e12	0.117796
$311$	−2.08261e13	−0.405907	−0.202954	−	0.979188i	$-0.565054\pi$
$311$	−2.08261e13	−0.405907	−0.202954	+	0.979188i	$0.565054\pi$
$312$	−1.53156e13	−0.293280
$313$	2.40315e13	0.452154	0.226077	−	0.974109i	$-0.427410\pi$
$313$	2.40315e13	0.452154	0.226077	+	0.974109i	$0.427410\pi$
$314$	−5.18941e12	−0.0959411
$315$	−5.63471e13	−1.02368
$316$	9.21793e12	0.164571
$317$	4.91354e13	0.862122	0.431061	−	0.902323i	$-0.358139\pi$
$317$	4.91354e13	0.862122	0.431061	+	0.902323i	$0.358139\pi$
$318$	−1.51639e13	−0.261494
$319$	−6.93915e12	−0.117614
$320$	−7.36634e13	−1.22723
$321$	−1.94068e13	−0.317816
$322$	−3.61902e13	−0.582618
$323$	5.01175e13	0.793187
$324$	−6.74191e12	−0.104902
$325$	1.62970e14	2.49315
$326$	2.13970e13	0.321852
$327$	−4.92793e13	−0.728872
$328$	−2.26263e13	−0.329084
$329$	1.71280e14	2.44980
$330$	2.54019e12	0.0357305
$331$	−9.52583e13	−1.31780	−0.658899	−	0.752231i	$-0.728978\pi$
$331$	−9.52583e13	−1.31780	−0.658899	+	0.752231i	$0.728978\pi$
$332$	1.27692e14	1.73742
$333$	−2.07929e12	−0.0278274
$334$	−3.09134e13	−0.406950
$335$	−1.88522e14	−2.44127
$336$	−6.44493e13	−0.821017
$337$	−8.43699e13	−1.05736	−0.528680	−	0.848821i	$-0.677313\pi$
$337$	−8.43699e13	−1.05736	−0.528680	+	0.848821i	$0.677313\pi$
$338$	4.25205e12	0.0524271
$339$	−4.16915e13	−0.505766
$340$	2.40885e14	2.87525
$341$	3.41202e12	0.0400740
$342$	−3.20394e12	−0.0370289
$343$	−1.34239e14	−1.52672
$344$	5.94803e13	0.665735
$345$	1.36944e14	1.50848
$346$	−1.75549e13	−0.190318
$347$	4.12347e12	0.0439998	0.0219999	−	0.999758i	$-0.492997\pi$
$347$	4.12347e12	0.0439998	0.0219999	+	0.999758i	$0.492997\pi$
$348$	4.20673e13	0.441834
$349$	1.74296e14	1.80197	0.900987	−	0.433847i	$-0.142844\pi$
$349$	1.74296e14	1.80197	0.900987	+	0.433847i	$0.142844\pi$
$350$	−8.91706e13	−0.907501
$351$	2.12327e13	0.212724
$352$	9.66621e12	0.0953393
$353$	1.48365e14	1.44069	0.720345	−	0.693616i	$-0.243983\pi$
$353$	1.48365e14	1.44069	0.720345	+	0.693616i	$0.243983\pi$
$354$	−1.85846e12	−0.0177679
$355$	2.32298e14	2.18671
$356$	−1.33890e14	−1.24100
$357$	1.81729e14	1.65863
$358$	1.63084e13	0.146573
$359$	2.14138e14	1.89528	0.947640	−	0.319341i	$-0.103462\pi$
$359$	2.14138e14	1.89528	0.947640	+	0.319341i	$0.103462\pi$
$360$	−3.17103e13	−0.276399
$361$	−9.07645e13	−0.779159
$362$	−3.48373e13	−0.294542
$363$	−6.78711e13	−0.565195
$364$	2.16549e14	1.77623
$365$	1.30517e14	1.05453
$366$	5.12770e12	0.0408110
$367$	7.54506e13	0.591560	0.295780	−	0.955256i	$-0.404420\pi$
$367$	7.54506e13	0.591560	0.295780	+	0.955256i	$0.404420\pi$
$368$	1.56635e14	1.20984
$369$	3.13679e13	0.238693
$370$	−4.74938e12	−0.0356064
$371$	4.41498e14	3.26116
$372$	−2.06848e13	−0.150544
$373$	4.45810e13	0.319706	0.159853	−	0.987141i	$-0.448898\pi$
$373$	4.45810e13	0.319706	0.159853	+	0.987141i	$0.448898\pi$
$374$	−8.19253e12	−0.0578927
$375$	1.87826e14	1.30793
$376$	9.63909e13	0.661459
$377$	−1.32485e14	−0.895962
$378$	−1.16177e13	−0.0774309
$379$	−2.12277e14	−1.39440	−0.697200	−	0.716877i	$-0.745571\pi$
$379$	−2.12277e14	−1.39440	−0.697200	+	0.716877i	$0.745571\pi$
$380$	1.23649e14	0.800533
$381$	−5.45536e13	−0.348125
$382$	−4.82094e13	−0.303237
$383$	−2.00563e14	−1.24354	−0.621768	−	0.783202i	$-0.713585\pi$
$383$	−2.00563e14	−1.24354	−0.621768	+	0.783202i	$0.713585\pi$
$384$	−7.72559e13	−0.472182
$385$	−7.39579e13	−0.445605
$386$	−5.06184e13	−0.300662
$387$	−8.24602e13	−0.482874
$388$	−1.96335e14	−1.13350
$389$	−1.28882e14	−0.733615	−0.366808	−	0.930297i	$-0.619549\pi$
$389$	−1.28882e14	−0.733615	−0.366808	+	0.930297i	$0.619549\pi$
$390$	4.84983e13	0.272190
$391$	−4.41668e14	−2.44413
$392$	−1.59766e14	−0.871787
$393$	4.73572e13	0.254816
$394$	−7.22421e13	−0.383320
$395$	−6.01066e13	−0.314513
$396$	−8.84903e12	−0.0456638
$397$	2.77310e14	1.41129	0.705647	−	0.708563i	$-0.250656\pi$
$397$	2.77310e14	1.41129	0.705647	+	0.708563i	$0.250656\pi$
$398$	2.41961e13	0.121448
$399$	9.32832e13	0.461798
