LMFDB - Embedded newform 403.2.h.b.118.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.6
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.837386 q^{2} +(0.883556 + 1.53036i) q^{3} -1.29878 q^{4} +(-2.21305 + 3.83311i) q^{5} +(-0.739877 - 1.28150i) q^{6} +(-1.99716 - 3.45918i) q^{7} +2.76236 q^{8} +(-0.0613409 + 0.106246i) q^{9} +O(q^{10})$	\(q-0.837386 q^{2} +(0.883556 + 1.53036i) q^{3} -1.29878 q^{4} +(-2.21305 + 3.83311i) q^{5} +(-0.739877 - 1.28150i) q^{6} +(-1.99716 - 3.45918i) q^{7} +2.76236 q^{8} +(-0.0613409 + 0.106246i) q^{9} +(1.85318 - 3.20980i) q^{10} +(-1.39540 + 2.41690i) q^{11} +(-1.14755 - 1.98761i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.67239 + 2.89667i) q^{14} -7.82141 q^{15} +0.284411 q^{16} +(-0.576858 - 0.999148i) q^{17} +(0.0513661 - 0.0889686i) q^{18} +(-1.68123 - 2.91198i) q^{19} +(2.87427 - 4.97839i) q^{20} +(3.52920 - 6.11275i) q^{21} +(1.16849 - 2.02388i) q^{22} +0.745639 q^{23} +(2.44070 + 4.22741i) q^{24} +(-7.29518 - 12.6356i) q^{25} +(0.418693 - 0.725198i) q^{26} +5.08454 q^{27} +(2.59388 + 4.49273i) q^{28} -5.02785 q^{29} +6.54954 q^{30} +(0.0190669 - 5.56773i) q^{31} -5.76287 q^{32} -4.93164 q^{33} +(0.483053 + 0.836672i) q^{34} +17.6792 q^{35} +(0.0796687 - 0.137990i) q^{36} +(-1.55308 - 2.69001i) q^{37} +(1.40784 + 2.43845i) q^{38} -1.76711 q^{39} +(-6.11323 + 10.5884i) q^{40} +(-4.81293 + 8.33625i) q^{41} +(-2.95530 + 5.11873i) q^{42} +(4.51314 + 7.81698i) q^{43} +(1.81232 - 3.13903i) q^{44} +(-0.271501 - 0.470254i) q^{45} -0.624387 q^{46} -9.11327 q^{47} +(0.251293 + 0.435252i) q^{48} +(-4.47727 + 7.75486i) q^{49} +(6.10888 + 10.5809i) q^{50} +(1.01937 - 1.76561i) q^{51} +(0.649392 - 1.12478i) q^{52} +(2.71344 - 4.69982i) q^{53} -4.25772 q^{54} +(-6.17617 - 10.6974i) q^{55} +(-5.51686 - 9.55548i) q^{56} +(2.97093 - 5.14580i) q^{57} +4.21025 q^{58} +(0.500931 + 0.867638i) q^{59} +10.1583 q^{60} -11.4247 q^{61} +(-0.0159664 + 4.66234i) q^{62} +0.490030 q^{63} +4.25693 q^{64} +(-2.21305 - 3.83311i) q^{65} +4.12969 q^{66} +(-0.828863 + 1.43563i) q^{67} +(0.749215 + 1.29768i) q^{68} +(0.658813 + 1.14110i) q^{69} -14.8043 q^{70} +(-0.716560 + 1.24112i) q^{71} +(-0.169446 + 0.293488i) q^{72} +(-6.94652 + 12.0317i) q^{73} +(1.30053 + 2.25258i) q^{74} +(12.8914 - 22.3285i) q^{75} +(2.18356 + 3.78204i) q^{76} +11.1473 q^{77} +1.47975 q^{78} +(1.40672 + 2.43651i) q^{79} +(-0.629416 + 1.09018i) q^{80} +(4.67650 + 8.09993i) q^{81} +(4.03028 - 6.98066i) q^{82} +(-5.39673 + 9.34741i) q^{83} +(-4.58367 + 7.93915i) q^{84} +5.10646 q^{85} +(-3.77924 - 6.54583i) q^{86} +(-4.44239 - 7.69444i) q^{87} +(-3.85458 + 6.67634i) q^{88} +2.37455 q^{89} +(0.227351 + 0.393784i) q^{90} +3.99431 q^{91} -0.968424 q^{92} +(8.53750 - 4.89022i) q^{93} +7.63133 q^{94} +14.8826 q^{95} +(-5.09182 - 8.81929i) q^{96} -4.35710 q^{97} +(3.74921 - 6.49381i) q^{98} +(-0.171190 - 0.296510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.837386			−0.592121			−0.296061	−	0.955169i	$-0.595673\pi$
$2$	−0.837386			−0.592121			−0.296061	+	0.955169i	$0.595673\pi$
$3$	0.883556	+	1.53036i	0.510121	+	0.883556i	0.999931	+	0.0117265i	$0.00373274\pi$
$3$	0.883556	+	1.53036i	0.510121	+	0.883556i	−0.489810	+	0.871829i	$0.662934\pi$
$4$	−1.29878			−0.649392
$5$	−2.21305	+	3.83311i	−0.989706	+	1.71422i	−0.370910	+	0.928669i	$0.620954\pi$
$5$	−2.21305	+	3.83311i	−0.989706	+	1.71422i	−0.618795	+	0.785552i	$0.712379\pi$
$6$	−0.739877	−	1.28150i	−0.302054	−	0.523172i
$7$	−1.99716	−	3.45918i	−0.754854	−	1.30745i	−0.945447	−	0.325777i	$-0.894374\pi$
$7$	−1.99716	−	3.45918i	−0.754854	−	1.30745i	0.190592	−	0.981669i	$-0.438959\pi$
$8$	2.76236			0.976640
$9$	−0.0613409	+	0.106246i	−0.0204470	+	0.0354152i
$10$	1.85318	−	3.20980i	0.586026	−	1.01503i
$11$	−1.39540	+	2.41690i	−0.420728	+	0.728722i	−0.996011	−	0.0892322i	$-0.971559\pi$
$11$	−1.39540	+	2.41690i	−0.420728	+	0.728722i	0.575283	+	0.817955i	$0.304892\pi$
$12$	−1.14755	−	1.98761i	−0.331269	−	0.573774i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	1.67239	+	2.89667i	0.446965	+	0.774167i
$15$	−7.82141			−2.01948
$16$	0.284411			0.0711027
$17$	−0.576858	−	0.999148i	−0.139909	−	0.242329i	0.787553	−	0.616247i	$-0.211348\pi$
$17$	−0.576858	−	0.999148i	−0.139909	−	0.242329i	−0.927462	+	0.373918i	$0.878014\pi$
$18$	0.0513661	−	0.0889686i	0.0121071	−	0.0209701i
$19$	−1.68123	−	2.91198i	−0.385701	−	0.668054i	0.606165	−	0.795339i	$-0.292707\pi$
$19$	−1.68123	−	2.91198i	−0.385701	−	0.668054i	−0.991866	+	0.127285i	$0.959374\pi$
$20$	2.87427	−	4.97839i	0.642707	−	1.11320i
$21$	3.52920	−	6.11275i	0.770134	−	1.33391i
$22$	1.16849	−	2.02388i	0.249122	−	0.431492i
$23$	0.745639			0.155476			0.0777382	−	0.996974i	$-0.475230\pi$
$23$	0.745639			0.155476			0.0777382	+	0.996974i	$0.475230\pi$
$24$	2.44070	+	4.22741i	0.498205	+	0.862916i
$25$	−7.29518	−	12.6356i	−1.45904	−	2.52712i
$26$	0.418693	−	0.725198i	0.0821125	−	0.142223i
$27$	5.08454			0.978520
$28$	2.59388	+	4.49273i	0.490197	+	0.849046i
$29$	−5.02785			−0.933649			−0.466824	−	0.884350i	$-0.654602\pi$
$29$	−5.02785			−0.933649			−0.466824	+	0.884350i	$0.654602\pi$
$30$	6.54954			1.19578
$31$	0.0190669	−	5.56773i	0.00342452	−	0.999994i
$31$	0.0190669	−	5.56773i	0.00342452	−	0.999994i
$32$	−5.76287			−1.01874
$33$	−4.93164			−0.858489
$34$	0.483053	+	0.836672i	0.0828429	+	0.143488i
$35$	17.6792			2.98834
$36$	0.0796687	−	0.137990i	0.0132781	−	0.0229984i
$37$	−1.55308	−	2.69001i	−0.255325	−	0.442235i	0.709659	−	0.704545i	$-0.248849\pi$
$37$	−1.55308	−	2.69001i	−0.255325	−	0.442235i	−0.964984	+	0.262310i	$0.915516\pi$
$38$	1.40784	+	2.43845i	0.228382	+	0.395569i
$39$	−1.76711			−0.282964
$40$	−6.11323	+	10.5884i	−0.966587	+	1.67418i
$41$	−4.81293	+	8.33625i	−0.751654	+	1.30190i	0.195367	+	0.980730i	$0.437410\pi$
$41$	−4.81293	+	8.33625i	−0.751654	+	1.30190i	−0.947021	+	0.321173i	$0.895923\pi$
$42$	−2.95530	+	5.11873i	−0.456013	+	0.789838i
$43$	4.51314	+	7.81698i	0.688247	+	1.19208i	0.972405	+	0.233301i	$0.0749528\pi$
$43$	4.51314	+	7.81698i	0.688247	+	1.19208i	−0.284158	+	0.958778i	$0.591714\pi$
$44$	1.81232	−	3.13903i	0.273218	−	0.473227i
$45$	−0.271501	−	0.470254i	−0.0404730	−	0.0701013i
$46$	−0.624387			−0.0920609
$47$	−9.11327			−1.32931			−0.664654	−	0.747151i	$-0.731421\pi$
$47$	−9.11327			−1.32931			−0.664654	+	0.747151i	$0.731421\pi$
$48$	0.251293	+	0.435252i	0.0362710	+	0.0628232i
$49$	−4.47727	+	7.75486i	−0.639610	+	1.10784i
$50$	6.10888	+	10.5809i	0.863926	+	1.49636i
$51$	1.01937	−	1.76561i	0.142741	−	0.247234i
$52$	0.649392	−	1.12478i	0.0900545	−	0.155979i
$53$	2.71344	−	4.69982i	0.372720	−	0.645570i	−0.617263	−	0.786757i	$-0.711759\pi$
$53$	2.71344	−	4.69982i	0.372720	−	0.645570i	0.989983	+	0.141187i	$0.0450919\pi$
$54$	−4.25772			−0.579403
$55$	−6.17617	−	10.6974i	−0.832794	−	1.44244i
$56$	−5.51686	−	9.55548i	−0.737221	−	1.27690i
$57$	2.97093	−	5.14580i	0.393509	−	0.681577i
$58$	4.21025			0.552833
$59$	0.500931	+	0.867638i	0.0652157	+	0.112957i	0.896790	−	0.442457i	$-0.145893\pi$
$59$	0.500931	+	0.867638i	0.0652157	+	0.112957i	−0.831574	+	0.555414i	$0.812560\pi$
$60$	10.1583			1.31143
$61$	−11.4247			−1.46279			−0.731394	−	0.681955i	$-0.761130\pi$
$61$	−11.4247			−1.46279			−0.731394	+	0.681955i	$0.761130\pi$
$62$	−0.0159664	+	4.66234i	−0.00202773	+	0.592118i
$63$	0.490030			0.0617380
$64$	4.25693			0.532116
$65$	−2.21305	−	3.83311i	−0.274495	−	0.475439i
$66$	4.12969			0.508330
$67$	−0.828863	+	1.43563i	−0.101262	+	0.175390i	−0.912205	−	0.409735i	$-0.865621\pi$
$67$	−0.828863	+	1.43563i	−0.101262	+	0.175390i	0.810943	+	0.585125i	$0.198955\pi$
$68$	0.749215	+	1.29768i	0.0908556	+	0.157367i
$69$	0.658813	+	1.14110i	0.0793118	+	0.137372i
$70$	−14.8043			−1.76946
$71$	−0.716560	+	1.24112i	−0.0850401	+	0.147294i	−0.905408	−	0.424542i	$-0.860435\pi$
$71$	−0.716560	+	1.24112i	−0.0850401	+	0.147294i	0.820368	+	0.571836i	$0.193768\pi$
$72$	−0.169446	+	0.293488i	−0.0199693	+	0.0345879i
$73$	−6.94652	+	12.0317i	−0.813029	+	1.40821i	0.0977055	+	0.995215i	$0.468850\pi$
$73$	−6.94652	+	12.0317i	−0.813029	+	1.40821i	−0.910735	+	0.412992i	$0.864484\pi$
$74$	1.30053	+	2.25258i	0.151183	+	0.261857i
$75$	12.8914	−	22.3285i	1.48857	−	2.57828i
$76$	2.18356	+	3.78204i	0.250472	+	0.433829i
$77$	11.1473			1.27035
$78$	1.47975			0.167549
