LMFDB - Embedded newform 177.12.a.c.1.6

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:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-64.1897 q^{2} -243.000 q^{3} +2072.32 q^{4} -6307.39 q^{5} +15598.1 q^{6} +84626.9 q^{7} -1560.87 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-64.1897 q^{2} -243.000 q^{3} +2072.32 q^{4} -6307.39 q^{5} +15598.1 q^{6} +84626.9 q^{7} -1560.87 q^{8} +59049.0 q^{9} +404869. q^{10} -902806. q^{11} -503573. q^{12} -1.37458e6 q^{13} -5.43217e6 q^{14} +1.53270e6 q^{15} -4.14391e6 q^{16} +6.10500e6 q^{17} -3.79034e6 q^{18} +1.53727e7 q^{19} -1.30709e7 q^{20} -2.05643e7 q^{21} +5.79509e7 q^{22} +5.45940e7 q^{23} +379292. q^{24} -9.04497e6 q^{25} +8.82338e7 q^{26} -1.43489e7 q^{27} +1.75374e8 q^{28} +3.20407e7 q^{29} -9.83833e7 q^{30} +2.01437e8 q^{31} +2.69193e8 q^{32} +2.19382e8 q^{33} -3.91878e8 q^{34} -5.33774e8 q^{35} +1.22368e8 q^{36} +6.20122e8 q^{37} -9.86768e8 q^{38} +3.34023e8 q^{39} +9.84503e6 q^{40} -1.18981e9 q^{41} +1.32002e9 q^{42} -2.91907e8 q^{43} -1.87090e9 q^{44} -3.72445e8 q^{45} -3.50437e9 q^{46} +6.14694e7 q^{47} +1.00697e9 q^{48} +5.18438e9 q^{49} +5.80594e8 q^{50} -1.48352e9 q^{51} -2.84856e9 q^{52} -3.65243e9 q^{53} +9.21052e8 q^{54} +5.69435e9 q^{55} -1.32092e8 q^{56} -3.73556e9 q^{57} -2.05668e9 q^{58} -7.14924e8 q^{59} +3.17623e9 q^{60} +1.13062e10 q^{61} -1.29302e10 q^{62} +4.99713e9 q^{63} -8.79269e9 q^{64} +8.67000e9 q^{65} -1.40821e10 q^{66} -8.11606e9 q^{67} +1.26515e10 q^{68} -1.32663e10 q^{69} +3.42628e10 q^{70} -1.75527e10 q^{71} -9.21680e7 q^{72} -1.78971e10 q^{73} -3.98055e10 q^{74} +2.19793e9 q^{75} +3.18571e10 q^{76} -7.64017e10 q^{77} -2.14408e10 q^{78} +2.32461e10 q^{79} +2.61373e10 q^{80} +3.48678e9 q^{81} +7.63737e10 q^{82} +8.67597e9 q^{83} -4.26158e10 q^{84} -3.85066e10 q^{85} +1.87374e10 q^{86} -7.78588e9 q^{87} +1.40917e9 q^{88} +7.88055e10 q^{89} +2.39071e10 q^{90} -1.16326e11 q^{91} +1.13136e11 q^{92} -4.89493e10 q^{93} -3.94570e9 q^{94} -9.69615e10 q^{95} -6.54139e10 q^{96} -6.50540e10 q^{97} -3.32784e11 q^{98} -5.33098e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * 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 $

$2$	−64.1897	−1.41841	−0.709203	−	0.705005i	$-0.750945\pi$
$2$	−64.1897	−1.41841	−0.709203	+	0.705005i	$0.750945\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2072.32	1.01187
$5$	−6307.39	−0.902640	−0.451320	−	0.892362i	$-0.649047\pi$
$5$	−6307.39	−0.902640	−0.451320	+	0.892362i	$0.649047\pi$
$6$	15598.1	0.818917
$7$	84626.9	1.90313	0.951566	−	0.307444i	$-0.0994737\pi$
$7$	84626.9	1.90313	0.951566	+	0.307444i	$0.0994737\pi$
$8$	−1560.87	−0.0168412
$9$	59049.0	0.333333
$10$	404869.	1.28031
$11$	−902806.	−1.69019	−0.845094	−	0.534618i	$-0.820455\pi$
$11$	−902806.	−1.69019	−0.845094	+	0.534618i	$0.820455\pi$
$12$	−503573.	−0.584205
$13$	−1.37458e6	−1.02679	−0.513394	−	0.858153i	$-0.671612\pi$
$13$	−1.37458e6	−1.02679	−0.513394	+	0.858153i	$0.671612\pi$
$14$	−5.43217e6	−2.69941
$15$	1.53270e6	0.521139
$16$	−4.14391e6	−0.987986
$17$	6.10500e6	1.04284	0.521419	−	0.853301i	$-0.325403\pi$
$17$	6.10500e6	1.04284	0.521419	+	0.853301i	$0.325403\pi$
$18$	−3.79034e6	−0.472802
$19$	1.53727e7	1.42431	0.712155	−	0.702022i	$-0.247719\pi$
$19$	1.53727e7	1.42431	0.712155	+	0.702022i	$0.247719\pi$
$20$	−1.30709e7	−0.913357
$21$	−2.05643e7	−1.09877
$22$	5.79509e7	2.39737
$23$	5.45940e7	1.76865	0.884324	−	0.466873i	$-0.154619\pi$
$23$	5.45940e7	1.76865	0.884324	+	0.466873i	$0.154619\pi$
$24$	379292.	0.00972326
$25$	−9.04497e6	−0.185241
$26$	8.82338e7	1.45640
$27$	−1.43489e7	−0.192450
$28$	1.75374e8	1.92573
$29$	3.20407e7	0.290076	0.145038	−	0.989426i	$-0.453669\pi$
$29$	3.20407e7	0.290076	0.145038	+	0.989426i	$0.453669\pi$
$30$	−9.83833e7	−0.739187
$31$	2.01437e8	1.26372	0.631860	−	0.775083i	$-0.282292\pi$
$31$	2.01437e8	1.26372	0.631860	+	0.775083i	$0.282292\pi$
$32$	2.69193e8	1.41821
$33$	2.19382e8	0.975830
$34$	−3.91878e8	−1.47917
$35$	−5.33774e8	−1.71784
$36$	1.22368e8	0.337291
$37$	6.20122e8	1.47017	0.735085	−	0.677975i	$-0.237142\pi$
$37$	6.20122e8	1.47017	0.735085	+	0.677975i	$0.237142\pi$
$38$	−9.86768e8	−2.02025
$39$	3.34023e8	0.592817
$40$	9.84503e6	0.0152015
$41$	−1.18981e9	−1.60386	−0.801932	−	0.597415i	$-0.796194\pi$
$41$	−1.18981e9	−1.60386	−0.801932	+	0.597415i	$0.796194\pi$
$42$	1.32002e9	1.55851
$43$	−2.91907e8	−0.302808	−0.151404	−	0.988472i	$-0.548380\pi$
$43$	−2.91907e8	−0.302808	−0.151404	+	0.988472i	$0.548380\pi$
$44$	−1.87090e9	−1.71026
$45$	−3.72445e8	−0.300880
$46$	−3.50437e9	−2.50866
$47$	6.14694e7	0.0390950	0.0195475	−	0.999809i	$-0.493777\pi$
$47$	6.14694e7	0.0390950	0.0195475	+	0.999809i	$0.493777\pi$
$48$	1.00697e9	0.570414
$49$	5.18438e9	2.62191
$50$	5.80594e8	0.262747
$51$	−1.48352e9	−0.602083
$52$	−2.84856e9	−1.03898
$53$	−3.65243e9	−1.19968	−0.599839	−	0.800120i	$-0.704769\pi$
$53$	−3.65243e9	−1.19968	−0.599839	+	0.800120i	$0.704769\pi$
$54$	9.21052e8	0.272972
$55$	5.69435e9	1.52563
$56$	−1.32092e8	−0.0320510
$57$	−3.73556e9	−0.822326
$58$	−2.05668e9	−0.411446
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	3.17623e9	0.527327
$61$	1.13062e10	1.71397	0.856987	−	0.515338i	$-0.172333\pi$
$61$	1.13062e10	1.71397	0.856987	+	0.515338i	$0.172333\pi$
$62$	−1.29302e10	−1.79247
$63$	4.99713e9	0.634377
$64$	−8.79269e9	−1.02360
$65$	8.67000e9	0.926821
$66$	−1.40821e10	−1.38412
$67$	−8.11606e9	−0.734402	−0.367201	−	0.930142i	$-0.619684\pi$
$67$	−8.11606e9	−0.734402	−0.367201	+	0.930142i	$0.619684\pi$
$68$	1.26515e10	1.05522
$69$	−1.32663e10	−1.02113
$70$	3.42628e10	2.43660
$71$	−1.75527e10	−1.15458	−0.577290	−	0.816539i	$-0.695890\pi$
$71$	−1.75527e10	−1.15458	−0.577290	+	0.816539i	$0.695890\pi$
$72$	−9.21680e7	−0.00561373
$73$	−1.78971e10	−1.01043	−0.505215	−	0.862994i	$-0.668587\pi$
$73$	−1.78971e10	−1.01043	−0.505215	+	0.862994i	$0.668587\pi$
$74$	−3.98055e10	−2.08530
$75$	2.19793e9	0.106949
$76$	3.18571e10	1.44122
$77$	−7.64017e10	−3.21665
