LMFDB - Embedded newform 950.2.q.f.407.2

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			407.2
Character	$\chi$	$=$	950.407
Dual form			950.2.q.f.943.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.17102 + 0.313773i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.606164 + 1.04991i) q^{6} +(1.88504 + 1.88504i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.32525 + 0.765131i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.17102 + 0.313773i) 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} +(-0.428469 + 1.59907i) q^{13} +(1.33292 - 2.30869i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-7.73985 + 2.07389i) q^{17} +(1.08206 + 1.08206i) q^{18} +(-1.52448 - 4.08362i) q^{19} +(-2.79888 - 1.61594i) q^{21} +(-1.31664 - 4.91377i) q^{22} +(-8.09508 - 2.16907i) q^{23} +(-1.04991 - 0.606164i) q^{24} +1.65548 q^{26} +(3.88354 - 3.88354i) q^{27} +(-2.57501 - 0.689971i) q^{28} +(0.858351 + 1.48671i) q^{29} +7.07909i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-5.95710 + 1.59620i) q^{33} +(4.00644 + 6.93936i) q^{34} +(0.765131 - 1.32525i) q^{36} +(0.618567 - 0.618567i) q^{37} +(-3.54991 + 2.52945i) q^{38} -2.00698i q^{39} +(4.93587 + 2.84972i) q^{41} +(-0.836470 + 3.12175i) q^{42} +(1.13429 + 4.23321i) q^{43} +(-4.40557 + 2.54356i) q^{44} +8.38064i q^{46} +(-2.67349 + 9.97760i) q^{47} +(-0.313773 + 1.17102i) q^{48} +0.106718i q^{49} +(8.41277 - 4.85711i) q^{51} +(-0.428469 - 1.59907i) q^{52} +(-1.66761 + 6.22361i) q^{53} +(-4.75635 - 2.74608i) q^{54} +2.66584i q^{56} +(3.06652 + 4.30366i) q^{57} +(1.21389 - 1.21389i) q^{58} +(-7.18753 + 12.4492i) q^{59} +(-2.82198 - 4.88781i) q^{61} +(6.83787 - 1.83220i) q^{62} +(-3.94044 - 1.05584i) q^{63} +1.00000i q^{64} +(3.08362 + 5.34099i) q^{66} +(-1.35824 - 0.363940i) q^{67} +(5.66596 - 5.66596i) q^{68} +10.1601 q^{69} +(-13.2313 - 7.63907i) q^{71} +(-1.47812 - 0.396061i) q^{72} +(-0.535526 - 1.99861i) q^{73} +(-0.757586 - 0.437393i) q^{74} +(3.36205 + 2.77428i) q^{76} +(9.58939 + 9.58939i) q^{77} +(-1.93859 + 0.519445i) q^{78} +(-2.01507 + 3.49020i) q^{79} +(-1.03375 + 1.79051i) q^{81} +(1.47513 - 5.50524i) 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} +(8.09508 - 2.16907i) q^{92} +(-2.22123 - 8.28974i) q^{93} +10.3296 q^{94} +1.21233 q^{96} +(2.68643 + 10.0259i) q^{97} +(0.103082 - 0.0276208i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.17102	+	0.313773i	−0.676088	+	0.181157i	−0.580495	−	0.814263i	$-0.697141\pi$
$3$	−1.17102	+	0.313773i	−0.676088	+	0.181157i	−0.0955921	+	0.995421i	$0.530474\pi$
$4$	−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	$-0.0819360\pi$
$7$	1.88504	+	1.88504i	0.712476	+	0.712476i	−0.254576	+	0.967053i	$0.581936\pi$
$8$	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
$13$	−0.428469	+	1.59907i	−0.118836	+	0.443502i	−0.999545	−	0.0301554i	$-0.990400\pi$
$13$	−0.428469	+	1.59907i	−0.118836	+	0.443502i	0.880709	+	0.473657i	$0.157066\pi$
$14$	1.33292	−	2.30869i	0.356238	−	0.617023i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−7.73985	+	2.07389i	−1.87719	+	0.502991i	−0.877461	+	0.479648i	$0.840764\pi$
$17$	−7.73985	+	2.07389i	−1.87719	+	0.502991i	−0.999728	+	0.0233430i	$0.992569\pi$
$18$	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
$22$	−1.31664	−	4.91377i	−0.280709	−	1.04762i
$23$	−8.09508	−	2.16907i	−1.68794	−	0.452282i	−0.718083	−	0.695957i	$-0.754980\pi$
$23$	−8.09508	−	2.16907i	−1.68794	−	0.452282i	−0.969857	+	0.243675i	$0.921647\pi$
$24$	−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
$28$	−2.57501	−	0.689971i	−0.486630	−	0.130392i
$29$	0.858351	+	1.48671i	0.159392	+	0.276075i	0.934649	−	0.355570i	$-0.115713\pi$
$29$	0.858351	+	1.48671i	0.159392	+	0.276075i	−0.775258	+	0.631645i	$0.782380\pi$
$30$		0			0
$31$			7.07909i			1.27144i	0.771919	+	0.635721i	$0.219297\pi$
$31$			7.07909i			1.27144i	−0.771919	+	0.635721i	$0.780703\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−5.95710	+	1.59620i	−1.03700	+	0.277863i
$34$	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	−0.654430	−	0.756122i	$-0.727092\pi$
$37$	0.618567	−	0.618567i	0.101692	−	0.101692i	0.756122	+	0.654430i	$0.227092\pi$
$38$	−3.54991	+	2.52945i	−0.575872	+	0.410331i
$39$		−	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	$0.519852\pi$
$42$	−0.836470	+	3.12175i	−0.129070	+	0.481697i
$43$	1.13429	+	4.23321i	0.172977	+	0.645559i	0.996887	+	0.0788388i	$0.0251212\pi$
$43$	1.13429	+	4.23321i	0.172977	+	0.645559i	−0.823910	+	0.566720i	$0.808212\pi$
$44$	−4.40557	+	2.54356i	−0.664164	+	0.383456i
$45$		0			0
$46$			8.38064i			1.23566i
$47$	−2.67349	+	9.97760i	−0.389968	+	1.45538i	0.440215	+	0.897892i	$0.354902\pi$
$47$	−2.67349	+	9.97760i	−0.389968	+	1.45538i	−0.830184	+	0.557490i	$0.811765\pi$
$48$	−0.313773	+	1.17102i	−0.0452893	+	0.169022i
$49$			0.106718i			0.0152455i
$50$		0			0
$51$	8.41277	−	4.85711i	1.17802	−	0.680132i
$52$	−0.428469	−	1.59907i	−0.0594180	−	0.221751i
$53$	−1.66761	+	6.22361i	−0.229064	+	0.854878i	0.751672	+	0.659538i	$0.229248\pi$
$53$	−1.66761	+	6.22361i	−0.229064	+	0.854878i	−0.980735	+	0.195340i	$0.937419\pi$
$54$	−4.75635	−	2.74608i	−0.647257	−	0.373694i
$55$		0			0
$56$			2.66584i			0.356238i
$57$	3.06652	+	4.30366i	0.406171	+	0.570033i
$58$	1.21389	−	1.21389i	0.159392	−	0.159392i
$59$	−7.18753	+	12.4492i	−0.935736	+	1.62074i	−0.162420	+	0.986722i	$0.551930\pi$
$59$	−7.18753	+	12.4492i	−0.935736	+	1.62074i	−0.773316	+	0.634021i	$0.781403\pi$
$60$		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	$0.951006\pi$
$62$	6.83787	−	1.83220i	0.868411	−	0.232690i
$63$	−3.94044	−	1.05584i	−0.496448	−	0.133023i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.08362	+	5.34099i	0.379568	+	0.657430i
$67$	−1.35824	−	0.363940i	−0.165936	−	0.0444624i	0.174895	−	0.984587i	$-0.444042\pi$
$67$	−1.35824	−	0.363940i	−0.165936	−	0.0444624i	−0.340830	+	0.940125i	$0.610708\pi$
$68$	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	$-0.694658\pi$