$79$	1.40672	+	2.43651i	0.158268	+	0.274128i	0.934244	−	0.356634i	$-0.116076\pi$
$79$	1.40672	+	2.43651i	0.158268	+	0.274128i	−0.775976	+	0.630762i	$0.782742\pi$
$80$	−0.629416	+	1.09018i	−0.0703708	+	0.121886i
$81$	4.67650	+	8.09993i	0.519611	+	0.899992i
$82$	4.03028	−	6.98066i	0.445070	−	0.770884i
$83$	−5.39673	+	9.34741i	−0.592368	+	1.02601i	0.401545	+	0.915839i	$0.368473\pi$
$83$	−5.39673	+	9.34741i	−0.592368	+	1.02601i	−0.993913	+	0.110172i	$0.964860\pi$
$84$	−4.58367	+	7.93915i	−0.500119	+	0.866232i
$85$	5.10646			0.553874
$86$	−3.77924	−	6.54583i	−0.407526	−	0.705855i
$87$	−4.44239	−	7.69444i	−0.476274	−	0.824931i
$88$	−3.85458	+	6.67634i	−0.410900	+	0.711700i
$89$	2.37455			0.251702			0.125851	−	0.992049i	$-0.459834\pi$
$89$	2.37455			0.251702			0.125851	+	0.992049i	$0.459834\pi$
$90$	0.227351	+	0.393784i	0.0239649	+	0.0415085i
$91$	3.99431			0.418718
$92$	−0.968424			−0.100965
$93$	8.53750	−	4.89022i	0.885297	−	0.507092i
$94$	7.63133			0.787111
$95$	14.8826			1.52692
$96$	−5.09182	−	8.81929i	−0.519682	−	0.900115i
$97$	−4.35710			−0.442397			−0.221198	−	0.975229i	$-0.570997\pi$
$97$	−4.35710			−0.442397			−0.221198	+	0.975229i	$0.570997\pi$
$98$	3.74921	−	6.49381i	0.378727	−	0.655974i
$99$	−0.171190	−	0.296510i	−0.0172052	−	0.0298003i
$100$	9.47486	+	16.4109i	0.947486	+	1.64109i
$101$	1.46025			0.145300			0.0726499	−	0.997358i	$-0.476854\pi$
$101$	1.46025			0.145300			0.0726499	+	0.997358i	$0.476854\pi$
$102$	−0.853608	+	1.47849i	−0.0845198	+	0.146393i
$103$	−5.46261	+	9.46152i	−0.538247	+	0.932271i	0.460752	+	0.887529i	$0.347580\pi$
$103$	−5.46261	+	9.46152i	−0.538247	+	0.932271i	−0.998999	+	0.0447418i	$0.985753\pi$
$104$	−1.38118	+	2.39227i	−0.135436	+	0.234581i
$105$	15.6206	+	27.0556i	1.52441	+	2.64036i
$106$	−2.27220	+	3.93556i	−0.220695	+	0.382256i
$107$	−7.77964	−	13.4747i	−0.752086	−	1.30265i	−0.946810	−	0.321793i	$-0.895714\pi$
$107$	−7.77964	−	13.4747i	−0.752086	−	1.30265i	0.194724	−	0.980858i	$-0.437619\pi$
$108$	−6.60372			−0.635444
$109$	−4.37993			−0.419522			−0.209761	−	0.977753i	$-0.567269\pi$
$109$	−4.37993			−0.419522			−0.209761	+	0.977753i	$0.567269\pi$
$110$	5.17184	+	8.95788i	0.493115	+	0.854100i
$111$	2.74446	−	4.75355i	0.260493	−	0.451187i
$112$	−0.568013	−	0.983828i	−0.0536722	−	0.0929630i
$113$	5.62626	−	9.74497i	0.529274	−	0.916730i	−0.470143	−	0.882590i	$-0.655798\pi$
$113$	5.62626	−	9.74497i	0.529274	−	0.916730i	0.999417	−	0.0341394i	$-0.0108690\pi$
$114$	−2.48781	+	4.30902i	−0.233005	+	0.403576i
$115$	−1.65014	+	2.85812i	−0.153876	+	0.266521i
$116$	6.53010			0.606304
$117$	−0.0613409	−	0.106246i	−0.00567097	−	0.00982241i
$118$	−0.419473	−	0.726548i	−0.0386156	−	0.0668842i
$119$	−2.30415	+	3.99091i	−0.211221	+	0.365846i
$120$	−21.6055			−1.97230
$121$	1.60573	+	2.78121i	0.145976	+	0.252837i
$122$	9.56692			0.866148
$123$	−17.0100			−1.53374
$124$	−0.0247638	+	7.23128i	−0.00222386	+	0.649389i
$125$	42.4479			3.79665
$126$	−0.410344			−0.0365564
$127$	1.05463	+	1.82667i	0.0935832	+	0.162091i	0.909016	−	0.416760i	$-0.136835\pi$
$127$	1.05463	+	1.82667i	0.0935832	+	0.162091i	−0.815433	+	0.578851i	$0.803501\pi$
$128$	7.96106			0.703665
$129$	−7.97521	+	13.8135i	−0.702179	+	1.21621i
$130$	1.85318	+	3.20980i	0.162534	+	0.281518i
$131$	−6.11480	−	10.5911i	−0.534252	−	0.925352i	−0.999199	−	0.0400134i	$-0.987260\pi$
$131$	−6.11480	−	10.5911i	−0.534252	−	0.925352i	0.464947	−	0.885339i	$-0.346073\pi$
$132$	6.40514			0.557496
$133$	−6.71537	+	11.6314i	−0.582297	+	1.00857i
$134$	0.694078	−	1.20218i	0.0599592	−	0.103852i
$135$	−11.2523	+	19.4896i	−0.968447	+	1.67740i
$136$	−1.59349	−	2.76000i	−0.136640	−	0.236668i
$137$	−1.70112	+	2.94642i	−0.145336	+	0.251730i	−0.929498	−	0.368826i	$-0.879760\pi$
$137$	−1.70112	+	2.94642i	−0.145336	+	0.251730i	0.784162	+	0.620556i	$0.213093\pi$
$138$	−0.551681	−	0.955540i	−0.0469622	−	0.0813409i
$139$	10.2497			0.869372			0.434686	−	0.900582i	$-0.356859\pi$
$139$	10.2497			0.869372			0.434686	+	0.900582i	$0.356859\pi$
$140$	−22.9615			−1.94060
$141$	−8.05208	−	13.9466i	−0.678108	−	1.17452i
$142$	0.600038	−	1.03930i	0.0503540	−	0.0872158i
$143$	−1.39540	−	2.41690i	−0.116689	−	0.202111i
$144$	−0.0174460	+	0.0302174i	−0.00145384	+	0.00251812i
$145$	11.1269	−	19.2723i	0.924038	−	1.60048i
$146$	5.81692	−	10.0752i	0.481412	−	0.833830i
$147$	−15.8237			−1.30511
$148$	2.01712	+	3.49375i	0.165806	+	0.287184i
$149$	−9.11796	−	15.7928i	−0.746972	−	1.29379i	−0.949268	−	0.314469i	$-0.898174\pi$
$149$	−9.11796	−	15.7928i	−0.746972	−	1.29379i	0.202296	−	0.979324i	$-0.435160\pi$
$150$	−10.7951	+	18.6976i	−0.881414	+	1.52665i
$151$	16.7337			1.36177			0.680887	−	0.732389i	$-0.261595\pi$
$151$	16.7337			1.36177			0.680887	+	0.732389i	$0.261595\pi$
$152$	−4.64417	−	8.04393i	−0.376692	−	0.652449i
$153$	0.141540			0.0114428
$154$	−9.33460			−0.752204
$155$	21.2996	+	12.3948i	1.71082	+	0.995570i
$156$	2.29510			0.183755
$157$	−15.2206			−1.21473			−0.607367	−	0.794421i	$-0.707774\pi$
$157$	−15.2206			−1.21473			−0.607367	+	0.794421i	$0.707774\pi$
$158$	−1.17797	−	2.04030i	−0.0937139	−	0.162317i
$159$	9.58991			0.760529
$160$	12.7535	−	22.0898i	1.00825	−	1.74635i
$161$	−1.48916	−	2.57930i	−0.117362	−	0.203277i
$162$	−3.91603	−	6.78277i	−0.307673	−	0.532905i
$163$	−1.56277			−0.122405			−0.0612026	−	0.998125i	$-0.519494\pi$
$163$	−1.56277			−0.122405			−0.0612026	+	0.998125i	$0.519494\pi$
$164$	6.25096	−	10.8270i	0.488118	−	0.845446i
$165$	10.9140	−	18.9036i	0.849652	−	1.47164i
$166$	4.51915	−	7.82739i	0.350754	−	0.607523i
$167$	0.981987	+	1.70085i	0.0759884	+	0.131616i	0.901516	−	0.432746i	$-0.142455\pi$
$167$	0.981987	+	1.70085i	0.0759884	+	0.131616i	−0.825527	+	0.564362i	$0.809122\pi$
$168$	9.74890	−	16.8856i	0.752144	−	1.30275i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−4.27608			−0.327960
$171$	0.412514			0.0315457
$172$	−5.86159	−	10.1526i	−0.446942	−	0.774127i
$173$	−1.42174	+	2.46252i	−0.108093	+	0.187222i	−0.914998	−	0.403459i	$-0.867808\pi$
$173$	−1.42174	+	2.46252i	−0.108093	+	0.187222i	0.806905	+	0.590681i	$0.201141\pi$
$174$	3.71999	+	6.44322i	0.282012	+	0.488459i
$175$	−29.1392	+	50.4706i	−2.20272	+	3.81522i
$176$	−0.396866	+	0.687393i	−0.0299149	+	0.0518142i
$177$	−0.885201	+	1.53321i	−0.0665358	+	0.115243i
$178$	−1.98841			−0.149038
$179$	10.2287	+	17.7166i	0.764528	+	1.32420i	0.940496	+	0.339805i	$0.110361\pi$
$179$	10.2287	+	17.7166i	0.764528	+	1.32420i	−0.175968	+	0.984396i	$0.556306\pi$
$180$	0.352621	+	0.610758i	0.0262829	+	0.0455232i
$181$	6.85586	−	11.8747i	0.509592	−	0.882640i	−0.490346	−	0.871528i	$-0.663130\pi$
$181$	6.85586	−	11.8747i	0.509592	−	0.882640i	0.999938	−	0.0111118i	$-0.00353708\pi$
$182$	−3.34478			−0.247932
$183$	−10.0944	−	17.4840i	−0.746199	−	1.29245i
$184$	2.05972			0.151845
$185$	13.7482			1.01079
$186$	−7.14918	+	4.09500i	−0.524203	+	0.300260i
$187$	3.21979			0.235454
$188$	11.8362			0.863242
$189$	−10.1546	−	17.5883i	−0.738640	−	1.27936i
$190$	−12.4625			−0.904124
$191$	3.58671	−	6.21237i	0.259525	−	0.449511i	−0.706589	−	0.707624i	$-0.749767\pi$
$191$	3.58671	−	6.21237i	0.259525	−	0.449511i	0.966115	+	0.258113i	$0.0831006\pi$
$192$	3.76123	+	6.51465i	0.271444	+	0.470154i
$193$	−11.8483	−	20.5219i	−0.852860	−	1.47720i	−0.878616	−	0.477529i	$-0.841532\pi$
$193$	−11.8483	−	20.5219i	−0.852860	−	1.47720i	0.0257554	−	0.999668i	$-0.491801\pi$
$194$	3.64858			0.261953
$195$	3.91070	−	6.77354i	0.280051	−	0.485063i
$196$	5.81501	−	10.0719i	0.415358	−	0.719421i
$197$	−8.93070	+	15.4684i	−0.636286	+	1.10208i	0.349955	+	0.936767i	$0.386197\pi$
$197$	−8.93070	+	15.4684i	−0.636286	+	1.10208i	−0.986241	+	0.165313i	$0.947136\pi$
$198$	0.143352	+	0.248293i	0.0101876	+	0.0176454i
$199$	−0.268331	+	0.464763i	−0.0190215	+	0.0329462i	−0.875379	−	0.483436i	$-0.839388\pi$
$199$	−0.268331	+	0.464763i	−0.0190215	+	0.0329462i	0.856358	+	0.516383i	$0.172722\pi$
$200$	−20.1519	−	34.9041i	−1.42495	−	2.46809i
$201$	−2.92939			−0.206623
$202$	−1.22279			−0.0860352
$203$	10.0414	+	17.3922i	0.704769	+	1.22070i
$204$	−1.32395	+	2.29314i	−0.0926947	+	0.160552i
$205$	−21.3025	−	36.8971i	−1.48783	−	2.57700i
$206$	4.57431	−	7.92294i	0.318707	−	0.552017i
$207$	−0.0457382	+	0.0792209i	−0.00317902	+	0.00550623i
$208$	−0.142205	+	0.246307i	−0.00986018	+	0.0170783i
