LMFDB - Embedded newform 950.2.q.f.293.7

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.7
Character	$\chi$	$=$	950.293
Dual form			950.2.q.f.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.313773 + 1.17102i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.606164 + 1.04991i) q^{6} +(-1.88504 + 1.88504i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.32525 - 0.765131i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.313773 + 1.17102i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.606164 + 1.04991i) q^{6} +(-1.88504 + 1.88504i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.32525 - 0.765131i) q^{9} +5.08711 q^{11} +(0.857245 + 0.857245i) q^{12} +(1.59907 + 0.428469i) q^{13} +(-1.33292 + 2.30869i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.07389 - 7.73985i) q^{17} +(1.08206 - 1.08206i) q^{18} +(1.52448 + 4.08362i) q^{19} +(-2.79888 - 1.61594i) q^{21} +(4.91377 - 1.31664i) q^{22} +(-2.16907 + 8.09508i) q^{23} +(1.04991 + 0.606164i) q^{24} +1.65548 q^{26} +(3.88354 + 3.88354i) q^{27} +(-0.689971 + 2.57501i) q^{28} +(-0.858351 - 1.48671i) q^{29} +7.07909i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.59620 + 5.95710i) q^{33} +(-4.00644 - 6.93936i) q^{34} +(0.765131 - 1.32525i) q^{36} +(0.618567 + 0.618567i) q^{37} +(2.52945 + 3.54991i) q^{38} +2.00698i q^{39} +(4.93587 + 2.84972i) q^{41} +(-3.12175 - 0.836470i) q^{42} +(4.23321 - 1.13429i) q^{43} +(4.40557 - 2.54356i) q^{44} +8.38064i q^{46} +(-9.97760 - 2.67349i) q^{47} +(1.17102 + 0.313773i) q^{48} -0.106718i q^{49} +(8.41277 - 4.85711i) q^{51} +(1.59907 - 0.428469i) q^{52} +(6.22361 + 1.66761i) q^{53} +(4.75635 + 2.74608i) q^{54} +2.66584i q^{56} +(-4.30366 + 3.06652i) q^{57} +(-1.21389 - 1.21389i) q^{58} +(7.18753 - 12.4492i) q^{59} +(-2.82198 - 4.88781i) q^{61} +(1.83220 + 6.83787i) q^{62} +(-1.05584 + 3.94044i) q^{63} -1.00000i q^{64} +(3.08362 + 5.34099i) q^{66} +(0.363940 - 1.35824i) q^{67} +(-5.66596 - 5.66596i) q^{68} -10.1601 q^{69} +(-13.2313 - 7.63907i) q^{71} +(0.396061 - 1.47812i) q^{72} +(-1.99861 + 0.535526i) q^{73} +(0.757586 + 0.437393i) q^{74} +(3.36205 + 2.77428i) q^{76} +(-9.58939 + 9.58939i) q^{77} +(0.519445 + 1.93859i) q^{78} +(2.01507 - 3.49020i) q^{79} +(-1.03375 + 1.79051i) q^{81} +(5.50524 + 1.47513i) q^{82} +(-3.12063 - 3.12063i) q^{83} -3.23187 q^{84} +(3.79539 - 2.19127i) q^{86} +(1.47163 - 1.47163i) q^{87} +(3.59713 - 3.59713i) q^{88} +(-5.26392 - 9.11738i) q^{89} +(-3.82198 + 2.20662i) q^{91} +(2.16907 + 8.09508i) q^{92} +(-8.28974 + 2.22123i) q^{93} -10.3296 q^{94} +1.21233 q^{96} +(-10.0259 + 2.68643i) q^{97} +(-0.0276208 - 0.103082i) q^{98} +(6.74168 - 3.89231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{6}+O(q^{10}) $ 32 * q + 4 * q^6	$ 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) $ 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.313773	+	1.17102i	0.181157	+	0.676088i	0.995421	+	0.0955921i	$0.0304744\pi$
$3$	0.313773	+	1.17102i	0.181157	+	0.676088i	−0.814263	+	0.580495i	$0.802859\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	0.606164	+	1.04991i	0.247465	+	0.428622i
$7$	−1.88504	+	1.88504i	−0.712476	+	0.712476i	−0.967053	−	0.254576i	$-0.918064\pi$
$7$	−1.88504	+	1.88504i	−0.712476	+	0.712476i	0.254576	+	0.967053i	$0.418064\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.32525	−	0.765131i	0.441749	−	0.255044i
$10$		0			0
$11$	5.08711			1.53382			0.766911	−	0.641753i	$-0.221793\pi$
$11$	5.08711			1.53382			0.766911	+	0.641753i	$0.221793\pi$
$12$	0.857245	+	0.857245i	0.247465	+	0.247465i
$13$	1.59907	+	0.428469i	0.443502	+	0.118836i	0.473657	−	0.880709i	$-0.342934\pi$
$13$	1.59907	+	0.428469i	0.443502	+	0.118836i	−0.0301554	+	0.999545i	$0.509600\pi$
$14$	−1.33292	+	2.30869i	−0.356238	+	0.617023i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.07389	−	7.73985i	−0.502991	−	1.87719i	−0.479648	−	0.877461i	$-0.659236\pi$
$17$	−2.07389	−	7.73985i	−0.502991	−	1.87719i	−0.0233430	−	0.999728i	$-0.507431\pi$
$18$	1.08206	−	1.08206i	0.255044	−	0.255044i
$19$	1.52448	+	4.08362i	0.349739	+	0.936847i
$19$	1.52448	+	4.08362i	0.349739	+	0.936847i
$20$		0			0
$21$	−2.79888	−	1.61594i	−0.610767	−	0.352626i
$22$	4.91377	−	1.31664i	1.04762	−	0.280709i
$23$	−2.16907	+	8.09508i	−0.452282	+	1.68794i	0.243675	+	0.969857i	$0.421647\pi$
$23$	−2.16907	+	8.09508i	−0.452282	+	1.68794i	−0.695957	+	0.718083i	$0.745020\pi$
$24$	1.04991	+	0.606164i	0.214311	+	0.123733i
$25$		0			0
$26$	1.65548			0.324666
$27$	3.88354	+	3.88354i	0.747388	+	0.747388i
$28$	−0.689971	+	2.57501i	−0.130392	+	0.486630i
$29$	−0.858351	−	1.48671i	−0.159392	−	0.276075i	0.775258	−	0.631645i	$-0.217620\pi$
$29$	−0.858351	−	1.48671i	−0.159392	−	0.276075i	−0.934649	+	0.355570i	$0.884287\pi$
$30$		0			0
$31$			7.07909i			1.27144i	0.771919	+	0.635721i	$0.219297\pi$
$31$			7.07909i			1.27144i	−0.771919	+	0.635721i	$0.780703\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.59620	+	5.95710i	0.277863	+	1.03700i
$34$	−4.00644	−	6.93936i	−0.687099	−	1.19009i
$35$		0			0
$36$	0.765131	−	1.32525i	0.127522	−	0.220874i
$37$	0.618567	+	0.618567i	0.101692	+	0.101692i	0.756122	−	0.654430i	$-0.227092\pi$
$37$	0.618567	+	0.618567i	0.101692	+	0.101692i	−0.654430	+	0.756122i	$0.727092\pi$
$38$	2.52945	+	3.54991i	0.410331	+	0.575872i
$39$			2.00698i			0.321374i
$40$		0			0
$41$	4.93587	+	2.84972i	0.770853	+	0.445052i	0.833179	−	0.553004i	$-0.186519\pi$
$41$	4.93587	+	2.84972i	0.770853	+	0.445052i	−0.0623260	+	0.998056i	$0.519852\pi$
$42$	−3.12175	−	0.836470i	−0.481697	−	0.129070i
$43$	4.23321	−	1.13429i	0.645559	−	0.172977i	0.0788388	−	0.996887i	$-0.474879\pi$
$43$	4.23321	−	1.13429i	0.645559	−	0.172977i	0.566720	+	0.823910i	$0.308212\pi$
$44$	4.40557	−	2.54356i	0.664164	−	0.383456i
$45$		0			0
$46$			8.38064i			1.23566i
$47$	−9.97760	−	2.67349i	−1.45538	−	0.389968i	−0.557490	−	0.830184i	$-0.688235\pi$
$47$	−9.97760	−	2.67349i	−1.45538	−	0.389968i	−0.897892	+	0.440215i	$0.854902\pi$
$48$	1.17102	+	0.313773i	0.169022	+	0.0452893i
$49$		−	0.106718i		−	0.0152455i
$50$		0			0
$51$	8.41277	−	4.85711i	1.17802	−	0.680132i
$52$	1.59907	−	0.428469i	0.221751	−	0.0594180i
$53$	6.22361	+	1.66761i	0.854878	+	0.229064i	0.659538	−	0.751672i	$-0.270752\pi$
$53$	6.22361	+	1.66761i	0.854878	+	0.229064i	0.195340	+	0.980735i	$0.437419\pi$
$54$	4.75635	+	2.74608i	0.647257	+	0.373694i
$55$		0			0
$56$			2.66584i			0.356238i
$57$	−4.30366	+	3.06652i	−0.570033	+	0.406171i
$58$	−1.21389	−	1.21389i	−0.159392	−	0.159392i
$59$	7.18753	−	12.4492i	0.935736	−	1.62074i	0.162420	−	0.986722i	$-0.448070\pi$
$59$	7.18753	−	12.4492i	0.935736	−	1.62074i	0.773316	−	0.634021i	$-0.218597\pi$
$60$		0			0
$61$	−2.82198	−	4.88781i	−0.361318	−	0.625820i	0.626860	−	0.779132i	$-0.284340\pi$
$61$	−2.82198	−	4.88781i	−0.361318	−	0.625820i	−0.988178	+	0.153311i	$0.951006\pi$
$62$	1.83220	+	6.83787i	0.232690	+	0.868411i
$63$	−1.05584	+	3.94044i	−0.133023	+	0.496448i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	3.08362	+	5.34099i	0.379568	+	0.657430i
$67$	0.363940	−	1.35824i	0.0444624	−	0.165936i	−0.940125	−	0.340830i	$-0.889292\pi$
$67$	0.363940	−	1.35824i	0.0444624	−	0.165936i	0.984587	+	0.174895i	$0.0559584\pi$
$68$	−5.66596	−	5.66596i	−0.687099	−	0.687099i
$69$	−10.1601			−1.22313
$70$		0			0
$71$	−13.2313	−	7.63907i	−1.57026	−	0.906591i	−0.996136	−	0.0878239i	$-0.972009\pi$
$71$	−13.2313	−	7.63907i	−1.57026	−	0.906591i	−0.574126	−	0.818767i	$-0.694658\pi$
$72$	0.396061	−	1.47812i	0.0466763	−	0.174198i
$73$	−1.99861	+	0.535526i	−0.233920	+	0.0626786i	−0.373874	−	0.927479i	$-0.621971\pi$
$73$	−1.99861	+	0.535526i	−0.233920	+	0.0626786i	0.139955	+	0.990158i	$0.455304\pi$
$74$	0.757586	+	0.437393i	0.0880676	+	0.0508459i
$75$		0			0
$76$	3.36205	+	2.77428i	0.385653	+	0.318232i
$77$	−9.58939	+	9.58939i	−1.09281	+	1.09281i
$78$	0.519445	+	1.93859i	0.0588155	+	0.219503i
$79$	2.01507	−	3.49020i	0.226713	−	0.392678i	−0.730119	−	0.683320i	$-0.760536\pi$
$79$	2.01507	−	3.49020i	0.226713	−	0.392678i	0.956832	+	0.290642i	$0.0938688\pi$