$72$	−1.47812	−	0.396061i	−0.174198	−	0.0466763i
$73$	−0.535526	−	1.99861i	−0.0626786	−	0.233920i	0.927479	−	0.373874i	$-0.121971\pi$
$73$	−0.535526	−	1.99861i	−0.0626786	−	0.233920i	−0.990158	+	0.139955i	$0.955304\pi$
$74$	−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
$78$	−1.93859	+	0.519445i	−0.219503	+	0.0588155i
$79$	−2.01507	+	3.49020i	−0.226713	+	0.392678i	−0.956832	−	0.290642i	$-0.906131\pi$
$79$	−2.01507	+	3.49020i	−0.226713	+	0.392678i	0.730119	+	0.683320i	$0.239464\pi$
$80$		0			0
$81$	−1.03375	+	1.79051i	−0.114861	+	0.198946i
$82$	1.47513	−	5.50524i	0.162900	−	0.607952i
$83$	3.12063	−	3.12063i	0.342534	−	0.342534i	−0.514785	−	0.857319i	$-0.672128\pi$
$83$	3.12063	−	3.12063i	0.342534	−	0.342534i	0.857319	+	0.514785i	$0.172128\pi$
$84$	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	$0.0217546\pi$
$89$	5.26392	+	9.11738i	0.557974	+	0.966440i	−0.439691	+	0.898149i	$0.644912\pi$
$90$		0			0
$91$	−3.82198	+	2.20662i	−0.400652	+	0.231317i
$92$	8.09508	−	2.16907i	0.843970	−	0.226141i
$93$	−2.22123	−	8.28974i	−0.230331	−	0.859606i
$94$	10.3296			1.06541
$95$		0			0
$96$	1.21233			0.123733
$97$	2.68643	+	10.0259i	0.272766	+	1.01798i	0.957324	+	0.289017i	$0.0933285\pi$
$97$	2.68643	+	10.0259i	0.272766	+	1.01798i	−0.684558	+	0.728958i	$0.740005\pi$
$98$	0.103082	−	0.0276208i	0.0104129	−	0.00279012i
$99$	−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	0.947741	−	0.319041i	$-0.103361\pi$
$103$	6.38060	+	6.38060i	0.628699	+	0.628699i	−0.319041	+	0.947741i	$0.603361\pi$
$104$	−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	−0.948842	−	0.315750i	$-0.897744\pi$
$107$	−6.54875	+	6.54875i	−0.633092	+	0.633092i	0.315750	+	0.948842i	$0.397744\pi$
$108$	−1.42148	+	5.30502i	−0.136782	+	0.510476i
$109$	−2.10586	+	3.64745i	−0.201705	+	0.349363i	−0.949078	−	0.315042i	$-0.897981\pi$
$109$	−2.10586	+	3.64745i	−0.201705	+	0.349363i	0.747373	+	0.664404i	$0.231315\pi$
$110$		0			0
$111$	−0.530263	+	0.918442i	−0.0503303	+	0.0871747i
$112$	2.57501	−	0.689971i	0.243315	−	0.0651961i
$113$	−6.93263	−	6.93263i	−0.652167	−	0.652167i	0.301347	−	0.953515i	$-0.402564\pi$
$113$	−6.93263	−	6.93263i	−0.652167	−	0.652167i	−0.953515	+	0.301347i	$0.902564\pi$
$114$	3.36334	−	4.07590i	0.315005	−	0.381743i
$115$		0			0
$116$	−1.48671	−	0.858351i	−0.138037	−	0.0796958i
$117$	−0.655670	−	2.44700i	−0.0606168	−	0.226225i
$118$	13.8852	+	3.72054i	1.27824	+	0.342503i
$119$	−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
$123$	−6.67416	−	1.78833i	−0.601788	−	0.161249i
$124$	−3.53954	−	6.13067i	−0.317860	−	0.550550i
$125$		0			0
$126$			4.07944i			0.363425i
$127$	−11.4266	−	3.06175i	−1.01395	−	0.271687i	−0.286670	−	0.958029i	$-0.592548\pi$
$127$	−11.4266	−	3.06175i	−1.01395	−	0.271687i	−0.727278	+	0.686343i	$0.759215\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−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
$133$	4.82408	−	10.5715i	0.418301	−	0.916662i
$134$			1.40616i			0.121474i
$135$		0			0
$136$	−6.93936	−	4.00644i	−0.595045	−	0.343549i
$137$	4.44559	−	16.5912i	0.379812	−	1.41748i	−0.466373	−	0.884588i	$-0.654439\pi$
$137$	4.44559	−	16.5912i	0.379812	−	1.41748i	0.846185	−	0.532890i	$-0.178894\pi$
$138$	−2.62962	−	9.81388i	−0.223848	−	0.835413i
$139$	11.7743	−	6.79791i	0.998686	−	0.576591i	0.0908265	−	0.995867i	$-0.471049\pi$
$139$	11.7743	−	6.79791i	0.998686	−	0.576591i	0.907859	+	0.419275i	$0.137716\pi$
$140$		0			0
$141$		−	12.5228i		−	1.05461i
$142$	−3.95427	+	14.7576i	−0.331835	+	1.23843i
$143$	−2.17967	+	8.13464i	−0.182273	+	0.680253i
$144$			1.53026i			0.127522i
$145$		0			0
$146$	−1.79190	+	1.03456i	−0.148299	+	0.0856205i
$147$	−0.0334854	−	0.124969i	−0.00276183	−	0.0103073i
$148$	−0.226411	+	0.844978i	−0.0186109	+	0.0694567i
$149$	8.23647	+	4.75533i	0.674758	+	0.389572i	0.797877	−	0.602820i	$-0.205956\pi$
$149$	8.23647	+	4.75533i	0.674758	+	0.389572i	−0.123119	+	0.992392i	$0.539290\pi$
$150$		0			0
$151$			6.21129i			0.505468i	0.967536	+	0.252734i	$0.0813297\pi$
$151$			6.21129i			0.505468i	−0.967536	+	0.252734i	$0.918670\pi$
$152$	1.80959	−	3.96552i	0.146777	−	0.321647i
$153$	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
$157$	13.8408	−	3.70862i	1.10461	−	0.295980i	0.339971	−	0.940436i	$-0.389583\pi$
$157$	13.8408	−	3.70862i	1.10461	−	0.295980i	0.764641	+	0.644456i	$0.222916\pi$
$158$	3.89281	+	1.04308i	0.309695	+	0.0829826i
$159$		−	7.81121i		−	0.619469i
$160$		0			0
$161$	−11.1707	−	19.3483i	−0.880377	−	1.52486i
$162$	1.99706	+	0.535110i	0.156904	+	0.0420422i
$163$	1.78065	−	1.78065i	0.139471	−	0.139471i	−0.633924	−	0.773395i	$-0.718557\pi$
$163$	1.78065	−	1.78065i	0.139471	−	0.139471i	0.773395	+	0.633924i	$0.218557\pi$
$164$	−5.69945			−0.445052
$165$		0			0
$166$	−3.82198	−	2.20662i	−0.296643	−	0.171267i
$167$	12.9661	+	3.47427i	1.00335	+	0.268847i	0.722849	−	0.691006i	$-0.242832\pi$
$167$	12.9661	+	3.47427i	1.00335	+	0.268847i	0.280502	+	0.959853i	$0.409499\pi$
$168$	−0.836470	−	3.12175i	−0.0645351	−	0.240848i
$169$	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
$173$	9.98909	−	2.67657i	0.759457	−	0.203496i	0.141748	−	0.989903i	$-0.454728\pi$
$173$	9.98909	−	2.67657i	0.759457	−	0.203496i	0.617709	+	0.786407i	$0.288061\pi$
$174$	−1.04060	+	1.80237i	−0.0788878	+	0.136638i
$175$		0			0
$176$	2.54356	−	4.40557i	0.191728	−	0.332082i
$177$	4.51051	−	16.8334i	0.339031	−	1.26528i
$178$	7.44431	−	7.44431i	0.557974	−	0.557974i
$179$	−15.2968			−1.14333			−0.571666	−	0.820486i	$-0.693703\pi$
$179$	−15.2968			−1.14333			−0.571666	+	0.820486i	$0.693703\pi$
$180$		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
$187$	−39.3735	+	10.5501i	−2.87927	+	0.771499i
$188$	−2.67349	−	9.97760i	−0.194984	−	0.727691i
$189$	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	$0.674723\pi$
$192$	−0.313773	−	1.17102i	−0.0226446	−	0.0845109i
$193$	7.42030	−	1.98826i	0.534125	−	0.143118i	0.0183327	−	0.999832i	$-0.494164\pi$
