LMFDB - Embedded newform 147.8.c.b.146.27

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			146.27
Character	$\chi$	$=$	147.146
Dual form			147.8.c.b.146.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-20.7644i q^{2} +(-43.7336 - 16.5643i) q^{3} -303.161 q^{4} -343.321 q^{5} +(-343.947 + 908.102i) q^{6} +3637.11i q^{8} +(1638.25 + 1448.83i) q^{9} +7128.85i q^{10} +1113.01i q^{11} +(13258.3 + 5021.63i) q^{12} -5040.70i q^{13} +(15014.6 + 5686.86i) q^{15} +36717.9 q^{16} -12799.2 q^{17} +(30084.1 - 34017.3i) q^{18} -28448.7i q^{19} +104081. q^{20} +23111.1 q^{22} +101790. i q^{23} +(60246.1 - 159064. i) q^{24} +39744.1 q^{25} -104667. q^{26} +(-47647.8 - 90498.9i) q^{27} +73697.1i q^{29} +(118084. - 311770. i) q^{30} +182120. i q^{31} -296875. i q^{32} +(18436.3 - 48676.1i) q^{33} +265767. i q^{34} +(-496653. - 439228. i) q^{36} +401039. q^{37} -590720. q^{38} +(-83495.4 + 220448. i) q^{39} -1.24870e6i q^{40} -424658. q^{41} -150211. q^{43} -337422. i q^{44} +(-562445. - 497413. i) q^{45} +2.11360e6 q^{46} -378601. q^{47} +(-1.60580e6 - 608204. i) q^{48} -825264. i q^{50} +(559753. + 212009. i) q^{51} +1.52814e6i q^{52} -737648. i q^{53} +(-1.87916e6 + 989377. i) q^{54} -382121. i q^{55} +(-471231. + 1.24416e6i) q^{57} +1.53028e6 q^{58} +1.08041e6 q^{59} +(-4.55185e6 - 1.72403e6i) q^{60} +376699. i q^{61} +3.78162e6 q^{62} -1.46454e6 q^{64} +1.73058e6i q^{65} +(-1.01073e6 - 382818. i) q^{66} -2.49206e6 q^{67} +3.88021e6 q^{68} +(1.68607e6 - 4.45162e6i) q^{69} -1.89722e6i q^{71} +(-5.26955e6 + 5.95850e6i) q^{72} +1.88543e6i q^{73} -8.32733e6i q^{74} +(-1.73815e6 - 658332. i) q^{75} +8.62452e6i q^{76} +(4.57747e6 + 1.73373e6i) q^{78} -4.27705e6 q^{79} -1.26060e7 q^{80} +(584759. + 4.74709e6i) q^{81} +8.81778e6i q^{82} -3.62840e6 q^{83} +4.39422e6 q^{85} +3.11905e6i q^{86} +(1.22074e6 - 3.22304e6i) q^{87} -4.04815e6 q^{88} +4.43094e6 q^{89} +(-1.03285e7 + 1.16788e7i) q^{90} -3.08586e7i q^{92} +(3.01669e6 - 7.96477e6i) q^{93} +7.86142e6i q^{94} +9.76702e6i q^{95} +(-4.91751e6 + 1.29834e7i) q^{96} -3.45013e6i q^{97} +(-1.61257e6 + 1.82340e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	20.7644i		−	1.83533i	−0.397353	−	0.917666i	$-0.630071\pi$
$2$		−	20.7644i		−	1.83533i	0.397353	−	0.917666i	$-0.369929\pi$
$3$	−43.7336	−	16.5643i	−0.935170	−	0.354199i
$3$	−43.7336	−	16.5643i	−0.935170	−	0.354199i
$4$	−303.161			−2.36844
$5$	−343.321			−1.22830			−0.614151	−	0.789189i	$-0.710501\pi$
$5$	−343.321			−1.22830			−0.614151	+	0.789189i	$0.710501\pi$
$6$	−343.947	+	908.102i	−0.650073	+	1.71635i
$7$		0			0
$7$		0			0
$8$			3637.11i			2.51155i
$9$	1638.25	+	1448.83i	0.749086	+	0.662473i
$10$			7128.85i			2.25434i
$11$			1113.01i			0.252131i	0.992022	+	0.126065i	$0.0402349\pi$
$11$			1113.01i			0.252131i	−0.992022	+	0.126065i	$0.959765\pi$
$12$	13258.3	+	5021.63i	2.21490	+	0.838901i
$13$		−	5040.70i		−	0.636339i	−0.948034	−	0.318170i	$-0.896932\pi$
$13$		−	5040.70i		−	0.636339i	0.948034	−	0.318170i	$-0.103068\pi$
$14$		0			0
$15$	15014.6	+	5686.86i	1.14867	+	0.435064i
$16$	36717.9			2.24108
$17$	−12799.2			−0.631845			−0.315923	−	0.948785i	$-0.602314\pi$
$17$	−12799.2			−0.631845			−0.315923	+	0.948785i	$0.602314\pi$
$18$	30084.1	−	34017.3i	1.21586	−	1.37482i
$19$		−	28448.7i		−	0.951534i	−0.879571	−	0.475767i	$-0.842171\pi$
$19$		−	28448.7i		−	0.951534i	0.879571	−	0.475767i	$-0.157829\pi$
$20$	104081.			2.90916
$21$		0			0
$22$	23111.1			0.462744
$23$			101790.i			1.74444i	0.489113	+	0.872220i	$0.337320\pi$
$23$			101790.i			1.74444i	−0.489113	+	0.872220i	$0.662680\pi$
$24$	60246.1	−	159064.i	0.889589	−	2.34872i
$25$	39744.1			0.508725
$26$	−104667.			−1.16789
$27$	−47647.8	−	90498.9i	−0.465875	−	0.884851i
$28$		0			0
$29$			73697.1i			0.561122i	0.959836	+	0.280561i	$0.0905205\pi$
$29$			73697.1i			0.561122i	−0.959836	+	0.280561i	$0.909480\pi$
$30$	118084.	−	311770.i	0.798486	−	2.10819i
$31$			182120.i			1.09798i	0.835831	+	0.548988i	$0.184987\pi$
$31$			182120.i			1.09798i	−0.835831	+	0.548988i	$0.815013\pi$
$32$		−	296875.i		−	1.60158i
$33$	18436.3	−	48676.1i	0.0893046	−	0.235785i
$34$			265767.i			1.15965i
$35$		0			0
$36$	−496653.	−	439228.i	−1.77417	−	1.56903i
$37$	401039.			1.30161			0.650804	−	0.759246i	$-0.274432\pi$
$37$	401039.			1.30161			0.650804	+	0.759246i	$0.274432\pi$
$38$	−590720.			−1.74638
$39$	−83495.4	+	220448.i	−0.225391	+	0.595086i
$40$		−	1.24870e6i		−	3.08494i
$41$	−424658.			−0.962268			−0.481134	−	0.876647i	$-0.659775\pi$
$41$	−424658.			−0.962268			−0.481134	+	0.876647i	$0.659775\pi$
$42$		0			0
$43$	−150211.			−0.288113			−0.144057	−	0.989569i	$-0.546015\pi$
$43$	−150211.			−0.288113			−0.144057	+	0.989569i	$0.546015\pi$
$44$		−	337422.i		−	0.597158i
$45$	−562445.	−	497413.i	−0.920103	−	0.813717i
$46$	2.11360e6			3.20163
$47$	−378601.			−0.531911			−0.265955	−	0.963985i	$-0.585687\pi$
$47$	−378601.			−0.531911			−0.265955	+	0.963985i	$0.585687\pi$
$48$	−1.60580e6	−	608204.i	−2.09579	−	0.793789i
$49$		0			0
$50$		−	825264.i		−	0.933679i
$51$	559753.	+	212009.i	0.590883	+	0.223799i
$52$			1.52814e6i			1.50713i
$53$		−	737648.i		−	0.680587i	−0.940319	−	0.340293i	$-0.889474\pi$
$53$		−	737648.i		−	0.680587i	0.940319	−	0.340293i	$-0.110526\pi$
$54$	−1.87916e6	+	989377.i	−1.62399	+	0.855035i
$55$		−	382121.i		−	0.309693i
$56$		0			0
$57$	−471231.	+	1.24416e6i	−0.337033	+	0.889846i
$58$	1.53028e6			1.02984
$59$	1.08041e6			0.684870			0.342435	−	0.939542i	$-0.388748\pi$
$59$	1.08041e6			0.684870			0.342435	+	0.939542i	$0.388748\pi$
$60$	−4.55185e6	−	1.72403e6i	−2.72056	−	1.03042i
$61$			376699.i			0.212491i	0.994340	+	0.106245i	$0.0338829\pi$
$61$			376699.i			0.212491i	−0.994340	+	0.106245i	$0.966117\pi$
$62$	3.78162e6			2.01515
$63$		0			0
$64$	−1.46454e6			−0.698349
$65$			1.73058e6i			0.781617i
$66$	−1.01073e6	−	382818.i	−0.432744	−	0.163904i
$67$	−2.49206e6			−1.01227			−0.506136	−	0.862454i	$-0.668927\pi$
$67$	−2.49206e6			−1.01227			−0.506136	+	0.862454i	$0.668927\pi$
$68$	3.88021e6			1.49649
$69$	1.68607e6	−	4.45162e6i	0.617880	−	1.63135i
$70$		0			0
$71$		−	1.89722e6i		−	0.629092i	−0.949242	−	0.314546i	$-0.898148\pi$
$71$		−	1.89722e6i		−	0.629092i	0.949242	−	0.314546i	$-0.101852\pi$
$72$	−5.26955e6	+	5.95850e6i	−1.66383	+	1.88136i
$73$			1.88543e6i			0.567258i	0.958934	+	0.283629i	$0.0915384\pi$
$73$			1.88543e6i			0.567258i	−0.958934	+	0.283629i	$0.908462\pi$
$74$		−	8.32733e6i		−	2.38888i
$75$	−1.73815e6	−	658332.i	−0.475744	−	0.180190i
$76$			8.62452e6i			2.25365i
$77$		0			0
$78$	4.57747e6	+	1.73373e6i	1.09218	+	0.413667i
$79$	−4.27705e6			−0.975999			−0.488000	−	0.872844i	$-0.662273\pi$
$79$	−4.27705e6			−0.975999			−0.488000	+	0.872844i	$0.662273\pi$
$80$	−1.26060e7			−2.75272
$81$	584759.	+	4.74709e6i	0.122259	+	0.992498i
$82$			8.81778e6i			1.76608i
$83$	−3.62840e6			−0.696533			−0.348267	−	0.937396i	$-0.613230\pi$
$83$	−3.62840e6			−0.696533			−0.348267	+	0.937396i	$0.613230\pi$
$84$		0			0
$85$	4.39422e6			0.776096
$86$			3.11905e6i			0.528784i
$87$	1.22074e6	−	3.22304e6i	0.198749	−	0.524744i