$209$	9.38395			0.649102
$210$	−13.0805	−	22.6560i	−0.902637	−	1.56341i
$211$	3.48976	+	6.04443i	0.240245	+	0.416116i	0.960784	−	0.277298i	$-0.0894390\pi$
$211$	3.48976	+	6.04443i	0.240245	+	0.416116i	−0.720539	+	0.693414i	$0.756106\pi$
$212$	−3.52418	+	6.10405i	−0.242042	+	0.419228i
$213$	−2.53248			−0.173523
$214$	6.51456	+	11.2835i	0.445326	+	0.771328i
$215$	−39.9512			−2.72465
$216$	14.0453			0.955662
$217$	−19.2979	+	11.0537i	−1.31002	+	0.750373i
$218$	3.66770			0.248408
$219$	−24.5506			−1.65897
$220$	8.02151	+	13.8937i	0.540810	+	0.936711i
$221$	1.15372			0.0776074
$222$	−2.29818	+	3.98056i	−0.154243	+	0.267157i
$223$	1.16130	+	2.01143i	0.0777662	+	0.134695i	0.902286	−	0.431138i	$-0.141888\pi$
$223$	1.16130	+	2.01143i	0.0777662	+	0.134695i	−0.824520	+	0.565833i	$0.808555\pi$
$224$	11.5094	+	19.9348i	0.769002	+	1.33195i
$225$	1.78997			0.119331
$226$	−4.71135	+	8.16030i	−0.313395	+	0.542815i
$227$	−6.02682	+	10.4388i	−0.400014	+	0.692844i	−0.993727	−	0.111832i	$-0.964328\pi$
$227$	−6.02682	+	10.4388i	−0.400014	+	0.692844i	0.593713	+	0.804677i	$0.297661\pi$
$228$	−3.85859	+	6.68328i	−0.255542	+	0.442611i
$229$	−8.82591	−	15.2869i	−0.583233	−	1.01019i	−0.995093	−	0.0989416i	$-0.968454\pi$
$229$	−8.82591	−	15.2869i	−0.583233	−	1.01019i	0.411861	−	0.911247i	$-0.364879\pi$
$230$	1.38180	−	2.39335i	0.0911132	−	0.157813i
$231$	9.84927	+	17.0594i	0.648034	+	1.12243i
$232$	−13.8887			−0.911839
$233$	−11.0803			−0.725895			−0.362947	−	0.931810i	$-0.618229\pi$
$233$	−11.0803			−0.725895			−0.362947	+	0.931810i	$0.618229\pi$
$234$	0.0513661	+	0.0889686i	0.00335790	+	0.00581606i
$235$	20.1681	−	34.9322i	1.31562	−	2.27873i
$236$	−0.650602	−	1.12687i	−0.0423506	−	0.0733533i
$237$	−2.48583	+	4.30558i	−0.161472	+	0.279677i
$238$	1.92947	−	3.34193i	0.125069	−	0.216625i
$239$	−5.37527	+	9.31025i	−0.347698	+	0.602230i	−0.985840	−	0.167688i	$-0.946370\pi$
$239$	−5.37527	+	9.31025i	−0.347698	+	0.602230i	0.638142	+	0.769918i	$0.279703\pi$
$240$	−2.22449			−0.143591
$241$	5.38850	+	9.33316i	0.347104	+	0.601202i	0.985734	−	0.168313i	$-0.0538318\pi$
$241$	5.38850	+	9.33316i	0.347104	+	0.601202i	−0.638630	+	0.769514i	$0.720498\pi$
$242$	−1.34462	−	2.32895i	−0.0864354	−	0.149710i
$243$	−0.637079	+	1.10345i	−0.0408687	+	0.0707866i
$244$	14.8383			0.949923
$245$	−19.8169	−	34.3238i	−1.26605	−	2.19287i
$246$	14.2439			0.908159
$247$	3.36247			0.213949
$248$	0.0526696	−	15.3801i	0.00334452	−	0.976635i
$249$	−19.0732			−1.20872
$250$	−35.5452			−2.24808
$251$	9.81046	+	16.9922i	0.619231	+	1.07254i	0.989626	+	0.143665i	$0.0458889\pi$
$251$	9.81046	+	16.9922i	0.619231	+	1.07254i	−0.370395	+	0.928874i	$0.620778\pi$
$252$	−0.636443			−0.0400922
$253$	−1.04046	+	1.80213i	−0.0654133	+	0.113299i
$254$	−0.883132	−	1.52963i	−0.0554126	−	0.0959775i
$255$	4.51184	+	7.81474i	0.282543	+	0.489378i
$256$	−15.1803			−0.948771
$257$	−6.27771	+	10.8733i	−0.391593	+	0.678259i	−0.992660	−	0.120940i	$-0.961409\pi$
$257$	−6.27771	+	10.8733i	−0.391593	+	0.678259i	0.601067	+	0.799199i	$0.294743\pi$
$258$	6.67833	−	11.5672i	0.415775	−	0.720143i
$259$	−6.20349	+	10.7448i	−0.385466	+	0.667646i
$260$	2.87427	+	4.97839i	0.178255	+	0.308747i
$261$	0.308413	−	0.534187i	0.0190903	−	0.0330654i
$262$	5.12044	+	8.86887i	0.316342	+	0.547921i
$263$	−28.1587			−1.73634			−0.868170	−	0.496266i	$-0.834704\pi$
$263$	−28.1587			−1.73634			−0.868170	+	0.496266i	$0.834704\pi$
$264$	−13.6230			−0.838435
$265$	12.0100	+	20.8019i	0.737766	+	1.27785i
$266$	5.62336	−	9.73995i	0.344790	−	0.597194i
$267$	2.09805	+	3.63392i	0.128398	+	0.222392i
$268$	1.07651	−	1.86458i	0.0657586	−	0.113897i
$269$	−3.10195	+	5.37274i	−0.189129	+	0.327582i	−0.944960	−	0.327185i	$-0.893900\pi$
$269$	−3.10195	+	5.37274i	−0.189129	+	0.327582i	0.755831	+	0.654767i	$0.227233\pi$
$270$	9.42255	−	16.3203i	0.573438	−	0.993224i
$271$	−1.44701			−0.0878995			−0.0439497	−	0.999034i	$-0.513994\pi$
$271$	−1.44701			−0.0878995			−0.0439497	+	0.999034i	$0.513994\pi$
$272$	−0.164065	−	0.284169i	−0.00994789	−	0.0172302i
$273$	3.52920	+	6.11275i	0.213597	+	0.369961i
$274$	1.42449	−	2.46729i	0.0860567	−	0.149055i
$275$	40.7187			2.45543
$276$	−0.855657	−	1.48204i	−0.0515045	−	0.0892084i
$277$	20.3836			1.22473			0.612367	−	0.790574i	$-0.290218\pi$
$277$	20.3836			1.22473			0.612367	+	0.790574i	$0.290218\pi$
$278$	−8.58299			−0.514774
$279$	0.590378	+	0.343556i	0.0353450	+	0.0205681i
$280$	48.8363			2.91853
$281$	20.0622			1.19681			0.598405	−	0.801194i	$-0.295801\pi$
$281$	20.0622			1.19681			0.598405	+	0.801194i	$0.295801\pi$
$282$	6.74270	+	11.6787i	0.401522	+	0.695457i
$283$	21.1954			1.25994			0.629968	−	0.776621i	$-0.283068\pi$
$283$	21.1954			1.25994			0.629968	+	0.776621i	$0.283068\pi$
$284$	0.930658	−	1.61195i	0.0552244	−	0.0956514i
$285$	13.1496	+	22.7758i	0.778916	+	1.34912i
$286$	1.16849	+	2.02388i	0.0690940	+	0.119674i
$287$	38.4487			2.26956
$288$	0.353500	−	0.612280i	0.0208302	−	0.0360790i
$289$	7.83447	−	13.5697i	0.460851	−	0.798218i
$290$	−9.31750	+	16.1384i	−0.547142	+	0.947679i
$291$	−3.84974	−	6.66795i	−0.225676	−	0.390882i
$292$	9.02204	−	15.6266i	0.527975	−	0.914479i
$293$	−0.263737	−	0.456805i	−0.0154077	−	0.0266868i	0.858219	−	0.513284i	$-0.171571\pi$
$293$	−0.263737	−	0.456805i	−0.0154077	−	0.0266868i	−0.873626	+	0.486597i	$0.838238\pi$
$294$	13.2505			0.772786
$295$	−4.43434			−0.258177
$296$	−4.29016	−	7.43077i	−0.249360	−	0.431905i
$297$	−7.09495	+	12.2888i	−0.411691	+	0.713070i
$298$	7.63525	+	13.2246i	0.442298	+	0.766083i
$299$	−0.372819	+	0.645742i	−0.0215607	+	0.0373442i
$300$	−16.7431	+	29.0000i	−0.966666	+	1.67431i
$301$	18.0269	−	31.2235i	1.03905	−	1.79969i
$302$	−14.0126			−0.806335
$303$	1.29021	+	2.23471i	0.0741205	+	0.128381i
$304$	−0.478161	−	0.828199i	−0.0274244	−	0.0475005i
$305$	25.2835	−	43.7923i	1.44773	−	2.50754i
$306$	−0.118524			−0.00677555
$307$	−5.06752	−	8.77720i	−0.289219	−	0.500941i	0.684405	−	0.729102i	$-0.260062\pi$
$307$	−5.06752	−	8.77720i	−0.289219	−	0.500941i	−0.973623	+	0.228161i	$0.926729\pi$
$308$	−14.4780			−0.824958
$309$	−19.3061			−1.09828
$310$	−17.8360	−	10.3792i	−1.01301	−	0.589498i
$311$	−23.4109			−1.32751			−0.663756	−	0.747949i	$-0.731039\pi$
$311$	−23.4109			−1.32751			−0.663756	+	0.747949i	$0.731039\pi$
$312$	−4.88139			−0.276354
$313$	13.4826	+	23.3526i	0.762083	+	1.31997i	0.941775	+	0.336244i	$0.109157\pi$
$313$	13.4826	+	23.3526i	0.762083	+	1.31997i	−0.179692	+	0.983723i	$0.557510\pi$
$314$	12.7455			0.719270
$315$	−1.08446	+	1.87834i	−0.0611024	+	0.105833i
$316$	−1.82702	−	3.16450i	−0.102778	−	0.178017i
$317$	9.08022	+	15.7274i	0.509996	+	0.883339i	0.999933	+	0.0115811i	$0.00368647\pi$
$317$	9.08022	+	15.7274i	0.509996	+	0.883339i	−0.489937	+	0.871758i	$0.662980\pi$
$318$	−8.03046			−0.450326
$319$	7.01585	−	12.1518i	0.392812	−	0.680371i
$320$	−9.42079	+	16.3173i	−0.526638	+	0.912164i
$321$	13.7475	−	23.8113i	0.767310	−	1.32902i
$322$	1.24700	+	2.15987i	0.0694926	+	0.120365i
$323$	−1.93967	+	3.35960i	−0.107926	+	0.186933i
$324$	−6.07376	−	10.5201i	−0.337431	−	0.584448i
$325$	14.5904			0.809327
$326$	1.30864			0.0724787
$327$	−3.86991	−	6.70289i	−0.214007	−	0.370671i
$328$	−13.2950	+	23.0277i	−0.734096	+	1.27149i
$329$	18.2006	+	31.5244i	1.00343	+	1.73800i
$330$	−9.13921	+	15.8296i	−0.503097	+	0.871389i
$331$	7.65564	−	13.2600i	0.420792	−	0.728833i	−0.575225	−	0.817995i	$-0.695085\pi$
$331$	7.65564	−	13.2600i	0.420792	−	0.728833i	0.996017	+	0.0891618i	$0.0284188\pi$
$332$	7.00919	−	12.1403i	0.384679	−	0.666284i
$333$	0.381069			0.0208825
$334$	−0.822302	−	1.42427i	−0.0449944	−	0.0779325i
$335$	−3.66863	−	6.35425i	−0.200439	−	0.347170i
$336$	1.00374	−	1.73853i	0.0547587	−	0.0948448i
$337$	−11.1650			−0.608196			−0.304098	−	0.952641i	$-0.598355\pi$
$337$	−11.1650			−0.608196			−0.304098	+	0.952641i	$0.598355\pi$
$338$	0.418693	+	0.725198i	0.0227739	+	0.0394455i
$339$	19.8845			1.07998
$340$	−6.63220			−0.359681
$341$	13.4300	+	7.81528i	0.727277	+	0.423221i
$342$	−0.345433			−0.0186789
$343$	7.80706			0.421542
$344$	12.4669	+	21.5933i	0.672170	+	1.16423i
$345$	−5.83195			−0.313981
$346$	1.19054	−	2.06208i	0.0640040	−	0.110858i
$347$	17.1043	+	29.6255i	0.918208	+	1.59038i	0.802136	+	0.597141i	$0.203697\pi$
$347$	17.1043	+	29.6255i	0.918208	+	1.59038i	0.116072	+	0.993241i	$0.462970\pi$
