LMFDB - Embedded newform 731.2.f.d.259.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, degree $2$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.19
Character	$\chi$	$=$	731.259
Dual form			731.2.f.d.302.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.374564i q^{2} +(-0.409333 + 0.409333i) q^{3} +1.85970 q^{4} +(2.01640 - 2.01640i) q^{5} +(-0.153322 - 0.153322i) q^{6} +(1.28867 + 1.28867i) q^{7} +1.44571i q^{8} +2.66489i q^{9} +O(q^{10})$	\(q+0.374564i q^{2} +(-0.409333 + 0.409333i) q^{3} +1.85970 q^{4} +(2.01640 - 2.01640i) q^{5} +(-0.153322 - 0.153322i) q^{6} +(1.28867 + 1.28867i) q^{7} +1.44571i q^{8} +2.66489i q^{9} +(0.755271 + 0.755271i) q^{10} +(3.49105 + 3.49105i) q^{11} +(-0.761237 + 0.761237i) q^{12} -6.01269 q^{13} +(-0.482689 + 0.482689i) q^{14} +1.65076i q^{15} +3.17789 q^{16} +(-4.03234 + 0.860353i) q^{17} -0.998174 q^{18} +0.526847i q^{19} +(3.74990 - 3.74990i) q^{20} -1.05499 q^{21} +(-1.30762 + 1.30762i) q^{22} +(0.860723 + 0.860723i) q^{23} +(-0.591775 - 0.591775i) q^{24} -3.13174i q^{25} -2.25214i q^{26} +(-2.31883 - 2.31883i) q^{27} +(2.39654 + 2.39654i) q^{28} +(4.98760 - 4.98760i) q^{29} -0.618315 q^{30} +(6.07859 - 6.07859i) q^{31} +4.08174i q^{32} -2.85801 q^{33} +(-0.322258 - 1.51037i) q^{34} +5.19694 q^{35} +4.95591i q^{36} +(-1.81495 + 1.81495i) q^{37} -0.197338 q^{38} +(2.46119 - 2.46119i) q^{39} +(2.91512 + 2.91512i) q^{40} +(-4.87418 - 4.87418i) q^{41} -0.395161i q^{42} -1.00000i q^{43} +(6.49232 + 6.49232i) q^{44} +(5.37349 + 5.37349i) q^{45} +(-0.322396 + 0.322396i) q^{46} -5.20861 q^{47} +(-1.30082 + 1.30082i) q^{48} -3.67866i q^{49} +1.17304 q^{50} +(1.29840 - 2.00274i) q^{51} -11.1818 q^{52} +3.10269i q^{53} +(0.868550 - 0.868550i) q^{54} +14.0787 q^{55} +(-1.86304 + 1.86304i) q^{56} +(-0.215656 - 0.215656i) q^{57} +(1.86818 + 1.86818i) q^{58} -7.12941i q^{59} +3.06992i q^{60} +(3.67007 + 3.67007i) q^{61} +(2.27682 + 2.27682i) q^{62} +(-3.43417 + 3.43417i) q^{63} +4.82691 q^{64} +(-12.1240 + 12.1240i) q^{65} -1.07051i q^{66} +0.463939 q^{67} +(-7.49896 + 1.60000i) q^{68} -0.704645 q^{69} +1.94659i q^{70} +(-8.81156 + 8.81156i) q^{71} -3.85265 q^{72} +(6.57572 - 6.57572i) q^{73} +(-0.679814 - 0.679814i) q^{74} +(1.28192 + 1.28192i) q^{75} +0.979778i q^{76} +8.99763i q^{77} +(0.921874 + 0.921874i) q^{78} +(-6.35639 - 6.35639i) q^{79} +(6.40790 - 6.40790i) q^{80} -6.09633 q^{81} +(1.82570 - 1.82570i) q^{82} -6.89378i q^{83} -1.96197 q^{84} +(-6.39600 + 9.86563i) q^{85} +0.374564 q^{86} +4.08318i q^{87} +(-5.04704 + 5.04704i) q^{88} +16.6983 q^{89} +(-2.01272 + 2.01272i) q^{90} +(-7.74836 - 7.74836i) q^{91} +(1.60069 + 1.60069i) q^{92} +4.97633i q^{93} -1.95096i q^{94} +(1.06233 + 1.06233i) q^{95} +(-1.67079 - 1.67079i) q^{96} +(6.01619 - 6.01619i) q^{97} +1.37790 q^{98} +(-9.30329 + 9.30329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$			0.374564i			0.264857i	0.991193	+	0.132428i	$0.0422775\pi$
$2$			0.374564i			0.264857i	−0.991193	+	0.132428i	$0.957723\pi$
$3$	−0.409333	+	0.409333i	−0.236329	+	0.236329i	−0.815328	−	0.578999i	$-0.803443\pi$
$3$	−0.409333	+	0.409333i	−0.236329	+	0.236329i	0.578999	+	0.815328i	$0.303443\pi$
$4$	1.85970			0.929851
$5$	2.01640	−	2.01640i	0.901761	−	0.901761i	−0.0938272	−	0.995589i	$-0.529910\pi$
$5$	2.01640	−	2.01640i	0.901761	−	0.901761i	0.995589	+	0.0938272i	$0.0299101\pi$
$6$	−0.153322	−	0.153322i	−0.0625932	−	0.0625932i
$7$	1.28867	+	1.28867i	0.487071	+	0.487071i	0.907381	−	0.420310i	$-0.138079\pi$
$7$	1.28867	+	1.28867i	0.487071	+	0.487071i	−0.420310	+	0.907381i	$0.638079\pi$
$8$			1.44571i			0.511134i
$9$			2.66489i			0.888298i
$10$	0.755271	+	0.755271i	0.238838	+	0.238838i
$11$	3.49105	+	3.49105i	1.05259	+	1.05259i	0.998538	+	0.0540544i	$0.0172144\pi$
$11$	3.49105	+	3.49105i	1.05259	+	1.05259i	0.0540544	+	0.998538i	$0.482786\pi$
$12$	−0.761237	+	0.761237i	−0.219750	+	0.219750i
$13$	−6.01269			−1.66762			−0.833810	−	0.552052i	$-0.813845\pi$
$13$	−6.01269			−1.66762			−0.833810	+	0.552052i	$0.813845\pi$
$14$	−0.482689	+	0.482689i	−0.129004	+	0.129004i
$15$			1.65076i			0.426224i
$16$	3.17789			0.794473
$17$	−4.03234	+	0.860353i	−0.977987	+	0.208666i
$17$	−4.03234	+	0.860353i	−0.977987	+	0.208666i
$18$	−0.998174			−0.235272
$19$			0.526847i			0.120867i	0.998172	+	0.0604335i	$0.0192483\pi$
$19$			0.526847i			0.120867i	−0.998172	+	0.0604335i	$0.980752\pi$
$20$	3.74990	−	3.74990i	0.838504	−	0.838504i
$21$	−1.05499			−0.230218
$22$	−1.30762	+	1.30762i	−0.278786	+	0.278786i
$23$	0.860723	+	0.860723i	0.179473	+	0.179473i	0.791126	−	0.611653i	$-0.209495\pi$
$23$	0.860723	+	0.860723i	0.179473	+	0.179473i	−0.611653	+	0.791126i	$0.709495\pi$
$24$	−0.591775	−	0.591775i	−0.120796	−	0.120796i
$25$		−	3.13174i		−	0.626347i
$26$		−	2.25214i		−	0.441680i
$27$	−2.31883	−	2.31883i	−0.446259	−	0.446259i
$28$	2.39654	+	2.39654i	0.452904	+	0.452904i
$29$	4.98760	−	4.98760i	0.926174	−	0.926174i	−0.0712819	−	0.997456i	$-0.522709\pi$
$29$	4.98760	−	4.98760i	0.926174	−	0.926174i	0.997456	+	0.0712819i	$0.0227090\pi$
$30$	−0.618315			−0.112888
$31$	6.07859	−	6.07859i	1.09175	−	1.09175i	0.0964041	−	0.995342i	$-0.469266\pi$
$31$	6.07859	−	6.07859i	1.09175	−	1.09175i	0.995342	−	0.0964041i	$-0.0307341\pi$
$32$			4.08174i			0.721556i
$33$	−2.85801			−0.497515
$34$	−0.322258	−	1.51037i	−0.0552667	−	0.259027i
$35$	5.19694			0.878444
$36$			4.95591i			0.825984i
$37$	−1.81495	+	1.81495i	−0.298376	+	0.298376i	−0.840377	−	0.542002i	$-0.817667\pi$
$37$	−1.81495	+	1.81495i	−0.298376	+	0.298376i	0.542002	+	0.840377i	$0.317667\pi$
$38$	−0.197338			−0.0320124
$39$	2.46119	−	2.46119i	0.394106	−	0.394106i
$40$	2.91512	+	2.91512i	0.460921	+	0.460921i
$41$	−4.87418	−	4.87418i	−0.761220	−	0.761220i	0.215323	−	0.976543i	$-0.430920\pi$
$41$	−4.87418	−	4.87418i	−0.761220	−	0.761220i	−0.976543	+	0.215323i	$0.930920\pi$
$42$		−	0.395161i		−	0.0609747i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	6.49232	+	6.49232i	0.978754	+	0.978754i
$45$	5.37349	+	5.37349i	0.801032	+	0.801032i
$46$	−0.322396	+	0.322396i	−0.0475347	+	0.0475347i
$47$	−5.20861			−0.759754			−0.379877	−	0.925037i	$-0.624034\pi$
$47$	−5.20861			−0.759754			−0.379877	+	0.925037i	$0.624034\pi$
$48$	−1.30082	+	1.30082i	−0.187757	+	0.187757i
$49$		−	3.67866i		−	0.525523i
$50$	1.17304			0.165892
$51$	1.29840	−	2.00274i	0.181812	−	0.280440i
$52$	−11.1818			−1.55064
$53$			3.10269i			0.426187i	0.977032	+	0.213094i	$0.0683539\pi$
$53$			3.10269i			0.426187i	−0.977032	+	0.213094i	$0.931646\pi$
$54$	0.868550	−	0.868550i	0.118195	−	0.118195i
$55$	14.0787			1.89837
$56$	−1.86304	+	1.86304i	−0.248959	+	0.248959i
$57$	−0.215656	−	0.215656i	−0.0285643	−	0.0285643i
$58$	1.86818	+	1.86818i	0.245304	+	0.245304i
$59$		−	7.12941i		−	0.928171i	−0.885791	−	0.464085i	$-0.846383\pi$
$59$		−	7.12941i		−	0.928171i	0.885791	−	0.464085i	$-0.153617\pi$
$60$			3.06992i			0.396325i
$61$	3.67007	+	3.67007i	0.469905	+	0.469905i	0.901884	−	0.431979i	$-0.142185\pi$
$61$	3.67007	+	3.67007i	0.469905	+	0.469905i	−0.431979	+	0.901884i	$0.642185\pi$
$62$	2.27682	+	2.27682i	0.289157	+	0.289157i
$63$	−3.43417	+	3.43417i	−0.432664	+	0.432664i
$64$	4.82691			0.603364
$65$	−12.1240	+	12.1240i	−1.50379	+	1.50379i
$66$		−	1.07051i		−	0.131770i
$67$	0.463939			0.0566792			0.0283396	−	0.999598i	$-0.490978\pi$
$67$	0.463939			0.0566792			0.0283396	+	0.999598i	$0.490978\pi$
$68$	−7.49896	+	1.60000i	−0.909382	+	0.194029i
$69$	−0.704645			−0.0848293
$70$			1.94659i			0.232662i
$71$	−8.81156	+	8.81156i	−1.04574	+	1.04574i	−0.0468367	+	0.998903i	$0.514914\pi$
$71$	−8.81156	+	8.81156i	−1.04574	+	1.04574i	−0.998903	+	0.0468367i	$0.985086\pi$
$72$	−3.85265			−0.454039
$73$	6.57572	−	6.57572i	0.769629	−	0.769629i	−0.208412	−	0.978041i	$-0.566829\pi$
$73$	6.57572	−	6.57572i	0.769629	−	0.769629i	0.978041	+	0.208412i	$0.0668294\pi$
$74$	−0.679814	−	0.679814i	−0.0790268	−	0.0790268i
$75$	1.28192	+	1.28192i	0.148024	+	0.148024i
