LMFDB - Embedded newform 630.2.j.k.211.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(211,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.211"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,1,-3,-3,1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.k.421.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.403374 + 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.25707 - 1.19154i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-2.67458 + 1.35891i) q^{9} +1.00000 q^{10} +(1.25707 + 2.17731i) q^{11} +(-1.66044 - 0.492881i) q^{12} +(-0.757068 + 1.31128i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-1.66044 - 0.492881i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.320884 q^{17} +(2.51414 + 1.63680i) q^{18} -2.70739 q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.25707 - 1.19154i) q^{21} +(1.25707 - 2.17731i) q^{22} +(-3.07795 + 5.33117i) q^{23} +(0.403374 + 1.68443i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.51414 q^{26} +(-3.36783 - 3.95698i) q^{27} +1.00000 q^{28} +(0.563816 + 0.976558i) q^{29} +(0.403374 + 1.68443i) q^{30} +(-0.193252 + 0.334723i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.16044 + 2.99571i) q^{33} +(0.160442 + 0.277894i) q^{34} +1.00000 q^{35} +(0.160442 - 2.99571i) q^{36} -5.86330 q^{37} +(1.35369 + 2.34467i) q^{38} +(-2.51414 - 0.746289i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-5.38470 + 9.32657i) q^{41} +(-1.66044 - 0.492881i) q^{42} +(-5.01414 - 8.68474i) q^{43} -2.51414 q^{44} +(0.160442 - 2.99571i) q^{45} +6.15591 q^{46} +(0.320884 + 0.555788i) q^{47} +(1.25707 - 1.19154i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.129436 - 0.540506i) q^{51} +(-0.757068 - 1.31128i) q^{52} +2.83502 q^{53} +(-1.74293 + 4.89512i) q^{54} -2.51414 q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.09209 - 4.56040i) q^{57} +(0.563816 - 0.976558i) q^{58} +(-6.16044 + 10.6702i) q^{59} +(1.25707 - 1.19154i) q^{60} +(0.0966262 + 0.167362i) q^{61} +0.386505 q^{62} +(2.51414 + 1.63680i) q^{63} +1.00000 q^{64} +(-0.757068 - 1.31128i) q^{65} +(4.17458 + 1.23917i) q^{66} +(0.546947 - 0.947340i) q^{67} +(0.160442 - 0.277894i) q^{68} +(-10.2215 - 3.03413i) q^{69} +(-0.500000 - 0.866025i) q^{70} +10.6363 q^{71} +(-2.67458 + 1.35891i) q^{72} +5.64177 q^{73} +(2.93165 + 5.07776i) q^{74} +(1.25707 - 1.19154i) q^{75} +(1.35369 - 2.34467i) q^{76} +(1.25707 - 2.17731i) q^{77} +(0.610763 + 2.55045i) q^{78} +(2.32088 + 4.01989i) q^{79} +1.00000 q^{80} +(5.30675 - 7.26900i) q^{81} +10.7694 q^{82} +(2.83502 + 4.91040i) q^{83} +(0.403374 + 1.68443i) q^{84} +(0.160442 - 0.277894i) q^{85} +(-5.01414 + 8.68474i) q^{86} +(-1.41751 + 1.34362i) q^{87} +(1.25707 + 2.17731i) q^{88} +16.0565 q^{89} +(-2.67458 + 1.35891i) q^{90} +1.51414 q^{91} +(-3.07795 - 5.33117i) q^{92} +(-0.641769 - 0.190501i) q^{93} +(0.320884 - 0.555788i) q^{94} +(1.35369 - 2.34467i) q^{95} +(-1.66044 - 0.492881i) q^{96} +(1.30675 + 2.26335i) q^{97} +1.00000 q^{98} +(-6.32088 - 4.11514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} - 3 q^{14} - 2 q^{15} - 3 q^{16} + 14 q^{17} + 2 q^{18} - 6 q^{19} - 3 q^{20}+ \cdots - 22 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + q^11 - 2 * q^12 + 2 * q^13 - 3 * q^14 - 2 * q^15 - 3 * q^16 + 14 * q^17 + 2 * q^18 - 6 * q^19 - 3 * q^20 + q^21 + q^22 + 4 * q^23 + q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 - 7 * q^34 + 6 * q^35 - 7 * q^36 + 20 * q^37 + 3 * q^38 - 2 * q^39 - 3 * q^40 - 7 * q^41 - 2 * q^42 - 17 * q^43 - 2 * q^44 - 7 * q^45 - 8 * q^46 - 14 * q^47 + q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 2 * q^52 - 12 * q^53 - 17 * q^54 - 2 * q^55 - 3 * q^56 + 29 * q^57 - 6 * q^58 - 29 * q^59 + q^60 + 2 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 + 2 * q^65 + 4 * q^66 + q^67 - 7 * q^68 - 38 * q^69 - 3 * q^70 + 20 * q^71 + 5 * q^72 + 2 * q^73 - 10 * q^74 + q^75 + 3 * q^76 + q^77 - 8 * q^78 - 2 * q^79 + 6 * q^80 + 29 * q^81 + 14 * q^82 - 12 * q^83 + q^84 - 7 * q^85 - 17 * q^86 + 6 * q^87 + q^88 + 44 * q^89 + 5 * q^90 - 4 * q^91 + 4 * q^92 + 28 * q^93 - 14 * q^94 + 3 * q^95 - 2 * q^96 + 5 * q^97 + 6 * q^98 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.403374	+	1.68443i	0.232888	+	0.972504i
$3$	0.403374	+	1.68443i	0.232888	+	0.972504i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.25707	−	1.19154i	0.513196	−	0.486446i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	−2.67458	+	1.35891i	−0.891526	+	0.452969i
$10$	1.00000			0.316228
$11$	1.25707	+	2.17731i	0.379020	+	0.656483i	0.990920	−	0.134453i	$-0.0429277\pi$
$11$	1.25707	+	2.17731i	0.379020	+	0.656483i	−0.611900	+	0.790935i	$0.709594\pi$
$12$	−1.66044	−	0.492881i	−0.479328	−	0.142282i
$13$	−0.757068	+	1.31128i	−0.209973	+	0.363684i	−0.951706	−	0.307012i	$-0.900671\pi$
$13$	−0.757068	+	1.31128i	−0.209973	+	0.363684i	0.741733	+	0.670696i	$0.234004\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	−1.66044	−	0.492881i	−0.428724	−	0.127261i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.320884			−0.0778259			−0.0389130	−	0.999243i	$-0.512390\pi$
$17$	−0.320884			−0.0778259			−0.0389130	+	0.999243i	$0.512390\pi$
$18$	2.51414	+	1.63680i	0.592588	+	0.385798i
$19$	−2.70739			−0.621118			−0.310559	−	0.950554i	$-0.600516\pi$
$19$	−2.70739			−0.621118			−0.310559	+	0.950554i	$0.600516\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	1.25707	−	1.19154i	0.274315	−	0.260016i
$22$	1.25707	−	2.17731i	0.268008	−	0.464203i
$23$	−3.07795	+	5.33117i	−0.641798	+	1.11163i	0.343234	+	0.939250i	$0.388478\pi$
$23$	−3.07795	+	5.33117i	−0.641798	+	1.11163i	−0.985031	+	0.172376i	$0.944856\pi$
$24$	0.403374	+	1.68443i	0.0823383	+	0.343832i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.51414			0.296947
$27$	−3.36783	−	3.95698i	−0.648139	−	0.761522i
$28$	1.00000			0.188982
$29$	0.563816	+	0.976558i	0.104698	+	0.181342i	0.913615	−	0.406581i	$-0.133279\pi$
$29$	0.563816	+	0.976558i	0.104698	+	0.181342i	−0.808917	+	0.587923i	$0.799946\pi$
$30$	0.403374	+	1.68443i	0.0736456	+	0.307533i
$31$	−0.193252	+	0.334723i	−0.0347092	+	0.0601180i	−0.882858	−	0.469640i	$-0.844384\pi$
$31$	−0.193252	+	0.334723i	−0.0347092	+	0.0601180i	0.848149	+	0.529758i	$0.177717\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.16044	+	2.99571i	−0.550162	+	0.521486i
$34$	0.160442	+	0.277894i	0.0275156	+	0.0476584i
$35$	1.00000			0.169031
$36$	0.160442	−	2.99571i	0.0267404	−	0.499284i
$37$	−5.86330			−0.963920			−0.481960	−	0.876193i	$-0.660075\pi$
$37$	−5.86330			−0.963920			−0.481960	+	0.876193i	$0.660075\pi$
$38$	1.35369	+	2.34467i	0.219598	+	0.380355i
$39$	−2.51414	−	0.746289i	−0.402584	−	0.119502i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−5.38470	+	9.32657i	−0.840949	+	1.45657i	0.0481444	+	0.998840i	$0.484669\pi$
$41$	−5.38470	+	9.32657i	−0.840949	+	1.45657i	−0.889093	+	0.457726i	$0.848664\pi$
$42$	−1.66044	−	0.492881i	−0.256212	−	0.0760532i
$43$	−5.01414	−	8.68474i	−0.764649	−	1.32441i	−0.940432	−	0.339982i	$-0.889579\pi$
$43$	−5.01414	−	8.68474i	−0.764649	−	1.32441i	0.175783	−	0.984429i	$-0.443754\pi$
$44$	−2.51414			−0.379020
$45$	0.160442	−	2.99571i	0.0239173	−	0.446574i
$46$	6.15591			0.907639
$47$	0.320884	+	0.555788i	0.0468058	+	0.0810700i	0.888479	−	0.458917i	$-0.151762\pi$
$47$	0.320884	+	0.555788i	0.0468058	+	0.0810700i	−0.841673	+	0.539987i	$0.818429\pi$
$48$	1.25707	−	1.19154i	0.181442	−	0.171985i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−0.129436	−	0.540506i	−0.0181247	−	0.0756860i
$52$	−0.757068	−	1.31128i	−0.104987	−	0.181842i
$53$	2.83502			0.389420			0.194710	−	0.980861i	$-0.437623\pi$
$53$	2.83502			0.389420			0.194710	+	0.980861i	$0.437623\pi$
$54$	−1.74293	+	4.89512i	−0.237183	+	0.666141i
$55$	−2.51414			−0.339006
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−1.09209	−	4.56040i	−0.144651	−	0.604039i
$58$	0.563816	−	0.976558i	0.0740327	−	0.128228i
$59$	−6.16044	+	10.6702i	−0.802021	+	1.38914i	0.116262	+	0.993219i	$0.462909\pi$
$59$	−6.16044	+	10.6702i	−0.802021	+	1.38914i	−0.918284	+	0.395923i	$0.870425\pi$
$60$	1.25707	−	1.19154i	0.162287	−	0.153828i
$61$	0.0966262	+	0.167362i	0.0123717	+	0.0214284i	0.872145	−	0.489248i	$-0.162729\pi$
$61$	0.0966262	+	0.167362i	0.0123717	+	0.0214284i	−0.859773	+	0.510676i	$0.829395\pi$
$62$	0.386505			0.0490862
$63$	2.51414	+	1.63680i	0.316751	+	0.206217i
$64$	1.00000			0.125000
$65$	−0.757068	−	1.31128i	−0.0939028	−	0.162644i
$66$	4.17458	+	1.23917i	0.513855	+	0.152531i
$67$	0.546947	−	0.947340i	0.0668202	−	0.115736i	−0.830680	−	0.556751i	$-0.812048\pi$
$67$	0.546947	−	0.947340i	0.0668202	−	0.115736i	0.897500	+	0.441015i	$0.145381\pi$
$68$	0.160442	−	0.277894i	0.0194565	−	0.0336996i
$69$	−10.2215	−	3.03413i	−1.23053	−	0.365266i
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	10.6363			1.26230			0.631149	−	0.775662i	$-0.282584\pi$
