LMFDB - Embedded newform 175.2.n.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(29,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("175.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.n (of order $10$, degree $4$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	175.29
Dual form			175.2.n.a.169.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44207 + 0.793475i) q^{2} +(-1.88310 + 2.59187i) q^{3} +(3.71604 + 2.69986i) q^{4} +(0.256301 - 2.22133i) q^{5} +(-6.65525 + 4.83532i) q^{6} -1.00000i q^{7} +(3.91399 + 5.38714i) q^{8} +(-2.24466 - 6.90836i) q^{9} +O(q^{10})$	\(q+(2.44207 + 0.793475i) q^{2} +(-1.88310 + 2.59187i) q^{3} +(3.71604 + 2.69986i) q^{4} +(0.256301 - 2.22133i) q^{5} +(-6.65525 + 4.83532i) q^{6} -1.00000i q^{7} +(3.91399 + 5.38714i) q^{8} +(-2.24466 - 6.90836i) q^{9} +(2.38847 - 5.22127i) q^{10} +(-0.140883 + 0.433593i) q^{11} +(-13.9954 + 4.54738i) q^{12} +(-2.11592 + 0.687503i) q^{13} +(0.793475 - 2.44207i) q^{14} +(5.27476 + 4.84730i) q^{15} +(2.44485 + 7.52447i) q^{16} +(1.36142 + 1.87383i) q^{17} -18.6517i q^{18} +(4.06801 - 2.95558i) q^{19} +(6.94972 - 7.56259i) q^{20} +(2.59187 + 1.88310i) q^{21} +(-0.688091 + 0.947076i) q^{22} +(1.71708 + 0.557914i) q^{23} -21.3332 q^{24} +(-4.86862 - 1.13866i) q^{25} -5.71272 q^{26} +(12.9917 + 4.22126i) q^{27} +(2.69986 - 3.71604i) q^{28} +(-3.05970 - 2.22300i) q^{29} +(9.03510 + 16.0228i) q^{30} +(-3.06113 + 2.22404i) q^{31} +6.99741i q^{32} +(-0.858520 - 1.18165i) q^{33} +(1.83783 + 5.65626i) q^{34} +(-2.22133 - 0.256301i) q^{35} +(10.3104 - 31.7320i) q^{36} +(-3.77053 + 1.22512i) q^{37} +(12.2795 - 3.98986i) q^{38} +(2.20257 - 6.77882i) q^{39} +(12.9698 - 7.31353i) q^{40} +(-3.31529 - 10.2034i) q^{41} +(4.83532 + 6.65525i) q^{42} +8.62633i q^{43} +(-1.69417 + 1.23089i) q^{44} +(-15.9211 + 3.21551i) q^{45} +(3.75054 + 2.72493i) q^{46} +(-0.101111 + 0.139167i) q^{47} +(-24.1063 - 7.83263i) q^{48} -1.00000 q^{49} +(-10.9860 - 6.64381i) q^{50} -7.42041 q^{51} +(-9.71901 - 3.15790i) q^{52} +(-0.497619 + 0.684914i) q^{53} +(28.3771 + 20.6172i) q^{54} +(0.927045 + 0.424078i) q^{55} +(5.38714 - 3.91399i) q^{56} +16.1094i q^{57} +(-5.70809 - 7.85651i) q^{58} +(1.82037 + 5.60254i) q^{59} +(6.51420 + 32.2539i) q^{60} +(-1.91871 + 5.90518i) q^{61} +(-9.24019 + 3.00232i) q^{62} +(-6.90836 + 2.24466i) q^{63} +(-0.662572 + 2.03919i) q^{64} +(0.984860 + 4.87636i) q^{65} +(-1.15895 - 3.56688i) q^{66} +(-3.43667 - 4.73018i) q^{67} +10.6389i q^{68} +(-4.67949 + 3.39985i) q^{69} +(-5.22127 - 2.38847i) q^{70} +(2.53925 + 1.84488i) q^{71} +(28.4307 - 39.1315i) q^{72} +(-4.61606 - 1.49985i) q^{73} -10.1800 q^{74} +(12.1194 - 10.4746i) q^{75} +23.0966 q^{76} +(0.433593 + 0.140883i) q^{77} +(10.7577 - 14.8066i) q^{78} +(-11.9870 - 8.70904i) q^{79} +(17.3409 - 3.50228i) q^{80} +(-17.7759 + 12.9150i) q^{81} -27.5480i q^{82} +(7.74495 + 10.6600i) q^{83} +(4.54738 + 13.9954i) q^{84} +(4.51133 - 2.54389i) q^{85} +(-6.84478 + 21.0661i) q^{86} +(11.5235 - 3.74420i) q^{87} +(-2.88724 + 0.938122i) q^{88} +(0.802112 - 2.46865i) q^{89} +(-41.4317 - 4.78046i) q^{90} +(0.687503 + 2.11592i) q^{91} +(4.87447 + 6.70913i) q^{92} -12.1221i q^{93} +(-0.357344 + 0.259626i) q^{94} +(-5.52269 - 9.79391i) q^{95} +(-18.1364 - 13.1768i) q^{96} +(2.98616 - 4.11009i) q^{97} +(-2.44207 - 0.793475i) q^{98} +3.31165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	2.44207	+	0.793475i	1.72680	+	0.561072i	0.992981	−	0.118273i	$-0.0377357\pi$
$2$	2.44207	+	0.793475i	1.72680	+	0.561072i	0.733820	+	0.679344i	$0.237736\pi$
$3$	−1.88310	+	2.59187i	−1.08721	+	1.49642i	−0.235884	+	0.971781i	$0.575799\pi$
$3$	−1.88310	+	2.59187i	−1.08721	+	1.49642i	−0.851327	+	0.524636i	$0.824201\pi$
$4$	3.71604	+	2.69986i	1.85802	+	1.34993i
$5$	0.256301	−	2.22133i	0.114621	−	0.993409i
$5$	0.256301	−	2.22133i	0.114621	−	0.993409i
$6$	−6.65525	+	4.83532i	−2.71699	+	1.97401i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	3.91399	+	5.38714i	1.38380	+	1.90464i
$9$	−2.24466	−	6.90836i	−0.748220	−	2.30279i
$10$	2.38847	−	5.22127i	0.755302	−	1.65111i
$11$	−0.140883	+	0.433593i	−0.0424778	+	0.130733i	−0.970046	−	0.242920i	$-0.921895\pi$
$11$	−0.140883	+	0.433593i	−0.0424778	+	0.130733i	0.927569	+	0.373653i	$0.121895\pi$
$12$	−13.9954	+	4.54738i	−4.04012	+	1.31272i
$13$	−2.11592	+	0.687503i	−0.586850	+	0.190679i	−0.587367	−	0.809321i	$-0.699835\pi$
$13$	−2.11592	+	0.687503i	−0.586850	+	0.190679i	0.000517035		1.00000i	$0.499835\pi$
$14$	0.793475	−	2.44207i	0.212065	−	0.652669i
$15$	5.27476	+	4.84730i	1.36194	+	1.25157i
$16$	2.44485	+	7.52447i	0.611212	+	1.88112i
$17$	1.36142	+	1.87383i	0.330192	+	0.454470i	0.941545	−	0.336888i	$-0.109374\pi$
$17$	1.36142	+	1.87383i	0.330192	+	0.454470i	−0.611353	+	0.791358i	$0.709374\pi$
$18$		−	18.6517i		−	4.39626i
$19$	4.06801	−	2.95558i	0.933265	−	0.678057i	−0.0135252	−	0.999909i	$-0.504305\pi$
$19$	4.06801	−	2.95558i	0.933265	−	0.678057i	0.946790	+	0.321852i	$0.104305\pi$
$20$	6.94972	−	7.56259i	1.55400	−	1.69105i
$21$	2.59187	+	1.88310i	0.565593	+	0.410927i
$22$	−0.688091	+	0.947076i	−0.146701	+	0.201917i
$23$	1.71708	+	0.557914i	0.358037	+	0.116333i	0.482512	−	0.875890i	$-0.339725\pi$
$23$	1.71708	+	0.557914i	0.358037	+	0.116333i	−0.124475	+	0.992223i	$0.539725\pi$
$24$	−21.3332			−4.35463
$25$	−4.86862	−	1.13866i	−0.973724	−	0.227732i
$26$	−5.71272			−1.12036
$27$	12.9917	+	4.22126i	2.50026	+	0.812383i
$28$	2.69986	−	3.71604i	0.510226	−	0.702266i
$29$	−3.05970	−	2.22300i	−0.568172	−	0.412801i	0.266269	−	0.963899i	$-0.414209\pi$
$29$	−3.05970	−	2.22300i	−0.568172	−	0.412801i	−0.834441	+	0.551098i	$0.814209\pi$
$30$	9.03510	+	16.0228i	1.64958	+	2.92535i
$31$	−3.06113	+	2.22404i	−0.549795	+	0.399449i	−0.827710	−	0.561156i	$-0.810357\pi$
$31$	−3.06113	+	2.22404i	−0.549795	+	0.399449i	0.277915	+	0.960606i	$0.410357\pi$
$32$			6.99741i			1.23698i
$33$	−0.858520	−	1.18165i	−0.149449	−	0.205699i
$34$	1.83783	+	5.65626i	0.315185	+	0.970041i
$35$	−2.22133	−	0.256301i	−0.375473	−	0.0433228i
$36$	10.3104	−	31.7320i	1.71839	−	5.28867i
$37$	−3.77053	+	1.22512i	−0.619871	+	0.201408i	−0.602083	−	0.798434i	$-0.705662\pi$
$37$	−3.77053	+	1.22512i	−0.619871	+	0.201408i	−0.0177878	+	0.999842i	$0.505662\pi$
$38$	12.2795	−	3.98986i	1.99200	−	0.647240i
$39$	2.20257	−	6.77882i	0.352694	−	1.08548i
$40$	12.9698	−	7.31353i	2.05070	−	1.15637i
$41$	−3.31529	−	10.2034i	−0.517761	−	1.59350i	−0.778201	−	0.628015i	$-0.783868\pi$
$41$	−3.31529	−	10.2034i	−0.517761	−	1.59350i	0.260440	−	0.965490i	$-0.416132\pi$
$42$	4.83532	+	6.65525i	0.746106	+	1.02693i
$43$			8.62633i			1.31550i	0.753235	+	0.657752i	$0.228492\pi$
$43$			8.62633i			1.31550i	−0.753235	+	0.657752i	$0.771508\pi$
$44$	−1.69417	+	1.23089i	−0.255406	+	0.185563i
$45$	−15.9211	+	3.21551i	−2.37337	+	0.479340i
$46$	3.75054	+	2.72493i	0.552987	+	0.401768i
$47$	−0.101111	+	0.139167i	−0.0147485	+	0.0202996i	−0.816328	−	0.577589i	$-0.803994\pi$
$47$	−0.101111	+	0.139167i	−0.0147485	+	0.0202996i	0.801579	+	0.597889i	$0.203994\pi$
$48$	−24.1063	−	7.83263i	−3.47945	−	1.13054i
$49$	−1.00000			−0.142857
$50$	−10.9860	−	6.64381i	−1.55365	−	0.939576i
$51$	−7.42041			−1.03907
$52$	−9.71901	−	3.15790i	−1.34778	−	0.437922i
$53$	−0.497619	+	0.684914i	−0.0683533	+	0.0940802i	−0.841825	−	0.539751i	$-0.818518\pi$
$53$	−0.497619	+	0.684914i	−0.0683533	+	0.0940802i	0.773472	+	0.633831i	$0.218518\pi$
$54$	28.3771	+	20.6172i	3.86164	+	2.80565i
$55$	0.927045	+	0.424078i	0.125003	+	0.0571827i
$56$	5.38714	−	3.91399i	0.719888	−	0.523029i
$57$			16.1094i			2.13374i
$58$	−5.70809	−	7.85651i	−0.749508	−	1.03161i
$59$	1.82037	+	5.60254i	0.236993	+	0.729388i	0.996851	+	0.0792994i	$0.0252683\pi$
$59$	1.82037	+	5.60254i	0.236993	+	0.729388i	−0.759858	+	0.650089i	$0.774732\pi$
$60$	6.51420	+	32.2539i	0.840979	+	4.16396i
$61$	−1.91871	+	5.90518i	−0.245666	+	0.756081i	0.749861	+	0.661596i	$0.230121\pi$
$61$	−1.91871	+	5.90518i	−0.245666	+	0.756081i	−0.995526	+	0.0944853i	$0.969879\pi$
$62$	−9.24019	+	3.00232i	−1.17351	+	0.381295i
$63$	−6.90836	+	2.24466i	−0.870371	+	0.282801i
$64$	−0.662572	+	2.03919i	−0.0828215	+	0.254898i
$65$	0.984860	+	4.87636i	0.122157	+	0.604838i
$66$	−1.15895	−	3.56688i	−0.142657	−	0.439053i
$67$	−3.43667	−	4.73018i	−0.419857	−	0.577883i	0.545731	−	0.837960i	$-0.316252\pi$
$67$	−3.43667	−	4.73018i	−0.419857	−	0.577883i	−0.965588	+	0.260077i	$0.916252\pi$
$68$			10.6389i			1.29015i
$69$	−4.67949	+	3.39985i	−0.563344	+	0.409293i
$70$	−5.22127	−	2.38847i	−0.624061	−	0.285477i
$71$	2.53925	+	1.84488i	0.301354	+	0.218946i	0.728178	−	0.685388i	$-0.240368\pi$
$71$	2.53925	+	1.84488i	0.301354	+	0.218946i	−0.426824	+	0.904335i	$0.640368\pi$
$72$	28.4307	−	39.1315i	3.35059	−	4.61170i
$73$	−4.61606	−	1.49985i	−0.540269	−	0.175544i	0.0261551	−	0.999658i	$-0.491674\pi$
$73$	−4.61606	−	1.49985i	−0.540269	−	0.175544i	−0.566424	+	0.824114i	$0.691674\pi$
