LMFDB - Embedded newform 950.2.q.e.407.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.5
Character	$\chi$	$=$	950.407
Dual form			950.2.q.e.943.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-1.47205 + 0.394434i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.761988 - 1.31980i) q^{6} +(-1.69567 - 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.586729 + 0.338748i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.47205 + 0.394434i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.761988 - 1.31980i) q^{6} +(-1.69567 - 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.586729 + 0.338748i) q^{9} +4.92692 q^{11} +(1.07761 - 1.07761i) q^{12} +(0.951806 - 3.55219i) q^{13} +(1.19902 - 2.07676i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.153111 + 0.0410260i) q^{17} +(-0.479062 - 0.479062i) q^{18} +(-0.533033 + 4.32618i) q^{19} +(3.16493 + 1.82727i) q^{21} +(1.27518 + 4.75904i) q^{22} +(2.31632 + 0.620657i) q^{23} +(1.31980 + 0.761988i) q^{24} +3.67750 q^{26} +(3.96292 - 3.96292i) q^{27} +(2.31632 + 0.620657i) q^{28} +(4.62539 + 8.01141i) q^{29} -6.10371i q^{31} +(0.965926 + 0.258819i) q^{32} +(-7.25267 + 1.94335i) q^{33} +(-0.0792561 - 0.137276i) q^{34} +(0.338748 - 0.586729i) q^{36} +(-2.44015 + 2.44015i) q^{37} +(-4.31673 + 0.604829i) q^{38} +5.60442i q^{39} +(6.51141 + 3.75937i) q^{41} +(-0.945867 + 3.53002i) q^{42} +(1.64858 + 6.15257i) q^{43} +(-4.26684 + 2.46346i) q^{44} +2.39804i q^{46} +(-0.702709 + 2.62255i) q^{47} +(-0.394434 + 1.47205i) q^{48} -1.24943i q^{49} +(0.209205 - 0.120784i) q^{51} +(0.951806 + 3.55219i) q^{52} +(-1.61747 + 6.03648i) q^{53} +(4.85357 + 2.80221i) q^{54} +2.39804i q^{56} +(-0.921745 - 6.57860i) q^{57} +(-6.54129 + 6.54129i) q^{58} +(1.77358 - 3.07193i) q^{59} +(2.36272 + 4.09236i) q^{61} +(5.89573 - 1.57976i) q^{62} +(1.56930 + 0.420493i) q^{63} +1.00000i q^{64} +(-3.75426 - 6.50256i) q^{66} +(8.84162 + 2.36911i) q^{67} +(0.112085 - 0.112085i) q^{68} -3.65455 q^{69} +(3.64869 + 2.10657i) q^{71} +(0.654411 + 0.175349i) q^{72} +(-0.847284 - 3.16211i) q^{73} +(-2.98856 - 1.72545i) q^{74} +(-1.70147 - 4.01310i) q^{76} +(-8.35442 - 8.35442i) q^{77} +(-5.41345 + 1.45053i) q^{78} +(7.39795 - 12.8136i) q^{79} +(-3.25426 + 5.63654i) q^{81} +(-1.94599 + 7.26254i) q^{82} +(2.27867 - 2.27867i) q^{83} -3.65455 q^{84} +(-5.51624 + 3.18480i) q^{86} +(-9.96877 - 9.96877i) q^{87} +(-3.48386 - 3.48386i) q^{88} +(-3.93005 - 6.80704i) q^{89} +(-7.63728 + 4.40938i) q^{91} +(-2.31632 + 0.620657i) q^{92} +(2.40751 + 8.98495i) q^{93} -2.71506 q^{94} -1.52398 q^{96} +(4.52503 + 16.8877i) q^{97} +(1.20685 - 0.323375i) q^{98} +(-2.89077 + 1.66898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{6}+O(q^{10}) $ 24 * q - 12 * q^6	$ 24 q - 12 q^{6} - 48 q^{11} + 12 q^{16} - 84 q^{21} + 24 q^{26} - 24 q^{36} + 48 q^{41} + 12 q^{51} + 12 q^{61} + 24 q^{71} + 36 q^{76} + 12 q^{81} - 36 q^{86} - 228 q^{91} - 24 q^{96}+O(q^{100}) $ 24 * q - 12 * q^6 - 48 * q^11 + 12 * q^16 - 84 * q^21 + 24 * q^26 - 24 * q^36 + 48 * q^41 + 12 * q^51 + 12 * q^61 + 24 * q^71 + 36 * q^76 + 12 * q^81 - 36 * q^86 - 228 * q^91 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−1.47205	+	0.394434i	−0.849887	+	0.227727i	−0.657371	−	0.753567i	$-0.728332\pi$
$3$	−1.47205	+	0.394434i	−0.849887	+	0.227727i	−0.192516	+	0.981294i	$0.561665\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.761988	−	1.31980i	−0.311080	−	0.538807i
$7$	−1.69567	−	1.69567i	−0.640902	−	0.640902i	0.309875	−	0.950777i	$-0.399713\pi$
$7$	−1.69567	−	1.69567i	−0.640902	−	0.640902i	−0.950777	+	0.309875i	$0.899713\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.586729	+	0.338748i	−0.195576	+	0.112916i
$10$		0			0
$11$	4.92692			1.48552			0.742761	−	0.669556i	$-0.233516\pi$
$11$	4.92692			1.48552			0.742761	+	0.669556i	$0.233516\pi$
$12$	1.07761	−	1.07761i	0.311080	−	0.311080i
$13$	0.951806	−	3.55219i	0.263983	−	0.985200i	−0.698886	−	0.715233i	$-0.746321\pi$
$13$	0.951806	−	3.55219i	0.263983	−	0.985200i	0.962870	−	0.269967i	$-0.0870127\pi$
$14$	1.19902	−	2.07676i	0.320451	−	0.555037i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.153111	+	0.0410260i	−0.0371349	+	0.00995026i	−0.277339	−	0.960772i	$-0.589452\pi$
$17$	−0.153111	+	0.0410260i	−0.0371349	+	0.00995026i	0.240204	+	0.970722i	$0.422786\pi$
$18$	−0.479062	−	0.479062i	−0.112916	−	0.112916i
$19$	−0.533033	+	4.32618i	−0.122286	+	0.992495i
$19$	−0.533033	+	4.32618i	−0.122286	+	0.992495i
$20$		0			0
$21$	3.16493	+	1.82727i	0.690645	+	0.398744i
$22$	1.27518	+	4.75904i	0.271870	+	1.01463i
$23$	2.31632	+	0.620657i	0.482987	+	0.129416i	0.492093	−	0.870543i	$-0.336232\pi$
$23$	2.31632	+	0.620657i	0.482987	+	0.129416i	−0.00910610	+	0.999959i	$0.502899\pi$
$24$	1.31980	+	0.761988i	0.269404	+	0.155540i
$25$		0			0
$26$	3.67750			0.721216
$27$	3.96292	−	3.96292i	0.762665	−	0.762665i
$28$	2.31632	+	0.620657i	0.437744	+	0.117293i
$29$	4.62539	+	8.01141i	0.858914	+	1.48768i	0.872966	+	0.487781i	$0.162193\pi$
$29$	4.62539	+	8.01141i	0.858914	+	1.48768i	−0.0140525	+	0.999901i	$0.504473\pi$
$30$		0			0
$31$		−	6.10371i		−	1.09626i	−0.836394	−	0.548129i	$-0.815340\pi$
$31$		−	6.10371i		−	1.09626i	0.836394	−	0.548129i	$-0.184660\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−7.25267	+	1.94335i	−1.26253	+	0.338293i
$34$	−0.0792561	−	0.137276i	−0.0135923	−	0.0235426i
$35$		0			0
$36$	0.338748	−	0.586729i	0.0564580	−	0.0977881i
$37$	−2.44015	+	2.44015i	−0.401159	+	0.401159i	−0.878641	−	0.477483i	$-0.841549\pi$
$37$	−2.44015	+	2.44015i	−0.401159	+	0.401159i	0.477483	+	0.878641i	$0.341549\pi$
$38$	−4.31673	+	0.604829i	−0.700267	+	0.0981162i
$39$			5.60442i			0.897425i
$40$		0			0
$41$	6.51141	+	3.75937i	1.01691	+	0.587114i	0.913208	−	0.407494i	$-0.133597\pi$
$41$	6.51141	+	3.75937i	1.01691	+	0.587114i	0.103704	+	0.994608i	$0.466931\pi$
$42$	−0.945867	+	3.53002i	−0.145950	+	0.544695i
$43$	1.64858	+	6.15257i	0.251406	+	0.938258i	0.970055	+	0.242886i	$0.0780940\pi$
$43$	1.64858	+	6.15257i	0.251406	+	0.938258i	−0.718649	+	0.695373i	$0.755239\pi$
$44$	−4.26684	+	2.46346i	−0.643250	+	0.371381i
$45$		0			0
$46$			2.39804i			0.353571i
$47$	−0.702709	+	2.62255i	−0.102501	+	0.382538i	−0.998050	−	0.0624252i	$-0.980117\pi$
$47$	−0.702709	+	2.62255i	−0.102501	+	0.382538i	0.895549	+	0.444963i	$0.146783\pi$
$48$	−0.394434	+	1.47205i	−0.0569317	+	0.212472i
$49$		−	1.24943i		−	0.178489i
$50$		0			0
$51$	0.209205	−	0.120784i	0.0292945	−	0.0169132i
$52$	0.951806	+	3.55219i	0.131992	+	0.492600i
$53$	−1.61747	+	6.03648i	−0.222177	+	0.829174i	0.761339	+	0.648354i	$0.224542\pi$
$53$	−1.61747	+	6.03648i	−0.222177	+	0.829174i	−0.983516	+	0.180821i	$0.942125\pi$
$54$	4.85357	+	2.80221i	0.660487	+	0.381332i
$55$		0			0
$56$			2.39804i			0.320451i
$57$	−0.921745	−	6.57860i	−0.122088	−	0.871357i
$58$	−6.54129	+	6.54129i	−0.858914	+	0.858914i
$59$	1.77358	−	3.07193i	0.230900	−	0.399931i	−0.727173	−	0.686454i	$-0.759166\pi$
$59$	1.77358	−	3.07193i	0.230900	−	0.399931i	0.958073	+	0.286523i	$0.0924995\pi$
$60$		0			0
$61$	2.36272	+	4.09236i	0.302516	+	0.523973i	0.976705	−	0.214586i	$-0.0688401\pi$
$61$	2.36272	+	4.09236i	0.302516	+	0.523973i	−0.674189	+	0.738559i	$0.735507\pi$
$62$	5.89573	−	1.57976i	0.748758	−	0.200629i
$63$	1.56930	+	0.420493i	0.197713	+	0.0529771i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−3.75426	−	6.50256i	−0.462117	−	0.800410i
$67$	8.84162	+	2.36911i	1.08018	+	0.289432i	0.754668	−	0.656107i	$-0.227798\pi$
$67$	8.84162	+	2.36911i	1.08018	+	0.289432i	0.325508	+	0.945539i	$0.394465\pi$
$68$	0.112085	−	0.112085i	0.0135923	−	0.0135923i
$69$	−3.65455			−0.439956
$70$		0			0
$71$	3.64869	+	2.10657i	0.433020	+	0.250004i	0.700632	−	0.713523i	$-0.252901\pi$
$71$	3.64869	+	2.10657i	0.433020	+	0.250004i	−0.267613	+	0.963527i	$0.586235\pi$
$72$	0.654411	+	0.175349i	0.0771231	+	0.0206651i
$73$	−0.847284	−	3.16211i	−0.0991671	−	0.370097i	0.898451	−	0.439073i	$-0.144693\pi$
$73$	−0.847284	−	3.16211i	−0.0991671	−	0.370097i	−0.997618	+	0.0689769i	$0.978027\pi$
$74$	−2.98856	−	1.72545i	−0.347414	−	0.200579i
$75$		0			0
$76$	−1.70147	−	4.01310i	−0.195172	−	0.460334i