$78$	−2.14408e10	−0.840855
$79$	2.32461e10	0.849963	0.424982	−	0.905202i	$-0.360281\pi$
$79$	2.32461e10	0.849963	0.424982	+	0.905202i	$0.360281\pi$
$80$	2.61373e10	0.891795
$81$	3.48678e9	0.111111
$82$	7.63737e10	2.27493
$83$	8.67597e9	0.241762	0.120881	−	0.992667i	$-0.461428\pi$
$83$	8.67597e9	0.241762	0.120881	+	0.992667i	$0.461428\pi$
$84$	−4.26158e10	−1.11182
$85$	−3.85066e10	−0.941307
$86$	1.87374e10	0.429505
$87$	−7.78588e9	−0.167476
$88$	1.40917e9	0.0284648
$89$	7.88055e10	1.49593	0.747966	−	0.663737i	$-0.231031\pi$
$89$	7.88055e10	1.49593	0.747966	+	0.663737i	$0.231031\pi$
$90$	2.39071e10	0.426770
$91$	−1.16326e11	−1.95412
$92$	1.13136e11	1.78965
$93$	−4.89493e10	−0.729609
$94$	−3.94570e9	−0.0554525
$95$	−9.69615e10	−1.28564
$96$	−6.54139e10	−0.818801
$97$	−6.50540e10	−0.769183	−0.384592	−	0.923087i	$-0.625658\pi$
$97$	−6.50540e10	−0.769183	−0.384592	+	0.923087i	$0.625658\pi$
$98$	−3.32784e11	−3.71893
$99$	−5.33098e10	−0.563396
$100$	−1.87440e10	−0.187440
$101$	−8.59215e10	−0.813457	−0.406728	−	0.913549i	$-0.633330\pi$
$101$	−8.59215e10	−0.813457	−0.406728	+	0.913549i	$0.633330\pi$
$102$	9.52264e10	0.853998
$103$	−4.71359e10	−0.400633	−0.200317	−	0.979731i	$-0.564197\pi$
$103$	−4.71359e10	−0.400633	−0.200317	+	0.979731i	$0.564197\pi$
$104$	2.14554e9	0.0172923
$105$	1.29707e11	0.991797
$106$	2.34449e11	1.70163
$107$	6.98844e10	0.481692	0.240846	−	0.970563i	$-0.422575\pi$
$107$	6.98844e10	0.481692	0.240846	+	0.970563i	$0.422575\pi$
$108$	−2.97355e10	−0.194735
$109$	−8.79549e9	−0.0547538	−0.0273769	−	0.999625i	$-0.508715\pi$
$109$	−8.79549e9	−0.0547538	−0.0273769	+	0.999625i	$0.508715\pi$
$110$	−3.65519e11	−2.16396
$111$	−1.50690e11	−0.848803
$112$	−3.50686e11	−1.88027
$113$	−1.78906e10	−0.0913468	−0.0456734	−	0.998956i	$-0.514543\pi$
$113$	−1.78906e10	−0.0913468	−0.0456734	+	0.998956i	$0.514543\pi$
$114$	2.39785e11	1.16639
$115$	−3.44345e11	−1.59645
$116$	6.63984e10	0.293521
$117$	−8.11675e10	−0.342263
$118$	4.58908e10	0.184661
$119$	5.16647e11	1.98466
$120$	−2.39234e9	−0.00877661
$121$	5.29748e11	1.85673
$122$	−7.25745e11	−2.43111
$123$	2.89125e11	0.925991
$124$	4.17442e11	1.27872
$125$	3.65028e11	1.06985
$126$	−3.20764e11	−0.899804
$127$	−4.11217e10	−0.110446	−0.0552231	−	0.998474i	$-0.517587\pi$
$127$	−4.11217e10	−0.110446	−0.0552231	+	0.998474i	$0.517587\pi$
$128$	1.30926e10	0.0336800
$129$	7.09334e10	0.174827
$130$	−5.56525e11	−1.31461
$131$	−7.36528e11	−1.66800	−0.834002	−	0.551762i	$-0.813956\pi$
$131$	−7.36528e11	−1.66800	−0.834002	+	0.551762i	$0.813956\pi$
$132$	4.54629e11	0.987417
$133$	1.30094e12	2.71065
$134$	5.20967e11	1.04168
$135$	9.05041e10	0.173713
$136$	−9.52914e9	−0.0175626
$137$	−5.15534e11	−0.912628	−0.456314	−	0.889819i	$-0.650831\pi$
$137$	−5.15534e11	−0.912628	−0.456314	+	0.889819i	$0.650831\pi$
$138$	8.51562e11	1.44838
$139$	3.25513e11	0.532092	0.266046	−	0.963960i	$-0.414283\pi$
$139$	3.25513e11	0.532092	0.266046	+	0.963960i	$0.414283\pi$
$140$	−1.10615e12	−1.73824
$141$	−1.49371e10	−0.0225715
$142$	1.12671e12	1.63766
$143$	1.24098e12	1.73547
$144$	−2.44694e11	−0.329329
$145$	−2.02093e11	−0.261835
$146$	1.14881e12	1.43320
$147$	−1.25980e12	−1.51376
$148$	1.28509e12	1.48763
$149$	1.16267e12	1.29697	0.648485	−	0.761227i	$-0.275403\pi$
$149$	1.16267e12	1.29697	0.648485	+	0.761227i	$0.275403\pi$
$150$	−1.41084e11	−0.151697
$151$	7.93846e11	0.822930	0.411465	−	0.911425i	$-0.365017\pi$
$151$	7.93846e11	0.822930	0.411465	+	0.911425i	$0.365017\pi$
$152$	−2.39948e10	−0.0239871
$153$	3.60494e11	0.347613
$154$	4.90420e12	4.56251
$155$	−1.27054e12	−1.14068
$156$	6.92201e11	0.599856
$157$	−1.68630e12	−1.41087	−0.705436	−	0.708774i	$-0.749249\pi$
$157$	−1.68630e12	−1.41087	−0.705436	+	0.708774i	$0.749249\pi$
$158$	−1.49216e12	−1.20559
$159$	8.87541e11	0.692635
$160$	−1.69791e12	−1.28013
$161$	4.62012e12	3.36597
$162$	−2.23816e11	−0.157601
$163$	−6.34506e11	−0.431921	−0.215960	−	0.976402i	$-0.569288\pi$
$163$	−6.34506e11	−0.431921	−0.215960	+	0.976402i	$0.569288\pi$
$164$	−2.46567e12	−1.62291
$165$	−1.38373e12	−0.880823
$166$	−5.56908e11	−0.342917
$167$	−1.56788e12	−0.934056	−0.467028	−	0.884242i	$-0.654675\pi$
$167$	−1.56788e12	−0.934056	−0.467028	+	0.884242i	$0.654675\pi$
$168$	3.20983e10	0.0185047
$169$	9.73062e10	0.0542955
$170$	2.47173e12	1.33516
$171$	9.07741e11	0.474770
$172$	−6.04924e11	−0.306404
$173$	−1.63986e12	−0.804550	−0.402275	−	0.915519i	$-0.631780\pi$
$173$	−1.63986e12	−0.804550	−0.402275	+	0.915519i	$0.631780\pi$
$174$	4.99773e11	0.237548
$175$	−7.65447e11	−0.352538
$176$	3.74115e12	1.66988
$177$	1.73727e11	0.0751646
$178$	−5.05850e12	−2.12184
$179$	−2.22928e12	−0.906718	−0.453359	−	0.891328i	$-0.649775\pi$
$179$	−2.22928e12	−0.906718	−0.453359	+	0.891328i	$0.649775\pi$
$180$	−7.71824e11	−0.304452
$181$	1.95784e12	0.749111	0.374555	−	0.927205i	$-0.377795\pi$
$181$	1.95784e12	0.749111	0.374555	+	0.927205i	$0.377795\pi$
$182$	7.46695e12	2.77173
$183$	−2.74742e12	−0.989564
$184$	−8.52143e10	−0.0297861
$185$	−3.91135e12	−1.32703
$186$	3.14204e12	1.03488
$187$	−5.51164e12	−1.76259
$188$	1.27384e11	0.0395592
$189$	−1.21430e12	−0.366258
$190$	6.22393e12	1.82356
$191$	−1.00786e12	−0.286891	−0.143446	−	0.989658i	$-0.545818\pi$
$191$	−1.00786e12	−0.286891	−0.143446	+	0.989658i	$0.545818\pi$
$192$	2.13662e12	0.590978
$193$	3.80074e12	1.02165	0.510826	−	0.859684i	$-0.329340\pi$
$193$	3.80074e12	1.02165	0.510826	+	0.859684i	$0.329340\pi$
$194$	4.17580e12	1.09101
$195$	−2.10681e12	−0.535100
$196$	1.07437e13	2.65304
$197$	−2.35828e12	−0.566280	−0.283140	−	0.959079i	$-0.591376\pi$
$197$	−2.35828e12	−0.566280	−0.283140	+	0.959079i	$0.591376\pi$
$198$	3.42194e12	0.799124
$199$	−1.25177e12	−0.284336	−0.142168	−	0.989843i	$-0.545407\pi$
$199$	−1.25177e12	−0.284336	−0.142168	+	0.989843i	$0.545407\pi$
$200$	1.41181e10	0.00311968
$201$	1.97220e12	0.424007
$202$	5.51528e12	1.15381
$203$	2.71150e12	0.552054
$204$	−3.07431e12	−0.609232
$205$	7.50461e12	1.44771