$193$	7.42030	−	1.98826i	0.534125	−	0.143118i	0.515793	+	0.856714i	$0.327498\pi$
$194$	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	−0.997236	−	0.0742953i	$-0.976329\pi$
$197$	−15.0397	−	15.0397i	−1.07153	−	1.07153i	−0.0742953	−	0.997236i	$-0.523671\pi$
$198$	5.50456	+	5.50456i	0.391192	+	0.391192i
$199$	3.99272	−	2.30520i	0.283036	−	0.163411i	−0.351761	−	0.936090i	$-0.614417\pi$
$199$	3.99272	−	2.30520i	0.283036	−	0.163411i	0.634797	+	0.772679i	$0.281084\pi$
$200$		0			0
$201$	1.70472			0.120242
$202$	−4.67426	+	4.67426i	−0.328879	+	0.328879i
$203$	−1.18447	+	4.42052i	−0.0831338	+	0.310259i
$204$	−4.85711	+	8.41277i	−0.340066	+	0.589012i
$205$		0			0
$206$	4.51177	−	7.81461i	0.314350	−	0.544470i
$207$	12.3876	−	3.31925i	0.860997	−	0.230704i
$208$	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	$0.691872\pi$
$212$	−1.66761	−	6.22361i	−0.114532	−	0.427439i
$213$	17.8910	+	4.79387i	1.22587	+	0.328471i
$214$	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
$218$	4.06820	+	1.09007i	0.275534	+	0.0738290i
$219$	1.25422	+	2.17237i	0.0847524	+	0.146795i
$220$		0			0
$221$		−	13.2651i		−	0.892310i
$222$	1.02439	+	0.274484i	0.0687525	+	0.0184222i
$223$	19.9298	−	5.34017i	1.33460	−	0.357604i	0.480169	−	0.877176i	$-0.340575\pi$
$223$	19.9298	−	5.34017i	1.33460	−	0.357604i	0.854427	+	0.519572i	$0.173909\pi$
$224$	−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	−0.779789	−	0.626043i	$-0.784674\pi$
$227$	−2.31642	+	2.31642i	−0.153746	+	0.153746i	0.626043	+	0.779789i	$0.284674\pi$
$228$	−4.80751	−	2.19381i	−0.318385	−	0.145289i
$229$			7.45517i			0.492651i	0.969187	+	0.246326i	$0.0792233\pi$
$229$			7.45517i			0.492651i	−0.969187	+	0.246326i	$0.920777\pi$
$230$		0			0
$231$	−14.2382	−	8.22045i	−0.936807	−	0.540866i
$232$	−0.444315	+	1.65821i	−0.0291707	+	0.108867i
$233$	2.91830	+	10.8912i	0.191184	+	0.713509i	0.993222	+	0.116236i	$0.0370828\pi$
$233$	2.91830	+	10.8912i	0.191184	+	0.713509i	−0.802037	+	0.597274i	$0.796251\pi$
$234$	−2.19392	+	1.26666i	−0.143421	+	0.0828040i
$235$		0			0
$236$		−	14.3751i		−	0.935736i
$237$	1.26455	−	4.71936i	0.0821412	−	0.306555i
$238$	−5.52865	+	20.6332i	−0.358369	+	1.33745i
$239$		−	13.3826i		−	0.865650i	−0.901478	−	0.432825i	$-0.857517\pi$
$239$		−	13.3826i		−	0.865650i	0.901478	−	0.432825i	$-0.142483\pi$
$240$		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	$0.539166\pi$
$242$	−3.85089	−	14.3717i	−0.247545	−	0.923850i
$243$	−3.61570	+	13.4940i	−0.231947	+	0.865639i
$244$	4.88781	+	2.82198i	0.312910	+	0.180659i
$245$		0			0
$246$			6.90959i			0.440540i
$247$	7.18318	−	0.688037i	0.457055	−	0.0437788i
$248$	−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	$0.636990\pi$
$252$	3.94044	−	1.05584i	0.248224	−	0.0665115i
$253$	−41.1806	−	11.0343i	−2.58900	−	0.693720i
$254$			11.8297i			0.742262i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.49161	+	0.399675i	0.0930438	+	0.0249310i	0.305041	−	0.952339i	$-0.401330\pi$
$257$	1.49161	+	0.399675i	0.0930438	+	0.0249310i	−0.211997	+	0.977270i	$0.567997\pi$
$258$	−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
$262$	5.60833	+	1.50275i	0.346484	+	0.0928400i
$263$	0.289870	+	1.08181i	0.0178741	+	0.0667072i	0.974287	−	0.225311i	$-0.0723398\pi$
$263$	0.289870	+	1.08181i	0.0178741	+	0.0667072i	−0.956413	+	0.292018i	$0.905673\pi$
$264$	−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
$268$	1.35824	−	0.363940i	0.0829680	−	0.0222312i
$269$	1.94303	−	3.36542i	0.118468	−	0.205193i	−0.800693	−	0.599076i	$-0.795535\pi$
$269$	1.94303	−	3.36542i	0.118468	−	0.205193i	0.919161	+	0.393882i	$0.128868\pi$
$270$		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	$0.137745\pi$
$272$	−2.07389	+	7.73985i	−0.125748	+	0.469297i
$273$	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	$-0.0124146\pi$
$277$	15.9817	+	15.9817i	0.960248	+	0.960248i	−0.0389918	+	0.999240i	$0.512415\pi$
$278$	−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	$0.0817385\pi$
$282$	−12.0961	+	3.24114i	−0.720313	+	0.193007i
$283$	2.27736	+	8.49923i	0.135375	+	0.505227i	0.999996	+	0.00280196i	$0.000891893\pi$
$283$	2.27736	+	8.49923i	0.135375	+	0.505227i	−0.864621	+	0.502425i	$0.832441\pi$
$284$	15.2781			0.906591
$285$		0			0
$286$	8.42160			0.497980
$287$	3.93245	+	14.6761i	0.232125	+	0.866304i
$288$	1.47812	−	0.396061i	0.0870991	−	0.0233381i
$289$	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	0.168619	−	0.985681i	$-0.446069\pi$
$293$	−13.9858	−	13.9858i	−0.817062	−	0.817062i	−0.985681	+	0.168619i	$0.946069\pi$
$294$	−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
$298$	2.46154	−	9.18659i	0.142593	−	0.532165i
$299$	6.93698	−	12.0152i	0.401176	−	0.694857i
$300$		0			0
$301$	−5.84159	+	10.1179i	−0.336703	+	0.583188i
$302$	5.99964	−	1.60760i	0.345241	−	0.0925070i
$303$	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
$307$	−3.20378	−	11.9567i	−0.182849	−	0.682404i	−0.995081	−	0.0990679i	$-0.968414\pi$
$307$	−3.20378	−	11.9567i	−0.182849	−	0.682404i	0.812231	−	0.583336i	$-0.198253\pi$
$308$	−13.0993	−	3.50996i	−0.746405	−	0.199999i
$309$	−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
$313$	−4.04681	−	1.08434i	−0.228739	−	0.0612904i	0.142629	−	0.989776i	$-0.454444\pi$
$313$	−4.04681	−	1.08434i	−0.228739	−	0.0612904i	−0.371368	+	0.928486i	$0.621111\pi$
$314$	−7.16450	−	12.4093i	−0.404316	−	0.700296i
$315$		0			0
$316$		−	4.03013i		−	0.226713i
$317$	−8.14871	−	2.18344i	−0.457677	−	0.122634i	0.0226121	−	0.999744i	$-0.492802\pi$
$317$	−8.14871	−	2.18344i	−0.457677	−	0.122634i	−0.480290	+	0.877110i	$0.659468\pi$
$318$	−7.54505	+	2.02169i	−0.423105	+	0.113371i
$319$	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
$323$	20.2682	+	28.4450i	1.12775	+	1.58272i
$324$		−	2.06751i		−	0.114861i
$325$		0			0
$326$	−2.18084	−	1.25911i	−0.120786	−	0.0697356i
$327$	1.32152	−	4.93199i	0.0730804	−	0.272740i
$328$	1.47513	+	5.50524i	0.0814502	+	0.303976i
