LMFDB - Embedded newform 702.2.bc.a.557.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(305,702)] 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("702.305"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.6
Character	$\chi$	$=$	702.557
Dual form			702.2.bc.a.305.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.970449 + 3.62177i) q^{5} +(2.29680 - 2.29680i) q^{7} +(0.707107 + 0.707107i) q^{8} +(3.24719 - 1.87476i) q^{10} +(2.11332 - 0.566263i) q^{11} +(-3.26412 + 1.53151i) q^{13} +(-2.81299 - 1.62408i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.50770 + 6.07551i) q^{17} +(4.70354 - 1.26031i) q^{19} +(-2.65132 - 2.65132i) q^{20} +(-1.09394 - 1.89475i) q^{22} -0.831757 q^{23} +(-7.84529 + 4.52948i) q^{25} +(2.32414 + 2.75652i) q^{26} +(-0.840685 + 3.13748i) q^{28} +(8.02571 + 4.63365i) q^{29} +(0.527973 - 0.141470i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(6.77635 + 1.81572i) q^{34} +(10.5474 + 6.08953i) q^{35} +(1.90093 + 0.509353i) q^{37} +(-2.43473 - 4.21708i) q^{38} +(-1.87476 + 3.24719i) q^{40} +(1.24565 - 1.24565i) q^{41} +0.0581115i q^{43} +(-1.54706 + 1.54706i) q^{44} +(0.215275 + 0.803416i) q^{46} +(-1.56367 + 5.83570i) q^{47} -3.55054i q^{49} +(6.40565 + 6.40565i) q^{50} +(2.06106 - 2.95839i) q^{52} -1.62324i q^{53} +(4.10174 + 7.10443i) q^{55} +3.24816 q^{56} +(2.39855 - 8.95152i) q^{58} +(0.755077 - 2.81798i) q^{59} +3.57998 q^{61} +(-0.273299 - 0.473367i) q^{62} +1.00000i q^{64} +(-8.71443 - 10.3356i) q^{65} +(9.19065 + 9.19065i) q^{67} -7.01540i q^{68} +(3.15217 - 11.7641i) q^{70} +(-2.31786 - 8.65035i) q^{71} +(3.38343 - 3.38343i) q^{73} -1.96799i q^{74} +(-3.44323 + 3.44323i) q^{76} +(3.55328 - 6.15446i) q^{77} +(-5.86001 - 10.1498i) q^{79} +(3.62177 + 0.970449i) q^{80} +(-1.52561 - 0.880809i) q^{82} +(-14.0250 - 3.75798i) q^{83} +(-25.4081 - 6.80809i) q^{85} +(0.0561314 - 0.0150404i) q^{86} +(1.89475 + 1.09394i) q^{88} +(3.50606 - 13.0848i) q^{89} +(-3.97946 + 11.0146i) q^{91} +(0.720323 - 0.415879i) q^{92} +6.04156 q^{94} +(9.12909 + 15.8121i) q^{95} +(6.97910 + 6.97910i) q^{97} +(-3.42956 + 0.918947i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.970449	+	3.62177i	0.433998	+	1.61970i	0.743452	+	0.668789i	$0.233187\pi$
$5$	0.970449	+	3.62177i	0.433998	+	1.61970i	−0.309454	+	0.950914i	$0.600146\pi$
$6$		0			0
$7$	2.29680	−	2.29680i	0.868107	−	0.868107i	−0.124156	−	0.992263i	$-0.539622\pi$
$7$	2.29680	−	2.29680i	0.868107	−	0.868107i	0.992263	+	0.124156i	$0.0396222\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	3.24719	−	1.87476i	1.02685	−	0.592852i
$11$	2.11332	−	0.566263i	0.637190	−	0.170735i	0.0742600	−	0.997239i	$-0.476341\pi$
$11$	2.11332	−	0.566263i	0.637190	−	0.170735i	0.562930	+	0.826504i	$0.309674\pi$
$12$		0			0
$13$	−3.26412	+	1.53151i	−0.905304	+	0.424764i
$13$	−3.26412	+	1.53151i	−0.905304	+	0.424764i
$14$	−2.81299	−	1.62408i	−0.751803	−	0.434054i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.50770	+	6.07551i	−0.850742	+	1.47353i	0.0297983	+	0.999556i	$0.490513\pi$
$17$	−3.50770	+	6.07551i	−0.850742	+	1.47353i	−0.880540	+	0.473972i	$0.842820\pi$
$18$		0			0
$19$	4.70354	−	1.26031i	1.07907	−	0.289135i	0.324853	−	0.945765i	$-0.394685\pi$
$19$	4.70354	−	1.26031i	1.07907	−	0.289135i	0.754213	+	0.656630i	$0.228019\pi$
$20$	−2.65132	−	2.65132i	−0.592852	−	0.592852i
$21$		0			0
$22$	−1.09394	−	1.89475i	−0.233228	−	0.403963i
$23$	−0.831757			−0.173433			−0.0867167	−	0.996233i	$-0.527637\pi$
$23$	−0.831757			−0.173433			−0.0867167	+	0.996233i	$0.527637\pi$
$24$		0			0
$25$	−7.84529	+	4.52948i	−1.56906	+	0.905896i
$26$	2.32414	+	2.75652i	0.455801	+	0.540597i
$27$		0			0
$28$	−0.840685	+	3.13748i	−0.158875	+	0.592928i
$29$	8.02571	+	4.63365i	1.49034	+	0.860447i	0.999939	−	0.0110518i	$-0.00351796\pi$
$29$	8.02571	+	4.63365i	1.49034	+	0.860447i	0.490398	+	0.871498i	$0.336851\pi$
$30$		0			0
$31$	0.527973	−	0.141470i	0.0948267	−	0.0254087i	−0.211094	−	0.977466i	$-0.567703\pi$
$31$	0.527973	−	0.141470i	0.0948267	−	0.0254087i	0.305920	+	0.952057i	$0.401036\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$	6.77635	+	1.81572i	1.16213	+	0.311393i
$35$	10.5474	+	6.08953i	1.78283	+	1.02932i
$36$		0			0
$37$	1.90093	+	0.509353i	0.312511	+	0.0837372i	0.411666	−	0.911335i	$-0.364947\pi$
$37$	1.90093	+	0.509353i	0.312511	+	0.0837372i	−0.0991544	+	0.995072i	$0.531614\pi$
$38$	−2.43473	−	4.21708i	−0.394966	−	0.684100i
$39$		0			0
$40$	−1.87476	+	3.24719i	−0.296426	+	0.513425i
$41$	1.24565	−	1.24565i	0.194538	−	0.194538i	−0.603116	−	0.797654i	$-0.706074\pi$
$41$	1.24565	−	1.24565i	0.194538	−	0.194538i	0.797654	+	0.603116i	$0.206074\pi$
$42$		0			0
$43$			0.0581115i			0.00886192i	0.999990	+	0.00443096i	$0.00141042\pi$
$43$			0.0581115i			0.00886192i	−0.999990	+	0.00443096i	$0.998590\pi$
$44$	−1.54706	+	1.54706i	−0.233228	+	0.233228i
$45$		0			0
$46$	0.215275	+	0.803416i	0.0317405	+	0.118457i
$47$	−1.56367	+	5.83570i	−0.228085	+	0.851224i	0.753060	+	0.657951i	$0.228577\pi$
$47$	−1.56367	+	5.83570i	−0.228085	+	0.851224i	−0.981145	+	0.193272i	$0.938090\pi$
$48$		0			0
$49$		−	3.55054i		−	0.507220i
$50$	6.40565	+	6.40565i	0.905896	+	0.905896i
$51$		0			0
$52$	2.06106	−	2.95839i	0.285817	−	0.410254i
$53$		−	1.62324i		−	0.222969i	−0.993766	−	0.111484i	$-0.964440\pi$
$53$		−	1.62324i		−	0.222969i	0.993766	−	0.111484i	$-0.0355605\pi$
$54$		0			0
$55$	4.10174	+	7.10443i	0.553079	+	0.957961i
$56$	3.24816			0.434054
$57$		0			0
$58$	2.39855	−	8.95152i	0.314945	−	1.17539i
$59$	0.755077	−	2.81798i	0.0983026	−	0.366870i	−0.899197	−	0.437544i	$-0.855848\pi$
$59$	0.755077	−	2.81798i	0.0983026	−	0.366870i	0.997499	+	0.0706740i	$0.0225150\pi$
$60$		0			0
$61$	3.57998			0.458369			0.229185	−	0.973383i	$-0.426394\pi$
$61$	3.57998			0.458369			0.229185	+	0.973383i	$0.426394\pi$
$62$	−0.273299	−	0.473367i	−0.0347090	−	0.0601177i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−8.71443	−	10.3356i	−1.08089	−	1.28198i
$66$		0			0
$67$	9.19065	+	9.19065i	1.12282	+	1.12282i	0.991316	+	0.131500i	$0.0419795\pi$
$67$	9.19065	+	9.19065i	1.12282	+	1.12282i	0.131500	+	0.991316i	$0.458021\pi$
$68$		−	7.01540i		−	0.850742i
$69$		0			0
$70$	3.15217	−	11.7641i	0.376757	−	1.40608i
$71$	−2.31786	−	8.65035i	−0.275079	−	1.02661i	−0.955789	−	0.294055i	$-0.904995\pi$
$71$	−2.31786	−	8.65035i	−0.275079	−	1.02661i	0.680710	−	0.732553i	$-0.261671\pi$
$72$		0			0
$73$	3.38343	−	3.38343i	0.396001	−	0.396001i	−0.480819	−	0.876820i	$-0.659661\pi$
$73$	3.38343	−	3.38343i	0.396001	−	0.396001i	0.876820	+	0.480819i	$0.159661\pi$
$74$		−	1.96799i		−	0.228774i
$75$		0			0
$76$	−3.44323	+	3.44323i	−0.394966	+	0.394966i
$77$	3.55328	−	6.15446i	0.404934	−	0.701366i
$78$		0			0
$79$	−5.86001	−	10.1498i	−0.659302	−	1.14194i	−0.980797	−	0.195033i	$-0.937518\pi$
$79$	−5.86001	−	10.1498i	−0.659302	−	1.14194i	0.321494	−	0.946911i	$-0.395815\pi$
$80$	3.62177	+	0.970449i	0.404926	+	0.108500i
$81$		0			0
$82$	−1.52561	−	0.880809i	−0.168475	−	0.0972691i
$83$	−14.0250	−	3.75798i	−1.53944	−	0.412492i	−0.613356	−	0.789807i	$-0.710181\pi$
$83$	−14.0250	−	3.75798i	−1.53944	−	0.412492i	−0.926085	+	0.377315i	$0.876848\pi$
$84$		0			0
$85$	−25.4081	−	6.80809i	−2.75590	−	0.738441i
$86$	0.0561314	−	0.0150404i	0.00605280	−	0.00162184i
$87$		0			0
$88$	1.89475	+	1.09394i	0.201981	+	0.116614i
