LMFDB - Embedded newform 637.2.bl.b.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.8
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17499 - 0.801092i) q^{2} +(2.33099 + 2.16284i) q^{3} +(0.00816248 + 0.0207977i) q^{4} +(3.42079 - 1.05518i) q^{5} +(-1.00624 - 4.40864i) q^{6} +(1.74821 - 1.98590i) q^{7} +(-0.625820 + 2.74190i) q^{8} +(0.531434 + 7.09150i) q^{9} +O(q^{10})$	\(q+(-1.17499 - 0.801092i) q^{2} +(2.33099 + 2.16284i) q^{3} +(0.00816248 + 0.0207977i) q^{4} +(3.42079 - 1.05518i) q^{5} +(-1.00624 - 4.40864i) q^{6} +(1.74821 - 1.98590i) q^{7} +(-0.625820 + 2.74190i) q^{8} +(0.531434 + 7.09150i) q^{9} +(-4.86468 - 1.50055i) q^{10} +(-0.0775072 + 1.03426i) q^{11} +(-0.0259554 + 0.0661333i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-3.64500 + 0.932926i) q^{14} +(10.2560 + 4.93903i) q^{15} +(2.96460 - 2.75074i) q^{16} +(3.12521 - 0.471049i) q^{17} +(5.05652 - 8.75814i) q^{18} +(0.645038 + 1.11724i) q^{19} +(0.0498674 + 0.0625317i) q^{20} +(8.37022 - 0.848008i) q^{21} +(0.919608 - 1.15315i) q^{22} +(-9.06434 - 1.36623i) q^{23} +(-7.38906 + 5.03778i) q^{24} +(6.45724 - 4.40247i) q^{25} +(1.40621 + 0.211952i) q^{26} +(-8.15122 + 10.2213i) q^{27} +(0.0555717 + 0.0201488i) q^{28} +(-4.03622 - 5.06126i) q^{29} +(-8.09405 - 14.0193i) q^{30} +(-3.17052 + 5.49150i) q^{31} +(-0.124969 + 0.0188360i) q^{32} +(-2.41761 + 2.24321i) q^{33} +(-4.04943 - 1.95010i) q^{34} +(3.88478 - 8.63800i) q^{35} +(-0.143149 + 0.0689368i) q^{36} +(1.47953 - 3.76979i) q^{37} +(0.137100 - 1.82948i) q^{38} +(-3.03857 - 0.937274i) q^{39} +(0.752380 + 10.0398i) q^{40} +(-0.721688 + 3.16192i) q^{41} +(-10.5142 - 5.70892i) q^{42} +(-1.97754 - 8.66417i) q^{43} +(-0.0221429 + 0.00683017i) q^{44} +(9.30070 + 23.6978i) q^{45} +(9.55600 + 8.86668i) q^{46} +(-4.66614 - 3.18132i) q^{47} +12.8599 q^{48} +(-0.887558 - 6.94350i) q^{49} -11.1140 q^{50} +(8.30362 + 5.66131i) q^{51} +(-0.0163779 - 0.0151965i) q^{52} +(4.36722 + 11.1275i) q^{53} +(17.7658 - 5.48002i) q^{54} +(0.826191 + 3.61978i) q^{55} +(4.35106 + 6.03621i) q^{56} +(-0.912834 + 3.99939i) q^{57} +(0.687968 + 9.18029i) q^{58} +(7.74533 + 2.38912i) q^{59} +(-0.0190059 + 0.253616i) q^{60} +(-1.01687 + 2.59095i) q^{61} +(8.12452 - 3.91256i) q^{62} +(15.0120 + 11.3420i) q^{63} +(-7.12544 - 3.43143i) q^{64} +(-2.62421 + 2.43491i) q^{65} +(4.63768 - 0.699018i) q^{66} +(-1.29910 + 2.25011i) q^{67} +(0.0353062 + 0.0611521i) q^{68} +(-18.1739 - 22.7894i) q^{69} +(-11.4844 + 7.03747i) q^{70} +(6.49774 - 8.14791i) q^{71} +(-19.7767 - 2.98086i) q^{72} +(1.92353 - 1.31144i) q^{73} +(-4.75838 + 3.24421i) q^{74} +(24.5736 + 3.70387i) q^{75} +(-0.0179709 + 0.0225347i) q^{76} +(1.91844 + 1.96202i) q^{77} +(2.81943 + 3.53546i) q^{78} +(-7.09422 - 12.2875i) q^{79} +(7.23876 - 12.5379i) q^{80} +(-20.0116 + 3.01626i) q^{81} +(3.38096 - 3.13708i) q^{82} +(3.42017 + 1.64707i) q^{83} +(0.0859584 + 0.167159i) q^{84} +(10.1936 - 4.90900i) q^{85} +(-4.61722 + 11.7645i) q^{86} +(1.53832 - 20.5274i) q^{87} +(-2.78733 - 0.859778i) q^{88} +(1.27957 + 17.0747i) q^{89} +(8.05592 - 35.2953i) q^{90} +(-0.713431 + 2.54775i) q^{91} +(-0.0455732 - 0.199669i) q^{92} +(-19.2677 + 5.94329i) q^{93} +(2.93412 + 7.47602i) q^{94} +(3.38543 + 3.14122i) q^{95} +(-0.332039 - 0.226381i) q^{96} -14.1181 q^{97} +(-4.51952 + 8.86954i) q^{98} -7.37565 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−1.17499	−	0.801092i	−0.830841	−	0.566458i	0.0715199	−	0.997439i	$-0.477215\pi$
$2$	−1.17499	−	0.801092i	−0.830841	−	0.566458i	−0.902361	+	0.430981i	$0.858167\pi$
$3$	2.33099	+	2.16284i	1.34580	+	1.24872i	0.942735	+	0.333544i	$0.108245\pi$
$3$	2.33099	+	2.16284i	1.34580	+	1.24872i	0.403062	+	0.915173i	$0.367946\pi$
$4$	0.00816248	+	0.0207977i	0.00408124	+	0.0103988i
$5$	3.42079	−	1.05518i	1.52983	−	0.471889i	0.588247	−	0.808682i	$-0.299818\pi$
$5$	3.42079	−	1.05518i	1.52983	−	0.471889i	0.941579	+	0.336793i	$0.109342\pi$
$6$	−1.00624	−	4.40864i	−0.410798	−	1.79982i
$7$	1.74821	−	1.98590i	0.660759	−	0.750598i
$7$	1.74821	−	1.98590i	0.660759	−	0.750598i
$8$	−0.625820	+	2.74190i	−0.221261	+	0.969407i
$9$	0.531434	+	7.09150i	0.177145	+	2.36383i
$10$	−4.86468	−	1.50055i	−1.53835	−	0.474517i
$11$	−0.0775072	+	1.03426i	−0.0233693	+	0.311841i	0.973254	+	0.229732i	$0.0737849\pi$
$11$	−0.0775072	+	1.03426i	−0.0233693	+	0.311841i	−0.996623	+	0.0821098i	$0.973834\pi$
$12$	−0.0259554	+	0.0661333i	−0.00749268	+	0.0190910i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	−3.64500	+	0.932926i	−0.974168	+	0.249335i
$15$	10.2560	+	4.93903i	2.64809	+	1.27525i
$16$	2.96460	−	2.75074i	0.741149	−	0.687686i
$17$	3.12521	−	0.471049i	0.757974	−	0.114246i	0.241326	−	0.970444i	$-0.422418\pi$
$17$	3.12521	−	0.471049i	0.757974	−	0.114246i	0.516648	+	0.856198i	$0.327180\pi$
$18$	5.05652	−	8.75814i	1.19183	−	2.06431i
$19$	0.645038	+	1.11724i	0.147982	+	0.256312i	0.930481	−	0.366339i	$-0.119389\pi$
$19$	0.645038	+	1.11724i	0.147982	+	0.256312i	−0.782500	+	0.622651i	$0.786056\pi$
$20$	0.0498674	+	0.0625317i	0.0111507	+	0.0139825i
$21$	8.37022	−	0.848008i	1.82653	−	0.185051i
$22$	0.919608	−	1.15315i	0.196061	−	0.245853i
$23$	−9.06434	−	1.36623i	−1.89005	−	0.284879i	−0.901152	−	0.433503i	$-0.857277\pi$
$23$	−9.06434	−	1.36623i	−1.89005	−	0.284879i	−0.988894	+	0.148624i	$0.952516\pi$
$24$	−7.38906	+	5.03778i	−1.50829	+	1.02833i
$25$	6.45724	−	4.40247i	1.29145	−	0.880495i
$26$	1.40621	+	0.211952i	0.275780	+	0.0415671i
$27$	−8.15122	+	10.2213i	−1.56870	+	1.96709i
$28$	0.0555717	+	0.0201488i	0.0105021	+	0.00380776i
$29$	−4.03622	−	5.06126i	−0.749507	−	0.939852i	0.250091	−	0.968222i	$-0.419540\pi$
$29$	−4.03622	−	5.06126i	−0.749507	−	0.939852i	−0.999597	+	0.0283706i	$0.990968\pi$
$30$	−8.09405	−	14.0193i	−1.47776	−	2.55956i
$31$	−3.17052	+	5.49150i	−0.569442	+	0.986303i	0.427179	+	0.904167i	$0.359507\pi$
$31$	−3.17052	+	5.49150i	−0.569442	+	0.986303i	−0.996621	+	0.0821358i	$0.973826\pi$
$32$	−0.124969	+	0.0188360i	−0.0220915	+	0.00332976i
$33$	−2.41761	+	2.24321i	−0.420852	+	0.390493i
$34$	−4.04943	−	1.95010i	−0.694471	−	0.334440i
$35$	3.88478	−	8.63800i	0.656648	−	1.46009i
$36$	−0.143149	+	0.0689368i	−0.0238581	+	0.0114895i
$37$	1.47953	−	3.76979i	0.243234	−	0.619749i	−0.756167	−	0.654379i	$-0.772930\pi$
$37$	1.47953	−	3.76979i	0.243234	−	0.619749i	0.999400	+	0.0346301i	$0.0110253\pi$
$38$	0.137100	−	1.82948i	0.0222406	−	0.296780i
$39$	−3.03857	−	0.937274i	−0.486560	−	0.150084i
$40$	0.752380	+	10.0398i	0.118962	+	1.58743i
$41$	−0.721688	+	3.16192i	−0.112709	+	0.493809i	0.886791	+	0.462171i	$0.152929\pi$
$41$	−0.721688	+	3.16192i	−0.112709	+	0.493809i	−0.999499	+	0.0316378i	$0.989928\pi$
$42$	−10.5142	−	5.70892i	−1.62238	−	0.880905i
$43$	−1.97754	−	8.66417i	−0.301572	−	1.32127i	−0.867754	−	0.496994i	$-0.834437\pi$
$43$	−1.97754	−	8.66417i	−0.301572	−	1.32127i	0.566182	−	0.824280i	$-0.308420\pi$
$44$	−0.0221429	+	0.00683017i	−0.00333816	+	0.00102969i
$45$	9.30070	+	23.6978i	1.38647	+	3.53266i
$46$	9.55600	+	8.86668i	1.40896	+	1.30732i
$47$	−4.66614	−	3.18132i	−0.680627	−	0.464043i	0.173005	−	0.984921i	$-0.444652\pi$
$47$	−4.66614	−	3.18132i	−0.680627	−	0.464043i	−0.853631	+	0.520878i	$0.825605\pi$
$48$	12.8599			1.85616
$49$	−0.887558	−	6.94350i	−0.126794	−	0.991929i
$50$	−11.1140			−1.57175
$51$	8.30362	+	5.66131i	1.16274	+	0.792742i
$52$	−0.0163779	−	0.0151965i	−0.00227121	−	0.00210737i
$53$	4.36722	+	11.1275i	0.599884	+	1.52848i	0.831415	+	0.555652i	$0.187531\pi$
$53$	4.36722	+	11.1275i	0.599884	+	1.52848i	−0.231531	+	0.972827i	$0.574374\pi$
$54$	17.7658	−	5.48002i	2.41762	−	0.745736i
$55$	0.826191	+	3.61978i	0.111404	+	0.488091i
$56$	4.35106	+	6.03621i	0.581434	+	0.806622i
$57$	−0.912834	+	3.99939i	−0.120908	+	0.529732i
$58$	0.687968	+	9.18029i	0.0903346	+	1.20543i
$59$	7.74533	+	2.38912i	1.00836	+	0.311037i	0.754567	−	0.656223i	$-0.227847\pi$
$59$	7.74533	+	2.38912i	1.00836	+	0.311037i	0.253789	+	0.967260i	$0.418323\pi$
$60$	−0.0190059	+	0.253616i	−0.00245365	+	0.0327417i
$61$	−1.01687	+	2.59095i	−0.130197	+	0.331737i	−0.981075	−	0.193626i	$-0.937975\pi$
$61$	−1.01687	+	2.59095i	−0.130197	+	0.331737i	0.850878	+	0.525363i	$0.176070\pi$
$62$	8.12452	−	3.91256i	1.03181	−	0.496896i
$63$	15.0120	+	11.3420i	1.89134	+	1.42896i
$64$	−7.12544	−	3.43143i	−0.890680	−	0.428929i
$65$	−2.62421	+	2.43491i	−0.325493	+	0.302013i
$66$	4.63768	−	0.699018i	0.570859	−	0.0860432i
$67$	−1.29910	+	2.25011i	−0.158711	+	0.274895i	−0.934404	−	0.356215i	$-0.884067\pi$
$67$	−1.29910	+	2.25011i	−0.158711	+	0.274895i	0.775693	+	0.631110i	$0.217400\pi$
$68$	0.0353062	+	0.0611521i	0.00428150	+	0.00741578i
$69$	−18.1739	−	22.7894i	−2.18788	−	2.74352i
$70$	−11.4844	+	7.03747i	−1.37265	+	0.841138i
$71$	6.49774	−	8.14791i	0.771140	−	0.966979i	−0.228839	−	0.973464i	$-0.573493\pi$
$71$	6.49774	−	8.14791i	0.771140	−	0.966979i	0.999979	+	0.00648522i	$0.00206432\pi$
$72$	−19.7767	−	2.98086i	−2.33071	−	0.351298i
$73$	1.92353	−	1.31144i	0.225132	−	0.153492i	−0.445502	−	0.895281i	$-0.646975\pi$
$73$	1.92353	−	1.31144i	0.225132	−	0.153492i	0.670634	+	0.741789i	$0.266022\pi$
$74$	−4.75838	+	3.24421i	−0.553150	+	0.377131i
$75$	24.5736	+	3.70387i	2.83751	+	0.427687i
$76$	−0.0179709	+	0.0225347i	−0.00206140	+	0.00258491i
$77$	1.91844	+	1.96202i	0.218626	+	0.223593i
$78$	2.81943	+	3.53546i	0.319238	+	0.400312i
