LMFDB - Embedded newform 980.2.s.g.619.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(19,980)] 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("980.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,-16,0,0,0,0,64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.30
Character	$\chi$	$=$	980.619
Dual form			980.2.s.g.19.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.346793 + 1.37103i) q^{2} +(0.366665 + 0.211694i) q^{3} +(-1.75947 + 0.950931i) q^{4} +(-2.08328 - 0.812373i) q^{5} +(-0.163083 + 0.576124i) q^{6} +(-1.91393 - 2.08252i) q^{8} +(-1.41037 - 2.44283i) q^{9} +(0.391324 - 3.13797i) q^{10} +(4.23964 + 2.44776i) q^{11} +(-0.846442 - 0.0237963i) q^{12} +2.54664 q^{13} +(-0.591890 - 0.738886i) q^{15} +(2.19146 - 3.34627i) q^{16} +(2.55715 - 4.42911i) q^{17} +(2.86010 - 2.78083i) q^{18} +(-3.13300 - 5.42652i) q^{19} +(4.43797 - 0.551709i) q^{20} +(-1.88568 + 6.66155i) q^{22} +(2.31555 + 4.01064i) q^{23} +(-0.260915 - 1.16875i) q^{24} +(3.68010 + 3.38480i) q^{25} +(0.883158 + 3.49153i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(0.807775 - 1.06774i) q^{30} +(0.738782 - 1.27961i) q^{31} +(5.34783 + 1.84411i) q^{32} +(1.03635 + 1.79501i) q^{33} +(6.95926 + 1.96995i) q^{34} +(4.80447 + 2.95693i) q^{36} +(-2.04313 + 1.17960i) q^{37} +(6.35344 - 6.17733i) q^{38} +(0.933764 + 0.539109i) q^{39} +(2.29547 + 5.89329i) q^{40} +7.05393i q^{41} +10.7790 q^{43} +(-9.78716 - 0.275150i) q^{44} +(0.953704 + 6.23485i) q^{45} +(-4.69571 + 4.56556i) q^{46} +(10.5781 - 6.10725i) q^{47} +(1.51192 - 0.763038i) q^{48} +(-3.36444 + 6.21937i) q^{50} +(1.87523 - 1.08267i) q^{51} +(-4.48074 + 2.42168i) q^{52} +(1.93661 + 1.11810i) q^{53} +(3.37882 - 0.854648i) q^{54} +(-6.84386 - 8.54352i) q^{55} -2.65295i q^{57} +(-0.655292 - 2.59067i) q^{58} +(2.84500 - 4.92768i) q^{59} +(1.74404 + 0.737201i) q^{60} +(-3.35156 + 1.93502i) q^{61} +(2.01059 + 0.569136i) q^{62} +(-0.673743 + 7.97158i) q^{64} +(-5.30536 - 2.06882i) q^{65} +(-2.10162 + 2.04337i) q^{66} +(0.444655 - 0.770165i) q^{67} +(-0.287446 + 10.2245i) q^{68} +1.96075i q^{69} -14.3310i q^{71} +(-2.38789 + 7.61254i) q^{72} +(3.93594 - 6.81724i) q^{73} +(-2.32581 - 2.39212i) q^{74} +(0.632822 + 2.02014i) q^{75} +(10.6727 + 6.56853i) q^{76} +(-0.415314 + 1.46718i) q^{78} +(-4.01812 + 2.31987i) q^{79} +(-7.28384 + 5.19092i) q^{80} +(-3.70941 + 6.42488i) q^{81} +(-9.67118 + 2.44625i) q^{82} -4.32876i q^{83} +(-8.92534 + 7.14971i) q^{85} +(3.73808 + 14.7784i) q^{86} +(-0.692841 - 0.400012i) q^{87} +(-3.01688 - 13.5139i) q^{88} +(1.89013 - 1.09127i) q^{89} +(-8.21746 + 3.46977i) q^{90} +(-7.88798 - 4.85468i) q^{92} +(0.541770 - 0.312791i) q^{93} +(12.0416 + 12.3849i) q^{94} +(2.11856 + 13.8501i) q^{95} +(1.57047 + 1.80827i) q^{96} +3.42330 q^{97} -13.8090i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) $ 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.346793	+	1.37103i	0.245220	+	0.969468i
$2$	0.346793	+	1.37103i	0.245220	+	0.969468i
$3$	0.366665	+	0.211694i	0.211694	+	0.122222i	0.602098	−	0.798422i	$-0.294331\pi$
$3$	0.366665	+	0.211694i	0.211694	+	0.122222i	−0.390404	+	0.920643i	$0.627665\pi$
$4$	−1.75947	+	0.950931i	−0.879734	+	0.475465i
$5$	−2.08328	−	0.812373i	−0.931671	−	0.363304i
$5$	−2.08328	−	0.812373i	−0.931671	−	0.363304i
$6$	−0.163083	+	0.576124i	−0.0665783	+	0.235202i
$7$		0			0
$7$		0			0
$8$	−1.91393	−	2.08252i	−0.676676	−	0.736280i
$9$	−1.41037	−	2.44283i	−0.470124	−	0.814278i
$10$	0.391324	−	3.13797i	0.123748	−	0.992314i
$11$	4.23964	+	2.44776i	1.27830	+	0.738026i	0.976535	−	0.215357i	$-0.0690914\pi$
$11$	4.23964	+	2.44776i	1.27830	+	0.738026i	0.301763	+	0.953383i	$0.402425\pi$
$12$	−0.846442	−	0.0237963i	−0.244347	−	0.00686940i
$13$	2.54664			0.706311			0.353156	−	0.935565i	$-0.385109\pi$
$13$	2.54664			0.706311			0.353156	+	0.935565i	$0.385109\pi$
$14$		0			0
$15$	−0.591890	−	0.738886i	−0.152825	−	0.190780i
$16$	2.19146	−	3.34627i	0.547866	−	0.836566i
$17$	2.55715	−	4.42911i	0.620199	−	1.07422i	−0.369249	−	0.929330i	$-0.620385\pi$
$17$	2.55715	−	4.42911i	0.620199	−	1.07422i	0.989448	−	0.144886i	$-0.0462816\pi$
$18$	2.86010	−	2.78083i	0.674133	−	0.655447i
$19$	−3.13300	−	5.42652i	−0.718760	−	1.24493i	−0.961491	−	0.274836i	$-0.911377\pi$
$19$	−3.13300	−	5.42652i	−0.718760	−	1.24493i	0.242731	−	0.970094i	$-0.421957\pi$
$20$	4.43797	−	0.551709i	0.992361	−	0.123366i
$21$		0			0
$22$	−1.88568	+	6.66155i	−0.402028	+	1.42025i
$23$	2.31555	+	4.01064i	0.482825	+	0.836277i	0.999806	−	0.0197200i	$-0.00627747\pi$
$23$	2.31555	+	4.01064i	0.482825	+	0.836277i	−0.516981	+	0.855997i	$0.672944\pi$
$24$	−0.260915	−	1.16875i	−0.0532590	−	0.238571i
$25$	3.68010	+	3.38480i	0.736020	+	0.676960i
$26$	0.883158	+	3.49153i	0.173202	+	0.684746i
$27$		−	2.46443i		−	0.474280i
$28$		0			0
$29$	−1.88958			−0.350886			−0.175443	−	0.984490i	$-0.556136\pi$
$29$	−1.88958			−0.350886			−0.175443	+	0.984490i	$0.556136\pi$
$30$	0.807775	−	1.06774i	0.147479	−	0.194942i
$31$	0.738782	−	1.27961i	0.132689	−	0.229824i	−0.792023	−	0.610491i	$-0.790972\pi$
$31$	0.738782	−	1.27961i	0.132689	−	0.229824i	0.924712	+	0.380667i	$0.124305\pi$
$32$	5.34783	+	1.84411i	0.945371	+	0.325995i
$33$	1.03635	+	1.79501i	0.180405	+	0.312471i
$34$	6.95926	+	1.96995i	1.19350	+	0.337844i
$35$		0			0
$36$	4.80447	+	2.95693i	0.800745	+	0.492821i
$37$	−2.04313	+	1.17960i	−0.335888	+	0.193925i	−0.658452	−	0.752623i	$-0.728789\pi$
$37$	−2.04313	+	1.17960i	−0.335888	+	0.193925i	0.322564	+	0.946548i	$0.395455\pi$
$38$	6.35344	−	6.17733i	1.03066	−	1.00210i
$39$	0.933764	+	0.539109i	0.149522	+	0.0863265i
$40$	2.29547	+	5.89329i	0.362946	+	0.931810i
$41$			7.05393i			1.10164i	0.834624	+	0.550819i	$0.185685\pi$
$41$			7.05393i			1.10164i	−0.834624	+	0.550819i	$0.814315\pi$
$42$		0			0
$43$	10.7790			1.64378			0.821890	−	0.569646i	$-0.192920\pi$
$43$	10.7790			1.64378			0.821890	+	0.569646i	$0.192920\pi$
$44$	−9.78716	−	0.275150i	−1.47547	−	0.0414804i
$45$	0.953704	+	6.23485i	0.142170	+	0.929437i
$46$	−4.69571	+	4.56556i	−0.692345	+	0.673155i
$47$	10.5781	−	6.10725i	1.54297	−	0.890834i	0.544320	−	0.838878i	$-0.316788\pi$
$47$	10.5781	−	6.10725i	1.54297	−	0.890834i	0.998649	−	0.0519561i	$-0.0165456\pi$
$48$	1.51192	−	0.763038i	0.218226	−	0.110135i
$49$		0			0
$50$	−3.36444	+	6.21937i	−0.475804	+	0.879552i
$51$	1.87523	−	1.08267i	0.262585	−	0.151603i
$52$	−4.48074	+	2.42168i	−0.621366	+	0.335826i
$53$	1.93661	+	1.11810i	0.266014	+	0.153583i	0.627075	−	0.778959i	$-0.284252\pi$
$53$	1.93661	+	1.11810i	0.266014	+	0.153583i	−0.361061	+	0.932542i	$0.617585\pi$
$54$	3.37882	−	0.854648i	0.459799	−	0.116303i
$55$	−6.84386	−	8.54352i	−0.922825	−	1.15201i
$56$		0			0
$57$		−	2.65295i		−	0.351392i
$58$	−0.655292	−	2.59067i	−0.0860441	−	0.340172i
$59$	2.84500	−	4.92768i	0.370387	−	0.641529i	−0.619238	−	0.785203i	$-0.712558\pi$
$59$	2.84500	−	4.92768i	0.370387	−	0.641529i	0.989625	+	0.143674i	$0.0458917\pi$
$60$	1.74404	+	0.737201i	0.225155	+	0.0951722i
$61$	−3.35156	+	1.93502i	−0.429123	+	0.247754i	−0.698973	−	0.715148i	$-0.746359\pi$
$61$	−3.35156	+	1.93502i	−0.429123	+	0.247754i	0.269850	+	0.962902i	$0.413026\pi$
$62$	2.01059	+	0.569136i	0.255345	+	0.0722803i
$63$		0			0
$64$	−0.673743	+	7.97158i	−0.0842179	+	0.996447i
$65$	−5.30536	−	2.06882i	−0.658049	−	0.256606i
$66$	−2.10162	+	2.04337i	−0.258692	+	0.251521i
$67$	0.444655	−	0.770165i	0.0543232	−	0.0940906i	−0.837585	−	0.546307i	$-0.816033\pi$
$67$	0.444655	−	0.770165i	0.0543232	−	0.0940906i	0.891908	+	0.452216i	$0.149367\pi$
$68$	−0.287446	+	10.2245i	−0.0348580	+	1.23991i
$69$			1.96075i			0.236046i
$70$		0			0
$71$		−	14.3310i		−	1.70078i	−0.526152	−	0.850391i	$-0.676366\pi$
$71$		−	14.3310i		−	1.70078i	0.526152	−	0.850391i	$-0.323634\pi$
$72$	−2.38789	+	7.61254i	−0.281416	+	0.897146i
$73$	3.93594	−	6.81724i	0.460667	−	0.797898i	−0.538328	−	0.842736i	$-0.680944\pi$
$73$	3.93594	−	6.81724i	0.460667	−	0.797898i	0.998994	+	0.0448377i	$0.0142771\pi$
$74$	−2.32581	−	2.39212i	−0.270370	−	0.278078i
$75$	0.632822	+	2.02014i	0.0730720	+	0.233266i
$76$	10.6727	+	6.56853i	1.22424	+	0.753462i
$77$		0			0
$78$	−0.415314	+	1.46718i	−0.0470250	+	0.166126i
$79$	−4.01812	+	2.31987i	−0.452074	+	0.261005i	−0.708706	−	0.705504i	$-0.750721\pi$
$79$	−4.01812	+	2.31987i	−0.452074	+	0.261005i	0.256632	+	0.966509i	$0.417387\pi$
$80$	−7.28384	+	5.19092i	−0.814358	+	0.580362i