$206$	3.02564e12	0.568260
$207$	3.22372e12	0.589550
$208$	5.69613e12	1.01445
$209$	−1.38786e13	−2.40735
$210$	−8.32586e12	−1.40677
$211$	−4.10909e12	−0.676382	−0.338191	−	0.941077i	$-0.609815\pi$
$211$	−4.10909e12	−0.676382	−0.338191	+	0.941077i	$0.609815\pi$
$212$	−7.56900e12	−1.21392
$213$	4.26532e12	0.666597
$214$	−4.48586e12	−0.683235
$215$	1.84117e12	0.273327
$216$	2.23968e10	0.00324109
$217$	1.70470e13	2.40503
$218$	5.64580e11	0.0776631
$219$	4.34899e12	0.583372
$220$	1.18005e13	1.54375
$221$	−8.39181e12	−1.07077
$222$	9.67272e12	1.20395
$223$	9.53747e12	1.15813	0.579064	−	0.815282i	$-0.303418\pi$
$223$	9.53747e12	1.15813	0.579064	+	0.815282i	$0.303418\pi$
$224$	2.27810e13	2.69903
$225$	−5.34096e11	−0.0617470
$226$	1.14839e12	0.129567
$227$	9.82918e12	1.08237	0.541184	−	0.840904i	$-0.317976\pi$
$227$	9.82918e12	1.08237	0.541184	+	0.840904i	$0.317976\pi$
$228$	−7.74127e12	−0.832090
$229$	−4.90493e12	−0.514681	−0.257340	−	0.966321i	$-0.582846\pi$
$229$	−4.90493e12	−0.514681	−0.257340	+	0.966321i	$0.582846\pi$
$230$	2.21034e13	2.26442
$231$	1.85656e13	1.85713
$232$	−5.00114e10	−0.00488523
$233$	1.38224e13	1.31863	0.659317	−	0.751865i	$-0.270845\pi$
$233$	1.38224e13	1.31863	0.659317	+	0.751865i	$0.270845\pi$
$234$	5.21012e12	0.485468
$235$	−3.87711e11	−0.0352887
$236$	−1.48155e12	−0.131735
$237$	−5.64879e12	−0.490727
$238$	−3.31634e13	−2.81505
$239$	−2.29756e12	−0.190581	−0.0952904	−	0.995450i	$-0.530378\pi$
$239$	−2.29756e12	−0.190581	−0.0952904	+	0.995450i	$0.530378\pi$
$240$	−6.35136e12	−0.514878
$241$	−4.33916e12	−0.343805	−0.171903	−	0.985114i	$-0.554991\pi$
$241$	−4.33916e12	−0.343805	−0.171903	+	0.985114i	$0.554991\pi$
$242$	−3.40044e13	−2.63360
$243$	−8.47289e11	−0.0641500
$244$	2.34301e13	1.73433
$245$	−3.26999e13	−2.36664
$246$	−1.85588e13	−1.31343
$247$	−2.11310e13	−1.46247
$248$	−3.14418e11	−0.0212825
$249$	−2.10826e12	−0.139581
$250$	−2.34310e13	−1.51748
$251$	8.15418e12	0.516624	0.258312	−	0.966062i	$-0.416834\pi$
$251$	8.15418e12	0.516624	0.258312	+	0.966062i	$0.416834\pi$
$252$	1.03556e13	0.641910
$253$	−4.92878e13	−2.98935
$254$	2.63959e12	0.156658
$255$	9.35711e12	0.543464
$256$	1.71670e13	0.975832
$257$	1.34438e13	0.747982	0.373991	−	0.927432i	$-0.377989\pi$
$257$	1.34438e13	0.747982	0.373991	+	0.927432i	$0.377989\pi$
$258$	−4.55319e12	−0.247975
$259$	5.24790e13	2.79793
$260$	1.79670e13	0.937825
$261$	1.89197e12	0.0966921
$262$	4.72775e13	2.36590
$263$	2.31137e13	1.13270	0.566348	−	0.824166i	$-0.308356\pi$
$263$	2.31137e13	1.13270	0.566348	+	0.824166i	$0.308356\pi$
$264$	−3.42427e11	−0.0164341
$265$	2.30373e13	1.08288
$266$	−8.35070e13	−3.84480
$267$	−1.91497e13	−0.863676
$268$	−1.68190e13	−0.743122
$269$	2.85981e13	1.23794	0.618970	−	0.785415i	$-0.287550\pi$
$269$	2.85981e13	1.23794	0.618970	+	0.785415i	$0.287550\pi$
$270$	−5.80943e12	−0.246396
$271$	−7.95747e12	−0.330707	−0.165354	−	0.986234i	$-0.552877\pi$
$271$	−7.95747e12	−0.330707	−0.165354	+	0.986234i	$0.552877\pi$
$272$	−2.52986e13	−1.03031
$273$	2.82673e13	1.12821
$274$	3.30919e13	1.29448
$275$	8.16586e12	0.313092
$276$	−2.74920e13	−1.03325
$277$	−1.29393e13	−0.476729	−0.238365	−	0.971176i	$-0.576611\pi$
$277$	−1.29393e13	−0.476729	−0.238365	+	0.971176i	$0.576611\pi$
$278$	−2.08946e13	−0.754722
$279$	1.18947e13	0.421240
$280$	8.33154e11	0.0289305
$281$	1.93697e13	0.659536	0.329768	−	0.944062i	$-0.393029\pi$
$281$	1.93697e13	0.659536	0.329768	+	0.944062i	$0.393029\pi$
$282$	9.58806e11	0.0320155
$283$	5.69672e13	1.86552	0.932759	−	0.360499i	$-0.117394\pi$
$283$	5.69672e13	1.86552	0.932759	+	0.360499i	$0.117394\pi$
$284$	−3.63748e13	−1.16829
$285$	2.35616e13	0.742265
$286$	−7.96580e13	−2.46159
$287$	−1.00690e14	−3.05237
$288$	1.58956e13	0.472735
$289$	2.99918e12	0.0875115
$290$	1.29723e13	0.371388
$291$	1.58081e13	0.444088
$292$	−3.70884e13	−1.02243
$293$	−4.46407e13	−1.20770	−0.603849	−	0.797098i	$-0.706367\pi$
$293$	−4.46407e13	−1.20770	−0.603849	+	0.797098i	$0.706367\pi$
$294$	8.08664e13	2.14713
$295$	4.50931e12	0.117514
$296$	−9.67932e11	−0.0247594
$297$	1.29543e13	0.325277
$298$	−7.46311e13	−1.83963
$299$	−7.50437e13	−1.81603
$300$	4.55480e12	0.108219
$301$	−2.47032e13	−0.576285
$302$	−5.09567e13	−1.16725
$303$	2.08789e13	0.469649
$304$	−6.37030e13	−1.40720
$305$	−7.13129e13	−1.54710
$306$	−2.31400e13	−0.493056
$307$	6.66583e13	1.39506	0.697530	−	0.716556i	$-0.254282\pi$
$307$	6.66583e13	1.39506	0.697530	+	0.716556i	$0.254282\pi$
$308$	−1.58328e14	−3.25484
$309$	1.14540e13	0.231306
$310$	8.15558e13	1.61795
$311$	−6.84643e13	−1.33439	−0.667194	−	0.744884i	$-0.732505\pi$
$311$	−6.84643e13	−1.33439	−0.667194	+	0.744884i	$0.732505\pi$
$312$	−5.21367e11	−0.00998374
$313$	1.48075e13	0.278603	0.139302	−	0.990250i	$-0.455514\pi$
$313$	1.48075e13	0.278603	0.139302	+	0.990250i	$0.455514\pi$
$314$	1.08243e14	2.00119
$315$	−3.15188e13	−0.572614
$316$	4.81732e13	0.860055
$317$	8.34508e13	1.46421	0.732107	−	0.681190i	$-0.238537\pi$
$317$	8.34508e13	1.46421	0.732107	+	0.681190i	$0.238537\pi$
$318$	−5.69710e13	−0.982437
$319$	−2.89265e13	−0.490284
$320$	5.54589e13	0.923946
$321$	−1.69819e13	−0.278105
$322$	−2.96564e14	−4.77431
$323$	9.38503e13	1.48533
$324$	7.22572e12	0.112430
$325$	1.24330e13	0.190203
$326$	4.07288e13	0.612639
$327$	2.13730e12	0.0316121
$328$	1.85715e12	0.0270110
$329$	5.20196e12	0.0744029
$330$	8.88210e13	1.24936
$331$	−4.81979e13	−0.666767	−0.333383	−	0.942791i	$-0.608190\pi$
$331$	−4.81979e13	−0.666767	−0.333383	+	0.942791i	$0.608190\pi$
$332$	1.79793e13	0.244633
$333$	3.66176e13	0.490057
$334$	1.00642e14	1.32487
$335$	5.11911e13	0.662901
$336$	8.52168e13	1.08557
$337$	7.78671e13	0.975865	0.487932	−	0.872881i	$-0.337751\pi$
$337$	7.78671e13	0.975865	0.487932	+	0.872881i	$0.337751\pi$
$338$	−6.24605e12	−0.0770130
$339$	4.34741e12	0.0527391
$340$	−7.97979e13	−0.952484
$341$	−1.81859e14	−2.13592
$342$	−5.82676e13	−0.673417
$343$	2.71403e14	3.08671
$344$	4.55630e11	0.00509965
$345$	8.36759e13	0.921713
