LMFDB - Embedded newform 980.2.x.m.67.1

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)

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);

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")

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			67.1
Character	$\chi$	$=$	980.67
Dual form			980.2.x.m.863.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41262 + 0.0671791i) q^{2} +(-2.38471 + 0.638980i) q^{3} +(1.99097 - 0.189797i) q^{4} +(0.525600 - 2.17342i) q^{5} +(3.32575 - 1.06284i) q^{6} +(-2.79973 + 0.401862i) q^{8} +(2.68045 - 1.54756i) q^{9} +(-0.596463 + 3.10552i) q^{10} +(-4.09588 - 2.36476i) q^{11} +(-4.62661 + 1.72480i) q^{12} +(-0.0592655 + 0.0592655i) q^{13} +(0.135370 + 5.51881i) q^{15} +(3.92795 - 0.755761i) q^{16} +(-4.77484 + 1.27942i) q^{17} +(-3.68249 + 2.36618i) q^{18} +(1.31544 + 2.27842i) q^{19} +(0.633947 - 4.42698i) q^{20} +(5.94478 + 3.06534i) q^{22} +(-0.292774 + 1.09265i) q^{23} +(6.41976 - 2.74730i) q^{24} +(-4.44749 - 2.28469i) q^{25} +(0.0797380 - 0.0877008i) q^{26} +(-0.166053 + 0.166053i) q^{27} -7.27332i q^{29} +(-0.561975 - 7.78687i) q^{30} +(4.01558 + 2.31840i) q^{31} +(-5.49792 + 1.33148i) q^{32} +(11.2785 + 3.02207i) q^{33} +(6.65908 - 2.12809i) q^{34} +(5.04299 - 3.58989i) q^{36} +(-0.596933 + 2.22779i) q^{37} +(-2.01128 - 3.13016i) q^{38} +(0.103461 - 0.179200i) q^{39} +(-0.598125 + 6.29621i) q^{40} +5.71767 q^{41} +(-1.57302 - 1.57302i) q^{43} +(-8.60362 - 3.93079i) q^{44} +(-1.95465 - 6.63914i) q^{45} +(0.340174 - 1.56316i) q^{46} +(-2.67468 - 0.716679i) q^{47} +(-8.88410 + 4.31215i) q^{48} +(6.43608 + 2.92862i) q^{50} +(10.5691 - 6.10206i) q^{51} +(-0.106748 + 0.129244i) q^{52} +(2.44441 + 9.12265i) q^{53} +(0.223414 - 0.245724i) q^{54} +(-7.29241 + 7.65915i) q^{55} +(-4.59281 - 4.59281i) q^{57} +(0.488615 + 10.2744i) q^{58} +(1.67748 - 2.90547i) q^{59} +(1.31697 + 10.9621i) q^{60} +(0.978771 + 1.69528i) q^{61} +(-5.82822 - 3.00524i) q^{62} +(7.67701 - 2.25021i) q^{64} +(0.0976587 + 0.159959i) q^{65} +(-16.1352 - 3.51135i) q^{66} +(-0.131802 - 0.491893i) q^{67} +(-9.26376 + 3.45353i) q^{68} -2.79272i q^{69} +14.4625i q^{71} +(-6.88265 + 5.40993i) q^{72} +(2.48257 + 9.26507i) q^{73} +(0.693578 - 3.18711i) q^{74} +(12.0658 + 2.60647i) q^{75} +(3.05145 + 4.28660i) q^{76} +(-0.134113 + 0.260092i) q^{78} +(3.05204 + 5.28630i) q^{79} +(0.421947 - 8.93431i) q^{80} +(-4.35280 + 7.53927i) q^{81} +(-8.07688 + 0.384108i) q^{82} +(5.62620 + 5.62620i) q^{83} +(0.271049 + 11.0502i) q^{85} +(2.32775 + 2.11640i) q^{86} +(4.64751 + 17.3447i) q^{87} +(12.4177 + 4.97472i) q^{88} +(-14.4482 + 8.34169i) q^{89} +(3.20718 + 9.24725i) q^{90} +(-0.375524 + 2.23100i) q^{92} +(-11.0574 - 2.96282i) q^{93} +(3.82645 + 0.832711i) q^{94} +(5.64335 - 1.66148i) q^{95} +(12.2601 - 6.68825i) 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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.41262	+	0.0671791i	−0.998871	+	0.0475028i
$2$	−1.41262	+	0.0671791i	−0.998871	+	0.0475028i
$3$	−2.38471	+	0.638980i	−1.37681	+	0.368915i	−0.869962	−	0.493119i	$-0.835857\pi$
$3$	−2.38471	+	0.638980i	−1.37681	+	0.368915i	−0.506849	+	0.862035i	$0.669190\pi$
$4$	1.99097	−	0.189797i	0.995487	−	0.0948984i
$5$	0.525600	−	2.17342i	0.235055	−	0.971982i
$5$	0.525600	−	2.17342i	0.235055	−	0.971982i
$6$	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
$10$	−0.596463	+	3.10552i	−0.188618	+	0.982051i
$11$	−4.09588	−	2.36476i	−1.23496	−	0.713002i	−0.266897	−	0.963725i	$-0.585998\pi$
$11$	−4.09588	−	2.36476i	−1.23496	−	0.713002i	−0.968059	+	0.250723i	$0.919332\pi$
$12$	−4.62661	+	1.72480i	−1.33559	+	0.497908i
$13$	−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
$16$	3.92795	−	0.755761i	0.981989	−	0.188940i
$17$	−4.77484	+	1.27942i	−1.15807	+	0.310304i	−0.786195	−	0.617979i	$-0.787952\pi$
$17$	−4.77484	+	1.27942i	−1.15807	+	0.310304i	−0.371875	+	0.928283i	$0.621285\pi$
$18$	−3.68249	+	2.36618i	−0.867971	+	0.557714i
$19$	1.31544	+	2.27842i	0.301784	+	0.522705i	0.976540	−	0.215336i	$-0.0690846\pi$
$19$	1.31544	+	2.27842i	0.301784	+	0.522705i	−0.674756	+	0.738041i	$0.735751\pi$
$20$	0.633947	−	4.42698i	0.141755	−	0.989902i
$21$		0			0
$22$	5.94478	+	3.06534i	1.26743	+	0.653533i
$23$	−0.292774	+	1.09265i	−0.0610475	+	0.227832i	−0.989709	−	0.143097i	$-0.954294\pi$
$23$	−0.292774	+	1.09265i	−0.0610475	+	0.227832i	0.928661	+	0.370929i	$0.120961\pi$
$24$	6.41976	−	2.74730i	1.31043	−	0.560790i
$25$	−4.44749	−	2.28469i	−0.889498	−	0.456939i
$26$	0.0797380	−	0.0877008i	0.0156379	−	0.0171995i
$27$	−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	$-0.235991\pi$
$30$	−0.561975	−	7.78687i	−0.102602	−	1.42168i
$31$	4.01558	+	2.31840i	0.721219	+	0.416396i	0.815201	−	0.579178i	$-0.196626\pi$
$31$	4.01558	+	2.31840i	0.721219	+	0.416396i	−0.0939821	+	0.995574i	$0.529960\pi$
$32$	−5.49792	+	1.33148i	−0.971905	+	0.235374i
$33$	11.2785	+	3.02207i	1.96334	+	0.526075i
$34$	6.65908	−	2.12809i	1.14202	−	0.364965i
$35$		0			0
$36$	5.04299	−	3.58989i	0.840498	−	0.598315i
$37$	−0.596933	+	2.22779i	−0.0981352	+	0.366246i	−0.997476	−	0.0710024i	$-0.977380\pi$
$37$	−0.596933	+	2.22779i	−0.0981352	+	0.366246i	0.899341	+	0.437248i	$0.144047\pi$
$38$	−2.01128	−	3.13016i	−0.326273	−	0.507779i
$39$	0.103461	−	0.179200i	0.0165671	−	0.0286950i
$40$	−0.598125	+	6.29621i	−0.0945718	+	0.995518i
$41$	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	$0.804255\pi$
$44$	−8.60362	−	3.93079i	−1.29704	−	0.592589i
$45$	−1.95465	−	6.63914i	−0.291382	−	0.989704i
$46$	0.340174	−	1.56316i	0.0501559	−	0.230475i
$47$	−2.67468	−	0.716679i	−0.390143	−	0.104538i	0.0584148	−	0.998292i	$-0.481395\pi$
$47$	−2.67468	−	0.716679i	−0.390143	−	0.104538i	−0.448558	+	0.893754i	$0.648062\pi$
$48$	−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
$52$	−0.106748	+	0.129244i	−0.0148032	+	0.0179230i
$53$	2.44441	+	9.12265i	0.335765	+	1.25309i	0.903037	+	0.429562i	$0.141332\pi$
$53$	2.44441	+	9.12265i	0.335765	+	1.25309i	−0.567272	+	0.823530i	$0.692001\pi$
$54$	0.223414	−	0.245724i	0.0304027	−	0.0334388i
$55$	−7.29241	+	7.65915i	−0.983308	+	1.03276i
$56$		0			0
$57$	−4.59281	−	4.59281i	−0.608333	−	0.608333i
$58$	0.488615	+	10.2744i	0.0641584	+	1.34910i
$59$	1.67748	−	2.90547i	0.218389	−	0.378260i	−0.735927	−	0.677061i	$-0.763253\pi$
$59$	1.67748	−	2.90547i	0.218389	−	0.378260i	0.954315	+	0.298801i	$0.0965866\pi$
$60$	1.31697	+	10.9621i	0.170020	+	1.41520i
$61$	0.978771	+	1.69528i	0.125319	+	0.217058i	0.921857	−	0.387529i	$-0.126671\pi$
$61$	0.978771	+	1.69528i	0.125319	+	0.217058i	−0.796539	+	0.604587i	$0.793338\pi$
$62$	−5.82822	−	3.00524i	−0.740185	−	0.381666i
$63$		0			0
$64$	7.67701	−	2.25021i	0.959627	−	0.281277i
$65$	0.0976587	+	0.159959i	0.0121131	+	0.0198404i
$66$	−16.1352	−	3.51135i	−1.98611	−	0.432217i
$67$	−0.131802	−	0.491893i	−0.0161022	−	0.0600943i	0.957407	−	0.288741i	$-0.0932366\pi$
$67$	−0.131802	−	0.491893i	−0.0161022	−	0.0600943i	−0.973509	+	0.228647i	$0.926570\pi$
$68$	−9.26376	+	3.45353i	−1.12340	+	0.418802i
$69$		−	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	$0.671588\pi$
$72$	−6.88265	+	5.40993i	−0.811128	+	0.637566i
$73$	2.48257	+	9.26507i	0.290563	+	1.08439i	0.944678	+	0.327999i	$0.106374\pi$