$79$	−7.09422	−	12.2875i	−0.798162	−	1.38246i	−0.920812	−	0.390007i	$-0.872473\pi$
$79$	−7.09422	−	12.2875i	−0.798162	−	1.38246i	0.122650	−	0.992450i	$-0.460861\pi$
$80$	7.23876	−	12.5379i	0.809318	−	1.40178i
$81$	−20.0116	+	3.01626i	−2.22351	+	0.335140i
$82$	3.38096	−	3.13708i	0.373365	−	0.346432i
$83$	3.42017	+	1.64707i	0.375413	+	0.180789i	0.612069	−	0.790804i	$-0.290337\pi$
$83$	3.42017	+	1.64707i	0.375413	+	0.180789i	−0.236657	+	0.971593i	$0.576052\pi$
$84$	0.0859584	+	0.167159i	0.00937883	+	0.0182386i
$85$	10.1936	−	4.90900i	1.10566	−	0.532456i
$86$	−4.61722	+	11.7645i	−0.497887	+	1.26860i
$87$	1.53832	−	20.5274i	0.164925	−	2.20077i
$88$	−2.78733	−	0.859778i	−0.297130	−	0.0916526i
$89$	1.27957	+	17.0747i	0.135634	+	1.80992i	0.486704	+	0.873567i	$0.338199\pi$
$89$	1.27957	+	17.0747i	0.135634	+	1.80992i	−0.351070	+	0.936349i	$0.614182\pi$
$90$	8.05592	−	35.2953i	0.849169	−	3.72045i
$91$	−0.713431	+	2.54775i	−0.0747879	+	0.267076i
$92$	−0.0455732	−	0.199669i	−0.00475133	−	0.0208169i
$93$	−19.2677	+	5.94329i	−1.99797	+	0.616291i
$94$	2.93412	+	7.47602i	0.302632	+	0.771093i
$95$	3.38543	+	3.14122i	0.347337	+	0.322282i
$96$	−0.332039	−	0.226381i	−0.0338886	−	0.0231049i
$97$	−14.1181			−1.43348			−0.716738	−	0.697342i	$-0.754366\pi$
$97$	−14.1181			−1.43348			−0.716738	+	0.697342i	$0.754366\pi$
$98$	−4.51952	+	8.86954i	−0.456540	+	0.895959i
$99$	−7.37565			−0.741281
$100$	0.144268	+	0.0983605i	0.0144268	+	0.00983605i
$101$	0.665699	+	0.617679i	0.0662396	+	0.0614613i	0.712598	−	0.701573i	$-0.247518\pi$
$101$	0.665699	+	0.617679i	0.0662396	+	0.0614613i	−0.646358	+	0.763034i	$0.723709\pi$
$102$	−5.22141	−	13.3039i	−0.516996	−	1.31729i
$103$	5.34676	−	1.64926i	0.526832	−	0.162506i	−0.0199185	−	0.999802i	$-0.506341\pi$
$103$	5.34676	−	1.64926i	0.526832	−	0.162506i	0.546751	+	0.837295i	$0.315864\pi$
$104$	−0.625820	−	2.74190i	−0.0613667	−	0.268865i
$105$	27.7380	−	11.7329i	2.70695	−	1.14501i
$106$	3.78273	−	16.5732i	0.367411	−	1.60973i
$107$	0.124843	+	1.66592i	0.0120691	+	0.161050i	0.999982	+	0.00603916i	$0.00192233\pi$
$107$	0.124843	+	1.66592i	0.0120691	+	0.161050i	−0.987913	+	0.155011i	$0.950459\pi$
$108$	−0.279114	−	0.0860951i	−0.0268577	−	0.00828451i
$109$	0.0784247	−	1.04650i	0.00751172	−	0.100237i	−0.992188	−	0.124754i	$-0.960186\pi$
$109$	0.0784247	−	1.04650i	0.00751172	−	0.100237i	0.999699	+	0.0245172i	$0.00780484\pi$
$110$	1.92901	−	4.91504i	0.183924	−	0.468631i
$111$	11.6022	−	5.58733i	1.10123	−	0.530326i
$112$	−0.279966	−	10.6962i	−0.0264543	−	1.01070i
$113$	5.63576	+	2.71404i	0.530168	+	0.255315i	0.679763	−	0.733432i	$-0.262083\pi$
$113$	5.63576	+	2.71404i	0.530168	+	0.255315i	−0.149595	+	0.988747i	$0.547797\pi$
$114$	4.27644	−	3.96796i	0.400526	−	0.371634i
$115$	−32.4489	+	4.89088i	−3.02587	+	0.456077i
$116$	0.0723168	−	0.125256i	0.00671445	−	0.0116298i
$117$	−3.55569	−	6.15864i	−0.328724	−	0.569366i
$118$	−7.18675	−	9.01190i	−0.661594	−	0.829613i
$119$	4.52805	−	7.02982i	0.415085	−	0.644423i
$120$	−19.9607	+	25.0300i	−1.82216	+	2.28491i
$121$	9.81345	+	1.47914i	0.892132	+	0.134467i
$122$	3.27040	−	2.22972i	0.296088	−	0.201870i
$123$	−8.52097	+	5.80950i	−0.768310	+	0.523825i
$124$	−0.140090	−	0.0211151i	−0.0125804	−	0.00189620i
$125$	6.28356	−	7.87933i	0.562018	−	0.704749i
$126$	−8.55293	−	25.3527i	−0.761955	−	2.25860i
$127$	−5.55975	−	6.97171i	−0.493348	−	0.618639i	0.471366	−	0.881938i	$-0.343761\pi$
$127$	−5.55975	−	6.97171i	−0.493348	−	0.618639i	−0.964714	+	0.263298i	$0.915190\pi$
$128$	5.74979	+	9.95892i	0.508214	+	0.880253i
$129$	14.1296	−	24.4732i	1.24404	−	2.15474i
$130$	5.03399	−	0.758752i	0.441510	−	0.0665470i
$131$	−2.70260	+	2.50765i	−0.236127	+	0.219094i	−0.789357	−	0.613935i	$-0.789586\pi$
$131$	−2.70260	+	2.50765i	−0.236127	+	0.219094i	0.553229	+	0.833029i	$0.313395\pi$
$132$	−0.0663873	−	0.0319705i	−0.00577828	−	0.00278267i
$133$	3.34638	+	0.672185i	0.290168	+	0.0582858i
$134$	3.32898	−	1.60315i	0.287580	−	0.138491i
$135$	−17.0984	+	43.5659i	−1.47159	+	3.74956i
$136$	−0.664249	+	8.86378i	−0.0569588	+	0.760063i
$137$	1.71999	+	0.530546i	0.146948	+	0.0453276i	0.367357	−	0.930080i	$-0.380263\pi$
$137$	1.71999	+	0.530546i	0.146948	+	0.0453276i	−0.220408	+	0.975408i	$0.570739\pi$
$138$	3.09772	+	41.3362i	0.263696	+	3.51877i
$139$	−0.103531	+	0.453599i	−0.00878138	+	0.0384738i	−0.979129	−	0.203241i	$-0.934853\pi$
$139$	−0.103531	+	0.453599i	−0.00878138	+	0.0384738i	0.970347	+	0.241714i	$0.0777097\pi$
$140$	0.211360	+	0.0102869i	0.0178632	+	0.000869400i
$141$	−3.99603	−	17.5077i	−0.336526	−	1.47442i
$142$	−14.1620	+	4.36839i	−1.18845	+	0.366588i
$143$	−0.378918	−	0.965466i	−0.0316867	−	0.0807363i
$144$	21.0824	+	19.5616i	1.75687	+	1.63013i
$145$	−19.1476	−	13.0546i	−1.59012	−	1.08413i
$146$	−3.31070			−0.273995
$147$	12.9488	−	18.1049i	1.06800	−	1.49326i
$148$	0.0904794			0.00743736
$149$	−14.4052	−	9.82129i	−1.18012	−	0.804591i	−0.195740	−	0.980656i	$-0.562711\pi$
$149$	−14.4052	−	9.82129i	−1.18012	−	0.804591i	−0.984379	+	0.176065i	$0.943663\pi$
$150$	−25.9065	−	24.0377i	−2.11526	−	1.96267i
$151$	−5.83327	−	14.8629i	−0.474705	−	1.20953i	−0.945015	−	0.327027i	$-0.893953\pi$
$151$	−5.83327	−	14.8629i	−0.474705	−	1.20953i	0.470310	−	0.882501i	$-0.344142\pi$
$152$	−3.46703	+	1.06944i	−0.281213	+	0.0867429i
$153$	5.00128	+	21.9121i	0.404330	+	1.77149i
$154$	−0.682376	−	3.84219i	−0.0549874	−	0.309613i
$155$	−5.05120	+	22.1308i	−0.405722	+	1.77758i
$156$	−0.00530915	−	0.0708456i	−0.000425072	−	0.00567219i
$157$	7.38864	+	2.27909i	0.589678	+	0.181891i	0.575213	−	0.818004i	$-0.304919\pi$
$157$	7.38864	+	2.27909i	0.589678	+	0.181891i	0.0144650	+	0.999895i	$0.495395\pi$
$158$	−1.50785	+	20.1208i	−0.119958	+	1.60073i
$159$	−13.8871	+	35.3837i	−1.10132	+	2.80611i
$160$	−0.407616	+	0.196298i	−0.0322249	+	0.0155187i
$161$	−18.5595	+	15.6124i	−1.46269	+	1.23043i
$162$	25.9296	+	12.4871i	2.03722	+	0.981076i
$163$	−10.3346	+	9.58908i	−0.809466	+	0.751075i	−0.971837	−	0.235655i	$-0.924276\pi$
$163$	−10.3346	+	9.58908i	−0.809466	+	0.751075i	0.162371	+	0.986730i	$0.448086\pi$
$164$	−0.0716513	+	0.0107997i	−0.00559503	+	0.000843315i
$165$	−5.90316	+	10.2246i	−0.459561	+	0.795982i
$166$	−2.69920	−	4.67516i	−0.209499	−	0.362863i
$167$	4.77946	+	5.99325i	0.369846	+	0.463772i	0.931575	−	0.363549i	$-0.118435\pi$
$167$	4.77946	+	5.99325i	0.369846	+	0.463772i	−0.561729	+	0.827321i	$0.689864\pi$
$168$	−2.91310	+	23.4810i	−0.224750	+	1.81160i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−15.9100	−	2.39804i	−1.22024	−	0.183921i
$171$	−7.58010	+	5.16803i	−0.579665	+	0.395209i
$172$	0.164053	−	0.111849i	0.0125089	−	0.00852844i
$173$	1.18236	+	0.178212i	0.0898933	+	0.0135492i	0.193835	−	0.981034i	$-0.437907\pi$
$173$	1.18236	+	0.178212i	0.0898933	+	0.0135492i	−0.103942	+	0.994583i	$0.533145\pi$
$174$	−18.2519	+	22.8871i	−1.38367	+	1.73507i
$175$	2.54573	−	20.5198i	0.192439	−	1.55115i
$176$	2.61521	+	3.27937i	0.197129	+	0.247192i
$177$	12.8870	+	22.3209i	0.968645	+	1.67774i
$178$	12.1749	−	21.0876i	0.912550	−	1.58058i
$179$	−14.0153	+	2.11247i	−1.04755	+	0.157893i	−0.650193	−	0.759769i	$-0.725312\pi$
$179$	−14.0153	+	2.11247i	−1.04755	+	0.157893i	−0.397361	+	0.917662i	$0.630074\pi$
$180$	−0.416942	+	0.386866i	−0.0310770	+	0.0288353i
$181$	−12.7403	−	6.13540i	−0.946979	−	0.456041i	−0.104353	−	0.994540i	$-0.533277\pi$
$181$	−12.7403	−	6.13540i	−0.946979	−	0.456041i	−0.842626	+	0.538500i	$0.818991\pi$
$182$	2.87925	−	2.42204i	0.213424	−	0.179534i
$183$	−7.97413	+	3.84014i	−0.589465	+	0.283871i
$184$	9.41871	−	23.9985i	0.694356	−	1.76919i
$185$	1.08339	−	14.4568i	0.0796524	−	1.06289i
$186$	27.4004	+	8.45190i	2.00909	+	0.619724i
$187$	0.244962	+	3.26879i	0.0179134	+	0.239038i
$188$	0.0280768	−	0.123012i	0.00204771	−	0.00897160i
$189$	6.04844	+	34.0564i	0.439959	+	2.47724i
$190$	−1.46143	−	6.40293i	−0.106023	−	0.464517i
$191$	0.151809	−	0.0468267i	0.0109845	−	0.00338826i	−0.289258	−	0.957251i	$-0.593409\pi$
$191$	0.151809	−	0.0468267i	0.0109845	−	0.00338826i	0.300243	+	0.953863i	$0.402932\pi$
$192$	−9.18768	−	23.4098i	−0.663064	−	1.68946i
$193$	4.43545	+	4.11550i	0.319271	+	0.296240i	0.823484	−	0.567339i	$-0.192027\pi$
$193$	4.43545	+	4.11550i	0.319271	+	0.296240i	−0.504214	+	0.863579i	$0.668218\pi$
$194$	16.5886	+	11.3099i	1.19099	+	0.812004i
$195$	−11.3833			−0.815175
$196$	0.137164	−	0.0751354i	0.00979743	−	0.00536681i
$197$	12.2579			0.873341			0.436671	−	0.899621i	$-0.356157\pi$
$197$	12.2579			0.873341			0.436671	+	0.899621i	$0.356157\pi$
$198$	8.66629	+	5.90858i	0.615886	+	0.419904i
$199$	−14.8725	−	13.7996i	−1.05428	−	0.978231i	−0.0544877	−	0.998514i	$-0.517353\pi$
$199$	−14.8725	−	13.7996i	−1.05428	−	0.978231i	−0.999794	+	0.0202838i	$0.993543\pi$
$200$	8.03005	+	20.4602i	0.567810	+	1.44676i
$201$	−7.89483	+	2.43523i	−0.556858	+	0.171768i
$202$	−0.287370	−	1.25905i	−0.0202193	−	0.0885865i
$203$	−17.1073	−	0.832610i	−1.20069	−	0.0584378i
$204$	−0.0499639	+	0.218906i	−0.00349818	+	0.0153265i
$205$	0.867635	+	11.5778i	0.0605983	+	0.808627i
$206$	−7.60358	−	2.34539i	−0.529767	−	0.163411i
$207$	4.87151	−	65.0058i	0.338594	−	4.51822i
$208$	−1.47751	+	3.76463i	−0.102447	+	0.261030i
$209$	−1.20551	+	0.580544i	−0.0833870	+	0.0401571i
$210$	−41.9909	−	8.43468i	−2.89765	−	0.582048i