$77$	−8.35442	−	8.35442i	−0.952074	−	0.952074i
$78$	−5.41345	+	1.45053i	−0.612953	+	0.164240i
$79$	7.39795	−	12.8136i	0.832334	−	1.44165i	−0.0638484	−	0.997960i	$-0.520337\pi$
$79$	7.39795	−	12.8136i	0.832334	−	1.44165i	0.896183	−	0.443685i	$-0.146329\pi$
$80$		0			0
$81$	−3.25426	+	5.63654i	−0.361584	+	0.626282i
$82$	−1.94599	+	7.26254i	−0.214899	+	0.802013i
$83$	2.27867	−	2.27867i	0.250117	−	0.250117i	−0.570902	−	0.821019i	$-0.693406\pi$
$83$	2.27867	−	2.27867i	0.250117	−	0.250117i	0.821019	+	0.570902i	$0.193406\pi$
$84$	−3.65455			−0.398744
$85$		0			0
$86$	−5.51624	+	3.18480i	−0.594832	+	0.343426i
$87$	−9.96877	−	9.96877i	−1.06876	−	1.06876i
$88$	−3.48386	−	3.48386i	−0.371381	−	0.371381i
$89$	−3.93005	−	6.80704i	−0.416584	−	0.721545i	0.579009	−	0.815321i	$-0.303439\pi$
$89$	−3.93005	−	6.80704i	−0.416584	−	0.721545i	−0.995593	+	0.0937763i	$0.970106\pi$
$90$		0			0
$91$	−7.63728	+	4.40938i	−0.800604	+	0.462229i
$92$	−2.31632	+	0.620657i	−0.241494	+	0.0647080i
$93$	2.40751	+	8.98495i	0.249647	+	0.931696i
$94$	−2.71506			−0.280037
$95$		0			0
$96$	−1.52398			−0.155540
$97$	4.52503	+	16.8877i	0.459447	+	1.71468i	0.674673	+	0.738117i	$0.264285\pi$
$97$	4.52503	+	16.8877i	0.459447	+	1.71468i	−0.215225	+	0.976564i	$0.569049\pi$
$98$	1.20685	−	0.323375i	0.121910	−	0.0326658i
$99$	−2.89077	+	1.66898i	−0.290533	+	0.167739i
$100$		0			0
$101$	3.87897	+	6.71857i	0.385972	+	0.668523i	0.991903	−	0.126994i	$-0.0405329\pi$
$101$	3.87897	+	6.71857i	0.385972	+	0.668523i	−0.605932	+	0.795517i	$0.707200\pi$
$102$	0.170815	+	0.170815i	0.0169132	+	0.0169132i
$103$	−3.63726	−	3.63726i	−0.358390	−	0.358390i	0.504829	−	0.863219i	$-0.331555\pi$
$103$	−3.63726	−	3.63726i	−0.358390	−	0.358390i	−0.863219	+	0.504829i	$0.831555\pi$
$104$	−3.18480	+	1.83875i	−0.312296	+	0.180304i
$105$		0			0
$106$	−6.24943			−0.606998
$107$	10.8399	−	10.8399i	1.04793	−	1.04793i	0.0491359	−	0.998792i	$-0.484353\pi$
$107$	10.8399	−	10.8399i	1.04793	−	1.04793i	0.998792	−	0.0491359i	$-0.0156468\pi$
$108$	−1.45053	+	5.41345i	−0.139577	+	0.520910i
$109$	−4.50461	+	7.80221i	−0.431463	+	0.747316i	−0.997000	−	0.0774073i	$-0.975336\pi$
$109$	−4.50461	+	7.80221i	−0.431463	+	0.747316i	0.565536	+	0.824723i	$0.308669\pi$
$110$		0			0
$111$	2.62954	−	4.55450i	0.249585	−	0.432294i
$112$	−2.31632	+	0.620657i	−0.218872	+	0.0586466i
$113$	13.1375	+	13.1375i	1.23588	+	1.23588i	0.961671	+	0.274205i	$0.0884146\pi$
$113$	13.1375	+	13.1375i	1.23588	+	1.23588i	0.274205	+	0.961671i	$0.411585\pi$
$114$	6.11587	−	2.59300i	0.572804	−	0.242857i
$115$		0			0
$116$	−8.01141	−	4.62539i	−0.743841	−	0.429457i
$117$	0.644845	+	2.40659i	0.0596159	+	0.222490i
$118$	3.42629	+	0.918072i	0.315416	+	0.0845154i
$119$	0.329192	+	0.190059i	0.0301770	+	0.0174227i
$120$		0			0
$121$	13.2746			1.20678
$122$	−3.34140	+	3.34140i	−0.302516	+	0.302516i
$123$	−11.0679	−	2.96564i	−0.997962	−	0.267403i
$124$	3.05185	+	5.28596i	0.274064	+	0.474694i
$125$		0			0
$126$			1.62466i			0.144736i
$127$	−7.71247	−	2.06655i	−0.684371	−	0.183377i	−0.100151	−	0.994972i	$-0.531933\pi$
$127$	−7.71247	−	2.06655i	−0.684371	−	0.183377i	−0.584220	+	0.811596i	$0.698599\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−4.85357	−	8.40663i	−0.427333	−	0.740162i
$130$		0			0
$131$	9.21772	−	15.9656i	0.805356	−	1.39492i	−0.110695	−	0.993854i	$-0.535308\pi$
$131$	9.21772	−	15.9656i	0.805356	−	1.39492i	0.916051	−	0.401062i	$-0.131359\pi$
$132$	5.30932	−	5.30932i	0.462117	−	0.462117i
$133$	8.23962	−	6.43192i	0.714465	−	0.557718i
$134$			9.15352i			0.790744i
$135$		0			0
$136$	0.137276	+	0.0792561i	0.0117713	+	0.00679616i
$137$	1.43518	−	5.35617i	0.122616	−	0.457608i	−0.877128	−	0.480257i	$-0.840543\pi$
$137$	1.43518	−	5.35617i	0.122616	−	0.457608i	0.999743	+	0.0226489i	$0.00720999\pi$
$138$	−0.945867	−	3.53002i	−0.0805176	−	0.300496i
$139$	5.00828	−	2.89153i	0.424797	−	0.245256i	−0.272331	−	0.962204i	$-0.587794\pi$
$139$	5.00828	−	2.89153i	0.424797	−	0.245256i	0.697127	+	0.716947i	$0.254461\pi$
$140$		0			0
$141$		−	4.13769i		−	0.348456i
$142$	−1.09044	+	4.06958i	−0.0915078	+	0.341512i
$143$	4.68947	−	17.5014i	0.392153	−	1.46354i
$144$			0.677496i			0.0564580i
$145$		0			0
$146$	2.83507	−	1.63683i	0.234632	−	0.135465i
$147$	0.492816	+	1.83921i	0.0406468	+	0.151696i
$148$	0.893158	−	3.33331i	0.0734171	−	0.273996i
$149$	−16.4960	−	9.52398i	−1.35141	−	0.780235i	−0.362959	−	0.931805i	$-0.618234\pi$
$149$	−16.4960	−	9.52398i	−1.35141	−	0.780235i	−0.988446	+	0.151570i	$0.951567\pi$
$150$		0			0
$151$			10.5073i			0.855072i	0.903998	+	0.427536i	$0.140618\pi$
$151$			10.5073i			0.855072i	−0.903998	+	0.427536i	$0.859382\pi$
$152$	3.43599	−	2.68216i	0.278695	−	0.217552i
$153$	0.0759372	−	0.0759372i	0.00613916	−	0.00613916i
$154$	5.90747	−	10.2320i	0.476037	−	0.824521i
$155$		0			0
$156$	−2.80221	−	4.85357i	−0.224356	−	0.388596i
$157$	−0.796403	+	0.213396i	−0.0635599	+	0.0170308i	−0.290459	−	0.956887i	$-0.593808\pi$
$157$	−0.796403	+	0.213396i	−0.0635599	+	0.0170308i	0.226899	+	0.973918i	$0.427141\pi$
$158$	14.2917	+	3.82946i	1.13699	+	0.304655i
$159$		−	9.52398i		−	0.755300i
$160$		0			0
$161$	−2.87529	−	4.98014i	−0.226604	−	0.392490i
$162$	−6.28674	−	1.68453i	−0.493933	−	0.132349i
$163$	0.165440	−	0.165440i	0.0129583	−	0.0129583i	−0.700598	−	0.713556i	$-0.747083\pi$
$163$	0.165440	−	0.165440i	0.0129583	−	0.0129583i	0.713556	+	0.700598i	$0.247083\pi$
$164$	−7.51873			−0.587114
$165$		0			0
$166$	2.79080	+	1.61127i	0.216608	+	0.125059i
$167$	−7.65682	−	2.05164i	−0.592502	−	0.158761i	−0.0499057	−	0.998754i	$-0.515892\pi$
$167$	−7.65682	−	2.05164i	−0.592502	−	0.158761i	−0.542597	+	0.839993i	$0.682559\pi$
$168$	−0.945867	−	3.53002i	−0.0729752	−	0.272347i
$169$	−0.453777	−	0.261988i	−0.0349059	−	0.0201529i
$170$		0			0
$171$	−1.15274	−	2.71886i	−0.0881523	−	0.207916i
$172$	−4.50399	−	4.50399i	−0.343426	−	0.343426i
$173$	2.46935	−	0.661662i	0.187742	−	0.0503052i	−0.163723	−	0.986506i	$-0.552350\pi$
$173$	2.46935	−	0.661662i	0.187742	−	0.0503052i	0.351465	+	0.936201i	$0.385684\pi$
$174$	7.04899	−	12.2092i	0.534382	−	0.925577i
$175$		0			0
$176$	2.46346	−	4.26684i	0.185690	−	0.321625i
$177$	−1.39912	+	5.22159i	−0.105164	+	0.392479i
$178$	5.55792	−	5.55792i	0.416584	−	0.416584i
$179$	21.3316			1.59440			0.797200	−	0.603715i	$-0.206314\pi$
$179$	21.3316			1.59440			0.797200	+	0.603715i	$0.206314\pi$
$180$		0			0
$181$	−6.16493	+	3.55933i	−0.458236	+	0.264563i	−0.711302	−	0.702886i	$-0.751894\pi$
$181$	−6.16493	+	3.55933i	−0.458236	+	0.264563i	0.253066	+	0.967449i	$0.418561\pi$
$182$	−6.23581	−	6.23581i	−0.462229	−	0.462229i
$183$	−5.09221	−	5.09221i	−0.376427	−	0.376427i
$184$	−1.19902	−	2.07676i	−0.0883928	−	0.153101i
$185$		0			0
$186$	−8.05569	+	4.65095i	−0.590672	+	0.341024i
$187$	−0.754366	+	0.202132i	−0.0551647	+	0.0147813i
$188$	−0.702709	−	2.62255i	−0.0512503	−	0.191269i
$189$	−13.4396			−0.977586
$190$		0			0
$191$	−25.8767			−1.87237			−0.936185	−	0.351508i	$-0.885669\pi$
$191$	−25.8767			−1.87237			−0.936185	+	0.351508i	$0.885669\pi$
$192$	−0.394434	−	1.47205i	−0.0284658	−	0.106236i
$193$	11.7857	−	3.15797i	0.848354	−	0.227316i	0.191649	−	0.981463i	$-0.438616\pi$
$193$	11.7857	−	3.15797i	0.848354	−	0.227316i	0.656705	+	0.754148i	$0.271950\pi$
$194$	−15.1411	+	8.74169i	−1.08706	+	0.627617i
$195$		0			0
$196$	0.624713	+	1.08203i	0.0446223	+	0.0772881i
$197$	−6.95348	−	6.95348i	−0.495415	−	0.495415i	0.414592	−	0.910007i	$-0.363924\pi$
$197$	−6.95348	−	6.95348i	−0.495415	−	0.495415i	−0.910007	+	0.414592i	$0.863924\pi$
$198$	−2.36030	−	2.36030i	−0.167739	−	0.167739i
$199$	22.8221	−	13.1763i	1.61782	−	0.934046i	0.630332	−	0.776326i	$-0.282919\pi$
$199$	22.8221	−	13.1763i	1.61782	−	0.934046i	0.987484	−	0.157721i	$-0.0504146\pi$
$200$		0			0
$201$	−13.9497			−0.983939
$202$	−5.48569	+	5.48569i	−0.385972	+	0.385972i
$203$	5.74157	−	21.4278i	0.402979	−	1.50394i
$204$	−0.120784	+	0.209205i	−0.00845660	+	0.0146473i
$205$		0			0
$206$	2.57193	−	4.45471i	0.179195	−	0.310374i
$207$	−1.56930	+	0.420493i	−0.109074	+	0.0292263i
$208$	−2.60038	−	2.60038i	−0.180304	−	0.180304i
$209$	−2.62621	+	21.3148i	−0.181659	+	1.47437i
