LMFDB - Embedded newform 196.9.h.c.129.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,9,Mod(117,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.117"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	196.h (of order $6$, degree $2$, not 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:	$79.8462075720$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.13
Character	$\chi$	$=$	196.129
Dual form			196.9.h.c.117.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(95.3296 + 55.0385i) q^{3} +(20.9063 - 12.0703i) q^{5} +(2777.98 + 4811.61i) q^{9} +(5764.63 - 9984.63i) q^{11} +16167.0i q^{13} +2657.32 q^{15} +(11823.0 + 6826.04i) q^{17} +(95678.7 - 55240.1i) q^{19} +(47748.3 + 82702.4i) q^{23} +(-195021. + 337786. i) q^{25} -110631. i q^{27} +968391. q^{29} +(-556669. - 321393. i) q^{31} +(1.09908e6 - 634554. i) q^{33} +(1.45709e6 + 2.52376e6i) q^{37} +(-889810. + 1.54120e6i) q^{39} +2.54503e6i q^{41} +4.32250e6 q^{43} +(116155. + 67062.1i) q^{45} +(8.23472e6 - 4.75432e6i) q^{47} +(751390. + 1.30145e6i) q^{51} +(-1.66496e6 + 2.88379e6i) q^{53} -278323. i q^{55} +1.21613e7 q^{57} +(1.22742e6 + 708648. i) q^{59} +(-9.79018e6 + 5.65236e6i) q^{61} +(195141. + 337993. i) q^{65} +(-3.61550e6 + 6.26223e6i) q^{67} +1.05120e7i q^{69} -4.54041e6 q^{71} +(1.47310e7 + 8.50494e6i) q^{73} +(-3.71826e7 + 2.14674e7i) q^{75} +(-2.65854e7 - 4.60472e7i) q^{79} +(2.43153e7 - 4.21154e7i) q^{81} +4.31758e7i q^{83} +329569. q^{85} +(9.23163e7 + 5.32988e7i) q^{87} +(-6.63688e7 + 3.83180e7i) q^{89} +(-3.53780e7 - 6.12765e7i) q^{93} +(1.33353e6 - 2.30974e6i) q^{95} -2.32937e7i q^{97} +6.40562e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 52264 q^{9} + 22776 q^{11} + 206064 q^{15} - 571560 q^{23} + 1030440 q^{25} - 5384256 q^{29} + 3376640 q^{37} + 10336136 q^{39} + 18525008 q^{43} + 16028856 q^{51} - 14106216 q^{53} - 4787360 q^{57}+ \cdots + 1119499328 q^{99}+O(q^{100}) $ 32 * q + 52264 * q^9 + 22776 * q^11 + 206064 * q^15 - 571560 * q^23 + 1030440 * q^25 - 5384256 * q^29 + 3376640 * q^37 + 10336136 * q^39 + 18525008 * q^43 + 16028856 * q^51 - 14106216 * q^53 - 4787360 * q^57 - 5623008 * q^65 - 82433680 * q^67 + 250685568 * q^71 + 138241200 * q^79 - 465637680 * q^81 + 880381104 * q^85 + 310654512 * q^93 - 811120872 * q^95 + 1119499328 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	95.3296	+	55.0385i	1.17691	+	0.679488i	0.955297	−	0.295647i	$-0.0955352\pi$
$3$	95.3296	+	55.0385i	1.17691	+	0.679488i	0.221611	+	0.975135i	$0.428869\pi$
$4$		0			0
$5$	20.9063	−	12.0703i	0.0334501	−	0.0193124i	−0.483182	−	0.875520i	$-0.660519\pi$
$5$	20.9063	−	12.0703i	0.0334501	−	0.0193124i	0.516632	+	0.856208i	$0.327186\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2777.98	+	4811.61i	0.423409	+	0.733365i
$10$		0			0
$11$	5764.63	−	9984.63i	0.393732	−	0.681964i	−0.599206	−	0.800595i	$-0.704517\pi$
$11$	5764.63	−	9984.63i	0.393732	−	0.681964i	0.992938	+	0.118631i	$0.0378505\pi$
$12$		0			0
$13$			16167.0i			0.566053i	0.959112	+	0.283026i	$0.0913384\pi$
$13$			16167.0i			0.566053i	−0.959112	+	0.283026i	$0.908662\pi$
$14$		0			0
$15$	2657.32			0.0524903
$16$		0			0
$17$	11823.0	+	6826.04i	0.141558	+	0.0817284i	0.569106	−	0.822264i	$-0.307289\pi$
$17$	11823.0	+	6826.04i	0.141558	+	0.0817284i	−0.427548	+	0.903992i	$0.640623\pi$
$18$		0			0
$19$	95678.7	−	55240.1i	0.734177	−	0.423877i	−0.0857712	−	0.996315i	$-0.527335\pi$
$19$	95678.7	−	55240.1i	0.734177	−	0.423877i	0.819948	+	0.572438i	$0.194002\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	47748.3	+	82702.4i	0.170626	+	0.295534i	0.938639	−	0.344901i	$-0.112088\pi$
$23$	47748.3	+	82702.4i	0.170626	+	0.295534i	−0.768013	+	0.640435i	$0.778754\pi$
$24$		0			0
$25$	−195021.	+	337786.i	−0.499254	+	0.864733i
$26$		0			0
$27$		−	110631.i		−	0.208172i
$28$		0			0
$29$	968391.			1.36917			0.684587	−	0.728931i	$-0.259983\pi$
$29$	968391.			1.36917			0.684587	+	0.728931i	$0.259983\pi$
$30$		0			0
$31$	−556669.	−	321393.i	−0.602768	−	0.348008i	0.167362	−	0.985896i	$-0.446475\pi$
$31$	−556669.	−	321393.i	−0.602768	−	0.348008i	−0.770130	+	0.637887i	$0.779808\pi$
$32$		0			0
$33$	1.09908e6	−	634554.i	0.926773	−	0.535072i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.45709e6	+	2.52376e6i	0.777464	+	1.34661i	0.933399	+	0.358840i	$0.116828\pi$
$37$	1.45709e6	+	2.52376e6i	0.777464	+	1.34661i	−0.155935	+	0.987767i	$0.549839\pi$
$38$		0			0
$39$	−889810.	+	1.54120e6i	−0.384626	+	0.666192i
$40$		0			0
$41$			2.54503e6i			0.900653i	0.892864	+	0.450326i	$0.148692\pi$
$41$			2.54503e6i			0.900653i	−0.892864	+	0.450326i	$0.851308\pi$
$42$		0			0
$43$	4.32250e6			1.26433			0.632166	−	0.774833i	$-0.282166\pi$
$43$	4.32250e6			1.26433			0.632166	+	0.774833i	$0.282166\pi$
$44$		0			0
$45$	116155.	+	67062.1i	0.0283261	+	0.0163541i
$46$		0			0
$47$	8.23472e6	−	4.75432e6i	1.68755	−	0.974309i	0.731170	−	0.682195i	$-0.238975\pi$
$47$	8.23472e6	−	4.75432e6i	1.68755	−	0.974309i	0.956383	−	0.292114i	$-0.0943587\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	751390.	+	1.30145e6i	0.111067	+	0.192374i
$52$		0			0
$53$	−1.66496e6	+	2.88379e6i	−0.211008	+	0.365477i	−0.952030	−	0.306004i	$-0.901008\pi$
$53$	−1.66496e6	+	2.88379e6i	−0.211008	+	0.365477i	0.741022	+	0.671481i	$0.234341\pi$
$54$		0			0
$55$		−	278323.i		−	0.0304157i
$56$		0			0
$57$	1.21613e7			1.15208
$58$		0			0
$59$	1.22742e6	+	708648.i	0.101294	+	0.0584821i	0.549791	−	0.835302i	$-0.314707\pi$
$59$	1.22742e6	+	708648.i	0.101294	+	0.0584821i	−0.448497	+	0.893784i	$0.648041\pi$
$60$		0			0
$61$	−9.79018e6	+	5.65236e6i	−0.707085	+	0.408236i	−0.809981	−	0.586457i	$-0.800522\pi$
$61$	−9.79018e6	+	5.65236e6i	−0.707085	+	0.408236i	0.102896	+	0.994692i	$0.467189\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	195141.	+	337993.i	0.0109319	+	0.0189345i
$66$		0			0
$67$	−3.61550e6	+	6.26223e6i	−0.179419	+	0.310763i	−0.941682	−	0.336505i	$-0.890755\pi$
$67$	−3.61550e6	+	6.26223e6i	−0.179419	+	0.310763i	0.762263	+	0.647268i	$0.224089\pi$
$68$		0			0
$69$			1.05120e7i			0.463755i
$70$		0			0
$71$	−4.54041e6			−0.178674			−0.0893370	−	0.996001i	$-0.528475\pi$
$71$	−4.54041e6			−0.178674			−0.0893370	+	0.996001i	$0.528475\pi$
$72$		0			0
$73$	1.47310e7	+	8.50494e6i	0.518729	+	0.299488i	0.736415	−	0.676531i	$-0.236517\pi$
$73$	1.47310e7	+	8.50494e6i	0.518729	+	0.299488i	−0.217685	+	0.976019i	$0.569851\pi$
$74$		0			0
$75$	−3.71826e7	+	2.14674e7i	−1.17515	+	0.678475i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.65854e7	−	4.60472e7i	−0.682549	−	1.18221i	−0.974200	−	0.225685i	$-0.927538\pi$