$211$	−13.0638	−	6.29120i	−0.899350	−	0.433104i	−0.0736960	−	0.997281i	$-0.523479\pi$
$211$	−13.0638	−	6.29120i	−0.899350	−	0.433104i	−0.825654	+	0.564177i	$0.809194\pi$
$212$	−0.195779	+	0.181656i	−0.0134461	+	0.0124762i
$213$	32.7688	−	4.93910i	2.24528	−	0.338422i
$214$	1.18787	−	2.05744i	0.0812008	−	0.140644i
$215$	−15.9070	−	27.5517i	−1.08485	−	1.87901i
$216$	−22.9246	−	28.7465i	−1.55982	−	1.95595i
$217$	5.36283	+	15.8966i	0.364052	+	1.07913i
$218$	−0.930495	+	1.16680i	−0.0630210	+	0.0790259i
$219$	7.32015	+	1.10333i	0.494650	+	0.0745564i
$220$	−0.0685392	+	0.0467292i	−0.00462091	+	0.00315048i
$221$	−2.61133	+	1.78038i	−0.175657	+	0.119761i
$222$	−18.1084	−	2.72940i	−1.21536	−	0.183186i
$223$	−2.79812	+	3.50874i	−0.187376	+	0.234962i	−0.866643	−	0.498929i	$-0.833727\pi$
$223$	−2.79812	+	3.50874i	−0.187376	+	0.234962i	0.679266	+	0.733892i	$0.262298\pi$
$224$	−0.181064	+	0.281104i	−0.0120979	+	0.0187820i
$225$	34.6517	+	43.4519i	2.31012	+	2.89679i
$226$	−4.44775	−	7.70372i	−0.295860	−	0.512444i
$227$	−0.100128	+	0.173428i	−0.00664576	+	0.0115108i	−0.869329	−	0.494234i	$-0.835449\pi$
$227$	−0.100128	+	0.173428i	−0.00664576	+	0.0115108i	0.862683	+	0.505744i	$0.168782\pi$
$228$	−0.0906289	+	0.0136601i	−0.00600205	+	0.000904663i
$229$	−4.24807	+	3.94163i	−0.280720	+	0.260470i	−0.807948	−	0.589254i	$-0.799422\pi$
$229$	−4.24807	+	3.94163i	−0.280720	+	0.260470i	0.527228	+	0.849724i	$0.323231\pi$
$230$	42.0450	+	20.2478i	2.77237	+	1.33510i
$231$	0.228310	+	8.72272i	0.0150217	+	0.573913i
$232$	16.4034	−	7.89945i	1.07693	−	0.518625i
$233$	10.2865	−	26.2095i	0.673890	−	1.71704i	−0.0228687	−	0.999738i	$-0.507280\pi$
$233$	10.2865	−	26.2095i	0.673890	−	1.71704i	0.696759	−	0.717306i	$-0.254625\pi$
$234$	−0.755748	+	10.0848i	−0.0494048	+	0.659261i
$235$	−19.3188	−	5.95905i	−1.26022	−	0.388725i
$236$	0.0135330	+	0.180586i	0.000880926	+	0.0117551i
$237$	10.0395	−	43.9858i	0.652133	−	2.85718i
$238$	−10.9519	+	4.63256i	−0.709908	+	0.300284i
$239$	−2.57196	−	11.2685i	−0.166366	−	0.728898i	−0.987429	−	0.158061i	$-0.949476\pi$
$239$	−2.57196	−	11.2685i	−0.166366	−	0.728898i	0.821063	−	0.570837i	$-0.193381\pi$
$240$	43.9909	−	13.5694i	2.83960	−	0.875901i
$241$	4.61238	+	11.7521i	0.297109	+	0.757022i	0.998999	+	0.0447365i	$0.0142448\pi$
$241$	4.61238	+	11.7521i	0.297109	+	0.757022i	−0.701889	+	0.712286i	$0.747660\pi$
$242$	−10.3457	−	9.59945i	−0.665050	−	0.617076i
$243$	−20.7648	−	14.1572i	−1.33207	−	0.908187i
$244$	−0.0621859			−0.00398105
$245$	−10.3628	−	22.8158i	−0.662053	−	1.45765i
$246$	14.6660			0.935068
$247$	−1.06591	−	0.726726i	−0.0678223	−	0.0462405i
$248$	−13.0730	−	12.1299i	−0.830133	−	0.770251i
$249$	4.41004	+	11.2366i	0.279475	+	0.712090i
$250$	−13.6952	+	4.22440i	−0.866158	+	0.267174i
$251$	5.87242	+	25.7287i	0.370664	+	1.62398i	0.724919	+	0.688835i	$0.241877\pi$
$251$	5.87242	+	25.7287i	0.370664	+	1.62398i	−0.354255	+	0.935149i	$0.615265\pi$
$252$	−0.113352	+	0.404794i	−0.00714052	+	0.0254996i
$253$	2.11559	−	9.26900i	0.133006	−	0.582737i
$254$	0.947652	+	12.6455i	0.0594610	+	0.793452i
$255$	34.3787	+	10.6044i	2.15287	+	0.664074i
$256$	0.0400661	−	0.534645i	0.00250413	−	0.0334153i
$257$	−9.77877	+	24.9159i	−0.609983	+	1.55421i	0.207486	+	0.978238i	$0.433472\pi$
$257$	−9.77877	+	24.9159i	−0.609983	+	1.55421i	−0.817469	+	0.575973i	$0.804623\pi$
$258$	−36.2074	+	17.4366i	−2.25417	+	1.08555i
$259$	−4.89987	−	9.52855i	−0.304463	−	0.592075i
$260$	−0.0720604	−	0.0347025i	−0.00446900	−	0.00215216i
$261$	33.7469	−	31.3126i	2.08888	−	1.93820i
$262$	5.18437	−	0.781419i	0.320292	−	0.0482762i
$263$	6.22747	−	10.7863i	0.384002	−	0.665112i	−0.607628	−	0.794222i	$-0.707879\pi$
$263$	6.22747	−	10.7863i	0.384002	−	0.665112i	0.991630	+	0.129110i	$0.0412121\pi$
$264$	−4.63767	−	8.03268i	−0.285429	−	0.494378i
$265$	26.6808	+	33.4567i	1.63899	+	2.05523i
$266$	−3.39347	−	3.47057i	−0.208067	−	0.212794i
$267$	−33.9472	+	42.5685i	−2.07754	+	2.60515i
$268$	−0.0574010	−	0.00865181i	−0.00350633	−	0.000528494i
$269$	5.41425	−	3.69137i	0.330113	−	0.225067i	−0.386909	−	0.922118i	$-0.626457\pi$
$269$	5.41425	−	3.69137i	0.330113	−	0.225067i	0.717022	+	0.697051i	$0.245505\pi$
$270$	54.9907	−	37.4920i	3.34663	−	2.28169i
$271$	7.83243	+	1.18055i	0.475786	+	0.0717132i	0.382558	−	0.923932i	$-0.375043\pi$
$271$	7.83243	+	1.18055i	0.475786	+	0.0717132i	0.0932283	+	0.995645i	$0.470281\pi$
$272$	7.96924	−	9.99311i	0.483206	−	0.605922i
$273$	−7.17337	+	4.39573i	−0.434152	+	0.266042i
$274$	−1.59594	−	2.00125i	−0.0964146	−	0.120900i
$275$	4.05282	+	7.01970i	0.244394	+	0.423304i
$276$	0.325622	−	0.563994i	0.0196001	−	0.0339484i
$277$	−7.14843	+	1.07745i	−0.429508	+	0.0647379i	−0.360239	−	0.932860i	$-0.617305\pi$
$277$	−7.14843	+	1.07745i	−0.429508	+	0.0647379i	−0.0692690	+	0.997598i	$0.522067\pi$
$278$	0.485022	−	0.450035i	0.0290897	−	0.0269913i
$279$	−40.6279	−	19.5654i	−2.43233	−	1.17135i
$280$	21.2533	+	16.0575i	1.27013	+	0.959619i
$281$	12.1872	−	5.86905i	0.727027	−	0.350118i	−0.0334870	−	0.999439i	$-0.510661\pi$
$281$	12.1872	−	5.86905i	0.727027	−	0.350118i	0.760514	+	0.649321i	$0.224947\pi$
$282$	−9.33004	+	23.7725i	−0.555596	+	1.41563i
$283$	−0.948474	+	12.6565i	−0.0563809	+	0.752351i	0.895339	+	0.445385i	$0.146933\pi$
$283$	−0.948474	+	12.6565i	−0.0563809	+	0.752351i	−0.951720	+	0.306967i	$0.900686\pi$
$284$	0.222495	+	0.0686307i	0.0132027	+	0.00407248i
$285$	1.09744	+	14.6443i	0.0650065	+	0.867452i
$286$	−0.328204	+	1.43796i	−0.0194071	+	0.0850282i
$287$	5.01758	+	6.96088i	0.296179	+	0.410888i
$288$	−0.199988	−	0.876204i	−0.0117844	−	0.0516308i
$289$	−6.69971	+	2.06659i	−0.394101	+	0.121564i
$290$	12.0402	+	30.6780i	0.707026	+	1.80147i
$291$	−32.9091	−	30.5352i	−1.92917	−	1.79001i
$292$	0.0429756	+	0.0293003i	0.00251496	+	0.00171467i
$293$	19.4723			1.13758			0.568792	−	0.822482i	$-0.307411\pi$
$293$	19.4723			1.13758			0.568792	+	0.822482i	$0.307411\pi$
$294$	−29.7183	+	10.8998i	−1.73321	+	0.635689i
$295$	29.0161			1.68938
$296$	9.41044	+	6.41593i	0.546971	+	0.372918i
$297$	−9.93972	−	9.22271i	−0.576761	−	0.535156i
$298$	9.05814	+	23.0798i	0.524724	+	1.33697i
$299$	8.75948	−	2.70194i	0.506574	−	0.156257i
$300$	0.123550	+	0.541306i	0.00713314	+	0.0312523i
$301$	−20.6633	−	11.2196i	−1.19101	−	0.646685i
$302$	−5.05256	+	22.1367i	−0.290742	+	1.27383i
$303$	0.215796	+	2.87960i	0.0123972	+	0.165429i
$304$	4.98552	+	1.53783i	0.285939	+	0.0882005i
$305$	−0.744607	+	9.93608i	−0.0426361	+	0.568939i
$306$	11.6771	−	29.7529i	0.667538	−	1.70086i
$307$	26.2746	−	12.6532i	1.49957	−	0.722155i	0.509206	−	0.860645i	$-0.329939\pi$
$307$	26.2746	−	12.6532i	1.49957	−	0.722155i	0.990364	+	0.138490i	$0.0442249\pi$
$308$	−0.0251463	+	0.0559140i	−0.00143284	+	0.00318599i
$309$	16.0303	+	7.71980i	0.911933	+	0.439164i
$310$	23.6639	−	21.9569i	1.34402	−	1.24707i
$311$	−22.9067	+	3.45263i	−1.29892	+	0.195780i	−0.761847	−	0.647757i	$-0.775707\pi$
$311$	−22.9067	+	3.45263i	−1.29892	+	0.195780i	−0.537071	+	0.843537i	$0.680469\pi$
$312$	4.47151	−	7.74487i	0.253149	−	0.438467i
$313$	−16.3240	−	28.2740i	−0.922687	−	1.59814i	−0.795239	−	0.606296i	$-0.792655\pi$
$313$	−16.3240	−	28.2740i	−0.922687	−	1.59814i	−0.127448	−	0.991845i	$-0.540679\pi$
$314$	−6.85579	−	8.59689i	−0.386894	−	0.485150i
$315$	63.3209	+	22.9584i	3.56773	+	1.29356i
$316$	0.197646	−	0.247840i	0.0111184	−	0.0139421i
$317$	−4.08238	−	0.615320i	−0.229289	−	0.0345598i	0.0333925	−	0.999442i	$-0.489369\pi$
$317$	−4.08238	−	0.615320i	−0.229289	−	0.0345598i	−0.262682	+	0.964883i	$0.584607\pi$
$318$	44.6627	−	30.4505i	2.50456	−	1.70758i
$319$	5.54750	−	3.78222i	0.310600	−	0.211764i
$320$	−27.9954	−	4.21963i	−1.56499	−	0.235885i
$321$	−3.31211	+	4.15325i	−0.184864	+	0.231812i
$322$	34.3141	−	3.47645i	1.91225	−	0.193735i
$323$	2.54215	+	3.18776i	0.141449	+	0.177372i
$324$	−0.226075	−	0.391574i	−0.0125597	−	0.0217541i
$325$	−3.90761	+	6.76818i	−0.216755	+	0.375431i
$326$	19.8247	−	2.98810i	1.09799	−	0.165495i
$327$	2.44623	−	2.26977i	0.135277	−	0.125519i
$328$	−8.21801	−	3.95758i	−0.453764	−	0.218521i
$329$	−14.4751	+	3.70487i	−0.798041	+	0.204256i
$330$	15.1270	−	7.28476i	0.832712	−	0.401013i
$331$	3.04643	−	7.76219i	0.167447	−	0.426648i	−0.822377	−	0.568943i	$-0.807353\pi$
$331$	3.04643	−	7.76219i	0.167447	−	0.426648i	0.989824	+	0.142294i	$0.0454479\pi$
$332$	−0.00633808	+	0.0845758i	−0.000347847	+	0.00464170i
$333$	27.5197	+	8.48870i	1.50807	+	0.465178i
$334$	−0.814652	−	10.8708i	−0.0445758	−	0.594823i
$335$	−2.06970	+	9.06795i	−0.113080	+	0.495435i
$336$	22.4817	−	25.5383i	1.22648	−	1.39323i
$337$	−1.10009	−	4.81983i	−0.0599259	−	0.262553i	0.936086	−	0.351771i	$-0.114420\pi$
$337$	−1.10009	−	4.81983i	−0.0599259	−	0.262553i	−0.996012	+	0.0892181i	$0.971563\pi$
$338$	−1.35891	+	0.419169i	−0.0739150	+	0.0227998i
$339$	7.26685	+	18.5156i	0.394681	+	1.00563i
$340$	0.185301	+	0.171934i	0.0100494	+	0.00932446i
$341$	−5.43391	−	3.70478i	−0.294263	−	0.200625i
$342$	13.0466			0.705479
$343$	−15.3407	−	10.3761i	−0.828320	−	0.560255i
$344$	24.9938			1.34758
$345$	−86.2161	−	58.7811i	−4.64172	−	3.16467i
$346$	−1.24650	−	1.15658i	−0.0670120	−	0.0621780i
$347$	2.30414	+	5.87086i	0.123693	+	0.315164i	0.979285	−	0.202486i	$-0.0649021\pi$
$347$	2.30414	+	5.87086i	0.123693	+	0.315164i	−0.855592	+	0.517650i	$0.826807\pi$
$348$	0.439479	−	0.135561i	0.0235586	−	0.00726685i
