LMFDB - Embedded newform 959.2.e.b.275.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [959,2,Mod(275,959)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(959, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("959.275");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 959 = 7 \cdot 137 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	959.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.65765355384$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			275.12
Character	$\chi$	$=$	959.275
Dual form			959.2.e.b.823.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809668 + 1.40239i) q^{2} +(1.09654 + 1.89926i) q^{3} +(-0.311125 - 0.538884i) q^{4} +(0.209785 - 0.363358i) q^{5} -3.55133 q^{6} +(-1.06146 + 2.42349i) q^{7} -2.23104 q^{8} +(-0.904790 + 1.56714i) q^{9} +O(q^{10})$	\(q+(-0.809668 + 1.40239i) q^{2} +(1.09654 + 1.89926i) q^{3} +(-0.311125 - 0.538884i) q^{4} +(0.209785 - 0.363358i) q^{5} -3.55133 q^{6} +(-1.06146 + 2.42349i) q^{7} -2.23104 q^{8} +(-0.904790 + 1.56714i) q^{9} +(0.339712 + 0.588399i) q^{10} +(-1.69902 - 2.94279i) q^{11} +(0.682320 - 1.18181i) q^{12} -5.14547 q^{13} +(-2.53924 - 3.45080i) q^{14} +0.920149 q^{15} +(2.42865 - 4.20655i) q^{16} +(-3.96027 - 6.85939i) q^{17} +(-1.46516 - 2.53773i) q^{18} +(2.47916 - 4.29402i) q^{19} -0.261077 q^{20} +(-5.76677 + 0.641464i) q^{21} +5.50256 q^{22} +(-3.99890 + 6.92630i) q^{23} +(-2.44642 - 4.23732i) q^{24} +(2.41198 + 4.17767i) q^{25} +(4.16612 - 7.21593i) q^{26} +2.61068 q^{27} +(1.63623 - 0.182005i) q^{28} +2.65159 q^{29} +(-0.745015 + 1.29040i) q^{30} +(0.886960 + 1.53626i) q^{31} +(1.70176 + 2.94754i) q^{32} +(3.72607 - 6.45375i) q^{33} +12.8260 q^{34} +(0.657917 + 0.894102i) q^{35} +1.12601 q^{36} +(-4.05997 + 7.03207i) q^{37} +(4.01459 + 6.95347i) q^{38} +(-5.64220 - 9.77258i) q^{39} +(-0.468039 + 0.810667i) q^{40} -11.2380 q^{41} +(3.76959 - 8.60661i) q^{42} -5.03758 q^{43} +(-1.05721 + 1.83115i) q^{44} +(0.379623 + 0.657526i) q^{45} +(-6.47556 - 11.2160i) q^{46} +(-3.29337 + 5.70428i) q^{47} +10.6524 q^{48} +(-4.74661 - 5.14487i) q^{49} -7.81161 q^{50} +(8.68517 - 15.0432i) q^{51} +(1.60088 + 2.77281i) q^{52} +(-3.08905 - 5.35039i) q^{53} +(-2.11379 + 3.66118i) q^{54} -1.42571 q^{55} +(2.36816 - 5.40691i) q^{56} +10.8739 q^{57} +(-2.14691 + 3.71855i) q^{58} +(7.28922 + 12.6253i) q^{59} +(-0.286281 - 0.495853i) q^{60} +(-6.85725 + 11.8771i) q^{61} -2.87257 q^{62} +(-2.83756 - 3.85621i) q^{63} +4.20315 q^{64} +(-1.07944 + 1.86965i) q^{65} +(6.03377 + 10.4508i) q^{66} +(-0.713832 - 1.23639i) q^{67} +(-2.46428 + 4.26825i) q^{68} -17.5398 q^{69} +(-1.78657 + 0.198729i) q^{70} +0.734250 q^{71} +(2.01862 - 3.49636i) q^{72} +(3.12859 + 5.41888i) q^{73} +(-6.57446 - 11.3873i) q^{74} +(-5.28966 + 9.16195i) q^{75} -3.08531 q^{76} +(8.93525 - 0.993909i) q^{77} +18.2732 q^{78} +(-1.92138 + 3.32792i) q^{79} +(-1.01899 - 1.76494i) q^{80} +(5.57708 + 9.65979i) q^{81} +(9.09906 - 15.7600i) q^{82} +3.03088 q^{83} +(2.13986 + 2.90804i) q^{84} -3.32322 q^{85} +(4.07877 - 7.06464i) q^{86} +(2.90757 + 5.03605i) q^{87} +(3.79058 + 6.56547i) q^{88} +(6.12117 - 10.6022i) q^{89} -1.22947 q^{90} +(5.46170 - 12.4700i) q^{91} +4.97663 q^{92} +(-1.94517 + 3.36914i) q^{93} +(-5.33307 - 9.23715i) q^{94} +(-1.04018 - 1.80164i) q^{95} +(-3.73210 + 6.46418i) q^{96} +0.502479 q^{97} +(11.0583 - 2.49095i) q^{98} +6.14902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) $ 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9	\( 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9} + 25 q^{10} + 33 q^{12} - 72 q^{13} - 38 q^{16} + 18 q^{17} + 5 q^{18} + 43 q^{19} - 20 q^{20} + 8 q^{21} + q^{23} + 20 q^{24} - 43 q^{25} + 2 q^{26} - 106 q^{27} + 7 q^{28} - 8 q^{29} + 12 q^{30} + 59 q^{31} + 11 q^{32} + 37 q^{33} - 96 q^{34} + 2 q^{35} + 28 q^{36} + 39 q^{38} - 16 q^{39} + 56 q^{40} - 30 q^{41} + 26 q^{42} - 2 q^{43} + 2 q^{44} + 28 q^{45} - 31 q^{46} + 58 q^{47} - 24 q^{48} + 15 q^{49} - 148 q^{50} + 5 q^{51} + 115 q^{52} - 10 q^{53} + 39 q^{54} - 162 q^{55} + 63 q^{56} - 36 q^{57} + 11 q^{58} + 41 q^{59} - 90 q^{60} + 40 q^{61} + 58 q^{62} + 53 q^{63} + 30 q^{64} + 9 q^{65} + 42 q^{66} + 56 q^{68} - 10 q^{69} + 84 q^{70} - 84 q^{71} + 11 q^{72} + 67 q^{73} - 39 q^{74} + 40 q^{75} - 136 q^{76} + 21 q^{77} - 156 q^{78} + 9 q^{79} + 14 q^{80} - 73 q^{81} + 34 q^{82} - 96 q^{83} + 28 q^{84} + 12 q^{85} + 13 q^{86} + 135 q^{87} - 47 q^{88} + 17 q^{89} + 88 q^{90} + 26 q^{91} - 122 q^{92} + q^{93} + 28 q^{94} - 47 q^{95} + 50 q^{96} - 162 q^{97} + 128 q^{98} - 70 q^{99}+O(q^{100}) \) 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9 + 25 * q^10 + 33 * q^12 - 72 * q^13 - 38 * q^16 + 18 * q^17 + 5 * q^18 + 43 * q^19 - 20 * q^20 + 8 * q^21 + q^23 + 20 * q^24 - 43 * q^25 + 2 * q^26 - 106 * q^27 + 7 * q^28 - 8 * q^29 + 12 * q^30 + 59 * q^31 + 11 * q^32 + 37 * q^33 - 96 * q^34 + 2 * q^35 + 28 * q^36 + 39 * q^38 - 16 * q^39 + 56 * q^40 - 30 * q^41 + 26 * q^42 - 2 * q^43 + 2 * q^44 + 28 * q^45 - 31 * q^46 + 58 * q^47 - 24 * q^48 + 15 * q^49 - 148 * q^50 + 5 * q^51 + 115 * q^52 - 10 * q^53 + 39 * q^54 - 162 * q^55 + 63 * q^56 - 36 * q^57 + 11 * q^58 + 41 * q^59 - 90 * q^60 + 40 * q^61 + 58 * q^62 + 53 * q^63 + 30 * q^64 + 9 * q^65 + 42 * q^66 + 56 * q^68 - 10 * q^69 + 84 * q^70 - 84 * q^71 + 11 * q^72 + 67 * q^73 - 39 * q^74 + 40 * q^75 - 136 * q^76 + 21 * q^77 - 156 * q^78 + 9 * q^79 + 14 * q^80 - 73 * q^81 + 34 * q^82 - 96 * q^83 + 28 * q^84 + 12 * q^85 + 13 * q^86 + 135 * q^87 - 47 * q^88 + 17 * q^89 + 88 * q^90 + 26 * q^91 - 122 * q^92 + q^93 + 28 * q^94 - 47 * q^95 + 50 * q^96 - 162 * q^97 + 128 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/959\mathbb{Z}\right)^\times$.

$n$	$414$	$549$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.809668	+	1.40239i	−0.572522	+	0.991637i	0.423784	+	0.905763i	$0.360701\pi$
$2$	−0.809668	+	1.40239i	−0.572522	+	0.991637i	−0.996306	+	0.0858737i	$0.972632\pi$
$3$	1.09654	+	1.89926i	0.633086	+	1.09654i	0.986917	+	0.161228i	$0.0515455\pi$
$3$	1.09654	+	1.89926i	0.633086	+	1.09654i	−0.353831	+	0.935309i	$0.615121\pi$
$4$	−0.311125	−	0.538884i	−0.155562	−	0.269442i
$5$	0.209785	−	0.363358i	0.0938187	−	0.162499i	−0.815296	−	0.579044i	$-0.803426\pi$
$5$	0.209785	−	0.363358i	0.0938187	−	0.162499i	0.909115	+	0.416545i	$0.136759\pi$
$6$	−3.55133			−1.44982
$7$	−1.06146	+	2.42349i	−0.401194	+	0.915993i
$7$	−1.06146	+	2.42349i	−0.401194	+	0.915993i
$8$	−2.23104			−0.788792
$9$	−0.904790	+	1.56714i	−0.301597	+	0.522381i
$10$	0.339712	+	0.588399i	0.107427	+	0.186068i
$11$	−1.69902	−	2.94279i	−0.512273	−	0.887283i	−0.999899	−	0.0142303i	$-0.995470\pi$
$11$	−1.69902	−	2.94279i	−0.512273	−	0.887283i	0.487626	−	0.873053i	$-0.337863\pi$
$12$	0.682320	−	1.18181i	0.196969	−	0.341160i
$13$	−5.14547			−1.42710			−0.713548	−	0.700606i	$-0.752913\pi$
$13$	−5.14547			−1.42710			−0.713548	+	0.700606i	$0.752913\pi$
$14$	−2.53924	−	3.45080i	−0.678641	−	0.922264i
$15$	0.920149			0.237581
$16$	2.42865	−	4.20655i	0.607163	−	1.05164i
$17$	−3.96027	−	6.85939i	−0.960506	−	1.66365i	−0.721232	−	0.692694i	$-0.756424\pi$
$17$	−3.96027	−	6.85939i	−0.960506	−	1.66365i	−0.239275	−	0.970952i	$-0.576910\pi$
$18$	−1.46516	−	2.53773i	−0.345341	−	0.598149i
$19$	2.47916	−	4.29402i	0.568757	−	0.985116i	−0.427932	−	0.903811i	$-0.640758\pi$
$19$	2.47916	−	4.29402i	0.568757	−	0.985116i	0.996689	−	0.0813055i	$-0.0259089\pi$
$20$	−0.261077			−0.0583787
$21$	−5.76677	+	0.641464i	−1.25841	+	0.139979i
$22$	5.50256			1.17315
$23$	−3.99890	+	6.92630i	−0.833828	+	1.44423i	0.0611524	+	0.998128i	$0.480522\pi$
$23$	−3.99890	+	6.92630i	−0.833828	+	1.44423i	−0.894981	+	0.446105i	$0.852811\pi$
$24$	−2.44642	−	4.23732i	−0.499373	−	0.864940i
$25$	2.41198	+	4.17767i	0.482396	+	0.835535i
$26$	4.16612	−	7.21593i	0.817044	−	1.41516i
$27$	2.61068			0.502426
$28$	1.63623	−	0.182005i	0.309218	−	0.0343957i
$29$	2.65159			0.492388			0.246194	−	0.969221i	$-0.420820\pi$
$29$	2.65159			0.492388			0.246194	+	0.969221i	$0.420820\pi$
$30$	−0.745015	+	1.29040i	−0.136021	+	0.235594i
$31$	0.886960	+	1.53626i	0.159303	+	0.275921i	0.934617	−	0.355655i	$-0.115742\pi$
$31$	0.886960	+	1.53626i	0.159303	+	0.275921i	−0.775315	+	0.631575i	$0.782409\pi$
$32$	1.70176	+	2.94754i	0.300832	+	0.521057i
$33$	3.72607	−	6.45375i	0.648626	−	1.12345i
$34$	12.8260			2.19964
$35$	0.657917	+	0.894102i	0.111208	+	0.151131i
$36$	1.12601			0.187668
$37$	−4.05997	+	7.03207i	−0.667455	+	1.15607i	0.311159	+	0.950358i	$0.399283\pi$
$37$	−4.05997	+	7.03207i	−0.667455	+	1.15607i	−0.978613	+	0.205708i	$0.934050\pi$
$38$	4.01459	+	6.95347i	0.651252	+	1.12800i
$39$	−5.64220	−	9.77258i	−0.903475	−	1.56486i
$40$	−0.468039	+	0.810667i	−0.0740035	+	0.128178i
$41$	−11.2380			−1.75508			−0.877541	−	0.479502i	$-0.840817\pi$
$41$	−11.2380			−1.75508			−0.877541	+	0.479502i	$0.840817\pi$
$42$	3.76959	−	8.60661i	0.581660	−	1.32803i
$43$	−5.03758			−0.768224			−0.384112	−	0.923287i	$-0.625492\pi$
$43$	−5.03758			−0.768224			−0.384112	+	0.923287i	$0.625492\pi$