$79$	−2.65854e7	−	4.60472e7i	−0.682549	−	1.18221i	0.291651	−	0.956525i	$-0.405795\pi$
$80$		0			0
$81$	2.43153e7	−	4.21154e7i	0.564859	−	0.978364i
$82$		0			0
$83$			4.31758e7i			0.909762i	0.890552	+	0.454881i	$0.150318\pi$
$83$			4.31758e7i			0.909762i	−0.890552	+	0.454881i	$0.849682\pi$
$84$		0			0
$85$	329569.			0.00631350
$86$		0			0
$87$	9.23163e7	+	5.32988e7i	1.61139	+	0.930338i
$88$		0			0
$89$	−6.63688e7	+	3.83180e7i	−1.05780	+	0.610721i	−0.924823	−	0.380398i	$-0.875787\pi$
$89$	−6.63688e7	+	3.83180e7i	−1.05780	+	0.610721i	−0.132977	+	0.991119i	$0.542454\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.53780e7	−	6.12765e7i	−0.472935	−	0.819147i
$94$		0			0
$95$	1.33353e6	−	2.30974e6i	0.0163722	−	0.0283575i
$96$		0			0
$97$		−	2.32937e7i		−	0.263118i	−0.991308	−	0.131559i	$-0.958002\pi$
$97$		−	2.32937e7i		−	0.263118i	0.991308	−	0.131559i	$-0.0419983\pi$
$98$		0			0
$99$	6.40562e7			0.666838
$100$		0			0
$101$	8.11435e7	+	4.68482e7i	0.779773	+	0.450202i	0.836350	−	0.548196i	$-0.184685\pi$
$101$	8.11435e7	+	4.68482e7i	0.779773	+	0.450202i	−0.0565766	+	0.998398i	$0.518019\pi$
$102$		0			0
$103$	−1.25657e8	+	7.25480e7i	−1.11644	+	0.644579i	−0.940491	−	0.339819i	$-0.889634\pi$
$103$	−1.25657e8	+	7.25480e7i	−1.11644	+	0.644579i	−0.175954	+	0.984398i	$0.556301\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.30680e7	−	3.99549e7i	−0.175984	−	0.304814i	0.764517	−	0.644604i	$-0.222978\pi$
$107$	−2.30680e7	−	3.99549e7i	−0.175984	−	0.304814i	−0.940502	+	0.339789i	$0.889644\pi$
$108$		0			0
$109$	−2.26788e7	+	3.92808e7i	−0.160662	+	0.278275i	−0.935106	−	0.354367i	$-0.884696\pi$
$109$	−2.26788e7	+	3.92808e7i	−0.160662	+	0.278275i	0.774444	+	0.632642i	$0.218030\pi$
$110$		0			0
$111$			3.20785e8i			2.11311i
$112$		0			0
$113$	3.21193e8			1.96994			0.984969	−	0.172733i	$-0.0552599\pi$
$113$	3.21193e8			1.96994			0.984969	+	0.172733i	$0.0552599\pi$
$114$		0			0
$115$	1.99648e6	+	1.15267e6i	0.0114150	+	0.00659043i
$116$		0			0
$117$	−7.77894e7	+	4.49118e7i	−0.415123	+	0.239672i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	4.07175e7	+	7.05248e7i	0.189950	+	0.329004i
$122$		0			0
$123$	−1.40075e8	+	2.42616e8i	−0.611983	+	1.05999i
$124$		0			0
$125$			1.88457e7i			0.0771921i
$126$		0			0
$127$	3.60956e8			1.38752			0.693761	−	0.720206i	$-0.255953\pi$
$127$	3.60956e8			1.38752			0.693761	+	0.720206i	$0.255953\pi$
$128$		0			0
$129$	4.12062e8	+	2.37904e8i	1.48800	+	0.859099i
$130$		0			0
$131$	3.09304e8	−	1.78577e8i	1.05027	−	0.606373i	0.127544	−	0.991833i	$-0.459290\pi$
$131$	3.09304e8	−	1.78577e8i	1.05027	−	0.606373i	0.922725	+	0.385460i	$0.125957\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.33535e6	−	2.31289e6i	−0.00402031	−	0.00696338i
$136$		0			0
$137$	6.56374e7	−	1.13687e8i	0.186324	−	0.322723i	−0.757698	−	0.652606i	$-0.773676\pi$
$137$	6.56374e7	−	1.13687e8i	0.186324	−	0.322723i	0.944022	+	0.329883i	$0.107009\pi$
$138$		0			0
$139$			5.79820e8i			1.55322i	0.629979	+	0.776612i	$0.283063\pi$
$139$			5.79820e8i			1.55322i	−0.629979	+	0.776612i	$0.716937\pi$
$140$		0			0
$141$	1.04668e9			2.64813
$142$		0			0
$143$	1.61422e8	+	9.31970e7i	0.386027	+	0.222873i
$144$		0			0
$145$	2.02455e7	−	1.16887e7i	0.0457990	−	0.0264421i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.32188e8	+	2.28956e8i	0.268193	+	0.464524i	0.968395	−	0.249421i	$-0.0802402\pi$
$149$	1.32188e8	+	2.28956e8i	0.268193	+	0.464524i	−0.700202	+	0.713944i	$0.746907\pi$
$150$		0			0
$151$	−2.65806e8	+	4.60390e8i	−0.511278	+	0.885559i	0.488637	+	0.872487i	$0.337494\pi$
$151$	−2.65806e8	+	4.60390e8i	−0.511278	+	0.885559i	−0.999915	+	0.0130720i	$0.995839\pi$
$152$		0			0
$153$			7.58505e7i			0.138418i
$154$		0			0
$155$	−1.55172e7			−0.0268835
$156$		0			0
$157$	5.50247e7	+	3.17685e7i	0.0905647	+	0.0522875i	0.544598	−	0.838697i	$-0.316682\pi$
$157$	5.50247e7	+	3.17685e7i	0.0905647	+	0.0522875i	−0.454034	+	0.890985i	$0.650015\pi$
$158$		0			0
$159$	−3.17439e8	+	1.83274e8i	−0.496675	+	0.286755i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.92321e8	−	5.06315e8i	−0.414104	−	0.717250i	0.581230	−	0.813740i	$-0.302572\pi$
$163$	−2.92321e8	−	5.06315e8i	−0.414104	−	0.717250i	−0.995334	+	0.0964898i	$0.969238\pi$
$164$		0			0
$165$	1.53185e7	−	2.65324e7i	0.0206671	−	0.0357965i
$166$		0			0
$167$			7.54928e8i			0.970598i	0.874348	+	0.485299i	$0.161289\pi$
$167$			7.54928e8i			0.970598i	−0.874348	+	0.485299i	$0.838711\pi$
$168$		0			0
$169$	5.54358e8			0.679584
$170$		0			0
$171$	5.31588e8	+	3.06912e8i	0.621714	+	0.358947i
$172$		0			0
$173$	−1.31118e9	+	7.57011e8i	−1.46379	+	0.845119i	−0.999184	−	0.0403982i	$-0.987137\pi$
$173$	−1.31118e9	+	7.57011e8i	−1.46379	+	0.845119i	−0.464606	+	0.885518i	$0.653804\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.80060e7	+	1.35110e8i	0.0794758	+	0.137656i
$178$		0			0
$179$	−1.97676e7	+	3.42385e7i	−0.0192549	+	0.0333505i	−0.875492	−	0.483232i	$-0.839463\pi$
$179$	−1.97676e7	+	3.42385e7i	−0.0192549	+	0.0333505i	0.856237	+	0.516583i	$0.172796\pi$
$180$		0			0
$181$		−	9.35971e8i		−	0.872063i	−0.899931	−	0.436032i	$-0.856384\pi$
$181$		−	9.35971e8i		−	0.872063i	0.899931	−	0.436032i	$-0.143616\pi$
$182$		0			0
$183$	−1.24439e9			−1.10956
$184$		0			0
$185$	6.09249e7	+	3.51750e7i	0.0520126	+	0.0300295i
$186$		0			0
$187$	1.36311e8	−	7.86991e7i	0.111472	−	0.0643581i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.09529e9	−	1.89710e9i	−0.822993	−	1.42547i	−0.903443	−	0.428708i	$-0.858969\pi$
$191$	−1.09529e9	−	1.89710e9i	−0.822993	−	1.42547i	0.0804501	−	0.996759i	$-0.474364\pi$
$192$		0			0
$193$	1.24858e9	−	2.16260e9i	0.899886	−	1.55865i	0.0722467	−	0.997387i	$-0.476983\pi$
$193$	1.24858e9	−	2.16260e9i	0.899886	−	1.55865i	0.827639	−	0.561261i	$-0.189684\pi$
$194$		0			0
$195$			4.29610e7i			0.0297123i
$196$		0			0
$197$	−7.82360e8			−0.519447			−0.259724	−	0.965683i	$-0.583632\pi$
$197$	−7.82360e8			−0.519447			−0.259724	+	0.965683i	$0.583632\pi$
$198$		0			0
$199$	6.59868e8	+	3.80975e8i	0.420770	+	0.242932i	0.695407	−	0.718616i	$-0.255224\pi$
$199$	6.59868e8	+	3.80975e8i	0.420770	+	0.242932i	−0.274637	+	0.961548i	$0.588558\pi$
$200$		0			0
$201$	−6.89328e8	+	3.97983e8i	−0.422320	+	0.243826i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.07192e7	+	5.32072e7i	0.0173938	+	0.0301269i
$206$		0			0
$207$	−2.65288e8	+	4.59492e8i	−0.144489	+	0.250263i
$208$		0			0
$209$		−	1.27376e9i		−	0.667576i