$349$	5.16325	+	22.6217i	0.276383	+	1.21091i	0.902330	+	0.431046i	$0.141855\pi$
$349$	5.16325	+	22.6217i	0.276383	+	1.21091i	−0.625947	+	0.779865i	$0.715287\pi$
$350$	−19.4295	+	22.0712i	−1.03855	+	1.17975i
$351$	2.90914	−	12.7458i	0.155278	−	0.680318i
$352$	−0.00979536	−	0.130710i	−0.000522095	−	0.00696687i
$353$	−15.2487	−	4.70361i	−0.811607	−	0.250348i	−0.138948	−	0.990300i	$-0.544372\pi$
$353$	−15.2487	−	4.70361i	−0.811607	−	0.250348i	−0.672660	+	0.739952i	$0.734848\pi$
$354$	2.73908	−	36.5504i	0.145580	−	1.94263i
$355$	13.6300	−	34.7286i	0.723403	−	1.84320i
$356$	−0.344670	+	0.165984i	−0.0182675	+	0.00879715i
$357$	25.7592	−	6.59298i	1.36332	−	0.348938i
$358$	18.1601	+	8.74544i	0.959791	+	0.462211i
$359$	−13.1372	+	12.1896i	−0.693355	+	0.643340i	−0.945980	−	0.324224i	$-0.894897\pi$
$359$	−13.1372	+	12.1896i	−0.693355	+	0.643340i	0.252625	+	0.967564i	$0.418706\pi$
$360$	−70.7975	+	10.6710i	−3.73135	+	0.562411i
$361$	8.66785	−	15.0132i	0.456203	−	0.790166i
$362$	10.0547	+	17.4152i	0.528461	+	0.915321i
$363$	19.6759	+	24.6728i	1.03272	+	1.29499i
$364$	−0.0588106	+	0.00595825i	−0.00308251	+	0.000312297i
$365$	5.19619	−	6.51582i	0.271981	−	0.341053i
$366$	12.4458	+	1.87590i	0.650552	+	0.0980550i
$367$	−11.0933	+	7.56330i	−0.579067	+	0.394801i	−0.817134	−	0.576448i	$-0.804438\pi$
$367$	−11.0933	+	7.56330i	−0.579067	+	0.394801i	0.238067	+	0.971249i	$0.423486\pi$
$368$	−30.6303	+	20.8834i	−1.59671	+	1.08862i
$369$	−22.8063	−	3.43749i	−1.18725	−	0.178949i
$370$	−12.8542	+	16.1187i	−0.668259	+	0.837970i
$371$	29.7328	+	10.7803i	1.54365	+	0.559685i
$372$	−0.280879	−	0.352211i	−0.0145629	−	0.0182613i
$373$	11.0032	+	19.0581i	0.569725	+	0.986792i	0.996593	+	0.0824785i	$0.0262836\pi$
$373$	11.0032	+	19.0581i	0.569725	+	0.986792i	−0.426868	+	0.904314i	$0.640383\pi$
$374$	2.33077	−	4.03702i	0.120521	−	0.208749i
$375$	31.6886	−	4.77629i	1.63639	−	0.246647i
$376$	11.6430	−	10.8031i	0.600443	−	0.557129i
$377$	5.83250	+	2.80879i	0.300389	+	0.144660i
$378$	20.1755	−	44.8612i	1.03772	−	2.30741i
$379$	11.6583	−	5.61436i	0.598849	−	0.288390i	−0.109798	−	0.993954i	$-0.535020\pi$
$379$	11.6583	−	5.61436i	0.598849	−	0.288390i	0.708647	+	0.705564i	$0.249306\pi$
$380$	−0.0376965	+	0.0960491i	−0.00193379	+	0.00492722i
$381$	2.11898	−	28.2758i	0.108559	−	1.44861i
$382$	−0.215886	−	0.0665919i	−0.0110457	−	0.00340714i
$383$	1.49287	+	19.9210i	0.0762823	+	1.01792i	0.895682	+	0.444695i	$0.146688\pi$
$383$	1.49287	+	19.9210i	0.0762823	+	1.01792i	−0.819400	+	0.573222i	$0.805693\pi$
$384$	−8.13688	+	35.6500i	−0.415233	+	1.81926i
$385$	8.63285	+	4.68739i	0.439971	+	0.238891i
$386$	−1.91470	−	8.38886i	−0.0974557	−	0.426982i
$387$	60.3910	−	18.6282i	3.06985	−	0.946923i
$388$	−0.115239	−	0.293624i	−0.00585036	−	0.0149065i
$389$	−1.13936	−	1.05717i	−0.0577677	−	0.0536005i	0.650761	−	0.759283i	$-0.274450\pi$
$389$	−1.13936	−	1.05717i	−0.0577677	−	0.0536005i	−0.708528	+	0.705682i	$0.750641\pi$
$390$	13.3752	+	9.11908i	0.677281	+	0.461762i
$391$	−28.9715			−1.46515
$392$	19.5938	+	1.91179i	0.989637	+	0.0965600i
$393$	−11.7234			−0.591366
$394$	−14.4029	−	9.81973i	−0.725608	−	0.494711i
$395$	−37.2334	−	34.5475i	−1.87341	−	1.73827i
$396$	−0.0602036	−	0.153396i	−0.00302535	−	0.00770846i
$397$	11.3941	−	3.51461i	0.571852	−	0.176393i	0.00467538	−	0.999989i	$-0.498512\pi$
$397$	11.3941	−	3.51461i	0.571852	−	0.176393i	0.567177	+	0.823596i	$0.308036\pi$
$398$	6.42017	+	28.1286i	0.321814	+	1.40996i
$399$	6.34654	+	8.80454i	0.317724	+	0.440778i
$400$	7.03304	−	30.8138i	0.351652	−	1.54069i
$401$	0.948765	+	12.6604i	0.0473791	+	0.632230i	0.969463	+	0.245239i	$0.0788665\pi$
$401$	0.948765	+	12.6604i	0.0473791	+	0.632230i	−0.922084	+	0.386991i	$0.873514\pi$
$402$	11.2272	+	3.46312i	0.559960	+	0.172725i
$403$	0.473867	−	6.32331i	0.0236050	−	0.314987i
$404$	−0.00741252	+	0.0188868i	−0.000368787	+	0.000939653i
$405$	−65.2728	+	31.4337i	−3.24343	+	1.56195i
$406$	19.4338	+	14.6828i	0.964483	+	0.728695i
$407$	3.78427	+	1.82241i	0.187579	+	0.0903334i
$408$	−20.7193	+	19.2247i	−1.02576	+	0.951765i
$409$	29.7741	−	4.48772i	1.47223	−	0.221903i	0.636601	−	0.771193i	$-0.280340\pi$
$409$	29.7741	−	4.48772i	1.47223	−	0.221903i	0.835632	+	0.549290i	$0.185102\pi$
$410$	8.25541	−	14.2988i	0.407706	−	0.706167i
$411$	2.86178	+	4.95675i	0.141161	+	0.244498i
$412$	0.0779436	+	0.0977382i	0.00384001	+	0.00481522i
$413$	18.2850	−	11.2047i	0.899744	−	0.551349i
$414$	−57.7996	+	72.4784i	−2.84070	+	3.56212i
$415$	13.4377	+	2.02540i	0.659629	+	0.0994230i
$416$	0.104420	−	0.0711924i	0.00511962	−	0.00349050i
$417$	−1.22239	+	0.833413i	−0.0598608	+	0.0408124i
$418$	1.88153	+	0.283595i	0.0920286	+	0.0138711i
$419$	−3.56434	+	4.46954i	−0.174129	+	0.218351i	−0.861236	−	0.508205i	$-0.830309\pi$
$419$	−3.56434	+	4.46954i	−0.174129	+	0.218351i	0.687107	+	0.726557i	$0.258881\pi$
$420$	0.470428	+	0.481116i	0.0229545	+	0.0234761i
$421$	11.2104	+	14.0574i	0.546361	+	0.685115i	0.975971	−	0.217899i	$-0.0699205\pi$
$421$	11.2104	+	14.0574i	0.546361	+	0.685115i	−0.429610	+	0.903014i	$0.641349\pi$
$422$	10.3100	+	17.8574i	0.501882	+	0.869285i
$423$	20.0806	−	34.7806i	0.976352	−	1.69109i
$424$	−33.2435	+	5.01066i	−1.61445	+	0.243339i
$425$	18.1064	−	16.8003i	0.878291	−	0.814935i
$426$	−42.4596	−	20.4474i	−2.05717	−	0.990682i
$427$	3.36765	+	6.54891i	0.162972	+	0.316924i
$428$	−0.0336282	+	0.0161945i	−0.00162548	+	0.000782790i
$429$	1.20490	−	3.07003i	0.0581730	−	0.148222i
$430$	−3.38096	+	45.1158i	−0.163045	+	2.17568i
$431$	−2.85222	−	0.879794i	−0.137387	−	0.0423782i	0.225299	−	0.974290i	$-0.427664\pi$
$431$	−2.85222	−	0.879794i	−0.137387	−	0.0423782i	−0.362686	+	0.931911i	$0.618140\pi$
$432$	3.95112	+	52.7240i	0.190098	+	2.53668i
$433$	8.37489	−	36.6928i	0.402471	−	1.76334i	−0.214865	−	0.976644i	$-0.568931\pi$
$433$	8.37489	−	36.6928i	0.402471	−	1.76334i	0.617337	−	0.786699i	$-0.288212\pi$
$434$	6.43339	−	22.9744i	0.308812	−	1.10281i
$435$	−16.3978	−	71.8433i	−0.786212	−	3.44462i
$436$	0.0224050	−	0.00691103i	0.00107300	−	0.000330978i
$437$	−4.32044	−	11.0083i	−0.206675	−	0.526599i
$438$	−7.71720	−	7.16052i	−0.368742	−	0.342143i
$439$	19.0935	+	13.0178i	0.911285	+	0.621304i	0.925563	−	0.378594i	$-0.123592\pi$
$439$	19.0935	+	13.0178i	0.911285	+	0.621304i	−0.0142775	+	0.999898i	$0.504545\pi$
$440$	−10.4421			−0.497808
$441$	48.7682	−	9.98413i	2.32229	−	0.475435i
$442$	4.49453			0.213783
$443$	21.6556	+	14.7646i	1.02889	+	0.701485i	0.955250	−	0.295799i	$-0.0955860\pi$
$443$	21.6556	+	14.7646i	1.02889	+	0.701485i	0.0736401	+	0.997285i	$0.476538\pi$
$444$	0.210906	+	0.195693i	0.0100092	+	0.00928716i
$445$	22.3940	+	57.0589i	1.06158	+	2.70485i
$446$	6.09858	−	1.88116i	0.288776	−	0.0890756i
$447$	−12.3364	−	54.0494i	−0.583493	−	2.55645i
$448$	−19.2712	+	8.15154i	−0.910479	+	0.385124i
$449$	−7.32557	+	32.0954i	−0.345715	+	1.51468i	0.441083	+	0.897466i	$0.354594\pi$
$449$	−7.32557	+	32.0954i	−0.345715	+	1.51468i	−0.786798	+	0.617210i	$0.788263\pi$
$450$	−5.90634	−	78.8146i	−0.278427	−	3.71536i
$451$	−3.21432	−	0.991485i	−0.151356	−	0.0466872i
$452$	−0.0104439	+	0.139364i	−0.000491239	+	0.00655513i
$453$	18.5489	−	47.2617i	0.871502	−	2.22055i
$454$	0.256581	−	0.123563i	0.0120419	−	0.00579909i
$455$	0.247820	+	9.46811i	0.0116180	+	0.443872i
$456$	−10.3946	−	5.00579i	−0.486773	−	0.234418i
$457$	−24.2745	+	22.5235i	−1.13551	+	1.05360i	−0.137508	+	0.990501i	$0.543909\pi$
$457$	−24.2745	+	22.5235i	−1.13551	+	1.05360i	−0.998007	+	0.0631030i	$0.979900\pi$
$458$	8.14903	−	1.22827i	0.380779	−	0.0573932i
$459$	−20.6595	+	35.7833i	−0.964303	+	1.67022i
$460$	−0.366582	−	0.634939i	−0.0170920	−	0.0296042i
$461$	6.35533	+	7.96934i	0.295997	+	0.371169i	0.907485	−	0.420085i	$-0.138000\pi$
$461$	6.35533	+	7.96934i	0.295997	+	0.371169i	−0.611487	+	0.791254i	$0.709428\pi$
$462$	6.71944	−	10.4320i	0.312617	−	0.485339i
$463$	11.1337	−	13.9612i	0.517428	−	0.648834i	−0.452633	−	0.891697i	$-0.649515\pi$
$463$	11.1337	−	13.9612i	0.517428	−	0.648834i	0.970061	+	0.242863i	$0.0780866\pi$
$464$	−25.8880	−	3.90199i	−1.20182	−	0.181145i
$465$	−59.6396	+	40.6616i	−2.76572	+	1.88564i
$466$	−33.0827	+	22.5554i	−1.53253	+	1.04486i
$467$	17.8974	+	2.69760i	0.828192	+	0.124830i	0.549440	−	0.835533i	$-0.314841\pi$
$467$	17.8974	+	2.69760i	0.828192	+	0.124830i	0.278752	+	0.960363i	$0.410079\pi$
$468$	0.0990621	−	0.124220i	0.00457915	−	0.00574207i
$469$	2.19739	+	6.51354i	0.101466	+	0.300767i
$470$	17.9255	+	22.4779i	0.826843	+	1.03683i
$471$	12.2935	+	21.2930i	0.566455	+	0.981129i
$472$	−11.3979	+	19.7417i	−0.524630	+	0.908687i
$473$	9.11429	−	1.37376i	0.419076	−	0.0631655i
$474$	−47.0329	+	43.6401i	−2.16029	+	2.00446i
$475$	9.08378	+	4.37452i	0.416793	+	0.200717i
$476$	0.183164	+	0.0367920i	0.00839531	+	0.00168636i
$477$	−76.5897	+	36.8837i	−3.50680	+	1.68879i
$478$	−6.00508	+	15.3007i	−0.274666	+	0.699838i
$479$	−1.47265	+	19.6511i	−0.0672869	+	0.897882i	0.856788	+	0.515669i	$0.172457\pi$
$479$	−1.47265	+	19.6511i	−0.0672869	+	0.897882i	−0.924075	+	0.382212i	$0.875162\pi$
$480$	−1.37471	−	0.424042i	−0.0627466	−	0.0193548i
$481$	0.302637	+	4.03840i	0.0137990	+	0.184135i
$482$	3.99507	−	17.5036i	0.181971	−	0.797265i
$483$	−77.0291	−	3.74900i	−3.50495	−	0.170586i
$484$	0.0493395	+	0.216170i	0.00224270	+	0.00982593i
