LMFDB - Embedded newform 147.8.c.b.146.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,8,Mod(146,147)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("147.146"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$45.9205987462$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.24
Character	$\chi$	$=$	147.146
Dual form			147.8.c.b.146.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+9.33246i q^{2} +(13.8782 + 44.6586i) q^{3} +40.9053 q^{4} -246.682 q^{5} +(-416.775 + 129.518i) q^{6} +1576.30i q^{8} +(-1801.79 + 1239.57i) q^{9} -2302.15i q^{10} +6681.89i q^{11} +(567.693 + 1826.77i) q^{12} +6161.99i q^{13} +(-3423.52 - 11016.5i) q^{15} -9474.88 q^{16} +31753.3 q^{17} +(-11568.2 - 16815.1i) q^{18} +6873.52i q^{19} -10090.6 q^{20} -62358.4 q^{22} +55675.8i q^{23} +(-70395.5 + 21876.3i) q^{24} -17272.8 q^{25} -57506.5 q^{26} +(-80363.0 - 63262.4i) q^{27} -167195. i q^{29} +(102811. - 31949.8i) q^{30} -229331. i q^{31} +113343. i q^{32} +(-298404. + 92732.8i) q^{33} +296336. i q^{34} +(-73702.7 + 50704.8i) q^{36} -280542. q^{37} -64146.8 q^{38} +(-275186. + 85517.5i) q^{39} -388846. i q^{40} +78668.6 q^{41} +118106. q^{43} +273324. i q^{44} +(444469. - 305779. i) q^{45} -519592. q^{46} +8356.96 q^{47} +(-131495. - 423135. i) q^{48} -161198. i q^{50} +(440680. + 1.41806e6i) q^{51} +252058. i q^{52} +177258. i q^{53} +(590394. - 749984. i) q^{54} -1.64830e6i q^{55} +(-306962. + 95392.4i) q^{57} +1.56034e6 q^{58} +234608. q^{59} +(-140040. - 450633. i) q^{60} -237235. i q^{61} +2.14022e6 q^{62} -2.27055e6 q^{64} -1.52005e6i q^{65} +(-865425. - 2.78484e6i) q^{66} -3.36488e6 q^{67} +1.29888e6 q^{68} +(-2.48641e6 + 772682. i) q^{69} +711242. i q^{71} +(-1.95393e6 - 2.84016e6i) q^{72} -5.36998e6i q^{73} -2.61814e6i q^{74} +(-239717. - 771381. i) q^{75} +281163. i q^{76} +(-798089. - 2.56816e6i) q^{78} +2.55196e6 q^{79} +2.33729e6 q^{80} +(1.70992e6 - 4.46688e6i) q^{81} +734172. i q^{82} +2.04843e6 q^{83} -7.83298e6 q^{85} +1.10222e6i q^{86} +(7.46669e6 - 2.32037e6i) q^{87} -1.05327e7 q^{88} +4.63762e6 q^{89} +(2.85367e6 + 4.14799e6i) q^{90} +2.27743e6i q^{92} +(1.02416e7 - 3.18271e6i) q^{93} +77990.9i q^{94} -1.69558e6i q^{95} +(-5.06173e6 + 1.57300e6i) q^{96} +217594. i q^{97} +(-8.28264e6 - 1.20393e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2300 q^{4} + 7032 q^{9} + 27576 q^{15} + 39188 q^{16} - 66996 q^{18} + 105132 q^{22} + 662504 q^{25} + 81324 q^{30} - 227244 q^{36} + 1237496 q^{37} - 3992208 q^{39} - 1416064 q^{43} + 6985680 q^{46}+ \cdots + 35642232 q^{99}+O(q^{100}) $ 32 * q - 2300 * q^4 + 7032 * q^9 + 27576 * q^15 + 39188 * q^16 - 66996 * q^18 + 105132 * q^22 + 662504 * q^25 + 81324 * q^30 - 227244 * q^36 + 1237496 * q^37 - 3992208 * q^39 - 1416064 * q^43 + 6985680 * q^46 - 1354680 * q^51 - 6279408 * q^57 + 4128684 * q^58 - 15042564 * q^60 - 589508 * q^64 + 3889456 * q^67 + 3088944 * q^72 + 1917432 * q^78 - 15252656 * q^79 - 17406072 * q^81 + 3418848 * q^85 - 24626796 * q^88 + 49664208 * q^93 + 35642232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$			9.33246i			0.824880i	0.910985	+	0.412440i	$0.135323\pi$
$2$			9.33246i			0.824880i	−0.910985	+	0.412440i	$0.864677\pi$
$3$	13.8782	+	44.6586i	0.296763	+	0.954951i
$3$	13.8782	+	44.6586i	0.296763	+	0.954951i
$4$	40.9053			0.319572
$5$	−246.682			−0.882558			−0.441279	−	0.897370i	$-0.645475\pi$
$5$	−246.682			−0.882558			−0.441279	+	0.897370i	$0.645475\pi$
$6$	−416.775	+	129.518i	−0.787720	+	0.244794i
$7$		0			0
$7$		0			0
$8$			1576.30i			1.08849i
$9$	−1801.79	+	1239.57i	−0.823863	+	0.566789i
$10$		−	2302.15i		−	0.728004i
$11$			6681.89i			1.51365i	0.653619	+	0.756824i	$0.273250\pi$
$11$			6681.89i			1.51365i	−0.653619	+	0.756824i	$0.726750\pi$
$12$	567.693	+	1826.77i	0.0948373	+	0.305176i
$13$			6161.99i			0.777891i	0.921261	+	0.388946i	$0.127161\pi$
$13$			6161.99i			0.777891i	−0.921261	+	0.388946i	$0.872839\pi$
$14$		0			0
$15$	−3423.52	−	11016.5i	−0.261911	−	0.842799i
$16$	−9474.88			−0.578301
$17$	31753.3			1.56754			0.783769	−	0.621053i	$-0.213295\pi$
$17$	31753.3			1.56754			0.783769	+	0.621053i	$0.213295\pi$
$18$	−11568.2	−	16815.1i	−0.467533	−	0.679589i
$19$			6873.52i			0.229901i	0.993371	+	0.114951i	$0.0366710\pi$
$19$			6873.52i			0.229901i	−0.993371	+	0.114951i	$0.963329\pi$
$20$	−10090.6			−0.282041
$21$		0			0
$22$	−62358.4			−1.24858
$23$			55675.8i			0.954155i	0.878861	+	0.477078i	$0.158304\pi$
$23$			55675.8i			0.954155i	−0.878861	+	0.477078i	$0.841696\pi$
$24$	−70395.5	+	21876.3i	−1.03945	+	0.323024i
$25$	−17272.8			−0.221092
$26$	−57506.5			−0.641667
$27$	−80363.0	−	63262.4i	−0.785748	−	0.618547i
$28$		0			0
$29$		−	167195.i		−	1.27300i	−0.771275	−	0.636502i	$-0.780381\pi$
$29$		−	167195.i		−	1.27300i	0.771275	−	0.636502i	$-0.219619\pi$
$30$	102811.	−	31949.8i	0.695209	−	0.216045i
$31$		−	229331.i		−	1.38260i	−0.722568	−	0.691300i	$-0.757038\pi$
$31$		−	229331.i		−	1.38260i	0.722568	−	0.691300i	$-0.242962\pi$
$32$			113343.i			0.611460i
$33$	−298404.	+	92732.8i	−1.44546	+	0.449195i
$34$			296336.i			1.29303i
$35$		0			0
$36$	−73702.7	+	50704.8i	−0.263284	+	0.181130i
$37$	−280542.			−0.910524			−0.455262	−	0.890358i	$-0.650454\pi$
$37$	−280542.			−0.910524			−0.455262	+	0.890358i	$0.650454\pi$
$38$	−64146.8			−0.189641
$39$	−275186.	+	85517.5i	−0.742848	+	0.230850i
$40$		−	388846.i		−	0.960654i
$41$	78668.6			0.178262			0.0891309	−	0.996020i	$-0.471591\pi$
$41$	78668.6			0.178262			0.0891309	+	0.996020i	$0.471591\pi$
$42$		0			0
$43$	118106.			0.226533			0.113266	−	0.993565i	$-0.463869\pi$
$43$	118106.			0.226533			0.113266	+	0.993565i	$0.463869\pi$
$44$			273324.i			0.483720i
$45$	444469.	−	305779.i	0.727107	−	0.500224i
$46$	−519592.			−0.787064
$47$	8356.96			0.0117410			0.00587051	−	0.999983i	$-0.498131\pi$
$47$	8356.96			0.0117410			0.00587051	+	0.999983i	$0.498131\pi$
$48$	−131495.	−	423135.i	−0.171618	−	0.552249i
$49$		0			0
$50$		−	161198.i		−	0.182375i
$51$	440680.	+	1.41806e6i	0.465187	+	1.49692i
$52$			252058.i			0.248593i
$53$			177258.i			0.163546i	0.996651	+	0.0817731i	$0.0260583\pi$
$53$			177258.i			0.163546i	−0.996651	+	0.0817731i	$0.973942\pi$
$54$	590394.	−	749984.i	0.510227	−	0.648148i
$55$		−	1.64830e6i		−	1.33588i
$56$		0			0
$57$	−306962.	+	95392.4i	−0.219545	+	0.0682263i
$58$	1.56034e6			1.05008
$59$	234608.			0.148717			0.0743586	−	0.997232i	$-0.476309\pi$
$59$	234608.			0.148717			0.0743586	+	0.997232i	$0.476309\pi$
$60$	−140040.	−	450633.i	−0.0836994	−	0.269335i
$61$		−	237235.i		−	0.133821i	−0.997759	−	0.0669105i	$-0.978686\pi$
$61$		−	237235.i		−	0.133821i	0.997759	−	0.0669105i	$-0.0213142\pi$
$62$	2.14022e6			1.14048
$63$		0			0
$64$	−2.27055e6			−1.08268
$65$		−	1.52005e6i		−	0.686534i
$66$	−865425.	−	2.78484e6i	−0.370532	−	1.19233i
$67$	−3.36488e6			−1.36681			−0.683403	−	0.730041i	$-0.739501\pi$
$67$	−3.36488e6			−1.36681			−0.683403	+	0.730041i	$0.739501\pi$
$68$	1.29888e6			0.500942
$69$	−2.48641e6	+	772682.i	−0.911172	+	0.283158i
$70$		0			0
$71$			711242.i			0.235838i	0.993023	+	0.117919i	$0.0376223\pi$
$71$			711242.i			0.235838i	−0.993023	+	0.117919i	$0.962378\pi$
$72$	−1.95393e6	−	2.84016e6i	−0.616943	−	0.896766i
$73$		−	5.36998e6i		−	1.61563i	−0.589435	−	0.807816i	$-0.700650\pi$
