LMFDB - Embedded newform 177.12.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-66.1318 q^{2} -243.000 q^{3} +2325.41 q^{4} +6882.52 q^{5} +16070.0 q^{6} +7668.92 q^{7} -18345.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-66.1318 q^{2} -243.000 q^{3} +2325.41 q^{4} +6882.52 q^{5} +16070.0 q^{6} +7668.92 q^{7} -18345.7 q^{8} +59049.0 q^{9} -455153. q^{10} +265231. q^{11} -565075. q^{12} -2.03008e6 q^{13} -507159. q^{14} -1.67245e6 q^{15} -3.54921e6 q^{16} -2.19078e6 q^{17} -3.90502e6 q^{18} +1.39158e7 q^{19} +1.60047e7 q^{20} -1.86355e6 q^{21} -1.75402e7 q^{22} -1.47893e7 q^{23} +4.45802e6 q^{24} -1.45904e6 q^{25} +1.34253e8 q^{26} -1.43489e7 q^{27} +1.78334e7 q^{28} +1.32726e8 q^{29} +1.10602e8 q^{30} -6.41414e7 q^{31} +2.72287e8 q^{32} -6.44512e7 q^{33} +1.44880e8 q^{34} +5.27815e7 q^{35} +1.37313e8 q^{36} +2.46731e8 q^{37} -9.20275e8 q^{38} +4.93310e8 q^{39} -1.26265e8 q^{40} -1.45972e7 q^{41} +1.23240e8 q^{42} +6.41487e7 q^{43} +6.16772e8 q^{44} +4.06406e8 q^{45} +9.78041e8 q^{46} +1.68292e9 q^{47} +8.62457e8 q^{48} -1.91851e9 q^{49} +9.64887e7 q^{50} +5.32358e8 q^{51} -4.72078e9 q^{52} +5.02137e9 q^{53} +9.48919e8 q^{54} +1.82546e9 q^{55} -1.40692e8 q^{56} -3.38153e9 q^{57} -8.77743e9 q^{58} -7.14924e8 q^{59} -3.88914e9 q^{60} +1.12753e9 q^{61} +4.24178e9 q^{62} +4.52842e8 q^{63} -1.07381e10 q^{64} -1.39721e10 q^{65} +4.26227e9 q^{66} -1.51714e10 q^{67} -5.09446e9 q^{68} +3.59379e9 q^{69} -3.49053e9 q^{70} -5.00236e9 q^{71} -1.08330e9 q^{72} +2.20994e10 q^{73} -1.63167e10 q^{74} +3.54546e8 q^{75} +3.23599e10 q^{76} +2.03404e9 q^{77} -3.26235e10 q^{78} -4.29957e10 q^{79} -2.44275e10 q^{80} +3.48678e9 q^{81} +9.65342e8 q^{82} -1.16822e10 q^{83} -4.33351e9 q^{84} -1.50781e10 q^{85} -4.24227e9 q^{86} -3.22525e10 q^{87} -4.86587e9 q^{88} -8.90945e10 q^{89} -2.68763e10 q^{90} -1.55685e10 q^{91} -3.43911e10 q^{92} +1.55864e10 q^{93} -1.11294e11 q^{94} +9.57757e10 q^{95} -6.61659e10 q^{96} +1.57286e11 q^{97} +1.26875e11 q^{98} +1.56616e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−66.1318	−1.46132	−0.730660	−	0.682742i	$-0.760787\pi$
$2$	−66.1318	−1.46132	−0.730660	+	0.682742i	$0.760787\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2325.41	1.13546
$5$	6882.52	0.984946	0.492473	−	0.870328i	$-0.336093\pi$
$5$	6882.52	0.984946	0.492473	+	0.870328i	$0.336093\pi$
$6$	16070.0	0.843693
$7$	7668.92	0.172463	0.0862313	−	0.996275i	$-0.472518\pi$
$7$	7668.92	0.172463	0.0862313	+	0.996275i	$0.472518\pi$
$8$	−18345.7	−0.197943
$9$	59049.0	0.333333
$10$	−455153.	−1.43932
$11$	265231.	0.496552	0.248276	−	0.968689i	$-0.420136\pi$
$11$	265231.	0.496552	0.248276	+	0.968689i	$0.420136\pi$
$12$	−565075.	−0.655555
$13$	−2.03008e6	−1.51644	−0.758220	−	0.651999i	$-0.773931\pi$
$13$	−2.03008e6	−1.51644	−0.758220	+	0.651999i	$0.773931\pi$
$14$	−507159.	−0.252023
$15$	−1.67245e6	−0.568659
$16$	−3.54921e6	−0.846197
$17$	−2.19078e6	−0.374222	−0.187111	−	0.982339i	$-0.559912\pi$
$17$	−2.19078e6	−0.374222	−0.187111	+	0.982339i	$0.559912\pi$
$18$	−3.90502e6	−0.487107
$19$	1.39158e7	1.28933	0.644663	−	0.764467i	$-0.276998\pi$
$19$	1.39158e7	1.28933	0.644663	+	0.764467i	$0.276998\pi$
$20$	1.60047e7	1.11836
$21$	−1.86355e6	−0.0995713
$22$	−1.75402e7	−0.725622
$23$	−1.47893e7	−0.479119	−0.239560	−	0.970882i	$-0.577003\pi$
$23$	−1.47893e7	−0.479119	−0.239560	+	0.970882i	$0.577003\pi$
$24$	4.45802e6	0.114282
$25$	−1.45904e6	−0.0298811
$26$	1.34253e8	2.21600
$27$	−1.43489e7	−0.192450
$28$	1.78334e7	0.195823
$29$	1.32726e8	1.20162	0.600811	−	0.799391i	$-0.294844\pi$
$29$	1.32726e8	1.20162	0.600811	+	0.799391i	$0.294844\pi$
$30$	1.10602e8	0.830992
$31$	−6.41414e7	−0.402392	−0.201196	−	0.979551i	$-0.564483\pi$
$31$	−6.41414e7	−0.402392	−0.201196	+	0.979551i	$0.564483\pi$
$32$	2.72287e8	1.43451
$33$	−6.44512e7	−0.286685
$34$	1.44880e8	0.546857
$35$	5.27815e7	0.169866
$36$	1.37313e8	0.378485
$37$	2.46731e8	0.584943	0.292471	−	0.956274i	$-0.405522\pi$
$37$	2.46731e8	0.584943	0.292471	+	0.956274i	$0.405522\pi$
$38$	−9.20275e8	−1.88412
$39$	4.93310e8	0.875517
$40$	−1.26265e8	−0.194963
$41$	−1.45972e7	−0.0196770	−0.00983852	−	0.999952i	$-0.503132\pi$
$41$	−1.45972e7	−0.0196770	−0.00983852	+	0.999952i	$0.503132\pi$
$42$	1.23240e8	0.145505
$43$	6.41487e7	0.0665444	0.0332722	−	0.999446i	$-0.489407\pi$
$43$	6.41487e7	0.0665444	0.0332722	+	0.999446i	$0.489407\pi$
$44$	6.16772e8	0.563813
$45$	4.06406e8	0.328315
$46$	9.78041e8	0.700146
$47$	1.68292e9	1.07035	0.535174	−	0.844742i	$-0.320246\pi$
$47$	1.68292e9	1.07035	0.535174	+	0.844742i	$0.320246\pi$
$48$	8.62457e8	0.488552
$49$	−1.91851e9	−0.970257
$50$	9.64887e7	0.0436658
$51$	5.32358e8	0.216057
$52$	−4.72078e9	−1.72185
$53$	5.02137e9	1.64932	0.824660	−	0.565629i	$-0.191367\pi$
$53$	5.02137e9	1.64932	0.824660	+	0.565629i	$0.191367\pi$
$54$	9.48919e8	0.281231
$55$	1.82546e9	0.489077
$56$	−1.40692e8	−0.0341378
$57$	−3.38153e9	−0.744393
$58$	−8.77743e9	−1.75595
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−3.88914e9	−0.645687
$61$	1.12753e9	0.170928	0.0854642	−	0.996341i	$-0.472763\pi$
$61$	1.12753e9	0.170928	0.0854642	+	0.996341i	$0.472763\pi$
$62$	4.24178e9	0.588023
$63$	4.52842e8	0.0574875
$64$	−1.07381e10	−1.25008
$65$	−1.39721e10	−1.49361
$66$	4.26227e9	0.418938
$67$	−1.51714e10	−1.37282	−0.686412	−	0.727213i	$-0.740815\pi$
$67$	−1.51714e10	−1.37282	−0.686412	+	0.727213i	$0.740815\pi$
$68$	−5.09446e9	−0.424912
$69$	3.59379e9	0.276620
$70$	−3.49053e9	−0.248229
$71$	−5.00236e9	−0.329044	−0.164522	−	0.986373i	$-0.552608\pi$
$71$	−5.00236e9	−0.329044	−0.164522	+	0.986373i	$0.552608\pi$
$72$	−1.08330e9	−0.0659810
$73$	2.20994e10	1.24768	0.623841	−	0.781551i	$-0.285571\pi$
$73$	2.20994e10	1.24768	0.623841	+	0.781551i	$0.285571\pi$
$74$	−1.63167e10	−0.854788
$75$	3.54546e8	0.0172518
$76$	3.23599e10	1.46397
$77$	2.03404e9	0.0856367
$78$	−3.26235e10	−1.27941
$79$	−4.29957e10	−1.57209	−0.786043	−	0.618172i	$-0.787873\pi$
$79$	−4.29957e10	−1.57209	−0.786043	+	0.618172i	$0.787873\pi$