$210$		0			0
$211$	−2.33535e9			−1.17821			−0.589103	−	0.808058i	$-0.700519\pi$
$211$	−2.33535e9			−1.17821			−0.589103	+	0.808058i	$0.700519\pi$
$212$		0			0
$213$	−4.32835e8	−	2.49897e8i	−0.210283	−	0.121407i
$214$		0			0
$215$	9.03677e7	−	5.21738e7i	0.0422921	−	0.0244174i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	9.36200e8	+	1.62155e9i	0.406998	+	0.704941i
$220$		0			0
$221$	−1.10357e8	+	1.91143e8i	−0.0462626	+	0.0801291i
$222$		0			0
$223$			1.59601e9i			0.645380i	0.946505	+	0.322690i	$0.104587\pi$
$223$			1.59601e9i			0.645380i	−0.946505	+	0.322690i	$0.895413\pi$
$224$		0			0
$225$	−2.16706e9			−0.845554
$226$		0			0
$227$	−3.57744e9	−	2.06544e9i	−1.34731	−	0.777872i	−0.359446	−	0.933166i	$-0.617034\pi$
$227$	−3.57744e9	−	2.06544e9i	−1.34731	−	0.777872i	−0.987868	+	0.155294i	$0.950368\pi$
$228$		0			0
$229$	1.11788e9	−	6.45408e8i	0.406493	−	0.234689i	−0.282789	−	0.959182i	$-0.591260\pi$
$229$	1.11788e9	−	6.45408e8i	0.406493	−	0.234689i	0.689282	+	0.724493i	$0.257926\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.07602e8	+	1.05240e9i	0.206156	+	0.357073i	0.950500	−	0.310723i	$-0.100571\pi$
$233$	6.07602e8	+	1.05240e9i	0.206156	+	0.357073i	−0.744344	+	0.667796i	$0.767238\pi$
$234$		0			0
$235$	1.14772e8	−	1.98791e8i	0.0376326	−	0.0651816i
$236$		0			0
$237$		−	5.85288e9i		−	1.85514i
$238$		0			0
$239$	1.18854e9			0.364267			0.182134	−	0.983274i	$-0.441700\pi$
$239$	1.18854e9			0.364267			0.182134	+	0.983274i	$0.441700\pi$
$240$		0			0
$241$	−3.74859e9	−	2.16425e9i	−1.11122	−	0.641562i	−0.172074	−	0.985084i	$-0.555047\pi$
$241$	−3.74859e9	−	2.16425e9i	−1.11122	−	0.641562i	−0.939145	+	0.343522i	$0.888380\pi$
$242$		0			0
$243$	4.00733e9	−	2.31364e9i	1.14929	−	0.663544i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.93069e8	+	1.54684e9i	0.239937	+	0.415583i
$248$		0			0
$249$	−2.37633e9	+	4.11593e9i	−0.618173	+	1.07071i
$250$		0			0
$251$		−	1.91790e9i		−	0.483205i	−0.970375	−	0.241602i	$-0.922327\pi$
$251$		−	1.91790e9i		−	0.483205i	0.970375	−	0.241602i	$-0.0776730\pi$
$252$		0			0
$253$	1.10100e9			0.268724
$254$		0			0
$255$	3.14176e7	+	1.81390e7i	0.00743041	+	0.00428995i
$256$		0			0
$257$	6.25843e9	−	3.61331e9i	1.43461	−	0.828271i	0.437140	−	0.899393i	$-0.355991\pi$
$257$	6.25843e9	−	3.61331e9i	1.43461	−	0.828271i	0.997468	+	0.0711223i	$0.0226581\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2.69017e9	+	4.65952e9i	0.579720	+	1.00410i
$262$		0			0
$263$	1.97015e9	−	3.41239e9i	0.411790	−	0.713241i	−0.583296	−	0.812260i	$-0.698237\pi$
$263$	1.97015e9	−	3.41239e9i	0.411790	−	0.713241i	0.995086	+	0.0990189i	$0.0315704\pi$
$264$		0			0
$265$			8.03860e7i			0.0163003i
$266$		0			0
$267$	−8.43587e9			−1.65991
$268$		0			0
$269$	−3.56210e9	−	2.05658e9i	−0.680294	−	0.392768i	0.119672	−	0.992814i	$-0.461816\pi$
$269$	−3.56210e9	−	2.05658e9i	−0.680294	−	0.392768i	−0.799966	+	0.600046i	$0.795149\pi$
$270$		0			0
$271$	6.09050e9	−	3.51635e9i	1.12921	−	0.651952i	0.185476	−	0.982649i	$-0.440617\pi$
$271$	6.09050e9	−	3.51635e9i	1.12921	−	0.651952i	0.943737	+	0.330697i	$0.107284\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.24845e9	+	3.89443e9i	0.393145	+	0.680946i
$276$		0			0
$277$	−1.03030e9	+	1.78453e9i	−0.175002	+	0.303113i	−0.940162	−	0.340728i	$-0.889327\pi$
$277$	−1.03030e9	+	1.78453e9i	−0.175002	+	0.303113i	0.765160	+	0.643840i	$0.222660\pi$
$278$		0			0
$279$		−	3.57129e9i		−	0.589398i
$280$		0			0
$281$	−1.05644e8			−0.0169442			−0.00847210	−	0.999964i	$-0.502697\pi$
$281$	−1.05644e8			−0.0169442			−0.00847210	+	0.999964i	$0.502697\pi$
$282$		0			0
$283$	−5.72282e9	−	3.30407e9i	−0.892205	−	0.515115i	−0.0175419	−	0.999846i	$-0.505584\pi$
$283$	−5.72282e9	−	3.30407e9i	−0.892205	−	0.515115i	−0.874663	+	0.484731i	$0.838917\pi$
$284$		0			0
$285$	2.54249e8	−	1.46791e8i	0.0385372	−	0.0222495i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.39469e9	−	5.87977e9i	−0.486641	−	0.842887i
$290$		0			0
$291$	1.28205e9	−	2.22058e9i	0.178786	−	0.309666i
$292$		0			0
$293$			3.40164e9i			0.461549i	0.973007	+	0.230774i	$0.0741259\pi$
$293$			3.40164e9i			0.461549i	−0.973007	+	0.230774i	$0.925874\pi$
$294$		0			0
$295$	3.42143e7			0.00451773
$296$		0			0
$297$	−1.10461e9	−	6.37747e8i	−0.141966	−	0.0819639i
$298$		0			0
$299$	−1.33705e9	+	7.71948e8i	−0.167288	+	0.0965836i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	5.15692e9	+	8.93204e9i	0.611814	+	1.05969i
$304$		0			0
$305$	−1.36451e8	+	2.36340e8i	−0.0157680	+	0.0273111i
$306$		0			0
$307$		−	1.01001e10i		−	1.13704i	−0.822671	−	0.568518i	$-0.807517\pi$
$307$		−	1.01001e10i		−	1.13704i	0.822671	−	0.568518i	$-0.192483\pi$
$308$		0			0
$309$	−1.59717e10			−1.75194
$310$		0			0
$311$	8.06784e8	+	4.65797e8i	0.0862414	+	0.0497915i	0.542501	−	0.840055i	$-0.317478\pi$
$311$	8.06784e8	+	4.65797e8i	0.0862414	+	0.0497915i	−0.456259	+	0.889847i	$0.650811\pi$
$312$		0			0
$313$	−1.19209e10	+	6.88251e9i	−1.24202	+	0.717083i	−0.969506	−	0.245068i	$-0.921190\pi$
$313$	−1.19209e10	+	6.88251e9i	−1.24202	+	0.717083i	−0.272518	+	0.962151i	$0.587857\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.06158e9	−	1.04990e10i	−0.600273	−	1.03970i	−0.992779	−	0.119954i	$-0.961725\pi$
$317$	−6.06158e9	−	1.04990e10i	−0.600273	−	1.03970i	0.392506	−	0.919749i	$-0.371608\pi$
$318$		0			0
$319$	5.58241e9	−	9.66902e9i	0.539088	−	0.933727i
$320$		0			0
$321$		−	5.07851e9i		−	0.478318i
$322$		0			0
$323$	1.50828e9			0.138571
$324$		0			0
$325$	−5.46101e9	−	3.15291e9i	−0.489485	−	0.282604i
$326$		0			0
$327$	−4.32392e9	+	2.49642e9i	−0.378170	+	0.218336i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.30685e9	−	1.43879e10i	−0.692030	−	1.19863i	−0.971172	−	0.238381i	$-0.923383\pi$
$331$	−8.30685e9	−	1.43879e10i	−0.692030	−	1.19863i	0.279142	−	0.960250i	$-0.409950\pi$
$332$		0			0
$333$	−8.09556e9	+	1.40219e10i	−0.658370	+	1.14033i
$334$		0			0
$335$			1.74560e8i			0.0138601i
$336$		0			0
$337$	−3.60721e9			−0.279674			−0.139837	−	0.990175i	$-0.544658\pi$
$337$	−3.60721e9			−0.279674			−0.139837	+	0.990175i	$0.544658\pi$
$338$		0			0
$339$	3.06192e10	+	1.76780e10i	2.31844	+	1.33855i
$340$		0			0
$341$	−6.41798e9	+	3.70542e9i	−0.474658	+	0.274044i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.26883e8	+	2.19767e8i	0.00895623	+	0.0155127i
$346$		0			0
$347$	1.33512e10	−	2.31250e10i	0.920882	−	1.59501i	0.122828	−	0.992428i	$-0.460804\pi$
$347$	1.33512e10	−	2.31250e10i	0.920882	−	1.59501i	0.798054	−	0.602586i	$-0.205863\pi$