$73$		−	5.36998e6i		−	1.61563i	0.589435	−	0.807816i	$-0.299350\pi$
$74$		−	2.61814e6i		−	0.751073i
$75$	−239717.	−	771381.i	−0.0656120	−	0.211132i
$76$			281163.i			0.0734702i
$77$		0			0
$78$	−798089.	−	2.56816e6i	−0.190423	−	0.612761i
$79$	2.55196e6			0.582343			0.291171	−	0.956671i	$-0.405955\pi$
$79$	2.55196e6			0.582343			0.291171	+	0.956671i	$0.405955\pi$
$80$	2.33729e6			0.510384
$81$	1.70992e6	−	4.46688e6i	0.357501	−	0.933913i
$82$			734172.i			0.147045i
$83$	2.04843e6			0.393231			0.196615	−	0.980481i	$-0.437005\pi$
$83$	2.04843e6			0.393231			0.196615	+	0.980481i	$0.437005\pi$
$84$		0			0
$85$	−7.83298e6			−1.38344
$86$			1.10222e6i			0.186862i
$87$	7.46669e6	−	2.32037e6i	1.21566	−	0.377781i
$88$	−1.05327e7			−1.64759
$89$	4.63762e6			0.697317			0.348658	−	0.937250i	$-0.386637\pi$
$89$	4.63762e6			0.697317			0.348658	+	0.937250i	$0.386637\pi$
$90$	2.85367e6	+	4.14799e6i	0.412625	+	0.599776i
$91$		0			0
$92$			2.27743e6i			0.304922i
$93$	1.02416e7	−	3.18271e6i	1.32032	−	0.410305i
$94$			77990.9i			0.00968493i
$95$		−	1.69558e6i		−	0.202901i
$96$	−5.06173e6	+	1.57300e6i	−0.583915	+	0.181459i
$97$			217594.i			0.0242073i	0.999927	+	0.0121036i	$0.00385280\pi$
$97$			217594.i			0.0242073i	−0.999927	+	0.0121036i	$0.996147\pi$
$98$		0			0
$99$	−8.28264e6	−	1.20393e7i	−0.857918	−	1.24704i
$100$	−706550.			−0.0706550
$101$	−4.06191e6			−0.392289			−0.196144	−	0.980575i	$-0.562842\pi$
$101$	−4.06191e6			−0.392289			−0.196144	+	0.980575i	$0.562842\pi$
$102$	−1.32340e7	+	4.11263e6i	−1.23478	+	0.383724i
$103$			3.97387e6i			0.358330i	0.983819	+	0.179165i	$0.0573396\pi$
$103$			3.97387e6i			0.358330i	−0.983819	+	0.179165i	$0.942660\pi$
$104$	−9.71314e6			−0.846726
$105$		0			0
$106$	−1.65425e6			−0.134906
$107$			1.23272e7i			0.972796i	0.873737	+	0.486398i	$0.161690\pi$
$107$			1.23272e7i			0.972796i	−0.873737	+	0.486398i	$0.838310\pi$
$108$	−3.28727e6	−	2.58777e6i	−0.251103	−	0.197671i
$109$	1.43296e7			1.05984			0.529922	−	0.848046i	$-0.322221\pi$
$109$	1.43296e7			1.05984			0.529922	+	0.848046i	$0.322221\pi$
$110$	1.53827e7			1.10194
$111$	−3.89342e6	−	1.25286e7i	−0.270210	−	0.869505i
$112$		0			0
$113$			2.51834e7i			1.64187i	0.571019	+	0.820937i	$0.306548\pi$
$113$			2.51834e7i			1.64187i	−0.571019	+	0.820937i	$0.693452\pi$
$114$	−890245.	−	2.86471e6i	−0.0562785	−	0.181098i
$115$		−	1.37342e7i		−	0.842097i
$116$		−	6.83915e6i		−	0.406817i
$117$	−7.63819e6	−	1.11026e7i	−0.440900	−	0.640876i
$118$			2.18947e6i			0.122674i
$119$		0			0
$120$	1.73653e7	−	5.39649e6i	0.917378	−	0.285087i
$121$	−2.51604e7			−1.29113
$122$	2.21398e6			0.110386
$123$	1.09178e6	+	3.51323e6i	0.0529015	+	0.170231i
$124$		−	9.38084e6i		−	0.441841i
$125$	2.35330e7			1.07768
$126$		0			0
$127$	2.57045e7			1.11352			0.556758	−	0.830675i	$-0.312045\pi$
$127$	2.57045e7			1.11352			0.556758	+	0.830675i	$0.312045\pi$
$128$		−	6.68195e6i		−	0.281623i
$129$	1.63910e6	+	5.27444e6i	0.0672266	+	0.216328i
$130$	1.41858e7			0.566308
$131$	−2.91128e7			−1.13145			−0.565724	−	0.824594i	$-0.691403\pi$
$131$	−2.91128e7			−1.13145			−0.565724	+	0.824594i	$0.691403\pi$
$132$	−1.22063e7	+	3.79326e6i	−0.461929	+	0.143550i
$133$		0			0
$134$		−	3.14025e7i		−	1.12745i
$135$	1.98241e7	+	1.56057e7i	0.693468	+	0.545903i
$136$			5.00528e7i			1.70625i
$137$			5.42048e7i			1.80101i	0.434847	+	0.900504i	$0.356802\pi$
$137$			5.42048e7i			1.80101i	−0.434847	+	0.900504i	$0.643198\pi$
$138$	−7.21102e6	−	2.32043e7i	−0.233572	−	0.751608i
$139$		−	2.23460e7i		−	0.705745i	−0.935671	−	0.352872i	$-0.885205\pi$
$139$		−	2.23460e7i		−	0.705745i	0.935671	−	0.352872i	$-0.114795\pi$
$140$		0			0
$141$	115980.	+	373210.i	0.00348430	+	0.0112121i
$142$	−6.63764e6			−0.194538
$143$	−4.11737e7			−1.17745
$144$	1.70717e7	−	1.17448e7i	0.476441	−	0.327774i
$145$			4.12440e7i			1.12350i
$146$	5.01151e7			1.33270
$147$		0			0
$148$	−1.14756e7			−0.290978
$149$			1.80962e7i			0.448163i	0.974570	+	0.224081i	$0.0719381\pi$
$149$			1.80962e7i			0.448163i	−0.974570	+	0.224081i	$0.928062\pi$
$150$	7.19888e6	−	2.23714e6i	0.174159	−	0.0541221i
$151$	−8.24073e6			−0.194781			−0.0973905	−	0.995246i	$-0.531050\pi$
$151$	−8.24073e6			−0.194781			−0.0973905	+	0.995246i	$0.531050\pi$
$152$	−1.08347e7			−0.250245
$153$	−5.72128e7	+	3.93604e7i	−1.29144	+	0.888462i
$154$		0			0
$155$			5.65719e7i			1.22022i
$156$	−1.12566e7	+	3.49812e6i	−0.237394	+	0.0737731i
$157$			5.34359e7i			1.10201i	0.834503	+	0.551003i	$0.185755\pi$
$157$			5.34359e7i			1.10201i	−0.834503	+	0.551003i	$0.814245\pi$
$158$			2.38160e7i			0.480363i
$159$	−7.91611e6	+	2.46003e6i	−0.156179	+	0.0485345i
$160$		−	2.79596e7i		−	0.539649i
$161$		0			0
$162$	4.16869e7	+	1.59577e7i	0.770366	+	0.294896i
$163$	−3.01140e7			−0.544643			−0.272322	−	0.962206i	$-0.587791\pi$
$163$	−3.01140e7			−0.544643			−0.272322	+	0.962206i	$0.587791\pi$
$164$	3.21796e6			0.0569675
$165$	7.36110e7	−	2.28755e7i	1.27570	−	0.396440i
$166$			1.91169e7i			0.324368i
$167$	−6.70162e7			−1.11345			−0.556726	−	0.830696i	$-0.687943\pi$
$167$	−6.70162e7			−1.11345			−0.556726	+	0.830696i	$0.687943\pi$
$168$		0			0
$169$	2.47784e7			0.394885
$170$		−	7.31010e7i		−	1.14117i
$171$	−8.52019e6	−	1.23846e7i	−0.130306	−	0.189407i
$172$	4.83114e6			0.0723936
$173$	7.28931e7			1.07035			0.535174	−	0.844742i	$-0.320246\pi$
$173$	7.28931e7			1.07035			0.535174	+	0.844742i	$0.320246\pi$
$174$	2.16547e7	+	6.96825e7i	0.311624	+	1.00277i
$175$		0			0
$176$		−	6.33101e7i		−	0.875344i
$177$	3.25595e6	+	1.04773e7i	0.0441338	+	0.142018i
$178$			4.32804e7i			0.575203i
$179$		−	1.04960e8i		−	1.36785i	−0.729550	−	0.683927i	$-0.760271\pi$
$179$		−	1.04960e8i		−	1.36785i	0.729550	−	0.683927i	$-0.239729\pi$
$180$	1.81811e7	−	1.25080e7i	0.232363	−	0.159858i
$181$			7.36629e7i			0.923366i	0.887045	+	0.461683i	$0.152754\pi$
$181$			7.36629e7i			0.923366i	−0.887045	+	0.461683i	$0.847246\pi$
$182$		0			0
$183$	1.05946e7	−	3.29240e6i	0.127792	−	0.0397131i
$184$	−8.77618e7			−1.03859
$185$	6.92046e7			0.803589
$186$	2.97025e7	+	9.55793e7i	0.338452	+	1.08910i
$187$			2.12172e8i			2.37270i
$188$	341844.			0.00375210
$189$		0			0
$190$	1.58239e7			0.167369
$191$		−	5.86519e6i		−	0.0609068i	−0.999536	−	0.0304534i	$-0.990305\pi$
$191$		−	5.86519e6i		−	0.0609068i	0.999536	−	0.0304534i	$-0.00969511\pi$
$192$	−3.15112e7	−	1.01400e8i	−0.321300	−	1.03391i
$193$	1.16324e8			1.16471			0.582355	−	0.812934i	$-0.302131\pi$
$193$	1.16324e8			1.16471			0.582355	+	0.812934i	$0.302131\pi$
$194$	−2.03069e6			−0.0199681
$195$	6.78835e7	−	2.10957e7i	0.655606	−	0.203738i
$196$		0			0
$197$			2.35040e7i			0.219033i	0.993985	+	0.109516i	$0.0349302\pi$
$197$			2.35040e7i			0.219033i	−0.993985	+	0.109516i	$0.965070\pi$
$198$	1.12357e8	−	7.72974e7i	1.02866	−	0.707680i
$199$			1.97440e8i			1.77602i	0.459822	+	0.888011i	$0.347913\pi$
$199$			1.97440e8i			1.77602i	−0.459822	+	0.888011i	$0.652087\pi$
$200$		−	2.72272e7i		−	0.240657i
$201$	−4.66985e7	−	1.50271e8i	−0.405618	−	1.30523i
$202$		−	3.79076e7i		−	0.323591i
$203$		0			0
$204$	1.80261e7	+	5.80061e7i	0.148661	+	0.478375i
$205$	−1.94062e7			−0.157326
$206$	−3.70859e7			−0.295579
$207$	−6.90139e7	−	1.00316e8i	−0.540804	−	0.786094i
$208$		−	5.83841e7i		−	0.449855i