$81$	−3.70941	+	6.42488i	−0.412156	+	0.713876i
$82$	−9.67118	+	2.44625i	−1.06800	+	0.270144i
$83$		−	4.32876i		−	0.475143i	−0.971370	−	0.237571i	$-0.923649\pi$
$83$		−	4.32876i		−	0.475143i	0.971370	−	0.237571i	$-0.0763514\pi$
$84$		0			0
$85$	−8.92534	+	7.14971i	−0.968089	+	0.775495i
$86$	3.73808	+	14.7784i	0.403087	+	1.59359i
$87$	−0.692841	−	0.400012i	−0.0742804	−	0.0428858i
$88$	−3.01688	−	13.5139i	−0.321600	−	1.44059i
$89$	1.89013	−	1.09127i	0.200354	−	0.115674i	−0.396467	−	0.918049i	$-0.629764\pi$
$89$	1.89013	−	1.09127i	0.200354	−	0.115674i	0.596820	+	0.802375i	$0.296430\pi$
$90$	−8.21746	+	3.46977i	−0.866196	+	0.365745i
$91$		0			0
$92$	−7.88798	−	4.85468i	−0.822378	−	0.506135i
$93$	0.541770	−	0.312791i	0.0561790	−	0.0324349i
$94$	12.0416	+	12.3849i	1.24200	+	1.27741i
$95$	2.11856	+	13.8501i	0.217360	+	1.42099i
$96$	1.57047	+	1.80827i	0.160286	+	0.184556i
$97$	3.42330			0.347584			0.173792	−	0.984782i	$-0.444398\pi$
$97$	3.42330			0.347584			0.173792	+	0.984782i	$0.444398\pi$
$98$		0			0
$99$		−	13.8090i		−	1.38785i
$100$	−9.69373	−	2.45593i	−0.969373	−	0.245593i
$101$	−6.32803	−	3.65349i	−0.629663	−	0.363536i	0.150959	−	0.988540i	$-0.451764\pi$
$101$	−6.32803	−	3.65349i	−0.629663	−	0.363536i	−0.780621	+	0.625004i	$0.785097\pi$
$102$	2.13469	+	2.19555i	0.211366	+	0.217391i
$103$	−5.84630	+	3.37536i	−0.576053	+	0.332584i	−0.759563	−	0.650434i	$-0.774587\pi$
$103$	−5.84630	+	3.37536i	−0.576053	+	0.332584i	0.183510	+	0.983018i	$0.441254\pi$
$104$	−4.87409	−	5.30342i	−0.477944	−	0.520043i
$105$		0			0
$106$	−0.861354	+	3.04291i	−0.0836621	+	0.295554i
$107$	−4.91497	−	8.51298i	−0.475148	−	0.822980i	0.524447	−	0.851443i	$-0.324272\pi$
$107$	−4.91497	−	8.51298i	−0.475148	−	0.822980i	−0.999595	+	0.0284627i	$0.990939\pi$
$108$	2.34350	+	4.33609i	0.225504	+	0.417241i
$109$	4.70610	−	8.15121i	0.450763	−	0.780744i	−0.547671	−	0.836694i	$-0.684485\pi$
$109$	4.70610	−	8.15121i	0.450763	−	0.780744i	0.998434	+	0.0559497i	$0.0178186\pi$
$110$	9.34006	−	12.3460i	0.890540	−	1.17714i
$111$	−0.998857			−0.0948073
$112$		0			0
$113$		−	15.9261i		−	1.49820i	−0.662455	−	0.749102i	$-0.730485\pi$
$113$		−	15.9261i		−	1.49820i	0.662455	−	0.749102i	$-0.269515\pi$
$114$	3.63729	−	0.920026i	0.340663	−	0.0861683i
$115$	−1.56579	−	10.2364i	−0.146011	−	0.954547i
$116$	3.32465	−	1.79686i	0.308686	−	0.166834i
$117$	−3.59171	−	6.22102i	−0.332054	−	0.575134i
$118$	7.74264	+	2.19170i	0.712768	+	0.201763i
$119$		0			0
$120$	−0.405905	+	2.64680i	−0.0370539	+	0.241618i
$121$	6.48302	+	11.2289i	0.589365	+	1.02081i
$122$	−3.81528	−	3.92405i	−0.345419	−	0.355267i
$123$	−1.49327	+	2.58643i	−0.134644	+	0.233210i
$124$	−0.0830457	+	2.95396i	−0.00745772	+	0.265273i
$125$	−4.91696	−	10.0411i	−0.439786	−	0.898103i
$126$		0			0
$127$	12.2192			1.08428			0.542138	−	0.840290i	$-0.317615\pi$
$127$	12.2192			1.08428			0.542138	+	0.840290i	$0.317615\pi$
$128$	−11.1630	+	1.84076i	−0.986675	+	0.162702i
$129$	3.95227	+	2.28185i	0.347978	+	0.200905i
$130$	0.996562	−	7.99129i	0.0874043	−	0.700882i
$131$	−4.92530	−	8.53087i	−0.430325	−	0.745345i	0.566576	−	0.824010i	$-0.308268\pi$
$131$	−4.92530	−	8.53087i	−0.430325	−	0.745345i	−0.996901	+	0.0786642i	$0.974935\pi$
$132$	−3.53036	−	2.17277i	−0.307278	−	0.189115i
$133$		0			0
$134$	1.21013	+	0.342549i	0.104539	+	0.0295917i
$135$	−2.00204	+	5.13410i	−0.172308	+	0.441873i
$136$	−14.1179	+	3.15171i	−1.21060	+	0.270256i
$137$	4.06585	+	2.34742i	0.347369	+	0.200554i	0.663526	−	0.748153i	$-0.269059\pi$
$137$	4.06585	+	2.34742i	0.347369	+	0.200554i	−0.316157	+	0.948707i	$0.602393\pi$
$138$	−2.68825	+	0.679974i	−0.228839	+	0.0578833i
$139$	−13.8745			−1.17682			−0.588409	−	0.808564i	$-0.700245\pi$
$139$	−13.8745			−1.17682			−0.588409	+	0.808564i	$0.700245\pi$
$140$		0			0
$141$	5.17147			0.435516
$142$	19.6483	−	4.96991i	1.64885	−	0.417065i
$143$	10.7968	+	6.23356i	0.902877	+	0.521276i
$144$	−11.2651	−	0.633903i	−0.938762	−	0.0528252i
$145$	3.93652	+	1.53504i	0.326910	+	0.127478i
$146$	10.7116	+	3.03213i	0.886501	+	0.250941i
$147$		0			0
$148$	2.47310	−	4.01834i	0.203288	−	0.330306i
$149$	2.73179	+	4.73161i	0.223797	+	0.387628i	0.955958	−	0.293504i	$-0.0948213\pi$
$149$	2.73179	+	4.73161i	0.223797	+	0.387628i	−0.732161	+	0.681132i	$0.761488\pi$
$150$	−2.55022	+	1.56819i	−0.208225	+	0.128042i
$151$	1.29567	+	0.748053i	0.105440	+	0.0608757i	0.551793	−	0.833981i	$-0.313944\pi$
$151$	1.29567	+	0.748053i	0.105440	+	0.0608757i	−0.446353	+	0.894857i	$0.647277\pi$
$152$	−5.30447	+	16.9105i	−0.430249	+	1.37162i
$153$	−14.4261			−1.16628
$154$		0			0
$155$	−2.57861	+	2.06561i	−0.207119	+	0.165914i
$156$	−2.15558	−	0.0606006i	−0.172585	−	0.00485193i
$157$	−11.4517	+	19.8350i	−0.913948	+	1.58300i	−0.105515	+	0.994418i	$0.533649\pi$
$157$	−11.4517	+	19.8350i	−0.913948	+	1.58300i	−0.808434	+	0.588587i	$0.799684\pi$
$158$	−4.57407	−	4.70447i	−0.363894	−	0.374268i
$159$	0.473392	+	0.819938i	0.0375424	+	0.0650253i
$160$	−9.64291	−	8.18622i	−0.762339	−	0.647178i
$161$		0			0
$162$	−10.0951	−	2.85762i	−0.793148	−	0.224516i
$163$	0.965256	+	1.67187i	0.0756047	+	0.130951i	0.901349	−	0.433093i	$-0.142578\pi$
$163$	0.965256	+	1.67187i	0.0756047	+	0.130951i	−0.825744	+	0.564045i	$0.809245\pi$
$164$	−6.70780	−	12.4112i	−0.523791	−	0.969150i
$165$	−0.700788	−	4.58141i	−0.0545563	−	0.356663i
$166$	5.93487	−	1.50118i	0.460635	−	0.116514i
$167$			16.9677i			1.31300i	0.754327	+	0.656499i	$0.227963\pi$
$167$			16.9677i			1.31300i	−0.754327	+	0.656499i	$0.772037\pi$
$168$		0			0
$169$	−6.51462			−0.501124
$170$	−12.8977	−	9.75747i	−0.989212	−	0.748364i
$171$	−8.83740	+	15.3068i	−0.675813	+	1.17054i
$172$	−18.9653	+	10.2501i	−1.44609	+	0.781560i
$173$	5.01816	+	8.69171i	0.381524	+	0.660818i	0.991280	−	0.131770i	$-0.0420661\pi$
$173$	5.01816	+	8.69171i	0.381524	+	0.660818i	−0.609757	+	0.792589i	$0.708733\pi$
$174$	0.308158	−	1.08863i	0.0233614	−	0.0825289i
$175$		0			0
$176$	17.4818	−	8.82279i	1.31774	−	0.665043i
$177$	2.08632	−	1.20454i	0.156818	−	0.0905386i
$178$	2.15165	+	2.21299i	0.161273	+	0.165871i
$179$	3.07683	+	1.77641i	0.229973	+	0.132775i	0.610560	−	0.791970i	$-0.290944\pi$
$179$	3.07683	+	1.77641i	0.229973	+	0.132775i	−0.380586	+	0.924745i	$0.624278\pi$
$180$	−7.60692	−	10.0631i	−0.566987	−	0.750061i
$181$			22.2716i			1.65543i	0.561148	+	0.827716i	$0.310360\pi$
$181$			22.2716i			1.65543i	−0.561148	+	0.827716i	$0.689640\pi$
$182$		0			0
$183$	−1.63853			−0.121124
$184$	3.92044	−	12.4983i	0.289018	−	0.921383i
$185$	5.21468	−	0.797654i	0.383391	−	0.0586447i
$186$	0.616730	+	0.634312i	0.0452208	+	0.0465100i
$187$	21.6828	−	12.5185i	1.58560	−	0.915447i
$188$	−12.8042	+	20.8045i	−0.933843	+	1.51733i
$189$		0			0
$190$	−18.2543	+	7.70775i	−1.32431	+	0.559179i
$191$	15.4551	−	8.92302i	1.11829	−	0.645647i	0.177328	−	0.984152i	$-0.443254\pi$
$191$	15.4551	−	8.92302i	1.11829	−	0.645647i	0.940965	+	0.338505i	$0.109921\pi$
$192$	−1.93457	+	2.78027i	−0.139616	+	0.200649i
$193$	−15.7903	−	9.11654i	−1.13661	−	0.656223i	−0.191022	−	0.981586i	$-0.561180\pi$
$193$	−15.7903	−	9.11654i	−1.13661	−	0.656223i	−0.945589	+	0.325363i	$0.894513\pi$
$194$	1.18718	+	4.69346i	0.0852344	+	0.336971i
$195$	−1.50733	−	1.88168i	−0.107942	−	0.134750i
$196$		0			0
$197$			11.3569i			0.809148i	0.914505	+	0.404574i	$0.132580\pi$
$197$			11.3569i			0.809148i	−0.914505	+	0.404574i	$0.867420\pi$
$198$	18.9326	−	4.78886i	1.34548	−	0.340329i
$199$	−4.51414	+	7.81873i	−0.319999	+	0.554255i	−0.980487	−	0.196581i	$-0.937016\pi$
$199$	−4.51414	+	7.81873i	−0.319999	+	0.554255i	0.660488	+	0.750836i	$0.270349\pi$
$200$	0.00544018	−	14.1421i	0.000384679	−	1.00000i
$201$	0.326079	−	0.188262i	0.0229998	−	0.0132789i
$202$	2.81454	−	9.94295i	0.198030	−	0.699584i
$203$		0			0
$204$	−2.26987	+	3.68813i	−0.158923	+	0.258221i
$205$	5.73042	−	14.6953i	0.400230	−	1.02636i
$206$	−6.65519	−	6.84492i	−0.463689	−	0.476908i
$207$	6.53156	−	11.3130i	0.453975	−	0.786307i
$208$	5.58087	−	8.52174i	0.386964	−	0.590876i
$209$		−	30.6753i		−	2.12186i
$210$		0			0
$211$			4.40164i			0.303021i	0.988456	+	0.151511i	$0.0484138\pi$
$211$			4.40164i			0.303021i	−0.988456	+	0.151511i	$0.951586\pi$
$212$	−4.47065	−	0.125685i	−0.307045	−	0.00863207i
$213$	3.03379	−	5.25469i	0.207872	−	0.360045i
$214$	9.96710	−	9.69083i	0.681337	−	0.662452i
$215$	−22.4556	−	8.75655i	−1.53146	−	0.597192i
$216$	−5.13222	+	4.71675i	−0.349203	+	0.320934i
$217$		0			0