$80$	−2.44275e10	−0.833458
$81$	3.48678e9	0.111111
$82$	9.65342e8	0.0287544
$83$	−1.16822e10	−0.325533	−0.162767	−	0.986665i	$-0.552042\pi$
$83$	−1.16822e10	−0.325533	−0.162767	+	0.986665i	$0.552042\pi$
$84$	−4.33351e9	−0.113059
$85$	−1.50781e10	−0.368588
$86$	−4.24227e9	−0.0972426
$87$	−3.22525e10	−0.693757
$88$	−4.86587e9	−0.0982891
$89$	−8.90945e10	−1.69124	−0.845621	−	0.533783i	$-0.820770\pi$
$89$	−8.90945e10	−1.69124	−0.845621	+	0.533783i	$0.820770\pi$
$90$	−2.68763e10	−0.479774
$91$	−1.55685e10	−0.261529
$92$	−3.43911e10	−0.544018
$93$	1.55864e10	0.232321
$94$	−1.11294e11	−1.56412
$95$	9.57757e10	1.26992
$96$	−6.61659e10	−0.828213
$97$	1.57286e11	1.85971	0.929853	−	0.367932i	$-0.119934\pi$
$97$	1.57286e11	1.85971	0.929853	+	0.367932i	$0.119934\pi$
$98$	1.26875e11	1.41786
$99$	1.56616e10	0.165517
$100$	−3.39286e9	−0.0339286
$101$	−2.07070e11	−1.96042	−0.980212	−	0.197951i	$-0.936571\pi$
$101$	−2.07070e11	−1.96042	−0.980212	+	0.197951i	$0.936571\pi$
$102$	−3.52058e10	−0.315728
$103$	2.11248e11	1.79551	0.897757	−	0.440491i	$-0.145196\pi$
$103$	2.11248e11	1.79551	0.897757	+	0.440491i	$0.145196\pi$
$104$	3.72434e10	0.300169
$105$	−1.28259e10	−0.0980724
$106$	−3.32072e11	−2.41018
$107$	−1.72110e9	−0.0118630	−0.00593150	−	0.999982i	$-0.501888\pi$
$107$	−1.72110e9	−0.0118630	−0.00593150	+	0.999982i	$0.501888\pi$
$108$	−3.33671e10	−0.218518
$109$	2.58436e11	1.60882	0.804411	−	0.594074i	$-0.202481\pi$
$109$	2.58436e11	1.60882	0.804411	+	0.594074i	$0.202481\pi$
$110$	−1.20721e11	−0.714698
$111$	−5.99555e10	−0.337717
$112$	−2.72186e10	−0.145937
$113$	−1.78825e11	−0.913054	−0.456527	−	0.889710i	$-0.650907\pi$
$113$	−1.78825e11	−0.913054	−0.456527	+	0.889710i	$0.650907\pi$
$114$	2.23627e11	1.08780
$115$	−1.01787e11	−0.471907
$116$	3.08643e11	1.36439
$117$	−1.19874e11	−0.505480
$118$	4.72792e10	0.190248
$119$	−1.68009e10	−0.0645392
$120$	3.06824e10	0.112562
$121$	−2.14964e11	−0.753436
$122$	−7.45656e10	−0.249781
$123$	3.54713e9	0.0113605
$124$	−1.49155e11	−0.456898
$125$	−3.46102e11	−1.01438
$126$	−2.99472e10	−0.0840076
$127$	1.23462e11	0.331599	0.165800	−	0.986159i	$-0.446980\pi$
$127$	1.23462e11	0.331599	0.165800	+	0.986159i	$0.446980\pi$
$128$	1.52483e11	0.392254
$129$	−1.55881e10	−0.0384194
$130$	9.23999e11	2.18264
$131$	4.74686e11	1.07502	0.537508	−	0.843259i	$-0.319366\pi$
$131$	4.74686e11	1.07502	0.537508	+	0.843259i	$0.319366\pi$
$132$	−1.49876e11	−0.325518
$133$	1.06719e11	0.222360
$134$	1.00331e12	2.00613
$135$	−9.87566e10	−0.189553
$136$	4.01914e10	0.0740746
$137$	8.43562e11	1.49332	0.746661	−	0.665204i	$-0.231656\pi$
$137$	8.43562e11	1.49332	0.746661	+	0.665204i	$0.231656\pi$
$138$	−2.37664e11	−0.404230
$139$	−3.30930e11	−0.540948	−0.270474	−	0.962727i	$-0.587180\pi$
$139$	−3.30930e11	−0.540948	−0.270474	+	0.962727i	$0.587180\pi$
$140$	1.22739e11	0.192876
$141$	−4.08949e11	−0.617966
$142$	3.30815e11	0.480839
$143$	−5.38442e11	−0.752992
$144$	−2.09577e11	−0.282066
$145$	9.13492e11	1.18353
$146$	−1.46147e12	−1.82326
$147$	4.66199e11	0.560178
$148$	5.73750e11	0.664176
$149$	7.63172e11	0.851330	0.425665	−	0.904881i	$-0.360040\pi$
$149$	7.63172e11	0.851330	0.425665	+	0.904881i	$0.360040\pi$
$150$	−2.34468e10	−0.0252105
$151$	−8.84524e11	−0.916930	−0.458465	−	0.888712i	$-0.651601\pi$
$151$	−8.84524e11	−0.916930	−0.458465	+	0.888712i	$0.651601\pi$
$152$	−2.55295e11	−0.255213
$153$	−1.29363e11	−0.124741
$154$	−1.34515e11	−0.125143
$155$	−4.41454e11	−0.396334
$156$	1.14715e12	0.994110
$157$	−1.22177e12	−1.02221	−0.511106	−	0.859518i	$-0.670764\pi$
$157$	−1.22177e12	−1.02221	−0.511106	+	0.859518i	$0.670764\pi$
$158$	2.84338e12	2.29732
$159$	−1.22019e12	−0.952235
$160$	1.87402e12	1.41291
$161$	−1.13418e11	−0.0826301
$162$	−2.30587e11	−0.162369
$163$	1.93527e12	1.31737	0.658687	−	0.752417i	$-0.271112\pi$
$163$	1.93527e12	1.31737	0.658687	+	0.752417i	$0.271112\pi$
$164$	−3.39446e10	−0.0223424
$165$	−4.43587e11	−0.282369
$166$	7.72565e11	0.475708
$167$	−1.66922e12	−0.994426	−0.497213	−	0.867628i	$-0.665643\pi$
$167$	−1.66922e12	−0.994426	−0.497213	+	0.867628i	$0.665643\pi$
$168$	3.41881e10	0.0197094
$169$	2.32907e12	1.29959
$170$	9.97139e11	0.538625
$171$	8.21713e11	0.429775
$172$	1.49172e11	0.0755581
$173$	1.28276e12	0.629347	0.314674	−	0.949200i	$-0.398105\pi$
$173$	1.28276e12	0.629347	0.314674	+	0.949200i	$0.398105\pi$
$174$	2.13291e12	1.01380
$175$	−1.11892e10	−0.00515337
$176$	−9.41361e11	−0.420181
$177$	1.73727e11	0.0751646
$178$	5.89198e12	2.47145
$179$	−1.09968e12	−0.447276	−0.223638	−	0.974672i	$-0.571793\pi$
$179$	−1.09968e12	−0.447276	−0.223638	+	0.974672i	$0.571793\pi$
$180$	9.45061e11	0.372787
$181$	2.45767e12	0.940353	0.470177	−	0.882572i	$-0.344190\pi$
$181$	2.45767e12	0.940353	0.470177	+	0.882572i	$0.344190\pi$
$182$	1.02957e12	0.382178
$183$	−2.73990e11	−0.0986855
$184$	2.71320e11	0.0948383
$185$	1.69813e12	0.576137
$186$	−1.03075e12	−0.339495
$187$	−5.81062e11	−0.185821
$188$	3.91348e12	1.21533
$189$	−1.10041e11	−0.0331904
$190$	−6.33381e12	−1.85575
$191$	−1.69206e12	−0.481650	−0.240825	−	0.970569i	$-0.577418\pi$
$191$	−1.69206e12	−0.481650	−0.240825	+	0.970569i	$0.577418\pi$
$192$	2.60935e12	0.721732
$193$	4.25498e11	0.114375	0.0571876	−	0.998363i	$-0.481787\pi$
$193$	4.25498e11	0.114375	0.0571876	+	0.998363i	$0.481787\pi$
$194$	−1.04016e13	−2.71762
$195$	3.39522e12	0.862337
$196$	−4.46134e12	−1.10168
$197$	3.94792e12	0.947990	0.473995	−	0.880527i	$-0.342811\pi$
$197$	3.94792e12	0.947990	0.473995	+	0.880527i	$0.342811\pi$
$198$	−1.03573e12	−0.241874
$199$	1.31854e12	0.299502	0.149751	−	0.988724i	$-0.452153\pi$
$199$	1.31854e12	0.299502	0.149751	+	0.988724i	$0.452153\pi$
$200$	2.67671e10	0.00591475
$201$	3.68666e12	0.792600
$202$	1.36939e13	2.86481
$203$	1.01787e12	0.207235
$204$	1.23795e12	0.245323
$205$	−1.00466e11	−0.0193808
$206$	−1.39702e13	−2.62382
$207$	−8.73292e11	−0.159706
$208$	7.20518e12	1.28321
$209$	3.69090e12	0.640218
$210$	8.48199e11	0.143315
$211$	5.99993e12	0.987626	0.493813	−	0.869568i	$-0.335603\pi$
