LMFDB - Embedded newform 225.2.q.a.211.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			211.4
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06085 - 0.917550i) q^{2} +(1.65499 - 0.510883i) q^{3} +(2.06695 + 2.29558i) q^{4} +(-2.23029 + 0.160691i) q^{5} +(-3.87945 - 0.465685i) q^{6} +(2.12428 + 3.67936i) q^{7} +(-0.759150 - 2.33642i) q^{8} +(2.47800 - 1.69101i) q^{9} +O(q^{10})$	\(q+(-2.06085 - 0.917550i) q^{2} +(1.65499 - 0.510883i) q^{3} +(2.06695 + 2.29558i) q^{4} +(-2.23029 + 0.160691i) q^{5} +(-3.87945 - 0.465685i) q^{6} +(2.12428 + 3.67936i) q^{7} +(-0.759150 - 2.33642i) q^{8} +(2.47800 - 1.69101i) q^{9} +(4.74373 + 1.71524i) q^{10} +(2.79930 + 1.24633i) q^{11} +(4.59355 + 2.74319i) q^{12} +(-2.17836 + 0.969869i) q^{13} +(-1.00183 - 9.53175i) q^{14} +(-3.60901 + 1.40536i) q^{15} +(0.0664873 - 0.632584i) q^{16} +(2.36985 + 7.29363i) q^{17} +(-6.65837 + 1.21124i) q^{18} +(-0.781940 - 2.40656i) q^{19} +(-4.97876 - 4.78765i) q^{20} +(5.39539 + 5.00406i) q^{21} +(-4.62537 - 5.13700i) q^{22} +(-0.656165 - 6.24299i) q^{23} +(-2.45003 - 3.47893i) q^{24} +(4.94836 - 0.716775i) q^{25} +5.37918 q^{26} +(3.23716 - 4.06458i) q^{27} +(-4.05548 + 12.4815i) q^{28} +(4.40315 - 0.935918i) q^{29} +(8.72712 + 0.415217i) q^{30} +(1.42509 + 0.302912i) q^{31} +(-3.17411 + 5.49772i) q^{32} +(5.26955 + 0.632551i) q^{33} +(1.80838 - 17.2055i) q^{34} +(-5.32900 - 7.86468i) q^{35} +(9.00374 + 2.19320i) q^{36} +(0.524265 + 0.380901i) q^{37} +(-0.596680 + 5.67703i) q^{38} +(-3.10968 + 2.71801i) q^{39} +(2.06856 + 5.08890i) q^{40} +(1.84882 - 0.823147i) q^{41} +(-6.52762 - 15.2632i) q^{42} +(0.433089 + 0.750133i) q^{43} +(2.92496 + 9.00211i) q^{44} +(-5.25491 + 4.16964i) q^{45} +(-4.37600 + 13.4679i) q^{46} +(-9.74091 + 2.07049i) q^{47} +(-0.213140 - 1.08089i) q^{48} +(-5.52514 + 9.56982i) q^{49} +(-10.8555 - 3.06320i) q^{50} +(7.64827 + 10.8602i) q^{51} +(-6.72897 - 2.99593i) q^{52} +(-0.161545 + 0.497185i) q^{53} +(-10.4008 + 5.40624i) q^{54} +(-6.44352 - 2.32985i) q^{55} +(6.98390 - 7.75641i) q^{56} +(-2.52357 - 3.58336i) q^{57} +(-9.93298 - 2.11132i) q^{58} +(1.08427 - 0.482747i) q^{59} +(-10.6857 - 5.37997i) q^{60} +(-9.93622 - 4.42389i) q^{61} +(-2.65896 - 1.93184i) q^{62} +(11.4858 + 5.52526i) q^{63} +(10.5566 - 7.66983i) q^{64} +(4.70252 - 2.51313i) q^{65} +(-10.2794 - 6.13867i) q^{66} +(2.36441 + 0.502571i) q^{67} +(-11.8448 + 20.5157i) q^{68} +(-4.27538 - 9.99688i) q^{69} +(3.76603 + 21.0975i) q^{70} +(-3.08718 + 9.50135i) q^{71} +(-5.83210 - 4.50592i) q^{72} +(-2.70313 + 1.96394i) q^{73} +(-0.730937 - 1.26602i) q^{74} +(7.82330 - 3.71429i) q^{75} +(3.90822 - 6.76924i) q^{76} +(1.36081 + 12.9472i) q^{77} +(8.90251 - 2.74813i) q^{78} +(1.44490 - 0.307122i) q^{79} +(-0.0466350 + 1.42153i) q^{80} +(3.28095 - 8.38066i) q^{81} -4.56542 q^{82} +(4.79891 - 5.32973i) q^{83} +(-0.335214 + 22.7286i) q^{84} +(-6.45746 - 15.8861i) q^{85} +(-0.204248 - 1.94329i) q^{86} +(6.80903 - 3.79843i) q^{87} +(0.786864 - 7.48651i) q^{88} +(0.415723 - 0.302040i) q^{89} +(14.6554 - 3.77135i) q^{90} +(-8.19595 - 5.95471i) q^{91} +(12.9750 - 14.4102i) q^{92} +(2.51326 - 0.226736i) q^{93} +(21.9743 + 4.67079i) q^{94} +(2.13066 + 5.24167i) q^{95} +(-2.44444 + 10.7203i) q^{96} +(-2.02334 + 0.430075i) q^{97} +(20.1673 - 14.6524i) q^{98} +(9.04423 - 1.64526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.06085	−	0.917550i	−1.45724	−	0.648806i	−0.483269	−	0.875472i	$-0.660551\pi$
$2$	−2.06085	−	0.917550i	−1.45724	−	0.648806i	−0.973972	+	0.226666i	$0.927217\pi$
$3$	1.65499	−	0.510883i	0.955510	−	0.294958i
$3$	1.65499	−	0.510883i	0.955510	−	0.294958i
$4$	2.06695	+	2.29558i	1.03347	+	1.14779i
$5$	−2.23029	+	0.160691i	−0.997414	+	0.0718633i
$5$	−2.23029	+	0.160691i	−0.997414	+	0.0718633i
$6$	−3.87945	−	0.465685i	−1.58378	−	0.190115i
$7$	2.12428	+	3.67936i	0.802903	+	1.39067i	0.917698	+	0.397279i	$0.130045\pi$
$7$	2.12428	+	3.67936i	0.802903	+	1.39067i	−0.114795	+	0.993389i	$0.536621\pi$
$8$	−0.759150	−	2.33642i	−0.268400	−	0.826050i
$9$	2.47800	−	1.69101i	0.825999	−	0.563671i
$10$	4.74373	+	1.71524i	1.50010	+	0.542406i
$11$	2.79930	+	1.24633i	0.844021	+	0.375783i	0.782748	−	0.622338i	$-0.213817\pi$
$11$	2.79930	+	1.24633i	0.844021	+	0.375783i	0.0612732	+	0.998121i	$0.480484\pi$
$12$	4.59355	+	2.74319i	1.32604	+	0.791892i
$13$	−2.17836	+	0.969869i	−0.604169	+	0.268993i	−0.685940	−	0.727658i	$-0.740609\pi$
$13$	−2.17836	+	0.969869i	−0.604169	+	0.268993i	0.0817713	+	0.996651i	$0.473942\pi$
$14$	−1.00183	−	9.53175i	−0.267750	−	2.54747i
$15$	−3.60901	+	1.40536i	−0.931843	+	0.362862i
$16$	0.0664873	−	0.632584i	0.0166218	−	0.158146i
$17$	2.36985	+	7.29363i	0.574772	+	1.76897i	0.636955	+	0.770901i	$0.280194\pi$
$17$	2.36985	+	7.29363i	0.574772	+	1.76897i	−0.0621827	+	0.998065i	$0.519806\pi$
$18$	−6.65837	+	1.21124i	−1.56939	+	0.285492i
$19$	−0.781940	−	2.40656i	−0.179389	−	0.552103i	0.820417	−	0.571765i	$-0.193741\pi$
$19$	−0.781940	−	2.40656i	−0.179389	−	0.552103i	−0.999807	+	0.0196617i	$0.993741\pi$
$20$	−4.97876	−	4.78765i	−1.11328	−	1.07055i
$21$	5.39539	+	5.00406i	1.17737	+	1.09197i
$22$	−4.62537	−	5.13700i	−0.986133	−	1.09521i
$23$	−0.656165	−	6.24299i	−0.136820	−	1.30175i	−0.820363	−	0.571844i	$-0.806228\pi$
$23$	−0.656165	−	6.24299i	−0.136820	−	1.30175i	0.683543	−	0.729910i	$-0.260438\pi$
$24$	−2.45003	−	3.47893i	−0.500109	−	0.710133i
$25$	4.94836	−	0.716775i	0.989671	−	0.143355i
$26$	5.37918			1.05494
$27$	3.23716	−	4.06458i	0.622991	−	0.782229i
$28$	−4.05548	+	12.4815i	−0.766414	+	2.35878i
$29$	4.40315	−	0.935918i	0.817644	−	0.173796i	0.219941	−	0.975513i	$-0.429413\pi$
$29$	4.40315	−	0.935918i	0.817644	−	0.173796i	0.597703	+	0.801718i	$0.296080\pi$
$30$	8.72712	+	0.415217i	1.59335	+	0.0758080i
$31$	1.42509	+	0.302912i	0.255953	+	0.0544046i	0.334101	−	0.942537i	$-0.391567\pi$
$31$	1.42509	+	0.302912i	0.255953	+	0.0544046i	−0.0781478	+	0.996942i	$0.524901\pi$
$32$	−3.17411	+	5.49772i	−0.561108	+	0.971868i
$33$	5.26955	+	0.632551i	0.917311	+	0.110113i
$34$	1.80838	−	17.2055i	0.310134	−	2.95073i
$35$	−5.32900	−	7.86468i	−0.900765	−	1.32937i
$36$	9.00374	+	2.19320i	1.50062	+	0.365533i
$37$	0.524265	+	0.380901i	0.0861887	+	0.0626198i	0.630045	−	0.776559i	$-0.283036\pi$
$37$	0.524265	+	0.380901i	0.0861887	+	0.0626198i	−0.543856	+	0.839178i	$0.683036\pi$
$38$	−0.596680	+	5.67703i	−0.0967943	+	0.920937i
$39$	−3.10968	+	2.71801i	−0.497948	+	0.435231i
$40$	2.06856	+	5.08890i	0.327069	+	0.804627i
$41$	1.84882	−	0.823147i	0.288737	−	0.128554i	−0.257257	−	0.966343i	$-0.582819\pi$
$41$	1.84882	−	0.823147i	0.288737	−	0.128554i	0.545994	+	0.837789i	$0.316152\pi$
$42$	−6.52762	−	15.2632i	−1.00723	−	2.35516i
$43$	0.433089	+	0.750133i	0.0660455	+	0.114394i	0.897157	−	0.441711i	$-0.145628\pi$
$43$	0.433089	+	0.750133i	0.0660455	+	0.114394i	−0.831112	+	0.556105i	$0.812295\pi$
$44$	2.92496	+	9.00211i	0.440955	+	1.35712i
$45$	−5.25491	+	4.16964i	−0.783356	+	0.621573i
$46$	−4.37600	+	13.4679i	−0.645206	+	1.98574i
$47$	−9.74091	+	2.07049i	−1.42086	+	0.302012i	−0.853342	−	0.521351i	$-0.825428\pi$
$47$	−9.74091	+	2.07049i	−1.42086	+	0.302012i	−0.567515	+	0.823363i	$0.692095\pi$
$48$	−0.213140	−	1.08089i	−0.0307642	−	0.156013i
$49$	−5.52514	+	9.56982i	−0.789305	+	1.36712i
$50$	−10.8555	−	3.06320i	−1.53520	−	0.433202i
$51$	7.64827	+	10.8602i	1.07097	+	1.52073i
$52$	−6.72897	−	2.99593i	−0.933140	−	0.415461i
$53$	−0.161545	+	0.497185i	−0.0221900	+	0.0682937i	−0.961538	−	0.274671i	$-0.911431\pi$
$53$	−0.161545	+	0.497185i	−0.0221900	+	0.0682937i	0.939348	+	0.342965i	$0.111431\pi$
$54$	−10.4008	+	5.40624i	−1.41536	+	0.735696i
$55$	−6.44352	−	2.32985i	−0.868844	−	0.314157i
$56$	6.98390	−	7.75641i	0.933263	−	1.03649i
$57$	−2.52357	−	3.58336i	−0.334256	−	0.474628i
$58$	−9.93298	−	2.11132i	−1.30426	−	0.277230i
$59$	1.08427	−	0.482747i	0.141160	−	0.0628484i	−0.334941	−	0.942239i	$-0.608716\pi$
$59$	1.08427	−	0.482747i	0.141160	−	0.0628484i	0.476101	+	0.879391i	$0.342050\pi$
$60$	−10.6857	−	5.37997i	−1.37952	−	0.694551i
$61$	−9.93622	−	4.42389i	−1.27220	−	0.566421i	−0.344166	−	0.938909i	$-0.611838\pi$
$61$	−9.93622	−	4.42389i	−1.27220	−	0.566421i	−0.928037	+	0.372488i	$0.878505\pi$
$62$	−2.65896	−	1.93184i	−0.337688	−	0.245345i
$63$	11.4858	+	5.52526i	1.44708	+	0.696118i
$64$	10.5566	−	7.66983i	1.31958	−	0.958728i
$65$	4.70252	−	2.51313i	0.583276	−	0.311715i
$66$	−10.2794	−	6.13867i	−1.26530	−	0.755618i
$67$	2.36441	+	0.502571i	0.288859	+	0.0613988i	0.350062	−	0.936727i	$-0.386161\pi$
$67$	2.36441	+	0.502571i	0.288859	+	0.0613988i	−0.0612034	+	0.998125i	$0.519494\pi$
$68$	−11.8448	+	20.5157i	−1.43639	+	2.48790i
$69$	−4.27538	−	9.99688i	−0.514696	−	1.20348i
$70$	3.76603	+	21.0975i	0.450127	+	2.52164i
$71$	−3.08718	+	9.50135i	−0.366380	+	1.12760i	0.582732	+	0.812665i	$0.301984\pi$
$71$	−3.08718	+	9.50135i	−0.366380	+	1.12760i	−0.949112	+	0.314938i	$0.898016\pi$
$72$	−5.83210	−	4.50592i	−0.687319	−	0.531028i
$73$	−2.70313	+	1.96394i	−0.316378	+	0.229862i	−0.734628	−	0.678470i	$-0.762643\pi$
$73$	−2.70313	+	1.96394i	−0.316378	+	0.229862i	0.418250	+	0.908332i	$0.362643\pi$
$74$	−0.730937	−	1.26602i	−0.0849697	−	0.147172i
$75$	7.82330	−	3.71429i	0.903357	−	0.428889i
$76$	3.90822	−	6.76924i	0.448304	−	0.776485i
$77$	1.36081	+	12.9472i	0.155078	+	1.47547i
