LMFDB - Embedded newform 980.2.x.m.667.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.12
Character	$\chi$	$=$	980.667
Dual form			980.2.x.m.263.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.764487 + 1.18977i) q^{2} +(0.638980 - 2.38471i) q^{3} +(-0.831118 + 1.81913i) q^{4} +(-2.14503 + 0.631526i) q^{5} +(3.32575 - 1.06284i) q^{6} +(-2.79973 + 0.401862i) q^{8} +(-2.68045 - 1.54756i) q^{9} +(-2.39122 - 2.06931i) q^{10} +(4.09588 - 2.36476i) q^{11} +(3.80703 + 3.14436i) q^{12} +(-0.0592655 + 0.0592655i) q^{13} +(0.135370 + 5.51881i) q^{15} +(-2.61849 - 3.02383i) q^{16} +(1.27942 - 4.77484i) q^{17} +(-0.207927 - 4.37222i) q^{18} +(1.31544 - 2.27842i) q^{19} +(0.633947 - 4.42698i) q^{20} +(5.94478 + 3.06534i) q^{22} +(1.09265 - 0.292774i) q^{23} +(-0.830651 + 6.93332i) q^{24} +(4.20235 - 2.70929i) q^{25} +(-0.115820 - 0.0252047i) q^{26} +(-0.166053 + 0.166053i) q^{27} -7.27332i q^{29} +(-6.46264 + 4.38012i) q^{30} +(-4.01558 + 2.31840i) q^{31} +(1.59587 - 5.42708i) q^{32} +(-3.02207 - 11.2785i) q^{33} +(6.65908 - 2.12809i) q^{34} +(5.04299 - 3.58989i) q^{36} +(2.22779 - 0.596933i) q^{37} +(3.71644 - 0.176741i) q^{38} +(0.103461 + 0.179200i) q^{39} +(5.75174 - 2.63011i) q^{40} +5.71767 q^{41} +(-1.57302 - 1.57302i) q^{43} +(0.897647 + 9.41635i) q^{44} +(6.72699 + 1.62679i) q^{45} +(1.18365 + 1.07618i) q^{46} +(0.716679 + 2.67468i) q^{47} +(-8.88410 + 4.31215i) q^{48} +(6.43608 + 2.92862i) q^{50} +(-10.5691 - 6.10206i) q^{51} +(-0.0585551 - 0.157068i) q^{52} +(-9.12265 - 2.44441i) q^{53} +(-0.324510 - 0.0706197i) q^{54} +(-7.29241 + 7.65915i) q^{55} +(-4.59281 - 4.59281i) q^{57} +(8.65360 - 5.56036i) q^{58} +(1.67748 + 2.90547i) q^{59} +(-10.1520 - 4.34053i) q^{60} +(0.978771 - 1.69528i) q^{61} +(-5.82822 - 3.00524i) q^{62} +(7.67701 - 2.25021i) q^{64} +(0.0896988 - 0.164554i) q^{65} +(11.1085 - 12.2179i) q^{66} +(0.491893 + 0.131802i) q^{67} +(7.62273 + 6.29589i) q^{68} -2.79272i q^{69} +14.4625i q^{71} +(8.12646 + 3.25558i) q^{72} +(-9.26507 - 2.48257i) q^{73} +(2.41333 + 2.19421i) q^{74} +(-3.77565 - 11.7526i) q^{75} +(3.05145 + 4.28660i) q^{76} +(-0.134113 + 0.260092i) q^{78} +(3.05204 - 5.28630i) q^{79} +(7.52637 + 4.83257i) q^{80} +(-4.35280 - 7.53927i) q^{81} +(4.37109 + 6.80273i) q^{82} +(5.62620 + 5.62620i) q^{83} +(0.271049 + 11.0502i) q^{85} +(0.668982 - 3.07409i) q^{86} +(-17.3447 - 4.64751i) q^{87} +(-10.5171 + 8.26668i) q^{88} +(14.4482 + 8.34169i) q^{89} +(3.20718 + 9.24725i) q^{90} +(-0.375524 + 2.23100i) q^{92} +(2.96282 + 11.0574i) q^{93} +(-2.63437 + 2.89745i) q^{94} +(-1.38279 + 5.71802i) q^{95} +(-11.9223 - 7.27348i) q^{96} +(-5.81505 - 5.81505i) q^{97} -14.6384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.764487	+	1.18977i	0.540574	+	0.841296i
$2$	0.764487	+	1.18977i	0.540574	+	0.841296i
$3$	0.638980	−	2.38471i	0.368915	−	1.37681i	−0.493119	−	0.869962i	$-0.664143\pi$
$3$	0.638980	−	2.38471i	0.368915	−	1.37681i	0.862035	−	0.506849i	$-0.169190\pi$
$4$	−0.831118	+	1.81913i	−0.415559	+	0.909566i
$5$	−2.14503	+	0.631526i	−0.959289	+	0.282427i
$5$	−2.14503	+	0.631526i	−0.959289	+	0.282427i
$6$	3.32575	−	1.06284i	1.35773	−	0.433901i
$7$		0			0
$7$		0			0
$8$	−2.79973	+	0.401862i	−0.989855	+	0.142080i
$9$	−2.68045	−	1.54756i	−0.893484	−	0.515853i
$10$	−2.39122	−	2.06931i	−0.756172	−	0.654373i
$11$	4.09588	−	2.36476i	1.23496	−	0.713002i	0.266897	−	0.963725i	$-0.414002\pi$
$11$	4.09588	−	2.36476i	1.23496	−	0.713002i	0.968059	+	0.250723i	$0.0806684\pi$
$12$	3.80703	+	3.14436i	1.09899	+	0.907699i
$13$	−0.0592655	+	0.0592655i	−0.0164373	+	0.0164373i	−0.715278	−	0.698840i	$-0.753700\pi$
$13$	−0.0592655	+	0.0592655i	−0.0164373	+	0.0164373i	0.698840	+	0.715278i	$0.253700\pi$
$14$		0			0
$15$	0.135370	+	5.51881i	0.0349524	+	1.42495i
$16$	−2.61849	−	3.02383i	−0.654621	−	0.755957i
$17$	1.27942	−	4.77484i	0.310304	−	1.15807i	−0.617979	−	0.786195i	$-0.712048\pi$
$17$	1.27942	−	4.77484i	0.310304	−	1.15807i	0.928283	−	0.371875i	$-0.121285\pi$
$18$	−0.207927	−	4.37222i	−0.0490090	−	1.03054i
$19$	1.31544	−	2.27842i	0.301784	−	0.522705i	−0.674756	−	0.738041i	$-0.735751\pi$
$19$	1.31544	−	2.27842i	0.301784	−	0.522705i	0.976540	+	0.215336i	$0.0690846\pi$
$20$	0.633947	−	4.42698i	0.141755	−	0.989902i
$21$		0			0
$22$	5.94478	+	3.06534i	1.26743	+	0.653533i
$23$	1.09265	−	0.292774i	0.227832	−	0.0610475i	−0.143097	−	0.989709i	$-0.545706\pi$
$23$	1.09265	−	0.292774i	0.227832	−	0.0610475i	0.370929	+	0.928661i	$0.379039\pi$
$24$	−0.830651	+	6.93332i	−0.169556	+	1.41526i
$25$	4.20235	−	2.70929i	0.840470	−	0.541858i
$26$	−0.115820	−	0.0252047i	−0.0227142	−	0.00494306i
$27$	−0.166053	+	0.166053i	−0.0319568	+	0.0319568i
$28$		0			0
$29$		−	7.27332i		−	1.35062i	−0.737533	−	0.675311i	$-0.764009\pi$
$29$		−	7.27332i		−	1.35062i	0.737533	−	0.675311i	$-0.235991\pi$
$30$	−6.46264	+	4.38012i	−1.17991	+	0.799697i
$31$	−4.01558	+	2.31840i	−0.721219	+	0.416396i	−0.815201	−	0.579178i	$-0.803374\pi$
$31$	−4.01558	+	2.31840i	−0.721219	+	0.416396i	0.0939821	+	0.995574i	$0.470040\pi$
$32$	1.59587	−	5.42708i	0.282112	−	0.959381i
$33$	−3.02207	−	11.2785i	−0.526075	−	1.96334i
$34$	6.65908	−	2.12809i	1.14202	−	0.364965i
$35$		0			0
$36$	5.04299	−	3.58989i	0.840498	−	0.598315i
$37$	2.22779	−	0.596933i	0.366246	−	0.0981352i	−0.0710024	−	0.997476i	$-0.522620\pi$
$37$	2.22779	−	0.596933i	0.366246	−	0.0981352i	0.437248	+	0.899341i	$0.355953\pi$
$38$	3.71644	−	0.176741i	0.602886	−	0.0286712i
$39$	0.103461	+	0.179200i	0.0165671	+	0.0286950i
$40$	5.75174	−	2.63011i	0.909430	−	0.415857i
$41$	5.71767			0.892950			0.446475	−	0.894796i	$-0.352679\pi$
$41$	5.71767			0.892950			0.446475	+	0.894796i	$0.352679\pi$
$42$		0			0
$43$	−1.57302	−	1.57302i	−0.239883	−	0.239883i	0.576918	−	0.816802i	$-0.304255\pi$
$43$	−1.57302	−	1.57302i	−0.239883	−	0.239883i	−0.816802	+	0.576918i	$0.804255\pi$
$44$	0.897647	+	9.41635i	0.135325	+	1.41957i
$45$	6.72699	+	1.62679i	1.00280	+	0.242508i
$46$	1.18365	+	1.07618i	0.174519	+	0.158674i
$47$	0.716679	+	2.67468i	0.104538	+	0.390143i	0.998292	−	0.0584148i	$-0.0186046\pi$
$47$	0.716679	+	2.67468i	0.104538	+	0.390143i	−0.893754	+	0.448558i	$0.851938\pi$
$48$	−8.88410	+	4.31215i	−1.28231	+	0.622406i
$49$		0			0
$50$	6.43608	+	2.92862i	0.910200	+	0.414169i
$51$	−10.5691	−	6.10206i	−1.47997	−	0.854459i
$52$	−0.0585551	−	0.157068i	−0.00812014	−	0.0217815i
$53$	−9.12265	−	2.44441i	−1.25309	−	0.335765i	−0.429562	−	0.903037i	$-0.641332\pi$
$53$	−9.12265	−	2.44441i	−1.25309	−	0.335765i	−0.823530	+	0.567272i	$0.807999\pi$
$54$	−0.324510	−	0.0706197i	−0.0441602	−	0.00961013i
$55$	−7.29241	+	7.65915i	−0.983308	+	1.03276i
$56$		0			0
$57$	−4.59281	−	4.59281i	−0.608333	−	0.608333i
$58$	8.65360	−	5.56036i	1.13627	−	0.730112i
$59$	1.67748	+	2.90547i	0.218389	+	0.378260i	0.954315	−	0.298801i	$-0.0965866\pi$
$59$	1.67748	+	2.90547i	0.218389	+	0.378260i	−0.735927	+	0.677061i	$0.763253\pi$
$60$	−10.1520	−	4.34053i	−1.31061	−	0.560360i
$61$	0.978771	−	1.69528i	0.125319	−	0.217058i	−0.796539	−	0.604587i	$-0.793338\pi$
$61$	0.978771	−	1.69528i	0.125319	−	0.217058i	0.921857	+	0.387529i	$0.126671\pi$
$62$	−5.82822	−	3.00524i	−0.740185	−	0.381666i
$63$		0			0
$64$	7.67701	−	2.25021i	0.959627	−	0.281277i
$65$	0.0896988	−	0.164554i	0.0111258	−	0.0204104i
$66$	11.1085	−	12.2179i	1.36737	−	1.50391i
$67$	0.491893	+	0.131802i	0.0600943	+	0.0161022i	0.288741	−	0.957407i	$-0.406763\pi$
$67$	0.491893	+	0.131802i	0.0600943	+	0.0161022i	−0.228647	+	0.973509i	$0.573430\pi$
$68$	7.62273	+	6.29589i	0.924392	+	0.763488i
$69$		−	2.79272i		−	0.336204i
$70$		0			0
$71$			14.4625i			1.71638i	0.513329	+	0.858192i	$0.328412\pi$
$71$			14.4625i			1.71638i	−0.513329	+	0.858192i	$0.671588\pi$
$72$	8.12646	+	3.25558i	0.957712	+	0.383674i
$73$	−9.26507	−	2.48257i	−1.08439	−	0.290563i	−0.327999	−	0.944678i	$-0.606374\pi$
$73$	−9.26507	−	2.48257i	−1.08439	−	0.290563i	−0.756395	+	0.654115i	$0.773041\pi$
$74$	2.41333	+	2.19421i	0.280544	+	0.255072i
$75$	−3.77565	−	11.7526i	−0.435974	−	1.35707i
$76$	3.05145	+	4.28660i	0.350026	+	0.491707i
$77$		0			0
$78$	−0.134113	+	0.260092i	−0.0151853	+	0.0294496i
$79$	3.05204	−	5.28630i	0.343382	−	0.594755i	−0.641677	−	0.766975i	$-0.721761\pi$
$79$	3.05204	−	5.28630i	0.343382	−	0.594755i	0.985058	+	0.172221i	$0.0550942\pi$
$80$	7.52637	+	4.83257i	0.841474	+	0.540298i
$81$	−4.35280	−	7.53927i	−0.483644	−	0.837696i
$82$	4.37109	+	6.80273i	0.482706	+	0.751235i
$83$	5.62620	+	5.62620i	0.617555	+	0.617555i	0.944904	−	0.327348i	$-0.106155\pi$
$83$	5.62620	+	5.62620i	0.617555	+	0.617555i	−0.327348	+	0.944904i	$0.606155\pi$
$84$		0			0
$85$	0.271049	+	11.0502i	0.0293994	+	1.19856i
$86$	0.668982	−	3.07409i	0.0721382	−	0.331488i