$329$	−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	$-0.0852230\pi$
$332$	−1.14223	+	4.26287i	−0.0626881	+	0.233955i
$333$	−0.346469	+	1.29304i	−0.0189864	+	0.0708580i
$334$		−	13.4235i		−	0.734504i
$335$		0			0
$336$	−2.79888	+	1.61594i	−0.152692	+	0.0881566i
$337$	−0.951182	−	3.54986i	−0.0518142	−	0.193373i	0.935168	−	0.354206i	$-0.115249\pi$
$337$	−0.951182	−	3.54986i	−0.0518142	−	0.193373i	−0.986982	+	0.160833i	$0.948582\pi$
$338$	2.65533	−	9.90981i	0.144431	−	0.539023i
$339$	10.2935	+	5.94296i	0.559067	+	0.322778i
$340$		0			0
$341$			36.0121i			1.95016i
$342$	2.76915	−	6.06830i	0.149738	−	0.328136i
$343$	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
$347$	0.415829	−	0.111421i	0.0223228	−	0.00598139i	−0.247640	−	0.968852i	$-0.579655\pi$
$347$	0.415829	−	0.111421i	0.0223228	−	0.00598139i	0.269963	+	0.962871i	$0.412988\pi$
$348$	2.01029	+	0.538655i	0.107763	+	0.0288749i
$349$			11.4552i			0.613181i	0.951841	+	0.306591i	$0.0991882\pi$
$349$			11.4552i			0.613181i	−0.951841	+	0.306591i	$0.900812\pi$
$350$		0			0
$351$	4.54607	+	7.87403i	0.242652	+	0.420285i
$352$	−4.91377	−	1.31664i	−0.261905	−	0.0701772i
$353$	21.7675	−	21.7675i	1.15857	−	1.15857i	0.173784	−	0.984784i	$-0.444400\pi$
$353$	21.7675	−	21.7675i	1.15857	−	1.15857i	0.984784	−	0.173784i	$-0.0555996\pi$
$354$	−17.4273			−0.926249
$355$		0			0
$356$	−9.11738	−	5.26392i	−0.483220	−	0.278987i
$357$	25.0142	+	6.70254i	1.32389	+	0.354736i
$358$	3.95909	+	14.7755i	0.209244	+	0.780911i
$359$	−32.2397	−	18.6136i	−1.70154	−	0.982387i	−0.944201	−	0.329371i	$-0.893163\pi$
$359$	−32.2397	−	18.6136i	−1.70154	−	0.982387i	−0.757344	−	0.653016i	$-0.773503\pi$
$360$		0			0
$361$	−14.3519	+	12.4508i	−0.755365	+	0.655304i
$362$	10.9231	+	10.9231i	0.574107	+	0.574107i
$363$	−17.4232	+	4.66854i	−0.914483	+	0.245035i
$364$	2.20662	−	3.82198i	0.115658	−	0.200326i
$365$		0			0
$366$	3.42116	−	5.92563i	0.178827	−	0.309738i
$367$	−0.242527	+	0.905122i	−0.0126598	+	0.0472470i	−0.971967	−	0.235118i	$-0.924452\pi$
$367$	−0.242527	+	0.905122i	−0.0126598	+	0.0472470i	0.959307	+	0.282365i	$0.0911190\pi$
$368$	−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	0.998730	−	0.0503814i	$-0.0160437\pi$
$373$	18.3157	+	18.3157i	0.948349	+	0.948349i	−0.0503814	+	0.998730i	$0.516044\pi$
$374$	20.3812	+	35.3013i	1.05389	+	1.82539i
$375$		0			0
$376$	−8.94567	+	5.16478i	−0.461338	+	0.266353i
$377$	−2.74512	+	0.735553i	−0.141381	+	0.0378829i
$378$	−3.78943	−	14.1423i	−0.194907	−	0.727404i
$379$	32.8155			1.68562			0.842810	−	0.538211i	$-0.180900\pi$
$379$	32.8155			1.68562			0.842810	+	0.538211i	$0.180900\pi$
$380$		0			0
$381$	14.3415			0.734736
$382$	3.73259	+	13.9302i	0.190976	+	0.712731i
$383$	10.4707	−	2.80563i	0.535030	−	0.143361i	0.0188199	−	0.999823i	$-0.494009\pi$
$383$	10.4707	−	2.80563i	0.535030	−	0.143361i	0.516210	+	0.856462i	$0.327342\pi$
$384$	−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	−0.893460	−	0.449143i	$-0.851729\pi$
$389$	−18.7610	+	10.8317i	−0.951220	+	0.549187i	−0.0577605	+	0.998330i	$0.518396\pi$
$390$		0			0
$391$	67.1530			3.39608
$392$	−0.0754613	+	0.0754613i	−0.00381137	+	0.00381137i
$393$	1.82182	−	6.79913i	0.0918987	−	0.342971i
$394$	−10.6346	+	18.4198i	−0.535766	+	0.927974i
$395$		0			0
$396$	3.89231	−	6.74168i	0.195596	−	0.338782i
$397$	24.0130	−	6.43427i	1.20518	−	0.322927i	0.400310	−	0.916380i	$-0.368902\pi$
$397$	24.0130	−	6.43427i	1.20518	−	0.322927i	0.804869	+	0.593453i	$0.202236\pi$
$398$	−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	$0.406897\pi$
$402$	−0.441215	−	1.64664i	−0.0220058	−	0.0821268i
$403$	−11.3199	−	3.03317i	−0.563887	−	0.151093i
$404$	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
$408$	9.38323	+	2.51423i	0.464539	+	0.124473i
$409$	6.42063	+	11.1209i	0.317480	+	0.549891i	0.979962	−	0.199187i	$-0.0638300\pi$
$409$	6.42063	+	11.1209i	0.317480	+	0.549891i	−0.662482	+	0.749078i	$0.730497\pi$
$410$		0			0
$411$			20.8234i			1.02714i
$412$	−8.71606	−	2.33546i	−0.429410	−	0.115060i
$413$	−37.0158	+	9.91837i	−1.82143	+	0.488051i
$414$	−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
$418$	−18.0588	+	12.8676i	−0.883285	+	0.629375i
$419$			17.7916i			0.869177i	0.900629	+	0.434588i	$0.143106\pi$
$419$			17.7916i			0.869177i	−0.900629	+	0.434588i	$0.856894\pi$
$420$		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	$0.354709\pi$
$422$	−0.594787	+	2.21978i	−0.0289538	+	0.108057i
$423$	−4.09114	−	15.2683i	−0.198918	−	0.742372i
$424$	−5.57993	+	3.22158i	−0.270985	+	0.156454i
$425$		0			0
$426$		−	18.5221i		−	0.897399i
$427$	3.89417	−	14.5332i	0.188452	−	0.703313i
$428$	2.39701	−	8.94576i	0.115864	−	0.432410i
$429$		−	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	$0.134172\pi$
$432$	−1.42148	−	5.30502i	−0.0683908	−	0.255238i
$433$	6.67057	−	24.8949i	0.320567	−	1.19637i	−0.598126	−	0.801402i	$-0.704088\pi$
$433$	6.67057	−	24.8949i	0.320567	−	1.19637i	0.918694	−	0.394971i	$-0.129245\pi$
$434$	16.3434	+	9.43587i	0.784508	+	0.452936i
$435$		0			0
$436$		−	4.21171i		−	0.201705i
$437$	3.48310	+	36.3639i	0.166619	+	1.73952i
$438$	1.77374	−	1.77374i	0.0847524	−	0.0847524i
$439$	−0.512599	+	0.887848i	−0.0244650	+	0.0423747i	−0.877999	−	0.478663i	$-0.841122\pi$
$439$	−0.512599	+	0.887848i	−0.0244650	+	0.0423747i	0.853534	+	0.521038i	$0.174455\pi$
$440$		0			0
$441$	−0.0816536	−	0.141428i	−0.00388827	−	0.00673468i
$442$	−12.8131	+	3.43327i	−0.609459	+	0.163304i
$443$	−8.01308	−	2.14710i	−0.380713	−	0.102012i	0.0633869	−	0.997989i	$-0.479810\pi$
$443$	−8.01308	−	2.14710i	−0.380713	−	0.102012i	−0.444100	+	0.895977i	$0.646476\pi$
$444$		−	1.06053i		−	0.0503303i
$445$		0			0
$446$	−10.3164	−	17.8685i	−0.488496	−	0.846100i
$447$	−11.1372	−	2.98419i	−0.526769	−	0.141147i
$448$	−1.88504	+	1.88504i	−0.0890596	+	0.0890596i
$449$	19.6032			0.925134			0.462567	−	0.886584i	$-0.346928\pi$
$449$	19.6032			0.925134			0.462567	+	0.886584i	$0.346928\pi$