$74$	−10.1800			−1.18340
$75$	12.1194	−	10.4746i	1.39942	−	1.20950i
$76$	23.0966			2.64936
$77$	0.433593	+	0.140883i	0.0494125	+	0.0160551i
$78$	10.7577	−	14.8066i	1.21806	−	1.67652i
$79$	−11.9870	−	8.70904i	−1.34864	−	0.979844i	−0.999078	−	0.0429306i	$-0.986331\pi$
$79$	−11.9870	−	8.70904i	−1.34864	−	0.979844i	−0.349562	−	0.936913i	$-0.613669\pi$
$80$	17.3409	−	3.50228i	1.93878	−	0.391567i
$81$	−17.7759	+	12.9150i	−1.97510	+	1.43500i
$82$		−	27.5480i		−	3.04217i
$83$	7.74495	+	10.6600i	0.850119	+	1.17009i	0.983837	+	0.179069i	$0.0573086\pi$
$83$	7.74495	+	10.6600i	0.850119	+	1.17009i	−0.133717	+	0.991020i	$0.542691\pi$
$84$	4.54738	+	13.9954i	0.496160	+	1.52702i
$85$	4.51133	−	2.54389i	0.489322	−	0.275924i
$86$	−6.84478	+	21.0661i	−0.738092	+	2.27161i
$87$	11.5235	−	3.74420i	1.23544	−	0.401420i
$88$	−2.88724	+	0.938122i	−0.307781	+	0.100004i
$89$	0.802112	−	2.46865i	0.0850237	−	0.261676i	−0.899502	−	0.436917i	$-0.856070\pi$
$89$	0.802112	−	2.46865i	0.0850237	−	0.261676i	0.984526	+	0.175241i	$0.0560704\pi$
$90$	−41.4317	−	4.78046i	−4.36728	−	0.503905i
$91$	0.687503	+	2.11592i	0.0720699	+	0.221808i
$92$	4.87447	+	6.70913i	0.508198	+	0.699475i
$93$		−	12.1221i		−	1.25701i
$94$	−0.357344	+	0.259626i	−0.0368573	+	0.0267784i
$95$	−5.52269	−	9.79391i	−0.566616	−	1.00483i
$96$	−18.1364	−	13.1768i	−1.85104	−	1.34486i
$97$	2.98616	−	4.11009i	0.303198	−	0.417316i	−0.630047	−	0.776557i	$-0.716964\pi$
$97$	2.98616	−	4.11009i	0.303198	−	0.417316i	0.933245	+	0.359241i	$0.116964\pi$
$98$	−2.44207	−	0.793475i	−0.246686	−	0.0801531i
$99$	3.31165			0.332833
$100$	−15.0178	−	17.3759i	−1.50178	−	1.73759i
$101$	17.9409			1.78519			0.892593	−	0.450863i	$-0.148884\pi$
$101$	17.9409			1.78519			0.892593	+	0.450863i	$0.148884\pi$
$102$	−18.1211	−	5.88791i	−1.79426	−	0.582990i
$103$	0.363075	−	0.499730i	0.0357748	−	0.0492399i	−0.790755	−	0.612133i	$-0.790312\pi$
$103$	0.363075	−	0.499730i	0.0357748	−	0.0492399i	0.826530	+	0.562893i	$0.190312\pi$
$104$	−11.9854	−	8.70787i	−1.17526	−	0.853877i
$105$	4.84730	−	5.27476i	0.473048	−	0.514764i
$106$	−1.75868	+	1.27776i	−0.170818	+	0.124107i
$107$			9.21399i			0.890750i	0.895344	+	0.445375i	$0.146930\pi$
$107$			9.21399i			0.890750i	−0.895344	+	0.445375i	$0.853070\pi$
$108$	36.8810	+	50.7623i	3.54887	+	4.88460i
$109$	1.13959	+	3.50729i	0.109153	+	0.335937i	0.990683	−	0.136191i	$-0.0434860\pi$
$109$	1.13959	+	3.50729i	0.109153	+	0.335937i	−0.881530	+	0.472128i	$0.843486\pi$
$110$	1.92741	+	1.77121i	0.183771	+	0.168879i
$111$	3.92495	−	12.0797i	0.372539	−	1.14656i
$112$	7.52447	−	2.44485i	0.710995	−	0.231016i
$113$	10.2261	−	3.32267i	0.961993	−	0.312571i	0.214414	−	0.976743i	$-0.431216\pi$
$113$	10.2261	−	3.32267i	0.961993	−	0.312571i	0.747579	+	0.664172i	$0.231216\pi$
$114$	−12.7824	+	39.3402i	−1.19718	+	3.68455i
$115$	1.67940	−	3.67122i	0.156605	−	0.342343i
$116$	−5.36817	−	16.5215i	−0.498423	−	1.53399i
$117$	9.49903	+	13.0743i	0.878186	+	1.20872i
$118$			15.1262i			1.39248i
$119$	1.87383	−	1.36142i	0.171774	−	0.124801i
$120$	−5.46773	+	47.3882i	−0.499134	+	4.32593i
$121$	8.73103	+	6.34347i	0.793730	+	0.576679i
$122$	−9.37123	+	12.8984i	−0.848431	+	1.16777i
$123$	32.6889	+	10.6213i	2.94746	+	0.957689i
$124$	−17.3799			−1.56076
$125$	−3.77717	+	10.5230i	−0.337841	+	0.941203i
$126$	−18.6517			−1.66163
$127$	−2.79125	−	0.906931i	−0.247683	−	0.0804771i	0.182544	−	0.983198i	$-0.441567\pi$
$127$	−2.79125	−	0.906931i	−0.247683	−	0.0804771i	−0.430228	+	0.902720i	$0.641567\pi$
$128$	4.98986	−	6.86795i	0.441045	−	0.607046i
$129$	−22.3583	−	16.2443i	−1.96854	−	1.43023i
$130$	−1.46418	+	12.6898i	−0.128417	+	1.11297i
$131$	−12.1802	+	8.84946i	−1.06419	+	0.773181i	−0.974859	−	0.222821i	$-0.928473\pi$
$131$	−12.1802	+	8.84946i	−1.06419	+	0.773181i	−0.0893328	+	0.996002i	$0.528473\pi$
$132$		−	6.70896i		−	0.583940i
$133$	−2.95558	−	4.06801i	−0.256281	−	0.352741i
$134$	−4.63931	−	14.2783i	−0.400775	−	1.23346i
$135$	12.7066	−	27.7770i	1.09361	−	2.39066i
$136$	−4.76602	+	14.6683i	−0.408683	+	1.25780i
$137$	−2.00590	+	0.651758i	−0.171376	+	0.0556834i	−0.393448	−	0.919347i	$-0.628718\pi$
$137$	−2.00590	+	0.651758i	−0.171376	+	0.0556834i	0.222072	+	0.975030i	$0.428718\pi$
$138$	−14.1253	+	4.58959i	−1.20243	+	0.390692i
$139$	−4.34123	+	13.3609i	−0.368218	+	1.13326i	0.579723	+	0.814814i	$0.303161\pi$
$139$	−4.34123	+	13.3609i	−0.368218	+	1.13326i	−0.947941	+	0.318445i	$0.896839\pi$
$140$	−7.56259	−	6.94972i	−0.639155	−	0.587358i
$141$	−0.170301	−	0.524132i	−0.0143419	−	0.0441398i
$142$	4.73716	+	6.52014i	0.397534	+	0.547158i
$143$		−	1.01430i		−	0.0848204i
$144$	46.4938	−	33.7797i	3.87449	−	2.81498i
$145$	−5.72222	+	6.22684i	−0.475205	+	0.517111i
$146$	−10.0826	−	7.32546i	−0.834444	−	0.606259i
$147$	1.88310	−	2.59187i	0.155316	−	0.213774i
$148$	−17.3191	−	5.62732i	−1.42362	−	0.462563i
$149$	21.0398			1.72365			0.861824	−	0.507207i	$-0.169322\pi$
$149$	21.0398			1.72365			0.861824	+	0.507207i	$0.169322\pi$
$150$	37.9077	−	15.9633i	3.09515	−	1.30340i
$151$	7.08895			0.576890			0.288445	−	0.957496i	$-0.406862\pi$
$151$	7.08895			0.576890			0.288445	+	0.957496i	$0.406862\pi$
$152$	31.8443	+	10.3468i	2.58291	+	0.839239i
$153$	9.88916	−	13.6113i	0.799491	−	1.10041i
$154$	0.947076	+	0.688091i	0.0763175	+	0.0554479i
$155$	4.15576	+	7.36980i	0.333798	+	0.591956i
$156$	26.4868	−	19.2438i	2.12064	−	1.54073i
$157$		−	17.4788i		−	1.39496i	−0.716604	−	0.697480i	$-0.754305\pi$
$157$		−	17.4788i		−	1.39496i	0.716604	−	0.697480i	$-0.245695\pi$
$158$	−22.3626	−	30.7794i	−1.77907	−	2.44868i
$159$	−0.838140	−	2.57953i	−0.0664688	−	0.204570i
$160$	15.5436	+	1.79344i	1.22883	+	0.141784i
$161$	0.557914	−	1.71708i	0.0439698	−	0.135325i
$162$	−53.6577	+	17.4344i	−4.21574	+	1.36978i
$163$	−18.5888	+	6.03988i	−1.45599	+	0.473080i	−0.926843	−	0.375450i	$-0.877488\pi$
$163$	−18.5888	+	6.03988i	−1.45599	+	0.473080i	−0.529147	+	0.848530i	$0.677488\pi$
$164$	15.2281	−	46.8672i	1.18911	−	3.65971i
$165$	−2.84488	+	1.60420i	−0.221473	+	0.124887i
$166$	10.4552	+	32.1779i	0.811483	+	2.49749i
$167$	−11.6371	−	16.0171i	−0.900508	−	1.23944i	−0.970306	−	0.241882i	$-0.922235\pi$
$167$	−11.6371	−	16.0171i	−0.900508	−	1.23944i	0.0697977	−	0.997561i	$-0.477765\pi$
$168$			21.3332i			1.64589i
$169$	−6.51278	+	4.73181i	−0.500983	+	0.363985i
$170$	13.0355	−	2.63272i	0.999775	−	0.201921i
$171$	−29.5495	−	21.4690i	−2.25971	−	1.64177i
$172$	−23.2899	+	32.0558i	−1.77584	+	2.44423i
$173$	12.3606	+	4.01620i	0.939759	+	0.305346i	0.738547	−	0.674202i	$-0.235512\pi$
$173$	12.3606	+	4.01620i	0.939759	+	0.305346i	0.201212	+	0.979548i	$0.435512\pi$
$174$	31.1120			2.35859
$175$	−1.13866	+	4.86862i	−0.0860746	+	0.368033i
$176$	−3.60699			−0.271887
$177$	−17.9490	−	5.83199i	−1.34913	−	0.438359i
$178$	3.91762	−	5.39214i	0.293638	−	0.404158i
$179$	17.9369	+	13.0319i	1.34067	+	0.974051i	0.999419	+	0.0340767i	$0.0108491\pi$
$179$	17.9369	+	13.0319i	1.34067	+	0.974051i	0.341246	+	0.939974i	$0.389151\pi$
$180$	−67.8448	−	31.0357i	−5.05685	−	2.31326i
$181$	−8.11941	+	5.89910i	−0.603511	+	0.438476i	−0.847123	−	0.531396i	$-0.821668\pi$
$181$	−8.11941	+	5.89910i	−0.603511	+	0.438476i	0.243612	+	0.969873i	$0.421668\pi$
$182$			5.71272i			0.423455i
$183$	−11.6923	−	16.0931i	−0.864323	−	1.18964i
$184$	3.71508	+	11.4338i	0.273879	+	0.842914i
$185$	1.75500	+	8.68958i	0.129030	+	0.638871i
$186$	9.61862	−	29.6031i	0.705271	−	2.17060i
$187$	−1.00428	+	0.326310i	−0.0734402	+	0.0238622i
$188$	−0.751464	+	0.244165i	−0.0548061	+	0.0178076i
$189$	4.22126	−	12.9917i	0.307052	−	0.945008i
$190$	−5.71554	−	28.2995i	−0.414649	−	2.05306i
$191$	2.72336	+	8.38164i	0.197055	+	0.606474i	0.999946	+	0.0103485i	$0.00329410\pi$
$191$	2.72336	+	8.38164i	0.197055	+	0.606474i	−0.802891	+	0.596126i	$0.796706\pi$
$192$	−4.03762	−	5.55730i	−0.291390	−	0.401064i
$193$			13.3896i			0.963804i	0.876225	+	0.481902i	$0.160054\pi$
$193$			13.3896i			0.963804i	−0.876225	+	0.481902i	$0.839946\pi$
$194$	10.5536	−	7.66767i	0.757707	−	0.550506i
$195$	−14.4935	−	6.63006i	−1.03790	−	0.474789i
$196$	−3.71604	−	2.69986i	−0.265432	−	0.192847i
$197$	9.67296	−	13.3137i	0.689170	−	0.948561i	−0.310828	−	0.950466i	$-0.600606\pi$
$197$	9.67296	−	13.3137i	0.689170	−	0.948561i	0.999998	+	0.00190523i	$0.000606455\pi$
$198$	8.08726	+	2.62771i	0.574737	+	0.186743i
$199$	21.3951			1.51666			0.758330	−	0.651870i	$-0.226015\pi$
$199$	21.3951			1.51666			0.758330	+	0.651870i	$0.226015\pi$
$200$	−12.9216	−	30.6847i	−0.913695	−	2.16973i
$201$	18.7316			1.32123
$202$	43.8128	+	14.2357i	3.08266	+	1.00162i
$203$	−2.22300	+	3.05970i	−0.156024	+	0.214749i
$204$	−27.5746	−	20.0341i	−1.93061	−	1.40267i
$205$	−23.5149	+	4.74921i	−1.64235	+	0.331699i
$206$	1.28318	−	0.932282i	0.0894031	−	0.0649552i
$207$		−	13.1145i		−	0.911524i
$208$	−10.3462	−	14.2403i	−0.717379	−	0.987388i
$209$	0.708406	+	2.18025i	0.0490015	+	0.150811i
$210$	16.0228	−	9.03510i	1.10568	−	0.623481i