$76$			0.979778i			0.112388i
$77$			8.99763i			1.02537i
$78$	0.921874	+	0.921874i	0.104382	+	0.104382i
$79$	−6.35639	−	6.35639i	−0.715150	−	0.715150i	0.252458	−	0.967608i	$-0.418761\pi$
$79$	−6.35639	−	6.35639i	−0.715150	−	0.715150i	−0.967608	+	0.252458i	$0.918761\pi$
$80$	6.40790	−	6.40790i	0.716425	−	0.716425i
$81$	−6.09633			−0.677370
$82$	1.82570	−	1.82570i	0.201614	−	0.201614i
$83$		−	6.89378i		−	0.756691i	−0.925664	−	0.378346i	$-0.876493\pi$
$83$		−	6.89378i		−	0.756691i	0.925664	−	0.378346i	$-0.123507\pi$
$84$	−1.96197			−0.214068
$85$	−6.39600	+	9.86563i	−0.693744	+	1.07008i
$86$	0.374564			0.0403903
$87$			4.08318i			0.437763i
$88$	−5.04704	+	5.04704i	−0.538016	+	0.538016i
$89$	16.6983			1.77002			0.885009	−	0.465574i	$-0.154152\pi$
$89$	16.6983			1.77002			0.885009	+	0.465574i	$0.154152\pi$
$90$	−2.01272	+	2.01272i	−0.212159	+	0.212159i
$91$	−7.74836	−	7.74836i	−0.812249	−	0.812249i
$92$	1.60069	+	1.60069i	0.166883	+	0.166883i
$93$			4.97633i			0.516022i
$94$		−	1.95096i		−	0.201226i
$95$	1.06233	+	1.06233i	0.108993	+	0.108993i
$96$	−1.67079	−	1.67079i	−0.170524	−	0.170524i
$97$	6.01619	−	6.01619i	0.610851	−	0.610851i	−0.332317	−	0.943168i	$-0.607830\pi$
$97$	6.01619	−	6.01619i	0.610851	−	0.610851i	0.943168	+	0.332317i	$0.107830\pi$
$98$	1.37790			0.139188
$99$	−9.30329	+	9.30329i	−0.935015	+	0.935015i
$100$		−	5.82409i		−	0.582409i
$101$	−0.665987			−0.0662682			−0.0331341	−	0.999451i	$-0.510549\pi$
$101$	−0.665987			−0.0662682			−0.0331341	+	0.999451i	$0.510549\pi$
$102$	0.750156	+	0.486334i	0.0742765	+	0.0481543i
$103$	12.6998			1.25135			0.625676	−	0.780083i	$-0.284823\pi$
$103$	12.6998			1.25135			0.625676	+	0.780083i	$0.284823\pi$
$104$		−	8.69258i		−	0.852377i
$105$	−2.12728	+	2.12728i	−0.207601	+	0.207601i
$106$	−1.16216			−0.112879
$107$	0.754779	−	0.754779i	0.0729673	−	0.0729673i	−0.669681	−	0.742649i	$-0.733569\pi$
$107$	0.754779	−	0.754779i	0.0729673	−	0.0729673i	0.742649	+	0.669681i	$0.233569\pi$
$108$	−4.31233	−	4.31233i	−0.414954	−	0.414954i
$109$	−2.72917	−	2.72917i	−0.261407	−	0.261407i	0.564219	−	0.825625i	$-0.309178\pi$
$109$	−2.72917	−	2.72917i	−0.261407	−	0.261407i	−0.825625	+	0.564219i	$0.809178\pi$
$110$			5.27339i			0.502798i
$111$		−	1.48584i		−	0.141029i
$112$	4.09525	+	4.09525i	0.386965	+	0.386965i
$113$	0.151373	+	0.151373i	0.0142400	+	0.0142400i	0.714191	−	0.699951i	$-0.246795\pi$
$113$	0.151373	+	0.151373i	0.0142400	+	0.0142400i	−0.699951	+	0.714191i	$0.746795\pi$
$114$	0.0807770	−	0.0807770i	0.00756545	−	0.00756545i
$115$	3.47112			0.323684
$116$	9.27545	−	9.27545i	0.861204	−	0.861204i
$117$		−	16.0232i		−	1.48134i
$118$	2.67042			0.245832
$119$	−6.30507	−	4.08765i	−0.577985	−	0.374714i
$120$	−2.38651			−0.217858
$121$			13.3749i			1.21590i
$122$	−1.37468	+	1.37468i	−0.124457	+	0.124457i
$123$	3.99033			0.359796
$124$	11.3044	−	11.3044i	1.01516	−	1.01516i
$125$	3.76717	+	3.76717i	0.336946	+	0.336946i
$126$	−1.28632	−	1.28632i	−0.114594	−	0.114594i
$127$		−	11.0096i		−	0.976942i	−0.872580	−	0.488471i	$-0.837555\pi$
$127$		−	11.0096i		−	0.976942i	0.872580	−	0.488471i	$-0.162445\pi$
$128$			9.97146i			0.881361i
$129$	0.409333	+	0.409333i	0.0360398	+	0.0360398i
$130$	−4.54121	−	4.54121i	−0.398290	−	0.398290i
$131$	−11.4880	+	11.4880i	−1.00371	+	1.00371i	−0.00371512	+	0.999993i	$0.501183\pi$
$131$	−11.4880	+	11.4880i	−1.00371	+	1.00371i	−0.999993	+	0.00371512i	$0.998817\pi$
$132$	−5.31504			−0.462615
$133$	−0.678931	+	0.678931i	−0.0588708	+	0.0588708i
$134$			0.173775i			0.0150119i
$135$	−9.35137			−0.804837
$136$	−1.24382	−	5.82958i	−0.106657	−	0.499883i
$137$	3.95001			0.337472			0.168736	−	0.985661i	$-0.446031\pi$
$137$	3.95001			0.337472			0.168736	+	0.985661i	$0.446031\pi$
$138$		−	0.263935i		−	0.0224676i
$139$	11.7913	−	11.7913i	1.00013	−	1.00013i	0.000127437	−	1.00000i	$-0.499959\pi$
$139$	11.7913	−	11.7913i	1.00013	−	1.00013i	1.00000		0.000127437i	$-4.05644e-5\pi$
$140$	9.66477			0.816822
$141$	2.13206	−	2.13206i	0.179552	−	0.179552i
$142$	−3.30049	−	3.30049i	−0.276971	−	0.276971i
$143$	−20.9906	−	20.9906i	−1.75532	−	1.75532i
$144$			8.46875i			0.705729i
$145$		−	20.1140i		−	1.67038i
$146$	2.46303	+	2.46303i	0.203842	+	0.203842i
$147$	1.50580	+	1.50580i	0.124196	+	0.124196i
$148$	−3.37526	+	3.37526i	−0.277445	+	0.277445i
$149$	−19.1681			−1.57031			−0.785155	−	0.619299i	$-0.787417\pi$
$149$	−19.1681			−1.57031			−0.785155	+	0.619299i	$0.787417\pi$
$150$	−0.480162	+	0.480162i	−0.0392051	+	0.0392051i
$151$		−	16.9313i		−	1.37785i	−0.724832	−	0.688925i	$-0.758083\pi$
$151$		−	16.9313i		−	1.37785i	0.724832	−	0.688925i	$-0.241917\pi$
$152$	−0.761666			−0.0617792
$153$	−2.29275	−	10.7458i	−0.185358	−	0.868743i
$154$	−3.37019			−0.271578
$155$		−	24.5137i		−	1.96899i
$156$	4.57708	−	4.57708i	0.366460	−	0.366460i
$157$	−5.44656			−0.434683			−0.217341	−	0.976096i	$-0.569739\pi$
$157$	−5.44656			−0.434683			−0.217341	+	0.976096i	$0.569739\pi$
$158$	2.38088	−	2.38088i	0.189412	−	0.189412i
$159$	−1.27003	−	1.27003i	−0.100720	−	0.100720i
$160$	8.23041	+	8.23041i	0.650671	+	0.650671i
$161$			2.21837i			0.174832i
$162$		−	2.28347i		−	0.179406i
$163$	−4.92547	−	4.92547i	−0.385793	−	0.385793i	0.487391	−	0.873184i	$-0.337949\pi$
$163$	−4.92547	−	4.92547i	−0.385793	−	0.385793i	−0.873184	+	0.487391i	$0.837949\pi$
$164$	−9.06453	−	9.06453i	−0.707821	−	0.707821i
$165$	−5.76288	+	5.76288i	−0.448640	+	0.448640i
$166$	2.58216			0.200415
$167$	−9.75062	+	9.75062i	−0.754526	+	0.754526i	−0.975320	−	0.220795i	$-0.929135\pi$
$167$	−9.75062	+	9.75062i	−0.754526	+	0.754526i	0.220795	+	0.975320i	$0.429135\pi$
$168$		−	1.52521i		−	0.117672i
$169$	23.1524			1.78095
$170$	−3.69531	−	2.39571i	−0.283418	−	0.183743i
$171$	−1.40399			−0.107366
$172$		−	1.85970i		−	0.141801i
$173$	−17.0666	+	17.0666i	−1.29755	+	1.29755i	−0.367543	+	0.930006i	$0.619801\pi$
$173$	−17.0666	+	17.0666i	−1.29755	+	1.29755i	−0.930006	+	0.367543i	$0.880199\pi$
$174$	−1.52941			−0.115945
$175$	4.03577	−	4.03577i	0.305076	−	0.305076i
$176$	11.0942	+	11.0942i	0.836257	+	0.836257i
$177$	2.91830	+	2.91830i	0.219353	+	0.219353i
$178$			6.25459i			0.468802i
$179$		−	11.1776i		−	0.835449i	−0.908574	−	0.417725i	$-0.862828\pi$
$179$		−	11.1776i		−	0.835449i	0.908574	−	0.417725i	$-0.137172\pi$
$180$	9.99309	+	9.99309i	0.744841	+	0.744841i
$181$	−11.0791	−	11.0791i	−0.823505	−	0.823505i	0.163104	−	0.986609i	$-0.447849\pi$
$181$	−11.0791	−	11.0791i	−0.823505	−	0.823505i	−0.986609	+	0.163104i	$0.947849\pi$
$182$	2.90226	−	2.90226i	0.215130	−	0.215130i
$183$	−3.00456			−0.222104
$184$	−1.24435	+	1.24435i	−0.0917349	+	0.0917349i
$185$			7.31932i			0.538127i
$186$	−1.86396			−0.136672
$187$	−17.0807	−	11.0736i	−1.24906	−	0.809781i
$188$	−9.68646			−0.706458
$189$		−	5.97640i		−	0.434719i
$190$	−0.397912	+	0.397912i	−0.0288676	+	0.0288676i
$191$	−14.6966			−1.06341			−0.531706	−	0.846929i	$-0.678449\pi$
$191$	−14.6966			−1.06341			−0.531706	+	0.846929i	$0.678449\pi$
$192$	−1.97582	+	1.97582i	−0.142592	+	0.142592i
$193$	16.8306	+	16.8306i	1.21149	+	1.21149i	0.970536	+	0.240955i	$0.0774607\pi$
$193$	16.8306	+	16.8306i	1.21149	+	1.21149i	0.240955	+	0.970536i	$0.422539\pi$
$194$	2.25345	+	2.25345i	0.161788	+	0.161788i
$195$		−	9.92549i		−	0.710779i
$196$		−	6.84122i		−	0.488658i
$197$	11.8366	+	11.8366i	0.843324	+	0.843324i	0.989290	−	0.145965i	$-0.0466288\pi$
$197$	11.8366	+	11.8366i	0.843324	+	0.843324i	−0.145965	+	0.989290i	$0.546629\pi$
$198$	−3.48468	−	3.48468i	−0.247645	−	0.247645i
$199$	−10.4347	+	10.4347i	−0.739694	+	0.739694i	−0.972519	−	0.232825i	$-0.925203\pi$
$199$	−10.4347	+	10.4347i	−0.739694	+	0.739694i	0.232825	+	0.972519i	$0.425203\pi$
$200$	4.52757			0.320147
$201$	−0.189906	+	0.189906i	−0.0133949	+	0.0133949i
$202$		−	0.249455i		−	0.0175516i
$203$	12.8547			0.902226
$204$	2.41464	−	3.72450i	0.169058	−	0.260767i
$205$	−19.6566			−1.37288
$206$			4.75690i			0.331429i
$207$	−2.29374	+	2.29374i	−0.159426	+	0.159426i