$348$	5.76971	+	9.99342i	0.309289	+	0.535704i
$349$	10.2919			0.550915			0.275458	−	0.961313i	$-0.411171\pi$
$349$	10.2919			0.550915			0.275458	+	0.961313i	$0.411171\pi$
$350$	24.4008	−	42.2634i	1.30428	−	2.25907i
$351$	−2.54227	+	4.40334i	−0.135696	+	0.235033i
$352$	8.04150	−	13.9283i	0.428613	−	0.742380i
$353$	0.0801093	+	0.138753i	0.00426379	+	0.00738510i	0.868149	−	0.496303i	$-0.165309\pi$
$353$	0.0801093	+	0.138753i	0.00426379	+	0.00738510i	−0.863886	+	0.503688i	$0.831976\pi$
$354$	0.741255	−	1.28389i	0.0393972	−	0.0682380i
$355$	−3.17157	−	5.49332i	−0.168329	−	0.291555i
$356$	−3.08403			−0.163453
$357$	−8.14339			−0.430994
$358$	−8.56535	−	14.8356i	−0.452693	−	0.784087i
$359$	1.27797	−	2.21351i	0.0674487	−	0.116825i	−0.830329	−	0.557274i	$-0.811847\pi$
$359$	1.27797	−	2.21351i	0.0674487	−	0.116825i	0.897778	+	0.440449i	$0.145181\pi$
$360$	−0.749983	−	1.29901i	−0.0395276	−	0.0684637i
$361$	3.84691	−	6.66304i	0.202469	−	0.350686i
$362$	−5.74100	+	9.94371i	−0.301740	+	0.522630i
$363$	−2.83751	+	4.91471i	−0.148931	+	0.257955i
$364$	−5.18775			−0.271912
$365$	−30.7460	−	53.2536i	−1.60932	−	2.78742i
$366$	8.45290	+	14.6409i	0.441840	+	0.765290i
$367$	−14.0952	+	24.4135i	−0.735762	+	1.27438i	0.218627	+	0.975809i	$0.429842\pi$
$367$	−14.0952	+	24.4135i	−0.735762	+	1.27438i	−0.954388	+	0.298568i	$0.903491\pi$
$368$	0.212068			0.0110548
$369$	−0.590460	−	1.02271i	−0.0307381	−	0.0532400i
$370$	−11.5125			−0.598507
$371$	−21.6767			−1.12540
$372$	−11.0884	+	6.35134i	−0.574905	+	0.329302i
$373$	−24.1839			−1.25219			−0.626097	−	0.779745i	$-0.715349\pi$
$373$	−24.1839			−1.25219			−0.626097	+	0.779745i	$0.715349\pi$
$374$	−2.69620			−0.139417
$375$	37.5050	+	64.9606i	1.93675	+	3.35455i
$376$	−25.1741			−1.29826
$377$	2.51393	−	4.35425i	0.129474	−	0.224255i
$378$	8.50334	+	14.7282i	0.437365	+	0.757538i
$379$	6.58924	+	11.4129i	0.338467	+	0.586241i	0.984145	−	0.177368i	$-0.0567584\pi$
$379$	6.58924	+	11.4129i	0.338467	+	0.586241i	−0.645678	+	0.763610i	$0.723425\pi$
$380$	−19.3293			−0.991573
$381$	−1.86365	+	3.22793i	−0.0954775	+	0.165372i
$382$	−3.00346	+	5.20215i	−0.153671	+	0.266165i
$383$	−1.86301	+	3.22682i	−0.0951952	+	0.164883i	−0.909690	−	0.415288i	$-0.863681\pi$
$383$	−1.86301	+	3.22682i	−0.0951952	+	0.164883i	0.814495	+	0.580171i	$0.197014\pi$
$384$	7.03404	+	12.1833i	0.358954	+	0.621727i
$385$	−24.6695	+	42.7289i	−1.25728	+	2.17767i
$386$	9.92161	+	17.1847i	0.504997	+	0.874680i
$387$	−1.10736			−0.0562903
$388$	5.65894			0.287289
$389$	−6.02389	−	10.4337i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$389$	−6.02389	−	10.4337i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$390$	−3.27477	+	5.67207i	−0.165824	+	0.287216i
$391$	−0.430128	−	0.745003i	−0.0217525	−	0.0376764i
$392$	−12.3678	+	21.4217i	−0.624669	+	1.08196i
$393$	10.8055	−	18.7157i	0.545067	−	0.944083i
$394$	7.47844	−	12.9530i	0.376759	−	0.652565i
$395$	−12.4525			−0.626556
$396$	0.222339	+	0.385102i	0.0111730	+	0.0193521i
$397$	16.5205	+	28.6143i	0.829140	+	1.43611i	0.898714	+	0.438536i	$0.144503\pi$
$397$	16.5205	+	28.6143i	0.829140	+	1.43611i	−0.0695737	+	0.997577i	$0.522164\pi$
$398$	0.224697	−	0.389186i	0.0112630	−	0.0195081i
$399$	−23.7336			−1.18817
$400$	−2.07483	−	3.59371i	−0.103741	−	0.179685i
$401$	−23.6856			−1.18280			−0.591401	−	0.806378i	$-0.701425\pi$
$401$	−23.6856			−1.18280			−0.591401	+	0.806378i	$0.701425\pi$
$402$	2.45303			0.122346
$403$	4.81226	+	2.80038i	0.239716	+	0.139497i
$404$	−1.89654			−0.0943566
$405$	−41.3973			−2.05705
$406$	−8.40854	−	14.5640i	−0.417309	−	0.722800i
$407$	8.66865			0.429689
$408$	2.81587	−	4.87723i	0.139406	−	0.241459i
$409$	−17.7737	−	30.7849i	−0.878851	−	1.52222i	−0.852603	−	0.522560i	$-0.824977\pi$
$409$	−17.7737	−	30.7849i	−0.878851	−	1.52222i	−0.0262488	−	0.999655i	$-0.508356\pi$
$410$	17.8384	+	30.8971i	0.880977	+	1.52590i
$411$	−6.01213			−0.296556
$412$	7.09475	−	12.2885i	0.349533	−	0.605410i
$413$	2.00088	−	3.46562i	0.0984567	−	0.170532i
$414$	0.0383005	−	0.0663384i	0.00188237	−	0.00326036i
$415$	−23.8865	−	41.3726i	−1.17254	−	2.03090i
$416$	2.88144	−	4.99080i	0.141274	−	0.244694i
$417$	9.05622	+	15.6858i	0.443485	+	0.768138i
$418$	−7.85799			−0.384347
$419$	23.4933			1.14772			0.573860	−	0.818953i	$-0.305445\pi$
$419$	23.4933			1.14772			0.573860	+	0.818953i	$0.305445\pi$
$420$	−20.2878	−	35.1395i	−0.989942	−	1.71463i
$421$	10.3395	−	17.9085i	0.503914	−	0.872805i	−0.496076	−	0.868279i	$-0.665226\pi$
$421$	10.3395	−	17.9085i	0.503914	−	0.872805i	0.999990	−	0.00452547i	$-0.00144051\pi$
$422$	−2.92227	−	5.06153i	−0.142254	−	0.246391i
$423$	0.559017	−	0.968246i	0.0271803	−	0.0470777i
$424$	7.49549	−	12.9826i	0.364013	−	0.630490i
$425$	−8.41657	+	14.5779i	−0.408263	+	0.707133i
$426$	2.12067			0.102747
$427$	22.8170	+	39.5202i	1.10419	+	1.91252i
$428$	10.1041	+	17.5008i	0.488399	+	0.845932i
$429$	2.46582	−	4.27093i	0.119051	−	0.206202i
$430$	33.4546			1.61332
$431$	−1.66248	−	2.87950i	−0.0800787	−	0.138700i	0.823205	−	0.567745i	$-0.192184\pi$
$431$	−1.66248	−	2.87950i	−0.0800787	−	0.138700i	−0.903284	+	0.429044i	$0.858851\pi$
$432$	1.44610			0.0695755
$433$	−29.7410			−1.42926			−0.714630	−	0.699502i	$-0.753405\pi$
$433$	−29.7410			−1.42926			−0.714630	+	0.699502i	$0.753405\pi$
$434$	16.1598	−	9.25620i	0.775693	−	0.444312i
$435$	39.3249			1.88548
$436$	5.68859			0.272434
$437$	−1.25359	−	2.17129i	−0.0599675	−	0.103867i
$438$	20.5583			0.982313
$439$	−12.0902	+	20.9409i	−0.577034	+	0.999453i	0.418783	+	0.908086i	$0.362457\pi$
$439$	−12.0902	+	20.9409i	−0.577034	+	0.999453i	−0.995817	+	0.0913666i	$0.970876\pi$
$440$	−17.0608	−	29.5501i	−0.813340	−	1.40875i
$441$	−0.549280	−	0.951381i	−0.0261562	−	0.0453039i
$442$	−0.966106			−0.0459530
$443$	8.41160	−	14.5693i	0.399647	−	0.692209i	−0.594035	−	0.804439i	$-0.702466\pi$
$443$	8.41160	−	14.5693i	0.399647	−	0.692209i	0.993682	+	0.112230i	$0.0357993\pi$
$444$	−3.56447	+	6.17384i	−0.169162	+	0.292997i
$445$	−5.25499	+	9.10191i	−0.249111	+	0.431472i
$446$	−0.972454	−	1.68434i	−0.0460470	−	0.0797558i
$447$	16.1124	−	27.9076i	0.762092	−	1.31998i
$448$	−8.50175	−	14.7255i	−0.401670	−	0.695713i
$449$	27.2969			1.28822			0.644109	−	0.764934i	$-0.277228\pi$
$449$	27.2969			1.28822			0.644109	+	0.764934i	$0.277228\pi$
$450$	−1.49890			−0.0706587
$451$	−13.4319	−	23.2647i	−0.632484	−	1.09549i
$452$	−7.30730	+	12.6566i	−0.343707	+	0.595317i
$453$	14.7852	+	25.6087i	0.694669	+	1.20320i
$454$	5.04677	−	8.74126i	0.236857	−	0.410248i
$455$	−8.83961	+	15.3107i	−0.414408	+	0.717775i
$456$	8.20676	−	14.2145i	0.384317	−	0.665656i
$457$	0.511763			0.0239393			0.0119696	−	0.999928i	$-0.496190\pi$
$457$	0.511763			0.0239393			0.0119696	+	0.999928i	$0.496190\pi$
$458$	7.39069	+	12.8011i	0.345344	+	0.598154i
$459$	−2.93306	−	5.08021i	−0.136903	−	0.237124i
$460$	2.14317	−	3.71208i	0.0999259	−	0.173077i
$461$	6.73481			0.313671			0.156836	−	0.987625i	$-0.449871\pi$
$461$	6.73481			0.313671			0.156836	+	0.987625i	$0.449871\pi$
$462$	−8.24764	−	14.2853i	−0.383715	−	0.664614i
$463$	9.38450			0.436135			0.218067	−	0.975934i	$-0.430025\pi$
$463$	9.38450			0.436135			0.218067	+	0.975934i	$0.430025\pi$
$464$	−1.42998			−0.0663850
$465$	−0.149130	+	43.5475i	−0.00691574	+	2.01947i
$466$	9.27849			0.429818
$467$	16.5236			0.764622			0.382311	−	0.924034i	$-0.375128\pi$
$467$	16.5236			0.764622			0.382311	+	0.924034i	$0.375128\pi$
$468$	0.0796687	+	0.137990i	0.00368269	+	0.00637860i
$469$	6.62148			0.305751
$470$	−16.8885	+	29.2518i	−0.779009	+	1.34928i
$471$	−13.4482	−	23.2930i	−0.619662	−	1.07329i
$472$	1.38375	+	2.39673i	0.0636923	+	0.110318i
$473$	−25.1905			−1.15826
$474$	2.08160	−	3.60543i	0.0956109	−	0.165603i
$475$	−24.5298	+	42.4868i	−1.12550	+	1.94943i
$476$	2.99260	−	5.18333i	0.137166	−	0.237578i
$477$	0.332890	+	0.576583i	0.0152420	+	0.0263999i
$478$	4.50118	−	7.79627i	0.205879	−	0.356593i
$479$	−1.66727	−	2.88779i	−0.0761794	−	0.131947i	0.825419	−	0.564520i	$-0.190939\pi$
$479$	−1.66727	−	2.88779i	−0.0761794	−	0.131947i	−0.901599	+	0.432574i	$0.857606\pi$
$480$	45.0738			2.05733
$481$	3.10616			0.141629
$482$	−4.51226	−	7.81546i	−0.205528	−	0.355984i
$483$	2.63151	−	4.55790i	0.119738	−	0.207392i
$484$	−2.08550	−	3.61220i	−0.0947955	−	0.164191i
