LMFDB - Embedded newform 525.2.bp.a.59.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(59,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("525.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bp (of order $30$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			59.20
Character	$\chi$	$=$	525.59
Dual form			525.2.bp.a.89.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.166978 + 1.58869i) q^{2} +(-1.07806 + 1.35565i) q^{3} +(-0.539759 - 0.114729i) q^{4} +(-0.154769 + 2.23071i) q^{5} +(-1.97370 - 1.93906i) q^{6} +(-2.37636 - 1.16314i) q^{7} +(-0.714876 + 2.20016i) q^{8} +(-0.675580 - 2.92294i) q^{9} +O(q^{10})$	\(q+(-0.166978 + 1.58869i) q^{2} +(-1.07806 + 1.35565i) q^{3} +(-0.539759 - 0.114729i) q^{4} +(-0.154769 + 2.23071i) q^{5} +(-1.97370 - 1.93906i) q^{6} +(-2.37636 - 1.16314i) q^{7} +(-0.714876 + 2.20016i) q^{8} +(-0.675580 - 2.92294i) q^{9} +(-3.51806 - 0.618358i) q^{10} +(-1.14988 - 2.58268i) q^{11} +(0.737425 - 0.608040i) q^{12} +(0.739425 - 0.537224i) q^{13} +(2.24468 - 3.58108i) q^{14} +(-2.85721 - 2.61464i) q^{15} +(-4.38423 - 1.95198i) q^{16} +(-2.67479 + 2.40839i) q^{17} +(4.75646 - 0.585219i) q^{18} +(0.499057 + 2.34788i) q^{19} +(0.339465 - 1.18629i) q^{20} +(4.13867 - 1.96758i) q^{21} +(4.29509 - 1.39556i) q^{22} +(-0.00342274 + 0.0325652i) q^{23} +(-2.21197 - 3.34102i) q^{24} +(-4.95209 - 0.690487i) q^{25} +(0.730014 + 1.26442i) q^{26} +(4.69080 + 2.23525i) q^{27} +(1.14922 + 0.900456i) q^{28} +(-0.897979 + 0.291771i) q^{29} +(4.63095 - 4.10263i) q^{30} +(3.39075 - 3.05305i) q^{31} +(1.51978 - 2.63234i) q^{32} +(4.74086 + 1.22544i) q^{33} +(-3.37955 - 4.65155i) q^{34} +(2.96242 - 5.12094i) q^{35} +(0.0293030 + 1.65519i) q^{36} +(-3.95576 + 8.88478i) q^{37} +(-3.81338 + 0.400802i) q^{38} +(-0.0688555 + 1.58156i) q^{39} +(-4.79727 - 1.93519i) q^{40} +(-4.36235 + 3.16943i) q^{41} +(2.43481 + 6.90361i) q^{42} -10.1283i q^{43} +(0.324351 + 1.52595i) q^{44} +(6.62478 - 1.05464i) q^{45} +(-0.0511645 - 0.0108753i) q^{46} +(6.17557 + 5.56051i) q^{47} +(7.37266 - 3.83913i) q^{48} +(4.29419 + 5.52810i) q^{49} +(1.92386 - 7.75204i) q^{50} +(-0.381358 - 6.22246i) q^{51} +(-0.460747 + 0.205138i) q^{52} +(-6.13365 - 1.30375i) q^{53} +(-4.33439 + 7.07900i) q^{54} +(5.93917 - 2.16533i) q^{55} +(4.25791 - 4.39687i) q^{56} +(-3.72091 - 1.85460i) q^{57} +(-0.313591 - 1.47533i) q^{58} +(-0.466981 - 4.44302i) q^{59} +(1.24223 + 1.73908i) q^{60} +(-2.12256 - 0.223090i) q^{61} +(4.28417 + 5.89665i) q^{62} +(-1.79438 + 7.73177i) q^{63} +(-3.83696 - 2.78772i) q^{64} +(1.08395 + 1.73258i) q^{65} +(-2.73847 + 7.32713i) q^{66} +(-4.69897 + 4.23097i) q^{67} +(1.72005 - 0.993073i) q^{68} +(-0.0404571 - 0.0397472i) q^{69} +(7.64094 + 5.56145i) q^{70} +(4.27261 - 1.38826i) q^{71} +(6.91390 + 0.603156i) q^{72} +(6.16025 - 2.74272i) q^{73} +(-13.4546 - 7.76804i) q^{74} +(6.27471 - 5.96892i) q^{75} -1.32454i q^{76} +(-0.271491 + 7.47487i) q^{77} +(-2.50111 - 0.373476i) q^{78} +(-4.93967 + 5.48606i) q^{79} +(5.03284 - 9.47781i) q^{80} +(-8.08718 + 3.94936i) q^{81} +(-4.30683 - 7.45964i) q^{82} +(-10.1603 - 3.30130i) q^{83} +(-2.45963 + 0.587192i) q^{84} +(-4.95843 - 6.33940i) q^{85} +(16.0908 + 1.69121i) q^{86} +(0.572534 - 1.53189i) q^{87} +(6.50434 - 0.683634i) q^{88} +(-1.61232 + 15.3402i) q^{89} +(0.569301 + 10.7008i) q^{90} +(-2.38201 + 0.416580i) q^{91} +(0.00558364 - 0.0171847i) q^{92} +(0.483437 + 7.88805i) q^{93} +(-9.86511 + 8.88259i) q^{94} +(-5.31466 + 0.749870i) q^{95} +(1.93012 + 4.89810i) q^{96} +(0.0882345 + 0.271558i) q^{97} +(-9.49948 + 5.89907i) q^{98} +(-6.77219 + 5.10585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.166978	+	1.58869i	−0.118071	+	1.12337i	0.761685	+	0.647948i	$0.224373\pi$
$2$	−0.166978	+	1.58869i	−0.118071	+	1.12337i	−0.879756	+	0.475426i	$0.842294\pi$
$3$	−1.07806	+	1.35565i	−0.622417	+	0.782686i
$3$	−1.07806	+	1.35565i	−0.622417	+	0.782686i
$4$	−0.539759	−	0.114729i	−0.269880	−	0.0573647i
$5$	−0.154769	+	2.23071i	−0.0692147	+	0.997602i
$5$	−0.154769	+	2.23071i	−0.0692147	+	0.997602i
$6$	−1.97370	−	1.93906i	−0.805759	−	0.791620i
$7$	−2.37636	−	1.16314i	−0.898180	−	0.439627i
$7$	−2.37636	−	1.16314i	−0.898180	−	0.439627i
$8$	−0.714876	+	2.20016i	−0.252747	+	0.777874i
$9$	−0.675580	−	2.92294i	−0.225193	−	0.974314i
$10$	−3.51806	−	0.618358i	−1.11251	−	0.195542i
$11$	−1.14988	−	2.58268i	−0.346703	−	0.778708i	−0.999771	−	0.0214085i	$-0.993185\pi$
$11$	−1.14988	−	2.58268i	−0.346703	−	0.778708i	0.653068	−	0.757300i	$-0.273482\pi$
$12$	0.737425	−	0.608040i	0.212876	−	0.175526i
$13$	0.739425	−	0.537224i	0.205080	−	0.148999i	−0.480505	−	0.876992i	$-0.659547\pi$
$13$	0.739425	−	0.537224i	0.205080	−	0.148999i	0.685585	+	0.727993i	$0.259547\pi$
$14$	2.24468	−	3.58108i	0.599915	−	0.957085i
$15$	−2.85721	−	2.61464i	−0.737728	−	0.675098i
$16$	−4.38423	−	1.95198i	−1.09606	−	0.487996i
$17$	−2.67479	+	2.40839i	−0.648731	+	0.584120i	−0.926393	−	0.376559i	$-0.877107\pi$
$17$	−2.67479	+	2.40839i	−0.648731	+	0.584120i	0.277662	+	0.960679i	$0.410441\pi$
$18$	4.75646	−	0.585219i	1.12111	−	0.137938i
$19$	0.499057	+	2.34788i	0.114491	+	0.538640i	0.997586	+	0.0694445i	$0.0221227\pi$
$19$	0.499057	+	2.34788i	0.114491	+	0.538640i	−0.883094	+	0.469195i	$0.844544\pi$
$20$	0.339465	−	1.18629i	0.0759067	−	0.265262i
$21$	4.13867	−	1.96758i	0.903133	−	0.429361i
$22$	4.29509	−	1.39556i	0.915716	−	0.297534i
$23$	−0.00342274	+	0.0325652i	−0.000713691	+	0.00679031i	−0.994873	−	0.101133i	$-0.967753\pi$
$23$	−0.00342274	+	0.0325652i	−0.000713691	+	0.00679031i	0.994159	+	0.107923i	$0.0344200\pi$
$24$	−2.21197	−	3.34102i	−0.451517	−	0.681984i
$25$	−4.95209	−	0.690487i	−0.990419	−	0.138097i
$26$	0.730014	+	1.26442i	0.143168	+	0.247973i
$27$	4.69080	+	2.23525i	0.902746	+	0.430175i
$28$	1.14922	+	0.900456i	0.217181	+	0.170170i
$29$	−0.897979	+	0.291771i	−0.166750	+	0.0541805i	−0.391202	−	0.920305i	$-0.627941\pi$
$29$	−0.897979	+	0.291771i	−0.166750	+	0.0541805i	0.224452	+	0.974485i	$0.427941\pi$
$30$	4.63095	−	4.10263i	0.845492	−	0.749034i
$31$	3.39075	−	3.05305i	0.608998	−	0.548344i	−0.305883	−	0.952069i	$-0.598952\pi$
$31$	3.39075	−	3.05305i	0.608998	−	0.548344i	0.914880	+	0.403725i	$0.132285\pi$
$32$	1.51978	−	2.63234i	0.268662	−	0.465336i
$33$	4.74086	+	1.22544i	0.825278	+	0.213322i
$34$	−3.37955	−	4.65155i	−0.579588	−	0.797735i
$35$	2.96242	−	5.12094i	0.500740	−	0.865598i
$36$	0.0293030	+	1.65519i	0.00488383	+	0.275866i
$37$	−3.95576	+	8.88478i	−0.650323	+	1.46065i	0.223647	+	0.974670i	$0.428204\pi$
$37$	−3.95576	+	8.88478i	−0.650323	+	1.46065i	−0.873970	+	0.485979i	$0.838463\pi$
$38$	−3.81338	+	0.400802i	−0.618612	+	0.0650187i
$39$	−0.0688555	+	1.58156i	−0.0110257	+	0.253252i
$40$	−4.79727	−	1.93519i	−0.758515	−	0.305981i
$41$	−4.36235	+	3.16943i	−0.681284	+	0.494982i	−0.873783	−	0.486315i	$-0.838341\pi$
$41$	−4.36235	+	3.16943i	−0.681284	+	0.494982i	0.192499	+	0.981297i	$0.438341\pi$
$42$	2.43481	+	6.90361i	0.375699	+	1.06525i
$43$		−	10.1283i		−	1.54456i	−0.635284	−	0.772279i	$-0.719117\pi$
$43$		−	10.1283i		−	1.54456i	0.635284	−	0.772279i	$-0.280883\pi$
$44$	0.324351	+	1.52595i	0.0488978	+	0.230046i
$45$	6.62478	−	1.05464i	0.987564	−	0.157216i
$46$	−0.0511645	−	0.0108753i	−0.00754379	−	0.00160348i
$47$	6.17557	+	5.56051i	0.900800	+	0.811084i	0.982632	−	0.185562i	$-0.0594107\pi$
$47$	6.17557	+	5.56051i	0.900800	+	0.811084i	−0.0818328	+	0.996646i	$0.526077\pi$
$48$	7.37266	−	3.83913i	1.06415	−	0.554130i
$49$	4.29419	+	5.52810i	0.613456	+	0.789729i
$50$	1.92386	−	7.75204i	0.272075	−	1.09630i
$51$	−0.381358	−	6.22246i	−0.0534008	−	0.871319i
$52$	−0.460747	+	0.205138i	−0.0638941	+	0.0284475i
$53$	−6.13365	−	1.30375i	−0.842521	−	0.179083i	−0.233619	−	0.972328i	$-0.575057\pi$
$53$	−6.13365	−	1.30375i	−0.842521	−	0.179083i	−0.608903	+	0.793245i	$0.708390\pi$
$54$	−4.33439	+	7.07900i	−0.589835	+	0.963329i
$55$	5.93917	−	2.16533i	0.800838	−	0.291974i
$56$	4.25791	−	4.39687i	0.568987	−	0.587557i
$57$	−3.72091	−	1.85460i	−0.492847	−	0.245648i
$58$	−0.313591	−	1.47533i	−0.0411765	−	0.193720i
$59$	−0.466981	−	4.44302i	−0.0607957	−	0.578432i	−0.981938	−	0.189205i	$-0.939409\pi$
$59$	−0.466981	−	4.44302i	−0.0607957	−	0.578432i	0.921142	−	0.389227i	$-0.127258\pi$
$60$	1.24223	+	1.73908i	0.160371	+	0.224515i
$61$	−2.12256	−	0.223090i	−0.271766	−	0.0285637i	−0.0323346	−	0.999477i	$-0.510294\pi$
$61$	−2.12256	−	0.223090i	−0.271766	−	0.0285637i	−0.239431	+	0.970913i	$0.576961\pi$
$62$	4.28417	+	5.89665i	0.544090	+	0.748875i
$63$	−1.79438	+	7.73177i	−0.226071	+	0.974111i
$64$	−3.83696	−	2.78772i	−0.479621	−	0.348465i
$65$	1.08395	+	1.73258i	0.134447	+	0.214901i
$66$	−2.73847	+	7.32713i	−0.337082	+	0.901908i
$67$	−4.69897	+	4.23097i	−0.574071	+	0.516895i	−0.904239	−	0.427027i	$-0.859561\pi$
$67$	−4.69897	+	4.23097i	−0.574071	+	0.516895i	0.330169	+	0.943922i	$0.392894\pi$
$68$	1.72005	−	0.993073i	0.208587	−	0.120428i
$69$	−0.0404571	−	0.0397472i	−0.00487047	−	0.00478500i
$70$	7.64094	+	5.56145i	0.913266	+	0.664720i
$71$	4.27261	−	1.38826i	0.507066	−	0.164756i	−0.0443016	−	0.999018i	$-0.514106\pi$
$71$	4.27261	−	1.38826i	0.507066	−	0.164756i	0.551367	+	0.834263i	$0.314106\pi$
$72$	6.91390	+	0.603156i	0.814811	+	0.0710827i
$73$	6.16025	−	2.74272i	0.721002	−	0.321011i	−0.0132270	−	0.999913i	$-0.504210\pi$
$73$	6.16025	−	2.74272i	0.721002	−	0.321011i	0.734229	+	0.678902i	$0.237544\pi$
$74$	−13.4546	−	7.76804i	−1.56407	−	0.903017i
