LMFDB - Embedded newform 575.2.p.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [575,2,Mod(49,575)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(575, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("575.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.p (of order $22$, degree $10$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			49.1
Root			$0.281733 + 0.959493i$ of defining polynomial
Character	$\chi$	$=$	575.49
Dual form			575.2.p.b.399.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.18119 + 0.313607i) q^{2} +(-2.28621 - 1.04408i) q^{3} +(2.74024 - 0.804606i) q^{4} +(5.31408 + 1.56036i) q^{6} +(1.28282 + 1.99611i) q^{7} +(-1.71568 + 0.783524i) q^{8} +(2.17208 + 2.50672i) q^{9} +(0.272084 - 1.89238i) q^{11} +(-7.10483 - 1.02152i) q^{12} +(-0.106222 + 0.165284i) q^{13} +(-3.42408 - 3.95159i) q^{14} +(-1.30862 + 0.840996i) q^{16} +(0.439476 - 1.49672i) q^{17} +(-5.52384 - 4.78644i) q^{18} +(-7.66103 + 2.24948i) q^{19} +(-0.848710 - 5.90291i) q^{21} +4.21297i q^{22} +(-1.10192 - 4.66752i) q^{23} +4.74046 q^{24} +(0.179855 - 0.393828i) q^{26} +(-0.224367 - 0.764125i) q^{27} +(5.12133 + 4.43766i) q^{28} +(4.77570 + 1.40227i) q^{29} +(0.740552 + 1.62158i) q^{31} +(5.44146 - 4.71506i) q^{32} +(-2.59784 + 4.04231i) q^{33} +(-0.489198 + 3.40244i) q^{34} +(7.96894 + 5.12133i) q^{36} +(-2.93475 + 2.54297i) q^{37} +(16.0047 - 7.30909i) q^{38} +(0.415415 - 0.266971i) q^{39} +(-0.279295 + 0.322324i) q^{41} +(3.70239 + 12.6092i) q^{42} +(4.05075 + 1.84991i) q^{43} +(-0.777050 - 5.40450i) q^{44} +(3.86725 + 9.83517i) q^{46} +2.58842i q^{47} +(3.86984 - 0.556399i) q^{48} +(0.569072 - 1.24609i) q^{49} +(-2.56743 + 2.96297i) q^{51} +(-0.158084 + 0.538385i) q^{52} +(5.30876 + 8.26060i) q^{53} +(0.729022 + 1.59634i) q^{54} +(-3.76492 - 2.41956i) q^{56} +(19.8634 + 2.85592i) q^{57} +(-10.8565 - 1.56092i) q^{58} +(6.07293 + 3.90283i) q^{59} +(3.08639 + 6.75826i) q^{61} +(-2.12382 - 3.30473i) q^{62} +(-2.21729 + 7.55141i) q^{63} +(-8.35283 + 9.63968i) q^{64} +(4.39867 - 9.63174i) q^{66} +(-7.19254 + 1.03413i) q^{67} -4.45497i q^{68} +(-2.35404 + 11.8214i) q^{69} +(0.103930 + 0.722850i) q^{71} +(-5.69067 - 2.59884i) q^{72} +(1.81558 + 6.18330i) q^{73} +(5.60373 - 6.46705i) q^{74} +(-19.1831 + 12.3282i) q^{76} +(4.12645 - 1.88449i) q^{77} +(-0.822373 + 0.712591i) q^{78} +(4.77671 + 3.06980i) q^{79} +(1.13126 - 7.86810i) q^{81} +(0.508112 - 0.790638i) q^{82} +(-9.74141 + 8.44098i) q^{83} +(-7.07518 - 15.4925i) q^{84} +(-9.41558 - 2.76466i) q^{86} +(-9.45418 - 8.19209i) q^{87} +(1.01592 + 3.45991i) q^{88} +(5.77436 - 12.6441i) q^{89} -0.466190 q^{91} +(-6.77503 - 11.9035i) q^{92} -4.48047i q^{93} +(-0.811746 - 5.64582i) q^{94} +(-17.3632 + 5.09830i) q^{96} +(3.26769 + 2.83147i) q^{97} +(-0.850468 + 2.89643i) q^{98} +(5.33466 - 3.42838i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{4} + 12 q^{6} + 4 q^{9} + 14 q^{11} - 18 q^{14} + 2 q^{16} - 4 q^{19} - 4 q^{21} + 76 q^{24} + 24 q^{26} - 28 q^{29} + 20 q^{31} - 58 q^{34} + 54 q^{36} - 2 q^{39} + 14 q^{41} + 68 q^{44} - 58 q^{46}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^4 + 12 * q^6 + 4 * q^9 + 14 * q^11 - 18 * q^14 + 2 * q^16 - 4 * q^19 - 4 * q^21 + 76 * q^24 + 24 * q^26 - 28 * q^29 + 20 * q^31 - 58 * q^34 + 54 * q^36 - 2 * q^39 + 14 * q^41 + 68 * q^44 - 58 * q^46 + 36 * q^49 + 14 * q^51 + 12 * q^54 - 4 * q^56 + 42 * q^59 + 6 * q^61 - 48 * q^64 + 4 * q^66 - 52 * q^69 - 28 * q^71 - 20 * q^74 - 32 * q^76 + 30 * q^79 - 88 * q^81 + 34 * q^84 - 22 * q^86 - 50 * q^89 - 8 * q^91 - 34 * q^94 - 102 * q^96 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$

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 $

$2$	−2.18119	+	0.313607i	−1.54233	+	0.221754i	−0.860384	−	0.509647i	$-0.829776\pi$
$2$	−2.18119	+	0.313607i	−1.54233	+	0.221754i	−0.681948	+	0.731401i	$0.738867\pi$
$3$	−2.28621	−	1.04408i	−1.31995	−	0.602799i	−0.374091	−	0.927392i	$-0.622045\pi$
$3$	−2.28621	−	1.04408i	−1.31995	−	0.602799i	−0.945854	+	0.324593i	$0.894773\pi$
$4$	2.74024	−	0.804606i	1.37012	−	0.402303i
$5$		0			0
$5$		0			0
$6$	5.31408	+	1.56036i	2.16947	+	0.637013i
$7$	1.28282	+	1.99611i	0.484862	+	0.754460i	0.994365	−	0.106009i	$-0.0338071\pi$
$7$	1.28282	+	1.99611i	0.484862	+	0.754460i	−0.509503	+	0.860469i	$0.670171\pi$
$8$	−1.71568	+	0.783524i	−0.606584	+	0.277017i
$9$	2.17208	+	2.50672i	0.724028	+	0.835573i
$10$		0			0
$11$	0.272084	−	1.89238i	0.0820363	−	0.570575i	−0.906799	−	0.421563i	$-0.861482\pi$
$11$	0.272084	−	1.89238i	0.0820363	−	0.570575i	0.988835	−	0.149012i	$-0.0476093\pi$
$12$	−7.10483	−	1.02152i	−2.05099	−	0.294888i
$13$	−0.106222	+	0.165284i	−0.0294606	+	0.0458416i	−0.855672	−	0.517519i	$-0.826856\pi$
$13$	−0.106222	+	0.165284i	−0.0294606	+	0.0458416i	0.826211	+	0.563361i	$0.190492\pi$
$14$	−3.42408	−	3.95159i	−0.915123	−	1.05611i
$15$		0			0
$16$	−1.30862	+	0.840996i	−0.327154	+	0.210249i
$17$	0.439476	−	1.49672i	0.106589	−	0.363008i	−0.888875	−	0.458150i	$-0.848512\pi$
$17$	0.439476	−	1.49672i	0.106589	−	0.363008i	0.995464	+	0.0951421i	$0.0303306\pi$
$18$	−5.52384	−	4.78644i	−1.30198	−	1.12817i
$19$	−7.66103	+	2.24948i	−1.75756	+	0.516066i	−0.991883	−	0.127157i	$-0.959415\pi$
$19$	−7.66103	+	2.24948i	−1.75756	+	0.516066i	−0.765678	+	0.643224i	$0.777597\pi$
$20$		0			0
$21$	−0.848710	−	5.90291i	−0.185204	−	1.28812i
$22$			4.21297i			0.898208i
$23$	−1.10192	−	4.66752i	−0.229765	−	0.973246i
$23$	−1.10192	−	4.66752i	−0.229765	−	0.973246i
$24$	4.74046			0.967643
$25$		0			0
$26$	0.179855	−	0.393828i	0.0352725	−	0.0772359i
$27$	−0.224367	−	0.764125i	−0.0431795	−	0.147056i
$28$	5.12133	+	4.43766i	0.967840	+	0.838638i
$29$	4.77570	+	1.40227i	0.886825	+	0.260395i	0.693256	−	0.720691i	$-0.256175\pi$
$29$	4.77570	+	1.40227i	0.886825	+	0.260395i	0.193569	+	0.981087i	$0.437994\pi$
$30$		0			0
$31$	0.740552	+	1.62158i	0.133007	+	0.291245i	0.964404	−	0.264435i	$-0.0851854\pi$
$31$	0.740552	+	1.62158i	0.133007	+	0.291245i	−0.831397	+	0.555680i	$0.812458\pi$
$32$	5.44146	−	4.71506i	0.961924	−	0.833512i
$33$	−2.59784	+	4.04231i	−0.452226	+	0.703677i
$34$	−0.489198	+	3.40244i	−0.0838967	+	0.583514i
$35$		0			0
$36$	7.96894	+	5.12133i	1.32816	+	0.853555i
$37$	−2.93475	+	2.54297i	−0.482469	+	0.418062i	−0.861838	−	0.507184i	$-0.830687\pi$
$37$	−2.93475	+	2.54297i	−0.482469	+	0.418062i	0.379369	+	0.925246i	$0.376141\pi$
$38$	16.0047	−	7.30909i	2.59630	−	1.18569i
$39$	0.415415	−	0.266971i	0.0665196	−	0.0427496i
$40$		0			0
$41$	−0.279295	+	0.322324i	−0.0436186	+	0.0503386i	−0.777140	−	0.629328i	$-0.783330\pi$
$41$	−0.279295	+	0.322324i	−0.0436186	+	0.0503386i	0.733521	+	0.679667i	$0.237876\pi$
$42$	3.70239	+	12.6092i	0.571291	+	1.94564i
$43$	4.05075	+	1.84991i	0.617733	+	0.282109i	0.699601	−	0.714534i	$-0.253361\pi$
$43$	4.05075	+	1.84991i	0.617733	+	0.282109i	−0.0818677	+	0.996643i	$0.526089\pi$
$44$	−0.777050	−	5.40450i	−0.117145	−	0.814759i
$45$		0			0
$46$	3.86725	+	9.83517i	0.570195	+	1.45012i
$47$			2.58842i			0.377559i	0.982019	+	0.188780i	$0.0604532\pi$
$47$			2.58842i			0.377559i	−0.982019	+	0.188780i	$0.939547\pi$
$48$	3.86984	−	0.556399i	0.558563	−	0.0803092i
$49$	0.569072	−	1.24609i	0.0812960	−	0.178013i
$50$		0			0
$51$	−2.56743	+	2.96297i	−0.359512	+	0.414898i
$52$	−0.158084	+	0.538385i	−0.0219223	+	0.0746605i
$53$	5.30876	+	8.26060i	0.729215	+	1.13468i	0.985762	+	0.168149i	$0.0537789\pi$
$53$	5.30876	+	8.26060i	0.729215	+	1.13468i	−0.256547	+	0.966532i	$0.582585\pi$
$54$	0.729022	+	1.59634i	0.0992074	+	0.217234i
$55$		0			0
$56$	−3.76492	−	2.41956i	−0.503108	−	0.323328i
$57$	19.8634	+	2.85592i	2.63097	+	0.378276i
$58$	−10.8565	−	1.56092i	−1.42552	−	0.204959i
$59$	6.07293	+	3.90283i	0.790628	+	0.508106i	0.872545	−	0.488533i	$-0.162468\pi$
$59$	6.07293	+	3.90283i	0.790628	+	0.508106i	−0.0819173	+	0.996639i	$0.526104\pi$
$60$		0			0
$61$	3.08639	+	6.75826i	0.395172	+	0.865306i	0.997737	+	0.0672363i	$0.0214181\pi$
$61$	3.08639	+	6.75826i	0.395172	+	0.865306i	−0.602565	+	0.798070i	$0.705855\pi$
$62$	−2.12382	−	3.30473i	−0.269726	−	0.419701i
$63$	−2.21729	+	7.55141i	−0.279353	+	0.951388i
$64$	−8.35283	+	9.63968i	−1.04410	+	1.20496i
$65$		0			0
$66$	4.39867	−	9.63174i	0.541439	−	1.18559i
$67$	−7.19254	+	1.03413i	−0.878708	+	0.126339i	−0.566881	−	0.823800i	$-0.691850\pi$
$67$	−7.19254	+	1.03413i	−0.878708	+	0.126339i	−0.311827	+	0.950139i	$0.600941\pi$
$68$		−	4.45497i		−	0.540244i
$69$	−2.35404	+	11.8214i	−0.283394	+	1.42313i
$70$		0			0
$71$	0.103930	+	0.722850i	0.0123342	+	0.0857866i	0.995059	−	0.0992879i	$-0.0316565\pi$
$71$	0.103930	+	0.722850i	0.0123342	+	0.0857866i	−0.982725	+	0.185074i	$0.940747\pi$