$211$	5.99993e12	0.987626	0.493813	+	0.869568i	$0.335603\pi$
$212$	1.16767e13	1.87273
$213$	1.21557e12	0.189974
$214$	1.13819e11	0.0173356
$215$	4.41505e11	0.0655426
$216$	2.63241e11	0.0380942
$217$	−4.91895e11	−0.0693975
$218$	−1.70909e13	−2.35100
$219$	−5.37015e12	−0.720350
$220$	4.24495e12	0.555325
$221$	4.44745e12	0.567485
$222$	3.96496e12	0.493512
$223$	2.51473e12	0.305362	0.152681	−	0.988276i	$-0.451209\pi$
$223$	2.51473e12	0.305362	0.152681	+	0.988276i	$0.451209\pi$
$224$	2.08815e12	0.247399
$225$	−8.61547e10	−0.00996036
$226$	1.18260e13	1.33426
$227$	1.57568e12	0.173510	0.0867552	−	0.996230i	$-0.472350\pi$
$227$	1.57568e12	0.173510	0.0867552	+	0.996230i	$0.472350\pi$
$228$	−7.86346e12	−0.845225
$229$	1.54637e13	1.62262	0.811310	−	0.584616i	$-0.198755\pi$
$229$	1.54637e13	1.62262	0.811310	+	0.584616i	$0.198755\pi$
$230$	6.73138e12	0.689606
$231$	−4.94271e11	−0.0494424
$232$	−2.43496e12	−0.237853
$233$	7.69781e12	0.734361	0.367181	−	0.930150i	$-0.380323\pi$
$233$	7.69781e12	0.734361	0.367181	+	0.930150i	$0.380323\pi$
$234$	7.92750e12	0.738668
$235$	1.15827e13	1.05424
$236$	−1.66249e12	−0.147824
$237$	1.04480e13	0.907644
$238$	1.11107e12	0.0943124
$239$	−9.02876e12	−0.748927	−0.374464	−	0.927242i	$-0.622173\pi$
$239$	−9.02876e12	−0.748927	−0.374464	+	0.927242i	$0.622173\pi$
$240$	5.93588e12	0.481197
$241$	−1.40911e13	−1.11648	−0.558238	−	0.829681i	$-0.688523\pi$
$241$	−1.40911e13	−1.11648	−0.558238	+	0.829681i	$0.688523\pi$
$242$	1.42159e13	1.10101
$243$	−8.47289e11	−0.0641500
$244$	2.62197e12	0.194081
$245$	−1.32042e13	−0.955651
$246$	−2.34578e11	−0.0166014
$247$	−2.82502e13	−1.95519
$248$	1.17672e12	0.0796507
$249$	2.83878e12	0.187947
$250$	2.28884e13	1.48233
$251$	−1.89090e12	−0.119802	−0.0599010	−	0.998204i	$-0.519078\pi$
$251$	−1.89090e12	−0.119802	−0.0599010	+	0.998204i	$0.519078\pi$
$252$	1.05304e12	0.0652745
$253$	−3.92258e12	−0.237908
$254$	−8.16477e12	−0.484573
$255$	3.66397e12	0.212804
$256$	1.19076e13	0.676868
$257$	−1.60395e12	−0.0892398	−0.0446199	−	0.999004i	$-0.514208\pi$
$257$	−1.60395e12	−0.0892398	−0.0446199	+	0.999004i	$0.514208\pi$
$258$	1.03087e12	0.0561430
$259$	1.89216e12	0.100881
$260$	−3.24908e13	−1.69593
$261$	7.83736e12	0.400541
$262$	−3.13918e13	−1.57094
$263$	−2.83907e13	−1.39130	−0.695648	−	0.718383i	$-0.744883\pi$
$263$	−2.83907e13	−1.39130	−0.695648	+	0.718383i	$0.744883\pi$
$264$	1.18241e12	0.0567473
$265$	3.45597e13	1.62449
$266$	−7.05751e12	−0.324940
$267$	2.16500e13	0.976439
$268$	−3.52798e13	−1.55878
$269$	−2.14423e13	−0.928185	−0.464093	−	0.885787i	$-0.653620\pi$
$269$	−2.14423e13	−0.928185	−0.464093	+	0.885787i	$0.653620\pi$
$270$	6.53095e12	0.276997
$271$	−2.63137e13	−1.09358	−0.546791	−	0.837269i	$-0.684151\pi$
$271$	−2.63137e13	−1.09358	−0.546791	+	0.837269i	$0.684151\pi$
$272$	7.77552e12	0.316665
$273$	3.78315e12	0.150994
$274$	−5.57862e13	−2.18222
$275$	−3.86982e11	−0.0148375
$276$	8.35705e12	0.314089
$277$	−3.69721e13	−1.36218	−0.681091	−	0.732199i	$-0.738494\pi$
$277$	−3.69721e13	−1.36218	−0.681091	+	0.732199i	$0.738494\pi$
$278$	2.18850e13	0.790498
$279$	−3.78748e12	−0.134131
$280$	−9.68315e11	−0.0336239
$281$	−1.62031e13	−0.551712	−0.275856	−	0.961199i	$-0.588961\pi$
$281$	−1.62031e13	−0.551712	−0.275856	+	0.961199i	$0.588961\pi$
$282$	2.70446e13	0.903046
$283$	5.24493e13	1.71757	0.858784	−	0.512338i	$-0.171220\pi$
$283$	5.24493e13	1.71757	0.858784	+	0.512338i	$0.171220\pi$
$284$	−1.16326e13	−0.373615
$285$	−2.32735e13	−0.733187
$286$	3.56081e13	1.10036
$287$	−1.11945e11	−0.00339355
$288$	1.60783e13	0.478169
$289$	−2.94724e13	−0.859958
$290$	−6.04108e13	−1.72952
$291$	−3.82204e13	−1.07370
$292$	5.13901e13	1.41669
$293$	−1.90369e13	−0.515019	−0.257510	−	0.966276i	$-0.582902\pi$
$293$	−1.90369e13	−0.515019	−0.257510	+	0.966276i	$0.582902\pi$
$294$	−3.08306e13	−0.818599
$295$	−4.92048e12	−0.128229
$296$	−4.52645e12	−0.115785
$297$	−3.80578e12	−0.0955616
$298$	−5.04699e13	−1.24406
$299$	3.00234e13	0.726556
$300$	8.24465e11	0.0195887
$301$	4.91951e11	0.0114764
$302$	5.84951e13	1.33993
$303$	5.03181e13	1.13185
$304$	−4.93900e13	−1.09102
$305$	7.76025e12	0.168355
$306$	8.55501e12	0.182286
$307$	−1.69753e13	−0.355268	−0.177634	−	0.984097i	$-0.556844\pi$
$307$	−1.69753e13	−0.355268	−0.177634	+	0.984097i	$0.556844\pi$
$308$	4.72997e12	0.0972366
$309$	−5.13334e13	−1.03664
$310$	2.91942e13	0.579171
$311$	−2.69573e13	−0.525406	−0.262703	−	0.964877i	$-0.584614\pi$
$311$	−2.69573e13	−0.525406	−0.262703	+	0.964877i	$0.584614\pi$
$312$	−9.05014e12	−0.173303
$313$	3.07747e13	0.579029	0.289514	−	0.957174i	$-0.406506\pi$
$313$	3.07747e13	0.579029	0.289514	+	0.957174i	$0.406506\pi$
$314$	8.07977e13	1.49378
$315$	3.11669e12	0.0566221
$316$	−9.99827e13	−1.78503
$317$	−2.86706e13	−0.503050	−0.251525	−	0.967851i	$-0.580932\pi$
$317$	−2.86706e13	−0.503050	−0.251525	+	0.967851i	$0.580932\pi$
$318$	8.06935e13	1.39152
$319$	3.52032e13	0.596669
$320$	−7.39050e13	−1.23126
$321$	4.18227e11	0.00684911
$322$	7.50051e12	0.120749
$323$	−3.04864e13	−0.482494
$324$	8.10821e12	0.126162
$325$	2.96196e12	0.0453129
$326$	−1.27983e14	−1.92510
$327$	−6.28000e13	−0.928853
$328$	2.67797e11	0.00389493
$329$	1.29062e13	0.184595
$330$	2.93352e13	0.412631
$331$	8.39875e13	1.16188	0.580939	−	0.813947i	$-0.302686\pi$
$331$	8.39875e13	1.16188	0.580939	+	0.813947i	$0.302686\pi$
$332$	−2.71660e13	−0.369629
$333$	1.45692e13	0.194981
$334$	1.10388e14	1.45317
$335$	−1.04418e14	−1.35216
$336$	6.61411e12	0.0842569
$337$	7.95960e12	0.0997532	0.0498766	−	0.998755i	$-0.484117\pi$
$337$	7.95960e12	0.0997532	0.0498766	+	0.998755i	$0.484117\pi$
$338$	−1.54026e14	−1.89912
$339$	4.34544e13	0.527152
$340$	−3.50627e13	−0.418515
$341$	−1.70123e13	−0.199809
$342$	−5.43413e13	−0.628039
$343$	−2.98769e13	−0.339795
$344$	−1.17686e12	−0.0131720
$345$	2.47343e13	0.272455
$346$	−8.48309e13	−0.919677
$347$	1.70126e13	0.181534	0.0907669	−	0.995872i	$-0.471068\pi$
$347$	1.70126e13	0.181534	0.0907669	+	0.995872i	$0.471068\pi$