$88$	−4.04815e6			−0.633239
$89$	4.43094e6			0.666241			0.333120	−	0.942884i	$-0.391898\pi$
$89$	4.43094e6			0.666241			0.333120	+	0.942884i	$0.391898\pi$
$90$	−1.03285e7	+	1.16788e7i	−1.49344	+	1.68869i
$91$		0			0
$92$		−	3.08586e7i		−	4.13161i
$93$	3.01669e6	−	7.96477e6i	0.388902	−	1.02679i
$94$			7.86142e6i			0.976233i
$95$			9.76702e6i			1.16877i
$96$	−4.91751e6	+	1.29834e7i	−0.567278	+	1.49775i
$97$		−	3.45013e6i		−	0.383826i	−0.981412	−	0.191913i	$-0.938531\pi$
$97$		−	3.45013e6i		−	0.383826i	0.981412	−	0.191913i	$-0.0614692\pi$
$98$		0			0
$99$	−1.61257e6	+	1.82340e6i	−0.167030	+	0.188868i
$100$	−1.20489e7			−1.20489
$101$	−1.34986e7			−1.30366			−0.651828	−	0.758367i	$-0.725998\pi$
$101$	−1.34986e7			−1.30366			−0.651828	+	0.758367i	$0.725998\pi$
$102$	4.40224e6	−	1.16230e7i	0.410746	−	1.08447i
$103$			2.67558e6i			0.241261i	0.992697	+	0.120631i	$0.0384917\pi$
$103$			2.67558e6i			0.241261i	−0.992697	+	0.120631i	$0.961508\pi$
$104$	1.83336e7			1.59820
$105$		0			0
$106$	−1.53168e7			−1.24910
$107$		−	8.35749e6i		−	0.659527i	−0.944064	−	0.329764i	$-0.893031\pi$
$107$		−	8.35749e6i		−	0.659527i	0.944064	−	0.329764i	$-0.106969\pi$
$108$	1.44449e7	+	2.74357e7i	1.10340	+	2.09572i
$109$	−2.01785e7			−1.49244			−0.746218	−	0.665702i	$-0.768132\pi$
$109$	−2.01785e7			−1.49244			−0.746218	+	0.665702i	$0.768132\pi$
$110$	−7.93451e6			−0.568389
$111$	−1.75389e7	−	6.64291e6i	−1.21723	−	0.461029i
$112$		0			0
$113$		−	1.07711e7i		−	0.702237i	−0.936331	−	0.351119i	$-0.885801\pi$
$113$		−	1.07711e7i		−	0.702237i	0.936331	−	0.351119i	$-0.114199\pi$
$114$	2.58343e7	+	9.78484e6i	1.63316	+	0.618567i
$115$		−	3.49465e7i		−	2.14270i
$116$		−	2.23421e7i		−	1.32899i
$117$	7.30311e6	−	8.25792e6i	0.421558	−	0.476673i
$118$		−	2.24342e7i		−	1.25696i
$119$		0			0
$120$	−2.06837e7	+	5.46099e7i	−1.09268	+	2.88494i
$121$	1.82484e7			0.936430
$122$	7.82193e6			0.389991
$123$	1.85718e7	+	7.03415e6i	0.899884	+	0.340835i
$124$		−	5.52117e7i		−	2.60049i
$125$	1.31769e7			0.603434
$126$		0			0
$127$	4.20872e7			1.82321			0.911606	−	0.411066i	$-0.134843\pi$
$127$	4.20872e7			1.82321			0.911606	+	0.411066i	$0.134843\pi$
$128$		−	7.58959e6i		−	0.319877i
$129$	6.56928e6	+	2.48814e6i	0.269435	+	0.102050i
$130$	3.59344e7			1.43453
$131$	2.12950e7			0.827614			0.413807	−	0.910365i	$-0.364199\pi$
$131$	2.12950e7			0.827614			0.413807	+	0.910365i	$0.364199\pi$
$132$	−5.58915e6	+	1.47567e7i	−0.211513	+	0.558444i
$133$		0			0
$134$			5.17462e7i			1.85785i
$135$	1.63585e7	+	3.10701e7i	0.572235	+	1.08686i
$136$		−	4.65520e7i		−	1.58691i
$137$		−	1.93619e7i		−	0.643319i	−0.946855	−	0.321659i	$-0.895759\pi$
$137$		−	1.93619e7i		−	0.643319i	0.946855	−	0.321659i	$-0.104241\pi$
$138$	−9.24354e7	−	3.50103e7i	−2.99407	−	1.13401i
$139$		−	4.20425e7i		−	1.32781i	−0.747816	−	0.663906i	$-0.768897\pi$
$139$		−	4.20425e7i		−	1.32781i	0.747816	−	0.663906i	$-0.231103\pi$
$140$		0			0
$141$	1.65576e7	+	6.27124e6i	0.497427	+	0.188403i
$142$	−3.93947e7			−1.15459
$143$	5.61036e6			0.160441
$144$	6.01531e7	+	5.31979e7i	1.67876	+	1.48466i
$145$		−	2.53017e7i		−	0.689227i
$146$	3.91498e7			1.04111
$147$		0			0
$148$	−1.21579e8			−3.08279
$149$		−	1.36435e7i		−	0.337889i	−0.985626	−	0.168945i	$-0.945964\pi$
$149$		−	1.36435e7i		−	0.337889i	0.985626	−	0.168945i	$-0.0540359\pi$
$150$	−1.36699e7	+	3.60917e7i	−0.330709	+	0.873149i
$151$	−5.21813e7			−1.23338			−0.616688	−	0.787207i	$-0.711526\pi$
$151$	−5.21813e7			−1.23338			−0.616688	+	0.787207i	$0.711526\pi$
$152$	1.03471e8			2.38982
$153$	−2.09682e7	−	1.85438e7i	−0.473306	−	0.418580i
$154$		0			0
$155$		−	6.25257e7i		−	1.34864i
$156$	2.53125e7	−	6.68311e7i	0.533826	−	1.40943i
$157$			3.74887e7i			0.773129i	0.922262	+	0.386565i	$0.126338\pi$
$157$			3.74887e7i			0.773129i	−0.922262	+	0.386565i	$0.873662\pi$
$158$			8.88104e7i			1.79128i
$159$	−1.22186e7	+	3.22600e7i	−0.241063	+	0.636464i
$160$			1.01923e8i			1.96722i
$161$		0			0
$162$	9.85705e7	−	1.21422e7i	1.82156	−	0.224385i
$163$	9.44168e7			1.70763			0.853813	−	0.520580i	$-0.174284\pi$
$163$	9.44168e7			1.70763			0.853813	+	0.520580i	$0.174284\pi$
$164$	1.28740e8			2.27908
$165$	−6.32955e6	+	1.67115e7i	−0.109693	+	0.289615i
$166$			7.53416e7i			1.27837i
$167$	−2.74004e7			−0.455249			−0.227625	−	0.973749i	$-0.573096\pi$
$167$	−2.74004e7			−0.455249			−0.227625	+	0.973749i	$0.573096\pi$
$168$		0			0
$169$	3.73399e7			0.595072
$170$		−	9.12434e7i		−	1.42439i
$171$	4.12173e7	−	4.66060e7i	0.630366	−	0.712781i
$172$	4.55382e7			0.682380
$173$	−6.32915e7			−0.929359			−0.464680	−	0.885479i	$-0.653831\pi$
$173$	−6.32915e7			−0.929359			−0.464680	+	0.885479i	$0.653831\pi$
$174$	−6.69244e7	−	2.53479e7i	−0.963080	−	0.364770i
$175$		0			0
$176$			4.08675e7i			0.565046i
$177$	−4.72503e7	−	1.78963e7i	−0.640470	−	0.242580i
$178$		−	9.20060e7i		−	1.22277i
$179$		−	2.05120e7i		−	0.267315i	−0.991028	−	0.133657i	$-0.957328\pi$
$179$		−	2.05120e7i		−	0.267315i	0.991028	−	0.133657i	$-0.0426721\pi$
$180$	1.70511e8	+	1.50796e8i	2.17921	+	1.92724i
$181$			6.65265e6i			0.0833911i	0.999130	+	0.0416956i	$0.0132760\pi$
$181$			6.65265e6i			0.0833911i	−0.999130	+	0.0416956i	$0.986724\pi$
$182$		0			0
$183$	6.23974e6	−	1.64744e7i	0.0752641	−	0.198715i
$184$	−3.70220e8			−4.38125
$185$	−1.37685e8			−1.59877
$186$	−1.65384e8	−	6.26398e7i	−1.88451	−	0.713764i
$187$		−	1.42457e7i		−	0.159308i
$188$	1.14777e8			1.25980
$189$		0			0
$190$	2.02806e8			2.14508
$191$			1.38193e8i			1.43506i	0.696527	+	0.717530i	$0.254727\pi$
$191$			1.38193e8i			1.43506i	−0.696527	+	0.717530i	$0.745273\pi$
$192$	6.40497e7	+	2.42591e7i	0.653075	+	0.247355i
$193$	1.36873e8			1.37046			0.685229	−	0.728328i	$-0.259702\pi$
$193$	1.36873e8			1.37046			0.685229	+	0.728328i	$0.259702\pi$
$194$	−7.16399e7			−0.704448
$195$	2.86657e7	−	7.56843e7i	0.276848	−	0.730945i
$196$		0			0
$197$			9.90561e6i			0.0923102i	0.998934	+	0.0461551i	$0.0146968\pi$
$197$			9.90561e6i			0.0923102i	−0.998934	+	0.0461551i	$0.985303\pi$
$198$	3.78617e7	+	3.34840e7i	0.346635	+	0.306555i
$199$			2.35572e7i			0.211903i	0.994371	+	0.105952i	$0.0337889\pi$
$199$			2.35572e7i			0.211903i	−0.994371	+	0.105952i	$0.966211\pi$
$200$			1.44554e8i			1.27769i
$201$	1.08987e8	+	4.12792e7i	0.946646	+	0.358546i
$202$			2.80290e8i			2.39264i
$203$		0			0
$204$	−1.69695e8	−	6.42728e7i	−1.39947	−	0.530056i
$205$	1.45794e8			1.18196
$206$	5.55568e7			0.442795
$207$	−1.47476e8	+	1.66757e8i	−1.15564	+	1.30674i
$208$		−	1.85084e8i		−	1.42609i
$209$	3.16638e7			0.239911
$210$		0			0
$211$	−8.68031e6			−0.0636131			−0.0318066	−	0.999494i	$-0.510126\pi$
$211$	−8.68031e6			−0.0636131			−0.0318066	+	0.999494i	$0.510126\pi$
$212$			2.23626e8i			1.61193i
$213$	−3.14261e7	+	8.29724e7i	−0.222824	+	0.588308i
$214$	−1.73538e8			−1.21045
$215$	5.15707e7			0.353890
$216$	3.29154e8	−	1.73300e8i	2.22234	−	1.17007i
$217$		0			0
$218$			4.18994e8i			2.73911i
$219$	3.12308e7	−	8.24566e7i	0.200922	−	0.530482i
$220$			1.15844e8i			0.733490i
$221$			6.45167e7i			0.402068i
