LMFDB - Embedded newform 750.2.g.f.601.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [750,2,Mod(151,750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("750.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(750, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,-4,-4,0,-4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5^{6} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			601.4
Root			$2.32349 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	750.601
Dual form			750.2.g.f.151.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} +3.23143 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.63788 - 5.04087i) q^{11} +(0.309017 + 0.951057i) q^{12} +(1.82456 + 5.61543i) q^{13} +(0.998566 - 3.07327i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.828995 + 0.602300i) q^{17} +1.00000 q^{18} +(3.64639 - 2.64926i) q^{19} +(-2.61428 - 1.89939i) q^{21} +(-4.28802 - 3.11543i) q^{22} +(0.595870 - 1.83390i) q^{23} +1.00000 q^{24} +5.90441 q^{26} +(0.309017 - 0.951057i) q^{27} +(-2.61428 - 1.89939i) q^{28} +(0.210961 + 0.153272i) q^{29} +(1.81386 - 1.31784i) q^{31} +1.00000 q^{32} +(-4.28802 + 3.11543i) q^{33} +(0.316648 + 0.974542i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-2.95221 - 9.08596i) q^{37} +(-1.39280 - 4.28659i) q^{38} +(1.82456 - 5.61543i) q^{39} +(-3.07816 - 9.47359i) q^{41} +(-2.61428 + 1.89939i) q^{42} -5.30164 q^{43} +(-4.28802 + 3.11543i) q^{44} +(-1.56001 - 1.13341i) q^{46} +(8.51747 + 6.18830i) q^{47} +(0.309017 - 0.951057i) q^{48} +3.44213 q^{49} +1.02469 q^{51} +(1.82456 - 5.61543i) q^{52} +(1.86970 + 1.35841i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-2.61428 + 1.89939i) q^{56} -4.50718 q^{57} +(0.210961 - 0.153272i) q^{58} +(-2.00615 - 6.17428i) q^{59} +(-1.21905 + 3.75186i) q^{61} +(-0.692831 - 2.13232i) q^{62} +(0.998566 + 3.07327i) q^{63} +(0.309017 - 0.951057i) q^{64} +(1.63788 + 5.04087i) q^{66} +(-7.51747 + 5.46176i) q^{67} +1.02469 q^{68} +(-1.56001 + 1.13341i) q^{69} +(-6.90715 - 5.01834i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(1.22192 - 3.76068i) q^{73} -9.55354 q^{74} -4.50718 q^{76} +(5.29269 - 16.2892i) q^{77} +(-4.77677 - 3.47053i) q^{78} +(10.8177 + 7.85950i) q^{79} +(-0.809017 + 0.587785i) q^{81} -9.96112 q^{82} +(-6.05709 + 4.40074i) q^{83} +(0.998566 + 3.07327i) q^{84} +(-1.63830 + 5.04216i) q^{86} +(-0.0805798 - 0.247999i) q^{87} +(1.63788 + 5.04087i) q^{88} +(-0.226687 + 0.697671i) q^{89} +(5.89595 + 18.1459i) q^{91} +(-1.56001 + 1.13341i) q^{92} -2.24205 q^{93} +(8.51747 - 6.18830i) q^{94} +(-0.809017 - 0.587785i) q^{96} +(13.9610 + 10.1432i) q^{97} +(1.06368 - 3.27366i) q^{98} +5.30029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26}+ \cdots + 12 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	3.23143			1.22136			0.610682	−	0.791876i	$-0.290895\pi$
$7$	3.23143			1.22136			0.610682	+	0.791876i	$0.290895\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	1.63788	−	5.04087i	0.493839	−	1.51988i	−0.324920	−	0.945742i	$-0.605337\pi$
$11$	1.63788	−	5.04087i	0.493839	−	1.51988i	0.818758	−	0.574138i	$-0.194663\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	1.82456	+	5.61543i	0.506043	+	1.55744i	0.799010	+	0.601318i	$0.205357\pi$
$13$	1.82456	+	5.61543i	0.506043	+	1.55744i	−0.292967	+	0.956122i	$0.594643\pi$
$14$	0.998566	−	3.07327i	0.266878	−	0.821366i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.828995	+	0.602300i	−0.201061	+	0.146079i	−0.683760	−	0.729707i	$-0.739656\pi$
$17$	−0.828995	+	0.602300i	−0.201061	+	0.146079i	0.482699	+	0.875786i	$0.339656\pi$
$18$	1.00000			0.235702
$19$	3.64639	−	2.64926i	0.836539	−	0.607781i	−0.0848627	−	0.996393i	$-0.527045\pi$
$19$	3.64639	−	2.64926i	0.836539	−	0.607781i	0.921402	+	0.388611i	$0.127045\pi$
$20$		0			0
$21$	−2.61428	−	1.89939i	−0.570483	−	0.414480i
$22$	−4.28802	−	3.11543i	−0.914209	−	0.664212i
$23$	0.595870	−	1.83390i	0.124247	−	0.382394i	−0.869516	−	0.493905i	$-0.835569\pi$
$23$	0.595870	−	1.83390i	0.124247	−	0.382394i	0.993763	+	0.111511i	$0.0355690\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	5.90441			1.15795
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−2.61428	−	1.89939i	−0.494053	−	0.358950i
$29$	0.210961	+	0.153272i	0.0391744	+	0.0284619i	0.607200	−	0.794549i	$-0.292293\pi$
$29$	0.210961	+	0.153272i	0.0391744	+	0.0284619i	−0.568026	+	0.823011i	$0.692293\pi$
$30$		0			0
$31$	1.81386	−	1.31784i	0.325778	−	0.236692i	−0.412859	−	0.910795i	$-0.635470\pi$
$31$	1.81386	−	1.31784i	0.325778	−	0.236692i	0.738637	+	0.674103i	$0.235470\pi$
$32$	1.00000			0.176777
$33$	−4.28802	+	3.11543i	−0.746449	+	0.542327i
$34$	0.316648	+	0.974542i	0.0543046	+	0.167133i
$35$		0			0
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−2.95221	−	9.08596i	−0.485340	−	1.49372i	−0.831488	−	0.555542i	$-0.812511\pi$
$37$	−2.95221	−	9.08596i	−0.485340	−	1.49372i	0.346149	−	0.938180i	$-0.387489\pi$
$38$	−1.39280	−	4.28659i	−0.225941	−	0.695376i
$39$	1.82456	−	5.61543i	0.292164	−	0.899188i
$40$		0			0
$41$	−3.07816	−	9.47359i	−0.480727	−	1.47953i	−0.838075	−	0.545555i	$-0.816319\pi$
$41$	−3.07816	−	9.47359i	−0.480727	−	1.47953i	0.357348	−	0.933971i	$-0.383681\pi$
$42$	−2.61428	+	1.89939i	−0.403392	+	0.293082i
$43$	−5.30164			−0.808492			−0.404246	−	0.914650i	$-0.632466\pi$
$43$	−5.30164			−0.808492			−0.404246	+	0.914650i	$0.632466\pi$
$44$	−4.28802	+	3.11543i	−0.646444	+	0.469669i
$45$		0			0
$46$	−1.56001	−	1.13341i	−0.230010	−	0.167112i
$47$	8.51747	+	6.18830i	1.24240	+	0.902657i	0.997756	−	0.0669561i	$-0.0213288\pi$
$47$	8.51747	+	6.18830i	1.24240	+	0.902657i	0.244644	+	0.969613i	$0.421329\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	3.44213			0.491732
$50$		0			0
$51$	1.02469			0.143486
$52$	1.82456	−	5.61543i	0.253021	−	0.778720i
$53$	1.86970	+	1.35841i	0.256823	+	0.186593i	0.708745	−	0.705465i	$-0.249262\pi$
$53$	1.86970	+	1.35841i	0.256823	+	0.186593i	−0.451923	+	0.892057i	$0.649262\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$		0			0
$56$	−2.61428	+	1.89939i	−0.349348	+	0.253816i
$57$	−4.50718			−0.596991
$58$	0.210961	−	0.153272i	0.0277005	−	0.0201256i
$59$	−2.00615	−	6.17428i	−0.261178	−	0.803823i	−0.992549	−	0.121844i	$-0.961119\pi$
$59$	−2.00615	−	6.17428i	−0.261178	−	0.803823i	0.731371	−	0.681979i	$-0.238881\pi$
$60$		0			0
$61$	−1.21905	+	3.75186i	−0.156084	+	0.480376i	−0.998269	−	0.0588118i	$-0.981269\pi$
$61$	−1.21905	+	3.75186i	−0.156084	+	0.480376i	0.842185	+	0.539188i	$0.181269\pi$
$62$	−0.692831	−	2.13232i	−0.0879897	−	0.270804i
$63$	0.998566	+	3.07327i	0.125808	+	0.387196i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$		0			0
$66$	1.63788	+	5.04087i	0.201609	+	0.620488i
$67$	−7.51747	+	5.46176i	−0.918405	+	0.667260i	−0.943126	−	0.332434i	$-0.892130\pi$
$67$	−7.51747	+	5.46176i	−0.918405	+	0.667260i	0.0247216	+	0.999694i	$0.492130\pi$
$68$	1.02469			0.124262
$69$	−1.56001	+	1.13341i	−0.187803	+	0.136447i
$70$		0			0
$71$	−6.90715	−	5.01834i	−0.819728	−	0.595567i	0.0969066	−	0.995293i	$-0.469105\pi$
$71$	−6.90715	−	5.01834i	−0.819728	−	0.595567i	−0.916635	+	0.399726i	$0.869105\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	1.22192	−	3.76068i	0.143015	−	0.440155i	−0.853735	−	0.520707i	$-0.825668\pi$
$73$	1.22192	−	3.76068i	0.143015	−	0.440155i	0.996750	+	0.0805522i	$0.0256684\pi$
$74$	−9.55354			−1.11058
$75$		0			0
$76$	−4.50718			−0.517010
$77$	5.29269	−	16.2892i	0.603158	−	1.85633i
$78$	−4.77677	−	3.47053i	−0.540863	−	0.392960i
$79$	10.8177	+	7.85950i	1.21708	+	0.884263i	0.995855	−	0.0909589i	$-0.0289932\pi$
$79$	10.8177	+	7.85950i	1.21708	+	0.884263i	0.221229	+	0.975222i	$0.428993\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−9.96112			−1.10002
$83$	−6.05709	+	4.40074i	−0.664852	+	0.483044i	−0.868298	−	0.496043i	$-0.834786\pi$