$485$	−48.2951	+	14.8971i	−2.19297	+	0.676441i
$486$	13.0572	+	33.2691i	0.592285	+	1.50912i
$487$	13.4955	+	12.5219i	0.611537	+	0.567424i	0.923945	−	0.382524i	$-0.124945\pi$
$487$	13.4955	+	12.5219i	0.611537	+	0.567424i	−0.312408	+	0.949948i	$0.601136\pi$
$488$	−6.46774	−	4.40963i	−0.292781	−	0.199614i
$489$	−44.8294			−2.02726
$490$	−6.10142	+	35.1097i	−0.275634	+	1.58610i
$491$	−30.3660			−1.37040			−0.685200	−	0.728355i	$-0.740285\pi$
$491$	−30.3660			−1.37040			−0.685200	+	0.728355i	$0.740285\pi$
$492$	−0.190376	−	0.129796i	−0.00858283	−	0.00585168i
$493$	−14.9981	−	13.9162i	−0.675481	−	0.626755i
$494$	0.670257	+	1.70779i	0.0301563	+	0.0768370i
$495$	−25.2306	+	7.78260i	−1.13403	+	0.349802i
$496$	5.70640	+	25.0014i	0.256225	+	1.12260i
$497$	−4.82151	−	27.1481i	−0.216274	−	1.21776i
$498$	3.81981	−	16.7357i	0.171170	−	0.749944i
$499$	0.332957	+	4.44300i	0.0149052	+	0.198896i	0.999685	+	0.0250905i	$0.00798739\pi$
$499$	0.332957	+	4.44300i	0.0149052	+	0.198896i	−0.984780	+	0.173806i	$0.944394\pi$
$500$	0.215161	+	0.0663684i	0.00962230	+	0.00296809i
$501$	−1.82159	+	24.3074i	−0.0813826	+	1.08598i
$502$	13.7111	−	34.9353i	0.611956	−	1.55924i
$503$	−11.9587	+	5.75899i	−0.533210	+	0.256781i	−0.681058	−	0.732230i	$-0.738480\pi$
$503$	−11.9587	+	5.75899i	−0.533210	+	0.256781i	0.147848	+	0.989010i	$0.452766\pi$
$504$	−40.4935	+	34.0634i	−1.80372	+	1.51730i
$505$	2.92898	+	1.41052i	0.130338	+	0.0627674i
$506$	−9.91112	+	9.19617i	−0.440603	+	0.408820i
$507$	3.14432	−	0.473931i	0.139644	−	0.0210480i
$508$	0.0996140	−	0.172536i	0.00441965	−	0.00765507i
$509$	12.0605	+	20.8895i	0.534574	+	0.925909i	0.999184	+	0.0403937i	$0.0128612\pi$
$509$	12.0605	+	20.8895i	0.534574	+	0.925909i	−0.464610	+	0.885515i	$0.653805\pi$
$510$	−31.8993	−	40.0005i	−1.41253	−	1.77125i
$511$	0.758340	−	6.11258i	0.0335470	−	0.270405i
$512$	13.8644	−	17.3854i	0.612724	−	0.768331i
$513$	−16.6775	−	2.51373i	−0.736329	−	0.110984i
$514$	31.4499	−	21.4422i	1.38719	−	0.945773i
$515$	16.5499	−	11.2835i	0.729277	−	0.497212i
$516$	0.624318	+	0.0941008i	0.0274841	+	0.00414256i
$517$	3.65198	−	4.57943i	0.160614	−	0.201403i
$518$	−1.87596	+	15.1212i	−0.0824251	+	0.664386i
$519$	2.37063	+	2.97267i	0.104059	+	0.130486i
$520$	−5.03398	−	8.71911i	−0.220755	−	0.382358i
$521$	17.0905	−	29.6017i	0.748750	−	1.29687i	−0.199672	−	0.979863i	$-0.563988\pi$
$521$	17.0905	−	29.6017i	0.748750	−	1.29687i	0.948422	−	0.317010i	$-0.102679\pi$
$522$	−64.7364	+	9.75744i	−2.83344	+	0.427072i
$523$	−24.8733	+	23.0790i	−1.08763	+	1.00917i	−0.0877169	+	0.996145i	$0.527957\pi$
$523$	−24.8733	+	23.0790i	−1.08763	+	1.00917i	−0.999915	+	0.0130295i	$0.995852\pi$
$524$	−0.0742131	−	0.0357392i	−0.00324202	−	0.00156127i
$525$	50.3152	−	42.3255i	2.19594	−	1.84723i
$526$	−15.9580	+	7.68497i	−0.695802	+	0.335081i
$527$	−7.32176	+	18.6555i	−0.318941	+	0.812648i
$528$	−0.996731	+	13.3005i	−0.0433772	+	0.578828i
$529$	58.3175	+	17.9886i	2.53555	+	0.782112i
$530$	−4.54771	−	60.6849i	−0.197540	−	2.63599i
$531$	−12.8263	+	56.1956i	−0.556613	+	2.43868i
$532$	0.0133349	+	0.0750836i	0.000578141	+	0.00325529i
$533$	−0.721688	−	3.16192i	−0.0312598	−	0.136958i
$534$	73.9888	−	22.8225i	3.20181	−	0.987627i
$535$	2.18490	+	5.56703i	0.0944614	+	0.240684i
$536$	−5.35657	−	4.97017i	−0.231369	−	0.214679i
$537$	−37.2385	−	25.3888i	−1.60696	−	1.09561i
$538$	−9.31881			−0.401762
$539$	7.25019	−	0.379796i	0.312288	−	0.0163590i
$540$	−1.04564			−0.0449970
$541$	7.90935	+	5.39250i	0.340050	+	0.231842i	0.721289	−	0.692635i	$-0.243550\pi$
$541$	7.90935	+	5.39250i	0.340050	+	0.231842i	−0.381239	+	0.924476i	$0.624503\pi$
$542$	−8.25727	−	7.66163i	−0.354680	−	0.329095i
$543$	−16.4276	−	41.8568i	−0.704975	−	1.79625i
$544$	−0.381680	+	0.117733i	−0.0163644	+	0.00504774i
$545$	−0.835971	−	3.66263i	−0.0358091	−	0.156890i
$546$	11.9500	+	0.581606i	0.511413	+	0.0248904i
$547$	5.76850	−	25.2735i	0.246643	−	1.08062i	−0.688191	−	0.725530i	$-0.741595\pi$
$547$	5.76850	−	25.2735i	0.246643	−	1.08062i	0.934834	−	0.355085i	$-0.115548\pi$
$548$	0.00300525	+	0.0401023i	0.000128378	+	0.00171308i
$549$	−18.9141	−	5.83423i	−0.807235	−	0.248999i
$550$	0.861411	−	11.4947i	0.0367307	−	0.490137i
$551$	3.05112	−	7.77413i	0.129982	−	0.331189i
$552$	73.8598	−	35.5690i	3.14368	−	1.51392i
$553$	−36.8039	−	7.39278i	−1.56506	−	0.314373i
$554$	9.26245	+	4.46056i	0.393524	+	0.189511i
$555$	33.7932	−	31.3555i	1.43444	−	1.33097i
$556$	−0.0102789	+	0.00154929i	−0.000435921	+	6.57046e-5i
$557$	10.8275	−	18.7538i	0.458775	−	0.794622i	−0.540121	−	0.841587i	$-0.681622\pi$
$557$	10.8275	−	18.7538i	0.458775	−	0.794622i	0.998897	+	0.0469649i	$0.0149549\pi$
$558$	32.0636	+	55.5357i	1.35736	+	2.35102i
$559$	5.54095	+	6.94813i	0.234357	+	0.293875i
$560$	−12.2441	−	36.2942i	−0.517408	−	1.53371i
$561$	−6.49887	+	8.14932i	−0.274382	+	0.344065i
$562$	−19.0214	−	2.86702i	−0.802371	−	0.120938i
$563$	25.2890	−	17.2418i	1.06581	−	0.726654i	0.102411	−	0.994742i	$-0.467344\pi$
$563$	25.2890	−	17.2418i	1.06581	−	0.726654i	0.963394	+	0.268088i	$0.0863919\pi$
$564$	0.331503	−	0.226015i	0.0139588	−	0.00951694i
$565$	22.1426	+	3.33745i	0.931544	+	0.140408i
$566$	11.2535	−	14.1114i	0.473019	−	0.593147i
$567$	−28.9944	+	45.0139i	−1.21765	+	1.89041i
$568$	18.2743	+	22.9153i	0.766773	+	0.961503i
$569$	17.4717	+	30.2618i	0.732450	+	1.26864i	0.955833	+	0.293910i	$0.0949565\pi$
$569$	17.4717	+	30.2618i	0.732450	+	1.26864i	−0.223383	+	0.974731i	$0.571710\pi$
$570$	10.4419	−	18.0860i	0.437365	−	0.757538i
$571$	−15.9935	+	2.41063i	−0.669306	+	0.100882i	−0.474901	−	0.880039i	$-0.657516\pi$
$571$	−15.9935	+	2.41063i	−0.669306	+	0.100882i	−0.194406	+	0.980921i	$0.562278\pi$
$572$	0.0169865	−	0.0157612i	0.000710243	−	0.000659009i
$573$	0.455143	+	0.219185i	0.0190139	+	0.00915659i
$574$	−0.319286	−	12.1985i	−0.0133267	−	0.509155i
$575$	−64.5454	+	31.0834i	−2.69173	+	1.29627i
$576$	20.5473	−	52.3537i	0.856137	−	2.18140i
$577$	0.401469	−	5.35723i	0.0167134	−	0.223024i	−0.982593	−	0.185774i	$-0.940521\pi$
$577$	0.401469	−	5.35723i	0.0167134	−	0.223024i	0.999306	−	0.0372508i	$-0.0118600\pi$
$578$	9.52760	+	2.93888i	0.396296	+	0.122241i
$579$	1.43782	+	19.1863i	0.0597537	+	0.797357i
$580$	0.115213	−	0.504783i	0.00478398	−	0.0209600i
$581$	9.25007	−	3.91269i	0.383758	−	0.162326i
$582$	14.2063	+	62.2417i	0.588869	+	2.58000i
$583$	−11.8472	+	3.65439i	−0.490662	+	0.151349i
$584$	2.39205	+	6.09483i	0.0989835	+	0.252206i
$585$	−18.6617	−	17.3156i	−0.771568	−	0.715910i
$586$	−22.8797	−	15.5991i	−0.945151	−	0.644393i
$587$	29.6293			1.22293			0.611465	−	0.791271i	$-0.290580\pi$
$587$	29.6293			1.22293			0.611465	+	0.791271i	$0.290580\pi$
$588$	0.482234	+	0.121524i	0.0198870	+	0.00501158i
$589$	−8.18043			−0.337069
$590$	−34.0935	−	23.2446i	−1.40361	−	0.956964i
$591$	28.5731	+	26.5120i	1.17534	+	1.09056i
$592$	−5.98350	−	15.2457i	−0.245920	−	0.626595i
$593$	16.2621	−	5.01619i	0.667804	−	0.205990i	0.0577272	−	0.998332i	$-0.481615\pi$
$593$	16.2621	−	5.01619i	0.667804	−	0.205990i	0.610077	+	0.792342i	$0.291138\pi$
$594$	4.29079	+	18.7992i	0.176053	+	0.771340i
$595$	8.07182	−	28.8255i	0.330912	−	1.18173i
$596$	0.0866778	−	0.379760i	0.00355046	−	0.0155556i
$597$	−4.82114	−	64.3336i	−0.197316	−	2.63300i
$598$	−12.4568	−	3.84240i	−0.509395	−	0.157128i
$599$	−2.69175	+	35.9190i	−0.109982	+	1.46761i	0.620247	+	0.784406i	$0.287032\pi$
$599$	−2.69175	+	35.9190i	−0.109982	+	1.46761i	−0.730229	+	0.683202i	$0.760587\pi$
$600$	−25.5343	+	65.0603i	−1.04243	+	2.65608i
$601$	2.20295	−	1.06089i	0.0898602	−	0.0432744i	−0.388414	−	0.921485i	$-0.626977\pi$
$601$	2.20295	−	1.06089i	0.0898602	−	0.0432744i	0.478274	+	0.878211i	$0.341263\pi$
$602$	15.2912	+	29.7360i	0.623222	+	1.21195i
$603$	−16.6471	−	8.01680i	−0.677921	−	0.326469i
$604$	0.261500	−	0.242637i	0.0106403	−	0.00987275i
$605$	35.1305	−	5.29508i	1.42826	−	0.215276i
$606$	2.05327	−	3.55637i	0.0834084	−	0.144468i
$607$	−5.63576	−	9.76142i	−0.228748	−	0.396204i	0.728689	−	0.684845i	$-0.240130\pi$
$607$	−5.63576	−	9.76142i	−0.228748	−	0.396204i	−0.957437	+	0.288641i	$0.906797\pi$
$608$	−0.101654	−	0.127470i	−0.00412261	−	0.00516958i
$609$	−38.0760	−	38.9411i	−1.54292	−	1.57797i
$610$	8.83462	−	11.0783i	0.357703	−	0.448546i
$611$	5.58437	+	0.841709i	0.225920	+	0.0340519i
$612$	−0.414897	+	0.282872i	−0.0167712	+	0.0114344i
$613$	10.2408	−	6.98203i	0.413620	−	0.282002i	−0.338578	−	0.940938i	$-0.609946\pi$
$613$	10.2408	−	6.98203i	0.413620	−	0.282002i	0.752198	+	0.658937i	$0.228994\pi$
$614$	−41.0086	−	6.18106i	−1.65497	−	0.249447i
$615$	−23.0185	+	28.8642i	−0.928194	+	1.16392i
$616$	−6.58025	+	4.03228i	−0.265126	+	0.162465i
$617$	16.3663	+	20.5227i	0.658884	+	0.826215i	0.993221	−	0.116239i	$-0.0370838\pi$
$617$	16.3663	+	20.5227i	0.658884	+	0.826215i	−0.334337	+	0.942454i	$0.608512\pi$
$618$	−12.6511	−	21.9124i	−0.508904	−	0.881447i
$619$	−8.32495	+	14.4192i	−0.334608	+	0.579558i	−0.983409	−	0.181400i	$-0.941937\pi$
$619$	−8.32495	+	14.4192i	−0.334608	+	0.579558i	0.648801	+	0.760958i	$0.275271\pi$
$620$	−0.501498	+	0.0755887i	−0.0201407	+	0.00303572i
$621$	87.8501	−	81.5130i	3.52530	−	3.27100i
$622$	29.6809	+	14.2936i	1.19010	+	0.573120i
$623$	36.1455	+	27.3090i	1.44814	+	1.09411i
$624$	−11.5863	+	5.57968i	−0.463825	+	0.223366i
$625$	−1.09543	+	2.79112i	−0.0438173	+	0.111645i