$222$	−1.37936e8	+	3.64184e8i	−0.846141	+	2.23401i
$223$		−	1.90665e8i		−	1.15134i	−0.817683	−	0.575669i	$-0.804742\pi$
$223$		−	1.90665e8i		−	1.15134i	0.817683	−	0.575669i	$-0.195258\pi$
$224$		0			0
$225$	6.51109e7	+	5.75825e7i	0.381079	+	0.337017i
$226$	−2.23655e8			−1.28884
$227$	3.06558e8			1.73949			0.869747	−	0.493499i	$-0.164282\pi$
$227$	3.06558e8			1.73949			0.869747	+	0.493499i	$0.164282\pi$
$228$	1.42859e8	−	3.77181e8i	0.798243	−	2.10755i
$229$		−	2.84885e8i		−	1.56764i	−0.620989	−	0.783820i	$-0.713269\pi$
$229$		−	2.84885e8i		−	1.56764i	0.620989	−	0.783820i	$-0.286731\pi$
$230$	−7.25643e8			−3.93256
$231$		0			0
$232$	−2.68044e8			−1.40928
$233$		−	424927.i		−	0.00220074i	−0.999999	−	0.00110037i	$-0.999650\pi$
$233$		−	424927.i		−	0.00220074i	0.999999	−	0.00110037i	$-0.000350259\pi$
$234$	−1.71471e8	−	1.51645e8i	−0.874853	−	0.773699i
$235$	1.29981e8			0.653347
$236$	−3.27539e8			−1.62208
$237$	1.87051e8	+	7.08462e7i	0.912725	+	0.345698i
$238$		0			0
$239$		−	1.59609e8i		−	0.756250i	−0.925755	−	0.378125i	$-0.876569\pi$
$239$		−	1.59609e8i		−	0.756250i	0.925755	−	0.378125i	$-0.123431\pi$
$240$	5.51306e8	+	2.08809e8i	2.57426	+	0.975013i
$241$			7.79671e7i			0.358799i	0.983776	+	0.179400i	$0.0574155\pi$
$241$			7.79671e7i			0.358799i	−0.983776	+	0.179400i	$0.942584\pi$
$242$		−	3.78917e8i		−	1.71866i
$243$	5.30584e7	−	2.17293e8i	0.237210	−	0.971458i
$244$		−	1.14200e8i		−	0.503272i
$245$		0			0
$246$	1.46060e8	−	3.85633e8i	0.625545	−	1.65159i
$247$	−1.43401e8			−0.605499
$248$	−6.62392e8			−2.75762
$249$	1.58683e8	+	6.01018e7i	0.651377	+	0.246712i
$250$		−	2.73612e8i		−	1.10750i
$251$	−1.08662e7			−0.0433730			−0.0216865	−	0.999765i	$-0.506904\pi$
$251$	−1.08662e7			−0.0433730			−0.0216865	+	0.999765i	$0.506904\pi$
$252$		0			0
$253$	−1.13293e8			−0.439827
$254$		−	8.73916e8i		−	3.34620i
$255$	−1.92175e8	−	7.27870e7i	−0.725782	−	0.274893i
$256$	−3.45055e8			−1.28543
$257$	8.16843e7			0.300174			0.150087	−	0.988673i	$-0.452045\pi$
$257$	8.16843e7			0.300174			0.150087	+	0.988673i	$0.452045\pi$
$258$	5.16648e7	−	1.36407e8i	0.187295	−	0.494503i
$259$		0			0
$260$		−	5.24643e8i		−	1.85122i
$261$	−1.06774e8	+	1.20734e8i	−0.371728	+	0.420328i
$262$		−	4.42178e8i		−	1.51895i
$263$		−	2.53072e8i		−	0.857824i	−0.903346	−	0.428912i	$-0.858897\pi$
$263$		−	2.53072e8i		−	0.857824i	0.903346	−	0.428912i	$-0.141103\pi$
$264$	1.77040e8	+	6.70547e7i	0.592186	+	0.224293i
$265$			2.53250e8i			0.835966i
$266$		0			0
$267$	−1.93781e8	−	7.33953e7i	−0.623048	−	0.235982i
$268$	7.55495e8			2.39751
$269$	5.61342e8			1.75831			0.879153	−	0.476540i	$-0.158109\pi$
$269$	5.61342e8			1.75831			0.879153	+	0.476540i	$0.158109\pi$
$270$	6.45153e8	−	3.39674e8i	1.99476	−	1.05024i
$271$			4.66736e8i			1.42455i	0.701899	+	0.712277i	$0.252336\pi$
$271$			4.66736e8i			1.42455i	−0.701899	+	0.712277i	$0.747664\pi$
$272$	−4.69958e8			−1.41602
$273$		0			0
$274$	−4.02039e8			−1.18070
$275$			4.42358e7i			0.128265i
$276$	−5.11150e8	+	1.34956e9i	−1.46341	+	3.86376i
$277$	1.28270e8			0.362615			0.181307	−	0.983426i	$-0.441967\pi$
$277$	1.28270e8			0.362615			0.181307	+	0.983426i	$0.441967\pi$
$278$	−8.72987e8			−2.43698
$279$	−2.63861e8	+	2.98359e8i	−0.727379	+	0.822477i
$280$		0			0
$281$			3.38344e7i			0.0909675i	0.998965	+	0.0454837i	$0.0144829\pi$
$281$			3.38344e7i			0.0909675i	−0.998965	+	0.0454837i	$0.985517\pi$
$282$	1.30219e8	−	3.43808e8i	0.345781	−	0.912944i
$283$		−	2.66184e8i		−	0.698120i	−0.937100	−	0.349060i	$-0.886501\pi$
$283$		−	2.66184e8i		−	0.698120i	0.937100	−	0.349060i	$-0.113499\pi$
$284$			5.75164e8i			1.48997i
$285$	1.61783e8	−	4.27147e8i	0.413978	−	1.09300i
$286$		−	1.16496e8i		−	0.294462i
$287$		0			0
$288$	4.30121e8	−	4.86355e8i	1.06100	−	1.19972i
$289$	−2.46520e8			−0.600772
$290$	−5.25376e8			−1.26496
$291$	−5.71489e7	+	1.50887e8i	−0.135951	+	0.358943i
$292$		−	5.71588e8i		−	1.34352i
$293$	3.87975e8			0.901088			0.450544	−	0.892754i	$-0.351230\pi$
$293$	3.87975e8			0.901088			0.450544	+	0.892754i	$0.351230\pi$
$294$		0			0
$295$	−3.70928e8			−0.841227
$296$			1.45862e9i			3.26905i
$297$	1.00726e8	−	5.30326e7i	0.223098	−	0.117461i
$298$	−2.83300e8			−0.620139
$299$	5.13091e8			1.11006
$300$	5.26940e8	+	1.99581e8i	1.12677	+	0.426770i
$301$		0			0
$302$			1.08351e9i			2.26366i
$303$	5.90341e8	+	2.23594e8i	1.21914	+	0.461754i
$304$		−	1.04457e9i		−	2.13247i
$305$		−	1.29329e8i		−	0.261003i
$306$	−3.85051e8	+	4.35393e8i	−0.768234	+	0.868674i
$307$			2.45426e8i			0.484101i	0.970264	+	0.242051i	$0.0778200\pi$
$307$			2.45426e8i			0.484101i	−0.970264	+	0.242051i	$0.922180\pi$
$308$		0			0
$309$	4.43190e7	−	1.17013e8i	0.0854546	−	0.225620i
$310$	−1.29831e9			−2.47521
$311$	−5.06429e8			−0.954678			−0.477339	−	0.878719i	$-0.658399\pi$
$311$	−5.06429e8			−0.954678			−0.477339	+	0.878719i	$0.658399\pi$
$312$	−8.01792e8	−	3.03682e8i	−1.49459	−	0.566080i
$313$			3.28338e8i			0.605223i	0.953114	+	0.302611i	$0.0978584\pi$
$313$			3.28338e8i			0.605223i	−0.953114	+	0.302611i	$0.902142\pi$
$314$	7.78432e8			1.41895
$315$		0			0
$316$	1.29663e9			2.31160
$317$			7.22758e8i			1.27434i	0.770723	+	0.637170i	$0.219895\pi$
$317$			7.22758e8i			1.27434i	−0.770723	+	0.637170i	$0.780105\pi$
$318$	6.69859e8	+	2.53712e8i	1.16812	+	0.442431i
$319$	−8.20259e7			−0.141476
$320$	5.02808e8			0.857783
$321$	−1.38436e8	+	3.65503e8i	−0.233604	+	0.616770i
$322$		0			0
$323$			3.64119e8i			0.601222i
$324$	−1.77276e8	−	1.43913e9i	−0.289563	−	2.35068i
$325$		−	2.00338e8i		−	0.323722i
$326$		−	1.96051e9i		−	3.13406i
$327$	8.82477e8	+	3.34242e8i	1.39568	+	0.528620i
$328$		−	1.54453e9i		−	2.41678i
$329$		0			0
$330$	3.47005e8	+	1.31429e8i	0.531540	+	0.201323i
$331$	−4.38696e8			−0.664914			−0.332457	−	0.943118i	$-0.607878\pi$
$331$	−4.38696e8			−0.664914			−0.332457	+	0.943118i	$0.607878\pi$
$332$	1.09999e9			1.64970
$333$	6.57002e8	+	5.81037e8i	0.975016	+	0.862281i
$334$			5.68953e8i			0.835534i
$335$	8.55576e8			1.24337
$336$		0			0
$337$	−3.32774e8			−0.473636			−0.236818	−	0.971554i	$-0.576105\pi$
$337$	−3.32774e8			−0.473636			−0.236818	+	0.971554i	$0.576105\pi$
$338$		−	7.75341e8i		−	1.09215i
$339$	−1.78415e8	+	4.71057e8i	−0.248732	+	0.656711i
$340$	−1.33216e9			−1.83814
$341$	−2.02702e8			−0.276833
$342$	−9.67747e8	−	8.55852e8i	−1.30819	−	1.15693i
$343$		0			0
$344$		−	5.46336e8i		−	0.723611i
$345$	−5.78863e8	+	1.52833e9i	−0.758943	+	2.00379i
$346$			1.31421e9i			1.70568i
$347$			1.44259e9i			1.85348i	0.375700	+	0.926741i	$0.377402\pi$
$347$			1.44259e9i			1.85348i	−0.375700	+	0.926741i	$0.622598\pi$
$348$	−3.70080e8	+	9.77098e8i	−0.470726	+	1.24283i
$349$			7.76311e8i			0.977568i	0.872405	+	0.488784i	$0.162559\pi$
$349$			7.76311e8i			0.977568i	−0.872405	+	0.488784i	$0.837441\pi$
$350$		0			0
$351$	−4.56177e8	+	2.40178e8i	−0.563065	+	0.296455i
$352$	3.30426e8			0.403808
$353$	2.37025e7			0.0286802			0.0143401	−	0.999897i	$-0.495435\pi$
$353$	2.37025e7			0.0286802			0.0143401	+	0.999897i	$0.495435\pi$
$354$	−3.71605e8	+	9.81126e8i	−0.445216	+	1.17547i
$355$			6.51357e8i			0.772715i
