LMFDB - Embedded newform 375.2.g.e.76.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not 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:	$2.99439007580$
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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			76.4
Root			$2.53767i$ of defining polynomial
Character	$\chi$	$=$	375.76
Dual form			375.2.g.e.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05302 + 1.49161i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.37197 + 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054 q^{7} +(-1.91324 + 5.88835i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(2.05302 + 1.49161i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.37197 + 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054 q^{7} +(-1.91324 + 5.88835i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.40360 - 1.74631i) q^{11} +(-3.59186 + 2.60964i) q^{12} +(4.58650 - 3.33228i) q^{13} +(-2.13624 - 1.55207i) q^{14} +(-5.52731 + 4.01583i) q^{16} +(1.57092 - 4.83480i) q^{17} -2.53767 q^{18} +(-1.65990 + 5.10866i) q^{19} +(-0.321543 - 0.989608i) q^{21} +(-2.32982 - 7.17044i) q^{22} +(3.12312 + 2.26908i) q^{23} -6.19138 q^{24} +14.3866 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.42758 - 4.39365i) q^{28} +(0.210038 + 0.646430i) q^{29} +(0.262699 - 0.808503i) q^{31} -4.95495 q^{32} +(0.918092 - 2.82560i) q^{33} +(10.4368 - 7.58275i) q^{34} +(-3.59186 - 2.60964i) q^{36} +(-1.30869 + 0.950818i) q^{37} +(-11.0279 + 8.01226i) q^{38} +(4.58650 + 3.33228i) q^{39} +(-0.942740 + 0.684941i) q^{41} +(0.815972 - 2.51130i) q^{42} -5.68601 q^{43} +(4.07613 - 12.5450i) q^{44} +(3.02725 + 9.31693i) q^{46} +(-1.01555 - 3.12556i) q^{47} +(-5.52731 - 4.01583i) q^{48} -5.91729 q^{49} +5.08361 q^{51} +(20.3631 + 14.7946i) q^{52} +(-3.92023 - 12.0652i) q^{53} +(-0.784184 - 2.41347i) q^{54} +(1.99080 - 6.12704i) q^{56} -5.37156 q^{57} +(-0.533007 + 1.64043i) q^{58} +(-2.59846 + 1.88789i) q^{59} +(4.38562 + 3.18634i) q^{61} +(1.74530 - 1.26803i) q^{62} +(0.841811 - 0.611611i) q^{63} +(0.881995 + 0.640807i) q^{64} +(6.09954 - 4.43157i) q^{66} +(0.287120 - 0.883665i) q^{67} +22.5702 q^{68} +(-1.19292 + 3.67145i) q^{69} +(-0.436821 - 1.34440i) q^{71} +(-1.91324 - 5.88835i) q^{72} +(9.16080 + 6.65571i) q^{73} -4.10501 q^{74} -23.8486 q^{76} +(2.50103 + 1.81710i) q^{77} +(4.44571 + 13.6825i) q^{78} +(-0.447171 - 1.37625i) q^{79} +(0.309017 - 0.951057i) q^{81} -2.95713 q^{82} +(3.54616 - 10.9140i) q^{83} +(3.73746 - 2.71542i) q^{84} +(-11.6735 - 8.48129i) q^{86} +(-0.549886 + 0.399516i) q^{87} +(14.8816 - 10.8121i) q^{88} +(-7.33961 - 5.33254i) q^{89} +(-4.77241 + 3.46736i) q^{91} +(-5.29633 + 16.3004i) q^{92} +0.850111 q^{93} +(2.57715 - 7.93164i) q^{94} +(-1.53117 - 4.71244i) q^{96} +(1.86315 + 5.73419i) q^{97} +(-12.1483 - 8.82627i) q^{98} +2.97101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.05302	+	1.49161i	1.45171	+	1.05473i	0.985429	+	0.170086i	$0.0544046\pi$
$2$	2.05302	+	1.49161i	1.45171	+	1.05473i	0.466276	+	0.884639i	$0.345595\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	1.37197	+	4.22249i	0.685985	+	2.11124i
$5$		0			0
$5$		0			0
$6$	−0.784184	+	2.41347i	−0.320142	+	0.985295i
$7$	−1.04054			−0.393285			−0.196643	−	0.980475i	$-0.563004\pi$
$7$	−1.04054			−0.393285			−0.196643	+	0.980475i	$0.563004\pi$
$8$	−1.91324	+	5.88835i	−0.676433	+	2.08185i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−2.40360	−	1.74631i	−0.724711	−	0.526533i	0.163175	−	0.986597i	$-0.447827\pi$
$11$	−2.40360	−	1.74631i	−0.724711	−	0.526533i	−0.887886	+	0.460064i	$0.847827\pi$
$12$	−3.59186	+	2.60964i	−1.03688	+	0.753338i
$13$	4.58650	−	3.33228i	1.27207	−	0.924209i	0.272782	−	0.962076i	$-0.412056\pi$
$13$	4.58650	−	3.33228i	1.27207	−	0.924209i	0.999283	+	0.0378663i	$0.0120561\pi$
$14$	−2.13624	−	1.55207i	−0.570934	−	0.414808i
$15$		0			0
$16$	−5.52731	+	4.01583i	−1.38183	+	1.00396i
$17$	1.57092	−	4.83480i	0.381005	−	1.17261i	−0.558333	−	0.829617i	$-0.688559\pi$
$17$	1.57092	−	4.83480i	0.381005	−	1.17261i	0.939337	−	0.342995i	$-0.111441\pi$
$18$	−2.53767			−0.598135
$19$	−1.65990	+	5.10866i	−0.380808	+	1.17201i	0.558668	+	0.829391i	$0.311313\pi$
$19$	−1.65990	+	5.10866i	−0.380808	+	1.17201i	−0.939476	+	0.342615i	$0.888687\pi$
$20$		0			0
$21$	−0.321543	−	0.989608i	−0.0701665	−	0.215950i
$22$	−2.32982	−	7.17044i	−0.496719	−	1.52874i
$23$	3.12312	+	2.26908i	0.651215	+	0.473135i	0.863685	−	0.504032i	$-0.168151\pi$
$23$	3.12312	+	2.26908i	0.651215	+	0.473135i	−0.212470	+	0.977168i	$0.568151\pi$
$24$	−6.19138			−1.26381
$25$		0			0
$26$	14.3866			2.82145
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.42758	−	4.39365i	−0.269788	−	0.830322i
$29$	0.210038	+	0.646430i	0.0390030	+	0.120039i	0.968662	−	0.248382i	$-0.0798987\pi$
$29$	0.210038	+	0.646430i	0.0390030	+	0.120039i	−0.929659	+	0.368421i	$0.879899\pi$
$30$		0			0
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	−0.924690	−	0.380721i	$-0.875676\pi$
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	0.971872	+	0.235509i	$0.0756759\pi$
$32$	−4.95495			−0.875921
$33$	0.918092	−	2.82560i	0.159819	−	0.491873i
$34$	10.4368	−	7.58275i	1.78989	−	1.30043i
$35$		0			0
$36$	−3.59186	−	2.60964i	−0.598644	−	0.434940i
$37$	−1.30869	+	0.950818i	−0.215147	+	0.156313i	−0.690139	−	0.723676i	$-0.742451\pi$
$37$	−1.30869	+	0.950818i	−0.215147	+	0.156313i	0.474992	+	0.879990i	$0.342451\pi$
$38$	−11.0279	+	8.01226i	−1.78897	+	1.29976i
$39$	4.58650	+	3.33228i	0.734427	+	0.533593i
$40$		0			0
$41$	−0.942740	+	0.684941i	−0.147231	+	0.106970i	−0.658962	−	0.752176i	$-0.729004\pi$
$41$	−0.942740	+	0.684941i	−0.147231	+	0.106970i	0.511731	+	0.859146i	$0.329004\pi$
$42$	0.815972	−	2.51130i	0.125907	−	0.387502i
$43$	−5.68601			−0.867109			−0.433554	−	0.901127i	$-0.642741\pi$
$43$	−5.68601			−0.867109			−0.433554	+	0.901127i	$0.642741\pi$
$44$	4.07613	−	12.5450i	0.614500	−	1.89124i
$45$		0			0
$46$	3.02725	+	9.31693i	0.446344	+	1.37371i
$47$	−1.01555	−	3.12556i	−0.148134	−	0.455909i	0.849267	−	0.527964i	$-0.177044\pi$
$47$	−1.01555	−	3.12556i	−0.148134	−	0.455909i	−0.997401	+	0.0720547i	$0.977044\pi$
$48$	−5.52731	−	4.01583i	−0.797798	−	0.579635i
$49$	−5.91729			−0.845327
$50$		0			0
$51$	5.08361			0.711848
$52$	20.3631	+	14.7946i	2.82385	+	2.05165i
$53$	−3.92023	−	12.0652i	−0.538485	−	1.65729i	−0.735996	−	0.676986i	$-0.763286\pi$
$53$	−3.92023	−	12.0652i	−0.538485	−	1.65729i	0.197511	−	0.980301i	$-0.436714\pi$
$54$	−0.784184	−	2.41347i	−0.106714	−	0.328432i
$55$		0			0
$56$	1.99080	−	6.12704i	0.266031	−	0.818760i
$57$	−5.37156			−0.711481
$58$	−0.533007	+	1.64043i	−0.0699873	+	0.215399i
$59$	−2.59846	+	1.88789i	−0.338290	+	0.245782i	−0.743940	−	0.668246i	$-0.767045\pi$
$59$	−2.59846	+	1.88789i	−0.338290	+	0.245782i	0.405650	+	0.914029i	$0.367045\pi$
$60$		0			0
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	0.832015	−	0.554753i	$-0.187187\pi$
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	−0.270494	+	0.962722i	$0.587187\pi$
$62$	1.74530	−	1.26803i	0.221653	−	0.161040i
$63$	0.841811	−	0.611611i	0.106058	−	0.0770558i
$64$	0.881995	+	0.640807i	0.110249	+	0.0801008i
$65$		0			0
$66$	6.09954	−	4.43157i	0.750801	−	0.545489i
$67$	0.287120	−	0.883665i	0.0350773	−	0.107957i	−0.931985	−	0.362497i	$-0.881924\pi$
$67$	0.287120	−	0.883665i	0.0350773	−	0.107957i	0.967062	+	0.254540i	$0.0819242\pi$
$68$	22.5702			2.73703
$69$	−1.19292	+	3.67145i	−0.143611	+	0.441990i
$70$		0			0
$71$	−0.436821	−	1.34440i	−0.0518412	−	0.159551i	0.921784	−	0.387703i	$-0.126731\pi$
$71$	−0.436821	−	1.34440i	−0.0518412	−	0.159551i	−0.973625	+	0.228153i	$0.926731\pi$
$72$	−1.91324	−	5.88835i	−0.225478	−	0.693949i
$73$	9.16080	+	6.65571i	1.07219	+	0.778992i	0.976305	−	0.216400i	$-0.0694315\pi$
$73$	9.16080	+	6.65571i	1.07219	+	0.778992i	0.0958862	+	0.995392i	$0.469432\pi$
$74$	−4.10501			−0.477198
$75$		0			0
$76$	−23.8486			−2.73562
