LMFDB - Embedded newform 980.2.s.g.619.38

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			619.38
Character	$\chi$	$=$	980.619
Dual form			980.2.s.g.19.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01395 + 0.985849i) q^{2} +(0.366665 + 0.211694i) q^{3} +(0.0562045 + 1.99921i) 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} +(-2.52190 + 1.90788i) q^{10} +(-4.23964 - 2.44776i) q^{11} +(-0.402613 + 0.744938i) q^{12} -2.54664 q^{13} +(-0.591890 + 0.738886i) q^{15} +(-3.99368 + 0.224729i) q^{16} +(-2.55715 + 4.42911i) q^{17} +(0.978214 - 3.86733i) 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} +(-1.14263 + 0.358418i) q^{24} +(-4.77137 - 1.49466i) q^{25} +(-2.58218 - 2.51060i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(-1.32858 + 0.165682i) q^{30} +(-0.738782 + 1.27961i) q^{31} +(-4.27096 - 3.70930i) 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} +(-2.17301 + 8.59091i) q^{38} +(-0.933764 - 0.539109i) q^{39} +(-3.95600 - 4.93458i) q^{40} +7.05393i q^{41} +10.7790 q^{43} +(4.65529 - 8.61350i) q^{44} +(5.87639 - 2.29149i) q^{45} +(-1.60603 + 6.34939i) 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} +(-0.143133 - 5.09127i) q^{52} +(-1.93661 - 1.11810i) q^{53} +(2.42956 - 2.49882i) q^{54} +(6.84386 - 8.54352i) q^{55} +2.65295i q^{57} +(-1.91594 - 1.86284i) q^{58} +(-2.84500 + 4.92768i) q^{59} +(-1.51046 - 1.14178i) 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} +(0.718799 - 2.84174i) q^{66} +(0.444655 - 0.770165i) q^{67} +(-8.99844 - 4.86334i) q^{68} +1.96075i q^{69} +14.3310i q^{71} +(7.78659 + 1.73829i) q^{72} +(-3.93594 + 6.81724i) q^{73} +(3.23454 + 0.818154i) 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} +(0.853547 - 8.90345i) q^{80} +(-3.70941 + 6.42488i) q^{81} +(-6.95411 + 7.15236i) q^{82} -4.32876i q^{83} +(-8.92534 - 7.14971i) q^{85} +(10.9294 + 10.6264i) q^{86} +(-0.692841 - 0.400012i) q^{87} +(13.2119 - 4.14428i) 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} +(16.7465 + 4.23590i) q^{94} +(-13.0538 + 5.09033i) q^{95} +(-0.780773 - 2.26421i) 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 $

$2$	1.01395	+	0.985849i	0.716974	+	0.697100i
$2$	1.01395	+	0.985849i	0.716974	+	0.697100i
$3$	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	$0.627665\pi$
$4$	0.0562045	+	1.99921i	0.0281022	+	0.999605i
$5$	−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
$10$	−2.52190	+	1.90788i	−0.797495	+	0.603325i
$11$	−4.23964	−	2.44776i	−1.27830	−	0.738026i	−0.301763	−	0.953383i	$-0.597575\pi$
$11$	−4.23964	−	2.44776i	−1.27830	−	0.738026i	−0.976535	+	0.215357i	$0.930909\pi$
$12$	−0.402613	+	0.744938i	−0.116224	+	0.215045i
$13$	−2.54664			−0.706311			−0.353156	−	0.935565i	$-0.614891\pi$
$13$	−2.54664			−0.706311			−0.353156	+	0.935565i	$0.614891\pi$
$14$		0			0
$15$	−0.591890	+	0.738886i	−0.152825	+	0.190780i
$16$	−3.99368	+	0.224729i	−0.998421	+	0.0561823i
$17$	−2.55715	+	4.42911i	−0.620199	+	1.07422i	0.369249	+	0.929330i	$0.379615\pi$
$17$	−2.55715	+	4.42911i	−0.620199	+	1.07422i	−0.989448	+	0.144886i	$0.953718\pi$
$18$	0.978214	−	3.86733i	0.230567	−	0.911539i
$19$	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	$0.578043\pi$
$20$	−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	$0.672944\pi$
$24$	−1.14263	+	0.358418i	−0.233238	+	0.0731617i
$25$	−4.77137	−	1.49466i	−0.954274	−	0.298932i
$26$	−2.58218	−	2.51060i	−0.506407	−	0.492370i
$27$		−	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	$0.556136\pi$
$30$	−1.32858	+	0.165682i	−0.242564	+	0.0302492i
$31$	−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	$0.209028\pi$
$32$	−4.27096	−	3.70930i	−0.755006	−	0.655718i
$33$	−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	$0.271211\pi$
$38$	−2.17301	+	8.59091i	−0.352509	+	1.39363i
$39$	−0.933764	−	0.539109i	−0.149522	−	0.0863265i
$40$	−3.95600	−	4.93458i	−0.625498	−	0.780225i
$41$			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	$0.192920\pi$
$44$	4.65529	−	8.61350i	0.701812	−	1.29853i
$45$	5.87639	−	2.29149i	0.876001	−	0.341596i
$46$	−1.60603	+	6.34939i	−0.236796	+	0.936166i
$47$	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
$52$	−0.143133	−	5.09127i	−0.0198489	−	0.706032i
$53$	−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	$0.715748\pi$
$54$	2.42956	−	2.49882i	0.330621	−	0.340046i
$55$	6.84386	−	8.54352i	0.922825	−	1.15201i
$56$		0			0
$57$			2.65295i			0.351392i
$58$	−1.91594	−	1.86284i	−0.251576	−	0.244602i
$59$	−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	$0.287442\pi$
$60$	−1.51046	−	1.14178i	−0.194999	−	0.147404i
$61$	−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
$65$	0.861029	−	5.62899i	0.106798	−	0.698190i
$66$	0.718799	−	2.84174i	0.0884780	−	0.349794i
$67$	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	$0.149367\pi$
$68$	−8.99844	−	4.86334i	−1.09122	−	0.589766i
$69$			1.96075i			0.236046i
$70$		0			0
$71$			14.3310i			1.70078i	0.526152	+	0.850391i	$0.323634\pi$
$71$			14.3310i			1.70078i	−0.526152	+	0.850391i	$0.676366\pi$
$72$	7.78659	+	1.73829i	0.917659	+	0.204860i
$73$	−3.93594	+	6.81724i	−0.460667	+	0.797898i	−0.998994	−	0.0448377i	$-0.985723\pi$
$73$	−3.93594	+	6.81724i	−0.460667	+	0.797898i	0.538328	+	0.842736i	$0.319056\pi$
$74$	3.23454	+	0.818154i	0.376008	+	0.0951085i
$75$	−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	−0.256632	−	0.966509i	$-0.582613\pi$