$211$	2.55134	−	7.85222i	0.175642	−	0.540569i	−0.824021	−	0.566560i	$-0.808274\pi$
$211$	2.55134	−	7.85222i	0.175642	−	0.540569i	0.999662	+	0.0259906i	$0.00827400\pi$
$212$	−3.69835	+	1.20167i	−0.254004	+	0.0825308i
$213$	−9.56336	+	3.10732i	−0.655271	+	0.212910i
$214$	−7.31107	+	22.5012i	−0.499774	+	1.53815i
$215$	19.1619	+	2.21094i	1.30683	+	0.150785i
$216$	28.1089	+	86.5102i	1.91257	+	5.88628i
$217$	2.22404	+	3.06113i	0.150978	+	0.207803i
$218$			9.46925i			0.641339i
$219$	12.5799	−	9.13986i	0.850074	−	0.617615i
$220$	2.29999	+	4.07879i	0.155065	+	0.274992i
$221$	−4.16891	−	3.02889i	−0.280431	−	0.203745i
$222$	19.1699	−	26.3852i	1.28660	−	1.77086i
$223$	−8.64450	−	2.80877i	−0.578879	−	0.188089i	0.00491943	−	0.999988i	$-0.498434\pi$
$223$	−8.64450	−	2.80877i	−0.578879	−	0.188089i	−0.583798	+	0.811899i	$0.698434\pi$
$224$	6.99741			0.467534
$225$	3.06213	+	36.1901i	0.204142	+	2.41267i
$226$	27.6093			1.83655
$227$	−21.9223	−	7.12297i	−1.45503	−	0.472768i	−0.528483	−	0.848944i	$-0.677239\pi$
$227$	−21.9223	−	7.12297i	−1.45503	−	0.472768i	−0.926548	+	0.376176i	$0.877239\pi$
$228$	−43.4932	+	59.8633i	−2.88041	+	3.96454i
$229$	−15.9581	−	11.5942i	−1.05454	−	0.766169i	−0.0814706	−	0.996676i	$-0.525962\pi$
$229$	−15.9581	−	11.5942i	−1.05454	−	0.766169i	−0.973071	+	0.230507i	$0.925962\pi$
$230$	7.01423	−	7.63278i	0.462504	−	0.503291i
$231$	−1.18165	+	0.858520i	−0.0777470	+	0.0564865i
$232$		−	25.1838i		−	1.65340i
$233$	3.15729	+	4.34563i	0.206841	+	0.284692i	0.899816	−	0.436269i	$-0.143701\pi$
$233$	3.15729	+	4.34563i	0.206841	+	0.284692i	−0.692975	+	0.720961i	$0.743701\pi$
$234$	12.8231	+	39.4655i	0.838274	+	2.57994i
$235$	0.283221	+	0.260269i	0.0184753	+	0.0169781i
$236$	−8.36150	+	25.7340i	−0.544287	+	1.67514i
$237$	45.1454	−	14.6686i	2.93251	−	0.952831i
$238$	5.65626	−	1.83783i	0.366641	−	0.119129i
$239$	8.21489	−	25.2828i	0.531377	−	1.63541i	−0.219972	−	0.975506i	$-0.570597\pi$
$239$	8.21489	−	25.2828i	0.531377	−	1.63541i	0.751349	−	0.659905i	$-0.229403\pi$
$240$	−23.5773	+	51.5406i	−1.52191	+	3.32693i
$241$	−5.66834	−	17.4454i	−0.365130	−	1.12375i	−0.949900	−	0.312555i	$-0.898815\pi$
$241$	−5.66834	−	17.4454i	−0.365130	−	1.12375i	0.584769	−	0.811200i	$-0.301185\pi$
$242$	16.2884	+	22.4190i	1.04706	+	1.44115i
$243$		−	29.4122i		−	1.88680i
$244$	−23.0732	+	16.7637i	−1.47711	+	1.07318i
$245$	−0.256301	+	2.22133i	−0.0163745	+	0.141916i
$246$	71.4008	+	51.8757i	4.55235	+	3.30748i
$247$	−6.57560	+	9.05053i	−0.418395	+	0.575871i
$248$	−23.9624	−	7.78587i	−1.52162	−	0.494403i
$249$	−42.2139			−2.67520
$250$	−17.5738	+	22.7007i	−1.11147	+	1.43572i
$251$	0.927993			0.0585744			0.0292872	−	0.999571i	$-0.490676\pi$
$251$	0.927993			0.0585744			0.0292872	+	0.999571i	$0.490676\pi$
$252$	−31.7320	−	10.3104i	−1.99893	−	0.649492i
$253$	−0.483815	+	0.665915i	−0.0304172	+	0.0418657i
$254$	−6.09678	−	4.42957i	−0.382546	−	0.277936i
$255$	−1.90186	+	16.4832i	−0.119099	+	1.03222i
$256$	21.1044	−	15.3332i	1.31902	−	0.958326i
$257$			23.9403i			1.49336i	0.665185	+	0.746678i	$0.268353\pi$
$257$			23.9403i			1.49336i	−0.665185	+	0.746678i	$0.731647\pi$
$258$	−41.7111	−	57.4104i	−2.59682	−	3.57421i
$259$	1.22512	+	3.77053i	0.0761251	+	0.234289i
$260$	−9.50573	+	20.7798i	−0.589520	+	1.28871i
$261$	−8.48930	+	26.1274i	−0.525474	+	1.61724i
$262$	−36.7668	+	11.9462i	−2.27146	+	0.738041i
$263$	−2.98781	+	0.970798i	−0.184236	+	0.0598620i	−0.399682	−	0.916654i	$-0.630879\pi$
$263$	−2.98781	+	0.970798i	−0.184236	+	0.0598620i	0.215446	+	0.976516i	$0.430879\pi$
$264$	3.00549	−	9.24994i	0.184975	−	0.569295i
$265$	1.39388	+	1.28092i	0.0856254	+	0.0786864i
$266$	−3.98986	−	12.2795i	−0.244634	−	0.752905i
$267$	4.88795	+	6.72769i	0.299138	+	0.411728i
$268$		−	26.8561i		−	1.64050i
$269$	13.3936	−	9.73102i	0.816622	−	0.593311i	−0.0991206	−	0.995075i	$-0.531603\pi$
$269$	13.3936	−	9.73102i	0.816622	−	0.593311i	0.915743	+	0.401764i	$0.131603\pi$
$270$	53.0707	−	57.7508i	3.22978	−	3.51460i
$271$	−16.4517	−	11.9529i	−0.999371	−	0.726086i	−0.0374181	−	0.999300i	$-0.511913\pi$
$271$	−16.4517	−	11.9529i	−0.999371	−	0.726086i	−0.961953	+	0.273214i	$0.911913\pi$
$272$	−10.7711	+	14.8252i	−0.653094	+	0.898907i
$273$	−6.77882	−	2.20257i	−0.410273	−	0.133306i
$274$	−5.41570			−0.327174
$275$	1.17962	−	1.95058i	0.0711338	−	0.117625i
$276$	−26.5683			−1.59922
$277$	3.20892	+	1.04264i	0.192805	+	0.0626462i	0.403828	−	0.914835i	$-0.367679\pi$
$277$	3.20892	+	1.04264i	0.192805	+	0.0626462i	−0.211023	+	0.977481i	$0.567679\pi$
$278$	−21.2031	+	29.1836i	−1.27168	+	1.75032i
$279$	22.2356	+	16.1551i	1.33121	+	0.967183i
$280$	−7.31353	−	12.9698i	−0.437067	−	0.775093i
$281$	1.67250	−	1.21514i	0.0997730	−	0.0724893i	−0.536780	−	0.843722i	$-0.680360\pi$
$281$	1.67250	−	1.21514i	0.0997730	−	0.0724893i	0.636553	+	0.771233i	$0.280360\pi$
$282$		−	1.41509i		−	0.0842675i
$283$	−3.09659	−	4.26209i	−0.184073	−	0.253355i	0.707001	−	0.707212i	$-0.250048\pi$
$283$	−3.09659	−	4.26209i	−0.184073	−	0.253355i	−0.891074	+	0.453857i	$0.850048\pi$
$284$	4.45507	+	13.7113i	0.264360	+	0.813615i
$285$	35.7843	+	4.12886i	2.11968	+	0.244573i
$286$	0.804825	−	2.47700i	0.0475903	−	0.146468i
$287$	−10.2034	+	3.31529i	−0.602288	+	0.195695i
$288$	48.3406	−	15.7068i	2.84849	−	0.925532i
$289$	3.59551	−	11.0658i	0.211500	−	0.650932i
$290$	−18.9149	+	10.6659i	−1.11072	+	0.626324i
$291$	5.02958	+	15.4795i	0.294839	+	0.907422i
$292$	−13.1041	−	18.0363i	−0.766860	−	1.05549i
$293$			8.45672i			0.494047i	0.969009	+	0.247024i	$0.0794525\pi$
$293$			8.45672i			0.494047i	−0.969009	+	0.247024i	$0.920547\pi$
$294$	6.65525	−	4.83532i	0.388142	−	0.282002i
$295$	12.9117	−	2.60772i	0.751745	−	0.151827i
$296$	−21.3577	−	15.5173i	−1.24139	−	0.901923i
$297$	−3.66062	+	5.03841i	−0.212411	+	0.292358i
$298$	51.3806	+	16.6946i	2.97640	+	0.967090i
$299$	−4.01677			−0.232296
$300$	73.3162	−	6.20347i	4.23291	−	0.358158i
$301$	8.62633			0.497214
$302$	17.3117	+	5.62490i	0.996175	+	0.323677i
$303$	−33.7846	+	46.5005i	−1.94087	+	2.67138i
$304$	32.1848	+	23.3836i	1.84593	+	1.34114i
$305$	12.6256	+	5.77560i	0.722940	+	0.330710i
$306$	34.9502	−	25.3928i	1.99797	−	1.45161i
$307$			16.2945i			0.929978i	0.885316	+	0.464989i	$0.153942\pi$
$307$			16.2945i			0.929978i	−0.885316	+	0.464989i	$0.846058\pi$
$308$	1.23089	+	1.69417i	0.0701363	+	0.0965343i
$309$	0.611527	+	1.88209i	0.0347886	+	0.107068i
$310$	4.30087	+	21.2950i	0.244273	+	1.20948i
$311$	−0.633051	+	1.94833i	−0.0358970	+	0.110480i	−0.967399	−	0.253255i	$-0.918499\pi$
$311$	−0.633051	+	1.94833i	−0.0358970	+	0.110480i	0.931502	+	0.363735i	$0.118499\pi$
$312$	45.1394	−	14.6667i	2.55551	−	0.830336i
$313$	3.24626	−	1.05478i	0.183490	−	0.0596194i	−0.215831	−	0.976431i	$-0.569246\pi$
$313$	3.24626	−	1.05478i	0.183490	−	0.0596194i	0.399321	+	0.916811i	$0.369246\pi$
$314$	13.8690	−	42.6843i	0.782672	−	2.40882i
$315$	3.21551	+	15.9211i	0.181174	+	0.897050i
$316$	−21.0309	−	64.7264i	−1.18308	−	3.64114i
$317$	−17.7849	−	24.4788i	−0.998898	−	1.37487i	−0.925999	−	0.377526i	$-0.876775\pi$
$317$	−17.7849	−	24.4788i	−0.998898	−	1.37487i	−0.0728988	−	0.997339i	$-0.523225\pi$
$318$		−	6.96442i		−	0.390545i
$319$	1.39494	−	1.01348i	0.0781015	−	0.0567441i
$320$	4.35989	+	1.99444i	0.243725	+	0.111492i
$321$	−23.8815	−	17.3509i	−1.33293	−	0.968433i
$322$	2.72493	−	3.75054i	0.151854	−	0.209009i
$323$	11.0765	+	3.59897i	0.616313	+	0.200252i
$324$	−100.925			−5.60693
$325$	11.0844	−	0.937882i	0.614853	−	0.0520243i
$326$	−50.1876			−2.77964
$327$	−11.2364	−	3.65092i	−0.621374	−	0.201897i
$328$	41.9912	−	57.7960i	2.31858	−	3.19125i
$329$	0.139167	+	0.101111i	0.00767252	+	0.00557441i
$330$	−8.22027	+	1.66022i	−0.452511	+	0.0913919i
$331$	11.7938	−	8.56870i	0.648246	−	0.470978i	−0.214427	−	0.976740i	$-0.568789\pi$
$331$	11.7938	−	8.56870i	0.648246	−	0.470978i	0.862673	+	0.505762i	$0.168789\pi$
$332$			60.5234i			3.32165i
$333$	16.9271	+	23.2982i	0.927600	+	1.27673i
$334$	−15.7094	−	48.3487i	−0.859582	−	2.64552i
$335$	−11.3881	+	6.42164i	−0.622199	+	0.350852i
$336$	−7.83263	+	24.1063i	−0.427305	+	1.31511i
$337$	−7.57206	+	2.46031i	−0.412477	+	0.134022i	−0.507902	−	0.861415i	$-0.669579\pi$
$337$	−7.57206	+	2.46031i	−0.412477	+	0.134022i	0.0954255	+	0.995437i	$0.469579\pi$
$338$	−19.6592	+	6.38766i	−1.06932	+	0.347443i
$339$	−10.6449	+	32.7617i	−0.578153	+	1.77937i
$340$	23.6325	+	2.72676i	1.28165	+	0.147879i
$341$	−0.533067	−	1.64061i	−0.0288672	−	0.0888442i
$342$	−55.1267	−	75.8754i	−2.98091	−	4.10287i
$343$			1.00000i			0.0539949i
$344$	−46.4713	+	33.7634i	−2.50556	+	1.82040i
$345$	6.35283	+	11.2661i	0.342025	+	0.606545i
$346$	26.9986	+	19.6157i	1.45146	+	1.05454i
$347$	16.2215	−	22.3270i	0.870815	−	1.19857i	−0.108066	−	0.994144i	$-0.534466\pi$
$347$	16.2215	−	22.3270i	0.870815	−	1.19857i	0.978881	−	0.204431i	$-0.0655343\pi$
$348$	52.9305	+	17.1982i	2.83737	+	0.921919i