$210$		0			0
$211$	−12.3233	−	7.11485i	−0.848370	−	0.489807i	0.0117307	−	0.999931i	$-0.496266\pi$
$211$	−12.3233	−	7.11485i	−0.848370	−	0.489807i	−0.860100	+	0.510125i	$0.829599\pi$
$212$	−1.61747	−	6.03648i	−0.111088	−	0.414587i
$213$	−6.20195	−	1.66181i	−0.424951	−	0.113865i
$214$	13.2761	+	7.66493i	0.907532	+	0.523964i
$215$		0			0
$216$	−5.60442			−0.381332
$217$	−10.3499	+	10.3499i	−0.702594	+	0.702594i
$218$	−8.70223	−	2.33176i	−0.589390	−	0.157926i
$219$	2.49449	+	4.32058i	0.168562	+	0.291957i
$220$		0			0
$221$			0.582928i			0.0392120i
$222$	5.07989	+	1.36115i	0.340940	+	0.0913545i
$223$	16.5519	−	4.43506i	1.10840	−	0.296994i	0.342216	−	0.939621i	$-0.388822\pi$
$223$	16.5519	−	4.43506i	1.10840	−	0.296994i	0.766179	+	0.642628i	$0.222156\pi$
$224$	−1.19902	−	2.07676i	−0.0801127	−	0.138759i
$225$		0			0
$226$	−9.28965	+	16.0901i	−0.617938	+	1.07030i
$227$	15.3513	−	15.3513i	1.01890	−	1.01890i	0.0190821	−	0.999818i	$-0.493926\pi$
$227$	15.3513	−	15.3513i	1.01890	−	1.01890i	0.999818	−	0.0190821i	$-0.00607439\pi$
$228$	4.08755	+	5.23636i	0.270705	+	0.346787i
$229$		−	29.5542i		−	1.95299i	−0.215531	−	0.976497i	$-0.569148\pi$
$229$		−	29.5542i		−	1.95299i	0.215531	−	0.976497i	$-0.430852\pi$
$230$		0			0
$231$	15.5934	+	9.00284i	1.02597	+	0.592343i
$232$	2.39428	−	8.93557i	0.157192	−	0.586649i
$233$	−1.19399	−	4.45603i	−0.0782209	−	0.291924i	0.915723	−	0.401809i	$-0.131618\pi$
$233$	−1.19399	−	4.45603i	−0.0782209	−	0.291924i	−0.993944	+	0.109885i	$0.964952\pi$
$234$	−2.15769	+	1.24574i	−0.141053	+	0.0814369i
$235$		0			0
$236$			3.54716i			0.230900i
$237$	−5.83601	+	21.7803i	−0.379089	+	1.41478i
$238$	−0.0983818	+	0.367166i	−0.00637714	+	0.0237998i
$239$			6.46056i			0.417899i	0.977926	+	0.208949i	$0.0670044\pi$
$239$			6.46056i			0.417899i	−0.977926	+	0.208949i	$0.932996\pi$
$240$		0			0
$241$	0.597834	−	0.345160i	0.0385099	−	0.0222337i	−0.480621	−	0.876928i	$-0.659589\pi$
$241$	0.597834	−	0.345160i	0.0385099	−	0.0222337i	0.519131	+	0.854694i	$0.326256\pi$
$242$	3.43571	+	12.8222i	0.220856	+	0.824244i
$243$	−1.78441	+	6.65951i	−0.114470	+	0.427208i
$244$	−4.09236	−	2.36272i	−0.261986	−	0.151258i
$245$		0			0
$246$		−	11.4584i		−	0.730559i
$247$	14.8601	+	6.01112i	0.945524	+	0.382479i
$248$	−4.31597	+	4.31597i	−0.274064	+	0.274064i
$249$	−2.45553	+	4.25311i	−0.155613	+	0.269530i
$250$		0			0
$251$	4.81477	+	8.33943i	0.303906	+	0.526380i	0.977017	−	0.213161i	$-0.0683759\pi$
$251$	4.81477	+	8.33943i	0.303906	+	0.526380i	−0.673111	+	0.739541i	$0.735043\pi$
$252$	−1.56930	+	0.420493i	−0.0988566	+	0.0264886i
$253$	11.4123	+	3.05793i	0.717488	+	0.192250i
$254$		−	7.98454i		−	0.500994i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.97548	+	0.797277i	0.185605	+	0.0497328i	0.350424	−	0.936591i	$-0.386037\pi$
$257$	2.97548	+	0.797277i	0.185605	+	0.0497328i	−0.164819	+	0.986324i	$0.552704\pi$
$258$	6.86398	−	6.86398i	0.427333	−	0.427333i
$259$	8.27538			0.514207
$260$		0			0
$261$	−5.42770	−	3.13368i	−0.335966	−	0.193970i
$262$	17.8073	+	4.77144i	1.10014	+	0.294781i
$263$	−4.08585	−	15.2486i	−0.251944	−	0.940269i	−0.969765	−	0.244041i	$-0.921527\pi$
$263$	−4.08585	−	15.2486i	−0.251944	−	0.940269i	0.717821	−	0.696228i	$-0.245140\pi$
$264$	6.50256	+	3.75426i	0.400205	+	0.231058i
$265$		0			0
$266$	8.34533	+	6.29415i	0.511685	+	0.385919i
$267$	8.47015	+	8.47015i	0.518364	+	0.518364i
$268$	−8.84162	+	2.36911i	−0.540088	+	0.144716i
$269$	−8.43845	+	14.6158i	−0.514502	+	0.891143i	0.485357	+	0.874316i	$0.338690\pi$
$269$	−8.43845	+	14.6158i	−0.514502	+	0.891143i	−0.999858	+	0.0168267i	$0.994644\pi$
$270$		0			0
$271$	−7.71404	+	13.3611i	−0.468594	+	0.811629i	−0.999356	−	0.0358922i	$-0.988573\pi$
$271$	−7.71404	+	13.3611i	−0.468594	+	0.811629i	0.530761	+	0.847521i	$0.321906\pi$
$272$	−0.0410260	+	0.153111i	−0.00248757	+	0.00928372i
$273$	9.50323	−	9.50323i	0.575161	−	0.575161i
$274$	5.54511			0.334993
$275$		0			0
$276$	3.16493	−	1.82727i	0.190507	−	0.109989i
$277$	−20.0894	−	20.0894i	−1.20706	−	1.20706i	−0.971976	−	0.235081i	$-0.924465\pi$
$277$	−20.0894	−	20.0894i	−1.20706	−	1.20706i	−0.235081	−	0.971976i	$-0.575535\pi$
$278$	4.08924	+	4.08924i	0.245256	+	0.245256i
$279$	2.06762	+	3.58122i	0.123785	+	0.214402i
$280$		0			0
$281$	−24.2579	+	14.0053i	−1.44711	+	0.835488i	−0.998308	−	0.0581450i	$-0.981481\pi$
$281$	−24.2579	+	14.0053i	−1.44711	+	0.835488i	−0.448799	+	0.893633i	$0.648148\pi$
$282$	3.99670	−	1.07091i	0.238000	−	0.0637719i
$283$	7.04953	+	26.3092i	0.419051	+	1.56392i	0.776581	+	0.630017i	$0.216952\pi$
$283$	7.04953	+	26.3092i	0.419051	+	1.56392i	−0.357530	+	0.933902i	$0.616381\pi$
$284$	−4.21314			−0.250004
$285$		0			0
$286$	18.1187			1.07138
$287$	−4.66656	−	17.4158i	−0.275458	−	1.02802i
$288$	−0.654411	+	0.175349i	−0.0385615	+	0.0103325i
$289$	−14.7007	+	8.48744i	−0.864745	+	0.499261i
$290$		0			0
$291$	−13.3221	−	23.0746i	−0.780957	−	1.35266i
$292$	2.31482	+	2.31482i	0.135465	+	0.135465i
$293$	−11.1535	−	11.1535i	−0.651593	−	0.651593i	0.301783	−	0.953377i	$-0.402418\pi$
$293$	−11.1535	−	11.1535i	−0.651593	−	0.651593i	−0.953377	+	0.301783i	$0.902418\pi$
$294$	−1.64899	+	0.952047i	−0.0961713	+	0.0555245i
$295$		0			0
$296$	3.45090			0.200579
$297$	19.5250	−	19.5250i	1.13296	−	1.13296i
$298$	4.92997	−	18.3989i	0.285586	−	1.06582i
$299$	4.40938	−	7.63728i	0.255001	−	0.441675i
$300$		0			0
$301$	7.63728	−	13.2281i	0.440205	−	0.762458i
$302$	−10.1493	+	2.71949i	−0.584025	+	0.156489i
$303$	−8.36006	−	8.36006i	−0.480273	−	0.480273i
$304$	3.48007	+	2.62471i	0.199596	+	0.150538i
$305$		0			0
$306$	0.0930037	+	0.0536957i	0.00531667	+	0.00306958i
$307$	6.21356	+	23.1893i	0.354627	+	1.32349i	0.880954	+	0.473203i	$0.156902\pi$
$307$	6.21356	+	23.1893i	0.354627	+	1.32349i	−0.526327	+	0.850282i	$0.676431\pi$
$308$	11.4123	+	3.05793i	0.650279	+	0.174242i
$309$	6.78888	+	3.91956i	0.386206	+	0.222976i
$310$		0			0
$311$	−5.75057			−0.326085			−0.163043	−	0.986619i	$-0.552131\pi$
$311$	−5.75057			−0.326085			−0.163043	+	0.986619i	$0.552131\pi$
$312$	3.96292	−	3.96292i	0.224356	−	0.224356i
$313$	1.36681	+	0.366236i	0.0772567	+	0.0207009i	0.297240	−	0.954803i	$-0.403934\pi$
$313$	1.36681	+	0.366236i	0.0772567	+	0.0207009i	−0.219984	+	0.975504i	$0.570600\pi$
$314$	−0.412249	−	0.714035i	−0.0232645	−	0.0402953i
$315$		0			0
$316$			14.7959i			0.832334i
$317$	20.0969	+	5.38496i	1.12876	+	0.302450i	0.774422	−	0.632669i	$-0.218041\pi$
$317$	20.0969	+	5.38496i	1.12876	+	0.302450i	0.354335	+	0.935119i	$0.384707\pi$
$318$	9.19945	−	2.46499i	0.515880	−	0.138230i
$319$	22.7889	+	39.4716i	1.27594	+	2.20999i
$320$		0			0
$321$	−11.6812	+	20.2324i	−0.651980	+	1.12926i
$322$	4.06627	−	4.06627i	0.226604	−	0.226604i
$323$	−0.0958728	−	0.684255i	−0.00533450	−	0.0380730i
$324$		−	6.50851i		−	0.361584i
$325$		0			0
$326$	0.202622	+	0.116984i	0.0112222	+	0.00647914i
$327$	3.55354	−	13.2620i	0.196511	−	0.733390i
$328$	−1.94599	−	7.26254i	−0.107449	−	0.401007i
$329$	5.63853	−	3.25541i	0.310862	−	0.179476i
$330$		0			0
$331$			2.19600i			0.120703i	0.998177	+	0.0603516i	$0.0192222\pi$
$331$			2.19600i			0.120703i	−0.998177	+	0.0603516i	$0.980778\pi$
$332$	−0.834053	+	3.11273i	−0.0457746	+	0.170833i
$333$	0.605111	−	2.25830i	0.0331599	−	0.123754i
$334$		−	7.92692i		−	0.433742i
$335$		0			0
$336$	3.16493	−	1.82727i	0.172661	−	0.0996860i
$337$	7.02475	+	26.2167i	0.382663	+	1.42812i	0.841818	+	0.539761i	$0.181485\pi$
$337$	7.02475	+	26.2167i	0.382663	+	1.42812i	−0.459156	+	0.888356i	$0.651848\pi$
$338$	0.135615	−	0.506122i	0.00737649	−	0.0275294i
$339$	−24.5210	−	14.1572i	−1.33180	−	0.768914i
$340$		0			0
$341$		−	30.0725i		−	1.62852i
$342$	2.32787	−	1.81715i	0.125877	−	0.0982605i
$343$	−13.9883	+	13.9883i	−0.755296	+	0.755296i
$344$	3.18480	−	5.51624i	0.171713	−	0.297416i
$345$		0			0
$346$	1.27823	+	2.21396i	0.0687182	+	0.119023i
$347$	−16.8834	+	4.52390i	−0.906350	+	0.242856i	−0.681742	−	0.731593i	$-0.738777\pi$
$347$	−16.8834	+	4.52390i	−0.906350	+	0.242856i	−0.224609	+	0.974449i	$0.572110\pi$
$348$	13.6176	+	3.64882i	0.729980	+	0.195598i
$349$		−	10.0383i		−	0.537337i	−0.963233	−	0.268669i	$-0.913416\pi$