$79$	4.01812	−	2.31987i	0.452074	−	0.261005i	0.708706	+	0.705504i	$0.249279\pi$
$80$	0.853547	−	8.90345i	0.0954295	−	0.995436i
$81$	−3.70941	+	6.42488i	−0.412156	+	0.713876i
$82$	−6.95411	+	7.15236i	−0.767953	+	0.789846i
$83$		−	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
$86$	10.9294	+	10.6264i	1.17855	+	1.14588i
$87$	−0.692841	−	0.400012i	−0.0742804	−	0.0428858i
$88$	13.2119	−	4.14428i	1.40839	−	0.441782i
$89$	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
$94$	16.7465	+	4.23590i	1.72727	+	0.436900i
$95$	−13.0538	+	5.09033i	−1.33930	+	0.522257i
$96$	−0.780773	−	2.26421i	−0.0796873	−	0.231090i
$97$	−3.42330			−0.347584			−0.173792	−	0.984782i	$-0.555602\pi$
$97$	−3.42330			−0.347584			−0.173792	+	0.984782i	$0.555602\pi$
$98$		0			0
$99$			13.8090i			1.38785i
$100$	2.71997	−	9.62298i	0.271997	−	0.962298i
$101$	−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	$0.785097\pi$
$102$	−2.96874	−	0.750922i	−0.293949	−	0.0743524i
$103$	−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	$0.990939\pi$
$108$	4.92692	−	0.138512i	0.474093	−	0.0133283i
$109$	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	$0.0178186\pi$
$110$	15.3620	−	1.91573i	1.46471	−	0.182658i
$111$	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	$0.730485\pi$
$114$	−2.61541	+	2.68997i	−0.244956	+	0.251939i
$115$	−9.64786	+	3.76217i	−0.899667	+	0.350825i
$116$	−0.106203	−	3.77766i	−0.00986067	−	0.350747i
$117$	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
$122$	−5.30597	−	1.34211i	−0.480380	−	0.121509i
$123$	−1.49327	+	2.58643i	−0.134644	+	0.233210i
$124$	−2.59973	−	1.40506i	−0.233462	−	0.126178i
$125$	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	$0.317615\pi$
$128$	7.17563	−	8.74702i	0.634242	−	0.773135i
$129$	3.95227	+	2.28185i	0.347978	+	0.200905i
$130$	6.42238	−	4.85869i	0.563280	−	0.426135i
$131$	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
$136$	−4.32949	−	13.8023i	−0.371250	−	1.18354i
$137$	−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	$0.730941\pi$
$138$	−1.93300	+	1.98811i	−0.164548	+	0.169239i
$139$	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
$142$	−14.1282	+	14.5310i	−1.18562	+	1.21942i
$143$	10.7968	+	6.23356i	0.902877	+	0.521276i
$144$	6.18155	+	9.43895i	0.515129	+	0.786579i
$145$	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	$0.761488\pi$
$150$	0.0829814	−	2.99266i	0.00677540	−	0.244349i
$151$	−1.29567	−	0.748053i	−0.105440	−	0.0608757i	0.446353	−	0.894857i	$-0.352723\pi$
$151$	−1.29567	−	0.748053i	−0.105440	−	0.0608757i	−0.551793	+	0.833981i	$0.686056\pi$
$152$	−17.2972	−	3.86145i	−1.40299	−	0.313205i
$153$	14.4261			1.16628
$154$		0			0
$155$	−2.57861	−	2.06561i	−0.207119	−	0.165914i
$156$	1.02531	−	1.89709i	0.0820905	−	0.151889i
$157$	11.4517	−	19.8350i	0.913948	−	1.58300i	0.105515	−	0.994418i	$-0.466351\pi$
$157$	11.4517	−	19.8350i	0.913948	−	1.58300i	0.808434	−	0.588587i	$-0.200316\pi$
$158$	6.36123	+	1.60903i	0.506072	+	0.128007i
$159$	−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	$0.809245\pi$
$164$	−14.1023	+	0.396462i	−1.10120	+	0.0309585i
$165$	4.31801	−	1.68381i	0.336157	−	0.131084i
$166$	4.26750	−	4.38916i	0.331222	−	0.340665i
$167$			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
$170$	−2.00135	−	16.0485i	−0.153496	−	1.23086i
$171$	8.83740	−	15.3068i	0.675813	−	1.17054i
$172$	0.605827	+	21.5495i	0.0461939	+	1.64313i
$173$	−5.01816	−	8.69171i	−0.381524	−	0.660818i	0.609757	−	0.792589i	$-0.291267\pi$
$173$	−5.01816	−	8.69171i	−0.381524	−	0.660818i	−0.991280	+	0.131770i	$0.957934\pi$
$174$	−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
$178$	2.99233	+	0.756890i	0.224285	+	0.0567313i
$179$	−3.07683	−	1.77641i	−0.229973	−	0.132775i	0.380586	−	0.924745i	$-0.375722\pi$
$179$	−3.07683	−	1.77641i	−0.229973	−	0.132775i	−0.610560	+	0.791970i	$0.709056\pi$
$180$	4.91146	+	11.6194i	0.366079	+	0.866055i
$181$			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
$184$	−12.7840	−	2.85393i	−0.942451	−	0.210395i
$185$	1.91655	+	4.91487i	0.140908	+	0.361348i
$186$	−0.857695	−	0.216948i	−0.0628893	−	0.0159074i
$187$	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	−0.940965	−	0.338505i	$-0.890079\pi$
$191$	−15.4551	+	8.92302i	−1.11829	+	0.645647i	−0.177328	+	0.984152i	$0.556746\pi$
$192$	1.44050	−	3.06552i	0.103959	−	0.221235i
$193$	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	$0.438820\pi$
$194$	−3.47107	−	3.37486i	−0.249208	−	0.242301i
$195$	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	$-0.132580\pi$
$198$	−13.6136	+	14.0017i	−0.967474	+	0.995055i
$199$	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	$0.0629840\pi$
$200$	12.2447	−	7.07578i	0.865833	−	0.500333i
$201$	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
$206$	−9.25547	−	2.34110i	−0.644859	−	0.163112i
$207$	6.53156	−	11.3130i	0.453975	−	0.786307i
$208$	10.1705	−	0.572304i	0.705196	−	0.0396822i
$209$		−	30.6753i		−	2.12186i
$210$		0			0
$211$		−	4.40164i		−	0.303021i	−0.988456	−	0.151511i	$-0.951586\pi$
$211$		−	4.40164i		−	0.303021i	0.988456	−	0.151511i	$-0.0484138\pi$
$212$	2.12648	−	3.93454i	0.146047	−	0.270225i
$213$	−3.03379	+	5.25469i	−0.207872	+	0.360045i
$214$	3.40896	−	13.4772i	0.233031	−	0.921281i
$215$	−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
$220$	17.4650	+	13.2021i	1.17749	+	0.890087i
