LMFDB - Embedded newform 605.2.g.j.511.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(81,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.1
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	605.511
Dual form			605.2.g.j.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0288961 + 0.0889332i) q^{2} +(-1.18661 - 0.862123i) q^{3} +(1.61096 - 1.17043i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.0423829 - 0.130441i) q^{6} +(-3.66042 + 2.65945i) q^{7} +(0.301943 + 0.219374i) q^{8} +(-0.262262 - 0.807160i) q^{9} +0.0935099 q^{10} -2.92064 q^{12} +(-0.353070 - 1.08664i) q^{13} +(-0.342285 - 0.248685i) q^{14} +(-1.18661 + 0.862123i) q^{15} +(1.21988 - 3.75440i) q^{16} +(1.04238 - 3.20812i) q^{17} +(0.0642049 - 0.0466476i) q^{18} +(-4.92268 - 3.57654i) q^{19} +(-0.615332 - 1.89380i) q^{20} +6.63626 q^{21} -5.45258 q^{23} +(-0.169161 - 0.520624i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.0864358 - 0.0627993i) q^{26} +(-1.74440 + 5.36872i) q^{27} +(-2.78408 + 8.56853i) q^{28} +(-2.68661 + 1.95194i) q^{29} +(-0.110960 - 0.0806171i) q^{30} +(0.553420 + 1.70325i) q^{31} +1.11558 q^{32} +0.315430 q^{34} +(1.39815 + 4.30308i) q^{35} +(-1.36722 - 0.993342i) q^{36} +(-1.20447 + 0.875099i) q^{37} +(0.175826 - 0.541138i) q^{38} +(-0.517859 + 1.59381i) q^{39} +(0.301943 - 0.219374i) q^{40} +(1.41356 + 1.02701i) q^{41} +(0.191762 + 0.590184i) q^{42} -0.263041 q^{43} -0.848698 q^{45} +(-0.157559 - 0.484916i) q^{46} +(-5.60222 - 4.07025i) q^{47} +(-4.68428 + 3.40333i) q^{48} +(4.16287 - 12.8120i) q^{49} +(0.0288961 - 0.0889332i) q^{50} +(-4.00270 + 2.90813i) q^{51} +(-1.84062 - 1.33729i) q^{52} +(-0.444910 - 1.36929i) q^{53} -0.527864 q^{54} -1.68865 q^{56} +(2.75789 + 8.48791i) q^{57} +(-0.251225 - 0.182525i) q^{58} +(5.71821 - 4.15452i) q^{59} +(-0.902527 + 2.77769i) q^{60} +(0.773299 - 2.37997i) q^{61} +(-0.135484 + 0.0984349i) q^{62} +(3.10659 + 2.25707i) q^{63} +(-2.40752 - 7.40959i) q^{64} -1.14256 q^{65} -0.516598 q^{67} +(-2.07565 - 6.38820i) q^{68} +(6.47010 + 4.70080i) q^{69} +(-0.342285 + 0.248685i) q^{70} +(-3.31584 + 10.2051i) q^{71} +(0.0978819 - 0.301250i) q^{72} +(4.59621 - 3.33934i) q^{73} +(-0.112630 - 0.0818304i) q^{74} +(0.453245 + 1.39494i) q^{75} -12.1163 q^{76} -0.156706 q^{78} +(-3.49293 - 10.7501i) q^{79} +(-3.19369 - 2.32035i) q^{80} +(4.63859 - 3.37014i) q^{81} +(-0.0504891 + 0.155390i) q^{82} +(1.38467 - 4.26157i) q^{83} +(10.6908 - 7.76729i) q^{84} +(-2.72899 - 1.98273i) q^{85} +(-0.00760088 - 0.0233931i) q^{86} +4.87077 q^{87} +13.2676 q^{89} +(-0.0245241 - 0.0754774i) q^{90} +(4.18224 + 3.03857i) q^{91} +(-8.78389 + 6.38187i) q^{92} +(0.811719 - 2.49821i) q^{93} +(0.200098 - 0.615837i) q^{94} +(-4.92268 + 3.57654i) q^{95} +(-1.32376 - 0.961771i) q^{96} +(-1.03723 - 3.19227i) q^{97} +1.25970 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{7} - 7 q^{8} + 5 q^{9} + 6 q^{10} - 28 q^{12} - 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} - 4 q^{17} - 16 q^{18} - 11 q^{19} - 6 q^{20} - 12 q^{21}+ \cdots - 84 q^{98}+O(q^{100}) $ 8 * q + q^2 + q^3 - q^4 - 2 * q^5 - 12 * q^6 - 8 * q^7 - 7 * q^8 + 5 * q^9 + 6 * q^10 - 28 * q^12 - 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 - 4 * q^17 - 16 * q^18 - 11 * q^19 - 6 * q^20 - 12 * q^21 - 18 * q^23 - 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 - 11 * q^28 - 11 * q^29 + 13 * q^30 - 9 * q^31 + 12 * q^32 - 20 * q^34 - 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 - 6 * q^39 - 7 * q^40 + 11 * q^41 - 31 * q^42 + 42 * q^43 + 29 * q^46 - q^47 + 21 * q^48 + q^50 - 22 * q^51 - q^52 + 8 * q^53 - 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 - 2 * q^61 + 27 * q^62 - 4 * q^63 + 21 * q^64 + 14 * q^65 - 2 * q^67 - 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 + 21 * q^72 + 32 * q^73 - 12 * q^74 + q^75 + 16 * q^76 + 12 * q^78 - 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 + 10 * q^83 + 51 * q^84 + q^85 + 34 * q^86 + 30 * q^87 + 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 - 22 * q^94 - 11 * q^95 + 3 * q^96 - 18 * q^97 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.0288961	+	0.0889332i	0.0204327	+	0.0628853i	0.960753	−	0.277405i	$-0.0894745\pi$
$2$	0.0288961	+	0.0889332i	0.0204327	+	0.0628853i	−0.940320	+	0.340291i	$0.889475\pi$
$3$	−1.18661	−	0.862123i	−0.685090	−	0.497747i	0.189952	−	0.981793i	$-0.439167\pi$
$3$	−1.18661	−	0.862123i	−0.685090	−	0.497747i	−0.875042	+	0.484046i	$0.839167\pi$
$4$	1.61096	−	1.17043i	0.805480	−	0.585215i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	0.0423829	−	0.130441i	0.0173027	−	0.0532524i
$7$	−3.66042	+	2.65945i	−1.38351	+	1.00518i	−0.386965	+	0.922094i	$0.626477\pi$
$7$	−3.66042	+	2.65945i	−1.38351	+	1.00518i	−0.996543	+	0.0830826i	$0.973523\pi$
$8$	0.301943	+	0.219374i	0.106753	+	0.0775605i
$9$	−0.262262	−	0.807160i	−0.0874207	−	0.269053i
$10$	0.0935099			0.0295704
$11$		0			0
$11$		0			0
$12$	−2.92064			−0.843116
$13$	−0.353070	−	1.08664i	−0.0979240	−	0.301379i	0.890081	−	0.455803i	$-0.150648\pi$
$13$	−0.353070	−	1.08664i	−0.0979240	−	0.301379i	−0.988005	+	0.154424i	$0.950648\pi$
$14$	−0.342285	−	0.248685i	−0.0914796	−	0.0664638i
$15$	−1.18661	+	0.862123i	−0.306382	+	0.222599i
$16$	1.21988	−	3.75440i	0.304970	−	0.938600i
$17$	1.04238	−	3.20812i	0.252815	−	0.778085i	−0.741437	−	0.671022i	$-0.765856\pi$
$17$	1.04238	−	3.20812i	0.252815	−	0.778085i	0.994252	−	0.107062i	$-0.0341445\pi$
$18$	0.0642049	−	0.0466476i	0.0151332	−	0.0109949i
$19$	−4.92268	−	3.57654i	−1.12934	−	0.820514i	−0.143741	−	0.989615i	$-0.545913\pi$
$19$	−4.92268	−	3.57654i	−1.12934	−	0.820514i	−0.985599	+	0.169102i	$0.945913\pi$
$20$	−0.615332	−	1.89380i	−0.137592	−	0.423466i
$21$	6.63626			1.44815
$22$		0			0
$23$	−5.45258			−1.13694			−0.568471	−	0.822703i	$-0.692465\pi$
$23$	−5.45258			−1.13694			−0.568471	+	0.822703i	$0.692465\pi$
$24$	−0.169161	−	0.520624i	−0.0345298	−	0.106272i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	0.0864358	−	0.0627993i	0.0169514	−	0.0123159i
$27$	−1.74440	+	5.36872i	−0.335711	+	1.03321i
$28$	−2.78408	+	8.56853i	−0.526142	+	1.61930i
$29$	−2.68661	+	1.95194i	−0.498891	+	0.362466i	−0.808593	−	0.588368i	$-0.799771\pi$
$29$	−2.68661	+	1.95194i	−0.498891	+	0.362466i	0.309702	+	0.950834i	$0.399771\pi$
$30$	−0.110960	−	0.0806171i	−0.0202584	−	0.0147186i
$31$	0.553420	+	1.70325i	0.0993972	+	0.305913i	0.988375	−	0.152038i	$-0.0485835\pi$
$31$	0.553420	+	1.70325i	0.0993972	+	0.305913i	−0.888977	+	0.457951i	$0.848584\pi$
$32$	1.11558			0.197209
$33$		0			0
$34$	0.315430			0.0540957
$35$	1.39815	+	4.30308i	0.236331	+	0.727353i
$36$	−1.36722	−	0.993342i	−0.227870	−	0.165557i
$37$	−1.20447	+	0.875099i	−0.198014	+	0.143865i	−0.682374	−	0.731003i	$-0.739052\pi$
$37$	−1.20447	+	0.875099i	−0.198014	+	0.143865i	0.484360	+	0.874869i	$0.339052\pi$
$38$	0.175826	−	0.541138i	0.0285228	−	0.0877841i
$39$	−0.517859	+	1.59381i	−0.0829238	+	0.255213i
$40$	0.301943	−	0.219374i	0.0477414	−	0.0346861i
$41$	1.41356	+	1.02701i	0.220762	+	0.160393i	0.692669	−	0.721255i	$-0.256434\pi$
$41$	1.41356	+	1.02701i	0.220762	+	0.160393i	−0.471908	+	0.881648i	$0.656434\pi$
$42$	0.191762	+	0.590184i	0.0295896	+	0.0910674i
$43$	−0.263041			−0.0401134			−0.0200567	−	0.999799i	$-0.506385\pi$
$43$	−0.263041			−0.0401134			−0.0200567	+	0.999799i	$0.506385\pi$
$44$		0			0
$45$	−0.848698			−0.126516
$46$	−0.157559	−	0.484916i	−0.0232308	−	0.0714969i
$47$	−5.60222	−	4.07025i	−0.817167	−	0.593707i	0.0987325	−	0.995114i	$-0.468521\pi$
$47$	−5.60222	−	4.07025i	−0.817167	−	0.593707i	−0.915900	+	0.401407i	$0.868521\pi$
$48$	−4.68428	+	3.40333i	−0.676118	+	0.491228i
$49$	4.16287	−	12.8120i	0.594695	−	1.83028i
$50$	0.0288961	−	0.0889332i	0.00408653	−	0.0125771i
$51$	−4.00270	+	2.90813i	−0.560490	+	0.407220i
$52$	−1.84062	−	1.33729i	−0.255247	−	0.185448i
$53$	−0.444910	−	1.36929i	−0.0611131	−	0.188087i	0.915839	−	0.401546i	$-0.131527\pi$
$53$	−0.444910	−	1.36929i	−0.0611131	−	0.188087i	−0.976952	+	0.213459i	$0.931527\pi$
$54$	−0.527864			−0.0718332
$55$		0			0
$56$	−1.68865			−0.225656
$57$	2.75789	+	8.48791i	0.365291	+	1.12425i
$58$	−0.251225	−	0.182525i	−0.0329874	−	0.0239668i
$59$	5.71821	−	4.15452i	0.744447	−	0.540873i	−0.149653	−	0.988739i	$-0.547816\pi$
$59$	5.71821	−	4.15452i	0.744447	−	0.540873i	0.894101	+	0.447866i	$0.147816\pi$
$60$	−0.902527	+	2.77769i	−0.116516	+	0.358599i
$61$	0.773299	−	2.37997i	0.0990108	−	0.304724i	−0.889267	−	0.457388i	$-0.848785\pi$
$61$	0.773299	−	2.37997i	0.0990108	−	0.304724i	0.988278	+	0.152664i	$0.0487851\pi$
$62$	−0.135484	+	0.0984349i	−0.0172065	+	0.0125012i
$63$	3.10659	+	2.25707i	0.391393	+	0.284364i
$64$	−2.40752	−	7.40959i	−0.300940	−	0.926199i
$65$	−1.14256			−0.141717
$66$		0			0
$67$	−0.516598			−0.0631124			−0.0315562	−	0.999502i	$-0.510046\pi$
$67$	−0.516598			−0.0631124			−0.0315562	+	0.999502i	$0.510046\pi$