$87$	−17.3447	−	4.64751i	−1.85955	−	0.498265i
$88$	−10.5171	+	8.26668i	−1.12112	+	0.881231i
$89$	14.4482	+	8.34169i	1.53151	+	0.884218i	0.999292	+	0.0376100i	$0.0119745\pi$
$89$	14.4482	+	8.34169i	1.53151	+	0.884218i	0.532217	+	0.846608i	$0.321359\pi$
$90$	3.20718	+	9.24725i	0.338067	+	0.974746i
$91$		0			0
$92$	−0.375524	+	2.23100i	−0.0391511	+	0.232598i
$93$	2.96282	+	11.0574i	0.307230	+	1.14660i
$94$	−2.63437	+	2.89745i	−0.271715	+	0.298849i
$95$	−1.38279	+	5.71802i	−0.141872	+	0.586657i
$96$	−11.9223	−	7.27348i	−1.21681	−	0.742346i
$97$	−5.81505	−	5.81505i	−0.590429	−	0.590429i	0.347318	−	0.937747i	$-0.387092\pi$
$97$	−5.81505	−	5.81505i	−0.590429	−	0.590429i	−0.937747	+	0.347318i	$0.887092\pi$
$98$		0			0
$99$	−14.6384			−1.47122
$100$	1.43591	+	9.89637i	0.143591	+	0.989637i
$101$	−4.28723	−	7.42571i	−0.426596	−	0.738885i	0.569972	−	0.821664i	$-0.306954\pi$
$101$	−4.28723	−	7.42571i	−0.426596	−	0.738885i	−0.996568	+	0.0827785i	$0.973621\pi$
$102$	−0.819862	−	17.2398i	−0.0811785	−	1.70699i
$103$	3.15482	−	0.845330i	0.310853	−	0.0832929i	−0.100020	−	0.994985i	$-0.531891\pi$
$103$	3.15482	−	0.845330i	0.310853	−	0.0832929i	0.410873	+	0.911693i	$0.365224\pi$
$104$	0.142111	−	0.189744i	0.0139351	−	0.0186059i
$105$		0			0
$106$	−4.06586	−	12.7226i	−0.394911	−	1.23573i
$107$	−1.75796	−	6.56081i	−0.169949	−	0.634257i	−0.997357	−	0.0726563i	$-0.976852\pi$
$107$	−1.75796	−	6.56081i	−0.169949	−	0.634257i	0.827408	−	0.561601i	$-0.189814\pi$
$108$	−0.164062	−	0.440081i	−0.0157869	−	0.0423468i
$109$	3.39423	−	1.95966i	0.325108	−	0.187701i	−0.328559	−	0.944483i	$-0.606563\pi$
$109$	3.39423	−	1.95966i	0.325108	−	0.187701i	0.653667	+	0.756782i	$0.273230\pi$
$110$	−14.6876	−	2.82098i	−1.40041	−	0.268970i
$111$		−	5.69404i		−	0.540455i
$112$		0			0
$113$	−0.0280186	+	0.0280186i	−0.00263577	+	0.00263577i	−0.708423	−	0.705788i	$-0.750593\pi$
$113$	−0.0280186	+	0.0280186i	−0.00263577	+	0.00263577i	0.705788	+	0.708423i	$0.250593\pi$
$114$	1.95326	−	8.97555i	0.182939	−	0.840637i
$115$	−2.15887	+	1.31804i	−0.201316	+	0.122908i
$116$	13.2311	+	6.04499i	1.22848	+	0.561263i
$117$	0.250575	−	0.0671414i	0.0231657	−	0.00620723i
$118$	−2.17444	+	4.21701i	−0.200174	+	0.388207i
$119$		0			0
$120$	−2.59680	−	15.3968i	−0.237054	−	1.40553i
$121$	5.68418	−	9.84529i	0.516744	−	0.895026i
$122$	2.76526	−	0.131506i	0.250355	−	0.0119060i
$123$	3.65348	−	13.6350i	0.329423	−	1.22942i
$124$	−0.880048	−	9.23173i	−0.0790306	−	0.829034i
$125$	−7.30320	+	8.46542i	−0.653218	+	0.757170i
$126$		0			0
$127$	−6.53450	+	6.53450i	−0.579843	+	0.579843i	−0.934860	−	0.355017i	$-0.884475\pi$
$127$	−6.53450	+	6.53450i	−0.579843	+	0.579843i	0.355017	+	0.934860i	$0.384475\pi$
$128$	8.54622	+	7.41364i	0.755386	+	0.655280i
$129$	−4.75632	+	2.74606i	−0.418770	+	0.241777i
$130$	0.264356	−	0.0190784i	0.0231855	−	0.00167329i
$131$	3.19588	+	1.84514i	0.279225	+	0.161211i	0.633073	−	0.774092i	$-0.281793\pi$
$131$	3.19588	+	1.84514i	0.279225	+	0.161211i	−0.353847	+	0.935303i	$0.615127\pi$
$132$	23.0288	+	3.87624i	2.00440	+	0.337383i
$133$		0			0
$134$	0.219231	+	0.686002i	0.0189387	+	0.0592616i
$135$	0.251322	−	0.461055i	0.0216304	−	0.0396813i
$136$	−1.66319	+	13.8824i	−0.142618	+	1.19041i
$137$	−5.13977	+	19.1819i	−0.439120	+	1.63882i	0.291890	+	0.956452i	$0.405716\pi$
$137$	−5.13977	+	19.1819i	−0.439120	+	1.63882i	−0.731010	+	0.682366i	$0.760951\pi$
$138$	3.32270	−	2.13500i	0.282847	−	0.181743i
$139$	−1.15593			−0.0980447			−0.0490223	−	0.998798i	$-0.515611\pi$
$139$	−1.15593			−0.0980447			−0.0490223	+	0.998798i	$0.515611\pi$
$140$		0			0
$141$	6.83628			0.575719
$142$	−17.2071	+	11.0564i	−1.44399	+	0.927833i
$143$	−0.102596	+	0.382893i	−0.00857950	+	0.0320191i
$144$	2.33917	+	12.1575i	0.194931	+	1.01312i
$145$	4.59330	+	15.6015i	0.381452	+	1.29564i
$146$	−4.12934	−	12.9212i	−0.341746	−	1.06937i
$147$		0			0
$148$	−0.765652	+	4.54876i	−0.0629362	+	0.373906i
$149$	5.37045	+	3.10063i	0.439965	+	0.254014i	0.703583	−	0.710613i	$-0.251582\pi$
$149$	5.37045	+	3.10063i	0.439965	+	0.254014i	−0.263618	+	0.964627i	$0.584916\pi$
$150$	11.0964	−	13.4768i	0.906020	−	1.10038i
$151$	−8.72300	+	5.03623i	−0.709868	+	0.409842i	−0.811012	−	0.585029i	$-0.801083\pi$
$151$	−8.72300	+	5.03623i	−0.709868	+	0.409842i	0.101144	+	0.994872i	$0.467750\pi$
$152$	−2.76729	+	6.90759i	−0.224457	+	0.560279i
$153$	−10.8188	+	10.8188i	−0.874646	+	0.874646i
$154$		0			0
$155$	7.14943	−	7.50898i	0.574256	−	0.603136i
$156$	−0.411977	+	0.0392732i	−0.0329846	+	0.00314438i
$157$	−3.77089	+	14.0732i	−0.300950	+	1.12316i	0.635426	+	0.772162i	$0.280825\pi$
$157$	−3.77089	+	14.0732i	−0.300950	+	1.12316i	−0.936376	+	0.350999i	$0.885842\pi$
$158$	8.62274	−	0.410067i	0.685988	−	0.0326232i
$159$	−11.6584	+	20.1929i	−0.924570	+	1.60140i
$160$	0.00414940	+	12.6491i	0.000328038	+	1.00000i
$161$		0			0
$162$	5.64235	−	10.9425i	0.443305	−	0.859725i
$163$	2.85106	−	0.763938i	0.223312	−	0.0598363i	−0.145428	−	0.989369i	$-0.546456\pi$
$163$	2.85106	−	0.763938i	0.223312	−	0.0598363i	0.368740	+	0.929533i	$0.379789\pi$
$164$	−4.75206	+	10.4012i	−0.371073	+	0.812197i
$165$	13.6051	+	22.2843i	1.05916	+	1.73483i
$166$	−2.39274	+	10.9950i	−0.185713	+	0.853381i
$167$	6.13096	−	6.13096i	0.474428	−	0.474428i	−0.428916	−	0.903344i	$-0.641105\pi$
$167$	6.13096	−	6.13096i	0.474428	−	0.474428i	0.903344	+	0.428916i	$0.141105\pi$
$168$		0			0
$169$			12.9930i			0.999460i
$170$	−12.9400	+	8.77022i	−0.992453	+	0.672645i
$171$	−7.05197	+	4.07146i	−0.539278	+	0.311352i
$172$	4.16890	−	1.55417i	0.317875	−	0.118504i
$173$	0.464708	+	1.73431i	0.0353311	+	0.131857i	0.981339	−	0.192287i	$-0.0615904\pi$
$173$	0.464708	+	1.73431i	0.0353311	+	0.131857i	−0.946008	+	0.324144i	$0.894924\pi$
$174$	−7.73035	−	24.1893i	−0.586037	−	1.83378i
$175$		0			0
$176$	−17.8756	−	6.19316i	−1.34743	−	0.466827i
$177$	8.00057	−	2.14375i	0.601360	−	0.161134i
$178$	1.12078	+	23.5672i	0.0840057	+	1.76644i
$179$	10.7713	+	18.6564i	0.805084	+	1.39445i	0.916234	+	0.400643i	$0.131213\pi$
$179$	10.7713	+	18.6564i	0.805084	+	1.39445i	−0.111150	+	0.993804i	$0.535453\pi$
$180$	−8.55027	+	10.8852i	−0.637300	+	0.811337i
$181$	16.2122			1.20504			0.602520	−	0.798104i	$-0.294163\pi$
$181$	16.2122			1.20504			0.602520	+	0.798104i	$0.294163\pi$
$182$		0			0
$183$	−3.41733	−	3.41733i	−0.252616	−	0.252616i
$184$	−2.94146	+	1.25878i	−0.216848	+	0.0927986i
$185$	−4.40170	+	2.68735i	−0.323619	+	0.197578i
$186$	−10.8907	+	11.9783i	−0.798548	+	0.878292i
$187$	−6.05102	−	22.5827i	−0.442495	−	1.65141i
$188$	−5.46125	−	0.919244i	−0.398303	−	0.0670427i
$189$		0			0
$190$	−7.86028	+	2.72614i	−0.570244	+	0.197775i
$191$	14.2331	+	8.21746i	1.02987	+	0.594595i	0.916947	−	0.399009i	$-0.130646\pi$
$191$	14.2331	+	8.21746i	1.02987	+	0.594595i	0.112921	+	0.993604i	$0.463979\pi$
$192$	−0.460637	−	19.7453i	−0.0332436	−	1.42499i
$193$	−4.79080	−	1.28369i	−0.344849	−	0.0924021i	0.0822374	−	0.996613i	$-0.473793\pi$
$193$	−4.79080	−	1.28369i	−0.344849	−	0.0924021i	−0.427087	+	0.904211i	$0.640460\pi$
$194$	2.47306	−	11.3641i	0.177555	−	0.815897i
$195$	−0.335098	−	0.319052i	−0.0239968	−	0.0228478i
$196$		0			0
$197$	−3.89922	−	3.89922i	−0.277808	−	0.277808i	0.554425	−	0.832233i	$-0.312938\pi$
$197$	−3.89922	−	3.89922i	−0.277808	−	0.277808i	−0.832233	+	0.554425i	$0.812938\pi$
$198$	−11.1909	−	17.4164i	−0.795302	−	1.23773i
$199$	−9.44788	−	16.3642i	−0.669743	−	1.16003i	−0.977976	−	0.208717i	$-0.933071\pi$
$199$	−9.44788	−	16.3642i	−0.669743	−	1.16003i	0.308233	−	0.951311i	$-0.400262\pi$
$200$	−10.6767	+	9.27406i	−0.754956	+	0.655775i
$201$	0.628620	−	1.08880i	0.0443394	−	0.0767981i
$202$	5.55737	−	10.7777i	0.391015	−	0.758316i
$203$		0			0
$204$	19.8846	−	14.1550i	1.39220	−	0.991050i
$205$	−12.2646	+	3.61086i	−0.856597	+	0.252193i
$206$	3.41757	+	3.10727i	0.238113	+	0.216494i
$207$	−3.38187	−	0.906169i	−0.235056	−	0.0629831i
$208$	0.334394	+	0.0240228i	0.0231861	+	0.00166568i
$209$		−	12.4428i		−	0.860690i
$210$		0			0
$211$			10.9795i			0.755859i	0.925834	+	0.377929i	$0.123364\pi$
$211$			10.9795i			0.755859i	−0.925834	+	0.377929i	$0.876636\pi$
$212$	12.0287	−	14.5637i	0.826135	−	1.00024i
$213$	34.4888	+	9.24126i	2.36314	+	0.633201i
$214$	6.46193	−	7.10723i	0.441728	−	0.485840i
$215$	4.36758	+	2.38078i	0.297867	+	0.162368i
$216$	0.398173	−	0.531633i	0.0270922	−	0.0361731i
$217$		0			0
$218$	4.92639	+	2.54022i	0.333657	+	0.172046i
$219$	−11.8404	+	20.5082i	−0.800099	+	1.38581i
$220$	−7.87216	−	19.6315i	−0.530741	−	1.32356i
$221$	0.207158	+	0.358809i	0.0139350	+	0.0241361i
$222$	6.77462	−	4.35302i	0.454683	−	0.292156i
$223$	−13.6990	−	13.6990i	−0.917356	−	0.917356i	0.0794806	−	0.996836i	$-0.474674\pi$