$209$	−4.59281e7			−0.347990
$210$		0			0
$211$	−1.62963e8			−1.19427			−0.597134	−	0.802142i	$-0.703694\pi$
$211$	−1.62963e8			−1.19427			−0.597134	+	0.802142i	$0.703694\pi$
$212$			7.25079e6i			0.0522649i
$213$	−3.17631e7	+	9.87079e6i	−0.225214	+	0.0699880i
$214$	−1.15043e8			−0.802441
$215$	−2.91346e7			−0.199928
$216$	9.97206e7	−	1.26676e8i	0.673282	−	0.855278i
$217$		0			0
$218$			1.33731e8i			0.874245i
$219$	2.39816e8	−	7.45258e7i	1.54285	−	0.479460i
$220$		−	6.74243e7i		−	0.426911i
$221$			1.95664e8i			1.21937i
$222$	1.16923e8	−	3.63352e7i	0.717238	−	0.222891i
$223$		−	1.23475e8i		−	0.745609i	−0.927910	−	0.372804i	$-0.878396\pi$
$223$		−	1.23475e8i		−	0.745609i	0.927910	−	0.372804i	$-0.121604\pi$
$224$		0			0
$225$	3.11220e7	−	2.14108e7i	0.182150	−	0.125313i
$226$	−2.35023e8			−1.35435
$227$	−1.30063e8			−0.738013			−0.369007	−	0.929427i	$-0.620302\pi$
$227$	−1.30063e8			−0.738013			−0.369007	+	0.929427i	$0.620302\pi$
$228$	−1.25564e7	+	3.90205e6i	−0.0701604	+	0.0218032i
$229$		−	1.27874e8i		−	0.703652i	−0.936065	−	0.351826i	$-0.885561\pi$
$229$		−	1.27874e8i		−	0.703652i	0.936065	−	0.351826i	$-0.114439\pi$
$230$	1.28174e8			0.694629
$231$		0			0
$232$	2.63549e8			1.38565
$233$			5.90812e7i			0.305988i	0.988227	+	0.152994i	$0.0488914\pi$
$233$			5.90812e7i			0.305988i	−0.988227	+	0.152994i	$0.951109\pi$
$234$	1.03614e8	−	7.12831e7i	0.528646	−	0.363690i
$235$	−2.06151e6			−0.0103621
$236$	9.59671e6			0.0475259
$237$	3.54167e7	+	1.13967e8i	0.172818	+	0.556109i
$238$		0			0
$239$		−	2.73993e8i		−	1.29822i	−0.760696	−	0.649109i	$-0.775142\pi$
$239$		−	2.73993e8i		−	1.29822i	0.760696	−	0.649109i	$-0.224858\pi$
$240$	3.24374e7	+	1.04380e8i	0.151463	+	0.487392i
$241$		−	8.65220e7i		−	0.398169i	−0.979982	−	0.199084i	$-0.936203\pi$
$241$		−	8.65220e7i		−	0.398169i	0.979982	−	0.199084i	$-0.0637967\pi$
$242$		−	2.34809e8i		−	1.06503i
$243$	2.23215e8	+	1.43702e7i	0.997934	+	0.0642452i
$244$		−	9.70416e6i		−	0.0427655i
$245$		0			0
$246$	−3.27871e7	+	1.01890e7i	−0.140420	+	0.0436374i
$247$	−4.23546e7			−0.178838
$248$	3.61494e8			1.50495
$249$	2.84286e7	+	9.14801e7i	0.116696	+	0.375516i
$250$			2.19620e8i			0.888960i
$251$	−3.83930e8			−1.53248			−0.766238	−	0.642557i	$-0.777874\pi$
$251$	−3.83930e8			−1.53248			−0.766238	+	0.642557i	$0.777874\pi$
$252$		0			0
$253$	−3.72019e8			−1.44425
$254$			2.39886e8i			0.918517i
$255$	−1.08708e8	−	3.49810e8i	−0.410555	−	1.32112i
$256$	−2.28271e8			−0.850377
$257$	−5.17897e8			−1.90317			−0.951585	−	0.307384i	$-0.900546\pi$
$257$	−5.17897e8			−1.90317			−0.951585	+	0.307384i	$0.900546\pi$
$258$	−4.92235e7	+	1.52968e7i	−0.178445	+	0.0554539i
$259$		0			0
$260$		−	6.21782e7i		−	0.219397i
$261$	2.07249e8	+	3.01250e8i	0.721524	+	1.04878i
$262$		−	2.71694e8i		−	0.933310i
$263$		−	7.81847e7i		−	0.265019i	−0.991182	−	0.132509i	$-0.957697\pi$
$263$		−	7.81847e7i		−	0.265019i	0.991182	−	0.132509i	$-0.0423035\pi$
$264$	−1.46175e8	−	4.70374e8i	−0.488944	−	1.57337i
$265$		−	4.37264e7i		−	0.144339i
$266$		0			0
$267$	6.43620e7	+	2.07110e8i	0.206938	+	0.665904i
$268$	−1.37641e8			−0.436794
$269$	5.93248e7			0.185825			0.0929123	−	0.995674i	$-0.470382\pi$
$269$	5.93248e7			0.185825			0.0929123	+	0.995674i	$0.470382\pi$
$270$	−1.45640e8	+	1.85008e8i	−0.450305	+	0.572028i
$271$			3.13781e8i			0.957710i	0.877894	+	0.478855i	$0.158948\pi$
$271$			3.13781e8i			0.957710i	−0.877894	+	0.478855i	$0.841052\pi$
$272$	−3.00859e8			−0.906509
$273$		0			0
$274$	−5.05864e8			−1.48562
$275$		−	1.15415e8i		−	0.334656i
$276$	−1.01707e8	+	3.16068e7i	−0.291185	+	0.0904896i
$277$	−6.63856e8			−1.87670			−0.938349	−	0.345689i	$-0.887645\pi$
$277$	−6.63856e8			−1.87670			−0.938349	+	0.345689i	$0.887645\pi$
$278$	2.08543e8			0.582155
$279$	2.84271e8	+	4.13206e8i	0.783642	+	1.13907i
$280$		0			0
$281$		−	4.05619e8i		−	1.09055i	−0.838257	−	0.545275i	$-0.816425\pi$
$281$		−	4.05619e8i		−	1.09055i	0.838257	−	0.545275i	$-0.183575\pi$
$282$	−3.48297e6	+	1.08238e6i	−0.00924864	+	0.00287413i
$283$			2.97292e8i			0.779707i	0.920877	+	0.389853i	$0.127474\pi$
$283$			2.97292e8i			0.779707i	−0.920877	+	0.389853i	$0.872526\pi$
$284$			2.90936e7i			0.0753673i
$285$	7.57222e7	−	2.35316e7i	0.193761	−	0.0602136i
$286$		−	3.84252e8i		−	0.971258i
$287$		0			0
$288$	−1.40496e8	−	2.04219e8i	−0.346569	−	0.503760i
$289$	5.97935e8			1.45717
$290$	−3.84908e8			−0.926752
$291$	−9.71745e6	+	3.01982e6i	−0.0231167	+	0.00718382i
$292$		−	2.19660e8i		−	0.516311i
$293$	6.28561e8			1.45986			0.729929	−	0.683522i	$-0.239553\pi$
$293$	6.28561e8			1.45986			0.729929	+	0.683522i	$0.239553\pi$
$294$		0			0
$295$	−5.78737e7			−0.131251
$296$		−	4.42218e8i		−	0.991095i
$297$	4.22712e8	−	5.36977e8i	0.936262	−	1.18934i
$298$	−1.68882e8			−0.369681
$299$	−3.43074e8			−0.742229
$300$	−9.80567e6	−	3.15536e7i	−0.0209678	−	0.0674720i
$301$		0			0
$302$		−	7.69063e7i		−	0.160671i
$303$	−5.63722e7	−	1.81400e8i	−0.116417	−	0.374617i
$304$		−	6.51258e7i		−	0.132952i
$305$			5.85217e7i			0.118105i
$306$	−3.67329e8	−	5.33936e8i	−0.732875	−	1.06528i
$307$			1.40498e7i			0.0277132i	0.999904	+	0.0138566i	$0.00441083\pi$
$307$			1.40498e7i			0.0277132i	−0.999904	+	0.0138566i	$0.995589\pi$
$308$		0			0
$309$	−1.77468e8	+	5.51503e7i	−0.342188	+	0.106339i
$310$	−5.27954e8			−1.00654
$311$	3.58535e8			0.675881			0.337941	−	0.941167i	$-0.390270\pi$
$311$	3.58535e8			0.675881			0.337941	+	0.941167i	$0.390270\pi$
$312$	−1.34801e8	−	4.33776e8i	−0.251277	−	0.808582i
$313$			8.60525e8i			1.58620i	0.609090	+	0.793101i	$0.291535\pi$
$313$			8.60525e8i			1.58620i	−0.609090	+	0.793101i	$0.708465\pi$
$314$	−4.98688e8			−0.909024
$315$		0			0
$316$	1.04389e8			0.186101
$317$			3.08439e8i			0.543828i	0.962322	+	0.271914i	$0.0876566\pi$
$317$			3.08439e8i			0.543828i	−0.962322	+	0.271914i	$0.912343\pi$
$318$	−2.29581e7	−	7.38767e7i	−0.0400352	−	0.128829i
$319$	1.11718e9			1.92688
$320$	5.60105e8			0.955530
$321$	−5.50517e8	+	1.71080e8i	−0.928973	+	0.288690i
$322$		0			0
$323$			2.18257e8i			0.360379i
$324$	6.99446e7	−	1.82719e8i	0.114248	−	0.298453i
$325$		−	1.06435e8i		−	0.171986i
$326$		−	2.81038e8i		−	0.449265i
$327$	1.98870e8	+	6.39941e8i	0.314523	+	1.01210i
$328$			1.24005e8i			0.194036i
$329$		0			0
$330$	2.13485e8	+	6.86971e8i	0.327016	+	1.05230i
$331$	−1.50536e8			−0.228162			−0.114081	−	0.993471i	$-0.536392\pi$
$331$	−1.50536e8			−0.228162			−0.114081	+	0.993471i	$0.536392\pi$
$332$	8.37915e7			0.125666
$333$	5.05477e8	−	3.47750e8i	0.750147	−	0.516074i
$334$		−	6.25425e8i		−	0.918465i
$335$	8.30055e8			1.20629
$336$		0			0
$337$	4.66726e8			0.664289			0.332145	−	0.943228i	$-0.392228\pi$
$337$	4.66726e8			0.664289			0.332145	+	0.943228i	$0.392228\pi$
$338$			2.31244e8i			0.325733i
$339$	−1.12466e9	+	3.49501e8i	−1.56791	+	0.487248i
$340$	−3.20410e8			−0.442110
$341$	1.53236e9			2.09277
$342$	1.15579e8	−	7.95143e7i	0.156238	−	0.107486i
$343$		0			0
$344$			1.86170e8i			0.246579i
$345$	6.13352e8	−	1.90607e8i	0.804161	−	0.249903i
$346$			6.80272e8i			0.882909i
$347$			6.69141e8i			0.859734i	0.902892	+	0.429867i	$0.141440\pi$
$347$			6.69141e8i			0.859734i	−0.902892	+	0.429867i	$0.858560\pi$
$348$	3.05427e8	−	9.49153e7i	0.388490	−	0.120728i