$77$	2.50103	+	1.81710i	0.285018	+	0.207078i
$78$	4.44571	+	13.6825i	0.503378	+	1.54924i
$79$	−0.447171	−	1.37625i	−0.0503106	−	0.154840i	0.922745	−	0.385412i	$-0.125941\pi$
$79$	−0.447171	−	1.37625i	−0.0503106	−	0.154840i	−0.973055	+	0.230571i	$0.925941\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−2.95713			−0.326560
$83$	3.54616	−	10.9140i	0.389242	−	1.19796i	−0.544114	−	0.839011i	$-0.683134\pi$
$83$	3.54616	−	10.9140i	0.389242	−	1.19796i	0.933356	−	0.358952i	$-0.116866\pi$
$84$	3.73746	−	2.71542i	0.407790	−	0.296277i
$85$		0			0
$86$	−11.6735	−	8.48129i	−1.25879	−	0.914561i
$87$	−0.549886	+	0.399516i	−0.0589540	+	0.0428326i
$88$	14.8816	−	10.8121i	1.58638	−	1.15257i
$89$	−7.33961	−	5.33254i	−0.777997	−	0.565248i	0.126380	−	0.991982i	$-0.459664\pi$
$89$	−7.33961	−	5.33254i	−0.777997	−	0.565248i	−0.904377	+	0.426734i	$0.859664\pi$
$90$		0			0
$91$	−4.77241	+	3.46736i	−0.500285	+	0.363478i
$92$	−5.29633	+	16.3004i	−0.552181	+	1.69944i
$93$	0.850111			0.0881524
$94$	2.57715	−	7.93164i	0.265812	−	0.818086i
$95$		0			0
$96$	−1.53117	−	4.71244i	−0.156274	−	0.480962i
$97$	1.86315	+	5.73419i	0.189174	+	0.582219i	0.999995	−	0.00307549i	$-0.000978961\pi$
$97$	1.86315	+	5.73419i	0.189174	+	0.582219i	−0.810821	+	0.585294i	$0.800979\pi$
$98$	−12.1483	−	8.82627i	−1.22716	−	0.891587i
$99$	2.97101			0.298597
$100$		0			0
$101$	−15.3408			−1.52647			−0.763236	−	0.646120i	$-0.776390\pi$
$101$	−15.3408			−1.52647			−0.763236	+	0.646120i	$0.776390\pi$
$102$	10.4368	+	7.58275i	1.03339	+	0.750804i
$103$	3.72642	+	11.4688i	0.367175	+	1.13005i	0.948608	+	0.316455i	$0.102493\pi$
$103$	3.72642	+	11.4688i	0.367175	+	1.13005i	−0.581432	+	0.813595i	$0.697507\pi$
$104$	10.8466	+	33.3824i	1.06360	+	3.27341i
$105$		0			0
$106$	9.94827	−	30.6176i	0.966261	−	2.97385i
$107$	−6.49787			−0.628173			−0.314086	−	0.949394i	$-0.601698\pi$
$107$	−6.49787			−0.628173			−0.314086	+	0.949394i	$0.601698\pi$
$108$	1.37197	−	4.22249i	0.132018	−	0.406309i
$109$	1.86929	−	1.35812i	0.179046	−	0.130084i	−0.494653	−	0.869091i	$-0.664705\pi$
$109$	1.86929	−	1.35812i	0.179046	−	0.130084i	0.673698	+	0.739006i	$0.264705\pi$
$110$		0			0
$111$	−1.30869	−	0.950818i	−0.124215	−	0.0902476i
$112$	5.75136	−	4.17861i	0.543453	−	0.394841i
$113$	−3.13317	+	2.27638i	−0.294744	+	0.214144i	−0.725323	−	0.688409i	$-0.758309\pi$
$113$	−3.13317	+	2.27638i	−0.294744	+	0.214144i	0.430579	+	0.902553i	$0.358309\pi$
$114$	−11.0279	−	8.01226i	−1.03286	−	0.750417i
$115$		0			0
$116$	−2.44138	+	1.77376i	−0.226676	+	0.164690i
$117$	−1.75189	+	5.39175i	−0.161962	+	0.498467i
$118$	−8.15067			−0.750330
$119$	−1.63460	+	5.03078i	−0.149844	+	0.461171i
$120$		0			0
$121$	−0.671530	−	2.06676i	−0.0610482	−	0.187887i
$122$	4.25101	+	13.0832i	0.384868	+	1.18450i
$123$	−0.942740	−	0.684941i	−0.0850040	−	0.0617590i
$124$	3.77431			0.338943
$125$		0			0
$126$	2.64054			0.235238
$127$	−9.46046	−	6.87342i	−0.839480	−	0.609918i	0.0827456	−	0.996571i	$-0.473631\pi$
$127$	−9.46046	−	6.87342i	−0.839480	−	0.609918i	−0.922225	+	0.386653i	$0.873631\pi$
$128$	3.91725	+	12.0561i	0.346239	+	1.06562i
$129$	−1.75707	−	5.40772i	−0.154702	−	0.476123i
$130$		0			0
$131$	−2.46042	+	7.57241i	−0.214968	+	0.661604i	0.784188	+	0.620524i	$0.213080\pi$
$131$	−2.46042	+	7.57241i	−0.214968	+	0.661604i	−0.999156	+	0.0410805i	$0.986920\pi$
$132$	13.1906			1.14810
$133$	1.72719	−	5.31574i	0.149766	−	0.460933i
$134$	1.90754	−	1.38591i	0.164787	−	0.119725i
$135$		0			0
$136$	25.4635	+	18.5003i	2.18348	+	1.58639i
$137$	8.94069	−	6.49579i	0.763854	−	0.554973i	−0.136236	−	0.990676i	$-0.543500\pi$
$137$	8.94069	−	6.49579i	0.763854	−	0.554973i	0.900090	+	0.435704i	$0.143500\pi$
$138$	−7.92545	+	5.75818i	−0.674659	+	0.490169i
$139$	9.92651	+	7.21204i	0.841956	+	0.611717i	0.922916	−	0.385000i	$-0.125799\pi$
$139$	9.92651	+	7.21204i	0.841956	+	0.611717i	−0.0809604	+	0.996717i	$0.525799\pi$
$140$		0			0
$141$	2.65876	−	1.93170i	0.223908	−	0.162678i
$142$	1.10851	−	3.41164i	0.0930241	−	0.286299i
$143$	−16.8433			−1.40851
$144$	2.11124	−	6.49774i	0.175937	−	0.541479i
$145$		0			0
$146$	8.87961	+	27.3286i	0.734882	+	2.26173i
$147$	−1.82854	−	5.62767i	−0.150816	−	0.464163i
$148$	−5.81030	−	4.22143i	−0.477604	−	0.346999i
$149$	−4.62832			−0.379167			−0.189584	−	0.981865i	$-0.560714\pi$
$149$	−4.62832			−0.379167			−0.189584	+	0.981865i	$0.560714\pi$
$150$		0			0
$151$	−4.67249			−0.380242			−0.190121	−	0.981761i	$-0.560888\pi$
$151$	−4.67249			−0.380242			−0.190121	+	0.981761i	$0.560888\pi$
$152$	−26.9058	−	19.5482i	−2.18235	−	1.58557i
$153$	1.57092	+	4.83480i	0.127002	+	0.390871i
$154$	2.42426	+	7.46110i	0.195352	+	0.601232i
$155$		0			0
$156$	−7.77800	+	23.9382i	−0.622738	+	1.91659i
$157$	14.9726			1.19494			0.597472	−	0.801890i	$-0.296172\pi$
$157$	14.9726			1.19494			0.597472	+	0.801890i	$0.296172\pi$
$158$	1.13477	−	3.49247i	0.0902777	−	0.277846i
$159$	10.2633	−	7.45672i	0.813932	−	0.591357i
$160$		0			0
$161$	−3.24972	−	2.36106i	−0.256113	−	0.186077i
$162$	2.05302	−	1.49161i	0.161301	−	0.117192i
$163$	−9.63637	+	7.00123i	−0.754779	+	0.548379i	−0.897304	−	0.441412i	$-0.854478\pi$
$163$	−9.63637	+	7.00123i	−0.754779	+	0.548379i	0.142526	+	0.989791i	$0.454478\pi$
$164$	−4.18557	−	3.04099i	−0.326838	−	0.237462i
$165$		0			0
$166$	23.5597	−	17.1171i	1.82859	−	1.32855i
$167$	−3.27809	+	10.0889i	−0.253666	+	0.780704i	0.740424	+	0.672141i	$0.234625\pi$
$167$	−3.27809	+	10.0889i	−0.253666	+	0.780704i	−0.994090	+	0.108563i	$0.965375\pi$
$168$	6.44235			0.497038
$169$	5.91461	−	18.2033i	0.454970	−	1.40025i
$170$		0			0
$171$	−1.65990	−	5.10866i	−0.126936	−	0.390669i
$172$	−7.80103	−	24.0091i	−0.594823	−	1.83068i
$173$	1.01401	+	0.736719i	0.0770935	+	0.0560117i	0.625664	−	0.780092i	$-0.284828\pi$
$173$	1.01401	+	0.736719i	0.0770935	+	0.0560117i	−0.548571	+	0.836104i	$0.684828\pi$
$174$	−1.72485			−0.130760
$175$		0			0
$176$	20.2983			1.53004
$177$	−2.59846	−	1.88789i	−0.195312	−	0.141902i
$178$	−7.11432	−	21.8956i	−0.533241	−	1.64115i
$179$	−6.43105	−	19.7927i	−0.480679	−	1.47938i	−0.838143	−	0.545451i	$-0.816358\pi$
$179$	−6.43105	−	19.7927i	−0.480679	−	1.47938i	0.357464	−	0.933927i	$-0.383642\pi$
$180$		0			0
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	−0.998554	−	0.0537591i	$-0.982880\pi$
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	0.839446	+	0.543443i	$0.182880\pi$
$182$	−14.9698			−1.10964
$183$	−1.67516	+	5.15561i	−0.123831	+	0.381113i
$184$	−19.3364	+	14.0487i	−1.42550	+	1.03569i
$185$		0			0
$186$	1.74530	+	1.26803i	0.127971	+	0.0929766i
$187$	−12.2189	+	8.87759i	−0.893538	+	0.649193i
$188$	11.8043	−	8.57633i	0.860918	−	0.625494i
$189$	0.841811	+	0.611611i	0.0612327	+	0.0444882i
$190$		0			0
$191$	−6.60494	+	4.79877i	−0.477916	+	0.347227i	−0.800518	−	0.599308i	$-0.795442\pi$
$191$	−6.60494	+	4.79877i	−0.477916	+	0.347227i	0.322602	+	0.946535i	$0.395442\pi$
$192$	−0.336892	+	1.03685i	−0.0243131	+	0.0748280i
$193$	−13.9629			−1.00507			−0.502537	−	0.864556i	$-0.667600\pi$
$193$	−13.9629			−1.00507			−0.502537	+	0.864556i	$0.667600\pi$
$194$	−4.72807	+	14.5515i	−0.339456	+	1.04474i
$195$		0			0
$196$	−8.11834	−	24.9857i	−0.579881	−	1.78469i
$197$	1.78071	+	5.48046i	0.126870	+	0.390467i	0.994237	−	0.107203i	$-0.0341893\pi$
$197$	1.78071	+	5.48046i	0.126870	+	0.390467i	−0.867367	+	0.497669i	$0.834189\pi$
$198$	6.09954	+	4.43157i	0.433475	+	0.314938i
$199$	−26.5748			−1.88384			−0.941919	−	0.335841i	$-0.890980\pi$
$199$	−26.5748			−1.88384			−0.941919	+	0.335841i	$0.890980\pi$
$200$		0			0
$201$	0.929140			0.0655365
$202$	−31.4951	−	22.8825i	−2.21599	−	1.61001i
$203$	−0.218552	−	0.672633i	−0.0153393	−	0.0472096i
$204$	6.97456	+	21.4655i	0.488317	+	1.50289i
$205$		0			0
$206$	−9.45644	+	29.1039i	−0.658862	+	2.02777i
$207$	−3.86039			−0.268315
$208$	−11.9691	+	36.8371i	−0.829909	+	2.55420i
$209$	12.9111	−	9.38043i	0.893076	−	0.648858i
$210$		0			0
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.979533	+	0.201285i	$0.0645116\pi$