$73$	2.48257	+	9.26507i	0.290563	+	1.08439i	−0.654115	+	0.756395i	$0.726959\pi$
$74$	0.693578	−	3.18711i	0.0806268	−	0.370494i
$75$	12.0658	+	2.60647i	1.39324	+	0.300969i
$76$	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	0.985058	−	0.172221i	$-0.0550942\pi$
$79$	3.05204	+	5.28630i	0.343382	+	0.594755i	−0.641677	+	0.766975i	$0.721761\pi$
$80$	0.421947	−	8.93431i	0.0471751	−	0.998887i
$81$	−4.35280	+	7.53927i	−0.483644	+	0.837696i
$82$	−8.07688	+	0.384108i	−0.891942	+	0.0424176i
$83$	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
$86$	2.32775	+	2.11640i	0.251008	+	0.228217i
$87$	4.64751	+	17.3447i	0.498265	+	1.85955i
$88$	12.4177	+	4.97472i	1.32373	+	0.530307i
$89$	−14.4482	+	8.34169i	−1.53151	+	0.884218i	−0.532217	+	0.846608i	$0.678641\pi$
$89$	−14.4482	+	8.34169i	−1.53151	+	0.884218i	−0.999292	+	0.0376100i	$0.988026\pi$
$90$	3.20718	+	9.24725i	0.338067	+	0.974746i
$91$		0			0
$92$	−0.375524	+	2.23100i	−0.0391511	+	0.232598i
$93$	−11.0574	−	2.96282i	−1.14660	−	0.307230i
$94$	3.82645	+	0.832711i	0.394668	+	0.0858875i
$95$	5.64335	−	1.66148i	0.578996	−	0.170464i
$96$	12.2601	−	6.68825i	1.25130	−	0.682616i
$97$	−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
$100$	−9.28846	−	3.70465i	−0.928846	−	0.370465i
$101$	−4.28723	+	7.42571i	−0.426596	+	0.738885i	−0.996568	−	0.0827785i	$-0.973621\pi$
$101$	−4.28723	+	7.42571i	−0.426596	+	0.738885i	0.569972	+	0.821664i	$0.306954\pi$
$102$	−14.5201	+	9.32990i	−1.43771	+	0.923798i
$103$	−0.845330	+	3.15482i	−0.0832929	+	0.310853i	−0.994985	−	0.100020i	$-0.968109\pi$
$103$	−0.845330	+	3.15482i	−0.0832929	+	0.310853i	0.911693	+	0.410873i	$0.134776\pi$
$104$	0.142111	−	0.189744i	0.0139351	−	0.0186059i
$105$		0			0
$106$	−4.06586	−	12.7226i	−0.394911	−	1.23573i
$107$	6.56081	+	1.75796i	0.634257	+	0.169949i	0.561601	−	0.827408i	$-0.310186\pi$
$107$	6.56081	+	1.75796i	0.634257	+	0.169949i	0.0726563	+	0.997357i	$0.476852\pi$
$108$	−0.299090	+	0.362123i	−0.0287800	+	0.0348453i
$109$	−3.39423	−	1.95966i	−0.325108	−	0.187701i	0.328559	−	0.944483i	$-0.393437\pi$
$109$	−3.39423	−	1.95966i	−0.325108	−	0.187701i	−0.653667	+	0.756782i	$0.726770\pi$
$110$	9.78684	−	11.3093i	0.933139	−	1.07830i
$111$		−	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	$0.250593\pi$
$114$	6.79643	+	6.17935i	0.636544	+	0.578749i
$115$	2.22089	+	1.21061i	0.207100	+	0.112890i
$116$	−1.38045	−	14.4810i	−0.128172	−	1.34453i
$117$	−0.0671414	+	0.250575i	−0.00620723	+	0.0231657i
$118$	−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
$122$	−1.49652	−	2.32903i	−0.135488	−	0.210860i
$123$	−13.6350	+	3.65348i	−1.22942	+	0.329423i
$124$	8.43494	+	3.85372i	0.757480	+	0.346074i
$125$	−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	$0.384475\pi$
$128$	−10.6935	+	3.69442i	−0.945182	+	0.326544i
$129$	4.75632	+	2.74606i	0.418770	+	0.241777i
$130$	−0.148700	−	0.219400i	−0.0130419	−	0.0192426i
$131$	−3.19588	+	1.84514i	−0.279225	+	0.161211i	−0.633073	−	0.774092i	$-0.718207\pi$
$131$	−3.19588	+	1.84514i	−0.279225	+	0.161211i	0.353847	+	0.935303i	$0.384873\pi$
$132$	23.0288	+	3.87624i	2.00440	+	0.337383i
$133$		0			0
$134$	0.219231	+	0.686002i	0.0189387	+	0.0592616i
$135$	0.273625	+	0.448179i	0.0235499	+	0.0385731i
$136$	12.8541	−	5.50085i	1.10223	−	0.471694i
$137$	19.1819	−	5.13977i	1.63882	−	0.439120i	0.682366	−	0.731010i	$-0.260951\pi$
$137$	19.1819	−	5.13977i	1.63882	−	0.439120i	0.956452	+	0.291890i	$0.0942843\pi$
$138$	0.187612	+	3.94504i	0.0159706	+	0.335824i
$139$	−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
$142$	−0.971579	−	20.4300i	−0.0815331	−	1.71445i
$143$	0.382893	−	0.102596i	0.0320191	−	0.00857950i
$144$	9.35911	−	8.10452i	0.779926	−	0.675377i
$145$	−15.8080	−	3.82286i	−1.31278	−	0.317471i
$146$	−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	$-0.748418\pi$
$149$	−5.37045	+	3.10063i	−0.439965	+	0.254014i	0.263618	+	0.964627i	$0.415084\pi$
$150$	−17.2195	−	2.87137i	−1.40597	−	0.234446i
$151$	8.72300	+	5.03623i	0.709868	+	0.409842i	0.811012	−	0.585029i	$-0.198917\pi$
$151$	8.72300	+	5.03623i	0.709868	+	0.409842i	−0.101144	+	0.994872i	$0.532250\pi$
$152$	−4.59850	−	5.85033i	−0.372988	−	0.474525i
$153$	−10.8188	+	10.8188i	−0.874646	+	0.874646i
$154$		0			0
$155$	7.14943	−	7.50898i	0.574256	−	0.603136i
$156$	0.171977	−	0.376420i	0.0137692	−	0.0301377i
$157$	14.0732	−	3.77089i	1.12316	−	0.300950i	0.350999	−	0.936376i	$-0.385842\pi$
$157$	14.0732	−	3.77089i	1.12316	−	0.300950i	0.772162	+	0.635426i	$0.219175\pi$
$158$	−4.66650	−	7.26248i	−0.371247	−	0.577772i
$159$	−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
$163$	−0.763938	+	2.85106i	−0.0598363	+	0.223312i	−0.989369	−	0.145428i	$-0.953544\pi$
$163$	−0.763938	+	2.85106i	−0.0598363	+	0.223312i	0.929533	+	0.368740i	$0.120211\pi$
$164$	11.3837	−	1.08519i	0.888920	−	0.0847395i
$165$	12.4962	−	22.9245i	0.972828	−	1.78467i
$166$	−8.32562	−	7.56970i	−0.646194	−	0.587522i
$167$	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
$170$	−1.12523	−	15.5915i	−0.0863012	−	1.19581i
$171$	7.05197	+	4.07146i	0.539278	+	0.311352i
$172$	−3.43039	−	2.83329i	−0.261565	−	0.216036i
$173$	−1.73431	−	0.464708i	−0.131857	−	0.0353311i	0.192287	−	0.981339i	$-0.438410\pi$
$173$	−1.73431	−	0.464708i	−0.131857	−	0.0353311i	−0.324144	+	0.946008i	$0.605076\pi$
$174$	−7.73035	−	24.1893i	−0.586037	−	1.83378i
$175$		0			0
$176$	−17.8756	−	6.19316i	−1.34743	−	0.466827i
$177$	−2.14375	+	8.00057i	−0.161134	+	0.601360i
$178$	19.8494	−	12.7542i	1.48778	−	0.955971i
$179$	10.7713	−	18.6564i	0.805084	−	1.39445i	−0.111150	−	0.993804i	$-0.535453\pi$
$179$	10.7713	−	18.6564i	0.805084	−	1.39445i	0.916234	−	0.400643i	$-0.131213\pi$
$180$	−5.15174	−	12.8474i	−0.383988	−	0.957586i
$181$	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
$184$	0.380595	−	3.17677i	0.0280578	−	0.234195i
$185$	4.52816	+	2.46831i	0.332917	+	0.181474i
$186$	15.8189	+	3.44250i	1.15990	+	0.252416i
$187$	22.5827	+	6.05102i	1.65141	+	0.442495i
$188$	−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	$-0.869354\pi$
$191$	−14.2331	+	8.21746i	−1.02987	+	0.594595i	−0.112921	+	0.993604i	$0.536021\pi$
$192$	−16.8696	+	10.2716i	−1.21746	+	0.741286i
$193$	1.28369	+	4.79080i	0.0924021	+	0.344849i	0.996613	−	0.0822374i	$-0.0262066\pi$
$193$	1.28369	+	4.79080i	0.0924021	+	0.344849i	−0.904211	+	0.427087i	$0.859540\pi$
$194$	8.60509	+	7.82379i	0.617810	+	0.561716i
$195$	−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	$0.812938\pi$
$198$	20.6785	−	0.983397i	1.46956	−	0.0698870i
$199$	−9.44788	+	16.3642i	−0.669743	+	1.16003i	0.308233	+	0.951311i	$0.400262\pi$
$199$	−9.44788	+	16.3642i	−0.669743	+	1.16003i	−0.977976	+	0.208717i	$0.933071\pi$
$200$	13.3699	+	4.60926i	0.945396	+	0.325924i
$201$	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
$205$	3.00520	−	12.4269i	0.209893	−	0.867931i
$206$	0.982190	−	4.51334i	0.0684324	−	0.314459i
$207$	0.906169	+	3.38187i	0.0629831	+	0.235056i
$208$	−0.188002	+	0.277583i	−0.0130356	+	0.0192469i
$209$		−	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	$0.876636\pi$
$212$	6.59820	+	17.6990i	0.453166	+	1.21557i
$213$	−9.24126	−	34.4888i	−0.633201	−	2.36314i
$214$	−9.38600	−	2.04258i	−0.641614	−	0.139628i