$349$		−	4.41794e8i		−	0.556327i	−0.960534	−	0.278164i	$-0.910274\pi$
$349$		−	4.41794e8i		−	0.556327i	0.960534	−	0.278164i	$-0.0897258\pi$
$350$		0			0
$351$	3.89822e8	−	4.95196e8i	0.481162	−	0.611226i
$352$	−7.57342e8			−0.925535
$353$	8.82746e8			1.06813			0.534065	−	0.845443i	$-0.320664\pi$
$353$	8.82746e8			1.06813			0.534065	+	0.845443i	$0.320664\pi$
$354$	−9.77788e7	+	3.03860e7i	−0.117148	+	0.0364051i
$355$		−	1.75451e8i		−	0.208140i
$356$	1.89703e8			0.222843
$357$		0			0
$358$	9.79538e8			1.12832
$359$		−	9.49168e8i		−	1.08271i	−0.840794	−	0.541356i	$-0.817911\pi$
$359$		−	9.49168e8i		−	1.08271i	0.840794	−	0.541356i	$-0.182089\pi$
$360$	4.82000e8	+	7.00618e8i	0.544488	+	0.791448i
$361$	8.46626e8			0.947145
$362$	−6.87456e8			−0.761666
$363$	−3.49182e8	−	1.12363e9i	−0.383159	−	1.23296i
$364$		0			0
$365$			1.32468e9i			1.42589i
$366$	3.07262e7	+	9.88735e7i	0.0327586	+	0.105414i
$367$			7.92567e8i			0.836961i	0.908226	+	0.418480i	$0.137437\pi$
$367$			7.92567e8i			0.836961i	−0.908226	+	0.418480i	$0.862563\pi$
$368$		−	5.27522e8i		−	0.551789i
$369$	−1.41744e8	+	9.75150e7i	−0.146863	+	0.101037i
$370$			6.45849e8i			0.662865i
$371$		0			0
$372$	4.18936e8	−	1.30190e8i	0.421936	−	0.131122i
$373$	8.24623e8			0.822762			0.411381	−	0.911463i	$-0.365046\pi$
$373$	8.24623e8			0.822762			0.411381	+	0.911463i	$0.365046\pi$
$374$	−1.98009e9			−1.95719
$375$	3.26596e8	+	1.05095e9i	0.319817	+	1.02914i
$376$			1.31731e7i			0.0127800i
$377$	1.03025e9			0.990258
$378$		0			0
$379$	−4.65185e8			−0.438923			−0.219461	−	0.975621i	$-0.570430\pi$
$379$	−4.65185e8			−0.438923			−0.219461	+	0.975621i	$0.570430\pi$
$380$		−	6.93580e7i		−	0.0648417i
$381$	3.56733e8	+	1.14793e9i	0.330450	+	1.06335i
$382$	5.47366e7			0.0502408
$383$	−1.00110e9			−0.910507			−0.455254	−	0.890362i	$-0.650451\pi$
$383$	−1.00110e9			−0.910507			−0.455254	+	0.890362i	$0.650451\pi$
$384$	2.98407e8	−	9.27338e7i	0.268937	−	0.0835754i
$385$		0			0
$386$			1.08559e9i			0.960747i
$387$	−2.12801e8	+	1.46400e8i	−0.186632	+	0.128396i
$388$			8.90074e6i			0.00773597i
$389$			9.10786e8i			0.784500i	0.919859	+	0.392250i	$0.128303\pi$
$389$			9.10786e8i			0.784500i	−0.919859	+	0.392250i	$0.871697\pi$
$390$	1.96874e8	+	6.33520e8i	0.168059	+	0.540797i
$391$			1.76789e9i			1.49567i
$392$		0			0
$393$	−4.04035e8	−	1.30014e9i	−0.335772	−	1.08048i
$394$	−2.19350e8			−0.180676
$395$	−6.29523e8			−0.513951
$396$	−3.38804e8	−	4.92473e8i	−0.274167	−	0.398519i
$397$			3.03278e8i			0.243262i	0.992575	+	0.121631i	$0.0388124\pi$
$397$			3.03278e8i			0.243262i	−0.992575	+	0.121631i	$0.961188\pi$
$398$	−1.84260e9			−1.46501
$399$		0			0
$400$	1.63658e8			0.127858
$401$			1.36917e9i			1.06036i	0.847886	+	0.530179i	$0.177875\pi$
$401$			1.36917e9i			1.06036i	−0.847886	+	0.530179i	$0.822125\pi$
$402$	1.40240e9	−	4.35812e8i	1.07666	−	0.334586i
$403$	1.41313e9			1.07551
$404$	−1.66154e8			−0.125365
$405$	−4.21806e8	+	1.10190e9i	−0.315515	+	0.824232i
$406$		0			0
$407$		−	1.87455e9i		−	1.37821i
$408$	−2.23529e9	+	6.94645e8i	−1.62938	+	0.506352i
$409$		−	4.74820e8i		−	0.343161i	−0.985170	−	0.171580i	$-0.945113\pi$
$409$		−	4.74820e8i		−	0.343161i	0.985170	−	0.171580i	$-0.0548874\pi$
$410$		−	1.81107e8i		−	0.129775i
$411$	−2.42071e9	+	7.52267e8i	−1.71988	+	0.534473i
$412$			1.62552e8i			0.114512i
$413$		0			0
$414$	9.36195e8	−	6.44069e8i	0.648433	−	0.446099i
$415$	−5.05311e8			−0.347049
$416$	−6.98415e8			−0.475650
$417$	9.97941e8	−	3.10123e8i	0.673952	−	0.209439i
$418$		−	4.28622e8i		−	0.287050i
$419$	−1.13110e9			−0.751197			−0.375598	−	0.926783i	$-0.622563\pi$
$419$	−1.13110e9			−0.751197			−0.375598	+	0.926783i	$0.622563\pi$
$420$		0			0
$421$	1.77782e9			1.16118			0.580592	−	0.814195i	$-0.302821\pi$
$421$	1.77782e9			1.16118			0.580592	+	0.814195i	$0.302821\pi$
$422$		−	1.52085e9i		−	0.985128i
$423$	−1.50575e7	+	1.03590e7i	−0.00967299	+	0.00665467i
$424$	−2.79412e8			−0.178018
$425$	−5.48470e8			−0.346570
$426$	−9.21187e7	−	2.96428e8i	−0.0577317	−	0.185774i
$427$		0			0
$428$			5.04248e8i			0.310879i
$429$	−5.71418e8	−	1.83876e9i	−0.349425	−	1.12441i
$430$		−	2.71897e8i		−	0.164917i
$431$		−	1.90415e8i		−	0.114559i	−0.998358	−	0.0572797i	$-0.981757\pi$
$431$		−	1.90415e8i		−	0.114559i	0.998358	−	0.0572797i	$-0.0182427\pi$
$432$	7.61430e8	+	5.99404e8i	0.454399	+	0.357706i
$433$		−	1.11786e9i		−	0.661729i	−0.943678	−	0.330864i	$-0.892660\pi$
$433$		−	1.11786e9i		−	0.661729i	0.943678	−	0.330864i	$-0.107340\pi$
$434$		0			0
$435$	−1.84190e9	+	5.72394e8i	−1.07289	+	0.333413i
$436$	5.86157e8			0.338697
$437$	−3.82689e8			−0.219362
$438$	6.95509e8	+	2.23807e9i	0.395497	+	1.27267i
$439$		−	6.18150e8i		−	0.348713i	−0.984683	−	0.174357i	$-0.944215\pi$
$439$		−	6.18150e8i		−	0.348713i	0.984683	−	0.174357i	$-0.0557845\pi$
$440$	2.59822e9			1.45409
$441$		0			0
$442$	−1.82602e9			−1.00584
$443$			2.61419e9i			1.42864i	0.699818	+	0.714322i	$0.253265\pi$
$443$			2.61419e9i			1.42864i	−0.699818	+	0.714322i	$0.746735\pi$
$444$	−1.59262e8	−	5.12486e8i	−0.0863516	−	0.277870i
$445$	−1.14402e9			−0.615422
$446$	1.15232e9			0.615038
$447$	−8.08152e8	+	2.51144e8i	−0.427973	+	0.132998i
$448$		0			0
$449$			8.76314e8i			0.456875i	0.973559	+	0.228438i	$0.0733617\pi$
$449$			8.76314e8i			0.456875i	−0.973559	+	0.228438i	$0.926638\pi$
$450$	1.99816e8	+	2.90445e8i	0.103368	+	0.150252i
$451$			5.25655e8i			0.269825i
$452$			1.03013e9i			0.524698i
$453$	−1.14367e8	−	3.68020e8i	−0.0578038	−	0.186006i
$454$		−	1.21381e9i		−	0.608773i
$455$		0			0
$456$	−1.50367e8	−	4.83865e8i	−0.0742636	−	0.238972i
$457$	2.30159e9			1.12803			0.564017	−	0.825763i	$-0.309255\pi$
$457$	2.30159e9			1.12803			0.564017	+	0.825763i	$0.309255\pi$
$458$	1.19338e9			0.580429
$459$	−2.55179e9	−	2.00879e9i	−1.23169	−	0.969596i
$460$		−	5.61803e8i		−	0.269111i
$461$	−1.26292e9			−0.600376			−0.300188	−	0.953880i	$-0.597049\pi$
$461$	−1.26292e9			−0.600376			−0.300188	+	0.953880i	$0.597049\pi$
$462$		0			0
$463$	1.16895e9			0.547346			0.273673	−	0.961823i	$-0.411761\pi$
$463$	1.16895e9			0.547346			0.273673	+	0.961823i	$0.411761\pi$
$464$			1.58415e9i			0.736179i
$465$	−2.52642e9	+	7.85118e8i	−1.16525	+	0.362118i
$466$	−5.51373e8			−0.252403
$467$	9.96991e8			0.452983			0.226492	−	0.974013i	$-0.427274\pi$
$467$	9.96991e8			0.452983			0.226492	+	0.974013i	$0.427274\pi$
$468$	−3.12442e8	−	4.54155e8i	−0.140899	−	0.204806i
$469$		0			0
$470$		−	1.92390e7i		−	0.00854751i
$471$	−2.38637e9	+	7.41596e8i	−1.05236	+	0.327035i
$472$			3.69813e8i			0.161877i
$473$			7.89169e8i			0.342891i
$474$	−1.06359e9	+	3.30525e8i	−0.458723	+	0.142554i
$475$		−	1.18725e8i		−	0.0508294i
$476$		0			0
$477$	−2.19723e8	−	3.19382e8i	−0.0926961	−	0.134740i
$478$	2.55703e9			1.07087
$479$	3.72553e9			1.54886			0.774432	−	0.632657i	$-0.218036\pi$
$479$	3.72553e9			1.54886			0.774432	+	0.632657i	$0.218036\pi$
$480$	1.24864e9	−	3.88030e8i	0.515338	−	0.160148i
$481$		−	1.72869e9i		−	0.708288i
$482$	8.07463e8			0.328441
$483$		0			0
$484$	−1.02919e9			−0.412609
$485$		−	5.36766e7i		−	0.0213643i
$486$	−1.34109e8	+	2.08315e9i	−0.0529946	+	0.823176i
$487$	−1.35403e9			−0.531224			−0.265612	−	0.964080i	$-0.585574\pi$
$487$	−1.35403e9			−0.531224			−0.265612	+	0.964080i	$0.585574\pi$
