LMFDB - Embedded newform 177.12.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.89171 q^{2} -243.000 q^{3} -1985.72 q^{4} -1405.99 q^{5} -1917.69 q^{6} +25105.4 q^{7} -31832.9 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+7.89171 q^{2} -243.000 q^{3} -1985.72 q^{4} -1405.99 q^{5} -1917.69 q^{6} +25105.4 q^{7} -31832.9 q^{8} +59049.0 q^{9} -11095.6 q^{10} +251890. q^{11} +482530. q^{12} +1.97716e6 q^{13} +198125. q^{14} +341655. q^{15} +3.81554e6 q^{16} +384296. q^{17} +465997. q^{18} -1.00048e7 q^{19} +2.79190e6 q^{20} -6.10062e6 q^{21} +1.98784e6 q^{22} +5.12407e7 q^{23} +7.73541e6 q^{24} -4.68513e7 q^{25} +1.56031e7 q^{26} -1.43489e7 q^{27} -4.98524e7 q^{28} -1.79135e8 q^{29} +2.69624e6 q^{30} -1.54653e8 q^{31} +9.53050e7 q^{32} -6.12092e7 q^{33} +3.03275e6 q^{34} -3.52980e7 q^{35} -1.17255e8 q^{36} +6.49876e8 q^{37} -7.89553e7 q^{38} -4.80449e8 q^{39} +4.47567e7 q^{40} -1.77958e8 q^{41} -4.81443e7 q^{42} +1.32372e9 q^{43} -5.00183e8 q^{44} -8.30222e7 q^{45} +4.04377e8 q^{46} -2.57114e9 q^{47} -9.27176e8 q^{48} -1.34704e9 q^{49} -3.69737e8 q^{50} -9.33839e7 q^{51} -3.92608e9 q^{52} -1.18778e9 q^{53} -1.13237e8 q^{54} -3.54154e8 q^{55} -7.99180e8 q^{56} +2.43118e9 q^{57} -1.41368e9 q^{58} -7.14924e8 q^{59} -6.78432e8 q^{60} +8.62224e9 q^{61} -1.22048e9 q^{62} +1.48245e9 q^{63} -7.06211e9 q^{64} -2.77986e9 q^{65} -4.83046e8 q^{66} -9.42876e8 q^{67} -7.63104e8 q^{68} -1.24515e10 q^{69} -2.78561e8 q^{70} +8.96360e9 q^{71} -1.87970e9 q^{72} -9.87272e9 q^{73} +5.12863e9 q^{74} +1.13849e10 q^{75} +1.98668e10 q^{76} +6.32381e9 q^{77} -3.79156e9 q^{78} -1.71048e10 q^{79} -5.36460e9 q^{80} +3.48678e9 q^{81} -1.40440e9 q^{82} +5.86777e10 q^{83} +1.21141e10 q^{84} -5.40315e8 q^{85} +1.04464e10 q^{86} +4.35299e10 q^{87} -8.01840e9 q^{88} -2.87521e10 q^{89} -6.55187e8 q^{90} +4.96374e10 q^{91} -1.01750e11 q^{92} +3.75807e10 q^{93} -2.02907e10 q^{94} +1.40667e10 q^{95} -2.31591e10 q^{96} +8.39510e10 q^{97} -1.06305e10 q^{98} +1.48738e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.89171	0.174384	0.0871919	−	0.996192i	$-0.472211\pi$
$2$	7.89171	0.174384	0.0871919	+	0.996192i	$0.472211\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1985.72	−0.969590
$5$	−1405.99	−0.201209	−0.100604	−	0.994927i	$-0.532078\pi$
$5$	−1405.99	−0.201209	−0.100604	+	0.994927i	$0.532078\pi$
$6$	−1917.69	−0.100681
$7$	25105.4	0.564584	0.282292	−	0.959329i	$-0.408905\pi$
$7$	25105.4	0.564584	0.282292	+	0.959329i	$0.408905\pi$
$8$	−31832.9	−0.343465
$9$	59049.0	0.333333
$10$	−11095.6	−0.0350875
$11$	251890.	0.471575	0.235788	−	0.971805i	$-0.424233\pi$
$11$	251890.	0.471575	0.235788	+	0.971805i	$0.424233\pi$
$12$	482530.	0.559793
$13$	1.97716e6	1.47691	0.738453	−	0.674305i	$-0.235557\pi$
$13$	1.97716e6	1.47691	0.738453	+	0.674305i	$0.235557\pi$
$14$	198125.	0.0984543
$15$	341655.	0.116168
$16$	3.81554e6	0.909696
$17$	384296.	0.0656442	0.0328221	−	0.999461i	$-0.489551\pi$
$17$	384296.	0.0656442	0.0328221	+	0.999461i	$0.489551\pi$
$18$	465997.	0.0581279
$19$	−1.00048e7	−0.926970	−0.463485	−	0.886105i	$-0.653401\pi$
$19$	−1.00048e7	−0.926970	−0.463485	+	0.886105i	$0.653401\pi$
$20$	2.79190e6	0.195090
$21$	−6.10062e6	−0.325963
$22$	1.98784e6	0.0822351
$23$	5.12407e7	1.66001	0.830007	−	0.557752i	$-0.188336\pi$
$23$	5.12407e7	1.66001	0.830007	+	0.557752i	$0.188336\pi$
$24$	7.73541e6	0.198299
$25$	−4.68513e7	−0.959515
$26$	1.56031e7	0.257548
$27$	−1.43489e7	−0.192450
$28$	−4.98524e7	−0.547415
$29$	−1.79135e8	−1.62178	−0.810890	−	0.585198i	$-0.801017\pi$
$29$	−1.79135e8	−1.62178	−0.810890	+	0.585198i	$0.801017\pi$
$30$	2.69624e6	0.0202578
$31$	−1.54653e8	−0.970218	−0.485109	−	0.874454i	$-0.661220\pi$
$31$	−1.54653e8	−0.970218	−0.485109	+	0.874454i	$0.661220\pi$
$32$	9.53050e7	0.502101
$33$	−6.12092e7	−0.272264
$34$	3.03275e6	0.0114473
$35$	−3.52980e7	−0.113599
$36$	−1.17255e8	−0.323197
$37$	6.49876e8	1.54071	0.770355	−	0.637615i	$-0.220079\pi$
$37$	6.49876e8	1.54071	0.770355	+	0.637615i	$0.220079\pi$
$38$	−7.89553e7	−0.161648
$39$	−4.80449e8	−0.852692
$40$	4.47567e7	0.0691080
$41$	−1.77958e8	−0.239887	−0.119944	−	0.992781i	$-0.538271\pi$
$41$	−1.77958e8	−0.239887	−0.119944	+	0.992781i	$0.538271\pi$
$42$	−4.81443e7	−0.0568426
$43$	1.32372e9	1.37315	0.686577	−	0.727057i	$-0.259113\pi$
$43$	1.32372e9	1.37315	0.686577	+	0.727057i	$0.259113\pi$
$44$	−5.00183e8	−0.457235
$45$	−8.30222e7	−0.0670695
$46$	4.04377e8	0.289480
$47$	−2.57114e9	−1.63526	−0.817632	−	0.575741i	$-0.804714\pi$
$47$	−2.57114e9	−1.63526	−0.817632	+	0.575741i	$0.804714\pi$
$48$	−9.27176e8	−0.525213
$49$	−1.34704e9	−0.681245
$50$	−3.69737e8	−0.167324
$51$	−9.33839e7	−0.0378997
$52$	−3.92608e9	−1.43199
$53$	−1.18778e9	−0.390138	−0.195069	−	0.980790i	$-0.562493\pi$
$53$	−1.18778e9	−0.390138	−0.195069	+	0.980790i	$0.562493\pi$
$54$	−1.13237e8	−0.0335602
$55$	−3.54154e8	−0.0948850
$56$	−7.99180e8	−0.193915
$57$	2.43118e9	0.535186
$58$	−1.41368e9	−0.282812
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−6.78432e8	−0.112635
$61$	8.62224e9	1.30709	0.653545	−	0.756887i	$-0.273281\pi$
$61$	8.62224e9	1.30709	0.653545	+	0.756887i	$0.273281\pi$
$62$	−1.22048e9	−0.169190
$63$	1.48245e9	0.188195
$64$	−7.06211e9	−0.822137
$65$	−2.77986e9	−0.297166
$66$	−4.83046e8	−0.0474784
$67$	−9.42876e8	−0.0853185	−0.0426592	−	0.999090i	$-0.513583\pi$
$67$	−9.42876e8	−0.0853185	−0.0426592	+	0.999090i	$0.513583\pi$
$68$	−7.63104e8	−0.0636480
$69$	−1.24515e10	−0.958410
$70$	−2.78561e8	−0.0198099
$71$	8.96360e9	0.589606	0.294803	−	0.955558i	$-0.404746\pi$
$71$	8.96360e9	0.589606	0.294803	+	0.955558i	$0.404746\pi$
$72$	−1.87970e9	−0.114488
$73$	−9.87272e9	−0.557393	−0.278696	−	0.960379i	$-0.589902\pi$
$73$	−9.87272e9	−0.557393	−0.278696	+	0.960379i	$0.589902\pi$
$74$	5.12863e9	0.268675
$75$	1.13849e10	0.553976
$76$	1.98668e10	0.898781
$77$	6.32381e9	0.266244
$78$	−3.79156e9	−0.148696
$79$	−1.71048e10	−0.625416	−0.312708	−	0.949849i	$-0.601236\pi$
$79$	−1.71048e10	−0.625416	−0.312708	+	0.949849i	$0.601236\pi$
