LMFDB - Embedded newform 294.2.j.a.251.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,2,Mod(41,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.41"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.9
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.781831 - 0.623490i) q^{2} +(1.38755 + 1.03668i) q^{3} +(0.222521 + 0.974928i) q^{4} +(1.24567 + 0.599884i) q^{5} +(-0.438472 - 1.67563i) q^{6} +(2.35011 - 1.21532i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.850594 + 2.87689i) q^{9} +(-0.599884 - 1.24567i) q^{10} +(-4.74543 - 3.78435i) q^{11} +(-0.701928 + 1.58344i) q^{12} +(3.67688 + 2.93221i) q^{13} +(-2.59513 - 0.515095i) q^{14} +(1.10655 + 2.12373i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.02928 + 4.50956i) q^{17} +(1.12869 - 2.77958i) q^{18} -0.830794i q^{19} +(-0.307656 + 1.34793i) q^{20} +(4.52079 + 0.749993i) q^{21} +(1.35062 + 5.91746i) q^{22} +(6.70486 - 1.53034i) q^{23} +(1.53605 - 0.800342i) q^{24} +(-1.92561 - 2.41464i) q^{25} +(-1.04649 - 4.58499i) q^{26} +(-1.80217 + 4.87362i) q^{27} +(1.70779 + 2.02075i) q^{28} +(-5.02565 - 1.14707i) q^{29} +(0.458992 - 2.35032i) q^{30} +3.29815i q^{31} +(0.974928 + 0.222521i) q^{32} +(-2.66137 - 10.1705i) q^{33} +(3.61639 - 2.88397i) q^{34} +(3.65651 - 0.104094i) q^{35} +(-2.61548 + 1.46944i) q^{36} +(0.766842 - 3.35975i) q^{37} +(-0.517992 + 0.649541i) q^{38} +(2.06209 + 7.88033i) q^{39} +(1.08095 - 0.862032i) q^{40} +(-3.21630 - 1.54889i) q^{41} +(-3.06688 - 3.40503i) q^{42} +(2.30191 - 1.10854i) q^{43} +(2.63352 - 5.46855i) q^{44} +(-0.666239 + 4.09392i) q^{45} +(-6.19623 - 2.98395i) q^{46} +(1.68186 - 2.10898i) q^{47} +(-1.69994 - 0.331980i) q^{48} +(4.04601 - 5.71225i) q^{49} +3.08844i q^{50} +(-6.10314 + 5.19022i) q^{51} +(-2.04051 + 4.23717i) q^{52} +(-8.03549 + 1.83405i) q^{53} +(4.44764 - 2.68672i) q^{54} +(-3.64108 - 7.56078i) q^{55} +(-0.0752892 - 2.64468i) q^{56} +(0.861267 - 1.15277i) q^{57} +(3.21403 + 4.03026i) q^{58} +(8.71118 - 4.19508i) q^{59} +(-1.82426 + 1.55138i) q^{60} +(-6.90429 - 1.57586i) q^{61} +(2.05636 - 2.57859i) q^{62} +(5.49532 + 5.72726i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(2.82120 + 5.85828i) q^{65} +(-4.26045 + 9.61093i) q^{66} -9.57648 q^{67} -4.62553 q^{68} +(10.8898 + 4.82736i) q^{69} +(-2.92368 - 2.19841i) q^{70} +(-1.12963 + 0.257831i) q^{71} +(2.96105 + 0.481877i) q^{72} +(-10.6284 + 8.47585i) q^{73} +(-2.69431 + 2.14864i) q^{74} +(-0.168677 - 5.34667i) q^{75} +(0.809965 - 0.184869i) q^{76} +(-15.7515 - 3.12644i) q^{77} +(3.30110 - 7.44678i) q^{78} -15.0627 q^{79} -1.38259 q^{80} +(-7.55298 + 4.89413i) q^{81} +(1.54889 + 3.21630i) q^{82} +(-2.44958 - 3.07168i) q^{83} +(0.274781 + 4.57433i) q^{84} +(-3.98736 + 4.99999i) q^{85} +(-2.49087 - 0.568525i) q^{86} +(-5.78420 - 6.80161i) q^{87} +(-5.46855 + 2.63352i) q^{88} +(5.74690 + 7.20638i) q^{89} +(3.07340 - 2.78536i) q^{90} +(12.2046 + 2.42244i) q^{91} +(2.98395 + 6.19623i) q^{92} +(-3.41912 + 4.57635i) q^{93} +(-2.62986 + 0.600248i) q^{94} +(0.498380 - 1.03490i) q^{95} +(1.12208 + 1.31945i) q^{96} -14.5502i q^{97} +(-6.72483 + 1.94337i) q^{98} +(6.85073 - 16.8710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$3$	1.38755	+	1.03668i	0.801103	+	0.598527i
$3$	1.38755	+	1.03668i	0.801103	+	0.598527i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	1.24567	+	0.599884i	0.557082	+	0.268276i	0.691169	−	0.722693i	$-0.257096\pi$
$5$	1.24567	+	0.599884i	0.557082	+	0.268276i	−0.134087	+	0.990970i	$0.542810\pi$
$6$	−0.438472	−	1.67563i	−0.179006	−	0.684074i
$7$	2.35011	−	1.21532i	0.888257	−	0.459347i
$7$	2.35011	−	1.21532i	0.888257	−	0.459347i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$	0.850594	+	2.87689i	0.283531	+	0.958963i
$10$	−0.599884	−	1.24567i	−0.189700	−	0.393916i
$11$	−4.74543	−	3.78435i	−1.43080	−	1.14103i	−0.966905	−	0.255136i	$-0.917880\pi$
$11$	−4.74543	−	3.78435i	−1.43080	−	1.14103i	−0.463896	−	0.885890i	$-0.653549\pi$
$12$	−0.701928	+	1.58344i	−0.202629	+	0.457101i
$13$	3.67688	+	2.93221i	1.01978	+	0.813249i	0.982539	−	0.186057i	$-0.0595709\pi$
$13$	3.67688	+	2.93221i	1.01978	+	0.813249i	0.0372432	+	0.999306i	$0.488142\pi$
$14$	−2.59513	−	0.515095i	−0.693576	−	0.137665i
$15$	1.10655	+	2.12373i	0.285709	+	0.548345i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−1.02928	+	4.50956i	−0.249637	+	1.09373i	0.682290	+	0.731082i	$0.260984\pi$
$17$	−1.02928	+	4.50956i	−0.249637	+	1.09373i	−0.931926	+	0.362648i	$0.881873\pi$
$18$	1.12869	−	2.77958i	0.266035	−	0.655153i
$19$		−	0.830794i		−	0.190597i	−0.995449	−	0.0952986i	$-0.969619\pi$
$19$		−	0.830794i		−	0.190597i	0.995449	−	0.0952986i	$-0.0303806\pi$
$20$	−0.307656	+	1.34793i	−0.0687939	+	0.301406i
$21$	4.52079	+	0.749993i	0.986516	+	0.163662i
$22$	1.35062	+	5.91746i	0.287953	+	1.26161i
$23$	6.70486	−	1.53034i	1.39806	−	0.319098i	0.543919	−	0.839138i	$-0.316940\pi$
$23$	6.70486	−	1.53034i	1.39806	−	0.319098i	0.854142	+	0.520040i	$0.174083\pi$
$24$	1.53605	−	0.800342i	0.313545	−	0.163369i
$25$	−1.92561	−	2.41464i	−0.385122	−	0.482928i
$26$	−1.04649	−	4.58499i	−0.205234	−	0.899191i
$27$	−1.80217	+	4.87362i	−0.346827	+	0.937929i
$28$	1.70779	+	2.02075i	0.322743	+	0.381886i
$29$	−5.02565	−	1.14707i	−0.933240	−	0.213006i	−0.271242	−	0.962511i	$-0.587434\pi$
$29$	−5.02565	−	1.14707i	−0.933240	−	0.213006i	−0.661998	+	0.749505i	$0.730291\pi$
$30$	0.458992	−	2.35032i	0.0838002	−	0.429108i
$31$			3.29815i			0.592365i	0.955131	+	0.296182i	$0.0957136\pi$
$31$			3.29815i			0.592365i	−0.955131	+	0.296182i	$0.904286\pi$
$32$	0.974928	+	0.222521i	0.172345	+	0.0393365i
$33$	−2.66137	−	10.1705i	−0.463284	−	1.77045i
$34$	3.61639	−	2.88397i	0.620205	−	0.494597i
$35$	3.65651	−	0.104094i	0.618064	−	0.0175951i
$36$	−2.61548	+	1.46944i	−0.435914	+	0.244906i
$37$	0.766842	−	3.35975i	0.126068	−	0.552340i	−0.871960	−	0.489576i	$-0.837151\pi$
$37$	0.766842	−	3.35975i	0.126068	−	0.552340i	0.998028	−	0.0627637i	$-0.0199914\pi$
$38$	−0.517992	+	0.649541i	−0.0840294	+	0.105369i
$39$	2.06209	+	7.88033i	0.330199	+	1.26186i
$40$	1.08095	−	0.862032i	0.170914	−	0.136299i
$41$	−3.21630	−	1.54889i	−0.502302	−	0.241896i	0.165535	−	0.986204i	$-0.447065\pi$
$41$	−3.21630	−	1.54889i	−0.502302	−	0.241896i	−0.667836	+	0.744308i	$0.732779\pi$
$42$	−3.06688	−	3.40503i	−0.473230	−	0.525408i
$43$	2.30191	−	1.10854i	0.351038	−	0.169051i	−0.250052	−	0.968232i	$-0.580448\pi$
$43$	2.30191	−	1.10854i	0.351038	−	0.169051i	0.601090	+	0.799182i	$0.294733\pi$
$44$	2.63352	−	5.46855i	0.397017	−	0.824415i
$45$	−0.666239	+	4.09392i	−0.0993170	+	0.610285i
$46$	−6.19623	−	2.98395i	−0.913584	−	0.439959i
$47$	1.68186	−	2.10898i	0.245324	−	0.307627i	−0.643890	−	0.765118i	$-0.722681\pi$
$47$	1.68186	−	2.10898i	0.245324	−	0.307627i	0.889214	+	0.457491i	$0.151252\pi$
$48$	−1.69994	−	0.331980i	−0.245365	−	0.0479171i
$49$	4.04601	−	5.71225i	0.578001	−	0.816036i
$50$			3.08844i			0.436771i
$51$	−6.10314	+	5.19022i	−0.854611	+	0.726776i
$52$	−2.04051	+	4.23717i	−0.282968	+	0.587590i
$53$	−8.03549	+	1.83405i	−1.10376	+	0.251926i	−0.735316	−	0.677724i	$-0.762966\pi$
$53$	−8.03549	+	1.83405i	−1.10376	+	0.251926i	−0.368443	+	0.929650i	$0.620109\pi$
$54$	4.44764	−	2.68672i	0.605248	−	0.365616i
$55$	−3.64108	−	7.56078i	−0.490963	−	1.01949i
$56$	−0.0752892	−	2.64468i	−0.0100609	−	0.353410i
$57$	0.861267	−	1.15277i	0.114078	−	0.152688i
$58$	3.21403	+	4.03026i	0.422022	+	0.529199i
$59$	8.71118	−	4.19508i	1.13410	−	0.546153i	0.229879	−	0.973219i	$-0.426167\pi$
$59$	8.71118	−	4.19508i	1.13410	−	0.546153i	0.904220	+	0.427066i	$0.140453\pi$
$60$	−1.82426	+	1.55138i	−0.235510	+	0.200282i
$61$	−6.90429	−	1.57586i	−0.884004	−	0.201768i	−0.243664	−	0.969860i	$-0.578349\pi$
$61$	−6.90429	−	1.57586i	−0.884004	−	0.201768i	−0.640340	+	0.768092i	$0.721207\pi$
$62$	2.05636	−	2.57859i	0.261158	−	0.327482i
$63$	5.49532	+	5.72726i	0.692345	+	0.721567i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	2.82120	+	5.85828i	0.349926	+	0.726630i
$66$	−4.26045	+	9.61093i	−0.524425	+	1.18302i
$67$	−9.57648			−1.16995			−0.584976	−	0.811050i	$-0.698896\pi$
$67$	−9.57648			−1.16995			−0.584976	+	0.811050i	$0.698896\pi$
$68$	−4.62553			−0.560928
$69$	10.8898	+	4.82736i	1.31098	+	0.581146i
$70$	−2.92368	−	2.19841i	−0.349446	−	0.262761i
$71$	−1.12963	+	0.257831i	−0.134063	+	0.0305989i	−0.289026	−	0.957321i	$-0.593331\pi$
$71$	−1.12963	+	0.257831i	−0.134063	+	0.0305989i	0.154963	+	0.987920i	$0.450474\pi$
$72$	2.96105	+	0.481877i	0.348963	+	0.0567897i
$73$	−10.6284	+	8.47585i	−1.24396	+	0.992023i	−0.244206	+	0.969723i	$0.578527\pi$
$73$	−10.6284	+	8.47585i	−1.24396	+	0.992023i	−0.999751	+	0.0222993i	$0.992901\pi$
$74$	−2.69431	+	2.14864i	−0.313208	+	0.249775i
$75$	−0.168677	−	5.34667i	−0.0194771	−	0.617381i
$76$	0.809965	−	0.184869i	0.0929093	−	0.0212059i
$77$	−15.7515	−	3.12644i	−1.79505	−	0.356291i
$78$	3.30110	−	7.44678i	0.373776	−	0.843182i
$79$	−15.0627			−1.69468			−0.847341	−	0.531049i	$-0.821798\pi$
$79$	−15.0627			−1.69468			−0.847341	+	0.531049i	$0.821798\pi$
$80$	−1.38259			−0.154578
$81$	−7.55298	+	4.89413i	−0.839220	+	0.543792i
