LMFDB - Embedded newform 177.12.a.c.1.21

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			1.21
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)

$f(q)$	$=$	$q+52.1944 q^{2} -243.000 q^{3} +676.260 q^{4} -195.395 q^{5} -12683.2 q^{6} -35236.2 q^{7} -71597.2 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+52.1944 q^{2} -243.000 q^{3} +676.260 q^{4} -195.395 q^{5} -12683.2 q^{6} -35236.2 q^{7} -71597.2 q^{8} +59049.0 q^{9} -10198.5 q^{10} -666403. q^{11} -164331. q^{12} -1.14980e6 q^{13} -1.83914e6 q^{14} +47481.0 q^{15} -5.12196e6 q^{16} -1.54672e6 q^{17} +3.08203e6 q^{18} -1.21328e7 q^{19} -132138. q^{20} +8.56241e6 q^{21} -3.47825e7 q^{22} +5.18586e7 q^{23} +1.73981e7 q^{24} -4.87899e7 q^{25} -6.00130e7 q^{26} -1.43489e7 q^{27} -2.38289e7 q^{28} +1.11766e8 q^{29} +2.47825e6 q^{30} -4.07927e7 q^{31} -1.20707e8 q^{32} +1.61936e8 q^{33} -8.07302e7 q^{34} +6.88499e6 q^{35} +3.99325e7 q^{36} -5.91190e8 q^{37} -6.33266e8 q^{38} +2.79401e8 q^{39} +1.39898e7 q^{40} +1.38792e8 q^{41} +4.46910e8 q^{42} +1.48167e8 q^{43} -4.50662e8 q^{44} -1.15379e7 q^{45} +2.70673e9 q^{46} +1.81801e8 q^{47} +1.24464e9 q^{48} -7.35734e8 q^{49} -2.54656e9 q^{50} +3.75853e8 q^{51} -7.77561e8 q^{52} -2.53793e8 q^{53} -7.48933e8 q^{54} +1.30212e8 q^{55} +2.52282e9 q^{56} +2.94828e9 q^{57} +5.83354e9 q^{58} -7.14924e8 q^{59} +3.21095e7 q^{60} +5.28118e9 q^{61} -2.12915e9 q^{62} -2.08066e9 q^{63} +4.18955e9 q^{64} +2.24665e8 q^{65} +8.45216e9 q^{66} -8.08767e9 q^{67} -1.04599e9 q^{68} -1.26016e10 q^{69} +3.59358e8 q^{70} +1.55122e10 q^{71} -4.22774e9 q^{72} -3.19603e9 q^{73} -3.08569e10 q^{74} +1.18560e10 q^{75} -8.20495e9 q^{76} +2.34815e10 q^{77} +1.45832e10 q^{78} -4.22126e10 q^{79} +1.00081e9 q^{80} +3.48678e9 q^{81} +7.24418e9 q^{82} -1.40372e9 q^{83} +5.79041e9 q^{84} +3.02222e8 q^{85} +7.73351e9 q^{86} -2.71590e10 q^{87} +4.77126e10 q^{88} +2.78818e10 q^{89} -6.02214e8 q^{90} +4.05145e10 q^{91} +3.50699e10 q^{92} +9.91263e9 q^{93} +9.48900e9 q^{94} +2.37070e9 q^{95} +2.93317e10 q^{96} +6.20731e10 q^{97} -3.84012e10 q^{98} -3.93504e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	52.1944	1.15335	0.576673	−	0.816975i	$-0.304351\pi$
$2$	52.1944	1.15335	0.576673	+	0.816975i	$0.304351\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	676.260	0.330205
$5$	−195.395	−0.0279627	−0.0139813	−	0.999902i	$-0.504451\pi$
$5$	−195.395	−0.0279627	−0.0139813	+	0.999902i	$0.504451\pi$
$6$	−12683.2	−0.665884
$7$	−35236.2	−0.792411	−0.396205	−	0.918162i	$-0.629673\pi$
$7$	−35236.2	−0.792411	−0.396205	+	0.918162i	$0.629673\pi$
$8$	−71597.2	−0.772505
$9$	59049.0	0.333333
$10$	−10198.5	−0.0322506
$11$	−666403.	−1.24761	−0.623803	−	0.781582i	$-0.714413\pi$
$11$	−666403.	−1.24761	−0.623803	+	0.781582i	$0.714413\pi$
$12$	−164331.	−0.190644
$13$	−1.14980e6	−0.858880	−0.429440	−	0.903095i	$-0.641289\pi$
$13$	−1.14980e6	−0.858880	−0.429440	+	0.903095i	$0.641289\pi$
$14$	−1.83914e6	−0.913923
$15$	47481.0	0.0161443
$16$	−5.12196e6	−1.22117
$17$	−1.54672e6	−0.264206	−0.132103	−	0.991236i	$-0.542173\pi$
$17$	−1.54672e6	−0.264206	−0.132103	+	0.991236i	$0.542173\pi$
$18$	3.08203e6	0.384448
$19$	−1.21328e7	−1.12413	−0.562066	−	0.827092i	$-0.689993\pi$
$19$	−1.21328e7	−1.12413	−0.562066	+	0.827092i	$0.689993\pi$
$20$	−132138.	−0.00923342
$21$	8.56241e6	0.457499
$22$	−3.47825e7	−1.43892
$23$	5.18586e7	1.68003	0.840015	−	0.542562i	$-0.182546\pi$
$23$	5.18586e7	1.68003	0.840015	+	0.542562i	$0.182546\pi$
$24$	1.73981e7	0.446006
$25$	−4.87899e7	−0.999218
$26$	−6.00130e7	−0.990585
$27$	−1.43489e7	−0.192450
$28$	−2.38289e7	−0.261658
$29$	1.11766e8	1.01186	0.505928	−	0.862575i	$-0.331150\pi$
$29$	1.11766e8	1.01186	0.505928	+	0.862575i	$0.331150\pi$
$30$	2.47825e6	0.0186199
$31$	−4.07927e7	−0.255914	−0.127957	−	0.991780i	$-0.540842\pi$
$31$	−4.07927e7	−0.255914	−0.127957	+	0.991780i	$0.540842\pi$
$32$	−1.20707e8	−0.635925
$33$	1.61936e8	0.720305
$34$	−8.07302e7	−0.304721
$35$	6.88499e6	0.0221579
$36$	3.99325e7	0.110068
$37$	−5.91190e8	−1.40158	−0.700790	−	0.713368i	$-0.747169\pi$
$37$	−5.91190e8	−1.40158	−0.700790	+	0.713368i	$0.747169\pi$
$38$	−6.33266e8	−1.29651
$39$	2.79401e8	0.495875
$40$	1.39898e7	0.0216013
$41$	1.38792e8	0.187091	0.0935457	−	0.995615i	$-0.470180\pi$
$41$	1.38792e8	0.187091	0.0935457	+	0.995615i	$0.470180\pi$
$42$	4.46910e8	0.527654
$43$	1.48167e8	0.153701	0.0768503	−	0.997043i	$-0.475514\pi$
$43$	1.48167e8	0.153701	0.0768503	+	0.997043i	$0.475514\pi$
$44$	−4.50662e8	−0.411966
$45$	−1.15379e7	−0.00932089
$46$	2.70673e9	1.93766
$47$	1.81801e8	0.115627	0.0578133	−	0.998327i	$-0.481587\pi$
$47$	1.81801e8	0.115627	0.0578133	+	0.998327i	$0.481587\pi$
$48$	1.24464e9	0.705043
$49$	−7.35734e8	−0.372085
$50$	−2.54656e9	−1.15244
$51$	3.75853e8	0.152539
$52$	−7.77561e8	−0.283606
$53$	−2.53793e8	−0.0833608	−0.0416804	−	0.999131i	$-0.513271\pi$
$53$	−2.53793e8	−0.0833608	−0.0416804	+	0.999131i	$0.513271\pi$
$54$	−7.48933e8	−0.221961
$55$	1.30212e8	0.0348864
$56$	2.52282e9	0.612141
$57$	2.94828e9	0.649018
$58$	5.83354e9	1.16702
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	3.21095e7	0.00533092
$61$	5.28118e9	0.800603	0.400302	−	0.916383i	$-0.368905\pi$
$61$	5.28118e9	0.800603	0.400302	+	0.916383i	$0.368905\pi$
$62$	−2.12915e9	−0.295157
$63$	−2.08066e9	−0.264137
$64$	4.18955e9	0.487728
$65$	2.24665e8	0.0240166
$66$	8.45216e9	0.830761
$67$	−8.08767e9	−0.731833	−0.365917	−	0.930648i	$-0.619245\pi$
$67$	−8.08767e9	−0.731833	−0.365917	+	0.930648i	$0.619245\pi$
$68$	−1.04599e9	−0.0872422
$69$	−1.26016e10	−0.969966
$70$	3.59358e8	0.0255557
$71$	1.55122e10	1.02036	0.510178	−	0.860069i	$-0.329580\pi$
$71$	1.55122e10	1.02036	0.510178	+	0.860069i	$0.329580\pi$
$72$	−4.22774e9	−0.257502
$73$	−3.19603e9	−0.180441	−0.0902206	−	0.995922i	$-0.528757\pi$
$73$	−3.19603e9	−0.180441	−0.0902206	+	0.995922i	$0.528757\pi$
$74$	−3.08569e10	−1.61651
$75$	1.18560e10	0.576899
$76$	−8.20495e9	−0.371194
$77$	2.34815e10	0.988616
$78$	1.45832e10	0.571915
$79$	−4.22126e10	−1.54345	−0.771727	−	0.635955i	$-0.780607\pi$