$223$	−13.6990	−	13.6990i	−0.917356	−	0.917356i	−0.996836	+	0.0794806i	$0.974674\pi$
$224$		0			0
$225$	−15.4570	+	0.758741i	−1.03047	+	0.0505828i
$226$	−0.0547556	−	0.0119159i	−0.00364229	−	0.000792634i
$227$	22.1724	+	5.94107i	1.47163	+	0.394322i	0.903490	−	0.428609i	$-0.140996\pi$
$227$	22.1724	+	5.94107i	1.47163	+	0.394322i	0.568141	+	0.822931i	$0.307663\pi$
$228$	12.1721	−	4.53776i	0.806117	−	0.300521i
$229$	−10.3396	−	5.96955i	−0.683258	−	0.394479i	0.117824	−	0.993035i	$-0.462408\pi$
$229$	−10.3396	−	5.96955i	−0.683258	−	0.394479i	−0.801081	+	0.598556i	$0.795742\pi$
$230$	−3.21860	−	1.56094i	−0.212228	−	0.102925i
$231$		0			0
$232$	2.92287	+	20.3634i	0.191896	+	1.33692i
$233$	−6.15761	−	22.9805i	−0.403399	−	1.50550i	−0.806990	−	0.590565i	$-0.798905\pi$
$233$	−6.15761	−	22.9805i	−0.403399	−	1.50550i	0.403592	−	0.914939i	$-0.367762\pi$
$234$	0.271445	+	0.246799i	0.0177449	+	0.0161337i
$235$	−3.22644	−	5.28469i	−0.210469	−	0.344735i
$236$	−6.67962	+	0.636759i	−0.434806	+	0.0414495i
$237$	−10.6561	−	10.6561i	−0.692186	−	0.692186i
$238$		0			0
$239$	1.50749			0.0975113			0.0487556	−	0.998811i	$-0.484474\pi$
$239$	1.50749			0.0975113			0.0487556	+	0.998811i	$0.484474\pi$
$240$	16.3335	−	14.8603i	1.05432	−	0.959226i
$241$	−9.26556	−	16.0484i	−0.596847	−	1.03377i	−0.993283	−	0.115708i	$-0.963086\pi$
$241$	−9.26556	−	16.0484i	−0.596847	−	1.03377i	0.396436	−	0.918062i	$-0.370247\pi$
$242$	16.0591	−	0.763716i	1.03232	−	0.0490935i
$243$	−21.4408	+	5.74504i	−1.37543	+	0.368544i
$244$	2.27047	+	3.18949i	0.145352	+	0.204186i
$245$		0			0
$246$	19.0155	−	6.07695i	1.21239	−	0.387452i
$247$	0.0570710	+	0.212992i	0.00363134	+	0.0135524i
$248$	10.3109	−	8.10460i	0.654741	−	0.514642i
$249$	17.0119	−	9.82180i	1.07808	−	0.622431i
$250$	−15.6551	−	2.21744i	−0.990117	−	0.140243i
$251$			18.0219i			1.13753i	0.822500	+	0.568765i	$0.192579\pi$
$251$			18.0219i			1.13753i	−0.822500	+	0.568765i	$0.807421\pi$
$252$		0			0
$253$	3.78301	−	3.78301i	0.237836	−	0.237836i
$254$	−12.7701	−	2.77903i	−0.801268	−	0.174372i
$255$	26.5247	+	6.41448i	1.66104	+	0.401690i
$256$	−2.28707	+	15.8357i	−0.142942	+	0.989731i
$257$	−14.4032	+	3.85933i	−0.898448	+	0.240738i	−0.678350	−	0.734739i	$-0.737304\pi$
$257$	−14.4032	+	3.85933i	−0.898448	+	0.240738i	−0.220098	+	0.975478i	$0.570638\pi$
$258$	−6.90333	−	3.55961i	−0.429783	−	0.221611i
$259$		0			0
$260$	0.224796	+	0.299938i	0.0139412	+	0.0186014i
$261$	−11.2559	+	19.4958i	−0.696723	+	1.20676i
$262$	0.247910	+	5.21295i	0.0153159	+	0.322057i
$263$	1.83499	−	6.84826i	0.113150	−	0.422282i	−0.885992	−	0.463701i	$-0.846521\pi$
$263$	1.83499	−	6.84826i	0.113150	−	0.422282i	0.999142	+	0.0414191i	$0.0131879\pi$
$264$	12.9934	+	30.3624i	0.799688	+	1.86868i
$265$	21.1121	−	0.517856i	1.29691	−	0.0318117i
$266$		0			0
$267$	29.1246	−	29.1246i	1.78240	−	1.78240i
$268$	−0.648587	+	0.785275i	−0.0396188	+	0.0479683i
$269$	5.23463	−	3.02221i	0.319161	−	0.184268i	−0.331858	−	0.943329i	$-0.607675\pi$
$269$	5.23463	−	3.02221i	0.319161	−	0.184268i	0.651019	+	0.759062i	$0.274342\pi$
$270$	0.740684	−	0.0534548i	0.0450766	−	0.00325316i
$271$	20.3476	+	11.7477i	1.23603	+	0.713622i	0.968280	−	0.249866i	$-0.0803866\pi$
$271$	20.3476	+	11.7477i	1.23603	+	0.713622i	0.267750	+	0.963488i	$0.413720\pi$
$272$	−17.7884	+	8.63413i	−1.07858	+	0.523521i
$273$		0			0
$274$	−26.7514	+	8.54914i	−1.61611	+	0.516473i
$275$	10.8055	−	21.0345i	0.651597	−	1.26843i
$276$	5.08032	+	2.32108i	0.305799	+	0.139712i
$277$	6.03684	−	22.5298i	0.362719	−	1.35369i	−0.507768	−	0.861494i	$-0.669529\pi$
$277$	6.03684	−	22.5298i	0.362719	−	1.35369i	0.870487	−	0.492191i	$-0.163804\pi$
$278$	−0.883694	−	1.37529i	−0.0530004	−	0.0824846i
$279$	14.3514			0.859197
$280$		0			0
$281$	−19.3011			−1.15141			−0.575703	−	0.817659i	$-0.695272\pi$
$281$	−19.3011			−1.15141			−0.575703	+	0.817659i	$0.695272\pi$
$282$	5.22625	+	8.13362i	0.311219	+	0.484350i
$283$	1.84508	−	6.88593i	0.109679	−	0.409326i	−0.889155	−	0.457606i	$-0.848707\pi$
$283$	1.84508	−	6.88593i	0.109679	−	0.409326i	0.998834	+	0.0482794i	$0.0153738\pi$
$284$	−26.3092	−	12.0201i	−1.56117	−	0.713259i
$285$	12.7522	+	6.95126i	0.755377	+	0.411757i
$286$	−0.533989	+	0.170651i	−0.0315754	+	0.0100908i
$287$		0			0
$288$	−12.6764	+	12.0773i	−0.746963	+	0.711663i
$289$	−6.43980	−	3.71802i	−0.378812	−	0.218707i
$290$	−15.0508	+	17.3922i	−0.883811	+	1.02130i
$291$	−17.5829	+	10.1515i	−1.03073	+	0.595091i
$292$	12.2165	−	14.7911i	0.714916	−	0.865583i
$293$	−1.29442	+	1.29442i	−0.0756208	+	0.0756208i	−0.743906	−	0.668285i	$-0.767029\pi$
$293$	−1.29442	+	1.29442i	−0.0756208	+	0.0756208i	0.668285	+	0.743906i	$0.267029\pi$
$294$		0			0
$295$	−5.43312	−	5.17297i	−0.316329	−	0.301182i
$296$	−5.99732	+	2.56652i	−0.348587	+	0.149176i
$297$	−0.287458	+	1.07281i	−0.0166800	+	0.0622506i
$298$	0.416596	+	8.76001i	0.0241327	+	0.507454i
$299$	−0.0474048	+	0.0821076i	−0.00274149	+	0.00474840i
$300$	24.5175	+	2.89936i	1.41552	+	0.167394i
$301$		0			0
$302$	−12.6606	−	6.52826i	−0.728535	−	0.375659i
$303$	−20.4476	+	5.47891i	−1.17468	+	0.314755i
$304$	−10.3340	+	1.98832i	−0.592696	+	0.114038i
$305$	−1.02888	+	4.25456i	−0.0589137	+	0.243615i
$306$	−21.1427	−	4.60106i	−1.20865	−	0.263025i
$307$	−3.86175	+	3.86175i	−0.220402	+	0.220402i	−0.808667	−	0.588266i	$-0.799811\pi$
$307$	−3.86175	+	3.86175i	−0.220402	+	0.220402i	0.588266	+	0.808667i	$0.299811\pi$
$308$		0			0
$309$		−	8.06346i		−	0.458714i
$310$	14.3996	+	2.76567i	0.817844	+	0.157080i
$311$	−17.7808	+	10.2657i	−1.00826	+	0.582116i	−0.910680	−	0.413112i	$-0.864442\pi$
$311$	−17.7808	+	10.2657i	−1.00826	+	0.582116i	−0.0975749	+	0.995228i	$0.531109\pi$
$312$	−0.361678	−	0.460136i	−0.0204760	−	0.0260501i
$313$	−7.22385	−	26.9598i	−0.408316	−	1.52386i	−0.797856	−	0.602847i	$-0.794033\pi$
$313$	−7.22385	−	26.9598i	−0.408316	−	1.52386i	0.389540	−	0.921009i	$-0.372634\pi$
$314$	−19.6267	+	6.27225i	−1.10760	+	0.353964i
$315$		0			0
$316$	7.07986	+	9.94561i	0.398273	+	0.559484i
$317$	12.5169	−	3.35388i	0.703016	−	0.188373i	0.110435	−	0.993883i	$-0.464776\pi$
$317$	12.5169	−	3.35388i	0.703016	−	0.188373i	0.592581	+	0.805511i	$0.298109\pi$
$318$	−32.9377	+	1.56640i	−1.84705	+	0.0878394i
$319$	−17.1997	−	29.7907i	−0.962996	−	1.66796i
$320$	−15.0464	+	9.67502i	−0.841119	+	0.540850i
$321$	−16.7689			−0.935949
$322$		0			0
$323$	−9.19609	−	9.19609i	−0.511684	−	0.511684i
$324$	17.3326	−	1.65229i	0.962923	−	0.0917941i
$325$	−0.0884867	+	0.409622i	−0.00490836	+	0.0227217i
$326$	3.08851	+	2.80809i	0.171057	+	0.155526i
$327$	−2.50436	−	9.34642i	−0.138492	−	0.516858i
$328$	−16.0079	+	2.29771i	−0.883891	+	0.126870i
$329$		0			0
$330$	−16.1123	+	33.2231i	−0.886953	+	1.82887i
$331$	6.41324	+	3.70269i	0.352504	+	0.203518i	0.665787	−	0.746142i	$-0.268096\pi$
$331$	6.41324	+	3.70269i	0.352504	+	0.203518i	−0.313284	+	0.949660i	$0.601429\pi$
$332$	−14.9108	+	5.55876i	−0.818338	+	0.305077i
$333$	−6.89526	−	1.84758i	−0.377858	−	0.101247i
$334$	11.9815	+	2.60741i	0.655598	+	0.142671i
$335$	−1.13836	+	0.0279228i	−0.0621955	+	0.00152559i
$336$		0			0
$337$	−5.81990	−	5.81990i	−0.317030	−	0.317030i	0.530595	−	0.847625i	$-0.321968\pi$
$337$	−5.81990	−	5.81990i	−0.317030	−	0.317030i	−0.847625	+	0.530595i	$0.821968\pi$
$338$	−15.4587	+	9.93297i	−0.840842	+	0.540282i
$339$	0.0489128	+	0.0847195i	0.00265658	+	0.00460133i
$340$	−20.3270	−	8.69094i	−1.10239	−	0.471333i
$341$	−10.9649	+	18.9918i	−0.593782	+	1.02846i
$342$	−10.2353	−	5.27767i	−0.553459	−	0.285384i
$343$		0			0
$344$	5.03617	+	3.77190i	0.271532	+	0.203367i
$345$	1.76367	+	5.99047i	0.0949530	+	0.322516i
$346$	−1.70817	+	1.87876i	−0.0918320	+	0.101003i
$347$	10.6671	+	2.85823i	0.572638	+	0.153438i	0.533506	−	0.845796i	$-0.320874\pi$
$347$	10.6671	+	2.85823i	0.572638	+	0.153438i	0.0391317	+	0.999234i	$0.487541\pi$
$348$	22.8700	−	27.6897i	1.22596	−	1.48433i
$349$			10.3995i			0.556672i	0.960484	+	0.278336i	$0.0897829\pi$
$349$			10.3995i			0.556672i	−0.960484	+	0.278336i	$0.910217\pi$
$350$		0			0
$351$		−	0.0196824i		−	0.00105057i
$352$	−6.29725	−	26.0025i	−0.335644	−	1.38594i
$353$	−7.28892	−	1.95306i	−0.387950	−	0.103951i	0.0595714	−	0.998224i	$-0.481027\pi$
$353$	−7.28892	−	1.95306i	−0.387950	−	0.103951i	−0.447522	+	0.894273i	$0.647693\pi$
$354$	8.66691	+	7.87999i	0.460641	+	0.418817i
$355$	−9.13346	−	31.0226i	−0.484754	−	1.64651i
$356$	−27.1828	+	19.3503i	−1.44069	+	1.02556i
$357$		0			0
$358$	−13.9624	+	27.0780i	−0.737935	+	1.43112i
$359$	−5.74179	+	9.94507i	−0.303040	+	0.524881i	−0.976823	−	0.214049i	$-0.931335\pi$
$359$	−5.74179	+	9.94507i	−0.303040	+	0.524881i	0.673783	+	0.738929i	$0.264668\pi$