$75$	6.27471	−	5.96892i	0.724541	−	0.689232i
$76$		−	1.32454i		−	0.151936i
$77$	−0.271491	+	7.47487i	−0.0309392	+	0.851840i
$78$	−2.50111	−	0.373476i	−0.283195	−	0.0422878i
$79$	−4.93967	+	5.48606i	−0.555756	+	0.617230i	−0.953911	−	0.300088i	$-0.902984\pi$
$79$	−4.93967	+	5.48606i	−0.555756	+	0.617230i	0.398155	+	0.917318i	$0.369650\pi$
$80$	5.03284	−	9.47781i	0.562689	−	1.05965i
$81$	−8.08718	+	3.94936i	−0.898576	+	0.438818i
$82$	−4.30683	−	7.45964i	−0.475610	−	0.823780i
$83$	−10.1603	−	3.30130i	−1.11524	−	0.362364i	−0.307292	−	0.951615i	$-0.599423\pi$
$83$	−10.1603	−	3.30130i	−1.11524	−	0.362364i	−0.807950	+	0.589251i	$0.799423\pi$
$84$	−2.45963	+	0.587192i	−0.268367	+	0.0640679i
$85$	−4.95843	−	6.33940i	−0.537817	−	0.687605i
$86$	16.0908	+	1.69121i	1.73512	+	0.182368i
$87$	0.572534	−	1.53189i	0.0613821	−	0.164236i
$88$	6.50434	−	0.683634i	0.693365	−	0.0728756i
$89$	−1.61232	+	15.3402i	−0.170905	+	1.62605i	0.487314	+	0.873227i	$0.337977\pi$
$89$	−1.61232	+	15.3402i	−0.170905	+	1.62605i	−0.658219	+	0.752827i	$0.728690\pi$
$90$	0.569301	+	10.7008i	0.0600096	+	1.12797i
$91$	−2.38201	+	0.416580i	−0.249702	+	0.0436694i
$92$	0.00558364	−	0.0171847i	0.000582134	−	0.00179163i
$93$	0.483437	+	7.88805i	0.0501301	+	0.817952i
$94$	−9.86511	+	8.88259i	−1.01751	+	0.916169i
$95$	−5.31466	+	0.749870i	−0.545273	+	0.0769351i
$96$	1.93012	+	4.89810i	0.196992	+	0.499911i
$97$	0.0882345	+	0.271558i	0.00895885	+	0.0275725i	0.955436	−	0.295198i	$-0.0953857\pi$
$97$	0.0882345	+	0.271558i	0.00895885	+	0.0275725i	−0.946477	+	0.322771i	$0.895386\pi$
$98$	−9.49948	+	5.89907i	−0.959592	+	0.595896i
$99$	−6.77219	+	5.10585i	−0.680631	+	0.513158i
$100$	2.59372	+	0.940847i	0.259372	+	0.0940847i
$101$	−6.65931	+	11.5343i	−0.662627	+	1.14770i	0.317296	+	0.948326i	$0.397225\pi$
$101$	−6.65931	+	11.5343i	−0.662627	+	1.14770i	−0.979923	+	0.199376i	$0.936108\pi$
$102$	9.94924	+	0.433154i	0.985121	+	0.0428887i
$103$	−3.12417	+	3.46974i	−0.307833	+	0.341883i	−0.877134	−	0.480246i	$-0.840547\pi$
$103$	−3.12417	+	3.46974i	−0.307833	+	0.341883i	0.569301	+	0.822129i	$0.307214\pi$
$104$	0.653381	+	2.01090i	0.0640693	+	0.197185i
$105$	3.74855	+	9.53668i	0.365821	+	0.930685i
$106$	3.09543	−	9.52677i	0.300655	−	0.925321i
$107$	7.59391	+	13.1530i	0.734131	+	1.27155i	0.955103	+	0.296272i	$0.0957436\pi$
$107$	7.59391	+	13.1530i	0.734131	+	1.27155i	−0.220972	+	0.975280i	$0.570923\pi$
$108$	−2.27546	−	1.74467i	−0.218956	−	0.167881i
$109$	−1.79106	−	17.0408i	−0.171553	−	1.63221i	−0.654145	−	0.756369i	$-0.726971\pi$
$109$	−1.79106	−	17.0408i	−0.171553	−	1.63221i	0.482593	−	0.875845i	$-0.339695\pi$
$110$	2.44833	+	9.79706i	0.233440	+	0.934113i
$111$	−7.78013	−	14.9409i	−0.738457	−	1.41813i
$112$	8.14807	+	9.73810i	0.769920	+	0.920164i
$113$	−16.2412	+	11.7999i	−1.52784	+	1.11004i	−0.570418	+	0.821355i	$0.693219\pi$
$113$	−16.2412	+	11.7999i	−1.52784	+	1.11004i	−0.957423	+	0.288687i	$0.906781\pi$
$114$	3.56770	−	5.60170i	0.334146	−	0.524647i
$115$	−0.0721136	−	0.0126752i	−0.00672463	−	0.00118197i
$116$	0.518167	−	0.0544615i	0.0481106	−	0.00505663i
$117$	−2.06981	−	1.79836i	−0.191354	−	0.166258i
$118$	7.13656			0.656974
$119$	9.15756	−	2.61204i	0.839472	−	0.239445i
$120$	7.79518	−	4.41717i	0.711600	−	0.403231i
$121$	2.01242	−	2.23502i	0.182947	−	0.203184i
$122$	0.708841	−	3.33483i	0.0641754	−	0.301922i
$123$	0.406223	−	9.33065i	0.0366279	−	0.841317i
$124$	−2.18047	+	1.25889i	−0.195812	+	0.113052i
$125$	2.30670	−	10.9398i	0.206318	−	0.978485i
$126$	−11.9838	−	4.14175i	−1.06760	−	0.368977i
$127$	−8.69790	+	11.9716i	−0.771814	+	1.06231i	0.224325	+	0.974514i	$0.427982\pi$
$127$	−8.69790	+	11.9716i	−0.771814	+	1.06231i	−0.996138	+	0.0877960i	$0.972018\pi$
$128$	9.13723	−	10.1479i	0.807625	−	0.896958i
$129$	13.7305	+	10.9189i	1.20890	+	0.961360i
$130$	−2.93353	+	1.43275i	−0.257288	+	0.125661i
$131$	−5.72385	+	1.21664i	−0.500095	+	0.106298i	−0.451051	−	0.892498i	$-0.648951\pi$
$131$	−5.72385	+	1.21664i	−0.500095	+	0.106298i	−0.0490438	+	0.998797i	$0.515617\pi$
$132$	−2.41833	−	1.20536i	−0.210488	−	0.104913i
$133$	1.54498	−	6.15988i	0.133967	−	0.534129i
$134$	−5.93708	−	8.17169i	−0.512885	−	0.705926i
$135$	−5.71218	+	10.1179i	−0.491626	+	0.870806i
$136$	−3.38670	−	7.60666i	−0.290407	−	0.652265i
$137$	0.000983626		0.00935858i	8.40368e−5		0.000799557i	0.994564	−	0.104129i	$-0.0332054\pi$
$137$	0.000983626		0.00935858i	8.40368e−5		0.000799557i	−0.994480	+	0.104928i	$0.966539\pi$
$138$	0.0699015	−	0.0576369i	0.00595041	−	0.00490638i
$139$	−4.19204	+	5.76984i	−0.355564	+	0.489392i	−0.948906	−	0.315559i	$-0.897808\pi$
$139$	−4.19204	+	5.76984i	−0.355564	+	0.489392i	0.593342	+	0.804950i	$0.297808\pi$
$140$	−2.18652	+	2.42420i	−0.184794	+	0.204882i
$141$	−14.1957	+	2.37737i	−1.19550	+	0.200210i
$142$	1.49208	+	7.01967i	0.125212	+	0.589077i
$143$	−2.23773	−	1.29195i	−0.187128	−	0.108039i
$144$	−2.74364	+	14.1336i	−0.228637	+	1.17780i
$145$	−0.511876	−	2.04828i	−0.0425090	−	0.170101i
$146$	3.32870	+	10.2447i	0.275485	+	0.847857i
$147$	−12.1236	−	0.138193i	−0.999935	−	0.0113980i
$148$	3.15450	−	4.34180i	0.259299	−	0.356894i
$149$	−8.38937	+	4.84361i	−0.687284	+	0.396804i	−0.802594	−	0.596526i	$-0.796547\pi$
$149$	−8.38937	+	4.84361i	−0.687284	+	0.396804i	0.115310	+	0.993330i	$0.463214\pi$
$150$	8.43503	+	10.9652i	0.688718	+	0.895308i
$151$	−4.03889	+	6.99557i	−0.328680	+	0.569291i	−0.982250	−	0.187575i	$-0.939937\pi$
$151$	−4.03889	+	6.99557i	−0.328680	+	0.569291i	0.653570	+	0.756866i	$0.273271\pi$
$152$	−5.52247	−	0.580435i	−0.447931	−	0.0470795i
$153$	8.84661	+	6.19119i	0.715206	+	0.500528i
$154$	−11.8299	−	1.67945i	−0.953282	−	0.135334i
$155$	6.28567	+	8.03629i	0.504877	+	0.645490i
$156$	0.218617	−	0.845762i	0.0175034	−	0.0677151i
$157$	−0.0789561	+	0.136756i	−0.00630138	+	0.0109143i	−0.869159	−	0.494533i	$-0.835339\pi$
$157$	−0.0789561	+	0.136756i	−0.00630138	+	0.0109143i	0.862858	+	0.505447i	$0.168672\pi$
$158$	−7.89083	−	8.76365i	−0.627760	−	0.697199i
$159$	8.37986	−	6.90957i	0.664566	−	0.547965i
$160$	5.63675	+	3.79758i	0.445624	+	0.300225i
$161$	0.0460117	−	0.0734055i	0.00362623	−	0.00578517i
$162$	−4.92393	−	13.5075i	−0.386860	−	1.06125i
$163$	9.04486	−	20.3151i	0.708448	−	1.59120i	−0.0947580	−	0.995500i	$-0.530208\pi$
$163$	9.04486	−	20.3151i	0.708448	−	1.59120i	0.803206	−	0.595701i	$-0.203126\pi$
$164$	2.71824	−	1.21024i	0.212259	−	0.0945039i
$165$	−3.46733	+	10.3858i	−0.269932	+	0.808533i
$166$	6.94129	−	15.5904i	0.538749	−	1.21005i
$167$	7.79374	+	2.53234i	0.603097	+	0.195958i	0.594621	−	0.804006i	$-0.297302\pi$
$167$	7.79374	+	2.53234i	0.603097	+	0.195958i	0.00847601	+	0.999964i	$0.497302\pi$
$168$	1.37035	+	10.5123i	0.105725	+	0.811043i
$169$	−3.75908	+	11.5693i	−0.289160	+	0.889943i
$170$	10.8993	−	6.81887i	0.835938	−	0.522983i
$171$	6.52556	−	3.04489i	0.499022	−	0.232849i
$172$	−1.16202	+	5.46687i	−0.0886031	+	0.416845i
$173$	5.95509	+	0.625906i	0.452757	+	0.0475867i	0.328163	−	0.944621i	$-0.393570\pi$
$173$	5.95509	+	0.625906i	0.452757	+	0.0475867i	0.124594	+	0.992208i	$0.460237\pi$
$174$	2.33810	+	1.16537i	0.177251	+	0.0883466i
$175$	10.9648	+	7.40085i	0.828863	+	0.559451i
$176$			13.5676i			1.02270i
$177$	6.52662	+	4.15678i	0.490571	+	0.312442i
$178$	−24.1015	−	5.12294i	−1.80649	−	0.383981i
$179$	1.57620	−	7.41545i	0.117811	−	0.554256i	−0.879163	−	0.476521i	$-0.841898\pi$
$179$	1.57620	−	7.41545i	0.117811	−	0.554256i	0.996974	−	0.0777356i	$-0.0247690\pi$
$180$	−3.69678	−	0.190806i	−0.275542	−	0.0142218i
$181$	1.13530	+	0.368880i	0.0843860	+	0.0274187i	0.350906	−	0.936411i	$-0.385874\pi$
$181$	1.13530	+	0.368880i	0.0843860	+	0.0274187i	−0.266520	+	0.963829i	$0.585874\pi$
$182$	−0.264073	−	3.85383i	−0.0195744	−	0.285665i
$183$	2.59067	−	2.63694i	0.191508	−	0.194928i
$184$	−0.0692018	−	0.0308106i	−0.00510163	−	0.00227139i
$185$	−19.2071	−	10.1992i	−1.41213	−	0.749862i
$186$	−12.6124	−	0.549098i	−0.924785	−	0.0402618i
$187$	9.29580	+	4.13876i	0.679776	+	0.302656i
$188$	−2.69537	−	3.70986i	−0.196580	−	0.270569i
$189$	−8.54713	−	10.7679i	−0.621712	−	0.783246i
$190$	−0.303880	−	8.56856i	−0.0220458	−	0.621629i
$191$	7.32096	−	16.4431i	0.529726	−	1.18978i	−0.428440	−	0.903570i	$-0.640937\pi$
$191$	7.32096	−	16.4431i	0.529726	−	1.18978i	0.958166	−	0.286214i	$-0.0923967\pi$
$192$	7.91564	−	2.19626i	0.571262	−	0.158502i
$193$	9.69137	+	5.59532i	0.697600	+	0.402760i	0.806453	−	0.591298i	$-0.201384\pi$
$193$	9.69137	+	5.59532i	0.697600	+	0.402760i	−0.108853	+	0.994058i	$0.534718\pi$
$194$	−0.446154	+	0.0948330i	−0.0320320	+	0.00680861i
$195$	−3.51734	−	0.398373i	−0.251882	−	0.0285281i
$196$	−1.68359	−	3.47651i	−0.120257	−	0.248322i
$197$	−7.81190	−	24.0425i	−0.556575	−	1.71296i	−0.691748	−	0.722139i	$-0.743159\pi$
$197$	−7.81190	−	24.0425i	−0.556575	−	1.71296i	0.135174	−	0.990822i	$-0.456841\pi$
$198$	−6.98081	−	11.6115i	−0.496105	−	0.825192i
$199$	20.7338	+	11.9707i	1.46978	+	0.848580i	0.999425	−	0.0338958i	$-0.0107914\pi$
$199$	20.7338	+	11.9707i	1.46978	+	0.848580i	0.470358	+	0.882476i	$0.344125\pi$
$200$	5.05931	−	10.4018i	0.357747	−	0.735518i
$201$	−0.669956	−	10.9314i	−0.0472551	−	0.771041i
$202$	−17.2124	−	12.5056i	−1.21106	−	0.879888i
$203$	2.47329	+	0.351125i	0.173591	+	0.0246442i
$204$	−0.508057	+	3.40238i	−0.0355711	+	0.238214i
$205$	−6.39491	−	10.2216i	−0.446640	−	0.713910i
$206$	−4.99067	−	5.54270i	−0.347716	−	0.386178i
$207$	0.0974985	−	0.0119959i	0.00677661	−	0.000833773i
$208$	−4.29046	+	0.911965i	−0.297490	+	0.0632334i