$221$	6.51214	−	11.2794i	0.438054	−	0.758731i
$222$	1.01279	+	0.984722i	0.0679743	+	0.0660902i
$223$		−	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
$226$	−15.7008	+	16.1484i	−1.04440	+	1.07417i
$227$	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	$0.547747\pi$
$228$	−5.30381	+	0.149108i	−0.351253	+	0.00987490i
$229$	−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	−0.877403	−	0.479754i	$-0.840726\pi$
$233$	−13.7475	+	7.93710i	−0.900626	+	0.519977i	−0.0232229	+	0.999730i	$0.507393\pi$
$234$	−2.49116	+	9.84871i	−0.162852	+	0.643831i
$235$	9.92273	+	25.4462i	0.647287	+	1.65993i
$236$	−10.0114	−	5.41079i	−0.651685	−	0.352213i
$237$	1.96441			0.127602
$238$		0			0
$239$		−	24.4934i		−	1.58435i	−0.610295	−	0.792174i	$-0.708949\pi$
$239$		−	24.4934i		−	1.58435i	0.610295	−	0.792174i	$-0.291051\pi$
$240$	2.19777	−	3.08389i	0.141866	−	0.199064i
$241$	−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	$0.878701\pi$
$242$	−4.49653	+	17.7769i	−0.289048	+	1.14274i
$243$	−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
$248$	−1.25083	−	3.98760i	−0.0794275	−	0.253213i
$249$	0.916372	−	1.58720i	0.0580727	−	0.100585i
$250$	14.8846	−	5.33383i	0.941383	−	0.337341i
$251$	−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
$254$	12.3897	+	12.0462i	0.777397	+	0.755848i
$255$	−1.75906	−	4.51099i	−0.110156	−	0.282489i
$256$	15.8990	−	1.79499i	0.993687	−	0.112187i
$257$	12.8260	+	22.2153i	0.800064	+	1.38575i	0.919573	+	0.392918i	$0.128534\pi$
$257$	12.8260	+	22.2153i	0.800064	+	1.38575i	−0.119509	+	0.992833i	$0.538132\pi$
$258$	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
$262$	−3.41612	+	13.5055i	−0.211049	+	0.834373i
$263$	−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	$0.266635\pi$
$264$	5.72164	+	1.27731i	0.352143	+	0.0786130i
$265$	3.12619	−	3.90257i	0.192040	−	0.239733i
$266$		0			0
$267$	0.924061			0.0565516
$268$	1.56471	+	0.845672i	0.0955801	+	0.0516576i
$269$	−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	$0.803754\pi$
$270$	4.70185	+	6.21506i	0.286145	+	0.378236i
$271$	−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
$276$	−3.91995	+	0.110203i	−0.235953	+	0.00663343i
$277$	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	$0.486972\pi$
$278$	14.0681	+	13.6781i	0.843747	+	0.820360i
$279$	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	$0.155250\pi$
$282$	5.24363	+	5.09829i	0.312254	+	0.303599i
$283$	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	$0.632749\pi$
$284$	−28.6508	+	0.805468i	−1.70011	+	0.0477957i
$285$	−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
$290$	4.76533	−	3.60509i	0.279830	−	0.211698i
$291$	−1.25520	−	0.724692i	−0.0735814	−	0.0424822i
$292$	−13.8503	−	7.48560i	−0.810528	−	0.438062i
$293$	−17.7739			−1.03836			−0.519180	−	0.854665i	$-0.673763\pi$
$293$	−17.7739			−1.03836			−0.519180	+	0.854665i	$0.673763\pi$
$294$		0			0
$295$	−9.93004	−	7.95453i	−0.578149	−	0.463131i
$296$	−1.45387	+	6.51252i	−0.0845043	+	0.378532i
$297$	−6.03233	+	10.4483i	−0.350031	+	0.606272i
$298$	−1.89474	+	7.49077i	−0.109759	+	0.433928i
$299$	−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
$304$	−13.7317	−	20.9677i	−0.787568	−	1.20258i
$305$	−3.14392	−	8.06239i	−0.180020	−	0.461651i
$306$	14.6274	+	14.2220i	0.836193	+	0.813015i
$307$			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
$310$	−0.578206	−	4.63655i	−0.0328399	−	0.263338i
$311$	−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	$0.976122\pi$
$312$	2.90986	−	0.912761i	0.164738	−	0.0516749i
$313$	3.18572	+	5.51783i	0.180068	+	0.311886i	0.941903	−	0.335884i	$-0.109035\pi$
$313$	3.18572	+	5.51783i	0.180068	+	0.311886i	−0.761836	+	0.647770i	$0.775702\pi$
$314$	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	$0.174887\pi$
$318$	0.328338	−	1.29807i	0.0184123	−	0.0727923i
$319$	8.01112	+	4.62522i	0.448537	+	0.258963i
$320$	17.8478	+	1.20601i	0.997725	+	0.0674178i
$321$		−	4.16188i		−	0.232293i
$322$		0			0
$323$	−32.0462			−1.78310
$324$	−13.0532	−	7.05478i	−0.725177	−	0.391932i
$325$	12.1510	+	3.80637i	0.674015	+	0.211139i
$326$	−0.669488	+	2.64680i	−0.0370795	+	0.146593i
$327$	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	−0.108669	−	0.994078i	$-0.534659\pi$
$331$	12.6971	−	7.33065i	0.697893	−	0.402929i	0.806562	+	0.591149i	$0.201326\pi$
$332$	8.65409	−	0.243295i	0.474955	−	0.0133526i
$333$	−5.76313	−	3.32735i	−0.315818	−	0.182338i
$334$	−16.7276	+	17.2044i	−0.915291	+	0.941385i
$335$	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	$0.863717\pi$
$338$	−6.60552	−	6.42243i	−0.359293	−	0.349334i
$339$	−3.37147	+	5.83955i	−0.183113	+	0.317161i
$340$	13.7921	−	18.2455i	0.747983	−	0.989500i
$341$	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
$346$	3.48053	−	13.7601i	0.187114	−	0.739750i
$347$	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	$-0.187609\pi$
$348$	0.760768	−	1.40762i	0.0407814	−	0.0754562i
$349$			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
$352$	9.02785	+	26.1804i	0.481186	+	1.39542i
$353$	11.3427	−	19.6461i	0.603711	−	1.04566i	−0.388543	−	0.921431i	$-0.627021\pi$
$353$	11.3427	−	19.6461i	0.603711	−	1.04566i	0.992254	−	0.124228i	$-0.0396453\pi$
$354$	−3.30293	−	0.835451i	−0.175549	−	0.0444037i
$355$	−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	−0.831592	−	0.555388i	$-0.812570\pi$
