LMFDB - Embedded newform 637.2.bl.b.625.22

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			625.22
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.b.53.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46759 - 1.00059i) q^{2} +(-0.670565 + 0.622193i) q^{3} +(0.421973 - 1.07517i) q^{4} +(-3.65935 - 1.12876i) q^{5} +(-0.361558 + 1.58409i) q^{6} +(2.44101 + 1.02053i) q^{7} +(0.333981 + 1.46327i) q^{8} +(-0.161658 + 2.15717i) q^{9} +O(q^{10})$	\(q+(1.46759 - 1.00059i) q^{2} +(-0.670565 + 0.622193i) q^{3} +(0.421973 - 1.07517i) q^{4} +(-3.65935 - 1.12876i) q^{5} +(-0.361558 + 1.58409i) q^{6} +(2.44101 + 1.02053i) q^{7} +(0.333981 + 1.46327i) q^{8} +(-0.161658 + 2.15717i) q^{9} +(-6.49987 + 2.00494i) q^{10} +(0.0318729 + 0.425314i) q^{11} +(0.386003 + 0.983520i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(4.60354 - 0.944727i) q^{14} +(3.15614 - 1.51992i) q^{15} +(3.64765 + 3.38452i) q^{16} +(3.25629 + 0.490807i) q^{17} +(1.92119 + 3.32760i) q^{18} +(-3.69716 + 6.40367i) q^{19} +(-2.75776 + 3.45812i) q^{20} +(-2.27182 + 0.834450i) q^{21} +(0.472341 + 0.592297i) q^{22} +(2.14315 - 0.323027i) q^{23} +(-1.13439 - 0.773415i) q^{24} +(7.98555 + 5.44446i) q^{25} +(-1.75640 + 0.264734i) q^{26} +(-2.94480 - 3.69266i) q^{27} +(2.12728 - 2.19386i) q^{28} +(-5.11394 + 6.41268i) q^{29} +(3.11112 - 5.38862i) q^{30} +(5.20193 + 9.01000i) q^{31} +(5.77151 + 0.869915i) q^{32} +(-0.286000 - 0.265369i) q^{33} +(5.27001 - 2.53790i) q^{34} +(-7.78058 - 6.48978i) q^{35} +(2.25111 + 1.08408i) q^{36} +(-2.40867 - 6.13719i) q^{37} +(0.981508 + 13.0973i) q^{38} +(0.874118 - 0.269630i) q^{39} +(0.429524 - 5.73159i) q^{40} +(-2.34361 - 10.2680i) q^{41} +(-2.49917 + 3.49779i) q^{42} +(0.221121 - 0.968795i) q^{43} +(0.470734 + 0.145202i) q^{44} +(3.02649 - 7.71137i) q^{45} +(2.82205 - 2.61848i) q^{46} +(-0.101886 + 0.0694649i) q^{47} -4.55181 q^{48} +(4.91705 + 4.98223i) q^{49} +17.1672 q^{50} +(-2.48893 + 1.69692i) q^{51} +(-0.846683 + 0.785607i) q^{52} +(2.41309 - 6.14845i) q^{53} +(-8.01661 - 2.47280i) q^{54} +(0.363443 - 1.59235i) q^{55} +(-0.678053 + 3.91269i) q^{56} +(-1.50513 - 6.59442i) q^{57} +(-1.08874 + 14.5282i) q^{58} +(-7.16946 + 2.21148i) q^{59} +(-0.302363 - 4.03475i) q^{60} +(-3.28680 - 8.37463i) q^{61} +(16.6496 + 8.01804i) q^{62} +(-2.59606 + 5.10069i) q^{63} +(0.374270 - 0.180239i) q^{64} +(2.80721 + 2.60471i) q^{65} +(-0.685258 - 0.103286i) q^{66} +(5.47285 + 9.47925i) q^{67} +(1.90177 - 3.29396i) q^{68} +(-1.23613 + 1.55006i) q^{69} +(-17.9123 - 1.73921i) q^{70} +(0.132786 + 0.166508i) q^{71} +(-3.21051 + 0.483906i) q^{72} +(-3.73720 - 2.54798i) q^{73} +(-9.67575 - 6.59681i) q^{74} +(-8.74234 + 1.31770i) q^{75} +(5.32493 + 6.67725i) q^{76} +(-0.356242 + 1.07072i) q^{77} +(1.01306 - 1.27034i) q^{78} +(-0.506776 + 0.877761i) q^{79} +(-9.52770 - 16.5025i) q^{80} +(-2.14494 - 0.323298i) q^{81} +(-13.7136 - 12.7243i) q^{82} +(9.97761 - 4.80496i) q^{83} +(-0.0614717 + 2.79471i) q^{84} +(-11.3619 - 5.47160i) q^{85} +(-0.644849 - 1.64305i) q^{86} +(-0.560697 - 7.48198i) q^{87} +(-0.611703 + 0.188685i) q^{88} +(-0.587651 + 7.84165i) q^{89} +(-3.27425 - 14.3454i) q^{90} +(-1.75648 - 1.97858i) q^{91} +(0.557041 - 2.44055i) q^{92} +(-9.09419 - 2.80519i) q^{93} +(-0.0800219 + 0.203893i) q^{94} +(20.7574 - 19.2601i) q^{95} +(-4.41143 + 3.00766i) q^{96} -11.9861 q^{97} +(12.2014 + 2.39195i) q^{98} -0.922627 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	1.46759	−	1.00059i	1.03775	−	0.707523i	0.0804871	−	0.996756i	$-0.474352\pi$
$2$	1.46759	−	1.00059i	1.03775	−	0.707523i	0.957259	+	0.289232i	$0.0934000\pi$
$3$	−0.670565	+	0.622193i	−0.387151	+	0.359223i	−0.849605	−	0.527420i	$-0.823160\pi$
$3$	−0.670565	+	0.622193i	−0.387151	+	0.359223i	0.462454	+	0.886643i	$0.346969\pi$
$4$	0.421973	−	1.07517i	0.210987	−	0.537585i
$5$	−3.65935	−	1.12876i	−1.63651	−	0.504797i	−0.666020	−	0.745934i	$-0.732004\pi$
$5$	−3.65935	−	1.12876i	−1.63651	−	0.504797i	−0.970491	+	0.241137i	$0.922480\pi$
$6$	−0.361558	+	1.58409i	−0.147605	+	0.646701i
$7$	2.44101	+	1.02053i	0.922615	+	0.385723i
$7$	2.44101	+	1.02053i	0.922615	+	0.385723i
$8$	0.333981	+	1.46327i	0.118080	+	0.517343i
$9$	−0.161658	+	2.15717i	−0.0538858	+	0.719057i
$10$	−6.49987	+	2.00494i	−2.05544	+	0.634019i
$11$	0.0318729	+	0.425314i	0.00961003	+	0.128237i	0.999945	−	0.0104570i	$-0.00332862\pi$
$11$	0.0318729	+	0.425314i	0.00961003	+	0.128237i	−0.990335	+	0.138694i	$0.955710\pi$
$12$	0.386003	+	0.983520i	0.111430	+	0.283918i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$14$	4.60354	−	0.944727i	1.23035	−	0.252489i
$15$	3.15614	−	1.51992i	0.814911	−	0.392441i
$16$	3.64765	+	3.38452i	0.911911	+	0.846130i
$17$	3.25629	+	0.490807i	0.789766	+	0.119038i	0.531525	−	0.847042i	$-0.321619\pi$
$17$	3.25629	+	0.490807i	0.789766	+	0.119038i	0.258241	+	0.966081i	$0.416857\pi$
$18$	1.92119	+	3.32760i	0.452829	+	0.784324i
$19$	−3.69716	+	6.40367i	−0.848186	+	1.46910i	0.0346389	+	0.999400i	$0.488972\pi$
$19$	−3.69716	+	6.40367i	−0.848186	+	1.46910i	−0.882825	+	0.469702i	$0.844361\pi$
$20$	−2.75776	+	3.45812i	−0.616653	+	0.773259i
$21$	−2.27182	+	0.834450i	−0.495752	+	0.182092i
$22$	0.472341	+	0.592297i	0.100703	+	0.126278i
$23$	2.14315	−	0.323027i	0.446877	−	0.0673558i	0.0782509	−	0.996934i	$-0.475066\pi$
$23$	2.14315	−	0.323027i	0.446877	−	0.0673558i	0.368626	+	0.929578i	$0.379828\pi$
$24$	−1.13439	−	0.773415i	−0.231557	−	0.157873i
$25$	7.98555	+	5.44446i	1.59711	+	1.08889i
$26$	−1.75640	+	0.264734i	−0.344458	+	0.0519186i
$27$	−2.94480	−	3.69266i	−0.566727	−	0.710653i
$28$	2.12728	−	2.19386i	0.402018	−	0.414601i
$29$	−5.11394	+	6.41268i	−0.949635	+	1.19080i	0.0318941	+	0.999491i	$0.489846\pi$
$29$	−5.11394	+	6.41268i	−0.949635	+	1.19080i	−0.981529	+	0.191313i	$0.938725\pi$
$30$	3.11112	−	5.38862i	0.568010	−	0.983823i
$31$	5.20193	+	9.01000i	0.934294	+	1.61824i	0.775888	+	0.630870i	$0.217302\pi$
$31$	5.20193	+	9.01000i	0.934294	+	1.61824i	0.158406	+	0.987374i	$0.449365\pi$
$32$	5.77151	+	0.869915i	1.02027	+	0.153781i
$33$	−0.286000	−	0.265369i	−0.0497863	−	0.0461949i
$34$	5.27001	−	2.53790i	0.903799	−	0.435247i
$35$	−7.78058	−	6.48978i	−1.31516	−	1.09697i
$36$	2.25111	+	1.08408i	0.375185	+	0.180679i
$37$	−2.40867	−	6.13719i	−0.395983	−	1.00895i	−0.980316	−	0.197434i	$-0.936739\pi$
$37$	−2.40867	−	6.13719i	−0.395983	−	1.00895i	0.584334	−	0.811514i	$-0.301356\pi$
$38$	0.981508	+	13.0973i	0.159222	+	2.12467i
$39$	0.874118	−	0.269630i	0.139971	−	0.0431753i
$40$	0.429524	−	5.73159i	0.0679136	−	0.906244i
$41$	−2.34361	−	10.2680i	−0.366011	−	1.60360i	−0.737624	−	0.675211i	$-0.764052\pi$
$41$	−2.34361	−	10.2680i	−0.366011	−	1.60360i	0.371613	−	0.928388i	$-0.378805\pi$
$42$	−2.49917	+	3.49779i	−0.385630	+	0.539721i
$43$	0.221121	−	0.968795i	0.0337207	−	0.147740i	−0.955265	−	0.295751i	$-0.904430\pi$
$43$	0.221121	−	0.968795i	0.0337207	−	0.147740i	0.988986	+	0.148011i	$0.0472872\pi$
$44$	0.470734	+	0.145202i	0.0709659	+	0.0218901i
$45$	3.02649	−	7.71137i	0.451162	−	1.14954i
$46$	2.82205	−	2.61848i	0.416089	−	0.386074i
$47$	−0.101886	+	0.0694649i	−0.0148616	+	0.0101325i	−0.570728	−	0.821139i	$-0.693339\pi$
$47$	−0.101886	+	0.0694649i	−0.0148616	+	0.0101325i	0.555866	+	0.831272i	$0.312387\pi$
$48$	−4.55181			−0.656997
$49$	4.91705	+	4.98223i	0.702436	+	0.711747i
$50$	17.1672			2.42781
$51$	−2.48893	+	1.69692i	−0.348520	+	0.237617i
$52$	−0.846683	+	0.785607i	−0.117414	+	0.108944i
$53$	2.41309	−	6.14845i	0.331463	−	0.844555i	−0.663851	−	0.747865i	$-0.731079\pi$
$53$	2.41309	−	6.14845i	0.331463	−	0.844555i	0.995315	−	0.0966899i	$-0.0308255\pi$
$54$	−8.01661	−	2.47280i	−1.09092	−	0.336505i
$55$	0.363443	−	1.59235i	0.0490067	−	0.214712i
$56$	−0.678053	+	3.91269i	−0.0906086	+	0.522855i
$57$	−1.50513	−	6.59442i	−0.199360	−	0.873452i
$58$	−1.08874	+	14.5282i	−0.142958	+	1.90764i
$59$	−7.16946	+	2.21148i	−0.933384	+	0.287911i	−0.723903	−	0.689902i	$-0.757654\pi$
$59$	−7.16946	+	2.21148i	−0.933384	+	0.287911i	−0.209481	+	0.977813i	$0.567177\pi$
$60$	−0.302363	−	4.03475i	−0.0390349	−	0.520884i
$61$	−3.28680	−	8.37463i	−0.420832	−	1.07226i	−0.971395	−	0.237468i	$-0.923682\pi$
$61$	−3.28680	−	8.37463i	−0.420832	−	1.07226i	0.550564	−	0.834793i	$-0.314413\pi$
$62$	16.6496	+	8.01804i	2.11451	+	1.01829i
$63$	−2.59606	+	5.10069i	−0.327073	+	0.642627i
$64$	0.374270	−	0.180239i	0.0467838	−	0.0225299i
$65$	2.80721	+	2.60471i	0.348192	+	0.323075i
$66$	−0.685258	−	0.103286i	−0.0843494	−	0.0127136i
$67$	5.47285	+	9.47925i	0.668615	+	1.15807i	0.978292	+	0.207233i	$0.0664458\pi$
$67$	5.47285	+	9.47925i	0.668615	+	1.15807i	−0.309677	+	0.950842i	$0.600221\pi$
$68$	1.90177	−	3.29396i	0.230623	−	0.399451i
$69$	−1.23613	+	1.55006i	−0.148813	+	0.186605i
$70$	−17.9123	−	1.73921i	−2.14093	−	0.207875i
$71$	0.132786	+	0.166508i	0.0157588	+	0.0197609i	0.789648	−	0.613560i	$-0.210263\pi$
$71$	0.132786	+	0.166508i	0.0157588	+	0.0197609i	−0.773890	+	0.633320i	$0.781692\pi$
$72$	−3.21051	+	0.483906i	−0.378362	+	0.0570289i
$73$	−3.73720	−	2.54798i	−0.437406	−	0.298218i	0.324524	−	0.945877i	$-0.394796\pi$
$73$	−3.73720	−	2.54798i	−0.437406	−	0.298218i	−0.761930	+	0.647659i	$0.775748\pi$
$74$	−9.67575	−	6.59681i	−1.12478	−	0.766864i
$75$	−8.74234	+	1.31770i	−1.00948	+	0.152154i
$76$	5.32493	+	6.67725i	0.610811	+	0.765933i