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.494125	+	0.869391i	$0.335488\pi$
$212$	45.5669	−	33.1063i	3.12954	−	2.27375i
$213$	1.14361	−	0.830884i	0.0783591	−	0.0569312i
$214$	−13.3403	−	9.69227i	−0.911922	−	0.662550i
$215$		0			0
$216$	5.00893	−	3.63920i	0.340815	−	0.247616i
$217$	−0.273347	+	0.841277i	−0.0185560	+	0.0571096i
$218$	5.86348			0.397125
$219$	−3.49912	+	10.7692i	−0.236448	+	0.727713i
$220$		0			0
$221$	−8.90591	−	27.4096i	−0.599076	−	1.84377i
$222$	−1.26852	−	3.90410i	−0.0851374	−	0.262026i
$223$	22.2039	+	16.1321i	1.48689	+	1.08029i	0.975255	+	0.221081i	$0.0709585\pi$
$223$	22.2039	+	16.1321i	1.48689	+	1.08029i	0.511631	+	0.859205i	$0.329042\pi$
$224$	5.15581			0.344487
$225$		0			0
$226$	−9.82792			−0.653744
$227$	−0.105302	−	0.0765066i	−0.00698916	−	0.00507792i	0.584285	−	0.811548i	$-0.301375\pi$
$227$	−0.105302	−	0.0765066i	−0.00698916	−	0.00507792i	−0.591274	+	0.806470i	$0.701375\pi$
$228$	−7.36962	−	22.6813i	−0.488065	−	1.50211i
$229$	0.873064	+	2.68702i	0.0576937	+	0.177563i	0.975750	−	0.218886i	$-0.0702423\pi$
$229$	0.873064	+	2.68702i	0.0576937	+	0.177563i	−0.918057	+	0.396449i	$0.870242\pi$
$230$		0			0
$231$	−0.955307	+	2.94013i	−0.0628546	+	0.193447i
$232$	−4.20826			−0.276286
$233$	2.46815	−	7.59617i	0.161694	−	0.497642i	−0.837084	−	0.547075i	$-0.815741\pi$
$233$	2.46815	−	7.59617i	0.161694	−	0.497642i	0.998777	+	0.0494328i	$0.0157414\pi$
$234$	−11.6390	+	8.45625i	−0.760867	+	0.552802i
$235$		0			0
$236$	−11.5366	−	8.38182i	−0.750968	−	0.545610i
$237$	1.17071	−	0.850569i	0.0760457	−	0.0552504i
$238$	−10.8598	+	7.89012i	−0.703938	+	0.511441i
$239$	15.4214	+	11.2043i	0.997528	+	0.724747i	0.961557	−	0.274606i	$-0.0885475\pi$
$239$	15.4214	+	11.2043i	0.997528	+	0.724747i	0.0359713	+	0.999353i	$0.488548\pi$
$240$		0			0
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.981162	−	0.193184i	$-0.938118\pi$
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.119467	+	0.992838i	$0.538118\pi$
$242$	1.70413	−	5.24476i	0.109545	−	0.337146i
$243$	1.00000			0.0641500
$244$	−7.43735	+	22.8898i	−0.476127	+	1.46537i
$245$		0			0
$246$	−0.913803	−	2.81240i	−0.0582619	−	0.179312i
$247$	9.41036	+	28.9621i	0.598767	+	1.84281i
$248$	4.25815	+	3.09373i	0.270393	+	0.196452i
$249$	11.4756			0.727238
$250$		0			0
$251$	30.2224			1.90762			0.953811	−	0.300408i	$-0.0971228\pi$
$251$	30.2224			1.90762			0.953811	+	0.300408i	$0.0971228\pi$
$252$	3.73746	+	2.71542i	0.235438	+	0.171056i
$253$	−3.54419	−	10.9079i	−0.222821	−	0.685773i
$254$	−9.17007	−	28.2226i	−0.575381	−	1.77084i
$255$		0			0
$256$	−9.26692	+	28.5207i	−0.579183	+	1.78254i
$257$	5.10215			0.318263			0.159132	−	0.987257i	$-0.449131\pi$
$257$	5.10215			0.318263			0.159132	+	0.987257i	$0.449131\pi$
$258$	4.45888	−	13.7230i	0.277598	−	0.854358i
$259$	1.36174	−	0.989360i	0.0846142	−	0.0614758i
$260$		0			0
$261$	−0.549886	−	0.399516i	−0.0340371	−	0.0247294i
$262$	−16.3464	+	11.8763i	−1.00988	+	0.733722i
$263$	−5.19017	+	3.77088i	−0.320040	+	0.232522i	−0.736192	−	0.676772i	$-0.763378\pi$
$263$	−5.19017	+	3.77088i	−0.320040	+	0.232522i	0.416153	+	0.909295i	$0.363378\pi$
$264$	14.8816	+	10.8121i	0.915898	+	0.665439i
$265$		0			0
$266$	11.4749	−	8.33704i	0.703574	−	0.511177i
$267$	2.80348	−	8.62823i	0.171570	−	0.528039i
$268$	4.12518			0.251986
$269$	−5.39518	+	16.6047i	−0.328950	+	1.01240i	0.640676	+	0.767811i	$0.278654\pi$
$269$	−5.39518	+	16.6047i	−0.328950	+	1.01240i	−0.969626	+	0.244592i	$0.921346\pi$
$270$		0			0
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	0.950159	−	0.311765i	$-0.100920\pi$
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	−0.951946	+	0.306266i	$0.900920\pi$
$272$	10.7328	+	33.0320i	0.650769	+	2.00286i
$273$	−4.77241	−	3.46736i	−0.288840	−	0.209854i
$274$	28.0446			1.69424
$275$		0			0
$276$	−17.1393			−1.03166
$277$	14.8865	+	10.8157i	0.894443	+	0.649851i	0.937033	−	0.349242i	$-0.113561\pi$
$277$	14.8865	+	10.8157i	0.894443	+	0.649851i	−0.0425895	+	0.999093i	$0.513561\pi$
$278$	9.62182	+	29.6129i	0.577078	+	1.77606i
$279$	0.262699	+	0.808503i	0.0157274	+	0.0484038i
$280$		0			0
$281$	5.54254	−	17.0582i	0.330640	−	1.01761i	−0.638189	−	0.769879i	$-0.720316\pi$
$281$	5.54254	−	17.0582i	0.330640	−	1.01761i	0.968830	−	0.247727i	$-0.0796837\pi$
$282$	8.33982			0.496629
$283$	−6.87252	+	21.1514i	−0.408529	+	1.25732i	0.509383	+	0.860540i	$0.329874\pi$
$283$	−6.87252	+	21.1514i	−0.408529	+	1.25732i	−0.917912	+	0.396783i	$0.870126\pi$
$284$	5.07740	−	3.68895i	0.301288	−	0.218899i
$285$		0			0
$286$	−34.5796	−	25.1236i	−2.04474	−	1.48559i
$287$	0.980955	−	0.712705i	0.0579039	−	0.0420697i
$288$	4.00864	−	2.91245i	0.236212	−	0.171618i
$289$	−7.15424	−	5.19786i	−0.420837	−	0.305756i
$290$		0			0
$291$	−4.87779	+	3.54392i	−0.285941	+	0.207749i
$292$	−15.5353	+	47.8128i	−0.909136	+	2.79803i
$293$	−18.7316			−1.09431			−0.547155	−	0.837031i	$-0.684289\pi$
$293$	−18.7316			−1.09431			−0.547155	+	0.837031i	$0.684289\pi$
$294$	4.64024	−	14.2812i	0.270624	−	0.832896i
$295$		0			0
$296$	−3.09491	−	9.52517i	−0.179888	−	0.553639i
$297$	0.918092	+	2.82560i	0.0532731	+	0.163958i
$298$	−9.50204	−	6.90364i	−0.550439	−	0.399917i
$299$	21.8854			1.26566
$300$		0			0
$301$	5.91650			0.341021
$302$	−9.59272	−	6.96952i	−0.551999	−	0.401051i
$303$	−4.74058	−	14.5900i	−0.272339	−	0.838174i
$304$	−11.3407	−	34.9030i	−0.650433	−	2.00183i
$305$		0			0
$306$	−3.98649	+	12.2692i	−0.227892	+	0.701381i
$307$	−7.03850			−0.401708			−0.200854	−	0.979621i	$-0.564372\pi$
$307$	−7.03850			−0.401708			−0.200854	+	0.979621i	$0.564372\pi$
$308$	−4.24136	+	13.0536i	−0.241674	+	0.743796i
$309$	−9.75590	+	7.08808i	−0.554994	+	0.403227i
$310$		0			0
$311$	23.6872	+	17.2098i	1.34318	+	0.975876i	0.999321	+	0.0368546i	$0.0117338\pi$
$311$	23.6872	+	17.2098i	1.34318	+	0.975876i	0.343858	+	0.939022i	$0.388266\pi$
$312$	−28.3967	+	20.6314i	−1.60765	+	1.16803i
$313$	12.6493	−	9.19024i	0.714980	−	0.519463i	−0.169796	−	0.985479i	$-0.554311\pi$
$313$	12.6493	−	9.19024i	0.714980	−	0.519463i	0.884776	+	0.466016i	$0.154311\pi$
$314$	30.7391	+	22.3333i	1.73471	+	1.26034i
$315$		0			0
$316$	5.19769	−	3.77635i	0.292393	−	0.212436i
$317$	−1.92871	+	5.93596i	−0.108327	+	0.333397i	−0.990497	−	0.137535i	$-0.956082\pi$
$317$	−1.92871	+	5.93596i	−0.108327	+	0.333397i	0.882170	+	0.470932i	$0.156082\pi$
$318$	32.1933			1.80531
$319$	0.624024	−	1.92055i	0.0349386	−	0.107530i
$320$		0			0
$321$	−2.00795	−	6.17984i	−0.112073	−	0.344925i
$322$	−3.14997	−	9.69460i	−0.175541	−	0.540259i
$323$	22.0918	+	16.0506i	1.22922	+	0.893080i
$324$	4.43979			0.246655
$325$		0			0
$326$	−30.2268			−1.67411
$327$	1.86929	+	1.35812i	0.103372	+	0.0751042i
$328$	−2.22948	−	6.86164i	−0.123103	−	0.378871i
$329$	1.05672	+	3.25225i	0.0582589	+	0.179302i
$330$		0			0
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	−0.585862	−	0.810411i	$-0.699244\pi$
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	0.950320	−	0.311275i	$-0.100756\pi$
$332$	50.9493			2.79621
$333$	0.499875	−	1.53846i	0.0273930	−	0.0843068i
$334$	−21.7787	+	15.8231i	−1.19168	+	0.865804i
$335$		0			0
$336$	5.75136	+	4.17861i	0.313763	+	0.227962i
$337$	28.1142	−	20.4262i	1.53148	−	1.11269i	0.576072	−	0.817399i	$-0.304585\pi$
$337$	28.1142	−	20.4262i	1.53148	−	1.11269i	0.955409	−	0.295287i	$-0.0954152\pi$
$338$	39.2950	−	28.5495i	2.13736	−	1.55289i
$339$	−3.13317	−	2.27638i	−0.170170	−	0.123636i
$340$		0			0
$341$	−2.04332	+	1.48456i	−0.110652	+	0.0803935i
$342$	4.21229	−	12.9641i	0.227775	−	0.701019i
$343$	13.4409			0.725740
$344$	10.8787	−	33.4812i	0.586541	−	1.80519i
$345$		0			0
$346$	0.982882	+	3.02500i	0.0528401	+	0.162625i
$347$	−8.87623	−	27.3182i	−0.476501	−	1.46652i	−0.843922	−	0.536465i	$-0.819759\pi$
$347$	−8.87623	−	27.3182i	−0.476501	−	1.46652i	0.367421	−	0.930055i	$-0.380241\pi$
$348$	−2.44138	−	1.77376i	−0.130871	−	0.0950837i
$349$	−12.2834			−0.657515			−0.328758	−	0.944414i	$-0.606630\pi$