$79$	−4.22126e10	−1.54345	−0.771727	+	0.635955i	$0.780607\pi$
$80$	1.00081e9	0.0341472
$81$	3.48678e9	0.111111
$82$	7.24418e9	0.215781
$83$	−1.40372e9	−0.0391156	−0.0195578	−	0.999809i	$-0.506226\pi$
$83$	−1.40372e9	−0.0391156	−0.0195578	+	0.999809i	$0.506226\pi$
$84$	5.79041e9	0.151068
$85$	3.02222e8	0.00738791
$86$	7.73351e9	0.177270
$87$	−2.71590e10	−0.584196
$88$	4.77126e10	0.963781
$89$	2.78818e10	0.529269	0.264634	−	0.964349i	$-0.414749\pi$
$89$	2.78818e10	0.529269	0.264634	+	0.964349i	$0.414749\pi$
$90$	−6.02214e8	−0.0107502
$91$	4.05145e10	0.680586
$92$	3.50699e10	0.554755
$93$	9.91263e9	0.147752
$94$	9.48900e9	0.133357
$95$	2.37070e9	0.0314337
$96$	2.93317e10	0.367152
$97$	6.20731e10	0.733938	0.366969	−	0.930233i	$-0.380396\pi$
$97$	6.20731e10	0.733938	0.366969	+	0.930233i	$0.380396\pi$
$98$	−3.84012e10	−0.429143
$99$	−3.93504e10	−0.415868
$100$	−3.29947e10	−0.329947
$101$	3.44423e10	0.326080	0.163040	−	0.986619i	$-0.447870\pi$
$101$	3.44423e10	0.326080	0.163040	+	0.986619i	$0.447870\pi$
$102$	1.96174e10	0.175931
$103$	9.70035e10	0.824485	0.412242	−	0.911074i	$-0.364746\pi$
$103$	9.70035e10	0.824485	0.412242	+	0.911074i	$0.364746\pi$
$104$	8.23222e10	0.663489
$105$	−1.67305e9	−0.0127929
$106$	−1.32466e10	−0.0961437
$107$	2.39751e11	1.65253	0.826264	−	0.563283i	$-0.190462\pi$
$107$	2.39751e11	1.65253	0.826264	+	0.563283i	$0.190462\pi$
$108$	−9.70359e9	−0.0635480
$109$	−8.63007e9	−0.0537240	−0.0268620	−	0.999639i	$-0.508551\pi$
$109$	−8.63007e9	−0.0537240	−0.0268620	+	0.999639i	$0.508551\pi$
$110$	6.79634e9	0.0402361
$111$	1.43659e11	0.809203
$112$	1.80478e11	0.967668
$113$	5.81717e10	0.297016	0.148508	−	0.988911i	$-0.452553\pi$
$113$	5.81717e10	0.297016	0.148508	+	0.988911i	$0.452553\pi$
$114$	1.53884e11	0.748542
$115$	−1.01329e10	−0.0469782
$116$	7.55826e10	0.334120
$117$	−6.78943e10	−0.286293
$118$	−3.73151e10	−0.150153
$119$	5.45006e10	0.209360
$120$	−3.39951e9	−0.0124715
$121$	1.58781e11	0.556519
$122$	2.75649e11	0.923372
$123$	−3.37265e10	−0.108017
$124$	−2.75865e10	−0.0845040
$125$	1.90741e10	0.0559035
$126$	−1.08599e11	−0.304641
$127$	−5.14365e10	−0.138150	−0.0690751	−	0.997611i	$-0.522005\pi$
$127$	−5.14365e10	−0.138150	−0.0690751	+	0.997611i	$0.522005\pi$
$128$	4.65879e11	1.19844
$129$	−3.60046e10	−0.0887391
$130$	1.17262e10	0.0276994
$131$	−4.21719e11	−0.955061	−0.477530	−	0.878615i	$-0.658468\pi$
$131$	−4.21719e11	−0.955061	−0.477530	+	0.878615i	$0.658468\pi$
$132$	1.09511e11	0.237848
$133$	4.27515e11	0.890774
$134$	−4.22132e11	−0.844057
$135$	2.80371e9	0.00538142
$136$	1.10741e11	0.204100
$137$	9.57825e10	0.169560	0.0847799	−	0.996400i	$-0.472981\pi$
$137$	9.57825e10	0.169560	0.0847799	+	0.996400i	$0.472981\pi$
$138$	−6.57735e11	−1.11871
$139$	2.49476e11	0.407800	0.203900	−	0.978992i	$-0.434638\pi$
$139$	2.49476e11	0.407800	0.203900	+	0.978992i	$0.434638\pi$
$140$	4.65604e9	0.00731666
$141$	−4.41776e10	−0.0667571
$142$	8.09649e11	1.17682
$143$	7.66228e11	1.07154
$144$	−3.02446e11	−0.407057
$145$	−2.18385e10	−0.0282942
$146$	−1.66815e11	−0.208111
$147$	1.78783e11	0.214824
$148$	−3.99798e11	−0.462809
$149$	1.19427e12	1.33223	0.666116	−	0.745848i	$-0.267956\pi$
$149$	1.19427e12	1.33223	0.666116	+	0.745848i	$0.267956\pi$
$150$	6.18815e11	0.665363
$151$	4.00230e11	0.414893	0.207447	−	0.978246i	$-0.433485\pi$
$151$	4.00230e11	0.414893	0.207447	+	0.978246i	$0.433485\pi$
$152$	8.68677e11	0.868397
$153$	−9.13323e10	−0.0880687
$154$	1.22561e12	1.14022
$155$	7.97070e9	0.00715603
$156$	1.88947e11	0.163740
$157$	−8.20755e10	−0.0686697	−0.0343349	−	0.999410i	$-0.510931\pi$
$157$	−8.20755e10	−0.0686697	−0.0343349	+	0.999410i	$0.510931\pi$
$158$	−2.20326e12	−1.78013
$159$	6.16716e10	0.0481284
$160$	2.35855e10	0.0177822
$161$	−1.82730e12	−1.33127
$162$	1.81991e11	0.128149
$163$	−9.67748e11	−0.658765	−0.329382	−	0.944197i	$-0.606840\pi$
$163$	−9.67748e11	−0.658765	−0.329382	+	0.944197i	$0.606840\pi$
$164$	9.38596e10	0.0617785
$165$	−3.16415e10	−0.0201417
$166$	−7.32663e10	−0.0451138
$167$	−1.26097e11	−0.0751213	−0.0375606	−	0.999294i	$-0.511959\pi$
$167$	−1.26097e11	−0.0751213	−0.0375606	+	0.999294i	$0.511959\pi$
$168$	−6.13044e11	−0.353420
$169$	−4.70129e11	−0.262325
$170$	1.57743e10	0.00852081
$171$	−7.16432e11	−0.374711
$172$	1.00200e11	0.0507527
$173$	−1.81179e12	−0.888900	−0.444450	−	0.895804i	$-0.646601\pi$
$173$	−1.81179e12	−0.888900	−0.444450	+	0.895804i	$0.646601\pi$
$174$	−1.41755e12	−0.673779
$175$	1.71917e12	0.791791
$176$	3.41329e12	1.52354
$177$	1.73727e11	0.0751646
$178$	1.45528e12	0.610430
$179$	3.76217e11	0.153020	0.0765098	−	0.997069i	$-0.475622\pi$
$179$	3.76217e11	0.153020	0.0765098	+	0.997069i	$0.475622\pi$
$180$	−7.80261e9	−0.00307781
$181$	1.02375e12	0.391709	0.195854	−	0.980633i	$-0.437252\pi$
$181$	1.02375e12	0.391709	0.195854	+	0.980633i	$0.437252\pi$
$182$	2.11463e12	0.784950
$183$	−1.28333e12	−0.462228
$184$	−3.71293e12	−1.29783
$185$	1.15516e11	0.0391919
$186$	5.17384e11	0.170409
$187$	1.03074e12	0.329625
$188$	1.22945e11	0.0381805
$189$	5.05602e11	0.152500
$190$	1.23737e11	0.0362540
$191$	−3.23344e12	−0.920409	−0.460205	−	0.887813i	$-0.652224\pi$
$191$	−3.23344e12	−0.920409	−0.460205	+	0.887813i	$0.652224\pi$
$192$	−1.01806e12	−0.281590
$193$	−4.65345e12	−1.25086	−0.625432	−	0.780279i	$-0.715077\pi$
$193$	−4.65345e12	−1.25086	−0.625432	+	0.780279i	$0.715077\pi$
$194$	3.23987e12	0.846483
$195$	−5.45935e10	−0.0138660
$196$	−4.97548e11	−0.122864
$197$	−5.36562e11	−0.128841	−0.0644207	−	0.997923i	$-0.520520\pi$
$197$	−5.36562e11	−0.128841	−0.0644207	+	0.997923i	$0.520520\pi$
$198$	−2.05387e12	−0.479640
$199$	−7.34848e12	−1.66919	−0.834594	−	0.550865i	$-0.814298\pi$
$199$	−7.34848e12	−1.66919	−0.834594	+	0.550865i	$0.814298\pi$
$200$	3.49322e12	0.771901
$201$	1.96531e12	0.422524
$202$	1.79770e12	0.376083
$203$	−3.93820e12	−0.801806
$204$	2.54174e11	0.0503693
$205$	−2.71193e10	−0.00523158
$206$	5.06304e12	0.950916
$207$	3.06220e12	0.560010
$208$	5.88921e12	1.04884
$209$	8.08536e12	1.40247