$218$	12.8076	+	3.62544i	0.867442	+	0.245546i
$219$	2.88634	−	1.66643i	0.195041	−	0.112607i
$220$	20.1659	+	8.52403i	1.35958	+	0.574690i
$221$	6.51214	−	11.2794i	0.438054	−	0.758731i
$222$	−0.346397	−	1.36947i	−0.0232486	−	0.0919126i
$223$		−	14.1103i		−	0.944899i	−0.881358	−	0.472449i	$-0.843370\pi$
$223$		−	14.1103i		−	0.944899i	0.881358	−	0.472449i	$-0.156630\pi$
$224$		0			0
$225$	3.07819	−	13.7637i	0.205213	−	0.917580i
$226$	21.8353	−	5.52307i	1.45246	−	0.367389i
$227$	9.52419	+	5.49880i	0.632143	+	0.364968i	0.781582	−	0.623803i	$-0.214413\pi$
$227$	9.52419	+	5.49880i	0.632143	+	0.364968i	−0.149439	+	0.988771i	$0.547747\pi$
$228$	2.52277	+	4.66779i	0.167075	+	0.309132i
$229$	−7.02292	+	4.05469i	−0.464088	+	0.267941i	−0.713762	−	0.700389i	$-0.753010\pi$
$229$	−7.02292	+	4.05469i	−0.464088	+	0.267941i	0.249674	+	0.968330i	$0.419677\pi$
$230$	13.4914	−	5.69666i	0.889598	−	0.375626i
$231$		0			0
$232$	3.61652	+	3.93507i	0.237436	+	0.258350i
$233$	13.7475	−	7.93710i	0.900626	−	0.519977i	0.0232229	−	0.999730i	$-0.492607\pi$
$233$	13.7475	−	7.93710i	0.900626	−	0.519977i	0.877403	+	0.479754i	$0.159274\pi$
$234$	7.28366	−	7.08177i	0.476147	−	0.462949i
$235$	−26.9984	+	4.12977i	−1.76118	+	0.269396i
$236$	−0.319803	+	11.3755i	−0.0208174	+	0.740482i
$237$	−1.96441			−0.127602
$238$		0			0
$239$			24.4934i			1.58435i	0.610295	+	0.792174i	$0.291051\pi$
$239$			24.4934i			1.58435i	−0.610295	+	0.792174i	$0.708949\pi$
$240$	−3.76961	+	0.361382i	−0.243328	+	0.0233271i
$241$	−16.6157	−	9.59308i	−1.07031	−	0.617945i	−0.142045	−	0.989860i	$-0.545368\pi$
$241$	−16.6157	−	9.59308i	−1.07031	−	0.617945i	−0.928267	+	0.371916i	$0.878701\pi$
$242$	−13.1470	+	12.7826i	−0.845119	+	0.821694i
$243$	−9.12300	+	5.26717i	−0.585241	+	0.337889i
$244$	4.05689	−	6.59171i	0.259716	−	0.421991i
$245$		0			0
$246$	−4.06394	−	1.15038i	−0.259107	−	0.0733452i
$247$	−7.97864	−	13.8194i	−0.507668	−	0.879308i
$248$	−4.07878	+	0.910555i	−0.259003	+	0.0578203i
$249$	0.916372	−	1.58720i	0.0580727	−	0.100585i
$250$	12.0615	−	10.2235i	0.762837	−	0.646591i
$251$	21.1323			1.33386			0.666929	−	0.745121i	$-0.267608\pi$
$251$	21.1323			1.33386			0.666929	+	0.745121i	$0.267608\pi$
$252$		0			0
$253$			22.6716i			1.42535i
$254$	4.23752	+	16.7529i	0.265886	+	1.05117i
$255$	−4.78616	+	0.732107i	−0.299721	+	0.0458463i
$256$	−6.39499	−	14.6664i	−0.399687	−	0.916652i
$257$	−12.8260	−	22.2153i	−0.800064	−	1.38575i	−0.919573	−	0.392918i	$-0.871466\pi$
$257$	−12.8260	−	22.2153i	−0.800064	−	1.38575i	0.119509	−	0.992833i	$-0.461868\pi$
$258$	−1.75787	+	6.21003i	−0.109440	+	0.386620i
$259$		0			0
$260$	11.3019	−	1.40500i	0.700916	−	0.0871346i
$261$	2.66501	+	4.61592i	0.164960	+	0.285719i
$262$	9.98805	−	9.71120i	0.617064	−	0.599960i
$263$	−5.00988	+	8.67737i	−0.308922	+	0.535069i	−0.978127	−	0.208009i	$-0.933302\pi$
$263$	−5.00988	+	8.67737i	−0.308922	+	0.535069i	0.669204	+	0.743078i	$0.266635\pi$
$264$	1.75464	−	5.59374i	0.107990	−	0.344271i
$265$	−3.12619	−	3.90257i	−0.192040	−	0.239733i
$266$		0			0
$267$	0.924061			0.0565516
$268$	−0.0499832	+	1.77792i	−0.00305321	+	0.108604i
$269$	−11.8597	−	6.84723i	−0.723102	−	0.417483i	0.0927916	−	0.995686i	$-0.470421\pi$
$269$	−11.8597	−	6.84723i	−0.723102	−	0.417483i	−0.815893	+	0.578203i	$0.803754\pi$
$270$	−7.73332	−	0.964392i	−0.470635	−	0.0586910i
$271$	7.68044	+	13.3029i	0.466554	+	0.808095i	0.999270	−	0.0381991i	$-0.0121621\pi$
$271$	7.68044	+	13.3029i	0.466554	+	0.808095i	−0.532716	+	0.846294i	$0.678829\pi$
$272$	−9.21708	−	18.2631i	−0.558868	−	1.10736i
$273$		0			0
$274$	−1.80838	+	6.38849i	−0.109249	+	0.385943i
$275$	7.31713	+	23.3583i	0.441240	+	1.40856i
$276$	−1.86454	−	3.44988i	−0.112232	−	0.207658i
$277$	−15.4230	−	8.90447i	−0.926678	−	0.535018i	−0.0409188	−	0.999162i	$-0.513028\pi$
$277$	−15.4230	−	8.90447i	−0.926678	−	0.535018i	−0.885759	+	0.464145i	$0.846362\pi$
$278$	−4.81157	−	19.0224i	−0.288579	−	1.14089i
$279$	−4.16783			−0.249521
$280$		0			0
$281$	29.6169			1.76680			0.883398	−	0.468624i	$-0.155250\pi$
$281$	29.6169			1.76680			0.883398	+	0.468624i	$0.155250\pi$
$282$	1.79343	+	7.09026i	0.106797	+	0.422219i
$283$	3.09887	+	1.78914i	0.184209	+	0.106353i	0.589269	−	0.807937i	$-0.299416\pi$
$283$	3.09887	+	1.78914i	0.184209	+	0.106353i	−0.405060	+	0.914290i	$0.632749\pi$
$284$	13.6278	+	25.2150i	0.808662	+	1.49624i
$285$	−2.15519	+	5.52684i	−0.127662	+	0.327382i
$286$	−4.80215	+	16.9646i	−0.283957	+	1.00314i
$287$		0			0
$288$	−3.03757	−	15.6647i	−0.178991	−	0.923053i
$289$	−4.57800	−	7.92933i	−0.269294	−	0.466431i
$290$	−0.739437	+	5.92944i	−0.0434212	+	0.348189i
$291$	1.25520	+	0.724692i	0.0735814	+	0.0424822i
$292$	−0.442434	+	15.7375i	−0.0258915	+	0.920969i
$293$	17.7739			1.03836			0.519180	−	0.854665i	$-0.326237\pi$
$293$	17.7739			1.03836			0.519180	+	0.854665i	$0.326237\pi$
$294$		0			0
$295$	−9.93004	+	7.95453i	−0.578149	+	0.463131i
$296$	6.36694	+	1.99717i	0.370071	+	0.116083i
$297$	6.03233	−	10.4483i	0.350031	−	0.606272i
$298$	−5.53983	+	5.38627i	−0.320913	+	0.312018i
$299$	5.89687	+	10.2137i	0.341025	+	0.590672i
$300$	−3.03444	−	2.95261i	−0.175194	−	0.170469i
$301$		0			0
$302$	−0.576278	+	2.03582i	−0.0331611	+	0.117148i
$303$	−1.54684	−	2.67921i	−0.0888639	−	0.153917i
$304$	−25.0244	−	1.40815i	−1.43525	−	0.0807632i
$305$	8.55419	−	1.30848i	0.489812	−	0.0749232i
$306$	−5.00288	−	19.7787i	−0.285995	−	1.13067i
$307$			32.8923i			1.87726i	0.344923	+	0.938631i	$0.387905\pi$
$307$			32.8923i			1.87726i	−0.344923	+	0.938631i	$0.612095\pi$
$308$		0			0
$309$	−2.85818			−0.162596
$310$	−3.72627	−	2.81902i	−0.211638	−	0.160109i
$311$	9.93741	−	17.2121i	0.563499	−	0.976009i	−0.433689	−	0.901063i	$-0.642788\pi$
$311$	9.93741	−	17.2121i	0.563499	−	0.976009i	0.997188	−	0.0749459i	$-0.0238784\pi$
$312$	−0.664456	−	2.97639i	−0.0376174	−	0.168505i
$313$	−3.18572	−	5.51783i	−0.180068	−	0.311886i	0.761836	−	0.647770i	$-0.224298\pi$
$313$	−3.18572	−	5.51783i	−0.180068	−	0.311886i	−0.941903	+	0.335884i	$0.890965\pi$
$314$	−31.1658	−	8.82208i	−1.75879	−	0.497859i
$315$		0			0
$316$	4.86373	−	7.90269i	0.273606	−	0.444561i
$317$	−14.7244	+	8.50113i	−0.827004	+	0.477471i	−0.852826	−	0.522196i	$-0.825113\pi$
$317$	−14.7244	+	8.50113i	−0.827004	+	0.477471i	0.0258220	+	0.999667i	$0.491780\pi$
$318$	−0.959994	+	0.933385i	−0.0538338	+	0.0523416i
$319$	−8.01112	−	4.62522i	−0.448537	−	0.258963i
$320$	7.87949	−	16.0597i	0.440477	−	0.897764i
$321$		−	4.16188i		−	0.232293i
$322$		0			0
$323$	−32.0462			−1.78310
$324$	0.416971	−	14.8318i	0.0231650	−	0.823987i
$325$	9.37190	+	8.61987i	0.519859	+	0.478144i
$326$	−1.95745	+	1.90319i	−0.108413	+	0.105408i
$327$	3.45112	−	1.99251i	0.190848	−	0.110186i
$328$	14.6899	−	13.5007i	0.811115	−	0.745453i
$329$		0			0
$330$	6.03824	−	2.54961i	0.332394	−	0.140351i
$331$	−12.6971	+	7.33065i	−0.697893	+	0.402929i	−0.806562	−	0.591149i	$-0.798674\pi$
$331$	−12.6971	+	7.33065i	−0.697893	+	0.402929i	0.108669	+	0.994078i	$0.465341\pi$
$332$	4.11635	+	7.61631i	0.225914	+	0.417999i
$333$	5.76313	+	3.32735i	0.315818	+	0.182338i
$334$	−23.2633	+	5.88427i	−1.27291	+	0.321973i
$335$	−1.55200	+	1.24324i	−0.0847949	+	0.0679256i
$336$		0			0
$337$		−	15.2435i		−	0.830368i	−0.909738	−	0.415184i	$-0.863717\pi$
$337$		−	15.2435i		−	0.830368i	0.909738	−	0.415184i	$-0.136283\pi$
$338$	−2.25922	−	8.93176i	−0.122886	−	0.485824i
$339$	3.37147	−	5.83955i	0.183113	−	0.317161i
$340$	8.90498	−	21.0671i	0.482940	−	1.14252i
$341$	6.26433	−	3.61671i	0.339233	−	0.195856i
$342$	−24.0509	−	6.80807i	−1.30052	−	0.368138i
$343$		0			0
$344$	−20.6302	−	22.4474i	−1.11231	−	1.21028i
$345$	1.59286	−	4.08479i	0.0857567	−	0.219918i
$346$	−10.1764	+	9.89429i	−0.547085	+	0.531921i
$347$	16.7097	−	28.9420i	0.897024	−	1.55369i	0.0657437	−	0.997837i	$-0.479058\pi$
$347$	16.7097	−	28.9420i	0.897024	−	1.55369i	0.831280	−	0.555854i	$-0.187609\pi$
$348$	1.59942	+	0.0449649i	0.0857377	+	0.00241037i
$349$			16.1586i			0.864951i	0.901646	+	0.432476i	$0.142360\pi$
$349$			16.1586i			0.864951i	−0.901646	+	0.432476i	$0.857640\pi$
$350$		0			0
$351$		−	6.27603i		−	0.334990i
$352$	18.1589	+	20.9085i	0.967874	+	1.11443i
$353$	−11.3427	+	19.6461i	−0.603711	+	1.04566i	0.388543	+	0.921431i	$0.372979\pi$
$353$	−11.3427	+	19.6461i	−0.603711	+	1.04566i	−0.992254	+	0.124228i	$0.960355\pi$
$354$	2.37498	+	2.44269i	0.126229	+	0.129828i
$355$	−11.6421	+	29.8555i	−0.617901	+	1.58457i