$83$	−6.05709	+	4.40074i	−0.664852	+	0.483044i	0.203446	+	0.979086i	$0.434786\pi$
$84$	0.998566	+	3.07327i	0.108952	+	0.335321i
$85$		0			0
$86$	−1.63830	+	5.04216i	−0.176662	+	0.543710i
$87$	−0.0805798	−	0.247999i	−0.00863906	−	0.0265883i
$88$	1.63788	+	5.04087i	0.174598	+	0.537359i
$89$	−0.226687	+	0.697671i	−0.0240288	+	0.0739529i	−0.962352	−	0.271807i	$-0.912379\pi$
$89$	−0.226687	+	0.697671i	−0.0240288	+	0.0739529i	0.938323	+	0.345760i	$0.112379\pi$
$90$		0			0
$91$	5.89595	+	18.1459i	0.618063	+	1.90220i
$92$	−1.56001	+	1.13341i	−0.162642	+	0.118166i
$93$	−2.24205			−0.232490
$94$	8.51747	−	6.18830i	0.878510	−	0.638275i
$95$		0			0
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	13.9610	+	10.1432i	1.41752	+	1.02989i	0.992175	+	0.124857i	$0.0398473\pi$
$97$	13.9610	+	10.1432i	1.41752	+	1.02989i	0.425345	+	0.905031i	$0.360153\pi$
$98$	1.06368	−	3.27366i	0.107447	−	0.330689i
$99$	5.30029			0.532699
$100$		0			0
$101$	11.8454			1.17866			0.589331	−	0.807892i	$-0.299391\pi$
$101$	11.8454			1.17866			0.589331	+	0.807892i	$0.299391\pi$
$102$	0.316648	−	0.974542i	0.0313528	−	0.0964940i
$103$	5.78515	+	4.20316i	0.570028	+	0.414150i	0.835115	−	0.550075i	$-0.185401\pi$
$103$	5.78515	+	4.20316i	0.570028	+	0.414150i	−0.265087	+	0.964224i	$0.585401\pi$
$104$	−4.77677	−	3.47053i	−0.468401	−	0.340313i
$105$		0			0
$106$	1.86970	−	1.35841i	0.181601	−	0.131941i
$107$	3.20058			0.309412			0.154706	−	0.987961i	$-0.450557\pi$
$107$	3.20058			0.309412			0.154706	+	0.987961i	$0.450557\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	3.05789	+	9.41123i	0.292893	+	0.901432i	0.983921	+	0.178604i	$0.0571581\pi$
$109$	3.05789	+	9.41123i	0.292893	+	0.901432i	−0.691028	+	0.722828i	$0.742842\pi$
$110$		0			0
$111$	−2.95221	+	9.08596i	−0.280211	+	0.862401i
$112$	0.998566	+	3.07327i	0.0943556	+	0.290397i
$113$	−1.31201	−	4.03794i	−0.123423	−	0.379858i	0.870187	−	0.492721i	$-0.163998\pi$
$113$	−1.31201	−	4.03794i	−0.123423	−	0.379858i	−0.993611	+	0.112863i	$0.963998\pi$
$114$	−1.39280	+	4.28659i	−0.130447	+	0.401476i
$115$		0			0
$116$	−0.0805798	−	0.247999i	−0.00748165	−	0.0230261i
$117$	−4.77677	+	3.47053i	−0.441613	+	0.320850i
$118$	−6.49202			−0.597639
$119$	−2.67884	+	1.94629i	−0.245569	+	0.178416i
$120$		0			0
$121$	−13.8285	−	10.0470i	−1.25714	−	0.913366i
$122$	3.19152	+	2.31878i	0.288947	+	0.209932i
$123$	−3.07816	+	9.47359i	−0.277548	+	0.854205i
$124$	−2.24205			−0.201342
$125$		0			0
$126$	3.23143			0.287878
$127$	−2.85868	+	8.79813i	−0.253667	+	0.780708i	0.740422	+	0.672142i	$0.234626\pi$
$127$	−2.85868	+	8.79813i	−0.253667	+	0.780708i	−0.994089	+	0.108565i	$0.965374\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	4.28912	+	3.11623i	0.377636	+	0.274368i
$130$		0			0
$131$	3.93584	−	2.85956i	0.343876	−	0.249841i	−0.402419	−	0.915455i	$-0.631831\pi$
$131$	3.93584	−	2.85956i	0.343876	−	0.249841i	0.746296	+	0.665615i	$0.231831\pi$
$132$	5.30029			0.461331
$133$	11.7830	−	8.56088i	1.02172	−	0.742323i
$134$	2.87142	+	8.83731i	0.248053	+	0.763428i
$135$		0			0
$136$	0.316648	−	0.974542i	0.0271523	−	0.0835663i
$137$	1.85925	+	5.72219i	0.158847	+	0.488879i	0.998530	−	0.0541963i	$-0.0172597\pi$
$137$	1.85925	+	5.72219i	0.158847	+	0.488879i	−0.839684	+	0.543076i	$0.817260\pi$
$138$	0.595870	+	1.83390i	0.0507238	+	0.156112i
$139$	−1.73890	+	5.35178i	−0.147492	+	0.453932i	−0.997323	−	0.0731222i	$-0.976704\pi$
$139$	−1.73890	+	5.35178i	−0.147492	+	0.453932i	0.849831	+	0.527055i	$0.176704\pi$
$140$		0			0
$141$	−3.25338	−	10.0129i	−0.273984	−	0.843237i
$142$	−6.90715	+	5.01834i	−0.579635	+	0.421130i
$143$	31.2951			2.61703
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$		0			0
$146$	−3.19903	−	2.32423i	−0.264754	−	0.192355i
$147$	−2.78474	−	2.02323i	−0.229681	−	0.166873i
$148$	−2.95221	+	9.08596i	−0.242670	+	0.746861i
$149$	−11.6556			−0.954863			−0.477432	−	0.878669i	$-0.658432\pi$
$149$	−11.6556			−0.954863			−0.477432	+	0.878669i	$0.658432\pi$
$150$		0			0
$151$	5.52354			0.449499			0.224750	−	0.974417i	$-0.427844\pi$
$151$	5.52354			0.449499			0.224750	+	0.974417i	$0.427844\pi$
$152$	−1.39280	+	4.28659i	−0.112971	+	0.347688i
$153$	−0.828995	−	0.602300i	−0.0670202	−	0.0486931i
$154$	−13.8564	−	10.0673i	−1.11658	−	0.811245i
$155$		0			0
$156$	−4.77677	+	3.47053i	−0.382448	+	0.277864i
$157$	−6.84307			−0.546136			−0.273068	−	0.961995i	$-0.588038\pi$
$157$	−6.84307			−0.546136			−0.273068	+	0.961995i	$0.588038\pi$
$158$	10.8177	−	7.85950i	0.860608	−	0.625268i
$159$	−0.714161	−	2.19796i	−0.0566366	−	0.174310i
$160$		0			0
$161$	1.92551	−	5.92611i	0.151751	−	0.467043i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−2.90080	−	8.92773i	−0.227208	−	0.699274i	−0.998060	−	0.0622597i	$-0.980169\pi$
$163$	−2.90080	−	8.92773i	−0.227208	−	0.699274i	0.770852	−	0.637014i	$-0.219831\pi$
$164$	−3.07816	+	9.47359i	−0.240364	+	0.739763i
$165$		0			0
$166$	2.31360	+	7.12054i	0.179570	+	0.552661i
$167$	−5.52464	+	4.01388i	−0.427509	+	0.310604i	−0.780652	−	0.624966i	$-0.785113\pi$
$167$	−5.52464	+	4.01388i	−0.427509	+	0.310604i	0.353143	+	0.935569i	$0.385113\pi$
$168$	3.23143			0.249310
$169$	−17.6868	+	12.8502i	−1.36052	+	0.988478i
$170$		0			0
$171$	3.64639	+	2.64926i	0.278846	+	0.202594i
$172$	4.28912	+	3.11623i	0.327042	+	0.237610i
$173$	5.82820	−	17.9373i	0.443110	−	1.36375i	−0.441434	−	0.897294i	$-0.645530\pi$
$173$	5.82820	−	17.9373i	0.443110	−	1.36375i	0.884544	−	0.466457i	$-0.154470\pi$
$174$	−0.260762			−0.0197683
$175$		0			0
$176$	5.30029			0.399524
$177$	−2.00615	+	6.17428i	−0.150791	+	0.464087i
$178$	0.593474	+	0.431184i	0.0444828	+	0.0323186i
$179$	−0.761557	−	0.553303i	−0.0569214	−	0.0413558i	0.558961	−	0.829194i	$-0.311200\pi$
$179$	−0.761557	−	0.553303i	−0.0569214	−	0.0413558i	−0.615882	+	0.787838i	$0.711200\pi$
$180$		0			0
$181$	−11.4118	+	8.29114i	−0.848231	+	0.616276i	−0.924658	−	0.380800i	$-0.875649\pi$
$181$	−11.4118	+	8.29114i	−0.848231	+	0.616276i	0.0764270	+	0.997075i	$0.475649\pi$
$182$	19.0797			1.41428
$183$	3.19152	−	2.31878i	0.235924	−	0.171409i
$184$	0.595870	+	1.83390i	0.0439281	+	0.135197i
$185$		0			0
$186$	−0.692831	+	2.13232i	−0.0508009	+	0.156349i
$187$	1.67832	+	5.16535i	0.122731	+	0.377728i
$188$	−3.25338	−	10.0129i	−0.237277	−	0.730265i
$189$	0.998566	−	3.07327i	0.0726350	−	0.223548i
$190$		0			0
$191$	7.87125	+	24.2252i	0.569544	+	1.75288i	0.654049	+	0.756453i	$0.273069\pi$
$191$	7.87125	+	24.2252i	0.569544	+	1.75288i	−0.0845047	+	0.996423i	$0.526931\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	−6.63439			−0.477554			−0.238777	−	0.971074i	$-0.576746\pi$
$193$	−6.63439			−0.477554			−0.238777	+	0.971074i	$0.576746\pi$
$194$	13.9610	−	10.1432i	1.00234	−	0.728241i
$195$		0			0
$196$	−2.78474	−	2.02323i	−0.198910	−	0.144517i
$197$	8.23396	+	5.98232i	0.586645	+	0.426223i	0.841114	−	0.540858i	$-0.181900\pi$
$197$	8.23396	+	5.98232i	0.586645	+	0.426223i	−0.254468	+	0.967081i	$0.581900\pi$
$198$	1.63788	−	5.04087i	0.116399	−	0.358239i
$199$	−2.52238			−0.178807			−0.0894035	−	0.995995i	$-0.528496\pi$
$199$	−2.52238			−0.178807			−0.0894035	+	0.995995i	$0.528496\pi$
$200$		0			0
$201$	9.29210			0.655414
$202$	3.66043	−	11.2656i	0.257547	−	0.792648i
$203$	0.681704	+	0.495287i	0.0478463	+	0.0347623i
$204$	−0.828995	−	0.602300i	−0.0580412	−	0.0421694i
$205$		0			0
$206$	5.78515	−	4.20316i	0.403071	−	0.292848i
$207$	1.92827			0.134024
$208$	−4.77677	+	3.47053i	−0.331209	+	0.240638i
$209$	−7.38222	−	22.7201i	−0.510639	−	1.57158i
$210$		0			0
$211$	4.87129	−	14.9923i	0.335353	−	1.03211i	−0.631194	−	0.775625i	$-0.717435\pi$
$211$	4.87129	−	14.9923i	0.335353	−	1.03211i	0.966548	−	0.256487i	$-0.0825650\pi$
$212$	−0.714161	−	2.19796i	−0.0490487	−	0.150957i
$213$	2.63830	+	8.11984i	0.180773	+	0.556362i
$214$	0.989034	−	3.04393i	0.0676090	−	0.208079i
$215$		0			0
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	5.86135	−	4.25852i	0.397894	−	0.289087i