$349$	−12.2834			−0.657515			−0.328758	+	0.944414i	$0.606630\pi$
$350$		0			0
$351$	−5.66922			−0.302601
$352$	11.9097	+	8.65291i	0.634789	+	0.461201i
$353$	8.33663	+	25.6575i	0.443714	+	1.36561i	0.883888	+	0.467699i	$0.154917\pi$
$353$	8.33663	+	25.6575i	0.443714	+	1.36561i	−0.440174	+	0.897913i	$0.645083\pi$
$354$	−2.51870	−	7.75175i	−0.133867	−	0.412001i
$355$		0			0
$356$	12.4469	−	38.3075i	0.659682	−	2.03029i
$357$	−5.28968			−0.279960
$358$	16.3199	−	50.2275i	0.862533	−	2.65461i
$359$	−13.2875	+	9.65393i	−0.701287	+	0.509515i	−0.880351	−	0.474322i	$-0.842693\pi$
$359$	−13.2875	+	9.65393i	−0.701287	+	0.509515i	0.179064	+	0.983837i	$0.442693\pi$
$360$		0			0
$361$	−7.97178	−	5.79184i	−0.419567	−	0.304834i
$362$	−14.2214	+	10.3325i	−0.747460	+	0.543062i
$363$	1.75809	−	1.27733i	0.0922758	−	0.0670423i
$364$	−21.1885	−	15.3943i	−1.11058	−	0.806883i
$365$		0			0
$366$	−11.1293	+	8.08589i	−0.581737	+	0.422656i
$367$	9.23816	−	28.4321i	0.482228	−	1.48415i	−0.353727	−	0.935349i	$-0.615086\pi$
$367$	9.23816	−	28.4321i	0.482228	−	1.48415i	0.835956	−	0.548797i	$-0.184914\pi$
$368$	−26.3747			−1.37487
$369$	0.360095	−	1.10826i	0.0187458	−	0.0576936i
$370$		0			0
$371$	4.07914	+	12.5543i	0.211778	+	0.651787i
$372$	1.16633	+	3.58958i	0.0604712	+	0.186111i
$373$	−20.0885	−	14.5951i	−1.04014	−	0.755706i	−0.0698276	−	0.997559i	$-0.522245\pi$
$373$	−20.0885	−	14.5951i	−1.04014	−	0.755706i	−0.970313	+	0.241853i	$0.922245\pi$
$374$	−38.3276			−1.98187
$375$		0			0
$376$	20.3474			1.04934
$377$	3.11742	+	2.26494i	0.160556	+	0.116650i
$378$	0.815972	+	2.51130i	0.0419690	+	0.129167i
$379$	5.99389	+	18.4473i	0.307885	+	0.947574i	0.978585	+	0.205845i	$0.0659941\pi$
$379$	5.99389	+	18.4473i	0.307885	+	0.947574i	−0.670699	+	0.741729i	$0.734006\pi$
$380$		0			0
$381$	3.61357	−	11.1214i	0.185129	−	0.569768i
$382$	−20.7179			−1.06002
$383$	3.47670	−	10.7002i	0.177651	−	0.546754i	−0.822094	−	0.569353i	$-0.807194\pi$
$383$	3.47670	−	10.7002i	0.177651	−	0.546754i	0.999745	+	0.0225986i	$0.00719397\pi$
$384$	−10.2555	+	7.45106i	−0.523349	+	0.380235i
$385$		0			0
$386$	−28.6662	−	20.8272i	−1.45907	−	1.06008i
$387$	4.60008	−	3.34215i	0.233835	−	0.169891i
$388$	−21.6564	+	15.7343i	−1.09944	+	0.798786i
$389$	−12.0558	−	8.75903i	−0.611252	−	0.444100i	0.238603	−	0.971117i	$-0.423310\pi$
$389$	−12.0558	−	8.75903i	−0.611252	−	0.444100i	−0.849855	+	0.527017i	$0.823310\pi$
$390$		0			0
$391$	15.8767	−	11.5351i	0.802920	−	0.583356i
$392$	11.3212	−	34.8431i	0.571807	−	1.75984i
$393$	−7.96210			−0.401635
$394$	−4.51886	+	13.9076i	−0.227657	+	0.700656i
$395$		0			0
$396$	4.07613	+	12.5450i	0.204833	+	0.630412i
$397$	−7.44626	−	22.9172i	−0.373717	−	1.15018i	−0.944340	−	0.328971i	$-0.893298\pi$
$397$	−7.44626	−	22.9172i	−0.373717	−	1.15018i	0.570623	−	0.821212i	$-0.306702\pi$
$398$	−54.5586	−	39.6392i	−2.73478	−	1.98693i
$399$	5.58930			0.279815
$400$		0			0
$401$	13.4580			0.672059			0.336030	−	0.941851i	$-0.390916\pi$
$401$	13.4580			0.672059			0.336030	+	0.941851i	$0.390916\pi$
$402$	1.90754	+	1.38591i	0.0951397	+	0.0691230i
$403$	−1.48930	−	4.58358i	−0.0741872	−	0.228325i
$404$	−21.0472	−	64.7765i	−1.04714	−	3.22275i
$405$		0			0
$406$	0.554613	−	1.70692i	0.0275250	−	0.0847132i
$407$	4.80598			0.238224
$408$	−9.72618	+	29.9341i	−0.481518	+	1.48196i
$409$	28.6988	−	20.8509i	1.41906	−	1.03101i	0.427140	−	0.904186i	$-0.359521\pi$
$409$	28.6988	−	20.8509i	1.41906	−	1.03101i	0.991925	−	0.126825i	$-0.0404788\pi$
$410$		0			0
$411$	8.94069	+	6.49579i	0.441012	+	0.320414i
$412$	−43.3141	+	31.4696i	−2.13393	+	1.55039i
$413$	2.70379	−	1.96441i	0.133045	−	0.0966625i
$414$	−7.92545	−	5.75818i	−0.389515	−	0.282999i
$415$		0			0
$416$	−22.7259	+	16.5113i	−1.11423	+	0.809534i
$417$	−3.79159	+	11.6693i	−0.185675	+	0.571449i
$418$	40.4986			1.98085
$419$	4.88617	−	15.0381i	0.238705	−	0.734659i	−0.757903	−	0.652367i	$-0.773776\pi$
$419$	4.88617	−	15.0381i	0.238705	−	0.734659i	0.996608	−	0.0822916i	$-0.0262239\pi$
$420$		0			0
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	0.999840	−	0.0178752i	$-0.00569015\pi$
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	−0.819394	+	0.573230i	$0.805690\pi$
$422$	20.7491	+	63.8590i	1.01005	+	3.10861i
$423$	2.65876	+	1.93170i	0.129273	+	0.0939225i
$424$	78.5447			3.81447
$425$		0			0
$426$	3.58721			0.173801
$427$	−4.56340	−	3.31550i	−0.220838	−	0.160448i
$428$	−8.91488	−	27.4372i	−0.430917	−	1.32623i
$429$	−5.20486	−	16.0189i	−0.251293	−	0.773401i
$430$		0			0
$431$	4.52486	−	13.9261i	0.217955	−	0.670797i	−0.780976	−	0.624562i	$-0.785278\pi$
$431$	4.52486	−	13.9261i	0.217955	−	0.670797i	0.998931	−	0.0462350i	$-0.0147223\pi$
$432$	6.83213			0.328711
$433$	1.32041	−	4.06380i	0.0634547	−	0.195294i	−0.914303	−	0.405031i	$-0.867261\pi$
$433$	1.32041	−	4.06380i	0.0634547	−	0.195294i	0.977758	+	0.209737i	$0.0672608\pi$
$434$	−1.81604	+	1.31943i	−0.0871728	+	0.0633347i
$435$		0			0
$436$	8.29926	+	6.02976i	0.397462	+	0.288773i
$437$	−16.7760	+	12.1885i	−0.802506	+	0.583055i
$438$	−23.2471	+	16.8900i	−1.11079	+	0.807037i
$439$	16.4289	+	11.9363i	0.784111	+	0.569690i	0.906210	−	0.422828i	$-0.138963\pi$
$439$	16.4289	+	11.9363i	0.784111	+	0.569690i	−0.122099	+	0.992518i	$0.538963\pi$
$440$		0			0
$441$	4.78718	−	3.47809i	0.227961	−	0.165623i
$442$	22.6003	−	69.5565i	1.07499	−	3.30847i
$443$	19.0543			0.905299			0.452649	−	0.891689i	$-0.350479\pi$
$443$	19.0543			0.905299			0.452649	+	0.891689i	$0.350479\pi$
$444$	2.21934	−	6.83041i	0.105325	−	0.324157i
$445$		0			0
$446$	21.5224	+	66.2391i	1.01912	+	3.13651i
$447$	−1.43023	−	4.40180i	−0.0676476	−	0.208198i
$448$	−0.917747	−	0.666782i	−0.0433595	−	0.0315025i
$449$	29.4793			1.39122			0.695608	−	0.718421i	$-0.255135\pi$
$449$	29.4793			1.39122			0.695608	+	0.718421i	$0.255135\pi$
$450$		0			0
$451$	3.46209			0.163023
$452$	−13.9106	−	10.1066i	−0.654299	−	0.475376i
$453$	−1.44388	−	4.44380i	−0.0678394	−	0.208788i
$454$	−0.102070	−	0.314139i	−0.00479038	−	0.0147433i
$455$		0			0
$456$	10.2771	−	31.6296i	0.481269	−	1.48119i
$457$	28.3015			1.32389			0.661945	−	0.749553i	$-0.269731\pi$
$457$	28.3015			1.32389			0.661945	+	0.749553i	$0.269731\pi$
$458$	−2.21555	+	6.81877i	−0.103526	+	0.318620i
$459$	−4.11273	+	2.98807i	−0.191966	+	0.139471i
$460$		0			0
$461$	13.3953	+	9.73223i	0.623879	+	0.453275i	0.854274	−	0.519822i	$-0.174002\pi$
$461$	13.3953	+	9.73223i	0.623879	+	0.453275i	−0.230395	+	0.973097i	$0.574002\pi$
$462$	−6.34679	+	4.61121i	−0.295279	+	0.214533i
$463$	−7.45051	+	5.41311i	−0.346254	+	0.251569i	−0.747296	−	0.664491i	$-0.768648\pi$
$463$	−7.45051	+	5.41311i	−0.346254	+	0.251569i	0.401042	+	0.916060i	$0.368648\pi$
$464$	−3.75689	−	2.72954i	−0.174409	−	0.126716i
$465$		0			0
$466$	16.3977	−	11.9136i	0.759607	−	0.551887i
$467$	3.27938	−	10.0929i	0.151752	−	0.467043i	−0.846066	−	0.533079i	$-0.821035\pi$
$467$	3.27938	−	10.0929i	0.151752	−	0.467043i	0.997817	+	0.0660353i	$0.0210350\pi$
$468$	−25.1701			−1.16349
$469$	−0.298759	+	0.919485i	−0.0137954	+	0.0424579i
$470$		0			0
$471$	4.62679	+	14.2398i	0.213191	+	0.656135i
$472$	−6.14508	−	18.9126i	−0.282850	−	0.870524i
$473$	13.6669	+	9.92956i	0.628403	+	0.456562i
$474$	3.67220			0.168670
$475$		0			0
$476$	−23.4850			−1.07644
$477$	10.2633	+	7.45672i	0.469924	+	0.341420i
$478$	14.9480	+	46.0054i	0.683708	+	2.10424i
$479$	10.3849	+	31.9613i	0.474496	+	1.46035i	0.846636	+	0.532172i	$0.178624\pi$
$479$	10.3849	+	31.9613i	0.474496	+	1.46035i	−0.372140	+	0.928177i	$0.621376\pi$
$480$		0			0
$481$	−2.83390	+	8.72184i	−0.129215	+	0.397682i
$482$	−53.5954			−2.44120
$483$	1.24128	−	3.82027i	0.0564802	−	0.173828i
$484$	7.80554	−	5.67106i	0.354797	−	0.257775i
$485$		0			0
$486$	2.05302	+	1.49161i	0.0931269	+	0.0676607i
$487$	−23.6626	+	17.1919i	−1.07226	+	0.779039i	−0.976316	−	0.216348i	$-0.930585\pi$
$487$	−23.6626	+	17.1919i	−1.07226	+	0.779039i	−0.0959389	+	0.995387i	$0.530585\pi$