$80$		0			0
$81$	−1.03375	+	1.79051i	−0.114861	+	0.198946i
$82$	5.50524	+	1.47513i	0.607952	+	0.162900i
$83$	−3.12063	−	3.12063i	−0.342534	−	0.342534i	0.514785	−	0.857319i	$-0.327872\pi$
$83$	−3.12063	−	3.12063i	−0.342534	−	0.342534i	−0.857319	+	0.514785i	$0.827872\pi$
$84$	−3.23187			−0.352626
$85$		0			0
$86$	3.79539	−	2.19127i	0.409268	−	0.236291i
$87$	1.47163	−	1.47163i	0.157776	−	0.157776i
$88$	3.59713	−	3.59713i	0.383456	−	0.383456i
$89$	−5.26392	−	9.11738i	−0.557974	−	0.966440i	−0.997665	−	0.0682908i	$-0.978245\pi$
$89$	−5.26392	−	9.11738i	−0.557974	−	0.966440i	0.439691	−	0.898149i	$-0.355088\pi$
$90$		0			0
$91$	−3.82198	+	2.20662i	−0.400652	+	0.231317i
$92$	2.16907	+	8.09508i	0.226141	+	0.843970i
$93$	−8.28974	+	2.22123i	−0.859606	+	0.230331i
$94$	−10.3296			−1.06541
$95$		0			0
$96$	1.21233			0.123733
$97$	−10.0259	+	2.68643i	−1.01798	+	0.272766i	−0.728958	−	0.684558i	$-0.759995\pi$
$97$	−10.0259	+	2.68643i	−1.01798	+	0.272766i	−0.289017	+	0.957324i	$0.593329\pi$
$98$	−0.0276208	−	0.103082i	−0.00279012	−	0.0104129i
$99$	6.74168	−	3.89231i	0.677564	−	0.391192i
$100$		0			0
$101$	−3.30520	−	5.72477i	−0.328879	−	0.569636i	0.653410	−	0.757004i	$-0.273338\pi$
$101$	−3.30520	−	5.72477i	−0.328879	−	0.569636i	−0.982290	+	0.187368i	$0.940004\pi$
$102$	6.86900	−	6.86900i	0.680132	−	0.680132i
$103$	6.38060	−	6.38060i	0.628699	−	0.628699i	−0.319041	−	0.947741i	$-0.603361\pi$
$103$	6.38060	−	6.38060i	0.628699	−	0.628699i	0.947741	+	0.319041i	$0.103361\pi$
$104$	1.43369	−	0.827739i	0.140584	−	0.0811665i
$105$		0			0
$106$	6.44315			0.625814
$107$	−6.54875	−	6.54875i	−0.633092	−	0.633092i	0.315750	−	0.948842i	$-0.397744\pi$
$107$	−6.54875	−	6.54875i	−0.633092	−	0.633092i	−0.948842	+	0.315750i	$0.897744\pi$
$108$	5.30502	+	1.42148i	0.510476	+	0.136782i
$109$	2.10586	−	3.64745i	0.201705	−	0.349363i	−0.747373	−	0.664404i	$-0.768685\pi$
$109$	2.10586	−	3.64745i	0.201705	−	0.349363i	0.949078	+	0.315042i	$0.102019\pi$
$110$		0			0
$111$	−0.530263	+	0.918442i	−0.0503303	+	0.0871747i
$112$	0.689971	+	2.57501i	0.0651961	+	0.243315i
$113$	−6.93263	+	6.93263i	−0.652167	+	0.652167i	−0.953515	−	0.301347i	$-0.902564\pi$
$113$	−6.93263	+	6.93263i	−0.652167	+	0.652167i	0.301347	+	0.953515i	$0.402564\pi$
$114$	−3.36334	+	4.07590i	−0.315005	+	0.381743i
$115$		0			0
$116$	−1.48671	−	0.858351i	−0.138037	−	0.0796958i
$117$	2.44700	−	0.655670i	0.226225	−	0.0606168i
$118$	3.72054	−	13.8852i	0.342503	−	1.27824i
$119$	18.4992	+	10.6805i	1.69582	+	0.979083i
$120$		0			0
$121$	14.8787			1.35261
$122$	−3.99088	−	3.99088i	−0.361318	−	0.361318i
$123$	−1.78833	+	6.67416i	−0.161249	+	0.601788i
$124$	3.53954	+	6.13067i	0.317860	+	0.550550i
$125$		0			0
$126$			4.07944i			0.363425i
$127$	3.06175	−	11.4266i	0.271687	−	1.01395i	−0.686343	−	0.727278i	$-0.740785\pi$
$127$	3.06175	−	11.4266i	0.271687	−	1.01395i	0.958029	−	0.286670i	$-0.0925483\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	2.65654	+	4.60126i	0.233895	+	0.405118i
$130$		0			0
$131$	−2.90308	+	5.02829i	−0.253644	+	0.439324i	−0.964526	−	0.263987i	$-0.914962\pi$
$131$	−2.90308	+	5.02829i	−0.253644	+	0.439324i	0.710883	+	0.703311i	$0.248296\pi$
$132$	4.36090	+	4.36090i	0.379568	+	0.379568i
$133$	−10.5715	−	4.82408i	−0.916662	−	0.418301i
$134$		−	1.40616i		−	0.121474i
$135$		0			0
$136$	−6.93936	−	4.00644i	−0.595045	−	0.343549i
$137$	16.5912	+	4.44559i	1.41748	+	0.379812i	0.884588	−	0.466373i	$-0.154439\pi$
$137$	16.5912	+	4.44559i	1.41748	+	0.379812i	0.532890	+	0.846185i	$0.321106\pi$
$138$	−9.81388	+	2.62962i	−0.835413	+	0.223848i
$139$	−11.7743	+	6.79791i	−0.998686	+	0.576591i	−0.907859	−	0.419275i	$-0.862284\pi$
$139$	−11.7743	+	6.79791i	−0.998686	+	0.576591i	−0.0908265	+	0.995867i	$0.528951\pi$
$140$		0			0
$141$		−	12.5228i		−	1.05461i
$142$	−14.7576	−	3.95427i	−1.23843	−	0.331835i
$143$	8.13464	+	2.17967i	0.680253	+	0.182273i
$144$		−	1.53026i		−	0.127522i
$145$		0			0
$146$	−1.79190	+	1.03456i	−0.148299	+	0.0856205i
$147$	0.124969	−	0.0334854i	0.0103073	−	0.00276183i
$148$	0.844978	+	0.226411i	0.0694567	+	0.0186109i
$149$	−8.23647	−	4.75533i	−0.674758	−	0.389572i	0.123119	−	0.992392i	$-0.460710\pi$
$149$	−8.23647	−	4.75533i	−0.674758	−	0.389572i	−0.797877	+	0.602820i	$0.794044\pi$
$150$		0			0
$151$			6.21129i			0.505468i	0.967536	+	0.252734i	$0.0813297\pi$
$151$			6.21129i			0.505468i	−0.967536	+	0.252734i	$0.918670\pi$
$152$	3.96552	+	1.80959i	0.321647	+	0.146777i
$153$	−8.67041	−	8.67041i	−0.700961	−	0.700961i
$154$	−6.78072	+	11.7446i	−0.546406	+	0.946403i
$155$		0			0
$156$	1.00349	+	1.73810i	0.0803435	+	0.139159i
$157$	3.70862	+	13.8408i	0.295980	+	1.10461i	0.940436	+	0.339971i	$0.110417\pi$
$157$	3.70862	+	13.8408i	0.295980	+	1.10461i	−0.644456	+	0.764641i	$0.722916\pi$
$158$	1.04308	−	3.89281i	0.0829826	−	0.309695i
$159$			7.81121i			0.619469i
$160$		0			0
$161$	−11.1707	−	19.3483i	−0.880377	−	1.52486i
$162$	−0.535110	+	1.99706i	−0.0420422	+	0.156904i
$163$	−1.78065	−	1.78065i	−0.139471	−	0.139471i	0.633924	−	0.773395i	$-0.281443\pi$
$163$	−1.78065	−	1.78065i	−0.139471	−	0.139471i	−0.773395	+	0.633924i	$0.781443\pi$
$164$	5.69945			0.445052
$165$		0			0
$166$	−3.82198	−	2.20662i	−0.296643	−	0.171267i
$167$	−3.47427	+	12.9661i	−0.268847	+	1.00335i	0.691006	+	0.722849i	$0.257168\pi$
$167$	−3.47427	+	12.9661i	−0.268847	+	1.00335i	−0.959853	+	0.280502i	$0.909499\pi$
$168$	−3.12175	+	0.836470i	−0.240848	+	0.0645351i
$169$	−8.88490	−	5.12970i	−0.683454	−	0.394592i
$170$		0			0
$171$	5.14482	+	4.24538i	0.393434	+	0.324652i
$172$	3.09893	−	3.09893i	0.236291	−	0.236291i
$173$	−2.67657	−	9.98909i	−0.203496	−	0.759457i	−0.989903	−	0.141748i	$-0.954728\pi$
$173$	−2.67657	−	9.98909i	−0.203496	−	0.759457i	0.786407	−	0.617709i	$-0.211939\pi$
$174$	1.04060	−	1.80237i	0.0788878	−	0.136638i
$175$		0			0
$176$	2.54356	−	4.40557i	0.191728	−	0.332082i
$177$	16.8334	+	4.51051i	1.26528	+	0.339031i
$178$	−7.44431	−	7.44431i	−0.557974	−	0.557974i
$179$	15.2968			1.14333			0.571666	−	0.820486i	$-0.306297\pi$
$179$	15.2968			1.14333			0.571666	+	0.820486i	$0.306297\pi$
$180$		0			0
$181$	−13.3780	+	7.72382i	−0.994382	+	0.574107i	−0.906581	−	0.422031i	$-0.861317\pi$
$181$	−13.3780	+	7.72382i	−0.994382	+	0.574107i	−0.0878009	+	0.996138i	$0.527984\pi$
$182$	−3.12063	+	3.12063i	−0.231317	+	0.231317i
$183$	4.83826	−	4.83826i	0.357654	−	0.357654i
$184$	4.19032	+	7.25785i	0.308914	+	0.535056i
$185$		0			0
$186$	−7.43238	+	4.29108i	−0.544968	+	0.314638i
$187$	−10.5501	−	39.3735i	−0.771499	−	2.87927i
$188$	−9.97760	+	2.67349i	−0.727691	+	0.194984i
$189$	−14.6412			−1.06499
$190$		0			0
$191$	−14.4216			−1.04351			−0.521755	−	0.853095i	$-0.674723\pi$
$191$	−14.4216			−1.04351			−0.521755	+	0.853095i	$0.674723\pi$
$192$	1.17102	−	0.313773i	0.0845109	−	0.0226446i
$193$	−1.98826	−	7.42030i	−0.143118	−	0.534125i	−0.999832	−	0.0183327i	$-0.994164\pi$
$193$	−1.98826	−	7.42030i	−0.143118	−	0.534125i	0.856714	−	0.515793i	$-0.172502\pi$
$194$	−8.98897	+	5.18979i	−0.645371	+	0.372605i
$195$		0			0
$196$	−0.0533592	−	0.0924208i	−0.00381137	−	0.00660149i
$197$	15.0397	−	15.0397i	1.07153	−	1.07153i	0.0742953	−	0.997236i	$-0.476329\pi$
$197$	15.0397	−	15.0397i	1.07153	−	1.07153i	0.997236	−	0.0742953i	$-0.0236708\pi$
$198$	5.50456	−	5.50456i	0.391192	−	0.391192i
$199$	−3.99272	+	2.30520i	−0.283036	+	0.163411i	−0.634797	−	0.772679i	$-0.718916\pi$
$199$	−3.99272	+	2.30520i	−0.283036	+	0.163411i	0.351761	+	0.936090i	$0.385583\pi$
$200$		0			0
$201$	1.70472			0.120242
$202$	−4.67426	−	4.67426i	−0.328879	−	0.328879i
$203$	4.42052	+	1.18447i	0.310259	+	0.0831338i
$204$	4.85711	−	8.41277i	0.340066	−	0.589012i
$205$		0			0
$206$	4.51177	−	7.81461i	0.314350	−	0.544470i
$207$	3.31925	+	12.3876i	0.230704	+	0.860997i
$208$	1.17060	−	1.17060i	0.0811665	−	0.0811665i
$209$	7.75519	+	20.7738i	0.536437	+	1.43696i
$210$		0			0
$211$	−1.99020	−	1.14904i	−0.137011	−	0.0791032i	0.429928	−	0.902863i	$-0.358539\pi$
$211$	−1.99020	−	1.14904i	−0.137011	−	0.0791032i	−0.566939	+	0.823760i	$0.691872\pi$