$80$	−5.36460e9	−0.183039
$81$	3.48678e9	0.111111
$82$	−1.40440e9	−0.0418325
$83$	5.86777e10	1.63510	0.817548	−	0.575860i	$-0.195333\pi$
$83$	5.86777e10	1.63510	0.817548	+	0.575860i	$0.195333\pi$
$84$	1.21141e10	0.316050
$85$	−5.40315e8	−0.0132082
$86$	1.04464e10	0.239456
$87$	4.35299e10	0.936336
$88$	−8.01840e9	−0.161969
$89$	−2.87521e10	−0.545788	−0.272894	−	0.962044i	$-0.587981\pi$
$89$	−2.87521e10	−0.545788	−0.272894	+	0.962044i	$0.587981\pi$
$90$	−6.55187e8	−0.0116958
$91$	4.96374e10	0.833837
$92$	−1.01750e11	−1.60953
$93$	3.75807e10	0.560156
$94$	−2.02907e10	−0.285164
$95$	1.40667e10	0.186514
$96$	−2.31591e10	−0.289888
$97$	8.39510e10	0.992617	0.496308	−	0.868146i	$-0.334689\pi$
$97$	8.39510e10	0.992617	0.496308	+	0.868146i	$0.334689\pi$
$98$	−1.06305e10	−0.118798
$99$	1.48738e10	0.157192
$100$	9.30337e10	0.930337
$101$	9.28263e10	0.878827	0.439413	−	0.898285i	$-0.355186\pi$
$101$	9.28263e10	0.878827	0.439413	+	0.898285i	$0.355186\pi$
$102$	−7.36958e8	−0.00660910
$103$	−1.89238e11	−1.60844	−0.804219	−	0.594333i	$-0.797416\pi$
$103$	−1.89238e11	−1.60844	−0.804219	+	0.594333i	$0.797416\pi$
$104$	−6.29387e10	−0.507265
$105$	8.57740e9	0.0655865
$106$	−9.37360e9	−0.0680337
$107$	−1.43004e11	−0.985680	−0.492840	−	0.870120i	$-0.664041\pi$
$107$	−1.43004e11	−0.985680	−0.492840	+	0.870120i	$0.664041\pi$
$108$	2.84929e10	0.186598
$109$	2.89853e11	1.80440	0.902199	−	0.431321i	$-0.141952\pi$
$109$	2.89853e11	1.80440	0.902199	+	0.431321i	$0.141952\pi$
$110$	−2.79488e9	−0.0165464
$111$	−1.57920e11	−0.889530
$112$	9.57908e10	0.513600
$113$	1.90809e11	0.974243	0.487122	−	0.873334i	$-0.338047\pi$
$113$	1.90809e11	0.974243	0.487122	+	0.873334i	$0.338047\pi$
$114$	1.91861e10	0.0933278
$115$	−7.20438e10	−0.334009
$116$	3.55713e11	1.57246
$117$	1.16749e11	0.492302
$118$	−5.64197e9	−0.0227028
$119$	9.64792e9	0.0370617
$120$	−1.08759e10	−0.0398995
$121$	−2.21863e11	−0.777617
$122$	6.80442e10	0.227935
$123$	4.32439e10	0.138499
$124$	3.07098e11	0.940714
$125$	1.34524e11	0.394271
$126$	1.16991e10	0.0328181
$127$	−1.82107e11	−0.489108	−0.244554	−	0.969636i	$-0.578642\pi$
$127$	−1.82107e11	−0.489108	−0.244554	+	0.969636i	$0.578642\pi$
$128$	−2.50917e11	−0.645468
$129$	−3.21664e11	−0.792791
$130$	−2.19378e10	−0.0518209
$131$	6.09391e11	1.38008	0.690039	−	0.723772i	$-0.257593\pi$
$131$	6.09391e11	1.38008	0.690039	+	0.723772i	$0.257593\pi$
$132$	1.21544e11	0.263985
$133$	−2.51176e11	−0.523352
$134$	−7.44090e9	−0.0148782
$135$	2.01744e10	0.0387226
$136$	−1.22333e10	−0.0225465
$137$	−7.08371e11	−1.25400	−0.627000	−	0.779019i	$-0.715718\pi$
$137$	−7.08371e11	−1.25400	−0.627000	+	0.779019i	$0.715718\pi$
$138$	−9.82635e10	−0.167131
$139$	3.39953e10	0.0555696	0.0277848	−	0.999614i	$-0.491155\pi$
$139$	3.39953e10	0.0555696	0.0277848	+	0.999614i	$0.491155\pi$
$140$	7.00919e10	0.110145
$141$	6.24788e11	0.944120
$142$	7.07381e10	0.102818
$143$	4.98026e11	0.696472
$144$	2.25304e11	0.303232
$145$	2.51862e11	0.326316
$146$	−7.79127e10	−0.0972002
$147$	3.27332e11	0.393317
$148$	−1.29047e12	−1.49386
$149$	1.33224e12	1.48613	0.743066	−	0.669219i	$-0.233371\pi$
$149$	1.33224e12	1.48613	0.743066	+	0.669219i	$0.233371\pi$
$150$	8.98461e10	0.0966045
$151$	−3.50958e11	−0.363816	−0.181908	−	0.983316i	$-0.558227\pi$
$151$	−3.50958e11	−0.363816	−0.181908	+	0.983316i	$0.558227\pi$
$152$	3.18484e11	0.318381
$153$	2.26923e10	0.0218814
$154$	4.99057e10	0.0464286
$155$	2.17441e11	0.195216
$156$	9.54038e11	0.826762
$157$	−8.04739e11	−0.673298	−0.336649	−	0.941630i	$-0.609294\pi$
$157$	−8.04739e11	−0.673298	−0.336649	+	0.941630i	$0.609294\pi$
$158$	−1.34986e11	−0.109062
$159$	2.88630e11	0.225246
$160$	−1.33998e11	−0.101027
$161$	1.28642e12	0.937218
$162$	2.75167e10	0.0193760
$163$	1.19198e12	0.811405	0.405702	−	0.914005i	$-0.367027\pi$
$163$	1.19198e12	0.811405	0.405702	+	0.914005i	$0.367027\pi$
$164$	3.53376e11	0.232592
$165$	8.60595e10	0.0547819
$166$	4.63067e11	0.285134
$167$	−8.90159e11	−0.530306	−0.265153	−	0.964206i	$-0.585423\pi$
$167$	−8.90159e11	−0.530306	−0.265153	+	0.964206i	$0.585423\pi$
$168$	1.94201e11	0.111957
$169$	2.11699e12	1.18125
$170$	−4.26401e9	−0.00230329
$171$	−5.90776e11	−0.308990
$172$	−2.62854e12	−1.33140
$173$	9.49944e11	0.466063	0.233032	−	0.972469i	$-0.425135\pi$
$173$	9.49944e11	0.466063	0.233032	+	0.972469i	$0.425135\pi$
$174$	3.43525e11	0.163282
$175$	−1.17622e12	−0.541727
$176$	9.61096e11	0.428990
$177$	1.73727e11	0.0751646
$178$	−2.26903e11	−0.0951766
$179$	−1.13637e12	−0.462197	−0.231099	−	0.972930i	$-0.574232\pi$
$179$	−1.13637e12	−0.462197	−0.231099	+	0.972930i	$0.574232\pi$
$180$	1.64859e11	0.0650300
$181$	1.56925e12	0.600425	0.300213	−	0.953872i	$-0.402942\pi$
$181$	1.56925e12	0.600425	0.300213	+	0.953872i	$0.402942\pi$
$182$	3.91724e11	0.145408
$183$	−2.09520e12	−0.754649
$184$	−1.63114e12	−0.570156
$185$	−9.13718e11	−0.310004
$186$	2.96576e11	0.0976821
$187$	9.68002e10	0.0309562
$188$	5.10557e12	1.58554
$189$	−3.60236e11	−0.108654
$190$	1.11010e11	0.0325251
$191$	6.19963e12	1.76475	0.882374	−	0.470549i	$-0.155944\pi$
$191$	6.19963e12	1.76475	0.882374	+	0.470549i	$0.155944\pi$
$192$	1.71609e12	0.474661
$193$	−1.65838e12	−0.445778	−0.222889	−	0.974844i	$-0.571549\pi$
$193$	−1.65838e12	−0.445778	−0.222889	+	0.974844i	$0.571549\pi$
$194$	6.62517e11	0.173096
$195$	6.75506e11	0.171569
$196$	2.67485e12	0.660528
$197$	−3.41122e12	−0.819117	−0.409559	−	0.912284i	$-0.634317\pi$
$197$	−3.41122e12	−0.819117	−0.409559	+	0.912284i	$0.634317\pi$
$198$	1.17380e11	0.0274117
$199$	7.79320e12	1.77021	0.885104	−	0.465394i	$-0.154087\pi$
$199$	7.79320e12	1.77021	0.885104	+	0.465394i	$0.154087\pi$
$200$	1.49142e12	0.329559
$201$	2.29119e11	0.0492586
$202$	7.32558e11	0.153253
$203$	−4.49727e12	−0.915632
$204$	1.85434e11	0.0367472
$205$	2.50207e11	0.0482674
$206$	−1.49341e12	−0.280485
$207$	3.02571e12	0.553338
$208$	7.54392e12	1.34353
$209$	−2.52012e12	−0.437136
$210$	6.76904e10	0.0114372
$211$	2.52623e12	0.415834	0.207917	−	0.978146i	$-0.433332\pi$
