LMFDB - Embedded newform 980.2.s.g.619.20

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			619.20
Character	$\chi$	$=$	980.619
Dual form			980.2.s.g.19.20

$q$-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} +(0.338104 - 2.21036i) q^{5} +(0.163083 - 0.576124i) q^{6} +(1.91393 + 2.08252i) q^{8} +(-1.41037 - 2.44283i) q^{9} +(-3.14773 + 0.302985i) 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} +(1.50701 + 4.21057i) q^{20} +(1.88568 - 6.66155i) q^{22} +(-2.31555 - 4.01064i) q^{23} +(0.260915 + 1.16875i) q^{24} +(-4.77137 - 1.49466i) q^{25} +(-0.883158 - 3.49153i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(-1.21830 - 0.555261i) 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} +(5.25021 - 3.52637i) q^{40} -7.05393i q^{41} -10.7790 q^{43} +(-9.78716 - 0.275150i) q^{44} +(-5.87639 + 2.29149i) q^{45} +(-4.69571 + 4.56556i) q^{46} +(10.5781 - 6.10725i) q^{47} +(1.51192 - 0.763038i) q^{48} +(-0.394553 + 7.06005i) 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} +(-0.338784 + 1.86289i) q^{60} +(3.35156 - 1.93502i) q^{61} +(2.01059 + 0.569136i) q^{62} +(-0.673743 + 7.97158i) q^{64} +(0.861029 - 5.62899i) 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} +(-1.43308 - 1.55811i) q^{75} +(-10.6727 - 6.56853i) q^{76} +(0.415314 - 1.46718i) q^{78} +(-4.01812 + 2.31987i) q^{79} +(-6.65551 - 5.97530i) 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} +(5.17961 + 7.26206i) q^{90} +(7.88798 + 4.85468i) q^{92} +(-0.541770 + 0.312791i) q^{93} +(-12.0416 - 12.3849i) q^{94} +(13.0538 - 5.09033i) 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
$5$	0.338104	−	2.21036i	0.151205	−	0.988502i
$5$	0.338104	−	2.21036i	0.151205	−	0.988502i
$6$	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
$10$	−3.14773	+	0.302985i	−0.995399	+	0.0958124i
$11$	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	$0.0886234\pi$
$19$	3.13300	+	5.42652i	0.718760	+	1.24493i	−0.242731	+	0.970094i	$0.578043\pi$
$20$	1.50701	+	4.21057i	0.336979	+	0.941512i
$21$		0			0
$22$	1.88568	−	6.66155i	0.402028	−	1.42025i
$23$	−2.31555	−	4.01064i	−0.482825	−	0.836277i	0.516981	−	0.855997i	$-0.327056\pi$
$23$	−2.31555	−	4.01064i	−0.482825	−	0.836277i	−0.999806	+	0.0197200i	$0.993723\pi$
$24$	0.260915	+	1.16875i	0.0532590	+	0.238571i
$25$	−4.77137	−	1.49466i	−0.954274	−	0.298932i
$26$	−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	$0.556136\pi$
$30$	−1.21830	−	0.555261i	−0.222430	−	0.101376i
$31$	−0.738782	+	1.27961i	−0.132689	+	0.229824i	−0.924712	−	0.380667i	$-0.875695\pi$
$31$	−0.738782	+	1.27961i	−0.132689	+	0.229824i	0.792023	+	0.610491i	$0.209028\pi$
$32$	−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	−0.322564	−	0.946548i	$-0.604545\pi$
$37$	2.04313	−	1.17960i	0.335888	−	0.193925i	0.658452	+	0.752623i	$0.271211\pi$
$38$	6.35344	−	6.17733i	1.03066	−	1.00210i
$39$	0.933764	+	0.539109i	0.149522	+	0.0863265i
$40$	5.25021	−	3.52637i	0.830132	−	0.557567i
$41$		−	7.05393i		−	1.10164i	−0.834624	−	0.550819i	$-0.814315\pi$
$41$		−	7.05393i		−	1.10164i	0.834624	−	0.550819i	$-0.185685\pi$
$42$		0			0
$43$	−10.7790			−1.64378			−0.821890	−	0.569646i	$-0.807080\pi$
$43$	−10.7790			−1.64378			−0.821890	+	0.569646i	$0.807080\pi$
$44$	−9.78716	−	0.275150i	−1.47547	−	0.0414804i
$45$	−5.87639	+	2.29149i	−0.876001	+	0.341596i
$46$	−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
$50$	−0.394553	+	7.06005i	−0.0557982	+	0.998442i
$51$	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	0.361061	−	0.932542i	$-0.382415\pi$
$53$	−1.93661	−	1.11810i	−0.266014	−	0.153583i	−0.627075	+	0.778959i	$0.715748\pi$
$54$	−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	−0.989625	−	0.143674i	$-0.954108\pi$
$59$	−2.84500	+	4.92768i	−0.370387	+	0.641529i	0.619238	+	0.785203i	$0.287442\pi$
$60$	−0.338784	+	1.86289i	−0.0437368	+	0.240499i
$61$	3.35156	−	1.93502i	0.429123	−	0.247754i	−0.269850	−	0.962902i	$-0.586974\pi$
$61$	3.35156	−	1.93502i	0.429123	−	0.247754i	0.698973	+	0.715148i	$0.253641\pi$
$62$	2.01059	+	0.569136i	0.255345	+	0.0722803i
$63$		0			0
$64$	−0.673743	+	7.97158i	−0.0842179	+	0.996447i
$65$	0.861029	−	5.62899i	0.106798	−	0.698190i
$66$	2.10162	−	2.04337i	0.258692	−	0.251521i
$67$	−0.444655	+	0.770165i	−0.0543232	+	0.0940906i	−0.891908	−	0.452216i	$-0.850633\pi$