$349$		−	10.0383i		−	0.537337i	0.963233	−	0.268669i	$-0.0865837\pi$
$350$		0			0
$351$	−10.3051	−	17.8490i	−0.550046	−	0.952708i
$352$	4.75904	+	1.27518i	0.253658	+	0.0679674i
$353$	−17.8161	+	17.8161i	−0.948257	+	0.948257i	−0.998726	−	0.0504691i	$-0.983928\pi$
$353$	−17.8161	+	17.8161i	−0.948257	+	0.948257i	0.0504691	+	0.998726i	$0.483928\pi$
$354$	−5.40579			−0.287314
$355$		0			0
$356$	6.80704	+	3.93005i	0.360772	+	0.208292i
$357$	−0.559552	−	0.149932i	−0.0296146	−	0.00793522i
$358$	5.52103	+	20.6048i	0.291795	+	1.08900i
$359$	4.17542	+	2.41068i	0.220370	+	0.127231i	0.606122	−	0.795372i	$-0.292724\pi$
$359$	4.17542	+	2.41068i	0.220370	+	0.127231i	−0.385752	+	0.922603i	$0.626058\pi$
$360$		0			0
$361$	−18.4318	−	4.61200i	−0.970092	−	0.242737i
$362$	−5.03365	−	5.03365i	−0.264563	−	0.264563i
$363$	−19.5408	+	5.23594i	−1.02562	+	0.274815i
$364$	4.40938	−	7.63728i	0.231114	−	0.400302i
$365$		0			0
$366$	3.60074	−	6.23666i	0.188213	−	0.325995i
$367$	−8.81188	+	32.8864i	−0.459977	+	1.71666i	0.213053	+	0.977041i	$0.431659\pi$
$367$	−8.81188	+	32.8864i	−0.459977	+	1.71666i	−0.673030	+	0.739615i	$0.735007\pi$
$368$	1.69567	−	1.69567i	0.0883928	−	0.0883928i
$369$	−5.09391			−0.265178
$370$		0			0
$371$	12.9786	−	7.49317i	0.673813	−	0.389026i
$372$	−6.57744	−	6.57744i	−0.341024	−	0.341024i
$373$	20.9496	+	20.9496i	1.08473	+	1.08473i	0.996061	+	0.0886693i	$0.0282614\pi$
$373$	20.9496	+	20.9496i	1.08473	+	1.08473i	0.0886693	+	0.996061i	$0.471739\pi$
$374$	−0.390489	−	0.676346i	−0.0201917	−	0.0349730i
$375$		0			0
$376$	2.35131	−	1.35753i	0.121260	−	0.0700093i
$377$	32.8605	−	8.80495i	1.69240	−	0.453478i
$378$	−3.47842	−	12.9816i	−0.178911	−	0.667704i
$379$	−33.6580			−1.72890			−0.864448	−	0.502723i	$-0.832332\pi$
$379$	−33.6580			−1.72890			−0.864448	+	0.502723i	$0.832332\pi$
$380$		0			0
$381$	12.1682			0.623398
$382$	−6.69737	−	24.9949i	−0.342668	−	1.27885i
$383$	−10.7713	+	2.88615i	−0.550385	+	0.147475i	−0.523285	−	0.852157i	$-0.675294\pi$
$383$	−10.7713	+	2.88615i	−0.550385	+	0.147475i	−0.0270998	+	0.999633i	$0.508627\pi$
$384$	1.31980	−	0.761988i	0.0673509	−	0.0388850i
$385$		0			0
$386$	6.10074	+	10.5668i	0.310519	+	0.537835i
$387$	−3.05144	−	3.05144i	−0.155113	−	0.155113i
$388$	−12.3626	−	12.3626i	−0.627617	−	0.627617i
$389$	4.69447	−	2.71035i	0.238019	−	0.137420i	−0.376247	−	0.926519i	$-0.622786\pi$
$389$	4.69447	−	2.71035i	0.238019	−	0.137420i	0.614266	+	0.789099i	$0.289452\pi$
$390$		0			0
$391$	−0.380118			−0.0192234
$392$	−0.883477	+	0.883477i	−0.0446223	+	0.0446223i
$393$	−7.27156	+	27.1378i	−0.366802	+	1.36892i
$394$	4.91686	−	8.51624i	0.247708	−	0.429042i
$395$		0			0
$396$	1.66898	−	2.89077i	0.0838696	−	0.145266i
$397$	−33.6334	+	9.01205i	−1.68801	+	0.452302i	−0.969876	−	0.243600i	$-0.921672\pi$
$397$	−33.6334	+	9.01205i	−1.68801	+	0.452302i	−0.718137	+	0.695902i	$0.755005\pi$
$398$	18.6342	+	18.6342i	0.934046	+	0.934046i
$399$	−9.59214	+	12.7181i	−0.480208	+	0.636701i
$400$		0			0
$401$	6.24689	+	3.60665i	0.311955	+	0.180107i	0.647801	−	0.761810i	$-0.275689\pi$
$401$	6.24689	+	3.60665i	0.311955	+	0.180107i	−0.335846	+	0.941917i	$0.609022\pi$
$402$	−3.61046	−	13.4744i	−0.180073	−	0.672043i
$403$	−21.6815	−	5.80954i	−1.08003	−	0.289394i
$404$	−6.71857	−	3.87897i	−0.334261	−	0.192986i
$405$		0			0
$406$	22.1837			1.10096
$407$	−12.0224	+	12.0224i	−0.595930	+	0.595930i
$408$	−0.233338	−	0.0625226i	−0.0115519	−	0.00309533i
$409$	0.332992	+	0.576760i	0.0164654	+	0.0285189i	0.874141	−	0.485673i	$-0.161425\pi$
$409$	0.332992	+	0.576760i	0.0164654	+	0.0285189i	−0.857675	+	0.514192i	$0.828092\pi$
$410$		0			0
$411$			8.45062i			0.416838i
$412$	4.96859	+	1.33133i	0.244785	+	0.0655898i
$413$	−8.21637	+	2.20157i	−0.404301	+	0.108332i
$414$	−0.812330	−	1.40700i	−0.0399238	−	0.0691501i
$415$		0			0
$416$	1.83875	−	3.18480i	0.0901520	−	0.156148i
$417$	−6.23191	+	6.23191i	−0.305178	+	0.305178i
$418$	−21.2682	+	2.97994i	−1.04026	+	0.145754i
$419$		−	10.2471i		−	0.500605i	−0.968168	−	0.250302i	$-0.919470\pi$
$419$		−	10.2471i		−	0.500605i	0.968168	−	0.250302i	$-0.0805300\pi$
$420$		0			0
$421$	23.5062	+	13.5713i	1.14562	+	0.661426i	0.947817	−	0.318816i	$-0.103285\pi$
$421$	23.5062	+	13.5713i	1.14562	+	0.661426i	0.197806	+	0.980241i	$0.436618\pi$
$422$	3.68292	−	13.7448i	0.179282	−	0.669088i
$423$	−0.476083	−	1.77676i	−0.0231479	−	0.0863893i
$424$	5.41216	−	3.12471i	0.262838	−	0.151749i
$425$		0			0
$426$		−	6.42073i		−	0.311085i
$427$	2.93288	−	10.9457i	0.141932	−	0.529698i
$428$	−3.96766	+	14.8075i	−0.191784	+	0.715748i
$429$			27.6125i			1.33315i
$430$		0			0
$431$	11.7908	−	6.80742i	0.567943	−	0.327902i	−0.188385	−	0.982095i	$-0.560325\pi$
$431$	11.7908	−	6.80742i	0.567943	−	0.327902i	0.756327	+	0.654194i	$0.226992\pi$
$432$	−1.45053	−	5.41345i	−0.0697887	−	0.260455i
$433$	−2.34119	+	8.73743i	−0.112510	+	0.419894i	−0.999089	−	0.0426844i	$-0.986409\pi$
$433$	−2.34119	+	8.73743i	−0.112510	+	0.419894i	0.886578	+	0.462579i	$0.153076\pi$
$434$	−12.6759	−	7.31845i	−0.608464	−	0.351297i
$435$		0			0
$436$		−	9.00921i		−	0.431463i
$437$	−3.91976	+	9.69002i	−0.187507	+	0.463536i
$438$	−3.52774	+	3.52774i	−0.168562	+	0.168562i
$439$	0.957449	−	1.65835i	0.0456965	−	0.0791487i	−0.842272	−	0.539052i	$-0.818783\pi$
$439$	0.957449	−	1.65835i	0.0456965	−	0.0791487i	0.887969	+	0.459903i	$0.152116\pi$
$440$		0			0
$441$	0.423240	+	0.733074i	0.0201543	+	0.0349083i
$442$	−0.563065	+	0.150873i	−0.0267823	+	0.00717629i
$443$	−18.5144	−	4.96093i	−0.879647	−	0.235701i	−0.209392	−	0.977832i	$-0.567149\pi$
$443$	−18.5144	−	4.96093i	−0.879647	−	0.235701i	−0.670255	+	0.742131i	$0.733815\pi$
$444$			5.25909i			0.249585i
$445$		0			0
$446$	8.56788	+	14.8400i	0.405701	+	0.702694i
$447$	28.0395	+	7.51316i	1.32622	+	0.355360i
$448$	1.69567	−	1.69567i	0.0801127	−	0.0801127i
$449$	20.7974			0.981488			0.490744	−	0.871304i	$-0.336725\pi$
$449$	20.7974			0.981488			0.490744	+	0.871304i	$0.336725\pi$
$450$		0			0
$451$	32.0812	+	18.5221i	1.51065	+	0.872172i
$452$	−17.9462	−	4.80867i	−0.844119	−	0.226181i
$453$	−4.14444	−	15.4672i	−0.194723	−	0.726715i
$454$	18.8014	+	10.8550i	0.882393	+	0.509450i
$455$		0			0
$456$	−4.00000	+	5.30354i	−0.187317	+	0.248361i
$457$	−9.00799	−	9.00799i	−0.421376	−	0.421376i	0.464301	−	0.885677i	$-0.346305\pi$
$457$	−9.00799	−	9.00799i	−0.421376	−	0.421376i	−0.885677	+	0.464301i	$0.846305\pi$
$458$	28.5471	−	7.64918i	1.33392	−	0.357423i
$459$	−0.444184	+	0.769350i	−0.0207328	+	0.0359102i
$460$		0			0
$461$	0.295626	−	0.512039i	0.0137687	−	0.0238480i	−0.859059	−	0.511877i	$-0.828950\pi$
$461$	0.295626	−	0.512039i	0.0137687	−	0.0238480i	0.872828	+	0.488029i	$0.162284\pi$
$462$	−4.66021	+	17.3921i	−0.216813	+	0.809156i
$463$	−11.5577	+	11.5577i	−0.537133	+	0.537133i	−0.922686	−	0.385553i	$-0.874011\pi$
$463$	−11.5577	+	11.5577i	−0.537133	+	0.537133i	0.385553	+	0.922686i	$0.374011\pi$
$464$	9.25078			0.429457
$465$		0			0
$466$	3.99517	−	2.30661i	0.185073	−	0.106852i
$467$	−21.0087	−	21.0087i	−0.972166	−	0.972166i	0.0274570	−	0.999623i	$-0.491259\pi$
$467$	−21.0087	−	21.0087i	−0.972166	−	0.972166i	−0.999623	+	0.0274570i	$0.991259\pi$
$468$	−1.76175	−	1.76175i	−0.0814369	−	0.0814369i
$469$	−10.9752	−	19.0097i	−0.506789	−	0.877785i
$470$		0			0
$471$	1.08817	−	0.628257i	0.0501404	−	0.0289486i
$472$	−3.42629	+	0.918072i	−0.157708	+	0.0422577i
$473$	8.12241	+	30.3132i	0.373469	+	1.39380i
$474$	−22.5486			−1.03569
$475$		0			0
$476$	−0.380118			−0.0174227
$477$	−1.09583	−	4.08969i	−0.0501746	−	0.187254i
$478$	−6.24042	+	1.67212i	−0.285430	+	0.0764808i
$479$	−0.940715	+	0.543122i	−0.0429824	+	0.0248159i	−0.521337	−	0.853351i	$-0.674567\pi$
$479$	−0.940715	+	0.543122i	−0.0429824	+	0.0248159i	0.478355	+	0.878167i	$0.341233\pi$
$480$		0			0
$481$	6.34533	+	10.9904i	0.289322	+	0.501121i
$482$	0.488130	+	0.488130i	0.0222337	+	0.0222337i
$483$	6.19690	+	6.19690i	0.281969	+	0.281969i
$484$	−11.4961	+	6.63728i	−0.522550	+	0.301694i
$485$		0			0
$486$	−6.89443			−0.312738
$487$	−7.21190	+	7.21190i	−0.326803	+	0.326803i	−0.851369	−	0.524567i	$-0.824227\pi$
$487$	−7.21190	+	7.21190i	−0.326803	+	0.326803i	0.524567	+	0.851369i	$0.324227\pi$
