LMFDB - Embedded newform 756.2.n.b.199.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(19,756)] 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("756.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [84] 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.10
Character	$\chi$	$=$	756.199
Dual form			756.2.n.b.19.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07941 + 0.913714i) q^{2} +(0.330255 - 1.97254i) q^{4} +3.48216i q^{5} +(-0.638585 - 2.56753i) q^{7} +(1.44586 + 2.43094i) q^{8} +(-3.18169 - 3.75868i) q^{10} -1.97557i q^{11} +(5.52258 + 3.18847i) q^{13} +(3.03528 + 2.18793i) q^{14} +(-3.78186 - 1.30288i) q^{16} +(-1.04054 - 0.600755i) q^{17} +(2.25453 + 3.90496i) q^{19} +(6.86871 + 1.15000i) q^{20} +(1.80511 + 2.13246i) q^{22} -0.590265i q^{23} -7.12541 q^{25} +(-8.87448 + 1.60440i) q^{26} +(-5.27546 + 0.411699i) q^{28} +(2.00631 + 3.47503i) q^{29} +(2.63991 + 4.57246i) q^{31} +(5.27265 - 2.04919i) q^{32} +(1.67209 - 0.302292i) q^{34} +(8.94054 - 2.22365i) q^{35} +(0.506783 + 0.877774i) q^{37} +(-6.00157 - 2.15506i) q^{38} +(-8.46493 + 5.03471i) q^{40} +(-4.54294 - 2.62287i) q^{41} +(-2.66552 + 1.53894i) q^{43} +(-3.89691 - 0.652443i) q^{44} +(0.539333 + 0.637139i) q^{46} +(0.174866 - 0.302877i) q^{47} +(-6.18442 + 3.27917i) q^{49} +(7.69124 - 6.51059i) q^{50} +(8.11325 - 9.84054i) q^{52} +(-3.01662 + 5.22494i) q^{53} +6.87926 q^{55} +(5.31822 - 5.26465i) q^{56} +(-5.34081 - 1.91779i) q^{58} +(7.25888 + 12.5727i) q^{59} +(3.42577 + 1.97787i) q^{61} +(-7.02746 - 2.52344i) q^{62} +(-3.81897 + 7.02961i) q^{64} +(-11.1027 + 19.2305i) q^{65} +(-4.23532 + 2.44526i) q^{67} +(-1.52866 + 1.85410i) q^{68} +(-7.61873 + 10.5693i) q^{70} -1.47342i q^{71} +(9.61590 + 5.55174i) q^{73} +(-1.34906 - 0.484424i) q^{74} +(8.44727 - 3.15753i) q^{76} +(-5.07235 + 1.26157i) q^{77} +(0.556744 + 0.321436i) q^{79} +(4.53685 - 13.1690i) q^{80} +(7.30024 - 1.31979i) q^{82} +(-1.00577 - 1.74205i) q^{83} +(2.09192 - 3.62331i) q^{85} +(1.47104 - 4.09667i) q^{86} +(4.80251 - 2.85640i) q^{88} +(3.27016 - 1.88803i) q^{89} +(4.65984 - 16.2155i) q^{91} +(-1.16432 - 0.194938i) q^{92} +(0.0879904 + 0.486706i) q^{94} +(-13.5977 + 7.85062i) q^{95} +(-14.8094 + 8.55023i) q^{97} +(3.67930 - 9.19036i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41}+ \cdots - 21 q^{98}+O(q^{100}) $ 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.07941	+	0.913714i	−0.763259	+	0.646093i
$2$	−1.07941	+	0.913714i	−0.763259	+	0.646093i
$3$		0			0
$3$		0			0
$4$	0.330255	−	1.97254i	0.165127	−	0.986272i
$5$			3.48216i			1.55727i	0.627479	+	0.778634i	$0.284087\pi$
$5$			3.48216i			1.55727i	−0.627479	+	0.778634i	$0.715913\pi$
$6$		0			0
$7$	−0.638585	−	2.56753i	−0.241362	−	0.970435i
$7$	−0.638585	−	2.56753i	−0.241362	−	0.970435i
$8$	1.44586	+	2.43094i	0.511189	+	0.859468i
$9$		0			0
$10$	−3.18169	−	3.75868i	−1.00614	−	1.18860i
$11$		−	1.97557i		−	0.595658i	−0.954619	−	0.297829i	$-0.903737\pi$
$11$		−	1.97557i		−	0.595658i	0.954619	−	0.297829i	$-0.0962625\pi$
$12$		0			0
$13$	5.52258	+	3.18847i	1.53169	+	0.884321i	0.999284	+	0.0378315i	$0.0120450\pi$
$13$	5.52258	+	3.18847i	1.53169	+	0.884321i	0.532405	+	0.846490i	$0.321288\pi$
$14$	3.03528	+	2.18793i	0.811213	+	0.584750i
$15$		0			0
$16$	−3.78186	−	1.30288i	−0.945466	−	0.325721i
$17$	−1.04054	−	0.600755i	−0.252367	−	0.145704i	0.368480	−	0.929636i	$-0.379878\pi$
$17$	−1.04054	−	0.600755i	−0.252367	−	0.145704i	−0.620848	+	0.783931i	$0.713212\pi$
$18$		0			0
$19$	2.25453	+	3.90496i	0.517224	+	0.895858i	0.999800	+	0.0200042i	$0.00636795\pi$
$19$	2.25453	+	3.90496i	0.517224	+	0.895858i	−0.482576	+	0.875854i	$0.660299\pi$
$20$	6.86871	+	1.15000i	1.53589	+	0.257147i
$21$		0			0
$22$	1.80511	+	2.13246i	0.384851	+	0.454641i
$23$		−	0.590265i		−	0.123079i	−0.998105	−	0.0615394i	$-0.980399\pi$
$23$		−	0.590265i		−	0.123079i	0.998105	−	0.0615394i	$-0.0196010\pi$
$24$		0			0
$25$	−7.12541			−1.42508
$26$	−8.87448	+	1.60440i	−1.74043	+	0.314648i
$27$		0			0
$28$	−5.27546	+	0.411699i	−0.996969	+	0.0778038i
$29$	2.00631	+	3.47503i	0.372562	+	0.645296i	0.989959	−	0.141356i	$-0.0451461\pi$
$29$	2.00631	+	3.47503i	0.372562	+	0.645296i	−0.617397	+	0.786652i	$0.711813\pi$
$30$		0			0
$31$	2.63991	+	4.57246i	0.474142	+	0.821237i	0.999562	−	0.0296057i	$-0.00942517\pi$
$31$	2.63991	+	4.57246i	0.474142	+	0.821237i	−0.525420	+	0.850843i	$0.676092\pi$
$32$	5.27265	−	2.04919i	0.932081	−	0.362250i
$33$		0			0
$34$	1.67209	−	0.302292i	0.286760	−	0.0518427i
$35$	8.94054	−	2.22365i	1.51123	−	0.375866i
$36$		0			0
$37$	0.506783	+	0.877774i	0.0833146	+	0.144305i	0.904672	−	0.426109i	$-0.140116\pi$
$37$	0.506783	+	0.877774i	0.0833146	+	0.144305i	−0.821357	+	0.570414i	$0.806783\pi$
$38$	−6.00157	−	2.15506i	−0.973584	−	0.349597i
$39$		0			0
$40$	−8.46493	+	5.03471i	−1.33842	+	0.796058i
$41$	−4.54294	−	2.62287i	−0.709488	−	0.409623i	0.101384	−	0.994847i	$-0.467673\pi$
$41$	−4.54294	−	2.62287i	−0.709488	−	0.409623i	−0.810871	+	0.585225i	$0.801006\pi$
$42$		0			0
$43$	−2.66552	+	1.53894i	−0.406488	+	0.234686i	−0.689280	−	0.724495i	$-0.742073\pi$
$43$	−2.66552	+	1.53894i	−0.406488	+	0.234686i	0.282792	+	0.959181i	$0.408739\pi$
$44$	−3.89691	−	0.652443i	−0.587481	−	0.0983594i
$45$		0			0
$46$	0.539333	+	0.637139i	0.0795204	+	0.0939410i
$47$	0.174866	−	0.302877i	0.0255068	−	0.0441791i	−0.852990	−	0.521927i	$-0.825213\pi$
$47$	0.174866	−	0.302877i	0.0255068	−	0.0441791i	0.878497	+	0.477748i	$0.158547\pi$
$48$		0			0
$49$	−6.18442	+	3.27917i	−0.883488	+	0.468453i
$50$	7.69124	−	6.51059i	1.08771	−	0.920736i
$51$		0			0
$52$	8.11325	−	9.84054i	1.12511	−	1.36464i
$53$	−3.01662	+	5.22494i	−0.414364	+	0.717700i	−0.995361	−	0.0962054i	$-0.969329\pi$
$53$	−3.01662	+	5.22494i	−0.414364	+	0.717700i	0.580997	+	0.813906i	$0.302663\pi$
$54$		0			0
$55$	6.87926			0.927599
$56$	5.31822	−	5.26465i	0.710676	−	0.703519i
$57$		0			0
$58$	−5.34081	−	1.91779i	−0.701282	−	0.251818i
$59$	7.25888	+	12.5727i	0.945025	+	1.63683i	0.755701	+	0.654917i	$0.227296\pi$
$59$	7.25888	+	12.5727i	0.945025	+	1.63683i	0.189324	+	0.981915i	$0.439370\pi$
$60$		0			0
$61$	3.42577	+	1.97787i	0.438625	+	0.253240i	0.703014	−	0.711176i	$-0.251837\pi$
$61$	3.42577	+	1.97787i	0.438625	+	0.253240i	−0.264389	+	0.964416i	$0.585170\pi$
$62$	−7.02746	−	2.52344i	−0.892488	−	0.320477i
$63$		0			0
$64$	−3.81897	+	7.02961i	−0.477372	+	0.878701i
$65$	−11.1027	+	19.2305i	−1.37712	+	2.38525i
$66$		0			0
$67$	−4.23532	+	2.44526i	−0.517426	+	0.298736i	−0.735881	−	0.677111i	$-0.763232\pi$
$67$	−4.23532	+	2.44526i	−0.517426	+	0.298736i	0.218455	+	0.975847i	$0.429898\pi$
$68$	−1.52866	+	1.85410i	−0.185377	+	0.224843i
$69$		0			0
$70$	−7.61873	+	10.5693i	−0.910613	+	1.26328i
$71$		−	1.47342i		−	0.174863i	−0.996171	−	0.0874313i	$-0.972134\pi$
$71$		−	1.47342i		−	0.174863i	0.996171	−	0.0874313i	$-0.0278658\pi$
$72$		0			0
$73$	9.61590	+	5.55174i	1.12546	+	0.649783i	0.942788	−	0.333392i	$-0.108193\pi$
$73$	9.61590	+	5.55174i	1.12546	+	0.649783i	0.182668	+	0.983175i	$0.441527\pi$
$74$	−1.34906	−	0.484424i	−0.156825	−	0.0563131i
$75$		0			0
$76$	8.44727	−	3.15753i	0.968968	−	0.362193i
$77$	−5.07235	+	1.26157i	−0.578047	+	0.143770i
$78$		0			0
$79$	0.556744	+	0.321436i	0.0626386	+	0.0361644i	0.530992	−	0.847377i	$-0.321819\pi$
$79$	0.556744	+	0.321436i	0.0626386	+	0.0361644i	−0.468354	+	0.883541i	$0.655153\pi$
$80$	4.53685	−	13.1690i	0.507235	−	1.47234i