$77$	−0.356242	+	1.07072i	−0.0405976	+	0.122020i
$78$	1.01306	−	1.27034i	0.114707	−	0.143838i
$79$	−0.506776	+	0.877761i	−0.0570167	+	0.0987558i	−0.893125	−	0.449809i	$-0.851492\pi$
$79$	−0.506776	+	0.877761i	−0.0570167	+	0.0987558i	0.836108	+	0.548565i	$0.184825\pi$
$80$	−9.52770	−	16.5025i	−1.06523	−	1.84503i
$81$	−2.14494	−	0.323298i	−0.238327	−	0.0359220i
$82$	−13.7136	−	12.7243i	−1.51441	−	1.40517i
$83$	9.97761	−	4.80496i	1.09518	−	0.527413i	0.203043	−	0.979170i	$-0.434917\pi$
$83$	9.97761	−	4.80496i	1.09518	−	0.527413i	0.892141	+	0.451757i	$0.149202\pi$
$84$	−0.0614717	+	2.79471i	−0.00670712	+	0.304928i
$85$	−11.3619	−	5.47160i	−1.23237	−	0.593479i
$86$	−0.644849	−	1.64305i	−0.0695359	−	0.177175i
$87$	−0.560697	−	7.48198i	−0.0601130	−	0.802152i
$88$	−0.611703	+	0.188685i	−0.0652078	+	0.0201139i
$89$	−0.587651	+	7.84165i	−0.0622908	+	0.831214i	0.875324	+	0.483537i	$0.160648\pi$
$89$	−0.587651	+	7.84165i	−0.0622908	+	0.831214i	−0.937615	+	0.347676i	$0.886971\pi$
$90$	−3.27425	−	14.3454i	−0.345136	−	1.51214i
$91$	−1.75648	−	1.97858i	−0.184129	−	0.207411i
$92$	0.557041	−	2.44055i	0.0580755	−	0.254445i
$93$	−9.09419	−	2.80519i	−0.943024	−	0.290884i
$94$	−0.0800219	+	0.203893i	−0.00825363	+	0.0210299i
$95$	20.7574	−	19.2601i	2.12966	−	1.97604i
$96$	−4.41143	+	3.00766i	−0.450239	+	0.306968i
$97$	−11.9861			−1.21700			−0.608502	−	0.793552i	$-0.708229\pi$
$97$	−11.9861			−1.21700			−0.608502	+	0.793552i	$0.708229\pi$
$98$	12.2014	+	2.39195i	1.23253	+	0.241624i
$99$	−0.922627			−0.0927275
$100$	9.22341	−	6.28841i	0.922341	−	0.628841i
$101$	0.244060	−	0.226454i	0.0242848	−	0.0225330i	−0.667937	−	0.744218i	$-0.732822\pi$
$101$	0.244060	−	0.226454i	0.0242848	−	0.0225330i	0.692222	+	0.721685i	$0.256632\pi$
$102$	−1.95482	+	4.98079i	−0.193556	+	0.493172i
$103$	8.41294	+	2.59505i	0.828951	+	0.255698i	0.680060	−	0.733156i	$-0.261954\pi$
$103$	8.41294	+	2.59505i	0.828951	+	0.255698i	0.148891	+	0.988854i	$0.452430\pi$
$104$	0.333981	−	1.46327i	0.0327496	−	0.143485i
$105$	9.25528	−	0.489204i	0.903223	−	0.0477414i
$106$	−2.61064	−	11.4379i	−0.253567	−	1.11095i
$107$	0.835337	−	11.1468i	0.0807551	−	1.07760i	−0.798734	−	0.601684i	$-0.794497\pi$
$107$	0.835337	−	11.1468i	0.0807551	−	1.07760i	0.879489	−	0.475918i	$-0.157884\pi$
$108$	−5.21287	+	1.60796i	−0.501608	+	0.154726i
$109$	0.865838	+	11.5538i	0.0829322	+	1.10665i	0.871071	+	0.491157i	$0.163426\pi$
$109$	0.865838	+	11.5538i	0.0829322	+	1.10665i	−0.788139	+	0.615497i	$0.788955\pi$
$110$	−1.05990	−	2.70058i	−0.101057	−	0.257490i
$111$	5.43368	+	2.61672i	0.515743	+	0.248369i
$112$	5.44994	+	11.9842i	0.514971	+	1.13240i
$113$	2.31494	−	1.11482i	0.217772	−	0.104873i	−0.321818	−	0.946802i	$-0.604294\pi$
$113$	2.31494	−	1.11482i	0.217772	−	0.104873i	0.539589	+	0.841928i	$0.318580\pi$
$114$	−8.80723	−	8.17191i	−0.824873	−	0.765370i
$115$	−8.20714	−	1.23703i	−0.765320	−	0.115353i
$116$	4.73677	+	8.20433i	0.439798	+	0.761753i
$117$	1.08161	−	1.87340i	0.0999948	−	0.173196i
$118$	−8.30907	+	10.4192i	−0.764912	+	0.959169i
$119$	7.44775	+	4.52120i	0.682734	+	0.414457i
$120$	3.27813	+	4.11065i	0.299251	+	0.375249i
$121$	10.6973	−	1.61235i	0.972478	−	0.146578i
$122$	−13.2033	−	9.00183i	−1.19537	−	0.814987i
$123$	7.96025	+	5.42721i	0.717752	+	0.489355i
$124$	11.8824	−	1.79098i	1.06707	−	0.160835i
$125$	−11.1382	−	13.9669i	−0.996234	−	1.24924i
$126$	1.29374	+	10.0833i	0.115255	+	0.898295i
$127$	0.489289	−	0.613549i	0.0434174	−	0.0544437i	−0.759649	−	0.650334i	$-0.774629\pi$
$127$	0.489289	−	0.613549i	0.0434174	−	0.0544437i	0.803066	+	0.595890i	$0.203201\pi$
$128$	−5.46777	+	9.47045i	−0.483287	+	0.837078i
$129$	0.454502	+	0.787220i	0.0400166	+	0.0693108i
$130$	6.72609	+	1.01380i	0.589917	+	0.0889157i
$131$	8.29978	+	7.70107i	0.725155	+	0.672846i	0.953725	−	0.300682i	$-0.0972142\pi$
$131$	8.29978	+	7.70107i	0.725155	+	0.672846i	−0.228569	+	0.973528i	$0.573405\pi$
$132$	−0.406002	+	0.195520i	−0.0353379	+	0.0170178i
$133$	−15.5599	+	11.8584i	−1.34922	+	1.02825i
$134$	17.5168	+	8.43562i	1.51322	+	0.728727i
$135$	6.60793	+	16.8367i	0.568720	+	1.44907i
$136$	0.369358	+	4.92874i	0.0316722	+	0.422636i
$137$	10.9713	−	3.38418i	0.937337	−	0.289130i	0.211800	−	0.977313i	$-0.432067\pi$
$137$	10.9713	−	3.38418i	0.937337	−	0.289130i	0.725537	+	0.688183i	$0.241591\pi$
$138$	−0.263167	+	3.51172i	−0.0224023	+	0.298938i
$139$	2.00129	+	8.76821i	0.169747	+	0.743710i	0.986099	+	0.166156i	$0.0531355\pi$
$139$	2.00129	+	8.76821i	0.169747	+	0.743710i	−0.816353	+	0.577554i	$0.804007\pi$
$140$	−10.2608	+	5.62693i	−0.867197	+	0.475562i
$141$	0.0251008	−	0.109974i	0.00211387	−	0.00926145i
$142$	0.361482	+	0.111503i	0.0303349	+	0.00935708i
$143$	0.155820	−	0.397024i	0.0130303	−	0.0332008i
$144$	−7.89065	+	7.32146i	−0.657554	+	0.610121i
$145$	25.9521	−	17.6938i	2.15520	−	1.46939i
$146$	−8.03417			−0.664913
$147$	−6.39711	−	0.281555i	−0.527625	−	0.0232223i
$148$	−7.61491			−0.625942
$149$	6.33764	−	4.32093i	0.519200	−	0.353985i	−0.275193	−	0.961389i	$-0.588742\pi$
$149$	6.33764	−	4.32093i	0.519200	−	0.353985i	0.794393	+	0.607405i	$0.207789\pi$
$150$	−11.5117	+	10.6813i	−0.939929	+	0.872127i
$151$	2.90215	−	7.39457i	0.236174	−	0.601762i	−0.762820	−	0.646611i	$-0.776186\pi$
$151$	2.90215	−	7.39457i	0.236174	−	0.601762i	0.998994	+	0.0448496i	$0.0142809\pi$
$152$	−10.6051	−	3.27123i	−0.860184	−	0.265332i
$153$	−1.58516	+	6.94503i	−0.128152	+	0.561472i
$154$	0.548533	+	1.92784i	0.0442021	+	0.155350i
$155$	−8.86555	−	38.8425i	−0.712098	−	3.11990i
$156$	0.0789565	−	1.05360i	0.00632158	−	0.0843556i
$157$	12.4389	−	3.83689i	0.992732	−	0.306217i	0.244496	−	0.969650i	$-0.421377\pi$
$157$	12.4389	−	3.83689i	0.992732	−	0.306217i	0.748236	+	0.663433i	$0.230901\pi$
$158$	0.134537	+	1.79527i	0.0107032	+	0.142824i
$159$	2.20739	+	5.62434i	0.175058	+	0.446039i
$160$	−20.1380	−	9.69797i	−1.59205	−	0.766692i
$161$	5.56109	+	1.39863i	0.438276	+	0.110227i
$162$	−3.47139	+	1.67173i	−0.272738	+	0.131344i
$163$	−8.39720	−	7.79146i	−0.657719	−	0.610274i	0.279027	−	0.960283i	$-0.409988\pi$
$163$	−8.39720	−	7.79146i	−0.657719	−	0.610274i	−0.936746	+	0.350009i	$0.886179\pi$
$164$	−12.0288	−	1.81306i	−0.939294	−	0.141576i
$165$	0.747037	+	1.29391i	0.0581567	+	0.100730i
$166$	9.83529	−	17.0352i	0.763366	−	1.32219i
$167$	6.11365	−	7.66627i	0.473088	−	0.593234i	−0.486836	−	0.873493i	$-0.661849\pi$
$167$	6.11365	−	7.66627i	0.473088	−	0.593234i	0.959924	+	0.280259i	$0.0904205\pi$
$168$	−1.97977	−	3.04559i	−0.152742	−	0.234972i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	−22.1495	+	3.33850i	−1.69879	+	0.256051i
$171$	−13.2161	−	9.01060i	−1.01066	−	0.689058i
$172$	−0.948312	−	0.646548i	−0.0723081	−	0.0492988i
$173$	5.94456	−	0.895998i	0.451956	−	0.0681215i	0.0808801	−	0.996724i	$-0.474227\pi$
$173$	5.94456	−	0.895998i	0.451956	−	0.0681215i	0.371076	+	0.928602i	$0.378989\pi$
$174$	−8.30926	−	10.4195i	−0.629923	−	0.789899i
$175$	13.9366	+	21.4394i	1.05351	+	1.62067i
$176$	−1.32322	+	1.65927i	−0.0997416	+	0.125072i
$177$	3.43162	−	5.94373i	0.257936	−	0.446758i
$178$	6.98384	+	12.0964i	0.523461	+	0.906661i
$179$	−3.76702	−	0.567787i	−0.281560	−	0.0424384i	0.00674385	−	0.999977i	$-0.497853\pi$
$179$	−3.76702	−	0.567787i	−0.281560	−	0.0424384i	−0.288304	+	0.957539i	$0.593091\pi$
$180$	−7.01393	−	6.50798i	−0.522788	−	0.485076i
$181$	22.3647	−	10.7703i	1.66235	−	0.800547i	0.663737	−	0.747966i	$-0.268969\pi$
$181$	22.3647	−	10.7703i	1.66235	−	0.800547i	0.998617	−	0.0525813i	$-0.0167449\pi$
$182$	−4.55755	−	1.14623i	−0.337828	−	0.0849643i
$183$	7.41465	+	3.57071i	0.548107	+	0.263954i
$184$	1.18845	+	3.02811i	0.0876134	+	0.223235i
$185$	1.88675	+	25.1769i	0.138717	+	1.85104i
$186$	−16.1534	+	4.98267i	−1.18443	+	0.365347i
$187$	−0.104960	+	1.40059i	−0.00767541	+	0.102421i
$188$	0.0316933	+	0.138857i	0.00231147	+	0.0101272i
$189$	−3.41982	−	12.0191i	−0.248755	−	0.874259i
$190$	11.1920	−	49.0356i	0.811957	−	3.55741i
$191$	−3.82331	−	1.17934i	−0.276645	−	0.0853337i	0.153328	−	0.988175i	$-0.451001\pi$
$191$	−3.82331	−	1.17934i	−0.276645	−	0.0853337i	−0.429973	+	0.902842i	$0.641477\pi$
$192$	−0.138829	+	0.353731i	−0.0100191	+	0.0255283i
$193$	−19.3697	+	17.9725i	−1.39426	+	1.29369i	−0.486828	+	0.873498i	$0.661846\pi$
$193$	−19.3697	+	17.9725i	−1.39426	+	1.29369i	−0.907436	+	0.420190i	$0.861963\pi$
$194$	−17.5907	+	11.9932i	−1.26294	+	0.861058i
$195$	−3.50305			−0.250859
$196$	7.43161	−	3.18430i	0.530829	−	0.227450i
$197$	−2.93745			−0.209284			−0.104642	−	0.994510i	$-0.533370\pi$
$197$	−2.93745			−0.209284			−0.104642	+	0.994510i	$0.533370\pi$
$198$	−1.35404	+	0.923170i	−0.0962276	+	0.0656068i
$199$	2.11645	−	1.96378i	0.150031	−	0.139209i	−0.601586	−	0.798808i	$-0.705464\pi$
$199$	2.11645	−	1.96378i	0.150031	−	0.139209i	0.751618	+	0.659599i	$0.229274\pi$
$200$	−5.29967	+	13.5033i	−0.374743	+	0.954831i
$201$	−9.56782	−	2.95128i	−0.674862	−	0.208167i
$202$	0.131593	−	0.576547i	0.00925885	−	0.0405657i
$203$	−19.0275	+	10.4345i	−1.33547	+	0.732358i
$204$	0.774220	+	3.39208i	0.0542062	+	0.237493i
$205$	−3.01405	+	40.2198i	−0.210511	+	2.80907i
$206$	14.9434	−	4.60941i	1.04115	−	0.321153i
$207$	0.350369	+	4.67535i	0.0243523	+	0.324959i
$208$	−1.81793	−	4.63200i	−0.126051	−	0.321171i
$209$	−2.84141	−	1.36835i	−0.196544	−	0.0946507i