$488$	1.22304	−	4.56443i	0.0553642	−	0.206622i
$489$	−0.178281	+	0.308791i	−0.00806213	+	0.0139640i
$490$		0			0
$491$	11.8502	−	20.5251i	0.534790	−	0.926284i	−0.464383	−	0.885634i	$-0.653724\pi$
$491$	11.8502	−	20.5251i	0.534790	−	0.926284i	0.999173	−	0.0406496i	$-0.0129427\pi$
$492$	11.0679	−	2.96564i	0.498981	−	0.133702i
$493$	−1.03687	−	1.03687i	−0.0466985	−	0.0466985i
$494$	−1.96023	+	15.9095i	−0.0881948	+	0.715803i
$495$		0			0
$496$	−5.28596	−	3.05185i	−0.237347	−	0.137032i
$497$	−2.61492	−	9.75901i	−0.117295	−	0.437751i
$498$	−4.74372	−	1.27108i	−0.212571	−	0.0569583i
$499$	24.0371	+	13.8778i	1.07605	+	0.621256i	0.929828	−	0.367996i	$-0.119956\pi$
$499$	24.0371	+	13.8778i	1.07605	+	0.621256i	0.146220	+	0.989252i	$0.453289\pi$
$500$		0			0
$501$	12.0804			0.539714
$502$	−6.80912	+	6.80912i	−0.303906	+	0.303906i
$503$	−30.8010	−	8.25311i	−1.37335	−	0.367988i	−0.504649	−	0.863324i	$-0.668378\pi$
$503$	−30.8010	−	8.25311i	−1.37335	−	0.367988i	−0.868701	+	0.495336i	$0.835045\pi$
$504$	−0.812330	−	1.40700i	−0.0361840	−	0.0626726i
$505$		0			0
$506$			11.8149i			0.525238i
$507$	0.771318	+	0.206674i	0.0342555	+	0.00917872i
$508$	7.71247	−	2.06655i	0.342185	−	0.0916883i
$509$	−1.49048	−	2.58159i	−0.0660644	−	0.114427i	0.831101	−	0.556121i	$-0.187711\pi$
$509$	−1.49048	−	2.58159i	−0.0660644	−	0.114427i	−0.897166	+	0.441694i	$0.854378\pi$
$510$		0			0
$511$	−3.92517	+	6.79859i	−0.173639	+	0.300752i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	15.0320	+	19.2567i	0.663677	+	0.850204i
$514$			3.08044i			0.135872i
$515$		0			0
$516$	8.40663	+	4.85357i	0.370081	+	0.213666i
$517$	−3.46219	+	12.9211i	−0.152267	+	0.568268i
$518$	2.14182	+	7.99340i	0.0941064	+	0.351210i
$519$	−3.37403	+	1.94800i	−0.148103	+	0.0855075i
$520$		0			0
$521$		−	34.7368i		−	1.52185i	−0.648841	−	0.760924i	$-0.724746\pi$
$521$		−	34.7368i		−	1.52185i	0.648841	−	0.760924i	$-0.275254\pi$
$522$	1.62211	−	6.05381i	0.0709980	−	0.264968i
$523$	5.35573	−	19.9879i	0.234190	−	0.874008i	−0.744323	−	0.667820i	$-0.767227\pi$
$523$	5.35573	−	19.9879i	0.234190	−	0.874008i	0.978512	−	0.206188i	$-0.0661059\pi$
$524$			18.4354i			0.805356i
$525$		0			0
$526$	13.6715	−	7.89325i	0.596106	−	0.344162i
$527$	0.250411	+	0.934545i	0.0109081	+	0.0407094i
$528$	−1.94335	+	7.25267i	−0.0845733	+	0.315632i
$529$	−14.9384	−	8.62471i	−0.649497	−	0.374988i
$530$		0			0
$531$			2.40319i			0.104289i
$532$	−3.91976	+	9.69002i	−0.169943	+	0.420116i
$533$	19.5516	−	19.5516i	0.846873	−	0.846873i
$534$	−5.98930	+	10.3738i	−0.259182	+	0.448917i
$535$		0			0
$536$	−4.57676	−	7.92718i	−0.197686	−	0.342402i
$537$	−31.4012	+	8.41392i	−1.35506	+	0.363087i
$538$	−16.3018	−	4.36806i	−0.702822	−	0.188321i
$539$		−	6.15582i		−	0.265150i
$540$		0			0
$541$	−5.13245	−	8.88966i	−0.220661	−	0.382196i	0.734348	−	0.678773i	$-0.237488\pi$
$541$	−5.13245	−	8.88966i	−0.220661	−	0.382196i	−0.955009	+	0.296577i	$0.904155\pi$
$542$	−14.9024	−	3.99308i	−0.640112	−	0.171517i
$543$	7.67116	−	7.67116i	0.329201	−	0.329201i
$544$	−0.158512			−0.00679616
$545$		0			0
$546$	11.6390	+	6.71980i	0.498104	+	0.287581i
$547$	24.8709	+	6.66414i	1.06340	+	0.284938i	0.747780	−	0.663946i	$-0.231120\pi$
$547$	24.8709	+	6.66414i	1.06340	+	0.284938i	0.315624	+	0.948884i	$0.397786\pi$
$548$	1.43518	+	5.35617i	0.0613079	+	0.228804i
$549$	−2.77256	−	1.60074i	−0.118330	−	0.0683178i
$550$		0			0
$551$	−37.1243	+	15.7400i	−1.58155	+	0.670544i
$552$	2.58416	+	2.58416i	0.109989	+	0.109989i
$553$	−34.2721	+	9.18318i	−1.45740	+	0.390509i
$554$	14.2054	−	24.6044i	0.603528	−	1.04534i
$555$		0			0
$556$	−2.89153	+	5.00828i	−0.122628	+	0.212398i
$557$	−6.88975	+	25.7129i	−0.291928	+	1.08949i	0.651698	+	0.758478i	$0.274057\pi$
$557$	−6.88975	+	25.7129i	−0.291928	+	1.08949i	−0.943626	+	0.331012i	$0.892610\pi$
$558$	−2.92405	+	2.92405i	−0.123785	+	0.123785i
$559$	23.4242			0.990739
$560$		0			0
$561$	1.03074	−	0.595096i	0.0435177	−	0.0251250i
$562$	−19.8065	−	19.8065i	−0.835488	−	0.835488i
$563$	−13.4241	−	13.4241i	−0.565758	−	0.565758i	0.365179	−	0.930937i	$-0.381008\pi$
$563$	−13.4241	−	13.4241i	−0.565758	−	0.565758i	−0.930937	+	0.365179i	$0.881008\pi$
$564$	2.06884	+	3.58334i	0.0871140	+	0.150886i
$565$		0			0
$566$	−23.5882	+	13.6186i	−0.991485	+	0.572434i
$567$	15.0758	−	4.03956i	0.633125	−	0.169645i
$568$	−1.09044	−	4.06958i	−0.0457539	−	0.170756i
$569$	−30.1939			−1.26579			−0.632897	−	0.774236i	$-0.718134\pi$
$569$	−30.1939			−1.26579			−0.632897	+	0.774236i	$0.718134\pi$
$570$		0			0
$571$	24.7196			1.03448			0.517242	−	0.855839i	$-0.326959\pi$
$571$	24.7196			1.03448			0.517242	+	0.855839i	$0.326959\pi$
$572$	4.68947	+	17.5014i	0.196077	+	0.731768i
$573$	38.0917	−	10.2066i	1.59130	−	0.426389i
$574$	15.6146	−	9.01509i	0.651741	−	0.376283i
$575$		0			0
$576$	−0.338748	−	0.586729i	−0.0141145	−	0.0244470i
$577$	26.4463	+	26.4463i	1.10098	+	1.10098i	0.994293	+	0.106682i	$0.0340227\pi$
$577$	26.4463	+	26.4463i	1.10098	+	1.10098i	0.106682	+	0.994293i	$0.465977\pi$
$578$	−12.0030	−	12.0030i	−0.499261	−	0.499261i
$579$	−16.1035	+	9.29738i	−0.669240	+	0.386386i
$580$		0			0
$581$	−7.72775			−0.320601
$582$	18.8403	−	18.8403i	0.780957	−	0.780957i
$583$	−7.96915	+	29.7413i	−0.330048	+	1.23176i
$584$	−1.63683	+	2.83507i	−0.0677324	+	0.117316i
$585$		0			0
$586$	7.88670	−	13.6602i	0.325797	−	0.564296i
$587$	36.5313	−	9.78854i	1.50781	−	0.404016i	0.592103	−	0.805863i	$-0.298298\pi$
$587$	36.5313	−	9.78854i	1.50781	−	0.404016i	0.915707	+	0.401846i	$0.131631\pi$
$588$	−1.34640	−	1.34640i	−0.0555245	−	0.0555245i
$589$	26.4058	+	3.25348i	1.08803	+	0.134057i
$590$		0			0
$591$	12.9786	+	7.49317i	0.533866	+	0.308228i
$592$	0.893158	+	3.33331i	0.0367086	+	0.136998i
$593$	15.0573	+	4.03459i	0.618329	+	0.165681i	0.554368	−	0.832272i	$-0.312960\pi$
$593$	15.0573	+	4.03459i	0.618329	+	0.165681i	0.0639609	+	0.997952i	$0.479627\pi$
$594$	23.9131	+	13.8063i	0.981168	+	0.566478i
$595$		0			0
$596$	19.0480			0.780235
$597$	−28.3980	+	28.3980i	−1.16225	+	1.16225i
$598$	8.51827	+	2.28246i	0.348338	+	0.0933369i
$599$	4.80824	+	8.32811i	0.196459	+	0.340277i	0.947378	−	0.320117i	$-0.103722\pi$
$599$	4.80824	+	8.32811i	0.196459	+	0.340277i	−0.750919	+	0.660395i	$0.770389\pi$
$600$		0			0
$601$		−	18.0184i		−	0.734987i	−0.930026	−	0.367494i	$-0.880216\pi$
$601$		−	18.0184i		−	0.734987i	0.930026	−	0.367494i	$-0.119784\pi$
$602$	14.7541	+	3.95334i	0.601332	+	0.161126i
$603$	−5.99016	+	1.60506i	−0.243938	+	0.0653631i
$604$	−5.25365	−	9.09959i	−0.213768	−	0.370257i
$605$		0			0
$606$	5.91146	−	10.2389i	0.240136	−	0.415929i
$607$	24.8718	−	24.8718i	1.00952	−	1.00952i	0.00956121	−	0.999954i	$-0.496957\pi$
$607$	24.8718	−	24.8718i	1.00952	−	1.00952i	0.999954	−	0.00956121i	$-0.00304347\pi$
$608$	−1.63457	+	4.04081i	−0.0662905	+	0.163877i
$609$			33.8074i			1.36995i
$610$		0			0
$611$	8.64694	+	4.99231i	0.349818	+	0.201967i
$612$	−0.0277949	+	0.103732i	−0.00112354	+	0.00419312i
$613$	6.78817	+	25.3338i	0.274172	+	1.02322i	0.956394	+	0.292078i	$0.0943468\pi$
$613$	6.78817	+	25.3338i	0.274172	+	1.02322i	−0.682223	+	0.731144i	$0.738987\pi$
$614$	−20.7910	+	12.0037i	−0.839056	+	0.484429i
$615$		0			0
$616$			11.8149i			0.476037i
$617$	0.474750	−	1.77179i	0.0191127	−	0.0713296i	−0.955711	−	0.294307i	$-0.904911\pi$
$617$	0.474750	−	1.77179i	0.0191127	−	0.0713296i	0.974824	+	0.222978i	$0.0715777\pi$
$618$	−2.02891	+	7.57201i	−0.0816149	+	0.304591i
$619$			15.4281i			0.620107i	0.950719	+	0.310053i	$0.100347\pi$
$619$			15.4281i			0.620107i	−0.950719	+	0.310053i	$0.899653\pi$
$620$		0			0
$621$	11.6390	−	6.71980i	0.467058	−	0.269656i
$622$	−1.48836	−	5.55463i	−0.0596777	−	0.222720i
$623$	−4.87842	+	18.2065i	−0.195450	+	0.729429i
$624$	4.85357	+	2.80221i	0.194298	+	0.112178i
$625$		0			0
$626$			1.41503i			0.0565558i
$627$	−4.54136	−	32.4122i	−0.181365	−	1.29442i
$628$	0.583007	−	0.583007i	0.0232645	−	0.0232645i
$629$	0.273505	−	0.473724i	0.0109053	−	0.0188886i
$630$		0			0
$631$	1.10364	+	1.91156i	0.0439351	+	0.0760979i	0.887157	−	0.461468i	$-0.152677\pi$
$631$	1.10364	+	1.91156i	0.0439351	+	0.0760979i	−0.843222	+	0.537566i	$0.819344\pi$