$488$	−27.1531	+	19.7279i	−1.22916	+	0.893038i
$489$	−9.63637	−	7.00123i	−0.435772	−	0.316607i
$490$		0			0
$491$	−11.2898	+	8.20251i	−0.509501	+	0.370174i	−0.812634	−	0.582774i	$-0.801967\pi$
$491$	−11.2898	+	8.20251i	−0.509501	+	0.370174i	0.303133	+	0.952948i	$0.401967\pi$
$492$	1.59874	−	4.92043i	0.0720769	−	0.221830i
$493$	3.45531			0.155619
$494$	−23.8804	+	73.4964i	−1.07443	+	3.30676i
$495$		0			0
$496$	1.79479	+	5.52380i	0.0805885	+	0.248026i
$497$	0.454528	+	1.39889i	0.0203884	+	0.0627490i
$498$	23.5597	+	17.1171i	1.05573	+	0.767036i
$499$	−35.7533			−1.60054			−0.800268	−	0.599642i	$-0.795310\pi$
$499$	−35.7533			−1.60054			−0.800268	+	0.599642i	$0.795310\pi$
$500$		0			0
$501$	−10.6081			−0.473936
$502$	62.0472	+	45.0800i	2.76930	+	2.01202i
$503$	−3.59828	−	11.0744i	−0.160439	−	0.493782i	0.838232	−	0.545314i	$-0.183590\pi$
$503$	−3.59828	−	11.0744i	−0.160439	−	0.493782i	−0.998671	+	0.0515323i	$0.983590\pi$
$504$	1.99080	+	6.12704i	0.0886771	+	0.272920i
$505$		0			0
$506$	8.99399	−	27.6807i	0.399832	−	1.23056i
$507$	19.1401			0.850040
$508$	16.0435	−	49.3768i	0.711815	−	2.19074i
$509$	6.90384	−	5.01594i	0.306007	−	0.222327i	−0.424174	−	0.905581i	$-0.639436\pi$
$509$	6.90384	−	5.01594i	0.306007	−	0.222327i	0.730181	+	0.683253i	$0.239436\pi$
$510$		0			0
$511$	−9.53214	−	6.92551i	−0.421677	−	0.306366i
$512$	−41.0558	+	29.8288i	−1.81443	+	1.31826i
$513$	4.34568	−	3.15732i	0.191867	−	0.139399i
$514$	10.4748	+	7.61040i	0.462025	+	0.335681i
$515$		0			0
$516$	20.4234	−	14.8384i	0.899089	−	0.653226i
$517$	−3.01722	+	9.28605i	−0.132697	+	0.408400i
$518$	4.27141			0.187675
$519$	−0.387316	+	1.19204i	−0.0170013	+	0.0523246i
$520$		0			0
$521$	0.390998	+	1.20337i	0.0171299	+	0.0527205i	0.959256	−	0.282538i	$-0.0911763\pi$
$521$	0.390998	+	1.20337i	0.0171299	+	0.0527205i	−0.942126	+	0.335259i	$0.891176\pi$
$522$	−0.533007	−	1.64043i	−0.0233291	−	0.0717996i
$523$	−22.0218	−	15.9998i	−0.962946	−	0.699621i	−0.00911285	−	0.999958i	$-0.502901\pi$
$523$	−22.0218	−	15.9998i	−0.962946	−	0.699621i	−0.953833	+	0.300337i	$0.902901\pi$
$524$	−35.3500			−1.54427
$525$		0			0
$526$	−16.2802			−0.709850
$527$	−3.49628	−	2.54019i	−0.152300	−	0.110653i
$528$	6.27252	+	19.3048i	0.272976	+	0.840135i
$529$	−2.50224	−	7.70110i	−0.108793	−	0.334831i
$530$		0			0
$531$	0.992522	−	3.05467i	0.0430718	−	0.132561i
$532$	24.8153			1.07588
$533$	−2.04146	+	6.28296i	−0.0884253	+	0.272145i
$534$	18.6255	−	13.5322i	0.806005	−	0.585597i
$535$		0			0
$536$	4.65400	+	3.38133i	0.201022	+	0.146051i
$537$	16.8367	−	12.2326i	0.726557	−	0.527875i
$538$	−35.8440	+	26.0422i	−1.54535	+	1.12276i
$539$	14.2228	+	10.3334i	0.612618	+	0.445093i
$540$		0			0
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.973492	−	0.228719i	$-0.926546\pi$
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.0833007	+	0.996524i	$0.526546\pi$
$542$	0.0746431	−	0.229728i	0.00320620	−	0.00986766i
$543$	−6.92706			−0.297269
$544$	−7.78385	+	23.9562i	−0.333730	+	1.02711i
$545$		0			0
$546$	−4.62592	−	14.2371i	−0.197971	−	0.609293i
$547$	3.51564	+	10.8200i	0.150318	+	0.462631i	0.997656	−	0.0684223i	$-0.0217965\pi$
$547$	3.51564	+	10.8200i	0.150318	+	0.462631i	−0.847339	+	0.531053i	$0.821797\pi$
$548$	39.6947	+	28.8399i	1.69568	+	1.23198i
$549$	−5.42093			−0.231360
$550$		0			0
$551$	−3.65103			−0.155539
$552$	−19.3364	−	14.0487i	−0.823012	−	0.597954i
$553$	0.465297	+	1.43204i	0.0197864	+	0.0608964i
$554$	14.4296	+	44.4096i	0.613053	+	1.88678i
$555$		0			0
$556$	−16.8339	+	51.8093i	−0.713914	+	2.19720i
$557$	−45.7532			−1.93862			−0.969312	−	0.245833i	$-0.920938\pi$
$557$	−45.7532			−1.93862			−0.969312	+	0.245833i	$0.920938\pi$
$558$	−0.666643	+	2.05172i	−0.0282213	+	0.0868561i
$559$	−26.0789	+	18.9474i	−1.10302	+	0.801390i
$560$		0			0
$561$	−12.2189	−	8.87759i	−0.515884	−	0.374812i
$562$	36.8231	−	26.7535i	1.55329	−	1.12853i
$563$	−7.23495	+	5.25650i	−0.304917	+	0.221535i	−0.729712	−	0.683754i	$-0.760346\pi$
$563$	−7.23495	+	5.25650i	−0.304917	+	0.221535i	0.424796	+	0.905289i	$0.360346\pi$
$564$	11.8043	+	8.57633i	0.497051	+	0.361129i
$565$		0			0
$566$	−45.6591	+	33.1733i	−1.91919	+	1.39438i
$567$	−0.321543	+	0.989608i	−0.0135035	+	0.0415596i
$568$	8.75203			0.367227
$569$	−0.707365	+	2.17704i	−0.0296543	+	0.0912665i	−0.964788	−	0.263028i	$-0.915279\pi$
$569$	−0.707365	+	2.17704i	−0.0296543	+	0.0912665i	0.935134	+	0.354294i	$0.115279\pi$
$570$		0			0
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	−0.926774	−	0.375618i	$-0.877430\pi$
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	0.528993	−	0.848626i	$-0.322570\pi$
$572$	−23.1085	−	71.1206i	−0.966214	−	2.97370i
$573$	−6.60494	−	4.79877i	−0.275925	−	0.200471i
$574$	3.07700			0.128431
$575$		0			0
$576$	−1.09021			−0.0454252
$577$	−5.33326	−	3.87484i	−0.222027	−	0.161312i	0.471212	−	0.882020i	$-0.343817\pi$
$577$	−5.33326	−	3.87484i	−0.222027	−	0.161312i	−0.693238	+	0.720708i	$0.743817\pi$
$578$	−6.93464	−	21.3426i	−0.288443	−	0.887736i
$579$	−4.31479	−	13.2795i	−0.179316	−	0.551879i
$580$		0			0
$581$	−3.68991	+	11.3564i	−0.153083	+	0.471141i
$582$	−15.3004			−0.634220
$583$	−11.6470	+	35.8459i	−0.482371	+	1.48458i
$584$	−56.7180	+	41.2081i	−2.34701	+	1.70520i
$585$		0			0
$586$	−38.4563	−	27.9401i	−1.58861	−	1.15420i
$587$	−4.48010	+	3.25499i	−0.184914	+	0.134348i	−0.676391	−	0.736543i	$-0.736457\pi$
$587$	−4.48010	+	3.25499i	−0.184914	+	0.134348i	0.491477	+	0.870890i	$0.336457\pi$
$588$	21.2541	−	15.4420i	0.876503	−	0.636817i
$589$	3.69431	+	2.68408i	0.152222	+	0.110595i
$590$		0			0
$591$	−4.66196	+	3.38711i	−0.191767	+	0.139327i
$592$	3.41521	−	10.5109i	0.140364	−	0.431997i
$593$	1.88122			0.0772524			0.0386262	−	0.999254i	$-0.487702\pi$
$593$	1.88122			0.0772524			0.0386262	+	0.999254i	$0.487702\pi$
$594$	−2.32982	+	7.17044i	−0.0955935	+	0.294207i
$595$		0			0
$596$	−6.34992	−	19.5430i	−0.260103	−	0.800514i
$597$	−8.21206	−	25.2741i	−0.336097	−	1.03440i
$598$	44.9311	+	32.6444i	1.83737	+	1.33493i
$599$	17.8272			0.728400			0.364200	−	0.931321i	$-0.381342\pi$
$599$	17.8272			0.728400			0.364200	+	0.931321i	$0.381342\pi$
$600$		0			0
$601$	33.0994			1.35015			0.675077	−	0.737747i	$-0.264110\pi$
$601$	33.0994			1.35015			0.675077	+	0.737747i	$0.264110\pi$
$602$	12.1467	+	8.82509i	0.495062	+	0.359684i
$603$	0.287120	+	0.883665i	0.0116924	+	0.0359856i
$604$	−6.41052	−	19.7295i	−0.260840	−	0.802784i
$605$		0			0
$606$	12.0300	−	37.0247i	0.488687	−	1.50402i
$607$	23.4603			0.952226			0.476113	−	0.879384i	$-0.342045\pi$
$607$	23.4603			0.952226			0.476113	+	0.879384i	$0.342045\pi$
$608$	8.22475	−	25.3132i	0.333558	−	1.02658i
$609$	0.572176	−	0.415710i	0.0231857	−	0.0168454i
$610$		0			0
$611$	−15.0731	−	10.9512i	−0.609792	−	0.443039i
$612$	−18.2596	+	13.2664i	−0.738102	+	0.536263i
$613$	38.2083	−	27.7600i	1.54322	−	1.12121i	0.594942	−	0.803769i	$-0.297175\pi$
$613$	38.2083	−	27.7600i	1.54322	−	1.12121i	0.948277	−	0.317445i	$-0.102825\pi$
$614$	−14.4502	−	10.4987i	−0.583162	−	0.423692i
$615$		0			0
$616$	−15.4848	+	11.2504i	−0.623901	+	0.453290i
$617$	−5.02765	+	15.4735i	−0.202406	+	0.622941i	0.797404	+	0.603446i	$0.206206\pi$
$617$	−5.02765	+	15.4735i	−0.202406	+	0.622941i	−0.999810	+	0.0194952i	$0.993794\pi$
$618$	−30.6017			−1.23098
$619$	10.9577	−	33.7244i	0.440428	−	1.35550i	−0.446993	−	0.894537i	$-0.647505\pi$
$619$	10.9577	−	33.7244i	0.440428	−	1.35550i	0.887421	−	0.460960i	$-0.152495\pi$
$620$		0			0
$621$	−1.19292	−	3.67145i	−0.0478704	−	0.147330i
$622$	22.9601	+	70.6640i	0.920617	+	2.83337i
$623$	7.63712	+	5.54869i	0.305975	+	0.222304i
$624$	−38.7329			−1.55056
$625$		0			0
$626$	39.6775			1.58583
$627$	12.9111	+	9.38043i	0.515618	+	0.374618i
$628$	20.5420	+	63.2217i	0.819714	+	2.52282i
$629$	2.54117	+	7.82091i	0.101323	+	0.311840i
$630$		0			0
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	0.593599	+	0.804761i	$0.297706\pi$
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	−0.953258	+	0.302156i	$0.902294\pi$