$212$	6.22361	−	1.66761i	0.427439	−	0.114532i
$213$	4.79387	−	17.8910i	0.328471	−	1.22587i
$214$	−8.02055	−	4.63067i	−0.548274	−	0.316546i
$215$		0			0
$216$	5.49216			0.373694
$217$	−13.3443	−	13.3443i	−0.905872	−	0.905872i
$218$	1.09007	−	4.06820i	0.0738290	−	0.275534i
$219$	−1.25422	−	2.17237i	−0.0847524	−	0.146795i
$220$		0			0
$221$		−	13.2651i		−	0.892310i
$222$	−0.274484	+	1.02439i	−0.0184222	+	0.0687525i
$223$	−5.34017	−	19.9298i	−0.357604	−	1.33460i	−0.877176	−	0.480169i	$-0.840575\pi$
$223$	−5.34017	−	19.9298i	−0.357604	−	1.33460i	0.519572	−	0.854427i	$-0.326091\pi$
$224$	1.33292	+	2.30869i	0.0890596	+	0.154256i
$225$		0			0
$226$	−4.90211	+	8.49071i	−0.326084	+	0.564794i
$227$	−2.31642	−	2.31642i	−0.153746	−	0.153746i	0.626043	−	0.779789i	$-0.284674\pi$
$227$	−2.31642	−	2.31642i	−0.153746	−	0.153746i	−0.779789	+	0.626043i	$0.784674\pi$
$228$	−2.19381	+	4.80751i	−0.145289	+	0.318385i
$229$		−	7.45517i		−	0.492651i	−0.969187	−	0.246326i	$-0.920777\pi$
$229$		−	7.45517i		−	0.492651i	0.969187	−	0.246326i	$-0.0792233\pi$
$230$		0			0
$231$	−14.2382	−	8.22045i	−0.936807	−	0.540866i
$232$	−1.65821	−	0.444315i	−0.108867	−	0.0291707i
$233$	10.8912	−	2.91830i	0.713509	−	0.191184i	0.116236	−	0.993222i	$-0.462917\pi$
$233$	10.8912	−	2.91830i	0.713509	−	0.191184i	0.597274	+	0.802037i	$0.296251\pi$
$234$	2.19392	−	1.26666i	0.143421	−	0.0828040i
$235$		0			0
$236$		−	14.3751i		−	0.935736i
$237$	4.71936	+	1.26455i	0.306555	+	0.0821412i
$238$	20.6332	+	5.52865i	1.33745	+	0.358369i
$239$			13.3826i			0.865650i	0.901478	+	0.432825i	$0.142483\pi$
$239$			13.3826i			0.865650i	−0.901478	+	0.432825i	$0.857517\pi$
$240$		0			0
$241$	−16.2007	+	9.35347i	−1.04358	+	0.602510i	−0.920845	−	0.389929i	$-0.872499\pi$
$241$	−16.2007	+	9.35347i	−1.04358	+	0.602510i	−0.122734	+	0.992440i	$0.539166\pi$
$242$	14.3717	−	3.85089i	0.923850	−	0.247545i
$243$	13.4940	+	3.61570i	0.865639	+	0.231947i
$244$	−4.88781	−	2.82198i	−0.312910	−	0.180659i
$245$		0			0
$246$			6.90959i			0.440540i
$247$	0.688037	+	7.18318i	0.0437788	+	0.457055i
$248$	5.00567	+	5.00567i	0.317860	+	0.317860i
$249$	2.67515	−	4.63349i	0.169531	−	0.293636i
$250$		0			0
$251$	9.16442	+	15.8732i	0.578453	+	1.00191i	0.995657	+	0.0930973i	$0.0296768\pi$
$251$	9.16442	+	15.8732i	0.578453	+	1.00191i	−0.417204	+	0.908813i	$0.636990\pi$
$252$	1.05584	+	3.94044i	0.0665115	+	0.248224i
$253$	−11.0343	+	41.1806i	−0.693720	+	2.58900i
$254$		−	11.8297i		−	0.742262i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.399675	+	1.49161i	−0.0249310	+	0.0930438i	−0.977270	−	0.211997i	$-0.932003\pi$
$257$	−0.399675	+	1.49161i	−0.0249310	+	0.0930438i	0.952339	+	0.305041i	$0.0986700\pi$
$258$	3.75691	+	3.75691i	0.233895	+	0.233895i
$259$	−2.33204			−0.144906
$260$		0			0
$261$	−2.27505	−	1.31350i	−0.140822	−	0.0813037i
$262$	−1.50275	+	5.60833i	−0.0928400	+	0.346484i
$263$	1.08181	−	0.289870i	0.0667072	−	0.0178741i	−0.225311	−	0.974287i	$-0.572340\pi$
$263$	1.08181	−	0.289870i	0.0667072	−	0.0178741i	0.292018	+	0.956413i	$0.405673\pi$
$264$	5.34099	+	3.08362i	0.328715	+	0.189784i
$265$		0			0
$266$	−11.4598	−	1.92361i	−0.702646	−	0.117944i
$267$	9.02493	−	9.02493i	0.552317	−	0.552317i
$268$	−0.363940	−	1.35824i	−0.0222312	−	0.0829680i
$269$	−1.94303	+	3.36542i	−0.118468	+	0.205193i	−0.919161	−	0.393882i	$-0.871132\pi$
$269$	−1.94303	+	3.36542i	−0.118468	+	0.205193i	0.800693	+	0.599076i	$0.204465\pi$
$270$		0			0
$271$	1.49369	−	2.58714i	0.0907350	−	0.157158i	−0.817086	−	0.576516i	$-0.804412\pi$
$271$	1.49369	−	2.58714i	0.0907350	−	0.157158i	0.907821	+	0.419359i	$0.137745\pi$
$272$	−7.73985	−	2.07389i	−0.469297	−	0.125748i
$273$	−3.78323	−	3.78323i	−0.228971	−	0.228971i
$274$	17.1764			1.03767
$275$		0			0
$276$	−8.79888	+	5.08004i	−0.529631	+	0.305782i
$277$	−15.9817	+	15.9817i	−0.960248	+	0.960248i	−0.999240	−	0.0389918i	$-0.987585\pi$
$277$	−15.9817	+	15.9817i	−0.960248	+	0.960248i	0.0389918	+	0.999240i	$0.487585\pi$
$278$	−9.61370	+	9.61370i	−0.576591	+	0.576591i
$279$	5.41643	+	9.38154i	0.324273	+	0.561658i
$280$		0			0
$281$	20.6331	−	11.9125i	1.23087	−	0.710641i	0.263655	−	0.964617i	$-0.415072\pi$
$281$	20.6331	−	11.9125i	1.23087	−	0.710641i	0.967210	+	0.253976i	$0.0817385\pi$
$282$	−3.24114	−	12.0961i	−0.193007	−	0.720313i
$283$	8.49923	−	2.27736i	0.505227	−	0.135375i	0.00280196	−	0.999996i	$-0.499108\pi$
$283$	8.49923	−	2.27736i	0.505227	−	0.135375i	0.502425	+	0.864621i	$0.332441\pi$
$284$	−15.2781			−0.906591
$285$		0			0
$286$	8.42160			0.497980
$287$	−14.6761	+	3.93245i	−0.866304	+	0.232125i
$288$	−0.396061	−	1.47812i	−0.0233381	−	0.0870991i
$289$	−40.8818	+	23.6031i	−2.40481	+	1.38842i
$290$		0			0
$291$	−6.29172	−	10.8976i	−0.368827	−	0.638827i
$292$	−1.46308	+	1.46308i	−0.0856205	+	0.0856205i
$293$	−13.9858	+	13.9858i	−0.817062	+	0.817062i	−0.985681	−	0.168619i	$-0.946069\pi$
$293$	−13.9858	+	13.9858i	−0.817062	+	0.817062i	0.168619	+	0.985681i	$0.446069\pi$
$294$	0.112044	−	0.0646888i	0.00653456	−	0.00377273i
$295$		0			0
$296$	0.874785			0.0508459
$297$	19.7560	+	19.7560i	1.14636	+	1.14636i
$298$	−9.18659	−	2.46154i	−0.532165	−	0.142593i
$299$	−6.93698	+	12.0152i	−0.401176	+	0.694857i
$300$		0			0
$301$	−5.84159	+	10.1179i	−0.336703	+	0.583188i
$302$	1.60760	+	5.99964i	0.0925070	+	0.345241i
$303$	5.66673	−	5.66673i	0.325545	−	0.325545i
$304$	4.29876	+	0.721575i	0.246551	+	0.0413852i
$305$		0			0
$306$	−10.6190	−	6.13091i	−0.607050	−	0.350481i
$307$	11.9567	−	3.20378i	0.682404	−	0.182849i	0.0990679	−	0.995081i	$-0.468414\pi$
$307$	11.9567	−	3.20378i	0.682404	−	0.182849i	0.583336	+	0.812231i	$0.301747\pi$
$308$	−3.50996	+	13.0993i	−0.199999	+	0.746405i
$309$	9.47386	+	5.46974i	0.538949	+	0.311162i
$310$		0			0
$311$	−12.9658			−0.735224			−0.367612	−	0.929979i	$-0.619825\pi$
$311$	−12.9658			−0.735224			−0.367612	+	0.929979i	$0.619825\pi$
$312$	1.41915	+	1.41915i	0.0803435	+	0.0803435i
$313$	−1.08434	+	4.04681i	−0.0612904	+	0.228739i	−0.989776	−	0.142629i	$-0.954444\pi$
$313$	−1.08434	+	4.04681i	−0.0612904	+	0.228739i	0.928486	+	0.371368i	$0.121111\pi$
$314$	7.16450	+	12.4093i	0.404316	+	0.700296i
$315$		0			0
$316$		−	4.03013i		−	0.226713i
$317$	2.18344	−	8.14871i	0.122634	−	0.457677i	−0.877110	−	0.480290i	$-0.840532\pi$
$317$	2.18344	−	8.14871i	0.122634	−	0.457677i	0.999744	+	0.0226121i	$0.00719827\pi$
$318$	2.02169	+	7.54505i	0.113371	+	0.423105i
$319$	−4.36653	−	7.56304i	−0.244479	−	0.423449i
$320$		0			0
$321$	5.61389	−	9.72353i	0.313337	−	0.542715i
$322$	−15.7978	−	15.7978i	−0.880377	−	0.880377i
$323$	28.4450	−	20.2682i	1.58272	−	1.12775i
$324$			2.06751i			0.114861i
$325$		0			0
$326$	−2.18084	−	1.25911i	−0.120786	−	0.0697356i
$327$	4.93199	+	1.32152i	0.272740	+	0.0730804i
$328$	5.50524	−	1.47513i	0.303976	−	0.0814502i
$329$	23.8477	−	13.7685i	1.31477	−	0.759082i
$330$		0			0
$331$		−	9.62608i		−	0.529097i	−0.964372	−	0.264549i	$-0.914777\pi$
$331$		−	9.62608i		−	0.529097i	0.964372	−	0.264549i	$-0.0852230\pi$
$332$	−4.26287	−	1.14223i	−0.233955	−	0.0626881i
$333$	1.29304	+	0.346469i	0.0708580	+	0.0189864i
$334$			13.4235i			0.734504i
$335$		0			0
$336$	−2.79888	+	1.61594i	−0.152692	+	0.0881566i
$337$	3.54986	−	0.951182i	0.193373	−	0.0518142i	−0.160833	−	0.986982i	$-0.551418\pi$
$337$	3.54986	−	0.951182i	0.193373	−	0.0518142i	0.354206	+	0.935168i	$0.384751\pi$
$338$	−9.90981	−	2.65533i	−0.539023	−	0.144431i
$339$	−10.2935	−	5.94296i	−0.559067	−	0.322778i
$340$		0			0
$341$			36.0121i			1.95016i
$342$	6.06830	+	2.76915i	0.328136	+	0.149738i
$343$	−12.9941	−	12.9941i	−0.701614	−	0.701614i
$344$	2.19127	−	3.79539i	0.118145	−	0.204634i
$345$		0			0
$346$	−5.17073	−	8.95597i	−0.277980	−	0.481476i
$347$	0.111421	+	0.415829i	0.00598139	+	0.0223228i	0.968852	−	0.247640i	$-0.0796551\pi$
$347$	0.111421	+	0.415829i	0.00598139	+	0.0223228i	−0.962871	+	0.269963i	$0.912988\pi$
$348$	0.538655	−	2.01029i	0.0288749	−	0.107763i
$349$		−	11.4552i		−	0.613181i	−0.951841	−	0.306591i	$-0.900812\pi$
$349$		−	11.4552i		−	0.613181i	0.951841	−	0.306591i	$-0.0991882\pi$
$350$		0			0