$348$		0			0
$349$			1.62645e10i			1.09633i	0.836372	+	0.548163i	$0.184673\pi$
$349$			1.62645e10i			1.09633i	−0.836372	+	0.548163i	$0.815327\pi$
$350$		0			0
$351$	1.78858e9			0.117836
$352$		0			0
$353$	−1.52579e10	−	8.80916e9i	−0.982644	−	0.567330i	−0.0795766	−	0.996829i	$-0.525357\pi$
$353$	−1.52579e10	−	8.80916e9i	−0.982644	−	0.567330i	−0.903067	+	0.429499i	$0.858690\pi$
$354$		0			0
$355$	−9.49232e7	+	5.48040e7i	−0.00597667	+	0.00345063i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.01184e9	−	3.48461e9i	−0.121120	−	0.209786i	0.799090	−	0.601212i	$-0.205315\pi$
$359$	−2.01184e9	−	3.48461e9i	−0.121120	−	0.209786i	−0.920210	+	0.391426i	$0.871982\pi$
$360$		0			0
$361$	−2.38884e9	+	4.13759e9i	−0.140656	+	0.243623i
$362$		0			0
$363$			8.96414e9i			0.516276i
$364$		0			0
$365$	4.10628e8			0.0231354
$366$		0			0
$367$	4.78514e9	+	2.76270e9i	0.263773	+	0.152289i	0.626055	−	0.779779i	$-0.284669\pi$
$367$	4.78514e9	+	2.76270e9i	0.263773	+	0.152289i	−0.362281	+	0.932069i	$0.618002\pi$
$368$		0			0
$369$	−1.22457e10	+	7.07005e9i	−0.660507	+	0.381344i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	3.60547e9	+	6.24485e9i	0.186263	+	0.322617i	0.944001	−	0.329942i	$-0.107029\pi$
$373$	3.60547e9	+	6.24485e9i	0.186263	+	0.322617i	−0.757739	+	0.652558i	$0.773696\pi$
$374$		0			0
$375$	−1.03724e9	+	1.79656e9i	−0.0524512	+	0.0908481i
$376$		0			0
$377$			1.56560e10i			0.775025i
$378$		0			0
$379$	3.64299e10			1.76563			0.882817	−	0.469717i	$-0.155644\pi$
$379$	3.64299e10			1.76563			0.882817	+	0.469717i	$0.155644\pi$
$380$		0			0
$381$	3.44098e10	+	1.98665e10i	1.63298	+	0.942804i
$382$		0			0
$383$	1.76564e9	−	1.01939e9i	0.0820554	−	0.0473747i	−0.458411	−	0.888740i	$-0.651581\pi$
$383$	1.76564e9	−	1.01939e9i	0.0820554	−	0.0473747i	0.540466	+	0.841366i	$0.318248\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.20078e10	+	2.07982e10i	0.535329	+	0.927218i
$388$		0			0
$389$	−1.65407e10	+	2.86493e10i	−0.722362	+	1.25117i	0.237688	+	0.971342i	$0.423610\pi$
$389$	−1.65407e10	+	2.86493e10i	−0.722362	+	1.25117i	−0.960050	+	0.279827i	$0.909723\pi$
$390$		0			0
$391$			1.30373e9i			0.0557801i
$392$		0			0
$393$	3.93144e10			1.64809
$394$		0			0
$395$	−1.11160e9	−	6.41785e8i	−0.0456627	−	0.0263634i
$396$		0			0
$397$	4.11682e9	−	2.37684e9i	0.165729	−	0.0956839i	−0.414841	−	0.909894i	$-0.636163\pi$
$397$	4.11682e9	−	2.37684e9i	0.165729	−	0.0956839i	0.580571	+	0.814210i	$0.302830\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.58852e10	−	2.75141e10i	−0.614351	−	1.06409i	−0.990498	−	0.137527i	$-0.956085\pi$
$401$	−1.58852e10	−	2.75141e10i	−0.614351	−	1.06409i	0.376147	−	0.926560i	$-0.377249\pi$
$402$		0			0
$403$	5.19597e9	−	8.99968e9i	0.196991	−	0.341198i
$404$		0			0
$405$		−	1.17397e9i		−	0.0436352i
$406$		0			0
$407$	3.35984e10			1.22445
$408$		0			0
$409$	−2.93924e10	−	1.69697e10i	−1.05037	−	0.606430i	−0.127615	−	0.991824i	$-0.540732\pi$
$409$	−2.93924e10	−	1.69697e10i	−1.05037	−	0.606430i	−0.922752	+	0.385394i	$0.874066\pi$
$410$		0			0
$411$	1.25144e10	−	7.22518e9i	0.438573	−	0.253210i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	5.21144e8	+	9.02647e8i	0.0175697	+	0.0304317i
$416$		0			0
$417$	−3.19125e10	+	5.52740e10i	−1.05540	+	1.82800i
$418$		0			0
$419$			4.35642e10i			1.41343i	0.707499	+	0.706714i	$0.249823\pi$
$419$			4.35642e10i			1.41343i	−0.707499	+	0.706714i	$0.750177\pi$
$420$		0			0
$421$	3.95300e10			1.25834			0.629170	−	0.777267i	$-0.283395\pi$
$421$	3.95300e10			1.25834			0.629170	+	0.777267i	$0.283395\pi$
$422$		0			0
$423$	4.57519e10	+	2.64148e10i	1.42905	+	0.825062i
$424$		0			0
$425$	−4.61148e9	+	2.66244e9i	−0.141347	+	0.0816064i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.02589e10	+	1.77689e10i	0.302879	+	0.524602i
$430$		0			0
$431$	1.59834e10	−	2.76840e10i	0.463190	−	0.802268i	−0.535928	−	0.844264i	$-0.680038\pi$
$431$	1.59834e10	−	2.76840e10i	0.463190	−	0.802268i	0.999118	+	0.0419955i	$0.0133715\pi$
$432$		0			0
$433$			1.48533e10i			0.422544i	0.977427	+	0.211272i	$0.0677606\pi$
$433$			1.48533e10i			0.422544i	−0.977427	+	0.211272i	$0.932239\pi$
$434$		0			0
$435$	2.57333e9			0.0718684
$436$		0			0
$437$	9.13698e9	+	5.27524e9i	0.250540	+	0.144649i
$438$		0			0
$439$	3.33751e10	−	1.92691e10i	0.898597	−	0.518805i	0.0218522	−	0.999761i	$-0.493044\pi$
$439$	3.33751e10	−	1.92691e10i	0.898597	−	0.518805i	0.876745	+	0.480956i	$0.159710\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.28056e10	+	2.21799e10i	0.332494	+	0.575896i	0.983000	−	0.183605i	$-0.0587767\pi$
$443$	1.28056e10	+	2.21799e10i	0.332494	+	0.575896i	−0.650506	+	0.759501i	$0.725443\pi$
$444$		0			0
$445$	−9.25018e8	+	1.60218e9i	−0.0235890	+	0.0408574i
$446$		0			0
$447$			2.91018e10i			0.728936i
$448$		0			0
$449$	4.06129e10			0.999260			0.499630	−	0.866239i	$-0.333469\pi$
$449$	4.06129e10			0.999260			0.499630	+	0.866239i	$0.333469\pi$
$450$		0			0
$451$	2.54112e10	+	1.46711e10i	0.614212	+	0.354616i
$452$		0			0
$453$	−5.06784e10	+	2.92592e10i	−1.20345	+	0.694815i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.40656e10	−	4.16829e10i	−0.551737	−	0.955637i	−0.998149	−	0.0608093i	$-0.980632\pi$
$457$	−2.40656e10	−	4.16829e10i	−0.551737	−	0.955637i	0.446412	−	0.894827i	$-0.352701\pi$
$458$		0			0
$459$	7.55171e8	−	1.30800e9i	0.0170135	−	0.0294683i
$460$		0			0
$461$		−	3.22835e10i		−	0.714787i	−0.933954	−	0.357394i	$-0.883665\pi$
$461$		−	3.22835e10i		−	0.714787i	0.933954	−	0.357394i	$-0.116335\pi$
$462$		0			0
$463$	−4.05811e10			−0.883080			−0.441540	−	0.897242i	$-0.645568\pi$
$463$	−4.05811e10			−0.883080			−0.441540	+	0.897242i	$0.645568\pi$
$464$		0			0
$465$	−1.47925e9	−	8.54044e8i	−0.0316395	−	0.0182670i
$466$		0			0
$467$	−1.16899e10	+	6.74919e9i	−0.245779	+	0.141900i	−0.617830	−	0.786312i	$-0.711988\pi$
$467$	−1.16899e10	+	6.74919e9i	−0.245779	+	0.141900i	0.372051	+	0.928212i	$0.378655\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.49699e9	+	6.05696e9i	0.0710575	+	0.123075i
$472$		0			0
$473$	2.49176e10	−	4.31586e10i	0.497808	−	0.862229i
$474$		0			0
$475$			4.30920e10i			0.846490i
$476$		0			0
$477$	−1.85009e10			−0.357371
$478$		0			0
$479$	−1.95583e10	−	1.12920e10i	−0.371526	−	0.214500i	0.302599	−	0.953118i	$-0.402146\pi$
$479$	−1.95583e10	−	1.12920e10i	−0.371526	−	0.214500i	−0.674125	+	0.738618i	$0.735479\pi$
$480$		0			0
$481$	−4.08017e10	+	2.35569e10i	−0.762251	+	0.440086i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.81161e8	−	4.86985e8i	−0.00508146	−	0.00880134i