$348$	−7.50003e13	−0.787730
$349$	1.55596e14	1.60864	0.804318	−	0.594200i	$-0.202531\pi$
$349$	1.55596e14	1.60864	0.804318	+	0.594200i	$0.202531\pi$
$350$	7.39964e11	0.00753071
$351$	2.91295e13	0.291839
$352$	7.22192e13	0.712308
$353$	9.94759e13	0.965955	0.482978	−	0.875633i	$-0.339555\pi$
$353$	9.94759e13	0.965955	0.482978	+	0.875633i	$0.339555\pi$
$354$	−1.14888e13	−0.109840
$355$	−3.44289e13	−0.324091
$356$	−2.07181e14	−1.92033
$357$	4.08261e12	0.0372617
$358$	7.27239e13	0.653613
$359$	1.64530e14	1.45622	0.728109	−	0.685462i	$-0.240400\pi$
$359$	1.64530e14	1.45622	0.728109	+	0.685462i	$0.240400\pi$
$360$	−7.45582e12	−0.0649878
$361$	7.71587e13	0.662362
$362$	−1.62530e14	−1.37416
$363$	5.22362e13	0.434996
$364$	−3.62032e13	−0.296955
$365$	1.52099e14	1.22890
$366$	1.81194e13	0.144211
$367$	1.37417e14	1.07740	0.538701	−	0.842497i	$-0.318915\pi$
$367$	1.37417e14	1.07740	0.538701	+	0.842497i	$0.318915\pi$
$368$	5.24902e13	0.405429
$369$	−8.61953e11	−0.00655901
$370$	−1.12300e14	−0.841920
$371$	3.85084e13	0.284446
$372$	3.62447e13	0.263790
$373$	1.09871e14	0.787925	0.393962	−	0.919127i	$-0.371104\pi$
$373$	1.09871e14	0.787925	0.393962	+	0.919127i	$0.371104\pi$
$374$	3.84267e13	0.271543
$375$	8.41029e13	0.585651
$376$	−3.08744e13	−0.211868
$377$	−2.69445e14	−1.82219
$378$	7.27718e12	0.0485018
$379$	2.48057e14	1.62943	0.814716	−	0.579860i	$-0.196893\pi$
$379$	2.48057e14	1.62943	0.814716	+	0.579860i	$0.196893\pi$
$380$	2.22718e14	1.44193
$381$	−3.00013e13	−0.191449
$382$	1.11899e14	0.703845
$383$	1.35785e14	0.841894	0.420947	−	0.907085i	$-0.361698\pi$
$383$	1.35785e14	0.841894	0.420947	+	0.907085i	$0.361698\pi$
$384$	−3.70535e13	−0.226468
$385$	1.39993e13	0.0843475
$386$	−2.81389e13	−0.167139
$387$	3.78792e12	0.0221815
$388$	3.65754e14	2.11161
$389$	7.94373e13	0.452170	0.226085	−	0.974108i	$-0.427407\pi$
$389$	7.94373e13	0.452170	0.226085	+	0.974108i	$0.427407\pi$
$390$	−2.24532e14	−1.26015
$391$	3.24000e13	0.179297
$392$	3.51966e13	0.192056
$393$	−1.15349e14	−0.620660
$394$	−2.61083e14	−1.38532
$395$	−2.95919e14	−1.54842
$396$	3.64198e13	0.187938
$397$	1.52289e13	0.0775035	0.0387518	−	0.999249i	$-0.487662\pi$
$397$	1.52289e13	0.0775035	0.0387518	+	0.999249i	$0.487662\pi$
$398$	−8.71971e13	−0.437668
$399$	−2.59327e13	−0.128380
$400$	5.17842e12	0.0252853
$401$	2.68365e14	1.29250	0.646252	−	0.763124i	$-0.276335\pi$
$401$	2.68365e14	1.29250	0.646252	+	0.763124i	$0.276335\pi$
$402$	−2.43805e14	−1.15824
$403$	1.30212e14	0.610203
$404$	−4.81523e14	−2.22597
$405$	2.39979e13	0.109438
$406$	−6.73134e13	−0.302836
$407$	6.54407e13	0.290455
$408$	−9.76651e12	−0.0427670
$409$	−3.75994e14	−1.62444	−0.812218	−	0.583355i	$-0.801740\pi$
$409$	−3.75994e14	−1.62444	−0.812218	+	0.583355i	$0.801740\pi$
$410$	6.64398e12	0.0283216
$411$	−2.04985e14	−0.862170
$412$	4.91240e14	2.03873
$413$	−5.48269e12	−0.0224527
$414$	5.77523e13	0.233382
$415$	−8.04031e13	−0.320633
$416$	−5.52766e14	−2.17534
$417$	8.04161e13	0.312316
$418$	−2.44086e14	−0.935563
$419$	5.07594e13	0.192017	0.0960083	−	0.995381i	$-0.469392\pi$
$419$	5.07594e13	0.192017	0.0960083	+	0.995381i	$0.469392\pi$
$420$	−2.98255e13	−0.111357
$421$	3.23595e14	1.19248	0.596238	−	0.802808i	$-0.296661\pi$
$421$	3.23595e14	1.19248	0.596238	+	0.802808i	$0.296661\pi$
$422$	−3.96786e14	−1.44324
$423$	9.93747e13	0.356783
$424$	−9.21207e13	−0.326471
$425$	3.19642e12	0.0111821
$426$	−8.03881e13	−0.277612
$427$	8.64693e12	0.0294787
$428$	−4.00226e12	−0.0134699
$429$	1.30841e14	0.434740
$430$	−2.91975e13	−0.0957787
$431$	−2.28987e14	−0.741628	−0.370814	−	0.928707i	$-0.620921\pi$
$431$	−2.28987e14	−0.741628	−0.370814	+	0.928707i	$0.620921\pi$
$432$	5.09272e13	0.162851
$433$	−2.16476e14	−0.683482	−0.341741	−	0.939794i	$-0.611017\pi$
$433$	−2.16476e14	−0.683482	−0.341741	+	0.939794i	$0.611017\pi$
$434$	3.25299e13	0.101412
$435$	−2.21978e14	−0.683313
$436$	6.00971e14	1.82674
$437$	−2.05804e14	−0.617741
$438$	3.55137e14	1.05266
$439$	3.66508e14	1.07283	0.536413	−	0.843956i	$-0.319779\pi$
$439$	3.66508e14	1.07283	0.536413	+	0.843956i	$0.319779\pi$
$440$	−3.34894e13	−0.0968095
$441$	−1.13286e14	−0.323419
$442$	−2.94118e14	−0.829276
$443$	3.26305e14	0.908664	0.454332	−	0.890832i	$-0.349878\pi$
$443$	3.26305e14	0.908664	0.454332	+	0.890832i	$0.349878\pi$
$444$	−1.39421e14	−0.383462
$445$	−6.13195e14	−1.66578
$446$	−1.66304e14	−0.446231
$447$	−1.85451e14	−0.491515
$448$	−8.23494e13	−0.215591
$449$	4.19927e13	0.108597	0.0542986	−	0.998525i	$-0.482708\pi$
$449$	4.19927e13	0.108597	0.0542986	+	0.998525i	$0.482708\pi$
$450$	5.69756e12	0.0145553
$451$	−3.87165e12	−0.00977068
$452$	−4.15841e14	−1.03673
$453$	2.14939e14	0.529390
$454$	−1.04202e14	−0.253554
$455$	−1.07151e14	−0.257592
$456$	6.20368e13	0.147347
$457$	1.76811e14	0.414926	0.207463	−	0.978243i	$-0.433479\pi$
$457$	1.76811e14	0.414926	0.207463	+	0.978243i	$0.433479\pi$
$458$	−1.02264e15	−2.37117
$459$	3.14352e13	0.0720190
$460$	−2.36698e14	−0.535829
$461$	6.73921e14	1.50749	0.753744	−	0.657168i	$-0.228246\pi$
$461$	6.73921e14	1.50749	0.753744	+	0.657168i	$0.228246\pi$
$462$	3.26870e13	0.0722511
$463$	5.54820e14	1.21187	0.605936	−	0.795514i	$-0.292799\pi$
$463$	5.54820e14	1.21187	0.605936	+	0.795514i	$0.292799\pi$
$464$	−4.71073e14	−1.01681
$465$	1.07273e14	0.228824
$466$	−5.09070e14	−1.07314
$467$	6.39614e14	1.33252	0.666262	−	0.745717i	$-0.267893\pi$
$467$	6.39614e14	1.33252	0.666262	+	0.745717i	$0.267893\pi$
$468$	−2.78757e14	−0.573950
$469$	−1.16348e14	−0.236761
$470$	−7.65986e14	−1.54058
$471$	2.96890e14	0.590174
$472$	1.31158e13	0.0257700
$473$	1.70142e13	0.0330428
$474$	−6.90942e14	−1.32636
$475$	−2.03036e13	−0.0385264
$476$	−3.90690e13	−0.0732814
$477$	2.96507e14	0.549773
$478$	5.97088e14	1.09442
$479$	4.30598e14	0.780238	0.390119	−	0.920764i	$-0.372434\pi$
$479$	4.30598e14	0.780238	0.390119	+	0.920764i	$0.372434\pi$
$480$	−4.55388e14	−0.815745
$481$	−5.00883e14	−0.887031
$482$	9.31866e14	1.63153
$483$	2.75605e13	0.0477065
