LMFDB - Embedded newform 250.2.d.c.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [250,2,Mod(51,250)] 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("250.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(250, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	250.101
Dual form			250.2.d.c.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.34786 - 1.70582i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.34786 - 1.70582i) q^{6} -1.07768 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.67557 + 5.15688i) q^{9} +(-0.638757 + 1.96589i) q^{11} +(0.896802 + 2.76007i) q^{12} +(1.79032 + 5.51005i) q^{13} +(0.333023 - 1.02494i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.666977 + 0.484587i) q^{17} -5.42226 q^{18} +(-2.76007 + 2.00531i) q^{19} +(2.53025 + 1.83833i) q^{21} +(-1.67229 - 1.21499i) q^{22} +(-0.606480 + 1.86655i) q^{23} -2.90211 q^{24} -5.79360 q^{26} +(2.17229 - 6.68562i) q^{27} +(0.871864 + 0.633446i) q^{28} +(0.847859 + 0.616005i) q^{29} +(-1.71113 + 1.24321i) q^{31} -1.00000 q^{32} +(4.85317 - 3.52603i) q^{33} +(-0.254763 - 0.784079i) q^{34} +(1.67557 - 5.15688i) q^{36} +(2.68712 + 8.27012i) q^{37} +(-1.05425 - 3.24466i) q^{38} +(5.19572 - 15.9908i) q^{39} +(-2.03150 - 6.25232i) q^{41} +(-2.53025 + 1.83833i) q^{42} +7.47684 q^{43} +(1.67229 - 1.21499i) q^{44} +(-1.58779 - 1.15359i) q^{46} +(-6.99942 - 5.08538i) q^{47} +(0.896802 - 2.76007i) q^{48} -5.83860 q^{49} +2.39259 q^{51} +(1.79032 - 5.51005i) q^{52} +(-2.07768 - 1.50953i) q^{53} +(5.68712 + 4.13194i) q^{54} +(-0.871864 + 0.633446i) q^{56} +9.90096 q^{57} +(-0.847859 + 0.616005i) q^{58} +(1.45309 + 4.47214i) q^{59} +(-2.86858 + 8.82859i) q^{61} +(-0.653594 - 2.01155i) q^{62} +(-1.80573 - 5.55748i) q^{63} +(0.309017 - 0.951057i) q^{64} +(1.85375 + 5.70524i) q^{66} +(3.52874 - 2.56378i) q^{67} +0.824429 q^{68} +(4.60793 - 3.34786i) q^{69} +(-3.96740 - 2.88249i) q^{71} +(4.38670 + 3.18712i) q^{72} +(0.401017 - 1.23420i) q^{73} -8.69572 q^{74} +3.41164 q^{76} +(0.688378 - 2.11861i) q^{77} +(13.6026 + 9.88284i) q^{78} +(5.82141 + 4.22950i) q^{79} +(-3.34458 + 2.42998i) q^{81} +6.57408 q^{82} +(-12.1094 + 8.79798i) q^{83} +(-0.966469 - 2.97449i) q^{84} +(-2.31047 + 7.11089i) q^{86} +(-0.939859 - 2.89259i) q^{87} +(0.638757 + 1.96589i) q^{88} +(-3.61803 + 11.1352i) q^{89} +(-1.92940 - 5.93809i) q^{91} +(1.58779 - 1.15359i) q^{92} +6.13818 q^{93} +(6.99942 - 5.08538i) q^{94} +(2.34786 + 1.70582i) q^{96} +(-0.413147 - 0.300169i) q^{97} +(1.80423 - 5.55284i) q^{98} -11.2081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} + 2 q^{8} + 4 q^{9} - 4 q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} - 4 q^{18} - 10 q^{19} + 16 q^{21} - 6 q^{22} - 12 q^{23} - 8 q^{24}+ \cdots + 28 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 + 2 * q^8 + 4 * q^9 - 4 * q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^17 - 4 * q^18 - 10 * q^19 + 16 * q^21 - 6 * q^22 - 12 * q^23 - 8 * q^24 - 28 * q^26 + 10 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^31 - 8 * q^32 + 16 * q^33 + 4 * q^34 + 4 * q^36 - 4 * q^37 - 10 * q^38 + 8 * q^39 - 14 * q^41 - 16 * q^42 + 28 * q^43 + 6 * q^44 - 8 * q^46 - 24 * q^47 - 2 * q^48 + 16 * q^49 + 16 * q^51 - 2 * q^52 + 8 * q^53 + 20 * q^54 + 4 * q^56 + 10 * q^58 - 14 * q^61 + 14 * q^62 - 12 * q^63 - 2 * q^64 + 24 * q^66 - 4 * q^67 + 16 * q^68 + 8 * q^69 - 34 * q^71 + 6 * q^72 - 12 * q^73 - 36 * q^74 - 18 * q^77 + 22 * q^78 - 12 * q^81 + 24 * q^82 - 32 * q^83 - 14 * q^84 + 22 * q^86 + 20 * q^87 + 4 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 + 16 * q^93 + 24 * q^94 + 2 * q^96 - 4 * q^97 - 16 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−2.34786	−	1.70582i	−1.35554	−	0.984855i	−0.998715	−	0.0506828i	$-0.983860\pi$
$3$	−2.34786	−	1.70582i	−1.35554	−	0.984855i	−0.356822	−	0.934172i	$-0.616140\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	2.34786	−	1.70582i	0.958509	−	0.696398i
$7$	−1.07768			−0.407326			−0.203663	−	0.979041i	$-0.565285\pi$
$7$	−1.07768			−0.407326			−0.203663	+	0.979041i	$0.565285\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.67557	+	5.15688i	0.558524	+	1.71896i
$10$		0			0
$11$	−0.638757	+	1.96589i	−0.192593	+	0.592739i	0.807404	+	0.589999i	$0.200872\pi$
$11$	−0.638757	+	1.96589i	−0.192593	+	0.592739i	−0.999996	+	0.00273957i	$0.999128\pi$
$12$	0.896802	+	2.76007i	0.258885	+	0.796765i
$13$	1.79032	+	5.51005i	0.496546	+	1.52821i	0.814533	+	0.580117i	$0.196993\pi$
$13$	1.79032	+	5.51005i	0.496546	+	1.52821i	−0.317987	+	0.948095i	$0.603007\pi$
$14$	0.333023	−	1.02494i	0.0890040	−	0.273926i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.666977	+	0.484587i	−0.161766	+	0.117530i	−0.665723	−	0.746199i	$-0.731877\pi$
$17$	−0.666977	+	0.484587i	−0.161766	+	0.117530i	0.503957	+	0.863729i	$0.331877\pi$
$18$	−5.42226			−1.27804
$19$	−2.76007	+	2.00531i	−0.633204	+	0.460050i	−0.857509	−	0.514469i	$-0.827989\pi$
$19$	−2.76007	+	2.00531i	−0.633204	+	0.460050i	0.224305	+	0.974519i	$0.427989\pi$
$20$		0			0
$21$	2.53025	+	1.83833i	0.552146	+	0.401157i
$22$	−1.67229	−	1.21499i	−0.356533	−	0.259036i
$23$	−0.606480	+	1.86655i	−0.126460	+	0.389203i	−0.994164	−	0.107877i	$-0.965595\pi$
$23$	−0.606480	+	1.86655i	−0.126460	+	0.389203i	0.867704	+	0.497081i	$0.165595\pi$
$24$	−2.90211			−0.592391
$25$		0			0
$26$	−5.79360			−1.13622
$27$	2.17229	−	6.68562i	0.418057	−	1.28665i
$28$	0.871864	+	0.633446i	0.164767	+	0.119710i
$29$	0.847859	+	0.616005i	0.157443	+	0.114389i	0.663718	−	0.747983i	$-0.268978\pi$
$29$	0.847859	+	0.616005i	0.157443	+	0.114389i	−0.506274	+	0.862373i	$0.668978\pi$
$30$		0			0
$31$	−1.71113	+	1.24321i	−0.307328	+	0.223287i	−0.730749	−	0.682646i	$-0.760829\pi$
$31$	−1.71113	+	1.24321i	−0.307328	+	0.223287i	0.423421	+	0.905933i	$0.360829\pi$
$32$	−1.00000			−0.176777
$33$	4.85317	−	3.52603i	0.844828	−	0.613804i
$34$	−0.254763	−	0.784079i	−0.0436914	−	0.134468i
$35$		0			0
$36$	1.67557	−	5.15688i	0.279262	−	0.859479i
$37$	2.68712	+	8.27012i	0.441761	+	1.35960i	0.885998	+	0.463690i	$0.153475\pi$
$37$	2.68712	+	8.27012i	0.441761	+	1.35960i	−0.444237	+	0.895909i	$0.646525\pi$
$38$	−1.05425	−	3.24466i	−0.171023	−	0.526354i
$39$	5.19572	−	15.9908i	0.831981	−	2.56057i
$40$		0			0
$41$	−2.03150	−	6.25232i	−0.317267	−	0.976449i	−0.974811	−	0.223032i	$-0.928404\pi$
$41$	−2.03150	−	6.25232i	−0.317267	−	0.976449i	0.657544	−	0.753416i	$-0.271596\pi$
$42$	−2.53025	+	1.83833i	−0.390426	+	0.283661i
$43$	7.47684			1.14021			0.570103	−	0.821573i	$-0.306903\pi$
$43$	7.47684			1.14021			0.570103	+	0.821573i	$0.306903\pi$
$44$	1.67229	−	1.21499i	0.252107	−	0.183166i
$45$		0			0
$46$	−1.58779	−	1.15359i	−0.234106	−	0.170088i
$47$	−6.99942	−	5.08538i	−1.02097	−	0.741779i	−0.0544892	−	0.998514i	$-0.517353\pi$
$47$	−6.99942	−	5.08538i	−1.02097	−	0.741779i	−0.966482	+	0.256736i	$0.917353\pi$
$48$	0.896802	−	2.76007i	0.129442	−	0.398382i
$49$	−5.83860			−0.834085
$50$		0			0
$51$	2.39259			0.335029
$52$	1.79032	−	5.51005i	0.248273	−	0.764106i
$53$	−2.07768	−	1.50953i	−0.285392	−	0.207349i	0.435874	−	0.900008i	$-0.356439\pi$
$53$	−2.07768	−	1.50953i	−0.285392	−	0.207349i	−0.721266	+	0.692658i	$0.756439\pi$
$54$	5.68712	+	4.13194i	0.773920	+	0.562286i
$55$		0			0
$56$	−0.871864	+	0.633446i	−0.116508	+	0.0846478i
$57$	9.90096			1.31141
$58$	−0.847859	+	0.616005i	−0.111329	+	0.0808855i
$59$	1.45309	+	4.47214i	0.189176	+	0.582223i	0.999995	−	0.00307347i	$-0.000978319\pi$
$59$	1.45309	+	4.47214i	0.189176	+	0.582223i	−0.810820	+	0.585296i	$0.800978\pi$
$60$		0			0
$61$	−2.86858	+	8.82859i	−0.367284	+	1.13038i	0.581254	+	0.813722i	$0.302562\pi$
$61$	−2.86858	+	8.82859i	−0.367284	+	1.13038i	−0.948538	+	0.316663i	$0.897438\pi$
$62$	−0.653594	−	2.01155i	−0.0830065	−	0.255468i
$63$	−1.80573	−	5.55748i	−0.227501	−	0.700177i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$		0			0
$66$	1.85375	+	5.70524i	0.228180	+	0.702267i
$67$	3.52874	−	2.56378i	0.431104	−	0.313216i	−0.350986	−	0.936381i	$-0.614154\pi$
$67$	3.52874	−	2.56378i	0.431104	−	0.313216i	0.782090	+	0.623165i	$0.214154\pi$
$68$	0.824429			0.0999768
$69$	4.60793	−	3.34786i	0.554730	−	0.403035i