$351$	4.54607	+	7.87403i	0.242652	+	0.420285i
$352$	1.31664	−	4.91377i	0.0701772	−	0.261905i
$353$	−21.7675	−	21.7675i	−1.15857	−	1.15857i	−0.984784	−	0.173784i	$-0.944400\pi$
$353$	−21.7675	−	21.7675i	−1.15857	−	1.15857i	−0.173784	−	0.984784i	$-0.555600\pi$
$354$	17.4273			0.926249
$355$		0			0
$356$	−9.11738	−	5.26392i	−0.483220	−	0.278987i
$357$	−6.70254	+	25.0142i	−0.354736	+	1.32389i
$358$	14.7755	−	3.95909i	0.780911	−	0.209244i
$359$	32.2397	+	18.6136i	1.70154	+	0.982387i	0.944201	+	0.329371i	$0.106837\pi$
$359$	32.2397	+	18.6136i	1.70154	+	0.982387i	0.757344	+	0.653016i	$0.226497\pi$
$360$		0			0
$361$	−14.3519	+	12.4508i	−0.755365	+	0.655304i
$362$	−10.9231	+	10.9231i	−0.574107	+	0.574107i
$363$	4.66854	+	17.4232i	0.245035	+	0.914483i
$364$	−2.20662	+	3.82198i	−0.115658	+	0.200326i
$365$		0			0
$366$	3.42116	−	5.92563i	0.178827	−	0.309738i
$367$	−0.905122	−	0.242527i	−0.0472470	−	0.0126598i	0.235118	−	0.971967i	$-0.424452\pi$
$367$	−0.905122	−	0.242527i	−0.0472470	−	0.0126598i	−0.282365	+	0.959307i	$0.591119\pi$
$368$	5.92601	+	5.92601i	0.308914	+	0.308914i
$369$	8.72165			0.454031
$370$		0			0
$371$	−14.8752	+	8.58821i	−0.772283	+	0.445878i
$372$	−6.06851	+	6.06851i	−0.314638	+	0.314638i
$373$	18.3157	−	18.3157i	0.948349	−	0.948349i	−0.0503814	−	0.998730i	$-0.516044\pi$
$373$	18.3157	−	18.3157i	0.948349	−	0.948349i	0.998730	+	0.0503814i	$0.0160437\pi$
$374$	−20.3812	−	35.3013i	−1.05389	−	1.82539i
$375$		0			0
$376$	−8.94567	+	5.16478i	−0.461338	+	0.266353i
$377$	−0.735553	−	2.74512i	−0.0378829	−	0.141381i
$378$	−14.1423	+	3.78943i	−0.727404	+	0.194907i
$379$	−32.8155			−1.68562			−0.842810	−	0.538211i	$-0.819100\pi$
$379$	−32.8155			−1.68562			−0.842810	+	0.538211i	$0.819100\pi$
$380$		0			0
$381$	14.3415			0.734736
$382$	−13.9302	+	3.73259i	−0.712731	+	0.190976i
$383$	−2.80563	−	10.4707i	−0.143361	−	0.535030i	−0.999823	−	0.0188199i	$-0.994009\pi$
$383$	−2.80563	−	10.4707i	−0.143361	−	0.535030i	0.856462	−	0.516210i	$-0.172658\pi$
$384$	1.04991	−	0.606164i	0.0535778	−	0.0309332i
$385$		0			0
$386$	−3.84103	−	6.65286i	−0.195503	−	0.338622i
$387$	4.74217	−	4.74217i	0.241058	−	0.241058i
$388$	−7.33947	+	7.33947i	−0.372605	+	0.372605i
$389$	18.7610	−	10.8317i	0.951220	−	0.549187i	0.0577605	−	0.998330i	$-0.481604\pi$
$389$	18.7610	−	10.8317i	0.951220	−	0.549187i	0.893460	+	0.449143i	$0.148271\pi$
$390$		0			0
$391$	67.1530			3.39608
$392$	−0.0754613	−	0.0754613i	−0.00381137	−	0.00381137i
$393$	−6.79913	−	1.82182i	−0.342971	−	0.0918987i
$394$	10.6346	−	18.4198i	0.535766	−	0.927974i
$395$		0			0
$396$	3.89231	−	6.74168i	0.195596	−	0.338782i
$397$	6.43427	+	24.0130i	0.322927	+	1.20518i	0.916380	+	0.400310i	$0.131098\pi$
$397$	6.43427	+	24.0130i	0.322927	+	1.20518i	−0.593453	+	0.804869i	$0.702236\pi$
$398$	−3.26004	+	3.26004i	−0.163411	+	0.163411i
$399$	2.33204	−	13.8930i	0.116748	−	0.695522i
$400$		0			0
$401$	25.2666	+	14.5877i	1.26175	+	0.728473i	0.973413	−	0.229056i	$-0.0735638\pi$
$401$	25.2666	+	14.5877i	1.26175	+	0.728473i	0.288339	+	0.957529i	$0.406897\pi$
$402$	1.64664	−	0.441215i	0.0821268	−	0.0220058i
$403$	−3.03317	+	11.3199i	−0.151093	+	0.563887i
$404$	−5.72477	−	3.30520i	−0.284818	−	0.164440i
$405$		0			0
$406$	4.57646			0.227126
$407$	3.14672	+	3.14672i	0.155977	+	0.155977i
$408$	2.51423	−	9.38323i	0.124473	−	0.464539i
$409$	−6.42063	−	11.1209i	−0.317480	−	0.549891i	0.662482	−	0.749078i	$-0.269503\pi$
$409$	−6.42063	−	11.1209i	−0.317480	−	0.549891i	−0.979962	+	0.199187i	$0.936170\pi$
$410$		0			0
$411$			20.8234i			1.02714i
$412$	2.33546	−	8.71606i	0.115060	−	0.429410i
$413$	9.91837	+	37.0158i	0.488051	+	1.82143i
$414$	6.41229	+	11.1064i	0.315147	+	0.545850i
$415$		0			0
$416$	0.827739	−	1.43369i	0.0405832	−	0.0702922i
$417$	−11.6549	−	11.6549i	−0.570745	−	0.570745i
$418$	12.8676	+	18.0588i	0.629375	+	0.883285i
$419$		−	17.7916i		−	0.869177i	−0.900629	−	0.434588i	$-0.856894\pi$
$419$		−	17.7916i		−	0.869177i	0.900629	−	0.434588i	$-0.143106\pi$
$420$		0			0
$421$	29.5157	+	17.0409i	1.43851	+	0.830522i	0.997746	−	0.0671023i	$-0.0213754\pi$
$421$	29.5157	+	17.0409i	1.43851	+	0.830522i	0.440761	+	0.897625i	$0.354709\pi$
$422$	−2.21978	−	0.594787i	−0.108057	−	0.0289538i
$423$	−15.2683	+	4.09114i	−0.742372	+	0.198918i
$424$	5.57993	−	3.22158i	0.270985	−	0.156454i
$425$		0			0
$426$		−	18.5221i		−	0.897399i
$427$	14.5332	+	3.89417i	0.703313	+	0.188452i
$428$	−8.94576	−	2.39701i	−0.432410	−	0.115864i
$429$			10.2097i			0.492931i
$430$		0			0
$431$	21.0591	−	12.1585i	1.01438	−	0.585652i	0.101908	−	0.994794i	$-0.467505\pi$
$431$	21.0591	−	12.1585i	1.01438	−	0.585652i	0.912471	+	0.409142i	$0.134172\pi$
$432$	5.30502	−	1.42148i	0.255238	−	0.0683908i
$433$	−24.8949	−	6.67057i	−1.19637	−	0.320567i	−0.394971	−	0.918694i	$-0.629245\pi$
$433$	−24.8949	−	6.67057i	−1.19637	−	0.320567i	−0.801402	+	0.598126i	$0.795912\pi$
$434$	−16.3434	−	9.43587i	−0.784508	−	0.452936i
$435$		0			0
$436$		−	4.21171i		−	0.201705i
$437$	−36.3639	+	3.48310i	−1.73952	+	0.166619i
$438$	−1.77374	−	1.77374i	−0.0847524	−	0.0847524i
$439$	0.512599	−	0.887848i	0.0244650	−	0.0423747i	−0.853534	−	0.521038i	$-0.825545\pi$
$439$	0.512599	−	0.887848i	0.0244650	−	0.0423747i	0.877999	+	0.478663i	$0.158878\pi$
$440$		0			0
$441$	−0.0816536	−	0.141428i	−0.00388827	−	0.00673468i
$442$	−3.43327	−	12.8131i	−0.163304	−	0.609459i
$443$	−2.14710	+	8.01308i	−0.102012	+	0.380713i	−0.997989	−	0.0633869i	$-0.979810\pi$
$443$	−2.14710	+	8.01308i	−0.102012	+	0.380713i	0.895977	+	0.444100i	$0.146476\pi$
$444$			1.06053i			0.0503303i
$445$		0			0
$446$	−10.3164	−	17.8685i	−0.488496	−	0.846100i
$447$	2.98419	−	11.1372i	0.141147	−	0.526769i
$448$	1.88504	+	1.88504i	0.0890596	+	0.0890596i
$449$	−19.6032			−0.925134			−0.462567	−	0.886584i	$-0.653072\pi$
$449$	−19.6032			−0.925134			−0.462567	+	0.886584i	$0.653072\pi$
$450$		0			0
$451$	25.1093	+	14.4969i	1.18235	+	0.682631i
$452$	−2.53752	+	9.47015i	−0.119355	+	0.445439i
$453$	−7.27353	+	1.94894i	−0.341740	+	0.0915691i
$454$	−2.83702	−	1.63795i	−0.133148	−	0.0768729i
$455$		0			0
$456$	−0.874785	+	5.21150i	−0.0409656	+	0.244051i
$457$	19.5026	−	19.5026i	0.912293	−	0.912293i	−0.0841597	−	0.996452i	$-0.526821\pi$
$457$	19.5026	−	19.5026i	0.912293	−	0.912293i	0.996452	+	0.0841597i	$0.0268206\pi$
$458$	−1.92954	−	7.20114i	−0.0901615	−	0.336487i
$459$	22.0040	−	38.1121i	1.02706	−	1.77892i
$460$		0			0
$461$	3.84973	−	6.66792i	0.179300	−	0.310556i	−0.762341	−	0.647175i	$-0.775950\pi$
$461$	3.84973	−	6.66792i	0.179300	−	0.310556i	0.941641	+	0.336619i	$0.109284\pi$
$462$	−15.8807	−	4.25522i	−0.738837	−	0.197971i
$463$	12.6250	+	12.6250i	0.586735	+	0.586735i	0.936746	−	0.350010i	$-0.113822\pi$
$463$	12.6250	+	12.6250i	0.586735	+	0.586735i	−0.350010	+	0.936746i	$0.613822\pi$
$464$	−1.71670			−0.0796958
$465$		0			0
$466$	9.76483	−	5.63773i	0.452347	−	0.261163i
$467$	−10.9349	+	10.9349i	−0.506008	+	0.506008i	−0.913299	−	0.407291i	$-0.866474\pi$
$467$	−10.9349	+	10.9349i	−0.506008	+	0.506008i	0.407291	+	0.913299i	$0.366474\pi$
$468$	1.79133	−	1.79133i	0.0828040	−	0.0828040i
$469$	1.87430	+	3.24638i	0.0865470	+	0.149904i
$470$		0			0
$471$	−15.0441	+	8.68572i	−0.693196	+	0.400217i
$472$	−3.72054	−	13.8852i	−0.171252	−	0.639120i
$473$	21.5348	−	5.77024i	0.990172	−	0.265316i
$474$	4.88584			0.224414
$475$		0			0
$476$	21.3611			0.979083
$477$	9.52375	−	2.55188i	0.436063	−	0.116843i
$478$	3.46368	+	12.9266i	0.158425	+	0.591250i
$479$	−2.12792	+	1.22856i	−0.0972272	+	0.0561341i	−0.547825	−	0.836593i	$-0.684544\pi$
$479$	−2.12792	+	1.22856i	−0.0972272	+	0.0561341i	0.450598	+	0.892727i	$0.351211\pi$
$480$		0			0
$481$	0.724094	+	1.25417i	0.0330158	+	0.0571851i
$482$	−13.2278	+	13.2278i	−0.602510	+	0.602510i
$483$	19.1521	−	19.1521i	0.871451	−	0.871451i
$484$	12.8853	−	7.43936i	0.585697	−	0.338153i
$485$		0			0
$486$	13.9700			0.633692
$487$	−7.28307	−	7.28307i	−0.330027	−	0.330027i	0.522569	−	0.852597i	$-0.324974\pi$
$487$	−7.28307	−	7.28307i	−0.330027	−	0.330027i	−0.852597	+	0.522569i	$0.824974\pi$