$450$		0			0
$451$	25.1093	+	14.4969i	1.18235	+	0.682631i
$452$	9.47015	+	2.53752i	0.445439	+	0.119355i
$453$	−1.94894	−	7.27353i	−0.0915691	−	0.341740i
$454$	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	$-0.473179\pi$
$457$	−19.5026	−	19.5026i	−0.912293	−	0.912293i	−0.996452	+	0.0841597i	$0.973179\pi$
$458$	7.20114	−	1.92954i	0.336487	−	0.0901615i
$459$	−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	$0.109284\pi$
$462$	−4.25522	+	15.8807i	−0.197971	+	0.738837i
$463$	−12.6250	+	12.6250i	−0.586735	+	0.586735i	−0.936746	−	0.350010i	$-0.886178\pi$
$463$	−12.6250	+	12.6250i	−0.586735	+	0.586735i	0.350010	+	0.936746i	$0.386178\pi$
$464$	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	$-0.133526\pi$
$467$	10.9349	+	10.9349i	0.506008	+	0.506008i	−0.407291	+	0.913299i	$0.633526\pi$
$468$	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
$472$	−13.8852	+	3.72054i	−0.639120	+	0.171252i
$473$	5.77024	+	21.5348i	0.265316	+	0.990172i
$474$	−4.88584			−0.224414
$475$		0			0
$476$	21.3611			0.979083
$477$	−2.55188	−	9.52375i	−0.116843	−	0.436063i
$478$	−12.9266	+	3.46368i	−0.591250	+	0.158425i
$479$	2.12792	−	1.22856i	0.0972272	−	0.0561341i	−0.450598	−	0.892727i	$-0.648789\pi$
$479$	2.12792	−	1.22856i	0.0972272	−	0.0561341i	0.547825	+	0.836593i	$0.315456\pi$
$480$		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	−0.852597	−	0.522569i	$-0.824974\pi$
$487$	−7.28307	+	7.28307i	−0.330027	+	0.330027i	0.522569	+	0.852597i	$0.324974\pi$
$488$	1.46076	−	5.45165i	0.0661257	−	0.246785i
$489$	−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	$0.323018\pi$
$492$	6.67416	−	1.78833i	0.300894	−	0.0806244i
$493$	−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
$497$	−10.5415	−	39.3413i	−0.472850	−	1.76470i
$498$	5.16799	+	1.38476i	0.231583	+	0.0620525i
$499$	−24.1791	−	13.9598i	−1.08241	−	0.624927i	−0.150861	−	0.988555i	$-0.548205\pi$
$499$	−24.1791	−	13.9598i	−1.08241	−	0.624927i	−0.931544	+	0.363628i	$0.881538\pi$
$500$		0			0
$501$	−16.2737			−0.727057
$502$	12.9604	−	12.9604i	0.578453	−	0.578453i
$503$	−0.741405	−	0.198659i	−0.0330576	−	0.00885777i	0.242252	−	0.970213i	$-0.422114\pi$
$503$	−0.741405	−	0.198659i	−0.0330576	−	0.00885777i	−0.275310	+	0.961356i	$0.588780\pi$
$504$	−2.03972	−	3.53290i	−0.0908564	−	0.157368i
$505$		0			0
$506$			42.6333i			1.89528i
$507$	−12.0139	−	3.21912i	−0.533558	−	0.142966i
$508$	11.4266	−	3.06175i	0.506974	−	0.135843i
$509$	9.55337	+	16.5469i	0.423446	+	0.733430i	0.996274	−	0.0862459i	$-0.0274871\pi$
$509$	9.55337	+	16.5469i	0.423446	+	0.733430i	−0.572828	+	0.819676i	$0.694154\pi$
$510$		0			0
$511$	2.75796	−	4.77694i	0.122005	−	0.211319i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−21.7793	−	9.93855i	−0.961580	−	0.438798i
$514$		−	1.54422i		−	0.0681128i
$515$		0			0
$516$	4.60126	+	2.65654i	0.202559	+	0.116948i
$517$	−13.6003	+	50.7572i	−0.598142	+	2.23230i
$518$	−0.603576	−	2.25258i	−0.0265196	−	0.0989726i
$519$	−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	$-0.119045\pi$
$522$	−0.679919	+	2.53749i	−0.0297592	+	0.111063i
$523$	−2.10296	+	7.84835i	−0.0919560	+	0.343185i	−0.996540	−	0.0831101i	$-0.973515\pi$
$523$	−2.10296	+	7.84835i	−0.0919560	+	0.343185i	0.904584	+	0.426295i	$0.140181\pi$
$524$		−	5.80617i		−	0.253644i
$525$		0			0
$526$	0.969923	−	0.559985i	0.0422907	−	0.0244165i
$527$	−14.6812	−	54.7910i	−0.639524	−	2.38674i
$528$	−1.59620	+	5.95710i	−0.0694657	+	0.259250i
$529$	40.9068	+	23.6176i	1.77856	+	1.02685i
$530$		0			0
$531$		−	21.9976i		−	0.954615i
$532$	1.10796	+	11.5672i	0.0480361	+	0.501502i
$533$	−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
$537$	17.9128	−	4.79971i	0.772993	−	0.207123i
$538$	−3.75364	−	1.00578i	−0.161831	−	0.0433624i
$539$			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	$0.867796\pi$
$542$	−2.88558	−	0.773189i	−0.123946	−	0.0332113i
$543$	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
$547$	41.0987	+	11.0124i	1.75725	+	0.470855i	0.986150	−	0.165854i	$-0.0530382\pi$
$547$	41.0987	+	11.0124i	1.75725	+	0.470855i	0.771104	+	0.636709i	$0.219705\pi$
$548$	4.44559	+	16.5912i	0.189906	+	0.708739i
$549$	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
$553$	−10.3776	+	2.78067i	−0.441301	+	0.118246i
$554$	11.3008	−	19.5735i	0.480124	−	0.831599i
$555$		0			0
$556$	−6.79791	+	11.7743i	−0.288296	+	0.499343i
$557$	9.69165	−	36.1697i	0.410648	−	1.53256i	−0.382747	−	0.923853i	$-0.625022\pi$
$557$	9.69165	−	36.1697i	0.410648	−	1.53256i	0.793395	−	0.608707i	$-0.208312\pi$
$558$	−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	0.766641	−	0.642076i	$-0.221927\pi$
$563$	2.95561	+	2.95561i	0.124564	+	0.124564i	−0.642076	+	0.766641i	$0.721927\pi$
$564$	6.26141	+	10.8451i	0.263653	+	0.456660i
$565$		0			0
$566$	7.62020	−	4.39952i	0.320301	−	0.184926i
$567$	−5.32384	+	1.42652i	−0.223580	+	0.0599082i
$568$	−3.95427	−	14.7576i	−0.165918	−	0.619213i
$569$	−8.11963			−0.340393			−0.170196	−	0.985410i	$-0.554440\pi$
$569$	−8.11963			−0.340393			−0.170196	+	0.985410i	$0.554440\pi$
$570$		0			0
$571$	−30.5277			−1.27754			−0.638772	−	0.769396i	$-0.720557\pi$
$571$	−30.5277			−1.27754			−0.638772	+	0.769396i	$0.720557\pi$
$572$	−2.17967	−	8.13464i	−0.0911366	−	0.340126i
$573$	16.8880	−	4.52511i	0.705504	−	0.189039i
$574$	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	$-0.285251\pi$
$577$	−3.75441	−	3.75441i	−0.156298	−	0.156298i	−0.780924	+	0.624626i	$0.785251\pi$
$578$	−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
$583$	−8.48332	+	31.6602i	−0.351343	+	1.31123i
$584$	1.03456	−	1.79190i	0.0428102	−	0.0741495i
$585$		0			0
$586$	−9.88949	+	17.1291i	−0.408531	+	0.707596i
$587$	−1.96581	+	0.526737i	−0.0811376	+	0.0217407i	−0.299159	−	0.954203i	$-0.596706\pi$
$587$	−1.96581	+	0.526737i	−0.0811376	+	0.0217407i	0.218022	+	0.975944i	$0.430040\pi$
$588$	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
$592$	−0.226411	−	0.844978i	−0.00930544	−	0.0347284i