$81$		0			0
$82$	7.30024	−	1.31979i	0.806177	−	0.145747i
$83$	−1.00577	−	1.74205i	−0.110398	−	0.191215i	0.805533	−	0.592551i	$-0.201879\pi$
$83$	−1.00577	−	1.74205i	−0.110398	−	0.191215i	−0.915931	+	0.401336i	$0.868546\pi$
$84$		0			0
$85$	2.09192	−	3.62331i	0.226901	−	0.393004i
$86$	1.47104	−	4.09667i	0.158626	−	0.441755i
$87$		0			0
$88$	4.80251	−	2.85640i	0.511949	−	0.304494i
$89$	3.27016	−	1.88803i	0.346636	−	0.200130i	−0.316567	−	0.948570i	$-0.602530\pi$
$89$	3.27016	−	1.88803i	0.346636	−	0.200130i	0.663203	+	0.748440i	$0.269197\pi$
$90$		0			0
$91$	4.65984	−	16.2155i	0.488484	−	1.69985i
$92$	−1.16432	−	0.194938i	−0.121389	−	0.0203237i
$93$		0			0
$94$	0.0879904	+	0.486706i	0.00907552	+	0.0501999i
$95$	−13.5977	+	7.85062i	−1.39509	+	0.805456i
$96$		0			0
$97$	−14.8094	+	8.55023i	−1.50367	+	0.868145i	−0.503679	+	0.863891i	$0.668021\pi$
$97$	−14.8094	+	8.55023i	−1.50367	+	0.868145i	−0.999991	+	0.00425389i	$0.998646\pi$
$98$	3.67930	−	9.19036i	0.371666	−	0.928367i
$99$		0			0
$100$	−2.35320	+	14.0552i	−0.235320	+	1.40552i
$101$		−	4.96913i		−	0.494447i	−0.968958	−	0.247224i	$-0.920482\pi$
$101$		−	4.96913i		−	0.494447i	0.968958	−	0.247224i	$-0.0795182\pi$
$102$		0			0
$103$	−15.1779			−1.49552			−0.747761	−	0.663968i	$-0.768871\pi$
$103$	−15.1779			−1.49552			−0.747761	+	0.663968i	$0.768871\pi$
$104$	0.233906	+	18.0352i	0.0229364	+	1.76849i
$105$		0			0
$106$	−1.51793	−	8.39618i	−0.147434	−	0.815509i
$107$	−9.66900	+	5.58240i	−0.934737	+	0.539671i	−0.888307	−	0.459251i	$-0.848118\pi$
$107$	−9.66900	+	5.58240i	−0.934737	+	0.539671i	−0.0464307	+	0.998922i	$0.514785\pi$
$108$		0			0
$109$	2.33905	−	4.05136i	0.224041	−	0.388050i	−0.731991	−	0.681315i	$-0.761409\pi$
$109$	2.33905	−	4.05136i	0.224041	−	0.388050i	0.956031	+	0.293265i	$0.0947419\pi$
$110$	−7.42554	+	6.28567i	−0.707998	+	0.599315i
$111$		0			0
$112$	−0.930152	+	10.5420i	−0.0878911	+	0.996130i
$113$	5.62554	−	9.74373i	0.529207	−	0.916613i	−0.470213	−	0.882553i	$-0.655823\pi$
$113$	5.62554	−	9.74373i	0.529207	−	0.916613i	0.999420	−	0.0340600i	$-0.0108437\pi$
$114$		0			0
$115$	2.05540			0.191667
$116$	7.51724	−	2.80989i	0.697958	−	0.260891i
$117$		0			0
$118$	−19.3232	−	6.93862i	−1.77884	−	0.638751i
$119$	−0.877984	+	3.05524i	−0.0804846	+	0.280074i
$120$		0			0
$121$	7.09711			0.645192
$122$	−5.50501	+	0.995239i	−0.498401	+	0.0901047i
$123$		0			0
$124$	9.89121	−	3.69726i	0.888257	−	0.332024i
$125$		−	7.40101i		−	0.661967i
$126$		0			0
$127$			10.7073i			0.950115i	0.879955	+	0.475058i	$0.157573\pi$
$127$			10.7073i			0.950115i	−0.879955	+	0.475058i	$0.842427\pi$
$128$	−2.30081	−	11.0773i	−0.203365	−	0.979103i
$129$		0			0
$130$	−5.58676	−	30.9023i	−0.489991	−	2.71031i
$131$	5.67606			0.495920			0.247960	−	0.968770i	$-0.420240\pi$
$131$	5.67606			0.495920			0.247960	+	0.968770i	$0.420240\pi$
$132$		0			0
$133$	8.58638	−	8.28221i	0.744534	−	0.718159i
$134$	2.33738	−	6.50931i	0.201919	−	0.562318i
$135$		0			0
$136$	−0.0440714	−	3.39810i	−0.00377909	−	0.291384i
$137$	7.79004			0.665548			0.332774	−	0.943007i	$-0.392015\pi$
$137$	7.79004			0.665548			0.332774	+	0.943007i	$0.392015\pi$
$138$		0			0
$139$	6.87438	−	11.9068i	0.583078	−	1.00992i	−0.412035	−	0.911168i	$-0.635182\pi$
$139$	6.87438	−	11.9068i	0.583078	−	1.00992i	0.995112	−	0.0987517i	$-0.0314850\pi$
$140$	−1.43360	−	18.3700i	−0.121161	−	1.55255i
$141$		0			0
$142$	1.34628	+	1.59042i	0.112978	+	0.133465i
$143$	6.29905	−	10.9103i	0.526753	−	0.912363i
$144$		0			0
$145$	−12.1006	+	6.98628i	−1.00490	+	0.580179i
$146$	−15.4522	+	2.79357i	−1.27883	+	0.231198i
$147$		0			0
$148$	1.89882	−	0.709763i	0.156082	−	0.0583422i
$149$	20.4898			1.67859			0.839293	−	0.543679i	$-0.182969\pi$
$149$	20.4898			1.67859			0.839293	+	0.543679i	$0.182969\pi$
$150$		0			0
$151$		−	22.0199i		−	1.79195i	−0.444100	−	0.895977i	$-0.646477\pi$
$151$		−	22.0199i		−	1.79195i	0.444100	−	0.895977i	$-0.353523\pi$
$152$	−6.23300	+	11.1267i	−0.505563	+	0.902491i
$153$		0			0
$154$	4.32243	−	5.99643i	0.348311	−	0.483206i
$155$	−15.9220	+	9.19257i	−1.27889	+	0.738365i
$156$		0			0
$157$	9.72123	−	5.61256i	0.775839	−	0.447931i	−0.0591146	−	0.998251i	$-0.518828\pi$
$157$	9.72123	−	5.61256i	0.775839	−	0.447931i	0.834954	+	0.550320i	$0.185494\pi$
$158$	−0.894656	+	0.161743i	−0.0711750	+	0.0128676i
$159$		0			0
$160$	7.13561	+	18.3602i	0.564120	+	1.45150i
$161$	−1.51552	+	0.376935i	−0.119440	+	0.0297066i
$162$		0			0
$163$	7.50110	−	4.33076i	0.587531	−	0.339211i	−0.176589	−	0.984285i	$-0.556506\pi$
$163$	7.50110	−	4.33076i	0.587531	−	0.339211i	0.764121	+	0.645073i	$0.223173\pi$
$164$	−6.67405	+	8.09493i	−0.521155	+	0.632108i
$165$		0			0
$166$	2.67738	+	0.961399i	0.207805	+	0.0746190i
$167$	12.3381	−	21.3703i	0.954754	−	1.65368i	0.219824	−	0.975540i	$-0.429452\pi$
$167$	12.3381	−	21.3703i	0.954754	−	1.65368i	0.734930	−	0.678143i	$-0.237215\pi$
$168$		0			0
$169$	13.8326	+	23.9588i	1.06405	+	1.84299i
$170$	1.05263	+	5.82246i	0.0807330	+	0.446562i
$171$		0			0
$172$	2.15532	+	5.76610i	0.164342	+	0.439661i
$173$	0.626093	+	0.361475i	0.0476010	+	0.0274824i	0.523612	−	0.851957i	$-0.324584\pi$
$173$	0.626093	+	0.361475i	0.0476010	+	0.0274824i	−0.476011	+	0.879440i	$0.657918\pi$
$174$		0			0
$175$	4.55018	+	18.2947i	0.343961	+	1.38295i
$176$	−2.57394	+	7.47135i	−0.194018	+	0.563174i
$177$		0			0
$178$	−1.80473	+	5.02594i	−0.135270	+	0.376710i
$179$	−10.2904	−	5.94116i	−0.769139	−	0.444063i	0.0634282	−	0.997986i	$-0.479797\pi$
$179$	−10.2904	−	5.94116i	−0.769139	−	0.444063i	−0.832568	+	0.553924i	$0.813130\pi$
$180$		0			0
$181$		−	5.23327i		−	0.388986i	−0.980904	−	0.194493i	$-0.937694\pi$
$181$		−	5.23327i		−	0.388986i	0.980904	−	0.194493i	$-0.0623062\pi$
$182$	9.78645	+	21.7609i	0.725420	+	1.61303i
$183$		0			0
$184$	1.43490	−	0.853441i	0.105782	−	0.0629165i
$185$	−3.05655	+	1.76470i	−0.224722	+	0.129743i
$186$		0			0
$187$	−1.18684	+	2.05566i	−0.0867900	+	0.150325i
$188$	−0.539687	−	0.444957i	−0.0393607	−	0.0324518i
$189$		0			0
$190$	7.50425	−	20.8984i	0.544416	−	1.51613i
$191$	13.7450	+	7.93569i	0.994555	+	0.574207i	0.906633	−	0.421921i	$-0.138644\pi$
$191$	13.7450	+	7.93569i	0.994555	+	0.574207i	0.0879222	+	0.996127i	$0.471977\pi$
$192$		0			0
$193$	0.442829	+	0.767002i	0.0318755	+	0.0552100i	0.881523	−	0.472141i	$-0.156519\pi$
$193$	0.442829	+	0.767002i	0.0318755	+	0.0552100i	−0.849648	+	0.527351i	$0.823185\pi$
$194$	8.17300	−	22.7608i	0.586787	−	1.63413i
$195$		0			0
$196$	4.42588	+	13.2820i	0.316134	+	0.948714i
$197$	2.17147			0.154711			0.0773553	−	0.997004i	$-0.475352\pi$
$197$	2.17147			0.154711			0.0773553	+	0.997004i	$0.475352\pi$
$198$		0			0
$199$	6.48062	−	11.2248i	0.459399	−	0.795702i	−0.539530	−	0.841966i	$-0.681398\pi$
$199$	6.48062	−	11.2248i	0.459399	−	0.795702i	0.998929	+	0.0462638i	$0.0147315\pi$
$200$	−10.3024	−	17.3215i	−0.728486	−	1.22481i
$201$		0			0
$202$	4.54037	+	5.36374i	0.319459	+	0.377391i
$203$	7.64104	−	7.37035i	0.536296	−	0.517297i
$204$		0			0
$205$	9.13323	−	15.8192i	0.637892	−	1.10486i
$206$	16.3832	−	13.8682i	1.14147	−	0.966246i
$207$		0			0
$208$	−16.7315	−	19.2536i	−1.16012	−	1.33500i
$209$	7.71453	−	4.45399i	0.533625	−	0.308089i
$210$		0			0
$211$	−8.89012	−	5.13271i	−0.612021	−	0.353350i	0.161735	−	0.986834i	$-0.448291\pi$
$211$	−8.89012	−	5.13271i	−0.612021	−	0.353350i	−0.773756	+	0.633484i	$0.781624\pi$