$488$	−5.45165	−	1.46076i	−0.246785	−	0.0661257i
$489$	1.52645	−	2.64389i	0.0690286	−	0.119561i
$490$		0			0
$491$	−10.4517	+	18.1028i	−0.471678	+	0.816970i	−0.999475	−	0.0324007i	$-0.989685\pi$
$491$	−10.4517	+	18.1028i	−0.471678	+	0.816970i	0.527797	+	0.849370i	$0.323018\pi$
$492$	1.78833	+	6.67416i	0.0806244	+	0.300894i
$493$	−9.72676	+	9.72676i	−0.438071	+	0.438071i
$494$	2.52374	+	6.76035i	0.113548	+	0.304162i
$495$		0			0
$496$	6.13067	+	3.53954i	0.275275	+	0.158930i
$497$	39.3413	−	10.5415i	1.76470	−	0.472850i
$498$	1.38476	−	5.16799i	0.0620525	−	0.231583i
$499$	24.1791	+	13.9598i	1.08241	+	0.624927i	0.931544	−	0.363628i	$-0.118462\pi$
$499$	24.1791	+	13.9598i	1.08241	+	0.624927i	0.150861	+	0.988555i	$0.451795\pi$
$500$		0			0
$501$	−16.2737			−0.727057
$502$	12.9604	+	12.9604i	0.578453	+	0.578453i
$503$	−0.198659	+	0.741405i	−0.00885777	+	0.0330576i	−0.970213	−	0.242252i	$-0.922114\pi$
$503$	−0.198659	+	0.741405i	−0.00885777	+	0.0330576i	0.961356	+	0.275310i	$0.0887805\pi$
$504$	2.03972	+	3.53290i	0.0908564	+	0.157368i
$505$		0			0
$506$			42.6333i			1.89528i
$507$	3.21912	−	12.0139i	0.142966	−	0.533558i
$508$	−3.06175	−	11.4266i	−0.135843	−	0.506974i
$509$	−9.55337	−	16.5469i	−0.423446	−	0.733430i	0.572828	−	0.819676i	$-0.305846\pi$
$509$	−9.55337	−	16.5469i	−0.423446	−	0.733430i	−0.996274	+	0.0862459i	$0.972513\pi$
$510$		0			0
$511$	2.75796	−	4.77694i	0.122005	−	0.211319i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−9.93855	+	21.7793i	−0.438798	+	0.961580i
$514$			1.54422i			0.0681128i
$515$		0			0
$516$	4.60126	+	2.65654i	0.202559	+	0.116948i
$517$	−50.7572	−	13.6003i	−2.23230	−	0.598142i
$518$	−2.25258	+	0.603576i	−0.0989726	+	0.0265196i
$519$	10.8576	−	6.26862i	0.476594	−	0.275162i
$520$		0			0
$521$		−	16.6777i		−	0.730665i	−0.930877	−	0.365332i	$-0.880955\pi$
$521$		−	16.6777i		−	0.730665i	0.930877	−	0.365332i	$-0.119045\pi$
$522$	−2.53749	−	0.679919i	−0.111063	−	0.0297592i
$523$	7.84835	+	2.10296i	0.343185	+	0.0919560i	0.426295	−	0.904584i	$-0.359819\pi$
$523$	7.84835	+	2.10296i	0.343185	+	0.0919560i	−0.0831101	+	0.996540i	$0.526485\pi$
$524$			5.80617i			0.253644i
$525$		0			0
$526$	0.969923	−	0.559985i	0.0422907	−	0.0244165i
$527$	54.7910	−	14.6812i	2.38674	−	0.639524i
$528$	5.95710	+	1.59620i	0.259250	+	0.0694657i
$529$	−40.9068	−	23.6176i	−1.77856	−	1.02685i
$530$		0			0
$531$		−	21.9976i		−	0.954615i
$532$	−11.5672	+	1.10796i	−0.501502	+	0.0480361i
$533$	6.67177	+	6.67177i	0.288986	+	0.288986i
$534$	6.38159	−	11.0532i	0.276158	−	0.478321i
$535$		0			0
$536$	−0.703079	−	1.21777i	−0.0303684	−	0.0525996i
$537$	4.79971	+	17.9128i	0.207123	+	0.772993i
$538$	−1.00578	+	3.75364i	−0.0433624	+	0.161831i
$539$		−	0.542888i		−	0.0233839i
$540$		0			0
$541$	−2.51329	−	4.35315i	−0.108055	−	0.187157i	0.806927	−	0.590651i	$-0.201129\pi$
$541$	−2.51329	−	4.35315i	−0.108055	−	0.187157i	−0.914982	+	0.403494i	$0.867796\pi$
$542$	0.773189	−	2.88558i	0.0332113	−	0.123946i
$543$	−13.2424	−	13.2424i	−0.568286	−	0.568286i
$544$	−8.01288			−0.343549
$545$		0			0
$546$	−4.63349	−	2.67515i	−0.198295	−	0.114486i
$547$	−11.0124	+	41.0987i	−0.470855	+	1.75725i	0.165854	+	0.986150i	$0.446962\pi$
$547$	−11.0124	+	41.0987i	−0.470855	+	1.75725i	−0.636709	+	0.771104i	$0.719705\pi$
$548$	16.5912	−	4.44559i	0.708739	−	0.189906i
$549$	−7.47964	−	4.31837i	−0.319223	−	0.184304i
$550$		0			0
$551$	4.76261	−	5.77163i	0.202894	−	0.245880i
$552$	−7.18426	+	7.18426i	−0.305782	+	0.305782i
$553$	2.78067	+	10.3776i	0.118246	+	0.441301i
$554$	−11.3008	+	19.5735i	−0.480124	+	0.831599i
$555$		0			0
$556$	−6.79791	+	11.7743i	−0.288296	+	0.499343i
$557$	36.1697	+	9.69165i	1.53256	+	0.410648i	0.923853	−	0.382747i	$-0.125022\pi$
$557$	36.1697	+	9.69165i	1.53256	+	0.410648i	0.608707	+	0.793395i	$0.291688\pi$
$558$	7.65999	+	7.65999i	0.324273	+	0.324273i
$559$	7.25520			0.306862
$560$		0			0
$561$	42.7967	−	24.7087i	1.80688	−	1.04320i
$562$	16.8468	−	16.8468i	0.710641	−	0.710641i
$563$	2.95561	−	2.95561i	0.124564	−	0.124564i	−0.642076	−	0.766641i	$-0.721927\pi$
$563$	2.95561	−	2.95561i	0.124564	−	0.124564i	0.766641	+	0.642076i	$0.221927\pi$
$564$	−6.26141	−	10.8451i	−0.263653	−	0.456660i
$565$		0			0
$566$	7.62020	−	4.39952i	0.320301	−	0.184926i
$567$	−1.42652	−	5.32384i	−0.0599082	−	0.223580i
$568$	−14.7576	+	3.95427i	−0.619213	+	0.165918i
$569$	8.11963			0.340393			0.170196	−	0.985410i	$-0.445560\pi$
$569$	8.11963			0.340393			0.170196	+	0.985410i	$0.445560\pi$
$570$		0			0
$571$	−30.5277			−1.27754			−0.638772	−	0.769396i	$-0.720557\pi$
$571$	−30.5277			−1.27754			−0.638772	+	0.769396i	$0.720557\pi$
$572$	8.13464	−	2.17967i	0.340126	−	0.0911366i
$573$	−4.52511	−	16.8880i	−0.189039	−	0.705504i
$574$	−13.1582	+	7.59692i	−0.549214	+	0.317089i
$575$		0			0
$576$	−0.765131	−	1.32525i	−0.0318805	−	0.0552186i
$577$	3.75441	−	3.75441i	0.156298	−	0.156298i	−0.624626	−	0.780924i	$-0.714749\pi$
$577$	3.75441	−	3.75441i	0.156298	−	0.156298i	0.780924	+	0.624626i	$0.214749\pi$
$578$	−33.3798	+	33.3798i	−1.38842	+	1.38842i
$579$	8.06545	−	4.65659i	0.335188	−	0.193521i
$580$		0			0
$581$	11.7650			0.488095
$582$	−8.89783	−	8.89783i	−0.368827	−	0.368827i
$583$	31.6602	+	8.48332i	1.31123	+	0.351343i
$584$	−1.03456	+	1.79190i	−0.0428102	+	0.0741495i
$585$		0			0
$586$	−9.88949	+	17.1291i	−0.408531	+	0.707596i
$587$	−0.526737	−	1.96581i	−0.0217407	−	0.0811376i	0.954203	−	0.299159i	$-0.0967063\pi$
$587$	−0.526737	−	1.96581i	−0.0217407	−	0.0811376i	−0.975944	+	0.218022i	$0.930040\pi$
$588$	0.0914838	−	0.0914838i	0.00377273	−	0.00377273i
$589$	−28.9083	+	10.7919i	−1.19115	+	0.444673i
$590$		0			0
$591$	22.3308	+	12.8927i	0.918565	+	0.530334i
$592$	0.844978	−	0.226411i	0.0347284	−	0.00930544i
$593$	−3.63727	+	13.5745i	−0.149365	+	0.557437i	0.850157	+	0.526529i	$0.176507\pi$
$593$	−3.63727	+	13.5745i	−0.149365	+	0.557437i	−0.999522	+	0.0309085i	$0.990160\pi$
$594$	24.1961	+	13.9696i	0.992778	+	0.573180i
$595$		0			0
$596$	−9.51066			−0.389572
$597$	−3.95224	−	3.95224i	−0.161754	−	0.161754i
$598$	−3.59085	+	13.4012i	−0.146841	+	0.548017i
$599$	20.6686	+	35.7990i	0.844495	+	1.46271i	0.886059	+	0.463573i	$0.153433\pi$
$599$	20.6686	+	35.7990i	0.844495	+	1.46271i	−0.0415632	+	0.999136i	$0.513234\pi$
$600$		0			0
$601$			41.7390i			1.70257i	0.524704	+	0.851285i	$0.324176\pi$
$601$			41.7390i			1.70257i	−0.524704	+	0.851285i	$0.675824\pi$
$602$	−3.02383	+	11.2851i	−0.123242	+	0.459945i
$603$	−0.556925	−	2.07847i	−0.0226797	−	0.0846419i
$604$	3.10564	+	5.37913i	0.126367	+	0.218874i
$605$		0			0
$606$	4.00698	−	6.94029i	0.162772	−	0.281930i
$607$	−16.1858	−	16.1858i	−0.656963	−	0.656963i	0.297697	−	0.954660i	$-0.403781\pi$
$607$	−16.1858	−	16.1858i	−0.656963	−	0.656963i	−0.954660	+	0.297697i	$0.903781\pi$
$608$	4.33904	−	0.415613i	0.175971	−	0.0168553i
$609$			5.54816i			0.224823i
$610$		0			0
$611$	−14.8094	−	8.55019i	−0.599122	−	0.345903i
$612$	−11.8440	−	3.17359i	−0.478765	−	0.128285i
$613$	−19.2434	+	5.15626i	−0.777235	+	0.208260i	−0.625566	−	0.780172i	$-0.715132\pi$
$613$	−19.2434	+	5.15626i	−0.777235	+	0.208260i	−0.151670	+	0.988431i	$0.548465\pi$
$614$	10.7201	−	6.18923i	0.432627	−	0.249777i
$615$		0			0
$616$			13.5614i			0.546406i
$617$	−14.9980	−	4.01870i	−0.603796	−	0.161787i	−0.0560454	−	0.998428i	$-0.517849\pi$
$617$	−14.9980	−	4.01870i	−0.603796	−	0.161787i	−0.547751	+	0.836642i	$0.684516\pi$
$618$	10.5667	+	2.83134i	0.425056	+	0.113893i
$619$			32.8578i			1.32067i	0.750973	+	0.660333i	$0.229585\pi$
$619$			32.8578i			1.32067i	−0.750973	+	0.660333i	$0.770415\pi$
$620$		0			0
$621$	−39.8613	+	23.0139i	−1.59958	+	0.923516i
$622$	−12.5240	+	3.35580i	−0.502168	+	0.134555i
$623$	27.1093	+	7.26390i	1.08611	+	0.291022i
$624$	1.73810	+	1.00349i	0.0695795	+	0.0401718i
$625$		0			0
$626$			4.18956i			0.167449i
$627$	−21.8932	+	15.5997i	−0.874329	+	0.622994i
$628$	10.1321	+	10.1321i	0.404316	+	0.404316i
$629$	3.50477	−	6.07045i	0.139744	−	0.242045i
$630$		0			0
$631$	16.1438	+	27.9620i	0.642676	+	1.11315i	0.984833	+	0.173505i	$0.0555093\pi$