$626$	−3.46960	+	46.2986i	−0.138673	+	1.85046i
$627$	−4.06566	−	1.25409i	−0.162367	−	0.0500835i
$628$	0.0129098	+	0.172270i	0.000515158	+	0.00687430i
$629$	2.84809	−	12.4783i	0.113561	−	0.497542i
$630$	−56.0094	−	77.7017i	−2.23147	−	3.09571i
$631$	−1.42730	−	6.25340i	−0.0568198	−	0.248944i	0.938540	−	0.345172i	$-0.112179\pi$
$631$	−1.42730	−	6.25340i	−0.0568198	−	0.248944i	−0.995359	+	0.0962280i	$0.969322\pi$
$632$	38.1309	−	11.7618i	1.51676	−	0.467860i
$633$	−16.8447	−	42.9197i	−0.669518	−	1.70590i
$634$	4.30381	+	3.99335i	0.170926	+	0.158596i
$635$	−26.3751	−	17.9823i	−1.04667	−	0.713605i
$636$	−0.849251			−0.0336750
$637$	3.81234	+	5.87078i	0.151050	+	0.232609i
$638$	−9.54814			−0.378015
$639$	61.2340	+	41.7486i	2.42238	+	1.65155i
$640$	30.1772	+	28.0004i	1.19286	+	1.10681i
$641$	−14.8570	−	37.8549i	−0.586815	−	1.49518i	−0.848056	−	0.529906i	$-0.822227\pi$
$641$	−14.8570	−	37.8549i	−0.586815	−	1.49518i	0.261241	−	0.965274i	$-0.415868\pi$
$642$	7.21882	−	2.22671i	0.284904	−	0.0878813i
$643$	0.750285	+	3.28721i	0.0295884	+	0.129635i	0.987565	−	0.157211i	$-0.0502503\pi$
$643$	0.750285	+	3.28721i	0.0295884	+	0.129635i	−0.957977	+	0.286846i	$0.907393\pi$
$644$	−0.476193	−	0.258559i	−0.0187646	−	0.0101886i
$645$	22.5110	−	98.6269i	0.886368	−	3.88343i
$646$	−0.433306	−	5.78207i	−0.0170482	−	0.227493i
$647$	−25.5755	−	7.88899i	−1.00548	−	0.310148i	−0.252073	−	0.967708i	$-0.581112\pi$
$647$	−25.5755	−	7.88899i	−1.00548	−	0.310148i	−0.753402	+	0.657560i	$0.771589\pi$
$648$	4.25337	−	56.7573i	0.167088	−	2.22964i
$649$	−3.07129	+	7.82552i	−0.120559	+	0.307178i
$650$	10.0133	−	4.82217i	0.392755	−	0.189141i
$651$	−21.8811	+	48.6537i	−0.857588	+	1.90689i
$652$	−0.283786	−	0.136664i	−0.0111139	−	0.00535219i
$653$	20.0807	−	18.6321i	0.785818	−	0.729132i	−0.181309	−	0.983426i	$-0.558034\pi$
$653$	20.0807	−	18.6321i	0.785818	−	0.729132i	0.967127	+	0.254294i	$0.0818431\pi$
$654$	−4.69258	+	0.707293i	−0.183494	+	0.0276573i
$655$	−6.59903	+	11.4299i	−0.257845	+	0.446601i
$656$	6.55812	+	11.3590i	0.256052	+	0.443494i
$657$	10.3223	+	12.9437i	0.402711	+	0.504983i
$658$	19.9760	+	7.24276i	0.778747	+	0.282352i
$659$	15.4804	−	19.4118i	0.603029	−	0.756174i	−0.382818	−	0.923824i	$-0.625046\pi$
$659$	15.4804	−	19.4118i	0.603029	−	0.756174i	0.985847	+	0.167649i	$0.0536177\pi$
$660$	−0.260832	−	0.0393141i	−0.0101529	−	0.00153030i
$661$	−1.21777	+	0.830262i	−0.0473658	+	0.0322935i	−0.586772	−	0.809753i	$-0.699601\pi$
$661$	−1.21777	+	0.830262i	−0.0473658	+	0.0322935i	0.539406	+	0.842046i	$0.318649\pi$
$662$	−9.79775	+	6.67999i	−0.380800	+	0.259625i
$663$	−9.93766	−	1.49786i	−0.385947	−	0.0581721i
$664$	−6.65650	+	8.34699i	−0.258322	+	0.323926i
$665$	12.1565	−	1.23161i	0.471411	−	0.0477598i
$666$	−25.5350	−	32.0199i	−0.989463	−	1.24075i
$667$	29.6708	+	51.3914i	1.14886	+	1.98988i
$668$	−0.0856335	+	0.148321i	−0.00331326	+	0.00573873i
$669$	−14.1112	+	2.12693i	−0.545572	+	0.0822317i
$670$	9.69614	−	8.99670i	0.374595	−	0.347573i
$671$	−2.60090	−	1.25253i	−0.100407	−	0.0483534i
$672$	−1.03004	+	0.263636i	−0.0397347	+	0.0101700i
$673$	−1.25692	+	0.605303i	−0.0484509	+	0.0233327i	−0.457952	−	0.888977i	$-0.651417\pi$
$673$	−1.25692	+	0.605303i	−0.0484509	+	0.0233327i	0.409501	+	0.912309i	$0.365703\pi$
$674$	−2.56853	+	6.54451i	−0.0989361	+	0.252085i
$675$	−7.63537	+	101.887i	−0.293886	+	3.92163i
$676$	0.0213495	+	0.00658545i	0.000821135	+	0.000253286i
$677$	−0.546838	−	7.29704i	−0.0210167	−	0.280448i	−0.997804	−	0.0662365i	$-0.978901\pi$
$677$	−0.546838	−	7.29704i	−0.0210167	−	0.280448i	0.976787	−	0.214212i	$-0.0687182\pi$
$678$	6.29428	−	27.5770i	0.241730	−	1.05909i
$679$	−24.6813	+	28.0371i	−0.947183	+	1.07596i
$680$	7.08058	+	31.0221i	0.271528	+	1.18964i
$681$	−0.608494	+	0.187696i	−0.0233175	+	0.00719251i
$682$	3.41690	+	8.70613i	0.130840	+	0.333375i
$683$	−7.70951	−	7.15338i	−0.294996	−	0.273717i	0.518764	−	0.854918i	$-0.326392\pi$
$683$	−7.70951	−	7.15338i	−0.294996	−	0.273717i	−0.813760	+	0.581201i	$0.802583\pi$
$684$	−0.169355	−	0.115465i	−0.00647547	−	0.00441490i
$685$	6.44354			0.246195
$686$	9.71293	+	24.4811i	0.370841	+	0.934691i
$687$	−18.4273			−0.703046
$688$	−29.6955	−	20.2461i	−1.13213	−	0.771874i
$689$	−8.76277	−	8.13066i	−0.333835	−	0.309754i
$690$	54.2136	+	138.134i	2.06388	+	5.25867i
$691$	−24.9203	+	7.68689i	−0.948012	+	0.292423i	−0.729941	−	0.683510i	$-0.760453\pi$
$691$	−24.9203	+	7.68689i	−0.948012	+	0.292423i	−0.218071	+	0.975933i	$0.569976\pi$
$692$	0.00594461	+	0.0260450i	0.000225980	+	0.000990084i
$693$	−12.8941	+	14.6473i	−0.489808	+	0.556404i
$694$	1.99576	−	8.74401i	0.0757582	−	0.331918i
$695$	0.124468	+	1.66091i	0.00472135	+	0.0630020i
$696$	55.3213	+	17.0644i	2.09695	+	0.646824i
$697$	−0.766003	+	10.2216i	−0.0290144	+	0.387171i
$698$	12.0553	−	30.7164i	0.456300	−	1.16263i
$699$	80.6647	−	38.8461i	3.05102	−	1.46929i
$700$	0.447544	−	0.114547i	0.0169156	−	0.00432949i
$701$	−15.9753	−	7.69332i	−0.603381	−	0.290573i	0.107146	−	0.994243i	$-0.465829\pi$
$701$	−15.9753	−	7.69332i	−0.603381	−	0.290573i	−0.710526	+	0.703671i	$0.751543\pi$
$702$	−13.6287	+	12.6456i	−0.514383	+	0.477278i
$703$	5.16611	−	0.778665i	0.194843	−	0.0293679i
$704$	4.10127	−	7.10361i	0.154572	−	0.267727i
$705$	−32.1433	−	55.6739i	−1.21059	−	2.09680i
$706$	14.1490	+	17.7423i	0.532505	+	0.667740i
$707$	2.39042	−	0.242180i	0.0899011	−	0.00910811i
$708$	−0.359033	+	0.450213i	−0.0134933	+	0.0169201i
$709$	10.2378	+	1.54310i	0.384489	+	0.0579524i	0.338443	−	0.940987i	$-0.390100\pi$
$709$	10.2378	+	1.54310i	0.384489	+	0.0579524i	0.0460461	+	0.998939i	$0.485338\pi$
$710$	−43.8358	+	29.8868i	−1.64513	+	1.12163i
$711$	83.3670	−	56.8386i	3.12651	−	2.13162i
$712$	−47.6179	−	7.17724i	−1.78456	−	0.268978i
$713$	36.2413	−	45.4452i	1.35725	−	1.70194i
$714$	−35.5483	−	12.8888i	−1.33036	−	0.482352i
$715$	−2.31493	−	2.90284i	−0.0865736	−	0.108560i
$716$	−0.158334	−	0.274243i	−0.00591723	−	0.0102489i
$717$	18.3767	−	31.8295i	0.686292	−	1.18869i
$718$	25.2010	−	3.79844i	0.940493	−	0.141757i
$719$	−21.6136	+	20.0545i	−0.806053	+	0.747907i	−0.971176	−	0.238366i	$-0.923388\pi$
$719$	−21.6136	+	20.0545i	−0.806053	+	0.747907i	0.165123	+	0.986273i	$0.447198\pi$
$720$	92.7594	+	44.6706i	3.45694	+	1.66477i
$721$	6.07199	−	13.5014i	0.226133	−	0.502817i
$722$	−22.2115	+	10.6965i	−0.826628	+	0.398083i
$723$	−14.6666	+	37.3700i	−0.545458	+	1.38980i
$724$	0.0236096	−	0.315049i	0.000877445	−	0.0117087i
$725$	−48.3449	−	14.9124i	−1.79548	−	0.553833i
$726$	−3.35373	−	44.7524i	−0.124469	−	1.66092i
$727$	4.82527	−	21.1409i	0.178959	−	0.784072i	−0.803153	−	0.595773i	$-0.796846\pi$
$727$	4.82527	−	21.1409i	0.178959	−	0.784072i	0.982112	−	0.188299i	$-0.0602972\pi$
$728$	−6.53918	−	3.55058i	−0.242358	−	0.131593i
$729$	−4.27288	−	18.7207i	−0.158255	−	0.693360i
$730$	−11.3252	+	3.49337i	−0.419165	+	0.129295i
$731$	−10.2615	−	26.1458i	−0.379534	−	0.967038i
$732$	−0.144955	−	0.134498i	−0.00535768	−	0.00497120i
$733$	38.1499	+	26.0101i	1.40910	+	0.960706i	0.998811	+	0.0487498i	$0.0155237\pi$
$733$	38.1499	+	26.0101i	1.40910	+	0.960706i	0.410287	+	0.911957i	$0.365429\pi$
$734$	19.0934			0.704750
$735$	25.1914	−	75.5963i	0.929198	−	2.78841i
$736$	1.15849			0.0427026
$737$	−2.22651	−	1.51801i	−0.0820147	−	0.0559167i
$738$	24.0433	+	22.3089i	0.885047	+	0.821204i
$739$	−2.72698	−	6.94824i	−0.100314	−	0.255595i	0.871903	−	0.489679i	$-0.162886\pi$
$739$	−2.72698	−	6.94824i	−0.100314	−	0.255595i	−0.972216	+	0.234084i	$0.924791\pi$
$740$	0.309511	−	0.0954716i	0.0113779	−	0.00350961i
$741$	−0.912834	−	3.99939i	−0.0335338	−	0.146921i
$742$	−26.2997	−	36.4855i	−0.965491	−	1.33942i
$743$	−0.476792	+	2.08896i	−0.0174918	+	0.0766366i	−0.982920	−	0.184031i	$-0.941085\pi$
$743$	−0.476792	+	2.08896i	−0.0174918	+	0.0766366i	0.965429	+	0.260667i	$0.0839426\pi$
$744$	−4.23779	−	56.5494i	−0.155365	−	2.07320i
$745$	−59.6403	−	18.3966i	−2.18505	−	0.674000i
$746$	2.33869	−	31.2076i	0.0856255	−	1.14259i
$747$	−9.86259	+	25.1295i	−0.360853	+	0.919439i
$748$	−0.0659837	+	0.0317761i	−0.00241260	+	0.00116185i
$749$	3.52659	+	2.66444i	0.128859	+	0.0973566i
$750$	−41.0600	−	19.7734i	−1.49930	−	0.722024i
$751$	−29.0237	+	26.9300i	−1.05909	+	0.982691i	−0.999879	−	0.0155546i	$-0.995049\pi$
$751$	−29.0237	+	26.9300i	−1.05909	+	0.982691i	−0.0592100	+	0.998246i	$0.518858\pi$
$752$	−22.5842	+	3.40403i	−0.823562	+	0.124132i
$753$	−41.9586	+	72.6745i	−1.52906	+	2.64840i
$754$	−4.60302	−	7.97266i	−0.167632	−	0.290347i
$755$	−35.6374	−	44.6879i	−1.29698	−	1.62636i
$756$	−0.658924	+	0.403778i	−0.0239648	+	0.0146853i
$757$	14.0828	−	17.6593i	0.511848	−	0.641837i	−0.457008	−	0.889463i	$-0.651079\pi$
$757$	14.0828	−	17.6593i	0.511848	−	0.641837i	0.968856	+	0.247626i	$0.0796504\pi$
$758$	−18.1960	−	2.74261i	−0.660909	−	0.0996160i
$759$	24.9788	−	17.0303i	0.906673	−	0.618159i
$760$	−10.7316	+	7.31665i	−0.389274	+	0.265403i
$761$	14.5923	+	2.19943i	0.528969	+	0.0797293i	0.408097	−	0.912939i	$-0.366193\pi$
$761$	14.5923	+	2.19943i	0.528969	+	0.0797293i	0.120873	+	0.992668i	$0.461431\pi$
$762$	−25.1413	+	31.5262i	−0.910774	+	1.14207i
$763$	−1.94115	−	1.98525i	−0.0702742	−	0.0718708i
$764$	0.00221302	+	0.00277504i	8.00643e−5	+	0.000100398i
$765$	40.2294	+	69.6794i	1.45450	+	2.51926i
$766$	14.2045	−	24.6029i	0.513229	−	0.888938i