$78$	8.90251	−	2.74813i	1.00801	−	0.311165i
$79$	1.44490	−	0.307122i	0.162564	−	0.0345540i	−0.125911	−	0.992042i	$-0.540185\pi$
$79$	1.44490	−	0.307122i	0.162564	−	0.0345540i	0.288474	+	0.957488i	$0.406852\pi$
$80$	−0.0466350	+	1.42153i	−0.00521395	+	0.158932i
$81$	3.28095	−	8.38066i	0.364550	−	0.931184i
$82$	−4.56542			−0.504166
$83$	4.79891	−	5.32973i	0.526748	−	0.585013i	−0.419783	−	0.907624i	$-0.637894\pi$
$83$	4.79891	−	5.32973i	0.526748	−	0.585013i	0.946532	+	0.322611i	$0.104561\pi$
$84$	−0.335214	+	22.7286i	−0.0365749	+	2.47990i
$85$	−6.45746	−	15.8861i	−0.700410	−	1.72309i
$86$	−0.204248	−	1.94329i	−0.0220247	−	0.209551i
$87$	6.80903	−	3.79843i	0.730005	−	0.407234i
$88$	0.786864	−	7.48651i	0.0838799	−	0.798064i
$89$	0.415723	−	0.302040i	0.0440665	−	0.0320162i	−0.565534	−	0.824725i	$-0.691330\pi$
$89$	0.415723	−	0.302040i	0.0440665	−	0.0320162i	0.609600	+	0.792709i	$0.291330\pi$
$90$	14.6554	−	3.77135i	1.54482	−	0.397536i
$91$	−8.19595	−	5.95471i	−0.859169	−	0.624223i
$92$	12.9750	−	14.4102i	1.35274	−	1.50237i
$93$	2.51326	−	0.226736i	0.260613	−	0.0235114i
$94$	21.9743	+	4.67079i	2.26648	+	0.481755i
$95$	2.13066	+	5.24167i	0.218601	+	0.537784i
$96$	−2.44444	+	10.7203i	−0.249484	+	1.09413i
$97$	−2.02334	+	0.430075i	−0.205439	+	0.0436675i	−0.309482	−	0.950905i	$-0.600156\pi$
$97$	−2.02334	+	0.430075i	−0.205439	+	0.0436675i	0.104042	+	0.994573i	$0.466822\pi$
$98$	20.1673	−	14.6524i	2.03720	−	1.48011i
$99$	9.04423	−	1.64526i	0.908979	−	0.165354i
$100$	11.8734	+	9.87780i	1.18734	+	0.987780i
$101$	−7.67282	−	13.2897i	−0.763474	−	1.32238i	−0.941049	−	0.338269i	$-0.890159\pi$
$101$	−7.67282	−	13.2897i	−0.763474	−	1.32238i	0.177575	−	0.984107i	$-0.443175\pi$
$102$	−5.79716	−	29.3989i	−0.574005	−	2.91093i
$103$	−6.17144	−	6.85407i	−0.608090	−	0.675352i	0.357952	−	0.933740i	$-0.383475\pi$
$103$	−6.17144	−	6.85407i	−0.608090	−	0.675352i	−0.966041	+	0.258388i	$0.916809\pi$
$104$	3.91973	+	4.35330i	0.384361	+	0.426876i
$105$	−12.8374	−	10.2935i	−1.25280	−	1.00454i
$106$	0.789113	−	0.876399i	0.0766454	−	0.0851234i
$107$	8.88999			0.859427			0.429714	−	0.902965i	$-0.358615\pi$
$107$	8.88999			0.859427			0.429714	+	0.902965i	$0.358615\pi$
$108$	16.0216	−	0.970126i	1.54168	−	0.0933504i
$109$	−1.19596	−	0.868915i	−0.114552	−	0.0832270i	0.529034	−	0.848600i	$-0.322554\pi$
$109$	−1.19596	−	0.868915i	−0.114552	−	0.0832270i	−0.643586	+	0.765373i	$0.722554\pi$
$110$	11.1414	+	10.7137i	1.06229	+	1.02151i
$111$	1.06225	+	0.362550i	0.100824	+	0.0344118i
$112$	2.46874	−	1.09916i	0.233274	−	0.103860i
$113$	−3.38269	+	1.50607i	−0.318216	+	0.141679i	−0.559628	−	0.828744i	$-0.689056\pi$
$113$	−3.38269	+	1.50607i	−0.318216	+	0.141679i	0.241412	+	0.970423i	$0.422389\pi$
$114$	1.91280	+	9.70028i	0.179150	+	0.908515i
$115$	2.46663	+	13.8182i	0.230014	+	1.28856i
$116$	11.2495	+	8.17327i	1.04449	+	0.758869i
$117$	−3.75792	+	6.08697i	−0.347419	+	0.562741i
$118$	−2.67746			−0.246480
$119$	−21.8017	+	24.2132i	−1.99856	+	2.21962i
$120$	6.02329	+	7.36530i	0.549849	+	0.672357i
$121$	−1.07768	−	1.19689i	−0.0979709	−	0.108808i
$122$	16.4179	+	18.2340i	1.48641	+	1.65083i
$123$	2.63925	−	2.30683i	0.237973	−	0.208000i
$124$	2.25022	+	3.89750i	0.202076	+	0.350006i
$125$	−10.9211	+	2.39377i	−0.976811	+	0.214105i
$126$	−18.6008	−	21.9255i	−1.65709	−	1.95328i
$127$	4.74186	−	3.44516i	0.420772	−	0.305709i	−0.357176	−	0.934037i	$-0.616261\pi$
$127$	4.74186	−	3.44516i	0.420772	−	0.305709i	0.777948	+	0.628328i	$0.216261\pi$
$128$	−16.3741	+	3.48041i	−1.44728	+	0.307628i
$129$	1.09999	+	1.02021i	0.0968487	+	0.0898242i
$130$	−11.9971	+	0.864387i	−1.05222	+	0.0758118i
$131$	6.27356	+	1.33349i	0.548124	+	0.116507i	0.473646	−	0.880715i	$-0.342938\pi$
$131$	6.27356	+	1.33349i	0.548124	+	0.116507i	0.0744779	+	0.997223i	$0.476271\pi$
$132$	9.43981	+	13.4041i	0.821630	+	1.16668i
$133$	7.19356	−	7.98925i	0.623760	−	0.692756i
$134$	−4.41156	−	3.20519i	−0.381101	−	0.276886i
$135$	−6.56665	+	9.58536i	−0.565167	+	0.824977i
$136$	15.2419	−	11.0739i	1.30699	−	0.949581i
$137$	1.45881	−	13.8797i	0.124635	−	1.18582i	−0.736138	−	0.676831i	$-0.763353\pi$
$137$	1.45881	−	13.8797i	0.124635	−	1.18582i	0.860773	−	0.508989i	$-0.169981\pi$
$138$	−0.361707	+	24.5250i	−0.0307906	+	2.08770i
$139$	−1.23615	−	11.7612i	−0.104849	−	0.997573i	−0.912823	−	0.408355i	$-0.866103\pi$
$139$	−1.23615	−	11.7612i	−0.104849	−	0.997573i	0.807974	−	0.589218i	$-0.200564\pi$
$140$	7.03922	−	28.4890i	0.594923	−	2.40776i
$141$	−15.0633	+	8.40311i	−1.26856	+	0.707669i
$142$	15.0802	−	16.7482i	1.26550	−	1.40548i
$143$	−7.30667			−0.611015
$144$	−0.904953	−	1.67997i	−0.0754127	−	0.139998i
$145$	−9.66989	+	2.79491i	−0.803041	+	0.232105i
$146$	7.37277	−	1.56713i	0.610175	−	0.129697i
$147$	−4.25500	+	18.6607i	−0.350947	+	1.53911i
$148$	0.209241	+	1.99079i	0.0171995	+	0.163642i
$149$	6.20150	−	10.7413i	0.508047	−	0.879963i	−0.491910	−	0.870646i	$-0.663701\pi$
$149$	6.20150	−	10.7413i	0.508047	−	0.879963i	0.999957	−	0.00931695i	$-0.00296572\pi$
$150$	−19.5307	+	0.476318i	−1.59468	+	0.0388912i
$151$	6.61985	+	11.4659i	0.538716	+	0.933083i	0.998974	+	0.0452978i	$0.0144237\pi$
$151$	6.61985	+	11.4659i	0.538716	+	0.933083i	−0.460258	+	0.887785i	$0.652243\pi$
$152$	−5.02914	+	3.65388i	−0.407917	+	0.296369i
$153$	18.2061	+	14.0662i	1.47188	+	1.13718i
$154$	9.07528	−	27.9309i	0.731307	−	2.25073i
$155$	−3.22703	−	0.446581i	−0.259201	−	0.0358703i
$156$	−12.6670	−	1.52053i	−1.01417	−	0.121740i
$157$	4.80131	−	8.31611i	0.383186	−	0.663698i	−0.608330	−	0.793684i	$-0.708160\pi$
$157$	4.80131	−	8.31611i	0.383186	−	0.663698i	0.991516	+	0.129987i	$0.0414935\pi$
$158$	−3.25952	−	0.692832i	−0.259313	−	0.0551188i
$159$	−0.0133529	+	0.905369i	−0.00105895	+	0.0718004i
$160$	6.19574	−	12.7715i	0.489816	−	1.00968i
$161$	21.5764	−	15.6761i	1.70045	−	1.23545i
$162$	−14.4512	+	14.2608i	−1.13539	+	1.12044i
$163$	−9.18728	−	6.67495i	−0.719603	−	0.522822i	0.166654	−	0.986015i	$-0.446704\pi$
$163$	−9.18728	−	6.67495i	−0.719603	−	0.522822i	−0.886257	+	0.463193i	$0.846704\pi$
$164$	5.71101	+	2.54270i	0.445955	+	0.198552i
$165$	−11.8543	−	0.563999i	−0.922853	−	0.0439073i
$166$	−14.7801	+	6.58053i	−1.14716	+	0.510748i
$167$	−18.1337	−	3.85444i	−1.40323	−	0.298266i	−0.556747	−	0.830682i	$-0.687951\pi$
$167$	−18.1337	−	3.85444i	−1.40323	−	0.298266i	−0.846482	+	0.532417i	$0.821284\pi$
$168$	7.59569	−	16.4047i	0.586020	−	1.26565i
$169$	−4.89408	+	5.43543i	−0.376468	+	0.418110i
$170$	−1.26842	+	38.6639i	−0.0972831	+	2.96538i
$171$	−6.00717	−	4.64119i	−0.459380	−	0.354920i
$172$	−0.826815	+	2.54467i	−0.0630440	+	0.194030i
$173$	8.23416	+	3.66608i	0.626032	+	0.278727i	0.695132	−	0.718883i	$-0.255346\pi$
$173$	8.23416	+	3.66608i	0.626032	+	0.278727i	−0.0691000	+	0.997610i	$0.522013\pi$
$174$	−17.5176	+	1.58037i	−1.32801	+	0.119807i
$175$	13.1490	+	16.6842i	0.993969	+	1.26120i
$176$	0.974526	−	1.68793i	0.0734577	−	0.127232i
$177$	1.54783	−	1.35288i	0.116342	−	0.101688i
$178$	−1.13388	+	0.241013i	−0.0849878	+	0.0180647i
$179$	5.80773	−	17.8744i	0.434090	−	1.33599i	−0.459926	−	0.887957i	$-0.652124\pi$
$179$	5.80773	−	17.8744i	0.434090	−	1.33599i	0.894016	−	0.448035i	$-0.147876\pi$
$180$	−20.4333	−	3.44464i	−1.52301	−	0.256748i
$181$	−0.674906	−	2.07715i	−0.0501653	−	0.154393i	0.922836	−	0.385194i	$-0.125865\pi$
$181$	−0.674906	−	2.07715i	−0.0501653	−	0.154393i	−0.973001	+	0.230801i	$0.925865\pi$
$182$	11.4269	+	19.7920i	0.847018	+	1.46708i
$183$	−18.7045	−	2.24526i	−1.38267	−	0.165975i
$184$	−14.0881	+	6.27245i	−1.03859	+	0.462411i
$185$	−1.23047	−	0.765274i	−0.0904659	−	0.0562641i
$186$	−5.38750	−	1.83877i	−0.395031	−	0.134825i
$187$	−2.45636	+	23.3707i	−0.179627	+	1.70903i
$188$	−24.8869	−	18.0814i	−1.81506	−	1.31872i
$189$	21.8317	+	3.27637i	1.58802	+	0.238321i
$190$	0.418519	−	12.7573i	0.0303626	−	0.925511i
$191$	1.30681	−	12.4335i	0.0945576	−	0.899655i	−0.839699	−	0.543053i	$-0.817268\pi$
$191$	1.30681	−	12.4335i	0.0945576	−	0.899655i	0.934256	−	0.356603i	$-0.116065\pi$
$192$	13.5527	−	18.0867i	0.978084	−	1.30529i
$193$	7.39092	−	12.8015i	0.532010	−	0.921469i	−0.467291	−	0.884103i	$-0.654770\pi$
$193$	7.39092	−	12.8015i	0.532010	−	0.921469i	0.999302	−	0.0373655i	$-0.0118966\pi$
$194$	4.56443	+	0.970199i	0.327707	+	0.0696562i
$195$	6.49872	−	6.56165i	0.465383	−	0.469889i
$196$	−33.3884	+	7.09692i	−2.38489	+	0.506923i
$197$	3.83767	−	11.8111i	0.273422	−	0.841507i	−0.716210	−	0.697885i	$-0.754125\pi$
$197$	3.83767	−	11.8111i	0.273422	−	0.841507i	0.989633	−	0.143623i	$-0.0458752\pi$
$198$	−20.1484	−	4.90790i	−1.43188	−	0.348789i
$199$	6.90105			0.489202			0.244601	−	0.969624i	$-0.421343\pi$
$199$	6.90105			0.489202			0.244601	+	0.969624i	$0.421343\pi$
$200$	−5.43123	−	11.0173i	−0.384046	−	0.779042i
$201$	4.16983	−	0.376185i	0.294117	−	0.0265341i
$202$	3.61856	+	34.4283i	0.254601	+	2.42237i
$203$	12.7971	+	14.2126i	0.898181	+	0.997531i
$204$	−9.12185	+	40.0046i	−0.638657	+	2.80088i
$205$	−3.99112	+	2.13294i	−0.278752	+	0.148971i
$206$	6.42945	+	19.7878i	0.447961	+	1.37868i
$207$	−12.1830	−	14.3605i	−0.846774	−	0.998127i
$208$	0.468691	+	1.44248i	0.0324978	+	0.100018i
$209$	0.810485	−	7.71125i	0.0560624	−	0.533398i
$210$	17.0111	+	32.9923i	1.17388	+	2.27668i