$70$		0			0
$71$	−3.96740	−	2.88249i	−0.470844	−	0.342088i	0.326926	−	0.945050i	$-0.393987\pi$
$71$	−3.96740	−	2.88249i	−0.470844	−	0.342088i	−0.797770	+	0.602962i	$0.793987\pi$
$72$	4.38670	+	3.18712i	0.516978	+	0.375606i
$73$	0.401017	−	1.23420i	0.0469355	−	0.144453i	−0.924842	−	0.380351i	$-0.875803\pi$
$73$	0.401017	−	1.23420i	0.0469355	−	0.144453i	0.971778	+	0.235898i	$0.0758032\pi$
$74$	−8.69572			−1.01086
$75$		0			0
$76$	3.41164			0.391342
$77$	0.688378	−	2.11861i	0.0784480	−	0.241438i
$78$	13.6026	+	9.88284i	1.54019	+	1.11901i
$79$	5.82141	+	4.22950i	0.654960	+	0.475856i	0.864957	−	0.501846i	$-0.167345\pi$
$79$	5.82141	+	4.22950i	0.654960	+	0.475856i	−0.209997	+	0.977702i	$0.567345\pi$
$80$		0			0
$81$	−3.34458	+	2.42998i	−0.371620	+	0.269997i
$82$	6.57408			0.725986
$83$	−12.1094	+	8.79798i	−1.32918	+	0.965704i	−0.329409	+	0.944187i	$0.606850\pi$
$83$	−12.1094	+	8.79798i	−1.32918	+	0.965704i	−0.999768	+	0.0215168i	$0.993150\pi$
$84$	−0.966469	−	2.97449i	−0.105450	−	0.324543i
$85$		0			0
$86$	−2.31047	+	7.11089i	−0.249144	+	0.766787i
$87$	−0.939859	−	2.89259i	−0.100763	−	0.310118i
$88$	0.638757	+	1.96589i	0.0680918	+	0.209565i
$89$	−3.61803	+	11.1352i	−0.383511	+	1.18032i	0.554044	+	0.832487i	$0.313084\pi$
$89$	−3.61803	+	11.1352i	−0.383511	+	1.18032i	−0.937555	+	0.347838i	$0.886916\pi$
$90$		0			0
$91$	−1.92940	−	5.93809i	−0.202256	−	0.622480i
$92$	1.58779	−	1.15359i	0.165538	−	0.120270i
$93$	6.13818			0.636500
$94$	6.99942	−	5.08538i	0.721935	−	0.524517i
$95$		0			0
$96$	2.34786	+	1.70582i	0.239627	+	0.174099i
$97$	−0.413147	−	0.300169i	−0.0419487	−	0.0304775i	0.566613	−	0.823984i	$-0.308253\pi$
$97$	−0.413147	−	0.300169i	−0.0419487	−	0.0304775i	−0.608562	+	0.793506i	$0.708253\pi$
$98$	1.80423	−	5.55284i	0.182254	−	0.560921i
$99$	−11.2081			−1.12646
$100$		0			0
$101$	−3.50766			−0.349025			−0.174513	−	0.984655i	$-0.555835\pi$
$101$	−3.50766			−0.349025			−0.174513	+	0.984655i	$0.555835\pi$
$102$	−0.739350	+	2.27549i	−0.0732066	+	0.225307i
$103$	−3.75528	−	2.72837i	−0.370019	−	0.268835i	0.387200	−	0.921996i	$-0.373442\pi$
$103$	−3.75528	−	2.72837i	−0.370019	−	0.268835i	−0.757219	+	0.653161i	$0.773442\pi$
$104$	4.68712	+	3.40540i	0.459610	+	0.333926i
$105$		0			0
$106$	2.07768	−	1.50953i	0.201802	−	0.146618i
$107$	−7.60189			−0.734902			−0.367451	−	0.930043i	$-0.619769\pi$
$107$	−7.60189			−0.734902			−0.367451	+	0.930043i	$0.619769\pi$
$108$	−5.68712	+	4.13194i	−0.547244	+	0.397596i
$109$	−0.922836	−	2.84020i	−0.0883917	−	0.272042i	0.897084	−	0.441861i	$-0.145682\pi$
$109$	−0.922836	−	2.84020i	−0.0883917	−	0.272042i	−0.985475	+	0.169819i	$0.945682\pi$
$110$		0			0
$111$	7.79834	−	24.0008i	0.740186	−	2.27806i
$112$	−0.333023	−	1.02494i	−0.0314677	−	0.0968475i
$113$	−6.24170	−	19.2100i	−0.587170	−	1.80712i	−0.590377	−	0.807128i	$-0.701021\pi$
$113$	−6.24170	−	19.2100i	−0.587170	−	1.80712i	0.00320699	−	0.999995i	$-0.498979\pi$
$114$	−3.05957	+	9.41637i	−0.286555	+	0.881924i
$115$		0			0
$116$	−0.323853	−	0.996718i	−0.0300690	−	0.0925429i
$117$	−25.4148	+	18.4649i	−2.34960	+	1.70708i
$118$	−4.70228			−0.432880
$119$	0.718791	−	0.522232i	0.0658914	−	0.0478729i
$120$		0			0
$121$	5.44246	+	3.95418i	0.494769	+	0.359471i
$122$	−7.51005	−	5.45637i	−0.679928	−	0.493996i
$123$	−5.89565	+	18.1449i	−0.531593	+	1.63607i
$124$	2.11507			0.189939
$125$		0			0
$126$	5.84348			0.520579
$127$	−6.59783	+	20.3060i	−0.585463	+	1.80187i	0.0119411	+	0.999929i	$0.496199\pi$
$127$	−6.59783	+	20.3060i	−0.585463	+	1.80187i	−0.597404	+	0.801940i	$0.703801\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−17.5546	−	12.7541i	−1.54559	−	1.12294i
$130$		0			0
$131$	7.28730	−	5.29454i	0.636695	−	0.462586i	−0.222018	−	0.975042i	$-0.571264\pi$
$131$	7.28730	−	5.29454i	0.636695	−	0.462586i	0.858713	+	0.512457i	$0.171264\pi$
$132$	−5.99885			−0.522133
$133$	2.97449	−	2.16109i	0.257921	−	0.187390i
$134$	1.34786	+	4.14828i	0.116437	+	0.358357i
$135$		0			0
$136$	−0.254763	+	0.784079i	−0.0218457	+	0.0672342i
$137$	−1.38795	−	4.27168i	−0.118581	−	0.364955i	0.874096	−	0.485753i	$-0.161455\pi$
$137$	−1.38795	−	4.27168i	−0.118581	−	0.364955i	−0.992677	+	0.120798i	$0.961455\pi$
$138$	1.76007	+	5.41695i	0.149827	+	0.461121i
$139$	4.14204	−	12.7479i	0.351323	−	1.08126i	−0.606788	−	0.794864i	$-0.707542\pi$
$139$	4.14204	−	12.7479i	0.351323	−	1.08126i	0.958111	−	0.286398i	$-0.0924578\pi$
$140$		0			0
$141$	7.75892	+	23.8795i	0.653419	+	2.01102i
$142$	3.96740	−	2.88249i	0.332937	−	0.241893i
$143$	−11.9757			−1.00146
$144$	−4.38670	+	3.18712i	−0.365558	+	0.265594i
$145$		0			0
$146$	1.04988	+	0.762779i	0.0868883	+	0.0631281i
$147$	13.7082	+	9.95959i	1.13063	+	0.821453i
$148$	2.68712	−	8.27012i	0.220880	−	0.679800i
$149$	13.6139			1.11529			0.557646	−	0.830079i	$-0.311705\pi$
$149$	13.6139			1.11529			0.557646	+	0.830079i	$0.311705\pi$
$150$		0			0
$151$	8.79830			0.715996			0.357998	−	0.933722i	$-0.383459\pi$
$151$	8.79830			0.715996			0.357998	+	0.933722i	$0.383459\pi$
$152$	−1.05425	+	3.24466i	−0.0855113	+	0.263177i
$153$	−3.61653	−	2.62756i	−0.292379	−	0.212426i
$154$	1.80220	+	1.30937i	0.145225	+	0.105512i
$155$		0			0
$156$	−13.6026	+	9.88284i	−1.08908	+	0.791261i
$157$	11.8558			0.946195			0.473097	−	0.881010i	$-0.343136\pi$
$157$	11.8558			0.946195			0.473097	+	0.881010i	$0.343136\pi$
$158$	−5.82141	+	4.22950i	−0.463127	+	0.336481i
$159$	2.30313	+	7.08831i	0.182650	+	0.562139i
$160$		0			0
$161$	0.653594	−	2.01155i	0.0515104	−	0.158533i
$162$	−1.27751	−	3.93179i	−0.100371	−	0.308910i
$163$	4.62257	+	14.2268i	0.362068	+	1.11433i	0.951797	+	0.306729i	$0.0992344\pi$
$163$	4.62257	+	14.2268i	0.362068	+	1.11433i	−0.589729	+	0.807601i	$0.700766\pi$
$164$	−2.03150	+	6.25232i	−0.158634	+	0.488224i
$165$		0			0
$166$	−4.62537	−	14.2354i	−0.358999	−	1.10488i
$167$	17.4504	−	12.6785i	1.35035	−	0.981090i	0.351361	−	0.936240i	$-0.385719\pi$
$167$	17.4504	−	12.6785i	1.35035	−	0.981090i	0.998994	−	0.0448496i	$-0.0142809\pi$
$168$	3.12756			0.241296
$169$	−16.6381	+	12.0883i	−1.27986	+	0.929870i
$170$		0			0
$171$	−14.9658	−	10.8733i	−1.14447	−	0.831503i
$172$	−6.04889	−	4.39477i	−0.461223	−	0.335098i
$173$	−1.38602	+	4.26574i	−0.105377	+	0.324318i	−0.989819	−	0.142333i	$-0.954540\pi$
$173$	−1.38602	+	4.26574i	−0.105377	+	0.324318i	0.884441	+	0.466651i	$0.154540\pi$
$174$	3.04145			0.230571
$175$		0			0
$176$	−2.06706			−0.155811
$177$	4.21702	−	12.9786i	0.316970	−	0.975535i
$178$	−9.47214	−	6.88191i	−0.709967	−	0.515821i
$179$	12.2423	+	8.89456i	0.915033	+	0.664811i	0.942283	−	0.334818i	$-0.108675\pi$
$179$	12.2423	+	8.89456i	0.915033	+	0.664811i	−0.0272495	+	0.999629i	$0.508675\pi$
$180$		0			0
$181$	7.94542	−	5.77269i	0.590579	−	0.429081i	−0.251944	−	0.967742i	$-0.581070\pi$
$181$	7.94542	−	5.77269i	0.590579	−	0.429081i	0.842522	+	0.538661i	$0.181070\pi$
$182$	6.24367			0.462812
$183$	21.7950	−	15.8350i	1.61113	−	1.17056i
$184$	0.606480	+	1.86655i	0.0447103	+	0.137604i
$185$		0			0
$186$	−1.89680	+	5.83776i	−0.139080	+	0.428045i
$187$	−0.526610	−	1.62074i	−0.0385096	−	0.118520i
$188$	2.67354	+	8.22832i	0.194988	+	0.600112i
$189$	−2.34104	+	7.20498i	−0.170286	+	0.524085i
$190$		0			0
$191$	6.01130	+	18.5009i	0.434962	+	1.33868i	0.893125	+	0.449808i	$0.148508\pi$
$191$	6.01130	+	18.5009i	0.434962	+	1.33868i	−0.458163	+	0.888868i	$0.651492\pi$
$192$	−2.34786	+	1.70582i	−0.169442	+	0.123107i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	0.413147	−	0.300169i	0.0296622	−	0.0215509i
$195$		0			0
$196$	4.72353	+	3.43184i	0.337395	+	0.245132i
$197$	1.13818	+	0.826937i	0.0810920	+	0.0589168i	0.627593	−	0.778542i	$-0.284040\pi$
$197$	1.13818	+	0.826937i	0.0810920	+	0.0589168i	−0.546501	+	0.837459i	$0.684040\pi$
$198$	3.46351	−	10.6596i	0.246141	−	0.757543i
$199$	13.7199			0.972575			0.486288	−	0.873799i	$-0.338351\pi$
$199$	13.7199			0.972575			0.486288	+	0.873799i	$0.338351\pi$
$200$		0			0
$201$	−12.6583			−0.892850
$202$	1.08393	−	3.33598i	0.0762648	−	0.234719i
$203$	−0.913723	−	0.663859i	−0.0641308	−	0.0465938i
$204$	−1.93564	−	1.40633i	−0.135522	−	0.0984626i
$205$		0			0
$206$	3.75528	−	2.72837i	0.261643	−	0.190095i