$89$	3.50606	−	13.0848i	0.371642	−	1.38699i	−0.486548	−	0.873654i	$-0.661744\pi$
$89$	3.50606	−	13.0848i	0.371642	−	1.38699i	0.858190	−	0.513332i	$-0.171589\pi$
$90$		0			0
$91$	−3.97946	+	11.0146i	−0.417160	+	1.15464i
$92$	0.720323	−	0.415879i	0.0750989	−	0.0433583i
$93$		0			0
$94$	6.04156			0.623139
$95$	9.12909	+	15.8121i	0.936625	+	1.62228i
$96$		0			0
$97$	6.97910	+	6.97910i	0.708620	+	0.708620i	0.966245	−	0.257625i	$-0.0829398\pi$
$97$	6.97910	+	6.97910i	0.708620	+	0.708620i	−0.257625	+	0.966245i	$0.582940\pi$
$98$	−3.42956	+	0.918947i	−0.346438	+	0.0928277i
$99$		0			0
$100$	4.52948	−	7.84529i	0.452948	−	0.784529i
$101$	−2.19946	+	3.80958i	−0.218855	+	0.379068i	−0.954458	−	0.298345i	$-0.903565\pi$
$101$	−2.19946	+	3.80958i	−0.218855	+	0.379068i	0.735603	+	0.677413i	$0.236899\pi$
$102$		0			0
$103$	8.09876	+	4.67582i	0.797994	+	0.460722i	0.842769	−	0.538275i	$-0.180924\pi$
$103$	8.09876	+	4.67582i	0.797994	+	0.460722i	−0.0447750	+	0.998997i	$0.514257\pi$
$104$	−3.39102	−	1.22514i	−0.332517	−	0.120135i
$105$		0			0
$106$	−1.56793	+	0.420125i	−0.152290	+	0.0408061i
$107$	4.41803	−	2.55075i	0.427107	−	0.246590i	−0.271007	−	0.962577i	$-0.587357\pi$
$107$	4.41803	−	2.55075i	0.427107	−	0.246590i	0.698113	+	0.715987i	$0.254023\pi$
$108$		0			0
$109$	−0.923072	−	0.923072i	−0.0884142	−	0.0884142i	0.661516	−	0.749931i	$-0.269913\pi$
$109$	−0.923072	−	0.923072i	−0.0884142	−	0.0884142i	−0.749931	+	0.661516i	$0.769913\pi$
$110$	5.80074	−	5.80074i	0.553079	−	0.553079i
$111$		0			0
$112$	−0.840685	−	3.13748i	−0.0794373	−	0.296464i
$113$	−10.0193	+	5.78467i	−0.942541	+	0.544176i	−0.890756	−	0.454482i	$-0.849824\pi$
$113$	−10.0193	+	5.78467i	−0.942541	+	0.544176i	−0.0517852	+	0.998658i	$0.516491\pi$
$114$		0			0
$115$	−0.807178	−	3.01243i	−0.0752698	−	0.280911i
$116$	−9.26729			−0.860447
$117$		0			0
$118$	−2.91739			−0.268568
$119$	5.89774	+	22.0107i	0.540645	+	2.01771i
$120$		0			0
$121$	−5.38080	+	3.10661i	−0.489164	+	0.282419i
$122$	−0.926566	−	3.45799i	−0.0838874	−	0.313072i
$123$		0			0
$124$	−0.386503	+	0.386503i	−0.0347090	+	0.0347090i
$125$	−10.7616	−	10.7616i	−0.962547	−	0.962547i
$126$		0			0
$127$	2.86070	−	1.65163i	0.253846	−	0.146558i	−0.367678	−	0.929953i	$-0.619847\pi$
$127$	2.86070	−	1.65163i	0.253846	−	0.146558i	0.621524	+	0.783395i	$0.286514\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	−7.72799	+	11.0925i	−0.677790	+	0.972881i
$131$	−9.54763	−	5.51233i	−0.834181	−	0.481614i	0.0211014	−	0.999777i	$-0.493283\pi$
$131$	−9.54763	−	5.51233i	−0.834181	−	0.481614i	−0.855282	+	0.518163i	$0.826616\pi$
$132$		0			0
$133$	7.90840	−	13.6977i	0.685745	−	1.18774i
$134$	6.49877	−	11.2562i	0.561408	−	0.972388i
$135$		0			0
$136$	−6.77635	+	1.81572i	−0.581067	+	0.155697i
$137$	8.04563	+	8.04563i	0.687384	+	0.687384i	0.961653	−	0.274269i	$-0.0884358\pi$
$137$	8.04563	+	8.04563i	0.687384	+	0.687384i	−0.274269	+	0.961653i	$0.588436\pi$
$138$		0			0
$139$	−1.83834	−	3.18410i	−0.155926	−	0.270072i	0.777470	−	0.628920i	$-0.216503\pi$
$139$	−1.83834	−	3.18410i	−0.155926	−	0.270072i	−0.933396	+	0.358849i	$0.883169\pi$
$140$	−12.1791			−1.02932
$141$		0			0
$142$	−7.75569	+	4.47775i	−0.650843	+	0.375765i
$143$	−6.03090	+	5.08492i	−0.504329	+	0.425222i
$144$		0			0
$145$	−8.99344	+	33.5640i	−0.746864	+	2.78734i
$146$	−4.14384	−	2.39245i	−0.342947	−	0.198000i
$147$		0			0
$148$	−1.90093	+	0.509353i	−0.156256	+	0.0418686i
$149$	−8.76537	−	2.34867i	−0.718087	−	0.192411i	−0.118769	−	0.992922i	$-0.537895\pi$
$149$	−8.76537	−	2.34867i	−0.718087	−	0.192411i	−0.599318	+	0.800511i	$0.704561\pi$
$150$		0			0
$151$	−18.2244	−	4.88320i	−1.48308	−	0.397389i	−0.575684	−	0.817672i	$-0.695264\pi$
$151$	−18.2244	−	4.88320i	−1.48308	−	0.397389i	−0.907393	+	0.420283i	$0.861931\pi$
$152$	4.21708	+	2.43473i	0.342050	+	0.197483i
$153$		0			0
$154$	−6.86441	−	1.83931i	−0.553150	−	0.148216i
$155$	1.02474	+	1.77490i	0.0823092	+	0.142564i
$156$		0			0
$157$	11.0256	−	19.0969i	0.879939	−	1.52410i	0.0285320	−	0.999593i	$-0.490917\pi$
$157$	11.0256	−	19.0969i	0.879939	−	1.52410i	0.851407	−	0.524506i	$-0.175750\pi$
$158$	−8.28730	+	8.28730i	−0.659302	+	0.659302i
$159$		0			0
$160$		−	3.74953i		−	0.296426i
$161$	−1.91038	+	1.91038i	−0.150559	+	0.150559i
$162$		0			0
$163$	−1.64426	−	6.13647i	−0.128789	−	0.480646i	0.871158	−	0.491003i	$-0.163370\pi$
$163$	−1.64426	−	6.13647i	−0.128789	−	0.480646i	−0.999946	+	0.0103577i	$0.996703\pi$
$164$	−0.455940	+	1.70159i	−0.0356030	+	0.132872i
$165$		0			0
$166$			14.5197i			1.12695i
$167$	6.22875	+	6.22875i	0.481995	+	0.481995i	0.905768	−	0.423773i	$-0.139295\pi$
$167$	6.22875	+	6.22875i	0.481995	+	0.481995i	−0.423773	+	0.905768i	$0.639295\pi$
$168$		0			0
$169$	8.30897	−	9.99805i	0.639151	−	0.769081i
$170$			26.3044i			2.01746i
$171$		0			0
$172$	−0.0290558	−	0.0503260i	−0.00221548	−	0.00383732i
$173$	0.0504820			0.00383808			0.00191904	−	0.999998i	$-0.499389\pi$
$173$	0.0504820			0.00383808			0.00191904	+	0.999998i	$0.499389\pi$
$174$		0			0
$175$	−7.61574	+	28.4223i	−0.575696	+	2.14853i
$176$	0.566263	−	2.11332i	0.0426837	−	0.159298i
$177$		0			0
$178$	−13.5464			−1.01534
$179$	−3.55609	−	6.15933i	−0.265795	−	0.460370i	0.701977	−	0.712200i	$-0.252301\pi$
$179$	−3.55609	−	6.15933i	−0.265795	−	0.460370i	−0.967772	+	0.251830i	$0.918968\pi$
$180$		0			0
$181$		−	20.6330i		−	1.53364i	−0.641863	−	0.766820i	$-0.721838\pi$
$181$		−	20.6330i		−	1.53364i	0.641863	−	0.766820i	$-0.278162\pi$
$182$	11.6692	+	0.993078i	0.864980	+	0.0736118i
$183$		0			0
$184$	−0.588141	−	0.588141i	−0.0433583	−	0.0433583i
$185$			7.37904i			0.542518i
$186$		0			0
$187$	−3.97256	+	14.8258i	−0.290502	+	1.08417i
$188$	−1.56367	−	5.83570i	−0.114042	−	0.425612i
$189$		0			0
$190$	12.9105	−	12.9105i	0.936625	−	0.936625i
$191$		−	22.4922i		−	1.62748i	−0.581232	−	0.813738i	$-0.697429\pi$
$191$		−	22.4922i		−	1.62748i	0.581232	−	0.813738i	$-0.302571\pi$
$192$		0			0
$193$	4.78081	−	4.78081i	0.344131	−	0.344131i	−0.513787	−	0.857918i	$-0.671758\pi$
$193$	4.78081	−	4.78081i	0.344131	−	0.344131i	0.857918	+	0.513787i	$0.171758\pi$
$194$	4.93497	−	8.54762i	0.354310	−	0.613683i
$195$		0			0
$196$	1.77527	+	3.07486i	0.126805	+	0.219633i
$197$	−5.95380	−	1.59532i	−0.424191	−	0.113662i	0.0404072	−	0.999183i	$-0.487134\pi$
$197$	−5.95380	−	1.59532i	−0.424191	−	0.113662i	−0.464598	+	0.885522i	$0.653801\pi$
$198$		0			0
$199$	3.29772	+	1.90394i	0.233769	+	0.134967i	0.612310	−	0.790618i	$-0.290241\pi$
$199$	3.29772	+	1.90394i	0.233769	+	0.134967i	−0.378541	+	0.925585i	$0.623574\pi$
$200$	−8.75029	−	2.34463i	−0.618739	−	0.165791i
$201$		0			0
$202$	4.24904	+	1.13853i	0.298961	+	0.0801064i
$203$	29.0760	−	7.79088i	2.04073	−	0.546813i
$204$		0			0
$205$	5.72030	+	3.30262i	0.399523	+	0.230665i
$206$	2.42038	−	9.03299i	0.168636	−	0.629358i
$207$		0			0
$208$	−0.305736	+	3.59257i	−0.0211989	+	0.249100i
$209$	9.22643	−	5.32688i	0.638205	−	0.368468i
$210$		0			0
$211$	−19.1877			−1.32094			−0.660469	−	0.750853i	$-0.729642\pi$
$211$	−19.1877			−1.32094			−0.660469	+	0.750853i	$0.729642\pi$
$212$	0.811618	+	1.40576i	0.0557422	+	0.0965483i
$213$		0			0
$214$	−3.60730	−	3.60730i	−0.246590	−	0.246590i
$215$	−0.210466	+	0.0563943i	−0.0143537	+	0.00384606i
$216$		0			0
$217$	0.887718	−	1.53757i	0.0602622	−	0.104377i