$346$	1.05262e14	1.14118
$347$	−9.04895e13	−0.965575	−0.482788	−	0.875737i	$-0.660376\pi$
$347$	−9.04895e13	−0.965575	−0.482788	+	0.875737i	$0.660376\pi$
$348$	−1.61348e13	−0.169464
$349$	7.98190e13	0.825214	0.412607	−	0.910909i	$-0.364618\pi$
$349$	7.98190e13	0.825214	0.412607	+	0.910909i	$0.364618\pi$
$350$	4.91338e13	0.500042
$351$	1.97237e13	0.197606
$352$	−2.43029e14	−2.39703
$353$	5.16894e13	0.501927	0.250964	−	0.967996i	$-0.419253\pi$
$353$	5.16894e13	0.501927	0.250964	+	0.967996i	$0.419253\pi$
$354$	−1.11515e13	−0.106614
$355$	1.10712e14	1.04217
$356$	1.63310e14	1.51369
$357$	−1.25545e14	−1.14584
$358$	1.43097e14	1.28609
$359$	1.14657e14	1.01480	0.507399	−	0.861711i	$-0.330607\pi$
$359$	1.14657e14	1.01480	0.507399	+	0.861711i	$0.330607\pi$
$360$	5.81339e11	0.00506718
$361$	1.19829e14	1.02866
$362$	−1.25673e14	−1.06254
$363$	−1.28729e14	−1.07199
$364$	−2.41065e14	−1.97732
$365$	1.12884e14	0.912054
$366$	1.76356e14	1.40360
$367$	−2.83999e12	−0.0222666	−0.0111333	−	0.999938i	$-0.503544\pi$
$367$	−2.83999e12	−0.0222666	−0.0111333	+	0.999938i	$0.503544\pi$
$368$	−2.26233e14	−1.74740
$369$	−7.02573e13	−0.534621
$370$	2.51068e14	1.88227
$371$	−3.09094e14	−2.28315
$372$	−1.01438e14	−0.738272
$373$	−7.99288e13	−0.573198	−0.286599	−	0.958051i	$-0.592525\pi$
$373$	−7.99288e13	−0.573198	−0.286599	+	0.958051i	$0.592525\pi$
$374$	3.53790e14	2.50007
$375$	−8.87018e13	−0.617676
$376$	−9.59460e10	−0.000658406 0
$377$	−4.40424e13	−0.297847
$378$	7.79457e13	0.519502
$379$	−1.32898e14	−0.872974	−0.436487	−	0.899711i	$-0.643778\pi$
$379$	−1.32898e14	−0.872974	−0.436487	+	0.899711i	$0.643778\pi$
$380$	−2.00935e14	−1.30090
$381$	9.99258e12	0.0637662
$382$	6.46944e13	0.406928
$383$	−3.98305e13	−0.246958	−0.123479	−	0.992347i	$-0.539405\pi$
$383$	−3.98305e13	−0.246958	−0.123479	+	0.992347i	$0.539405\pi$
$384$	−3.18151e12	−0.0194452
$385$	4.81895e14	2.90348
$386$	−2.43968e14	−1.44912
$387$	−1.72368e13	−0.100936
$388$	−1.34813e14	−0.778316
$389$	1.63688e14	0.931736	0.465868	−	0.884854i	$-0.345742\pi$
$389$	1.63688e14	0.931736	0.465868	+	0.884854i	$0.345742\pi$
$390$	1.35236e14	0.758989
$391$	3.33296e14	1.84441
$392$	−8.09216e12	−0.0441561
$393$	1.78976e14	0.963022
$394$	1.51377e14	0.803214
$395$	−1.46622e14	−0.767211
$396$	−1.10475e14	−0.570085
$397$	2.15879e13	0.109866	0.0549328	−	0.998490i	$-0.482506\pi$
$397$	2.15879e13	0.109866	0.0549328	+	0.998490i	$0.482506\pi$
$398$	8.03505e13	0.403303
$399$	−3.16129e14	−1.56500
$400$	3.74816e13	0.183015
$401$	6.97618e13	0.335988	0.167994	−	0.985788i	$-0.446271\pi$
$401$	6.97618e13	0.335988	0.167994	+	0.985788i	$0.446271\pi$
$402$	−1.26595e14	−0.601414
$403$	−2.76891e14	−1.29757
$404$	−1.78057e14	−0.823115
$405$	−2.19925e13	−0.100293
$406$	−1.74050e14	−0.783036
$407$	−5.59850e14	−2.48486
$408$	2.31558e12	0.0101398
$409$	−1.49949e14	−0.647838	−0.323919	−	0.946085i	$-0.605001\pi$
$409$	−1.49949e14	−0.647838	−0.323919	+	0.946085i	$0.605001\pi$
$410$	−4.81719e14	−2.05344
$411$	1.25275e14	0.526906
$412$	−9.76805e13	−0.405390
$413$	−6.05018e13	−0.247767
$414$	−2.06930e14	−0.836220
$415$	−5.47227e13	−0.218224
$416$	−3.70027e14	−1.45620
$417$	−7.90996e13	−0.307203
$418$	8.90860e14	3.41460
$419$	−8.76706e13	−0.331647	−0.165824	−	0.986155i	$-0.553028\pi$
$419$	−8.76706e13	−0.331647	−0.165824	+	0.986155i	$0.553028\pi$
$420$	2.68794e14	1.00357
$421$	1.73321e14	0.638705	0.319352	−	0.947636i	$-0.396535\pi$
$421$	1.73321e14	0.638705	0.319352	+	0.947636i	$0.396535\pi$
$422$	2.63761e14	0.959384
$423$	3.62971e12	0.0130317
$424$	5.70099e12	0.0202040
$425$	−5.52196e13	−0.193176
$426$	−2.73789e14	−0.945505
$427$	9.56812e14	3.26192
$428$	1.44823e14	0.487411
$429$	−3.01558e14	−1.00197
$430$	−1.18184e14	−0.387688
$431$	1.13774e14	0.368484	0.184242	−	0.982881i	$-0.441017\pi$
$431$	1.13774e14	0.368484	0.184242	+	0.982881i	$0.441017\pi$
$432$	5.94606e13	0.190138
$433$	2.00411e14	0.632758	0.316379	−	0.948633i	$-0.397533\pi$
$433$	2.00411e14	0.632758	0.316379	+	0.948633i	$0.397533\pi$
$434$	−1.09424e15	−3.41130
$435$	4.91086e13	0.151170
$436$	−1.82270e13	−0.0554039
$437$	8.39256e14	2.51911
$438$	−2.79160e14	−0.827458
$439$	−4.94116e14	−1.44635	−0.723176	−	0.690664i	$-0.757318\pi$
$439$	−4.94116e14	−1.44635	−0.723176	+	0.690664i	$0.757318\pi$
$440$	−8.88816e12	−0.0256934
$441$	3.06132e14	0.873971
$442$	5.38668e14	1.51879
$443$	−1.92652e14	−0.536479	−0.268240	−	0.963352i	$-0.586442\pi$
$443$	−1.92652e14	−0.536479	−0.268240	+	0.963352i	$0.586442\pi$
$444$	−3.12277e14	−0.858882
$445$	−4.97057e14	−1.35029
$446$	−6.12207e14	−1.64269
$447$	−2.82528e14	−0.748806
$448$	−7.44098e14	−1.94805
$449$	7.18393e14	1.85783	0.928917	−	0.370287i	$-0.120741\pi$
$449$	7.18393e14	1.85783	0.928917	+	0.370287i	$0.120741\pi$
$450$	3.42835e13	0.0875823
$451$	1.07417e15	2.71083
$452$	−3.70750e13	−0.0924314
$453$	−1.92905e14	−0.475119
$454$	−6.30932e14	−1.53524
$455$	7.33715e14	1.76386
$456$	5.83074e12	0.0138490
$457$	2.86012e14	0.671189	0.335595	−	0.942006i	$-0.391063\pi$
$457$	2.86012e14	0.671189	0.335595	+	0.942006i	$0.391063\pi$
$458$	3.14846e14	0.730026
$459$	−8.76001e13	−0.200694
$460$	−7.13593e14	−1.61541
$461$	−2.80949e14	−0.628451	−0.314226	−	0.949348i	$-0.601745\pi$
$461$	−2.80949e14	−0.628451	−0.314226	+	0.949348i	$0.601745\pi$
$462$	−1.19172e15	−2.63417
$463$	−5.41341e14	−1.18243	−0.591215	−	0.806514i	$-0.701352\pi$
$463$	−5.41341e14	−1.18243	−0.591215	+	0.806514i	$0.701352\pi$
$464$	−1.32774e14	−0.286591
$465$	3.08742e14	0.658574
$466$	−8.87253e14	−1.87036
$467$	−3.33665e14	−0.695133	−0.347567	−	0.937655i	$-0.612992\pi$
$467$	−3.33665e14	−0.695133	−0.347567	+	0.937655i	$0.612992\pi$
$468$	−1.68205e14	−0.346327
$469$	−6.86837e14	−1.39766
$470$	2.48871e13	0.0500536
$471$	4.09772e14	0.814567
$472$	1.11591e12	0.00219254
$473$	2.63536e14	0.511803
$474$	3.62594e14	0.696049
$475$	−1.39045e14	−0.263841
$476$	1.07066e15	2.00822
$477$	−2.15673e14	−0.399893
$478$	1.47480e14	0.270321
$479$	6.72462e14	1.21849	0.609245	−	0.792982i	$-0.291473\pi$