$68$	−2.07565	−	6.38820i	−0.251710	−	0.774683i
$69$	6.47010	+	4.70080i	0.778908	+	0.565910i
$70$	−0.342285	+	0.248685i	−0.0409109	+	0.0297235i
$71$	−3.31584	+	10.2051i	−0.393518	+	1.21112i	0.536592	+	0.843842i	$0.319711\pi$
$71$	−3.31584	+	10.2051i	−0.393518	+	1.21112i	−0.930110	+	0.367281i	$0.880289\pi$
$72$	0.0978819	−	0.301250i	0.0115355	−	0.0355026i
$73$	4.59621	−	3.33934i	0.537946	−	0.390841i	−0.285376	−	0.958416i	$-0.592118\pi$
$73$	4.59621	−	3.33934i	0.537946	−	0.390841i	0.823322	+	0.567575i	$0.192118\pi$
$74$	−0.112630	−	0.0818304i	−0.0130930	−	0.00951259i
$75$	0.453245	+	1.39494i	0.0523362	+	0.161074i
$76$	−12.1163			−1.38984
$77$		0			0
$78$	−0.156706			−0.0177435
$79$	−3.49293	−	10.7501i	−0.392985	−	1.20948i	−0.930520	−	0.366242i	$-0.880644\pi$
$79$	−3.49293	−	10.7501i	−0.392985	−	1.20948i	0.537535	−	0.843241i	$-0.319356\pi$
$80$	−3.19369	−	2.32035i	−0.357065	−	0.259423i
$81$	4.63859	−	3.37014i	0.515399	−	0.374460i
$82$	−0.0504891	+	0.155390i	−0.00557559	+	0.0171599i
$83$	1.38467	−	4.26157i	0.151987	−	0.467768i	−0.845856	−	0.533411i	$-0.820910\pi$
$83$	1.38467	−	4.26157i	0.151987	−	0.467768i	0.997843	+	0.0656431i	$0.0209099\pi$
$84$	10.6908	−	7.76729i	1.16646	−	0.847481i
$85$	−2.72899	−	1.98273i	−0.296001	−	0.215057i
$86$	−0.00760088	−	0.0233931i	−0.000819625	−	0.00252254i
$87$	4.87077			0.522202
$88$		0			0
$89$	13.2676			1.40637			0.703183	−	0.711009i	$-0.251762\pi$
$89$	13.2676			1.40637			0.703183	+	0.711009i	$0.251762\pi$
$90$	−0.0245241	−	0.0754774i	−0.00258507	−	0.00795602i
$91$	4.18224	+	3.03857i	0.438418	+	0.318529i
$92$	−8.78389	+	6.38187i	−0.915784	+	0.665356i
$93$	0.811719	−	2.49821i	0.0841713	−	0.259053i
$94$	0.200098	−	0.615837i	0.0206385	−	0.0635188i
$95$	−4.92268	+	3.57654i	−0.505056	+	0.366945i
$96$	−1.32376	−	0.961771i	−0.135106	−	0.0981604i
$97$	−1.03723	−	3.19227i	−0.105315	−	0.324126i	0.884489	−	0.466560i	$-0.154507\pi$
$97$	−1.03723	−	3.19227i	−0.105315	−	0.324126i	−0.989804	+	0.142434i	$0.954507\pi$
$98$	1.25970			0.127249
$99$		0			0
$100$	−1.99126			−0.199126
$101$	−2.88467	−	8.87810i	−0.287035	−	0.883404i	−0.985781	−	0.168034i	$-0.946258\pi$
$101$	−2.88467	−	8.87810i	−0.287035	−	0.883404i	0.698746	−	0.715370i	$-0.253742\pi$
$102$	−0.374292	−	0.271939i	−0.0370605	−	0.0269260i
$103$	11.2583	−	8.17961i	1.10931	−	0.805960i	0.126755	−	0.991934i	$-0.459544\pi$
$103$	11.2583	−	8.17961i	1.10931	−	0.805960i	0.982555	+	0.185974i	$0.0595439\pi$
$104$	0.131773	−	0.405557i	0.0129214	−	0.0397681i
$105$	2.05072	−	6.31146i	0.200130	−	0.615936i
$106$	0.108919	−	0.0791345i	0.0105792	−	0.00768622i
$107$	13.5820	+	9.86792i	1.31302	+	0.953968i	0.999991	+	0.00422546i	$0.00134501\pi$
$107$	13.5820	+	9.86792i	1.31302	+	0.953968i	0.313033	+	0.949742i	$0.398655\pi$
$108$	3.47355	+	10.6905i	0.334243	+	1.02869i
$109$	−3.65293			−0.349888			−0.174944	−	0.984578i	$-0.555974\pi$
$109$	−3.65293			−0.349888			−0.174944	+	0.984578i	$0.555974\pi$
$110$		0			0
$111$	2.18368			0.207266
$112$	5.51937	+	16.9869i	0.521532	+	1.60511i
$113$	9.62919	+	6.99602i	0.905838	+	0.658130i	0.939959	−	0.341288i	$-0.110863\pi$
$113$	9.62919	+	6.99602i	0.905838	+	0.658130i	−0.0341209	+	0.999418i	$0.510863\pi$
$114$	−0.675165	+	0.490536i	−0.0632350	+	0.0459429i
$115$	−1.68494	+	5.18572i	−0.157122	+	0.483570i
$116$	−2.04341	+	6.28898i	−0.189726	+	0.583918i
$117$	−0.784493	+	0.569967i	−0.0725264	+	0.0526935i
$118$	0.534709	+	0.388489i	0.0492240	+	0.0357633i
$119$	4.71629	+	14.5152i	0.432341	+	1.33061i
$120$	−0.547416			−0.0499721
$121$		0			0
$122$	0.234004			0.0211857
$123$	−0.791938	−	2.43733i	−0.0714066	−	0.219767i
$124$	2.88508	+	2.09613i	0.259088	+	0.188238i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	−0.110960	+	0.341499i	−0.00988509	+	0.0304232i
$127$	6.10700	−	18.7954i	0.541908	−	1.66782i	−0.186321	−	0.982489i	$-0.559656\pi$
$127$	6.10700	−	18.7954i	0.541908	−	1.66782i	0.728229	−	0.685333i	$-0.240344\pi$
$128$	2.39444	−	1.73967i	0.211641	−	0.153766i
$129$	0.312128	+	0.226774i	0.0274813	+	0.0199664i
$130$	−0.0330155	−	0.101611i	−0.00289565	−	0.00891190i
$131$	−1.93479			−0.169043			−0.0845215	−	0.996422i	$-0.526936\pi$
$131$	−1.93479			−0.169043			−0.0845215	+	0.996422i	$0.526936\pi$
$132$		0			0
$133$	27.5307			2.38721
$134$	−0.0149277	−	0.0459427i	−0.00128956	−	0.00396884i
$135$	4.56691	+	3.31805i	0.393057	+	0.285572i
$136$	1.01852	−	0.739998i	0.0873374	−	0.0634543i
$137$	−3.87363	+	11.9218i	−0.330947	+	1.01855i	0.637738	+	0.770254i	$0.279870\pi$
$137$	−3.87363	+	11.9218i	−0.330947	+	1.01855i	−0.968684	+	0.248295i	$0.920130\pi$
$138$	−0.231096	+	0.711241i	−0.0196722	+	0.0605449i
$139$	9.09743	−	6.60967i	0.771634	−	0.560625i	−0.130822	−	0.991406i	$-0.541762\pi$
$139$	9.09743	−	6.60967i	0.771634	−	0.560625i	0.902457	+	0.430781i	$0.141762\pi$
$140$	7.28883	+	5.29564i	0.616018	+	0.447563i
$141$	3.13859	+	9.65960i	0.264317	+	0.813485i
$142$	−1.00339			−0.0842024
$143$		0			0
$144$	−3.35033			−0.279194
$145$	1.02619	+	3.15830i	0.0852208	+	0.262283i
$146$	0.429791	+	0.312262i	0.0355698	+	0.0258430i
$147$	−15.9852	+	11.6139i	−1.31844	+	0.957901i
$148$	−0.916110	+	2.81950i	−0.0753038	+	0.231761i
$149$	−5.35640	+	16.4853i	−0.438813	+	1.35053i	0.450315	+	0.892870i	$0.351312\pi$
$149$	−5.35640	+	16.4853i	−0.438813	+	1.35053i	−0.889128	+	0.457658i	$0.848688\pi$
$150$	−0.110960	+	0.0806171i	−0.00905983	+	0.00658236i
$151$	0.00437205	+	0.00317648i	0.000355792	+	0.000258498i	0.587963	−	0.808888i	$-0.299930\pi$
$151$	0.00437205	+	0.00317648i	0.000355792	+	0.000258498i	−0.587607	+	0.809146i	$0.699930\pi$
$152$	−0.701768	−	2.15982i	−0.0569209	−	0.175184i
$153$	−2.86285			−0.231447
$154$		0			0
$155$	1.79091			0.143849
$156$	1.03119	+	3.17367i	0.0825612	+	0.254097i
$157$	−0.448873	−	0.326125i	−0.0358240	−	0.0260276i	0.569729	−	0.821832i	$-0.307048\pi$
$157$	−0.448873	−	0.326125i	−0.0358240	−	0.0260276i	−0.605553	+	0.795805i	$0.707048\pi$
$158$	0.855110	−	0.621274i	0.0680289	−	0.0494259i
$159$	−0.652563	+	2.00838i	−0.0517516	+	0.159275i
$160$	0.344735	−	1.06098i	0.0272537	−	0.0838781i
$161$	19.9587	−	14.5009i	1.57297	−	1.14283i
$162$	0.433755	+	0.315141i	0.0340790	+	0.0247598i
$163$	−2.46110	−	7.57448i	−0.192768	−	0.593279i	−0.999995	−	0.00303852i	$-0.999033\pi$
$163$	−2.46110	−	7.57448i	−0.192768	−	0.593279i	0.807227	−	0.590241i	$-0.200967\pi$
$164$	3.47924			0.271683
$165$		0			0
$166$	0.419007			0.0325212
$167$	1.05882	+	3.25873i	0.0819343	+	0.252168i	0.983629	−	0.180205i	$-0.0576763\pi$
$167$	1.05882	+	3.25873i	0.0819343	+	0.252168i	−0.901695	+	0.432373i	$0.857676\pi$
$168$	2.00377	+	1.45583i	0.154594	+	0.112319i
$169$	9.46110	−	6.87389i	0.727777	−	0.528761i
$170$	0.0974731	−	0.299991i	0.00747585	−	0.0230083i
$171$	−1.59580	+	4.91138i	−0.122034	+	0.375582i
$172$	−0.423749	+	0.307872i	−0.0323106	+	0.0234750i
$173$	−16.6390	−	12.0889i	−1.26504	−	0.919103i	−0.266044	−	0.963961i	$-0.585717\pi$
$173$	−16.6390	−	12.0889i	−1.26504	−	0.919103i	−0.998993	+	0.0448577i	$0.985717\pi$
$174$	0.140747	+	0.433173i	0.0106700	+	0.0328388i
$175$	4.52452			0.342022
$176$		0			0
$177$	−10.3670			−0.779231
$178$	0.383383	+	1.17993i	0.0287358	+	0.0884397i
$179$	2.07458	+	1.50727i	0.155061	+	0.112659i	0.662611	−	0.748964i	$-0.269448\pi$
$179$	2.07458	+	1.50727i	0.155061	+	0.112659i	−0.507549	+	0.861623i	$0.669448\pi$
$180$	−1.36722	+	0.993342i	−0.101906	+	0.0740393i
$181$	4.14604	−	12.7602i	0.308173	−	0.948458i	−0.670302	−	0.742089i	$-0.733835\pi$
$181$	4.14604	−	12.7602i	0.308173	−	0.948458i	0.978474	−	0.206369i	$-0.0661648\pi$
$182$	−0.149380	+	0.459743i	−0.0110727	+	0.0340784i
$183$	−2.96943	+	2.15742i	−0.219507	+	0.159481i
$184$	−1.64637	−	1.19616i	−0.121372	−	0.0881819i
$185$	0.460067	+	1.41594i	0.0338248	+	0.104102i
$186$	0.245630			0.0180104
$187$		0			0
$188$	−13.7889			−1.00566
$189$	−7.89259	−	24.2909i	−0.574102	−	1.76690i
$190$	−0.460319	−	0.334441i	−0.0333951	−	0.0242629i
$191$	−14.7159	+	10.6917i	−1.06480	+	0.773625i	−0.974971	−	0.222332i	$-0.928633\pi$
$191$	−14.7159	+	10.6917i	−1.06480	+	0.773625i	−0.0898325	+	0.995957i	$0.528633\pi$
$192$	−3.53119	+	10.8679i	−0.254842	+	0.784322i
$193$	4.84806	−	14.9208i	0.348971	−	1.07402i	−0.610452	−	0.792053i	$-0.709012\pi$
$193$	4.84806	−	14.9208i	0.348971	−	1.07402i	0.959423	−	0.281969i	$-0.0909876\pi$
$194$	0.253927	−	0.184489i	0.0182309	−	0.0132455i
$195$	1.35577	+	0.985026i	0.0970888	+	0.0705392i
$196$	−8.28933	−	25.5119i	−0.592095	−	1.82228i
$197$	−21.8486			−1.55665			−0.778325	−	0.627862i	$-0.783930\pi$
$197$	−21.8486			−1.55665			−0.778325	+	0.627862i	$0.783930\pi$
$198$		0			0
$199$	−4.55200			−0.322683			−0.161341	−	0.986899i	$-0.551582\pi$
$199$	−4.55200			−0.322683			−0.161341	+	0.986899i	$0.551582\pi$
$200$	−0.115332	−	0.354955i	−0.00815520	−	0.0250991i
$201$	0.613000	+	0.445371i	0.0432377	+	0.0314140i
$202$	0.706202	−	0.513085i	0.0496882	−	0.0361006i
$203$	4.64304	−	14.2898i	0.325878	−	1.00295i