$210$	−8.73241e10	−0.0147546
$211$	6.24939e11	0.102869	0.0514345	−	0.998676i	$-0.483621\pi$
$211$	6.24939e11	0.102869	0.0514345	+	0.998676i	$0.483621\pi$
$212$	−1.71630e11	−0.0275261
$213$	−3.76946e12	−0.589103
$214$	1.25137e13	1.90594
$215$	−2.89512e10	−0.00429788
$216$	1.02734e12	0.148669
$217$	1.43738e12	0.202789
$218$	−4.50442e11	−0.0619624
$219$	7.76636e11	0.104178
$220$	8.80571e10	0.0115197
$221$	1.77841e12	0.226921
$222$	7.49821e12	0.933290
$223$	3.35270e12	0.407116	0.203558	−	0.979063i	$-0.434749\pi$
$223$	3.35270e12	0.407116	0.203558	+	0.979063i	$0.434749\pi$
$224$	4.25325e12	0.503914
$225$	−2.88100e12	−0.333073
$226$	3.03624e12	0.342562
$227$	9.56208e12	1.05296	0.526478	−	0.850189i	$-0.323512\pi$
$227$	9.56208e12	1.05296	0.526478	+	0.850189i	$0.323512\pi$
$228$	1.99380e12	0.214309
$229$	−8.28264e12	−0.869108	−0.434554	−	0.900646i	$-0.643094\pi$
$229$	−8.28264e12	−0.869108	−0.434554	+	0.900646i	$0.643094\pi$
$230$	−5.28882e11	−0.0541820
$231$	−5.70601e12	−0.570778
$232$	−8.00210e12	−0.781664
$233$	2.99323e12	0.285550	0.142775	−	0.989755i	$-0.454397\pi$
$233$	2.99323e12	0.285550	0.142775	+	0.989755i	$0.454397\pi$
$234$	−3.54371e12	−0.330195
$235$	−3.55230e10	−0.00323323
$236$	−4.83475e11	−0.0429890
$237$	1.02577e13	0.891113
$238$	2.84463e12	0.241464
$239$	1.43639e13	1.19147	0.595734	−	0.803182i	$-0.296861\pi$
$239$	1.43639e13	1.19147	0.595734	+	0.803182i	$0.296861\pi$
$240$	−2.43196e11	−0.0197149
$241$	5.77363e12	0.457462	0.228731	−	0.973490i	$-0.426542\pi$
$241$	5.77363e12	0.457462	0.228731	+	0.973490i	$0.426542\pi$
$242$	8.28751e12	0.641859
$243$	−8.47289e11	−0.0641500
$244$	3.57145e12	0.264363
$245$	1.43759e11	0.0104045
$246$	−1.76034e12	−0.124581
$247$	1.39503e13	0.965495
$248$	2.92065e12	0.197695
$249$	3.41104e11	0.0225834
$250$	9.95562e11	0.0644760
$251$	1.07314e13	0.679908	0.339954	−	0.940442i	$-0.389589\pi$
$251$	1.07314e13	0.679908	0.339954	+	0.940442i	$0.389589\pi$
$252$	−1.40707e12	−0.0872193
$253$	−3.45587e13	−2.09602
$254$	−2.68470e12	−0.159335
$255$	−7.34399e10	−0.00426541
$256$	1.57361e13	0.894492
$257$	6.26349e12	0.348485	0.174243	−	0.984703i	$-0.444252\pi$
$257$	6.26349e12	0.348485	0.174243	+	0.984703i	$0.444252\pi$
$258$	−1.87924e12	−0.102347
$259$	2.08313e13	1.11063
$260$	1.51932e11	0.00793040
$261$	6.59965e12	0.337286
$262$	−2.20114e13	−1.10151
$263$	1.41722e13	0.694515	0.347257	−	0.937770i	$-0.387113\pi$
$263$	1.41722e13	0.694515	0.347257	+	0.937770i	$0.387113\pi$
$264$	−1.15942e13	−0.556439
$265$	4.95899e10	0.00233099
$266$	2.23139e13	1.02737
$267$	−6.77529e12	−0.305574
$268$	−5.46937e12	−0.241655
$269$	1.61109e13	0.697401	0.348700	−	0.937234i	$-0.386623\pi$
$269$	1.61109e13	0.697401	0.348700	+	0.937234i	$0.386623\pi$
$270$	1.46338e11	0.00620664
$271$	3.01958e13	1.25492	0.627460	−	0.778649i	$-0.284095\pi$
$271$	3.01958e13	1.25492	0.627460	+	0.778649i	$0.284095\pi$
$272$	7.92224e12	0.322640
$273$	−9.84502e12	−0.392936
$274$	4.99931e12	0.195561
$275$	3.25138e13	1.24663
$276$	−8.52198e12	−0.320288
$277$	−2.63710e13	−0.971601	−0.485800	−	0.874070i	$-0.661472\pi$
$277$	−2.63710e13	−0.971601	−0.485800	+	0.874070i	$0.661472\pi$
$278$	1.30213e13	0.470334
$279$	−2.40877e12	−0.0853046
$280$	−4.92946e11	−0.0171171
$281$	9.81038e12	0.334042	0.167021	−	0.985953i	$-0.446585\pi$
$281$	9.81038e12	0.334042	0.167021	+	0.985953i	$0.446585\pi$
$282$	−2.30583e12	−0.0769940
$283$	−2.37771e13	−0.778634	−0.389317	−	0.921104i	$-0.627289\pi$
$283$	−2.37771e13	−0.778634	−0.389317	+	0.921104i	$0.627289\pi$
$284$	1.04903e13	0.336927
$285$	−5.76079e11	−0.0181483
$286$	3.99928e13	1.23586
$287$	−4.89052e12	−0.148253
$288$	−7.12760e12	−0.211975
$289$	−3.18796e13	−0.930195
$290$	−1.13985e12	−0.0326330
$291$	−1.50838e13	−0.423739
$292$	−2.16135e12	−0.0595826
$293$	−3.44772e13	−0.932739	−0.466370	−	0.884590i	$-0.654438\pi$
$293$	−3.44772e13	−0.932739	−0.466370	+	0.884590i	$0.654438\pi$
$294$	9.33150e12	0.247766
$295$	1.39693e11	0.00364043
$296$	4.23276e13	1.08273
$297$	9.56216e12	0.240102
$298$	6.23345e13	1.53652
$299$	−5.96268e13	−1.44295
$300$	8.01771e12	0.190495
$301$	−5.22086e12	−0.121794
$302$	2.08898e13	0.478515
$303$	−8.36948e12	−0.188262
$304$	6.21438e13	1.37276
$305$	−1.03192e12	−0.0223870
$306$	−4.76704e12	−0.101574
$307$	−5.35986e13	−1.12174	−0.560870	−	0.827904i	$-0.689533\pi$
$307$	−5.35986e13	−1.12174	−0.560870	+	0.827904i	$0.689533\pi$
$308$	1.58796e13	0.326446
$309$	−2.35719e13	−0.476017
$310$	4.16026e11	0.00825338
$311$	−3.96142e13	−0.772092	−0.386046	−	0.922480i	$-0.626159\pi$
$311$	−3.96142e13	−0.772092	−0.386046	+	0.922480i	$0.626159\pi$
$312$	−2.00043e13	−0.383066
$313$	−4.08874e13	−0.769299	−0.384650	−	0.923063i	$-0.625678\pi$
$313$	−4.08874e13	−0.769299	−0.384650	+	0.923063i	$0.625678\pi$
$314$	−4.28388e12	−0.0791999
$315$	4.06552e11	0.00738598
$316$	−2.85467e13	−0.509656
$317$	−7.02915e13	−1.23332	−0.616662	−	0.787228i	$-0.711515\pi$
$317$	−7.02915e13	−1.23332	−0.616662	+	0.787228i	$0.711515\pi$
$318$	3.21891e12	0.0555086
$319$	−7.44809e13	−1.26240
$320$	−8.18619e11	−0.0136382
$321$	−5.82594e13	−0.954088
$322$	−9.53749e13	−1.53542
$323$	1.87661e13	0.297003
$324$	2.35797e12	0.0366894
$325$	5.60985e13	0.858208
$326$	−5.05110e13	−0.759783
$327$	2.09711e12	0.0310176
$328$	−9.93713e12	−0.144529
$329$	−6.40598e12	−0.0916238
$330$	−1.65151e12	−0.0232303
$331$	−2.73371e13	−0.378180	−0.189090	−	0.981960i	$-0.560554\pi$
$331$	−2.73371e13	−0.378180	−0.189090	+	0.981960i	$0.560554\pi$
$332$	−9.49279e11	−0.0129162
$333$	−3.49092e13	−0.467193
$334$	−6.58155e12	−0.0866408
$335$	1.58029e12	0.0204640
$336$	−4.38563e13	−0.558683
$337$	−5.16909e13	−0.647813	−0.323907	−	0.946089i	$-0.604996\pi$
$337$	−5.16909e13	−0.647813	−0.323907	+	0.946089i	$0.604996\pi$
$338$	−2.45381e13	−0.302551
$339$	−1.41357e13	−0.171482
$340$	2.04380e11	0.00243953
$341$	2.71844e13	0.319279
$342$	−3.73937e13	−0.432171
$343$	9.55981e13	1.08726
$344$	−1.06084e13	−0.118735
$345$	2.46230e12	0.0271229
$346$	−9.45651e13	−1.02521
$347$	−3.92799e13	−0.419139	−0.209570	−	0.977794i	$-0.567206\pi$