$218$	9.89555			0.670211
$219$	−3.19903	+	2.32423i	−0.216170	+	0.157057i
$220$		0			0
$221$	−4.89473	−	3.55623i	−0.329255	−	0.239218i
$222$	7.72898	+	5.61543i	0.518735	+	0.376883i
$223$	−2.87242	+	8.84040i	−0.192351	+	0.591997i	0.807646	+	0.589668i	$0.200741\pi$
$223$	−2.87242	+	8.84040i	−0.192351	+	0.591997i	−0.999997	+	0.00232890i	$0.999259\pi$
$224$	3.23143			0.215909
$225$		0			0
$226$	−4.24575			−0.282423
$227$	−1.12423	+	3.46003i	−0.0746178	+	0.229650i	−0.981408	−	0.191931i	$-0.938525\pi$
$227$	−1.12423	+	3.46003i	−0.0746178	+	0.229650i	0.906791	+	0.421582i	$0.138525\pi$
$228$	3.64639	+	2.64926i	0.241488	+	0.175451i
$229$	−8.03500	−	5.83777i	−0.530968	−	0.385771i	0.289752	−	0.957102i	$-0.406427\pi$
$229$	−8.03500	−	5.83777i	−0.530968	−	0.385771i	−0.820720	+	0.571331i	$0.806427\pi$
$230$		0			0
$231$	−13.8564	+	10.0673i	−0.911686	+	0.662379i
$232$	−0.260762			−0.0171198
$233$	−15.2009	+	11.0441i	−0.995844	+	0.723523i	−0.961193	−	0.275877i	$-0.911032\pi$
$233$	−15.2009	+	11.0441i	−0.995844	+	0.723523i	−0.0346507	+	0.999399i	$0.511032\pi$
$234$	1.82456	+	5.61543i	0.119275	+	0.367092i
$235$		0			0
$236$	−2.00615	+	6.17428i	−0.130589	+	0.401912i
$237$	−4.13198	−	12.7169i	−0.268401	−	0.826054i
$238$	1.02322	+	3.14916i	0.0663258	+	0.204130i
$239$	−3.01349	+	9.27457i	−0.194926	+	0.599922i	0.805051	+	0.593206i	$0.202138\pi$
$239$	−3.01349	+	9.27457i	−0.194926	+	0.599922i	−0.999977	+	0.00671626i	$0.997862\pi$
$240$		0			0
$241$	5.84694	+	17.9950i	0.376634	+	1.15916i	0.942369	+	0.334574i	$0.108592\pi$
$241$	5.84694	+	17.9950i	0.376634	+	1.15916i	−0.565735	+	0.824587i	$0.691408\pi$
$242$	−13.8285	+	10.0470i	−0.888933	+	0.645848i
$243$	1.00000			0.0641500
$244$	3.19152	−	2.31878i	0.204316	−	0.148444i
$245$		0			0
$246$	8.05872	+	5.85500i	0.513805	+	0.373301i
$247$	21.5298	+	15.6423i	1.36991	+	0.995296i
$248$	−0.692831	+	2.13232i	−0.0439948	+	0.135402i
$249$	7.48698			0.474468
$250$		0			0
$251$	−1.98608			−0.125360			−0.0626801	−	0.998034i	$-0.519965\pi$
$251$	−1.98608			−0.125360			−0.0626801	+	0.998034i	$0.519965\pi$
$252$	0.998566	−	3.07327i	0.0629038	−	0.193598i
$253$	−8.26848	−	6.00740i	−0.519835	−	0.377682i
$254$	7.48413	+	5.43754i	0.469596	+	0.341182i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−19.2797			−1.20263			−0.601317	−	0.799010i	$-0.705357\pi$
$257$	−19.2797			−1.20263			−0.601317	+	0.799010i	$0.705357\pi$
$258$	4.28912	−	3.11623i	0.267029	−	0.194008i
$259$	−9.53984	−	29.3606i	−0.592777	−	1.82438i
$260$		0			0
$261$	−0.0805798	+	0.247999i	−0.00498777	+	0.0153508i
$262$	−1.50336	−	4.62686i	−0.0928778	−	0.285848i
$263$	3.87188	+	11.9164i	0.238751	+	0.734799i	0.996602	+	0.0823713i	$0.0262493\pi$
$263$	3.87188	+	11.9164i	0.238751	+	0.734799i	−0.757851	+	0.652428i	$0.773751\pi$
$264$	1.63788	−	5.04087i	0.100804	−	0.310244i
$265$		0			0
$266$	−4.50072	−	13.8518i	−0.275957	−	0.849308i
$267$	0.593474	−	0.431184i	0.0363200	−	0.0263880i
$268$	9.29210			0.567605
$269$	−10.9160	+	7.93096i	−0.665562	+	0.483559i	−0.868537	−	0.495625i	$-0.834939\pi$
$269$	−10.9160	+	7.93096i	−0.665562	+	0.483559i	0.202975	+	0.979184i	$0.434939\pi$
$270$		0			0
$271$	21.6926	+	15.7606i	1.31773	+	0.957387i	0.999957	+	0.00922023i	$0.00293493\pi$
$271$	21.6926	+	15.7606i	1.31773	+	0.957387i	0.317773	+	0.948167i	$0.397065\pi$
$272$	−0.828995	−	0.602300i	−0.0502652	−	0.0365198i
$273$	5.89595	−	18.1459i	0.356839	−	1.09824i
$274$	6.01666			0.363480
$275$		0			0
$276$	1.92827			0.116068
$277$	2.52382	−	7.76751i	0.151641	−	0.466704i	−0.846164	−	0.532923i	$-0.821094\pi$
$277$	2.52382	−	7.76751i	0.151641	−	0.466704i	0.997805	+	0.0662188i	$0.0210935\pi$
$278$	4.55250	+	3.30758i	0.273041	+	0.198376i
$279$	1.81386	+	1.31784i	0.108593	+	0.0788972i
$280$		0			0
$281$	−25.3561	+	18.4223i	−1.51262	+	1.09898i	−0.547615	+	0.836730i	$0.684464\pi$
$281$	−25.3561	+	18.4223i	−1.51262	+	1.09898i	−0.965000	+	0.262249i	$0.915536\pi$
$282$	−10.5282			−0.626943
$283$	13.2277	−	9.61049i	0.786306	−	0.571284i	−0.120559	−	0.992706i	$-0.538469\pi$
$283$	13.2277	−	9.61049i	0.786306	−	0.571284i	0.906865	+	0.421422i	$0.138469\pi$
$284$	2.63830	+	8.11984i	0.156554	+	0.481824i
$285$		0			0
$286$	9.67071	−	29.7634i	0.571841	−	1.75995i
$287$	−9.94684	−	30.6132i	−0.587143	−	1.80704i
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	−4.92882	+	15.1694i	−0.289931	+	0.892315i
$290$		0			0
$291$	−5.33261	−	16.4121i	−0.312603	−	0.962093i
$292$	−3.19903	+	2.32423i	−0.187209	+	0.136015i
$293$	−28.1867			−1.64669			−0.823343	−	0.567545i	$-0.807893\pi$
$293$	−28.1867			−1.64669			−0.823343	+	0.567545i	$0.807893\pi$
$294$	−2.78474	+	2.02323i	−0.162409	+	0.117997i
$295$		0			0
$296$	7.72898	+	5.61543i	0.449238	+	0.326390i
$297$	−4.28802	−	3.11543i	−0.248816	−	0.180776i
$298$	−3.60178	+	11.0851i	−0.208645	+	0.642144i
$299$	11.3853			0.658431
$300$		0			0
$301$	−17.1319			−0.987464
$302$	1.70687	−	5.25320i	0.0982192	−	0.302288i
$303$	−9.58313	−	6.96255i	−0.550537	−	0.399988i
$304$	3.64639	+	2.64926i	0.209135	+	0.151945i
$305$		0			0
$306$	−0.828995	+	0.602300i	−0.0473905	+	0.0344312i
$307$	−14.5372			−0.829680			−0.414840	−	0.909894i	$-0.636163\pi$
$307$	−14.5372			−0.829680			−0.414840	+	0.909894i	$0.636163\pi$
$308$	−13.8564	+	10.0673i	−0.789543	+	0.573637i
$309$	−2.20973	−	6.80085i	−0.125707	−	0.386887i
$310$		0			0
$311$	4.47841	−	13.7831i	0.253947	−	0.781570i	−0.740088	−	0.672510i	$-0.765216\pi$
$311$	4.47841	−	13.7831i	0.253947	−	0.781570i	0.994035	−	0.109060i	$-0.0347839\pi$
$312$	1.82456	+	5.61543i	0.103296	+	0.317911i
$313$	−9.74294	−	29.9857i	−0.550703	−	1.69489i	−0.707029	−	0.707185i	$-0.749965\pi$
$313$	−9.74294	−	29.9857i	−0.550703	−	1.69489i	0.156325	−	0.987706i	$-0.450035\pi$
$314$	−2.11462	+	6.50814i	−0.119335	+	0.367276i
$315$		0			0
$316$	−4.13198	−	12.7169i	−0.232442	−	0.715384i
$317$	12.1199	−	8.80564i	0.680722	−	0.494574i	−0.192875	−	0.981223i	$-0.561781\pi$
$317$	12.1199	−	8.80564i	0.680722	−	0.494574i	0.873597	+	0.486650i	$0.161781\pi$
$318$	−2.31107			−0.129598
$319$	1.11815	−	0.812385i	0.0626045	−	0.0454848i
$320$		0			0
$321$	−2.58932	−	1.88125i	−0.144522	−	0.105001i
$322$	−5.04105	−	3.66254i	−0.280927	−	0.204105i
$323$	−1.42719	+	4.39244i	−0.0794110	+	0.244402i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−9.38717			−0.519907
$327$	3.05789	−	9.41123i	0.169102	−	0.520442i
$328$	8.05872	+	5.85500i	0.444968	+	0.323288i
$329$	27.5236	+	19.9971i	1.51742	+	1.10247i
$330$		0			0
$331$	17.4888	−	12.7064i	0.961273	−	0.698406i	0.00782724	−	0.999969i	$-0.497508\pi$
$331$	17.4888	−	12.7064i	0.961273	−	0.698406i	0.953446	+	0.301563i	$0.0975085\pi$
$332$	7.48698			0.410901
$333$	7.72898	−	5.61543i	0.423545	−	0.307724i
$334$	2.11022	+	6.49460i	0.115466	+	0.355369i
$335$		0			0
$336$	0.998566	−	3.07327i	0.0544762	−	0.167661i
$337$	−2.34697	−	7.22323i	−0.127848	−	0.393474i	0.866562	−	0.499070i	$-0.166325\pi$
$337$	−2.34697	−	7.22323i	−0.127848	−	0.393474i	−0.994409	+	0.105596i	$0.966325\pi$
$338$	6.75576	+	20.7921i	0.367465	+	1.13094i
$339$	−1.31201	+	4.03794i	−0.0712585	+	0.219311i
$340$		0			0
$341$	−3.67220	−	11.3019i	−0.198861	−	0.612031i
$342$	3.64639	−	2.64926i	0.197174	−	0.143255i
$343$	−11.4970			−0.620780
$344$	4.28912	−	3.11623i	0.231254	−	0.168016i
$345$		0			0
$346$	−15.2584	−	11.0859i	−0.820298	−	0.595981i
$347$	6.09436	+	4.42781i	0.327162	+	0.237697i	0.739226	−	0.673458i	$-0.235192\pi$
$347$	6.09436	+	4.42781i	0.327162	+	0.237697i	−0.412063	+	0.911155i	$0.635192\pi$
$348$	−0.0805798	+	0.247999i	−0.00431953	+	0.0132942i
$349$	18.7527			1.00381			0.501904	−	0.864923i	$-0.332633\pi$
$349$	18.7527			1.00381			0.501904	+	0.864923i	$0.332633\pi$
$350$		0			0
$351$	5.90441			0.315154
$352$	1.63788	−	5.04087i	0.0872992	−	0.268679i
$353$	−3.53223	−	2.56631i	−0.188001	−	0.136591i	0.489803	−	0.871833i	$-0.337069\pi$