$72$	−5.69067	−	2.59884i	−0.670652	−	0.306276i
$73$	1.81558	+	6.18330i	0.212498	+	0.723700i	0.994895	+	0.100920i	$0.0321787\pi$
$73$	1.81558	+	6.18330i	0.212498	+	0.723700i	−0.782397	+	0.622780i	$0.786003\pi$
$74$	5.60373	−	6.46705i	0.651421	−	0.751780i
$75$		0			0
$76$	−19.1831	+	12.3282i	−2.20045	+	1.41414i
$77$	4.12645	−	1.88449i	0.470253	−	0.214757i
$78$	−0.822373	+	0.712591i	−0.0931154	+	0.0806850i
$79$	4.77671	+	3.06980i	0.537422	+	0.345380i	0.781030	−	0.624494i	$-0.214695\pi$
$79$	4.77671	+	3.06980i	0.537422	+	0.345380i	−0.243608	+	0.969874i	$0.578331\pi$
$80$		0			0
$81$	1.13126	−	7.86810i	0.125696	−	0.874233i
$82$	0.508112	−	0.790638i	0.0561116	−	0.0873113i
$83$	−9.74141	+	8.44098i	−1.06926	+	0.926518i	−0.997483	−	0.0709025i	$-0.977412\pi$
$83$	−9.74141	+	8.44098i	−1.06926	+	0.926518i	−0.0717758	+	0.997421i	$0.522867\pi$
$84$	−7.07518	−	15.4925i	−0.771966	−	1.69037i
$85$		0			0
$86$	−9.41558	−	2.76466i	−1.01531	−	0.298121i
$87$	−9.45418	−	8.19209i	−1.01359	−	0.878284i
$88$	1.01592	+	3.45991i	0.108297	+	0.368827i
$89$	5.77436	−	12.6441i	0.612081	−	1.34027i	−0.309060	−	0.951043i	$-0.600014\pi$
$89$	5.77436	−	12.6441i	0.612081	−	1.34027i	0.921141	−	0.389228i	$-0.127258\pi$
$90$		0			0
$91$	−0.466190			−0.0488700
$92$	−6.77503	−	11.9035i	−0.706346	−	1.24103i
$93$		−	4.48047i		−	0.464603i
$94$	−0.811746	−	5.64582i	−0.0837252	−	0.582322i
$95$		0			0
$96$	−17.3632	+	5.09830i	−1.77213	+	0.520343i
$97$	3.26769	+	2.83147i	0.331783	+	0.287492i	0.804781	−	0.593572i	$-0.202283\pi$
$97$	3.26769	+	2.83147i	0.331783	+	0.287492i	−0.472998	+	0.881064i	$0.656828\pi$
$98$	−0.850468	+	2.89643i	−0.0859103	+	0.292583i
$99$	5.33466	−	3.42838i	0.536154	−	0.344565i
$100$		0			0
$101$	1.19203	+	1.37567i	0.118611	+	0.136885i	0.811950	−	0.583727i	$-0.198406\pi$
$101$	1.19203	+	1.37567i	0.118611	+	0.136885i	−0.693338	+	0.720612i	$0.743861\pi$
$102$	4.67083	−	7.26795i	0.462481	−	0.719634i
$103$	15.1574	+	2.17930i	1.49350	+	0.214733i	0.840163	−	0.542335i	$-0.182459\pi$
$103$	15.1574	+	2.17930i	1.49350	+	0.214733i	0.653337	+	0.757067i	$0.273369\pi$
$104$	0.0527381	−	0.366802i	0.00517140	−	0.0359679i
$105$		0			0
$106$	−14.1700	−	16.3530i	−1.37631	−	1.58835i
$107$	1.80865	−	0.825981i	0.174848	−	0.0798506i	−0.326068	−	0.945346i	$-0.605724\pi$
$107$	1.80865	−	0.825981i	0.174848	−	0.0798506i	0.500916	+	0.865496i	$0.332996\pi$
$108$	−1.22964	−	1.91336i	−0.118322	−	0.184113i
$109$	14.9631	+	4.39356i	1.43320	+	0.420826i	0.903950	−	0.427638i	$-0.140654\pi$
$109$	14.9631	+	4.39356i	1.43320	+	0.420826i	0.529253	+	0.848464i	$0.322472\pi$
$110$		0			0
$111$	9.36451	−	2.74967i	0.888840	−	0.260987i
$112$	−3.35745	−	1.53330i	−0.317249	−	0.144883i
$113$	−1.47310	+	0.211799i	−0.138577	+	0.0199244i	−0.211254	−	0.977431i	$-0.567755\pi$
$113$	−1.47310	+	0.211799i	−0.138577	+	0.0199244i	0.0726771	+	0.997356i	$0.476846\pi$
$114$	−44.2213			−4.14171
$115$		0			0
$116$	14.2148			1.31981
$117$	−0.645043	+	0.0927432i	−0.0596343	+	0.00857412i
$118$	−14.4701	−	6.60829i	−1.33208	−	0.608343i
$119$	3.55139	−	1.04278i	0.325556	−	0.0955917i
$120$		0			0
$121$	7.04733	+	2.06928i	0.640667	+	0.188117i
$122$	−8.85143	−	13.7731i	−0.801371	−	1.24696i
$123$	0.975060	−	0.445295i	0.0879182	−	0.0401509i
$124$	3.33402	+	3.84767i	0.299404	+	0.345531i
$125$		0			0
$126$	2.46815	−	17.1664i	0.219881	−	1.52930i
$127$	5.93335	+	0.853087i	0.526500	+	0.0756993i	0.400439	−	0.916323i	$-0.368858\pi$
$127$	5.93335	+	0.853087i	0.526500	+	0.0756993i	0.126061	+	0.992023i	$0.459767\pi$
$128$	7.41067	−	11.5312i	0.655017	−	1.01923i
$129$	−7.32941	−	8.45859i	−0.645319	−	0.744737i
$130$		0			0
$131$	−10.7418	+	6.90335i	−0.938517	+	0.603148i	−0.917974	−	0.396641i	$-0.870176\pi$
$131$	−10.7418	+	6.90335i	−0.938517	+	0.603148i	−0.0205431	+	0.999789i	$0.506540\pi$
$132$	−3.86622	+	13.1671i	−0.336511	+	1.14605i
$133$	−14.3180	−	12.4066i	−1.24153	−	1.07579i
$134$	15.3640	−	4.51126i	1.32724	−	0.389714i
$135$		0			0
$136$	0.418715	+	2.91223i	0.0359045	+	0.249721i
$137$		−	0.697560i		−	0.0595966i	−0.999556	−	0.0297983i	$-0.990514\pi$
$137$		−	0.697560i		−	0.0595966i	0.999556	−	0.0297983i	$-0.00948649\pi$
$138$	1.42732	−	26.5230i	0.121502	−	2.25779i
$139$	−13.9559			−1.18372			−0.591862	−	0.806039i	$-0.701607\pi$
$139$	−13.9559			−1.18372			−0.591862	+	0.806039i	$0.701607\pi$
$140$		0			0
$141$	2.70251	−	5.91767i	0.227592	−	0.498358i
$142$	−0.453382	−	1.54408i	−0.0380470	−	0.129576i
$143$	0.283880	+	0.245983i	0.0237392	+	0.0205702i
$144$	−4.95056	−	1.45362i	−0.412547	−	0.121135i
$145$		0			0
$146$	−5.89924	−	12.9175i	−0.488225	−	1.06906i
$147$	−2.60204	+	2.25468i	−0.214613	+	0.185963i
$148$	−5.99581	+	9.32966i	−0.492852	+	0.766893i
$149$	−2.36798	+	16.4697i	−0.193993	+	1.34925i	0.627317	+	0.778764i	$0.284153\pi$
$149$	−2.36798	+	16.4697i	−0.193993	+	1.34925i	−0.821309	+	0.570483i	$0.806756\pi$
$150$		0			0
$151$	11.0961	+	7.13103i	0.902988	+	0.580315i	0.907675	−	0.419674i	$-0.137855\pi$
$151$	11.0961	+	7.13103i	0.902988	+	0.580315i	−0.00468679	+	0.999989i	$0.501492\pi$
$152$	11.3813	−	9.86198i	0.923148	−	0.799913i
$153$	4.70643	−	2.14935i	0.380492	−	0.173765i
$154$	−8.40957	+	5.40450i	−0.677662	+	0.435507i
$155$		0			0
$156$	0.923529	−	1.06581i	0.0739415	−	0.0853330i
$157$	1.16318	+	3.96143i	0.0928320	+	0.316157i	0.992798	−	0.119804i	$-0.0382267\pi$
$157$	1.16318	+	3.96143i	0.0928320	+	0.316157i	−0.899965	+	0.435961i	$0.856409\pi$
$158$	−11.3816	−	5.19780i	−0.905471	−	0.413515i
$159$	−3.51225	−	24.4282i	−0.278540	−	1.93729i
$160$		0			0
$161$	7.90335	−	8.18717i	0.622871	−	0.645239i
$162$			17.5166i			1.37623i
$163$	−14.6388	+	2.10474i	−1.14660	+	0.164856i	−0.689312	−	0.724464i	$-0.742087\pi$
$163$	−14.6388	+	2.10474i	−1.14660	+	0.164856i	−0.457285	+	0.889320i	$0.651178\pi$
$164$	−0.505992	+	1.10797i	−0.0395113	+	0.0865177i
$165$		0			0
$166$	18.6007	−	21.4663i	1.44369	−	1.66611i
$167$	−0.374632	+	1.27588i	−0.0289899	+	0.0987306i	−0.972717	−	0.231994i	$-0.925475\pi$
$167$	−0.374632	+	1.27588i	−0.0289899	+	0.0987306i	0.943727	+	0.330725i	$0.107293\pi$
$168$	6.08118	+	9.46250i	0.469173	+	0.730048i
$169$	5.38436	+	11.7901i	0.414181	+	0.906931i
$170$		0			0
$171$	−22.2792	−	14.3180i	−1.70373	−	1.09492i
$172$	12.5885	+	1.80995i	0.959861	+	0.138007i
$173$	16.7637	+	2.41025i	1.27452	+	0.183248i	0.746156	−	0.665771i	$-0.231897\pi$
$173$	16.7637	+	2.41025i	1.27452	+	0.183248i	0.528362	+	0.849019i	$0.322806\pi$
$174$	23.1904	+	14.9036i	1.75806	+	1.12984i
$175$		0			0
$176$	1.23543	+	2.70522i	0.0931244	+	0.203914i
$177$	−9.80914	−	15.2633i	−0.737300	−	1.14726i
$178$	−8.62968	+	29.3900i	−0.646822	+	2.20287i
$179$	−0.937335	+	1.08174i	−0.0700597	+	0.0808532i	−0.789697	−	0.613497i	$-0.789762\pi$
$179$	−0.937335	+	1.08174i	−0.0700597	+	0.0808532i	0.719638	+	0.694350i	$0.244308\pi$
$180$		0			0
$181$	−6.70121	+	14.6736i	−0.498097	+	1.09068i	0.478986	+	0.877822i	$0.341004\pi$
$181$	−6.70121	+	14.6736i	−0.498097	+	1.09068i	−0.977083	+	0.212858i	$0.931723\pi$
$182$	1.01685	−	0.146201i	0.0753737	−	0.0108371i
$183$		−	18.6732i		−	1.38037i
$184$	5.54765	+	7.14459i	0.408978	+	0.526706i
$185$		0			0
$186$	1.40511	+	9.77275i	0.103028	+	0.716573i
$187$	−2.71279	−	1.23889i	−0.198379	−	0.0905967i
$188$	2.08266	+	7.09288i	0.151893	+	0.517301i
$189$	1.23746	−	1.42810i	0.0900118	−	0.103879i
$190$		0			0
$191$	−17.4514	+	11.2153i	−1.26274	+	0.811512i	−0.988656	−	0.150195i	$-0.952010\pi$
$191$	−17.4514	+	11.2153i	−1.26274	+	0.811512i	−0.274081	+	0.961707i	$0.588374\pi$
$192$	29.1609	−	13.3173i	2.10451	−	0.961096i
$193$	11.0734	−	9.59519i	0.797083	−	0.690677i	−0.157861	−	0.987461i	$-0.550460\pi$
$193$	11.0734	−	9.59519i	0.797083	−	0.690677i	0.954944	+	0.296785i	$0.0959144\pi$
$194$	−8.01540	−	5.15119i	−0.575472	−	0.369834i
$195$		0			0
$196$	0.556778	−	3.87247i	0.0397698	−	0.276605i
$197$	6.31355	−	9.82407i	0.449822	−	0.699936i	−0.540092	−	0.841606i	$-0.681611\pi$
$197$	6.31355	−	9.82407i	0.449822	−	0.699936i	0.989914	+	0.141669i	$0.0452470\pi$
$198$	−10.5607	+	9.15092i	−0.750518	+	0.650328i
$199$	2.37759	+	5.20620i	0.168543	+	0.369057i	0.974990	−	0.222249i	$-0.0713397\pi$
$199$	2.37759	+	5.20620i	0.168543	+	0.369057i	−0.806447	+	0.591306i	$0.798612\pi$
$200$		0			0
$201$	17.5234	+	5.14533i	1.23600	+	0.362923i
$202$	−3.03146	−	2.62677i	−0.213293	−	0.184819i
$203$	3.32729	+	11.3317i	0.233530	+	0.795330i
$204$	−4.65133	+	10.1850i	−0.325659	+	0.713093i
$205$		0			0
$206$	−33.7445			−2.35109
$207$	9.30671	−	12.9004i	0.646861	−	0.896643i
$208$		−	0.305626i		−	0.0211913i
$209$	2.17244	+	15.1097i	0.150271	+	1.04516i
$210$		0			0
$211$	13.4979	−	3.96334i	0.929234	−	0.272848i	0.218118	−	0.975922i	$-0.430008\pi$