$356$	−1.34329e9			−1.57795
$357$		0			0
$358$	−4.25920e8			−0.490611
$359$		−	9.81756e7i		−	0.111988i	−0.998431	−	0.0559942i	$-0.982167\pi$
$359$		−	9.81756e7i		−	0.111988i	0.998431	−	0.0559942i	$-0.0178328\pi$
$360$	1.80915e9	−	2.04568e9i	2.04369	−	2.31088i
$361$	8.45447e7			0.0945826
$362$	1.38138e8			0.153050
$363$	−7.98066e8	−	3.02271e8i	−0.875721	−	0.331683i
$364$		0			0
$365$		−	6.47307e8i		−	0.696764i
$366$	−3.42081e8	−	1.29565e8i	−0.364708	−	0.138135i
$367$			1.69767e9i			1.79276i	0.443291	+	0.896378i	$0.353811\pi$
$367$			1.69767e9i			1.79276i	−0.443291	+	0.896378i	$0.646189\pi$
$368$			3.73750e9i			3.90943i
$369$	−6.95696e8	−	6.15257e8i	−0.720821	−	0.637477i
$370$			2.85895e9i			2.93427i
$371$		0			0
$372$	−9.14542e8	+	2.41461e9i	−0.921093	+	2.43190i
$373$	1.86808e7			0.0186386			0.00931932	−	0.999957i	$-0.497034\pi$
$373$	1.86808e7			0.0186386			0.00931932	+	0.999957i	$0.497034\pi$
$374$	−2.95803e8			−0.292383
$375$	−5.76275e8	−	2.18266e8i	−0.564313	−	0.213736i
$376$		−	1.37701e9i		−	1.33592i
$377$	3.71485e8			0.357064
$378$		0			0
$379$	1.03410e9			0.975719			0.487860	−	0.872922i	$-0.337778\pi$
$379$	1.03410e9			0.975719			0.487860	+	0.872922i	$0.337778\pi$
$380$		−	2.96098e9i		−	2.76817i
$381$	−1.84062e9	−	6.97144e8i	−1.70501	−	0.645780i
$382$	2.86950e9			2.63381
$383$	6.16484e8			0.560694			0.280347	−	0.959899i	$-0.409550\pi$
$383$	6.16484e8			0.560694			0.280347	+	0.959899i	$0.409550\pi$
$384$	−1.25716e8	+	3.31920e8i	−0.113300	+	0.299139i
$385$		0			0
$386$		−	2.84208e9i		−	2.51525i
$387$	−2.46084e8	−	2.17631e8i	−0.215822	−	0.190867i
$388$			1.04594e9i			0.909071i
$389$		−	7.02287e8i		−	0.604910i	−0.953164	−	0.302455i	$-0.902194\pi$
$389$		−	7.02287e8i		−	0.604910i	0.953164	−	0.302455i	$-0.0978063\pi$
$390$	−1.57154e9	−	5.95227e8i	−1.34153	−	0.508108i
$391$		−	1.30282e9i		−	1.10222i
$392$		0			0
$393$	−9.31305e8	−	3.52736e8i	−0.773959	−	0.293140i
$394$	2.05684e8			0.169420
$395$	1.46840e9			1.19882
$396$	4.88867e8	−	5.52782e8i	0.395601	−	0.447322i
$397$		−	5.89861e8i		−	0.473133i	−0.971615	−	0.236566i	$-0.923978\pi$
$397$		−	5.89861e8i		−	0.473133i	0.971615	−	0.236566i	$-0.0760221\pi$
$398$	4.89151e8			0.388913
$399$		0			0
$400$	1.45932e9			1.14009
$401$		−	2.17272e8i		−	0.168267i	−0.996454	−	0.0841336i	$-0.973188\pi$
$401$		−	2.17272e8i		−	0.168267i	0.996454	−	0.0841336i	$-0.0268122\pi$
$402$	8.57138e8	−	2.26305e9i	0.658051	−	1.73741i
$403$	9.18013e8			0.698685
$404$	4.09224e9			3.08764
$405$	−2.00760e8	−	1.62977e9i	−0.150170	−	1.21909i
$406$		0			0
$407$			4.46362e8i			0.328176i
$408$	−7.71100e8	+	2.03588e9i	−0.562082	+	1.48403i
$409$		−	1.84741e9i		−	1.33515i	−0.744541	−	0.667577i	$-0.767331\pi$
$409$		−	1.84741e9i		−	1.33515i	0.744541	−	0.667577i	$-0.232669\pi$
$410$		−	3.02733e9i		−	2.16928i
$411$	−3.20716e8	+	8.46766e8i	−0.227863	+	0.601613i
$412$		−	8.11131e8i		−	0.571414i
$413$		0			0
$414$	3.46261e9	+	3.06225e9i	2.39829	+	2.12099i
$415$	1.24571e9			0.855553
$416$	−1.49646e9			−1.01915
$417$	−6.96403e8	+	1.83867e9i	−0.470310	+	1.24173i
$418$		−	6.57479e8i		−	0.440317i
$419$	2.39246e9			1.58890			0.794448	−	0.607333i	$-0.207760\pi$
$419$	2.39246e9			1.58890			0.794448	+	0.607333i	$0.207760\pi$
$420$		0			0
$421$	−2.88856e9			−1.88666			−0.943331	−	0.331853i	$-0.892326\pi$
$421$	−2.88856e9			−1.88666			−0.943331	+	0.331853i	$0.892326\pi$
$422$			1.80242e8i			0.116751i
$423$	−6.20243e8	−	5.48528e8i	−0.398447	−	0.352377i
$424$	2.68291e9			1.70933
$425$	−5.08692e8			−0.321435
$426$	1.72287e9	+	6.52545e8i	1.07974	+	0.408956i
$427$		0			0
$428$			2.53366e9i			1.56205i
$429$	−2.45361e8	−	9.29316e7i	−0.150039	−	0.0568280i
$430$		−	1.07084e9i		−	0.649506i
$431$		−	2.78813e9i		−	1.67742i	−0.544575	−	0.838712i	$-0.683309\pi$
$431$		−	2.78813e9i		−	1.67742i	0.544575	−	0.838712i	$-0.316691\pi$
$432$	−1.74952e9	−	3.32293e9i	−1.04406	−	1.98302i
$433$			2.17509e9i			1.28757i	0.765207	+	0.643784i	$0.222637\pi$
$433$			2.17509e9i			1.28757i	−0.765207	+	0.643784i	$0.777363\pi$
$434$		0			0
$435$	−4.19105e8	+	1.10654e9i	−0.244124	+	0.644544i
$436$	6.11732e9			3.53475
$437$	2.89578e9			1.65989
$438$	−1.71216e9	−	6.48488e8i	−0.973611	−	0.368759i
$439$		−	3.33046e9i		−	1.87879i	−0.342837	−	0.939395i	$-0.611388\pi$
$439$		−	3.33046e9i		−	1.87879i	0.342837	−	0.939395i	$-0.388612\pi$
$440$	1.38982e9			0.777808
$441$		0			0
$442$	1.33965e9			0.737928
$443$		−	5.69632e8i		−	0.311302i	−0.987812	−	0.155651i	$-0.950253\pi$
$443$		−	5.69632e8i		−	0.311302i	0.987812	−	0.155651i	$-0.0497475\pi$
$444$	5.31709e9	+	2.01387e9i	2.88293	+	1.09192i
$445$	−1.52124e9			−0.818345
$446$	−3.95904e9			−2.11309
$447$	−2.25995e8	+	5.96680e8i	−0.119680	+	0.315984i
$448$		0			0
$449$		−	3.83593e7i		−	0.0199990i	−0.999950	−	0.00999950i	$-0.996817\pi$
$449$		−	3.83593e7i		−	0.0199990i	0.999950	−	0.00999950i	$-0.00318299\pi$
$450$	1.19567e9	−	1.35199e9i	0.618537	−	0.699406i
$451$		−	4.72650e8i		−	0.242617i
$452$			3.26536e9i			1.66321i
$453$	2.28208e9	+	8.64345e8i	1.15342	+	0.436861i
$454$		−	6.36550e9i		−	3.19255i
$455$		0			0
$456$	−4.52515e9	−	1.71392e9i	−2.23489	−	0.846474i
$457$	−3.35569e8			−0.164466			−0.0822329	−	0.996613i	$-0.526205\pi$
$457$	−3.35569e8			−0.164466			−0.0822329	+	0.996613i	$0.526205\pi$
$458$	−5.91548e9			−2.87714
$459$	6.09852e8	+	1.15831e9i	0.294361	+	0.559089i
$460$			1.05944e10i			5.07486i
$461$	−1.91384e9			−0.909815			−0.454907	−	0.890539i	$-0.650328\pi$
$461$	−1.91384e9			−0.909815			−0.454907	+	0.890539i	$0.650328\pi$
$462$		0			0
$463$	2.37251e9			1.11090			0.555450	−	0.831550i	$-0.312546\pi$
$463$	2.37251e9			1.11090			0.555450	+	0.831550i	$0.312546\pi$
$464$			2.70600e9i			1.25752i
$465$	−1.03569e9	+	2.73447e9i	−0.477689	+	1.26121i
$466$	−8.82337e6			−0.00403909
$467$	1.68770e9			0.766809			0.383404	−	0.923581i	$-0.374752\pi$
$467$	1.68770e9			0.766809			0.383404	+	0.923581i	$0.374752\pi$
$468$	−2.21402e9	+	2.50348e9i	−0.998436	+	1.12897i
$469$		0			0
$470$		−	2.69899e9i		−	1.19911i
$471$	6.20973e8	−	1.63952e9i	0.273842	−	0.723007i
$472$			3.92958e9i			1.72008i
$473$		−	1.67187e8i		−	0.0726423i
$474$	1.47108e9	−	3.88400e9i	0.634471	−	1.67515i
$475$		−	1.13067e9i		−	0.484069i
$476$		0			0
$477$	1.06873e9	−	1.20845e9i	0.450871	−	0.509818i
$478$	−3.31419e9			−1.38797
$479$	2.55452e9			1.06202			0.531012	−	0.847364i	$-0.321812\pi$
$479$	2.55452e9			1.06202			0.531012	+	0.847364i	$0.321812\pi$
$480$	1.68828e9	−	4.45747e9i	0.696789	−	1.83969i
$481$		−	2.02151e9i		−	0.828265i
$482$	1.61894e9			0.658516
$483$		0			0
$484$	−5.53219e9			−2.21788
$485$			1.18450e9i			0.471454i
$486$	−4.51197e9	−	1.10173e9i	−1.78295	−	0.435358i
$487$	2.78226e9			1.09156			0.545778	−	0.837930i	$-0.316234\pi$
$487$	2.78226e9			1.09156			0.545778	+	0.837930i	$0.316234\pi$
$488$	−1.37010e9			−0.533681
$489$	−4.12918e9	−	1.56394e9i	−1.59692	−	0.604840i
$490$		0			0
$491$		−	4.40912e9i		−	1.68100i	−0.541815	−	0.840498i	$-0.682263\pi$
$491$		−	4.40912e9i		−	1.68100i	0.541815	−	0.840498i	$-0.317737\pi$
$492$	−5.63025e9	−	2.13248e9i	−2.13132	−	0.807248i