$209$	5.48996	−	3.98869i	0.379749	−	0.275904i
$210$	−15.7768	+	4.36287i	−1.08870	+	0.301067i
$211$	21.0985	+	15.3289i	1.45248	+	1.05529i	0.985244	+	0.171153i	$0.0547493\pi$
$211$	21.0985	+	15.3289i	1.45248	+	1.05529i	0.467234	+	0.884134i	$0.345251\pi$
$212$	3.16111	+	1.40742i	0.217106	+	0.0966619i
$213$	−2.72414	+	7.28879i	−0.186655	+	0.499420i
$214$	−22.1641	+	9.86810i	−1.51511	+	0.674570i
$215$	22.5934	+	1.56755i	1.54085	+	0.106906i
$216$	−8.27126	+	8.72260i	−0.562788	+	0.593497i
$217$	−11.6088	+	3.31121i	−0.788056	+	0.224780i
$218$	27.3716			1.85384
$219$	−2.92294	+	11.3080i	−0.197514	+	0.764121i
$220$	−3.45415	+	0.487362i	−0.232879	+	0.0328579i
$221$	−0.683960	+	3.21778i	−0.0460081	+	0.216451i
$222$	25.0356	−	9.86540i	1.68028	−	0.662122i
$223$	7.95037	+	5.77628i	0.532396	+	0.386808i	0.821253	−	0.570564i	$-0.193275\pi$
$223$	7.95037	+	5.77628i	0.532396	+	0.386808i	−0.288857	+	0.957372i	$0.593275\pi$
$224$	−6.67333	+	4.48766i	−0.445881	+	0.299844i
$225$	1.32728	+	14.9412i	0.0884853	+	0.996077i
$226$	−16.0345	−	27.7725i	−1.06660	−	1.84740i
$227$	−5.02958	−	11.2966i	−0.333825	−	0.749783i	−0.999992	−	0.00398084i	$-0.998733\pi$
$227$	−5.02958	−	11.2966i	−0.333825	−	0.749783i	0.666167	−	0.745803i	$-0.267934\pi$
$228$	1.79562	+	1.42794i	0.118918	+	0.0945674i
$229$	21.5229	+	19.3793i	1.42227	+	1.28062i	0.905401	+	0.424558i	$0.139571\pi$
$229$	21.5229	+	19.3793i	1.42227	+	1.28062i	0.516873	+	0.856062i	$0.327096\pi$
$230$	0.0321784	−	0.112450i	0.00212178	−	0.00741471i
$231$	−9.84063	−	8.42639i	−0.647466	−	0.554416i
$232$		−	2.18428i		−	0.143405i
$233$	23.1246	−	4.91528i	1.51494	−	0.322011i	0.625923	−	0.779885i	$-0.284722\pi$
$233$	23.1246	−	4.91528i	1.51494	−	0.322011i	0.889017	+	0.457874i	$0.151389\pi$
$234$	3.20265	−	2.98801i	0.209364	−	0.195332i
$235$	−13.3596	+	12.9153i	−0.871487	+	0.842501i
$236$	−0.257688	+	2.45174i	−0.0167741	+	0.159595i
$237$	−2.11193	−	12.6108i	−0.137184	−	0.819157i
$238$	2.62061	+	14.9847i	0.169869	+	0.971313i
$239$	1.56571	−	2.15501i	0.101277	−	0.139396i	−0.755370	−	0.655298i	$-0.772543\pi$
$239$	1.56571	−	2.15501i	0.101277	−	0.139396i	0.856648	+	0.515902i	$0.172543\pi$
$240$	7.42291	+	17.0404i	0.479147	+	1.09995i
$241$	20.6145	−	2.16667i	1.32790	−	0.139568i	0.586126	−	0.810220i	$-0.300652\pi$
$241$	20.6145	−	2.16667i	1.32790	−	0.139568i	0.741772	+	0.670652i	$0.233986\pi$
$242$	3.21472	+	3.57031i	0.206650	+	0.229508i
$243$	3.36450	−	15.2210i	0.215833	−	0.976430i
$244$	1.12007	+	0.363934i	0.0717054	+	0.0232985i
$245$	−12.9962	+	8.72350i	−0.830295	+	0.557324i
$246$	14.7557	+	2.20338i	0.940788	+	0.140482i
$247$	1.63035	+	1.46797i	0.103737	+	0.0934049i
$248$	4.29323	+	9.64276i	0.272620	+	0.612316i
$249$	15.4289	−	10.2149i	0.977764	−	0.647342i
$250$	16.9948	+	5.49134i	1.07484	+	0.347303i
$251$	−7.72394			−0.487531			−0.243765	−	0.969834i	$-0.578383\pi$
$251$	−7.72394			−0.487531			−0.243765	+	0.969834i	$0.578383\pi$
$252$	1.85559	−	3.96742i	0.116891	−	0.249924i
$253$	0.0880413	−	0.0286064i	0.00553511	−	0.00179847i
$254$	−17.5669	−	15.8173i	−1.10224	−	0.992463i
$255$	13.9395	+	0.112345i	0.872925	+	0.00703532i
$256$	8.24915	+	9.16161i	0.515572	+	0.572601i
$257$	−26.1696	+	15.1091i	−1.63242	+	0.942477i	−0.649073	+	0.760726i	$0.724843\pi$
$257$	−26.1696	+	15.1091i	−1.63242	+	0.942477i	−0.983345	+	0.181750i	$0.941824\pi$
$258$	−19.6395	+	19.9903i	−1.22270	+	1.24454i
$259$	19.7346	−	16.5123i	1.22625	−	1.02603i
$260$	−0.386292	−	1.05954i	−0.0239568	−	0.0657098i
$261$	1.45949	+	2.42763i	0.0903399	+	0.150266i
$262$	−0.977109	−	9.29657i	−0.0603660	−	0.574344i
$263$	−2.93669	−	27.9407i	−0.181084	−	1.72290i	−0.587512	−	0.809215i	$-0.699893\pi$
$263$	−2.93669	−	27.9407i	−0.181084	−	1.72290i	0.406429	−	0.913683i	$-0.366774\pi$
$264$	−6.08529	+	9.55461i	−0.374524	+	0.588046i
$265$	3.85757	−	13.4806i	0.236969	−	0.828105i
$266$	9.52816	+	3.48306i	0.584209	+	0.213560i
$267$	−19.0577	−	18.7233i	−1.16631	−	1.14585i
$268$	3.02173	−	1.74460i	0.184581	−	0.106568i
$269$	18.8909	+	20.9805i	1.15180	+	1.27920i	0.954283	+	0.298904i	$0.0966210\pi$
$269$	18.8909	+	20.9805i	1.15180	+	1.27920i	0.197517	+	0.980300i	$0.436712\pi$
$270$	−15.1203	−	10.7643i	−0.920194	−	0.655097i
$271$	10.0755	+	9.07198i	0.612041	+	0.551084i	0.915785	−	0.401670i	$-0.131570\pi$
$271$	10.0755	+	9.07198i	0.612041	+	0.551084i	−0.303744	+	0.952754i	$0.598237\pi$
$272$	16.4280	−	5.33778i	0.996094	−	0.323651i
$273$	2.00321	−	3.67827i	0.121240	−	0.222619i
$274$	−0.0150321			−0.000908124
$275$	3.91103	+	13.5837i	0.235844	+	0.819126i
$276$	0.0172769	+	0.0260955i	0.00103995	+	0.00157077i
$277$	3.08198	+	6.92223i	0.185178	+	0.415917i	0.982150	−	0.188100i	$-0.0602328\pi$
$277$	3.08198	+	6.92223i	0.185178	+	0.415917i	−0.796972	+	0.604016i	$0.793566\pi$
$278$	−8.46652	−	7.62329i	−0.507788	−	0.457214i
$279$	−11.2146	−	7.84840i	−0.671401	−	0.469872i
$280$	9.14914	+	10.1786i	0.546766	+	0.608290i
$281$	−0.111141	−	0.0361117i	−0.00663009	−	0.00215425i	0.305700	−	0.952128i	$-0.401110\pi$
$281$	−0.111141	−	0.0361117i	−0.00663009	−	0.00215425i	−0.312330	+	0.949974i	$0.601110\pi$
$282$	−1.40652	−	22.9496i	−0.0837570	−	1.36663i
$283$	2.28949	+	2.54274i	0.136096	+	0.151150i	0.807340	−	0.590087i	$-0.200906\pi$
$283$	2.28949	+	2.54274i	0.136096	+	0.151150i	−0.671244	+	0.741236i	$0.734240\pi$
$284$	−2.46546	+	0.259130i	−0.146298	+	0.0153765i
$285$	4.71295	−	8.01323i	0.279171	−	0.474663i
$286$	2.42617	−	3.33933i	0.143462	−	0.197459i
$287$	14.0530	−	2.45768i	0.829524	−	0.145072i
$288$	−8.72090	−	2.66388i	−0.513884	−	0.156970i
$289$	−0.422837	+	4.02302i	−0.0248728	+	0.236648i
$290$	3.33956	−	0.471194i	0.196106	−	0.0276695i
$291$	−0.463259	−	0.173140i	−0.0271567	−	0.0101496i
$292$	−3.63972	+	0.773646i	−0.212998	+	0.0452742i
$293$			16.7958i			0.981221i	0.871379	+	0.490611i	$0.163226\pi$
$293$			16.7958i			0.981221i	−0.871379	+	0.490611i	$0.836774\pi$
$294$	2.24392	−	19.2375i	0.130868	−	1.12195i
$295$	9.98335	−	0.354055i	0.581253	−	0.0206139i
$296$	−16.7201	−	15.0548i	−0.971835	−	0.875044i
$297$	0.379066	−	14.6851i	0.0219956	−	0.852118i
$298$	−6.29415	−	14.1369i	−0.364610	−	0.818928i
$299$	0.0149639	+	0.0259183i	0.000865386	+	0.00149889i
$300$	−4.07164	+	2.50189i	−0.235076	+	0.144447i
$301$	−11.7807	+	24.0686i	−0.679030	+	1.38729i
$302$	−10.4394	−	7.58465i	−0.600719	−	0.436448i
$303$	−8.45732	−	21.4623i	−0.485860	−	1.23298i
$304$	2.39504	−	11.2678i	0.137365	−	0.646251i
$305$	0.826153	−	4.70027i	0.0473054	−	0.269137i
$306$	−11.3131	+	13.0207i	−0.646725	+	0.744346i
$307$	−22.8699			−1.30525			−0.652626	−	0.757680i	$-0.726333\pi$
$307$	−22.8699			−1.30525			−0.652626	+	0.757680i	$0.726333\pi$
$308$	1.00413	−	4.00348i	0.0572154	−	0.228120i
$309$	−1.33572	−	7.97586i	−0.0759864	−	0.453731i
$310$	−13.8167	+	8.64410i	−0.784738	+	0.490952i
$311$	9.86057	−	4.39021i	0.559142	−	0.248946i	−0.107651	−	0.994189i	$-0.534333\pi$
$311$	9.86057	−	4.39021i	0.559142	−	0.248946i	0.666793	+	0.745243i	$0.267666\pi$
$312$	−3.43046	−	1.28211i	−0.194212	−	0.0725853i
$313$	−24.0230	−	10.6957i	−1.35786	−	0.604557i	−0.406785	−	0.913524i	$-0.633350\pi$
$313$	−24.0230	−	10.6957i	−1.35786	−	0.604557i	−0.951073	+	0.308967i	$0.900017\pi$
$314$	−0.204079	−	0.148272i	−0.0115168	−	0.00836747i
$315$	−16.9696	−	5.19937i	−0.956127	−	0.292951i
$316$	3.29564	−	2.39442i	0.185394	−	0.134697i
$317$	−4.98279	+	1.05912i	−0.279861	+	0.0594864i	−0.345704	−	0.938344i	$-0.612360\pi$
$317$	−4.98279	+	1.05912i	−0.279861	+	0.0594864i	0.0658426	+	0.997830i	$0.479026\pi$
$318$	9.57791	+	14.4667i	0.537103	+	0.811255i
$319$	1.78612	+	1.98369i	0.100004	+	0.111065i
$320$	6.81242	−	8.12768i	0.380826	−	0.454351i
$321$	−26.0176	−	3.88505i	−1.45216	−	0.216843i
$322$	0.108936	+	0.0853554i	0.00607075	+	0.00475667i
$323$	−6.98947	−	5.07815i	−0.388904	−	0.282556i
$324$	4.81824	−	1.20387i	0.267680	−	0.0668814i
$325$	−4.03265	+	2.14982i	−0.223691	+	0.119250i
$326$	30.7641	+	17.7617i	1.70387	+	0.983727i
$327$	25.0323	+	15.9429i	1.38429	+	0.881647i
$328$	−3.85472	−	11.8636i	−0.212841	−	0.655059i
$329$	−8.20772	−	20.3969i	−0.452506	−	1.12452i
$330$	−15.9208	−	7.24272i	−0.876414	−	0.398699i
$331$	−9.84489	+	2.09260i	−0.541124	+	0.115019i	−0.470362	−	0.882474i	$-0.655877\pi$
$331$	−9.84489	+	2.09260i	−0.541124	+	0.115019i	−0.0707623	+	0.997493i	$0.522543\pi$
$332$	5.10538	+	2.94759i	0.280194	+	0.161770i
$333$	28.6421	+	5.56008i	1.56958	+	0.304691i
$334$	−5.32448	+	11.9590i	−0.291343	+	0.654367i
$335$	−8.71080	−	11.1368i	−0.475922	−	0.608471i
$336$	−21.9856	+	0.547692i	−1.19941	+	0.0298790i
$337$	13.6905	+	18.8433i	0.745767	+	1.02646i	0.998266	+	0.0588628i	$0.0187474\pi$
$337$	13.6905	+	18.8433i	0.745767	+	1.02646i	−0.252499	+	0.967597i	$0.581253\pi$
$338$	−17.7523	−	7.90383i	−0.965597	−	0.429912i
$339$	1.51238	−	34.7384i	0.0821415	−	1.88673i
$340$	1.94904	+	3.99063i	0.105702	+	0.216422i
$341$	−11.7840	−	5.24659i	−0.638141	−	0.284119i
$342$	3.74776	+	10.8755i	0.202656	+	0.588081i
$343$	−3.77457	−	18.1315i	−0.203808	−	0.979011i
$344$	22.2840	+	7.24050i	1.20147	+	0.390382i
$345$	0.0949258	−	0.0840963i	0.00511064	−	0.00452759i
$346$	−1.98874	+	9.35629i	−0.106915	+	0.502997i
$347$	−16.8001	−	3.57098i	−0.901879	−	0.191700i	−0.266440	−	0.963852i	$-0.585847\pi$
$347$	−16.8001	−	3.57098i	−0.901879	−	0.191700i	−0.635439	+	0.772151i	$0.719181\pi$
$348$	−0.484783	+	0.761166i	−0.0259871	+	0.0408028i
$349$		−	15.5564i		−	0.832715i	−0.909201	−	0.416357i	$-0.863307\pi$