$211$	13.4979	−	3.96334i	0.929234	−	0.272848i	0.711116	+	0.703075i	$0.248190\pi$
$212$	21.1938	+	18.3645i	1.45560	+	1.26128i
$213$	0.517106	−	1.76110i	0.0354315	−	0.120669i
$214$	−3.68596	+	2.36882i	−0.251967	+	0.161929i
$215$		0			0
$216$	0.983652	+	1.13520i	0.0669291	+	0.0772403i
$217$	−2.28687	+	3.55843i	−0.155243	+	0.241562i
$218$	−34.0151	−	4.89064i	−2.30379	−	0.331236i
$219$	2.30504	−	16.0319i	0.155760	−	1.08334i
$220$		0			0
$221$	0.200702	+	0.231623i	0.0135007	+	0.0155806i
$222$	−19.5634	+	8.93432i	−1.31301	+	0.599632i
$223$	−2.27263	−	3.53628i	−0.152187	−	0.236807i	0.756786	−	0.653663i	$-0.226768\pi$
$223$	−2.27263	−	3.53628i	−0.152187	−	0.236807i	−0.908973	+	0.416856i	$0.863132\pi$
$224$	16.3922	+	4.81319i	1.09525	+	0.321595i
$225$		0			0
$226$	3.14668	−	0.923948i	0.209314	−	0.0614601i
$227$	−16.7652	−	7.65642i	−1.11275	−	0.508174i	−0.227726	−	0.973725i	$-0.573129\pi$
$227$	−16.7652	−	7.65642i	−1.11275	−	0.508174i	−0.885021	+	0.465551i	$0.845856\pi$
$228$	56.7282	−	8.15629i	3.75692	−	0.540163i
$229$	−10.9247			−0.721923			−0.360961	−	0.932581i	$-0.617551\pi$
$229$	−10.9247			−0.721923			−0.360961	+	0.932581i	$0.617551\pi$
$230$		0			0
$231$	−11.4015			−0.750163
$232$	−9.29227	+	1.33603i	−0.610068	+	0.0877145i
$233$	3.78846	+	1.73013i	0.248190	+	0.113345i	0.535626	−	0.844455i	$-0.320076\pi$
$233$	3.78846	+	1.73013i	0.248190	+	0.113345i	−0.287436	+	0.957800i	$0.592803\pi$
$234$	1.37787	−	0.404581i	0.0900745	−	0.0264483i
$235$		0			0
$236$	19.7815	+	5.80837i	1.28767	+	0.378093i
$237$	−7.71545	−	12.0055i	−0.501172	−	0.779839i
$238$	−7.41922	+	3.38825i	−0.480917	+	0.219627i
$239$	−14.7456	−	17.0173i	−0.953813	−	1.10076i	−0.994825	−	0.101601i	$-0.967604\pi$
$239$	−14.7456	−	17.0173i	−0.953813	−	1.10076i	0.0410120	−	0.999159i	$-0.486942\pi$
$240$		0			0
$241$	−0.843804	+	5.86878i	−0.0543542	+	0.378042i	0.944429	+	0.328717i	$0.106616\pi$
$241$	−0.843804	+	5.86878i	−0.0543542	+	0.378042i	−0.998783	+	0.0493250i	$0.984293\pi$
$242$	−16.0205	−	2.30340i	−1.02984	−	0.148068i
$243$	−12.0929	+	18.8169i	−0.775759	+	1.20710i
$244$	13.8952	+	16.0359i	0.889548	+	1.02659i
$245$		0			0
$246$	−1.98714	+	1.27706i	−0.126695	+	0.0814222i
$247$	0.441964	−	1.50519i	0.0281215	−	0.0957730i
$248$	−2.54110	−	2.20187i	−0.161360	−	0.139819i
$249$	31.0840	−	9.12708i	1.96987	−	0.578405i
$250$		0			0
$251$	0.220675	+	1.53483i	0.0139289	+	0.0968775i	0.995600	−	0.0937056i	$-0.0298712\pi$
$251$	0.220675	+	1.53483i	0.0139289	+	0.0968775i	−0.981671	+	0.190583i	$0.938962\pi$
$252$			22.4767i			1.41590i
$253$	−9.13256	+	0.815292i	−0.574159	+	0.0512570i
$254$	−13.2093			−0.828824
$255$		0			0
$256$	−1.95044	+	4.27088i	−0.121903	+	0.266930i
$257$	7.73578	+	26.3456i	0.482545	+	1.64340i	0.736690	+	0.676230i	$0.236388\pi$
$257$	7.73578	+	26.3456i	0.482545	+	1.64340i	−0.254145	+	0.967166i	$0.581794\pi$
$258$	18.6395	+	16.1512i	1.16044	+	1.00553i
$259$	−8.84083	−	2.59590i	−0.549342	−	0.161301i
$260$		0			0
$261$	6.85812	+	15.0172i	0.424507	+	0.929540i
$262$	21.2650	−	18.4262i	1.31375	−	1.13837i
$263$	6.99627	−	10.8864i	0.431408	−	0.671285i	−0.555692	−	0.831388i	$-0.687547\pi$
$263$	6.99627	−	10.8864i	0.431408	−	0.671285i	0.987100	+	0.160104i	$0.0511829\pi$
$264$	1.28980	−	8.97078i	0.0793819	−	0.552113i
$265$		0			0
$266$	35.1210	+	22.5709i	2.15341	+	1.38391i
$267$	−26.4028	+	22.8782i	−1.61583	+	1.40012i
$268$	−18.8772	+	8.62092i	−1.15311	+	0.526607i
$269$	8.41057	−	5.40514i	0.512801	−	0.329557i	−0.258517	−	0.966007i	$-0.583234\pi$
$269$	8.41057	−	5.40514i	0.512801	−	0.329557i	0.771319	+	0.636449i	$0.219598\pi$
$270$		0			0
$271$	−2.88885	+	3.33391i	−0.175485	+	0.202520i	−0.836678	−	0.547696i	$-0.815505\pi$
$271$	−2.88885	+	3.33391i	−0.175485	+	0.202520i	0.661193	+	0.750216i	$0.270051\pi$
$272$	0.683629	+	2.32823i	0.0414511	+	0.141169i
$273$	1.06581	+	0.486739i	0.0645057	+	0.0294588i
$274$	0.218760	+	1.52151i	0.0132158	+	0.0919177i
$275$		0			0
$276$	3.06096	+	34.2876i	0.184248	+	2.06387i
$277$			30.8042i			1.85085i	0.378935	+	0.925423i	$0.376290\pi$
$277$			30.8042i			1.85085i	−0.378935	+	0.925423i	$0.623710\pi$
$278$	30.4404	−	4.37667i	1.82570	−	0.262495i
$279$	−2.45631	+	5.37857i	−0.147055	+	0.322006i
$280$		0			0
$281$	2.34395	−	2.70506i	0.139828	−	0.161370i	−0.681516	−	0.731803i	$-0.738679\pi$
$281$	2.34395	−	2.70506i	0.139828	−	0.161370i	0.821344	+	0.570433i	$0.193225\pi$
$282$	−4.03885	+	13.7551i	−0.240510	+	0.819102i
$283$	7.99089	+	12.4341i	0.475009	+	0.739129i	0.993236	−	0.116115i	$-0.0370440\pi$
$283$	7.99089	+	12.4341i	0.475009	+	0.739129i	−0.518227	+	0.855243i	$0.673408\pi$
$284$	0.866403	+	1.89716i	0.0514116	+	0.112576i
$285$		0			0
$286$	−0.696337	−	0.447509i	−0.0411753	−	0.0264618i
$287$	−1.00168	−	0.144020i	−0.0591275	−	0.00850125i
$288$	23.6386	+	3.39872i	1.39292	+	0.200272i
$289$	12.2543	+	7.87535i	0.720840	+	0.463256i
$290$		0			0
$291$	−4.51435	−	9.88506i	−0.264636	−	0.579472i
$292$	9.95024	+	15.4829i	0.582294	+	0.906067i
$293$	6.06104	−	20.6420i	0.354090	−	1.20592i	−0.569324	−	0.822113i	$-0.692795\pi$
$293$	6.06104	−	20.6420i	0.354090	−	1.20592i	0.923414	−	0.383806i	$-0.125387\pi$
$294$	4.96845	−	5.73389i	0.289766	−	0.334408i
$295$		0			0
$296$	3.04260	−	6.66236i	0.176847	−	0.387242i
$297$	−1.50707	+	0.216683i	−0.0874488	+	0.0125732i
$298$		−	36.6660i		−	2.12401i
$299$	0.888516	+	0.313663i	0.0513842	+	0.0181396i
$300$		0			0
$301$	1.50376	+	10.4589i	0.0866752	+	0.602839i
$302$	−26.4390	−	12.0743i	−1.52139	−	0.694797i
$303$	−1.28892	−	4.38965i	−0.0740464	−	0.252179i
$304$	8.13354	−	9.38660i	0.466490	−	0.538359i
$305$		0			0
$306$	−9.59155	+	6.16411i	−0.548312	+	0.352379i
$307$	12.8667	−	5.87602i	0.734341	−	0.335362i	−0.0128989	−	0.999917i	$-0.504106\pi$
$307$	12.8667	−	5.87602i	0.734341	−	0.335362i	0.747240	+	0.664555i	$0.231379\pi$
$308$	9.79118	−	8.48411i	0.557904	−	0.483427i
$309$	−32.3776	−	20.8078i	−1.84190	−	1.18371i
$310$		0			0
$311$	−0.0811393	+	0.564336i	−0.00460099	+	0.0320006i	−0.991993	−	0.126296i	$-0.959691\pi$
$311$	−0.0811393	+	0.564336i	−0.00460099	+	0.0320006i	0.987392	+	0.158297i	$0.0506002\pi$
$312$	−0.503540	+	0.783524i	−0.0285073	+	0.0443583i
$313$	−15.9711	+	13.8390i	−0.902738	+	0.782227i	−0.976605	−	0.215041i	$-0.931011\pi$
$313$	−15.9711	+	13.8390i	−0.902738	+	0.782227i	0.0738672	+	0.997268i	$0.476466\pi$
$314$	−3.77945	−	8.27584i	−0.213287	−	0.467033i
$315$		0			0
$316$	15.5593	+	4.56862i	0.875279	+	0.257005i
$317$	−6.65977	−	5.77072i	−0.374050	−	0.324116i	0.447467	−	0.894301i	$-0.352326\pi$
$317$	−6.65977	−	5.77072i	−0.374050	−	0.324116i	−0.821517	+	0.570185i	$0.806872\pi$
$318$	15.3217	+	52.1811i	0.859201	+	2.92617i
$319$	3.95303	−	8.65592i	0.221327	−	0.484639i
$320$		0			0
$321$	−4.99734			−0.278924
$322$	−14.6711	+	20.3363i	−0.817589	+	1.13330i
$323$			12.4550i			0.693015i
$324$	−3.23080	−	22.4707i	−0.179489	−	1.24837i
$325$		0			0
$326$	31.2698	−	9.18165i	1.73188	−	0.508525i
$327$	−29.6216	−	25.6672i	−1.63808	−	1.41940i
$328$	0.226632	−	0.771839i	0.0125137	−	0.0426177i
$329$	−5.16678	+	3.32049i	−0.284854	+	0.183064i
$330$		0			0
$331$	−19.7686	−	22.8142i	−1.08658	−	1.25398i	−0.965239	−	0.261371i	$-0.915826\pi$
$331$	−19.7686	−	22.8142i	−1.08658	−	1.25398i	−0.121342	−	0.992611i	$-0.538720\pi$
$332$	−19.9021	+	30.9683i	−1.09227	+	1.69961i
$333$	−12.7490	−	1.83303i	−0.698642	−	0.100450i
$334$	0.417017	−	2.90042i	0.0228182	−	0.158704i
$335$		0			0
$336$	6.07496	+	7.01088i	0.331416	+	0.382475i
$337$	−4.50792	+	2.05870i	−0.245562	+	0.112145i	−0.534394	−	0.845235i	$-0.679460\pi$
$337$	−4.50792	+	2.05870i	−0.245562	+	0.112145i	0.288832	+	0.957380i	$0.406733\pi$
$338$	−15.4418	−	24.0278i	−0.839920	−	1.30694i
$339$	3.58895	+	1.05381i	0.194925	+	0.0572351i
$340$		0			0
$341$	3.27015	−	0.960202i	0.177088	−	0.0519979i
$342$	53.0853	+	24.2433i	2.87053	+	1.31093i
$343$	19.6578	−	2.82637i	1.06142	−	0.152609i
$344$	−8.39923			−0.452856
$345$		0			0
$346$	−37.3205			−2.00636
$347$	6.69808	−	0.963038i	0.359572	−	0.0516986i	0.0398383	−	0.999206i	$-0.487316\pi$
$347$	6.69808	−	0.963038i	0.359572	−	0.0516986i	0.319733	+	0.947508i	$0.396407\pi$
$348$	−32.4981	−	14.8414i	−1.74208	−	0.795582i
$349$	9.68306	−	2.84320i	0.518322	−	0.152193i	−0.0121000	−	0.999927i	$-0.503852\pi$
$349$	9.68306	−	2.84320i	0.518322	−	0.152193i	0.530422	+	0.847734i	$0.322033\pi$
$350$		0			0
$351$	0.150131	+	0.0440823i	0.00801338	+	0.00235294i
$352$	−7.44216	−	11.5802i	−0.396669	−	0.617228i
$353$	−22.2580	+	10.1649i	−1.18468	+	0.541023i	−0.907604	−	0.419827i	$-0.862091\pi$
$353$	−22.2580	+	10.1649i	−1.18468	+	0.541023i	−0.277071	+	0.960850i	$0.589364\pi$