$356$	−2.28791	+	3.71744i	−0.121259	+	0.197024i
$357$		0			0
$358$	−1.36850	+	4.83449i	−0.0723272	+	0.255511i
$359$	14.5214	−	8.38391i	0.766408	−	0.442486i	−0.0651839	−	0.997873i	$-0.520763\pi$
$359$	14.5214	−	8.38391i	0.766408	−	0.442486i	0.831592	+	0.555388i	$0.187430\pi$
$360$	11.1589	−	13.9192i	0.588123	−	0.733605i
$361$	−10.1314	+	17.5481i	−0.533233	+	0.923586i
$362$	−30.5351	+	7.72362i	−1.60489	+	0.405945i
$363$			5.48966i			0.288133i
$364$		0			0
$365$	−13.7378	+	11.0048i	−0.719069	+	0.576016i
$366$	−0.568231	−	2.24648i	−0.0297019	−	0.117426i
$367$	−13.5474	−	7.82159i	−0.707168	−	0.408284i	0.102844	−	0.994698i	$-0.467206\pi$
$367$	−13.5474	−	7.82159i	−0.707168	−	0.408284i	−0.810012	+	0.586414i	$0.800539\pi$
$368$	18.4951	+	1.04074i	0.964124	+	0.0542524i
$369$	17.2316	−	9.94866i	0.897041	−	0.517907i
$370$	2.90203	+	6.87288i	0.150869	+	0.357304i
$371$		0			0
$372$	−0.655785	+	1.06553i	−0.0340009	+	0.0552453i
$373$	−14.8129	+	8.55225i	−0.766985	+	0.442819i	−0.831798	−	0.555079i	$-0.812688\pi$
$373$	−14.8129	+	8.55225i	−0.766985	+	0.442819i	0.0648133	+	0.997897i	$0.479355\pi$
$374$	24.6828	+	25.3864i	1.27632	+	1.31270i
$375$	0.322764	−	4.72261i	0.0166675	−	0.243874i
$376$	−32.9641	−	10.3401i	−1.69999	−	0.533252i
$377$	−4.81207			−0.247834
$378$		0			0
$379$			10.3762i			0.532990i	0.963836	+	0.266495i	$0.0858655\pi$
$379$			10.3762i			0.532990i	−0.963836	+	0.266495i	$0.914134\pi$
$380$	−16.8980	−	22.3543i	−0.866852	−	1.14675i
$381$	4.48034	+	2.58672i	0.229535	+	0.132522i
$382$	17.5935	+	18.0951i	0.900161	+	0.925823i
$383$	−8.00016	+	4.61890i	−0.408789	+	0.236015i	−0.690269	−	0.723552i	$-0.742508\pi$
$383$	−8.00016	+	4.61890i	−0.408789	+	0.236015i	0.281480	+	0.959567i	$0.409175\pi$
$384$	−4.48274	−	1.68819i	−0.228759	−	0.0861500i
$385$		0			0
$386$	7.02311	−	24.8106i	0.357467	−	1.26283i
$387$	−15.2024	−	26.3313i	−0.772780	−	1.33849i
$388$	−6.02319	+	3.25532i	−0.305781	+	0.165264i
$389$	−8.54214	+	14.7954i	−0.433104	+	0.750158i	−0.997139	−	0.0755930i	$-0.975915\pi$
$389$	−8.54214	+	14.7954i	−0.433104	+	0.750158i	0.564035	+	0.825751i	$0.309248\pi$
$390$	2.05711	−	2.71916i	0.104166	−	0.137690i
$391$	23.6848			1.19779
$392$		0			0
$393$		−	4.17063i		−	0.210380i
$394$	−15.5707	+	3.93851i	−0.784442	+	0.198419i
$395$	10.2555	−	1.56871i	0.516009	−	0.0789304i
$396$	13.1314	+	24.2965i	0.659877	+	1.22094i
$397$	16.7682	+	29.0434i	0.841573	+	1.45765i	0.888564	+	0.458752i	$0.151703\pi$
$397$	16.7682	+	29.0434i	0.841573	+	1.45765i	−0.0469909	+	0.998895i	$0.514963\pi$
$398$	−12.2852	−	3.47756i	−0.615802	−	0.174315i
$399$		0			0
$400$	19.3912	−	4.89694i	0.969562	−	0.244847i
$401$	6.41428	+	11.1099i	0.320314	+	0.554800i	0.980553	−	0.196256i	$-0.0628784\pi$
$401$	6.41428	+	11.1099i	0.320314	+	0.554800i	−0.660239	+	0.751056i	$0.729545\pi$
$402$	0.371195	+	0.381777i	0.0185135	+	0.0190413i
$403$	1.88141	−	3.25870i	0.0937198	−	0.162327i
$404$	14.6082	+	0.410685i	0.726785	+	0.0204323i
$405$	12.9471	−	10.3714i	0.643348	−	0.515359i
$406$		0			0
$407$	−11.5495			−0.572487
$408$	−5.84373	−	1.83305i	−0.289308	−	0.0907497i
$409$	18.7038	+	10.7986i	0.924841	+	0.533957i	0.885176	−	0.465256i	$-0.154038\pi$
$409$	18.7038	+	10.7986i	0.924841	+	0.533957i	0.0396649	+	0.999213i	$0.487371\pi$
$410$	22.1350	+	2.76037i	1.09317	+	0.136325i
$411$	0.993870	+	1.72143i	0.0490240	+	0.0849121i
$412$	7.07664	−	11.4983i	0.348641	−	0.566479i
$413$		0			0
$414$	17.7756	+	5.03172i	0.873623	+	0.247296i
$415$	−3.51656	+	9.01801i	−0.172621	+	0.442677i
$416$	13.6190	+	4.69628i	0.667726	+	0.230254i
$417$	−5.08728	−	2.93714i	−0.249125	−	0.143833i
$418$	42.0569	−	10.6380i	2.05707	−	0.520321i
$419$	18.7281			0.914929			0.457464	−	0.889228i	$-0.348758\pi$
$419$	18.7281			0.914929			0.457464	+	0.889228i	$0.348758\pi$
$420$		0			0
$421$	−18.9665			−0.924371			−0.462186	−	0.886783i	$-0.652935\pi$
$421$	−18.9665			−0.924371			−0.462186	+	0.886783i	$0.652935\pi$
$422$	−6.03479	+	1.52646i	−0.293769	+	0.0743068i
$423$	−29.8380	−	17.2270i	−1.45077	−	0.837604i
$424$	−1.37807	−	6.17300i	−0.0669251	−	0.299787i
$425$	24.4022	−	7.64414i	1.18368	−	0.370795i
$426$	8.25645	+	2.33715i	0.400026	+	0.113235i
$427$		0			0
$428$	16.7430	+	10.3045i	0.809303	+	0.498088i
$429$	2.63921	+	4.57125i	0.127422	+	0.220702i
$430$	4.21808	−	33.8241i	0.203414	−	1.63115i
$431$	−23.4036	−	13.5121i	−1.12731	−	0.650854i	−0.184055	−	0.982916i	$-0.558923\pi$
$431$	−23.4036	−	13.5121i	−1.12731	−	0.650854i	−0.943258	+	0.332061i	$0.892256\pi$
$432$	−8.24665	−	5.40071i	−0.396767	−	0.259842i
$433$	−15.0015			−0.720928			−0.360464	−	0.932773i	$-0.617382\pi$
$433$	−15.0015			−0.720928			−0.360464	+	0.932773i	$0.617382\pi$
$434$		0			0
$435$	1.11842	+	1.39618i	0.0536243	+	0.0669418i
$436$	−0.529008	+	18.8170i	−0.0253349	+	0.901170i
$437$	14.5092	−	25.1307i	0.694071	−	1.20217i
$438$	3.28569	+	3.37936i	0.156996	+	0.161472i
$439$	9.21899	+	15.9678i	0.439998	+	0.762099i	0.997689	−	0.0679495i	$-0.0216457\pi$
$439$	9.21899	+	15.9678i	0.439998	+	0.762099i	−0.557690	+	0.830049i	$0.688312\pi$
$440$	−4.69336	+	30.6041i	−0.223747	+	1.45900i
$441$		0			0
$442$	17.7227	+	5.01676i	0.842985	+	0.238623i
$443$	10.4298	+	18.0649i	0.495533	+	0.858289i	0.999987	−	0.00514984i	$-0.00163925\pi$
$443$	10.4298	+	18.0649i	0.495533	+	0.858289i	−0.504453	+	0.863439i	$0.668306\pi$
$444$	1.75746	−	0.949844i	0.0834052	−	0.0450776i
$445$	−4.82419	+	0.737925i	−0.228689	+	0.0349810i
$446$	19.3458	−	4.89337i	0.916048	−	0.231708i
$447$			2.31322i			0.109411i
$448$		0			0
$449$	14.6483			0.691298			0.345649	−	0.938364i	$-0.387659\pi$
$449$	14.6483			0.691298			0.345649	+	0.938364i	$0.387659\pi$
$450$	19.9380	−	0.552848i	0.939886	−	0.0260615i
$451$	−17.2663	+	29.9061i	−0.813038	+	1.40822i
$452$	15.1446	+	28.0215i	0.712344	+	1.31802i
$453$	0.316717	+	0.548569i	0.0148806	+	0.0257740i
$454$	−4.23611	+	14.9649i	−0.198811	+	0.702339i
$455$		0			0
$456$	−5.52481	+	5.07756i	−0.258723	+	0.237779i
$457$	−1.03058	+	0.595004i	−0.0482084	+	0.0278331i	−0.523910	−	0.851773i	$-0.675527\pi$
$457$	−1.03058	+	0.595004i	−0.0482084	+	0.0278331i	0.475702	+	0.879606i	$0.342194\pi$
$458$	−7.99462	−	8.22253i	−0.373564	−	0.384214i
$459$	−10.9152	−	6.30192i	−0.509480	−	0.294148i
$460$	12.4890	+	16.5216i	0.582305	+	0.770325i
$461$			14.5645i			0.678336i	0.940726	+	0.339168i	$0.110146\pi$
$461$			14.5645i			0.678336i	−0.940726	+	0.339168i	$0.889854\pi$
$462$		0			0
$463$	−4.69391			−0.218145			−0.109072	−	0.994034i	$-0.534788\pi$
$463$	−4.69391			−0.218145			−0.109072	+	0.994034i	$0.534788\pi$
$464$	−4.14094	+	6.32303i	−0.192238	+	0.293539i
$465$	−1.38276	+	0.211512i	−0.0641241	+	0.00980863i
$466$	15.6496	+	16.0957i	0.724952	+	0.745619i
$467$	21.8947	−	12.6409i	1.01317	−	0.584952i	0.101050	−	0.994881i	$-0.467780\pi$
$467$	21.8947	−	12.6409i	1.01317	−	0.584952i	0.912117	+	0.409929i	$0.134447\pi$
$468$	12.2353	+	7.53023i	0.565575	+	0.348085i
$469$		0			0
$470$	−15.0249	−	35.5836i	−0.693048	−	1.64135i
$471$	−8.39790	+	4.84853i	−0.386955	+	0.223408i
$472$	−15.7071	+	3.50648i	−0.722978	+	0.161399i
$473$	45.6990	+	26.3843i	2.10124	+	1.21315i
$474$	−0.681243	−	2.69327i	−0.0312905	−	0.123706i
$475$	6.83791	−	30.5747i	0.313745	−	1.40286i
$476$		0			0
$477$		−	6.30776i		−	0.288813i
$478$	−33.5813	+	8.49416i	−1.53597	+	0.388514i
$479$	2.05143	−	3.55318i	0.0937322	−	0.162349i	−0.815347	−	0.578973i	$-0.803454\pi$
$479$	2.05143	−	3.55318i	0.0937322	−	0.162349i	0.909079	+	0.416624i	$0.136787\pi$
$480$	−1.80274	−	5.04295i	−0.0822836	−	0.230178i
$481$	−5.20311	+	3.00402i	−0.237241	+	0.136971i
$482$	7.39023	−	26.1075i	0.336616	−	1.18916i
$483$		0			0
$484$	−22.0846	−	13.5920i	−1.00385	−	0.617820i
$485$	−7.13169	−	2.78100i	−0.323833	−	0.126279i
$486$	−10.3853	−	10.6813i	−0.471085	−	0.484515i
$487$	16.9058	−	29.2816i	0.766073	−	1.32688i	−0.173605	−	0.984815i	$-0.555542\pi$
$487$	16.9058	−	29.2816i	0.766073	−	1.32688i	0.939678	−	0.342062i	$-0.111125\pi$
$488$	10.4444	+	3.27617i	0.472794	+	0.148305i
$489$			0.817356i			0.0369621i
$490$		0			0
$491$			25.9116i			1.16937i	0.811259	+	0.584686i	$0.198782\pi$
$491$			25.9116i			1.16937i	−0.811259	+	0.584686i	$0.801218\pi$
$492$	0.167857	−	5.97074i	0.00756760	−	0.269182i
$493$	−4.83193	+	8.36914i	−0.217619	+	0.376927i
$494$	16.1799	−	15.7315i	0.727970	−	0.707792i
$495$	−11.2180	+	28.7680i	−0.504213	+	1.29302i
$496$	−2.66289	−	5.27637i	−0.119567	−	0.236916i