$632$	8.95939			0.356385
$633$	−8.17641	+	25.1644i	−0.324983	+	1.00020i
$634$	−12.8138	+	9.30978i	−0.508901	+	0.369738i
$635$		0			0
$636$	45.5669	+	33.1063i	1.80684	+	1.31275i
$637$	−27.1396	+	19.7181i	−1.07531	+	0.781259i
$638$	4.14583	−	3.01213i	0.164135	−	0.119251i
$639$	1.14361	+	0.830884i	0.0452406	+	0.0328692i
$640$		0			0
$641$	12.7145	−	9.23764i	0.502194	−	0.364865i	−0.307661	−	0.951496i	$-0.599546\pi$
$641$	12.7145	−	9.23764i	0.502194	−	0.364865i	0.809854	+	0.586631i	$0.199546\pi$
$642$	5.09553	−	15.6824i	0.201104	−	0.618936i
$643$	−8.08055			−0.318666			−0.159333	−	0.987225i	$-0.550934\pi$
$643$	−8.08055			−0.318666			−0.159333	+	0.987225i	$0.550934\pi$
$644$	5.51102	−	16.9612i	0.217165	−	0.668364i
$645$		0			0
$646$	21.4137	+	65.9045i	0.842510	+	2.59298i
$647$	3.40516	+	10.4800i	0.133870	+	0.412011i	0.995413	−	0.0956751i	$-0.0305010\pi$
$647$	3.40516	+	10.4800i	0.133870	+	0.412011i	−0.861542	+	0.507686i	$0.830501\pi$
$648$	5.00893	+	3.63920i	0.196769	+	0.142961i
$649$	9.54248			0.374575
$650$		0			0
$651$	−0.884570			−0.0346691
$652$	−42.7834	−	31.0840i	−1.67553	−	1.21734i
$653$	−9.60613	−	29.5646i	−0.375917	−	1.15695i	−0.942858	−	0.333195i	$-0.891873\pi$
$653$	−9.60613	−	29.5646i	−0.375917	−	1.15695i	0.566941	−	0.823758i	$-0.308127\pi$
$654$	1.81191	+	5.57650i	0.0708515	+	0.218058i
$655$		0			0
$656$	2.46021	−	7.57176i	0.0960552	−	0.295628i
$657$	−11.3234			−0.441767
$658$	−2.68161	+	8.25315i	−0.104540	+	0.321741i
$659$	−26.2325	+	19.0590i	−1.02187	+	0.742435i	−0.966666	−	0.256040i	$-0.917582\pi$
$659$	−26.2325	+	19.0590i	−1.02187	+	0.742435i	−0.0552080	+	0.998475i	$0.517582\pi$
$660$		0			0
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	0.314490	−	0.949261i	$-0.398166\pi$
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	−0.805618	+	0.592436i	$0.798166\pi$
$662$	44.0527	−	32.0061i	1.71216	−	1.24395i
$663$	23.3160	−	16.9400i	0.905517	−	0.657897i
$664$	57.4806	+	41.7621i	2.23068	+	1.62068i
$665$		0			0
$666$	3.32102	−	2.41287i	0.128687	−	0.0934966i
$667$	−0.810827	+	2.49547i	−0.0313953	+	0.0966249i
$668$	−47.0978			−1.82227
$669$	−8.48115	+	26.1023i	−0.327900	+	1.00917i
$670$		0			0
$671$	−4.97691	−	15.3173i	−0.192131	−	0.591320i
$672$	1.59323	+	4.90346i	0.0614602	+	0.189155i
$673$	−25.1014	−	18.2373i	−0.967589	−	0.702995i	−0.0126883	−	0.999919i	$-0.504039\pi$
$673$	−25.1014	−	18.2373i	−0.967589	−	0.702995i	−0.954901	+	0.296925i	$0.904039\pi$
$674$	88.1870			3.39684
$675$		0			0
$676$	84.9778			3.26838
$677$	18.6796	+	13.5716i	0.717917	+	0.521597i	0.885718	−	0.464224i	$-0.153667\pi$
$677$	18.6796	+	13.5716i	0.717917	+	0.521597i	−0.167801	+	0.985821i	$0.553667\pi$
$678$	−3.03700	−	9.34691i	−0.116635	−	0.358966i
$679$	−1.93868	−	5.96663i	−0.0743995	−	0.228978i
$680$		0			0
$681$	0.0402219	−	0.123790i	0.00154131	−	0.00474365i
$682$	−6.40936			−0.245427
$683$	−12.7791	+	39.3301i	−0.488979	+	1.50492i	0.337154	+	0.941449i	$0.390536\pi$
$683$	−12.7791	+	39.3301i	−0.488979	+	1.50492i	−0.826134	+	0.563474i	$0.809464\pi$
$684$	19.2939	−	14.0178i	0.737721	−	0.535986i
$685$		0			0
$686$	27.5944	+	20.0485i	1.05356	+	0.765457i
$687$	−2.28571	+	1.66067i	−0.0872053	+	0.0633584i
$688$	31.4283	−	22.8340i	1.19819	−	0.870539i
$689$	−58.1849	−	42.2738i	−2.21667	−	1.61050i
$690$		0			0
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	−0.654429	−	0.756123i	$-0.727091\pi$
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	0.516886	+	0.856054i	$0.327091\pi$
$692$	−1.71960	+	5.29239i	−0.0653694	+	0.201186i
$693$	−3.09144			−0.117434
$694$	22.5250	−	69.3248i	0.855037	−	2.63153i
$695$		0			0
$696$	−1.30042	−	4.00229i	−0.0492924	−	0.151707i
$697$	1.83058	+	5.63395i	0.0693382	+	0.213401i
$698$	−25.2181	−	18.3220i	−0.954518	−	0.693498i
$699$	7.98709			0.302099
$700$		0			0
$701$	−25.2265			−0.952791			−0.476396	−	0.879231i	$-0.658057\pi$
$701$	−25.2265			−0.952791			−0.476396	+	0.879231i	$0.658057\pi$
$702$	−11.6390	−	8.45625i	−0.439287	−	0.319161i
$703$	−2.68511	−	8.26391i	−0.101271	−	0.311679i
$704$	−1.00091	−	3.08048i	−0.0377231	−	0.116100i
$705$		0			0
$706$	−21.1556	+	65.1104i	−0.796203	+	2.45046i
$707$	15.9627			0.600339
$708$	4.40658	−	13.5621i	0.165610	−	0.509694i
$709$	−1.26199	+	0.916889i	−0.0473950	+	0.0344345i	−0.611231	−	0.791453i	$-0.709325\pi$
$709$	−1.26199	+	0.916889i	−0.0473950	+	0.0344345i	0.563836	+	0.825887i	$0.309325\pi$
$710$		0			0
$711$	1.17071	+	0.850569i	0.0439050	+	0.0318988i
$712$	45.4423	−	33.0158i	1.70302	−	1.23732i
$713$	2.65500	−	1.92897i	0.0994304	−	0.0722404i
$714$	−10.8598	−	7.89012i	−0.406419	−	0.295280i
$715$		0			0
$716$	74.7514	−	54.3100i	2.79359	−	2.02966i
$717$	−5.89045	+	18.1290i	−0.219983	+	0.677038i
$718$	−41.6794			−1.55546
$719$	8.94304	−	27.5238i	0.333519	−	1.02647i	−0.633928	−	0.773392i	$-0.718558\pi$
$719$	8.94304	−	27.5238i	0.333519	−	1.02647i	0.967447	−	0.253074i	$-0.0814416\pi$
$720$		0			0
$721$	−3.87748	−	11.9336i	−0.144405	−	0.444432i
$722$	−7.72709	−	23.7815i	−0.287572	−	0.885057i
$723$	−17.0864	−	12.4140i	−0.635448	−	0.461680i
$724$	−30.7547			−1.14299
$725$		0			0
$726$	5.51466			0.204668
$727$	−29.9008	−	21.7242i	−1.10896	−	0.805707i	−0.126461	−	0.991972i	$-0.540362\pi$
$727$	−29.9008	−	21.7242i	−1.10896	−	0.805707i	−0.982500	+	0.186265i	$0.940362\pi$
$728$	−11.2863	−	34.7355i	−0.418297	−	1.28739i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−8.93229	+	27.4907i	−0.330372	+	1.01678i
$732$	−24.0678			−0.889570
$733$	1.28601	−	3.95793i	0.0474998	−	0.146189i	−0.924494	−	0.381198i	$-0.875512\pi$
$733$	1.28601	−	3.95793i	0.0474998	−	0.146189i	0.971993	+	0.235008i	$0.0755117\pi$
$734$	61.3757	−	44.5921i	2.26542	−	1.64592i
$735$		0			0
$736$	−15.4749	−	11.2432i	−0.570413	−	0.414429i
$737$	−2.23328	+	1.62257i	−0.0822638	+	0.0597682i
$738$	2.39237	−	1.73816i	0.0880642	−	0.0639824i
$739$	−15.3371	−	11.1431i	−0.564184	−	0.409904i	0.268804	−	0.963195i	$-0.413372\pi$
$739$	−15.3371	−	11.1431i	−0.564184	−	0.409904i	−0.832988	+	0.553291i	$0.813372\pi$
$740$		0			0
$741$	−24.6366	+	17.8996i	−0.905050	+	0.657557i
$742$	−10.3515	+	31.8587i	−0.380016	+	1.16957i
$743$	11.7060			0.429452			0.214726	−	0.976674i	$-0.431114\pi$
$743$	11.7060			0.429452			0.214726	+	0.976674i	$0.431114\pi$
$744$	−1.62647	+	5.00575i	−0.0596292	+	0.183520i
$745$		0			0
$746$	−19.4718	−	59.9281i	−0.712915	−	2.19413i
$747$	3.54616	+	10.9140i	0.129747	+	0.399321i
$748$	−54.2495	−	39.4146i	−1.98356	−	1.44114i
$749$	6.76126			0.247051
$750$		0			0
$751$	−4.95672			−0.180873			−0.0904367	−	0.995902i	$-0.528826\pi$
$751$	−4.95672			−0.180873			−0.0904367	+	0.995902i	$0.528826\pi$
$752$	18.1650	+	13.1976i	0.662408	+	0.481268i
$753$	9.33924	+	28.7432i	0.340341	+	1.04746i
$754$	3.02174	+	9.29995i	0.110045	+	0.338684i
$755$		0			0
$756$	−1.42758	+	4.39365i	−0.0519207	+	0.159795i
$757$	−18.6020			−0.676101			−0.338051	−	0.941128i	$-0.609768\pi$
$757$	−18.6020			−0.676101			−0.338051	+	0.941128i	$0.609768\pi$
$758$	−15.2105	+	46.8132i	−0.552472	+	1.70033i
$759$	9.27881	−	6.74145i	0.336799	−	0.244699i
$760$		0			0
$761$	9.18925	+	6.67638i	0.333110	+	0.242019i	0.741749	−	0.670677i	$-0.233997\pi$
$761$	9.18925	+	6.67638i	0.333110	+	0.242019i	−0.408639	+	0.912696i	$0.633997\pi$
$762$	24.0075	−	17.4425i	0.869702	−	0.631875i
$763$	−1.94507	+	1.41317i	−0.0704161	+	0.0511603i
$764$	−29.3245	−	21.3055i	−1.06092	−	0.770806i
$765$		0			0
$766$	23.0982	−	16.7818i	0.834572	−	0.606352i
$767$	−5.62682	+	17.3176i	−0.203173	+	0.625302i
$768$	−29.9884			−1.08211
$769$	2.24803	−	6.91872i	0.0810660	−	0.249495i	−0.902307	−	0.431095i	$-0.858127\pi$
$769$	2.24803	−	6.91872i	0.0810660	−	0.249495i	0.983373	+	0.181599i	$0.0581274\pi$
$770$		0			0
$771$	1.57665	+	4.85243i	0.0567817	+	0.174756i
$772$	−19.1567	−	58.9584i	−0.689466	−	2.12196i
$773$	7.54237	+	5.47985i	0.271280	+	0.197097i	0.715105	−	0.699017i	$-0.246379\pi$
$773$	7.54237	+	5.47985i	0.271280	+	0.197097i	−0.443825	+	0.896114i	$0.646379\pi$