$354$	26.1822	+	30.2159i	1.39157	+	1.60596i
$355$		0			0
$356$	5.64961	−	39.2939i	0.299429	−	2.08257i
$357$	−9.20798	−	1.32391i	−0.487338	−	0.0700686i
$358$	1.70526	−	2.65343i	0.0901257	−	0.140238i
$359$	0.274264	+	0.316518i	0.0144751	+	0.0167052i	0.762941	−	0.646468i	$-0.223755\pi$
$359$	0.274264	+	0.316518i	0.0144751	+	0.0167052i	−0.748466	+	0.663173i	$0.769209\pi$
$360$		0			0
$361$	37.6474	−	24.1945i	1.98144	−	1.27340i
$362$	10.0148	−	34.1074i	0.526368	−	1.79265i
$363$	−13.9512	−	12.0888i	−0.732248	−	0.634497i
$364$	−1.27747	+	0.375099i	−0.0669577	+	0.0196606i
$365$		0			0
$366$	5.85606	+	40.7298i	0.306101	+	2.12898i
$367$		−	28.5682i		−	1.49125i	−0.666367	−	0.745624i	$-0.732151\pi$
$367$		−	28.5682i		−	1.49125i	0.666367	−	0.745624i	$-0.267849\pi$
$368$	5.36735	+	5.18129i	0.279793	+	0.270093i
$369$	−1.41463			−0.0736426
$370$		0			0
$371$	−9.67888	+	21.1938i	−0.502503	+	1.10033i
$372$	−3.60502	−	12.2776i	−0.186911	−	0.636562i
$373$	−10.8887	−	9.43508i	−0.563794	−	0.488530i	0.325703	−	0.945472i	$-0.394399\pi$
$373$	−10.8887	−	9.43508i	−0.563794	−	0.488530i	−0.889496	+	0.456942i	$0.848945\pi$
$374$	6.30563	+	1.85150i	0.326056	+	0.0957388i
$375$		0			0
$376$	−2.02809	−	4.44089i	−0.104591	−	0.229021i
$377$	−0.739056	+	0.640396i	−0.0380633	+	0.0329821i
$378$	−2.25126	+	3.50303i	−0.115792	+	0.180176i
$379$	−0.800823	+	5.56985i	−0.0411355	+	0.286104i	0.958862	+	0.283873i	$0.0916193\pi$
$379$	−0.800823	+	5.56985i	−0.0411355	+	0.286104i	−0.999998	+	0.00223119i	$0.999290\pi$
$380$		0			0
$381$	−12.6742	−	8.14522i	−0.649320	−	0.417292i
$382$	34.5475	−	29.9356i	1.76760	−	1.53164i
$383$	−0.210725	+	0.0962350i	−0.0107676	+	0.00491738i	−0.420792	−	0.907157i	$-0.638248\pi$
$383$	−0.210725	+	0.0962350i	−0.0107676	+	0.00491738i	0.410024	+	0.912075i	$0.365520\pi$
$384$	−28.9819	+	18.6255i	−1.47898	+	0.950480i
$385$		0			0
$386$	−21.1441	+	24.4016i	−1.07621	+	1.24201i
$387$	4.16135	+	14.1722i	0.211533	+	0.720416i
$388$	11.2325	+	5.12969i	0.570241	+	0.260421i
$389$	−4.29361	−	29.8627i	−0.217695	−	1.51410i	−0.746516	−	0.665367i	$-0.768275\pi$
$389$	−4.29361	−	29.8627i	−0.217695	−	1.51410i	0.528821	−	0.848733i	$-0.322634\pi$
$390$		0			0
$391$	−7.47023	−	0.402007i	−0.377786	−	0.0203304i
$392$			2.58378i			0.130500i
$393$	31.7657	−	4.56722i	1.60237	−	0.230386i
$394$	−10.6901	+	23.4081i	−0.538561	+	1.17928i
$395$		0			0
$396$	11.8597	−	13.6869i	0.595975	−	0.687791i
$397$	3.67528	−	12.5168i	0.184457	−	0.628202i	−0.814396	−	0.580310i	$-0.802931\pi$
$397$	3.67528	−	12.5168i	0.184457	−	0.628202i	0.998853	−	0.0478924i	$-0.0152504\pi$
$398$	−6.81867	−	10.6101i	−0.341789	−	0.531834i
$399$	19.7805	+	43.3132i	0.990263	+	2.16837i
$400$		0			0
$401$	−17.9404	−	11.5296i	−0.895899	−	0.575759i	0.00967246	−	0.999953i	$-0.496921\pi$
$401$	−17.9404	−	11.5296i	−0.895899	−	0.575759i	−0.905571	+	0.424194i	$0.860557\pi$
$402$	−39.8354	−	5.72746i	−1.98681	−	0.285660i
$403$	−0.346685	−	0.0498457i	−0.0172696	−	0.00248299i
$404$	4.37332	+	2.81056i	0.217581	+	0.139831i
$405$		0			0
$406$	−10.8111	−	23.6731i	−0.536548	−	1.17488i
$407$	4.01378	+	6.24557i	0.198956	+	0.309581i
$408$	2.08332	−	7.09514i	0.103140	−	0.351262i
$409$	−5.99134	+	6.91437i	−0.296253	+	0.341894i	−0.884288	−	0.466941i	$-0.845356\pi$
$409$	−5.99134	+	6.91437i	−0.296253	+	0.341894i	0.588036	+	0.808835i	$0.299901\pi$
$410$		0			0
$411$	−0.728307	+	1.59477i	−0.0359247	+	0.0786642i
$412$	43.2882	−	6.22391i	2.13266	−	0.306630i
$413$			17.1289i			0.842859i
$414$	−16.2540	+	31.0569i	−0.798840	+	1.52636i
$415$		0			0
$416$	0.201323	+	1.40023i	0.00987065	+	0.0686519i
$417$	31.9062	+	14.5711i	1.56245	+	0.713548i
$418$	−9.47700	−	32.2757i	−0.463535	−	1.57866i
$419$	−5.87685	+	6.78225i	−0.287103	+	0.331334i	−0.880920	−	0.473266i	$-0.843075\pi$
$419$	−5.87685	+	6.78225i	−0.287103	+	0.331334i	0.593817	+	0.804600i	$0.297620\pi$
$420$		0			0
$421$	26.4762	−	17.0152i	1.29037	−	0.829270i	0.298241	−	0.954491i	$-0.403600\pi$
$421$	26.4762	−	17.0152i	1.29037	−	0.829270i	0.992129	+	0.125221i	$0.0399638\pi$
$422$	−28.1985	+	12.8778i	−1.37268	+	0.626882i
$423$	−6.48843	+	5.62226i	−0.315478	+	0.273364i
$424$	−15.5805	−	10.0130i	−0.756656	−	0.486273i
$425$		0			0
$426$	−0.575610	+	4.00346i	−0.0278884	+	0.193968i
$427$	−9.53095	+	14.8305i	−0.461235	+	0.717696i
$428$	4.29153	−	3.71863i	0.207439	−	0.179747i
$429$	−0.392184	−	0.858763i	−0.0189348	−	0.0414615i
$430$		0			0
$431$	21.2071	+	6.22697i	1.02151	+	0.299942i	0.749254	−	0.662283i	$-0.230412\pi$
$431$	21.2071	+	6.22697i	1.02151	+	0.299942i	0.272256	+	0.962225i	$0.412230\pi$
$432$	0.936237	+	0.811254i	0.0450447	+	0.0390315i
$433$	−3.57666	−	12.1810i	−0.171884	−	0.585382i	−0.999703	−	0.0243864i	$-0.992237\pi$
$433$	−3.57666	−	12.1810i	−0.171884	−	0.585382i	0.827819	−	0.560995i	$-0.189581\pi$
$434$	3.87213	−	8.47878i	0.185868	−	0.406994i
$435$		0			0
$436$	44.5375			2.13296
$437$	18.9413	+	33.2793i	0.906086	+	1.59196i
$438$			35.6915i			1.70541i
$439$	2.62158	+	18.2335i	0.125121	+	0.870238i	0.951615	+	0.307292i	$0.0994229\pi$
$439$	2.62158	+	18.2335i	0.125121	+	0.870238i	−0.826494	+	0.562946i	$0.809668\pi$
$440$		0			0
$441$	4.35968	−	1.28012i	0.207604	−	0.0609580i
$442$	−0.510407	−	0.442270i	−0.0242776	−	0.0210366i
$443$	−3.91968	+	13.3492i	−0.186230	+	0.634240i	0.812458	+	0.583020i	$0.198129\pi$
$443$	−3.91968	+	13.3492i	−0.186230	+	0.634240i	−0.998687	+	0.0512201i	$0.983689\pi$
$444$	23.4486	−	15.0695i	1.11282	−	0.715166i
$445$		0			0
$446$	6.06603	+	7.00057i	0.287235	+	0.331487i
$447$	22.6093	−	35.1808i	1.06938	−	1.66399i
$448$	−29.9571	−	4.30718i	−1.41534	−	0.203495i
$449$	4.28260	−	29.7862i	0.202109	−	1.40570i	−0.595904	−	0.803056i	$-0.703206\pi$
$449$	4.28260	−	29.7862i	0.202109	−	1.40570i	0.798013	−	0.602641i	$-0.205885\pi$
$450$		0			0
$451$	0.533969	+	0.616233i	0.0251436	+	0.0290173i
$452$	−3.86622	+	1.76564i	−0.181852	+	0.0830489i
$453$	−17.9227	−	27.8883i	−0.842082	−	1.31030i
$454$	38.9692	+	11.4424i	1.82891	+	0.537017i
$455$		0			0
$456$	−36.3168	+	10.6636i	−1.70069	+	0.499368i
$457$	−34.6093	−	15.8055i	−1.61895	−	0.739351i	−0.619978	−	0.784619i	$-0.712859\pi$
$457$	−34.6093	−	15.8055i	−1.61895	−	0.739351i	−0.998975	+	0.0452680i	$0.985586\pi$
$458$	23.8287	−	3.42606i	1.11344	−	0.160089i
$459$	−1.24228			−0.0579849
$460$		0			0
$461$	8.76016			0.408001			0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016			0.408001			0.204001	+	0.978971i	$0.434606\pi$
$462$	24.8688	−	3.57559i	1.15700	−	0.166352i
$463$	−25.3212	−	11.5638i	−1.17677	−	0.537415i	−0.271581	−	0.962416i	$-0.587547\pi$
$463$	−25.3212	−	11.5638i	−1.17677	−	0.537415i	−0.905193	+	0.425001i	$0.860274\pi$
$464$	−7.42886	+	2.18131i	−0.344876	+	0.101265i
$465$		0			0
$466$	−8.80592	−	2.58565i	−0.407926	−	0.119778i
$467$	9.38895	+	14.6095i	0.434469	+	0.676047i	0.987590	−	0.157054i	$-0.0501997\pi$
$467$	9.38895	+	14.6095i	0.434469	+	0.676047i	−0.553121	+	0.833101i	$0.686563\pi$
$468$	−1.69295	+	0.773144i	−0.0782566	+	0.0357386i
$469$	−11.2910	−	13.0305i	−0.521370	−	0.601693i
$470$		0			0
$471$	1.47677	−	10.2711i	0.0680458	−	0.473269i
$472$	−13.4771	−	1.93772i	−0.620336	−	0.0891909i
$473$	4.60289	−	7.16224i	0.211641	−	0.329320i
$474$	20.5938	+	23.7666i	0.945906	+	1.09163i
$475$		0			0
$476$	8.89263	−	5.71494i	0.407593	−	0.261944i
$477$	−9.17591	+	31.2503i	−0.420136	+	1.43085i
$478$	37.4996	+	32.4936i	1.71519	+	1.48622i
$479$	−24.4458	+	7.17792i	−1.11695	+	0.327968i	−0.787568	−	0.616228i	$-0.788660\pi$
$479$	−24.4458	+	7.17792i	−1.11695	+	0.327968i	−0.329387	+	0.944195i	$0.606842\pi$
$480$		0			0
$481$	−0.108579	−	0.755186i	−0.00495079	−	0.0344335i
$482$		−	13.0655i		−	0.595119i
$483$	−26.6168	+	10.4659i	−1.21110	+	0.476214i
$484$	20.9763			0.953469
$485$		0			0
$486$	20.4757	−	44.8356i	0.928797	−	2.03378i
$487$	−1.73577	−	5.91151i	−0.0786555	−	0.267876i	0.910771	−	0.412912i	$-0.135488\pi$
$487$	−1.73577	−	5.91151i	−0.0786555	−	0.267876i	−0.989426	+	0.145036i	$0.953670\pi$
$488$	−10.5905	−	9.17673i	−0.479410	−	0.415411i
$489$	35.6649	+	10.4721i	1.61282	+	0.473567i
$490$		0			0
$491$	−13.5623	−	29.6973i	−0.612058	−	1.34022i	−0.921157	−	0.389191i	$-0.872755\pi$
$491$	−13.5623	−	29.6973i	−0.612058	−	1.34022i	0.309099	−	0.951030i	$-0.399973\pi$
$492$	2.31361	−	2.00475i	0.104306	−	0.0903812i
$493$	4.19761	−	6.53161i	0.189051	−	0.294169i
$494$	−0.491967	+	3.42171i	−0.0221346	+	0.153950i
$495$		0			0
$496$	−2.33284	−	1.49923i	−0.104748	−	0.0673172i
$497$	−1.30957	+	1.13475i	−0.0587421	+	0.0509004i
$498$	−64.9376	+	29.6560i	−2.90992	+	1.32892i
$499$	7.21265	−	4.63529i	0.322882	−	0.207504i	−0.369151	−	0.929369i	$-0.620351\pi$