$767$	−8.01490	+	1.20805i	−0.289401	+	0.0436202i
$768$	1.24974	−	1.15959i	0.0450963	−	0.0418432i
$769$	38.8912	+	18.7290i	1.40245	+	0.675385i	0.973657	−	0.228017i	$-0.0732242\pi$
$769$	38.8912	+	18.7290i	1.40245	+	0.675385i	0.428794	+	0.903402i	$0.358938\pi$
$770$	−6.38845	−	12.4233i	−0.230224	−	0.447705i
$771$	−76.6833	+	36.9287i	−2.76168	+	1.32996i
$772$	−0.0493884	+	0.125840i	−0.00177753	+	0.00452907i
$773$	1.84468	−	24.6156i	0.0663487	−	0.885361i	−0.860386	−	0.509644i	$-0.829777\pi$
$773$	1.84468	−	24.6156i	0.0663487	−	0.885361i	0.926734	−	0.375718i	$-0.122604\pi$
$774$	−85.8815	−	26.4909i	−3.08695	−	0.952197i
$775$	3.70337	+	49.4181i	0.133029	+	1.77515i
$776$	8.83539	−	38.7104i	0.317172	−	1.38962i
$777$	9.18720	−	32.8086i	0.329589	−	1.17700i
$778$	0.491839	+	2.15489i	0.0176333	+	0.0772565i
$779$	−3.99814	+	1.23326i	−0.143248	+	0.0441862i
$780$	−0.0929161	−	0.236746i	−0.00332693	−	0.00847688i
$781$	7.92345	+	7.35188i	0.283523	+	0.263071i
$782$	34.0411	+	23.2088i	1.21731	+	0.829947i
$783$	84.6327			3.02453
$784$	−21.7311	−	18.1432i	−0.776109	−	0.647973i
$785$	27.6799			0.987936
$786$	13.7748	+	9.39150i	0.491331	+	0.334984i
$787$	−23.7149	−	22.0042i	−0.845344	−	0.784364i	0.133051	−	0.991109i	$-0.457523\pi$
$787$	−23.7149	−	22.0042i	−0.845344	−	0.784364i	−0.978395	+	0.206745i	$0.933713\pi$
$788$	0.100055	+	0.254936i	0.00356432	+	0.00908174i
$789$	37.8452	−	11.6737i	1.34732	−	0.415595i
$790$	16.0730	+	70.4202i	0.571850	+	2.50544i
$791$	15.2423	−	6.44733i	0.541952	−	0.229241i
$792$	4.61583	−	20.2233i	0.164016	−	0.718603i
$793$	−0.208000	−	2.77557i	−0.00738630	−	0.0985634i
$794$	−16.2034	−	4.99809i	−0.575037	−	0.177376i
$795$	−10.1688	+	135.693i	−0.360651	+	4.81255i
$796$	0.165604	−	0.421952i	0.00586968	−	0.0149557i
$797$	25.6654	−	12.3598i	0.909116	−	0.437807i	0.0799430	−	0.996799i	$-0.474526\pi$
$797$	25.6654	−	12.3598i	0.909116	−	0.437807i	0.829173	+	0.558992i	$0.188812\pi$
$798$	−0.403852	−	15.4294i	−0.0142962	−	0.546194i
$799$	−16.0812	−	7.74430i	−0.568912	−	0.273974i
$800$	−0.724027	+	0.671799i	−0.0255982	+	0.0237517i
$801$	−120.405	+	18.1482i	−4.25431	+	0.641234i
$802$	9.02736	−	15.6358i	0.318767	−	0.552121i
$803$	1.20728	+	2.09107i	0.0426041	+	0.0737924i
$804$	−0.115089	−	0.144317i	−0.00405886	−	0.00508965i
$805$	−47.0145	+	72.9903i	−1.65704	+	2.57257i
$806$	−5.62234	+	7.05019i	−0.198039	+	0.248332i
$807$	20.6044	+	3.10562i	0.725310	+	0.109323i
$808$	−2.11022	+	1.43872i	−0.0742372	+	0.0506141i
$809$	−9.47825	+	6.46216i	−0.333238	+	0.227198i	−0.718366	−	0.695666i	$-0.755110\pi$
$809$	−9.47825	+	6.46216i	−0.333238	+	0.227198i	0.385128	+	0.922863i	$0.374157\pi$
$810$	101.876	+	15.3553i	3.57956	+	0.539531i
$811$	5.82057	−	7.29876i	0.204388	−	0.256294i	−0.669064	−	0.743205i	$-0.733305\pi$
$811$	5.82057	−	7.29876i	0.204388	−	0.256294i	0.873452	+	0.486911i	$0.161876\pi$
$812$	−0.122321	−	0.362587i	−0.00429264	−	0.0127243i
$813$	15.7040	+	19.6921i	0.550762	+	0.690633i
$814$	−2.98655	−	5.17285i	−0.104678	−	0.181308i
$815$	−25.2343	+	43.7071i	−0.883918	+	1.53099i
$816$	40.1897	−	6.05763i	1.40692	−	0.212059i
$817$	8.40437	−	7.79811i	0.294032	−	0.272821i
$818$	−38.5792	−	18.5788i	−1.34889	−	0.649591i
$819$	−18.4465	−	3.70533i	−0.644572	−	0.129475i
$820$	−0.233709	+	0.112548i	−0.00816147	+	0.00393036i
$821$	8.12245	−	20.6957i	0.283476	−	0.722284i	−0.716226	−	0.697868i	$-0.754132\pi$
$821$	8.12245	−	20.6957i	0.283476	−	0.722284i	0.999702	−	0.0244160i	$-0.00777261\pi$
$822$	0.608260	−	8.11667i	0.0212155	−	0.283101i
$823$	−5.57517	−	1.71971i	−0.194338	−	0.0599454i	0.196058	−	0.980592i	$-0.437186\pi$
$823$	−5.57517	−	1.71971i	−0.194338	−	0.0599454i	−0.390396	+	0.920647i	$0.627662\pi$
$824$	1.17598	+	15.6924i	0.0409673	+	0.546671i
$825$	−5.73540	+	25.1284i	−0.199681	+	0.874860i
$826$	−30.4606	−	1.48252i	−1.05986	−	0.0515834i
$827$	3.21298	+	14.0770i	0.111726	+	0.489505i	0.999569	+	0.0293578i	$0.00934623\pi$
$827$	3.21298	+	14.0770i	0.111726	+	0.489505i	−0.887843	+	0.460147i	$0.847797\pi$
$828$	1.39173	−	0.429293i	0.0483661	−	0.0149190i
$829$	7.97612	+	20.3228i	0.277022	+	0.705841i	0.999890	+	0.0148543i	$0.00472844\pi$
$829$	7.97612	+	20.3228i	0.277022	+	0.705841i	−0.722868	+	0.690987i	$0.757176\pi$
$830$	−14.1665	−	13.1446i	−0.491727	−	0.456256i
$831$	−18.9933	−	12.9494i	−0.658869	−	0.449210i
$832$	7.90865			0.274183
$833$	−6.04453	−	21.2818i	−0.209431	−	0.737370i
$834$	2.10393			0.0728533
$835$	22.6735	+	15.4585i	0.784648	+	0.534964i
$836$	−0.0219139	−	0.0203332i	−0.000757910	−	0.000703237i
$837$	−30.2867	−	77.1693i	−1.04686	−	2.66736i
$838$	7.76856	−	2.39628i	0.268361	−	0.0827783i
$839$	−11.7768	−	51.5975i	−0.406580	−	1.78134i	−0.599761	−	0.800179i	$-0.704738\pi$
$839$	−11.7768	−	51.5975i	−0.406580	−	1.78134i	0.193181	−	0.981163i	$-0.438119\pi$
$840$	14.8114	+	83.3974i	0.511043	+	2.87748i
$841$	−2.87216	+	12.5838i	−0.0990400	+	0.433923i
$842$	−1.91080	−	25.4978i	−0.0658504	−	0.878712i
$843$	41.1020	+	12.6783i	1.41563	+	0.436664i
$844$	0.0242092	−	0.323049i	0.000833314	−	0.0111198i
$845$	1.30786	−	3.33238i	0.0449918	−	0.114637i
$846$	−51.4569	+	24.7803i	−1.76912	+	0.851965i
$847$	20.0933	−	16.9026i	0.690415	−	0.580782i
$848$	43.5559	+	20.9754i	1.49572	+	0.720299i
$849$	−29.5849	+	27.4508i	−1.01535	+	0.942108i
$850$	−34.7334	+	5.23522i	−1.19135	+	0.179567i
$851$	−18.5614	+	32.1492i	−0.636276	+	1.10206i
$852$	0.370197	+	0.641199i	0.0126827	+	0.0219671i
$853$	−3.06384	−	3.84193i	−0.104904	−	0.131545i	0.726608	−	0.687052i	$-0.241096\pi$
$853$	−3.06384	−	3.84193i	−0.104904	−	0.131545i	−0.831512	+	0.555507i	$0.812524\pi$
$854$	1.28934	−	10.3927i	0.0441203	−	0.355630i
$855$	−20.4768	+	25.6771i	−0.700292	+	0.878138i
$856$	−4.64590	−	0.700257i	−0.158794	−	0.0239343i
$857$	−18.8286	+	12.8371i	−0.643172	+	0.438507i	−0.840486	−	0.541833i	$-0.817730\pi$
$857$	−18.8286	+	12.8371i	−0.643172	+	0.438507i	0.197314	+	0.980340i	$0.436778\pi$
$858$	−3.87511	+	2.64201i	−0.132294	+	0.0901967i
$859$	−6.50239	−	0.980077i	−0.221859	−	0.0334398i	0.0371722	−	0.999309i	$-0.488165\pi$
$859$	−6.50239	−	0.980077i	−0.221859	−	0.0334398i	−0.259031	+	0.965869i	$0.583403\pi$
$860$	0.443171	−	0.555719i	0.0151120	−	0.0189498i
$861$	−3.35935	+	27.0780i	−0.114486	+	0.922814i
$862$	2.64653	+	3.31864i	0.0901410	+	0.113033i
$863$	−1.46951	−	2.54526i	−0.0500226	−	0.0866417i	0.839930	−	0.542695i	$-0.182596\pi$
$863$	−1.46951	−	2.54526i	−0.0500226	−	0.0866417i	−0.889953	+	0.456053i	$0.849263\pi$
$864$	0.826118	−	1.43088i	0.0281051	−	0.0486794i
$865$	4.23266	−	0.637971i	0.143915	−	0.0216917i
$866$	−39.2347	+	36.4045i	−1.33325	+	1.23707i
$867$	−20.0866	−	9.67322i	−0.682178	−	0.328520i
$868$	−0.286838	+	0.241290i	−0.00973592	+	0.00818992i
$869$	13.2584	−	6.38490i	0.449760	−	0.216593i
$870$	−38.2859	+	97.5510i	−1.29802	+	3.30729i
$871$	0.194164	−	2.59094i	0.00657900	−	0.0877907i
$872$	2.82033	+	0.869956i	0.0955083	+	0.0294604i
$873$	−7.50284	−	100.119i	−0.253933	−	3.38850i
$874$	−3.74221	+	16.3957i	−0.126582	+	0.554592i
$875$	−4.66258	−	26.2532i	−0.157624	−	0.887519i
$876$	0.0368038	+	0.161248i	0.00124348	+	0.00544806i
$877$	−14.0776	+	4.34236i	−0.475366	+	0.146631i	−0.523175	−	0.852225i	$-0.675253\pi$
$877$	−14.0776	+	4.34236i	−0.475366	+	0.146631i	0.0478084	+	0.998857i	$0.484776\pi$
$878$	−12.0062	−	30.5914i	−0.405191	−	1.03241i
$879$	45.3897	+	42.1155i	1.53096	+	1.42052i
$880$	12.4064	+	8.45854i	0.418220	+	0.285137i
$881$	−28.1296			−0.947710			−0.473855	−	0.880603i	$-0.657138\pi$
$881$	−28.1296			−0.947710			−0.473855	+	0.880603i	$0.657138\pi$
$882$	−65.3001	−	27.3366i	−2.19877	−	0.920470i
$883$	31.1388			1.04790			0.523952	−	0.851748i	$-0.324457\pi$
$883$	31.1388			1.04790			0.523952	+	0.851748i	$0.324457\pi$
$884$	−0.0583427	−	0.0397773i	−0.00196228	−	0.00133786i
$885$	67.6362	+	62.7572i	2.27357	+	2.10956i
$886$	−13.6173	−	34.6963i	−0.457482	−	1.16565i
$887$	5.75447	−	1.77502i	0.193216	−	0.0595993i	−0.196637	−	0.980476i	$-0.563002\pi$
$887$	5.75447	−	1.77502i	0.193216	−	0.0595993i	0.389853	+	0.920877i	$0.372526\pi$
$888$	8.05899	+	35.3087i	0.270442	+	1.18488i
$889$	−23.5647	−	1.14689i	−0.790334	−	0.0384655i
$890$	19.3968	−	84.9831i	0.650183	−	2.84864i
$891$	−1.56856	−	20.9310i	−0.0525487	−	0.701214i
$892$	−0.0958132	−	0.0295545i	−0.00320806	−	0.000989556i
$893$	0.544457	−	7.26527i	0.0182196	−	0.243123i
$894$	−28.8034	+	73.3899i	−0.963331	+	2.45453i
$895$	−45.7145	+	22.0149i	−1.52807	+	0.735878i
$896$	29.8292	+	5.99177i	0.996523	+	0.200171i
$897$	26.2621	+	12.6472i	0.876866	+	0.422276i
$898$	34.3188	−	31.8432i	1.14523	−	1.06262i
$899$	40.5908	−	6.11808i	1.35378	−	0.204049i
$900$	−0.620854	+	1.07535i	−0.0206951	+	0.0358450i
$901$	18.8901	+	32.7185i	0.629319	+	1.09001i
$902$	2.98251	+	3.73994i	0.0993066	+	0.124527i
$903$	−23.8997	−	70.8441i	−0.795334	−	2.35754i
$904$	−10.9686	+	13.7542i	−0.364810	+	0.457457i
$905$	−50.0558	−	7.54470i	−1.66391	−	0.250794i
$906$	−59.6557	+	40.6725i	−1.98193	+	1.35125i
$907$	−22.7774	+	15.5294i	−0.756310	+	0.515644i	−0.879012	−	0.476800i	$-0.841797\pi$
$907$	−22.7774	+	15.5294i	−0.756310	+	0.515644i	0.122702	+	0.992444i	$0.460844\pi$
$908$	−0.00442419		0.000666839i	−0.000146822		2.21298e-5i
$909$	−4.02649	+	5.04906i	−0.133550	+	0.167467i
$910$	7.29365	−	11.3234i	0.241782	−	0.375368i