$484$	−4.99880e14	−0.855492
$485$	1.08252e15	1.83171
$486$	5.60327e13	0.0937437
$487$	1.84161e14	0.304641	0.152321	−	0.988331i	$-0.451325\pi$
$487$	1.84161e14	0.304641	0.152321	+	0.988331i	$0.451325\pi$
$488$	−2.06854e13	−0.0338341
$489$	−4.70270e14	−0.760586
$490$	8.73218e14	1.39651
$491$	4.53217e13	0.0716734	0.0358367	−	0.999358i	$-0.488590\pi$
$491$	4.53217e13	0.0716734	0.0358367	+	0.999358i	$0.488590\pi$
$492$	8.24854e12	0.0128994
$493$	−2.90774e14	−0.449673
$494$	1.86823e15	2.85715
$495$	1.07792e14	0.163026
$496$	2.27651e14	0.340503
$497$	−3.83627e13	−0.0567478
$498$	−1.87733e14	−0.274650
$499$	−4.58426e14	−0.663310	−0.331655	−	0.943401i	$-0.607607\pi$
$499$	−4.58426e14	−0.663310	−0.331655	+	0.943401i	$0.607607\pi$
$500$	−8.04831e14	−1.15178
$501$	4.05620e14	0.574132
$502$	1.25049e14	0.175069
$503$	−5.06253e14	−0.701042	−0.350521	−	0.936555i	$-0.613995\pi$
$503$	−5.06253e14	−0.701042	−0.350521	+	0.936555i	$0.613995\pi$
$504$	−8.30772e12	−0.0113793
$505$	−1.42516e15	−1.93091
$506$	2.59407e14	0.347659
$507$	−5.65965e14	−0.750319
$508$	2.87100e14	0.376516
$509$	−7.38876e14	−0.958570	−0.479285	−	0.877659i	$-0.659104\pi$
$509$	−7.38876e14	−0.958570	−0.479285	+	0.877659i	$0.659104\pi$
$510$	−2.42305e14	−0.310975
$511$	1.69478e14	0.215178
$512$	−1.09976e15	−1.38137
$513$	−1.99676e14	−0.248131
$514$	1.06072e14	0.130408
$515$	1.45392e15	1.76848
$516$	−3.62488e13	−0.0436235
$517$	4.46363e14	0.531484
$518$	−1.25132e14	−0.147419
$519$	−3.11710e14	−0.363354
$520$	2.56328e14	0.295650
$521$	1.57532e15	1.79789	0.898943	−	0.438066i	$-0.144336\pi$
$521$	1.57532e15	1.79789	0.898943	+	0.438066i	$0.144336\pi$
$522$	−5.18298e14	−0.585318
$523$	1.23678e15	1.38208	0.691039	−	0.722818i	$-0.257153\pi$
$523$	1.23678e15	1.38208	0.691039	+	0.722818i	$0.257153\pi$
$524$	1.10384e15	1.22063
$525$	2.71898e12	0.00297530
$526$	1.87753e15	2.03313
$527$	1.40519e14	0.150584
$528$	2.28751e14	0.242592
$529$	−7.34087e14	−0.770445
$530$	−2.28549e15	−2.37390
$531$	−4.22156e13	−0.0433963
$532$	2.48166e14	0.252480
$533$	2.96336e13	0.0298390
$534$	−1.43175e15	−1.42689
$535$	−1.18455e13	−0.0116844
$536$	2.78331e14	0.271741
$537$	2.67223e14	0.258235
$538$	1.41802e15	1.35638
$539$	−5.08850e14	−0.481783
$540$	−2.29650e14	−0.215229
$541$	1.52839e15	1.41791	0.708957	−	0.705251i	$-0.249166\pi$
$541$	1.52839e15	1.41791	0.708957	+	0.705251i	$0.249166\pi$
$542$	1.74017e15	1.59807
$543$	−5.97213e14	−0.542913
$544$	−5.96521e14	−0.536824
$545$	1.77869e15	1.58460
$546$	−2.50187e14	−0.220650
$547$	2.00393e15	1.74965	0.874827	−	0.484436i	$-0.160975\pi$
$547$	2.00393e15	1.74965	0.874827	+	0.484436i	$0.160975\pi$
$548$	1.96163e15	1.69560
$549$	6.65795e13	0.0569761
$550$	2.55918e13	0.0216824
$551$	1.84699e15	1.54928
$552$	−6.59308e13	−0.0547549
$553$	−3.29730e14	−0.271126
$554$	2.44503e15	1.99058
$555$	−4.12645e14	−0.332633
$556$	−7.69550e14	−0.614222
$557$	−8.50142e14	−0.671874	−0.335937	−	0.941884i	$-0.609053\pi$
$557$	−8.50142e14	−0.671874	−0.335937	+	0.941884i	$0.609053\pi$
$558$	2.50473e14	0.196008
$559$	−1.30227e14	−0.100911
$560$	−1.87332e14	−0.143740
$561$	1.41198e14	0.107284
$562$	1.07154e15	0.806228
$563$	1.76992e15	1.31873	0.659367	−	0.751821i	$-0.270824\pi$
$563$	1.76992e15	1.31873	0.659367	+	0.751821i	$0.270824\pi$
$564$	−9.50976e14	−0.701673
$565$	−1.23077e15	−0.899309
$566$	−3.46856e15	−2.50992
$567$	2.67399e13	0.0191625
$568$	9.17721e13	0.0651320
$569$	−7.42644e14	−0.521991	−0.260996	−	0.965340i	$-0.584051\pi$
$569$	−7.42644e14	−0.521991	−0.260996	+	0.965340i	$0.584051\pi$
$570$	1.53912e15	1.07142
$571$	1.42799e15	0.984527	0.492263	−	0.870446i	$-0.336170\pi$
$571$	1.42799e15	0.984527	0.492263	+	0.870446i	$0.336170\pi$
$572$	−1.25210e15	−0.854989
$573$	4.11170e14	0.278081
$574$	7.40312e12	0.00495906
$575$	2.15781e13	0.0143166
$576$	−6.34073e14	−0.416692
$577$	−5.49111e14	−0.357432	−0.178716	−	0.983901i	$-0.557194\pi$
$577$	−5.49111e14	−0.357432	−0.178716	+	0.983901i	$0.557194\pi$
$578$	1.94906e15	1.25667
$579$	−1.03396e14	−0.0660346
$580$	2.12424e15	1.34385
$581$	−8.95899e13	−0.0561423
$582$	2.52758e15	1.56902
$583$	1.33182e15	0.818973
$584$	−4.05429e14	−0.246970
$585$	−8.25038e14	−0.497871
$586$	1.25894e15	0.752608
$587$	1.98082e15	1.17310	0.586550	−	0.809913i	$-0.300486\pi$
$587$	1.98082e15	1.17310	0.586550	+	0.809913i	$0.300486\pi$
$588$	1.08410e15	0.636057
$589$	−8.92578e14	−0.518814
$590$	3.25400e14	0.187384
$591$	−9.59344e14	−0.547322
$592$	−8.75698e14	−0.494977
$593$	3.24270e15	1.81596	0.907981	−	0.419012i	$-0.137624\pi$
$593$	3.24270e15	1.81596	0.907981	+	0.419012i	$0.137624\pi$
$594$	2.51683e14	0.139646
$595$	−1.15632e14	−0.0635676
$596$	1.77469e15	0.966646
$597$	−3.20404e14	−0.172918
$598$	−1.98550e15	−1.06173
$599$	3.16947e15	1.67934	0.839670	−	0.543098i	$-0.182749\pi$
$599$	3.16947e15	1.67934	0.839670	+	0.543098i	$0.182749\pi$
$600$	−6.50441e12	−0.00341488
$601$	−3.20242e15	−1.66598	−0.832989	−	0.553290i	$-0.813372\pi$
$601$	−3.20242e15	−1.66598	−0.832989	+	0.553290i	$0.813372\pi$
$602$	−3.25336e13	−0.0167707
$603$	−8.95857e14	−0.457608
$604$	−2.05688e15	−1.04113
$605$	−1.47949e15	−0.742094
$606$	−3.32762e15	−1.65400
$607$	−3.31168e14	−0.163121	−0.0815606	−	0.996668i	$-0.525990\pi$
$607$	−3.31168e14	−0.163121	−0.0815606	+	0.996668i	$0.525990\pi$
$608$	3.78909e15	1.84955
$609$	−2.47342e14	−0.119647
$610$	−5.13199e14	−0.246021
$611$	−3.41647e15	−1.62312
$612$	−3.00823e14	−0.141637
$613$	1.67829e15	0.783131	0.391566	−	0.920150i	$-0.371934\pi$
$613$	1.67829e15	0.783131	0.391566	+	0.920150i	$0.371934\pi$
$614$	1.12261e15	0.519160
$615$	2.44132e13	0.0111895
$616$	−3.73159e13	−0.0169512
$617$	−2.13368e15	−0.960640	−0.480320	−	0.877093i	$-0.659480\pi$
$617$	−2.13368e15	−0.960640	−0.480320	+	0.877093i	$0.659480\pi$
$618$	3.39477e15	1.51486
$619$	−1.97750e14	−0.0874617	−0.0437309	−	0.999043i	$-0.513924\pi$
$619$	−1.97750e14	−0.0874617	−0.0437309	+	0.999043i	$0.513924\pi$
$620$	−1.02656e15	−0.450020
$621$	2.12210e14	0.0922065
$622$	1.78274e15	0.767786