$67$	−0.444655	+	0.770165i	−0.0543232	+	0.0940906i	0.837585	+	0.546307i	$0.183967\pi$
$68$	−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
$75$	−1.43308	−	1.55811i	−0.165478	−	0.179915i
$76$	−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	$0.417387\pi$
$80$	−6.65551	−	5.97530i	−0.744108	−	0.668059i
$81$	−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	−0.596820	−	0.802375i	$-0.703570\pi$
$89$	−1.89013	+	1.09127i	−0.200354	+	0.115674i	0.396467	+	0.918049i	$0.370236\pi$
$90$	5.17961	+	7.26206i	0.545979	+	0.765488i
$91$		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
$95$	13.0538	−	5.09033i	1.33930	−	0.522257i
$96$	−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
$100$	9.81640	−	1.90743i	0.981640	−	0.190743i
$101$	6.32803	+	3.65349i	0.629663	+	0.363536i	0.780621	−	0.625004i	$-0.214903\pi$
$101$	6.32803	+	3.65349i	0.629663	+	0.363536i	−0.150959	+	0.988540i	$0.548236\pi$
$102$	−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	0.999595	−	0.0284627i	$-0.00906119\pi$
$107$	4.91497	+	8.51298i	0.475148	+	0.822980i	−0.524447	+	0.851443i	$0.675728\pi$
$108$	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	$0.0178186\pi$
$110$	−14.0869	−	6.42032i	−1.34313	−	0.612154i
$111$	0.998857			0.0948073
$112$		0			0
$113$			15.9261i			1.49820i	0.662455	+	0.749102i	$0.269515\pi$
$113$			15.9261i			1.49820i	−0.662455	+	0.749102i	$0.730485\pi$
$114$	3.63729	−	0.920026i	0.340663	−	0.0861683i
$115$	−9.64786	+	3.76217i	−0.899667	+	0.350825i
$116$	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
$120$	2.67158	−	0.181555i	0.243881	−	0.0165736i
$121$	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	$-0.682385\pi$
$127$	−12.2192			−1.08428			−0.542138	+	0.840290i	$0.682385\pi$
$128$	11.1630	−	1.84076i	0.986675	−	0.162702i
$129$	−3.95227	−	2.28185i	−0.347978	−	0.200905i
$130$	−8.01614	+	0.771595i	−0.703062	+	0.0676734i
$131$	4.92530	+	8.53087i	0.430325	+	0.745345i	0.996901	−	0.0786642i	$-0.0250655\pi$
$131$	4.92530	+	8.53087i	0.430325	+	0.745345i	−0.566576	+	0.824010i	$0.691732\pi$
$132$	−3.53036	−	2.17277i	−0.307278	−	0.189115i
$133$		0			0
$134$	1.21013	+	0.342549i	0.104539	+	0.0295917i
$135$	−5.44728	−	0.833234i	−0.468827	−	0.0717134i
$136$	14.1179	−	3.15171i	1.21060	−	0.270256i
$137$	−4.06585	−	2.34742i	−0.347369	−	0.200554i	0.316157	−	0.948707i	$-0.397607\pi$
$137$	−4.06585	−	2.34742i	−0.347369	−	0.200554i	−0.663526	+	0.748153i	$0.730941\pi$
$138$	−2.68825	+	0.679974i	−0.228839	+	0.0578833i
$139$	13.8745			1.17682			0.588409	−	0.808564i	$-0.299755\pi$
$139$	13.8745			1.17682			0.588409	+	0.808564i	$0.299755\pi$
$140$		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
$145$	−0.638873	+	4.17664i	−0.0530555	+	0.346851i
$146$	−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	$0.761488\pi$
$150$	−1.63924	+	2.50515i	−0.133843	+	0.204544i
$151$	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
$160$	−5.88426	+	11.1971i	−0.465192	+	0.885210i
$161$		0			0
$162$	10.0951	+	2.85762i	0.793148	+	0.224516i
$163$	−0.965256	−	1.67187i	−0.0756047	−	0.130951i	0.825744	−	0.564045i	$-0.190755\pi$
$163$	−0.965256	−	1.67187i	−0.0756047	−	0.130951i	−0.901349	+	0.433093i	$0.857422\pi$
$164$	6.70780	+	12.4112i	0.523791	+	0.969150i
$165$	4.31801	−	1.68381i	0.336157	−	0.131084i
$166$	−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
$170$	−6.70725	+	14.7164i	−0.514423	+	1.12870i
$171$	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	$0.624278\pi$
$180$	8.16028	−	9.61986i	0.608231	−	0.717022i
$181$		−	22.2716i		−	1.65543i	−0.561148	−	0.827716i	$-0.689640\pi$
$181$		−	22.2716i		−	1.65543i	0.561148	−	0.827716i	$-0.310360\pi$
$182$		0			0
$183$	1.63853			0.121124
$184$	3.92044	−	12.4983i	0.289018	−	0.921383i
$185$	−1.91655	−	4.91487i	−0.140908	−	0.361348i
$186$	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
$190$	−11.5060	−	16.1320i	−0.834733	−	1.17034i
$191$	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	0.945589	−	0.325363i	$-0.105487\pi$
$193$	15.7903	+	9.11654i	1.13661	+	0.656223i	0.191022	+	0.981586i	$0.438820\pi$
$194$	−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	$-0.867420\pi$
$197$		−	11.3569i		−	0.809148i	0.914505	−	0.404574i	$-0.132580\pi$
$198$	−18.9326	+	4.78886i	−1.34548	+	0.340329i