$360$	−19.4875	−	1.85127i	−1.02708	−	0.0975703i
$361$	6.03921	+	10.4602i	0.317853	+	0.550538i
$362$	12.3940	+	19.2888i	0.651413	+	1.01380i
$363$	−19.8460	−	19.8460i	−1.04165	−	1.04165i
$364$		0			0
$365$	21.4417	−	0.525941i	1.12231	−	0.0275290i
$366$	1.45334	−	6.67835i	0.0759673	−	0.349083i
$367$	12.2312	+	3.27735i	0.638465	+	0.171076i	0.563508	−	0.826111i	$-0.309451\pi$
$367$	12.2312	+	3.27735i	0.638465	+	0.171076i	0.0749570	+	0.997187i	$0.476118\pi$
$368$	−3.74637	−	2.53735i	−0.195293	−	0.132269i
$369$	−15.3259	−	8.84843i	−0.797836	−	0.460631i
$370$	−6.56238	−	3.18258i	−0.341162	−	0.165454i
$371$		0			0
$372$	−22.5773	−	3.80024i	−1.17058	−	0.197033i
$373$	−6.44552	−	24.0550i	−0.333737	−	1.24552i	−0.905232	−	0.424917i	$-0.860303\pi$
$373$	−6.44552	−	24.0550i	−0.333737	−	1.24552i	0.571496	−	0.820605i	$-0.306363\pi$
$374$	22.2424	−	24.4635i	1.15013	−	1.26498i
$375$	15.5209	+	22.8252i	0.801498	+	1.17869i
$376$	−3.08137	−	7.20040i	−0.158909	−	0.371332i
$377$	0.431057	+	0.431057i	0.0222006	+	0.0222006i
$378$		0			0
$379$	4.18354			0.214894			0.107447	−	0.994211i	$-0.465732\pi$
$379$	4.18354			0.214894			0.107447	+	0.994211i	$0.465732\pi$
$380$	−9.25257	−	7.26784i	−0.474647	−	0.372832i
$381$	11.4074	+	19.7583i	0.584421	+	1.01225i
$382$	1.10408	+	23.2163i	0.0564898	+	1.18785i
$383$	12.9702	−	3.47535i	0.662745	−	0.177582i	0.0882604	−	0.996097i	$-0.471869\pi$
$383$	12.9702	−	3.47535i	0.662745	−	0.177582i	0.574484	+	0.818515i	$0.305203\pi$
$384$	23.1402	−	15.6431i	1.18087	−	0.798282i
$385$		0			0
$386$	−2.13521	−	6.68133i	−0.108679	−	0.340071i
$387$	1.78206	+	6.65075i	0.0905873	+	0.338076i
$388$	15.4113	−	5.74535i	0.782393	−	0.291676i
$389$	15.5106	−	8.95506i	0.786419	−	0.454039i	−0.0522811	−	0.998632i	$-0.516649\pi$
$389$	15.5106	−	8.95506i	0.786419	−	0.454039i	0.838700	+	0.544593i	$0.183316\pi$
$390$	0.123422	−	0.642602i	0.00624970	−	0.0325394i
$391$		−	5.59179i		−	0.282789i
$392$		0			0
$393$	6.44222	−	6.44222i	0.324967	−	0.324967i
$394$	1.65828	−	7.62009i	0.0835430	−	0.383895i
$395$	−3.20831	+	13.2667i	−0.161427	+	0.667522i
$396$	12.1663	−	26.6292i	0.611378	−	1.33817i
$397$	−5.90626	+	1.58258i	−0.296427	+	0.0794273i	−0.403967	−	0.914773i	$-0.632369\pi$
$397$	−5.90626	+	1.58258i	−0.296427	+	0.0794273i	0.107541	+	0.994201i	$0.465702\pi$
$398$	12.2469	−	23.7511i	0.613882	−	1.19053i
$399$		0			0
$400$	−19.1962	−	5.61294i	−0.959811	−	0.280647i
$401$	−9.81777	+	17.0049i	−0.490276	+	0.849183i	−0.999937	−	0.0111923i	$-0.996437\pi$
$401$	−9.81777	+	17.0049i	−0.490276	+	0.849183i	0.509662	+	0.860375i	$0.329771\pi$
$402$	1.77600	−	0.0844603i	0.0885788	−	0.00421250i
$403$	0.100584	−	0.375386i	0.00501046	−	0.0186993i
$404$	17.0715	−	1.62741i	0.849341	−	0.0809665i
$405$	14.0981	+	13.4231i	0.700542	+	0.666998i
$406$		0			0
$407$	7.71315	−	7.71315i	0.382327	−	0.382327i
$408$	32.0428	+	12.8368i	1.58635	+	0.635518i
$409$	8.70611	−	5.02647i	0.430489	−	0.248543i	−0.269066	−	0.963122i	$-0.586715\pi$
$409$	8.70611	−	5.02647i	0.430489	−	0.248543i	0.699555	+	0.714579i	$0.253382\pi$
$410$	−13.6722	−	11.8316i	−0.675223	−	0.584323i
$411$	42.4589	+	24.5137i	2.09434	+	1.20917i
$412$	−1.08426	+	6.44160i	−0.0534175	+	0.317355i
$413$		0			0
$414$	−1.50726	−	4.71641i	−0.0740779	−	0.231799i
$415$	−15.6215	−	8.51529i	−0.766828	−	0.417999i
$416$	0.227059	+	0.416218i	0.0111325	+	0.0204068i
$417$	−0.738616	+	2.75655i	−0.0361702	+	0.134989i
$418$	14.8042	−	9.51240i	0.724095	−	0.465267i
$419$	17.7853			0.868870			0.434435	−	0.900703i	$-0.356948\pi$
$419$	17.7853			0.868870			0.434435	+	0.900703i	$0.356948\pi$
$420$		0			0
$421$	39.6482			1.93234			0.966168	−	0.257913i	$-0.0830348\pi$
$421$	39.6482			1.93234			0.966168	+	0.257913i	$0.0830348\pi$
$422$	−13.0631	+	8.39368i	−0.635901	+	0.408598i
$423$	2.21821	−	8.27847i	0.107853	−	0.402513i
$424$	26.5233	+	3.17764i	1.28809	+	0.154320i
$425$	−7.55990	−	23.5319i	−0.366709	−	1.14146i
$426$	15.3713	+	48.0987i	0.744741	+	2.33039i
$427$		0			0
$428$	13.3960	+	2.25484i	0.647522	+	0.108992i
$429$	0.847531	+	0.489322i	0.0409192	+	0.0236247i
$430$	0.506378	+	7.01651i	0.0244197	+	0.338366i
$431$	−21.7939	+	12.5827i	−1.04977	+	0.606087i	−0.922586	−	0.385792i	$-0.873928\pi$
$431$	−21.7939	+	12.5827i	−1.04977	+	0.606087i	−0.127187	+	0.991879i	$0.540595\pi$
$432$	0.936921	+	0.0673082i	0.0450776	+	0.00323837i
$433$	−9.19231	+	9.19231i	−0.441754	+	0.441754i	−0.892601	−	0.450847i	$-0.851122\pi$
$433$	−9.19231	+	9.19231i	−0.441754	+	0.441754i	0.450847	+	0.892601i	$0.351122\pi$
$434$		0			0
$435$	40.1401	−	0.984591i	1.92457	−	0.0472075i
$436$	0.743873	+	7.80325i	0.0356251	+	0.373708i
$437$	0.770255	−	2.87463i	0.0368463	−	0.137512i
$438$	−33.4519	+	1.59085i	−1.59839	+	0.0760139i
$439$	−14.8997	+	25.8071i	−0.711125	+	1.23170i	0.253310	+	0.967385i	$0.418481\pi$
$439$	−14.8997	+	25.8071i	−0.711125	+	1.23170i	−0.964435	+	0.264320i	$0.914853\pi$
$440$	17.3389	−	24.3741i	0.826598	−	1.16199i
$441$		0			0
$442$	−0.268531	+	0.520776i	−0.0127727	+	0.0247708i
$443$	39.4412	−	10.5682i	1.87391	−	0.502112i	0.874039	−	0.485856i	$-0.161492\pi$
$443$	39.4412	−	10.5682i	1.87391	−	0.502112i	0.999868	−	0.0162556i	$-0.00517456\pi$
$444$	10.3582	+	4.73242i	0.491579	+	0.224591i
$445$	−36.2600	−	8.76878i	−1.71889	−	0.415680i
$446$	5.82600	−	26.7715i	0.275869	−	1.26767i
$447$	10.8257	−	10.8257i	0.512039	−	0.512039i
$448$		0			0
$449$		−	20.7052i		−	0.977139i	−0.872525	−	0.488570i	$-0.837519\pi$
$449$		−	20.7052i		−	0.977139i	0.872525	−	0.488570i	$-0.162481\pi$
$450$	−12.7194	−	17.8103i	−0.599598	−	0.839583i
$451$	23.4189	−	13.5209i	1.10275	−	0.636675i
$452$	−0.0276828	−	0.0742563i	−0.00130209	−	0.00349272i
$453$	6.43610	+	24.0199i	0.302394	+	1.12855i
$454$	9.88197	+	30.9219i	0.463784	+	1.45124i
$455$		0			0
$456$	14.7043	+	11.0130i	0.688593	+	0.515730i
$457$	−3.61891	+	0.969683i	−0.169285	+	0.0453599i	−0.342466	−	0.939530i	$-0.611262\pi$
$457$	−3.61891	+	0.969683i	−0.169285	+	0.0453599i	0.173181	+	0.984890i	$0.444596\pi$
$458$	−0.802058	−	16.8654i	−0.0374777	−	0.788067i
$459$	0.580425	+	1.00533i	0.0270919	+	0.0469246i
$460$	−0.603422	−	5.02272i	−0.0281347	−	0.234186i
$461$	6.66823			0.310570			0.155285	−	0.987870i	$-0.450370\pi$
$461$	6.66823			0.310570			0.155285	+	0.987870i	$0.450370\pi$
$462$		0			0
$463$	−14.7884	−	14.7884i	−0.687277	−	0.687277i	0.274353	−	0.961629i	$-0.411536\pi$
$463$	−14.7884	−	14.7884i	−0.687277	−	0.687277i	−0.961629	+	0.274353i	$0.911536\pi$
$464$	−21.9933	+	19.0451i	−1.02101	+	0.884146i
$465$	−13.3384	−	21.8474i	−0.618552	−	1.01315i
$466$	22.6342	−	24.8945i	1.04851	−	1.15321i
$467$	7.26895	+	27.1281i	0.336367	+	1.25534i	0.902380	+	0.430941i	$0.141818\pi$
$467$	7.26895	+	27.1281i	0.336367	+	1.25534i	−0.566013	+	0.824396i	$0.691515\pi$
$468$	−0.0861184	+	0.511632i	−0.00398083	+	0.0236502i
$469$		0			0
$470$	3.82101	−	7.87880i	0.176250	−	0.363422i
$471$	31.1509	+	17.9850i	1.43536	+	0.828703i
$472$	−5.86408	−	7.46043i	−0.269916	−	0.343394i
$473$	−10.1627	−	2.72309i	−0.467282	−	0.125208i
$474$	4.53187	−	20.8247i	0.208156	−	0.956511i
$475$	−0.644940	−	13.1386i	−0.0295919	−	0.602842i
$476$		0			0
$477$	20.6700	+	20.6700i	0.946413	+	0.946413i
$478$	1.15246	+	1.79357i	0.0527121	+	0.0820359i
$479$	5.27141	+	9.13034i	0.240857	+	0.417176i	0.960959	−	0.276692i	$-0.0892383\pi$
$479$	5.27141	+	9.13034i	0.240857	+	0.417176i	−0.720102	+	0.693868i	$0.755905\pi$
$480$	30.1671	+	8.07263i	1.37693	+	0.368464i
$481$	−0.0966532	+	0.167408i	−0.00440701	+	0.00763316i
$482$	12.0106	−	23.2927i	0.547067	−	1.06096i
$483$		0			0
$484$	13.1857	+	18.5229i	0.599348	+	0.841949i
$485$	16.1459	+	8.80113i	0.733145	+	0.399639i
$486$	−23.2265	−	21.1176i	−1.05358	−	0.957916i
$487$	36.7636	+	9.85078i	1.66592	+	0.446381i	0.964006	−	0.265882i	$-0.0856630\pi$
$487$	36.7636	+	9.85078i	1.66592	+	0.446381i	0.701913	+	0.712263i	$0.252330\pi$
$488$	−2.05903	+	5.13966i	−0.0932078	+	0.232662i
$489$		−	7.28707i		−	0.329533i
$490$		0			0
$491$		−	3.59770i		−	0.162362i	−0.996699	−	0.0811809i	$-0.974131\pi$
$491$		−	3.59770i		−	0.162362i	0.996699	−	0.0811809i	$-0.0258691\pi$
$492$	21.7673	+	17.9784i	0.981347	+	0.810530i
$493$	−34.7290	−	9.30560i	−1.56411	−	0.419103i
$494$	−0.209782	+	0.230731i	−0.00943854	+	0.0103811i
$495$	31.3999	−	9.24455i	1.41132	−	0.415512i
$496$	17.5252	+	6.07173i	0.786903	+	0.272629i
$497$		0			0
$498$	24.6910	+	12.7316i	1.10643	+	0.570516i
$499$	−5.11616	+	8.86145i	−0.229031	+	0.396693i	−0.957521	−	0.288363i	$-0.906889\pi$
$499$	−5.11616	+	8.86145i	−0.229031	+	0.396693i	0.728490	+	0.685056i	$0.240222\pi$
$500$	−9.32990	−	20.3212i	−0.417246	−	0.908794i
$501$	−10.7030	−	18.5381i	−0.478174	−	0.828221i
$502$	−21.4419	+	13.7775i	−0.957000	+	0.614920i