$349$		−	15.5564i		−	0.832715i	0.909201	−	0.416357i	$-0.136693\pi$
$350$	−13.5885	+	16.1839i	−0.726338	+	0.865068i
$351$	4.66933	−	0.867209i	0.249230	−	0.0462882i
$352$	−8.54606	−	0.898227i	−0.455506	−	0.0478757i
$353$	1.03778	−	4.88238i	0.0552356	−	0.259863i	−0.941862	−	0.336001i	$-0.890926\pi$
$353$	1.03778	−	4.88238i	0.0552356	−	0.259863i	0.997097	+	0.0761377i	$0.0242589\pi$
$354$	−7.69363	+	9.67469i	−0.408912	+	0.514204i
$355$	2.43552	+	9.74580i	0.129264	+	0.517253i
$356$	2.63023	−	8.09501i	0.139402	−	0.429035i
$357$	−6.33137	+	15.2304i	−0.335092	+	0.806078i
$358$	11.5177	+	3.74231i	0.608727	+	0.197787i
$359$	−0.681150	+	1.52989i	−0.0359497	+	0.0807444i	−0.930628	−	0.365967i	$-0.880738\pi$
$359$	−0.681150	+	1.52989i	−0.0359497	+	0.0807444i	0.894678	+	0.446711i	$0.147405\pi$
$360$	−2.41552	+	15.3295i	−0.127309	+	0.807937i
$361$	12.0939	−	5.38455i	0.636521	−	0.283397i
$362$	−0.775606	+	1.74204i	−0.0407650	+	0.0915596i
$363$	0.860400	+	5.13762i	0.0451593	+	0.269655i
$364$	1.33351	+	0.0484335i	0.0698947	+	0.00253861i
$365$	5.16478	+	14.1662i	0.270337	+	0.741492i
$366$	3.75670	+	4.55609i	0.196366	+	0.238150i
$367$	−21.2826	−	23.6367i	−1.11094	−	1.23383i	−0.969816	−	0.243837i	$-0.921594\pi$
$367$	−21.2826	−	23.6367i	−1.11094	−	1.23383i	−0.141128	−	0.989991i	$-0.545073\pi$
$368$	0.0785728	−	0.136092i	0.00409589	−	0.00709429i
$369$	12.2112	+	10.6097i	0.635689	+	0.552318i
$370$	19.4106	−	28.8111i	1.00911	−	1.49782i
$371$	13.0593	+	10.2325i	0.678006	+	0.531244i
$372$	0.644051	−	4.31311i	0.0333925	−	0.223624i
$373$	7.43181	+	0.781115i	0.384805	+	0.0404446i	0.294956	−	0.955511i	$-0.404695\pi$
$373$	7.43181	+	0.781115i	0.384805	+	0.0404446i	0.0898487	+	0.995955i	$0.471362\pi$
$374$	−8.12739	+	14.0771i	−0.420258	+	0.727907i
$375$	12.3438	+	14.9208i	0.637430	+	0.770508i
$376$	−16.6488	+	9.61218i	−0.858595	+	0.495710i
$377$	−0.507241	+	0.698158i	−0.0261243	+	0.0359570i
$378$	18.5340	−	11.7807i	0.953284	−	0.605936i
$379$	2.38872	+	7.35173i	0.122700	+	0.377633i	0.993475	−	0.114049i	$-0.0363822\pi$
$379$	2.38872	+	7.35173i	0.122700	+	0.377633i	−0.870775	+	0.491682i	$0.836382\pi$
$380$	2.95467	+	0.204998i	0.151571	+	0.0105162i
$381$	−6.85251	−	24.6974i	−0.351065	−	1.26529i
$382$	24.9006	+	14.3764i	1.27403	+	0.735559i
$383$	−0.848397	−	3.99139i	−0.0433511	−	0.203951i	0.951142	−	0.308754i	$-0.0999120\pi$
$383$	−0.848397	−	3.99139i	−0.0433511	−	0.203951i	−0.994493	+	0.104803i	$0.966579\pi$
$384$	3.90657	+	23.3270i	0.199356	+	1.19040i
$385$	−16.6322	−	1.76249i	−0.847656	−	0.0898249i
$386$	−10.5075	+	14.4623i	−0.534816	+	0.736111i
$387$	−29.6046	+	6.84250i	−1.50488	+	0.347824i
$388$	−0.0164697	−	0.156699i	−0.000836123	−	0.00795518i
$389$	0.869063	+	1.95195i	0.0440632	+	0.0989676i	0.934236	−	0.356656i	$-0.116083\pi$
$389$	0.869063	+	1.95195i	0.0440632	+	0.0989676i	−0.890173	+	0.455623i	$0.849416\pi$
$390$	1.22021	−	5.52144i	0.0617877	−	0.279589i
$391$	−0.0692745	−	0.0953482i	−0.00350336	−	0.00482197i
$392$	−15.2325	+	5.49601i	−0.769359	+	0.277590i
$393$	4.52130	−	9.07115i	0.228069	−	0.457579i
$394$	39.5006	−	8.39611i	1.99001	−	0.422990i
$395$	−11.4733	−	11.8680i	−0.577283	−	0.597144i
$396$	4.24114	−	1.97896i	0.213126	−	0.0994466i
$397$	−6.82578	+	7.58079i	−0.342576	+	0.380469i	−0.889672	−	0.456601i	$-0.849067\pi$
$397$	−6.82578	+	7.58079i	−0.342576	+	0.380469i	0.547096	+	0.837070i	$0.315733\pi$
$398$	−22.4798	+	30.9408i	−1.12681	+	1.55092i
$399$	6.68507	+	8.73516i	0.334672	+	0.437305i
$400$	20.3633	+	12.6937i	1.01816	+	0.634683i
$401$	11.7840	−	6.80350i	0.588465	−	0.339750i	−0.176025	−	0.984386i	$-0.556324\pi$
$401$	11.7840	−	6.80350i	0.588465	−	0.339750i	0.764490	+	0.644635i	$0.222991\pi$
$402$	17.4785	+	0.760950i	0.871747	+	0.0379528i
$403$	0.867038	−	4.07909i	0.0431902	−	0.203194i
$404$	4.91774	−	5.46171i	0.244667	−	0.271730i
$405$	−7.55822	−	18.6514i	−0.375571	−	0.926794i
$406$	−0.970815	+	3.87067i	−0.0481807	+	0.192098i
$407$	27.4952			1.36289
$408$	13.9630	+	3.60924i	0.691273	+	0.178684i
$409$	−22.0156	+	2.31393i	−1.08860	+	0.114417i	−0.631784	−	0.775144i	$-0.717677\pi$
$409$	−22.0156	+	2.31393i	−1.08860	+	0.114417i	−0.456817	+	0.889561i	$0.651010\pi$
$410$	17.3068	−	8.45274i	0.854723	−	0.417451i
$411$	−0.0137474	−	0.00875564i	−0.000678108	−	0.000431884i
$412$	2.08438	−	1.51439i	0.102690	−	0.0746086i
$413$	−4.05816	+	11.1014i	−0.199689	+	0.546264i
$414$	0.00277767	+	0.156898i	0.000136515	+	0.00771111i
$415$	8.93672	−	22.1538i	0.438686	−	1.08749i
$416$	−0.290390	−	2.76288i	−0.0142375	−	0.135461i
$417$	−3.30263	−	11.9032i	−0.161731	−	0.582901i
$418$	5.42009	+	9.38787i	0.265105	+	0.459176i
$419$	0.000499553	−	0.00153747i	2.44048e−5	−	7.51102e-5i	−0.951044	−	0.309055i	$-0.899987\pi$
$419$	0.000499553	−	0.00153747i	2.44048e−5	−	7.51102e-5i	0.951069	+	0.308979i	$0.0999874\pi$
$420$	−0.929179	−	5.57758i	−0.0453393	−	0.272158i
$421$	0.535000	+	1.64656i	0.0260743	+	0.0802484i	0.963247	−	0.268618i	$-0.0865668\pi$
$421$	0.535000	+	1.64656i	0.0260743	+	0.0802484i	−0.937173	+	0.348866i	$0.886567\pi$
$422$	−27.8759	+	30.9593i	−1.35698	+	1.50708i
$423$	12.0810	−	21.8074i	0.587396	−	1.06031i
$424$	7.25325	−	12.5630i	0.352249	−	0.610113i
$425$	14.9088	−	10.0797i	0.723181	−	0.488935i
$426$	−11.1248	−	5.54488i	−0.538997	−	0.268650i
$427$	4.78448	+	2.99898i	0.231537	+	0.145131i
$428$	−2.58984	−	7.97072i	−0.125185	−	0.385279i
$429$	4.16384	−	1.64078i	0.201032	−	0.0792176i
$430$	−6.26295	+	35.6321i	−0.302026	+	1.71833i
$431$	−11.8206	+	10.6434i	−0.569380	+	0.512672i	−0.902774	−	0.430115i	$-0.858473\pi$
$431$	−11.8206	+	10.6434i	−0.569380	+	0.512672i	0.333394	+	0.942788i	$0.391806\pi$
$432$	−16.2024	−	18.9562i	−0.779537	−	0.912032i
$433$	−7.19502	+	22.1440i	−0.345770	+	1.06417i	0.615400	+	0.788215i	$0.288995\pi$
$433$	−7.19502	+	22.1440i	−0.345770	+	1.06417i	−0.961170	+	0.275957i	$0.911005\pi$
$434$	−3.32208	−	18.9957i	−0.159465	−	0.911822i
$435$	3.32859	+	1.51424i	0.159594	+	0.0726024i
$436$	−0.988340	+	9.40342i	−0.0473329	+	0.450342i
$437$	−0.0781672	+	0.00821570i	−0.00373924	+	0.000393010i
$438$	−17.4768	−	6.53182i	−0.835072	−	0.312102i
$439$	−10.7721	−	1.13219i	−0.514122	−	0.0540364i	−0.156085	−	0.987744i	$-0.549887\pi$
$439$	−10.7721	−	1.13219i	−0.514122	−	0.0540364i	−0.358038	+	0.933707i	$0.616554\pi$
$440$	0.518317	+	14.6151i	0.0247098	+	0.696746i
$441$	13.2573	−	16.2863i	0.631298	−	0.775540i
$442$	−4.99785	−	1.62390i	−0.237723	−	0.0772410i
$443$	18.6031	+	32.2215i	0.883861	+	1.53089i	0.847014	+	0.531571i	$0.178398\pi$
$443$	18.6031	+	32.2215i	0.883861	+	1.53089i	0.0368466	+	0.999321i	$0.488269\pi$
$444$	2.48523	+	8.95712i	0.117944	+	0.425086i
$445$	−33.9698	−	5.97078i	−1.61033	−	0.283042i
$446$	−10.5043	+	11.6662i	−0.497391	+	0.552409i
$447$	2.47799	−	16.5948i	0.117205	−	0.784905i
$448$	5.87550	+	11.0876i	0.277591	+	0.523838i
$449$			3.78197i			0.178482i	0.996010	+	0.0892411i	$0.0284441\pi$
$449$			3.78197i			0.178482i	−0.996010	+	0.0892411i	$0.971556\pi$
$450$	−23.9585	−	0.386211i	−1.12941	−	0.0182062i
$451$	13.2018	+	7.62208i	0.621650	+	0.358910i
$452$	10.1201	−	4.50577i	0.476010	−	0.211933i
$453$	−5.12939	−	13.0170i	−0.241000	−	0.611590i
$454$	18.7867	−	6.10416i	0.881702	−	0.286482i
$455$	−0.560606	−	5.37803i	−0.0262816	−	0.252126i
$456$	6.74041	−	6.86080i	0.315649	−	0.321286i
$457$	20.2283	−	11.6788i	0.946238	−	0.546311i	0.0543277	−	0.998523i	$-0.482698\pi$
$457$	20.2283	−	11.6788i	0.946238	−	0.546311i	0.891910	+	0.452212i	$0.149365\pi$
$458$	−34.3816	+	30.9573i	−1.60654	+	1.44654i
$459$	−17.9303	+	5.31846i	−0.836913	+	0.248244i
$460$	0.0374698	+	0.0151151i	0.00174704	+	0.000704745i
$461$	7.19098	+	5.22455i	0.334917	+	0.243332i	0.742514	−	0.669830i	$-0.233633\pi$
$461$	7.19098	+	5.22455i	0.334917	+	0.243332i	−0.407597	+	0.913162i	$0.633633\pi$
$462$	15.0301	−	14.2267i	0.699263	−	0.661886i
$463$	7.31576	+	10.0693i	0.339992	+	0.467959i	0.944439	−	0.328686i	$-0.106606\pi$
$463$	7.31576	+	10.0693i	0.339992	+	0.467959i	−0.604447	+	0.796645i	$0.706606\pi$
$464$	4.50647	+	0.473649i	0.209208	+	0.0219886i
$465$	−17.6707	−	0.142417i	−0.819460	−	0.00660442i
$466$	3.94756	+	37.5585i	0.182867	+	1.73986i
$467$	7.27016	+	34.2034i	0.336423	+	1.58275i	0.743104	+	0.669176i	$0.233353\pi$
$467$	7.27016	+	34.2034i	0.336423	+	1.58275i	−0.406681	+	0.913570i	$0.633314\pi$
$468$	0.910876	+	1.20815i	0.0421053	+	0.0558467i
$469$	16.0877	−	4.58874i	0.742860	−	0.211888i
$470$	−18.2876	−	23.3809i	−0.843545	−	1.07848i
$471$	−0.100274	−	0.254468i	−0.00462039	−	0.0117253i
$472$	10.1092	+	2.14878i	0.465314	+	0.0989054i
$473$	−26.1583	+	11.6464i	−1.20276	+	0.535503i
$474$	20.3872	−	1.24948i	0.936416	−	0.0573905i
$475$	−0.850196	−	11.9715i	−0.0390097	−	0.549290i
$476$	−5.24256	+	0.359231i	−0.240292	+	0.0164653i
$477$	0.332990	+	18.8091i	0.0152466	+	0.861209i
$478$	3.16221	+	2.84727i	0.144636	+	0.130231i
$479$	6.44223	+	1.36934i	0.294353	+	0.0625666i	0.352721	−	0.935728i	$-0.385256\pi$
$479$	6.44223	+	1.36934i	0.294353	+	0.0625666i	−0.0583683	+	0.998295i	$0.518590\pi$
$480$	−11.2249	+	3.54745i	−0.512346	+	0.161918i
$481$	1.84813	+	8.69476i	0.0842674	+	0.396447i
$482$			33.1119i			1.50820i
$483$	0.0499090	+	0.141511i	0.00227094	+	0.00643898i
$484$	−1.34265	+	0.975489i	−0.0610293	+	0.0443404i
$485$	−0.619421	+	0.154796i	−0.0281265	+	0.00702894i
$486$	23.6197	+	7.88673i	1.07141	+	0.357749i
$487$	13.6799	−	1.43782i	0.619898	−	0.0651539i	0.210626	−	0.977567i	$-0.432450\pi$