$623$	−6.83258e14	−0.291676
$624$	−1.75086e15	−0.740860
$625$	−2.31081e15	−0.969226
$626$	−2.03519e15	−0.846146
$627$	−8.96889e14	−0.369630
$628$	−2.84111e15	−1.16068
$629$	−5.40531e14	−0.218898
$630$	−2.06112e14	−0.0827430
$631$	−5.35469e13	−0.0213095	−0.0106547	−	0.999943i	$-0.503392\pi$
$631$	−5.35469e13	−0.0213095	−0.0106547	+	0.999943i	$0.503392\pi$
$632$	7.88788e14	0.311183
$633$	−1.45798e15	−0.570206
$634$	1.89604e15	0.735116
$635$	8.49731e14	0.326607
$636$	−2.83745e15	−1.08122
$637$	3.89474e15	1.47134
$638$	−2.32805e15	−0.871924
$639$	−2.95385e14	−0.109681
$640$	1.04947e15	0.386349
$641$	1.18003e14	0.0430699	0.0215350	−	0.999768i	$-0.493145\pi$
$641$	1.18003e14	0.0430699	0.0215350	+	0.999768i	$0.493145\pi$
$642$	−2.76581e13	−0.0100087
$643$	−5.38608e15	−1.93247	−0.966234	−	0.257666i	$-0.917047\pi$
$643$	−5.38608e15	−1.93247	−0.966234	+	0.257666i	$0.917047\pi$
$644$	−2.63743e14	−0.0938228
$645$	−1.07286e14	−0.0378411
$646$	2.01612e15	0.705077
$647$	−2.44963e15	−0.849429	−0.424714	−	0.905327i	$-0.639625\pi$
$647$	−2.44963e15	−0.849429	−0.424714	+	0.905327i	$0.639625\pi$
$648$	−6.39676e13	−0.0219937
$649$	−1.89620e14	−0.0646456
$650$	−1.95880e14	−0.0662166
$651$	1.19530e14	0.0400667
$652$	4.50029e15	1.49582
$653$	−1.91375e15	−0.630758	−0.315379	−	0.948966i	$-0.602132\pi$
$653$	−1.91375e15	−0.630758	−0.315379	+	0.948966i	$0.602132\pi$
$654$	4.15308e15	1.35735
$655$	3.26704e15	1.05883
$656$	5.18086e13	0.0166506
$657$	1.30495e15	0.415894
$658$	−8.53508e14	−0.269752
$659$	5.66582e14	0.177580	0.0887898	−	0.996050i	$-0.471700\pi$
$659$	5.66582e14	0.177580	0.0887898	+	0.996050i	$0.471700\pi$
$660$	−1.03152e15	−0.320617
$661$	1.39801e15	0.430924	0.215462	−	0.976512i	$-0.430874\pi$
$661$	1.39801e15	0.430924	0.215462	+	0.976512i	$0.430874\pi$
$662$	−5.55424e15	−1.69787
$663$	−1.08073e15	−0.327637
$664$	2.14319e14	0.0644371
$665$	7.34495e14	0.219013
$666$	−9.63486e14	−0.284929
$667$	−1.96293e15	−0.575721
$668$	−3.88162e15	−1.12913
$669$	−6.11079e14	−0.176301
$670$	6.90532e15	1.97593
$671$	2.99056e14	0.0848749
$672$	−5.07420e14	−0.142836
$673$	2.62224e15	0.732133	0.366067	−	0.930589i	$-0.380704\pi$
$673$	2.62224e15	0.732133	0.366067	+	0.930589i	$0.380704\pi$
$674$	−5.26383e14	−0.145771
$675$	2.09356e13	0.00575062
$676$	5.41606e15	1.47563
$677$	−1.68017e15	−0.454062	−0.227031	−	0.973888i	$-0.572902\pi$
$677$	−1.68017e15	−0.454062	−0.227031	+	0.973888i	$0.572902\pi$
$678$	−2.87372e15	−0.770338
$679$	1.20621e15	0.320730
$680$	2.76618e14	0.0729595
$681$	−3.82890e14	−0.100176
$682$	1.12505e15	0.291984
$683$	6.60997e14	0.170171	0.0850855	−	0.996374i	$-0.472884\pi$
$683$	6.60997e14	0.170171	0.0850855	+	0.996374i	$0.472884\pi$
$684$	1.91082e15	0.487991
$685$	5.80583e15	1.47084
$686$	1.97581e15	0.496550
$687$	−3.75767e15	−0.936821
$688$	−2.27677e14	−0.0563096
$689$	−1.01938e16	−2.50109
$690$	−1.63573e15	−0.398144
$691$	3.54965e15	0.857149	0.428574	−	0.903507i	$-0.359016\pi$
$691$	3.54965e15	0.857149	0.428574	+	0.903507i	$0.359016\pi$
$692$	2.98293e15	0.714595
$693$	1.20108e14	0.0285456
$694$	−1.12507e15	−0.265279
$695$	−2.27764e15	−0.532804
$696$	5.91696e14	0.137324
$697$	3.19793e13	0.00736357
$698$	−1.02898e16	−2.35073
$699$	−1.87057e15	−0.423984
$700$	−2.60196e13	−0.00585142
$701$	−3.81648e15	−0.851558	−0.425779	−	0.904827i	$-0.640000\pi$
$701$	−3.81648e15	−0.851558	−0.425779	+	0.904827i	$0.640000\pi$
$702$	−1.92638e15	−0.426470
$703$	3.43345e15	0.754182
$704$	−2.84808e15	−0.620729
$705$	−2.81460e15	−0.608663
$706$	−6.57852e15	−1.41157
$707$	−1.58800e15	−0.338100
$708$	4.03986e14	0.0853460
$709$	4.42457e15	0.927507	0.463753	−	0.885964i	$-0.346502\pi$
$709$	4.42457e15	0.927507	0.463753	+	0.885964i	$0.346502\pi$
$710$	2.27684e15	0.473600
$711$	−2.53885e15	−0.524028
$712$	1.63450e15	0.334770
$713$	9.48604e14	0.192794
$714$	−2.69990e14	−0.0544513
$715$	−3.70584e15	−0.741657
$716$	−2.55721e15	−0.507861
$717$	2.19399e15	0.432393
$718$	−1.08807e16	−2.12800
$719$	−3.23176e15	−0.627235	−0.313617	−	0.949549i	$-0.601541\pi$
$719$	−3.23176e15	−0.627235	−0.313617	+	0.949549i	$0.601541\pi$
$720$	−1.44242e15	−0.277819
$721$	1.62005e15	0.309659
$722$	−5.10264e15	−0.967923
$723$	3.42413e15	0.644598
$724$	5.71509e15	1.06773
$725$	−1.93653e14	−0.0359058
$726$	−3.45448e15	−0.635669
$727$	4.85991e15	0.887543	0.443771	−	0.896140i	$-0.353640\pi$
$727$	4.85991e15	0.887543	0.443771	+	0.896140i	$0.353640\pi$
$728$	2.85616e14	0.0517679
$729$	2.05891e14	0.0370370
$730$	−1.00586e16	−1.79582
$731$	−1.40535e14	−0.0249023
$732$	−6.37139e14	−0.112053
$733$	−7.63492e15	−1.33270	−0.666350	−	0.745639i	$-0.732144\pi$
$733$	−7.63492e15	−1.33270	−0.666350	+	0.745639i	$0.732144\pi$
$734$	−9.08765e15	−1.57443
$735$	3.20862e15	0.551745
$736$	−4.02693e15	−0.687300
$737$	−4.02394e15	−0.681679
$738$	5.70025e13	0.00958481
$739$	5.02289e15	0.838319	0.419159	−	0.907913i	$-0.362325\pi$
$739$	5.02289e15	0.838319	0.419159	+	0.907913i	$0.362325\pi$
$740$	3.94885e15	0.654178
$741$	6.86479e15	1.12883
$742$	−2.54663e15	−0.415666
$743$	4.65787e15	0.754655	0.377328	−	0.926080i	$-0.376843\pi$
$743$	4.65787e15	0.754655	0.377328	+	0.926080i	$0.376843\pi$
$744$	−2.85943e14	−0.0459863
$745$	5.25254e15	0.838514
$746$	−7.26597e15	−1.15141
$747$	−6.89823e14	−0.108511
$748$	−1.35121e15	−0.210991
$749$	−1.31990e13	−0.00204592
$750$	−5.56187e15	−0.855823
$751$	−3.09246e15	−0.472373	−0.236186	−	0.971708i	$-0.575898\pi$
$751$	−3.09246e15	−0.472373	−0.236186	+	0.971708i	$0.575898\pi$
$752$	−5.97303e15	−0.905726
$753$	4.59489e14	0.0691677
$754$	1.78189e16	2.66280
$755$	−6.08775e15	−0.903127
$756$	−2.55890e14	−0.0376862
$757$	−7.13211e15	−1.04278	−0.521388	−	0.853320i	$-0.674585\pi$
$757$	−7.13211e15	−1.04278	−0.521388	+	0.853320i	$0.674585\pi$
$758$	−1.64045e16	−2.38112
$759$	9.53187e14	0.137356
$760$	−1.75708e15	−0.251371
$761$	−2.50666e15	−0.356024	−0.178012	−	0.984028i	$-0.556967\pi$
$761$	−2.50666e15	−0.356024	−0.178012	+	0.984028i	$0.556967\pi$
$762$	1.98404e15	0.279768