$499$	7.21265	−	4.63529i	0.322882	−	0.207504i	0.692033	+	0.721866i	$0.256715\pi$
$500$		0			0
$501$	2.18861	−	2.52579i	0.0977797	−	0.112844i
$502$	−0.962667	−	3.27854i	−0.0429659	−	0.146329i
$503$	6.14505	+	2.80635i	0.273994	+	0.125129i	0.547674	−	0.836692i	$-0.315513\pi$
$503$	6.14505	+	2.80635i	0.273994	+	0.125129i	−0.273679	+	0.961821i	$0.588241\pi$
$504$	−2.11255	−	14.6931i	−0.0941003	−	0.654482i
$505$		0			0
$506$	19.6641	−	4.64234i	0.874177	−	0.206377i
$507$		−	32.5764i		−	1.44677i
$508$	16.9452	−	2.43635i	0.751821	−	0.108096i
$509$	−17.0206	+	37.2699i	−0.754425	+	1.65196i	0.00382066	+	0.999993i	$0.498784\pi$
$509$	−17.0206	+	37.2699i	−0.754425	+	1.65196i	−0.758246	+	0.651968i	$0.773943\pi$
$510$		0			0
$511$	−10.0135	+	11.5562i	−0.442971	+	0.511216i
$512$	−4.80863	+	16.3767i	−0.212513	+	0.723754i
$513$	3.43777	+	5.34928i	0.151781	+	0.236176i
$514$	−25.1354	−	55.0388i	−1.10867	−	2.42766i
$515$		0			0
$516$	−26.8902	−	17.2813i	−1.18377	−	0.760765i
$517$	4.89828	+	0.704266i	0.215426	+	0.0309736i
$518$	20.0976	+	2.88960i	0.883037	+	0.126962i
$519$	−35.8088	−	23.0129i	−1.57183	−	1.01016i
$520$		0			0
$521$	−7.77941	−	17.0345i	−0.340822	−	0.746297i	0.659162	−	0.752001i	$-0.270911\pi$
$521$	−7.77941	−	17.0345i	−0.340822	−	0.746297i	−0.999984	+	0.00570487i	$0.998184\pi$
$522$	−19.6683	−	30.6045i	−0.860859	−	1.33952i
$523$	6.63875	−	22.6095i	0.290292	−	0.988644i	−0.677212	−	0.735788i	$-0.736812\pi$
$523$	6.63875	−	22.6095i	0.290292	−	0.988644i	0.967504	−	0.252856i	$-0.0813699\pi$
$524$	−23.8807	+	27.5597i	−1.04323	+	1.20395i
$525$		0			0
$526$	−11.8461	+	25.9394i	−0.516515	+	1.13101i
$527$	2.75251	−	0.395751i	0.119901	−	0.0172392i
$528$		−	7.47461i		−	0.325291i
$529$	−20.5716	+	10.2864i	−0.894416	+	0.447237i
$530$		0			0
$531$	3.40760	+	23.7004i	0.147877	+	1.02851i
$532$	−49.2171	−	22.4767i	−2.13383	−	0.974488i
$533$	−0.0236078	−	0.0804009i	−0.00102257	−	0.00348255i
$534$	50.4147	−	58.1817i	2.18166	−	2.51777i
$535$		0			0
$536$	11.5298	−	7.40976i	0.498012	−	0.320053i
$537$	3.27237	−	1.49444i	0.141213	−	0.0644899i
$538$	−16.6499	+	14.4272i	−0.717829	+	0.622002i
$539$	−2.20325	−	1.41595i	−0.0949009	−	0.0609891i
$540$		0			0
$541$	−0.135667	+	0.943585i	−0.00583278	+	0.0405679i	−0.992530	−	0.122001i	$-0.961069\pi$
$541$	−0.135667	+	0.943585i	−0.00583278	+	0.0405679i	0.986697	+	0.162569i	$0.0519780\pi$
$542$	5.25558	−	8.17784i	0.225746	−	0.351268i
$543$	30.6408	−	26.5504i	1.31492	−	1.13939i
$544$	−4.66572	−	10.2165i	−0.200041	−	0.438029i
$545$		0			0
$546$	−2.47737	−	0.727422i	−0.106022	−	0.0311308i
$547$	22.5108	+	19.5057i	0.962491	+	0.834003i	0.986173	−	0.165717i	$-0.0529937\pi$
$547$	22.5108	+	19.5057i	0.962491	+	0.834003i	−0.0236827	+	0.999720i	$0.507539\pi$
$548$	−0.561261	−	1.91148i	−0.0239759	−	0.0816544i
$549$	−10.2371	+	22.4162i	−0.436911	+	0.956701i
$550$		0			0
$551$	−39.7412			−1.69303
$552$	−5.22359	−	22.1262i	−0.222331	−	0.941754i
$553$			13.4729i			0.572925i
$554$	−9.66043	−	67.1897i	−0.410432	−	2.85462i
$555$		0			0
$556$	−38.2425	+	11.2290i	−1.62184	+	0.476216i
$557$	−4.54108	−	3.93487i	−0.192412	−	0.166726i	0.553327	−	0.832964i	$-0.313358\pi$
$557$	−4.54108	−	3.93487i	−0.192412	−	0.166726i	−0.745739	+	0.666238i	$0.767903\pi$
$558$	3.67091	−	12.5020i	0.155402	−	0.529251i
$559$	−0.736039	+	0.473023i	−0.0311311	+	0.0200068i
$560$		0			0
$561$	4.90852	+	5.66473i	0.207238	+	0.239165i
$562$	−4.26426	+	6.63532i	−0.179877	+	0.279894i
$563$	−0.0882822	−	0.0126931i	−0.00372065	−	0.000534949i	0.140454	−	0.990087i	$-0.455144\pi$
$563$	−0.0882822	−	0.0126931i	−0.00372065	−	0.000534949i	−0.144175	+	0.989552i	$0.546053\pi$
$564$	2.64412	−	18.3903i	0.111338	−	0.774370i
$565$		0			0
$566$	−21.3290	−	24.6150i	−0.896526	−	1.03465i
$567$	17.1568	−	7.83526i	0.720519	−	0.329050i
$568$	−0.744681	−	1.15875i	−0.0312461	−	0.0486199i
$569$	−39.6842	−	11.6523i	−1.66365	−	0.488491i	−0.691406	−	0.722466i	$-0.743009\pi$
$569$	−39.6842	−	11.6523i	−1.66365	−	0.488491i	−0.972243	+	0.233975i	$0.924827\pi$
$570$		0			0
$571$	−24.7458	+	7.26602i	−1.03558	+	0.304073i	−0.754977	−	0.655751i	$-0.772352\pi$
$571$	−24.7458	+	7.26602i	−1.03558	+	0.304073i	−0.280602	+	0.959824i	$0.590534\pi$
$572$	0.975819	+	0.445641i	0.0408010	+	0.0186332i
$573$	51.6072	−	7.42000i	2.15592	−	0.309975i
$574$	2.23002			0.0930793
$575$		0			0
$576$	−42.3070			−1.76279
$577$	−26.8679	+	3.86302i	−1.11853	+	0.160820i	−0.676684	−	0.736273i	$-0.736584\pi$
$577$	−26.8679	+	3.86302i	−1.11853	+	0.160820i	−0.441842	+	0.897093i	$0.645675\pi$
$578$	−29.1986	−	13.3346i	−1.21450	−	0.554645i
$579$	−35.3343	+	10.3751i	−1.46845	+	0.431174i
$580$		0			0
$581$	−29.3457	−	8.61667i	−1.21746	−	0.357480i
$582$	12.9467	+	20.1454i	0.536657	+	0.835054i
$583$	17.0767	−	7.79865i	0.707243	−	0.322987i
$584$	−7.95971	−	9.18600i	−0.329375	−	0.380119i
$585$		0			0
$586$	−6.74678	+	46.9249i	−0.278707	+	1.93845i
$587$	31.3128	+	4.50210i	1.29242	+	0.185822i	0.754010	−	0.656863i	$-0.228117\pi$
$587$	31.3128	+	4.50210i	1.29242	+	0.185822i	0.538407	+	0.842685i	$0.319026\pi$
$588$	−5.31608	+	8.27197i	−0.219231	+	0.341130i
$589$	−9.32111	−	10.7571i	−0.384070	−	0.443240i
$590$		0			0
$591$	−24.6912	+	15.8681i	−1.01566	+	0.652726i
$592$	1.70182	−	5.79588i	0.0699446	−	0.238209i
$593$	19.4575	+	16.8600i	0.799024	+	0.692358i	0.955392	−	0.295341i	$-0.0954331\pi$
$593$	19.4575	+	16.8600i	0.799024	+	0.692358i	−0.156368	+	0.987699i	$0.549979\pi$
$594$	3.21924	−	0.945253i	0.132087	−	0.0387842i
$595$		0			0
$596$	6.76277	+	47.0361i	0.277014	+	1.92667i
$597$		−	14.3849i		−	0.588733i
$598$	−2.03638	−	0.405513i	−0.0832740	−	0.0165826i
$599$	−16.9434			−0.692289			−0.346144	−	0.938181i	$-0.612509\pi$
$599$	−16.9434			−0.692289			−0.346144	+	0.938181i	$0.612509\pi$
$600$		0			0
$601$	−4.01081	+	8.78246i	−0.163605	+	0.358244i	−0.973624	−	0.228159i	$-0.926729\pi$
$601$	−4.01081	+	8.78246i	−0.163605	+	0.358244i	0.810019	+	0.586403i	$0.199457\pi$
$602$	−6.55995	−	22.3411i	−0.267364	−	0.910557i
$603$	−18.2151	−	15.7834i	−0.741775	−	0.642752i
$604$	36.1436	+	10.6127i	1.47066	+	0.431826i
$605$		0			0
$606$	4.18800	+	9.17043i	0.170126	+	0.372523i
$607$	−2.45261	+	2.12520i	−0.0995484	+	0.0862592i	−0.703213	−	0.710979i	$-0.748252\pi$
$607$	−2.45261	+	2.12520i	−0.0995484	+	0.0862592i	0.603665	+	0.797238i	$0.293707\pi$
$608$	−31.0808	+	48.3627i	−1.26049	+	1.96136i
$609$	4.22430	−	29.3806i	0.171177	−	1.19056i
$610$		0			0
$611$	−0.427825	−	0.274946i	−0.0173079	−	0.0111231i
$612$	11.1673	−	9.67656i	0.451413	−	0.391152i
$613$	29.9399	−	13.6731i	1.20926	−	0.552251i	0.294269	−	0.955723i	$-0.404924\pi$
$613$	29.9399	−	13.6731i	1.20926	−	0.552251i	0.914992	+	0.403471i	$0.132197\pi$
$614$	−26.2219	+	16.8518i	−1.05823	+	0.680083i
$615$		0			0
$616$	−5.60312	+	6.46634i	−0.225756	+	0.260536i
$617$	0.852079	+	2.90191i	0.0343034	+	0.116827i	0.974865	−	0.222797i	$-0.0715186\pi$
$617$	0.852079	+	2.90191i	0.0343034	+	0.116827i	−0.940562	+	0.339623i	$0.889700\pi$
$618$	77.1470	+	35.2319i	3.10331	+	1.41723i
$619$	1.48326	+	10.3163i	0.0596172	+	0.414647i	0.997674	+	0.0681655i	$0.0217146\pi$
$619$	1.48326	+	10.3163i	0.0596172	+	0.414647i	−0.938057	+	0.346482i	$0.887376\pi$
$620$		0			0
$621$	−3.31934	+	1.88924i	−0.133200	+	0.0758127i
$622$		−	1.25637i		−	0.0503758i
$623$	32.6465	−	4.69386i	1.30796	−	0.188056i
$624$	−0.319097	+	0.698725i	−0.0127741	+	0.0279714i
$625$		0			0
$626$	30.4958	−	35.1941i	1.21886	−	1.40664i
$627$	10.8090	−	36.8121i	0.431670	−	1.47013i
$628$	6.37479	+	9.91937i	0.254382	+	0.395826i
$629$	2.51636	+	5.51006i	0.100334	+	0.219701i
$630$		0			0
$631$	28.6878	+	18.4366i	1.14205	+	0.733948i	0.968040	−	0.250797i	$-0.0806926\pi$
$631$	28.6878	+	18.4366i	1.14205	+	0.733948i	0.174005	+	0.984745i	$0.444329\pi$
$632$	−10.6006	−	1.52413i	−0.421667	−	0.0606266i
$633$	−34.9971	−	5.03182i	−1.39101	−	0.199997i
$634$	16.3359	+	10.4985i	0.648783	+	0.416947i
$635$		0			0
$636$	−29.2795	−	64.1132i	−1.16101	−	2.54225i
$637$	0.145512	+	0.226421i	0.00576539	+	0.00897113i
$638$	−5.90773	+	20.1199i	−0.233889	+	0.796553i
$639$	−1.58624	+	1.83062i	−0.0627506	+	0.0724180i
$640$		0			0
$641$	−3.74109	+	8.19184i	−0.147764	+	0.323558i	−0.969012	−	0.247013i	$-0.920551\pi$
$641$	−3.74109	+	8.19184i	−0.147764	+	0.323558i	0.821248	+	0.570571i	$0.193278\pi$
$642$	10.9001	−	1.56720i	0.430194	−	0.0618525i
$643$		−	22.9522i		−	0.905146i	−0.891727	−	0.452573i	$-0.850506\pi$
$643$		−	22.9522i		−	0.905146i	0.891727	−	0.452573i	$-0.149494\pi$
$644$	15.0696	−	28.7939i	0.593825	−	1.13464i
$645$		0			0
$646$	−3.90598	−	27.1667i	−0.153679	−	1.06886i
$647$	40.8919	+	18.6747i	1.60763	+	0.734178i	0.998274	−	0.0587216i	$-0.0187024\pi$