$353$	−3.53223	−	2.56631i	−0.188001	−	0.136591i	−0.677805	+	0.735242i	$0.737069\pi$
$354$	5.25216	+	3.81592i	0.279149	+	0.202814i
$355$		0			0
$356$	0.593474	−	0.431184i	0.0314541	−	0.0228527i
$357$	3.31122			0.175249
$358$	−0.761557	+	0.553303i	−0.0402495	+	0.0292430i
$359$	0.227811	+	0.701130i	0.0120234	+	0.0370042i	0.956888	−	0.290456i	$-0.0938071\pi$
$359$	0.227811	+	0.701130i	0.0120234	+	0.0370042i	−0.944865	+	0.327461i	$0.893807\pi$
$360$		0			0
$361$	0.406269	−	1.25037i	0.0213826	−	0.0658088i
$362$	4.35891	+	13.4153i	0.229099	+	0.705095i
$363$	5.28204	+	16.2564i	0.277235	+	0.853242i
$364$	5.89595	−	18.1459i	0.309032	−	0.951101i
$365$		0			0
$366$	−1.21905	−	3.75186i	−0.0637209	−	0.196113i
$367$	−15.2581	+	11.0856i	−0.796466	+	0.578666i	−0.909875	−	0.414882i	$-0.863823\pi$
$367$	−15.2581	+	11.0856i	−0.796466	+	0.578666i	0.113410	+	0.993548i	$0.463823\pi$
$368$	1.92827			0.100518
$369$	8.05872	−	5.85500i	0.419520	−	0.304799i
$370$		0			0
$371$	6.04179	+	4.38962i	0.313674	+	0.227898i
$372$	1.81386	+	1.31784i	0.0940441	+	0.0683270i
$373$	−9.22003	+	28.3763i	−0.477395	+	1.46927i	0.365305	+	0.930888i	$0.380965\pi$
$373$	−9.22003	+	28.3763i	−0.477395	+	1.46927i	−0.842700	+	0.538383i	$0.819035\pi$
$374$	5.43117			0.280839
$375$		0			0
$376$	−10.5282			−0.542949
$377$	−0.475776	+	1.46429i	−0.0245037	+	0.0754147i
$378$	−2.61428	−	1.89939i	−0.134464	−	0.0976939i
$379$	−20.6159	−	14.9783i	−1.05897	−	0.769384i	−0.0850692	−	0.996375i	$-0.527111\pi$
$379$	−20.6159	−	14.9783i	−1.05897	−	0.769384i	−0.973897	+	0.226991i	$0.927111\pi$
$380$		0			0
$381$	7.48413	−	5.43754i	0.383424	−	0.278574i
$382$	25.4719			1.30326
$383$	−25.6000	+	18.5995i	−1.30810	+	0.950389i	−1.00000		0.000965638i	$-0.999693\pi$
$383$	−25.6000	+	18.5995i	−1.30810	+	0.950389i	−0.308098	+	0.951354i	$0.599693\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$		0			0
$386$	−2.05014	+	6.30968i	−0.104349	+	0.321154i
$387$	−1.63830	−	5.04216i	−0.0832793	−	0.256307i
$388$	−5.33261	−	16.4121i	−0.270722	−	0.833197i
$389$	3.72304	−	11.4583i	0.188766	−	0.580961i	−0.811227	−	0.584731i	$-0.801200\pi$
$389$	3.72304	−	11.4583i	0.188766	−	0.580961i	0.999993	+	0.00377022i	$0.00120010\pi$
$390$		0			0
$391$	0.610584	+	1.87918i	0.0308786	+	0.0950344i
$392$	−2.78474	+	2.02323i	−0.140651	+	0.102189i
$393$	−4.86497			−0.245405
$394$	8.23396	−	5.98232i	0.414821	−	0.301385i
$395$		0			0
$396$	−4.28802	−	3.11543i	−0.215481	−	0.156556i
$397$	−20.8374	−	15.1393i	−1.04580	−	0.759819i	−0.0743920	−	0.997229i	$-0.523702\pi$
$397$	−20.8374	−	15.1393i	−1.04580	−	0.759819i	−0.971410	+	0.237410i	$0.923702\pi$
$398$	−0.779460	+	2.39893i	−0.0390708	+	0.120247i
$399$	−14.5646			−0.729144
$400$		0			0
$401$	26.3196			1.31434			0.657169	−	0.753743i	$-0.271754\pi$
$401$	26.3196			1.31434			0.657169	+	0.753743i	$0.271754\pi$
$402$	2.87142	−	8.83731i	0.143213	−	0.440765i
$403$	10.7098	+	7.78109i	0.533491	+	0.387604i
$404$	−9.58313	−	6.96255i	−0.476779	−	0.346400i
$405$		0			0
$406$	0.681704	−	0.495287i	0.0338324	−	0.0245807i
$407$	−50.6365			−2.50996
$408$	−0.828995	+	0.602300i	−0.0410414	+	0.0298183i
$409$	11.3630	+	34.9716i	0.561863	+	1.72924i	0.677093	+	0.735897i	$0.263239\pi$
$409$	11.3630	+	34.9716i	0.561863	+	1.72924i	−0.115230	+	0.993339i	$0.536761\pi$
$410$		0			0
$411$	1.85925	−	5.72219i	0.0917101	−	0.282255i
$412$	−2.20973	−	6.80085i	−0.108866	−	0.335054i
$413$	−6.48272	−	19.9517i	−0.318994	−	0.981761i
$414$	0.595870	−	1.83390i	0.0292854	−	0.0901312i
$415$		0			0
$416$	1.82456	+	5.61543i	0.0894566	+	0.275319i
$417$	4.55250	−	3.30758i	0.222937	−	0.161973i
$418$	−23.8894			−1.16847
$419$	25.6657	−	18.6472i	1.25385	−	0.910975i	0.255411	−	0.966833i	$-0.417789\pi$
$419$	25.6657	−	18.6472i	1.25385	−	0.910975i	0.998439	+	0.0558572i	$0.0177891\pi$
$420$		0			0
$421$	−7.13332	−	5.18266i	−0.347657	−	0.252587i	0.400229	−	0.916415i	$-0.368931\pi$
$421$	−7.13332	−	5.18266i	−0.347657	−	0.252587i	−0.747885	+	0.663828i	$0.768931\pi$
$422$	−12.7532	−	9.26574i	−0.620816	−	0.451049i
$423$	−3.25338	+	10.0129i	−0.158185	+	0.486843i
$424$	−2.31107			−0.112236
$425$		0			0
$426$	8.53771			0.413653
$427$	−3.93928	+	12.1239i	−0.190635	+	0.586715i
$428$	−2.58932	−	1.88125i	−0.125160	−	0.0909339i
$429$	−25.3182	−	18.3948i	−1.22238	−	0.888108i
$430$		0			0
$431$	−19.0172	+	13.8168i	−0.916026	+	0.665532i	−0.942532	−	0.334117i	$-0.891562\pi$
$431$	−19.0172	+	13.8168i	−0.916026	+	0.665532i	0.0265058	+	0.999649i	$0.491562\pi$
$432$	1.00000			0.0481125
$433$	6.79827	−	4.93923i	0.326704	−	0.237364i	−0.412327	−	0.911036i	$-0.635284\pi$
$433$	6.79827	−	4.93923i	0.326704	−	0.237364i	0.739031	+	0.673672i	$0.235284\pi$
$434$	−2.23883	−	6.89042i	−0.107468	−	0.330751i
$435$		0			0
$436$	3.05789	−	9.41123i	0.146447	−	0.450716i
$437$	−2.68569	−	8.26572i	−0.128474	−	0.395403i
$438$	1.22192	+	3.76068i	0.0583856	+	0.179692i
$439$	11.0111	−	33.8885i	0.525529	−	1.61741i	−0.237739	−	0.971329i	$-0.576406\pi$
$439$	11.0111	−	33.8885i	0.525529	−	1.61741i	0.763268	−	0.646083i	$-0.223594\pi$
$440$		0			0
$441$	1.06368	+	3.27366i	0.0506512	+	0.155888i
$442$	−4.89473	+	3.55623i	−0.232818	+	0.169152i
$443$	−6.79550			−0.322864			−0.161432	−	0.986884i	$-0.551611\pi$
$443$	−6.79550			−0.322864			−0.161432	+	0.986884i	$0.551611\pi$
$444$	7.72898	−	5.61543i	0.366801	−	0.266497i
$445$		0			0
$446$	7.52009	+	5.46366i	0.356087	+	0.258712i
$447$	9.42957	+	6.85098i	0.446003	+	0.324040i
$448$	0.998566	−	3.07327i	0.0471778	−	0.145198i
$449$	8.75011			0.412943			0.206472	−	0.978453i	$-0.433802\pi$
$449$	8.75011			0.412943			0.206472	+	0.978453i	$0.433802\pi$
$450$		0			0
$451$	−52.7968			−2.48610
$452$	−1.31201	+	4.03794i	−0.0617117	+	0.189929i
$453$	−4.46864	−	3.24666i	−0.209955	−	0.152541i
$454$	2.94327	+	2.13841i	0.138135	+	0.100361i
$455$		0			0
$456$	3.64639	−	2.64926i	0.170758	−	0.124063i
$457$	38.1474			1.78446			0.892230	−	0.451581i	$-0.149140\pi$
$457$	38.1474			1.78446			0.892230	+	0.451581i	$0.149140\pi$
$458$	−8.03500	+	5.83777i	−0.375451	+	0.272781i
$459$	0.316648	+	0.974542i	0.0147799	+	0.0454877i
$460$		0			0
$461$	−0.392689	+	1.20857i	−0.0182893	+	0.0562888i	−0.959785	−	0.280737i	$-0.909421\pi$
$461$	−0.392689	+	1.20857i	−0.0182893	+	0.0562888i	0.941495	+	0.337026i	$0.109421\pi$
$462$	5.29269	+	16.2892i	0.246238	+	0.757843i
$463$	−2.76060	−	8.49626i	−0.128296	−	0.394855i	0.866191	−	0.499713i	$-0.166561\pi$
$463$	−2.76060	−	8.49626i	−0.128296	−	0.394855i	−0.994487	+	0.104858i	$0.966561\pi$
$464$	−0.0805798	+	0.247999i	−0.00374082	+	0.0115131i
$465$		0			0
$466$	5.80623	+	17.8697i	0.268968	+	0.827799i
$467$	−4.65737	+	3.38378i	−0.215517	+	0.156582i	−0.690306	−	0.723517i	$-0.742524\pi$
$467$	−4.65737	+	3.38378i	−0.215517	+	0.156582i	0.474789	+	0.880100i	$0.342524\pi$
$468$	5.90441			0.272932
$469$	−24.2922	+	17.6493i	−1.12171	+	0.814968i
$470$		0			0
$471$	5.53616	+	4.02225i	0.255093	+	0.185336i
$472$	5.25216	+	3.81592i	0.241750	+	0.175642i
$473$	−8.68344	+	26.7249i	−0.399265	+	1.22881i
$474$	−13.3714			−0.614168
$475$		0			0
$476$	3.31122			0.151770
$477$	−0.714161	+	2.19796i	−0.0326992	+	0.100638i
$478$	7.88942	+	5.73200i	0.360854	+	0.262175i
$479$	3.74616	+	2.72175i	0.171167	+	0.124360i	0.670070	−	0.742298i	$-0.266264\pi$
$479$	3.74616	+	2.72175i	0.171167	+	0.124360i	−0.498904	+	0.866657i	$0.666264\pi$
$480$		0			0
$481$	45.6351	−	33.1558i	2.08078	−	1.51177i
$482$	18.9211			0.861832
$483$	−5.04105	+	3.66254i	−0.229376	+	0.166651i
$484$	5.28204	+	16.2564i	0.240093	+	0.738929i
$485$		0			0
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−4.92064	−	15.1442i	−0.222975	−	0.686248i	−0.998491	−	0.0549192i	$-0.982510\pi$
$487$	−4.92064	−	15.1442i	−0.222975	−	0.686248i	0.775515	−	0.631329i	$-0.217490\pi$
$488$	−1.21905	−	3.75186i	−0.0551839	−	0.169839i
$489$	−2.90080	+	8.92773i	−0.131178	+	0.403726i