$211$	2.52623e12	0.415834	0.207917	+	0.978146i	$0.433332\pi$
$212$	2.35860e12	0.378274
$213$	−2.17816e12	−0.340409
$214$	−1.12854e12	−0.171887
$215$	−1.86113e12	−0.276290
$216$	4.56768e11	0.0660998
$217$	−3.88264e12	−0.547770
$218$	2.28744e12	0.314658
$219$	2.39907e12	0.321811
$220$	7.03251e11	0.0919996
$221$	7.59813e11	0.0969503
$222$	−1.24626e12	−0.155120
$223$	1.16037e13	1.40903	0.704513	−	0.709691i	$-0.251166\pi$
$223$	1.16037e13	1.40903	0.704513	+	0.709691i	$0.251166\pi$
$224$	2.39267e12	0.283478
$225$	−2.76652e12	−0.319838
$226$	1.50581e12	0.169892
$227$	1.77498e13	1.95457	0.977283	−	0.211939i	$-0.0679778\pi$
$227$	1.77498e13	1.95457	0.977283	+	0.211939i	$0.0679778\pi$
$228$	−4.82764e12	−0.518911
$229$	6.45345e12	0.677169	0.338584	−	0.940936i	$-0.390052\pi$
$229$	6.45345e12	0.677169	0.338584	+	0.940936i	$0.390052\pi$
$230$	−5.68549e11	−0.0582458
$231$	−1.53669e12	−0.153716
$232$	5.70241e12	0.557024
$233$	−1.56906e13	−1.49686	−0.748432	−	0.663212i	$-0.769193\pi$
$233$	−1.56906e13	−1.49686	−0.748432	+	0.663212i	$0.769193\pi$
$234$	9.21350e11	0.0858494
$235$	3.61500e12	0.329029
$236$	1.41964e12	0.126230
$237$	4.15646e12	0.361084
$238$	7.61385e10	0.00646296
$239$	−8.80380e12	−0.730267	−0.365134	−	0.930955i	$-0.618977\pi$
$239$	−8.80380e12	−0.730267	−0.365134	+	0.930955i	$0.618977\pi$
$240$	1.30360e12	0.105677
$241$	−1.06050e13	−0.840264	−0.420132	−	0.907463i	$-0.638016\pi$
$241$	−1.06050e13	−0.840264	−0.420132	+	0.907463i	$0.638016\pi$
$242$	−1.75088e12	−0.135604
$243$	−8.47289e11	−0.0641500
$244$	−1.71214e13	−1.26734
$245$	1.89393e12	0.137072
$246$	3.41268e11	0.0241520
$247$	−1.97811e13	−1.36905
$248$	4.92307e12	0.333236
$249$	−1.42587e13	−0.944023
$250$	1.06163e12	0.0687545
$251$	2.79673e13	1.77192	0.885962	−	0.463758i	$-0.153499\pi$
$251$	2.79673e13	1.77192	0.885962	+	0.463758i	$0.153499\pi$
$252$	−2.94373e12	−0.182472
$253$	1.29070e13	0.782822
$254$	−1.43713e12	−0.0852926
$255$	1.31297e11	0.00762575
$256$	1.24830e13	0.709578
$257$	2.75903e13	1.53506	0.767528	−	0.641015i	$-0.221487\pi$
$257$	2.75903e13	1.53506	0.767528	+	0.641015i	$0.221487\pi$
$258$	−2.53848e12	−0.138250
$259$	1.63154e13	0.869861
$260$	5.52002e12	0.288129
$261$	−1.05778e13	−0.540594
$262$	4.80913e12	0.240663
$263$	−4.32633e12	−0.212013	−0.106007	−	0.994365i	$-0.533806\pi$
$263$	−4.32633e12	−0.212013	−0.106007	+	0.994365i	$0.533806\pi$
$264$	1.94847e12	0.0935131
$265$	1.67000e12	0.0784991
$266$	−1.98221e12	−0.0912642
$267$	6.98676e12	0.315111
$268$	1.87229e12	0.0827240
$269$	−1.99206e13	−0.862315	−0.431157	−	0.902277i	$-0.641895\pi$
$269$	−1.99206e13	−0.862315	−0.431157	+	0.902277i	$0.641895\pi$
$270$	1.59210e11	0.00675260
$271$	4.12737e13	1.71531	0.857654	−	0.514227i	$-0.171921\pi$
$271$	4.12737e13	1.71531	0.857654	+	0.514227i	$0.171921\pi$
$272$	1.46630e12	0.0597163
$273$	−1.20619e13	−0.481416
$274$	−5.59026e12	−0.218677
$275$	−1.18014e13	−0.452484
$276$	2.47252e13	0.929265
$277$	4.39141e13	1.61795	0.808976	−	0.587842i	$-0.200022\pi$
$277$	4.39141e13	1.61795	0.808976	+	0.587842i	$0.200022\pi$
$278$	2.68281e11	0.00969043
$279$	−9.13211e12	−0.323406
$280$	1.12364e12	0.0390173
$281$	9.21235e12	0.313679	0.156840	−	0.987624i	$-0.449869\pi$
$281$	9.21235e12	0.313679	0.156840	+	0.987624i	$0.449869\pi$
$282$	4.93064e12	0.164639
$283$	−2.81171e13	−0.920758	−0.460379	−	0.887723i	$-0.652286\pi$
$283$	−2.81171e13	−0.920758	−0.460379	+	0.887723i	$0.652286\pi$
$284$	−1.77992e13	−0.571676
$285$	−3.41821e12	−0.107684
$286$	3.93027e12	0.121453
$287$	−4.46773e12	−0.135437
$288$	5.62767e12	0.167367
$289$	−3.41242e13	−0.995691
$290$	1.98762e12	0.0569043
$291$	−2.04001e13	−0.573087
$292$	1.96045e13	0.540443
$293$	−4.90947e13	−1.32820	−0.664098	−	0.747645i	$-0.731184\pi$
$293$	−4.90947e13	−1.32820	−0.664098	+	0.747645i	$0.731184\pi$
$294$	2.58321e12	0.0685881
$295$	1.00518e12	0.0261951
$296$	−2.06875e13	−0.529180
$297$	−3.61434e12	−0.0907547
$298$	1.05136e13	0.259157
$299$	1.01311e14	2.45168
$300$	−2.26072e13	−0.537130
$301$	3.32325e13	0.775261
$302$	−2.76966e12	−0.0634436
$303$	−2.25568e13	−0.507391
$304$	−3.81739e13	−0.843260
$305$	−1.21228e13	−0.262998
$306$	1.79081e11	0.00381576
$307$	−5.09295e13	−1.06588	−0.532940	−	0.846153i	$-0.678913\pi$
$307$	−5.09295e13	−1.06588	−0.532940	+	0.846153i	$0.678913\pi$
$308$	−1.25573e13	−0.258148
$309$	4.59849e13	0.928632
$310$	1.71598e12	0.0340426
$311$	−1.84718e13	−0.360021	−0.180010	−	0.983665i	$-0.557613\pi$
$311$	−1.84718e13	−0.360021	−0.180010	+	0.983665i	$0.557613\pi$
$312$	1.52941e13	0.292869
$313$	2.10290e13	0.395663	0.197831	−	0.980236i	$-0.436610\pi$
$313$	2.10290e13	0.395663	0.197831	+	0.980236i	$0.436610\pi$
$314$	−6.35077e12	−0.117412
$315$	−2.08431e12	−0.0378664
$316$	3.39653e13	0.606397
$317$	2.81419e13	0.493774	0.246887	−	0.969044i	$-0.420592\pi$
$317$	2.81419e13	0.493774	0.246887	+	0.969044i	$0.420592\pi$
$318$	2.27778e12	0.0392793
$319$	−4.51224e13	−0.764792
$320$	9.92924e12	0.165421
$321$	3.47499e13	0.569083
$322$	1.01521e13	0.163436
$323$	−3.84482e12	−0.0608502
$324$	−6.92378e12	−0.107732
$325$	−9.26324e13	−1.41711
$326$	9.40677e12	0.141496
$327$	−7.04343e13	−1.04177
$328$	5.66494e12	0.0823928
$329$	−6.45497e13	−0.923245
$330$	6.79156e11	0.00955307
$331$	−1.08032e14	−1.49451	−0.747253	−	0.664540i	$-0.768628\pi$
$331$	−1.08032e14	−1.49451	−0.747253	+	0.664540i	$0.768628\pi$
$332$	−1.16517e14	−1.58537
$333$	3.83745e13	0.513570
$334$	−7.02487e12	−0.0924768
$335$	1.32567e12	0.0171668
$336$	−2.32772e13	−0.296527
$337$	1.05771e14	1.32556	0.662782	−	0.748812i	$-0.269376\pi$
$337$	1.05771e14	1.32556	0.662782	+	0.748812i	$0.269376\pi$
$338$	1.67066e13	0.205991
$339$	−4.63666e13	−0.562480
$340$	1.07292e12	0.0128065
$341$	−3.89556e13	−0.457531
$342$	−4.66223e12	−0.0538828
$343$	−8.34598e13	−0.949204
$344$	−4.21379e13	−0.471630
$345$	1.75066e13	0.192840
$346$	7.49668e12	0.0812738
$347$	−1.77689e14	−1.89605	−0.948025	−	0.318197i	$-0.896923\pi$
$347$	−1.77689e14	−1.89605	−0.948025	+	0.318197i	$0.896923\pi$
$348$	−8.64382e13	−0.907862