$199$	4.51414	−	7.81873i	0.319999	−	0.554255i	−0.660488	−	0.750836i	$-0.729651\pi$
$199$	4.51414	−	7.81873i	0.319999	−	0.554255i	0.980487	+	0.196581i	$0.0629840\pi$
$200$	−6.01942	−	12.7971i	−0.425637	−	0.904894i
$201$	−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
$205$	−15.5917	−	2.38496i	−1.08897	−	0.166573i
$206$	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
$215$	−3.64442	+	23.8254i	−0.248547	+	1.62488i
$216$	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
$220$	−3.91725	+	21.5401i	−0.264101	+	1.45223i
$221$	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	−0.249674	−	0.968330i	$-0.580323\pi$
$229$	7.02292	−	4.05469i	0.464088	−	0.267941i	0.713762	+	0.700389i	$0.246990\pi$
$230$	8.50388	+	11.9228i	0.560729	+	0.786169i
$231$		0			0
$232$	−3.61652	−	3.93507i	−0.237436	−	0.258350i
$233$	−13.7475	+	7.93710i	−0.900626	+	0.519977i	−0.877403	−	0.479754i	$-0.840726\pi$
$233$	−13.7475	+	7.93710i	−0.900626	+	0.519977i	−0.0232229	+	0.999730i	$0.507393\pi$
$234$	−7.28366	+	7.08177i	−0.476147	+	0.462949i
$235$	−9.92273	−	25.4462i	−0.647287	−	1.65993i
$236$	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	$0.708949\pi$
$240$	−1.17540	−	3.59986i	−0.0758720	−	0.232370i
$241$	16.6157	+	9.59308i	1.07031	+	0.617945i	0.928267	−	0.371916i	$-0.121299\pi$
$241$	16.6157	+	9.59308i	1.07031	+	0.617945i	0.142045	+	0.989860i	$0.454632\pi$
$242$	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
$250$	15.4718	+	3.25913i	0.978526	+	0.206126i
$251$	−21.1323			−1.33386			−0.666929	−	0.745121i	$-0.732392\pi$
$251$	−21.1323			−1.33386			−0.666929	+	0.745121i	$0.732392\pi$
$252$		0			0
$253$		−	22.6716i		−	1.42535i
$254$	4.23752	+	16.7529i	0.265886	+	1.05117i
$255$	−1.75906	−	4.51099i	−0.110156	−	0.282489i
$256$	−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
$260$	3.83783	+	10.7228i	0.238012	+	0.665001i
$261$	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	−0.669204	−	0.743078i	$-0.733365\pi$
$263$	5.00988	−	8.67737i	0.308922	−	0.535069i	0.978127	+	0.208009i	$0.0666983\pi$
$264$	−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	0.815893	−	0.578203i	$-0.196246\pi$
$269$	11.8597	+	6.84723i	0.723102	+	0.417483i	−0.0927916	+	0.995686i	$0.529579\pi$
$270$	0.746687	+	7.75737i	0.0454419	+	0.472098i
$271$	−7.68044	−	13.3029i	−0.466554	−	0.808095i	0.532716	−	0.846294i	$-0.321171\pi$
$271$	−7.68044	−	13.3029i	−0.466554	−	0.808095i	−0.999270	+	0.0381991i	$0.987838\pi$
$272$	−9.21708	−	18.2631i	−0.558868	−	1.10736i
$273$		0			0
$274$	−1.80838	+	6.38849i	−0.109249	+	0.385943i
$275$	−16.5703	−	18.0160i	−0.999228	−	1.08640i
$276$	1.86454	+	3.44988i	0.112232	+	0.207658i
$277$	15.4230	+	8.90447i	0.926678	+	0.535018i	0.885759	−	0.464145i	$-0.153638\pi$
$277$	15.4230	+	8.90447i	0.926678	+	0.535018i	0.0409188	+	0.999162i	$0.486972\pi$
$278$	−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
$285$	5.86398	+	0.896973i	0.347352	+	0.0531321i
$286$	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
$290$	5.94788	−	0.572514i	0.349271	−	0.0336192i
$291$	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
$300$	4.00312	+	1.37868i	0.231120	+	0.0795984i
$301$		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
$305$	−3.14392	−	8.06239i	−0.180020	−	0.461651i
$306$	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
$310$	1.93778	−	4.25170i	0.110059	−	0.241480i
$311$	−9.93741	+	17.2121i	−0.563499	+	0.976009i	0.433689	+	0.901063i	$0.357212\pi$
$311$	−9.93741	+	17.2121i	−0.563499	+	0.976009i	−0.997188	+	0.0749459i	$0.976122\pi$
$312$	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	−0.0258220	−	0.999667i	$-0.508220\pi$
$317$	14.7244	−	8.50113i	0.827004	−	0.477471i	0.852826	+	0.522196i	$0.174887\pi$
$318$	−0.959994	+	0.933385i	−0.0538338	+	0.0523416i
$319$	−8.01112	−	4.62522i	−0.448537	−	0.258963i
$320$	17.3923	+	4.18444i	0.972257	+	0.233917i
$321$			4.16188i			0.232293i
$322$		0			0
$323$	32.0462			1.78310
$324$	0.416971	−	14.8318i	0.0231650	−	0.823987i
$325$	−12.1510	−	3.80637i	−0.674015	−	0.211139i
$326$	−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
$330$	−3.80601	−	5.33621i	−0.209514	−	0.293749i
$331$	−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	$0.136283\pi$
$337$			15.2435i			0.830368i	−0.909738	+	0.415184i	$0.863717\pi$