$207$	−10.6418			−0.739655
$208$	−4.68712	+	3.40540i	−0.324994	+	0.236122i
$209$	−2.17921	−	6.70692i	−0.150739	−	0.463927i
$210$		0			0
$211$	−5.18484	+	15.9573i	−0.356939	+	1.09855i	0.597937	+	0.801543i	$0.295987\pi$
$211$	−5.18484	+	15.9573i	−0.356939	+	1.09855i	−0.954877	+	0.297003i	$0.904013\pi$
$212$	0.793604	+	2.44246i	0.0545050	+	0.167749i
$213$	4.39790	+	13.5353i	0.301339	+	0.927426i
$214$	2.34911	−	7.22982i	0.160582	−	0.494221i
$215$		0			0
$216$	−2.17229	−	6.68562i	−0.147805	−	0.454899i
$217$	1.84406	−	1.33979i	0.125183	−	0.0909506i
$218$	2.98636			0.202262
$219$	−3.04686	+	2.21367i	−0.205888	+	0.149586i
$220$		0			0
$221$	−3.86420	−	2.80751i	−0.259934	−	0.188853i
$222$	20.4163	+	14.8333i	1.37025	+	0.995547i
$223$	3.61054	−	11.1121i	0.241779	−	0.744121i	−0.754370	−	0.656449i	$-0.772058\pi$
$223$	3.61054	−	11.1121i	0.241779	−	0.744121i	0.996149	−	0.0876712i	$-0.0279425\pi$
$224$	1.07768			0.0720058
$225$		0			0
$226$	20.1986			1.34359
$227$	0.220299	−	0.678012i	0.0146218	−	0.0450012i	−0.943479	−	0.331431i	$-0.892469\pi$
$227$	0.220299	−	0.678012i	0.0146218	−	0.0450012i	0.958101	+	0.286430i	$0.0924686\pi$
$228$	−8.01005	−	5.81964i	−0.530478	−	0.385415i
$229$	−16.5176	−	12.0008i	−1.09152	−	0.793034i	−0.111862	−	0.993724i	$-0.535682\pi$
$229$	−16.5176	−	12.0008i	−1.09152	−	0.793034i	−0.979655	+	0.200690i	$0.935682\pi$
$230$		0			0
$231$	−5.23018	+	3.79995i	−0.344121	+	0.250018i
$232$	1.04801			0.0688053
$233$	12.1679	−	8.84046i	0.797143	−	0.579158i	−0.112932	−	0.993603i	$-0.536024\pi$
$233$	12.1679	−	8.84046i	0.797143	−	0.579158i	0.910074	+	0.414445i	$0.136024\pi$
$234$	−9.70759	−	29.8769i	−0.634605	−	1.95311i
$235$		0			0
$236$	1.45309	−	4.47214i	0.0945878	−	0.291111i
$237$	−6.45309	−	19.8606i	−0.419173	−	1.29008i
$238$	0.274554	+	0.844989i	0.0177967	+	0.0547725i
$239$	1.29364	−	3.98141i	0.0836786	−	0.257536i	−0.900460	−	0.434940i	$-0.856770\pi$
$239$	1.29364	−	3.98141i	0.0836786	−	0.257536i	0.984138	+	0.177403i	$0.0567697\pi$
$240$		0			0
$241$	−9.09011	−	27.9765i	−0.585546	−	1.80212i	−0.597068	−	0.802191i	$-0.703668\pi$
$241$	−9.09011	−	27.9765i	−0.585546	−	1.80212i	0.0115222	−	0.999934i	$-0.496332\pi$
$242$	−5.44246	+	3.95418i	−0.349855	+	0.254184i
$243$	−9.09132			−0.583209
$244$	7.51005	−	5.45637i	0.480781	−	0.349308i
$245$		0			0
$246$	−15.4350	−	11.2142i	−0.984100	−	0.714991i
$247$	−15.9908	−	11.6180i	−1.01747	−	0.739234i
$248$	−0.653594	+	2.01155i	−0.0415032	+	0.127734i
$249$	43.4389			2.75283
$250$		0			0
$251$	−23.6695			−1.49400			−0.747002	−	0.664822i	$-0.768508\pi$
$251$	−23.6695			−1.49400			−0.747002	+	0.664822i	$0.768508\pi$
$252$	−1.80573	+	5.55748i	−0.113751	+	0.350088i
$253$	−3.28205	−	2.38455i	−0.206341	−	0.149915i
$254$	−17.2733	−	12.5498i	−1.08383	−	0.787446i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−4.34928			−0.271300			−0.135650	−	0.990757i	$-0.543312\pi$
$257$	−4.34928			−0.271300			−0.135650	+	0.990757i	$0.543312\pi$
$258$	17.5546	−	12.7541i	1.09290	−	0.794037i
$259$	−2.89587	−	8.91257i	−0.179941	−	0.553800i
$260$		0			0
$261$	−1.75602	+	5.40446i	−0.108695	+	0.334528i
$262$	2.78350	+	8.56674i	0.171965	+	0.529255i
$263$	0.697446	+	2.14652i	0.0430064	+	0.132360i	0.970254	−	0.242088i	$-0.0778322\pi$
$263$	0.697446	+	2.14652i	0.0430064	+	0.132360i	−0.927248	+	0.374448i	$0.877832\pi$
$264$	1.85375	−	5.70524i	0.114090	−	0.351133i
$265$		0			0
$266$	1.13615	+	3.49672i	0.0696620	+	0.214398i
$267$	27.4892	−	19.9721i	1.68231	−	1.22227i
$268$	−4.36176			−0.266437
$269$	6.92470	−	5.03109i	0.422206	−	0.306751i	−0.356319	−	0.934365i	$-0.615968\pi$
$269$	6.92470	−	5.03109i	0.422206	−	0.306751i	0.778525	+	0.627614i	$0.215968\pi$
$270$		0			0
$271$	19.3808	+	14.0809i	1.17730	+	0.855356i	0.991864	−	0.127300i	$-0.0406312\pi$
$271$	19.3808	+	14.0809i	1.17730	+	0.855356i	0.185433	+	0.982657i	$0.440631\pi$
$272$	−0.666977	−	0.484587i	−0.0404414	−	0.0293824i
$273$	−5.59934	+	17.2330i	−0.338887	+	1.04299i
$274$	4.49151			0.271342
$275$		0			0
$276$	−5.69572			−0.342842
$277$	−2.20234	+	6.77810i	−0.132326	+	0.407257i	−0.995164	−	0.0982226i	$-0.968684\pi$
$277$	−2.20234	+	6.77810i	−0.132326	+	0.407257i	0.862839	+	0.505479i	$0.168684\pi$
$278$	10.8440	+	7.87863i	0.650380	+	0.472529i
$279$	−9.27819	−	6.74100i	−0.555471	−	0.403573i
$280$		0			0
$281$	−1.82620	+	1.32681i	−0.108942	+	0.0791511i	−0.640922	−	0.767606i	$-0.721448\pi$
$281$	−1.82620	+	1.32681i	−0.108942	+	0.0791511i	0.531980	+	0.846757i	$0.321448\pi$
$282$	−25.1084			−1.49518
$283$	7.86171	−	5.71186i	0.467330	−	0.339535i	−0.329070	−	0.944306i	$-0.606735\pi$
$283$	7.86171	−	5.71186i	0.467330	−	0.339535i	0.796400	+	0.604771i	$0.206735\pi$
$284$	1.51541	+	4.66396i	0.0899232	+	0.276755i
$285$		0			0
$286$	3.70071	−	11.3896i	0.218827	−	0.673481i
$287$	2.18932	+	6.73802i	0.129231	+	0.397733i
$288$	−1.67557	−	5.15688i	−0.0987339	−	0.303872i
$289$	−5.04325	+	15.5215i	−0.296662	+	0.913032i
$290$		0			0
$291$	0.457977	+	1.40951i	0.0268471	+	0.0826269i
$292$	−1.04988	+	0.762779i	−0.0614393	+	0.0446383i
$293$	6.52369			0.381118			0.190559	−	0.981676i	$-0.438970\pi$
$293$	6.52369			0.381118			0.190559	+	0.981676i	$0.438970\pi$
$294$	−13.7082	+	9.95959i	−0.799479	+	0.580855i
$295$		0			0
$296$	7.03498	+	5.11121i	0.408900	+	0.297083i
$297$	11.7556	+	8.54097i	0.682131	+	0.495597i
$298$	−4.20692	+	12.9476i	−0.243700	+	0.750032i
$299$	−11.3706			−0.657578
$300$		0			0
$301$	−8.05766			−0.464436
$302$	−2.71883	+	8.36768i	−0.156451	+	0.481506i
$303$	8.23549	+	5.98343i	0.473117	+	0.343739i
$304$	−2.76007	−	2.00531i	−0.158301	−	0.115012i
$305$		0			0
$306$	3.61653	−	2.62756i	0.206743	−	0.150208i
$307$	−20.7081			−1.18187			−0.590937	−	0.806718i	$-0.701242\pi$
$307$	−20.7081			−1.18187			−0.590937	+	0.806718i	$0.701242\pi$
$308$	−1.80220	+	1.30937i	−0.102690	+	0.0746085i
$309$	4.16276	+	12.8117i	0.236811	+	0.728830i
$310$		0			0
$311$	2.46261	−	7.57914i	0.139642	−	0.429773i	−0.856641	−	0.515912i	$-0.827453\pi$
$311$	2.46261	−	7.57914i	0.139642	−	0.429773i	0.996283	+	0.0861391i	$0.0274530\pi$
$312$	−5.19572	−	15.9908i	−0.294150	−	0.905299i
$313$	−1.44938	−	4.46075i	−0.0819240	−	0.252136i	0.901702	−	0.432358i	$-0.142318\pi$
$313$	−1.44938	−	4.46075i	−0.0819240	−	0.252136i	−0.983626	+	0.180222i	$0.942318\pi$
$314$	−3.66364	+	11.2755i	−0.206751	+	0.636314i
$315$		0			0
$316$	−2.22358	−	6.84348i	−0.125086	−	0.384976i
$317$	11.5686	−	8.40508i	0.649758	−	0.472077i	−0.213431	−	0.976958i	$-0.568464\pi$
$317$	11.5686	−	8.40508i	0.649758	−	0.472077i	0.863189	+	0.504882i	$0.168464\pi$
$318$	−7.45309			−0.417948
$319$	−1.75258	+	1.27332i	−0.0981255	+	0.0712923i
$320$		0			0
$321$	17.8482	+	12.9674i	0.996187	+	0.723772i
$322$	1.71113	+	1.24321i	0.0953575	+	0.0692813i
$323$	0.869158	−	2.67499i	0.0483613	−	0.148841i
$324$	4.13412			0.229674
$325$		0			0
$326$	−14.9590			−0.828500
$327$	−2.67818	+	8.24258i	−0.148103	+	0.455815i
$328$	−5.31854	−	3.86415i	−0.293667	−	0.213362i
$329$	7.54316	+	5.48043i	0.415868	+	0.302146i
$330$		0			0
$331$	−28.7771	+	20.9078i	−1.58174	+	1.14920i	−0.667063	+	0.745002i	$0.732449\pi$
$331$	−28.7771	+	20.9078i	−1.58174	+	1.14920i	−0.914672	+	0.404196i	$0.867551\pi$
$332$	14.9680			0.821477
$333$	−38.1455	+	27.7143i	−2.09036	+	1.51874i
$334$	6.66547	+	20.5142i	0.364718	+	1.12249i
$335$		0			0
$336$	−0.966469	+	2.97449i	−0.0527252	+	0.162272i
$337$	−2.33686	−	7.19211i	−0.127297	−	0.391779i	0.867016	−	0.498281i	$-0.166035\pi$
$337$	−2.33686	−	7.19211i	−0.127297	−	0.391779i	−0.994313	+	0.106501i	$0.966035\pi$
$338$	−6.35520	−	19.5593i	−0.345677	−	1.06389i
$339$	−18.1141	+	55.7495i	−0.983824	+	3.02790i
$340$		0			0
$341$	−1.35102	−	4.15801i	−0.0731617	−	0.225169i
$342$	14.9658	−	10.8733i	0.809260	−	0.587962i
$343$	13.8359			0.747071
$344$	6.04889	−	4.39477i	0.326134	−	0.236950i
$345$		0			0
$346$	−3.62866	−	2.63637i	−0.195078	−	0.141732i
$347$	11.9295	+	8.66728i	0.640409	+	0.465284i	0.859991	−	0.510310i	$-0.170469\pi$
$347$	11.9295	+	8.66728i	0.640409	+	0.465284i	−0.219582	+	0.975594i	$0.570469\pi$
$348$	−0.939859	+	2.89259i	−0.0503817	+	0.155059i
$349$	−7.61178			−0.407449			−0.203725	−	0.979028i	$-0.565305\pi$