$349$	9.19114e13	0.950232	0.475116	−	0.879923i	$-0.342406\pi$
$349$	9.19114e13	0.950232	0.475116	+	0.879923i	$0.342406\pi$
$350$	−9.28241e12	−0.0944684
$351$	−2.83700e13	−0.284231
$352$	2.40064e13	0.236778
$353$	−1.12600e14	−1.09340	−0.546699	−	0.837329i	$-0.684116\pi$
$353$	−1.12600e14	−1.09340	−0.546699	+	0.837329i	$0.684116\pi$
$354$	1.37100e12	0.0131075
$355$	−1.26027e13	−0.118634
$356$	5.70936e13	0.529191
$357$	−2.34444e12	−0.0213976
$358$	−8.96788e12	−0.0805997
$359$	−1.66558e13	−0.147416	−0.0737081	−	0.997280i	$-0.523483\pi$
$359$	−1.66558e13	−0.147416	−0.0737081	+	0.997280i	$0.523483\pi$
$360$	2.64284e12	0.0230360
$361$	−1.63933e13	−0.140727
$362$	1.23840e13	0.104704
$363$	5.39127e13	0.448957
$364$	−9.85660e13	−0.808481
$365$	1.38809e13	0.112152
$366$	−1.65347e13	−0.131599
$367$	−1.46428e14	−1.14805	−0.574027	−	0.818836i	$-0.694620\pi$
$367$	−1.46428e14	−1.14805	−0.574027	+	0.818836i	$0.694620\pi$
$368$	1.95511e14	1.51011
$369$	−1.05083e13	−0.0799625
$370$	−7.21080e12	−0.0540597
$371$	−2.98197e13	−0.220266
$372$	−7.46248e13	−0.543122
$373$	2.08804e14	1.49740	0.748702	−	0.662906i	$-0.230677\pi$
$373$	2.08804e14	1.49740	0.748702	+	0.662906i	$0.230677\pi$
$374$	7.63919e11	0.00539826
$375$	−3.26894e13	−0.227633
$376$	8.18471e13	0.561655
$377$	−3.54179e14	−2.39522
$378$	−2.84287e12	−0.0189475
$379$	8.51228e13	0.559153	0.279576	−	0.960123i	$-0.409806\pi$
$379$	8.51228e13	0.559153	0.279576	+	0.960123i	$0.409806\pi$
$380$	−2.79325e13	−0.180842
$381$	4.42519e13	0.282387
$382$	4.89257e13	0.307743
$383$	2.25630e14	1.39895	0.699476	−	0.714656i	$-0.253417\pi$
$383$	2.25630e14	1.39895	0.699476	+	0.714656i	$0.253417\pi$
$384$	6.09728e13	0.372661
$385$	−8.89120e12	−0.0535706
$386$	−1.30875e13	−0.0777365
$387$	7.81643e13	0.457718
$388$	−1.66703e14	−0.962431
$389$	1.19250e14	0.678789	0.339394	−	0.940644i	$-0.389778\pi$
$389$	1.19250e14	0.678789	0.339394	+	0.940644i	$0.389778\pi$
$390$	5.33089e12	0.0299188
$391$	1.96916e13	0.108970
$392$	4.28804e13	0.233983
$393$	−1.48082e14	−0.796788
$394$	−2.69204e13	−0.142841
$395$	2.40491e13	0.125839
$396$	−2.95353e13	−0.152412
$397$	−2.31280e14	−1.17704	−0.588518	−	0.808484i	$-0.700288\pi$
$397$	−2.31280e14	−1.17704	−0.588518	+	0.808484i	$0.700288\pi$
$398$	6.15017e13	0.308695
$399$	6.10358e13	0.302158
$400$	−1.78763e14	−0.872867
$401$	−5.79434e12	−0.0279068	−0.0139534	−	0.999903i	$-0.504442\pi$
$401$	−5.79434e12	−0.0279068	−0.0139534	+	0.999903i	$0.504442\pi$
$402$	1.80814e12	0.00858991
$403$	−3.05774e14	−1.43292
$404$	−1.84327e14	−0.852102
$405$	−4.90238e12	−0.0223565
$406$	−3.54912e13	−0.159671
$407$	1.63697e14	0.726561
$408$	2.97268e12	0.0130172
$409$	2.40534e14	1.03920	0.519600	−	0.854410i	$-0.326081\pi$
$409$	2.40534e14	1.03920	0.519600	+	0.854410i	$0.326081\pi$
$410$	1.97456e12	0.00841705
$411$	1.72134e14	0.723998
$412$	3.75774e14	1.55953
$413$	−1.79485e13	−0.0735026
$414$	2.38780e13	0.0964932
$415$	−8.25001e13	−0.328996
$416$	1.88433e14	0.741555
$417$	−8.26085e12	−0.0320831
$418$	−1.98880e13	−0.0762294
$419$	−2.03602e13	−0.0770203	−0.0385101	−	0.999258i	$-0.512261\pi$
$419$	−2.03602e13	−0.0770203	−0.0385101	+	0.999258i	$0.512261\pi$
$420$	−1.70323e13	−0.0635921
$421$	−3.06582e13	−0.112978	−0.0564891	−	0.998403i	$-0.517991\pi$
$421$	−3.06582e13	−0.112978	−0.0564891	+	0.998403i	$0.517991\pi$
$422$	1.99363e13	0.0725147
$423$	−1.51823e14	−0.545088
$424$	3.78105e13	0.133999
$425$	−1.80048e13	−0.0629866
$426$	−1.71894e13	−0.0593618
$427$	2.16465e14	0.737963
$428$	2.83965e14	0.955706
$429$	−1.21020e14	−0.402108
$430$	−1.46875e13	−0.0481806
$431$	−3.65677e14	−1.18433	−0.592165	−	0.805816i	$-0.701727\pi$
$431$	−3.65677e14	−1.18433	−0.592165	+	0.805816i	$0.701727\pi$
$432$	−5.47488e13	−0.175071
$433$	4.13063e14	1.30417	0.652083	−	0.758148i	$-0.273895\pi$
$433$	4.13063e14	1.30417	0.652083	+	0.758148i	$0.273895\pi$
$434$	−3.06406e13	−0.0955222
$435$	−6.12025e13	−0.188399
$436$	−5.75567e14	−1.74953
$437$	−5.12655e14	−1.53878
$438$	1.89328e13	0.0561186
$439$	−6.75685e13	−0.197783	−0.0988916	−	0.995098i	$-0.531530\pi$
$439$	−6.75685e13	−0.197783	−0.0988916	+	0.995098i	$0.531530\pi$
$440$	1.12738e13	0.0325896
$441$	−7.95416e13	−0.227082
$442$	5.99622e12	0.0169066
$443$	−6.24507e13	−0.173907	−0.0869535	−	0.996212i	$-0.527713\pi$
$443$	−6.24507e13	−0.173907	−0.0869535	+	0.996212i	$0.527713\pi$
$444$	3.13585e14	0.862479
$445$	4.04251e13	0.109817
$446$	9.15728e13	0.245711
$447$	−3.23734e14	−0.858018
$448$	−1.77297e14	−0.464166
$449$	4.13909e14	1.07041	0.535205	−	0.844722i	$-0.320234\pi$
$449$	4.13909e14	1.07041	0.535205	+	0.844722i	$0.320234\pi$
$450$	−2.18326e13	−0.0557746
$451$	−4.48259e13	−0.113125
$452$	−3.78893e14	−0.944617
$453$	8.52827e13	0.210049
$454$	1.40076e14	0.340845
$455$	−6.97896e13	−0.167775
$456$	−7.73915e13	−0.183818
$457$	4.01500e14	0.942207	0.471104	−	0.882078i	$-0.343856\pi$
$457$	4.01500e14	0.942207	0.471104	+	0.882078i	$0.343856\pi$
$458$	5.09288e13	0.118087
$459$	−5.51422e12	−0.0126332
$460$	1.43059e14	0.323852
$461$	−4.86101e13	−0.108735	−0.0543677	−	0.998521i	$-0.517314\pi$
$461$	−4.86101e13	−0.108735	−0.0543677	+	0.998521i	$0.517314\pi$
$462$	−1.21271e13	−0.0268056
$463$	7.54487e14	1.64800	0.823998	−	0.566593i	$-0.191739\pi$
$463$	7.54487e14	1.64800	0.823998	+	0.566593i	$0.191739\pi$
$464$	−6.83498e14	−1.47533
$465$	−5.28380e13	−0.112708
$466$	−1.23826e14	−0.261029
$467$	9.12970e14	1.90201	0.951007	−	0.309170i	$-0.100051\pi$
$467$	9.12970e14	1.90201	0.951007	+	0.309170i	$0.100051\pi$
$468$	−2.31831e14	−0.477331
$469$	−2.36713e13	−0.0481695
$470$	2.85285e13	0.0573774
$471$	1.95552e14	0.388729
$472$	2.27581e13	0.0447153
$473$	3.33431e14	0.647545
$474$	3.28016e13	0.0629672
$475$	4.68740e14	0.889441
$476$	−1.91581e13	−0.0359347
$477$	−7.01371e13	−0.130046
$478$	−6.94770e13	−0.127347
$479$	7.41424e13	0.134345	0.0671724	−	0.997741i	$-0.478602\pi$
$479$	7.41424e13	0.134345	0.0671724	+	0.997741i	$0.478602\pi$
$480$	3.25614e13	0.0583280
$481$	1.28491e15	2.27548
$482$	−8.36913e13	−0.146528
$483$	−3.12600e14	−0.541103