$208$	−19.1077			−1.32488
$209$	−1.83925	+	1.83925i	−0.127224	+	0.127224i
$210$	−0.796803	−	0.796803i	−0.0549847	−	0.0549847i
$211$	2.19372	+	2.19372i	0.151022	+	0.151022i	0.778574	−	0.627552i	$-0.215943\pi$
$211$	2.19372	+	2.19372i	0.151022	+	0.151022i	−0.627552	+	0.778574i	$0.715943\pi$
$212$			5.77008i			0.396290i
$213$		−	7.21372i		−	0.494276i
$214$	0.282713	+	0.282713i	0.0193259	+	0.0193259i
$215$	−2.01640	−	2.01640i	−0.137517	−	0.137517i
$216$	3.35234	−	3.35234i	0.228098	−	0.228098i
$217$	15.6666			1.06352
$218$	1.02225	−	1.02225i	0.0692354	−	0.0692354i
$219$			5.38332i			0.363771i
$220$	26.1822			1.76520
$221$	24.2452	−	5.17304i	1.63091	−	0.347976i
$222$	0.556541			0.0373526
$223$			11.5049i			0.770426i	0.922828	+	0.385213i	$0.125872\pi$
$223$			11.5049i			0.770426i	−0.922828	+	0.385213i	$0.874128\pi$
$224$	−5.26001	+	5.26001i	−0.351449	+	0.351449i
$225$	8.34574			0.556383
$226$	−0.0566989	+	0.0566989i	−0.00377156	+	0.00377156i
$227$	−13.5567	−	13.5567i	−0.899789	−	0.899789i	0.0956278	−	0.995417i	$-0.469514\pi$
$227$	−13.5567	−	13.5567i	−0.899789	−	0.899789i	−0.995417	+	0.0956278i	$0.969514\pi$
$228$	−0.401055	−	0.401055i	−0.0265605	−	0.0265605i
$229$			15.8825i			1.04955i	0.851242	+	0.524773i	$0.175850\pi$
$229$			15.8825i			1.04955i	−0.851242	+	0.524773i	$0.824150\pi$
$230$			1.30016i			0.0857299i
$231$	−3.68303	−	3.68303i	−0.242325	−	0.242325i
$232$	7.21061	+	7.21061i	0.473399	+	0.473399i
$233$	−5.05942	+	5.05942i	−0.331454	+	0.331454i	−0.853138	−	0.521685i	$-0.825304\pi$
$233$	−5.05942	+	5.05942i	−0.331454	+	0.331454i	0.521685	+	0.853138i	$0.325304\pi$
$234$	6.00170			0.392344
$235$	−10.5026	+	10.5026i	−0.685117	+	0.685117i
$236$		−	13.2586i		−	0.863060i
$237$	5.20376			0.338021
$238$	1.53109	−	2.36165i	0.0992456	−	0.153083i
$239$	2.00557			0.129730			0.0648648	−	0.997894i	$-0.479338\pi$
$239$	2.00557			0.129730			0.0648648	+	0.997894i	$0.479338\pi$
$240$			5.24593i			0.338623i
$241$	−12.6564	+	12.6564i	−0.815268	+	0.815268i	−0.985418	−	0.170150i	$-0.945575\pi$
$241$	−12.6564	+	12.6564i	−0.815268	+	0.815268i	0.170150	+	0.985418i	$0.445575\pi$
$242$	−5.00977			−0.322040
$243$	9.45191	−	9.45191i	0.606341	−	0.606341i
$244$	6.82524	+	6.82524i	0.436941	+	0.436941i
$245$	−7.41766	−	7.41766i	−0.473897	−	0.473897i
$246$			1.49463i			0.0952944i
$247$		−	3.16776i		−	0.201560i
$248$	8.78785	+	8.78785i	0.558029	+	0.558029i
$249$	2.82185	+	2.82185i	0.178828	+	0.178828i
$250$	−1.41105	+	1.41105i	−0.0892424	+	0.0892424i
$251$	−5.18730			−0.327420			−0.163710	−	0.986509i	$-0.552346\pi$
$251$	−5.18730			−0.327420			−0.163710	+	0.986509i	$0.552346\pi$
$252$	−6.38652	+	6.38652i	−0.402313	+	0.402313i
$253$			6.00966i			0.377824i
$254$	4.12379			0.258750
$255$	−1.42024	−	6.65642i	−0.0889386	−	0.416841i
$256$	5.91887			0.369930
$257$		−	16.8498i		−	1.05106i	−0.850775	−	0.525531i	$-0.823867\pi$
$257$		−	16.8498i		−	1.05106i	0.850775	−	0.525531i	$-0.176133\pi$
$258$	−0.153322	+	0.153322i	−0.00954538	+	0.00954538i
$259$	−4.67773			−0.290660
$260$	−22.5470	+	22.5470i	−1.39830	+	1.39830i
$261$	13.2914	+	13.2914i	0.822718	+	0.822718i
$262$	−4.30298	−	4.30298i	−0.265839	−	0.265839i
$263$		−	29.0789i		−	1.79308i	−0.442963	−	0.896540i	$-0.646073\pi$
$263$		−	29.0789i		−	1.79308i	0.442963	−	0.896540i	$-0.353927\pi$
$264$		−	4.13184i		−	0.254297i
$265$	6.25626	+	6.25626i	0.384319	+	0.384319i
$266$	−0.254303	−	0.254303i	−0.0155923	−	0.0155923i
$267$	−6.83517	+	6.83517i	−0.418306	+	0.418306i
$268$	0.862789			0.0527032
$269$	−5.70832	+	5.70832i	−0.348042	+	0.348042i	−0.859380	−	0.511338i	$-0.829150\pi$
$269$	−5.70832	+	5.70832i	−0.348042	+	0.348042i	0.511338	+	0.859380i	$0.329150\pi$
$270$		−	3.50269i		−	0.213167i
$271$	8.21767			0.499188			0.249594	−	0.968351i	$-0.419703\pi$
$271$	8.21767			0.499188			0.249594	+	0.968351i	$0.419703\pi$
$272$	−12.8144	+	2.73411i	−0.776985	+	0.165780i
$273$	6.34332			0.383915
$274$			1.47953i			0.0893819i
$275$	10.9331	−	10.9331i	0.659288	−	0.659288i
$276$	−1.31043			−0.0788786
$277$	5.57349	−	5.57349i	0.334878	−	0.334878i	−0.519557	−	0.854436i	$-0.673903\pi$
$277$	5.57349	−	5.57349i	0.334878	−	0.334878i	0.854436	+	0.519557i	$0.173903\pi$
$278$	4.41661	+	4.41661i	0.264891	+	0.264891i
$279$	16.1988	+	16.1988i	0.969796	+	0.969796i
$280$			7.51325i			0.449003i
$281$			8.97244i			0.535251i	0.963523	+	0.267625i	$0.0862389\pi$
$281$			8.97244i			0.535251i	−0.963523	+	0.267625i	$0.913761\pi$
$282$	0.798592	+	0.798592i	0.0475555	+	0.0475555i
$283$	−3.47702	−	3.47702i	−0.206688	−	0.206688i	0.596170	−	0.802858i	$-0.296688\pi$
$283$	−3.47702	−	3.47702i	−0.206688	−	0.206688i	−0.802858	+	0.596170i	$0.796688\pi$
$284$	−16.3869	+	16.3869i	−0.972382	+	0.972382i
$285$	−0.869697			−0.0515164
$286$	7.86233	−	7.86233i	0.464909	−	0.464909i
$287$		−	12.5624i		−	0.741536i
$288$	−10.8774			−0.640957
$289$	15.5196	−	6.93848i	0.912917	−	0.408146i
$290$	7.53398			0.442411
$291$			4.92525i			0.288723i
$292$	12.2289	−	12.2289i	0.715640	−	0.715640i
$293$	−23.4720			−1.37125			−0.685625	−	0.727955i	$-0.740471\pi$
$293$	−23.4720			−1.37125			−0.685625	+	0.727955i	$0.740471\pi$
$294$	−0.564018	+	0.564018i	−0.0328942	+	0.0328942i
$295$	−14.3757	−	14.3757i	−0.836988	−	0.836988i
$296$	−2.62388	−	2.62388i	−0.152510	−	0.152510i
$297$		−	16.1903i		−	0.939457i
$298$		−	7.17968i		−	0.415908i
$299$	−5.17526	−	5.17526i	−0.299293	−	0.299293i
$300$	2.38399	+	2.38399i	0.137640	+	0.137640i
$301$	1.28867	−	1.28867i	0.0742777	−	0.0742777i
$302$	6.34186			0.364933
$303$	0.272610	−	0.272610i	0.0156611	−	0.0156611i
$304$			1.67426i			0.0960256i
$305$	14.8007			0.847484
$306$	4.02498	−	0.858782i	0.230093	−	0.0490933i
$307$	12.7393			0.727070			0.363535	−	0.931580i	$-0.381570\pi$
$307$	12.7393			0.727070			0.363535	+	0.931580i	$0.381570\pi$
$308$			16.7329i			0.953446i
$309$	−5.19846	+	5.19846i	−0.295730	+	0.295730i
$310$	9.18196			0.521500
$311$	−18.6115	+	18.6115i	−1.05536	+	1.05536i	−0.0569837	+	0.998375i	$0.518148\pi$
$311$	−18.6115	+	18.6115i	−1.05536	+	1.05536i	−0.998375	+	0.0569837i	$0.981852\pi$
$312$	3.55816	+	3.55816i	0.201441	+	0.201441i
$313$	10.7881	+	10.7881i	0.609781	+	0.609781i	0.942889	−	0.333108i	$-0.108097\pi$
$313$	10.7881	+	10.7881i	0.609781	+	0.609781i	−0.333108	+	0.942889i	$0.608097\pi$
$314$		−	2.04009i		−	0.115129i
$315$			13.8493i			0.780320i
$316$	−11.8210	−	11.8210i	−0.664983	−	0.664983i
$317$	−5.64570	−	5.64570i	−0.317094	−	0.317094i	0.530556	−	0.847650i	$-0.321983\pi$
$317$	−5.64570	−	5.64570i	−0.317094	−	0.317094i	−0.847650	+	0.530556i	$0.821983\pi$
$318$	0.475709	−	0.475709i	0.0266764	−	0.0266764i
$319$	34.8240			1.94977
$320$	9.73299	−	9.73299i	0.544091	−	0.544091i
$321$			0.617912i			0.0344885i
$322$	−0.830924			−0.0463056
$323$	−0.453274	−	2.12443i	−0.0252209	−	0.118206i
$324$	−11.3374			−0.629853
$325$			18.8301i			1.04451i
$326$	1.84491	−	1.84491i	0.102180	−	0.102180i
$327$	2.23428			0.123556
$328$	7.04664	−	7.04664i	0.389086	−	0.389086i
$329$	−6.71218	−	6.71218i	−0.370054	−	0.370054i
$330$	−2.15857	−	2.15857i	−0.118825	−	0.118825i
$331$			11.0714i			0.608541i	0.952586	+	0.304270i	$0.0984126\pi$
$331$			11.0714i			0.608541i	−0.952586	+	0.304270i	$0.901587\pi$
$332$		−	12.8204i		−	0.703610i
$333$	−4.83664	−	4.83664i	−0.265046	−	0.265046i
$334$	−3.65223	−	3.65223i	−0.199841	−	0.199841i
$335$	0.935487	−	0.935487i	0.0511111	−	0.0511111i
$336$	−3.35264			−0.182902
$337$	−5.32812	+	5.32812i	−0.290241	+	0.290241i	−0.837176	−	0.546934i	$-0.815795\pi$
$337$	−5.32812	+	5.32812i	−0.290241	+	0.290241i	0.546934	+	0.837176i	$0.315795\pi$
$338$			8.67206i			0.471698i
$339$	−0.123924			−0.00673062
$340$	−11.8947	+	18.3471i	−0.645078	+	0.995013i
$341$	42.4414			2.29833
$342$		−	0.525885i		−	0.0284366i
$343$	13.7613	−	13.7613i	0.743038	−	0.743038i
$344$	1.44571			0.0779473
$345$	−1.42085	+	1.42085i	−0.0764958	+	0.0764958i
$346$	−6.39254	−	6.39254i	−0.343665	−	0.343665i