$210$	13.0935	−	9.97868i	0.903538	−	0.688594i
$211$	9.25907	−	4.45893i	0.637420	−	0.306965i	−0.0871200	−	0.996198i	$-0.527766\pi$
$211$	9.25907	−	4.45893i	0.637420	−	0.306965i	0.724540	+	0.689232i	$0.242052\pi$
$212$	−5.59237	−	5.18896i	−0.384086	−	0.356379i
$213$	−0.192642	−	0.0290361i	−0.0131996	−	0.00198952i
$214$	−9.92743	−	17.1948i	−0.678625	−	1.17541i
$215$	−1.90270	+	3.29557i	−0.129763	+	0.224756i
$216$	4.41985	−	5.54231i	0.300732	−	0.377107i
$217$	3.50300	+	27.3022i	0.237799	+	1.85339i
$218$	12.8313	+	16.0900i	0.869046	+	1.08975i
$219$	4.09137	−	0.616675i	0.276469	−	0.0416710i
$220$	−1.55868	−	1.06269i	−0.105086	−	0.0716467i
$221$	−2.72086	−	1.85505i	−0.183025	−	0.124784i
$222$	10.5927	−	1.59659i	0.710936	−	0.107156i
$223$	−8.66239	−	10.8623i	−0.580076	−	0.727393i	0.402050	−	0.915618i	$-0.368298\pi$
$223$	−8.66239	−	10.8623i	−0.580076	−	0.727393i	−0.982126	+	0.188225i	$0.939727\pi$
$224$	13.2005	+	8.01345i	0.881998	+	0.535421i
$225$	−13.0355	+	16.3461i	−0.869036	+	1.08974i
$226$	2.28192	−	3.95241i	0.151791	−	0.262910i
$227$	5.77905	+	10.0096i	0.383569	+	0.664361i	0.991570	−	0.129575i	$-0.0413614\pi$
$227$	5.77905	+	10.0096i	0.383569	+	0.664361i	−0.608000	+	0.793937i	$0.708028\pi$
$228$	−7.72525	−	1.16439i	−0.511617	−	0.0771139i
$229$	3.79415	+	3.52046i	0.250725	+	0.232638i	0.795515	−	0.605934i	$-0.207200\pi$
$229$	3.79415	+	3.52046i	0.250725	+	0.232638i	−0.544791	+	0.838572i	$0.683391\pi$
$230$	−13.2825	+	6.39652i	−0.875823	+	0.421774i
$231$	−0.427312	−	0.939640i	−0.0281151	−	0.0618238i
$232$	−11.0914	−	5.34135i	−0.728188	−	0.350677i
$233$	−3.97674	−	10.1326i	−0.260525	−	0.663806i	0.739431	−	0.673232i	$-0.235095\pi$
$233$	−3.97674	−	10.1326i	−0.260525	−	0.663806i	−0.999956	+	0.00942649i	$0.996999\pi$
$234$	−0.287142	−	3.83164i	−0.0187710	−	0.250482i
$235$	0.451247	−	0.139191i	0.0294361	−	0.00907983i
$236$	−0.647596	+	8.64157i	−0.0421549	+	0.562519i
$237$	−0.206311	−	0.903908i	−0.0134013	−	0.0587151i
$238$	15.4541	−	0.816855i	1.00174	−	0.0529489i
$239$	4.38075	−	19.1933i	0.283367	−	1.24151i	−0.610078	−	0.792341i	$-0.708862\pi$
$239$	4.38075	−	19.1933i	0.283367	−	1.24151i	0.893445	−	0.449172i	$-0.148281\pi$
$240$	16.6567	+	5.13790i	1.07518	+	0.331650i
$241$	−5.39291	+	13.7409i	−0.347388	+	0.885130i	0.645245	+	0.763975i	$0.276755\pi$
$241$	−5.39291	+	13.7409i	−0.347388	+	0.885130i	−0.992634	+	0.121155i	$0.961340\pi$
$242$	14.0859	−	13.0698i	0.905479	−	0.840161i
$243$	13.3467	−	9.09962i	0.856190	−	0.583741i
$244$	−10.3911			−0.665222
$245$	−12.3695	−	23.7819i	−0.790256	−	1.51937i
$246$	17.1128			1.09107
$247$	6.10947	−	4.16537i	0.388736	−	0.265036i
$248$	−11.4467	+	10.6210i	−0.726866	+	0.674433i
$249$	−3.70102	+	9.43004i	−0.234542	+	0.597604i
$250$	−30.3215	−	9.35295i	−1.91770	−	0.591533i
$251$	−5.19929	+	22.7796i	−0.328176	+	1.43784i	0.494427	+	0.869219i	$0.335378\pi$
$251$	−5.19929	+	22.7796i	−0.328176	+	1.43784i	−0.822603	+	0.568616i	$0.807479\pi$
$252$	4.38865	+	4.94356i	0.276459	+	0.311415i
$253$	0.205696	+	0.901214i	0.0129320	+	0.0566588i
$254$	0.104168	−	1.39002i	0.00653605	−	0.0872176i
$255$	11.0233	−	3.40023i	0.690305	−	0.212931i
$256$	1.51365	+	20.1983i	0.0946032	+	1.26239i
$257$	4.06048	+	10.3459i	0.253286	+	0.645361i	0.999800	−	0.0200084i	$-0.00636930\pi$
$257$	4.06048	+	10.3459i	0.253286	+	0.645361i	−0.746514	+	0.665369i	$0.768274\pi$
$258$	1.45471	+	0.700550i	0.0905661	+	0.0436143i
$259$	0.383585	−	17.4390i	0.0238348	−	1.08361i
$260$	3.98507	−	1.91911i	0.247144	−	0.119018i
$261$	−13.0065	−	12.0683i	−0.805084	−	0.747009i
$262$	19.8863	+	2.99738i	1.22858	+	0.185179i
$263$	−12.2699	−	21.2521i	−0.756595	−	1.31046i	−0.944578	−	0.328288i	$-0.893528\pi$
$263$	−12.2699	−	21.2521i	−0.756595	−	1.31046i	0.187983	−	0.982172i	$-0.439805\pi$
$264$	0.292788	−	0.507123i	0.0180198	−	0.0312113i
$265$	−15.7705	+	19.7755i	−0.968772	+	1.21480i
$266$	−10.9703	+	32.9723i	−0.672632	+	2.02166i
$267$	−4.48497	−	5.62397i	−0.274475	−	0.344181i
$268$	12.5012	−	1.88425i	0.763632	−	0.115099i
$269$	22.4895	+	15.3331i	1.37121	+	0.934876i	0.999980	+	0.00633636i	$0.00201694\pi$
$269$	22.4895	+	15.3331i	1.37121	+	0.934876i	0.371232	+	0.928540i	$0.378935\pi$
$270$	26.5444	+	18.0977i	1.61544	+	1.10139i
$271$	30.2806	−	4.56407i	1.83942	−	0.277248i	0.864964	−	0.501834i	$-0.167341\pi$
$271$	30.2806	−	4.56407i	1.83942	−	0.277248i	0.974454	+	0.224586i	$0.0721031\pi$
$272$	10.2166	+	12.8113i	0.619475	+	0.776797i
$273$	2.40889	+	0.233893i	0.145793	+	0.0141558i
$274$	12.7152	−	15.9443i	0.768152	−	0.963232i
$275$	−2.06108	+	3.56990i	−0.124288	+	0.215273i
$276$	1.14496	+	1.98314i	0.0689188	+	0.119371i
$277$	26.6750	+	4.02061i	1.60275	+	0.241575i	0.888689	−	0.458511i	$-0.151617\pi$
$277$	26.6750	+	4.02061i	1.60275	+	0.241575i	0.714059	+	0.700086i	$0.246855\pi$
$278$	11.7105	+	10.8657i	0.702346	+	0.651682i
$279$	−20.2770	+	9.76491i	−1.21395	+	0.584610i
$280$	6.89772	−	13.5525i	0.412217	−	0.809919i
$281$	−6.67879	−	3.21634i	−0.398423	−	0.191871i	0.223933	−	0.974605i	$-0.428110\pi$
$281$	−6.67879	−	3.21634i	−0.398423	−	0.191871i	−0.622356	+	0.782734i	$0.713825\pi$
$282$	−0.0732007	−	0.186512i	−0.00435904	−	0.0111066i
$283$	0.912456	+	12.1759i	0.0542399	+	0.723781i	0.956340	+	0.292255i	$0.0944055\pi$
$283$	0.912456	+	12.1759i	0.0542399	+	0.723781i	−0.902101	+	0.431526i	$0.857975\pi$
$284$	0.235057	−	0.0725054i	0.0139481	−	0.00430241i
$285$	−1.93571	+	25.8302i	−0.114661	+	1.53005i
$286$	−0.168576	−	0.738582i	−0.00996814	−	0.0436733i
$287$	4.75804	−	27.4561i	0.280858	−	1.62068i
$288$	−2.80956	+	12.3095i	−0.165555	+	0.725344i
$289$	−5.88221	−	1.81442i	−0.346012	−	0.106731i
$290$	20.3829	−	51.9347i	1.19692	−	3.04971i
$291$	8.03745	−	7.45767i	0.471164	−	0.437176i
$292$	−4.31651	+	2.94294i	−0.252604	+	0.172223i
$293$	12.6189			0.737207			0.368603	−	0.929587i	$-0.379836\pi$
$293$	12.6189			0.737207			0.368603	+	0.929587i	$0.379836\pi$
$294$	−9.67008	+	5.98767i	−0.563971	+	0.349208i
$295$	28.7318			1.67283
$296$	8.17590	−	5.57423i	0.475214	−	0.323996i
$297$	1.47668	−	1.37016i	0.0856858	−	0.0795048i
$298$	4.97761	−	12.6828i	0.288345	−	0.734692i
$299$	−2.07106	−	0.638838i	−0.119773	−	0.0369450i
$300$	−2.27228	+	9.95553i	−0.131190	+	0.574783i
$301$	1.52844	−	2.13918i	0.0880978	−	0.123300i
$302$	−3.13974	−	13.7561i	−0.180672	−	0.791574i
$303$	−0.0227595	+	0.303705i	−0.00130750	+	0.0174474i
$304$	−35.1593	+	10.8452i	−2.01652	+	0.622015i
$305$	2.57461	+	34.3557i	0.147421	+	1.96720i
$306$	4.62275	+	11.7786i	0.264265	+	0.673336i
$307$	−8.32758	−	4.01035i	−0.475280	−	0.228883i	0.180879	−	0.983505i	$-0.442106\pi$
$307$	−8.32758	−	4.01035i	−0.475280	−	0.228883i	−0.656159	+	0.754622i	$0.727820\pi$
$308$	1.00088	+	0.834837i	0.0570306	+	0.0475693i
$309$	−7.25604	+	3.49432i	−0.412782	+	0.198785i
$310$	−51.8764	−	48.1343i	−2.94638	−	2.73384i
$311$	−21.2374	−	3.20102i	−1.20426	−	0.181513i	−0.483907	−	0.875119i	$-0.660783\pi$
$311$	−21.2374	−	3.20102i	−1.20426	−	0.181513i	−0.720354	+	0.693606i	$0.756021\pi$
$312$	0.686479	+	1.18902i	0.0388642	+	0.0673148i
$313$	12.6941	−	21.9867i	0.717510	−	1.24276i	−0.244473	−	0.969656i	$-0.578615\pi$
$313$	12.6941	−	21.9867i	0.717510	−	1.24276i	0.961983	−	0.273108i	$-0.0880516\pi$
$314$	14.4161	−	18.0772i	0.813547	−	1.02016i
$315$	15.2573	−	15.7349i	0.859654	−	0.886561i
$316$	0.729897	+	0.915262i	0.0410599	+	0.0514875i
$317$	−4.57524	+	0.689606i	−0.256971	+	0.0387322i	−0.276264	−	0.961082i	$-0.589096\pi$
$317$	−4.57524	+	0.689606i	−0.256971	+	0.0387322i	0.0192932	+	0.999814i	$0.493858\pi$
$318$	8.86721	+	6.04556i	0.497248	+	0.339018i
$319$	−2.89040	−	1.97064i	−0.161831	−	0.110335i
$320$	−1.57303	+	0.237097i	−0.0879353	+	0.0132541i
$321$	6.37532	+	7.99439i	0.355835	+	0.446204i
$322$	9.56088	−	3.51175i	0.532807	−	0.195702i
$323$	−15.1820	+	19.0376i	−0.844748	+	1.05928i
$324$	−1.25271	+	2.16975i	−0.0695949	+	0.120542i
$325$	−4.83247	−	8.37009i	−0.268057	−	0.464289i
$326$	−20.1197	−	3.03256i	−1.11433	−	0.167958i
$327$	−7.76930	−	7.20886i	−0.429643	−	0.398651i
$328$	14.2422	−	6.85867i	0.786392	−	0.378707i
$329$	−0.319596	+	0.0655867i	−0.0176199	+	0.00361591i
$330$	2.39101	+	1.15145i	0.131621	+	0.0633853i
$331$	5.36176	+	13.6615i	0.294709	+	0.750906i	0.999153	+	0.0411465i	$0.0131010\pi$
$331$	5.36176	+	13.6615i	0.294709	+	0.750906i	−0.704444	+	0.709759i	$0.748804\pi$
$332$	−0.955869	−	12.7552i	−0.0524601	−	0.700032i
$333$	13.6283	−	4.20378i	0.746828	−	0.230366i
$334$	1.30157	−	17.3682i	0.0712187	−	0.950347i
$335$	−9.32727	−	40.8654i	−0.509603	−	2.23272i
$336$	−11.1110	−	4.64524i	−0.606155	−	0.253419i
$337$	−1.23025	+	5.39006i	−0.0670158	+	0.293616i	−0.997319	−	0.0731758i	$-0.976687\pi$
$337$	−1.23025	+	5.39006i	−0.0670158	+	0.293616i	0.930303	+	0.366791i	$0.119544\pi$
$338$	1.69732	+	0.523555i	0.0923222	+	0.0284776i
$339$	−0.858688	+	2.18790i	−0.0466375	+	0.118830i
$340$	−10.6773	+	9.90711i	−0.579059	+	0.537288i
$341$	−3.66628	+	2.49963i	−0.198540	+	0.135362i
$342$	−28.4118			−1.53633
$343$	6.91806	+	17.1797i	0.373540	+	0.927614i
$344$	1.49146			0.0804139
$345$	6.27309	−	4.27692i	0.337732	−	0.230262i
$346$	7.82768	−	7.26302i	0.420818	−	0.390462i
$347$	11.0322	−	28.1097i	0.592242	−	1.50901i	−0.249086	−	0.968481i	$-0.580130\pi$
$347$	11.0322	−	28.1097i	0.592242	−	1.50901i	0.841327	−	0.540526i	$-0.181775\pi$