$493$		−	9.43261e8i		−	0.354542i
$494$			2.97764e9i			1.11129i
$495$	5.53628e8	−	6.26009e8i	0.205163	−	0.231986i
$496$			6.68707e9i			2.46065i
$497$		0			0
$498$	1.24798e9	−	3.29496e9i	0.452798	−	1.19549i
$499$	8.76642e8			0.315842			0.157921	−	0.987452i	$-0.449521\pi$
$499$	8.76642e8			0.315842			0.157921	+	0.987452i	$0.449521\pi$
$500$	−3.99473e9			−1.42920
$501$	1.19832e9	+	4.53868e8i	0.425736	+	0.161249i
$502$			2.25630e8i			0.0796039i
$503$	−2.66652e9			−0.934235			−0.467118	−	0.884195i	$-0.654708\pi$
$503$	−2.66652e9			−0.934235			−0.467118	+	0.884195i	$0.654708\pi$
$504$		0			0
$505$	4.63434e9			1.60128
$506$			2.35247e9i			0.807229i
$507$	−1.63301e9	−	6.18508e8i	−0.556494	−	0.210774i
$508$	−1.27592e10			−4.31817
$509$	−5.29487e9			−1.77969			−0.889843	−	0.456267i	$-0.849186\pi$
$509$	−5.29487e9			−1.77969			−0.889843	+	0.456267i	$0.849186\pi$
$510$	−1.51138e9	+	3.99040e9i	−0.504520	+	1.33205i
$511$		0			0
$512$			6.19340e9i			2.03931i
$513$	−2.57457e9	+	1.35552e9i	−0.841966	+	0.443296i
$514$		−	1.69613e9i		−	0.550919i
$515$		−	9.18582e8i		−	0.296342i
$516$	−1.99155e9	−	7.54307e8i	−0.638142	−	0.241699i
$517$		−	4.21388e8i		−	0.134111i
$518$		0			0
$519$	2.76796e9	+	1.04838e9i	0.869109	+	0.329179i
$520$	−6.29429e9			−1.96307
$521$	−4.10919e9			−1.27299			−0.636494	−	0.771282i	$-0.719616\pi$
$521$	−4.10919e9			−1.27299			−0.636494	+	0.771282i	$0.719616\pi$
$522$	2.50698e9	+	2.21711e9i	0.771442	+	0.682245i
$523$			5.01077e9i			1.53161i	0.643073	+	0.765805i	$0.277659\pi$
$523$			5.01077e9i			1.53161i	−0.643073	+	0.765805i	$0.722341\pi$
$524$	−6.45580e9			−1.96016
$525$		0			0
$526$	−5.25488e9			−1.57439
$527$		−	2.33099e9i		−	0.693750i
$528$	6.76940e8	−	1.78728e9i	0.200139	−	0.528414i
$529$	−6.95630e9			−2.04307
$530$	5.25858e9			1.53428
$531$	1.76999e9	+	1.56533e9i	0.513026	+	0.453708i
$532$		0			0
$533$			2.14057e9i			0.612329i
$534$	−1.52401e9	+	4.02375e9i	−0.433106	+	1.14350i
$535$			2.86930e9i			0.810098i
$536$		−	9.06390e9i		−	2.54237i
$537$	−3.39766e8	+	8.97063e8i	−0.0946826	+	0.249984i
$538$		−	1.16559e10i		−	3.22707i
$539$		0			0
$540$	−4.95924e9	−	9.41925e9i	−1.35531	−	2.57417i
$541$	4.68219e9			1.27133			0.635665	−	0.771965i	$-0.280726\pi$
$541$	4.68219e9			1.27133			0.635665	+	0.771965i	$0.280726\pi$
$542$	9.69150e9			2.61453
$543$	1.10196e8	−	2.90944e8i	0.0295371	−	0.0779849i
$544$			3.79975e9i			1.01195i
$545$	6.92769e9			1.83316
$546$		0			0
$547$	1.79128e9			0.467958			0.233979	−	0.972242i	$-0.424825\pi$
$547$	1.79128e9			0.467958			0.233979	+	0.972242i	$0.424825\pi$
$548$			5.86977e9i			1.52366i
$549$	−5.45772e8	+	6.17127e8i	−0.140769	+	0.159174i
$550$	9.18530e8			0.235409
$551$	2.09658e9			0.533927
$552$	1.61910e10	+	6.13242e9i	4.09721	+	1.55183i
$553$		0			0
$554$		−	2.66345e9i		−	0.665519i
$555$	6.02145e9	+	2.28065e9i	1.49512	+	0.566282i
$556$			1.27456e10i			3.14485i
$557$		−	2.56562e9i		−	0.629069i	−0.949246	−	0.314535i	$-0.898152\pi$
$557$		−	2.56562e9i		−	0.629069i	0.949246	−	0.314535i	$-0.101848\pi$
$558$	6.19524e9	+	5.47892e9i	1.50952	+	1.33498i
$559$			7.57170e8i			0.183338i
$560$		0			0
$561$	−2.35969e8	+	6.23013e8i	−0.0564267	+	0.148980i
$562$	7.02551e8			0.166956
$563$	6.11987e9			1.44532			0.722658	−	0.691206i	$-0.242920\pi$
$563$	6.11987e9			1.44532			0.722658	+	0.691206i	$0.242920\pi$
$564$	−5.01960e9	−	1.90119e9i	−1.17813	−	0.446221i
$565$			3.69793e9i			0.862559i
$566$	−5.52716e9			−1.28128
$567$		0			0
$568$	6.90041e9			1.58000
$569$		−	7.66269e9i		−	1.74377i	−0.489714	−	0.871883i	$-0.662899\pi$
$569$		−	7.66269e9i		−	1.74377i	0.489714	−	0.871883i	$-0.337101\pi$
$570$	−8.86945e9	−	3.35934e9i	−2.00602	−	0.759787i
$571$	2.20883e9			0.496520			0.248260	−	0.968693i	$-0.420141\pi$
$571$	2.20883e9			0.496520			0.248260	+	0.968693i	$0.420141\pi$
$572$	−1.70084e9			−0.379995
$573$	2.28907e9	−	6.04369e9i	0.508297	−	1.34203i
$574$		0			0
$575$			4.04554e9i			0.887440i
$576$	−2.39929e9	−	2.12187e9i	−0.523123	−	0.462638i
$577$		−	8.82063e9i		−	1.91154i	−0.294109	−	0.955772i	$-0.595023\pi$
$577$		−	8.82063e9i		−	1.91154i	0.294109	−	0.955772i	$-0.404977\pi$
$578$			5.11884e9i			1.10262i
$579$	−5.98592e9	−	2.26719e9i	−1.28161	−	0.485415i
$580$			7.67049e9i			1.63240i
$581$		0			0
$582$	3.13307e9	+	1.18666e9i	0.658779	+	0.249515i
$583$	8.21012e8			0.171597
$584$	−6.85752e9			−1.42469
$585$	−2.50731e9	+	2.83512e9i	−0.517800	+	0.585498i
$586$		−	8.05608e9i		−	1.65380i
$587$	2.02419e9			0.413064			0.206532	−	0.978440i	$-0.433782\pi$
$587$	2.02419e9			0.413064			0.206532	+	0.978440i	$0.433782\pi$
$588$		0			0
$589$	5.18108e9			1.04476
$590$			7.70211e9i			1.54393i
$591$	1.64079e8	−	4.33208e8i	0.0326962	−	0.0863257i
$592$	1.47253e10			2.91701
$593$	−6.17648e9			−1.21632			−0.608162	−	0.793813i	$-0.708093\pi$
$593$	−6.17648e9			−1.21632			−0.608162	+	0.793813i	$0.708093\pi$
$594$	−1.10119e9	−	2.09153e9i	−0.215581	−	0.409459i
$595$		0			0
$596$			4.13618e9i			0.800272i
$597$	3.90208e8	−	1.03024e9i	0.0750561	−	0.198166i
$598$		−	1.06540e10i		−	2.03732i
$599$		−	1.93063e9i		−	0.367034i	−0.983017	−	0.183517i	$-0.941252\pi$
$599$		−	1.93063e9i		−	0.367034i	0.983017	−	0.183517i	$-0.0587482\pi$
$600$	2.39443e9	−	6.32185e9i	0.452556	−	1.19485i
$601$		−	2.31165e9i		−	0.434371i	−0.976130	−	0.217186i	$-0.930312\pi$
$601$		−	2.31165e9i		−	0.434371i	0.976130	−	0.217186i	$-0.0696877\pi$
$602$		0			0
$603$	−4.08262e9	−	3.61057e9i	−0.758278	−	0.670603i
$604$	1.58193e10			2.92118
$605$	−6.26504e9			−1.15022
$606$	4.64280e9	−	1.22581e10i	0.847472	−	2.23753i
$607$			1.47091e9i			0.266947i	0.991052	+	0.133474i	$0.0426132\pi$
$607$			1.47091e9i			0.266947i	−0.991052	+	0.133474i	$0.957387\pi$
$608$	−8.44570e9			−1.52396
$609$		0			0
$610$	−2.68543e9			−0.479027
$611$			1.90841e9i			0.338476i
$612$	6.35675e9	+	5.62176e9i	1.12100	+	0.991384i
$613$	6.52558e9			1.14422			0.572108	−	0.820179i	$-0.306126\pi$
$613$	6.52558e9			1.14422			0.572108	+	0.820179i	$0.306126\pi$
$614$	5.09613e9			0.888487
$615$	−6.37609e9	−	2.41497e9i	−1.10533	−	0.418648i
$616$		0			0
$617$		−	2.15423e8i		−	0.0369228i	−0.999830	−	0.0184614i	$-0.994123\pi$
$617$		−	2.15423e8i		−	0.0369228i	0.999830	−	0.0184614i	$-0.00587678\pi$
$618$	−2.42970e9	−	9.20258e8i	−0.414088	−	0.156838i
$619$			8.91605e9i			1.51097i	0.655167	+	0.755484i	$0.272598\pi$
$619$			8.91605e9i			1.51097i	−0.655167	+	0.755484i	$0.727402\pi$
$620$			1.89553e10i			3.19419i
$621$	9.21185e9	−	4.85005e9i	1.54357	−	0.812691i
$622$			1.05157e10i			1.75215i
$623$		0			0
$624$	−3.06577e9	+	8.09437e9i	−0.505119	+	1.33363i
$625$	−7.62893e9			−1.24992
$626$	6.81774e9			1.11078
$627$	−1.38477e9	−	5.24487e8i	−0.224358	−	0.0849764i
$628$		−	1.13651e10i		−	1.83111i
$629$	−5.13296e9			−0.822415
$630$		0			0
$631$	2.86880e9			0.454567			0.227284	−	0.973829i	$-0.427016\pi$
$631$	2.86880e9			0.454567			0.227284	+	0.973829i	$0.427016\pi$
$632$		−	1.55561e10i		−	2.45127i
$633$	3.79621e8	+	1.43783e8i	0.0594891	+	0.0225317i
$634$	1.50076e10			2.33884
$635$	−1.44494e10			−2.23945