$347$	−3.92799e13	−0.419139	−0.209570	+	0.977794i	$0.567206\pi$
$348$	−1.83666e13	−0.192904
$349$	−1.13790e14	−1.17643	−0.588214	−	0.808705i	$-0.700169\pi$
$349$	−1.13790e14	−1.17643	−0.588214	+	0.808705i	$0.700169\pi$
$350$	8.97313e13	0.913208
$351$	1.64983e13	0.165292
$352$	8.04392e13	0.793384
$353$	1.00625e14	0.977112	0.488556	−	0.872533i	$-0.337524\pi$
$353$	1.00625e14	0.977112	0.488556	+	0.872533i	$0.337524\pi$
$354$	9.06756e12	0.0866907
$355$	−3.03100e12	−0.0285319
$356$	1.88554e13	0.174767
$357$	−1.32437e13	−0.120874
$358$	1.96364e13	0.176484
$359$	4.74384e13	0.419866	0.209933	−	0.977716i	$-0.432675\pi$
$359$	4.74384e13	0.419866	0.209933	+	0.977716i	$0.432675\pi$
$360$	8.26081e11	0.00720044
$361$	3.07153e13	0.263673
$362$	5.34343e13	0.451776
$363$	−3.85839e13	−0.321306
$364$	2.73983e13	0.224733
$365$	6.24490e11	0.00504562
$366$	−6.69826e13	−0.533109
$367$	−1.95201e14	−1.53045	−0.765223	−	0.643765i	$-0.777371\pi$
$367$	−1.95201e14	−1.53045	−0.765223	+	0.643765i	$0.777371\pi$
$368$	−2.65617e14	−2.05160
$369$	8.19554e12	0.0623638
$370$	6.02928e12	0.0452018
$371$	8.94270e12	0.0660560
$372$	6.70352e12	0.0487884
$373$	−4.77630e13	−0.342525	−0.171263	−	0.985225i	$-0.554785\pi$
$373$	−4.77630e13	−0.342525	−0.171263	+	0.985225i	$0.554785\pi$
$374$	5.37989e13	0.380171
$375$	−4.63501e12	−0.0322759
$376$	−1.30164e13	−0.0893222
$377$	−1.28508e14	−0.869064
$378$	2.63896e13	0.175885
$379$	8.87683e13	0.583099	0.291549	−	0.956556i	$-0.405829\pi$
$379$	8.87683e13	0.583099	0.291549	+	0.956556i	$0.405829\pi$
$380$	1.60321e12	0.0103796
$381$	1.24991e13	0.0797610
$382$	−1.68768e14	−1.06155
$383$	−5.24378e13	−0.325126	−0.162563	−	0.986698i	$-0.551976\pi$
$383$	−5.24378e13	−0.325126	−0.162563	+	0.986698i	$0.551976\pi$
$384$	−1.13208e14	−0.691922
$385$	−4.58818e12	−0.0276444
$386$	−2.42884e14	−1.44268
$387$	8.74913e12	0.0512336
$388$	4.19776e13	0.242350
$389$	−1.75475e14	−0.998830	−0.499415	−	0.866363i	$-0.666452\pi$
$389$	−1.75475e14	−0.998830	−0.499415	+	0.866363i	$0.666452\pi$
$390$	−2.84948e12	−0.0159923
$391$	−8.02107e13	−0.443874
$392$	5.26765e13	0.287438
$393$	1.02478e14	0.551404
$394$	−2.80055e13	−0.148599
$395$	8.24815e12	0.0431591
$396$	−2.66111e13	−0.137322
$397$	1.62729e14	0.828167	0.414083	−	0.910239i	$-0.364102\pi$
$397$	1.62729e14	0.828167	0.414083	+	0.910239i	$0.364102\pi$
$398$	−3.83550e14	−1.92515
$399$	−1.03886e14	−0.514289
$400$	2.49900e14	1.22021
$401$	−3.57263e14	−1.72066	−0.860329	−	0.509739i	$-0.829742\pi$
$401$	−3.57263e14	−1.72066	−0.860329	+	0.509739i	$0.829742\pi$
$402$	1.02578e14	0.487316
$403$	4.69033e13	0.219799
$404$	2.32919e13	0.107673
$405$	−6.81301e11	−0.00310696
$406$	−2.05552e14	−0.924759
$407$	3.93971e14	1.74862
$408$	−2.69100e13	−0.117837
$409$	3.25002e14	1.40413	0.702066	−	0.712112i	$-0.252261\pi$
$409$	3.25002e14	1.40413	0.702066	+	0.712112i	$0.252261\pi$
$410$	−1.41548e12	−0.00603382
$411$	−2.32751e13	−0.0978954
$412$	6.55996e13	0.272249
$413$	2.51912e13	0.103163
$414$	1.59830e14	0.645885
$415$	2.74280e11	0.00109378
$416$	1.38788e14	0.546184
$417$	−6.06226e13	−0.235443
$418$	4.22011e14	1.61754
$419$	3.14362e14	1.18919	0.594597	−	0.804024i	$-0.297312\pi$
$419$	3.14362e14	1.18919	0.594597	+	0.804024i	$0.297312\pi$
$420$	−1.13142e12	−0.00422428
$421$	−1.11428e14	−0.410622	−0.205311	−	0.978697i	$-0.565821\pi$
$421$	−1.11428e14	−0.410622	−0.205311	+	0.978697i	$0.565821\pi$
$422$	3.26184e13	0.118643
$423$	1.07352e13	0.0385422
$424$	1.81708e13	0.0643966
$425$	7.54644e13	0.264000
$426$	−1.96745e14	−0.679439
$427$	−1.86089e14	−0.634406
$428$	1.62134e14	0.545673
$429$	−1.86193e14	−0.618656
$430$	−1.51109e12	−0.00495694
$431$	−2.10838e14	−0.682848	−0.341424	−	0.939909i	$-0.610909\pi$
$431$	−2.10838e14	−0.682848	−0.341424	+	0.939909i	$0.610909\pi$
$432$	7.34945e13	0.235014
$433$	−3.80292e14	−1.20070	−0.600349	−	0.799738i	$-0.704972\pi$
$433$	−3.80292e14	−1.20070	−0.600349	+	0.799738i	$0.704972\pi$
$434$	7.50234e13	0.233885
$435$	5.30675e12	0.0163357
$436$	−5.83617e12	−0.0177400
$437$	−6.29191e14	−1.88858
$438$	4.05361e13	0.120153
$439$	8.54458e13	0.250113	0.125056	−	0.992150i	$-0.460089\pi$
$439$	8.54458e13	0.250113	0.125056	+	0.992150i	$0.460089\pi$
$440$	−9.32281e12	−0.0269499
$441$	−4.34444e13	−0.124028
$442$	9.28233e13	0.261719
$443$	1.55349e14	0.432601	0.216301	−	0.976327i	$-0.430601\pi$
$443$	1.55349e14	0.432601	0.216301	+	0.976327i	$0.430601\pi$
$444$	9.71510e13	0.267203
$445$	−5.44798e12	−0.0147998
$446$	1.74993e14	0.469546
$447$	−2.90209e14	−0.769164
$448$	−1.47624e14	−0.386481
$449$	6.71217e14	1.73583	0.867917	−	0.496710i	$-0.165459\pi$
$449$	6.71217e14	1.73583	0.867917	+	0.496710i	$0.165459\pi$
$450$	−1.50372e14	−0.384148
$451$	−9.24916e13	−0.233416
$452$	3.93392e13	0.0980763
$453$	−9.72559e13	−0.239539
$454$	4.99088e14	1.21442
$455$	−7.91634e12	−0.0190310
$456$	−2.11088e14	−0.501369
$457$	−3.94792e14	−0.926465	−0.463233	−	0.886237i	$-0.653311\pi$
$457$	−3.94792e14	−0.926465	−0.463233	+	0.886237i	$0.653311\pi$
$458$	−4.32308e14	−1.00238
$459$	2.21938e13	0.0508465
$460$	−6.85248e12	−0.0155124
$461$	2.70666e14	0.605450	0.302725	−	0.953078i	$-0.402104\pi$
$461$	2.70666e14	0.605450	0.302725	+	0.953078i	$0.402104\pi$
$462$	−2.97822e14	−0.658304
$463$	4.02389e14	0.878923	0.439462	−	0.898261i	$-0.355169\pi$
$463$	4.02389e14	0.878923	0.439462	+	0.898261i	$0.355169\pi$
$464$	−5.72459e14	−1.23565
$465$	−1.93688e12	−0.00413154
$466$	1.56230e14	0.329338
$467$	5.63819e14	1.17462	0.587309	−	0.809363i	$-0.300187\pi$
$467$	5.63819e14	1.17462	0.587309	+	0.809363i	$0.300187\pi$
$468$	−4.59142e13	−0.0945355
$469$	2.84979e14	0.579913
$470$	−1.85411e12	−0.00372903
$471$	1.99443e13	0.0396465
$472$	5.11866e13	0.100572
$473$	−9.87391e13	−0.191758
$474$	5.35393e14	1.02776
$475$	5.91960e14	1.12325
$476$	3.68566e13	0.0691316
$477$	−1.49862e13	−0.0277869
$478$	7.49713e14	1.37417
$479$	−2.55309e14	−0.462616	−0.231308	−	0.972881i	$-0.574300\pi$
$479$	−2.55309e14	−0.462616	−0.231308	+	0.972881i	$0.574300\pi$
$480$	−5.73127e12	−0.0102665