$82$	1.54889	+	3.21630i	0.171046	+	0.355181i
$83$	−2.44958	−	3.07168i	−0.268877	−	0.337161i	0.629002	−	0.777404i	$-0.283464\pi$
$83$	−2.44958	−	3.07168i	−0.268877	−	0.337161i	−0.897879	+	0.440243i	$0.854892\pi$
$84$	0.274781	+	4.57433i	0.0299810	+	0.499100i
$85$	−3.98736	+	4.99999i	−0.432490	+	0.542325i
$86$	−2.49087	−	0.568525i	−0.268597	−	0.0613056i
$87$	−5.78420	−	6.80161i	−0.620132	−	0.729209i
$88$	−5.46855	+	2.63352i	−0.582949	+	0.280734i
$89$	5.74690	+	7.20638i	0.609170	+	0.763875i	0.986776	−	0.162091i	$-0.0518240\pi$
$89$	5.74690	+	7.20638i	0.609170	+	0.763875i	−0.377606	+	0.925966i	$0.623253\pi$
$90$	3.07340	−	2.78536i	0.323965	−	0.293603i
$91$	12.2046	+	2.42244i	1.27939	+	0.253941i
$92$	2.98395	+	6.19623i	0.311098	+	0.646001i
$93$	−3.41912	+	4.57635i	−0.354546	+	0.474545i
$94$	−2.62986	+	0.600248i	−0.271249	+	0.0619109i
$95$	0.498380	−	1.03490i	0.0511328	−	0.106178i
$96$	1.12208	+	1.31945i	0.114522	+	0.134665i
$97$		−	14.5502i		−	1.47735i	−0.674064	−	0.738673i	$-0.735453\pi$
$97$		−	14.5502i		−	1.47735i	0.674064	−	0.738673i	$-0.264547\pi$
$98$	−6.72483	+	1.94337i	−0.679310	+	0.196310i
$99$	6.85073	−	16.8710i	0.688525	−	1.69560i
$100$	1.92561	−	2.41464i	0.192561	−	0.241464i
$101$	−9.32141	−	4.48895i	−0.927515	−	0.446667i	−0.0917665	−	0.995781i	$-0.529251\pi$
$101$	−9.32141	−	4.48895i	−0.927515	−	0.446667i	−0.835748	+	0.549113i	$0.814966\pi$
$102$	8.00768	−	0.252626i	0.792878	−	0.0250137i
$103$	5.22239	−	10.8444i	0.514577	−	1.06853i	−0.468181	−	0.883633i	$-0.655090\pi$
$103$	5.22239	−	10.8444i	0.514577	−	1.06853i	0.982758	−	0.184898i	$-0.0591953\pi$
$104$	4.23717	−	2.04051i	0.415489	−	0.200089i
$105$	5.18151	+	3.64619i	0.505664	+	0.355832i
$106$	7.42591	+	3.57613i	0.721268	+	0.347344i
$107$	1.62625	−	1.29689i	0.157216	−	0.125376i	−0.541722	−	0.840557i	$-0.682228\pi$
$107$	1.62625	−	1.29689i	0.157216	−	0.125376i	0.698938	+	0.715182i	$0.253656\pi$
$108$	−5.15245	−	0.672501i	−0.495795	−	0.0647114i
$109$	10.0298	−	12.5770i	0.960682	−	1.20466i	−0.0181179	−	0.999836i	$-0.505767\pi$
$109$	10.0298	−	12.5770i	0.960682	−	1.20466i	0.978799	−	0.204821i	$-0.0656611\pi$
$110$	−1.86736	+	8.18143i	−0.178046	+	0.780068i
$111$	4.54702	−	3.86686i	0.431584	−	0.367026i
$112$	−1.59007	+	2.11464i	−0.150247	+	0.199814i
$113$	3.80437	−	3.03389i	0.357885	−	0.285404i	−0.427997	−	0.903780i	$-0.640781\pi$
$113$	3.80437	−	3.03389i	0.357885	−	0.285404i	0.785882	+	0.618376i	$0.212209\pi$
$114$	−1.39211	+	0.364280i	−0.130383	+	0.0341180i
$115$	9.27009	+	2.11584i	0.864441	+	0.197303i
$116$		−	5.15490i		−	0.478620i
$117$	−5.30812	+	13.0721i	−0.490736	+	1.20851i
$118$	−9.42627	−	2.15148i	−0.867758	−	0.198060i
$119$	3.06163	+	11.8489i	0.280659	+	1.08618i
$120$	2.39353	−	0.0755111i	0.218498	−	0.00689319i
$121$	5.75004	+	25.1926i	0.522731	+	2.29023i
$122$	4.41546	+	5.53681i	0.399757	+	0.501279i
$123$	−2.85708	−	5.48343i	−0.257614	−	0.494424i
$124$	−3.21545	+	0.733907i	−0.288756	+	0.0659068i
$125$	−2.48845	−	10.9026i	−0.222574	−	0.975161i
$126$	−0.725527	−	7.90402i	−0.0646351	−	0.704147i
$127$	−1.33968	+	5.86954i	−0.118878	+	0.520837i	0.880064	+	0.474854i	$0.157499\pi$
$127$	−1.33968	+	5.86954i	−0.118878	+	0.520837i	−0.998942	+	0.0459832i	$0.985358\pi$
$128$			1.00000i			0.0883883i
$129$	4.34322	+	0.848183i	0.382399	+	0.0746784i
$130$	1.44687	−	6.33917i	0.126899	−	0.555982i
$131$	5.66821	−	2.72967i	0.495234	−	0.238492i	−0.169559	−	0.985520i	$-0.554234\pi$
$131$	5.66821	−	2.72967i	0.495234	−	0.238492i	0.664793	+	0.747028i	$0.268520\pi$
$132$	9.32327	−	4.85778i	0.811486	−	0.422816i
$133$	−1.00968	−	1.95246i	−0.0875502	−	0.169299i
$134$	7.48719	+	5.97084i	0.646795	+	0.515802i
$135$	−5.16852	+	4.98984i	−0.444835	+	0.429457i
$136$	3.61639	+	2.88397i	0.310103	+	0.247299i
$137$	9.69084	+	20.1232i	0.827945	+	1.71925i	0.683776	+	0.729692i	$0.260336\pi$
$137$	9.69084	+	20.1232i	0.827945	+	1.71925i	0.144169	+	0.989553i	$0.453949\pi$
$138$	−5.50419	−	10.5639i	−0.468547	−	0.899256i
$139$	−0.346981	+	0.720513i	−0.0294305	+	0.0611131i	−0.915166	−	0.403078i	$-0.867940\pi$
$139$	−0.346981	+	0.720513i	−0.0294305	+	0.0611131i	0.885735	+	0.464191i	$0.153655\pi$
$140$	0.915135	+	3.54167i	0.0773430	+	0.299326i
$141$	4.52000	−	1.18277i	0.380653	−	0.0996076i
$142$	1.04394	+	0.502734i	0.0876053	+	0.0421885i
$143$	−6.35184	−	27.8292i	−0.531167	−	2.32720i
$144$	−2.01459	−	2.22293i	−0.167883	−	0.185244i
$145$	−5.57221	−	4.44369i	−0.462747	−	0.369028i
$146$	13.5942			1.12506
$147$	11.5358	−	3.73162i	0.951458	−	0.307779i
$148$	3.44616			0.283272
$149$	9.36588	+	7.46904i	0.767283	+	0.611888i	0.926907	−	0.375290i	$-0.122457\pi$
$149$	9.36588	+	7.46904i	0.767283	+	0.611888i	−0.159624	+	0.987178i	$0.551028\pi$
$150$	−3.20172	+	4.28537i	−0.261419	+	0.349899i
$151$	−0.0178195	−	0.0780722i	−0.00145013	−	0.00635342i	0.974198	−	0.225696i	$-0.0724658\pi$
$151$	−0.0178195	−	0.0780722i	−0.00145013	−	0.00635342i	−0.975648	+	0.219343i	$0.929609\pi$
$152$	−0.748520	−	0.360468i	−0.0607130	−	0.0292378i
$153$	−13.8490	+	0.874688i	−1.11963	+	0.0707143i
$154$	10.3657	+	12.2652i	0.835291	+	0.988360i
$155$	−1.97851	+	4.10841i	−0.158917	+	0.329995i
$156$	−7.22390	+	3.76393i	−0.578375	+	0.301356i
$157$	−0.754870	−	1.56750i	−0.0602452	−	0.125100i	0.868672	−	0.495387i	$-0.164974\pi$
$157$	−0.754870	−	1.56750i	−0.0602452	−	0.125100i	−0.928918	+	0.370287i	$0.879259\pi$
$158$	11.7765	+	9.39142i	0.936886	+	0.747141i
$159$	−13.0510	−	5.78539i	−1.03501	−	0.458811i
$160$	1.08095	+	0.862032i	0.0854569	+	0.0681496i
$161$	13.8973	−	11.7450i	1.09526	−	0.925636i
$162$	8.95660	+	0.882822i	0.703697	+	0.0693610i
$163$	16.4133	−	7.90424i	1.28559	−	0.619108i	0.338769	−	0.940869i	$-0.389989\pi$
$163$	16.4133	−	7.90424i	1.28559	−	0.619108i	0.946821	+	0.321762i	$0.104275\pi$
$164$	0.794360	−	3.48032i	0.0620291	−	0.271767i
$165$	2.78592	−	14.2656i	0.216883	−	1.11057i
$166$			3.92883i			0.304936i
$167$	−1.87055	+	8.19541i	−0.144748	+	0.634180i	0.849547	+	0.527513i	$0.176875\pi$
$167$	−1.87055	+	8.19541i	−0.144748	+	0.634180i	−0.994295	+	0.106668i	$0.965982\pi$
$168$	2.63722	−	3.74768i	0.203466	−	0.289140i
$169$	2.02879	+	8.88870i	0.156061	+	0.683746i
$170$	6.23489	−	1.42307i	0.478194	−	0.109145i
$171$	2.39010	−	0.706669i	0.182776	−	0.0540403i
$172$	1.59297	+	1.99752i	0.121463	+	0.152310i
$173$	−1.09089	−	4.77951i	−0.0829389	−	0.363379i	0.916379	−	0.400312i	$-0.131098\pi$
$173$	−1.09089	−	4.77951i	−0.0829389	−	0.363379i	−0.999318	+	0.0369330i	$0.988241\pi$
$174$	0.281538	+	8.92410i	0.0213433	+	0.676534i
$175$	−7.45994	−	3.33443i	−0.563919	−	0.252060i
$176$	5.91746	+	1.35062i	0.446045	+	0.101807i
$177$	16.4362	+	3.20981i	1.23542	+	0.241264i
$178$		−	9.21731i		−	0.690866i
$179$	−5.74722	−	1.31176i	−0.429567	−	0.0980459i	0.00227013	−	0.999997i	$-0.499277\pi$
$179$	−5.74722	−	1.31176i	−0.429567	−	0.0980459i	−0.431837	+	0.901952i	$0.642135\pi$
$180$	−4.13953	+	0.261448i	−0.308542	+	0.0194872i
$181$	−6.48699	+	5.17320i	−0.482174	+	0.384521i	−0.834194	−	0.551472i	$-0.814067\pi$
$181$	−6.48699	+	5.17320i	−0.482174	+	0.384521i	0.352019	+	0.935993i	$0.385495\pi$
$182$	−8.03159	−	9.50340i	−0.595341	−	0.704439i
$183$	−7.94639	−	9.34412i	−0.587414	−	0.690737i
$184$	1.53034	−	6.70486i	0.112818	−	0.494289i
$185$	2.97070	−	3.72514i	0.218410	−	0.273877i
$186$	5.52648	−	1.44615i	0.405221	−	0.106037i
$187$	21.9502	−	17.5047i	1.60515	−	1.28007i
$188$	2.43036	+	1.17040i	0.177252	+	0.0853600i
$189$	1.68771	+	13.6437i	0.122763	+	0.992436i
$190$	−1.03490	+	0.498380i	−0.0750794	+	0.0361563i
$191$	−4.47394	+	9.29022i	−0.323723	+	0.672217i	−0.997790	−	0.0664534i	$-0.978832\pi$
$191$	−4.47394	+	9.29022i	−0.323723	+	0.672217i	0.674067	+	0.738670i	$0.264546\pi$
$192$	−0.0546156	−	1.73119i	−0.00394154	−	0.124938i
$193$	−9.21730	−	4.43882i	−0.663476	−	0.319513i	0.0716639	−	0.997429i	$-0.477169\pi$
$193$	−9.21730	−	4.43882i	−0.663476	−	0.319513i	−0.735140	+	0.677916i	$0.762883\pi$
$194$	−9.07188	+	11.3758i	−0.651323	+	0.816733i
$195$	−2.15860	+	11.0533i	−0.154580	+	0.791545i
$196$	6.46935	+	2.67347i	0.462097	+	0.190962i
$197$		−	4.24217i		−	0.302242i	−0.988515	−	0.151121i	$-0.951712\pi$
$197$		−	4.24217i		−	0.302242i	0.988515	−	0.151121i	$-0.0482883\pi$
$198$	−15.8750	+	8.91894i	−1.12819	+	0.633841i
$199$	−8.37738	+	17.3958i	−0.593857	+	1.23316i	0.360016	+	0.932946i	$0.382771\pi$
$199$	−8.37738	+	17.3958i	−0.593857	+	1.23316i	−0.953873	+	0.300211i	$0.902943\pi$
$200$	−3.01101	+	0.687242i	−0.212910	+	0.0485954i
$201$	−13.2878	−	9.92773i	−0.937253	−	0.700248i
$202$	4.48895	+	9.32141i	0.315842	+	0.655852i
$203$	−13.2049	+	3.41202i	−0.926801	+	0.239477i
$204$	−6.41816	−	4.79519i	−0.449361	−	0.335731i
$205$	−3.07730	−	3.85882i	−0.214928	−	0.269511i
$206$	−10.8444	+	5.22239i	−0.755565	+	0.363861i
$207$	10.1057	+	17.9875i	0.702397	+	1.25021i
$208$	−4.58499	−	1.04649i	−0.317912	−	0.0725613i
$209$	−3.14402	+	3.94248i	−0.217476	+	0.272707i
$210$	−1.77770	−	6.08133i	−0.122673	−	0.419652i
$211$	4.39127	+	5.50648i	0.302308	+	0.379082i	0.909662	−	0.415349i	$-0.136341\pi$
$211$	4.39127	+	5.50648i	0.302308	+	0.379082i	−0.607354	+	0.794431i	$0.707769\pi$