$349$	10.2387			0.548068			0.274034	−	0.961720i	$-0.411642\pi$
$349$	10.2387			0.548068			0.274034	+	0.961720i	$0.411642\pi$
$350$	−6.64381	+	10.9860i	−0.355126	+	0.587226i
$351$	−30.3915			−1.62218
$352$	−3.03403	−	0.985815i	−0.161714	−	0.0525441i
$353$	2.27140	−	3.12632i	0.120895	−	0.166397i	−0.744280	−	0.667867i	$-0.767207\pi$
$353$	2.27140	−	3.12632i	0.120895	−	0.166397i	0.865175	+	0.501470i	$0.167207\pi$
$354$	−39.2051	−	28.4842i	−2.08373	−	1.51392i
$355$	4.74889	−	5.16768i	0.252045	−	0.274272i
$356$	9.64569	−	7.00801i	0.511221	−	0.371424i
$357$			7.42041i			0.392730i
$358$	33.4625	+	46.0572i	1.76855	+	2.43420i
$359$	4.33787	+	13.3506i	0.228944	+	0.704617i	0.997867	+	0.0652759i	$0.0207927\pi$
$359$	4.33787	+	13.3506i	0.228944	+	0.704617i	−0.768923	+	0.639341i	$0.779207\pi$
$360$	−79.6373	−	73.1835i	−4.19725	−	3.85711i
$361$	1.94190	−	5.97657i	0.102205	−	0.314556i
$362$	−24.5089	+	7.96343i	−1.28816	+	0.418548i
$363$	−32.8829	+	10.6843i	−1.72590	+	0.560780i
$364$	−3.15790	+	9.71901i	−0.165519	+	0.509414i
$365$	−4.51476	+	9.86939i	−0.236314	+	0.516587i
$366$	−15.7840	−	48.5780i	−0.825041	−	2.53921i
$367$	5.69689	+	7.84110i	0.297375	+	0.409302i	0.931392	−	0.364017i	$-0.118595\pi$
$367$	5.69689	+	7.84110i	0.297375	+	0.409302i	−0.634017	+	0.773319i	$0.718595\pi$
$368$			14.2841i			0.744613i
$369$	−63.0471	+	45.8064i	−3.28210	+	2.38458i
$370$	−2.60914	+	22.6131i	−0.135643	+	1.17560i
$371$	0.684914	+	0.497619i	0.0355590	+	0.0258351i
$372$	32.7281	−	45.0464i	1.69688	−	2.33555i
$373$	−19.5558	−	6.35408i	−1.01256	−	0.329002i	−0.244688	−	0.969602i	$-0.578686\pi$
$373$	−19.5558	−	6.35408i	−1.01256	−	0.329002i	−0.767875	+	0.640600i	$0.778686\pi$
$374$	−2.71144			−0.140205
$375$	−20.1614	−	29.6058i	−1.04113	−	1.52884i
$376$	−1.14546			−0.0590725
$377$	8.00239	+	2.60013i	0.412144	+	0.133914i
$378$	20.6172	−	28.3771i	1.06043	−	1.45956i
$379$	28.9117	+	21.0056i	1.48509	+	1.07898i	0.975871	+	0.218347i	$0.0700664\pi$
$379$	28.9117	+	21.0056i	1.48509	+	1.07898i	0.509221	+	0.860636i	$0.329934\pi$
$380$	5.91968	−	51.3051i	0.303673	−	2.63190i
$381$	7.60686	−	5.52671i	0.389711	−	0.283142i
$382$			22.6294i			1.15782i
$383$	−11.5425	−	15.8868i	−0.589793	−	0.811780i	0.404934	−	0.914346i	$-0.367295\pi$
$383$	−11.5425	−	15.8868i	−0.589793	−	0.811780i	−0.994726	+	0.102566i	$0.967295\pi$
$384$	8.40441	+	25.8661i	0.428886	+	1.31997i
$385$	0.424078	−	0.927045i	0.0216130	−	0.0472466i
$386$	−10.6243	+	32.6982i	−0.540763	+	1.66430i
$387$	59.5938	−	19.3632i	3.02932	−	0.984286i
$388$	22.1934	−	7.21106i	1.12670	−	0.366086i
$389$	−1.75238	+	5.39327i	−0.0888492	+	0.273450i	−0.985602	−	0.169082i	$-0.945920\pi$
$389$	−1.75238	+	5.39327i	−0.0888492	+	0.273450i	0.896753	+	0.442532i	$0.145920\pi$
$390$	−30.1332	−	27.6913i	−1.52586	−	1.40220i
$391$	1.29223	+	3.97707i	0.0653509	+	0.201129i
$392$	−3.91399	−	5.38714i	−0.197686	−	0.272092i
$393$		−	48.2341i		−	2.43309i
$394$	34.1861	−	24.8376i	1.72227	−	1.25130i
$395$	−22.4179	+	24.3949i	−1.12797	+	1.22744i
$396$	12.3062	+	8.94101i	0.618412	+	0.449303i
$397$	0.245372	−	0.337726i	0.0123149	−	0.0169500i	−0.802815	−	0.596228i	$-0.796665\pi$
$397$	0.245372	−	0.337726i	0.0123149	−	0.0169500i	0.815130	+	0.579278i	$0.196665\pi$
$398$	52.2483	+	16.9765i	2.61897	+	0.850955i
$399$	16.1094			0.806479
$400$	−3.33523	−	39.4176i	−0.166761	−	1.97088i
$401$	−13.0748			−0.652926			−0.326463	−	0.945210i	$-0.605857\pi$
$401$	−13.0748			−0.652926			−0.326463	+	0.945210i	$0.605857\pi$
$402$	45.7438	+	14.8631i	2.28150	+	0.741303i
$403$	4.94806	−	6.81042i	0.246480	−	0.339251i
$404$	66.6692	+	48.4380i	3.31692	+	2.40988i
$405$	24.1324	+	42.7963i	1.19915	+	2.12657i
$406$	−7.85651	+	5.70809i	−0.389912	+	0.283288i
$407$		−	1.80747i		−	0.0895931i
$408$	−29.0434	−	39.9748i	−1.43786	−	1.97905i
$409$	−6.30083	−	19.3920i	−0.311556	−	0.958871i	−0.977149	−	0.212556i	$-0.931821\pi$
$409$	−6.30083	−	19.3920i	−0.311556	−	0.958871i	0.665593	−	0.746315i	$-0.268179\pi$
$410$	−61.1932	−	7.06058i	−3.02212	−	0.348697i
$411$	2.08805	−	6.42637i	0.102996	−	0.316989i
$412$	2.69841	−	0.876765i	0.132941	−	0.0431951i
$413$	5.60254	−	1.82037i	0.275683	−	0.0895748i
$414$	10.4061	−	32.0266i	0.511430	−	1.57402i
$415$	25.6645	−	14.4719i	1.25982	−	0.710399i
$416$	−4.81074	−	14.8059i	−0.235866	−	0.725920i
$417$	−26.4548	−	36.4119i	−1.29550	−	1.78310i
$418$			5.88642i			0.287914i
$419$	−5.41166	+	3.93180i	−0.264377	+	0.192081i	−0.712074	−	0.702104i	$-0.752244\pi$
$419$	−5.41166	+	3.93180i	−0.264377	+	0.192081i	0.447698	+	0.894185i	$0.352244\pi$
$420$	32.2539	−	6.51420i	1.57383	−	0.317860i
$421$	−16.5595	−	12.0312i	−0.807063	−	0.586365i	0.105915	−	0.994375i	$-0.466223\pi$
$421$	−16.5595	−	12.0312i	−0.807063	−	0.586365i	−0.912978	+	0.408010i	$0.866223\pi$
$422$	12.4611	−	17.1512i	0.606596	−	0.834908i
$423$	1.18837	+	0.386126i	0.0577807	+	0.0187741i
$424$	−5.63741			−0.273777
$425$	−4.49457	−	10.6732i	−0.218018	−	0.517724i
$426$	−25.8199			−1.25098
$427$	5.90518	+	1.91871i	0.285772	+	0.0928529i
$428$	−24.8765	+	34.2396i	−1.20245	+	1.65503i
$429$	2.62895	+	1.91004i	0.126927	+	0.0922177i
$430$	45.0404	+	20.6038i	2.17204	+	0.993602i
$431$	17.3287	−	12.5901i	0.834695	−	0.606442i	−0.0861884	−	0.996279i	$-0.527469\pi$
$431$	17.3287	−	12.5901i	0.834695	−	0.606442i	0.920884	+	0.389837i	$0.127469\pi$
$432$			108.076i			5.19981i
$433$	15.3230	+	21.0903i	0.736375	+	1.01353i	0.998819	+	0.0485865i	$0.0154717\pi$
$433$	15.3230	+	21.0903i	0.736375	+	1.01353i	−0.262444	+	0.964947i	$0.584528\pi$
$434$	3.00232	+	9.24019i	0.144116	+	0.443543i
$435$	−5.36363	−	26.5571i	−0.257166	−	1.27331i
$436$	−5.23444	+	16.1100i	−0.250684	+	0.771527i
$437$	8.63407	−	2.80538i	0.413023	−	0.134199i
$438$	37.9733	−	12.3383i	1.81443	−	0.589545i
$439$	−3.78774	+	11.6575i	−0.180779	+	0.556380i	−0.999850	−	0.0173116i	$-0.994489\pi$
$439$	−3.78774	+	11.6575i	−0.180779	+	0.556380i	0.819071	+	0.573692i	$0.194489\pi$
$440$	1.34388	+	6.65396i	0.0640668	+	0.317215i
$441$	2.24466	+	6.90836i	0.106889	+	0.328969i
$442$	−7.77740	−	10.7047i	−0.369933	−	0.509169i
$443$		−	0.640696i		−	0.0304404i	−0.999884	−	0.0152202i	$-0.995155\pi$
$443$		−	0.640696i		−	0.0304404i	0.999884	−	0.0152202i	$-0.00484492\pi$
$444$	47.1989	−	34.2920i	2.23996	−	1.62743i
$445$	−5.27810	−	2.41447i	−0.250206	−	0.114457i
$446$	−18.8818	−	13.7184i	−0.894077	−	0.649585i
$447$	−39.6202	+	54.5325i	−1.87397	+	2.57930i
$448$	2.03919	+	0.662572i	0.0963425	+	0.0313036i
$449$	15.2380			0.719126			0.359563	−	0.933121i	$-0.382926\pi$
$449$	15.2380			0.719126			0.359563	+	0.933121i	$0.382926\pi$
$450$	−21.2380	+	90.8082i	−1.00117	+	4.28074i
$451$	4.89120			0.230317
$452$	46.9715	+	15.2620i	2.20935	+	0.717863i
$453$	−13.3492	+	18.3736i	−0.627201	+	0.863269i
$454$	−47.8837	−	34.7895i	−2.24729	−	1.63275i
$455$	4.87636	−	0.984860i	0.228607	−	0.0461709i
$456$	−86.7837	+	63.0521i	−4.06402	+	2.95268i
$457$		−	25.2090i		−	1.17923i	−0.807685	−	0.589614i	$-0.799280\pi$
$457$		−	25.2090i		−	1.17923i	0.807685	−	0.589614i	$-0.200720\pi$
$458$	−29.7710	−	40.9763i	−1.39111	−	1.91469i
$459$	9.77721	+	30.0912i	0.456361	+	1.40453i
$460$	16.1525	−	9.10824i	0.753115	−	0.424674i
$461$	−2.16831	+	6.67338i	−0.100988	+	0.310810i	−0.988768	−	0.149459i	$-0.952247\pi$
$461$	−2.16831	+	6.67338i	−0.100988	+	0.310810i	0.887780	+	0.460269i	$0.152247\pi$
$462$	−3.56688	+	1.15895i	−0.165946	+	0.0539193i
$463$	−13.8867	+	4.51207i	−0.645371	+	0.209694i	−0.613372	−	0.789794i	$-0.710187\pi$
$463$	−13.8867	+	4.51207i	−0.645371	+	0.209694i	−0.0319990	+	0.999488i	$0.510187\pi$
$464$	9.24640	−	28.4575i	0.429253	−	1.32111i
$465$	−26.9273	−	3.10692i	−1.24872	−	0.144080i
$466$	4.26215	+	13.1175i	0.197440	+	0.607658i
$467$	−5.00980	−	6.89540i	−0.231826	−	0.319081i	0.677217	−	0.735783i	$-0.263186\pi$
$467$	−5.00980	−	6.89540i	−0.231826	−	0.319081i	−0.909043	+	0.416702i	$0.863186\pi$
$468$			74.2308i			3.43132i
$469$	−4.73018	+	3.43667i	−0.218419	+	0.158691i
$470$	0.485127	+	0.860322i	0.0223772	+	0.0396837i
$471$	45.3028	+	32.9144i	2.08744	+	1.51661i
$472$	−23.0568	+	31.7349i	−1.06127	+	1.46072i
$473$	−3.74032	−	1.21530i	−0.171980	−	0.0558797i
$474$	121.887			5.59847
$475$	−23.1710	+	9.75752i	−1.06316	+	0.447706i
$476$	10.6389			0.487632
$477$	5.84862	+	1.90033i	0.267790	+	0.0870102i
$478$	40.1226	−	55.2240i	1.83517	−	2.52589i
$479$	11.2198	+	8.15163i	0.512644	+	0.372458i	0.813826	−	0.581109i	$-0.197381\pi$
$479$	11.2198	+	8.15163i	0.512644	+	0.372458i	−0.301182	+	0.953567i	$0.597381\pi$
$480$	−33.9185	+	36.9096i	−1.54816	+	1.68469i
$481$	7.13585	−	5.18450i	0.325367	−	0.236393i
$482$		−	47.1004i		−	2.14536i
$483$	3.39985	+	4.67949i	0.154698	+	0.212924i
$484$	15.3184	+	47.1452i	0.696291	+	2.14296i
$485$	−8.36451	−	7.68666i	−0.379813	−	0.349033i
$486$	23.3379	−	71.8266i	1.05863	−	3.25812i
$487$	−13.1793	+	4.28222i	−0.597212	+	0.194046i	−0.591997	−	0.805940i	$-0.701660\pi$