$211$	2.36206	+	22.4735i	0.162611	+	1.54714i	0.706337	+	0.707875i	$0.250346\pi$
$211$	2.36206	+	22.4735i	0.162611	+	1.54714i	−0.543727	+	0.839262i	$0.682987\pi$
$212$	−1.47523	+	0.656816i	−0.101319	+	0.0451103i
$213$	−0.255177	+	17.3018i	−0.0174844	+	1.18550i
$214$	−18.3209	−	8.15700i	−1.25239	−	0.557601i
$215$	−1.08645	−	1.60342i	−0.0740955	−	0.109352i
$216$	−11.9541	−	4.47774i	−0.813371	−	0.304672i
$217$	1.91276	+	5.88688i	0.129847	+	0.399628i
$218$	1.66742	+	2.88806i	0.112932	+	0.195604i
$219$	−3.47032	+	4.63129i	−0.234503	+	0.312954i
$220$	−7.97006	−	19.6073i	−0.537342	−	1.32192i
$221$	−12.2363	−	13.5897i	−0.823100	−	0.914145i
$222$	−1.85648	−	1.72183i	−0.124599	−	0.115562i
$223$	5.21313	+	2.32103i	0.349097	+	0.155428i	0.573792	−	0.819001i	$-0.305472\pi$
$223$	5.21313	+	2.32103i	0.349097	+	0.155428i	−0.224695	+	0.974429i	$0.572139\pi$
$224$	−26.9708			−1.80206
$225$	11.0499	−	10.1439i	0.736663	−	0.676260i
$226$	8.35310			0.555640
$227$	−11.8328	−	5.26831i	−0.785372	−	0.349670i	−0.0254432	−	0.999676i	$-0.508100\pi$
$227$	−11.8328	−	5.26831i	−0.785372	−	0.349670i	−0.759929	+	0.650006i	$0.774766\pi$
$228$	3.00979	−	13.1997i	0.199328	−	0.874170i
$229$	5.11674	+	5.68271i	0.338123	+	0.375524i	0.888096	−	0.459659i	$-0.152028\pi$
$229$	5.11674	+	5.68271i	0.338123	+	0.375524i	−0.549972	+	0.835183i	$0.685362\pi$
$230$	7.59555	−	30.7406i	0.500836	−	2.02697i
$231$	8.86662	+	20.7323i	0.583381	+	1.36409i
$232$	−5.52935	−	9.57712i	−0.363020	−	0.628769i
$233$	0.0969674	+	0.298435i	0.00635254	+	0.0195511i	0.954183	−	0.299225i	$-0.0967282\pi$
$233$	0.0969674	+	0.298435i	0.00635254	+	0.0195511i	−0.947830	+	0.318776i	$0.896728\pi$
$234$	13.3296	−	9.09627i	0.871383	−	0.594642i
$235$	21.3923	−	6.18307i	1.39548	−	0.403339i
$236$	3.34931	+	1.49121i	0.218021	+	0.0970694i
$237$	2.23439	−	1.24646i	0.145139	−	0.0809662i
$238$	67.1469	−	29.8957i	4.35249	−	1.93785i
$239$	2.36316	+	22.4840i	0.152860	+	1.45437i	0.754867	+	0.655878i	$0.227701\pi$
$239$	2.36316	+	22.4840i	0.152860	+	1.45437i	−0.602007	+	0.798491i	$0.705632\pi$
$240$	0.649053	+	2.37644i	0.0418962	+	0.153399i
$241$	−1.68606	+	16.0418i	−0.108609	+	1.03334i	0.795474	+	0.605988i	$0.207222\pi$
$241$	−1.68606	+	16.0418i	−0.108609	+	1.03334i	−0.904083	+	0.427357i	$0.859445\pi$
$242$	1.12274	+	3.45543i	0.0721722	+	0.222123i
$243$	1.14841	−	15.5461i	0.0736706	−	0.997283i
$244$	−10.3823	−	31.9533i	−0.664656	−	2.04560i
$245$	10.7849	−	22.2313i	0.689019	−	1.42030i
$246$	−7.55573	+	2.33239i	−0.481736	+	0.148708i
$247$	4.03740	+	4.48399i	0.256894	+	0.285309i
$248$	−0.374125	−	3.55956i	−0.0237570	−	0.226033i
$249$	5.21929	−	11.2723i	0.330759	−	0.714355i
$250$	24.7031	+	5.08743i	1.56236	+	0.321757i
$251$	−18.3401			−1.15762			−0.578809	−	0.815463i	$-0.696482\pi$
$251$	−18.3401			−1.15762			−0.578809	+	0.815463i	$0.696482\pi$
$252$	11.0569	+	37.7870i	0.696519	+	2.38036i
$253$	5.94402	−	18.2938i	0.373698	−	1.15012i
$254$	−12.9334	+	2.74907i	−0.811512	+	0.172492i
$255$	−18.8030	−	22.9923i	−1.17749	−	1.43984i
$256$	11.4109	+	2.42545i	0.713179	+	0.151591i
$257$	−11.2959	+	19.5650i	−0.704616	+	1.22043i	0.262214	+	0.965010i	$0.415547\pi$
$257$	−11.2959	+	19.5650i	−0.704616	+	1.22043i	−0.966830	+	0.255421i	$0.917786\pi$
$258$	−1.33082	−	3.11179i	−0.0828535	−	0.193731i
$259$	−0.287786	+	2.73810i	−0.0178822	+	0.170137i
$260$	15.4889	+	5.60050i	0.960584	+	0.347328i
$261$	9.32834	−	9.76499i	0.577410	−	0.604438i
$262$	−11.7053	−	8.50443i	−0.723158	−	0.525405i
$263$	0.238572	−	2.26986i	0.0147110	−	0.139965i	−0.984701	−	0.174252i	$-0.944249\pi$
$263$	0.238572	−	2.26986i	0.0147110	−	0.139965i	0.999412	+	0.0342866i	$0.0109159\pi$
$264$	−2.52247	−	12.7921i	−0.155247	−	0.787300i
$265$	0.280399	−	1.13482i	0.0172248	−	0.0697117i
$266$	−22.1554	+	9.86421i	−1.35843	+	0.604814i
$267$	0.533711	−	0.712260i	0.0326626	−	0.0435896i
$268$	3.73342	+	6.46647i	0.228055	+	0.395002i
$269$	−0.759927	−	2.33881i	−0.0463335	−	0.142600i	0.925213	−	0.379447i	$-0.123886\pi$
$269$	−0.759927	−	2.33881i	−0.0463335	−	0.142600i	−0.971547	+	0.236847i	$0.923886\pi$
$270$	22.3279	−	13.7288i	1.35883	−	0.835506i
$271$	−4.44549	+	13.6818i	−0.270044	+	0.831111i	0.720444	+	0.693513i	$0.243938\pi$
$271$	−4.44549	+	13.6818i	−0.270044	+	0.831111i	−0.990488	+	0.137598i	$0.956062\pi$
$272$	4.77140	−	1.01419i	0.289309	−	0.0614945i
$273$	−16.6064	−	5.66783i	−1.00506	−	0.343032i
$274$	−15.7417	+	27.2654i	−0.950990	+	1.64716i
$275$	14.7453	+	4.16081i	0.889174	+	0.250907i
$276$	14.1116	−	30.4775i	0.849419	−	1.83453i
$277$	−25.6221	−	11.4077i	−1.53949	−	0.685423i	−0.550691	−	0.834709i	$-0.685636\pi$
$277$	−25.6221	−	11.4077i	−1.53949	−	0.685423i	−0.988794	+	0.149286i	$0.952303\pi$
$278$	−8.24397	+	25.3723i	−0.494441	+	1.52173i
$279$	4.04359	−	1.65923i	0.242084	−	0.0993354i
$280$	−14.3297	+	18.4213i	−0.856364	+	1.10088i
$281$	8.00633	−	8.89193i	0.477618	−	0.530448i	−0.455396	−	0.890289i	$-0.650502\pi$
$281$	8.00633	−	8.89193i	0.477618	−	0.530448i	0.933014	+	0.359841i	$0.117169\pi$
$282$	38.7536	−	3.49619i	2.30774	−	0.208195i
$283$	−30.4217	−	6.46633i	−1.80838	−	0.384383i	−0.824884	−	0.565302i	$-0.808760\pi$
$283$	−30.4217	−	6.46633i	−1.80838	−	0.384383i	−0.983498	+	0.180919i	$0.942093\pi$
$284$	−28.1921	+	12.5519i	−1.67289	+	0.744820i
$285$	6.20411	+	7.58641i	0.367500	+	0.449380i
$286$	15.0580	+	6.70424i	0.890396	+	0.396430i
$287$	6.95607	+	5.05388i	0.410604	+	0.298321i
$288$	1.43128	+	18.9908i	0.0843389	+	1.11904i
$289$	−33.8276	+	24.5772i	−1.98986	+	1.44572i
$290$	22.4927	+	3.11271i	1.32082	+	0.182784i
$291$	−3.12890	+	1.74546i	−0.183419	+	0.102321i
$292$	−10.0956	−	2.14589i	−0.590801	−	0.125579i
$293$	9.75305	−	16.8928i	0.569779	−	0.986886i	−0.426808	−	0.904342i	$-0.640362\pi$
$293$	9.75305	−	16.8928i	0.569779	−	0.986886i	0.996587	−	0.0825441i	$-0.0263045\pi$
$294$	25.8910	−	34.5527i	1.50999	−	2.01515i
$295$	−2.34066	+	1.25090i	−0.136278	+	0.0728301i
$296$	0.491950	−	1.51407i	0.0285940	−	0.0880034i
$297$	14.1276	−	7.34342i	0.819766	−	0.426109i
$298$	−22.6361	+	16.4461i	−1.31127	+	0.952695i
$299$	7.48425	+	12.9631i	0.432826	+	0.749676i
$300$	24.6968	+	10.2818i	1.42587	+	0.593618i
$301$	−1.84001	+	3.18699i	−0.106056	+	0.183695i
$302$	−3.12197	−	29.7036i	−0.179649	−	1.70925i
$303$	−19.4879	−	18.0745i	−1.11955	−	1.03835i
$304$	−1.57434	+	0.334637i	−0.0902947	+	0.0191927i
$305$	22.8715	+	8.26988i	1.30962	+	0.473532i
$306$	−24.6137	−	45.6933i	−1.40707	−	2.61211i
$307$	27.0345			1.54294			0.771469	−	0.636267i	$-0.219522\pi$
$307$	27.0345			1.54294			0.771469	+	0.636267i	$0.219522\pi$
$308$	−26.9086	+	29.8850i	−1.53326	+	1.70286i
$309$	−13.7153	−	8.19056i	−0.780236	−	0.465945i
$310$	6.24067	+	3.88130i	0.354446	+	0.220443i
$311$	2.19188	+	20.8544i	0.124290	+	1.18254i	0.861815	+	0.507222i	$0.169328\pi$
$311$	2.19188	+	20.8544i	0.124290	+	1.18254i	−0.737525	+	0.675320i	$0.764006\pi$
$312$	8.71115	+	5.20216i	0.493172	+	0.294514i
$313$	2.87675	−	27.3705i	0.162604	−	1.54707i	−0.543772	−	0.839233i	$-0.683004\pi$
$313$	2.87675	−	27.3705i	0.162604	−	1.54707i	0.706376	−	0.707837i	$-0.250329\pi$
$314$	−17.5252	+	12.7328i	−0.989005	+	0.718554i
$315$	−26.5045	−	10.4773i	−1.49336	−	0.590326i
$316$	3.69155	+	2.68207i	0.207666	+	0.150878i
$317$	−4.19062	+	4.65416i	−0.235369	+	0.261403i	−0.849245	−	0.527999i	$-0.822943\pi$
$317$	−4.19062	+	4.65416i	−0.235369	+	0.261403i	0.613876	+	0.789402i	$0.289609\pi$
$318$	0.858239	−	1.85358i	0.0481277	−	0.103943i
$319$	13.4922	+	2.86786i	0.755419	+	0.160569i
$320$	−22.3118	+	18.8023i	−1.24727	+	1.05108i
$321$	14.7129	−	4.54174i	0.821192	−	0.253495i
$322$	−58.8493	+	12.5088i	−3.27954	+	0.697088i
$323$	15.6995	−	11.4064i	0.873544	−	0.634667i
$324$	26.0200	−	9.79070i	1.44555	−	0.543928i
$325$	−10.0841	+	6.36066i	−0.559367	+	0.352826i
$326$	12.8090	+	22.1859i	0.709426	+	1.22876i
$327$	−2.42322	−	0.827053i	−0.134004	−	0.0457361i
$328$	−3.32675	−	3.69473i	−0.183689	−	0.204007i
$329$	−28.3105	−	31.4420i	−1.56081	−	1.73345i
$330$	23.9124	+	12.0392i	1.31633	+	0.662736i
$331$	−1.60189	+	1.77908i	−0.0880478	+	0.0977870i	−0.785559	−	0.618787i	$-0.787624\pi$
$331$	−1.60189	+	1.77908i	−0.0880478	+	0.0977870i	0.697511	+	0.716574i	$0.254291\pi$
$332$	22.1539			1.21585
$333$	1.94324	+	0.0573323i	0.106489	+	0.00314179i
$334$	33.8342	+	24.5820i	1.85133	+	1.34507i
$335$	−5.35407	−	0.740937i	−0.292524	−	0.0404817i
$336$	3.52421	−	3.08033i	0.192262	−	0.168046i
$337$	−6.42544	+	2.86079i	−0.350016	+	0.155837i	−0.574211	−	0.818707i	$-0.694691\pi$
$337$	−6.42544	+	2.86079i	−0.350016	+	0.155837i	0.224195	+	0.974544i	$0.428025\pi$
$338$	15.0732	−	6.71104i	0.819876	−	0.365033i
$339$	−4.82889	+	4.22069i	−0.262269	+	0.229236i
$340$	23.1205	−	47.6593i	1.25388	−	2.58469i
$341$	3.61172	+	2.62407i	0.195586	+	0.142101i
$342$	8.12137	+	15.0767i	0.439153	+	0.815253i
$343$	−17.2078			−0.929135
$344$	1.42385	−	1.58134i	0.0767688	−	0.0852603i
$345$	11.1417	+	21.6089i	0.599851	+	1.16338i
$346$	−13.6056	−	15.1105i	−0.731439	−	0.812346i
$347$	7.78217	+	8.64298i	0.417769	+	0.463979i	0.914891	−	0.403701i	$-0.132277\pi$
$347$	7.78217	+	8.64298i	0.417769	+	0.463979i	−0.497122	+	0.867681i	$0.665610\pi$
$348$	22.7935	+	7.77950i	1.22186	+	0.417025i
$349$	9.48461	+	16.4278i	0.507700	+	0.879362i	0.999960	+	0.00891382i	$0.00283739\pi$
$349$	9.48461	+	16.4278i	0.507700	+	0.879362i	−0.492261	+	0.870448i	$0.663829\pi$