$636$	3.70420e9	−	9.77996e9i	0.570945	−	1.50743i
$637$		0			0
$638$			1.70322e9i			0.259656i
$639$	2.74875e9	−	3.10813e9i	0.416757	−	0.471244i
$640$			2.60566e9i			0.392906i
$641$		−	7.55117e9i		−	1.13243i	−0.824258	−	0.566215i	$-0.808407\pi$
$641$		−	7.55117e9i		−	1.13243i	0.824258	−	0.566215i	$-0.191593\pi$
$642$	7.58945e9	+	2.87454e9i	1.13198	+	0.428741i
$643$			1.35180e7i			0.00200528i	0.999999	+	0.00100264i	$0.000319150\pi$
$643$			1.35180e7i			0.00200528i	−0.999999	+	0.00100264i	$0.999681\pi$
$644$		0			0
$645$	−2.25537e9	−	8.54231e8i	−0.330947	−	0.125348i
$646$	7.56073e9			1.10344
$647$	−1.65844e8			−0.0240733			−0.0120367	−	0.999928i	$-0.503831\pi$
$647$	−1.65844e8			−0.0240733			−0.0120367	+	0.999928i	$0.503831\pi$
$648$	−1.72657e10	+	2.12683e9i	−2.49271	+	0.307058i
$649$			1.20252e9i			0.172677i
$650$	−4.15990e9			−0.594137
$651$		0			0
$652$	−2.86235e10			−4.04441
$653$		−	9.63138e9i		−	1.35361i	−0.736164	−	0.676803i	$-0.763365\pi$
$653$		−	9.63138e9i		−	1.35361i	0.736164	−	0.676803i	$-0.236635\pi$
$654$	6.94033e9	−	1.83241e10i	0.970193	−	2.56154i
$655$	−7.31101e9			−1.01656
$656$	−1.55925e10			−2.15652
$657$	−2.73167e9	+	3.08881e9i	−0.375793	+	0.424925i
$658$		0			0
$659$		−	5.54548e9i		−	0.754814i	−0.926048	−	0.377407i	$-0.876816\pi$
$659$		−	5.54548e9i		−	0.754814i	0.926048	−	0.377407i	$-0.123184\pi$
$660$	1.91887e9	−	5.06627e9i	0.259802	−	0.685938i
$661$			1.79370e9i			0.241571i	0.992679	+	0.120785i	$0.0385413\pi$
$661$			1.79370e9i			0.241571i	−0.992679	+	0.120785i	$0.961459\pi$
$662$			9.10926e9i			1.22034i
$663$	1.06867e9	−	2.82155e9i	0.142412	−	0.376002i
$664$		−	1.31969e10i		−	1.74938i
$665$		0			0
$666$	1.20649e10	−	1.36423e10i	1.58257	−	1.78948i
$667$	−7.50160e9			−0.978844
$668$	8.30673e9			1.07823
$669$	−3.15822e9	+	8.33844e9i	−0.407803	+	1.07670i
$670$		−	1.77655e10i		−	2.28201i
$671$	−4.19271e8			−0.0535755
$672$		0			0
$673$	−9.01100e9			−1.13952			−0.569758	−	0.821813i	$-0.692963\pi$
$673$	−9.01100e9			−1.13952			−0.569758	+	0.821813i	$0.692963\pi$
$674$			6.90986e9i			0.869280i
$675$	−1.89372e9	−	3.59680e9i	−0.237002	−	0.450146i
$676$	−1.13200e10			−1.40939
$677$	5.17968e9			0.641567			0.320784	−	0.947152i	$-0.396054\pi$
$677$	5.17968e9			0.641567			0.320784	+	0.947152i	$0.396054\pi$
$678$	9.78122e9	+	3.70468e9i	1.20528	+	0.456506i
$679$		0			0
$680$			1.59823e10i			1.94920i
$681$	−1.34069e10	−	5.07791e9i	−1.62672	−	0.616127i
$682$			4.20900e9i			0.508081i
$683$		−	4.37372e9i		−	0.525265i	−0.964896	−	0.262633i	$-0.915409\pi$
$683$		−	4.37372e9i		−	0.525265i	0.964896	−	0.262633i	$-0.0845907\pi$
$684$	−1.24955e10	+	1.41291e10i	−1.49299	+	1.68818i
$685$			6.64735e9i			0.790190i
$686$		0			0
$687$	−4.71892e9	+	1.24591e10i	−0.555257	+	1.46601i
$688$	−5.51545e9			−0.645686
$689$	−3.71826e9			−0.433084
$690$	3.17350e10	+	1.20197e10i	3.67762	+	1.39291i
$691$			4.68467e9i			0.540139i	0.962841	+	0.270070i	$0.0870467\pi$
$691$			4.68467e9i			0.540139i	−0.962841	+	0.270070i	$0.912953\pi$
$692$	1.91875e10			2.20114
$693$		0			0
$694$	2.99544e10			3.40176
$695$			1.44341e10i			1.63095i
$696$	1.17225e10	+	4.43996e9i	1.31792	+	0.499168i
$697$	5.43527e9			0.608004
$698$	1.61196e10			1.79416
$699$	−7.03861e6	+	1.85836e7i	−0.000779501	+	0.00205807i
$700$		0			0
$701$		−	5.56974e8i		−	0.0610692i	−0.999534	−	0.0305346i	$-0.990279\pi$
$701$		−	5.56974e8i		−	0.0610692i	0.999534	−	0.0305346i	$-0.00972098\pi$
$702$	4.98715e9	+	9.47225e9i	0.544092	+	1.03341i
$703$		−	1.14090e10i		−	1.23852i
$704$		−	1.63006e9i		−	0.176075i
$705$	−5.68455e9	−	2.15305e9i	−0.610991	−	0.231415i
$706$		−	4.92169e8i		−	0.0526378i
$707$		0			0
$708$	1.43245e10	+	5.42544e9i	1.51692	+	0.574538i
$709$	3.88299e9			0.409171			0.204585	−	0.978849i	$-0.434415\pi$
$709$	3.88299e9			0.409171			0.204585	+	0.978849i	$0.434415\pi$
$710$	1.35250e10			1.41819
$711$	−7.00688e9	−	6.19671e9i	−0.731107	−	0.646573i
$712$			1.61158e10i			1.67330i
$713$	−1.85380e10			−1.91535
$714$		0			0
$715$	−1.92615e9			−0.197070
$716$			6.21844e9i			0.633119i
$717$	−2.64381e9	+	6.98028e9i	−0.267863	+	0.707222i
$718$	−2.03856e9			−0.205536
$719$	1.64202e10			1.64751			0.823756	−	0.566944i	$-0.191875\pi$
$719$	1.64202e10			1.64751			0.823756	+	0.566944i	$0.191875\pi$
$720$	−2.06518e10	−	1.82639e10i	−2.06203	−	1.82361i
$721$		0			0
$722$		−	1.75552e9i		−	0.173591i
$723$	1.29147e9	−	3.40978e9i	0.127086	−	0.335538i
$724$		−	2.01682e9i		−	0.197507i
$725$			2.92903e9i			0.285457i
$726$	−6.27648e9	+	1.65714e10i	−0.608748	+	1.60724i
$727$			4.75159e9i			0.458636i	0.973351	+	0.229318i	$0.0736497\pi$
$727$			4.75159e9i			0.458636i	−0.973351	+	0.229318i	$0.926350\pi$
$728$		0			0
$729$	−5.91974e9	+	8.62414e9i	−0.565921	+	0.824459i
$730$	−1.34410e10			−1.27879
$731$	1.92258e9			0.182043
$732$	−1.89164e9	+	4.99439e9i	−0.178259	+	0.470645i
$733$			6.95925e9i			0.652677i	0.945253	+	0.326338i	$0.105815\pi$
$733$			6.95925e9i			0.652677i	−0.945253	+	0.326338i	$0.894185\pi$
$734$	3.52510e10			3.29030
$735$		0			0
$736$	3.02188e10			2.79386
$737$		−	2.77370e9i		−	0.255225i
$738$	−1.27754e10	+	1.44457e10i	−1.16998	+	1.32295i
$739$	−5.47550e9			−0.499078			−0.249539	−	0.968365i	$-0.580279\pi$
$739$	−5.47550e9			−0.499078			−0.249539	+	0.968365i	$0.580279\pi$
$740$	4.17407e10			3.78659
$741$	6.27144e9	+	2.37533e9i	0.566244	+	0.214467i
$742$		0			0
$743$			1.33440e10i			1.19351i	0.802424	+	0.596755i	$0.203543\pi$
$743$			1.33440e10i			1.19351i	−0.802424	+	0.596755i	$0.796457\pi$
$744$	2.89688e10	+	1.09720e10i	2.57884	+	0.976746i
$745$			4.68410e9i			0.415030i
$746$		−	3.87895e8i		−	0.0342081i
$747$	−5.94423e9	−	5.25693e9i	−0.521763	−	0.461435i
$748$			4.31872e9i			0.377311i
$749$		0			0
$750$	−4.53217e9	+	1.19660e10i	−0.392276	+	1.03570i
$751$	−1.20933e10			−1.04185			−0.520926	−	0.853602i	$-0.674413\pi$
$751$	−1.20933e10			−1.04185			−0.520926	+	0.853602i	$0.674413\pi$
$752$	−1.39014e10			−1.19206
$753$	4.75218e8	+	1.79991e8i	0.0405612	+	0.0153627i
$754$		−	7.71366e9i		−	0.655331i
$755$	1.79149e10			1.51496
$756$		0			0
$757$	−5.16465e9			−0.432719			−0.216359	−	0.976314i	$-0.569418\pi$
$757$	−5.16465e9			−0.432719			−0.216359	+	0.976314i	$0.569418\pi$
$758$		−	2.14725e10i		−	1.79077i
$759$	4.95472e9	+	1.87662e9i	0.411313	+	0.155787i
$760$	−3.55237e10			−2.93542
$761$	−5.85978e9			−0.481987			−0.240993	−	0.970527i	$-0.577473\pi$
$761$	−5.85978e9			−0.481987			−0.240993	+	0.970527i	$0.577473\pi$
$762$	−1.44758e10	+	3.82195e10i	−1.18522	+	3.12926i
$763$		0			0
$764$		−	4.18948e10i		−	3.39886i
$765$	7.19883e9	+	6.36647e9i	0.581363	+	0.514143i
$766$		−	1.28009e10i		−	1.02906i
$767$		−	5.44604e9i		−	0.435810i
$768$	1.50905e10	+	5.71558e9i	1.20210	+	0.455298i
$769$			1.46138e10i			1.15883i	0.815033	+	0.579415i	$0.196719\pi$
$769$			1.46138e10i			1.15883i	−0.815033	+	0.579415i	$0.803281\pi$
$770$		0			0
$771$	−3.57235e9	−	1.35304e9i	−0.280714	−	0.106321i
$772$	−4.14944e10			−3.24585
$773$	1.42212e10			1.10741			0.553706	−	0.832712i	$-0.313213\pi$
$773$	1.42212e10			1.10741			0.553706	+	0.832712i	$0.313213\pi$