$212$	9.31017	+	7.67597i	0.639425	+	0.527188i
$213$		0			0
$214$	5.33611	−	14.8604i	0.364769	−	1.01584i
$215$	−5.35882	−	9.28176i	−0.365469	−	0.633010i
$216$		0			0
$217$	10.0541	−	9.69795i	0.682517	−	0.658339i
$218$	1.17698	+	6.51030i	0.0797153	+	0.440933i
$219$		0			0
$220$	2.27191	−	13.5696i	0.153172	−	0.914865i
$221$	−3.83097	−	6.63544i	−0.257699	−	0.446348i
$222$		0			0
$223$	−9.27475	−	16.0643i	−0.621083	−	1.07575i	−0.989284	−	0.146001i	$-0.953360\pi$
$223$	−9.27475	−	16.0643i	−0.621083	−	1.07575i	0.368201	−	0.929746i	$-0.379974\pi$
$224$	−8.62840	−	12.2291i	−0.576509	−	0.817091i
$225$		0			0
$226$	2.83071	+	15.6576i	0.188296	+	1.04153i
$227$	−6.02921			−0.400172			−0.200086	−	0.979778i	$-0.564122\pi$
$227$	−6.02921			−0.400172			−0.200086	+	0.979778i	$0.564122\pi$
$228$		0			0
$229$		−	2.91153i		−	0.192399i	−0.995362	−	0.0961995i	$-0.969331\pi$
$229$		−	2.91153i		−	0.192399i	0.995362	−	0.0961995i	$-0.0306687\pi$
$230$	−2.21862	+	1.87804i	−0.146291	+	0.123834i
$231$		0			0
$232$	−5.54675	+	9.90162i	−0.364162	+	0.650073i
$233$	4.64505	+	8.04547i	0.304308	+	0.527076i	0.977107	−	0.212749i	$-0.0682416\pi$
$233$	4.64505	+	8.04547i	0.304308	+	0.527076i	−0.672799	+	0.739825i	$0.734908\pi$
$234$		0			0
$235$	1.05466	+	0.608910i	0.0687987	+	0.0397209i
$236$	27.1976	−	10.1662i	1.77041	−	0.661766i
$237$		0			0
$238$	−1.84391	−	4.10009i	−0.119523	−	0.265769i
$239$	−4.84551	−	2.79756i	−0.313430	−	0.180959i	0.335030	−	0.942207i	$-0.391253\pi$
$239$	−4.84551	−	2.79756i	−0.313430	−	0.180959i	−0.648460	+	0.761248i	$0.724587\pi$
$240$		0			0
$241$			2.16706i			0.139593i	0.997561	+	0.0697963i	$0.0222349\pi$
$241$			2.16706i			0.139593i	−0.997561	+	0.0697963i	$0.977765\pi$
$242$	−7.66069	+	6.48472i	−0.492448	+	0.416854i
$243$		0			0
$244$	5.03281	−	6.10428i	0.322192	−	0.390786i
$245$	−11.4186	−	21.5351i	−0.729507	−	1.37583i
$246$		0			0
$247$			28.7539i			1.82957i
$248$	−7.29844	+	13.0286i	−0.463452	+	0.827317i
$249$		0			0
$250$	6.76241	+	7.98873i	0.427692	+	0.505252i
$251$	14.3444			0.905410			0.452705	−	0.891660i	$-0.350459\pi$
$251$	14.3444			0.905410			0.452705	+	0.891660i	$0.350459\pi$
$252$		0			0
$253$	−1.16611			−0.0733129
$254$	−9.78336	−	11.5575i	−0.613863	−	0.725184i
$255$		0			0
$256$	12.6050	+	9.85466i	0.787812	+	0.615916i
$257$		−	1.08665i		−	0.0677832i	−0.999426	−	0.0338916i	$-0.989210\pi$
$257$		−	1.08665i		−	0.0677832i	0.999426	−	0.0338916i	$-0.0107901\pi$
$258$		0			0
$259$	1.93009	−	1.86171i	0.119930	−	0.115681i
$260$	34.2663	+	28.2516i	2.12510	+	1.75209i
$261$		0			0
$262$	−6.12680	+	5.18630i	−0.378515	+	0.320411i
$263$		−	3.61167i		−	0.222705i	−0.993781	−	0.111352i	$-0.964482\pi$
$263$		−	3.61167i		−	0.222705i	0.993781	−	0.111352i	$-0.0355182\pi$
$264$		0			0
$265$	−18.1940	−	10.5043i	−1.11765	−	0.645276i
$266$	−1.70066	+	16.7854i	−0.104274	+	1.02918i
$267$		0			0
$268$	3.42465	+	9.16191i	0.209194	+	0.559652i
$269$	−18.9812	−	10.9588i	−1.15731	−	0.668171i	−0.206649	−	0.978415i	$-0.566256\pi$
$269$	−18.9812	−	10.9588i	−1.15731	−	0.668171i	−0.950657	+	0.310244i	$0.899589\pi$
$270$		0			0
$271$	7.49415	+	12.9802i	0.455237	+	0.788494i	0.998702	−	0.0509383i	$-0.0162212\pi$
$271$	7.49415	+	12.9802i	0.455237	+	0.788494i	−0.543465	+	0.839432i	$0.682888\pi$
$272$	3.15246	+	3.62767i	0.191146	+	0.219960i
$273$		0			0
$274$	−8.40866	+	7.11787i	−0.507986	+	0.430006i
$275$			14.0768i			0.848862i
$276$		0			0
$277$	−17.6898			−1.06288			−0.531439	−	0.847097i	$-0.678348\pi$
$277$	−17.6898			−1.06288			−0.531439	+	0.847097i	$0.678348\pi$
$278$	3.45911	+	19.1335i	0.207463	+	1.14755i
$279$		0			0
$280$	18.3323	+	18.5189i	1.09557	+	1.10671i
$281$	5.96654	+	10.3343i	0.355934	+	0.616495i	0.987277	−	0.159008i	$-0.0508296\pi$
$281$	5.96654	+	10.3343i	0.355934	+	0.616495i	−0.631344	+	0.775503i	$0.717496\pi$
$282$		0			0
$283$	9.08689	+	15.7390i	0.540160	+	0.935584i	0.998894	+	0.0470106i	$0.0149694\pi$
$283$	9.08689	+	15.7390i	0.540160	+	0.935584i	−0.458735	+	0.888573i	$0.651697\pi$
$284$	−2.90638	−	0.486603i	−0.172462	−	0.0288746i
$285$		0			0
$286$	3.16961	+	17.5322i	0.187423	+	1.03670i
$287$	−3.83323	+	13.3391i	−0.226269	+	0.787379i
$288$		0			0
$289$	−7.77819	−	13.4722i	−0.457540	−	0.792483i
$290$	6.67804	−	18.5975i	0.392148	−	1.09208i
$291$		0			0
$292$	14.1268	−	17.1343i	0.826706	−	1.00271i
$293$	−11.7151	−	6.76373i	−0.684405	−	0.395141i	0.117108	−	0.993119i	$-0.462638\pi$
$293$	−11.7151	−	6.76373i	−0.684405	−	0.395141i	−0.801513	+	0.597978i	$0.795971\pi$
$294$		0			0
$295$	−43.7802	+	25.2765i	−2.54898	+	1.47166i
$296$	−1.40108	+	2.50110i	−0.0814362	+	0.145373i
$297$		0			0
$298$	−22.1169	+	18.7218i	−1.28120	+	1.08452i
$299$	1.88204	−	3.25979i	0.108841	−	0.188518i
$300$		0			0
$301$	5.65343	+	5.86106i	0.325858	+	0.337826i
$302$	20.1199	+	23.7685i	1.15777	+	1.36772i
$303$		0			0
$304$	−3.43861	−	17.7054i	−0.197218	−	1.01547i
$305$	−6.88724	+	11.9291i	−0.394362	+	0.683056i
$306$		0			0
$307$	−30.1730			−1.72206			−0.861031	−	0.508553i	$-0.830181\pi$
$307$	−30.1730			−1.72206			−0.861031	+	0.508553i	$0.830181\pi$
$308$	0.813342	+	10.4221i	0.0463445	+	0.593852i
$309$		0			0
$310$	8.78700	−	24.4707i	0.499068	−	1.38984i
$311$	−10.6227	−	18.3990i	−0.602357	−	1.04331i	−0.992463	−	0.122543i	$-0.960895\pi$
$311$	−10.6227	−	18.3990i	−0.602357	−	1.04331i	0.390106	−	0.920770i	$-0.372438\pi$
$312$		0			0
$313$	−5.89379	−	3.40278i	−0.333137	−	0.192336i	0.324096	−	0.946024i	$-0.394940\pi$
$313$	−5.89379	−	3.40278i	−0.333137	−	0.192336i	−0.657233	+	0.753688i	$0.728273\pi$
$314$	−5.36493	+	14.9407i	−0.302761	+	0.843151i
$315$		0			0
$316$	0.817915	−	0.992046i	0.0460113	−	0.0558070i
$317$	5.88259	−	10.1889i	0.330399	−	0.572268i	−0.652191	−	0.758055i	$-0.726150\pi$
$317$	5.88259	−	10.1889i	0.330399	−	0.572268i	0.982590	+	0.185786i	$0.0594833\pi$
$318$		0			0
$319$	6.86517	−	3.96361i	0.384376	−	0.221919i
$320$	−24.4782	−	13.2983i	−1.36837	−	0.743396i
$321$		0			0
$322$	1.29146	−	1.79162i	0.0719704	−	0.0998432i
$323$		−	5.41767i		−	0.301447i
$324$		0			0
$325$	−39.3507	−	22.7191i	−2.18278	−	1.26023i
$326$	−4.13969	+	11.5285i	−0.229276	+	0.638506i
$327$		0			0
$328$	−0.192414	−	14.8359i	−0.0106243	−	0.819177i
$329$	−0.889312	−	0.255561i	−0.0490293	−	0.0140895i
$330$		0			0
$331$	−7.21741	−	4.16697i	−0.396705	−	0.229038i	0.288356	−	0.957523i	$-0.406891\pi$
$331$	−7.21741	−	4.16697i	−0.396705	−	0.229038i	−0.685061	+	0.728486i	$0.740225\pi$
$332$	−3.76843	+	1.40861i	−0.206820	+	0.0773076i
$333$		0			0
$334$	6.20840	+	34.3408i	0.339709	+	1.87905i
$335$	−8.51478	−	14.7480i	−0.465212	−	0.805771i
$336$		0			0
$337$	−8.90728	+	15.4279i	−0.485210	+	0.840409i	−0.999856	−	0.0169941i	$-0.994590\pi$
$337$	−8.90728	+	15.4279i	−0.485210	+	0.840409i	0.514645	+	0.857403i	$0.327924\pi$
$338$	−36.8226	−	13.2223i	−2.00288	−	0.719200i
$339$		0			0
$340$	−6.45628	−	5.32303i	−0.350141	−	0.288682i
$341$	9.03322	−	5.21533i	0.489177	−	0.282426i
$342$		0			0
$343$	12.3687	+	13.7846i	0.667844	+	0.744301i
$344$	−7.59504	−	4.25464i	−0.409497	−	0.229395i
$345$		0			0
$346$	−1.00610	+	0.181890i	−0.0540881	+	0.00977846i
$347$	−10.4898	+	6.05632i	−0.563125	+	0.325120i	−0.754399	−	0.656417i	$-0.772071\pi$
$347$	−10.4898	+	6.05632i	−0.563125	+	0.325120i	0.191274	+	0.981537i	$0.438738\pi$
$348$		0			0
$349$	9.68839	−	5.59359i	0.518607	−	0.299418i	−0.217757	−	0.976003i	$-0.569874\pi$
$349$	9.68839	−	5.59359i	0.518607	−	0.299418i	0.736365	+	0.676585i	$0.236541\pi$