$593$	−13.5745	−	3.63727i	−0.557437	−	0.149365i	−0.0309085	−	0.999522i	$-0.509840\pi$
$593$	−13.5745	−	3.63727i	−0.557437	−	0.149365i	−0.526529	+	0.850157i	$0.676507\pi$
$594$	−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
$598$	−13.4012	−	3.59085i	−0.548017	−	0.146841i
$599$	−20.6686	−	35.7990i	−0.844495	−	1.46271i	−0.886059	−	0.463573i	$-0.846567\pi$
$599$	−20.6686	−	35.7990i	−0.844495	−	1.46271i	0.0415632	−	0.999136i	$-0.486766\pi$
$600$		0			0
$601$			41.7390i			1.70257i	0.524704	+	0.851285i	$0.324176\pi$
$601$			41.7390i			1.70257i	−0.524704	+	0.851285i	$0.675824\pi$
$602$	11.2851	+	3.02383i	0.459945	+	0.123242i
$603$	2.07847	−	0.556925i	0.0846419	−	0.0226797i
$604$	−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	−0.954660	−	0.297697i	$-0.903781\pi$
$607$	−16.1858	+	16.1858i	−0.656963	+	0.656963i	0.297697	+	0.954660i	$0.403781\pi$
$608$	0.415613	+	4.33904i	0.0168553	+	0.175971i
$609$		−	5.54816i		−	0.224823i
$610$		0			0
$611$	−14.8094	−	8.55019i	−0.599122	−	0.345903i
$612$	−3.17359	+	11.8440i	−0.128285	+	0.478765i
$613$	−5.15626	−	19.2434i	−0.208260	−	0.777235i	−0.988431	−	0.151670i	$-0.951535\pi$
$613$	−5.15626	−	19.2434i	−0.208260	−	0.777235i	0.780172	−	0.625566i	$-0.215132\pi$
$614$	−10.7201	+	6.18923i	−0.432627	+	0.249777i
$615$		0			0
$616$			13.5614i			0.546406i
$617$	−4.01870	+	14.9980i	−0.161787	+	0.603796i	0.836642	+	0.547751i	$0.184516\pi$
$617$	−4.01870	+	14.9980i	−0.161787	+	0.603796i	−0.998428	+	0.0560454i	$0.982151\pi$
$618$	−2.83134	+	10.5667i	−0.113893	+	0.425056i
$619$		−	32.8578i		−	1.32067i	−0.750973	−	0.660333i	$-0.770415\pi$
$619$		−	32.8578i		−	1.32067i	0.750973	−	0.660333i	$-0.229585\pi$
$620$		0			0
$621$	−39.8613	+	23.0139i	−1.59958	+	0.923516i
$622$	3.35580	+	12.5240i	0.134555	+	0.502168i
$623$	−7.26390	+	27.1093i	−0.291022	+	1.08611i
$624$	−1.73810	−	1.00349i	−0.0695795	−	0.0401718i
$625$		0			0
$626$			4.18956i			0.167449i
$627$	15.5997	+	21.8932i	0.622994	+	0.874329i
$628$	−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	$0.611157\pi$
$632$	−3.89281	+	1.04308i	−0.154848	+	0.0414913i
$633$	2.69110	+	0.721077i	0.106961	+	0.0286602i
$634$			8.43617i			0.335043i
$635$		0			0
$636$	3.90560	+	6.76470i	0.154867	+	0.268238i
$637$	−0.170650	−	0.0457255i	−0.00676140	−	0.00181171i
$638$	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	$0.703559\pi$
$642$	−10.8452	−	2.90596i	−0.428026	−	0.114689i
$643$	−2.86125	−	10.6783i	−0.112837	−	0.421113i	0.886279	−	0.463151i	$-0.153281\pi$
$643$	−2.86125	−	10.6783i	−0.112837	−	0.421113i	−0.999116	+	0.0420388i	$0.986615\pi$
$644$	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	$-0.0170703\pi$
$647$	24.0362	+	24.0362i	0.944960	+	0.944960i	−0.0536023	+	0.998562i	$0.517070\pi$
$648$	−1.99706	+	0.535110i	−0.0784518	+	0.0210211i
$649$	−36.5637	+	63.3303i	−1.43525	+	2.48593i
$650$		0			0
$651$	11.4394	−	19.8135i	0.448344	−	0.776554i
$652$	−0.651763	+	2.43241i	−0.0255250	+	0.0952606i
$653$	−2.19175	+	2.19175i	−0.0857697	+	0.0857697i	−0.748690	−	0.662920i	$-0.769317\pi$
$653$	−2.19175	+	2.19175i	−0.0857697	+	0.0857697i	0.662920	+	0.748690i	$0.269317\pi$
$654$	−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	0.824218	−	0.566273i	$-0.191615\pi$
$659$	−2.00998	−	3.48139i	−0.0782978	−	0.135616i	−0.902516	+	0.430657i	$0.858282\pi$
$660$		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	$0.401500\pi$
$662$	−9.29808	+	2.49141i	−0.361380	+	0.0968315i
$663$	4.16225	+	15.5337i	0.161648	+	0.603280i
$664$	4.41324			0.171267
$665$		0			0
$666$	1.33865			0.0518717
$667$	−3.72364	−	13.8968i	−0.144180	−	0.538087i
$668$	−12.9661	+	3.47427i	−0.501675	+	0.134424i
$669$	−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	0.834176	−	0.551498i	$-0.185944\pi$
$673$	7.33331	+	7.33331i	0.282679	+	0.282679i	−0.551498	+	0.834176i	$0.685944\pi$
$674$	−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	−0.186550	−	0.982445i	$-0.559731\pi$
$677$	20.7086	−	20.7086i	0.795895	−	0.795895i	0.982445	+	0.186550i	$0.0597307\pi$
$678$	3.07630	−	11.4809i	0.118145	−	0.440922i
$679$	−13.8352	+	23.9632i	−0.530944	+	0.919623i
$680$		0			0
$681$	1.98573	−	3.43939i	0.0760935	−	0.131798i
$682$	34.7850	−	9.32062i	1.33199	−	0.356905i
$683$	24.6294	+	24.6294i	0.942417	+	0.942417i	0.998430	−	0.0560135i	$-0.0178390\pi$
$683$	24.6294	+	24.6294i	0.942417	+	0.942417i	−0.0560135	+	0.998430i	$0.517839\pi$
$684$	−6.57823	−	1.10420i	−0.251525	−	0.0422201i
$685$		0			0
$686$	−15.9144	−	9.18820i	−0.607616	−	0.350807i
$687$	−2.33923	−	8.73014i	−0.0892473	−	0.333075i
$688$	4.23321	+	1.13429i	0.161390	+	0.0432442i
$689$	−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
$693$	−20.0454	−	5.37116i	−0.761464	−	0.204034i
$694$	−0.215249	−	0.372822i	−0.00817073	−	0.0141521i
$695$		0			0
$696$		−	2.08120i		−	0.0788878i
$697$	−44.1128	−	11.8200i	−1.67089	−	0.447714i
$698$	11.0648	−	2.96482i	0.418810	−	0.112220i
$699$	−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
$703$	−3.46898	−	1.58300i	−0.130835	−	0.0597040i
$704$			5.08711i			0.191728i
$705$		0			0
$706$	−26.6597	−	15.3920i	−1.00335	−	0.579284i
$707$	4.56098	−	17.0218i	0.171533	−	0.640171i
$708$	4.51051	+	16.8334i	0.169515	+	0.632640i
$709$	23.3759	−	13.4961i	0.877901	−	0.506856i	0.00793506	−	0.999969i	$-0.497474\pi$
$709$	23.3759	−	13.4961i	0.877901	−	0.506856i	0.869966	+	0.493112i	$0.164141\pi$
$710$		0			0
$711$		−	6.16716i		−	0.231287i
$712$	−2.72481	+	10.1691i	−0.102116	+	0.381104i
$713$	15.3550	−	57.3057i	0.575050	−	2.14612i
$714$		−	25.8966i		−	0.969156i
$715$		0			0
$716$	13.2474	−	7.64838i	0.495078	−	0.285833i
$717$	4.19911	+	15.6713i	0.156819	+	0.585255i
$718$	−9.63510	+	35.9587i	−0.359579	+	1.34197i
$719$	−5.21897	−	3.01318i	−0.194635	−	0.112372i	0.399516	−	0.916726i	$-0.369178\pi$
$719$	−5.21897	−	3.01318i	−0.194635	−	0.112372i	−0.594151	+	0.804354i	$0.702512\pi$
$720$		0			0
$721$			24.0553i			0.895867i
$722$	15.7411	+	10.6404i	0.585822	+	0.395995i