$490$		0			0
$491$	−1.97176	−	6.06846i	−0.0889844	−	0.273866i	0.896655	−	0.442730i	$-0.145990\pi$
$491$	−1.97176	−	6.06846i	−0.0889844	−	0.273866i	−0.985639	+	0.168864i	$0.945990\pi$
$492$	8.05872	−	5.85500i	0.363315	−	0.263964i
$493$	−0.267201			−0.0120341
$494$	21.5298	−	15.6423i	0.968671	−	0.703780i
$495$		0			0
$496$	1.81386	+	1.31784i	0.0814445	+	0.0591729i
$497$	−22.3200	−	16.2164i	−1.00119	−	0.727405i
$498$	2.31360	−	7.12054i	0.103675	−	0.319079i
$499$	12.9135			0.578087			0.289044	−	0.957316i	$-0.406663\pi$
$499$	12.9135			0.578087			0.289044	+	0.957316i	$0.406663\pi$
$500$		0			0
$501$	6.82883			0.305090
$502$	−0.613732	+	1.88887i	−0.0273922	+	0.0843046i
$503$	−1.17472	−	0.853483i	−0.0523781	−	0.0380549i	0.561288	−	0.827620i	$-0.310306\pi$
$503$	−1.17472	−	0.853483i	−0.0523781	−	0.0380549i	−0.613666	+	0.789566i	$0.710306\pi$
$504$	−2.61428	−	1.89939i	−0.116449	−	0.0846054i
$505$		0			0
$506$	−8.26848	+	6.00740i	−0.367579	+	0.267062i
$507$	21.8621			0.970929
$508$	7.48413	−	5.43754i	0.332055	−	0.241252i
$509$	−3.83481	−	11.8023i	−0.169975	−	0.523130i	0.829393	−	0.558665i	$-0.188686\pi$
$509$	−3.83481	−	11.8023i	−0.169975	−	0.523130i	−0.999368	+	0.0355355i	$0.988686\pi$
$510$		0			0
$511$	3.94855	−	12.1524i	0.174673	−	0.537590i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.39280	−	4.28659i	−0.0614935	−	0.189257i
$514$	−5.95775	+	18.3361i	−0.262785	+	0.808770i
$515$		0			0
$516$	−1.63830	−	5.04216i	−0.0721220	−	0.221969i
$517$	45.1450	−	32.7998i	1.98548	−	1.44253i
$518$	−30.8716			−1.35642
$519$	−15.2584	+	11.0859i	−0.669770	+	0.486617i
$520$		0			0
$521$	−6.42857	−	4.67063i	−0.281641	−	0.204624i	0.437992	−	0.898979i	$-0.355690\pi$
$521$	−6.42857	−	4.67063i	−0.281641	−	0.204624i	−0.719633	+	0.694355i	$0.755690\pi$
$522$	0.210961	+	0.153272i	0.00923350	+	0.00670853i
$523$	10.7632	−	33.1258i	0.470643	−	1.44849i	−0.381101	−	0.924533i	$-0.624455\pi$
$523$	10.7632	−	33.1258i	0.470643	−	1.44849i	0.851745	−	0.523957i	$-0.175545\pi$
$524$	−4.86497			−0.212527
$525$		0			0
$526$	12.5297			0.546320
$527$	−0.709940	+	2.18497i	−0.0309255	+	0.0951788i
$528$	−4.28802	−	3.11543i	−0.186612	−	0.135582i
$529$	15.5993	+	11.3335i	0.678229	+	0.492762i
$530$		0			0
$531$	5.25216	−	3.81592i	0.227924	−	0.165597i
$532$	−14.5646			−0.631457
$533$	47.5820	−	34.5703i	2.06100	−	1.49741i
$534$	−0.226687	−	0.697671i	−0.00980970	−	0.0301912i
$535$		0			0
$536$	2.87142	−	8.83731i	0.124026	−	0.381714i
$537$	0.290889	+	0.895264i	0.0125528	+	0.0386335i
$538$	4.16955	+	12.8326i	0.179762	+	0.553251i
$539$	5.63778	−	17.3513i	0.242837	−	0.747374i
$540$		0			0
$541$	8.70571	+	26.7934i	0.374288	+	1.15194i	0.943958	+	0.330065i	$0.107071\pi$
$541$	8.70571	+	26.7934i	0.374288	+	1.15194i	−0.569670	+	0.821873i	$0.692929\pi$
$542$	21.6926	−	15.7606i	0.931776	−	0.676975i
$543$	14.1057			0.605335
$544$	−0.828995	+	0.602300i	−0.0355429	+	0.0258234i
$545$		0			0
$546$	−15.4358	−	11.2148i	−0.660591	−	0.479947i
$547$	−21.9873	−	15.9747i	−0.940108	−	0.683029i	0.00833839	−	0.999965i	$-0.497346\pi$
$547$	−21.9873	−	15.9747i	−0.940108	−	0.683029i	−0.948447	+	0.316937i	$0.897346\pi$
$548$	1.85925	−	5.72219i	0.0794233	−	0.244440i
$549$	−3.94494			−0.168366
$550$		0			0
$551$	1.17530			0.0500695
$552$	0.595870	−	1.83390i	0.0253619	−	0.0780559i
$553$	34.9565	+	25.3974i	1.48650	+	1.08001i
$554$	−6.60744	−	4.80058i	−0.280723	−	0.203957i
$555$		0			0
$556$	4.55250	−	3.30758i	0.193069	−	0.140273i
$557$	−6.74857			−0.285946			−0.142973	−	0.989727i	$-0.545666\pi$
$557$	−6.74857			−0.285946			−0.142973	+	0.989727i	$0.545666\pi$
$558$	1.81386	−	1.31784i	0.0767867	−	0.0557888i
$559$	−9.67318	−	29.7710i	−0.409132	−	1.25918i
$560$		0			0
$561$	1.67832	−	5.16535i	0.0708589	−	0.218081i
$562$	9.68515	+	29.8078i	0.408543	+	1.25737i
$563$	3.49426	+	10.7542i	0.147265	+	0.453236i	0.997295	−	0.0734982i	$-0.0234163\pi$
$563$	3.49426	+	10.7542i	0.147265	+	0.453236i	−0.850030	+	0.526734i	$0.823416\pi$
$564$	−3.25338	+	10.0129i	−0.136992	+	0.421618i
$565$		0			0
$566$	−5.05253	−	15.5501i	−0.212374	−	0.653620i
$567$	−2.61428	+	1.89939i	−0.109789	+	0.0797667i
$568$	8.53771			0.358234
$569$	−20.4022	+	14.8231i	−0.855304	+	0.621415i	−0.926603	−	0.376040i	$-0.877286\pi$
$569$	−20.4022	+	14.8231i	−0.855304	+	0.621415i	0.0712991	+	0.997455i	$0.477286\pi$
$570$		0			0
$571$	22.4908	+	16.3405i	0.941209	+	0.683828i	0.948711	−	0.316144i	$-0.102388\pi$
$571$	22.4908	+	16.3405i	0.941209	+	0.683828i	−0.00750262	+	0.999972i	$0.502388\pi$
$572$	−25.3182	−	18.3948i	−1.05861	−	0.769124i
$573$	7.87125	−	24.2252i	0.328826	−	1.01202i
$574$	−32.1886			−1.34353
$575$		0			0
$576$	1.00000			0.0416667
$577$	−3.55168	+	10.9309i	−0.147858	+	0.455061i	−0.997367	−	0.0725129i	$-0.976898\pi$
$577$	−3.55168	+	10.9309i	−0.147858	+	0.455061i	0.849509	+	0.527574i	$0.176898\pi$
$578$	12.9038	+	9.37518i	0.536728	+	0.389956i
$579$	5.36734	+	3.89960i	0.223059	+	0.162062i
$580$		0			0
$581$	−19.5731	+	14.2207i	−0.812027	+	0.589972i
$582$	−17.2567			−0.715313
$583$	9.90993	−	7.19998i	0.410427	−	0.298193i
$584$	1.22192	+	3.76068i	0.0505634	+	0.155618i
$585$		0			0
$586$	−8.71017	+	26.8072i	−0.359814	+	1.10739i
$587$	13.0492	+	40.1613i	0.538598	+	1.65763i	0.735745	+	0.677259i	$0.236832\pi$
$587$	13.0492	+	40.1613i	0.538598	+	1.65763i	−0.197147	+	0.980374i	$0.563168\pi$
$588$	1.06368	+	3.27366i	0.0438652	+	0.135003i
$589$	3.12272	−	9.61074i	0.128669	−	0.396004i
$590$		0			0
$591$	−3.14509	−	9.67960i	−0.129372	−	0.398166i
$592$	7.72898	−	5.61543i	0.317659	−	0.230793i
$593$	−0.0131121			−0.000538451			−0.000269225	−	1.00000i	$-0.500086\pi$
$593$	−0.0131121			−0.000538451			−0.000269225		1.00000i	$0.500086\pi$
$594$	−4.28802	+	3.11543i	−0.175940	+	0.127828i
$595$		0			0
$596$	9.42957	+	6.85098i	0.386250	+	0.280627i
$597$	2.04065	+	1.48262i	0.0835183	+	0.0606796i
$598$	3.51826	−	10.8281i	0.143872	−	0.442794i
$599$	2.38072			0.0972738			0.0486369	−	0.998817i	$-0.484512\pi$
$599$	2.38072			0.0972738			0.0486369	+	0.998817i	$0.484512\pi$
$600$		0			0
$601$	−19.6020			−0.799581			−0.399790	−	0.916607i	$-0.630917\pi$
$601$	−19.6020			−0.799581			−0.399790	+	0.916607i	$0.630917\pi$
$602$	−5.29404	+	16.2934i	−0.215769	+	0.664068i
$603$	−7.51747	−	5.46176i	−0.306135	−	0.222420i
$604$	−4.46864	−	3.24666i	−0.181826	−	0.132105i
$605$		0			0
$606$	−9.58313	+	6.96255i	−0.389288	+	0.282834i
$607$	10.7155			0.434930			0.217465	−	0.976068i	$-0.430221\pi$
$607$	10.7155			0.434930			0.217465	+	0.976068i	$0.430221\pi$
$608$	3.64639	−	2.64926i	0.147881	−	0.107442i
$609$	−0.260388	−	0.801391i	−0.0105514	−	0.0324740i
$610$		0			0
$611$	−19.2093	+	59.1202i	−0.777126	+	2.39175i
$612$	0.316648	+	0.974542i	0.0127997	+	0.0393935i
$613$	0.359801	+	1.10735i	0.0145322	+	0.0447256i	0.958060	−	0.286569i	$-0.0925147\pi$
$613$	0.359801	+	1.10735i	0.0145322	+	0.0447256i	−0.943527	+	0.331294i	$0.892515\pi$
$614$	−4.49223	+	13.8257i	−0.181292	+	0.557959i
$615$		0			0
$616$	5.29269	+	16.2892i	0.213248	+	0.656311i
$617$	−18.3190	+	13.3095i	−0.737495	+	0.535821i	−0.891926	−	0.452182i	$-0.850646\pi$
$617$	−18.3190	+	13.3095i	−0.737495	+	0.535821i	0.154431	+	0.988004i	$0.450646\pi$
$618$	−7.15084			−0.287649
$619$	−20.0413	+	14.5609i	−0.805529	+	0.585251i	−0.912531	−	0.409008i	$-0.865875\pi$
$619$	−20.0413	+	14.5609i	−0.805529	+	0.585251i	0.107002	+	0.994259i	$0.465875\pi$
$620$		0			0
$621$	−1.56001	−	1.13341i	−0.0626009	−	0.0454822i
$622$	−11.7246	−	8.51844i	−0.470115	−	0.341559i
$623$	−0.732522	+	2.25447i	−0.0293479	+	0.0903235i
$624$	5.90441			0.236366
$625$		0			0
$626$	−31.5288			−1.26014
$627$	−7.38222	+	22.7201i	−0.294817	+	0.907355i
$628$	5.53616	+	4.02225i	0.220917	+	0.160505i
$629$	7.91983	+	5.75410i	0.315784	+	0.229431i
$630$		0			0
$631$	26.4156	−	19.1920i	1.05159	−	0.764023i	0.0790740	−	0.996869i	$-0.474804\pi$