$359$	−14.5214	+	8.38391i	−0.766408	+	0.442486i	0.0651839	+	0.997873i	$0.479237\pi$
$360$	−6.47493	+	16.6234i	−0.341259	+	0.876132i
$361$	−10.1314	+	17.5481i	−0.533233	+	0.923586i
$362$	−21.9564	+	22.5823i	−1.15400	+	1.18690i
$363$			5.48966i			0.288133i
$364$		0			0
$365$	−13.7378	−	11.0048i	−0.719069	−	0.576016i
$366$	−1.66139	−	1.61534i	−0.0868425	−	0.0844354i
$367$	−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	$0.800539\pi$
$368$	−10.1489	−	15.4969i	−0.529046	−	0.807830i
$369$	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	−0.0648133	−	0.997897i	$-0.520645\pi$
$373$	14.8129	−	8.55225i	0.766985	−	0.442819i	0.831798	+	0.555079i	$0.187312\pi$
$374$	34.3267	+	8.68269i	1.77499	+	0.448971i
$375$	3.92851	−	2.64082i	0.202868	−	0.136372i
$376$	−7.52724	+	33.7178i	−0.388188	+	1.73886i
$377$	4.81207			0.247834
$378$		0			0
$379$		−	10.3762i		−	0.532990i	−0.963836	−	0.266495i	$-0.914134\pi$
$379$		−	10.3762i		−	0.532990i	0.963836	−	0.266495i	$-0.0858655\pi$
$380$	−10.9103	−	25.8113i	−0.559688	−	1.32409i
$381$	4.48034	+	2.58672i	0.229535	+	0.132522i
$382$	−24.4675	−	6.18888i	−1.25187	−	0.316651i
$383$	−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
$388$	−0.192405	−	6.84390i	−0.00976787	−	0.347446i
$389$	−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	$0.309248\pi$
$390$	3.38342	−	0.421932i	0.171326	−	0.0213654i
$391$	−23.6848			−1.19779
$392$		0			0
$393$			4.17063i			0.210380i
$394$	11.1962	−	11.5154i	0.564057	−	0.580138i
$395$	3.76919	+	9.66585i	0.189649	+	0.486342i
$396$	−27.6071	+	0.776126i	−1.38731	+	0.0390018i
$397$	−16.7682	−	29.0434i	−0.841573	−	1.45765i	−0.888564	−	0.458752i	$-0.848297\pi$
$397$	−16.7682	−	29.0434i	−0.841573	−	1.45765i	0.0469909	−	0.998895i	$-0.485037\pi$
$398$	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	$0.729545\pi$
$402$	0.516226	+	0.130576i	0.0257470	+	0.00651252i
$403$	1.88141	−	3.25870i	0.0937198	−	0.162327i
$404$	6.94843	−	12.8564i	0.345697	−	0.639630i
$405$	−12.9471	−	10.3714i	−0.643348	−	0.515359i
$406$		0			0
$407$	−11.5495			−0.572487
$408$	1.33439	−	5.97734i	0.0660624	−	0.295923i
$409$	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	$0.487371\pi$
$410$	−13.4581	−	17.7893i	−0.664647	−	0.878552i
$411$	−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
$416$	10.8766	+	9.44626i	0.533269	+	0.463141i
$417$	5.08728	+	2.93714i	0.249125	+	0.143833i
$418$	30.2412	−	31.1033i	1.47915	−	1.52131i
$419$	−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	$0.652935\pi$
$422$	4.33935	−	4.46306i	0.211236	−	0.217258i
$423$	−29.8380	−	17.2270i	−1.45077	−	0.837604i
$424$	6.03501	−	1.89305i	0.293086	−	0.0919348i
$425$	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
$430$	−27.1835	+	20.5650i	−1.31091	+	0.991734i
$431$	23.4036	+	13.5121i	1.12731	+	0.650854i	0.943258	−	0.332061i	$-0.107744\pi$
$431$	23.4036	+	13.5121i	1.12731	+	0.650854i	0.184055	+	0.982916i	$0.441077\pi$
$432$	0.553830	+	9.84216i	0.0266461	+	0.473531i
$433$	15.0015			0.720928			0.360464	−	0.932773i	$-0.382618\pi$
$433$	15.0015			0.720928			0.360464	+	0.932773i	$0.382618\pi$
$434$		0			0
$435$	1.11842	−	1.39618i	0.0536243	−	0.0669418i
$436$	16.5605	+	8.95036i	0.793103	+	0.428644i
$437$	−14.5092	+	25.1307i	−0.694071	+	1.20217i
$438$	−4.56946	−	1.15581i	−0.218337	−	0.0552268i
$439$	−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	$0.978354\pi$
$440$	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	$0.668306\pi$
$444$	0.0561402	+	1.99692i	0.00266430	+	0.0947699i
$445$	1.77304	+	4.54684i	0.0840499	+	0.215541i
$446$	13.9107	−	14.3072i	0.658689	−	0.677467i
$447$			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	$0.387659\pi$
$450$	−10.4478	+	16.9904i	−0.492513	+	0.800935i
$451$	17.2663	−	29.9061i	0.813038	−	1.40822i
$452$	−31.8397	+	0.895119i	−1.49761	+	0.0421029i
$453$	−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	$0.324473\pi$
$458$	−11.1182	−	2.81228i	−0.519521	−	0.131409i
$459$	10.9152	+	6.30192i	0.509480	+	0.294148i
$460$	−8.06363	−	19.0766i	−0.375969	−	0.889453i
$461$			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	$0.534788\pi$
$464$	7.54637	−	0.424643i	0.350331	−	0.0197136i
$465$	−0.508206	−	1.30326i	−0.0235675	−	0.0604374i
$466$	−21.7641	−	5.50506i	−1.00820	−	0.255017i
$467$	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
$472$	−4.81685	−	15.3560i	−0.221713	−	0.706817i
$473$	−45.6990	−	26.3843i	−2.10124	−	1.21315i
$474$	1.99182	+	1.93661i	0.0914872	+	0.0889513i
$475$	−6.83791	−	30.5747i	−0.313745	−	1.40286i
$476$		0			0
$477$			6.30776i			0.288813i
$478$	24.1468	−	24.8352i	1.10445	−	1.13594i
$479$	−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	$0.196546\pi$
$480$	5.26869	−	0.960251i	0.240482	−	0.0438293i
$481$	−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
$486$	−14.4429	−	3.65324i	−0.655145	−	0.165714i
$487$	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	$-0.111125\pi$
$488$	2.38493	−	10.6832i	0.107961	−	0.483604i
$489$			0.817356i			0.0369621i
$490$		0			0
$491$		−	25.9116i		−	1.16937i	−0.811259	−	0.584686i	$-0.801218\pi$
$491$		−	25.9116i		−	1.16937i	0.811259	−	0.584686i	$-0.198782\pi$
$492$	−5.25474	−	2.84000i	−0.236902	−	0.128037i
$493$	4.83193	−	8.36914i	0.217619	−	0.376927i
$494$	5.53387	−	21.8780i	0.248981	−	0.984336i
$495$	−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	0.0515304	−	0.998671i	$-0.483590\pi$