$204$	−3.04442	+	9.36977i	−0.213152	+	0.656015i
$205$	1.41356	−	1.02701i	0.0987276	−	0.0717298i
$206$	1.05276	+	0.764874i	0.0733492	+	0.0532913i
$207$	1.43001	+	4.40111i	0.0993923	+	0.305898i
$208$	−4.51038			−0.312738
$209$		0			0
$210$	0.620556			0.0428225
$211$	5.85910	+	18.0324i	0.403357	+	1.24140i	0.922259	+	0.386571i	$0.126341\pi$
$211$	5.85910	+	18.0324i	0.403357	+	1.24140i	−0.518903	+	0.854833i	$0.673659\pi$
$212$	−2.31939	−	1.68514i	−0.159297	−	0.115736i
$213$	12.7327	−	9.25082i	0.872428	−	0.633856i
$214$	−0.485117	+	1.49304i	−0.0331619	+	0.102062i
$215$	−0.0812843	+	0.250167i	−0.00554354	+	0.0170613i
$216$	−1.70447	+	1.23837i	−0.115974	+	0.0842604i
$217$	−6.55546	−	4.76282i	−0.445014	−	0.323321i
$218$	−0.105556	−	0.324867i	−0.00714913	−	0.0220028i
$219$	−8.33284			−0.563081
$220$		0			0
$221$	−3.85410			−0.259255
$222$	0.0630999	+	0.194202i	0.00423499	+	0.0130340i
$223$	−3.94761	−	2.86811i	−0.264352	−	0.192063i	0.447712	−	0.894178i	$-0.352239\pi$
$223$	−3.94761	−	2.86811i	−0.264352	−	0.192063i	−0.712063	+	0.702115i	$0.752239\pi$
$224$	−4.08350	+	2.96684i	−0.272841	+	0.198230i
$225$	−0.262262	+	0.807160i	−0.0174841	+	0.0538106i
$226$	−0.343932	+	1.05851i	−0.0228780	+	0.0704112i
$227$	−13.2055	+	9.59433i	−0.876477	+	0.636798i	−0.932317	−	0.361642i	$-0.882216\pi$
$227$	−13.2055	+	9.59433i	−0.876477	+	0.636798i	0.0558398	+	0.998440i	$0.482216\pi$
$228$	14.3774	+	10.4458i	0.952164	+	0.691788i
$229$	−1.49307	−	4.59519i	−0.0986647	−	0.303659i	0.889527	−	0.456883i	$-0.151034\pi$
$229$	−1.49307	−	4.59519i	−0.0986647	−	0.303659i	−0.988191	+	0.153224i	$0.951034\pi$
$230$	−0.509871			−0.0336199
$231$		0			0
$232$	−1.23941			−0.0813711
$233$	−2.60185	−	8.00766i	−0.170453	−	0.524599i	0.828944	−	0.559331i	$-0.188942\pi$
$233$	−2.60185	−	8.00766i	−0.170453	−	0.524599i	−0.999397	+	0.0347325i	$0.988942\pi$
$234$	−0.0733578	−	0.0532976i	−0.00479555	−	0.00348417i
$235$	−5.60222	+	4.07025i	−0.365448	+	0.265514i
$236$	4.34922	−	13.3855i	0.283110	−	0.871324i
$237$	−5.12319	+	15.7675i	−0.332787	+	1.02421i
$238$	−1.15460	+	0.838869i	−0.0748419	+	0.0543758i
$239$	18.3588	+	13.3385i	1.18753	+	0.862795i	0.993002	−	0.118101i	$-0.0376807\pi$
$239$	18.3588	+	13.3385i	1.18753	+	0.862795i	0.194533	+	0.980896i	$0.437681\pi$
$240$	1.78924	+	5.50670i	0.115495	+	0.355456i
$241$	11.6065			0.747638			0.373819	−	0.927502i	$-0.378048\pi$
$241$	11.6065			0.747638			0.373819	+	0.927502i	$0.378048\pi$
$242$		0			0
$243$	8.52534			0.546901
$244$	−1.53984	−	4.73913i	−0.0985780	−	0.303392i
$245$	−10.8985	−	7.91824i	−0.696281	−	0.505878i
$246$	0.193876	−	0.140859i	0.0123611	−	0.00898085i
$247$	−2.14835	+	6.61193i	−0.136696	+	0.420707i
$248$	−0.206549	+	0.635691i	−0.0131158	+	0.0403664i
$249$	−5.31706	+	3.86307i	−0.336955	+	0.244812i
$250$	−0.0756511	−	0.0549637i	−0.00478460	−	0.00347621i
$251$	1.02379	+	3.15090i	0.0646210	+	0.198883i	0.978154	−	0.207882i	$-0.0666569\pi$
$251$	1.02379	+	3.15090i	0.0646210	+	0.198883i	−0.913533	+	0.406765i	$0.866657\pi$
$252$	7.64633			0.481674
$253$		0			0
$254$	1.84800			0.115954
$255$	1.52890	+	4.70546i	0.0957432	+	0.294667i
$256$	−12.3820	−	8.99608i	−0.773878	−	0.562255i
$257$	21.7194	−	15.7800i	1.35482	−	0.984332i	0.356061	−	0.934463i	$-0.384120\pi$
$257$	21.7194	−	15.7800i	1.35482	−	0.984332i	0.998756	−	0.0498689i	$-0.0158803\pi$
$258$	−0.0111485	+	0.0343114i	−0.000694073	+	0.00213614i
$259$	2.08158	−	6.40645i	0.129343	−	0.398077i
$260$	−1.84062	+	1.33729i	−0.114150	+	0.0829349i
$261$	2.28012	+	1.65660i	0.141136	+	0.102541i
$262$	−0.0559079	−	0.172067i	−0.00345400	−	0.0106303i
$263$	12.1682			0.750324			0.375162	−	0.926959i	$-0.377587\pi$
$263$	12.1682			0.750324			0.375162	+	0.926959i	$0.377587\pi$
$264$		0			0
$265$	−1.43976			−0.0884436
$266$	0.795530	+	2.44839i	0.0487771	+	0.150120i
$267$	−15.7435	−	11.4383i	−0.963487	−	0.700015i
$268$	−0.832218	+	0.604642i	−0.0508358	+	0.0369344i
$269$	−0.646930	+	1.99105i	−0.0394440	+	0.121396i	−0.968840	−	0.247689i	$-0.920329\pi$
$269$	−0.646930	+	1.99105i	−0.0394440	+	0.121396i	0.929396	+	0.369085i	$0.120329\pi$
$270$	−0.163119	+	0.502029i	−0.00992710	+	0.0305525i
$271$	−12.2508	+	8.90071i	−0.744182	+	0.540680i	−0.894018	−	0.448031i	$-0.852125\pi$
$271$	−12.2508	+	8.90071i	−0.744182	+	0.540680i	0.149836	+	0.988711i	$0.452125\pi$
$272$	−10.7730	−	7.82705i	−0.653210	−	0.474585i
$273$	−2.34306	−	7.21121i	−0.141809	−	0.436442i
$274$	−1.17218			−0.0708138
$275$		0			0
$276$	15.9250			0.958574
$277$	2.55577	+	7.86586i	0.153562	+	0.472614i	0.998012	−	0.0630194i	$-0.0200730\pi$
$277$	2.55577	+	7.86586i	0.153562	+	0.472614i	−0.844451	+	0.535633i	$0.820073\pi$
$278$	0.850700	+	0.618070i	0.0510216	+	0.0370694i
$279$	1.22966	−	0.893397i	0.0736175	−	0.0534863i
$280$	−0.521822	+	1.60600i	−0.0311848	+	0.0959770i
$281$	0.756235	−	2.32745i	0.0451132	−	0.138844i	−0.925963	−	0.377615i	$-0.876744\pi$
$281$	0.756235	−	2.32745i	0.0451132	−	0.138844i	0.971076	+	0.238771i	$0.0767444\pi$
$282$	−0.768366	+	0.558251i	−0.0457555	+	0.0332433i
$283$	−21.1111	−	15.3381i	−1.25492	−	0.911756i	−0.256428	−	0.966563i	$-0.582546\pi$
$283$	−21.1111	−	15.3381i	−1.25492	−	0.911756i	−0.998497	+	0.0548072i	$0.982546\pi$
$284$	6.60268	+	20.3210i	0.391797	+	1.20583i
$285$	8.92472			0.528655
$286$		0			0
$287$	−7.90553			−0.466648
$288$	−0.292575	−	0.900455i	−0.0172402	−	0.0530598i
$289$	4.54779	+	3.30416i	0.267517	+	0.194362i
$290$	−0.251225	+	0.182525i	−0.0147524	+	0.0107183i
$291$	−1.52134	+	4.68220i	−0.0891825	+	0.274476i
$292$	3.49584	−	10.7591i	0.204579	−	0.629629i
$293$	−10.8837	+	7.90744i	−0.635830	+	0.461958i	−0.858415	−	0.512956i	$-0.828551\pi$
$293$	−10.8837	+	7.90744i	−0.635830	+	0.461958i	0.222585	+	0.974913i	$0.428551\pi$
$294$	−1.49478	−	1.08602i	−0.0871771	−	0.0633379i
$295$	−2.18416	−	6.72216i	−0.127167	−	0.391379i
$296$	−0.555655			−0.0322968
$297$		0			0
$298$	−1.62087			−0.0938944
$299$	1.92514	+	5.92498i	0.111334	+	0.342650i
$300$	2.36285	+	1.71671i	0.136419	+	0.0991142i
$301$	0.962841	−	0.699545i	0.0554973	−	0.0403211i
$302$	−0.000156159	0	0.000480608i	−8.98595e−6	0	2.76559e-5i
$303$	−4.23103	+	13.0218i	−0.243067	+	0.748082i
$304$	−19.4328	+	14.1188i	−1.11455	+	0.809767i
$305$	−2.02452	−	1.47090i	−0.115924	−	0.0842237i
$306$	−0.0827252	−	0.254602i	−0.00472909	−	0.0145546i
$307$	27.1844			1.55150			0.775748	−	0.631042i	$-0.217373\pi$
$307$	27.1844			1.55150			0.775748	+	0.631042i	$0.217373\pi$
$308$		0			0
$309$	−20.4110			−1.16114
$310$	0.0517503	+	0.159271i	0.00293922	+	0.00904598i
$311$	10.6782	+	7.75819i	0.605507	+	0.439927i	0.847829	−	0.530269i	$-0.177909\pi$
$311$	10.6782	+	7.75819i	0.605507	+	0.439927i	−0.242322	+	0.970196i	$0.577909\pi$
$312$	−0.506004	+	0.367633i	−0.0286468	+	0.0208131i
$313$	4.99739	−	15.3804i	0.282469	−	0.869352i	−0.704676	−	0.709529i	$-0.748908\pi$
$313$	4.99739	−	15.3804i	0.282469	−	0.869352i	0.987146	−	0.159823i	$-0.0510922\pi$
$314$	0.0160327	−	0.0493435i	0.000904776	−	0.00278461i
$315$	3.10659	−	2.25707i	0.175036	−	0.127171i
$316$	−18.2092	−	13.2298i	−1.02435	−	0.744234i
$317$	−1.66287	−	5.11778i	−0.0933959	−	0.287443i	0.893436	−	0.449190i	$-0.148287\pi$
$317$	−1.66287	−	5.11778i	−0.0933959	−	0.287443i	−0.986832	+	0.161747i	$0.948287\pi$
$318$	−0.197469			−0.0110735
$319$		0			0
$320$	−7.79091			−0.435525
$321$	−7.60922	−	23.4188i	−0.424705	−	1.30711i
$322$	1.86634	+	1.35597i	0.104007	+	0.0755655i
$323$	−16.6053	+	12.0644i	−0.923943	+	0.671284i
$324$	3.52808	−	10.8583i	0.196004	−	0.603239i
$325$	−0.353070	+	1.08664i	−0.0195848	+	0.0602758i
$326$	0.602507	−	0.437747i	0.0333698	−	0.0242445i
$327$	4.33461	+	3.14928i	0.239705	+	0.174156i
$328$	0.201515	+	0.620199i	0.0111268	+	0.0342448i
$329$	31.3311			1.72734
$330$		0			0
$331$	−18.5702			−1.02071			−0.510356	−	0.859963i	$-0.670486\pi$
$331$	−18.5702			−1.02071			−0.510356	+	0.859963i	$0.670486\pi$
$332$	−2.75723	−	8.48588i	−0.151323	−	0.465723i
$333$	1.02223	+	0.742694i	0.0560179	+	0.0406994i
$334$	−0.259213	+	0.188329i	−0.0141835	+	0.0103049i
$335$	−0.159637	+	0.491314i	−0.00872193	+	0.0268433i
$336$	8.09544	−	24.9152i	0.441642	−	1.35924i
$337$	−7.28612	+	5.29368i	−0.396900	+	0.288365i	−0.768277	−	0.640117i	$-0.778886\pi$
$337$	−7.28612	+	5.29368i	−0.396900	+	0.288365i	0.371377	+	0.928482i	$0.378886\pi$
$338$	0.884706	+	0.642777i	0.0481217	+	0.0349624i
$339$	−5.39467	−	16.6031i	−0.292998	−	0.901756i
$340$	−6.71695			−0.364278
$341$		0			0
$342$	−0.482897			−0.0261121
$343$	9.04790	+	27.8466i	0.488541	+	1.50357i
$344$	−0.0794235	−	0.0577045i	−0.00428223	−	0.00311122i
$345$	6.47010	−	4.70080i	0.348338	−	0.253083i
$346$	0.594304	−	1.82908i	0.0319500	−	0.0983319i
$347$	3.17390	−	9.76827i	0.170384	−	0.524388i	−0.829009	−	0.559236i	$-0.811095\pi$
$347$	3.17390	−	9.76827i	0.170384	−	0.524388i	0.999393	+	0.0348477i	$0.0110946\pi$
$348$	7.84662	−	5.70090i	0.420623	−	0.305600i
$349$	−13.9647	−	10.1459i	−0.747511	−	0.543098i	0.147544	−	0.989056i	$-0.452863\pi$