$212$	−3.57613	−	7.42591i	−0.245610	−	0.510013i
$213$	−1.83471	−	0.813312i	−0.125712	−	0.0557272i
$214$	−2.08006			−0.142190
$215$	3.53242			0.240909
$216$	3.60905	+	3.73828i	0.245565	+	0.254358i
$217$	4.00829	+	7.75100i	0.272101	+	0.526172i
$218$	−15.6832	+	3.57960i	−1.06220	+	0.242441i
$219$	−23.5341	+	0.742455i	−1.59029	+	0.0501705i
$220$	6.56100	−	5.23222i	0.442342	−	0.352756i
$221$	−17.0075	+	13.5630i	−1.14405	+	0.912349i
$222$	−5.96595	+	0.188214i	−0.400408	+	0.0126321i
$223$	15.5958	−	3.55963i	1.04437	−	0.238371i	0.334275	−	0.942476i	$-0.391509\pi$
$223$	15.5958	−	3.55963i	1.04437	−	0.238371i	0.710096	+	0.704105i	$0.248652\pi$
$224$	2.56162	−	0.661898i	0.171155	−	0.0442249i
$225$	5.30874	−	7.59364i	0.353916	−	0.506243i
$226$	−4.86597			−0.323680
$227$	8.39289			0.557055			0.278528	−	0.960428i	$-0.410154\pi$
$227$	8.39289			0.557055			0.278528	+	0.960428i	$0.410154\pi$
$228$	1.31552	+	0.583158i	0.0871222	+	0.0386206i
$229$	11.4881	+	23.8554i	0.759158	+	1.57641i	0.816019	+	0.578025i	$0.196176\pi$
$229$	11.4881	+	23.8554i	0.759158	+	1.57641i	−0.0568614	+	0.998382i	$0.518109\pi$
$230$	−5.92845	−	7.43404i	−0.390910	−	0.490186i
$231$	−18.6148	−	20.6673i	−1.22477	−	1.35981i
$232$	−3.21403	+	4.03026i	−0.211011	+	0.264600i
$233$	8.71642	+	1.98947i	0.571031	+	0.130334i	0.498280	−	0.867016i	$-0.333965\pi$
$233$	8.71642	+	1.98947i	0.571031	+	0.130334i	0.0727511	+	0.997350i	$0.476822\pi$
$234$	12.3004	−	6.91061i	0.804100	−	0.451761i
$235$	3.36019	−	1.61818i	0.219195	−	0.105559i
$236$	6.02832	+	7.55928i	0.392410	+	0.492067i
$237$	−20.9002	−	15.6152i	−1.35761	−	1.01431i
$238$	4.99396	−	11.1727i	0.323710	−	0.724219i
$239$	4.79479	+	9.95649i	0.310149	+	0.644032i	0.996532	−	0.0832086i	$-0.0265168\pi$
$239$	4.79479	+	9.95649i	0.310149	+	0.644032i	−0.686383	+	0.727241i	$0.740802\pi$
$240$	−1.91842	−	1.43330i	−0.123833	−	0.0925194i
$241$	−7.58309	+	1.73079i	−0.488470	+	0.111490i	−0.459660	−	0.888095i	$-0.652029\pi$
$241$	−7.58309	+	1.73079i	−0.488470	+	0.111490i	−0.0288096	+	0.999585i	$0.509172\pi$
$242$	11.2118	−	23.2814i	0.720719	−	1.49659i
$243$	−15.5538	−	1.03916i	−0.997776	−	0.0666623i
$244$		−	7.08185i		−	0.453369i
$245$	8.46669	−	4.68845i	0.540917	−	0.299534i
$246$	−1.18511	+	6.06848i	−0.0755598	+	0.386912i
$247$	2.43606	−	3.05473i	0.155003	−	0.194368i
$248$	2.97153	+	1.43101i	0.188692	+	0.0908694i
$249$	−0.214575	−	6.80155i	−0.0135982	−	0.431031i
$250$	−4.85213	+	10.0755i	−0.306875	+	0.637233i
$251$	21.6571	−	10.4295i	1.36699	−	0.658306i	0.400803	−	0.916164i	$-0.368731\pi$
$251$	21.6571	−	10.4295i	1.36699	−	0.658306i	0.966183	+	0.257859i	$0.0830169\pi$
$252$	−4.36084	+	6.63197i	−0.274707	+	0.417775i
$253$	−37.6088	−	18.1115i	−2.36445	−	1.13866i
$254$	4.70701	−	3.75371i	0.295344	−	0.235529i
$255$	−10.7160	+	2.80413i	−0.671065	+	0.175601i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−5.32276	+	23.3205i	−0.332025	+	1.45470i	0.483179	+	0.875521i	$0.339482\pi$
$257$	−5.32276	+	23.3205i	−0.332025	+	1.45470i	−0.815204	+	0.579174i	$0.803375\pi$
$258$	−2.86683	−	3.37109i	−0.178481	−	0.209875i
$259$	−2.28100	−	8.82774i	−0.141735	−	0.548529i
$260$	−5.08362	+	4.05405i	−0.315273	+	0.251422i
$261$	−0.974790	−	15.4339i	−0.0603380	−	0.955337i
$262$	−6.13351	−	1.39993i	−0.378929	−	0.0864882i
$263$			3.51437i			0.216705i	0.994113	+	0.108353i	$0.0345575\pi$
$263$			3.51437i			0.216705i	−0.994113	+	0.108353i	$0.965442\pi$
$264$	−10.3180	−	2.01499i	−0.635029	−	0.124014i
$265$	−11.1098	−	2.53574i	−0.682470	−	0.155769i
$266$	−0.427938	+	2.15602i	−0.0262386	+	0.132194i
$267$	0.503409	+	15.9569i	0.0308081	+	0.976547i
$268$	−2.13097	−	9.33637i	−0.130170	−	0.570310i
$269$	3.99917	+	5.01481i	0.243834	+	0.305758i	0.888656	−	0.458575i	$-0.151640\pi$
$269$	3.99917	+	5.01481i	0.243834	+	0.305758i	−0.644822	+	0.764333i	$0.723068\pi$
$270$	7.15203	−	0.678699i	0.435259	−	0.0413043i
$271$	−1.14194	+	0.260641i	−0.0693682	+	0.0158328i	−0.257064	−	0.966394i	$-0.582755\pi$
$271$	−1.14194	+	0.260641i	−0.0693682	+	0.0158328i	0.187696	+	0.982227i	$0.439898\pi$
$272$	−1.02928	−	4.50956i	−0.0624092	−	0.273432i
$273$	14.4232	+	16.0135i	0.872934	+	0.969183i
$274$	4.97003	−	21.7751i	0.300251	−	1.31548i
$275$			18.7457i			1.13041i
$276$	−2.28312	+	11.6910i	−0.137428	+	0.703714i
$277$	−5.53892	+	24.2676i	−0.332801	+	1.45810i	0.480880	+	0.876787i	$0.340317\pi$
$277$	−5.53892	+	24.2676i	−0.332801	+	1.45810i	−0.813681	+	0.581312i	$0.802540\pi$
$278$	0.720513	−	0.346981i	0.0432135	−	0.0208105i
$279$	−9.48840	+	2.80538i	−0.568056	+	0.167954i
$280$	1.49272	−	3.33957i	0.0892069	−	0.199577i
$281$	11.8913	+	9.48300i	0.709376	+	0.565708i	0.910325	−	0.413893i	$-0.135831\pi$
$281$	11.8913	+	9.48300i	0.709376	+	0.565708i	−0.200950	+	0.979602i	$0.564403\pi$
$282$	−4.27133	−	1.89344i	−0.254354	−	0.112753i
$283$	−11.3731	−	9.06971i	−0.676058	−	0.539138i	0.224174	−	0.974549i	$-0.428032\pi$
$283$	−11.3731	−	9.06971i	−0.676058	−	0.539138i	−0.900232	+	0.435411i	$0.856603\pi$
$284$	−0.502734	−	1.04394i	−0.0298318	−	0.0619463i
$285$	1.76438	−	0.919313i	0.104513	−	0.0544554i
$286$	−12.3852	+	25.7181i	−0.732350	+	1.52074i
$287$	−9.44104	+	0.268769i	−0.557287	+	0.0158649i
$288$	0.189100	+	2.99403i	0.0111428	+	0.176425i
$289$	−3.96027	−	1.90717i	−0.232957	−	0.112186i
$290$	1.58593	+	6.94843i	0.0931292	+	0.408026i
$291$	15.0838	−	20.1891i	0.884231	−	1.18351i
$292$	−10.6284	−	8.47585i	−0.621979	−	0.496011i
$293$	4.09342			0.239140			0.119570	−	0.992826i	$-0.461848\pi$
$293$	4.09342			0.239140			0.119570	+	0.992826i	$0.461848\pi$
$294$	−11.3457	−	4.27496i	−0.661694	−	0.249321i
$295$	13.3678			0.778306
$296$	−2.69431	−	2.14864i	−0.156604	−	0.124887i
$297$	26.9956	−	16.3074i	1.56644	−	0.946251i
$298$	−2.66567	−	11.6791i	−0.154418	−	0.676550i
$299$	29.1402	+	14.0332i	1.68522	+	0.811561i
$300$	5.17509	−	1.35419i	0.298784	−	0.0781845i
$301$	4.06250	−	5.40274i	0.234159	−	0.311409i
$302$	−0.0347454	+	0.0721495i	−0.00199937	+	0.00415174i
$303$	−8.28032	−	15.8920i	−0.475692	−	0.912969i
$304$	0.360468	+	0.748520i	0.0206743	+	0.0429306i
$305$	−7.65515	−	6.10478i	−0.438333	−	0.349559i
$306$	11.3729	+	7.95086i	0.650148	+	0.454520i
$307$	−5.41326	−	4.31693i	−0.308951	−	0.246380i	0.456723	−	0.889609i	$-0.349023\pi$
$307$	−5.41326	−	4.31693i	−0.308951	−	0.246380i	−0.765674	+	0.643229i	$0.777594\pi$
$308$	−0.456978	−	16.0522i	−0.0260387	−	0.914661i
$309$	18.4885	−	9.63321i	1.05177	−	0.548014i
$310$	4.10841	−	1.97851i	0.233342	−	0.112372i
$311$	3.10733	−	13.6141i	0.176201	−	0.771985i	−0.807162	−	0.590330i	$-0.798998\pi$
$311$	3.10733	−	13.6141i	0.176201	−	0.771985i	0.983362	−	0.181655i	$-0.0581453\pi$
$312$	7.99464	+	1.56127i	0.452607	+	0.0883894i
$313$			17.0194i			0.961993i	0.876723	+	0.480996i	$0.159725\pi$
$313$			17.0194i			0.961993i	−0.876723	+	0.480996i	$0.840275\pi$
$314$	−0.387142	+	1.69618i	−0.0218477	+	0.0957209i
$315$	3.40968	+	10.4308i	0.192113	+	0.587711i
$316$	−3.35176	−	14.6850i	−0.188551	−	0.826097i
$317$	−6.65967	+	1.52003i	−0.374044	+	0.0853732i	−0.405410	−	0.914135i	$-0.632871\pi$
$317$	−6.65967	+	1.52003i	−0.374044	+	0.0853732i	0.0313661	+	0.999508i	$0.490014\pi$
$318$	6.59653	+	12.6603i	0.369915	+	0.709957i
$319$	19.5080	+	24.4622i	1.09224	+	1.36962i
$320$	−0.307656	−	1.34793i	−0.0171985	−	0.0753514i
$321$	3.60097	−	0.113604i	0.200987	−	0.00634073i
$322$	−18.1882	+	0.517786i	−1.01359	+	0.0288551i
$323$	3.74652	+	0.855119i	0.208462	+	0.0475801i
$324$	−6.45212	−	6.27456i	−0.358451	−	0.348587i
$325$		−	14.5246i		−	0.805681i
$326$	−17.7607	−	4.05375i	−0.983672	−	0.224517i
$327$	26.9552	−	7.05351i	1.49062	−	0.390060i
$328$	−2.79100	+	2.22575i	−0.154107	+	0.122896i
$329$	1.38946	−	7.00033i	0.0766036	−	0.385941i
$330$	−11.0726	+	9.41630i	−0.609525	+	0.518350i
$331$	0.780623	−	3.42013i	0.0429069	−	0.187988i	−0.948933	−	0.315478i	$-0.897835\pi$
$331$	0.780623	−	3.42013i	0.0429069	−	0.187988i	0.991840	+	0.127491i	$0.0406923\pi$
$332$	2.44958	−	3.07168i	0.134438	−	0.168580i
$333$	10.3179	−	0.651667i	0.565418	−	0.0357112i
$334$	6.57221	−	5.24116i	0.359615	−	0.286784i
$335$	−11.9292	−	5.74478i	−0.651759	−	0.313871i
$336$	−4.39850	+	1.28578i	−0.239958	+	0.0701448i
$337$	−1.66645	+	0.802519i	−0.0907771	+	0.0437160i	−0.478721	−	0.877967i	$-0.658900\pi$
$337$	−1.66645	+	0.802519i	−0.0907771	+	0.0437160i	0.387944	+	0.921683i	$0.373185\pi$
$338$	3.95584	−	8.21439i	0.215169	−	0.446804i
$339$	8.42392	−	0.265758i	0.457525	−	0.0144340i
$340$	−5.76190	−	2.77479i	−0.312483	−	0.150484i
$341$	12.4814	−	15.6511i	0.675903	−	0.847556i
$342$	−2.30926	−	0.937709i	−0.124870	−	0.0507055i
$343$	2.56637	−	18.3416i	0.138571	−	0.990353i
$344$		−	2.55493i		−	0.137752i
$345$	10.6693	+	12.5459i	0.574415	+	0.675451i
$346$	−2.12708	+	4.41693i	−0.114353	+	0.237456i
$347$	0.724949	−	0.165465i	0.0389173	−	0.00888262i	−0.203018	−	0.979175i	$-0.565075\pi$
$347$	0.724949	−	0.165465i	0.0389173	−	0.00888262i	0.241935	+	0.970292i	$0.422218\pi$
$348$	5.34397	−	7.15268i	0.286467	−	0.383424i
$349$	5.19524	+	10.7880i	0.278095	+	0.577470i	0.992498	−	0.122265i	$-0.0390157\pi$