$632$	−14.2917	+	3.82946i	−0.568495	+	0.152328i
$633$	20.9468	+	5.61268i	0.832561	+	0.223084i
$634$			20.8059i			0.826307i
$635$		0			0
$636$	4.76199	+	8.24801i	0.188825	+	0.327055i
$637$	−4.43819	−	1.18921i	−0.175848	−	0.0471182i
$638$	−32.2284	+	32.2284i	−1.27594	+	1.27594i
$639$	−2.85439			−0.112918
$640$		0			0
$641$	−11.6878	−	6.74793i	−0.461639	−	0.266527i	0.251094	−	0.967963i	$-0.419210\pi$
$641$	−11.6878	−	6.74793i	−0.461639	−	0.266527i	−0.712733	+	0.701435i	$0.752543\pi$
$642$	−22.5663	−	6.04662i	−0.890621	−	0.238641i
$643$	−11.2535	−	41.9986i	−0.443794	−	1.65626i	−0.719101	−	0.694906i	$-0.755446\pi$
$643$	−11.2535	−	41.9986i	−0.443794	−	1.65626i	0.275306	−	0.961357i	$-0.411221\pi$
$644$	4.98014	+	2.87529i	0.196245	+	0.113302i
$645$		0			0
$646$	0.636126	−	0.269704i	0.0250280	−	0.0106114i
$647$	2.24253	+	2.24253i	0.0881628	+	0.0881628i	0.749813	−	0.661650i	$-0.230144\pi$
$647$	2.24253	+	2.24253i	0.0881628	+	0.0881628i	−0.661650	+	0.749813i	$0.730144\pi$
$648$	6.28674	−	1.68453i	0.246966	−	0.0661745i
$649$	8.73828	−	15.1352i	0.343008	−	0.594107i
$650$		0			0
$651$	11.1531	−	19.3178i	0.437126	−	0.757125i
$652$	−0.0605553	+	0.225996i	−0.00237153	+	0.00885067i
$653$	−32.7942	+	32.7942i	−1.28334	+	1.28334i	−0.344581	+	0.938757i	$0.611979\pi$
$653$	−32.7942	+	32.7942i	−1.28334	+	1.28334i	−0.938757	+	0.344581i	$0.888021\pi$
$654$	13.7298			0.536879
$655$		0			0
$656$	6.51141	−	3.75937i	0.254228	−	0.146779i
$657$	1.56828	+	1.56828i	0.0611845	+	0.0611845i
$658$	4.60384	+	4.60384i	0.179476	+	0.179476i
$659$	−19.3919	−	33.5878i	−0.755402	−	1.30840i	−0.945174	−	0.326567i	$-0.894108\pi$
$659$	−19.3919	−	33.5878i	−0.755402	−	1.30840i	0.189772	−	0.981828i	$-0.439225\pi$
$660$		0			0
$661$	22.2873	−	12.8676i	0.866877	−	0.500492i	0.000568016	−	1.00000i	$-0.499819\pi$
$661$	22.2873	−	12.8676i	0.866877	−	0.500492i	0.866309	+	0.499508i	$0.166486\pi$
$662$	−2.12118	+	0.568368i	−0.0824419	+	0.0220902i
$663$	−0.229927	−	0.858098i	−0.00892961	−	0.0333258i
$664$	−3.22253			−0.125059
$665$		0			0
$666$	2.33797			0.0905945
$667$	5.74157	+	21.4278i	0.222314	+	0.829688i
$668$	7.65682	−	2.05164i	0.296251	−	0.0793803i
$669$	−22.6158	+	13.0572i	−0.874378	+	0.504822i
$670$		0			0
$671$	11.6410	+	20.1627i	0.449394	+	0.778373i
$672$	2.58416	+	2.58416i	0.0996860	+	0.0996860i
$673$	3.40401	+	3.40401i	0.131215	+	0.131215i	0.769664	−	0.638449i	$-0.220424\pi$
$673$	3.40401	+	3.40401i	0.131215	+	0.131215i	−0.638449	+	0.769664i	$0.720424\pi$
$674$	−23.5053	+	13.5708i	−0.905390	+	0.522727i
$675$		0			0
$676$	0.523976			0.0201529
$677$	31.6199	−	31.6199i	1.21525	−	1.21525i	0.245977	−	0.969276i	$-0.420891\pi$
$677$	31.6199	−	31.6199i	1.21525	−	1.21525i	0.969276	−	0.245977i	$-0.0791089\pi$
$678$	7.32831	−	27.3496i	0.281442	−	1.05036i
$679$	20.9629	−	36.3088i	0.804482	−	1.39340i
$680$		0			0
$681$	−16.5428	+	28.6529i	−0.633920	+	1.09798i
$682$	29.0478	−	7.78333i	1.11230	−	0.298039i
$683$	−20.7232	−	20.7232i	−0.792951	−	0.792951i	0.189022	−	0.981973i	$-0.439468\pi$
$683$	−20.7232	−	20.7232i	−0.792951	−	0.792951i	−0.981973	+	0.189022i	$0.939468\pi$
$684$	2.35773	+	1.77823i	0.0901502	+	0.0679924i
$685$		0			0
$686$	−17.1321	−	9.89121i	−0.654106	−	0.377648i
$687$	11.6572	+	43.5052i	0.444749	+	1.65983i
$688$	6.15257	+	1.64858i	0.234565	+	0.0628514i
$689$	19.9032	+	11.4911i	0.758252	+	0.437777i
$690$		0			0
$691$	−39.3446			−1.49674			−0.748369	−	0.663282i	$-0.769163\pi$
$691$	−39.3446			−1.49674			−0.748369	+	0.663282i	$0.769163\pi$
$692$	−1.80769	+	1.80769i	−0.0687182	+	0.0687182i
$693$	7.73182	+	2.07173i	0.293708	+	0.0786987i
$694$	−8.73951	−	15.1373i	−0.331747	−	0.574603i
$695$		0			0
$696$			14.0980i			0.534382i
$697$	−1.15120	−	0.308463i	−0.0436049	−	0.0116839i
$698$	9.69625	−	2.59810i	0.367008	−	0.0983396i
$699$	3.51522	+	6.08854i	0.132958	+	0.230290i
$700$		0			0
$701$	0.708055	−	1.22639i	0.0267429	−	0.0463200i	−0.852344	−	0.522981i	$-0.824820\pi$
$701$	0.708055	−	1.22639i	0.0267429	−	0.0463200i	0.879087	+	0.476661i	$0.158153\pi$
$702$	14.5736	−	14.5736i	0.550046	−	0.550046i
$703$	−9.25587	−	11.8572i	−0.349092	−	0.447204i
$704$			4.92692i			0.185690i
$705$		0			0
$706$	−21.8202	−	12.5979i	−0.821214	−	0.474128i
$707$	4.81502	−	17.9699i	0.181087	−	0.675828i
$708$	−1.39912	−	5.22159i	−0.0525822	−	0.196239i
$709$	42.6724	−	24.6369i	1.60259	−	0.925258i	0.611629	−	0.791145i	$-0.290515\pi$
$709$	42.6724	−	24.6369i	1.60259	−	0.925258i	0.990966	−	0.134113i	$-0.0428186\pi$
$710$		0			0
$711$			10.0242i			0.375935i
$712$	−2.03434	+	7.59227i	−0.0762402	+	0.284532i
$713$	3.78831	−	14.1382i	0.141873	−	0.529478i
$714$		−	0.579291i		−	0.0216794i
$715$		0			0
$716$	−18.4737	+	10.6658i	−0.690395	+	0.398600i
$717$	−2.54826	−	9.51025i	−0.0951667	−	0.355167i
$718$	−1.24786	+	4.65707i	−0.0465697	+	0.173800i
$719$	25.3850	+	14.6561i	0.946702	+	0.546578i	0.892055	−	0.451927i	$-0.149263\pi$
$719$	25.3850	+	14.6561i	0.946702	+	0.546578i	0.0546469	+	0.998506i	$0.482597\pi$
$720$		0			0
$721$			12.3352i			0.459385i
$722$	−0.315640	−	18.9974i	−0.0117469	−	0.707009i
$723$	−0.743898	+	0.743898i	−0.0276659	+	0.0276659i
$724$	3.55933	−	6.16493i	0.132281	−	0.229118i
$725$		0			0
$726$	−10.1151	−	17.5198i	−0.375405	−	0.650220i
$727$	−27.8600	+	7.46505i	−1.03327	+	0.276863i	−0.735321	−	0.677719i	$-0.762969\pi$
$727$	−27.8600	+	7.46505i	−1.03327	+	0.276863i	−0.297947	+	0.954582i	$0.596302\pi$
$728$	8.51827	+	2.28246i	0.315708	+	0.0845938i
$729$		−	30.0325i		−	1.11231i
$730$		0			0
$731$	−0.504831	−	0.874392i	−0.0186718	−	0.0323406i
$732$	6.95609	+	1.86388i	0.257104	+	0.0688909i
$733$	20.8178	−	20.8178i	0.768925	−	0.768925i	−0.208993	−	0.977917i	$-0.567018\pi$
$733$	20.8178	−	20.8178i	0.768925	−	0.768925i	0.977917	+	0.208993i	$0.0670184\pi$
$734$	−34.0465			−1.25668
$735$		0			0
$736$	2.07676	+	1.19902i	0.0765504	+	0.0441964i
$737$	43.5620	+	11.6724i	1.60463	+	0.429958i
$738$	−1.31840	−	4.92034i	−0.0485310	−	0.181120i
$739$	−6.92621	−	3.99885i	−0.254785	−	0.147100i	0.367168	−	0.930154i	$-0.380327\pi$
$739$	−6.92621	−	3.99885i	−0.254785	−	0.147100i	−0.621953	+	0.783054i	$0.713661\pi$
$740$		0			0
$741$	−24.2457	−	2.98734i	−0.890690	−	0.109743i
$742$	10.5969	+	10.5969i	0.389026	+	0.389026i
$743$	11.8320	−	3.17038i	0.434075	−	0.116310i	−0.0351632	−	0.999382i	$-0.511195\pi$
$743$	11.8320	−	3.17038i	0.434075	−	0.116310i	0.469239	+	0.883071i	$0.344528\pi$
$744$	4.65095	−	8.05569i	0.170512	−	0.295336i
$745$		0			0
$746$	−14.8136	+	25.6579i	−0.542365	+	0.939404i
$747$	−0.565067	+	2.10886i	−0.0206747	+	0.0771592i
$748$	0.552234	−	0.552234i	0.0201917	−	0.0201917i
$749$	−36.7616			−1.34324
$750$		0			0
$751$	−25.3395	+	14.6298i	−0.924652	+	0.533848i	−0.885116	−	0.465370i	$-0.845921\pi$
$751$	−25.3395	+	14.6298i	−0.924652	+	0.533848i	−0.0395361	+	0.999218i	$0.512588\pi$
$752$	1.91984	+	1.91984i	0.0700093	+	0.0700093i
$753$	−10.3769	−	10.3769i	−0.378156	−	0.378156i
$754$	17.0099	+	29.4619i	0.619463	+	1.07294i
$755$		0			0
$756$	11.6390	−	6.71980i	0.423307	−	0.244397i
$757$	22.2323	−	5.95712i	0.808045	−	0.216515i	0.168932	−	0.985628i	$-0.445968\pi$
$757$	22.2323	−	5.95712i	0.808045	−	0.216515i	0.639113	+	0.769113i	$0.279301\pi$
$758$	−8.71133	−	32.5111i	−0.316410	−	1.18086i
$759$	−18.0057			−0.653565
$760$		0			0
$761$	−43.2641			−1.56832			−0.784162	−	0.620556i	$-0.786907\pi$
$761$	−43.2641			−1.56832			−0.784162	+	0.620556i	$0.786907\pi$
$762$	3.14937	+	11.7536i	0.114090	+	0.425789i
$763$	20.8683	−	5.59163i	0.755482	−	0.202431i
$764$	22.4099	−	12.9383i	0.810760	−	0.468093i
$765$		0			0
$766$	−5.57561	−	9.65724i	−0.201455	−	0.348930i
$767$	−9.22397	−	9.22397i	−0.333058	−	0.333058i
$768$	1.07761	+	1.07761i	0.0388850	+	0.0388850i
$769$	12.8970	−	7.44607i	0.465076	−	0.268512i	−0.249100	−	0.968478i	$-0.580135\pi$
$769$	12.8970	−	7.44607i	0.465076	−	0.268512i	0.714176	+	0.699966i	$0.246801\pi$
$770$		0			0
$771$	−4.69452			−0.169069
$772$	−8.62774	+	8.62774i	−0.310519	+	0.310519i
$773$	4.76494	−	17.7830i	0.171383	−	0.639610i	−0.825757	−	0.564027i	$-0.809252\pi$
$773$	4.76494	−	17.7830i	0.171383	−	0.639610i	0.997140	−	0.0755831i	$-0.0240818\pi$