$350$	−21.6276	−	15.5899i	−1.15605	−	0.833317i
$351$		0			0
$352$	−4.04833	−	10.4165i	−0.215777	−	0.555202i
$353$		−	30.1679i		−	1.60568i	−0.596197	−	0.802838i	$-0.703322\pi$
$353$		−	30.1679i		−	1.60568i	0.596197	−	0.802838i	$-0.296678\pi$
$354$		0			0
$355$	5.13067			0.272308
$356$	−2.64423	−	7.07406i	−0.140144	−	0.374925i
$357$		0			0
$358$	16.5361	−	2.98952i	0.873958	−	0.158001i
$359$	−24.5853	+	14.1944i	−1.29757	+	0.749150i	−0.979983	−	0.199081i	$-0.936204\pi$
$359$	−24.5853	+	14.1944i	−1.29757	+	0.749150i	−0.317582	+	0.948231i	$0.602871\pi$
$360$		0			0
$361$	−0.665788	+	1.15318i	−0.0350415	+	0.0606936i
$362$	4.78171	+	5.64885i	0.251321	+	0.296897i
$363$		0			0
$364$	−30.4469	−	14.5470i	−1.59585	−	0.762469i
$365$	−19.3320	+	33.4841i	−1.01189	+	1.75264i
$366$		0			0
$367$	35.2632			1.84072			0.920362	−	0.391066i	$-0.127894\pi$
$367$	35.2632			1.84072			0.920362	+	0.391066i	$0.127894\pi$
$368$	−0.769047	+	2.23230i	−0.0400894	+	0.116367i
$369$		0			0
$370$	1.68684	−	4.69764i	0.0876946	−	0.244219i
$371$	15.3415	+	4.40869i	0.796493	+	0.228888i
$372$		0			0
$373$	−11.4118			−0.590880			−0.295440	−	0.955361i	$-0.595466\pi$
$373$	−11.4118			−0.590880			−0.295440	+	0.955361i	$0.595466\pi$
$374$	−0.597201	−	3.30333i	−0.0308805	−	0.170811i
$375$		0			0
$376$	0.989108	−	0.0128282i	0.0510093	−	0.000661563i
$377$			25.5882i			1.31786i
$378$		0			0
$379$		−	14.3418i		−	0.736686i	−0.929690	−	0.368343i	$-0.879925\pi$
$379$		−	14.3418i		−	0.736686i	0.929690	−	0.368343i	$-0.120075\pi$
$380$	10.9950	+	29.4147i	0.564031	+	1.50894i
$381$		0			0
$382$	−22.0875	+	3.99314i	−1.13009	+	0.204307i
$383$	−18.6443			−0.952678			−0.476339	−	0.879262i	$-0.658037\pi$
$383$	−18.6443			−0.952678			−0.476339	+	0.879262i	$0.658037\pi$
$384$		0			0
$385$	−4.39299	−	17.6627i	−0.223888	−	0.900174i
$386$	−1.17881	−	0.423291i	−0.0600001	−	0.0215450i
$387$		0			0
$388$	11.9748	+	32.0360i	0.607930	+	1.62638i
$389$	15.9211			0.807231			0.403615	−	0.914929i	$-0.367753\pi$
$389$	15.9211			0.807231			0.403615	+	0.914929i	$0.367753\pi$
$390$		0			0
$391$	−0.354605	+	0.614193i	−0.0179331	+	0.0310611i
$392$	−16.9133	−	10.2927i	−0.854250	−	0.519862i
$393$		0			0
$394$	−2.34390	+	1.98410i	−0.118084	+	0.0999574i
$395$	−1.11929	+	1.93867i	−0.0563177	+	0.0975450i
$396$		0			0
$397$	−4.13873	+	2.38950i	−0.207717	+	0.119925i	−0.600250	−	0.799813i	$-0.704932\pi$
$397$	−4.13873	+	2.38950i	−0.207717	+	0.119925i	0.392533	+	0.919738i	$0.371599\pi$
$398$	3.26097	+	18.0376i	0.163458	+	0.904141i
$399$		0			0
$400$	26.9473	+	9.28358i	1.34737	+	0.464179i
$401$	33.2918			1.66251			0.831256	−	0.555890i	$-0.187622\pi$
$401$	33.2918			1.66251			0.831256	+	0.555890i	$0.187622\pi$
$402$		0			0
$403$			33.6690i			1.67717i
$404$	−9.80184	−	1.64108i	−0.487660	−	0.0816468i
$405$		0			0
$406$	−1.51342	+	14.9374i	−0.0751099	+	0.741329i
$407$	1.73411	−	1.00119i	0.0859565	−	0.0496270i
$408$		0			0
$409$	8.34763	−	4.81951i	0.412764	−	0.238309i	−0.279213	−	0.960229i	$-0.590073\pi$
$409$	8.34763	−	4.81951i	0.412764	−	0.238309i	0.691977	+	0.721920i	$0.256740\pi$
$410$	4.59573	+	25.4206i	0.226967	+	1.25543i
$411$		0			0
$412$	−5.01257	+	29.9391i	−0.246952	+	1.47499i
$413$	27.6455	−	26.6661i	1.36034	−	1.31216i
$414$		0			0
$415$	6.06609	−	3.50226i	0.297773	−	0.171919i
$416$	35.6524	+	5.49481i	1.74800	+	0.269405i
$417$		0			0
$418$	−4.25748	+	11.8566i	−0.208240	+	0.579923i
$419$	−5.29413	+	9.16971i	−0.258635	+	0.447970i	−0.965877	−	0.259003i	$-0.916606\pi$
$419$	−5.29413	+	9.16971i	−0.258635	+	0.447970i	0.707241	+	0.706972i	$0.249939\pi$
$420$		0			0
$421$	−12.4805	−	21.6168i	−0.608261	−	1.05354i	−0.991527	−	0.129901i	$-0.958534\pi$
$421$	−12.4805	−	21.6168i	−0.608261	−	1.05354i	0.383266	−	0.923638i	$-0.374799\pi$
$422$	14.2859	−	2.58272i	0.695428	−	0.125725i
$423$		0			0
$424$	−17.0631	+	0.221299i	−0.828659	+	0.0107472i
$425$	7.41426	+	4.28062i	0.359644	+	0.207641i
$426$		0			0
$427$	2.89059	−	10.0588i	0.139885	−	0.486779i
$428$	7.81830	+	20.9161i	0.377912	+	1.01102i
$429$		0			0
$430$	14.2652	+	5.12239i	0.687931	+	0.247024i
$431$	25.0572	+	14.4668i	1.20696	+	0.696841i	0.962095	−	0.272715i	$-0.0879215\pi$
$431$	25.0572	+	14.4668i	1.20696	+	0.696841i	0.244870	+	0.969556i	$0.421255\pi$
$432$		0			0
$433$			11.0967i			0.533275i	0.963797	+	0.266637i	$0.0859126\pi$
$433$			11.0967i			0.533275i	−0.963797	+	0.266637i	$0.914087\pi$
$434$	−1.99137	+	19.6546i	−0.0955887	+	0.943453i
$435$		0			0
$436$	−7.21900	−	5.95186i	−0.345727	−	0.285043i
$437$	2.30496	−	1.33077i	0.110261	−	0.0636593i
$438$		0			0
$439$	6.98423	−	12.0970i	0.333339	−	0.577361i	−0.649825	−	0.760084i	$-0.725158\pi$
$439$	6.98423	−	12.0970i	0.333339	−	0.577361i	0.983164	+	0.182723i	$0.0584912\pi$
$440$	9.94645	+	16.7231i	0.474178	+	0.797242i
$441$		0			0
$442$	10.1981	+	3.66195i	0.485073	+	0.174181i
$443$	1.79243	+	1.03486i	0.0851609	+	0.0491676i	0.541976	−	0.840394i	$-0.317676\pi$
$443$	1.79243	+	1.03486i	0.0851609	+	0.0491676i	−0.456815	+	0.889562i	$0.651010\pi$
$444$		0			0
$445$	6.57440	+	11.3872i	0.311657	+	0.539805i
$446$	24.6895	+	8.86555i	1.16908	+	0.419796i
$447$		0			0
$448$	20.4875	+	5.31633i	0.967942	+	0.251173i
$449$	−15.9634			−0.753361			−0.376680	−	0.926343i	$-0.622934\pi$
$449$	−15.9634			−0.753361			−0.376680	+	0.926343i	$0.622934\pi$
$450$		0			0
$451$	−5.18167	+	8.97491i	−0.243995	+	0.422612i
$452$	−17.3621	−	14.3145i	−0.816643	−	0.673300i
$453$		0			0
$454$	6.50799	−	5.50897i	0.305435	−	0.258549i
$455$	56.4649	+	16.2263i	2.64712	+	0.760700i
$456$		0			0
$457$	−6.54273	+	11.3323i	−0.306056	+	0.530104i	−0.977496	−	0.210955i	$-0.932343\pi$
$457$	−6.54273	+	11.3323i	−0.306056	+	0.530104i	0.671440	+	0.741059i	$0.265676\pi$
$458$	2.66030	+	3.14273i	0.124308	+	0.146850i
$459$		0			0
$460$	0.678804	−	4.05436i	0.0316494	−	0.189035i
$461$	−4.13795	+	2.38905i	−0.192724	+	0.111269i	−0.593257	−	0.805013i	$-0.702158\pi$
$461$	−4.13795	+	2.38905i	−0.192724	+	0.111269i	0.400533	+	0.916282i	$0.368825\pi$
$462$		0			0
$463$	−14.5389	−	8.39406i	−0.675681	−	0.390105i	0.122545	−	0.992463i	$-0.460895\pi$
$463$	−14.5389	−	8.39406i	−0.675681	−	0.390105i	−0.798226	+	0.602358i	$0.794228\pi$
$464$	−3.06002	−	15.7561i	−0.142058	−	0.731457i
$465$		0			0
$466$	−12.3652	−	4.44012i	−0.572806	−	0.205684i
$467$	17.1928	+	29.7788i	0.795587	+	1.37800i	0.922466	+	0.386079i	$0.126171\pi$
$467$	17.1928	+	29.7788i	0.795587	+	1.37800i	−0.126879	+	0.991918i	$0.540496\pi$
$468$		0			0
$469$	8.98289	+	9.31279i	0.414791	+	0.430025i
$470$	−1.69478	+	0.306396i	−0.0781746	+	0.0141330i
$471$		0			0
$472$	−20.0683	+	35.8243i	−0.923719	+	1.64895i
$473$	3.04029	+	5.26593i	0.139793	+	0.242128i
$474$		0			0
$475$	−16.0644	−	27.8244i	−0.737087	−	1.27667i
$476$	5.73665	+	2.74087i	0.262939	+	0.125628i
$477$		0			0
$478$	7.78647	−	1.40770i	0.356145	−	0.0643866i
$479$	10.2893			0.470130			0.235065	−	0.971980i	$-0.424470\pi$
$479$	10.2893			0.470130			0.235065	+	0.971980i	$0.424470\pi$
$480$		0			0
$481$			6.46344i			0.294707i
$482$	−1.98007	−	2.33915i	−0.0901899	−	0.106545i
$483$		0			0
$484$	2.34385	−	13.9994i	0.106539	−	0.636334i
$485$	−29.7732	−	51.5688i	−1.35193	−	2.34162i
$486$		0			0
$487$	23.9091	+	13.8039i	1.08343	+	0.625516i	0.931818	−	0.362925i	$-0.118222\pi$
$487$	23.9091	+	13.8039i	1.08343	+	0.625516i	0.151607	+	0.988441i	$0.451555\pi$
$488$	0.145097	+	11.1876i	0.00656821	+	0.506437i