$347$	−5.69888	−	5.69888i	−0.305932	−	0.305932i	0.537397	−	0.843329i	$-0.319408\pi$
$347$	−5.69888	−	5.69888i	−0.305932	−	0.305932i	−0.843329	+	0.537397i	$0.819408\pi$
$348$			7.59350i			0.407054i
$349$			15.6938i			0.840067i	0.907508	+	0.420034i	$0.137982\pi$
$349$			15.6938i			0.840067i	−0.907508	+	0.420034i	$0.862018\pi$
$350$	1.51166	+	1.51166i	0.0808014	+	0.0808014i
$351$	13.9424	+	13.9424i	0.744189	+	0.744189i
$352$	−14.2496	+	14.2496i	−0.759504	+	0.759504i
$353$	17.7862			0.946662			0.473331	−	0.880885i	$-0.343051\pi$
$353$	17.7862			0.946662			0.473331	+	0.880885i	$0.343051\pi$
$354$	−1.09309	+	1.09309i	−0.0580972	+	0.0580972i
$355$			35.5352i			1.88601i
$356$	31.0539			1.64585
$357$	4.25408	−	0.907664i	0.225150	−	0.0480387i
$358$	4.18671			0.221275
$359$		−	2.27727i		−	0.120190i	−0.998193	−	0.0600949i	$-0.980860\pi$
$359$		−	2.27727i		−	0.120190i	0.998193	−	0.0600949i	$-0.0191403\pi$
$360$	−7.76849	+	7.76849i	−0.409435	+	0.409435i
$361$	18.7224			0.985391
$362$	4.14984	−	4.14984i	0.218111	−	0.218111i
$363$	−5.47479	−	5.47479i	−0.287352	−	0.287352i
$364$	−14.4096	−	14.4096i	−0.755271	−	0.755271i
$365$		−	26.5185i		−	1.38804i
$366$		−	1.12540i		−	0.0588257i
$367$	8.10645	+	8.10645i	0.423153	+	0.423153i	0.886288	−	0.463135i	$-0.153275\pi$
$367$	8.10645	+	8.10645i	0.423153	+	0.423153i	−0.463135	+	0.886288i	$0.653275\pi$
$368$	2.73529	+	2.73529i	0.142587	+	0.142587i
$369$	12.9892	−	12.9892i	0.676190	−	0.676190i
$370$	−2.74156			−0.142527
$371$	−3.99834	+	3.99834i	−0.207583	+	0.207583i
$372$			9.25449i			0.479823i
$373$	−19.9575			−1.03336			−0.516680	−	0.856178i	$-0.672832\pi$
$373$	−19.9575			−1.03336			−0.516680	+	0.856178i	$0.672832\pi$
$374$	4.14777	−	6.39781i	0.214476	−	0.330823i
$375$	−3.08405			−0.159260
$376$		−	7.53012i		−	0.388336i
$377$	−29.9889	+	29.9889i	−1.54451	+	1.54451i
$378$	2.23855			0.115138
$379$	15.7712	−	15.7712i	0.810113	−	0.810113i	−0.174537	−	0.984651i	$-0.555843\pi$
$379$	15.7712	−	15.7712i	0.810113	−	0.810113i	0.984651	+	0.174537i	$0.0558430\pi$
$380$	1.97562	+	1.97562i	0.101347	+	0.101347i
$381$	4.50658	+	4.50658i	0.230879	+	0.230879i
$382$		−	5.50484i		−	0.281652i
$383$		−	11.5855i		−	0.591993i	−0.955189	−	0.295996i	$-0.904348\pi$
$383$		−	11.5855i		−	0.591993i	0.955189	−	0.295996i	$-0.0956516\pi$
$384$	−4.08165	−	4.08165i	−0.208291	−	0.208291i
$385$	18.1428	+	18.1428i	0.924643	+	0.924643i
$386$	−6.30413	+	6.30413i	−0.320872	+	0.320872i
$387$	2.66489			0.135464
$388$	11.1883	−	11.1883i	0.568000	−	0.568000i
$389$			17.9914i			0.912198i	0.889929	+	0.456099i	$0.150754\pi$
$389$			17.9914i			0.912198i	−0.889929	+	0.456099i	$0.849246\pi$
$390$	3.71773			0.188255
$391$	−4.21126	−	2.73021i	−0.212972	−	0.138072i
$392$	5.31827			0.268613
$393$		−	9.40481i		−	0.474410i
$394$	−4.43357	+	4.43357i	−0.223360	+	0.223360i
$395$	−25.6341			−1.28979
$396$	−17.3013	+	17.3013i	−0.869425	+	0.869425i
$397$	−19.9072	−	19.9072i	−0.999114	−	0.999114i	0.000885863	−	1.00000i	$-0.499718\pi$
$397$	−19.9072	−	19.9072i	−0.999114	−	0.999114i	−1.00000		0.000885863i	$0.999718\pi$
$398$	−3.90845	−	3.90845i	−0.195913	−	0.195913i
$399$		−	0.555818i		−	0.0278257i
$400$		−	9.95232i		−	0.497616i
$401$	−16.3361	−	16.3361i	−0.815787	−	0.815787i	0.169708	−	0.985494i	$-0.445718\pi$
$401$	−16.3361	−	16.3361i	−0.815787	−	0.815787i	−0.985494	+	0.169708i	$0.945718\pi$
$402$	−0.0711319	−	0.0711319i	−0.00354774	−	0.00354774i
$403$	−36.5486	+	36.5486i	−1.82062	+	1.82062i
$404$	−1.23854			−0.0616195
$405$	−12.2926	+	12.2926i	−0.610826	+	0.610826i
$406$			4.81492i			0.238961i
$407$	−12.6722			−0.628136
$408$	2.89538	+	1.87711i	0.143343	+	0.0929305i
$409$	−31.2281			−1.54413			−0.772064	−	0.635545i	$-0.780776\pi$
$409$	−31.2281			−1.54413			−0.772064	+	0.635545i	$0.780776\pi$
$410$		−	7.36266i		−	0.363616i
$411$	−1.61687	+	1.61687i	−0.0797543	+	0.0797543i
$412$	23.6179			1.16357
$413$	9.18746	−	9.18746i	0.452085	−	0.452085i
$414$	−0.859151	−	0.859151i	−0.0422250	−	0.0422250i
$415$	−13.9006	−	13.9006i	−0.682355	−	0.682355i
$416$		−	24.5422i		−	1.20328i
$417$			9.65316i			0.472717i
$418$	−0.688918	−	0.688918i	−0.0336961	−	0.0336961i
$419$	6.72867	+	6.72867i	0.328717	+	0.328717i	0.852098	−	0.523381i	$-0.175330\pi$
$419$	6.72867	+	6.72867i	0.328717	+	0.328717i	−0.523381	+	0.852098i	$0.675330\pi$
$420$	−3.95611	+	3.95611i	−0.193038	+	0.193038i
$421$	−14.4959			−0.706488			−0.353244	−	0.935531i	$-0.614921\pi$
$421$	−14.4959			−0.706488			−0.353244	+	0.935531i	$0.614921\pi$
$422$	−0.821690	+	0.821690i	−0.0399992	+	0.0399992i
$423$		−	13.8804i		−	0.674888i
$424$	−4.48558			−0.217839
$425$	2.69440	+	12.6282i	0.130698	+	0.612559i
$426$	2.70200			0.130912
$427$			9.45902i			0.457754i
$428$	1.40366	−	1.40366i	0.0678487	−	0.0678487i
$429$	17.1843			0.829666
$430$	0.755271	−	0.755271i	0.0364224	−	0.0364224i
$431$	22.6999	+	22.6999i	1.09341	+	1.09341i	0.995161	+	0.0982534i	$0.0313256\pi$
$431$	22.6999	+	22.6999i	1.09341	+	1.09341i	0.0982534	+	0.995161i	$0.468674\pi$
$432$	−7.36899	−	7.36899i	−0.354541	−	0.354541i
$433$		−	25.4679i		−	1.22391i	−0.790892	−	0.611955i	$-0.790383\pi$
$433$		−	25.4679i		−	1.22391i	0.790892	−	0.611955i	$-0.209617\pi$
$434$			5.86814i			0.281680i
$435$	8.23332	+	8.23332i	0.394758	+	0.394758i
$436$	−5.07544	−	5.07544i	−0.243069	−	0.243069i
$437$	−0.453469	+	0.453469i	−0.0216924	+	0.0216924i
$438$	−2.01640			−0.0963472
$439$	1.25624	−	1.25624i	0.0599573	−	0.0599573i	−0.676492	−	0.736450i	$-0.736501\pi$
$439$	1.25624	−	1.25624i	0.0599573	−	0.0599573i	0.736450	+	0.676492i	$0.236501\pi$
$440$			20.3537i			0.970324i
$441$	9.80324			0.466821
$442$	1.93763	+	9.08139i	0.0921639	+	0.431958i
$443$	18.5355			0.880648			0.440324	−	0.897839i	$-0.354864\pi$
$443$	18.5355			0.880648			0.440324	+	0.897839i	$0.354864\pi$
$444$		−	2.76321i		−	0.131136i
$445$	33.6705	−	33.6705i	1.59613	−	1.59613i
$446$	−4.30933			−0.204053
$447$	7.84613	−	7.84613i	0.371109	−	0.371109i
$448$	6.22030	+	6.22030i	0.293881	+	0.293881i
$449$	4.73336	+	4.73336i	0.223381	+	0.223381i	0.809921	−	0.586540i	$-0.199510\pi$
$449$	4.73336	+	4.73336i	0.223381	+	0.223381i	−0.586540	+	0.809921i	$0.699510\pi$
$450$			3.12602i			0.147362i
$451$		−	34.0321i		−	1.60251i
$452$	0.281509	+	0.281509i	0.0132411	+	0.0132411i
$453$	6.93055	+	6.93055i	0.325625	+	0.325625i
$454$	5.07785	−	5.07785i	0.238315	−	0.238315i
$455$	−31.2476			−1.46491
$456$	0.311775	−	0.311775i	0.0146002	−	0.0146002i
$457$			26.1651i			1.22395i	0.790876	+	0.611976i	$0.209625\pi$
$457$			26.1651i			1.22395i	−0.790876	+	0.611976i	$0.790375\pi$
$458$	−5.94902			−0.277979
$459$	11.3453	+	7.35530i	0.529554	+	0.343316i
$460$	6.45525			0.300978
$461$			34.3460i			1.59965i	0.600232	+	0.799826i	$0.295075\pi$
$461$			34.3460i			1.59965i	−0.600232	+	0.799826i	$0.704925\pi$
$462$	1.37953	−	1.37953i	0.0641815	−	0.0641815i
$463$	−12.3835			−0.575510			−0.287755	−	0.957704i	$-0.592909\pi$
$463$	−12.3835			−0.575510			−0.287755	+	0.957704i	$0.592909\pi$
$464$	15.8501	−	15.8501i	0.735821	−	0.735821i
$465$	10.0343	+	10.0343i	0.465328	+	0.465328i
$466$	−1.89508	−	1.89508i	−0.0877879	−	0.0877879i
$467$			33.1677i			1.53482i	0.641159	+	0.767408i	$0.278454\pi$
$467$			33.1677i			1.53482i	−0.641159	+	0.767408i	$0.721546\pi$
$468$		−	29.7983i		−	1.37743i
$469$	0.597865	+	0.597865i	0.0276068	+	0.0276068i
$470$	−3.93391	−	3.93391i	−0.181458	−	0.181458i
$471$	2.22946	−	2.22946i	0.102728	−	0.102728i
$472$	10.3070			0.474420
$473$	3.49105	−	3.49105i	0.160519	−	0.160519i
$474$			1.94914i			0.0895271i
$475$	1.64994			0.0757047
$476$	−11.7255	−	7.60180i	−0.537439	−	0.348428i
$477$	−8.26833			−0.378581
$478$			0.751215i			0.0343598i
$479$	−18.3480	+	18.3480i	−0.838344	+	0.838344i	−0.988641	−	0.150297i	$-0.951977\pi$
$479$	−18.3480	+	18.3480i	−0.838344	+	0.838344i	0.150297	+	0.988641i	$0.451977\pi$
$480$	−6.73796			−0.307544
$481$	10.9127	−	10.9127i	0.497577	−	0.497577i
$482$	−4.74062	−	4.74062i	−0.215929	−	0.215929i