$774$	−4.51897e9	+	5.10979e9i	−0.350305	+	0.396104i
$775$			7.23822e9i			0.558567i
$776$	1.25485e10			0.963998
$777$		0			0
$778$	−1.45826e10			−1.11021
$779$			1.20810e10i			0.915631i
$780$	−8.69032e9	+	2.29445e10i	−0.655699	+	1.73120i
$781$	2.11164e9			0.158614
$782$	−2.70524e10			−2.02293
$783$	6.66950e9	−	3.51150e9i	0.496509	−	0.261413i
$784$		0			0
$785$		−	1.28707e10i		−	0.949636i
$786$	−7.32435e9	+	1.93380e10i	−0.538010	+	1.42047i
$787$		−	1.44143e10i		−	1.05410i	−0.849833	−	0.527052i	$-0.823297\pi$
$787$		−	1.44143e10i		−	1.05410i	0.849833	−	0.527052i	$-0.176703\pi$
$788$		−	3.00299e9i		−	0.218631i
$789$	−4.19194e9	+	1.10677e10i	−0.303841	+	0.802211i
$790$		−	3.04905e10i		−	2.20024i
$791$		0			0
$792$	−6.63189e9	−	5.86508e9i	−0.474350	−	0.419504i
$793$	1.89882e9			0.135216
$794$	−1.22481e10			−0.868356
$795$	4.19490e9	−	1.10755e10i	0.296099	−	0.781770i
$796$		−	7.14162e9i		−	0.501881i
$797$	−8.69993e9			−0.608712			−0.304356	−	0.952558i	$-0.598441\pi$
$797$	−8.69993e9			−0.608712			−0.304356	+	0.952558i	$0.598441\pi$
$798$		0			0
$799$	4.84578e9			0.336085
$800$		−	1.17990e10i		−	0.814764i
$801$	7.25900e9	+	6.41968e9i	0.499072	+	0.441367i
$802$	−4.51153e9			−0.308826
$803$	−2.09851e9			−0.143023
$804$	−3.30405e10	−	1.25142e10i	−2.24208	−	0.849196i
$805$		0			0
$806$		−	1.90620e10i		−	1.28232i
$807$	−2.45495e10	−	9.29821e9i	−1.64431	−	0.622791i
$808$		−	4.90958e10i		−	3.27419i
$809$		−	7.73407e9i		−	0.513557i	−0.966470	−	0.256778i	$-0.917339\pi$
$809$		−	7.73407e9i		−	0.513557i	0.966470	−	0.256778i	$-0.0826611\pi$
$810$	−3.38413e10	+	4.16866e9i	−2.23743	+	0.275613i
$811$		−	2.54241e9i		−	0.167368i	−0.996492	−	0.0836841i	$-0.973331\pi$
$811$		−	2.54241e9i		−	0.167368i	0.996492	−	0.0836841i	$-0.0266687\pi$
$812$		0			0
$813$	7.73114e9	−	2.04120e10i	0.504576	−	1.33220i
$814$	9.26844e9			0.602311
$815$	−3.24152e10			−2.09748
$816$	2.05530e10	+	7.78451e9i	1.32422	+	0.501552i
$817$			4.27332e9i			0.274150i
$818$	−3.83604e10			−2.45045
$819$		0			0
$820$	−4.41990e10			−2.79939
$821$		−	2.73759e10i		−	1.72650i	−0.504776	−	0.863250i	$-0.668425\pi$
$821$		−	2.73759e10i		−	1.72650i	0.504776	−	0.863250i	$-0.331575\pi$
$822$	1.75826e10	+	6.65948e9i	1.10416	+	0.418205i
$823$	1.01376e10			0.633922			0.316961	−	0.948439i	$-0.397338\pi$
$823$	1.01376e10			0.633922			0.316961	+	0.948439i	$0.397338\pi$
$824$	−9.73138e9			−0.605939
$825$	7.32733e8	−	1.93459e9i	0.0454315	−	0.119950i
$826$		0			0
$827$			1.43439e10i			0.881858i	0.897542	+	0.440929i	$0.145351\pi$
$827$			1.43439e10i			0.881858i	−0.897542	+	0.440929i	$0.854649\pi$
$828$	4.47089e10	−	5.05541e10i	2.73708	−	3.09493i
$829$			1.74580e10i			1.06428i	0.846658	+	0.532138i	$0.178611\pi$
$829$			1.74580e10i			1.06428i	−0.846658	+	0.532138i	$0.821389\pi$
$830$		−	2.58663e10i		−	1.57022i
$831$	−5.60970e9	−	2.12470e9i	−0.339107	−	0.128438i
$832$			7.38232e9i			0.444387i
$833$		0			0
$834$	3.81789e10	+	1.44604e10i	2.27899	+	0.863175i
$835$	9.40713e9			0.559184
$836$	−9.59921e9			−0.568216
$837$	1.64817e10	−	8.67762e9i	0.971544	−	0.511519i
$838$		−	4.96780e10i		−	2.91615i
$839$	2.21478e10			1.29468			0.647341	−	0.762200i	$-0.275881\pi$
$839$	2.21478e10			1.29468			0.647341	+	0.762200i	$0.275881\pi$
$840$		0			0
$841$	1.18186e10			0.685142
$842$			5.99793e10i			3.46265i
$843$	5.60442e8	−	1.47970e9i	0.0322206	−	0.0850701i
$844$	2.63153e9			0.150664
$845$	−1.28196e10			−0.730928
$846$	−1.13899e10	+	1.28790e10i	−0.646728	+	0.731282i
$847$		0			0
$848$		−	2.70849e10i		−	1.52525i
$849$	−4.40915e9	+	1.16412e10i	−0.247274	+	0.652861i
$850$			1.05627e10i			0.589941i
$851$			4.08216e10i			2.27058i
$852$	9.52717e9	−	2.51540e10i	0.527746	−	1.39338i
$853$			2.54298e10i			1.40288i	0.712727	+	0.701442i	$0.247460\pi$
$853$			2.54298e10i			1.40288i	−0.712727	+	0.701442i	$0.752540\pi$
$854$		0			0
$855$	−1.41507e10	+	1.60008e10i	−0.774279	+	0.875510i
$856$	3.03971e10			1.65643
$857$	1.03844e10			0.563571			0.281786	−	0.959477i	$-0.409073\pi$
$857$	1.03844e10			0.563571			0.281786	+	0.959477i	$0.409073\pi$
$858$	−1.92967e9	+	5.09478e9i	−0.104298	+	0.275372i
$859$		−	1.97174e9i		−	0.106139i	−0.998591	−	0.0530694i	$-0.983100\pi$
$859$		−	1.97174e9i		−	0.106139i	0.998591	−	0.0530694i	$-0.0169005\pi$
$860$	−1.56342e10			−0.838169
$861$		0			0
$862$	−5.78939e10			−3.07863
$863$			1.72039e10i			0.911149i	0.890198	+	0.455574i	$0.150566\pi$
$863$			1.72039e10i			0.911149i	−0.890198	+	0.455574i	$0.849434\pi$
$864$	−2.68668e10	+	1.41454e10i	−1.41716	+	0.746136i
$865$	2.17293e10			1.14153
$866$	4.51645e10			2.36312
$867$	1.07812e10	+	4.08342e9i	0.561824	+	0.212793i
$868$		0			0
$869$		−	4.76042e9i		−	0.246080i
$870$	2.29766e10	+	8.70246e9i	1.18295	+	0.448048i
$871$			1.25617e10i			0.644148i
$872$		−	7.33913e10i		−	3.74832i
$873$	4.99865e9	−	5.65218e9i	0.254275	−	0.287519i
$874$		−	6.01292e10i		−	3.04646i
$875$		0			0
$876$	−9.46794e9	+	2.49976e10i	−0.475873	+	1.25642i
$877$	2.12852e10			1.06557			0.532783	−	0.846252i	$-0.321146\pi$
$877$	2.12852e10			1.06557			0.532783	+	0.846252i	$0.321146\pi$
$878$	−6.91550e10			−3.44820
$879$	−1.69675e10	−	6.42652e9i	−0.842671	−	0.319165i
$880$		−	1.40307e10i		−	0.694047i
$881$	1.34320e10			0.661798			0.330899	−	0.943666i	$-0.392648\pi$
$881$	1.34320e10			0.661798			0.330899	+	0.943666i	$0.392648\pi$
$882$		0			0
$883$	2.56922e9			0.125585			0.0627927	−	0.998027i	$-0.479999\pi$
$883$	2.56922e9			0.125585			0.0627927	+	0.998027i	$0.479999\pi$
$884$		−	1.95589e10i		−	0.952275i
$885$	1.62220e10	+	6.14416e9i	0.786690	+	0.297962i
$886$	−1.18281e10			−0.571342
$887$	3.37177e9			0.162228			0.0811138	−	0.996705i	$-0.474152\pi$
$887$	3.37177e9			0.162228			0.0811138	+	0.996705i	$0.474152\pi$
$888$	2.41610e10	−	6.37908e10i	1.15790	−	3.05712i
$889$		0			0
$890$			3.15876e10i			1.50193i
$891$	−5.28357e9	+	6.50845e8i	−0.250240	+	0.0308252i
$892$			5.78020e10i			2.72688i
$893$			1.07707e10i			0.506131i
$894$	1.23897e10	+	4.69265e9i	0.579935	+	0.219653i
$895$			7.04220e9i			0.328343i
$896$		0			0
$897$	−2.24393e10	−	8.49897e9i	−1.03809	−	0.393181i
$898$	−7.96508e8			−0.0367048
$899$	−1.34217e10			−0.616098
$900$	−1.97391e10	−	1.74567e10i	−0.902563	−	0.798205i
$901$			9.44128e9i			0.430025i
$902$	−9.81431e9			−0.445284
$903$		0			0
$904$	3.91755e10			1.76370
$905$		−	2.28399e9i		−	0.102429i
$906$	1.79476e10	−	4.73860e10i	0.801785	−	2.11690i
$907$	−3.61933e9			−0.161065			−0.0805327	−	0.996752i	$-0.525662\pi$
$907$	−3.61933e9			−0.161065			−0.0805327	+	0.996752i	$0.525662\pi$
$908$	−9.29365e10			−4.11989
$909$	−2.21140e10	−	1.95571e10i	−0.976550	−	0.863637i
$910$		0			0
$911$			3.28292e10i			1.43862i	0.694688	+	0.719311i	$0.255542\pi$
$911$			3.28292e10i			1.43862i	−0.694688	+	0.719311i	$0.744458\pi$
$912$	−1.73026e10	+	4.56830e10i	−0.755318	+	1.99422i
$913$		−	4.03846e9i		−	0.175618i
$914$			6.96790e9i			0.301849i
$915$	−2.14223e9	+	5.65600e9i	−0.0924470	+	0.244082i
$916$			8.63661e10i			3.71286i
$917$		0			0
$918$	2.40516e10	−	1.26632e10i	1.02611	−	0.540250i