$503$	30.0943	+	30.0943i	1.34184	+	1.34184i	0.894231	+	0.447605i	$0.147723\pi$
$503$	30.0943	+	30.0943i	1.34184	+	1.34184i	0.447605	+	0.894231i	$0.352277\pi$
$504$		0			0
$505$	13.8858	+	13.2209i	0.617910	+	0.588322i
$506$	7.39299	+	1.60886i	0.328659	+	0.0715225i
$507$	30.9844	+	8.30225i	1.37607	+	0.368716i
$508$	−6.45618	−	17.3181i	−0.286447	−	0.768365i
$509$	0.0145211	+	0.00838376i	0.000643637	+	0.000371604i	0.500322	−	0.865840i	$-0.333215\pi$
$509$	0.0145211	+	0.00838376i	0.000643637	+	0.000371604i	−0.499678	+	0.866211i	$0.666548\pi$
$510$	12.6460	+	36.4621i	0.559974	+	1.61457i
$511$		0			0
$512$	−20.5893	+	9.38510i	−0.909928	+	0.414767i
$513$	0.159904	+	0.596770i	0.00705994	+	0.0263481i
$514$	−15.6028	−	14.1861i	−0.688210	−	0.625724i
$515$	−6.23334	+	3.80561i	−0.274674	+	0.167695i
$516$	−1.04239	−	10.9347i	−0.0458885	−	0.481372i
$517$	9.26042	+	9.26042i	0.407273	+	0.407273i
$518$		0			0
$519$	4.43276			0.194577
$520$	−0.185005	+	0.496755i	−0.00811299	+	0.0217841i
$521$	−0.00830997	−	0.0143933i	−0.000364066	−	0.000630582i	0.865843	−	0.500315i	$-0.166783\pi$
$521$	−0.00830997	−	0.0143933i	−0.000364066	−	0.000630582i	−0.866207	+	0.499685i	$0.833449\pi$
$522$	−31.8006	+	1.51232i	−1.39187	+	0.0661926i
$523$	−29.8717	+	8.00409i	−1.30620	+	0.349994i	−0.843790	−	0.536674i	$-0.819681\pi$
$523$	−29.8717	+	8.00409i	−1.30620	+	0.349994i	−0.462407	+	0.886668i	$0.653014\pi$
$524$	−6.01271	+	4.28019i	−0.262666	+	0.186981i
$525$		0			0
$526$	9.55070	−	3.05219i	0.416430	−	0.133082i
$527$	5.93238	+	22.1400i	0.258419	+	0.964432i
$528$	−26.1910	+	38.6708i	−1.13982	+	1.68293i
$529$	−18.8104	+	10.8602i	−0.817845	+	0.472183i
$530$	16.7561	+	24.7227i	0.727837	+	1.07389i
$531$		−	10.3840i		−	0.450626i
$532$		0			0
$533$	−0.338860	+	0.338860i	−0.0146777	+	0.0146777i
$534$	56.9171	+	12.3863i	2.46304	+	0.536007i
$535$	7.91421	+	12.9630i	0.342161	+	0.560438i
$536$	−1.43014	−	0.171338i	−0.0617725	−	0.00740069i
$537$	51.3727	−	13.7653i	2.21690	−	0.594016i
$538$	7.59756	+	3.91757i	0.327554	+	0.168899i
$539$		0			0
$540$	0.629842	+	0.840380i	0.0271041	+	0.0361642i
$541$	−14.5885	+	25.2681i	−0.627211	+	1.08636i	0.360898	+	0.932605i	$0.382470\pi$
$541$	−14.5885	+	25.2681i	−0.627211	+	1.08636i	−0.988109	+	0.153756i	$0.950863\pi$
$542$	1.57840	+	33.1900i	0.0677981	+	1.42563i
$543$	10.3592	−	38.6612i	0.444558	−	1.65911i
$544$	−23.8717	−	14.5635i	−1.02349	−	0.624406i
$545$	−6.04316	+	6.34708i	−0.258860	+	0.271879i
$546$		0			0
$547$	0.913792	−	0.913792i	0.0390709	−	0.0390709i	−0.687301	−	0.726372i	$-0.741205\pi$
$547$	0.913792	−	0.913792i	0.0390709	−	0.0390709i	0.726372	+	0.687301i	$0.241205\pi$
$548$	−30.6226	−	25.2923i	−1.30813	−	1.08043i
$549$	−5.24710	+	3.02941i	−0.223941	+	0.129292i
$550$	33.2869	−	3.22450i	1.41936	−	0.137493i
$551$	−16.5717	−	9.56766i	−0.705977	−	0.407596i
$552$	1.12229	+	7.81886i	0.0477677	+	0.332793i
$553$		0			0
$554$	31.4204	−	10.0413i	1.33493	−	0.426613i
$555$	3.59594	+	12.2139i	0.152639	+	0.518452i
$556$	0.960714	−	2.10279i	0.0407434	−	0.0891781i
$557$	0.744970	−	2.78027i	0.0315654	−	0.117804i	−0.948346	−	0.317239i	$-0.897244\pi$
$557$	0.744970	−	2.78027i	0.0315654	−	0.117804i	0.979911	+	0.199436i	$0.0639109\pi$
$558$	10.9715	+	17.0749i	0.464460	+	0.722839i
$559$	0.186452			0.00788606
$560$		0			0
$561$	−57.7196			−2.43693
$562$	−14.7554	−	22.9639i	−0.622421	−	0.968674i
$563$	7.23315	−	26.9945i	0.304841	−	1.13768i	−0.628241	−	0.778018i	$-0.716225\pi$
$563$	7.23315	−	26.9945i	0.304841	−	1.13768i	0.933082	−	0.359663i	$-0.117108\pi$
$564$	−5.68176	+	12.4361i	−0.239245	+	0.523654i
$565$	0.0424064	−	0.0777954i	0.00178405	−	0.00327288i
$566$	9.60324	−	3.06898i	0.403654	−	0.128999i
$567$		0			0
$568$	−5.81193	−	40.4912i	−0.243863	−	1.69897i
$569$	31.8950	+	18.4146i	1.33711	+	0.771981i	0.986378	−	0.164495i	$-0.0525996\pi$
$569$	31.8950	+	18.4146i	1.33711	+	0.771981i	0.350732	+	0.936476i	$0.385933\pi$
$570$	1.47849	+	20.4864i	0.0619273	+	0.858081i
$571$	35.5147	−	20.5044i	1.48624	−	0.858084i	0.486367	−	0.873754i	$-0.338322\pi$
$571$	35.5147	−	20.5044i	1.48624	−	0.858084i	0.999877	+	0.0156706i	$0.00498830\pi$
$572$	−0.611264	−	0.504865i	−0.0255582	−	0.0211095i
$573$	28.6909	−	28.6909i	1.19858	−	1.19858i
$574$		0			0
$575$	3.79847	−	4.19063i	0.158407	−	0.174762i
$576$	−24.0602	−	5.84905i	−1.00251	−	0.243710i
$577$	−5.52692	+	20.6267i	−0.230089	+	0.858703i	0.750213	+	0.661196i	$0.229951\pi$
$577$	−5.52692	+	20.6267i	−0.230089	+	0.858703i	−0.980302	+	0.197506i	$0.936716\pi$
$578$	−0.499547	−	10.5043i	−0.0207784	−	0.436921i
$579$	−6.12245	+	10.6044i	−0.254440	+	0.440704i
$580$	−32.1988	−	4.61090i	−1.33698	−	0.191457i
$581$		0			0
$582$	−25.5199	−	13.1590i	−1.05783	−	0.545457i
$583$	−43.1458	+	11.5609i	−1.78691	+	0.478802i
$584$	26.9374	+	3.22725i	1.11468	+	0.133545i
$585$	−0.495091	+	0.302265i	−0.0204695	+	0.0124971i
$586$	−2.52963	−	0.550498i	−0.104498	−	0.0227408i
$587$	0.870374	−	0.870374i	0.0359242	−	0.0359242i	−0.688917	−	0.724841i	$-0.741913\pi$
$587$	0.870374	−	0.870374i	0.0359242	−	0.0359242i	0.724841	+	0.688917i	$0.241913\pi$
$588$		0			0
$589$			12.1989i			0.502646i
$590$	2.00110	−	10.4189i	0.0823841	−	0.428937i
$591$	−11.7900	+	6.80697i	−0.484977	+	0.280001i
$592$	−7.63845	−	5.17338i	−0.313938	−	0.212625i
$593$	−0.547190	−	2.04214i	−0.0224704	−	0.0838607i	0.953780	−	0.300505i	$-0.0971553\pi$
$593$	−0.547190	−	2.04214i	−0.0224704	−	0.0838607i	−0.976251	+	0.216645i	$0.930489\pi$
$594$	−1.49615	+	0.478138i	−0.0613880	+	0.0196182i
$595$		0			0
$596$	−10.1039	+	7.19257i	−0.413874	+	0.294619i
$597$	−45.0608	+	12.0740i	−1.84422	+	0.494157i
$598$	−0.133930	+	0.00636923i	−0.00547679	+	0.000260457i
$599$	−12.9248	−	22.3864i	−0.528092	−	0.914683i	−0.999464	−	0.0327479i	$-0.989574\pi$
$599$	−12.9248	−	22.3864i	−0.528092	−	0.914683i	0.471371	−	0.881935i	$-0.343759\pi$
$600$	15.2937	+	31.3867i	0.624363	+	1.28136i
$601$	−20.5570			−0.838537			−0.419269	−	0.907862i	$-0.637713\pi$
$601$	−20.5570			−0.838537			−0.419269	+	0.907862i	$0.637713\pi$
$602$		0			0
$603$	−1.11452	−	1.11452i	−0.0453869	−	0.0453869i
$604$	−1.91172	−	20.0540i	−0.0777868	−	0.815986i
$605$	−5.97520	+	24.7082i	−0.242927	+	1.00453i
$606$	−22.1506	−	20.1394i	−0.899806	−	0.818108i
$607$	5.79881	+	21.6414i	0.235366	+	0.878399i	0.977983	+	0.208683i	$0.0669177\pi$
$607$	5.79881	+	21.6414i	0.235366	+	0.878399i	−0.742617	+	0.669716i	$0.766416\pi$
$608$	−10.2659	−	10.7751i	−0.416336	−	0.436987i
$609$		0			0
$610$	−5.84852	+	2.02842i	−0.236800	+	0.0821282i
$611$	−0.200991	−	0.116042i	−0.00813122	−	0.00469456i
$612$	−10.6891	−	28.6725i	−0.432081	−	1.15902i
$613$	31.9774	+	8.56832i	1.29156	+	0.346071i	0.838251	−	0.545285i	$-0.183578\pi$
$613$	31.9774	+	8.56832i	1.29156	+	0.346071i	0.453304	+	0.891356i	$0.350245\pi$
$614$	−7.54686	−	1.64234i	−0.304566	−	0.0662796i
$615$	0.774002	+	31.5547i	0.0312108	+	1.27241i
$616$		0			0
$617$	27.2948	+	27.2948i	1.09885	+	1.09885i	0.994546	+	0.104300i	$0.0332603\pi$
$617$	27.2948	+	27.2948i	1.09885	+	1.09885i	0.104300	+	0.994546i	$0.466740\pi$
$618$	9.59368	−	6.16441i	0.385914	−	0.247969i
$619$	−18.1903	−	31.5065i	−0.731130	−	1.26635i	−0.956400	−	0.292059i	$-0.905660\pi$
$619$	−18.1903	−	31.5065i	−0.731130	−	1.26635i	0.225270	−	0.974296i	$-0.427674\pi$
$620$	7.71781	+	19.2466i	0.309955	+	0.772962i
$621$	−0.132821	+	0.230053i	−0.00532992	+	0.00923169i
$622$	−25.8071	−	13.3071i	−1.03477	−	0.533564i
$623$		0			0
$624$	0.270959	−	0.782082i	0.0108470	−	0.0313083i
$625$	10.3195	−	22.7708i	0.412779	−	0.910831i
$626$	26.5535	−	29.2052i	1.06129	−	1.16727i
$627$	−29.6725	−	7.95073i	−1.18501	−	0.317522i
$628$	−22.4669	−	18.5562i	−0.896527	−	0.740474i
$629$		−	11.4011i		−	0.454590i
$630$		0			0
$631$			10.6984i			0.425897i	0.977063	+	0.212949i	$0.0683067\pi$
$631$			10.6984i			0.425897i	−0.977063	+	0.212949i	$0.931693\pi$
$632$	−6.42055	+	16.0267i	−0.255396	+	0.637509i
$633$	26.1828	+	7.01567i	1.04067	+	0.278848i
$634$	13.5593	+	12.3282i	0.538510	+	0.489616i
$635$	9.89002	−	18.1434i	0.392473	−	0.720000i
$636$	−27.0441	−	37.9908i	−1.07237	−	1.50643i
$637$		0			0
$638$	22.2952	−	43.2383i	0.882676	−	1.71182i
$639$	22.3816	−	38.7661i	0.885402	−	1.53356i
$640$	−23.0139	−	10.5054i	−0.909702	−	0.415261i
$641$	−2.64450	−	4.58042i	−0.104452	−	0.180916i	0.809062	−	0.587723i	$-0.199975\pi$
$641$	−2.64450	−	4.58042i	−0.104452	−	0.180916i	−0.913514	+	0.406807i	$0.866642\pi$
$642$	−12.8196	−	19.9512i	−0.505950	−	0.787410i
$643$	6.36844	+	6.36844i	0.251147	+	0.251147i	0.821441	−	0.570294i	$-0.193171\pi$
$643$	6.36844	+	6.36844i	0.251147	+	0.251147i	−0.570294	+	0.821441i	$0.693171\pi$
$644$		0			0
$645$	8.46826	−	8.89414i	0.333437	−	0.350206i