$481$	6.79749e14	1.20379
$482$	3.01352e14	0.527612
$483$	4.44034e14	0.768612
$484$	1.07378e14	0.183765
$485$	−1.21288e13	−0.0205229
$486$	−4.42238e13	−0.0739871
$487$	8.94639e14	1.47992	0.739960	−	0.672651i	$-0.234844\pi$
$487$	8.94639e14	1.47992	0.739960	+	0.672651i	$0.234844\pi$
$488$	−3.78118e14	−0.618470
$489$	2.35163e14	0.380338
$490$	7.50342e12	0.0120000
$491$	1.59955e14	0.252958	0.126479	−	0.991969i	$-0.459632\pi$
$491$	1.59955e14	0.252958	0.126479	+	0.991969i	$0.459632\pi$
$492$	−2.28079e13	−0.0356678
$493$	−1.72870e14	−0.267339
$494$	7.28127e14	1.11355
$495$	7.68889e12	0.0116288
$496$	2.08939e14	0.312514
$497$	−5.46591e14	−0.808541
$498$	1.78037e13	0.0260465
$499$	−7.41397e13	−0.107275	−0.0536374	−	0.998560i	$-0.517082\pi$
$499$	−7.41397e13	−0.107275	−0.0536374	+	0.998560i	$0.517082\pi$
$500$	1.28990e13	0.0184596
$501$	3.06415e13	0.0433713
$502$	5.60118e14	0.784169
$503$	1.85219e14	0.256485	0.128243	−	0.991743i	$-0.459066\pi$
$503$	1.85219e14	0.256485	0.128243	+	0.991743i	$0.459066\pi$
$504$	1.48970e14	0.204047
$505$	−6.72986e12	−0.00911808
$506$	−1.80377e15	−2.41743
$507$	1.14241e14	0.151453
$508$	−3.47845e13	−0.0456179
$509$	−1.46862e15	−1.90529	−0.952644	−	0.304088i	$-0.901648\pi$
$509$	−1.46862e15	−1.90529	−0.952644	+	0.304088i	$0.901648\pi$
$510$	−3.83315e12	−0.00491949
$511$	1.12616e14	0.142984
$512$	−1.32784e14	−0.166787
$513$	1.74093e14	0.216339
$514$	3.26920e14	0.401924
$515$	−1.89540e13	−0.0230548
$516$	−2.43485e13	−0.0293021
$517$	−1.21153e14	−0.144256
$518$	1.08728e15	1.28094
$519$	4.40264e14	0.513207
$520$	−1.60854e13	−0.0185529
$521$	1.07000e14	0.122117	0.0610585	−	0.998134i	$-0.480552\pi$
$521$	1.07000e14	0.122117	0.0610585	+	0.998134i	$0.480552\pi$
$522$	3.44465e14	0.389007
$523$	6.04277e14	0.675269	0.337635	−	0.941277i	$-0.390373\pi$
$523$	6.04277e14	0.675269	0.337635	+	0.941277i	$0.390373\pi$
$524$	−2.85192e14	−0.315366
$525$	−4.17759e14	−0.457141
$526$	7.39711e14	0.801015
$527$	6.30950e13	0.0676140
$528$	−8.29429e14	−0.879615
$529$	1.73650e15	1.82250
$530$	2.58831e12	0.00268844
$531$	−4.22156e13	−0.0433963
$532$	2.89111e14	0.294138
$533$	−1.59583e14	−0.160689
$534$	−3.53632e14	−0.352432
$535$	−4.68461e13	−0.0462091
$536$	5.79055e14	0.565345
$537$	−9.14208e13	−0.0883459
$538$	8.40900e14	0.804344
$539$	4.90296e14	0.464216
$540$	1.89603e12	0.00177697
$541$	−1.75974e15	−1.63254	−0.816271	−	0.577669i	$-0.803962\pi$
$541$	−1.75974e15	−1.63254	−0.816271	+	0.577669i	$0.803962\pi$
$542$	1.57605e15	1.44736
$543$	−2.48772e14	−0.226153
$544$	1.86699e14	0.168015
$545$	1.68627e12	0.00150227
$546$	−5.13856e14	−0.453191
$547$	1.10384e15	0.963775	0.481887	−	0.876233i	$-0.339951\pi$
$547$	1.10384e15	0.963775	0.481887	+	0.876233i	$0.339951\pi$
$548$	6.47739e13	0.0559895
$549$	3.11849e14	0.266868
$550$	1.69704e15	1.43779
$551$	−1.35603e15	−1.13746
$552$	9.02241e14	0.749304
$553$	1.48741e15	1.22305
$554$	−1.37642e15	−1.12059
$555$	−2.80703e13	−0.0226275
$556$	1.68710e14	0.134658
$557$	−8.18349e14	−0.646748	−0.323374	−	0.946271i	$-0.604817\pi$
$557$	−8.18349e14	−0.646748	−0.323374	+	0.946271i	$0.604817\pi$
$558$	−1.25724e14	−0.0983856
$559$	−1.70362e14	−0.132010
$560$	−3.52646e13	−0.0270586
$561$	−2.50470e14	−0.190309
$562$	5.12047e14	0.385266
$563$	−7.90376e14	−0.588895	−0.294447	−	0.955668i	$-0.595136\pi$
$563$	−7.90376e14	−0.588895	−0.294447	+	0.955668i	$0.595136\pi$
$564$	−2.98756e13	−0.0220435
$565$	−1.13665e13	−0.00830538
$566$	−1.24103e15	−0.898034
$567$	−1.22861e14	−0.0880456
$568$	−1.11063e15	−0.788230
$569$	−2.79979e15	−1.96792	−0.983961	−	0.178383i	$-0.942913\pi$
$569$	−2.79979e15	−1.96792	−0.983961	+	0.178383i	$0.942913\pi$
$570$	−3.00681e13	−0.0209312
$571$	−3.59745e14	−0.248026	−0.124013	−	0.992281i	$-0.539576\pi$
$571$	−3.59745e14	−0.248026	−0.124013	+	0.992281i	$0.539576\pi$
$572$	5.18169e14	0.353829
$573$	7.85726e14	0.531399
$574$	−2.55258e14	−0.170987
$575$	−2.53018e15	−1.67872
$576$	2.47389e14	0.162576
$577$	2.88711e15	1.87930	0.939650	−	0.342136i	$-0.111150\pi$
$577$	2.88711e15	1.87930	0.939650	+	0.342136i	$0.111150\pi$
$578$	−1.66394e15	−1.07284
$579$	1.13079e15	0.722187
$580$	−1.47685e13	−0.00934290
$581$	4.94618e13	0.0309957
$582$	−7.87289e14	−0.488717
$583$	1.69128e14	0.104001
$584$	2.28827e14	0.139392
$585$	1.32662e13	0.00800553
$586$	−1.79952e15	−1.07577
$587$	−1.53997e15	−0.912016	−0.456008	−	0.889976i	$-0.650721\pi$
$587$	−1.53997e15	−0.912016	−0.456008	+	0.889976i	$0.650721\pi$
$588$	1.20904e14	0.0709358
$589$	4.94931e14	0.287681
$590$	7.29119e12	0.00419867
$591$	1.30385e14	0.0743866
$592$	3.02805e15	1.71157
$593$	3.28167e15	1.83778	0.918891	−	0.394512i	$-0.129086\pi$
$593$	3.28167e15	1.83778	0.918891	+	0.394512i	$0.129086\pi$
$594$	4.99091e14	0.276920
$595$	−1.06492e13	−0.00585426
$596$	8.07640e14	0.439910
$597$	1.78568e15	0.963707
$598$	−3.11219e15	−1.66421
$599$	1.10082e14	0.0583268	0.0291634	−	0.999575i	$-0.490716\pi$
$599$	1.10082e14	0.0583268	0.0291634	+	0.999575i	$0.490716\pi$
$600$	−8.48853e14	−0.445657
$601$	2.22928e15	1.15973	0.579863	−	0.814714i	$-0.303106\pi$
$601$	2.22928e15	1.15973	0.579863	+	0.814714i	$0.303106\pi$
$602$	−2.72500e14	−0.140471
$603$	−4.77569e14	−0.243944
$604$	2.70660e14	0.137000
$605$	−3.10251e13	−0.0155618
$606$	−4.36840e14	−0.217132
$607$	−3.75115e15	−1.84768	−0.923839	−	0.382781i	$-0.874966\pi$
$607$	−3.75115e15	−1.84768	−0.923839	+	0.382781i	$0.874966\pi$
$608$	1.46451e15	0.714864
$609$	9.56982e14	0.462923
$610$	−5.38604e13	−0.0258200
$611$	−2.09034e14	−0.0993094
$612$	−6.17644e13	−0.0290807
$613$	1.70579e15	0.795961	0.397981	−	0.917394i	$-0.369711\pi$
$613$	1.70579e15	0.795961	0.397981	+	0.917394i	$0.369711\pi$
$614$	−2.79755e15	−1.29375
$615$	6.59000e12	0.00302045
$616$	−1.68121e15	−0.763710
$617$	2.06411e15	0.929320	0.464660	−	0.885489i	$-0.346177\pi$
$617$	2.06411e15	0.929320	0.464660	+	0.885489i	$0.346177\pi$
$618$	−1.23032e15	−0.549011
$619$	1.68302e15	0.744371	0.372186	−	0.928158i	$-0.378608\pi$
$619$	1.68302e15	0.744371	0.372186	+	0.928158i	$0.378608\pi$