$338$	2.25922	+	8.93176i	0.122886	+	0.485824i
$339$	−3.37147	+	5.83955i	−0.183113	+	0.317161i
$340$	22.5027	+	4.09232i	1.22038	+	0.221937i
$341$	−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
$345$	−4.33396	−	0.662937i	−0.233333	−	0.0356913i
$346$	10.1764	−	9.89429i	0.547085	−	0.531921i
$347$	−16.7097	+	28.9420i	−0.897024	+	1.55369i	−0.0657437	+	0.997837i	$0.520942\pi$
$347$	−16.7097	+	28.9420i	−0.897024	+	1.55369i	−0.831280	+	0.555854i	$0.812391\pi$
$348$	1.59942	+	0.0449649i	0.0857377	+	0.00241037i
$349$		−	16.1586i		−	0.864951i	−0.901646	−	0.432476i	$-0.857640\pi$
$349$		−	16.1586i		−	0.864951i	0.901646	−	0.432476i	$-0.142360\pi$
$350$		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
$355$	−31.6767	−	4.84538i	−1.68123	−	0.257166i
$356$	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	$0.187430\pi$
$360$	−16.0191	−	7.85192i	−0.844280	−	0.413833i
$361$	−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
$370$	−6.07381	+	4.33210i	−0.315762	+	0.225215i
$371$		0			0
$372$	0.655785	−	1.06553i	0.0340009	−	0.0552453i
$373$	14.8129	−	8.55225i	0.766985	−	0.442819i	−0.0648133	−	0.997897i	$-0.520645\pi$
$373$	14.8129	−	8.55225i	0.766985	−	0.442819i	0.831798	+	0.555079i	$0.187312\pi$
$374$	−24.6828	−	25.3864i	−1.27632	−	1.31270i
$375$	−3.92851	+	2.64082i	−0.202868	+	0.136372i
$376$	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	$0.914134\pi$
$380$	−18.1273	+	21.3696i	−0.929909	+	1.09624i
$381$	−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	$0.309248\pi$
$390$	−3.10258	−	1.41405i	−0.157105	−	0.0716033i
$391$	−23.6848			−1.19779
$392$		0			0
$393$			4.17063i			0.210380i
$394$	−15.5707	+	3.93851i	−0.784442	+	0.198419i
$395$	3.76919	+	9.66585i	0.189649	+	0.486342i
$396$	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
$400$	−15.4578	+	12.6908i	−0.772891	+	0.634539i
$401$	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	−0.0396649	−	0.999213i	$-0.512629\pi$
$409$	−18.7038	−	10.7986i	−0.924841	−	0.533957i	−0.885176	+	0.465256i	$0.845962\pi$
$410$	2.13724	+	22.2039i	0.105551	+	1.09657i
$411$	−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
$415$	−9.56811	−	1.46357i	−0.469680	−	0.0718438i
$416$	−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	$-0.651242\pi$
$419$	−18.7281			−0.914929			−0.457464	+	0.889228i	$0.651242\pi$
$420$		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
$425$	−18.8211	+	17.3109i	−0.912958	+	0.839700i
$426$	−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
$430$	33.9293	−	3.26588i	1.63622	−	0.157495i
$431$	−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	0.557690	−	0.830049i	$-0.311688\pi$
$439$	−9.21899	−	15.9678i	−0.439998	−	0.762099i	−0.997689	+	0.0679495i	$0.978354\pi$
$440$	30.8907	−	2.09927i	1.47266	−	0.100079i
$441$		0			0
$442$	−17.7227	−	5.01676i	−0.842985	−	0.238623i
$443$	−10.4298	−	18.0649i	−0.495533	−	0.858289i	0.504453	−	0.863439i	$-0.331694\pi$
$443$	−10.4298	−	18.0649i	−0.495533	−	0.858289i	−0.999987	+	0.00514984i	$0.998361\pi$
$444$	−1.75746	+	0.949844i	−0.0834052	+	0.0450776i
$445$	1.77304	+	4.54684i	0.0840499	+	0.215541i
$446$	−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	$0.387659\pi$
$450$	17.8030	−	8.99347i	0.839242	−	0.423956i
$451$	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	−0.475702	−	0.879606i	$-0.657806\pi$
$457$	1.03058	−	0.595004i	0.0482084	−	0.0278331i	0.523910	+	0.851773i	$0.324473\pi$
$458$	−7.99462	−	8.22253i	−0.373564	−	0.384214i
$459$	−10.9152	−	6.30192i	−0.509480	−	0.294148i
$460$	13.3975	−	15.7939i	0.624663	−	0.736393i
$461$		−	14.5645i		−	0.678336i	−0.940726	−	0.339168i	$-0.889854\pi$
$461$		−	14.5645i		−	0.678336i	0.940726	−	0.339168i	$-0.110146\pi$
$462$		0			0
$463$	4.69391			0.218145			0.109072	−	0.994034i	$-0.465212\pi$
$463$	4.69391			0.218145			0.109072	+	0.994034i	$0.465212\pi$
$464$	−4.14094	+	6.32303i	−0.192238	+	0.293539i
$465$	0.508206	+	1.30326i	0.0235675	+	0.0604374i
$466$	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
$470$	−31.4465	+	22.4290i	−1.45052	+	1.03457i
$471$	−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	−0.909079	−	0.416624i	$-0.863213\pi$
$479$	−2.05143	+	3.55318i	−0.0937322	+	0.162349i	0.815347	+	0.578973i	$0.196546\pi$
$480$	−4.52791	+	2.85993i	−0.206670	+	0.130537i