$348$	−8.28099	−	2.55435i	−0.443908	−	0.136927i
$349$	−6.23259	+	27.3068i	−0.333623	+	1.46170i	0.478436	+	0.878122i	$0.341204\pi$
$349$	−6.23259	+	27.3068i	−0.333623	+	1.46170i	−0.812059	+	0.583575i	$0.801653\pi$
$350$	41.9053	+	17.5196i	2.23993	+	0.936463i
$351$	1.05099	+	4.60468i	0.0560975	+	0.245779i
$352$	−0.186032	+	2.48243i	−0.00991556	+	0.132314i
$353$	−16.2489	+	5.01211i	−0.864840	+	0.266768i	−0.695268	−	0.718750i	$-0.744714\pi$
$353$	−16.2489	+	5.01211i	−0.864840	+	0.266768i	−0.169571	+	0.985518i	$0.554238\pi$
$354$	−0.911013	−	12.1566i	−0.0484198	−	0.646117i
$355$	−0.297962	−	0.759196i	−0.0158142	−	0.0402939i
$356$	8.18314	+	3.94079i	0.433705	+	0.208862i
$357$	−7.80726	+	1.60219i	−0.413204	+	0.0847966i
$358$	−6.09658	+	2.93596i	−0.322214	+	0.155170i
$359$	−15.8094	−	14.6690i	−0.834389	−	0.774200i	0.142081	−	0.989855i	$-0.454621\pi$
$359$	−15.8094	−	14.6690i	−0.834389	−	0.774200i	−0.976470	+	0.215655i	$0.930811\pi$
$360$	12.2946	+	1.85311i	0.647981	+	0.0976675i
$361$	−17.8380	−	30.8962i	−0.938840	−	1.62612i
$362$	22.0457	−	38.1842i	1.15870	−	2.00692i
$363$	−6.17001	+	7.73695i	−0.323842	+	0.406085i
$364$	−2.86850	+	1.05361i	−0.150350	+	0.0552242i
$365$	10.7997	+	13.5423i	0.565280	+	0.708839i
$366$	14.4545	−	2.17867i	0.755549	−	0.113881i
$367$	17.4896	+	11.9242i	0.912949	+	0.622438i	0.926019	−	0.377476i	$-0.123208\pi$
$367$	17.4896	+	11.9242i	0.912949	+	0.622438i	−0.0130701	+	0.999915i	$0.504160\pi$
$368$	8.91073	+	6.07523i	0.464504	+	0.316693i
$369$	22.5288	−	3.39567i	1.17280	−	0.176771i
$370$	27.9607	+	35.0617i	1.45361	+	1.82277i
$371$	12.1650	−	12.5458i	0.631577	−	0.651345i
$372$	−6.85356	+	8.59409i	−0.355340	+	0.445583i
$373$	−1.78326	+	3.08870i	−0.0923339	+	0.159927i	−0.908493	−	0.417901i	$-0.862766\pi$
$373$	−1.78326	+	3.08870i	−0.0923339	+	0.159927i	0.816159	+	0.577828i	$0.196099\pi$
$374$	1.24738	+	2.16052i	0.0645002	+	0.111718i
$375$	16.1590	+	2.43558i	0.834448	+	0.125773i
$376$	−0.135674	−	0.125887i	−0.00699684	−	0.00649212i
$377$	7.38986	−	3.55877i	0.380597	−	0.183286i
$378$	−17.0451	−	14.2173i	−0.876703	−	0.731258i
$379$	−12.9971	−	6.25907i	−0.667616	−	0.321507i	0.0691978	−	0.997603i	$-0.477956\pi$
$379$	−12.9971	−	6.25907i	−0.667616	−	0.321507i	−0.736813	+	0.676096i	$0.763670\pi$
$380$	−11.9488	−	30.4450i	−0.612959	−	1.56179i
$381$	0.0536461	+	0.715857i	0.00274837	+	0.0366745i
$382$	−6.79110	+	2.09478i	−0.347463	+	0.107178i
$383$	−1.48013	+	19.7509i	−0.0756309	+	1.00922i	0.822290	+	0.569068i	$0.192696\pi$
$383$	−1.48013	+	19.7509i	−0.0756309	+	1.00922i	−0.897921	+	0.440156i	$0.854923\pi$
$384$	−2.22596	−	9.75256i	−0.113593	−	0.497683i
$385$	2.51220	−	3.51604i	0.128034	−	0.179194i
$386$	−10.4438	+	45.7575i	−0.531578	+	2.32899i
$387$	2.05411	+	0.633609i	0.104416	+	0.0322081i
$388$	−5.05781	+	12.8871i	−0.256771	+	0.654243i
$389$	−6.19137	+	5.74475i	−0.313915	+	0.291270i	−0.821356	−	0.570416i	$-0.806782\pi$
$389$	−6.19137	+	5.74475i	−0.313915	+	0.291270i	0.507441	+	0.861686i	$0.330591\pi$
$390$	−5.14106	+	3.50511i	−0.260327	+	0.177488i
$391$	7.13724			0.360946
$392$	−5.64814	+	8.85893i	−0.285274	+	0.447443i
$393$	−10.3571			−0.522446
$394$	−4.31098	+	2.93918i	−0.217184	+	0.148074i
$395$	2.84525	−	2.64001i	0.143160	−	0.132833i
$396$	−0.389324	+	0.991981i	−0.0195643	+	0.0498489i
$397$	−22.9460	−	7.07789i	−1.15162	−	0.355229i	−0.340581	−	0.940215i	$-0.610624\pi$
$397$	−22.9460	−	7.07789i	−1.15162	−	0.355229i	−0.811043	+	0.584986i	$0.801100\pi$
$398$	1.14116	−	4.99973i	0.0572009	−	0.250614i
$399$	3.05574	−	17.6331i	0.152978	−	0.882757i
$400$	10.7016	+	46.8867i	0.535079	+	2.34434i
$401$	1.52849	−	20.3962i	0.0763289	−	1.01854i	−0.819192	−	0.573519i	$-0.805578\pi$
$401$	1.52849	−	20.3962i	0.0763289	−	1.01854i	0.895521	−	0.445019i	$-0.146803\pi$
$402$	−16.9947	+	5.24217i	−0.847619	+	0.261456i
$403$	−0.777481	−	10.3748i	−0.0387291	−	0.516804i
$404$	−0.140490	−	0.357963i	−0.00698965	−	0.0178093i
$405$	7.48417	+	3.60419i	0.371891	+	0.179093i
$406$	−17.4840	+	34.3523i	−0.867716	+	1.70488i
$407$	2.53346	−	1.22005i	0.125579	−	0.0604756i
$408$	−3.31431	−	3.07523i	−0.164083	−	0.152247i
$409$	−33.3809	−	5.03136i	−1.65058	−	0.248785i	−0.743190	−	0.669080i	$-0.766688\pi$
$409$	−33.3809	−	5.03136i	−1.65058	−	0.248785i	−0.907387	+	0.420296i	$0.861926\pi$
$410$	35.8200	+	62.0421i	1.76903	+	3.06404i
$411$	−5.25132	+	9.09555i	−0.259028	+	0.448650i
$412$	6.34015	−	7.95030i	0.312357	−	0.391683i
$413$	−19.7576	−	1.91837i	−0.972208	−	0.0943969i
$414$	5.19230	+	6.51094i	0.255188	+	0.319995i
$415$	−41.9352	+	6.32072i	−2.05852	+	0.310272i
$416$	−4.82251	−	3.28793i	−0.236443	−	0.161204i
$417$	−6.79751	−	4.63447i	−0.332876	−	0.226951i
$418$	−5.53919	+	0.834898i	−0.270931	+	0.0408362i
$419$	−4.71961	−	5.91820i	−0.230568	−	0.289123i	0.653066	−	0.757301i	$-0.273482\pi$
$419$	−4.71961	−	5.91820i	−0.230568	−	0.289123i	−0.883634	+	0.468177i	$0.844911\pi$
$420$	3.37950	−	10.1574i	0.164903	−	0.495632i
$421$	−7.77814	+	9.75348i	−0.379084	+	0.475356i	−0.934370	−	0.356303i	$-0.884037\pi$
$421$	−7.77814	+	9.75348i	−0.379084	+	0.475356i	0.555287	+	0.831659i	$0.312608\pi$
$422$	9.12700	−	15.8084i	0.444295	−	0.769542i
$423$	−0.133377	−	0.231015i	−0.00648500	−	0.0112324i
$424$	9.80275	+	1.47753i	0.476064	+	0.0717551i
$425$	23.3311	+	21.6481i	1.13172	+	1.05009i
$426$	−0.311773	+	0.150142i	−0.0151055	+	0.00727441i
$427$	0.523429	−	23.7968i	0.0253305	−	1.15161i
$428$	−11.6322	−	5.60178i	−0.562264	−	0.270772i
$429$	0.142538	+	0.363180i	0.00688179	+	0.0175345i
$430$	0.505121	+	6.74037i	0.0243591	+	0.325050i
$431$	19.5439	−	6.02848i	0.941395	−	0.290382i	0.214182	−	0.976794i	$-0.431291\pi$
$431$	19.5439	−	6.02848i	0.941395	−	0.290382i	0.727213	+	0.686412i	$0.240815\pi$
$432$	1.75631	−	23.4363i	0.0845003	−	1.12758i
$433$	8.06963	+	35.3554i	0.387802	+	1.69907i	0.672204	+	0.740366i	$0.265348\pi$
$433$	8.06963	+	35.3554i	0.387802	+	1.69907i	−0.284403	+	0.958705i	$0.591795\pi$
$434$	32.4593	+	36.5635i	1.55809	+	1.75510i
$435$	−6.39357	+	28.0121i	−0.306548	+	1.34308i
$436$	12.7877	+	3.94447i	0.612418	+	0.188906i
$437$	−5.85499	+	14.9183i	−0.280082	+	0.713638i
$438$	5.38743	−	4.99881i	0.257421	−	0.238852i
$439$	28.4706	−	19.4109i	1.35883	−	0.926431i	0.358850	−	0.933395i	$-0.383169\pi$
$439$	28.4706	−	19.4109i	1.35883	−	0.926431i	0.999976	+	0.00696389i	$0.00221669\pi$
$440$	2.45142			0.116867
$441$	−11.5424	+	9.80149i	−0.549638	+	0.466738i
$442$	−5.84927			−0.278221
$443$	−0.455687	+	0.310682i	−0.0216504	+	0.0147610i	−0.574097	−	0.818787i	$-0.694647\pi$
$443$	−0.455687	+	0.310682i	−0.0216504	+	0.0147610i	0.552447	+	0.833548i	$0.313694\pi$
$444$	5.10629	−	4.73795i	0.242334	−	0.224853i
$445$	11.0018	−	28.0320i	0.521534	−	1.32885i
$446$	−23.5816	−	7.27395i	−1.11662	−	0.344431i
$447$	−1.56135	+	6.84070i	−0.0738491	+	0.323554i
$448$	1.09754	−	0.0580122i	0.0518537	−	0.00274082i
$449$	−1.41961	−	6.21971i	−0.0669955	−	0.293526i	0.930320	−	0.366748i	$-0.119529\pi$
$449$	−1.41961	−	6.21971i	−0.0669955	−	0.293526i	−0.997316	+	0.0732219i	$0.976672\pi$
$450$	−2.77521	+	37.0326i	−0.130825	+	1.74573i
$451$	4.29244	−	1.32404i	0.202123	−	0.0623468i
$452$	−0.221775	−	2.95938i	−0.0104314	−	0.139198i
$453$	2.65477	+	6.76424i	0.124732	+	0.317812i
$454$	18.4968	+	8.90760i	0.868099	+	0.418054i
$455$	4.19425	+	9.22296i	0.196629	+	0.432379i
$456$	9.14671	−	4.40482i	0.428334	−	0.206275i
$457$	−4.33391	−	4.02128i	−0.202732	−	0.188107i	0.572273	−	0.820063i	$-0.306062\pi$
$457$	−4.33391	−	4.02128i	−0.202732	−	0.188107i	−0.775004	+	0.631956i	$0.782252\pi$
$458$	9.09081	+	1.37022i	0.424785	+	0.0640261i
$459$	−7.77674	−	13.4697i	−0.362987	−	0.628712i
$460$	−4.79321	+	8.30208i	−0.223484	+	0.387086i
$461$	5.41133	−	6.78559i	0.252031	−	0.316036i	−0.639681	−	0.768641i	$-0.720934\pi$
$461$	5.41133	−	6.78559i	0.252031	−	0.316036i	0.891712	+	0.452604i	$0.149505\pi$
$462$	−1.56731	−	0.951447i	−0.0729181	−	0.0442653i
$463$	7.09912	+	8.90201i	0.329924	+	0.413711i	0.918932	−	0.394415i	$-0.129053\pi$
$463$	7.09912	+	8.90201i	0.329924	+	0.413711i	−0.589008	+	0.808127i	$0.700481\pi$
$464$	−40.3577	+	6.08294i	−1.87356	+	0.282393i
$465$	30.1125	+	20.5303i	1.39643	+	0.952071i
$466$	−15.9748	−	10.8914i	−0.740016	−	0.504535i
$467$	18.4760	−	2.78481i	0.854966	−	0.128865i	0.293088	−	0.956085i	$-0.405317\pi$
$467$	18.4760	−	2.78481i	0.854966	−	0.128865i	0.561878	+	0.827220i	$0.310079\pi$
$468$	−1.55782	−	1.95344i	−0.0720101	−	0.0902978i
$469$	3.68544	+	28.7241i	0.170178	+	1.32636i
$470$	0.522974	−	0.655789i	0.0241230	−	0.0302493i
$471$	−5.95380	+	10.3123i	−0.274336	+	0.475165i
$472$	−5.63046	−	9.75224i	−0.259163	−	0.448883i
$473$	0.419090	+	0.0631676i	0.0192698	+	0.00290445i
$474$	−1.20722	−	1.12014i	−0.0554495	−	0.0514496i
$475$	−64.3883	+	31.0078i	−2.95434	+	1.42274i
$476$	8.00380	−	6.09977i	0.366854	−	0.279583i
$477$	12.8732	+	6.19938i	0.589421	+	0.283850i
$478$	−12.7755	−	32.5514i	−0.584336	−	1.48886i
$479$	−1.58175	−	21.1069i	−0.0722718	−	0.964400i	−0.909004	−	0.416788i	$-0.863156\pi$
$479$	−1.58175	−	21.1069i	−0.0722718	−	0.964400i	0.836732	−	0.547612i	$-0.184463\pi$
$480$	19.5379	−	6.02664i	0.891778	−	0.275077i
$481$	−0.492690	+	6.57450i	−0.0224647	+	0.299771i
$482$	5.83440	+	25.5622i	0.265750	+	1.16433i
$483$	−4.59929	+	2.52221i	−0.209275	+	0.114764i
$484$	2.78040	−	12.1817i	0.126382	−	0.553716i