$647$	40.8919	+	18.6747i	1.60763	+	0.734178i	0.609352	+	0.792900i	$0.291430\pi$
$648$	4.22396	+	14.3855i	0.165933	+	0.565115i
$649$	9.03801	−	10.4304i	0.354773	−	0.409430i
$650$		0			0
$651$	8.94354	−	5.74766i	0.350525	−	0.225269i
$652$	−38.4202	+	17.5459i	−1.50465	+	0.687152i
$653$	−22.1914	+	19.2289i	−0.868415	+	0.752486i	−0.970196	−	0.242321i	$-0.922091\pi$
$653$	−22.1914	+	19.2289i	−0.868415	+	0.752486i	0.101781	+	0.994807i	$0.467546\pi$
$654$	72.6596	+	46.6955i	2.84121	+	1.82594i
$655$		0			0
$656$	0.0944170	−	0.656685i	0.00368636	−	0.0256392i
$657$	−11.5562	+	17.9818i	−0.450850	+	0.701536i
$658$	10.2284	−	8.86294i	0.398744	−	0.345513i
$659$	16.6805	+	36.5251i	0.649778	+	1.42282i	0.891748	+	0.452532i	$0.149479\pi$
$659$	16.6805	+	36.5251i	0.649778	+	1.42282i	−0.241970	+	0.970284i	$0.577794\pi$
$660$		0			0
$661$	−9.56288	−	2.80792i	−0.371953	−	0.109215i	0.0904132	−	0.995904i	$-0.471181\pi$
$661$	−9.56288	−	2.80792i	−0.371953	−	0.109215i	−0.462366	+	0.886689i	$0.652999\pi$
$662$	50.2737	+	43.5624i	1.95394	+	1.69310i
$663$	−0.217015	−	0.739087i	−0.00842818	−	0.0287037i
$664$	10.0994	−	22.1146i	0.391933	−	0.858214i
$665$		0			0
$666$	28.3829			1.09981
$667$	1.28272	−	23.8359i	0.0496669	−	0.922929i
$668$			3.79764i			0.146935i
$669$	1.50356	+	10.4575i	0.0581310	+	0.404310i
$670$		0			0
$671$	13.6290	−	4.00183i	0.526141	−	0.154489i
$672$	−32.4508	−	28.1188i	−1.25182	−	1.08470i
$673$	−9.59489	+	32.6772i	−0.369856	+	1.25961i	0.538930	+	0.842351i	$0.318829\pi$
$673$	−9.59489	+	32.6772i	−0.369856	+	1.25961i	−0.908786	+	0.417263i	$0.862989\pi$
$674$	9.18700	−	5.90412i	0.353870	−	0.227418i
$675$		0			0
$676$	24.2408	+	27.9754i	0.932339	+	1.07598i
$677$	−13.5112	+	21.0239i	−0.519278	+	0.808012i	−0.997532	−	0.0702091i	$-0.977633\pi$
$677$	−13.5112	+	21.0239i	−0.519278	+	0.808012i	0.478254	+	0.878221i	$0.341270\pi$
$678$	−8.15864	−	1.17304i	−0.313331	−	0.0450502i
$679$	−1.46006	+	10.1550i	−0.0560320	+	0.389711i
$680$		0			0
$681$	30.3349	+	35.0084i	1.16244	+	1.34152i
$682$	−6.83168	+	3.11992i	−0.261598	+	0.119468i
$683$	18.6392	+	29.0032i	0.713210	+	1.10978i	0.988908	+	0.148532i	$0.0474548\pi$
$683$	18.6392	+	29.0032i	0.713210	+	1.10978i	−0.275698	+	0.961244i	$0.588909\pi$
$684$	−72.5707	−	21.3087i	−2.77481	−	0.814757i
$685$		0			0
$686$	−41.9910	+	12.3297i	−1.60322	+	0.470749i
$687$	24.9761	+	11.4062i	0.952898	+	0.435174i
$688$	−6.85664	+	0.985836i	−0.261407	+	0.0375846i
$689$	−1.92925			−0.0734987
$690$		0			0
$691$	−21.2259			−0.807470			−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259			−0.807470			−0.403735	+	0.914876i	$0.632288\pi$
$692$	47.8757	−	6.88349i	1.81996	−	0.261671i
$693$	13.6869	+	6.25059i	0.519921	+	0.237440i
$694$	−14.3077	+	4.20113i	−0.543114	+	0.159473i
$695$		0			0
$696$	22.6390	+	6.64742i	0.858130	+	0.251970i
$697$	0.359685	+	0.559680i	0.0136240	+	0.0211994i
$698$	−20.2289	+	9.23823i	−0.765675	+	0.349672i
$699$	−6.85483	−	7.91090i	−0.259274	−	0.299218i
$700$		0			0
$701$	3.43351	−	23.8806i	0.129682	−	0.901957i	−0.816275	−	0.577664i	$-0.803965\pi$
$701$	3.43351	−	23.8806i	0.129682	−	0.901957i	0.945957	−	0.324293i	$-0.105126\pi$
$702$	−0.341287	−	0.0490697i	−0.0128811	−	0.00185202i
$703$	16.7628	−	26.0834i	0.632221	−	0.983756i
$704$	15.9693	+	18.4296i	0.601866	+	0.694590i
$705$		0			0
$706$	45.3611	−	29.1518i	1.70719	−	1.09714i
$707$	−1.21684	+	4.14417i	−0.0457639	+	0.155858i
$708$	−39.1603	−	33.9326i	−1.47173	−	1.27527i
$709$	6.75188	−	1.98253i	0.253572	−	0.0744556i	−0.152476	−	0.988307i	$-0.548725\pi$
$709$	6.75188	−	1.98253i	0.253572	−	0.0744556i	0.406048	+	0.913852i	$0.366906\pi$
$710$		0			0
$711$	2.68028	+	18.6417i	0.100518	+	0.699119i
$712$			26.2175i			0.982544i
$713$	6.75275	−	5.24339i	0.252892	−	0.196367i
$714$	20.4995			0.767175
$715$		0			0
$716$	−1.69814	+	3.71841i	−0.0634626	+	0.138964i
$717$	15.9441	+	54.3008i	0.595445	+	2.02790i
$718$	−0.697483	−	0.604373i	−0.0260298	−	0.0225550i
$719$	25.4920	+	7.48514i	0.950693	+	0.279149i	0.720075	−	0.693896i	$-0.244107\pi$
$719$	25.4920	+	7.48514i	0.950693	+	0.279149i	0.230618	+	0.973044i	$0.425925\pi$
$720$		0			0
$721$	15.0941	+	33.0515i	0.562134	+	1.23090i
$722$	−74.5284	+	64.5792i	−2.77366	+	2.40339i
$723$	8.05658	−	12.5363i	0.299628	−	0.466230i
$724$	−6.55643	+	45.6010i	−0.243668	+	1.69475i
$725$		0			0
$726$	34.2213	+	21.9927i	1.27007	+	0.816226i
$727$	3.95072	−	3.42332i	0.146524	−	0.126964i	−0.578514	−	0.815672i	$-0.696367\pi$
$727$	3.95072	−	3.42332i	0.146524	−	0.126964i	0.725039	+	0.688708i	$0.241822\pi$
$728$	0.799832	−	0.365271i	0.0296437	−	0.0135378i
$729$	27.2318	−	17.5008i	1.00859	−	0.648179i
$730$		0			0
$731$	4.54901	−	5.24983i	0.168251	−	0.194172i
$732$	−15.0246	−	51.1691i	−0.555325	−	1.89126i
$733$	−24.2771	−	11.0870i	−0.896694	−	0.409506i	−0.0868973	−	0.996217i	$-0.527695\pi$
$733$	−24.2771	−	11.0870i	−0.896694	−	0.409506i	−0.809796	+	0.586711i	$0.800422\pi$
$734$	8.95920	+	62.3126i	0.330690	+	2.30000i
$735$		0			0
$736$	−28.0037	−	20.2026i	−1.03223	−	0.744677i
$737$			13.8924i			0.511734i
$738$	3.08557	−	0.443638i	0.113581	−	0.0163305i
$739$	0.930342	−	2.03716i	0.0342232	−	0.0749383i	−0.891748	−	0.452532i	$-0.850521\pi$
$739$	0.930342	−	2.03716i	0.0342232	−	0.0749383i	0.925972	+	0.377593i	$0.123248\pi$
$740$		0			0
$741$	−2.58196	+	2.97974i	−0.0948507	+	0.109464i
$742$	14.4649	−	49.2630i	0.531024	−	1.80850i
$743$	9.80730	+	15.2605i	0.359795	+	0.559852i	0.973213	−	0.229907i	$-0.0738422\pi$
$743$	9.80730	+	15.2605i	0.359795	+	0.559852i	−0.613418	+	0.789759i	$0.710206\pi$
$744$	3.51056	+	7.68705i	0.128703	+	0.281821i
$745$		0			0
$746$	26.7091	+	17.1649i	0.977890	+	0.628452i
$747$	−42.3183	−	6.08446i	−1.54835	−	0.222619i
$748$	−8.43051	−	1.21212i	−0.308250	−	0.0443197i
$749$	3.96893	+	2.55068i	0.145022	+	0.0931997i
$750$		0			0
$751$	11.7258	+	25.6759i	0.427880	+	0.936927i	0.993666	+	0.112375i	$0.0358457\pi$
$751$	11.7258	+	25.6759i	0.427880	+	0.936927i	−0.565786	+	0.824552i	$0.691427\pi$
$752$	−2.17685	−	3.38724i	−0.0793815	−	0.123520i
$753$	1.09797	−	3.73935i	0.0400123	−	0.136269i
$754$	1.41119	−	1.62860i	0.0513924	−	0.0593100i
$755$		0			0
$756$	2.24187	−	4.90900i	0.0815359	−	0.178539i
$757$	−0.120772	+	0.0173643i	−0.00438952	+	0.000631118i	−0.144509	−	0.989503i	$-0.546160\pi$
$757$	−0.120772	+	0.0173643i	−0.00438952	+	0.000631118i	0.140120	+	0.990135i	$0.455251\pi$
$758$		−	12.4000i		−	0.450389i
$759$	21.7302	+	7.67118i	0.788756	+	0.278446i
$760$		0			0
$761$	3.80057	+	26.4336i	0.137771	+	0.958216i	0.935027	+	0.354576i	$0.115375\pi$
$761$	3.80057	+	26.4336i	0.137771	+	0.958216i	−0.797257	+	0.603640i	$0.793716\pi$
$762$	30.1992	+	13.7915i	1.09400	+	0.499614i
$763$	10.4250	+	35.5042i	0.377409	+	1.28534i
$764$	−38.7970	+	44.7741i	−1.40363	+	1.61987i
$765$		0			0
$766$	0.429451	−	0.275992i	0.0155167	−	0.00997198i
$767$	−1.29015	+	0.589194i	−0.0465848	+	0.0212745i
$768$	8.91825	−	7.72771i	0.321810	−	0.278850i
$769$	6.60471	+	4.24459i	0.238172	+	0.153064i	0.654283	−	0.756250i	$-0.272971\pi$
$769$	6.60471	+	4.24459i	0.238172	+	0.153064i	−0.416111	+	0.909314i	$0.636607\pi$
$770$		0			0
$771$	9.82128	−	68.3085i	0.353705	−	2.46007i
$772$	22.6235	−	35.2028i	0.814237	−	1.26698i
$773$	−25.9084	+	22.4497i	−0.931859	+	0.807460i	−0.981531	−	0.191305i	$-0.938728\pi$
$773$	−25.9084	+	22.4497i	−0.931859	+	0.807460i	0.0496716	+	0.998766i	$0.484183\pi$
$774$	−13.5212	−	29.6073i	−0.486009	−	1.06421i
$775$		0			0
$776$	−7.82482	−	2.29757i	−0.280895	−	0.0824781i
$777$	17.5017	+	15.1653i	0.627869	+	0.544052i
$778$	18.7303	+	63.7897i	0.671515	+	2.28697i
$779$	1.41463	−	3.09760i	0.0506843	−	0.110983i
$780$		0			0
$781$	1.39619			0.0499596
$782$	16.4200	−	1.46587i	0.587180	−	0.0524193i
$783$		−	3.96386i		−	0.141657i
$784$	0.303264	+	2.10925i	0.0108308	+	0.0753302i
$785$		0			0
$786$	−67.8546	+	19.9239i	−2.42029	+	0.710662i
$787$	12.1015	+	10.4860i	0.431370	+	0.373785i	0.843311	−	0.537426i	$-0.180603\pi$
$787$	12.1015	+	10.4860i	0.431370	+	0.373785i	−0.411940	+	0.911211i	$0.635149\pi$
$788$	9.39611	−	32.0002i	0.334723	−	1.13996i
$789$	−27.3612	+	17.5840i	−0.974085	+	0.626006i
$790$		0			0
$791$	−2.31250	−	2.66877i	−0.0822231	−	0.0948905i
$792$	−6.46634	+	10.0618i	−0.229772	+	0.357531i
$793$	−1.44488	−	0.207742i	−0.0513090	−	0.00737712i
$794$	−4.09109	+	28.4542i	−0.145187	+	1.00980i
$795$		0			0
$796$	10.7041	+	12.3532i	0.379397	+	0.437847i
$797$	19.5787	−	8.94128i	0.693512	−	0.316716i	−0.0372914	−	0.999304i	$-0.511873\pi$
$797$	19.5787	−	8.94128i	0.693512	−	0.316716i	0.730803	+	0.682588i	$0.239146\pi$
$798$	−56.7282	−	88.2709i	−2.00816	−	3.12475i