$631$	26.4156	−	19.1920i	1.05159	−	0.764023i	0.972514	+	0.232845i	$0.0748036\pi$
$632$	−13.3714			−0.531885
$633$	−12.7532	+	9.26574i	−0.506894	+	0.368280i
$634$	−4.62940	−	14.2478i	−0.183857	−	0.565853i
$635$		0			0
$636$	−0.714161	+	2.19796i	−0.0283183	+	0.0871548i
$637$	6.28038	+	19.3290i	0.248838	+	0.765844i
$638$	−0.427096	−	1.31447i	−0.0169089	−	0.0520402i
$639$	2.63830	−	8.11984i	0.104369	−	0.321216i
$640$		0			0
$641$	−8.29842	−	25.5399i	−0.327768	−	1.00877i	−0.970176	−	0.242403i	$-0.922064\pi$
$641$	−8.29842	−	25.5399i	−0.327768	−	1.00877i	0.642408	−	0.766363i	$-0.277936\pi$
$642$	−2.58932	+	1.88125i	−0.102193	+	0.0742472i
$643$	17.1051			0.674559			0.337279	−	0.941405i	$-0.390493\pi$
$643$	17.1051			0.674559			0.337279	+	0.941405i	$0.390493\pi$
$644$	−5.04105	+	3.66254i	−0.198645	+	0.144324i
$645$		0			0
$646$	3.73643	+	2.71468i	0.147008	+	0.106808i
$647$	37.0639	+	26.9285i	1.45713	+	1.05867i	0.984098	+	0.177626i	$0.0568418\pi$
$647$	37.0639	+	26.9285i	1.45713	+	1.05867i	0.473036	+	0.881043i	$0.343158\pi$
$648$	0.309017	−	0.951057i	0.0121393	−	0.0373610i
$649$	−34.4096			−1.35069
$650$		0			0
$651$	−7.24502			−0.283955
$652$	−2.90080	+	8.92773i	−0.113604	+	0.349637i
$653$	9.26769	+	6.73337i	0.362673	+	0.263497i	0.754166	−	0.656684i	$-0.228041\pi$
$653$	9.26769	+	6.73337i	0.362673	+	0.263497i	−0.391493	+	0.920181i	$0.628041\pi$
$654$	−8.00567	−	5.81646i	−0.313046	−	0.227442i
$655$		0			0
$656$	8.05872	−	5.85500i	0.314640	−	0.228599i
$657$	3.95422			0.154269
$658$	27.5236	−	19.9971i	1.07298	−	0.779566i
$659$	12.3601	+	38.0405i	0.481482	+	1.48185i	0.837013	+	0.547183i	$0.184300\pi$
$659$	12.3601	+	38.0405i	0.481482	+	1.48185i	−0.355531	+	0.934664i	$0.615700\pi$
$660$		0			0
$661$	−1.75871	+	5.41276i	−0.0684060	+	0.210532i	−0.979416	−	0.201852i	$-0.935304\pi$
$661$	−1.75871	+	5.41276i	−0.0684060	+	0.210532i	0.911010	+	0.412384i	$0.135304\pi$
$662$	−6.68014	−	20.5594i	−0.259631	−	0.799062i
$663$	1.86962	+	5.75410i	0.0726100	+	0.223471i
$664$	2.31360	−	7.12054i	0.0897852	−	0.276331i
$665$		0			0
$666$	−2.95221	−	9.08596i	−0.114396	−	0.352074i
$667$	0.406790	−	0.295550i	0.0157510	−	0.0114438i
$668$	6.82883			0.264215
$669$	7.52009	−	5.46366i	0.290743	−	0.211237i
$670$		0			0
$671$	16.9160	+	12.2902i	0.653034	+	0.474457i
$672$	−2.61428	−	1.89939i	−0.100848	−	0.0732704i
$673$	−14.9727	+	46.0813i	−0.577156	+	1.77630i	0.0515628	+	0.998670i	$0.483580\pi$
$673$	−14.9727	+	46.0813i	−0.577156	+	1.77630i	−0.628719	+	0.777633i	$0.716420\pi$
$674$	−7.59495			−0.292547
$675$		0			0
$676$	21.8621			0.840849
$677$	−5.71966	+	17.6033i	−0.219824	+	0.676550i	0.778951	+	0.627084i	$0.215752\pi$
$677$	−5.71966	+	17.6033i	−0.219824	+	0.676550i	−0.998776	+	0.0494656i	$0.984248\pi$
$678$	3.43488	+	2.49559i	0.131916	+	0.0958424i
$679$	45.1138	+	32.7771i	1.73131	+	1.25787i
$680$		0			0
$681$	2.94327	−	2.13841i	0.112787	−	0.0819442i
$682$	−11.8835			−0.455043
$683$	−29.1442	+	21.1745i	−1.11517	+	0.810219i	−0.983470	−	0.181070i	$-0.942044\pi$
$683$	−29.1442	+	21.1745i	−1.11517	+	0.810219i	−0.131701	+	0.991289i	$0.542044\pi$
$684$	−1.39280	−	4.28659i	−0.0532549	−	0.163902i
$685$		0			0
$686$	−3.55277	+	10.9343i	−0.135645	+	0.417474i
$687$	3.06910	+	9.44571i	0.117093	+	0.360376i
$688$	−1.63830	−	5.04216i	−0.0624595	−	0.192231i
$689$	−4.21670	+	12.9777i	−0.160643	+	0.494410i
$690$		0			0
$691$	−4.47133	−	13.7613i	−0.170097	−	0.523506i	0.829278	−	0.558836i	$-0.188752\pi$
$691$	−4.47133	−	13.7613i	−0.170097	−	0.523506i	−0.999376	+	0.0353301i	$0.988752\pi$
$692$	−15.2584	+	11.0859i	−0.580038	+	0.421422i
$693$	17.1275			0.650620
$694$	6.09436	−	4.42781i	0.231339	−	0.168077i
$695$		0			0
$696$	0.210961	+	0.153272i	0.00799644	+	0.00580976i
$697$	8.25772	+	5.99958i	0.312783	+	0.227250i
$698$	5.79489	−	17.8349i	0.219340	−	0.675059i
$699$	18.7893			0.710678
$700$		0			0
$701$	8.31284			0.313972			0.156986	−	0.987601i	$-0.449822\pi$
$701$	8.31284			0.313972			0.156986	+	0.987601i	$0.449822\pi$
$702$	1.82456	−	5.61543i	0.0688637	−	0.211941i
$703$	−34.8359	−	25.3098i	−1.31386	−	0.954576i
$704$	−4.28802	−	3.11543i	−0.161611	−	0.117417i
$705$		0			0
$706$	−3.53223	+	2.56631i	−0.132937	+	0.0965845i
$707$	38.2776			1.43958
$708$	5.25216	−	3.81592i	0.197388	−	0.143411i
$709$	−2.77255	−	8.53302i	−0.104125	−	0.320464i	0.885399	−	0.464832i	$-0.153885\pi$
$709$	−2.77255	−	8.53302i	−0.104125	−	0.320464i	−0.989524	+	0.144368i	$0.953885\pi$
$710$		0			0
$711$	−4.13198	+	12.7169i	−0.154962	+	0.476923i
$712$	−0.226687	−	0.697671i	−0.00849545	−	0.0261463i
$713$	−1.33597	−	4.11169i	−0.0500324	−	0.153984i
$714$	1.02322	−	3.14916i	0.0382932	−	0.117854i
$715$		0			0
$716$	0.290889	+	0.895264i	0.0108710	+	0.0334576i
$717$	7.88942	−	5.73200i	0.294636	−	0.214065i
$718$	0.737212			0.0275125
$719$	−22.7445	+	16.5249i	−0.848228	+	0.616274i	−0.924657	−	0.380801i	$-0.875648\pi$
$719$	−22.7445	+	16.5249i	−0.848228	+	0.616274i	0.0764289	+	0.997075i	$0.475648\pi$
$720$		0			0
$721$	18.6943	+	13.5822i	0.696212	+	0.505828i
$722$	−1.06363	−	0.772769i	−0.0395840	−	0.0287595i
$723$	5.84694	−	17.9950i	0.217450	−	0.669242i
$724$	14.1057			0.524235
$725$		0			0
$726$	17.0930			0.634382
$727$	7.68734	−	23.6592i	0.285108	−	0.877471i	−0.701259	−	0.712907i	$-0.747378\pi$
$727$	7.68734	−	23.6592i	0.285108	−	0.877471i	0.986366	−	0.164564i	$-0.0526217\pi$
$728$	−15.4358	−	11.2148i	−0.572088	−	0.415647i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	4.39503	−	3.19318i	0.162556	−	0.118104i
$732$	−3.94494			−0.145809
$733$	5.46572	−	3.97108i	0.201881	−	0.146675i	−0.482252	−	0.876033i	$-0.660181\pi$
$733$	5.46572	−	3.97108i	0.201881	−	0.146675i	0.684133	+	0.729358i	$0.260181\pi$
$734$	5.82807	+	17.9370i	0.215118	+	0.662065i
$735$		0			0
$736$	0.595870	−	1.83390i	0.0219640	−	0.0675984i
$737$	15.2193	+	46.8403i	0.560611	+	1.72538i
$738$	−3.07816	−	9.47359i	−0.113308	−	0.348728i
$739$	−1.57339	+	4.84241i	−0.0578783	+	0.178131i	−0.975816	−	0.218593i	$-0.929853\pi$
$739$	−1.57339	+	4.84241i	−0.0578783	+	0.178131i	0.917938	+	0.396724i	$0.129853\pi$
$740$		0			0
$741$	−8.22365	−	25.3098i	−0.302103	−	0.929778i
$742$	6.04179	−	4.38962i	0.221801	−	0.161148i
$743$	16.0999			0.590647			0.295324	−	0.955397i	$-0.404573\pi$
$743$	16.0999			0.590647			0.295324	+	0.955397i	$0.404573\pi$
$744$	1.81386	−	1.31784i	0.0664992	−	0.0483145i
$745$		0			0
$746$	24.1383	+	17.5375i	0.883768	+	0.642095i
$747$	−6.05709	−	4.40074i	−0.221617	−	0.161015i
$748$	1.67832	−	5.16535i	0.0613656	−	0.188864i
$749$	10.3424			0.377905
$750$		0			0
$751$	−25.4366			−0.928196			−0.464098	−	0.885784i	$-0.653622\pi$
$751$	−25.4366			−0.928196			−0.464098	+	0.885784i	$0.653622\pi$
$752$	−3.25338	+	10.0129i	−0.118639	+	0.365132i
$753$	1.60677	+	1.16739i	0.0585540	+	0.0425420i
$754$	1.24560	+	0.904981i	0.0453620	+	0.0329575i
$755$		0			0
$756$	−2.61428	+	1.89939i	−0.0950804	+	0.0690800i
$757$	−12.4947			−0.454129			−0.227064	−	0.973880i	$-0.572913\pi$
$757$	−12.4947			−0.454129			−0.227064	+	0.973880i	$0.572913\pi$
$758$	−20.6159	+	14.9783i	−0.748802	+	0.544037i
$759$	3.15828	+	9.72018i	0.114638	+	0.352820i
$760$		0			0
$761$	−3.58120	+	11.0218i	−0.129818	+	0.399540i	−0.994748	−	0.102353i	$-0.967363\pi$
$761$	−3.58120	+	11.0218i	−0.129818	+	0.399540i	0.864930	+	0.501893i	$0.167363\pi$
$762$	−2.85868	−	8.79813i	−0.103559	−	0.318723i
$763$	9.88136	+	30.4117i	0.357729	+	1.10098i
$764$	7.87125	−	24.2252i	0.284772	−	0.876438i
$765$		0			0
$766$	9.77832	+	30.0946i	0.353305	+	1.08736i
$767$	31.0109	−	22.5307i	1.11974	−	0.813538i
$768$	1.00000			0.0360844
$769$	19.2155	−	13.9609i	0.692927	−	0.503441i	−0.184694	−	0.982796i	$-0.559129\pi$
$769$	19.2155	−	13.9609i	0.692927	−	0.503441i	0.877621	+	0.479355i	$0.159129\pi$
$770$		0			0
$771$	15.5976	+	11.3323i	0.561734	+	0.408124i
$772$	5.36734	+	3.89960i	0.193175	+	0.140350i