$44$	−1.05721	+	1.83115i	−0.159381	+	0.276056i
$45$	0.379623	+	0.657526i	0.0565908	+	0.0980182i
$46$	−6.47556	−	11.2160i	−0.954770	−	1.65371i
$47$	−3.29337	+	5.70428i	−0.480387	+	0.832055i	−0.999747	−	0.0225009i	$-0.992837\pi$
$47$	−3.29337	+	5.70428i	−0.480387	+	0.832055i	0.519360	+	0.854556i	$0.326170\pi$
$48$	10.6524			1.53755
$49$	−4.74661	−	5.14487i	−0.678087	−	0.734981i
$50$	−7.81161			−1.10473
$51$	8.68517	−	15.0432i	1.21617	−	2.10646i
$52$	1.60088	+	2.77281i	0.222003	+	0.384520i
$53$	−3.08905	−	5.35039i	−0.424314	−	0.734933i	0.572043	−	0.820224i	$-0.306151\pi$
$53$	−3.08905	−	5.35039i	−0.424314	−	0.734933i	−0.996356	+	0.0852913i	$0.972818\pi$
$54$	−2.11379	+	3.66118i	−0.287650	+	0.498224i
$55$	−1.42571			−0.192243
$56$	2.36816	−	5.40691i	0.316458	−	0.722528i
$57$	10.8739			1.44029
$58$	−2.14691	+	3.71855i	−0.281903	+	0.488270i
$59$	7.28922	+	12.6253i	0.948976	+	1.64367i	0.747589	+	0.664162i	$0.231212\pi$
$59$	7.28922	+	12.6253i	0.948976	+	1.64367i	0.201387	+	0.979512i	$0.435455\pi$
$60$	−0.286281	−	0.495853i	−0.0369587	−	0.0640144i
$61$	−6.85725	+	11.8771i	−0.877981	+	1.52071i	−0.0244282	+	0.999702i	$0.507776\pi$
$61$	−6.85725	+	11.8771i	−0.877981	+	1.52071i	−0.853553	+	0.521006i	$0.825557\pi$
$62$	−2.87257			−0.364817
$63$	−2.83756	−	3.85621i	−0.357499	−	0.485836i
$64$	4.20315			0.525394
$65$	−1.07944	+	1.86965i	−0.133888	+	0.231901i
$66$	6.03377	+	10.4508i	0.742705	+	1.28640i
$67$	−0.713832	−	1.23639i	−0.0872085	−	0.151049i	0.819122	−	0.573620i	$-0.194461\pi$
$67$	−0.713832	−	1.23639i	−0.0872085	−	0.151049i	−0.906330	+	0.422570i	$0.861128\pi$
$68$	−2.46428	+	4.26825i	−0.298837	+	0.517602i
$69$	−17.5398			−2.11154
$70$	−1.78657	+	0.198729i	−0.213536	+	0.0237526i
$71$	0.734250			0.0871394			0.0435697	−	0.999050i	$-0.486127\pi$
$71$	0.734250			0.0871394			0.0435697	+	0.999050i	$0.486127\pi$
$72$	2.01862	−	3.49636i	0.237897	−	0.412050i
$73$	3.12859	+	5.41888i	0.366174	+	0.634232i	0.988964	−	0.148157i	$-0.0473341\pi$
$73$	3.12859	+	5.41888i	0.366174	+	0.634232i	−0.622790	+	0.782389i	$0.714001\pi$
$74$	−6.57446	−	11.3873i	−0.764265	−	1.32375i
$75$	−5.28966	+	9.16195i	−0.610797	+	1.05793i
$76$	−3.08531			−0.353909
$77$	8.93525	−	0.993909i	1.01827	−	0.113266i
$78$	18.2732			2.06904
$79$	−1.92138	+	3.32792i	−0.216172	+	0.374421i	−0.953634	−	0.300967i	$-0.902690\pi$
$79$	−1.92138	+	3.32792i	−0.216172	+	0.374421i	0.737463	+	0.675388i	$0.236024\pi$
$80$	−1.01899	−	1.76494i	−0.113927	−	0.197327i
$81$	5.57708	+	9.65979i	0.619676	+	1.07331i
$82$	9.09906	−	15.7600i	1.00482	−	1.74040i
$83$	3.03088			0.332682			0.166341	−	0.986068i	$-0.446805\pi$
$83$	3.03088			0.332682			0.166341	+	0.986068i	$0.446805\pi$
$84$	2.13986	+	2.90804i	0.233478	+	0.317293i
$85$	−3.32322			−0.360454
$86$	4.07877	−	7.06464i	0.439825	−	0.761799i
$87$	2.90757	+	5.03605i	0.311724	+	0.539922i
$88$	3.79058	+	6.56547i	0.404077	+	0.699882i
$89$	6.12117	−	10.6022i	0.648843	−	1.12383i	−0.334557	−	0.942376i	$-0.608587\pi$
$89$	6.12117	−	10.6022i	0.648843	−	1.12383i	0.983400	−	0.181453i	$-0.0580801\pi$
$90$	−1.22947			−0.129598
$91$	5.46170	−	12.4700i	0.572542	−	1.30721i
$92$	4.97663			0.518849
$93$	−1.94517	+	3.36914i	−0.201705	+	0.349363i
$94$	−5.33307	−	9.23715i	−0.550064	−	0.952739i
$95$	−1.04018	−	1.80164i	−0.106720	−	0.184845i
$96$	−3.73210	+	6.46418i	−0.380905	+	0.659748i
$97$	0.502479			0.0510190			0.0255095	−	0.999675i	$-0.491879\pi$
$97$	0.502479			0.0510190			0.0255095	+	0.999675i	$0.491879\pi$
$98$	11.0583	−	2.49095i	1.11705	−	0.251624i
$99$	6.14902			0.617999
$100$	1.50085	−	2.59956i	0.150085	−	0.259956i
$101$	−0.241789	−	0.418790i	−0.0240589	−	0.0416712i	0.853745	−	0.520691i	$-0.174326\pi$
$101$	−0.241789	−	0.418790i	−0.0240589	−	0.0416712i	−0.877804	+	0.479020i	$0.840992\pi$
$102$	14.0642	+	24.3599i	1.39256	+	2.41199i
$103$	0.0768908	−	0.133179i	0.00757628	−	0.0131225i	−0.862212	−	0.506547i	$-0.830922\pi$
$103$	0.0768908	−	0.133179i	0.00757628	−	0.0131225i	0.869789	+	0.493424i	$0.164255\pi$
$104$	11.4797			1.12568
$105$	−0.976700	+	2.22997i	−0.0953161	+	0.217623i
$106$	10.0044			0.971715
$107$	−0.943675	+	1.63449i	−0.0912285	+	0.158012i	−0.908028	−	0.418909i	$-0.862413\pi$
$107$	−0.943675	+	1.63449i	−0.0912285	+	0.158012i	0.816800	+	0.576921i	$0.195746\pi$
$108$	−0.812248	−	1.40685i	−0.0781586	−	0.135375i
$109$	3.97879	+	6.89147i	0.381099	+	0.660083i	0.991220	−	0.132226i	$-0.0422124\pi$
$109$	3.97879	+	6.89147i	0.381099	+	0.660083i	−0.610121	+	0.792309i	$0.708879\pi$
$110$	1.15435	−	1.99940i	0.110063	−	0.190635i
$111$	−17.8076			−1.69023
$112$	7.61662	+	10.3509i	0.719703	+	0.978067i
$113$	−7.48623			−0.704245			−0.352123	−	0.935954i	$-0.614540\pi$
$113$	−7.48623			−0.704245			−0.352123	+	0.935954i	$0.614540\pi$
$114$	−8.80429	+	15.2495i	−0.824597	+	1.42824i
$115$	1.67782	+	2.90607i	0.156457	+	0.270992i
$116$	−0.824975	−	1.42890i	−0.0765970	−	0.132670i
$117$	4.65557	−	8.06368i	0.430407	−	0.745487i
$118$	−23.6074			−2.17324
$119$	20.8273	−	2.31672i	1.90924	−	0.212373i
$120$	−2.05289			−0.187402
$121$	−0.273323	+	0.473409i	−0.0248475	+	0.0430372i
$122$	−11.1042	−	19.2330i	−1.00533	−	1.74128i
$123$	−12.3229	−	21.3439i	−1.11112	−	1.92451i
$124$	0.551911	−	0.955938i	0.0495631	−	0.0858457i
$125$	4.12184			0.368669
$126$	7.70537	−	0.857104i	0.686449	−	0.0763569i
$127$	−6.25447			−0.554994			−0.277497	−	0.960726i	$-0.589505\pi$
$127$	−6.25447			−0.554994			−0.277497	+	0.960726i	$0.589505\pi$
$128$	−6.80669	+	11.7895i	−0.601632	+	1.04206i
$129$	−5.52390	−	9.56767i	−0.486352	−	0.842387i
$130$	−1.74798	−	3.02759i	−0.153308	−	0.265537i
$131$	6.75834	−	11.7058i	0.590479	−	1.02274i	−0.403689	−	0.914896i	$-0.632272\pi$
$131$	6.75834	−	11.7058i	0.590479	−	1.02274i	0.994168	−	0.107843i	$-0.0343944\pi$
$132$	−4.63710			−0.403607
$133$	7.77500	+	10.5661i	0.674178	+	0.916200i
$134$	2.31187			0.199715
$135$	0.547682	−	0.948613i	0.0471369	−	0.0816436i
$136$	8.83552	+	15.3036i	0.757640	+	1.31227i
$137$	0.500000	+	0.866025i	0.0427179	+	0.0739895i
$137$	0.500000	+	0.866025i	0.0427179	+	0.0739895i
$138$	14.2014	−	24.5975i	1.20890	−	2.09388i
$139$	−4.73947			−0.401996			−0.200998	−	0.979592i	$-0.564419\pi$
$139$	−4.73947			−0.401996			−0.200998	+	0.979592i	$0.564419\pi$
$140$	0.277123	−	0.632718i	0.0234211	−	0.0534745i
$141$	−14.4452			−1.21651
$142$	−0.594498	+	1.02970i	−0.0498892	+	0.0864106i
$143$	8.74224	+	15.1420i	0.731063	+	1.26624i
$144$	4.39484	+	7.61209i	0.366237	+	0.634341i
$145$	0.556264	−	0.963477i	0.0461952	−	0.0800124i
$146$	−10.1325			−0.838571
$147$	4.56660	−	14.6566i	0.376647	−	1.20885i
$148$	5.05263			0.415324
$149$	−0.280610	+	0.486031i	−0.0229885	+	0.0398172i	−0.877291	−	0.479959i	$-0.840651\pi$
$149$	−0.280610	+	0.486031i	−0.0229885	+	0.0398172i	0.854302	+	0.519776i	$0.173985\pi$
$150$	−8.56573	−	14.8363i	−0.699389	−	1.21138i
$151$	2.93650	+	5.08617i	0.238969	+	0.413907i	0.960419	−	0.278560i	$-0.0898572\pi$
$151$	2.93650	+	5.08617i	0.238969	+	0.413907i	−0.721450	+	0.692467i	$0.756524\pi$
$152$	−5.53110	+	9.58014i	−0.448631	+	0.777052i
$153$	14.3328			1.15874
$154$	−5.84074	+	13.3354i	−0.470660	+	1.07460i
$155$	0.744284			0.0597823
$156$	−3.51086	+	6.08098i	−0.281093	+	0.486868i
$157$	−3.41170	−	5.90923i	−0.272283	−	0.471608i	0.697163	−	0.716913i	$-0.254445\pi$
$157$	−3.41170	−	5.90923i	−0.272283	−	0.471608i	−0.969446	+	0.245305i	$0.921112\pi$
$158$	−3.11136	−	5.38903i	−0.247526	−	0.428728i
$159$	6.77452	−	11.7338i	0.537254	−	0.930552i
$160$	1.42802			0.112895
$161$	−12.5412	−	17.0433i	−0.988381	−	1.34320i
$162$	−18.0623			−1.41911
$163$	2.86708	−	4.96592i	0.224567	−	0.388961i	−0.731623	−	0.681710i	$-0.761237\pi$
$163$	2.86708	−	4.96592i	0.224567	−	0.388961i	0.956189	+	0.292749i	$0.0945700\pi$
$164$	3.49642	+	6.05598i	0.273025	+	0.472893i
$165$	−1.56335	−	2.70780i	−0.121707	−	0.210802i
$166$	−2.45400	+	4.25046i	−0.190468	+	0.329900i
$167$	−4.71958			−0.365212			−0.182606	−	0.983186i	$-0.558453\pi$
$167$	−4.71958			−0.365212			−0.182606	+	0.983186i	$0.558453\pi$
$168$	12.8659	−	1.43113i	0.992625	−	0.110414i
$169$	13.4758			1.03660
$170$	2.69071	−	4.66044i	0.206368	−	0.357439i
$171$	4.48623	+	7.77038i	0.343070	+	0.594216i
$172$	1.56732	+	2.71467i	0.119507	+	0.206992i
$173$	11.0584	−	19.1538i	0.840756	−	1.45623i	−0.0484996	−	0.998823i	$-0.515444\pi$
$173$	11.0584	−	19.1538i	0.840756	−	1.45623i	0.889256	−	0.457410i	$-0.151223\pi$
$174$	−9.41666			−0.713875
$175$	−12.6848	+	1.41099i	−0.958878	+	0.106660i
$176$	−16.5053			−1.24413
$177$	−15.9858	+	27.6882i	−1.20157	+	2.08117i
$178$	9.91223	+	17.1685i	0.742953	+	1.28683i
$179$	−1.55507	−	2.69346i	−0.116231	−	0.201319i	0.802040	−	0.597270i	$-0.203748\pi$
$179$	−1.55507	−	2.69346i	−0.116231	−	0.201319i	−0.918271	+	0.395952i	$0.870415\pi$
$180$	0.236220	−	0.409145i	0.0176068	−	0.0304959i
$181$	4.34949			0.323295			0.161648	−	0.986849i	$-0.448319\pi$
$181$	4.34949			0.323295			0.161648	+	0.986849i	$0.448319\pi$
$182$	13.0656	+	17.7560i	0.968485	+	1.31616i
$183$	−30.0769			−2.22335
$184$	8.92171	−	15.4529i	0.657717	−	1.13920i