$499$	21.0465	−	12.1512i	0.942170	−	0.543962i	0.890640	+	0.454709i	$0.150257\pi$
$500$	20.3506	+	9.26568i	0.910107	+	0.414374i
$501$	−3.59195	+	6.22145i	−0.160477	+	0.277954i
$502$	−21.4272	−	20.8332i	−0.956341	−	0.929833i
$503$			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
$506$	22.3507	−	22.9879i	0.993612	−	1.02194i
$507$	−2.38868	−	1.37911i	−0.106085	−	0.0612482i
$508$	0.686771	+	24.4287i	0.0304705	+	1.08385i
$509$	−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
$514$	−8.89594	+	35.1698i	−0.392383	+	1.55127i
$515$	−5.48410	−	14.0636i	−0.241658	−	0.619718i
$516$	−4.33976	+	8.02968i	−0.191047	+	0.353487i
$517$	−59.7962			−2.62983
$518$		0			0
$519$		−	4.24926i		−	0.186522i
$520$	10.0745	+	12.5666i	0.441797	+	0.551082i
$521$	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	$0.543091\pi$
$522$	−1.84841	+	7.30763i	−0.0809028	+	0.319846i
$523$	−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
$528$	4.54225	+	6.93581i	0.197676	+	0.301842i
$529$	0.776490	−	1.34492i	0.0337605	−	0.0584748i
$530$	7.01715	−	0.875081i	0.304806	−	0.0380111i
$531$	16.0500			0.696511
$532$		0			0
$533$		−	17.9638i		−	0.778100i
$534$	0.936955	+	0.910984i	0.0405460	+	0.0394221i
$535$	20.4785	−	7.98557i	0.885363	−	0.345247i
$536$	0.752842	+	2.40004i	0.0325178	+	0.103666i
$537$	−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	$0.962687\pi$
$542$	5.32705	−	21.0603i	0.228816	−	0.904617i
$543$	−4.71475	+	8.16619i	−0.202329	+	0.350445i
$544$	27.3504	−	9.43131i	1.17264	−	0.404364i
$545$	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	$0.367215\pi$
$548$	4.46447	−	8.26043i	0.190713	−	0.352868i
$549$	9.45388	+	5.45820i	0.403482	+	0.232950i
$550$	−0.959490	+	34.6032i	−0.0409128	+	1.47549i
$551$	−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
$556$	0.779807	+	27.7380i	0.0330712	+	1.17635i
$557$	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	$0.484914\pi$
$558$	4.22598	+	4.10885i	0.178900	+	0.173941i
$559$	−27.4502			−1.16102
$560$		0			0
$561$	10.6004			0.447549
$562$	30.0302	+	29.1978i	1.26675	+	1.23163i
$563$	−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	$0.897369\pi$
$564$	0.290660	+	10.3389i	0.0122390	+	0.435344i
$565$	−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	$0.945280\pi$
$570$	−5.06152	−	6.69048i	−0.212004	−	0.280233i
$571$	−12.9962	−	7.50335i	−0.543873	−	0.314005i	0.202774	−	0.979226i	$-0.435004\pi$
$571$	−12.9962	−	7.50335i	−0.543873	−	0.314005i	−0.746647	+	0.665220i	$0.768338\pi$
$572$	−11.8554	+	21.9355i	−0.495697	+	0.917169i
$573$	−7.55580			−0.315648
$574$		0			0
$575$	−5.05378	−	22.5972i	−0.210757	−	0.942370i
$576$	−18.5230	+	12.8887i	−0.771793	+	0.537030i
$577$	−1.24966	+	2.16447i	−0.0520240	+	0.0901082i	−0.890865	−	0.454269i	$-0.849901\pi$
$577$	−1.24966	+	2.16447i	−0.0520240	+	0.0901082i	0.838841	+	0.544377i	$0.183234\pi$
$578$	3.17524	−	12.5532i	0.132073	−	0.522144i
$579$	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
$584$	−6.66391	−	21.2444i	−0.275754	−	0.879098i
$585$	−14.9651	+	5.83562i	−0.618729	+	0.241273i
$586$	−18.0219	−	17.5224i	−0.744477	−	0.723842i
$587$			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
$590$	−2.22663	−	17.8550i	−0.0916690	−	0.735081i
$591$	2.40419	−	4.16419i	0.0988953	−	0.171292i
$592$	−7.89451	+	5.17010i	−0.324462	+	0.212490i
$593$	14.3251	+	24.8118i	0.588262	+	1.01890i	0.994460	+	0.105115i	$0.0335211\pi$
$593$	14.3251	+	24.8118i	0.588262	+	1.01890i	−0.406198	+	0.913785i	$0.633146\pi$
$594$	−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
$598$	4.08999	−	16.1696i	0.167252	−	0.661224i
$599$	−14.2033	−	8.20030i	−0.580333	−	0.335055i	0.180933	−	0.983495i	$-0.442088\pi$
$599$	−14.2033	−	8.20030i	−0.580333	−	0.335055i	−0.761266	+	0.648440i	$0.775422\pi$
$600$	5.98761	−	0.00230331i	0.244443	−	9.40322e-5i
$601$		−	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
$604$	1.42269	−	2.63235i	0.0578885	−	0.107109i
$605$	−27.0119	+	10.5333i	−1.09819	+	0.428238i
$606$	1.07287	−	4.24155i	0.0435824	−	0.172301i
$607$	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
$612$	0.810812	+	28.8408i	0.0327751	+	1.16582i
$613$	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	$0.587777\pi$
$614$	−32.4268	+	33.3513i	−1.30864	+	1.34595i
$615$	−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	$0.896120\pi$
$618$	−2.89806	−	2.81773i	−0.116577	−	0.113346i
$619$	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	$0.141800\pi$
$620$	3.98466	−	5.27127i	0.160028	−	0.211699i
$621$	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
$626$	−2.20957	+	8.73546i	−0.0883123	+	0.349139i
$627$	6.49378	−	11.2476i	0.259337	−	0.449184i
$628$	40.2980	+	21.7796i	1.60806	+	0.869101i
$629$			12.0656i			0.481089i
$630$		0			0
$631$		−	12.2743i		−	0.488633i	−0.969696	−	0.244316i	$-0.921436\pi$
$631$		−	12.2743i		−	0.488633i	0.969696	−	0.244316i	$-0.0785636\pi$
$632$	−2.85925	+	12.8079i	−0.113735	+	0.509470i
$633$	0.931800	−	1.61393i	0.0370357	−	0.0641478i
$634$	23.3107	+	5.89626i	0.925785	+	0.234171i
$635$	−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
$640$	16.9079	+	18.8181i	0.668345	+	0.743851i
$641$	−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	$0.261259\pi$
$642$	4.10298	−	4.21995i	0.161932	−	0.166548i
$643$		−	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
$646$	−32.4934	−	31.5927i	−1.27843	−	1.24300i