$486$		0			0
$487$	2.09348e10	−	3.62602e10i	0.372180	−	0.644635i	−0.617720	−	0.786398i	$-0.711944\pi$
$487$	2.09348e10	−	3.62602e10i	0.372180	−	0.644635i	0.989901	+	0.141763i	$0.0452770\pi$
$488$		0			0
$489$		−	6.43557e10i		−	1.12552i
$490$		0			0
$491$	−4.04271e10			−0.695580			−0.347790	−	0.937573i	$-0.613068\pi$
$491$	−4.04271e10			−0.695580			−0.347790	+	0.937573i	$0.613068\pi$
$492$		0			0
$493$	1.14493e10	+	6.61027e9i	0.193817	+	0.111900i
$494$		0			0
$495$	1.33918e9	−	7.73176e8i	0.0223058	−	0.0128783i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−5.29476e10	−	9.17080e10i	−0.853973	−	1.47912i	−0.877594	−	0.479404i	$-0.840853\pi$
$499$	−5.29476e10	−	9.17080e10i	−0.853973	−	1.47912i	0.0236213	−	0.999721i	$-0.492480\pi$
$500$		0			0
$501$	−4.15501e10	+	7.19669e10i	−0.659510	+	1.14231i
$502$		0			0
$503$			4.31315e9i			0.0673786i	0.999432	+	0.0336893i	$0.0107257\pi$
$503$			4.31315e9i			0.0673786i	−0.999432	+	0.0336893i	$0.989274\pi$
$504$		0			0
$505$	2.26188e9			0.0347780
$506$		0			0
$507$	5.28467e10	+	3.05110e10i	0.799808	+	0.461770i
$508$		0			0
$509$	−6.95245e10	+	4.01400e10i	−1.03578	+	0.598007i	−0.918635	−	0.395108i	$-0.870707\pi$
$509$	−6.95245e10	+	4.01400e10i	−1.03578	+	0.598007i	−0.117144	+	0.993115i	$0.537374\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−6.11127e9	−	1.05850e10i	−0.0882393	−	0.152835i
$514$		0			0
$515$	−1.75135e9	+	3.03342e9i	−0.0248968	+	0.0431225i
$516$		0			0
$517$		−	1.09628e11i		−	1.53447i
$518$		0			0
$519$	−1.66659e11			−2.29699
$520$		0			0
$521$	−1.12411e11	−	6.49004e10i	−1.52566	−	0.880838i	−0.999537	−	0.0304279i	$-0.990313\pi$
$521$	−1.12411e11	−	6.49004e10i	−1.52566	−	0.880838i	−0.526120	−	0.850410i	$-0.676354\pi$
$522$		0			0
$523$	3.98775e10	−	2.30233e10i	0.532992	−	0.307723i	−0.209242	−	0.977864i	$-0.567100\pi$
$523$	3.98775e10	−	2.30233e10i	0.532992	−	0.307723i	0.742234	+	0.670141i	$0.233766\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.38768e9	−	7.59968e9i	−0.0568843	−	0.0985264i
$528$		0			0
$529$	3.45957e10	−	5.99215e10i	0.441773	−	0.765174i
$530$		0			0
$531$			7.87446e9i			0.0990473i
$532$		0			0
$533$	−4.11456e10			−0.509817
$534$		0			0
$535$	−9.64534e8	−	5.56874e8i	−0.0117734	−	0.00679738i
$536$		0			0
$537$	−3.76887e9	+	2.17596e9i	−0.0453226	+	0.0261670i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	7.00454e10	+	1.21322e11i	0.817693	+	1.41629i	0.907378	+	0.420316i	$0.138081\pi$
$541$	7.00454e10	+	1.21322e11i	0.817693	+	1.41629i	−0.0896847	+	0.995970i	$0.528586\pi$
$542$		0			0
$543$	5.15145e10	−	8.92257e10i	0.592557	−	1.02634i
$544$		0			0
$545$			1.09496e9i			0.0124111i
$546$		0			0
$547$	−1.68525e10			−0.188241			−0.0941207	−	0.995561i	$-0.530004\pi$
$547$	−1.68525e10			−0.188241			−0.0941207	+	0.995561i	$0.530004\pi$
$548$		0			0
$549$	−5.43939e10	−	3.14044e10i	−0.598771	−	0.345701i
$550$		0			0
$551$	9.26544e10	−	5.34940e10i	1.00522	−	0.580362i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.87197e9	+	6.70644e9i	0.0408093	+	0.0706839i
$556$		0			0
$557$	−1.97581e10	+	3.42220e10i	−0.205269	+	0.355536i	−0.950218	−	0.311585i	$-0.899140\pi$
$557$	−1.97581e10	+	3.42220e10i	−0.205269	+	0.355536i	0.744949	+	0.667121i	$0.232474\pi$
$558$		0			0
$559$			6.98820e10i			0.715679i
$560$		0			0
$561$	1.73259e10			0.174922
$562$		0			0
$563$	−9.52435e9	−	5.49889e9i	−0.0947986	−	0.0547320i	0.451851	−	0.892093i	$-0.350764\pi$
$563$	−9.52435e9	−	5.49889e9i	−0.0947986	−	0.0547320i	−0.546650	+	0.837361i	$0.684097\pi$
$564$		0			0
$565$	6.71497e9	−	3.87689e9i	0.0658947	−	0.0380443i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.74390e10	+	4.75257e10i	0.261769	+	0.453398i	0.966712	−	0.255866i	$-0.0823607\pi$
$569$	2.74390e10	+	4.75257e10i	0.261769	+	0.453398i	−0.704943	+	0.709264i	$0.749027\pi$
$570$		0			0
$571$	−7.04519e9	+	1.22026e10i	−0.0662748	+	0.114791i	−0.897259	−	0.441505i	$-0.854445\pi$
$571$	−7.04519e9	+	1.22026e10i	−0.0662748	+	0.114791i	0.830984	+	0.556296i	$0.187778\pi$
$572$		0			0
$573$		−	2.41133e11i		−	2.23686i
$574$		0			0
$575$	−3.72477e10			−0.340744
$576$		0			0
$577$	−1.31690e11	−	7.60313e10i	−1.18809	−	0.685945i	−0.230219	−	0.973139i	$-0.573944\pi$
$577$	−1.31690e11	−	7.60313e10i	−1.18809	−	0.685945i	−0.957872	+	0.287194i	$0.907277\pi$
$578$		0			0
$579$	2.38053e11	−	1.37440e11i	2.11817	−	1.22292i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.91957e10	+	3.32480e10i	0.166161	+	0.287800i
$584$		0			0
$585$	−1.08419e9	+	1.87788e9i	−0.00925729	+	0.0160341i
$586$		0			0
$587$			6.94891e10i			0.585281i	0.956223	+	0.292640i	$0.0945339\pi$
$587$			6.94891e10i			0.585281i	−0.956223	+	0.292640i	$0.905466\pi$
$588$		0			0
$589$	−7.10151e10			−0.590051
$590$		0			0
$591$	−7.45820e10	−	4.30600e10i	−0.611342	−	0.352958i
$592$		0			0
$593$	4.40368e10	−	2.54246e10i	0.356120	−	0.205606i	−0.311257	−	0.950326i	$-0.600750\pi$
$593$	4.40368e10	−	2.54246e10i	0.356120	−	0.205606i	0.667378	+	0.744720i	$0.267417\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.19366e10	+	7.26364e10i	0.330139	+	0.571817i
$598$		0			0
$599$	−6.18447e10	+	1.07118e11i	−0.480392	+	0.832063i	−0.999747	−	0.0224958i	$-0.992839\pi$
$599$	−6.18447e10	+	1.07118e11i	−0.480392	+	0.832063i	0.519355	+	0.854558i	$0.326172\pi$
$600$		0			0
$601$		−	1.28493e11i		−	0.984875i	−0.870348	−	0.492437i	$-0.836106\pi$
$601$		−	1.28493e11i		−	0.984875i	0.870348	−	0.492437i	$-0.163894\pi$
$602$		0			0
$603$	−4.01752e10			−0.303870
$604$		0			0
$605$	1.70251e9	+	9.82944e8i	0.0127077	+	0.00733681i
$606$		0			0
$607$	9.04953e10	−	5.22475e10i	0.666609	−	0.384867i	−0.128181	−	0.991751i	$-0.540914\pi$
$607$	9.04953e10	−	5.22475e10i	0.666609	−	0.384867i	0.794791	+	0.606884i	$0.207581\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.68632e10	+	1.33131e11i	0.551511	+	0.955244i
$612$		0			0
$613$	−1.22363e11	+	2.11940e11i	−0.866583	+	1.50097i	−0.00111547	+	0.999999i	$0.500355\pi$
$613$	−1.22363e11	+	2.11940e11i	−0.866583	+	1.50097i	−0.865467	+	0.500966i	$0.832978\pi$
$614$		0			0
$615$			6.76296e9i			0.0472755i
$616$		0			0
$617$	1.19891e11			0.827268			0.413634	−	0.910443i	$-0.364259\pi$
$617$	1.19891e11			0.827268			0.413634	+	0.910443i	$0.364259\pi$
$618$		0			0
$619$	−6.14066e10	−	3.54531e10i	−0.418266	−	0.241486i	0.276069	−	0.961138i	$-0.410968\pi$
$619$	−6.14066e10	−	3.54531e10i	−0.418266	−	0.241486i	−0.694335	+	0.719652i	$0.744301\pi$
$620$		0			0