$479$	6.72462e14	1.21849	0.609245	+	0.792982i	$0.291473\pi$
$480$	4.12591e14	0.739083
$481$	−8.52407e14	−1.50956
$482$	2.78530e14	0.487655
$483$	−1.12269e15	−1.94335
$484$	1.09781e15	1.87878
$485$	4.10321e14	0.694295
$486$	5.43872e13	0.0909907
$487$	−2.16358e14	−0.357901	−0.178950	−	0.983858i	$-0.557270\pi$
$487$	−2.16358e14	−0.357901	−0.178950	+	0.983858i	$0.557270\pi$
$488$	−1.76476e13	−0.0288654
$489$	1.54185e14	0.249370
$490$	2.09900e15	3.35686
$491$	5.66577e14	0.896006	0.448003	−	0.894032i	$-0.352135\pi$
$491$	5.66577e14	0.896006	0.448003	+	0.894032i	$0.352135\pi$
$492$	5.99158e14	0.936986
$493$	1.95608e14	0.302503
$494$	1.35639e15	2.07437
$495$	3.36246e14	0.508544
$496$	−8.34739e14	−1.24854
$497$	−1.48543e15	−2.19732
$498$	1.35329e14	0.197983
$499$	−4.60728e14	−0.666641	−0.333320	−	0.942814i	$-0.608169\pi$
$499$	−4.60728e14	−0.666641	−0.333320	+	0.942814i	$0.608169\pi$
$500$	7.56454e14	1.08255
$501$	3.80996e14	0.539278
$502$	−5.23414e14	−0.732782
$503$	5.36485e14	0.742906	0.371453	−	0.928452i	$-0.378860\pi$
$503$	5.36485e14	0.742906	0.371453	+	0.928452i	$0.378860\pi$
$504$	−7.79989e12	−0.0106837
$505$	5.41940e14	0.734258
$506$	3.16377e15	4.24011
$507$	−2.36454e13	−0.0313475
$508$	−8.52173e13	−0.111758
$509$	1.27284e15	1.65131	0.825653	−	0.564179i	$-0.190807\pi$
$509$	1.27284e15	1.65131	0.825653	+	0.564179i	$0.190807\pi$
$510$	−6.00630e14	−0.770852
$511$	−1.51457e15	−1.92298
$512$	−1.12876e15	−1.41781
$513$	−2.20581e14	−0.274109
$514$	−8.62956e14	−1.06094
$515$	2.97304e14	0.361628
$516$	1.46996e14	0.176902
$517$	−5.54950e13	−0.0660778
$518$	−3.36861e15	−3.96860
$519$	3.98486e14	0.464507
$520$	−1.35328e13	−0.0156088
$521$	4.23962e14	0.483860	0.241930	−	0.970294i	$-0.422220\pi$
$521$	4.23962e14	0.483860	0.241930	+	0.970294i	$0.422220\pi$
$522$	−1.21445e14	−0.137149
$523$	1.41638e15	1.58278	0.791390	−	0.611312i	$-0.209358\pi$
$523$	1.41638e15	1.58278	0.791390	+	0.611312i	$0.209358\pi$
$524$	−1.52632e15	−1.68781
$525$	1.86004e14	0.203538
$526$	−1.48366e15	−1.60662
$527$	1.22978e15	1.31785
$528$	−9.09100e14	−0.964106
$529$	2.02769e15	2.12812
$530$	−1.47876e15	−1.53596
$531$	−4.22156e13	−0.0433963
$532$	2.69596e15	2.74284
$533$	1.63549e15	1.64683
$534$	1.22922e15	1.22504
$535$	−4.40788e14	−0.434795
$536$	1.26681e13	0.0123682
$537$	5.41714e14	0.523494
$538$	−1.83570e15	−1.75590
$539$	−4.68049e15	−4.43152
$540$	1.87553e14	0.175776
$541$	3.05136e14	0.283079	0.141540	−	0.989933i	$-0.454795\pi$
$541$	3.05136e14	0.283079	0.141540	+	0.989933i	$0.454795\pi$
$542$	5.10788e14	0.469077
$543$	−4.75756e14	−0.432499
$544$	1.64343e15	1.47896
$545$	5.54766e13	0.0494230
$546$	−1.81447e15	−1.60026
$547$	−5.80672e14	−0.506991	−0.253496	−	0.967337i	$-0.581580\pi$
$547$	−5.80672e14	−0.506991	−0.253496	+	0.967337i	$0.581580\pi$
$548$	−1.06835e15	−0.923464
$549$	6.67623e14	0.571325
$550$	−5.24164e14	−0.444091
$551$	4.92551e14	0.413159
$552$	2.07071e13	0.0171970
$553$	1.96724e15	1.61759
$554$	8.30569e14	0.676195
$555$	9.50458e14	0.766164
$556$	6.74566e14	0.538410
$557$	1.27295e15	1.00602	0.503011	−	0.864280i	$-0.332225\pi$
$557$	1.27295e15	1.00602	0.503011	+	0.864280i	$0.332225\pi$
$558$	−7.63515e14	−0.597489
$559$	4.01249e14	0.310920
$560$	2.21191e15	1.69720
$561$	1.33933e15	1.01763
$562$	−1.24334e15	−0.935490
$563$	1.15682e15	0.861923	0.430961	−	0.902370i	$-0.358175\pi$
$563$	1.15682e15	0.861923	0.430961	+	0.902370i	$0.358175\pi$
$564$	−3.09543e13	−0.0228395
$565$	1.12843e14	0.0824532
$566$	−3.65671e15	−2.64606
$567$	2.95076e14	0.211459
$568$	2.73976e13	0.0194445
$569$	2.09256e15	1.47082	0.735412	−	0.677620i	$-0.236989\pi$
$569$	2.09256e15	1.47082	0.735412	+	0.677620i	$0.236989\pi$
$570$	−1.51241e15	−1.05283
$571$	−2.47949e14	−0.170948	−0.0854740	−	0.996340i	$-0.527240\pi$
$571$	−2.47949e14	−0.170948	−0.0854740	+	0.996340i	$0.527240\pi$
$572$	2.57170e15	1.75607
$573$	2.44910e14	0.165637
$574$	6.46327e15	4.32949
$575$	−4.93801e14	−0.327626
$576$	−5.19200e14	−0.341201
$577$	3.09646e14	0.201557	0.100778	−	0.994909i	$-0.467867\pi$
$577$	3.09646e14	0.201557	0.100778	+	0.994909i	$0.467867\pi$
$578$	−1.92517e14	−0.124127
$579$	−9.23579e14	−0.589851
$580$	−4.18800e14	−0.264943
$581$	7.34220e14	0.460105
$582$	−1.01472e15	−0.629897
$583$	3.29744e15	2.02768
$584$	2.79350e13	0.0170168
$585$	5.11955e14	0.308940
$586$	2.86547e15	1.71301
$587$	−2.08360e15	−1.23397	−0.616986	−	0.786974i	$-0.711647\pi$
$587$	−2.08360e15	−1.23397	−0.616986	+	0.786974i	$0.711647\pi$
$588$	−2.61071e15	−1.53174
$589$	3.09663e15	1.79993
$590$	−2.89451e14	−0.166682
$591$	5.73062e14	0.326942
$592$	−2.56973e15	−1.45251
$593$	2.43608e15	1.36424	0.682119	−	0.731241i	$-0.261059\pi$
$593$	2.43608e15	1.36424	0.682119	+	0.731241i	$0.261059\pi$
$594$	−8.31532e14	−0.461374
$595$	−3.25870e15	−1.79143
$596$	2.40941e15	1.31237
$597$	3.04179e14	0.164161
$598$	4.81703e15	2.57586
$599$	−6.60050e14	−0.349727	−0.174863	−	0.984593i	$-0.555948\pi$
$599$	−6.60050e14	−0.349727	−0.174863	+	0.984593i	$0.555948\pi$
$600$	−3.43069e12	−0.00180115
$601$	3.71095e14	0.193052	0.0965261	−	0.995330i	$-0.469227\pi$
$601$	3.71095e14	0.193052	0.0965261	+	0.995330i	$0.469227\pi$
$602$	1.58569e15	0.817405
$603$	−4.79245e14	−0.244801
$604$	1.64510e15	0.832701
$605$	−3.34133e15	−1.67596
$606$	−1.34021e15	−0.666153
$607$	−2.04336e15	−1.00648	−0.503242	−	0.864146i	$-0.667859\pi$
$607$	−2.04336e15	−1.00648	−0.503242	+	0.864146i	$0.667859\pi$
$608$	4.13822e15	2.01997
$609$	−6.58895e14	−0.318728
$610$	4.57755e15	2.19442
$611$	−8.44945e13	−0.0401423
$612$	7.47059e14	0.351740
$613$	−2.66338e15	−1.24280	−0.621399	−	0.783494i	$-0.713435\pi$
$613$	−2.66338e15	−1.24280	−0.621399	+	0.783494i	$0.713435\pi$
$614$	−4.27877e15	−1.97876
$615$	−1.82362e15	−0.835837
$616$	1.19253e14	0.0541722
$617$	−3.42504e15	−1.54205	−0.771024	−	0.636806i	$-0.780255\pi$
$617$	−3.42504e15	−1.54205	−0.771024	+	0.636806i	$0.780255\pi$
$618$	−7.35230e14	−0.328085