$723$	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
$727$	−1.28175	+	0.343444i	−0.0475375	+	0.0127376i	−0.282509	−	0.959265i	$-0.591167\pi$
$727$	−1.28175	+	0.343444i	−0.0475375	+	0.0127376i	0.234972	+	0.972002i	$0.424500\pi$
$728$	−4.26287	−	1.14223i	−0.157992	−	0.0423339i
$729$		−	23.1387i		−	0.856989i
$730$		0			0
$731$	−17.5584	−	30.4120i	−0.649421	−	1.12483i
$732$	−6.60918	−	1.77092i	−0.244282	−	0.0654553i
$733$	−23.2056	+	23.2056i	−0.857120	+	0.857120i	−0.990998	−	0.133878i	$-0.957257\pi$
$733$	−23.2056	+	23.2056i	−0.857120	+	0.857120i	0.133878	+	0.990998i	$0.457257\pi$
$734$	0.937051			0.0345872
$735$		0			0
$736$	7.25785	+	4.19032i	0.267528	+	0.154457i
$737$	−6.90954	−	1.85141i	−0.254516	−	0.0681974i
$738$	2.25733	+	8.42447i	0.0830935	+	0.310109i
$739$	−1.10497	−	0.637953i	−0.0406469	−	0.0234675i	0.479539	−	0.877521i	$-0.340804\pi$
$739$	−1.10497	−	0.637953i	−0.0406469	−	0.0234675i	−0.520186	+	0.854053i	$0.674137\pi$
$740$		0			0
$741$	−8.19575	+	3.05960i	−0.301078	+	0.112397i
$742$	12.1456	+	12.1456i	0.445878	+	0.445878i
$743$	−0.264268	+	0.0708104i	−0.00969505	+	0.00259778i	−0.263663	−	0.964615i	$-0.584931\pi$
$743$	−0.264268	+	0.0708104i	−0.00969505	+	0.00259778i	0.253968	+	0.967213i	$0.418264\pi$
$744$	4.29108	−	7.43238i	0.157319	−	0.272484i
$745$		0			0
$746$	12.9511	−	22.4320i	0.474174	−	0.821294i
$747$	−1.74791	+	6.52331i	−0.0639528	+	0.238675i
$748$	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
$757$	24.9364	−	6.68168i	0.906328	−	0.242850i	0.224596	−	0.974452i	$-0.427894\pi$
$757$	24.9364	−	6.68168i	0.906328	−	0.242850i	0.681732	+	0.731602i	$0.261227\pi$
$758$	−8.49328	−	31.6974i	−0.308490	−	1.15130i
$759$	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	$0.292367\pi$
$762$	−3.71185	−	13.8528i	−0.134466	−	0.501834i
$763$	−10.8452	+	2.90596i	−0.392622	+	0.105203i
$764$	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	0.478294	−	0.878200i	$-0.341255\pi$
$769$	40.9858	−	23.6631i	1.47798	−	0.853315i	0.999690	+	0.0248847i	$0.00792186\pi$
$770$		0			0
$771$	−1.87210			−0.0674222
$772$	−5.43204	+	5.43204i	−0.195503	+	0.195503i
$773$	−8.33051	+	31.0899i	−0.299628	+	1.11823i	0.637845	+	0.770165i	$0.279826\pi$
$773$	−8.33051	+	31.0899i	−0.299628	+	1.11823i	−0.937472	+	0.348060i	$0.886840\pi$
$774$	−3.35322	+	5.80795i	−0.120529	+	0.208763i
$775$		0			0
$776$	−5.18979	+	8.98897i	−0.186302	+	0.322685i
$777$	−2.73086	+	0.731732i	−0.0979691	+	0.0262507i
$778$	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
$782$	−17.3805	−	64.8649i	−0.621525	−	2.31956i
$783$	9.10713	+	2.44025i	0.325462	+	0.0872074i
$784$	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	−0.973829	−	0.227282i	$-0.927016\pi$
$787$	−20.9433	+	20.9433i	−0.746547	+	0.746547i	0.227282	+	0.973829i	$0.427016\pi$
$788$	20.5446	+	5.50490i	0.731870	+	0.196104i
$789$	−0.678886	−	1.17586i	−0.0241690	−	0.0418619i
$790$		0			0
$791$		−	26.1365i		−	0.929308i
$792$	−7.51937	−	2.01481i	−0.267189	−	0.0715931i
$793$	9.02508	−	2.41826i	0.320490	−	0.0858751i
$794$	−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	−0.974576	−	0.224056i	$-0.928070\pi$
$797$	−21.1881	+	21.1881i	−0.750521	+	0.750521i	0.224056	+	0.974576i	$0.428070\pi$
$798$	14.0232	−	1.34321i	0.496417	−	0.0475490i
$799$		−	82.7696i		−	2.92818i
$800$		0			0
$801$	−13.9520	−	8.05518i	−0.492969	−	0.284616i
$802$	7.55113	−	28.1812i	0.266640	−	0.995112i
$803$	−2.72428	−	10.1672i	−0.0961377	−	0.358791i
$804$	−1.47633	+	0.852362i	−0.0520663	+	0.0300605i
$805$		0			0
$806$			11.7193i			0.412794i
$807$	−1.21934	+	4.55064i	−0.0429228	+	0.160190i
$808$	1.71090	−	6.38515i	0.0601891	−	0.224629i
$809$		−	17.3630i		−	0.610451i	−0.952280	−	0.305226i	$-0.901268\pi$
$809$		−	17.3630i		−	0.610451i	0.952280	−	0.305226i	$-0.0987319\pi$
$810$		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	$0.379843\pi$
$812$	−1.18447	−	4.42052i	−0.0415669	−	0.155130i
$813$	−0.937358	+	3.49827i	−0.0328746	+	0.122690i
$814$	−3.85393	−	2.22507i	−0.135080	−	0.0779885i
$815$		0			0
$816$		−	9.71423i		−	0.340066i
$817$	15.5576	−	11.0854i	0.544293	−	0.387830i
$818$	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	$0.755772\pi$
$822$	20.1139	−	5.38951i	0.701553	−	0.187981i
$823$	−1.13611	−	0.304420i	−0.0396023	−	0.0106114i	0.238963	−	0.971029i	$-0.423192\pi$
$823$	−1.13611	−	0.304420i	−0.0396023	−	0.0106114i	−0.278566	+	0.960417i	$0.589859\pi$
$824$			9.02353i			0.314350i
$825$		0			0
$826$	19.1608	+	33.1875i	0.666690	+	1.15474i
$827$	31.3991	+	8.41337i	1.09185	+	0.292562i	0.759444	−	0.650573i	$-0.225471\pi$
$827$	31.3991	+	8.41337i	1.09185	+	0.292562i	0.332411	+	0.943135i	$0.392138\pi$
$828$	−9.06835	+	9.06835i	−0.315147	+	0.315147i
$829$	23.1927			0.805516			0.402758	−	0.915307i	$-0.368052\pi$
$829$	23.1927			0.805516			0.402758	+	0.915307i	$0.368052\pi$
$830$		0			0
$831$	−23.7295	−	13.7002i	−0.823167	−	0.475256i
$832$	−1.59907	−	0.428469i	−0.0554377	−	0.0148545i
$833$	−0.221322	−	0.825984i	−0.00766834	−	0.0286186i
$834$	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
$838$	17.1854	−	4.60480i	0.593659	−	0.159070i
$839$	−25.4002	+	43.9944i	−0.876912	+	1.51886i	−0.0222001	+	0.999754i	$0.507067\pi$
$839$	−25.4002	+	43.9944i	−0.876912	+	1.51886i	−0.854712	+	0.519103i	$0.826266\pi$
$840$		0			0
$841$	13.0265	−	22.5625i	0.449189	−	0.778017i
$842$	8.82102	−	32.9205i	0.303992	−	1.13451i
$843$	−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
$852$	−17.8910	+	4.79387i	−0.612935	+	0.164235i
$853$	9.40178	+	35.0879i	0.321911	+	1.20139i	0.917381	+	0.398010i	$0.130299\pi$
$853$	9.40178	+	35.0879i	0.321911	+	1.20139i	−0.595470	+	0.803377i	$0.703034\pi$
$854$	−15.0459			−0.514861
$855$		0			0
$856$	−9.26134			−0.316546
$857$	−4.21201	−	15.7194i	−0.143880	−	0.536966i	−0.999803	−	0.0198628i	$-0.993677\pi$
$857$	−4.21201	−	15.7194i	−0.143880	−	0.536966i	0.855923	−	0.517103i	$-0.172990\pi$
$858$	−9.86185	+	2.64247i	−0.336678	+	0.0902126i