$71$	10.6363			1.26230			0.631149	+	0.775662i	$0.282584\pi$
$72$	−2.67458	+	1.35891i	−0.315202	+	0.160149i
$73$	5.64177			0.660319			0.330160	−	0.943925i	$-0.392897\pi$
$73$	5.64177			0.660319			0.330160	+	0.943925i	$0.392897\pi$
$74$	2.93165	+	5.07776i	0.340797	+	0.590278i
$75$	1.25707	−	1.19154i	0.145154	−	0.137588i
$76$	1.35369	−	2.34467i	0.155279	−	0.268952i
$77$	1.25707	−	2.17731i	0.143256	−	0.248127i
$78$	0.610763	+	2.55045i	0.0691553	+	0.288782i
$79$	2.32088	+	4.01989i	0.261120	+	0.452273i	0.966540	−	0.256517i	$-0.0825749\pi$
$79$	2.32088	+	4.01989i	0.261120	+	0.452273i	−0.705420	+	0.708790i	$0.749242\pi$
$80$	1.00000			0.111803
$81$	5.30675	−	7.26900i	0.589639	−	0.807667i
$82$	10.7694			1.18928
$83$	2.83502	+	4.91040i	0.311184	+	0.538987i	0.978619	−	0.205682i	$-0.0659411\pi$
$83$	2.83502	+	4.91040i	0.311184	+	0.538987i	−0.667435	+	0.744668i	$0.732608\pi$
$84$	0.403374	+	1.68443i	0.0440117	+	0.183786i
$85$	0.160442	−	0.277894i	0.0174024	−	0.0301419i
$86$	−5.01414	+	8.68474i	−0.540688	+	0.936500i
$87$	−1.41751	+	1.34362i	−0.151973	+	0.144052i
$88$	1.25707	+	2.17731i	0.134004	+	0.232102i
$89$	16.0565			1.70199			0.850995	−	0.525173i	$-0.175999\pi$
$89$	16.0565			1.70199			0.850995	+	0.525173i	$0.175999\pi$
$90$	−2.67458	+	1.35891i	−0.281925	+	0.143241i
$91$	1.51414			0.158725
$92$	−3.07795	−	5.33117i	−0.320899	−	0.555813i
$93$	−0.641769	−	0.190501i	−0.0665483	−	0.0197540i
$94$	0.320884	−	0.555788i	0.0330967	−	0.0573252i
$95$	1.35369	−	2.34467i	0.138886	−	0.240558i
$96$	−1.66044	−	0.492881i	−0.169468	−	0.0503044i
$97$	1.30675	+	2.26335i	0.132680	+	0.229809i	0.924709	−	0.380675i	$-0.124308\pi$
$97$	1.30675	+	2.26335i	0.132680	+	0.229809i	−0.792029	+	0.610484i	$0.790975\pi$
$98$	1.00000			0.101015
$99$	−6.32088	−	4.11514i	−0.635273	−	0.413587i
$100$	1.00000			0.100000
$101$	7.54241	+	13.0638i	0.750498	+	1.29990i	0.947582	+	0.319514i	$0.103520\pi$
$101$	7.54241	+	13.0638i	0.750498	+	1.29990i	−0.197084	+	0.980387i	$0.563147\pi$
$102$	−0.403374	+	0.382348i	−0.0399400	+	0.0378581i
$103$	1.71012	−	2.96202i	0.168503	−	0.291856i	−0.769391	−	0.638779i	$-0.779440\pi$
$103$	1.71012	−	2.96202i	0.168503	−	0.291856i	0.937894	+	0.346922i	$0.112773\pi$
$104$	−0.757068	+	1.31128i	−0.0742367	+	0.128582i
$105$	0.403374	+	1.68443i	0.0393653	+	0.164383i
$106$	−1.41751	−	2.45520i	−0.137681	−	0.238470i
$107$	−11.0192			−1.06527			−0.532633	−	0.846346i	$-0.678797\pi$
$107$	−11.0192			−1.06527			−0.532633	+	0.846346i	$0.678797\pi$
$108$	5.11076	−	0.938136i	0.491783	−	0.0902722i
$109$	16.5990			1.58989			0.794946	−	0.606680i	$-0.207499\pi$
$109$	16.5990			1.58989			0.794946	+	0.606680i	$0.207499\pi$
$110$	1.25707	+	2.17731i	0.119857	+	0.207598i
$111$	−2.36510	−	9.87628i	−0.224485	−	0.937415i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	5.88197	−	10.1879i	0.553329	−	0.958394i	−0.444702	−	0.895678i	$-0.646691\pi$
$113$	5.88197	−	10.1879i	0.553329	−	0.958394i	0.998031	−	0.0627156i	$-0.0199761\pi$
$114$	−3.40337	+	3.22598i	−0.318755	+	0.302140i
$115$	−3.07795	−	5.33117i	−0.287021	−	0.497134i
$116$	−1.12763			−0.104698
$117$	0.242932	−	4.53591i	0.0224590	−	0.419345i
$118$	12.3209			1.13423
$119$	0.160442	+	0.277894i	0.0147077	+	0.0254745i
$120$	−1.66044	−	0.492881i	−0.151577	−	0.0449937i
$121$	2.33956	−	4.05223i	0.212687	−	0.368385i
$122$	0.0966262	−	0.167362i	0.00874813	−	0.0151522i
$123$	−17.8820	−	5.30803i	−1.61236	−	0.478609i
$124$	−0.193252	−	0.334723i	−0.0173546	−	0.0300590i
$125$	1.00000			0.0894427
$126$	0.160442	−	2.99571i	0.0142933	−	0.266879i
$127$	5.90064			0.523597			0.261799	−	0.965123i	$-0.415684\pi$
$127$	5.90064			0.523597			0.261799	+	0.965123i	$0.415684\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	12.6062	−	11.9491i	1.10992	−	1.05206i
$130$	−0.757068	+	1.31128i	−0.0663993	+	0.115007i
$131$	−7.98133	+	13.8241i	−0.697332	+	1.20781i	0.272057	+	0.962281i	$0.412296\pi$
$131$	−7.98133	+	13.8241i	−0.697332	+	1.20781i	−0.969388	+	0.245533i	$0.921037\pi$
$132$	−1.01414	−	4.23488i	−0.0882693	−	0.368599i
$133$	1.35369	+	2.34467i	0.117380	+	0.203308i
$134$	−1.09389			−0.0944981
$135$	5.11076	−	0.938136i	0.439864	−	0.0807419i
$136$	−0.320884			−0.0275156
$137$	−11.1017	−	19.2287i	−0.948481	−	1.64282i	−0.748626	−	0.662993i	$-0.769286\pi$
$137$	−11.1017	−	19.2287i	−0.948481	−	1.64282i	−0.199856	−	0.979825i	$-0.564047\pi$
$138$	2.48313	+	10.3692i	0.211378	+	0.882682i
$139$	−3.62763	+	6.28324i	−0.307692	+	0.532938i	−0.977857	−	0.209274i	$-0.932890\pi$
$139$	−3.62763	+	6.28324i	−0.307692	+	0.532938i	0.670165	+	0.742212i	$0.266223\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	−0.806748	+	0.764696i	−0.0679404	+	0.0643991i
$142$	−5.31815	−	9.21131i	−0.446289	−	0.772996i
$143$	−3.80675			−0.318336
$144$	2.51414	+	1.63680i	0.209511	+	0.136400i
$145$	−1.12763			−0.0936447
$146$	−2.82088	−	4.88592i	−0.233458	−	0.404361i
$147$	−1.66044	−	0.492881i	−0.136951	−	0.0406521i
$148$	2.93165	−	5.07776i	0.240980	−	0.417390i
$149$	5.83502	−	10.1066i	0.478024	−	0.827961i	−0.521659	−	0.853154i	$-0.674687\pi$
$149$	5.83502	−	10.1066i	0.478024	−	0.827961i	0.999683	+	0.0251929i	$0.00802001\pi$
$150$	−1.66044	−	0.492881i	−0.135575	−	0.0402436i
$151$	0.292611	+	0.506816i	0.0238123	+	0.0412441i	0.877686	−	0.479236i	$-0.159086\pi$
$151$	0.292611	+	0.506816i	0.0238123	+	0.0412441i	−0.853874	+	0.520480i	$0.825753\pi$
$152$	−2.70739			−0.219598
$153$	0.858231	−	0.436052i	0.0693839	−	0.0352527i
$154$	−2.51414			−0.202595
$155$	−0.193252	−	0.334723i	−0.0155224	−	0.0268856i
$156$	1.90337	−	1.80416i	0.152392	−	0.144449i
$157$	2.97859	−	5.15908i	0.237718	−	0.411739i	−0.722341	−	0.691537i	$-0.756934\pi$
$157$	2.97859	−	5.15908i	0.237718	−	0.411739i	0.960059	+	0.279798i	$0.0902673\pi$
$158$	2.32088	−	4.01989i	0.184640	−	0.319805i
$159$	1.14357	+	4.77538i	0.0906913	+	0.378712i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	6.15591			0.485153
$162$	−8.94852	−	0.961276i	−0.703062	−	0.0755250i
$163$	−15.7639			−1.23473			−0.617363	−	0.786678i	$-0.711799\pi$
$163$	−15.7639			−1.23473			−0.617363	+	0.786678i	$0.711799\pi$
$164$	−5.38470	−	9.32657i	−0.420474	−	0.728283i
$165$	−1.01414	−	4.23488i	−0.0789505	−	0.329685i
$166$	2.83502	−	4.91040i	0.220040	−	0.381121i
$167$	−3.61076	+	6.25403i	−0.279409	+	0.483951i	−0.971238	−	0.238111i	$-0.923472\pi$
$167$	−3.61076	+	6.25403i	−0.279409	+	0.483951i	0.691829	+	0.722062i	$0.256805\pi$
$168$	1.25707	−	1.19154i	0.0969849	−	0.0919297i
$169$	5.35369	+	9.27287i	0.411823	+	0.713298i
$170$	−0.320884			−0.0246107
$171$	7.24113	−	3.67909i	0.553743	−	0.281347i
$172$	10.0283			0.764649
$173$	3.80675	+	6.59348i	0.289422	+	0.501293i	0.973672	−	0.227954i	$-0.0732037\pi$
$173$	3.80675	+	6.59348i	0.289422	+	0.501293i	−0.684250	+	0.729247i	$0.739870\pi$
$174$	1.87237	+	0.555788i	0.141944	+	0.0421342i
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	1.25707	−	2.17731i	0.0947551	−	0.164121i
$177$	−20.4581	−	6.07273i	−1.53773	−	0.456454i
$178$	−8.02827	−	13.9054i	−0.601745	−	1.04225i
$179$	3.32088			0.248215			0.124107	−	0.992269i	$-0.460393\pi$
$179$	3.32088			0.248215			0.124107	+	0.992269i	$0.460393\pi$
$180$	2.51414	+	1.63680i	0.187393	+	0.122000i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−0.757068	−	1.31128i	−0.0561176	−	0.0971986i
$183$	−0.242932	+	0.230269i	−0.0179580	+	0.0170220i
$184$	−3.07795	+	5.33117i	−0.226910	+	0.393019i
$185$	2.93165	−	5.07776i	0.215539	−	0.373325i
$186$	0.155906	+	0.651039i	0.0114316	+	0.0477365i
$187$	−0.403374	−	0.698664i	−0.0294976	−	0.0510914i
$188$	−0.641769			−0.0468058
$189$	−1.74293	+	4.89512i	−0.126780	+	0.356068i
$190$	−2.70739			−0.196415
$191$	−3.48586	−	6.03769i	−0.252228	−	0.436872i	0.711911	−	0.702270i	$-0.247830\pi$
$191$	−3.48586	−	6.03769i	−0.252228	−	0.436872i	−0.964139	+	0.265398i	$0.914497\pi$
$192$	0.403374	+	1.68443i	0.0291110	+	0.121563i
$193$	−2.69598	+	4.66958i	−0.194061	+	0.336124i	−0.946592	−	0.322433i	$-0.895499\pi$
$193$	−2.69598	+	4.66958i	−0.194061	+	0.336124i	0.752531	+	0.658557i	$0.228833\pi$
$194$	1.30675	−	2.26335i	0.0938190	−	0.162499i
$195$	1.90337	−	1.80416i	0.136303	−	0.129199i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	13.6755			0.974340			0.487170	−	0.873307i	$-0.338029\pi$
$197$	13.6755			0.974340			0.487170	+	0.873307i	$0.338029\pi$
$198$	−0.403374	+	7.53162i	−0.0286665	+	0.535249i
$199$	26.4677			1.87625			0.938123	−	0.346301i	$-0.112562\pi$
$199$	26.4677			1.87625			0.938123	+	0.346301i	$0.112562\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	1.81635	+	0.539160i	0.128115	+	0.0380294i
$202$	7.54241	−	13.0638i	0.530682	−	0.919168i
$203$	0.563816	−	0.976558i	0.0395721	−	0.0685409i
$204$	0.532810	+	0.158158i	0.0373042	+	0.0110733i
$205$	−5.38470	−	9.32657i	−0.376084	−	0.651396i
$206$	−3.42024			−0.238300
$207$	0.987667	−	18.4413i	0.0686476	−	1.28176i