$215$	−4.24561	+	2.59205i	−0.289548	+	0.176776i
$216$	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
$220$	−13.0653	+	16.6332i	−0.880863	+	1.12141i
$221$	0.207158	−	0.358809i	0.0139350	−	0.0241361i
$222$	0.382521	+	8.04350i	0.0256731	+	0.539845i
$223$	−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
$226$	0.0376973	−	0.0414618i	0.00250759	−	0.00275800i
$227$	−5.94107	−	22.1724i	−0.394322	−	1.47163i	−0.822931	−	0.568141i	$-0.807663\pi$
$227$	−5.94107	−	22.1724i	−0.394322	−	1.47163i	0.428609	−	0.903490i	$-0.359004\pi$
$228$	−10.0159	−	8.27247i	−0.663317	−	0.547858i
$229$	10.3396	−	5.96955i	0.683258	−	0.394479i	−0.117824	−	0.993035i	$-0.537592\pi$
$229$	10.3396	−	5.96955i	0.683258	−	0.394479i	0.801081	+	0.598556i	$0.204258\pi$
$230$	−3.21860	−	1.56094i	−0.212228	−	0.102925i
$231$		0			0
$232$	2.92287	+	20.3634i	0.191896	+	1.33692i
$233$	22.9805	+	6.15761i	1.50550	+	0.403399i	0.914939	−	0.403592i	$-0.132238\pi$
$233$	22.9805	+	6.15761i	1.50550	+	0.403399i	0.590565	+	0.806990i	$0.298905\pi$
$234$	0.0780117	−	0.358477i	0.00509978	−	0.0234344i
$235$	−2.96346	+	5.43652i	−0.193315	+	0.354639i
$236$	2.78836	−	6.10310i	0.181507	−	0.397278i
$237$	−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	$0.484474\pi$
$240$	4.70263	+	21.5753i	0.303553	+	1.39268i
$241$	−9.26556	+	16.0484i	−0.596847	+	1.03377i	0.396436	+	0.918062i	$0.370247\pi$
$241$	−9.26556	+	16.0484i	−0.596847	+	1.03377i	−0.993283	+	0.115708i	$0.963086\pi$
$242$	−8.69097	−	13.5258i	−0.558676	−	0.869469i
$243$	5.74504	−	21.4408i	0.368544	−	1.37543i
$244$	2.27047	+	3.18949i	0.145352	+	0.204186i
$245$		0			0
$246$	19.0155	−	6.07695i	1.21239	−	0.387452i
$247$	−0.212992	−	0.0570710i	−0.0135524	−	0.00363134i
$248$	−12.1742	−	4.87718i	−0.773064	−	0.309701i
$249$	−17.0119	−	9.82180i	−1.07808	−	0.622431i
$250$	9.74792	−	12.4490i	0.616513	−	0.787345i
$251$			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
$254$	8.79176	−	9.66973i	0.551644	−	0.606733i
$255$	−7.70722	−	26.1783i	−0.482645	−	1.63935i
$256$	14.8577	−	5.93719i	0.928603	−	0.371074i
$257$	3.85933	−	14.4032i	0.240738	−	0.898448i	−0.734739	−	0.678350i	$-0.762696\pi$
$257$	3.85933	−	14.4032i	0.240738	−	0.898448i	0.975478	−	0.220098i	$-0.0706378\pi$
$258$	−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
$262$	4.39060	−	2.82117i	0.271252	−	0.174293i
$263$	−6.84826	+	1.83499i	−0.422282	+	0.113150i	−0.463701	−	0.885992i	$-0.653479\pi$
$263$	−6.84826	+	1.83499i	−0.422282	+	0.113150i	0.0414191	+	0.999142i	$0.486812\pi$
$264$	−32.7913	−	3.92858i	−2.01816	−	0.241787i
$265$	21.1121	−	0.517856i	1.29691	−	0.0318117i
$266$		0			0
$267$	29.1246	−	29.1246i	1.78240	−	1.78240i
$268$	−0.355775	−	0.954331i	−0.0217324	−	0.0582950i
$269$	−5.23463	−	3.02221i	−0.319161	−	0.184268i	0.331858	−	0.943329i	$-0.392325\pi$
$269$	−5.23463	−	3.02221i	−0.319161	−	0.184268i	−0.651019	+	0.759062i	$0.725658\pi$
$270$	−0.416635	−	0.614723i	−0.0253556	−	0.0374109i
$271$	−20.3476	+	11.7477i	−1.23603	+	0.713622i	−0.968280	−	0.249866i	$-0.919613\pi$
$271$	−20.3476	+	11.7477i	−1.23603	+	0.713622i	−0.267750	+	0.963488i	$0.586280\pi$
$272$	−17.7884	+	8.63413i	−1.07858	+	0.523521i
$273$		0			0
$274$	−26.7514	+	8.54914i	−1.61611	+	0.516473i
$275$	12.8137	+	19.8751i	0.772692	+	1.19851i
$276$	−0.530048	−	5.56023i	−0.0319052	−	0.334686i
$277$	−22.5298	+	6.03684i	−1.35369	+	0.362719i	−0.861494	−	0.507768i	$-0.830471\pi$
$277$	−22.5298	+	6.03684i	−1.35369	+	0.362719i	−0.492191	+	0.870487i	$0.663804\pi$
$278$	1.63289	−	0.0776543i	0.0979340	−	0.00465740i
$279$	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	$0.695272\pi$
$282$	−9.65704	+	0.459255i	−0.575069	+	0.0273483i
$283$	−6.88593	+	1.84508i	−0.409326	+	0.109679i	−0.457606	−	0.889155i	$-0.651293\pi$
$283$	−6.88593	+	1.84508i	−0.409326	+	0.109679i	0.0482794	+	0.998834i	$0.484626\pi$
$284$	2.74494	+	28.7945i	0.162882	+	1.70864i
$285$	−12.3961	+	7.56812i	−0.734281	+	0.448297i
$286$	−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
$290$	22.5874	+	4.33827i	1.32638	+	0.254752i
$291$	17.5829	+	10.1515i	1.03073	+	0.595091i
$292$	6.70121	+	17.9753i	0.392159	+	1.05193i
$293$	−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
$296$	0.775992	−	6.47709i	0.0451036	−	0.376473i
$297$	1.07281	−	0.287458i	0.0622506	−	0.0166800i
$298$	7.37810	−	4.74079i	0.427402	−	0.274627i
$299$	−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
$303$	5.47891	−	20.4476i	0.314755	−	1.17468i
$304$	6.88895	+	7.95536i	0.395108	+	0.456271i
$305$	4.19899	−	1.23624i	0.240434	−	0.0707868i
$306$	14.5560	−	16.0096i	0.832110	−	0.915206i
$307$	−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
$310$	−9.59496	+	11.0876i	−0.544957	+	0.629734i
$311$	17.7808	+	10.2657i	1.00826	+	0.582116i	0.910680	−	0.413112i	$-0.135558\pi$
$311$	17.7808	+	10.2657i	1.00826	+	0.582116i	0.0975749	+	0.995228i	$0.468891\pi$
$312$	−0.217650	+	0.543290i	−0.0123220	+	0.0307577i
$313$	26.9598	+	7.22385i	1.52386	+	0.408316i	0.921009	−	0.389540i	$-0.127366\pi$
$313$	26.9598	+	7.22385i	1.52386	+	0.408316i	0.602847	+	0.797856i	$0.294033\pi$
$314$	−19.6267	+	6.27225i	−1.10760	+	0.353964i
$315$		0			0
$316$	7.07986	+	9.94561i	0.398273	+	0.559484i
$317$	−3.35388	+	12.5169i	−0.188373	+	0.703016i	0.805511	+	0.592581i	$0.201891\pi$
$317$	−3.35388	+	12.5169i	−0.188373	+	0.703016i	−0.993883	+	0.110435i	$0.964776\pi$
$318$	17.8254	+	27.7417i	0.999597	+	1.55567i
$319$	−17.1997	+	29.7907i	−0.962996	+	1.66796i
$320$	−0.855618	−	17.8681i	−0.0478305	−	0.998855i
$321$	−16.7689			−0.935949
$322$		0			0
$323$	−9.19609	−	9.19609i	−0.511684	−	0.511684i
$324$	−7.23538	+	15.8366i	−0.401965	+	0.879813i
$325$	0.398986	−	0.128179i	0.0221318	−	0.00711010i
$326$	0.887621	−	4.07877i	0.0491608	−	0.225902i
$327$	9.34642	+	2.50436i	0.516858	+	0.138492i
$328$	−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	$-0.731904\pi$
$331$	−6.41324	+	3.70269i	−0.352504	+	0.203518i	0.313284	+	0.949660i	$0.398571\pi$
$332$	12.2694	+	10.1338i	0.673373	+	0.556163i
$333$	1.84758	+	6.89526i	0.101247	+	0.377858i
$334$	−8.24882	+	9.07257i	−0.451356	+	0.496429i
$335$	−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	$0.821968\pi$
$338$	−0.872857	−	18.3541i	−0.0474771	−	0.998331i
$339$	0.0489128	−	0.0847195i	0.00265658	−	0.00460133i
$340$	2.63694	+	21.9492i	0.143008	+	1.19036i
$341$	−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
$345$	−6.06974	−	1.46785i	−0.326784	−	0.0790264i
$346$	2.48114	+	0.539944i	0.133387	+	0.0290276i
$347$	−2.85823	−	10.6671i	−0.153438	−	0.572638i	−0.999234	−	0.0391317i	$-0.987541\pi$
$347$	−2.85823	−	10.6671i	−0.153438	−	0.572638i	0.845796	−	0.533506i	$-0.179126\pi$
$348$	12.5450	+	33.6508i	0.672485	+	1.80387i
$349$			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
$352$	25.6675	+	7.54769i	1.36808	+	0.402293i
$353$	1.95306	+	7.28892i	0.103951	+	0.387950i	0.998224	−	0.0595714i	$-0.0189734\pi$
$353$	1.95306	+	7.28892i	0.103951	+	0.387950i	−0.894273	+	0.447522i	$0.852307\pi$
$354$	2.49082	−	11.4458i	0.132386	−	0.608335i
$355$	31.4331	+	7.60149i	1.66829	+	0.403445i
$356$	−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	0.673783	−	0.738929i	$-0.264668\pi$
$359$	−5.74179	−	9.94507i	−0.303040	−	0.524881i	−0.976823	+	0.214049i	$0.931335\pi$