$185$	1.70344	+	2.95045i	0.125240	+	0.216921i
$186$	−3.14989	−	5.45576i	−0.230961	−	0.400036i
$187$	−13.4571	+	23.3084i	−0.984083	+	1.70448i
$188$	4.09859			0.298921
$189$	−2.77113	+	6.32696i	−0.201570	+	0.460219i
$190$	3.36880			0.244398
$191$	9.46469	−	16.3933i	0.684841	−	1.18618i	−0.288646	−	0.957436i	$-0.593205\pi$
$191$	9.46469	−	16.3933i	0.684841	−	1.18618i	0.973487	−	0.228743i	$-0.0734615\pi$
$192$	4.60892	+	7.98288i	0.332620	+	0.576115i
$193$	9.74144	+	16.8727i	0.701204	+	1.21452i	0.968044	+	0.250780i	$0.0806871\pi$
$193$	9.74144	+	16.8727i	0.701204	+	1.21452i	−0.266840	+	0.963741i	$0.585980\pi$
$194$	−0.406841	+	0.704670i	−0.0292095	+	0.0505924i
$195$	−4.73460			−0.339051
$196$	−1.29570	+	4.15857i	−0.0925499	+	0.297041i
$197$	−25.2037			−1.79569			−0.897844	−	0.440313i	$-0.854867\pi$
$197$	−25.2037			−1.79569			−0.897844	+	0.440313i	$0.854867\pi$
$198$	−4.97866	+	8.62330i	−0.353818	+	0.612831i
$199$	−11.8360	−	20.5005i	−0.839030	−	1.45324i	−0.890706	−	0.454579i	$-0.849790\pi$
$199$	−11.8360	−	20.5005i	−0.839030	−	1.45324i	0.0516764	−	0.998664i	$-0.483544\pi$
$200$	−5.38123	−	9.32056i	−0.380510	−	0.659063i
$201$	1.56549	−	2.71150i	0.110421	−	0.191255i
$202$	0.783074			0.0550969
$203$	−2.81455	+	6.42610i	−0.197543	+	0.451024i
$204$	−10.8087			−0.756760
$205$	−2.35757	+	4.08342i	−0.164660	+	0.285199i
$206$	0.124512	+	0.215661i	0.00867517	+	0.0150258i
$207$	−7.23633	−	12.5337i	−0.502960	−	0.871152i
$208$	−12.4966	+	21.6447i	−0.866480	+	1.50079i
$209$	−16.8485			−1.16544
$210$	−2.33648	−	3.17525i	−0.161232	−	0.219113i
$211$	7.90378			0.544119			0.272059	−	0.962280i	$-0.412295\pi$
$211$	7.90378			0.544119			0.272059	+	0.962280i	$0.412295\pi$
$212$	−1.92216	+	3.32928i	−0.132014	+	0.228656i
$213$	0.805132	+	1.39453i	0.0551668	+	0.0955516i
$214$	−1.52813	−	2.64679i	−0.104461	−	0.180931i
$215$	−1.05681	+	1.83045i	−0.0720738	+	0.124835i
$216$	−5.82454			−0.396310
$217$	−4.66458	+	0.518863i	−0.316653	+	0.0352227i
$218$	−12.8860			−0.872750
$219$	−6.86124	+	11.8840i	−0.463640	+	0.803048i
$220$	0.443575	+	0.768294i	0.0299058	+	0.0517984i
$221$	20.3774	+	35.2948i	1.37073	+	2.37418i
$222$	14.4183	−	24.9732i	0.967691	−	1.67609i
$223$	−8.94426			−0.598952			−0.299476	−	0.954104i	$-0.596812\pi$
$223$	−8.94426			−0.598952			−0.299476	+	0.954104i	$0.596812\pi$
$224$	−8.94969	+	0.995516i	−0.597976	+	0.0665157i
$225$	−8.72934			−0.581956
$226$	6.06136	−	10.4986i	0.403196	−	0.698355i
$227$	−0.822484	−	1.42458i	−0.0545902	−	0.0945529i	0.837439	−	0.546531i	$-0.184052\pi$
$227$	−0.822484	−	1.42458i	−0.0545902	−	0.0945529i	−0.892029	+	0.451978i	$0.850719\pi$
$228$	−3.38316	−	5.85980i	−0.224055	−	0.388075i
$229$	−11.8198	+	20.4726i	−0.781077	+	1.35286i	0.150238	+	0.988650i	$0.451996\pi$
$229$	−11.8198	+	20.4726i	−0.781077	+	1.35286i	−0.931315	+	0.364215i	$0.881337\pi$
$230$	−5.43391			−0.358301
$231$	11.6855	+	15.8805i	0.768851	+	1.04486i
$232$	−5.91580			−0.388392
$233$	0.505226	−	0.875076i	0.0330984	−	0.0573282i	−0.849002	−	0.528390i	$-0.822796\pi$
$233$	0.505226	−	0.875076i	0.0330984	−	0.0573282i	0.882100	+	0.471062i	$0.156129\pi$
$234$	7.53893	+	13.0578i	0.492835	+	0.853615i
$235$	1.38180	+	2.39334i	0.0901386	+	0.156125i
$236$	4.53571	−	7.85609i	0.295250	−	0.511388i
$237$	−8.42745			−0.547422
$238$	−13.6143	+	31.0837i	−0.882483	+	2.01486i
$239$	−27.5533			−1.78228			−0.891138	−	0.453733i	$-0.850092\pi$
$239$	−27.5533			−1.78228			−0.891138	+	0.453733i	$0.850092\pi$
$240$	2.23472	−	3.87065i	0.144251	−	0.249849i
$241$	10.6834	+	18.5042i	0.688177	+	1.19196i	0.972427	+	0.233208i	$0.0749222\pi$
$241$	10.6834	+	18.5042i	0.688177	+	1.19196i	−0.284250	+	0.958750i	$0.591744\pi$
$242$	−0.442601	−	0.766608i	−0.0284515	−	0.0492794i
$243$	−8.31494	+	14.4019i	−0.533403	+	0.923882i
$244$	8.53385			0.546323
$245$	−2.86520	+	0.645404i	−0.183051	+	0.0412334i
$246$	39.9098			2.54456
$247$	−12.7564	+	22.0948i	−0.811671	+	1.40586i
$248$	−1.97885	−	3.42746i	−0.125657	−	0.217644i
$249$	3.32347	+	5.75642i	0.210616	+	0.364798i
$250$	−3.33732	+	5.78041i	−0.211071	+	0.365585i
$251$	20.3196			1.28256			0.641280	−	0.767307i	$-0.278404\pi$
$251$	20.3196			1.28256			0.641280	+	0.767307i	$0.278404\pi$
$252$	−1.19521	+	2.72888i	−0.0752914	+	0.171903i
$253$	27.1768			1.70859
$254$	5.06404	−	8.77118i	0.317746	−	0.550353i
$255$	−3.64404	−	6.31166i	−0.228198	−	0.395251i
$256$	−6.81916	−	11.8111i	−0.426198	−	0.738196i
$257$	11.4670	−	19.8613i	0.715289	−	1.23892i	−0.247559	−	0.968873i	$-0.579629\pi$
$257$	11.4670	−	19.8613i	0.715289	−	1.23892i	0.962848	−	0.270044i	$-0.0870381\pi$
$258$	17.8901			1.11379
$259$	−12.7327	−	17.3036i	−0.791170	−	1.07519i
$260$	1.34336			0.0833120
$261$	−2.39913	+	4.15542i	−0.148502	+	0.257214i
$262$	10.9440	+	18.9556i	0.676124	+	1.17108i
$263$	−2.01519	−	3.49041i	−0.124262	−	0.215228i	0.797182	−	0.603739i	$-0.206323\pi$
$263$	−2.01519	−	3.49041i	−0.124262	−	0.215228i	−0.921444	+	0.388511i	$0.872990\pi$
$264$	−8.31302	+	14.3986i	−0.511631	+	0.886171i
$265$	−2.59214			−0.159234
$266$	−21.1130	+	2.34849i	−1.29452	+	0.143995i
$267$	26.8484			1.64309
$268$	−0.444182	+	0.769345i	−0.0271327	+	0.0469952i
$269$	11.7218	+	20.3027i	0.714689	+	1.23788i	0.963079	+	0.269217i	$0.0867650\pi$
$269$	11.7218	+	20.3027i	0.714689	+	1.23788i	−0.248391	+	0.968660i	$0.579902\pi$
$270$	0.886881	+	1.53612i	0.0539739	+	0.0934855i
$271$	10.4233	−	18.0536i	0.633168	−	1.09668i	−0.353732	−	0.935347i	$-0.615087\pi$
$271$	10.4233	−	18.0536i	0.633168	−	1.09668i	0.986900	−	0.161333i	$-0.0515793\pi$
$272$	−38.4725			−2.33274
$273$	29.6727	−	3.30063i	1.79587	−	0.199763i
$274$	−1.61934			−0.0978277
$275$	8.19600	−	14.1959i	0.494237	−	0.856044i
$276$	5.45706	+	9.45191i	0.328477	+	0.568938i
$277$	−4.20167	−	7.27750i	−0.252454	−	0.437262i	0.711747	−	0.702436i	$-0.247904\pi$
$277$	−4.20167	−	7.27750i	−0.252454	−	0.437262i	−0.964201	+	0.265173i	$0.914571\pi$
$278$	3.83740	−	6.64656i	0.230152	−	0.398634i
$279$	−3.21005			−0.192181
$280$	−1.46784	−	1.99478i	−0.0877202	−	0.119211i
$281$	−16.2523			−0.969532			−0.484766	−	0.874644i	$-0.661095\pi$
$281$	−16.2523			−0.969532			−0.484766	+	0.874644i	$0.661095\pi$
$282$	11.6958	−	20.2578i	0.696476	−	1.20633i
$283$	14.3947	+	24.9324i	0.855677	+	1.48208i	0.876016	+	0.482283i	$0.160192\pi$
$283$	14.3947	+	24.9324i	0.855677	+	1.48208i	−0.0203385	+	0.999793i	$0.506474\pi$
$284$	−0.228443	−	0.395675i	−0.0135556	−	0.0234790i
$285$	2.28119	−	3.95114i	0.135126	−	0.234045i
$286$	−28.3133			−1.67420
$287$	11.9287	−	27.2352i	0.704128	−	1.60764i
$288$	−6.15895			−0.362920
$289$	−22.8675	+	39.6076i	−1.34514	+	2.32986i
$290$	0.900778	+	1.56019i	0.0528955	+	0.0916177i
$291$	0.550987	+	0.954338i	0.0322995	+	0.0559443i
$292$	1.94677	−	3.37190i	0.113926	−	0.197325i
$293$	19.5272			1.14079			0.570397	−	0.821369i	$-0.306789\pi$
$293$	19.5272			1.14079			0.570397	+	0.821369i	$0.306789\pi$
$294$	16.8568	+	18.2711i	0.983107	+	1.06559i
$295$	6.11668			0.356127
$296$	9.05796	−	15.6888i	0.526483	−	0.911895i
$297$	−4.43559	−	7.68267i	−0.257379	−	0.445794i
$298$	−0.454403	−	0.787048i	−0.0263228	−	0.0455925i
$299$	20.5762	−	35.6390i	1.18995	−	2.06106i
$300$	6.58297			0.380068
$301$	5.34718	−	12.2085i	0.308207	−	0.703688i
$302$	−9.51036			−0.547260
$303$	0.530261	−	0.918438i	0.0304627	−	0.0527629i
$304$	−12.0420	−	20.8574i	−0.690657	−	1.19625i
$305$	2.87710	+	4.98328i	0.164742	+	0.285342i
$306$	−11.6048	+	20.1002i	−0.663405	+	1.14905i
$307$	−2.62600			−0.149874			−0.0749369	−	0.997188i	$-0.523876\pi$
$307$	−2.62600			−0.149874			−0.0749369	+	0.997188i	$0.523876\pi$
$308$	−3.31558	−	4.50583i	−0.188923	−	0.256744i
$309$	0.337255			0.0191858
$310$	−0.602623	+	1.04377i	−0.0342267	+	0.0592824i
$311$	−5.72831	−	9.92172i	−0.324823	−	0.562609i	0.656654	−	0.754192i	$-0.271971\pi$
$311$	−5.72831	−	9.92172i	−0.324823	−	0.562609i	−0.981476	+	0.191583i	$0.938638\pi$
$312$	12.5880	+	21.8030i	0.712654	+	1.23435i
$313$	−10.2317	+	17.7218i	−0.578328	+	1.00169i	0.417343	+	0.908749i	$0.362961\pi$
$313$	−10.2317	+	17.7218i	−0.578328	+	1.00169i	−0.995671	+	0.0929444i	$0.970372\pi$
$314$	11.0494			0.623552
$315$	−1.99646	+	0.222076i	−0.112488	+	0.0125125i
$316$	2.39115			0.134513
$317$	−13.8844	+	24.0485i	−0.779827	+	1.35070i	0.152214	+	0.988348i	$0.451360\pi$
$317$	−13.8844	+	24.0485i	−0.779827	+	1.35070i	−0.932041	+	0.362353i	$0.881974\pi$
$318$	10.9702	+	19.0010i	0.615180	+	1.06552i
$319$	−4.50510	−	7.80306i	−0.252237	−	0.436887i
$320$	0.881759	−	1.52725i	0.0492918	−	0.0853759i
$321$	−4.13910			−0.231022
$322$	34.0554	−	3.78814i	1.89783	−	0.211105i
$323$	−39.2725			−2.18518
$324$	3.47034	−	6.01080i	0.192796	−	0.333933i
$325$	−12.4108	−	21.4961i	−0.688425	−	1.19239i
$326$	4.64276	+	8.04149i	0.257139	+	0.445377i
$327$	−8.72579	+	15.1135i	−0.482537	+	0.835779i
$328$	25.0725			1.38439
$329$	−10.3285	−	14.0363i	−0.569428	−	0.773846i
$330$	5.06318			0.278719
$331$	−1.14160	+	1.97731i	−0.0627480	+	0.108683i	−0.895693	−	0.444673i	$-0.853320\pi$
$331$	−1.14160	+	1.97731i	−0.0627480	+	0.108683i	0.832945	+	0.553356i	$0.186653\pi$