$350$	−11.7895	−	46.4484i	−0.630176	−	2.48277i
$351$	−3.10959	+	11.9937i	−0.165978	+	0.640179i
$352$	−15.7373	+	11.4338i	−0.838799	+	0.609423i
$353$	−17.9763	+	3.82097i	−0.956780	+	0.203370i	−0.659739	−	0.751495i	$-0.729333\pi$
$353$	−17.9763	+	3.82097i	−0.956780	+	0.203370i	−0.297041	+	0.954865i	$0.596000\pi$
$354$	−4.43117	+	1.36787i	−0.235514	+	0.0727013i
$355$	5.35850	−	21.6868i	0.284400	−	1.15102i
$356$	1.55263	+	0.330022i	0.0822894	+	0.0174911i
$357$	−23.7115	+	51.2108i	−1.25495	+	2.71037i
$358$	−28.3695	+	31.5075i	−1.49937	+	1.66522i
$359$	−9.64076	−	7.00442i	−0.508820	−	0.369679i	0.303556	−	0.952814i	$-0.401826\pi$
$359$	−9.64076	−	7.00442i	−0.508820	−	0.369679i	−0.812376	+	0.583134i	$0.801826\pi$
$360$	13.7313	+	9.11233i	0.723703	+	0.480262i
$361$	10.1912	−	7.40435i	0.536379	−	0.389702i
$362$	−0.515005	+	4.89995i	−0.0270681	+	0.257536i
$363$	−2.39502	−	1.43027i	−0.125706	−	0.0750696i
$364$	−3.27111	−	31.1225i	−0.171453	−	1.63126i
$365$	5.71318	−	4.81452i	0.299041	−	0.252004i
$366$	36.4870	+	21.7894i	1.90720	+	1.13895i
$367$	17.3734	−	19.2951i	0.906885	−	1.00720i	−0.0930481	−	0.995662i	$-0.529661\pi$
$367$	17.3734	−	19.2951i	0.906885	−	1.00720i	0.999933	−	0.0115366i	$-0.00367231\pi$
$368$	−3.99285			−0.208141
$369$	3.18942	−	5.16614i	0.166034	−	0.268938i
$370$	1.83364	+	2.70613i	0.0953263	+	0.140685i
$371$	−2.17249	+	0.461778i	−0.112790	+	0.0239743i
$372$	5.71527	+	5.30073i	0.296323	+	0.274830i
$373$	3.95418	+	37.6215i	0.204740	+	1.94797i	0.303440	+	0.952850i	$0.401865\pi$
$373$	3.95418	+	37.6215i	0.204740	+	1.94797i	−0.0987007	+	0.995117i	$0.531469\pi$
$374$	26.5060	−	45.9097i	1.37059	−	2.37393i
$375$	−16.8514	+	9.54106i	−0.870200	+	0.492698i
$376$	12.2324	+	21.1871i	0.630836	+	1.09264i
$377$	−8.68394	+	6.30925i	−0.447245	+	0.324943i
$378$	−41.9856	−	26.7838i	−2.15951	−	1.37761i
$379$	−8.50160	+	26.1652i	−0.436698	+	1.34402i	0.454639	+	0.890676i	$0.349768\pi$
$379$	−8.50160	+	26.1652i	−0.436698	+	1.34402i	−0.891337	+	0.453342i	$0.850232\pi$
$380$	−7.62870	+	15.7254i	−0.391344	+	0.806694i
$381$	6.08766	−	8.12425i	0.311881	−	0.416218i
$382$	−14.1015	+	24.4245i	−0.721495	+	1.24967i
$383$	28.8177	+	6.12539i	1.47251	+	0.312993i	0.873137	−	0.487474i	$-0.162082\pi$
$383$	28.8177	+	6.12539i	1.47251	+	0.312993i	0.599377	+	0.800467i	$0.295415\pi$
$384$	−25.3209	+	14.1253i	−1.29215	+	0.720828i
$385$	−5.11549	−	28.6573i	−0.260709	−	1.46051i
$386$	−26.9776	+	19.6003i	−1.37312	+	0.997631i
$387$	2.34168	+	1.12647i	0.119034	+	0.0572616i
$388$	−5.16941	−	3.75580i	−0.262437	−	0.190672i
$389$	27.9229	+	12.4321i	1.41575	+	0.630331i	0.964983	−	0.262312i	$-0.0844850\pi$
$389$	27.9229	+	12.4321i	1.41575	+	0.630331i	0.450764	+	0.892643i	$0.351152\pi$
$390$	−19.4135	+	7.55967i	−0.983043	+	0.382799i
$391$	43.9791	−	19.5808i	2.22412	−	0.990241i
$392$	26.5535	+	5.64413i	1.34116	+	0.285072i
$393$	11.0640	−	0.998144i	0.558103	−	0.0503497i
$394$	−18.7461	+	20.8197i	−0.944417	+	1.04888i
$395$	−3.17318	+	0.917153i	−0.159660	+	0.0461470i
$396$	22.4707	+	17.3611i	1.12920	+	0.872426i
$397$	−2.97055	+	9.14241i	−0.149088	+	0.458844i	−0.997514	−	0.0704690i	$-0.977550\pi$
$397$	−2.97055	+	9.14241i	−0.149088	+	0.458844i	0.848426	+	0.529313i	$0.177550\pi$
$398$	−14.2220	−	6.33205i	−0.712886	−	0.317397i
$399$	7.82371	−	16.8972i	0.391675	−	0.845919i
$400$	−0.124418	−	3.17791i	−0.00622088	−	0.158895i
$401$	4.31447	−	7.47289i	0.215454	−	0.373178i	−0.737959	−	0.674846i	$-0.764210\pi$
$401$	4.31447	−	7.47289i	0.215454	−	0.373178i	0.953413	+	0.301668i	$0.0975434\pi$
$402$	−8.93857	−	3.05077i	−0.445816	−	0.152159i
$403$	−3.39814	+	0.722298i	−0.169274	+	0.0359802i
$404$	14.6482	−	45.0827i	0.728778	−	2.24295i
$405$	−5.97076	+	19.2185i	−0.296689	+	0.954974i
$406$	−13.3321	−	41.0321i	−0.661663	−	2.03639i
$407$	0.992849	+	1.71967i	0.0492137	+	0.0852406i
$408$	19.5678	−	26.1141i	0.968752	−	1.29284i
$409$	21.7649	−	9.69034i	1.07620	−	0.479157i	0.209412	−	0.977827i	$-0.432845\pi$
$409$	21.7649	−	9.69034i	1.07620	−	0.479157i	0.866791	+	0.498671i	$0.166178\pi$
$410$	10.1822	−	0.733623i	0.502863	−	0.0362310i
$411$	−4.67656	−	23.7160i	−0.230678	−	1.16983i
$412$	2.97802	−	28.3340i	0.146717	−	1.39592i
$413$	4.07949	+	2.96392i	0.200739	+	0.145845i
$414$	11.9308	+	40.7734i	0.586364	+	2.00390i
$415$	−9.84650	+	12.6580i	−0.483346	+	0.621355i
$416$	1.58229	−	15.0545i	0.0775782	−	0.738107i
$417$	−8.05443	−	18.8332i	−0.394427	−	0.922265i
$418$	−8.74575	+	15.1481i	−0.427768	+	0.740917i
$419$	−5.80677	−	1.23427i	−0.283679	−	0.0602979i	0.0638744	−	0.997958i	$-0.479654\pi$
$419$	−5.80677	−	1.23427i	−0.283679	−	0.0602979i	−0.347554	+	0.937660i	$0.612988\pi$
$420$	−2.90467	−	50.7453i	−0.141733	−	2.47612i
$421$	15.0822	−	3.20582i	0.735061	−	0.156242i	0.174853	−	0.984594i	$-0.444055\pi$
$421$	15.0822	−	3.20582i	0.735061	−	0.156242i	0.560207	+	0.828353i	$0.310722\pi$
$422$	15.7527	−	48.4818i	0.766829	−	2.36006i
$423$	−20.6367	+	21.6027i	−1.00339	+	1.05036i
$424$	1.28427			0.0623698
$425$	16.9547	+	34.3929i	0.822425	+	1.66830i
$426$	16.4012	−	35.4224i	0.794640	−	1.71622i
$427$	−4.83023	−	45.9565i	−0.233751	−	2.22399i
$428$	18.3751	+	20.4076i	0.888195	+	0.986440i
$429$	−12.0925	+	3.73285i	−0.583831	+	0.180224i
$430$	0.767802	+	4.30128i	0.0370267	+	0.207426i
$431$	−3.02158	−	9.29948i	−0.145545	−	0.447940i	0.851536	−	0.524296i	$-0.175671\pi$
$431$	−3.02158	−	9.29948i	−0.145545	−	0.447940i	−0.997081	+	0.0763560i	$0.975671\pi$
$432$	−2.35596	−	2.31802i	−0.113351	−	0.111526i
$433$	−5.55389	−	17.0931i	−0.266903	−	0.821443i	−0.991249	−	0.132006i	$-0.957858\pi$
$433$	−5.55389	−	17.0931i	−0.266903	−	0.821443i	0.724346	−	0.689437i	$-0.242142\pi$
$434$	1.45959	−	13.8870i	0.0700624	−	0.666599i
$435$	−14.5757	+	9.56574i	−0.698852	+	0.458642i
$436$	−0.477322	−	4.54142i	−0.0228596	−	0.217494i
$437$	−14.5111	+	6.46075i	−0.694159	+	0.309059i
$438$	11.4013	−	6.36021i	0.544773	−	0.303903i
$439$	26.8307	+	11.9458i	1.28056	+	0.570142i	0.930399	−	0.366548i	$-0.119460\pi$
$439$	26.8307	+	11.9458i	1.28056	+	0.570142i	0.350160	+	0.936690i	$0.386127\pi$
$440$	−0.551916	+	16.8235i	−0.0263115	+	0.802029i
$441$	2.49141	+	33.0571i	0.118639	+	1.57415i
$442$	12.7478	+	39.2338i	0.606353	+	1.86616i
$443$	−5.20445	−	9.01437i	−0.247271	−	0.428285i	0.715497	−	0.698616i	$-0.246200\pi$
$443$	−5.20445	−	9.01437i	−0.247271	−	0.428285i	−0.962768	+	0.270331i	$0.912867\pi$
$444$	1.36335	+	3.18785i	0.0647019	+	0.151289i
$445$	−0.878646	+	0.740439i	−0.0416518	+	0.0351002i
$446$	−8.61381	−	9.56660i	−0.407876	−	0.452992i
$447$	4.77589	−	20.9450i	0.225892	−	0.990666i
$448$	50.6453	+	22.5487i	2.39276	+	1.06533i
$449$	11.4000			0.538000			0.269000	−	0.963140i	$-0.413307\pi$
$449$	11.4000			0.538000			0.269000	+	0.963140i	$0.413307\pi$
$450$	−32.0798	+	10.7662i	−1.51226	+	0.507523i
$451$	6.20132			0.292009
$452$	−10.4491	−	4.65225i	−0.491485	−	0.218823i
$453$	16.8135	+	15.5940i	0.789969	+	0.732672i
$454$	19.5517	+	21.7144i	0.917609	+	1.01911i
$455$	19.2362	+	11.9637i	0.901807	+	0.560866i
$456$	−6.45648	+	8.61645i	−0.302352	+	0.403502i
$457$	−9.11863	−	15.7939i	−0.426552	−	0.738809i	0.570012	−	0.821636i	$-0.306938\pi$
$457$	−9.11863	−	15.7939i	−0.426552	−	0.738809i	−0.996564	+	0.0828271i	$0.973605\pi$
$458$	−5.33066	−	16.4061i	−0.249085	−	0.766606i
$459$	37.3171	+	13.9782i	1.74181	+	0.652447i
$460$	−26.6224	+	34.2239i	−1.24128	+	1.59570i
$461$	−34.8569	−	15.5193i	−1.62345	−	0.722806i	−0.625116	−	0.780532i	$-0.714948\pi$
$461$	−34.8569	−	15.5193i	−1.62345	−	0.722806i	−0.998332	+	0.0577259i	$0.981615\pi$
$462$	0.750137	−	50.8617i	0.0348995	−	2.36630i
$463$	−14.5875	+	6.49477i	−0.677939	+	0.301838i	−0.716670	−	0.697412i	$-0.754335\pi$
$463$	−14.5875	+	6.49477i	−0.677939	+	0.301838i	0.0387319	+	0.999250i	$0.487668\pi$
$464$	−0.299294	−	2.84759i	−0.0138944	−	0.132196i
$465$	−5.56886	+	0.909545i	−0.258250	+	0.0421792i
$466$	0.0739936	−	0.704002i	0.00342769	−	0.0326123i
$467$	−2.63535	−	8.11077i	−0.121949	−	0.375321i	0.871384	−	0.490602i	$-0.163223\pi$
$467$	−2.63535	−	8.11077i	−0.121949	−	0.375321i	−0.993333	+	0.115281i	$0.963223\pi$
$468$	−21.7405	+	3.95487i	−1.00496	+	0.182814i
$469$	3.17353	+	9.76712i	0.146540	+	0.451004i
$470$	−49.7596	−	6.88612i	−2.29524	−	0.317633i
$471$	3.69757	−	16.2160i	0.170375	−	0.747194i
$472$	−1.95102	−	2.16683i	−0.0898032	−	0.0997365i
$473$	0.277435	+	2.63962i	0.0127565	+	0.121370i
$474$	−5.74843	+	0.518600i	−0.264034	+	0.0238201i
$475$	−5.59428	−	11.3481i	−0.256683	−	0.520684i
$476$	−100.646			−4.61312
$477$	0.440438	+	1.50520i	0.0201663	+	0.0689184i
$478$	15.7601	−	48.5045i	0.720848	−	2.21854i
$479$	−7.93651	+	1.68696i	−0.362629	+	0.0770791i	−0.385623	−	0.922657i	$-0.626013\pi$
$479$	−7.93651	+	1.68696i	−0.362629	+	0.0770791i	0.0229942	+	0.999736i	$0.492680\pi$
$480$	3.72914	−	24.3021i	0.170211	−	1.10923i
$481$	−1.51146	−	0.321272i	−0.0689169	−	0.0146487i
$482$	18.1939	−	31.5128i	0.828709	−	1.43537i
$483$	27.7000	−	36.9669i	1.26039	−	1.68205i
$484$	0.520034	−	4.94779i	0.0236379	−	0.224900i
$485$	4.44353	−	1.28432i	0.201770	−	0.0583182i
$486$	−16.6310	+	30.9845i	−0.754398	+	1.40548i
$487$	12.1898	+	8.85644i	0.552374	+	0.401323i	0.828660	−	0.559752i	$-0.189104\pi$
$487$	12.1898	+	8.85644i	0.552374	+	0.401323i	−0.276286	+	0.961076i	$0.589104\pi$