$489$		0			0
$490$	32.0023	+	12.8119i	1.44572	+	0.578783i
$491$	−28.0754	−	16.2093i	−1.26702	−	0.731516i	−0.292599	−	0.956235i	$-0.594520\pi$
$491$	−28.0754	−	16.2093i	−1.26702	−	0.731516i	−0.974424	+	0.224719i	$0.927854\pi$
$492$		0			0
$493$		−	4.82119i		−	0.217136i
$494$	−26.2729	−	31.0373i	−1.18207	−	1.39643i
$495$		0			0
$496$	−4.02639	−	20.7319i	−0.180790	−	0.930890i
$497$	−3.78305	+	0.940903i	−0.169693	+	0.0422053i
$498$		0			0
$499$		−	7.13521i		−	0.319416i	−0.987164	−	0.159708i	$-0.948945\pi$
$499$		−	7.13521i		−	0.319416i	0.987164	−	0.159708i	$-0.0510552\pi$
$500$	−14.5988	−	2.44422i	−0.652879	−	0.109309i
$501$		0			0
$502$	−15.4835	+	13.1067i	−0.691062	+	0.584979i
$503$	−13.4502			−0.599716			−0.299858	−	0.953984i	$-0.596939\pi$
$503$	−13.4502			−0.599716			−0.299858	+	0.953984i	$0.596939\pi$
$504$		0			0
$505$	17.3033			0.769987
$506$	1.25871	−	1.06549i	0.0559567	−	0.0473669i
$507$		0			0
$508$	21.1205	+	3.53612i	0.937072	+	0.156890i
$509$			5.90623i			0.261789i	0.991396	+	0.130895i	$0.0417849\pi$
$509$			5.90623i			0.261789i	−0.991396	+	0.130895i	$0.958215\pi$
$510$		0			0
$511$	8.11370	−	28.2344i	0.358929	−	1.24902i
$512$	−22.6103	+	0.880124i	−0.999243	+	0.0388963i
$513$		0			0
$514$	0.992884	+	1.17294i	0.0437942	+	0.0517361i
$515$		−	52.8518i		−	2.32893i
$516$		0			0
$517$	−0.598355	−	0.345461i	−0.0263156	−	0.0151933i
$518$	−0.382282	+	3.77310i	−0.0167965	+	0.165780i
$519$		0			0
$520$	−62.8013	+	0.814497i	−2.75402	+	0.0357181i
$521$	37.1446	+	21.4454i	1.62733	+	0.939542i	0.984884	+	0.173215i	$0.0554155\pi$
$521$	37.1446	+	21.4454i	1.62733	+	0.939542i	0.642451	+	0.766327i	$0.277918\pi$
$522$		0			0
$523$	4.11355	+	7.12488i	0.179873	+	0.311549i	0.941837	−	0.336070i	$-0.109098\pi$
$523$	4.11355	+	7.12488i	0.179873	+	0.311549i	−0.761964	+	0.647619i	$0.775765\pi$
$524$	1.87455	−	11.1963i	0.0818900	−	0.489112i
$525$		0			0
$526$	3.30003	+	3.89847i	0.143888	+	0.169981i
$527$		−	6.34375i		−	0.276338i
$528$		0			0
$529$	22.6516			0.984852
$530$	29.2368	−	5.28565i	1.26997	−	0.229594i
$531$		0			0
$532$	−13.5013	−	19.6723i	−0.585357	−	0.852901i
$533$	−16.7258	−	28.9700i	−0.724476	−	1.25483i
$534$		0			0
$535$	−19.4388	−	33.6690i	−0.840412	−	1.45564i
$536$	−12.0680	−	6.76031i	−0.521257	−	0.292001i
$537$		0			0
$538$	30.5018	−	5.51434i	1.31502	−	0.237740i
$539$	6.47825	+	12.2178i	0.279038	+	0.526257i
$540$		0			0
$541$	5.48118	+	9.49369i	0.235654	+	0.408165i	0.959463	−	0.281836i	$-0.0909433\pi$
$541$	5.48118	+	9.49369i	0.235654	+	0.408165i	−0.723808	+	0.690001i	$0.757610\pi$
$542$	−19.9495	−	7.16351i	−0.856904	−	0.307699i
$543$		0			0
$544$	−6.71745	−	1.03530i	−0.288008	−	0.0443883i
$545$	14.1075	+	8.14494i	0.604297	+	0.348891i
$546$		0			0
$547$	−4.82709	+	2.78692i	−0.206391	+	0.119160i	−0.599633	−	0.800275i	$-0.704687\pi$
$547$	−4.82709	+	2.78692i	−0.206391	+	0.119160i	0.393242	+	0.919435i	$0.371354\pi$
$548$	2.57270	−	15.3662i	0.109900	−	0.656412i
$549$		0			0
$550$	−12.8621	−	15.1946i	−0.548444	−	0.647901i
$551$	−9.04655	+	15.6691i	−0.385396	+	0.667525i
$552$		0			0
$553$	0.469769	−	1.63472i	0.0199766	−	0.0695154i
$554$	19.0946	−	16.1634i	0.811251	−	0.686718i
$555$		0			0
$556$	−21.2164	−	17.4923i	−0.899774	−	0.741839i
$557$	−14.6473	+	25.3699i	−0.620626	+	1.07496i	0.368743	+	0.929531i	$0.379788\pi$
$557$	−14.6473	+	25.3699i	−0.620626	+	1.07496i	−0.989369	+	0.145425i	$0.953545\pi$
$558$		0			0
$559$	−19.6274			−0.830151
$560$	−36.7091	−	3.23893i	−1.55124	−	0.136870i
$561$		0			0
$562$	−15.8830	−	5.70329i	−0.669983	−	0.240579i
$563$	4.68201	+	8.10948i	0.197323	+	0.341774i	0.947660	−	0.319282i	$-0.103442\pi$
$563$	4.68201	+	8.10948i	0.197323	+	0.341774i	−0.750336	+	0.661056i	$0.770108\pi$
$564$		0			0
$565$	33.9292	+	19.5890i	1.42741	+	0.824116i
$566$	−24.1894	−	8.68598i	−1.01676	−	0.365099i
$567$		0			0
$568$	3.58180	−	2.13036i	0.150289	−	0.0893878i
$569$	−13.9962	+	24.2421i	−0.586750	+	1.01628i	0.407905	+	0.913025i	$0.366260\pi$
$569$	−13.9962	+	24.2421i	−0.586750	+	1.01628i	−0.994655	+	0.103257i	$0.967074\pi$
$570$		0			0
$571$	−10.7880	+	6.22848i	−0.451466	+	0.260654i	−0.708449	−	0.705762i	$-0.750605\pi$
$571$	−10.7880	+	6.22848i	−0.451466	+	0.260654i	0.256983	+	0.966416i	$0.417271\pi$
$572$	−19.4407	−	16.0283i	−0.812857	−	0.670178i
$573$		0			0
$574$	−8.05044	−	17.9008i	−0.336019	−	0.747165i
$575$			4.20588i			0.175397i
$576$		0			0
$577$	−23.8836	−	13.7892i	−0.994289	−	0.574053i	−0.0877357	−	0.996144i	$-0.527963\pi$
$577$	−23.8836	−	13.7892i	−0.994289	−	0.574053i	−0.906554	+	0.422091i	$0.861296\pi$
$578$	20.7056	+	7.43502i	0.861240	+	0.309256i
$579$		0			0
$580$	9.78446	+	26.1762i	0.406278	+	1.08691i
$581$	−3.83049	+	3.69480i	−0.158916	+	0.153286i
$582$		0			0
$583$	10.3222	+	5.95955i	0.427504	+	0.246819i
$584$	0.407276	+	31.4028i	0.0168532	+	1.29946i
$585$		0			0
$586$	18.8255	−	3.40343i	0.777676	−	0.140594i
$587$	0.790747	+	1.36961i	0.0326376	+	0.0565300i	0.881883	−	0.471469i	$-0.156276\pi$
$587$	0.790747	+	1.36961i	0.0326376	+	0.0565300i	−0.849245	+	0.527999i	$0.822943\pi$
$588$		0			0
$589$	−11.9035	+	20.6175i	−0.490475	+	0.849527i
$590$	24.1613	−	67.2864i	0.994707	−	2.77014i
$591$		0			0
$592$	−0.772946	−	3.97990i	−0.0317679	−	0.163573i
$593$	15.1545	−	8.74947i	0.622322	−	0.359298i	−0.155450	−	0.987844i	$-0.549683\pi$
$593$	15.1545	−	8.74947i	0.622322	−	0.359298i	0.777773	+	0.628546i	$0.216350\pi$
$594$		0			0
$595$	−10.6388	−	3.05728i	−0.436150	−	0.125336i
$596$	6.76684	−	40.4169i	0.277180	−	1.65554i
$597$		0			0
$598$	0.947020	+	5.23830i	0.0387265	+	0.214210i
$599$	8.75858	−	5.05677i	0.357866	−	0.206614i	−0.310278	−	0.950646i	$-0.600422\pi$
$599$	8.75858	−	5.05677i	0.357866	−	0.206614i	0.668144	+	0.744032i	$0.267089\pi$
$600$		0			0
$601$	−3.06836	+	1.77152i	−0.125161	+	0.0722618i	−0.561273	−	0.827630i	$-0.689688\pi$
$601$	−3.06836	+	1.77152i	−0.125161	+	0.0722618i	0.436112	+	0.899892i	$0.356355\pi$
$602$	−11.4577	−	1.16087i	−0.466981	−	0.0473135i
$603$		0			0
$604$	−43.4352	−	7.27218i	−1.76735	−	0.295901i
$605$			24.7132i			1.00474i
$606$		0			0
$607$	−18.5731			−0.753857			−0.376929	−	0.926242i	$-0.623020\pi$
$607$	−18.5731			−0.753857			−0.376929	+	0.926242i	$0.623020\pi$
$608$	19.8893	+	15.9695i	0.806619	+	0.647648i
$609$		0			0
$610$	−3.46558	−	19.1693i	−0.140317	−	0.776143i
$611$	1.93142	−	1.11511i	0.0781370	−	0.0451124i
$612$		0			0
$613$	13.5566	−	23.4808i	0.547548	−	0.948381i	−0.450894	−	0.892578i	$-0.648895\pi$
$613$	13.5566	−	23.4808i	0.547548	−	0.948381i	0.998442	−	0.0558032i	$-0.0177719\pi$
$614$	32.5690	−	27.5694i	1.31438	−	1.11261i
$615$		0			0
$616$	−10.4007	−	10.5065i	−0.419057	−	0.423320i
$617$	10.1963	−	17.6606i	0.410489	−	0.710987i	−0.584454	−	0.811427i	$-0.698691\pi$
$617$	10.1963	−	17.6606i	0.410489	−	0.710987i	0.994943	+	0.100439i	$0.0320248\pi$
$618$		0			0
$619$	24.0272			0.965734			0.482867	−	0.875694i	$-0.339595\pi$
$619$	24.0272			0.965734			0.482867	+	0.875694i	$0.339595\pi$
$620$	12.8744	+	34.4428i	0.517050	+	1.38325i
$621$		0			0
$622$	28.2777	+	10.1540i	1.13383	+	0.407139i
$623$	−6.93584	−	7.19056i	−0.277879	−	0.288084i
$624$		0			0
$625$	−9.85557			−0.394223
$626$	9.47098	−	1.71224i	0.378537	−	0.0684348i
$627$		0			0
$628$	−7.86054	−	21.0291i	−0.313670	−	0.839154i
$629$		−	1.21781i		−	0.0485572i
$630$		0			0
$631$		−	17.1069i		−	0.681016i	−0.940242	−	0.340508i	$-0.889401\pi$