$497$		0			0
$498$	2.49390	+	0.705946i	0.111754	+	0.0316342i
$499$	−21.0465	+	12.1512i	−0.942170	+	0.543962i	−0.890640	−	0.454709i	$-0.849743\pi$
$499$	−21.0465	+	12.1512i	−0.942170	+	0.543962i	−0.0515304	+	0.998671i	$0.516410\pi$
$500$	18.1996	+	12.9913i	0.813912	+	0.580989i
$501$	−3.59195	+	6.22145i	−0.160477	+	0.277954i
$502$	7.32853	+	28.9731i	0.327088	+	1.29313i
$503$			11.5222i			0.513750i	0.966445	+	0.256875i	$0.0826928\pi$
$503$			11.5222i			0.513750i	−0.966445	+	0.256875i	$0.917307\pi$
$504$		0			0
$505$	10.2151	+	12.7520i	0.454564	+	0.567455i
$506$	−31.0835	+	7.86235i	−1.38183	+	0.349524i
$507$	−2.38868	−	1.37911i	−0.106085	−	0.0612482i
$508$	−21.4992	+	11.6196i	−0.953874	+	0.515535i
$509$	−23.4965	+	13.5657i	−1.04147	+	0.601290i	−0.920248	−	0.391336i	$-0.872013\pi$
$509$	−23.4965	+	13.5657i	−1.04147	+	0.601290i	−0.121218	+	0.992626i	$0.538680\pi$
$510$	−2.66355	−	6.30810i	−0.117944	−	0.279327i
$511$		0			0
$512$	17.8904	−	13.8540i	0.790653	−	0.612264i
$513$	−13.3733	+	7.72108i	−0.590445	+	0.340894i
$514$	26.0099	−	25.2890i	1.14725	−	1.11545i
$515$	14.9215	−	2.28245i	0.657521	−	0.100577i
$516$	−9.12378	−	0.256500i	−0.401652	−	0.0112918i
$517$	59.7962			2.62983
$518$		0			0
$519$			4.24926i			0.186522i
$520$	5.84574	+	15.0081i	0.256353	+	0.658148i
$521$	14.9657	+	8.64045i	0.655659	+	0.378545i	0.790621	−	0.612306i	$-0.209758\pi$
$521$	14.9657	+	8.64045i	0.655659	+	0.378545i	−0.134962	+	0.990851i	$0.543091\pi$
$522$	−5.40438	+	5.25458i	−0.236543	+	0.229987i
$523$	−16.4944	+	9.52305i	−0.721250	+	0.416414i	−0.815213	−	0.579162i	$-0.803380\pi$
$523$	−16.4944	+	9.52305i	−0.721250	+	0.416414i	0.0939627	+	0.995576i	$0.470047\pi$
$524$	16.7782	+	10.3262i	0.732958	+	0.451101i
$525$		0			0
$526$	−13.6344	−	3.85946i	−0.594486	−	0.168281i
$527$	−3.77835	−	6.54429i	−0.164587	−	0.285074i
$528$	8.27771	+	0.465796i	0.360241	+	0.0202712i
$529$	0.776490	−	1.34492i	0.0337605	−	0.0584748i
$530$	4.26642	−	5.63949i	0.185321	−	0.244964i
$531$	−16.0500			−0.696511
$532$		0			0
$533$			17.9638i			0.778100i
$534$	0.320458	+	1.26692i	0.0138676	+	0.0548249i
$535$	3.32354	+	21.7277i	0.143689	+	0.939370i
$536$	−2.45492	+	0.548041i	−0.106036	+	0.0236718i
$537$	0.752111	+	1.30269i	0.0324560	+	0.0562154i
$538$	5.27490	−	18.6347i	0.227417	−	0.803399i
$539$		0			0
$540$	−1.35965	−	10.9371i	−0.0585100	−	0.470657i
$541$	−9.19403	−	15.9245i	−0.395282	−	0.684649i	0.597855	−	0.801604i	$-0.296020\pi$
$541$	−9.19403	−	15.9245i	−0.395282	−	0.684649i	−0.993137	+	0.116955i	$0.962687\pi$
$542$	−15.5752	+	15.1435i	−0.669013	+	0.650469i
$543$	−4.71475	+	8.16619i	−0.202329	+	0.350445i
$544$	21.8429	−	18.9705i	0.936508	−	0.813352i
$545$	−16.4259	+	13.1581i	−0.703610	+	0.563632i
$546$		0			0
$547$	18.9519			0.810323			0.405161	−	0.914245i	$-0.367215\pi$
$547$	18.9519			0.810323			0.405161	+	0.914245i	$0.367215\pi$
$548$	−9.38598	−	0.263871i	−0.400949	−	0.0112720i
$549$	9.45388	+	5.45820i	0.403482	+	0.232950i
$550$	−29.4875	+	18.1325i	−1.25735	+	0.773174i
$551$	5.92005	+	10.2538i	0.252203	+	0.436828i
$552$	4.08329	−	3.75274i	0.173796	−	0.159727i
$553$		0			0
$554$	6.85974	−	24.2335i	0.291443	−	1.02958i
$555$	2.08090	+	0.811444i	0.0883292	+	0.0344439i
$556$	24.4117	−	13.1937i	1.03529	−	0.559536i
$557$	−22.0931	−	12.7555i	−0.936116	−	0.540467i	−0.0473751	−	0.998877i	$-0.515086\pi$
$557$	−22.0931	−	12.7555i	−0.936116	−	0.540467i	−0.888741	+	0.458411i	$0.848419\pi$
$558$	−1.44537	−	5.71423i	−0.0611875	−	0.241903i
$559$	27.4502			1.16102
$560$		0			0
$561$	10.6004			0.447549
$562$	10.2709	+	40.6058i	0.433253	+	1.71285i
$563$	−27.2462	−	15.7306i	−1.14829	−	0.662965i	−0.199819	−	0.979833i	$-0.564035\pi$
$563$	−27.2462	−	15.7306i	−1.14829	−	0.662965i	−0.948470	+	0.316868i	$0.897369\pi$
$564$	−9.09904	+	4.91771i	−0.383139	+	0.207073i
$565$	−12.9380	+	33.1786i	−0.544304	+	1.39583i
$566$	−1.37830	+	4.86912i	−0.0579342	+	0.204665i
$567$		0			0
$568$	−29.8446	+	27.4286i	−1.25225	+	1.15088i
$569$	−8.21728	−	14.2327i	−0.344486	−	0.596668i	0.640774	−	0.767729i	$-0.278614\pi$
$569$	−8.21728	−	14.2327i	−0.344486	−	0.596668i	−0.985260	+	0.171062i	$0.945280\pi$
$570$	−8.32489	−	1.03816i	−0.348691	−	0.0434839i
$571$	12.9962	+	7.50335i	0.543873	+	0.314005i	0.746647	−	0.665220i	$-0.231662\pi$
$571$	12.9962	+	7.50335i	0.543873	+	0.314005i	−0.202774	+	0.979226i	$0.564996\pi$
$572$	−24.9244	−	0.700707i	−1.04214	−	0.0292981i
$573$	7.55580			0.315648
$574$		0			0
$575$	−5.05378	+	22.5972i	−0.210757	+	0.942370i
$576$	20.4235	−	9.59704i	0.850978	−	0.399877i
$577$	1.24966	−	2.16447i	0.0520240	−	0.0901082i	−0.838841	−	0.544377i	$-0.816766\pi$
$577$	1.24966	−	2.16447i	0.0520240	−	0.0901082i	0.890865	+	0.454269i	$0.150099\pi$
$578$	9.28376	−	9.02643i	0.386154	−	0.375450i
$579$	−3.85983	−	6.68543i	−0.160409	−	0.277837i
$580$	−8.38589	+	1.04250i	−0.348205	+	0.0432873i
$581$		0			0
$582$	−0.558282	+	1.97225i	−0.0231415	+	0.0817522i
$583$	5.47369	+	9.48071i	0.226697	+	0.392651i
$584$	−21.7301	+	4.85107i	−0.899199	+	0.200739i
$585$	2.42874	+	15.8779i	0.100416	+	0.656472i
$586$	6.16386	+	24.3686i	0.254627	+	1.00666i
$587$			22.1562i			0.914482i	0.889343	+	0.457241i	$0.151162\pi$
$587$			22.1562i			0.914482i	−0.889343	+	0.457241i	$0.848838\pi$
$588$		0			0
$589$	−9.25842			−0.381487
$590$	−14.3496	−	10.8558i	−0.590764	−	0.446928i
$591$	−2.40419	+	4.16419i	−0.0988953	+	0.171292i
$592$	−0.530181	+	9.42189i	−0.0217903	+	0.387237i
$593$	−14.3251	−	24.8118i	−0.588262	−	1.01890i	−0.994460	−	0.105115i	$-0.966479\pi$
$593$	−14.3251	−	24.8118i	−0.588262	−	1.01890i	0.406198	−	0.913785i	$-0.366854\pi$
$594$	16.4169	+	4.64713i	0.673596	+	0.190674i
$595$		0			0
$596$	−9.30594	−	5.72737i	−0.381186	−	0.234602i
$597$	−3.31036	+	1.91123i	−0.135484	+	0.0782216i
$598$	−11.9583	+	11.6268i	−0.489011	+	0.475457i
$599$	14.2033	+	8.20030i	0.580333	+	0.335055i	0.761266	−	0.648440i	$-0.224578\pi$
$599$	14.2033	+	8.20030i	0.580333	+	0.335055i	−0.180933	+	0.983495i	$0.557912\pi$
$600$	2.99580	−	5.18427i	0.122303	−	0.211647i
$601$		−	22.1672i		−	0.904220i	−0.891962	−	0.452110i	$-0.850671\pi$
$601$		−	22.1672i		−	0.904220i	0.891962	−	0.452110i	$-0.149329\pi$
$602$		0			0
$603$	−2.50851			−0.102155
$604$	−2.99103	−	0.0840878i	−0.121703	−	0.00342149i
$605$	−4.38387	−	28.6596i	−0.178230	−	1.16518i
$606$	3.13686	−	3.04991i	0.127426	−	0.123894i
$607$	24.8986	−	14.3752i	1.01060	−	0.583472i	0.0992347	−	0.995064i	$-0.468361\pi$
$607$	24.8986	−	14.3752i	1.01060	−	0.583472i	0.911368	+	0.411592i	$0.135027\pi$
$608$	−6.74768	−	34.7977i	−0.273654	−	1.41123i
$609$		0			0
$610$	4.76050	+	11.2743i	0.192747	+	0.456484i
$611$	26.9385	−	15.5530i	1.08982	−	0.629206i
$612$	25.3823	−	13.7182i	1.02602	−	0.554526i
$613$	−10.5198	−	6.07359i	−0.424890	−	0.245310i	0.272278	−	0.962219i	$-0.412223\pi$
$613$	−10.5198	−	6.07359i	−0.424890	−	0.245310i	−0.697167	+	0.716909i	$0.745556\pi$
$614$	−45.0965	+	11.4068i	−1.81994	+	0.460342i
$615$	5.21205	−	4.17515i	0.210170	−	0.168358i
$616$		0			0
$617$		−	15.9265i		−	0.641175i	−0.947219	−	0.320588i	$-0.896120\pi$
$617$		−	15.9265i		−	0.641175i	0.947219	−	0.320588i	$-0.103880\pi$
$618$	−0.991196	−	3.91866i	−0.0398717	−	0.157631i
$619$	−1.94167	+	3.36308i	−0.0780424	+	0.135173i	−0.902405	−	0.430888i	$-0.858200\pi$
$619$	−1.94167	+	3.36308i	−0.0780424	+	0.135173i	0.824363	+	0.566062i	$0.191534\pi$
$620$	2.57272	−	6.08646i	0.103323	−	0.244438i
$621$	9.88396	−	5.70651i	0.396630	−	0.228994i
$622$	27.0446	+	7.65549i	1.08439	+	0.306957i
$623$		0			0
$624$	3.85031	−	1.94319i	0.154136	−	0.0777897i
$625$	2.08628	+	24.9128i	0.0834513	+	0.996512i
$626$	6.46035	−	6.28128i	0.258207	−	0.251050i
$627$	6.49378	−	11.2476i	0.259337	−	0.449184i
$628$	1.28728	−	45.7889i	0.0513680	−	1.82717i
$629$			12.0656i			0.481089i
$630$		0			0
$631$			12.2743i			0.488633i	0.969696	+	0.244316i	$0.0785636\pi$
$631$			12.2743i			0.488633i	−0.969696	+	0.244316i	$0.921436\pi$
$632$	12.5216	+	3.92775i	0.498081	+	0.156237i
$633$	−0.931800	+	1.61393i	−0.0370357	+	0.0641478i
$634$	−16.7616	−	17.2395i	−0.665690	−	0.684668i
$635$	−25.4559	−	9.92651i	−1.01019	−	0.393922i
$636$	−1.61262	−	0.992493i	−0.0639446	−	0.0393549i
$637$		0			0
$638$	3.56314	−	12.5875i	0.141066	−	0.498345i
$639$	−35.0084	+	20.2121i	−1.38491	+	0.799578i
$640$	24.7509	+	5.23366i	0.978367	+	0.206878i
$641$	−7.41350	+	12.8406i	−0.292816	+	0.507172i	−0.974474	−	0.224499i	$-0.927926\pi$