$483$	−0.908054	−	0.908054i	−0.0413179	−	0.0413179i
$484$			24.8734i			1.13061i
$485$		−	24.2621i		−	1.10168i
$486$	3.54035	+	3.54035i	0.160593	+	0.160593i
$487$	28.5872	+	28.5872i	1.29541	+	1.29541i	0.931393	+	0.364015i	$0.118594\pi$
$487$	28.5872	+	28.5872i	1.29541	+	1.29541i	0.364015	+	0.931393i	$0.381406\pi$
$488$	−5.30585	+	5.30585i	−0.240184	+	0.240184i
$489$	4.03232			0.182348
$490$	2.77839	−	2.77839i	0.125515	−	0.125515i
$491$			16.3872i			0.739543i	0.929123	+	0.369771i	$0.120564\pi$
$491$			16.3872i			0.739543i	−0.929123	+	0.369771i	$0.879436\pi$
$492$	7.42082			0.334556
$493$	−15.8206	+	24.4028i	−0.712525	+	1.09905i
$494$	1.18653			0.0533846
$495$			37.5183i			1.68632i
$496$	19.3171	−	19.3171i	0.867363	−	0.867363i
$497$	−22.7104			−1.01870
$498$	−1.05697	+	1.05697i	−0.0473637	+	0.0473637i
$499$	18.3368	+	18.3368i	0.820866	+	0.820866i	0.986232	−	0.165366i	$-0.0528806\pi$
$499$	18.3368	+	18.3368i	0.820866	+	0.820866i	−0.165366	+	0.986232i	$0.552881\pi$
$500$	7.00581	+	7.00581i	0.313309	+	0.313309i
$501$		−	7.98250i		−	0.356632i
$502$		−	1.94298i		−	0.0867193i
$503$	11.6567	+	11.6567i	0.519749	+	0.519749i	0.917495	−	0.397747i	$-0.130208\pi$
$503$	11.6567	+	11.6567i	0.519749	+	0.519749i	−0.397747	+	0.917495i	$0.630208\pi$
$504$	−4.96479	−	4.96479i	−0.221150	−	0.221150i
$505$	−1.34290	+	1.34290i	−0.0597581	+	0.0597581i
$506$	−2.25100			−0.100069
$507$	−9.47704	+	9.47704i	−0.420890	+	0.420890i
$508$		−	20.4745i		−	0.908410i
$509$	40.5848			1.79889			0.899444	−	0.437035i	$-0.143971\pi$
$509$	40.5848			1.79889			0.899444	+	0.437035i	$0.143971\pi$
$510$	2.49326	−	0.531969i	0.110403	−	0.0235560i
$511$	16.9478			0.749729
$512$			22.1599i			0.979340i
$513$	1.22167	−	1.22167i	0.0539379	−	0.0539379i
$514$	6.31133			0.278381
$515$	25.6079	−	25.6079i	1.12842	−	1.12842i
$516$	0.761237	+	0.761237i	0.0335116	+	0.0335116i
$517$	−18.1835	−	18.1835i	−0.799711	−	0.799711i
$518$		−	1.75211i		−	0.0769834i
$519$		−	13.9718i		−	0.613296i
$520$	−17.5277	−	17.5277i	−0.768641	−	0.768641i
$521$	0.0240937	+	0.0240937i	0.00105556	+	0.00105556i	0.707634	−	0.706579i	$-0.249762\pi$
$521$	0.0240937	+	0.0240937i	0.00105556	+	0.00105556i	−0.706579	+	0.707634i	$0.749762\pi$
$522$	−4.97849	+	4.97849i	−0.217903	+	0.217903i
$523$	32.6317			1.42689			0.713443	−	0.700714i	$-0.247135\pi$
$523$	32.6317			1.42689			0.713443	+	0.700714i	$0.247135\pi$
$524$	−21.3642	+	21.3642i	−0.933299	+	0.933299i
$525$			3.30395i			0.144196i
$526$	10.8919			0.474909
$527$	−19.2812	+	29.7407i	−0.839903	+	1.29552i
$528$	−9.08244			−0.395263
$529$		−	21.5183i		−	0.935579i
$530$	−2.34337	+	2.34337i	−0.101790	+	0.101790i
$531$	18.9991			0.824492
$532$	−1.26261	+	1.26261i	−0.0547411	+	0.0547411i
$533$	29.3069	+	29.3069i	1.26942	+	1.26942i
$534$	−2.56021	−	2.56021i	−0.110791	−	0.110791i
$535$		−	3.04387i		−	0.131598i
$536$			0.670720i			0.0289707i
$537$	4.57534	+	4.57534i	0.197441	+	0.197441i
$538$	−2.13813	−	2.13813i	−0.0921814	−	0.0921814i
$539$	12.8424	−	12.8424i	0.553162	−	0.553162i
$540$	−17.3908			−0.748379
$541$	−22.7856	+	22.7856i	−0.979630	+	0.979630i	−0.999797	−	0.0201664i	$-0.993580\pi$
$541$	−22.7856	+	22.7856i	−0.979630	+	0.979630i	0.0201664	+	0.999797i	$0.493580\pi$
$542$			3.07804i			0.132213i
$543$	9.07010			0.389235
$544$	−3.51174	−	16.4590i	−0.150564	−	0.705672i
$545$	−11.0062			−0.471453
$546$			2.37598i			0.101683i
$547$	−4.11881	+	4.11881i	−0.176108	+	0.176108i	−0.789657	−	0.613549i	$-0.789741\pi$
$547$	−4.11881	+	4.11881i	−0.176108	+	0.176108i	0.613549	+	0.789657i	$0.289741\pi$
$548$	7.34584			0.313799
$549$	−9.78035	+	9.78035i	−0.417415	+	0.417415i
$550$	4.09513	+	4.09513i	0.174617	+	0.174617i
$551$	2.62770	+	2.62770i	0.111944	+	0.111944i
$552$		−	1.01871i		−	0.0433592i
$553$		−	16.3826i		−	0.696658i
$554$	2.08763	+	2.08763i	0.0886949	+	0.0886949i
$555$	−2.99604	−	2.99604i	−0.127175	−	0.127175i
$556$	21.9284	−	21.9284i	0.929969	−	0.929969i
$557$	−8.23539			−0.348945			−0.174472	−	0.984662i	$-0.555822\pi$
$557$	−8.23539			−0.348945			−0.174472	+	0.984662i	$0.555822\pi$
$558$	−6.06748	+	6.06748i	−0.256857	+	0.256857i
$559$			6.01269i			0.254310i
$560$	16.5153			0.697900
$561$	11.5245	−	2.45890i	0.486563	−	0.103815i
$562$	−3.36075			−0.141765
$563$		−	14.1764i		−	0.597463i	−0.954337	−	0.298732i	$-0.903436\pi$
$563$		−	14.1764i		−	0.597463i	0.954337	−	0.298732i	$-0.0965636\pi$
$564$	3.96499	−	3.96499i	0.166956	−	0.166956i
$565$	0.610457			0.0256821
$566$	1.30237	−	1.30237i	0.0547426	−	0.0547426i
$567$	−7.85616	−	7.85616i	−0.329928	−	0.329928i
$568$	−12.7389	−	12.7389i	−0.534513	−	0.534513i
$569$		−	42.4109i		−	1.77796i	−0.457948	−	0.888979i	$-0.651415\pi$
$569$		−	42.4109i		−	1.77796i	0.457948	−	0.888979i	$-0.348585\pi$
$570$		−	0.325757i		−	0.0136445i
$571$	−26.2663	−	26.2663i	−1.09921	−	1.09921i	−0.994503	−	0.104707i	$-0.966610\pi$
$571$	−26.2663	−	26.2663i	−1.09921	−	1.09921i	−0.104707	−	0.994503i	$-0.533390\pi$
$572$	−39.0363	−	39.0363i	−1.63219	−	1.63219i
$573$	6.01582	−	6.01582i	0.251315	−	0.251315i
$574$	4.70543			0.196401
$575$	2.69556	−	2.69556i	0.112413	−	0.112413i
$576$			12.8632i			0.535967i
$577$	−5.32596			−0.221723			−0.110861	−	0.993836i	$-0.535361\pi$
$577$	−5.32596			−0.221723			−0.110861	+	0.993836i	$0.535361\pi$
$578$	2.59891	+	5.81308i	0.108100	+	0.241792i
$579$	−13.7786			−0.572620
$580$		−	37.4060i		−	1.55320i
$581$	8.88381	−	8.88381i	0.368562	−	0.368562i
$582$	−1.84482			−0.0764703
$583$	−10.8317	+	10.8317i	−0.448601	+	0.448601i
$584$	9.50655	+	9.50655i	0.393384	+	0.393384i
$585$	−32.3091	−	32.3091i	−1.33582	−	1.33582i
$586$		−	8.79178i		−	0.363185i
$587$			3.91634i			0.161645i	0.996729	+	0.0808223i	$0.0257546\pi$
$587$			3.91634i			0.161645i	−0.996729	+	0.0808223i	$0.974245\pi$
$588$	2.80034	+	2.80034i	0.115484	+	0.115484i
$589$	3.20248	+	3.20248i	0.131956	+	0.131956i
$590$	5.38464	−	5.38464i	0.221682	−	0.221682i
$591$	−9.69024			−0.398603
$592$	−5.76771	+	5.76771i	−0.237051	+	0.237051i
$593$			24.0356i			0.987022i	0.869739	+	0.493511i	$0.164287\pi$
$593$			24.0356i			0.987022i	−0.869739	+	0.493511i	$0.835713\pi$
$594$	6.06431			0.248822
$595$	−20.9559	+	4.47121i	−0.859107	+	0.183302i
$596$	−35.6469			−1.46015
$597$		−	8.54250i		−	0.349621i
$598$	1.93847	−	1.93847i	0.0792698	−	0.0792698i
$599$	1.60564			0.0656048			0.0328024	−	0.999462i	$-0.489557\pi$
$599$	1.60564			0.0656048			0.0328024	+	0.999462i	$0.489557\pi$
$600$	−1.85328	+	1.85328i	−0.0756600	+	0.0756600i
$601$	−24.4932	−	24.4932i	−0.999099	−	0.999099i	0.000900903	−	1.00000i	$-0.499713\pi$
$601$	−24.4932	−	24.4932i	−0.999099	−	0.999099i	−1.00000		0.000900903i	$0.999713\pi$
$602$	0.482689	+	0.482689i	0.0196730	+	0.0196730i
$603$			1.23635i			0.0503480i
$604$		−	31.4872i		−	1.28120i
$605$	26.9692	+	26.9692i	1.09645	+	1.09645i
$606$	0.102110	+	0.102110i	0.00414794	+	0.00414794i
$607$	−19.7439	+	19.7439i	−0.801380	+	0.801380i	−0.983311	−	0.181931i	$-0.941765\pi$
$607$	−19.7439	+	19.7439i	−0.801380	+	0.801380i	0.181931	+	0.983311i	$0.441765\pi$
$608$	−2.15045			−0.0872123
$609$	−5.26187	+	5.26187i	−0.213222	+	0.213222i
$610$			5.54380i			0.224462i
$611$	31.3178			1.26698
$612$	−4.26383	−	19.9839i	−0.172355	−	0.807802i
$613$	−14.3176			−0.578282			−0.289141	−	0.957287i	$-0.593370\pi$
$613$	−14.3176			−0.578282			−0.289141	+	0.957287i	$0.593370\pi$
$614$			4.77169i			0.192570i
$615$	8.04610	−	8.04610i	0.324450	−	0.324450i
$616$	−13.0079			−0.524104
$617$	8.86659	−	8.86659i	0.356955	−	0.356955i	−0.505734	−	0.862689i	$-0.668778\pi$
$617$	8.86659	−	8.86659i	0.356955	−	0.356955i	0.862689	+	0.505734i	$0.168778\pi$
$618$	−1.94716	−	1.94716i	−0.0783261	−	0.0783261i
$619$	−19.6259	−	19.6259i	−0.788833	−	0.788833i	0.192470	−	0.981303i	$-0.438350\pi$
$619$	−19.6259	−	19.6259i	−0.788833	−	0.788833i	−0.981303	+	0.192470i	$0.938350\pi$
$620$		−	45.5882i		−	1.83087i
$621$		−	3.99174i		−	0.160183i
$622$	−6.97119	−	6.97119i	−0.279519	−	0.279519i