$484$	4.40558e14	0.753970
$485$	−1.18034e14	−0.199723
$486$	−6.68655e12	−0.0111867
$487$	9.63385e14	1.59364	0.796820	−	0.604216i	$-0.206514\pi$
$487$	9.63385e14	1.59364	0.796820	+	0.604216i	$0.206514\pi$
$488$	−2.74471e14	−0.448939
$489$	−2.89651e14	−0.468465
$490$	1.49463e13	0.0239032
$491$	−5.31814e14	−0.841030	−0.420515	−	0.907286i	$-0.638151\pi$
$491$	−5.31814e14	−0.841030	−0.420515	+	0.907286i	$0.638151\pi$
$492$	−8.58703e13	−0.134287
$493$	−6.88409e13	−0.106461
$494$	−1.56107e14	−0.238739
$495$	−2.09125e13	−0.0316283
$496$	−5.90085e14	−0.882603
$497$	2.25035e14	0.332882
$498$	−1.12525e14	−0.164622
$499$	−7.62146e14	−1.10277	−0.551385	−	0.834251i	$-0.685901\pi$
$499$	−7.62146e14	−1.10277	−0.551385	+	0.834251i	$0.685901\pi$
$500$	−2.67127e14	−0.382282
$501$	2.16309e14	0.306172
$502$	2.20710e14	0.308995
$503$	−3.50610e14	−0.485513	−0.242756	−	0.970087i	$-0.578052\pi$
$503$	−3.50610e14	−0.485513	−0.242756	+	0.970087i	$0.578052\pi$
$504$	−4.71908e13	−0.0646382
$505$	−1.30513e14	−0.176828
$506$	1.01858e14	0.136511
$507$	−5.14428e14	−0.681994
$508$	3.61613e14	0.474235
$509$	−5.65144e14	−0.733181	−0.366591	−	0.930382i	$-0.619475\pi$
$509$	−5.65144e14	−0.733181	−0.366591	+	0.930382i	$0.619475\pi$
$510$	1.03615e12	0.00132981
$511$	−2.47859e14	−0.314695
$512$	6.12390e14	0.769207
$513$	1.43559e14	0.178395
$514$	2.17735e14	0.267689
$515$	2.66067e14	0.323632
$516$	6.38734e14	0.768682
$517$	−6.47645e14	−0.771150
$518$	1.28757e14	0.151690
$519$	−2.30837e14	−0.269082
$520$	8.84911e13	0.102066
$521$	−2.17536e14	−0.248270	−0.124135	−	0.992265i	$-0.539616\pi$
$521$	−2.17536e14	−0.248270	−0.124135	+	0.992265i	$0.539616\pi$
$522$	−8.34766e13	−0.0942708
$523$	5.34086e14	0.596832	0.298416	−	0.954436i	$-0.403542\pi$
$523$	5.34086e14	0.596832	0.298416	+	0.954436i	$0.403542\pi$
$524$	−1.21008e15	−1.33811
$525$	2.85822e14	0.312766
$526$	−3.41421e13	−0.0369717
$527$	−5.94326e13	−0.0636892
$528$	−2.33546e14	−0.247677
$529$	1.67280e15	1.75565
$530$	1.31792e13	0.0136890
$531$	−4.22156e13	−0.0433963
$532$	4.98766e14	0.507437
$533$	−3.51852e14	−0.354291
$534$	5.51374e13	0.0549503
$535$	2.01061e14	0.198327
$536$	3.00145e13	0.0293039
$537$	2.76137e14	0.266850
$538$	−1.57208e14	−0.150374
$539$	−3.39307e14	−0.321258
$540$	−4.00607e13	−0.0375451
$541$	1.01852e15	0.944898	0.472449	−	0.881358i	$-0.343370\pi$
$541$	1.01852e15	0.944898	0.472449	+	0.881358i	$0.343370\pi$
$542$	3.25720e14	0.299122
$543$	−3.81327e14	−0.346656
$544$	3.66253e13	0.0329600
$545$	−4.07530e14	−0.363060
$546$	−9.51889e13	−0.0839512
$547$	5.00644e14	0.437118	0.218559	−	0.975824i	$-0.429864\pi$
$547$	5.00644e14	0.437118	0.218559	+	0.975824i	$0.429864\pi$
$548$	1.40663e15	1.21587
$549$	5.09134e14	0.435697
$550$	−9.31330e13	−0.0789058
$551$	1.79222e15	1.50334
$552$	3.96368e14	0.329180
$553$	−4.29423e14	−0.353100
$554$	3.46557e14	0.282144
$555$	2.22033e14	0.178981
$556$	−6.75051e13	−0.0538797
$557$	−1.12979e15	−0.892886	−0.446443	−	0.894812i	$-0.647309\pi$
$557$	−1.12979e15	−0.892886	−0.446443	+	0.894812i	$0.647309\pi$
$558$	−7.20680e13	−0.0563968
$559$	2.61720e15	2.02802
$560$	−1.34681e14	−0.103341
$561$	−2.35225e13	−0.0178726
$562$	7.27012e13	0.0547006
$563$	1.26181e15	0.940152	0.470076	−	0.882626i	$-0.344226\pi$
$563$	1.26181e15	0.940152	0.470076	+	0.882626i	$0.344226\pi$
$564$	−1.24065e15	−0.915410
$565$	−2.68275e14	−0.196026
$566$	−2.21892e14	−0.160565
$567$	8.75373e13	0.0627316
$568$	−2.85338e14	−0.202509
$569$	2.42444e15	1.70410	0.852048	−	0.523464i	$-0.175361\pi$
$569$	2.42444e15	1.70410	0.852048	+	0.523464i	$0.175361\pi$
$570$	−2.69755e13	−0.0187784
$571$	2.53107e15	1.74504	0.872521	−	0.488576i	$-0.162484\pi$
$571$	2.53107e15	1.74504	0.872521	+	0.488576i	$0.162484\pi$
$572$	−9.88940e14	−0.675292
$573$	−1.50651e15	−1.01888
$574$	−3.52580e13	−0.0236179
$575$	−2.40069e15	−1.59281
$576$	−4.17010e14	−0.274046
$577$	1.93944e15	1.26244	0.631219	−	0.775604i	$-0.282555\pi$
$577$	1.93944e15	1.26244	0.631219	+	0.775604i	$0.282555\pi$
$578$	−2.69298e14	−0.173632
$579$	4.02986e14	0.257370
$580$	−5.00128e14	−0.316393
$581$	1.47313e15	0.923150
$582$	−1.60992e14	−0.0999371
$583$	−2.99189e14	−0.183979
$584$	3.14278e14	0.191445
$585$	−1.64148e14	−0.0990554
$586$	−3.87441e14	−0.231616
$587$	−1.27549e15	−0.755383	−0.377691	−	0.925932i	$-0.623282\pi$
$587$	−1.27549e15	−0.755383	−0.377691	+	0.925932i	$0.623282\pi$
$588$	−6.49989e14	−0.381356
$589$	1.54728e15	0.899363
$590$	7.93255e12	0.00456801
$591$	8.28928e14	0.472918
$592$	2.47963e15	1.40158
$593$	2.98297e15	1.67051	0.835253	−	0.549866i	$-0.185321\pi$
$593$	2.98297e15	1.67051	0.835253	+	0.549866i	$0.185321\pi$
$594$	−2.85234e13	−0.0158261
$595$	−1.35649e13	−0.00745713
$596$	−2.64545e15	−1.44094
$597$	−1.89375e15	−1.02203
$598$	7.99516e14	0.427534
$599$	6.46227e14	0.342403	0.171202	−	0.985236i	$-0.445235\pi$
$599$	6.46227e14	0.342403	0.171202	+	0.985236i	$0.445235\pi$
$600$	−3.62414e14	−0.190271
$601$	3.46992e15	1.80513	0.902567	−	0.430549i	$-0.141680\pi$
$601$	3.46992e15	1.80513	0.902567	+	0.430549i	$0.141680\pi$
$602$	2.62262e14	0.135193
$603$	−5.56759e13	−0.0284395
$604$	6.96904e14	0.352752
$605$	3.11937e14	0.156463
$606$	−1.78012e14	−0.0884808
$607$	2.95267e14	0.145438	0.0727188	−	0.997352i	$-0.476832\pi$
$607$	2.95267e14	0.145438	0.0727188	+	0.997352i	$0.476832\pi$
$608$	−9.53512e14	−0.465432
$609$	1.09284e15	0.528640
$610$	−9.56693e13	−0.0458626
$611$	−5.08355e15	−2.41513
$612$	−4.50605e13	−0.0212160
$613$	−9.01113e14	−0.420481	−0.210241	−	0.977650i	$-0.567425\pi$
$613$	−9.01113e14	−0.420481	−0.210241	+	0.977650i	$0.567425\pi$
$614$	−4.01921e14	−0.185872
$615$	−6.08004e13	−0.0278672
$616$	−2.01305e14	−0.0914454
$617$	−3.98663e14	−0.179489	−0.0897444	−	0.995965i	$-0.528605\pi$
$617$	−3.98663e14	−0.179489	−0.0897444	+	0.995965i	$0.528605\pi$
$618$	3.62899e14	0.161938
$619$	2.59898e15	1.14949	0.574744	−	0.818333i	$-0.305101\pi$
$619$	2.59898e15	1.14949	0.574744	+	0.818333i	$0.305101\pi$
$620$	−4.31776e14	−0.189280
$621$	−7.35248e14	−0.319470