$400$	3.85941e14	1.88448
$401$	−3.34964e13	−0.161326	−0.0806631	−	0.996741i	$-0.525704\pi$
$401$	−3.34964e13	−0.161326	−0.0806631	+	0.996741i	$0.525704\pi$
$402$	−3.88695e13	−0.184657
$403$	6.51438e13	0.305278
$404$	−2.38118e14	−1.10077
$405$	4.39614e13	0.200479
$406$	7.24905e13	0.326128
$407$	−2.72915e12	−0.0121132
$408$	1.02271e14	0.447839
$409$	−8.55004e13	−0.369394	−0.184697	−	0.982795i	$-0.559130\pi$
$409$	−8.55004e13	−0.369394	−0.184697	+	0.982795i	$0.559130\pi$
$410$	7.16485e13	0.305419
$411$	−5.63150e13	−0.236861
$412$	2.10569e14	0.873896
$413$	5.41094e13	0.221589
$414$	2.82352e13	0.114101
$415$	−8.32634e14	−3.32039
$416$	1.84551e14	0.726280
$417$	−1.86358e14	−0.723770
$418$	−4.20530e12	−0.0161186
$419$	3.83763e14	1.45173	0.725865	−	0.687837i	$-0.241439\pi$
$419$	3.83763e14	1.45173	0.725865	+	0.687837i	$0.241439\pi$
$420$	4.48356e14	1.67399
$421$	6.87047e13	0.253183	0.126592	−	0.991955i	$-0.459596\pi$
$421$	6.87047e13	0.253183	0.126592	+	0.991955i	$0.459596\pi$
$422$	2.31500e13	0.0842039
$423$	−1.33631e14	−0.479772
$424$	2.48460e14	0.880532
$425$	−1.08824e15	−3.80704
$426$	4.78954e13	0.165402
$427$	−1.49294e14	−0.508965
$428$	1.54421e14	0.519714
$429$	2.78687e13	0.0925982
$430$	−1.88350e14	−0.617860
$431$	3.82711e14	1.23950	0.619749	−	0.784800i	$-0.287234\pi$
$431$	3.82711e14	1.23950	0.619749	+	0.784800i	$0.287234\pi$
$432$	5.02827e13	0.160789
$433$	−2.01869e14	−0.637364	−0.318682	−	0.947862i	$-0.603240\pi$
$433$	−2.01869e14	−0.637364	−0.318682	+	0.947862i	$0.603240\pi$
$434$	−3.56441e13	−0.111120
$435$	−2.74305e14	−0.844390
$436$	3.92117e14	1.19190
$437$	−2.26712e14	−0.680498
$438$	2.69101e13	0.0797641
$439$	−6.71377e13	−0.196522	−0.0982611	−	0.995161i	$-0.531328\pi$
$439$	−6.71377e13	−0.196522	−0.0982611	+	0.995161i	$0.531328\pi$
$440$	−4.16211e13	−0.120316
$441$	2.21491e14	0.632329
$442$	−1.56415e14	−0.441018
$443$	−1.02274e14	−0.284803	−0.142401	−	0.989809i	$-0.545482\pi$
$443$	−1.02274e14	−0.284803	−0.142401	+	0.989809i	$0.545482\pi$
$444$	1.65450e13	0.0455051
$445$	8.73044e14	2.37168
$446$	1.54146e13	0.0413611
$447$	−9.96243e13	−0.264043
$448$	4.42199e14	1.15768
$449$	3.03892e13	0.0785894	0.0392947	−	0.999228i	$-0.487489\pi$
$449$	3.03892e13	0.0785894	0.0392947	+	0.999228i	$0.487489\pi$
$450$	6.95699e13	0.177727
$451$	4.11716e13	0.103903
$452$	3.31741e14	0.827061
$453$	−2.66586e14	−0.656595
$454$	−8.69022e13	−0.211458
$455$	−1.41203e15	−3.39455
$456$	5.24967e13	0.124688
$457$	3.10511e14	0.728681	0.364340	−	0.931266i	$-0.381295\pi$
$457$	3.10511e14	0.728681	0.364340	+	0.931266i	$0.381295\pi$
$458$	1.46124e14	0.338814
$459$	−1.41783e14	−0.324828
$460$	−1.08967e15	−2.46676
$461$	−1.47681e14	−0.330347	−0.165173	−	0.986265i	$-0.552818\pi$
$461$	−1.47681e14	−0.330347	−0.165173	+	0.986265i	$0.552818\pi$
$462$	−1.52487e13	−0.0337055
$463$	5.29520e14	1.15661	0.578305	−	0.815821i	$-0.303715\pi$
$463$	5.29520e14	1.15661	0.578305	+	0.815821i	$0.303715\pi$
$464$	−3.13748e14	−0.677223
$465$	1.34878e14	0.287706
$466$	6.79069e13	0.143150
$467$	2.82042e14	0.587585	0.293792	−	0.955869i	$-0.405083\pi$
$467$	2.82042e14	0.587585	0.293792	+	0.955869i	$0.405083\pi$
$468$	−1.68949e14	−0.347860
$469$	1.13169e15	2.30291
$470$	−3.05231e14	−0.613891
$471$	−1.17879e14	−0.234326
$472$	3.04510e13	0.0598302
$473$	−1.08232e14	−0.210194
$474$	−1.23928e13	−0.0237897
$475$	−5.58606e14	−1.05996
$476$	−1.44602e15	−2.71230
$477$	−3.44452e14	−0.638672
$478$	9.91958e13	0.181819
$479$	7.44418e14	1.34888	0.674438	−	0.738332i	$-0.264386\pi$
$479$	7.44418e14	1.34888	0.674438	+	0.738332i	$0.264386\pi$
$480$	3.82106e14	0.684475
$481$	−5.21061e13	−0.0922764
$482$	1.07127e14	0.187560
$483$	−8.22071e14	−1.42298
$484$	5.40053e14	0.924244
$485$	1.28023e15	2.16624
$486$	9.06398e12	0.0151642
$487$	2.90278e14	0.480181	0.240090	−	0.970751i	$-0.422823\pi$
$487$	2.90278e14	0.480181	0.240090	+	0.970751i	$0.422823\pi$
$488$	−8.40175e13	−0.137423
$489$	4.86039e14	0.786090