$623$	21.5186	+	21.5186i	0.862125	+	0.862125i
$624$	7.82140	−	7.82140i	0.313107	−	0.313107i
$625$	30.8509			1.23404
$626$	−4.04084	+	4.04084i	−0.161505	+	0.161505i
$627$		−	1.50573i		−	0.0601331i
$628$	−10.1290			−0.404190
$629$	5.75699	−	8.87999i	0.229546	−	0.354068i
$630$	−5.18745			−0.206673
$631$		−	5.04688i		−	0.200913i	−0.994941	−	0.100457i	$-0.967970\pi$
$631$		−	5.04688i		−	0.200913i	0.994941	−	0.100457i	$-0.0320303\pi$
$632$	9.18948	−	9.18948i	0.365538	−	0.365538i
$633$	−1.79593			−0.0713816
$634$	2.11468	−	2.11468i	0.0839845	−	0.0839845i
$635$	−22.1997	−	22.1997i	−0.880969	−	0.880969i
$636$	−2.36188	−	2.36188i	−0.0936547	−	0.0936547i
$637$			22.1186i			0.876373i
$638$			13.0438i			0.516410i
$639$	−23.4819	−	23.4819i	−0.928928	−	0.928928i
$640$	20.1065	+	20.1065i	0.794778	+	0.794778i
$641$	−26.2346	+	26.2346i	−1.03620	+	1.03620i	−0.0368854	+	0.999320i	$0.511744\pi$
$641$	−26.2346	+	26.2346i	−1.03620	+	1.03620i	−0.999320	+	0.0368854i	$0.988256\pi$
$642$	−0.231448			−0.00913451
$643$	21.7801	−	21.7801i	0.858925	−	0.858925i	−0.132287	−	0.991212i	$-0.542232\pi$
$643$	21.7801	−	21.7801i	0.858925	−	0.858925i	0.991212	+	0.132287i	$0.0422319\pi$
$644$			4.12552i			0.162568i
$645$	1.65076			0.0649985
$646$	0.795734	−	0.169780i	0.0313078	−	0.00667992i
$647$	−18.5602			−0.729676			−0.364838	−	0.931071i	$-0.618876\pi$
$647$	−18.5602			−0.729676			−0.364838	+	0.931071i	$0.618876\pi$
$648$		−	8.81351i		−	0.346227i
$649$	24.8892	−	24.8892i	0.976985	−	0.976985i
$650$	−7.05310			−0.276645
$651$	−6.41285	+	6.41285i	−0.251339	+	0.251339i
$652$	−9.15991	−	9.15991i	−0.358730	−	0.358730i
$653$	4.07616	+	4.07616i	0.159512	+	0.159512i	0.782351	−	0.622838i	$-0.214021\pi$
$653$	4.07616	+	4.07616i	0.159512	+	0.159512i	−0.622838	+	0.782351i	$0.714021\pi$
$654$			0.836880i			0.0327246i
$655$			46.3287i			1.81021i
$656$	−15.4896	−	15.4896i	−0.604769	−	0.604769i
$657$	17.5236	+	17.5236i	0.683660	+	0.683660i
$658$	2.51414	−	2.51414i	0.0980115	−	0.0980115i
$659$	−14.5350			−0.566203			−0.283102	−	0.959090i	$-0.591363\pi$
$659$	−14.5350			−0.566203			−0.283102	+	0.959090i	$0.591363\pi$
$660$	−10.7172	+	10.7172i	−0.417168	+	0.417168i
$661$			32.4066i			1.26047i	0.776405	+	0.630235i	$0.217041\pi$
$661$			32.4066i			1.26047i	−0.776405	+	0.630235i	$0.782959\pi$
$662$	−4.14696			−0.161176
$663$	−7.80687	+	12.0419i	−0.303194	+	0.467667i
$664$	9.96638			0.386771
$665$			2.73799i			0.106175i
$666$	1.81163	−	1.81163i	0.0701993	−	0.0701993i
$667$	8.58589			0.332447
$668$	−18.1332	+	18.1332i	−0.701596	+	0.701596i
$669$	−4.70934	−	4.70934i	−0.182074	−	0.182074i
$670$	0.350400	+	0.350400i	0.0135371	+	0.0135371i
$671$			25.6248i			0.989236i
$672$		−	4.30619i		−	0.166115i
$673$	18.6819	+	18.6819i	0.720133	+	0.720133i	0.968632	−	0.248499i	$-0.0799374\pi$
$673$	18.6819	+	18.6819i	0.720133	+	0.720133i	−0.248499	+	0.968632i	$0.579937\pi$
$674$	−1.99572	−	1.99572i	−0.0768724	−	0.0768724i
$675$	−7.26195	+	7.26195i	−0.279513	+	0.279513i
$676$	43.0566			1.65602
$677$	13.2748	−	13.2748i	0.510191	−	0.510191i	−0.404394	−	0.914585i	$-0.632517\pi$
$677$	13.2748	−	13.2748i	0.510191	−	0.510191i	0.914585	+	0.404394i	$0.132517\pi$
$678$		−	0.0464175i		−	0.00178265i
$679$	15.5057			0.595056
$680$	−14.2628	−	9.24674i	−0.546954	−	0.354596i
$681$	11.0984			0.425292
$682$			15.8970i			0.608728i
$683$	−0.657604	+	0.657604i	−0.0251625	+	0.0251625i	−0.719576	−	0.694414i	$-0.755664\pi$
$683$	−0.657604	+	0.657604i	−0.0251625	+	0.0251625i	0.694414	+	0.719576i	$0.255664\pi$
$684$	−2.61100			−0.0998342
$685$	7.96480	−	7.96480i	0.304319	−	0.304319i
$686$	5.15448	+	5.15448i	0.196799	+	0.196799i
$687$	−6.50123	−	6.50123i	−0.248038	−	0.248038i
$688$		−	3.17789i		−	0.121156i
$689$		−	18.6555i		−	0.710718i
$690$	−0.532198	−	0.532198i	−0.0202604	−	0.0202604i
$691$	−27.2708	−	27.2708i	−1.03743	−	1.03743i	−0.999272	−	0.0381586i	$-0.987851\pi$
$691$	−27.2708	−	27.2708i	−1.03743	−	1.03743i	−0.0381586	−	0.999272i	$-0.512149\pi$
$692$	−31.7388	+	31.7388i	−1.20653	+	1.20653i
$693$	−23.9777			−0.910838
$694$	2.13460	−	2.13460i	0.0810281	−	0.0810281i
$695$		−	47.5521i		−	1.80375i
$696$	−5.90308			−0.223756
$697$	23.8479	+	15.4609i	0.903304	+	0.585622i
$698$	−5.87832			−0.222498
$699$		−	4.14198i		−	0.156664i
$700$	7.50533	−	7.50533i	0.283675	−	0.283675i
$701$	7.45148			0.281438			0.140719	−	0.990050i	$-0.455059\pi$
$701$	7.45148			0.281438			0.140719	+	0.990050i	$0.455059\pi$
$702$	−5.22232	+	5.22232i	−0.197104	+	0.197104i
$703$	−0.956199	−	0.956199i	−0.0360637	−	0.0360637i
$704$	16.8510	+	16.8510i	0.635097	+	0.635097i
$705$		−	8.59816i		−	0.323825i
$706$			6.66206i			0.250730i
$707$	−0.858237	−	0.858237i	−0.0322773	−	0.0322773i
$708$	5.42718	+	5.42718i	0.203966	+	0.203966i
$709$	12.3881	−	12.3881i	0.465244	−	0.465244i	−0.435126	−	0.900370i	$-0.643296\pi$
$709$	12.3881	−	12.3881i	0.465244	−	0.465244i	0.900370	+	0.435126i	$0.143296\pi$
$710$	−13.3102			−0.499524
$711$	16.9391	−	16.9391i	0.635266	−	0.635266i
$712$			24.1409i			0.904717i
$713$	10.4640			0.391878
$714$	0.339978	+	1.59343i	0.0127234	+	0.0596325i
$715$	−84.6509			−3.16577
$716$		−	20.7869i		−	0.776843i
$717$	−0.820947	+	0.820947i	−0.0306588	+	0.0306588i
$718$	0.852985			0.0318331
$719$	25.0947	−	25.0947i	0.935874	−	0.935874i	−0.0621904	−	0.998064i	$-0.519809\pi$
$719$	25.0947	−	25.0947i	0.935874	−	0.935874i	0.998064	+	0.0621904i	$0.0198086\pi$
$720$	17.0764	+	17.0764i	0.636399	+	0.636399i
$721$	16.3659	+	16.3659i	0.609497	+	0.609497i
$722$			7.01275i			0.260988i
$723$		−	10.3613i		−	0.385342i
$724$	−20.6039	−	20.6039i	−0.765737	−	0.765737i
$725$	−15.6198	−	15.6198i	−0.580107	−	0.580107i
$726$	2.05066	−	2.05066i	0.0761072	−	0.0761072i
$727$	−13.3167			−0.493890			−0.246945	−	0.969029i	$-0.579427\pi$
$727$	−13.3167			−0.493890			−0.246945	+	0.969029i	$0.579427\pi$
$728$	11.2019	−	11.2019i	0.415168	−	0.415168i
$729$		−	10.5510i		−	0.390779i
$730$	9.93290			0.367633
$731$	0.860353	+	4.03234i	0.0318213	+	0.149142i
$732$	−5.58759			−0.206523
$733$		−	20.0872i		−	0.741937i	−0.928646	−	0.370968i	$-0.879026\pi$
$733$		−	20.0872i		−	0.741937i	0.928646	−	0.370968i	$-0.120974\pi$
$734$	−3.03639	+	3.03639i	−0.112075	+	0.112075i
$735$	6.07258			0.223991
$736$	−3.51325	+	3.51325i	−0.129500	+	0.129500i
$737$	1.61964	+	1.61964i	0.0596601	+	0.0596601i
$738$	4.86528	+	4.86528i	0.179094	+	0.179094i
$739$		−	13.4126i		−	0.493389i	−0.969093	−	0.246695i	$-0.920656\pi$
$739$		−	13.4126i		−	0.493389i	0.969093	−	0.246695i	$-0.0793445\pi$
$740$			13.6117i			0.500378i
$741$	1.29667	+	1.29667i	0.0476344	+	0.0476344i
$742$	−1.49764	−	1.49764i	−0.0549799	−	0.0549799i
$743$	29.7281	−	29.7281i	1.09062	−	1.09062i	0.0951539	−	0.995463i	$-0.469666\pi$
$743$	29.7281	−	29.7281i	1.09062	−	1.09062i	0.995463	−	0.0951539i	$-0.0303343\pi$
$744$	−7.19431			−0.263756
$745$	−38.6505	+	38.6505i	−1.41605	+	1.41605i
$746$		−	7.47537i		−	0.273693i
$747$	18.3712			0.672167
$748$	−31.7649	−	20.5936i	−1.16144	−	0.752975i
$749$	1.94532			0.0710805
$750$		−	1.15518i		−	0.0421811i
$751$	3.01665	−	3.01665i	0.110079	−	0.110079i	−0.649922	−	0.760001i	$-0.725198\pi$
$751$	3.01665	−	3.01665i	0.110079	−	0.110079i	0.760001	+	0.649922i	$0.225198\pi$
$752$	−16.5524			−0.603604
$753$	2.12333	−	2.12333i	0.0773786	−	0.0773786i
$754$	−11.2328	−	11.2328i	−0.409073	−	0.409073i
$755$	−34.1403	−	34.1403i	−1.24249	−	1.24249i
$756$		−	11.1143i		−	0.404224i
$757$		−	6.29426i		−	0.228769i	−0.993437	−	0.114384i	$-0.963510\pi$
$757$		−	6.29426i		−	0.228769i	0.993437	−	0.114384i	$-0.0364896\pi$
$758$	5.90733	+	5.90733i	0.214564	+	0.214564i
$759$	−2.45995	−	2.45995i	−0.0892906	−	0.0892906i
$760$	−1.53582	+	1.53582i	−0.0557101	+	0.0557101i
$761$	22.8183			0.827162			0.413581	−	0.910467i	$-0.364278\pi$
$761$	22.8183			0.827162			0.413581	+	0.910467i	$0.364278\pi$
$762$	−1.68801	+	1.68801i	−0.0611500	+	0.0611500i
$763$		−	7.03399i		−	0.254647i
$764$	−27.3314			−0.988814