$360$	8.14052	+	17.8023i	0.429043	+	0.938265i
$361$	6.03921	−	10.4602i	0.317853	−	0.550538i
$362$	−22.9016	+	1.08912i	−1.20368	+	0.0572428i
$363$	−19.8460	−	19.8460i	−1.04165	−	1.04165i
$364$		0			0
$365$	21.4417	−	0.525941i	1.12231	−	0.0275290i
$366$	5.05695	+	4.59781i	0.264331	+	0.240331i
$367$	−3.27735	−	12.2312i	−0.171076	−	0.638465i	−0.997187	−	0.0749570i	$-0.976118\pi$
$367$	−3.27735	−	12.2312i	−0.171076	−	0.638465i	0.826111	−	0.563508i	$-0.190549\pi$
$368$	−0.324222	+	4.51313i	−0.0169013	+	0.235263i
$369$	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
$373$	24.0550	+	6.44552i	1.24552	+	0.333737i	0.820605	−	0.571496i	$-0.193637\pi$
$373$	24.0550	+	6.44552i	1.24552	+	0.333737i	0.424917	+	0.905232i	$0.360303\pi$
$374$	−32.3072	−	7.03069i	−1.67057	−	0.363548i
$375$	12.0067	−	24.8541i	0.620025	−	1.28346i
$376$	7.77641	+	0.931657i	0.401038	+	0.0480466i
$377$	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	$0.465732\pi$
$380$	10.9204	−	4.37905i	0.560206	−	0.224640i
$381$	11.4074	−	19.7583i	0.584421	−	1.01225i
$382$	19.5538	−	12.5643i	1.00046	−	0.642845i
$383$	−3.47535	+	12.9702i	−0.177582	+	0.662745i	0.818515	+	0.574484i	$0.194797\pi$
$383$	−3.47535	+	12.9702i	−0.177582	+	0.662745i	−0.996097	+	0.0882604i	$0.971869\pi$
$384$	23.1402	−	15.6431i	1.18087	−	0.798282i
$385$		0			0
$386$	−2.13521	−	6.68133i	−0.108679	−	0.340071i
$387$	−6.65075	−	1.78206i	−0.338076	−	0.0905873i
$388$	−12.6813	−	10.4739i	−0.643795	−	0.531734i
$389$	−15.5106	−	8.95506i	−0.786419	−	0.454039i	0.0522811	−	0.998632i	$-0.483351\pi$
$389$	−15.5106	−	8.95506i	−0.786419	−	0.454039i	−0.838700	+	0.544593i	$0.816684\pi$
$390$	0.494798	+	0.428187i	0.0250551	+	0.0216821i
$391$		−	5.59179i		−	0.282789i
$392$		0			0
$393$	6.44222	−	6.44222i	0.324967	−	0.324967i
$394$	5.77005	+	5.24616i	0.290691	+	0.264298i
$395$	13.0935	−	3.85489i	0.658805	−	0.193961i
$396$	−29.1447	+	2.77833i	−1.46458	+	0.139616i
$397$	1.58258	−	5.90626i	0.0794273	−	0.296427i	−0.914773	−	0.403967i	$-0.867631\pi$
$397$	1.58258	−	5.90626i	0.0794273	−	0.296427i	0.994201	+	0.107541i	$0.0342976\pi$
$398$	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	0.509662	−	0.860375i	$-0.329771\pi$
$401$	−9.81777	−	17.0049i	−0.490276	−	0.849183i	−0.999937	+	0.0111923i	$0.996437\pi$
$402$	−0.961144	−	1.49583i	−0.0479375	−	0.0746052i
$403$	−0.375386	+	0.100584i	−0.0186993	+	0.00501046i
$404$	−7.12640	+	15.5981i	−0.354551	+	0.776034i
$405$	14.0981	+	13.4231i	0.700542	+	0.666998i
$406$		0			0
$407$	7.71315	−	7.71315i	0.382327	−	0.382327i
$408$	−27.1384	+	21.3315i	−1.34355	+	1.05606i
$409$	−8.70611	−	5.02647i	−0.430489	−	0.248543i	0.269066	−	0.963122i	$-0.413285\pi$
$409$	−8.70611	−	5.02647i	−0.430489	−	0.248543i	−0.699555	+	0.714579i	$0.746618\pi$
$410$	−3.41038	+	17.7563i	−0.168426	+	0.876922i
$411$	−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
$415$	15.1852	−	9.27095i	0.745412	−	0.455093i
$416$	0.246926	−	0.404748i	0.0121066	−	0.0198444i
$417$	2.75655	−	0.738616i	0.134989	−	0.0361702i
$418$	0.835899	+	17.5770i	0.0408852	+	0.859718i
$419$	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	$0.0830348\pi$
$422$	−0.737592	−	15.5098i	−0.0359054	−	0.755006i
$423$	−8.27847	+	2.21821i	−0.402513	+	0.107853i
$424$	−10.5097	−	24.5587i	−0.510398	−	1.19267i
$425$	24.1591	+	5.21887i	1.17189	+	0.253153i
$426$	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
$430$	5.82329	−	3.94679i	0.280824	−	0.190331i
$431$	21.7939	+	12.5827i	1.04977	+	0.606087i	0.922586	−	0.385792i	$-0.126072\pi$
$431$	21.7939	+	12.5827i	1.04977	+	0.606087i	0.127187	+	0.991879i	$0.459405\pi$
$432$	−0.526751	+	0.777743i	−0.0253433	+	0.0374192i
$433$	−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
$436$	−7.12975	−	3.25741i	−0.341453	−	0.156002i
$437$	−2.87463	+	0.770255i	−0.137512	+	0.0368463i
$438$	18.1037	+	28.1747i	0.865026	+	1.34624i
$439$	−14.8997	−	25.8071i	−0.711125	−	1.23170i	−0.964435	−	0.264320i	$-0.914853\pi$
$439$	−14.8997	−	25.8071i	−0.711125	−	1.23170i	0.253310	−	0.967385i	$-0.418481\pi$
$440$	17.3389	−	24.3741i	0.826598	−	1.16199i
$441$		0			0
$442$	−0.268531	+	0.520776i	−0.0127727	+	0.0247708i
$443$	−10.5682	+	39.4412i	−0.502112	+	1.87391i	−0.0162556	+	0.999868i	$0.505175\pi$
$443$	−10.5682	+	39.4412i	−0.502112	+	1.87391i	−0.485856	+	0.874039i	$0.661492\pi$
$444$	−1.08071	−	11.3367i	−0.0512883	−	0.538016i
$445$	10.5360	+	35.7864i	0.499454	+	1.69644i
$446$	20.2718	+	18.4312i	0.959897	+	0.872743i
$447$	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	$-0.162481\pi$
$450$	21.7838	−	2.11020i	1.02690	−	0.0994757i
$451$	−23.4189	−	13.5209i	−1.10275	−	0.636675i
$452$	−0.0504665	+	0.0611021i	−0.00237374	+	0.00287400i
$453$	−24.0199	−	6.43610i	−1.12855	−	0.302394i
$454$	9.88197	+	30.9219i	0.463784	+	1.45124i
$455$		0			0
$456$	14.7043	+	11.0130i	0.688593	+	0.515730i
$457$	0.969683	−	3.61891i	0.0453599	−	0.169285i	−0.939530	−	0.342466i	$-0.888738\pi$
$457$	0.969683	−	3.61891i	0.0453599	−	0.169285i	0.984890	+	0.173181i	$0.0554045\pi$
$458$	−14.2048	+	9.12729i	−0.663748	+	0.426490i
$459$	0.580425	−	1.00533i	0.0270919	−	0.0469246i
$460$	4.65151	+	1.98878i	0.216878	+	0.0927274i
$461$	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	$0.911536\pi$
$464$	−5.49689	−	28.5693i	−0.255187	−	1.32630i
$465$	−12.2512	+	22.4751i	−0.568136	+	1.04226i
$466$	−32.8763	−	7.15454i	−1.52297	−	0.331428i
$467$	−27.1281	−	7.26895i	−1.25534	−	0.336367i	−0.430941	−	0.902380i	$-0.641818\pi$
$467$	−27.1281	−	7.26895i	−1.25534	−	0.336367i	−0.824396	+	0.566013i	$0.808485\pi$
$468$	−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
$472$	−3.52888	+	8.80866i	−0.162430	+	0.405451i
$473$	2.72309	+	10.1627i	0.125208	+	0.467282i
$474$	15.7688	+	14.3371i	0.724285	+	0.658524i
$475$	−0.644940	−	13.1386i	−0.0295919	−	0.602842i
$476$		0			0
$477$	20.6700	+	20.6700i	0.946413	+	0.946413i
$478$	−2.12950	+	0.101272i	−0.0974012	+	0.00463206i
$479$	5.27141	−	9.13034i	0.240857	−	0.417176i	−0.720102	−	0.693868i	$-0.755905\pi$
$479$	5.27141	−	9.13034i	0.240857	−	0.417176i	0.960959	+	0.276692i	$0.0892383\pi$
$480$	−8.09242	−	30.1618i	−0.369367	−	1.37669i
$481$	−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
$485$	−15.6949	+	9.58215i	−0.712670	+	0.435103i
$486$	−6.67517	+	30.6736i	−0.302792	+	1.39138i
$487$	−9.85078	−	36.7636i	−0.446381	−	1.66592i	−0.712263	−	0.701913i	$-0.752330\pi$
$487$	−9.85078	−	36.7636i	−0.446381	−	1.66592i	0.265882	−	0.964006i	$-0.414337\pi$
$488$	−3.42157	−	4.35300i	−0.154887	−	0.197051i
$489$		−	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	$-0.0258691\pi$
$492$	−26.4534	+	9.86185i	−1.19261	+	0.444606i
$493$	9.30560	+	34.7290i	0.419103	+	1.56411i
$494$	0.304710	+	0.0663109i	0.0137096	+	0.00298347i
$495$	−7.69395	+	31.8154i	−0.345817	+	1.43000i
$496$	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	0.728490	−	0.685056i	$-0.240222\pi$
$499$	−5.11616	−	8.86145i	−0.229031	−	0.396693i	−0.957521	+	0.288363i	$0.906889\pi$
$500$	−12.9338	+	18.2406i	−0.578415	+	0.815742i
$501$	−10.7030	+	18.5381i	−0.478174	+	0.828221i
$502$	−1.21069	−	25.4580i	−0.0540359	−	1.13625i
$503$	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
$506$	−5.08981	+	5.59809i	−0.226270	+	0.248865i