$218$	−0.652710	+	1.13053i	−0.0442071	+	0.0765690i
$219$		0			0
$220$	−7.10443	−	4.10174i	−0.478980	−	0.276539i
$221$	2.14486	−	25.2033i	0.144279	−	1.69536i
$222$		0			0
$223$	−0.270983	+	0.0726098i	−0.0181464	+	0.00486231i	−0.267881	−	0.963452i	$-0.586323\pi$
$223$	−0.270983	+	0.0726098i	−0.0181464	+	0.00486231i	0.249734	+	0.968314i	$0.419657\pi$
$224$	−2.81299	+	1.62408i	−0.187951	+	0.108513i
$225$		0			0
$226$	8.18076	+	8.18076i	0.544176	+	0.544176i
$227$	−9.00891	+	9.00891i	−0.597942	+	0.597942i	−0.939765	−	0.341822i	$-0.888956\pi$
$227$	−9.00891	+	9.00891i	−0.597942	+	0.597942i	0.341822	+	0.939765i	$0.388956\pi$
$228$		0			0
$229$	−1.11470	−	4.16011i	−0.0736613	−	0.274908i	0.919265	−	0.393639i	$-0.128784\pi$
$229$	−1.11470	−	4.16011i	−0.0736613	−	0.274908i	−0.992926	+	0.118731i	$0.962117\pi$
$230$	−2.70087	+	1.55935i	−0.178090	+	0.102820i
$231$		0			0
$232$	2.39855	+	8.95152i	0.157473	+	0.587696i
$233$	−21.0744			−1.38063			−0.690313	−	0.723511i	$-0.742527\pi$
$233$	−21.0744			−1.38063			−0.690313	+	0.723511i	$0.742527\pi$
$234$		0			0
$235$	−22.6530			−1.47772
$236$	0.755077	+	2.81798i	0.0491513	+	0.183435i
$237$		0			0
$238$	19.7342	−	11.3936i	1.27918	−	0.738535i
$239$	−3.36892	−	12.5730i	−0.217917	−	0.813278i	−0.985119	−	0.171873i	$-0.945018\pi$
$239$	−3.36892	−	12.5730i	−0.217917	−	0.813278i	0.767202	−	0.641406i	$-0.221648\pi$
$240$		0			0
$241$	0.881282	−	0.881282i	0.0567684	−	0.0567684i	−0.678153	−	0.734921i	$-0.737219\pi$
$241$	0.881282	−	0.881282i	0.0567684	−	0.0567684i	0.734921	+	0.678153i	$0.237219\pi$
$242$	4.39341	+	4.39341i	0.282419	+	0.282419i
$243$		0			0
$244$	−3.10035	+	1.78999i	−0.198480	+	0.114592i
$245$	12.8592	−	3.44562i	0.821545	−	0.220132i
$246$		0			0
$247$	−13.4227	+	11.3173i	−0.854069	+	0.720103i
$248$	0.473367	+	0.273299i	0.0300588	+	0.0173545i
$249$		0			0
$250$	−7.60960	+	13.1802i	−0.481273	+	0.833590i
$251$	5.64794	−	9.78252i	0.356495	−	0.617467i	−0.630878	−	0.775882i	$-0.717305\pi$
$251$	5.64794	−	9.78252i	0.356495	−	0.617467i	0.987373	+	0.158415i	$0.0506384\pi$
$252$		0			0
$253$	−1.75777	+	0.470993i	−0.110510	+	0.0296111i
$254$	−2.33575	−	2.33575i	−0.146558	−	0.146558i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.62623			0.101442			0.0507209	−	0.998713i	$-0.483848\pi$
$257$	1.62623			0.101442			0.0507209	+	0.998713i	$0.483848\pi$
$258$		0			0
$259$	5.53593	−	3.19617i	0.343986	−	0.198601i
$260$	12.7147	+	4.59371i	0.788534	+	0.284890i
$261$		0			0
$262$	−2.85339	+	10.6490i	−0.176283	+	0.657897i
$263$	−9.85242	−	5.68830i	−0.607526	−	0.350755i	0.164470	−	0.986382i	$-0.447409\pi$
$263$	−9.85242	−	5.68830i	−0.607526	−	0.350755i	−0.771997	+	0.635627i	$0.780742\pi$
$264$		0			0
$265$	5.87898	−	1.57527i	0.361143	−	0.0967680i
$266$	−15.2778	−	4.09369i	−0.936745	−	0.251000i
$267$		0			0
$268$	−12.5547	−	3.36401i	−0.766898	−	0.205490i
$269$	10.3721	+	5.98835i	0.632400	+	0.365116i	0.781681	−	0.623678i	$-0.214363\pi$
$269$	10.3721	+	5.98835i	0.632400	+	0.365116i	−0.149281	+	0.988795i	$0.547696\pi$
$270$		0			0
$271$	23.9876	+	6.42745i	1.45714	+	0.390440i	0.898502	−	0.438970i	$-0.144657\pi$
$271$	23.9876	+	6.42745i	1.45714	+	0.390440i	0.558640	+	0.829410i	$0.311323\pi$
$272$	3.50770	+	6.07551i	0.212685	+	0.368382i
$273$		0			0
$274$	5.68912	−	9.85384i	0.343692	−	0.595292i
$275$	−14.0147	+	14.0147i	−0.845121	+	0.845121i
$276$		0			0
$277$		−	15.6518i		−	0.940425i	−0.882553	−	0.470212i	$-0.844177\pi$
$277$		−	15.6518i		−	0.940425i	0.882553	−	0.470212i	$-0.155823\pi$
$278$	−2.59981	+	2.59981i	−0.155926	+	0.155926i
$279$		0			0
$280$	3.15217	+	11.7641i	0.188378	+	0.703038i
$281$	−1.13987	+	4.25406i	−0.0679991	+	0.253776i	−0.991555	−	0.129688i	$-0.958602\pi$
$281$	−1.13987	+	4.25406i	−0.0679991	+	0.253776i	0.923556	+	0.383464i	$0.125269\pi$
$282$		0			0
$283$		−	18.2539i		−	1.08508i	−0.840030	−	0.542540i	$-0.817463\pi$
$283$		−	18.2539i		−	1.08508i	0.840030	−	0.542540i	$-0.182537\pi$
$284$	6.33250	+	6.33250i	0.375765	+	0.375765i
$285$		0			0
$286$	6.47257	+	4.50933i	0.382731	+	0.266642i
$287$		−	5.72202i		−	0.337760i
$288$		0			0
$289$	−16.1079	−	27.8997i	−0.947523	−	1.64116i
$290$	34.7480			2.04047
$291$		0			0
$292$	−1.23842	+	4.62186i	−0.0724732	+	0.270474i
$293$	2.89268	−	10.7956i	0.168992	−	0.630688i	−0.828505	−	0.559982i	$-0.810808\pi$
$293$	2.89268	−	10.7956i	0.168992	−	0.630688i	0.997497	−	0.0707062i	$-0.0225253\pi$
$294$		0			0
$295$	10.9388			0.636884
$296$	0.983995	+	1.70433i	0.0571936	+	0.0990622i
$297$		0			0
$298$			9.07458i			0.525676i
$299$	2.71496	−	1.27384i	0.157010	−	0.0736682i
$300$		0			0
$301$	0.133470	+	0.133470i	0.00769310	+	0.00769310i
$302$			18.8672i			1.08569i
$303$		0			0
$304$	1.26031	−	4.70354i	0.0722837	−	0.269767i
$305$	3.47419	+	12.9658i	0.198931	+	0.742422i
$306$		0			0
$307$	−14.9777	+	14.9777i	−0.854823	+	0.854823i	−0.990723	−	0.135900i	$-0.956608\pi$
$307$	−14.9777	+	14.9777i	−0.854823	+	0.854823i	0.135900	+	0.990723i	$0.456608\pi$
$308$			7.10656i			0.404934i
$309$		0			0
$310$	1.44920	−	1.44920i	0.0823092	−	0.0823092i
$311$	6.94304	−	12.0257i	0.393704	−	0.681915i	−0.599231	−	0.800576i	$-0.704527\pi$
$311$	6.94304	−	12.0257i	0.393704	−	0.681915i	0.992935	+	0.118661i	$0.0378603\pi$
$312$		0			0
$313$	4.79094	+	8.29816i	0.270800	+	0.469040i	0.969067	−	0.246798i	$-0.0793784\pi$
$313$	4.79094	+	8.29816i	0.270800	+	0.469040i	−0.698267	+	0.715838i	$0.746045\pi$
$314$	−21.2998	−	5.70727i	−1.20202	−	0.322080i
$315$		0			0
$316$	10.1498	+	5.86001i	0.570972	+	0.329651i
$317$	−15.5549	−	4.16793i	−0.873653	−	0.234095i	−0.205986	−	0.978555i	$-0.566040\pi$
$317$	−15.5549	−	4.16793i	−0.873653	−	0.234095i	−0.667667	+	0.744460i	$0.732707\pi$
$318$		0			0
$319$	19.5848	+	5.24772i	1.09654	+	0.293816i
$320$	−3.62177	+	0.970449i	−0.202463	+	0.0542498i
$321$		0			0
$322$	2.33972	+	1.35084i	0.130388	+	0.0752794i
$323$	−8.84157	+	32.9972i	−0.491958	+	1.83601i
$324$		0			0
$325$	18.6710	−	26.7999i	1.03568	−	1.48659i
$326$	−5.50181	+	3.17647i	−0.304717	+	0.175928i
$327$		0			0
$328$	1.76162			0.0972691
$329$	9.81197	+	16.9948i	0.540951	+	0.936955i
$330$		0			0
$331$	5.22945	+	5.22945i	0.287437	+	0.287437i	0.836066	−	0.548629i	$-0.184850\pi$
$331$	5.22945	+	5.22945i	0.287437	+	0.287437i	−0.548629	+	0.836066i	$0.684850\pi$
$332$	14.0250	−	3.75798i	0.769721	−	0.206246i
$333$		0			0
$334$	4.40439	−	7.62863i	0.240998	−	0.417420i
$335$	−24.3673	+	42.2054i	−1.33133	+	2.30593i
$336$		0			0
$337$	16.2869	+	9.40326i	0.887205	+	0.512228i	0.873027	−	0.487671i	$-0.162154\pi$
$337$	16.2869	+	9.40326i	0.887205	+	0.512228i	0.0141778	+	0.999899i	$0.495487\pi$
$338$	−11.8079	−	5.43816i	−0.642265	−	0.295797i
$339$		0			0
$340$	25.4081	−	6.80809i	1.37795	−	0.369220i
$341$	1.03567	−	0.597942i	0.0560845	−	0.0323804i
$342$		0			0
$343$	7.92271	+	7.92271i	0.427786	+	0.427786i
$344$	−0.0410910	+	0.0410910i	−0.00221548	+	0.00221548i
$345$		0			0
$346$	−0.0130657	−	0.0487619i	−0.000702417	−	0.00262145i
$347$	21.4424	−	12.3798i	1.15109	−	0.664582i	0.201937	−	0.979398i	$-0.435276\pi$
$347$	21.4424	−	12.3798i	1.15109	−	0.664582i	0.949153	+	0.314817i	$0.101943\pi$
$348$		0			0
$349$	0.883920	+	3.29884i	0.0473152	+	0.176583i	0.985540	−	0.169444i	$-0.0541973\pi$
$349$	0.883920	+	3.29884i	0.0473152	+	0.176583i	−0.938225	+	0.346027i	$0.887531\pi$
$350$	29.4250			1.57283