$631$	16.1438	+	27.9620i	0.642676	+	1.11315i	−0.342157	+	0.939643i	$0.611157\pi$
$632$	−1.04308	−	3.89281i	−0.0414913	−	0.154848i
$633$	0.721077	−	2.69110i	0.0286602	−	0.106961i
$634$		−	8.43617i		−	0.335043i
$635$		0			0
$636$	3.90560	+	6.76470i	0.154867	+	0.268238i
$637$	0.0457255	−	0.170650i	0.00181171	−	0.00676140i
$638$	−6.17520	−	6.17520i	−0.244479	−	0.244479i
$639$	−23.3796			−0.924882
$640$		0			0
$641$	−5.07111	−	2.92781i	−0.200297	−	0.115642i	0.396497	−	0.918036i	$-0.370226\pi$
$641$	−5.07111	−	2.92781i	−0.200297	−	0.115642i	−0.596794	+	0.802394i	$0.703559\pi$
$642$	2.90596	−	10.8452i	0.114689	−	0.428026i
$643$	−10.6783	+	2.86125i	−0.421113	+	0.112837i	−0.463151	−	0.886279i	$-0.653281\pi$
$643$	−10.6783	+	2.86125i	−0.421113	+	0.112837i	0.0420388	+	0.999116i	$0.486615\pi$
$644$	−19.3483	−	11.1707i	−0.762429	−	0.440189i
$645$		0			0
$646$	22.2300	−	26.9397i	0.874627	−	1.05993i
$647$	−24.0362	+	24.0362i	−0.944960	+	0.944960i	−0.998562	−	0.0536023i	$-0.982930\pi$
$647$	−24.0362	+	24.0362i	−0.944960	+	0.944960i	0.0536023	+	0.998562i	$0.482930\pi$
$648$	0.535110	+	1.99706i	0.0210211	+	0.0784518i
$649$	36.5637	−	63.3303i	1.43525	−	2.48593i
$650$		0			0
$651$	11.4394	−	19.8135i	0.448344	−	0.776554i
$652$	−2.43241	−	0.651763i	−0.0952606	−	0.0255250i
$653$	2.19175	+	2.19175i	0.0857697	+	0.0857697i	0.748690	−	0.662920i	$-0.230683\pi$
$653$	2.19175	+	2.19175i	0.0857697	+	0.0857697i	−0.662920	+	0.748690i	$0.730683\pi$
$654$	5.10598			0.199659
$655$		0			0
$656$	4.93587	−	2.84972i	0.192713	−	0.111263i
$657$	−2.23890	+	2.23890i	−0.0873479	+	0.0873479i
$658$	19.4716	−	19.4716i	0.759082	−	0.759082i
$659$	2.00998	+	3.48139i	0.0782978	+	0.135616i	0.902516	−	0.430657i	$-0.141718\pi$
$659$	2.00998	+	3.48139i	0.0782978	+	0.135616i	−0.824218	+	0.566273i	$0.808385\pi$
$660$		0			0
$661$	−9.46361	+	5.46382i	−0.368092	+	0.212518i	−0.672624	−	0.739984i	$-0.734833\pi$
$661$	−9.46361	+	5.46382i	−0.368092	+	0.212518i	0.304533	+	0.952502i	$0.401500\pi$
$662$	−2.49141	−	9.29808i	−0.0968315	−	0.361380i
$663$	15.5337	−	4.16225i	0.603280	−	0.161648i
$664$	−4.41324			−0.171267
$665$		0			0
$666$	1.33865			0.0518717
$667$	13.8968	−	3.72364i	0.538087	−	0.144180i
$668$	3.47427	+	12.9661i	0.134424	+	0.501675i
$669$	21.6625	−	12.5069i	0.837521	−	0.483543i
$670$		0			0
$671$	−14.3557	−	24.8649i	−0.554197	−	0.959897i
$672$	−2.28528	+	2.28528i	−0.0881566	+	0.0881566i
$673$	7.33331	−	7.33331i	0.282679	−	0.282679i	−0.551498	−	0.834176i	$-0.685944\pi$
$673$	7.33331	−	7.33331i	0.282679	−	0.282679i	0.834176	+	0.551498i	$0.185944\pi$
$674$	3.18272	−	1.83754i	0.122594	−	0.0707795i
$675$		0			0
$676$	−10.2594			−0.394592
$677$	20.7086	+	20.7086i	0.795895	+	0.795895i	0.982445	−	0.186550i	$-0.0597307\pi$
$677$	20.7086	+	20.7086i	0.795895	+	0.795895i	−0.186550	+	0.982445i	$0.559731\pi$
$678$	−11.4809	−	3.07630i	−0.440922	−	0.118145i
$679$	13.8352	−	23.9632i	0.530944	−	0.919623i
$680$		0			0
$681$	1.98573	−	3.43939i	0.0760935	−	0.131798i
$682$	9.32062	+	34.7850i	0.356905	+	1.33199i
$683$	24.6294	−	24.6294i	0.942417	−	0.942417i	−0.0560135	−	0.998430i	$-0.517839\pi$
$683$	24.6294	−	24.6294i	0.942417	−	0.942417i	0.998430	+	0.0560135i	$0.0178390\pi$
$684$	6.57823	+	1.10420i	0.251525	+	0.0422201i
$685$		0			0
$686$	−15.9144	−	9.18820i	−0.607616	−	0.350807i
$687$	8.73014	−	2.33923i	0.333075	−	0.0892473i
$688$	1.13429	−	4.23321i	0.0432442	−	0.161390i
$689$	9.23745	+	5.33325i	0.351919	+	0.203180i
$690$		0			0
$691$	−25.0871			−0.954359			−0.477179	−	0.878806i	$-0.658341\pi$
$691$	−25.0871			−0.954359			−0.477179	+	0.878806i	$0.658341\pi$
$692$	−7.31252	−	7.31252i	−0.277980	−	0.277980i
$693$	−5.37116	+	20.0454i	−0.204034	+	0.761464i
$694$	0.215249	+	0.372822i	0.00817073	+	0.0141521i
$695$		0			0
$696$		−	2.08120i		−	0.0788878i
$697$	11.8200	−	44.1128i	0.447714	−	1.67089i
$698$	−2.96482	−	11.0648i	−0.112220	−	0.418810i
$699$	6.83477	+	11.8382i	0.258515	+	0.447761i
$700$		0			0
$701$	−5.67140	+	9.82316i	−0.214206	+	0.371016i	−0.953027	−	0.302887i	$-0.902050\pi$
$701$	−5.67140	+	9.82316i	−0.214206	+	0.371016i	0.738821	+	0.673902i	$0.235383\pi$
$702$	6.42912	+	6.42912i	0.242652	+	0.242652i
$703$	−1.58300	+	3.46898i	−0.0597040	+	0.130835i
$704$		−	5.08711i		−	0.191728i
$705$		0			0
$706$	−26.6597	−	15.3920i	−1.00335	−	0.579284i
$707$	17.0218	+	4.56098i	0.640171	+	0.171533i
$708$	16.8334	−	4.51051i	0.632640	−	0.169515i
$709$	−23.3759	+	13.4961i	−0.877901	+	0.506856i	−0.869966	−	0.493112i	$-0.835859\pi$
$709$	−23.3759	+	13.4961i	−0.877901	+	0.506856i	−0.00793506	+	0.999969i	$0.502526\pi$
$710$		0			0
$711$		−	6.16716i		−	0.231287i
$712$	−10.1691	−	2.72481i	−0.381104	−	0.102116i
$713$	−57.3057	−	15.3550i	−2.14612	−	0.575050i
$714$			25.8966i			0.969156i
$715$		0			0
$716$	13.2474	−	7.64838i	0.495078	−	0.285833i
$717$	−15.6713	+	4.19911i	−0.585255	+	0.156819i
$718$	35.9587	+	9.63510i	1.34197	+	0.359579i
$719$	5.21897	+	3.01318i	0.194635	+	0.112372i	0.594151	−	0.804354i	$-0.297488\pi$
$719$	5.21897	+	3.01318i	0.194635	+	0.112372i	−0.399516	+	0.916726i	$0.630822\pi$
$720$		0			0
$721$			24.0553i			0.895867i
$722$	−10.6404	+	15.7411i	−0.395995	+	0.585822i
$723$	−16.0364	−	16.0364i	−0.596401	−	0.596401i
$724$	−7.72382	+	13.3780i	−0.287053	+	0.497191i
$725$		0			0
$726$	9.01893	+	15.6213i	0.334724	+	0.579759i
$727$	−0.343444	−	1.28175i	−0.0127376	−	0.0475375i	0.959265	−	0.282509i	$-0.0911668\pi$
$727$	−0.343444	−	1.28175i	−0.0127376	−	0.0475375i	−0.972002	+	0.234972i	$0.924500\pi$
$728$	−1.14223	+	4.26287i	−0.0423339	+	0.157992i
$729$			23.1387i			0.856989i
$730$		0			0
$731$	−17.5584	−	30.4120i	−0.649421	−	1.12483i
$732$	1.77092	−	6.60918i	0.0654553	−	0.244282i
$733$	23.2056	+	23.2056i	0.857120	+	0.857120i	0.990998	−	0.133878i	$-0.0427430\pi$
$733$	23.2056	+	23.2056i	0.857120	+	0.857120i	−0.133878	+	0.990998i	$0.542743\pi$
$734$	−0.937051			−0.0345872
$735$		0			0
$736$	7.25785	+	4.19032i	0.267528	+	0.154457i
$737$	1.85141	−	6.90954i	0.0681974	−	0.254516i
$738$	8.42447	−	2.25733i	0.310109	−	0.0830935i
$739$	1.10497	+	0.637953i	0.0406469	+	0.0234675i	0.520186	−	0.854053i	$-0.325863\pi$
$739$	1.10497	+	0.637953i	0.0406469	+	0.0234675i	−0.479539	+	0.877521i	$0.659196\pi$
$740$		0			0
$741$	−8.19575	+	3.05960i	−0.301078	+	0.112397i
$742$	−12.1456	+	12.1456i	−0.445878	+	0.445878i
$743$	0.0708104	+	0.264268i	0.00259778	+	0.00969505i	0.967213	−	0.253968i	$-0.0817359\pi$
$743$	0.0708104	+	0.264268i	0.00259778	+	0.00969505i	−0.964615	+	0.263663i	$0.915069\pi$
$744$	−4.29108	+	7.43238i	−0.157319	+	0.272484i
$745$		0			0
$746$	12.9511	−	22.4320i	0.474174	−	0.821294i
$747$	−6.52331	−	1.74791i	−0.238675	−	0.0639528i
$748$	−28.8234	−	28.8234i	−1.05389	−	1.05389i
$749$	24.6893			0.902126
$750$		0			0
$751$	8.25436	−	4.76566i	0.301206	−	0.173901i	−0.341779	−	0.939780i	$-0.611029\pi$
$751$	8.25436	−	4.76566i	0.301206	−	0.173901i	0.642984	+	0.765879i	$0.277696\pi$
$752$	−7.30411	+	7.30411i	−0.266353	+	0.266353i
$753$	−15.7123	+	15.7123i	−0.572588	+	0.572588i
$754$	−1.42098	−	2.46121i	−0.0517490	−	0.0896320i
$755$		0			0
$756$	−12.6797	+	7.32062i	−0.461156	+	0.266248i
$757$	6.68168	+	24.9364i	0.242850	+	0.906328i	0.974452	+	0.224596i	$0.0721063\pi$
$757$	6.68168	+	24.9364i	0.242850	+	0.906328i	−0.731602	+	0.681732i	$0.761227\pi$
$758$	−31.6974	+	8.49328i	−1.15130	+	0.308490i
$759$	−51.6855			−1.87606
$760$		0			0
$761$	33.4904			1.21403			0.607014	−	0.794691i	$-0.292367\pi$
$761$	33.4904			1.21403			0.607014	+	0.794691i	$0.292367\pi$
$762$	13.8528	−	3.71185i	0.501834	−	0.134466i
$763$	2.90596	+	10.8452i	0.105203	+	0.392622i
$764$	−12.4895	+	7.21080i	−0.451853	+	0.260878i
$765$		0			0
$766$	−5.42005	−	9.38781i	−0.195835	−	0.339195i
$767$	16.8274	−	16.8274i	0.607603	−	0.607603i
$768$	0.857245	−	0.857245i	0.0309332	−	0.0309332i
$769$	−40.9858	+	23.6631i	−1.47798	+	0.853315i	−0.999690	−	0.0248847i	$-0.992078\pi$
$769$	−40.9858	+	23.6631i	−1.47798	+	0.853315i	−0.478294	+	0.878200i	$0.658745\pi$
$770$		0			0
$771$	−1.87210			−0.0674222
$772$	−5.43204	−	5.43204i	−0.195503	−	0.195503i