$485$	43.8613	+	13.5294i	1.99164	+	0.614340i
$486$	10.4825	−	26.7091i	0.475498	−	1.21155i
$487$	5.17642	−	4.80301i	0.234566	−	0.217645i	−0.554128	−	0.832432i	$-0.686948\pi$
$487$	5.17642	−	4.80301i	0.234566	−	0.217645i	0.788694	+	0.614786i	$0.210758\pi$
$488$	11.1566	−	7.60644i	0.505035	−	0.344327i
$489$	10.4787			0.473861
$490$	−41.9493	−	22.5254i	−1.89507	−	1.01760i
$491$	9.14179			0.412563			0.206281	−	0.978493i	$-0.433864\pi$
$491$	9.14179			0.412563			0.206281	+	0.978493i	$0.433864\pi$
$492$	9.19418	−	6.26849i	0.414506	−	0.282605i
$493$	−19.7999	+	18.3716i	−0.891741	+	0.827414i
$494$	4.79841	−	12.2261i	0.215890	−	0.550080i
$495$	3.37621	+	1.04142i	0.151750	+	0.0468085i
$496$	−11.5198	+	50.4713i	−0.517252	+	2.26623i
$497$	0.154205	+	0.541960i	0.00691706	+	0.0243102i
$498$	4.00400	+	17.5427i	0.179423	+	0.786106i
$499$	1.74810	−	23.3267i	0.0782556	−	1.04425i	−0.810461	−	0.585792i	$-0.800784\pi$
$499$	1.74810	−	23.3267i	0.0782556	−	1.04425i	0.888717	−	0.458456i	$-0.151597\pi$
$500$	−19.7168	+	6.08184i	−0.881763	+	0.271988i
$501$	0.670305	+	8.94460i	0.0299470	+	0.399615i
$502$	15.1626	+	38.6336i	0.676738	+	1.72430i
$503$	−15.5705	−	7.49837i	−0.694255	−	0.334336i	0.0532597	−	0.998581i	$-0.483039\pi$
$503$	−15.5705	−	7.49837i	−0.694255	−	0.334336i	−0.747515	+	0.664245i	$0.768753\pi$
$504$	−8.33071	−	2.09519i	−0.371080	−	0.0933272i
$505$	−1.14871	+	0.553191i	−0.0511170	+	0.0246167i
$506$	1.20362	+	1.11680i	0.0535076	+	0.0496478i
$507$	−0.904541	−	0.136338i	−0.0401721	−	0.00605496i
$508$	−0.453203	−	0.784971i	−0.0201076	−	0.0348274i
$509$	−4.50033	+	7.79480i	−0.199474	+	0.345498i	−0.948358	−	0.317202i	$-0.897257\pi$
$509$	−4.50033	+	7.79480i	−0.199474	+	0.345498i	0.748884	+	0.662701i	$0.230590\pi$
$510$	12.7755	−	16.0199i	0.565708	−	0.709375i
$511$	−6.52225	−	10.0335i	−0.288527	−	0.443858i
$512$	8.79520	+	11.0288i	0.388696	+	0.487410i
$513$	34.5340	−	5.20516i	1.52471	−	0.229813i
$514$	16.3111	+	11.1208i	0.719454	+	0.490515i
$515$	−27.8567	−	18.9924i	−1.22751	−	0.836904i
$516$	1.03818	−	0.156481i	0.0457034	−	0.00688869i
$517$	−0.0327918	−	0.0411196i	−0.00144218	−	0.00180844i
$518$	−16.8864	−	25.9772i	−0.741944	−	1.14137i
$519$	−3.42873	+	4.29949i	−0.150504	+	0.188727i
$520$	−2.87383	+	4.97762i	−0.126026	+	0.218283i
$521$	−9.35743	−	16.2075i	−0.409957	−	0.710066i	0.584928	−	0.811085i	$-0.301123\pi$
$521$	−9.35743	−	16.2075i	−0.409957	−	0.710066i	−0.994884	+	0.101020i	$0.967789\pi$
$522$	−31.1637	−	4.69717i	−1.36400	−	0.205590i
$523$	−19.2522	−	17.8635i	−0.841842	−	0.781115i	0.135945	−	0.990716i	$-0.456593\pi$
$523$	−19.2522	−	17.8635i	−0.841842	−	0.781115i	−0.977787	+	0.209602i	$0.932783\pi$
$524$	11.7822	−	5.67403i	0.514710	−	0.247871i
$525$	−22.6849	−	5.70529i	−0.990049	−	0.248999i
$526$	−39.2719	−	18.9123i	−1.71233	−	0.824617i
$527$	12.5168	+	31.8923i	0.545241	+	1.38925i
$528$	−0.145079	−	1.93595i	−0.00631376	−	0.0842513i
$529$	−17.4894	+	5.39478i	−0.760411	+	0.234556i
$530$	−3.35746	+	44.8022i	−0.145839	+	1.94608i
$531$	−3.61155	−	15.8232i	−0.156728	−	0.686670i
$532$	6.18388	+	21.7335i	0.268105	+	0.942265i
$533$	−2.34361	+	10.2680i	−0.101513	+	0.444758i
$534$	−12.2094	−	3.76610i	−0.528352	−	0.162975i
$535$	−15.6389	+	39.8472i	−0.676127	+	1.72274i
$536$	−12.0429	+	11.1741i	−0.520172	+	0.482649i
$537$	2.87931	−	1.96308i	0.124251	−	0.0847130i
$538$	48.3477			2.08442
$539$	−1.96229	+	2.25009i	−0.0845219	+	0.0969181i
$540$	20.8907			0.898993
$541$	11.8750	−	8.09626i	0.510547	−	0.348085i	−0.280486	−	0.959858i	$-0.590496\pi$
$541$	11.8750	−	8.09626i	0.510547	−	0.348085i	0.791034	+	0.611773i	$0.209543\pi$
$542$	39.8729	−	36.9967i	1.71269	−	1.58914i
$543$	−8.29578	+	21.1373i	−0.356006	+	0.907089i
$544$	18.3667	+	5.66539i	0.787468	+	0.242902i
$545$	9.87307	−	43.2567i	0.422916	−	1.85292i
$546$	3.76931	−	2.06705i	0.161311	−	0.0884617i
$547$	4.21612	+	18.4720i	0.180268	+	0.789808i	0.981501	+	0.191455i	$0.0613206\pi$
$547$	4.21612	+	18.4720i	0.180268	+	0.789808i	−0.801233	+	0.598353i	$0.795822\pi$
$548$	0.991001	−	13.2240i	0.0423335	−	0.564901i
$549$	18.5968	−	5.73636i	0.793694	−	0.244822i
$550$	0.547168	+	7.30146i	0.0233313	+	0.311335i
$551$	−22.1576	−	56.4567i	−0.943946	−	2.40513i
$552$	−2.68100	−	1.29110i	−0.114111	−	0.0549529i
$553$	−2.13282	+	1.62544i	−0.0906968	+	0.0691209i
$554$	43.1711	−	20.7901i	1.83417	−	0.883287i
$555$	−16.9301	−	15.7088i	−0.718643	−	0.666803i
$556$	10.2718	+	1.54823i	0.435622	+	0.0656594i
$557$	1.79991	+	3.11753i	0.0762645	+	0.132094i	0.901635	−	0.432497i	$-0.142367\pi$
$557$	1.79991	+	3.11753i	0.0762645	+	0.132094i	−0.825371	+	0.564591i	$0.809034\pi$
$558$	−19.9878	+	34.6199i	−0.846151	+	1.46558i
$559$	−0.619568	+	0.776913i	−0.0262049	+	0.0328599i
$560$	−6.41599	−	50.0059i	−0.271125	−	2.11314i
$561$	−0.801054	−	1.00449i	−0.0338205	−	0.0424096i
$562$	−13.0200	+	1.96245i	−0.549215	+	0.0827809i
$563$	28.6897	+	19.5603i	1.20913	+	0.824369i	0.988534	−	0.150998i	$-0.0482485\pi$
$563$	28.6897	+	19.5603i	1.20913	+	0.824369i	0.220592	+	0.975366i	$0.429201\pi$
$564$	−0.107649	−	0.0733935i	−0.00453282	−	0.00309042i
$565$	−9.72955	+	1.46649i	−0.409325	+	0.0616959i
$566$	13.5222	+	16.9563i	0.568379	+	0.712724i
$567$	−4.90589	−	2.97814i	−0.206028	−	0.125070i
$568$	−0.199298	+	0.249912i	−0.00836237	+	0.0104861i
$569$	14.6127	−	25.3100i	0.612598	−	1.06105i	−0.378203	−	0.925723i	$-0.623458\pi$
$569$	14.6127	−	25.3100i	0.612598	−	1.06105i	0.990801	−	0.135328i	$-0.0432089\pi$
$570$	23.0046	+	39.8451i	0.963557	+	1.66893i
$571$	−7.46813	−	1.12564i	−0.312532	−	0.0471066i	−0.00909635	−	0.999959i	$-0.502895\pi$
$571$	−7.46813	−	1.12564i	−0.312532	−	0.0471066i	−0.303435	+	0.952852i	$0.598134\pi$
$572$	−0.361116	−	0.335067i	−0.0150990	−	0.0140098i
$573$	3.29755	−	1.58802i	0.137757	−	0.0663404i
$574$	−20.4894	−	45.0553i	−0.855212	−	1.88057i
$575$	18.8729	+	9.08871i	0.787055	+	0.379026i
$576$	0.328303	+	0.836502i	0.0136793	+	0.0348542i
$577$	2.60316	+	34.7368i	0.108371	+	1.44611i	0.740921	+	0.671592i	$0.234389\pi$
$577$	2.60316	+	34.7368i	0.108371	+	1.44611i	−0.632550	+	0.774520i	$0.717992\pi$
$578$	−10.4482	+	3.22284i	−0.434587	+	0.134052i
$579$	1.80630	−	24.1034i	0.0750674	−	1.00170i
$580$	−8.07279	−	35.3692i	−0.335204	−	1.46863i
$581$	29.2590	−	1.54654i	1.21387	−	0.0641611i
$582$	4.33366	−	18.9870i	0.179636	−	0.787037i
$583$	2.69193	+	0.830351i	0.111488	+	0.0343896i
$584$	2.48022	−	6.31950i	0.102632	−	0.261503i
$585$	−6.07261	+	5.63456i	−0.251071	+	0.232960i
$586$	18.5195	−	12.6264i	0.765033	−	0.521591i
$587$	−24.8910			−1.02736			−0.513681	−	0.857982i	$-0.671718\pi$
$587$	−24.8910			−1.02736			−0.513681	+	0.857982i	$0.671718\pi$
$588$	−3.00213	+	6.75917i	−0.123806	+	0.278744i
$589$	−76.9294			−3.16982
$590$	42.1666	−	28.7487i	1.73597	−	1.18357i
$591$	1.96975	−	1.82766i	0.0810246	−	0.0751799i
$592$	11.9855	−	30.5385i	0.492600	−	1.25512i
$593$	−22.0694	−	6.80752i	−0.906283	−	0.279551i	−0.193636	−	0.981074i	$-0.562028\pi$
$593$	−22.0694	−	6.80752i	−0.906283	−	0.279551i	−0.712648	+	0.701522i	$0.752504\pi$
$594$	0.796203	−	3.48839i	0.0326686	−	0.143130i
$595$	−22.1506	−	24.9514i	−0.908085	−	1.02291i
$596$	−1.97142	−	8.63736i	−0.0807526	−	0.353800i
$597$	−0.197367	+	2.63368i	−0.00807770	+	0.107789i
$598$	−3.67870	+	1.13473i	−0.150433	+	0.0464025i
$599$	1.32901	+	17.7345i	0.0543020	+	0.724610i	0.956210	+	0.292682i	$0.0945476\pi$
$599$	1.32901	+	17.7345i	0.0543020	+	0.724610i	−0.901908	+	0.431928i	$0.857833\pi$
$600$	−4.84792	−	12.3523i	−0.197915	−	0.504280i
$601$	−16.3820	−	7.88913i	−0.668234	−	0.321804i	0.0688292	−	0.997628i	$-0.478074\pi$
$601$	−16.3820	−	7.88913i	−0.668234	−	0.321804i	−0.737063	+	0.675824i	$0.763788\pi$
$602$	0.102693	−	4.66878i	0.00418547	−	0.190285i
$603$	−21.3331	+	10.2735i	−0.868750	+	0.418368i
$604$	−6.72579	−	6.24062i	−0.273668	−	0.253927i
$605$	−40.9650	−	6.17448i	−1.66546	−	0.251028i
$606$	0.270482	+	0.468488i	0.0109876	+	0.0190310i
$607$	−0.448655	+	0.777093i	−0.0182103	+	0.0315412i	−0.874987	−	0.484146i	$-0.839130\pi$
$607$	−0.448655	+	0.777093i	−0.0182103	+	0.0315412i	0.856777	+	0.515688i	$0.172464\pi$
$608$	−26.9088	+	33.7426i	−1.09130	+	1.36844i
$609$	6.26689	−	18.8358i	0.253947	−	0.763264i
$610$	38.1544	+	47.8441i	1.54483	+	1.93715i
$611$	0.121936	−	0.0183789i	0.00493300	−	0.000743531i
$612$	6.79819	+	4.63493i	0.274801	+	0.187356i
$613$	−0.144411	−	0.0984580i	−0.00583272	−	0.00397668i	0.560400	−	0.828222i	$-0.310647\pi$
$613$	−0.144411	−	0.0984580i	−0.00583272	−	0.00397668i	−0.566233	+	0.824245i	$0.691600\pi$
$614$	−16.2342	+	2.44692i	−0.655160	+	0.0987495i
$615$	−23.0033	−	28.8453i	−0.927584	−	1.16315i
$616$	−1.68573	−	0.163677i	−0.0679200	−	0.00659473i
$617$	15.4449	−	19.3673i	0.621788	−	0.779697i	−0.366807	−	0.930297i	$-0.619549\pi$
$617$	15.4449	−	19.3673i	0.621788	−	0.779697i	0.988595	+	0.150600i	$0.0481204\pi$
$618$	−7.15254	+	12.3886i	−0.287717	+	0.498341i
$619$	−7.63986	−	13.2326i	−0.307072	−	0.531864i	0.670649	−	0.741775i	$-0.266016\pi$
$619$	−7.63986	−	13.2326i	−0.307072	−	0.531864i	−0.977720	+	0.209911i	$0.932683\pi$
$620$	−45.5033	−	6.85852i	−1.82746	−	0.275445i
$621$	−7.50397	−	6.96266i	−0.301124	−	0.279402i
$622$	−34.3708	+	16.5521i	−1.37814	+	0.663678i
$623$	−9.43708	+	18.5418i	−0.378089	+	0.742863i
$624$	4.10104	+	1.97496i	0.164173	+	0.0790615i