$490$	5.05915e14	0.809094
$491$	4.36016e13	0.0689532	0.0344766	−	0.999406i	$-0.489024\pi$
$491$	4.36016e13	0.0689532	0.0344766	+	0.999406i	$0.489024\pi$
$492$	−2.49595e14	−0.390327
$493$	8.84680e14	1.36813
$494$	−8.02894e13	−0.122789
$495$	5.77012e13	0.0872682
$496$	1.54272e14	0.230748
$497$	−1.39448e15	−2.06277
$498$	−1.71673e14	−0.251154
$499$	−3.22220e14	−0.466229	−0.233115	−	0.972449i	$-0.574892\pi$
$499$	−3.22220e14	−0.466229	−0.233115	+	0.972449i	$0.574892\pi$
$500$	−1.49454e15	−2.13881
$501$	−7.02206e14	−0.993933
$502$	−5.01322e13	−0.0701853
$503$	9.03185e14	1.25070	0.625350	−	0.780345i	$-0.284956\pi$
$503$	9.03185e14	1.25070	0.625350	+	0.780345i	$0.284956\pi$
$504$	1.90356e14	0.260734
$505$	1.55268e15	2.10368
$506$	3.70598e13	0.0496679
$507$	9.65865e13	0.128048
$508$	4.34085e14	0.569278
$509$	−4.38071e14	−0.568325	−0.284162	−	0.958776i	$-0.591715\pi$
$509$	−4.38071e14	−0.568325	−0.284162	+	0.958776i	$0.591715\pi$
$510$	−3.23851e14	−0.415633
$511$	−7.83490e14	−0.994760
$512$	7.42732e14	0.932926
$513$	−7.27785e13	−0.0904394
$514$	−1.73764e14	−0.213630
$515$	−1.37304e15	−1.67010
$516$	6.56139e14	0.789628
$517$	−1.75396e14	−0.208844
$518$	2.85104e13	0.0335884
$519$	−3.98765e14	−0.464833
$520$	−7.94646e14	−0.916548
$521$	−1.19830e14	−0.136759	−0.0683797	−	0.997659i	$-0.521783\pi$
$521$	−1.19830e14	−0.136759	−0.0683797	+	0.997659i	$0.521783\pi$
$522$	−5.65563e13	−0.0638695
$523$	1.22735e15	1.37154	0.685771	−	0.727818i	$-0.259465\pi$
$523$	1.22735e15	1.37154	0.685771	+	0.727818i	$0.259465\pi$
$524$	−3.76823e14	−0.416692
$525$	−2.02554e15	−2.21648
$526$	1.87288e14	0.202809
$527$	−4.35003e14	−0.466158
$528$	6.59980e13	0.0699913
$529$	1.04512e15	1.09689
$530$	−7.86775e14	−0.817210
$531$	−4.22156e13	−0.0433963
$532$	−7.42258e14	−0.755163
$533$	7.86065e14	0.791514
$534$	1.80005e14	0.179393
$535$	−1.00692e15	−0.993227
$536$	6.36877e14	0.621798
$537$	3.70450e14	0.357990
$538$	3.02914e14	0.289745
$539$	2.90715e14	0.275252
$540$	−3.49803e14	−0.327837
$541$	9.04575e14	0.839188	0.419594	−	0.907712i	$-0.362172\pi$
$541$	9.04575e14	0.839188	0.419594	+	0.907712i	$0.362172\pi$
$542$	3.38241e14	0.310621
$543$	−7.91340e14	−0.719390
$544$	−1.23236e15	−1.10903
$545$	−2.55685e15	−2.27784
$546$	−2.91134e14	−0.256763
$547$	−1.57116e15	−1.37180	−0.685900	−	0.727696i	$-0.740591\pi$
$547$	−1.57116e15	−1.37180	−0.685900	+	0.727696i	$0.740591\pi$
$548$	4.48101e14	0.387331
$549$	1.16477e14	0.0996766
$550$	9.13133e13	0.0773641
$551$	4.54115e14	0.380918
$552$	−4.62634e14	−0.384214
$553$	3.60818e14	0.296688
$554$	−4.81050e14	−0.391639
$555$	−1.07884e14	−0.0869650
$556$	1.48286e15	1.18356
$557$	−1.14870e15	−0.907830	−0.453915	−	0.891045i	$-0.649973\pi$
$557$	−1.14870e15	−0.907830	−0.453915	+	0.891045i	$0.649973\pi$
$558$	2.78091e13	0.0217620
$559$	−2.06642e15	−1.60123
$560$	−3.34394e15	−2.56581
$561$	−1.86096e14	−0.141397
$562$	−2.17321e12	−0.00163513
$563$	−3.34715e14	−0.249390	−0.124695	−	0.992195i	$-0.539795\pi$
$563$	−3.34715e14	−0.249390	−0.124695	+	0.992195i	$0.539795\pi$
$564$	1.06331e15	0.784556
$565$	−2.16316e15	−1.58060
$566$	−4.10448e14	−0.297008
$567$	−2.63899e14	−0.189117
$568$	−7.84766e14	−0.556961
$569$	8.92451e14	0.627288	0.313644	−	0.949541i	$-0.398450\pi$
$569$	8.92451e14	0.627288	0.313644	+	0.949541i	$0.398450\pi$
$570$	−1.66236e14	−0.115721
$571$	−1.26374e15	−0.871283	−0.435642	−	0.900120i	$-0.643478\pi$
$571$	−1.26374e15	−0.871283	−0.435642	+	0.900120i	$0.643478\pi$
$572$	−2.21753e14	−0.151423
$573$	−1.09509e15	−0.740627
$574$	−4.30103e14	−0.288109
$575$	4.92280e15	3.26617
$576$	−3.44999e14	−0.226722
$577$	−1.00358e15	−0.653261	−0.326631	−	0.945152i	$-0.605913\pi$
$577$	−1.00358e15	−0.653261	−0.326631	+	0.945152i	$0.605913\pi$
$578$	6.77846e14	0.437047
$579$	−1.14981e15	−0.734336
$580$	2.18266e15	1.38080
$581$	4.99827e15	3.13221
$582$	2.63957e14	0.163854
$583$	−4.52107e14	−0.278013
$584$	−4.40922e14	−0.268591
$585$	1.10165e15	0.664795