$488$	3.73954e8			0.145663
$489$	−4.17930e8	−	1.34485e9i	−0.161630	−	0.520108i
$490$		0			0
$491$			1.16862e9i			0.445540i	0.974871	+	0.222770i	$0.0715099\pi$
$491$			1.16862e9i			0.445540i	−0.974871	+	0.222770i	$0.928490\pi$
$492$	4.46596e7	+	1.43710e8i	0.0169059	+	0.0544012i
$493$		−	5.30899e9i		−	1.99548i
$494$		−	3.95272e8i		−	0.147520i
$495$	2.04318e9	+	2.96989e9i	0.757162	+	1.10058i
$496$			2.17288e9i			0.799559i
$497$		0			0
$498$	−8.53734e8	+	2.65309e8i	−0.309756	+	0.0962606i
$499$	1.28940e9			0.464554			0.232277	−	0.972650i	$-0.425382\pi$
$499$	1.28940e9			0.464554			0.232277	+	0.972650i	$0.425382\pi$
$500$	9.62622e8			0.344398
$501$	−9.30066e8	−	2.99285e9i	−0.330432	−	1.06329i
$502$		−	3.58301e9i		−	1.26411i
$503$	3.67733e9			1.28838			0.644191	−	0.764864i	$-0.277194\pi$
$503$	3.67733e9			1.28838			0.644191	+	0.764864i	$0.277194\pi$
$504$		0			0
$505$	1.00200e9			0.346218
$506$		−	3.47185e9i		−	1.19134i
$507$	3.43881e8	+	1.10657e9i	0.117187	+	0.377096i
$508$	1.05145e9			0.355849
$509$	−1.73776e8			−0.0584088			−0.0292044	−	0.999573i	$-0.509297\pi$
$509$	−1.73776e8			−0.0584088			−0.0292044	+	0.999573i	$0.509297\pi$
$510$	3.26459e9	−	1.01451e9i	1.08977	−	0.338658i
$511$		0			0
$512$		−	2.98562e9i		−	0.983083i
$513$	4.34836e8	−	5.52377e8i	0.142205	−	0.180645i
$514$		−	4.83325e9i		−	1.56989i
$515$		−	9.80283e8i		−	0.316247i
$516$	6.70478e7	+	2.15752e8i	0.0214838	+	0.0691324i
$517$			5.58402e7i			0.0177718i
$518$		0			0
$519$	1.01163e9	+	3.25531e9i	0.317640	+	1.02213i
$520$	2.39606e9			0.747285
$521$	−2.71271e9			−0.840370			−0.420185	−	0.907438i	$-0.638035\pi$
$521$	−2.71271e9			−0.840370			−0.420185	+	0.907438i	$0.638035\pi$
$522$	−2.81140e9	+	1.93414e9i	−0.865119	+	0.595171i
$523$		−	1.76487e9i		−	0.539456i	−0.962937	−	0.269728i	$-0.913066\pi$
$523$		−	1.76487e9i		−	0.539456i	0.962937	−	0.269728i	$-0.0869337\pi$
$524$	−1.19087e9			−0.361580
$525$		0			0
$526$	7.29655e8			0.218609
$527$		−	7.28202e9i		−	2.16728i
$528$	2.82734e9	−	8.78633e8i	0.835910	−	0.259770i
$529$	3.05030e8			0.0895874
$530$	4.08075e8			0.119062
$531$	−4.22714e8	+	2.90813e8i	−0.122523	+	0.0842912i
$532$		0			0
$533$			4.84755e8i			0.138668i
$534$	−1.93284e9	+	6.00656e8i	−0.549291	+	0.170699i
$535$		−	3.04091e9i		−	0.858549i
$536$		−	5.30406e9i		−	1.48775i
$537$	4.68739e9	−	1.45667e9i	1.30623	−	0.405929i
$538$			5.53646e8i			0.153283i
$539$		0			0
$540$	8.10912e8	+	6.38356e8i	0.221613	+	0.174456i
$541$	−1.46669e9			−0.398244			−0.199122	−	0.979975i	$-0.563809\pi$
$541$	−1.46669e9			−0.398244			−0.199122	+	0.979975i	$0.563809\pi$
$542$	−2.92835e9			−0.789996
$543$	−3.28968e9	+	1.02231e9i	−0.881769	+	0.274021i
$544$			3.59900e9i			0.958487i
$545$	−3.53486e9			−0.935373
$546$		0			0
$547$	−6.14008e9			−1.60405			−0.802026	−	0.597290i	$-0.796244\pi$
$547$	−6.14008e9			−1.60405			−0.802026	+	0.597290i	$0.796244\pi$
$548$			2.21726e9i			0.575553i
$549$	2.94069e8	+	4.27447e8i	0.0758482	+	0.110250i
$550$	1.07711e9			0.276051
$551$	1.14922e9			0.292665
$552$	−1.21798e9	−	3.91932e9i	−0.308215	−	0.991801i
$553$		0			0
$554$		−	6.19540e9i		−	1.54805i
$555$	9.60439e8	+	3.09059e9i	0.238476	+	0.767389i
$556$		−	9.14068e8i		−	0.225537i
$557$		−	3.53089e9i		−	0.865747i	−0.901455	−	0.432874i	$-0.857500\pi$
$557$		−	3.53089e9i		−	0.865747i	0.901455	−	0.432874i	$-0.142500\pi$
$558$	−3.85622e9	+	2.65295e9i	−0.939599	+	0.646411i
$559$			7.27765e8i			0.176218i
$560$		0			0
$561$	−9.47532e9	+	2.94457e9i	−2.26581	+	0.704130i
$562$	3.78542e9			0.899574
$563$	−7.95921e8			−0.187971			−0.0939855	−	0.995574i	$-0.529961\pi$
$563$	−7.95921e8			−0.187971			−0.0939855	+	0.995574i	$0.529961\pi$
$564$	4.74419e6	+	1.52663e7i	0.00111349	+	0.00358308i
$565$		−	6.21230e9i		−	1.44905i
$566$	−2.77447e9			−0.643165
$567$		0			0
$568$	−1.12113e9			−0.256707
$569$			6.43234e9i			1.46378i	0.681422	+	0.731891i	$0.261362\pi$
$569$			6.43234e9i			1.46378i	−0.681422	+	0.731891i	$0.738638\pi$
$570$	2.19608e8	+	7.06674e8i	0.0496690	+	0.159829i
$571$	−6.12867e9			−1.37765			−0.688827	−	0.724926i	$-0.741874\pi$
$571$	−6.12867e9			−1.37765			−0.688827	+	0.724926i	$0.741874\pi$
$572$	−1.68422e9			−0.376282
$573$	2.61932e8	−	8.13986e7i	0.0581630	−	0.0180749i
$574$		0			0
$575$		−	9.61679e8i		−	0.210956i
$576$	4.09105e9	−	2.81450e9i	0.891982	−	0.613652i
$577$			1.88633e9i			0.408792i	0.978888	+	0.204396i	$0.0655230\pi$
$577$			1.88633e9i			0.408792i	−0.978888	+	0.204396i	$0.934477\pi$
$578$			5.58020e9i			1.20199i
$579$	1.61437e9	+	5.19486e9i	0.345643	+	1.11224i
$580$			1.68710e9i			0.359039i
$581$		0			0
$582$	−2.81823e7	−	9.06876e7i	−0.00592579	−	0.0190685i
$583$	−1.18442e9			−0.247551
$584$	8.46470e9			1.75860
$585$	1.88421e9	+	2.73881e9i	0.389120	+	0.565610i
$586$			5.86602e9i			1.20421i
$587$	1.57758e9			0.321927			0.160964	−	0.986960i	$-0.448540\pi$
$587$	1.57758e9			0.321927			0.160964	+	0.986960i	$0.448540\pi$
$588$		0			0
$589$	1.57631e9			0.317862
$590$		−	5.40104e8i		−	0.108267i
$591$	−1.04966e9	+	3.26194e8i	−0.209166	+	0.0650009i
$592$	2.65810e9			0.526557
$593$	−6.62562e9			−1.30477			−0.652387	−	0.757886i	$-0.726232\pi$
$593$	−6.62562e9			−1.30477			−0.652387	+	0.757886i	$0.726232\pi$
$594$	5.01131e9	+	3.94494e9i	0.981067	+	0.772304i
$595$		0			0
$596$			7.40230e8i			0.143220i
$597$	−8.81738e9	+	2.74011e9i	−1.69601	+	0.527058i
$598$		−	3.20172e9i		−	0.612250i
$599$		−	3.13094e8i		−	0.0595225i	−0.999557	−	0.0297612i	$-0.990525\pi$
$599$		−	3.13094e8i		−	0.0595225i	0.999557	−	0.0297612i	$-0.00947469\pi$
$600$	1.21593e9	−	3.77865e8i	0.229815	−	0.0714180i
$601$			3.12363e7i			0.00586947i	0.999996	+	0.00293474i	$0.000934157\pi$
$601$			3.12363e7i			0.00586947i	−0.999996	+	0.00293474i	$0.999066\pi$
$602$		0			0
$603$	6.06279e9	−	4.17099e9i	1.12606	−	0.774691i
$604$	−3.37089e8			−0.0622466
$605$	6.20663e9			1.13949
$606$	1.69290e9	−	5.26091e8i	0.309014	−	0.0960300i
$607$		−	5.77536e9i		−	1.04814i	−0.851676	−	0.524069i	$-0.824413\pi$
$607$		−	5.77536e9i		−	1.04814i	0.851676	−	0.524069i	$-0.175587\pi$
$608$	−7.79063e8			−0.140576
$609$		0			0
$610$	−5.46151e8			−0.0974222
$611$			5.14954e7i			0.00913323i
$612$	−2.34030e9	+	1.61005e9i	−0.412707	+	0.283928i
$613$	1.08666e9			0.190538			0.0952691	−	0.995452i	$-0.469629\pi$
$613$	1.08666e9			0.190538			0.0952691	+	0.995452i	$0.469629\pi$
$614$	−1.31119e8			−0.0228601
$615$	−2.69323e8	−	8.66653e8i	−0.0466886	−	0.150239i
$616$		0			0
$617$		−	4.36859e9i		−	0.748761i	−0.927275	−	0.374381i	$-0.877855\pi$
$617$		−	4.36859e9i		−	0.748761i	0.927275	−	0.374381i	$-0.122145\pi$
$618$	−5.14688e8	−	1.65621e9i	−0.0877171	−	0.282264i
$619$			8.97007e9i			1.52012i	0.649851	+	0.760061i	$0.274831\pi$
$619$			8.97007e9i			1.52012i	−0.649851	+	0.760061i	$0.725169\pi$
$620$			2.31409e9i			0.389950i
$621$	3.52219e9	−	4.47428e9i	0.590190	−	0.749725i
$622$			3.34601e9i			0.557521i
$623$		0			0
$624$	2.60735e9	−	8.10269e8i	0.429590	−	0.133501i
$625$	−4.45573e9			−0.730026
$626$	−8.03081e9			−1.30843
$627$	−6.37401e8	−	2.05109e9i	−0.103271	−	0.332313i
$628$			2.18581e9i			0.352171i
$629$	−8.90813e9			−1.42728
$630$		0			0
$631$	1.18971e10			1.88512			0.942558	−	0.334043i	$-0.108413\pi$
$631$	1.18971e10			1.88512			0.942558	+	0.334043i	$0.108413\pi$