$208$	1.51414			0.104987
$209$	−3.40337	−	5.89482i	−0.235416	−	0.407753i
$210$	1.25707	−	1.19154i	0.0867460	−	0.0822244i
$211$	−1.41478	+	2.45047i	−0.0973974	+	0.168697i	−0.910607	−	0.413274i	$-0.864385\pi$
$211$	−1.41478	+	2.45047i	−0.0973974	+	0.168697i	0.813209	+	0.581971i	$0.197718\pi$
$212$	−1.41751	+	2.45520i	−0.0973550	+	0.168624i
$213$	4.29041	+	17.9161i	0.293974	+	1.22759i
$214$	5.50960	+	9.54291i	0.376629	+	0.652340i
$215$	10.0283			0.683923
$216$	−3.36783	−	3.95698i	−0.229152	−	0.269239i
$217$	0.386505			0.0262377
$218$	−8.29948	−	14.3751i	−0.562112	−	0.973606i
$219$	2.27574	+	9.50314i	0.153780	+	0.642163i
$220$	1.25707	−	2.17731i	0.0847515	−	0.146794i
$221$	0.242932	−	0.420770i	0.0163413	−	0.0283040i
$222$	−7.37056	+	6.98638i	−0.494680	+	0.468895i
$223$	6.73840	+	11.6712i	0.451236	+	0.781564i	0.998463	−	0.0554201i	$-0.0176498\pi$
$223$	6.73840	+	11.6712i	0.451236	+	0.781564i	−0.547227	+	0.836984i	$0.684316\pi$
$224$	1.00000			0.0668153
$225$	2.51414	+	1.63680i	0.167609	+	0.109120i
$226$	−11.7639			−0.782525
$227$	−4.21012	−	7.29214i	−0.279436	−	0.483997i	0.691809	−	0.722081i	$-0.256814\pi$
$227$	−4.21012	−	7.29214i	−0.279436	−	0.483997i	−0.971245	+	0.238084i	$0.923481\pi$
$228$	4.49546	+	1.33442i	0.297719	+	0.0883741i
$229$	11.7667	−	20.3805i	0.777563	−	1.34678i	−0.155779	−	0.987792i	$-0.549789\pi$
$229$	11.7667	−	20.3805i	0.777563	−	1.34678i	0.933342	−	0.358987i	$-0.116878\pi$
$230$	−3.07795	+	5.33117i	−0.202954	+	0.351527i
$231$	4.17458	+	1.23917i	0.274667	+	0.0815314i
$232$	0.563816	+	0.976558i	0.0370163	+	0.0641142i
$233$	2.32635			0.152404			0.0762021	−	0.997092i	$-0.475721\pi$
$233$	2.32635			0.152404			0.0762021	+	0.997092i	$0.475721\pi$
$234$	−4.04968	+	2.05757i	−0.264736	+	0.134508i
$235$	−0.641769			−0.0418644
$236$	−6.16044	−	10.6702i	−0.401011	−	0.694571i
$237$	−5.83502	+	5.53088i	−0.379025	+	0.359269i
$238$	0.160442	−	0.277894i	0.0103999	−	0.0180132i
$239$	−2.19325	+	3.79882i	−0.141870	+	0.245726i	−0.928201	−	0.372080i	$-0.878645\pi$
$239$	−2.19325	+	3.79882i	−0.141870	+	0.245726i	0.786331	+	0.617805i	$0.211978\pi$
$240$	0.403374	+	1.68443i	0.0260377	+	0.108729i
$241$	1.11076	+	1.92390i	0.0715505	+	0.123929i	0.899581	−	0.436754i	$-0.143872\pi$
$241$	1.11076	+	1.92390i	0.0715505	+	0.123929i	−0.828030	+	0.560683i	$0.810539\pi$
$242$	−4.67912			−0.300785
$243$	14.3847	+	6.00670i	0.922779	+	0.385330i
$244$	−0.193252			−0.0123717
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	4.34409	+	18.1403i	0.276969	+	1.15658i
$247$	2.04968	−	3.55015i	0.130418	−	0.225891i
$248$	−0.193252	+	0.334723i	−0.0122715	+	0.0212549i
$249$	−7.12763	+	6.75611i	−0.451695	+	0.428151i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−17.5671			−1.10882			−0.554412	−	0.832242i	$-0.687057\pi$
$251$	−17.5671			−1.10882			−0.554412	+	0.832242i	$0.687057\pi$
$252$	−2.67458	+	1.35891i	−0.168483	+	0.0856030i
$253$	−15.4768			−0.973017
$254$	−2.95032	−	5.11011i	−0.185120	−	0.320637i
$255$	0.532810	+	0.158158i	0.0333659	+	0.00990423i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.68418	−	16.7735i	0.604083	−	1.04630i	−0.388113	−	0.921612i	$-0.626873\pi$
$257$	9.68418	−	16.7735i	0.604083	−	1.04630i	0.992196	−	0.124690i	$-0.0397936\pi$
$258$	−16.6514	−	4.94274i	−1.03667	−	0.307722i
$259$	2.93165	+	5.07776i	0.182164	+	0.315517i
$260$	1.51414			0.0939028
$261$	−2.83502	−	1.84571i	−0.175483	−	0.114246i
$262$	15.9627			0.986176
$263$	3.56382	+	6.17271i	0.219754	+	0.380626i	0.954733	−	0.297465i	$-0.0961411\pi$
$263$	3.56382	+	6.17271i	0.219754	+	0.380626i	−0.734978	+	0.678090i	$0.762808\pi$
$264$	−3.16044	+	2.99571i	−0.194512	+	0.184373i
$265$	−1.41751	+	2.45520i	−0.0870770	+	0.150822i
$266$	1.35369	−	2.34467i	0.0830003	−	0.143761i
$267$	6.47679	+	27.0461i	0.396373	+	1.65519i
$268$	0.546947	+	0.947340i	0.0334101	+	0.0578680i
$269$	15.6646			0.955086			0.477543	−	0.878608i	$-0.341527\pi$
$269$	15.6646			0.955086			0.477543	+	0.878608i	$0.341527\pi$
$270$	−3.36783	−	3.95698i	−0.204960	−	0.240814i
$271$	−21.1842			−1.28685			−0.643424	−	0.765510i	$-0.722487\pi$
$271$	−21.1842			−1.28685			−0.643424	+	0.765510i	$0.722487\pi$
$272$	0.160442	+	0.277894i	0.00972824	+	0.0168498i
$273$	0.610763	+	2.55045i	0.0369651	+	0.154360i
$274$	−11.1017	+	19.2287i	−0.670678	+	1.16165i
$275$	1.25707	−	2.17731i	0.0758041	−	0.131297i
$276$	7.73840	−	7.33504i	0.465797	−	0.441517i
$277$	14.9627	+	25.9161i	0.899019	+	1.55715i	0.828751	+	0.559618i	$0.189052\pi$
$277$	14.9627	+	25.9161i	0.899019	+	1.55715i	0.0702680	+	0.997528i	$0.477615\pi$
$278$	7.25526			0.435142
$279$	0.0620117	−	1.15786i	0.00371254	−	0.0693190i
$280$	1.00000			0.0597614
$281$	15.4298	+	26.7253i	0.920467	+	1.59430i	0.798693	+	0.601738i	$0.205525\pi$
$281$	15.4298	+	26.7253i	0.920467	+	1.59430i	0.121774	+	0.992558i	$0.461142\pi$
$282$	1.06562	+	0.316316i	0.0634568	+	0.0188363i
$283$	−10.2498	+	17.7532i	−0.609287	+	1.05532i	0.382071	+	0.924133i	$0.375211\pi$
$283$	−10.2498	+	17.7532i	−0.609287	+	1.05532i	−0.991358	+	0.131184i	$0.958122\pi$
$284$	−5.31815	+	9.21131i	−0.315574	+	0.546591i
$285$	4.49546	+	1.33442i	0.266288	+	0.0790442i
$286$	1.90337	+	3.29674i	0.112549	+	0.194940i
$287$	10.7694			0.635698
$288$	0.160442	−	2.99571i	0.00945415	−	0.176524i
$289$	−16.8970			−0.993943
$290$	0.563816	+	0.976558i	0.0331084	+	0.0573455i
$291$	−3.28534	+	3.11410i	−0.192590	+	0.182552i
$292$	−2.82088	+	4.88592i	−0.165080	+	0.285927i
$293$	−4.14357	+	7.17688i	−0.242070	+	0.419278i	−0.961304	−	0.275490i	$-0.911160\pi$
$293$	−4.14357	+	7.17688i	−0.242070	+	0.419278i	0.719234	+	0.694768i	$0.244493\pi$
$294$	0.403374	+	1.68443i	0.0235252	+	0.0982377i
$295$	−6.16044	−	10.6702i	−0.358675	−	0.621243i
$296$	−5.86330			−0.340797
$297$	4.38197	−	12.3070i	0.254268	−	0.714125i
$298$	−11.6700			−0.676027
$299$	−4.66044	−	8.07212i	−0.269520	−	0.466823i
$300$	0.403374	+	1.68443i	0.0232888	+	0.0972504i
$301$	−5.01414	+	8.68474i	−0.289010	+	0.500580i
$302$	0.292611	−	0.506816i	0.0168379	−	0.0291640i
$303$	−18.9627	+	17.9742i	−1.08938	+	1.03259i
$304$	1.35369	+	2.34467i	0.0776397	+	0.134476i
$305$	−0.193252			−0.0110656
$306$	−0.806748	−	0.525224i	−0.0461187	−	0.0300251i
$307$	9.21245			0.525783			0.262891	−	0.964825i	$-0.415324\pi$
$307$	9.21245			0.525783			0.262891	+	0.964825i	$0.415324\pi$
$308$	1.25707	+	2.17731i	0.0716281	+	0.124064i
$309$	5.67912	+	1.68577i	0.323074	+	0.0959002i
$310$	−0.193252	+	0.334723i	−0.0109760	+	0.0190110i
$311$	−16.6983	+	28.9223i	−0.946875	+	1.64004i	−0.194921	+	0.980819i	$0.562445\pi$
$311$	−16.6983	+	28.9223i	−0.946875	+	1.64004i	−0.751954	+	0.659216i	$0.770888\pi$
$312$	−2.51414	−	0.746289i	−0.142335	−	0.0422503i
$313$	−4.38743	−	7.59926i	−0.247992	−	0.429535i	0.714976	−	0.699149i	$-0.246437\pi$
$313$	−4.38743	−	7.59926i	−0.247992	−	0.429535i	−0.962969	+	0.269613i	$0.913104\pi$
$314$	−5.95719			−0.336184
$315$	−2.67458	+	1.35891i	−0.150695	+	0.0765657i
$316$	−4.64177			−0.261120
$317$	−14.1532	−	24.5140i	−0.794921	−	1.37684i	−0.922889	−	0.385066i	$-0.874179\pi$
$317$	−14.1532	−	24.5140i	−0.794921	−	1.37684i	0.127968	−	0.991778i	$-0.459155\pi$
$318$	3.56382	−	3.37805i	0.199849	−	0.189432i
$319$	−1.41751	+	2.45520i	−0.0793654	+	0.137465i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−4.44486	−	18.5610i	−0.248088	−	1.03598i
$322$	−3.07795	−	5.33117i	−0.171528	−	0.297095i
$323$	0.868759			0.0483391
$324$	3.64177	+	8.23028i	0.202320	+	0.457238i
$325$	1.51414			0.0839892
$326$	7.88197	+	13.6520i	0.436542	+	0.756113i
$327$	6.69558	+	27.9597i	0.370267	+	1.54618i
$328$	−5.38470	+	9.32657i	−0.297320	+	0.514974i
$329$	0.320884	−	0.555788i	0.0176909	−	0.0306416i
$330$	−3.16044	+	2.99571i	−0.173977	+	0.164908i
$331$	−2.44852	−	4.24096i	−0.134583	−	0.233104i	0.790855	−	0.612003i	$-0.209636\pi$
$331$	−2.44852	−	4.24096i	−0.134583	−	0.233104i	−0.925438	+	0.378899i	$0.876303\pi$
$332$	−5.67004			−0.311184
$333$	15.6818	−	7.96767i	0.859360	−	0.436626i
$334$	7.22153			0.395144
$335$	0.546947	+	0.947340i	0.0298829	+	0.0517587i
$336$	−1.66044	−	0.492881i	−0.0905846	−	0.0268889i
$337$	−12.5876	+	21.8023i	−0.685688	+	1.18765i	0.287532	+	0.957771i	$0.407165\pi$
$337$	−12.5876	+	21.8023i	−0.685688	+	1.18765i	−0.973220	+	0.229875i	$0.926168\pi$
$338$	5.35369	−	9.27287i	0.291203	−	0.504378i
$339$	19.5333	+	5.79822i	1.06091	+	0.314916i
$340$	0.160442	+	0.277894i	0.00870120	+	0.0150709i
$341$	−0.971726			−0.0526219
$342$	−6.80675	−	4.43146i	−0.368067	−	0.239626i
$343$	1.00000			0.0539949
$344$	−5.01414	−	8.68474i	−0.270344	−	0.468250i
$345$	7.73840	−	7.33504i	0.416621	−	0.394905i
$346$	3.80675	−	6.59348i	0.204652	−	0.354468i
$347$	7.77394	−	13.4649i	0.417327	−	0.722831i	−0.578343	−	0.815794i	$-0.696300\pi$
$347$	7.77394	−	13.4649i	0.417327	−	0.722831i	0.995670	+	0.0929626i	$0.0296337\pi$
$348$	−0.454857	−	1.89941i	−0.0243829	−	0.101819i