$859$	−26.5596	+	15.3342i	−0.906201	+	0.523196i	−0.879207	−	0.476440i	$-0.841927\pi$
$859$	−26.5596	+	15.3342i	−0.906201	+	0.523196i	−0.0269944	+	0.999636i	$0.508594\pi$
$860$		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	0.564539	−	0.825407i	$-0.309054\pi$
$863$	−7.66348	−	7.66348i	−0.260868	−	0.260868i	−0.825407	+	0.564539i	$0.809054\pi$
$864$	−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
$868$	4.88436	−	18.2287i	0.165786	−	0.618722i
$869$	−10.2509	+	17.7550i	−0.347737	+	0.602298i
$870$		0			0
$871$	1.16393	−	2.01599i	0.0394383	−	0.0683092i
$872$	−4.06820	+	1.09007i	−0.137767	+	0.0369145i
$873$	−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
$877$	−3.61868	−	13.5051i	−0.122194	−	0.456035i	0.877530	−	0.479522i	$-0.159190\pi$
$877$	−3.61868	−	13.5051i	−0.122194	−	0.456035i	−0.999724	+	0.0234870i	$0.992523\pi$
$878$	0.990266	+	0.265341i	0.0334198	+	0.00895482i
$879$	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
$883$	7.01327	+	1.87920i	0.236015	+	0.0632401i	0.374888	−	0.927070i	$-0.377681\pi$
$883$	7.01327	+	1.87920i	0.236015	+	0.0632401i	−0.138873	+	0.990310i	$0.544348\pi$
$884$	6.63257	+	11.4879i	0.223077	+	0.386382i
$885$		0			0
$886$			8.29575i			0.278701i
$887$	−14.9940	−	4.01762i	−0.503449	−	0.134899i	−0.00184854	−	0.999998i	$-0.500588\pi$
$887$	−14.9940	−	4.01762i	−0.503449	−	0.134899i	−0.501600	+	0.865100i	$0.667255\pi$
$888$	−1.02439	+	0.274484i	−0.0343763	+	0.00921109i
$889$	−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
$893$	44.8204	−	4.29310i	1.49986	−	0.143663i
$894$			11.5300i			0.385622i
$895$		0			0
$896$	2.30869	+	1.33292i	0.0771278	+	0.0445298i
$897$	−4.35328	+	16.2467i	−0.145352	+	0.542460i
$898$	−5.07369	−	18.9353i	−0.169311	−	0.631878i
$899$	−10.5245	+	6.07634i	−0.351013	+	0.202657i
$900$		0			0
$901$		−	51.6282i		−	1.71998i
$902$	7.50413	−	28.0058i	0.249860	−	0.932491i
$903$	3.66587	−	13.6812i	0.121992	−	0.455282i
$904$		−	9.80423i		−	0.326084i
$905$		0			0
$906$	−6.52127	+	3.76506i	−0.216655	+	0.125086i
$907$	−8.65791	−	32.3118i	−0.287481	−	1.07289i	−0.947007	−	0.321213i	$-0.895909\pi$
$907$	−8.65791	−	32.3118i	−0.287481	−	1.07289i	0.659526	−	0.751682i	$-0.270757\pi$
$908$	0.847867	−	3.16428i	0.0281375	−	0.105010i
$909$	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	$0.879446\pi$
$912$	5.26034	−	0.503858i	0.174187	−	0.0166844i
$913$	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
$917$	−14.9509	+	4.00609i	−0.493723	+	0.132293i
$918$	42.5085	+	11.3901i	1.40299	+	0.375930i
$919$			50.0242i			1.65015i	0.565027	+	0.825073i	$0.308866\pi$
$919$			50.0242i			1.65015i	−0.565027	+	0.825073i	$0.691134\pi$
$920$		0			0
$921$	7.50337	+	12.9962i	0.247245	+	0.428240i
$922$	−7.43710	−	1.99276i	−0.244928	−	0.0656282i
$923$	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
$927$	−13.3379	−	3.57387i	−0.438073	−	0.117381i
$928$	−0.444315	−	1.65821i	−0.0145854	−	0.0544333i
$929$	−11.8563	−	6.84526i	−0.388994	−	0.224586i	0.292730	−	0.956195i	$-0.405436\pi$
$929$	−11.8563	−	6.84526i	−0.388994	−	0.224586i	−0.681724	+	0.731609i	$0.738770\pi$
$930$		0			0
$931$	0.435798	−	0.162690i	0.0142827	−	0.00533194i
$932$	−7.97295	−	7.97295i	−0.261163	−	0.261163i
$933$	15.1832	−	4.06833i	0.497076	−	0.133191i
$934$	7.73216	−	13.3925i	0.253004	−	0.438216i
$935$		0			0
$936$	1.26666	−	2.19392i	0.0414020	−	0.0717104i
$937$	1.15881	−	4.32476i	0.0378568	−	0.141284i	−0.944411	−	0.328768i	$-0.893367\pi$
$937$	1.15881	−	4.32476i	0.0378568	−	0.141284i	0.982268	+	0.187484i	$0.0600333\pi$
$938$	−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
$947$	−49.0334	+	13.1384i	−1.59337	+	0.426942i	−0.943032	−	0.332703i	$-0.892039\pi$
$947$	−49.0334	+	13.1384i	−1.59337	+	0.426942i	−0.650338	+	0.759645i	$0.725373\pi$
$948$	1.26455	+	4.71936i	0.0410706	+	0.153278i
$949$	3.42537			0.111192
$950$		0			0
$951$	10.2274			0.331646
$952$	−5.52865	−	20.6332i	−0.179185	−	0.668726i
$953$	−9.53536	+	2.55499i	−0.308881	+	0.0827643i	−0.409930	−	0.912117i	$-0.634447\pi$
$953$	−9.53536	+	2.55499i	−0.308881	+	0.0827643i	0.101049	+	0.994881i	$0.467780\pi$
$954$	−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
$963$	3.66806	−	13.6894i	0.118201	−	0.441134i
$964$	9.35347	−	16.2007i	0.301255	−	0.521789i
$965$		0			0
$966$	13.5426	−	23.4564i	0.435726	−	0.754699i
$967$	−21.0294	+	5.63481i	−0.676260	+	0.181203i	−0.580573	−	0.814208i	$-0.697172\pi$
$967$	−21.0294	+	5.63481i	−0.676260	+	0.181203i	−0.0956872	+	0.995411i	$0.530505\pi$
$968$	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	$0.761449\pi$
$972$	−3.61570	−	13.4940i	−0.115974	−	0.432819i
$973$	35.0093	+	9.38072i	1.12235	+	0.300732i
$974$	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	−0.660929	−	0.750449i	$-0.729838\pi$
$977$	2.79812	−	2.79812i	0.0895197	−	0.0895197i	0.750449	+	0.660929i	$0.229838\pi$
$978$	2.94888	+	0.790150i	0.0942948	+	0.0252662i
$979$	26.7781	+	46.3811i	0.855833	+	1.48235i
$980$		0			0
$981$		−	6.44503i		−	0.205774i
$982$	20.1911	+	5.41019i	0.644324	+	0.172646i
$983$	5.93687	−	1.59078i	0.189357	−	0.0507380i	−0.162894	−	0.986644i	$-0.552083\pi$
$983$	5.93687	−	1.59078i	0.189357	−	0.0507380i	0.352251	+	0.935906i	$0.385416\pi$
$984$	−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
$988$	−5.87680	+	4.18745i	−0.186966	+	0.133221i
$989$		−	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	$0.684837\pi$
$992$	1.83220	−	6.83787i	0.0581725	−	0.217103i
$993$	3.02041	+	11.2723i	0.0958498	+	0.357716i
$994$	−35.2725	+	20.3646i	−1.11877	+	0.645925i
$995$		0			0
$996$		−	5.35029i		−	0.169531i
$997$	−5.09479	+	19.0140i	−0.161354	+	0.602180i	0.837124	+	0.547014i	$0.184236\pi$
$997$	−5.09479	+	19.0140i	−0.161354	+	0.602180i	−0.998477	+	0.0551662i	$0.982431\pi$
$998$	−7.22613	+	26.9683i	−0.228739	+	0.853666i
$999$		−	4.80446i		−	0.152006i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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