$507$	−8.30225	−	30.9844i	−0.368716	−	1.37607i
$508$	−11.7698	+	14.2502i	−0.522200	+	0.632252i
$509$	−0.0145211	+	0.00838376i	−0.000643637	+	0.000371604i	−0.500322	−	0.865840i	$-0.666785\pi$
$509$	−0.0145211	+	0.00838376i	−0.000643637	+	0.000371604i	0.499678	+	0.866211i	$0.333452\pi$
$510$	12.6460	+	36.4621i	0.559974	+	1.61457i
$511$		0			0
$512$	−20.5893	+	9.38510i	−0.909928	+	0.414767i
$513$	−0.596770	−	0.159904i	−0.0263481	−	0.00705994i
$514$	−4.48416	+	20.6055i	−0.197788	+	0.908869i
$515$	6.41243	+	3.49543i	0.282565	+	0.154027i
$516$	9.99090	+	4.56460i	0.439825	+	0.200945i
$517$	9.26042	+	9.26042i	0.407273	+	0.407273i
$518$		0			0
$519$	4.43276			0.194577
$520$	−0.337700	−	0.408596i	−0.0148091	−	0.0179181i
$521$	−0.00830997	+	0.0143933i	−0.000364066	+	0.000630582i	−0.866207	−	0.499685i	$-0.833449\pi$
$521$	−0.00830997	+	0.0143933i	−0.000364066	+	0.000630582i	0.865843	+	0.500315i	$0.166783\pi$
$522$	17.2100	+	26.7839i	0.753261	+	1.17230i
$523$	8.00409	−	29.8717i	0.349994	−	1.30620i	−0.536674	−	0.843790i	$-0.680319\pi$
$523$	8.00409	−	29.8717i	0.349994	−	1.30620i	0.886668	−	0.462407i	$-0.153014\pi$
$524$	−6.01271	+	4.28019i	−0.262666	+	0.186981i
$525$		0			0
$526$	9.55070	−	3.05219i	0.416430	−	0.133082i
$527$	−22.1400	−	5.93238i	−0.964432	−	0.258419i
$528$	46.5855	+	3.34669i	2.02737	+	0.145646i
$529$	18.8104	+	10.8602i	0.817845	+	0.472183i
$530$	−29.7885	+	2.14983i	−1.29393	+	0.0933825i
$531$		−	10.3840i		−	0.450626i
$532$		0			0
$533$	−0.338860	+	0.338860i	−0.0146777	+	0.0146777i
$534$	−39.1854	+	43.0985i	−1.69572	+	1.86505i
$535$	7.26914	−	13.3354i	0.314272	−	0.576539i
$536$	0.566685	+	1.32420i	0.0244771	+	0.0571969i
$537$	−13.7653	+	51.3727i	−0.594016	+	2.21690i
$538$	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	−0.988109	−	0.153756i	$-0.950863\pi$
$541$	−14.5885	−	25.2681i	−0.627211	−	1.08636i	0.360898	−	0.932605i	$-0.382470\pi$
$542$	27.9542	−	17.9619i	1.20074	−	0.771532i
$543$	−38.6612	+	10.3592i	−1.65911	+	0.444558i
$544$	24.5482	−	13.3917i	1.05250	−	0.574166i
$545$	−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	$0.241205\pi$
$548$	37.2151	−	13.8738i	1.58975	−	0.592659i
$549$	5.24710	+	3.02941i	0.223941	+	0.129292i
$550$	−19.4360	−	27.2151i	−0.828753	−	1.16046i
$551$	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
$555$	−12.3755	−	2.99279i	−0.525312	−	0.127037i
$556$	−2.30143	+	0.219392i	−0.0976022	+	0.00930428i
$557$	−2.78027	+	0.744970i	−0.117804	+	0.0315654i	−0.317239	−	0.948346i	$-0.602756\pi$
$557$	−2.78027	+	0.744970i	−0.117804	+	0.0315654i	0.199436	+	0.979911i	$0.436089\pi$
$558$	−20.2731	+	0.964116i	−0.858227	+	0.0408143i
$559$	0.186452			0.00788606
$560$		0			0
$561$	−57.7196			−2.43693
$562$	27.2651	−	1.29663i	1.15011	−	0.0546951i
$563$	−26.9945	+	7.23315i	−1.13768	+	0.304841i	−0.778018	−	0.628241i	$-0.783775\pi$
$563$	−26.9945	+	7.23315i	−1.13768	+	0.304841i	−0.359663	+	0.933082i	$0.617108\pi$
$564$	13.6109	−	1.29750i	0.573120	−	0.0546348i
$565$	0.0461696	+	0.0756227i	0.00194237	+	0.00318147i
$566$	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	$-0.947400\pi$
$569$	−31.8950	+	18.4146i	−1.33711	+	0.771981i	−0.350732	+	0.936476i	$0.614067\pi$
$570$	17.0025	−	11.5236i	0.712156	−	0.482671i
$571$	−35.5147	−	20.5044i	−1.48624	−	0.858084i	−0.486367	−	0.873754i	$-0.661678\pi$
$571$	−35.5147	−	20.5044i	−1.48624	−	0.858084i	−0.999877	+	0.0156706i	$0.995012\pi$
$572$	0.742858	−	0.276938i	0.0310605	−	0.0115793i
$573$	28.6909	−	28.6909i	1.19858	−	1.19858i
$574$		0			0
$575$	3.79847	−	4.19063i	0.158407	−	0.174762i
$576$	17.0955	−	17.9122i	0.712314	−	0.746343i
$577$	20.6267	−	5.52692i	0.858703	−	0.230089i	0.197506	−	0.980302i	$-0.436716\pi$
$577$	20.6267	−	5.52692i	0.858703	−	0.230089i	0.661196	+	0.750213i	$0.270049\pi$
$578$	−8.84720	+	5.68476i	−0.367995	+	0.236455i
$579$	−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
$583$	11.5609	−	43.1458i	0.478802	−	1.78691i
$584$	−10.6738	−	24.9421i	−0.441685	−	1.03211i
$585$	0.509315	+	0.277629i	0.0210576	+	0.0114785i
$586$	1.74156	−	1.91548i	0.0719432	−	0.0791276i
$587$	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
$590$	8.02244	+	6.94243i	0.330279	+	0.285815i
$591$	11.7900	+	6.80697i	0.484977	+	0.280001i
$592$	−0.661054	+	9.20178i	−0.0271692	+	0.378191i
$593$	2.04214	+	0.547190i	0.0838607	+	0.0224704i	0.300505	−	0.953780i	$-0.402845\pi$
$593$	2.04214	+	0.547190i	0.0838607	+	0.0224704i	−0.216645	+	0.976251i	$0.569511\pi$
$594$	−1.49615	+	0.478138i	−0.0613880	+	0.0196182i
$595$		0			0
$596$	−10.1039	+	7.19257i	−0.413874	+	0.294619i
$597$	12.0740	−	45.0608i	0.494157	−	1.84422i
$598$	0.0724808	+	0.112802i	0.00296396	+	0.00461281i
$599$	−12.9248	+	22.3864i	−0.528092	+	0.914683i	0.471371	+	0.881935i	$0.343759\pi$
$599$	−12.9248	+	22.3864i	−0.528092	+	0.914683i	−0.999464	+	0.0327479i	$0.989574\pi$
$600$	−34.8286	−	2.44862i	−1.42187	−	0.0999644i
$601$	−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
$604$	18.3231	+	8.37140i	0.745558	+	0.340627i
$605$	24.3855	−	7.17942i	0.991412	−	0.291885i
$606$	−6.36596	+	29.2527i	−0.258599	+	1.18831i
$607$	−21.6414	−	5.79881i	−0.878399	−	0.235366i	−0.208683	−	0.977983i	$-0.566918\pi$
$607$	−21.6414	−	5.79881i	−0.878399	−	0.235366i	−0.669716	+	0.742617i	$0.733584\pi$
$608$	−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
$612$	−19.4865	+	23.5933i	−0.787696	+	0.953701i
$613$	−8.56832	−	31.9774i	−0.346071	−	1.29156i	−0.891356	−	0.453304i	$-0.850245\pi$
$613$	−8.56832	−	31.9774i	−0.346071	−	1.29156i	0.545285	−	0.838251i	$-0.316422\pi$
$614$	5.19574	−	5.71460i	0.209683	−	0.230622i
$615$	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	$0.466740\pi$
$618$	0.541696	+	11.3906i	0.0217902	+	0.458196i
$619$	−18.1903	+	31.5065i	−0.731130	+	1.26635i	0.225270	+	0.974296i	$0.427674\pi$
$619$	−18.1903	+	31.5065i	−0.731130	+	1.26635i	−0.956400	+	0.292059i	$0.905660\pi$
$620$	12.8091	−	16.3071i	0.514428	−	0.654910i
$621$	−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
$625$	14.5603	+	20.3223i	0.582414	+	0.812893i
$626$	−38.5691	−	8.39340i	−1.54153	−	0.335468i
$627$	7.95073	+	29.6725i	0.317522	+	1.18501i
$628$	27.3036	−	10.1788i	1.08953	−	0.406178i
$629$		−	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	$0.931693\pi$
$632$	−10.6693	−	13.5737i	−0.424401	−	0.539934i
$633$	−7.01567	−	26.1828i	−0.278848	−	1.04067i
$634$	3.89688	−	17.9068i	0.154765	−	0.711171i
$635$	10.7677	+	17.6367i	0.427302	+	0.699892i
$636$	−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
$640$	2.40902	+	25.1833i	0.0952249	+	0.995456i
$641$	−2.64450	+	4.58042i	−0.104452	+	0.180916i	−0.913514	−	0.406807i	$-0.866642\pi$
$641$	−2.64450	+	4.58042i	−0.104452	+	0.180916i	0.809062	+	0.587723i	$0.199975\pi$
$642$	23.6880	−	1.12652i	0.934892	−	0.0444602i
$643$	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
$646$	13.6083	+	12.3728i	0.535413	+	0.486800i
$647$	−1.58576	−	5.91812i	−0.0623425	−	0.232665i	0.927724	−	0.373268i	$-0.121763\pi$
$647$	−1.58576	−	5.91812i	−0.0623425	−	0.232665i	−0.990066	+	0.140602i	$0.955096\pi$
$648$	9.15693	−	22.8572i	0.359718	−	0.897914i
$649$	−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
$653$	−37.7871	−	10.1250i	−1.47872	−	0.396223i	−0.572812	−	0.819687i	$-0.694147\pi$