$763$	1.98193e15	0.277461
$764$	−3.93473e15	−0.546892
$765$	−8.90344e14	−0.122863
$766$	−8.97968e15	−1.23028
$767$	1.45136e15	0.197424
$768$	−2.89354e15	−0.390790
$769$	−1.13780e16	−1.52571	−0.762856	−	0.646569i	$-0.776203\pi$
$769$	−1.13780e16	−1.52571	−0.762856	+	0.646569i	$0.776203\pi$
$770$	−9.25799e14	−0.123259
$771$	3.89760e14	0.0515226
$772$	9.89457e14	0.129868
$773$	5.28918e15	0.689288	0.344644	−	0.938733i	$-0.388000\pi$
$773$	5.28918e15	0.689288	0.344644	+	0.938733i	$0.388000\pi$
$774$	−2.50502e14	−0.0324142
$775$	9.35846e13	0.0120239
$776$	−2.88552e15	−0.368116
$777$	−4.59794e14	−0.0582435
$778$	−5.25333e15	−0.660765
$779$	−2.03132e14	−0.0253701
$780$	7.89528e15	0.979145
$781$	−1.32678e15	−0.163388
$782$	−2.14267e15	−0.262010
$783$	−1.90448e15	−0.231252
$784$	6.80921e15	0.821028
$785$	−8.40885e15	−1.00682
$786$	7.62822e15	0.906983
$787$	5.05298e15	0.596605	0.298302	−	0.954471i	$-0.403580\pi$
$787$	5.05298e15	0.596605	0.298302	+	0.954471i	$0.403580\pi$
$788$	9.18053e15	1.07640
$789$	6.89894e15	0.803265
$790$	1.95696e16	2.26274
$791$	−1.37139e15	−0.157468
$792$	−2.87325e14	−0.0327630
$793$	−2.28898e15	−0.259203
$794$	−1.00712e15	−0.113257
$795$	−8.39800e15	−0.937900
$796$	3.06614e15	0.340071
$797$	1.24735e16	1.37394	0.686970	−	0.726686i	$-0.258940\pi$
$797$	1.24735e16	1.37394	0.686970	+	0.726686i	$0.258940\pi$
$798$	1.71498e15	0.187604
$799$	−3.68690e15	−0.400547
$800$	−3.97277e14	−0.0428646
$801$	−5.26094e15	−0.563748
$802$	−1.77475e16	−1.88876
$803$	5.86144e15	0.619540
$804$	8.57299e15	0.899962
$805$	−7.80599e14	−0.0813862
$806$	−8.61117e15	−0.891701
$807$	5.21049e15	0.535888
$808$	3.79886e15	0.388052
$809$	5.04702e15	0.512057	0.256029	−	0.966669i	$-0.417586\pi$
$809$	5.04702e15	0.512057	0.256029	+	0.966669i	$0.417586\pi$
$810$	−1.58702e15	−0.159925
$811$	1.93186e15	0.193358	0.0966789	−	0.995316i	$-0.469178\pi$
$811$	1.93186e15	0.193358	0.0966789	+	0.995316i	$0.469178\pi$
$812$	2.36696e15	0.235306
$813$	6.39424e15	0.631380
$814$	−4.32771e15	−0.424447
$815$	1.33195e16	1.29754
$816$	−1.88945e15	−0.182827
$817$	8.92679e14	0.0857974
$818$	2.48651e16	2.37382
$819$	−9.19306e14	−0.0871764
$820$	−2.33624e14	−0.0220060
$821$	4.37286e15	0.409146	0.204573	−	0.978851i	$-0.434419\pi$
$821$	4.37286e15	0.409146	0.204573	+	0.978851i	$0.434419\pi$
$822$	1.35561e16	1.25991
$823$	7.49452e15	0.691902	0.345951	−	0.938253i	$-0.387556\pi$
$823$	7.49452e15	0.691902	0.345951	+	0.938253i	$0.387556\pi$
$824$	−3.87551e15	−0.355410
$825$	9.40367e13	0.00856645
$826$	3.62580e14	0.0328106
$827$	−1.90369e16	−1.71126	−0.855629	−	0.517590i	$-0.826829\pi$
$827$	−1.90369e16	−1.71126	−0.855629	+	0.517590i	$0.826829\pi$
$828$	−2.03076e15	−0.181339
$829$	−7.72884e15	−0.685590	−0.342795	−	0.939410i	$-0.611374\pi$
$829$	−7.72884e15	−0.685590	−0.342795	+	0.939410i	$0.611374\pi$
$830$	5.31720e15	0.468547
$831$	8.98421e15	0.786456
$832$	2.17992e16	1.89567
$833$	4.20303e15	0.363091
$834$	−5.31806e15	−0.456394
$835$	−1.14884e16	−0.979457
$836$	8.58287e15	0.726939
$837$	9.20359e14	0.0774403
$838$	−3.35681e15	−0.280598
$839$	1.44536e16	1.20029	0.600145	−	0.799891i	$-0.295110\pi$
$839$	1.44536e16	1.20029	0.600145	+	0.799891i	$0.295110\pi$
$840$	2.35301e14	0.0194127
$841$	5.41577e15	0.443897
$842$	−2.13999e16	−1.74259
$843$	3.93734e15	0.318531
$844$	1.39523e16	1.12141
$845$	1.60299e16	1.28003
$846$	−6.57183e15	−0.521374
$847$	−1.64854e15	−0.129939
$848$	−1.78219e16	−1.39565
$849$	−1.27452e16	−0.991638
$850$	−2.11385e14	−0.0163407
$851$	−3.64896e15	−0.280257
$852$	2.82671e15	0.215707
$853$	−8.00796e15	−0.607159	−0.303579	−	0.952806i	$-0.598182\pi$
$853$	−8.00796e15	−0.607159	−0.303579	+	0.952806i	$0.598182\pi$
$854$	−5.71837e14	−0.0430779
$855$	5.65546e15	0.423306
$856$	3.15748e13	0.00234820
$857$	1.37390e16	1.01522	0.507610	−	0.861587i	$-0.330529\pi$
$857$	1.37390e16	1.01522	0.507610	+	0.861587i	$0.330529\pi$
$858$	−8.65277e15	−0.635294
$859$	1.35946e16	0.991755	0.495878	−	0.868392i	$-0.334846\pi$
$859$	1.35946e16	0.991755	0.495878	+	0.868392i	$0.334846\pi$
$860$	1.02668e15	0.0744207
$861$	2.72026e13	0.00195927
$862$	1.51433e16	1.08375
$863$	1.57105e16	1.11720	0.558601	−	0.829437i	$-0.311338\pi$
$863$	1.57105e16	1.11720	0.558601	+	0.829437i	$0.311338\pi$
$864$	−3.90703e15	−0.276071
$865$	8.82859e15	0.619873
$866$	1.43160e16	0.998785
$867$	7.16179e15	0.496497
$868$	−1.14386e15	−0.0787977
$869$	−1.14038e16	−0.780623
$870$	1.46798e16	0.998539
$871$	3.07992e16	2.08181
$872$	−4.74121e15	−0.318455
$873$	9.28755e15	0.619902
$874$	1.36102e16	0.902717
$875$	−2.65423e15	−0.174942
$876$	−1.24878e16	−0.817925
$877$	−7.13883e15	−0.464654	−0.232327	−	0.972638i	$-0.574634\pi$
$877$	−7.13883e15	−0.464654	−0.232327	+	0.972638i	$0.574634\pi$
$878$	−2.42378e16	−1.56774
$879$	4.62596e15	0.297346
$880$	−6.47894e15	−0.413856
$881$	−2.56583e15	−0.162877	−0.0814387	−	0.996678i	$-0.525951\pi$
$881$	−2.56583e15	−0.162877	−0.0814387	+	0.996678i	$0.525951\pi$
$882$	7.49183e15	0.472618
$883$	1.85749e16	1.16451	0.582254	−	0.813007i	$-0.302171\pi$
$883$	1.85749e16	1.16451	0.582254	+	0.813007i	$0.302171\pi$
$884$	1.03422e16	0.644353
$885$	1.19568e15	0.0740331
$886$	−2.15791e16	−1.32785
$887$	−5.83734e15	−0.356973	−0.178486	−	0.983942i	$-0.557120\pi$
$887$	−5.83734e15	−0.356973	−0.178486	+	0.983942i	$0.557120\pi$
$888$	1.09993e15	0.0668487
$889$	9.46821e14	0.0571885
$890$	4.05517e16	2.43424
$891$	9.24805e14	0.0551725
$892$	5.84778e15	0.346725
$893$	2.34191e16	1.38003
$894$	1.22642e16	0.718261
$895$	−7.56858e15	−0.440543
$896$	1.16938e15	0.0676492
$897$	−7.29569e15	−0.419477
$898$	−2.77705e15	−0.158695
$899$	−8.51325e15	−0.483523
$900$	−2.00345e14	−0.0113095
$901$	−1.10007e16	−0.617211
$902$	2.56039e14	0.0142781
$903$	−1.19544e14	−0.00662591
$904$	3.28067e15	0.180733
$905$	1.69149e16	0.926197
$906$	−1.42143e16	−0.773608
$907$	−6.91706e15	−0.374181	−0.187090	−	0.982343i	$-0.559906\pi$
$907$	−6.91706e15	−0.374181	−0.187090	+	0.982343i	$0.559906\pi$
$908$	3.66410e15	0.197013