$619$	3.05390e15	1.35069	0.675347	−	0.737500i	$-0.263994\pi$
$619$	3.05390e15	1.35069	0.675347	+	0.737500i	$0.263994\pi$
$620$	−2.63297e15	−1.15423
$621$	−7.83364e14	−0.340377
$622$	4.39470e15	1.89270
$623$	6.66906e15	2.84696
$624$	−1.38416e15	−0.585695
$625$	−1.86073e15	−0.780445
$626$	−9.50486e14	−0.395173
$627$	3.37249e15	1.38989
$628$	−3.49455e15	−1.42762
$629$	3.78585e15	1.53315
$630$	2.02319e15	0.812199
$631$	2.34415e15	0.932877	0.466438	−	0.884554i	$-0.345537\pi$
$631$	2.34415e15	0.932877	0.466438	+	0.884554i	$0.345537\pi$
$632$	−3.62841e13	−0.0143144
$633$	9.98509e14	0.390509
$634$	−5.35668e15	−2.07685
$635$	2.59371e14	0.0996932
$636$	1.83927e15	0.700859
$637$	−7.12633e15	−2.69215
$638$	1.85678e15	0.695421
$639$	−1.03647e15	−0.384860
$640$	−8.25803e13	−0.0304009
$641$	1.76636e14	0.0644703	0.0322351	−	0.999480i	$-0.489737\pi$
$641$	1.76636e14	0.0644703	0.0322351	+	0.999480i	$0.489737\pi$
$642$	1.09006e15	0.394466
$643$	5.68123e14	0.203837	0.101918	−	0.994793i	$-0.467502\pi$
$643$	5.68123e14	0.203837	0.101918	+	0.994793i	$0.467502\pi$
$644$	9.57434e15	3.40594
$645$	−4.47405e14	−0.157805
$646$	−6.02422e15	−2.10679
$647$	−4.50332e15	−1.56156	−0.780782	−	0.624804i	$-0.785179\pi$
$647$	−4.50332e15	−1.56156	−0.780782	+	0.624804i	$0.785179\pi$
$648$	−5.44243e12	−0.00187124
$649$	6.45438e14	0.220044
$650$	−7.98072e14	−0.269785
$651$	−4.14242e15	−1.38854
$652$	−1.31490e15	−0.437049
$653$	1.31034e15	0.431879	0.215939	−	0.976407i	$-0.430719\pi$
$653$	1.31034e15	0.431879	0.215939	+	0.976407i	$0.430719\pi$
$654$	−1.37193e14	−0.0448388
$655$	4.64557e15	1.50561
$656$	4.93048e15	1.58459
$657$	−1.05680e15	−0.336810
$658$	−3.33912e14	−0.105533
$659$	−4.17876e15	−1.30972	−0.654858	−	0.755752i	$-0.727272\pi$
$659$	−4.17876e15	−1.30972	−0.654858	+	0.755752i	$0.727272\pi$
$660$	−2.86752e15	−0.891282
$661$	−9.57421e14	−0.295117	−0.147559	−	0.989053i	$-0.547142\pi$
$661$	−9.57421e14	−0.295117	−0.147559	+	0.989053i	$0.547142\pi$
$662$	3.09381e15	0.945745
$663$	2.03921e15	0.618212
$664$	−1.35421e13	−0.00407156
$665$	−8.20554e15	−2.44674
$666$	−2.35047e15	−0.695099
$667$	1.74923e15	0.513043
$668$	−3.24915e15	−0.945147
$669$	−2.31761e15	−0.668645
$670$	−3.28594e15	−0.940262
$671$	−1.02074e16	−2.89694
$672$	−5.53577e15	−1.55829
$673$	4.38576e15	1.22451	0.612255	−	0.790660i	$-0.290263\pi$
$673$	4.38576e15	1.22451	0.612255	+	0.790660i	$0.290263\pi$
$674$	−4.99827e15	−1.38417
$675$	1.29785e14	0.0356496
$676$	2.01649e14	0.0549401
$677$	1.46162e15	0.395001	0.197500	−	0.980303i	$-0.436718\pi$
$677$	1.46162e15	0.395001	0.197500	+	0.980303i	$0.436718\pi$
$678$	−2.79059e14	−0.0748054
$679$	−5.50532e15	−1.46386
$680$	6.01040e13	0.0158527
$681$	−2.38849e15	−0.624906
$682$	1.16735e16	3.02960
$683$	7.08973e14	0.182522	0.0912612	−	0.995827i	$-0.470910\pi$
$683$	7.08973e14	0.182522	0.0912612	+	0.995827i	$0.470910\pi$
$684$	1.88113e15	0.480407
$685$	3.25167e15	0.823775
$686$	−1.74212e16	−4.37821
$687$	1.19190e15	0.297151
$688$	1.20964e15	0.299170
$689$	5.02056e15	1.23182
$690$	−5.37113e15	−1.30736
$691$	−6.30474e15	−1.52243	−0.761216	−	0.648499i	$-0.775397\pi$
$691$	−6.30474e15	−1.52243	−0.761216	+	0.648499i	$0.775397\pi$
$692$	−3.39831e15	−0.814102
$693$	−4.51144e15	−1.07222
$694$	5.80849e15	1.36958
$695$	−2.05314e15	−0.480288
$696$	1.21528e13	0.00282049
$697$	−7.26382e15	−1.67257
$698$	−5.12356e15	−1.17049
$699$	−3.35883e15	−0.761314
$700$	−1.58625e15	−0.356724
$701$	3.31122e15	0.738820	0.369410	−	0.929267i	$-0.379560\pi$
$701$	3.31122e15	0.738820	0.369410	+	0.929267i	$0.379560\pi$
$702$	−1.26606e15	−0.280285
$703$	9.53294e15	2.09398
$704$	7.93810e15	1.73008
$705$	9.42139e13	0.0203739
$706$	−3.31793e15	−0.711937
$707$	−7.27127e15	−1.54812
$708$	3.60017e14	0.0760571
$709$	2.87126e15	0.601892	0.300946	−	0.953641i	$-0.402698\pi$
$709$	2.87126e15	0.601892	0.300946	+	0.953641i	$0.402698\pi$
$710$	−7.10657e15	−1.47822
$711$	1.37266e15	0.283321
$712$	−1.23005e14	−0.0251933
$713$	1.09973e16	2.23508
$714$	8.05871e15	1.62527
$715$	−7.82733e15	−1.56650
$716$	−4.61977e15	−0.917484
$717$	5.58308e14	0.110032
$718$	−7.35978e15	−1.43940
$719$	7.29124e14	0.141512	0.0707558	−	0.997494i	$-0.477459\pi$
$719$	7.29124e14	0.141512	0.0707558	+	0.997494i	$0.477459\pi$
$720$	1.54338e15	0.297265
$721$	−3.98896e15	−0.762458
$722$	−7.69179e15	−1.45906
$723$	1.05442e15	0.198496
$724$	4.05727e15	0.758005
$725$	−2.89807e14	−0.0537340
$726$	8.26306e15	1.52051
$727$	3.25997e15	0.595352	0.297676	−	0.954667i	$-0.403788\pi$
$727$	3.25997e15	0.595352	0.297676	+	0.954667i	$0.403788\pi$
$728$	1.81571e14	0.0329096
$729$	2.05891e14	0.0370370
$730$	−7.24597e15	−1.29366
$731$	−1.78209e15	−0.315780
$732$	−5.69352e15	−1.00131
$733$	−8.09179e15	−1.41245	−0.706224	−	0.707988i	$-0.749603\pi$
$733$	−8.09179e15	−1.41245	−0.706224	+	0.707988i	$0.749603\pi$
$734$	1.82298e14	0.0315831
$735$	7.94607e15	1.36638
$736$	1.46963e16	2.50831
$737$	7.32723e15	1.24128
$738$	4.50979e15	0.758310
$739$	−3.12675e15	−0.521853	−0.260927	−	0.965359i	$-0.584028\pi$
$739$	−3.12675e15	−0.521853	−0.260927	+	0.965359i	$0.584028\pi$
$740$	−8.10556e15	−1.34279
$741$	5.13482e15	0.844356
$742$	1.98406e16	3.23843
$743$	−2.31503e15	−0.375075	−0.187537	−	0.982257i	$-0.560051\pi$
$743$	−2.31503e15	−0.375075	−0.187537	+	0.982257i	$0.560051\pi$
$744$	7.64036e13	0.0122875
$745$	−7.33338e15	−1.17070
$746$	5.13060e15	0.813027
$747$	5.12307e14	0.0805874
$748$	−1.14219e16	−1.78352
$749$	5.91410e15	0.916724
$750$	5.69374e15	0.876115
$751$	9.42887e15	1.44026	0.720129	−	0.693840i	$-0.244083\pi$
$751$	9.42887e15	1.44026	0.720129	+	0.693840i	$0.244083\pi$
$752$	−2.54724e14	−0.0386253
$753$	−1.98147e15	−0.298273
$754$	2.82707e15	0.422468
$755$	−5.00710e15	−0.742810
$756$	−2.51642e15	−0.370607
$757$	1.92231e15	0.281058	0.140529	−	0.990077i	$-0.455120\pi$
$757$	1.92231e15	0.281058	0.140529	+	0.990077i	$0.455120\pi$
$758$	8.53065e15	1.23823
$759$	1.19769e16	1.72590
$760$	1.51345e14	0.0216517
$761$	−5.23339e15	−0.743306	−0.371653	−	0.928372i	$-0.621209\pi$