$349$	−7.61178			−0.407449			−0.203725	+	0.979028i	$0.565305\pi$
$350$		0			0
$351$	40.7271			2.17385
$352$	0.638757	−	1.96589i	0.0340459	−	0.104782i
$353$	26.0230	+	18.9068i	1.38506	+	1.00631i	0.996387	+	0.0849343i	$0.0270680\pi$
$353$	26.0230	+	18.9068i	1.38506	+	1.00631i	0.388678	+	0.921374i	$0.372932\pi$
$354$	11.0403	+	8.02124i	0.586785	+	0.426324i
$355$		0			0
$356$	9.47214	−	6.88191i	0.502022	−	0.364740i
$357$	−2.57845			−0.136466
$358$	−12.2423	+	8.89456i	−0.647026	+	0.470092i
$359$	−10.7988	−	33.2352i	−0.569937	−	1.75408i	−0.652807	−	0.757524i	$-0.726409\pi$
$359$	−10.7988	−	33.2352i	−0.569937	−	1.75408i	0.0828704	−	0.996560i	$-0.473591\pi$
$360$		0			0
$361$	−2.27459	+	7.00046i	−0.119715	+	0.368445i
$362$	3.03488	+	9.34041i	0.159510	+	0.490921i
$363$	−6.03302	−	18.5677i	−0.316651	−	0.974552i
$364$	−1.92940	+	5.93809i	−0.101128	+	0.311240i
$365$		0			0
$366$	8.32495	+	25.6216i	0.435152	+	1.33926i
$367$	−8.93423	+	6.49110i	−0.466363	+	0.338832i	−0.796022	−	0.605268i	$-0.793066\pi$
$367$	−8.93423	+	6.49110i	−0.466363	+	0.338832i	0.329659	+	0.944100i	$0.393066\pi$
$368$	−1.96261			−0.102308
$369$	28.8385	−	20.9524i	1.50127	−	1.09074i
$370$		0			0
$371$	2.23909	+	1.62679i	0.116248	+	0.0844588i
$372$	−4.96589	−	3.60793i	−0.257470	−	0.187063i
$373$	6.31632	−	19.4396i	0.327047	−	1.00655i	−0.643462	−	0.765478i	$-0.722502\pi$
$373$	6.31632	−	19.4396i	0.327047	−	1.00655i	0.970508	−	0.241068i	$-0.0774976\pi$
$374$	1.70415			0.0881193
$375$		0			0
$376$	−8.65176			−0.446181
$377$	−1.87628	+	5.77459i	−0.0966332	+	0.297406i
$378$	−6.12892	−	4.45292i	−0.315238	−	0.229034i
$379$	2.82662	+	2.05366i	0.145193	+	0.105489i	0.658011	−	0.753009i	$-0.271398\pi$
$379$	2.82662	+	2.05366i	0.145193	+	0.105489i	−0.512817	+	0.858498i	$0.671398\pi$
$380$		0			0
$381$	50.1292	−	36.4210i	2.56820	−	1.86590i
$382$	−19.4530			−0.995301
$383$	−15.8471	+	11.5136i	−0.809751	+	0.588318i	−0.913758	−	0.406258i	$-0.866833\pi$
$383$	−15.8471	+	11.5136i	−0.809751	+	0.588318i	0.104008	+	0.994577i	$0.466833\pi$
$384$	−0.896802	−	2.76007i	−0.0457647	−	0.140849i
$385$		0			0
$386$	−1.85410	+	5.70634i	−0.0943713	+	0.290445i
$387$	12.5280	+	38.5571i	0.636832	+	1.95997i
$388$	0.157808	+	0.485684i	0.00801150	+	0.0246569i
$389$	3.15799	−	9.71930i	0.160117	−	0.492788i	−0.838527	−	0.544861i	$-0.816583\pi$
$389$	3.15799	−	9.71930i	0.160117	−	0.492788i	0.998643	+	0.0520722i	$0.0165826\pi$
$390$		0			0
$391$	−0.500000	−	1.53884i	−0.0252861	−	0.0778226i
$392$	−4.72353	+	3.43184i	−0.238574	+	0.173334i
$393$	−26.1411			−1.31864
$394$	−1.13818	+	0.826937i	−0.0573407	+	0.0416605i
$395$		0			0
$396$	9.06758	+	6.58798i	0.455663	+	0.331059i
$397$	18.2073	+	13.2284i	0.913797	+	0.663912i	0.941972	−	0.335691i	$-0.108970\pi$
$397$	18.2073	+	13.2284i	0.913797	+	0.663912i	−0.0281755	+	0.999603i	$0.508970\pi$
$398$	−4.23967	+	13.0484i	−0.212516	+	0.654056i
$399$	−10.6701			−0.534173
$400$		0			0
$401$	30.3084			1.51353			0.756765	−	0.653687i	$-0.226779\pi$
$401$	30.3084			1.51353			0.756765	+	0.653687i	$0.226779\pi$
$402$	3.91164	−	12.0388i	0.195095	−	0.600440i
$403$	−9.91361	−	7.20266i	−0.493832	−	0.358790i
$404$	2.83776	+	2.06175i	0.141184	+	0.102576i
$405$		0			0
$406$	0.913723	−	0.663859i	0.0453473	−	0.0329468i
$407$	−17.9746			−0.890967
$408$	1.93564	−	1.40633i	0.0958287	−	0.0696236i
$409$	−4.76281	−	14.6584i	−0.235506	−	0.724813i	−0.997054	−	0.0767043i	$-0.975560\pi$
$409$	−4.76281	−	14.6584i	−0.235506	−	0.724813i	0.761548	−	0.648109i	$-0.224440\pi$
$410$		0			0
$411$	−4.02800	+	12.3969i	−0.198687	+	0.611494i
$412$	1.43439	+	4.41460i	0.0706673	+	0.217492i
$413$	−1.56597	−	4.81955i	−0.0770561	−	0.237154i
$414$	3.28849	−	10.1209i	0.161621	−	0.497417i
$415$		0			0
$416$	−1.79032	−	5.51005i	−0.0877778	−	0.270152i
$417$	−31.4705	+	22.8647i	−1.54112	+	1.11969i
$418$	7.05207			0.344928
$419$	−17.1755	+	12.4787i	−0.839076	+	0.609624i	−0.922112	−	0.386922i	$-0.873538\pi$
$419$	−17.1755	+	12.4787i	−0.839076	+	0.609624i	0.0830364	+	0.996547i	$0.473538\pi$
$420$		0			0
$421$	−26.5536	−	19.2923i	−1.29414	−	0.940249i	−0.294261	−	0.955725i	$-0.595074\pi$
$421$	−26.5536	−	19.2923i	−1.29414	−	0.940249i	−0.999880	+	0.0154761i	$0.995074\pi$
$422$	−13.5741	−	9.86215i	−0.660776	−	0.480082i
$423$	14.4966	−	44.6161i	0.704851	−	2.16931i
$424$	−2.56816			−0.124721
$425$		0			0
$426$	−14.2319			−0.689538
$427$	3.09142	−	9.51442i	0.149604	−	0.460435i
$428$	6.15006	+	4.46828i	0.297274	+	0.215982i
$429$	28.1173	+	20.4284i	1.35752	+	0.986295i
$430$		0			0
$431$	0.680214	−	0.494204i	0.0327647	−	0.0238050i	−0.571282	−	0.820754i	$-0.693554\pi$
$431$	0.680214	−	0.494204i	0.0327647	−	0.0238050i	0.604047	+	0.796949i	$0.293554\pi$
$432$	7.02967			0.338215
$433$	−27.5350	+	20.0053i	−1.32325	+	0.961394i	−0.323360	+	0.946276i	$0.604813\pi$
$433$	−27.5350	+	20.0053i	−1.32325	+	0.961394i	−0.999886	+	0.0151184i	$0.995187\pi$
$434$	0.704367	+	2.16782i	0.0338107	+	0.104059i
$435$		0			0
$436$	−0.922836	+	2.84020i	−0.0441958	+	0.136021i
$437$	−2.06909	−	6.36801i	−0.0989780	−	0.304623i
$438$	−1.16380	−	3.58180i	−0.0556083	−	0.171145i
$439$	−0.492305	+	1.51516i	−0.0234964	+	0.0723145i	−0.962117	−	0.272636i	$-0.912104\pi$
$439$	−0.492305	+	1.51516i	−0.0234964	+	0.0723145i	0.938621	+	0.344951i	$0.112104\pi$
$440$		0			0
$441$	−9.78298	−	30.1089i	−0.465856	−	1.43376i
$442$	3.86420	−	2.80751i	0.183801	−	0.133540i
$443$	24.6238			1.16991			0.584955	−	0.811065i	$-0.301112\pi$
$443$	24.6238			1.16991			0.584955	+	0.811065i	$0.301112\pi$
$444$	−20.4163	+	14.8333i	−0.968916	+	0.703958i
$445$		0			0
$446$	9.45251	+	6.86765i	0.447589	+	0.325193i
$447$	−31.9634	−	23.2228i	−1.51182	−	1.09840i
$448$	−0.333023	+	1.02494i	−0.0157338	+	0.0484238i
$449$	−34.1186			−1.61016			−0.805078	−	0.593169i	$-0.797876\pi$
$449$	−34.1186			−1.61016			−0.805078	+	0.593169i	$0.797876\pi$
$450$		0			0
$451$	13.5890			0.639882
$452$	−6.24170	+	19.2100i	−0.293585	+	0.903561i
$453$	−20.6572	−	15.0083i	−0.970559	−	0.705152i
$454$	0.576751	+	0.419034i	0.0270683	+	0.0196663i
$455$		0			0
$456$	8.01005	−	5.81964i	0.375105	−	0.272530i
$457$	3.48932			0.163224			0.0816118	−	0.996664i	$-0.473993\pi$
$457$	3.48932			0.163224			0.0816118	+	0.996664i	$0.473993\pi$
$458$	16.5176	−	12.0008i	0.771819	−	0.560759i
$459$	1.79090	+	5.51182i	0.0835920	+	0.257270i
$460$		0			0
$461$	4.16714	−	12.8251i	0.194083	−	0.597326i	−0.805903	−	0.592048i	$-0.798320\pi$
$461$	4.16714	−	12.8251i	0.194083	−	0.597326i	0.999986	−	0.00527875i	$-0.00168028\pi$
$462$	−1.99775	−	6.14845i	−0.0929438	−	0.286052i
$463$	0.576011	+	1.77278i	0.0267695	+	0.0823881i	0.963549	−	0.267533i	$-0.0862084\pi$
$463$	0.576011	+	1.77278i	0.0267695	+	0.0823881i	−0.936779	+	0.349921i	$0.886208\pi$
$464$	−0.323853	+	0.996718i	−0.0150345	+	0.0462715i
$465$		0			0
$466$	4.64771	+	14.3042i	0.215301	+	0.662628i
$467$	−10.5508	+	7.66561i	−0.488233	+	0.354722i	−0.804504	−	0.593947i	$-0.797569\pi$
$467$	−10.5508	+	7.66561i	−0.488233	+	0.354722i	0.316271	+	0.948669i	$0.397569\pi$
$468$	31.4144			1.45213
$469$	−3.80287	+	2.76294i	−0.175600	+	0.127581i
$470$		0			0
$471$	−27.8357	−	20.2238i	−1.28260	−	0.931865i
$472$	3.80423	+	2.76393i	0.175104	+	0.127220i
$473$	−4.77588	+	14.6987i	−0.219595	+	0.675845i
$474$	20.8826			0.959171
$475$		0			0
$476$	−0.888474			−0.0407231
$477$	4.30313	−	13.2437i	0.197027	−	0.606386i
$478$	3.38679	+	2.46065i	0.154908	+	0.112547i
$479$	−10.0171	−	7.27787i	−0.457694	−	0.332534i	0.334932	−	0.942242i	$-0.391287\pi$
$479$	−10.0171	−	7.27787i	−0.457694	−	0.332534i	−0.792626	+	0.609708i	$0.791287\pi$
$480$		0			0
$481$	−40.7579	+	29.6124i	−1.85840	+	1.35021i
$482$	29.4162			1.33987
$483$	−4.96589	+	3.60793i	−0.225956	+	0.164167i
$484$	−2.07884	−	6.39800i	−0.0944925	−	0.290818i
$485$		0			0
$486$	2.80937	−	8.64636i	0.127436	−	0.392207i
$487$	−1.39647	−	4.29789i	−0.0632800	−	0.194756i	0.914418	−	0.404771i	$-0.132649\pi$
$487$	−1.39647	−	4.29789i	−0.0632800	−	0.194756i	−0.977698	+	0.210015i	$0.932649\pi$
$488$	2.86858	+	8.82859i	0.129855	+	0.399651i
$489$	13.4152	−	41.2878i	0.606657	−	1.86710i
$490$		0			0
$491$	8.48797	+	26.1233i	0.383057	+	1.17893i	0.937880	+	0.346959i	$0.112786\pi$