$488$	−2.79300	+	26.5736i	−0.126433	+	1.20293i
$489$	−18.6150	−	6.35337i	−0.841799	−	0.287309i
$490$	−42.6243	+	35.9197i	−1.92557	+	1.62269i
$491$	−3.50680	+	1.56133i	−0.158260	+	0.0704618i	−0.484338	−	0.874881i	$-0.660939\pi$
$491$	−3.50680	+	1.56133i	−0.158260	+	0.0704618i	0.326078	+	0.945343i	$0.394273\pi$
$492$	10.7507	+	1.29050i	0.484679	+	0.0581803i
$493$	17.2610	+	29.8970i	0.777398	+	1.34649i
$494$	−4.20620	−	12.9453i	−0.189246	−	0.582438i
$495$	−19.9068	+	5.12272i	−0.894746	+	0.230249i
$496$	0.286367	−	0.881348i	0.0128583	−	0.0395737i
$497$	−41.5169	+	8.82470i	−1.86229	+	0.395842i
$498$	−21.0991	+	18.4416i	−0.945473	+	0.826389i
$499$	−8.93474	+	15.4754i	−0.399974	+	0.692775i	−0.993722	−	0.111876i	$-0.964314\pi$
$499$	−8.93474	+	15.4754i	−0.399974	+	0.692775i	0.593748	+	0.804651i	$0.297648\pi$
$500$	−28.0684	−	20.1224i	−1.25525	−	0.899899i
$501$	−31.9803	+	2.88513i	−1.42878	+	0.128898i
$502$	37.7962	+	16.8280i	1.68693	+	0.751069i
$503$	−12.3252	+	37.9329i	−0.549552	+	1.69135i	0.160363	+	0.987058i	$0.448734\pi$
$503$	−12.3252	+	37.9329i	−0.549552	+	1.69135i	−0.709915	+	0.704288i	$0.751266\pi$
$504$	4.18990	−	31.0302i	0.186633	−	1.38220i
$505$	19.2481	+	28.4069i	0.856531	+	1.26409i
$506$	−29.0352	+	32.2469i	−1.29077	+	1.43355i
$507$	−5.32280	+	11.4959i	−0.236394	+	0.510550i
$508$	17.7098	+	3.76433i	0.785745	+	0.167015i
$509$	2.90742	−	1.29447i	0.128869	−	0.0573762i	−0.341289	−	0.939958i	$-0.610864\pi$
$509$	2.90742	−	1.29447i	0.128869	−	0.0573762i	0.470158	+	0.882582i	$0.344197\pi$
$510$	17.6535	+	64.6364i	0.781709	+	2.86215i
$511$	−12.9683	−	5.77385i	−0.573683	−	0.255420i
$512$	5.79508	+	4.21037i	0.256109	+	0.186074i
$513$	−12.3129	−	4.61217i	−0.543629	−	0.203632i
$514$	41.2309	−	29.9560i	1.81862	−	1.32130i
$515$	14.8655	+	14.2949i	0.655050	+	0.629907i
$516$	−0.0683421	+	4.63382i	−0.00300859	+	0.203993i
$517$	−29.8483	−	6.34444i	−1.31272	−	0.279028i
$518$	3.10543	−	5.37876i	0.136445	−	0.236329i
$519$	15.5004	+	1.86065i	0.680392	+	0.0816735i
$520$	−9.44166	−	9.07924i	−0.414044	−	0.398151i
$521$	5.21002	−	16.0348i	0.228255	−	0.702497i	−0.769690	−	0.638418i	$-0.779589\pi$
$521$	5.21002	−	16.0348i	0.228255	−	0.702497i	0.997945	−	0.0640786i	$-0.0204109\pi$
$522$	−28.1842	+	11.5650i	−1.23359	+	0.506185i
$523$	4.47138	−	3.24865i	0.195520	−	0.142053i	−0.485718	−	0.874115i	$-0.661442\pi$
$523$	4.47138	−	3.24865i	0.195520	−	0.142053i	0.681238	+	0.732062i	$0.261442\pi$
$524$	9.90600	+	17.1577i	0.432746	+	0.749537i
$525$	30.2851	+	20.8946i	1.32175	+	0.911914i
$526$	−2.57437	+	4.45894i	−0.112248	+	0.194419i
$527$	1.16791	+	11.1119i	0.0508750	+	0.484043i
$528$	0.750500	−	3.29138i	0.0326613	−	0.143239i
$529$	−16.0470	+	3.41090i	−0.697697	+	0.148300i
$530$	−1.61912	+	2.08142i	−0.0703300	+	0.0904113i
$531$	1.87048	−	3.02976i	0.0811720	−	0.131480i
$532$	33.2086			1.43978
$533$	−3.22905	+	3.58623i	−0.139866	+	0.155337i
$534$	−1.75343	+	0.978155i	−0.0758784	+	0.0423289i
$535$	−19.8272	+	1.42854i	−0.857205	+	0.0617613i
$536$	−0.620723	−	5.90579i	−0.0268112	−	0.255091i
$537$	0.480050	−	32.5490i	0.0207157	−	1.40459i
$538$	−0.579883	+	5.51722i	−0.0250005	+	0.237864i
$539$	−27.3937	+	19.9027i	−1.17993	+	0.857269i
$540$	−35.5768	+	4.73819i	−1.53098	+	0.203899i
$541$	−3.34560	−	2.43072i	−0.143838	−	0.104505i	0.513539	−	0.858066i	$-0.328334\pi$
$541$	−3.34560	−	2.43072i	−0.143838	−	0.104505i	−0.657377	+	0.753562i	$0.728334\pi$
$542$	21.7152	−	24.1172i	0.932749	−	1.03592i
$543$	−2.17814	−	3.09286i	−0.0934730	−	0.132727i
$544$	−47.6205	−	10.1220i	−2.04171	−	0.433979i
$545$	2.80696	+	1.74575i	0.120237	+	0.0747797i
$546$	29.0228	+	26.9177i	1.24206	+	1.15197i
$547$	41.5266	−	8.82676i	1.77555	−	0.377405i	0.800490	−	0.599346i	$-0.204573\pi$
$547$	41.5266	−	8.82676i	1.77555	−	0.377405i	0.975060	+	0.221941i	$0.0712392\pi$
$548$	34.8771	−	25.3397i	1.48988	−	1.08246i
$549$	−32.1028	+	5.83989i	−1.37011	+	0.249241i
$550$	−26.5701	−	22.1044i	−1.13295	−	0.942533i
$551$	−5.69534	−	9.86462i	−0.242630	−	0.420247i
$552$	−20.1113	+	17.5782i	−0.855993	+	0.748180i
$553$	4.19938	+	4.66389i	0.178576	+	0.198329i
$554$	42.3363	+	47.0192i	1.79870	+	1.99765i
$555$	−2.42738	−	0.637897i	−0.103037	−	0.0270772i
$556$	24.4437	−	27.1475i	1.03664	−	1.15131i
$557$	−15.6043			−0.661177			−0.330588	−	0.943775i	$-0.607247\pi$
$557$	−15.6043			−0.661177			−0.330588	+	0.943775i	$0.607247\pi$
$558$	−9.85566	−	0.290777i	−0.417224	−	0.0123096i
$559$	−1.67096	−	1.21402i	−0.0706740	−	0.0513476i
$560$	−5.32938	+	2.84814i	−0.225207	+	0.120356i
$561$	7.87443	+	39.9332i	0.332459	+	1.68598i
$562$	−24.6586	+	10.9787i	−1.04016	+	0.463110i
$563$	−38.2572	+	17.0332i	−1.61235	+	0.717865i	−0.997492	−	0.0707733i	$-0.977453\pi$
$563$	−38.2572	+	17.0332i	−1.61235	+	0.717865i	−0.614858	+	0.788638i	$0.710787\pi$
$564$	−50.4251	−	17.2103i	−2.12328	−	0.724683i
$565$	7.30235	−	3.90253i	0.307212	−	0.164181i
$566$	56.7614	+	41.2396i	2.38586	+	1.73343i
$567$	37.8051	−	5.73107i	1.58767	−	0.240682i
$568$	24.5428			1.02979
$569$	16.0904	−	17.8702i	0.674546	−	0.749159i	−0.304564	−	0.952492i	$-0.598511\pi$
$569$	16.0904	−	17.8702i	0.674546	−	0.749159i	0.979110	+	0.203333i	$0.0651774\pi$
$570$	−5.82483	−	21.3270i	−0.243975	−	0.893291i
$571$	11.0384	+	12.2594i	0.461944	+	0.513041i	0.928440	−	0.371482i	$-0.121150\pi$
$571$	11.0384	+	12.2594i	0.461944	+	0.513041i	−0.466496	+	0.884523i	$0.654484\pi$
$572$	−15.1025	−	16.7730i	−0.631467	−	0.701315i
$573$	−4.18929	−	21.2449i	−0.175010	−	0.887520i
$574$	−9.69823	−	16.7978i	−0.404796	−	0.701128i
$575$	−7.72176	−	30.4222i	−0.322020	−	1.26869i
$576$	13.1895	−	36.8572i	0.549562	−	1.53572i
$577$	−6.91645	+	5.02510i	−0.287936	+	0.209198i	−0.722371	−	0.691505i	$-0.756948\pi$
$577$	−6.91645	+	5.02510i	−0.287936	+	0.209198i	0.434436	+	0.900703i	$0.356948\pi$
$578$	92.2645	−	19.6114i	3.83770	−	0.815728i
$579$	5.69188	−	24.9622i	0.236546	−	1.03739i
$580$	−26.4031	−	16.4210i	−1.09633	−	0.681846i
$581$	29.8042	+	6.33508i	1.23649	+	0.262823i
$582$	8.04975	−	0.726215i	0.333673	−	0.0301026i
$583$	−1.07187	+	1.19043i	−0.0443924	+	0.0493027i
$584$	6.64069	+	4.82474i	0.274794	+	0.199649i
$585$	7.40311	−	14.1796i	0.306081	−	0.586253i
$586$	−35.5995	+	25.8646i	−1.47060	+	1.06846i
$587$	1.54336	−	14.6841i	0.0637014	−	0.606078i	−0.915377	−	0.402597i	$-0.868108\pi$
$587$	1.54336	−	14.6841i	0.0637014	−	0.606078i	0.979079	−	0.203482i	$-0.0652257\pi$
$588$	−51.6318	+	28.8029i	−2.12926	+	1.18781i
$589$	−0.385356	−	3.66642i	−0.0158783	−	0.151072i
$590$	5.97150	−	0.430244i	0.245843	−	0.0177129i
$591$	0.317210	−	21.5079i	0.0130483	−	0.884717i
$592$	0.275809	−	0.306317i	0.0113357	−	0.0125895i
$593$	39.0327			1.60288			0.801441	−	0.598074i	$-0.204067\pi$
$593$	39.0327			1.60288			0.801441	+	0.598074i	$0.204067\pi$
$594$	−35.8528	+	2.17093i	−1.47106	+	0.0890743i
$595$	44.7332	−	57.5058i	1.83388	−	2.35751i
$596$	37.4757	−	7.96570i	1.53506	−	0.326288i
$597$	11.4212	−	3.52563i	0.467438	−	0.144294i
$598$	−3.52963	−	33.5822i	−0.144337	−	1.37328i
$599$	2.16975	−	3.75811i	0.0886534	−	0.153552i	−0.818289	−	0.574807i	$-0.805077\pi$
$599$	2.16975	−	3.75811i	0.0886534	−	0.153552i	0.906942	+	0.421255i	$0.138410\pi$
$600$	−14.6172	−	15.4588i	−0.596745	−	0.631105i
$601$	7.63713	+	13.2279i	0.311525	+	0.539577i	0.978693	−	0.205331i	$-0.0658270\pi$
$601$	7.63713	+	13.2279i	0.311525	+	0.539577i	−0.667168	+	0.744907i	$0.732494\pi$
$602$	6.71620	−	4.87960i	0.273732	−	0.198878i
$603$	6.70886	−	2.75288i	0.273206	−	0.112106i
$604$	−12.6380	+	38.8958i	−0.514233	+	1.58265i
$605$	2.59586	+	2.49622i	0.105537	+	0.101486i
$606$	23.5775	+	55.1299i	0.957771	+	2.23950i
$607$	−16.3162	+	28.2605i	−0.662255	+	1.14706i	0.317766	+	0.948169i	$0.397067\pi$
$607$	−16.3162	+	28.2605i	−0.662255	+	1.14706i	−0.980022	+	0.198891i	$0.936266\pi$
$608$	15.7126	+	3.33981i	0.637229	+	0.135447i
$609$	28.4401	+	16.9840i	1.15245	+	0.688225i
$610$	−39.5467	−	38.0287i	−1.60120	−	1.53974i
$611$	19.2111	−	13.9577i	0.777199	−	0.564668i
$612$	5.34107	+	70.8675i	0.215900	+	2.86465i
$613$	−13.4253	−	9.75406i	−0.542243	−	0.393963i	0.282674	−	0.959216i	$-0.408778\pi$
$613$	−13.4253	−	9.75406i	−0.542243	−	0.393963i	−0.824917	+	0.565253i	$0.808778\pi$
$614$	−55.7140	−	24.8055i	−2.24843	−	1.00107i
$615$	−5.51560	+	5.56900i	−0.222410	+	0.224564i
$616$	29.2171	−	13.0083i	1.17719	−	0.524119i
$617$	−36.6450	−	7.78913i	−1.47527	−	0.313578i	−0.601091	−	0.799181i	$-0.705267\pi$
$617$	−36.6450	−	7.78913i	−1.47527	−	0.313578i	−0.874180	+	0.485602i	$0.838600\pi$
$618$	20.7499	+	29.4640i	0.834685	+	1.18522i
$619$	−10.6559	+	11.8346i	−0.428296	+	0.475671i	−0.918207	−	0.396102i	$-0.870363\pi$
$619$	−10.6559	+	11.8346i	−0.428296	+	0.475671i	0.489910	+	0.871773i	$0.337029\pi$
$620$	−5.64494	−	8.33095i	−0.226706	−	0.334579i
$621$	−27.4993	−	17.5425i	−1.10351	−	0.703957i
$622$	14.6178	−	44.9889i	0.586119	−	1.80389i
$623$	1.99443	+	0.887976i	0.0799050	+	0.0355760i
$624$	1.51262	+	2.14785i	0.0605532	+	0.0859828i
$625$	23.9725	−	7.09371i	0.958899	−	0.283749i
$626$	−31.0423	+	53.7669i	−1.24070	+	2.14896i
$627$	−2.59820	−	13.1761i	−0.103762	−	0.526204i
$628$	29.0143	−	6.16718i	1.15780	−	0.246097i
$629$	−1.53573	+	4.72648i	−0.0612334	+	0.188457i
$630$	45.0084	+	45.9113i	1.79318	+	1.82915i