$351$		0			0
$352$	−2.18787			−0.116614
$353$	1.15015	+	4.29243i	0.0612165	+	0.228463i	0.989756	−	0.142771i	$-0.0456013\pi$
$353$	1.15015	+	4.29243i	0.0612165	+	0.228463i	−0.928539	+	0.371234i	$0.878935\pi$
$354$		0			0
$355$	29.0802	−	16.7895i	1.54342	−	0.891092i
$356$	3.50606	+	13.0848i	0.185821	+	0.693493i
$357$		0			0
$358$	−5.02907	+	5.02907i	−0.265795	+	0.265795i
$359$	−1.76025	−	1.76025i	−0.0929022	−	0.0929022i	0.659128	−	0.752031i	$-0.270925\pi$
$359$	−1.76025	−	1.76025i	−0.0929022	−	0.0929022i	−0.752031	+	0.659128i	$0.770925\pi$
$360$		0			0
$361$	4.08043	−	2.35584i	0.214759	−	0.123991i
$362$	−19.9300	+	5.34021i	−1.04750	+	0.280675i
$363$		0			0
$364$	−2.06098	−	11.5286i	−0.108025	−	0.604265i
$365$	15.5375	+	8.97055i	0.813268	+	0.469540i
$366$		0			0
$367$	−4.07549	+	7.05896i	−0.212739	+	0.368475i	−0.952571	−	0.304317i	$-0.901572\pi$
$367$	−4.07549	+	7.05896i	−0.212739	+	0.368475i	0.739832	+	0.672792i	$0.234905\pi$
$368$	−0.415879	+	0.720323i	−0.0216792	+	0.0375494i
$369$		0			0
$370$	7.12760	−	1.90984i	0.370546	−	0.0992876i
$371$	−3.72824	−	3.72824i	−0.193561	−	0.193561i
$372$		0			0
$373$	−11.8381	−	20.5043i	−0.612956	−	1.06167i	−0.990740	−	0.135776i	$-0.956647\pi$
$373$	−11.8381	−	20.5043i	−0.612956	−	1.06167i	0.377784	−	0.925894i	$-0.376686\pi$
$374$	15.3488			0.793667
$375$		0			0
$376$	−5.23214	+	3.02078i	−0.269827	+	0.155785i
$377$	−33.2934	−	2.83334i	−1.71470	−	0.145925i
$378$		0			0
$379$	2.92796	−	10.9273i	0.150399	−	0.561297i	−0.849057	−	0.528302i	$-0.822829\pi$
$379$	2.92796	−	10.9273i	0.150399	−	0.561297i	0.999456	−	0.0329946i	$-0.0105044\pi$
$380$	−15.8121	−	9.12909i	−0.811141	−	0.468313i
$381$		0			0
$382$	−21.7258	+	5.82140i	−1.11159	+	0.297849i
$383$	29.0188	+	7.77555i	1.48279	+	0.397312i	0.907296	−	0.420494i	$-0.138143\pi$
$383$	29.0188	+	7.77555i	1.48279	+	0.397312i	0.575494	+	0.817806i	$0.304810\pi$
$384$		0			0
$385$	25.7383	+	6.89655i	1.31174	+	0.351481i
$386$	−5.85528	−	3.38055i	−0.298026	−	0.172065i
$387$		0			0
$388$	−9.53363	−	2.55453i	−0.483997	−	0.129687i
$389$	4.55590	+	7.89104i	0.230993	+	0.400092i	0.958101	−	0.286432i	$-0.0924692\pi$
$389$	4.55590	+	7.89104i	0.230993	+	0.400092i	−0.727108	+	0.686524i	$0.759136\pi$
$390$		0			0
$391$	2.91755	−	5.05335i	0.147547	−	0.255559i
$392$	2.51061	−	2.51061i	0.126805	−	0.126805i
$393$		0			0
$394$			6.16383i			0.310529i
$395$	31.0735	−	31.0735i	1.56348	−	1.56348i
$396$		0			0
$397$	−2.78992	−	10.4121i	−0.140022	−	0.522570i	−0.999927	−	0.0121147i	$-0.996144\pi$
$397$	−2.78992	−	10.4121i	−0.140022	−	0.522570i	0.859904	−	0.510455i	$-0.170523\pi$
$398$	0.985551	−	3.67812i	0.0494012	−	0.184368i
$399$		0			0
$400$			9.05896i			0.452948i
$401$	−8.39762	−	8.39762i	−0.419357	−	0.419357i	0.465625	−	0.884982i	$-0.345830\pi$
$401$	−8.39762	−	8.39762i	−0.419357	−	0.419357i	−0.884982	+	0.465625i	$0.845830\pi$
$402$		0			0
$403$	−1.50670	+	1.27037i	−0.0750543	+	0.0632816i
$404$		−	4.39893i		−	0.218855i
$405$		0			0
$406$	−15.0508	−	26.0688i	−0.746960	−	1.29377i
$407$	4.30571			0.213426
$408$		0			0
$409$	−5.55756	+	20.7411i	−0.274804	+	1.02558i	0.681169	+	0.732126i	$0.261472\pi$
$409$	−5.55756	+	20.7411i	−0.274804	+	1.02558i	−0.955973	+	0.293455i	$0.905195\pi$
$410$	1.70956	−	6.38017i	0.0844292	−	0.315094i
$411$		0			0
$412$	−9.35164			−0.460722
$413$	−4.73808	−	8.20659i	−0.233146	−	0.403820i
$414$		0			0
$415$		−	54.4421i		−	2.67246i
$416$	3.54928	−	0.634506i	0.174018	−	0.0311092i
$417$		0			0
$418$	−7.53335	−	7.53335i	−0.368468	−	0.368468i
$419$			10.7983i			0.527530i	0.964587	+	0.263765i	$0.0849644\pi$
$419$			10.7983i			0.527530i	−0.964587	+	0.263765i	$0.915036\pi$
$420$		0			0
$421$	−1.69956	+	6.34283i	−0.0828313	+	0.309131i	−0.994895	−	0.100919i	$-0.967822\pi$
$421$	−1.69956	+	6.34283i	−0.0828313	+	0.309131i	0.912063	+	0.410049i	$0.134488\pi$
$422$	4.96615	+	18.5339i	0.241748	+	0.902217i
$423$		0			0
$424$	1.14780	−	1.14780i	0.0557422	−	0.0557422i
$425$		−	63.5522i		−	3.08273i
$426$		0			0
$427$	8.22248	−	8.22248i	0.397913	−	0.397913i
$428$	−2.55075	+	4.41803i	−0.123295	+	0.213553i
$429$		0			0
$430$	0.108945	+	0.188699i	0.00525381	+	0.00909987i
$431$	5.36331	+	1.43709i	0.258341	+	0.0692224i	0.385665	−	0.922639i	$-0.373972\pi$
$431$	5.36331	+	1.43709i	0.258341	+	0.0692224i	−0.127324	+	0.991861i	$0.540639\pi$
$432$		0			0
$433$	31.1666	+	17.9940i	1.49777	+	0.864737i	0.999997	−	0.00257012i	$-0.000818096\pi$
$433$	31.1666	+	17.9940i	1.49777	+	0.864737i	0.497773	+	0.867308i	$0.334151\pi$
$434$	−1.71494	−	0.459516i	−0.0823197	−	0.0220575i
$435$		0			0
$436$	1.26094	+	0.337868i	0.0603881	+	0.0161809i
$437$	−3.91220	+	1.04827i	−0.187146	+	0.0501456i
$438$		0			0
$439$	17.5924	+	10.1570i	0.839640	+	0.484767i	0.857142	−	0.515080i	$-0.172238\pi$
$439$	17.5924	+	10.1570i	0.839640	+	0.484767i	−0.0175016	+	0.999847i	$0.505571\pi$
$440$	−2.12322	+	7.92396i	−0.101220	+	0.377760i
$441$		0			0
$442$	−24.8996	+	4.45131i	−1.18435	+	0.211727i
$443$	16.2468	−	9.38011i	0.771910	−	0.445662i	−0.0616456	−	0.998098i	$-0.519635\pi$
$443$	16.2468	−	9.38011i	0.771910	−	0.445662i	0.833556	+	0.552436i	$0.186302\pi$
$444$		0			0
$445$	50.7925			2.40780
$446$	0.140271	+	0.242957i	0.00664204	+	0.0115044i
$447$		0			0
$448$	2.29680	+	2.29680i	0.108513	+	0.108513i
$449$	15.3460	−	4.11194i	0.724221	−	0.194055i	0.122167	−	0.992510i	$-0.461016\pi$
$449$	15.3460	−	4.11194i	0.724221	−	0.194055i	0.602054	+	0.798455i	$0.294349\pi$
$450$		0			0
$451$	1.92710	−	3.33783i	0.0907435	−	0.157172i
$452$	5.78467	−	10.0193i	0.272088	−	0.471271i
$453$		0			0
$454$	11.0336	+	6.37026i	0.517833	+	0.298971i
$455$	−43.7541	−	3.72357i	−2.05122	−	0.174564i
$456$		0			0
$457$	0.847454	−	0.227075i	0.0396422	−	0.0106221i	−0.238943	−	0.971033i	$-0.576801\pi$
$457$	0.847454	−	0.227075i	0.0396422	−	0.0106221i	0.278586	+	0.960411i	$0.410134\pi$
$458$	−3.72985	+	2.15343i	−0.174285	+	0.100623i
$459$		0			0
$460$	2.20525	+	2.20525i	0.102820	+	0.102820i
$461$	−16.4709	+	16.4709i	−0.767127	+	0.767127i	−0.977600	−	0.210473i	$-0.932500\pi$
$461$	−16.4709	+	16.4709i	−0.767127	+	0.767127i	0.210473	+	0.977600i	$0.432500\pi$
$462$		0			0
$463$	4.66680	+	17.4167i	0.216885	+	0.809424i	0.985495	+	0.169707i	$0.0542820\pi$
$463$	4.66680	+	17.4167i	0.216885	+	0.809424i	−0.768610	+	0.639718i	$0.779051\pi$
$464$	8.02571	−	4.63365i	0.372584	−	0.215112i
$465$		0			0
$466$	5.45444	+	20.3563i	0.252672	+	0.942986i
$467$	24.8989			1.15218			0.576091	−	0.817386i	$-0.304577\pi$
$467$	24.8989			1.15218			0.576091	+	0.817386i	$0.304577\pi$
$468$		0			0
$469$	42.2181			1.94945
$470$	5.86303	+	21.8811i	0.270441	+	1.00930i
$471$		0			0
$472$	2.52654	−	1.45870i	0.116293	−	0.0671419i
$473$	0.0329064	+	0.122808i	0.00151304	+	0.00564673i
$474$		0			0
$475$	−31.1921	+	31.1921i	−1.43119	+	1.43119i
$476$	−16.1129	−	16.1129i	−0.738535	−	0.738535i
$477$		0			0
$478$	−11.2726	+	6.50825i	−0.515598	+	0.297681i
$479$	7.34248	−	1.96741i	0.335487	−	0.0898934i	−0.0871431	−	0.996196i	$-0.527774\pi$
$479$	7.34248	−	1.96741i	0.335487	−	0.0898934i	0.422630	+	0.906302i	$0.361107\pi$
$480$		0			0
$481$	−6.98495	+	1.24870i	−0.318486	+	0.0569359i
$482$	−1.07935	−	0.623161i	−0.0491629	−	0.0283842i
$483$		0			0
$484$	3.10661	−	5.38080i	0.141209	−	0.244582i
$485$	−18.5038	+	32.0495i	−0.840215	+	1.45529i
$486$		0			0