$332$	−0.942981	−	1.63329i	−0.0517528	−	0.0896385i
$333$	−7.34684	−	12.7251i	−0.402604	−	0.697331i
$334$	3.82130	−	6.61868i	0.209092	−	0.362158i
$335$	−0.599005			−0.0327271
$336$	−11.3071	+	25.8161i	−0.616854	+	1.40838i
$337$	−7.51550			−0.409396			−0.204698	−	0.978825i	$-0.565621\pi$
$337$	−7.51550			−0.409396			−0.204698	+	0.978825i	$0.565621\pi$
$338$	−10.9110	+	18.8983i	−0.593478	+	1.02793i
$339$	−8.20893	−	14.2183i	−0.445848	−	0.772231i
$340$	1.03394	+	1.79083i	0.0560731	+	0.0971214i
$341$	3.01392	−	5.22027i	0.163213	−	0.282693i
$342$	−14.5294			−0.785661
$343$	17.5069	−	6.04230i	0.945282	−	0.326254i
$344$	11.2391			0.605969
$345$	−3.67958	+	6.37322i	−0.198102	+	0.343123i
$346$	17.9073	+	31.0164i	0.962703	+	1.66745i
$347$	13.7225	+	23.7681i	0.736663	+	1.27594i	0.953990	+	0.299838i	$0.0969327\pi$
$347$	13.7225	+	23.7681i	0.736663	+	1.27594i	−0.217327	+	0.976099i	$0.569734\pi$
$348$	1.80923	−	3.13368i	0.0969851	−	0.167983i
$349$	−16.1888			−0.866564			−0.433282	−	0.901258i	$-0.642645\pi$
$349$	−16.1888			−0.866564			−0.433282	+	0.901258i	$0.642645\pi$
$350$	8.29170	−	18.9314i	0.443210	−	1.01192i
$351$	−13.4332			−0.717010
$352$	5.78265	−	10.0158i	0.308216	−	0.533847i
$353$	−4.59725	−	7.96266i	−0.244687	−	0.423810i	0.717357	−	0.696706i	$-0.245352\pi$
$353$	−4.59725	−	7.96266i	−0.244687	−	0.423810i	−0.962043	+	0.272896i	$0.912018\pi$
$354$	−25.8864	−	44.8366i	−1.37585	−	2.38304i
$355$	0.154035	−	0.266796i	0.00817531	−	0.0141600i
$356$	−7.61779			−0.403742
$357$	27.2380	+	37.0161i	1.44159	+	1.95910i
$358$	5.03636			0.266180
$359$	−8.34680	+	14.4571i	−0.440528	+	0.763016i	−0.997729	−	0.0673616i	$-0.978542\pi$
$359$	−8.34680	+	14.4571i	−0.440528	+	0.763016i	0.557201	+	0.830378i	$0.311875\pi$
$360$	−0.846954	−	1.46697i	−0.0446384	−	0.0773159i
$361$	−2.79242	−	4.83662i	−0.146970	−	0.254559i
$362$	−3.52164	+	6.09967i	−0.185093	+	0.320591i
$363$	−1.19883			−0.0629225
$364$	−8.41915	+	0.936501i	−0.441283	+	0.0490860i
$365$	2.62533			0.137416
$366$	24.3523	−	42.1795i	1.27292	−	2.20476i
$367$	−5.59459	−	9.69011i	−0.292035	−	0.505819i	0.682256	−	0.731114i	$-0.260999\pi$
$367$	−5.59459	−	9.69011i	−0.292035	−	0.505819i	−0.974291	+	0.225294i	$0.927666\pi$
$368$	19.4239	+	33.6431i	1.01254	+	1.75377i
$369$	10.1680	−	17.6116i	0.529327	−	0.916821i
$370$	−5.51689			−0.286809
$371$	16.2455	−	1.80706i	0.843425	−	0.0938181i
$372$	2.42076			0.125511
$373$	1.34655	−	2.33229i	0.0697216	−	0.120761i	−0.829057	−	0.559164i	$-0.811122\pi$
$373$	1.34655	−	2.33229i	0.0697216	−	0.120761i	0.898779	+	0.438403i	$0.144456\pi$
$374$	−21.7916	−	37.7442i	−1.12682	−	1.95171i
$375$	4.51975	+	7.82844i	0.233399	+	0.404259i
$376$	7.34764	−	12.7265i	0.378925	−	0.656318i
$377$	−13.6437			−0.702684
$378$	−6.62915	−	9.00893i	−0.340967	−	0.463370i
$379$	−21.6320			−1.11116			−0.555582	−	0.831462i	$-0.687504\pi$
$379$	−21.6320			−1.11116			−0.555582	+	0.831462i	$0.687504\pi$
$380$	−0.647251	+	1.12107i	−0.0332033	+	0.0575098i
$381$	−6.85826	−	11.8789i	−0.351359	−	0.608572i
$382$	15.3265	+	26.5463i	0.784172	+	1.35823i
$383$	−3.78885	+	6.56248i	−0.193601	+	0.335327i	−0.946441	−	0.322877i	$-0.895350\pi$
$383$	−3.78885	+	6.56248i	−0.193601	+	0.335327i	0.752840	+	0.658204i	$0.228683\pi$
$384$	−29.8552			−1.52354
$385$	1.51334	−	3.45520i	0.0771267	−	0.176093i
$386$	−31.5493			−1.60582
$387$	4.55795	−	7.89461i	0.231694	−	0.401305i
$388$	−0.156334	−	0.270778i	−0.00793665	−	0.0137467i
$389$	2.40240	+	4.16109i	0.121807	+	0.210975i	0.920480	−	0.390789i	$-0.127798\pi$
$389$	2.40240	+	4.16109i	0.121807	+	0.210975i	−0.798673	+	0.601765i	$0.794465\pi$
$390$	3.83345	−	6.63973i	0.194114	−	0.336216i
$391$	63.3469			3.20359
$392$	10.5899	+	11.4784i	0.534870	+	0.579747i
$393$	29.6431			1.49530
$394$	20.4066	−	35.3453i	1.02807	−	1.78067i
$395$	0.806152	+	1.39630i	0.0405619	+	0.0702553i
$396$	−1.91311	−	3.31361i	−0.0961375	−	0.166515i
$397$	0.944574	−	1.63605i	0.0474068	−	0.0821110i	−0.841348	−	0.540493i	$-0.818238\pi$
$397$	0.944574	−	1.63605i	0.0474068	−	0.0821110i	0.888755	+	0.458382i	$0.151571\pi$
$398$	38.3328			1.92145
$399$	−11.5422	+	26.3529i	−0.577835	+	1.31930i
$400$	23.4314			1.17157
$401$	8.75080	−	15.1568i	0.436994	−	0.756896i	−0.560462	−	0.828180i	$-0.689376\pi$
$401$	8.75080	−	15.1568i	0.436994	−	0.756896i	0.997456	+	0.0712841i	$0.0227097\pi$
$402$	2.53505	+	4.39084i	0.126437	+	0.218995i
$403$	−4.56383	−	7.90478i	−0.227340	−	0.393765i
$404$	−0.150453	+	0.260592i	−0.00748531	+	0.0129649i
$405$	4.67995			0.232549
$406$	−6.73302	−	9.15010i	−0.334154	−	0.454112i
$407$	27.5918			1.36768
$408$	−19.3770	+	33.5619i	−0.959303	+	1.66156i
$409$	5.40770	+	9.36642i	0.267394	+	0.463139i	0.968188	−	0.250224i	$-0.0805043\pi$
$409$	5.40770	+	9.36642i	0.267394	+	0.463139i	−0.700794	+	0.713363i	$0.747171\pi$
$410$	−3.81769	−	6.61243i	−0.188542	−	0.326565i
$411$	−1.09654	+	1.89926i	−0.0540882	+	0.0936835i
$412$	−0.0956906			−0.00471434
$413$	−38.3345	+	4.26412i	−1.88632	+	0.209824i
$414$	23.4361			1.15182
$415$	0.635833	−	1.10129i	0.0312118	−	0.0540604i
$416$	−8.75637	−	15.1665i	−0.429316	−	0.743598i
$417$	−5.19700	−	9.00148i	−0.254498	−	0.440804i
$418$	13.6417	−	23.6281i	0.667238	−	1.15569i
$419$	−5.87733			−0.287126			−0.143563	−	0.989641i	$-0.545856\pi$
$419$	−5.87733			−0.287126			−0.143563	+	0.989641i	$0.545856\pi$
$420$	1.50557	−	0.167472i	0.0734644	−	0.00817178i
$421$	26.5879			1.29582			0.647909	−	0.761718i	$-0.275644\pi$
$421$	26.5879			1.29582			0.647909	+	0.761718i	$0.275644\pi$
$422$	−6.39944	+	11.0842i	−0.311520	+	0.539568i
$423$	−5.95961	−	10.3223i	−0.289766	−	0.501890i
$424$	6.89180	+	11.9369i	0.334695	+	0.579709i
$425$	19.1042	−	33.0894i	0.926689	−	1.60507i
$426$	−2.60756			−0.126337
$427$	−21.5054	−	29.2255i	−1.04072	−	1.41432i
$428$	1.17440			0.0567669
$429$	−19.1724	+	33.2076i	−0.925652	+	1.60328i
$430$	−1.71133	−	2.96411i	−0.0825276	−	0.142942i
$431$	9.34933	+	16.1935i	0.450341	+	0.780014i	0.998407	−	0.0564213i	$-0.0179690\pi$
$431$	9.34933	+	16.1935i	0.450341	+	0.780014i	−0.548066	+	0.836435i	$0.684636\pi$
$432$	6.34044	−	10.9820i	0.305054	−	0.528370i
$433$	−26.8000			−1.28792			−0.643962	−	0.765057i	$-0.722711\pi$
$433$	−26.8000			−1.28792			−0.643962	+	0.765057i	$0.722711\pi$
$434$	3.04912	−	6.96166i	0.146362	−	0.334170i
$435$	2.43986			0.116982
$436$	2.47580	−	4.28821i	0.118569	−	0.205368i
$437$	19.8278	+	34.3427i	0.948492	+	1.64284i
$438$	−11.1107	−	19.2442i	−0.530888	−	0.919525i
$439$	4.25262	−	7.36575i	0.202966	−	0.351548i	−0.746516	−	0.665367i	$-0.768275\pi$
$439$	4.25262	−	7.36575i	0.202966	−	0.351548i	0.949483	+	0.313819i	$0.101608\pi$
$440$	3.18083			0.151640
$441$	12.3574	−	2.78359i	0.588449	−	0.132552i
$442$	−65.9958			−3.13910
$443$	6.86158	−	11.8846i	0.326003	−	0.564654i	−0.655712	−	0.755012i	$-0.727631\pi$
$443$	6.86158	−	11.8846i	0.326003	−	0.564654i	0.981715	+	0.190357i	$0.0609646\pi$
$444$	5.54040	+	9.59625i	0.262936	+	0.455418i
$445$	−2.56826	−	4.44836i	−0.121747	−	0.210872i
$446$	7.24188	−	12.5433i	0.342913	−	0.593943i
$447$	−1.23080			−0.0582148
$448$	−4.46147	+	10.1863i	−0.210785	+	0.481258i
$449$	−39.3469			−1.85689			−0.928447	−	0.371465i	$-0.878856\pi$
$449$	−39.3469			−1.85689			−0.928447	+	0.371465i	$0.878856\pi$
$450$	7.06787	−	12.2419i	0.333183	−	0.577089i
$451$	19.0936	+	33.0710i	0.899081	+	1.55725i
$452$	2.32915	+	4.03421i	0.109554	+	0.189753i
$453$	−6.43997	+	11.1544i	−0.302576	+	0.524077i
$454$	2.66376			0.125016
$455$	−3.38529	−	4.60057i	−0.158705	−	0.215678i
$456$	−24.2602			−1.13609
$457$	−2.64296	+	4.57773i	−0.123632	+	0.214137i	−0.921197	−	0.389095i	$-0.872788\pi$
$457$	−2.64296	+	4.57773i	−0.123632	+	0.214137i	0.797565	+	0.603233i	$0.206121\pi$
$458$	−19.1403	−	33.1520i	−0.894367	−	1.54909i
$459$	−10.3390	−	17.9077i	−0.482583	−	0.835859i
$460$	1.04402	−	1.80830i	0.0486778	−	0.0843124i
$461$	23.7615			1.10668			0.553341	−	0.832954i	$-0.313352\pi$
$461$	23.7615			1.10668			0.553341	+	0.832954i	$0.313352\pi$
$462$	−31.7320	+	3.52970i	−1.47631	+	0.164216i
$463$	7.70601			0.358129			0.179064	−	0.983837i	$-0.442693\pi$
$463$	7.70601			0.358129			0.179064	+	0.983837i	$0.442693\pi$
$464$	6.43979	−	11.1540i	0.298960	−	0.517813i
$465$	0.816135	+	1.41359i	0.0378474	+	0.0655536i
$466$	0.818130	+	1.41704i	0.0378991	+	0.0656432i
$467$	−8.35414	+	14.4698i	−0.386584	+	0.669583i	−0.991988	−	0.126336i	$-0.959678\pi$
$467$	−8.35414	+	14.4698i	−0.386584	+	0.669583i	0.605404	+	0.795918i	$0.293012\pi$
$468$	−5.79385			−0.267821
$469$	3.75409	−	0.417585i	0.173348	−	0.0192823i
$470$	−4.47519			−0.206425
$471$	7.48211	−	12.9594i	0.344757	−	0.597137i
$472$	−16.2625	−	28.1676i	−0.748544	−	1.29652i
$473$	8.55894	+	14.8245i	0.393540	+	0.681632i
$474$	6.82344	−	11.8185i	0.313411	−	0.542844i
$475$	23.9187			1.09747
$476$	−7.72834	−	10.5027i	−0.354228	−	0.481391i
$477$	11.1798			0.511886
$478$	22.3090	−	38.6404i	1.02039	−	1.76737i
$479$	7.02898	+	12.1746i	0.321162	+	0.556269i	0.980728	−	0.195377i	$-0.0625932\pi$
$479$	7.02898	+	12.1746i	0.321162	+	0.556269i	−0.659566	+	0.751647i	$0.729260\pi$