$349$	5.19524	+	10.7880i	0.278095	+	0.577470i	−0.714402	+	0.699735i	$0.753301\pi$
$350$	3.75343	+	7.25816i	0.200629	+	0.387965i
$351$	−20.9168	+	12.6354i	−1.11646	+	0.674426i
$352$	−3.78435	−	4.74543i	−0.201707	−	0.252932i
$353$	−12.0433	+	5.79973i	−0.640999	+	0.308689i	−0.726003	−	0.687692i	$-0.758624\pi$
$353$	−12.0433	+	5.79973i	−0.640999	+	0.308689i	0.0850040	+	0.996381i	$0.472910\pi$
$354$	−10.8490	−	12.7573i	−0.576619	−	0.678043i
$355$	−1.56182	−	0.356475i	−0.0828929	−	0.0189198i
$356$	−5.74690	+	7.20638i	−0.304585	+	0.381937i
$357$	−8.03529	+	19.6148i	−0.425273	+	1.03813i
$358$	3.67548	+	4.60891i	0.194255	+	0.243588i
$359$	−11.6948	−	24.2846i	−0.617230	−	1.28169i	−0.941909	−	0.335867i	$-0.890971\pi$
$359$	−11.6948	−	24.2846i	−0.617230	−	1.28169i	0.324680	−	0.945824i	$-0.394744\pi$
$360$	3.39942	+	2.37655i	0.179165	+	0.125255i
$361$	18.3098			0.963673
$362$	8.29717			0.436090
$363$	−18.1381	+	40.9169i	−0.952005	+	2.14758i
$364$	0.354078	+	12.4377i	0.0185587	+	0.651911i
$365$	−18.3240	+	4.18233i	−0.959122	+	0.218913i
$366$	0.386779	+	12.2600i	0.0202173	+	0.640842i
$367$	17.7763	−	14.1761i	0.927915	−	0.739988i	−0.0378830	−	0.999282i	$-0.512061\pi$
$367$	17.7763	−	14.1761i	0.927915	−	0.739988i	0.965798	+	0.259294i	$0.0834900\pi$
$368$	−5.37688	+	4.28792i	−0.280289	+	0.223523i
$369$	1.72021	−	10.5704i	0.0895508	−	0.550274i
$370$	−4.64517	+	1.06023i	−0.241491	+	0.0551187i
$371$	−16.6553	+	14.0759i	−0.864701	+	0.730783i
$372$	−5.22243	−	2.31506i	−0.270770	−	0.120030i
$373$	−9.45599			−0.489613			−0.244806	−	0.969572i	$-0.578724\pi$
$373$	−9.45599			−0.489613			−0.244806	+	0.969572i	$0.578724\pi$
$374$	−28.0753			−1.45174
$375$	7.84967	−	17.7077i	0.405355	−	0.914421i
$376$	−1.17040	−	2.43036i	−0.0603586	−	0.125336i
$377$	−15.1152	−	18.9539i	−0.778475	−	0.976177i
$378$	7.18723	−	11.7194i	0.369671	−	0.602780i
$379$	−16.2076	+	20.3237i	−0.832528	+	1.04396i	0.165800	+	0.986159i	$0.446979\pi$
$379$	−16.2076	+	20.3237i	−0.832528	+	1.04396i	−0.998328	+	0.0577977i	$0.981592\pi$
$380$	1.11985	+	0.255599i	0.0574471	+	0.0131119i
$381$	−7.94371	+	6.75546i	−0.406968	+	0.346093i
$382$	9.29022	−	4.47394i	0.475329	−	0.228906i
$383$	0.874932	+	1.09713i	0.0447069	+	0.0560607i	0.803682	−	0.595059i	$-0.202871\pi$
$383$	0.874932	+	1.09713i	0.0447069	+	0.0560607i	−0.758975	+	0.651119i	$0.774300\pi$
$384$	−1.03668	+	1.38755i	−0.0529028	+	0.0708082i
$385$	−17.7457	−	13.3436i	−0.904403	−	0.680051i
$386$	4.43882	+	9.21730i	0.225930	+	0.469148i
$387$	5.14714	+	5.67942i	0.261644	+	0.288701i
$388$	14.1854	−	3.23772i	0.720153	−	0.164370i
$389$	−9.23029	+	19.1669i	−0.467994	+	0.971800i	0.524716	+	0.851277i	$0.324171\pi$
$389$	−9.23029	+	19.1669i	−0.467994	+	0.971800i	−0.992711	+	0.120523i	$0.961543\pi$
$390$	8.57930	−	7.29598i	0.434430	−	0.369446i
$391$			31.8112i			1.60876i
$392$	−3.39106	−	6.12378i	−0.171274	−	0.309298i
$393$	10.6947	+	2.08856i	0.539477	+	0.105354i
$394$	−2.64495	+	3.31666i	−0.133251	+	0.167091i
$395$	−18.7632	−	9.03586i	−0.944077	−	0.454643i
$396$	17.9725	+	2.92481i	0.903150	+	0.146977i
$397$	−4.51275	+	9.37081i	−0.226488	+	0.470308i	−0.982984	−	0.183691i	$-0.941195\pi$
$397$	−4.51275	+	9.37081i	−0.226488	+	0.470308i	0.756496	+	0.653999i	$0.226910\pi$
$398$	17.3958	−	8.37738i	0.871974	−	0.419920i
$399$	0.623090	−	3.75584i	0.0311935	−	0.188027i
$400$	2.78259	+	1.34002i	0.139129	+	0.0670012i
$401$	22.6214	−	18.0400i	1.12966	−	0.900873i	0.133730	−	0.991018i	$-0.457304\pi$
$401$	22.6214	−	18.0400i	1.12966	−	0.900873i	0.995929	+	0.0901449i	$0.0287330\pi$
$402$	4.19902	+	16.0467i	0.209428	+	0.800334i
$403$	−9.67086	+	12.1269i	−0.481740	+	0.604083i
$404$	2.30220	−	10.0866i	0.114539	−	0.501826i
$405$	−12.3444	+	1.56557i	−0.613401	+	0.0777937i
$406$	12.4513	+	5.56549i	0.617950	+	0.276210i
$407$	−16.3535	+	13.0415i	−0.810613	+	0.646442i
$408$	2.02817	+	7.75069i	0.100409	+	0.383716i
$409$	27.4471	+	6.26463i	1.35717	+	0.309766i	0.838358	−	0.545120i	$-0.183516\pi$
$409$	27.4471	+	6.26463i	1.35717	+	0.309766i	0.518816	+	0.854886i	$0.326373\pi$
$410$			4.93561i			0.243752i
$411$	−7.41481	+	37.9683i	−0.365745	+	1.87284i
$412$	11.7346	+	2.67835i	0.578122	+	0.131953i
$413$	15.3739	−	20.4457i	0.756498	−	1.00607i
$414$	3.31401	−	20.3640i	0.162875	−	1.00084i
$415$	−1.20873	−	5.29578i	−0.0593340	−	0.259959i
$416$	2.93221	+	3.67688i	0.143763	+	0.180274i
$417$	−1.22839	+	0.640041i	−0.0601547	+	0.0313429i
$418$	4.91619	−	1.12209i	0.240459	−	0.0548831i
$419$	3.80551	+	16.6730i	0.185911	+	0.814531i	0.978743	+	0.205090i	$0.0657488\pi$
$419$	3.80551	+	16.6730i	0.185911	+	0.814531i	−0.792832	+	0.609441i	$0.791394\pi$
$420$	−2.40178	+	5.86295i	−0.117195	+	0.286083i
$421$	8.47058	−	37.1120i	0.412831	−	1.80873i	−0.157739	−	0.987481i	$-0.550420\pi$
$421$	8.47058	−	37.1120i	0.412831	−	1.80873i	0.570570	−	0.821249i	$-0.306722\pi$
$422$		−	7.04305i		−	0.342850i
$423$	7.49789	+	3.04463i	0.364560	+	0.148035i
$424$	−1.83405	+	8.03549i	−0.0890692	+	0.390238i
$425$	12.8710	−	6.19832i	0.624333	−	0.300663i
$426$	0.927343	+	1.77980i	0.0449299	+	0.0862314i
$427$	−18.1410	+	4.68746i	−0.877904	+	0.226842i
$428$	1.62625	+	1.29689i	0.0786080	+	0.0626878i
$429$	20.0365	−	45.1993i	0.967369	−	2.18224i
$430$	−2.76176	−	2.20243i	−0.133184	−	0.106211i
$431$	1.66281	+	3.45286i	0.0800948	+	0.166319i	0.937170	−	0.348872i	$-0.113435\pi$
$431$	1.66281	+	3.45286i	0.0800948	+	0.166319i	−0.857075	+	0.515191i	$0.827721\pi$
$432$	−0.490889	−	5.17291i	−0.0236179	−	0.248882i
$433$	7.19915	−	14.9492i	0.345969	−	0.718412i	−0.653282	−	0.757115i	$-0.726608\pi$
$433$	7.19915	−	14.9492i	0.345969	−	0.718412i	0.999251	+	0.0387030i	$0.0123226\pi$
$434$	1.69886	−	8.55910i	0.0815478	−	0.410850i
$435$	−3.12504	−	11.9424i	−0.149834	−	0.572596i
$436$	14.4935	+	6.97970i	0.694113	+	0.334267i
$437$	−1.27140	−	5.57036i	−0.0608193	−	0.266467i
$438$	18.8626	+	14.0928i	0.901292	+	0.673381i
$439$	12.5092	+	9.97577i	0.597032	+	0.476117i	0.874769	−	0.484540i	$-0.161013\pi$
$439$	12.5092	+	9.97577i	0.597032	+	0.476117i	−0.277737	+	0.960657i	$0.589584\pi$
$440$	−8.39183			−0.400065
$441$	19.8750	+	6.78112i	0.946430	+	0.322910i
$442$	21.7534			1.03471
$443$	−8.87808	−	7.08003i	−0.421810	−	0.336383i	0.389471	−	0.921039i	$-0.372658\pi$
$443$	−8.87808	−	7.08003i	−0.421810	−	0.336383i	−0.811281	+	0.584656i	$0.801229\pi$
$444$	4.78172	+	3.57256i	0.226930	+	0.169546i
$445$	2.83576	+	12.4243i	0.134428	+	0.588967i
$446$	−14.4127	−	6.94077i	−0.682459	−	0.328655i
$447$	5.25264	+	20.0731i	0.248441	+	0.949425i
$448$	−2.41544	−	1.07965i	−0.114119	−	0.0510087i
$449$	−5.71113	+	11.8593i	−0.269525	+	0.559675i	−0.991171	−	0.132587i	$-0.957671\pi$
$449$	−5.71113	+	11.8593i	−0.269525	+	0.559675i	0.721646	+	0.692262i	$0.243386\pi$
$450$	−8.88510	+	2.62701i	−0.418847	+	0.123838i
$451$	9.40119	+	19.5218i	0.442685	+	0.919244i
$452$	3.80437	+	3.03389i	0.178943	+	0.142702i
$453$	0.0562104	−	0.126802i	0.00264099	−	0.00595769i
$454$	−6.56182	−	5.23288i	−0.307962	−	0.245591i
$455$	13.7498	+	10.3389i	0.644599	+	0.484696i
$456$	−0.664920	−	1.27614i	−0.0311377	−	0.0597609i
$457$	5.57952	−	2.68695i	0.260999	−	0.125690i	−0.298809	−	0.954313i	$-0.596589\pi$
$457$	5.57952	−	2.68695i	0.260999	−	0.125690i	0.559808	+	0.828623i	$0.310875\pi$
$458$	5.89179	−	25.8136i	0.275305	−	1.20619i
$459$	−20.1230	−	13.1433i	−0.939260	−	0.613477i
$460$			9.50849i			0.443336i
$461$	6.01050	−	26.3337i	0.279937	−	1.22648i	−0.617935	−	0.786229i	$-0.712031\pi$
$461$	6.01050	−	26.3337i	0.279937	−	1.22648i	0.897872	−	0.440256i	$-0.145112\pi$
$462$	1.66782	+	27.7645i	0.0775939	+	1.29172i
$463$	3.18065	+	13.9354i	0.147817	+	0.647631i	0.993489	+	0.113927i	$0.0363430\pi$
$463$	3.18065	+	13.9354i	0.147817	+	0.647631i	−0.845672	+	0.533704i	$0.820800\pi$
$464$	5.02565	−	1.14707i	0.233310	−	0.0532515i
$465$	−7.00438	+	3.64955i	−0.324820	+	0.169244i
$466$	−5.57436	−	6.99002i	−0.258227	−	0.323807i
$467$	0.827790	+	3.62678i	0.0383055	+	0.167828i	0.990463	−	0.137781i	$-0.0439971\pi$
$467$	0.827790	+	3.62678i	0.0383055	+	0.167828i	−0.952157	+	0.305609i	$0.901140\pi$
$468$	−13.9255	−	2.26622i	−0.643707	−	0.104756i
$469$	−22.5058	+	11.6385i	−1.03922	+	0.537414i
$470$	−3.63602	−	0.829898i	−0.167717	−	0.0382804i
$471$	0.577578	−	2.95755i	0.0266134	−	0.136277i
$472$		−	9.66868i		−	0.445037i
$473$	−15.1187	−	3.45074i	−0.695157	−	0.158665i
$474$	6.60456	+	25.2395i	0.303358	+	1.15929i
$475$	−2.00607	+	1.59979i	−0.0920447	+	0.0734032i
$476$	−10.8705	+	5.62149i	−0.498249	+	0.257661i
$477$	−12.1113	−	21.5572i	−0.554538	−	0.987035i
$478$	2.45905	−	10.7738i	0.112474	−	0.492782i
$479$	−11.5472	+	14.4797i	−0.527605	+	0.661596i	−0.972204	−	0.234134i	$-0.924775\pi$
$479$	−11.5472	+	14.4797i	−0.527605	+	0.661596i	0.444600	+	0.895729i	$0.353346\pi$
$480$	0.606228	+	2.31672i	0.0276704	+	0.105743i
$481$	12.6711	−	10.1049i	0.577752	−	0.460742i
$482$	7.00783	+	3.37479i	0.319198	+	0.153718i
$483$	31.4590	−	1.88975i	1.43143	−	0.0859864i
$484$	−23.2814	+	11.2118i	−1.05825	+	0.509625i
$485$	8.72842	−	18.1247i	0.396337	−	0.823002i
$486$	11.5125	+	10.5101i	0.522219	+	0.476747i