$487$	−32.0391	+	8.58485i	−1.45183	+	0.389017i	−0.896660	−	0.442720i	$-0.854014\pi$
$487$	−32.0391	+	8.58485i	−1.45183	+	0.389017i	−0.555171	+	0.831736i	$0.687347\pi$
$488$	2.53143	+	2.53143i	0.114592	+	0.114592i
$489$		0			0
$490$	−6.65642	−	11.5293i	−0.300706	−	0.520839i
$491$	25.8478			1.16650			0.583248	−	0.812294i	$-0.301782\pi$
$491$	25.8478			1.16650			0.583248	+	0.812294i	$0.301782\pi$
$492$		0			0
$493$	−56.3035	+	32.5069i	−2.53578	+	1.46404i
$494$	14.4057	+	10.0362i	0.648145	+	0.451552i
$495$		0			0
$496$	0.141470	−	0.527973i	0.00635218	−	0.0237067i
$497$	−25.1917	−	14.5445i	−1.13000	−	0.652408i
$498$		0			0
$499$	15.7626	−	4.22357i	0.705629	−	0.189073i	0.111879	−	0.993722i	$-0.464313\pi$
$499$	15.7626	−	4.22357i	0.705629	−	0.189073i	0.593751	+	0.804649i	$0.297647\pi$
$500$	14.7006	+	3.93902i	0.657432	+	0.176158i
$501$		0			0
$502$	−10.9110	−	2.92359i	−0.486981	−	0.130486i
$503$	−6.80210	−	3.92720i	−0.303291	−	0.175105i	0.340630	−	0.940198i	$-0.389360\pi$
$503$	−6.80210	−	3.92720i	−0.303291	−	0.175105i	−0.643920	+	0.765093i	$0.722693\pi$
$504$		0			0
$505$	−15.9319	−	4.26894i	−0.708960	−	0.189965i
$506$	0.909889	+	1.57597i	0.0404495	+	0.0700606i
$507$		0			0
$508$	−1.65163	+	2.86070i	−0.0732790	+	0.126923i
$509$	−18.3184	+	18.3184i	−0.811947	+	0.811947i	−0.984926	−	0.172979i	$-0.944661\pi$
$509$	−18.3184	+	18.3184i	−0.811947	+	0.811947i	0.172979	+	0.984926i	$0.444661\pi$
$510$		0			0
$511$		−	15.5421i		−	0.687542i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−0.420900	−	1.57082i	−0.0185651	−	0.0692860i
$515$	−9.07529	+	33.8695i	−0.399905	+	1.49247i
$516$		0			0
$517$			13.2182i			0.581334i
$518$	−4.52007	−	4.52007i	−0.198601	−	0.198601i
$519$		0			0
$520$	1.14636	−	13.4704i	0.0502714	−	0.590717i
$521$			44.6910i			1.95795i	0.203981	+	0.978975i	$0.434612\pi$
$521$			44.6910i			1.95795i	−0.203981	+	0.978975i	$0.565388\pi$
$522$		0			0
$523$	2.38397	+	4.12916i	0.104244	+	0.180556i	0.913429	−	0.406998i	$-0.133424\pi$
$523$	2.38397	+	4.12916i	0.104244	+	0.180556i	−0.809185	+	0.587554i	$0.800091\pi$
$524$	11.0247			0.481614
$525$		0			0
$526$	−2.94448	+	10.9889i	−0.128385	+	0.479141i
$527$	−0.992467	+	3.70394i	−0.0432325	+	0.161346i
$528$		0			0
$529$	−22.3082			−0.969921
$530$	−3.04319	−	5.27095i	−0.132188	−	0.228956i
$531$		0			0
$532$			15.8168i			0.685745i
$533$	−2.15823	+	5.97369i	−0.0934834	+	0.258749i
$534$		0			0
$535$	13.5257	+	13.5257i	0.584766	+	0.584766i
$536$			12.9975i			0.561408i
$537$		0			0
$538$	3.09980	−	11.5686i	0.133642	−	0.498758i
$539$	−2.01054	−	7.50343i	−0.0866000	−	0.323196i
$540$		0			0
$541$	−31.0921	+	31.0921i	−1.33675	+	1.33675i	−0.437565	+	0.899187i	$0.644159\pi$
$541$	−31.0921	+	31.0921i	−1.33675	+	1.33675i	−0.899187	+	0.437565i	$0.855841\pi$
$542$		−	24.8338i		−	1.06670i
$543$		0			0
$544$	4.96063	−	4.96063i	0.212685	−	0.212685i
$545$	2.44736	−	4.23894i	0.104833	−	0.181576i
$546$		0			0
$547$	7.14869	+	12.3819i	0.305656	+	0.529412i	0.977407	−	0.211365i	$-0.0677910\pi$
$547$	7.14869	+	12.3819i	0.305656	+	0.529412i	−0.671751	+	0.740777i	$0.734458\pi$
$548$	−10.9905	−	2.94490i	−0.469492	−	0.125800i
$549$		0			0
$550$	17.1645	+	9.90992i	0.731896	+	0.422561i
$551$	43.5891	+	11.6797i	1.85696	+	0.497570i
$552$		0			0
$553$	−36.7713	−	9.85284i	−1.56368	−	0.418986i
$554$	−15.1185	+	4.05098i	−0.642322	+	0.172110i
$555$		0			0
$556$	3.18410	+	1.83834i	0.135036	+	0.0779630i
$557$	11.2642	−	42.0386i	0.477280	−	1.78123i	−0.135277	−	0.990808i	$-0.543193\pi$
$557$	11.2642	−	42.0386i	0.477280	−	1.78123i	0.612557	−	0.790426i	$-0.290141\pi$
$558$		0			0
$559$	−0.0889982	−	0.189683i	−0.00376422	−	0.00802273i
$560$	10.5474	−	6.08953i	0.445708	−	0.257330i
$561$		0			0
$562$	4.40413			0.185777
$563$	−3.73481	−	6.46888i	−0.157403	−	0.272631i	0.776528	−	0.630083i	$-0.216979\pi$
$563$	−3.73481	−	6.46888i	−0.157403	−	0.272631i	−0.933932	+	0.357452i	$0.883646\pi$
$564$		0			0
$565$	−30.6740	−	30.6740i	−1.29047	−	1.29047i
$566$	−17.6319	+	4.72445i	−0.741124	+	0.198583i
$567$		0			0
$568$	4.47775	−	7.75569i	0.187882	−	0.325422i
$569$	20.6528	−	35.7717i	0.865810	−	1.49963i	−0.000430492	−	1.00000i	$-0.500137\pi$
$569$	20.6528	−	35.7717i	0.865810	−	1.49963i	0.866241	−	0.499627i	$-0.166530\pi$
$570$		0			0
$571$	−38.0908	−	21.9917i	−1.59405	−	0.920326i	−0.992602	−	0.121415i	$-0.961257\pi$
$571$	−38.0908	−	21.9917i	−1.59405	−	0.920326i	−0.601449	−	0.798911i	$-0.705410\pi$
$572$	2.68045	−	7.41912i	0.112075	−	0.310209i
$573$		0			0
$574$	−5.52704	+	1.48097i	−0.230694	+	0.0618144i
$575$	6.52538	−	3.76743i	0.272127	−	0.157113i
$576$		0			0
$577$	−27.8109	−	27.8109i	−1.15778	−	1.15778i	−0.984952	−	0.172831i	$-0.944709\pi$
$577$	−27.8109	−	27.8109i	−1.15778	−	1.15778i	−0.172831	−	0.984952i	$-0.555291\pi$
$578$	−22.7800	+	22.7800i	−0.947523	+	0.947523i
$579$		0			0
$580$	−8.99344	−	33.5640i	−0.373432	−	1.39367i
$581$	−40.8438	+	23.5812i	−1.69449	+	0.978313i
$582$		0			0
$583$	−0.919179	−	3.43042i	−0.0380685	−	0.142074i
$584$	4.78490			0.198000
$585$		0			0
$586$	−11.1765			−0.461696
$587$	2.71700	+	10.1400i	0.112143	+	0.418522i	0.999057	−	0.0434112i	$-0.0138225\pi$
$587$	2.71700	+	10.1400i	0.112143	+	0.418522i	−0.886915	+	0.461933i	$0.847156\pi$
$588$		0			0
$589$	2.30504	−	1.33082i	0.0949777	−	0.0548354i
$590$	−2.83118	−	10.5661i	−0.116558	−	0.435000i
$591$		0			0
$592$	1.39158	−	1.39158i	0.0571936	−	0.0571936i
$593$	24.8672	+	24.8672i	1.02117	+	1.02117i	0.999771	+	0.0214039i	$0.00681360\pi$
$593$	24.8672	+	24.8672i	1.02117	+	1.02117i	0.0214039	+	0.999771i	$0.493186\pi$
$594$		0			0
$595$	−73.9940	+	42.7205i	−3.03346	+	1.75137i
$596$	8.76537	−	2.34867i	0.359044	−	0.0962054i
$597$		0			0
$598$	−1.93312	−	2.29275i	−0.0790512	−	0.0937576i
$599$	−5.46701	−	3.15638i	−0.223376	−	0.128966i	0.384137	−	0.923276i	$-0.374499\pi$
$599$	−5.46701	−	3.15638i	−0.223376	−	0.128966i	−0.607512	+	0.794310i	$0.707833\pi$
$600$		0			0
$601$	−16.8743	+	29.2272i	−0.688318	+	1.19220i	0.284064	+	0.958805i	$0.408317\pi$
$601$	−16.8743	+	29.2272i	−0.688318	+	1.19220i	−0.972382	+	0.233396i	$0.925016\pi$
$602$	0.0943777	−	0.163467i	0.00384655	−	0.00666242i
$603$		0			0
$604$	18.2244	−	4.88320i	0.741539	−	0.198695i
$605$	−16.4732	−	16.4732i	−0.669731	−	0.669731i
$606$		0			0
$607$	−12.9072	−	22.3560i	−0.523888	−	0.907401i	−0.999613	−	0.0278069i	$-0.991148\pi$
$607$	−12.9072	−	22.3560i	−0.523888	−	0.907401i	0.475725	−	0.879594i	$-0.342186\pi$
$608$	−4.86946			−0.197483
$609$		0			0
$610$	11.6249	−	6.71161i	0.470677	−	0.271745i
$611$	−3.83341	−	21.4432i	−0.155083	−	0.867499i
$612$		0			0
$613$	4.39253	−	16.3932i	0.177413	−	0.662113i	−0.818715	−	0.574200i	$-0.805313\pi$
$613$	4.39253	−	16.3932i	0.177413	−	0.662113i	0.996128	−	0.0879138i	$-0.0280200\pi$
$614$	18.3439	+	10.5908i	0.740299	+	0.427412i
$615$		0			0
$616$	6.86441	−	1.83931i	0.276575	−	0.0741080i
$617$	−44.7003	−	11.9774i	−1.79957	−	0.482193i	−0.805657	−	0.592383i	$-0.798187\pi$
$617$	−44.7003	−	11.9774i	−1.79957	−	0.482193i	−0.993911	+	0.110190i	$0.964854\pi$
$618$		0			0
$619$	33.1257	+	8.87599i	1.33143	+	0.356756i	0.853249	−	0.521504i	$-0.174629\pi$
$619$	33.1257	+	8.87599i	1.33143	+	0.356756i	0.478183	+	0.878260i	$0.341295\pi$
$620$	−1.77490	−	1.02474i	−0.0712819	−	0.0411546i
$621$		0			0
$622$	−13.4129	−	3.59398i	−0.537809	−	0.144106i