$774$	2.15769	−	3.73723i	0.0775567	−	0.134332i
$775$		0			0
$776$	8.74169	−	15.1411i	0.313808	−	0.543532i
$777$	−12.1818	+	3.26409i	−0.437018	+	0.117099i
$778$	3.83302	+	3.83302i	0.137420	+	0.137420i
$779$	−19.7345	+	26.1657i	−0.707062	+	0.937484i
$780$		0			0
$781$	17.9768	+	10.3789i	0.643261	+	0.371387i
$782$	−0.0983818	−	0.367166i	−0.00351813	−	0.0131298i
$783$	50.0787	+	13.4185i	1.78967	+	0.479539i
$784$	−1.08203	−	0.624713i	−0.0386441	−	0.0223112i
$785$		0			0
$786$	−28.0952			−1.00212
$787$	−24.3605	+	24.3605i	−0.868357	+	0.868357i	−0.992290	−	0.123934i	$-0.960449\pi$
$787$	−24.3605	+	24.3605i	−0.868357	+	0.868357i	0.123934	+	0.992290i	$0.460449\pi$
$788$	9.49864	+	2.54515i	0.338375	+	0.0906673i
$789$	12.0291	+	20.8351i	0.428248	+	0.741748i
$790$		0			0
$791$		−	44.5538i		−	1.58415i
$792$	3.22423	+	0.863930i	0.114568	+	0.0306984i
$793$	16.7857	−	4.49771i	0.596077	−	0.159718i
$794$	−17.4099	−	30.1549i	−0.617856	−	1.07016i
$795$		0			0
$796$	−13.1763	+	22.8221i	−0.467023	+	0.808908i
$797$	29.3671	−	29.3671i	1.04024	−	1.04024i	0.0410799	−	0.999156i	$-0.486920\pi$
$797$	29.3671	−	29.3671i	1.04024	−	1.04024i	0.999156	−	0.0410799i	$-0.0130798\pi$
$798$	−14.7674	−	5.97362i	−0.522759	−	0.211464i
$799$		−	0.430370i		−	0.0152254i
$800$		0			0
$801$	4.61174	+	2.66259i	0.162948	+	0.0940780i
$802$	−1.86694	+	6.96750i	−0.0659238	+	0.246031i
$803$	−4.17450	−	15.5794i	−0.147315	−	0.549787i
$804$	12.0808	−	6.97487i	0.426058	−	0.245985i
$805$		0			0
$806$		−	22.4464i		−	0.790639i
$807$	6.65683	−	24.8436i	0.234331	−	0.874537i
$808$	2.00790	−	7.49359i	0.0706377	−	0.263624i
$809$			46.8264i			1.64633i	0.567803	+	0.823165i	$0.307794\pi$
$809$			46.8264i			1.64633i	−0.567803	+	0.823165i	$0.692206\pi$
$810$		0			0
$811$	14.4298	−	8.33106i	0.506700	−	0.292543i	−0.224776	−	0.974410i	$-0.572165\pi$
$811$	14.4298	−	8.33106i	0.506700	−	0.292543i	0.731476	+	0.681867i	$0.238832\pi$
$812$	5.74157	+	21.4278i	0.201489	+	0.751969i
$813$	6.08536	−	22.7109i	0.213423	−	0.796505i
$814$	−14.7244	−	8.50115i	−0.516091	−	0.297965i
$815$		0			0
$816$		−	0.241569i		−	0.00845660i
$817$	−27.4959	+	3.85252i	−0.961960	+	0.134783i
$818$	−0.470922	+	0.470922i	−0.0164654	+	0.0164654i
$819$	2.98734	−	5.17422i	0.104386	−	0.180802i
$820$		0			0
$821$	3.66783	+	6.35288i	0.128008	+	0.221717i	0.922905	−	0.385028i	$-0.125808\pi$
$821$	3.66783	+	6.35288i	0.128008	+	0.221717i	−0.794897	+	0.606745i	$0.792475\pi$
$822$	−8.16267	+	2.18718i	−0.284706	+	0.0762867i
$823$	−29.8554	−	7.99972i	−1.04069	−	0.278853i	−0.302292	−	0.953215i	$-0.597752\pi$
$823$	−29.8554	−	7.99972i	−1.04069	−	0.278853i	−0.738401	+	0.674362i	$0.764419\pi$
$824$			5.14386i			0.179195i
$825$		0			0
$826$	−4.25311	−	7.36660i	−0.147984	−	0.256317i
$827$	−15.8605	−	4.24980i	−0.551523	−	0.147780i	−0.0277138	−	0.999616i	$-0.508823\pi$
$827$	−15.8605	−	4.24980i	−0.551523	−	0.147780i	−0.523809	+	0.851836i	$0.675489\pi$
$828$	1.14881	−	1.14881i	0.0399238	−	0.0399238i
$829$	−46.5326			−1.61614			−0.808071	−	0.589084i	$-0.799489\pi$
$829$	−46.5326			−1.61614			−0.808071	+	0.589084i	$0.799489\pi$
$830$		0			0
$831$	37.4966	+	21.6486i	1.30074	+	0.750983i
$832$	3.55219	+	0.951806i	0.123150	+	0.0329979i
$833$	0.0512589	+	0.191301i	0.00177602	+	0.00662818i
$834$	−7.63250	−	4.40663i	−0.264292	−	0.152589i
$835$		0			0
$836$	−8.38302	−	19.7722i	−0.289933	−	0.683837i
$837$	−24.1885	−	24.1885i	−0.836077	−	0.836077i
$838$	9.89796	−	2.65215i	0.341919	−	0.0916170i
$839$	−1.39526	+	2.41666i	−0.0481697	+	0.0834323i	−0.889105	−	0.457703i	$-0.848672\pi$
$839$	−1.39526	+	2.41666i	−0.0481697	+	0.0834323i	0.840935	+	0.541136i	$0.182005\pi$
$840$		0			0
$841$	−28.2885	+	48.9971i	−0.975465	+	1.68956i
$842$	−7.02503	+	26.2178i	−0.242099	+	0.903524i
$843$	30.1847	−	30.1847i	1.03962	−	1.03962i
$844$	14.2297			0.489807
$845$		0			0
$846$	1.59300	−	0.919721i	0.0547686	−	0.0316207i
$847$	−22.5092	−	22.5092i	−0.773426	−	0.773426i
$848$	4.41901	+	4.41901i	0.151749	+	0.151749i
$849$	−20.7545	−	35.9478i	−0.712292	−	1.23373i
$850$		0			0
$851$	−7.16669	+	4.13769i	−0.245671	+	0.141838i
$852$	6.20195	−	1.66181i	0.212475	−	0.0569326i
$853$	−6.98897	−	26.0832i	−0.239298	−	0.893072i	−0.976164	−	0.217033i	$-0.930362\pi$
$853$	−6.98897	−	26.0832i	−0.239298	−	0.893072i	0.736866	−	0.676038i	$-0.236305\pi$
$854$	11.3318			0.387766
$855$		0			0
$856$	−15.3299			−0.523964
$857$	0.634339	+	2.36739i	0.0216686	+	0.0808683i	0.975913	−	0.218158i	$-0.0700048\pi$
$857$	0.634339	+	2.36739i	0.0216686	+	0.0808683i	−0.954245	+	0.299026i	$0.903338\pi$
$858$	−26.6716	+	7.14665i	−0.910555	+	0.243982i
$859$	−18.7669	+	10.8351i	−0.640318	+	0.369688i	−0.784737	−	0.619829i	$-0.787202\pi$
$859$	−18.7669	+	10.8351i	−0.640318	+	0.369688i	0.144419	+	0.989517i	$0.453869\pi$
$860$		0			0
$861$	13.7388	+	23.7963i	0.468217	+	0.810975i
$862$	9.62714	+	9.62714i	0.327902	+	0.327902i
$863$	12.0651	+	12.0651i	0.410702	+	0.410702i	0.881983	−	0.471281i	$-0.156208\pi$
$863$	12.0651	+	12.0651i	0.410702	+	0.410702i	−0.471281	+	0.881983i	$0.656208\pi$
$864$	4.85357	−	2.80221i	0.165122	−	0.0953331i
$865$		0			0
$866$	−9.04565			−0.307384
$867$	18.2924	−	18.2924i	0.621241	−	0.621241i
$868$	3.78831	−	14.1382i	0.128584	−	0.479881i
$869$	36.4491	−	63.1317i	1.23645	−	2.14160i
$870$		0			0
$871$	16.8310	−	29.1522i	0.570297	−	0.987784i
$872$	8.70223	−	2.33176i	0.294695	−	0.0789632i
$873$	−8.37563	−	8.37563i	−0.283472	−	0.283472i
$874$	−10.3743	−	1.27823i	−0.350917	−	0.0432368i
$875$		0			0
$876$	−4.32058	−	2.49449i	−0.145979	−	0.0842808i
$877$	−3.26167	−	12.1727i	−0.110139	−	0.411043i	0.888739	−	0.458414i	$-0.151582\pi$
$877$	−3.26167	−	12.1727i	−0.110139	−	0.411043i	−0.998877	+	0.0473710i	$0.984916\pi$
$878$	1.84965	+	0.495612i	0.0624226	+	0.0167261i
$879$	20.8178	+	12.0191i	0.702166	+	0.405396i
$880$		0			0
$881$	25.1454			0.847171			0.423585	−	0.905856i	$-0.360771\pi$
$881$	25.1454			0.847171			0.423585	+	0.905856i	$0.360771\pi$
$882$	−0.598552	+	0.598552i	−0.0201543	+	0.0201543i
$883$	44.5556	+	11.9386i	1.49941	+	0.401767i	0.912904	−	0.408174i	$-0.133834\pi$
$883$	44.5556	+	11.9386i	1.49941	+	0.401767i	0.586511	+	0.809941i	$0.300501\pi$
$884$	−0.291464	−	0.504831i	−0.00980300	−	0.0169793i
$885$		0			0
$886$		−	19.1676i		−	0.643946i
$887$	−7.69380	−	2.06155i	−0.258333	−	0.0692200i	0.127328	−	0.991861i	$-0.459360\pi$
$887$	−7.69380	−	2.06155i	−0.258333	−	0.0692200i	−0.385661	+	0.922641i	$0.626027\pi$
$888$	−5.07989	+	1.36115i	−0.170470	+	0.0456773i
$889$	9.57360	+	16.5820i	0.321088	+	0.556141i
$890$		0			0
$891$	−16.0335	+	27.7708i	−0.537141	+	0.930356i
$892$	−12.1168	+	12.1168i	−0.405701	+	0.405701i
$893$	−10.9711	−	4.43795i	−0.367132	−	0.148510i
$894$			29.0286i			0.970863i
$895$		0			0
$896$	2.07676	+	1.19902i	0.0693797	+	0.0400564i
$897$	−3.47842	+	12.9816i	−0.116141	+	0.433445i
$898$	5.38275	+	20.0887i	0.179625	+	0.670369i
$899$	48.8993	−	28.2320i	1.63088	−	0.941591i
$900$		0			0
$901$		−	0.990610i		−	0.0330020i
$902$	−9.58774	+	35.7820i	−0.319237	+	1.19141i
$903$	−6.02480	+	22.4849i	−0.200493	+	0.748250i
$904$		−	18.5793i		−	0.617938i
$905$		0			0
$906$	13.8676	−	8.00644i	0.460719	−	0.265996i
$907$	−3.93974	−	14.7033i	−0.130817	−	0.488216i	0.869163	−	0.494526i	$-0.164658\pi$
$907$	−3.93974	−	14.7033i	−0.130817	−	0.488216i	−0.999980	+	0.00630979i	$0.997992\pi$
$908$	−5.61896	+	20.9702i	−0.186472	+	0.695922i
$909$	−4.55180	−	2.62799i	−0.150974	−	0.0871648i
$910$		0			0
$911$		−	12.4861i		−	0.413682i	−0.978375	−	0.206841i	$-0.933682\pi$
$911$		−	12.4861i		−	0.413682i	0.978375	−	0.206841i	$-0.0663183\pi$
$912$	−6.15811	−	2.49105i	−0.203915	−	0.0824867i
$913$	11.2269	−	11.2269i	0.371555	−	0.371555i
$914$	6.36961	−	11.0325i	0.210688	−	0.364922i
$915$		0			0
$916$	14.7771	+	25.5947i	0.488249	+	0.845671i
$917$	−42.7024	+	11.4421i	−1.41016	+	0.377851i
$918$	−0.858098	−	0.229927i	−0.0283215	−	0.00758871i
$919$			5.76604i			0.190204i	0.995468	+	0.0951021i	$0.0303177\pi$
$919$			5.76604i			0.190204i	−0.995468	+	0.0951021i	$0.969682\pi$
$920$		0			0
$921$	−18.2933	−	31.6850i	−0.602786	−	1.04406i
$922$	0.571105	+	0.153027i	0.0188083	+	0.00503968i