$773$	31.0899	+	8.33051i	1.11823	+	0.299628i	0.770165	−	0.637845i	$-0.220174\pi$
$773$	31.0899	+	8.33051i	1.11823	+	0.299628i	0.348060	+	0.937472i	$0.386840\pi$
$774$	3.35322	−	5.80795i	0.120529	−	0.208763i
$775$		0			0
$776$	−5.18979	+	8.98897i	−0.186302	+	0.322685i
$777$	−0.731732	−	2.73086i	−0.0262507	−	0.0979691i
$778$	15.3183	−	15.3183i	0.549187	−	0.549187i
$779$	−4.11258	+	24.5005i	−0.147348	+	0.877823i
$780$		0			0
$781$	−67.3089	−	38.8608i	−2.40850	−	1.39055i
$782$	64.8649	−	17.3805i	2.31956	−	0.621525i
$783$	2.44025	−	9.10713i	0.0872074	−	0.325462i
$784$	−0.0924208	−	0.0533592i	−0.00330074	−	0.00190569i
$785$		0			0
$786$	−7.03898			−0.251072
$787$	−20.9433	−	20.9433i	−0.746547	−	0.746547i	0.227282	−	0.973829i	$-0.427016\pi$
$787$	−20.9433	−	20.9433i	−0.746547	−	0.746547i	−0.973829	+	0.227282i	$0.927016\pi$
$788$	5.50490	−	20.5446i	0.196104	−	0.731870i
$789$	0.678886	+	1.17586i	0.0241690	+	0.0418619i
$790$		0			0
$791$		−	26.1365i		−	0.929308i
$792$	2.01481	−	7.51937i	0.0715931	−	0.267189i
$793$	−2.41826	−	9.02508i	−0.0858751	−	0.320490i
$794$	12.4300	+	21.5295i	0.441126	+	0.764053i
$795$		0			0
$796$	−2.30520	+	3.99272i	−0.0817056	+	0.141518i
$797$	−21.1881	−	21.1881i	−0.750521	−	0.750521i	0.224056	−	0.974576i	$-0.428070\pi$
$797$	−21.1881	−	21.1881i	−0.750521	−	0.750521i	−0.974576	+	0.224056i	$0.928070\pi$
$798$	−1.34321	−	14.0232i	−0.0475490	−	0.496417i
$799$			82.7696i			2.92818i
$800$		0			0
$801$	−13.9520	−	8.05518i	−0.492969	−	0.284616i
$802$	28.1812	+	7.55113i	0.995112	+	0.266640i
$803$	−10.1672	+	2.72428i	−0.358791	+	0.0961377i
$804$	1.47633	−	0.852362i	0.0520663	−	0.0300605i
$805$		0			0
$806$			11.7193i			0.412794i
$807$	−4.55064	−	1.21934i	−0.160190	−	0.0429228i
$808$	−6.38515	−	1.71090i	−0.224629	−	0.0601891i
$809$			17.3630i			0.610451i	0.952280	+	0.305226i	$0.0987319\pi$
$809$			17.3630i			0.610451i	−0.952280	+	0.305226i	$0.901268\pi$
$810$		0			0
$811$	−7.18151	+	4.14625i	−0.252177	+	0.145594i	−0.620761	−	0.784000i	$-0.713176\pi$
$811$	−7.18151	+	4.14625i	−0.252177	+	0.145594i	0.368584	+	0.929595i	$0.379843\pi$
$812$	4.42052	−	1.18447i	0.155130	−	0.0415669i
$813$	3.49827	+	0.937358i	0.122690	+	0.0328746i
$814$	3.85393	+	2.22507i	0.135080	+	0.0779885i
$815$		0			0
$816$		−	9.71423i		−	0.340066i
$817$	11.0854	+	15.5576i	0.387830	+	0.544293i
$818$	−9.08015	−	9.08015i	−0.317480	−	0.317480i
$819$	−3.37671	+	5.84864i	−0.117992	+	0.204368i
$820$		0			0
$821$	6.91289	+	11.9735i	0.241261	+	0.417877i	0.961074	−	0.276292i	$-0.0891055\pi$
$821$	6.91289	+	11.9735i	0.241261	+	0.417877i	−0.719812	+	0.694169i	$0.755772\pi$
$822$	5.38951	+	20.1139i	0.187981	+	0.701553i
$823$	−0.304420	+	1.13611i	−0.0106114	+	0.0396023i	−0.971029	−	0.238963i	$-0.923192\pi$
$823$	−0.304420	+	1.13611i	−0.0106114	+	0.0396023i	0.960417	+	0.278566i	$0.0898590\pi$
$824$		−	9.02353i		−	0.314350i
$825$		0			0
$826$	19.1608	+	33.1875i	0.666690	+	1.15474i
$827$	−8.41337	+	31.3991i	−0.292562	+	1.09185i	0.650573	+	0.759444i	$0.274529\pi$
$827$	−8.41337	+	31.3991i	−0.292562	+	1.09185i	−0.943135	+	0.332411i	$0.892138\pi$
$828$	9.06835	+	9.06835i	0.315147	+	0.315147i
$829$	−23.1927			−0.805516			−0.402758	−	0.915307i	$-0.631948\pi$
$829$	−23.1927			−0.805516			−0.402758	+	0.915307i	$0.631948\pi$
$830$		0			0
$831$	−23.7295	−	13.7002i	−0.823167	−	0.475256i
$832$	0.428469	−	1.59907i	0.0148545	−	0.0554377i
$833$	−0.825984	+	0.221322i	−0.0286186	+	0.00766834i
$834$	−14.2743	−	8.24129i	−0.494280	−	0.285373i
$835$		0			0
$836$	17.1031	+	14.1131i	0.591523	+	0.488111i
$837$	−27.4919	+	27.4919i	−0.950261	+	0.950261i
$838$	−4.60480	−	17.1854i	−0.159070	−	0.593659i
$839$	25.4002	−	43.9944i	0.876912	−	1.51886i	0.0222001	−	0.999754i	$-0.492933\pi$
$839$	25.4002	−	43.9944i	0.876912	−	1.51886i	0.854712	−	0.519103i	$-0.173734\pi$
$840$		0			0
$841$	13.0265	−	22.5625i	0.449189	−	0.778017i
$842$	32.9205	+	8.82102i	1.13451	+	0.303992i
$843$	20.4239	+	20.4239i	0.703435	+	0.703435i
$844$	−2.29808			−0.0791032
$845$		0			0
$846$	−13.6892	+	7.90348i	−0.470645	+	0.271727i
$847$	−28.0469	+	28.0469i	−0.963703	+	0.963703i
$848$	4.55600	−	4.55600i	0.156454	−	0.156454i
$849$	5.33366	+	9.23817i	0.183051	+	0.317053i
$850$		0			0
$851$	−6.34906	+	3.66563i	−0.217643	+	0.125656i
$852$	−4.79387	−	17.8910i	−0.164235	−	0.612935i
$853$	35.0879	−	9.40178i	1.20139	−	0.321911i	0.398010	−	0.917381i	$-0.369701\pi$
$853$	35.0879	−	9.40178i	1.20139	−	0.321911i	0.803377	+	0.595470i	$0.203034\pi$
$854$	15.0459			0.514861
$855$		0			0
$856$	−9.26134			−0.316546
$857$	15.7194	−	4.21201i	0.536966	−	0.143880i	0.0198628	−	0.999803i	$-0.493677\pi$
$857$	15.7194	−	4.21201i	0.536966	−	0.143880i	0.517103	+	0.855923i	$0.327010\pi$
$858$	2.64247	+	9.86185i	0.0902126	+	0.336678i
$859$	26.5596	−	15.3342i	0.906201	−	0.523196i	0.0269944	−	0.999636i	$-0.491406\pi$
$859$	26.5596	−	15.3342i	0.906201	−	0.523196i	0.879207	+	0.476440i	$0.158073\pi$
$860$		0			0
$861$	−9.20995	−	15.9521i	−0.313874	−	0.543646i
$862$	17.1947	−	17.1947i	0.585652	−	0.585652i
$863$	−7.66348	+	7.66348i	−0.260868	+	0.260868i	−0.825407	−	0.564539i	$-0.809054\pi$
$863$	−7.66348	+	7.66348i	−0.260868	+	0.260868i	0.564539	+	0.825407i	$0.309054\pi$
$864$	4.75635	−	2.74608i	0.161814	−	0.0934235i
$865$		0			0
$866$	−25.7731			−0.875806
$867$	−40.4673	−	40.4673i	−1.37434	−	1.37434i
$868$	−18.2287	−	4.88436i	−0.618722	−	0.165786i
$869$	10.2509	−	17.7550i	0.347737	−	0.602298i
$870$		0			0
$871$	1.16393	−	2.01599i	0.0394383	−	0.0683092i
$872$	−1.09007	−	4.06820i	−0.0369145	−	0.137767i
$873$	−11.2313	+	11.2313i	−0.380122	+	0.380122i
$874$	−34.2234	+	12.7761i	−1.15762	+	0.432158i
$875$		0			0
$876$	−2.17237	−	1.25422i	−0.0733977	−	0.0423762i
$877$	13.5051	−	3.61868i	0.456035	−	0.122194i	−0.0234870	−	0.999724i	$-0.507477\pi$
$877$	13.5051	−	3.61868i	0.456035	−	0.122194i	0.479522	+	0.877530i	$0.340810\pi$
$878$	0.265341	−	0.990266i	0.00895482	−	0.0334198i
$879$	−20.7661	−	11.9893i	−0.700422	−	0.404389i
$880$		0			0
$881$	24.2524			0.817085			0.408542	−	0.912739i	$-0.366037\pi$
$881$	24.2524			0.817085			0.408542	+	0.912739i	$0.366037\pi$
$882$	−0.115476	−	0.115476i	−0.00388827	−	0.00388827i
$883$	1.87920	−	7.01327i	0.0632401	−	0.236015i	−0.927070	−	0.374888i	$-0.877681\pi$
$883$	1.87920	−	7.01327i	0.0632401	−	0.236015i	0.990310	+	0.138873i	$0.0443479\pi$
$884$	−6.63257	−	11.4879i	−0.223077	−	0.386382i
$885$		0			0
$886$			8.29575i			0.278701i
$887$	4.01762	−	14.9940i	0.134899	−	0.503449i	−0.865100	−	0.501600i	$-0.832745\pi$
$887$	4.01762	−	14.9940i	0.134899	−	0.503449i	0.999998	−	0.00184854i	$-0.000588408\pi$
$888$	0.274484	+	1.02439i	0.00921109	+	0.0343763i
$889$	15.7681	+	27.3111i	0.528844	+	0.915985i
$890$		0			0
$891$	−5.25882	+	9.10854i	−0.176177	+	0.305148i
$892$	−14.5896	−	14.5896i	−0.488496	−	0.488496i
$893$	−4.29310	−	44.8204i	−0.143663	−	1.49986i
$894$		−	11.5300i		−	0.385622i
$895$		0			0
$896$	2.30869	+	1.33292i	0.0771278	+	0.0445298i
$897$	−16.2467	−	4.35328i	−0.542460	−	0.145352i
$898$	−18.9353	+	5.07369i	−0.631878	+	0.169311i
$899$	10.5245	−	6.07634i	0.351013	−	0.202657i
$900$		0			0
$901$		−	51.6282i		−	1.71998i
$902$	28.0058	+	7.50413i	0.932491	+	0.249860i
$903$	−13.6812	−	3.66587i	−0.455282	−	0.121992i
$904$			9.80423i			0.326084i
$905$		0			0
$906$	−6.52127	+	3.76506i	−0.216655	+	0.125086i
$907$	32.3118	−	8.65791i	1.07289	−	0.287481i	0.321213	−	0.947007i	$-0.395909\pi$
$907$	32.3118	−	8.65791i	1.07289	−	0.287481i	0.751682	+	0.659526i	$0.229243\pi$
$908$	−3.16428	−	0.847867i	−0.105010	−	0.0281375i
$909$	−8.76040	−	5.05782i	−0.290564	−	0.167757i
$910$		0			0
$911$			22.3197i			0.739486i	0.929134	+	0.369743i	$0.120554\pi$
$911$			22.3197i			0.739486i	−0.929134	+	0.369743i	$0.879446\pi$
$912$	0.503858	+	5.26034i	0.0166844	+	0.174187i
$913$	−15.8750	−	15.8750i	−0.525386	−	0.525386i
$914$	13.7904	−	23.8857i	0.456146	−	0.790069i
$915$		0			0
$916$	−3.72758	−	6.45636i	−0.123163	−	0.213324i
$917$	−4.00609	−	14.9509i	−0.132293	−	0.493723i
$918$	11.3901	−	42.5085i	0.375930	−	1.40299i