$349$	−13.9647	−	10.1459i	−0.747511	−	0.543098i	−0.895054	+	0.445957i	$0.852863\pi$
$350$	0.130741	+	0.402380i	0.00698842	+	0.0215081i
$351$	6.44975			0.344262
$352$		0			0
$353$	−22.8096			−1.21403			−0.607017	−	0.794689i	$-0.707634\pi$
$353$	−22.8096			−1.21403			−0.607017	+	0.794689i	$0.707634\pi$
$354$	−0.299566	−	0.921970i	−0.0159218	−	0.0490022i
$355$	8.68098	+	6.30710i	0.460738	+	0.334746i
$356$	21.3736	−	15.5288i	1.13280	−	0.823027i
$357$	6.91753	−	21.2900i	0.366114	−	1.12678i
$358$	−0.0740990	+	0.228053i	−0.00391626	+	0.0120530i
$359$	13.0047	−	9.44847i	0.686362	−	0.498671i	−0.189100	−	0.981958i	$-0.560557\pi$
$359$	13.0047	−	9.44847i	0.686362	−	0.498671i	0.875462	+	0.483287i	$0.160557\pi$
$360$	−0.256258	−	0.186183i	−0.0135060	−	0.00981268i
$361$	5.56984	+	17.1422i	0.293149	+	0.902221i
$362$	1.25461			0.0659408
$363$		0			0
$364$	10.2939			0.539545
$365$	−1.75560	−	5.40317i	−0.0918921	−	0.282815i
$366$	−0.277671	−	0.201740i	−0.0145141	−	0.0105451i
$367$	−17.7963	+	12.9298i	−0.928961	+	0.674930i	−0.945738	−	0.324930i	$-0.894659\pi$
$367$	−17.7963	+	12.9298i	−0.928961	+	0.674930i	0.0167772	+	0.999859i	$0.494659\pi$
$368$	−6.65149	+	20.4712i	−0.346733	+	1.06713i
$369$	0.458240	−	1.41032i	0.0238550	−	0.0734183i
$370$	−0.112630	+	0.0818304i	−0.00585535	+	0.00425416i
$371$	5.27012	+	3.82896i	0.273611	+	0.198790i
$372$	−1.61634	−	4.97458i	−0.0838033	−	0.257920i
$373$	−20.2604			−1.04905			−0.524523	−	0.851396i	$-0.675756\pi$
$373$	−20.2604			−1.04905			−0.524523	+	0.851396i	$0.675756\pi$
$374$		0			0
$375$	1.46673			0.0757417
$376$	−0.798641	−	2.45796i	−0.0411868	−	0.126760i
$377$	3.06961	+	2.23020i	0.158093	+	0.114861i
$378$	1.93220	−	1.40383i	0.0993818	−	0.0722051i
$379$	−1.15193	+	3.54526i	−0.0591704	+	0.182108i	−0.976273	−	0.216544i	$-0.930522\pi$
$379$	−1.15193	+	3.54526i	−0.0591704	+	0.182108i	0.917103	+	0.398651i	$0.130522\pi$
$380$	−3.74415	+	11.5233i	−0.192071	+	0.591133i
$381$	−23.4506	+	17.0378i	−1.20141	+	0.872875i
$382$	−1.37608	−	0.999781i	−0.0704064	−	0.0511532i
$383$	−3.39838	−	10.4592i	−0.173649	−	0.534438i	0.825920	−	0.563787i	$-0.190656\pi$
$383$	−3.39838	−	10.4592i	−0.173649	−	0.534438i	−0.999569	+	0.0293499i	$0.990656\pi$
$384$	−4.34108			−0.221530
$385$		0			0
$386$	1.46704			0.0746706
$387$	0.0689858	+	0.212316i	0.00350675	+	0.0107927i
$388$	−5.40727	−	3.92861i	−0.274513	−	0.199445i
$389$	−7.59036	+	5.51472i	−0.384847	+	0.279607i	−0.763340	−	0.645996i	$-0.776442\pi$
$389$	−7.59036	+	5.51472i	−0.384847	+	0.279607i	0.378494	+	0.925604i	$0.376442\pi$
$390$	−0.0484249	+	0.149037i	−0.00245209	+	0.00754676i
$391$	−5.68368	+	17.4926i	−0.287436	+	0.884637i
$392$	4.06757	−	2.95526i	0.205443	−	0.149263i
$393$	2.29584	+	1.66802i	0.115810	+	0.0841407i
$394$	−0.631341	−	1.94307i	−0.0318065	−	0.0978903i
$395$	−11.3033			−0.568733
$396$		0			0
$397$	22.3136			1.11989			0.559945	−	0.828530i	$-0.310822\pi$
$397$	22.3136			1.11989			0.559945	+	0.828530i	$0.310822\pi$
$398$	−0.131535	−	0.404824i	−0.00659327	−	0.0202920i
$399$	−32.6682	−	23.7348i	−1.63546	−	1.18823i
$400$	−3.19369	+	2.32035i	−0.159684	+	0.116017i
$401$	−7.62722	+	23.4742i	−0.380885	+	1.17224i	0.558536	+	0.829480i	$0.311363\pi$
$401$	−7.62722	+	23.4742i	−0.380885	+	1.17224i	−0.939421	+	0.342764i	$0.888637\pi$
$402$	−0.0218949	+	0.0673856i	−0.00109202	+	0.00336089i
$403$	1.65542	−	1.20273i	0.0824624	−	0.0599125i
$404$	−15.0383	−	10.9260i	−0.748182	−	0.543586i
$405$	−1.77179	−	5.45300i	−0.0880407	−	0.270962i
$406$	1.40500			0.0697292
$407$		0			0
$408$	−1.84656			−0.0914182
$409$	9.11772	+	28.0615i	0.450842	+	1.38755i	0.875948	+	0.482406i	$0.160237\pi$
$409$	9.11772	+	28.0615i	0.450842	+	1.38755i	−0.425105	+	0.905144i	$0.639763\pi$
$410$	0.132182	+	0.0960360i	0.00652802	+	0.00474288i
$411$	14.8746	−	10.8070i	0.733708	−	0.533070i
$412$	8.56294	−	26.3540i	0.421866	−	1.29837i
$413$	−9.88229	+	30.4146i	−0.486276	+	1.49660i
$414$	−0.350083	+	0.254350i	−0.0172056	+	0.0125006i
$415$	−3.62511	−	2.63380i	−0.177950	−	0.129288i
$416$	−0.393879	−	1.21224i	−0.0193115	−	0.0594348i
$417$	−16.4935			−0.807689
$418$		0			0
$419$	9.03564			0.441420			0.220710	−	0.975339i	$-0.429163\pi$
$419$	9.03564			0.441420			0.220710	+	0.975339i	$0.429163\pi$
$420$	−4.08350	−	12.5677i	−0.199255	−	0.613243i
$421$	−11.5043	−	8.35839i	−0.560687	−	0.407363i	0.271023	−	0.962573i	$-0.412638\pi$
$421$	−11.5043	−	8.35839i	−0.560687	−	0.407363i	−0.831710	+	0.555210i	$0.812638\pi$
$422$	−1.43438	+	1.04214i	−0.0698244	+	0.0507304i
$423$	−1.81609	+	5.58935i	−0.0883014	+	0.271764i
$424$	0.166050	−	0.511050i	0.00806410	−	0.0248188i
$425$	−2.72899	+	1.98273i	−0.132376	+	0.0961765i
$426$	1.19063	+	0.865044i	0.0576862	+	0.0419115i
$427$	3.49881	+	10.7682i	0.169319	+	0.521111i
$428$	33.4298			1.61589
$429$		0			0
$430$	−0.0245970			−0.00118617
$431$	−0.535080	−	1.64681i	−0.0257739	−	0.0793239i	0.937342	−	0.348410i	$-0.113278\pi$
$431$	−0.535080	−	1.64681i	−0.0257739	−	0.0793239i	−0.963116	+	0.269086i	$0.913278\pi$
$432$	18.0284	+	13.0984i	0.867391	+	0.630196i
$433$	−14.9244	+	10.8432i	−0.717222	+	0.521092i	−0.885496	−	0.464648i	$-0.846181\pi$
$433$	−14.9244	+	10.8432i	−0.717222	+	0.521092i	0.168273	+	0.985740i	$0.446181\pi$
$434$	0.234145	−	0.720625i	0.0112393	−	0.0345911i
$435$	1.50515	−	4.63238i	0.0721665	−	0.222106i
$436$	−5.88473	+	4.27551i	−0.281827	+	0.204760i
$437$	26.8413	+	19.5014i	1.28399	+	0.932877i
$438$	−0.240787	−	0.741066i	−0.0115052	−	0.0354095i
$439$	−17.1704			−0.819499			−0.409750	−	0.912198i	$-0.634384\pi$
$439$	−17.1704			−0.819499			−0.409750	+	0.912198i	$0.634384\pi$
$440$		0			0
$441$	−11.4331			−0.544432
$442$	−0.111369	−	0.342758i	−0.00529727	−	0.0163033i
$443$	−29.6094	−	21.5125i	−1.40678	−	1.02209i	−0.993780	−	0.111360i	$-0.964479\pi$
$443$	−29.6094	−	21.5125i	−1.40678	−	1.02209i	−0.413005	−	0.910729i	$-0.635521\pi$
$444$	3.51782	−	2.55585i	0.166948	−	0.121295i
$445$	4.09992	−	12.6183i	0.194355	−	0.598163i
$446$	0.140999	−	0.433951i	0.00667651	−	0.0205482i
$447$	20.5683	−	14.9438i	0.972848	−	0.706815i
$448$	28.5180	+	20.7195i	1.34735	+	0.978905i
$449$	−5.13059	−	15.7903i	−0.242127	−	0.745191i	−0.996096	−	0.0882804i	$-0.971863\pi$
$449$	−5.13059	−	15.7903i	−0.242127	−	0.745191i	0.753968	−	0.656911i	$-0.228137\pi$
$450$	−0.0793616			−0.00374114
$451$		0			0
$452$	23.7006			1.11478
$453$	−0.00244940	−	0.00753849i	−0.000115083	−	0.000354189i
$454$	−1.23484	−	0.897165i	−0.0579540	−	0.0421060i
$455$	4.18224	−	3.03857i	0.196066	−	0.142451i
$456$	−1.02930	+	3.16787i	−0.0482016	+	0.148349i
$457$	−9.78512	+	30.1155i	−0.457728	+	1.40874i	0.410173	+	0.912008i	$0.365468\pi$
$457$	−9.78512	+	30.1155i	−0.457728	+	1.40874i	−0.867902	+	0.496736i	$0.834532\pi$
$458$	0.365521	−	0.265567i	0.0170797	−	0.0124091i
$459$	15.4052	+	11.1925i	0.719053	+	0.522422i
$460$	3.35515	+	10.3261i	0.156435	+	0.481456i
$461$	−25.4351			−1.18463			−0.592315	−	0.805706i	$-0.701786\pi$
$461$	−25.4351			−1.18463			−0.592315	+	0.805706i	$0.701786\pi$
$462$		0			0
$463$	−16.3319			−0.759007			−0.379503	−	0.925190i	$-0.623905\pi$
$463$	−16.3319			−0.759007			−0.379503	+	0.925190i	$0.623905\pi$
$464$	4.05102	+	12.4677i	0.188064	+	0.578801i
$465$	−2.12511	−	1.54398i	−0.0985495	−	0.0716004i
$466$	0.636963	−	0.462781i	0.0295067	−	0.0214379i
$467$	2.63564	−	8.11167i	0.121963	−	0.375363i	−0.871373	−	0.490622i	$-0.836770\pi$
$467$	2.63564	−	8.11167i	0.121963	−	0.375363i	0.993336	+	0.115259i	$0.0367697\pi$
$468$	−0.596679	+	1.83639i	−0.0275815	+	0.0848871i
$469$	1.89096	−	1.37386i	0.0873165	−	0.0634392i
$470$	−0.523863	−	0.380608i	−0.0241640	−	0.0175562i
$471$	0.251477	+	0.773968i	0.0115875	+	0.0356626i
$472$	2.63797			0.121422
$473$		0			0
$474$	−1.55030			−0.0712076
$475$	1.88030	+	5.78696i	0.0862739	+	0.265524i
$476$	24.5868	+	17.8634i	1.12694	+	0.818767i
$477$	−0.988554	+	0.718226i	−0.0452628	+	0.0328853i
$478$	−0.655734	+	2.01814i	−0.0299926	+	0.0923076i
$479$	9.25438	−	28.4821i	0.422844	−	1.30138i	−0.482200	−	0.876061i	$-0.660162\pi$
$479$	9.25438	−	28.4821i	0.422844	−	1.30138i	0.905044	−	0.425318i	$-0.139838\pi$
$480$	−1.32376	+	0.961771i	−0.0604213	+	0.0438987i
$481$	1.37618	+	0.999851i	0.0627483	+	0.0455893i
$482$	0.335382	+	1.03220i	0.0152762	+	0.0470154i
$483$	−36.1848			−1.64646
$484$		0			0
$485$	−3.35655			−0.152413
$486$	0.246350	+	0.758186i	0.0111746	+	0.0343920i
$487$	15.8592	+	11.5224i	0.718650	+	0.522130i	0.885952	−	0.463776i	$-0.153506\pi$
$487$	15.8592	+	11.5224i	0.718650	+	0.522130i	−0.167303	+	0.985906i	$0.553506\pi$
$488$	0.755597	−	0.548973i	0.0342043	−	0.0248508i
$489$	−3.60977	+	11.1097i	−0.163240	+	0.502400i
$490$	0.389269	−	1.19805i	0.0175854	−	0.0541223i
$491$	12.7737	−	9.28061i	0.576468	−	0.418828i	−0.260981	−	0.965344i	$-0.584046\pi$
$491$	12.7737	−	9.28061i	0.576468	−	0.418828i	0.837449	+	0.546516i	$0.184046\pi$
$492$	−4.12851	−	2.99954i	−0.186128	−	0.135230i