$631$		−	17.1069i		−	0.681016i	0.940242	−	0.340508i	$-0.110599\pi$
$632$	0.0235806	+	1.81817i	0.000937985	+	0.0723227i
$633$		0			0
$634$	2.96005	+	16.3731i	0.117559	+	0.650257i
$635$	−37.2843			−1.47958
$636$		0			0
$637$	−44.6095	−	1.60930i	−1.76749	−	0.0637626i
$638$	−3.78874	+	10.5512i	−0.149997	+	0.417725i
$639$		0			0
$640$	38.5728	−	8.01178i	1.52473	−	0.316693i
$641$	−30.3467			−1.19862			−0.599311	−	0.800516i	$-0.704559\pi$
$641$	−30.3467			−1.19862			−0.599311	+	0.800516i	$0.704559\pi$
$642$		0			0
$643$	−2.71240	+	4.69801i	−0.106967	+	0.185272i	−0.914540	−	0.404496i	$-0.867447\pi$
$643$	−2.71240	+	4.69801i	−0.106967	+	0.185272i	0.807573	+	0.589767i	$0.200780\pi$
$644$	0.243012	+	3.11392i	0.00957600	+	0.122706i
$645$		0			0
$646$	4.95020	+	5.84789i	0.194763	+	0.230082i
$647$	9.98684	−	17.2977i	0.392623	−	0.680043i	−0.600171	−	0.799871i	$-0.704901\pi$
$647$	9.98684	−	17.2977i	0.392623	−	0.680043i	0.992795	+	0.119828i	$0.0382343\pi$
$648$		0			0
$649$	24.8384	−	14.3404i	0.974992	−	0.562912i
$650$	63.2343	−	11.4320i	2.48025	−	0.448399i
$651$		0			0
$652$	−6.06535	−	16.2265i	−0.237537	−	0.635479i
$653$	−32.1932			−1.25982			−0.629909	−	0.776669i	$-0.716908\pi$
$653$	−32.1932			−1.25982			−0.629909	+	0.776669i	$0.716908\pi$
$654$		0			0
$655$			19.7649i			0.772280i
$656$	13.7635	+	15.8382i	0.537374	+	0.618379i
$657$		0			0
$658$	1.19344	−	0.536721i	0.0465252	−	0.0209236i
$659$	3.30688	−	1.90923i	0.128818	−	0.0743729i	−0.434206	−	0.900813i	$-0.642971\pi$
$659$	3.30688	−	1.90923i	0.128818	−	0.0743729i	0.563024	+	0.826440i	$0.309638\pi$
$660$		0			0
$661$	35.9322	−	20.7455i	1.39760	−	0.806906i	0.403460	−	0.914997i	$-0.367807\pi$
$661$	35.9322	−	20.7455i	1.39760	−	0.806906i	0.994141	+	0.108092i	$0.0344740\pi$
$662$	11.5980	−	2.09677i	0.450768	−	0.0814933i
$663$		0			0
$664$	2.78062	−	4.96374i	0.107909	−	0.192630i
$665$	28.8400	+	29.8991i	1.11837	+	1.15944i
$666$		0			0
$667$	2.05119	−	1.18425i	0.0794223	−	0.0458545i
$668$	−38.0791	−	31.3952i	−1.47333	−	1.21472i
$669$		0			0
$670$	22.6664	+	8.13911i	0.875680	+	0.314441i
$671$	3.90742	−	6.76786i	0.150844	−	0.261270i
$672$		0			0
$673$	−3.35200	−	5.80584i	−0.129210	−	0.223799i	0.794161	−	0.607708i	$-0.207911\pi$
$673$	−3.35200	−	5.80584i	−0.129210	−	0.223799i	−0.923371	+	0.383909i	$0.874578\pi$
$674$	−4.48203	−	24.7917i	−0.172642	−	0.954941i
$675$		0			0
$676$	51.8281	−	19.3730i	1.99339	−	0.745114i
$677$	−15.7745	−	9.10739i	−0.606262	−	0.350025i	0.165239	−	0.986253i	$-0.447160\pi$
$677$	−15.7745	−	9.10739i	−0.606262	−	0.350025i	−0.771501	+	0.636228i	$0.780494\pi$
$678$		0			0
$679$	31.4101	+	32.5636i	1.20541	+	1.24968i
$680$	11.8327	−	0.153464i	0.453763	−	0.00588506i
$681$		0			0
$682$	−4.98524	+	13.8833i	−0.190895	+	0.531618i
$683$	−41.8382	−	24.1553i	−1.60090	−	0.924278i	−0.991308	−	0.131559i	$-0.958002\pi$
$683$	−41.8382	−	24.1553i	−1.60090	−	0.924278i	−0.609588	−	0.792719i	$-0.708665\pi$
$684$		0			0
$685$			27.1262i			1.03644i
$686$	−25.9461	−	3.57789i	−0.990626	−	0.136604i
$687$		0			0
$688$	12.0857	−	2.34719i	0.460763	−	0.0894859i
$689$	−33.3191	+	19.2368i	−1.26935	+	0.732862i
$690$		0			0
$691$	−2.71691	+	4.70582i	−0.103356	+	0.179018i	−0.913065	−	0.407813i	$-0.866291\pi$
$691$	−2.71691	+	4.70582i	−0.103356	+	0.179018i	0.809709	+	0.586831i	$0.199625\pi$
$692$	0.919796	−	1.11562i	0.0349654	−	0.0424094i
$693$		0			0
$694$	5.78911	−	16.1220i	0.219752	−	0.611982i
$695$	41.4613	+	23.9377i	1.57272	+	0.908008i
$696$		0			0
$697$	3.15140	+	5.45838i	0.119368	+	0.206751i
$698$	−5.34681	+	14.8902i	−0.202380	+	0.563602i
$699$		0			0
$700$	37.5898	−	2.93352i	1.42076	−	0.110877i
$701$	17.6328			0.665980			0.332990	−	0.942930i	$-0.391942\pi$
$701$	17.6328			0.665980			0.332990	+	0.942930i	$0.391942\pi$
$702$		0			0
$703$	−2.28511	+	3.95793i	−0.0861846	+	0.149276i
$704$	13.8875	+	7.54467i	0.523406	+	0.284350i
$705$		0			0
$706$	27.5648	+	32.5636i	1.03742	+	1.22555i
$707$	−12.7584	+	3.17322i	−0.479829	+	0.119341i
$708$		0			0
$709$	−8.40413	+	14.5564i	−0.315624	+	0.546677i	−0.979570	−	0.201104i	$-0.935547\pi$
$709$	−8.40413	+	14.5564i	−0.315624	+	0.546677i	0.663946	+	0.747780i	$0.268880\pi$
$710$	−5.53810	+	4.68797i	−0.207841	+	0.175936i
$711$		0			0
$712$	9.31788	+	5.21975i	0.349202	+	0.195618i
$713$	2.69896	−	1.55825i	0.101077	−	0.0583568i
$714$		0			0
$715$	37.9913	+	21.9343i	1.42079	+	0.820295i
$716$	−15.1176	+	18.3361i	−0.564973	+	0.685254i
$717$		0			0
$718$	13.5681	−	37.7855i	0.506357	−	1.41014i
$719$	−15.1910	−	26.3116i	−0.566530	−	0.981258i	−0.996906	−	0.0786083i	$-0.974952\pi$
$719$	−15.1910	−	26.3116i	−0.566530	−	0.981258i	0.430376	−	0.902650i	$-0.358381\pi$
$720$		0			0
$721$	9.69238	+	38.9697i	0.360963	+	1.45131i
$722$	−0.335016	−	1.85309i	−0.0124680	−	0.0689650i
$723$		0			0
$724$	−10.3229	−	1.72831i	−0.383646	−	0.0642322i
$725$	−14.2958	−	24.7610i	−0.530931	−	0.919600i
$726$		0			0
$727$	2.64995	+	4.58985i	0.0982812	+	0.170228i	0.910973	−	0.412465i	$-0.135332\pi$
$727$	2.64995	+	4.58985i	0.0982812	+	0.170228i	−0.812692	+	0.582693i	$0.801999\pi$
$728$	46.1565	−	12.1176i	1.71067	−	0.449106i
$729$		0			0
$730$	−9.72765	−	53.8070i	−0.360036	−	1.99149i
$731$	3.69810			0.136779
$732$		0			0
$733$		−	49.1128i		−	1.81402i	−0.421105	−	0.907012i	$-0.638358\pi$
$733$		−	49.1128i		−	1.81402i	0.421105	−	0.907012i	$-0.361642\pi$
$734$	−38.0635	+	32.2205i	−1.40495	+	1.18928i
$735$		0			0
$736$	−1.20957	−	3.11226i	−0.0445853	−	0.114719i
$737$	4.83079	+	8.36718i	0.177945	+	0.308209i
$738$		0			0
$739$	−24.0001	−	13.8565i	−0.882859	−	0.509719i	−0.0112591	−	0.999937i	$-0.503584\pi$
$739$	−24.0001	−	13.8565i	−0.882859	−	0.509719i	−0.871600	+	0.490218i	$0.836917\pi$
$740$	2.47151	+	6.61197i	0.0908543	+	0.243061i
$741$		0			0
$742$	−20.5881	+	9.25899i	−0.755813	+	0.339908i
$743$	−32.0177	−	18.4854i	−1.17461	−	0.678164i	−0.219852	−	0.975533i	$-0.570557\pi$
$743$	−32.0177	−	18.4854i	−1.17461	−	0.678164i	−0.954763	+	0.297369i	$0.903891\pi$
$744$		0			0
$745$			71.3485i			2.61401i
$746$	12.3180	−	10.4271i	0.450994	−	0.381764i
$747$		0			0
$748$	3.66292	+	3.01998i	0.133930	+	0.110421i
$749$	20.5075	+	21.2606i	0.749326	+	0.776846i
$750$		0			0
$751$		−	25.6840i		−	0.937222i	−0.883405	−	0.468611i	$-0.844755\pi$
$751$		−	25.6840i		−	0.937222i	0.883405	−	0.468611i	$-0.155245\pi$
$752$	−1.05593	+	0.917608i	−0.0385059	+	0.0334617i
$753$		0			0
$754$	−23.3803	−	27.6201i	−0.851459	−	1.00587i
$755$	76.6767			2.79055
$756$		0			0
$757$	32.8332			1.19334			0.596671	−	0.802486i	$-0.296490\pi$
$757$	32.8332			1.19334			0.596671	+	0.802486i	$0.296490\pi$
$758$	13.1043	+	15.4806i	0.475968	+	0.562282i
$759$		0			0
$760$	−38.7447	−	21.7043i	−1.40542	−	0.787296i
$761$		−	13.3912i		−	0.485432i	−0.970097	−	0.242716i	$-0.921962\pi$
$761$		−	13.3912i		−	0.485432i	0.970097	−	0.242716i	$-0.0780382\pi$
$762$		0			0
$763$	−11.8957	−	3.41845i	−0.430652	−	0.123756i
$764$	20.1929	−	24.4919i	0.730552	−	0.886085i
$765$		0			0
$766$	20.1248	−	17.0355i	0.727140	−	0.615519i
$767$			92.5787i			3.34282i
$768$		0			0
$769$	−1.88139	−	1.08622i	−0.0678447	−	0.0391702i	0.465694	−	0.884946i	$-0.345805\pi$
$769$	−1.88139	−	1.08622i	−0.0678447	−	0.0391702i	−0.533539	+	0.845776i	$0.679138\pi$
$770$	20.8805	+	15.0514i	0.752481	+	0.542414i
$771$		0			0
$772$	1.65919	−	0.620193i	0.0597156	−	0.0223212i
$773$	9.28632	+	5.36146i	0.334006	+	0.192838i	0.657618	−	0.753351i	$-0.271564\pi$