$481$	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
$485$	1.15743	−	7.56672i	0.0525562	−	0.343587i
$486$	10.3853	+	10.6813i	0.471085	+	0.484515i
$487$	−16.9058	+	29.2816i	−0.766073	+	1.32688i	0.173605	+	0.984815i	$0.444458\pi$
$487$	−16.9058	+	29.2816i	−0.766073	+	1.32688i	−0.939678	+	0.342062i	$0.888875\pi$
$488$	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
$495$	−30.5228	−	4.66887i	−1.37190	−	0.209850i
$496$	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	$0.516410\pi$
$500$	−0.897147	−	22.3427i	−0.0401217	−	0.999195i
$501$	−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	0.121218	−	0.992626i	$-0.461320\pi$
$509$	23.4965	−	13.5657i	1.04147	−	0.601290i	0.920248	+	0.391336i	$0.127987\pi$
$510$	−5.57469	+	3.97611i	−0.246851	+	0.176065i
$511$		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
$515$	5.48410	+	14.0636i	0.241658	+	0.619718i
$516$	9.12378	+	0.256500i	0.401652	+	0.0112918i
$517$	59.7962			2.62983
$518$		0			0
$519$			4.24926i			0.186522i
$520$	13.3704	−	8.98039i	0.586331	−	0.393816i
$521$	−14.9657	−	8.64045i	−0.655659	−	0.378545i	0.134962	−	0.990851i	$-0.456909\pi$
$521$	−14.9657	−	8.64045i	−0.655659	−	0.378545i	−0.790621	+	0.612306i	$0.790242\pi$
$522$	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
$530$	6.43470	+	2.93272i	0.279505	+	0.127389i
$531$	16.0500			0.696511
$532$		0			0
$533$		−	17.9638i		−	0.778100i
$534$	0.320458	+	1.26692i	0.0138676	+	0.0548249i
$535$	20.4785	−	7.98557i	0.885363	−	0.345247i
$536$	−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
$540$	10.3767	−	3.71394i	0.446541	−	0.159822i
$541$	−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	$-0.632785\pi$
$547$	−18.9519			−0.810323			−0.405161	+	0.914245i	$0.632785\pi$
$548$	9.38598	+	0.263871i	0.400949	+	0.0112720i
$549$	−9.45388	−	5.45820i	−0.403482	−	0.232950i
$550$	−18.9540	+	28.9663i	−0.808203	+	1.23513i
$551$	−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
$555$	0.337717	−	2.20783i	0.0143353	−	0.0937172i
$556$	−24.4117	+	13.1937i	−1.03529	+	0.559536i
$557$	22.0931	+	12.7555i	0.936116	+	0.540467i	0.888741	−	0.458411i	$-0.151581\pi$
$557$	22.0931	+	12.7555i	0.936116	+	0.540467i	0.0473751	+	0.998877i	$0.484914\pi$
$558$	−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
$565$	35.2025	+	5.38468i	1.48098	+	0.226535i
$566$	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	$0.945280\pi$
$570$	−0.803806	−	8.35078i	−0.0336677	−	0.349775i
$571$	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
$580$	−2.84762	−	7.95620i	−0.118241	−	0.330363i
$581$		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
$585$	−14.9651	+	5.83562i	−0.618729	+	0.241273i
$586$	−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
$590$	7.46227	−	16.3730i	0.307217	−	0.674066i
$591$	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	$0.557912\pi$
$600$	0.501969	−	5.96653i	0.0204928	−	0.243583i
$601$			22.1672i			0.904220i	0.891962	+	0.452110i	$0.149329\pi$
$601$			22.1672i			0.904220i	−0.891962	+	0.452110i	$0.850671\pi$
$602$		0			0
$603$	2.50851			0.102155
$604$	−2.99103	−	0.0840878i	−0.121703	−	0.00342149i
$605$	27.0119	−	10.5333i	1.09819	−	0.428238i
$606$	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
$610$	−9.96351	+	7.10640i	−0.403411	+	0.287730i
$611$	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	0.697167	−	0.716909i	$-0.254444\pi$
$613$	10.5198	+	6.07359i	0.424890	+	0.245310i	−0.272278	+	0.962219i	$0.587777\pi$
$614$	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	$0.103880\pi$
$617$			15.9265i			0.641175i	−0.947219	+	0.320588i	$0.896120\pi$
$618$	0.991196	+	3.91866i	0.0398717	+	0.157631i
$619$	1.94167	−	3.36308i	0.0780424	−	0.135173i	−0.824363	−	0.566062i	$-0.808466\pi$
$619$	1.94167	−	3.36308i	0.0780424	−	0.135173i	0.902405	+	0.430888i	$0.141800\pi$
$620$	−6.50123	−	1.18231i	−0.261096	−	0.0474825i
$621$	−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
$625$	20.5320	+	14.2632i	0.821279	+	0.570527i
$626$	−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
$635$	−4.13134	+	27.0087i	−0.163947	+	1.07181i
$636$	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
$640$	−0.294511	−	25.2965i	−0.0116416	−	0.999932i
$641$	−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