$632$			4.02265e9i			0.633874i
$633$	−2.26165e9	−	7.27773e9i	−0.354415	−	1.14047i
$634$	−2.87849e9			−0.448593
$635$	−6.34085e9			−0.982741
$636$	−3.23810e8	+	1.00628e8i	−0.0499104	+	0.0155103i
$637$		0			0
$638$			1.04260e10i			1.58944i
$639$	−8.81633e8	−	1.28151e9i	−0.133670	−	0.194298i
$640$			1.64832e9i			0.248549i
$641$			6.70756e9i			1.00592i	0.864311	+	0.502958i	$0.167755\pi$
$641$			6.70756e9i			1.00592i	−0.864311	+	0.502958i	$0.832245\pi$
$642$	−1.59660e9	−	5.13768e9i	−0.238135	−	0.766292i
$643$		−	9.24553e9i		−	1.37149i	−0.727840	−	0.685747i	$-0.759476\pi$
$643$		−	9.24553e9i		−	1.37149i	0.727840	−	0.685747i	$-0.240524\pi$
$644$		0			0
$645$	−4.04337e8	−	1.30111e9i	−0.0593313	−	0.190922i
$646$	−2.03688e9			−0.297270
$647$	−5.77075e9			−0.837659			−0.418830	−	0.908065i	$-0.637560\pi$
$647$	−5.77075e9			−0.837659			−0.418830	+	0.908065i	$0.637560\pi$
$648$	7.04114e9	+	2.69534e9i	1.01655	+	0.389136i
$649$			1.56763e9i			0.225105i
$650$	9.93299e8			0.141868
$651$		0			0
$652$	−1.23182e9			−0.174053
$653$		−	3.77885e9i		−	0.531084i	−0.964099	−	0.265542i	$-0.914449\pi$
$653$		−	3.77885e9i		−	0.531084i	0.964099	−	0.265542i	$-0.0855510\pi$
$654$	−5.97223e9	+	1.85594e9i	−0.834861	+	0.259444i
$655$	7.18162e9			0.998569
$656$	−7.45376e8			−0.103089
$657$	6.65644e9	+	9.67556e9i	0.915722	+	1.33106i
$658$		0			0
$659$			1.25248e10i			1.70479i	0.522897	+	0.852396i	$0.324851\pi$
$659$			1.25248e10i			1.70479i	−0.522897	+	0.852396i	$0.675149\pi$
$660$	3.01108e9	−	9.35730e8i	0.407679	−	0.126691i
$661$			5.05342e9i			0.680582i	0.940320	+	0.340291i	$0.110526\pi$
$661$			5.05342e9i			0.680582i	−0.940320	+	0.340291i	$0.889474\pi$
$662$		−	1.40487e9i		−	0.188206i
$663$	−8.73807e9	+	2.71547e9i	−1.16444	+	0.361865i
$664$			3.22894e9i			0.428028i
$665$		0			0
$666$	3.24536e9	+	4.71734e9i	0.425700	+	0.618781i
$667$	9.30870e9			1.21464
$668$	−2.74131e9			−0.355829
$669$	5.51421e9	−	1.71361e9i	0.712020	−	0.221269i
$670$			7.74645e9i			0.995041i
$671$	1.58518e9			0.202558
$672$		0			0
$673$	4.68666e9			0.592667			0.296333	−	0.955085i	$-0.404236\pi$
$673$	4.68666e9			0.592667			0.296333	+	0.955085i	$0.404236\pi$
$674$			4.35570e9i			0.547959i
$675$	1.38810e9	+	1.09272e9i	0.173723	+	0.136756i
$676$	1.01357e9			0.126194
$677$	9.99726e9			1.23829			0.619143	−	0.785279i	$-0.287480\pi$
$677$	9.99726e9			1.23829			0.619143	+	0.785279i	$0.287480\pi$
$678$	−3.26171e9	−	1.04958e10i	−0.401921	−	1.29334i
$679$		0			0
$680$		−	1.23471e10i		−	1.50586i
$681$	−1.80505e9	−	5.80845e9i	−0.219015	−	0.704766i
$682$			1.43007e10i			1.72628i
$683$			2.74470e9i			0.329626i	0.986325	+	0.164813i	$0.0527021\pi$
$683$			2.74470e9i			0.329626i	−0.986325	+	0.164813i	$0.947298\pi$
$684$	−3.48521e8	−	5.06597e8i	−0.0416421	−	0.0605294i
$685$		−	1.33714e10i		−	1.58949i
$686$		0			0
$687$	5.71068e9	−	1.77467e9i	0.671954	−	0.208818i
$688$	−1.11904e9			−0.131004
$689$	−1.09226e9			−0.127221
$690$	1.77883e9	+	5.72408e9i	0.206140	+	0.663337i
$691$		−	7.67170e9i		−	0.884542i	−0.896881	−	0.442271i	$-0.854173\pi$
$691$		−	7.67170e9i		−	0.884542i	0.896881	−	0.442271i	$-0.145827\pi$
$692$	2.98171e9			0.342054
$693$		0			0
$694$	−6.24473e9			−0.709178
$695$			5.51236e9i			0.622860i
$696$	3.65760e9	+	1.17697e10i	0.411210	+	1.32323i
$697$	2.49799e9			0.279432
$698$	4.12302e9			0.458903
$699$	−2.63849e9	+	8.19943e8i	−0.292203	+	0.0908058i
$700$		0			0
$701$		−	1.08816e10i		−	1.19311i	−0.802571	−	0.596556i	$-0.796535\pi$
$701$		−	1.08816e10i		−	1.19311i	0.802571	−	0.596556i	$-0.203465\pi$
$702$	4.62139e9	+	3.63800e9i	0.504189	+	0.396901i
$703$		−	1.92831e9i		−	0.209331i
$704$		−	1.51716e10i		−	1.63880i
$705$	−2.86102e7	−	9.20644e7i	−0.00307510	−	0.00989532i
$706$			8.23819e9i			0.881080i
$707$		0			0
$708$	1.33185e8	+	4.28576e8i	0.0141039	+	0.0453849i
$709$	−1.28719e10			−1.35638			−0.678189	−	0.734887i	$-0.737235\pi$
$709$	−1.28719e10			−1.35638			−0.678189	+	0.734887i	$0.737235\pi$
$710$	1.63739e9			0.171691
$711$	−4.59809e9	+	3.16332e9i	−0.479771	+	0.330065i
$712$			7.31029e9i			0.759022i
$713$	1.27682e10			1.31922
$714$		0			0
$715$	1.01568e10			1.03917
$716$		−	4.29343e9i		−	0.437129i
$717$	1.22362e10	−	3.80255e9i	1.23973	−	0.385263i
$718$	8.85807e9			0.893107
$719$	7.91923e9			0.794569			0.397285	−	0.917695i	$-0.369953\pi$
$719$	7.91923e9			0.794569			0.397285	+	0.917695i	$0.369953\pi$
$720$	−4.21130e9	+	2.89722e9i	−0.420487	+	0.289280i
$721$		0			0
$722$			7.90110e9i			0.781282i
$723$	3.86396e9	−	1.20077e9i	0.380231	−	0.118162i
$724$			3.01320e9i			0.295082i
$725$			2.88793e9i			0.281451i
$726$	1.04862e10	−	3.25873e9i	1.01705	−	0.316060i
$727$			1.17473e10i			1.13389i	0.823757	+	0.566943i	$0.191874\pi$
$727$			1.17473e10i			1.13389i	−0.823757	+	0.566943i	$0.808126\pi$
$728$		0			0
$729$	2.45608e9	+	1.01679e10i	0.234799	+	0.972044i
$730$	−1.23625e10			−1.17619
$731$	3.75025e9			0.355099
$732$	4.33375e8	−	1.34677e8i	0.0408390	−	0.0126912i
$733$			6.37551e9i			0.597931i	0.954264	+	0.298965i	$0.0966415\pi$
$733$			6.37551e9i			0.597931i	−0.954264	+	0.298965i	$0.903359\pi$
$734$	−7.39660e9			−0.690392
$735$		0			0
$736$	−6.31044e9			−0.583428
$737$		−	2.24837e10i		−	2.06886i
$738$	−9.10055e8	−	1.32282e9i	−0.0833432	−	0.121145i
$739$	−6.02664e8			−0.0549312			−0.0274656	−	0.999623i	$-0.508744\pi$
$739$	−6.02664e8			−0.0549312			−0.0274656	+	0.999623i	$0.508744\pi$
$740$	2.83083e9			0.256805
$741$	−5.87807e8	−	1.89150e9i	−0.0530727	−	0.170782i
$742$		0			0
$743$			1.48198e10i			1.32550i	0.748839	+	0.662752i	$0.230612\pi$
$743$			1.48198e10i			1.32550i	−0.748839	+	0.662752i	$0.769388\pi$
$744$	5.01691e9	+	1.61439e10i	0.446612	+	1.43715i
$745$		−	4.46401e9i		−	0.395529i
$746$			7.69576e9i			0.678681i
$747$	−3.69084e9	+	2.53916e9i	−0.323968	+	0.222879i
$748$			8.67895e9i			0.758249i
$749$		0			0
$750$	−9.80794e9	+	3.04794e9i	−0.848914	+	0.263811i
$751$	−1.77496e10			−1.52915			−0.764573	−	0.644537i	$-0.777050\pi$
$751$	−1.77496e10			−1.52915			−0.764573	+	0.644537i	$0.777050\pi$
$752$	−7.91812e7			−0.00678984
$753$	−5.32827e9	−	1.71458e10i	−0.454783	−	1.46344i
$754$			9.61478e9i			0.816845i
$755$	2.03284e9			0.171905
$756$		0			0
$757$	−8.54076e9			−0.715585			−0.357792	−	0.933801i	$-0.616470\pi$
$757$	−8.54076e9			−0.715585			−0.357792	+	0.933801i	$0.616470\pi$
$758$		−	4.34132e9i		−	0.362059i
$759$	−5.16297e9	−	1.66139e10i	−0.428602	−	1.37919i
$760$	2.67274e9			0.220856
$761$	−1.20899e10			−0.994435			−0.497217	−	0.867626i	$-0.665645\pi$
$761$	−1.20899e10			−0.994435			−0.497217	+	0.867626i	$0.665645\pi$
$762$	−1.07130e10	+	3.32920e9i	−0.877139	+	0.272582i
$763$		0			0
$764$		−	2.39917e8i		−	0.0194641i
$765$	1.41134e10	−	9.70951e9i	1.13977	−	0.784119i
$766$		−	9.34276e9i		−	0.751060i
$767$			1.44565e9i			0.115686i
$768$	−3.16800e9	−	1.01943e10i	−0.252361	−	0.812068i
$769$		−	1.19507e10i		−	0.947656i	−0.880617	−	0.473828i	$-0.842872\pi$
$769$		−	1.19507e10i		−	0.947656i	0.880617	−	0.473828i	$-0.157128\pi$
$770$		0			0
$771$	−7.18751e9	−	2.31286e10i	−0.564791	−	1.81744i
$772$	4.75826e9			0.372209
$773$	−4.32773e9			−0.337001			−0.168501	−	0.985702i	$-0.553893\pi$
$773$	−4.32773e9			−0.337001			−0.168501	+	0.985702i	$0.553893\pi$
$774$	−1.36627e9	−	1.98596e9i	−0.105912	−	0.153949i