$623$	−22.0004	−	38.1058i	−0.881428	−	1.52668i
$624$		0			0
$625$	5.88500	−	10.1931i	0.235400	−	0.407725i
$626$	6.77542	−	6.77542i	0.270800	−	0.270800i
$627$		0			0
$628$			22.0512i			0.879939i
$629$	−9.76248	+	9.76248i	−0.389256	+	0.389256i
$630$		0			0
$631$	−2.50134	−	9.33512i	−0.0995767	−	0.371625i	0.898097	−	0.439798i	$-0.144950\pi$
$631$	−2.50134	−	9.33512i	−0.0995767	−	0.371625i	−0.997674	+	0.0681724i	$0.978283\pi$
$632$	3.03336	−	11.3207i	0.120661	−	0.450312i
$633$		0			0
$634$			16.1037i			0.639558i
$635$	8.75797	+	8.75797i	0.347549	+	0.347549i
$636$		0			0
$637$	5.43768	+	11.5894i	0.215449	+	0.459188i
$638$		−	20.2756i		−	0.802721i
$639$		0			0
$640$	1.87476	+	3.24719i	0.0741066	+	0.128356i
$641$	22.3227			0.881695			0.440848	−	0.897582i	$-0.354678\pi$
$641$	22.3227			0.881695			0.440848	+	0.897582i	$0.354678\pi$
$642$		0			0
$643$	−9.67643	+	36.1129i	−0.381601	+	1.42415i	0.461855	+	0.886956i	$0.347184\pi$
$643$	−9.67643	+	36.1129i	−0.381601	+	1.42415i	−0.843456	+	0.537199i	$0.819483\pi$
$644$	0.699246	−	2.60962i	0.0275542	−	0.102834i
$645$		0			0
$646$	34.1612			1.34405
$647$	−1.97324	−	3.41775i	−0.0775760	−	0.134366i	0.824628	−	0.565676i	$-0.191385\pi$
$647$	−1.97324	−	3.41775i	−0.0775760	−	0.134366i	−0.902204	+	0.431310i	$0.858051\pi$
$648$		0			0
$649$		−	6.38288i		−	0.250550i
$650$	−30.7191	−	11.0985i	−1.20490	−	0.435320i
$651$		0			0
$652$	4.49221	+	4.49221i	0.175928	+	0.175928i
$653$		−	14.8536i		−	0.581266i	−0.956835	−	0.290633i	$-0.906134\pi$
$653$		−	14.8536i		−	0.581266i	0.956835	−	0.290633i	$-0.0938659\pi$
$654$		0			0
$655$	10.6989	−	39.9287i	0.418039	−	1.56014i
$656$	−0.455940	−	1.70159i	−0.0178015	−	0.0664360i
$657$		0			0
$658$	13.8762	−	13.8762i	0.540951	−	0.540951i
$659$			40.0270i			1.55923i	0.626259	+	0.779615i	$0.284585\pi$
$659$			40.0270i			1.55923i	−0.626259	+	0.779615i	$0.715415\pi$
$660$		0			0
$661$	3.62807	−	3.62807i	0.141116	−	0.141116i	−0.633020	−	0.774136i	$-0.718185\pi$
$661$	3.62807	−	3.62807i	0.141116	−	0.141116i	0.774136	+	0.633020i	$0.218185\pi$
$662$	3.69778	−	6.40474i	0.143718	−	0.248927i
$663$		0			0
$664$	−7.25986	−	12.5744i	−0.281737	−	0.487983i
$665$	57.2847	+	15.3494i	2.22141	+	0.595224i
$666$		0			0
$667$	−6.67544	−	3.85407i	−0.258474	−	0.149230i
$668$	−8.50863	−	2.27988i	−0.329209	−	0.0882112i
$669$		0			0
$670$	47.0741	+	12.6135i	1.81863	+	0.487300i
$671$	7.56564	−	2.02721i	0.292068	−	0.0782595i
$672$		0			0
$673$	35.1333	+	20.2842i	1.35429	+	0.781899i	0.988847	−	0.148936i	$-0.0475847\pi$
$673$	35.1333	+	20.2842i	1.35429	+	0.781899i	0.365441	+	0.930834i	$0.380918\pi$
$674$	4.86748	−	18.1657i	0.187489	−	0.699717i
$675$		0			0
$676$	−2.19675	+	12.8131i	−0.0844904	+	0.492810i
$677$	11.0747	−	6.39397i	0.425635	−	0.245740i	−0.271851	−	0.962339i	$-0.587636\pi$
$677$	11.0747	−	6.39397i	0.425635	−	0.245740i	0.697485	+	0.716599i	$0.254302\pi$
$678$		0			0
$679$	32.0591			1.23032
$680$	−13.1522	−	22.7803i	−0.504364	−	0.873585i
$681$		0			0
$682$	−0.845618	−	0.845618i	−0.0323804	−	0.0323804i
$683$	−31.3371	+	8.39675i	−1.19908	+	0.321293i	−0.802469	−	0.596693i	$-0.796481\pi$
$683$	−31.3371	+	8.39675i	−1.19908	+	0.321293i	−0.396612	+	0.917986i	$0.629814\pi$
$684$		0			0
$685$	−21.3315	+	36.9473i	−0.815035	+	1.41168i
$686$	5.60220	−	9.70330i	0.213893	−	0.370474i
$687$		0			0
$688$	0.0503260	+	0.0290558i	0.00191866	+	0.00110774i
$689$	2.48600	+	5.29844i	0.0947091	+	0.201855i
$690$		0			0
$691$	9.31482	−	2.49590i	0.354353	−	0.0949485i	−0.0772515	−	0.997012i	$-0.524614\pi$
$691$	9.31482	−	2.49590i	0.354353	−	0.0949485i	0.431604	+	0.902063i	$0.357948\pi$
$692$	−0.0437187	+	0.0252410i	−0.00166194	+	0.000959519i
$693$		0			0
$694$	−17.5077	−	17.5077i	−0.664582	−	0.664582i
$695$	9.74804	−	9.74804i	0.369764	−	0.369764i
$696$		0			0
$697$	3.19860	+	11.9373i	0.121156	+	0.452159i
$698$	2.95766	−	1.70760i	0.111949	−	0.0646337i
$699$		0			0
$700$	−7.61574	−	28.4223i	−0.287848	−	1.07426i
$701$	−45.7174			−1.72672			−0.863360	−	0.504588i	$-0.831645\pi$
$701$	−45.7174			−1.72672			−0.863360	+	0.504588i	$0.831645\pi$
$702$		0			0
$703$	9.58306			0.361432
$704$	0.566263	+	2.11332i	0.0213418	+	0.0796488i
$705$		0			0
$706$	3.84849	−	2.22193i	0.144840	−	0.0836233i
$707$	3.69811	+	13.8016i	0.139082	+	0.519061i
$708$		0			0
$709$	11.3342	−	11.3342i	0.425664	−	0.425664i	−0.461484	−	0.887148i	$-0.652683\pi$
$709$	11.3342	−	11.3342i	0.425664	−	0.425664i	0.887148	+	0.461484i	$0.152683\pi$
$710$	−23.7439	−	23.7439i	−0.891092	−	0.891092i
$711$		0			0
$712$	11.7315	−	6.77319i	0.439657	−	0.253836i
$713$	−0.439145	+	0.117669i	−0.0164461	+	0.00440672i
$714$		0			0
$715$	−24.2691	−	16.9079i	−0.907612	−	0.632318i
$716$	6.15933	+	3.55609i	0.230185	+	0.132897i
$717$		0			0
$718$	−1.24468	+	2.15585i	−0.0464511	+	0.0804557i
$719$	−10.0799	+	17.4589i	−0.375917	+	0.651107i	−0.990464	−	0.137773i	$-0.956006\pi$
$719$	−10.0799	+	17.4589i	−0.375917	+	0.651107i	0.614547	+	0.788880i	$0.289339\pi$
$720$		0			0
$721$	29.3406	−	7.86179i	1.09270	−	0.292788i
$722$	−3.33165	−	3.33165i	−0.123991	−	0.123991i
$723$		0			0
$724$	10.3165	+	17.8687i	0.383410	+	0.664085i
$725$	−83.9521			−3.11790
$726$		0			0
$727$	19.8457	−	11.4579i	0.736036	−	0.424950i	−0.0845905	−	0.996416i	$-0.526958\pi$
$727$	19.8457	−	11.4579i	0.736036	−	0.424950i	0.820626	+	0.571465i	$0.193625\pi$
$728$	−10.6024	+	4.97458i	−0.392950	+	0.184370i
$729$		0			0
$730$	4.64350	−	17.3298i	0.171864	−	0.641404i
$731$	−0.353057	−	0.203838i	−0.0130583	−	0.00753921i
$732$		0			0
$733$	−26.3034	+	7.04796i	−0.971536	+	0.260322i	−0.709476	−	0.704729i	$-0.751069\pi$
$733$	−26.3034	+	7.04796i	−0.971536	+	0.260322i	−0.262060	+	0.965052i	$0.584402\pi$
$734$	7.87325	+	2.10963i	0.290607	+	0.0778679i
$735$		0			0
$736$	0.803416	+	0.215275i	0.0296143	+	0.00793513i
$737$	24.6271	+	14.2185i	0.907152	+	0.523744i
$738$		0			0
$739$	23.3006	+	6.24337i	0.857126	+	0.229666i	0.660513	−	0.750815i	$-0.270339\pi$
$739$	23.3006	+	6.24337i	0.857126	+	0.229666i	0.196613	+	0.980481i	$0.437006\pi$
$740$	−3.68952	−	6.39043i	−0.135629	−	0.234917i
$741$		0			0
$742$	−2.63627	+	4.56615i	−0.0967804	+	0.167628i
$743$	−32.2692	+	32.2692i	−1.18384	+	1.18384i	−0.205101	+	0.978741i	$0.565752\pi$
$743$	−32.2692	+	32.2692i	−1.18384	+	1.18384i	−0.978741	+	0.205101i	$0.934248\pi$
$744$		0			0
$745$		−	34.0254i		−	1.24659i
$746$	−16.7417	+	16.7417i	−0.612956	+	0.612956i
$747$		0			0
$748$	−3.97256	−	14.8258i	−0.145251	−	0.542084i
$749$	4.28875	−	16.0058i	0.156708	−	0.584841i
$750$		0			0
$751$		−	31.2358i		−	1.13981i	−0.821711	−	0.569905i	$-0.806980\pi$
$751$		−	31.2358i		−	1.13981i	0.821711	−	0.569905i	$-0.193020\pi$
$752$	4.27203	+	4.27203i	0.155785	+	0.155785i
$753$		0			0
$754$	5.88016	+	32.8922i	0.214143	+	1.19786i
$755$		−	70.7433i		−	2.57461i
$756$		0			0
$757$	11.2648	+	19.5112i	0.409426	+	0.709147i	0.994826	−	0.101598i	$-0.0323956\pi$
$757$	11.2648	+	19.5112i	0.409426	+	0.709147i	−0.585399	+	0.810745i	$0.699062\pi$
$758$	−11.3128			−0.410898
$759$		0			0
$760$	−4.72557	+	17.6361i	−0.171414	+	0.639727i
$761$	8.52630	−	31.8206i	0.309078	−	1.15350i	−0.620300	−	0.784365i	$-0.712989\pi$
$761$	8.52630	−	31.8206i	0.309078	−	1.15350i	0.929378	−	0.369130i	$-0.120344\pi$
$762$		0			0
$763$	−4.24021			−0.153506
$764$	11.2461	+	19.4788i	0.406869	+	0.704718i
$765$		0			0