$650$	−1.00478	+	17.9794i	−0.0394109	+	0.705211i
$651$		0			0
$652$	3.28817	+	2.02372i	0.128775	+	0.0792549i
$653$	−24.4111	+	14.0937i	−0.955279	+	0.551531i	−0.894717	−	0.446634i	$-0.852623\pi$
$653$	−24.4111	+	14.0937i	−0.955279	+	0.551531i	−0.0605622	+	0.998164i	$0.519289\pi$
$654$	−3.92862	−	4.04062i	−0.153621	−	0.158001i
$655$	20.5215	−	8.00236i	0.801843	−	0.312678i
$656$	−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	$0.938922\pi$
$660$	−5.99623	+	7.06874i	−0.233403	+	0.275150i
$661$	0.707548	+	0.408503i	0.0275204	+	0.0158889i	0.513697	−	0.857972i	$-0.328276\pi$
$661$	0.707548	+	0.408503i	0.0275204	+	0.0158889i	−0.486177	+	0.873861i	$0.661609\pi$
$662$	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
$670$	1.16630	−	2.55899i	0.0450583	−	0.0988626i
$671$	18.9459			0.731397
$672$		0			0
$673$		−	9.43129i		−	0.363550i	−0.983340	−	0.181775i	$-0.941816\pi$
$673$		−	9.43129i		−	0.363550i	0.983340	−	0.181775i	$-0.0581842\pi$
$674$	20.8994	−	5.28635i	0.805015	−	0.203623i
$675$	−3.68349	+	11.7587i	−0.141778	+	0.452594i
$676$	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
$680$	−2.19309	−	32.2712i	−0.0841010	−	1.23754i
$681$	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	−0.628928	−	0.777464i	$-0.716506\pi$
$683$	9.37801	−	16.2432i	0.358840	−	0.621528i	0.987767	+	0.155935i	$0.0498392\pi$
$684$	−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
$690$	0.594078	+	6.17191i	0.0226162	+	0.234961i
$691$	−2.11063	−	3.65572i	−0.0802923	−	0.139070i	0.823083	−	0.567921i	$-0.192252\pi$
$691$	−2.11063	−	3.65572i	−0.0802923	−	0.139070i	−0.903375	+	0.428851i	$0.858919\pi$
$692$	−17.0945	−	10.5209i	−0.649836	−	0.399943i
$693$		0			0
$694$	45.4753	+	12.8727i	1.72622	+	0.488640i
$695$	4.69101	−	30.6676i	0.177940	−	1.16329i
$696$	−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
$705$	1.74849	−	11.4308i	0.0658521	−	0.430509i
$706$	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	$0.850892\pi$
$710$	4.34210	+	45.1102i	0.162956	+	1.69296i
$711$	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	$0.180025\pi$
$719$	23.7638	+	41.1601i	0.886240	+	1.53501i	0.0419549	+	0.999120i	$0.486641\pi$
$720$	−5.20994	+	24.6857i	−0.194163	+	0.919982i
$721$		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
$725$	9.01587	+	2.82428i	0.334841	+	0.104891i
$726$	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
$730$	−10.3237	+	22.6514i	−0.382099	+	0.838365i
$731$	−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	$0.824869\pi$
$740$	8.04581	+	6.82506i	0.295770	+	0.250894i
$741$			6.75612i			0.248192i
$742$		0			0
$743$	11.2976			0.414470			0.207235	−	0.978291i	$-0.433554\pi$
$743$	11.2976			0.414470			0.207235	+	0.978291i	$0.433554\pi$
$744$	−1.68830	−	0.529585i	−0.0618962	−	0.0194155i
$745$	11.3822	−	4.43847i	0.417011	−	0.162613i
$746$	−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
$750$	4.98304	+	4.47031i	0.181955	+	0.163233i
$751$	−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	$-0.836451\pi$
$757$		−	27.0456i		−	0.982990i	0.870880	−	0.491495i	$-0.163549\pi$
$758$	14.2261	−	3.59839i	0.516716	−	0.130700i
$759$	4.79944	−	8.31287i	0.174208	−	0.301738i
$760$	35.5848	+	17.4423i	1.29080	+	0.632698i
$761$	22.3558	−	12.9071i	0.810396	−	0.467883i	−0.0366971	−	0.999326i	$-0.511684\pi$
$761$	22.3558	−	12.9071i	0.810396	−	0.467883i	0.847094	+	0.531444i	$0.178350\pi$
$762$	−1.99274	+	7.03975i	−0.0721892	+	0.255023i
$763$		0			0
$764$	−18.7076	+	30.3965i	−0.676818	+	1.09971i
$765$	−4.87752	+	31.8869i	−0.176347	+	1.15287i
$766$	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	$-0.967868\pi$
$769$		−	5.58909i		−	0.201548i	0.994909	−	0.100774i	$-0.0321319\pi$
$770$		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
$775$	5.43758	−	5.00125i	0.195324	−	0.179650i
$776$	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
$780$	−0.862760	+	4.74412i	−0.0308918	+	0.169867i
$781$	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
$790$	11.9451	−	8.51974i	0.424987	−	0.303119i
$791$		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
$795$	−1.97241	+	0.769141i	−0.0699543	+	0.0272786i
$796$	−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
$800$	22.7602	+	16.7921i	0.804693	+	0.593691i
$801$	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	$0.984704\pi$