$775$			3.96119e9i			0.305682i
$776$	−3.42993e8			−0.0263493
$777$		0			0
$778$	−8.49987e9			−0.647119
$779$			5.40731e8i			0.0409826i
$780$	2.77679e9	−	8.62924e8i	0.209514	−	0.0651090i
$781$	−4.75244e9			−0.356975
$782$	−1.64988e10			−1.23375
$783$	−1.05771e10	+	1.34363e10i	−0.787412	+	1.00026i
$784$		0			0
$785$		−	1.31817e10i		−	0.972584i
$786$	1.21335e10	−	3.77064e9i	0.891265	−	0.276972i
$787$			1.17095e10i			0.856299i	0.903708	+	0.428149i	$0.140834\pi$
$787$			1.17095e10i			0.856299i	−0.903708	+	0.428149i	$0.859166\pi$
$788$			9.61436e8i			0.0699969i
$789$	3.49162e9	−	1.08507e9i	0.253080	−	0.0786478i
$790$		−	5.87500e9i		−	0.423948i
$791$		0			0
$792$	1.89776e10	−	1.30559e10i	1.35739	−	0.933835i
$793$	1.46184e9			0.104098
$794$	−2.83033e9			−0.200662
$795$	1.95276e9	−	6.06846e8i	0.137837	−	0.0428345i
$796$			8.07632e9i			0.567568i
$797$	2.83668e10			1.98475			0.992377	−	0.123238i	$-0.0393279\pi$
$797$	2.83668e10			1.98475			0.992377	+	0.123238i	$0.0393279\pi$
$798$		0			0
$799$	2.65361e8			0.0184045
$800$		−	1.95775e9i		−	0.135189i
$801$	−8.35601e9	+	5.74864e9i	−0.574494	+	0.395231i
$802$	−1.27777e10			−0.874668
$803$	3.58816e10			2.44550
$804$	−1.91022e9	−	6.14687e9i	−0.129624	−	0.417117i
$805$		0			0
$806$			1.31880e10i			0.887169i
$807$	8.23324e8	+	2.64937e9i	0.0551459	+	0.177453i
$808$		−	6.40280e9i		−	0.427002i
$809$			1.17287e9i			0.0778809i	0.999242	+	0.0389404i	$0.0123983\pi$
$809$			1.17287e9i			0.0778809i	−0.999242	+	0.0389404i	$0.987602\pi$
$810$	−1.02834e10	−	3.93649e9i	−0.679892	−	0.260262i
$811$		−	1.21163e8i		−	0.00797623i	−0.999992	−	0.00398811i	$-0.998731\pi$
$811$		−	1.21163e8i		−	0.00797623i	0.999992	−	0.00398811i	$-0.00126946\pi$
$812$		0			0
$813$	−1.40130e10	+	4.35473e9i	−0.914566	+	0.284213i
$814$	1.74941e10			1.13686
$815$	7.42860e9			0.480679
$816$	−4.17539e9	−	1.34360e10i	−0.269018	−	0.865671i
$817$			8.11802e8i			0.0520802i
$818$	4.43124e9			0.283067
$819$		0			0
$820$	−7.93814e8			−0.0502771
$821$			2.10170e10i			1.32547i	0.748853	+	0.662736i	$0.230605\pi$
$821$			2.10170e10i			1.32547i	−0.748853	+	0.662736i	$0.769395\pi$
$822$	−7.02050e9	−	2.25912e10i	−0.440876	−	1.41869i
$823$	−7.98981e9			−0.499617			−0.249808	−	0.968295i	$-0.580368\pi$
$823$	−7.98981e9			−0.499617			−0.249808	+	0.968295i	$0.580368\pi$
$824$	−6.26401e9			−0.390038
$825$	5.15428e9	−	1.60176e9i	0.319580	−	0.0993135i
$826$		0			0
$827$		−	8.63581e9i		−	0.530926i	−0.964121	−	0.265463i	$-0.914475\pi$
$827$		−	8.63581e9i		−	0.530926i	0.964121	−	0.265463i	$-0.0855247\pi$
$828$	−2.82303e9	−	4.10346e9i	−0.172826	−	0.251214i
$829$			1.26323e10i			0.770092i	0.922897	+	0.385046i	$0.125814\pi$
$829$			1.26323e10i			0.770092i	−0.922897	+	0.385046i	$0.874186\pi$
$830$		−	4.71579e9i		−	0.286274i
$831$	−9.21315e9	−	2.96469e10i	−0.556935	−	1.79216i
$832$		−	1.39911e10i		−	0.842209i
$833$		0			0
$834$	2.89421e9	+	9.31324e9i	0.172762	+	0.555930i
$835$	1.65317e10			0.982686
$836$	−1.87870e9			−0.111208
$837$	−1.45080e10	+	1.84297e10i	−0.855203	+	1.08637i
$838$		−	1.05560e10i		−	0.619648i
$839$	−2.36975e10			−1.38527			−0.692637	−	0.721287i	$-0.743551\pi$
$839$	−2.36975e10			−1.38527			−0.692637	+	0.721287i	$0.743551\pi$
$840$		0			0
$841$	−1.07042e10			−0.620538
$842$			1.65915e10i			0.957838i
$843$	1.81144e10	−	5.62927e9i	1.04142	−	0.323635i
$844$	−6.66606e9			−0.381655
$845$	−6.11241e9			−0.348509
$846$	−9.66750e7	−	1.40523e8i	−0.00548931	−	0.00797906i
$847$		0			0
$848$		−	1.67950e9i		−	0.0945789i
$849$	−1.32767e10	+	4.12590e9i	−0.744582	+	0.231388i
$850$		−	5.11857e9i		−	0.285879i
$851$		−	1.56194e10i		−	0.868781i
$852$	−1.29928e9	+	4.03768e8i	−0.0719721	+	0.0223662i
$853$		−	3.02762e10i		−	1.67024i	−0.550065	−	0.835122i	$-0.685397\pi$
$853$		−	3.02762e10i		−	1.67024i	0.550065	−	0.835122i	$-0.314603\pi$
$854$		0			0
$855$	2.10178e9	+	3.05507e9i	0.115002	+	0.167163i
$856$	−1.94314e10			−1.05888
$857$	1.30491e10			0.708185			0.354093	−	0.935210i	$-0.384790\pi$
$857$	1.30491e10			0.708185			0.354093	+	0.935210i	$0.384790\pi$
$858$	1.71602e10	−	5.33274e9i	0.927504	−	0.288234i
$859$		−	8.57626e9i		−	0.461659i	−0.972994	−	0.230830i	$-0.925856\pi$
$859$		−	8.57626e9i		−	0.461659i	0.972994	−	0.230830i	$-0.0741440\pi$
$860$	−1.19176e9			−0.0638916
$861$		0			0
$862$	1.77704e9			0.0944978
$863$			2.04345e10i			1.08225i	0.840943	+	0.541124i	$0.182001\pi$
$863$			2.04345e10i			1.08225i	−0.840943	+	0.541124i	$0.817999\pi$
$864$	7.17033e9	−	9.10855e9i	0.378217	−	0.480453i
$865$	−1.79814e10			−0.944644
$866$	1.04324e10			0.545847
$867$	8.29828e9	+	2.67029e10i	0.432435	+	1.39153i
$868$		0			0
$869$			1.70519e10i			0.881462i
$870$	−5.34184e9	−	1.71895e10i	−0.275026	−	0.885003i
$871$		−	2.07343e10i		−	1.06323i
$872$			2.25878e10i			1.15363i
$873$	−2.69722e8	−	3.92058e8i	−0.0137204	−	0.0199435i
$874$		−	3.57143e9i		−	0.180947i
$875$		0			0
$876$	9.80973e9	−	3.04850e9i	0.493052	−	0.153222i
$877$	−2.47321e10			−1.23812			−0.619061	−	0.785343i	$-0.712487\pi$
$877$	−2.47321e10			−1.23812			−0.619061	+	0.785343i	$0.712487\pi$
$878$	5.76886e9			0.287647
$879$	8.72332e9	+	2.80707e10i	0.433232	+	1.39409i
$880$			1.56175e10i			0.772541i
$881$	−6.10025e9			−0.300560			−0.150280	−	0.988643i	$-0.548018\pi$
$881$	−6.10025e9			−0.300560			−0.150280	+	0.988643i	$0.548018\pi$
$882$		0			0
$883$	7.46738e9			0.365011			0.182505	−	0.983205i	$-0.441579\pi$
$883$	7.46738e9			0.365011			0.182505	+	0.983205i	$0.441579\pi$
$884$			8.00367e9i			0.389678i
$885$	−8.03185e8	−	2.58456e9i	−0.0389506	−	0.125339i
$886$	−2.43968e10			−1.17846
$887$	7.39914e9			0.355999			0.178000	−	0.984031i	$-0.443037\pi$
$887$	7.39914e9			0.355999			0.178000	+	0.984031i	$0.443037\pi$
$888$	1.97489e10	−	6.13721e9i	0.946447	−	0.294121i
$889$		0			0
$890$		−	1.06765e10i		−	0.507650i
$891$	2.98471e10	+	1.14255e10i	1.41361	+	0.541131i
$892$		−	5.05077e9i		−	0.238276i
$893$			5.74417e7i			0.00269928i
$894$	−2.34379e9	−	7.54204e9i	−0.109708	−	0.353027i
$895$			2.58919e10i			1.20721i
$896$		0			0
$897$	−4.76126e9	−	1.53212e10i	−0.220266	−	0.708793i
$898$	−8.17816e9			−0.376867
$899$	−3.83429e10			−1.76005
$900$	1.27305e9	−	8.75816e8i	0.0582100	−	0.0400464i
$901$			5.62853e9i			0.256365i
$902$	−4.90565e9			−0.222574
$903$		0			0
$904$	−3.96966e10			−1.78716
$905$		−	1.81713e10i		−	0.814923i
$906$	3.43453e9	−	1.06732e9i	0.153433	−	0.0476812i
$907$	−1.14080e10			−0.507674			−0.253837	−	0.967247i	$-0.581693\pi$
$907$	−1.14080e10			−0.507674			−0.253837	+	0.967247i	$0.581693\pi$
$908$	−5.32027e9			−0.235849
$909$	7.31871e9	−	5.03502e9i	0.323192	−	0.222345i
$910$		0			0
$911$			9.95158e9i			0.436091i	0.975939	+	0.218046i	$0.0699682\pi$
$911$			9.95158e9i			0.436091i	−0.975939	+	0.218046i	$0.930032\pi$
$912$	2.90843e9	−	9.03832e8i	0.126963	−	0.0394553i
$913$			1.36874e10i			0.595213i
$914$			2.14795e10i			0.930493i
$915$	−2.61350e9	+	8.12178e8i	−0.112784	+	0.0350491i
$916$		−	5.23072e9i		−	0.224868i
$917$		0			0
$918$	1.87470e10	−	2.38145e10i	0.799800	−	1.01600i
$919$	3.18281e10			1.35271			0.676357	−	0.736574i	$-0.263557\pi$
$919$	3.18281e10			1.35271			0.676357	+	0.736574i	$0.263557\pi$
$920$	2.16493e10			0.916614
$921$	−6.27446e8	+	1.94987e8i	−0.0264648	+	0.00822426i