$761$	−5.23339e15	−0.743306	−0.371653	+	0.928372i	$0.621209\pi$
$762$	−6.41421e14	−0.0904463
$763$	−7.44335e14	−0.104204
$764$	−2.08861e15	−0.290298
$765$	−2.27378e15	−0.313769
$766$	2.55671e15	0.350286
$767$	9.82720e14	0.133677
$768$	−4.17159e15	−0.563397
$769$	−2.22888e15	−0.298877	−0.149438	−	0.988771i	$-0.547747\pi$
$769$	−2.22888e15	−0.298877	−0.149438	+	0.988771i	$0.547747\pi$
$770$	−3.09327e16	−4.11831
$771$	−3.26685e15	−0.431848
$772$	7.87633e15	1.03378
$773$	−6.35866e15	−0.828664	−0.414332	−	0.910126i	$-0.635985\pi$
$773$	−6.35866e15	−0.828664	−0.414332	+	0.910126i	$0.635985\pi$
$774$	1.10643e15	0.143168
$775$	−1.82199e15	−0.234093
$776$	1.01541e14	0.0129540
$777$	−1.27524e16	−1.61539
$778$	−1.05071e16	−1.32158
$779$	−1.82906e16	−2.28440
$780$	−4.36598e15	−0.541454
$781$	1.58467e16	1.95146
$782$	−2.13942e16	−2.61613
$783$	−4.59748e14	−0.0558252
$784$	−2.14836e16	−2.59041
$785$	1.06362e16	1.27351
$786$	−1.14884e16	−1.36596
$787$	−4.68159e15	−0.552755	−0.276378	−	0.961049i	$-0.589134\pi$
$787$	−4.68159e15	−0.552755	−0.276378	+	0.961049i	$0.589134\pi$
$788$	−4.88710e15	−0.573003
$789$	−5.61664e15	−0.653962
$790$	9.41162e15	1.08822
$791$	−1.51402e15	−0.173845
$792$	8.32099e13	0.00948826
$793$	−1.55413e16	−1.75989
$794$	−1.38572e15	−0.155834
$795$	−5.59807e15	−0.625200
$796$	−2.59406e15	−0.287712
$797$	9.28783e15	1.02304	0.511521	−	0.859271i	$-0.329082\pi$
$797$	9.28783e15	1.02304	0.511521	+	0.859271i	$0.329082\pi$
$798$	2.02922e16	2.21980
$799$	3.75271e14	0.0407697
$800$	−2.43484e15	−0.262710
$801$	4.65339e15	0.498644
$802$	−4.47799e15	−0.476567
$803$	1.61576e16	1.70782
$804$	4.08703e15	0.429042
$805$	−2.91409e16	−3.03826
$806$	1.77736e16	1.84048
$807$	−6.94933e15	−0.714725
$808$	1.34113e14	0.0136996
$809$	6.57580e15	0.667163	0.333581	−	0.942721i	$-0.391743\pi$
$809$	6.57580e15	0.667163	0.333581	+	0.942721i	$0.391743\pi$
$810$	1.41169e15	0.142257
$811$	8.94290e15	0.895084	0.447542	−	0.894263i	$-0.352299\pi$
$811$	8.94290e15	0.895084	0.447542	+	0.894263i	$0.352299\pi$
$812$	5.61909e15	0.558609
$813$	1.93367e15	0.190934
$814$	3.59366e16	3.52454
$815$	4.00208e15	0.389869
$816$	6.14756e15	0.594849
$817$	−4.48739e15	−0.431293
$818$	9.62521e15	0.918897
$819$	−6.86895e15	−0.651372
$820$	1.55519e16	1.46490
$821$	−6.28129e15	−0.587708	−0.293854	−	0.955850i	$-0.594938\pi$
$821$	−6.28129e15	−0.587708	−0.293854	+	0.955850i	$0.594938\pi$
$822$	−8.04134e15	−0.747366
$823$	1.30428e16	1.20413	0.602063	−	0.798449i	$-0.294346\pi$
$823$	1.30428e16	1.20413	0.602063	+	0.798449i	$0.294346\pi$
$824$	7.35731e13	0.00674714
$825$	−1.98430e15	−0.180764
$826$	3.88359e15	0.351434
$827$	3.68427e15	0.331185	0.165593	−	0.986194i	$-0.447046\pi$
$827$	3.68427e15	0.331185	0.165593	+	0.986194i	$0.447046\pi$
$828$	6.68057e15	0.596550
$829$	8.52482e15	0.756198	0.378099	−	0.925765i	$-0.376578\pi$
$829$	8.52482e15	0.756198	0.378099	+	0.925765i	$0.376578\pi$
$830$	3.51263e15	0.309530
$831$	3.14425e15	0.275240
$832$	1.20862e16	1.05103
$833$	3.16506e16	2.73423
$834$	5.07738e15	0.435739
$835$	9.88925e15	0.843117
$836$	−2.87608e16	−2.43594
$837$	−2.89041e15	−0.243203
$838$	5.62755e15	0.470410
$839$	1.13665e16	0.943920	0.471960	−	0.881620i	$-0.343547\pi$
$839$	1.13665e16	0.943920	0.471960	+	0.881620i	$0.343547\pi$
$840$	−2.02456e14	−0.0167030
$841$	−1.11739e16	−0.915856
$842$	−1.11254e16	−0.905942
$843$	−4.70684e15	−0.380784
$844$	−8.51534e15	−0.684413
$845$	−6.13748e14	−0.0490093
$846$	−2.32990e14	−0.0184842
$847$	4.48309e16	3.53361
$848$	1.51354e16	1.18527
$849$	−1.38430e16	−1.07706
$850$	3.54453e15	0.274002
$851$	3.38549e16	2.60022
$852$	8.83909e15	0.674512
$853$	−2.38523e16	−1.80847	−0.904235	−	0.427035i	$-0.859558\pi$
$853$	−2.38523e16	−1.80847	−0.904235	+	0.427035i	$0.859558\pi$
$854$	−6.14175e16	−4.62672
$855$	−5.72548e15	−0.428547
$856$	−1.09081e14	−0.00811227
$857$	−1.55491e16	−1.14897	−0.574486	−	0.818514i	$-0.694798\pi$
$857$	−1.55491e16	−1.14897	−0.574486	+	0.818514i	$0.694798\pi$
$858$	1.93569e16	1.42120
$859$	2.58000e16	1.88216	0.941080	−	0.338184i	$-0.109813\pi$
$859$	2.58000e16	1.88216	0.941080	+	0.338184i	$0.109813\pi$
$860$	3.81549e15	0.276572
$861$	2.44677e16	1.76228
$862$	−7.30313e15	−0.522660
$863$	6.23324e15	0.443256	0.221628	−	0.975131i	$-0.428863\pi$
$863$	6.23324e15	0.443256	0.221628	+	0.975131i	$0.428863\pi$
$864$	−3.86263e15	−0.272934
$865$	1.03432e16	0.726219
$866$	−1.28643e16	−0.897507
$867$	−7.28802e14	−0.0505248
$868$	3.53268e16	2.43358
$869$	−2.09867e16	−1.43660
$870$	−3.15226e15	−0.214421
$871$	1.11562e16	0.754076
$872$	1.37286e13	0.000922119 0
$873$	−3.84138e15	−0.256394
$874$	−5.38716e16	−3.57311
$875$	3.08912e16	2.03606
$876$	9.01248e15	0.590298
$877$	2.58853e16	1.68483	0.842413	−	0.538832i	$-0.181134\pi$
$877$	2.58853e16	1.68483	0.842413	+	0.538832i	$0.181134\pi$
$878$	3.17171e16	2.05151
$879$	1.08477e16	0.697265
$880$	−2.35969e16	−1.50730
$881$	−1.51066e16	−0.958955	−0.479478	−	0.877554i	$-0.659174\pi$
$881$	−1.51066e16	−0.958955	−0.479478	+	0.877554i	$0.659174\pi$
$882$	−1.96505e16	−1.23964
$883$	1.59585e16	1.00048	0.500240	−	0.865887i	$-0.333245\pi$
$883$	1.59585e16	1.00048	0.500240	+	0.865887i	$0.333245\pi$
$884$	−1.73905e16	−1.08349
$885$	−1.09576e15	−0.0678466
$886$	1.23663e16	0.760945
$887$	7.58241e15	0.463690	0.231845	−	0.972753i	$-0.425524\pi$
$887$	7.58241e15	0.463690	0.231845	+	0.972753i	$0.425524\pi$
$888$	2.35208e14	0.0142949
$889$	−3.48000e15	−0.210194
$890$	3.19059e16	1.91525
$891$	−3.14789e15	−0.187799
$892$	1.97647e16	1.17188
$893$	9.44950e14	0.0556834
$894$	1.81354e16	1.06211
$895$	1.40609e16	0.818440
$896$	1.10799e15	0.0640975
$897$	1.82356e16	1.04848
$898$	−4.61134e16	−2.63516
$899$	6.45419e15	0.366575
$900$	−1.10682e15	−0.0624801
$901$	−2.22981e16	−1.25107
$902$	−6.89507e16	−3.84506
$903$	6.00287e15	0.332718
$904$	2.79249e13	0.00153839
$905$	−1.23489e16	−0.676177
$906$	1.23825e16	0.673911
$907$	1.27789e16	0.691279	0.345639	−	0.938367i	$-0.387662\pi$