$631$	−3.82191	−	11.7626i	−0.152148	−	0.468263i	0.845713	−	0.533638i	$-0.179176\pi$
$631$	−3.82191	−	11.7626i	−0.152148	−	0.468263i	−0.997861	+	0.0653753i	$0.979176\pi$
$632$	−1.81446	−	3.14274i	−0.0721754	−	0.125012i
$633$	15.3905	+	35.9867i	0.611717	+	1.43034i
$634$	12.9067	−	5.74642i	0.512589	−	0.228219i
$635$	−10.0221	+	8.44567i	−0.397715	+	0.335156i
$636$	−2.10594	+	1.84070i	−0.0835060	+	0.0729883i
$637$	2.75428	−	26.2052i	0.109128	−	1.03829i
$638$	−25.1740	−	18.2900i	−0.996649	−	0.724108i
$639$	8.41690	+	28.7648i	0.332967	+	1.13792i
$640$	35.9596	−	10.3935i	1.42143	−	0.410839i
$641$	−2.44347	+	23.2481i	−0.0965114	+	0.918244i	0.833946	+	0.551845i	$0.186076\pi$
$641$	−2.44347	+	23.2481i	−0.0965114	+	0.918244i	−0.930458	+	0.366399i	$0.880591\pi$
$642$	−34.4883	−	4.13993i	−1.36114	−	0.163390i
$643$	−1.29303	+	2.23959i	−0.0509921	+	0.0883208i	−0.890395	−	0.455189i	$-0.849572\pi$
$643$	−1.29303	+	2.23959i	−0.0509921	+	0.0883208i	0.839403	+	0.543510i	$0.182905\pi$
$644$	80.5829	+	17.1284i	3.17541	+	0.674955i
$645$	−2.61723	−	2.09859i	−0.103053	−	0.0826321i
$646$	−42.8203	+	9.10173i	−1.68474	+	0.358103i
$647$	−5.47796	+	16.8594i	−0.215361	+	0.662812i	0.783767	+	0.621055i	$0.213296\pi$
$647$	−5.47796	+	16.8594i	−0.215361	+	0.662812i	−0.999128	+	0.0417574i	$0.986704\pi$
$648$	−22.0715	−	1.30351i	−0.867050	−	0.0512066i
$649$	3.63686			0.142759
$650$	26.6181	−	3.85566i	1.04405	−	0.151232i
$651$	6.17312	+	8.76555i	0.241944	+	0.343549i
$652$	−3.66676	−	34.8869i	−0.143601	−	1.36628i
$653$	−2.36951	−	2.63160i	−0.0927259	−	0.102983i	0.694996	−	0.719014i	$-0.255406\pi$
$653$	−2.36951	−	2.63160i	−0.0927259	−	0.102983i	−0.787722	+	0.616031i	$0.788740\pi$
$654$	4.23502	+	3.92785i	0.165603	+	0.153591i
$655$	−14.2061	−	1.96595i	−0.555079	−	0.0768161i
$656$	−0.397787	−	1.22426i	−0.0155310	−	0.0477994i
$657$	−3.37731	+	9.43768i	−0.131761	+	0.368199i
$658$	29.4941	+	90.7736i	1.14980	+	3.53872i
$659$	−1.37129	+	13.0470i	−0.0534179	+	0.508237i	0.934799	+	0.355177i	$0.115579\pi$
$659$	−1.37129	+	13.0470i	−0.0534179	+	0.508237i	−0.988217	+	0.153060i	$0.951087\pi$
$660$	−23.2074	−	28.3781i	−0.903347	−	1.10462i
$661$	−4.11615	−	39.1625i	−0.160100	−	1.52325i	−0.719585	−	0.694405i	$-0.755668\pi$
$661$	−4.11615	−	39.1625i	−0.160100	−	1.52325i	0.559485	−	0.828840i	$-0.310999\pi$
$662$	4.93365	−	2.19660i	0.191752	−	0.0853734i
$663$	−27.1937	−	16.2396i	−1.05611	−	0.630695i
$664$	−16.0956	−	7.16622i	−0.624630	−	0.278103i
$665$	−14.7599	+	18.9743i	−0.572364	+	0.735790i
$666$	−3.95212	−	1.90117i	−0.153141	−	0.0736689i
$667$	−8.73212	−	26.8747i	−0.338109	−	1.04059i
$668$	−28.6333	−	49.5943i	−1.10785	−	1.91886i
$669$	9.81346	+	1.17800i	0.379410	+	0.0455440i
$670$	10.3541	+	6.43959i	0.400013	+	0.248783i
$671$	−22.3009	−	24.7676i	−0.860915	−	0.956143i
$672$	−44.6364	+	13.7789i	−1.72189	+	0.531533i
$673$	−39.4094	−	17.5462i	−1.51912	−	0.676356i	−0.533573	−	0.845754i	$-0.679151\pi$
$673$	−39.4094	−	17.5462i	−1.51912	−	0.676356i	−0.985548	+	0.169398i	$0.945818\pi$
$674$	15.8668			0.611166
$675$	13.1052	−	22.4333i	0.504420	−	0.863458i
$676$	−22.5932			−0.868971
$677$	27.8062	+	12.3801i	1.06868	+	0.475807i	0.864244	−	0.503072i	$-0.167797\pi$
$677$	27.8062	+	12.3801i	1.06868	+	0.475807i	0.204437	+	0.978880i	$0.434464\pi$
$678$	13.8243	−	4.26745i	0.530920	−	0.163891i
$679$	−5.88055	−	6.53102i	−0.225675	−	0.250637i
$680$	−32.2144	+	27.1473i	−1.23537	+	1.04105i
$681$	−22.2747	−	2.67383i	−0.853569	−	0.102461i
$682$	−5.03551	−	8.72175i	−0.192820	−	0.333973i
$683$	15.4441	+	47.5321i	0.590952	+	1.81876i	0.573924	+	0.818909i	$0.305420\pi$
$683$	15.4441	+	47.5321i	0.590952	+	1.81876i	0.0170281	+	0.999855i	$0.494580\pi$
$684$	−1.76231	−	23.3830i	−0.0673835	−	0.894072i
$685$	−1.02323	+	31.1901i	−0.0390956	+	1.19171i
$686$	35.4628	+	15.7890i	1.35397	+	0.602828i
$687$	11.3714	+	6.79079i	0.433844	+	0.259085i
$688$	0.503317	−	0.224091i	0.0191888	−	0.00854340i
$689$	−0.130301	−	1.23973i	−0.00496406	−	0.0472299i
$690$	−3.13423	−	54.7558i	−0.119318	−	2.08452i
$691$	1.95655	−	18.6153i	0.0744305	−	0.708159i	−0.892140	−	0.451759i	$-0.850797\pi$
$691$	1.95655	−	18.6153i	0.0744305	−	0.708159i	0.966571	−	0.256400i	$-0.0825365\pi$
$692$	8.60379	+	26.4797i	0.327067	+	1.00661i
$693$	25.2660	+	29.7820i	0.959775	+	1.13132i
$694$	−8.10753	−	24.9524i	−0.307758	−	0.947181i
$695$	4.64690	+	26.0322i	0.176267	+	0.987459i
$696$	−14.0438	−	13.0252i	−0.532329	−	0.493719i
$697$	10.3852	+	11.5339i	0.393366	+	0.436877i
$698$	−4.47302	−	42.5579i	−0.169306	−	1.61084i
$699$	0.312945	+	0.444368i	0.0118367	+	0.0168076i
$700$	−11.1216	+	64.6697i	−0.420355	+	2.44429i
$701$	37.2362			1.40639			0.703195	−	0.710997i	$-0.251756\pi$
$701$	37.2362			1.40639			0.703195	+	0.710997i	$0.251756\pi$
$702$	17.4133	−	21.8641i	0.657221	−	0.825208i
$703$	0.506719	−	1.55952i	0.0191113	−	0.0588184i
$704$	39.1103	−	8.31315i	1.47402	−	0.313314i
$705$	32.2453	−	21.1619i	1.21443	−	0.797003i
$706$	40.5523	+	8.61967i	1.52621	+	0.324405i
$707$	32.5985	−	56.4622i	1.22599	−	2.12348i
$708$	6.30491	+	0.756834i	0.236953	+	0.0284436i
$709$	5.22998	−	49.7599i	0.196416	−	1.86877i	−0.242373	−	0.970183i	$-0.577926\pi$
$709$	5.22998	−	49.7599i	0.196416	−	1.86877i	0.438789	−	0.898590i	$-0.355407\pi$
$710$	−30.9418	+	39.7766i	−1.16123	+	1.49279i
$711$	3.06111	−	3.20439i	0.114800	−	0.120174i
$712$	−1.02129	−	0.742010i	−0.0382744	−	0.0278080i
$713$	0.955983	−	9.09557i	0.0358019	−	0.340632i
$714$	95.8544	−	83.7814i	3.58726	−	3.13544i
$715$	16.2960	−	1.17412i	0.609435	−	0.0439095i
$716$	53.0362	−	23.6132i	1.98206	−	0.882468i
$717$	15.3977	+	36.0035i	0.575037	+	1.34458i
$718$	13.4413	+	23.2809i	0.501623	+	0.868837i
$719$	12.5051	+	38.4868i	0.466362	+	1.43532i	0.857261	+	0.514882i	$0.172164\pi$
$719$	12.5051	+	38.4868i	0.466362	+	1.43532i	−0.390899	+	0.920434i	$0.627836\pi$
$720$	2.28826	+	3.60140i	0.0852785	+	0.134216i
$721$	12.1088	−	37.2669i	0.450954	−	1.38789i
$722$	−27.7964	+	5.90831i	−1.03448	+	0.219885i
$723$	5.40507	+	27.4105i	0.201017	+	1.01941i
$724$	3.37325	−	5.84265i	0.125366	−	0.217140i
$725$	21.1175	−	7.78732i	0.784285	−	0.289214i
$726$	3.62344	+	5.14512i	0.134478	+	0.190953i
$727$	19.5293	+	8.69500i	0.724301	+	0.322480i	0.735562	−	0.677457i	$-0.236918\pi$
$727$	19.5293	+	8.69500i	0.724301	+	0.322480i	−0.0112613	+	0.999937i	$0.503585\pi$
$728$	−7.69076	+	23.6697i	−0.285039	+	0.877259i
$729$	−6.04162	−	26.3154i	−0.223764	−	0.974643i
$730$	−16.1916	+	4.67989i	−0.599277	+	0.173211i
$731$	−4.44484	+	4.93650i	−0.164398	+	0.182583i
$732$	−33.5069	−	47.5784i	−1.23845	−	1.75855i
$733$	15.0890	+	3.20726i	0.557324	+	0.118463i	0.477958	−	0.878383i	$-0.341377\pi$
$733$	15.0890	+	3.20726i	0.557324	+	0.118463i	0.0793660	+	0.996846i	$0.474710\pi$
$734$	−53.5083	+	23.8234i	−1.97503	+	0.879339i
$735$	6.49127	−	42.3024i	0.239434	−	1.56035i
$736$	36.4050	+	16.2085i	1.34190	+	0.597454i
$737$	5.99233	+	4.35368i	0.220730	+	0.160370i
$738$	−11.3131	+	7.72019i	−0.416441	+	0.284184i
$739$	−25.1767	+	18.2919i	−0.926139	+	0.672879i	−0.945044	−	0.326942i	$-0.893982\pi$
$739$	−25.1767	+	18.2919i	−0.926139	+	0.672879i	0.0189056	+	0.999821i	$0.493982\pi$
$740$	−0.786570	−	4.40642i	−0.0289149	−	0.161983i
$741$	8.97266	+	5.35832i	0.329619	+	0.196843i
$742$	4.90089	+	1.04172i	0.179917	+	0.0382426i
$743$	−14.4868	+	25.0919i	−0.531470	+	0.920533i	0.467856	+	0.883805i	$0.345027\pi$
$743$	−14.4868	+	25.0919i	−0.531470	+	0.920533i	−0.999325	+	0.0367277i	$0.988307\pi$
$744$	−2.43769	−	5.69992i	−0.0893702	−	0.208969i
$745$	−12.1051	+	24.9527i	−0.443496	+	0.914198i
$746$	26.3706	−	81.1605i	0.965497	−	2.97150i
$747$	2.87904	−	21.3221i	0.105339	−	0.780134i
$748$	−58.7264	+	42.6672i	−2.14725	+	1.56007i
$749$	18.8848	+	32.7095i	0.690036	+	1.19518i
$750$	43.4825	−	4.20074i	1.58776	−	0.153389i
$751$	−10.6074	+	18.3726i	−0.387070	+	0.670425i	−0.992054	−	0.125813i	$-0.959846\pi$
$751$	−10.6074	+	18.3726i	−0.387070	+	0.670425i	0.604984	+	0.796238i	$0.293179\pi$
$752$	0.662115	+	6.29960i	0.0241448	+	0.229723i
$753$	−30.3528	+	9.36965i	−1.10612	+	0.341449i
$754$	23.6853	−	5.03448i	0.862569	−	0.183345i
$755$	−16.6066	−	24.5085i	−0.604377	−	0.891957i
$756$	37.6038	+	56.8884i	1.36764	+	2.06901i
$757$	35.8369			1.30251			0.651257	−	0.758857i	$-0.274242\pi$
$757$	35.8369			1.30251			0.651257	+	0.758857i	$0.274242\pi$
$758$	41.5284	−	46.1220i	1.50838	−	1.67523i
$759$	0.491316	−	33.3128i	0.0178336	−	1.20918i
$760$	10.6293	−	8.95735i	0.385564	−	0.324917i
$761$	4.23275	+	40.2719i	0.153437	+	1.45986i	0.752203	+	0.658931i	$0.228991\pi$
$761$	4.23275	+	40.2719i	0.153437	+	1.45986i	−0.598766	+	0.800924i	$0.704342\pi$
$762$	−20.0002	+	11.1571i	−0.724530	+	0.404180i
$763$	0.656501	−	6.24619i	0.0237669	−	0.226127i
$764$	31.2431	−	22.6995i	1.13034	−	0.821237i
$765$	−42.8651	−	28.4460i	−1.54979	−	1.02847i
$766$	−53.7686	−	39.0652i	−1.94274	−	1.41148i
$767$	−1.89373	+	2.10320i	−0.0683785	+	0.0759421i
$768$	20.1240	−	1.81550i	0.726162	−	0.0655113i
$769$	−20.3031	−	4.31556i	−0.732150	−	0.155623i	−0.173273	−	0.984874i	$-0.555434\pi$
$769$	−20.3031	−	4.31556i	−0.732150	−	0.155623i	−0.558877	+	0.829251i	$0.688768\pi$
$770$	−15.7522	+	63.7521i	−0.567671	+	2.29747i
$771$	−8.69913	+	38.1508i	−0.313292	+	1.37397i
$772$	44.6634	−	9.49349i	1.60747	−	0.341678i