$922$		−	1.17862e10i		−	0.495238i
$923$	−4.38267e9			−0.183456
$924$		0			0
$925$	4.84575e9			0.201310
$926$			1.09092e10i			0.451495i
$927$	−4.92587e9	−	7.16007e9i	−0.203097	−	0.295215i
$928$	1.89503e10			0.778391
$929$	−3.34390e10			−1.36835			−0.684177	−	0.729316i	$-0.739839\pi$
$929$	−3.34390e10			−1.36835			−0.684177	+	0.729316i	$0.739839\pi$
$930$	−7.32708e9	−	2.35777e10i	−0.298704	−	0.961195i
$931$		0			0
$932$			2.41673e9i			0.0977852i
$933$	4.97584e9	+	1.60117e10i	0.200577	+	0.645434i
$934$			9.30437e9i			0.373657i
$935$		−	5.23391e10i		−	2.09404i
$936$	1.75010e10	−	1.20401e10i	0.697587	−	0.479915i
$937$		−	2.48503e10i		−	0.986832i	−0.869793	−	0.493416i	$-0.835748\pi$
$937$		−	2.48503e10i		−	0.986832i	0.869793	−	0.493416i	$-0.164252\pi$
$938$		0			0
$939$	−3.84299e10	+	1.19426e10i	−1.51475	+	0.470726i
$940$	−8.43268e7			−0.00331145
$941$	−1.96550e10			−0.768971			−0.384485	−	0.923131i	$-0.625621\pi$
$941$	−1.96550e10			−0.768971			−0.384485	+	0.923131i	$0.625621\pi$
$942$	−6.92091e9	−	2.22707e10i	−0.269765	−	0.868073i
$943$			4.37994e9i			0.170089i
$944$	−2.22289e9			−0.0860033
$945$		0			0
$946$	−7.36488e9			−0.282844
$947$		−	3.64835e10i		−	1.39596i	−0.716119	−	0.697979i	$-0.754083\pi$
$947$		−	3.64835e10i		−	1.39596i	0.716119	−	0.697979i	$-0.245917\pi$
$948$	1.44873e9	+	4.66185e9i	0.0552278	+	0.177717i
$949$	3.30897e10			1.25679
$950$	1.10800e9			0.0419282
$951$	−1.37745e10	+	4.28059e9i	−0.519329	+	0.161388i
$952$		0			0
$953$		−	1.60579e10i		−	0.600984i	−0.953784	−	0.300492i	$-0.902849\pi$
$953$		−	1.60579e10i		−	0.600984i	0.953784	−	0.300492i	$-0.0971508\pi$
$954$	2.98061e9	−	2.05056e9i	0.111144	−	0.0764632i
$955$			1.44684e9i			0.0537537i
$956$		−	1.12078e10i		−	0.414874i
$957$	1.55044e10	+	4.98916e10i	0.571826	+	1.84007i
$958$			3.47683e10i			1.27763i
$959$		0			0
$960$	7.77327e9	+	2.50135e10i	0.283566	+	0.912484i
$961$	−2.50800e10			−0.911583
$962$	1.61330e10			0.584253
$963$	−1.52804e10	−	2.22110e10i	−0.551370	−	0.801451i
$964$		−	3.53921e9i		−	0.127244i
$965$	−2.86950e10			−1.02792
$966$		0			0
$967$	5.02193e10			1.78599			0.892993	−	0.450071i	$-0.148601\pi$
$967$	5.02193e10			1.78599			0.892993	+	0.450071i	$0.148601\pi$
$968$		−	3.96604e10i		−	1.40538i
$969$	−9.74707e9	+	3.02903e9i	−0.344144	+	0.106947i
$970$	5.00934e8			0.0176230
$971$	−2.45564e10			−0.860791			−0.430396	−	0.902640i	$-0.641626\pi$
$971$	−2.45564e10			−0.860791			−0.430396	+	0.902640i	$0.641626\pi$
$972$	9.13068e9	+	5.87817e8i	0.318912	+	0.0205310i
$973$		0			0
$974$		−	1.26364e10i		−	0.438196i
$975$	4.75324e9	−	1.47713e9i	0.164238	−	0.0510390i
$976$			2.24777e9i			0.0773888i
$977$			6.17851e9i			0.211959i	0.994368	+	0.105980i	$0.0337978\pi$
$977$			6.17851e9i			0.211959i	−0.994368	+	0.105980i	$0.966202\pi$
$978$	1.25508e10	−	3.90031e9i	0.429027	−	0.133325i
$979$			3.09881e10i			1.05549i
$980$		0			0
$981$	−2.58190e10	+	1.77625e10i	−0.873167	+	0.600708i
$982$	−1.09061e10			−0.367517
$983$	3.38979e10			1.13824			0.569122	−	0.822253i	$-0.307283\pi$
$983$	3.38979e10			1.13824			0.569122	+	0.822253i	$0.307283\pi$
$984$	−5.53791e9	+	1.72098e9i	−0.185295	+	0.0575827i
$985$		−	5.79801e9i		−	0.193309i
$986$	4.95459e10			1.64603
$987$		0			0
$988$	−1.73252e9			−0.0571518
$989$			6.57563e9i			0.216148i
$990$	−2.77164e10	+	1.90679e10i	−0.907849	+	0.624568i
$991$	3.70960e10			1.21079			0.605395	−	0.795925i	$-0.293015\pi$
$991$	3.70960e10			1.21079			0.605395	+	0.795925i	$0.293015\pi$
$992$	2.59930e10			0.845405
$993$	−2.08918e9	−	6.72275e9i	−0.0677101	−	0.217884i
$994$		0			0
$995$		−	4.87049e10i		−	1.56744i
$996$	1.16288e9	+	3.74202e9i	0.0372930	+	0.120005i
$997$		−	6.89036e9i		−	0.220196i	−0.993921	−	0.110098i	$-0.964884\pi$
$997$		−	6.89036e9i		−	0.220196i	0.993921	−	0.110098i	$-0.0351164\pi$
$998$			1.20333e10i			0.383201i
$999$	2.25452e10	+	1.77477e10i	0.715442	+	0.563202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.8.c.b.146.24		32
3.2	odd	2	inner	147.8.c.b.146.9		32
7.2	even	3		21.8.g.b.17.11	yes	32
7.3	odd	6		21.8.g.b.5.6	✓	32
7.6	odd	2	inner	147.8.c.b.146.10		32
21.2	odd	6		21.8.g.b.17.6	yes	32
21.17	even	6		21.8.g.b.5.11	yes	32
21.20	even	2	inner	147.8.c.b.146.23		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.6	✓	32	7.3	odd	6
21.8.g.b.5.11	yes	32	21.17	even	6
21.8.g.b.17.6	yes	32	21.2	odd	6
21.8.g.b.17.11	yes	32	7.2	even	3
147.8.c.b.146.9		32	3.2	odd	2	inner
147.8.c.b.146.10		32	7.6	odd	2	inner
147.8.c.b.146.23		32	21.20	even	2	inner
147.8.c.b.146.24		32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+9.33246i q^{2} +(13.8782 + 44.6586i) q^{3} +40.9053 q^{4} -246.682 q^{5} +(-416.775 + 129.518i) q^{6} +1576.30i q^{8} +(-1801.79 + 1239.57i) q^{9} -2302.15i q^{10} +6681.89i q^{11} +(567.693 + 1826.77i) q^{12} +6161.99i q^{13} +(-3423.52 - 11016.5i) q^{15} -9474.88 q^{16} +31753.3 q^{17} +(-11568.2 - 16815.1i) q^{18} +6873.52i q^{19} -10090.6 q^{20} -62358.4 q^{22} +55675.8i q^{23} +(-70395.5 + 21876.3i) q^{24} -17272.8 q^{25} -57506.5 q^{26} +(-80363.0 - 63262.4i) q^{27} -167195. i q^{29} +(102811. - 31949.8i) q^{30} -229331. i q^{31} +113343. i q^{32} +(-298404. + 92732.8i) q^{33} +296336. i q^{34} +(-73702.7 + 50704.8i) q^{36} -280542. q^{37} -64146.8 q^{38} +(-275186. + 85517.5i) q^{39} -388846. i q^{40} +78668.6 q^{41} +118106. q^{43} +273324. i q^{44} +(444469. - 305779. i) q^{45} -519592. q^{46} +8356.96 q^{47} +(-131495. - 423135. i) q^{48} -161198. i q^{50} +(440680. + 1.41806e6i) q^{51} +252058. i q^{52} +177258. i q^{53} +(590394. - 749984. i) q^{54} -1.64830e6i q^{55} +(-306962. + 95392.4i) q^{57} +1.56034e6 q^{58} +234608. q^{59} +(-140040. - 450633. i) q^{60} -237235. i q^{61} +2.14022e6 q^{62} -2.27055e6 q^{64} -1.52005e6i q^{65} +(-865425. - 2.78484e6i) q^{66} -3.36488e6 q^{67} +1.29888e6 q^{68} +(-2.48641e6 + 772682. i) q^{69} +711242. i q^{71} +(-1.95393e6 - 2.84016e6i) q^{72} -5.36998e6i q^{73} -2.61814e6i q^{74} +(-239717. - 771381. i) q^{75} +281163. i q^{76} +(-798089. - 2.56816e6i) q^{78} +2.55196e6 q^{79} +2.33729e6 q^{80} +(1.70992e6 - 4.46688e6i) q^{81} +734172. i q^{82} +2.04843e6 q^{83} -7.83298e6 q^{85} +1.10222e6i q^{86} +(7.46669e6 - 2.32037e6i) q^{87} -1.05327e7 q^{88} +4.63762e6 q^{89} +(2.85367e6 + 4.14799e6i) q^{90} +2.27743e6i q^{92} +(1.02416e7 - 3.18271e6i) q^{93} +77990.9i q^{94} -1.69558e6i q^{95} +(-5.06173e6 + 1.57300e6i) q^{96} +217594. i q^{97} +(-8.28264e6 - 1.20393e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2300 q^{4} + 7032 q^{9} + 27576 q^{15} + 39188 q^{16} - 66996 q^{18} + 105132 q^{22} + 662504 q^{25} + 81324 q^{30} - 227244 q^{36} + 1237496 q^{37} - 3992208 q^{39} - 1416064 q^{43} + 6985680 q^{46}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 32 * q - 2300 * q^4 + 7032 * q^9 + 27576 * q^15 + 39188 * q^16 - 66996 * q^18 + 105132 * q^22 + 662504 * q^25 + 81324 * q^30 - 227244 * q^36 + 1237496 * q^37 - 3992208 * q^39 - 1416064 * q^43 + 6985680 * q^46 - 1354680 * q^51 - 6279408 * q^57 + 4128684 * q^58 - 15042564 * q^60 - 589508 * q^64 + 3889456 * q^67 + 3088944 * q^72 + 1917432 * q^78 - 15252656 * q^79 - 17406072 * q^81 + 3418848 * q^85 - 24626796 * q^88 + 49664208 * q^93 + 35642232 * q^99

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