$641$	−7.41350	+	12.8406i	−0.292816	+	0.507172i	0.681659	+	0.731670i	$0.261259\pi$
$642$	5.70608	−	1.44331i	0.225201	−	0.0569629i
$643$		−	11.8058i		−	0.465577i	−0.972527	−	0.232789i	$-0.925215\pi$
$643$		−	11.8058i		−	0.465577i	0.972527	−	0.232789i	$-0.0747850\pi$
$644$		0			0
$645$	−6.37998	−	7.96444i	−0.251211	−	0.313600i
$646$	−11.1134	−	43.9364i	−0.437251	−	1.72866i
$647$	29.9706	+	17.3035i	1.17827	+	0.680272i	0.955613	−	0.294626i	$-0.0951950\pi$
$647$	29.9706	+	17.3035i	1.17827	+	0.680272i	0.222653	+	0.974898i	$0.428528\pi$
$648$	20.4795	−	4.57188i	0.804510	−	0.179600i
$649$	24.1235	−	13.9277i	0.946931	−	0.546711i
$650$	−8.56802	+	15.8385i	−0.336065	+	0.621237i
$651$		0			0
$652$	−3.28817	−	2.02372i	−0.128775	−	0.0792549i
$653$	24.4111	−	14.0937i	0.955279	−	0.551531i	0.0605622	−	0.998164i	$-0.480711\pi$
$653$	24.4111	−	14.0937i	0.955279	−	0.551531i	0.894717	+	0.446634i	$0.147377\pi$
$654$	3.92862	+	4.04062i	0.153621	+	0.158001i
$655$	3.33053	+	21.7734i	0.130134	+	0.850755i
$656$	23.6043	+	15.4584i	0.921594	+	0.603550i
$657$	−22.2045			−0.866281
$658$		0			0
$659$			9.79123i			0.381412i	0.981647	+	0.190706i	$0.0610777\pi$
$659$			9.79123i			0.381412i	−0.981647	+	0.190706i	$0.938922\pi$
$660$	5.58962	+	7.39445i	0.217576	+	0.287829i
$661$	−0.707548	−	0.408503i	−0.0275204	−	0.0158889i	0.486177	−	0.873861i	$-0.338391\pi$
$661$	−0.707548	−	0.408503i	−0.0275204	−	0.0158889i	−0.513697	+	0.857972i	$0.671724\pi$
$662$	−14.4538	−	14.8659i	−0.561763	−	0.577778i
$663$	4.77554	−	2.75716i	0.185467	−	0.107079i
$664$	−9.01470	+	8.28494i	−0.349838	+	0.321518i
$665$		0			0
$666$	−2.56329	+	9.05536i	−0.0993255	+	0.350888i
$667$	−4.37540	−	7.57842i	−0.169416	−	0.293438i
$668$	−16.1351	−	29.8541i	−0.624285	−	1.15509i
$669$	2.98708	−	5.17377i	0.115487	−	0.200029i
$670$	−2.24275	−	1.69670i	−0.0866451	−	0.0655492i
$671$	−18.9459			−0.731397
$672$		0			0
$673$			9.43129i			0.363550i	0.983340	+	0.181775i	$0.0581842\pi$
$673$			9.43129i			0.363550i	−0.983340	+	0.181775i	$0.941816\pi$
$674$	20.8994	−	5.28635i	0.805015	−	0.203623i
$675$	8.34161	−	9.06936i	0.321069	−	0.349080i
$676$	11.4623	−	6.19495i	0.440856	−	0.238267i
$677$	−1.23700	−	2.14255i	−0.0475418	−	0.0823449i	0.841275	−	0.540607i	$-0.181805\pi$
$677$	−1.23700	−	2.14255i	−0.0475418	−	0.0823449i	−0.888817	+	0.458262i	$0.848472\pi$
$678$	9.17542	+	2.59728i	0.352380	+	0.0997479i
$679$		0			0
$680$	31.9719	+	4.90311i	1.22606	+	0.188026i
$681$	2.32812	+	4.03243i	0.0892139	+	0.154523i
$682$	7.13107	+	7.33436i	0.273063	+	0.280847i
$683$	−9.37801	+	16.2432i	−0.358840	+	0.621528i	−0.987767	−	0.155935i	$-0.950161\pi$
$683$	−9.37801	+	16.2432i	−0.358840	+	0.621528i	0.628928	+	0.777464i	$0.283494\pi$
$684$	0.993402	−	35.3356i	0.0379837	−	1.35109i
$685$	−6.56332	−	8.19332i	−0.250772	−	0.313051i
$686$		0			0
$687$	−3.43341			−0.130993
$688$	23.6217	−	36.0693i	0.900570	−	1.37513i
$689$	4.93186	+	2.84741i	0.187889	+	0.108478i
$690$	6.15278	+	0.767288i	0.234232	+	0.0292102i
$691$	2.11063	+	3.65572i	0.0802923	+	0.139070i	0.903375	−	0.428851i	$-0.141081\pi$
$691$	2.11063	+	3.65572i	0.0802923	+	0.139070i	−0.823083	+	0.567921i	$0.807748\pi$
$692$	−17.0945	−	10.5209i	−0.649836	−	0.399943i
$693$		0			0
$694$	45.4753	+	12.8727i	1.72622	+	0.488640i
$695$	28.9044	+	11.2712i	1.09641	+	0.427543i
$696$	0.493018	+	2.20845i	0.0186878	+	0.0837110i
$697$	31.2426	+	18.0379i	1.18340	+	0.683236i
$698$	−22.1540	+	5.60370i	−0.838542	+	0.212103i
$699$	6.72095			0.254210
$700$		0			0
$701$	−12.2843			−0.463971			−0.231985	−	0.972719i	$-0.574522\pi$
$701$	−12.2843			−0.463971			−0.231985	+	0.972719i	$0.574522\pi$
$702$	8.60465	−	2.17648i	0.324761	−	0.0821461i
$703$	12.8022	+	7.39138i	0.482846	+	0.278771i
$704$	−22.3689	+	32.1474i	−0.843060	+	1.21160i
$705$	−10.7736	−	4.20116i	−0.405758	−	0.158225i
$706$	−30.8691	−	8.73809i	−1.16177	−	0.328862i
$707$		0			0
$708$	−2.52539	+	4.10329i	−0.0949098	+	0.154211i
$709$	−1.46808	−	2.54279i	−0.0551348	−	0.0954963i	0.837141	−	0.546988i	$-0.184226\pi$
$709$	−1.46808	−	2.54279i	−0.0551348	−	0.0954963i	−0.892276	+	0.451491i	$0.850892\pi$
$710$	−44.9704	−	5.60808i	−1.68771	−	0.210467i
$711$	11.3341	+	6.54374i	0.425062	+	0.245410i
$712$	−5.89017	−	1.84762i	−0.220743	−	0.0692425i
$713$	6.84273			0.256262
$714$		0			0
$715$	−17.4288	−	21.7573i	−0.651802	−	0.813677i
$716$	−7.10284	−	0.199685i	−0.265446	−	0.00746256i
$717$	−5.18511	+	8.98088i	−0.193642	+	0.335397i
$718$	16.5305	+	17.0018i	0.616914	+	0.634501i
$719$	−23.7638	−	41.1601i	−0.886240	−	1.53501i	−0.844285	−	0.535894i	$-0.819975\pi$
$719$	−23.7638	−	41.1601i	−0.886240	−	1.53501i	−0.0419549	−	0.999120i	$-0.513359\pi$
$720$	22.9535	+	10.4721i	0.855426	+	0.390272i
$721$		0			0
$722$	−27.5726	−	7.80495i	−1.02615	−	0.290470i
$723$	−4.06160	−	7.03489i	−0.151052	−	0.261630i
$724$	−21.1787	−	39.1861i	−0.787100	−	1.45634i
$725$	−6.95383	−	6.39584i	−0.258259	−	0.237535i
$726$	−7.52652	+	1.90378i	−0.279335	+	0.0706558i
$727$			8.28795i			0.307383i	0.988119	+	0.153692i	$0.0491162\pi$
$727$			8.28795i			0.307383i	−0.988119	+	0.153692i	$0.950884\pi$
$728$		0			0
$729$	17.7963			0.659124
$730$	−19.8521	−	15.0186i	−0.734759	−	0.555864i
$731$	27.5634	−	47.7413i	1.01947	−	1.76578i
$732$	2.88294	−	1.55813i	0.106557	−	0.0575901i
$733$	20.9930	+	36.3610i	0.775395	+	1.34302i	0.934572	+	0.355773i	$0.115782\pi$
$733$	20.9930	+	36.3610i	0.775395	+	1.34302i	−0.159178	+	0.987250i	$0.550884\pi$
$734$	6.02552	−	21.2864i	0.222406	−	0.785696i
$735$		0			0
$736$	4.98709	+	25.7184i	0.183826	+	0.947991i
$737$	3.77035	−	2.17681i	0.138883	−	0.0801840i
$738$	19.6157	+	20.1750i	0.722066	+	0.742651i
$739$	−22.4500	−	12.9615i	−0.825836	−	0.476796i	0.0265891	−	0.999646i	$-0.491535\pi$
$739$	−22.4500	−	12.9615i	−0.825836	−	0.476796i	−0.852425	+	0.522850i	$0.824869\pi$
$740$	−8.41655	+	6.36224i	−0.309398	+	0.233881i
$741$		−	6.75612i		−	0.248192i
$742$		0			0
$743$	−11.2976			−0.414470			−0.207235	−	0.978291i	$-0.566446\pi$
$743$	−11.2976			−0.414470			−0.207235	+	0.978291i	$0.566446\pi$
$744$	−1.68830	−	0.529585i	−0.0618962	−	0.0194155i
$745$	−1.84726	−	12.0765i	−0.0676784	−	0.442448i
$746$	−16.8625	−	17.3432i	−0.617378	−	0.634979i
$747$	−10.5744	+	6.10515i	−0.386898	+	0.223376i
$748$	−26.2459	+	42.6448i	−0.959644	+	1.55925i
$749$		0			0
$750$	6.58679	−	1.19525i	0.240515	−	0.0436442i
$751$	−4.86553	+	2.80911i	−0.177546	+	0.102506i	−0.586139	−	0.810210i	$-0.699353\pi$
$751$	−4.86553	+	2.80911i	−0.177546	+	0.102506i	0.408593	+	0.912717i	$0.366019\pi$
$752$	2.74495	−	48.7808i	0.100098	−	1.77885i
$753$	7.74847	+	4.47358i	0.282370	+	0.163026i
$754$	−1.66879	−	6.59752i	−0.0607739	−	0.240267i
$755$	−2.09153	−	2.61097i	−0.0761187	−	0.0950228i
$756$		0			0
$757$			27.0456i			0.982990i	0.870880	+	0.491495i	$0.163549\pi$
$757$			27.0456i			0.982990i	−0.870880	+	0.491495i	$0.836451\pi$
$758$	−14.2261	+	3.59839i	−0.516716	+	0.130700i
$759$	−4.79944	+	8.31287i	−0.174208	+	0.301738i
$760$	24.7883	−	30.9201i	0.899167	−	1.12159i
$761$	−22.3558	+	12.9071i	−0.810396	+	0.467883i	−0.847094	−	0.531444i	$-0.821650\pi$
$761$	−22.3558	+	12.9071i	−0.810396	+	0.467883i	0.0366971	+	0.999326i	$0.488316\pi$
$762$	−1.99274	+	7.03975i	−0.0721892	+	0.255023i
$763$		0			0
$764$	−18.7076	+	30.3965i	−0.676818	+	1.09971i
$765$	30.0536	+	11.7194i	1.08659	+	0.423715i
$766$	−9.10707	−	9.36669i	−0.329052	−	0.338432i
$767$	7.24519	−	12.5490i	0.261609	−	0.453119i
$768$	0.759979	−	6.73144i	0.0274234	−	0.242900i
$769$			5.58909i			0.201548i	0.994909	+	0.100774i	$0.0321319\pi$
$769$			5.58909i			0.201548i	−0.994909	+	0.100774i	$0.967868\pi$
$770$		0			0
$771$		−	10.8608i		−	0.391140i
$772$	36.4517	+	1.02478i	1.31193	+	0.0368826i
$773$	−4.38608	+	7.59692i	−0.157756	+	0.273242i	−0.934059	−	0.357118i	$-0.883759\pi$
$773$	−4.38608	+	7.59692i	−0.157756	+	0.273242i	0.776303	+	0.630360i	$0.217093\pi$
$774$	30.8290	−	29.9745i	1.10813	−	1.07741i
$775$	7.05000	−	2.20846i	0.253244	−	0.0793301i
$776$	−6.55196	−	7.12908i	−0.235202	−	0.255919i
$777$		0			0
$778$	−23.2474	−	6.58062i	−0.833459	−	0.235927i
$779$	38.2783	−	22.1000i	1.37146	−	0.791814i
$780$	4.44145	+	1.87739i	0.159029	+	0.0672212i
$781$	35.0789	−	60.7584i	1.25522	−	2.17411i
$782$	8.21372	+	32.4726i	0.293722	+	1.16122i
$783$			4.65674i			0.166418i
$784$		0			0
$785$	39.9706	−	32.0187i	1.42661	−	1.14280i
$786$	5.71807	−	1.44634i	0.203957	−	0.0515894i