$493$	3.46158	+	10.6536i	0.155902	+	0.479816i
$494$	−0.650099			−0.0292494
$495$		0			0
$496$	7.06980			0.317443
$497$	−15.0026	−	46.1732i	−0.672958	−	2.07115i
$498$	−0.497198	−	0.361235i	−0.0222800	−	0.0161873i
$499$	−9.06757	+	6.58797i	−0.405920	+	0.294918i	−0.771948	−	0.635686i	$-0.780717\pi$
$499$	−9.06757	+	6.58797i	−0.405920	+	0.294918i	0.366028	+	0.930604i	$0.380717\pi$
$500$	−0.615332	+	1.89380i	−0.0275185	+	0.0846932i
$501$	1.55301	−	4.77968i	0.0693834	−	0.213540i
$502$	−0.250636	+	0.182098i	−0.0111864	+	0.00812742i
$503$	0.277419	+	0.201557i	0.0123695	+	0.00898696i	0.593953	−	0.804500i	$-0.297567\pi$
$503$	0.277419	+	0.201557i	0.0123695	+	0.00898696i	−0.581583	+	0.813487i	$0.697567\pi$
$504$	0.442869	+	1.36301i	0.0197270	+	0.0607133i
$505$	−9.33498			−0.415401
$506$		0			0
$507$	−17.1528			−0.761782
$508$	−12.1606	−	37.4265i	−0.539539	−	1.66053i
$509$	15.8265	+	11.4986i	0.701497	+	0.509667i	0.880419	−	0.474196i	$-0.157261\pi$
$509$	15.8265	+	11.4986i	0.701497	+	0.509667i	−0.178923	+	0.983863i	$0.557261\pi$
$510$	−0.374292	+	0.271939i	−0.0165739	+	0.0120417i
$511$	−7.94324	+	24.4468i	−0.351388	+	1.08146i
$512$	2.27145	−	6.99080i	0.100385	−	0.308953i
$513$	27.7886	−	20.1896i	1.22689	−	0.891391i
$514$	2.03097	+	1.47559i	0.0895825	+	0.0650855i
$515$	−4.30027	−	13.2349i	−0.189493	−	0.583198i
$516$	0.768249			0.0338203
$517$		0			0
$518$	0.629896			0.0276760
$519$	9.32184	+	28.6897i	0.409183	+	1.25934i
$520$	−0.344987	−	0.250648i	−0.0151287	−	0.0109916i
$521$	−34.0001	+	24.7025i	−1.48957	+	1.08224i	−0.515260	+	0.857034i	$0.672305\pi$
$521$	−34.0001	+	24.7025i	−1.48957	+	1.08224i	−0.974312	+	0.225203i	$0.927695\pi$
$522$	−0.0814404	+	0.250648i	−0.00356455	+	0.0109706i
$523$	9.27377	−	28.5417i	0.405513	−	1.24804i	−0.514952	−	0.857219i	$-0.672190\pi$
$523$	9.27377	−	28.5417i	0.405513	−	1.24804i	0.920466	−	0.390823i	$-0.127810\pi$
$524$	−3.11686	+	2.26453i	−0.136161	+	0.0989266i
$525$	−5.36885	−	3.90070i	−0.234316	−	0.170240i
$526$	0.351614	+	1.08216i	0.0153311	+	0.0471843i
$527$	6.04112			0.263155
$528$		0			0
$529$	6.73067			0.292638
$530$	−0.0416035	−	0.128042i	−0.00180714	−	0.00556180i
$531$	−4.85303	−	3.52593i	−0.210604	−	0.153012i
$532$	44.3508	−	32.2227i	1.92285	−	1.39703i
$533$	0.616905	−	1.89864i	0.0267211	−	0.0822392i
$534$	0.562321	−	1.73064i	0.0243340	−	0.0748923i
$535$	13.5820	−	9.86792i	0.587202	−	0.426627i
$536$	−0.155983	−	0.113328i	−0.00673744	−	0.00489504i
$537$	−1.16227	−	3.57709i	−0.0501555	−	0.154363i
$538$	−0.195764			−0.00843998
$539$		0			0
$540$	11.2407			0.483721
$541$	−3.19017	−	9.81832i	−0.137156	−	0.422123i	0.858763	−	0.512373i	$-0.171233\pi$
$541$	−3.19017	−	9.81832i	−0.137156	−	0.422123i	−0.995919	+	0.0902502i	$0.971233\pi$
$542$	−1.14557	−	0.832305i	−0.0492064	−	0.0357505i
$543$	−15.9206	+	11.5670i	−0.683218	+	0.496387i
$544$	1.16287	−	3.57893i	0.0498575	−	0.153446i
$545$	−1.12882	+	3.47415i	−0.0483533	+	0.148816i
$546$	0.573611	−	0.416752i	0.0245483	−	0.0178354i
$547$	−33.8305	−	24.5793i	−1.44649	−	1.05094i	−0.986636	−	0.162941i	$-0.947902\pi$
$547$	−33.8305	−	24.5793i	−1.44649	−	1.05094i	−0.459853	−	0.887995i	$-0.652098\pi$
$548$	7.71339	+	23.7394i	0.329500	+	1.01410i
$549$	−2.12382			−0.0906426
$550$		0			0
$551$	20.2065			0.860826
$552$	0.922364	+	2.83875i	0.0392584	+	0.120825i
$553$	41.3750	+	30.0607i	1.75944	+	1.27831i
$554$	−0.625684	+	0.454586i	−0.0265828	+	0.0193135i
$555$	0.674794	−	2.07680i	0.0286434	−	0.0881554i
$556$	6.91944	−	21.2958i	0.293449	−	0.903145i
$557$	31.1333	−	22.6196i	1.31916	−	0.958425i	0.319216	−	0.947682i	$-0.396580\pi$
$557$	31.1333	−	22.6196i	1.31916	−	0.958425i	0.999942	−	0.0107427i	$-0.00341958\pi$
$558$	0.114985	+	0.0835414i	0.00486770	+	0.00353659i
$559$	0.0928720	+	0.285831i	0.00392807	+	0.0120893i
$560$	17.8611			0.754768
$561$		0			0
$562$	0.228840			0.00965303
$563$	9.48262	+	29.1845i	0.399645	+	1.22998i	0.925285	+	0.379273i	$0.123826\pi$
$563$	9.48262	+	29.1845i	0.399645	+	1.22998i	−0.525640	+	0.850707i	$0.676174\pi$
$564$	16.3620	+	11.8877i	0.688966	+	0.500563i
$565$	9.62919	−	6.99602i	0.405103	−	0.294325i
$566$	0.754038	−	2.32069i	0.0316946	−	0.0975459i
$567$	−8.01649	+	24.6722i	−0.336661	+	1.03614i
$568$	−3.23993	+	2.35395i	−0.135944	+	0.0987695i
$569$	−10.5564	−	7.66970i	−0.442549	−	0.321530i	0.344098	−	0.938934i	$-0.388185\pi$
$569$	−10.5564	−	7.66970i	−0.442549	−	0.321530i	−0.786647	+	0.617403i	$0.788185\pi$
$570$	0.257890	+	0.793704i	0.0108018	+	0.0332446i
$571$	16.1300			0.675018			0.337509	−	0.941322i	$-0.390416\pi$
$571$	16.1300			0.675018			0.337509	+	0.941322i	$0.390416\pi$
$572$		0			0
$573$	26.6796			1.11456
$574$	−0.228439	−	0.703064i	−0.00953487	−	0.0293453i
$575$	4.41123	+	3.20495i	0.183961	+	0.133656i
$576$	−5.34932	+	3.88651i	−0.222888	+	0.161938i
$577$	−4.50282	+	13.8583i	−0.187455	+	0.576927i	−0.999982	−	0.00599662i	$-0.998091\pi$
$577$	−4.50282	+	13.8583i	−0.187455	+	0.576927i	0.812527	+	0.582923i	$0.198091\pi$
$578$	−0.162436	+	0.499927i	−0.00675645	+	0.0207942i
$579$	−18.6163	+	13.5256i	−0.773668	+	0.562103i
$580$	5.34973	+	3.88681i	0.222135	+	0.161391i
$581$	6.26496	+	19.2816i	0.259915	+	0.799935i
$582$	−0.460364			−0.0190827
$583$		0			0
$584$	2.12036			0.0877411
$585$	0.299650	+	0.922227i	0.0123890	+	0.0381294i
$586$	−1.01773	−	0.739424i	−0.0420420	−	0.0305453i
$587$	22.5507	−	16.3840i	0.930767	−	0.676242i	−0.0154134	−	0.999881i	$-0.504906\pi$
$587$	22.5507	−	16.3840i	0.930767	−	0.676242i	0.946181	+	0.323639i	$0.104906\pi$
$588$	−12.1582	+	37.4192i	−0.501397	+	1.54314i
$589$	3.36743	−	10.3639i	0.138753	−	0.427037i
$590$	0.534709	−	0.388489i	0.0220136	−	0.0159938i
$591$	25.9258	+	18.8362i	1.06645	+	0.774818i
$592$	1.81616	+	5.58958i	0.0746439	+	0.229730i
$593$	15.1037			0.620236			0.310118	−	0.950698i	$-0.399631\pi$
$593$	15.1037			0.620236			0.310118	+	0.950698i	$0.399631\pi$
$594$		0			0
$595$	15.2622			0.625690
$596$	10.6660	+	32.8264i	0.436894	+	1.34462i
$597$	5.40146	+	3.92439i	0.221067	+	0.160615i
$598$	−0.471298	+	0.342418i	−0.0192728	+	0.0140025i
$599$	−7.99602	+	24.6092i	−0.326709	+	1.00551i	0.643955	+	0.765063i	$0.277292\pi$
$599$	−7.99602	+	24.6092i	−0.326709	+	1.00551i	−0.970663	+	0.240442i	$0.922708\pi$
$600$	−0.169161	+	0.520624i	−0.00690597	+	0.0212544i
$601$	38.0455	−	27.6417i	1.55191	−	1.12753i	0.609635	−	0.792682i	$-0.291316\pi$
$601$	38.0455	−	27.6417i	1.55191	−	1.12753i	0.942273	−	0.334845i	$-0.108684\pi$
$602$	0.0900352	+	0.0654144i	0.00366956	+	0.00266609i
$603$	0.135484	+	0.416977i	0.00551733	+	0.0169806i
$604$	0.0107610			0.000437861
$605$		0			0
$606$	−1.28033			−0.0520098
$607$	−10.8848	−	33.4999i	−0.441800	−	1.35972i	−0.885955	−	0.463770i	$-0.846496\pi$
$607$	−10.8848	−	33.4999i	−0.441800	−	1.35972i	0.444156	−	0.895950i	$-0.353504\pi$
$608$	−5.49166	−	3.98993i	−0.222716	−	0.161813i
$609$	−17.8291	+	12.9536i	−0.722470	+	0.524905i
$610$	0.0723111	−	0.222551i	0.00292779	−	0.00901082i
$611$	−2.44491	+	7.52466i	−0.0989105	+	0.304415i
$612$	−4.61193	+	3.35076i	−0.186426	+	0.135447i
$613$	18.9405	+	13.7611i	0.764998	+	0.555804i	0.900439	−	0.434982i	$-0.143245\pi$
$613$	18.9405	+	13.7611i	0.764998	+	0.555804i	−0.135441	+	0.990785i	$0.543245\pi$
$614$	0.785525	+	2.41760i	0.0317012	+	0.0975663i
$615$	−2.56276			−0.103341
$616$		0			0
$617$	22.8910			0.921557			0.460778	−	0.887515i	$-0.347570\pi$
$617$	22.8910			0.921557			0.460778	+	0.887515i	$0.347570\pi$
$618$	−0.589799	−	1.81522i	−0.0237252	−	0.0730187i
$619$	−1.72120	−	1.25053i	−0.0691810	−	0.0502629i	0.552657	−	0.833409i	$-0.313614\pi$
$619$	−1.72120	−	1.25053i	−0.0691810	−	0.0502629i	−0.621838	+	0.783146i	$0.713614\pi$
$620$	2.88508	−	2.09613i	0.115867	−	0.0841826i
$621$	9.51150	−	29.2734i	0.381684	−	1.17470i
$622$	−0.381401	+	1.17383i	−0.0152928	+	0.0470664i
$623$	−48.5650	+	35.2846i	−1.94572	+	1.41365i
$624$	5.35206	+	3.88850i	0.214254	+	0.155665i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	1.51223			0.0604410
$627$		0			0
$628$	−1.10482			−0.0440873
$629$	1.55191	+	4.77628i	0.0618786	+	0.190443i
$630$	0.290497	+	0.211058i	0.0115737	+	0.00840876i
$631$	−12.5064	+	9.08644i	−0.497872	+	0.361725i	−0.808204	−	0.588903i	$-0.799560\pi$
$631$	−12.5064	+	9.08644i	−0.497872	+	0.361725i	0.310331	+	0.950628i	$0.399560\pi$
$632$	1.30364	−	4.01218i	0.0518559	−	0.159596i
$633$	8.59372	−	26.4488i	0.341570	−	1.05124i
$634$	0.407090	−	0.295768i	0.0161676	−	0.0117464i
$635$	−15.9883	−	11.6162i	−0.634477	−	0.460975i
$636$	1.29942	+	3.99921i	0.0515254	+	0.158579i
$637$	−15.3918			−0.609844
$638$		0			0
$639$	9.10676			0.360258
$640$	−0.914596	−	2.81484i	−0.0361526	−	0.111266i
$641$	−11.4723	−	8.33508i	−0.453127	−	0.329216i	0.337702	−	0.941253i	$-0.390350\pi$
$641$	−11.4723	−	8.33508i	−0.453127	−	0.329216i	−0.790829	+	0.612037i	$0.790350\pi$
$642$	1.86283	−	1.35342i	0.0735200	−	0.0534154i