$349$	16.3802	+	28.3713i	0.876810	+	1.51868i	0.854822	+	0.518921i	$0.173666\pi$
$349$	16.3802	+	28.3713i	0.876810	+	1.51868i	0.0219881	+	0.999758i	$0.493000\pi$
$350$	1.00000			0.0534522
$351$	7.73840	−	1.42047i	0.413045	−	0.0758189i
$352$	−2.51414			−0.134004
$353$	−4.66498	−	8.07998i	−0.248292	−	0.430054i	0.714760	−	0.699370i	$-0.246536\pi$
$353$	−4.66498	−	8.07998i	−0.248292	−	0.430054i	−0.963052	+	0.269316i	$0.913203\pi$
$354$	4.96992	+	20.7536i	0.264148	+	1.10304i
$355$	−5.31815	+	9.21131i	−0.282258	+	0.488886i
$356$	−8.02827	+	13.9054i	−0.425498	+	0.736984i
$357$	−0.403374	+	0.382348i	−0.0213488	+	0.0202360i
$358$	−1.66044	−	2.87597i	−0.0877571	−	0.152000i
$359$	24.7038			1.30382			0.651908	−	0.758298i	$-0.273969\pi$
$359$	24.7038			1.30382			0.651908	+	0.758298i	$0.273969\pi$
$360$	0.160442	−	2.99571i	0.00845605	−	0.157888i
$361$	−11.6700			−0.614213
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$	7.76940	+	2.30625i	0.407788	+	0.121047i
$364$	−0.757068	+	1.31128i	−0.0396812	+	0.0687298i
$365$	−2.82088	+	4.88592i	−0.147652	+	0.255740i
$366$	0.320884	+	0.0952504i	0.0167729	+	0.00497882i
$367$	8.60169	+	14.8986i	0.449005	+	0.777699i	0.998321	−	0.0579153i	$-0.0184453\pi$
$367$	8.60169	+	14.8986i	0.449005	+	0.777699i	−0.549317	+	0.835614i	$0.685112\pi$
$368$	6.15591			0.320899
$369$	1.72787	−	32.2620i	0.0899492	−	1.67949i
$370$	−5.86330			−0.304818
$371$	−1.41751	−	2.45520i	−0.0735935	−	0.127468i
$372$	0.485863	−	0.460538i	0.0251908	−	0.0238778i
$373$	−6.50506	+	11.2671i	−0.336819	+	0.583388i	−0.983833	−	0.179090i	$-0.942685\pi$
$373$	−6.50506	+	11.2671i	−0.336819	+	0.583388i	0.647013	+	0.762479i	$0.276018\pi$
$374$	−0.403374	+	0.698664i	−0.0208580	+	0.0361270i
$375$	0.403374	+	1.68443i	0.0208301	+	0.0869834i
$376$	0.320884	+	0.555788i	0.0165484	+	0.0286626i
$377$	−1.70739			−0.0879350
$378$	5.11076	−	0.938136i	0.262869	−	0.0482525i
$379$	−26.8633			−1.37987			−0.689937	−	0.723869i	$-0.742362\pi$
$379$	−26.8633			−1.37987			−0.689937	+	0.723869i	$0.742362\pi$
$380$	1.35369	+	2.34467i	0.0694431	+	0.120279i
$381$	2.38016	+	9.93919i	0.121940	+	0.509200i
$382$	−3.48586	+	6.03769i	−0.178352	+	0.308915i
$383$	1.87237	−	3.24304i	0.0956735	−	0.165711i	−0.814216	−	0.580562i	$-0.802833\pi$
$383$	1.87237	−	3.24304i	0.0956735	−	0.165711i	0.909890	+	0.414851i	$0.136166\pi$
$384$	1.25707	−	1.19154i	0.0641495	−	0.0608058i
$385$	1.25707	+	2.17731i	0.0640661	+	0.110966i
$386$	5.39197			0.274444
$387$	25.2125	+	16.4143i	1.28162	+	0.834385i
$388$	−2.61350			−0.132680
$389$	1.70739	+	2.95729i	0.0865681	+	0.149940i	0.906058	−	0.423153i	$-0.139077\pi$
$389$	1.70739	+	2.95729i	0.0865681	+	0.149940i	−0.819490	+	0.573093i	$0.805743\pi$
$390$	−2.51414	−	0.746289i	−0.127308	−	0.0377898i
$391$	0.987667	−	1.71069i	0.0499485	−	0.0865133i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−26.5051	−	7.86769i	−1.33700	−	0.396872i
$394$	−6.83775	−	11.8433i	−0.344481	−	0.596659i
$395$	−4.64177			−0.233553
$396$	6.72426	−	3.41648i	0.337907	−	0.171684i
$397$	−13.0711			−0.656019			−0.328009	−	0.944674i	$-0.606378\pi$
$397$	−13.0711			−0.656019			−0.328009	+	0.944674i	$0.606378\pi$
$398$	−13.2339	−	22.9217i	−0.663353	−	1.14896i
$399$	−3.40337	+	3.22598i	−0.170382	+	0.161501i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	4.91478	−	8.51265i	0.245432	−	0.425101i	−0.716821	−	0.697258i	$-0.754403\pi$
$401$	4.91478	−	8.51265i	0.245432	−	0.425101i	0.962253	+	0.272156i	$0.0877368\pi$
$402$	−0.441248	−	1.84258i	−0.0220075	−	0.0918997i
$403$	−0.292611	−	0.506816i	−0.0145760	−	0.0252463i
$404$	−15.0848			−0.750498
$405$	3.64177	+	8.23028i	0.180961	+	0.408966i
$406$	−1.12763			−0.0559634
$407$	−7.37056	−	12.7662i	−0.365345	−	0.632797i
$408$	−0.129436	−	0.540506i	−0.00640806	−	0.0267590i
$409$	15.6628	−	27.1287i	0.774474	−	1.34143i	−0.160615	−	0.987017i	$-0.551348\pi$
$409$	15.6628	−	27.1287i	0.774474	−	1.34143i	0.935089	−	0.354412i	$-0.115319\pi$
$410$	−5.38470	+	9.32657i	−0.265931	+	0.460607i
$411$	27.9112	−	26.4563i	1.37676	−	1.30499i
$412$	1.71012	+	2.96202i	0.0842516	+	0.145928i
$413$	12.3209			0.606271
$414$	−16.4645	+	8.36530i	−0.809184	+	0.411132i
$415$	−5.67004			−0.278331
$416$	−0.757068	−	1.31128i	−0.0371183	−	0.0642908i
$417$	−12.0469	−	3.57598i	−0.589942	−	0.175117i
$418$	−3.40337	+	5.89482i	−0.166464	+	0.288325i
$419$	−13.9813	+	24.2164i	−0.683033	+	1.18305i	0.291018	+	0.956717i	$0.406006\pi$
$419$	−13.9813	+	24.2164i	−0.683033	+	1.18305i	−0.974051	+	0.226330i	$0.927327\pi$
$420$	−1.66044	−	0.492881i	−0.0810213	−	0.0240501i
$421$	−4.30494	−	7.45638i	−0.209810	−	0.363402i	0.741844	−	0.670572i	$-0.233951\pi$
$421$	−4.30494	−	7.45638i	−0.209810	−	0.363402i	−0.951655	+	0.307170i	$0.900618\pi$
$422$	2.82956			0.137741
$423$	−1.61350	−	1.05045i	−0.0784508	−	0.0510745i
$424$	2.83502			0.137681
$425$	0.160442	+	0.277894i	0.00778259	+	0.0134798i
$426$	13.3706	−	12.6736i	0.647806	−	0.614040i
$427$	0.0966262	−	0.167362i	0.00467607	−	0.00809919i
$428$	5.50960	−	9.54291i	0.266317	−	0.461274i
$429$	−1.53554	−	6.41218i	−0.0741367	−	0.309583i
$430$	−5.01414	−	8.68474i	−0.241803	−	0.418815i
$431$	−37.5953			−1.81090			−0.905452	−	0.424448i	$-0.860468\pi$
$431$	−37.5953			−1.81090			−0.905452	+	0.424448i	$0.860468\pi$
$432$	−1.74293	+	4.89512i	−0.0838568	+	0.235517i
$433$	28.5279			1.37096			0.685481	−	0.728090i	$-0.259592\pi$
$433$	28.5279			1.37096			0.685481	+	0.728090i	$0.259592\pi$
$434$	−0.193252	−	0.334723i	−0.00927641	−	0.0160672i
$435$	−0.454857	−	1.89941i	−0.0218087	−	0.0910699i
$436$	−8.29948	+	14.3751i	−0.397473	+	0.688443i
$437$	8.33322	−	14.4336i	0.398632	−	0.690451i
$438$	7.09209	−	6.72242i	0.338873	−	0.321210i
$439$	−14.6113	−	25.3075i	−0.697359	−	1.20786i	−0.969379	−	0.245569i	$-0.921025\pi$
$439$	−14.6113	−	25.3075i	−0.697359	−	1.20786i	0.272020	−	0.962292i	$-0.412308\pi$
$440$	−2.51414			−0.119857
$441$	0.160442	−	2.99571i	0.00764011	−	0.142653i
$442$	−0.485863			−0.0231101
$443$	8.30675	+	14.3877i	0.394665	+	0.683581i	0.993058	−	0.117622i	$-0.0375271\pi$
$443$	8.30675	+	14.3877i	0.394665	+	0.683581i	−0.598393	+	0.801203i	$0.704194\pi$
$444$	9.73566	+	2.88991i	0.462034	+	0.137149i
$445$	−8.02827	+	13.9054i	−0.380577	+	0.659178i
$446$	6.73840	−	11.6712i	0.319072	−	0.552649i
$447$	19.3774	+	5.75194i	0.916521	+	0.272057i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−8.43398			−0.398024			−0.199012	−	0.979997i	$-0.563773\pi$
$449$	−8.43398			−0.398024			−0.199012	+	0.979997i	$0.563773\pi$
$450$	0.160442	−	2.99571i	0.00756332	−	0.141219i
$451$	−27.0757			−1.27495
$452$	5.88197	+	10.1879i	0.276665	+	0.479197i
$453$	−0.735663	+	0.697317i	−0.0345645	+	0.0327628i
$454$	−4.21012	+	7.29214i	−0.197591	+	0.342237i
$455$	−0.757068	+	1.31128i	−0.0354919	+	0.0614738i
$456$	−1.09209	−	4.56040i	−0.0511418	−	0.213560i
$457$	−10.7621	−	18.6406i	−0.503431	−	0.871969i	−0.999992	−	0.00396671i	$-0.998737\pi$
$457$	−10.7621	−	18.6406i	−0.503431	−	0.871969i	0.496561	−	0.868002i	$-0.334596\pi$
$458$	−23.5333			−1.09964
$459$	1.08068	+	1.26973i	0.0504421	+	0.0592661i
$460$	6.15591			0.287021
$461$	−5.06835	−	8.77864i	−0.236057	−	0.408862i	0.723523	−	0.690301i	$-0.242522\pi$
$461$	−5.06835	−	8.77864i	−0.236057	−	0.408862i	−0.959579	+	0.281439i	$0.909188\pi$
$462$	−1.01414	−	4.23488i	−0.0471819	−	0.197024i
$463$	1.83502	−	3.17835i	0.0852807	−	0.147710i	−0.820230	−	0.572034i	$-0.806155\pi$
$463$	1.83502	−	3.17835i	0.0852807	−	0.147710i	0.905511	+	0.424323i	$0.139488\pi$
$464$	0.563816	−	0.976558i	0.0261745	−	0.0453356i
$465$	0.485863	−	0.460538i	0.0225314	−	0.0213569i
$466$	−1.16317	−	2.01468i	−0.0538830	−	0.0933281i
$467$	9.70378			0.449037			0.224519	−	0.974470i	$-0.427919\pi$
$467$	9.70378			0.449037			0.224519	+	0.974470i	$0.427919\pi$
$468$	3.80675	+	2.47834i	0.175967	+	0.114561i
$469$	−1.09389			−0.0505113
$470$	0.320884	+	0.555788i	0.0148013	+	0.0256366i
$471$	9.89157	+	2.93618i	0.455779	+	0.135292i
$472$	−6.16044	+	10.6702i	−0.283557	+	0.491136i
$473$	12.6062	−	21.8346i	0.579635	−	1.00396i
$474$	7.70739	+	2.28784i	0.354012	+	0.105084i
$475$	1.35369	+	2.34467i	0.0621118	+	0.107581i
$476$	−0.320884			−0.0147077
$477$	−7.58249	+	3.85253i	−0.347178	+	0.176395i
$478$	4.38650			0.200634
$479$	−14.6541	−	25.3816i	−0.669563	−	1.15972i	−0.978026	−	0.208481i	$-0.933148\pi$
$479$	−14.6541	−	25.3816i	−0.669563	−	1.15972i	0.308463	−	0.951236i	$-0.400185\pi$
$480$	1.25707	−	1.19154i	0.0573771	−	0.0543863i
$481$	4.43892	−	7.68843i	0.202397	−	0.350562i
$482$	1.11076	−	1.92390i	0.0505939	−	0.0876312i
$483$	2.48313	+	10.3692i	0.112986	+	0.471813i
$484$	2.33956	+	4.05223i	0.106344	+	0.184192i
$485$	−2.61350			−0.118673
$486$	−1.99040	−	15.4609i	−0.0902863	−	0.701319i
$487$	16.4431			0.745106			0.372553	−	0.928011i	$-0.378483\pi$
$487$	16.4431			0.745106			0.372553	+	0.928011i	$0.378483\pi$