$487$	−13.1793	+	4.28222i	−0.597212	+	0.194046i	−0.00521540	+	0.999986i	$0.501660\pi$
$488$	−39.3219	+	12.7765i	−1.78002	+	0.578363i
$489$	19.3501	−	59.5536i	0.875043	−	2.69311i
$490$	−2.38847	+	5.22127i	−0.107900	+	0.235873i
$491$	−4.84934	−	14.9247i	−0.218848	−	0.673543i	−0.998858	−	0.0477770i	$-0.984786\pi$
$491$	−4.84934	−	14.9247i	−0.218848	−	0.673543i	0.780011	−	0.625766i	$-0.215214\pi$
$492$	92.7976	+	127.725i	4.18364	+	5.75828i
$493$		−	8.75978i		−	0.394521i
$494$	−23.2394	+	16.8844i	−1.04559	+	0.759666i
$495$	0.848780	−	7.35627i	0.0381498	−	0.330640i
$496$	−24.2187	−	17.5959i	−1.08745	−	0.790080i
$497$	1.84488	−	2.53925i	0.0827540	−	0.113901i
$498$	−103.089	−	33.4957i	−4.61954	−	1.50098i
$499$	−29.3023			−1.31175			−0.655877	−	0.754868i	$-0.727701\pi$
$499$	−29.3023			−1.31175			−0.655877	+	0.754868i	$0.727701\pi$
$500$	−42.4467	+	28.9060i	−1.89828	+	1.29272i
$501$	63.4283			2.83377
$502$	2.26622	+	0.736339i	0.101146	+	0.0328644i
$503$	0.159071	−	0.218942i	0.00709260	−	0.00976213i	−0.805456	−	0.592656i	$-0.798080\pi$
$503$	0.159071	−	0.218942i	0.00709260	−	0.00976213i	0.812549	+	0.582893i	$0.198080\pi$
$504$	−39.1315	−	28.4307i	−1.74306	−	1.26641i
$505$	4.59827	−	39.8527i	0.204621	−	1.77342i
$506$	−1.70990	+	1.24231i	−0.0760141	+	0.0552275i
$507$		−	25.7908i		−	1.14541i
$508$	−7.92381	−	10.9062i	−0.351562	−	0.483884i
$509$	2.43438	+	7.49224i	0.107902	+	0.332088i	0.990401	−	0.138227i	$-0.0441404\pi$
$509$	2.43438	+	7.49224i	0.107902	+	0.332088i	−0.882499	+	0.470315i	$0.844140\pi$
$510$	−17.7235	+	38.7439i	−0.784808	+	1.71561i
$511$	−1.49985	+	4.61606i	−0.0663494	+	0.204203i
$512$	47.5573	−	15.4523i	2.10175	−	0.682901i
$513$	65.3267	−	21.2259i	2.88424	−	0.937147i
$514$	−18.9961	+	58.4638i	−0.837880	+	2.57873i
$515$	−1.01701	−	0.934591i	−0.0448148	−	0.0411830i
$516$	−39.2272	−	120.729i	−1.72688	−	5.31480i
$517$	−0.0460970	−	0.0634471i	−0.00202735	−	0.00279040i
$518$			10.1800i			0.447282i
$519$	−33.6858	+	24.4741i	−1.47864	+	1.07430i
$520$	−22.4149	+	24.3916i	−0.982959	+	1.06964i
$521$	−7.52517	−	5.46736i	−0.329684	−	0.239529i	0.410613	−	0.911810i	$-0.365315\pi$
$521$	−7.52517	−	5.46736i	−0.329684	−	0.239529i	−0.740296	+	0.672281i	$0.765315\pi$
$522$	−41.4628	+	57.0687i	−1.81478	+	2.49783i
$523$	0.690957	+	0.224505i	0.0302134	+	0.00981694i	0.324085	−	0.946028i	$-0.394944\pi$
$523$	0.690957	+	0.224505i	0.0302134	+	0.00981694i	−0.293871	+	0.955845i	$0.594944\pi$
$524$	−69.1546			−3.02103
$525$	−10.4746	−	12.1194i	−0.457150	−	0.528933i
$526$	−8.06673			−0.351726
$527$	−8.33494	−	2.70819i	−0.363076	−	0.117970i
$528$	6.79235	−	9.34886i	0.295599	−	0.406857i
$529$	−15.9703	−	11.6031i	−0.694360	−	0.504482i
$530$	2.38757	+	4.23410i	0.103709	+	0.183918i
$531$	34.6182	−	25.1516i	1.50230	−	1.09149i
$532$		−	23.0966i		−	1.00136i
$533$	14.0298	+	19.3103i	0.607696	+	0.836422i
$534$	6.59844	+	20.3079i	0.285543	+	0.878810i
$535$	20.4673	+	2.36156i	0.884879	+	0.102099i
$536$	12.0310	−	37.0277i	0.519662	−	1.59935i
$537$	−67.5540	+	21.9496i	−2.91517	+	0.947197i
$538$	40.4294	−	13.1363i	1.74303	−	0.566346i
$539$	0.140883	−	0.433593i	0.00606826	−	0.0186762i
$540$	122.212	−	68.9144i	5.25919	−	2.96560i
$541$	−6.96644	−	21.4405i	−0.299510	−	0.921798i	−0.981669	−	0.190594i	$-0.938959\pi$
$541$	−6.96644	−	21.4405i	−0.299510	−	0.921798i	0.682158	−	0.731204i	$-0.261041\pi$
$542$	−30.6919	−	42.2438i	−1.31833	−	1.81452i
$543$		−	32.1531i		−	1.37982i
$544$	−13.1119	+	9.52638i	−0.562170	+	0.408440i
$545$	8.08292	−	1.63248i	0.346234	−	0.0699276i
$546$	−14.8066	−	10.7577i	−0.633666	−	0.460385i
$547$	−6.09144	+	8.38415i	−0.260451	+	0.358480i	−0.919137	−	0.393938i	$-0.871113\pi$
$547$	−6.09144	+	8.38415i	−0.260451	+	0.358480i	0.658686	+	0.752418i	$0.271113\pi$
$548$	−9.21369	−	2.99371i	−0.393589	−	0.127885i
$549$	45.1020			1.92490
$550$	4.42845	−	3.82745i	0.188830	−	0.163203i
$551$	−19.0171			−0.810157
$552$	−36.6309	−	11.9021i	−1.55912	−	0.506588i
$553$	−8.70904	+	11.9870i	−0.370346	+	0.509738i
$554$	7.00908	+	5.09239i	0.297787	+	0.216355i
$555$	−25.8271	−	11.8147i	−1.09630	−	0.501504i
$556$	−52.2049	+	37.9291i	−2.21398	+	1.60855i
$557$		−	12.8068i		−	0.542641i	−0.962489	−	0.271321i	$-0.912540\pi$
$557$		−	12.8068i		−	0.542641i	0.962489	−	0.271321i	$-0.0874604\pi$
$558$	41.4822	+	57.0953i	1.75608	+	2.41704i
$559$	−5.93063	−	18.2526i	−0.250839	−	0.772003i
$560$	−3.50228	−	17.3409i	−0.147999	−	0.732789i
$561$	1.04541	−	3.21744i	0.0441372	−	0.135840i
$562$	5.04854	−	1.64037i	0.212960	−	0.0691948i
$563$	−2.28223	+	0.741543i	−0.0961847	+	0.0312523i	−0.356714	−	0.934214i	$-0.616103\pi$
$563$	−2.28223	+	0.741543i	−0.0961847	+	0.0312523i	0.260529	+	0.965466i	$0.416103\pi$
$564$	0.782239	−	2.40749i	0.0329382	−	0.101373i
$565$	−4.75978	−	23.5672i	−0.200245	−	0.991480i
$566$	−4.18021	−	12.8654i	−0.175707	−	0.540771i
$567$	12.9150	+	17.7759i	0.542378	+	0.746519i
$568$			20.9002i			0.876951i
$569$	−28.3521	+	20.5990i	−1.18858	+	0.863556i	−0.993114	−	0.117154i	$-0.962623\pi$
$569$	−28.3521	+	20.5990i	−1.18858	+	0.863556i	−0.195469	+	0.980710i	$0.562623\pi$
$570$	84.1115	+	38.4769i	3.52304	+	1.61162i
$571$	14.7239	+	10.6975i	0.616175	+	0.447677i	0.851583	−	0.524219i	$-0.175643\pi$
$571$	14.7239	+	10.6975i	0.616175	+	0.447677i	−0.235408	+	0.971897i	$0.575643\pi$
$572$	2.73849	−	3.76920i	0.114502	−	0.157598i
$573$	−26.8525	−	8.72491i	−1.12178	−	0.364488i
$574$	−27.5480			−1.14983
$575$	−7.72455	−	4.67144i	−0.322136	−	0.194813i
$576$	15.5747			0.648945
$577$	13.0751	+	4.24834i	0.544322	+	0.176861i	0.568255	−	0.822853i	$-0.307619\pi$
$577$	13.0751	+	4.24834i	0.544322	+	0.176861i	−0.0239331	+	0.999714i	$0.507619\pi$
$578$	17.5609	−	24.1705i	0.730438	−	1.00536i
$579$	−34.7041	−	25.2140i	−1.44225	−	1.04786i
$580$	−38.0757	+	7.69000i	−1.58101	+	0.319310i
$581$	10.6600	−	7.74495i	0.442252	−	0.321315i
$582$			41.7927i			1.73236i
$583$	−0.226868	−	0.312257i	−0.00939591	−	0.0129324i
$584$	−9.98731	−	30.7378i	−0.413278	−	1.27194i
$585$	31.4769	−	17.7495i	1.30141	−	0.733853i
$586$	−6.71020	+	20.6519i	−0.277196	+	0.853121i
$587$	−16.5410	+	5.37450i	−0.682721	+	0.221830i	−0.629786	−	0.776768i	$-0.716858\pi$
$587$	−16.5410	+	5.37450i	−0.682721	+	0.221830i	−0.0529347	+	0.998598i	$0.516858\pi$
$588$	13.9954	−	4.54738i	0.577161	−	0.187531i
$589$	−5.87936	+	18.0948i	−0.242255	+	0.745584i
$590$	33.6003	+	3.87686i	1.38330	+	0.159608i
$591$	16.2922	+	50.1421i	0.670170	+	2.06257i
$592$	−18.4367	−	25.3760i	−0.757745	−	1.04295i
$593$		−	7.50257i		−	0.308093i	−0.988064	−	0.154047i	$-0.950769\pi$
$593$		−	7.50257i		−	0.308093i	0.988064	−	0.154047i	$-0.0492306\pi$
$594$	−12.9373	+	9.39952i	−0.530825	+	0.385667i
$595$	−2.54389	−	4.51133i	−0.104289	−	0.184946i
$596$	78.1849	+	56.8047i	3.20258	+	2.32681i
$597$	−40.2893	+	55.4534i	−1.64893	+	2.26956i
$598$	−9.80922	−	3.18721i	−0.401129	−	0.130335i
$599$	−15.7587			−0.643883			−0.321942	−	0.946760i	$-0.604335\pi$
$599$	−15.7587			−0.643883			−0.321942	+	0.946760i	$0.604335\pi$
$600$	103.863	+	24.2913i	4.24021	+	0.991688i
$601$	23.9509			0.976979			0.488489	−	0.872570i	$-0.337548\pi$
$601$	23.9509			0.976979			0.488489	+	0.872570i	$0.337548\pi$
$602$	21.0661	+	6.84478i	0.858589	+	0.278972i
$603$	−24.9636	+	34.3594i	−1.01660	+	1.39922i
$604$	26.3429	+	19.1392i	1.07188	+	0.778763i
$605$	16.3287	−	17.7687i	0.663856	−	0.722399i
$606$	−119.401	+	86.7500i	−4.85034	+	3.52398i
$607$			4.85624i			0.197109i	0.995132	+	0.0985544i	$0.0314219\pi$
$607$			4.85624i			0.197109i	−0.995132	+	0.0985544i	$0.968578\pi$
$608$	20.6814	+	28.4655i	0.838741	+	1.15443i
$609$	−3.74420	−	11.5235i	−0.151723	−	0.466954i
$610$	26.2497	+	24.1225i	1.06282	+	0.976691i
$611$	0.118264	−	0.363980i	0.00478445	−	0.0147250i
$612$	73.4971	−	23.8807i	2.97095	−	0.965319i
$613$	−17.7656	+	5.77239i	−0.717545	+	0.233144i	−0.644958	−	0.764218i	$-0.723125\pi$
$613$	−17.7656	+	5.77239i	−0.717545	+	0.233144i	−0.0725865	+	0.997362i	$0.523125\pi$
$614$	−12.9293	+	39.7923i	−0.521784	+	1.60589i
$615$	31.9716	−	69.8907i	1.28922	−	2.81827i
$616$	0.938122	+	2.88724i	0.0377980	+	0.116330i
$617$	−25.1266	−	34.5838i	−1.01156	−	1.39229i	−0.917957	−	0.396681i	$-0.870162\pi$
$617$	−25.1266	−	34.5838i	−1.01156	−	1.39229i	−0.0936019	−	0.995610i	$-0.529838\pi$
$618$			5.08141i			0.204404i
$619$	24.1152	−	17.5207i	0.969273	−	0.704218i	0.0139869	−	0.999902i	$-0.495548\pi$
$619$	24.1152	−	17.5207i	0.969273	−	0.704218i	0.955286	+	0.295684i	$0.0955477\pi$
$620$	−4.45449	+	38.6065i	−0.178896	+	1.55047i
$621$	19.9527	+	14.4965i	0.800676	+	0.581725i
$622$	−3.09190	+	4.25564i	−0.123974	+	0.170636i
$623$	−2.46865	−	0.802112i	−0.0989042	−	0.0321359i
$624$	56.3920			2.25749
$625$	22.4069	+	11.0874i	0.896276	+	0.443496i
$626$	8.76453			0.350301
$627$	−6.98493	−	2.26954i	−0.278951	−	0.0906368i
$628$	47.1904	−	64.9520i	1.88310	−	2.59187i
$629$	−7.42892	−	5.39743i	−0.296210	−	0.215209i
$630$	−4.78046	+	41.4317i	−0.190458	+	1.65068i