$643$	−3.82997	+	11.7874i	−0.151039	+	0.464851i	−0.997738	−	0.0672213i	$-0.978587\pi$
$643$	−3.82997	+	11.7874i	−0.151039	+	0.464851i	0.846699	+	0.532073i	$0.178587\pi$
$644$	15.1805	−	46.7206i	0.598194	−	1.84105i
$645$	0.312128	−	0.226774i	0.0122900	−	0.00892923i
$646$	−1.55276	−	1.12815i	−0.0610925	−	0.0443863i
$647$	10.2737	+	31.6193i	0.403902	+	1.24308i	0.921809	+	0.387645i	$0.126711\pi$
$647$	10.2737	+	31.6193i	0.403902	+	1.24308i	−0.517907	+	0.855437i	$0.673289\pi$
$648$	2.13991			0.0840637
$649$		0			0
$650$	−0.106840			−0.00419063
$651$	3.67264	+	11.3032i	0.143942	+	0.443009i
$652$	−12.8301	−	9.32164i	−0.502467	−	0.365064i
$653$	28.1591	−	20.4588i	1.10195	−	0.800615i	0.120574	−	0.992704i	$-0.461526\pi$
$653$	28.1591	−	20.4588i	1.10195	−	0.800615i	0.981377	+	0.192090i	$0.0615265\pi$
$654$	−0.154822	+	0.476493i	−0.00605402	+	0.0186323i
$655$	−0.597882	+	1.84009i	−0.0233612	+	0.0718983i
$656$	5.58020	−	4.05425i	0.217870	−	0.158292i
$657$	−3.90080	−	2.83409i	−0.152185	−	0.110569i
$658$	0.905347	+	2.78637i	0.0352941	+	0.108624i
$659$	−34.4953			−1.34375			−0.671873	−	0.740666i	$-0.734510\pi$
$659$	−34.4953			−1.34375			−0.671873	+	0.740666i	$0.734510\pi$
$660$		0			0
$661$	1.77827			0.0691668			0.0345834	−	0.999402i	$-0.488990\pi$
$661$	1.77827			0.0691668			0.0345834	+	0.999402i	$0.488990\pi$
$662$	−0.536608	−	1.65151i	−0.0208559	−	0.0641878i
$663$	4.57332	+	3.32271i	0.177613	+	0.129043i
$664$	1.35297	−	0.982990i	0.0525054	−	0.0381474i
$665$	8.50744	−	26.1832i	0.329905	−	1.01534i
$666$	−0.0365116	+	0.112371i	−0.00141480	+	0.00435430i
$667$	14.6490	−	10.6431i	0.567210	−	0.412102i
$668$	5.51984	+	4.01040i	0.213569	+	0.155167i
$669$	2.21162	+	6.80666i	0.0855060	+	0.263161i
$670$	−0.0483070			−0.00186626
$671$		0			0
$672$	7.40331			0.285589
$673$	5.96292	+	18.3520i	0.229854	+	0.707417i	0.997762	+	0.0668581i	$0.0212975\pi$
$673$	5.96292	+	18.3520i	0.229854	+	0.707417i	−0.767909	+	0.640559i	$0.778703\pi$
$674$	−0.681325	−	0.495011i	−0.0262436	−	0.0190671i
$675$	4.56691	−	3.31805i	0.175780	−	0.127712i
$676$	7.19604	−	22.1471i	0.276771	−	0.851812i
$677$	−5.22550	+	16.0824i	−0.200832	+	0.618098i	0.799027	+	0.601296i	$0.205349\pi$
$677$	−5.22550	+	16.0824i	−0.200832	+	0.618098i	−0.999859	+	0.0168023i	$0.994651\pi$
$678$	1.32068	−	0.959531i	0.0507205	−	0.0368506i
$679$	12.2864	+	8.92658i	0.471508	+	0.342571i
$680$	−0.389040	−	1.19734i	−0.0149190	−	0.0459160i
$681$	23.9412			0.917430
$682$		0			0
$683$	4.14018			0.158420			0.0792098	−	0.996858i	$-0.474760\pi$
$683$	4.14018			0.158420			0.0792098	+	0.996858i	$0.474760\pi$
$684$	3.17765	+	9.77981i	0.121501	+	0.373940i
$685$	10.1413	+	7.36808i	0.387479	+	0.281520i
$686$	−2.21504	+	1.60932i	−0.0845705	+	0.0614441i
$687$	−2.18993	+	6.73991i	−0.0835510	+	0.257144i
$688$	−0.320879	+	0.987563i	−0.0122334	+	0.0376505i
$689$	−1.33084	+	0.966911i	−0.0507009	+	0.0368364i
$690$	0.605018	+	0.439571i	0.0230326	+	0.0167342i
$691$	−14.3236	−	44.0834i	−0.544894	−	1.67701i	−0.721242	−	0.692683i	$-0.756429\pi$
$691$	−14.3236	−	44.0834i	−0.544894	−	1.67701i	0.176348	−	0.984328i	$-0.443571\pi$
$692$	−40.9539			−1.55684
$693$		0			0
$694$	0.960437			0.0364577
$695$	−3.47491	−	10.6947i	−0.131811	−	0.405672i
$696$	1.47070	+	1.06852i	0.0557466	+	0.0405022i
$697$	4.76827	−	3.46435i	0.180611	−	0.131222i
$698$	0.498784	−	1.53510i	0.0188792	−	0.0581044i
$699$	−3.81621	+	11.7451i	−0.144342	+	0.444240i
$700$	7.28883	−	5.29564i	0.275492	−	0.200156i
$701$	36.7741	+	26.7180i	1.38894	+	1.00912i	0.995981	+	0.0895673i	$0.0285484\pi$
$701$	36.7741	+	26.7180i	1.38894	+	1.00912i	0.392959	+	0.919556i	$0.371452\pi$
$702$	0.186373	+	0.573597i	0.00703419	+	0.0216490i
$703$	9.05904			0.341668
$704$		0			0
$705$	10.1567			0.382524
$706$	−0.659111	−	2.02853i	−0.0248060	−	0.0763449i
$707$	34.1699	+	24.8259i	1.28509	+	0.933674i
$708$	−16.7008	+	12.1339i	−0.627655	+	0.456018i
$709$	−4.33370	+	13.3377i	−0.162755	+	0.500910i	−0.998864	−	0.0476545i	$-0.984825\pi$
$709$	−4.33370	+	13.3377i	−0.162755	+	0.500910i	0.836108	+	0.548564i	$0.184825\pi$
$710$	−0.310064	+	0.954278i	−0.0116365	+	0.0358134i
$711$	−7.76100	+	5.63870i	−0.291060	+	0.211468i
$712$	4.00607	+	2.91058i	0.150134	+	0.109078i
$713$	−3.01757	−	9.28713i	−0.113009	−	0.347806i
$714$	2.09327			0.0783388
$715$		0			0
$716$	5.10622			0.190829
$717$	−10.2854	−	31.6552i	−0.384115	−	1.18218i
$718$	1.21607	+	0.883525i	0.0453833	+	0.0329729i
$719$	−10.6292	+	7.72256i	−0.396402	+	0.288003i	−0.768074	−	0.640361i	$-0.778785\pi$
$719$	−10.6292	+	7.72256i	−0.396402	+	0.288003i	0.371672	+	0.928364i	$0.378785\pi$
$720$	−1.03531	+	3.18635i	−0.0385837	+	0.118748i
$721$	−19.4567	+	59.8815i	−0.724605	+	2.23010i
$722$	−1.36356	+	0.990687i	−0.0507466	+	0.0368696i
$723$	−13.7723	−	10.0062i	−0.512199	−	0.372134i
$724$	−8.25583	−	25.4088i	−0.306825	−	0.944311i
$725$	3.32083			0.123333
$726$		0			0
$727$	−18.3635			−0.681063			−0.340532	−	0.940233i	$-0.610607\pi$
$727$	−18.3635			−0.681063			−0.340532	+	0.940233i	$0.610607\pi$
$728$	0.596212	+	1.83495i	0.0220971	+	0.0680078i
$729$	−24.0320	−	17.4603i	−0.890076	−	0.646678i
$730$	0.429791	−	0.312262i	0.0159073	−	0.0115573i
$731$	−0.274190	+	0.843870i	−0.0101413	+	0.0312117i
$732$	−2.25853	+	6.95103i	−0.0834776	+	0.256918i
$733$	29.9318	−	21.7467i	1.10555	−	0.803232i	0.123597	−	0.992333i	$-0.460557\pi$
$733$	29.9318	−	21.7467i	1.10555	−	0.803232i	0.981958	+	0.189100i	$0.0605571\pi$
$734$	−1.66413	−	1.20906i	−0.0614243	−	0.0446274i
$735$	6.10581	+	18.7917i	0.225216	+	0.693144i
$736$	−6.08282			−0.224216
$737$		0			0
$738$	0.138666			0.00510435
$739$	3.04392	+	9.36822i	0.111972	+	0.344616i	0.991304	−	0.131595i	$-0.0420099\pi$
$739$	3.04392	+	9.36822i	0.111972	+	0.344616i	−0.879331	+	0.476211i	$0.842010\pi$
$740$	2.39841	+	1.74255i	0.0881672	+	0.0640572i
$741$	8.24955	−	5.99365i	0.303055	−	0.220182i
$742$	−0.188236	+	0.579330i	−0.00691036	+	0.0212679i
$743$	8.48162	−	26.1037i	0.311161	−	0.957654i	−0.666146	−	0.745822i	$-0.732057\pi$
$743$	8.48162	−	26.1037i	0.311161	−	0.957654i	0.977306	−	0.211832i	$-0.0679429\pi$
$744$	0.793137	−	0.576248i	0.0290778	−	0.0211263i
$745$	14.0232	+	10.1885i	0.513771	+	0.373277i
$746$	−0.585449	−	1.80183i	−0.0214348	−	0.0659695i
$747$	−3.80291			−0.139141
$748$		0			0
$749$	−75.9591			−2.77549
$750$	0.0423829	+	0.130441i	0.00154760	+	0.00476304i
$751$	−11.1065	−	8.06936i	−0.405283	−	0.294455i	0.366406	−	0.930455i	$-0.380588\pi$
$751$	−11.1065	−	8.06936i	−0.405283	−	0.294455i	−0.771689	+	0.636000i	$0.780588\pi$
$752$	−22.1154	+	16.0678i	−0.806465	+	0.585931i
$753$	1.50162	−	4.62153i	0.0547223	−	0.168418i
$754$	−0.109639	+	0.337434i	−0.00399282	+	0.0122886i
$755$	0.00437205	−	0.00317648i	0.000159115	−	0.000115604i
$756$	−41.1455	−	29.8939i	−1.49645	−	1.08723i
$757$	−7.08573	−	21.8076i	−0.257535	−	0.792612i	−0.993320	−	0.115396i	$-0.963186\pi$
$757$	−7.08573	−	21.8076i	−0.257535	−	0.792612i	0.735784	−	0.677216i	$-0.236814\pi$
$758$	−0.348578			−0.0126609
$759$		0			0
$760$	−2.27097			−0.0823767
$761$	−6.39104	−	19.6696i	−0.231675	−	0.713022i	−0.997545	−	0.0700268i	$-0.977692\pi$
$761$	−6.39104	−	19.6696i	−0.231675	−	0.713022i	0.765870	−	0.642995i	$-0.222308\pi$
$762$	−2.19286	−	1.59321i	−0.0794390	−	0.0577158i
$763$	13.3713	−	9.71479i	0.484072	−	0.351699i
$764$	−11.1928	+	34.4478i	−0.404941	+	1.24628i
$765$	−0.884668	+	2.72273i	−0.0319852	+	0.0984405i
$766$	0.831965	−	0.604458i	0.0300601	−	0.0218400i
$767$	−6.53339	−	4.74678i	−0.235907	−	0.171396i
$768$	6.93694	+	21.3497i	0.250315	+	0.770391i
$769$	38.4306			1.38584			0.692922	−	0.721013i	$-0.256323\pi$
$769$	38.4306			1.38584			0.692922	+	0.721013i	$0.256323\pi$
$770$		0			0
$771$	−39.3768			−1.41812
$772$	−9.65373	−	29.7111i	−0.347445	−	1.06933i
$773$	−40.4028	−	29.3544i	−1.45319	−	1.05580i	−0.985073	−	0.172136i	$-0.944933\pi$
$773$	−40.4028	−	29.3544i	−1.45319	−	1.05580i	−0.468115	−	0.883667i	$-0.655067\pi$
$774$	−0.0168886	+	0.0122703i	−0.000607047	+	0.000441045i
$775$	0.553420	−	1.70325i	0.0198794	−	0.0611826i
$776$	0.387117	−	1.19143i	0.0138967	−	0.0427697i
$777$	−7.99318	+	5.80738i	−0.286754	+	0.208339i
$778$	−0.709774	−	0.515681i	−0.0254466	−	0.0184881i
$779$	−3.28537	−	10.1113i	−0.117711	−	0.362276i
$780$	3.33700			0.119484
$781$		0			0
$782$	−1.71991			−0.0615037
$783$	−5.79287	−	17.8286i	−0.207020	−	0.637143i
$784$	−43.0231	−	31.2581i	−1.53654	−	1.11636i
$785$	−0.448873	+	0.326125i	−0.0160210	+	0.0116399i
$786$	−0.0820019	+	0.252376i	−0.00292491	+	0.00900195i
$787$	−4.80645	+	14.7927i	−0.171331	+	0.527304i	−0.999447	−	0.0332537i	$-0.989413\pi$
$787$	−4.80645	+	14.7927i	−0.171331	+	0.527304i	0.828116	+	0.560557i	$0.189413\pi$
$788$	−35.1973	+	25.5723i	−1.25385	+	0.910975i
$789$	−14.4389	−	10.4905i	−0.514040	−	0.373472i
$790$	−0.326623	−	1.00524i	−0.0116207	−	0.0357649i
$791$	−53.8524			−1.91477
$792$		0			0
$793$	−2.85919			−0.101533
$794$	0.644778	+	1.98442i	0.0228823	+	0.0704246i