$653$	−37.7871	−	10.1250i	−1.47872	−	0.396223i	−0.905913	+	0.423464i	$0.860814\pi$
$654$	−13.3711	−	2.90982i	−0.522853	−	0.113783i
$655$	2.33051	+	7.91578i	0.0910606	+	0.309295i
$656$	22.4587	−	4.32119i	0.876867	−	0.168714i
$657$	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	$0.549574\pi$
$660$	20.5286	−	48.0139i	0.799075	−	1.86894i
$661$	17.8362	−	30.8932i	0.693748	−	1.20161i	−0.276854	−	0.960912i	$-0.589292\pi$
$661$	17.8362	−	30.8932i	0.693748	−	1.20161i	0.970601	−	0.240694i	$-0.0773750\pi$
$662$	8.81071	−	5.66131i	0.342438	−	0.220033i
$663$	−0.264740	+	0.988023i	−0.0102817	+	0.0383716i
$664$	−18.0128	−	13.4909i	−0.699032	−	0.523548i
$665$		0			0
$666$	−3.07314	−	9.61625i	−0.119082	−	0.372622i
$667$	7.94717	+	2.12944i	0.307716	+	0.0824521i
$668$	11.0429	−	13.3702i	0.427264	−	0.517309i
$669$	41.4216	+	23.9148i	1.60145	+	0.924599i
$670$	1.60620	−	0.115919i	0.0620528	−	0.00447832i
$671$		−	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	$0.952873\pi$
$674$	8.61226	+	7.83031i	0.331732	+	0.301612i
$675$	1.11790	−	0.359138i	0.0430279	−	0.0138232i
$676$	2.46602	+	25.8687i	0.0948471	+	0.994949i
$677$	−11.9320	+	44.5308i	−0.458584	+	1.71146i	0.218750	+	0.975781i	$0.429802\pi$
$677$	−11.9320	+	44.5308i	−0.458584	+	1.71146i	−0.677333	+	0.735676i	$0.736864\pi$
$678$	−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
$682$	16.7650	+	26.0915i	0.641967	+	0.999094i
$683$	40.1276	−	10.7522i	1.53544	−	0.411420i	0.610652	−	0.791899i	$-0.290907\pi$
$683$	40.1276	−	10.7522i	1.53544	−	0.411420i	0.924790	+	0.380479i	$0.124241\pi$
$684$	14.8130	+	6.76773i	0.566391	+	0.258771i
$685$	−1.08888	−	44.3917i	−0.0416039	−	1.69612i
$686$		0			0
$687$	−20.8424	+	20.8424i	−0.795187	+	0.795187i
$688$	−7.36758	−	4.98992i	−0.280886	−	0.190239i
$689$	−0.685527	−	0.395789i	−0.0261165	−	0.0150784i
$690$	8.67283	+	1.66575i	0.330169	+	0.0634141i
$691$	−15.8798	+	9.16821i	−0.604096	+	0.348775i	−0.770651	−	0.637257i	$-0.780069\pi$
$691$	−15.8798	+	9.16821i	−0.604096	+	0.348775i	0.166555	+	0.986032i	$0.446736\pi$
$692$	−3.54117	−	0.596054i	−0.134615	−	0.0226586i
$693$		0			0
$694$	4.75419	+	14.8765i	0.180466	+	0.564703i
$695$	−0.607556	+	2.51232i	−0.0230459	+	0.0952977i
$696$	−19.9820	−	46.6930i	−0.757415	−	1.76989i
$697$	−27.3010	+	7.31528i	−1.03410	+	0.277086i
$698$	−0.698628	−	14.6905i	−0.0264435	−	0.556043i
$699$	−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	$0.479390\pi$
$702$	0.00132224	+	0.0278037i	4.99049e−5	+	0.00104938i
$703$	−5.86106	+	1.57047i	−0.221054	+	0.0592312i
$704$	−36.7654	−	8.93768i	−1.38565	−	0.336852i
$705$	3.59315	−	14.8581i	0.135326	−	0.559588i
$706$	−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	$-0.469067\pi$
$709$	26.8261	−	15.4881i	1.00748	−	0.581667i	0.910452	+	0.413615i	$0.135734\pi$
$710$	−44.9136	−	8.62635i	−1.68558	−	0.323741i
$711$	16.3617	+	9.44644i	0.613612	+	0.354269i
$712$	37.0990	−	29.1607i	1.39034	−	1.09284i
$713$	−3.70884	+	3.70884i	−0.138897	+	0.138897i
$714$		0			0
$715$	−0.0217353	−	0.886111i	−0.000812854	−	0.0331387i
$716$	17.9044	−	39.1888i	0.669120	−	1.46456i
$717$	−3.59492	+	0.963255i	−0.134255	+	0.0359734i
$718$	8.77905	+	13.6628i	0.327631	+	0.509893i
$719$	21.3674	+	37.0094i	0.796869	+	1.38022i	0.921646	+	0.388033i	$0.126845\pi$
$719$	21.3674	+	37.0094i	0.796869	+	1.38022i	−0.124777	+	0.992185i	$0.539821\pi$
$720$	−12.6954	−	24.6010i	−0.473129	−	0.916825i
$721$		0			0
$722$	−7.82838	+	15.1820i	−0.291342	+	0.565015i
$723$	11.8410	−	44.1913i	0.440372	−	1.64349i
$724$	32.2780	−	3.07701i	1.19960	−	0.114356i
$725$	−16.6173	+	32.3480i	−0.617152	+	1.20138i
$726$	29.3681	+	26.7016i	1.08995	+	0.990990i
$727$	−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
$730$	−30.2536	+	2.18339i	−1.11974	+	0.0808108i
$731$	9.52347	+	5.49838i	0.352238	+	0.203365i
$732$	−7.45242	−	6.15522i	−0.275449	−	0.227503i
$733$	3.68215	+	0.986629i	0.136003	+	0.0364420i	0.326179	−	0.945308i	$-0.394239\pi$
$733$	3.68215	+	0.986629i	0.136003	+	0.0364420i	−0.190175	+	0.981750i	$0.560906\pi$
$734$	5.45132	+	17.0579i	0.201212	+	0.629618i
$735$		0			0
$736$	0.154814	−	6.39711i	0.00570652	−	0.235800i
$737$	−0.623362	+	2.32642i	−0.0229618	+	0.0856947i
$738$	−21.0553	+	13.5290i	−0.775054	+	0.498011i
$739$	6.00177	−	10.3954i	0.220779	−	0.382400i	−0.734266	−	0.678862i	$-0.762474\pi$
$739$	6.00177	−	10.3954i	0.220779	−	0.382400i	0.955045	+	0.296462i	$0.0958068\pi$
$740$	9.48393	+	4.05491i	0.348636	+	0.149061i
$741$	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	$0.815362\pi$
$744$	32.1484	+	3.85156i	1.17862	+	0.141205i
$745$	3.91626	+	13.3019i	0.143481	+	0.487345i
$746$	−34.4135	−	7.48906i	−1.25997	−	0.274194i
$747$	23.7876	+	6.37387i	0.870344	+	0.233208i
$748$	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	$-0.659931\pi$
$751$	1.00430	−	0.579834i	0.0366475	−	0.0211584i	0.518212	+	0.855252i	$0.326598\pi$
$752$	−11.0477	−	0.793663i	−0.402867	−	0.0289419i
$753$	−11.5156	−	42.9769i	−0.419653	−	1.56616i
$754$	−0.637876	−	0.579960i	−0.0232301	−	0.0211209i
$755$	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	$0.882590\pi$
$758$	−5.90974	+	0.281047i	−0.214652	+	0.0102081i
$759$	−6.60410	+	11.4386i	−0.239714	+	0.415196i
$760$	−15.1322	+	6.91954i	−0.548902	+	0.250998i
$761$	−9.62047	−	16.6631i	−0.348742	−	0.604039i	0.637284	−	0.770629i	$-0.280058\pi$
$761$	−9.62047	−	16.6631i	−0.348742	−	0.604039i	−0.986026	+	0.166590i	$0.946724\pi$
$762$	−14.7870	+	28.6772i	−0.535677	+	1.03887i
$763$		0			0
$764$	−26.7780	+	19.0621i	−0.968794	+	0.689644i
$765$	17.8274	+	29.2000i	0.644550	+	1.05573i
$766$	4.03801	−	18.5554i	0.145899	−	0.670432i
$767$	0.0727778	+	0.271611i	0.00262786	+	0.00980729i
$768$	−31.6374	+	23.6522i	−1.14162	+	0.853475i
$769$			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
$772$	3.46507	+	9.29472i	0.124711	+	0.334524i
$773$	4.19873	+	15.6699i	0.151018	+	0.563607i	0.999414	+	0.0342438i	$0.0109023\pi$
$773$	4.19873	+	15.6699i	0.151018	+	0.563607i	−0.848396	+	0.529363i	$0.822431\pi$
$774$	9.51467	+	2.07058i	0.341998	+	0.0744254i
$775$	−12.5624	−	19.4854i	−0.451255	−	0.699937i
$776$	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
$780$	−0.727726	−	0.571624i	−0.0260568	−	0.0204674i
$781$	34.2004	−	59.2368i	1.22379	−	2.11966i
$782$	0.375652	+	7.89906i	0.0134333	+	0.282470i
$783$	1.20775	+	1.20775i	0.0431616	+	0.0431616i
$784$		0			0
$785$	−0.798877	−	32.5689i	−0.0285132	−	1.16243i
$786$	−8.66761	+	9.53317i	−0.309163	+	0.340037i
$787$	10.8721	+	40.5750i	0.387547	+	1.44634i	0.834113	+	0.551594i	$0.185980\pi$
$787$	10.8721	+	40.5750i	0.387547	+	1.44634i	−0.446566	+	0.894751i	$0.647353\pi$
$788$	−8.50331	−	7.02319i	−0.302918	−	0.250191i
$789$	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
$793$	−0.158479	−	0.0424643i	−0.00562775	−	0.00150795i
$794$	−1.83880	+	8.44960i	−0.0652565	+	0.299865i
$795$	−50.0153	+	14.7252i	−1.77386	+	0.522247i
$796$	−15.7046	+	34.3739i	−0.556635	+	1.21835i
$797$	−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
$800$	27.4940	+	6.63935i	0.972059	+	0.234736i
$801$	−25.8185	+	44.7190i	−0.912253	+	1.58007i
$802$	15.0111	+	23.3618i	0.530061	+	0.824935i
$803$	11.7414	−	43.8193i	0.414343	−	1.54635i