$799$	3.87413	+	1.13755i	0.137057	+	0.0402435i
$800$		0			0
$801$	44.2376	−	12.9893i	1.56306	−	0.458955i
$802$	42.7470	+	19.5219i	1.50945	+	0.689343i
$803$	12.1952	−	1.75340i	0.430358	−	0.0618761i
$804$	52.1582			1.83948
$805$		0			0
$806$	0.771816			0.0271860
$807$	−24.8717	+	3.57601i	−0.875526	+	0.125882i
$808$	−3.12301	−	1.42623i	−0.109867	−	0.0501746i
$809$	23.1479	−	6.79683i	0.813836	−	0.238964i	0.151776	−	0.988415i	$-0.451501\pi$
$809$	23.1479	−	6.79683i	0.813836	−	0.238964i	0.662060	+	0.749451i	$0.269682\pi$
$810$		0			0
$811$	−13.7575	−	4.03956i	−0.483091	−	0.141848i	0.0311137	−	0.999516i	$-0.490095\pi$
$811$	−13.7575	−	4.03956i	−0.483091	−	0.141848i	−0.514205	+	0.857668i	$0.671913\pi$
$812$	18.2351	+	28.3744i	0.639927	+	0.995747i
$813$	10.0854	−	4.60584i	0.353710	−	0.161534i
$814$	−10.7135	−	12.3640i	−0.375507	−	0.433358i
$815$		0			0
$816$	0.867929	−	6.03658i	0.0303836	−	0.211323i
$817$	−35.1942	−	5.06017i	−1.23129	−	0.177033i
$818$	10.8998	−	16.9605i	0.381103	−	0.593008i
$819$	−1.01260	−	1.16861i	−0.0353832	−	0.0408344i
$820$		0			0
$821$	11.9529	−	7.68167i	0.417160	−	0.268092i	−0.315180	−	0.949032i	$-0.602065\pi$
$821$	11.9529	−	7.68167i	0.417160	−	0.268092i	0.732339	+	0.680940i	$0.238428\pi$
$822$	1.08844	−	3.70689i	0.0379638	−	0.129293i
$823$	−12.1095	−	10.4929i	−0.422109	−	0.365760i	0.417752	−	0.908561i	$-0.362818\pi$
$823$	−12.1095	−	10.4929i	−0.422109	−	0.365760i	−0.839861	+	0.542802i	$0.817364\pi$
$824$	−27.7127	+	8.13718i	−0.965417	+	0.283472i
$825$		0			0
$826$	−5.37175	−	37.3613i	−0.186907	−	1.29997i
$827$		−	35.1240i		−	1.22138i	−0.791870	−	0.610690i	$-0.790892\pi$
$827$		−	35.1240i		−	1.22138i	0.791870	−	0.610690i	$-0.209108\pi$
$828$	15.1228	−	42.8385i	0.525554	−	1.48874i
$829$	2.29604			0.0797447			0.0398723	−	0.999205i	$-0.487305\pi$
$829$	2.29604			0.0797447			0.0398723	+	0.999205i	$0.487305\pi$
$830$		0			0
$831$	32.1620	−	70.4250i	1.11569	−	2.44302i
$832$	−0.706035	−	2.40453i	−0.0244774	−	0.0833622i
$833$	−1.61496	−	1.39937i	−0.0559550	−	0.0484853i
$834$	−74.1629	−	21.7762i	−2.56805	−	0.754048i
$835$		0			0
$836$	18.1103	+	39.6561i	0.626359	+	1.37153i
$837$	1.07294	−	0.929704i	0.0370861	−	0.0321353i
$838$	10.6915	−	16.6364i	0.369333	−	0.574694i
$839$	5.49501	−	38.2187i	0.189709	−	1.31945i	−0.643052	−	0.765822i	$-0.722332\pi$
$839$	5.49501	−	38.2187i	0.189709	−	1.31945i	0.832761	−	0.553632i	$-0.186759\pi$
$840$		0			0
$841$	−3.55542	−	2.28493i	−0.122601	−	0.0787906i
$842$	−52.4134	+	45.4164i	−1.80628	+	1.56515i
$843$	−8.18306	+	3.73708i	−0.281839	+	0.128712i
$844$	33.7985	−	21.7210i	1.16339	−	0.747667i
$845$		0			0
$846$	12.3893	−	14.2980i	0.425953	−	0.491576i
$847$	4.90997	+	16.7218i	0.168708	+	0.574568i
$848$	−13.8943	−	6.34530i	−0.477131	−	0.217898i
$849$	−5.28673	−	36.7700i	−0.181440	−	1.26194i
$850$		0			0
$851$	15.1032	+	10.8959i	0.517732	+	0.373505i
$852$		−	5.24190i		−	0.179584i
$853$	−38.0382	+	5.46907i	−1.30240	+	0.187257i	−0.758380	−	0.651812i	$-0.774009\pi$
$853$	−38.0382	+	5.46907i	−1.30240	+	0.187257i	−0.544024	+	0.839070i	$0.683100\pi$
$854$	16.1378	−	35.3369i	0.552226	−	1.20921i
$855$		0			0
$856$	−2.45588	+	2.83423i	−0.0839402	+	0.0968721i
$857$	14.3372	−	48.8281i	0.489750	−	1.66794i	−0.229598	−	0.973286i	$-0.573741\pi$
$857$	14.3372	−	48.8281i	0.489750	−	1.66794i	0.719348	−	0.694650i	$-0.244441\pi$
$858$	1.12474	+	1.75013i	0.0383980	+	0.0597485i
$859$	−3.79985	−	8.32050i	−0.129649	−	0.283892i	0.833664	−	0.552272i	$-0.186239\pi$
$859$	−3.79985	−	8.32050i	−0.129649	−	0.283892i	−0.963313	+	0.268380i	$0.913512\pi$
$860$		0			0
$861$	2.13969	+	1.37510i	0.0729205	+	0.0468631i
$862$	−48.2094	−	6.93147i	−1.64202	−	0.236087i
$863$	−12.2133	−	1.75600i	−0.415744	−	0.0597750i	−0.0687310	−	0.997635i	$-0.521895\pi$
$863$	−12.2133	−	1.75600i	−0.415744	−	0.0597750i	−0.347013	+	0.937860i	$0.612804\pi$
$864$	−4.82378	−	3.10006i	−0.164108	−	0.105466i
$865$		0			0
$866$	11.6214	+	25.4474i	0.394912	+	0.864737i
$867$	−19.7934	−	30.7991i	−0.672219	−	1.04599i
$868$	−3.40342	+	11.5910i	−0.115519	+	0.393423i
$869$	7.10891	−	8.20412i	0.241153	−	0.278306i
$870$		0			0
$871$	0.593078	−	1.29866i	0.0200957	−	0.0440034i
$872$	−29.1143	+	4.18600i	−0.985934	+	0.141756i
$873$			14.3414i			0.485381i
$874$	−51.7512	−	66.6482i	−1.75051	−	2.25441i
$875$		0			0
$876$	−6.58303	−	45.7860i	−0.222420	−	1.54696i
$877$	−2.09870	−	0.958445i	−0.0708681	−	0.0323644i	0.379666	−	0.925124i	$-0.376039\pi$
$877$	−2.09870	−	0.958445i	−0.0708681	−	0.0323644i	−0.450534	+	0.892759i	$0.648766\pi$
$878$	−11.4363	−	38.9485i	−0.385957	−	1.31445i
$879$	−35.4087	+	40.8638i	−1.19431	+	1.37830i
$880$		0			0
$881$	−29.9489	+	19.2470i	−1.00901	+	0.648448i	−0.937135	−	0.348966i	$-0.886533\pi$
$881$	−29.9489	+	19.2470i	−1.00901	+	0.648448i	−0.0718697	+	0.997414i	$0.522897\pi$
$882$	−9.10782	+	4.15940i	−0.306676	+	0.140054i
$883$	23.0311	−	19.9566i	0.775059	−	0.671592i	−0.174684	−	0.984625i	$-0.555890\pi$
$883$	23.0311	−	19.9566i	0.775059	−	0.671592i	0.949742	+	0.313032i	$0.101345\pi$
$884$	0.736336	+	0.473214i	0.0247657	+	0.0159159i
$885$		0			0
$886$	4.36315	−	30.3464i	0.146583	−	1.01951i
$887$	11.2405	−	17.4906i	0.377421	−	0.587278i	−0.599632	−	0.800276i	$-0.704686\pi$
$887$	11.2405	−	17.4906i	0.377421	−	0.587278i	0.977053	+	0.212998i	$0.0683227\pi$
$888$	−13.9121	+	12.0549i	−0.466858	+	0.404535i
$889$	5.90859	+	12.9380i	0.198168	+	0.433927i
$890$		0			0
$891$	−14.5817	−	4.28156i	−0.488504	−	0.143438i
$892$	−9.07286	−	7.86168i	−0.303782	−	0.263228i
$893$	−5.82260	−	19.8299i	−0.194846	−	0.663584i
$894$	−38.2822	+	83.8263i	−1.28035	+	2.80357i
$895$		0			0
$896$	32.5243			1.08656
$897$	−1.70385	−	1.64478i	−0.0568898	−	0.0549176i
$898$			66.3122i			2.21287i
$899$	1.26275	+	8.78264i	0.0421152	+	0.292918i
$900$		0			0
$901$	14.6969	−	4.31539i	0.489624	−	0.143766i
$902$	−1.35794	−	1.17666i	−0.0452145	−	0.0391786i
$903$	7.48196	−	25.4812i	0.248984	−	0.847962i
$904$	2.36141	−	1.51759i	0.0785393	−	0.0504742i
$905$		0			0
$906$	47.8387	+	55.2088i	1.58933	+	1.83419i
$907$	−12.2789	+	19.1064i	−0.407715	+	0.634417i	−0.983015	−	0.183525i	$-0.941249\pi$
$907$	−12.2789	+	19.1064i	−0.407715	+	0.634417i	0.575300	+	0.817943i	$0.304885\pi$
$908$	−52.1011	−	7.49100i	−1.72903	−	0.248598i
$909$	−0.859242	+	5.97616i	−0.0284992	+	0.198217i
$910$		0			0
$911$	−0.546182	−	0.630328i	−0.0180958	−	0.0208837i	0.746630	−	0.665240i	$-0.231671\pi$
$911$	−0.546182	−	0.630328i	−0.0180958	−	0.0208837i	−0.764725	+	0.644356i	$0.777125\pi$
$912$	−28.3953	+	12.9677i	−0.940264	+	0.429404i
$913$	13.3231	+	20.7312i	0.440930	+	0.686101i
$914$	80.4460	+	23.6211i	2.66092	+	0.781315i
$915$		0			0
$916$	−29.9362	+	8.79006i	−0.989120	+	0.290432i
$917$	−27.5597	−	12.5861i	−0.910103	−	0.415630i
$918$	2.70965	−	0.389589i	0.0894319	−	0.0128584i
$919$	45.3320			1.49537			0.747683	−	0.664056i	$-0.231166\pi$
$919$	45.3320			1.49537			0.747683	+	0.664056i	$0.231166\pi$
$920$		0			0
$921$	−35.5510			−1.17145
$922$	−19.1075	+	2.74725i	−0.629273	+	0.0904758i
$923$	−0.130515	−	0.0596044i	−0.00429597	−	0.00196190i
$924$	−31.2428	+	9.17371i	−1.02781	+	0.301793i
$925$		0			0
$926$	58.8566	+	17.2819i	1.93415	+	0.567918i
$927$	27.4602	+	42.7289i	0.901910	+	1.40340i
$928$	32.5986	−	14.8873i	1.07010	−	0.488699i
$929$	−11.5958	−	13.3822i	−0.380445	−	0.439056i	0.532941	−	0.846153i	$-0.321087\pi$
$929$	−11.5958	−	13.3822i	−0.380445	−	0.439056i	−0.913385	+	0.407096i	$0.866541\pi$
$930$		0			0
$931$	−1.55661	+	10.8265i	−0.0510159	+	0.354824i
$932$	11.7734	+	1.69275i	0.385649	+	0.0554480i
$933$	0.774713	−	1.20548i	0.0253630	−	0.0394655i
$934$	−25.0607	−	28.9216i	−0.820011	−	0.946343i
$935$		0			0
$936$	1.03402	−	0.664524i	0.0337980	−	0.0217207i
$937$	6.57170	−	22.3812i	0.214688	−	0.731161i	−0.779774	−	0.626062i	$-0.784666\pi$
$937$	6.57170	−	22.3812i	0.214688	−	0.731161i	0.994462	−	0.105099i	$-0.0335160\pi$
$938$	28.7143	+	24.8810i	0.937554	+	0.812395i
$939$	50.9622	−	14.9639i	1.66309	−	0.488327i
$940$		0			0
$941$	−1.65295	−	11.4965i	−0.0538847	−	0.374776i	−0.998864	−	0.0476470i	$-0.984828\pi$
$941$	−1.65295	−	11.4965i	−0.0538847	−	0.374776i	0.944980	−	0.327130i	$-0.106081\pi$
$942$			22.8664i			0.745027i
$943$	1.81222	+	0.948444i	0.0590139	+	0.0308856i
$944$	−11.2294			−0.365486
$945$		0			0
$946$	−7.79363	+	17.0657i	−0.253393	+	0.554853i
$947$	1.68981	+	5.75498i	0.0549116	+	0.187012i	0.982382	−	0.186886i	$-0.0598394\pi$
$947$	1.68981	+	5.75498i	0.0549116	+	0.187012i	−0.927470	+	0.373897i	$0.878021\pi$
$948$	−30.8018	−	26.6899i	−1.00040	−	0.866849i
$949$	−1.21486	−	0.356714i	−0.0394359	−	0.0115794i
$950$		0			0
$951$	9.20056	+	20.1464i	0.298348	+	0.653292i