$646$	3.91096	−	17.9715i	0.153875	−	0.707081i
$647$	5.91812	+	1.58576i	0.232665	+	0.0623425i	0.373268	−	0.927724i	$-0.378237\pi$
$647$	5.91812	+	1.58576i	0.232665	+	0.0623425i	−0.140602	+	0.990066i	$0.544904\pi$
$648$	15.2164	+	19.3587i	0.597757	+	0.760482i
$649$	13.7415	+	7.93365i	0.539401	+	0.311423i
$650$	−0.555004	+	0.207872i	−0.0217690	+	0.00815339i
$651$		0			0
$652$	−0.979860	+	5.82137i	−0.0383743	+	0.227983i
$653$	10.1250	+	37.7871i	0.396223	+	1.47872i	0.819687	+	0.572812i	$0.194147\pi$
$653$	10.1250	+	37.7871i	0.396223	+	1.47872i	−0.423464	+	0.905913i	$0.639186\pi$
$654$	9.20555	−	10.1248i	0.359966	−	0.395913i
$655$	−8.02052	−	1.93961i	−0.313388	−	0.0757869i
$656$	−14.9716	−	17.2892i	−0.584544	−	0.675032i
$657$	20.9927	+	20.9927i	0.819001	+	0.819001i
$658$		0			0
$659$	−7.96382			−0.310226			−0.155113	−	0.987897i	$-0.549574\pi$
$659$	−7.96382			−0.310226			−0.155113	+	0.987897i	$0.549574\pi$
$660$	−51.8455	+	6.22864i	−2.01808	+	0.242449i
$661$	17.8362	+	30.8932i	0.693748	+	1.20161i	0.970601	+	0.240694i	$0.0773750\pi$
$661$	17.8362	+	30.8932i	0.693748	+	1.20161i	−0.276854	+	0.960912i	$0.589292\pi$
$662$	0.497486	+	10.4610i	0.0193354	+	0.406577i
$663$	0.988023	−	0.264740i	0.0383716	−	0.0102817i
$664$	−18.0128	−	13.4909i	−0.699032	−	0.523548i
$665$		0			0
$666$	−3.07314	−	9.61625i	−0.119082	−	0.372622i
$667$	−2.12944	−	7.94717i	−0.0824521	−	0.307716i
$668$	6.05747	+	16.2486i	0.234371	+	0.628676i
$669$	−41.4216	+	23.9148i	−1.60145	+	0.924599i
$670$	−0.903487	−	1.33305i	−0.0349048	−	0.0515002i
$671$		−	9.25823i		−	0.357410i
$672$		0			0
$673$	−29.4853	+	29.4853i	−1.13657	+	1.13657i	−0.147515	+	0.989060i	$0.547127\pi$
$673$	−29.4853	+	29.4853i	−1.13657	+	1.13657i	−0.989060	+	0.147515i	$0.952873\pi$
$674$	2.47512	−	11.3736i	0.0953380	−	0.438094i
$675$	−0.247926	+	1.14770i	−0.00954268	+	0.0441748i
$676$	−23.6359	−	10.7987i	−0.909075	−	0.415335i
$677$	44.5308	−	11.9320i	1.71146	−	0.458584i	0.735676	−	0.677333i	$-0.236864\pi$
$677$	44.5308	−	11.9320i	1.71146	−	0.458584i	0.975781	+	0.218750i	$0.0701978\pi$
$678$	−0.0634037	+	0.122962i	−0.00243500	+	0.00472233i
$679$		0			0
$680$	−5.19952	−	30.8287i	−0.199392	−	1.18223i
$681$	28.3354	−	49.0783i	1.08581	−	1.88069i
$682$	−30.9784	+	1.47322i	−1.18622	+	0.0564127i
$683$	−10.7522	+	40.1276i	−0.411420	+	1.53544i	0.380479	+	0.924790i	$0.375759\pi$
$683$	−10.7522	+	40.1276i	−0.411420	+	1.53544i	−0.791899	+	0.610652i	$0.790907\pi$
$684$	−1.54550	−	16.2123i	−0.0590936	−	0.619894i
$685$	−1.08888	−	44.3917i	−0.0416039	−	1.69612i
$686$		0			0
$687$	−20.8424	+	20.8424i	−0.795187	+	0.795187i
$688$	−0.637612	+	8.87547i	−0.0243087	+	0.338374i
$689$	0.685527	−	0.395789i	0.0261165	−	0.0150784i
$690$	−5.77900	+	6.67801i	−0.220003	+	0.254228i
$691$	15.8798	+	9.16821i	0.604096	+	0.348775i	0.770651	−	0.637257i	$-0.219931\pi$
$691$	15.8798	+	9.16821i	0.604096	+	0.348775i	−0.166555	+	0.986032i	$0.553264\pi$
$692$	−3.54117	−	0.596054i	−0.134615	−	0.0226586i
$693$		0			0
$694$	4.75419	+	14.8765i	0.180466	+	0.564703i
$695$	2.47951	−	0.730000i	0.0940532	−	0.0276905i
$696$	50.4283	+	6.04159i	1.91148	+	0.229006i
$697$	7.31528	−	27.3010i	0.277086	−	1.03410i
$698$	−12.3730	+	7.95028i	−0.468326	+	0.300922i
$699$	−58.7364			−2.22161
$700$		0			0
$701$	3.42628			0.129409			0.0647045	−	0.997904i	$-0.479390\pi$
$701$	3.42628			0.129409			0.0647045	+	0.997904i	$0.479390\pi$
$702$	0.0234176	−	0.0150469i	0.000883839	−	0.000567910i
$703$	1.57047	−	5.86106i	0.0592312	−	0.221054i
$704$	26.1229	−	27.3709i	0.984546	−	1.03158i
$705$	−14.6641	+	4.31729i	−0.552280	+	0.162599i
$706$	−3.24859	−	10.1653i	−0.122262	−	0.382574i
$707$		0			0
$708$	−2.74966	+	16.3358i	−0.103339	+	0.613937i
$709$	−26.8261	−	15.4881i	−1.00748	−	0.581667i	−0.0970248	−	0.995282i	$-0.530933\pi$
$709$	−26.8261	−	15.4881i	−1.00748	−	0.581667i	−0.910452	+	0.413615i	$0.864266\pi$
$710$	29.9274	−	34.5831i	1.12316	−	1.29788i
$711$	−16.3617	+	9.44644i	−0.613612	+	0.354269i
$712$	−43.8034	−	17.5483i	−1.64160	−	0.657651i
$713$	−3.70884	+	3.70884i	−0.138897	+	0.138897i
$714$		0			0
$715$	−0.0217353	−	0.886111i	−0.000812854	−	0.0331387i
$716$	−42.8907	+	4.08871i	−1.60290	+	0.152802i
$717$	0.963255	−	3.59492i	0.0359734	−	0.134255i
$718$	−16.2219	+	0.771456i	−0.605396	+	0.0287905i
$719$	21.3674	−	37.0094i	0.796869	−	1.38022i	−0.124777	−	0.992185i	$-0.539821\pi$
$719$	21.3674	−	37.0094i	0.796869	−	1.38022i	0.921646	−	0.388033i	$-0.126845\pi$
$720$	−12.6954	−	24.6010i	−0.473129	−	0.916825i
$721$		0			0
$722$	−7.82838	+	15.1820i	−0.291342	+	0.565015i
$723$	−44.1913	+	11.8410i	−1.64349	+	0.440372i
$724$	−13.4742	+	29.4920i	−0.500765	+	1.09606i
$725$	−19.7056	−	30.5650i	−0.731846	−	1.13516i
$726$	8.44023	−	38.7843i	0.313246	−	1.43942i
$727$	−21.7303	+	21.7303i	−0.805931	+	0.805931i	−0.984015	−	0.178084i	$-0.943010\pi$
$727$	−21.7303	+	21.7303i	−0.805931	+	0.805931i	0.178084	+	0.984015i	$0.443010\pi$
$728$		0			0
$729$			28.6841i			1.06238i
$730$	17.0177	+	25.1087i	0.629852	+	0.929314i
$731$	−9.52347	+	5.49838i	−0.352238	+	0.203365i
$732$	9.05678	−	3.37637i	0.334748	−	0.124794i
$733$	−0.986629	−	3.68215i	−0.0364420	−	0.136003i	0.945308	−	0.326179i	$-0.105761\pi$
$733$	−0.986629	−	3.68215i	−0.0364420	−	0.136003i	−0.981750	+	0.190175i	$0.939094\pi$
$734$	5.45132	+	17.0579i	0.201212	+	0.629618i
$735$		0			0
$736$	0.154814	−	6.39711i	0.00570652	−	0.235800i
$737$	2.32642	−	0.623362i	0.0856947	−	0.0229618i
$738$	−1.18886	−	24.9989i	−0.0437625	−	0.920222i
$739$	6.00177	+	10.3954i	0.220779	+	0.382400i	0.955045	−	0.296462i	$-0.0958068\pi$
$739$	6.00177	+	10.3954i	0.220779	+	0.382400i	−0.734266	+	0.678862i	$0.762474\pi$
$740$	−1.23031	−	10.2408i	−0.0452271	−	0.376458i
$741$	0.544391			0.0199987
$742$		0			0
$743$	−7.86007	−	7.86007i	−0.288358	−	0.288358i	0.548073	−	0.836431i	$-0.315362\pi$
$743$	−7.86007	−	7.86007i	−0.288358	−	0.288358i	−0.836431	+	0.548073i	$0.815362\pi$
$744$	−12.7386	−	29.7671i	−0.467021	−	1.09131i
$745$	−13.4779	−	3.25938i	−0.493794	−	0.119415i
$746$	23.6925	−	26.0585i	0.867443	−	0.954068i
$747$	−6.37387	−	23.7876i	−0.233208	−	0.870344i
$748$	46.1101	+	7.76130i	1.68595	+	0.283781i
$749$		0			0
$750$	−15.2912	+	35.9160i	−0.558357	+	1.31147i
$751$	−1.00430	−	0.579834i	−0.0366475	−	0.0211584i	0.481564	−	0.876411i	$-0.340069\pi$
$751$	−1.00430	−	0.579834i	−0.0366475	−	0.0211584i	−0.518212	+	0.855252i	$0.673402\pi$
$752$	6.21117	−	9.17074i	0.226498	−	0.334422i
$753$	42.9769	+	11.5156i	1.56616	+	0.419653i
$754$	−0.183322	+	0.842397i	−0.00667620	+	0.0306783i
$755$	15.5306	−	16.3117i	0.565218	−	0.593643i
$756$		0			0
$757$	−15.7431	−	15.7431i	−0.572192	−	0.572192i	0.360549	−	0.932740i	$-0.382590\pi$
$757$	−15.7431	−	15.7431i	−0.572192	−	0.572192i	−0.932740	+	0.360549i	$0.882590\pi$
$758$	3.19827	+	4.97747i	0.116166	+	0.180790i
$759$	−6.60410	−	11.4386i	−0.239714	−	0.415196i
$760$	1.57360	−	16.5646i	0.0570805	−	0.600862i
$761$	−9.62047	+	16.6631i	−0.348742	+	0.604039i	−0.986026	−	0.166590i	$-0.946724\pi$
$761$	−9.62047	+	16.6631i	−0.348742	+	0.604039i	0.637284	+	0.770629i	$0.280058\pi$
$762$	−14.7870	+	28.6772i	−0.535677	+	1.03887i
$763$		0			0
$764$	−26.7780	+	19.0621i	−0.968794	+	0.689644i
$765$	16.3743	−	30.0390i	0.592014	−	1.08606i
$766$	14.0504	+	12.7747i	0.507662	+	0.461569i
$767$	−0.271611	−	0.0727778i	−0.00980729	−	0.00262786i
$768$	36.3021	+	15.5727i	1.30994	+	0.561931i
$769$			30.8833i			1.11368i	0.830620	+	0.556840i	$0.187986\pi$
$769$			30.8833i			1.11368i	−0.830620	+	0.556840i	$0.812014\pi$
$770$		0			0
$771$			36.8135i			1.32580i
$772$	6.31693	−	7.64820i	0.227351	−	0.275265i
$773$	−15.6699	−	4.19873i	−0.563607	−	0.151018i	−0.0342438	−	0.999414i	$-0.510902\pi$
$773$	−15.6699	−	4.19873i	−0.563607	−	0.151018i	−0.529363	+	0.848396i	$0.677569\pi$
$774$	−6.55051	+	7.20466i	−0.235453	+	0.258966i
$775$	−10.5937	+	20.6221i	−0.380535	+	0.740767i
$776$	18.6174	+	13.9437i	0.668327	+	0.500551i
$777$		0			0
$778$	22.5122	+	11.6081i	0.807100	+	0.416170i
$779$	7.52128	−	13.0272i	0.269478	−	0.466749i
$780$	0.858904	−	0.344417i	0.0307537	−	0.0123321i
$781$	34.2004	+	59.2368i	1.22379	+	2.11966i
$782$	6.65296	−	4.27486i	0.237910	−	0.152869i
$783$	1.20775	+	1.20775i	0.0431616	+	0.0431616i
$784$		0			0
$785$	−0.798877	−	32.5689i	−0.0285132	−	1.16243i
$786$	12.5898	+	2.73978i	0.449062	+	0.0977248i
$787$	−40.5750	−	10.8721i	−1.44634	−	0.387547i	−0.551594	−	0.834113i	$-0.685980\pi$
$787$	−40.5750	−	10.8721i	−1.44634	−	0.387547i	−0.894751	+	0.446566i	$0.852647\pi$
$788$	10.3339	−	3.85249i	0.368130	−	0.137239i
$789$	−15.1586	−	8.75180i	−0.539659	−	0.311572i
$790$	−18.2371	+	6.32510i	−0.648847	+	0.225037i
$791$		0			0
$792$	40.9837	−	5.88263i	1.45629	−	0.209030i