$625$	7.33840	+	18.6980i	0.293536	+	0.747918i
$626$	−3.36997	−	44.9691i	−0.134691	−	1.79733i
$627$	2.75673	−	0.850337i	0.110093	−	0.0339592i
$628$	1.12357	−	14.9930i	0.0448353	−	0.598285i
$629$	−4.83115	−	21.1666i	−0.192631	−	0.843970i
$630$	6.64743	−	38.3588i	0.264840	−	1.52825i
$631$	4.67339	−	20.4755i	0.186045	−	0.815116i	−0.792630	−	0.609702i	$-0.791289\pi$
$631$	4.67339	−	20.4755i	0.186045	−	0.815116i	0.978675	−	0.205413i	$-0.0658539\pi$
$632$	−1.45365	−	0.448392i	−0.0578232	−	0.0178361i
$633$	−3.43449	+	8.75093i	−0.136509	+	0.347818i
$634$	−6.02458	+	5.59000i	−0.239267	+	0.222007i
$635$	−2.48303	+	1.69290i	−0.0985361	+	0.0671808i
$636$	6.97858			0.276719
$637$	−2.26840	−	6.62226i	−0.0898772	−	0.262384i
$638$	−6.21373			−0.246004
$639$	−0.380653	+	0.259524i	−0.0150584	+	0.0102666i
$640$	30.6983	−	28.4839i	1.21346	−	1.12593i
$641$	−18.0773	+	46.0603i	−0.714012	+	1.81927i	−0.159302	+	0.987230i	$0.550924\pi$
$641$	−18.0773	+	46.0603i	−0.714012	+	1.81927i	−0.554710	+	0.832043i	$0.687171\pi$
$642$	17.3555	+	5.35346i	0.684966	+	0.211284i
$643$	6.28596	−	27.5406i	0.247894	−	1.08609i	−0.685734	−	0.727852i	$-0.740519\pi$
$643$	6.28596	−	27.5406i	0.247894	−	1.08609i	0.933628	−	0.358243i	$-0.116624\pi$
$644$	3.85039	−	5.38894i	0.151727	−	0.212354i
$645$	−0.774598	−	3.39374i	−0.0304998	−	0.133628i
$646$	−3.23218	+	43.1304i	−0.127168	+	1.69694i
$647$	−21.1193	+	6.51443i	−0.830284	+	0.256109i	−0.680628	−	0.732629i	$-0.738293\pi$
$647$	−21.1193	+	6.51443i	−0.830284	+	0.256109i	−0.149656	+	0.988738i	$0.547817\pi$
$648$	−0.243299	−	3.24660i	−0.00955768	−	0.127538i
$649$	−1.16909	−	2.97878i	−0.0458907	−	0.116927i
$650$	−15.4671	−	7.44858i	−0.606671	−	0.292157i
$651$	−19.3362	−	16.1284i	−0.757847	−	0.632120i
$652$	−11.9205	+	5.74063i	−0.466844	+	0.224820i
$653$	14.5550	+	13.5050i	0.569580	+	0.528493i	0.911534	−	0.411224i	$-0.134898\pi$
$653$	14.5550	+	13.5050i	0.569580	+	0.528493i	−0.341955	+	0.939716i	$0.611089\pi$
$654$	−18.6153	−	2.80580i	−0.727915	−	0.109716i
$655$	−21.6791	−	37.5494i	−0.847074	−	1.46718i
$656$	26.2037	−	45.3862i	1.02308	−	1.77203i
$657$	6.10057	−	7.64987i	0.238006	−	0.298450i
$658$	−0.403412	+	0.416039i	−0.0157266	+	0.0162189i
$659$	17.6828	+	22.1735i	0.688824	+	0.863758i	0.996134	−	0.0878514i	$-0.0280001\pi$
$659$	17.6828	+	22.1735i	0.688824	+	0.863758i	−0.307309	+	0.951610i	$0.599429\pi$
$660$	1.70640	−	0.257198i	0.0664214	−	0.0100114i
$661$	32.1011	+	21.8862i	1.24859	+	0.851273i	0.993297	−	0.115592i	$-0.0368764\pi$
$661$	32.1011	+	21.8862i	1.24859	+	0.851273i	0.255291	+	0.966864i	$0.417829\pi$
$662$	21.5385	+	14.6847i	0.837116	+	0.570736i
$663$	2.97872	−	0.448969i	0.115684	−	0.0174365i
$664$	10.3633	+	12.9951i	0.402173	+	0.504309i
$665$	70.3244	−	25.8305i	2.72706	−	1.00166i
$666$	15.7946	−	19.8058i	0.612029	−	0.767460i
$667$	−8.88845	+	15.3952i	−0.344162	+	0.596106i
$668$	−5.66275	−	9.80817i	−0.219098	−	0.379490i
$669$	12.5671	+	1.89419i	0.485874	+	0.0732336i
$670$	−54.5782	−	50.6411i	−2.10854	−	1.95644i
$671$	3.45709	−	1.66485i	0.133459	−	0.0642706i
$672$	−13.8377	+	2.83974i	−0.533802	+	0.109545i
$673$	0.727399	+	0.350297i	0.0280392	+	0.0135029i	0.447851	−	0.894108i	$-0.352190\pi$
$673$	0.727399	+	0.350297i	0.0280392	+	0.0135029i	−0.419812	+	0.907611i	$0.637904\pi$
$674$	3.58774	+	9.14140i	0.138194	+	0.352114i
$675$	−3.41131	−	45.5208i	−0.131301	−	1.75210i
$676$	1.10370	−	0.340446i	0.0424499	−	0.0130941i
$677$	−0.181045	+	2.41588i	−0.00695814	+	0.0928499i	−0.999602	−	0.0282241i	$-0.991015\pi$
$677$	−0.181045	+	2.41588i	−0.00695814	+	0.0928499i	0.992643	+	0.121074i	$0.0386338\pi$
$678$	0.928984	+	4.07014i	0.0356774	+	0.156313i
$679$	−29.2582	−	12.2321i	−1.12283	−	0.469426i
$680$	4.21176	−	18.4529i	0.161514	−	0.707637i
$681$	−10.1031	−	3.11641i	−0.387153	−	0.119421i
$682$	−2.87951	+	7.33688i	−0.110262	+	0.280944i
$683$	−0.568958	+	0.527916i	−0.0217706	+	0.0202001i	−0.690983	−	0.722871i	$-0.742822\pi$
$683$	−0.568958	+	0.527916i	−0.0217706	+	0.0202001i	0.669212	+	0.743071i	$0.266632\pi$
$684$	−15.2648	+	10.4073i	−0.583663	+	0.397935i
$685$	−43.9676			−1.67992
$686$	27.3427	+	18.2906i	1.04395	+	0.698340i
$687$	−4.73463			−0.180637
$688$	4.08548	−	2.78543i	0.155757	−	0.106194i
$689$	−4.84183	+	4.49256i	−0.184459	+	0.171153i
$690$	4.92691	−	12.5536i	0.187564	−	0.477906i
$691$	−22.8695	−	7.05430i	−0.869996	−	0.268358i	−0.172555	−	0.985000i	$-0.555202\pi$
$691$	−22.8695	−	7.05430i	−0.869996	−	0.268358i	−0.697442	+	0.716642i	$0.745678\pi$
$692$	1.54509	−	6.76950i	0.0587357	−	0.257338i
$693$	−2.25214	−	0.941566i	−0.0855517	−	0.0357671i
$694$	−11.9354	−	52.2924i	−0.453061	−	1.98499i
$695$	2.57380	−	34.3449i	0.0976297	−	1.30278i
$696$	10.7609	−	3.31929i	0.407890	−	0.125817i
$697$	−2.59186	−	34.5860i	−0.0981737	−	1.31004i
$698$	18.1759	+	46.3115i	0.687969	+	1.75292i
$699$	8.97107	+	4.32024i	0.339317	+	0.163406i
$700$	28.9319	−	5.93733i	1.09352	−	0.224410i
$701$	−34.2488	+	16.4934i	−1.29356	+	0.622946i	−0.948839	−	0.315759i	$-0.897741\pi$
$701$	−34.2488	+	16.4934i	−1.29356	+	0.622946i	−0.344721	+	0.938705i	$0.612027\pi$
$702$	6.14981	+	5.70619i	0.232110	+	0.215366i
$703$	48.2057	+	7.26584i	1.81811	+	0.274036i
$704$	0.0885873	+	0.153438i	0.00333876	+	0.00578290i
$705$	−0.215986	+	0.374099i	−0.00813452	+	0.0140894i
$706$	−18.8317	+	23.6142i	−0.708740	+	0.888731i
$707$	0.826855	−	0.303707i	0.0310971	−	0.0114221i
$708$	−4.94247	−	6.19767i	−0.185750	−	0.232923i
$709$	−10.8907	+	1.64151i	−0.409010	+	0.0616483i	−0.350325	−	0.936628i	$-0.613929\pi$
$709$	−10.8907	+	1.64151i	−0.409010	+	0.0616483i	−0.0586848	+	0.998277i	$0.518691\pi$
$710$	−1.19693	−	0.816054i	−0.0449200	−	0.0306259i
$711$	−1.81156	−	1.23510i	−0.0679386	−	0.0463198i
$712$	−11.6707	+	1.75907i	−0.437378	+	0.0659241i
$713$	14.0590	+	17.6294i	0.526512	+	0.660226i
$714$	−9.85476	+	10.1632i	−0.368805	+	0.380349i
$715$	−1.01835	+	1.27697i	−0.0380840	+	0.0477558i
$716$	−2.20005	+	3.81060i	−0.0822197	+	0.142409i
$717$	9.00438	+	15.5960i	0.336275	+	0.582445i
$718$	−37.8794	−	5.70941i	−1.41365	−	0.213073i
$719$	9.78051	+	9.07499i	0.364751	+	0.338440i	0.841162	−	0.540783i	$-0.181872\pi$
$719$	9.78051	+	9.07499i	0.364751	+	0.338440i	−0.476411	+	0.879223i	$0.658062\pi$
$720$	37.1388	−	17.8851i	1.38408	−	0.666539i
$721$	17.8877	+	14.9202i	0.666174	+	0.555656i
$722$	−57.0933	−	27.4947i	−2.12479	−	1.02325i
$723$	−4.93321	−	12.5696i	−0.183468	−	0.467469i
$724$	−2.14257	−	28.5906i	−0.0796280	−	1.06256i
$725$	−75.7512	+	23.3662i	−2.81333	+	0.867797i
$726$	−1.31357	+	17.5284i	−0.0487511	+	0.650538i
$727$	−8.62671	−	37.7961i	−0.319947	−	1.40178i	−0.837644	−	0.546216i	$-0.816068\pi$
$727$	−8.62671	−	37.7961i	−0.319947	−	1.40178i	0.517697	−	0.855564i	$-0.326789\pi$
$728$	2.30856	−	3.23101i	0.0855608	−	0.119749i
$729$	−1.84004	+	8.06175i	−0.0681497	+	0.298583i
$730$	29.3998	+	9.06865i	1.08814	+	0.335646i
$731$	1.19553	−	3.04615i	0.0442181	−	0.112666i
$732$	6.96790	−	6.46527i	0.257541	−	0.238963i
$733$	4.26072	−	2.90491i	0.157373	−	0.107295i	−0.482073	−	0.876131i	$-0.660116\pi$
$733$	4.26072	−	2.90491i	0.157373	−	0.107295i	0.639446	+	0.768836i	$0.279164\pi$
$734$	37.5988			1.38780
$735$	23.0915	+	8.25111i	0.851741	+	0.304347i
$736$	12.6502			0.466292
$737$	−3.85722	+	2.62981i	−0.142083	+	0.0968703i
$738$	29.6654	−	27.5255i	1.09200	−	1.01323i
$739$	−4.80370	+	12.2396i	−0.176707	+	0.450242i	−0.991596	−	0.129375i	$-0.958703\pi$
$739$	−4.80370	+	12.2396i	−0.176707	+	0.450242i	0.814889	+	0.579618i	$0.196798\pi$
$740$	27.8656	+	8.59541i	1.02436	+	0.315974i
$741$	−1.50513	+	6.59442i	−0.0552925	+	0.242252i
$742$	5.30014	−	30.5843i	0.194574	−	1.12279i
$743$	8.77150	+	38.4305i	0.321795	+	1.40988i	0.834356	+	0.551226i	$0.185840\pi$
$743$	8.77150	+	38.4305i	0.321795	+	1.40988i	−0.512561	+	0.858651i	$0.671303\pi$
$744$	1.06745	−	14.2441i	0.0391346	−	0.522215i
$745$	−28.0690	+	8.65813i	−1.02837	+	0.317209i
$746$	0.473414	+	6.31728i	0.0173329	+	0.231292i
$747$	8.75216	+	22.3001i	0.320225	+	0.815920i
$748$	1.46158	+	0.703860i	0.0534407	+	0.0257357i
$749$	13.4147	−	26.3570i	0.490162	−	0.963062i
$750$	26.1519	−	12.5941i	0.954932	−	0.459871i
$751$	27.1531	+	25.1944i	0.990832	+	0.919358i	0.996745	−	0.0806246i	$-0.0256915\pi$
$751$	27.1531	+	25.1944i	0.990832	+	0.919358i	−0.00591237	+	0.999983i	$0.501882\pi$
$752$	−0.606750	−	0.0914529i	−0.0221259	−	0.00333494i
$753$	−10.6868	−	18.5102i	−0.389450	−	0.674548i
$754$	7.28445	−	12.6170i	0.265284	−	0.459485i
$755$	−18.9667	+	23.7835i	−0.690269	+	0.865570i
$756$	−14.3656	−	1.39484i	−0.522473	−	0.0507297i
$757$	−16.6387	−	20.8643i	−0.604745	−	0.758327i	0.381364	−	0.924425i	$-0.375455\pi$
$757$	−16.6387	−	20.8643i	−0.604745	−	0.758327i	−0.986109	+	0.166098i	$0.946883\pi$
$758$	−25.3372	+	3.81897i	−0.920289	+	0.138711i
$759$	−0.698662	−	0.476339i	−0.0253598	−	0.0172900i
$760$	35.1152	+	23.9411i	1.27376	+	0.868436i
$761$	10.0623	−	1.51664i	0.364757	−	0.0549782i	0.0358931	−	0.999356i	$-0.488572\pi$
$761$	10.0623	−	1.51664i	0.364757	−	0.0549782i	0.328864	+	0.944377i	$0.393334\pi$
$762$	0.795010	+	0.996910i	0.0288002	+	0.0361143i
$763$	−9.67745	+	29.0865i	−0.350347	+	1.05300i
$764$	−2.88132	+	3.61306i	−0.104243	+	0.130716i
$765$	13.6399	−	23.6250i	0.493152	−	0.854165i
$766$	17.5903	+	30.4673i	0.635564	+	1.10083i