$622$	−1.45774e14	−0.0627818
$623$	−7.21834e14	−0.308143
$624$	−1.83317e15	−0.775690
$625$	2.09852e15	0.880184
$626$	1.65955e14	0.0689972
$627$	6.12389e14	0.252381
$628$	1.59799e15	0.652823
$629$	2.49745e14	0.101139
$630$	−1.64488e13	−0.00660329
$631$	−6.97014e13	−0.0277383	−0.0138691	−	0.999904i	$-0.504415\pi$
$631$	−6.97014e13	−0.0277383	−0.0138691	+	0.999904i	$0.504415\pi$
$632$	5.44496e14	0.214808
$633$	−6.13875e14	−0.240082
$634$	2.22088e14	0.0861062
$635$	2.56040e14	0.0984128
$636$	−5.73139e14	−0.218397
$637$	−2.66332e15	−1.00613
$638$	−3.56093e14	−0.133367
$639$	5.29292e14	0.196535
$640$	3.52786e14	0.129874
$641$	−3.70395e15	−1.35190	−0.675952	−	0.736946i	$-0.736267\pi$
$641$	−3.70395e15	−1.35190	−0.675952	+	0.736946i	$0.736267\pi$
$642$	2.74236e14	0.0992388
$643$	3.57318e14	0.128202	0.0641009	−	0.997943i	$-0.479582\pi$
$643$	3.57318e14	0.128202	0.0641009	+	0.997943i	$0.479582\pi$
$644$	−2.55447e15	−0.908718
$645$	4.52255e14	0.159516
$646$	−3.03422e13	−0.0106113
$647$	1.55248e14	0.0538333	0.0269167	−	0.999638i	$-0.491431\pi$
$647$	1.55248e14	0.0538333	0.0269167	+	0.999638i	$0.491431\pi$
$648$	−1.10995e14	−0.0381627
$649$	−1.80082e14	−0.0613939
$650$	−7.31028e14	−0.247121
$651$	9.43481e14	0.316255
$652$	−2.36694e15	−0.786730
$653$	−2.43695e15	−0.803200	−0.401600	−	0.915815i	$-0.631546\pi$
$653$	−2.43695e15	−0.803200	−0.401600	+	0.915815i	$0.631546\pi$
$654$	−5.55847e14	−0.181668
$655$	−8.56796e14	−0.277684
$656$	−6.79008e14	−0.218224
$657$	−5.82974e14	−0.185798
$658$	−5.09407e14	−0.160999
$659$	4.86047e14	0.152338	0.0761690	−	0.997095i	$-0.475731\pi$
$659$	4.86047e14	0.152338	0.0761690	+	0.997095i	$0.475731\pi$
$660$	−1.70890e14	−0.0531160
$661$	−3.09073e15	−0.952694	−0.476347	−	0.879257i	$-0.658039\pi$
$661$	−3.09073e15	−0.952694	−0.476347	+	0.879257i	$0.658039\pi$
$662$	−8.52556e14	−0.260618
$663$	−1.84635e14	−0.0559743
$664$	−1.86788e15	−0.561598
$665$	3.53151e14	0.105303
$666$	3.02841e14	0.0895583
$667$	−9.17902e15	−2.69218
$668$	1.76761e15	0.514180
$669$	−2.81969e15	−0.813501
$670$	1.04618e13	0.00299361
$671$	2.17185e15	0.616392
$672$	−5.81420e14	−0.163666
$673$	5.15556e15	1.43944	0.719719	−	0.694266i	$-0.244271\pi$
$673$	5.15556e15	1.43944	0.719719	+	0.694266i	$0.244271\pi$
$674$	8.34711e14	0.231157
$675$	6.72265e14	0.184659
$676$	−4.20375e15	−1.14533
$677$	−1.78330e15	−0.481934	−0.240967	−	0.970533i	$-0.577464\pi$
$677$	−1.78330e15	−0.481934	−0.240967	+	0.970533i	$0.577464\pi$
$678$	−3.65912e14	−0.0980873
$679$	2.10763e15	0.560416
$680$	1.71998e13	0.00453654
$681$	−4.31319e15	−1.12847
$682$	−3.07426e14	−0.0797860
$683$	6.38541e15	1.64390	0.821949	−	0.569561i	$-0.192887\pi$
$683$	6.38541e15	1.64390	0.821949	+	0.569561i	$0.192887\pi$
$684$	1.17312e15	0.299594
$685$	9.95961e14	0.252316
$686$	−6.58640e14	−0.165526
$687$	−1.56819e15	−0.390964
$688$	5.05070e15	1.24915
$689$	−2.34842e15	−0.576197
$690$	1.38157e14	0.0336282
$691$	−3.04808e15	−0.736033	−0.368016	−	0.929819i	$-0.619963\pi$
$691$	−3.04808e15	−0.736033	−0.368016	+	0.929819i	$0.619963\pi$
$692$	−1.88632e15	−0.451890
$693$	3.73415e14	0.0887480
$694$	−1.40227e15	−0.330640
$695$	−4.77969e13	−0.0111811
$696$	−1.38568e15	−0.321598
$697$	−6.83887e13	−0.0157472
$698$	7.25338e14	0.165705
$699$	3.81282e15	0.864215
$700$	2.33565e15	0.525253
$701$	−1.60759e15	−0.358696	−0.179348	−	0.983786i	$-0.557399\pi$
$701$	−1.60759e15	−0.358696	−0.179348	+	0.983786i	$0.557399\pi$
$702$	−2.23888e14	−0.0495652
$703$	−6.50191e15	−1.42819
$704$	−1.77887e15	−0.387700
$705$	−8.78444e14	−0.189965
$706$	−8.88607e14	−0.190671
$707$	2.33044e15	0.496172
$708$	−3.44973e14	−0.0728789
$709$	1.47197e15	0.308564	0.154282	−	0.988027i	$-0.450694\pi$
$709$	1.47197e15	0.308564	0.154282	+	0.988027i	$0.450694\pi$
$710$	−9.94570e13	−0.0206878
$711$	−1.01002e15	−0.208472
$712$	9.15264e14	0.187459
$713$	−7.92454e15	−1.61058
$714$	−1.85017e13	−0.00373139
$715$	−7.00218e14	−0.140136
$716$	2.25651e15	0.448142
$717$	2.13932e15	0.421620
$718$	−1.31442e14	−0.0257070
$719$	−2.97725e14	−0.0577838	−0.0288919	−	0.999583i	$-0.509198\pi$
$719$	−2.97725e14	−0.0577838	−0.0288919	+	0.999583i	$0.509198\pi$
$720$	−3.16775e14	−0.0610129
$721$	−4.75091e15	−0.908098
$722$	−1.29371e14	−0.0245405
$723$	2.57701e15	0.485126
$724$	−3.11609e15	−0.582167
$725$	8.39273e15	1.55612
$726$	4.25464e14	0.0782909
$727$	−1.05253e16	−1.92219	−0.961097	−	0.276212i	$-0.910921\pi$
$727$	−1.05253e16	−1.92219	−0.961097	+	0.276212i	$0.910921\pi$
$728$	−1.58010e15	−0.286394
$729$	2.05891e14	0.0370370
$730$	1.09544e14	0.0195575
$731$	5.08700e14	0.0901396
$732$	4.16049e15	0.731701
$733$	−1.44108e15	−0.251545	−0.125773	−	0.992059i	$-0.540141\pi$
$733$	−1.44108e15	−0.251545	−0.125773	+	0.992059i	$0.540141\pi$
$734$	−1.15557e15	−0.200202
$735$	−4.60224e14	−0.0791387
$736$	4.88350e15	0.833495
$737$	−2.37501e14	−0.0402341
$738$	−8.29282e13	−0.0139442
$739$	5.43782e15	0.907571	0.453786	−	0.891111i	$-0.350073\pi$
$739$	5.43782e15	0.907571	0.453786	+	0.891111i	$0.350073\pi$
$740$	1.81439e15	0.300577
$741$	4.80682e15	0.790419
$742$	−2.35328e14	−0.0384108
$743$	5.32566e15	0.862849	0.431425	−	0.902149i	$-0.358011\pi$
$743$	5.32566e15	0.862849	0.431425	+	0.902149i	$0.358011\pi$
$744$	−1.19631e15	−0.192394
$745$	−1.87311e15	−0.299022
$746$	1.64782e15	0.261123
$747$	3.46486e15	0.545032
$748$	−1.92218e14	−0.0300148
$749$	−3.59017e15	−0.556499
$750$	−2.57975e14	−0.0396954
$751$	3.43705e15	0.525008	0.262504	−	0.964931i	$-0.415452\pi$
$751$	3.43705e15	0.525008	0.262504	+	0.964931i	$0.415452\pi$
$752$	−9.81030e15	−1.48759
$753$	−6.79605e15	−1.02302
$754$	−2.79507e15	−0.417687
$755$	4.93443e14	0.0732029
$756$	7.15328e14	0.105350
$757$	1.01041e16	1.47731	0.738654	−	0.674085i	$-0.235462\pi$
$757$	1.01041e16	1.47731	0.738654	+	0.674085i	$0.235462\pi$
$758$	6.71764e14	0.0975071
$759$	−3.13640e15	−0.451962
$760$	−4.47784e14	−0.0640611
$761$	7.59905e15	1.07930	0.539652	−	0.841888i	$-0.318556\pi$
$761$	7.59905e15	1.07930	0.539652	+	0.841888i	$0.318556\pi$
$762$	3.49223e14	0.0492437