$487$	8.99791	+	4.33317i	0.407734	+	0.196354i	0.626497	−	0.779424i	$-0.284488\pi$
$487$	8.99791	+	4.33317i	0.407734	+	0.196354i	−0.218763	+	0.975778i	$0.570202\pi$
$488$	−4.41546	+	5.53681i	−0.199878	+	0.250640i
$489$	30.9685	+	6.04781i	1.40044	+	0.273491i
$490$	−9.54273	−	1.61331i	−0.431097	−	0.0728821i
$491$		−	16.5398i		−	0.746429i	−0.927745	−	0.373214i	$-0.878256\pi$
$491$		−	16.5398i		−	0.746429i	0.927745	−	0.373214i	$-0.121744\pi$
$492$	4.71019	−	4.00562i	0.212352	−	0.180588i
$493$	10.3456	−	21.4828i	0.465942	−	0.967538i
$494$	−3.80918	+	0.869421i	−0.171383	+	0.0391171i
$495$	18.6544	−	16.9061i	0.838454	−	0.759874i
$496$	−1.43101	−	2.97153i	−0.0642543	−	0.133426i
$497$	−2.34141	+	1.97879i	−0.105027	+	0.0887610i
$498$	−4.07293	+	5.45145i	−0.182513	+	0.244285i
$499$	−17.2470	−	21.6271i	−0.772083	−	0.968161i	0.227902	−	0.973684i	$-0.426813\pi$
$499$	−17.2470	−	21.6271i	−0.772083	−	0.968161i	−0.999985	+	0.00552287i	$0.998242\pi$
$500$	10.0755	−	4.85213i	0.450592	−	0.216994i
$501$	−11.0915	+	9.43239i	−0.495531	+	0.421408i
$502$	−23.4349	−	5.34887i	−1.04595	−	0.238732i
$503$	−1.52518	+	1.91251i	−0.0680043	+	0.0852747i	−0.814670	−	0.579925i	$-0.803082\pi$
$503$	−1.52518	+	1.91251i	−0.0680043	+	0.0852747i	0.746666	+	0.665199i	$0.231653\pi$
$504$	7.54441	−	2.46615i	0.336055	−	0.109851i
$505$	−8.91857	−	11.1835i	−0.396871	−	0.497661i
$506$	18.1115	+	37.6088i	0.805152	+	1.67192i
$507$	−6.39968	+	14.4367i	−0.284220	+	0.641157i
$508$	−6.02049			−0.267116
$509$	−16.8173			−0.745415			−0.372707	−	0.927949i	$-0.621571\pi$
$509$	−16.8173			−0.745415			−0.372707	+	0.927949i	$0.621571\pi$
$510$	10.1265	+	4.48899i	0.448408	+	0.198776i
$511$	−14.6770	+	32.8360i	−0.649272	+	1.45258i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$	4.04898	+	1.49723i	0.178767	+	0.0661043i
$514$	18.7016	−	14.9140i	0.824893	−	0.657830i
$515$	13.0108	−	10.3757i	0.573323	−	0.457210i
$516$	0.139539	+	4.42306i	0.00614285	+	0.194714i
$517$	−15.9623	+	3.64329i	−0.702020	+	0.160232i
$518$	−3.72064	+	8.32399i	−0.163476	+	0.365735i
$519$	3.44115	−	7.76271i	0.151050	−	0.340745i
$520$	6.50220			0.285140
$521$	39.5633			1.73330			0.866651	−	0.498915i	$-0.166268\pi$
$521$	39.5633			1.73330			0.866651	+	0.498915i	$0.166268\pi$
$522$	−8.86078	+	12.6745i	−0.387826	+	0.554748i
$523$	6.56141	+	13.6249i	0.286911	+	0.595776i	0.993754	−	0.111594i	$-0.0355957\pi$
$523$	6.56141	+	13.6249i	0.286911	+	0.595776i	−0.706843	+	0.707370i	$0.749881\pi$
$524$	3.92253	+	4.91869i	0.171356	+	0.214874i
$525$	−6.89431	−	12.3603i	−0.300892	−	0.539446i
$526$	2.19117	−	2.74764i	0.0955396	−	0.119803i
$527$	−14.8732	−	3.39471i	−0.647887	−	0.147876i
$528$	6.81061	+	8.00856i	0.296394	+	0.348528i
$529$	21.8910	−	10.5421i	0.951781	−	0.458354i
$530$	7.10498	+	8.90937i	0.308621	+	0.386998i
$531$	19.4785	+	21.4928i	0.845293	+	0.932707i
$532$	1.67883	−	1.41883i	0.0727865	−	0.0615139i
$533$	−7.28427	−	15.1259i	−0.315517	−	0.655177i
$534$	9.55539	−	12.7895i	0.413502	−	0.553455i
$535$	2.80377	−	0.639942i	0.121217	−	0.0276671i
$536$	−4.15508	+	8.62811i	−0.179472	+	0.372677i
$537$	−6.61468	−	7.77816i	−0.285444	−	0.335652i
$538$		−	6.41418i		−	0.276535i
$539$	−40.8172	+	11.7955i	−1.75812	+	0.508070i
$540$	−6.01484	−	3.92859i	−0.258838	−	0.169060i
$541$	−16.5668	+	20.7741i	−0.712263	+	0.893150i	−0.997872	−	0.0651963i	$-0.979233\pi$
$541$	−16.5668	+	20.7741i	−0.712263	+	0.893150i	0.285609	+	0.958346i	$0.407804\pi$
$542$	1.05532	+	0.508213i	0.0453297	+	0.0218296i
$543$	−14.3640	+	0.453155i	−0.616417	+	0.0194467i
$544$	−2.00694	+	4.16746i	−0.0860470	+	0.178678i
$545$	20.0386	−	9.65008i	0.858359	−	0.413364i
$546$	−1.29227	−	21.5126i	−0.0553039	−	0.920655i
$547$	−42.0688	−	20.2593i	−1.79873	−	0.866224i	−0.925235	−	0.379395i	$-0.876132\pi$
$547$	−42.0688	−	20.2593i	−1.79873	−	0.866224i	−0.873497	−	0.486829i	$-0.838154\pi$
$548$	−17.4623	+	13.9257i	−0.745952	+	0.594877i
$549$	−1.33918	−	21.2033i	−0.0571546	−	0.904935i
$550$	11.6877	−	14.6560i	0.498367	−	0.624933i
$551$	−0.952981	+	4.17528i	−0.0405984	+	0.177873i
$552$	9.07422	−	7.71687i	0.386224	−	0.328452i
$553$	−35.3989	+	18.3059i	−1.50531	+	0.778447i
$554$	19.4611	−	15.5197i	0.826823	−	0.659369i
$555$	7.98376	−	2.08916i	0.338892	−	0.0886798i
$556$	−0.779659	−	0.177952i	−0.0330649	−	0.00754685i
$557$		−	34.5348i		−	1.46329i	−0.681688	−	0.731643i	$-0.738754\pi$
$557$		−	34.5348i		−	1.46329i	0.681688	−	0.731643i	$-0.261246\pi$
$558$	9.16746	+	3.72258i	0.388089	+	0.157590i
$559$	11.7143	+	2.67371i	0.495463	+	0.113086i
$560$	−3.24924	+	1.68029i	−0.137305	+	0.0710051i
$561$	48.6037	−	1.53335i	2.05205	−	0.0647380i
$562$	−3.38444	−	14.8282i	−0.142764	−	0.625491i
$563$	−16.1077	−	20.1984i	−0.678857	−	0.851260i	0.316391	−	0.948629i	$-0.397529\pi$
$563$	−16.1077	−	20.1984i	−0.678857	−	0.851260i	−0.995248	+	0.0973689i	$0.968957\pi$
$564$	2.15891	+	4.14348i	0.0909067	+	0.174472i
$565$	6.55898	−	1.49704i	0.275938	−	0.0629812i
$566$	3.23694	+	14.1820i	0.136059	+	0.596112i
$567$	−11.8024	+	20.6810i	−0.495654	+	0.868520i
$568$	−0.257831	+	1.12963i	−0.0108184	+	0.0473983i
$569$		−	0.199932i		−	0.00838160i	−0.999991	−	0.00419080i	$-0.998666\pi$
$569$		−	0.199932i		−	0.00838160i	0.999991	−	0.00419080i	$-0.00133398\pi$
$570$	−1.95263	−	0.381328i	−0.0817868	−	0.0159721i
$571$	10.1609	−	44.5177i	0.425219	−	1.86301i	−0.0751135	−	0.997175i	$-0.523932\pi$
$571$	10.1609	−	44.5177i	0.425219	−	1.86301i	0.500333	−	0.865833i	$-0.333211\pi$
$572$	25.7181	−	12.3852i	1.07533	−	0.517850i
$573$	−15.8388	+	8.25262i	−0.661675	+	0.344758i
$574$	7.54888	+	5.67626i	0.315084	+	0.236923i
$575$	−16.6062	−	13.2430i	−0.692525	−	0.552271i
$576$	1.71891	−	2.45873i	0.0716211	−	0.102447i
$577$	22.9857	+	18.3305i	0.956906	+	0.763107i	0.971562	−	0.236785i	$-0.0760938\pi$
$577$	22.9857	+	18.3305i	0.956906	+	0.763107i	−0.0146558	+	0.999893i	$0.504665\pi$
$578$	1.90717	+	3.96027i	0.0793276	+	0.164726i
$579$	−8.18784	−	15.7145i	−0.340275	−	0.653071i
$580$	3.09234	−	6.42131i	0.128402	−	0.266630i
$581$	−9.48985	−	4.24176i	−0.393705	−	0.175978i
$582$	−24.3807	+	6.37984i	−1.01061	+	0.264453i
$583$	45.0725	+	21.7058i	1.86671	+	0.898962i
$584$	3.02499	+	13.2534i	0.125175	+	0.548428i
$585$	−14.4539	+	13.0993i	−0.597596	+	0.541589i
$586$	−3.20037	−	2.55221i	−0.132206	−	0.105431i
$587$	−1.85828			−0.0766994			−0.0383497	−	0.999264i	$-0.512210\pi$
$587$	−1.85828			−0.0766994			−0.0383497	+	0.999264i	$0.512210\pi$
$588$	6.20502	+	10.4162i	0.255891	+	0.429558i
$589$	2.74008			0.112903
$590$	−10.4514	−	8.33471i	−0.430277	−	0.343135i
$591$	4.39777	−	5.88623i	0.180900	−	0.242127i
$592$	0.766842	+	3.35975i	0.0315170	+	0.138085i
$593$	−19.6723	−	9.47366i	−0.807843	−	0.389037i	−0.0160844	−	0.999871i	$-0.505120\pi$
$593$	−19.6723	−	9.47366i	−0.807843	−	0.389037i	−0.791759	+	0.610834i	$0.790834\pi$
$594$	−31.2735	−	4.08183i	−1.28317	−	0.167480i
$595$	−3.29415	+	16.5964i	−0.135047	+	0.680387i
$596$	−5.19767	+	10.7931i	−0.212905	+	0.442102i
$597$	−29.6579	+	15.4529i	−1.21382	+	0.632446i
$598$	−14.0332	−	29.1402i	−0.573860	−	1.19163i
$599$	−20.3117	−	16.1981i	−0.829915	−	0.661835i	0.113467	−	0.993542i	$-0.463804\pi$
$599$	−20.3117	−	16.1981i	−0.829915	−	0.661835i	−0.943383	+	0.331706i	$0.892376\pi$
$600$	−4.89037	−	2.16786i	−0.199649	−	0.0885026i
$601$	1.73478	+	1.38344i	0.0707633	+	0.0564319i	0.658233	−	0.752815i	$-0.271304\pi$
$601$	1.73478	+	1.38344i	0.0707633	+	0.0564319i	−0.587469	+	0.809246i	$0.699876\pi$
$602$	−6.54475	+	1.69110i	−0.266744	+	0.0689241i
$603$	−8.14569	−	27.5505i	−0.331718	−	1.12194i
$604$	0.0721495	−	0.0347454i	0.00293572	−	0.00141377i
$605$	−7.94996	+	34.8311i	−0.323212	+	1.41608i
$606$	−3.43465	+	17.5875i	−0.139523	+	0.714444i
$607$			3.37845i			0.137127i	0.997647	+	0.0685635i	$0.0218416\pi$
$607$			3.37845i			0.137127i	−0.997647	+	0.0685635i	$0.978158\pi$
$608$	0.184869	−	0.809965i	0.00749743	−	0.0328484i
$609$	−21.8596	−	8.95487i	−0.885796	−	0.362870i
$610$	2.17877	+	9.54582i	0.0882159	+	0.386499i
$611$	12.3680	−	2.82291i	0.500354	−	0.114203i
$612$	−3.93445	−	13.3071i	−0.159041	−	0.537910i
$613$	10.8275	+	13.5772i	0.437318	+	0.548379i	0.950834	−	0.309701i	$-0.100229\pi$
$613$	10.8275	+	13.5772i	0.437318	+	0.548379i	−0.513516	+	0.858080i	$0.671657\pi$
$614$	1.54069	+	6.75022i	0.0621774	+	0.272417i
$615$	−0.269561	−	8.54448i	−0.0108698	−	0.344547i
$616$	−9.65113	+	12.8351i	−0.388855	+	0.517140i
$617$	23.2938	+	5.31666i	0.937774	+	0.214041i	0.663982	−	0.747748i	$-0.268865\pi$
$617$	23.2938	+	5.31666i	0.937774	+	0.214041i	0.273792	+	0.961789i	$0.411722\pi$
$618$	−20.4611	−	3.99583i	−0.823066	−	0.160736i
$619$		−	10.3257i		−	0.415025i	−0.978232	−	0.207512i	$-0.933463\pi$
$619$		−	10.3257i		−	0.415025i	0.978232	−	0.207512i	$-0.0665367\pi$
$620$	−4.44566	−	1.01469i	−0.178542	−	0.0407511i
$621$	−4.62498	+	35.4349i	−0.185594	+	1.42195i
$622$	−10.9177	+	8.70655i	−0.437758	+	0.349101i
$623$	22.2639	+	9.95147i	0.891983	+	0.398697i
$624$	−5.27703	−	6.20523i	−0.211250	−	0.248408i
$625$	0.00430567	−	0.0188644i	0.000172227	−	0.000754575i
$626$	10.6114	−	13.3063i	0.424118	−	0.531827i