$774$	14.4292			0.518648
$775$		0			0
$776$	−37.3296			−1.34005
$777$	1.36174	+	0.989360i	0.0488520	+	0.0354931i
$778$	−11.6857	−	35.9649i	−0.418953	−	1.28941i
$779$	−1.93427	−	5.95307i	−0.0693024	−	0.213291i
$780$		0			0
$781$	−1.29780	+	3.99421i	−0.0464389	+	0.142924i
$782$	49.8011			1.78088
$783$	0.210038	−	0.646430i	0.00750614	−	0.0231015i
$784$	32.7067	−	23.7628i	1.16810	−	0.848671i
$785$		0			0
$786$	−16.3464	−	11.8763i	−0.583055	−	0.423615i
$787$	−12.0266	+	8.73787i	−0.428704	+	0.311471i	−0.781130	−	0.624368i	$-0.785357\pi$
$787$	−12.0266	+	8.73787i	−0.428704	+	0.311471i	0.352427	+	0.935839i	$0.385357\pi$
$788$	−20.6981	+	15.0381i	−0.737339	+	0.535708i
$789$	−5.19017	−	3.77088i	−0.184775	−	0.134247i
$790$		0			0
$791$	3.26017	−	2.36865i	0.115918	−	0.0842196i
$792$	−5.68426	+	17.4943i	−0.201981	+	0.621634i
$793$	30.7324			1.09134
$794$	18.8962	−	58.1565i	0.670600	−	2.06390i
$795$		0			0
$796$	−36.4598	−	112.212i	−1.29228	−	3.97724i
$797$	−2.95898	−	9.10680i	−0.104812	−	0.322580i	0.884874	−	0.465831i	$-0.154244\pi$
$797$	−2.95898	−	9.10680i	−0.104812	−	0.322580i	−0.989686	+	0.143251i	$0.954244\pi$
$798$	11.4749	+	8.33704i	0.406209	+	0.295128i
$799$	−16.7068			−0.591044
$800$		0			0
$801$	9.07225			0.320552
$802$	27.6295	+	20.0740i	0.975632	+	0.708838i
$803$	−10.3959	−	31.9953i	−0.366863	−	1.12909i
$804$	1.27475	+	3.92328i	0.0449570	+	0.138364i
$805$		0			0
$806$	3.77935	−	11.6316i	0.133122	−	0.409707i
$807$	−17.4592			−0.614592
$808$	29.3508	−	90.3323i	1.03256	−	3.17788i
$809$	−33.2859	+	24.1836i	−1.17027	+	0.850250i	−0.991041	−	0.133557i	$-0.957360\pi$
$809$	−33.2859	+	24.1836i	−1.17027	+	0.850250i	−0.179228	+	0.983808i	$0.557360\pi$
$810$		0			0
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.236868	−	0.971542i	$-0.576121\pi$
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.997187	+	0.0749479i	$0.976121\pi$
$812$	2.54034	−	1.84566i	0.0891484	−	0.0647701i
$813$	0.0770069	−	0.0559488i	0.00270075	−	0.00196221i
$814$	9.86679	+	7.16864i	0.345831	+	0.251261i
$815$		0			0
$816$	−28.0987	+	20.4149i	−0.983651	+	0.714665i
$817$	9.43823	−	29.0479i	0.330202	−	1.01626i
$818$	90.0206			3.14750
$819$	1.82290	−	5.61031i	0.0636973	−	0.196040i
$820$		0			0
$821$	5.39595	+	16.6070i	0.188320	+	0.579589i	0.999990	−	0.00452746i	$-0.00144114\pi$
$821$	5.39595	+	16.6070i	0.188320	+	0.579589i	−0.811670	+	0.584116i	$0.801441\pi$
$822$	8.66625	+	26.6720i	0.302270	+	0.930292i
$823$	1.79970	+	1.30756i	0.0627337	+	0.0455787i	0.618710	−	0.785619i	$-0.287656\pi$
$823$	1.79970	+	1.30756i	0.0627337	+	0.0455787i	−0.555976	+	0.831198i	$0.687656\pi$
$824$	−74.6616			−2.60096
$825$		0			0
$826$	8.48106			0.295094
$827$	−25.4476	−	18.4888i	−0.884900	−	0.642918i	0.0496432	−	0.998767i	$-0.484192\pi$
$827$	−25.4476	−	18.4888i	−0.884900	−	0.642918i	−0.934543	+	0.355849i	$0.884192\pi$
$828$	−5.29633	−	16.3004i	−0.184060	−	0.566479i
$829$	16.4690	+	50.6862i	0.571990	+	1.76041i	0.646206	+	0.763163i	$0.276355\pi$
$829$	16.4690	+	50.6862i	0.571990	+	1.76041i	−0.0742155	+	0.997242i	$0.523645\pi$
$830$		0			0
$831$	−5.68614	+	17.5001i	−0.197250	+	0.607073i
$832$	6.18061			0.214274
$833$	−9.29560	+	28.6089i	−0.322073	+	0.991240i
$834$	−25.1903	+	18.3018i	−0.872267	+	0.633739i
$835$		0			0
$836$	57.3223	+	41.6471i	1.98253	+	1.44040i
$837$	−0.687754	+	0.499683i	−0.0237723	+	0.0172716i
$838$	32.4623	−	23.5853i	1.12139	−	0.814739i
$839$	6.77415	+	4.92171i	0.233870	+	0.169916i	0.698548	−	0.715563i	$-0.253830\pi$
$839$	6.77415	+	4.92171i	0.233870	+	0.169916i	−0.464678	+	0.885480i	$0.653830\pi$
$840$		0			0
$841$	23.0877	−	16.7742i	0.796129	−	0.578421i
$842$	−9.39558	+	28.9166i	−0.323793	+	0.996532i
$843$	17.9361			0.617750
$844$	−36.3015	+	111.725i	−1.24955	+	3.84572i
$845$		0			0
$846$	2.57715	+	7.93164i	0.0886041	+	0.272695i
$847$	0.698751	+	2.15054i	0.0240094	+	0.0738933i
$848$	70.1202	+	50.9453i	2.40794	+	1.74947i
$849$	−22.2399			−0.763273
$850$		0			0
$851$	−6.24467			−0.214064
$852$	5.07740	+	3.68895i	0.173949	+	0.126381i
$853$	−0.378146	−	1.16381i	−0.0129475	−	0.0398482i	0.944374	−	0.328873i	$-0.106669\pi$
$853$	−0.378146	−	1.16381i	−0.0129475	−	0.0398482i	−0.957322	+	0.289025i	$0.906669\pi$
$854$	−4.42332	−	13.6136i	−0.151363	−	0.465847i
$855$		0			0
$856$	12.4320	−	38.2618i	0.424917	−	1.30776i
$857$	−14.3684			−0.490816			−0.245408	−	0.969420i	$-0.578922\pi$
$857$	−14.3684			−0.490816			−0.245408	+	0.969420i	$0.578922\pi$
$858$	13.2082	−	40.6508i	0.450922	−	1.38780i
$859$	8.34015	−	6.05947i	0.284562	−	0.206747i	−0.436343	−	0.899781i	$-0.643726\pi$
$859$	8.34015	−	6.05947i	0.284562	−	0.206747i	0.720905	+	0.693034i	$0.243726\pi$
$860$		0			0
$861$	0.980955	+	0.712705i	0.0334308	+	0.0242889i
$862$	30.0619	−	21.8413i	1.02391	−	0.743916i
$863$	−24.4909	+	17.7937i	−0.833679	+	0.605703i	−0.920598	−	0.390512i	$-0.872298\pi$
$863$	−24.4909	+	17.7937i	−0.833679	+	0.605703i	0.0869190	+	0.996215i	$0.472298\pi$
$864$	4.00864	+	2.91245i	0.136377	+	0.0990835i
$865$		0			0
$866$	8.77241	−	6.37353i	0.298099	−	0.216581i
$867$	2.73268	−	8.41031i	0.0928065	−	0.285629i
$868$	−3.92730			−0.133301
$869$	−1.32855	+	4.08885i	−0.0450679	+	0.138705i
$870$		0			0
$871$	−1.62775	−	5.00969i	−0.0551541	−	0.169747i
$872$	4.42068	+	13.6055i	0.149703	+	0.460739i
$873$	−4.87779	−	3.54392i	−0.165088	−	0.119944i
$874$	−52.6220			−1.77996
$875$		0			0
$876$	−50.2734			−1.69858
$877$	−24.7839	−	18.0065i	−0.836892	−	0.608037i	0.0846091	−	0.996414i	$-0.473036\pi$
$877$	−24.7839	−	18.0065i	−0.836892	−	0.608037i	−0.921501	+	0.388377i	$0.873036\pi$
$878$	15.9247	+	49.0111i	0.537431	+	1.65404i
$879$	−5.78837	−	17.8148i	−0.195237	−	0.600877i
$880$		0			0
$881$	4.70359	−	14.4762i	0.158468	−	0.487714i	−0.840028	−	0.542543i	$-0.817461\pi$
$881$	4.70359	−	14.4762i	0.158468	−	0.487714i	0.998496	+	0.0548293i	$0.0174615\pi$
$882$	15.0161			0.505620
$883$	12.4220	−	38.2310i	0.418034	−	1.28658i	−0.491475	−	0.870892i	$-0.663542\pi$
$883$	12.4220	−	38.2310i	0.418034	−	1.28658i	0.909509	−	0.415684i	$-0.136458\pi$
$884$	103.518	−	75.2102i	3.48169	−	2.52959i
$885$		0			0
$886$	39.1189	+	28.4216i	1.31423	+	0.954842i
$887$	25.7617	−	18.7169i	0.864992	−	0.628453i	−0.0642465	−	0.997934i	$-0.520464\pi$
$887$	25.7617	−	18.7169i	0.864992	−	0.628453i	0.929238	+	0.369481i	$0.120464\pi$
$888$	8.10259	−	5.88688i	0.271905	−	0.197551i
$889$	9.84394	+	7.15204i	0.330155	+	0.239872i
$890$		0			0
$891$	−2.40360	+	1.74631i	−0.0805235	+	0.0585037i
$892$	−37.6545	+	115.889i	−1.26077	+	3.88024i
$893$	17.6531			0.590739
$894$	3.62946	−	11.1703i	0.121387	−	0.373591i
$895$		0			0
$896$	−4.07604	−	12.5448i	−0.136171	−	0.419091i
$897$	6.76296	+	20.8142i	0.225809	+	0.694967i
$898$	60.5217	+	43.9716i	2.01964	+	1.46735i
$899$	0.577817			0.0192713
$900$		0			0
$901$	−64.4914			−2.14852
$902$	7.10774	+	5.16407i	0.236662	+	0.171945i
$903$	1.82830	+	5.62692i	0.0608419	+	0.187252i
$904$	−7.40962	−	22.8045i	−0.246440	−	0.758465i
$905$		0			0
$906$	3.66409	−	11.2769i	0.121731	−	0.374651i
$907$	−28.8507			−0.957970			−0.478985	−	0.877823i	$-0.658995\pi$
$907$	−28.8507			−0.957970			−0.478985	+	0.877823i	$0.658995\pi$
$908$	0.178577	−	0.549602i	0.00592627	−	0.0182392i
$909$	12.4110	−	9.01712i	0.411647	−	0.299079i
$910$		0			0
$911$	−39.1370	−	28.4347i	−1.29667	−	0.942084i	−0.296750	−	0.954955i	$-0.595903\pi$
$911$	−39.1370	−	28.4347i	−1.29667	−	0.942084i	−0.999917	+	0.0128711i	$0.995903\pi$
$912$	29.6903	−	21.5713i	0.983143	−	0.714296i
$913$	−27.5827	+	20.0400i	−0.912855	+	0.663228i
$914$	58.1036	+	42.2148i	1.92190	+	1.39634i
$915$		0			0
$916$	−10.1481	+	7.37301i	−0.335302	+	0.243611i
$917$	2.56016	−	7.87936i	0.0845439	−	0.260199i
$918$	−12.9006			−0.425782
$919$	−2.58963	+	7.97006i	−0.0854240	+	0.262908i	−0.984640	−	0.174597i	$-0.944138\pi$
$919$	−2.58963	+	7.97006i	−0.0854240	+	0.262908i	0.899216	+	0.437505i	$0.144138\pi$
$920$		0			0
$921$	−2.17501	−	6.69401i	−0.0716692	−	0.220575i