$795$	1.70843	+	1.24125i	0.0605919	+	0.0440226i
$796$	−7.33309	+	5.32780i	−0.259915	+	0.188839i
$797$	14.2478	−	43.8501i	0.504682	−	1.55325i	−0.296622	−	0.954995i	$-0.595860\pi$
$797$	14.2478	−	43.8501i	0.504682	−	1.55325i	0.801304	−	0.598257i	$-0.204140\pi$
$798$	1.16683	−	3.59113i	0.0413053	−	0.127125i
$799$	−18.8975	+	13.7298i	−0.668546	+	0.485727i
$800$	−0.902527	−	0.655724i	−0.0319091	−	0.0231834i
$801$	−3.47960	−	10.7091i	−0.122945	−	0.378387i
$802$	−2.30803			−0.0814994
$803$		0			0
$804$	1.50879			0.0532111
$805$	−7.62356	−	23.4629i	−0.268695	−	0.826958i
$806$	0.154798	+	0.112468i	0.00545254	+	0.00396150i
$807$	2.48418	−	1.80486i	0.0874473	−	0.0635342i
$808$	1.07662	−	3.31350i	0.0378754	−	0.116569i
$809$	−11.6003	+	35.7021i	−0.407845	+	1.25522i	0.510651	+	0.859788i	$0.329404\pi$
$809$	−11.6003	+	35.7021i	−0.407845	+	1.25522i	−0.918496	+	0.395430i	$0.870596\pi$
$810$	0.433755	−	0.315141i	0.0152406	−	0.0110729i
$811$	−5.82935	−	4.23527i	−0.204696	−	0.148720i	0.480715	−	0.876877i	$-0.340377\pi$
$811$	−5.82935	−	4.23527i	−0.204696	−	0.148720i	−0.685411	+	0.728157i	$0.740377\pi$
$812$	−9.24548	−	28.4547i	−0.324453	−	0.998563i
$813$	22.2104			0.778953
$814$		0			0
$815$	−7.96428			−0.278977
$816$	6.03549	+	18.5753i	0.211284	+	0.650266i
$817$	1.29487	+	0.940777i	0.0453017	+	0.0329136i
$818$	−2.23213	+	1.62174i	−0.0780445	+	0.0567027i
$819$	1.35577	−	4.17264i	0.0473745	−	0.145804i
$820$	1.07515	−	3.30896i	0.0375457	−	0.115554i
$821$	6.98510	−	5.07497i	0.243782	−	0.177118i	−0.459185	−	0.888341i	$-0.651858\pi$
$821$	6.98510	−	5.07497i	0.243782	−	0.177118i	0.702966	+	0.711223i	$0.251858\pi$
$822$	1.39092	+	1.01056i	0.0485139	+	0.0352474i
$823$	−7.72915	−	23.7879i	−0.269421	−	0.829193i	−0.990642	−	0.136488i	$-0.956419\pi$
$823$	−7.72915	−	23.7879i	−0.269421	−	0.829193i	0.721221	−	0.692706i	$-0.243581\pi$
$824$	5.19375			0.180933
$825$		0			0
$826$	−2.99042			−0.104050
$827$	15.1024	+	46.4805i	0.525163	+	1.61629i	0.763993	+	0.645224i	$0.223236\pi$
$827$	15.1024	+	46.4805i	0.525163	+	1.61629i	−0.238830	+	0.971061i	$0.576764\pi$
$828$	7.45487	+	5.41628i	0.259075	+	0.188229i
$829$	−4.28107	+	3.11038i	−0.148688	+	0.108028i	−0.659642	−	0.751580i	$-0.729292\pi$
$829$	−4.28107	+	3.11038i	−0.148688	+	0.108028i	0.510954	+	0.859608i	$0.329292\pi$
$830$	0.129480	−	0.398499i	0.00449432	−	0.0138321i
$831$	3.74863	−	11.5371i	0.130039	−	0.400218i
$832$	−7.20152	+	5.23221i	−0.249668	+	0.181394i
$833$	−36.7631	−	26.7100i	−1.27377	−	0.925446i
$834$	−0.476598	−	1.46682i	−0.0165032	−	0.0507917i
$835$	3.42643			0.118576
$836$		0			0
$837$	−10.1097			−0.349441
$838$	0.261095	+	0.803568i	0.00901938	+	0.0277588i
$839$	10.7129	+	7.78337i	0.369850	+	0.268712i	0.757149	−	0.653243i	$-0.226592\pi$
$839$	10.7129	+	7.78337i	0.369850	+	0.268712i	−0.387299	+	0.921954i	$0.626592\pi$
$840$	2.00377	−	1.45583i	0.0691367	−	0.0502308i
$841$	−5.55367	+	17.0924i	−0.191506	+	0.589395i
$842$	0.410907	−	1.26464i	0.0141608	−	0.0435825i
$843$	−2.90391	+	2.10981i	−0.100016	+	0.0726658i
$844$	30.5445	+	22.1919i	1.05139	+	0.763876i
$845$	−3.61382	−	11.1222i	−0.124319	−	0.382615i
$846$	−0.549557			−0.0188942
$847$		0			0
$848$	−5.68361			−0.195176
$849$	11.8273	+	36.4007i	0.405913	+	1.24927i
$850$	−0.255188	−	0.185405i	−0.00875287	−	0.00635933i
$851$	6.56747	−	4.77155i	0.225130	−	0.163567i
$852$	9.68436	−	29.8054i	0.331781	−	1.02112i
$853$	0.685662	−	2.11025i	0.0234766	−	0.0722536i	−0.938632	−	0.344921i	$-0.887906\pi$
$853$	0.685662	−	2.11025i	0.0234766	−	0.0722536i	0.962108	+	0.272667i	$0.0879058\pi$
$854$	−0.856551	+	0.622321i	−0.0293106	+	0.0212954i
$855$	4.17787	+	3.03540i	0.142880	+	0.103808i
$856$	1.93623	+	5.95910i	0.0661789	+	0.203678i
$857$	31.4625			1.07474			0.537368	−	0.843348i	$-0.319418\pi$
$857$	31.4625			1.07474			0.537368	+	0.843348i	$0.319418\pi$
$858$		0			0
$859$	9.07676			0.309695			0.154848	−	0.987938i	$-0.450511\pi$
$859$	9.07676			0.309695			0.154848	+	0.987938i	$0.450511\pi$
$860$	0.161858	+	0.498147i	0.00551931	+	0.0169867i
$861$	9.38078	+	6.81554i	0.319696	+	0.232273i
$862$	0.130994	−	0.0951727i	0.00446167	−	0.00324159i
$863$	13.1283	−	40.4049i	0.446894	−	1.37540i	−0.433500	−	0.901154i	$-0.642721\pi$
$863$	13.1283	−	40.4049i	0.446894	−	1.37540i	0.880393	−	0.474244i	$-0.157279\pi$
$864$	−1.94603	+	5.98926i	−0.0662053	+	0.203759i
$865$	−16.6390	+	12.0889i	−0.565742	+	0.411035i
$866$	−1.39558	−	1.01395i	−0.0474238	−	0.0344554i
$867$	−2.54786	−	7.84151i	−0.0865299	−	0.266312i
$868$	−16.1351			−0.547662
$869$		0			0
$870$	0.455465			0.0154417
$871$	0.182395	+	0.561354i	0.00618022	+	0.0190208i
$872$	−1.10298	−	0.801360i	−0.0373515	−	0.0271375i
$873$	−2.30464	+	1.67442i	−0.0780004	+	0.0566706i
$874$	−0.958707	+	2.95060i	−0.0324288	+	0.0998055i
$875$	1.39815	−	4.30308i	0.0472663	−	0.145471i
$876$	−13.4239	+	9.75301i	−0.453551	+	0.329524i
$877$	25.3304	+	18.4036i	0.855348	+	0.621447i	0.926615	−	0.376010i	$-0.122704\pi$
$877$	25.3304	+	18.4036i	0.855348	+	0.621447i	−0.0712673	+	0.997457i	$0.522704\pi$
$878$	−0.496159	−	1.52702i	−0.0167446	−	0.0515344i
$879$	19.7319			0.665539
$880$		0			0
$881$	21.5189			0.724990			0.362495	−	0.931986i	$-0.381925\pi$
$881$	21.5189			0.724990			0.362495	+	0.931986i	$0.381925\pi$
$882$	−0.330372	−	1.01678i	−0.0111242	−	0.0342368i
$883$	0.527926	+	0.383561i	0.0177661	+	0.0129078i	0.596633	−	0.802514i	$-0.296505\pi$
$883$	0.527926	+	0.383561i	0.0177661	+	0.0129078i	−0.578867	+	0.815422i	$0.696505\pi$
$884$	−6.20880	+	4.51096i	−0.208825	+	0.151720i
$885$	−3.20358	+	9.85960i	−0.107687	+	0.331427i
$886$	1.05758	−	3.25489i	0.0355300	−	0.109350i
$887$	11.8490	−	8.60882i	0.397851	−	0.289056i	−0.370814	−	0.928707i	$-0.620921\pi$
$887$	11.8490	−	8.60882i	0.397851	−	0.289056i	0.768665	+	0.639651i	$0.220921\pi$
$888$	0.659347	+	0.479043i	0.0221262	+	0.0160756i
$889$	27.6313	+	85.0403i	0.926722	+	2.85216i
$890$	1.24065			0.0415868
$891$		0			0
$892$	−9.71637			−0.325328
$893$	13.0205	+	40.0730i	0.435715	+	1.34099i
$894$	1.92334	+	1.39739i	0.0643261	+	0.0467357i
$895$	2.07458	−	1.50727i	0.0693456	−	0.0503825i
$896$	−4.13811	+	12.7358i	−0.138245	+	0.425473i
$897$	2.82367	−	8.69036i	0.0942795	−	0.290163i
$898$	1.25603	−	0.912559i	0.0419142	−	0.0304525i
$899$	−4.81147	−	3.49573i	−0.160471	−	0.116589i
$900$	0.522231	+	1.60726i	0.0174077	+	0.0535754i
$901$	−4.85662			−0.161798
$902$		0			0
$903$	−1.74561			−0.0580903
$904$	1.37272	+	4.22479i	0.0456559	+	0.140515i
$905$	−10.8545	−	7.88624i	−0.360815	−	0.262147i
$906$	0.000599644	0	0.000435667i	1.99218e−5	0	1.44741e-5i
$907$	8.88269	−	27.3381i	0.294945	−	0.907747i	−0.688295	−	0.725431i	$-0.741641\pi$
$907$	8.88269	−	27.3381i	0.294945	−	0.907747i	0.983240	−	0.182316i	$-0.0583594\pi$
$908$	−10.0440	+	30.9122i	−0.333321	+	1.02586i
$909$	−6.40950	+	4.65678i	−0.212590	+	0.154455i
$910$	0.391081	+	0.284137i	0.0129642	+	0.00941904i
$911$	5.34039	+	16.4360i	0.176935	+	0.544550i	0.999717	−	0.0238080i	$-0.00757903\pi$
$911$	5.34039	+	16.4360i	0.176935	+	0.544550i	−0.822782	+	0.568358i	$0.807579\pi$
$912$	35.2313			1.16663
$913$		0			0
$914$	−2.96102			−0.0979418
$915$	1.13422	+	3.49078i	0.0374962	+	0.115402i
$916$	−7.78362	−	5.65513i	−0.257178	−	0.186851i
$917$	7.08213	−	5.14547i	0.233872	−	0.169918i
$918$	−0.550236	+	1.69345i	−0.0181605	+	0.0558923i
$919$	−0.679359	+	2.09085i	−0.0224100	+	0.0689709i	−0.961636	−	0.274328i	$-0.911544\pi$
$919$	−0.679359	+	2.09085i	−0.0224100	+	0.0689709i	0.939226	+	0.343299i	$0.111544\pi$
$920$	−1.64637	+	1.19616i	−0.0542792	+	0.0394361i
$921$	−32.2573	−	23.4363i	−1.06292	−	0.772253i
$922$	−0.734976	−	2.26202i	−0.0242052	−	0.0744958i
$923$	12.2600			0.403542
$924$		0			0
$925$	1.48881			0.0489517
$926$	−0.471928	−	1.45245i	−0.0155085	−	0.0477303i
$927$	−9.55486	−	6.94201i	−0.313823	−	0.228006i
$928$	−2.99714	+	2.17755i	−0.0983860	+	0.0714816i
$929$	7.48142	−	23.0254i	0.245457	−	0.755440i	−0.750103	−	0.661321i	$-0.769996\pi$
$929$	7.48142	−	23.0254i	0.245457	−	0.755440i	0.995561	−	0.0941198i	$-0.0300037\pi$
$930$	0.0759038	−	0.233608i	0.00248898	−	0.00766030i
$931$	−66.3150	+	48.1806i	−2.17339	+	1.57906i
$932$	−13.5639	−	9.85473i	−0.444300	−	0.322802i
$933$	−5.98239	−	18.4119i	−0.195855	−	0.602779i
$934$	0.797556			0.0260968
$935$		0			0
$936$	−0.361908			−0.0118293
$937$	−6.43458	−	19.8036i	−0.210209	−	0.646955i	−0.999459	−	0.0328841i	$-0.989531\pi$
$937$	−6.43458	−	19.8036i	−0.210209	−	0.646955i	0.789251	−	0.614071i	$-0.210469\pi$
$938$	0.176824	+	0.128470i	0.00577350	+	0.00419469i
$939$	−19.1898	+	13.9422i	−0.626234	+	0.454986i
$940$	−4.26100	+	13.1140i	−0.138979	+	0.427732i
$941$	10.5723	−	32.5383i	0.344648	−	1.06072i	−0.617124	−	0.786866i	$-0.711702\pi$
$941$	10.5723	−	32.5383i	0.344648	−	1.06072i	0.961772	−	0.273852i	$-0.0882978\pi$
$942$	−0.0615647	+	0.0447294i	−0.00200589	+	0.00145736i
$943$	−7.70758	−	5.59988i	−0.250993	−	0.182357i
$944$	−8.62222	−	26.5365i	−0.280629	−	0.863689i