$766$		−	30.0424i		−	1.08548i
$767$	1.85110	+	10.3546i	0.0668395	+	0.373885i
$768$		0			0
$769$	36.9455	+	36.9455i	1.33229	+	1.33229i	0.903320	+	0.428968i	$0.141123\pi$
$769$	36.9455	+	36.9455i	1.33229	+	1.33229i	0.428968	+	0.903320i	$0.358877\pi$
$770$		−	26.6462i		−	0.960264i
$771$		0			0
$772$	−1.74990	+	6.53071i	−0.0629803	+	0.235046i
$773$	−10.2286	−	38.1735i	−0.367896	−	1.37301i	−0.863452	−	0.504431i	$-0.831702\pi$
$773$	−10.2286	−	38.1735i	−0.367896	−	1.37301i	0.495556	−	0.868576i	$-0.334964\pi$
$774$		0			0
$775$	−3.50131	+	3.50131i	−0.125771	+	0.125771i
$776$			9.86994i			0.354310i
$777$		0			0
$778$	6.44301	−	6.44301i	0.230993	−	0.230993i
$779$	4.28907	−	7.42888i	0.153672	−	0.266167i
$780$		0			0
$781$	−9.79675	−	16.9685i	−0.350555	−	0.607179i
$782$	−5.63628	−	1.51024i	−0.201553	−	0.0540060i
$783$		0			0
$784$	−3.07486	−	1.77527i	−0.109816	−	0.0634025i
$785$	79.8643	+	21.3996i	2.85048	+	0.763784i
$786$		0			0
$787$	−0.829056	−	0.222145i	−0.0295527	−	0.00791861i	0.244012	−	0.969772i	$-0.421536\pi$
$787$	−0.829056	−	0.222145i	−0.0295527	−	0.00791861i	−0.273565	+	0.961853i	$0.588203\pi$
$788$	5.95380	−	1.59532i	0.212095	−	0.0568308i
$789$		0			0
$790$	−38.0571	−	21.9723i	−1.35401	−	0.781738i
$791$	−9.72618	+	36.2986i	−0.345823	+	1.29063i
$792$		0			0
$793$	−11.6855	+	5.48276i	−0.414963	+	0.194699i
$794$	−9.33526	+	5.38971i	−0.331296	+	0.191274i
$795$		0			0
$796$	−3.80788			−0.134967
$797$	11.0723	+	19.1778i	0.392201	+	0.679311i	0.992740	−	0.120284i	$-0.0383806\pi$
$797$	11.0723	+	19.1778i	0.392201	+	0.679311i	−0.600539	+	0.799596i	$0.705047\pi$
$798$		0			0
$799$	−29.9700	−	29.9700i	−1.06026	−	1.06026i
$800$	8.75029	−	2.34463i	0.309369	−	0.0828953i
$801$		0			0
$802$	−5.93801	+	10.2849i	−0.209678	+	0.363174i
$803$	5.23437	−	9.06620i	0.184717	−	0.319939i
$804$		0			0
$805$	−8.77286	−	5.06501i	−0.309203	−	0.178518i
$806$	1.61705	+	1.12657i	0.0569580	+	0.0396817i
$807$		0			0
$808$	−4.24904	+	1.13853i	−0.149481	+	0.0400532i
$809$	43.7042	−	25.2326i	1.53656	−	0.887132i	0.537521	−	0.843251i	$-0.319361\pi$
$809$	43.7042	−	25.2326i	1.53656	−	0.887132i	0.999037	−	0.0438813i	$-0.0139723\pi$
$810$		0			0
$811$	28.9155	+	28.9155i	1.01536	+	1.01536i	0.999880	+	0.0154811i	$0.00492798\pi$
$811$	28.9155	+	28.9155i	1.01536	+	1.01536i	0.0154811	+	0.999880i	$0.495072\pi$
$812$	−21.2851	+	21.2851i	−0.746960	+	0.746960i
$813$		0			0
$814$	−1.11440	−	4.15900i	−0.0390597	−	0.145773i
$815$	20.6292	−	11.9103i	0.722609	−	0.417199i
$816$		0			0
$817$	0.0732385	+	0.273330i	0.00256229	+	0.00956260i
$818$	21.4728			0.750777
$819$		0			0
$820$	−6.60524			−0.230665
$821$	−0.909000	−	3.39244i	−0.0317243	−	0.118397i	0.948248	−	0.317531i	$-0.102854\pi$
$821$	−0.909000	−	3.39244i	−0.0317243	−	0.118397i	−0.979972	+	0.199134i	$0.936187\pi$
$822$		0			0
$823$	−43.9396	+	25.3685i	−1.53164	+	0.884291i	−0.532350	+	0.846524i	$0.678691\pi$
$823$	−43.9396	+	25.3685i	−1.53164	+	0.884291i	−0.999287	+	0.0377668i	$0.987976\pi$
$824$	2.42038	+	9.03299i	0.0843180	+	0.314679i
$825$		0			0
$826$	−6.70065	+	6.70065i	−0.233146	+	0.233146i
$827$	3.62799	+	3.62799i	0.126158	+	0.126158i	0.767366	−	0.641209i	$-0.221567\pi$
$827$	3.62799	+	3.62799i	0.126158	+	0.126158i	−0.641209	+	0.767366i	$0.721567\pi$
$828$		0			0
$829$	−18.3968	+	10.6214i	−0.638949	+	0.368897i	−0.784209	−	0.620496i	$-0.786931\pi$
$829$	−18.3968	+	10.6214i	−0.638949	+	0.368897i	0.145261	+	0.989393i	$0.453598\pi$
$830$	−52.5870	+	14.0907i	−1.82532	+	0.489094i
$831$		0			0
$832$	−1.53151	−	3.26412i	−0.0530955	−	0.113163i
$833$	21.5713	+	12.4542i	0.747402	+	0.431513i
$834$		0			0
$835$	−16.5144	+	28.6038i	−0.571504	+	0.989874i
$836$	−5.32688	+	9.22643i	−0.184234	+	0.319103i
$837$		0			0
$838$	10.4303	−	2.79480i	0.360310	−	0.0965447i
$839$	−14.5388	−	14.5388i	−0.501934	−	0.501934i	0.410105	−	0.912039i	$-0.365492\pi$
$839$	−14.5388	−	14.5388i	−0.501934	−	0.501934i	−0.912039	+	0.410105i	$0.865492\pi$
$840$		0			0
$841$	28.4414	+	49.2619i	0.980737	+	1.69869i
$842$	6.56658			0.226299
$843$		0			0
$844$	16.6171	−	9.59387i	0.571983	−	0.330234i
$845$	44.2740	+	20.3905i	1.52307	+	0.701456i
$846$		0			0
$847$	−5.22336	+	19.4939i	−0.179477	+	0.669817i
$848$	−1.40576	−	0.811618i	−0.0482741	−	0.0278711i
$849$		0			0
$850$	−61.3867	+	16.4485i	−2.10555	+	0.564180i
$851$	−1.58111	−	0.423658i	−0.0541999	−	0.0145228i
$852$		0			0
$853$	−17.5934	−	4.71414i	−0.602387	−	0.161409i	−0.0552788	−	0.998471i	$-0.517605\pi$
$853$	−17.5934	−	4.71414i	−0.602387	−	0.161409i	−0.547108	+	0.837062i	$0.684271\pi$
$854$	−10.0704	−	5.81417i	−0.344603	−	0.198957i
$855$		0			0
$856$	4.92767	+	1.32036i	0.168424	+	0.0451291i
$857$	8.45527	+	14.6450i	0.288826	+	0.500262i	0.973530	−	0.228560i	$-0.0734016\pi$
$857$	8.45527	+	14.6450i	0.288826	+	0.500262i	−0.684703	+	0.728822i	$0.740068\pi$
$858$		0			0
$859$	14.3028	−	24.7732i	0.488007	−	0.845252i	−0.511898	−	0.859046i	$-0.671058\pi$
$859$	14.3028	−	24.7732i	0.488007	−	0.845252i	0.999905	+	0.0137939i	$0.00439089\pi$
$860$	0.154072	−	0.154072i	0.00525381	−	0.00525381i
$861$		0			0
$862$		−	5.55250i		−	0.189119i
$863$	7.73986	−	7.73986i	0.263468	−	0.263468i	−0.562993	−	0.826461i	$-0.690350\pi$
$863$	7.73986	−	7.73986i	0.263468	−	0.263468i	0.826461	+	0.562993i	$0.190350\pi$
$864$		0			0
$865$	0.0489902	+	0.182834i	0.00166572	+	0.00621654i
$866$	9.31439	−	34.7618i	0.316516	−	1.18125i
$867$		0			0
$868$			1.77544i			0.0602622i
$869$	−18.1315	−	18.1315i	−0.615071	−	0.615071i
$870$		0			0
$871$	−44.0749	−	15.9238i	−1.49342	−	0.539559i
$872$		−	1.30542i		−	0.0442071i
$873$		0			0
$874$	2.02511	+	3.50759i	0.0685002	+	0.118646i
$875$	−49.4344			−1.67119
$876$		0			0
$877$	12.1816	−	45.4622i	0.411342	−	1.53515i	−0.380710	−	0.924695i	$-0.624320\pi$
$877$	12.1816	−	45.4622i	0.411342	−	1.53515i	0.792052	−	0.610454i	$-0.209013\pi$
$878$	5.25764	−	19.6218i	0.177437	−	0.662204i
$879$		0			0
$880$	8.20349			0.276539
$881$	9.67727	+	16.7615i	0.326036	+	0.564710i	0.981721	−	0.190324i	$-0.0609537\pi$
$881$	9.67727	+	16.7615i	0.326036	+	0.564710i	−0.655686	+	0.755034i	$0.727620\pi$
$882$		0			0
$883$			20.5335i			0.691007i	0.938417	+	0.345504i	$0.112292\pi$
$883$			20.5335i			0.691007i	−0.938417	+	0.345504i	$0.887708\pi$
$884$	10.7441	+	22.8991i	0.361364	+	0.770180i
$885$		0			0
$886$	−13.2655	−	13.2655i	−0.445662	−	0.445662i
$887$			21.8501i			0.733655i	0.930289	+	0.366828i	$0.119556\pi$
$887$			21.8501i			0.733655i	−0.930289	+	0.366828i	$0.880444\pi$
$888$		0			0
$889$	2.77700	−	10.3639i	0.0931374	−	0.347594i
$890$	−13.1461	−	49.0618i	−0.440658	−	1.64456i
$891$		0			0
$892$	0.198374	−	0.198374i	0.00664204	−	0.00664204i
$893$			29.4191i			0.984474i
$894$		0			0
$895$	18.8566	−	18.8566i	0.630308	−	0.630308i
$896$	1.62408	−	2.81299i	0.0542567	−	0.0939753i
$897$		0			0
$898$	−7.94366	−	13.7588i	−0.265083	−	0.459138i
$899$	4.89288	+	1.31104i	0.163187	+	0.0437257i
$900$		0			0
$901$	9.86199	+	5.69382i	0.328551	+	0.189689i
$902$	−3.72287	−	0.997539i	−0.123958	−	0.0332144i
$903$		0			0
$904$	−11.1751	−	2.99437i	−0.371679	−	0.0995912i
$905$	74.7279	−	20.0233i	2.48404	−	0.665597i
$906$		0			0
$907$	22.9458	+	13.2478i	0.761903	+	0.439885i	0.829978	−	0.557796i	$-0.188353\pi$
$907$	22.9458	+	13.2478i	0.761903	+	0.439885i	−0.0680759	+	0.997680i	$0.521686\pi$
$908$	3.29749	−	12.3064i	0.109431	−	0.408402i