$763$	7.27689e15	1.01873
$764$	−1.23107e16	−1.71108
$765$	−3.19051e13	−0.00440273
$766$	1.78060e15	0.243955
$767$	−1.41352e15	−0.192277
$768$	−3.03338e15	−0.409675
$769$	1.12501e16	1.50856	0.754281	−	0.656551i	$-0.227985\pi$
$769$	1.12501e16	1.50856	0.754281	+	0.656551i	$0.227985\pi$
$770$	−7.01668e13	−0.00934184
$771$	−6.70444e15	−0.886265
$772$	3.29308e15	0.432222
$773$	−4.90363e15	−0.639044	−0.319522	−	0.947579i	$-0.603522\pi$
$773$	−4.90363e15	−0.639044	−0.319522	+	0.947579i	$0.603522\pi$
$774$	6.16850e14	0.0798186
$775$	7.24571e15	0.930939
$776$	−2.67241e15	−0.340929
$777$	−3.96465e15	−0.502214
$778$	9.41084e14	0.118370
$779$	1.78045e15	0.222368
$780$	−1.34137e15	−0.166352
$781$	2.25784e15	0.278043
$782$	1.55400e14	0.0190027
$783$	2.57040e15	0.312112
$784$	−5.13970e15	−0.619725
$785$	1.13145e15	0.135473
$786$	−1.16862e15	−0.138947
$787$	−9.33119e15	−1.10173	−0.550866	−	0.834594i	$-0.685702\pi$
$787$	−9.33119e15	−1.10173	−0.550866	+	0.834594i	$0.685702\pi$
$788$	6.77374e15	0.794208
$789$	1.05130e15	0.122406
$790$	1.89789e14	0.0219443
$791$	4.79034e15	0.550042
$792$	−4.73478e14	−0.0539898
$793$	1.70475e16	1.93045
$794$	−1.82519e15	−0.205256
$795$	−4.05810e14	−0.0453215
$796$	−1.54751e16	−1.71638
$797$	9.30024e15	1.02441	0.512204	−	0.858864i	$-0.328829\pi$
$797$	9.30024e15	1.02441	0.512204	+	0.858864i	$0.328829\pi$
$798$	4.81677e14	0.0526914
$799$	−9.88080e14	−0.107346
$800$	−4.46517e15	−0.481773
$801$	−1.69778e15	−0.181929
$802$	−4.57272e13	−0.00486649
$803$	−2.48684e15	−0.262853
$804$	−4.54966e14	−0.0477607
$805$	−1.80869e15	−0.188576
$806$	−2.41308e15	−0.249878
$807$	4.84072e15	0.497858
$808$	−2.95493e15	−0.301846
$809$	−1.14715e16	−1.16387	−0.581935	−	0.813235i	$-0.697704\pi$
$809$	−1.14715e16	−1.16387	−0.581935	+	0.813235i	$0.697704\pi$
$810$	−3.86881e13	−0.00389861
$811$	1.30920e16	1.31036	0.655179	−	0.755473i	$-0.272593\pi$
$811$	1.30920e16	1.31036	0.655179	+	0.755473i	$0.272593\pi$
$812$	8.93033e15	0.887788
$813$	−1.00295e16	−0.990334
$814$	1.29185e15	0.126700
$815$	−1.67591e15	−0.163262
$816$	−3.56310e14	−0.0344772
$817$	−1.32436e16	−1.27287
$818$	1.89823e15	0.181220
$819$	2.93104e15	0.277946
$820$	−4.96842e14	−0.0467996
$821$	−9.77412e15	−0.914514	−0.457257	−	0.889335i	$-0.651168\pi$
$821$	−9.77412e15	−0.914514	−0.457257	+	0.889335i	$0.651168\pi$
$822$	1.35843e15	0.126253
$823$	9.15167e15	0.844892	0.422446	−	0.906388i	$-0.361172\pi$
$823$	9.15167e15	0.844892	0.422446	+	0.906388i	$0.361172\pi$
$824$	6.02401e15	0.552441
$825$	2.86773e15	0.261242
$826$	−1.41644e14	−0.0128177
$827$	−1.75245e16	−1.57531	−0.787654	−	0.616117i	$-0.788705\pi$
$827$	−1.75245e16	−1.57531	−0.787654	+	0.616117i	$0.788705\pi$
$828$	−6.00822e15	−0.536511
$829$	−1.97295e16	−1.75011	−0.875056	−	0.484022i	$-0.839175\pi$
$829$	−1.97295e16	−1.75011	−0.875056	+	0.484022i	$0.839175\pi$
$830$	−6.51067e14	−0.0573715
$831$	−1.06711e16	−0.934125
$832$	−1.39629e16	−1.21422
$833$	−5.17663e14	−0.0447198
$834$	−6.51922e13	−0.00559477
$835$	1.25155e15	0.106702
$836$	5.00425e15	0.423843
$837$	2.21910e15	0.186719
$838$	−1.60677e14	−0.0134311
$839$	5.08692e15	0.422439	0.211219	−	0.977439i	$-0.432257\pi$
$839$	5.08692e15	0.422439	0.211219	+	0.977439i	$0.432257\pi$
$840$	−2.73044e14	−0.0225267
$841$	1.98889e16	1.63017
$842$	−2.41945e14	−0.0197016
$843$	−2.23860e15	−0.181103
$844$	−5.01639e15	−0.403189
$845$	−2.97646e15	−0.237678
$846$	−1.19815e15	−0.0950545
$847$	−5.56997e15	−0.439030
$848$	−4.53202e15	−0.354907
$849$	6.83246e15	0.531600
$850$	−1.42088e14	−0.0109838
$851$	3.33001e16	2.55760
$852$	4.32521e15	0.330057
$853$	1.72061e16	1.30455	0.652277	−	0.757981i	$-0.273814\pi$
$853$	1.72061e16	1.30455	0.652277	+	0.757981i	$0.273814\pi$
$854$	1.70828e15	0.128689
$855$	8.30624e14	0.0621714
$856$	4.55222e15	0.338546
$857$	−1.38966e16	−1.02687	−0.513434	−	0.858129i	$-0.671627\pi$
$857$	−1.38966e16	−1.02687	−0.513434	+	0.858129i	$0.671627\pi$
$858$	−9.55057e14	−0.0701212
$859$	−1.08043e15	−0.0788199	−0.0394100	−	0.999223i	$-0.512548\pi$
$859$	−1.08043e15	−0.0788199	−0.0394100	+	0.999223i	$0.512548\pi$
$860$	3.69569e15	0.267889
$861$	1.08566e15	0.0781944
$862$	−2.88582e15	−0.206528
$863$	−2.25406e16	−1.60290	−0.801448	−	0.598064i	$-0.795937\pi$
$863$	−2.25406e16	−1.60290	−0.801448	+	0.598064i	$0.795937\pi$
$864$	−1.36752e15	−0.0966293
$865$	−1.33561e15	−0.0937759
$866$	3.25977e15	0.227425
$867$	8.29218e15	0.574862
$868$	7.70983e15	0.531112
$869$	−4.30852e15	−0.294931
$870$	−4.82992e14	−0.0328537
$871$	−1.86421e15	−0.126007
$872$	−9.22688e15	−0.619747
$873$	4.95722e15	0.330872
$874$	−4.04573e15	−0.268339
$875$	3.37729e15	0.222599
$876$	−4.76389e15	−0.312025
$877$	2.44292e15	0.159006	0.0795028	−	0.996835i	$-0.474667\pi$
$877$	2.44292e15	0.159006	0.0795028	+	0.996835i	$0.474667\pi$
$878$	−5.33231e14	−0.0344902
$879$	1.19300e16	0.766834
$880$	−1.35129e15	−0.0863165
$881$	−2.77508e16	−1.76160	−0.880801	−	0.473487i	$-0.842995\pi$
$881$	−2.77508e16	−1.76160	−0.880801	+	0.473487i	$0.842995\pi$
$882$	−6.27719e14	−0.0395993
$883$	2.43119e16	1.52417	0.762086	−	0.647475i	$-0.224175\pi$
$883$	2.43119e16	1.52417	0.762086	+	0.647475i	$0.224175\pi$
$884$	−1.50878e15	−0.0940021
$885$	−2.44258e14	−0.0151238
$886$	−4.92843e14	−0.0303265
$887$	1.62559e16	0.994103	0.497051	−	0.867721i	$-0.334416\pi$
$887$	1.62559e16	0.994103	0.497051	+	0.867721i	$0.334416\pi$
$888$	5.02706e15	0.305522
$889$	−4.57187e15	−0.276143
$890$	3.19023e14	0.0191504
$891$	8.78286e14	0.0523973
$892$	−2.30417e16	−1.36618
$893$	2.57239e16	1.51584
$894$	−2.55481e15	−0.149624
$895$	1.59772e15	0.0929980
$896$	−6.29938e15	−0.364421
$897$	−2.46185e16	−1.41548
$898$	3.26645e15	0.186662
$899$	2.77038e16	1.57348
$900$	5.49354e15	0.310112
$901$	−4.56458e14	−0.0256103
$902$	−3.53753e14	−0.0197272
$903$	−8.07551e15	−0.447597
$904$	−6.07401e15	−0.334618
$905$	−2.20634e15	−0.120811
$906$	6.73027e14	0.0366292
$907$	1.95882e16	1.05963	0.529815	−	0.848113i	$-0.322261\pi$
$907$	1.95882e16	1.05963	0.529815	+	0.848113i	$0.322261\pi$