$647$	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	$0.428528\pi$
$648$	−6.28037	−	20.0217i	−0.246716	−	0.786526i
$649$	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	−0.894717	−	0.446634i	$-0.852623\pi$
$653$	−24.4111	+	14.0937i	−0.955279	+	0.551531i	−0.0605622	+	0.998164i	$0.519289\pi$
$654$	5.46359	+	1.38198i	0.213643	+	0.0540396i
$655$	−20.5215	+	8.00236i	−0.801843	+	0.312678i
$656$	−1.58522	−	28.1712i	−0.0618926	−	1.09990i
$657$	22.2045			0.866281
$658$		0			0
$659$		−	9.79123i		−	0.381412i	−0.981647	−	0.190706i	$-0.938922\pi$
$659$		−	9.79123i		−	0.381412i	0.981647	−	0.190706i	$-0.0610777\pi$
$660$	3.60897	+	8.53798i	0.140479	+	0.332340i
$661$	−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	$0.671724\pi$
$662$	20.1011	+	5.08444i	0.781253	+	0.197612i
$663$	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
$668$	−33.9219	+	0.953659i	−1.31248	+	0.0368982i
$669$	2.98708	−	5.17377i	0.115487	−	0.200029i
$670$	0.348008	+	2.79063i	0.0134447	+	0.107811i
$671$	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	$-0.0581842\pi$
$674$	−15.0278	+	15.4562i	−0.578850	+	0.595352i
$675$	−3.68349	+	11.7587i	−0.141778	+	0.452594i
$676$	−0.366151	−	13.0241i	−0.0140827	−	0.500927i
$677$	1.23700	+	2.14255i	0.0475418	+	0.0823449i	0.888817	−	0.458262i	$-0.151528\pi$
$677$	1.23700	+	2.14255i	0.0475418	+	0.0823449i	−0.841275	+	0.540607i	$0.818195\pi$
$678$	−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
$682$	9.91728	+	2.50850i	0.379752	+	0.0960556i
$683$	−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	$0.283494\pi$
$684$	31.0982	+	16.8075i	1.18907	+	0.642651i
$685$	6.56332	−	8.19332i	0.250772	−	0.313051i
$686$		0			0
$687$	−3.43341			−0.130993
$688$	−43.0478	+	2.42235i	−1.64118	+	0.0923513i
$689$	4.93186	+	2.84741i	0.187889	+	0.108478i
$690$	−3.74088	−	4.94482i	−0.142413	−	0.188246i
$691$	−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
$696$	2.15908	−	0.677258i	0.0818398	−	0.0256714i
$697$	−31.2426	−	18.0379i	−1.18340	−	0.683236i
$698$	−15.9300	+	16.3841i	−0.602958	+	0.620147i
$699$	−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	$0.574522\pi$
$702$	−6.18721	+	6.36360i	−0.233521	+	0.240179i
$703$	12.8022	+	7.39138i	0.482846	+	0.278771i
$704$	−16.6561	+	35.4458i	−0.627749	+	1.33591i
$705$	−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	$0.850892\pi$
$710$	−27.3419	−	36.1415i	−1.02612	−	1.35636i
$711$	−11.3341	−	6.54374i	−0.425062	−	0.245410i
$712$	−1.34500	+	6.02485i	−0.0504060	+	0.225791i
$713$	−6.84273			−0.256262
$714$		0			0
$715$	−17.4288	+	21.7573i	−0.651802	+	0.813677i
$716$	3.37849	−	6.25108i	0.126260	−	0.233614i
$717$	5.18511	−	8.98088i	0.193642	−	0.335397i
$718$	−22.9892	−	5.81496i	−0.857951	−	0.217013i
$719$	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	$0.486641\pi$
$720$	−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
$724$	−44.5255	+	1.25176i	−1.65478	+	0.0465213i
$725$	9.01587	+	2.82428i	0.334841	+	0.104891i
$726$	−5.41198	+	5.56627i	−0.200857	+	0.206584i
$727$			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
$730$	−3.08045	−	24.7017i	−0.114013	−	0.914251i
$731$	−27.5634	+	47.7413i	−1.01947	+	1.76578i
$732$	−0.0920928	−	3.27577i	−0.00340385	−	0.121076i
$733$	−20.9930	−	36.3610i	−0.775395	−	1.34302i	−0.934572	−	0.355773i	$-0.884218\pi$
$733$	−20.9930	−	36.3610i	−0.775395	−	1.34302i	0.159178	−	0.987250i	$-0.449116\pi$
$734$	−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
$738$	27.2799	+	6.90026i	1.00419	+	0.254002i
$739$	22.4500	+	12.9615i	0.825836	+	0.476796i	0.852425	−	0.522850i	$-0.175131\pi$
$739$	22.4500	+	12.9615i	0.825836	+	0.476796i	−0.0265891	+	0.999646i	$0.508465\pi$
$740$	−9.71814	+	4.10782i	−0.357246	+	0.151007i
$741$		−	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	$0.566446\pi$
$744$	0.385518	−	1.72691i	0.0141338	−	0.0633115i
$745$	−11.3822	+	4.43847i	−0.417011	+	0.162613i
$746$	23.4509	+	5.93172i	0.858597	+	0.217176i
$747$	−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	−0.408593	−	0.912717i	$-0.633981\pi$
$751$	4.86553	−	2.80911i	0.177546	−	0.102506i	0.586139	+	0.810210i	$0.300647\pi$
$752$	−40.8730	+	26.7676i	−1.49048	+	0.976114i
$753$	−7.74847	−	4.47358i	−0.282370	−	0.163026i
$754$	4.87922	+	4.74398i	0.177691	+	0.172765i
$755$	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	$-0.163549\pi$
$758$	10.2294	−	10.5210i	0.371547	−	0.382139i
$759$	4.79944	−	8.31287i	0.174208	−	0.301738i
$760$	14.3834	−	36.9274i	0.521742	−	1.33950i
$761$	−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
$765$	−4.87752	+	31.8869i	−0.176347	+	1.15287i
$766$	−12.6653	−	3.20360i	−0.457617	−	0.115751i
$767$	7.24519	−	12.5490i	0.261609	−	0.453119i
$768$	6.20959	+	2.70756i	0.224069	+	0.0977007i
$769$			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
$772$	−17.3384	+	32.0805i	−0.624022	+	1.15460i
$773$	4.38608	−	7.59692i	0.157756	−	0.273242i	−0.776303	−	0.630360i	$-0.782907\pi$
$773$	4.38608	−	7.59692i	0.157756	−	0.273242i	0.934059	+	0.357118i	$0.116241\pi$
$774$	10.5442	−	41.6859i	0.379002	−	1.49837i
$775$	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
$780$	3.84659	+	2.90772i	0.137730	+	0.104113i
$781$	35.0789	−	60.7584i	1.25522	−	2.17411i
$782$	−24.0153	−	23.3496i	−0.858784	−	0.834980i
$783$			4.65674i			0.166418i
$784$		0			0
$785$	39.9706	+	32.0187i	1.42661	+	1.14280i