$491$	8.48797	+	26.1233i	0.383057	+	1.17893i	−0.554824	+	0.831968i	$0.687214\pi$
$492$	15.4350	−	11.2142i	0.695864	−	0.505575i
$493$	−0.864011			−0.0389131
$494$	15.9908	−	11.6180i	0.719459	−	0.522718i
$495$		0			0
$496$	−1.71113	−	1.24321i	−0.0768320	−	0.0558217i
$497$	4.27560	+	3.10641i	0.191787	+	0.139341i
$498$	−13.4234	+	41.3128i	−0.601515	+	1.85127i
$499$	13.4814			0.603510			0.301755	−	0.953385i	$-0.402427\pi$
$499$	13.4814			0.603510			0.301755	+	0.953385i	$0.402427\pi$
$500$		0			0
$501$	−62.5983			−2.79669
$502$	7.31427	−	22.5110i	0.326452	−	1.00472i
$503$	22.5145	+	16.3577i	1.00387	+	0.729355i	0.962915	−	0.269806i	$-0.0869597\pi$
$503$	22.5145	+	16.3577i	1.00387	+	0.729355i	0.0409559	+	0.999161i	$0.486960\pi$
$504$	−4.72747	−	3.43471i	−0.210578	−	0.152994i
$505$		0			0
$506$	3.28205	−	2.38455i	0.145905	−	0.106006i
$507$	59.6844			2.65068
$508$	17.2733	−	12.5498i	0.766381	−	0.556808i
$509$	−6.20182	−	19.0873i	−0.274891	−	0.846028i	−0.989248	−	0.146246i	$-0.953281\pi$
$509$	−6.20182	−	19.0873i	−0.274891	−	0.846028i	0.714357	−	0.699781i	$-0.246719\pi$
$510$		0			0
$511$	−0.432169	+	1.33008i	−0.0191180	+	0.0588393i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	7.41106	+	22.8089i	0.327206	+	1.00704i
$514$	1.34400	−	4.13641i	0.0592813	−	0.182449i
$515$		0			0
$516$	6.70524	+	20.6366i	0.295182	+	0.908476i
$517$	14.4682	−	10.5118i	0.636313	−	0.462308i
$518$	9.37123			0.411748
$519$	10.5308	−	7.65105i	0.462249	−	0.335844i
$520$		0			0
$521$	23.5901	+	17.1392i	1.03350	+	0.750881i	0.969006	−	0.247037i	$-0.0794569\pi$
$521$	23.5901	+	17.1392i	1.03350	+	0.750881i	0.0644931	+	0.997918i	$0.479457\pi$
$522$	−4.59731	−	3.34014i	−0.201219	−	0.146194i
$523$	−3.61732	+	11.1330i	−0.158174	+	0.486811i	−0.998469	−	0.0553197i	$-0.982382\pi$
$523$	−3.61732	+	11.1330i	−0.158174	+	0.486811i	0.840294	+	0.542131i	$0.182382\pi$
$524$	−9.00760			−0.393499
$525$		0			0
$526$	−2.25698			−0.0984092
$527$	0.538842	−	1.65838i	0.0234723	−	0.0722404i
$528$	4.85317	+	3.52603i	0.211207	+	0.153451i
$529$	15.4912	+	11.2550i	0.673530	+	0.489348i
$530$		0			0
$531$	−20.6275	+	14.9868i	−0.895157	+	0.650370i
$532$	−3.67667			−0.159404
$533$	30.8135	−	22.3873i	1.33468	−	0.969703i
$534$	10.4999	+	32.3155i	0.454377	+	1.39843i
$535$		0			0
$536$	1.34786	−	4.14828i	0.0582186	−	0.179179i
$537$	−13.5707	−	41.7663i	−0.585619	−	1.80235i
$538$	2.64500	+	8.14047i	0.114034	+	0.350961i
$539$	3.72945	−	11.4781i	0.160639	−	0.494395i
$540$		0			0
$541$	−9.24566	−	28.4552i	−0.397502	−	1.22339i	−0.926996	−	0.375072i	$-0.877618\pi$
$541$	−9.24566	−	28.4552i	−0.397502	−	1.22339i	0.529494	−	0.848314i	$-0.322382\pi$
$542$	−19.3808	+	14.0809i	−0.832475	+	0.604828i
$543$	−28.5019			−1.22313
$544$	0.666977	−	0.484587i	0.0285964	−	0.0207765i
$545$		0			0
$546$	−14.6593	−	10.6506i	−0.627358	−	0.455803i
$547$	−1.53050	−	1.11198i	−0.0654396	−	0.0475447i	0.554585	−	0.832127i	$-0.312877\pi$
$547$	−1.53050	−	1.11198i	−0.0654396	−	0.0475447i	−0.620024	+	0.784583i	$0.712877\pi$
$548$	−1.38795	+	4.27168i	−0.0592905	+	0.182477i
$549$	−50.3344			−2.14822
$550$		0			0
$551$	−3.57543			−0.152319
$552$	1.76007	−	5.41695i	0.0749137	−	0.230561i
$553$	−6.27364	−	4.55807i	−0.266782	−	0.193829i
$554$	−5.76580	−	4.18910i	−0.244965	−	0.177978i
$555$		0			0
$556$	−10.8440	+	7.87863i	−0.459888	+	0.334128i
$557$	−2.95618			−0.125257			−0.0626287	−	0.998037i	$-0.519948\pi$
$557$	−2.95618			−0.125257			−0.0626287	+	0.998037i	$0.519948\pi$
$558$	9.27819	−	6.74100i	0.392777	−	0.285369i
$559$	13.3859	+	41.1977i	0.566165	+	1.74248i
$560$		0			0
$561$	−1.52828	+	4.70357i	−0.0645241	+	0.198585i
$562$	−0.697547	−	2.14683i	−0.0294243	−	0.0905586i
$563$	−2.86862	−	8.82870i	−0.120898	−	0.372085i	0.872234	−	0.489089i	$-0.162671\pi$
$563$	−2.86862	−	8.82870i	−0.120898	−	0.372085i	−0.993131	+	0.117004i	$0.962671\pi$
$564$	7.75892	−	23.8795i	0.326710	−	1.00551i
$565$		0			0
$566$	3.00290	+	9.24199i	0.126221	+	0.388470i
$567$	3.60440	−	2.61875i	0.151370	−	0.109977i
$568$	−4.90398			−0.205766
$569$	11.7064	−	8.50522i	0.490759	−	0.356557i	−0.314717	−	0.949186i	$-0.601910\pi$
$569$	11.7064	−	8.50522i	0.490759	−	0.356557i	0.805476	+	0.592628i	$0.201910\pi$
$570$		0			0
$571$	4.11663	+	2.99091i	0.172276	+	0.125166i	0.670582	−	0.741835i	$-0.266044\pi$
$571$	4.11663	+	2.99091i	0.172276	+	0.125166i	−0.498306	+	0.867001i	$0.666044\pi$
$572$	9.68858	+	7.03916i	0.405100	+	0.294322i
$573$	17.4455	−	53.6916i	0.728795	−	2.24300i
$574$	−7.08478			−0.295713
$575$		0			0
$576$	5.42226			0.225928
$577$	−5.21453	+	16.0487i	−0.217084	+	0.668116i	0.781915	+	0.623385i	$0.214243\pi$
$577$	−5.21453	+	16.0487i	−0.217084	+	0.668116i	−0.998999	+	0.0447308i	$0.985757\pi$
$578$	−13.2034	−	9.59284i	−0.549190	−	0.399010i
$579$	−14.0872	−	10.2349i	−0.585442	−	0.425349i
$580$		0			0
$581$	13.0501	−	9.48144i	0.541409	−	0.393356i
$582$	−1.48205			−0.0614328
$583$	4.29470	−	3.12028i	0.177868	−	0.129229i
$584$	−0.401017	−	1.23420i	−0.0165942	−	0.0510717i
$585$		0			0
$586$	−2.01593	+	6.20440i	−0.0832774	+	0.256301i
$587$	13.6260	+	41.9364i	0.562403	+	1.73090i	0.675543	+	0.737320i	$0.263909\pi$
$587$	13.6260	+	41.9364i	0.562403	+	1.73090i	−0.113140	+	0.993579i	$0.536091\pi$
$588$	−5.23607	−	16.1150i	−0.215932	−	0.664570i
$589$	2.22982	−	6.86269i	0.0918783	−	0.282772i
$590$		0			0
$591$	−1.26168	−	3.88306i	−0.0518987	−	0.159728i
$592$	−7.03498	+	5.11121i	−0.289136	+	0.210070i
$593$	−31.1398			−1.27876			−0.639380	−	0.768891i	$-0.720809\pi$
$593$	−31.1398			−1.27876			−0.639380	+	0.768891i	$0.720809\pi$
$594$	−11.7556	+	8.54097i	−0.482340	+	0.350440i
$595$		0			0
$596$	−11.0138	−	8.00203i	−0.451145	−	0.327776i
$597$	−32.2123	−	23.4036i	−1.31836	−	0.957846i
$598$	3.51371	−	10.8141i	0.143686	−	0.442220i
$599$	28.6194			1.16936			0.584678	−	0.811265i	$-0.301221\pi$
$599$	28.6194			1.16936			0.584678	+	0.811265i	$0.301221\pi$
$600$		0			0
$601$	38.8122			1.58318			0.791592	−	0.611050i	$-0.209253\pi$
$601$	38.8122			1.58318			0.791592	+	0.611050i	$0.209253\pi$
$602$	2.48995	−	7.66329i	0.101483	−	0.312332i
$603$	19.1337	+	13.9015i	0.779186	+	0.566112i
$604$	−7.11798	−	5.17151i	−0.289626	−	0.210426i
$605$		0			0
$606$	−8.23549	+	5.98343i	−0.334544	+	0.243060i
$607$	6.78331			0.275326			0.137663	−	0.990479i	$-0.456041\pi$
$607$	6.78331			0.275326			0.137663	+	0.990479i	$0.456041\pi$
$608$	2.76007	−	2.00531i	0.111936	−	0.0813261i
$609$	1.01287	+	3.11729i	0.0410436	+	0.126319i
$610$		0			0
$611$	15.4894	−	47.6716i	0.626636	−	1.92859i
$612$	1.38139	+	4.25148i	0.0558394	+	0.171856i
$613$	10.4525	+	32.1696i	0.422174	+	1.29932i	0.905674	+	0.423974i	$0.139365\pi$
$613$	10.4525	+	32.1696i	0.422174	+	1.29932i	−0.483500	+	0.875344i	$0.660635\pi$
$614$	6.39915	−	19.6946i	0.258249	−	0.794808i
$615$		0			0
$616$	−0.688378	−	2.11861i	−0.0277355	−	0.0853612i
$617$	−10.6287	+	7.72217i	−0.427894	+	0.310883i	−0.780806	−	0.624773i	$-0.785191\pi$
$617$	−10.6287	+	7.72217i	−0.427894	+	0.310883i	0.352913	+	0.935656i	$0.385191\pi$
$618$	−13.4710			−0.541882
$619$	22.6836	−	16.4806i	0.911732	−	0.662412i	−0.0297205	−	0.999558i	$-0.509462\pi$
$619$	22.6836	−	16.4806i	0.911732	−	0.662412i	0.941452	+	0.337146i	$0.109462\pi$
$620$		0			0
$621$	11.1616	+	8.10938i	0.447900	+	0.325418i
$622$	6.44720	+	4.68416i	0.258509	+	0.187818i
$623$	3.89910	−	12.0002i	0.156214	−	0.480777i
$624$	16.8137			0.673086
$625$		0			0
$626$	4.69031			0.187462
$627$	−6.32431	+	19.4642i	−0.252569	+	0.777326i
$628$	−9.59153	−	6.96866i	−0.382744	−	0.278080i
$629$	−5.79985	−	4.21384i	−0.231255	−	0.168017i
$630$		0			0
$631$	23.0144	−	16.7209i	0.916187	−	0.665649i	−0.0263851	−	0.999652i	$-0.508400\pi$
$631$	23.0144	−	16.7209i	0.916187	−	0.665649i	0.942572	+	0.334003i	$0.108400\pi$
$632$	7.19566			0.286228
$633$	39.3935	−	28.6211i	1.56575	−	1.13759i
$634$	4.41881	+	13.5997i	0.175494	+	0.540114i
$635$		0			0
$636$	2.30313	−	7.08831i	0.0913250	−	0.281070i
$637$	−10.4530	−	32.1709i	−0.414162	−	1.27466i
$638$	−0.669425	−	2.06028i	−0.0265028	−	0.0815672i
$639$	8.21696	−	25.2892i	0.325058	−	1.00043i
$640$		0			0
$641$	7.87785	+	24.2455i	0.311156	+	0.957641i	0.977308	+	0.211824i	$0.0679405\pi$