$487$	13.6799	−	1.43782i	0.619898	−	0.0651539i	0.409271	+	0.912413i	$0.365783\pi$
$488$	2.00820	−	4.51048i	0.0909068	−	0.204180i
$489$	17.7893	+	34.1625i	0.804459	+	1.54488i
$490$	−11.6889	−	22.1035i	−0.528049	−	0.998536i
$491$	−18.0022	−	24.7780i	−0.812430	−	1.11821i	−0.990944	−	0.134276i	$-0.957129\pi$
$491$	−18.0022	−	24.7780i	−0.812430	−	1.11821i	0.178514	−	0.983937i	$-0.442871\pi$
$492$	−1.28976	+	4.98970i	−0.0581470	+	0.224953i
$493$	1.69920	−	2.94311i	0.0765283	−	0.132551i
$494$	−2.60439	+	2.34500i	−0.117177	+	0.105507i
$495$	−10.3415	−	15.8970i	−0.464817	−	0.714517i
$496$	−20.8253	+	6.76656i	−0.935085	+	0.303828i
$497$	−11.7680	−	1.67067i	−0.527868	−	0.0749396i
$498$	13.6520	+	26.2173i	0.611761	+	1.17483i
$499$	5.25173	+	9.09626i	0.235100	+	0.407204i	0.959302	−	0.282383i	$-0.0911250\pi$
$499$	5.25173	+	9.09626i	0.235100	+	0.407204i	−0.724202	+	0.689588i	$0.757792\pi$
$500$	−2.50018	+	5.64021i	−0.111811	+	0.252238i
$501$	−11.8351	+	7.83558i	−0.528752	+	0.350068i
$502$	1.28973	−	12.2709i	0.0575634	−	0.547679i
$503$	12.3838	−	4.02373i	0.552165	−	0.179409i	−0.0196279	−	0.999807i	$-0.506248\pi$
$503$	12.3838	−	4.02373i	0.552165	−	0.179409i	0.571793	+	0.820398i	$0.306248\pi$
$504$	−15.7284	−	9.47518i	−0.700597	−	0.422058i
$505$	−24.6989	−	16.6401i	−1.09909	−	0.740475i
$506$	0.0307457	+	0.144647i	0.00136681	+	0.00643034i
$507$	−11.6314	−	17.5683i	−0.516567	−	0.780238i
$508$	6.06827	−	5.46389i	0.269236	−	0.242421i
$509$	−31.8801	−	14.1939i	−1.41306	−	0.629136i	−0.448690	−	0.893687i	$-0.648109\pi$
$509$	−31.8801	−	14.1939i	−1.41306	−	0.629136i	−0.964372	+	0.264552i	$0.914776\pi$
$510$	−2.50607	+	22.1268i	−0.110971	+	0.979790i
$511$	−17.8292	−	0.647563i	−0.788715	−	0.0286465i
$512$	6.16248	−	4.47730i	0.272346	−	0.197871i
$513$	−2.90712	+	12.1289i	−0.128353	+	0.535506i
$514$	−19.6338	−	44.0983i	−0.866012	−	1.94509i
$515$	−7.25644	−	7.50610i	−0.319757	−	0.330758i
$516$	−6.15844	−	7.46889i	−0.271110	−	0.328800i
$517$	7.25984	−	22.3435i	0.319287	−	0.982665i
$518$	22.9377	+	34.1094i	1.00783	+	1.49868i
$519$	−7.26845	+	7.39827i	−0.319050	+	0.324748i
$520$	−4.58685	+	1.14628i	−0.201147	+	0.0502676i
$521$	3.53521	+	0.751433i	0.154881	+	0.0329209i	0.284699	−	0.958617i	$-0.408106\pi$
$521$	3.53521	+	0.751433i	0.154881	+	0.0329209i	−0.129819	+	0.991538i	$0.541440\pi$
$522$	−4.10045	+	1.91331i	−0.179472	+	0.0837433i
$523$	−2.28691	+	21.7585i	−0.0999995	+	0.951431i	0.823366	+	0.567510i	$0.192093\pi$
$523$	−2.28691	+	21.7585i	−0.0999995	+	0.951431i	−0.923366	+	0.383921i	$0.874573\pi$
$524$	3.22908			0.141063
$525$	−21.8537	+	6.88594i	−0.953773	+	0.300527i
$526$	44.8795			1.95684
$527$	−1.71662	+	16.3325i	−0.0747770	+	0.711455i
$528$	−18.3930	−	14.6267i	−0.800451	−	0.636545i
$529$	22.4963	+	4.78175i	0.978102	+	0.207902i
$530$	20.7723	+	8.37945i	0.902293	+	0.363980i
$531$	−12.6712	+	4.36657i	−0.549884	+	0.189493i
$532$	−1.54064	+	3.14760i	−0.0667950	+	0.136466i
$533$	−1.52293	+	4.68711i	−0.0659656	+	0.203021i
$534$	32.9278	−	27.1504i	1.42492	−	1.17491i
$535$	−30.5159	+	14.9041i	−1.31932	+	0.644360i
$536$	−5.94964	−	13.3631i	−0.256985	−	0.577198i
$537$	8.35352	+	10.1311i	0.360481	+	0.437188i
$538$	−36.4859	+	26.5085i	−1.57302	+	1.14286i
$539$	9.33951	−	17.4472i	0.402281	−	0.751505i
$540$	4.24402	−	4.80585i	0.182633	−	0.206811i
$541$	−6.21476	−	2.76699i	−0.267193	−	0.118962i	0.268767	−	0.963205i	$-0.413384\pi$
$541$	−6.21476	−	2.76699i	−0.267193	−	0.118962i	−0.535961	+	0.844243i	$0.680050\pi$
$542$	−16.0950	+	14.4920i	−0.691337	+	0.622483i
$543$	−1.72399	+	1.14139i	−0.0739835	+	0.0489818i
$544$	2.27460	+	10.7012i	0.0975227	+	0.458808i
$545$	38.2902	−	1.35795i	1.64017	−	0.0581680i
$546$	5.50914	+	3.79667i	0.235769	+	0.162482i
$547$	18.5144	−	6.01568i	0.791617	−	0.257212i	0.114824	−	0.993386i	$-0.463369\pi$
$547$	18.5144	−	6.01568i	0.791617	−	0.257212i	0.676792	+	0.736174i	$0.263369\pi$
$548$	0.000542782	−	0.00516423i	2.31865e−5	−	0.000220605i
$549$	0.781878	+	6.35483i	0.0333697	+	0.271217i
$550$	−22.2333	+	3.94523i	−0.948031	+	0.168225i
$551$	−1.13318	−	1.96273i	−0.0482753	−	0.0836152i
$552$	0.116372	−	0.0605979i	0.00495312	−	0.00257922i
$553$	18.1195	−	7.29131i	0.770520	−	0.310058i
$554$	−11.5119	+	3.74044i	−0.489094	+	0.158916i
$555$	34.5330	−	15.0428i	1.46584	−	0.638530i
$556$	2.92466	−	2.63338i	0.124033	−	0.111680i
$557$	2.40418	−	4.16417i	0.101869	−	0.176441i	−0.810586	−	0.585620i	$-0.800851\pi$
$557$	2.40418	−	4.16417i	0.101869	−	0.176441i	0.912454	+	0.409178i	$0.134185\pi$
$558$	14.3413	−	16.5060i	0.607115	−	0.698756i
$559$	−5.44118	−	7.48915i	−0.230138	−	0.316757i
$560$	−22.9839	+	16.6688i	−0.971247	+	0.704385i
$561$	−15.6321	+	8.14004i	−0.659989	+	0.343673i
$562$	0.0759284	−	0.170538i	0.00320285	−	0.00719371i
$563$	−27.8610	+	2.92831i	−1.17420	+	0.123413i	−0.671471	−	0.741031i	$-0.734337\pi$
$563$	−27.8610	+	2.92831i	−1.17420	+	0.123413i	−0.502729	+	0.864444i	$0.667671\pi$
$564$	7.93503	+	0.345463i	0.334125	+	0.0145466i
$565$	−23.8085	−	38.0555i	−1.00163	−	1.60101i
$566$	−4.42191	+	3.21271i	−0.185867	+	0.135040i
$567$	23.8118	+	0.0214513i	1.00000	+	0.000900870i
$568$			10.3929i			0.436075i
$569$	−6.44525	−	30.3225i	−0.270199	−	1.27119i	−0.878601	−	0.477557i	$-0.841522\pi$
$569$	−6.44525	−	30.3225i	−0.270199	−	1.27119i	0.608402	−	0.793629i	$-0.291811\pi$
$570$	11.9436	+	8.82545i	0.500261	+	0.369658i
$571$	−0.364644	−	0.0775074i	−0.0152599	−	0.00324358i	0.200275	−	0.979740i	$-0.435816\pi$
$571$	−0.364644	−	0.0775074i	−0.0152599	−	0.00324358i	−0.215535	+	0.976496i	$0.569150\pi$
$572$	1.05961	+	0.954078i	0.0443045	+	0.0398920i
$573$	14.3987	+	27.6513i	0.601516	+	1.15515i
$574$	1.55794	+	22.7363i	0.0650271	+	0.948994i
$575$	0.0394356	−	0.158903i	0.00164458	−	0.00662669i
$576$	−5.55616	+	13.0985i	−0.231507	+	0.545773i
$577$	26.3665	−	11.7391i	1.09765	−	0.488706i	0.223670	−	0.974665i	$-0.428196\pi$
$577$	26.3665	−	11.7391i	1.09765	−	0.488706i	0.873982	+	0.485959i	$0.161529\pi$
$578$	−6.32073	−	1.34351i	−0.262908	−	0.0558828i
$579$	−18.0332	+	7.10604i	−0.749433	+	0.295317i
$580$	0.0412916	+	1.16431i	0.00171454	+	0.0483452i
$581$	20.3048	+	19.6630i	0.842384	+	0.815759i
$582$	0.352420	−	0.707065i	0.0146083	−	0.0293088i
$583$	3.68582	+	17.3404i	0.152651	+	0.718167i
$584$	1.63061	+	15.5142i	0.0674752	+	0.641984i
$585$	4.33195	−	4.33881i	0.179104	−	0.179388i
$586$	−26.6833	−	2.80453i	−1.10228	−	0.115854i
$587$	2.21369	+	3.04688i	0.0913688	+	0.125758i	0.852254	−	0.523128i	$-0.175235\pi$
$587$	2.21369	+	3.04688i	0.0913688	+	0.125758i	−0.760885	+	0.648886i	$0.775235\pi$
$588$	6.52795	+	1.46552i	0.269208	+	0.0604370i
$589$	8.86036	+	6.43743i	0.365085	+	0.265250i
$590$	−1.10452	+	15.9196i	−0.0454722	+	0.655398i
$591$	41.0150	+	15.3291i	1.68713	+	0.630554i
$592$	34.6859	−	31.2313i	1.42558	−	1.28360i
$593$	−7.38790	+	4.26540i	−0.303385	+	0.175159i	−0.643962	−	0.765057i	$-0.722711\pi$
$593$	−7.38790	+	4.26540i	−0.303385	+	0.175159i	0.340578	+	0.940216i	$0.389377\pi$
$594$	23.2668	+	3.05431i	0.954650	+	0.125320i
$595$	4.40939	+	20.8321i	0.180767	+	0.854032i
$596$	5.08394	−	1.65187i	0.208246	−	0.0676634i
$597$	−38.5804	+	15.2028i	−1.57899	+	0.622207i
$598$	−0.0436748	+	0.0194453i	−0.00178599	+	0.000795176i
$599$	32.8869	+	18.9873i	1.34372	+	0.775799i	0.987352	−	0.158546i	$-0.0506806\pi$
$599$	32.8869	+	18.9873i	1.34372	+	0.775799i	0.356371	+	0.934345i	$0.384014\pi$
$600$	8.64696	+	18.0724i	0.353011	+	0.737803i
$601$			30.5665i			1.24683i	0.781889	+	0.623417i	$0.214256\pi$
$601$			30.5665i			1.24683i	−0.781889	+	0.623417i	$0.785744\pi$
$602$	−36.2704	−	22.7348i	−1.47827	−	0.926603i
$603$	15.5414	+	10.8765i	0.632895	+	0.442924i
$604$	2.98263	−	3.31254i	0.121361	−	0.134785i
$605$	4.67421	+	4.83503i	0.190034	+	0.196572i
$606$	35.5092	−	9.85232i	1.44246	−	0.400223i
$607$	−4.68736	−	8.11874i	−0.190254	−	0.329529i	0.755080	−	0.655632i	$-0.227598\pi$
$607$	−4.68736	−	8.11874i	−0.190254	−	0.329529i	−0.945334	+	0.326103i	$0.894264\pi$
$608$	6.93886	+	2.25457i	0.281408	+	0.0914349i
$609$	−3.14236	+	2.97439i	−0.127335	+	0.120528i
$610$	7.32932	+	2.09734i	0.296756	+	0.0849189i
$611$	7.55361	+	0.793916i	0.305586	+	0.0321184i
$612$	−4.06473	−	4.35672i	−0.164307	−	0.176110i
$613$	26.1683	−	2.75040i	1.05693	−	0.111087i	0.439913	−	0.898040i	$-0.355009\pi$
$613$	26.1683	−	2.75040i	1.05693	−	0.111087i	0.617013	+	0.786953i	$0.288342\pi$
$614$	3.81876	−	36.3331i	0.154113	−	1.46628i
$615$	20.7511	+	2.35026i	0.836764	+	0.0947716i
$616$	−16.2518	−	5.94092i	−0.654805	−	0.239367i
$617$	−11.7963	+	36.3053i	−0.474902	+	1.46160i	0.371189	+	0.928557i	$0.378950\pi$
$617$	−11.7963	+	36.3053i	−0.474902	+	1.46160i	−0.846090	+	0.533039i	$0.821050\pi$
$618$	12.8942	−	0.790251i	0.518681	−	0.0317886i
$619$	−2.05861	+	1.85358i	−0.0827425	+	0.0745016i	−0.709464	−	0.704742i	$-0.751063\pi$
$619$	−2.05861	+	1.85358i	−0.0827425	+	0.0745016i	0.626722	+	0.779243i	$0.284396\pi$
$620$	−2.47075	−	5.05881i	−0.0992277	−	0.203167i
$621$	−0.0888468	+	0.145106i	−0.00356530	+	0.00582291i
$622$	5.32818	+	16.3985i	0.213641	+	0.657518i
$623$	21.6743	−	34.5784i	0.868361	−	1.38536i
$624$	3.38906	−	6.79951i	0.135671	−	0.272198i
$625$	24.0465	+	6.83871i	0.961858	+	0.273549i
$626$	21.0035	−	36.3791i	0.839468	−	1.45400i
$627$	−0.511227	+	11.7425i	−0.0204165	+	0.468951i
$628$	0.0583072	−	0.0647567i	0.00232671	−	0.00258407i
$629$	−10.8172	−	33.2919i	−0.431310	−	1.32744i
$630$	11.0937	−	26.0912i	0.441985	−	1.03950i