$765$	−26.2909	−	17.0447i	−0.950548	−	0.616251i
$766$	4.33952			0.156793
$767$			42.8669i			1.54784i
$768$	−2.42279	+	2.42279i	−0.0874249	+	0.0874249i
$769$	−11.2784			−0.406711			−0.203355	−	0.979105i	$-0.565185\pi$
$769$	−11.2784			−0.406711			−0.203355	+	0.979105i	$0.565185\pi$
$770$	−6.79565	+	6.79565i	−0.244898	+	0.244898i
$771$	6.89718	+	6.89718i	0.248396	+	0.248396i
$772$	31.2999	+	31.2999i	1.12651	+	1.12651i
$773$		−	15.7658i		−	0.567057i	−0.958964	−	0.283529i	$-0.908495\pi$
$773$		−	15.7658i		−	0.567057i	0.958964	−	0.283529i	$-0.0915051\pi$
$774$			0.998174i			0.0358786i
$775$	−19.0365	−	19.0365i	−0.683812	−	0.683812i
$776$	8.69764	+	8.69764i	0.312227	+	0.312227i
$777$	1.91475	−	1.91475i	0.0686913	−	0.0686913i
$778$	−6.73892			−0.241602
$779$	2.56795	−	2.56795i	0.0920063	−	0.0920063i
$780$		−	18.4584i		−	0.660918i
$781$	−61.5232			−2.20147
$782$	1.02264	−	1.57739i	0.0365694	−	0.0564072i
$783$	−23.1308			−0.826627
$784$		−	11.6904i		−	0.417514i
$785$	−10.9824	+	10.9824i	−0.391980	+	0.391980i
$786$	3.52270			0.125651
$787$	−6.82688	+	6.82688i	−0.243352	+	0.243352i	−0.818235	−	0.574883i	$-0.805047\pi$
$787$	−6.82688	+	6.82688i	−0.243352	+	0.243352i	0.574883	+	0.818235i	$0.305047\pi$
$788$	22.0126	+	22.0126i	0.784166	+	0.784166i
$789$	11.9029	+	11.9029i	0.423756	+	0.423756i
$790$		−	9.60160i		−	0.341610i
$791$			0.390139i			0.0138718i
$792$	−13.4498	−	13.4498i	−0.477918	−	0.477918i
$793$	−22.0670	−	22.0670i	−0.783622	−	0.783622i
$794$	7.45653	−	7.45653i	0.264622	−	0.264622i
$795$	−5.12179			−0.181651
$796$	−19.4054	+	19.4054i	−0.687805	+	0.687805i
$797$			38.9111i			1.37830i	0.724618	+	0.689151i	$0.242016\pi$
$797$			38.9111i			1.37830i	−0.724618	+	0.689151i	$0.757984\pi$
$798$	0.208190			0.00736983
$799$	21.0029	−	4.48125i	0.743030	−	0.158535i
$800$	12.7829			0.451945
$801$			44.4992i			1.57230i
$802$	6.11892	−	6.11892i	0.216067	−	0.216067i
$803$	45.9124			1.62021
$804$	−0.353168	+	0.353168i	−0.0124553	+	0.0124553i
$805$	4.47313	+	4.47313i	0.157657	+	0.157657i
$806$	−13.6898	−	13.6898i	−0.482203	−	0.482203i
$807$		−	4.67320i		−	0.164505i
$808$		−	0.962822i		−	0.0338719i
$809$	16.6814	+	16.6814i	0.586486	+	0.586486i	0.936678	−	0.350192i	$-0.113884\pi$
$809$	16.6814	+	16.6814i	0.586486	+	0.586486i	−0.350192	+	0.936678i	$0.613884\pi$
$810$	−4.60439	−	4.60439i	−0.161782	−	0.161782i
$811$	−20.8200	+	20.8200i	−0.731091	+	0.731091i	−0.970836	−	0.239745i	$-0.922936\pi$
$811$	−20.8200	+	20.8200i	−0.731091	+	0.731091i	0.239745	+	0.970836i	$0.422936\pi$
$812$	23.9060			0.838935
$813$	−3.36376	+	3.36376i	−0.117972	+	0.117972i
$814$		−	4.74654i		−	0.166366i
$815$	−19.8634			−0.695786
$816$	4.12618	−	6.36450i	0.144445	−	0.222802i
$817$	0.526847			0.0184320
$818$		−	11.6969i		−	0.408973i
$819$	20.6486	−	20.6486i	0.721519	−	0.721519i
$820$	−36.5554			−1.27657
$821$	10.0527	−	10.0527i	0.350842	−	0.350842i	−0.509581	−	0.860423i	$-0.670199\pi$
$821$	10.0527	−	10.0527i	0.350842	−	0.350842i	0.860423	+	0.509581i	$0.170199\pi$
$822$	−0.605622	−	0.605622i	−0.0211235	−	0.0211235i
$823$	−19.8078	−	19.8078i	−0.690455	−	0.690455i	0.271877	−	0.962332i	$-0.412356\pi$
$823$	−19.8078	−	19.8078i	−0.690455	−	0.690455i	−0.962332	+	0.271877i	$0.912356\pi$
$824$			18.3602i			0.639609i
$825$			8.95052i			0.311617i
$826$	3.44129	+	3.44129i	0.119738	+	0.119738i
$827$	−1.03531	−	1.03531i	−0.0360012	−	0.0360012i	0.688877	−	0.724878i	$-0.258104\pi$
$827$	−1.03531	−	1.03531i	−0.0360012	−	0.0360012i	−0.724878	+	0.688877i	$0.758104\pi$
$828$	−4.26566	+	4.26566i	−0.148242	+	0.148242i
$829$	53.9382			1.87335			0.936676	−	0.350197i	$-0.113885\pi$
$829$	53.9382			1.87335			0.936676	+	0.350197i	$0.113885\pi$
$830$	5.20668	−	5.20668i	0.180726	−	0.180726i
$831$			4.56282i			0.158283i
$832$	−29.0227			−1.00618
$833$	3.16495	+	14.8336i	0.109659	+	0.513955i
$834$	−3.61573			−0.125202
$835$			39.3223i			1.36080i
$836$	−3.42046	+	3.42046i	−0.118299	+	0.118299i
$837$	−28.1904			−0.974402
$838$	−2.52032	+	2.52032i	−0.0870630	+	0.0870630i
$839$	13.1333	+	13.1333i	0.453411	+	0.453411i	0.896485	−	0.443074i	$-0.146112\pi$
$839$	13.1333	+	13.1333i	0.453411	+	0.453411i	−0.443074	+	0.896485i	$0.646112\pi$
$840$	−3.07542	−	3.07542i	−0.106112	−	0.106112i
$841$		−	20.7523i		−	0.715598i
$842$		−	5.42965i		−	0.187118i
$843$	−3.67271	−	3.67271i	−0.126495	−	0.126495i
$844$	4.07967	+	4.07967i	0.140428	+	0.140428i
$845$	46.6845	−	46.6845i	1.60600	−	1.60600i
$846$	5.19910			0.178749
$847$	−17.2358	+	17.2358i	−0.592231	+	0.592231i
$848$			9.86002i			0.338594i
$849$	2.84652			0.0976923
$850$	−4.73008	+	1.00923i	−0.162241	+	0.0346162i
$851$	−3.12433			−0.107101
$852$		−	13.4154i		−	0.459603i
$853$	8.43699	−	8.43699i	0.288877	−	0.288877i	−0.547759	−	0.836636i	$-0.684519\pi$
$853$	8.43699	−	8.43699i	0.288877	−	0.288877i	0.836636	+	0.547759i	$0.184519\pi$
$854$	−3.54301			−0.121239
$855$	−2.83101	+	2.83101i	−0.0968184	+	0.0968184i
$856$	1.09119	+	1.09119i	0.0372961	+	0.0372961i
$857$	−14.2735	−	14.2735i	−0.487573	−	0.487573i	0.419966	−	0.907540i	$-0.362042\pi$
$857$	−14.2735	−	14.2735i	−0.487573	−	0.487573i	−0.907540	+	0.419966i	$0.862042\pi$
$858$			6.43662i			0.219743i
$859$		−	23.7786i		−	0.811316i	−0.914025	−	0.405658i	$-0.867042\pi$
$859$		−	23.7786i		−	0.811316i	0.914025	−	0.405658i	$-0.132958\pi$
$860$	−3.74990	−	3.74990i	−0.127871	−	0.127871i
$861$	5.14221	+	5.14221i	0.175246	+	0.175246i
$862$	−8.50256	+	8.50256i	−0.289598	+	0.289598i
$863$	40.0314			1.36269			0.681343	−	0.731964i	$-0.261396\pi$
$863$	40.0314			1.36269			0.681343	+	0.731964i	$0.261396\pi$
$864$	9.46485	−	9.46485i	0.322001	−	0.322001i
$865$			68.8262i			2.34016i
$866$	9.53937			0.324161
$867$	−3.51253	+	9.19283i	−0.119292	+	0.312205i
$868$	29.1352			0.988912
$869$		−	44.3810i		−	1.50552i
$870$	−3.08391	+	3.08391i	−0.104554	+	0.104554i
$871$	−2.78952			−0.0945194
$872$	3.94557	−	3.94557i	0.133614	−	0.133614i
$873$	16.0325	+	16.0325i	0.542618	+	0.542618i
$874$	−0.169853	−	0.169853i	−0.00574538	−	0.00574538i
$875$			9.70927i			0.328233i
$876$			10.0114i			0.338253i
$877$	12.4931	+	12.4931i	0.421863	+	0.421863i	0.885845	−	0.463982i	$-0.153580\pi$
$877$	12.4931	+	12.4931i	0.421863	+	0.421863i	−0.463982	+	0.885845i	$0.653580\pi$
$878$	0.470544	+	0.470544i	0.0158801	+	0.0158801i
$879$	9.60787	−	9.60787i	0.324065	−	0.324065i
$880$	44.7407			1.50821
$881$	−15.9411	+	15.9411i	−0.537068	+	0.537068i	−0.922667	−	0.385598i	$-0.873995\pi$
$881$	−15.9411	+	15.9411i	−0.537068	+	0.537068i	0.385598	+	0.922667i	$0.373995\pi$
$882$			3.67194i			0.123641i
$883$	10.5148			0.353853			0.176926	−	0.984224i	$-0.443385\pi$
$883$	10.5148			0.353853			0.176926	+	0.984224i	$0.443385\pi$
$884$	45.0889	−	9.62030i	1.51650	−	0.323566i
$885$	11.7689			0.395608
$886$			6.94273i			0.233246i
$887$	18.7884	−	18.7884i	0.630854	−	0.630854i	−0.317428	−	0.948282i	$-0.602819\pi$
$887$	18.7884	−	18.7884i	0.630854	−	0.630854i	0.948282	+	0.317428i	$0.102819\pi$
$888$	2.14808			0.0720849
$889$	14.1877	−	14.1877i	0.475840	−	0.475840i
$890$	12.6118	+	12.6118i	0.422747	+	0.422747i
$891$	−21.2826	−	21.2826i	−0.712995	−	0.712995i
$892$			21.3957i			0.716381i
$893$		−	2.74414i		−	0.0918292i
$894$	2.93888	+	2.93888i	0.0982908	+	0.0982908i
$895$	−22.5384	−	22.5384i	−0.753376	−	0.753376i
$896$	−12.8499	+	12.8499i	−0.429286	+	0.429286i
$897$	4.23681			0.141463
$898$	−1.77295	+	1.77295i	−0.0591640	+	0.0591640i
$899$		−	60.6351i		−	2.02230i
$900$	15.5206			0.517353
$901$	−2.66941	−	12.5111i	−0.0889309	−	0.416805i
$902$	12.7472			0.424435
$903$			1.05499i			0.0351079i
$904$	−0.218841	+	0.218841i	−0.00727854	+	0.00727854i
$905$	−44.6799			−1.48521
$906$	−2.59593	+	2.59593i	−0.0862441	+	0.0862441i
$907$	−23.5932	−	23.5932i	−0.783400	−	0.783400i	0.197003	−	0.980403i	$-0.436879\pi$
$907$	−23.5932	−	23.5932i	−0.783400	−	0.783400i	−0.980403	+	0.197003i	$0.936879\pi$
$908$	−25.2114	−	25.2114i	−0.836670	−	0.836670i
$909$		−	1.77478i		−	0.0588659i