$485$	9.64249	−	16.7013i	0.437843	−	0.758366i
$486$	0.533481	−	0.924017i	0.0241992	−	0.0419143i
$487$	10.1354	−	17.5549i	0.459277	−	0.795490i	−0.539646	−	0.841892i	$-0.681442\pi$
$487$	10.1354	−	17.5549i	0.459277	−	0.795490i	0.998923	+	0.0464015i	$0.0147754\pi$
$488$	−31.5592			−1.42862
$489$	−1.38079	−	2.39160i	−0.0624415	−	0.108152i
$490$	16.5944	+	28.7423i	0.749656	+	1.29844i
$491$	−11.7204	+	20.3003i	−0.528934	+	0.916141i	0.470496	+	0.882402i	$0.344075\pi$
$491$	−11.7204	+	20.3003i	−0.528934	+	0.916141i	−0.999431	+	0.0337392i	$0.989258\pi$
$492$	22.0923			0.995998
$493$	2.90036	+	5.02357i	0.130626	+	0.226250i
$494$	−2.81568			−0.126684
$495$	1.51541			0.0681125
$496$	0.00542284	−	1.58352i	0.000243493	−	0.0711023i
$497$	5.72434			0.256772
$498$	15.9717			0.715707
$499$	−4.49905	−	7.79258i	−0.201405	−	0.348844i	0.747576	−	0.664176i	$-0.231217\pi$
$499$	−4.49905	−	7.79258i	−0.201405	−	0.348844i	−0.948981	+	0.315332i	$0.897884\pi$
$500$	−55.1306			−2.46552
$501$	−1.73528	+	3.00559i	−0.0775266	+	0.134280i
$502$	−8.21515	−	14.2290i	−0.366660	−	0.635074i
$503$	15.1227	+	26.1933i	0.674287	+	1.16790i	0.976677	+	0.214715i	$0.0688823\pi$
$503$	15.1227	+	26.1933i	0.674287	+	1.16790i	−0.302390	+	0.953184i	$0.597784\pi$
$504$	1.35364			0.0602958
$505$	−3.23160	+	5.59729i	−0.143804	+	0.249076i
$506$	0.871269	−	1.50908i	0.0387326	−	0.0670868i
$507$	0.883556	−	1.53036i	0.0392401	−	0.0679658i
$508$	−1.36974	−	2.37245i	−0.0607722	−	0.105261i
$509$	6.70207	−	11.6083i	0.297064	−	0.514530i	−0.678399	−	0.734694i	$-0.737326\pi$
$509$	6.70207	−	11.6083i	0.297064	−	0.514530i	0.975463	+	0.220164i	$0.0706592\pi$
$510$	−3.77816	−	6.54396i	−0.167300	−	0.289771i
$511$	55.4932			2.45487
$512$	−3.21031			−0.141877
$513$	−8.54830	−	14.8061i	−0.377417	−	0.653705i
$514$	5.25687	−	9.10516i	0.231871	−	0.401612i
$515$	−24.1780	−	41.8776i	−1.06541	−	1.84535i
$516$	10.3581	−	17.9407i	0.455989	−	0.789797i
$517$	12.7166	−	22.0259i	0.559277	−	0.968696i
$518$	5.19471	−	8.99751i	0.228243	−	0.395328i
$519$	−5.02474			−0.220561
$520$	−6.11323	−	10.5884i	−0.268083	−	0.464333i
$521$	1.96817	+	3.40897i	0.0862271	+	0.149350i	0.905913	−	0.423463i	$-0.139186\pi$
$521$	1.96817	+	3.40897i	0.0862271	+	0.149350i	−0.819686	+	0.572813i	$0.805852\pi$
$522$	−0.258261	+	0.447321i	−0.0113038	+	0.0195787i
$523$	−6.28091			−0.274645			−0.137323	−	0.990526i	$-0.543850\pi$
$523$	−6.28091			−0.274645			−0.137323	+	0.990526i	$0.543850\pi$
$524$	7.94180	+	13.7556i	0.346939	+	0.600916i
$525$	−102.985			−4.49461
$526$	23.5797			1.02812
$527$	−5.57399	+	3.19274i	−0.242807	+	0.139078i
$528$	−1.40261			−0.0610409
$529$	−22.4440			−0.975827
$530$	−10.0570	−	17.4192i	−0.436847	−	0.756642i
$531$	−0.122910			−0.00533385
$532$	8.72182	−	15.1066i	0.378139	−	0.654956i
$533$	−4.81293	−	8.33625i	−0.208471	−	0.361083i
$534$	−1.75687	−	3.04299i	−0.0760274	−	0.131683i
$535$	68.8669			2.97738
$536$	−2.28961	+	3.96573i	−0.0988963	+	0.171293i
$537$	−18.0752	+	31.3072i	−0.780003	+	1.35101i
$538$	2.59753	−	4.49905i	0.111987	−	0.193968i
$539$	−12.4951	−	21.6422i	−0.538204	−	0.932197i
$540$	14.6144	−	25.3128i	0.628902	−	1.08929i
$541$	0.630481	+	1.09203i	0.0271065	+	0.0469498i	0.879260	−	0.476341i	$-0.158037\pi$
$541$	0.630481	+	1.09203i	0.0271065	+	0.0469498i	−0.852154	+	0.523291i	$0.824704\pi$
$542$	1.21170			0.0520472
$543$	24.2301			1.03981
$544$	3.32436	+	5.75796i	0.142531	+	0.246871i
$545$	9.69301	−	16.7888i	0.415203	−	0.719153i
$546$	−2.95530	−	5.11873i	−0.126475	−	0.219062i
$547$	−7.17125	+	12.4210i	−0.306620	+	0.531082i	−0.977621	−	0.210375i	$-0.932532\pi$
$547$	−7.17125	+	12.4210i	−0.306620	+	0.531082i	0.671000	+	0.741457i	$0.265865\pi$
$548$	2.20939	−	3.82677i	0.0943803	−	0.163471i
$549$	0.700804	−	1.21383i	0.0299096	−	0.0518049i
$550$	−34.0973			−1.45391
$551$	8.45299	+	14.6410i	0.360110	+	0.623728i
$552$	1.81988	+	3.15212i	0.0774591	+	0.134163i
$553$	5.61887	−	9.73217i	0.238939	−	0.413854i
$554$	−17.0690			−0.725191
$555$	12.1473	+	21.0397i	0.515623	+	0.893085i
$556$	−13.3122			−0.564563
$557$	−5.94358			−0.251838			−0.125919	−	0.992041i	$-0.540188\pi$
$557$	−5.94358			−0.251838			−0.125919	+	0.992041i	$0.540188\pi$
$558$	−0.494374	−	0.287689i	−0.0209285	−	0.0121788i
$559$	−9.02627			−0.381771
$560$	5.02817			0.212479
$561$	2.84486	+	4.92744i	0.120110	+	0.208037i
$562$	−16.7998			−0.708657
$563$	9.46829	−	16.3996i	0.399041	−	0.691159i	−0.594567	−	0.804046i	$-0.702677\pi$
$563$	9.46829	−	16.3996i	0.399041	−	0.691159i	0.993608	+	0.112887i	$0.0360098\pi$
$564$	10.4579	+	18.1137i	0.440358	+	0.762723i
$565$	24.9024	+	43.1322i	1.04765	+	1.81459i
$566$	−17.7487			−0.746035
$567$	18.6794	−	32.3537i	0.784461	−	1.35873i
$568$	−1.97940	+	3.42841i	−0.0830536	+	0.143853i
$569$	4.70474	−	8.14884i	0.197233	−	0.341617i	−0.750397	−	0.660987i	$-0.770138\pi$
$569$	4.70474	−	8.14884i	0.197233	−	0.341617i	0.947630	+	0.319370i	$0.103471\pi$
$570$	−11.0113	−	19.0721i	−0.461213	−	0.798844i
$571$	−18.1155	+	31.3770i	−0.758111	+	1.31309i	0.185701	+	0.982606i	$0.440544\pi$
$571$	−18.1155	+	31.3770i	−0.758111	+	1.31309i	−0.943813	+	0.330481i	$0.892789\pi$
$572$	1.81232	+	3.13903i	0.0757769	+	0.131249i
$573$	12.6762			0.529557
$574$	−32.1964			−1.34385
$575$	−5.43957	−	9.42161i	−0.226846	−	0.392908i
$576$	−0.261124	+	0.452280i	−0.0108802	+	0.0188450i
$577$	0.0752435	+	0.130326i	0.00313243	+	0.00542552i	0.867587	−	0.497285i	$-0.165670\pi$
$577$	0.0752435	+	0.130326i	0.00313243	+	0.00542552i	−0.864455	+	0.502710i	$0.832336\pi$
$578$	−6.56047	+	11.3631i	−0.272880	+	0.472642i
$579$	20.9373	−	36.2645i	0.870124	−	1.50710i
$580$	−14.4514	+	25.0306i	−0.600063	+	1.03934i
$581$	43.1125			1.78861
$582$	3.22372	+	5.58365i	0.133628	+	0.231450i
$583$	7.57266	+	13.1162i	0.313628	+	0.543219i
$584$	−19.1888	+	33.2359i	−0.794037	+	1.37531i
$585$	0.543002			0.0224504
$586$	0.220849	+	0.382522i	0.00912320	+	0.0158018i
$587$	35.1844			1.45222			0.726108	−	0.687581i	$-0.241327\pi$
$587$	35.1844			1.45222			0.726108	+	0.687581i	$0.241327\pi$
$588$	20.5515			0.847532
$589$	−16.2452	+	9.30513i	−0.669371	+	0.383411i
$590$	3.71326			0.152872
$591$	−31.5631			−1.29833
$592$	−0.441713	−	0.765069i	−0.0181543	−	0.0314441i
$593$	−7.69506			−0.315998			−0.157999	−	0.987439i	$-0.550504\pi$
$593$	−7.69506			−0.315998			−0.157999	+	0.987439i	$0.550504\pi$
$594$	5.94122	−	10.2905i	0.243771	−	0.422224i
$595$	−10.1984	−	17.6642i	−0.418094	−	0.724160i
$596$	11.8423	+	20.5114i	0.485078	+	0.840180i
$597$	−0.948342			−0.0388131
$598$	0.312194	−	0.540735i	0.0127666	−	0.0221123i
$599$	5.81768	−	10.0765i	0.237704	−	0.411715i	−0.722351	−	0.691526i	$-0.756939\pi$
$599$	5.81768	−	10.0765i	0.237704	−	0.411715i	0.960055	+	0.279811i	$0.0902719\pi$
$600$	35.6106	−	61.6794i	1.45380	−	2.51805i
$601$	−20.1823	−	34.9568i	−0.823255	−	1.42592i	−0.903246	−	0.429123i	$-0.858823\pi$
$601$	−20.1823	−	34.9568i	−0.823255	−	1.42592i	0.0799911	−	0.996796i	$-0.474511\pi$
$602$	−15.0955	+	26.1461i	−0.615245	+	1.06564i
$603$	−0.101686	−	0.176126i	−0.00414099	−	0.00717241i
$604$	−21.7335			−0.884325
$605$	−14.2143			−0.577892
$606$	−1.08040	−	1.87131i	−0.0438883	−	0.0760168i
$607$	−9.55423	+	16.5484i	−0.387794	+	0.671679i	−0.992153	−	0.125033i	$-0.960096\pi$
$607$	−9.55423	+	16.5484i	−0.387794	+	0.671679i	0.604358	+	0.796713i	$0.293430\pi$
$608$	9.68874	+	16.7814i	0.392930	+	0.680575i
$609$	−17.7443	+	30.7340i	−0.719035	+	1.24541i
$610$	−21.1721	+	36.6711i	−0.857232	+	1.48477i
$611$	4.55664	−	7.89233i	0.184342	−	0.319289i
$612$	−0.183830			−0.00743089
$613$	2.84581	+	4.92909i	0.114941	+	0.199084i	0.917756	−	0.397144i	$-0.129999\pi$
$613$	2.84581	+	4.92909i	0.114941	+	0.199084i	−0.802815	+	0.596228i	$0.796665\pi$
$614$	4.24347	+	7.34991i	0.171253	+	0.296618i
$615$	37.6439	−	65.2012i	1.51795	−	2.62917i
$616$	30.7928			1.24068
$617$	1.21982	+	2.11278i	0.0491079	+	0.0850574i	0.889534	−	0.456868i	$-0.151029\pi$
$617$	1.21982	+	2.11278i	0.0491079	+	0.0850574i	−0.840427	+	0.541925i	$0.817696\pi$
$618$	16.1666			0.650318
$619$	29.6368			1.19120			0.595601	−	0.803281i	$-0.296914\pi$
$619$	29.6368			1.19120			0.595601	+	0.803281i	$0.296914\pi$
$620$	−27.6635	−	16.0981i	−1.11099	−	0.646516i
$621$	3.79123			0.152137
$622$	19.6040			0.786048
$623$	−4.74235	−	8.21398i	−0.189998	−	0.329086i
$624$	−0.502586			−0.0201195