$488$	0.0966262	+	0.167362i	0.00437406	+	0.00757610i
$489$	−6.35876	−	26.5532i	−0.287553	−	1.20078i
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	3.49727	−	6.05745i	0.157829	−	0.273369i	−0.776256	−	0.630418i	$-0.782884\pi$
$491$	3.49727	−	6.05745i	0.157829	−	0.273369i	0.934086	+	0.357049i	$0.116217\pi$
$492$	13.5379	−	12.8322i	0.610335	−	0.578521i
$493$	−0.180920	−	0.313362i	−0.00814822	−	0.0141131i
$494$	−4.09936			−0.184439
$495$	6.72426	−	3.41648i	0.302233	−	0.153559i
$496$	0.386505			0.0173546
$497$	−5.31815	−	9.21131i	−0.238552	−	0.413184i
$498$	9.41478	+	2.79466i	0.421886	+	0.125232i
$499$	13.5406	−	23.4530i	0.606161	−	1.04990i	−0.385706	−	0.922622i	$-0.626042\pi$
$499$	13.5406	−	23.4530i	0.606161	−	1.04990i	0.991867	−	0.127280i	$-0.0406245\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−11.9909	−	3.55935i	−0.535715	−	0.159020i
$502$	8.78354	+	15.2135i	0.392028	+	0.679013i
$503$	12.1878			0.543427			0.271713	−	0.962378i	$-0.412410\pi$
$503$	12.1878			0.543427			0.271713	+	0.962378i	$0.412410\pi$
$504$	2.51414	+	1.63680i	0.111989	+	0.0729089i
$505$	−15.0848			−0.671266
$506$	7.73840	+	13.4033i	0.344014	+	0.595849i
$507$	−13.4599	+	12.7583i	−0.597776	+	0.566617i
$508$	−2.95032	+	5.11011i	−0.130899	+	0.226724i
$509$	4.34643	−	7.52823i	0.192652	−	0.333683i	−0.753476	−	0.657475i	$-0.771624\pi$
$509$	4.34643	−	7.52823i	0.192652	−	0.333683i	0.946128	+	0.323792i	$0.104958\pi$
$510$	−0.129436	−	0.540506i	−0.00573154	−	0.0239340i
$511$	−2.82088	−	4.88592i	−0.124789	−	0.216140i
$512$	1.00000			0.0441942
$513$	9.11803	+	10.7131i	0.402571	+	0.472995i
$514$	−19.3684			−0.854302
$515$	1.71012	+	2.96202i	0.0753570	+	0.130522i
$516$	4.04514	+	16.8919i	0.178077	+	0.743624i
$517$	−0.806748	+	1.39733i	−0.0354807	+	0.0614544i
$518$	2.93165	−	5.07776i	0.128809	−	0.223104i
$519$	−9.57068	+	9.07182i	−0.420106	+	0.398209i
$520$	−0.757068	−	1.31128i	−0.0331996	−	0.0575035i
$521$	15.2498			0.668106			0.334053	−	0.942554i	$-0.391584\pi$
$521$	15.2498			0.668106			0.334053	+	0.942554i	$0.391584\pi$
$522$	−0.180920	+	3.37805i	−0.00791865	+	0.147853i
$523$	−20.1323			−0.880324			−0.440162	−	0.897918i	$-0.645079\pi$
$523$	−20.1323			−0.880324			−0.440162	+	0.897918i	$0.645079\pi$
$524$	−7.98133	−	13.8241i	−0.348666	−	0.603907i
$525$	−1.66044	−	0.492881i	−0.0724676	−	0.0215111i
$526$	3.56382	−	6.17271i	0.155390	−	0.269143i
$527$	0.0620117	−	0.107407i	0.00270127	−	0.00467874i
$528$	4.17458	+	1.23917i	0.181675	+	0.0539280i
$529$	−7.44759	−	12.8996i	−0.323808	−	0.560852i
$530$	2.83502			0.123145
$531$	1.97679	−	36.9098i	0.0857854	−	1.60175i
$532$	−2.70739			−0.117380
$533$	−8.15317	−	14.1217i	−0.353153	−	0.611679i
$534$	20.1842	−	19.1321i	0.873455	−	0.827927i
$535$	5.50960	−	9.54291i	0.238201	−	0.412576i
$536$	0.546947	−	0.947340i	0.0236245	−	0.0409189i
$537$	1.33956	+	5.59378i	0.0578062	+	0.241390i
$538$	−7.83229	−	13.5659i	−0.337674	−	0.584868i
$539$	−2.51414			−0.108292
$540$	−1.74293	+	4.89512i	−0.0750038	+	0.210652i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	10.5921	+	18.3460i	0.454969	+	0.788030i
$543$	−4.03374	−	16.8443i	−0.173104	−	0.722856i
$544$	0.160442	−	0.277894i	0.00687890	−	0.0119146i
$545$	−8.29948	+	14.3751i	−0.355511	+	0.615762i
$546$	1.90337	−	1.80416i	0.0814569	−	0.0772110i
$547$	19.9713	+	34.5914i	0.853912	+	1.47902i	0.877650	+	0.479301i	$0.159110\pi$
$547$	19.9713	+	34.5914i	0.853912	+	1.47902i	−0.0237382	+	0.999718i	$0.507557\pi$
$548$	22.2034			0.948481
$549$	−0.485863	−	0.316316i	−0.0207361	−	0.0135000i
$550$	−2.51414			−0.107203
$551$	−1.52647	−	2.64392i	−0.0650298	−	0.112635i
$552$	−10.2215	−	3.03413i	−0.435057	−	0.129141i
$553$	2.32088	−	4.01989i	0.0986940	−	0.170943i
$554$	14.9627	−	25.9161i	0.635702	−	1.10107i
$555$	9.73566	+	2.88991i	0.413256	+	0.122670i
$556$	−3.62763	−	6.28324i	−0.153846	−	0.266469i
$557$	−19.4713			−0.825027			−0.412513	−	0.910952i	$-0.635349\pi$
$557$	−19.4713			−0.825027			−0.412513	+	0.910952i	$0.635349\pi$
$558$	−1.03374	+	0.525224i	−0.0437616	+	0.0222345i
$559$	15.1842			0.642222
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$	1.01414	−	0.961276i	0.0428169	−	0.0405851i
$562$	15.4298	−	26.7253i	0.650869	−	1.12734i
$563$	−21.6910	+	37.5700i	−0.914169	+	1.58339i	−0.106055	+	0.994360i	$0.533822\pi$
$563$	−21.6910	+	37.5700i	−0.914169	+	1.58339i	−0.808114	+	0.589026i	$0.799511\pi$
$564$	−0.258873	−	1.08101i	−0.0109005	−	0.0455188i
$565$	5.88197	+	10.1879i	0.247456	+	0.428607i
$566$	20.4996			0.861662
$567$	−8.94852	−	0.961276i	−0.375802	−	0.0403698i
$568$	10.6363			0.446289
$569$	−16.1459	−	27.9655i	−0.676872	−	1.17238i	−0.975918	−	0.218137i	$-0.930002\pi$
$569$	−16.1459	−	27.9655i	−0.676872	−	1.17238i	0.299046	−	0.954239i	$-0.403331\pi$
$570$	−1.09209	−	4.56040i	−0.0457426	−	0.191014i
$571$	16.2667	−	28.1747i	0.680739	−	1.17907i	−0.294017	−	0.955800i	$-0.594992\pi$
$571$	16.2667	−	28.1747i	0.680739	−	1.17907i	0.974756	−	0.223274i	$-0.0716745\pi$
$572$	1.90337	−	3.29674i	0.0795841	−	0.137844i
$573$	8.76394	−	8.30712i	0.366119	−	0.347035i
$574$	−5.38470	−	9.32657i	−0.224753	−	0.389284i
$575$	6.15591			0.256719
$576$	−2.67458	+	1.35891i	−0.111441	+	0.0566211i
$577$	1.86690			0.0777202			0.0388601	−	0.999245i	$-0.487627\pi$
$577$	1.86690			0.0777202			0.0388601	+	0.999245i	$0.487627\pi$
$578$	8.44852	+	14.6333i	0.351412	+	0.608663i
$579$	−8.95305	−	2.65760i	−0.372076	−	0.110446i
$580$	0.563816	−	0.976558i	0.0234112	−	0.0405494i
$581$	2.83502	−	4.91040i	0.117617	−	0.203718i
$582$	4.33956	+	1.28814i	0.179880	+	0.0533952i
$583$	3.56382	+	6.17271i	0.147598	+	0.255648i
$584$	5.64177			0.233458
$585$	3.80675	+	2.47834i	0.157390	+	0.102467i
$586$	8.28715			0.342339
$587$	0.0583520	+	0.101069i	0.00240845	+	0.00417155i	0.867227	−	0.497913i	$-0.165900\pi$
$587$	0.0583520	+	0.101069i	0.00240845	+	0.00417155i	−0.864819	+	0.502084i	$0.832567\pi$
$588$	1.25707	−	1.19154i	0.0518406	−	0.0491385i
$589$	0.523210	−	0.906226i	0.0215585	−	0.0373404i
$590$	−6.16044	+	10.6702i	−0.253621	+	0.439285i
$591$	5.51634	+	23.0354i	0.226912	+	0.947549i
$592$	2.93165	+	5.07776i	0.120490	+	0.208695i
$593$	−12.2179			−0.501730			−0.250865	−	0.968022i	$-0.580715\pi$
$593$	−12.2179			−0.501730			−0.250865	+	0.968022i	$0.580715\pi$
$594$	−12.8492	+	2.35860i	−0.527207	+	0.0967747i
$595$	−0.320884			−0.0131550
$596$	5.83502	+	10.1066i	0.239012	+	0.413981i
$597$	10.6764	+	44.5829i	0.436955	+	1.82466i
$598$	−4.66044	+	8.07212i	−0.190580	+	0.330094i
$599$	−8.99093	+	15.5727i	−0.367359	+	0.636285i	−0.989152	−	0.146897i	$-0.953071\pi$
$599$	−8.99093	+	15.5727i	−0.367359	+	0.636285i	0.621792	+	0.783182i	$0.286405\pi$
$600$	1.25707	−	1.19154i	0.0513196	−	0.0486446i
$601$	18.8988	+	32.7337i	0.770900	+	1.33524i	0.937070	+	0.349140i	$0.113526\pi$
$601$	18.8988	+	32.7337i	0.770900	+	1.33524i	−0.166171	+	0.986097i	$0.553140\pi$
$602$	10.0283			0.408722
$603$	−0.175507	+	3.27699i	−0.00714719	+	0.133449i
$604$	−0.585221			−0.0238123
$605$	2.33956	+	4.05223i	0.0951165	+	0.164747i
$606$	25.0475	+	7.43502i	1.01748	+	0.302027i
$607$	−8.05655	+	13.9543i	−0.327005	+	0.566390i	−0.981916	−	0.189316i	$-0.939373\pi$
$607$	−8.05655	+	13.9543i	−0.327005	+	0.566390i	0.654911	+	0.755706i	$0.272706\pi$
$608$	1.35369	−	2.34467i	0.0548996	−	0.0950888i
$609$	1.87237	+	0.555788i	0.0758722	+	0.0225217i
$610$	0.0966262	+	0.167362i	0.00391228	+	0.00677627i
$611$	−0.971726			−0.0393118
$612$	−0.0514834	+	0.961276i	−0.00208109	+	0.0388573i
$613$	38.1696			1.54166			0.770829	−	0.637042i	$-0.219842\pi$
$613$	38.1696			1.54166			0.770829	+	0.637042i	$0.219842\pi$
$614$	−4.60623	−	7.97822i	−0.185892	−	0.321975i
$615$	13.5379	−	12.8322i	0.545900	−	0.517445i
$616$	1.25707	−	2.17731i	0.0506487	−	0.0877262i
$617$	−0.176384	+	0.305505i	−0.00710093	+	0.0122992i	−0.869554	−	0.493838i	$-0.835594\pi$
$617$	−0.176384	+	0.305505i	−0.00710093	+	0.0122992i	0.862453	+	0.506137i	$0.168927\pi$
$618$	−1.37964	−	5.76114i	−0.0554971	−	0.231747i
$619$	−14.7407	−	25.5317i	−0.592480	−	1.02621i	−0.993897	−	0.110310i	$-0.964816\pi$
$619$	−14.7407	−	25.5317i	−0.592480	−	1.02621i	0.401417	−	0.915895i	$-0.368518\pi$
$620$	0.386505			0.0155224
$621$	31.4614	−	5.77508i	1.26250	−	0.231746i
$622$	33.3966			1.33908
$623$	−8.02827	−	13.9054i	−0.321646	−	0.557107i
$624$	0.610763	+	2.55045i	0.0244501	+	0.102100i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.38743	+	7.59926i	−0.175357	+	0.303727i
$627$	8.55655	−	8.11054i	0.341716	−	0.323904i
$628$	2.97859	+	5.15908i	0.118859	+	0.205870i
$629$	1.88144			0.0750179
$630$	2.51414	+	1.63680i	0.100166	+	0.0652117i
$631$	−8.63631			−0.343806			−0.171903	−	0.985114i	$-0.554992\pi$
$631$	−8.63631			−0.343806			−0.171903	+	0.985114i	$0.554992\pi$
$632$	2.32088	+	4.01989i	0.0923198	+	0.159903i
$633$	−4.69832	−	1.39463i	−0.186741	−	0.0554318i