$919$	1.27468e10			0.541749			0.270875	−	0.962615i	$-0.412687\pi$
$919$	1.27468e10			0.541749			0.270875	+	0.962615i	$0.412687\pi$
$920$	1.27104e11			5.38149
$921$	4.06530e9	−	1.07334e10i	0.171468	−	0.452717i
$922$			3.97398e10i			1.66981i
$923$	−9.56333e9			−0.400316
$924$		0			0
$925$	1.59389e10			0.662161
$926$		−	4.92638e10i		−	2.03887i
$927$	−3.87646e9	+	4.38327e9i	−0.159829	+	0.180725i
$928$	2.18788e10			0.898681
$929$	2.13873e10			0.875185			0.437593	−	0.899173i	$-0.355831\pi$
$929$	2.13873e10			0.875185			0.437593	+	0.899173i	$0.355831\pi$
$930$	5.67797e10	+	2.15055e10i	2.31474	+	0.876718i
$931$		0			0
$932$			1.28821e8i			0.00521233i
$933$	2.21479e10	+	8.38862e9i	0.892786	+	0.338146i
$934$		−	3.50442e10i		−	1.40735i
$935$			4.89083e9i			0.195678i
$936$	3.00350e10	+	2.65622e10i	1.19719	+	1.05876i
$937$			1.55091e10i			0.615884i	0.951405	+	0.307942i	$0.0996402\pi$
$937$			1.55091e10i			0.615884i	−0.951405	+	0.307942i	$0.900360\pi$
$938$		0			0
$939$	5.43867e9	−	1.43594e10i	0.214370	−	0.565986i
$940$	−3.94053e10			−1.54742
$941$	−9.51405e9			−0.372222			−0.186111	−	0.982529i	$-0.559588\pi$
$941$	−9.51405e9			−0.372222			−0.186111	+	0.982529i	$0.559588\pi$
$942$	−3.40436e10	−	1.28941e10i	−1.32696	−	0.502591i
$943$		−	4.32258e10i		−	1.67862i
$944$	3.96705e10			1.53485
$945$		0			0
$946$	−3.47155e9			−0.133323
$947$		−	1.14360e9i		−	0.0437572i	−0.999761	−	0.0218786i	$-0.993035\pi$
$947$		−	1.14360e9i		−	0.0437572i	0.999761	−	0.0218786i	$-0.00696474\pi$
$948$	−5.67064e10	−	2.14778e10i	−2.16174	−	0.818767i
$949$	9.50388e9			0.360968
$950$	−2.34777e10			−0.888428
$951$	1.19719e10	−	3.16088e10i	0.451370	−	1.19172i
$952$		0			0
$953$		−	2.71794e10i		−	1.01722i	−0.860997	−	0.508611i	$-0.830159\pi$
$953$		−	2.71794e10i		−	1.01722i	0.860997	−	0.508611i	$-0.169841\pi$
$954$	−2.50928e10	−	2.21915e10i	−0.935685	−	0.827497i
$955$		−	4.74446e10i		−	1.76269i
$956$			4.83872e10i			1.79113i
$957$	3.58728e9	+	1.35870e9i	0.132304	+	0.0501108i
$958$		−	5.30430e10i		−	1.94917i
$959$		0			0
$960$	−2.19896e10	−	8.32865e9i	−0.802173	−	0.303826i
$961$	−5.65520e9			−0.205549
$962$	−4.19756e10			−1.52014
$963$	1.21086e10	−	1.36917e10i	0.436919	−	0.494042i
$964$		−	2.36366e10i		−	0.849796i
$965$	−4.69912e10			−1.68334
$966$		0			0
$967$	3.61731e10			1.28645			0.643226	−	0.765676i	$-0.277596\pi$
$967$	3.61731e10			1.28645			0.643226	+	0.765676i	$0.277596\pi$
$968$			6.63713e10i			2.35189i
$969$	6.03137e9	−	1.59242e10i	0.212953	−	0.562245i
$970$	2.45955e10			0.865275
$971$	4.42111e10			1.54976			0.774880	−	0.632109i	$-0.217810\pi$
$971$	4.42111e10			1.54976			0.774880	+	0.632109i	$0.217810\pi$
$972$	−1.60852e10	+	6.58748e10i	−0.561818	+	2.30084i
$973$		0			0
$974$		−	5.77720e10i		−	2.00337i
$975$	−3.31845e9	+	8.76150e9i	−0.114662	+	0.302735i
$976$			1.38316e10i			0.476209i
$977$			1.85701e10i			0.637064i	0.947912	+	0.318532i	$0.103190\pi$
$977$			1.85701e10i			0.637064i	−0.947912	+	0.318532i	$0.896810\pi$
$978$	−3.24744e10	+	8.57401e10i	−1.11008	+	2.93088i
$979$			4.93170e9i			0.167980i
$980$		0			0
$981$	−3.30574e10	−	2.92352e10i	−1.11796	−	0.988699i
$982$	−9.15527e10			−3.08518
$983$	4.53728e10			1.52356			0.761778	−	0.647838i	$-0.224327\pi$
$983$	4.53728e10			1.52356			0.761778	+	0.647838i	$0.224327\pi$
$984$	−2.55840e10	+	6.75477e10i	−0.856023	+	2.26010i
$985$		−	3.40080e9i		−	0.113385i
$986$	−1.95863e10			−0.650703
$987$		0			0
$988$	4.34736e10			1.43409
$989$		−	1.52900e10i		−	0.502597i
$990$	−1.29987e10	−	1.14957e10i	−0.425772	−	0.376543i
$991$	−1.93474e10			−0.631489			−0.315744	−	0.948844i	$-0.602254\pi$
$991$	−1.93474e10			−0.631489			−0.315744	+	0.948844i	$0.602254\pi$
$992$	5.40669e10			1.75849
$993$	1.91857e10	+	7.26667e9i	0.621808	+	0.235512i
$994$		0			0
$995$		−	8.08768e9i		−	0.260281i
$996$	−4.81064e10	−	1.82205e10i	−1.54275	−	0.584323i
$997$			5.71238e10i			1.82551i	0.408507	+	0.912755i	$0.366049\pi$
$997$			5.71238e10i			1.82551i	−0.408507	+	0.912755i	$0.633951\pi$
$998$		−	1.82030e10i		−	0.579676i
$999$	−1.91086e10	−	3.62936e10i	−0.606387	−	1.15173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.8.c.b.146.27		32
3.2	odd	2	inner	147.8.c.b.146.6		32
7.4	even	3		21.8.g.b.5.16	yes	32
7.5	odd	6		21.8.g.b.17.1	yes	32
7.6	odd	2	inner	147.8.c.b.146.5		32
21.5	even	6		21.8.g.b.17.16	yes	32
21.11	odd	6		21.8.g.b.5.1	✓	32
21.20	even	2	inner	147.8.c.b.146.28		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.1	✓	32	21.11	odd	6
21.8.g.b.5.16	yes	32	7.4	even	3
21.8.g.b.17.1	yes	32	7.5	odd	6
21.8.g.b.17.16	yes	32	21.5	even	6
147.8.c.b.146.5		32	7.6	odd	2	inner
147.8.c.b.146.6		32	3.2	odd	2	inner
147.8.c.b.146.27		32	1.1	even	1	trivial
147.8.c.b.146.28		32	21.20	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-20.7644i q^{2} +(-43.7336 - 16.5643i) q^{3} -303.161 q^{4} -343.321 q^{5} +(-343.947 + 908.102i) q^{6} +3637.11i q^{8} +(1638.25 + 1448.83i) q^{9} +7128.85i q^{10} +1113.01i q^{11} +(13258.3 + 5021.63i) q^{12} -5040.70i q^{13} +(15014.6 + 5686.86i) q^{15} +36717.9 q^{16} -12799.2 q^{17} +(30084.1 - 34017.3i) q^{18} -28448.7i q^{19} +104081. q^{20} +23111.1 q^{22} +101790. i q^{23} +(60246.1 - 159064. i) q^{24} +39744.1 q^{25} -104667. q^{26} +(-47647.8 - 90498.9i) q^{27} +73697.1i q^{29} +(118084. - 311770. i) q^{30} +182120. i q^{31} -296875. i q^{32} +(18436.3 - 48676.1i) q^{33} +265767. i q^{34} +(-496653. - 439228. i) q^{36} +401039. q^{37} -590720. q^{38} +(-83495.4 + 220448. i) q^{39} -1.24870e6i q^{40} -424658. q^{41} -150211. q^{43} -337422. i q^{44} +(-562445. - 497413. i) q^{45} +2.11360e6 q^{46} -378601. q^{47} +(-1.60580e6 - 608204. i) q^{48} -825264. i q^{50} +(559753. + 212009. i) q^{51} +1.52814e6i q^{52} -737648. i q^{53} +(-1.87916e6 + 989377. i) q^{54} -382121. i q^{55} +(-471231. + 1.24416e6i) q^{57} +1.53028e6 q^{58} +1.08041e6 q^{59} +(-4.55185e6 - 1.72403e6i) q^{60} +376699. i q^{61} +3.78162e6 q^{62} -1.46454e6 q^{64} +1.73058e6i q^{65} +(-1.01073e6 - 382818. i) q^{66} -2.49206e6 q^{67} +3.88021e6 q^{68} +(1.68607e6 - 4.45162e6i) q^{69} -1.89722e6i q^{71} +(-5.26955e6 + 5.95850e6i) q^{72} +1.88543e6i q^{73} -8.32733e6i q^{74} +(-1.73815e6 - 658332. i) q^{75} +8.62452e6i q^{76} +(4.57747e6 + 1.73373e6i) q^{78} -4.27705e6 q^{79} -1.26060e7 q^{80} +(584759. + 4.74709e6i) q^{81} +8.81778e6i q^{82} -3.62840e6 q^{83} +4.39422e6 q^{85} +3.11905e6i q^{86} +(1.22074e6 - 3.22304e6i) q^{87} -4.04815e6 q^{88} +4.43094e6 q^{89} +(-1.03285e7 + 1.16788e7i) q^{90} -3.08586e7i q^{92} +(3.01669e6 - 7.96477e6i) q^{93} +7.86142e6i q^{94} +9.76702e6i q^{95} +(-4.91751e6 + 1.29834e7i) q^{96} -3.45013e6i q^{97} +(-1.61257e6 + 1.82340e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2300 q^{4} + 7032 q^{9} + 27576 q^{15} + 39188 q^{16} - 66996 q^{18} + 105132 q^{22} + 662504 q^{25} + 81324 q^{30} - 227244 q^{36} + 1237496 q^{37} - 3992208 q^{39} - 1416064 q^{43} + 6985680 q^{46}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 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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