$620$	5.39027e12	0.00236296
$621$	−7.44114e14	−0.323322
$622$	−2.06764e15	−0.890488
$623$	−9.82451e14	−0.419398
$624$	−1.43108e15	−0.605547
$625$	2.37859e15	0.997655
$626$	−2.13409e15	−0.887268
$627$	−1.96474e15	−0.809718
$628$	−5.55043e13	−0.0226751
$629$	9.14406e14	0.370306
$630$	2.12197e13	0.00851858
$631$	2.86991e15	1.14211	0.571054	−	0.820913i	$-0.306535\pi$
$631$	2.86991e15	1.14211	0.571054	+	0.820913i	$0.306535\pi$
$632$	3.02231e15	1.19232
$633$	−1.51860e14	−0.0593914
$634$	−3.66883e15	−1.42245
$635$	1.00505e13	0.00386305
$636$	4.17060e13	0.0158922
$637$	8.45945e14	0.319577
$638$	−3.88749e15	−1.45598
$639$	9.15978e14	0.340119
$640$	−9.10304e13	−0.0335117
$641$	3.51229e15	1.28195	0.640975	−	0.767562i	$-0.278530\pi$
$641$	3.51229e15	1.28195	0.640975	+	0.767562i	$0.278530\pi$
$642$	−3.04082e15	−1.10039
$643$	−2.49598e15	−0.895533	−0.447766	−	0.894151i	$-0.647780\pi$
$643$	−2.49598e15	−0.895533	−0.447766	+	0.894151i	$0.647780\pi$
$644$	−1.23573e15	−0.439594
$645$	7.03513e12	0.00248138
$646$	9.79486e14	0.342546
$647$	−2.61131e14	−0.0905492	−0.0452746	−	0.998975i	$-0.514416\pi$
$647$	−2.61131e14	−0.0905492	−0.0452746	+	0.998975i	$0.514416\pi$
$648$	−2.49644e14	−0.0858339
$649$	4.76428e14	0.162424
$650$	2.92803e15	0.989811
$651$	−3.49284e14	−0.117080
$652$	−6.54449e14	−0.217527
$653$	−6.16620e13	−0.0203233	−0.0101617	−	0.999948i	$-0.503235\pi$
$653$	−6.16620e13	−0.0203233	−0.0101617	+	0.999948i	$0.503235\pi$
$654$	1.09457e14	0.0357740
$655$	8.24018e13	0.0267061
$656$	−7.10888e14	−0.228470
$657$	−1.88723e14	−0.0601471
$658$	−3.34357e14	−0.105674
$659$	2.76813e15	0.867593	0.433796	−	0.901011i	$-0.357174\pi$
$659$	2.76813e15	0.867593	0.433796	+	0.901011i	$0.357174\pi$
$660$	−2.13979e13	−0.00665088
$661$	−5.23330e14	−0.161312	−0.0806561	−	0.996742i	$-0.525702\pi$
$661$	−5.23330e14	−0.161312	−0.0806561	+	0.996742i	$0.525702\pi$
$662$	−1.42684e15	−0.436172
$663$	−4.32155e14	−0.131013
$664$	1.00502e14	0.0302170
$665$	−8.35344e13	−0.0249084
$666$	−1.82207e15	−0.538835
$667$	5.79600e15	1.69995
$668$	−8.52741e13	−0.0248054
$669$	−8.14707e14	−0.235049
$670$	8.24825e13	0.0236021
$671$	−3.51940e15	−0.998837
$672$	−1.03354e15	−0.290935
$673$	−1.92287e15	−0.536868	−0.268434	−	0.963298i	$-0.586506\pi$
$673$	−1.92287e15	−0.536868	−0.268434	+	0.963298i	$0.586506\pi$
$674$	−2.69798e15	−0.747152
$675$	7.00082e14	0.192300
$676$	−3.17929e14	−0.0866211
$677$	−6.67886e12	−0.00180495	−0.000902474	−	1.00000i	$-0.500287\pi$
$677$	−6.67886e12	−0.00180495	−0.000902474		1.00000i	$0.500287\pi$
$678$	−7.37806e14	−0.197778
$679$	−2.18722e15	−0.581580
$680$	−2.16382e13	−0.00570720
$681$	−2.32359e15	−0.607925
$682$	1.41887e15	0.368239
$683$	3.56170e15	0.916944	0.458472	−	0.888709i	$-0.348397\pi$
$683$	3.56170e15	0.916944	0.458472	+	0.888709i	$0.348397\pi$
$684$	−4.84494e14	−0.123731
$685$	−1.87154e13	−0.00474135
$686$	4.98969e15	1.25398
$687$	2.01268e15	0.501780
$688$	−7.58906e14	−0.187695
$689$	2.91810e14	0.0715969
$690$	1.28518e14	0.0312820
$691$	4.69830e15	1.13452	0.567259	−	0.823540i	$-0.308004\pi$
$691$	4.69830e15	1.13452	0.567259	+	0.823540i	$0.308004\pi$
$692$	−1.22524e15	−0.293519
$693$	1.38656e15	0.329539
$694$	−2.05019e15	−0.483412
$695$	−4.87464e13	−0.0114032
$696$	1.94451e15	0.451294
$697$	−2.14673e14	−0.0494307
$698$	−5.93922e15	−1.35683
$699$	−7.27355e14	−0.164863
$700$	1.16261e15	0.261453
$701$	−5.52473e14	−0.123271	−0.0616357	−	0.998099i	$-0.519632\pi$
$701$	−5.52473e14	−0.123271	−0.0616357	+	0.998099i	$0.519632\pi$
$702$	8.61121e14	0.190638
$703$	7.17281e15	1.57556
$704$	−2.79193e15	−0.608492
$705$	8.63210e12	0.00186671
$706$	5.25206e15	1.12695
$707$	−1.21362e15	−0.258389
$708$	1.17484e14	0.0248197
$709$	3.91516e15	0.820721	0.410361	−	0.911923i	$-0.365403\pi$
$709$	3.91516e15	0.820721	0.410361	+	0.911923i	$0.365403\pi$
$710$	−1.58202e14	−0.0329071
$711$	−2.49261e15	−0.514484
$712$	−1.99626e15	−0.408863
$713$	−2.11545e15	−0.429943
$714$	−6.91245e14	−0.139409
$715$	−1.49717e14	−0.0299632
$716$	2.54421e14	0.0505278
$717$	−3.49042e15	−0.687895
$718$	2.47602e15	0.484251
$719$	−5.11652e15	−0.993038	−0.496519	−	0.868026i	$-0.665389\pi$
$719$	−5.11652e15	−0.993038	−0.496519	+	0.868026i	$0.665389\pi$
$720$	5.90966e13	0.0113824
$721$	−3.41804e15	−0.653331
$722$	1.60317e15	0.304106
$723$	−1.40299e15	−0.264116
$724$	6.92324e14	0.129344
$725$	−5.45304e15	−1.01107
$726$	−2.01386e15	−0.370577
$727$	9.00816e15	1.64512	0.822558	−	0.568681i	$-0.192546\pi$
$727$	9.00816e15	1.64512	0.822558	+	0.568681i	$0.192546\pi$
$728$	−2.90073e15	−0.525756
$729$	2.05891e14	0.0370370
$730$	3.25949e13	0.00581934
$731$	−2.29173e14	−0.0406087
$732$	−8.67863e14	−0.152630
$733$	4.15701e15	0.725619	0.362810	−	0.931863i	$-0.381818\pi$
$733$	4.15701e15	0.725619	0.362810	+	0.931863i	$0.381818\pi$
$734$	−1.01884e16	−1.76513
$735$	−3.49334e13	−0.00600704
$736$	−6.25967e15	−1.06837
$737$	5.38965e15	0.913039
$738$	4.27762e14	0.0719270
$739$	4.43765e15	0.740642	0.370321	−	0.928904i	$-0.379248\pi$
$739$	4.43765e15	0.740642	0.370321	+	0.928904i	$0.379248\pi$
$740$	7.81187e13	0.0129414
$741$	−3.38992e15	−0.557429
$742$	4.66759e14	0.0761853
$743$	5.62873e15	0.911952	0.455976	−	0.889992i	$-0.349290\pi$
$743$	5.62873e15	0.911952	0.455976	+	0.889992i	$0.349290\pi$
$744$	−7.09717e14	−0.114139
$745$	−2.33356e14	−0.0372528
$746$	−2.49296e15	−0.395050
$747$	−8.28882e13	−0.0130385
$748$	6.97048e14	0.108844
$749$	−8.44791e15	−1.30948
$750$	−2.41922e14	−0.0372253
$751$	5.56239e15	0.849653	0.424826	−	0.905275i	$-0.360335\pi$
$751$	5.56239e15	0.849653	0.424826	+	0.905275i	$0.360335\pi$
$752$	−9.31177e14	−0.141200
$753$	−2.60773e15	−0.392545
$754$	−6.70739e15	−1.00233
$755$	−7.82030e13	−0.0116015
$756$	3.41918e14	0.0503561
$757$	−1.11556e15	−0.163104	−0.0815520	−	0.996669i	$-0.525988\pi$
$757$	−1.11556e15	−0.163104	−0.0815520	+	0.996669i	$0.525988\pi$
$758$	4.63321e15	0.672514
$759$	8.39776e15	1.21014
$760$	−1.69735e14	−0.0242827
$761$	1.01423e16	1.44052	0.720259	−	0.693705i	$-0.244023\pi$
$761$	1.01423e16	1.44052	0.720259	+	0.693705i	$0.244023\pi$