$634$	−14.1532	+	24.5140i	−0.562094	+	0.973576i
$635$	−2.95032	+	5.11011i	−0.117080	+	0.202788i
$636$	−4.70739	−	1.39733i	−0.186660	−	0.0554077i
$637$	−0.757068	−	1.31128i	−0.0299961	−	0.0519548i
$638$	2.83502			0.112240
$639$	−28.4476	+	14.4537i	−1.12537	+	0.571781i
$640$	1.00000			0.0395285
$641$	16.0611	+	27.8186i	0.634375	+	1.09877i	0.986647	+	0.162872i	$0.0520757\pi$
$641$	16.0611	+	27.8186i	0.634375	+	1.09877i	−0.352273	+	0.935897i	$0.614591\pi$
$642$	−13.8519	+	13.1299i	−0.546691	+	0.518195i
$643$	20.4791	−	35.4709i	0.807618	−	1.39883i	−0.106892	−	0.994271i	$-0.534090\pi$
$643$	20.4791	−	35.4709i	0.807618	−	1.39883i	0.914510	−	0.404564i	$-0.132577\pi$
$644$	−3.07795	+	5.33117i	−0.121288	+	0.210078i
$645$	4.04514	+	16.8919i	0.159277	+	0.665117i
$646$	−0.434380	−	0.752368i	−0.0170904	−	0.0296015i
$647$	6.20418			0.243912			0.121956	−	0.992536i	$-0.461083\pi$
$647$	6.20418			0.243912			0.121956	+	0.992536i	$0.461083\pi$
$648$	5.30675	−	7.26900i	0.208469	−	0.285553i
$649$	−30.9764			−1.21593
$650$	−0.757068	−	1.31128i	−0.0296947	−	0.0514327i
$651$	0.155906	+	0.651039i	0.00611044	+	0.0255162i
$652$	7.88197	−	13.6520i	0.308682	−	0.534652i
$653$	3.97173	−	6.87923i	0.155426	−	0.269205i	−0.777788	−	0.628526i	$-0.783658\pi$
$653$	3.97173	−	6.87923i	0.155426	−	0.269205i	0.933214	+	0.359321i	$0.116992\pi$
$654$	20.8660	−	19.7784i	0.815926	−	0.773397i
$655$	−7.98133	−	13.8241i	−0.311856	−	0.540151i
$656$	10.7694			0.420474
$657$	−15.0894	+	7.66664i	−0.588692	+	0.299104i
$658$	−0.641769			−0.0250188
$659$	−2.67912	−	4.64036i	−0.104364	−	0.180763i	0.809114	−	0.587651i	$-0.199947\pi$
$659$	−2.67912	−	4.64036i	−0.104364	−	0.180763i	−0.913478	+	0.406888i	$0.866614\pi$
$660$	4.17458	+	1.23917i	0.162495	+	0.0482346i
$661$	−5.95719	+	10.3182i	−0.231708	+	0.401330i	−0.958311	−	0.285728i	$-0.907765\pi$
$661$	−5.95719	+	10.3182i	−0.231708	+	0.401330i	0.726603	+	0.687058i	$0.241098\pi$
$662$	−2.44852	+	4.24096i	−0.0951643	+	0.164829i
$663$	0.806748	+	0.239473i	0.0313315	+	0.00930035i
$664$	2.83502	+	4.91040i	0.110020	+	0.190561i
$665$	−2.70739			−0.104988
$666$	−14.7411	−	9.59704i	−0.571207	−	0.371878i
$667$	−6.94160			−0.268780
$668$	−3.61076	−	6.25403i	−0.139705	−	0.241976i
$669$	−16.9412	+	16.0582i	−0.654986	+	0.620846i
$670$	0.546947	−	0.947340i	0.0211304	−	0.0365989i
$671$	−0.242932	+	0.420770i	−0.00937827	+	0.0162436i
$672$	0.403374	+	1.68443i	0.0155605	+	0.0649781i
$673$	−5.54241	−	9.59974i	−0.213644	−	0.370043i	0.739208	−	0.673477i	$-0.235200\pi$
$673$	−5.54241	−	9.59974i	−0.213644	−	0.370043i	−0.952852	+	0.303434i	$0.901867\pi$
$674$	25.1751			0.969709
$675$	−1.74293	+	4.89512i	−0.0670855	+	0.188413i
$676$	−10.7074			−0.411823
$677$	4.52647	+	7.84008i	0.173966	+	0.301319i	0.939803	−	0.341717i	$-0.111008\pi$
$677$	4.52647	+	7.84008i	0.173966	+	0.301319i	−0.765837	+	0.643035i	$0.777675\pi$
$678$	−4.74526	−	19.8155i	−0.182241	−	0.761009i
$679$	1.30675	−	2.26335i	0.0501484	−	0.0868595i
$680$	0.160442	−	0.277894i	0.00615268	−	0.0106568i
$681$	10.5848	−	10.0331i	0.405611	−	0.384469i
$682$	0.485863	+	0.841540i	0.0186047	+	0.0322242i
$683$	−1.74659			−0.0668315			−0.0334157	−	0.999442i	$-0.510639\pi$
$683$	−1.74659			−0.0668315			−0.0334157	+	0.999442i	$0.510639\pi$
$684$	−0.434380	+	8.11054i	−0.0166089	+	0.310114i
$685$	22.2034			0.848348
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	39.0757	+	11.5991i	1.49083	+	0.442534i
$688$	−5.01414	+	8.68474i	−0.191162	+	0.331103i
$689$	−2.14631	+	3.71751i	−0.0817677	+	0.141626i
$690$	−10.2215	−	3.03413i	−0.389127	−	0.115507i
$691$	−11.2835	−	19.5437i	−0.429246	−	0.743476i	0.567560	−	0.823332i	$-0.307887\pi$
$691$	−11.2835	−	19.5437i	−0.429246	−	0.743476i	−0.996806	+	0.0798559i	$0.974554\pi$
$692$	−7.61350			−0.289422
$693$	−0.403374	+	7.53162i	−0.0153229	+	0.286102i
$694$	−15.5479			−0.590189
$695$	−3.62763	−	6.28324i	−0.137604	−	0.238337i
$696$	−1.41751	+	1.34362i	−0.0537306	+	0.0509299i
$697$	1.72787	−	2.99275i	0.0654476	−	0.113359i
$698$	16.3802	−	28.3713i	0.619998	−	1.07387i
$699$	0.938388	+	3.91856i	0.0354931	+	0.148214i
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	41.4778			1.56660			0.783298	−	0.621646i	$-0.213536\pi$
$701$	41.4778			1.56660			0.783298	+	0.621646i	$0.213536\pi$
$702$	−5.09936	−	5.99141i	−0.192463	−	0.226131i
$703$	15.8742			0.598708
$704$	1.25707	+	2.17731i	0.0473776	+	0.0820603i
$705$	−0.258873	−	1.08101i	−0.00974971	−	0.0407133i
$706$	−4.66498	+	8.07998i	−0.175569	+	0.304094i
$707$	7.54241	−	13.0638i	0.283662	−	0.491316i
$708$	15.4882	−	14.6809i	0.582082	−	0.551741i
$709$	23.0780	+	39.9722i	0.866711	+	1.50119i	0.865338	+	0.501188i	$0.167103\pi$
$709$	23.0780	+	39.9722i	0.866711	+	1.50119i	0.00137226	+	0.999999i	$0.499563\pi$
$710$	10.6363			0.399173
$711$	−11.6700	−	7.59765i	−0.437661	−	0.284934i
$712$	16.0565			0.601745
$713$	−1.18964	−	2.06052i	−0.0445525	−	0.0771672i
$714$	0.532810	+	0.158158i	0.0199399	+	0.00591891i
$715$	1.90337	−	3.29674i	0.0711821	−	0.123291i
$716$	−1.66044	+	2.87597i	−0.0620536	+	0.107480i
$717$	−7.28354	−	2.16202i	−0.272009	−	0.0807423i
$718$	−12.3519	−	21.3941i	−0.460968	−	0.798421i
$719$	−20.7230			−0.772837			−0.386418	−	0.922324i	$-0.626288\pi$
$719$	−20.7230			−0.772837			−0.386418	+	0.922324i	$0.626288\pi$
$720$	−2.67458	+	1.35891i	−0.0996757	+	0.0506434i
$721$	−3.42024			−0.127376
$722$	5.83502	+	10.1066i	0.217157	+	0.376127i
$723$	−2.79261	+	2.64705i	−0.103858	+	0.0984448i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	0.563816	−	0.976558i	0.0209396	−	0.0362685i
$726$	−1.88743	−	7.88162i	−0.0700492	−	0.292514i
$727$	7.86603	+	13.6244i	0.291735	+	0.505300i	0.974220	−	0.225600i	$-0.0724342\pi$
$727$	7.86603	+	13.6244i	0.291735	+	0.505300i	−0.682485	+	0.730899i	$0.739101\pi$
$728$	1.51414			0.0561176
$729$	−4.31542	+	26.6529i	−0.159830	+	0.987144i
$730$	5.64177			0.208811
$731$	1.60896	+	2.78680i	0.0595095	+	0.103073i
$732$	−0.0779530	−	0.325519i	−0.00288122	−	0.0120315i
$733$	−17.0406	+	29.5152i	−0.629409	+	1.09017i	0.358261	+	0.933621i	$0.383370\pi$
$733$	−17.0406	+	29.5152i	−0.629409	+	1.09017i	−0.987670	+	0.156547i	$0.949964\pi$
$734$	8.60169	−	14.8986i	0.317494	−	0.549916i
$735$	1.25707	−	1.19154i	0.0463677	−	0.0439508i
$736$	−3.07795	−	5.33117i	−0.113455	−	0.196510i
$737$	2.75020			0.101305
$738$	−28.8036	+	14.6346i	−1.06028	+	0.538707i
$739$	−8.50321			−0.312796			−0.156398	−	0.987694i	$-0.549988\pi$
$739$	−8.50321			−0.312796			−0.156398	+	0.987694i	$0.549988\pi$
$740$	2.93165	+	5.07776i	0.107770	+	0.186662i
$741$	6.80675	+	2.02050i	0.250052	+	0.0742247i
$742$	−1.41751	+	2.45520i	−0.0520385	+	0.0901332i
$743$	14.6700	−	25.4093i	0.538192	−	0.932175i	−0.460810	−	0.887499i	$-0.652441\pi$
$743$	14.6700	−	25.4093i	0.538192	−	0.932175i	0.999002	−	0.0446764i	$-0.0142257\pi$
$744$	−0.641769	−	0.190501i	−0.0235284	−	0.00698410i
$745$	5.83502	+	10.1066i	0.213779	+	0.370275i
$746$	13.0101			0.476335
$747$	−14.2553	−	9.28073i	−0.521573	−	0.339564i
$748$	0.806748			0.0294976
$749$	5.50960	+	9.54291i	0.201316	+	0.348690i
$750$	1.25707	−	1.19154i	0.0459017	−	0.0435091i
$751$	17.6017	−	30.4870i	0.642295	−	1.11249i	−0.342624	−	0.939472i	$-0.611316\pi$
$751$	17.6017	−	30.4870i	0.642295	−	1.11249i	0.984919	−	0.173015i	$-0.0553508\pi$
$752$	0.320884	−	0.555788i	0.0117015	−	0.0202675i
$753$	−7.08610	−	29.5904i	−0.258232	−	1.07834i
$754$	0.853695	+	1.47864i	0.0310897	+	0.0538490i
$755$	−0.585221			−0.0212984
$756$	−3.36783	−	3.95698i	−0.122487	−	0.143914i
$757$	−36.8350			−1.33879			−0.669396	−	0.742906i	$-0.733447\pi$
$757$	−36.8350			−1.33879			−0.669396	+	0.742906i	$0.733447\pi$
$758$	13.4316	+	23.2643i	0.487859	+	0.844997i
$759$	−6.24293	−	26.0695i	−0.226604	−	0.946263i
$760$	1.35369	−	2.34467i	0.0491037	−	0.0850500i
$761$	−3.40571	+	5.89886i	−0.123457	+	0.213833i	−0.921129	−	0.389258i	$-0.872731\pi$
$761$	−3.40571	+	5.89886i	−0.123457	+	0.213833i	0.797672	+	0.603092i	$0.206065\pi$
$762$	7.41751	−	7.03088i	0.268708	−	0.254702i
$763$	−8.29948	−	14.3751i	−0.300461	−	0.520414i
$764$	6.97173			0.252228
$765$	−0.0514834	+	0.961276i	−0.00186139	+	0.0347550i
$766$	−3.74474			−0.135303
$767$	−9.32775	−	16.1561i	−0.336806	−	0.583364i
$768$	−1.66044	−	0.492881i	−0.0599160	−	0.0177853i
$769$	14.9476	−	25.8900i	0.539024	−	0.933617i	−0.459933	−	0.887954i	$-0.652127\pi$
$769$	14.9476	−	25.8900i	0.539024	−	0.933617i	0.998957	−	0.0456631i	$-0.0145401\pi$
$770$	1.25707	−	2.17731i	0.0453016	−	0.0784647i
$771$	32.1600	+	9.54629i	1.15822	+	0.343801i
$772$	−2.69598	−	4.66958i	−0.0970306	−	0.168062i
$773$	−42.0137			−1.51113			−0.755565	−	0.655074i	$-0.772637\pi$
$773$	−42.0137			−1.51113			−0.755565	+	0.655074i	$0.772637\pi$
$774$	1.60896	−	30.0418i	0.0578328	−	1.07983i
$775$	0.386505			0.0138837
$776$	1.30675	+	2.26335i	0.0469095	+	0.0812496i
$777$	−7.37056	+	6.98638i	−0.264417	+	0.250635i