$631$	12.2119	−	8.87247i	0.486148	−	0.353207i	−0.317553	−	0.948241i	$-0.602861\pi$
$631$	12.2119	−	8.87247i	0.486148	−	0.353207i	0.803701	+	0.595033i	$0.202861\pi$
$632$		−	98.6627i		−	3.92459i
$633$	15.5475	+	21.3993i	0.617958	+	0.850546i
$634$	−24.0085	−	73.8906i	−0.953500	−	2.93457i
$635$	−2.72999	+	5.96784i	−0.108337	+	0.236826i
$636$	3.84982	−	11.8485i	0.152655	−	0.469824i
$637$	2.11592	−	0.687503i	0.0838357	−	0.0272399i
$638$	4.21070	−	1.36814i	0.166703	−	0.0541652i
$639$	7.04530	−	21.6832i	0.278708	−	0.857774i
$640$	−13.9771	−	12.8444i	−0.552492	−	0.507719i
$641$	13.3976	+	41.2337i	0.529175	+	1.62863i	0.755910	+	0.654676i	$0.227195\pi$
$641$	13.3976	+	41.2337i	0.529175	+	1.62863i	−0.226735	+	0.973956i	$0.572805\pi$
$642$	−44.5526	−	61.3214i	−1.75835	−	2.42016i
$643$		−	43.7468i		−	1.72521i	−0.505881	−	0.862603i	$-0.668833\pi$
$643$		−	43.7468i		−	1.72521i	0.505881	−	0.862603i	$-0.331167\pi$
$644$	6.70913	−	4.87447i	0.264377	−	0.192081i
$645$	−41.8144	+	45.5018i	−1.64644	+	1.79163i
$646$	24.1938	+	17.5779i	0.951894	+	0.691592i
$647$	3.66274	−	5.04132i	0.143997	−	0.198195i	−0.730926	−	0.682456i	$-0.760912\pi$
$647$	3.66274	−	5.04132i	0.143997	−	0.198195i	0.874923	+	0.484262i	$0.160912\pi$
$648$	−139.150	−	45.2124i	−5.46631	−	1.77611i
$649$	−2.68568			−0.105422
$650$	27.8131	+	6.50485i	1.09092	+	0.255141i
$651$	−12.1221			−0.475104
$652$	−85.3838	−	27.7429i	−3.34389	−	1.08650i
$653$	12.1829	−	16.7683i	0.476753	−	0.656194i	−0.501124	−	0.865375i	$-0.667080\pi$
$653$	12.1829	−	16.7683i	0.476753	−	0.656194i	0.977877	+	0.209182i	$0.0670800\pi$
$654$	−24.5431	−	17.8316i	−0.959710	−	0.697270i
$655$	16.5358	+	29.3245i	0.646106	+	1.14580i
$656$	68.6698	−	49.8915i	2.68111	−	1.94794i
$657$			35.2560i			1.37547i
$658$	0.259626	+	0.357344i	0.0101213	+	0.0139307i
$659$	0.939000	+	2.88994i	0.0365782	+	0.112576i	0.967678	−	0.252187i	$-0.0811499\pi$
$659$	0.939000	+	2.88994i	0.0365782	+	0.112576i	−0.931100	+	0.364763i	$0.881150\pi$
$660$	−14.9028	−	1.71951i	−0.580091	−	0.0669320i
$661$	3.55001	−	10.9258i	0.138079	−	0.424965i	−0.857977	−	0.513688i	$-0.828279\pi$
$661$	3.55001	−	10.9258i	0.138079	−	0.424965i	0.996056	+	0.0887237i	$0.0282788\pi$
$662$	35.6003	−	11.5672i	1.38364	−	0.449573i
$663$	15.7010	−	5.10156i	0.609775	−	0.198128i
$664$	−27.1134	+	83.4464i	−1.05220	+	3.23835i
$665$	−9.79391	+	5.52269i	−0.379791	+	0.214161i
$666$	22.8506	+	70.3269i	0.885442	+	2.72511i
$667$	−4.01351	−	5.52413i	−0.155404	−	0.213895i
$668$		−	90.9391i		−	3.51854i
$669$	23.5585	−	17.1162i	0.910823	−	0.661752i
$670$	−32.9059	+	6.64588i	−1.27127	+	0.256753i
$671$	−2.29013	−	1.66388i	−0.0884096	−	0.0642333i
$672$	−13.1768	+	18.1364i	−0.508308	+	0.699626i
$673$	18.9025	+	6.14180i	0.728639	+	0.236749i	0.649765	−	0.760135i	$-0.274867\pi$
$673$	18.9025	+	6.14180i	0.728639	+	0.236749i	0.0788742	+	0.996885i	$0.474867\pi$
$674$	−20.4437			−0.787461
$675$	−58.4451	−	35.3449i	−2.24955	−	1.36042i
$676$	−36.9770			−1.42219
$677$	1.13417	+	0.368514i	0.0435896	+	0.0141631i	0.330731	−	0.943725i	$-0.392705\pi$
$677$	1.13417	+	0.368514i	0.0435896	+	0.0141631i	−0.287141	+	0.957888i	$0.592705\pi$
$678$	−51.9912	+	71.5598i	−1.99671	+	2.74824i
$679$	−4.11009	−	2.98616i	−0.157731	−	0.114598i
$680$	31.3616	+	14.3464i	1.20266	+	0.550160i
$681$	59.7437	−	43.4063i	2.28938	−	1.66333i
$682$		−	4.42946i		−	0.169613i
$683$	2.69580	+	3.71045i	0.103152	+	0.141976i	0.857472	−	0.514530i	$-0.172034\pi$
$683$	2.69580	+	3.71045i	0.103152	+	0.141976i	−0.754321	+	0.656506i	$0.772034\pi$
$684$	−51.8439	−	159.559i	−1.98230	−	6.10090i
$685$	0.933654	+	4.62282i	0.0356731	+	0.176629i
$686$	−0.793475	+	2.44207i	−0.0302950	+	0.0932385i
$687$	60.1016	−	19.5282i	2.29302	−	0.745047i
$688$	−64.9085	+	21.0901i	−2.47461	+	0.804051i
$689$	0.582041	−	1.79134i	0.0221740	−	0.0682445i
$690$	6.57466	+	32.5533i	0.250293	+	1.23928i
$691$	8.69342	+	26.7556i	0.330713	+	1.01783i	0.968795	+	0.247862i	$0.0797281\pi$
$691$	8.69342	+	26.7556i	0.330713	+	1.01783i	−0.638082	+	0.769968i	$0.720272\pi$
$692$	35.0893	+	48.2963i	1.33390	+	1.83595i
$693$		−	3.31165i		−	0.125799i
$694$	57.3298	−	41.6526i	2.17621	−	1.58111i
$695$	28.5664	+	13.0677i	1.08358	+	0.495687i
$696$	65.2733	+	47.4238i	2.47418	+	1.79759i
$697$	14.6060	−	20.1034i	0.553240	−	0.761470i
$698$	25.0037	+	8.12419i	0.946404	+	0.307505i
$699$	−17.2088			−0.650897
$700$	−17.3759	+	15.0178i	−0.656748	+	0.567619i
$701$	−2.34546			−0.0885867			−0.0442934	−	0.999019i	$-0.514104\pi$
$701$	−2.34546			−0.0885867			−0.0442934	+	0.999019i	$0.514104\pi$
$702$	−74.2181	−	24.1149i	−2.80118	−	0.910159i
$703$	−11.7176	+	16.1279i	−0.441937	+	0.608275i
$704$	−0.790832	−	0.574573i	−0.0298056	−	0.0216550i
$705$	−1.20792	+	0.243959i	−0.0454928	+	0.00918801i
$706$	8.02757	−	5.83237i	0.302122	−	0.219504i
$707$		−	17.9409i		−	0.674737i
$708$	−50.9537	−	70.1318i	−1.91496	−	2.63572i
$709$	15.8662	+	48.8312i	0.595868	+	1.83389i	0.550357	+	0.834930i	$0.314492\pi$
$709$	15.8662	+	48.8312i	0.595868	+	1.83389i	0.0455115	+	0.998964i	$0.485508\pi$
$710$	15.6975	−	8.85168i	0.589118	−	0.332198i
$711$	−33.2585	+	102.359i	−1.24729	+	3.83877i
$712$	16.4384	−	5.34116i	0.616056	−	0.200169i
$713$	−6.49703	+	2.11101i	−0.243316	+	0.0790581i
$714$	−5.88791	+	18.1211i	−0.220350	+	0.678166i
$715$	−2.25311	−	0.259968i	−0.0842614	−	0.00972223i
$716$	31.4699	+	96.8543i	1.17608	+	3.61962i
$717$	50.0604	+	68.9022i	1.86954	+	2.57320i
$718$			36.0450i			1.34519i
$719$	30.2991	−	22.0136i	1.12997	−	0.820968i	0.144276	−	0.989538i	$-0.453915\pi$
$719$	30.2991	−	22.0136i	1.12997	−	0.820968i	0.985690	+	0.168570i	$0.0539148\pi$
$720$	−63.1196	−	111.936i	−2.35233	−	4.17161i
$721$	−0.499730	−	0.363075i	−0.0186109	−	0.0135216i
$722$	9.48451	−	13.0543i	0.352977	−	0.485831i
$723$	55.8902	+	18.1598i	2.07858	+	0.675371i
$724$	−46.0988			−1.71325
$725$	12.3653	+	14.3069i	0.459234	+	0.531345i
$726$	−88.7799			−3.29493
$727$	5.15639	+	1.67541i	0.191240	+	0.0621376i	0.403071	−	0.915169i	$-0.367943\pi$
$727$	5.15639	+	1.67541i	0.191240	+	0.0621376i	−0.211831	+	0.977306i	$0.567943\pi$
$728$	−8.70787	+	11.9854i	−0.322735	+	0.444207i
$729$	22.9049	+	16.6414i	0.848331	+	0.616349i
$730$	−18.8565	+	20.5193i	−0.697909	+	0.759454i
$731$	−16.1643	+	11.7440i	−0.597857	+	0.434369i
$732$		−	91.3705i		−	3.37715i
$733$	16.1265	+	22.1962i	0.595646	+	0.819836i	0.995301	−	0.0968294i	$-0.0308701\pi$
$733$	16.1265	+	22.1962i	0.595646	+	0.819836i	−0.399655	+	0.916666i	$0.630870\pi$
$734$	7.69046	+	23.6688i	0.283860	+	0.873632i
$735$	−5.27476	−	4.84730i	−0.194562	−	0.178795i
$736$	−3.90395	+	12.0151i	−0.143902	+	0.442883i
$737$	2.53514	−	0.823717i	0.0933831	−	0.0303420i
$738$	−190.311	+	61.8359i	−7.00546	+	2.27621i
$739$	−13.8328	+	42.5730i	−0.508848	+	1.56607i	0.285355	+	0.958422i	$0.407889\pi$
$739$	−13.8328	+	42.5730i	−0.508848	+	1.56607i	−0.794203	+	0.607652i	$0.792111\pi$
$740$	−16.9390	+	37.0292i	−0.622691	+	1.36122i
$741$	−11.0753	−	34.0862i	−0.406860	−	1.25219i
$742$	1.27776	+	1.75868i	0.0469079	+	0.0645632i
$743$		−	31.7813i		−	1.16594i	−0.812493	−	0.582972i	$-0.801890\pi$
$743$		−	31.7813i		−	1.16594i	0.812493	−	0.582972i	$-0.198110\pi$
$744$	65.3037	−	47.4459i	2.39415	−	1.73945i
$745$	5.39253	−	46.7364i	0.197567	−	1.71229i
$746$	−42.7148	−	31.0341i	−1.56390	−	1.13624i
$747$	56.2584	−	77.4330i	2.05839	−	2.83313i
$748$	−4.61294	−	1.49884i	−0.168666	−	0.0548029i
$749$	9.21399			0.336672
$750$	−25.7439	−	88.2968i	−0.940035	−	3.22414i
$751$	−23.8194			−0.869184			−0.434592	−	0.900628i	$-0.643107\pi$
$751$	−23.8194			−0.869184			−0.434592	+	0.900628i	$0.643107\pi$
$752$	−1.29436	−	0.420562i	−0.0472003	−	0.0153363i
$753$	−1.74751	+	2.40524i	−0.0636827	+	0.0876517i
$754$	17.4792	+	12.6994i	0.636555	+	0.462485i
$755$	1.81691	−	15.7469i	0.0661240	−	0.573088i
$756$	50.7623	−	36.8810i	1.84621	−	1.34135i
$757$			41.8011i			1.51929i	0.650340	+	0.759644i	$0.274627\pi$
$757$			41.8011i			1.51929i	−0.650340	+	0.759644i	$0.725373\pi$
$758$	53.9368	+	74.2376i	1.95907	+	2.69643i
$759$	−0.814890	−	2.50797i	−0.0295786	−	0.0910337i
$760$	31.1455	−	68.0848i	1.12976	−	2.46969i
$761$	15.0150	−	46.2115i	0.544294	−	1.67516i	−0.178368	−	0.983964i	$-0.557082\pi$
$761$	15.0150	−	46.2115i	0.544294	−	1.67516i	0.722662	−	0.691201i	$-0.242918\pi$
$762$	22.9617	−	7.46072i	0.831816	−	0.270274i
$763$	3.50729	−	1.13959i	0.126972	−	0.0412558i
$764$	−12.5092	+	38.4993i	−0.452566	+	1.39285i
$765$	−27.7005	−	25.4557i	−1.00151	−	0.920352i
$766$	−15.5816	−	47.9554i	−0.562988	−	1.73270i
$767$	−7.70352	−	10.6030i	−0.278158	−	0.382852i
$768$			83.5738i			3.01571i
$769$	6.41362	−	4.65977i	0.231281	−	0.168035i	−0.466109	−	0.884727i	$-0.654345\pi$
$769$	6.41362	−	4.65977i	0.231281	−	0.168035i	0.697390	+	0.716692i	$0.254345\pi$
$770$	1.77121	−	1.92741i	0.0638301	−	0.0694590i
$771$	−62.0502	−	45.0821i	−2.23468	−	1.62359i
$772$	−36.1501	+	49.7563i	−1.30107	+	1.79077i