$773$	9.28632	+	5.36146i	0.334006	+	0.192838i	−0.323612	+	0.946190i	$0.604897\pi$
$774$		0			0
$775$	−18.8104	−	32.5806i	−0.675691	−	1.17033i
$776$	−42.1975	−	23.6385i	−1.51480	−	0.848571i
$777$		0			0
$778$	−17.1854	+	14.5473i	−0.616126	+	0.521546i
$779$		−	23.6533i		−	0.847467i
$780$		0			0
$781$	−2.91085			−0.104158
$782$	−0.178433	−	0.986974i	−0.00638074	−	0.0352941i
$783$		0			0
$784$	27.6610	−	4.34380i	0.987893	−	0.155136i
$785$	19.5438	+	33.8509i	0.697548	+	1.20819i
$786$		0			0
$787$	−12.2911	−	21.2888i	−0.438130	−	0.758863i	0.559416	−	0.828887i	$-0.311026\pi$
$787$	−12.2911	−	21.2888i	−0.438130	−	0.758863i	−0.997545	+	0.0700244i	$0.977692\pi$
$788$	0.717137	−	4.28331i	0.0255469	−	0.152587i
$789$		0			0
$790$	−0.563214	−	3.11533i	−0.0200382	−	0.110839i
$791$	−28.6097	−	8.22155i	−1.01724	−	0.292325i
$792$		0			0
$793$	12.6127	+	21.8459i	0.447891	+	0.775770i
$794$	2.28407	−	6.36086i	0.0810587	−	0.225739i
$795$		0			0
$796$	−20.0011	−	16.4903i	−0.708920	−	0.584485i
$797$	−29.3180	−	16.9267i	−1.03850	−	0.599576i	−0.119089	−	0.992884i	$-0.537997\pi$
$797$	−29.3180	−	16.9267i	−1.03850	−	0.599576i	−0.919407	+	0.393308i	$0.871331\pi$
$798$		0			0
$799$	−0.363909	+	0.210103i	−0.0128742	+	0.00743291i
$800$	−37.5698	+	14.6013i	−1.32829	+	0.516236i
$801$		0			0
$802$	−35.9355	+	30.4191i	−1.26893	+	1.07414i
$803$	10.9679	−	18.9969i	0.387048	−	0.670387i
$804$		0			0
$805$	−1.31255	−	5.27729i	−0.0462611	−	0.186000i
$806$	−30.7638	−	36.3427i	−1.08361	−	1.28012i
$807$		0			0
$808$	12.0797	−	7.18468i	0.424962	−	0.252756i
$809$	11.2283	−	19.4481i	0.394768	−	0.683758i	−0.598304	−	0.801269i	$-0.704158\pi$
$809$	11.2283	−	19.4481i	0.394768	−	0.683758i	0.993072	+	0.117512i	$0.0374917\pi$
$810$		0			0
$811$	47.6072			1.67172			0.835858	−	0.548946i	$-0.184971\pi$
$811$	47.6072			1.67172			0.835858	+	0.548946i	$0.184971\pi$
$812$	−12.0149	−	17.5064i	−0.421639	−	0.614353i
$813$		0			0
$814$	−0.957015	+	2.66517i	−0.0335434	+	0.0934141i
$815$	15.0804	+	26.1200i	0.528243	+	0.914944i
$816$		0			0
$817$	−12.0190	−	6.93916i	−0.420491	−	0.242770i
$818$	−4.60687	+	12.8296i	−0.161076	+	0.448576i
$819$		0			0
$820$	−28.1878	−	23.2401i	−0.984361	−	0.811578i
$821$	12.5572	−	21.7496i	0.438248	−	0.759068i	−0.559307	−	0.828961i	$-0.688933\pi$
$821$	12.5572	−	21.7496i	0.438248	−	0.759068i	0.997554	+	0.0698933i	$0.0222659\pi$
$822$		0			0
$823$	2.43553	−	1.40615i	0.0848972	−	0.0490154i	−0.456950	−	0.889492i	$-0.651058\pi$
$823$	2.43553	−	1.40615i	0.0848972	−	0.0490154i	0.541848	+	0.840477i	$0.317725\pi$
$824$	−21.9451	−	36.8966i	−0.764494	−	1.28535i
$825$		0			0
$826$	−5.47560	+	54.0438i	−0.190521	+	1.88042i
$827$		−	36.6231i		−	1.27351i	−0.771066	−	0.636756i	$-0.780276\pi$
$827$		−	36.6231i		−	1.27351i	0.771066	−	0.636756i	$-0.219724\pi$
$828$		0			0
$829$	15.8020	+	9.12326i	0.548825	+	0.316864i	0.748648	−	0.662968i	$-0.230703\pi$
$829$	15.8020	+	9.12326i	0.548825	+	0.316864i	−0.199823	+	0.979832i	$0.564037\pi$
$830$	−3.34774	+	9.32305i	−0.116202	+	0.323608i
$831$		0			0
$832$	−43.5043	+	26.6449i	−1.50824	+	0.923747i
$833$	8.40510	+	0.303215i	0.291219	+	0.0105058i
$834$		0			0
$835$	74.4147	+	42.9633i	2.57523	+	1.48681i
$836$	−6.23793	−	16.6882i	−0.215743	−	0.577174i
$837$		0			0
$838$	−2.66394	−	14.7352i	−0.0920244	−	0.509019i
$839$	−12.4481	−	21.5607i	−0.429755	−	0.744358i	0.567096	−	0.823652i	$-0.308067\pi$
$839$	−12.4481	−	21.5607i	−0.429755	−	0.744358i	−0.996851	+	0.0792938i	$0.974733\pi$
$840$		0			0
$841$	6.44946	−	11.1708i	0.222395	−	0.385200i
$842$	33.2231	+	11.9298i	1.14494	+	0.411129i
$843$		0			0
$844$	−13.0605	+	15.8411i	−0.449561	+	0.545271i
$845$	−83.4283	+	48.1674i	−2.87002	+	1.65701i
$846$		0			0
$847$	−4.53211	−	18.2220i	−0.155725	−	0.626116i
$848$	18.2159	−	15.8297i	0.625537	−	0.543594i
$849$		0			0
$850$	−11.9143	+	2.15396i	−0.408657	+	0.0738802i
$851$	0.518119	−	0.299136i	0.0177609	−	0.0102543i
$852$		0			0
$853$	38.8466	−	22.4281i	1.33008	−	0.767924i	0.344771	−	0.938687i	$-0.387956\pi$
$853$	38.8466	−	22.4281i	1.33008	−	0.767924i	0.985312	+	0.170763i	$0.0546232\pi$
$854$	6.07073	+	13.4987i	0.207736	+	0.461917i
$855$		0			0
$856$	−27.5505	−	15.4334i	−0.941657	−	0.527504i
$857$			7.51550i			0.256725i	0.991727	+	0.128362i	$0.0409721\pi$
$857$			7.51550i			0.256725i	−0.991727	+	0.128362i	$0.959028\pi$
$858$		0			0
$859$	30.9241			1.05512			0.527559	−	0.849519i	$-0.323107\pi$
$859$	30.9241			1.05512			0.527559	+	0.849519i	$0.323107\pi$
$860$	−20.0785	+	7.50518i	−0.684670	+	0.255924i
$861$		0			0
$862$	−40.2656	+	7.27952i	−1.37145	+	0.247941i
$863$	−37.2047	+	21.4801i	−1.26646	+	0.731192i	−0.974317	−	0.225181i	$-0.927703\pi$
$863$	−37.2047	+	21.4801i	−1.26646	+	0.731192i	−0.292146	+	0.956374i	$0.594369\pi$
$864$		0			0
$865$	−1.25871	+	2.18015i	−0.0427975	+	0.0741274i
$866$	−10.1392	−	11.9779i	−0.344545	−	0.407027i
$867$		0			0
$868$	−15.8092	−	23.0350i	−0.536600	−	0.781858i
$869$	0.635021	−	1.09989i	0.0215416	−	0.0373112i
$870$		0			0
$871$	−31.1865			−1.05671
$872$	13.2306	−	0.171593i	0.448043	−	0.00581087i
$873$		0			0
$874$	−1.27206	+	3.54252i	−0.0430279	+	0.119828i
$875$	−19.0023	+	4.72618i	−0.642396	+	0.159774i
$876$		0			0
$877$	8.25082			0.278610			0.139305	−	0.990249i	$-0.455513\pi$
$877$	8.25082			0.278610			0.139305	+	0.990249i	$0.455513\pi$
$878$	3.51438	+	19.4393i	0.118605	+	0.656044i
$879$		0			0
$880$	−26.0164	−	8.96288i	−0.877013	−	0.302138i
$881$		−	22.1964i		−	0.747816i	−0.927466	−	0.373908i	$-0.878018\pi$
$881$		−	22.1964i		−	0.747816i	0.927466	−	0.373908i	$-0.121982\pi$
$882$		0			0
$883$			48.0915i			1.61841i	0.587529	+	0.809203i	$0.300101\pi$
$883$			48.0915i			1.61841i	−0.587529	+	0.809203i	$0.699899\pi$
$884$	−14.3539	+	5.36538i	−0.482774	+	0.180457i
$885$		0			0
$886$	−2.88033	+	0.520729i	−0.0967666	+	0.0174942i
$887$	42.7483			1.43535			0.717674	−	0.696379i	$-0.245207\pi$
$887$	42.7483			1.43535			0.717674	+	0.696379i	$0.245207\pi$
$888$		0			0
$889$	27.4912	−	6.83749i	0.922025	−	0.229322i
$890$	−17.5011	−	6.28434i	−0.586639	−	0.210652i
$891$		0			0
$892$	−34.7506	+	12.9895i	−1.16354	+	0.434922i
$893$	1.57696			0.0527710
$894$		0			0
$895$	20.6880	−	35.8327i	0.691525	−	1.19776i
$896$	−26.9720	+	12.9812i	−0.901071	+	0.433671i
$897$		0			0
$898$	17.2311	−	14.5860i	0.575009	−	0.486741i
$899$	−10.5929	+	18.3475i	−0.353294	+	0.611923i
$900$		0			0
$901$	6.27781	−	3.62450i	0.209144	−	0.120749i
$902$	−2.60735	−	14.4222i	−0.0868153	−	0.480206i
$903$		0			0
$904$	31.8202	−	0.412690i	1.05832	−	0.0137259i
$905$	18.2231			0.605755
$906$		0			0
$907$			16.3986i			0.544508i	0.962225	+	0.272254i	$0.0877690\pi$
$907$			16.3986i			0.544508i	−0.962225	+	0.272254i	$0.912231\pi$
$908$	−1.99117	+	11.8929i	−0.0660794	+	0.394679i
$909$		0			0
$910$	−75.7750	+	34.0779i	−2.51192	+	1.12967i
$911$	−6.37439	+	3.68026i	−0.211193	+	0.121932i	−0.601866	−	0.798597i	$-0.705576\pi$
$911$	−6.37439	+	3.68026i	−0.211193	+	0.121932i	0.390673	+	0.920530i	$0.372242\pi$
$912$		0			0
$913$	−3.44155	+	1.98698i	−0.113899	+	0.0657594i
$914$	−3.29222	−	18.2104i	−0.108897	−	0.602347i
$915$		0			0
$916$	−5.74312	−	0.961545i	−0.189758	−	0.0317703i
$917$	−3.62465	−	14.5735i	−0.119696	−	0.481258i
$918$		0			0
$919$	−10.1235	+	5.84481i	−0.333944	+	0.192802i	−0.657591	−	0.753375i	$-0.728424\pi$
$919$	−10.1235	+	5.84481i	−0.333944	+	0.192802i	0.323647	+	0.946178i	$0.395091\pi$