$778$	1.70739	−	2.95729i	0.0612129	−	0.106024i
$779$	14.5785	−	25.2507i	0.522328	−	0.904699i
$780$	0.610763	+	2.55045i	0.0218688	+	0.0913208i
$781$	13.3706	+	23.1585i	0.478436	+	0.828676i
$782$	−1.97533			−0.0706378
$783$	1.96539	−	5.51989i	0.0702371	−	0.197265i
$784$	1.00000			0.0357143
$785$	2.97859	+	5.15908i	0.106311	+	0.184135i
$786$	6.43892	+	26.8879i	0.229669	+	0.959060i
$787$	−20.7603	+	35.9579i	−0.740026	+	1.28176i	0.212457	+	0.977170i	$0.431853\pi$
$787$	−20.7603	+	35.9579i	−0.740026	+	1.28176i	−0.952483	+	0.304592i	$0.901480\pi$
$788$	−6.83775	+	11.8433i	−0.243585	+	0.421901i
$789$	−8.95992	+	8.49289i	−0.318982	+	0.302355i
$790$	2.32088	+	4.01989i	0.0825734	+	0.143021i
$791$	−11.7639			−0.418277
$792$	−6.32088	−	4.11514i	−0.224603	−	0.146225i
$793$	−0.292611			−0.0103909
$794$	6.53554	+	11.3199i	0.231938	+	0.401728i
$795$	−4.70739	−	1.39733i	−0.166954	−	0.0495581i
$796$	−13.2339	+	22.9217i	−0.469062	+	0.812439i
$797$	−17.5051	+	30.3197i	−0.620061	+	1.07398i	0.369413	+	0.929265i	$0.379559\pi$
$797$	−17.5051	+	30.3197i	−0.620061	+	1.07398i	−0.989474	+	0.144712i	$0.953774\pi$
$798$	4.49546	+	1.33442i	0.159138	+	0.0472380i
$799$	−0.102967	−	0.178344i	−0.00364271	−	0.00630935i
$800$	1.00000			0.0353553
$801$	−42.9445	+	21.8193i	−1.51737	+	0.770949i
$802$	−9.82956			−0.347094
$803$	7.09209	+	12.2839i	0.250274	+	0.433488i
$804$	−1.37510	+	1.30342i	−0.0484960	+	0.0459682i
$805$	−3.07795	+	5.33117i	−0.108484	+	0.187899i
$806$	−0.292611	+	0.506816i	−0.0103068	+	0.0178518i
$807$	6.31868	+	26.3858i	0.222428	+	0.928825i
$808$	7.54241	+	13.0638i	0.265341	+	0.459584i
$809$	−50.1040			−1.76156			−0.880782	−	0.473522i	$-0.842982\pi$
$809$	−50.1040			−1.76156			−0.880782	+	0.473522i	$0.842982\pi$
$810$	5.30675	−	7.26900i	0.186460	−	0.255407i
$811$	−34.7749			−1.22111			−0.610555	−	0.791974i	$-0.709054\pi$
$811$	−34.7749			−1.22111			−0.610555	+	0.791974i	$0.709054\pi$
$812$	0.563816	+	0.976558i	0.0197861	+	0.0342705i
$813$	−8.54514	−	35.6832i	−0.299691	−	1.25146i
$814$	−7.37056	+	12.7662i	−0.258338	+	0.447455i
$815$	7.88197	−	13.6520i	0.276093	−	0.478208i
$816$	−0.403374	+	0.382348i	−0.0141209	+	0.0133849i
$817$	13.5752	+	23.5130i	0.474937	+	0.822615i
$818$	−31.3255			−1.09527
$819$	−4.04968	+	2.05757i	−0.141507	+	0.0718973i
$820$	10.7694			0.376084
$821$	17.4271	+	30.1846i	0.608210	+	1.05345i	0.991535	+	0.129838i	$0.0414456\pi$
$821$	17.4271	+	30.1846i	0.608210	+	1.05345i	−0.383325	+	0.923614i	$0.625221\pi$
$822$	−36.8674	−	10.9436i	−1.28590	−	0.381703i
$823$	11.7425	−	20.3387i	0.409319	−	0.708961i	−0.585495	−	0.810676i	$-0.699100\pi$
$823$	11.7425	−	20.3387i	0.409319	−	0.708961i	0.994814	+	0.101715i	$0.0324330\pi$
$824$	1.71012	−	2.96202i	0.0595749	−	0.103187i
$825$	4.17458	+	1.23917i	0.145340	+	0.0431424i
$826$	−6.16044	−	10.6702i	−0.214349	−	0.371264i
$827$	−33.6327			−1.16952			−0.584762	−	0.811205i	$-0.698812\pi$
$827$	−33.6327			−1.16952			−0.584762	+	0.811205i	$0.698812\pi$
$828$	15.4768	+	10.0760i	0.537856	+	0.350165i
$829$	52.4249			1.82079			0.910396	−	0.413738i	$-0.135777\pi$
$829$	52.4249			1.82079			0.910396	+	0.413738i	$0.135777\pi$
$830$	2.83502	+	4.91040i	0.0984050	+	0.170443i
$831$	−37.6182	+	35.6573i	−1.30496	+	1.23694i
$832$	−0.757068	+	1.31128i	−0.0262466	+	0.0454605i
$833$	0.160442	−	0.277894i	0.00555899	−	0.00962846i
$834$	2.92658	+	12.2210i	0.101339	+	0.423177i
$835$	−3.61076	−	6.25403i	−0.124956	−	0.216429i
$836$	6.80675			0.235416
$837$	1.97533	−	0.362594i	0.0682776	−	0.0125331i
$838$	27.9627			0.965954
$839$	−1.22373	−	2.11956i	−0.0422479	−	0.0731754i	0.844128	−	0.536141i	$-0.180119\pi$
$839$	−1.22373	−	2.11956i	−0.0422479	−	0.0731754i	−0.886376	+	0.462966i	$0.846785\pi$
$840$	0.403374	+	1.68443i	0.0139177	+	0.0581182i
$841$	13.8642	−	24.0135i	0.478077	−	0.828053i
$842$	−4.30494	+	7.45638i	−0.148358	+	0.256964i
$843$	−38.7927	+	36.7707i	−1.33609	+	1.26645i
$844$	−1.41478	−	2.45047i	−0.0486987	−	0.0843486i
$845$	−10.7074			−0.368345
$846$	−0.102967	+	1.92255i	−0.00354007	+	0.0660987i
$847$	−4.67912			−0.160776
$848$	−1.41751	−	2.45520i	−0.0486775	−	0.0843119i
$849$	−34.0384	−	10.1039i	−1.16819	−	0.346764i
$850$	0.160442	−	0.277894i	0.00550312	−	0.00953169i
$851$	18.0469	−	31.2582i	0.618641	−	1.07152i
$852$	−17.6610	−	5.24243i	−0.605055	−	0.179603i
$853$	6.35462	+	11.0065i	0.217578	+	0.376856i	0.954067	−	0.299593i	$-0.0968510\pi$
$853$	6.35462	+	11.0065i	0.217578	+	0.376856i	−0.736489	+	0.676450i	$0.763518\pi$
$854$	−0.193252			−0.00661296
$855$	−0.434380	+	8.11054i	−0.0148555	+	0.277375i
$856$	−11.0192			−0.376629
$857$	−20.0041	−	34.6482i	−0.683328	−	1.18356i	−0.973959	−	0.226724i	$-0.927198\pi$
$857$	−20.0041	−	34.6482i	−0.683328	−	1.18356i	0.290631	−	0.956835i	$-0.406135\pi$
$858$	−4.78534	+	4.53591i	−0.163369	+	0.154853i
$859$	21.0292	−	36.4236i	0.717507	−	1.24276i	−0.244477	−	0.969655i	$-0.578616\pi$
$859$	21.0292	−	36.4236i	0.717507	−	1.24276i	0.961985	−	0.273104i	$-0.0880502\pi$
$860$	−5.01414	+	8.68474i	−0.170981	+	0.296147i
$861$	4.34409	+	18.1403i	0.148046	+	0.618218i
$862$	18.7977	+	32.5585i	0.640251	+	1.10895i
$863$	−12.6599			−0.430948			−0.215474	−	0.976510i	$-0.569130\pi$
$863$	−12.6599			−0.430948			−0.215474	+	0.976510i	$0.569130\pi$
$864$	5.11076	−	0.938136i	0.173872	−	0.0319161i
$865$	−7.61350			−0.258867
$866$	−14.2639	−	24.7059i	−0.484708	−	0.839539i
$867$	−6.81582	−	28.4618i	−0.231477	−	0.966613i
$868$	−0.193252	+	0.334723i	−0.00655941	+	0.0113612i
$869$	−5.83502	+	10.1066i	−0.197940	+	0.342841i
$870$	−1.41751	+	1.34362i	−0.0480581	+	0.0455531i
$871$	0.828153	+	1.43440i	0.0280609	+	0.0486029i
$872$	16.5990			0.562112
$873$	−6.57068	−	4.27777i	−0.222384	−	0.144781i
$874$	−16.6664			−0.563751
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	−9.36783	−	2.78072i	−0.316510	−	0.0939518i
$877$	24.8004	−	42.9556i	0.837450	−	1.45051i	−0.0545695	−	0.998510i	$-0.517379\pi$
$877$	24.8004	−	42.9556i	0.837450	−	1.45051i	0.892020	−	0.451996i	$-0.149288\pi$
$878$	−14.6113	+	25.3075i	−0.493107	+	0.854087i
$879$	−13.7603	−	4.08458i	−0.464124	−	0.137769i
$880$	1.25707	+	2.17731i	0.0423758	+	0.0733970i
$881$	−6.87783			−0.231720			−0.115860	−	0.993266i	$-0.536962\pi$
$881$	−6.87783			−0.231720			−0.115860	+	0.993266i	$0.536962\pi$
$882$	−2.67458	+	1.35891i	−0.0900578	+	0.0457568i
$883$	51.6044			1.73663			0.868314	−	0.496016i	$-0.165204\pi$
$883$	51.6044			1.73663			0.868314	+	0.496016i	$0.165204\pi$
$884$	0.242932	+	0.420770i	0.00817067	+	0.0141520i
$885$	15.4882	−	14.6809i	0.520630	−	0.493493i
$886$	8.30675	−	14.3877i	0.279071	−	0.483365i
$887$	−5.34916	+	9.26501i	−0.179607	+	0.311089i	−0.941746	−	0.336325i	$-0.890816\pi$
$887$	−5.34916	+	9.26501i	−0.179607	+	0.311089i	0.762139	+	0.647414i	$0.224149\pi$
$888$	−2.36510	−	9.87628i	−0.0793675	−	0.331426i
$889$	−2.95032	−	5.11011i	−0.0989506	−	0.171387i
$890$	16.0565			0.538217
$891$	22.4978	+	2.41678i	0.753705	+	0.0809651i
$892$	−13.4768			−0.451236
$893$	−0.868759	−	1.50474i	−0.0290719	−	0.0503540i
$894$	−4.70739	−	19.6573i	−0.157439	−	0.657439i
$895$	−1.66044	+	2.87597i	−0.0555025	+	0.0961331i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	11.7170	−	11.1063i	0.391219	−	0.370827i
$898$	4.21699	+	7.30404i	0.140723	+	0.243739i
$899$	−0.435835			−0.0145359
$900$	−2.67458	+	1.35891i	−0.0891526	+	0.0452969i
$901$	−0.909714			−0.0303070
$902$	13.5379	+	23.4483i	0.450762	+	0.780743i
$903$	−16.6514	−	4.94274i	−0.554123	−	0.164484i
$904$	5.88197	−	10.1879i	0.195631	−	0.338843i
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$	0.971726	+	0.288444i	0.0322834	+	0.00958292i
$907$	−16.5752	−	28.7091i	−0.550371	−	0.953271i	−0.998248	−	0.0591754i	$-0.981153\pi$
$907$	−16.5752	−	28.7091i	−0.550371	−	0.953271i	0.447876	−	0.894095i	$-0.352180\pi$
$908$	8.42024			0.279436
$909$	−37.9253	−	24.6908i	−1.25790	−	0.818944i
$910$	1.51414			0.0501932
$911$	3.04008	+	5.26557i	0.100722	+	0.174456i	0.911982	−	0.410229i	$-0.134551\pi$
$911$	3.04008	+	5.26557i	0.100722	+	0.174456i	−0.811260	+	0.584685i	$0.801218\pi$
$912$	−3.40337	+	3.22598i	−0.112697	+	0.106823i
$913$	−7.12763	+	12.3454i	−0.235890	+	0.408574i
$914$	−10.7621	+	18.6406i	−0.355980	+	0.616575i
$915$	−0.0779530	−	0.325519i	−0.00257705	−	0.0107613i
$916$	11.7667	+	20.3805i	0.388782	+	0.673390i
$917$	15.9627			0.527133
$918$	0.559280	−	1.57077i	0.0184590	−	0.0518431i
$919$	47.3165			1.56083			0.780413	−	0.625264i	$-0.215009\pi$
$919$	47.3165			1.56083			0.780413	+	0.625264i	$0.215009\pi$
$920$	−3.07795	−	5.33117i	−0.101477	−	0.175764i
$921$	3.71606	+	15.5177i	0.122448	+	0.511325i
$922$	−5.06835	+	8.77864i	−0.166917	+	0.289109i
$923$	−8.05241	+	13.9472i	−0.265048	+	0.459077i
$924$	−3.16044	+	2.99571i	−0.103971	+	0.0985515i
$925$	2.93165	+	5.07776i	0.0963920	+	0.166956i
$926$	−3.67004			−0.120605
$927$	−0.548751	+	10.2460i	−0.0180234	+	0.336524i