$625$	−57.4633	+	99.5294i	−2.29853	+	3.98118i
$626$	−11.2902	−	19.5551i	−0.451246	−	0.781580i
$627$	8.29124	+	14.3609i	0.331120	+	0.573517i
$628$	19.7683			0.788840
$629$	−1.79181	+	3.10351i	−0.0714443	+	0.123745i
$630$	0.908112	−	1.57290i	0.0361801	−	0.0626657i
$631$	0.837471	−	1.45054i	0.0333392	−	0.0577452i	−0.848874	−	0.528595i	$-0.822719\pi$
$631$	0.837471	−	1.45054i	0.0333392	−	0.0577452i	0.882214	+	0.470849i	$0.156053\pi$
$632$	3.88586	+	6.73050i	0.154571	+	0.267725i
$633$	−6.16679	+	10.6812i	−0.245108	+	0.424539i
$634$	−7.60365	−	13.1699i	−0.301980	−	0.523044i
$635$	−9.33579			−0.370479
$636$	−12.4552			−0.493882
$637$	−4.47727	−	7.75486i	−0.177396	−	0.307259i
$638$	−5.87498	+	10.1758i	−0.232593	+	0.402862i
$639$	−0.0879090	−	0.152263i	−0.00347763	−	0.00602343i
$640$	−17.6182	+	30.5156i	−0.696421	+	1.20624i
$641$	−2.15900	+	3.73950i	−0.0852754	+	0.147701i	−0.905509	−	0.424328i	$-0.860510\pi$
$641$	−2.15900	+	3.73950i	−0.0852754	+	0.147701i	0.820233	+	0.572029i	$0.193844\pi$
$642$	−11.5120	+	19.9393i	−0.454341	+	0.786941i
$643$	39.2702			1.54867			0.774333	−	0.632778i	$-0.218085\pi$
$643$	39.2702			1.54867			0.774333	+	0.632778i	$0.218085\pi$
$644$	1.93410	+	3.34995i	0.0762140	+	0.132007i
$645$	−35.2991	−	61.1398i	−1.38990	−	2.40738i
$646$	1.62425	−	2.81328i	0.0639052	−	0.110687i
$647$	−27.1603			−1.06778			−0.533891	−	0.845554i	$-0.679271\pi$
$647$	−27.1603			−1.06778			−0.533891	+	0.845554i	$0.679271\pi$
$648$	12.9182	+	22.3749i	0.507473	+	0.878969i
$649$	−2.79599			−0.109752
$650$	−12.2178			−0.479220
$651$	−33.9669	−	19.7662i	−1.33127	−	0.774698i
$652$	2.02970			0.0794890
$653$	−40.9577			−1.60280			−0.801400	−	0.598129i	$-0.795911\pi$
$653$	−40.9577			−1.60280			−0.801400	+	0.598129i	$0.795911\pi$
$654$	3.24061	+	5.61291i	0.126718	+	0.219482i
$655$	54.1294			2.11501
$656$	−1.36885	+	2.37092i	−0.0534447	+	0.0925689i
$657$	−0.852213	−	1.47608i	−0.0332480	−	0.0575872i
$658$	−15.2410	−	26.3981i	−0.594155	−	1.02911i
$659$	−8.47471			−0.330128			−0.165064	−	0.986283i	$-0.552783\pi$
$659$	−8.47471			−0.330128			−0.165064	+	0.986283i	$0.552783\pi$
$660$	−14.1749	+	24.5516i	−0.551757	+	0.955672i
$661$	4.32047	−	7.48328i	0.168047	−	0.291066i	−0.769686	−	0.638422i	$-0.779587\pi$
$661$	4.32047	−	7.48328i	0.168047	−	0.291066i	0.937733	+	0.347357i	$0.112921\pi$
$662$	−6.41073	+	11.1037i	−0.249160	+	0.431558i
$663$	1.01937	+	1.76561i	0.0395892	+	0.0685704i
$664$	−14.9077	+	25.8209i	−0.578530	+	1.00204i
$665$	−29.7229	−	51.4816i	−1.15261	−	1.99637i
$666$	−0.319102			−0.0123650
$667$	−3.74896			−0.145160
$668$	−1.27539	−	2.20904i	−0.0493463	−	0.0854703i
$669$	−2.05214	+	3.55441i	−0.0793404	+	0.137422i
$670$	3.07206	+	5.32096i	0.118684	+	0.205567i
$671$	15.9420	−	27.6124i	0.615436	−	1.06597i
$672$	−20.3383	+	35.2270i	−0.784568	+	1.35891i
$673$	15.4873	−	26.8249i	0.596993	−	1.03402i	−0.396269	−	0.918134i	$-0.629695\pi$
$673$	15.4873	−	26.8249i	0.596993	−	1.03402i	0.993262	−	0.115888i	$-0.0369713\pi$
$674$	9.34941			0.360126
$675$	−37.0926	−	64.2463i	−1.42770	−	2.47284i
$676$	0.649392	+	1.12478i	0.0249766	+	0.0432608i
$677$	5.98801	−	10.3715i	0.230138	−	0.398610i	−0.727711	−	0.685884i	$-0.759416\pi$
$677$	5.98801	−	10.3715i	0.230138	−	0.398610i	0.957848	+	0.287274i	$0.0927490\pi$
$678$	−16.6510			−0.639477
$679$	8.70182	+	15.0720i	0.333945	+	0.578410i
$680$	14.1059			0.540935
$681$	−21.3001			−0.816222
$682$	−11.2461	−	6.54441i	−0.430636	−	0.250598i
$683$	−50.5559			−1.93447			−0.967234	−	0.253888i	$-0.918291\pi$
$683$	−50.5559			−1.93447			−0.967234	+	0.253888i	$0.918291\pi$
$684$	−0.535767			−0.0204855
$685$	−7.52932	−	13.0412i	−0.287680	−	0.498277i
$686$	−6.53753			−0.249604
$687$	15.5964	−	27.0137i	0.595038	−	1.03064i
$688$	1.28359	+	2.22324i	0.0489362	+	0.0847601i
$689$	2.71344	+	4.69982i	0.103374	+	0.179049i
$690$	4.88359			0.185915
$691$	−2.55778	+	4.43021i	−0.0973027	+	0.168533i	−0.910567	−	0.413361i	$-0.864355\pi$
$691$	−2.55778	+	4.43021i	−0.0973027	+	0.168533i	0.813265	+	0.581894i	$0.197688\pi$
$692$	1.84653	−	3.19829i	0.0701946	−	0.121581i
$693$	−0.683786	+	1.18435i	−0.0259749	+	0.0449898i
$694$	−14.3229	−	24.8080i	−0.543690	−	0.941699i
$695$	−22.6832	+	39.2884i	−0.860422	+	1.49030i
$696$	−12.2715	−	21.2548i	−0.465148	−	0.805661i
$697$	11.1055			0.420652
$698$	−8.61833			−0.326209
$699$	−9.79006	−	16.9569i	−0.370294	−	0.641368i
$700$	37.8456	−	65.5505i	1.43043	−	2.47757i
$701$	−11.0044	−	19.0602i	−0.415632	−	0.719895i	0.579863	−	0.814714i	$-0.303106\pi$
$701$	−11.0044	−	19.0602i	−0.415632	−	0.719895i	−0.995495	+	0.0948188i	$0.969773\pi$
$702$	2.12886	−	3.68730i	0.0803487	−	0.139168i
$703$	−5.22218	+	9.04508i	−0.196958	+	0.341141i
$704$	−5.94011	+	10.2886i	−0.223876	+	0.387765i
$705$	71.2787			2.68451
$706$	−0.0670824	−	0.116190i	−0.00252468	−	0.00437288i
$707$	−2.91634	−	5.05125i	−0.109680	−	0.189972i
$708$	1.14969	−	1.99131i	0.0432078	−	0.0748381i
$709$	24.0908			0.904748			0.452374	−	0.891828i	$-0.350577\pi$
$709$	24.0908			0.904748			0.452374	+	0.891828i	$0.350577\pi$
$710$	2.65583	+	4.60003i	0.0996714	+	0.172636i
$711$	−0.345158			−0.0129444
$712$	6.55935			0.245822
$713$	0.0142170	−	4.15152i	0.000532432	−	0.155476i
$714$	6.81916			0.255201
$715$	12.3523			0.461951
$716$	−13.2849	−	23.0100i	−0.496478	−	0.859926i
$717$	−18.9974			−0.709471
$718$	−1.07015	+	1.85356i	−0.0399378	+	0.0691743i
$719$	2.69660	+	4.67065i	0.100566	+	0.174186i	0.911918	−	0.410372i	$-0.134601\pi$
$719$	2.69660	+	4.67065i	0.100566	+	0.174186i	−0.811352	+	0.584558i	$0.801268\pi$
$720$	−0.0772179	−	0.133745i	−0.00287774	−	0.00498439i
$721$	43.6388			1.62519
$722$	−3.22135	+	5.57954i	−0.119886	+	0.207649i
$723$	−9.52208	+	16.4927i	−0.354130	+	0.613371i
$724$	−8.90429	+	15.4227i	−0.330925	+	0.573179i
$725$	36.6791	+	63.5300i	1.36223	+	2.35945i
$726$	2.37609	−	4.11551i	0.0881850	−	0.152741i
$727$	−14.4282	−	24.9904i	−0.535113	−	0.926843i	−0.999158	−	0.0410310i	$-0.986936\pi$
$727$	−14.4282	−	24.9904i	−0.535113	−	0.926843i	0.464045	−	0.885812i	$-0.346398\pi$
$728$	11.0337			0.408937
$729$	25.8074			0.955830
$730$	25.7463	+	44.5938i	0.952912	+	1.65049i
$731$	5.20688	−	9.01858i	0.192583	−	0.333564i
$732$	13.1104	+	22.7080i	0.484576	+	0.839310i
$733$	−3.04248	+	5.26973i	−0.112377	+	0.194642i	−0.916728	−	0.399512i	$-0.869180\pi$
$733$	−3.04248	+	5.26973i	−0.112377	+	0.194642i	0.804351	+	0.594154i	$0.202513\pi$
$734$	11.8031	−	20.4436i	0.435660	−	0.754585i
$735$	35.0186	−	60.6540i	1.29168	−	2.23725i
$736$	−4.29702			−0.158390
$737$	−2.31319	−	4.00656i	−0.0852073	−	0.147583i
$738$	0.494443	+	0.856400i	0.0182007	+	0.0315245i
$739$	19.9983	−	34.6381i	0.735650	−	1.27418i	−0.218787	−	0.975773i	$-0.570210\pi$
$739$	19.9983	−	34.6381i	0.735650	−	1.27418i	0.954437	−	0.298411i	$-0.0964566\pi$
$740$	−17.8559			−0.656396
$741$	2.97093	+	5.14580i	0.109140	+	0.189036i
$742$	18.1518			0.666372
$743$	−31.9389			−1.17172			−0.585862	−	0.810411i	$-0.699244\pi$
$743$	−31.9389			−1.17172			−0.585862	+	0.810411i	$0.699244\pi$
$744$	23.5836	−	13.5085i	0.864617	−	0.495247i
$745$	80.7140			2.95713
$746$	20.2513			0.741451
$747$	−0.662081	−	1.14676i	−0.0242243	−	0.0419577i
$748$	−4.18181			−0.152902
$749$	−31.0743	+	53.8223i	−1.13543	+	1.96662i
$750$	−31.4062	−	54.3971i	−1.14679	−	1.98630i
$751$	6.94224	+	12.0243i	0.253326	+	0.438773i	0.964439	−	0.264304i	$-0.0851422\pi$
$751$	6.94224	+	12.0243i	0.253326	+	0.438773i	−0.711114	+	0.703077i	$0.751809\pi$
$752$	−2.59192			−0.0945174
$753$	−17.3362	+	30.0271i	−0.631766	+	1.09425i
$754$	−2.10513	+	3.64619i	−0.0766642	+	0.132786i
$755$	−37.0326	+	64.1424i	−1.34775	+	2.33438i
$756$	13.1887	+	22.8435i	0.479667	+	0.830808i
$757$	20.8327	−	36.0833i	0.757178	−	1.31147i	−0.187106	−	0.982340i	$-0.559911\pi$
$757$	20.8327	−	36.0833i	0.757178	−	1.31147i	0.944284	−	0.329132i	$-0.106756\pi$
$758$	−5.51774	−	9.55700i	−0.200413	−	0.347126i
$759$	−3.67722			−0.133475
$760$	41.1111			1.49126
$761$	11.4653	+	19.8585i	0.415616	+	0.719869i	0.995493	−	0.0948356i	$-0.0302325\pi$
$761$	11.4653	+	19.8585i	0.415616	+	0.719869i	−0.579876	+	0.814704i	$0.696899\pi$
$762$	1.56059	−	2.70303i	0.0565343	−	0.0979203i
$763$	8.74741	+	15.1510i	0.316678	+	0.548502i
$764$	−4.65837	+	8.06853i	−0.168534	+	0.291909i
$765$	−0.313235	+	0.542539i	−0.0113250	+	0.0196156i