$773$	−15.1118	−	4.91013i	−0.543535	−	0.176605i	0.0243646	−	0.999703i	$-0.492244\pi$
$773$	−15.1118	−	4.91013i	−0.543535	−	0.176605i	−0.567899	+	0.823098i	$0.692244\pi$
$774$	160.896			5.78329
$775$	17.4359	−	7.34242i	0.626315	−	0.263747i
$776$	33.8294			1.21441
$777$	−12.0797	−	3.92495i	−0.433358	−	0.140807i
$778$	−8.55885	+	11.7802i	−0.306850	+	0.422342i
$779$	−43.6436	−	31.7089i	−1.56369	−	1.13609i
$780$	−35.9582	−	63.7681i	−1.28751	−	2.28326i
$781$	−1.15766	+	0.841092i	−0.0414244	+	0.0300966i
$782$			10.7376i			0.383977i
$783$	−30.3669	−	41.7964i	−1.08522	−	1.49368i
$784$	−2.44485	−	7.52447i	−0.0873160	−	0.268731i
$785$	−38.8262	−	4.47984i	−1.38577	−	0.159892i
$786$	38.2725	−	117.791i	1.36514	−	4.20145i
$787$	−10.1563	+	3.29999i	−0.362033	+	0.117632i	−0.484385	−	0.874855i	$-0.660957\pi$
$787$	−10.1563	+	3.29999i	−0.362033	+	0.117632i	0.122351	+	0.992487i	$0.460957\pi$
$788$	71.8903	−	23.3586i	2.56099	−	0.832115i
$789$	3.11017	−	9.57213i	0.110725	−	0.340777i
$790$	−74.1028	+	41.7858i	−2.63646	+	1.48667i
$791$	−3.32267	−	10.2261i	−0.118141	−	0.363599i
$792$	12.9618	+	17.8403i	0.460576	+	0.633929i
$793$		−	13.8140i		−	0.490549i
$794$	0.867192	−	0.630052i	0.0307755	−	0.0223597i
$795$	−5.94480	+	1.20065i	−0.210840	+	0.0425826i
$796$	79.5053	+	57.7640i	2.81799	+	2.04739i
$797$	−24.9143	+	34.2917i	−0.882511	+	1.21467i	0.0932075	+	0.995647i	$0.470288\pi$
$797$	−24.9143	+	34.2917i	−0.882511	+	1.21467i	−0.975719	+	0.219026i	$0.929712\pi$
$798$	39.3402	+	12.7824i	1.39263	+	0.452493i
$799$	−0.398429			−0.0140954
$800$	7.96766	−	34.0677i	0.281699	−	1.20448i
$801$	−18.8548			−0.666200
$802$	−31.9296	−	10.3745i	−1.12747	−	0.366338i
$803$	1.30065	−	1.79019i	0.0458989	−	0.0631744i
$804$	69.6076	+	50.5729i	2.45487	+	1.78357i
$805$	−3.67122	−	1.67940i	−0.129393	−	0.0591911i
$806$	17.4874	−	12.7053i	0.615966	−	0.447526i
$807$			53.0390i			1.86706i
$808$	70.2205	+	96.6502i	2.47035	+	3.40014i
$809$	12.5412	+	38.5978i	0.440925	+	1.35703i	0.886891	+	0.461978i	$0.152860\pi$
$809$	12.5412	+	38.5978i	0.440925	+	1.35703i	−0.445966	+	0.895050i	$0.647140\pi$
$810$	24.9751	+	123.660i	0.877536	+	4.34497i
$811$	−16.4431	+	50.6067i	−0.577395	+	1.77704i	0.0504787	+	0.998725i	$0.483925\pi$
$811$	−16.4431	+	50.6067i	−0.577395	+	1.77704i	−0.627874	+	0.778315i	$0.716075\pi$
$812$	−16.5215	+	5.36817i	−0.579792	+	0.188386i
$813$	61.9606	−	20.1322i	2.17305	−	0.706068i
$814$	1.43418	−	4.41397i	0.0502681	−	0.154709i
$815$	8.65223	+	42.8400i	0.303074	+	1.50062i
$816$	−18.1418	−	55.8346i	−0.635089	−	1.95460i
$817$	25.4958	+	35.0920i	0.891986	+	1.22771i
$818$		−	52.3560i		−	1.83058i
$819$	13.0743	−	9.49903i	0.456853	−	0.331923i
$820$	−100.204	−	45.8387i	−3.49929	−	1.60076i
$821$	−14.1326	−	10.2680i	−0.493232	−	0.358354i	0.313194	−	0.949689i	$-0.398601\pi$
$821$	−14.1326	−	10.2680i	−0.493232	−	0.358354i	−0.806426	+	0.591335i	$0.798601\pi$
$822$	10.1983	−	14.0368i	0.355708	−	0.489589i
$823$	−22.5387	−	7.32327i	−0.785650	−	0.255273i	−0.111399	−	0.993776i	$-0.535533\pi$
$823$	−22.5387	−	7.32327i	−0.785650	−	0.255273i	−0.674251	+	0.738503i	$0.735533\pi$
$824$	4.11319			0.143290
$825$	2.83431	+	6.73057i	0.0986780	+	0.234328i
$826$	15.1262			0.526307
$827$	7.18745	+	2.33534i	0.249932	+	0.0812078i	0.431304	−	0.902207i	$-0.358054\pi$
$827$	7.18745	+	2.33534i	0.249932	+	0.0812078i	−0.181372	+	0.983415i	$0.558054\pi$
$828$	35.4075	−	48.7343i	1.23050	−	1.69363i
$829$	−4.96058	−	3.60407i	−0.172288	−	0.125175i	0.498300	−	0.867005i	$-0.333958\pi$
$829$	−4.96058	−	3.60407i	−0.172288	−	0.125175i	−0.670588	+	0.741830i	$0.733958\pi$
$830$	74.1574	−	14.9773i	2.57404	−	0.519869i
$831$	−8.74512	+	6.35370i	−0.303365	+	0.220407i
$832$		−	4.77027i		−	0.165379i
$833$	−1.36142	−	1.87383i	−0.0471703	−	0.0649243i
$834$	−35.7124	−	109.911i	−1.23662	−	3.80592i
$835$	−38.5620	+	21.7447i	−1.33449	+	0.752506i
$836$	−3.25391	+	10.0145i	−0.112539	+	0.346359i
$837$	−49.1575	+	15.9723i	−1.69913	+	0.552082i
$838$	−16.3354	+	5.30770i	−0.564297	+	0.183351i
$839$	−8.69647	+	26.7650i	−0.300235	+	0.924029i	0.681177	+	0.732119i	$0.261468\pi$
$839$	−8.69647	+	26.7650i	−0.300235	+	0.924029i	−0.981412	+	0.191911i	$0.938532\pi$
$840$	47.3882	+	5.46773i	1.63505	+	0.188655i
$841$	−4.54147	−	13.9772i	−0.156602	−	0.481973i
$842$	−30.8930	−	42.5206i	−1.06464	−	1.46536i
$843$			6.62314i			0.228113i
$844$	30.6808	−	22.2909i	1.05608	−	0.767286i
$845$	8.84168	+	15.6798i	0.304163	+	0.539401i
$846$	2.59570	+	1.88589i	0.0892422	+	0.0648382i
$847$	6.34347	−	8.73103i	0.217964	−	0.300002i
$848$	−6.37022	−	2.06981i	−0.218754	−	0.0710775i
$849$	16.8780			0.579251
$850$	−2.50714	−	29.6309i	−0.0859943	−	1.01633i
$851$	−7.15782			−0.245367
$852$	−43.9272	−	14.2728i	−1.50492	−	0.488979i
$853$	5.22265	−	7.18836i	0.178820	−	0.246125i	−0.710192	−	0.704008i	$-0.751392\pi$
$853$	5.22265	−	7.18836i	0.178820	−	0.246125i	0.889013	+	0.457883i	$0.151392\pi$
$854$	12.8984	+	9.37123i	0.441374	+	0.320677i
$855$	−55.2632	+	60.1367i	−1.88996	+	2.05663i
$856$	−49.6371	+	36.0635i	−1.69656	+	1.23262i
$857$			2.02525i			0.0691811i	0.999402	+	0.0345906i	$0.0110127\pi$
$857$			2.02525i			0.0691811i	−0.999402	+	0.0345906i	$0.988987\pi$
$858$	4.90449	+	6.75045i	0.167436	+	0.230457i
$859$	−0.713207	−	2.19502i	−0.0243343	−	0.0748933i	0.938152	−	0.346224i	$-0.112536\pi$
$859$	−0.713207	−	2.19502i	−0.0243343	−	0.0748933i	−0.962486	+	0.271331i	$0.912536\pi$
$860$	65.2374	+	59.9506i	2.22458	+	2.04430i
$861$	10.6213	−	32.6889i	0.361972	−	1.11404i
$862$	52.3078	−	16.9958i	1.78161	−	0.578880i
$863$	−25.6232	+	8.32548i	−0.872223	+	0.283403i	−0.710725	−	0.703470i	$-0.751633\pi$
$863$	−25.6232	+	8.32548i	−0.872223	+	0.283403i	−0.161499	+	0.986873i	$0.551633\pi$
$864$	−29.5379	+	90.9083i	−1.00490	+	3.09276i
$865$	12.0893	−	26.4276i	0.411050	−	0.898566i
$866$	20.6851	+	63.6622i	0.702909	+	2.16333i
$867$	21.9105	+	30.1572i	0.744120	+	1.02419i
$868$			17.3799i			0.589912i
$869$	5.46494	−	3.97051i	0.185385	−	0.134690i
$870$	7.97404	−	69.1100i	0.270345	−	2.34305i
$871$	10.5237	+	7.64594i	0.356583	+	0.259073i
$872$	−14.4339	+	19.8666i	−0.488794	+	0.672768i
$873$	−35.0969	−	11.4037i	−1.18785	−	0.385956i
$874$	23.3109			0.788505
$875$	10.5230	+	3.77717i	0.355741	+	0.127692i
$876$	71.4240			2.41319
$877$	19.5555	+	6.35396i	0.660342	+	0.214558i	0.619969	−	0.784627i	$-0.287145\pi$
$877$	19.5555	+	6.35396i	0.660342	+	0.214558i	0.0403733	+	0.999185i	$0.487145\pi$
$878$	−18.4998	+	25.4628i	−0.624338	+	0.859328i
$879$	−21.9187	−	15.9249i	−0.739301	−	0.537133i
$880$	−0.924477	+	8.01233i	−0.0311641	+	0.270095i
$881$	−23.5133	+	17.0834i	−0.792185	+	0.575556i	−0.908611	−	0.417643i	$-0.862856\pi$
$881$	−23.5133	+	17.0834i	−0.792185	+	0.575556i	0.116426	+	0.993199i	$0.462856\pi$
$882$			18.6517i			0.628037i
$883$	4.03889	+	5.55906i	0.135920	+	0.187077i	0.871551	−	0.490305i	$-0.163115\pi$
$883$	4.03889	+	5.55906i	0.135920	+	0.187077i	−0.735632	+	0.677382i	$0.763115\pi$
$884$	−7.31426	−	22.5110i	−0.246005	−	0.757126i
$885$	−17.5551	+	38.3759i	−0.590109	+	1.28999i
$886$	0.508376	−	1.56462i	0.0170792	−	0.0525645i
$887$	−23.1016	+	7.50617i	−0.775676	+	0.252032i	−0.669993	−	0.742367i	$-0.733703\pi$
$887$	−23.1016	+	7.50617i	−0.775676	+	0.252032i	−0.105683	+	0.994400i	$0.533703\pi$
$888$	80.4375	−	26.1357i	2.69931	−	0.877058i
$889$	−0.906931	+	2.79125i	−0.0304175	+	0.0936154i
$890$	−10.9736	−	10.0843i	−0.367837	−	0.338028i
$891$	−3.09552	−	9.52702i	−0.103704	−	0.319167i
$892$	−24.5401	−	33.7765i	−0.821662	−	1.13092i
$893$			0.864973i			0.0289452i
$894$	−140.025	+	101.734i	−4.68314	+	3.40250i
$895$	33.5454	−	36.5037i	1.12130	−	1.22018i
$896$	−6.86795	−	4.98986i	−0.229442	−	0.166699i
$897$	7.56400	−	10.4110i	0.252555	−	0.347612i
$898$	37.2122	+	12.0910i	1.24179	+	0.403481i
$899$	14.3102			0.477271
$900$	−86.3292	+	142.751i	−2.87764	+	4.75837i
$901$	−1.96088			−0.0653264
$902$	11.9446	+	3.88104i	0.397712	+	0.129225i
$903$	−16.2443	+	22.3583i	−0.540576	+	0.744039i
$904$	57.9247	+	42.0847i	1.92655	+	1.39972i
$905$	11.0228	+	19.5478i	0.366411	+	0.649792i
$906$	−47.1787	+	34.2773i	−1.56741	+	1.13879i
$907$			1.01804i			0.0338034i	0.999857	+	0.0169017i	$0.00538023\pi$
$907$			1.01804i			0.0338034i	−0.999857	+	0.0169017i	$0.994620\pi$
$908$	−62.2330	−	85.6564i	−2.06528	−	2.84261i
$909$	−40.2712	−	123.942i	−1.33571	−	4.11090i
$910$	12.6898	+	1.46418i	0.420664	+	0.0485370i
$911$	−11.9294	+	36.7150i	−0.395240	+	1.21642i	0.533534	+	0.845778i	$0.320864\pi$
$911$	−11.9294	+	36.7150i	−0.395240	+	1.21642i	−0.928774	+	0.370645i	$0.879136\pi$
$912$	−121.215	+	39.3851i	−4.01382	+	1.30417i
$913$	−5.71324	+	1.85634i	−0.189081	+	0.0614360i
$914$	20.0027	−	61.5621i	0.661632	−	2.03629i
$915$	−38.7449	+	21.8479i	−1.28087	+	0.722268i
$916$	−27.9982	−	86.1695i	−0.925085	−	2.84712i
$917$	8.84946	+	12.1802i	0.292235	+	0.402227i
$918$			81.2425i			2.68140i
$919$	13.7348	−	9.97895i	0.453071	−	0.329175i	−0.337736	−	0.941241i	$-0.609661\pi$