$911$	26.6044	+	33.3609i	0.881443	+	1.10529i	0.993751	+	0.111621i	$0.0356044\pi$
$911$	26.6044	+	33.3609i	0.881443	+	1.10529i	−0.112308	+	0.993673i	$0.535824\pi$
$912$	8.29510	+	14.3675i	0.274678	+	0.475757i
$913$	−1.96859	+	3.40969i	−0.0651507	+	0.112844i
$914$	46.5656	−	7.01864i	1.54025	−	0.232156i
$915$	−23.2258	+	21.5504i	−0.767822	+	0.712435i
$916$	−0.116652	−	0.0561764i	−0.00385428	−	0.00185612i
$917$	0.255224	+	9.75096i	0.00842823	+	0.322005i
$918$	52.9404	−	25.4947i	1.74729	−	0.841452i
$919$	−4.44124	+	11.3161i	−0.146503	+	0.373284i	−0.985222	−	0.171280i	$-0.945210\pi$
$919$	−4.44124	+	11.3161i	−0.146503	+	0.373284i	0.838719	+	0.544564i	$0.183305\pi$
$920$	6.89686	−	92.0322i	0.227383	−	3.03421i
$921$	88.6125	+	27.3333i	2.91988	+	0.900664i
$922$	−1.08326	−	14.4551i	−0.0356752	−	0.476052i
$923$	−2.31902	+	10.1603i	−0.0763314	+	0.334430i
$924$	−0.179549	+	0.0759474i	−0.00590672	+	0.00249849i
$925$	−7.04268	−	30.8560i	−0.231562	−	1.01454i
$926$	−24.2662	+	7.48513i	−0.797437	+	0.245977i
$927$	14.5372	+	37.0401i	0.477463	+	1.21656i
$928$	0.599734	+	0.556472i	0.0196872	+	0.0182671i
$929$	−28.9565	−	19.7422i	−0.950032	−	0.647721i	−0.0140995	−	0.999901i	$-0.504488\pi$
$929$	−28.9565	−	19.7422i	−0.950032	−	0.647721i	−0.935932	+	0.352180i	$0.885441\pi$
$930$	102.649			3.36601
$931$	7.18505	−	5.47044i	0.235480	−	0.179286i
$932$	0.629061			0.0206056
$933$	−60.8627	−	41.4955i	−1.99255	−	1.35850i
$934$	−18.8682	−	17.5071i	−0.617385	−	0.572849i
$935$	4.28711	+	10.9234i	0.140203	+	0.357233i
$936$	19.1116	−	5.89514i	0.624681	−	0.192689i
$937$	−1.27062	−	5.56694i	−0.0415093	−	0.181864i	0.949923	−	0.312483i	$-0.101161\pi$
$937$	−1.27062	−	5.56694i	−0.0415093	−	0.181864i	−0.991433	+	0.130619i	$0.958304\pi$
$938$	2.63605	−	9.41364i	0.0860699	−	0.307366i
$939$	23.1011	−	101.213i	0.753876	−	3.30295i
$940$	−0.0337548	−	0.450426i	−0.00110096	−	0.0146913i
$941$	−31.2813	−	9.64900i	−1.01974	−	0.314549i	−0.260581	−	0.965452i	$-0.583914\pi$
$941$	−31.2813	−	9.64900i	−1.01974	−	0.314549i	−0.759161	+	0.650903i	$0.774390\pi$
$942$	2.61294	−	34.8672i	0.0851341	−	1.13604i
$943$	10.8615	−	27.6747i	0.353700	−	0.901213i
$944$	29.5336	−	14.2226i	0.961238	−	0.462908i
$945$	56.6259	+	110.118i	1.84204	+	3.58213i
$946$	−11.8097	−	5.68724i	−0.383966	−	0.184908i
$947$	37.3415	−	34.6479i	1.21344	−	1.12591i	0.224987	−	0.974362i	$-0.427766\pi$
$947$	37.3415	−	34.6479i	1.21344	−	1.12591i	0.988451	−	0.151543i	$-0.0484243\pi$
$948$	0.996749	−	0.150236i	0.0323729	−	0.00487943i
$949$	−1.16403	+	2.01615i	−0.0377859	+	0.0654470i
$950$	−7.16893	−	12.4170i	−0.232591	−	0.402859i
$951$	−8.18514	−	10.2638i	−0.265421	−	0.332828i
$952$	16.4413	+	16.8148i	0.532866	+	0.544972i
$953$	−28.5897	+	35.8504i	−0.926113	+	1.16131i	0.0604902	+	0.998169i	$0.480734\pi$
$953$	−28.5897	+	35.8504i	−0.926113	+	1.16131i	−0.986603	+	0.163140i	$0.947838\pi$
$954$	119.539	+	18.0176i	3.87022	+	0.583342i
$955$	0.469895	−	0.320369i	0.0152055	−	0.0103669i
$956$	0.213365	−	0.145470i	0.00690071	−	0.00470483i
$957$	21.1115	+	3.18204i	0.682437	+	0.102861i
$958$	17.4727	−	21.9100i	0.564517	−	0.707882i
$959$	4.06050	−	2.48821i	0.131120	−	0.0803485i
$960$	−56.1306	−	70.3856i	−1.81161	−	2.27168i
$961$	−4.60440	−	7.97506i	−0.148529	−	0.257260i
$962$	2.87954	−	4.98751i	0.0928401	−	0.160804i
$963$	−11.7475	+	1.77065i	−0.378558	+	0.0570585i
$964$	−0.206769	+	0.191853i	−0.00665958	+	0.00617918i
$965$	19.5153	+	9.39809i	0.628221	+	0.302535i
$966$	87.5049	+	66.1124i	2.81542	+	2.12713i
$967$	33.9585	−	16.3535i	1.09203	−	0.525894i	0.200886	−	0.979615i	$-0.435618\pi$
$967$	33.9585	−	16.3535i	1.09203	−	0.525894i	0.891144	+	0.453720i	$0.149904\pi$
$968$	−10.1971	+	25.9818i	−0.327747	+	0.835086i
$969$	−0.968887	+	12.9289i	−0.0311251	+	0.415336i
$970$	68.6800	+	21.1850i	2.20518	+	0.680209i
$971$	−2.05678	−	27.4458i	−0.0660052	−	0.880778i	−0.927694	−	0.373341i	$-0.878212\pi$
$971$	−2.05678	−	27.4458i	−0.0660052	−	0.880778i	0.861689	−	0.507437i	$-0.169407\pi$
$972$	0.124945	−	0.547419i	0.00400760	−	0.0175585i
$973$	0.719806	+	0.998586i	0.0230759	+	0.0320132i
$974$	−5.82574	−	25.5242i	−0.186669	−	0.817849i
$975$	−23.7471	+	7.32501i	−0.760516	+	0.234588i
$976$	4.11242	+	10.4783i	0.131635	+	0.335402i
$977$	−1.16324	−	1.07933i	−0.0372153	−	0.0345307i	0.661346	−	0.750081i	$-0.269986\pi$
$977$	−1.16324	−	1.07933i	−0.0372153	−	0.0345307i	−0.698561	+	0.715550i	$0.746176\pi$
$978$	52.6740	+	35.9125i	1.68433	+	1.14835i
$979$	−17.7589			−0.567577
$980$	0.389929	−	0.401755i	0.0124558	−	0.0128336i
$981$	7.46296			0.238274
$982$	35.6797	+	24.3260i	1.13858	+	0.776274i
$983$	41.5899	+	38.5898i	1.32651	+	1.23082i	0.952917	+	0.303232i	$0.0980656\pi$
$983$	41.5899	+	38.5898i	1.32651	+	1.23082i	0.373595	+	0.927592i	$0.378125\pi$
$984$	−10.5965	−	26.9993i	−0.337803	−	0.860707i
$985$	41.9319	−	12.9343i	1.33606	−	0.412120i
$986$	6.47441	+	28.3662i	0.206187	+	0.903365i
$987$	−41.7544	−	22.6714i	−1.32906	−	0.721640i
$988$	0.00641373	−	0.0281004i	0.000204048	−	0.000893992i
$989$	6.08786	+	81.2368i	0.193583	+	2.58318i
$990$	35.8802	+	11.0676i	1.14035	+	0.351750i
$991$	1.75947	−	23.4784i	0.0558913	−	0.745817i	−0.896908	−	0.442217i	$-0.854192\pi$
$991$	1.75947	−	23.4784i	0.0558913	−	0.745817i	0.952799	−	0.303600i	$-0.0981888\pi$
$992$	0.292778	−	0.745985i	0.00929570	−	0.0236850i
$993$	23.8896	−	11.5046i	0.758113	−	0.365088i
$994$	−16.0829	+	35.7611i	−0.510118	+	1.13427i
$995$	−65.4367	−	31.5127i	−2.07448	−	0.999019i
$996$	−0.197698	+	0.183437i	−0.00626430	+	0.00581242i
$997$	26.9049	−	4.05527i	0.852088	−	0.128432i	0.291545	−	0.956557i	$-0.405831\pi$
$997$	26.9049	−	4.05527i	0.852088	−	0.128432i	0.560543	+	0.828126i	$0.310593\pi$
$998$	3.16803	−	5.48720i	0.100282	−	0.173694i
$999$	26.4721	+	45.8511i	0.837541	+	1.45066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.8	✓	348
49.37	even	21	inner	637.2.bl.b.625.8	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.8	✓	348	1.1	even	1	trivial
637.2.bl.b.625.8	yes	348	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17499 - 0.801092i) q^{2} +(2.33099 + 2.16284i) q^{3} +(0.00816248 + 0.0207977i) q^{4} +(3.42079 - 1.05518i) q^{5} +(-1.00624 - 4.40864i) q^{6} +(1.74821 - 1.98590i) q^{7} +(-0.625820 + 2.74190i) q^{8} +(0.531434 + 7.09150i) q^{9} +O(q^{10})\)	\(q+(-1.17499 - 0.801092i) q^{2} +(2.33099 + 2.16284i) q^{3} +(0.00816248 + 0.0207977i) q^{4} +(3.42079 - 1.05518i) q^{5} +(-1.00624 - 4.40864i) q^{6} +(1.74821 - 1.98590i) q^{7} +(-0.625820 + 2.74190i) q^{8} +(0.531434 + 7.09150i) q^{9} +(-4.86468 - 1.50055i) q^{10} +(-0.0775072 + 1.03426i) q^{11} +(-0.0259554 + 0.0661333i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-3.64500 + 0.932926i) q^{14} +(10.2560 + 4.93903i) q^{15} +(2.96460 - 2.75074i) q^{16} +(3.12521 - 0.471049i) q^{17} +(5.05652 - 8.75814i) q^{18} +(0.645038 + 1.11724i) q^{19} +(0.0498674 + 0.0625317i) q^{20} +(8.37022 - 0.848008i) q^{21} +(0.919608 - 1.15315i) q^{22} +(-9.06434 - 1.36623i) q^{23} +(-7.38906 + 5.03778i) q^{24} +(6.45724 - 4.40247i) q^{25} +(1.40621 + 0.211952i) q^{26} +(-8.15122 + 10.2213i) q^{27} +(0.0555717 + 0.0201488i) q^{28} +(-4.03622 - 5.06126i) q^{29} +(-8.09405 - 14.0193i) q^{30} +(-3.17052 + 5.49150i) q^{31} +(-0.124969 + 0.0188360i) q^{32} +(-2.41761 + 2.24321i) q^{33} +(-4.04943 - 1.95010i) q^{34} +(3.88478 - 8.63800i) q^{35} +(-0.143149 + 0.0689368i) q^{36} +(1.47953 - 3.76979i) q^{37} +(0.137100 - 1.82948i) q^{38} +(-3.03857 - 0.937274i) q^{39} +(0.752380 + 10.0398i) q^{40} +(-0.721688 + 3.16192i) q^{41} +(-10.5142 - 5.70892i) q^{42} +(-1.97754 - 8.66417i) q^{43} +(-0.0221429 + 0.00683017i) q^{44} +(9.30070 + 23.6978i) q^{45} +(9.55600 + 8.86668i) q^{46} +(-4.66614 - 3.18132i) q^{47} +12.8599 q^{48} +(-0.887558 - 6.94350i) q^{49} -11.1140 q^{50} +(8.30362 + 5.66131i) q^{51} +(-0.0163779 - 0.0151965i) q^{52} +(4.36722 + 11.1275i) q^{53} +(17.7658 - 5.48002i) q^{54} +(0.826191 + 3.61978i) q^{55} +(4.35106 + 6.03621i) q^{56} +(-0.912834 + 3.99939i) q^{57} +(0.687968 + 9.18029i) q^{58} +(7.74533 + 2.38912i) q^{59} +(-0.0190059 + 0.253616i) q^{60} +(-1.01687 + 2.59095i) q^{61} +(8.12452 - 3.91256i) q^{62} +(15.0120 + 11.3420i) q^{63} +(-7.12544 - 3.43143i) q^{64} +(-2.62421 + 2.43491i) q^{65} +(4.63768 - 0.699018i) q^{66} +(-1.29910 + 2.25011i) q^{67} +(0.0353062 + 0.0611521i) q^{68} +(-18.1739 - 22.7894i) q^{69} +(-11.4844 + 7.03747i) q^{70} +(6.49774 - 8.14791i) q^{71} +(-19.7767 - 2.98086i) q^{72} +(1.92353 - 1.31144i) q^{73} +(-4.75838 + 3.24421i) q^{74} +(24.5736 + 3.70387i) q^{75} +(-0.0179709 + 0.0225347i) q^{76} +(1.91844 + 1.96202i) q^{77} +(2.81943 + 3.53546i) q^{78} +(-7.09422 - 12.2875i) q^{79} +(7.23876 - 12.5379i) q^{80} +(-20.0116 + 3.01626i) q^{81} +(3.38096 - 3.13708i) q^{82} +(3.42017 + 1.64707i) q^{83} +(0.0859584 + 0.167159i) q^{84} +(10.1936 - 4.90900i) q^{85} +(-4.61722 + 11.7645i) q^{86} +(1.53832 - 20.5274i) q^{87} +(-2.78733 - 0.859778i) q^{88} +(1.27957 + 17.0747i) q^{89} +(8.05592 - 35.2953i) q^{90} +(-0.713431 + 2.54775i) q^{91} +(-0.0455732 - 0.199669i) q^{92} +(-19.2677 + 5.94329i) q^{93} +(2.93412 + 7.47602i) q^{94} +(3.38543 + 3.14122i) q^{95} +(-0.332039 - 0.226381i) q^{96} -14.1181 q^{97} +(-4.51952 + 8.86954i) q^{98} -7.37565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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