$586$	4.47674e13	0.0267624
$587$	2.44010e15	1.44510	0.722549	−	0.691320i	$-0.242970\pi$
$587$	2.44010e15	1.44510	0.722549	+	0.691320i	$0.242970\pi$
$588$	−1.76241e15	−1.03403
$589$	−2.23291e14	−0.129789
$590$	−9.64261e13	−0.0555275
$591$	−1.64100e15	−0.936219
$592$	−1.23396e14	−0.0697482
$593$	−6.01651e14	−0.336933	−0.168467	−	0.985707i	$-0.553882\pi$
$593$	−6.01651e14	−0.336933	−0.168467	+	0.985707i	$0.553882\pi$
$594$	1.18968e13	0.00660095
$595$	9.42897e15	5.18347
$596$	7.92715e14	0.431780
$597$	5.49623e14	0.296624
$598$	7.07562e14	0.378362
$599$	−1.52053e15	−0.805650	−0.402825	−	0.915277i	$-0.631972\pi$
$599$	−1.52053e15	−0.805650	−0.402825	+	0.915277i	$0.631972\pi$
$600$	−1.13990e15	−0.598462
$601$	9.06559e14	0.471614	0.235807	−	0.971800i	$-0.424227\pi$
$601$	9.06559e14	0.471614	0.235807	+	0.971800i	$0.424227\pi$
$602$	1.13066e15	0.582843
$603$	−8.82932e14	−0.451006
$604$	2.12124e15	1.07371
$605$	−3.52148e15	−1.76632
$606$	3.20132e14	0.159122
$607$	−3.24469e14	−0.159822	−0.0799108	−	0.996802i	$-0.525464\pi$
$607$	−3.24469e14	−0.159822	−0.0799108	+	0.996802i	$0.525464\pi$
$608$	−6.32580e14	−0.308778
$609$	1.64664e15	0.796535
$610$	2.66050e14	0.127541
$611$	−3.34873e15	−1.59094
$612$	1.12817e15	0.531181
$613$	1.86652e15	0.870963	0.435482	−	0.900198i	$-0.356578\pi$
$613$	1.86652e15	0.870963	0.435482	+	0.900198i	$0.356578\pi$
$614$	−3.35332e14	−0.155077
$615$	1.62752e15	0.745955
$616$	2.49850e14	0.113497
$617$	1.21806e15	0.548406	0.274203	−	0.961672i	$-0.411586\pi$
$617$	1.21806e15	0.548406	0.274203	+	0.961672i	$0.411586\pi$
$618$	−2.83094e14	−0.126326
$619$	−2.04250e15	−0.903367	−0.451684	−	0.892178i	$-0.649176\pi$
$619$	−2.04250e15	−0.903367	−0.451684	+	0.892178i	$0.649176\pi$
$620$	−1.07323e15	−0.470476
$621$	6.41371e14	0.278680
$622$	−2.22790e14	−0.0959510
$623$	−5.24085e15	−2.23727
$624$	1.26006e15	0.533183
$625$	4.36767e15	1.83193
$626$	2.57080e14	0.106883
$627$	−9.55248e13	−0.0393681
$628$	9.37967e14	0.383186
$629$	3.47943e14	0.140906
$630$	−6.02781e14	−0.241984
$631$	−7.92447e14	−0.315361	−0.157681	−	0.987490i	$-0.550402\pi$
$631$	−7.92447e14	−0.315361	−0.157681	+	0.987490i	$0.550402\pi$
$632$	2.03056e14	0.0801074
$633$	5.25859e14	0.205660
$634$	5.25633e14	0.203794
$635$	−2.83050e15	−1.08795
$636$	2.74082e15	1.04440
$637$	5.55046e15	2.09682
$638$	−7.42325e13	−0.0278023
$639$	1.08796e15	0.403978
$640$	−4.00841e15	−1.47565
$641$	−1.96917e15	−0.718725	−0.359363	−	0.933198i	$-0.617006\pi$
$641$	−1.96917e15	−0.718725	−0.359363	+	0.933198i	$0.617006\pi$
$642$	−2.07607e14	−0.0751275
$643$	−2.86477e15	−1.02785	−0.513924	−	0.857836i	$-0.671809\pi$
$643$	−2.86477e15	−1.02785	−0.513924	+	0.857836i	$0.671809\pi$
$644$	6.54125e15	2.32696
$645$	−4.27843e15	−1.50906
$646$	5.36139e14	0.187499
$647$	−4.81632e15	−1.67010	−0.835048	−	0.550177i	$-0.814560\pi$
$647$	−4.81632e15	−1.67010	−0.835048	+	0.550177i	$0.814560\pi$
$648$	−1.48514e14	−0.0510627
$649$	−5.54096e13	−0.0188903
$650$	1.74339e15	0.589348
$651$	−8.09666e14	−0.271400
$652$	−3.86743e15	−1.28547
$653$	1.26231e15	0.416049	0.208024	−	0.978124i	$-0.433297\pi$
$653$	1.26231e15	0.416049	0.208024	+	0.978124i	$0.433297\pi$
$654$	−5.27171e14	−0.172296
$655$	2.45712e15	0.796341
$656$	1.86154e15	0.598275
$657$	6.11270e14	0.194816
$658$	1.83229e15	0.579099
$659$	−3.64839e15	−1.14349	−0.571744	−	0.820432i	$-0.693733\pi$
$659$	−3.64839e15	−1.14349	−0.571744	+	0.820432i	$0.693733\pi$
$660$	−4.59130e14	−0.142707
$661$	4.10991e15	1.26685	0.633424	−	0.773805i	$-0.281649\pi$
$661$	4.10991e15	1.26685	0.633424	+	0.773805i	$0.281649\pi$
$662$	−1.01904e15	−0.311510
$663$	−3.55302e15	−1.07714
$664$	2.81286e15	0.845715
$665$	4.83998e15	1.44319
$666$	−2.22435e13	−0.00657801
$667$	−4.00195e15	−1.17376
$668$	5.58748e15	1.62535
$669$	3.50148e14	0.101020
$670$	−2.01674e15	−0.577082
$671$	1.52881e14	0.0433890
$672$	−2.29377e15	−0.645682
$673$	4.16376e14	0.116253	0.0581264	−	0.998309i	$-0.481487\pi$