$909$		0			0
$910$	7.72770	+	43.2269i	0.256171	+	1.43296i
$911$	−15.5279	+	8.96501i	−0.514461	+	0.297024i	−0.734665	−	0.678430i	$-0.762661\pi$
$911$	−15.5279	+	8.96501i	−0.514461	+	0.297024i	0.220205	+	0.975454i	$0.429327\pi$
$912$		0			0
$913$	−31.7673			−1.05134
$914$	−0.438675	−	0.759807i	−0.0145101	−	0.0251322i
$915$		0			0
$916$	3.04541	+	3.04541i	0.100623	+	0.100623i
$917$	−34.5896	+	9.26827i	−1.14225	+	0.306065i
$918$		0			0
$919$	20.4782	−	35.4692i	0.675512	−	1.17002i	−0.300806	−	0.953685i	$-0.597256\pi$
$919$	20.4782	−	35.4692i	0.675512	−	1.17002i	0.976319	−	0.216337i	$-0.0694108\pi$
$920$	1.55935	−	2.70087i	0.0514102	−	0.0890451i
$921$		0			0
$922$	20.1727	+	11.6467i	0.664352	+	0.383564i
$923$	20.8138	+	24.6860i	0.685096	+	0.812549i
$924$		0			0
$925$	−17.2205	+	4.61421i	−0.566206	+	0.151714i
$926$	15.6154	−	9.01556i	0.513154	−	0.296270i
$927$		0			0
$928$	−6.55297	−	6.55297i	−0.215112	−	0.215112i
$929$	−15.9697	+	15.9697i	−0.523949	+	0.523949i	−0.918762	−	0.394813i	$-0.870809\pi$
$929$	−15.9697	+	15.9697i	−0.523949	+	0.523949i	0.394813	+	0.918762i	$0.370809\pi$
$930$		0			0
$931$	−4.47478	−	16.7001i	−0.146655	−	0.547324i
$932$	18.2509	−	10.5372i	0.597829	−	0.345157i
$933$		0			0
$934$	−6.44430	−	24.0504i	−0.210864	−	0.786955i
$935$	−57.5507			−1.88211
$936$		0			0
$937$	−6.24073			−0.203876			−0.101938	−	0.994791i	$-0.532504\pi$
$937$	−6.24073			−0.203876			−0.101938	+	0.994791i	$0.532504\pi$
$938$	−10.9268	−	40.7795i	−0.356774	−	1.33150i
$939$		0			0
$940$	19.6181	−	11.3265i	0.639871	−	0.369430i
$941$	−5.40991	−	20.1901i	−0.176358	−	0.658177i	−0.996316	−	0.0857538i	$-0.972670\pi$
$941$	−5.40991	−	20.1901i	−0.176358	−	0.658177i	0.819958	−	0.572423i	$-0.193997\pi$
$942$		0			0
$943$	−1.03608	+	1.03608i	−0.0337394	+	0.0337394i
$944$	−2.06291	−	2.06291i	−0.0671419	−	0.0671419i
$945$		0			0
$946$	0.110107	−	0.0635703i	0.00357988	−	0.00206685i
$947$	−9.48726	+	2.54210i	−0.308295	+	0.0826073i	−0.409649	−	0.912243i	$-0.634349\pi$
$947$	−9.48726	+	2.54210i	−0.308295	+	0.0826073i	0.101355	+	0.994850i	$0.467682\pi$
$948$		0			0
$949$	−5.86218	+	16.2257i	−0.190294	+	0.526708i
$950$	38.2024	+	22.0561i	1.23945	+	0.715596i
$951$		0			0
$952$	−11.3936	+	19.7342i	−0.369267	+	0.639590i
$953$	−16.8681	+	29.2164i	−0.546410	+	0.946410i	0.452106	+	0.891964i	$0.350673\pi$
$953$	−16.8681	+	29.2164i	−0.546410	+	0.946410i	−0.998517	+	0.0544464i	$0.982661\pi$
$954$		0			0
$955$	81.4614	−	21.8275i	2.63603	−	0.706322i
$956$	9.20406	+	9.20406i	0.297681	+	0.297681i
$957$		0			0
$958$	−3.80075	−	6.58309i	−0.122797	−	0.212690i
$959$	36.9583			1.19345
$960$		0			0
$961$	−26.5880	+	15.3506i	−0.857679	+	0.495181i
$962$	3.01399	+	6.42376i	0.0971750	+	0.207110i
$963$		0			0
$964$	−0.322572	+	1.20385i	−0.0103893	+	0.0387735i
$965$	21.9545	+	12.6755i	0.706741	+	0.408037i
$966$		0			0
$967$	−55.4982	+	14.8707i	−1.78470	+	0.478209i	−0.991428	−	0.130658i	$-0.958291\pi$
$967$	−55.4982	+	14.8707i	−1.78470	+	0.478209i	−0.793273	+	0.608867i	$0.791624\pi$
$968$	−6.00151	−	1.60810i	−0.192896	−	0.0516863i
$969$		0			0
$970$	35.7466	+	9.57827i	1.14775	+	0.307540i
$971$	1.03496	+	0.597536i	0.0332135	+	0.0191758i	0.516515	−	0.856278i	$-0.327229\pi$
$971$	1.03496	+	0.597536i	0.0332135	+	0.0191758i	−0.483301	+	0.875454i	$0.660562\pi$
$972$		0			0
$973$	−11.5355	−	3.09093i	−0.369812	−	0.0990907i
$974$	16.5847	+	28.7255i	0.531407	+	0.920424i
$975$		0			0
$976$	1.78999	−	3.10035i	0.0572961	−	0.0992398i
$977$	8.58538	−	8.58538i	0.274671	−	0.274671i	−0.556307	−	0.830977i	$-0.687782\pi$
$977$	8.58538	−	8.58538i	0.274671	−	0.274671i	0.830977	+	0.556307i	$0.187782\pi$
$978$		0			0
$979$		−	29.6377i		−	0.947227i
$980$	−9.41360	+	9.41360i	−0.300706	+	0.300706i
$981$		0			0
$982$	−6.68991	−	24.9671i	−0.213484	−	0.796732i
$983$	−0.201299	+	0.751256i	−0.00642043	+	0.0239614i	−0.969062	−	0.246818i	$-0.920615\pi$
$983$	−0.201299	+	0.751256i	−0.00642043	+	0.0239614i	0.962641	+	0.270780i	$0.0872815\pi$
$984$		0			0
$985$		−	23.1115i		−	0.736392i
$986$	45.9717	+	45.9717i	1.46404	+	1.46404i
$987$		0			0
$988$	5.96578	−	16.5125i	0.189797	−	0.525331i
$989$		−	0.0483347i		−	0.00153695i
$990$		0			0
$991$	12.0018	+	20.7877i	0.381250	+	0.660344i	0.991241	−	0.132064i	$-0.0421604\pi$
$991$	12.0018	+	20.7877i	0.381250	+	0.660344i	−0.609991	+	0.792408i	$0.708827\pi$
$992$	−0.546597			−0.0173545
$993$		0			0
$994$	−7.52876	+	28.0977i	−0.238798	+	0.891206i
$995$	−3.69535	+	13.7912i	−0.117150	+	0.437211i
$996$		0			0
$997$	7.43166			0.235363			0.117681	−	0.993051i	$-0.462454\pi$
$997$	7.43166			0.235363			0.117681	+	0.993051i	$0.462454\pi$
$998$	−8.15931	−	14.1323i	−0.258278	−	0.447351i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.557.6		56
3.2	odd	2		234.2.z.a.167.9	yes	56
9.2	odd	6		702.2.bb.a.89.13		56
9.7	even	3		234.2.y.a.11.6	✓	56
13.6	odd	12		702.2.bb.a.71.13		56
39.32	even	12		234.2.y.a.149.6	yes	56
117.97	odd	12		234.2.z.a.227.9	yes	56
117.110	even	12	inner	702.2.bc.a.305.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.6	✓	56	9.7	even	3
234.2.y.a.149.6	yes	56	39.32	even	12
234.2.z.a.167.9	yes	56	3.2	odd	2
234.2.z.a.227.9	yes	56	117.97	odd	12
702.2.bb.a.71.13		56	13.6	odd	12
702.2.bb.a.89.13		56	9.2	odd	6
702.2.bc.a.305.6		56	117.110	even	12	inner
702.2.bc.a.557.6		56	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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.970449 + 3.62177i) q^{5} +(2.29680 - 2.29680i) q^{7} +(0.707107 + 0.707107i) q^{8} +(3.24719 - 1.87476i) q^{10} +(2.11332 - 0.566263i) q^{11} +(-3.26412 + 1.53151i) q^{13} +(-2.81299 - 1.62408i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.50770 + 6.07551i) q^{17} +(4.70354 - 1.26031i) q^{19} +(-2.65132 - 2.65132i) q^{20} +(-1.09394 - 1.89475i) q^{22} -0.831757 q^{23} +(-7.84529 + 4.52948i) q^{25} +(2.32414 + 2.75652i) q^{26} +(-0.840685 + 3.13748i) q^{28} +(8.02571 + 4.63365i) q^{29} +(0.527973 - 0.141470i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(6.77635 + 1.81572i) q^{34} +(10.5474 + 6.08953i) q^{35} +(1.90093 + 0.509353i) q^{37} +(-2.43473 - 4.21708i) q^{38} +(-1.87476 + 3.24719i) q^{40} +(1.24565 - 1.24565i) q^{41} +0.0581115i q^{43} +(-1.54706 + 1.54706i) q^{44} +(0.215275 + 0.803416i) q^{46} +(-1.56367 + 5.83570i) q^{47} -3.55054i q^{49} +(6.40565 + 6.40565i) q^{50} +(2.06106 - 2.95839i) q^{52} -1.62324i q^{53} +(4.10174 + 7.10443i) q^{55} +3.24816 q^{56} +(2.39855 - 8.95152i) q^{58} +(0.755077 - 2.81798i) q^{59} +3.57998 q^{61} +(-0.273299 - 0.473367i) q^{62} +1.00000i q^{64} +(-8.71443 - 10.3356i) q^{65} +(9.19065 + 9.19065i) q^{67} -7.01540i q^{68} +(3.15217 - 11.7641i) q^{70} +(-2.31786 - 8.65035i) q^{71} +(3.38343 - 3.38343i) q^{73} -1.96799i q^{74} +(-3.44323 + 3.44323i) q^{76} +(3.55328 - 6.15446i) q^{77} +(-5.86001 - 10.1498i) q^{79} +(3.62177 + 0.970449i) q^{80} +(-1.52561 - 0.880809i) q^{82} +(-14.0250 - 3.75798i) q^{83} +(-25.4081 - 6.80809i) q^{85} +(0.0561314 - 0.0150404i) q^{86} +(1.89475 + 1.09394i) q^{88} +(3.50606 - 13.0848i) q^{89} +(-3.97946 + 11.0146i) q^{91} +(0.720323 - 0.415879i) q^{92} +6.04156 q^{94} +(9.12909 + 15.8121i) q^{95} +(6.97910 + 6.97910i) q^{97} +(-3.42956 + 0.918947i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

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