$762$	6.52382e14	0.0919920
$763$	3.04091e14	0.0425715
$764$	−2.18664e15	−0.303924
$765$	1.78459e13	0.00246264
$766$	−2.73696e15	−0.374982
$767$	8.22017e14	0.111817
$768$	−3.82386e15	−0.516435
$769$	3.35879e15	0.450390	0.225195	−	0.974314i	$-0.427698\pi$
$769$	3.35879e15	0.450390	0.225195	+	0.974314i	$0.427698\pi$
$770$	−2.39477e14	−0.0318835
$771$	−1.52203e15	−0.201198
$772$	−3.14694e15	−0.413042
$773$	1.03234e15	0.134535	0.0672673	−	0.997735i	$-0.478572\pi$
$773$	1.03234e15	0.134535	0.0672673	+	0.997735i	$0.478572\pi$
$774$	4.56656e14	0.0590900
$775$	1.99028e15	0.255714
$776$	−4.44426e15	−0.566970
$777$	−5.06201e15	−0.641221
$778$	−9.15880e15	−1.15200
$779$	−1.68394e15	−0.210315
$780$	−3.69194e13	−0.00457862
$781$	−1.03374e16	−1.27300
$782$	−4.18655e15	−0.511940
$783$	−1.60371e15	−0.194732
$784$	3.76840e15	0.454379
$785$	1.60372e13	0.00192019
$786$	5.34877e15	0.635960
$787$	1.44266e15	0.170335	0.0851673	−	0.996367i	$-0.472858\pi$
$787$	1.44266e15	0.170335	0.0851673	+	0.996367i	$0.472858\pi$
$788$	−3.62855e14	−0.0425441
$789$	−3.44385e15	−0.400978
$790$	4.30507e14	0.0497773
$791$	−2.04975e15	−0.235359
$792$	2.81738e15	0.321260
$793$	−6.07229e15	−0.687622
$794$	8.49356e15	0.955162
$795$	−1.20503e13	−0.00134580
$796$	−4.96948e15	−0.551175
$797$	1.16381e16	1.28192	0.640958	−	0.767576i	$-0.278537\pi$
$797$	1.16381e16	1.28192	0.640958	+	0.767576i	$0.278537\pi$
$798$	−5.42228e15	−0.593152
$799$	−2.81195e14	−0.0305493
$800$	5.88927e15	0.635428
$801$	1.64639e15	0.176423
$802$	−1.86472e16	−1.98451
$803$	2.12985e15	0.225119
$804$	1.32906e15	0.139520
$805$	3.57046e14	0.0372260
$806$	2.44809e15	0.253504
$807$	−3.91495e15	−0.402645
$808$	−2.46597e15	−0.251899
$809$	1.25498e16	1.27327	0.636635	−	0.771165i	$-0.280326\pi$
$809$	1.25498e16	1.27327	0.636635	+	0.771165i	$0.280326\pi$
$810$	−3.55601e13	−0.00358340
$811$	−1.15718e16	−1.15820	−0.579101	−	0.815256i	$-0.696596\pi$
$811$	−1.15718e16	−1.15820	−0.579101	+	0.815256i	$0.696596\pi$
$812$	−2.66325e15	−0.264760
$813$	−7.33759e15	−0.724528
$814$	2.05631e16	2.01676
$815$	1.89093e14	0.0184208
$816$	−1.92510e15	−0.186277
$817$	−1.79769e15	−0.172780
$818$	1.69633e16	1.61945
$819$	2.39234e15	0.226862
$820$	−1.83397e13	−0.00172749
$821$	1.29680e16	1.21335	0.606673	−	0.794951i	$-0.292504\pi$
$821$	1.29680e16	1.21335	0.606673	+	0.794951i	$0.292504\pi$
$822$	−1.21483e15	−0.112907
$823$	2.61179e15	0.241123	0.120561	−	0.992706i	$-0.461531\pi$
$823$	2.61179e15	0.241123	0.120561	+	0.992706i	$0.461531\pi$
$824$	−6.94518e15	−0.636919
$825$	−7.90085e15	−0.719742
$826$	1.31484e15	0.118983
$827$	2.02861e16	1.82355	0.911777	−	0.410685i	$-0.134710\pi$
$827$	2.02861e16	1.82355	0.911777	+	0.410685i	$0.134710\pi$
$828$	2.07084e15	0.184918
$829$	−2.08267e16	−1.84744	−0.923718	−	0.383073i	$-0.874866\pi$
$829$	−2.08267e16	−1.84744	−0.923718	+	0.383073i	$0.874866\pi$
$830$	1.43159e13	0.00126150
$831$	6.40815e15	0.560954
$832$	−4.81713e15	−0.418900
$833$	1.13798e15	0.0983072
$834$	−3.16416e15	−0.271547
$835$	2.46387e13	0.00210059
$836$	5.46780e15	0.463104
$837$	5.85331e14	0.0492506
$838$	1.64079e16	1.37155
$839$	1.71854e16	1.42715	0.713574	−	0.700580i	$-0.247075\pi$
$839$	1.71854e16	1.42715	0.713574	+	0.700580i	$0.247075\pi$
$840$	1.19786e14	0.00988257
$841$	2.91037e14	0.0238545
$842$	−5.81592e15	−0.473589
$843$	−2.38392e15	−0.192859
$844$	4.22621e14	0.0339678
$845$	9.18609e13	0.00733531
$846$	5.60316e14	0.0444525
$847$	−5.59486e15	−0.440992
$848$	1.29991e15	0.101798
$849$	5.77783e15	0.449545
$850$	3.93882e15	0.304483
$851$	−3.06583e16	−2.35470
$852$	−2.54913e15	−0.194525
$853$	−1.66180e16	−1.25997	−0.629983	−	0.776609i	$-0.716938\pi$
$853$	−1.66180e16	−1.25997	−0.629983	+	0.776609i	$0.716938\pi$
$854$	−9.71282e15	−0.731690
$855$	1.39987e14	0.0104779
$856$	−1.71655e16	−1.27659
$857$	−1.43054e16	−1.05707	−0.528536	−	0.848911i	$-0.677259\pi$
$857$	−1.43054e16	−1.05707	−0.528536	+	0.848911i	$0.677259\pi$
$858$	−9.71826e15	−0.713524
$859$	2.56536e16	1.87148	0.935740	−	0.352690i	$-0.114733\pi$
$859$	2.56536e16	1.87148	0.935740	+	0.352690i	$0.114733\pi$
$860$	−1.95785e13	−0.00141918
$861$	1.18840e15	0.0855940
$862$	−1.10046e16	−0.787560
$863$	1.11692e16	0.794259	0.397129	−	0.917763i	$-0.370006\pi$
$863$	1.11692e16	0.794259	0.397129	+	0.917763i	$0.370006\pi$
$864$	1.73201e15	0.122384
$865$	3.54014e14	0.0248560
$866$	−1.98491e16	−1.38482
$867$	7.74673e15	0.537048
$868$	9.72044e14	0.0669619
$869$	2.81306e16	1.92562
$870$	2.76983e14	0.0188407
$871$	9.29918e15	0.628557
$872$	6.17889e14	0.0415021
$873$	3.66536e15	0.244646
$874$	−3.28403e16	−2.17818
$875$	−6.72100e14	−0.0442985
$876$	5.25208e14	0.0344000
$877$	−1.35345e16	−0.880935	−0.440468	−	0.897769i	$-0.645187\pi$
$877$	−1.35345e16	−0.880935	−0.440468	+	0.897769i	$0.645187\pi$
$878$	4.45980e15	0.288466
$879$	8.37796e15	0.538517
$880$	−6.66940e14	−0.0426022
$881$	−4.03052e15	−0.255855	−0.127927	−	0.991784i	$-0.540832\pi$
$881$	−4.03052e15	−0.255855	−0.127927	+	0.991784i	$0.540832\pi$
$882$	−2.26755e15	−0.143048
$883$	−2.76624e16	−1.73423	−0.867114	−	0.498109i	$-0.834028\pi$
$883$	−2.76624e16	−1.73423	−0.867114	+	0.498109i	$0.834028\pi$
$884$	1.20267e15	0.0749306
$885$	−3.39453e13	−0.00210180
$886$	8.10835e15	0.498939
$887$	−1.48914e16	−0.910658	−0.455329	−	0.890323i	$-0.650478\pi$
$887$	−1.48914e16	−0.910658	−0.455329	+	0.890323i	$0.650478\pi$
$888$	−1.02856e16	−0.625113
$889$	1.81243e15	0.109472
$890$	−2.84354e14	−0.0170693
$891$	−2.32360e15	−0.138623
$892$	2.26730e15	0.134432
$893$	−2.20576e15	−0.129980
$894$	−1.51473e16	−0.887112
$895$	−7.35110e13	−0.00427884
$896$	−1.64158e16	−0.949660
$897$	1.44893e16	0.833085
$898$	3.50338e16	2.00201
$899$	−4.55922e15	−0.258948
$900$	−1.94830e15	−0.109982
$901$	3.92546e14	0.0220244
$902$	−4.82755e15	−0.269210
$903$	1.26867e15	0.0703178
$904$	−4.16493e15	−0.229447
$905$	−2.00037e14	−0.0109532
$906$	−5.07622e15	−0.276271
$907$	−9.16687e15	−0.495885	−0.247943	−	0.968775i	$-0.579754\pi$
$907$	−9.16687e15	−0.495885	−0.247943	+	0.968775i	$0.579754\pi$