$787$	−8.56726	−	4.94631i	−0.305390	−	0.176317i	0.339472	−	0.940616i	$-0.389752\pi$
$787$	−8.56726	−	4.94631i	−0.305390	−	0.176317i	−0.644862	+	0.764299i	$0.723085\pi$
$788$	−10.7997	−	19.9822i	−0.384722	−	0.711835i
$789$	−3.67389	+	2.12112i	−0.130794	+	0.0755140i
$790$	5.70728	+	13.5166i	0.203056	+	0.480898i
$791$		0			0
$792$	−28.7574	+	26.4294i	−1.02185	+	0.939129i
$793$	−8.53522	+	4.92781i	−0.303094	+	0.174992i
$794$	−34.0044	+	33.0619i	−1.20677	+	1.17332i
$795$	−0.320111	−	2.09273i	−0.0113532	−	0.0742215i
$796$	0.507430	−	18.0494i	0.0179854	−	0.639746i
$797$	−31.5699			−1.11826			−0.559132	−	0.829079i	$-0.688865\pi$
$797$	−31.5699			−1.11826			−0.559132	+	0.829079i	$0.688865\pi$
$798$		0			0
$799$		−	62.4685i		−	2.20998i
$800$	13.4386	+	24.8878i	0.475127	+	0.879917i
$801$	−5.33158	−	3.07819i	−0.188382	−	0.108762i
$802$	−13.0076	+	12.6470i	−0.459313	+	0.446582i
$803$	33.3739	−	19.2684i	1.17774	−	0.679968i
$804$	−0.394702	+	0.641319i	−0.0139200	+	0.0226176i
$805$		0			0
$806$	5.12025	+	1.44938i	0.180353	+	0.0510524i
$807$	−2.89903	−	5.02128i	−0.102051	−	0.176757i
$808$	4.50296	+	20.1708i	0.158414	+	0.709605i
$809$	−15.3882	+	26.6532i	−0.541021	+	0.937076i	0.457824	+	0.889043i	$0.348629\pi$
$809$	−15.3882	+	26.6532i	−0.541021	+	0.937076i	−0.998846	+	0.0480338i	$0.984704\pi$
$810$	18.7095	+	14.1542i	0.657386	+	0.497329i
$811$	−19.0962			−0.670557			−0.335278	−	0.942119i	$-0.608830\pi$
$811$	−19.0962			−0.670557			−0.335278	+	0.942119i	$0.608830\pi$
$812$		0			0
$813$			6.50362i			0.228092i
$814$	−4.00528	−	15.8347i	−0.140385	−	0.555007i
$815$	−0.652714	−	4.26712i	−0.0228636	−	0.149471i
$816$	0.486613	−	8.64764i	0.0170349	−	0.302728i
$817$	−33.7706	−	58.4924i	−1.18148	−	2.04639i
$818$	−8.31894	+	29.3884i	−0.290865	+	1.02754i
$819$		0			0
$820$	3.89171	+	31.3052i	0.135905	+	1.09322i
$821$	−24.0855	−	41.7174i	−0.840591	−	1.45595i	−0.889396	−	0.457137i	$-0.848875\pi$
$821$	−24.0855	−	41.7174i	−0.840591	−	1.45595i	0.0488054	−	0.998808i	$-0.484459\pi$
$822$	−2.01548	+	1.95961i	−0.0702978	+	0.0683493i
$823$	−4.76754	+	8.25762i	−0.166186	+	0.287843i	−0.937076	−	0.349126i	$-0.886479\pi$
$823$	−4.76754	+	8.25762i	−0.166186	+	0.287843i	0.770890	+	0.636969i	$0.219812\pi$
$824$	18.2186	+	5.71480i	0.634677	+	0.199085i
$825$	−2.26188	+	10.1137i	−0.0787485	+	0.352113i
$826$		0			0
$827$	0.650873			0.0226331			0.0113165	−	0.999936i	$-0.496398\pi$
$827$	0.650873			0.0226331			0.0113165	+	0.999936i	$0.496398\pi$
$828$	−0.734206	+	26.1159i	−0.0255154	+	0.907591i
$829$	−40.5282	−	23.3989i	−1.40760	−	0.812679i	−0.412445	−	0.910983i	$-0.635325\pi$
$829$	−40.5282	−	23.3989i	−1.40760	−	0.812679i	−0.995156	+	0.0983034i	$0.968658\pi$
$830$	−13.5835	−	1.69395i	−0.471491	−	0.0587977i
$831$	−3.77005	−	6.52991i	−0.130781	−	0.226520i
$832$	−1.71578	+	20.3008i	−0.0594841	+	0.703802i
$833$		0			0
$834$	2.26269	−	7.99342i	0.0783505	−	0.276789i
$835$	13.7841	−	35.3484i	0.477018	−	1.22328i
$836$	29.1701	+	53.9723i	1.00887	+	1.86667i
$837$	−3.15351	−	1.82068i	−0.109001	−	0.0629318i
$838$	6.49479	+	25.6769i	0.224359	+	0.886994i
$839$	−50.2124			−1.73353			−0.866763	−	0.498720i	$-0.833803\pi$
$839$	−50.2124			−1.73353			−0.866763	+	0.498720i	$0.833803\pi$
$840$		0			0
$841$	−25.4295			−0.876879
$842$	−6.57746	−	26.0037i	−0.226674	−	0.896148i
$843$	10.8595	+	6.26972i	0.374020	+	0.215941i
$844$	−4.18565	−	7.74454i	−0.144076	−	0.266578i
$845$	13.5718	+	5.29230i	0.466883	+	0.182061i
$846$	13.2712	−	46.8831i	0.456272	−	1.61187i
$847$		0			0
$848$	7.98548	−	4.03014i	0.274223	−	0.138395i
$849$	0.757499	+	1.31203i	0.0259973	+	0.0450286i
$850$	18.9429	+	30.8053i	0.649736	+	1.05661i
$851$	−9.46191	−	5.46284i	−0.324350	−	0.187264i
$852$	−0.341026	+	12.1304i	−0.0116833	+	0.415580i
$853$	−12.0132			−0.411323			−0.205661	−	0.978623i	$-0.565935\pi$
$853$	−12.0132			−0.411323			−0.205661	+	0.978623i	$0.565935\pi$
$854$		0			0
$855$	30.8456	−	24.7091i	1.05490	−	0.845034i
$856$	−8.32150	+	26.5287i	−0.284423	+	0.906734i
$857$	−13.5132	+	23.4056i	−0.461603	+	0.799519i	−0.999041	−	0.0437838i	$-0.986059\pi$
$857$	−13.5132	+	23.4056i	−0.461603	+	0.799519i	0.537438	+	0.843303i	$0.319392\pi$
$858$	−5.35208	+	5.20373i	−0.182717	+	0.177652i
$859$	10.2882	+	17.8197i	0.351030	+	0.608002i	0.986430	−	0.164181i	$-0.0524982\pi$
$859$	10.2882	+	17.8197i	0.351030	+	0.608002i	−0.635400	+	0.772183i	$0.719165\pi$
$860$	47.8369	−	5.94686i	1.63122	−	0.202786i
$861$		0			0
$862$	10.4093	−	36.7731i	0.354543	−	1.25250i
$863$	4.73195	+	8.19598i	0.161078	+	0.278994i	0.935255	−	0.353974i	$-0.115170\pi$
$863$	4.73195	+	8.19598i	0.161078	+	0.278994i	−0.774178	+	0.632968i	$0.781836\pi$
$864$	4.54468	−	13.1794i	0.154613	−	0.448371i
$865$	−3.39332	−	22.1839i	−0.115376	−	0.754274i
$866$	−5.20243	−	20.5676i	−0.176786	−	0.698916i
$867$		−	3.87654i		−	0.131654i
$868$		0			0
$869$	−22.7139			−0.770515
$870$	−1.52635	+	2.01758i	−0.0517482	+	0.0684024i
$871$	1.13238	−	1.96133i	0.0383691	−	0.0664573i
$872$	−25.9822	+	5.80031i	−0.879868	+	0.196423i
$873$	−4.82813	−	8.36256i	−0.163407	−	0.283030i
$874$	39.4868	+	11.1775i	1.33566	+	0.378084i
$875$		0			0
$876$	−3.49377	+	5.67674i	−0.118043	+	0.191799i
$877$	17.5315	−	10.1218i	0.591996	−	0.341789i	−0.173890	−	0.984765i	$-0.555634\pi$
$877$	17.5315	−	10.1218i	0.591996	−	0.341789i	0.765886	+	0.642976i	$0.222300\pi$
$878$	−18.6953	+	18.1771i	−0.630934	+	0.613446i
$879$	6.51705	+	3.76262i	0.219815	+	0.126910i
$880$	−43.5870	+	4.17855i	−1.46932	+	0.140859i
$881$		−	58.2514i		−	1.96254i	−0.192638	−	0.981270i	$-0.561704\pi$
$881$		−	58.2514i		−	1.96254i	0.192638	−	0.981270i	$-0.438296\pi$
$882$		0			0
$883$	39.7551			1.33786			0.668932	−	0.743323i	$-0.266752\pi$
$883$	39.7551			1.33786			0.668932	+	0.743323i	$0.266752\pi$
$884$	−0.732022	+	26.0383i	−0.0246206	+	0.875761i
$885$	−5.32492	+	0.814518i	−0.178995	+	0.0273797i
$886$	−21.1506	+	20.5644i	−0.710569	+	0.690873i
$887$	39.2114	−	22.6387i	1.31659	−	0.760134i	0.333412	−	0.942781i	$-0.391800\pi$
$887$	39.2114	−	22.6387i	1.31659	−	0.760134i	0.983178	+	0.182648i	$0.0584667\pi$
$888$	1.91174	+	2.08014i	0.0641539	+	0.0698048i
$889$		0			0
$890$	−2.68472	−	6.35823i	−0.0899919	−	0.213128i
$891$	−31.4531	+	18.1595i	−1.05372	+	0.608365i
$892$	13.4180	+	24.8267i	0.449266	+	0.831260i
$893$	−66.2822	−	38.2681i	−2.21805	−	1.28059i
$894$	−3.17150	+	0.802208i	−0.106071	+	0.0268299i
$895$	−4.96680	−	6.20030i	−0.166022	−	0.207253i
$896$		0			0
$897$			4.99333i			0.166722i
$898$	5.07994	+	20.0834i	0.169520	+	0.670191i
$899$	−1.39598	+	2.41792i	−0.0465587	+	0.0806420i
$900$	7.67234	+	27.1440i	0.255745	+	0.904798i
$901$	9.90440	−	5.71831i	0.329963	−	0.190504i
$902$	−46.9901	−	13.3015i	−1.56460	−	0.442890i
$903$		0			0
$904$	−33.1664	+	30.4815i	−1.10310	+	1.01380i
$905$	18.0928	−	46.3978i	0.601425	−	1.54232i
$906$	−0.642272	+	0.624469i	−0.0213381	+	0.0207466i
$907$	−25.2789	+	43.7844i	−0.839373	+	1.45384i	0.0510468	+	0.998696i	$0.483744\pi$
$907$	−25.2789	+	43.7844i	−0.839373	+	1.45384i	−0.890420	+	0.455140i	$0.849589\pi$
$908$	−21.9865	−	0.618114i	−0.729648	−	0.0205128i
$909$			20.6111i			0.683627i
$910$		0			0
$911$			0.524910i			0.0173910i	0.999962	+	0.00869552i	$0.00276790\pi$
$911$			0.524910i			0.0173910i	−0.999962	+	0.00869552i	$0.997232\pi$
$912$	−8.87748	−	5.81384i	−0.293963	−	0.192516i
$913$	10.5957	−	18.3524i	0.350668	−	0.607374i
$914$	−1.17317	−	1.20661i	−0.0388050	−	0.0399112i
$915$	3.41352	+	1.33110i	0.112847	+	0.0440048i
$916$	8.50089	−	13.8124i	0.280877	−	0.456375i
$917$		0			0
$918$	4.85481	−	17.1506i	0.160233	−	0.566055i
$919$	18.6304	−	10.7563i	0.614561	−	0.354817i	−0.160187	−	0.987087i	$-0.551210\pi$
$919$	18.6304	−	10.7563i	0.614561	−	0.354817i	0.774749	+	0.632269i	$0.217876\pi$
$920$	−18.3206	+	22.8525i	−0.604012	+	0.753424i
$921$	−6.96310	+	12.0604i	−0.229442	+	0.397405i
$922$	−19.9684	+	5.05087i	−0.657625	+	0.166341i
$923$		−	36.4960i		−	1.20128i
$924$		0			0
$925$	−11.5116	−	2.57453i	−0.378500	−	0.0846499i
$926$	−1.62782	−	6.43552i	−0.0534934	−	0.211484i
$927$	16.4909	+	9.52103i	0.541632	+	0.312711i
$928$	−10.1051	−	3.48458i	−0.331717	−	0.114387i
$929$	−13.5117	+	7.80096i	−0.443303	+	0.255941i	−0.704998	−	0.709210i	$-0.749052\pi$
$929$	−13.5117	+	7.80096i	−0.443303	+	0.255941i	0.261695	+	0.965151i	$0.415719\pi$
$930$	−0.769522	−	1.82246i	−0.0252336	−	0.0597609i
$931$		0			0
$932$	−16.6406	+	27.0380i	−0.545081	+	0.885658i