$910$		−	11.7042i		−	0.387991i
$911$	30.0255	+	30.0255i	0.994790	+	0.994790i	0.999986	−	0.00519635i	$-0.00165406\pi$
$911$	30.0255	+	30.0255i	0.994790	+	0.994790i	−0.00519635	+	0.999986i	$0.501654\pi$
$912$	−0.685331	−	0.685331i	−0.0226936	−	0.0226936i
$913$	24.0666	−	24.0666i	0.796487	−	0.796487i
$914$	−9.80051			−0.324172
$915$	−6.05840	+	6.05840i	−0.200285	+	0.200285i
$916$			29.5367i			0.975921i
$917$	−29.6084			−0.977755
$918$	−2.75503	+	4.24955i	−0.0909296	+	0.140256i
$919$	37.8583			1.24883			0.624414	−	0.781093i	$-0.285338\pi$
$919$	37.8583			1.24883			0.624414	+	0.781093i	$0.285338\pi$
$920$			5.01823i			0.165446i
$921$	−5.21462	+	5.21462i	−0.171827	+	0.171827i
$922$	−12.8648			−0.423679
$923$	52.9811	−	52.9811i	1.74389	−	1.74389i
$924$	−6.84933	−	6.84933i	−0.225326	−	0.225326i
$925$	5.68393	+	5.68393i	0.186887	+	0.186887i
$926$		−	4.63842i		−	0.152428i
$927$			33.8437i			1.11157i
$928$	20.3581	+	20.3581i	0.668287	+	0.668287i
$929$	25.4086	+	25.4086i	0.833630	+	0.833630i	0.988011	−	0.154381i	$-0.0493383\pi$
$929$	25.4086	+	25.4086i	0.833630	+	0.833630i	−0.154381	+	0.988011i	$0.549338\pi$
$930$	−3.75848	+	3.75848i	−0.123245	+	0.123245i
$931$	1.93809			0.0635184
$932$	−9.40902	+	9.40902i	−0.308203	+	0.308203i
$933$		−	15.2366i		−	0.498823i
$934$	−12.4234			−0.406507
$935$	−56.7702	+	12.1127i	−1.85659	+	0.396127i
$936$	23.1648			0.757165
$937$			40.6569i			1.32820i	0.747642	+	0.664102i	$0.231186\pi$
$937$			40.6569i			1.32820i	−0.747642	+	0.664102i	$0.768814\pi$
$938$	−0.223939	+	0.223939i	−0.00731186	+	0.00731186i
$939$	−8.83187			−0.288217
$940$	−19.5318	+	19.5318i	−0.637057	+	0.637057i
$941$	−0.0494928	−	0.0494928i	−0.00161342	−	0.00161342i	0.706300	−	0.707913i	$-0.250363\pi$
$941$	−0.0494928	−	0.0494928i	−0.00161342	−	0.00161342i	−0.707913	+	0.706300i	$0.750363\pi$
$942$	0.835075	+	0.835075i	0.0272082	+	0.0272082i
$943$		−	8.39065i		−	0.273237i
$944$		−	22.6565i		−	0.737407i
$945$	−12.0508	−	12.0508i	−0.392013	−	0.392013i
$946$	1.30762	+	1.30762i	0.0425145	+	0.0425145i
$947$	−41.2250	+	41.2250i	−1.33963	+	1.33963i	−0.443219	+	0.896413i	$0.646164\pi$
$947$	−41.2250	+	41.2250i	−1.33963	+	1.33963i	−0.896413	+	0.443219i	$0.853836\pi$
$948$	9.67745			0.314309
$949$	−39.5377	+	39.5377i	−1.28345	+	1.28345i
$950$			0.618010i			0.0200509i
$951$	4.62194			0.149877
$952$	5.90953	−	9.11527i	0.191529	−	0.295428i
$953$	10.3959			0.336755			0.168378	−	0.985723i	$-0.446147\pi$
$953$	10.3959			0.336755			0.168378	+	0.985723i	$0.446147\pi$
$954$		−	3.09702i		−	0.100270i
$955$	−29.6343	+	29.6343i	−0.958944	+	0.958944i
$956$	3.72977			0.120629
$957$	−14.2546	+	14.2546i	−0.460786	+	0.460786i
$958$	−6.87252	−	6.87252i	−0.222041	−	0.222041i
$959$	5.09026	+	5.09026i	0.164373	+	0.164373i
$960$			7.96807i			0.257168i
$961$		−	42.8984i		−	1.38382i
$962$	4.08751	+	4.08751i	0.131787	+	0.131787i
$963$	2.01141	+	2.01141i	0.0648166	+	0.0648166i
$964$	−23.5371	+	23.5371i	−0.758077	+	0.758077i
$965$	67.8743			2.18495
$966$	0.340125	−	0.340125i	0.0109433	−	0.0109433i
$967$		−	49.7242i		−	1.59902i	−0.600652	−	0.799511i	$-0.705092\pi$
$967$		−	49.7242i		−	1.59902i	0.600652	−	0.799511i	$-0.294908\pi$
$968$	−19.3362			−0.621489
$969$	1.05514	+	0.684058i	0.0338959	+	0.0219751i
$970$	9.08770			0.291789
$971$		−	1.22118i		−	0.0391897i	−0.999808	−	0.0195948i	$-0.993762\pi$
$971$		−	1.22118i		−	0.0391897i	0.999808	−	0.0195948i	$-0.00623763\pi$
$972$	17.5777	−	17.5777i	0.563806	−	0.563806i
$973$	30.3902			0.974266
$974$	−10.7077	+	10.7077i	−0.343098	+	0.343098i
$975$	−7.70780	−	7.70780i	−0.246847	−	0.246847i
$976$	11.6631	+	11.6631i	0.373327	+	0.373327i
$977$		−	40.3333i		−	1.29038i	−0.764023	−	0.645189i	$-0.776779\pi$
$977$		−	40.3333i		−	1.29038i	0.764023	−	0.645189i	$-0.223221\pi$
$978$			1.51036i			0.0482961i
$979$	58.2947	+	58.2947i	1.86311	+	1.86311i
$980$	−13.7946	−	13.7946i	−0.440653	−	0.440653i
$981$	7.27294	−	7.27294i	0.232207	−	0.232207i
$982$	−6.13805			−0.195873
$983$	−9.72625	+	9.72625i	−0.310219	+	0.310219i	−0.844994	−	0.534775i	$-0.820396\pi$
$983$	−9.72625	+	9.72625i	−0.310219	+	0.310219i	0.534775	+	0.844994i	$0.320396\pi$
$984$			5.76884i			0.183904i
$985$	47.7347			1.52095
$986$	−9.14042	−	5.92584i	−0.291090	−	0.188717i
$987$	5.49503			0.174909
$988$		−	5.89110i		−	0.187421i
$989$	0.860723	−	0.860723i	0.0273694	−	0.0273694i
$990$	−14.0530			−0.446634
$991$	−24.5400	+	24.5400i	−0.779539	+	0.779539i	−0.979752	−	0.200213i	$-0.935836\pi$
$991$	−24.5400	+	24.5400i	−0.779539	+	0.779539i	0.200213	+	0.979752i	$0.435836\pi$
$992$	24.8112	+	24.8112i	0.787756	+	0.787756i
$993$	−4.53190	−	4.53190i	−0.143815	−	0.143815i
$994$		−	8.50649i		−	0.269809i
$995$			42.0809i			1.33405i
$996$	5.24780	+	5.24780i	0.166283	+	0.166283i
$997$	3.11134	+	3.11134i	0.0985370	+	0.0985370i	0.754657	−	0.656120i	$-0.227803\pi$
$997$	3.11134	+	3.11134i	0.0985370	+	0.0985370i	−0.656120	+	0.754657i	$0.727803\pi$
$998$	−6.86829	+	6.86829i	−0.217412	+	0.217412i
$999$	8.41710			0.266305

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.d.259.19	✓	68
17.13	even	4	inner	731.2.f.d.302.16	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.d.259.19	✓	68	1.1	even	1	trivial
731.2.f.d.302.16	yes	68	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.374564i q^{2} +(-0.409333 + 0.409333i) q^{3} +1.85970 q^{4} +(2.01640 - 2.01640i) q^{5} +(-0.153322 - 0.153322i) q^{6} +(1.28867 + 1.28867i) q^{7} +1.44571i q^{8} +2.66489i q^{9} +O(q^{10})\)	\(q+0.374564i q^{2} +(-0.409333 + 0.409333i) q^{3} +1.85970 q^{4} +(2.01640 - 2.01640i) q^{5} +(-0.153322 - 0.153322i) q^{6} +(1.28867 + 1.28867i) q^{7} +1.44571i q^{8} +2.66489i q^{9} +(0.755271 + 0.755271i) q^{10} +(3.49105 + 3.49105i) q^{11} +(-0.761237 + 0.761237i) q^{12} -6.01269 q^{13} +(-0.482689 + 0.482689i) q^{14} +1.65076i q^{15} +3.17789 q^{16} +(-4.03234 + 0.860353i) q^{17} -0.998174 q^{18} +0.526847i q^{19} +(3.74990 - 3.74990i) q^{20} -1.05499 q^{21} +(-1.30762 + 1.30762i) q^{22} +(0.860723 + 0.860723i) q^{23} +(-0.591775 - 0.591775i) q^{24} -3.13174i q^{25} -2.25214i q^{26} +(-2.31883 - 2.31883i) q^{27} +(2.39654 + 2.39654i) q^{28} +(4.98760 - 4.98760i) q^{29} -0.618315 q^{30} +(6.07859 - 6.07859i) q^{31} +4.08174i q^{32} -2.85801 q^{33} +(-0.322258 - 1.51037i) q^{34} +5.19694 q^{35} +4.95591i q^{36} +(-1.81495 + 1.81495i) q^{37} -0.197338 q^{38} +(2.46119 - 2.46119i) q^{39} +(2.91512 + 2.91512i) q^{40} +(-4.87418 - 4.87418i) q^{41} -0.395161i q^{42} -1.00000i q^{43} +(6.49232 + 6.49232i) q^{44} +(5.37349 + 5.37349i) q^{45} +(-0.322396 + 0.322396i) q^{46} -5.20861 q^{47} +(-1.30082 + 1.30082i) q^{48} -3.67866i q^{49} +1.17304 q^{50} +(1.29840 - 2.00274i) q^{51} -11.1818 q^{52} +3.10269i q^{53} +(0.868550 - 0.868550i) q^{54} +14.0787 q^{55} +(-1.86304 + 1.86304i) q^{56} +(-0.215656 - 0.215656i) q^{57} +(1.86818 + 1.86818i) q^{58} -7.12941i q^{59} +3.06992i q^{60} +(3.67007 + 3.67007i) q^{61} +(2.27682 + 2.27682i) q^{62} +(-3.43417 + 3.43417i) q^{63} +4.82691 q^{64} +(-12.1240 + 12.1240i) q^{65} -1.07051i q^{66} +0.463939 q^{67} +(-7.49896 + 1.60000i) q^{68} -0.704645 q^{69} +1.94659i q^{70} +(-8.81156 + 8.81156i) q^{71} -3.85265 q^{72} +(6.57572 - 6.57572i) q^{73} +(-0.679814 - 0.679814i) q^{74} +(1.28192 + 1.28192i) q^{75} +0.979778i q^{76} +8.99763i q^{77} +(0.921874 + 0.921874i) q^{78} +(-6.35639 - 6.35639i) q^{79} +(6.40790 - 6.40790i) q^{80} -6.09633 q^{81} +(1.82570 - 1.82570i) q^{82} -6.89378i q^{83} -1.96197 q^{84} +(-6.39600 + 9.86563i) q^{85} +0.374564 q^{86} +4.08318i q^{87} +(-5.04704 + 5.04704i) q^{88} +16.6983 q^{89} +(-2.01272 + 2.01272i) q^{90} +(-7.74836 - 7.74836i) q^{91} +(1.60069 + 1.60069i) q^{92} +4.97633i q^{93} -1.95096i q^{94} +(1.06233 + 1.06233i) q^{95} +(-1.67079 - 1.67079i) q^{96} +(6.01619 - 6.01619i) q^{97} +1.37790 q^{98} +(-9.30329 + 9.30329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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