$673$	4.16376e14	0.116253	0.0581264	+	0.998309i	$0.481487\pi$
$674$	−9.02558e14	−0.249946
$675$	1.58030e15	0.434080
$676$	−7.68543e14	−0.209393
$677$	−8.56154e14	−0.231374	−0.115687	−	0.993286i	$-0.536907\pi$
$677$	−8.56154e14	−0.231374	−0.115687	+	0.993286i	$0.536907\pi$
$678$	−4.46000e14	−0.119556
$679$	−7.68515e15	−2.04347
$680$	5.30631e15	1.39957
$681$	−1.97401e15	−0.516464
$682$	3.65006e13	0.00947296
$683$	2.03764e15	0.524583	0.262291	−	0.964989i	$-0.415522\pi$
$683$	2.03764e15	0.524583	0.262291	+	0.964989i	$0.415522\pi$
$684$	5.79102e14	0.147893
$685$	−2.92190e15	−0.740230
$686$	−1.43604e15	−0.360896
$687$	3.31925e15	0.827519
$688$	−4.89363e15	−1.21030
$689$	−8.63182e15	−2.11786
$690$	1.46498e15	0.356584
$691$	−4.83876e15	−1.16844	−0.584218	−	0.811597i	$-0.698599\pi$
$691$	−4.83876e15	−1.16844	−0.584218	+	0.811597i	$0.698599\pi$
$692$	3.17299e15	0.760125
$693$	−3.46378e14	−0.0823223
$694$	4.41114e13	0.0104010
$695$	−9.66917e15	−2.26190
$696$	9.26677e14	0.215069
$697$	−5.24901e15	−1.20864
$698$	1.86456e15	0.425962
$699$	1.54253e15	0.349629
$700$	1.61173e16	3.62454
$701$	4.38418e15	0.978226	0.489113	−	0.872221i	$-0.337321\pi$
$701$	4.38418e15	0.978226	0.489113	+	0.872221i	$0.337321\pi$
$702$	2.27139e14	0.0502850
$703$	1.78602e14	0.0392313
$704$	−4.52825e14	−0.0986916
$705$	−6.93343e15	−1.49937
$706$	1.58716e15	0.340560
$707$	−9.32068e15	−1.98445
$708$	3.35911e14	0.0709645
$709$	3.57448e15	0.749305	0.374653	−	0.927165i	$-0.377762\pi$
$709$	3.57448e15	0.749305	0.374653	+	0.927165i	$0.377762\pi$
$710$	2.48504e15	0.516908
$711$	−2.81506e14	−0.0581039
$712$	−2.94938e15	−0.604075
$713$	1.96778e15	0.399931
$714$	1.94407e15	0.392077
$715$	1.44597e15	0.289384
$716$	−2.94769e15	−0.585410
$717$	2.25326e15	0.444075
$718$	2.29076e15	0.448019
$719$	1.68219e15	0.326488	0.163244	−	0.986586i	$-0.447804\pi$
$719$	1.68219e15	0.326488	0.163244	+	0.986586i	$0.447804\pi$
$720$	2.60891e15	0.502493
$721$	8.24231e15	1.57545
$722$	−9.70965e14	−0.184183
$723$	2.43342e15	0.458096
$724$	6.29673e15	1.17639
$725$	−9.86058e15	−1.82828
$726$	−7.26060e14	−0.133604
$727$	7.58110e15	1.38450	0.692250	−	0.721658i	$-0.256620\pi$
$727$	7.58110e15	1.38450	0.692250	+	0.721658i	$0.256620\pi$
$728$	4.77023e15	0.864603
$729$	2.05891e14	0.0370370
$730$	1.39622e15	0.249276
$731$	1.37987e16	2.44507
$732$	−9.26814e14	−0.162998
$733$	−8.07548e13	−0.0140960	−0.00704801	−	0.999975i	$-0.502243\pi$
$733$	−8.07548e13	−0.0140960	−0.00704801	+	0.999975i	$0.502243\pi$
$734$	8.07142e14	0.139837
$735$	1.14920e16	1.97613
$736$	5.57470e15	0.951467
$737$	−1.15888e15	−0.196322
$738$	3.35562e14	0.0564239
$739$	8.64960e15	1.44362	0.721808	−	0.692094i	$-0.243311\pi$
$739$	8.64960e15	1.44362	0.721808	+	0.692094i	$0.243311\pi$
$740$	8.58435e14	0.142211
$741$	−1.82380e15	−0.299900
$742$	4.72298e15	0.770895
$743$	−9.43377e15	−1.52843	−0.764217	−	0.644959i	$-0.776875\pi$
$743$	−9.43377e15	−1.52843	−0.764217	+	0.644959i	$0.776875\pi$
$744$	−4.55653e14	−0.0732796
$745$	−5.16899e15	−0.825175
$746$	4.76911e14	0.0755742
$747$	−3.89960e15	−0.613418
$748$	1.48077e15	0.231222
$749$	6.04450e15	0.936936
$750$	2.00929e15	0.309176
$751$	1.86122e14	0.0284301	0.0142150	−	0.999899i	$-0.495475\pi$
$751$	1.86122e14	0.0284301	0.0142150	+	0.999899i	$0.495475\pi$
$752$	−7.93038e15	−1.20253
$753$	−1.13877e15	−0.171421
$754$	−1.41728e15	−0.211793
$755$	−1.38318e16	−2.05196
$756$	2.09985e15	0.309257
$757$	−8.94198e15	−1.30739	−0.653696	−	0.756757i	$-0.726783\pi$
$757$	−8.94198e15	−1.30739	−0.653696	+	0.756757i	$0.726783\pi$
$758$	−2.27086e15	−0.329617
$759$	8.41826e14	0.121309
$760$	2.72378e15	0.389670
$761$	−6.68066e14	−0.0948864	−0.0474432	−	0.998874i	$-0.515107\pi$
$761$	−6.68066e14	−0.0948864	−0.0474432	+	0.998874i	$0.515107\pi$
$762$	−5.83594e14	−0.0822922
$763$	1.53487e16	2.14875
$764$	8.71367e15	1.21112
$765$	−7.35638e15	−1.01514
$766$	−2.14555e15	−0.293955
$767$	−1.05790e15	−0.143904
$768$	2.08119e15	0.281076