$767$	7.41899	+	1.11823i	0.267884	+	0.0403770i
$768$	−13.5822	−	12.6025i	−0.490106	−	0.454752i
$769$	42.5720	−	20.5016i	1.53518	−	0.739306i	0.540410	−	0.841402i	$-0.318269\pi$
$769$	42.5720	−	20.5016i	1.53518	−	0.739306i	0.994775	+	0.102096i	$0.0325548\pi$
$770$	0.168791	−	7.67380i	0.00608281	−	0.276544i
$771$	−9.15998	−	4.41121i	−0.329888	−	0.158866i
$772$	11.1500	+	28.4097i	0.401296	+	1.02249i
$773$	0.942442	+	12.5760i	0.0338973	+	0.452328i	0.988167	+	0.153381i	$0.0490162\pi$
$773$	0.942442	+	12.5760i	0.0338973	+	0.452328i	−0.954270	+	0.298947i	$0.903365\pi$
$774$	3.64858	−	1.12544i	0.131146	−	0.0404530i
$775$	−7.51431	+	100.272i	−0.269922	+	3.60186i
$776$	−4.00313	−	17.5389i	−0.143704	−	0.629609i
$777$	10.5932	+	11.9327i	0.380030	+	0.428082i
$778$	−3.33828	+	14.6260i	−0.119683	+	0.524367i
$779$	74.4178	+	22.9549i	2.66630	+	0.822443i
$780$	−1.47819	+	3.76637i	−0.0529278	+	0.134858i
$781$	−0.0665860	+	0.0617828i	−0.00238264	+	0.00221076i
$782$	10.4746	−	7.14145i	0.374570	−	0.255378i
$783$	38.7394			1.38443
$784$	1.07319	+	34.8153i	0.0383281	+	1.24340i
$785$	−49.8492			−1.77919
$786$	−15.2000	+	10.3632i	−0.542167	+	0.369643i
$787$	26.2676	−	24.3728i	0.936340	−	0.868797i	−0.0552162	−	0.998474i	$-0.517585\pi$
$787$	26.2676	−	24.3728i	0.936340	−	0.868797i	0.991556	+	0.129678i	$0.0413943\pi$
$788$	−1.23952	+	3.15826i	−0.0441562	+	0.112508i
$789$	21.4507	+	6.61666i	0.763664	+	0.235559i
$790$	1.53411	−	6.72139i	0.0545813	−	0.239136i
$791$	6.78850	−	0.358818i	0.241371	−	0.0127581i
$792$	−0.308140	−	1.35005i	−0.0109493	−	0.0479719i
$793$	−0.672311	+	8.97137i	−0.0238745	+	0.318583i
$794$	−40.7574	+	12.5720i	−1.44643	+	0.446164i
$795$	−1.72909	−	23.0731i	−0.0613244	−	0.818317i
$796$	−1.21831	−	3.10421i	−0.0431819	−	0.110026i
$797$	24.8255	+	11.9554i	0.879366	+	0.423480i	0.818393	−	0.574659i	$-0.194865\pi$
$797$	24.8255	+	11.9554i	0.879366	+	0.423480i	0.0609730	+	0.998139i	$0.480580\pi$
$798$	−13.1589	−	28.9357i	−0.465819	−	1.02431i
$799$	−0.365865	+	0.176191i	−0.0129434	+	0.00623320i
$800$	41.3525	+	38.3695i	1.46203	+	1.35657i
$801$	−16.8208	−	2.53532i	−0.594333	−	0.0895813i
$802$	−18.1650	−	31.4628i	−0.641430	−	1.11099i
$803$	0.964575	−	1.67069i	0.0340391	−	0.0589575i
$804$	−7.21050	+	9.04168i	−0.254295	+	0.318875i
$805$	−18.7713	−	11.3952i	−0.661601	−	0.401628i
$806$	−11.5219	−	14.4480i	−0.405842	−	0.508909i
$807$	−24.6209	+	3.71100i	−0.866695	+	0.130633i
$808$	0.412875	+	0.281493i	0.0145249	+	0.00990289i
$809$	−12.6117	−	8.59853i	−0.443405	−	0.302308i	0.320959	−	0.947093i	$-0.395995\pi$
$809$	−12.6117	−	8.59853i	−0.443405	−	0.302308i	−0.764364	+	0.644785i	$0.776947\pi$
$810$	14.5900	−	2.19909i	0.512641	−	0.0772683i
$811$	−20.3493	−	25.5172i	−0.714559	−	0.896029i	0.283457	−	0.958985i	$-0.408519\pi$
$811$	−20.3493	−	25.5172i	−0.714559	−	0.896029i	−0.998016	+	0.0629563i	$0.979947\pi$
$812$	3.18976	+	24.8609i	0.111939	+	0.872445i
$813$	−17.4654	+	21.9009i	−0.612538	+	0.768099i
$814$	2.49732	−	4.32549i	0.0875311	−	0.151608i
$815$	21.9336	+	37.9901i	0.768301	+	1.33074i
$816$	−14.8220	−	2.23406i	−0.518874	−	0.0782077i
$817$	5.38632	+	4.99777i	0.188443	+	0.174850i
$818$	−54.0239	+	26.0165i	−1.88890	+	0.909647i
$819$	4.55208	−	3.46918i	0.159062	−	0.121223i
$820$	41.9712	+	20.2123i	1.46570	+	0.705843i
$821$	0.287507	+	0.732556i	0.0100341	+	0.0255664i	0.935803	−	0.352523i	$-0.114676\pi$
$821$	0.287507	+	0.732556i	0.0100341	+	0.0255664i	−0.925769	+	0.378090i	$0.876581\pi$
$822$	1.39410	+	18.6030i	0.0486249	+	0.648854i
$823$	43.1869	−	13.3214i	1.50540	−	0.464354i	0.571111	−	0.820873i	$-0.306512\pi$
$823$	43.1869	−	13.3214i	1.50540	−	0.464354i	0.934288	+	0.356518i	$0.116036\pi$
$824$	−0.987485	+	13.1771i	−0.0344007	+	0.459045i
$825$	−0.839077	−	3.67624i	−0.0292129	−	0.127990i
$826$	−30.9156	+	16.9538i	−1.07569	+	0.589899i
$827$	−0.0609122	+	0.266874i	−0.00211813	+	0.00928011i	−0.975976	−	0.217878i	$-0.930086\pi$
$827$	−0.0609122	+	0.266874i	−0.00211813	+	0.00928011i	0.973858	+	0.227158i	$0.0729435\pi$
$828$	5.17464	+	1.59617i	0.179831	+	0.0554706i
$829$	−6.72252	+	17.1287i	−0.233483	+	0.594905i	−0.998812	−	0.0487347i	$-0.984481\pi$
$829$	−6.72252	+	17.1287i	−0.233483	+	0.594905i	0.765329	+	0.643639i	$0.222576\pi$
$830$	−55.2194	+	51.2361i	−1.91669	+	1.77843i
$831$	−20.3889	+	13.9009i	−0.707284	+	0.482218i
$832$	−0.415409			−0.0144017
$833$	13.5660	+	18.6369i	0.470035	+	0.645731i
$834$	−14.6132			−0.506013
$835$	−31.0254	+	21.1527i	−1.07368	+	0.732020i
$836$	−2.67021	+	2.47759i	−0.0923510	+	0.0856892i
$837$	17.9523	−	45.7416i	0.620521	−	1.58106i
$838$	−12.8482	−	3.96313i	−0.443832	−	0.136904i
$839$	−2.64448	+	11.5862i	−0.0912978	+	0.400002i	−0.999842	−	0.0177875i	$-0.994338\pi$
$839$	−2.64448	+	11.5862i	−0.0912978	+	0.400002i	0.908544	+	0.417789i	$0.137195\pi$
$840$	3.80693	+	13.3796i	0.131351	+	0.461639i
$841$	−8.51695	−	37.3152i	−0.293688	−	1.28673i
$842$	−1.65593	+	22.0969i	−0.0570672	+	0.761509i
$843$	6.47975	−	1.99874i	0.223174	−	0.0688402i
$844$	−0.887032	−	11.8366i	−0.0305329	−	0.407433i
$845$	−1.39907	−	3.56477i	−0.0481294	−	0.122632i
$846$	−0.426895	−	0.205582i	−0.0146769	−	0.00706804i
$847$	27.7576	+	6.98108i	0.953761	+	0.239873i
$848$	29.6116	−	14.2602i	1.01687	−	0.489698i
$849$	−8.18761	−	7.59699i	−0.280998	−	0.260728i
$850$	55.9014	+	8.42578i	1.91740	+	0.289002i
$851$	−7.14460	−	12.3748i	−0.244914	−	0.424203i
$852$	−0.112508	+	0.194870i	−0.00385448	+	0.00667615i
$853$	19.6512	−	24.6418i	0.672843	−	0.843719i	−0.321830	−	0.946797i	$-0.604298\pi$
$853$	19.6512	−	24.6418i	0.672843	−	0.843719i	0.994673	+	0.103079i	$0.0328694\pi$
$854$	−23.0427	−	35.4478i	−0.788503	−	1.21300i
$855$	38.1916	+	47.8908i	1.30613	+	1.63783i
$856$	16.5897	−	2.50050i	0.567026	−	0.0854654i
$857$	−2.36073	−	1.60952i	−0.0806409	−	0.0549801i	0.522328	−	0.852744i	$-0.325064\pi$
$857$	−2.36073	−	1.60952i	−0.0806409	−	0.0549801i	−0.602969	+	0.797764i	$0.706016\pi$
$858$	0.572582	+	0.390380i	0.0195476	+	0.0133273i
$859$	−19.5756	+	2.95055i	−0.667911	+	0.100671i	−0.474241	−	0.880395i	$-0.657277\pi$
$859$	−19.5756	+	2.95055i	−0.667911	+	0.100671i	−0.193670	+	0.981067i	$0.562039\pi$
$860$	2.74041	+	3.43636i	0.0934472	+	0.117179i
$861$	13.8924	+	21.3715i	0.473453	+	0.728339i
$862$	22.6504	−	28.4027i	0.771477	−	0.967401i
$863$	0.479507	−	0.830531i	0.0163226	−	0.0282716i	−0.857749	−	0.514069i	$-0.828137\pi$
$863$	0.479507	−	0.830531i	0.0163226	−	0.0282716i	0.874071	+	0.485798i	$0.161471\pi$
$864$	−13.7836	−	23.8740i	−0.468929	−	0.812209i
$865$	−22.7646	−	3.43121i	−0.774019	−	0.116665i
$866$	47.2191	+	43.8130i	1.60457	+	1.48882i
$867$	5.07332	−	2.44318i	0.172299	−	0.0829748i
$868$	30.8327	+	7.75448i	1.04653	+	0.263204i
$869$	−0.389476	−	0.187562i	−0.0132121	−	0.00636260i
$870$	18.6454	+	47.5077i	0.632138	+	1.61066i
$871$	−0.817973	−	10.9151i	−0.0277160	−	0.369844i
$872$	−16.6171	+	5.12571i	−0.562727	+	0.173578i
$873$	1.93764	−	25.8560i	0.0655793	−	0.875094i
$874$	6.33431	+	27.7524i	0.214261	+	0.938739i
$875$	−12.9349	−	45.4602i	−0.437280	−	1.53684i
$876$	1.06342	−	4.65914i	0.0359295	−	0.157418i
$877$	−5.06697	−	1.56295i	−0.171099	−	0.0527771i	0.208022	−	0.978124i	$-0.433297\pi$
$877$	−5.06697	−	1.56295i	−0.171099	−	0.0527771i	−0.379121	+	0.925347i	$0.623774\pi$
$878$	22.3609	−	56.9746i	0.754644	−	1.92280i
$879$	−8.46182	+	7.85142i	−0.285410	+	0.264822i
$880$	6.71505	−	4.57824i	0.226364	−	0.154333i
$881$	−21.4733			−0.723452			−0.361726	−	0.932284i	$-0.617812\pi$
$881$	−21.4733			−0.723452			−0.361726	+	0.932284i	$0.617812\pi$
$882$	−7.13229	+	25.9338i	−0.240157	+	0.873237i
$883$	14.0770			0.473728			0.236864	−	0.971543i	$-0.423880\pi$
$883$	14.0770			0.473728			0.236864	+	0.971543i	$0.423880\pi$
$884$	−3.14263	+	2.14261i	−0.105698	+	0.0720637i
$885$	−19.2665	+	17.8767i	−0.647637	+	0.600920i
$886$	−0.357899	+	0.911912i	−0.0120239	+	0.0306363i
$887$	14.8661	+	4.58559i	0.499155	+	0.153969i	0.534102	−	0.845420i	$-0.320650\pi$
$887$	14.8661	+	4.58559i	0.499155	+	0.153969i	−0.0349466	+	0.999389i	$0.511126\pi$
$888$	−2.01422	+	8.82487i	−0.0675928	+	0.296143i
$889$	1.82050	−	0.998347i	0.0610577	−	0.0334835i
$890$	−11.9024	−	52.1479i	−0.398970	−	1.74800i
$891$	0.0691377	−	0.922578i	0.00231620	−	0.0309075i
$892$	−15.3341	+	4.72994i	−0.513424	+	0.158370i
$893$	−0.0681402	−	0.909268i	−0.00228023	−	0.0304275i
$894$	4.55331	+	11.6016i	0.152285	+	0.388017i
$895$	13.1440	+	6.32980i	0.439354	+	0.211582i
$896$	−23.0117	+	17.5375i	−0.768768	+	0.585885i
$897$	1.78626	−	0.860219i	0.0596416	−	0.0287219i
$898$	−8.30679	−	7.70757i	−0.277201	−	0.257205i
$899$	−84.3806	−	12.7183i	−2.81425	−	0.424180i
$900$	12.0741	+	20.9130i	0.402471	+	0.697101i
$901$	10.8754	−	18.8368i	0.362313	−	0.627544i
$902$	4.97474	−	6.23813i	0.165641	−	0.207707i
$903$	0.306063	+	2.38544i	0.0101851	+	0.0793825i
$904$	2.40443	+	3.01505i	0.0799700	+	0.100279i
$905$	−93.9973	+	14.1678i	−3.12457	+	0.470954i
$906$	10.6643	+	7.27083i	0.354299	+	0.241557i
$907$	24.3331	+	16.5900i	0.807968	+	0.550863i	0.895377	−	0.445309i	$-0.146906\pi$
$907$	24.3331	+	16.5900i	0.807968	+	0.550863i	−0.0874088	+	0.996173i	$0.527859\pi$
$908$	13.2006	−	1.98968i	0.438079	−	0.0660297i
$909$	0.449046	+	0.563086i	0.0148939	+	0.0186764i
$910$	15.3838	+	9.33884i	0.509969	+	0.309580i
$911$	−33.5207	+	42.0337i	−1.11059	+	1.39264i	−0.199767	+	0.979843i	$0.564019\pi$