$773$	−9.77770	+	7.10392i	−0.351679	+	0.255510i	−0.749573	−	0.661921i	$-0.769741\pi$
$773$	−9.77770	+	7.10392i	−0.351679	+	0.255510i	0.397894	+	0.917431i	$0.369741\pi$
$774$	−3.79226	−	4.47009i	−0.136310	−	0.160674i
$775$	7.26896	+	0.477449i	0.261109	+	0.0171505i
$776$	2.54086	+	4.40090i	0.0912115	+	0.157983i
$777$	0.922565	+	4.67856i	0.0330968	+	0.167843i
$778$	−46.1379	−	51.2413i	−1.65412	−	1.83709i
$779$	−3.42662	−	3.80565i	−0.122771	−	0.136351i
$780$	28.4953	+	1.35574i	1.02029	+	0.0485434i
$781$	−20.4838	+	22.7495i	−0.732966	+	0.814042i
$782$	−108.601			−3.88355
$783$	10.4496	−	20.9267i	0.373437	−	0.747858i
$784$	5.68636	+	4.13138i	0.203084	+	0.147549i
$785$	−9.37196	+	19.3188i	−0.334500	+	0.689519i
$786$	−23.7170	−	8.09470i	−0.845958	−	0.288729i
$787$	19.6223	−	8.73643i	0.699461	−	0.311420i	−0.0260210	−	0.999661i	$-0.508284\pi$
$787$	19.6223	−	8.73643i	0.699461	−	0.311420i	0.725482	+	0.688241i	$0.241617\pi$
$788$	35.0456	−	15.6033i	1.24845	−	0.555844i
$789$	−0.764797	−	3.87848i	−0.0272275	−	0.138078i
$790$	7.38099	+	1.02144i	0.262604	+	0.0363411i
$791$	−12.7271	−	9.24681i	−0.452525	−	0.328779i
$792$	−10.7099	−	19.8821i	−0.380561	−	0.706481i
$793$	25.9353			0.920989
$794$	14.5105	−	16.1155i	0.514957	−	0.571918i
$795$	−0.115704	−	2.02138i	−0.00410360	−	0.0716909i
$796$	14.2641	+	15.8419i	0.505577	+	0.561501i
$797$	11.4866	+	12.7572i	0.406876	+	0.451882i	0.911403	−	0.411514i	$-0.135000\pi$
$797$	11.4866	+	12.7572i	0.406876	+	0.451882i	−0.504527	+	0.863396i	$0.668333\pi$
$798$	−31.6275	+	27.6440i	−1.11960	+	0.978587i
$799$	−38.1859	−	66.1399i	−1.35092	−	2.33986i
$800$	−11.7660	+	29.4798i	−0.415991	+	1.04227i
$801$	0.519406	−	1.45145i	0.0183523	−	0.0512844i
$802$	−15.7482	+	11.4418i	−0.556089	+	0.404022i
$803$	−10.0146	+	2.12867i	−0.353408	+	0.0751192i
$804$	9.48238	+	8.79462i	0.334418	+	0.310162i
$805$	−45.6024	+	38.4294i	−1.60727	+	1.35446i
$806$	7.66581	+	1.62942i	0.270017	+	0.0573938i
$807$	−2.45253	−	3.48248i	−0.0863332	−	0.122589i
$808$	−25.2256	+	28.0158i	−0.887433	+	0.985594i
$809$	17.1785	+	12.4809i	0.603965	+	0.438806i	0.847284	−	0.531140i	$-0.178236\pi$
$809$	17.1785	+	12.4809i	0.603965	+	0.438806i	−0.243319	+	0.969946i	$0.578236\pi$
$810$	29.9387	−	34.1280i	1.05194	−	1.19913i
$811$	−18.5739	+	13.4947i	−0.652216	+	0.473863i	−0.864025	−	0.503448i	$-0.832064\pi$
$811$	−18.5739	+	13.4947i	−0.652216	+	0.473863i	0.211809	+	0.977311i	$0.432064\pi$
$812$	−6.17524	+	58.7535i	−0.216708	+	2.06184i
$813$	−0.367451	+	24.9144i	−0.0128871	+	0.873787i
$814$	−0.468235	−	4.45496i	−0.0164116	−	0.156146i
$815$	21.5629	+	13.4107i	0.755315	+	0.469758i
$816$	7.37850	−	4.11611i	0.258299	−	0.144093i
$817$	1.46659	−	1.62882i	0.0513096	−	0.0569850i
$818$	−53.7455			−1.87917
$819$	−30.3791	−	0.896288i	−1.06153	−	0.0313189i
$820$	−13.1458	−	4.75325i	−0.459070	−	0.165991i
$821$	−1.39822	+	0.297201i	−0.0487982	+	0.0103724i	−0.232246	−	0.972657i	$-0.574607\pi$
$821$	−1.39822	+	0.297201i	−0.0487982	+	0.0103724i	0.183448	+	0.983029i	$0.441274\pi$
$822$	−12.1230	+	53.1662i	−0.422836	+	1.85438i
$823$	1.60428	+	15.2637i	0.0559218	+	0.532061i	0.986241	+	0.165311i	$0.0528628\pi$
$823$	1.60428	+	15.2637i	0.0559218	+	0.532061i	−0.930320	+	0.366750i	$0.880471\pi$
$824$	−11.3290	+	19.6224i	−0.394663	+	0.683577i
$825$	26.5290	−	0.646994i	0.923622	−	0.0225254i
$826$	−5.68768	−	9.85134i	−0.197900	−	0.342772i
$827$	22.1538	−	16.0957i	0.770362	−	0.559701i	−0.131709	−	0.991288i	$-0.542046\pi$
$827$	22.1538	−	16.0957i	0.770362	−	0.559701i	0.902071	+	0.431587i	$0.142046\pi$
$828$	7.78419	−	57.6494i	0.270519	−	2.00345i
$829$	10.7441	−	33.0668i	0.373157	−	1.14846i	−0.571557	−	0.820562i	$-0.693660\pi$
$829$	10.7441	−	33.0668i	0.373157	−	1.14846i	0.944714	−	0.327896i	$-0.106340\pi$
$830$	31.9065	−	17.0515i	1.10749	−	0.591867i
$831$	−48.2324	−	5.78977i	−1.67317	−	0.200845i
$832$	−15.5574	+	26.9462i	−0.539356	+	0.934191i
$833$	−82.8925	−	17.6193i	−2.87205	−	0.610474i
$834$	−0.681423	+	46.2027i	−0.0235957	+	1.59987i
$835$	41.0628	+	5.68258i	1.42104	+	0.196654i
$836$	19.3770	−	14.0782i	0.670167	−	0.486905i
$837$	5.84444	−	4.81181i	0.202014	−	0.166320i
$838$	10.8344	+	7.87165i	0.374268	+	0.271921i
$839$	−2.78353	−	1.23931i	−0.0960982	−	0.0427857i	0.358125	−	0.933674i	$-0.383416\pi$
$839$	−2.78353	−	1.23931i	−0.0960982	−	0.0427857i	−0.454223	+	0.890888i	$0.650083\pi$
$840$	−14.3045	+	37.8078i	−0.493551	+	1.30449i
$841$	−7.98104	+	3.55339i	−0.275208	+	0.122531i
$842$	−34.0236	−	7.23194i	−1.17253	−	0.249229i
$843$	8.70768	−	18.8064i	0.299908	−	0.647726i
$844$	−46.7073	+	51.8737i	−1.60773	+	1.78557i
$845$	10.0418	−	12.9090i	0.345448	−	0.444083i
$846$	62.3507	−	25.5847i	2.14366	−	0.879620i
$847$	2.11448	−	6.50770i	0.0726543	−	0.223607i
$848$	0.303771	+	0.135248i	0.0104315	+	0.00464442i
$849$	−53.6512	+	4.84019i	−1.84130	+	0.166115i
$850$	−3.38401	−	86.4354i	−0.116071	−	2.96471i
$851$	2.03396	−	3.52292i	0.0697232	−	0.120764i
$852$	−40.2451	+	35.1762i	−1.37878	+	1.20512i
$853$	−48.7695	+	10.3663i	−1.66984	+	0.354935i	−0.943235	−	0.332125i	$-0.892235\pi$
$853$	−48.7695	+	10.3663i	−1.66984	+	0.354935i	−0.726601	+	0.687059i	$0.758901\pi$
$854$	−32.2130	+	99.1416i	−1.10231	+	3.39255i
$855$	14.1435	+	9.38588i	0.483698	+	0.320990i
$856$	−6.74883	−	20.7708i	−0.230670	−	0.709930i
$857$	1.98749	+	3.44243i	0.0678913	+	0.117591i	0.897973	−	0.440051i	$-0.145040\pi$
$857$	1.98749	+	3.44243i	0.0678913	+	0.117591i	−0.830082	+	0.557642i	$0.811706\pi$
$858$	28.3459	+	3.40261i	0.967713	+	0.116163i
$859$	−3.78685	+	1.68602i	−0.129206	+	0.0575261i	−0.470321	−	0.882495i	$-0.655862\pi$
$859$	−3.78685	+	1.68602i	−0.129206	+	0.0575261i	0.341115	+	0.940021i	$0.389195\pi$
$860$	1.43513	−	5.80822i	0.0489374	−	0.198058i
$861$	14.0942	+	4.81040i	0.480328	+	0.163938i
$862$	−2.30570	+	21.9373i	−0.0785325	+	0.747187i
$863$	−38.2211	−	27.7693i	−1.30106	−	0.945277i	−0.301097	−	0.953593i	$-0.597353\pi$
$863$	−38.2211	−	27.7693i	−1.30106	−	0.945277i	−0.999965	+	0.00831611i	$0.997353\pi$
$864$	12.0708	+	30.6984i	0.410658	+	1.04438i
$865$	−18.9536	−	6.85326i	−0.644443	−	0.233018i
$866$	−4.23805	+	40.3223i	−0.144015	+	1.37021i
$867$	−43.4284	+	57.9571i	−1.47491	+	1.96832i
$868$	−9.56021	+	16.5588i	−0.324495	+	0.562041i
$869$	4.42748	+	0.941090i	0.150192	+	0.0319243i
$870$	38.8154	−	6.33961i	1.31597	−	0.214933i
$871$	−5.63797	+	1.19839i	−0.191035	+	0.0406058i
$872$	−1.12224	+	3.45390i	−0.0380039	+	0.116964i
$873$	−4.28658	+	4.48723i	−0.145079	+	0.151870i
$874$	35.8332			1.21208
$875$	−32.0070	−	35.0975i	−1.08203	−	1.18651i
$876$	−17.8045	+	1.60624i	−0.601557	+	0.0542700i
$877$	−3.27962	−	31.2035i	−0.110745	−	1.05367i	−0.898889	−	0.438177i	$-0.855624\pi$
$877$	−3.27962	−	31.2035i	−0.110745	−	1.05367i	0.788144	−	0.615491i	$-0.211042\pi$
$878$	−44.3332	−	49.2370i	−1.49617	−	1.66167i
$879$	7.51099	−	32.9401i	0.253339	−	1.11104i
$880$	−1.90224	+	3.92116i	−0.0641244	+	0.132182i
$881$	1.32647	+	4.08247i	0.0446901	+	0.137542i	0.970912	−	0.239437i	$-0.0769629\pi$
$881$	1.32647	+	4.08247i	0.0446901	+	0.137542i	−0.926222	+	0.376979i	$0.876963\pi$
$882$	25.1971	−	70.4117i	0.848430	−	2.37088i
$883$	−4.46274	−	13.7349i	−0.150183	−	0.462216i	0.847458	−	0.530863i	$-0.178132\pi$
$883$	−4.46274	−	13.7349i	−0.150183	−	0.462216i	−0.997641	+	0.0686462i	$0.978132\pi$
$884$	5.90460	−	56.1785i	0.198593	−	1.88949i
$885$	−3.23471	+	3.26603i	−0.108733	+	0.109786i
$886$	2.45446	+	23.3526i	0.0824591	+	0.784546i
$887$	−8.04828	+	3.58333i	−0.270235	+	0.120316i	−0.537381	−	0.843340i	$-0.680586\pi$
$887$	−8.04828	+	3.58333i	−0.270235	+	0.120316i	0.267146	+	0.963656i	$0.413919\pi$
$888$	0.0406632	−	2.75710i	0.00136457	−	0.0925222i
$889$	22.7490	+	10.1285i	0.762978	+	0.339700i
$890$	2.49015	−	0.719734i	0.0834699	−	0.0241255i
$891$	19.6294	−	19.3708i	0.657610	−	0.648948i
$892$	5.44714	+	16.7646i	0.182384	+	0.561320i
$893$	12.5996	+	21.8231i	0.421629	+	0.730282i
$894$	−29.0605	+	38.7825i	−0.971929	+	1.29708i
$895$	−10.0807	+	40.7982i	−0.336959	+	1.36373i
$896$	−47.5888	−	52.8527i	−1.58983	−	1.76569i
$897$	19.0090	+	17.6303i	0.634692	+	0.588658i
$898$	−23.4937	−	10.4601i	−0.783996	−	0.349057i
$899$	6.55837			0.218734
$900$	46.1257	+	4.39908i	1.53752	+	0.146636i
$901$	−4.00913			−0.133563
$902$	−12.7800	−	5.69002i	−0.425527	−	0.189457i
$903$	−1.41702	+	6.21446i	−0.0471555	+	0.206804i
$904$	6.08678	+	6.76005i	0.202443	+	0.224836i
$905$	1.83901	+	4.52418i	0.0611308	+	0.150389i
$906$	−20.3419	−	47.5642i	−0.675814	−	1.58022i
$907$	10.0081	+	17.3345i	0.332312	+	0.575582i	0.982965	−	0.183794i	$-0.0588378\pi$
$907$	10.0081	+	17.3345i	0.332312	+	0.575582i	−0.650652	+	0.759376i	$0.725505\pi$
$908$	−12.3640	−	38.0525i	−0.410314	−	1.26282i
$909$	−41.4863	−	19.9570i	−1.37601	−	0.661933i
$910$	−28.6656	−	42.3055i	−0.950257	−	1.40242i
$911$	−40.5899	−	18.0718i	−1.34480	−	0.598745i	−0.397064	−	0.917791i	$-0.629971\pi$
$911$	−40.5899	−	18.0718i	−1.34480	−	0.598745i	−0.947739	+	0.319046i	$0.896638\pi$
$912$	−2.43456	+	1.35813i	−0.0806165	+	0.0449720i
$913$	20.0762	−	8.93849i	0.664425	−	0.295821i
$914$	4.30042	+	40.9157i	0.142245	+	1.35337i
$915$	42.0771	+	2.00194i	1.39103	+	0.0661820i
$916$	−2.46908	+	23.4917i	−0.0815807	+	0.776188i
$917$	8.42043	+	25.9154i	0.278067	+	0.855802i
$918$	−64.0793	−	63.0473i	−2.11493	−	2.08087i