$920$	2.97182	+	4.99655i	0.0979778	+	0.164731i
$921$		0			0
$922$	2.28364	−	6.35966i	0.0752078	−	0.209444i
$923$	4.69794	−	8.13708i	0.154635	−	0.267835i
$924$		0			0
$925$	−3.61104	−	6.25450i	−0.118730	−	0.205647i
$926$	23.3632	−	4.22379i	0.767764	−	0.138802i
$927$		0			0
$928$	17.6996	+	14.2113i	0.581016	+	0.466508i
$929$	24.5685	+	14.1846i	0.806065	+	0.465382i	0.845588	−	0.533837i	$-0.179250\pi$
$929$	24.5685	+	14.1846i	0.806065	+	0.465382i	−0.0395223	+	0.999219i	$0.512584\pi$
$930$		0			0
$931$	−26.7480	−	16.7569i	−0.876629	−	0.549185i
$932$	17.4041	−	6.50552i	0.570090	−	0.213095i
$933$		0			0
$934$	−45.7673	−	16.4342i	−1.49755	−	0.537745i
$935$	−7.15813	−	4.13275i	−0.234096	−	0.135155i
$936$		0			0
$937$			49.8946i			1.62999i	0.579470	+	0.814993i	$0.303259\pi$
$937$			49.8946i			1.62999i	−0.579470	+	0.814993i	$0.696741\pi$
$938$	−18.2054	−	1.84454i	−0.594429	−	0.0602263i
$939$		0			0
$940$	1.54941	−	1.87928i	0.0505362	−	0.0612952i
$941$	10.8025	−	6.23683i	0.352151	−	0.203315i	−0.313481	−	0.949594i	$-0.601495\pi$
$941$	10.8025	−	6.23683i	0.352151	−	0.203315i	0.665632	+	0.746280i	$0.268162\pi$
$942$		0			0
$943$	−1.54819	+	2.68154i	−0.0504159	+	0.0873229i
$944$	−11.0713	−	57.0059i	−0.360339	−	1.85538i
$945$		0			0
$946$	−8.09327	−	2.90615i	−0.263135	−	0.0944871i
$947$	−24.4507	−	14.1166i	−0.794541	−	0.458728i	0.0470178	−	0.998894i	$-0.485028\pi$
$947$	−24.4507	−	14.1166i	−0.794541	−	0.458728i	−0.841559	+	0.540166i	$0.818362\pi$
$948$		0			0
$949$	35.4031	+	61.3200i	1.14923	+	1.99053i
$950$	42.7637	+	15.3557i	1.38744	+	0.498204i
$951$		0			0
$952$	−8.69657	+	2.28313i	−0.281857	+	0.0739966i
$953$	2.77543			0.0899050			0.0449525	−	0.998989i	$-0.485686\pi$
$953$	2.77543			0.0899050			0.0449525	+	0.998989i	$0.485686\pi$
$954$		0			0
$955$	−27.6333	+	47.8623i	−0.894193	+	1.54879i
$956$	−7.11856	+	8.63409i	−0.230231	+	0.279246i
$957$		0			0
$958$	−11.1064	+	9.40147i	−0.358831	+	0.303748i
$959$	−4.97461	−	20.0012i	−0.160638	−	0.645871i
$960$		0			0
$961$	1.56177	−	2.70506i	0.0503796	−	0.0872601i
$962$	−5.90573	−	6.97671i	−0.190408	−	0.224938i
$963$		0			0
$964$	4.27462	+	0.715682i	0.137676	+	0.0230506i
$965$	−2.67082	+	1.54200i	−0.0859767	+	0.0496387i
$966$		0			0
$967$	−33.2406	−	19.1915i	−1.06894	−	0.617156i	−0.141052	−	0.990002i	$-0.545048\pi$
$967$	−33.2406	−	19.1915i	−1.06894	−	0.617156i	−0.927893	+	0.372847i	$0.878382\pi$
$968$	10.2614	+	17.2527i	0.329815	+	0.554522i
$969$		0			0
$970$	79.2566	+	28.4597i	2.54478	+	0.913785i
$971$	22.7039	+	39.3244i	0.728604	+	1.26198i	0.957473	+	0.288522i	$0.0931637\pi$
$971$	22.7039	+	39.3244i	0.728604	+	1.26198i	−0.228870	+	0.973457i	$0.573503\pi$
$972$		0			0
$973$	−34.9609	−	10.0467i	−1.12079	−	0.322082i
$974$	−38.4206	+	6.94597i	−1.23107	+	0.222563i
$975$		0			0
$976$	−10.3789	−	11.9434i	−0.332219	−	0.382299i
$977$	19.2557	+	33.3519i	0.616046	+	1.06702i	0.990200	+	0.139656i	$0.0445997\pi$
$977$	19.2557	+	33.3519i	0.616046	+	1.06702i	−0.374154	+	0.927366i	$0.622067\pi$
$978$		0			0
$979$	−3.72994	−	6.46044i	−0.119209	−	0.206477i
$980$	−46.2500	+	15.4116i	−1.47740	+	0.492306i
$981$		0			0
$982$	45.1155	−	8.15633i	1.43969	−	0.260279i
$983$	6.34126			0.202255			0.101127	−	0.994873i	$-0.467755\pi$
$983$	6.34126			0.202255			0.101127	+	0.994873i	$0.467755\pi$
$984$		0			0
$985$			7.56138i			0.240926i
$986$	4.40519	+	5.20405i	0.140290	+	0.165731i
$987$		0			0
$988$	56.7184	+	9.49612i	1.80445	+	0.302112i
$989$	0.908382	+	1.57336i	0.0288849	+	0.0500300i
$990$		0			0
$991$	−39.7136	−	22.9287i	−1.26154	−	0.728353i	−0.288171	−	0.957579i	$-0.593047\pi$
$991$	−39.7136	−	22.9287i	−1.26154	−	0.728353i	−0.973373	+	0.229226i	$0.926380\pi$
$992$	23.2892	+	18.6993i	0.739431	+	0.593702i
$993$		0			0
$994$	3.22374	−	4.47224i	0.102251	−	0.141851i
$995$	39.0864	+	22.5665i	1.23912	+	0.715407i
$996$		0			0
$997$		−	41.3718i		−	1.31026i	−0.755518	−	0.655128i	$-0.772615\pi$
$997$		−	41.3718i		−	1.31026i	0.755518	−	0.655128i	$-0.227385\pi$
$998$	6.51954	+	7.70182i	0.206372	+	0.243797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.199.10		84
3.2	odd	2		252.2.n.b.31.33	yes	84
4.3	odd	2	inner	756.2.n.b.199.20		84
7.5	odd	6		756.2.bj.b.523.38		84
9.2	odd	6		252.2.bj.b.115.5	yes	84
9.7	even	3		756.2.bj.b.451.38		84
12.11	even	2		252.2.n.b.31.23	✓	84
21.5	even	6		252.2.bj.b.103.5	yes	84
28.19	even	6		756.2.bj.b.523.37		84
36.7	odd	6		756.2.bj.b.451.37		84
36.11	even	6		252.2.bj.b.115.6	yes	84
63.47	even	6		252.2.n.b.187.23	yes	84
63.61	odd	6	inner	756.2.n.b.19.20		84
84.47	odd	6		252.2.bj.b.103.6	yes	84
252.47	odd	6		252.2.n.b.187.33	yes	84
252.187	even	6	inner	756.2.n.b.19.10		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.23	✓	84	12.11	even	2
252.2.n.b.31.33	yes	84	3.2	odd	2
252.2.n.b.187.23	yes	84	63.47	even	6
252.2.n.b.187.33	yes	84	252.47	odd	6
252.2.bj.b.103.5	yes	84	21.5	even	6
252.2.bj.b.103.6	yes	84	84.47	odd	6
252.2.bj.b.115.5	yes	84	9.2	odd	6
252.2.bj.b.115.6	yes	84	36.11	even	6
756.2.n.b.19.10		84	252.187	even	6	inner
756.2.n.b.19.20		84	63.61	odd	6	inner
756.2.n.b.199.10		84	1.1	even	1	trivial
756.2.n.b.199.20		84	4.3	odd	2	inner
756.2.bj.b.451.37		84	36.7	odd	6
756.2.bj.b.451.38		84	9.7	even	3
756.2.bj.b.523.37		84	28.19	even	6
756.2.bj.b.523.38		84	7.5	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.07941 + 0.913714i) q^{2} +(0.330255 - 1.97254i) q^{4} +3.48216i q^{5} +(-0.638585 - 2.56753i) q^{7} +(1.44586 + 2.43094i) q^{8} +(-3.18169 - 3.75868i) q^{10} -1.97557i q^{11} +(5.52258 + 3.18847i) q^{13} +(3.03528 + 2.18793i) q^{14} +(-3.78186 - 1.30288i) q^{16} +(-1.04054 - 0.600755i) q^{17} +(2.25453 + 3.90496i) q^{19} +(6.86871 + 1.15000i) q^{20} +(1.80511 + 2.13246i) q^{22} -0.590265i q^{23} -7.12541 q^{25} +(-8.87448 + 1.60440i) q^{26} +(-5.27546 + 0.411699i) q^{28} +(2.00631 + 3.47503i) q^{29} +(2.63991 + 4.57246i) q^{31} +(5.27265 - 2.04919i) q^{32} +(1.67209 - 0.302292i) q^{34} +(8.94054 - 2.22365i) q^{35} +(0.506783 + 0.877774i) q^{37} +(-6.00157 - 2.15506i) q^{38} +(-8.46493 + 5.03471i) q^{40} +(-4.54294 - 2.62287i) q^{41} +(-2.66552 + 1.53894i) q^{43} +(-3.89691 - 0.652443i) q^{44} +(0.539333 + 0.637139i) q^{46} +(0.174866 - 0.302877i) q^{47} +(-6.18442 + 3.27917i) q^{49} +(7.69124 - 6.51059i) q^{50} +(8.11325 - 9.84054i) q^{52} +(-3.01662 + 5.22494i) q^{53} +6.87926 q^{55} +(5.31822 - 5.26465i) q^{56} +(-5.34081 - 1.91779i) q^{58} +(7.25888 + 12.5727i) q^{59} +(3.42577 + 1.97787i) q^{61} +(-7.02746 - 2.52344i) q^{62} +(-3.81897 + 7.02961i) q^{64} +(-11.1027 + 19.2305i) q^{65} +(-4.23532 + 2.44526i) q^{67} +(-1.52866 + 1.85410i) q^{68} +(-7.61873 + 10.5693i) q^{70} -1.47342i q^{71} +(9.61590 + 5.55174i) q^{73} +(-1.34906 - 0.484424i) q^{74} +(8.44727 - 3.15753i) q^{76} +(-5.07235 + 1.26157i) q^{77} +(0.556744 + 0.321436i) q^{79} +(4.53685 - 13.1690i) q^{80} +(7.30024 - 1.31979i) q^{82} +(-1.00577 - 1.74205i) q^{83} +(2.09192 - 3.62331i) q^{85} +(1.47104 - 4.09667i) q^{86} +(4.80251 - 2.85640i) q^{88} +(3.27016 - 1.88803i) q^{89} +(4.65984 - 16.2155i) q^{91} +(-1.16432 - 0.194938i) q^{92} +(0.0879904 + 0.486706i) q^{94} +(-13.5977 + 7.85062i) q^{95} +(-14.8094 + 8.55023i) q^{97} +(3.67930 - 9.19036i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41}+ \cdots - 21 q^{98}+O(q^{100}) \) 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

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