$786$	−4.11161	+	4.22882i	−0.146656	+	0.150837i
$787$	−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	$0.723085\pi$
$788$	22.7049	−	0.638310i	0.808828	−	0.0227389i
$789$	−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
$794$	11.6302	−	45.9796i	0.412741	−	1.63176i
$795$	1.97241	−	0.769141i	0.0699543	−	0.0272786i
$796$	15.8850	+	8.58527i	0.563029	+	0.304297i
$797$	31.5699			1.11826			0.559132	−	0.829079i	$-0.311135\pi$
$797$	31.5699			1.11826			0.559132	+	0.829079i	$0.311135\pi$
$798$		0			0
$799$			62.4685i			2.20998i
$800$	14.8342	+	24.0821i	0.524467	+	0.851431i
$801$	−5.33158	−	3.07819i	−0.188382	−	0.108762i
$802$	−4.44885	+	17.5884i	−0.157095	+	0.621067i
$803$	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
$808$	19.7199	−	6.18570i	0.693742	−	0.217612i
$809$	−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	$0.984704\pi$
$810$	−2.90316	−	23.2800i	−0.102007	−	0.817977i
$811$	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
$814$	−11.7106	−	11.3860i	−0.410458	−	0.399081i
$815$	−4.02180	+	1.56830i	−0.140877	+	0.0549350i
$816$	7.24577	−	4.74524i	0.253653	−	0.166117i
$817$	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	$-0.484459\pi$
$822$	0.689335	−	2.72526i	0.0240433	−	0.0950543i
$823$	−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	$0.219812\pi$
$824$	4.16016	−	18.6352i	0.144926	−	0.649188i
$825$	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	$0.496398\pi$
$828$	22.9842	+	12.4221i	0.798755	+	0.431699i
$829$	−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	$0.968658\pi$
$830$	8.25876	+	10.9167i	0.286666	+	0.378924i
$831$	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
$836$	61.3264	−	1.72409i	2.12102	−	0.0596289i
$837$	3.15351	+	1.82068i	0.109001	+	0.0629318i
$838$	−18.9895	−	18.4631i	−0.655980	−	0.637797i
$839$	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
$842$	−19.2312	−	18.6981i	−0.662750	−	0.644379i
$843$	10.8595	+	6.26972i	0.374020	+	0.215941i
$844$	8.79980	−	0.247392i	0.302901	−	0.00851557i
$845$	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
$850$	36.1496	+	1.00237i	1.23992	+	0.0343810i
$851$	9.46191	+	5.46284i	0.324350	+	0.187264i
$852$	−10.6757	−	5.76986i	−0.365745	−	0.197672i
$853$	12.0132			0.411323			0.205661	−	0.978623i	$-0.434065\pi$
$853$	12.0132			0.411323			0.205661	+	0.978623i	$0.434065\pi$
$854$		0			0
$855$	30.8456	+	24.7091i	1.05490	+	0.845034i
$856$	27.1353	+	6.05774i	0.927466	+	0.207049i
$857$	13.5132	−	23.4056i	0.461603	−	0.799519i	−0.537438	−	0.843303i	$-0.680608\pi$
$857$	13.5132	−	23.4056i	0.461603	−	0.799519i	0.999041	+	0.0437838i	$0.0139413\pi$
$858$	−1.83052	+	7.23690i	−0.0624930	+	0.247064i
$859$	−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	$0.947502\pi$
$860$	−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	$0.781836\pi$
$864$	−9.14132	+	10.5255i	−0.310994	+	0.358084i
$865$	20.9085	−	8.15323i	0.710909	−	0.277218i
$866$	15.2109	+	14.7892i	0.516886	+	0.502559i
$867$		−	3.87654i		−	0.131654i
$868$		0			0
$869$	−22.7139			−0.770515
$870$	2.51045	−	0.313069i	0.0851123	−	0.0106140i
$871$	−1.13238	+	1.96133i	−0.0383691	+	0.0664573i
$872$	7.96787	+	25.4014i	0.269826	+	0.860199i
$873$	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	$0.444366\pi$
$878$	6.39417	−	25.2791i	0.215793	−	0.853128i
$879$	−6.51705	−	3.76262i	−0.219815	−	0.126910i
$880$	−25.4122	+	35.6581i	−0.856645	+	1.20204i
$881$		−	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	$0.266752\pi$
$884$	22.9158	+	12.3852i	0.770742	+	0.416559i
$885$	−1.95707	−	5.01878i	−0.0657861	−	0.168704i
$886$	−7.23395	+	28.5991i	−0.243029	+	0.960807i
$887$	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
$892$	28.2095	−	0.793064i	0.944525	−	0.0265538i
$893$	66.2822	+	38.2681i	2.21805	+	1.28059i
$894$	−2.28048	+	2.34550i	−0.0762708	+	0.0784451i
$895$	4.96680	−	6.20030i	0.166022	−	0.207253i
$896$		0			0
$897$		−	4.99333i		−	0.166722i
$898$	14.8527	+	14.4410i	0.495642	+	0.481904i
$899$	1.39598	−	2.41792i	0.0465587	−	0.0806420i
$900$	−27.3435	+	6.92754i	−0.911451	+	0.230918i
$901$	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
$906$	0.219670	−	0.868459i	0.00729806	−	0.0288526i
$907$	−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	$0.849589\pi$
$908$	−10.4579	+	19.3499i	−0.347059	+	0.642150i
$909$			20.6111i			0.683627i
$910$		0			0
$911$		−	0.524910i		−	0.0173910i	−0.999962	−	0.00869552i	$-0.997232\pi$
$911$		−	0.524910i		−	0.0173910i	0.999962	−	0.00869552i	$-0.00276790\pi$
$912$	−0.596196	−	10.5950i	−0.0197420	−	0.350837i
$913$	−10.5957	+	18.3524i	−0.350668	+	0.607374i
$914$	1.63154	+	0.412687i	0.0539666	+	0.0136505i
$915$	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	−0.774749	−	0.632269i	$-0.782124\pi$
$919$	−18.6304	+	10.7563i	−0.614561	+	0.354817i	0.160187	+	0.987087i	$0.448790\pi$
$920$	10.6305	−	27.2924i	0.350478	−	0.899802i
$921$	−6.96310	+	12.0604i	−0.229442	+	0.397405i
$922$	−14.3584	+	14.7677i	−0.472868	+	0.486349i
$923$		−	36.4960i		−	1.20128i
$924$		0			0
$925$	−11.5116	+	2.57453i	−0.378500	+	0.0846499i
$926$	−4.75941	−	4.62749i	−0.156404	−	0.152069i
$927$	16.4909	+	9.52103i	0.541632	+	0.312711i
$928$	8.07030	+	7.00901i	0.264921	+	0.230082i
$929$	−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
$934$	34.6623	+	8.76757i	1.13418	+	0.286884i
$935$	20.3394	+	52.1592i	0.665171	+	1.70579i