$773$	−3.73754	+	11.5030i	−0.134430	+	0.413732i	−0.995501	−	0.0947521i	$-0.969794\pi$
$773$	−3.73754	+	11.5030i	−0.134430	+	0.413732i	0.861071	+	0.508485i	$0.169794\pi$
$774$	−5.30164			−0.190564
$775$		0			0
$776$	−17.2567			−0.619479
$777$	−9.53984	+	29.3606i	−0.342240	+	1.05331i
$778$	−9.74704	−	7.08164i	−0.349448	−	0.253889i
$779$	−36.3221	−	26.3896i	−1.30138	−	0.945504i
$780$		0			0
$781$	−36.6099	+	26.5986i	−1.31000	+	0.951774i
$782$	1.97589			0.0706577
$783$	0.210961	−	0.153272i	0.00753912	−	0.00547749i
$784$	1.06368	+	3.27366i	0.0379884	+	0.116916i
$785$		0			0
$786$	−1.50336	+	4.62686i	−0.0536230	+	0.165035i
$787$	6.27371	+	19.3085i	0.223634	+	0.688274i	0.998427	+	0.0560597i	$0.0178537\pi$
$787$	6.27371	+	19.3085i	0.223634	+	0.688274i	−0.774794	+	0.632214i	$0.782146\pi$
$788$	−3.14509	−	9.67960i	−0.112039	−	0.344821i
$789$	3.87188	−	11.9164i	0.137843	−	0.424236i
$790$		0			0
$791$	−4.23966	−	13.0483i	−0.150745	−	0.463945i
$792$	−4.28802	+	3.11543i	−0.152368	+	0.110702i
$793$	−23.2925			−0.827142
$794$	−20.8374	+	15.1393i	−0.739493	+	0.537273i
$795$		0			0
$796$	2.04065	+	1.48262i	0.0723290	+	0.0525501i
$797$	−25.6479	−	18.6343i	−0.908493	−	0.660059i	0.0321399	−	0.999483i	$-0.489768\pi$
$797$	−25.6479	−	18.6343i	−0.908493	−	0.660059i	−0.940633	+	0.339424i	$0.889768\pi$
$798$	−4.50072	+	13.8518i	−0.159324	+	0.490348i
$799$	−10.7881			−0.381657
$800$		0			0
$801$	−0.733574			−0.0259196
$802$	8.13321	−	25.0314i	0.287194	−	0.883891i
$803$	−16.9558	−	12.3191i	−0.598356	−	0.434731i
$804$	−7.51747	−	5.46176i	−0.265121	−	0.192621i
$805$		0			0
$806$	10.7098	−	7.78109i	0.377235	−	0.274077i
$807$	13.4929			0.474974
$808$	−9.58313	+	6.96255i	−0.337133	+	0.244942i
$809$	2.69637	+	8.29856i	0.0947992	+	0.291762i	0.987201	−	0.159479i	$-0.0509815\pi$
$809$	2.69637	+	8.29856i	0.0947992	+	0.291762i	−0.892402	+	0.451241i	$0.850981\pi$
$810$		0			0
$811$	4.69774	−	14.4581i	0.164960	−	0.507694i	−0.834074	−	0.551653i	$-0.813997\pi$
$811$	4.69774	−	14.4581i	0.164960	−	0.507694i	0.999033	+	0.0439592i	$0.0139972\pi$
$812$	−0.260388	−	0.801391i	−0.00913782	−	0.0281233i
$813$	−8.28583	−	25.5012i	−0.290597	−	0.894365i
$814$	−15.6475	+	48.1582i	−0.548446	+	1.68794i
$815$		0			0
$816$	0.316648	+	0.974542i	0.0110849	+	0.0341158i
$817$	−19.3318	+	14.0454i	−0.676336	+	0.491387i
$818$	36.7714			1.28568
$819$	−15.4358	+	11.2148i	−0.539370	+	0.391875i
$820$		0			0
$821$	−13.3160	−	9.67465i	−0.464732	−	0.337648i	0.330653	−	0.943753i	$-0.392731\pi$
$821$	−13.3160	−	9.67465i	−0.464732	−	0.337648i	−0.795385	+	0.606105i	$0.792731\pi$
$822$	−4.86758	−	3.53651i	−0.169776	−	0.123350i
$823$	7.10692	−	21.8728i	0.247732	−	0.762439i	−0.747444	−	0.664325i	$-0.768719\pi$
$823$	7.10692	−	21.8728i	0.247732	−	0.762439i	0.995175	−	0.0981141i	$-0.0312810\pi$
$824$	−7.15084			−0.249111
$825$		0			0
$826$	−20.9785			−0.729936
$827$	7.64257	−	23.5214i	0.265758	−	0.817919i	−0.725760	−	0.687948i	$-0.758512\pi$
$827$	7.64257	−	23.5214i	0.265758	−	0.817919i	0.991518	−	0.129971i	$-0.0414884\pi$
$828$	−1.56001	−	1.13341i	−0.0542140	−	0.0393888i
$829$	−16.8789	−	12.2632i	−0.586227	−	0.425919i	0.254736	−	0.967011i	$-0.418011\pi$
$829$	−16.8789	−	12.2632i	−0.586227	−	0.425919i	−0.840964	+	0.541091i	$0.818011\pi$
$830$		0			0
$831$	−6.60744	+	4.80058i	−0.229209	+	0.166530i
$832$	5.90441			0.204699
$833$	−2.85350	+	2.07319i	−0.0988681	+	0.0718319i
$834$	−1.73890	−	5.35178i	−0.0602132	−	0.185317i
$835$		0			0
$836$	−7.38222	+	22.7201i	−0.255319	+	0.785792i
$837$	−0.692831	−	2.13232i	−0.0239478	−	0.0737036i
$838$	−9.80341	−	30.1718i	−0.338653	−	1.04227i
$839$	−7.29166	+	22.4414i	−0.251736	+	0.774764i	0.742719	+	0.669603i	$0.233536\pi$
$839$	−7.29166	+	22.4414i	−0.251736	+	0.774764i	−0.994455	+	0.105161i	$0.966464\pi$
$840$		0			0
$841$	−8.94048	−	27.5160i	−0.308292	−	0.948827i
$842$	−7.13332	+	5.18266i	−0.245830	+	0.178606i
$843$	31.3418			1.07947
$844$	−12.7532	+	9.26574i	−0.438983	+	0.318940i
$845$		0			0
$846$	8.51747	+	6.18830i	0.292837	+	0.212758i
$847$	−44.6860	−	32.4663i	−1.53543	−	1.11555i
$848$	−0.714161	+	2.19796i	−0.0245244	+	0.0754783i
$849$	−16.3503			−0.561142
$850$		0			0
$851$	−18.4218			−0.631493
$852$	2.63830	−	8.11984i	0.0903866	−	0.278181i
$853$	21.3280	+	15.4957i	0.730257	+	0.530563i	0.889645	−	0.456653i	$-0.150952\pi$
$853$	21.3280	+	15.4957i	0.730257	+	0.530563i	−0.159388	+	0.987216i	$0.550952\pi$
$854$	10.3132	+	7.49296i	0.352910	+	0.256404i
$855$		0			0
$856$	−2.58932	+	1.88125i	−0.0885013	+	0.0643000i
$857$	−16.0891			−0.549593			−0.274797	−	0.961502i	$-0.588611\pi$
$857$	−16.0891			−0.549593			−0.274797	+	0.961502i	$0.588611\pi$
$858$	−25.3182	+	18.3948i	−0.864351	+	0.627987i
$859$	3.26846	+	10.0593i	0.111519	+	0.343219i	0.991205	−	0.132335i	$-0.0422476\pi$
$859$	3.26846	+	10.0593i	0.111519	+	0.343219i	−0.879686	+	0.475554i	$0.842248\pi$
$860$		0			0
$861$	−9.94684	+	30.6132i	−0.338987	+	1.04330i
$862$	7.26392	+	22.3560i	0.247410	+	0.761450i
$863$	12.9051	+	39.7177i	0.439293	+	1.35201i	0.888622	+	0.458640i	$0.151663\pi$
$863$	12.9051	+	39.7177i	0.439293	+	1.35201i	−0.449329	+	0.893366i	$0.648337\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$		0			0
$866$	−2.59671	−	7.99185i	−0.0882397	−	0.271574i
$867$	12.9038	−	9.37518i	0.438237	−	0.318398i
$868$	−7.24502			−0.245912
$869$	57.3368	−	41.6576i	1.94502	−	1.41314i
$870$		0			0
$871$	−44.3862	−	32.2485i	−1.50397	−	1.09270i
$872$	−8.00567	−	5.81646i	−0.271106	−	0.196970i
$873$	−5.33261	+	16.4121i	−0.180481	+	0.555465i
$874$	−8.69109			−0.293980
$875$		0			0
$876$	3.95422			0.133601
$877$	−9.83498	+	30.2690i	−0.332104	+	1.02211i	0.636027	+	0.771667i	$0.280577\pi$
$877$	−9.83498	+	30.2690i	−0.332104	+	1.02211i	−0.968131	+	0.250444i	$0.919423\pi$
$878$	−28.8273	−	20.9443i	−0.972875	−	0.706835i
$879$	22.8035	+	16.5677i	0.769144	+	0.558816i
$880$		0			0
$881$	40.1535	−	29.1732i	1.35280	−	0.982870i	0.353938	−	0.935269i	$-0.384842\pi$
$881$	40.1535	−	29.1732i	1.35280	−	0.982870i	0.998866	−	0.0476012i	$-0.0151577\pi$
$882$	3.44213			0.115902
$883$	4.09442	−	2.97477i	0.137788	−	0.100109i	−0.516756	−	0.856133i	$-0.672861\pi$
$883$	4.09442	−	2.97477i	0.137788	−	0.100109i	0.654544	+	0.756024i	$0.272861\pi$
$884$	1.86962	+	5.75410i	0.0628821	+	0.193531i
$885$		0			0
$886$	−2.09992	+	6.46290i	−0.0705483	+	0.217125i
$887$	3.41594	+	10.5132i	0.114696	+	0.352998i	0.991884	−	0.127150i	$-0.0405829\pi$
$887$	3.41594	+	10.5132i	0.114696	+	0.352998i	−0.877187	+	0.480148i	$0.840583\pi$
$888$	−2.95221	−	9.08596i	−0.0990696	−	0.304905i
$889$	−9.23763	+	28.4305i	−0.309820	+	0.953529i
$890$		0			0
$891$	1.63788	+	5.04087i	0.0548710	+	0.168876i
$892$	7.52009	−	5.46366i	0.251791	−	0.182937i
$893$	47.4524			1.58793
$894$	9.42957	−	6.85098i	0.315372	−	0.229131i
$895$		0			0
$896$	−2.61428	−	1.89939i	−0.0873370	−	0.0634540i
$897$	−9.21092	−	6.69213i	−0.307544	−	0.223444i
$898$	2.70393	−	8.32185i	0.0902314	−	0.277704i
$899$	0.584641			0.0194989
$900$		0			0
$901$	−2.36814			−0.0788942
$902$	−16.3151	+	50.2127i	−0.543234	+	1.67190i
$903$	13.8600	+	10.0699i	0.461231	+	0.335104i
$904$	3.43488	+	2.49559i	0.114242	+	0.0830020i
$905$		0			0
$906$	−4.46864	+	3.24666i	−0.148461	+	0.107863i
$907$	−7.57086			−0.251386			−0.125693	−	0.992069i	$-0.540115\pi$
$907$	−7.57086			−0.251386			−0.125693	+	0.992069i	$0.540115\pi$
$908$	2.94327	−	2.13841i	0.0976760	−	0.0709658i
$909$	3.66043	+	11.2656i	0.121409	+	0.373658i
$910$		0			0
$911$	11.0530	−	34.0177i	0.366203	−	1.12706i	−0.583021	−	0.812457i	$-0.698129\pi$
$911$	11.0530	−	34.0177i	0.366203	−	1.12706i	0.949224	−	0.314601i	$-0.101871\pi$
$912$	−1.39280	−	4.28659i	−0.0461201	−	0.141943i
$913$	12.2628	+	37.7409i	0.405838	+	1.24904i
$914$	11.7882	−	36.2803i	0.389919	−	1.20005i
$915$		0			0
$916$	3.06910	+	9.44571i	0.101406	+	0.312095i
$917$	12.7184	−	9.24046i	0.419998	−	0.305147i