$627$	−8.44957	+	2.21105i	−0.337443	+	0.0883007i
$628$	1.36023	−	1.08475i	0.0542791	−	0.0432861i
$629$	14.3617	+	6.91624i	0.572640	+	0.275769i
$630$	3.83773	−	10.2811i	0.152899	−	0.409607i
$631$	33.6812	−	16.2200i	1.34083	−	0.645708i	0.380551	−	0.924760i	$-0.375734\pi$
$631$	33.6812	−	16.2200i	1.34083	−	0.645708i	0.960276	+	0.279052i	$0.0900201\pi$
$632$	−6.53545	+	13.5710i	−0.259966	+	0.539825i
$633$	0.384660	+	12.1929i	0.0152889	+	0.484623i
$634$	6.15446	+	2.96383i	0.244425	+	0.117709i
$635$	−5.18985	+	6.50787i	−0.205953	+	0.258257i
$636$	2.73622	−	14.0111i	0.108498	−	0.555577i
$637$	31.6262	−	9.13948i	1.25308	−	0.362119i
$638$		−	31.2883i		−	1.23872i
$639$	−1.70261	−	3.03052i	−0.0673542	−	0.119885i
$640$	−0.599884	+	1.24567i	−0.0237125	+	0.0492395i
$641$	23.6755	−	5.40378i	0.935126	−	0.213436i	0.272302	−	0.962212i	$-0.412215\pi$
$641$	23.6755	−	5.40378i	0.935126	−	0.213436i	0.662824	+	0.748775i	$0.269358\pi$
$642$	−2.88619	−	2.15635i	−0.113909	−	0.0851044i
$643$	−15.9437	−	33.1074i	−0.628757	−	1.30563i	−0.935329	−	0.353780i	$-0.884896\pi$
$643$	−15.9437	−	33.1074i	−0.628757	−	1.30563i	0.306572	−	0.951848i	$-0.400818\pi$
$644$	14.5430	+	10.9354i	0.573073	+	0.430913i
$645$	4.90141	+	3.66199i	0.192993	+	0.144191i
$646$	−2.39599	−	3.00448i	−0.0942689	−	0.118209i
$647$	26.0330	−	12.5368i	1.02346	−	0.492874i	0.154626	−	0.987973i	$-0.450583\pi$
$647$	26.0330	−	12.5368i	1.02346	−	0.492874i	0.868836	+	0.495099i	$0.164868\pi$
$648$	1.13234	+	8.92848i	0.0444826	+	0.350744i
$649$	−57.2140	−	13.0587i	−2.24585	−	0.512600i
$650$	−9.05596	+	11.3558i	−0.355204	+	0.445412i
$651$	−2.47359	+	14.9102i	−0.0969475	+	0.584377i
$652$	11.3584	+	14.2429i	0.444828	+	0.557797i
$653$	7.58709	+	15.7548i	0.296906	+	0.616531i	0.995044	−	0.0994314i	$-0.0317024\pi$
$653$	7.58709	+	15.7548i	0.296906	+	0.616531i	−0.698139	+	0.715963i	$0.745988\pi$
$654$	−25.4722	−	11.2916i	−0.996041	−	0.441537i
$655$	8.69822			0.339868
$656$	3.56982			0.139378
$657$	−33.4245	−	23.3671i	−1.30401	−	0.911639i
$658$	−5.45096	+	4.60676i	−0.212501	+	0.179590i
$659$	−19.0078	+	4.33840i	−0.740438	+	0.169000i	−0.576072	−	0.817399i	$-0.695415\pi$
$659$	−19.0078	+	4.33840i	−0.740438	+	0.169000i	−0.164366	+	0.986399i	$0.552558\pi$
$660$	14.5278	−	0.458324i	0.565496	−	0.0178403i
$661$	−32.3616	+	25.8076i	−1.25872	+	1.00380i	−0.259446	+	0.965758i	$0.583540\pi$
$661$	−32.3616	+	25.8076i	−1.25872	+	1.00380i	−0.999276	+	0.0380399i	$0.987889\pi$
$662$	−2.74273	+	2.18726i	−0.106599	+	0.0850102i
$663$	−37.6593	+	1.18808i	−1.46257	+	0.0461411i
$664$	−3.83032	+	0.874247i	−0.148645	+	0.0339273i
$665$	−0.0864809	−	3.03781i	−0.00335359	−	0.117801i
$666$	−8.47317	−	5.92362i	−0.328329	−	0.229536i
$667$	−35.4517			−1.37270
$668$	−8.40618			−0.325245
$669$	25.3301	+	11.2286i	0.979319	+	0.434124i
$670$	5.74478	+	11.9292i	0.221940	+	0.460863i
$671$	26.8002	+	33.6064i	1.03461	+	1.29736i
$672$	4.24055	+	1.73716i	0.163583	+	0.0670124i
$673$	−17.9759	+	22.5411i	−0.692920	+	0.868894i	−0.996472	−	0.0839208i	$-0.973256\pi$
$673$	−17.9759	+	22.5411i	−0.692920	+	0.868894i	0.303553	+	0.952815i	$0.401827\pi$
$674$	1.80324	+	0.411578i	0.0694583	+	0.0158534i
$675$	15.2383	−	5.03311i	0.586523	−	0.193725i
$676$	−8.21439	+	3.95584i	−0.315938	+	0.152148i
$677$	−29.3180	−	36.7636i	−1.12678	−	1.41294i	−0.898296	−	0.439392i	$-0.855194\pi$
$677$	−29.3180	−	36.7636i	−1.12678	−	1.41294i	−0.228486	−	0.973547i	$-0.573377\pi$
$678$	−6.75179	−	5.04445i	−0.259301	−	0.193731i
$679$	−17.6831	−	34.1945i	−0.678614	−	1.31226i
$680$	2.77479	+	5.76190i	0.106408	+	0.220959i
$681$	11.6456	+	8.70073i	0.446259	+	0.333413i
$682$	−19.5166	+	4.45454i	−0.747331	+	0.170573i
$683$	−6.92481	+	14.3795i	−0.264971	+	0.550217i	−0.990425	−	0.138053i	$-0.955915\pi$
$683$	−6.92481	+	14.3795i	−0.264971	+	0.550217i	0.725454	+	0.688270i	$0.241630\pi$
$684$	1.22080	+	2.17293i	0.0466784	+	0.0830840i
$685$			30.8804i			1.17988i
$686$	−13.4423	+	12.7399i	−0.513228	+	0.486413i
$687$	−8.78998	+	45.0100i	−0.335359	+	1.71724i
$688$	−1.59297	+	1.99752i	−0.0607314	+	0.0761548i
$689$	−34.9233	−	16.8182i	−1.33047	−	0.640722i
$690$	−0.519312	−	16.4610i	−0.0197699	−	0.626659i
$691$	−0.799031	+	1.65921i	−0.0303966	+	0.0631191i	−0.915614	−	0.402058i	$-0.868295\pi$
$691$	−0.799031	+	1.65921i	−0.0303966	+	0.0631191i	0.885218	+	0.465177i	$0.154009\pi$
$692$	4.41693	−	2.12708i	0.167906	−	0.0808595i
$693$	−4.40368	−	47.9745i	−0.167282	−	1.82240i
$694$	−0.669953	−	0.322632i	−0.0254311	−	0.0122470i
$695$	−0.864449	+	0.689375i	−0.0327904	+	0.0261495i
$696$	−8.63771	+	2.26028i	−0.327412	+	0.0856756i
$697$	10.2953	−	12.9099i	0.389961	−	0.488996i
$698$	2.66443	−	11.6736i	0.100850	−	0.441853i
$699$	10.0320	+	11.7966i	0.379446	+	0.446189i
$700$	1.59084	−	8.01489i	0.0601281	−	0.302934i
$701$	5.66440	−	4.51721i	0.213941	−	0.170613i	−0.510656	−	0.859785i	$-0.670597\pi$
$701$	5.66440	−	4.51721i	0.213941	−	0.170613i	0.724597	+	0.689173i	$0.242026\pi$
$702$	24.2315	+	3.16270i	0.914558	+	0.119369i
$703$	−2.79126	−	0.637088i	−0.105275	−	0.0240282i
$704$			6.06963i			0.228758i
$705$	6.33997	+	1.23813i	0.238777	+	0.0466306i
$706$	13.0319	+	2.97444i	0.490461	+	0.111945i
$707$	−27.3618	+	0.778940i	−1.02905	+	0.0292951i
$708$	0.528061	+	16.7383i	0.0198457	+	0.629064i
$709$	0.312107	+	1.36743i	0.0117214	+	0.0513549i	0.980450	−	0.196766i	$-0.0630440\pi$
$709$	0.312107	+	1.36743i	0.0117214	+	0.0513549i	−0.968729	+	0.248121i	$0.920187\pi$
$710$	0.998822	+	1.25248i	0.0374851	+	0.0470049i
$711$	−12.8122	−	43.3336i	−0.480496	−	1.62514i
$712$	8.98621	−	2.05104i	0.336773	−	0.0768661i
$713$	5.04729	+	22.1136i	0.189023	+	0.828162i
$714$	18.5119	−	10.3256i	0.692790	−	0.386424i
$715$	8.78200	−	38.4764i	0.328428	−	1.43894i
$716$		−	5.89502i		−	0.220307i
$717$	−3.66867	+	18.7858i	−0.137009	+	0.701569i
$718$	−5.99780	+	26.2781i	−0.223836	+	0.980688i
$719$	−45.0298	+	21.6852i	−1.67933	+	0.808723i	−0.682353	+	0.731023i	$0.739043\pi$
$719$	−45.0298	+	21.6852i	−1.67933	+	0.808723i	−0.996977	+	0.0777000i	$0.975242\pi$
$720$	−1.17602	−	3.97756i	−0.0438278	−	0.148235i
$721$	−0.906209	−	31.8324i	−0.0337490	−	1.18550i
$722$	−14.3152	−	11.4160i	−0.532755	−	0.424858i
$723$	−12.3162	−	5.45967i	−0.458044	−	0.203047i
$724$	−6.48699	−	5.17320i	−0.241087	−	0.192261i
$725$	6.90768	+	14.3439i	0.256545	+	0.532721i
$726$	39.6923	−	20.6812i	1.47312	−	0.767551i
$727$	14.5220	−	30.1553i	0.538592	−	1.11840i	−0.437132	−	0.899397i	$-0.644006\pi$
$727$	14.5220	−	30.1553i	0.538592	−	1.11840i	0.975725	−	0.219001i	$-0.0702799\pi$
$728$	7.47793	−	9.94493i	0.277151	−	0.368583i
$729$	−20.5044	−	17.5662i	−0.759422	−	0.650599i
$730$	16.9339	+	8.15495i	0.626753	+	0.301828i
$731$	2.62973	+	11.5216i	0.0972641	+	0.426142i
$732$	7.34160	−	9.82642i	0.271353	−	0.363195i
$733$	−5.64315	−	4.50026i	−0.208434	−	0.166221i	0.513709	−	0.857965i	$-0.328271\pi$
$733$	−5.64315	−	4.50026i	−0.208434	−	0.166221i	−0.722143	+	0.691744i	$0.756843\pi$
$734$	−22.7367			−0.839228
$735$	16.6084	+	2.27177i	0.612610	+	0.0837956i
$736$	6.87729			0.253500
$737$	45.4445	+	36.2408i	1.67397	+	1.33495i
$738$	−7.93546	+	7.19175i	−0.292108	+	0.264732i
$739$	10.2150	+	44.7547i	0.375764	+	1.64633i	0.710265	+	0.703934i	$0.248575\pi$
$739$	10.2150	+	44.7547i	0.375764	+	1.64633i	−0.334501	+	0.942395i	$0.608568\pi$
$740$	4.29278	+	2.06729i	0.157806	+	0.0759953i
$741$	6.54694	−	1.71317i	0.240508	−	0.0629350i
$742$	21.7978	−	0.620544i	0.800223	−	0.0227809i
$743$	0.569921	−	1.18345i	0.0209084	−	0.0434167i	−0.890253	−	0.455466i	$-0.849473\pi$
$743$	0.569921	−	1.18345i	0.0209084	−	0.0434167i	0.911161	+	0.412049i	$0.135187\pi$
$744$	2.63964	+	5.06612i	0.0967741	+	0.185733i
$745$	7.18626	+	14.9224i	0.263284	+	0.546715i
$746$	7.39299	+	5.89571i	0.270677	+	0.215857i
$747$	6.75329	−	9.65994i	0.247090	−	0.353439i
$748$	21.9502	+	17.5047i	0.802577	+	0.640034i
$749$	2.24574	−	5.02426i	0.0820574	−	0.183582i
$750$	−17.1777	+	8.95023i	−0.627240	+	0.326816i
$751$	−18.9268	+	9.11468i	−0.690649	+	0.332599i	−0.746073	−	0.665864i	$-0.768063\pi$
$751$	−18.9268	+	9.11468i	−0.690649	+	0.332599i	0.0554240	+	0.998463i	$0.482349\pi$
$752$	−0.600248	+	2.62986i	−0.0218888	+	0.0959011i
$753$	40.8624	+	7.97999i	1.48911	+	0.290807i
$754$			24.2430i			0.882877i
$755$	0.0246371	−	0.107942i	0.000896634	−	0.00392841i
$756$	−12.9261	+	4.68141i	−0.470118	+	0.170261i
$757$	1.27098	+	5.56851i	0.0461944	+	0.202391i	0.992759	−	0.120123i	$-0.0383290\pi$
$757$	1.27098	+	5.56851i	0.0461944	+	0.202391i	−0.946565	+	0.322514i	$0.895472\pi$
$758$	25.3432	−	5.78442i	0.920507	−	0.210100i
$759$	−33.4084	−	64.1188i	−1.21265	−	2.32737i
$760$	−0.716171	−	0.898051i	−0.0259783	−	0.0325757i
$761$	0.858326	+	3.76057i	0.0311143	+	0.136321i	0.988099	−	0.153816i	$-0.0491563\pi$
$761$	0.858326	+	3.76057i	0.0311143	+	0.136321i	−0.956985	+	0.290137i	$0.906299\pi$
$762$	10.4226	−	0.328812i	0.377571	−	0.0119116i
$763$	8.28611	−	41.7467i	0.299977	−	1.51133i
$764$	−10.0528	−	2.29450i	−0.363699	−	0.0830119i
$765$	−17.7760	−	7.21823i	−0.642694	−	0.260976i
$766$		−	1.40328i		−	0.0507026i
$767$	44.3308	+	10.1182i	1.60069	+	0.365348i