$922$	12.9841	+	39.9609i	0.427608	+	1.31604i
$923$	−6.48340	−	4.71046i	−0.213404	−	0.155047i
$924$	−13.7253			−0.451530
$925$		0			0
$926$	−23.3703			−0.767995
$927$	−9.75590	−	7.08808i	−0.320426	−	0.232803i
$928$	−1.04073	−	3.20303i	−0.0341636	−	0.105145i
$929$	4.42283	+	13.6121i	0.145108	+	0.446597i	0.997025	−	0.0770801i	$-0.0245597\pi$
$929$	4.42283	+	13.6121i	0.145108	+	0.446597i	−0.851917	+	0.523677i	$0.824560\pi$
$930$		0			0
$931$	9.82212	−	30.2294i	0.321907	−	0.990728i
$932$	35.4610			1.16156
$933$	−9.04771	+	27.8460i	−0.296209	+	0.911637i
$934$	21.7873	−	15.8294i	0.712901	−	0.517953i
$935$		0			0
$936$	−28.3967	−	20.6314i	−0.928177	−	0.674360i
$937$	17.7372	−	12.8869i	0.579451	−	0.420996i	−0.259075	−	0.965857i	$-0.583418\pi$
$937$	17.7372	−	12.8869i	0.579451	−	0.420996i	0.838526	+	0.544862i	$0.183418\pi$
$938$	−1.98487	+	1.44209i	−0.0648082	+	0.0470859i
$939$	12.6493	+	9.19024i	0.412794	+	0.299912i
$940$		0			0
$941$	−18.1167	+	13.1625i	−0.590586	+	0.429086i	−0.842525	−	0.538657i	$-0.818932\pi$
$941$	−18.1167	+	13.1625i	−0.590586	+	0.429086i	0.251939	+	0.967743i	$0.418932\pi$
$942$	−11.7413	+	36.1360i	−0.382552	+	1.17737i
$943$	−4.49847			−0.146490
$944$	6.78104	−	20.8699i	0.220704	−	0.679257i
$945$		0			0
$946$	13.2474	+	40.7712i	0.430709	+	1.32559i
$947$	13.4619	+	41.4316i	0.437454	+	1.34635i	0.890550	+	0.454884i	$0.150319\pi$
$947$	13.4619	+	41.4316i	0.437454	+	1.34635i	−0.453096	+	0.891462i	$0.649681\pi$
$948$	5.19769	+	3.77635i	0.168813	+	0.122650i
$949$	64.1947			2.08385
$950$		0			0
$951$	−6.24144			−0.202393
$952$	−26.4957	−	19.2502i	−0.858729	−	0.623903i
$953$	0.732893	+	2.25561i	0.0237407	+	0.0730664i	0.962225	−	0.272256i	$-0.0877697\pi$
$953$	0.732893	+	2.25561i	0.0237407	+	0.0730664i	−0.938484	+	0.345322i	$0.887770\pi$
$954$	9.94827	+	30.6176i	0.322087	+	0.991282i
$955$		0			0
$956$	−26.1524	+	80.4887i	−0.845828	+	2.60319i
$957$	2.01938			0.0652774
$958$	−26.3534	+	81.1073i	−0.851439	+	2.62046i
$959$	−9.30310	+	6.75910i	−0.300413	+	0.218263i
$960$		0			0
$961$	24.4949	+	17.7966i	0.790157	+	0.574082i
$962$	−18.8276	+	13.6791i	−0.607027	+	0.441031i
$963$	5.25689	−	3.81935i	0.169401	−	0.123077i
$964$	−75.8598	−	55.1154i	−2.44328	−	1.77515i
$965$		0			0
$966$	8.24672	−	5.99159i	0.265334	−	0.192776i
$967$	−6.11413	+	18.8174i	−0.196617	+	0.605125i	0.803337	+	0.595525i	$0.203056\pi$
$967$	−6.11413	+	18.8174i	−0.196617	+	0.605125i	−0.999954	+	0.00960036i	$0.996944\pi$
$968$	13.4546			0.432447
$969$	−8.43831	+	25.9704i	−0.271077	+	0.834291i
$970$		0			0
$971$	15.2604	+	46.9668i	0.489731	+	1.50724i	0.825010	+	0.565118i	$0.191169\pi$
$971$	15.2604	+	46.9668i	0.489731	+	1.50724i	−0.335279	+	0.942119i	$0.608831\pi$
$972$	1.37197	+	4.22249i	0.0440059	+	0.135436i
$973$	−10.3289	−	7.50438i	−0.331129	−	0.240579i
$974$	−74.2234			−2.37827
$975$		0			0
$976$	−37.0365			−1.18551
$977$	38.6429	+	28.0757i	1.23630	+	0.898221i	0.997346	−	0.0728110i	$-0.0231970\pi$
$977$	38.6429	+	28.0757i	1.23630	+	0.898221i	0.238949	+	0.971032i	$0.423197\pi$
$978$	−9.34058	−	28.7474i	−0.298679	−	0.919239i
$979$	8.32916	+	25.6345i	0.266201	+	0.819283i
$980$		0			0
$981$	−0.714006	+	2.19749i	−0.0227965	+	0.0701603i
$982$	−35.4131			−1.13008
$983$	16.0467	−	49.3867i	0.511810	−	1.57519i	−0.277201	−	0.960812i	$-0.589407\pi$
$983$	16.0467	−	49.3867i	0.511810	−	1.57519i	0.789011	−	0.614379i	$-0.210593\pi$
$984$	5.83686	−	4.24073i	0.186072	−	0.135190i
$985$		0			0
$986$	7.09383	+	5.15397i	0.225914	+	0.164136i
$987$	−2.76653	+	2.01000i	−0.0880596	+	0.0639791i
$988$	−109.381	+	79.4703i	−3.47989	+	2.52829i
$989$	−17.7581	−	12.9020i	−0.564674	−	0.410260i
$990$		0			0
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	−0.357083	−	0.934073i	$-0.616229\pi$
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	0.778011	+	0.628250i	$0.216229\pi$
$992$	−1.30166	+	4.00610i	−0.0413277	+	0.127194i
$993$	21.4575			0.680933
$994$	−1.15344	+	3.54994i	−0.0365850	+	0.112597i
$995$		0			0
$996$	15.7442	+	48.4557i	0.498874	+	1.53538i
$997$	−6.87610	−	21.1625i	−0.217768	−	0.670222i	−0.998945	−	0.0459126i	$-0.985380\pi$
$997$	−6.87610	−	21.1625i	−0.217768	−	0.670222i	0.781177	−	0.624309i	$-0.214620\pi$
$998$	−73.4022	−	53.3299i	−2.32351	−	1.68813i
$999$	1.61763			0.0511795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.e.76.4		16
5.2	odd	4		375.2.i.c.49.1		16
5.3	odd	4		75.2.i.a.34.4	✓	16
5.4	even	2		375.2.g.d.76.1		16
15.8	even	4		225.2.m.b.109.1		16
25.2	odd	20		75.2.i.a.64.4	yes	16
25.6	even	5		1875.2.a.m.1.1		8
25.8	odd	20		1875.2.b.h.1249.16		16
25.11	even	5	inner	375.2.g.e.301.4		16
25.14	even	10		375.2.g.d.301.1		16
25.17	odd	20		1875.2.b.h.1249.1		16
25.19	even	10		1875.2.a.p.1.8		8
25.23	odd	20		375.2.i.c.199.1		16
75.2	even	20		225.2.m.b.64.1		16
75.44	odd	10		5625.2.a.t.1.1		8
75.56	odd	10		5625.2.a.bd.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.4	✓	16	5.3	odd	4
75.2.i.a.64.4	yes	16	25.2	odd	20
225.2.m.b.64.1		16	75.2	even	20
225.2.m.b.109.1		16	15.8	even	4
375.2.g.d.76.1		16	5.4	even	2
375.2.g.d.301.1		16	25.14	even	10
375.2.g.e.76.4		16	1.1	even	1	trivial
375.2.g.e.301.4		16	25.11	even	5	inner
375.2.i.c.49.1		16	5.2	odd	4
375.2.i.c.199.1		16	25.23	odd	20
1875.2.a.m.1.1		8	25.6	even	5
1875.2.a.p.1.8		8	25.19	even	10
1875.2.b.h.1249.1		16	25.17	odd	20
1875.2.b.h.1249.16		16	25.8	odd	20
5625.2.a.t.1.1		8	75.44	odd	10
5625.2.a.bd.1.8		8	75.56	odd	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.05302 + 1.49161i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.37197 + 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054 q^{7} +(-1.91324 + 5.88835i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.05302 + 1.49161i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.37197 + 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054 q^{7} +(-1.91324 + 5.88835i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.40360 - 1.74631i) q^{11} +(-3.59186 + 2.60964i) q^{12} +(4.58650 - 3.33228i) q^{13} +(-2.13624 - 1.55207i) q^{14} +(-5.52731 + 4.01583i) q^{16} +(1.57092 - 4.83480i) q^{17} -2.53767 q^{18} +(-1.65990 + 5.10866i) q^{19} +(-0.321543 - 0.989608i) q^{21} +(-2.32982 - 7.17044i) q^{22} +(3.12312 + 2.26908i) q^{23} -6.19138 q^{24} +14.3866 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.42758 - 4.39365i) q^{28} +(0.210038 + 0.646430i) q^{29} +(0.262699 - 0.808503i) q^{31} -4.95495 q^{32} +(0.918092 - 2.82560i) q^{33} +(10.4368 - 7.58275i) q^{34} +(-3.59186 - 2.60964i) q^{36} +(-1.30869 + 0.950818i) q^{37} +(-11.0279 + 8.01226i) q^{38} +(4.58650 + 3.33228i) q^{39} +(-0.942740 + 0.684941i) q^{41} +(0.815972 - 2.51130i) q^{42} -5.68601 q^{43} +(4.07613 - 12.5450i) q^{44} +(3.02725 + 9.31693i) q^{46} +(-1.01555 - 3.12556i) q^{47} +(-5.52731 - 4.01583i) q^{48} -5.91729 q^{49} +5.08361 q^{51} +(20.3631 + 14.7946i) q^{52} +(-3.92023 - 12.0652i) q^{53} +(-0.784184 - 2.41347i) q^{54} +(1.99080 - 6.12704i) q^{56} -5.37156 q^{57} +(-0.533007 + 1.64043i) q^{58} +(-2.59846 + 1.88789i) q^{59} +(4.38562 + 3.18634i) q^{61} +(1.74530 - 1.26803i) q^{62} +(0.841811 - 0.611611i) q^{63} +(0.881995 + 0.640807i) q^{64} +(6.09954 - 4.43157i) q^{66} +(0.287120 - 0.883665i) q^{67} +22.5702 q^{68} +(-1.19292 + 3.67145i) q^{69} +(-0.436821 - 1.34440i) q^{71} +(-1.91324 - 5.88835i) q^{72} +(9.16080 + 6.65571i) q^{73} -4.10501 q^{74} -23.8486 q^{76} +(2.50103 + 1.81710i) q^{77} +(4.44571 + 13.6825i) q^{78} +(-0.447171 - 1.37625i) q^{79} +(0.309017 - 0.951057i) q^{81} -2.95713 q^{82} +(3.54616 - 10.9140i) q^{83} +(3.73746 - 2.71542i) q^{84} +(-11.6735 - 8.48129i) q^{86} +(-0.549886 + 0.399516i) q^{87} +(14.8816 - 10.8121i) q^{88} +(-7.33961 - 5.33254i) q^{89} +(-4.77241 + 3.46736i) q^{91} +(-5.29633 + 16.3004i) q^{92} +0.850111 q^{93} +(2.57715 - 7.93164i) q^{94} +(-1.53117 - 4.71244i) q^{96} +(1.86315 + 5.73419i) q^{97} +(-12.1483 - 8.82627i) q^{98} +2.97101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more