$641$	7.87785	+	24.2455i	0.311156	+	0.957641i	−0.666151	+	0.745817i	$0.732059\pi$
$642$	−17.8482	+	12.9674i	−0.704411	+	0.511784i
$643$	13.7340			0.541617			0.270809	−	0.962633i	$-0.412709\pi$
$643$	13.7340			0.541617			0.270809	+	0.962633i	$0.412709\pi$
$644$	−1.71113	+	1.24321i	−0.0674280	+	0.0489893i
$645$		0			0
$646$	2.27549	+	1.65324i	0.0895278	+	0.0650458i
$647$	31.1702	+	22.6465i	1.22543	+	0.890324i	0.996539	−	0.0831286i	$-0.0264912\pi$
$647$	31.1702	+	22.6465i	1.22543	+	0.890324i	0.228887	+	0.973453i	$0.426491\pi$
$648$	−1.27751	+	3.93179i	−0.0501855	+	0.154455i
$649$	−9.71991			−0.381540
$650$		0			0
$651$	−6.61502			−0.259263
$652$	4.62257	−	14.2268i	0.181034	−	0.557165i
$653$	−11.2149	−	8.14808i	−0.438872	−	0.318859i	0.346315	−	0.938118i	$-0.387433\pi$
$653$	−11.2149	−	8.14808i	−0.438872	−	0.318859i	−0.785187	+	0.619259i	$0.787433\pi$
$654$	−7.01155	−	5.09419i	−0.274173	−	0.199199i
$655$		0			0
$656$	5.31854	−	3.86415i	0.207654	−	0.150870i
$657$	7.03656			0.274523
$658$	−7.54316	+	5.48043i	−0.294063	+	0.213649i
$659$	8.36885	+	25.7567i	0.326004	+	1.00334i	0.970985	+	0.239139i	$0.0768651\pi$
$659$	8.36885	+	25.7567i	0.326004	+	1.00334i	−0.644981	+	0.764198i	$0.723135\pi$
$660$		0			0
$661$	−7.25043	+	22.3145i	−0.282009	+	0.867934i	0.705270	+	0.708938i	$0.250826\pi$
$661$	−7.25043	+	22.3145i	−0.282009	+	0.867934i	−0.987279	+	0.158996i	$0.949174\pi$
$662$	−10.9919	−	33.8296i	−0.427212	−	1.31482i
$663$	4.28350	+	13.1833i	0.166357	+	0.511996i
$664$	−4.62537	+	14.2354i	−0.179499	+	0.552442i
$665$		0			0
$666$	−14.5703	−	44.8427i	−0.564587	−	1.73762i
$667$	−1.66402	+	1.20898i	−0.0644310	+	0.0468118i
$668$	−21.5699			−0.834565
$669$	−27.4322	+	19.9307i	−1.06059	+	0.770565i
$670$		0			0
$671$	−15.5237	−	11.2786i	−0.599287	−	0.435407i
$672$	−2.53025	−	1.83833i	−0.0976065	−	0.0709152i
$673$	−3.39760	+	10.4567i	−0.130968	+	0.403078i	−0.994941	−	0.100460i	$-0.967969\pi$
$673$	−3.39760	+	10.4567i	−0.130968	+	0.403078i	0.863973	+	0.503538i	$0.167969\pi$
$674$	7.56224			0.291286
$675$		0			0
$676$	20.5659			0.790994
$677$	11.3279	−	34.8638i	0.435368	−	1.33992i	−0.457341	−	0.889291i	$-0.651198\pi$
$677$	11.3279	−	34.8638i	0.435368	−	1.33992i	0.892709	−	0.450633i	$-0.148802\pi$
$678$	−47.4234	−	34.4551i	−1.82128	−	1.32324i
$679$	0.445242	+	0.323487i	0.0170868	+	0.0124143i
$680$		0			0
$681$	−1.67380	+	1.21608i	−0.0641400	+	0.0466005i
$682$	4.37199			0.167412
$683$	−8.26475	+	6.00469i	−0.316242	+	0.229763i	−0.734570	−	0.678533i	$-0.762616\pi$
$683$	−8.26475	+	6.00469i	−0.316242	+	0.229763i	0.418328	+	0.908296i	$0.362616\pi$
$684$	5.71644	+	17.5934i	0.218574	+	0.672700i
$685$		0			0
$686$	−4.27554	+	13.1588i	−0.163241	+	0.502404i
$687$	18.3100	+	56.3522i	0.698568	+	2.14997i
$688$	2.31047	+	7.11089i	0.0880858	+	0.271100i
$689$	4.59783	−	14.1507i	0.175163	−	0.539097i
$690$		0			0
$691$	1.68239	+	5.17786i	0.0640011	+	0.196975i	0.977944	−	0.208868i	$-0.0669779\pi$
$691$	1.68239	+	5.17786i	0.0640011	+	0.196975i	−0.913943	+	0.405843i	$0.866978\pi$
$692$	3.62866	−	2.63637i	0.137941	−	0.100220i
$693$	12.0788			0.458837
$694$	−11.9295	+	8.66728i	−0.452837	+	0.329006i
$695$		0			0
$696$	−2.46058	−	1.78772i	−0.0932681	−	0.0677633i
$697$	4.38476	+	3.18572i	0.166085	+	0.120668i
$698$	2.35217	−	7.23924i	0.0890310	−	0.274009i
$699$	−43.6486			−1.65094
$700$		0			0
$701$	13.9633			0.527387			0.263694	−	0.964606i	$-0.415059\pi$
$701$	13.9633			0.527387			0.263694	+	0.964606i	$0.415059\pi$
$702$	−12.5854	+	38.7338i	−0.475005	+	1.46191i
$703$	−24.0008	−	17.4376i	−0.905208	−	0.657672i
$704$	1.67229	+	1.21499i	0.0630267	+	0.0457916i
$705$		0			0
$706$	−26.0230	+	18.9068i	−0.979388	+	0.711567i
$707$	3.78015			0.142167
$708$	−11.0403	+	8.02124i	−0.414920	+	0.301457i
$709$	5.98835	+	18.4302i	0.224897	+	0.692162i	0.998302	+	0.0582499i	$0.0185520\pi$
$709$	5.98835	+	18.4302i	0.224897	+	0.692162i	−0.773405	+	0.633912i	$0.781448\pi$
$710$		0			0
$711$	−12.0568	+	37.1071i	−0.452167	+	1.39163i
$712$	3.61803	+	11.1352i	0.135592	+	0.417308i
$713$	−1.28275	−	3.94790i	−0.0480393	−	0.147850i
$714$	0.796786	−	2.45225i	0.0298190	−	0.0917733i
$715$		0			0
$716$	−4.67615	−	14.3917i	−0.174756	−	0.537843i
$717$	−9.82885	+	7.14108i	−0.367065	+	0.266688i
$718$	34.9455			1.30415
$719$	−7.97223	+	5.79216i	−0.297314	+	0.216011i	−0.726434	−	0.687236i	$-0.758824\pi$
$719$	−7.97223	+	5.79216i	−0.297314	+	0.216011i	0.429120	+	0.903247i	$0.358824\pi$
$720$		0			0
$721$	4.04701	+	2.94032i	0.150718	+	0.109503i
$722$	−5.95495	−	4.32652i	−0.221620	−	0.161017i
$723$	−26.3805	+	81.1909i	−0.981103	+	3.01952i
$724$	−9.82108			−0.364998
$725$		0			0
$726$	19.5233			0.724576
$727$	10.9658	−	33.7494i	0.406700	−	1.25169i	−0.512767	−	0.858528i	$-0.671380\pi$
$727$	10.9658	−	33.7494i	0.406700	−	1.25169i	0.919467	−	0.393167i	$-0.128620\pi$
$728$	−5.05124	−	3.66994i	−0.187211	−	0.136017i
$729$	31.3789	+	22.7981i	1.16218	+	0.844373i
$730$		0			0
$731$	−4.98688	+	3.62318i	−0.184446	+	0.134008i
$732$	−26.9401			−0.995735
$733$	−22.3126	+	16.2111i	−0.824135	+	0.598769i	−0.917894	−	0.396826i	$-0.870112\pi$
$733$	−22.3126	+	16.2111i	−0.824135	+	0.598769i	0.0937592	+	0.995595i	$0.470112\pi$
$734$	−3.41257	−	10.5028i	−0.125960	−	0.387666i
$735$		0			0
$736$	0.606480	−	1.86655i	0.0223551	−	0.0688021i
$737$	2.78611	+	8.57476i	0.102628	+	0.315855i
$738$	11.0153	+	33.9017i	0.405480	+	1.24794i
$739$	−11.9642	+	36.8219i	−0.440109	+	1.35452i	0.447651	+	0.894208i	$0.352261\pi$
$739$	−11.9642	+	36.8219i	−0.440109	+	1.35452i	−0.887760	+	0.460307i	$0.847739\pi$
$740$		0			0
$741$	17.7259	+	54.5547i	0.651178	+	2.00412i
$742$	−2.23909	+	1.62679i	−0.0821994	+	0.0597214i
$743$	−13.3434			−0.489520			−0.244760	−	0.969584i	$-0.578709\pi$
$743$	−13.3434			−0.489520			−0.244760	+	0.969584i	$0.578709\pi$
$744$	4.96589	−	3.60793i	0.182058	−	0.132273i
$745$		0			0
$746$	16.5363	+	12.0144i	0.605439	+	0.439877i
$747$	−65.6602	−	47.7050i	−2.40238	−	1.74543i
$748$	−0.526610	+	1.62074i	−0.0192548	+	0.0592601i
$749$	8.19243			0.299345
$750$		0			0
$751$	13.3487			0.487099			0.243550	−	0.969888i	$-0.421688\pi$
$751$	13.3487			0.487099			0.243550	+	0.969888i	$0.421688\pi$
$752$	2.67354	−	8.22832i	0.0974940	−	0.300056i
$753$	55.5726	+	40.3759i	2.02518	+	1.47138i
$754$	−4.91216	−	3.56889i	−0.178890	−	0.129971i
$755$		0			0
$756$	6.12892	−	4.45292i	0.222907	−	0.161951i
$757$	33.3735			1.21298			0.606490	−	0.795091i	$-0.292577\pi$
$757$	33.3735			1.21298			0.606490	+	0.795091i	$0.292577\pi$
$758$	−2.82662	+	2.05366i	−0.102667	+	0.0745922i
$759$	3.63818	+	11.1972i	0.132058	+	0.406432i
$760$		0			0
$761$	−0.678475	+	2.08813i	−0.0245947	+	0.0756947i	−0.962600	−	0.270925i	$-0.912671\pi$
$761$	−0.678475	+	2.08813i	−0.0245947	+	0.0756947i	0.938006	+	0.346620i	$0.112671\pi$
$762$	19.1477	+	58.9304i	0.693646	+	2.13482i
$763$	0.994526	+	3.06083i	0.0360042	+	0.110810i
$764$	6.01130	−	18.5009i	0.217481	−	0.669338i
$765$		0			0
$766$	−6.05307	−	18.6294i	−0.218706	−	0.673108i
$767$	−22.0402	+	16.0131i	−0.795825	+	0.578201i
$768$	2.90211			0.104721
$769$	−14.0154	+	10.1828i	−0.505408	+	0.367200i	−0.811079	−	0.584937i	$-0.801119\pi$
$769$	−14.0154	+	10.1828i	−0.505408	+	0.367200i	0.305671	+	0.952137i	$0.401119\pi$
$770$		0			0
$771$	10.2115	+	7.41908i	0.367758	+	0.267192i
$772$	−4.85410	−	3.52671i	−0.174703	−	0.126929i
$773$	−5.05119	+	15.5460i	−0.181679	+	0.559150i	−0.999875	−	0.0157888i	$-0.994974\pi$
$773$	−5.05119	+	15.5460i	−0.181679	+	0.559150i	0.818197	+	0.574939i	$0.194974\pi$
$774$	−40.5413			−1.45723
$775$		0			0
$776$	−0.510678			−0.0183323
$777$	−8.40414	+	25.8653i	−0.301497	+	0.927912i
$778$	8.26773	+	6.00686i	0.296413	+	0.215356i
$779$	18.1449	+	13.1831i	0.650110	+	0.472333i
$780$		0			0
$781$	8.20086	−	5.95828i	0.293450	−	0.213204i
$782$	1.61803			0.0578608
$783$	5.96017	−	4.33032i	0.212999	−	0.154753i
$784$	−1.80423	−	5.55284i	−0.0644366	−	0.198316i
$785$		0			0
$786$	8.07804	−	24.8616i	0.288134	−	0.886786i
$787$	−15.1572	−	46.6492i	−0.540297	−	1.66286i	−0.731917	−	0.681394i	$-0.761374\pi$
$787$	−15.1572	−	46.6492i	−0.540297	−	1.66286i	0.191620	−	0.981469i	$-0.438626\pi$