$768$	1.67563	−	0.438472i	0.0604642	−	0.0158220i
$769$	22.4353	−	17.8916i	0.809038	−	0.645186i	−0.129029	−	0.991641i	$-0.541186\pi$
$769$	22.4353	−	17.8916i	0.809038	−	0.645186i	0.938067	+	0.346454i	$0.112614\pi$
$770$	5.55454	+	21.4967i	0.200172	+	0.774686i
$771$	−31.5615	+	26.8404i	−1.13666	+	0.966635i
$772$	2.27648	−	9.97393i	0.0819325	−	0.358970i
$773$	−28.2228	+	35.3903i	−1.01511	+	1.27290i	−0.0534701	+	0.998569i	$0.517028\pi$
$773$	−28.2228	+	35.3903i	−1.01511	+	1.27290i	−0.961635	+	0.274332i	$0.911543\pi$
$774$	−0.483136	−	7.64954i	−0.0173660	−	0.274957i
$775$	7.96383	−	6.35094i	0.286069	−	0.228133i
$776$	−13.1092	−	6.31308i	−0.470595	−	0.226626i
$777$	5.98652	−	14.6136i	0.214765	−	0.524260i
$778$	19.1669	−	9.23029i	0.687167	−	0.330922i
$779$	−1.28681	+	2.67208i	−0.0461047	+	0.0957373i
$780$	−11.2565	+	0.355121i	−0.403049	+	0.0127154i
$781$	6.33632	+	3.05141i	0.226731	+	0.109188i
$782$	19.8339	−	24.8710i	0.709260	−	0.889384i
$783$	14.6475	−	22.4259i	0.523458	−	0.801437i
$784$	−1.16688	+	6.90206i	−0.0416742	+	0.246502i
$785$		−	2.40543i		−	0.0858535i
$786$	−7.05927	−	8.30096i	−0.251796	−	0.296085i
$787$	−0.198716	+	0.412637i	−0.00708345	+	0.0147089i	−0.904481	−	0.426515i	$-0.859741\pi$
$787$	−0.198716	+	0.412637i	−0.00708345	+	0.0147089i	0.897397	+	0.441224i	$0.145455\pi$
$788$	4.13581	−	0.943972i	0.147332	−	0.0336276i
$789$	−3.64327	+	4.87636i	−0.129704	+	0.173603i
$790$	9.03586	+	18.7632i	0.321481	+	0.667563i
$791$	5.25355	−	11.7535i	0.186795	−	0.417905i
$792$	−12.2278	−	13.4924i	−0.434498	−	0.479430i
$793$	−20.7655	−	26.0391i	−0.737404	−	0.924675i
$794$	9.37081	−	4.51275i	0.332558	−	0.160151i
$795$	−12.7867	−	15.0358i	−0.453496	−	0.533264i
$796$	−18.8238	−	4.29641i	−0.667192	−	0.152282i
$797$	8.30571	−	10.4150i	0.294203	−	0.368919i	−0.612658	−	0.790348i	$-0.709900\pi$
$797$	8.30571	−	10.4150i	0.294203	−	0.368919i	0.906862	+	0.421429i	$0.138471\pi$
$798$	−2.82888	+	2.54795i	−0.100141	+	0.0901963i
$799$	7.77949	+	9.75517i	0.275219	+	0.345113i
$800$	−1.34002	−	2.78259i	−0.0473770	−	0.0983793i
$801$	−15.8437	+	22.6629i	−0.559809	+	0.800754i
$802$	−28.9339			−1.02169
$803$	82.5118			2.91178
$804$	6.72200	−	15.1638i	0.237067	−	0.534787i
$805$	24.3571	−	6.29365i	0.858476	−	0.221822i
$806$	15.1220	−	3.45149i	0.532649	−	0.121574i
$807$	0.350314	+	11.1042i	0.0123316	+	0.390885i
$808$	−8.08881	+	6.45061i	−0.284563	+	0.226932i
$809$	−7.87011	+	6.27621i	−0.276698	+	0.220660i	−0.752000	−	0.659163i	$-0.770911\pi$
$809$	−7.87011	+	6.27621i	−0.276698	+	0.220660i	0.475301	+	0.879823i	$0.342339\pi$
$810$	10.6274	+	6.47263i	0.373409	+	0.227425i
$811$	7.95750	−	1.81625i	0.279426	−	0.0637771i	−0.0805113	−	0.996754i	$-0.525655\pi$
$811$	7.95750	−	1.81625i	0.279426	−	0.0637771i	0.359937	+	0.932977i	$0.382798\pi$
$812$	−6.26483	−	12.1146i	−0.219853	−	0.425138i
$813$	−1.85471	−	0.822177i	−0.0650475	−	0.0288350i
$814$	20.9169			0.733137
$815$	25.1872			0.882271
$816$	3.24679	−	7.32428i	0.113660	−	0.256401i
$817$	−0.920969	−	1.91241i	−0.0322206	−	0.0669069i
$818$	−17.5531	−	22.0109i	−0.613730	−	0.769593i
$819$	3.41208	+	37.1719i	0.119228	+	1.29889i
$820$	3.07730	−	3.85882i	0.107464	−	0.134756i
$821$	−33.4681	−	7.63887i	−1.16804	−	0.266598i	−0.405845	−	0.913942i	$-0.633023\pi$
$821$	−33.4681	−	7.63887i	−1.16804	−	0.266598i	−0.762198	+	0.647344i	$0.775880\pi$
$822$	29.4700	−	25.0618i	1.02788	−	0.874130i
$823$	−25.1416	+	12.1075i	−0.876380	+	0.422042i	−0.817301	−	0.576211i	$-0.804531\pi$
$823$	−25.1416	+	12.1075i	−0.876380	+	0.422042i	−0.0590788	+	0.998253i	$0.518816\pi$
$824$	−7.50456	−	9.41042i	−0.261434	−	0.327827i
$825$	−19.4333	+	26.0106i	−0.676579	+	0.905573i
$826$	−24.7675	+	6.39968i	−0.861771	+	0.222673i
$827$	21.0682	+	43.7485i	0.732612	+	1.52128i	0.849181	+	0.528101i	$0.177096\pi$
$827$	21.0682	+	43.7485i	0.732612	+	1.52128i	−0.116570	+	0.993182i	$0.537190\pi$
$828$	−15.2877	+	13.8550i	−0.531285	+	0.481493i
$829$	−7.49540	+	1.71078i	−0.260326	+	0.0594177i	−0.350692	−	0.936491i	$-0.614054\pi$
$829$	−7.49540	+	1.71078i	−0.260326	+	0.0594177i	0.0903658	+	0.995909i	$0.471196\pi$
$830$	−2.35684	+	4.89403i	−0.0818072	+	0.169874i
$831$	−32.8432	+	27.9304i	−1.13932	+	0.968896i
$832$		−	4.70290i		−	0.163044i
$833$	21.5953	+	24.1252i	0.748232	+	0.835890i
$834$	1.35946	+	0.265487i	0.0470741	+	0.00919307i
$835$	−7.24639	+	9.08669i	−0.250772	+	0.314458i
$836$	−4.54324	−	2.18791i	−0.157131	−	0.0756704i
$837$	−16.0739	−	5.94381i	−0.555596	−	0.205448i
$838$	7.42020	−	15.4082i	0.256327	−	0.532268i
$839$	19.1269	−	9.21104i	0.660334	−	0.318000i	−0.0735333	−	0.997293i	$-0.523428\pi$
$839$	19.1269	−	9.21104i	0.660334	−	0.318000i	0.733868	+	0.679293i	$0.237713\pi$
$840$	5.53328	−	3.08636i	0.190916	−	0.106489i
$841$	−2.18669	−	1.05305i	−0.0754031	−	0.0363122i
$842$	−29.7615	+	23.7340i	−1.02565	+	0.817929i
$843$	6.66896	+	25.4856i	0.229691	+	0.877771i
$844$	−4.39127	+	5.50648i	−0.151154	+	0.189541i
$845$	−2.80499	+	12.2894i	−0.0964944	+	0.422770i
$846$	−3.96379	−	7.05524i	−0.136278	−	0.242564i
$847$	44.1302	+	52.2171i	1.51633	+	1.79420i
$848$	6.44396	−	5.13889i	0.221287	−	0.176470i
$849$	−6.37831	−	24.3749i	−0.218903	−	0.836544i
$850$	−13.9275	−	3.17886i	−0.477710	−	0.109034i
$851$		−	23.7002i		−	0.812433i
$852$	0.384659	−	1.96969i	0.0131782	−	0.0674805i
$853$	37.7925	+	8.62589i	1.29399	+	0.295345i	0.813454	−	0.581630i	$-0.197585\pi$
$853$	37.7925	+	8.62589i	1.29399	+	0.295345i	0.480537	+	0.876975i	$0.340442\pi$
$854$	17.1058	+	7.64592i	0.585348	+	0.261638i
$855$	3.40121	+	0.553507i	0.116319	+	0.0189296i
$856$	−0.462856	−	2.02791i	−0.0158201	−	0.0693124i
$857$	23.4390	+	29.3916i	0.800662	+	1.00400i	0.999712	+	0.0240095i	$0.00764318\pi$
$857$	23.4390	+	29.3916i	0.800662	+	1.00400i	−0.199049	+	0.979989i	$0.563785\pi$
$858$	−43.8464	+	22.8457i	−1.49689	+	0.779938i
$859$	42.7070	−	9.74760i	1.45714	−	0.332584i	0.580712	−	0.814109i	$-0.302774\pi$
$859$	42.7070	−	9.74760i	1.45714	−	0.332584i	0.876432	+	0.481525i	$0.159917\pi$
$860$	0.786038	+	3.44386i	0.0268037	+	0.117434i
$861$	−13.3785	−	9.41440i	−0.455940	−	0.320842i
$862$	0.852787	−	3.73630i	0.0290460	−	0.127259i
$863$		−	4.69971i		−	0.159980i	−0.996796	−	0.0799900i	$-0.974511\pi$
$863$		−	4.69971i		−	0.159980i	0.996796	−	0.0799900i	$-0.0254888\pi$
$864$	−2.84147	+	4.35041i	−0.0966686	+	0.148004i
$865$	1.50826	−	6.60811i	0.0512823	−	0.224682i
$866$	−14.9492	+	7.19915i	−0.507994	+	0.244637i
$867$	−3.51796	−	6.75182i	−0.119476	−	0.229304i
$868$	−6.66474	+	5.63256i	−0.226216	+	0.191181i
$869$	71.4789	+	57.0025i	2.42475	+	1.93368i
$870$	−5.00272	+	11.2854i	−0.169608	+	0.382611i
$871$	−35.2115	−	28.0803i	−1.19310	−	0.951463i
$872$	−6.97970	−	14.4935i	−0.236362	−	0.490812i
$873$	41.8592	−	12.3763i	1.41672	−	0.418874i
$874$	−2.47904	+	5.14779i	−0.0838549	+	0.174127i
$875$	−19.0983	−	22.5981i	−0.645640	−	0.763955i
$876$	−5.96068	−	22.7789i	−0.201393	−	0.769627i
$877$	−1.72902	−	0.832654i	−0.0583850	−	0.0281167i	0.404463	−	0.914554i	$-0.367458\pi$
$877$	−1.72902	−	0.832654i	−0.0583850	−	0.0281167i	−0.462848	+	0.886437i	$0.653173\pi$
$878$	−3.56031	−	15.5987i	−0.120155	−	0.526432i
$879$	5.67983	+	4.24357i	0.191576	+	0.143132i
$880$	6.56100	+	5.23222i	0.221171	+	0.176378i
$881$	−55.9337			−1.88445			−0.942227	−	0.334974i	$-0.891272\pi$
$881$	−55.9337			−1.88445			−0.942227	+	0.334974i	$0.891272\pi$
$882$	−11.3110	−	17.6936i	−0.380860	−	0.595773i
$883$	53.7876			1.81010			0.905048	−	0.425309i	$-0.139834\pi$
$883$	53.7876			1.81010			0.905048	+	0.425309i	$0.139834\pi$
$884$	−17.0075	−	13.5630i	−0.572025	−	0.456175i
$885$	18.5486	+	13.8582i	0.623503	+	0.465837i
$886$	2.52683	+	11.0708i	0.0848907	+	0.371930i
$887$	−36.2732	−	17.4683i	−1.21794	−	0.586527i	−0.289200	−	0.957269i	$-0.593389\pi$
$887$	−36.2732	−	17.4683i	−1.21794	−	0.586527i	−0.928736	+	0.370741i	$0.879104\pi$
$888$	−1.51104	−	5.77449i	−0.0507073	−	0.193779i
$889$	3.98495	+	15.4222i	0.133651	+	0.517244i
$890$	5.52932	−	11.4817i	0.185343	−	0.384869i
$891$	54.3633	+	5.35840i	1.82124	+	0.179513i
$892$	6.94077	+	14.4127i	0.232394	+	0.482572i
$893$	−1.75213	−	1.39728i	−0.0586328	−	0.0467581i
$894$	8.40869	−	18.9687i	0.281229	−	0.634410i
$895$	−6.37224	−	5.08169i	−0.213001	−	0.169862i
$896$	1.21532	+	2.35011i	0.0406009	+	0.0785116i
$897$	25.8856	+	49.6809i	0.864296	+	1.65880i
$898$	11.8593	−	5.71113i	0.395750	−	0.190583i
$899$	3.78321	−	16.5753i	0.126177	−	0.552818i
$900$	8.58456	+	3.48589i	0.286152	+	0.116196i
$901$		−	38.1243i		−	1.27010i
$902$	4.82148	−	21.1243i	0.160538	−	0.703361i
$903$	11.2378	−	3.28506i	0.373972	−	0.109320i
$904$	−1.08278	−	4.74397i	−0.0360128	−	0.157782i
$905$	−11.1840	+	2.55267i	−0.371768	+	0.0848537i
$906$	−0.123007	+	0.0640913i	−0.00408663	+	0.00212929i
$907$	−6.55727	−	8.22255i	−0.217730	−	0.273025i	0.660956	−	0.750425i	$-0.270151\pi$
$907$	−6.55727	−	8.22255i	−0.217730	−	0.273025i	−0.878686	+	0.477399i	$0.841580\pi$
$908$	1.86759	+	8.18246i	0.0619782	+	0.271544i
$909$	4.98549	−	30.6349i	0.165358	−	1.01610i
$910$	−4.30379	−	16.6561i	−0.142669	−	0.552146i