$631$	6.75313	−	20.7840i	0.268838	−	0.827398i	−0.721946	−	0.691949i	$-0.756752\pi$
$631$	6.75313	−	20.7840i	0.268838	−	0.827398i	0.990784	−	0.135449i	$-0.0432477\pi$
$632$	−8.53896	−	14.7899i	−0.339661	−	0.588311i
$633$	−43.5261	+	12.0767i	−1.73001	+	0.480005i
$634$	−0.850604	−	8.09296i	−0.0337818	−	0.321412i
$635$	−25.3590	−	21.2553i	−1.00634	−	0.843490i
$636$	−5.31583	+	2.76809i	−0.210787	+	0.109762i
$637$	6.14506	+	1.78068i	0.243476	+	0.0705529i
$638$	−3.44971	+	2.50636i	−0.136575	+	0.0992279i
$639$	−6.94428	−	11.5507i	−0.274712	−	0.456940i
$640$	21.2229	+	21.9531i	0.838908	+	0.867771i
$641$	39.7082	−	4.17350i	1.56838	−	0.164843i	0.719902	−	0.694076i	$-0.244187\pi$
$641$	39.7082	−	4.17350i	1.56838	−	0.164843i	0.848477	+	0.529232i	$0.177520\pi$
$642$	10.5165	−	40.6852i	0.415054	−	1.60572i
$643$	−35.2691			−1.39088			−0.695439	−	0.718586i	$-0.744790\pi$
$643$	−35.2691			−1.39088			−0.695439	+	0.718586i	$0.744790\pi$
$644$	−0.0332570	+	0.0343424i	−0.00131051	+	0.00135328i
$645$	−26.4820	+	28.9388i	−1.04273	+	1.13946i
$646$	9.23469	−	10.2562i	0.363334	−	0.403523i
$647$	4.60936	−	21.6853i	0.181213	−	0.852539i	−0.789773	−	0.613400i	$-0.789801\pi$
$647$	4.60936	−	21.6853i	0.181213	−	0.852539i	0.970985	−	0.239139i	$-0.0768652\pi$
$648$	−2.90790	−	20.6164i	−0.114233	−	0.809889i
$649$	−10.9379	+	6.31503i	−0.429352	+	0.247886i
$650$	−2.74203	−	6.76560i	−0.107551	−	0.265369i
$651$	8.02611	−	19.3072i	0.314568	−	0.756707i
$652$	−7.21279	+	9.92755i	−0.282474	+	0.388793i
$653$	22.4103	−	24.8891i	0.876982	−	0.973987i	−0.122848	−	0.992425i	$-0.539203\pi$
$653$	22.4103	−	24.8891i	0.876982	−	0.973987i	0.999830	+	0.0184384i	$0.00586945\pi$
$654$	−29.5082	+	37.1064i	−1.15386	+	1.45097i
$655$	−1.82809	−	12.9565i	−0.0714296	−	0.506253i
$656$	25.3122	−	5.38027i	0.988275	−	0.210064i
$657$	−12.1785	−	16.1531i	−0.475130	−	0.630193i
$658$	33.7748	−	9.63369i	1.31668	−	0.375560i
$659$	−13.9420	−	19.1895i	−0.543104	−	0.747518i	0.445953	−	0.895057i	$-0.352865\pi$
$659$	−13.9420	−	19.1895i	−0.543104	−	0.747518i	−0.989056	+	0.147539i	$0.952865\pi$
$660$	3.06308	−	5.20803i	0.119230	−	0.202722i
$661$	3.73550	+	8.39008i	0.145294	+	0.326336i	0.971503	−	0.237028i	$-0.0761734\pi$
$661$	3.73550	+	8.39008i	0.145294	+	0.326336i	−0.826209	+	0.563364i	$0.809507\pi$
$662$	−1.68061	−	15.9899i	−0.0653186	−	0.621465i
$663$	−3.62484	−	4.39617i	−0.140777	−	0.170733i
$664$	14.5268	−	19.9944i	0.563748	−	0.775932i
$665$	13.5018	+	4.39975i	0.523576	+	0.170615i
$666$	−13.6159	+	44.5751i	−0.527604	+	1.72725i
$667$	−0.00642803	−	0.0302415i	−0.000248894	−	0.00117096i
$668$	−3.91621	−	2.26102i	−0.151523	−	0.0874816i
$669$	−16.4016	+	4.55076i	−0.634122	+	0.175942i
$670$	19.1475	−	11.9791i	0.739732	−	0.462795i
$671$	1.86452	+	5.73842i	0.0719792	+	0.221529i
$672$	1.11054	−	13.8847i	0.0428401	−	0.535613i
$673$	−21.1924	+	29.1689i	−0.816908	+	1.12438i	0.173313	+	0.984867i	$0.444553\pi$
$673$	−21.1924	+	29.1689i	−0.816908	+	1.12438i	−0.990221	+	0.139510i	$0.955447\pi$
$674$	−32.2222	+	18.6035i	−1.24115	+	0.716579i
$675$	−21.6859	−	14.3081i	−0.834690	−	0.550720i
$676$	3.35633	−	5.81334i	0.129090	−	0.223590i
$677$	20.8553	+	2.19198i	0.801536	+	0.0842448i	0.496433	−	0.868075i	$-0.334643\pi$
$677$	20.8553	+	2.19198i	0.801536	+	0.0842448i	0.305102	+	0.952320i	$0.401309\pi$
$678$	54.9359	+	8.20325i	2.10980	+	0.315044i
$679$	0.106184	−	0.747949i	0.00407496	−	0.0287036i
$680$	17.4924	−	6.37746i	0.670802	−	0.244564i
$681$	20.7365	+	5.36007i	0.794623	+	0.205398i
$682$	10.3029	−	17.8451i	0.394518	−	0.683325i
$683$	−1.07552	−	1.19448i	−0.0411534	−	0.0457055i	0.722217	−	0.691667i	$-0.243123\pi$
$683$	−1.07552	−	1.19448i	−0.0411534	−	0.0457055i	−0.763370	+	0.645961i	$0.776457\pi$
$684$	−3.87157	+	0.894835i	−0.148033	+	0.0342149i
$685$	−0.0210285		0.000745764i	−0.000803456		2.84942e-5i
$686$	29.4357	−	2.96906i	1.12386	−	0.113359i
$687$	−49.4745	+	8.28552i	−1.88757	+	0.316112i
$688$	−19.7704	+	44.4049i	−0.753738	+	1.69292i
$689$	−5.23577	+	2.33112i	−0.199467	+	0.0888085i
$690$	0.117752	+	0.164850i	0.00448276	+	0.00627573i
$691$	5.35691	−	12.0318i	0.203786	−	0.457712i	−0.782522	−	0.622623i	$-0.786067\pi$
$691$	5.35691	−	12.0318i	0.203786	−	0.457712i	0.986308	+	0.164911i	$0.0527337\pi$
$692$	−3.14251	−	1.02106i	−0.119460	−	0.0388150i
$693$	22.0320	−	4.25632i	0.836928	−	0.161684i
$694$	8.47843	−	26.0939i	0.321837	−	0.990512i
$695$	−12.2220	−	10.2442i	−0.463608	−	0.388584i
$696$	2.96112	+	2.35478i	0.112241	+	0.0892576i
$697$	4.03513	−	18.9838i	0.152841	−	0.719062i
$698$	24.7143	+	2.59758i	0.935450	+	0.0983197i
$699$	−18.2662	+	36.6478i	−0.690892	+	1.38615i
$700$	−5.06927	−	5.25266i	−0.191600	−	0.198532i
$701$			12.1280i			0.458069i	0.973418	+	0.229035i	$0.0735569\pi$
$701$			12.1280i			0.458069i	−0.973418	+	0.229035i	$0.926443\pi$
$702$	0.598052	+	7.56292i	0.0225720	+	0.285444i
$703$	−22.8345	−	4.85363i	−0.861221	−	0.183058i
$704$	−2.78772	+	13.1152i	−0.105066	+	0.494298i
$705$	−3.10614	−	32.0345i	−0.116984	−	1.20649i
$706$	7.58331	+	2.46397i	0.285402	+	0.0927326i
$707$	29.2410	−	19.6639i	1.09972	−	0.739535i
$708$	−3.04590	−	2.99245i	−0.114472	−	0.112463i
$709$	−1.15578	−	0.514585i	−0.0434061	−	0.0193257i	0.384919	−	0.922950i	$-0.374229\pi$
$709$	−1.15578	−	0.514585i	−0.0434061	−	0.0193257i	−0.428325	+	0.903625i	$0.640896\pi$
$710$	−15.8897	+	2.24196i	−0.596331	+	0.0841391i
$711$	19.3726	+	10.7321i	0.726528	+	0.402485i
$712$	−32.5982	−	14.5137i	−1.22167	−	0.543922i
$713$	0.0878175	+	0.120870i	0.00328879	+	0.00452663i
$714$	−23.1392	−	12.6017i	−0.865962	−	0.471608i
$715$	3.22830	−	4.79176i	0.120732	−	0.179202i
$716$	−1.70154	+	3.82172i	−0.0635895	+	0.142824i
$717$	1.23352	+	4.44579i	0.0460667	+	0.166031i
$718$	−2.31678	−	1.33759i	−0.0864615	−	0.0499186i
$719$	−9.23393	+	1.96273i	−0.344368	+	0.0731976i	−0.376849	−	0.926275i	$-0.622992\pi$
$719$	−9.23393	+	1.96273i	−0.344368	+	0.0731976i	0.0324813	+	0.999472i	$0.489659\pi$
$720$	−31.1032	−	8.30769i	−1.15915	−	0.309609i
$721$	11.4600	−	4.61150i	0.426791	−	0.171741i
$722$	6.53496	+	20.1126i	0.243206	+	0.748512i
$723$	−19.2864	+	30.2819i	−0.717269	+	1.12620i
$724$	−0.570465	−	0.329358i	−0.0212012	−	0.0122405i
$725$	4.64834	−	0.824834i	0.172635	−	0.0306336i
$726$	−8.30576	+	0.509038i	−0.308256	+	0.0188922i
$727$	−26.3177	−	19.1209i	−0.976068	−	0.709155i	−0.0192418	−	0.999815i	$-0.506125\pi$
$727$	−26.3177	−	19.1209i	−0.976068	−	0.709155i	−0.956826	+	0.290660i	$0.906125\pi$
$728$	0.786297	−	5.53861i	0.0291421	−	0.205274i
$729$	17.0073	+	20.9703i	0.629900	+	0.776677i
$730$	−23.3681	+	5.83980i	−0.864891	+	0.216141i
$731$	24.3930	+	27.0912i	0.902207	+	1.00200i
$732$	−1.70087	+	1.12609i	−0.0628661	+	0.0416214i
$733$	−48.9291	+	10.4002i	−1.80724	+	0.384140i	−0.983220	−	0.182424i	$-0.941606\pi$
$733$	−48.9291	+	10.4002i	−1.80724	+	0.384140i	−0.824018	+	0.566564i	$0.808272\pi$
$734$	41.1052	−	29.8647i	1.51722	−	1.10233i
$735$	2.18462	−	27.0227i	0.0805809	−	0.996748i
$736$	0.0805207	+	0.0585017i	0.00296803	+	0.00215640i
$737$	16.3305	+	7.27082i	0.601543	+	0.267824i
$738$	−18.8945	+	17.6282i	−0.695516	+	0.648903i
$739$	−40.6086	+	18.0801i	−1.49381	+	0.665088i	−0.981105	−	0.193476i	$-0.938024\pi$
$739$	−40.6086	+	18.0801i	−1.49381	+	0.665088i	−0.512706	+	0.858564i	$0.671357\pi$
$740$	9.19706	+	7.70874i	0.338091	+	0.283379i
$741$	−3.74767	+	0.627624i	−0.137674	+	0.0230563i
$742$	−18.4369	+	19.0386i	−0.676839	+	0.698929i
$743$	−32.3644			−1.18733			−0.593667	−	0.804711i	$-0.702321\pi$
$743$	−32.3644			−1.18733			−0.593667	+	0.804711i	$0.702321\pi$
$744$	−17.7006	−	4.57533i	−0.648934	−	0.167740i
$745$	−9.50625	−	19.4639i	−0.348282	−	0.713101i
$746$	−2.48190	+	11.6764i	−0.0908688	+	0.427504i
$747$	−2.78538	+	31.9284i	−0.101912	+	1.16820i
$748$	−4.54265	−	3.30043i	−0.166096	−	0.120676i
$749$	−2.74700	−	40.0892i	−0.100373	−	1.46483i
$750$	−25.7657	+	17.1190i	−0.940831	+	0.625097i
$751$	−9.97668	−	17.2801i	−0.364054	−	0.630561i	0.624570	−	0.780969i	$-0.285274\pi$
$751$	−9.97668	−	17.2801i	−0.364054	−	0.630561i	−0.988624	+	0.150408i	$0.951941\pi$
$752$	−16.2211	−	36.4331i	−0.591522	−	1.32858i
$753$	8.32686	−	10.4710i	0.303447	−	0.381583i
$754$	−1.02446	−	0.922426i	−0.0373086	−	0.0335928i
$755$	−14.9800	−	10.0923i	−0.545176	−	0.367295i
$756$	3.37800	+	6.79265i	0.122857	+	0.247046i
$757$		−	22.0396i		−	0.801041i	−0.916288	−	0.400521i	$-0.868829\pi$
$757$		−	22.0396i		−	0.801041i	0.916288	−	0.400521i	$-0.131171\pi$
$758$	−12.0785	+	2.56736i	−0.438710	+	0.0932507i
$759$	−0.0561334	+	0.150193i	−0.00203752	+	0.00545165i
$760$	2.14949	−	12.2292i	0.0779700	−	0.443599i
$761$	4.04287	−	38.4653i	0.146554	−	1.39437i	−0.635955	−	0.771726i	$-0.719393\pi$
$761$	4.04287	−	38.4653i	0.146554	−	1.39437i	0.782509	−	0.622640i	$-0.213940\pi$
$762$	40.3808	−	6.76258i	1.46284	−	0.244983i
$763$	−15.5647	+	42.5784i	−0.563480	+	1.54144i
$764$	−5.83806	+	8.03541i	−0.211214	+	0.290711i
$765$	−15.1799	+	18.7760i	−0.548830	+	0.678847i
$766$	6.48275	−	0.681365i	0.234231	−	0.0246187i
$767$	−2.73219	−	3.03441i	−0.0986538	−	0.109566i
$768$	−21.3130	+	1.30622i	−0.769067	+	0.0471341i
$769$	25.0632	+	8.14352i	0.903801	+	0.293663i	0.723805	−	0.690004i	$-0.242391\pi$
$769$	25.0632	+	8.14352i	0.903801	+	0.293663i	0.179996	+	0.983667i	$0.442391\pi$
$770$	5.57727	−	26.1291i	0.200991	−	0.941629i
$771$	7.72981	−	51.7653i	0.278382	−	1.86428i
$772$	−4.58906	−	4.13201i	−0.165164	−	0.148714i
$773$	0.957110	+	2.14970i	0.0344249	+	0.0773195i	0.929940	−	0.367713i	$-0.119859\pi$