$621$	9.14946e9	−	5.28244e9i	0.0615218	−	0.0355196i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7.59527e10	−	1.31554e11i	−0.497763	−	0.862151i
$626$		0			0
$627$	7.01056e10	−	1.21427e11i	0.453610	−	0.785676i
$628$		0			0
$629$			3.97847e10i			0.254164i
$630$		0			0
$631$	−8.29136e9			−0.0523008			−0.0261504	−	0.999658i	$-0.508325\pi$
$631$	−8.29136e9			−0.0523008			−0.0261504	+	0.999658i	$0.508325\pi$
$632$		0			0
$633$	−2.22627e11	−	1.28534e11i	−1.38664	−	0.800577i
$634$		0			0
$635$	7.54627e9	−	4.35684e9i	0.0464128	−	0.0267964i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.26132e10	−	2.18467e10i	−0.0756521	−	0.131033i
$640$		0			0
$641$	1.06154e11	−	1.83864e11i	0.628788	−	1.08909i	−0.359007	−	0.933335i	$-0.616885\pi$
$641$	1.06154e11	−	1.83864e11i	0.628788	−	1.08909i	0.987795	−	0.155758i	$-0.0497821\pi$
$642$		0			0
$643$		−	1.95015e11i		−	1.14084i	−0.821354	−	0.570419i	$-0.806781\pi$
$643$		−	1.95015e11i		−	1.14084i	0.821354	−	0.570419i	$-0.193219\pi$
$644$		0			0
$645$	1.14863e10			0.0663652
$646$		0			0
$647$	5.79725e10	+	3.34705e10i	0.330830	+	0.191005i	0.656210	−	0.754579i	$-0.272159\pi$
$647$	5.79725e10	+	3.34705e10i	0.330830	+	0.191005i	−0.325379	+	0.945584i	$0.605492\pi$
$648$		0			0
$649$	1.41512e10	−	8.17019e9i	0.0797653	−	0.0460525i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.10311e11	+	1.91064e11i	0.606687	+	1.05081i	0.991782	+	0.127936i	$0.0408353\pi$
$653$	1.10311e11	+	1.91064e11i	0.606687	+	1.05081i	−0.385095	+	0.922877i	$0.625831\pi$
$654$		0			0
$655$	4.31094e9	−	7.46677e9i	0.0234211	−	0.0405665i
$656$		0			0
$657$			9.45064e10i			0.507224i
$658$		0			0
$659$	−3.45078e11			−1.82968			−0.914840	−	0.403816i	$-0.867684\pi$
$659$	−3.45078e11			−1.82968			−0.914840	+	0.403816i	$0.867684\pi$
$660$		0			0
$661$	2.37254e11	+	1.36978e11i	1.24282	+	0.717540i	0.969667	−	0.244431i	$-0.0786012\pi$
$661$	2.37254e11	+	1.36978e11i	1.24282	+	0.717540i	0.273150	+	0.961972i	$0.411935\pi$
$662$		0			0
$663$	−2.10405e10	+	1.21478e10i	−0.108894	+	0.0628698i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.62390e10	+	8.00883e10i	0.233617	+	0.404637i
$668$		0			0
$669$	−8.78419e10	+	1.52147e11i	−0.438528	+	0.759553i
$670$		0			0
$671$			1.30335e11i			0.642941i
$672$		0			0
$673$	9.43930e10			0.460129			0.230065	−	0.973175i	$-0.426106\pi$
$673$	9.43930e10			0.460129			0.230065	+	0.973175i	$0.426106\pi$
$674$		0			0
$675$	3.73697e10	+	2.15754e10i	0.180013	+	0.103931i
$676$		0			0
$677$	−2.53956e11	+	1.46622e11i	−1.20894	+	0.697980i	−0.962527	−	0.271185i	$-0.912584\pi$
$677$	−2.53956e11	+	1.46622e11i	−1.20894	+	0.697980i	−0.246410	+	0.969166i	$0.579251\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.27357e11	−	3.93794e11i	−1.05711	−	1.83097i
$682$		0			0
$683$	1.62775e11	−	2.81935e11i	0.748006	−	1.29558i	−0.200771	−	0.979638i	$-0.564345\pi$
$683$	1.62775e11	−	2.81935e11i	0.748006	−	1.29558i	0.948777	−	0.315946i	$-0.102322\pi$
$684$		0			0
$685$		−	3.16905e9i		−	0.0143935i
$686$		0			0
$687$	1.42089e11			0.637873
$688$		0			0
$689$	−4.66223e10	−	2.69174e10i	−0.206879	−	0.119442i
$690$		0			0
$691$	−1.37818e11	+	7.95694e10i	−0.604498	+	0.349007i	−0.770809	−	0.637066i	$-0.780148\pi$
$691$	−1.37818e11	+	7.95694e10i	−0.604498	+	0.349007i	0.166311	+	0.986073i	$0.446814\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.99859e9	+	1.21219e10i	0.0299965	+	0.0519555i
$696$		0			0
$697$	−1.73725e10	+	3.00900e10i	−0.0736089	+	0.127494i
$698$		0			0
$699$			1.33766e11i			0.560322i
$700$		0			0
$701$	−2.81697e11			−1.16657			−0.583284	−	0.812269i	$-0.698232\pi$
$701$	−2.81697e11			−1.16657			−0.583284	+	0.812269i	$0.698232\pi$
$702$		0			0
$703$	2.78826e11	+	1.60980e11i	1.14159	+	0.659099i
$704$		0			0
$705$	2.18823e10	−	1.26338e10i	0.0885802	−	0.0511418i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.27876e11	−	2.21487e11i	−0.506062	−	0.876525i	−0.999975	−	0.00701367i	$-0.997767\pi$
$709$	−1.27876e11	−	2.21487e11i	−0.506062	−	0.876525i	0.493914	−	0.869511i	$-0.335566\pi$
$710$		0			0
$711$	1.47707e11	−	2.55837e11i	0.577994	−	1.00112i
$712$		0			0
$713$		−	6.13838e10i		−	0.237517i
$714$		0			0
$715$	4.49965e9			0.0172169
$716$		0			0
$717$	1.13303e11	+	6.54152e10i	0.428709	+	0.247515i
$718$		0			0
$719$	−3.07636e11	+	1.77614e11i	−1.15112	+	0.664601i	−0.949161	−	0.314792i	$-0.898065\pi$
$719$	−3.07636e11	+	1.77614e11i	−1.15112	+	0.664601i	−0.201962	+	0.979393i	$0.564732\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−2.38234e11	−	4.12634e11i	−0.871868	−	1.51012i
$724$		0			0
$725$	−1.88857e11	+	3.27109e11i	−0.683566	+	1.18397i
$726$		0			0
$727$		−	7.85098e10i		−	0.281052i	−0.990077	−	0.140526i	$-0.955121\pi$
$727$		−	7.85098e10i		−	0.281052i	0.990077	−	0.140526i	$-0.0448793\pi$
$728$		0			0
$729$	1.90291e11			0.673764
$730$		0			0
$731$	5.11051e10	+	2.95056e10i	0.178976	+	0.103332i
$732$		0			0
$733$	−1.10682e11	+	6.39023e10i	−0.383408	+	0.221361i	−0.679300	−	0.733861i	$-0.737717\pi$
$733$	−1.10682e11	+	6.39023e10i	−0.383408	+	0.221361i	0.295892	+	0.955221i	$0.404383\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.16840e10	+	7.21988e10i	0.141286	+	0.244715i
$738$		0			0
$739$	−1.04862e11	+	1.81627e11i	−0.351594	+	0.608979i	−0.986529	−	0.163587i	$-0.947694\pi$
$739$	−1.04862e11	+	1.81627e11i	−0.351594	+	0.608979i	0.634935	+	0.772566i	$0.281027\pi$
$740$		0			0
$741$			1.96613e11i			0.652137i
$742$		0			0
$743$	5.88745e11			1.93184			0.965922	−	0.258833i	$-0.0833380\pi$
$743$	5.88745e11			1.93184			0.965922	+	0.258833i	$0.0833380\pi$
$744$		0			0
$745$	5.52714e9	+	3.19109e9i	0.0179422	+	0.0103589i
$746$		0			0
$747$	−2.07745e11	+	1.19942e11i	−0.667188	+	0.385201i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.60439e11	+	2.77889e11i	0.504372	+	0.873598i	0.999987	+	0.00505549i	$0.00160922\pi$
$751$	1.60439e11	+	2.77889e11i	0.504372	+	0.873598i	−0.495615	+	0.868542i	$0.665057\pi$
$752$		0			0
$753$	1.05558e11	−	1.82833e11i	0.328332	−	0.568688i
$754$		0			0
$755$			1.28334e10i			0.0394961i
$756$		0			0
$757$	−2.41933e11			−0.736735			−0.368368	−	0.929680i	$-0.620083\pi$
$757$	−2.41933e11			−0.736735			−0.368368	+	0.929680i	$0.620083\pi$
$758$		0			0
$759$	1.04958e11	+	6.05977e10i	0.316264	+	0.182595i
$760$		0			0
$761$	−3.40642e11	+	1.96670e11i	−1.01569	+	0.586407i	−0.912852	−	0.408292i	$-0.866125\pi$
$761$	−3.40642e11	+	1.96670e11i	−1.01569	+	0.586407i	−0.102835	+	0.994698i	$0.532791\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	9.15536e8	+	1.58575e9i	0.00267319	+	0.00463010i
$766$		0			0