$909$	−1.22273e16	−0.653475
$910$	7.08607e15	0.376424
$911$	1.08098e16	0.570778	0.285389	−	0.958412i	$-0.407877\pi$
$911$	1.08098e16	0.570778	0.285389	+	0.958412i	$0.407877\pi$
$912$	1.20018e16	0.629903
$913$	−3.09849e15	−0.161644
$914$	−1.16928e16	−0.606339
$915$	−1.88574e15	−0.0971999
$916$	3.59594e16	1.84241
$917$	3.64033e15	0.185400
$918$	−2.07887e15	−0.105243
$919$	−8.23865e15	−0.414592	−0.207296	−	0.978278i	$-0.566466\pi$
$919$	−8.23865e15	−0.414592	−0.207296	+	0.978278i	$0.566466\pi$
$920$	1.86737e15	0.0934107
$921$	4.12500e15	0.205114
$922$	−4.45676e16	−2.20292
$923$	1.01552e16	0.498976
$924$	−1.14938e15	−0.0561396
$925$	−3.59989e14	−0.0174787
$926$	−3.66912e16	−1.77093
$927$	1.24740e16	0.598505
$928$	3.61397e16	1.72374
$929$	−2.99868e16	−1.42182	−0.710909	−	0.703284i	$-0.751716\pi$
$929$	−2.99868e16	−1.42182	−0.710909	+	0.703284i	$0.751716\pi$
$930$	−7.09418e15	−0.334384
$931$	−2.66976e16	−1.25098
$932$	1.79006e16	0.833834
$933$	6.55063e15	0.303343
$934$	−4.22988e16	−1.94724
$935$	−3.99917e15	−0.183023
$936$	2.19918e15	0.100056
$937$	2.94975e16	1.33419	0.667095	−	0.744973i	$-0.267538\pi$
$937$	2.94975e16	1.33419	0.667095	+	0.744973i	$0.267538\pi$
$938$	7.69432e15	0.345983
$939$	−7.47826e15	−0.334302
$940$	2.69346e16	1.19704
$941$	−3.09688e16	−1.36830	−0.684150	−	0.729341i	$-0.739827\pi$
$941$	−3.09688e16	−1.36830	−0.684150	+	0.729341i	$0.739827\pi$
$942$	−1.96338e16	−0.862433
$943$	2.15883e14	0.00942765
$944$	2.53741e15	0.110165
$945$	−7.57356e14	−0.0326908
$946$	−1.12518e15	−0.0482861
$947$	−1.68641e15	−0.0719514	−0.0359757	−	0.999353i	$-0.511454\pi$
$947$	−1.68641e15	−0.0719514	−0.0359757	+	0.999353i	$0.511454\pi$
$948$	2.42958e16	1.03059
$949$	−4.48635e16	−1.89204
$950$	1.34272e15	0.0562995
$951$	6.96696e15	0.290436
$952$	3.08224e14	0.0127751
$953$	1.59140e14	0.00655794	0.00327897	−	0.999995i	$-0.498956\pi$
$953$	1.59140e14	0.00655794	0.00327897	+	0.999995i	$0.498956\pi$
$954$	−1.96085e16	−0.803394
$955$	−1.16456e16	−0.474399
$956$	−2.09956e16	−0.850373
$957$	−8.55437e15	−0.344487
$958$	−2.84762e16	−1.14018
$959$	6.46920e15	0.257542
$960$	1.79589e16	0.710867
$961$	−2.12944e16	−0.838081
$962$	3.31243e16	1.29624
$963$	−1.01629e14	−0.00395434
$964$	−3.27675e16	−1.26771
$965$	2.92850e15	0.112653
$966$	−1.82262e15	−0.0697145
$967$	2.51928e16	0.958146	0.479073	−	0.877775i	$-0.340973\pi$
$967$	2.51928e16	0.958146	0.479073	+	0.877775i	$0.340973\pi$
$968$	3.94367e15	0.149137
$969$	7.40818e15	0.278568
$970$	−7.15890e16	−2.67671
$971$	3.97901e16	1.47934	0.739672	−	0.672967i	$-0.234981\pi$
$971$	3.97901e16	1.47934	0.739672	+	0.672967i	$0.234981\pi$
$972$	−1.97030e15	−0.0728395
$973$	−2.53788e15	−0.0932932
$974$	−1.21789e16	−0.445178
$975$	−7.19757e14	−0.0261614
$976$	−4.00184e15	−0.144639
$977$	−1.75457e16	−0.630594	−0.315297	−	0.948993i	$-0.602104\pi$
$977$	−1.75457e16	−0.630594	−0.315297	+	0.948993i	$0.602104\pi$
$978$	3.10998e16	1.11146
$979$	−2.36307e16	−0.839791
$980$	−3.07052e16	−1.08510
$981$	1.52604e16	0.536274
$982$	−2.99721e15	−0.104738
$983$	−4.06557e16	−1.41279	−0.706395	−	0.707818i	$-0.749680\pi$
$983$	−4.06557e16	−1.41279	−0.706395	+	0.707818i	$0.749680\pi$
$984$	−6.50747e13	−0.00224874
$985$	2.71716e16	0.933719
$986$	1.92294e16	0.657116
$987$	−3.13620e15	−0.106576
$988$	−6.56933e16	−2.22003
$989$	−9.48712e14	−0.0318827
$990$	−7.12845e15	−0.238233
$991$	3.73863e15	0.124253	0.0621266	−	0.998068i	$-0.480212\pi$
$991$	3.73863e15	0.124253	0.0621266	+	0.998068i	$0.480212\pi$
$992$	−1.74649e16	−0.577234
$993$	−2.04090e16	−0.670810
$994$	2.53699e15	0.0829267
$995$	9.07485e15	0.294993
$996$	6.60133e15	0.213405
$997$	3.08638e16	0.992261	0.496131	−	0.868248i	$-0.334754\pi$
$997$	3.08638e16	0.992261	0.496131	+	0.868248i	$0.334754\pi$
$998$	3.03165e16	0.969307
$999$	−3.54031e15	−0.112572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.5	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-66.1318 q^{2} -243.000 q^{3} +2325.41 q^{4} +6882.52 q^{5} +16070.0 q^{6} +7668.92 q^{7} -18345.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-66.1318 q^{2} -243.000 q^{3} +2325.41 q^{4} +6882.52 q^{5} +16070.0 q^{6} +7668.92 q^{7} -18345.7 q^{8} +59049.0 q^{9} -455153. q^{10} +265231. q^{11} -565075. q^{12} -2.03008e6 q^{13} -507159. q^{14} -1.67245e6 q^{15} -3.54921e6 q^{16} -2.19078e6 q^{17} -3.90502e6 q^{18} +1.39158e7 q^{19} +1.60047e7 q^{20} -1.86355e6 q^{21} -1.75402e7 q^{22} -1.47893e7 q^{23} +4.45802e6 q^{24} -1.45904e6 q^{25} +1.34253e8 q^{26} -1.43489e7 q^{27} +1.78334e7 q^{28} +1.32726e8 q^{29} +1.10602e8 q^{30} -6.41414e7 q^{31} +2.72287e8 q^{32} -6.44512e7 q^{33} +1.44880e8 q^{34} +5.27815e7 q^{35} +1.37313e8 q^{36} +2.46731e8 q^{37} -9.20275e8 q^{38} +4.93310e8 q^{39} -1.26265e8 q^{40} -1.45972e7 q^{41} +1.23240e8 q^{42} +6.41487e7 q^{43} +6.16772e8 q^{44} +4.06406e8 q^{45} +9.78041e8 q^{46} +1.68292e9 q^{47} +8.62457e8 q^{48} -1.91851e9 q^{49} +9.64887e7 q^{50} +5.32358e8 q^{51} -4.72078e9 q^{52} +5.02137e9 q^{53} +9.48919e8 q^{54} +1.82546e9 q^{55} -1.40692e8 q^{56} -3.38153e9 q^{57} -8.77743e9 q^{58} -7.14924e8 q^{59} -3.88914e9 q^{60} +1.12753e9 q^{61} +4.24178e9 q^{62} +4.52842e8 q^{63} -1.07381e10 q^{64} -1.39721e10 q^{65} +4.26227e9 q^{66} -1.51714e10 q^{67} -5.09446e9 q^{68} +3.59379e9 q^{69} -3.49053e9 q^{70} -5.00236e9 q^{71} -1.08330e9 q^{72} +2.20994e10 q^{73} -1.63167e10 q^{74} +3.54546e8 q^{75} +3.23599e10 q^{76} +2.03404e9 q^{77} -3.26235e10 q^{78} -4.29957e10 q^{79} -2.44275e10 q^{80} +3.48678e9 q^{81} +9.65342e8 q^{82} -1.16822e10 q^{83} -4.33351e9 q^{84} -1.50781e10 q^{85} -4.24227e9 q^{86} -3.22525e10 q^{87} -4.86587e9 q^{88} -8.90945e10 q^{89} -2.68763e10 q^{90} -1.55685e10 q^{91} -3.43911e10 q^{92} +1.55864e10 q^{93} -1.11294e11 q^{94} +9.57757e10 q^{95} -6.61659e10 q^{96} +1.57286e11 q^{97} +1.26875e11 q^{98} +1.56616e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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

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