$788$	−0.434746	−	1.33801i	−0.0154872	−	0.0476647i
$789$	2.02407	−	6.22944i	0.0720587	−	0.221774i
$790$		0			0
$791$	6.72658	+	20.7023i	0.239170	+	0.736088i
$792$	−9.06758	+	6.58798i	−0.322202	+	0.234094i
$793$	−53.7816			−1.90984
$794$	−18.2073	+	13.2284i	−0.646152	+	0.469457i
$795$		0			0
$796$	−11.0996	−	8.06433i	−0.393415	−	0.285833i
$797$	31.3513	+	22.7780i	1.11052	+	0.806840i	0.982745	−	0.184963i	$-0.0592167\pi$
$797$	31.3513	+	22.7780i	1.11052	+	0.806840i	0.127774	+	0.991803i	$0.459217\pi$
$798$	3.29724	−	10.1479i	0.116721	−	0.359231i
$799$	7.13277			0.252339
$800$		0			0
$801$	−63.4849			−2.24313
$802$	−9.36582	+	28.8250i	−0.330719	+	1.01785i
$803$	2.17016	+	1.57671i	0.0765832	+	0.0556410i
$804$	10.2408	+	7.44038i	0.361165	+	0.262402i
$805$		0			0
$806$	9.91361	−	7.20266i	0.349192	−	0.253703i
$807$	−24.8404			−0.874422
$808$	−2.83776	+	2.06175i	−0.0998319	+	0.0725322i
$809$	3.57476	+	11.0020i	0.125682	+	0.386809i	0.994025	−	0.109156i	$-0.0348147\pi$
$809$	3.57476	+	11.0020i	0.125682	+	0.386809i	−0.868343	+	0.495964i	$0.834815\pi$
$810$		0			0
$811$	13.7829	−	42.4193i	0.483982	−	1.48954i	−0.349468	−	0.936948i	$-0.613638\pi$
$811$	13.7829	−	42.4193i	0.483982	−	1.48954i	0.833450	−	0.552595i	$-0.186362\pi$
$812$	0.349011	+	1.07415i	0.0122479	+	0.0376951i
$813$	−21.4837	−	66.1201i	−0.753467	−	2.31893i
$814$	5.55445	−	17.0948i	0.194683	−	0.599174i
$815$		0			0
$816$	0.739350	+	2.27549i	0.0258824	+	0.0796579i
$817$	−20.6366	+	14.9934i	−0.721984	+	0.524552i
$818$	15.4128			0.538896
$819$	27.3891	−	19.8994i	0.957053	−	0.695340i
$820$		0			0
$821$	−30.8655	−	22.4251i	−1.07721	−	0.782640i	−0.100017	−	0.994986i	$-0.531890\pi$
$821$	−30.8655	−	22.4251i	−1.07721	−	0.782640i	−0.977195	+	0.212346i	$0.931890\pi$
$822$	−10.5454	−	7.66171i	−0.367814	−	0.267233i
$823$	15.7372	−	48.4340i	0.548563	−	1.68830i	−0.163801	−	0.986493i	$-0.552376\pi$
$823$	15.7372	−	48.4340i	0.548563	−	1.68830i	0.712364	−	0.701810i	$-0.247624\pi$
$824$	−4.64178			−0.161704
$825$		0			0
$826$	5.06757			0.176323
$827$	9.86857	−	30.3723i	0.343164	−	1.05615i	−0.619396	−	0.785079i	$-0.712622\pi$
$827$	9.86857	−	30.3723i	0.343164	−	1.05615i	0.962560	−	0.271070i	$-0.0873776\pi$
$828$	8.60938	+	6.25508i	0.299197	+	0.217379i
$829$	26.0284	+	18.9107i	0.904004	+	0.656797i	0.939491	−	0.342573i	$-0.111298\pi$
$829$	26.0284	+	18.9107i	0.904004	+	0.656797i	−0.0354873	+	0.999370i	$0.511298\pi$
$830$		0			0
$831$	16.7330	−	12.1572i	0.580461	−	0.421730i
$832$	5.79360			0.200857
$833$	3.89421	−	2.82931i	0.134926	−	0.0980298i
$834$	−12.0207	−	36.9958i	−0.416242	−	1.28106i
$835$		0			0
$836$	−2.17921	+	6.70692i	−0.0753695	+	0.231964i
$837$	4.59455	+	14.1406i	0.158811	+	0.488769i
$838$	−6.56044	−	20.1910i	−0.226627	−	0.697485i
$839$	−9.31121	+	28.6570i	−0.321459	+	0.989348i	0.651555	+	0.758601i	$0.274117\pi$
$839$	−9.31121	+	28.6570i	−0.321459	+	0.989348i	−0.973014	+	0.230747i	$0.925883\pi$
$840$		0			0
$841$	−8.62209	−	26.5361i	−0.297313	−	0.915037i
$842$	26.5536	−	19.2923i	0.915096	−	0.664856i
$843$	6.55097			0.225627
$844$	13.5741	−	9.86215i	0.467239	−	0.339469i
$845$		0			0
$846$	37.9527	+	27.5742i	1.30484	+	0.948022i
$847$	−5.86525	−	4.26136i	−0.201532	−	0.146422i
$848$	0.793604	−	2.44246i	0.0272525	−	0.0838745i
$849$	−28.2016			−0.967876
$850$		0			0
$851$	−17.0663			−0.585025
$852$	4.39790	−	13.5353i	0.150670	−	0.463713i
$853$	17.3966	+	12.6394i	0.595649	+	0.432765i	0.844332	−	0.535820i	$-0.179998\pi$
$853$	17.3966	+	12.6394i	0.595649	+	0.432765i	−0.248683	+	0.968585i	$0.579998\pi$
$854$	8.09345	+	5.88024i	0.276952	+	0.201218i
$855$		0			0
$856$	−6.15006	+	4.46828i	−0.210205	+	0.152723i
$857$	−40.1894			−1.37284			−0.686422	−	0.727204i	$-0.740819\pi$
$857$	−40.1894			−1.37284			−0.686422	+	0.727204i	$0.740819\pi$
$858$	−28.1173	+	20.4284i	−0.959910	+	0.697416i
$859$	−16.4439	−	50.6091i	−0.561058	−	1.72676i	−0.679382	−	0.733785i	$-0.737752\pi$
$859$	−16.4439	−	50.6091i	−0.561058	−	1.72676i	0.118323	−	0.992975i	$-0.462248\pi$
$860$		0			0
$861$	6.35364	−	19.5545i	0.216532	−	0.666416i
$862$	0.259819	+	0.799639i	0.00884945	+	0.0272358i
$863$	3.37194	+	10.3778i	0.114782	+	0.353264i	0.991902	−	0.127009i	$-0.0405377\pi$
$863$	3.37194	+	10.3778i	0.114782	+	0.353264i	−0.877119	+	0.480273i	$0.840538\pi$
$864$	−2.17229	+	6.68562i	−0.0739027	+	0.227449i
$865$		0			0
$866$	−10.5174	−	32.3693i	−0.357396	−	1.09995i
$867$	38.3178	−	27.8395i	1.30134	−	0.945479i
$868$	−2.27938			−0.0773672
$869$	−12.0332	+	8.74265i	−0.408199	+	0.296574i
$870$		0			0
$871$	20.4441	+	14.8535i	0.692723	+	0.503293i
$872$	−2.41602	−	1.75534i	−0.0818167	−	0.0594433i
$873$	0.855677	−	2.63350i	0.0289603	−	0.0891306i
$874$	6.69572			0.226486
$875$		0			0
$876$	3.76612			0.127246
$877$	−1.74877	+	5.38217i	−0.0590519	+	0.181743i	−0.976231	−	0.216732i	$-0.930460\pi$
$877$	−1.74877	+	5.38217i	−0.0590519	+	0.181743i	0.917179	+	0.398475i	$0.130460\pi$
$878$	−1.28887	−	0.936419i	−0.0434973	−	0.0316026i
$879$	−15.3167	−	11.1282i	−0.516620	−	0.375346i
$880$		0			0
$881$	−12.3606	+	8.98051i	−0.416440	+	0.302561i	−0.776204	−	0.630482i	$-0.782857\pi$
$881$	−12.3606	+	8.98051i	−0.416440	+	0.302561i	0.359764	+	0.933043i	$0.382857\pi$
$882$	31.6584			1.06599
$883$	−20.6662	+	15.0149i	−0.695473	+	0.505291i	−0.878455	−	0.477826i	$-0.841425\pi$
$883$	−20.6662	+	15.0149i	−0.695473	+	0.505291i	0.182982	+	0.983116i	$0.441425\pi$
$884$	1.47599	+	4.54264i	0.0496431	+	0.152786i
$885$		0			0
$886$	−7.60916	+	23.4186i	−0.255635	+	0.786763i
$887$	−0.521792	−	1.60591i	−0.0175201	−	0.0539212i	0.941914	−	0.335853i	$-0.109025\pi$
$887$	−0.521792	−	1.60591i	−0.0175201	−	0.0539212i	−0.959434	+	0.281932i	$0.909025\pi$
$888$	−7.79834	−	24.0008i	−0.261695	−	0.805415i
$889$	7.11037	−	21.8835i	0.238474	−	0.733948i
$890$		0			0
$891$	−2.64070	−	8.12724i	−0.0884668	−	0.272273i
$892$	−9.45251	+	6.86765i	−0.316493	+	0.229946i
$893$	29.5167			0.987738
$894$	31.9634	−	23.2228i	1.06902	−	0.776686i
$895$		0			0
$896$	−0.871864	−	0.633446i	−0.0291269	−	0.0211620i
$897$	26.6965	+	19.3962i	0.891371	+	0.647619i
$898$	10.5432	−	32.4487i	0.351832	−	1.08283i
$899$	−2.21662			−0.0739284
$900$		0			0
$901$	2.11727			0.0705363
$902$	−4.19924	+	12.9239i	−0.139819	+	0.430320i
$903$	18.9183	+	13.7449i	0.629560	+	0.457402i
$904$	−16.3410	−	11.8724i	−0.543493	−	0.394871i
$905$		0			0
$906$	20.6572	−	15.0083i	0.686289	−	0.498618i
$907$	−1.58315			−0.0525677			−0.0262838	−	0.999655i	$-0.508367\pi$
$907$	−1.58315			−0.0525677			−0.0262838	+	0.999655i	$0.508367\pi$
$908$	−0.576751	+	0.419034i	−0.0191402	+	0.0139061i
$909$	−5.87733	−	18.0886i	−0.194939	−	0.599960i
$910$		0			0
$911$	−1.28770	+	3.96315i	−0.0426635	+	0.131305i	−0.970120	−	0.242627i	$-0.921991\pi$
$911$	−1.28770	+	3.96315i	−0.0426635	+	0.131305i	0.927456	+	0.373932i	$0.121991\pi$
$912$	3.05957	+	9.41637i	0.101312	+	0.311807i
$913$	−9.56093	−	29.4255i	−0.316421	−	0.973843i
$914$	−1.07826	+	3.31854i	−0.0356657	+	0.109768i
$915$		0			0
$916$	6.30918	+	19.4177i	0.208461	+	0.641578i
$917$	−7.85341	+	5.70584i	−0.259342	+	0.188423i
$918$	−5.79547			−0.191279
$919$	29.8895	−	21.7160i	0.985963	−	0.716344i	0.0269300	−	0.999637i	$-0.491427\pi$
$919$	29.8895	−	21.7160i	0.985963	−	0.716344i	0.959033	+	0.283293i	$0.0914269\pi$
$920$		0			0
$921$	48.6197	+	35.3243i	1.60207	+	1.16397i
$922$	10.9097	+	7.92637i	0.359292	+	0.261041i
$923$	8.77970	−	27.0211i	0.288987	−	0.889412i
$924$	6.46486			0.212678
$925$		0			0
$926$	−1.86401			−0.0612552
$927$	7.77764	−	23.9371i	0.255451	−	0.786198i
$928$	−0.847859	−	0.616005i	−0.0278323	−	0.0202214i
$929$	10.7812	+	7.83301i	0.353720	+	0.256993i	0.750428	−	0.660952i	$-0.229847\pi$
$929$	10.7812	+	7.83301i	0.353720	+	0.256993i	−0.396708	+	0.917945i	$0.629847\pi$
$930$		0			0
$931$	16.1150	−	11.7082i	0.528146	−	0.383721i
$932$	−15.0403			−0.492661
$933$	−18.7105	+	13.5940i	−0.612554	+	0.445047i
$934$	−4.03005	−	12.4032i	−0.131867	−	0.405846i
$935$		0			0
$936$	−9.70759	+	29.8769i	−0.317303	+	0.976557i
$937$	14.6167	+	44.9856i	0.477507	+	1.46961i	0.842547	+	0.538623i	$0.181055\pi$
$937$	14.6167	+	44.9856i	0.477507	+	1.46961i	−0.365040	+	0.930992i	$0.618945\pi$