$793$	0.0424643	+	0.158479i	0.00150795	+	0.00562775i
$794$	−6.39817	−	5.81724i	−0.227062	−	0.206446i
$795$	12.2553	−	50.6771i	0.434650	−	1.79733i
$796$	37.6210	−	3.58635i	1.33344	−	0.127115i
$797$	−5.01705	−	5.01705i	−0.177713	−	0.177713i	0.612645	−	0.790358i	$-0.290106\pi$
$797$	−5.01705	−	5.01705i	−0.177713	−	0.177713i	−0.790358	+	0.612645i	$0.790106\pi$
$798$		0			0
$799$	13.6881			0.484251
$800$	−7.99715	−	27.1302i	−0.282742	−	0.959196i
$801$	−25.8185	−	44.7190i	−0.912253	−	1.58007i
$802$	−27.7375	+	1.31910i	−0.979445	+	0.0465790i
$803$	−43.8193	+	11.7414i	−1.54635	+	0.414343i
$804$	1.45822	+	2.04847i	0.0514273	+	0.0722438i
$805$		0			0
$806$	0.523519	−	0.167305i	0.0184402	−	0.00589308i
$807$	−3.86227	−	14.4142i	−0.135958	−	0.507403i
$808$	14.9872	+	19.0671i	0.527249	+	0.670779i
$809$	16.3576	−	9.44409i	0.575104	−	0.332036i	−0.184081	−	0.982911i	$-0.558931\pi$
$809$	16.3576	−	9.44409i	0.575104	−	0.332036i	0.759185	+	0.650875i	$0.225598\pi$
$810$	−5.19256	+	27.0354i	−0.182448	+	0.949926i
$811$		−	21.4189i		−	0.752118i	−0.926596	−	0.376059i	$-0.877279\pi$
$811$		−	21.4189i		−	0.752118i	0.926596	−	0.376059i	$-0.122721\pi$
$812$		0			0
$813$	41.0166	−	41.0166i	1.43851	−	1.43851i
$814$	15.0735	+	3.28029i	0.528326	+	0.114974i
$815$	−5.63317	+	3.43919i	−0.197321	+	0.120470i
$816$	9.22340	+	47.9372i	0.322883	+	1.67814i
$817$	−5.65322	+	1.51477i	−0.197781	+	0.0529953i
$818$	12.6361	+	6.51561i	0.441810	+	0.227813i
$819$		0			0
$820$	3.62470	−	25.3120i	0.126580	−	0.883933i
$821$	20.8528	−	36.1180i	0.727766	−	1.26053i	−0.230059	−	0.973177i	$-0.573892\pi$
$821$	20.8528	−	36.1180i	0.727766	−	1.26053i	0.957825	−	0.287351i	$-0.0927747\pi$
$822$	3.29361	+	69.2569i	0.114878	+	2.41561i
$823$	−10.4750	+	39.0933i	−0.365136	+	1.36271i	0.502100	+	0.864809i	$0.332561\pi$
$823$	−10.4750	+	39.0933i	−0.365136	+	1.36271i	−0.867236	+	0.497897i	$0.834106\pi$
$824$	−8.49294	+	3.63450i	−0.295865	+	0.126614i
$825$	−43.2566	−	39.2086i	−1.50600	−	1.36507i
$826$		0			0
$827$	−30.7849	+	30.7849i	−1.07050	+	1.07050i	−0.0731766	+	0.997319i	$0.523314\pi$
$827$	−30.7849	+	30.7849i	−1.07050	+	1.07050i	−0.997319	+	0.0731766i	$0.976686\pi$
$828$	4.45918	−	5.39894i	0.154967	−	0.187626i
$829$	36.1486	−	20.8704i	1.25549	−	0.724859i	0.283298	−	0.959032i	$-0.408571\pi$
$829$	36.1486	−	20.8704i	1.25549	−	0.724859i	0.972195	+	0.234172i	$0.0752380\pi$
$830$	−1.81116	−	25.0958i	−0.0628661	−	0.871089i
$831$	−49.8696	−	28.7922i	−1.72996	−	0.998790i
$832$	−0.321622	+	0.588342i	−0.0111502	+	0.0203971i
$833$		0			0
$834$	−3.84433	+	1.22856i	−0.133118	+	0.0425417i
$835$	−9.27926	+	17.0230i	−0.321122	+	0.589105i
$836$	22.6352	+	10.3415i	0.782854	+	0.357667i
$837$	0.281822	−	1.05177i	0.00974118	−	0.0363546i
$838$	13.5967	+	21.1605i	0.469689	+	0.730977i
$839$	20.9842			0.724456			0.362228	−	0.932090i	$-0.382016\pi$
$839$	20.9842			0.724456			0.362228	+	0.932090i	$0.382016\pi$
$840$		0			0
$841$	−23.9012			−0.824180
$842$	30.3106	+	47.1724i	1.04457	+	1.62567i
$843$	−12.3330	+	46.0274i	−0.424772	+	1.58527i
$844$	−19.9731	−	9.12525i	−0.687504	−	0.314104i
$845$	−8.20541	−	27.8704i	−0.282275	−	0.958770i
$846$	11.5453	−	3.68962i	0.396935	−	0.126852i
$847$		0			0
$848$	16.4961	+	33.9860i	0.566477	+	1.16708i
$849$	−15.2420	−	8.79995i	−0.523103	−	0.302014i
$850$	22.2181	−	26.9844i	0.762076	−	0.925557i
$851$	2.25941	−	1.30447i	0.0774517	−	0.0447168i
$852$	−45.4754	+	55.0592i	−1.55796	+	1.88630i
$853$	−19.9509	+	19.9509i	−0.683106	+	0.683106i	−0.960699	−	0.277593i	$-0.910463\pi$
$853$	−19.9509	+	19.9509i	−0.683106	+	0.683106i	0.277593	+	0.960699i	$0.410463\pi$
$854$		0			0
$855$	12.5555	−	13.1869i	0.429389	−	0.450983i
$856$	7.55837	+	17.6620i	0.258340	+	0.603676i
$857$	9.92835	−	37.0531i	0.339146	−	1.26571i	−0.560158	−	0.828386i	$-0.689260\pi$
$857$	9.92835	−	37.0531i	0.339146	−	1.26571i	0.899304	−	0.437324i	$-0.144074\pi$
$858$	0.0657445	+	1.38245i	0.00224448	+	0.0471961i
$859$	−3.51740	+	6.09232i	−0.120012	+	0.207867i	−0.919772	−	0.392453i	$-0.871627\pi$
$859$	−3.51740	+	6.09232i	−0.120012	+	0.207867i	0.799760	+	0.600320i	$0.204960\pi$
$860$	−7.96093	+	5.96651i	−0.271465	+	0.203456i
$861$		0			0
$862$	−31.6317	−	16.3104i	−1.07738	−	0.555536i
$863$	43.2762	−	11.5958i	1.47314	−	0.394726i	0.569132	−	0.822246i	$-0.307279\pi$
$863$	43.2762	−	11.5958i	1.47314	−	0.394726i	0.904006	+	0.427520i	$0.140613\pi$
$864$	0.636183	+	1.16618i	0.0216434	+	0.0396742i
$865$	−2.09208	−	3.42669i	−0.0711328	−	0.116511i
$866$	−17.9642	−	3.90936i	−0.610447	−	0.132845i
$867$	−12.9813	+	12.9813i	−0.440868	+	0.440868i
$868$		0			0
$869$		−	28.8694i		−	0.979328i
$870$	31.8580	+	47.0049i	1.08009	+	1.59361i
$871$	−0.0369636	+	0.0213410i	−0.00125246	+	0.000723111i
$872$	−8.71542	+	6.85053i	−0.295141	+	0.231988i
$873$	6.58783	+	24.5861i	0.222964	+	0.832114i
$874$	4.00901	−	1.28119i	0.135607	−	0.0433369i
$875$		0			0
$876$	−27.4663	−	38.5839i	−0.928000	−	1.30363i
$877$	−5.54663	+	1.48622i	−0.187297	+	0.0501860i	−0.351248	−	0.936282i	$-0.614243\pi$
$877$	−5.54663	+	1.48622i	−0.187297	+	0.0501860i	0.163951	+	0.986468i	$0.447576\pi$
$878$	−42.0952	+	2.00190i	−1.42064	+	0.0675609i
$879$	2.25970	+	3.91392i	0.0762179	+	0.132013i
$880$	42.2550	+	1.99561i	1.42442	+	0.0672719i
$881$	−3.68416			−0.124122			−0.0620612	−	0.998072i	$-0.519767\pi$
$881$	−3.68416			−0.124122			−0.0620612	+	0.998072i	$0.519767\pi$
$882$		0			0
$883$	−10.4605	−	10.4605i	−0.352023	−	0.352023i	0.508839	−	0.860862i	$-0.330075\pi$
$883$	−10.4605	−	10.4605i	−0.352023	−	0.352023i	−0.860862	+	0.508839i	$0.830075\pi$
$884$	−0.824893	+	0.0786359i	−0.0277442	+	0.00264481i
$885$	−15.8077	+	9.65098i	−0.531369	+	0.324414i
$886$	42.7261	+	38.8468i	1.43541	+	1.30508i
$887$	−8.27950	−	30.8995i	−0.277998	−	1.03750i	−0.953805	−	0.300426i	$-0.902871\pi$
$887$	−8.27950	−	30.8995i	−0.277998	−	1.03750i	0.675807	−	0.737079i	$-0.263795\pi$
$888$	2.28822	+	15.9418i	0.0767876	+	0.534972i
$889$		0			0
$890$	−17.2874	−	49.8447i	−0.579476	−	1.67080i
$891$	−35.6571	−	20.5866i	−1.19456	−	0.689678i
$892$	36.3059	−	13.5348i	1.21561	−	0.453180i
$893$	7.03680	+	1.88550i	0.235477	+	0.0630960i
$894$	21.1563	+	4.60402i	0.707571	+	0.153981i
$895$	−34.8868	−	33.2163i	−1.16614	−	1.11030i
$896$		0			0
$897$	0.165512	+	0.165512i	0.00552627	+	0.00552627i
$898$	24.6345	−	15.8289i	0.822064	−	0.528216i
$899$	16.8624	+	29.2066i	0.562394	+	0.974095i
$900$	11.4663	−	28.7489i	0.382211	−	0.958297i
$901$	−23.3433	+	40.4318i	−0.777679	+	1.34698i
$902$	33.9903	+	17.5266i	1.13175	+	0.583572i
$903$		0			0
$904$	0.0671850	−	0.0897042i	0.00223454	−	0.00298352i
$905$	−34.7756	+	10.2384i	−1.15598	+	0.340336i
$906$	−23.6578	+	26.0204i	−0.785979	+	0.864469i
$907$	−13.3895	−	3.58771i	−0.444592	−	0.119128i	0.0295760	−	0.999563i	$-0.490584\pi$
$907$	−13.3895	−	3.58771i	−0.444592	−	0.119128i	−0.474168	+	0.880435i	$0.657251\pi$
$908$	−29.2354	+	35.3967i	−0.970212	+	1.17468i
$909$			26.5390i			0.880243i
$910$		0			0
$911$		−	47.8573i		−	1.58558i	−0.609494	−	0.792791i	$-0.708627\pi$
$911$		−	47.8573i		−	1.58558i	0.609494	−	0.792791i	$-0.291373\pi$
$912$	−1.86166	+	25.9141i	−0.0616458	+	0.858101i
$913$	36.3488	+	9.73964i	1.20297	+	0.322335i
$914$	−3.92031	−	3.56437i	−0.129672	−	0.117899i
$915$	9.48843	+	5.17216i	0.313678	+	0.170986i
$916$	19.4528	−	13.8476i	0.642739	−	0.457539i
$917$		0			0
$918$	−0.752382	+	1.45913i	−0.0248323	+	0.0481586i
$919$	−3.56719	+	6.17855i	−0.117671	+	0.203812i	−0.918844	−	0.394620i	$-0.870876\pi$
$919$	−3.56719	+	6.17855i	−0.117671	+	0.203812i	0.801173	+	0.598432i	$0.204209\pi$
$920$	5.51459	−	4.55774i	0.181811	−	0.150264i
$921$	6.74155	+	11.6767i	0.222142	+	0.384761i
$922$	5.09778	+	7.93367i	0.167886	+	0.261282i
$923$	−0.857128	−	0.857128i	−0.0282127	−	0.0282127i
$924$		0			0
$925$	7.74467	−	8.54424i	0.254643	−	0.280933i
$926$	6.28930	−	28.9004i	0.206679	−	0.949727i
$927$	−9.76453	−	2.61640i	−0.320709	−	0.0859338i
$928$	−39.4729	−	11.6073i	−1.29576	−	0.381027i
$929$	−22.9712	−	13.2625i	−0.753662	−	0.435127i	0.0733534	−	0.997306i	$-0.476630\pi$
$929$	−22.9712	−	13.2625i	−0.753662	−	0.435127i	−0.827016	+	0.562179i	$0.809963\pi$
$930$	15.7964	−	32.5717i	0.517984	−	1.06807i
$931$		0			0
$932$	46.9223	+	7.89802i	1.53699	+	0.258708i
$933$	13.1192	+	48.9615i	0.429503	+	1.60293i
$934$	−26.7192	+	29.3875i	−0.874280	+	0.961587i
$935$	27.2412	+	44.6193i	0.890884	+	1.45921i
$936$	−0.674562	+	0.288675i	−0.0220487	+	0.00943563i
$937$	−4.34151	−	4.34151i	−0.141831	−	0.141831i	0.632626	−	0.774457i	$-0.281977\pi$
$937$	−4.34151	−	4.34151i	−0.141831	−	0.141831i	−0.774457	+	0.632626i	$0.781977\pi$
$938$		0			0
$939$	−68.9071			−2.24870
$940$	12.2951	−	1.47711i	0.401022	−	0.0481781i