$919$	−11.0598	−	34.0387i	−0.364830	−	1.12283i	−0.950087	−	0.311984i	$-0.899006\pi$
$919$	−11.0598	−	34.0387i	−0.364830	−	1.12283i	0.585257	−	0.810848i	$-0.300994\pi$
$920$	30.4127	−	16.2532i	1.00268	−	0.535852i
$921$	44.7418	−	13.8114i	1.47429	−	0.455102i
$922$	57.5952	+	63.9659i	1.89680	+	2.10661i
$923$	−2.49008	−	23.6915i	−0.0819620	−	0.779817i
$924$	−29.2658	+	63.2066i	−0.962773	+	2.07934i
$925$	2.86727	+	1.50905i	0.0942753	+	0.0496174i
$926$	36.0219			1.18375
$927$	−26.8831	−	6.54840i	−0.882958	−	0.215078i
$928$	−8.83066	+	27.1780i	−0.289881	+	0.892161i
$929$	−26.3655	+	5.60416i	−0.865024	+	0.183867i	−0.618994	−	0.785396i	$-0.712460\pi$
$929$	−26.3655	+	5.60416i	−0.865024	+	0.183867i	−0.246030	+	0.969262i	$0.579126\pi$
$930$	12.3111	+	3.23527i	0.403698	+	0.106089i
$931$	27.3507	+	5.81357i	0.896382	+	0.190532i
$932$	−0.484654	+	0.839445i	−0.0158754	+	0.0274969i
$933$	14.2817	+	33.3940i	0.467561	+	1.09327i
$934$	−2.01097	+	19.1331i	−0.0658011	+	0.626055i
$935$	1.72292	−	52.5181i	0.0563455	−	1.71752i
$936$	17.0746	+	4.15915i	0.558100	+	0.135946i
$937$	29.3765	+	21.3433i	0.959689	+	0.697255i	0.953079	−	0.302723i	$-0.0978957\pi$
$937$	29.3765	+	21.3433i	0.959689	+	0.697255i	0.00661075	+	0.999978i	$0.497896\pi$
$938$	2.42165	−	23.0404i	0.0790696	−	0.752297i
$939$	−9.22209	−	46.7676i	−0.300952	−	1.52620i
$940$	58.4104	+	36.3276i	1.90514	+	1.18488i
$941$	−3.93925	+	1.75387i	−0.128416	+	0.0571744i	−0.469939	−	0.882699i	$-0.655724\pi$
$941$	−3.93925	+	1.75387i	−0.128416	+	0.0571744i	0.341523	+	0.939873i	$0.389057\pi$
$942$	−22.4991	+	30.0260i	−0.733061	+	0.978301i
$943$	−6.35204	−	11.0020i	−0.206851	−	0.358276i
$944$	−0.233288	−	0.717987i	−0.00759289	−	0.0233685i
$945$	−49.2174	−	3.79908i	−1.60104	−	0.123584i
$946$	1.85023	−	5.69443i	0.0601562	−	0.185142i
$947$	−21.0325	+	4.47059i	−0.683464	+	0.145275i	−0.536542	−	0.843874i	$-0.680270\pi$
$947$	−21.0325	+	4.47059i	−0.683464	+	0.145275i	−0.146921	+	0.989148i	$0.546936\pi$
$948$	7.47971	+	2.55285i	0.242930	+	0.0829128i
$949$	3.98364	−	6.89987i	0.129314	−	0.223979i
$950$	1.11657	+	28.5197i	0.0362262	+	0.925300i
$951$	−4.55772	+	9.84351i	−0.147794	+	0.319198i
$952$	73.1232	+	32.5565i	2.36993	+	1.05516i
$953$	−0.379043	+	1.16658i	−0.0122784	+	0.0377891i	−0.957008	−	0.290061i	$-0.906324\pi$
$953$	−0.379043	+	1.16658i	−0.0122784	+	0.0377891i	0.944730	+	0.327851i	$0.106324\pi$
$954$	0.473418	−	3.50612i	0.0153275	−	0.113515i
$955$	−0.916614	+	27.9402i	−0.0296609	+	0.904124i
$956$	−46.7292	+	51.8980i	−1.51133	+	1.67850i
$957$	23.7946	−	2.14665i	0.769171	−	0.0693914i
$958$	17.9038	+	3.80558i	0.578447	+	0.122953i
$959$	54.1673	−	24.1168i	1.74915	−	0.778773i
$960$	−27.3201	+	42.5163i	−0.881752	+	1.37221i
$961$	−26.3808	−	11.7455i	−0.850993	−	0.378887i
$962$	2.82012	+	2.04894i	0.0909243	+	0.0660604i
$963$	22.0294	−	15.0331i	0.709886	−	0.484434i
$964$	−40.3102	+	29.2871i	−1.29831	+	0.943274i
$965$	−14.4268	+	29.7386i	−0.464415	+	0.957318i
$966$	−91.0046	+	50.7670i	−2.92802	+	1.63340i
$967$	−7.19410	−	1.52915i	−0.231347	−	0.0491743i	0.0907794	−	0.995871i	$-0.471064\pi$
$967$	−7.19410	−	1.52915i	−0.231347	−	0.0491743i	−0.322126	+	0.946697i	$0.604398\pi$
$968$	−1.97831	+	3.42653i	−0.0635853	+	0.110133i
$969$	20.1553	−	26.8980i	0.647480	−	0.864090i
$970$	−10.3359	−	1.43036i	−0.331865	−	0.0459260i
$971$	1.42441	−	4.38389i	0.0457116	−	0.140686i	−0.925596	−	0.378513i	$-0.876435\pi$
$971$	1.42441	−	4.38389i	0.0457116	−	0.140686i	0.971307	+	0.237828i	$0.0764354\pi$
$972$	38.0610	−	29.4967i	1.22081	−	0.946107i
$973$	40.6478	−	29.5324i	1.30311	−	0.946765i
$974$	−16.9952	−	29.4366i	−0.544562	−	0.943209i
$975$	−13.4396	+	15.6786i	−0.430412	+	0.502118i
$976$	−3.45912	+	5.99136i	−0.110724	+	0.191779i
$977$	−1.04406	−	9.93352i	−0.0334023	−	0.317802i	−0.998447	−	0.0557152i	$-0.982256\pi$
$977$	−1.04406	−	9.93352i	−0.0334023	−	0.317802i	0.965044	−	0.262086i	$-0.0844105\pi$
$978$	32.5332	+	30.1735i	1.04030	+	0.964843i
$979$	1.54018	−	0.327374i	0.0492242	−	0.0104629i
$980$	73.3253	−	21.1934i	2.34229	−	0.676998i
$981$	−4.43293	−	0.130787i	−0.141533	−	0.00417571i
$982$	8.65959			0.276339
$983$	1.46212	−	1.62385i	0.0466343	−	0.0517927i	−0.719376	−	0.694621i	$-0.755572\pi$
$983$	1.46212	−	1.62385i	0.0466343	−	0.0517927i	0.766011	+	0.642828i	$0.222239\pi$
$984$	−7.39332	−	4.41517i	−0.235691	−	0.140751i
$985$	−6.66115	+	26.9589i	−0.212242	+	0.858981i
$986$	−8.14043	−	77.4510i	−0.259244	−	2.46654i
$987$	−62.9168	−	37.5729i	−2.00267	−	1.19596i
$988$	−1.94825	+	18.5363i	−0.0619819	+	0.589719i
$989$	4.39890	−	3.19599i	0.139877	−	0.101626i
$990$	45.7254	+	7.70836i	1.45325	+	0.244988i
$991$	−5.74036	−	4.17062i	−0.182349	−	0.132484i	0.492866	−	0.870105i	$-0.335949\pi$
$991$	−5.74036	−	4.17062i	−0.182349	−	0.132484i	−0.675215	+	0.737621i	$0.735949\pi$
$992$	−6.18871	+	6.87326i	−0.196492	+	0.218226i
$993$	−1.74221	+	3.76274i	−0.0552875	+	0.119407i
$994$	93.6573	+	19.9075i	2.97063	+	0.631427i
$995$	−15.3913	+	1.10894i	−0.487937	+	0.0351557i
$996$	36.6645	−	11.3180i	1.16176	−	0.358625i
$997$	1.44820	−	0.307825i	0.0458651	−	0.00974892i	−0.184922	−	0.982753i	$-0.559203\pi$
$997$	1.44820	−	0.307825i	0.0458651	−	0.00974892i	0.230787	+	0.973004i	$0.425870\pi$
$998$	32.6126	−	23.6945i	1.03234	−	0.750036i
$999$	3.24533	−	0.897882i	0.102678	−	0.0284077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.211.4	yes	224
3.2	odd	2		675.2.r.a.361.25		224
9.2	odd	6		675.2.r.a.586.4		224
9.7	even	3	inner	225.2.q.a.61.25	yes	224
25.16	even	5	inner	225.2.q.a.166.25	yes	224
75.41	odd	10		675.2.r.a.91.4		224
225.16	even	15	inner	225.2.q.a.16.4	✓	224
225.191	odd	30		675.2.r.a.316.25		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.4	✓	224	225.16	even	15	inner
225.2.q.a.61.25	yes	224	9.7	even	3	inner
225.2.q.a.166.25	yes	224	25.16	even	5	inner
225.2.q.a.211.4	yes	224	1.1	even	1	trivial
675.2.r.a.91.4		224	75.41	odd	10
675.2.r.a.316.25		224	225.191	odd	30
675.2.r.a.361.25		224	3.2	odd	2
675.2.r.a.586.4		224	9.2	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06085 - 0.917550i) q^{2} +(1.65499 - 0.510883i) q^{3} +(2.06695 + 2.29558i) q^{4} +(-2.23029 + 0.160691i) q^{5} +(-3.87945 - 0.465685i) q^{6} +(2.12428 + 3.67936i) q^{7} +(-0.759150 - 2.33642i) q^{8} +(2.47800 - 1.69101i) q^{9} +O(q^{10})\)	\(q+(-2.06085 - 0.917550i) q^{2} +(1.65499 - 0.510883i) q^{3} +(2.06695 + 2.29558i) q^{4} +(-2.23029 + 0.160691i) q^{5} +(-3.87945 - 0.465685i) q^{6} +(2.12428 + 3.67936i) q^{7} +(-0.759150 - 2.33642i) q^{8} +(2.47800 - 1.69101i) q^{9} +(4.74373 + 1.71524i) q^{10} +(2.79930 + 1.24633i) q^{11} +(4.59355 + 2.74319i) q^{12} +(-2.17836 + 0.969869i) q^{13} +(-1.00183 - 9.53175i) q^{14} +(-3.60901 + 1.40536i) q^{15} +(0.0664873 - 0.632584i) q^{16} +(2.36985 + 7.29363i) q^{17} +(-6.65837 + 1.21124i) q^{18} +(-0.781940 - 2.40656i) q^{19} +(-4.97876 - 4.78765i) q^{20} +(5.39539 + 5.00406i) q^{21} +(-4.62537 - 5.13700i) q^{22} +(-0.656165 - 6.24299i) q^{23} +(-2.45003 - 3.47893i) q^{24} +(4.94836 - 0.716775i) q^{25} +5.37918 q^{26} +(3.23716 - 4.06458i) q^{27} +(-4.05548 + 12.4815i) q^{28} +(4.40315 - 0.935918i) q^{29} +(8.72712 + 0.415217i) q^{30} +(1.42509 + 0.302912i) q^{31} +(-3.17411 + 5.49772i) q^{32} +(5.26955 + 0.632551i) q^{33} +(1.80838 - 17.2055i) q^{34} +(-5.32900 - 7.86468i) q^{35} +(9.00374 + 2.19320i) q^{36} +(0.524265 + 0.380901i) q^{37} +(-0.596680 + 5.67703i) q^{38} +(-3.10968 + 2.71801i) q^{39} +(2.06856 + 5.08890i) q^{40} +(1.84882 - 0.823147i) q^{41} +(-6.52762 - 15.2632i) q^{42} +(0.433089 + 0.750133i) q^{43} +(2.92496 + 9.00211i) q^{44} +(-5.25491 + 4.16964i) q^{45} +(-4.37600 + 13.4679i) q^{46} +(-9.74091 + 2.07049i) q^{47} +(-0.213140 - 1.08089i) q^{48} +(-5.52514 + 9.56982i) q^{49} +(-10.8555 - 3.06320i) q^{50} +(7.64827 + 10.8602i) q^{51} +(-6.72897 - 2.99593i) q^{52} +(-0.161545 + 0.497185i) q^{53} +(-10.4008 + 5.40624i) q^{54} +(-6.44352 - 2.32985i) q^{55} +(6.98390 - 7.75641i) q^{56} +(-2.52357 - 3.58336i) q^{57} +(-9.93298 - 2.11132i) q^{58} +(1.08427 - 0.482747i) q^{59} +(-10.6857 - 5.37997i) q^{60} +(-9.93622 - 4.42389i) q^{61} +(-2.65896 - 1.93184i) q^{62} +(11.4858 + 5.52526i) q^{63} +(10.5566 - 7.66983i) q^{64} +(4.70252 - 2.51313i) q^{65} +(-10.2794 - 6.13867i) q^{66} +(2.36441 + 0.502571i) q^{67} +(-11.8448 + 20.5157i) q^{68} +(-4.27538 - 9.99688i) q^{69} +(3.76603 + 21.0975i) q^{70} +(-3.08718 + 9.50135i) q^{71} +(-5.83210 - 4.50592i) q^{72} +(-2.70313 + 1.96394i) q^{73} +(-0.730937 - 1.26602i) q^{74} +(7.82330 - 3.71429i) q^{75} +(3.90822 - 6.76924i) q^{76} +(1.36081 + 12.9472i) q^{77} +(8.90251 - 2.74813i) q^{78} +(1.44490 - 0.307122i) q^{79} +(-0.0466350 + 1.42153i) q^{80} +(3.28095 - 8.38066i) q^{81} -4.56542 q^{82} +(4.79891 - 5.32973i) q^{83} +(-0.335214 + 22.7286i) q^{84} +(-6.45746 - 15.8861i) q^{85} +(-0.204248 - 1.94329i) q^{86} +(6.80903 - 3.79843i) q^{87} +(0.786864 - 7.48651i) q^{88} +(0.415723 - 0.302040i) q^{89} +(14.6554 - 3.77135i) q^{90} +(-8.19595 - 5.95471i) q^{91} +(12.9750 - 14.4102i) q^{92} +(2.51326 - 0.226736i) q^{93} +(21.9743 + 4.67079i) q^{94} +(2.13066 + 5.24167i) q^{95} +(-2.44444 + 10.7203i) q^{96} +(-2.02334 + 0.430075i) q^{97} +(20.1673 - 14.6524i) q^{98} +(9.04423 - 1.64526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more