$773$	0.957110	+	2.14970i	0.0344249	+	0.0773195i	−0.895515	+	0.445032i	$0.853192\pi$
$774$	−5.92730	−	48.1750i	−0.213053	−	1.73162i
$775$	−18.8994	+	12.7777i	−0.678887	+	0.458989i
$776$	−0.660547			−0.0237123
$777$	1.10992	+	44.5545i	0.0398180	+	1.59838i
$778$	−3.24615	+	1.05474i	−0.116380	+	0.0378142i
$779$	−9.61849	−	8.66053i	−0.344618	−	0.310296i
$780$	1.85281	+	0.618567i	0.0663413	+	0.0221483i
$781$	−8.49844	−	9.43847i	−0.304098	−	0.337735i
$782$	0.163046	−	0.0941347i	0.00583052	−	0.00336625i
$783$	−4.86442	−	0.638569i	−0.173840	−	0.0228206i
$784$	−8.03594	−	32.6186i	−0.286998	−	1.16495i
$785$	−0.292842	−	0.197293i	−0.0104520	−	0.00704170i
$786$	13.6563	+	8.69763i	0.487103	+	0.310234i
$787$	−3.71588	−	35.3542i	−0.132457	−	1.26024i	−0.835658	−	0.549251i	$-0.814913\pi$
$787$	−3.71588	−	35.3542i	−0.132457	−	1.26024i	0.703201	−	0.710991i	$-0.251754\pi$
$788$	1.45816	+	13.8734i	0.0519447	+	0.494221i
$789$	41.0438	+	26.1406i	1.46120	+	0.930630i
$790$	20.7704	−	16.2458i	0.738977	−	0.577999i
$791$	52.3199	−	9.15002i	1.86028	−	0.325337i
$792$	−6.39242	−	18.5500i	−0.227145	−	0.659144i
$793$	−1.68932	+	0.975329i	−0.0599895	+	0.0346350i
$794$	−10.9038	−	12.1099i	−0.386960	−	0.429763i
$795$	14.1163	+	19.7624i	0.500653	+	0.700899i
$796$	−9.81789	−	8.84007i	−0.347986	−	0.313328i
$797$	4.97594	−	1.61678i	0.176257	−	0.0572694i	−0.219559	−	0.975599i	$-0.570462\pi$
$797$	4.97594	−	1.61678i	0.176257	−	0.0572694i	0.395816	+	0.918330i	$0.370462\pi$
$798$	−14.9937	+	9.16192i	−0.530772	+	0.324328i
$799$	−29.9102			−1.05815
$800$	−9.34368	+	11.9862i	−0.330349	+	0.423776i
$801$	45.9277	−	5.65079i	1.62277	−	0.199661i
$802$	8.84098	+	19.8572i	0.312186	+	0.701181i
$803$	−14.1671	−	12.7562i	−0.499948	−	0.450155i
$804$	−0.892537	+	5.97719i	−0.0314774	+	0.210799i
$805$	0.156625	+	0.113999i	0.00552030	+	0.00401795i
$806$	6.33564	+	2.05857i	0.223163	+	0.0725102i
$807$	−48.8078	+	2.99130i	−1.71811	+	0.105299i
$808$	−20.6167	−	22.8971i	−0.725292	−	0.805518i
$809$	14.6785	−	1.54277i	0.516069	−	0.0542411i	0.157086	−	0.987585i	$-0.449790\pi$
$809$	14.6785	−	1.54277i	0.516069	−	0.0542411i	0.358983	+	0.933344i	$0.383123\pi$
$810$	30.8933	−	8.89329i	1.08548	−	0.312479i
$811$	29.5654	−	40.6932i	1.03818	−	1.42893i	0.139556	−	0.990214i	$-0.455433\pi$
$811$	29.5654	−	40.6932i	1.03818	−	1.42893i	0.898625	−	0.438718i	$-0.144567\pi$
$812$	−1.29470	−	0.473282i	−0.0454350	−	0.0166090i
$813$	−23.1604	+	3.87868i	−0.812270	+	0.136031i
$814$	−4.59110	+	43.6814i	−0.160918	+	1.53103i
$815$	43.9171	+	23.3206i	1.53835	+	0.816884i
$816$	−10.4742	+	28.0251i	−0.366670	+	0.981074i
$817$	23.7801	−	5.05462i	0.831960	−	0.176839i
$818$		−	35.3623i		−	1.23641i
$819$	2.82688	+	6.68104i	0.0987790	+	0.233455i
$820$	2.27899	+	6.25091i	0.0795858	+	0.218291i
$821$	−37.4909	−	33.7570i	−1.30844	−	1.17813i	−0.971617	−	0.236558i	$-0.923981\pi$
$821$	−37.4909	−	33.7570i	−1.30844	−	1.17813i	−0.336824	−	0.941568i	$-0.609353\pi$
$822$	0.0162055	−	0.0203783i	0.000565232	−	0.000710775i
$823$	−21.5355	−	48.3695i	−0.750681	−	1.68606i	−0.727290	−	0.686330i	$-0.759221\pi$
$823$	−21.5355	−	48.3695i	−0.750681	−	1.68606i	−0.0233903	−	0.999726i	$-0.507446\pi$
$824$	−5.40059	−	9.35410i	−0.188138	−	0.325865i
$825$	−22.6310	−	9.34200i	−0.787911	−	0.325247i
$826$	−16.9591	−	8.30085i	−0.590081	−	0.288824i
$827$	9.14702	+	6.64570i	0.318073	+	0.231093i	0.735353	−	0.677685i	$-0.237017\pi$
$827$	9.14702	+	6.64570i	0.318073	+	0.231093i	−0.417280	+	0.908778i	$0.637017\pi$
$828$	−0.0540020	−	0.00471104i	−0.00187670	−	0.000163720i
$829$	−3.13670	+	14.7570i	−0.108942	+	0.512533i	0.889510	+	0.456916i	$0.151046\pi$
$829$	−3.13670	+	14.7570i	−0.108942	+	0.512533i	−0.998452	+	0.0556170i	$0.982287\pi$
$830$	33.7033	+	17.8969i	1.16986	+	0.621210i
$831$	−12.7067	−	3.28449i	−0.440790	−	0.113938i
$832$	−4.33477			−0.150281
$833$	−24.7999	−	4.44441i	−0.859264	−	0.153990i
$834$	19.4619	−	3.25929i	0.673911	−	0.112860i
$835$	−6.85513	+	16.9936i	−0.237231	+	0.588088i
$836$	−3.42088	+	1.52307i	−0.118314	+	0.0526766i
$837$	22.7297	−	6.74206i	0.785653	−	0.233040i
$838$	0.00235914	+	0.00105036i	8.14953e−5	+	3.62840e-5i
$839$	−18.0147	−	13.0884i	−0.621936	−	0.451863i	0.231661	−	0.972796i	$-0.425584\pi$
$839$	−18.0147	−	13.0884i	−0.621936	−	0.451863i	−0.853597	+	0.520934i	$0.825584\pi$
$840$	−23.6620	+	1.42988i	−0.816416	+	0.0493355i
$841$	−22.7403	+	16.5218i	−0.784147	+	0.569716i
$842$	−2.70521	+	0.575009i	−0.0932276	+	0.0198161i
$843$	0.168771	−	0.111737i	0.00581278	−	0.00384843i
$844$	−9.62941	−	10.6945i	−0.331458	−	0.368121i
$845$	−25.2258	−	10.1760i	−0.867795	−	0.350064i
$846$	32.6280	+	22.8343i	1.12177	+	0.785058i
$847$	−7.38189	+	2.97048i	−0.253645	+	0.102067i
$848$	24.3464	+	17.6887i	0.836059	+	0.607432i
$849$	−5.91527	+	0.362531i	−0.203011	+	0.0124420i
$850$	13.5240	+	25.3685i	0.463870	+	0.870131i
$851$	−0.275795	−	0.159230i	−0.00945414	−	0.00545835i
$852$	2.30662	−	3.62165i	0.0790234	−	0.124076i
$853$	−12.3728	−	38.0795i	−0.423636	−	1.30382i	−0.904294	−	0.426910i	$-0.859602\pi$
$853$	−12.3728	−	38.0795i	−0.423636	−	1.30382i	0.480658	−	0.876908i	$-0.340398\pi$
$854$	−5.56335	+	7.10029i	−0.190374	+	0.242967i
$855$	5.78230	+	15.0278i	0.197751	+	0.513942i
$856$	−34.3675	+	7.30504i	−1.17466	+	0.249681i
$857$	32.0174	+	18.4852i	1.09369	+	0.631443i	0.934557	−	0.355813i	$-0.115796\pi$
$857$	32.0174	+	18.4852i	1.09369	+	0.631443i	0.159135	+	0.987257i	$0.449129\pi$
$858$	1.91142	+	6.88903i	0.0652548	+	0.235188i
$859$	−2.44631	+	5.49451i	−0.0834671	+	0.187470i	−0.950457	−	0.310855i	$-0.899385\pi$
$859$	−2.44631	+	5.49451i	−0.0834671	+	0.187470i	0.866990	+	0.498325i	$0.166051\pi$
$860$	−12.0151	−	3.43822i	−0.409712	−	0.117242i
$861$	−11.8182	+	21.7005i	−0.402764	+	0.739551i
$862$	−14.9352	−	20.5565i	−0.508695	−	0.700159i
$863$	−14.1191	−	6.28622i	−0.480619	−	0.213985i	0.152103	−	0.988365i	$-0.451396\pi$
$863$	−14.1191	−	6.28622i	−0.480619	−	0.213985i	−0.632722	+	0.774379i	$0.718062\pi$
$864$	13.0129	−	8.95068i	0.442709	−	0.304508i
$865$	−2.31787	+	13.1872i	−0.0788101	+	0.448378i
$866$	−33.9785	−	15.1282i	−1.15464	−	0.514078i
$867$	−4.99797	−	4.91027i	−0.169740	−	0.166762i
$868$	6.64585	−	0.455388i	0.225575	−	0.0154569i
$869$	19.8488	+	6.44926i	0.673324	+	0.218776i
$870$	−2.96146	+	5.03525i	−0.100403	+	0.170711i
$871$	−1.20156	+	5.65288i	−0.0407132	+	0.191541i
$872$	38.7729	+	8.24144i	1.31302	+	0.279090i
$873$	0.734138	−	0.441363i	0.0248468	−	0.0149379i
$874$		−	0.125555i		−	0.00424697i
$875$	−18.2061	+	23.3139i	−0.615479	+	0.788153i
$876$	2.87504	−	5.76823i	0.0971385	−	0.194890i
$877$	−14.0876	−	1.48067i	−0.475705	−	0.0499986i	−0.136357	−	0.990660i	$-0.543540\pi$
$877$	−14.0876	−	1.48067i	−0.475705	−	0.0499986i	−0.339347	+	0.940661i	$0.610206\pi$
$878$	3.59740	−	16.9244i	0.121406	−	0.571171i
$879$	−22.7692	−	18.1069i	−0.767988	−	0.610729i
$880$	−30.2654	−	2.09984i	−1.02025	−	0.0707857i
$881$	0.274642	−	0.845262i	0.00925294	−	0.0284776i	−0.946323	−	0.323221i	$-0.895234\pi$
$881$	0.274642	−	0.845262i	0.00925294	−	0.0284776i	0.955576	+	0.294744i	$0.0952342\pi$
$882$	23.6603	+	23.7811i	0.796683	+	0.800752i
$883$	29.7746	+	9.67437i	1.00200	+	0.325568i	0.763663	−	0.645615i	$-0.223399\pi$
$883$	29.7746	+	9.67437i	1.00200	+	0.325568i	0.238334	+	0.971183i	$0.423399\pi$
$884$	0.738348	−	1.65836i	0.0248333	−	0.0557765i
$885$	−10.2827	+	13.9156i	−0.345648	+	0.467769i
$886$	−54.2963	+	24.1743i	−1.82412	+	0.812151i
$887$	3.80506	−	8.54630i	0.127761	−	0.286957i	−0.838327	−	0.545167i	$-0.816466\pi$
$887$	3.80506	−	8.54630i	0.127761	−	0.286957i	0.966089	+	0.258211i	$0.0831328\pi$
$888$	38.4343	−	6.43661i	1.28977	−	0.215998i
$889$	34.5941	−	18.3320i	1.16025	−	0.614836i
$890$	15.1579	−	52.9706i	0.508095	−	1.77558i
$891$	19.4993	+	16.3453i	0.653250	+	0.547589i
$892$	−3.62857	−	4.02994i	−0.121494	−	0.134932i
$893$	−9.97343	+	17.2745i	−0.333748	+	0.578069i
$894$	25.9501	+	6.70772i	0.867903	+	0.224340i
$895$	16.2977	+	4.66372i	0.544773	+	0.155891i
$896$	−33.5169	+	13.4872i	−1.11972	+	0.450576i
$897$	−0.0512681	−	0.00765556i	−0.00171179	−	0.000255612i
$898$	−6.00837	−	0.631506i	−0.200502	−	0.0210736i
$899$	−2.15403	+	3.73090i	−0.0718411	+	0.124432i
$900$	0.997779	−	8.21691i	0.0332593	−	0.273897i
$901$	19.5461	−	11.2850i	0.651176	−	0.375957i
$902$	−14.3135	+	19.7009i	−0.476589	+	0.655968i
$903$	−19.9283	−	41.9179i	−0.663173	−	1.39494i
$904$	−14.3513	−	44.1687i	−0.477316	−	1.46903i
$905$	−0.998572	+	2.47542i	−0.0331937	+	0.0822858i
$906$	21.5364	−	5.97546i	0.715499	−	0.198521i
$907$	12.2832	+	7.09168i	0.407855	+	0.235475i	0.689868	−	0.723935i	$-0.257669\pi$
$907$	12.2832	+	7.09168i	0.407855	+	0.235475i	−0.282012	+	0.959411i	$0.591002\pi$
$908$	1.41871	+	6.67450i	0.0470815	+	0.221501i
$909$	38.2129	+	11.6725i	1.26744	+	0.387152i
$910$	8.63764	+	0.00738383i	0.286335	+	0.000244772i
$911$	−9.33917	+	12.8543i	−0.309420	+	0.425881i	−0.935200	−	0.354119i	$-0.884781\pi$
$911$	−9.33917	+	12.8543i	−0.309420	+	0.425881i	0.625780	+	0.780000i	$0.284781\pi$
$912$	12.6932	+	15.3942i	0.420313	+	0.509751i
$913$	3.15702	+	30.0371i	0.104482	+	0.994081i
$914$	15.1763	+	34.0865i	0.501987	+	1.12748i
$915$	5.48129	+	6.18714i	0.181206	+	0.204541i
$916$	−9.39381	−	12.9295i	−0.310380	−	0.427202i
$917$	15.0171	+	3.76648i	0.495907	+	0.124380i
$918$	−5.45542	−	29.3737i	−0.180056	−	0.969476i
$919$	−35.8316	+	7.61624i	−1.18197	+	0.251236i	−0.756660	−	0.653809i	$-0.773170\pi$