$919$	13.7348	−	9.97895i	0.453071	−	0.329175i	0.790807	+	0.612066i	$0.209661\pi$
$920$	26.3505	−	5.32192i	0.868751	−	0.175458i
$921$	−42.2333	−	30.6843i	−1.39164	−	1.01108i
$922$	−10.5903	+	14.5763i	−0.348773	+	0.480045i
$923$	−6.64121	−	2.15786i	−0.218598	−	0.0710268i
$924$	−6.70896			−0.220709
$925$	19.7522	−	1.67129i	0.649450	−	0.0549516i
$926$	−37.4925			−1.23208
$927$	−4.26729	−	1.38653i	−0.140156	−	0.0455395i
$928$	15.5552	−	21.4099i	0.510626	−	0.702816i
$929$	41.1612	+	29.9054i	1.35046	+	0.981164i	0.998989	+	0.0449638i	$0.0143172\pi$
$929$	41.1612	+	29.9054i	1.35046	+	0.981164i	0.351468	+	0.936200i	$0.385683\pi$
$930$	−63.2929	−	28.9534i	−2.07546	−	0.949420i
$931$	−4.06801	+	2.95558i	−0.133324	+	0.0968652i
$932$			24.6728i			0.808185i
$933$	−3.85772	−	5.30970i	−0.126296	−	0.173832i
$934$	−6.76293	−	20.8142i	−0.221290	−	0.681060i
$935$	0.467445	+	2.31447i	0.0152871	+	0.0756913i
$936$	−33.2540	+	102.345i	−1.08694	+	3.34526i
$937$	−1.24526	+	0.404609i	−0.0406809	+	0.0132180i	−0.329287	−	0.944230i	$-0.606808\pi$
$937$	−1.24526	+	0.404609i	−0.0406809	+	0.0132180i	0.288606	+	0.957448i	$0.406808\pi$
$938$	−14.2783	+	4.63931i	−0.466204	+	0.151479i
$939$	−3.37921	+	10.4001i	−0.110276	+	0.339396i
$940$	0.349771	+	1.73183i	0.0114083	+	0.0564860i
$941$	−3.00688	−	9.25423i	−0.0980215	−	0.301679i	0.890008	−	0.455945i	$-0.150699\pi$
$941$	−3.00688	−	9.25423i	−0.0980215	−	0.301679i	−0.988029	+	0.154266i	$0.950699\pi$
$942$	84.5156	+	116.326i	2.75367	+	3.79010i
$943$		−	19.3697i		−	0.630766i
$944$	−37.7056	+	27.3947i	−1.22721	+	0.891621i
$945$	−27.7770	−	12.7066i	−0.903585	−	0.413346i
$946$	−8.16979	−	5.93570i	−0.265623	−	0.192986i
$947$	8.85406	−	12.1866i	0.287718	−	0.396010i	−0.640553	−	0.767914i	$-0.721295\pi$
$947$	8.85406	−	12.1866i	0.287718	−	0.396010i	0.928271	+	0.371904i	$0.121295\pi$
$948$	207.366	+	67.3772i	6.73493	+	2.18831i
$949$	10.7984			0.350529
$950$	−64.3274	+	5.44291i	−2.08706	+	0.176591i
$951$	96.9366			3.14338
$952$	14.6683	+	4.76602i	0.475402	+	0.154468i
$953$	−1.08856	+	1.49828i	−0.0352620	+	0.0485339i	−0.826284	−	0.563254i	$-0.809549\pi$
$953$	−1.08856	+	1.49828i	−0.0352620	+	0.0485339i	0.791022	+	0.611788i	$0.209549\pi$
$954$	12.7748	+	9.28146i	0.413601	+	0.300498i
$955$	19.3164	−	3.90126i	0.625064	−	0.126242i
$956$	98.7872	−	71.7731i	3.19501	−	2.32131i
$957$			5.52399i			0.178565i
$958$	20.9313	+	28.8094i	0.676258	+	0.930790i
$959$	0.651758	+	2.00590i	0.0210463	+	0.0647740i
$960$	−13.3795	+	7.54454i	−0.431820	+	0.243499i
$961$	−5.15538	+	15.8666i	−0.166303	+	0.511827i
$962$	21.5400	−	6.99876i	0.694477	−	0.225649i
$963$	63.6535	−	20.6823i	2.05121	−	0.666477i
$964$	26.0363	−	80.1315i	0.838573	−	2.58086i
$965$	29.7427	+	3.43177i	0.957451	+	0.110473i
$966$	4.58959	+	14.1253i	0.147668	+	0.454474i
$967$	27.6787	+	38.0964i	0.890086	+	1.22510i	0.973524	+	0.228586i	$0.0734101\pi$
$967$	27.6787	+	38.0964i	0.890086	+	1.22510i	−0.0834375	+	0.996513i	$0.526590\pi$
$968$			71.8636i			2.30978i
$969$	−30.1863	+	21.9316i	−0.969723	+	0.704545i
$970$	−14.3275	−	25.4084i	−0.460029	−	0.815813i
$971$	−35.9440	−	26.1149i	−1.15350	−	0.838066i	−0.164556	−	0.986368i	$-0.552619\pi$
$971$	−35.9440	−	26.1149i	−1.15350	−	0.838066i	−0.988942	+	0.148302i	$0.952619\pi$
$972$	79.4091	−	109.297i	2.54705	−	3.50571i
$973$	13.3609	+	4.34123i	0.428332	+	0.139173i
$974$	−35.5826			−1.14014
$975$	−18.4423	+	30.4955i	−0.590625	+	0.976639i
$976$	−49.1243			−1.57243
$977$	−13.1809	−	4.28273i	−0.421693	−	0.137017i	0.0904805	−	0.995898i	$-0.471160\pi$
$977$	−13.1809	−	4.28273i	−0.421693	−	0.137017i	−0.512174	+	0.858882i	$0.671160\pi$
$978$	94.5086	−	130.080i	3.02205	−	4.15950i
$979$	0.957384	+	0.695580i	0.0305981	+	0.0222308i
$980$	−6.94972	+	7.56259i	−0.222001	+	0.241578i
$981$	21.6716	−	15.7453i	0.691921	−	0.502710i
$982$		−	40.2950i		−	1.28586i
$983$	−12.7126	−	17.4975i	−0.405470	−	0.558082i	0.556636	−	0.830757i	$-0.312092\pi$
$983$	−12.7126	−	17.4975i	−0.405470	−	0.558082i	−0.962106	+	0.272674i	$0.912092\pi$
$984$	70.7258	+	217.672i	2.25466	+	6.93912i
$985$	−27.0949	−	24.8992i	−0.863315	−	0.793353i
$986$	6.95067	−	21.3920i	0.221354	−	0.681259i
$987$	−0.524132	+	0.170301i	−0.0166833	+	0.00542073i
$988$	−48.8704	+	15.8790i	−1.55478	+	0.505177i
$989$	−4.81275	+	14.8121i	−0.153037	+	0.470998i
$990$	7.90979	−	17.2910i	0.251390	−	0.549544i
$991$	4.14973	+	12.7716i	0.131820	+	0.405702i	0.995082	−	0.0990553i	$-0.0315821\pi$
$991$	4.14973	+	12.7716i	0.131820	+	0.405702i	−0.863261	+	0.504757i	$0.831582\pi$
$992$	−15.5625	−	21.4199i	−0.494110	−	0.680084i
$993$			46.7038i			1.48210i
$994$	6.52014	−	4.73716i	0.206806	−	0.150254i
$995$	5.48360	−	47.5257i	0.173842	−	1.50666i
$996$	−156.869	−	113.972i	−4.97058	−	3.61134i
$997$	27.2191	−	37.4638i	0.862036	−	1.18649i	−0.119044	−	0.992889i	$-0.537983\pi$
$997$	27.2191	−	37.4638i	0.862036	−	1.18649i	0.981080	−	0.193602i	$-0.0620172\pi$
$998$	−71.5582	−	23.2507i	−2.26514	−	0.735987i
$999$	−54.1571			−1.71346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.n.a.29.14	✓	56
5.2	odd	4		875.2.h.e.351.2		56
5.3	odd	4		875.2.h.d.351.13		56
5.4	even	2		875.2.n.c.274.1		56
25.6	even	5		875.2.n.c.99.1		56
25.8	odd	20		875.2.h.d.526.13		56
25.12	odd	20		4375.2.a.o.1.4		28
25.13	odd	20		4375.2.a.p.1.25		28
25.17	odd	20		875.2.h.e.526.2		56
25.19	even	10	inner	175.2.n.a.169.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.14	✓	56	1.1	even	1	trivial
175.2.n.a.169.14	yes	56	25.19	even	10	inner
875.2.h.d.351.13		56	5.3	odd	4
875.2.h.d.526.13		56	25.8	odd	20
875.2.h.e.351.2		56	5.2	odd	4
875.2.h.e.526.2		56	25.17	odd	20
875.2.n.c.99.1		56	25.6	even	5
875.2.n.c.274.1		56	5.4	even	2
4375.2.a.o.1.4		28	25.12	odd	20
4375.2.a.p.1.25		28	25.13	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44207 + 0.793475i) q^{2} +(-1.88310 + 2.59187i) q^{3} +(3.71604 + 2.69986i) q^{4} +(0.256301 - 2.22133i) q^{5} +(-6.65525 + 4.83532i) q^{6} -1.00000i q^{7} +(3.91399 + 5.38714i) q^{8} +(-2.24466 - 6.90836i) q^{9} +O(q^{10})\)	\(q+(2.44207 + 0.793475i) q^{2} +(-1.88310 + 2.59187i) q^{3} +(3.71604 + 2.69986i) q^{4} +(0.256301 - 2.22133i) q^{5} +(-6.65525 + 4.83532i) q^{6} -1.00000i q^{7} +(3.91399 + 5.38714i) q^{8} +(-2.24466 - 6.90836i) q^{9} +(2.38847 - 5.22127i) q^{10} +(-0.140883 + 0.433593i) q^{11} +(-13.9954 + 4.54738i) q^{12} +(-2.11592 + 0.687503i) q^{13} +(0.793475 - 2.44207i) q^{14} +(5.27476 + 4.84730i) q^{15} +(2.44485 + 7.52447i) q^{16} +(1.36142 + 1.87383i) q^{17} -18.6517i q^{18} +(4.06801 - 2.95558i) q^{19} +(6.94972 - 7.56259i) q^{20} +(2.59187 + 1.88310i) q^{21} +(-0.688091 + 0.947076i) q^{22} +(1.71708 + 0.557914i) q^{23} -21.3332 q^{24} +(-4.86862 - 1.13866i) q^{25} -5.71272 q^{26} +(12.9917 + 4.22126i) q^{27} +(2.69986 - 3.71604i) q^{28} +(-3.05970 - 2.22300i) q^{29} +(9.03510 + 16.0228i) q^{30} +(-3.06113 + 2.22404i) q^{31} +6.99741i q^{32} +(-0.858520 - 1.18165i) q^{33} +(1.83783 + 5.65626i) q^{34} +(-2.22133 - 0.256301i) q^{35} +(10.3104 - 31.7320i) q^{36} +(-3.77053 + 1.22512i) q^{37} +(12.2795 - 3.98986i) q^{38} +(2.20257 - 6.77882i) q^{39} +(12.9698 - 7.31353i) q^{40} +(-3.31529 - 10.2034i) q^{41} +(4.83532 + 6.65525i) q^{42} +8.62633i q^{43} +(-1.69417 + 1.23089i) q^{44} +(-15.9211 + 3.21551i) q^{45} +(3.75054 + 2.72493i) q^{46} +(-0.101111 + 0.139167i) q^{47} +(-24.1063 - 7.83263i) q^{48} -1.00000 q^{49} +(-10.9860 - 6.64381i) q^{50} -7.42041 q^{51} +(-9.71901 - 3.15790i) q^{52} +(-0.497619 + 0.684914i) q^{53} +(28.3771 + 20.6172i) q^{54} +(0.927045 + 0.424078i) q^{55} +(5.38714 - 3.91399i) q^{56} +16.1094i q^{57} +(-5.70809 - 7.85651i) q^{58} +(1.82037 + 5.60254i) q^{59} +(6.51420 + 32.2539i) q^{60} +(-1.91871 + 5.90518i) q^{61} +(-9.24019 + 3.00232i) q^{62} +(-6.90836 + 2.24466i) q^{63} +(-0.662572 + 2.03919i) q^{64} +(0.984860 + 4.87636i) q^{65} +(-1.15895 - 3.56688i) q^{66} +(-3.43667 - 4.73018i) q^{67} +10.6389i q^{68} +(-4.67949 + 3.39985i) q^{69} +(-5.22127 - 2.38847i) q^{70} +(2.53925 + 1.84488i) q^{71} +(28.4307 - 39.1315i) q^{72} +(-4.61606 - 1.49985i) q^{73} -10.1800 q^{74} +(12.1194 - 10.4746i) q^{75} +23.0966 q^{76} +(0.433593 + 0.140883i) q^{77} +(10.7577 - 14.8066i) q^{78} +(-11.9870 - 8.70904i) q^{79} +(17.3409 - 3.50228i) q^{80} +(-17.7759 + 12.9150i) q^{81} -27.5480i q^{82} +(7.74495 + 10.6600i) q^{83} +(4.54738 + 13.9954i) q^{84} +(4.51133 - 2.54389i) q^{85} +(-6.84478 + 21.0661i) q^{86} +(11.5235 - 3.74420i) q^{87} +(-2.88724 + 0.938122i) q^{88} +(0.802112 - 2.46865i) q^{89} +(-41.4317 - 4.78046i) q^{90} +(0.687503 + 2.11592i) q^{91} +(4.87447 + 6.70913i) q^{92} -12.1221i q^{93} +(-0.357344 + 0.259626i) q^{94} +(-5.52269 - 9.79391i) q^{95} +(-18.1364 - 13.1768i) q^{96} +(2.98616 - 4.11009i) q^{97} +(-2.44207 - 0.793475i) q^{98} +3.31165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

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