$769$	3.76569e13	0.00504951	0.00252476	−	0.999997i	$-0.499196\pi$
$769$	3.76569e13	0.00504951	0.00252476	+	0.999997i	$0.499196\pi$
$770$	−7.91174e14	−0.105335
$771$	−3.94709e15	−0.521769
$772$	9.14910e15	1.20084
$773$	1.24856e15	0.162713	0.0813564	−	0.996685i	$-0.474075\pi$
$773$	1.24856e15	0.162713	0.0813564	+	0.996685i	$0.474075\pi$
$774$	−8.82129e14	−0.114145
$775$	4.84851e15	0.622944
$776$	−4.32495e15	−0.551749
$777$	6.47622e14	0.0820363
$778$	−1.37873e15	−0.173417
$779$	−2.69437e15	−0.336512
$780$	−8.76591e15	−1.08712
$781$	1.42799e15	0.175851
$782$	−4.72480e15	−0.577758
$783$	−1.28469e15	−0.155995
$784$	1.31444e16	1.58491
$785$	−6.11613e15	−0.732308
$786$	5.06610e14	0.0602351
$787$	1.12544e16	1.32881	0.664405	−	0.747373i	$-0.268685\pi$
$787$	1.12544e16	1.32881	0.664405	+	0.747373i	$0.268685\pi$
$788$	1.30575e16	1.53097
$789$	4.25429e15	0.495341
$790$	−6.42999e14	−0.0743466
$791$	1.29854e16	1.49102
$792$	−1.94930e14	−0.0222275
$793$	2.91887e15	0.330531
$794$	2.96656e15	0.333611
$795$	−1.78718e16	−1.99595
$796$	−4.37337e15	−0.485059
$797$	7.79466e15	0.858571	0.429286	−	0.903169i	$-0.358765\pi$
$797$	7.79466e15	0.858571	0.429286	+	0.903169i	$0.358765\pi$
$798$	9.97909e14	0.109163
$799$	2.23614e16	2.42936
$800$	1.37358e16	1.48203
$801$	4.08886e15	0.438150
$802$	−3.58333e14	−0.0381353
$803$	8.02317e14	0.0848029
$804$	7.02553e15	0.737515
$805$	−4.26530e16	−4.44706
$806$	6.96884e14	0.0721635
$807$	6.88077e15	0.707673
$808$	−5.24537e15	−0.535813
$809$	1.09980e16	1.11583	0.557914	−	0.829899i	$-0.311602\pi$
$809$	1.09980e16	1.11583	0.557914	+	0.829899i	$0.311602\pi$
$810$	4.70283e14	0.0473906
$811$	−1.55405e16	−1.55543	−0.777713	−	0.628620i	$-0.783620\pi$
$811$	−1.55405e16	−1.55543	−0.777713	+	0.628620i	$0.783620\pi$
$812$	−1.31024e16	−1.30255
$813$	7.68325e15	0.758660
$814$	−2.91955e13	−0.00286340
$815$	2.52180e16	2.45666
$816$	−8.41416e15	−0.814169
$817$	7.08298e15	0.680761
$818$	−9.14652e14	−0.0873198
$819$	−6.61319e15	−0.627118
$820$	−1.29502e16	−1.21983
$821$	7.17636e15	0.671455	0.335727	−	0.941959i	$-0.391018\pi$
$821$	7.17636e15	0.671455	0.335727	+	0.941959i	$0.391018\pi$
$822$	−6.02437e14	−0.0559908
$823$	−1.15146e16	−1.06304	−0.531521	−	0.847045i	$-0.678379\pi$
$823$	−1.15146e16	−1.06304	−0.531521	+	0.847045i	$0.678379\pi$
$824$	4.63850e15	0.425381
$825$	2.07421e15	0.188954
$826$	5.78842e14	0.0523805
$827$	4.41263e15	0.396659	0.198330	−	0.980135i	$-0.436448\pi$
$827$	4.41263e15	0.396659	0.198330	+	0.980135i	$0.436448\pi$
$828$	−5.10342e15	−0.455716
$829$	3.94618e15	0.350047	0.175024	−	0.984564i	$-0.444000\pi$
$829$	3.94618e15	0.350047	0.175024	+	0.984564i	$0.444000\pi$
$830$	−8.90722e15	−0.784897
$831$	−1.09272e16	−0.956539
$832$	−8.64551e15	−0.751818
$833$	−3.70636e16	−3.20185
$834$	−1.99359e15	−0.171089
$835$	−3.64339e16	−3.10620
$836$	7.60094e14	0.0643773
$837$	6.31692e14	0.0531515
$838$	4.10536e15	0.343170
$839$	1.83103e16	1.52056	0.760280	−	0.649595i	$-0.225062\pi$
$839$	1.83103e16	1.52056	0.760280	+	0.649595i	$0.225062\pi$
$840$	9.87658e15	0.814837
$841$	−4.18443e15	−0.342972
$842$	7.34978e14	0.0598491
$843$	−4.93651e13	−0.00399364
$844$	−4.18428e15	−0.336308
$845$	5.01138e15	0.400171
$846$	−1.42954e15	−0.113412
$847$	2.11393e16	1.66622
$848$	−2.04416e16	−1.60081
$849$	−9.32346e15	−0.725412
$850$	−1.16416e16	−0.899932
$851$	−1.57396e15	−0.120887
$852$	−8.65692e15	−0.660611
$853$	8.39617e15	0.636593	0.318296	−	0.947991i	$-0.396889\pi$
$853$	8.39617e15	0.636593	0.318296	+	0.947991i	$0.396889\pi$
$854$	−1.59709e15	−0.120312
$855$	−3.77610e15	−0.282638
$856$	3.40164e15	0.252978
$857$	1.97835e16	1.46187	0.730933	−	0.682449i	$-0.239085\pi$
$857$	1.97835e16	1.46187	0.730933	+	0.682449i	$0.239085\pi$
$858$	2.98130e14	0.0218890
$859$	3.67738e15	0.268273	0.134136	−	0.990963i	$-0.457174\pi$
$859$	3.67738e15	0.268273	0.134136	+	0.990963i	$0.457174\pi$
$860$	3.40437e16	2.46771
$861$	−9.76993e15	−0.703678