$918$	1.02469			0.0338199
$919$	40.1464	−	29.1680i	1.32431	−	0.962165i	0.324438	−	0.945907i	$-0.394825\pi$
$919$	40.1464	−	29.1680i	1.32431	−	0.962165i	0.999868	−	0.0162579i	$-0.00517529\pi$
$920$		0			0
$921$	11.7608	+	8.54474i	0.387532	+	0.281559i
$922$	1.02807	+	0.746939i	0.0338578	+	0.0245991i
$923$	15.5776	−	47.9429i	0.512743	−	1.57806i
$924$	17.1275			0.563453
$925$		0			0
$926$	−8.93349			−0.293573
$927$	−2.20973	+	6.80085i	−0.0725771	+	0.223369i
$928$	0.210961	+	0.153272i	0.00692512	+	0.00503140i
$929$	13.1559	+	9.55836i	0.431633	+	0.313599i	0.782301	−	0.622900i	$-0.214046\pi$
$929$	13.1559	+	9.55836i	0.431633	+	0.313599i	−0.350669	+	0.936500i	$0.614046\pi$
$930$		0			0
$931$	12.5513	−	9.11908i	0.411353	−	0.298866i
$932$	18.7893			0.615465
$933$	−11.7246	+	8.51844i	−0.383847	+	0.278881i
$934$	1.77896	+	5.47507i	0.0582092	+	0.179150i
$935$		0			0
$936$	1.82456	−	5.61543i	0.0596377	−	0.183546i
$937$	0.176101	+	0.541982i	0.00575296	+	0.0177058i	0.953892	−	0.300151i	$-0.0970370\pi$
$937$	0.176101	+	0.541982i	0.00575296	+	0.0177058i	−0.948139	+	0.317857i	$0.897037\pi$
$938$	9.27878	+	28.5571i	0.302963	+	0.932424i
$939$	−9.74294	+	29.9857i	−0.317949	+	0.978545i
$940$		0			0
$941$	2.16169	+	6.65300i	0.0704691	+	0.216882i	0.980089	−	0.198561i	$-0.0636267\pi$
$941$	2.16169	+	6.65300i	0.0704691	+	0.216882i	−0.909619	+	0.415443i	$0.863627\pi$
$942$	5.53616	−	4.02225i	0.180378	−	0.131052i
$943$	−19.2078			−0.625491
$944$	5.25216	−	3.81592i	0.170943	−	0.124198i
$945$		0			0
$946$	22.7335	+	16.5169i	0.739131	+	0.537010i
$947$	−27.8804	−	20.2563i	−0.905991	−	0.658241i	0.0340070	−	0.999422i	$-0.489173\pi$
$947$	−27.8804	−	20.2563i	−0.905991	−	0.658241i	−0.939998	+	0.341181i	$0.889173\pi$
$948$	−4.13198	+	12.7169i	−0.134201	+	0.413027i
$949$	23.3473			0.757886
$950$		0			0
$951$	−14.9810			−0.485794
$952$	1.02322	−	3.14916i	0.0331629	−	0.102065i
$953$	−34.0081	−	24.7083i	−1.10163	−	0.800382i	−0.120305	−	0.992737i	$-0.538387\pi$
$953$	−34.0081	−	24.7083i	−1.10163	−	0.800382i	−0.981325	+	0.192355i	$0.938387\pi$
$954$	1.86970	+	1.35841i	0.0605337	+	0.0439803i
$955$		0			0
$956$	7.88942	−	5.73200i	0.255162	−	0.185386i
$957$	−1.38211			−0.0446773
$958$	3.74616	−	2.72175i	0.121033	−	0.0879356i
$959$	6.00804	+	18.4908i	0.194010	+	0.597100i
$960$		0			0
$961$	−8.02616	+	24.7020i	−0.258909	+	0.796839i
$962$	−17.4310	−	53.6472i	−0.561999	−	1.72966i
$963$	0.989034	+	3.04393i	0.0318712	+	0.0980894i
$964$	5.84694	−	17.9950i	0.188317	−	0.579580i
$965$		0			0
$966$	1.92551	+	5.92611i	0.0619523	+	0.190669i
$967$	9.68283	−	7.03499i	0.311379	−	0.226230i	−0.421109	−	0.907010i	$-0.638359\pi$
$967$	9.68283	−	7.03499i	0.311379	−	0.226230i	0.732488	+	0.680780i	$0.238359\pi$
$968$	17.0930			0.549391
$969$	3.73643	−	2.71468i	0.120031	−	0.0872080i
$970$		0			0
$971$	−1.09374	−	0.794651i	−0.0350999	−	0.0255016i	0.570097	−	0.821577i	$-0.306906\pi$
$971$	−1.09374	−	0.794651i	−0.0350999	−	0.0255016i	−0.605197	+	0.796076i	$0.706906\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−5.61913	+	17.2939i	−0.180141	+	0.554417i
$974$	−15.9235			−0.510223
$975$		0			0
$976$	−3.94494			−0.126274
$977$	5.73065	−	17.6371i	0.183340	−	0.564262i	−0.816576	−	0.577238i	$-0.804131\pi$
$977$	5.73065	−	17.6371i	0.183340	−	0.564262i	0.999916	+	0.0129761i	$0.00413053\pi$
$978$	7.59438	+	5.51764i	0.242842	+	0.176435i
$979$	3.14558	+	2.28540i	0.100533	+	0.0730417i
$980$		0			0
$981$	−8.00567	+	5.81646i	−0.255601	+	0.185705i
$982$	−6.38076			−0.203618
$983$	13.2534	−	9.62915i	0.422718	−	0.307122i	−0.356013	−	0.934481i	$-0.615864\pi$
$983$	13.2534	−	9.62915i	0.422718	−	0.307122i	0.778730	+	0.627359i	$0.215864\pi$
$984$	−3.07816	−	9.47359i	−0.0981280	−	0.302007i
$985$		0			0
$986$	−0.0825696	+	0.254123i	−0.00262955	+	0.00809293i
$987$	−10.5131	−	32.3559i	−0.334635	−	1.02990i
$988$	−8.22365	−	25.3098i	−0.261629	−	0.805211i
$989$	−3.15909	+	9.72267i	−0.100453	+	0.309163i
$990$		0			0
$991$	6.12790	+	18.8597i	0.194659	+	0.599099i	0.999980	+	0.00626045i	$0.00199278\pi$
$991$	6.12790	+	18.8597i	0.194659	+	0.599099i	−0.805321	+	0.592839i	$0.798007\pi$
$992$	1.81386	−	1.31784i	0.0575900	−	0.0418416i
$993$	−21.6174			−0.686007
$994$	−22.3200	+	16.2164i	−0.707946	+	0.514353i
$995$		0			0
$996$	−6.05709	−	4.40074i	−0.191926	−	0.139443i
$997$	8.46835	+	6.15262i	0.268195	+	0.194855i	0.713752	−	0.700398i	$-0.246994\pi$
$997$	8.46835	+	6.15262i	0.268195	+	0.194855i	−0.445557	+	0.895254i	$0.646994\pi$
$998$	3.99049	−	12.2815i	0.126317	−	0.388763i
$999$	−9.55354			−0.302261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.f.601.4		16
5.2	odd	4		150.2.h.b.79.3	yes	16
5.3	odd	4		750.2.h.d.649.1		16
5.4	even	2		750.2.g.g.601.1		16
15.2	even	4		450.2.l.c.379.2		16
25.6	even	5	inner	750.2.g.f.151.4		16
25.8	odd	20		150.2.h.b.19.3	✓	16
25.9	even	10		3750.2.a.u.1.2		8
25.12	odd	20		3750.2.c.k.1249.15		16
25.13	odd	20		3750.2.c.k.1249.2		16
25.16	even	5		3750.2.a.v.1.7		8
25.17	odd	20		750.2.h.d.349.2		16
25.19	even	10		750.2.g.g.151.1		16
75.8	even	20		450.2.l.c.19.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.3	✓	16	25.8	odd	20
150.2.h.b.79.3	yes	16	5.2	odd	4
450.2.l.c.19.2		16	75.8	even	20
450.2.l.c.379.2		16	15.2	even	4
750.2.g.f.151.4		16	25.6	even	5	inner
750.2.g.f.601.4		16	1.1	even	1	trivial
750.2.g.g.151.1		16	25.19	even	10
750.2.g.g.601.1		16	5.4	even	2
750.2.h.d.349.2		16	25.17	odd	20
750.2.h.d.649.1		16	5.3	odd	4
3750.2.a.u.1.2		8	25.9	even	10
3750.2.a.v.1.7		8	25.16	even	5
3750.2.c.k.1249.2		16	25.13	odd	20
3750.2.c.k.1249.15		16	25.12	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} +3.23143 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.63788 - 5.04087i) q^{11} +(0.309017 + 0.951057i) q^{12} +(1.82456 + 5.61543i) q^{13} +(0.998566 - 3.07327i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.828995 + 0.602300i) q^{17} +1.00000 q^{18} +(3.64639 - 2.64926i) q^{19} +(-2.61428 - 1.89939i) q^{21} +(-4.28802 - 3.11543i) q^{22} +(0.595870 - 1.83390i) q^{23} +1.00000 q^{24} +5.90441 q^{26} +(0.309017 - 0.951057i) q^{27} +(-2.61428 - 1.89939i) q^{28} +(0.210961 + 0.153272i) q^{29} +(1.81386 - 1.31784i) q^{31} +1.00000 q^{32} +(-4.28802 + 3.11543i) q^{33} +(0.316648 + 0.974542i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-2.95221 - 9.08596i) q^{37} +(-1.39280 - 4.28659i) q^{38} +(1.82456 - 5.61543i) q^{39} +(-3.07816 - 9.47359i) q^{41} +(-2.61428 + 1.89939i) q^{42} -5.30164 q^{43} +(-4.28802 + 3.11543i) q^{44} +(-1.56001 - 1.13341i) q^{46} +(8.51747 + 6.18830i) q^{47} +(0.309017 - 0.951057i) q^{48} +3.44213 q^{49} +1.02469 q^{51} +(1.82456 - 5.61543i) q^{52} +(1.86970 + 1.35841i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-2.61428 + 1.89939i) q^{56} -4.50718 q^{57} +(0.210961 - 0.153272i) q^{58} +(-2.00615 - 6.17428i) q^{59} +(-1.21905 + 3.75186i) q^{61} +(-0.692831 - 2.13232i) q^{62} +(0.998566 + 3.07327i) q^{63} +(0.309017 - 0.951057i) q^{64} +(1.63788 + 5.04087i) q^{66} +(-7.51747 + 5.46176i) q^{67} +1.02469 q^{68} +(-1.56001 + 1.13341i) q^{69} +(-6.90715 - 5.01834i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(1.22192 - 3.76068i) q^{73} -9.55354 q^{74} -4.50718 q^{76} +(5.29269 - 16.2892i) q^{77} +(-4.77677 - 3.47053i) q^{78} +(10.8177 + 7.85950i) q^{79} +(-0.809017 + 0.587785i) q^{81} -9.96112 q^{82} +(-6.05709 + 4.40074i) q^{83} +(0.998566 + 3.07327i) q^{84} +(-1.63830 + 5.04216i) q^{86} +(-0.0805798 - 0.247999i) q^{87} +(1.63788 + 5.04087i) q^{88} +(-0.226687 + 0.697671i) q^{89} +(5.89595 + 18.1459i) q^{91} +(-1.56001 + 1.13341i) q^{92} -2.24205 q^{93} +(8.51747 - 6.18830i) q^{94} +(-0.809017 - 0.587785i) q^{96} +(13.9610 + 10.1432i) q^{97} +(1.06368 - 3.27366i) q^{98} +5.30029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26}+ \cdots + 12 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more