$804$	1.45822	+	2.04847i	0.0514273	+	0.0722438i
$805$		0			0
$806$	0.523519	−	0.167305i	0.0184402	−	0.00589308i
$807$	14.4142	+	3.86227i	0.507403	+	0.135958i
$808$	9.01900	−	22.5129i	0.317287	−	0.792000i
$809$	−16.3576	−	9.44409i	−0.575104	−	0.332036i	0.184081	−	0.982911i	$-0.441069\pi$
$809$	−16.3576	−	9.44409i	−0.575104	−	0.332036i	−0.759185	+	0.650875i	$0.774402\pi$
$810$	−20.8170	−	18.0146i	−0.731436	−	0.632968i
$811$		−	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
$814$	−10.3776	+	11.4139i	−0.363733	+	0.400057i
$815$	5.79501	+	3.15887i	0.202990	+	0.110650i
$816$	36.9032	−	31.9563i	1.29187	−	1.11869i
$817$	1.51477	−	5.65322i	0.0529953	−	0.197781i
$818$	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	0.957825	+	0.287351i	$0.0927747\pi$
$821$	20.8528	+	36.1180i	0.727766	+	1.26053i	−0.230059	+	0.973177i	$0.573892\pi$
$822$	58.3314	−	37.4808i	2.03454	−	1.30729i
$823$	39.0933	−	10.4750i	1.36271	−	0.365136i	0.497897	−	0.867236i	$-0.334106\pi$
$823$	39.0933	−	10.4750i	1.36271	−	0.365136i	0.864809	+	0.502100i	$0.167439\pi$
$824$	1.09890	−	9.17235i	0.0382820	−	0.319534i
$825$	−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	$0.976686\pi$
$828$	2.44603	+	6.56123i	0.0850053	+	0.228018i
$829$	−36.1486	−	20.8704i	−1.25549	−	0.724859i	−0.283298	−	0.959032i	$-0.591429\pi$
$829$	−36.1486	−	20.8704i	−1.25549	−	0.724859i	−0.972195	+	0.234172i	$0.924762\pi$
$830$	−20.8281	+	14.1164i	−0.722952	+	0.489988i
$831$	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
$835$	−10.1027	−	16.5476i	−0.349619	−	0.572652i
$836$	−2.36161	−	24.7734i	−0.0816780	−	0.856805i
$837$	−1.05177	+	0.281822i	−0.0363546	+	0.00974118i
$838$	−25.1239	+	1.19480i	−0.867889	+	0.0412738i
$839$	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
$842$	−56.0078	+	2.66353i	−1.93015	+	0.0917914i
$843$	46.0274	−	12.3330i	1.58527	−	0.424772i
$844$	2.08387	+	21.8599i	0.0717298	+	0.752448i
$845$	28.2392	+	6.82910i	0.971457	+	0.234928i
$846$	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
$850$	−34.4782	−	5.74928i	−1.18259	−	0.197199i
$851$	−2.25941	−	1.30447i	−0.0774517	−	0.0447168i
$852$	−24.9450	−	66.9124i	−0.854601	−	2.29238i
$853$	−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
$856$	−19.0750	−	2.28529i	−0.651969	−	0.0781095i
$857$	−37.0531	+	9.92835i	−1.26571	+	0.339146i	−0.828386	−	0.560158i	$-0.810740\pi$
$857$	−37.0531	+	9.92835i	−1.26571	+	0.339146i	−0.437324	+	0.899304i	$0.644074\pi$
$858$	1.16436	−	0.748161i	0.0397507	−	0.0255418i
$859$	−3.51740	−	6.09232i	−0.120012	−	0.207867i	0.799760	−	0.600320i	$-0.204960\pi$
$859$	−3.51740	−	6.09232i	−0.120012	−	0.207867i	−0.919772	+	0.392453i	$0.871627\pi$
$860$	−7.96093	+	5.96651i	−0.271465	+	0.203456i
$861$		0			0
$862$	−31.6317	−	16.3104i	−1.07738	−	0.555536i
$863$	−11.5958	+	43.2762i	−0.394726	+	1.47314i	0.427520	+	0.904006i	$0.359387\pi$
$863$	−11.5958	+	43.2762i	−0.394726	+	1.47314i	−0.822246	+	0.569132i	$0.807279\pi$
$864$	0.691849	−	1.13404i	0.0235372	−	0.0385808i
$865$	−1.92156	+	3.52514i	−0.0653349	+	0.119858i
$866$	12.3677	−	13.6027i	0.420271	−	0.462240i
$867$	−12.9813	+	12.9813i	−0.440868	+	0.440868i
$868$		0			0
$869$		−	28.8694i		−	0.979328i
$870$	−56.6364	+	4.08743i	−1.92016	+	0.138577i
$871$	0.0369636	+	0.0213410i	0.00125246	+	0.000723111i
$872$	10.2904	+	4.12251i	0.348478	+	0.139606i
$873$	−24.5861	−	6.58783i	−0.832114	−	0.222964i
$874$	4.00901	−	1.28119i	0.135607	−	0.0433369i
$875$		0			0
$876$	−27.4663	−	38.5839i	−0.928000	−	1.30363i
$877$	1.48622	−	5.54663i	0.0501860	−	0.187297i	−0.936282	−	0.351248i	$-0.885757\pi$
$877$	1.48622	−	5.54663i	0.0501860	−	0.187297i	0.986468	+	0.163951i	$0.0524241\pi$
$878$	22.7813	+	35.4546i	0.768832	+	1.19653i
$879$	2.25970	−	3.91392i	0.0762179	−	0.132013i
$880$	−22.8558	+	35.5961i	−0.770467	+	1.19994i
$881$	−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	$0.830075\pi$
$884$	0.344346	−	0.753697i	0.0115816	−	0.0253496i
$885$	16.2618	+	8.86435i	0.546635	+	0.297972i
$886$	12.2792	−	56.4252i	0.412529	−	1.89564i
$887$	30.8995	+	8.27950i	1.03750	+	0.277998i	0.737079	−	0.675807i	$-0.236205\pi$
$887$	30.8995	+	8.27950i	1.03750	+	0.277998i	0.300426	+	0.953805i	$0.402871\pi$
$888$	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
$892$	−29.8745	−	24.6744i	−1.00027	−	0.826160i
$893$	−1.88550	−	7.03680i	−0.0630960	−	0.235477i
$894$	−14.5653	+	16.0198i	−0.487137	+	0.535784i
$895$	−34.8868	−	33.2163i	−1.16614	−	1.11030i
$896$		0			0
$897$	0.165512	+	0.165512i	0.00552627	+	0.00552627i
$898$	1.39096	+	29.2485i	0.0464169	+	0.976036i
$899$	16.8624	−	29.2066i	0.562394	−	0.974095i
$900$	−30.6305	+	4.44432i	−1.02102	+	0.148144i
$901$	−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
$905$	8.52110	−	35.2358i	0.283251	−	1.17128i
$906$	34.3632	+	7.47811i	1.14164	+	0.248444i
$907$	3.58771	+	13.3895i	0.119128	+	0.444592i	0.999563	−	0.0295760i	$-0.00941571\pi$
$907$	3.58771	+	13.3895i	0.119128	+	0.444592i	−0.880435	+	0.474168i	$0.842749\pi$
$908$	−16.0368	−	43.0170i	−0.532198	−	1.42757i
$909$			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	$-0.291373\pi$
$912$	−21.5114	−	14.5693i	−0.712315	−	0.482437i
$913$	−9.73964	−	36.3488i	−0.322335	−	1.20297i
$914$	−1.12668	+	5.17727i	−0.0372671	+	0.171249i
$915$	−9.22344	+	5.63114i	−0.304917	+	0.186160i
$916$	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	0.801173	−	0.598432i	$-0.204209\pi$
$919$	−3.56719	−	6.17855i	−0.117671	−	0.203812i	−0.918844	+	0.394620i	$0.870876\pi$
$920$	−6.70441	−	2.49690i	−0.221038	−	0.0823204i
$921$	6.74155	−	11.6767i	0.222142	−	0.384761i
$922$	−9.41965	+	0.447966i	−0.310220	+	0.0147530i
$923$	−0.857128	−	0.857128i	−0.0282127	−	0.0282127i
$924$		0			0
$925$	7.74467	−	8.54424i	0.254643	−	0.280933i
$926$	21.8839	+	19.8969i	0.719148	+	0.653853i
$927$	2.61640	+	9.76453i	0.0859338	+	0.320709i
$928$	9.68426	+	39.9882i	0.317902	+	1.31268i
$929$	22.9712	−	13.2625i	0.753662	−	0.435127i	−0.0733534	−	0.997306i	$-0.523370\pi$
$929$	22.9712	−	13.2625i	0.753662	−	0.435127i	0.827016	+	0.562179i	$0.190037\pi$
$930$	15.7964	−	32.5717i	0.517984	−	1.06807i
$931$		0			0
$932$	46.9223	+	7.89802i	1.53699	+	0.258708i
$933$	−48.9615	−	13.1192i	−1.60293	−	0.429503i
$934$	38.8099	+	8.44580i	1.26990	+	0.276355i
$935$	25.0209	−	45.9013i	0.818270	−	1.50113i
$936$	0.0872814	−	0.728525i	0.00285288	−	0.0238126i
$937$	−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
$940$	−4.86833	+	11.3864i	−0.158787	+	0.371384i
$941$	12.9331	−	22.4008i	0.421607	−	0.730245i	−0.574490	−	0.818512i	$-0.694800\pi$
$941$	12.9331	−	22.4008i	0.421607	−	0.730245i	0.996097	+	0.0882670i	$0.0281329\pi$
$942$	42.7960	−	27.4985i	1.39437	−	0.895951i
$943$	−1.67398	+	6.24739i	−0.0545124	+	0.203443i
$944$	4.39320	−	12.6803i	0.142987	−	0.412710i
$945$		0			0
$946$	−4.52941	−	14.1731i	−0.147264	−	0.460807i
$947$	28.6706	+	7.68227i	0.931670	+	0.249640i	0.692567	−	0.721354i	$-0.256480\pi$
$947$	28.6706	+	7.68227i	0.931670	+	0.249640i	0.239103	+	0.970994i	$0.423147\pi$
$948$	−23.2384	−	19.1935i	−0.754750	−	0.623375i
$949$	−0.696229	−	0.401968i	−0.0226006	−	0.0130484i
$950$	1.79369	+	18.5165i	0.0581951	+	0.600755i
$951$		−	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	$0.966027\pi$
$954$	−30.5873	−	27.8102i	−0.990301	−	0.900387i