$480$	1.56588	+	2.71218i	0.0714721	+	0.123793i
$481$	20.8904	−	36.1833i	0.952522	−	1.64982i
$482$	−34.6000			−1.57599
$483$	18.6177	−	42.5075i	0.847137	−	1.93416i
$484$	0.340150			0.0154614
$485$	0.105413	−	0.182580i	0.00478654	−	0.00829053i
$486$	−13.4647	−	23.3215i	−0.610770	−	1.05788i
$487$	9.51005	+	16.4719i	0.430941	+	0.746412i	0.996955	−	0.0779837i	$-0.0248482\pi$
$487$	9.51005	+	16.4719i	0.430941	+	0.746412i	−0.566013	+	0.824396i	$0.691515\pi$
$488$	15.2988	−	26.4983i	0.692545	−	1.19952i
$489$	12.5754			0.568680
$490$	1.41475	−	4.54068i	0.0639121	−	0.205127i
$491$	−26.9653			−1.21693			−0.608464	−	0.793581i	$-0.708214\pi$
$491$	−26.9653			−1.21693			−0.608464	+	0.793581i	$0.708214\pi$
$492$	−7.66792	+	13.2812i	−0.345697	+	0.598764i
$493$	−10.5010	−	18.1883i	−0.472942	−	0.819159i
$494$	−20.6569	−	35.7788i	−0.929399	−	1.60977i
$495$	1.28997	−	2.23430i	0.0579799	−	0.100424i
$496$	8.61647			0.386891
$497$	−0.779375	+	1.77945i	−0.0349598	+	0.0798191i
$498$	−10.7636			−0.482330
$499$	1.94235	−	3.36426i	0.0869517	−	0.150605i	−0.819269	−	0.573409i	$-0.805621\pi$
$499$	1.94235	−	3.36426i	0.0869517	−	0.150605i	0.906221	+	0.422804i	$0.138954\pi$
$500$	−1.28241	−	2.22119i	−0.0573510	−	0.0993348i
$501$	−5.17520	−	8.96371i	−0.231211	−	0.400469i
$502$	−16.4521	+	28.4959i	−0.734294	+	1.27183i
$503$	35.9405			1.60251			0.801255	−	0.598324i	$-0.204166\pi$
$503$	35.9405			1.60251			0.801255	+	0.598324i	$0.204166\pi$
$504$	6.33071	+	8.60335i	0.281992	+	0.383224i
$505$	−0.202894			−0.00902869
$506$	−22.0042	+	38.1124i	−0.978206	+	1.69430i
$507$	14.7768	+	25.5941i	0.656259	+	1.13667i
$508$	1.94592	+	3.37043i	0.0863363	+	0.149539i
$509$	−11.9008	+	20.6128i	−0.527495	+	0.913648i	0.471992	+	0.881603i	$0.343535\pi$
$509$	−11.9008	+	20.6128i	−0.527495	+	0.913648i	−0.999486	+	0.0320448i	$0.989798\pi$
$510$	11.8018			0.522594
$511$	−16.4535	+	1.83020i	−0.727859	+	0.0809632i
$512$	−5.14172			−0.227234
$513$	6.47228	−	11.2103i	0.285758	−	0.494948i
$514$	18.5688	+	32.1622i	0.819037	+	1.41861i
$515$	−0.0322611	−	0.0558778i	−0.00142159	−	0.00246227i
$516$	−3.43724	+	5.95348i	−0.151316	+	0.262087i
$517$	22.3820			0.984357
$518$	34.5755	−	3.84599i	1.51916	−	0.168983i
$519$	48.5039			2.12909
$520$	2.40828	−	4.17126i	0.105610	−	0.182922i
$521$	1.07799	+	1.86713i	0.0472274	+	0.0818003i	0.888673	−	0.458542i	$-0.151628\pi$
$521$	1.07799	+	1.86713i	0.0472274	+	0.0818003i	−0.841445	+	0.540342i	$0.818295\pi$
$522$	−3.88500	−	6.72902i	−0.170042	−	0.294521i
$523$	10.7689	−	18.6523i	0.470892	−	0.815609i	−0.528553	−	0.848900i	$-0.677265\pi$
$523$	10.7689	−	18.6523i	0.470892	−	0.815609i	0.999446	+	0.0332907i	$0.0105987\pi$
$524$	−8.41075			−0.367425
$525$	−16.5892	−	22.5445i	−0.724010	−	0.983921i
$526$	6.52653			0.284570
$527$	7.02520	−	12.1680i	0.306023	−	0.530047i
$528$	−18.0987	−	31.3478i	−0.787644	−	1.36424i
$529$	−20.4824	−	35.4766i	−0.890540	−	1.54246i
$530$	2.09878	−	3.63519i	0.0911650	−	0.157902i
$531$	−26.3808			−1.14483
$532$	3.27493	−	7.47721i	0.141986	−	0.324178i
$533$	57.8248			2.50467
$534$	−21.7383	+	37.6518i	−0.940707	+	1.62935i
$535$	0.395938	+	0.685784i	0.0171179	+	0.0296490i
$536$	1.59259	+	2.75844i	0.0687893	+	0.119147i
$537$	3.41038	−	5.90696i	0.147169	−	0.254904i
$538$	−37.9630			−1.63670
$539$	−7.07567	+	22.7095i	−0.304770	+	0.978167i
$540$	−0.681590			−0.0293310
$541$	4.62153	−	8.00472i	0.198695	−	0.344150i	−0.749411	−	0.662106i	$-0.769663\pi$
$541$	4.62153	−	8.00472i	0.198695	−	0.344150i	0.948106	+	0.317956i	$0.102996\pi$
$542$	16.8788	+	29.2349i	0.725005	+	1.25575i
$543$	4.76938	+	8.26081i	0.204674	+	0.354505i
$544$	13.4789	−	23.3461i	0.577902	−	1.00096i
$545$	3.33876			0.143017
$546$	−19.3963	+	44.2850i	−0.830084	+	1.89522i
$547$	−35.7206			−1.52730			−0.763652	−	0.645628i	$-0.776596\pi$
$547$	−35.7206			−1.52730			−0.763652	+	0.645628i	$0.776596\pi$
$548$	0.311125	−	0.538884i	0.0132906	−	0.0230200i
$549$	−12.4087	−	21.4926i	−0.529592	−	0.917281i
$550$	13.2721	+	22.9879i	0.565923	+	0.980207i
$551$	6.57370	−	11.3860i	0.280049	−	0.485059i
$552$	39.1320			1.66557
$553$	−6.02573	−	8.18889i	−0.256240	−	0.348227i
$554$	13.6078			0.578141
$555$	−3.73578	+	6.47055i	−0.158575	+	0.274660i
$556$	1.47457	+	2.55402i	0.0625355	+	0.108315i
$557$	−11.9507	−	20.6992i	−0.506366	−	0.877052i	−0.999973	−	0.00736692i	$-0.997655\pi$
$557$	−11.9507	−	20.6992i	−0.506366	−	0.877052i	0.493606	−	0.869685i	$-0.335678\pi$
$558$	2.59908	−	4.50173i	0.110028	−	0.190574i
$559$	25.9207			1.09633
$560$	5.35894	−	0.596099i	0.226456	−	0.0251898i
$561$	−59.0250			−2.49204
$562$	13.1590	−	22.7920i	0.555078	−	0.961424i
$563$	−18.2682	−	31.6415i	−0.769913	−	1.33353i	−0.937610	−	0.347690i	$-0.886966\pi$
$563$	−18.2682	−	31.6415i	−0.769913	−	1.33353i	0.167696	−	0.985839i	$-0.446367\pi$
$564$	4.49426	+	7.78429i	0.189243	+	0.327778i
$565$	−1.57050	+	2.72018i	−0.0660714	+	0.114439i
$566$	−46.6198			−1.95958
$567$	−29.3302	+	3.26254i	−1.23175	+	0.137014i
$568$	−1.63814			−0.0687349
$569$	1.92303	−	3.33078i	0.0806175	−	0.139634i	−0.822898	−	0.568189i	$-0.807644\pi$
$569$	1.92303	−	3.33078i	0.0806175	−	0.139634i	0.903515	+	0.428556i	$0.140977\pi$
$570$	3.69402	+	6.39822i	0.154725	+	0.267992i
$571$	14.7947	+	25.6252i	0.619140	+	1.07238i	0.989643	+	0.143551i	$0.0458521\pi$
$571$	14.7947	+	25.6252i	0.619140	+	1.07238i	−0.370503	+	0.928831i	$0.620815\pi$
$572$	5.43986	−	9.42211i	0.227452	−	0.393958i
$573$	41.5135			1.73425
$574$	28.5360	+	38.7801i	1.19107	+	1.61865i
$575$	−38.5811			−1.60894
$576$	−3.80297	+	6.58694i	−0.158457	+	0.274456i
$577$	9.59400	+	16.6173i	0.399403	+	0.691787i	0.993652	−	0.112494i	$-0.0358840\pi$
$577$	9.59400	+	16.6173i	0.399403	+	0.691787i	−0.594249	+	0.804281i	$0.702551\pi$
$578$	−37.0301	−	64.1380i	−1.54025	−	2.66779i
$579$	−21.3637	+	37.0030i	−0.887845	+	1.53779i
$580$	−0.692270			−0.0287449
$581$	−3.21715	+	7.34530i	−0.133470	+	0.304735i
$582$	−1.78447			−0.0739686
$583$	−10.4967	+	18.1808i	−0.434729	+	0.752972i
$584$	−6.98002	−	12.0898i	−0.288835	−	0.500278i
$585$	−1.95334	−	3.38328i	−0.0807605	−	0.139881i
$586$	−15.8106	+	27.3847i	−0.653129	+	1.13125i
$587$	−7.80758			−0.322253			−0.161127	−	0.986934i	$-0.551513\pi$
$587$	−7.80758			−0.322253			−0.161127	+	0.986934i	$0.551513\pi$
$588$	−9.31898	+	2.09916i	−0.384308	+	0.0865679i
$589$	8.79565			0.362418
$590$	−4.95248	+	8.57794i	−0.203890	+	0.353148i
$591$	−27.6368	−	47.8683i	−1.13683	−	1.96904i
$592$	19.7205	+	34.1569i	0.810508	+	1.40384i
$593$	10.8878	−	18.8583i	0.447109	−	0.774416i	−0.551087	−	0.834448i	$-0.685787\pi$
$593$	10.8878	−	18.8583i	0.447109	−	0.774416i	0.998196	+	0.0600315i	$0.0191201\pi$
$594$	14.3654			0.589421
$595$	3.52746	−	8.05379i	0.144612	−	0.330173i
$596$	0.349219			0.0143046
$597$	25.9572	−	44.9592i	1.06236	−	1.84006i
$598$	33.3198	+	57.7116i	1.36255	+	2.36000i
$599$	23.5342	+	40.7624i	0.961580	+	1.66551i	0.718534	+	0.695492i	$0.244813\pi$
$599$	23.5342	+	40.7624i	0.961580	+	1.66551i	0.243046	+	0.970015i	$0.421853\pi$
$600$	11.8014	−	20.4407i	0.481792	−	0.834488i
$601$	15.5272			0.633366			0.316683	−	0.948531i	$-0.397431\pi$
$601$	15.5272			0.633366			0.316683	+	0.948531i	$0.397431\pi$
$602$	12.7916	+	17.3837i	0.521348	+	0.708506i
$603$	2.58347			0.105207
$604$	1.82724	−	3.16487i	0.0743492	−	0.128777i
$605$	0.114678	+	0.198628i	0.00466232	+	0.00807538i
$606$	0.858670	+	1.48726i	0.0348811	+	0.0604158i
$607$	18.0521	−	31.2672i	0.732713	−	1.26910i	−0.223007	−	0.974817i	$-0.571587\pi$
$607$	18.0521	−	31.2672i	0.732713	−	1.26910i	0.955720	−	0.294279i	$-0.0950794\pi$
$608$	16.8757			0.684402
$609$	−15.2911	+	1.70090i	−0.619626	+	0.0689239i
$610$	−9.31797			−0.377274
$611$	16.9459	−	29.3512i	0.685558	−	1.18742i
$612$	−4.45930	−	7.72374i	−0.180257	−	0.312214i
$613$	5.98414	+	10.3648i	0.241697	+	0.418632i	0.961198	−	0.275860i	$-0.0889626\pi$
$613$	5.98414	+	10.3648i	0.241697	+	0.418632i	−0.719501	+	0.694492i	$0.755629\pi$
$614$	2.12619	−	3.68267i	0.0858061	−	0.148620i
$615$	−10.3406			−0.416975
$616$	−19.9349	+	2.21745i	−0.803200	+	0.0893437i
$617$	13.3488			0.537404			0.268702	−	0.963223i	$-0.413405\pi$
$617$	13.3488			0.537404			0.268702	+	0.963223i	$0.413405\pi$
$618$	−0.273064	+	0.472961i	−0.0109843	+	0.0190253i
$619$	−17.0148	−	29.4704i	−0.683881	−	1.18452i	−0.973787	−	0.227461i	$-0.926958\pi$
$619$	−17.0148	−	29.4704i	−0.683881	−	1.18452i	0.289907	−	0.957055i	$-0.406376\pi$
$620$	−0.231565	−	0.401083i	−0.00929988	−	0.0161079i
$621$	−10.4399	+	18.0824i	−0.418937	+	0.725620i
$622$	18.5521			0.743872
$623$	19.1969	+	26.0884i	0.769108	+	1.04521i
$624$	−54.8118			−2.19423
$625$	−11.1952	+	19.3907i	−0.447808	+	0.775626i
$626$	−16.5685	−	28.6975i	−0.662211	−	1.14698i
$627$	−18.4750	−	31.9997i	−0.737822	−	1.27794i
$628$	−2.12293	+	3.67702i	−0.0847140	+	0.146729i
$629$	64.3143			2.56438
$630$	1.30504	−	2.97962i	0.0519938	−	0.118711i
$631$	0.0706885			0.00281406			0.00140703	−	0.999999i	$-0.499552\pi$
$631$	0.0706885			0.00281406			0.00140703	+	0.999999i	$0.499552\pi$
$632$	4.28667	−	7.42473i	0.170515	−	0.295340i