$938$	−1.45257	−	4.47054i	−0.0474279	−	0.145968i
$939$	−4.20628	+	12.9456i	−0.137267	+	0.422463i
$940$		0			0
$941$	6.21002	+	19.1125i	0.202441	+	0.623049i	0.999809	+	0.0195553i	$0.00622505\pi$
$941$	6.21002	+	19.1125i	0.202441	+	0.623049i	−0.797368	+	0.603493i	$0.793775\pi$
$942$	27.8357	−	20.2238i	0.906936	−	0.658928i
$943$	12.9024			0.420159
$944$	−3.80423	+	2.76393i	−0.123817	+	0.0899583i
$945$		0			0
$946$	−12.5034	−	9.08427i	−0.406521	−	0.295355i
$947$	−25.5742	−	18.5807i	−0.831049	−	0.603793i	0.0888068	−	0.996049i	$-0.471695\pi$
$947$	−25.5742	−	18.5807i	−0.831049	−	0.603793i	−0.919856	+	0.392256i	$0.871695\pi$
$948$	−6.45309	+	19.8606i	−0.209586	+	0.645041i
$949$	7.51846			0.244060
$950$		0			0
$951$	−41.4990			−1.34570
$952$	0.274554	−	0.844989i	0.00889833	−	0.0273863i
$953$	−24.7901	−	18.0111i	−0.803031	−	0.583436i	0.108771	−	0.994067i	$-0.465308\pi$
$953$	−24.7901	−	18.0111i	−0.803031	−	0.583436i	−0.911802	+	0.410631i	$0.865308\pi$
$954$	11.2657	+	8.18504i	0.364742	+	0.265000i
$955$		0			0
$956$	−3.38679	+	2.46065i	−0.109537	+	0.0795831i
$957$	6.28686			0.203225
$958$	10.0171	−	7.27787i	0.323639	−	0.235137i
$959$	1.49578	+	4.60352i	0.0483011	+	0.148656i
$960$		0			0
$961$	−8.19713	+	25.2282i	−0.264424	+	0.813812i
$962$	−15.5681	−	47.9138i	−0.501937	−	1.54480i
$963$	−12.7375	−	39.2020i	−0.410460	−	1.26327i
$964$	−9.09011	+	27.9765i	−0.292773	+	0.901062i
$965$		0			0
$966$	−1.89680	−	5.83776i	−0.0610286	−	0.187827i
$967$	12.8779	−	9.35631i	0.414124	−	0.300879i	−0.361145	−	0.932510i	$-0.617614\pi$
$967$	12.8779	−	9.35631i	0.414124	−	0.300879i	0.775269	+	0.631631i	$0.217614\pi$
$968$	6.72725			0.216222
$969$	−6.60372	+	4.79788i	−0.212142	+	0.154130i
$970$		0			0
$971$	−41.1459	−	29.8942i	−1.32043	−	0.959351i	−0.999927	−	0.0121047i	$-0.996147\pi$
$971$	−41.1459	−	29.8942i	−1.32043	−	0.959351i	−0.320507	−	0.947246i	$-0.603853\pi$
$972$	7.35503	+	5.34375i	0.235913	+	0.171401i
$973$	−4.46381	+	13.7382i	−0.143103	+	0.440426i
$974$	4.51906			0.144800
$975$		0			0
$976$	−9.28293			−0.297139
$977$	5.12432	−	15.7710i	0.163942	−	0.504560i	−0.835015	−	0.550227i	$-0.814541\pi$
$977$	5.12432	−	15.7710i	0.163942	−	0.504560i	0.998957	+	0.0456666i	$0.0145412\pi$
$978$	35.1215	+	25.5173i	1.12306	+	0.815952i
$979$	−19.5795	−	14.2253i	−0.625763	−	0.454644i
$980$		0			0
$981$	13.1003	−	9.51790i	0.418259	−	0.303883i
$982$	−27.4676			−0.876528
$983$	−2.17446	+	1.57984i	−0.0693546	+	0.0503891i	−0.621922	−	0.783079i	$-0.713648\pi$
$983$	−2.17446	+	1.57984i	−0.0693546	+	0.0503891i	0.552568	+	0.833468i	$0.313648\pi$
$984$	5.89565	+	18.1449i	0.187946	+	0.578440i
$985$		0			0
$986$	0.266994	−	0.821724i	0.00850283	−	0.0261690i
$987$	−8.36166	−	25.7345i	−0.266155	−	0.819140i
$988$	6.10793	+	18.7983i	0.194319	+	0.598053i
$989$	−4.53455	+	13.9559i	−0.144190	+	0.443772i
$990$		0			0
$991$	−5.94835	−	18.3071i	−0.188956	−	0.581545i	0.811038	−	0.584993i	$-0.198903\pi$
$991$	−5.94835	−	18.3071i	−0.188956	−	0.581545i	−0.999994	+	0.00344733i	$0.998903\pi$
$992$	1.71113	−	1.24321i	0.0543284	−	0.0394719i
$993$	103.230			3.27589
$994$	−4.27560	+	3.10641i	−0.135614	+	0.0985293i
$995$		0			0
$996$	−35.1428	−	25.5327i	−1.11354	−	0.809036i
$997$	34.7455	+	25.2441i	1.10040	+	0.799489i	0.981125	−	0.193372i	$-0.0619425\pi$
$997$	34.7455	+	25.2441i	1.10040	+	0.799489i	0.119277	+	0.992861i	$0.461942\pi$
$998$	−4.16598	+	12.8216i	−0.131872	+	0.405860i
$999$	61.1280			1.93401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.d.c.101.1		8
5.2	odd	4		50.2.e.a.29.1	yes	8
5.3	odd	4		250.2.e.a.149.2		8
5.4	even	2		250.2.d.b.101.2		8
15.2	even	4		450.2.l.b.379.2		8
20.7	even	4		400.2.y.a.129.2		8
25.6	even	5	inner	250.2.d.c.151.1		8
25.8	odd	20		50.2.e.a.19.1	✓	8
25.9	even	10		1250.2.a.i.1.1		4
25.12	odd	20		1250.2.b.c.1249.1		8
25.13	odd	20		1250.2.b.c.1249.8		8
25.16	even	5		1250.2.a.h.1.4		4
25.17	odd	20		250.2.e.a.99.2		8
25.19	even	10		250.2.d.b.151.2		8
75.8	even	20		450.2.l.b.19.2		8
100.59	odd	10		10000.2.a.bb.1.4		4
100.83	even	20		400.2.y.a.369.2		8
100.91	odd	10		10000.2.a.o.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.19.1	✓	8	25.8	odd	20
50.2.e.a.29.1	yes	8	5.2	odd	4
250.2.d.b.101.2		8	5.4	even	2
250.2.d.b.151.2		8	25.19	even	10
250.2.d.c.101.1		8	1.1	even	1	trivial
250.2.d.c.151.1		8	25.6	even	5	inner
250.2.e.a.99.2		8	25.17	odd	20
250.2.e.a.149.2		8	5.3	odd	4
400.2.y.a.129.2		8	20.7	even	4
400.2.y.a.369.2		8	100.83	even	20
450.2.l.b.19.2		8	75.8	even	20
450.2.l.b.379.2		8	15.2	even	4
1250.2.a.h.1.4		4	25.16	even	5
1250.2.a.i.1.1		4	25.9	even	10
1250.2.b.c.1249.1		8	25.12	odd	20
1250.2.b.c.1249.8		8	25.13	odd	20
10000.2.a.o.1.1		4	100.91	odd	10
10000.2.a.bb.1.4		4	100.59	odd	10

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.34786 - 1.70582i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.34786 - 1.70582i) q^{6} -1.07768 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.67557 + 5.15688i) q^{9} +(-0.638757 + 1.96589i) q^{11} +(0.896802 + 2.76007i) q^{12} +(1.79032 + 5.51005i) q^{13} +(0.333023 - 1.02494i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.666977 + 0.484587i) q^{17} -5.42226 q^{18} +(-2.76007 + 2.00531i) q^{19} +(2.53025 + 1.83833i) q^{21} +(-1.67229 - 1.21499i) q^{22} +(-0.606480 + 1.86655i) q^{23} -2.90211 q^{24} -5.79360 q^{26} +(2.17229 - 6.68562i) q^{27} +(0.871864 + 0.633446i) q^{28} +(0.847859 + 0.616005i) q^{29} +(-1.71113 + 1.24321i) q^{31} -1.00000 q^{32} +(4.85317 - 3.52603i) q^{33} +(-0.254763 - 0.784079i) q^{34} +(1.67557 - 5.15688i) q^{36} +(2.68712 + 8.27012i) q^{37} +(-1.05425 - 3.24466i) q^{38} +(5.19572 - 15.9908i) q^{39} +(-2.03150 - 6.25232i) q^{41} +(-2.53025 + 1.83833i) q^{42} +7.47684 q^{43} +(1.67229 - 1.21499i) q^{44} +(-1.58779 - 1.15359i) q^{46} +(-6.99942 - 5.08538i) q^{47} +(0.896802 - 2.76007i) q^{48} -5.83860 q^{49} +2.39259 q^{51} +(1.79032 - 5.51005i) q^{52} +(-2.07768 - 1.50953i) q^{53} +(5.68712 + 4.13194i) q^{54} +(-0.871864 + 0.633446i) q^{56} +9.90096 q^{57} +(-0.847859 + 0.616005i) q^{58} +(1.45309 + 4.47214i) q^{59} +(-2.86858 + 8.82859i) q^{61} +(-0.653594 - 2.01155i) q^{62} +(-1.80573 - 5.55748i) q^{63} +(0.309017 - 0.951057i) q^{64} +(1.85375 + 5.70524i) q^{66} +(3.52874 - 2.56378i) q^{67} +0.824429 q^{68} +(4.60793 - 3.34786i) q^{69} +(-3.96740 - 2.88249i) q^{71} +(4.38670 + 3.18712i) q^{72} +(0.401017 - 1.23420i) q^{73} -8.69572 q^{74} +3.41164 q^{76} +(0.688378 - 2.11861i) q^{77} +(13.6026 + 9.88284i) q^{78} +(5.82141 + 4.22950i) q^{79} +(-3.34458 + 2.42998i) q^{81} +6.57408 q^{82} +(-12.1094 + 8.79798i) q^{83} +(-0.966469 - 2.97449i) q^{84} +(-2.31047 + 7.11089i) q^{86} +(-0.939859 - 2.89259i) q^{87} +(0.638757 + 1.96589i) q^{88} +(-3.61803 + 11.1352i) q^{89} +(-1.92940 - 5.93809i) q^{91} +(1.58779 - 1.15359i) q^{92} +6.13818 q^{93} +(6.99942 - 5.08538i) q^{94} +(2.34786 + 1.70582i) q^{96} +(-0.413147 - 0.300169i) q^{97} +(1.80423 - 5.55284i) q^{98} -11.2081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} + 2 q^{8} + 4 q^{9} - 4 q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} - 4 q^{18} - 10 q^{19} + 16 q^{21} - 6 q^{22} - 12 q^{23} - 8 q^{24}+ \cdots + 28 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 + 2 * q^8 + 4 * q^9 - 4 * q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^17 - 4 * q^18 - 10 * q^19 + 16 * q^21 - 6 * q^22 - 12 * q^23 - 8 * q^24 - 28 * q^26 + 10 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^31 - 8 * q^32 + 16 * q^33 + 4 * q^34 + 4 * q^36 - 4 * q^37 - 10 * q^38 + 8 * q^39 - 14 * q^41 - 16 * q^42 + 28 * q^43 + 6 * q^44 - 8 * q^46 - 24 * q^47 - 2 * q^48 + 16 * q^49 + 16 * q^51 - 2 * q^52 + 8 * q^53 + 20 * q^54 + 4 * q^56 + 10 * q^58 - 14 * q^61 + 14 * q^62 - 12 * q^63 - 2 * q^64 + 24 * q^66 - 4 * q^67 + 16 * q^68 + 8 * q^69 - 34 * q^71 + 6 * q^72 - 12 * q^73 - 36 * q^74 - 18 * q^77 + 22 * q^78 - 12 * q^81 + 24 * q^82 - 32 * q^83 - 14 * q^84 + 22 * q^86 + 20 * q^87 + 4 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 + 16 * q^93 + 24 * q^94 + 2 * q^96 - 4 * q^97 - 16 * q^98 + 28 * q^99

Introduction

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