$952$	−5.27600	+	4.57168i	−0.170996	+	0.148169i
$953$	9.68107	−	15.0640i	0.313601	−	0.487972i	−0.648295	−	0.761389i	$-0.724518\pi$
$953$	9.68107	−	15.0640i	0.313601	−	0.487972i	0.961896	+	0.273417i	$0.0881539\pi$
$954$	10.2141	−	71.0403i	0.330692	−	2.30002i
$955$		0			0
$956$	−54.0987	−	34.7671i	−1.74968	−	1.12445i
$957$	−18.0749	+	15.6620i	−0.584279	+	0.506281i
$958$	51.0697	−	23.3227i	1.64999	−	0.753524i
$959$	1.39241	−	0.894847i	0.0449632	−	0.0288961i
$960$		0			0
$961$	18.2196	−	21.0265i	0.587728	−	0.678274i
$962$	0.473664	+	1.61315i	0.0152715	+	0.0520101i
$963$	5.99903	+	2.73967i	0.193316	+	0.0882845i
$964$	2.40984	+	16.7608i	0.0776156	+	0.539829i
$965$		0			0
$966$	54.7739	−	31.1753i	1.76232	−	1.00305i
$967$		−	33.5068i		−	1.07751i	−0.842464	−	0.538753i	$-0.818896\pi$
$967$		−	33.5068i		−	1.07751i	0.842464	−	0.538753i	$-0.181104\pi$
$968$	−13.7123	+	1.97153i	−0.440730	+	0.0633673i
$969$	13.0040	−	28.4748i	0.417748	−	0.914741i
$970$		0			0
$971$	−38.8241	+	44.8054i	−1.24592	+	1.43787i	−0.389964	+	0.920830i	$0.627513\pi$
$971$	−38.8241	+	44.8054i	−1.24592	+	1.43787i	−0.855960	+	0.517042i	$0.827033\pi$
$972$	−17.9972	+	61.2928i	−0.577260	+	1.96597i
$973$	−17.9030	−	27.8576i	−0.573943	−	0.893073i
$974$	5.63994	+	12.3497i	0.180715	+	0.395711i
$975$		0			0
$976$	−9.72257	−	6.24832i	−0.311212	−	0.200004i
$977$	−12.5133	−	1.79914i	−0.400336	−	0.0575596i	−0.0607934	−	0.998150i	$-0.519363\pi$
$977$	−12.5133	−	1.79914i	−0.400336	−	0.0575596i	−0.339542	+	0.940591i	$0.610272\pi$
$978$	−81.0758	−	11.6569i	−2.59252	−	0.372748i
$979$	−22.3564	−	14.3676i	−0.714513	−	0.459189i
$980$		0			0
$981$	21.4877	+	47.0514i	0.686048	+	1.50224i
$982$	38.8952	+	60.5221i	1.24120	+	1.93134i
$983$	−16.4433	+	56.0008i	−0.524461	+	1.78615i	0.0885469	+	0.996072i	$0.471778\pi$
$983$	−16.4433	+	56.0008i	−0.524461	+	1.78615i	−0.613008	+	0.790077i	$0.710040\pi$
$984$	−1.32399	+	1.52797i	−0.0422072	+	0.0487097i
$985$		0			0
$986$	−7.10741	+	15.5631i	−0.226346	+	0.495629i
$987$	15.2792	−	2.19682i	0.486342	−	0.0699254i
$988$		−	4.48019i		−	0.142534i
$989$	4.17093	−	20.9454i	0.132628	−	0.666025i
$990$		0			0
$991$	6.51675	+	45.3250i	0.207011	+	1.43980i	0.782839	+	0.622224i	$0.213771\pi$
$991$	6.51675	+	45.3250i	0.207011	+	1.43980i	−0.575828	+	0.817571i	$0.695320\pi$
$992$	11.6755	+	5.33204i	0.370699	+	0.169292i
$993$	21.3754	+	72.7980i	0.678329	+	2.31018i
$994$	2.50055	−	2.88578i	0.0793125	−	0.0915315i
$995$		0			0
$996$	77.8338	−	50.0207i	2.46626	−	1.58497i
$997$	−35.7959	+	16.3475i	−1.13367	+	0.517729i	−0.891732	−	0.452563i	$-0.850510\pi$
$997$	−35.7959	+	16.3475i	−1.13367	+	0.517729i	−0.241936	+	0.970292i	$0.577782\pi$
$998$	−14.2785	+	12.3724i	−0.451977	+	0.391640i
$999$	2.60161	+	1.67195i	0.0823113	+	0.0528983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.p.b.49.1		20
5.2	odd	4		23.2.c.a.3.1	✓	10
5.3	odd	4		575.2.k.b.26.1		10
5.4	even	2	inner	575.2.p.b.49.2		20
15.2	even	4		207.2.i.c.118.1		10
20.7	even	4		368.2.m.c.49.1		10
23.8	even	11	inner	575.2.p.b.399.2		20
115.2	odd	44		529.2.c.i.334.1		10
115.7	even	44		529.2.c.c.170.1		10
115.8	odd	44		575.2.k.b.376.1		10
115.12	odd	44		529.2.c.b.501.1		10
115.17	even	44		529.2.c.e.177.1		10
115.22	even	4		529.2.c.a.118.1		10
115.27	odd	44		529.2.c.i.255.1		10
115.32	odd	44		529.2.c.d.266.1		10
115.37	even	44		529.2.c.e.266.1		10
115.42	even	44		529.2.c.h.255.1		10
115.52	odd	44		529.2.c.d.177.1		10
115.54	even	22	inner	575.2.p.b.399.1		20
115.57	even	44		529.2.c.c.501.1		10
115.62	odd	44		529.2.c.b.170.1		10
115.67	even	44		529.2.c.h.334.1		10
115.72	odd	44		529.2.c.g.487.1		10
115.77	odd	44		23.2.c.a.8.1	yes	10
115.82	odd	44		529.2.a.i.1.5		5
115.87	odd	44		529.2.c.g.466.1		10
115.97	even	44		529.2.c.f.466.1		10
115.102	even	44		529.2.a.j.1.5		5
115.107	even	44		529.2.c.a.399.1		10
115.112	even	44		529.2.c.f.487.1		10
345.77	even	44		207.2.i.c.100.1		10
345.197	even	44		4761.2.a.bo.1.1		5
345.332	odd	44		4761.2.a.bn.1.1		5
460.307	even	44		368.2.m.c.353.1		10
460.427	even	44		8464.2.a.bs.1.5		5
460.447	odd	44		8464.2.a.bt.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	5.2	odd	4
23.2.c.a.8.1	yes	10	115.77	odd	44
207.2.i.c.100.1		10	345.77	even	44
207.2.i.c.118.1		10	15.2	even	4
368.2.m.c.49.1		10	20.7	even	4
368.2.m.c.353.1		10	460.307	even	44
529.2.a.i.1.5		5	115.82	odd	44
529.2.a.j.1.5		5	115.102	even	44
529.2.c.a.118.1		10	115.22	even	4
529.2.c.a.399.1		10	115.107	even	44
529.2.c.b.170.1		10	115.62	odd	44
529.2.c.b.501.1		10	115.12	odd	44
529.2.c.c.170.1		10	115.7	even	44
529.2.c.c.501.1		10	115.57	even	44
529.2.c.d.177.1		10	115.52	odd	44
529.2.c.d.266.1		10	115.32	odd	44
529.2.c.e.177.1		10	115.17	even	44
529.2.c.e.266.1		10	115.37	even	44
529.2.c.f.466.1		10	115.97	even	44
529.2.c.f.487.1		10	115.112	even	44
529.2.c.g.466.1		10	115.87	odd	44
529.2.c.g.487.1		10	115.72	odd	44
529.2.c.h.255.1		10	115.42	even	44
529.2.c.h.334.1		10	115.67	even	44
529.2.c.i.255.1		10	115.27	odd	44
529.2.c.i.334.1		10	115.2	odd	44
575.2.k.b.26.1		10	5.3	odd	4
575.2.k.b.376.1		10	115.8	odd	44
575.2.p.b.49.1		20	1.1	even	1	trivial
575.2.p.b.49.2		20	5.4	even	2	inner
575.2.p.b.399.1		20	115.54	even	22	inner
575.2.p.b.399.2		20	23.8	even	11	inner
4761.2.a.bn.1.1		5	345.332	odd	44
4761.2.a.bo.1.1		5	345.197	even	44
8464.2.a.bs.1.5		5	460.427	even	44
8464.2.a.bt.1.5		5	460.447	odd	44

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.p (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.18119 + 0.313607i) q^{2} +(-2.28621 - 1.04408i) q^{3} +(2.74024 - 0.804606i) q^{4} +(5.31408 + 1.56036i) q^{6} +(1.28282 + 1.99611i) q^{7} +(-1.71568 + 0.783524i) q^{8} +(2.17208 + 2.50672i) q^{9} +(0.272084 - 1.89238i) q^{11} +(-7.10483 - 1.02152i) q^{12} +(-0.106222 + 0.165284i) q^{13} +(-3.42408 - 3.95159i) q^{14} +(-1.30862 + 0.840996i) q^{16} +(0.439476 - 1.49672i) q^{17} +(-5.52384 - 4.78644i) q^{18} +(-7.66103 + 2.24948i) q^{19} +(-0.848710 - 5.90291i) q^{21} +4.21297i q^{22} +(-1.10192 - 4.66752i) q^{23} +4.74046 q^{24} +(0.179855 - 0.393828i) q^{26} +(-0.224367 - 0.764125i) q^{27} +(5.12133 + 4.43766i) q^{28} +(4.77570 + 1.40227i) q^{29} +(0.740552 + 1.62158i) q^{31} +(5.44146 - 4.71506i) q^{32} +(-2.59784 + 4.04231i) q^{33} +(-0.489198 + 3.40244i) q^{34} +(7.96894 + 5.12133i) q^{36} +(-2.93475 + 2.54297i) q^{37} +(16.0047 - 7.30909i) q^{38} +(0.415415 - 0.266971i) q^{39} +(-0.279295 + 0.322324i) q^{41} +(3.70239 + 12.6092i) q^{42} +(4.05075 + 1.84991i) q^{43} +(-0.777050 - 5.40450i) q^{44} +(3.86725 + 9.83517i) q^{46} +2.58842i q^{47} +(3.86984 - 0.556399i) q^{48} +(0.569072 - 1.24609i) q^{49} +(-2.56743 + 2.96297i) q^{51} +(-0.158084 + 0.538385i) q^{52} +(5.30876 + 8.26060i) q^{53} +(0.729022 + 1.59634i) q^{54} +(-3.76492 - 2.41956i) q^{56} +(19.8634 + 2.85592i) q^{57} +(-10.8565 - 1.56092i) q^{58} +(6.07293 + 3.90283i) q^{59} +(3.08639 + 6.75826i) q^{61} +(-2.12382 - 3.30473i) q^{62} +(-2.21729 + 7.55141i) q^{63} +(-8.35283 + 9.63968i) q^{64} +(4.39867 - 9.63174i) q^{66} +(-7.19254 + 1.03413i) q^{67} -4.45497i q^{68} +(-2.35404 + 11.8214i) q^{69} +(0.103930 + 0.722850i) q^{71} +(-5.69067 - 2.59884i) q^{72} +(1.81558 + 6.18330i) q^{73} +(5.60373 - 6.46705i) q^{74} +(-19.1831 + 12.3282i) q^{76} +(4.12645 - 1.88449i) q^{77} +(-0.822373 + 0.712591i) q^{78} +(4.77671 + 3.06980i) q^{79} +(1.13126 - 7.86810i) q^{81} +(0.508112 - 0.790638i) q^{82} +(-9.74141 + 8.44098i) q^{83} +(-7.07518 - 15.4925i) q^{84} +(-9.41558 - 2.76466i) q^{86} +(-9.45418 - 8.19209i) q^{87} +(1.01592 + 3.45991i) q^{88} +(5.77436 - 12.6441i) q^{89} -0.466190 q^{91} +(-6.77503 - 11.9035i) q^{92} -4.48047i q^{93} +(-0.811746 - 5.64582i) q^{94} +(-17.3632 + 5.09830i) q^{96} +(3.26769 + 2.83147i) q^{97} +(-0.850468 + 2.89643i) q^{98} +(5.33466 - 3.42838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4} + 12 q^{6} + 4 q^{9} + 14 q^{11} - 18 q^{14} + 2 q^{16} - 4 q^{19} - 4 q^{21} + 76 q^{24} + 24 q^{26} - 28 q^{29} + 20 q^{31} - 58 q^{34} + 54 q^{36} - 2 q^{39} + 14 q^{41} + 68 q^{44} - 58 q^{46}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^4 + 12 * q^6 + 4 * q^9 + 14 * q^11 - 18 * q^14 + 2 * q^16 - 4 * q^19 - 4 * q^21 + 76 * q^24 + 24 * q^26 - 28 * q^29 + 20 * q^31 - 58 * q^34 + 54 * q^36 - 2 * q^39 + 14 * q^41 + 68 * q^44 - 58 * q^46 + 36 * q^49 + 14 * q^51 + 12 * q^54 - 4 * q^56 + 42 * q^59 + 6 * q^61 - 48 * q^64 + 4 * q^66 - 52 * q^69 - 28 * q^71 - 20 * q^74 - 32 * q^76 + 30 * q^79 - 88 * q^81 + 34 * q^84 - 22 * q^86 - 50 * q^89 - 8 * q^91 - 34 * q^94 - 102 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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