$911$	−24.7524	−	5.64956i	−0.820082	−	0.187178i	−0.208158	−	0.978095i	$-0.566747\pi$
$911$	−24.7524	−	5.64956i	−0.820082	−	0.187178i	−0.611924	+	0.790917i	$0.709604\pi$
$912$	−0.275807	+	1.41230i	−0.00913288	+	0.0467659i
$913$			23.8465i			0.789206i
$914$	−6.03753	−	1.37803i	−0.199704	−	0.0455811i
$915$	−4.29322	−	16.4066i	−0.141929	−	0.542386i
$916$	−20.7009	+	16.5084i	−0.683977	+	0.545454i
$917$	10.0035	−	13.3037i	0.330345	−	0.439326i
$918$	7.53806	+	22.8223i	0.248793	+	0.753249i
$919$	−10.9651	+	48.0411i	−0.361704	+	1.58473i	0.387164	+	0.922011i	$0.373455\pi$
$919$	−10.9651	+	48.0411i	−0.361704	+	1.58473i	−0.748868	+	0.662719i	$0.769402\pi$
$920$	5.92845	−	7.43404i	0.195455	−	0.245093i
$921$	−3.03590	−	11.6018i	−0.100036	−	0.382291i
$922$	−21.1180	+	16.8411i	−0.695485	+	0.554631i
$923$	−4.90954	−	2.36431i	−0.161599	−	0.0778221i
$924$	16.0069	−	22.7470i	0.526590	−	0.748322i
$925$	−9.58923	+	4.61793i	−0.315292	+	0.151837i
$926$	6.20181	−	12.8782i	0.203804	−	0.423204i
$927$	35.6403	+	5.80005i	1.17058	+	0.190499i
$928$	−4.64440	−	2.23663i	−0.152460	−	0.0734208i
$929$	−23.2979	+	29.2147i	−0.764380	+	0.958503i	−0.999911	−	0.0133644i	$-0.995746\pi$
$929$	−23.2979	+	29.2147i	−0.764380	+	0.958503i	0.235530	+	0.971867i	$0.424317\pi$
$930$	7.75170	+	1.51382i	0.254188	+	0.0496403i
$931$	−4.74571	−	3.36140i	−0.155534	−	0.110166i
$932$			8.94058i			0.292858i
$933$	18.4250	−	15.6690i	0.603208	−	0.512979i
$934$	1.61407	−	3.35165i	0.0528140	−	0.109669i
$935$	37.8435	−	8.63753i	1.23761	−	0.282477i
$936$	9.47444	+	10.4542i	0.309682	+	0.341707i
$937$	3.68446	+	7.65087i	0.120366	+	0.249943i	0.952443	−	0.304718i	$-0.0985622\pi$
$937$	3.68446	+	7.65087i	0.120366	+	0.249943i	−0.832076	+	0.554661i	$0.812848\pi$
$938$	24.8522	+	4.93280i	0.811452	+	0.161062i
$939$	−17.6436	+	23.6153i	−0.575779	+	0.770655i
$940$	2.32532	+	2.91586i	0.0758437	+	0.0951050i
$941$	37.4120	−	18.0167i	1.21960	−	0.587326i	0.290397	−	0.956906i	$-0.406213\pi$
$941$	37.4120	−	18.0167i	1.21960	−	0.587326i	0.929199	+	0.369580i	$0.120498\pi$
$942$	−2.29557	+	1.95219i	−0.0747937	+	0.0636058i
$943$	−23.9352	−	5.46305i	−0.779437	−	0.177901i
$944$	−6.02832	+	7.55928i	−0.196205	+	0.246034i
$945$	−6.08233	+	18.0081i	−0.197858	+	0.585802i
$946$	9.66875	+	12.1242i	0.314358	+	0.394193i
$947$	−20.1529	−	41.8480i	−0.654882	−	1.35988i	−0.918566	−	0.395268i	$-0.870652\pi$
$947$	−20.1529	−	41.8480i	−0.654882	−	1.35988i	0.263684	−	0.964609i	$-0.415062\pi$
$948$	10.5729	−	23.8509i	0.343392	−	0.774641i
$949$	−63.9322			−2.07533
$950$	2.56586			0.0832474
$951$	−10.8164	−	4.79482i	−0.350746	−	0.155483i
$952$	12.0038	+	2.38259i	0.389047	+	0.0772202i
$953$	26.9086	−	6.14171i	0.871655	−	0.198950i	0.236779	−	0.971564i	$-0.423908\pi$
$953$	26.9086	−	6.14171i	0.871655	−	0.198950i	0.634876	+	0.772614i	$0.281051\pi$
$954$	−3.97169	+	24.4053i	−0.128588	+	0.790152i
$955$	−11.1461	+	8.88873i	−0.360680	+	0.287633i
$956$	−8.63992	+	6.89011i	−0.279435	+	0.222842i
$957$	1.70883	+	54.1660i	0.0552386	+	1.75094i
$958$	18.0559	−	4.12115i	0.583360	−	0.133148i
$959$	47.2306	+	35.5143i	1.52516	+	1.14682i
$960$	0.970480	−	2.18926i	0.0313221	−	0.0706580i
$961$	20.1222			0.649104
$962$	−16.2069			−0.522533
$963$	5.11431	+	3.57542i	0.164806	+	0.115216i
$964$	−3.37479	−	7.00783i	−0.108695	−	0.225707i
$965$	−8.81896	−	11.0586i	−0.283892	−	0.355990i
$966$	−25.7739	−	18.1369i	−0.829261	−	0.583545i
$967$	−12.4216	+	15.5762i	−0.399453	+	0.500898i	−0.940358	−	0.340185i	$-0.889510\pi$
$967$	−12.4216	+	15.5762i	−0.399453	+	0.500898i	0.540906	+	0.841083i	$0.318082\pi$
$968$	25.1926	+	5.75004i	0.809720	+	0.184813i
$969$	4.31200	+	5.07046i	0.138521	+	0.162887i
$970$	−18.1247	+	8.72842i	−0.581950	+	0.280253i
$971$	15.5220	+	19.4639i	0.498123	+	0.624627i	0.965805	−	0.259270i	$-0.0834820\pi$
$971$	15.5220	+	19.4639i	0.498123	+	0.624627i	−0.467681	+	0.883897i	$0.654911\pi$
$972$	−2.44793	−	15.3951i	−0.0785175	−	0.493797i
$973$	0.0602094	+	2.11497i	0.00193023	+	0.0678030i
$974$	−4.33317	−	8.99791i	−0.138844	−	0.288312i
$975$	15.0574	−	20.1537i	0.482222	−	0.645434i
$976$	6.90429	−	1.57586i	0.221001	−	0.0504420i
$977$	3.71165	−	7.70733i	0.118746	−	0.246579i	−0.833120	−	0.553092i	$-0.813448\pi$
$977$	3.71165	−	7.70733i	0.118746	−	0.246579i	0.951867	+	0.306513i	$0.0991621\pi$
$978$	−20.4414	−	24.0369i	−0.653643	−	0.768615i
$979$		−	55.9457i		−	1.78803i
$980$	6.45492	+	7.21114i	0.206195	+	0.230351i
$981$	44.7139	+	18.1567i	1.42760	+	0.579700i
$982$	−10.3124	+	12.9313i	−0.329081	+	0.412654i
$983$	27.5426	+	13.2638i	0.878471	+	0.423050i	0.818066	−	0.575124i	$-0.195046\pi$
$983$	27.5426	+	13.2638i	0.878471	+	0.423050i	0.0604054	+	0.998174i	$0.480761\pi$
$984$	−6.18004	+	0.194968i	−0.197013	+	0.00621535i
$985$	2.54481	−	5.28435i	0.0810844	−	0.168374i
$986$	−21.4828	+	10.3456i	−0.684153	+	0.329471i
$987$	9.18504	−	8.27288i	0.292363	−	0.263329i
$988$	3.52022	+	1.69525i	0.111993	+	0.0539330i
$989$	13.7375	−	10.9553i	0.436828	−	0.348359i
$990$	−25.1254	+	1.58689i	−0.798538	+	0.0504348i
$991$	19.8869	−	24.9374i	0.631729	−	0.792163i	−0.358212	−	0.933640i	$-0.616614\pi$
$991$	19.8869	−	24.9374i	0.631729	−	0.792163i	0.989942	+	0.141477i	$0.0451851\pi$
$992$	−0.733907	+	3.21545i	−0.0233016	+	0.102091i
$993$	4.62873	−	3.93635i	0.146888	−	0.124916i
$994$	3.06435	−	0.0872363i	0.0971952	−	0.00276697i
$995$	−20.8710	+	16.6440i	−0.661654	+	0.527651i
$996$	6.58327	−	1.72268i	0.208599	−	0.0545853i
$997$	19.8963	+	4.54121i	0.630123	+	0.143822i	0.525643	−	0.850705i	$-0.323825\pi$
$997$	19.8963	+	4.54121i	0.630123	+	0.143822i	0.104481	+	0.994527i	$0.466682\pi$
$998$			27.6621i			0.875628i
$999$	14.9922	+	9.79214i	0.474332	+	0.309809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.9	yes	120
3.2	odd	2	inner	294.2.j.a.251.12	yes	120
49.41	odd	14	inner	294.2.j.a.41.12	yes	120
147.41	even	14	inner	294.2.j.a.41.9	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.9	✓	120	147.41	even	14	inner
294.2.j.a.41.12	yes	120	49.41	odd	14	inner
294.2.j.a.251.9	yes	120	1.1	even	1	trivial
294.2.j.a.251.12	yes	120	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.781831 - 0.623490i) q^{2} +(1.38755 + 1.03668i) q^{3} +(0.222521 + 0.974928i) q^{4} +(1.24567 + 0.599884i) q^{5} +(-0.438472 - 1.67563i) q^{6} +(2.35011 - 1.21532i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.850594 + 2.87689i) q^{9} +(-0.599884 - 1.24567i) q^{10} +(-4.74543 - 3.78435i) q^{11} +(-0.701928 + 1.58344i) q^{12} +(3.67688 + 2.93221i) q^{13} +(-2.59513 - 0.515095i) q^{14} +(1.10655 + 2.12373i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.02928 + 4.50956i) q^{17} +(1.12869 - 2.77958i) q^{18} -0.830794i q^{19} +(-0.307656 + 1.34793i) q^{20} +(4.52079 + 0.749993i) q^{21} +(1.35062 + 5.91746i) q^{22} +(6.70486 - 1.53034i) q^{23} +(1.53605 - 0.800342i) q^{24} +(-1.92561 - 2.41464i) q^{25} +(-1.04649 - 4.58499i) q^{26} +(-1.80217 + 4.87362i) q^{27} +(1.70779 + 2.02075i) q^{28} +(-5.02565 - 1.14707i) q^{29} +(0.458992 - 2.35032i) q^{30} +3.29815i q^{31} +(0.974928 + 0.222521i) q^{32} +(-2.66137 - 10.1705i) q^{33} +(3.61639 - 2.88397i) q^{34} +(3.65651 - 0.104094i) q^{35} +(-2.61548 + 1.46944i) q^{36} +(0.766842 - 3.35975i) q^{37} +(-0.517992 + 0.649541i) q^{38} +(2.06209 + 7.88033i) q^{39} +(1.08095 - 0.862032i) q^{40} +(-3.21630 - 1.54889i) q^{41} +(-3.06688 - 3.40503i) q^{42} +(2.30191 - 1.10854i) q^{43} +(2.63352 - 5.46855i) q^{44} +(-0.666239 + 4.09392i) q^{45} +(-6.19623 - 2.98395i) q^{46} +(1.68186 - 2.10898i) q^{47} +(-1.69994 - 0.331980i) q^{48} +(4.04601 - 5.71225i) q^{49} +3.08844i q^{50} +(-6.10314 + 5.19022i) q^{51} +(-2.04051 + 4.23717i) q^{52} +(-8.03549 + 1.83405i) q^{53} +(4.44764 - 2.68672i) q^{54} +(-3.64108 - 7.56078i) q^{55} +(-0.0752892 - 2.64468i) q^{56} +(0.861267 - 1.15277i) q^{57} +(3.21403 + 4.03026i) q^{58} +(8.71118 - 4.19508i) q^{59} +(-1.82426 + 1.55138i) q^{60} +(-6.90429 - 1.57586i) q^{61} +(2.05636 - 2.57859i) q^{62} +(5.49532 + 5.72726i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(2.82120 + 5.85828i) q^{65} +(-4.26045 + 9.61093i) q^{66} -9.57648 q^{67} -4.62553 q^{68} +(10.8898 + 4.82736i) q^{69} +(-2.92368 - 2.19841i) q^{70} +(-1.12963 + 0.257831i) q^{71} +(2.96105 + 0.481877i) q^{72} +(-10.6284 + 8.47585i) q^{73} +(-2.69431 + 2.14864i) q^{74} +(-0.168677 - 5.34667i) q^{75} +(0.809965 - 0.184869i) q^{76} +(-15.7515 - 3.12644i) q^{77} +(3.30110 - 7.44678i) q^{78} -15.0627 q^{79} -1.38259 q^{80} +(-7.55298 + 4.89413i) q^{81} +(1.54889 + 3.21630i) q^{82} +(-2.44958 - 3.07168i) q^{83} +(0.274781 + 4.57433i) q^{84} +(-3.98736 + 4.99999i) q^{85} +(-2.49087 - 0.568525i) q^{86} +(-5.78420 - 6.80161i) q^{87} +(-5.46855 + 2.63352i) q^{88} +(5.74690 + 7.20638i) q^{89} +(3.07340 - 2.78536i) q^{90} +(12.2046 + 2.42244i) q^{91} +(2.98395 + 6.19623i) q^{92} +(-3.41912 + 4.57635i) q^{93} +(-2.62986 + 0.600248i) q^{94} +(0.498380 - 1.03490i) q^{95} +(1.12208 + 1.31945i) q^{96} -14.5502i q^{97} +(-6.72483 + 1.94337i) q^{98} +(6.85073 - 16.8710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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