$919$		−	50.0242i		−	1.65015i	−0.565027	−	0.825073i	$-0.691134\pi$
$919$		−	50.0242i		−	1.65015i	0.565027	−	0.825073i	$-0.308866\pi$
$920$		0			0
$921$	7.50337	+	12.9962i	0.247245	+	0.428240i
$922$	1.99276	−	7.43710i	0.0656282	−	0.244928i
$923$	−17.8846	−	17.8846i	−0.588678	−	0.588678i
$924$	−16.4409			−0.540866
$925$		0			0
$926$	15.4625	+	8.92725i	0.508128	+	0.293368i
$927$	3.57387	−	13.3379i	0.117381	−	0.438073i
$928$	−1.65821	+	0.444315i	−0.0544333	+	0.0145854i
$929$	11.8563	+	6.84526i	0.388994	+	0.224586i	0.681724	−	0.731609i	$-0.261230\pi$
$929$	11.8563	+	6.84526i	0.388994	+	0.224586i	−0.292730	+	0.956195i	$0.594564\pi$
$930$		0			0
$931$	0.435798	−	0.162690i	0.0142827	−	0.00533194i
$932$	7.97295	−	7.97295i	0.261163	−	0.261163i
$933$	−4.06833	−	15.1832i	−0.133191	−	0.497076i
$934$	−7.73216	+	13.3925i	−0.253004	+	0.438216i
$935$		0			0
$936$	1.26666	−	2.19392i	0.0414020	−	0.0717104i
$937$	4.32476	+	1.15881i	0.141284	+	0.0378568i	0.328768	−	0.944411i	$-0.393367\pi$
$937$	4.32476	+	1.15881i	0.141284	+	0.0378568i	−0.187484	+	0.982268i	$0.560033\pi$
$938$	2.65066	+	2.65066i	0.0865470	+	0.0865470i
$939$	−5.07912			−0.165751
$940$		0			0
$941$	−29.3527	+	16.9468i	−0.956871	+	0.552450i	−0.895209	−	0.445648i	$-0.852973\pi$
$941$	−29.3527	+	16.9468i	−0.956871	+	0.552450i	−0.0616622	+	0.998097i	$0.519640\pi$
$942$	−12.2835	+	12.2835i	−0.400217	+	0.400217i
$943$	−33.7750	+	33.7750i	−1.09986	+	1.09986i
$944$	−7.18753	−	12.4492i	−0.233934	−	0.405186i
$945$		0			0
$946$	19.3076	−	11.1472i	0.627744	−	0.362428i
$947$	−13.1384	−	49.0334i	−0.426942	−	1.59337i	−0.759645	−	0.650338i	$-0.774627\pi$
$947$	−13.1384	−	49.0334i	−0.426942	−	1.59337i	0.332703	−	0.943032i	$-0.392039\pi$
$948$	4.71936	−	1.26455i	0.153278	−	0.0410706i
$949$	−3.42537			−0.111192
$950$		0			0
$951$	10.2274			0.331646
$952$	20.6332	−	5.52865i	0.668726	−	0.179185i
$953$	2.55499	+	9.53536i	0.0827643	+	0.308881i	0.994881	−	0.101049i	$-0.0322199\pi$
$953$	2.55499	+	9.53536i	0.0827643	+	0.308881i	−0.912117	+	0.409930i	$0.865553\pi$
$954$	8.53876	−	4.92986i	0.276453	−	0.159610i
$955$		0			0
$956$	6.69131	+	11.5897i	0.216413	+	0.374837i
$957$	7.48636	−	7.48636i	0.242000	−	0.242000i
$958$	−1.73744	+	1.73744i	−0.0561341	+	0.0561341i
$959$	−39.6550	+	22.8948i	−1.28053	+	0.739313i
$960$		0			0
$961$	−19.1135			−0.616563
$962$	1.02402	+	1.02402i	0.0330158	+	0.0330158i
$963$	−13.6894	−	3.66806i	−0.441134	−	0.118201i
$964$	−9.35347	+	16.2007i	−0.301255	+	0.521789i
$965$		0			0
$966$	13.5426	−	23.4564i	0.435726	−	0.754699i
$967$	−5.63481	−	21.0294i	−0.181203	−	0.676260i	−0.995411	−	0.0956872i	$-0.969495\pi$
$967$	−5.63481	−	21.0294i	−0.181203	−	0.676260i	0.814208	−	0.580573i	$-0.197172\pi$
$968$	10.5208	−	10.5208i	0.338153	−	0.338153i
$969$	32.6597	+	26.9500i	1.04918	+	0.865759i
$970$		0			0
$971$	−15.8347	−	9.14215i	−0.508159	−	0.293386i	0.223918	−	0.974608i	$-0.428115\pi$
$971$	−15.8347	−	9.14215i	−0.508159	−	0.293386i	−0.732077	+	0.681222i	$0.761449\pi$
$972$	13.4940	−	3.61570i	0.432819	−	0.115974i
$973$	9.38072	−	35.0093i	0.300732	−	1.12235i
$974$	−8.91990	−	5.14991i	−0.285812	−	0.165014i
$975$		0			0
$976$	−5.64396			−0.180659
$977$	2.79812	+	2.79812i	0.0895197	+	0.0895197i	0.750449	−	0.660929i	$-0.229838\pi$
$977$	2.79812	+	2.79812i	0.0895197	+	0.0895197i	−0.660929	+	0.750449i	$0.729838\pi$
$978$	0.790150	−	2.94888i	0.0252662	−	0.0942948i
$979$	−26.7781	−	46.3811i	−0.855833	−	1.48235i
$980$		0			0
$981$		−	6.44503i		−	0.205774i
$982$	−5.41019	+	20.1911i	−0.172646	+	0.644324i
$983$	−1.59078	−	5.93687i	−0.0507380	−	0.189357i	0.935906	−	0.352251i	$-0.114584\pi$
$983$	−1.59078	−	5.93687i	−0.0507380	−	0.189357i	−0.986644	+	0.162894i	$0.947917\pi$
$984$	3.45480	+	5.98388i	0.110135	+	0.190759i
$985$		0			0
$986$	−6.87786	+	11.9128i	−0.219036	+	0.379381i
$987$	23.6060	+	23.6060i	0.751386	+	0.751386i
$988$	4.18745	+	5.87680i	0.133221	+	0.186966i
$989$			36.7285i			1.16790i
$990$		0			0
$991$	−3.11089	−	1.79607i	−0.0988205	−	0.0570541i	0.449775	−	0.893142i	$-0.351504\pi$
$991$	−3.11089	−	1.79607i	−0.0988205	−	0.0570541i	−0.548596	+	0.836088i	$0.684837\pi$
$992$	6.83787	+	1.83220i	0.217103	+	0.0581725i
$993$	11.2723	−	3.02041i	0.357716	−	0.0958498i
$994$	35.2725	−	20.3646i	1.11877	−	0.645925i
$995$		0			0
$996$		−	5.35029i		−	0.169531i
$997$	−19.0140	−	5.09479i	−0.602180	−	0.161354i	−0.0551662	−	0.998477i	$-0.517569\pi$
$997$	−19.0140	−	5.09479i	−0.602180	−	0.161354i	−0.547014	+	0.837124i	$0.684236\pi$
$998$	26.9683	+	7.22613i	0.853666	+	0.228739i
$999$			4.80446i			0.152006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.f.293.7	yes	32
5.2	odd	4	inner	950.2.q.f.407.7	yes	32
5.3	odd	4	inner	950.2.q.f.407.2	yes	32
5.4	even	2	inner	950.2.q.f.293.2	yes	32
19.12	odd	6	inner	950.2.q.f.943.7	yes	32
95.12	even	12	inner	950.2.q.f.107.7	yes	32
95.69	odd	6	inner	950.2.q.f.943.2	yes	32
95.88	even	12	inner	950.2.q.f.107.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.f.107.2	✓	32	95.88	even	12	inner
950.2.q.f.107.7	yes	32	95.12	even	12	inner
950.2.q.f.293.2	yes	32	5.4	even	2	inner
950.2.q.f.293.7	yes	32	1.1	even	1	trivial
950.2.q.f.407.2	yes	32	5.3	odd	4	inner
950.2.q.f.407.7	yes	32	5.2	odd	4	inner
950.2.q.f.943.2	yes	32	95.69	odd	6	inner
950.2.q.f.943.7	yes	32	19.12	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.313773 + 1.17102i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.606164 + 1.04991i) q^{6} +(-1.88504 + 1.88504i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.32525 - 0.765131i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.313773 + 1.17102i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.606164 + 1.04991i) q^{6} +(-1.88504 + 1.88504i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.32525 - 0.765131i) q^{9} +5.08711 q^{11} +(0.857245 + 0.857245i) q^{12} +(1.59907 + 0.428469i) q^{13} +(-1.33292 + 2.30869i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.07389 - 7.73985i) q^{17} +(1.08206 - 1.08206i) q^{18} +(1.52448 + 4.08362i) q^{19} +(-2.79888 - 1.61594i) q^{21} +(4.91377 - 1.31664i) q^{22} +(-2.16907 + 8.09508i) q^{23} +(1.04991 + 0.606164i) q^{24} +1.65548 q^{26} +(3.88354 + 3.88354i) q^{27} +(-0.689971 + 2.57501i) q^{28} +(-0.858351 - 1.48671i) q^{29} +7.07909i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.59620 + 5.95710i) q^{33} +(-4.00644 - 6.93936i) q^{34} +(0.765131 - 1.32525i) q^{36} +(0.618567 + 0.618567i) q^{37} +(2.52945 + 3.54991i) q^{38} +2.00698i q^{39} +(4.93587 + 2.84972i) q^{41} +(-3.12175 - 0.836470i) q^{42} +(4.23321 - 1.13429i) q^{43} +(4.40557 - 2.54356i) q^{44} +8.38064i q^{46} +(-9.97760 - 2.67349i) q^{47} +(1.17102 + 0.313773i) q^{48} -0.106718i q^{49} +(8.41277 - 4.85711i) q^{51} +(1.59907 - 0.428469i) q^{52} +(6.22361 + 1.66761i) q^{53} +(4.75635 + 2.74608i) q^{54} +2.66584i q^{56} +(-4.30366 + 3.06652i) q^{57} +(-1.21389 - 1.21389i) q^{58} +(7.18753 - 12.4492i) q^{59} +(-2.82198 - 4.88781i) q^{61} +(1.83220 + 6.83787i) q^{62} +(-1.05584 + 3.94044i) q^{63} -1.00000i q^{64} +(3.08362 + 5.34099i) q^{66} +(0.363940 - 1.35824i) q^{67} +(-5.66596 - 5.66596i) q^{68} -10.1601 q^{69} +(-13.2313 - 7.63907i) q^{71} +(0.396061 - 1.47812i) q^{72} +(-1.99861 + 0.535526i) q^{73} +(0.757586 + 0.437393i) q^{74} +(3.36205 + 2.77428i) q^{76} +(-9.58939 + 9.58939i) q^{77} +(0.519445 + 1.93859i) q^{78} +(2.01507 - 3.49020i) q^{79} +(-1.03375 + 1.79051i) q^{81} +(5.50524 + 1.47513i) q^{82} +(-3.12063 - 3.12063i) q^{83} -3.23187 q^{84} +(3.79539 - 2.19127i) q^{86} +(1.47163 - 1.47163i) q^{87} +(3.59713 - 3.59713i) q^{88} +(-5.26392 - 9.11738i) q^{89} +(-3.82198 + 2.20662i) q^{91} +(2.16907 + 8.09508i) q^{92} +(-8.28974 + 2.22123i) q^{93} -10.3296 q^{94} +1.21233 q^{96} +(-10.0259 + 2.68643i) q^{97} +(-0.0276208 - 0.103082i) q^{98} +(6.74168 - 3.89231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{6}+O(q^{10}) \) 32 * q + 4 * q^6	\( 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) \) 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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