$941$	12.9331	+	22.4008i	0.421607	+	0.730245i	0.996097	−	0.0882670i	$-0.0281329\pi$
$941$	12.9331	+	22.4008i	0.421607	+	0.730245i	−0.574490	+	0.818512i	$0.694800\pi$
$942$	2.41643	+	50.8117i	0.0787314	+	1.65553i
$943$	6.24739	−	1.67398i	0.203443	−	0.0545124i
$944$	4.39320	−	12.6803i	0.142987	−	0.412710i
$945$		0			0
$946$	−4.52941	−	14.1731i	−0.147264	−	0.460807i
$947$	−7.68227	−	28.6706i	−0.249640	−	0.931670i	−0.970994	−	0.239103i	$-0.923147\pi$
$947$	−7.68227	−	28.6706i	−0.249640	−	0.931670i	0.721354	−	0.692567i	$-0.243520\pi$
$948$	28.2413	−	10.5283i	0.917233	−	0.341945i
$949$	0.696229	−	0.401968i	0.0226006	−	0.0130484i
$950$	15.1389	−	10.8116i	0.491172	−	0.350776i
$951$		−	31.9921i		−	1.03741i
$952$		0			0
$953$	−33.9836	+	33.9836i	−1.10084	+	1.10084i	−0.106528	+	0.994310i	$0.533973\pi$
$953$	−33.9836	+	33.9836i	−1.10084	+	1.10084i	−0.994310	+	0.106528i	$0.966027\pi$
$954$	−8.79063	+	40.3945i	−0.284607	+	1.30782i
$955$	−35.7200	−	8.63819i	−1.15587	−	0.279525i
$956$	−1.25290	+	2.74232i	−0.0405217	+	0.0886930i
$957$	−82.0323	+	21.9805i	−2.65173	+	0.710528i
$958$	−6.83311	+	13.2518i	−0.220768	+	0.428146i
$959$		0			0
$960$	13.4577	+	42.0634i	0.434347	+	1.35759i
$961$	−4.75009	+	8.22739i	−0.153229	+	0.265400i
$962$	−0.273068	+	0.0129862i	−0.00880407	+	0.000418691i
$963$	−5.44110	+	20.3065i	−0.175337	+	0.654367i
$964$	36.8950	−	3.51715i	1.18831	−	0.113280i
$965$	11.0871	−	0.271955i	0.356907	−	0.00875453i
$966$		0			0
$967$	26.2766	−	26.2766i	0.844999	−	0.844999i	−0.144505	−	0.989504i	$-0.546159\pi$
$967$	26.2766	−	26.2766i	0.844999	−	0.844999i	0.989504	+	0.144505i	$0.0461589\pi$
$968$	−11.9577	+	29.8484i	−0.384336	+	0.959365i
$969$	−27.8061	+	16.0539i	−0.893260	+	0.515724i
$970$	1.87195	+	25.9382i	0.0601047	+	0.832827i
$971$	40.7412	+	23.5219i	1.30745	+	0.754855i	0.981670	−	0.190591i	$-0.0610404\pi$
$971$	40.7412	+	23.5219i	1.30745	+	0.754855i	0.325778	+	0.945446i	$0.394374\pi$
$972$	7.36883	−	43.7784i	0.236355	−	1.40419i
$973$		0			0
$974$	16.3851	+	51.2711i	0.525013	+	1.64283i
$975$	0.920286	+	0.472755i	0.0294727	+	0.0151403i
$976$	−7.68913	+	1.47943i	−0.246123	+	0.0473555i
$977$	−5.73007	+	21.3849i	−0.183321	+	0.684163i	0.811663	+	0.584126i	$0.198563\pi$
$977$	−5.73007	+	21.3849i	−0.183321	+	0.684163i	−0.994984	+	0.100037i	$0.968104\pi$
$978$	8.66996	−	5.57087i	0.277235	−	0.178137i
$979$	78.9044			2.52180
$980$		0			0
$981$	−12.1307			−0.387305
$982$	4.28044	−	2.75039i	0.136594	−	0.0877686i
$983$	−4.57305	+	17.0668i	−0.145858	+	0.544348i	0.853858	+	0.520506i	$0.174257\pi$
$983$	−4.57305	+	17.0668i	−0.145858	+	0.544348i	−0.999716	+	0.0238421i	$0.992410\pi$
$984$	−4.74939	+	39.6424i	−0.151405	+	1.26376i
$985$	10.8264	+	5.90150i	0.344959	+	0.188038i
$986$	−15.4783	−	48.4336i	−0.492930	−	1.54244i
$987$		0			0
$988$	−0.434893	−	0.0732017i	−0.0138358	−	0.00232886i
$989$	−2.17929	−	1.25821i	−0.0692975	−	0.0400089i
$990$	35.0038	+	30.2914i	1.11249	+	0.962725i
$991$	3.59673	−	2.07657i	0.114254	−	0.0659645i	−0.441784	−	0.897121i	$-0.645654\pi$
$991$	3.59673	−	2.07657i	0.114254	−	0.0659645i	0.556038	+	0.831157i	$0.312321\pi$
$992$	6.17378	+	25.4927i	0.196018	+	0.809395i
$993$	12.9278	−	12.9278i	0.410250	−	0.410250i
$994$		0			0
$995$	30.6005	+	29.1352i	0.970100	+	0.923649i
$996$	3.72829	+	39.1099i	0.118135	+	1.23924i
$997$	6.26677	−	23.3879i	0.198471	−	0.740702i	−0.792870	−	0.609390i	$-0.791414\pi$
$997$	6.26677	−	23.3879i	0.198471	−	0.740702i	0.991341	−	0.131312i	$-0.0419190\pi$
$998$	−14.4544	+	0.687398i	−0.457545	+	0.0217592i
$999$	−0.270807	+	0.469052i	−0.00856796	+	0.0148401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.667.12		72
4.3	odd	2	inner	980.2.x.m.667.9		72
5.3	odd	4	inner	980.2.x.m.863.15		72
7.2	even	3		980.2.k.j.687.14		36
7.3	odd	6		140.2.w.b.67.1	yes	72
7.4	even	3	inner	980.2.x.m.67.1		72
7.5	odd	6		980.2.k.k.687.14		36
7.6	odd	2		140.2.w.b.107.12	yes	72
20.3	even	4	inner	980.2.x.m.863.1		72
28.3	even	6		140.2.w.b.67.15	yes	72
28.11	odd	6	inner	980.2.x.m.67.15		72
28.19	even	6		980.2.k.k.687.4		36
28.23	odd	6		980.2.k.j.687.4		36
28.27	even	2		140.2.w.b.107.9	yes	72
35.3	even	12		140.2.w.b.123.9	yes	72
35.13	even	4		140.2.w.b.23.15	yes	72
35.17	even	12		700.2.be.e.543.10		72
35.18	odd	12	inner	980.2.x.m.263.9		72
35.23	odd	12		980.2.k.j.883.4		36
35.24	odd	6		700.2.be.e.207.18		72
35.27	even	4		700.2.be.e.443.4		72
35.33	even	12		980.2.k.k.883.4		36
35.34	odd	2		700.2.be.e.107.7		72
140.3	odd	12		140.2.w.b.123.12	yes	72
140.23	even	12		980.2.k.j.883.14		36
140.27	odd	4		700.2.be.e.443.18		72
140.59	even	6		700.2.be.e.207.4		72
140.83	odd	4		140.2.w.b.23.1	✓	72
140.87	odd	12		700.2.be.e.543.7		72
140.103	odd	12		980.2.k.k.883.14		36
140.123	even	12	inner	980.2.x.m.263.12		72
140.139	even	2		700.2.be.e.107.10		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.1	✓	72	140.83	odd	4
140.2.w.b.23.15	yes	72	35.13	even	4
140.2.w.b.67.1	yes	72	7.3	odd	6
140.2.w.b.67.15	yes	72	28.3	even	6
140.2.w.b.107.9	yes	72	28.27	even	2
140.2.w.b.107.12	yes	72	7.6	odd	2
140.2.w.b.123.9	yes	72	35.3	even	12
140.2.w.b.123.12	yes	72	140.3	odd	12
700.2.be.e.107.7		72	35.34	odd	2
700.2.be.e.107.10		72	140.139	even	2
700.2.be.e.207.4		72	140.59	even	6
700.2.be.e.207.18		72	35.24	odd	6
700.2.be.e.443.4		72	35.27	even	4
700.2.be.e.443.18		72	140.27	odd	4
700.2.be.e.543.7		72	140.87	odd	12
700.2.be.e.543.10		72	35.17	even	12
980.2.k.j.687.4		36	28.23	odd	6
980.2.k.j.687.14		36	7.2	even	3
980.2.k.j.883.4		36	35.23	odd	12
980.2.k.j.883.14		36	140.23	even	12
980.2.k.k.687.4		36	28.19	even	6
980.2.k.k.687.14		36	7.5	odd	6
980.2.k.k.883.4		36	35.33	even	12
980.2.k.k.883.14		36	140.103	odd	12
980.2.x.m.67.1		72	7.4	even	3	inner
980.2.x.m.67.15		72	28.11	odd	6	inner
980.2.x.m.263.9		72	35.18	odd	12	inner
980.2.x.m.263.12		72	140.123	even	12	inner
980.2.x.m.667.9		72	4.3	odd	2	inner
980.2.x.m.667.12		72	1.1	even	1	trivial
980.2.x.m.863.1		72	20.3	even	4	inner
980.2.x.m.863.15		72	5.3	odd	4	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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.764487 + 1.18977i) q^{2} +(0.638980 - 2.38471i) q^{3} +(-0.831118 + 1.81913i) q^{4} +(-2.14503 + 0.631526i) q^{5} +(3.32575 - 1.06284i) q^{6} +(-2.79973 + 0.401862i) q^{8} +(-2.68045 - 1.54756i) q^{9} +(-2.39122 - 2.06931i) q^{10} +(4.09588 - 2.36476i) q^{11} +(3.80703 + 3.14436i) q^{12} +(-0.0592655 + 0.0592655i) q^{13} +(0.135370 + 5.51881i) q^{15} +(-2.61849 - 3.02383i) q^{16} +(1.27942 - 4.77484i) q^{17} +(-0.207927 - 4.37222i) q^{18} +(1.31544 - 2.27842i) q^{19} +(0.633947 - 4.42698i) q^{20} +(5.94478 + 3.06534i) q^{22} +(1.09265 - 0.292774i) q^{23} +(-0.830651 + 6.93332i) q^{24} +(4.20235 - 2.70929i) q^{25} +(-0.115820 - 0.0252047i) q^{26} +(-0.166053 + 0.166053i) q^{27} -7.27332i q^{29} +(-6.46264 + 4.38012i) q^{30} +(-4.01558 + 2.31840i) q^{31} +(1.59587 - 5.42708i) q^{32} +(-3.02207 - 11.2785i) q^{33} +(6.65908 - 2.12809i) q^{34} +(5.04299 - 3.58989i) q^{36} +(2.22779 - 0.596933i) q^{37} +(3.71644 - 0.176741i) q^{38} +(0.103461 + 0.179200i) q^{39} +(5.75174 - 2.63011i) q^{40} +5.71767 q^{41} +(-1.57302 - 1.57302i) q^{43} +(0.897647 + 9.41635i) q^{44} +(6.72699 + 1.62679i) q^{45} +(1.18365 + 1.07618i) q^{46} +(0.716679 + 2.67468i) q^{47} +(-8.88410 + 4.31215i) q^{48} +(6.43608 + 2.92862i) q^{50} +(-10.5691 - 6.10206i) q^{51} +(-0.0585551 - 0.157068i) q^{52} +(-9.12265 - 2.44441i) q^{53} +(-0.324510 - 0.0706197i) q^{54} +(-7.29241 + 7.65915i) q^{55} +(-4.59281 - 4.59281i) q^{57} +(8.65360 - 5.56036i) q^{58} +(1.67748 + 2.90547i) q^{59} +(-10.1520 - 4.34053i) q^{60} +(0.978771 - 1.69528i) q^{61} +(-5.82822 - 3.00524i) q^{62} +(7.67701 - 2.25021i) q^{64} +(0.0896988 - 0.164554i) q^{65} +(11.1085 - 12.2179i) q^{66} +(0.491893 + 0.131802i) q^{67} +(7.62273 + 6.29589i) q^{68} -2.79272i q^{69} +14.4625i q^{71} +(8.12646 + 3.25558i) q^{72} +(-9.26507 - 2.48257i) q^{73} +(2.41333 + 2.19421i) q^{74} +(-3.77565 - 11.7526i) q^{75} +(3.05145 + 4.28660i) q^{76} +(-0.134113 + 0.260092i) q^{78} +(3.05204 - 5.28630i) q^{79} +(7.52637 + 4.83257i) q^{80} +(-4.35280 - 7.53927i) q^{81} +(4.37109 + 6.80273i) q^{82} +(5.62620 + 5.62620i) q^{83} +(0.271049 + 11.0502i) q^{85} +(0.668982 - 3.07409i) q^{86} +(-17.3447 - 4.64751i) q^{87} +(-10.5171 + 8.26668i) q^{88} +(14.4482 + 8.34169i) q^{89} +(3.20718 + 9.24725i) q^{90} +(-0.375524 + 2.23100i) q^{92} +(2.96282 + 11.0574i) q^{93} +(-2.63437 + 2.89745i) q^{94} +(-1.38279 + 5.71802i) q^{95} +(-11.9223 - 7.27348i) q^{96} +(-5.81505 - 5.81505i) q^{97} -14.6384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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