$945$	−25.5410			−0.830848
$946$		0			0
$947$	33.8128			1.09877			0.549383	−	0.835570i	$-0.314863\pi$
$947$	33.8128			1.09877			0.549383	+	0.835570i	$0.314863\pi$
$948$	10.2016	+	31.3972i	0.331332	+	1.01973i
$949$	−5.25144	−	3.81539i	−0.170469	−	0.123853i
$950$	−0.460319	+	0.334441i	−0.0149347	+	0.0108507i
$951$	−2.43898	+	7.50641i	−0.0790893	+	0.243412i
$952$	−1.76022	+	5.41740i	−0.0570491	+	0.175579i
$953$	−20.7094	+	15.0462i	−0.670842	+	0.487395i	−0.870307	−	0.492510i	$-0.836080\pi$
$953$	−20.7094	+	15.0462i	−0.670842	+	0.487395i	0.199465	+	0.979905i	$0.436080\pi$
$954$	−0.0924396	−	0.0671613i	−0.00299284	−	0.00217443i
$955$	5.62097	+	17.2996i	0.181890	+	0.559800i
$956$	45.1871			1.46146
$957$		0			0
$958$	2.80042			0.0904774
$959$	−17.5263	−	53.9405i	−0.565955	−	1.74183i
$960$	9.24477	+	6.71672i	0.298374	+	0.216781i
$961$	22.4847	−	16.3361i	0.725314	−	0.526971i
$962$	−0.0491537	+	0.151280i	−0.00158478	+	0.00487745i
$963$	4.40294	−	13.5508i	0.141883	−	0.436670i
$964$	18.6975	−	13.5846i	0.602207	−	0.437529i
$965$	−12.6924	−	9.22156i	−0.408582	−	0.296852i
$966$	−1.04560	−	3.21803i	−0.0336417	−	0.103538i
$967$	43.8942			1.41154			0.705772	−	0.708439i	$-0.250600\pi$
$967$	43.8942			1.41154			0.705772	+	0.708439i	$0.250600\pi$
$968$		0			0
$969$	30.1051			0.967114
$970$	−0.0969914	−	0.298509i	−0.00311421	−	0.00958454i
$971$	−29.4245	−	21.3782i	−0.944278	−	0.686058i	0.00516893	−	0.999987i	$-0.498355\pi$
$971$	−29.4245	−	21.3782i	−0.944278	−	0.686058i	−0.949447	+	0.313929i	$0.898355\pi$
$972$	13.7340	−	9.97832i	0.440518	−	0.320055i
$973$	−15.7223	+	48.3883i	−0.504034	+	1.55126i
$974$	−0.566453	+	1.74336i	−0.0181503	+	0.0558610i
$975$	1.35577	−	0.985026i	0.0434195	−	0.0315461i
$976$	−7.99204	−	5.80655i	−0.255819	−	0.185863i
$977$	3.19882	+	9.84496i	0.102339	+	0.314968i	0.989097	−	0.147267i	$-0.0470476\pi$
$977$	3.19882	+	9.84496i	0.102339	+	0.314968i	−0.886757	+	0.462235i	$0.847048\pi$
$978$	−1.09233			−0.0349289
$979$		0			0
$980$	−26.8248			−0.856888
$981$	0.958026	+	2.94850i	0.0305874	+	0.0941384i
$982$	1.19446	+	0.867829i	0.0381169	+	0.0276935i
$983$	17.8921	−	12.9994i	0.570669	−	0.414615i	−0.264679	−	0.964336i	$-0.585266\pi$
$983$	17.8921	−	12.9994i	0.570669	−	0.414615i	0.835348	+	0.549721i	$0.185266\pi$
$984$	0.295568	−	0.909666i	0.00942238	−	0.0289991i
$985$	−6.75160	+	20.7793i	−0.215124	+	0.662083i
$986$	−0.847437	+	0.615699i	−0.0269879	+	0.0196078i
$987$	−37.1778	−	27.0112i	−1.18338	−	0.859777i
$988$	4.27791	+	13.1661i	0.136098	+	0.418868i
$989$	1.43426			0.0456067
$990$		0			0
$991$	−55.5911			−1.76591			−0.882955	−	0.469457i	$-0.844450\pi$
$991$	−55.5911			−1.76591			−0.882955	+	0.469457i	$0.844450\pi$
$992$	0.617387	+	1.90012i	0.0196021	+	0.0603289i
$993$	22.0356	+	16.0098i	0.699280	+	0.508057i
$994$	3.67282	−	2.66846i	0.116495	−	0.0846383i
$995$	−1.40665	+	4.32921i	−0.0445937	+	0.137245i
$996$	−4.04411	+	12.4465i	−0.128143	+	0.394383i
$997$	−8.73022	+	6.34287i	−0.276489	+	0.200881i	−0.717384	−	0.696678i	$-0.754661\pi$
$997$	−8.73022	+	6.34287i	−0.276489	+	0.200881i	0.440896	+	0.897558i	$0.354661\pi$
$998$	−0.847907	−	0.616041i	−0.0268400	−	0.0195004i
$999$	−2.59708	−	7.99299i	−0.0821679	−	0.252887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.j.511.1		8
11.2	odd	10		605.2.g.g.251.2		8
11.3	even	5		605.2.a.l.1.2		4
11.4	even	5		55.2.g.a.36.2	yes	8
11.5	even	5		55.2.g.a.26.2	✓	8
11.6	odd	10		605.2.g.n.81.1		8
11.7	odd	10		605.2.g.n.366.1		8
11.8	odd	10		605.2.a.i.1.3		4
11.9	even	5	inner	605.2.g.j.251.1		8
11.10	odd	2		605.2.g.g.511.2		8
33.5	odd	10		495.2.n.f.136.1		8
33.8	even	10		5445.2.a.bu.1.2		4
33.14	odd	10		5445.2.a.bg.1.3		4
33.26	odd	10		495.2.n.f.91.1		8
44.3	odd	10		9680.2.a.cs.1.1		4
44.15	odd	10		880.2.bo.e.641.1		8
44.19	even	10		9680.2.a.cv.1.1		4
44.27	odd	10		880.2.bo.e.81.1		8
55.4	even	10		275.2.h.b.201.1		8
55.14	even	10		3025.2.a.v.1.3		4
55.19	odd	10		3025.2.a.be.1.2		4
55.27	odd	20		275.2.z.b.224.3		16
55.37	odd	20		275.2.z.b.124.2		16
55.38	odd	20		275.2.z.b.224.2		16
55.48	odd	20		275.2.z.b.124.3		16
55.49	even	10		275.2.h.b.26.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	11.5	even	5
55.2.g.a.36.2	yes	8	11.4	even	5
275.2.h.b.26.1		8	55.49	even	10
275.2.h.b.201.1		8	55.4	even	10
275.2.z.b.124.2		16	55.37	odd	20
275.2.z.b.124.3		16	55.48	odd	20
275.2.z.b.224.2		16	55.38	odd	20
275.2.z.b.224.3		16	55.27	odd	20
495.2.n.f.91.1		8	33.26	odd	10
495.2.n.f.136.1		8	33.5	odd	10
605.2.a.i.1.3		4	11.8	odd	10
605.2.a.l.1.2		4	11.3	even	5
605.2.g.g.251.2		8	11.2	odd	10
605.2.g.g.511.2		8	11.10	odd	2
605.2.g.j.251.1		8	11.9	even	5	inner
605.2.g.j.511.1		8	1.1	even	1	trivial
605.2.g.n.81.1		8	11.6	odd	10
605.2.g.n.366.1		8	11.7	odd	10
880.2.bo.e.81.1		8	44.27	odd	10
880.2.bo.e.641.1		8	44.15	odd	10
3025.2.a.v.1.3		4	55.14	even	10
3025.2.a.be.1.2		4	55.19	odd	10
5445.2.a.bg.1.3		4	33.14	odd	10
5445.2.a.bu.1.2		4	33.8	even	10
9680.2.a.cs.1.1		4	44.3	odd	10
9680.2.a.cv.1.1		4	44.19	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0288961 + 0.0889332i) q^{2} +(-1.18661 - 0.862123i) q^{3} +(1.61096 - 1.17043i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.0423829 - 0.130441i) q^{6} +(-3.66042 + 2.65945i) q^{7} +(0.301943 + 0.219374i) q^{8} +(-0.262262 - 0.807160i) q^{9} +0.0935099 q^{10} -2.92064 q^{12} +(-0.353070 - 1.08664i) q^{13} +(-0.342285 - 0.248685i) q^{14} +(-1.18661 + 0.862123i) q^{15} +(1.21988 - 3.75440i) q^{16} +(1.04238 - 3.20812i) q^{17} +(0.0642049 - 0.0466476i) q^{18} +(-4.92268 - 3.57654i) q^{19} +(-0.615332 - 1.89380i) q^{20} +6.63626 q^{21} -5.45258 q^{23} +(-0.169161 - 0.520624i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.0864358 - 0.0627993i) q^{26} +(-1.74440 + 5.36872i) q^{27} +(-2.78408 + 8.56853i) q^{28} +(-2.68661 + 1.95194i) q^{29} +(-0.110960 - 0.0806171i) q^{30} +(0.553420 + 1.70325i) q^{31} +1.11558 q^{32} +0.315430 q^{34} +(1.39815 + 4.30308i) q^{35} +(-1.36722 - 0.993342i) q^{36} +(-1.20447 + 0.875099i) q^{37} +(0.175826 - 0.541138i) q^{38} +(-0.517859 + 1.59381i) q^{39} +(0.301943 - 0.219374i) q^{40} +(1.41356 + 1.02701i) q^{41} +(0.191762 + 0.590184i) q^{42} -0.263041 q^{43} -0.848698 q^{45} +(-0.157559 - 0.484916i) q^{46} +(-5.60222 - 4.07025i) q^{47} +(-4.68428 + 3.40333i) q^{48} +(4.16287 - 12.8120i) q^{49} +(0.0288961 - 0.0889332i) q^{50} +(-4.00270 + 2.90813i) q^{51} +(-1.84062 - 1.33729i) q^{52} +(-0.444910 - 1.36929i) q^{53} -0.527864 q^{54} -1.68865 q^{56} +(2.75789 + 8.48791i) q^{57} +(-0.251225 - 0.182525i) q^{58} +(5.71821 - 4.15452i) q^{59} +(-0.902527 + 2.77769i) q^{60} +(0.773299 - 2.37997i) q^{61} +(-0.135484 + 0.0984349i) q^{62} +(3.10659 + 2.25707i) q^{63} +(-2.40752 - 7.40959i) q^{64} -1.14256 q^{65} -0.516598 q^{67} +(-2.07565 - 6.38820i) q^{68} +(6.47010 + 4.70080i) q^{69} +(-0.342285 + 0.248685i) q^{70} +(-3.31584 + 10.2051i) q^{71} +(0.0978819 - 0.301250i) q^{72} +(4.59621 - 3.33934i) q^{73} +(-0.112630 - 0.0818304i) q^{74} +(0.453245 + 1.39494i) q^{75} -12.1163 q^{76} -0.156706 q^{78} +(-3.49293 - 10.7501i) q^{79} +(-3.19369 - 2.32035i) q^{80} +(4.63859 - 3.37014i) q^{81} +(-0.0504891 + 0.155390i) q^{82} +(1.38467 - 4.26157i) q^{83} +(10.6908 - 7.76729i) q^{84} +(-2.72899 - 1.98273i) q^{85} +(-0.00760088 - 0.0233931i) q^{86} +4.87077 q^{87} +13.2676 q^{89} +(-0.0245241 - 0.0754774i) q^{90} +(4.18224 + 3.03857i) q^{91} +(-8.78389 + 6.38187i) q^{92} +(0.811719 - 2.49821i) q^{93} +(0.200098 - 0.615837i) q^{94} +(-4.92268 + 3.57654i) q^{95} +(-1.32376 - 0.961771i) q^{96} +(-1.03723 - 3.19227i) q^{97} +1.25970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{7} - 7 q^{8} + 5 q^{9} + 6 q^{10} - 28 q^{12} - 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} - 4 q^{17} - 16 q^{18} - 11 q^{19} - 6 q^{20} - 12 q^{21}+ \cdots - 84 q^{98}+O(q^{100}) \) 8 * q + q^2 + q^3 - q^4 - 2 * q^5 - 12 * q^6 - 8 * q^7 - 7 * q^8 + 5 * q^9 + 6 * q^10 - 28 * q^12 - 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 - 4 * q^17 - 16 * q^18 - 11 * q^19 - 6 * q^20 - 12 * q^21 - 18 * q^23 - 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 - 11 * q^28 - 11 * q^29 + 13 * q^30 - 9 * q^31 + 12 * q^32 - 20 * q^34 - 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 - 6 * q^39 - 7 * q^40 + 11 * q^41 - 31 * q^42 + 42 * q^43 + 29 * q^46 - q^47 + 21 * q^48 + q^50 - 22 * q^51 - q^52 + 8 * q^53 - 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 - 2 * q^61 + 27 * q^62 - 4 * q^63 + 21 * q^64 + 14 * q^65 - 2 * q^67 - 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 + 21 * q^72 + 32 * q^73 - 12 * q^74 + q^75 + 16 * q^76 + 12 * q^78 - 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 + 10 * q^83 + 51 * q^84 + q^85 + 34 * q^86 + 30 * q^87 + 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 - 22 * q^94 - 11 * q^95 + 3 * q^96 - 18 * q^97 - 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more