$766$	1.56006	−	2.70210i	0.0563671	−	0.0976307i
$767$	−1.00186			−0.0361751
$768$	−13.4127	−	23.2314i	−0.483988	−	0.838292i
$769$	−20.1493	−	34.8996i	−0.726601	−	1.25851i	−0.958312	−	0.285725i	$-0.907765\pi$
$769$	−20.1493	−	34.8996i	−0.726601	−	1.25851i	0.231710	−	0.972785i	$-0.425568\pi$
$770$	20.6579	−	35.7806i	0.744460	−	1.28944i
$771$	−22.1868			−0.799039
$772$	15.3884	+	26.6535i	0.553841	+	0.959281i
$773$	−1.31154			−0.0471726			−0.0235863	−	0.999722i	$-0.507508\pi$
$773$	−1.31154			−0.0471726			−0.0235863	+	0.999722i	$0.507508\pi$
$774$	0.927288			0.0333307
$775$	−70.4908	+	40.3767i	−2.53211	+	1.45037i
$776$	−12.0359			−0.432063
$777$	−21.9245			−0.786537
$778$	5.04432	+	8.73703i	0.180848	+	0.313238i
$779$	32.3667			1.15966
$780$	−5.07916	+	8.79737i	−0.181863	+	0.314996i
$781$	−1.99977	−	3.46371i	−0.0715575	−	0.123941i
$782$	0.360183	+	0.623855i	0.0128801	+	0.0223090i
$783$	−25.5643			−0.913594
$784$	−1.27339	+	2.20557i	−0.0454780	+	0.0787703i
$785$	33.6839	−	58.3422i	1.20223	−	2.08232i
$786$	−9.04840	+	15.6723i	−0.322746	+	0.559012i
$787$	−1.54321	−	2.67292i	−0.0550096	−	0.0952794i	0.837209	−	0.546883i	$-0.184186\pi$
$787$	−1.54321	−	2.67292i	−0.0550096	−	0.0952794i	−0.892219	+	0.451603i	$0.850852\pi$
$788$	11.5991	−	20.0902i	0.413199	−	0.715682i
$789$	−24.8798	−	43.0931i	−0.885744	−	1.53415i
$790$	10.4276			0.370997
$791$	−44.9461			−1.59810
$792$	−0.472888	−	0.819065i	−0.0168033	−	0.0291042i
$793$	5.71237	−	9.89411i	0.202852	−	0.351350i
$794$	−13.8340	−	23.9612i	−0.490951	−	0.850353i
$795$	−21.2229	+	36.7592i	−0.752700	+	1.30372i
$796$	0.348504	−	0.603627i	0.0123524	−	0.0213950i
$797$	−22.4317	+	38.8529i	−0.794573	+	1.37624i	0.128538	+	0.991705i	$0.458972\pi$
$797$	−22.4317	+	38.8529i	−0.794573	+	1.37624i	−0.923110	+	0.384535i	$0.874362\pi$
$798$	19.8742			0.703539
$799$	5.25707	+	9.10551i	0.185982	+	0.322130i
$800$	42.0412	+	72.8175i	1.48638	+	2.57449i
$801$	−0.145657	+	0.252285i	−0.00514654	+	0.00891407i
$802$	19.8340			0.700362
$803$	−19.3863	−	33.5781i	−0.684128	−	1.18494i
$804$	3.80464			0.134179
$805$	13.1823			0.464616
$806$	−4.02972	−	2.34500i	−0.141941	−	0.0825990i
$807$	−10.9630			−0.385915
$808$	4.03372			0.141906
$809$	1.06689	+	1.84791i	0.0375100	+	0.0649692i	0.884171	−	0.467164i	$-0.154724\pi$
$809$	1.06689	+	1.84791i	0.0375100	+	0.0649692i	−0.846661	+	0.532133i	$0.821391\pi$
$810$	34.6655			1.21802
$811$	−9.27723	+	16.0686i	−0.325768	+	0.564246i	−0.981667	−	0.190602i	$-0.938956\pi$
$811$	−9.27723	+	16.0686i	−0.325768	+	0.564246i	0.655900	+	0.754848i	$0.272289\pi$
$812$	−13.0416	−	22.5888i	−0.457672	−	0.792710i
$813$	−1.27851	−	2.21445i	−0.0448394	−	0.0776641i
$814$	−7.25901			−0.254428
$815$	3.45848	−	5.99026i	0.121145	−	0.209830i
$816$	0.289921	−	0.502157i	0.0101493	−	0.0175790i
$817$	15.1753	−	26.2843i	0.530916	−	0.919573i
$818$	14.8834	+	25.7788i	0.520387	+	0.901336i
$819$	−0.245015	+	0.424378i	−0.00856152	+	0.0148290i
$820$	27.6674	+	47.9213i	0.966187	+	1.67349i
$821$	47.2678			1.64966			0.824828	−	0.565383i	$-0.191272\pi$
$821$	47.2678			1.64966			0.824828	+	0.565383i	$0.191272\pi$
$822$	5.03447			0.175597
$823$	10.1029	+	17.4988i	0.352166	+	0.609969i	0.986629	−	0.162985i	$-0.0521121\pi$
$823$	10.1029	+	17.4988i	0.352166	+	0.609969i	−0.634463	+	0.772953i	$0.718779\pi$
$824$	−15.0897	+	26.1361i	−0.525674	+	0.910493i
$825$	35.9772	+	62.3144i	1.25257	+	2.16951i
$826$	−1.67551	+	2.90206i	−0.0582983	+	0.100976i
$827$	−19.9405	+	34.5379i	−0.693399	+	1.20100i	0.277319	+	0.960778i	$0.410554\pi$
$827$	−19.9405	+	34.5379i	−0.693399	+	1.20100i	−0.970717	+	0.240224i	$0.922779\pi$
$828$	0.0594041	−	0.102891i	0.00206443	−	0.00357570i
$829$	−30.1828			−1.04829			−0.524146	−	0.851628i	$-0.675615\pi$
$829$	−30.1828			−1.04829			−0.524146	+	0.851628i	$0.675615\pi$
$830$	20.0022	+	34.6448i	0.694286	+	1.20254i
$831$	18.0101	+	31.1944i	0.624762	+	1.08212i
$832$	−2.12846	+	3.68661i	−0.0737912	+	0.127810i
$833$	10.3310			0.357948
$834$	−7.58355	−	13.1351i	−0.262597	−	0.454831i
$835$	−8.69274			−0.300825
$836$	−12.1877			−0.421522
$837$	0.0969465	−	28.3094i	0.00335096	−	0.978515i
$838$	−19.6729			−0.679590
$839$	25.6696			0.886213			0.443106	−	0.896469i	$-0.353876\pi$
$839$	25.6696			0.886213			0.443106	+	0.896469i	$0.353876\pi$
$840$	43.1496	+	74.7373i	1.48880	+	2.57868i
$841$	−3.72069			−0.128300
$842$	−8.65811	+	14.9963i	−0.298378	+	0.516806i
$843$	17.7261	+	30.7024i	0.610518	+	1.05745i
$844$	−4.53244	−	7.85042i	−0.156013	−	0.270223i
$845$	4.42610			0.152262
$846$	−0.468113	+	0.810795i	−0.0160941	+	0.0278757i
$847$	6.41380	−	11.1090i	0.220381	−	0.381711i
$848$	0.771733	−	1.33668i	0.0265014	−	0.0459018i
$849$	18.7273	+	32.4367i	0.642720	+	1.11322i
$850$	7.04791	−	12.2073i	0.241741	−	0.418708i
$851$	−1.15804	−	2.00578i	−0.0396970	−	0.0687572i
$852$	3.28915			0.112684
$853$	−53.5450			−1.83334			−0.916672	−	0.399640i	$-0.869135\pi$
$853$	−53.5450			−1.83334			−0.916672	+	0.399640i	$0.869135\pi$
$854$	−19.1066	−	33.0937i	−0.653816	−	1.13244i
$855$	−0.912913	+	1.58121i	−0.0312210	+	0.0540763i
$856$	−21.4901	−	37.2220i	−0.734518	−	1.27222i
$857$	−2.57343	+	4.45732i	−0.0879068	+	0.152259i	−0.906626	−	0.421935i	$-0.861351\pi$
$857$	−2.57343	+	4.45732i	−0.0879068	+	0.152259i	0.818719	+	0.574194i	$0.194684\pi$
$858$	−2.06484	+	3.57642i	−0.0704926	+	0.122097i
$859$	−12.3698	+	21.4252i	−0.422053	+	0.731017i	−0.996140	−	0.0877770i	$-0.972024\pi$
$859$	−12.3698	+	21.4252i	−0.422053	+	0.731017i	0.574087	+	0.818794i	$0.305357\pi$
$860$	51.8880			1.76937
$861$	33.9716	+	58.8405i	1.15775	+	2.00528i
$862$	1.39214	+	2.41125i	0.0474163	+	0.0821275i
$863$	6.89602	−	11.9443i	0.234743	−	0.406587i	−0.724455	−	0.689322i	$-0.757908\pi$
$863$	6.89602	−	11.9443i	0.234743	−	0.406587i	0.959198	+	0.282735i	$0.0912418\pi$
$864$	−29.3016			−0.996860
$865$	−6.29275	−	10.8994i	−0.213960	−	0.370590i
$866$	24.9047			0.846296
$867$	27.6888			0.940359
$868$	25.0638	−	14.3563i	0.850719	−	0.487286i
$869$	−7.85172			−0.266351
$870$	−32.9301			−1.11644
$871$	−0.828863	−	1.43563i	−0.0280849	−	0.0486446i
$872$	−12.0989			−0.409722
$873$	0.267269	−	0.462923i	0.00904568	−	0.0156676i
$874$	1.04974	+	1.81820i	0.0355080	+	0.0615017i
$875$	−84.7750	−	146.835i	−2.86592	−	4.96392i
$876$	31.8859			1.07732
$877$	−22.1956	+	38.4439i	−0.749492	+	1.29816i	0.198575	+	0.980086i	$0.436369\pi$
$877$	−22.1956	+	38.4439i	−0.749492	+	1.29816i	−0.948067	+	0.318072i	$0.896965\pi$
$878$	10.1242	−	17.5356i	0.341674	−	0.591797i
$879$	0.466052	−	0.807225i	0.0157195	−	0.0272270i
$880$	−1.75657	−	3.04247i	−0.0592139	−	0.102562i
$881$	15.7694	−	27.3135i	0.531286	−	0.920214i	−0.468048	−	0.883703i	$-0.655042\pi$
$881$	15.7694	−	27.3135i	0.531286	−	0.920214i	0.999333	−	0.0365103i	$-0.0116242\pi$
$882$	0.459960	+	0.796673i	0.0154876	+	0.0268254i
$883$	3.14330			0.105781			0.0528903	−	0.998600i	$-0.483157\pi$
$883$	3.14330			0.105781			0.0528903	+	0.998600i	$0.483157\pi$
$884$	−1.49843			−0.0503976
$885$	−3.91799	−	6.78615i	−0.131702	−	0.228114i
$886$	−7.04376	+	12.2001i	−0.236640	+	0.409872i
$887$	−4.22821	−	7.32347i	−0.141969	−	0.245898i	0.786269	−	0.617885i	$-0.212010\pi$
$887$	−4.22821	−	7.32347i	−0.141969	−	0.245898i	−0.928238	+	0.371986i	$0.878677\pi$
$888$	7.58119	−	13.1310i	0.254408	−	0.440647i
$889$	4.21252	−	7.29630i	0.141283	−	0.244710i
$890$	4.40046	−	7.62182i	0.147504	−	0.255484i
$891$	−26.1023			−0.874459
$892$	−1.50828	−	2.61241i	−0.0505008	−	0.0874699i
$893$	15.3215	+	26.5377i	0.512716	+	0.888050i
$894$	−13.4923	+	23.3694i	−0.451251	+	0.781590i
$895$	−90.5463			−3.02663
$896$	−15.8995	−	27.5387i	−0.531164	−	0.920004i
$897$	−1.31763			−0.0439943
$898$	−22.8580			−0.762781
$899$	−0.0958656	+	27.9937i	−0.00319730	+	0.933643i
$900$	−2.32479			−0.0774929
$901$	−6.26109			−0.208587
$902$	11.2477	+	19.4816i	0.374507	+	0.648665i
$903$	63.7110			2.12017
$904$	15.5417	−	26.9191i	0.516910	−	0.895315i
$905$	30.3447	+	52.5586i	1.00869	+	1.74711i
$906$	−12.3809	−	21.4444i	−0.411328	−	0.712442i
$907$	−7.07756			−0.235007			−0.117503	−	0.993072i	$-0.537489\pi$
$907$	−7.07756			−0.235007			−0.117503	+	0.993072i	$0.537489\pi$
$908$	7.82754	−	13.5577i	0.259766	−	0.449928i
$909$	−0.0895729	+	0.155145i	−0.00297094	+	0.00514583i
$910$	7.40217	−	12.8209i	0.245380	−	0.425010i