$923$	10.9558	−	10.9558i	0.360614	−	0.360614i
$924$	−18.0057			−0.592343
$925$		0			0
$926$	−14.1553	−	8.17255i	−0.465171	−	0.268567i
$927$	3.36620	+	0.901970i	0.110560	+	0.0296246i
$928$	2.39428	+	8.93557i	0.0785961	+	0.293324i
$929$	6.29795	+	3.63613i	0.206629	+	0.119297i	0.599744	−	0.800192i	$-0.295269\pi$
$929$	6.29795	+	3.63613i	0.206629	+	0.119297i	−0.393115	+	0.919489i	$0.628602\pi$
$930$		0			0
$931$	5.40524	+	0.665985i	0.177150	+	0.0218268i
$932$	3.26204	+	3.26204i	0.106852	+	0.106852i
$933$	8.46512	−	2.26822i	0.277136	−	0.0742583i
$934$	14.8554	−	25.7303i	0.486083	−	0.841920i
$935$		0			0
$936$	1.24574	−	2.15769i	0.0407184	−	0.0705264i
$937$	9.48813	−	35.4102i	0.309964	−	1.15680i	−0.618624	−	0.785687i	$-0.712310\pi$
$937$	9.48813	−	35.4102i	0.309964	−	1.15680i	0.928588	−	0.371113i	$-0.121024\pi$
$938$	15.5213	−	15.5213i	0.506789	−	0.506789i
$939$	−2.15647			−0.0703736
$940$		0			0
$941$	41.6812	−	24.0646i	1.35877	−	0.784485i	0.369310	−	0.929306i	$-0.379594\pi$
$941$	41.6812	−	24.0646i	1.35877	−	0.784485i	0.989458	+	0.144822i	$0.0462608\pi$
$942$	0.888490	+	0.888490i	0.0289486	+	0.0289486i
$943$	12.7493	+	12.7493i	0.415173	+	0.415173i
$944$	−1.77358	−	3.07193i	−0.0577251	−	0.0999828i
$945$		0			0
$946$	−27.1781	+	15.6913i	−0.883636	+	0.510168i
$947$	−49.5438	+	13.2752i	−1.60996	+	0.431387i	−0.948030	−	0.318180i	$-0.896928\pi$
$947$	−49.5438	+	13.2752i	−1.60996	+	0.431387i	−0.661928	+	0.749567i	$0.730262\pi$
$948$	−5.83601	−	21.7803i	−0.189545	−	0.707390i
$949$	−12.0388			−0.390798
$950$		0			0
$951$	−31.7077			−1.02819
$952$	−0.0983818	−	0.367166i	−0.00318857	−	0.0118999i
$953$	12.8316	−	3.43821i	0.415655	−	0.111374i	−0.0449297	−	0.998990i	$-0.514306\pi$
$953$	12.8316	−	3.43821i	0.415655	−	0.111374i	0.460585	+	0.887616i	$0.347640\pi$
$954$	3.66672	−	2.11698i	0.118714	−	0.0685398i
$955$		0			0
$956$	−3.23028	−	5.59501i	−0.104475	−	0.180955i
$957$	−49.1154	−	49.1154i	−1.58767	−	1.58767i
$958$	−0.768091	−	0.768091i	−0.0248159	−	0.0248159i
$959$	−11.5159	+	6.64869i	−0.371867	+	0.214697i
$960$		0			0
$961$	−6.25523			−0.201782
$962$	−8.97365	+	8.97365i	−0.289322	+	0.289322i
$963$	−2.68807	+	10.0320i	−0.0866220	+	0.323278i
$964$	−0.345160	+	0.597834i	−0.0111168	+	0.0192549i
$965$		0			0
$966$	−4.38187	+	7.58962i	−0.140984	+	0.244192i
$967$	−21.2025	+	5.68120i	−0.681827	+	0.182695i	−0.583077	−	0.812417i	$-0.698151\pi$
$967$	−21.2025	+	5.68120i	−0.681827	+	0.182695i	−0.0987505	+	0.995112i	$0.531485\pi$
$968$	−9.38653	−	9.38653i	−0.301694	−	0.301694i
$969$	0.411023	+	0.969441i	0.0132040	+	0.0311429i
$970$		0			0
$971$	−10.7469	−	6.20472i	−0.344884	−	0.199119i	0.317546	−	0.948243i	$-0.397141\pi$
$971$	−10.7469	−	6.20472i	−0.344884	−	0.199119i	−0.662430	+	0.749124i	$0.730475\pi$
$972$	−1.78441	−	6.65951i	−0.0572350	−	0.213604i
$973$	−13.3955	−	3.58930i	−0.429438	−	0.115068i
$974$	−8.83274	−	5.09959i	−0.283019	−	0.163401i
$975$		0			0
$976$	4.72545			0.151258
$977$	32.3787	−	32.3787i	1.03589	−	1.03589i	0.0365554	−	0.999332i	$-0.488361\pi$
$977$	32.3787	−	32.3787i	1.03589	−	1.03589i	0.999332	−	0.0365554i	$-0.0116385\pi$
$978$	−0.344412	−	0.0922849i	−0.0110131	−	0.00295095i
$979$	−19.3630	−	33.5377i	−0.618845	−	1.07187i
$980$		0			0
$981$		−	6.10371i		−	0.194876i
$982$	22.8928	+	6.13409i	0.730537	+	0.195747i
$983$	6.52989	−	1.74968i	0.208271	−	0.0558061i	−0.153175	−	0.988199i	$-0.548950\pi$
$983$	6.52989	−	1.74968i	0.208271	−	0.0558061i	0.361446	+	0.932393i	$0.382283\pi$
$984$	5.72919	+	9.92324i	0.182640	+	0.316341i
$985$		0			0
$986$	0.733181	−	1.26991i	0.0233492	−	0.0404421i
$987$	−7.01614	+	7.01614i	−0.223326	+	0.223326i
$988$	−15.8748	+	2.22426i	−0.505044	+	0.0707630i
$989$			15.2746i			0.485702i
$990$		0			0
$991$	20.3856	+	11.7696i	0.647568	+	0.373874i	0.787524	−	0.616284i	$-0.211363\pi$
$991$	20.3856	+	11.7696i	0.647568	+	0.373874i	−0.139956	+	0.990158i	$0.544696\pi$
$992$	1.57976	−	5.89573i	0.0501573	−	0.187190i
$993$	−0.866179	−	3.23262i	−0.0274874	−	0.102584i
$994$	8.74969	−	5.05163i	0.277523	−	0.160228i
$995$		0			0
$996$		−	4.91106i		−	0.155613i
$997$	−1.21155	+	4.52157i	−0.0383702	+	0.143200i	−0.982454	−	0.186507i	$-0.940283\pi$
$997$	−1.21155	+	4.52157i	−0.0383702	+	0.143200i	0.944083	+	0.329707i	$0.106950\pi$
$998$	−7.18369	+	26.8099i	−0.227396	+	0.848652i
$999$			19.3403i			0.611899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.e.407.5	yes	24
5.2	odd	4	inner	950.2.q.e.293.2	yes	24
5.3	odd	4	inner	950.2.q.e.293.5	yes	24
5.4	even	2	inner	950.2.q.e.407.2	yes	24
19.12	odd	6	inner	950.2.q.e.107.5	yes	24
95.12	even	12	inner	950.2.q.e.943.2	yes	24
95.69	odd	6	inner	950.2.q.e.107.2	✓	24
95.88	even	12	inner	950.2.q.e.943.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.e.107.2	✓	24	95.69	odd	6	inner
950.2.q.e.107.5	yes	24	19.12	odd	6	inner
950.2.q.e.293.2	yes	24	5.2	odd	4	inner
950.2.q.e.293.5	yes	24	5.3	odd	4	inner
950.2.q.e.407.2	yes	24	5.4	even	2	inner
950.2.q.e.407.5	yes	24	1.1	even	1	trivial
950.2.q.e.943.2	yes	24	95.12	even	12	inner
950.2.q.e.943.5	yes	24	95.88	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.47205 + 0.394434i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.761988 - 1.31980i) q^{6} +(-1.69567 - 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.586729 + 0.338748i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.47205 + 0.394434i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.761988 - 1.31980i) q^{6} +(-1.69567 - 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.586729 + 0.338748i) q^{9} +4.92692 q^{11} +(1.07761 - 1.07761i) q^{12} +(0.951806 - 3.55219i) q^{13} +(1.19902 - 2.07676i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.153111 + 0.0410260i) q^{17} +(-0.479062 - 0.479062i) q^{18} +(-0.533033 + 4.32618i) q^{19} +(3.16493 + 1.82727i) q^{21} +(1.27518 + 4.75904i) q^{22} +(2.31632 + 0.620657i) q^{23} +(1.31980 + 0.761988i) q^{24} +3.67750 q^{26} +(3.96292 - 3.96292i) q^{27} +(2.31632 + 0.620657i) q^{28} +(4.62539 + 8.01141i) q^{29} -6.10371i q^{31} +(0.965926 + 0.258819i) q^{32} +(-7.25267 + 1.94335i) q^{33} +(-0.0792561 - 0.137276i) q^{34} +(0.338748 - 0.586729i) q^{36} +(-2.44015 + 2.44015i) q^{37} +(-4.31673 + 0.604829i) q^{38} +5.60442i q^{39} +(6.51141 + 3.75937i) q^{41} +(-0.945867 + 3.53002i) q^{42} +(1.64858 + 6.15257i) q^{43} +(-4.26684 + 2.46346i) q^{44} +2.39804i q^{46} +(-0.702709 + 2.62255i) q^{47} +(-0.394434 + 1.47205i) q^{48} -1.24943i q^{49} +(0.209205 - 0.120784i) q^{51} +(0.951806 + 3.55219i) q^{52} +(-1.61747 + 6.03648i) q^{53} +(4.85357 + 2.80221i) q^{54} +2.39804i q^{56} +(-0.921745 - 6.57860i) q^{57} +(-6.54129 + 6.54129i) q^{58} +(1.77358 - 3.07193i) q^{59} +(2.36272 + 4.09236i) q^{61} +(5.89573 - 1.57976i) q^{62} +(1.56930 + 0.420493i) q^{63} +1.00000i q^{64} +(-3.75426 - 6.50256i) q^{66} +(8.84162 + 2.36911i) q^{67} +(0.112085 - 0.112085i) q^{68} -3.65455 q^{69} +(3.64869 + 2.10657i) q^{71} +(0.654411 + 0.175349i) q^{72} +(-0.847284 - 3.16211i) q^{73} +(-2.98856 - 1.72545i) q^{74} +(-1.70147 - 4.01310i) q^{76} +(-8.35442 - 8.35442i) q^{77} +(-5.41345 + 1.45053i) q^{78} +(7.39795 - 12.8136i) q^{79} +(-3.25426 + 5.63654i) q^{81} +(-1.94599 + 7.26254i) q^{82} +(2.27867 - 2.27867i) q^{83} -3.65455 q^{84} +(-5.51624 + 3.18480i) q^{86} +(-9.96877 - 9.96877i) q^{87} +(-3.48386 - 3.48386i) q^{88} +(-3.93005 - 6.80704i) q^{89} +(-7.63728 + 4.40938i) q^{91} +(-2.31632 + 0.620657i) q^{92} +(2.40751 + 8.98495i) q^{93} -2.71506 q^{94} -1.52398 q^{96} +(4.52503 + 16.8877i) q^{97} +(1.20685 - 0.323375i) q^{98} +(-2.89077 + 1.66898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{6}+O(q^{10}) \) 24 * q - 12 * q^6	\( 24 q - 12 q^{6} - 48 q^{11} + 12 q^{16} - 84 q^{21} + 24 q^{26} - 24 q^{36} + 48 q^{41} + 12 q^{51} + 12 q^{61} + 24 q^{71} + 36 q^{76} + 12 q^{81} - 36 q^{86} - 228 q^{91} - 24 q^{96}+O(q^{100}) \) 24 * q - 12 * q^6 - 48 * q^11 + 12 * q^16 - 84 * q^21 + 24 * q^26 - 24 * q^36 + 48 * q^41 + 12 * q^51 + 12 * q^61 + 24 * q^71 + 36 * q^76 + 12 * q^81 - 36 * q^86 - 228 * q^91 - 24 * q^96

Introduction

L-functions

Modular forms

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