$767$	−1.14567e10	+	1.98437e10i	−0.0331039	+	0.0573377i
$768$		0			0
$769$			6.91982e11i			1.97874i	0.145411	+	0.989371i	$0.453549\pi$
$769$			6.91982e11i			1.97874i	−0.145411	+	0.989371i	$0.546451\pi$
$770$		0			0
$771$	7.95485e11			2.25120
$772$		0			0
$773$	3.40927e11	+	1.96835e11i	0.954869	+	0.551294i	0.894590	−	0.446887i	$-0.147468\pi$
$773$	3.40927e11	+	1.96835e11i	0.954869	+	0.551294i	0.0602792	+	0.998182i	$0.480801\pi$
$774$		0			0
$775$	2.17124e11	−	1.25357e11i	0.601868	−	0.347489i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.40588e11	+	2.43505e11i	0.381766	+	0.661239i
$780$		0			0
$781$	−2.61738e10	+	4.53343e10i	−0.0703497	+	0.121849i
$782$		0			0
$783$		−	1.07134e11i		−	0.285023i
$784$		0			0
$785$	1.53382e9			0.00403920
$786$		0			0
$787$	2.91851e11	+	1.68500e11i	0.760786	+	0.439240i	0.829578	−	0.558391i	$-0.188581\pi$
$787$	2.91851e11	+	1.68500e11i	0.760786	+	0.439240i	−0.0687921	+	0.997631i	$0.521915\pi$
$788$		0			0
$789$	3.75627e11	−	2.16868e11i	0.969278	−	0.559613i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−9.13820e10	−	1.58278e11i	−0.231083	−	0.400247i
$794$		0			0
$795$	−4.42433e9	+	7.66316e9i	−0.0110759	+	0.0191840i
$796$		0			0
$797$			5.26594e11i			1.30510i	0.757747	+	0.652548i	$0.226300\pi$
$797$			5.26594e11i			1.30510i	−0.757747	+	0.652548i	$0.773700\pi$
$798$		0			0
$799$	1.29813e11			0.318515
$800$		0			0
$801$	−3.68743e11	−	2.12894e11i	−0.895763	−	0.517169i
$802$		0			0
$803$	1.69837e11	−	9.80557e10i	0.408480	−	0.235836i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.26382e11	−	3.92105e11i	−0.533762	−	0.924504i
$808$		0			0
$809$	−2.72962e11	+	4.72784e11i	−0.637247	+	1.10374i	0.348787	+	0.937202i	$0.386594\pi$
$809$	−2.72962e11	+	4.72784e11i	−0.637247	+	1.10374i	−0.986034	+	0.166543i	$0.946740\pi$
$810$		0			0
$811$		−	4.26131e11i		−	0.985054i	−0.870297	−	0.492527i	$-0.836073\pi$
$811$		−	4.26131e11i		−	0.985054i	0.870297	−	0.492527i	$-0.163927\pi$
$812$		0			0
$813$	7.74140e11			1.77197
$814$		0			0
$815$	−1.22227e10	−	7.05679e9i	−0.0277037	−	0.0159947i
$816$		0			0
$817$	4.13571e11	−	2.38776e11i	0.928244	−	0.535922i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4.32999e11	+	7.49977e11i	0.953047	+	1.65073i	0.738775	+	0.673952i	$0.235405\pi$
$821$	4.32999e11	+	7.49977e11i	0.953047	+	1.65073i	0.214272	+	0.976774i	$0.431262\pi$
$822$		0			0
$823$	2.34123e10	−	4.05513e10i	0.0510323	−	0.0883905i	−0.839381	−	0.543544i	$-0.817082\pi$
$823$	2.34123e10	−	4.05513e10i	0.0510323	−	0.0883905i	0.890413	+	0.455153i	$0.150416\pi$
$824$		0			0
$825$			4.95005e11i			1.06855i
$826$		0			0
$827$	2.16092e11			0.461974			0.230987	−	0.972957i	$-0.425805\pi$
$827$	2.16092e11			0.461974			0.230987	+	0.972957i	$0.425805\pi$
$828$		0			0
$829$	6.36661e11	+	3.67576e11i	1.34800	+	0.778268i	0.987966	−	0.154671i	$-0.0494317\pi$
$829$	6.36661e11	+	3.67576e11i	1.34800	+	0.778268i	0.360034	+	0.932939i	$0.382765\pi$
$830$		0			0
$831$	−1.96435e11	+	1.13412e11i	−0.411923	+	0.237824i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	9.11219e9	+	1.57828e10i	0.0187446	+	0.0324666i
$836$		0			0
$837$	−3.55560e10	+	6.15848e10i	−0.0724455	+	0.125479i
$838$		0			0
$839$			6.65490e11i			1.34306i	0.740979	+	0.671528i	$0.234362\pi$
$839$			6.65490e11i			1.34306i	−0.740979	+	0.671528i	$0.765638\pi$
$840$		0			0
$841$	4.37534e11			0.874637
$842$		0			0
$843$	−1.00710e10	−	5.81451e9i	−0.0199418	−	0.0115134i
$844$		0			0
$845$	1.15896e10	−	6.69125e9i	0.0227322	−	0.0131244i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.63703e11	−	6.29952e11i	−0.700029	−	1.21249i
$850$		0			0
$851$	−1.39147e11	+	2.41010e11i	−0.265312	+	0.459534i
$852$		0			0
$853$		−	7.76989e11i		−	1.46764i	−0.679345	−	0.733819i	$-0.737736\pi$
$853$		−	7.76989e11i		−	1.46764i	0.679345	−	0.733819i	$-0.262264\pi$
$854$		0			0
$855$	1.48181e10			0.0277285
$856$		0			0
$857$	−4.27209e11	−	2.46649e11i	−0.791986	−	0.457253i	0.0486755	−	0.998815i	$-0.484500\pi$
$857$	−4.27209e11	−	2.46649e11i	−0.791986	−	0.457253i	−0.840661	+	0.541562i	$0.817833\pi$
$858$		0			0
$859$	5.33204e10	−	3.07845e10i	0.0979311	−	0.0565406i	−0.450235	−	0.892910i	$-0.648660\pi$
$859$	5.33204e10	−	3.07845e10i	0.0979311	−	0.0565406i	0.548166	+	0.836370i	$0.315326\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.02953e11	+	8.71140e11i	0.906743	+	1.57053i	0.818560	+	0.574421i	$0.194773\pi$
$863$	5.02953e11	+	8.71140e11i	0.906743	+	1.57053i	0.0881834	+	0.996104i	$0.471894\pi$
$864$		0			0
$865$	−1.82747e10	+	3.16527e10i	−0.0326426	+	0.0565387i
$866$		0			0
$867$		−	7.47355e11i		−	1.32267i
$868$		0			0
$869$	−6.13019e11			−1.07497
$870$		0			0
$871$	−1.01242e11	−	5.84519e10i	−0.175908	−	0.101561i
$872$		0			0
$873$	1.12080e11	−	6.47094e10i	0.192962	−	0.111407i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.26686e10	−	2.19427e10i	−0.0214156	−	0.0370929i	0.855119	−	0.518432i	$-0.173484\pi$
$877$	−1.26686e10	−	2.19427e10i	−0.0214156	−	0.0370929i	−0.876535	+	0.481339i	$0.840151\pi$
$878$		0			0
$879$	−1.87221e11	+	3.24277e11i	−0.313617	+	0.543201i
$880$		0			0
$881$			3.46215e11i			0.574701i	0.957825	+	0.287351i	$0.0927745\pi$
$881$			3.46215e11i			0.574701i	−0.957825	+	0.287351i	$0.907225\pi$
$882$		0			0
$883$	1.74934e11			0.287761			0.143881	−	0.989595i	$-0.454042\pi$
$883$	1.74934e11			0.287761			0.143881	+	0.989595i	$0.454042\pi$
$884$		0			0
$885$	3.26164e9	+	1.88311e9i	0.00531695	+	0.00306974i
$886$		0			0
$887$	−7.46608e11	+	4.31055e11i	−1.20614	+	0.696366i	−0.961914	−	0.273352i	$-0.911868\pi$
$887$	−7.46608e11	+	4.31055e11i	−1.20614	+	0.696366i	−0.244228	+	0.969718i	$0.578534\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.80338e11	−	4.85559e11i	−0.444806	−	0.770427i
$892$		0			0
$893$	5.25258e11	−	9.09774e11i	0.825975	−	1.43063i
$894$		0			0
$895$			9.54402e8i			0.00148744i
$896$		0			0
$897$	−1.69948e11			−0.262510
$898$		0			0
$899$	−5.39073e11	−	3.11234e11i	−0.825294	−	0.476483i
$900$		0			0
$901$	−3.93697e10	+	2.27301e10i	−0.0597397	+	0.0344907i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.12974e10	−	1.95677e10i	−0.0168417	−	0.0291706i
$906$		0			0
$907$	−1.32062e11	+	2.28738e11i	−0.195141	+	0.337994i	−0.946947	−	0.321391i	$-0.895850\pi$
$907$	−1.32062e11	+	2.28738e11i	−0.195141	+	0.337994i	0.751806	+	0.659384i	$0.229183\pi$
$908$		0			0
$909$			5.20575e11i			0.762478i
$910$		0			0
$911$	−7.18346e11			−1.04294			−0.521471	−	0.853269i	$-0.674617\pi$
$911$	−7.18346e11			−1.04294			−0.521471	+	0.853269i	$0.674617\pi$
$912$		0			0