$810$	9.72957	−	21.3477i	0.341862	−	0.750081i
$811$	19.0962			0.670557			0.335278	−	0.942119i	$-0.391170\pi$
$811$	19.0962			0.670557			0.335278	+	0.942119i	$0.391170\pi$
$812$		0			0
$813$		−	6.50362i		−	0.228092i
$814$	−4.00528	−	15.8347i	−0.140385	−	0.555007i
$815$	−4.02180	+	1.56830i	−0.140877	+	0.0549350i
$816$	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
$820$	29.7011	−	10.6304i	1.03721	−	0.371229i
$821$	−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	−0.770890	−	0.636969i	$-0.780188\pi$
$823$	4.76754	−	8.25762i	0.166186	−	0.287843i	0.937076	+	0.349126i	$0.113521\pi$
$824$	−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	$-0.503602\pi$
$827$	−0.650873			−0.0226331			−0.0113165	+	0.999936i	$0.503602\pi$
$828$	0.734206	−	26.1159i	0.0255154	−	0.907591i
$829$	40.5282	+	23.3989i	1.40760	+	0.812679i	0.995156	−	0.0983034i	$-0.0313416\pi$
$829$	40.5282	+	23.3989i	1.40760	+	0.812679i	0.412445	+	0.910983i	$0.364675\pi$
$830$	1.31155	+	13.6258i	0.0455246	+	0.472957i
$831$	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
$835$	37.5046	+	5.73684i	1.29790	+	0.198531i
$836$	−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	$-0.166197\pi$
$839$	50.2124			1.73353			0.866763	+	0.498720i	$0.166197\pi$
$840$		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
$845$	−2.20262	+	14.3996i	−0.0757723	+	0.495363i
$846$	−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
$850$	30.2608	+	19.8011i	1.03794	+	0.679172i
$851$	−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	0.635400	−	0.772183i	$-0.280835\pi$
$859$	−10.2882	−	17.8197i	−0.351030	−	0.608002i	−0.986430	+	0.164181i	$0.947502\pi$
$860$	−16.2441	−	45.3857i	−0.553919	−	1.54764i
$861$		0			0
$862$	−10.4093	+	36.7731i	−0.354543	+	1.25250i
$863$	−4.73195	−	8.19598i	−0.161078	−	0.278994i	0.774178	−	0.632968i	$-0.218164\pi$
$863$	−4.73195	−	8.19598i	−0.161078	−	0.278994i	−0.935255	+	0.353974i	$0.884830\pi$
$864$	−4.54468	+	13.1794i	−0.154613	+	0.448371i
$865$	20.9085	−	8.15323i	0.710909	−	0.277218i
$866$	5.20243	+	20.5676i	0.176786	+	0.698916i
$867$		−	3.87654i		−	0.131654i
$868$		0			0
$869$	−22.7139			−0.770515
$870$	2.30207	+	1.04921i	0.0780476	+	0.0355715i
$871$	−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	−0.765886	−	0.642976i	$-0.777700\pi$
$877$	−17.5315	+	10.1218i	−0.591996	+	0.341789i	0.173890	+	0.984765i	$0.444366\pi$
$878$	−18.6953	+	18.1771i	−0.630934	+	0.613446i
$879$	6.51705	+	3.76262i	0.219815	+	0.126910i
$880$	−13.5908	−	41.6242i	−0.458147	−	1.40315i
$881$			58.2514i			1.96254i	0.192638	+	0.981270i	$0.438296\pi$
$881$			58.2514i			1.96254i	−0.192638	+	0.981270i	$0.561704\pi$
$882$		0			0
$883$	−39.7551			−1.33786			−0.668932	−	0.743323i	$-0.733248\pi$
$883$	−39.7551			−1.33786			−0.668932	+	0.743323i	$0.733248\pi$
$884$	−0.732022	+	26.0383i	−0.0246206	+	0.875761i
$885$	1.95707	+	5.01878i	0.0657861	+	0.168704i
$886$	−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
$890$	5.61899	−	4.00770i	0.188349	−	0.134339i
$891$	−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
$900$	−18.5043	−	21.2897i	−0.616810	−	0.709655i
$901$	−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
$905$	−49.2281	−	7.53010i	−1.63640	−	0.250309i
$906$	0.642272	−	0.624469i	0.0213381	−	0.0207466i
$907$	25.2789	−	43.7844i	0.839373	−	1.45384i	−0.0510468	−	0.998696i	$-0.516256\pi$
$907$	25.2789	−	43.7844i	0.839373	−	1.45384i	0.890420	−	0.455140i	$-0.150411\pi$
$908$	−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
$915$	0.553994	−	3.62174i	0.0183145	−	0.119731i
$916$	−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	$0.217876\pi$
$920$	−26.3001	−	12.8913i	−0.867089	−	0.425013i
$921$	−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	−0.261695	−	0.965151i	$-0.584281\pi$
$929$	13.5117	−	7.80096i	0.443303	−	0.255941i	0.704998	+	0.709210i	$0.250948\pi$
$930$	1.61058	−	1.14873i	0.0528129	−	0.0376684i
$931$		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
$935$	−20.3394	−	52.1592i	−0.665171	−	1.70579i
$936$	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
$940$	41.6563	+	35.3360i	1.35868	+	1.15253i
$941$	−6.17342	−	3.56423i	−0.201248	−	0.116191i	0.395990	−	0.918255i	$-0.370402\pi$
$941$	−6.17342	−	3.56423i	−0.201248	−	0.116191i	−0.597237	+	0.802065i	$0.703735\pi$