$919$	−35.8316	+	7.61624i	−1.18197	+	0.251236i	−0.425315	+	0.905045i	$0.639837\pi$
$920$	0.0794397	−	0.149600i	0.00261905	−	0.00493218i
$921$	24.6550	−	31.0035i	0.812411	−	1.02160i
$922$	−9.50093	+	10.5519i	−0.312896	+	0.347507i
$923$	2.41347	−	3.32186i	0.0794404	−	0.109340i
$924$	4.34482	+	5.67723i	0.142934	+	0.186767i
$925$	25.7241	−	41.2669i	0.845804	−	1.35685i
$926$	−17.2185	+	9.94113i	−0.565837	+	0.326686i
$927$	12.2525	+	6.78767i	0.402424	+	0.222936i
$928$	−0.596691	+	2.80721i	−0.0195873	+	0.0921511i
$929$	−23.2869	+	25.8628i	−0.764019	+	0.848529i	−0.992144	−	0.125103i	$-0.960074\pi$
$929$	−23.2869	+	25.8628i	−0.764019	+	0.848529i	0.228125	+	0.973632i	$0.426741\pi$
$930$	3.17688	−	28.0495i	0.104174	−	0.919780i
$931$	−10.8363	+	12.8411i	−0.355144	+	0.420849i
$932$	−13.0456			−0.427324
$933$	−4.67868	+	18.1004i	−0.153173	+	0.592580i
$934$	−55.5526	+	5.83882i	−1.81774	+	0.191052i
$935$	−10.6710	+	20.0956i	−0.348980	+	0.657198i
$936$	5.43634	−	3.26832i	0.177692	−	0.106828i
$937$	−39.4839	+	28.6868i	−1.28988	+	0.937156i	−0.999803	−	0.0198463i	$-0.993682\pi$
$937$	−39.4839	+	28.6868i	−1.28988	+	0.937156i	−0.290081	+	0.957002i	$0.593682\pi$
$938$	4.60380	+	26.3246i	0.150319	+	0.859527i
$939$	40.3978	−	21.0361i	1.31833	−	0.686489i
$940$	8.69275	−	5.43840i	0.283526	−	0.177381i
$941$	3.49498	+	33.2525i	0.113933	+	1.08400i	0.890819	+	0.454359i	$0.150132\pi$
$941$	3.49498	+	33.2525i	0.113933	+	1.08400i	−0.776886	+	0.629642i	$0.783202\pi$
$942$	0.421014	−	0.116814i	0.0137174	−	0.00380600i
$943$	−0.0882819	−	0.152909i	−0.00287486	−	0.00497940i
$944$	−6.62536	+	20.3908i	−0.215637	+	0.663663i
$945$	25.3427	−	17.3996i	0.824399	−	0.566009i
$946$	−14.1347	−	43.5021i	−0.459559	−	1.41438i
$947$	−3.89038	+	4.32070i	−0.126420	+	0.140404i	−0.803032	−	0.595936i	$-0.796781\pi$
$947$	−3.89038	+	4.32070i	−0.126420	+	0.140404i	0.676611	+	0.736340i	$0.263448\pi$
$948$	−0.306891	+	7.04907i	−0.00996737	+	0.228943i
$949$	3.08159	−	5.33746i	0.100033	−	0.173261i
$950$	19.1610	+	0.648279i	0.621664	+	0.0210329i
$951$	3.93593	−	7.89672i	0.127631	−	0.256069i
$952$	−0.799609	+	22.0154i	−0.0259155	+	0.713523i
$953$	−11.7839	−	36.2672i	−0.381718	−	1.17481i	−0.938833	−	0.344373i	$-0.888092\pi$
$953$	−11.7839	−	36.2672i	−0.381718	−	1.17481i	0.557115	−	0.830436i	$-0.311908\pi$
$954$	−29.9374	−	2.61169i	−0.969259	−	0.0845565i
$955$	35.5467	+	18.8758i	1.15027	+	0.610806i
$956$	−1.09235	+	0.983556i	−0.0353291	+	0.0318105i
$957$	−4.61474	+	0.282825i	−0.149173	+	0.00914244i
$958$	−3.25116	+	10.0061i	−0.105040	+	0.323281i
$959$	0.00854792	−	0.0233835i	0.000276027	−	0.000755091i
$960$	3.67412	+	17.9974i	0.118582	+	0.580863i
$961$	−1.06427	+	10.1259i	−0.0343314	+	0.326642i
$962$	−14.1219	+	1.48427i	−0.455307	+	0.0478547i
$963$	33.3153	−	31.0825i	1.07357	−	1.00162i
$964$	−11.3755	−	1.19561i	−0.366379	−	0.0385080i
$965$	−13.9814	+	20.7526i	−0.450078	+	0.668050i
$966$	−0.233151	+	0.0556607i	−0.00750152	+	0.00179085i
$967$	33.4813	+	10.8787i	1.07669	+	0.349837i	0.793089	−	0.609106i	$-0.208472\pi$
$967$	33.4813	+	10.8787i	1.07669	+	0.349837i	0.283599	+	0.958943i	$0.408472\pi$
$968$	3.47877	+	6.02541i	0.111812	+	0.193664i
$969$	14.4193	−	4.00074i	0.463213	−	0.128522i
$970$	−0.142494	−	1.00992i	−0.00457520	−	0.0324264i
$971$	3.84453	−	4.26978i	0.123377	−	0.137024i	−0.678292	−	0.734793i	$-0.737279\pi$
$971$	3.84453	−	4.26978i	0.123377	−	0.137024i	0.801668	+	0.597769i	$0.203946\pi$
$972$	−3.56232	+	7.82969i	−0.114262	+	0.251137i
$973$	16.6730	−	8.83530i	0.534511	−	0.283247i
$974$			21.9733i			0.704069i
$975$	1.43303	−	7.78449i	0.0458936	−	0.249303i
$976$	8.87030	+	5.12127i	0.283931	+	0.163928i
$977$	4.00273	−	1.78213i	0.128059	−	0.0570154i	−0.341707	−	0.939807i	$-0.611005\pi$
$977$	4.00273	−	1.78213i	0.128059	−	0.0570154i	0.469766	+	0.882791i	$0.344338\pi$
$978$	−57.2441	+	22.5573i	−1.83046	+	0.721302i
$979$	41.4727	−	13.4753i	1.32547	−	0.430673i
$980$	8.01565	−	3.21755i	0.256050	−	0.102781i
$981$	−48.5993	+	16.7476i	−1.55166	+	0.534710i
$982$	42.3705	−	24.4626i	1.35210	−	0.780633i
$983$	14.0679	−	12.6668i	0.448697	−	0.404009i	−0.413562	−	0.910476i	$-0.635716\pi$
$983$	14.0679	−	12.6668i	0.448697	−	0.404009i	0.862259	+	0.506467i	$0.169049\pi$
$984$	20.2385	+	7.56401i	0.645181	+	0.241132i
$985$	54.8409	−	13.7050i	1.74738	−	0.436678i
$986$	4.39195	+	3.19094i	0.139868	+	0.101620i
$987$	36.4994	+	10.8622i	1.16179	+	0.345748i
$988$	−0.711576	−	0.979401i	−0.0226383	−	0.0311589i
$989$	0.329831	+	0.0346667i	0.0104880	+	0.00110234i
$990$	26.9822	−	13.7750i	0.857551	−	0.437799i
$991$	−3.51334	−	33.4272i	−0.111605	−	1.06185i	−0.896750	−	0.442537i	$-0.854078\pi$
$991$	−3.51334	−	33.4272i	−0.111605	−	1.06185i	0.785145	−	0.619312i	$-0.212588\pi$
$992$	−2.88345	−	13.5656i	−0.0915496	−	0.430707i
$993$	7.77653	−	15.6022i	0.246781	−	0.495120i
$994$	4.61917	−	18.4168i	0.146511	−	0.584144i
$995$	−29.9120	+	44.3984i	−0.948275	+	1.40752i
$996$	−9.49981	+	3.74344i	−0.301013	+	0.118615i
$997$	−13.6066	−	2.89216i	−0.430924	−	0.0915958i	−0.0126572	−	0.999920i	$-0.504029\pi$
$997$	−13.6066	−	2.89216i	−0.430924	−	0.0915958i	−0.418267	+	0.908324i	$0.637362\pi$
$998$	−15.3281	+	6.82449i	−0.485201	+	0.216025i
$999$	−38.4154	+	32.8347i	−1.21541	+	1.03884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bp.a.59.20	✓	608
3.2	odd	2	inner	525.2.bp.a.59.57	yes	608
7.5	odd	6	inner	525.2.bp.a.509.57	yes	608
21.5	even	6	inner	525.2.bp.a.509.20	yes	608
25.14	even	10	inner	525.2.bp.a.164.20	yes	608
75.14	odd	10	inner	525.2.bp.a.164.57	yes	608
175.89	odd	30	inner	525.2.bp.a.89.57	yes	608
525.89	even	30	inner	525.2.bp.a.89.20	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bp.a.59.20	✓	608	1.1	even	1	trivial
525.2.bp.a.59.57	yes	608	3.2	odd	2	inner
525.2.bp.a.89.20	yes	608	525.89	even	30	inner
525.2.bp.a.89.57	yes	608	175.89	odd	30	inner
525.2.bp.a.164.20	yes	608	25.14	even	10	inner
525.2.bp.a.164.57	yes	608	75.14	odd	10	inner
525.2.bp.a.509.20	yes	608	21.5	even	6	inner
525.2.bp.a.509.57	yes	608	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bp (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.166978 + 1.58869i) q^{2} +(-1.07806 + 1.35565i) q^{3} +(-0.539759 - 0.114729i) q^{4} +(-0.154769 + 2.23071i) q^{5} +(-1.97370 - 1.93906i) q^{6} +(-2.37636 - 1.16314i) q^{7} +(-0.714876 + 2.20016i) q^{8} +(-0.675580 - 2.92294i) q^{9} +O(q^{10})\)	\(q+(-0.166978 + 1.58869i) q^{2} +(-1.07806 + 1.35565i) q^{3} +(-0.539759 - 0.114729i) q^{4} +(-0.154769 + 2.23071i) q^{5} +(-1.97370 - 1.93906i) q^{6} +(-2.37636 - 1.16314i) q^{7} +(-0.714876 + 2.20016i) q^{8} +(-0.675580 - 2.92294i) q^{9} +(-3.51806 - 0.618358i) q^{10} +(-1.14988 - 2.58268i) q^{11} +(0.737425 - 0.608040i) q^{12} +(0.739425 - 0.537224i) q^{13} +(2.24468 - 3.58108i) q^{14} +(-2.85721 - 2.61464i) q^{15} +(-4.38423 - 1.95198i) q^{16} +(-2.67479 + 2.40839i) q^{17} +(4.75646 - 0.585219i) q^{18} +(0.499057 + 2.34788i) q^{19} +(0.339465 - 1.18629i) q^{20} +(4.13867 - 1.96758i) q^{21} +(4.29509 - 1.39556i) q^{22} +(-0.00342274 + 0.0325652i) q^{23} +(-2.21197 - 3.34102i) q^{24} +(-4.95209 - 0.690487i) q^{25} +(0.730014 + 1.26442i) q^{26} +(4.69080 + 2.23525i) q^{27} +(1.14922 + 0.900456i) q^{28} +(-0.897979 + 0.291771i) q^{29} +(4.63095 - 4.10263i) q^{30} +(3.39075 - 3.05305i) q^{31} +(1.51978 - 2.63234i) q^{32} +(4.74086 + 1.22544i) q^{33} +(-3.37955 - 4.65155i) q^{34} +(2.96242 - 5.12094i) q^{35} +(0.0293030 + 1.65519i) q^{36} +(-3.95576 + 8.88478i) q^{37} +(-3.81338 + 0.400802i) q^{38} +(-0.0688555 + 1.58156i) q^{39} +(-4.79727 - 1.93519i) q^{40} +(-4.36235 + 3.16943i) q^{41} +(2.43481 + 6.90361i) q^{42} -10.1283i q^{43} +(0.324351 + 1.52595i) q^{44} +(6.62478 - 1.05464i) q^{45} +(-0.0511645 - 0.0108753i) q^{46} +(6.17557 + 5.56051i) q^{47} +(7.37266 - 3.83913i) q^{48} +(4.29419 + 5.52810i) q^{49} +(1.92386 - 7.75204i) q^{50} +(-0.381358 - 6.22246i) q^{51} +(-0.460747 + 0.205138i) q^{52} +(-6.13365 - 1.30375i) q^{53} +(-4.33439 + 7.07900i) q^{54} +(5.93917 - 2.16533i) q^{55} +(4.25791 - 4.39687i) q^{56} +(-3.72091 - 1.85460i) q^{57} +(-0.313591 - 1.47533i) q^{58} +(-0.466981 - 4.44302i) q^{59} +(1.24223 + 1.73908i) q^{60} +(-2.12256 - 0.223090i) q^{61} +(4.28417 + 5.89665i) q^{62} +(-1.79438 + 7.73177i) q^{63} +(-3.83696 - 2.78772i) q^{64} +(1.08395 + 1.73258i) q^{65} +(-2.73847 + 7.32713i) q^{66} +(-4.69897 + 4.23097i) q^{67} +(1.72005 - 0.993073i) q^{68} +(-0.0404571 - 0.0397472i) q^{69} +(7.64094 + 5.56145i) q^{70} +(4.27261 - 1.38826i) q^{71} +(6.91390 + 0.603156i) q^{72} +(6.16025 - 2.74272i) q^{73} +(-13.4546 - 7.76804i) q^{74} +(6.27471 - 5.96892i) q^{75} -1.32454i q^{76} +(-0.271491 + 7.47487i) q^{77} +(-2.50111 - 0.373476i) q^{78} +(-4.93967 + 5.48606i) q^{79} +(5.03284 - 9.47781i) q^{80} +(-8.08718 + 3.94936i) q^{81} +(-4.30683 - 7.45964i) q^{82} +(-10.1603 - 3.30130i) q^{83} +(-2.45963 + 0.587192i) q^{84} +(-4.95843 - 6.33940i) q^{85} +(16.0908 + 1.69121i) q^{86} +(0.572534 - 1.53189i) q^{87} +(6.50434 - 0.683634i) q^{88} +(-1.61232 + 15.3402i) q^{89} +(0.569301 + 10.7008i) q^{90} +(-2.38201 + 0.416580i) q^{91} +(0.00558364 - 0.0171847i) q^{92} +(0.483437 + 7.88805i) q^{93} +(-9.86511 + 8.88259i) q^{94} +(-5.31466 + 0.749870i) q^{95} +(1.93012 + 4.89810i) q^{96} +(0.0882345 + 0.271558i) q^{97} +(-9.49948 + 5.89907i) q^{98} +(-6.77219 + 5.10585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Introduction

L-functions

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