$928$	−1.12763			−0.0370163
$929$	9.48586	+	16.4300i	0.311221	+	0.539051i	0.978627	−	0.205643i	$-0.0659287\pi$
$929$	9.48586	+	16.4300i	0.311221	+	0.539051i	−0.667406	+	0.744694i	$0.732595\pi$
$930$	−0.641769	−	0.190501i	−0.0210444	−	0.00624677i
$931$	1.35369	−	2.34467i	0.0443656	−	0.0768434i
$932$	−1.16317	+	2.01468i	−0.0381010	+	0.0659929i
$933$	−55.4532	−	16.4606i	−1.81546	−	0.538895i
$934$	−4.85189	−	8.40372i	−0.158759	−	0.274978i
$935$	0.806748			0.0263835
$936$	0.242932	−	4.53591i	0.00794047	−	0.148261i
$937$	−2.33823			−0.0763867			−0.0381933	−	0.999270i	$-0.512160\pi$
$937$	−2.33823			−0.0763867			−0.0381933	+	0.999270i	$0.512160\pi$
$938$	0.546947	+	0.947340i	0.0178585	+	0.0309318i
$939$	11.0306	−	10.4556i	0.359970	−	0.341207i
$940$	0.320884	−	0.555788i	0.0104661	−	0.0181278i
$941$	−5.42024	+	9.38814i	−0.176695	+	0.306044i	−0.940747	−	0.339111i	$-0.889874\pi$
$941$	−5.42024	+	9.38814i	−0.176695	+	0.306044i	0.764052	+	0.645155i	$0.223207\pi$
$942$	−2.40297	−	10.0344i	−0.0782931	−	0.326940i
$943$	−33.1477	−	57.4135i	−1.07944	−	1.86964i
$944$	12.3209			0.401011
$945$	−3.36783	−	3.95698i	−0.109556	−	0.128721i
$946$	−25.2125			−0.819728
$947$	21.8720	+	37.8834i	0.710743	+	1.23104i	0.964578	+	0.263796i	$0.0849747\pi$
$947$	21.8720	+	37.8834i	0.710743	+	1.23104i	−0.253835	+	0.967248i	$0.581692\pi$
$948$	−1.87237	−	7.81871i	−0.0608117	−	0.253940i
$949$	−4.27121	+	7.39794i	−0.138649	+	0.240147i
$950$	1.35369	−	2.34467i	0.0439197	−	0.0760711i
$951$	35.5830	−	33.7283i	1.15386	−	1.09371i
$952$	0.160442	+	0.277894i	0.00519996	+	0.00900660i
$953$	−18.0529			−0.584792			−0.292396	−	0.956297i	$-0.594453\pi$
$953$	−18.0529			−0.584792			−0.292396	+	0.956297i	$0.594453\pi$
$954$	7.12763	+	4.64036i	0.230766	+	0.150237i
$955$	6.97173			0.225600
$956$	−2.19325	−	3.79882i	−0.0709349	−	0.122863i
$957$	−4.70739	−	1.39733i	−0.152168	−	0.0451692i
$958$	−14.6541	+	25.3816i	−0.473453	+	0.820044i
$959$	−11.1017	+	19.2287i	−0.358492	+	0.620927i
$960$	−1.66044	−	0.492881i	−0.0535905	−	0.0159077i
$961$	15.4253	+	26.7174i	0.497591	+	0.861852i
$962$	−8.87783			−0.286233
$963$	29.4717	−	14.9741i	0.949713	−	0.482532i
$964$	−2.22153			−0.0715505
$965$	−2.69598	−	4.66958i	−0.0867868	−	0.150319i
$966$	7.73840	−	7.33504i	0.248979	−	0.236001i
$967$	17.1468	−	29.6992i	0.551405	−	0.955061i	−0.446769	−	0.894650i	$-0.647425\pi$
$967$	17.1468	−	29.6992i	0.551405	−	0.955061i	0.998174	−	0.0604119i	$-0.0192414\pi$
$968$	2.33956	−	4.05223i	0.0751962	−	0.130244i
$969$	0.350435	+	1.46336i	0.0112576	+	0.0470099i
$970$	1.30675	+	2.26335i	0.0419571	+	0.0726719i
$971$	−51.8506			−1.66397			−0.831983	−	0.554802i	$-0.812794\pi$
$971$	−51.8506			−1.66397			−0.831983	+	0.554802i	$0.812794\pi$
$972$	−12.3943	+	9.45417i	−0.397547	+	0.303243i
$973$	7.25526			0.232593
$974$	−8.22153	−	14.2401i	−0.263435	−	0.456282i
$975$	0.610763	+	2.55045i	0.0195601	+	0.0816798i
$976$	0.0966262	−	0.167362i	0.00309293	−	0.00535711i
$977$	20.3378	−	35.2260i	0.650662	−	1.12698i	−0.332300	−	0.943174i	$-0.607825\pi$
$977$	20.3378	−	35.2260i	0.650662	−	1.12698i	0.982962	−	0.183807i	$-0.0588420\pi$
$978$	−19.8163	+	18.7834i	−0.633657	+	0.600628i
$979$	20.1842	+	34.9600i	0.645089	+	1.11733i
$980$	1.00000			0.0319438
$981$	−44.3952	+	22.5564i	−1.41743	+	0.720171i
$982$	−6.99454			−0.223205
$983$	10.3865	+	17.9900i	0.331278	+	0.573790i	0.982763	−	0.184871i	$-0.0591869\pi$
$983$	10.3865	+	17.9900i	0.331278	+	0.573790i	−0.651485	+	0.758662i	$0.725854\pi$
$984$	−17.8820	−	5.30803i	−0.570056	−	0.169214i
$985$	−6.83775	+	11.8433i	−0.217869	+	0.377360i
$986$	−0.180920	+	0.313362i	−0.00576166	+	0.00997949i
$987$	1.06562	+	0.316316i	0.0339191	+	0.0100684i
$988$	2.04968	+	3.55015i	0.0652090	+	0.112945i
$989$	61.7331			1.96300
$990$	−6.32088	−	4.11514i	−0.200891	−	0.130788i
$991$	28.0675			0.891593			0.445796	−	0.895134i	$-0.352921\pi$
$991$	28.0675			0.891593			0.445796	+	0.895134i	$0.352921\pi$
$992$	−0.193252	−	0.334723i	−0.00613577	−	0.0106275i
$993$	6.15591	−	5.83503i	0.195352	−	0.185169i
$994$	−5.31815	+	9.21131i	−0.168682	+	0.292165i
$995$	−13.2339	+	22.9217i	−0.419542	+	0.726667i
$996$	−2.28715	−	9.55077i	−0.0724710	−	0.302628i
$997$	22.5051	+	38.9799i	0.712743	+	1.23451i	0.963824	+	0.266540i	$0.0858805\pi$
$997$	22.5051	+	38.9799i	0.712743	+	1.23451i	−0.251081	+	0.967966i	$0.580786\pi$
$998$	−27.0812			−0.857241
$999$	19.7466	+	23.2010i	0.624754	+	0.734046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.k.211.2	✓	6
3.2	odd	2		1890.2.j.j.631.1		6
9.2	odd	6		1890.2.j.j.1261.1		6
9.4	even	3		5670.2.a.bt.1.1		3
9.5	odd	6		5670.2.a.bp.1.3		3
9.7	even	3	inner	630.2.j.k.421.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.k.211.2	✓	6	1.1	even	1	trivial
630.2.j.k.421.2	yes	6	9.7	even	3	inner
1890.2.j.j.631.1		6	3.2	odd	2
1890.2.j.j.1261.1		6	9.2	odd	6
5670.2.a.bp.1.3		3	9.5	odd	6
5670.2.a.bt.1.1		3	9.4	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.403374 + 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.25707 - 1.19154i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-2.67458 + 1.35891i) q^{9} +1.00000 q^{10} +(1.25707 + 2.17731i) q^{11} +(-1.66044 - 0.492881i) q^{12} +(-0.757068 + 1.31128i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-1.66044 - 0.492881i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.320884 q^{17} +(2.51414 + 1.63680i) q^{18} -2.70739 q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.25707 - 1.19154i) q^{21} +(1.25707 - 2.17731i) q^{22} +(-3.07795 + 5.33117i) q^{23} +(0.403374 + 1.68443i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.51414 q^{26} +(-3.36783 - 3.95698i) q^{27} +1.00000 q^{28} +(0.563816 + 0.976558i) q^{29} +(0.403374 + 1.68443i) q^{30} +(-0.193252 + 0.334723i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.16044 + 2.99571i) q^{33} +(0.160442 + 0.277894i) q^{34} +1.00000 q^{35} +(0.160442 - 2.99571i) q^{36} -5.86330 q^{37} +(1.35369 + 2.34467i) q^{38} +(-2.51414 - 0.746289i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-5.38470 + 9.32657i) q^{41} +(-1.66044 - 0.492881i) q^{42} +(-5.01414 - 8.68474i) q^{43} -2.51414 q^{44} +(0.160442 - 2.99571i) q^{45} +6.15591 q^{46} +(0.320884 + 0.555788i) q^{47} +(1.25707 - 1.19154i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.129436 - 0.540506i) q^{51} +(-0.757068 - 1.31128i) q^{52} +2.83502 q^{53} +(-1.74293 + 4.89512i) q^{54} -2.51414 q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.09209 - 4.56040i) q^{57} +(0.563816 - 0.976558i) q^{58} +(-6.16044 + 10.6702i) q^{59} +(1.25707 - 1.19154i) q^{60} +(0.0966262 + 0.167362i) q^{61} +0.386505 q^{62} +(2.51414 + 1.63680i) q^{63} +1.00000 q^{64} +(-0.757068 - 1.31128i) q^{65} +(4.17458 + 1.23917i) q^{66} +(0.546947 - 0.947340i) q^{67} +(0.160442 - 0.277894i) q^{68} +(-10.2215 - 3.03413i) q^{69} +(-0.500000 - 0.866025i) q^{70} +10.6363 q^{71} +(-2.67458 + 1.35891i) q^{72} +5.64177 q^{73} +(2.93165 + 5.07776i) q^{74} +(1.25707 - 1.19154i) q^{75} +(1.35369 - 2.34467i) q^{76} +(1.25707 - 2.17731i) q^{77} +(0.610763 + 2.55045i) q^{78} +(2.32088 + 4.01989i) q^{79} +1.00000 q^{80} +(5.30675 - 7.26900i) q^{81} +10.7694 q^{82} +(2.83502 + 4.91040i) q^{83} +(0.403374 + 1.68443i) q^{84} +(0.160442 - 0.277894i) q^{85} +(-5.01414 + 8.68474i) q^{86} +(-1.41751 + 1.34362i) q^{87} +(1.25707 + 2.17731i) q^{88} +16.0565 q^{89} +(-2.67458 + 1.35891i) q^{90} +1.51414 q^{91} +(-3.07795 - 5.33117i) q^{92} +(-0.641769 - 0.190501i) q^{93} +(0.320884 - 0.555788i) q^{94} +(1.35369 - 2.34467i) q^{95} +(-1.66044 - 0.492881i) q^{96} +(1.30675 + 2.26335i) q^{97} +1.00000 q^{98} +(-6.32088 - 4.11514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} - 3 q^{14} - 2 q^{15} - 3 q^{16} + 14 q^{17} + 2 q^{18} - 6 q^{19} - 3 q^{20}+ \cdots - 22 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + q^11 - 2 * q^12 + 2 * q^13 - 3 * q^14 - 2 * q^15 - 3 * q^16 + 14 * q^17 + 2 * q^18 - 6 * q^19 - 3 * q^20 + q^21 + q^22 + 4 * q^23 + q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 - 7 * q^34 + 6 * q^35 - 7 * q^36 + 20 * q^37 + 3 * q^38 - 2 * q^39 - 3 * q^40 - 7 * q^41 - 2 * q^42 - 17 * q^43 - 2 * q^44 - 7 * q^45 - 8 * q^46 - 14 * q^47 + q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 2 * q^52 - 12 * q^53 - 17 * q^54 - 2 * q^55 - 3 * q^56 + 29 * q^57 - 6 * q^58 - 29 * q^59 + q^60 + 2 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 + 2 * q^65 + 4 * q^66 + q^67 - 7 * q^68 - 38 * q^69 - 3 * q^70 + 20 * q^71 + 5 * q^72 + 2 * q^73 - 10 * q^74 + q^75 + 3 * q^76 + q^77 - 8 * q^78 - 2 * q^79 + 6 * q^80 + 29 * q^81 + 14 * q^82 - 12 * q^83 + q^84 - 7 * q^85 - 17 * q^86 + 6 * q^87 + q^88 + 44 * q^89 + 5 * q^90 - 4 * q^91 + 4 * q^92 + 28 * q^93 - 14 * q^94 + 3 * q^95 - 2 * q^96 + 5 * q^97 + 6 * q^98 - 22 * q^99

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