$908$	6.46645e15	0.347691
$909$	2.03378e15	0.108693
$910$	−4.13189e14	−0.0219493
$911$	2.45548e16	1.29654	0.648269	−	0.761411i	$-0.275493\pi$
$911$	2.45548e16	1.29654	0.648269	+	0.761411i	$0.275493\pi$
$912$	−1.51010e16	−0.792561
$913$	9.35442e14	0.0488009
$914$	−2.06059e16	−1.06853
$915$	2.50756e14	0.0129251
$916$	−5.60122e15	−0.286984
$917$	1.48598e16	0.756800
$918$	1.15839e15	0.0586436
$919$	1.48958e16	0.749596	0.374798	−	0.927107i	$-0.377712\pi$
$919$	1.48958e16	0.749596	0.374798	+	0.927107i	$0.377712\pi$
$920$	7.25488e14	0.0362909
$921$	1.30245e16	0.647637
$922$	1.41273e16	0.698293
$923$	−1.78358e16	−0.876363
$924$	−3.85875e15	−0.188474
$925$	2.88441e16	1.40048
$926$	2.10025e16	1.01370
$927$	5.72796e15	0.274828
$928$	−1.34908e16	−0.643465
$929$	2.02159e16	0.958533	0.479267	−	0.877669i	$-0.340903\pi$
$929$	2.02159e16	0.958533	0.479267	+	0.877669i	$0.340903\pi$
$930$	−1.01094e14	−0.00476509
$931$	8.92654e15	0.418273
$932$	2.02420e15	0.0942902
$933$	9.62625e15	0.445767
$934$	2.94282e16	1.35474
$935$	−2.01402e14	−0.00921720
$936$	4.86104e15	0.221163
$937$	3.40549e16	1.54032	0.770161	−	0.637849i	$-0.220176\pi$
$937$	3.40549e16	1.54032	0.770161	+	0.637849i	$0.220176\pi$
$938$	1.48743e16	0.668839
$939$	9.93563e15	0.444155
$940$	−2.40228e13	−0.00106763
$941$	−3.52843e16	−1.55897	−0.779486	−	0.626420i	$-0.784519\pi$
$941$	−3.52843e16	−1.55897	−0.779486	+	0.626420i	$0.784519\pi$
$942$	1.04098e15	0.0457261
$943$	7.19756e15	0.314319
$944$	3.66181e15	0.158983
$945$	−9.87921e13	−0.00426430
$946$	−5.15363e15	−0.221163
$947$	−1.53182e16	−0.653557	−0.326778	−	0.945101i	$-0.605963\pi$
$947$	−1.53182e16	−0.653557	−0.326778	+	0.945101i	$0.605963\pi$
$948$	6.93685e15	0.294250
$949$	3.67479e15	0.154977
$950$	3.08970e16	1.29550
$951$	1.70808e16	0.712059
$952$	−3.90209e15	−0.161731
$953$	3.59136e16	1.47995	0.739976	−	0.672633i	$-0.234837\pi$
$953$	3.59136e16	1.47995	0.739976	+	0.672633i	$0.234837\pi$
$954$	−7.82196e14	−0.0320479
$955$	6.31798e14	0.0257371
$956$	9.71370e15	0.393429
$957$	1.80989e16	0.728846
$958$	−1.33257e16	−0.533556
$959$	−3.37501e15	−0.134361
$960$	1.98924e14	0.00787401
$961$	−2.37444e16	−0.934508
$962$	3.54791e16	1.38838
$963$	1.41570e16	0.550843
$964$	3.90448e15	0.151056
$965$	9.09262e14	0.0349775
$966$	2.31761e16	0.886475
$967$	1.14254e16	0.434535	0.217268	−	0.976112i	$-0.430286\pi$
$967$	1.14254e16	0.434535	0.217268	+	0.976112i	$0.430286\pi$
$968$	−1.13683e16	−0.429914
$969$	−4.56016e15	−0.171475
$970$	−6.33055e14	−0.0236699
$971$	−2.45147e16	−0.911423	−0.455712	−	0.890127i	$-0.650615\pi$
$971$	−2.45147e16	−0.911423	−0.455712	+	0.890127i	$0.650615\pi$
$972$	−5.72987e14	−0.0211827
$973$	−8.79059e15	−0.323145
$974$	4.66952e16	1.70686
$975$	−1.36319e16	−0.495487
$976$	−2.70500e16	−0.977672
$977$	2.72152e16	0.978117	0.489058	−	0.872251i	$-0.337341\pi$
$977$	2.72152e16	0.978117	0.489058	+	0.872251i	$0.337341\pi$
$978$	1.22742e16	0.438661
$979$	−1.85805e16	−0.660319
$980$	9.72184e13	0.00343562
$981$	−5.09597e14	−0.0179080
$982$	8.34874e15	0.291748
$983$	1.91607e16	0.665834	0.332917	−	0.942956i	$-0.391967\pi$
$983$	1.91607e16	0.665834	0.332917	+	0.942956i	$0.391967\pi$
$984$	2.41472e15	0.0834439
$985$	1.04842e14	0.00360275
$986$	−9.02286e15	−0.308334
$987$	1.55665e15	0.0528990
$988$	9.43402e15	0.318811
$989$	7.68374e15	0.258222
$990$	4.01317e14	0.0134120
$991$	3.37436e16	1.12147	0.560733	−	0.827997i	$-0.310519\pi$
$991$	3.37436e16	1.12147	0.560733	+	0.827997i	$0.310519\pi$
$992$	4.92395e15	0.162742
$993$	6.64291e15	0.218342
$994$	−2.85290e16	−0.932527
$995$	1.43586e15	0.0466750
$996$	2.30675e14	0.00745716
$997$	2.58202e16	0.830112	0.415056	−	0.909796i	$-0.363762\pi$
$997$	2.58202e16	0.830112	0.415056	+	0.909796i	$0.363762\pi$
$998$	−3.86968e15	−0.123725
$999$	8.48294e15	0.269734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.21	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.21	✓	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)

\(f(q)\)	\(=\)	\(q+52.1944 q^{2} -243.000 q^{3} +676.260 q^{4} -195.395 q^{5} -12683.2 q^{6} -35236.2 q^{7} -71597.2 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+52.1944 q^{2} -243.000 q^{3} +676.260 q^{4} -195.395 q^{5} -12683.2 q^{6} -35236.2 q^{7} -71597.2 q^{8} +59049.0 q^{9} -10198.5 q^{10} -666403. q^{11} -164331. q^{12} -1.14980e6 q^{13} -1.83914e6 q^{14} +47481.0 q^{15} -5.12196e6 q^{16} -1.54672e6 q^{17} +3.08203e6 q^{18} -1.21328e7 q^{19} -132138. q^{20} +8.56241e6 q^{21} -3.47825e7 q^{22} +5.18586e7 q^{23} +1.73981e7 q^{24} -4.87899e7 q^{25} -6.00130e7 q^{26} -1.43489e7 q^{27} -2.38289e7 q^{28} +1.11766e8 q^{29} +2.47825e6 q^{30} -4.07927e7 q^{31} -1.20707e8 q^{32} +1.61936e8 q^{33} -8.07302e7 q^{34} +6.88499e6 q^{35} +3.99325e7 q^{36} -5.91190e8 q^{37} -6.33266e8 q^{38} +2.79401e8 q^{39} +1.39898e7 q^{40} +1.38792e8 q^{41} +4.46910e8 q^{42} +1.48167e8 q^{43} -4.50662e8 q^{44} -1.15379e7 q^{45} +2.70673e9 q^{46} +1.81801e8 q^{47} +1.24464e9 q^{48} -7.35734e8 q^{49} -2.54656e9 q^{50} +3.75853e8 q^{51} -7.77561e8 q^{52} -2.53793e8 q^{53} -7.48933e8 q^{54} +1.30212e8 q^{55} +2.52282e9 q^{56} +2.94828e9 q^{57} +5.83354e9 q^{58} -7.14924e8 q^{59} +3.21095e7 q^{60} +5.28118e9 q^{61} -2.12915e9 q^{62} -2.08066e9 q^{63} +4.18955e9 q^{64} +2.24665e8 q^{65} +8.45216e9 q^{66} -8.08767e9 q^{67} -1.04599e9 q^{68} -1.26016e10 q^{69} +3.59358e8 q^{70} +1.55122e10 q^{71} -4.22774e9 q^{72} -3.19603e9 q^{73} -3.08569e10 q^{74} +1.18560e10 q^{75} -8.20495e9 q^{76} +2.34815e10 q^{77} +1.45832e10 q^{78} -4.22126e10 q^{79} +1.00081e9 q^{80} +3.48678e9 q^{81} +7.24418e9 q^{82} -1.40372e9 q^{83} +5.79041e9 q^{84} +3.02222e8 q^{85} +7.73351e9 q^{86} -2.71590e10 q^{87} +4.77126e10 q^{88} +2.78818e10 q^{89} -6.02214e8 q^{90} +4.05145e10 q^{91} +3.50699e10 q^{92} +9.91263e9 q^{93} +9.48900e9 q^{94} +2.37070e9 q^{95} +2.93317e10 q^{96} +6.20731e10 q^{97} -3.84012e10 q^{98} -3.93504e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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