$911$	−33.5207	+	42.0337i	−1.11059	+	1.39264i	−0.910824	+	0.412794i	$0.864553\pi$
$912$	16.8288	−	29.1483i	0.557256	−	0.965195i
$913$	2.36163	+	4.09047i	0.0781586	+	0.135375i
$914$	−10.3841	−	1.56515i	−0.343474	−	0.0517704i
$915$	−23.1023	−	21.4358i	−0.763740	−	0.708647i
$916$	5.38612	−	2.59382i	0.177962	−	0.0857022i
$917$	12.4007	+	27.2685i	0.409507	+	0.900487i
$918$	−24.8907	−	11.9867i	−0.821517	−	0.395622i
$919$	−12.3910	−	31.5719i	−0.408743	−	1.04146i	−0.975971	−	0.217899i	$-0.930080\pi$
$919$	−12.3910	−	31.5719i	−0.408743	−	1.04146i	0.567229	−	0.823560i	$-0.308016\pi$
$920$	−0.930929	−	12.4224i	−0.0306918	−	0.409554i
$921$	8.07940	−	2.49216i	0.266225	−	0.0821196i
$922$	1.15205	−	15.3730i	0.0379407	−	0.506283i
$923$	−0.0473908	−	0.207632i	−0.00155989	−	0.00683431i
$924$	−1.19059	+	0.0629306i	−0.0391674	+	0.00207026i
$925$	14.1791	−	62.1227i	0.466206	−	2.04258i
$926$	19.3259	+	5.96124i	0.635088	+	0.195899i
$927$	−6.95797	+	17.7286i	−0.228530	+	0.582284i
$928$	−35.0936	+	32.5621i	−1.15201	+	1.06890i
$929$	22.3594	−	15.2444i	0.733589	−	0.500153i	−0.137974	−	0.990436i	$-0.544059\pi$
$929$	22.3594	−	15.2444i	0.733589	−	0.500153i	0.871563	+	0.490283i	$0.163107\pi$
$930$	64.7353			2.12275
$931$	−50.0837	+	13.0670i	−1.64143	+	0.428255i
$932$	−12.5723			−0.411819
$933$	16.2327	−	11.0673i	0.531434	−	0.362326i
$934$	24.3288	−	22.5738i	0.796062	−	0.738638i
$935$	1.96501	−	5.00677i	0.0642628	−	0.163739i
$936$	3.10253	+	0.957002i	0.101409	+	0.0312806i
$937$	−3.55300	+	15.5667i	−0.116072	+	0.508543i	0.883150	+	0.469091i	$0.155418\pi$
$937$	−3.55300	+	15.5667i	−0.116072	+	0.508543i	−0.999221	+	0.0394519i	$0.987439\pi$
$938$	34.1498	+	38.4678i	1.11503	+	1.25602i
$939$	5.16782	+	22.6417i	0.168645	+	0.738883i
$940$	0.0407598	−	0.543902i	0.00132944	−	0.0177401i
$941$	−18.9328	+	5.83998i	−0.617191	+	0.190378i	−0.587557	−	0.809183i	$-0.699910\pi$
$941$	−18.9328	+	5.83998i	−0.617191	+	0.190378i	−0.0296335	+	0.999561i	$0.509434\pi$
$942$	1.58059	+	21.0915i	0.0514985	+	0.687200i
$943$	−8.33956	−	21.2489i	−0.271574	−	0.691958i
$944$	−33.6365	−	16.1985i	−1.09477	−	0.527215i
$945$	−1.05232	+	47.8422i	−0.0342321	+	1.55631i
$946$	0.678259	−	0.326632i	0.0220521	−	0.0106197i
$947$	−3.87104	−	3.59180i	−0.125792	−	0.116718i	0.614769	−	0.788708i	$-0.289249\pi$
$947$	−3.87104	−	3.59180i	−0.125792	−	0.116718i	−0.740561	+	0.671990i	$0.765440\pi$
$948$	−1.05891	−	0.159605i	−0.0343919	−	0.00518374i
$949$	2.26157	+	3.91716i	0.0734137	+	0.127156i
$950$	−63.4699	+	109.933i	−2.05924	+	3.56670i
$951$	2.63893	−	3.30911i	0.0855730	−	0.107305i
$952$	−4.12831	+	12.4080i	−0.133799	+	0.402147i
$953$	21.7170	+	27.2323i	0.703483	+	0.882139i	0.997278	−	0.0737290i	$-0.0234900\pi$
$953$	21.7170	+	27.2323i	0.703483	+	0.882139i	−0.293796	+	0.955868i	$0.594919\pi$
$954$	25.0956	−	3.78255i	0.812500	−	0.122465i
$955$	12.6596	+	8.63120i	0.409657	+	0.279299i
$956$	−18.7875	−	12.8091i	−0.607632	−	0.414277i
$957$	3.16432	−	0.476944i	0.102288	−	0.0154174i
$958$	−23.4407	−	29.3937i	−0.757335	−	0.949668i
$959$	30.2346	+	2.93564i	0.976325	+	0.0947967i
$960$	0.907301	−	1.13772i	0.0292830	−	0.0367197i
$961$	−38.6201	+	66.8920i	−1.24581	+	2.15781i
$962$	5.85530	+	10.1417i	0.188782	+	0.326981i
$963$	23.9105	+	3.60393i	0.770505	+	0.116135i
$964$	12.4982	+	11.5966i	0.402539	+	0.373501i
$965$	91.1673	−	43.9039i	2.93478	−	1.41331i
$966$	−4.22620	+	8.30357i	−0.135976	+	0.267163i
$967$	3.75245	+	1.80708i	0.120671	+	0.0581119i	0.493245	−	0.869890i	$-0.335811\pi$
$967$	3.75245	+	1.80708i	0.120671	+	0.0581119i	−0.372574	+	0.928002i	$0.621525\pi$
$968$	5.93199	+	15.1145i	0.190661	+	0.485797i
$969$	−1.66456	−	22.2121i	−0.0534735	−	0.713554i
$970$	77.9080	−	24.0314i	2.50148	−	0.771603i
$971$	−1.94269	+	25.9234i	−0.0623439	+	0.831921i	0.875135	+	0.483879i	$0.160772\pi$
$971$	−1.94269	+	25.9234i	−0.0623439	+	0.831921i	−0.937479	+	0.348042i	$0.886847\pi$
$972$	−4.15169	−	18.1897i	−0.133166	−	0.583436i
$973$	−4.06304	+	23.4456i	−0.130255	+	0.751633i
$974$	2.79104	−	12.2283i	0.0894307	−	0.391821i
$975$	8.44830	+	2.60596i	0.270562	+	0.0834574i
$976$	16.3550	−	41.6719i	0.523512	−	1.33389i
$977$	−33.1318	+	30.7418i	−1.05998	+	0.983517i	−0.999892	−	0.0146763i	$-0.995328\pi$
$977$	−33.1318	+	30.7418i	−1.05998	+	0.983517i	−0.0600868	+	0.998193i	$0.519138\pi$
$978$	15.3784	−	10.4848i	0.491748	−	0.335268i
$979$	−3.35389			−0.107191
$980$	−30.7892	+	3.26395i	−0.983524	+	0.104263i
$981$	−25.0635			−0.800215
$982$	13.4164	−	9.14717i	0.428136	−	0.291898i
$983$	17.3790	−	16.1254i	0.554305	−	0.514320i	−0.352533	−	0.935799i	$-0.614679\pi$
$983$	17.3790	−	16.1254i	0.554305	−	0.514320i	0.906838	+	0.421479i	$0.138489\pi$
$984$	−5.28288	+	13.4606i	−0.168412	+	0.429107i
$985$	10.7491	+	3.31567i	0.342496	+	0.105646i
$986$	−10.6758	+	46.7735i	−0.339985	+	1.48957i
$987$	0.173502	−	0.242831i	0.00552264	−	0.00772938i
$988$	−1.90044	−	8.32639i	−0.0604612	−	0.264898i
$989$	0.160948	−	2.14770i	0.00511784	−	0.0682928i
$990$	5.99695	−	1.84981i	0.190596	−	0.0587910i
$991$	2.46056	+	32.8339i	0.0781623	+	1.04300i	0.889053	+	0.457805i	$0.151364\pi$
$991$	2.46056	+	32.8339i	0.0781623	+	1.04300i	−0.810890	+	0.585198i	$0.801017\pi$
$992$	22.1850	+	56.5266i	0.704376	+	1.79472i
$993$	−12.0955	−	5.82489i	−0.383840	−	0.184847i
$994$	0.768590	+	0.641081i	0.0243782	+	0.0203339i
$995$	−9.96147	+	4.79719i	−0.315800	+	0.152081i
$996$	8.57716	+	7.95844i	0.271778	+	0.252173i
$997$	1.31735	+	0.198558i	0.0417209	+	0.00628841i	0.169870	−	0.985467i	$-0.445665\pi$
$997$	1.31735	+	0.198558i	0.0417209	+	0.00628841i	−0.128149	+	0.991755i	$0.540903\pi$
$998$	−20.7750	−	35.9833i	−0.657621	−	1.13903i
$999$	−15.5695	+	26.9672i	−0.492598	+	0.853204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.625.22	yes	348
49.4	even	21	inner	637.2.bl.b.53.22	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.22	✓	348	49.4	even	21	inner
637.2.bl.b.625.22	yes	348	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.46759 - 1.00059i) q^{2} +(-0.670565 + 0.622193i) q^{3} +(0.421973 - 1.07517i) q^{4} +(-3.65935 - 1.12876i) q^{5} +(-0.361558 + 1.58409i) q^{6} +(2.44101 + 1.02053i) q^{7} +(0.333981 + 1.46327i) q^{8} +(-0.161658 + 2.15717i) q^{9} +O(q^{10})\)	\(q+(1.46759 - 1.00059i) q^{2} +(-0.670565 + 0.622193i) q^{3} +(0.421973 - 1.07517i) q^{4} +(-3.65935 - 1.12876i) q^{5} +(-0.361558 + 1.58409i) q^{6} +(2.44101 + 1.02053i) q^{7} +(0.333981 + 1.46327i) q^{8} +(-0.161658 + 2.15717i) q^{9} +(-6.49987 + 2.00494i) q^{10} +(0.0318729 + 0.425314i) q^{11} +(0.386003 + 0.983520i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(4.60354 - 0.944727i) q^{14} +(3.15614 - 1.51992i) q^{15} +(3.64765 + 3.38452i) q^{16} +(3.25629 + 0.490807i) q^{17} +(1.92119 + 3.32760i) q^{18} +(-3.69716 + 6.40367i) q^{19} +(-2.75776 + 3.45812i) q^{20} +(-2.27182 + 0.834450i) q^{21} +(0.472341 + 0.592297i) q^{22} +(2.14315 - 0.323027i) q^{23} +(-1.13439 - 0.773415i) q^{24} +(7.98555 + 5.44446i) q^{25} +(-1.75640 + 0.264734i) q^{26} +(-2.94480 - 3.69266i) q^{27} +(2.12728 - 2.19386i) q^{28} +(-5.11394 + 6.41268i) q^{29} +(3.11112 - 5.38862i) q^{30} +(5.20193 + 9.01000i) q^{31} +(5.77151 + 0.869915i) q^{32} +(-0.286000 - 0.265369i) q^{33} +(5.27001 - 2.53790i) q^{34} +(-7.78058 - 6.48978i) q^{35} +(2.25111 + 1.08408i) q^{36} +(-2.40867 - 6.13719i) q^{37} +(0.981508 + 13.0973i) q^{38} +(0.874118 - 0.269630i) q^{39} +(0.429524 - 5.73159i) q^{40} +(-2.34361 - 10.2680i) q^{41} +(-2.49917 + 3.49779i) q^{42} +(0.221121 - 0.968795i) q^{43} +(0.470734 + 0.145202i) q^{44} +(3.02649 - 7.71137i) q^{45} +(2.82205 - 2.61848i) q^{46} +(-0.101886 + 0.0694649i) q^{47} -4.55181 q^{48} +(4.91705 + 4.98223i) q^{49} +17.1672 q^{50} +(-2.48893 + 1.69692i) q^{51} +(-0.846683 + 0.785607i) q^{52} +(2.41309 - 6.14845i) q^{53} +(-8.01661 - 2.47280i) q^{54} +(0.363443 - 1.59235i) q^{55} +(-0.678053 + 3.91269i) q^{56} +(-1.50513 - 6.59442i) q^{57} +(-1.08874 + 14.5282i) q^{58} +(-7.16946 + 2.21148i) q^{59} +(-0.302363 - 4.03475i) q^{60} +(-3.28680 - 8.37463i) q^{61} +(16.6496 + 8.01804i) q^{62} +(-2.59606 + 5.10069i) q^{63} +(0.374270 - 0.180239i) q^{64} +(2.80721 + 2.60471i) q^{65} +(-0.685258 - 0.103286i) q^{66} +(5.47285 + 9.47925i) q^{67} +(1.90177 - 3.29396i) q^{68} +(-1.23613 + 1.55006i) q^{69} +(-17.9123 - 1.73921i) q^{70} +(0.132786 + 0.166508i) q^{71} +(-3.21051 + 0.483906i) q^{72} +(-3.73720 - 2.54798i) q^{73} +(-9.67575 - 6.59681i) q^{74} +(-8.74234 + 1.31770i) q^{75} +(5.32493 + 6.67725i) q^{76} +(-0.356242 + 1.07072i) q^{77} +(1.01306 - 1.27034i) q^{78} +(-0.506776 + 0.877761i) q^{79} +(-9.52770 - 16.5025i) q^{80} +(-2.14494 - 0.323298i) q^{81} +(-13.7136 - 12.7243i) q^{82} +(9.97761 - 4.80496i) q^{83} +(-0.0614717 + 2.79471i) q^{84} +(-11.3619 - 5.47160i) q^{85} +(-0.644849 - 1.64305i) q^{86} +(-0.560697 - 7.48198i) q^{87} +(-0.611703 + 0.188685i) q^{88} +(-0.587651 + 7.84165i) q^{89} +(-3.27425 - 14.3454i) q^{90} +(-1.75648 - 1.97858i) q^{91} +(0.557041 - 2.44055i) q^{92} +(-9.09419 - 2.80519i) q^{93} +(-0.0800219 + 0.203893i) q^{94} +(20.7574 - 19.2601i) q^{95} +(-4.41143 + 3.00766i) q^{96} -11.9861 q^{97} +(12.2014 + 2.39195i) q^{98} -0.922627 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

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