$911$	−26.4954	−	45.8913i	−0.877830	−	1.52045i	−0.853717	−	0.520737i	$-0.825657\pi$
$911$	−26.4954	−	45.8913i	−0.877830	−	1.52045i	−0.0241133	−	0.999709i	$-0.507676\pi$
$912$	0.844964	−	1.46352i	0.0279796	−	0.0484620i
$913$	−15.0612	−	26.0867i	−0.498452	−	0.863344i
$914$	−0.428543			−0.0141750
$915$	89.3576			2.95407
$916$	11.4630	+	19.8544i	0.378747	+	0.656009i
$917$	−24.4244	+	42.3043i	−0.806565	+	1.39701i
$918$	2.45610	+	4.25409i	0.0810635	+	0.140406i
$919$	5.08334	−	8.80460i	0.167684	−	0.290437i	−0.769921	−	0.638139i	$-0.779705\pi$
$919$	5.08334	−	8.80460i	0.167684	−	0.290437i	0.937605	+	0.347702i	$0.113038\pi$
$920$	−4.55826	+	7.89514i	−0.150281	+	0.260295i
$921$	8.95487	−	15.5103i	0.295073	−	0.511081i
$922$	−5.63963			−0.185731
$923$	−0.716560	−	1.24112i	−0.0235859	−	0.0408519i
$924$	−12.7921	−	22.1565i	−0.420828	−	0.728896i
$925$	−22.6600	+	39.2482i	−0.745055	+	1.29047i
$926$	−7.85845			−0.258245
$927$	−0.670163	−	1.16076i	−0.0220110	−	0.0381243i
$928$	28.9749			0.951147
$929$	35.4529			1.16317			0.581586	−	0.813485i	$-0.302432\pi$
$929$	35.4529			1.16317			0.581586	+	0.813485i	$0.302432\pi$
$930$	0.124879	−	36.4661i	0.00409496	−	1.19577i
$931$	30.1094			0.986794
$932$	14.3909			0.471390
$933$	−20.6849	−	35.8272i	−0.677192	−	1.17293i
$934$	−13.8366			−0.452749
$935$	−7.12554	+	12.3418i	−0.233030	+	0.403620i
$936$	−0.169446	−	0.293488i	−0.00553850	−	0.00959296i
$937$	−0.226680	−	0.392621i	−0.00740530	−	0.0128264i	0.862299	−	0.506399i	$-0.169024\pi$
$937$	−0.226680	−	0.392621i	−0.00740530	−	0.0128264i	−0.869704	+	0.493573i	$0.835691\pi$
$938$	−5.54473			−0.181042
$939$	−23.8253	+	41.2666i	−0.777509	+	1.34669i
$940$	−26.1941	+	45.3694i	−0.854356	+	1.47979i
$941$	3.38337	−	5.86016i	0.110295	−	0.191036i	−0.805594	−	0.592467i	$-0.798154\pi$
$941$	3.38337	−	5.86016i	0.110295	−	0.191036i	0.915889	+	0.401432i	$0.131487\pi$
$942$	11.2614	+	19.5053i	0.366915	+	0.635515i
$943$	−3.58871	+	6.21583i	−0.116864	+	0.202415i
$944$	0.142470	+	0.246766i	0.00463701	+	0.00803154i
$945$	89.8908			2.92415
$946$	21.0942			0.685830
$947$	−15.8759	−	27.4979i	−0.515898	−	0.893562i	−0.999830	−	0.0184561i	$-0.994125\pi$
$947$	−15.8759	−	27.4979i	−0.515898	−	0.893562i	0.483931	−	0.875106i	$-0.339208\pi$
$948$	3.22855	−	5.59202i	0.104859	−	0.181620i
$949$	−6.94652	−	12.0317i	−0.225494	−	0.390567i
$950$	20.5409	−	35.5779i	0.666435	−	1.15430i
$951$	−16.0458	+	27.7921i	−0.520319	+	0.901220i
$952$	−6.36489	+	11.0243i	−0.206287	+	0.357300i
$953$	−46.3825			−1.50248			−0.751238	−	0.660031i	$-0.770543\pi$
$953$	−46.3825			−1.50248			−0.751238	+	0.660031i	$0.770543\pi$
$954$	−0.278758	−	0.482822i	−0.00902511	−	0.0156320i
$955$	15.8751	+	27.4966i	0.513708	+	0.889768i
$956$	6.98132	−	12.0920i	0.225792	−	0.391083i
$957$	24.7956			0.801527
$958$	1.39615	+	2.41820i	0.0451074	+	0.0781284i
$959$	13.5896			0.438831
$960$	−33.2952			−1.07460
$961$	−30.9993	−	0.212319i	−0.999977	−	0.00684900i
$962$	−2.60105			−0.0838613
$963$	1.90884			0.0615116
$964$	−6.99850	−	12.1218i	−0.225407	−	0.390416i
$965$	104.884			3.37632
$966$	−2.20359	+	3.81673i	−0.0708993	+	0.122801i
$967$	−26.6890	−	46.2268i	−0.858262	−	1.48655i	−0.873586	−	0.486670i	$-0.838211\pi$
$967$	−26.6890	−	46.2268i	−0.858262	−	1.48655i	0.0153239	−	0.999883i	$-0.495122\pi$
$968$	4.43561	+	7.68270i	0.142566	+	0.246931i
$969$	−6.85521			−0.220221
$970$	−8.07448	+	13.9854i	−0.259256	+	0.449045i
$971$	−13.4105	+	23.2277i	−0.430364	+	0.745412i	−0.996904	−	0.0786221i	$-0.974948\pi$
$971$	−13.4105	+	23.2277i	−0.430364	+	0.745412i	0.566541	+	0.824034i	$0.308281\pi$
$972$	0.827429	−	1.43315i	0.0265398	−	0.0459683i
$973$	−20.4703	−	35.4557i	−0.656249	−	1.13666i
$974$	−8.48720	+	14.7003i	−0.271947	+	0.471027i
$975$	12.8914	+	22.3285i	0.412855	+	0.715086i
$976$	−3.24932			−0.104008
$977$	−16.0439			−0.513289			−0.256645	−	0.966506i	$-0.582617\pi$
$977$	−16.0439			−0.513289			−0.256645	+	0.966506i	$0.582617\pi$
$978$	1.15625	+	2.00269i	0.0369729	+	0.0640390i
$979$	−3.31344	+	5.73904i	−0.105898	+	0.183421i
$980$	25.7378	+	44.5792i	0.822165	+	1.42403i
$981$	0.268669	−	0.465349i	0.00857795	−	0.0148574i
$982$	9.81450	−	16.9992i	0.313193	−	0.542467i
$983$	27.2122	−	47.1329i	0.867934	−	1.50331i	0.00383020	−	0.999993i	$-0.498781\pi$
$983$	27.2122	−	47.1329i	0.867934	−	1.50331i	0.864104	−	0.503313i	$-0.167886\pi$
$984$	−46.9876			−1.49791
$985$	−39.5282	−	68.4648i	−1.25947	−	2.18147i
$986$	−2.42872	−	4.20667i	−0.0773462	−	0.133968i
$987$	−32.1626	+	55.7072i	−1.02375	+	1.77318i
$988$	−4.36712			−0.138937
$989$	3.36517	+	5.82865i	0.107006	+	0.185340i
$990$	−1.26898			−0.0403309
$991$	10.8957			0.346114			0.173057	−	0.984912i	$-0.444635\pi$
$991$	10.8957			0.346114			0.173057	+	0.984912i	$0.444635\pi$
$992$	−0.109880	+	32.0861i	−0.00348870	+	1.01874i
$993$	27.0567			0.858620
$994$	−4.79348			−0.152040
$995$	−1.18766	−	2.05709i	−0.0376514	−	0.0652141i
$996$	24.7720			0.784932
$997$	−9.33568	+	16.1699i	−0.295664	+	0.512105i	−0.975139	−	0.221594i	$-0.928874\pi$
$997$	−9.33568	+	16.1699i	−0.295664	+	0.512105i	0.679475	+	0.733698i	$0.262208\pi$
$998$	3.76744	+	6.52540i	0.119256	+	0.206558i
$999$	−7.89669	−	13.6775i	−0.249840	−	0.432736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.6	✓	34
31.5	even	3	inner	403.2.h.b.222.6	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.6	✓	34	1.1	even	1	trivial
403.2.h.b.222.6	yes	34	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.837386 q^{2} +(0.883556 + 1.53036i) q^{3} -1.29878 q^{4} +(-2.21305 + 3.83311i) q^{5} +(-0.739877 - 1.28150i) q^{6} +(-1.99716 - 3.45918i) q^{7} +2.76236 q^{8} +(-0.0613409 + 0.106246i) q^{9} +O(q^{10})\)	\(q-0.837386 q^{2} +(0.883556 + 1.53036i) q^{3} -1.29878 q^{4} +(-2.21305 + 3.83311i) q^{5} +(-0.739877 - 1.28150i) q^{6} +(-1.99716 - 3.45918i) q^{7} +2.76236 q^{8} +(-0.0613409 + 0.106246i) q^{9} +(1.85318 - 3.20980i) q^{10} +(-1.39540 + 2.41690i) q^{11} +(-1.14755 - 1.98761i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.67239 + 2.89667i) q^{14} -7.82141 q^{15} +0.284411 q^{16} +(-0.576858 - 0.999148i) q^{17} +(0.0513661 - 0.0889686i) q^{18} +(-1.68123 - 2.91198i) q^{19} +(2.87427 - 4.97839i) q^{20} +(3.52920 - 6.11275i) q^{21} +(1.16849 - 2.02388i) q^{22} +0.745639 q^{23} +(2.44070 + 4.22741i) q^{24} +(-7.29518 - 12.6356i) q^{25} +(0.418693 - 0.725198i) q^{26} +5.08454 q^{27} +(2.59388 + 4.49273i) q^{28} -5.02785 q^{29} +6.54954 q^{30} +(0.0190669 - 5.56773i) q^{31} -5.76287 q^{32} -4.93164 q^{33} +(0.483053 + 0.836672i) q^{34} +17.6792 q^{35} +(0.0796687 - 0.137990i) q^{36} +(-1.55308 - 2.69001i) q^{37} +(1.40784 + 2.43845i) q^{38} -1.76711 q^{39} +(-6.11323 + 10.5884i) q^{40} +(-4.81293 + 8.33625i) q^{41} +(-2.95530 + 5.11873i) q^{42} +(4.51314 + 7.81698i) q^{43} +(1.81232 - 3.13903i) q^{44} +(-0.271501 - 0.470254i) q^{45} -0.624387 q^{46} -9.11327 q^{47} +(0.251293 + 0.435252i) q^{48} +(-4.47727 + 7.75486i) q^{49} +(6.10888 + 10.5809i) q^{50} +(1.01937 - 1.76561i) q^{51} +(0.649392 - 1.12478i) q^{52} +(2.71344 - 4.69982i) q^{53} -4.25772 q^{54} +(-6.17617 - 10.6974i) q^{55} +(-5.51686 - 9.55548i) q^{56} +(2.97093 - 5.14580i) q^{57} +4.21025 q^{58} +(0.500931 + 0.867638i) q^{59} +10.1583 q^{60} -11.4247 q^{61} +(-0.0159664 + 4.66234i) q^{62} +0.490030 q^{63} +4.25693 q^{64} +(-2.21305 - 3.83311i) q^{65} +4.12969 q^{66} +(-0.828863 + 1.43563i) q^{67} +(0.749215 + 1.29768i) q^{68} +(0.658813 + 1.14110i) q^{69} -14.8043 q^{70} +(-0.716560 + 1.24112i) q^{71} +(-0.169446 + 0.293488i) q^{72} +(-6.94652 + 12.0317i) q^{73} +(1.30053 + 2.25258i) q^{74} +(12.8914 - 22.3285i) q^{75} +(2.18356 + 3.78204i) q^{76} +11.1473 q^{77} +1.47975 q^{78} +(1.40672 + 2.43651i) q^{79} +(-0.629416 + 1.09018i) q^{80} +(4.67650 + 8.09993i) q^{81} +(4.03028 - 6.98066i) q^{82} +(-5.39673 + 9.34741i) q^{83} +(-4.58367 + 7.93915i) q^{84} +5.10646 q^{85} +(-3.77924 - 6.54583i) q^{86} +(-4.44239 - 7.69444i) q^{87} +(-3.85458 + 6.67634i) q^{88} +2.37455 q^{89} +(0.227351 + 0.393784i) q^{90} +3.99431 q^{91} -0.968424 q^{92} +(8.53750 - 4.89022i) q^{93} +7.63133 q^{94} +14.8826 q^{95} +(-5.09182 - 8.81929i) q^{96} -4.35710 q^{97} +(3.74921 - 6.49381i) q^{98} +(-0.171190 - 0.296510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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