$933$	7.28740	−	4.20738i	0.238579	−	0.137743i
$934$	24.9241	+	25.6346i	0.815541	+	0.838791i
$935$	−55.3409	+	8.46514i	−1.80984	+	0.276840i
$936$	−6.08110	+	19.3864i	−0.198767	+	0.633664i
$937$	−7.15521			−0.233751			−0.116875	−	0.993147i	$-0.537288\pi$
$937$	−7.15521			−0.233751			−0.116875	+	0.993147i	$0.537288\pi$
$938$		0			0
$939$		−	2.69759i		−	0.0880326i
$940$	43.5758	−	32.9398i	1.42128	−	1.07438i
$941$	6.17342	+	3.56423i	0.201248	+	0.116191i	0.597237	−	0.802065i	$-0.296265\pi$
$941$	6.17342	+	3.56423i	0.201248	+	0.116191i	−0.395990	+	0.918255i	$0.629598\pi$
$942$	−9.55983	−	9.83237i	−0.311476	−	0.320356i
$943$	−28.2908	+	16.3337i	−0.921275	+	0.531899i
$944$	−10.2546	−	20.3189i	−0.333760	−	0.661325i
$945$		0			0
$946$	−20.3257	+	71.8048i	−0.660846	+	2.33457i
$947$	11.5507	+	20.0064i	0.375348	+	0.650122i	0.990379	−	0.138381i	$-0.0441899\pi$
$947$	11.5507	+	20.0064i	0.375348	+	0.650122i	−0.615031	+	0.788503i	$0.710857\pi$
$948$	3.45631	−	1.86801i	0.112256	−	0.0606703i
$949$	10.0234	−	17.3611i	0.325374	−	0.563564i
$950$	44.2903	−	1.22810i	1.43697	−	0.0398448i
$951$	−7.19855			−0.233429
$952$		0			0
$953$		−	36.2840i		−	1.17535i	−0.809096	−	0.587677i	$-0.800043\pi$
$953$		−	36.2840i		−	1.17535i	0.809096	−	0.587677i	$-0.199957\pi$
$954$	8.64816	−	2.18749i	0.279994	−	0.0708226i
$955$	−39.4461	+	6.03381i	−1.27645	+	0.195250i
$956$	−23.2916	−	43.0954i	−0.753303	−	1.39381i
$957$	−1.95826	−	3.39181i	−0.0633017	−	0.109642i
$958$	5.58295	+	1.58036i	0.180377	+	0.0510592i
$959$		0			0
$960$	6.28887	−	4.22048i	0.202972	−	0.136215i
$961$	14.4084	+	24.9561i	0.464787	+	0.805035i
$962$	−5.92301	−	6.09187i	−0.190966	−	0.196410i
$963$	−13.8639	+	24.0129i	−0.446757	+	0.773805i
$964$	38.3572	+	1.07835i	1.23540	+	0.0347312i
$965$	25.4896	+	31.8199i	0.820539	+	1.02432i
$966$		0			0
$967$	41.0345			1.31958			0.659790	−	0.751450i	$-0.270645\pi$
$967$	41.0345			1.31958			0.659790	+	0.751450i	$0.270645\pi$
$968$	10.9764	−	34.9923i	0.352793	−	1.12470i
$969$	−11.7502	−	6.78399i	−0.377471	−	0.217933i
$970$	1.33962	−	10.7422i	0.0430126	−	0.344912i
$971$	−22.1241	−	38.3201i	−0.709997	−	1.22975i	−0.964858	−	0.262773i	$-0.915363\pi$
$971$	−22.1241	−	38.3201i	−0.709997	−	1.22975i	0.254860	−	0.966978i	$-0.417970\pi$
$972$	11.0429	−	17.9428i	0.354202	−	0.575514i
$973$		0			0
$974$	46.0089	+	13.0237i	1.47422	+	0.417306i
$975$	1.61157	+	5.14458i	0.0516116	+	0.164758i
$976$	−0.869712	+	15.4557i	−0.0278388	+	0.494726i
$977$	−9.99116	−	5.76840i	−0.319646	−	0.184547i	0.331589	−	0.943424i	$-0.392415\pi$
$977$	−9.99116	−	5.76840i	−0.319646	−	0.184547i	−0.651235	+	0.758876i	$0.725749\pi$
$978$	−1.12062	+	0.283453i	−0.0358336	+	0.00906384i
$979$	10.6846			0.341483
$980$		0			0
$981$	−26.5494			−0.847658
$982$	−35.5256	+	8.98595i	−1.13367	+	0.286753i
$983$	13.6399	+	7.87503i	0.435047	+	0.251174i	0.701494	−	0.712675i	$-0.252517\pi$
$983$	13.6399	+	7.87503i	0.435047	+	0.251174i	−0.266448	+	0.963849i	$0.585850\pi$
$984$	8.24430	−	1.84047i	0.262819	−	0.0586722i
$985$	9.22606	−	23.6597i	0.293967	−	0.753859i
$986$	−13.1501	−	3.72237i	−0.418783	−	0.118545i
$987$		0			0
$988$	27.1795	+	16.7277i	0.864694	+	0.532178i
$989$	24.9592	+	43.2307i	0.793658	+	1.37466i
$990$	−43.3322	−	5.40379i	−1.37719	−	0.171744i
$991$	2.35222	+	1.35806i	0.0747208	+	0.0431401i	0.536895	−	0.843649i	$-0.319597\pi$
$991$	2.35222	+	1.35806i	0.0747208	+	0.0431401i	−0.462174	+	0.886789i	$0.652930\pi$
$992$	6.31061	−	5.48073i	0.200362	−	0.174013i
$993$	−6.20742			−0.196986
$994$		0			0
$995$	15.7559	−	12.6214i	0.499497	−	0.400126i
$996$	−0.103008	+	3.66404i	−0.00326395	+	0.116100i
$997$	−4.48080	+	7.76097i	−0.141908	+	0.245792i	−0.928215	−	0.372044i	$-0.878657\pi$
$997$	−4.48080	+	7.76097i	−0.141908	+	0.245792i	0.786307	+	0.617836i	$0.211990\pi$
$998$	−23.9585	−	24.6415i	−0.758393	−	0.780013i
$999$	2.90704	+	5.03515i	0.0919748	+	0.159305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.g.619.30		96
4.3	odd	2	inner	980.2.s.g.619.11		96
5.4	even	2	inner	980.2.s.g.619.19		96
7.2	even	3	inner	980.2.s.g.19.37		96
7.3	odd	6		980.2.c.e.979.6	yes	48
7.4	even	3		980.2.c.e.979.5	✓	48
7.5	odd	6	inner	980.2.s.g.19.38		96
7.6	odd	2	inner	980.2.s.g.619.29		96
20.19	odd	2	inner	980.2.s.g.619.38		96
28.3	even	6		980.2.c.e.979.41	yes	48
28.11	odd	6		980.2.c.e.979.42	yes	48
28.19	even	6	inner	980.2.s.g.19.19		96
28.23	odd	6	inner	980.2.s.g.19.20		96
28.27	even	2	inner	980.2.s.g.619.12		96
35.4	even	6		980.2.c.e.979.44	yes	48
35.9	even	6	inner	980.2.s.g.19.12		96
35.19	odd	6	inner	980.2.s.g.19.11		96
35.24	odd	6		980.2.c.e.979.43	yes	48
35.34	odd	2	inner	980.2.s.g.619.20		96
140.19	even	6	inner	980.2.s.g.19.30		96
140.39	odd	6		980.2.c.e.979.7	yes	48
140.59	even	6		980.2.c.e.979.8	yes	48
140.79	odd	6	inner	980.2.s.g.19.29		96
140.139	even	2	inner	980.2.s.g.619.37		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.c.e.979.5	✓	48	7.4	even	3
980.2.c.e.979.6	yes	48	7.3	odd	6
980.2.c.e.979.7	yes	48	140.39	odd	6
980.2.c.e.979.8	yes	48	140.59	even	6
980.2.c.e.979.41	yes	48	28.3	even	6
980.2.c.e.979.42	yes	48	28.11	odd	6
980.2.c.e.979.43	yes	48	35.24	odd	6
980.2.c.e.979.44	yes	48	35.4	even	6
980.2.s.g.19.11		96	35.19	odd	6	inner
980.2.s.g.19.12		96	35.9	even	6	inner
980.2.s.g.19.19		96	28.19	even	6	inner
980.2.s.g.19.20		96	28.23	odd	6	inner
980.2.s.g.19.29		96	140.79	odd	6	inner
980.2.s.g.19.30		96	140.19	even	6	inner
980.2.s.g.19.37		96	7.2	even	3	inner
980.2.s.g.19.38		96	7.5	odd	6	inner
980.2.s.g.619.11		96	4.3	odd	2	inner
980.2.s.g.619.12		96	28.27	even	2	inner
980.2.s.g.619.19		96	5.4	even	2	inner
980.2.s.g.619.20		96	35.34	odd	2	inner
980.2.s.g.619.29		96	7.6	odd	2	inner
980.2.s.g.619.30		96	1.1	even	1	trivial
980.2.s.g.619.37		96	140.139	even	2	inner
980.2.s.g.619.38		96	20.19	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.346793 + 1.37103i) q^{2} +(0.366665 + 0.211694i) q^{3} +(-1.75947 + 0.950931i) q^{4} +(-2.08328 - 0.812373i) q^{5} +(-0.163083 + 0.576124i) q^{6} +(-1.91393 - 2.08252i) q^{8} +(-1.41037 - 2.44283i) q^{9} +(0.391324 - 3.13797i) q^{10} +(4.23964 + 2.44776i) q^{11} +(-0.846442 - 0.0237963i) q^{12} +2.54664 q^{13} +(-0.591890 - 0.738886i) q^{15} +(2.19146 - 3.34627i) q^{16} +(2.55715 - 4.42911i) q^{17} +(2.86010 - 2.78083i) q^{18} +(-3.13300 - 5.42652i) q^{19} +(4.43797 - 0.551709i) q^{20} +(-1.88568 + 6.66155i) q^{22} +(2.31555 + 4.01064i) q^{23} +(-0.260915 - 1.16875i) q^{24} +(3.68010 + 3.38480i) q^{25} +(0.883158 + 3.49153i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(0.807775 - 1.06774i) q^{30} +(0.738782 - 1.27961i) q^{31} +(5.34783 + 1.84411i) q^{32} +(1.03635 + 1.79501i) q^{33} +(6.95926 + 1.96995i) q^{34} +(4.80447 + 2.95693i) q^{36} +(-2.04313 + 1.17960i) q^{37} +(6.35344 - 6.17733i) q^{38} +(0.933764 + 0.539109i) q^{39} +(2.29547 + 5.89329i) q^{40} +7.05393i q^{41} +10.7790 q^{43} +(-9.78716 - 0.275150i) q^{44} +(0.953704 + 6.23485i) q^{45} +(-4.69571 + 4.56556i) q^{46} +(10.5781 - 6.10725i) q^{47} +(1.51192 - 0.763038i) q^{48} +(-3.36444 + 6.21937i) q^{50} +(1.87523 - 1.08267i) q^{51} +(-4.48074 + 2.42168i) q^{52} +(1.93661 + 1.11810i) q^{53} +(3.37882 - 0.854648i) q^{54} +(-6.84386 - 8.54352i) q^{55} -2.65295i q^{57} +(-0.655292 - 2.59067i) q^{58} +(2.84500 - 4.92768i) q^{59} +(1.74404 + 0.737201i) q^{60} +(-3.35156 + 1.93502i) q^{61} +(2.01059 + 0.569136i) q^{62} +(-0.673743 + 7.97158i) q^{64} +(-5.30536 - 2.06882i) q^{65} +(-2.10162 + 2.04337i) q^{66} +(0.444655 - 0.770165i) q^{67} +(-0.287446 + 10.2245i) q^{68} +1.96075i q^{69} -14.3310i q^{71} +(-2.38789 + 7.61254i) q^{72} +(3.93594 - 6.81724i) q^{73} +(-2.32581 - 2.39212i) q^{74} +(0.632822 + 2.02014i) q^{75} +(10.6727 + 6.56853i) q^{76} +(-0.415314 + 1.46718i) q^{78} +(-4.01812 + 2.31987i) q^{79} +(-7.28384 + 5.19092i) q^{80} +(-3.70941 + 6.42488i) q^{81} +(-9.67118 + 2.44625i) q^{82} -4.32876i q^{83} +(-8.92534 + 7.14971i) q^{85} +(3.73808 + 14.7784i) q^{86} +(-0.692841 - 0.400012i) q^{87} +(-3.01688 - 13.5139i) q^{88} +(1.89013 - 1.09127i) q^{89} +(-8.21746 + 3.46977i) q^{90} +(-7.88798 - 4.85468i) q^{92} +(0.541770 - 0.312791i) q^{93} +(12.0416 + 12.3849i) q^{94} +(2.11856 + 13.8501i) q^{95} +(1.57047 + 1.80827i) q^{96} +3.42330 q^{97} -13.8090i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) \) 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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