$913$	4.31094e11	+	2.48892e11i	0.620425	+	0.358202i
$914$		0			0
$915$	−2.60157e10	+	1.50202e10i	−0.0371151	+	0.0214284i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.18816e11	−	5.52206e11i	−0.446970	−	0.774175i	0.551217	−	0.834362i	$-0.314164\pi$
$919$	−3.18816e11	−	5.52206e11i	−0.446970	−	0.774175i	−0.998187	+	0.0601868i	$0.980830\pi$
$920$		0			0
$921$	5.55897e11	−	9.62843e11i	0.772603	−	1.33819i
$922$		0			0
$923$		−	7.34049e10i		−	0.101139i
$924$		0			0
$925$	−1.13666e12			−1.55261
$926$		0			0
$927$	−6.98145e11	−	4.03074e11i	−0.945424	−	0.545841i
$928$		0			0
$929$	−1.19209e11	+	6.88253e10i	−0.160046	+	0.0924028i	−0.577884	−	0.816119i	$-0.696121\pi$
$929$	−1.19209e11	+	6.88253e10i	−0.160046	+	0.0924028i	0.417838	+	0.908522i	$0.362788\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	5.12736e10	+	8.88084e10i	0.0676655	+	0.117200i
$934$		0			0
$935$	1.89984e9	−	3.29062e9i	0.00248583	−	0.00430558i
$936$		0			0
$937$		−	1.07909e12i		−	1.39990i	−0.714191	−	0.699951i	$-0.753205\pi$
$937$		−	1.07909e12i		−	1.39990i	0.714191	−	0.699951i	$-0.246795\pi$
$938$		0			0
$939$	−1.51521e12			−1.94900
$940$		0			0
$941$	6.31889e11	+	3.64821e11i	0.805902	+	0.465288i	0.845531	−	0.533927i	$-0.179284\pi$
$941$	6.31889e11	+	3.64821e11i	0.805902	+	0.465288i	−0.0396289	+	0.999214i	$0.512618\pi$
$942$		0			0
$943$	−2.10480e11	+	1.21521e11i	−0.266173	+	0.153675i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.00302e11	+	3.46933e11i	0.249049	+	0.431366i	0.963262	−	0.268562i	$-0.0865485\pi$
$947$	2.00302e11	+	3.46933e11i	0.249049	+	0.431366i	−0.714213	+	0.699928i	$0.753215\pi$
$948$		0			0
$949$	−1.37500e11	+	2.38157e11i	−0.169526	+	0.293628i
$950$		0			0
$951$		−	1.33448e12i		−	1.63151i
$952$		0			0
$953$	−2.84049e11			−0.344367			−0.172183	−	0.985065i	$-0.555082\pi$
$953$	−2.84049e11			−0.344367			−0.172183	+	0.985065i	$0.555082\pi$
$954$		0			0
$955$	−4.57971e10	−	2.64409e10i	−0.0550585	−	0.0317880i
$956$		0			0
$957$	1.06434e12	−	6.14496e11i	1.26891	−	0.732607i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.19859e11	−	3.80807e11i	−0.257781	−	0.446490i
$962$		0			0
$963$	1.28165e11	−	2.21988e11i	0.149027	−	0.258122i
$964$		0			0
$965$		−	6.02828e10i		−	0.0695160i
$966$		0			0
$967$	−5.13167e11			−0.586885			−0.293442	−	0.955977i	$-0.594801\pi$
$967$	−5.13167e11			−0.586885			−0.293442	+	0.955977i	$0.594801\pi$
$968$		0			0
$969$	1.43784e11	+	8.30138e10i	0.163086	+	0.0941575i
$970$		0			0
$971$	−3.29471e11	+	1.90220e11i	−0.370629	+	0.213983i	−0.673733	−	0.738975i	$-0.735310\pi$
$971$	−3.29471e11	+	1.90220e11i	−0.370629	+	0.213983i	0.303104	+	0.952957i	$0.401977\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.47064e11	−	6.01132e11i	−0.384052	−	0.665198i
$976$		0			0
$977$	7.42574e11	−	1.28618e12i	0.815007	−	1.41163i	−0.0943151	−	0.995542i	$-0.530066\pi$
$977$	7.42574e11	−	1.28618e12i	0.815007	−	1.41163i	0.909323	−	0.416092i	$-0.136601\pi$
$978$		0			0
$979$			8.83557e11i			0.961842i
$980$		0			0
$981$	−2.52005e11			−0.272103
$982$		0			0
$983$	−1.27994e12	−	7.38976e11i	−1.37081	−	0.791437i	−0.379779	−	0.925077i	$-0.624000\pi$
$983$	−1.27994e12	−	7.38976e11i	−1.37081	−	0.791437i	−0.991030	+	0.133641i	$0.957333\pi$
$984$		0			0
$985$	−1.63563e10	+	9.44330e9i	−0.0173756	+	0.0100318i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.06392e11	+	3.57481e11i	0.215729	+	0.373653i
$990$		0			0
$991$	−3.22057e11	+	5.57819e11i	−0.333917	+	0.578361i	−0.983276	−	0.182121i	$-0.941704\pi$
$991$	−3.22057e11	+	5.57819e11i	−0.333917	+	0.578361i	0.649359	+	0.760482i	$0.275037\pi$
$992$		0			0
$993$		−	1.82879e12i		−	1.88090i
$994$		0			0
$995$	1.83939e10			0.0187664
$996$		0			0
$997$	−7.72684e11	−	4.46109e11i	−0.782026	−	0.451503i	0.0551215	−	0.998480i	$-0.482445\pi$
$997$	−7.72684e11	−	4.46109e11i	−0.782026	−	0.451503i	−0.837148	+	0.546976i	$0.815779\pi$
$998$		0			0
$999$	2.79206e11	−	1.61200e11i	0.280326	−	0.161846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.9.h.c.129.13		32
7.2	even	3	inner	196.9.h.c.117.4		32
7.3	odd	6		196.9.b.b.97.13	yes	16
7.4	even	3		196.9.b.b.97.4	✓	16
7.5	odd	6	inner	196.9.h.c.117.13		32
7.6	odd	2	inner	196.9.h.c.129.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.9.b.b.97.4	✓	16	7.4	even	3
196.9.b.b.97.13	yes	16	7.3	odd	6
196.9.h.c.117.4		32	7.2	even	3	inner
196.9.h.c.117.13		32	7.5	odd	6	inner
196.9.h.c.129.4		32	7.6	odd	2	inner
196.9.h.c.129.13		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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	196.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(95.3296 + 55.0385i) q^{3} +(20.9063 - 12.0703i) q^{5} +(2777.98 + 4811.61i) q^{9} +(5764.63 - 9984.63i) q^{11} +16167.0i q^{13} +2657.32 q^{15} +(11823.0 + 6826.04i) q^{17} +(95678.7 - 55240.1i) q^{19} +(47748.3 + 82702.4i) q^{23} +(-195021. + 337786. i) q^{25} -110631. i q^{27} +968391. q^{29} +(-556669. - 321393. i) q^{31} +(1.09908e6 - 634554. i) q^{33} +(1.45709e6 + 2.52376e6i) q^{37} +(-889810. + 1.54120e6i) q^{39} +2.54503e6i q^{41} +4.32250e6 q^{43} +(116155. + 67062.1i) q^{45} +(8.23472e6 - 4.75432e6i) q^{47} +(751390. + 1.30145e6i) q^{51} +(-1.66496e6 + 2.88379e6i) q^{53} -278323. i q^{55} +1.21613e7 q^{57} +(1.22742e6 + 708648. i) q^{59} +(-9.79018e6 + 5.65236e6i) q^{61} +(195141. + 337993. i) q^{65} +(-3.61550e6 + 6.26223e6i) q^{67} +1.05120e7i q^{69} -4.54041e6 q^{71} +(1.47310e7 + 8.50494e6i) q^{73} +(-3.71826e7 + 2.14674e7i) q^{75} +(-2.65854e7 - 4.60472e7i) q^{79} +(2.43153e7 - 4.21154e7i) q^{81} +4.31758e7i q^{83} +329569. q^{85} +(9.23163e7 + 5.32988e7i) q^{87} +(-6.63688e7 + 3.83180e7i) q^{89} +(-3.53780e7 - 6.12765e7i) q^{93} +(1.33353e6 - 2.30974e6i) q^{95} -2.32937e7i q^{97} +6.40562e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 52264 q^{9} + 22776 q^{11} + 206064 q^{15} - 571560 q^{23} + 1030440 q^{25} - 5384256 q^{29} + 3376640 q^{37} + 10336136 q^{39} + 18525008 q^{43} + 16028856 q^{51} - 14106216 q^{53} - 4787360 q^{57}+ \cdots + 1119499328 q^{99}+O(q^{100}) \) 32 * q + 52264 * q^9 + 22776 * q^11 + 206064 * q^15 - 571560 * q^23 + 1030440 * q^25 - 5384256 * q^29 + 3376640 * q^37 + 10336136 * q^39 + 18525008 * q^43 + 16028856 * q^51 - 14106216 * q^53 - 4787360 * q^57 - 5623008 * q^65 - 82433680 * q^67 + 250685568 * q^71 + 138241200 * q^79 - 465637680 * q^81 + 880381104 * q^85 + 310654512 * q^93 - 811120872 * q^95 + 1119499328 * q^99

Introduction

L-functions

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