$862$	4.09410e15	0.293001
$863$	9.74477e15	0.692967	0.346483	−	0.938056i	$-0.387376\pi$
$863$	9.74477e15	0.692967	0.346483	+	0.938056i	$0.387376\pi$
$864$	1.78958e15	0.126452
$865$	−2.06899e16	−1.45268
$866$	−2.15953e15	−0.150664
$867$	1.53975e16	1.06744
$868$	6.44254e15	0.443812
$869$	−3.69488e14	−0.0252925
$870$	−2.93442e15	−0.199602
$871$	−2.21259e16	−1.49555
$872$	8.63772e15	0.580174
$873$	5.99587e15	0.400197
$874$	−2.42528e15	−0.160861
$875$	−5.85007e16	−3.85582
$876$	−4.86390e15	−0.318575
$877$	−2.29169e16	−1.49162	−0.745808	−	0.666161i	$-0.767937\pi$
$877$	−2.29169e16	−1.49162	−0.745808	+	0.666161i	$0.767937\pi$
$878$	−7.18214e14	−0.0464552
$879$	1.01691e15	0.0653645
$880$	3.42430e15	0.218734
$881$	−9.38155e15	−0.595535	−0.297767	−	0.954638i	$-0.596242\pi$
$881$	−9.38155e15	−0.595535	−0.297767	+	0.954638i	$0.596242\pi$
$882$	2.36943e15	0.149474
$883$	−2.38795e16	−1.49707	−0.748533	−	0.663097i	$-0.769242\pi$
$883$	−2.38795e16	−1.49707	−0.748533	+	0.663097i	$0.769242\pi$
$884$	2.82715e16	1.76141
$885$	−2.19035e15	−0.135620
$886$	−1.09409e15	−0.0673235
$887$	−1.22475e16	−0.748976	−0.374488	−	0.927232i	$-0.622182\pi$
$887$	−1.22475e16	−0.748976	−0.374488	+	0.927232i	$0.622182\pi$
$888$	3.64460e14	0.0221503
$889$	1.69914e16	1.02629
$890$	9.33951e15	0.560633
$891$	2.70240e14	0.0161221
$892$	−2.78614e15	−0.165195
$893$	1.14783e16	0.676388
$894$	−1.06574e15	−0.0624161
$895$	1.92208e16	1.11878
$896$	2.40623e16	1.39201
$897$	1.60725e16	0.924112
$898$	3.25092e14	0.0185775
$899$	−3.94156e15	−0.223867
$900$	−1.25745e16	−0.709836
$901$	5.76396e16	3.23396
$902$	4.40439e14	0.0245612
$903$	2.56833e16	1.42353
$904$	7.30773e15	0.402583
$905$	−4.10586e16	−2.24821
$906$	−2.85184e15	−0.155210
$907$	−6.19815e15	−0.335291	−0.167645	−	0.985847i	$-0.553616\pi$
$907$	−6.19815e15	−0.335291	−0.167645	+	0.985847i	$0.553616\pi$
$908$	1.57073e16	0.844557
$909$	7.27189e15	0.388639
$910$	−1.51054e16	−0.802427
$911$	6.49524e15	0.342961	0.171480	−	0.985188i	$-0.445145\pi$
$911$	6.49524e15	0.342961	0.171480	+	0.985188i	$0.445145\pi$
$912$	−4.31907e15	−0.226683
$913$	−5.11838e15	−0.267020
$914$	3.32173e15	0.172250
$915$	6.04341e15	0.311506
$916$	−2.64114e16	−1.35321
$917$	−1.47500e16	−0.751209
$918$	−1.51674e15	−0.0767851
$919$	−5.32116e15	−0.267775	−0.133888	−	0.990997i	$-0.542746\pi$
$919$	−5.32116e15	−0.267775	−0.133888	+	0.990997i	$0.542746\pi$
$920$	−2.40037e16	−1.20073
$921$	−7.61716e15	−0.378761
$922$	−1.57984e15	−0.0780896
$923$	2.72637e16	1.33960
$924$	2.75614e15	0.134619
$925$	−3.87814e15	−0.188297
$926$	5.66461e15	0.273407
$927$	−6.43056e15	−0.308539
$928$	−1.11664e16	−0.532596
$929$	−2.10013e16	−0.995772	−0.497886	−	0.867242i	$-0.665890\pi$
$929$	−2.10013e16	−0.995772	−0.497886	+	0.867242i	$0.665890\pi$
$930$	1.44287e15	0.0680098
$931$	−1.90251e16	−0.891465
$932$	−1.22739e16	−0.571737
$933$	−5.06075e15	−0.234351
$934$	3.01718e15	0.138897
$935$	−9.65555e15	−0.441889
$936$	−3.72168e15	−0.169326
$937$	−7.65855e15	−0.346401	−0.173200	−	0.984887i	$-0.555411\pi$
$937$	−7.65855e15	−0.346401	−0.173200	+	0.984887i	$0.555411\pi$
$938$	1.21064e16	0.544377
$939$	5.83965e15	0.261051
$940$	5.51695e16	2.45186
$941$	−1.63583e16	−0.722760	−0.361380	−	0.932419i	$-0.617694\pi$
$941$	−1.63583e16	−0.722760	−0.361380	+	0.932419i	$0.617694\pi$
$942$	−1.26103e15	−0.0553916
$943$	2.37445e16	1.03693
$944$	−2.50530e15	−0.108771
$945$	−1.36924e16	−0.591021
$946$	−1.15783e15	−0.0496871
$947$	1.74846e16	0.745988	0.372994	−	0.927834i	$-0.378331\pi$
$947$	1.74846e16	0.745988	0.372994	+	0.927834i	$0.378331\pi$
$948$	2.23996e15	0.0950154
$949$	1.53182e16	0.646015
$950$	−5.97576e15	−0.250561
$951$	1.19399e16	0.497746
$952$	−3.18536e16	−1.32025
$953$	4.34637e15	0.179108	0.0895542	−	0.995982i	$-0.471456\pi$
$953$	4.34637e15	0.179108	0.0895542	+	0.995982i	$0.471456\pi$
$954$	−3.68482e15	−0.150973
$955$	−5.68186e16	−2.31458
$956$	−1.79293e16	−0.726181
$957$	−1.68621e15	−0.0679042