$907$	1.27789e16	0.691279	0.345639	+	0.938367i	$0.387662\pi$
$908$	2.03692e16	1.09522
$909$	−5.07358e15	−0.271152
$910$	−4.70969e16	−2.50187
$911$	−2.17665e16	−1.14931	−0.574655	−	0.818396i	$-0.694864\pi$
$911$	−2.17665e16	−1.14931	−0.574655	+	0.818396i	$0.694864\pi$
$912$	1.54798e16	0.812447
$913$	−7.83272e15	−0.408623
$914$	−1.83590e16	−0.952018
$915$	1.73290e16	0.893220
$916$	−1.01646e16	−0.520792
$917$	−6.23300e16	−3.17443
$918$	5.62303e15	0.284666
$919$	−1.17338e16	−0.590476	−0.295238	−	0.955424i	$-0.595399\pi$
$919$	−1.17338e16	−0.590476	−0.295238	+	0.955424i	$0.595399\pi$
$920$	5.37480e14	0.0268862
$921$	−1.61980e16	−0.805438
$922$	1.80340e16	0.891399
$923$	2.41276e16	1.18551
$924$	3.84738e16	1.87918
$925$	−5.60899e15	−0.272336
$926$	3.47485e16	1.67717
$927$	−2.78333e15	−0.133544
$928$	8.62513e15	0.411388
$929$	3.02918e16	1.43628	0.718138	−	0.695900i	$-0.244995\pi$
$929$	3.02918e16	1.43628	0.718138	+	0.695900i	$0.244995\pi$
$930$	−1.98181e16	−0.934125
$931$	7.96978e16	3.73442
$932$	2.86443e16	1.33429
$933$	1.66368e16	0.770409
$934$	2.14179e16	0.985980
$935$	3.47640e16	1.59099
$936$	1.26692e14	0.00576411
$937$	−4.00930e16	−1.81343	−0.906715	−	0.421743i	$-0.861418\pi$
$937$	−4.00930e16	−1.81343	−0.906715	+	0.421743i	$0.861418\pi$
$938$	4.40878e16	1.98245
$939$	−3.59821e15	−0.160852
$940$	−8.03461e14	−0.0357077
$941$	−1.61072e16	−0.711667	−0.355834	−	0.934549i	$-0.615803\pi$
$941$	−1.61072e16	−0.711667	−0.355834	+	0.934549i	$0.615803\pi$
$942$	−2.63031e16	−1.15539
$943$	−6.49566e16	−2.83667
$944$	2.96258e15	0.128625
$945$	7.65908e15	0.330599
$946$	−1.69163e16	−0.725944
$947$	−1.00119e16	−0.427162	−0.213581	−	0.976925i	$-0.568513\pi$
$947$	−1.00119e16	−0.427162	−0.213581	+	0.976925i	$0.568513\pi$
$948$	−1.17061e16	−0.496553
$949$	2.46009e16	1.03750
$950$	8.92528e15	0.374233
$951$	−2.02785e16	−0.845364
$952$	−8.06421e14	−0.0334240
$953$	7.97340e15	0.328574	0.164287	−	0.986413i	$-0.447468\pi$
$953$	7.97340e15	0.328574	0.164287	+	0.986413i	$0.447468\pi$
$954$	1.38440e16	0.567210
$955$	6.35698e15	0.258960
$956$	−4.76128e15	−0.192844
$957$	7.02914e15	0.283065
$958$	−4.31651e16	−1.72831
$959$	−4.36280e16	−1.73685
$960$	−1.34765e16	−0.533440
$961$	1.51685e16	0.596987
$962$	5.47157e16	2.14116
$963$	4.12660e15	0.160564
$964$	−8.99212e15	−0.347887
$965$	−2.39727e16	−0.922184
$966$	7.20650e16	2.75645
$967$	1.81277e16	0.689440	0.344720	−	0.938706i	$-0.387974\pi$
$967$	1.81277e16	0.689440	0.344720	+	0.938706i	$0.387974\pi$
$968$	−8.26869e14	−0.0312696
$969$	−2.28056e16	−0.857553
$970$	−2.63384e16	−0.984792
$971$	−3.66253e16	−1.36168	−0.680841	−	0.732431i	$-0.738386\pi$
$971$	−3.66253e16	−1.36168	−0.680841	+	0.732431i	$0.738386\pi$
$972$	−1.75585e15	−0.0649117
$973$	2.75471e16	1.01264
$974$	1.38879e16	0.507649
$975$	−3.02122e15	−0.109814
$976$	−4.68521e16	−1.69338
$977$	4.10970e16	1.47703	0.738516	−	0.674236i	$-0.235527\pi$
$977$	4.10970e16	1.47703	0.738516	+	0.674236i	$0.235527\pi$
$978$	−9.89709e15	−0.353707
$979$	−7.11461e16	−2.52840
$980$	−6.77645e16	−2.39474
$981$	−5.19365e14	−0.0182513
$982$	−3.63684e16	−1.27090
$983$	3.22372e16	1.12024	0.560122	−	0.828410i	$-0.310754\pi$
$983$	3.22372e16	1.12024	0.560122	+	0.828410i	$0.310754\pi$
$984$	−4.51287e14	−0.0155948
$985$	1.48746e16	0.511147
$986$	−1.25560e16	−0.429072
$987$	−1.26408e15	−0.0429565
$988$	−4.37900e16	−1.47983
$989$	−1.59364e16	−0.535562
$990$	−2.15835e16	−0.721321
$991$	−5.59817e15	−0.186055	−0.0930274	−	0.995664i	$-0.529654\pi$
$991$	−5.59817e15	−0.186055	−0.0930274	+	0.995664i	$0.529654\pi$
$992$	5.42255e16	1.79221
$993$	1.17121e16	0.384958
$994$	9.53495e16	3.11669
$995$	7.89538e15	0.256653
$996$	−4.36898e15	−0.141239
$997$	−4.95070e16	−1.59163	−0.795817	−	0.605538i	$-0.792958\pi$
$997$	−4.95070e16	−1.59163	−0.795817	+	0.605538i	$0.792958\pi$
$998$	2.95740e16	0.945567
$999$	−8.89808e15	−0.282934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.6	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-64.1897 q^{2} -243.000 q^{3} +2072.32 q^{4} -6307.39 q^{5} +15598.1 q^{6} +84626.9 q^{7} -1560.87 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-64.1897 q^{2} -243.000 q^{3} +2072.32 q^{4} -6307.39 q^{5} +15598.1 q^{6} +84626.9 q^{7} -1560.87 q^{8} +59049.0 q^{9} +404869. q^{10} -902806. q^{11} -503573. q^{12} -1.37458e6 q^{13} -5.43217e6 q^{14} +1.53270e6 q^{15} -4.14391e6 q^{16} +6.10500e6 q^{17} -3.79034e6 q^{18} +1.53727e7 q^{19} -1.30709e7 q^{20} -2.05643e7 q^{21} +5.79509e7 q^{22} +5.45940e7 q^{23} +379292. q^{24} -9.04497e6 q^{25} +8.82338e7 q^{26} -1.43489e7 q^{27} +1.75374e8 q^{28} +3.20407e7 q^{29} -9.83833e7 q^{30} +2.01437e8 q^{31} +2.69193e8 q^{32} +2.19382e8 q^{33} -3.91878e8 q^{34} -5.33774e8 q^{35} +1.22368e8 q^{36} +6.20122e8 q^{37} -9.86768e8 q^{38} +3.34023e8 q^{39} +9.84503e6 q^{40} -1.18981e9 q^{41} +1.32002e9 q^{42} -2.91907e8 q^{43} -1.87090e9 q^{44} -3.72445e8 q^{45} -3.50437e9 q^{46} +6.14694e7 q^{47} +1.00697e9 q^{48} +5.18438e9 q^{49} +5.80594e8 q^{50} -1.48352e9 q^{51} -2.84856e9 q^{52} -3.65243e9 q^{53} +9.21052e8 q^{54} +5.69435e9 q^{55} -1.32092e8 q^{56} -3.73556e9 q^{57} -2.05668e9 q^{58} -7.14924e8 q^{59} +3.17623e9 q^{60} +1.13062e10 q^{61} -1.29302e10 q^{62} +4.99713e9 q^{63} -8.79269e9 q^{64} +8.67000e9 q^{65} -1.40821e10 q^{66} -8.11606e9 q^{67} +1.26515e10 q^{68} -1.32663e10 q^{69} +3.42628e10 q^{70} -1.75527e10 q^{71} -9.21680e7 q^{72} -1.78971e10 q^{73} -3.98055e10 q^{74} +2.19793e9 q^{75} +3.18571e10 q^{76} -7.64017e10 q^{77} -2.14408e10 q^{78} +2.32461e10 q^{79} +2.61373e10 q^{80} +3.48678e9 q^{81} +7.63737e10 q^{82} +8.67597e9 q^{83} -4.26158e10 q^{84} -3.85066e10 q^{85} +1.87374e10 q^{86} -7.78588e9 q^{87} +1.40917e9 q^{88} +7.88055e10 q^{89} +2.39071e10 q^{90} -1.16326e11 q^{91} +1.13136e11 q^{92} -4.89493e10 q^{93} -3.94570e9 q^{94} -9.69615e10 q^{95} -6.54139e10 q^{96} -6.50540e10 q^{97} -3.32784e11 q^{98} -5.33098e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more