$955$	10.3791	+	35.2535i	0.335859	+	1.14078i
$956$	3.00137	−	0.286116i	0.0970712	−	0.00925366i
$957$	21.9805	−	82.0323i	0.710528	−	2.65173i
$958$	−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
$962$	0.147780	+	0.229991i	0.00476463	+	0.00741520i
$963$	20.3065	−	5.44110i	0.654367	−	0.175337i
$964$	−15.4016	+	33.7106i	−0.496051	+	1.08574i
$965$	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	$0.0461589\pi$
$968$	−19.8706	−	25.2799i	−0.638666	−	0.812527i
$969$	27.8061	+	16.0539i	0.893260	+	0.515724i
$970$	21.5272	−	14.5903i	0.691197	−	0.468466i
$971$	−40.7412	+	23.5219i	−1.30745	+	0.754855i	−0.981670	−	0.190591i	$-0.938960\pi$
$971$	−40.7412	+	23.5219i	−1.30745	+	0.754855i	−0.325778	+	0.945446i	$0.605626\pi$
$972$	7.36883	−	43.7784i	0.236355	−	1.40419i
$973$		0			0
$974$	16.3851	+	51.2711i	0.525013	+	1.64283i
$975$	−0.869561	+	0.560614i	−0.0278482	+	0.0179540i
$976$	5.12579	+	5.91927i	0.164073	+	0.189471i
$977$	21.3849	−	5.73007i	0.684163	−	0.183321i	0.100037	−	0.994984i	$-0.468104\pi$
$977$	21.3849	−	5.73007i	0.684163	−	0.183321i	0.584126	+	0.811663i	$0.301437\pi$
$978$	0.489539	+	10.2938i	0.0156537	+	0.329161i
$979$	78.9044			2.52180
$980$		0			0
$981$	−12.1307			−0.387305
$982$	0.241690	+	5.08217i	0.00771264	+	0.162178i
$983$	17.0668	−	4.57305i	0.544348	−	0.145858i	0.0238421	−	0.999716i	$-0.492410\pi$
$983$	17.0668	−	4.57305i	0.544348	−	0.145858i	0.520506	+	0.853858i	$0.325743\pi$
$984$	36.7061	−	15.7081i	1.17015	−	0.500757i
$985$	−10.5241	+	6.42521i	−0.335325	+	0.204724i
$986$	−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
$990$	8.73128	−	45.4599i	0.277498	−	1.44481i
$991$	−3.59673	−	2.07657i	−0.114254	−	0.0659645i	0.441784	−	0.897121i	$-0.354346\pi$
$991$	−3.59673	−	2.07657i	−0.114254	−	0.0659645i	−0.556038	+	0.831157i	$0.687679\pi$
$992$	−25.1642	−	7.39971i	−0.798965	−	0.234941i
$993$	12.9278	−	12.9278i	0.410250	−	0.410250i
$994$		0			0
$995$	30.6005	+	29.1352i	0.970100	+	0.923649i
$996$	−35.7343	−	16.3261i	−1.13228	−	0.517314i
$997$	−23.3879	+	6.26677i	−0.740702	+	0.198471i	−0.609390	−	0.792870i	$-0.708586\pi$
$997$	−23.3879	+	6.26677i	−0.740702	+	0.198471i	−0.131312	+	0.991341i	$0.541919\pi$
$998$	7.82248	+	12.1741i	0.247616	+	0.385366i
$999$	−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.67.1		72
4.3	odd	2	inner	980.2.x.m.67.15		72
5.3	odd	4	inner	980.2.x.m.263.9		72
7.2	even	3	inner	980.2.x.m.667.12		72
7.3	odd	6		980.2.k.k.687.14		36
7.4	even	3		980.2.k.j.687.14		36
7.5	odd	6		140.2.w.b.107.12	yes	72
7.6	odd	2		140.2.w.b.67.1	yes	72
20.3	even	4	inner	980.2.x.m.263.12		72
28.3	even	6		980.2.k.k.687.4		36
28.11	odd	6		980.2.k.j.687.4		36
28.19	even	6		140.2.w.b.107.9	yes	72
28.23	odd	6	inner	980.2.x.m.667.9		72
28.27	even	2		140.2.w.b.67.15	yes	72
35.3	even	12		980.2.k.k.883.4		36
35.12	even	12		700.2.be.e.443.4		72
35.13	even	4		140.2.w.b.123.9	yes	72
35.18	odd	12		980.2.k.j.883.4		36
35.19	odd	6		700.2.be.e.107.7		72
35.23	odd	12	inner	980.2.x.m.863.15		72
35.27	even	4		700.2.be.e.543.10		72
35.33	even	12		140.2.w.b.23.15	yes	72
35.34	odd	2		700.2.be.e.207.18		72
140.3	odd	12		980.2.k.k.883.14		36
140.19	even	6		700.2.be.e.107.10		72
140.23	even	12	inner	980.2.x.m.863.1		72
140.27	odd	4		700.2.be.e.543.7		72
140.47	odd	12		700.2.be.e.443.18		72
140.83	odd	4		140.2.w.b.123.12	yes	72
140.103	odd	12		140.2.w.b.23.1	✓	72
140.123	even	12		980.2.k.j.883.14		36
140.139	even	2		700.2.be.e.207.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.1	✓	72	140.103	odd	12
140.2.w.b.23.15	yes	72	35.33	even	12
140.2.w.b.67.1	yes	72	7.6	odd	2
140.2.w.b.67.15	yes	72	28.27	even	2
140.2.w.b.107.9	yes	72	28.19	even	6
140.2.w.b.107.12	yes	72	7.5	odd	6
140.2.w.b.123.9	yes	72	35.13	even	4
140.2.w.b.123.12	yes	72	140.83	odd	4
700.2.be.e.107.7		72	35.19	odd	6
700.2.be.e.107.10		72	140.19	even	6
700.2.be.e.207.4		72	140.139	even	2
700.2.be.e.207.18		72	35.34	odd	2
700.2.be.e.443.4		72	35.12	even	12
700.2.be.e.443.18		72	140.47	odd	12
700.2.be.e.543.7		72	140.27	odd	4
700.2.be.e.543.10		72	35.27	even	4
980.2.k.j.687.4		36	28.11	odd	6
980.2.k.j.687.14		36	7.4	even	3
980.2.k.j.883.4		36	35.18	odd	12
980.2.k.j.883.14		36	140.123	even	12
980.2.k.k.687.4		36	28.3	even	6
980.2.k.k.687.14		36	7.3	odd	6
980.2.k.k.883.4		36	35.3	even	12
980.2.k.k.883.14		36	140.3	odd	12
980.2.x.m.67.1		72	1.1	even	1	trivial
980.2.x.m.67.15		72	4.3	odd	2	inner
980.2.x.m.263.9		72	5.3	odd	4	inner
980.2.x.m.263.12		72	20.3	even	4	inner
980.2.x.m.667.9		72	28.23	odd	6	inner
980.2.x.m.667.12		72	7.2	even	3	inner
980.2.x.m.863.1		72	140.23	even	12	inner
980.2.x.m.863.15		72	35.23	odd	12	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+(-1.41262 + 0.0671791i) q^{2} +(-2.38471 + 0.638980i) q^{3} +(1.99097 - 0.189797i) q^{4} +(0.525600 - 2.17342i) q^{5} +(3.32575 - 1.06284i) q^{6} +(-2.79973 + 0.401862i) q^{8} +(2.68045 - 1.54756i) q^{9} +(-0.596463 + 3.10552i) q^{10} +(-4.09588 - 2.36476i) q^{11} +(-4.62661 + 1.72480i) q^{12} +(-0.0592655 + 0.0592655i) q^{13} +(0.135370 + 5.51881i) q^{15} +(3.92795 - 0.755761i) q^{16} +(-4.77484 + 1.27942i) q^{17} +(-3.68249 + 2.36618i) q^{18} +(1.31544 + 2.27842i) q^{19} +(0.633947 - 4.42698i) q^{20} +(5.94478 + 3.06534i) q^{22} +(-0.292774 + 1.09265i) q^{23} +(6.41976 - 2.74730i) q^{24} +(-4.44749 - 2.28469i) q^{25} +(0.0797380 - 0.0877008i) q^{26} +(-0.166053 + 0.166053i) q^{27} -7.27332i q^{29} +(-0.561975 - 7.78687i) q^{30} +(4.01558 + 2.31840i) q^{31} +(-5.49792 + 1.33148i) q^{32} +(11.2785 + 3.02207i) q^{33} +(6.65908 - 2.12809i) q^{34} +(5.04299 - 3.58989i) q^{36} +(-0.596933 + 2.22779i) q^{37} +(-2.01128 - 3.13016i) q^{38} +(0.103461 - 0.179200i) q^{39} +(-0.598125 + 6.29621i) q^{40} +5.71767 q^{41} +(-1.57302 - 1.57302i) q^{43} +(-8.60362 - 3.93079i) q^{44} +(-1.95465 - 6.63914i) q^{45} +(0.340174 - 1.56316i) q^{46} +(-2.67468 - 0.716679i) q^{47} +(-8.88410 + 4.31215i) q^{48} +(6.43608 + 2.92862i) q^{50} +(10.5691 - 6.10206i) q^{51} +(-0.106748 + 0.129244i) q^{52} +(2.44441 + 9.12265i) q^{53} +(0.223414 - 0.245724i) q^{54} +(-7.29241 + 7.65915i) q^{55} +(-4.59281 - 4.59281i) q^{57} +(0.488615 + 10.2744i) q^{58} +(1.67748 - 2.90547i) q^{59} +(1.31697 + 10.9621i) q^{60} +(0.978771 + 1.69528i) q^{61} +(-5.82822 - 3.00524i) q^{62} +(7.67701 - 2.25021i) q^{64} +(0.0976587 + 0.159959i) q^{65} +(-16.1352 - 3.51135i) q^{66} +(-0.131802 - 0.491893i) q^{67} +(-9.26376 + 3.45353i) q^{68} -2.79272i q^{69} +14.4625i q^{71} +(-6.88265 + 5.40993i) q^{72} +(2.48257 + 9.26507i) q^{73} +(0.693578 - 3.18711i) q^{74} +(12.0658 + 2.60647i) q^{75} +(3.05145 + 4.28660i) q^{76} +(-0.134113 + 0.260092i) q^{78} +(3.05204 + 5.28630i) q^{79} +(0.421947 - 8.93431i) q^{80} +(-4.35280 + 7.53927i) q^{81} +(-8.07688 + 0.384108i) q^{82} +(5.62620 + 5.62620i) q^{83} +(0.271049 + 11.0502i) q^{85} +(2.32775 + 2.11640i) q^{86} +(4.64751 + 17.3447i) q^{87} +(12.4177 + 4.97472i) q^{88} +(-14.4482 + 8.34169i) q^{89} +(3.20718 + 9.24725i) q^{90} +(-0.375524 + 2.23100i) q^{92} +(-11.0574 - 2.96282i) q^{93} +(3.82645 + 0.832711i) q^{94} +(5.64335 - 1.66148i) q^{95} +(12.2601 - 6.68825i) 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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