$908$	−3.52461e16	−1.89513
$909$	5.48130e15	0.292942
$910$	−5.50759e14	−0.0292573
$911$	−6.40605e15	−0.338251	−0.169125	−	0.985595i	$-0.554094\pi$
$911$	−6.40605e15	−0.338251	−0.169125	+	0.985595i	$0.554094\pi$
$912$	9.27625e15	0.486857
$913$	1.47803e16	0.771071
$914$	3.16852e15	0.164306
$915$	2.94583e15	0.151842
$916$	−1.28148e16	−0.656576
$917$	1.52990e16	0.779170
$918$	−4.35167e13	−0.00220303
$919$	9.03519e15	0.454676	0.227338	−	0.973816i	$-0.426998\pi$
$919$	9.03519e15	0.454676	0.227338	+	0.973816i	$0.426998\pi$
$920$	2.29337e15	0.114720
$921$	1.23759e16	0.615386
$922$	−3.83617e14	−0.0189617
$923$	1.77224e16	0.870792
$924$	3.05143e15	0.149042
$925$	−3.04476e16	−1.47834
$926$	5.95419e15	0.287384
$927$	−1.11743e16	−0.536146
$928$	−1.70725e16	−0.814297
$929$	2.26269e16	1.07285	0.536424	−	0.843949i	$-0.319775\pi$
$929$	2.26269e16	1.07285	0.536424	+	0.843949i	$0.319775\pi$
$930$	−4.16982e14	−0.0196545
$931$	1.34770e16	0.631493
$932$	3.11572e16	1.45134
$933$	4.48865e15	0.207858
$934$	7.20489e15	0.331680
$935$	−1.36100e14	−0.00622865
$936$	−3.71647e15	−0.169088
$937$	3.99367e16	1.80636	0.903180	−	0.429262i	$-0.141226\pi$
$937$	3.99367e16	1.80636	0.903180	+	0.429262i	$0.141226\pi$
$938$	−1.86807e14	−0.00839997
$939$	−5.11005e15	−0.228436
$940$	−7.17837e15	−0.319024
$941$	4.19219e16	1.85224	0.926122	−	0.377223i	$-0.123121\pi$
$941$	4.19219e16	1.85224	0.926122	+	0.377223i	$0.123121\pi$
$942$	1.54324e15	0.0677880
$943$	−9.11871e15	−0.398217
$944$	−2.72782e15	−0.118432
$945$	5.06487e14	0.0218622
$946$	2.63134e15	0.112921
$947$	−1.38333e16	−0.590201	−0.295100	−	0.955466i	$-0.595353\pi$
$947$	−1.38333e16	−0.590201	−0.295100	+	0.955466i	$0.595353\pi$
$948$	−8.25358e15	−0.350103
$949$	−1.95199e16	−0.823216
$950$	3.69916e15	0.155104
$951$	−6.83849e15	−0.285081
$952$	−3.07122e14	−0.0127294
$953$	−8.04510e15	−0.331528	−0.165764	−	0.986165i	$-0.553009\pi$
$953$	−8.04510e15	−0.331528	−0.165764	+	0.986165i	$0.553009\pi$
$954$	−5.53502e14	−0.0226779
$955$	−8.71661e15	−0.355082
$956$	1.74819e16	0.708060
$957$	1.09647e16	0.441553
$958$	5.85110e14	0.0234276
$959$	−1.77840e16	−0.707989
$960$	−2.41280e15	−0.0955059
$961$	−1.49088e15	−0.0586763
$962$	1.01401e16	0.396807
$963$	−8.44421e15	−0.328560
$964$	2.10585e16	0.814712
$965$	2.33166e15	0.0896944
$966$	−2.46695e15	−0.0943596
$967$	9.74385e14	0.0370582	0.0185291	−	0.999828i	$-0.494102\pi$
$967$	9.74385e14	0.0370582	0.0185291	+	0.999828i	$0.494102\pi$
$968$	7.06256e15	0.267084
$969$	9.34291e14	0.0351319
$970$	−9.31491e14	−0.0348285
$971$	3.42108e16	1.27191	0.635957	−	0.771725i	$-0.280606\pi$
$971$	3.42108e16	1.27191	0.635957	+	0.771725i	$0.280606\pi$
$972$	1.68248e15	0.0621992
$973$	8.53466e14	0.0313737
$974$	7.60275e15	0.277905
$975$	2.25097e16	0.818170
$976$	3.28985e16	1.18905
$977$	7.60864e14	0.0273456	0.0136728	−	0.999907i	$-0.495648\pi$
$977$	7.60864e14	0.0273456	0.0136728	+	0.999907i	$0.495648\pi$
$978$	−2.28584e15	−0.0816926
$979$	−7.24236e15	−0.257380
$980$	−3.76081e15	−0.132904
$981$	1.71155e16	0.601466
$982$	−4.19692e15	−0.146662
$983$	−3.75600e15	−0.130521	−0.0652607	−	0.997868i	$-0.520788\pi$
$983$	−3.75600e15	−0.130521	−0.0652607	+	0.997868i	$0.520788\pi$
$984$	−1.37658e15	−0.0475695
$985$	4.79614e15	0.164813
$986$	−5.43273e14	−0.0185650
$987$	1.56856e16	0.533035
$988$	3.92798e16	1.32741
$989$	6.78283e16	2.27946
$990$	−1.65035e14	−0.00551547
$991$	1.43031e16	0.475362	0.237681	−	0.971343i	$-0.423613\pi$
$991$	1.43031e16	0.475362	0.237681	+	0.971343i	$0.423613\pi$
$992$	−1.47392e16	−0.487147
$993$	2.62517e16	0.862853
$994$	1.77591e15	0.0580492
$995$	−1.09572e16	−0.356181
$996$	2.83137e16	0.915316
$997$	−1.74274e15	−0.0560287	−0.0280143	−	0.999608i	$-0.508918\pi$
$997$	−1.74274e15	−0.0560287	−0.0280143	+	0.999608i	$0.508918\pi$
$998$	−6.01463e15	−0.192305
$999$	−9.32501e15	−0.296510

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.16	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+7.89171 q^{2} -243.000 q^{3} -1985.72 q^{4} -1405.99 q^{5} -1917.69 q^{6} +25105.4 q^{7} -31832.9 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+7.89171 q^{2} -243.000 q^{3} -1985.72 q^{4} -1405.99 q^{5} -1917.69 q^{6} +25105.4 q^{7} -31832.9 q^{8} +59049.0 q^{9} -11095.6 q^{10} +251890. q^{11} +482530. q^{12} +1.97716e6 q^{13} +198125. q^{14} +341655. q^{15} +3.81554e6 q^{16} +384296. q^{17} +465997. q^{18} -1.00048e7 q^{19} +2.79190e6 q^{20} -6.10062e6 q^{21} +1.98784e6 q^{22} +5.12407e7 q^{23} +7.73541e6 q^{24} -4.68513e7 q^{25} +1.56031e7 q^{26} -1.43489e7 q^{27} -4.98524e7 q^{28} -1.79135e8 q^{29} +2.69624e6 q^{30} -1.54653e8 q^{31} +9.53050e7 q^{32} -6.12092e7 q^{33} +3.03275e6 q^{34} -3.52980e7 q^{35} -1.17255e8 q^{36} +6.49876e8 q^{37} -7.89553e7 q^{38} -4.80449e8 q^{39} +4.47567e7 q^{40} -1.77958e8 q^{41} -4.81443e7 q^{42} +1.32372e9 q^{43} -5.00183e8 q^{44} -8.30222e7 q^{45} +4.04377e8 q^{46} -2.57114e9 q^{47} -9.27176e8 q^{48} -1.34704e9 q^{49} -3.69737e8 q^{50} -9.33839e7 q^{51} -3.92608e9 q^{52} -1.18778e9 q^{53} -1.13237e8 q^{54} -3.54154e8 q^{55} -7.99180e8 q^{56} +2.43118e9 q^{57} -1.41368e9 q^{58} -7.14924e8 q^{59} -6.78432e8 q^{60} +8.62224e9 q^{61} -1.22048e9 q^{62} +1.48245e9 q^{63} -7.06211e9 q^{64} -2.77986e9 q^{65} -4.83046e8 q^{66} -9.42876e8 q^{67} -7.63104e8 q^{68} -1.24515e10 q^{69} -2.78561e8 q^{70} +8.96360e9 q^{71} -1.87970e9 q^{72} -9.87272e9 q^{73} +5.12863e9 q^{74} +1.13849e10 q^{75} +1.98668e10 q^{76} +6.32381e9 q^{77} -3.79156e9 q^{78} -1.71048e10 q^{79} -5.36460e9 q^{80} +3.48678e9 q^{81} -1.40440e9 q^{82} +5.86777e10 q^{83} +1.21141e10 q^{84} -5.40315e8 q^{85} +1.04464e10 q^{86} +4.35299e10 q^{87} -8.01840e9 q^{88} -2.87521e10 q^{89} -6.55187e8 q^{90} +4.96374e10 q^{91} -1.01750e11 q^{92} +3.75807e10 q^{93} -2.02907e10 q^{94} +1.40667e10 q^{95} -2.31591e10 q^{96} +8.39510e10 q^{97} -1.06305e10 q^{98} +1.48738e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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

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