$633$	8.66679	+	15.0113i	0.344474	+	0.596646i
$634$	−22.4836	−	38.9427i	−0.892936	−	1.54661i
$635$	−1.31209	+	2.27261i	−0.0520689	+	0.0901859i
$636$	−8.43088			−0.334306
$637$	24.4235	+	26.4728i	0.967696	+	1.04889i
$638$	14.5905			0.577645
$639$	−0.664342	+	1.15067i	−0.0262809	+	0.0455199i
$640$	2.85588	+	4.94653i	0.112889	+	0.195529i
$641$	−1.66501	−	2.88388i	−0.0657639	−	0.113906i	0.831269	−	0.555871i	$-0.187615\pi$
$641$	−1.66501	−	2.88388i	−0.0657639	−	0.113906i	−0.897033	+	0.441964i	$0.854282\pi$
$642$	3.35130	−	5.80462i	0.132265	−	0.229090i
$643$	24.8940			0.981723			0.490861	−	0.871238i	$-0.336682\pi$
$643$	24.8940			0.981723			0.490861	+	0.871238i	$0.336682\pi$
$644$	−5.28249	+	12.0608i	−0.208159	+	0.475263i
$645$	−4.63532			−0.182516
$646$	31.7977	−	55.0752i	1.25106	−	2.16690i
$647$	−22.0899	−	38.2609i	−0.868445	−	1.50419i	−0.863586	−	0.504202i	$-0.831787\pi$
$647$	−22.0899	−	38.2609i	−0.868445	−	1.50419i	−0.00485919	−	0.999988i	$-0.501547\pi$
$648$	−12.4427	−	21.5514i	−0.488795	−	0.846618i
$649$	24.7690	−	42.9012i	0.972269	−	1.68402i
$650$	40.1944			1.57655
$651$	−6.10035	−	8.29030i	−0.239092	−	0.324923i
$652$	−3.56807			−0.139737
$653$	−15.0713	+	26.1043i	−0.589786	+	1.02154i	0.404474	+	0.914549i	$0.367455\pi$
$653$	−15.0713	+	26.1043i	−0.589786	+	1.02154i	−0.994260	+	0.106990i	$0.965879\pi$
$654$	−14.1300	−	24.4738i	−0.552526	−	0.957003i
$655$	−2.83560	−	4.91140i	−0.110796	−	0.191904i
$656$	−27.2932	+	47.2732i	−1.06562	+	1.84571i
$657$	−11.3229			−0.441748
$658$	28.0470	−	3.11979i	1.09338	−	0.121622i
$659$	5.18577			0.202009			0.101004	−	0.994886i	$-0.467794\pi$
$659$	5.18577			0.202009			0.101004	+	0.994886i	$0.467794\pi$
$660$	−0.972793	+	1.68493i	−0.0378659	+	0.0655857i
$661$	−5.38072	−	9.31969i	−0.209286	−	0.362494i	0.742204	−	0.670174i	$-0.233781\pi$
$661$	−5.38072	−	9.31969i	−0.209286	−	0.362494i	−0.951490	+	0.307680i	$0.900447\pi$
$662$	−1.84863	−	3.20193i	−0.0718491	−	0.124446i
$663$	−44.6893	+	77.4041i	−1.73559	+	3.00612i
$664$	−6.76201			−0.262417
$665$	5.47037	−	0.608495i	0.212132	−	0.0235964i
$666$	23.7940			0.921999
$667$	−10.6034	+	18.3657i	−0.410567	+	0.711123i
$668$	1.46838	+	2.54331i	0.0568133	+	0.0984035i
$669$	−9.80772	−	16.9875i	−0.379188	−	0.656773i
$670$	0.484995	−	0.840036i	0.0187370	−	0.0324534i
$671$	46.6024			1.79906
$672$	−11.7044	−	15.9062i	−0.451508	−	0.613593i
$673$	34.7697			1.34027			0.670137	−	0.742238i	$-0.266235\pi$
$673$	34.7697			1.34027			0.670137	+	0.742238i	$0.266235\pi$
$674$	6.08506	−	10.5396i	0.234388	−	0.405972i
$675$	6.29691	+	10.9066i	0.242368	+	0.419794i
$676$	−4.19267	−	7.26191i	−0.161256	−	0.279304i
$677$	−12.8159	+	22.1978i	−0.492556	+	0.853133i	−0.999963	−	0.00857396i	$-0.997271\pi$
$677$	−12.8159	+	22.1978i	−0.492556	+	0.853133i	0.507407	+	0.861707i	$0.330604\pi$
$678$	26.5860			1.02103
$679$	−0.533361	+	1.21775i	−0.0204685	+	0.0467331i
$680$	7.41424			0.284323
$681$	1.80377	−	3.12422i	0.0691206	−	0.119720i
$682$	4.88055	+	8.45337i	0.186886	+	0.323696i
$683$	−11.4482	−	19.8289i	−0.438053	−	0.758730i	0.559486	−	0.828840i	$-0.310999\pi$
$683$	−11.4482	−	19.8289i	−0.438053	−	0.758730i	−0.997539	+	0.0701093i	$0.977665\pi$
$684$	2.79155	−	4.83511i	0.106738	−	0.184875i
$685$	0.419570			0.0160309
$686$	−5.70111	+	29.4437i	−0.217669	+	1.12416i
$687$	−51.8436			−1.97796
$688$	−12.2345	+	21.1908i	−0.466437	+	0.807893i
$689$	15.8946	+	27.5303i	0.605536	+	1.04882i
$690$	−5.95848	−	10.3204i	−0.226836	−	0.392891i
$691$	−12.5319	+	21.7059i	−0.476736	+	0.825732i	−0.999645	−	0.0266572i	$-0.991514\pi$
$691$	−12.5319	+	21.7059i	−0.476736	+	0.825732i	0.522908	+	0.852389i	$0.324847\pi$
$692$	−13.7622			−0.523160
$693$	−6.52693	+	14.9021i	−0.247937	+	0.566083i
$694$	−44.4427			−1.68702
$695$	−0.994269	+	1.72212i	−0.0377148	+	0.0653239i
$696$	−6.48690	−	11.2356i	−0.245885	−	0.425886i
$697$	44.5055	+	77.0858i	1.68577	+	2.91983i
$698$	13.1075	−	22.7029i	0.496127	−	0.859317i
$699$	2.21600			0.0838167
$700$	4.70690	+	6.39663i	0.177904	+	0.241770i
$701$	−35.6715			−1.34730			−0.673648	−	0.739053i	$-0.735274\pi$
$701$	−35.6715			−1.34730			−0.673648	+	0.739053i	$0.735274\pi$
$702$	10.8764	−	18.8385i	0.410504	−	0.711013i
$703$	20.1306	+	34.8672i	0.759240	+	1.31504i
$704$	−7.14123	−	12.3690i	−0.269145	−	0.466173i
$705$	−3.03039	+	5.24879i	−0.114131	+	0.197681i
$706$	14.8890			0.560354
$707$	1.27158	−	0.141444i	0.0478228	−	0.00531955i
$708$	19.8943			0.747675
$709$	−14.9784	+	25.9434i	−0.562526	+	0.974324i	0.434749	+	0.900552i	$0.356837\pi$
$709$	−14.9784	+	25.9434i	−0.562526	+	0.974324i	−0.997275	+	0.0737721i	$0.976496\pi$
$710$	0.249434	+	0.432032i	0.00936108	+	0.0162139i
$711$	−3.47689	−	6.02214i	−0.130393	−	0.225848i
$712$	−13.6566	+	23.6539i	−0.511802	+	0.886467i
$713$	−14.1875			−0.531325
$714$	−73.9646	+	8.22743i	−2.76806	+	0.307904i
$715$	7.33596			0.274350
$716$	−0.967642	+	1.67600i	−0.0361625	+	0.0626352i
$717$	−30.2132	−	52.3309i	−1.12833	−	1.95433i
$718$	−13.5163	−	23.4109i	−0.504423	−	0.873687i
$719$	−2.84080	+	4.92042i	−0.105944	+	0.183501i	−0.914124	−	0.405436i	$-0.867120\pi$
$719$	−2.84080	+	4.92042i	−0.105944	+	0.183501i	0.808179	+	0.588936i	$0.200453\pi$
$720$	3.68789			0.137439
$721$	0.241141	+	0.327708i	0.00898057	+	0.0122045i
$722$	9.04374			0.336573
$723$	−23.4295	+	40.5810i	−0.871351	+	1.50922i
$724$	−1.35323	−	2.34387i	−0.0502926	−	0.0871093i
$725$	6.39558	+	11.0775i	0.237526	+	0.411407i
$726$	0.970658	−	1.68123i	0.0360245	−	0.0623963i
$727$	−22.3497			−0.828904			−0.414452	−	0.910071i	$-0.636027\pi$
$727$	−22.3497			−0.828904			−0.414452	+	0.910071i	$0.636027\pi$
$728$	−12.1853	+	27.8211i	−0.451616	+	1.03112i
$729$	−3.00808			−0.111410
$730$	−2.12565	+	3.68173i	−0.0786737	+	0.136267i
$731$	19.9502	+	34.5547i	0.737884	+	1.27805i
$732$	9.35768	+	16.2080i	0.345870	+	0.599064i
$733$	22.4867	−	38.9480i	0.830563	−	1.43858i	−0.0670287	−	0.997751i	$-0.521352\pi$
$733$	22.4867	−	38.9480i	0.830563	−	1.43858i	0.897592	−	0.440827i	$-0.145315\pi$
$734$	18.1190			0.668786
$735$	−4.36759	−	4.73404i	−0.161101	−	0.174618i
$736$	−27.2207			−1.00337
$737$	−2.42563	+	4.20131i	−0.0893491	+	0.154757i
$738$	16.4655	+	28.5190i	0.606102	+	1.04980i
$739$	−10.4585	−	18.1147i	−0.384723	−	0.666360i	0.607008	−	0.794696i	$-0.292370\pi$
$739$	−10.4585	−	18.1147i	−0.384723	−	0.666360i	−0.991731	+	0.128336i	$0.959036\pi$
$740$	1.05997	−	1.83591i	0.0389651	−	0.0674896i
$741$	−55.9515			−2.05543
$742$	−10.6193	+	24.2456i	−0.389846	+	0.890084i
$743$	−25.7906			−0.946166			−0.473083	−	0.881018i	$-0.656859\pi$
$743$	−25.7906			−0.946166			−0.473083	+	0.881018i	$0.656859\pi$
$744$	4.33976	−	7.51668i	0.159103	−	0.275575i
$745$	0.117736	+	0.203924i	0.00431350	+	0.00747120i
$746$	2.18051	+	3.77676i	0.0798343	+	0.138277i
$747$	−2.74231	+	4.74982i	−0.100336	+	0.173787i
$748$	16.7474			0.612345
$749$	−2.95951	−	4.02193i	−0.108138	−	0.146958i
$750$	−14.6380			−0.534504
$751$	0.763307	−	1.32209i	0.0278535	−	0.0482436i	−0.851763	−	0.523928i	$-0.824466\pi$
$751$	0.763307	−	1.32209i	0.0278535	−	0.0482436i	0.879616	+	0.475684i	$0.157799\pi$
$752$	15.9969	+	27.7074i	0.583347	+	1.01039i
$753$	22.2812	+	38.5921i	0.811971	+	1.40638i
$754$	11.0468	−	19.1337i	0.402302	−	0.696808i
$755$	2.46414			0.0896791
$756$	4.27167	−	0.475157i	0.155359	−	0.0172813i
$757$	15.8366			0.575592			0.287796	−	0.957692i	$-0.407077\pi$
$757$	15.8366			0.575592			0.287796	+	0.957692i	$0.407077\pi$
$758$	17.5148	−	30.3365i	0.636165	−	1.10187i
$759$	29.8004	+	51.6158i	1.08169	+	1.87353i
$760$	2.32068	+	4.01954i	0.0841800	+	0.145804i
$761$	−26.0872	+	45.1843i	−0.945659	+	1.63793i	−0.191231	+	0.981545i	$0.561248\pi$
$761$	−26.0872	+	45.1843i	−0.945659	+	1.63793i	−0.754427	+	0.656384i	$0.772085\pi$
$762$	22.2117			0.804644
$763$	−20.9247	+	2.32755i	−0.757526	+	0.0842631i
$764$	−11.7788			−0.426142
$765$	3.00682	−	5.20796i	0.108712	−	0.188294i
$766$	−6.13542	−	10.6269i	−0.221682	−	0.383964i
$767$	−37.5064	−	64.9631i	−1.35428	−	2.34568i
$768$	14.9549	−	25.9027i	0.539640	−	0.934683i
$769$	26.6952			0.962654			0.481327	−	0.876541i	$-0.340155\pi$
$769$	26.6952			0.962654			0.481327	+	0.876541i	$0.340155\pi$
$770$	3.62023	+	4.91985i	0.130464	+	0.177299i
$771$	50.2958			1.81136
$772$	6.06161	−	10.4990i	0.218162	−	0.377868i
$773$	6.20767	+	10.7520i	0.223274	+	0.386722i	0.955800	−	0.294017i	$-0.0949921\pi$
$773$	6.20767	+	10.7520i	0.223274	+	0.386722i	−0.732526	+	0.680739i	$0.761659\pi$
$774$	7.38086	+	12.7840i	0.265299	+	0.459512i
$775$	−4.27866	+	7.41086i	−0.153694	+	0.266206i
$776$	−1.12105			−0.0402434
$777$	18.9021	−	43.1566i	0.678108	−	1.54824i
$778$	−7.78060			−0.278948
$779$	−27.8608	+	48.2563i	−0.998215	+	1.72896i
$780$	1.47305	+	2.55140i	0.0527437	+	0.0913547i
$781$	−1.24750	−	2.16074i	−0.0446392	−	0.0773173i
$782$	−51.2900	+	88.8368i	−1.83413	+	3.17680i
$783$	6.92245			0.247388
$784$	−33.1700	+	7.47176i	−1.18464	+	0.266849i
$785$	−2.86289			−0.102181
$786$	−24.0011	+	41.5711i	−0.856090	+	1.48279i
$787$	−2.90086	−	5.02444i	−0.103404	−	0.179102i	0.809681	−	0.586871i	$-0.199640\pi$