$958$	7.96352e15	0.318856
$959$	1.75400e16	0.698278
$960$	−1.79002e16	−0.708543
$961$	−2.34704e16	−0.923723
$962$	−5.57412e14	−0.0218129
$963$	−4.71585e15	−0.183491
$964$	−1.93628e16	−0.749110
$965$	−5.96578e16	−2.29492
$966$	−8.79422e15	−0.336374
$967$	−3.47539e16	−1.32177	−0.660887	−	0.750485i	$-0.729820\pi$
$967$	−3.47539e16	−1.32177	−0.660887	+	0.750485i	$0.729820\pi$
$968$	1.18965e16	0.449889
$969$	1.21786e16	0.457947
$970$	1.36954e16	0.512070
$971$	1.18674e15	0.0441214	0.0220607	−	0.999757i	$-0.492977\pi$
$971$	1.18674e15	0.0441214	0.0220607	+	0.999757i	$0.492977\pi$
$972$	−1.63828e15	−0.0605654
$973$	5.80437e16	2.13370
$974$	3.10529e15	0.113508
$975$	3.96017e16	1.43942
$976$	6.91239e15	0.249835
$977$	−1.83386e16	−0.659092	−0.329546	−	0.944139i	$-0.606896\pi$
$977$	−1.83386e16	−0.659092	−0.329546	+	0.944139i	$0.606896\pi$
$978$	5.19947e15	0.185821
$979$	5.36679e15	0.190726
$980$	−9.14424e16	−3.23150
$981$	−1.19749e16	−0.420815
$982$	4.66434e14	0.0162996
$983$	5.64873e15	0.196294	0.0981468	−	0.995172i	$-0.468709\pi$
$983$	5.64873e15	0.196294	0.0981468	+	0.995172i	$0.468709\pi$
$984$	−5.49819e15	−0.189997
$985$	−8.51431e16	−2.92584
$986$	9.46398e15	0.323408
$987$	4.16211e16	1.41439
$988$	1.45120e16	0.490416
$989$	−6.24198e16	−2.09770
$990$	6.17266e14	0.0206290
$991$	−3.41359e16	−1.13450	−0.567252	−	0.823544i	$-0.691993\pi$
$991$	−3.41359e16	−1.13450	−0.567252	+	0.823544i	$0.691993\pi$
$992$	5.49058e15	0.181470
$993$	−2.31478e16	−0.760831
$994$	−1.49176e16	−0.487612
$995$	2.85171e16	0.926997
$996$	3.10293e16	1.00310
$997$	5.30851e16	1.70667	0.853335	−	0.521364i	$-0.174577\pi$
$997$	5.30851e16	1.70667	0.853335	+	0.521364i	$0.174577\pi$
$998$	−3.44699e15	−0.110210
$999$	−5.05268e14	−0.0160661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.16	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.16	✓	27	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+10.6976 q^{2} +243.000 q^{3} -1933.56 q^{4} +12608.0 q^{5} +2599.53 q^{6} -75685.5 q^{7} -42593.3 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+10.6976 q^{2} +243.000 q^{3} -1933.56 q^{4} +12608.0 q^{5} +2599.53 q^{6} -75685.5 q^{7} -42593.3 q^{8} +59049.0 q^{9} +134876. q^{10} +77504.2 q^{11} -469855. q^{12} +1.47974e6 q^{13} -809655. q^{14} +3.06375e6 q^{15} +3.50428e6 q^{16} -9.88109e6 q^{17} +631685. q^{18} -5.07206e6 q^{19} -2.43784e7 q^{20} -1.83916e7 q^{21} +829112. q^{22} +4.46983e7 q^{23} -1.03502e7 q^{24} +1.10134e8 q^{25} +1.58297e7 q^{26} +1.43489e7 q^{27} +1.46342e8 q^{28} -8.95326e7 q^{29} +3.27749e7 q^{30} +4.40237e7 q^{31} +1.24719e8 q^{32} +1.88335e7 q^{33} -1.05704e8 q^{34} -9.54244e8 q^{35} -1.14175e8 q^{36} -3.52130e7 q^{37} -5.42590e7 q^{38} +3.59577e8 q^{39} -5.37017e8 q^{40} +5.31218e8 q^{41} -1.96746e8 q^{42} -1.39647e9 q^{43} -1.49859e8 q^{44} +7.44491e8 q^{45} +4.78166e8 q^{46} -2.26305e9 q^{47} +8.51541e8 q^{48} +3.75096e9 q^{49} +1.17817e9 q^{50} -2.40111e9 q^{51} -2.86117e9 q^{52} -5.83333e9 q^{53} +1.53499e8 q^{54} +9.77174e8 q^{55} +3.22369e9 q^{56} -1.23251e9 q^{57} -9.57786e8 q^{58} -7.14924e8 q^{59} -5.92394e9 q^{60} +1.97255e9 q^{61} +4.70950e8 q^{62} -4.46915e9 q^{63} -5.84258e9 q^{64} +1.86566e10 q^{65} +2.01474e8 q^{66} -1.49525e10 q^{67} +1.91057e10 q^{68} +1.08617e10 q^{69} -1.02081e10 q^{70} +1.84247e10 q^{71} -2.51509e9 q^{72} +1.03519e10 q^{73} -3.76695e8 q^{74} +2.67626e10 q^{75} +9.80714e9 q^{76} -5.86594e9 q^{77} +3.84663e9 q^{78} -4.76733e9 q^{79} +4.41821e10 q^{80} +3.48678e9 q^{81} +5.68277e9 q^{82} -6.60401e10 q^{83} +3.55612e10 q^{84} -1.24581e11 q^{85} -1.49389e10 q^{86} -2.17564e10 q^{87} -3.30116e9 q^{88} +6.92452e10 q^{89} +7.96429e9 q^{90} -1.11995e11 q^{91} -8.64268e10 q^{92} +1.06978e10 q^{93} -2.42093e10 q^{94} -6.39486e10 q^{95} +3.03066e10 q^{96} +1.01541e11 q^{97} +4.01264e10 q^{98} +4.57655e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

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