$942$	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	0.615031	−	0.788503i	$-0.289143\pi$
$947$	−11.5507	−	20.0064i	−0.375348	−	0.650122i	−0.990379	+	0.138381i	$0.955810\pi$
$948$	3.45631	−	1.86801i	0.112256	−	0.0606703i
$949$	10.0234	−	17.3611i	0.325374	−	0.563564i
$950$	−39.5477	+	19.9781i	−1.28310	+	0.648176i
$951$	7.19855			0.233429
$952$		0			0
$953$			36.2840i			1.17535i	0.809096	+	0.587677i	$0.199957\pi$
$953$			36.2840i			1.17535i	−0.809096	+	0.587677i	$0.800043\pi$
$954$	8.64816	−	2.18749i	0.279994	−	0.0708226i
$955$	−14.4976	−	37.1783i	−0.469132	−	1.20306i
$956$	−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
$960$	5.49131	+	5.21612i	0.177231	+	0.168350i
$961$	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	$-0.729355\pi$
$967$	−41.0345			−1.31958			−0.659790	+	0.751450i	$0.729355\pi$
$968$	−10.9764	+	34.9923i	−0.352793	+	1.12470i
$969$	11.7502	+	6.78399i	0.377471	+	0.217933i
$970$	−10.7756	+	1.03721i	−0.345984	+	0.0333028i
$971$	22.1241	+	38.3201i	0.709997	+	1.22975i	0.964858	+	0.262773i	$0.0846372\pi$
$971$	22.1241	+	38.3201i	0.709997	+	1.22975i	−0.254860	+	0.966978i	$0.582030\pi$
$972$	11.0429	−	17.9428i	0.354202	−	0.575514i
$973$		0			0
$974$	46.0089	+	13.0237i	1.47422	+	0.417306i
$975$	−3.64955	−	3.96795i	−0.116879	−	0.127076i
$976$	0.869712	−	15.4557i	0.0278388	−	0.494726i
$977$	9.99116	+	5.76840i	0.319646	+	0.184547i	0.651235	−	0.758876i	$-0.274251\pi$
$977$	9.99116	+	5.76840i	0.319646	+	0.184547i	−0.331589	+	0.943424i	$0.607585\pi$
$978$	−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
$985$	−25.1029	−	3.83982i	−0.799845	−	0.122347i
$986$	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
$990$	4.18392	+	43.4669i	0.132974	+	1.38147i
$991$	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.619.20		96
4.3	odd	2	inner	980.2.s.g.619.37		96
5.4	even	2	inner	980.2.s.g.619.29		96
7.2	even	3	inner	980.2.s.g.19.11		96
7.3	odd	6		980.2.c.e.979.44	yes	48
7.4	even	3		980.2.c.e.979.43	yes	48
7.5	odd	6	inner	980.2.s.g.19.12		96
7.6	odd	2	inner	980.2.s.g.619.19		96
20.19	odd	2	inner	980.2.s.g.619.12		96
28.3	even	6		980.2.c.e.979.7	yes	48
28.11	odd	6		980.2.c.e.979.8	yes	48
28.19	even	6	inner	980.2.s.g.19.29		96
28.23	odd	6	inner	980.2.s.g.19.30		96
28.27	even	2	inner	980.2.s.g.619.38		96
35.4	even	6		980.2.c.e.979.6	yes	48
35.9	even	6	inner	980.2.s.g.19.38		96
35.19	odd	6	inner	980.2.s.g.19.37		96
35.24	odd	6		980.2.c.e.979.5	✓	48
35.34	odd	2	inner	980.2.s.g.619.30		96
140.19	even	6	inner	980.2.s.g.19.20		96
140.39	odd	6		980.2.c.e.979.41	yes	48
140.59	even	6		980.2.c.e.979.42	yes	48
140.79	odd	6	inner	980.2.s.g.19.19		96
140.139	even	2	inner	980.2.s.g.619.11		96

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
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} +(0.338104 - 2.21036i) q^{5} +(0.163083 - 0.576124i) q^{6} +(1.91393 + 2.08252i) q^{8} +(-1.41037 - 2.44283i) q^{9} +(-3.14773 + 0.302985i) 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} +(1.50701 + 4.21057i) q^{20} +(1.88568 - 6.66155i) q^{22} +(-2.31555 - 4.01064i) q^{23} +(0.260915 + 1.16875i) q^{24} +(-4.77137 - 1.49466i) q^{25} +(-0.883158 - 3.49153i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(-1.21830 - 0.555261i) 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} +(5.25021 - 3.52637i) q^{40} -7.05393i q^{41} -10.7790 q^{43} +(-9.78716 - 0.275150i) q^{44} +(-5.87639 + 2.29149i) q^{45} +(-4.69571 + 4.56556i) q^{46} +(10.5781 - 6.10725i) q^{47} +(1.51192 - 0.763038i) q^{48} +(-0.394553 + 7.06005i) 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} +(-0.338784 + 1.86289i) q^{60} +(3.35156 - 1.93502i) q^{61} +(2.01059 + 0.569136i) q^{62} +(-0.673743 + 7.97158i) q^{64} +(0.861029 - 5.62899i) 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} +(-1.43308 - 1.55811i) q^{75} +(-10.6727 - 6.56853i) q^{76} +(0.415314 - 1.46718i) q^{78} +(-4.01812 + 2.31987i) q^{79} +(-6.65551 - 5.97530i) 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} +(5.17961 + 7.26206i) q^{90} +(7.88798 + 4.85468i) q^{92} +(-0.541770 + 0.312791i) q^{93} +(-12.0416 - 12.3849i) q^{94} +(13.0538 - 5.09033i) 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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