$787$	−2.90086	−	5.02444i	−0.103404	−	0.179102i	−0.913085	+	0.407769i	$0.866307\pi$
$788$	7.84149	+	13.5819i	0.279342	+	0.483834i
$789$	4.41946	−	7.65473i	0.157337	−	0.272515i
$790$	−2.61086			−0.0928903
$791$	7.94632	−	18.1428i	0.282539	−	0.645084i
$792$	−13.7187			−0.487473
$793$	35.2838	−	61.1133i	1.25296	−	2.17020i
$794$	1.52958	+	2.64931i	0.0542829	+	0.0940207i
$795$	−2.84238	−	4.92315i	−0.100809	−	0.174606i
$796$	−7.36493	+	12.7564i	−0.261043	+	0.452140i
$797$	39.9000			1.41333			0.706665	−	0.707548i	$-0.250199\pi$
$797$	39.9000			1.41333			0.706665	+	0.707548i	$0.250199\pi$
$798$	−27.6116	−	37.5238i	−0.977439	−	1.32833i
$799$	52.1705			1.84566
$800$	−8.20924	+	14.2188i	−0.290241	+	0.502711i
$801$	11.0767	+	19.1855i	0.391378	+	0.677886i
$802$	14.1705	+	24.5440i	0.500377	+	0.866679i
$803$	10.6311	−	18.4136i	0.375163	−	0.649801i
$804$	−1.94825			−0.0687094
$805$	−8.82376	+	0.981508i	−0.310997	+	0.0345936i
$806$	14.7807			0.520629
$807$	−25.7067	+	44.5253i	−0.904919	+	1.56737i
$808$	0.539440	+	0.934338i	0.0189774	+	0.0328699i
$809$	11.1928	+	19.3864i	0.393516	+	0.681590i	0.992911	−	0.118864i	$-0.0379251\pi$
$809$	11.1928	+	19.3864i	0.393516	+	0.681590i	−0.599394	+	0.800454i	$0.704592\pi$
$810$	−3.78921	+	6.56310i	−0.133139	+	0.230604i
$811$	−31.5020			−1.10618			−0.553092	−	0.833120i	$-0.686552\pi$
$811$	−31.5020			−1.10618			−0.553092	+	0.833120i	$0.686552\pi$
$812$	4.33860	−	0.482603i	0.152255	−	0.0169360i
$813$	45.7180			1.60340
$814$	−22.3402	+	38.6944i	−0.783025	+	1.35624i
$815$	−1.20294	−	2.08355i	−0.0421371	−	0.0729836i
$816$	−42.1865	−	73.0692i	−1.47682	−	2.55793i
$817$	−12.4889	+	21.6315i	−0.436933	+	0.756790i
$818$	−17.5138			−0.612355
$819$	14.6006	+	19.8420i	0.510185	+	0.693335i
$820$	2.93399			0.102459
$821$	−14.6295	+	25.3391i	−0.510574	+	0.884341i	0.489351	+	0.872087i	$0.337234\pi$
$821$	−14.6295	+	25.3391i	−0.510574	+	0.884341i	−0.999925	+	0.0122534i	$0.996100\pi$
$822$	−1.77566	−	3.07554i	−0.0619334	−	0.107272i
$823$	20.4190	+	35.3668i	0.711762	+	1.23281i	0.964195	+	0.265193i	$0.0854358\pi$
$823$	20.4190	+	35.3668i	0.711762	+	1.23281i	−0.252433	+	0.967614i	$0.581231\pi$
$824$	−0.171547	+	0.297127i	−0.00597611	+	0.0103509i
$825$	35.9489			1.25158
$826$	25.0583	−	57.2123i	0.871889	−	1.99067i
$827$	15.9485			0.554582			0.277291	−	0.960786i	$-0.410563\pi$
$827$	15.9485			0.554582			0.277291	+	0.960786i	$0.410563\pi$
$828$	−4.50280	+	7.79908i	−0.156483	+	0.271037i
$829$	−20.8952	−	36.1915i	−0.725719	−	1.25698i	−0.958677	−	0.284496i	$-0.908174\pi$
$829$	−20.8952	−	36.1915i	−0.725719	−	1.25698i	0.232958	−	0.972487i	$-0.425159\pi$
$830$	1.02963	+	1.78337i	0.0357389	+	0.0619015i
$831$	9.21457	−	15.9601i	0.319650	−	0.553650i
$832$	−21.6272			−0.749788
$833$	−16.4928	+	52.9339i	−0.571441	+	1.83405i
$834$	16.8314			0.582824
$835$	−0.990098	+	1.71490i	−0.0342637	+	0.0593465i
$836$	5.24199	+	9.07940i	0.181298	+	0.314017i
$837$	2.31557	+	4.01069i	0.0800379	+	0.138630i
$838$	4.75868	−	8.24228i	0.164386	−	0.284725i
$839$	−41.8382			−1.44441			−0.722207	−	0.691677i	$-0.756872\pi$
$839$	−41.8382			−1.44441			−0.722207	+	0.691677i	$0.756872\pi$
$840$	2.17906	−	4.97516i	0.0751846	−	0.171659i
$841$	−21.9691			−0.757554
$842$	−21.5274	+	37.2866i	−0.741884	+	1.28498i
$843$	−17.8213	−	30.8674i	−0.613798	−	1.06313i
$844$	−2.45906	−	4.25922i	−0.0846444	−	0.146608i
$845$	2.82703	−	4.89656i	0.0972527	−	0.168447i
$846$	19.3012			0.663590
$847$	−0.857181	−	1.16490i	−0.0294531	−	0.0400264i
$848$	−30.0089			−1.03051
$849$	−31.5687	+	54.6786i	−1.08343	+	1.87656i
$850$	30.9361	+	53.5829i	1.06110	+	1.83788i
$851$	−32.4708	−	56.2411i	−1.11309	−	1.92792i
$852$	0.500993	−	0.867746i	0.0171638	−	0.0297285i
$853$	6.90252			0.236338			0.118169	−	0.992994i	$-0.462298\pi$
$853$	6.90252			0.236338			0.118169	+	0.992994i	$0.462298\pi$
$854$	58.3977	−	6.49585i	1.99833	−	0.222283i
$855$	3.76457			0.128746
$856$	2.10538	−	3.64662i	0.0719603	−	0.124639i
$857$	3.55993	+	6.16597i	0.121605	+	0.210626i	0.920401	−	0.390976i	$-0.127863\pi$
$857$	3.55993	+	6.16597i	0.121605	+	0.210626i	−0.798796	+	0.601602i	$0.794529\pi$
$858$	−31.0465	−	53.7742i	−1.05991	−	1.83582i
$859$	16.1640	−	27.9968i	0.551507	−	0.955239i	−0.446659	−	0.894704i	$-0.647386\pi$
$859$	16.1640	−	27.9968i	0.551507	−	0.955239i	0.998166	−	0.0605345i	$-0.0192805\pi$
$860$	1.31520			0.0448479
$861$	64.8069	−	7.20878i	2.20861	−	0.245674i
$862$	−30.2794			−1.03132
$863$	2.31559	−	4.01073i	0.0788238	−	0.136527i	−0.823919	−	0.566708i	$-0.808217\pi$
$863$	2.31559	−	4.01073i	0.0788238	−	0.136527i	0.902743	+	0.430181i	$0.141550\pi$
$864$	4.44276	+	7.69509i	0.151146	+	0.261792i
$865$	−4.63978	−	8.03634i	−0.157757	−	0.273244i
$866$	21.6991	−	37.5839i	0.737365	−	1.27715i
$867$	−100.300			−3.40637
$868$	1.73088	+	2.35224i	0.0587497	+	0.0798402i
$869$	13.0578			0.442956
$870$	−1.97547	+	3.42162i	−0.0669748	+	0.116004i
$871$	3.67300	+	6.36182i	0.124455	+	0.215562i
$872$	−8.87684	−	15.3751i	−0.300608	−	0.520668i
$873$	−0.454638	+	0.787456i	−0.0153872	+	0.0266514i
$874$	−64.2157			−2.17213
$875$	−4.37516	+	9.98924i	−0.147907	+	0.337698i
$876$	8.53881			0.288500
$877$	−3.84593	+	6.66134i	−0.129868	+	0.224937i	−0.923625	−	0.383297i	$-0.874789\pi$
$877$	−3.84593	+	6.66134i	−0.129868	+	0.224937i	0.793757	+	0.608234i	$0.208122\pi$
$878$	6.88642	+	11.9276i	0.232405	+	0.402538i
$879$	21.4124	+	37.0873i	0.722221	+	1.25092i
$880$	−3.46256	+	5.99734i	−0.116723	+	0.202170i
$881$	−15.2681			−0.514394			−0.257197	−	0.966359i	$-0.582799\pi$
$881$	−15.2681			−0.514394			−0.257197	+	0.966359i	$0.582799\pi$
$882$	−6.10175	+	19.5837i	−0.205456	+	0.659416i
$883$	−35.8290			−1.20574			−0.602870	−	0.797839i	$-0.705976\pi$
$883$	−35.8290			−1.20574			−0.602870	+	0.797839i	$0.705976\pi$
$884$	12.6799	−	21.9622i	0.426470	−	0.738667i
$885$	6.70717	+	11.6172i	0.225459	+	0.390506i
$886$	11.1112	+	19.2452i	0.373288	+	0.646554i
$887$	6.86610	−	11.8924i	0.230541	−	0.399309i	−0.727426	−	0.686186i	$-0.759284\pi$
$887$	6.86610	−	11.8924i	0.230541	−	0.399309i	0.957967	+	0.286877i	$0.0926170\pi$
$888$	39.7296			1.33324
$889$	6.63886	−	15.1576i	0.222660	−	0.508371i
$890$	8.31775			0.278812
$891$	18.9511	−	32.8243i	0.634886	−	1.09966i
$892$	2.78278	+	4.81992i	0.0931744	+	0.161383i
$893$	16.3295	+	28.2836i	0.546447	+	0.946474i
$894$	0.996539	−	1.72606i	0.0333292	−	0.0577280i
$895$	−1.30492			−0.0436187
$896$	−21.3468	−	29.0100i	−0.713146	−	0.969157i
$897$	90.2504			3.01337
$898$	31.8579	−	55.1795i	1.06311	−	1.84136i
$899$	2.35185	+	4.07353i	0.0784387	+	0.135860i
$900$	2.71592	+	4.70410i	0.0905305	+	0.156803i
$901$	−24.4669	+	42.3780i	−0.815112	+	1.41181i
$902$	−61.8378			−2.05897
$903$	29.0505	−	3.23143i	0.966742	−	0.107535i
$904$	16.7021			0.555503
$905$	0.912458	−	1.58042i	0.0303311	−	0.0525351i
$906$	−10.4285	−	18.0626i	−0.346463	−	0.600091i
$907$	−11.4123	−	19.7667i	−0.378939	−	0.656341i	0.611969	−	0.790881i	$-0.290378\pi$
$907$	−11.4123	−	19.7667i	−0.378939	−	0.656341i	−0.990908	+	0.134540i	$0.957044\pi$
$908$	−0.511790	+	0.886447i	−0.0169844	+	0.0294178i
$909$	0.875071			0.0290243
$910$	9.19274	−	1.02255i	0.304736	−	0.0338972i
$911$	17.7721			0.588817			0.294409	−	0.955680i	$-0.404877\pi$
$911$	17.7721			0.588817			0.294409	+	0.955680i	$0.404877\pi$
$912$	26.4090	−	45.7418i	0.874491	−	1.51466i
$913$	−5.14951	−	8.91922i	−0.170424	−	0.295183i
$914$	−4.27983	−	7.41289i	−0.141564	−	0.245197i
$915$	−6.30969	+	10.9287i	−0.208592	+	0.361292i
$916$	14.7098			0.486025
$917$	21.1952	+	28.8040i	0.699926	+	0.951191i
$918$	33.4846			1.10516
$919$	−3.54369	+	6.13785i	−0.116896	+	0.202469i	−0.918536	−	0.395338i	$-0.870628\pi$
$919$	−3.54369	+	6.13785i	−0.116896	+	0.202469i	0.801640	+	0.597807i	$0.203961\pi$
$920$	−3.74328	−	6.48355i	−0.123412	−	0.213756i
$921$	−2.87951	−	4.98746i	−0.0948831	−	0.164342i
$922$	−19.2389	+	33.3228i	−0.633600	+	1.09743i
$923$	−3.77806			−0.124356
$924$	4.92209	−	11.2380i	0.161925	−	0.369702i
$925$	−39.1703			−1.28791
$926$	−6.23931	+	10.8068i	−0.205036	+	0.355133i
$927$	0.139140	+	0.240998i	0.00456996	+	0.00791540i
$928$	4.51238	+	7.81567i	0.148126	+	0.256562i
$929$	−14.0054	+	24.2581i	−0.459503	+	0.795882i	−0.998935	−	0.0461473i	$-0.985306\pi$
$929$	−14.0054	+	24.2581i	−0.459503	+	0.795882i	0.539432	+	0.842029i	$0.318639\pi$
$930$	−2.64320			−0.0866738
$931$	−33.8598	+	7.62713i	−1.10971	+	0.249969i
$932$	−0.628753			−0.0205955
$933$	12.5626	−	21.7591i	0.411282	−	0.712361i
$934$	−13.5282	−	23.4315i	−0.442655	−	0.766701i
$935$	5.64621	+	9.77952i	0.184651	+	0.319825i
$936$	−10.3868	+	17.9904i	−0.339502	+	0.588034i
$937$	20.5948			0.672803			0.336402	−	0.941719i	$-0.390790\pi$
$937$	20.5948			0.672803			0.336402	+	0.941719i	$0.390790\pi$
$938$	−2.45395	+	5.60279i	−0.0801244	+	0.182938i
$939$	−44.8776			−1.46453
$940$	0.859824	−	1.48926i	0.0280444	−	0.0485742i
$941$	−3.49455	−	6.05274i	−0.113919	−	0.197314i	0.803428	−	0.595402i	$-0.203007\pi$
$941$	−3.49455	−	6.05274i	−0.113919	−	0.197314i	−0.917347	+	0.398088i	$0.869674\pi$