$936$	−19.8297	−	4.42681i	−0.648153	−	0.144695i
$937$	7.15521			0.233751			0.116875	−	0.993147i	$-0.462712\pi$
$937$	7.15521			0.233751			0.116875	+	0.993147i	$0.462712\pi$
$938$		0			0
$939$			2.69759i			0.0880326i
$940$	−50.3146	+	21.2678i	−1.64108	+	0.693679i
$941$	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	$0.629598\pi$
$942$	13.2950	+	3.36287i	0.433174	+	0.109568i
$943$	−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	$0.710857\pi$
$948$	0.110408	+	3.92726i	0.00358590	+	0.127552i
$949$	10.0234	−	17.3611i	0.325374	−	0.563564i
$950$	23.2087	−	37.7425i	0.752991	−	1.22453i
$951$	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	$0.800043\pi$
$954$	−6.21850	+	6.39578i	−0.201331	+	0.207071i
$955$	−14.4976	−	37.1783i	−0.469132	−	1.20306i
$956$	48.9675	−	1.37664i	1.58372	−	0.0445237i
$957$	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
$962$	−8.23722	−	2.08355i	−0.265579	−	0.0671762i
$963$	−13.8639	+	24.0129i	−0.446757	+	0.773805i
$964$	18.2447	−	33.7575i	0.587622	−	1.08725i
$965$	−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	$0.270645\pi$
$968$	−35.7924	−	7.99037i	−1.15041	−	0.256820i
$969$	−11.7502	−	6.78399i	−0.377471	−	0.217933i
$970$	8.63323	−	6.53126i	0.277196	−	0.209706i
$971$	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
$976$	12.9502	−	8.48106i	0.414526	−	0.271472i
$977$	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	$0.607585\pi$
$978$	−0.805789	+	0.828761i	−0.0257663	+	0.0265009i
$979$	−10.6846			−0.341483
$980$		0			0
$981$	−26.5494			−0.847658
$982$	25.5449	−	26.2731i	0.815170	−	0.838409i
$983$	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	$0.585850\pi$
$984$	−2.52825	−	8.06001i	−0.0805978	−	0.256944i
$985$	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
$990$	−26.3459	−	34.8249i	−0.837328	−	1.10681i
$991$	−2.35222	−	1.35806i	−0.0747208	−	0.0431401i	0.462174	−	0.886789i	$-0.347070\pi$
$991$	−2.35222	−	1.35806i	−0.0747208	−	0.0431401i	−0.536895	+	0.843649i	$0.680403\pi$
$992$	7.90176	−	2.72479i	0.250881	−	0.0865120i
$993$	6.20742			0.196986
$994$		0			0
$995$	15.7559	+	12.6214i	0.499497	+	0.400126i
$996$	3.22466	+	1.74281i	0.102177	+	0.0552231i
$997$	4.48080	−	7.76097i	0.141908	−	0.245792i	−0.786307	−	0.617836i	$-0.788010\pi$
$997$	4.48080	−	7.76097i	0.141908	−	0.245792i	0.928215	+	0.372044i	$0.121343\pi$
$998$	33.3194	+	8.42791i	1.05471	+	0.266781i
$999$	−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.619.38		96
4.3	odd	2	inner	980.2.s.g.619.19		96
5.4	even	2	inner	980.2.s.g.619.11		96
7.2	even	3	inner	980.2.s.g.19.29		96
7.3	odd	6		980.2.c.e.979.8	yes	48
7.4	even	3		980.2.c.e.979.7	yes	48
7.5	odd	6	inner	980.2.s.g.19.30		96
7.6	odd	2	inner	980.2.s.g.619.37		96
20.19	odd	2	inner	980.2.s.g.619.30		96
28.3	even	6		980.2.c.e.979.43	yes	48
28.11	odd	6		980.2.c.e.979.44	yes	48
28.19	even	6	inner	980.2.s.g.19.11		96
28.23	odd	6	inner	980.2.s.g.19.12		96
28.27	even	2	inner	980.2.s.g.619.20		96
35.4	even	6		980.2.c.e.979.42	yes	48
35.9	even	6	inner	980.2.s.g.19.20		96
35.19	odd	6	inner	980.2.s.g.19.19		96
35.24	odd	6		980.2.c.e.979.41	yes	48
35.34	odd	2	inner	980.2.s.g.619.12		96
140.19	even	6	inner	980.2.s.g.19.38		96
140.39	odd	6		980.2.c.e.979.5	✓	48
140.59	even	6		980.2.c.e.979.6	yes	48
140.79	odd	6	inner	980.2.s.g.19.37		96
140.139	even	2	inner	980.2.s.g.619.29		96

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.01395 + 0.985849i) q^{2} +(0.366665 + 0.211694i) q^{3} +(0.0562045 + 1.99921i) 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} +(-2.52190 + 1.90788i) q^{10} +(-4.23964 - 2.44776i) q^{11} +(-0.402613 + 0.744938i) q^{12} -2.54664 q^{13} +(-0.591890 + 0.738886i) q^{15} +(-3.99368 + 0.224729i) q^{16} +(-2.55715 + 4.42911i) q^{17} +(0.978214 - 3.86733i) 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} +(-1.14263 + 0.358418i) q^{24} +(-4.77137 - 1.49466i) q^{25} +(-2.58218 - 2.51060i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(-1.32858 + 0.165682i) q^{30} +(-0.738782 + 1.27961i) q^{31} +(-4.27096 - 3.70930i) 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} +(-2.17301 + 8.59091i) q^{38} +(-0.933764 - 0.539109i) q^{39} +(-3.95600 - 4.93458i) q^{40} +7.05393i q^{41} +10.7790 q^{43} +(4.65529 - 8.61350i) q^{44} +(5.87639 - 2.29149i) q^{45} +(-1.60603 + 6.34939i) 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} +(-0.143133 - 5.09127i) q^{52} +(-1.93661 - 1.11810i) q^{53} +(2.42956 - 2.49882i) q^{54} +(6.84386 - 8.54352i) q^{55} +2.65295i q^{57} +(-1.91594 - 1.86284i) q^{58} +(-2.84500 + 4.92768i) q^{59} +(-1.51046 - 1.14178i) 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} +(0.718799 - 2.84174i) q^{66} +(0.444655 - 0.770165i) q^{67} +(-8.99844 - 4.86334i) q^{68} +1.96075i q^{69} +14.3310i q^{71} +(7.78659 + 1.73829i) q^{72} +(-3.93594 + 6.81724i) q^{73} +(3.23454 + 0.818154i) 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} +(0.853547 - 8.90345i) q^{80} +(-3.70941 + 6.42488i) q^{81} +(-6.95411 + 7.15236i) q^{82} -4.32876i q^{83} +(-8.92534 - 7.14971i) q^{85} +(10.9294 + 10.6264i) q^{86} +(-0.692841 - 0.400012i) q^{87} +(13.2119 - 4.14428i) 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} +(16.7465 + 4.23590i) q^{94} +(-13.0538 + 5.09033i) q^{95} +(-0.780773 - 2.26421i) 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

Related objects

Downloads

Learn more