$942$	12.1161	+	20.9856i	0.394762	+	0.683748i
$943$	44.9397	−	77.8378i	1.46344	−	2.53475i
$944$	70.8119			2.30473
$945$	1.71761	+	2.33421i	0.0558739	+	0.0759320i
$946$	−27.7196			−0.901242
$947$	−4.36883	+	7.56704i	−0.141968	+	0.245896i	−0.928238	−	0.371988i	$-0.878676\pi$
$947$	−4.36883	+	7.56704i	−0.141968	+	0.245896i	0.786270	+	0.617883i	$0.212010\pi$
$948$	2.62199	+	4.54142i	0.0851583	+	0.147498i
$949$	−16.0981	−	27.8827i	−0.522566	−	0.905111i
$950$	−19.3662	+	33.5433i	−0.628323	+	1.08829i
$951$	−60.8992			−1.97479
$952$	−46.4666	+	5.16870i	−1.50599	+	0.167518i
$953$	21.4663			0.695361			0.347681	−	0.937613i	$-0.386969\pi$
$953$	21.4663			0.695361			0.347681	+	0.937613i	$0.386969\pi$
$954$	−9.05190	+	15.6783i	−0.293066	+	0.507605i
$955$	−3.97110	−	6.87814i	−0.128502	−	0.222572i
$956$	8.57252	+	14.8480i	0.277255	+	0.480220i
$957$	9.88002	−	17.1127i	0.319376	−	0.553175i
$958$	−22.7646			−0.735490
$959$	−2.62953	+	0.292495i	−0.0849121	+	0.00944516i
$960$	3.86753			0.124824
$961$	13.9266	−	24.1216i	0.449245	−	0.778116i
$962$	33.8286	+	58.5929i	1.09068	+	1.88911i
$963$	−1.70766	−	2.95775i	−0.0550284	−	0.0953120i
$964$	6.64773	−	11.5142i	0.214109	−	0.370848i
$965$	8.17443			0.263144
$966$	44.5377	+	60.5262i	1.43298	+	1.94740i
$967$	−17.4926			−0.562525			−0.281263	−	0.959631i	$-0.590753\pi$
$967$	−17.4926			−0.562525			−0.281263	+	0.959631i	$0.590753\pi$
$968$	0.609794	−	1.05619i	0.0195995	−	0.0339474i
$969$	−43.0638	−	74.5886i	−1.38341	−	2.39613i
$970$	0.170698	+	0.295658i	0.00548080	+	0.00949302i
$971$	−6.75793	+	11.7051i	−0.216872	+	0.375634i	−0.953850	−	0.300283i	$-0.902919\pi$
$971$	−6.75793	+	11.7051i	−0.216872	+	0.375634i	0.736978	+	0.675917i	$0.236252\pi$
$972$	10.3479			0.331910
$973$	5.03075	−	11.4861i	0.161278	−	0.368226i
$974$	−30.7999			−0.986893
$975$	27.2177	−	47.1425i	0.871666	−	1.50977i
$976$	33.3078	+	57.6907i	1.06616	+	1.84664i
$977$	−18.7278	−	32.4375i	−0.599155	−	1.03777i	−0.992946	−	0.118567i	$-0.962170\pi$
$977$	−18.7278	−	32.4375i	−0.599155	−	1.03777i	0.393791	−	0.919200i	$-0.371163\pi$
$978$	−10.1819	+	17.6356i	−0.325582	+	0.563924i
$979$	−41.5999			−1.32954
$980$	1.23923	+	1.34321i	0.0395858	+	0.0429072i
$981$	−14.3999			−0.459753
$982$	21.8330	−	37.8158i	0.696718	−	1.20675i
$983$	12.6658	+	21.9378i	0.403976	+	0.699708i	0.994202	−	0.107531i	$-0.0342944\pi$
$983$	12.6658	+	21.9378i	0.403976	+	0.699708i	−0.590225	+	0.807239i	$0.700961\pi$
$984$	27.4929	+	47.6191i	0.876441	+	1.51804i
$985$	−5.28736	+	9.15797i	−0.168469	+	0.291797i
$986$	34.0093			1.08308
$987$	15.3330	−	35.0078i	0.488054	−	1.11431i
$988$	15.8753			0.505062
$989$	20.1448	−	34.8918i	0.640567	−	1.10949i
$990$	2.08890	+	3.61808i	0.0663895	+	0.114990i
$991$	−5.46542	−	9.46639i	−0.173615	−	0.300710i	0.766066	−	0.642762i	$-0.222211\pi$
$991$	−5.46542	−	9.46639i	−0.173615	−	0.300710i	−0.939681	+	0.342052i	$0.888878\pi$
$992$	−3.01879	+	5.22871i	−0.0958468	+	0.166012i
$993$	−5.00723			−0.158899
$994$	−1.86444	−	2.53375i	−0.0591363	−	0.0803656i
$995$	−9.93204			−0.314867
$996$	2.06803	−	3.58193i	0.0655280	−	0.113498i
$997$	7.15363	+	12.3904i	0.226558	+	0.392409i	0.956786	−	0.290794i	$-0.0939195\pi$
$997$	7.15363	+	12.3904i	0.226558	+	0.392409i	−0.730228	+	0.683204i	$0.760586\pi$
$998$	3.14532	+	5.44786i	0.0995635	+	0.172449i
$999$	−10.5993	+	18.3585i	−0.335347	+	0.580837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	959.2.e.b.275.12	✓	90
7.2	even	3		6713.2.a.k.1.34		45
7.4	even	3	inner	959.2.e.b.823.12	yes	90
7.5	odd	6		6713.2.a.l.1.34		45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.2.e.b.275.12	✓	90	1.1	even	1	trivial
959.2.e.b.823.12	yes	90	7.4	even	3	inner
6713.2.a.k.1.34		45	7.2	even	3
6713.2.a.l.1.34		45	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 959 = 7 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	959.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809668 + 1.40239i) q^{2} +(1.09654 + 1.89926i) q^{3} +(-0.311125 - 0.538884i) q^{4} +(0.209785 - 0.363358i) q^{5} -3.55133 q^{6} +(-1.06146 + 2.42349i) q^{7} -2.23104 q^{8} +(-0.904790 + 1.56714i) q^{9} +O(q^{10})\)	\(q+(-0.809668 + 1.40239i) q^{2} +(1.09654 + 1.89926i) q^{3} +(-0.311125 - 0.538884i) q^{4} +(0.209785 - 0.363358i) q^{5} -3.55133 q^{6} +(-1.06146 + 2.42349i) q^{7} -2.23104 q^{8} +(-0.904790 + 1.56714i) q^{9} +(0.339712 + 0.588399i) q^{10} +(-1.69902 - 2.94279i) q^{11} +(0.682320 - 1.18181i) q^{12} -5.14547 q^{13} +(-2.53924 - 3.45080i) q^{14} +0.920149 q^{15} +(2.42865 - 4.20655i) q^{16} +(-3.96027 - 6.85939i) q^{17} +(-1.46516 - 2.53773i) q^{18} +(2.47916 - 4.29402i) q^{19} -0.261077 q^{20} +(-5.76677 + 0.641464i) q^{21} +5.50256 q^{22} +(-3.99890 + 6.92630i) q^{23} +(-2.44642 - 4.23732i) q^{24} +(2.41198 + 4.17767i) q^{25} +(4.16612 - 7.21593i) q^{26} +2.61068 q^{27} +(1.63623 - 0.182005i) q^{28} +2.65159 q^{29} +(-0.745015 + 1.29040i) q^{30} +(0.886960 + 1.53626i) q^{31} +(1.70176 + 2.94754i) q^{32} +(3.72607 - 6.45375i) q^{33} +12.8260 q^{34} +(0.657917 + 0.894102i) q^{35} +1.12601 q^{36} +(-4.05997 + 7.03207i) q^{37} +(4.01459 + 6.95347i) q^{38} +(-5.64220 - 9.77258i) q^{39} +(-0.468039 + 0.810667i) q^{40} -11.2380 q^{41} +(3.76959 - 8.60661i) q^{42} -5.03758 q^{43} +(-1.05721 + 1.83115i) q^{44} +(0.379623 + 0.657526i) q^{45} +(-6.47556 - 11.2160i) q^{46} +(-3.29337 + 5.70428i) q^{47} +10.6524 q^{48} +(-4.74661 - 5.14487i) q^{49} -7.81161 q^{50} +(8.68517 - 15.0432i) q^{51} +(1.60088 + 2.77281i) q^{52} +(-3.08905 - 5.35039i) q^{53} +(-2.11379 + 3.66118i) q^{54} -1.42571 q^{55} +(2.36816 - 5.40691i) q^{56} +10.8739 q^{57} +(-2.14691 + 3.71855i) q^{58} +(7.28922 + 12.6253i) q^{59} +(-0.286281 - 0.495853i) q^{60} +(-6.85725 + 11.8771i) q^{61} -2.87257 q^{62} +(-2.83756 - 3.85621i) q^{63} +4.20315 q^{64} +(-1.07944 + 1.86965i) q^{65} +(6.03377 + 10.4508i) q^{66} +(-0.713832 - 1.23639i) q^{67} +(-2.46428 + 4.26825i) q^{68} -17.5398 q^{69} +(-1.78657 + 0.198729i) q^{70} +0.734250 q^{71} +(2.01862 - 3.49636i) q^{72} +(3.12859 + 5.41888i) q^{73} +(-6.57446 - 11.3873i) q^{74} +(-5.28966 + 9.16195i) q^{75} -3.08531 q^{76} +(8.93525 - 0.993909i) q^{77} +18.2732 q^{78} +(-1.92138 + 3.32792i) q^{79} +(-1.01899 - 1.76494i) q^{80} +(5.57708 + 9.65979i) q^{81} +(9.09906 - 15.7600i) q^{82} +3.03088 q^{83} +(2.13986 + 2.90804i) q^{84} -3.32322 q^{85} +(4.07877 - 7.06464i) q^{86} +(2.90757 + 5.03605i) q^{87} +(3.79058 + 6.56547i) q^{88} +(6.12117 - 10.6022i) q^{89} -1.22947 q^{90} +(5.46170 - 12.4700i) q^{91} +4.97663 q^{92} +(-1.94517 + 3.36914i) q^{93} +(-5.33307 - 9.23715i) q^{94} +(-1.04018 - 1.80164i) q^{95} +(-3.73210 + 6.46418i) q^{96} +0.502479 q^{97} +(11.0583 - 2.49095i) q^{98} +6.14902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) \) 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9	\( 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9} + 25 q^{10} + 33 q^{12} - 72 q^{13} - 38 q^{16} + 18 q^{17} + 5 q^{18} + 43 q^{19} - 20 q^{20} + 8 q^{21} + q^{23} + 20 q^{24} - 43 q^{25} + 2 q^{26} - 106 q^{27} + 7 q^{28} - 8 q^{29} + 12 q^{30} + 59 q^{31} + 11 q^{32} + 37 q^{33} - 96 q^{34} + 2 q^{35} + 28 q^{36} + 39 q^{38} - 16 q^{39} + 56 q^{40} - 30 q^{41} + 26 q^{42} - 2 q^{43} + 2 q^{44} + 28 q^{45} - 31 q^{46} + 58 q^{47} - 24 q^{48} + 15 q^{49} - 148 q^{50} + 5 q^{51} + 115 q^{52} - 10 q^{53} + 39 q^{54} - 162 q^{55} + 63 q^{56} - 36 q^{57} + 11 q^{58} + 41 q^{59} - 90 q^{60} + 40 q^{61} + 58 q^{62} + 53 q^{63} + 30 q^{64} + 9 q^{65} + 42 q^{66} + 56 q^{68} - 10 q^{69} + 84 q^{70} - 84 q^{71} + 11 q^{72} + 67 q^{73} - 39 q^{74} + 40 q^{75} - 136 q^{76} + 21 q^{77} - 156 q^{78} + 9 q^{79} + 14 q^{80} - 73 q^{81} + 34 q^{82} - 96 q^{83} + 28 q^{84} + 12 q^{85} + 13 q^{86} + 135 q^{87} - 47 q^{88} + 17 q^{89} + 88 q^{90} + 26 q^{91} - 122 q^{92} + q^{93} + 28 q^{94} - 47 q^{95} + 50 q^{96} - 162 q^{97} + 128 q^{98} - 70 q^{99}+O(q^{100}) \) 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9 + 25 * q^10 + 33 * q^12 - 72 * q^13 - 38 * q^16 + 18 * q^17 + 5 * q^18 + 43 * q^19 - 20 * q^20 + 8 * q^21 + q^23 + 20 * q^24 - 43 * q^25 + 2 * q^26 - 106 * q^27 + 7 * q^28 - 8 * q^29 + 12 * q^30 + 59 * q^31 + 11 * q^32 + 37 * q^33 - 96 * q^34 + 2 * q^35 + 28 * q^36 + 39 * q^38 - 16 * q^39 + 56 * q^40 - 30 * q^41 + 26 * q^42 - 2 * q^43 + 2 * q^44 + 28 * q^45 - 31 * q^46 + 58 * q^47 - 24 * q^48 + 15 * q^49 - 148 * q^50 + 5 * q^51 + 115 * q^52 - 10 * q^53 + 39 * q^54 - 162 * q^55 + 63 * q^56 - 36 * q^57 + 11 * q^58 + 41 * q^59 - 90 * q^60 + 40 * q^61 + 58 * q^62 + 53 * q^63 + 30 * q^64 + 9 * q^65 + 42 * q^66 + 56 * q^68 - 10 * q^69 + 84 * q^70 - 84 * q^71 + 11 * q^72 + 67 * q^73 - 39 * q^74 + 40 * q^75 - 136 * q^76 + 21 * q^77 - 156 * q^78 + 9 * q^79 + 14 * q^80 - 73 * q^81 + 34 * q^82 - 96 * q^83 + 28 * q^84 + 12 * q^85 + 13 * q^86 + 135 * q^87 - 47 * q^88 + 17 * q^89 + 88 * q^90 + 26 * q^91 - 122 * q^92 + q^93 + 28 * q^94 - 47 * q^95 + 50 * q^96 - 162 * q^97 + 128 * q^98 - 70 * q^99

Introduction

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