LMFDB - Embedded newform 260.2.bg.c.23.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	260.23
Dual form			260.2.bg.c.147.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31533 - 0.519519i) q^{2} +(3.04677 + 0.816378i) q^{3} +(1.46020 + 1.36668i) q^{4} +(-0.215330 + 2.22568i) q^{5} +(-3.58339 - 2.65666i) q^{6} +(-0.0424015 - 0.158244i) q^{7} +(-1.21063 - 2.55624i) q^{8} +(6.01823 + 3.47463i) q^{9} +(1.43951 - 2.81564i) q^{10} +(-1.67952 - 2.90902i) q^{11} +(3.33316 + 5.35603i) q^{12} +(-0.302905 + 3.59281i) q^{13} +(-0.0264389 + 0.230172i) q^{14} +(-2.47305 + 6.60532i) q^{15} +(0.264369 + 3.99125i) q^{16} +(-1.11891 - 4.17582i) q^{17} +(-6.11084 - 7.69687i) q^{18} +(-1.77930 - 1.02728i) q^{19} +(-3.35621 + 2.95565i) q^{20} -0.516749i q^{21} +(0.697841 + 4.69887i) q^{22} +(-1.12010 - 0.300129i) q^{23} +(-1.60165 - 8.77660i) q^{24} +(-4.90727 - 0.958509i) q^{25} +(2.26495 - 4.56837i) q^{26} +(8.80836 + 8.80836i) q^{27} +(0.154355 - 0.289018i) q^{28} +(0.663797 - 0.383243i) q^{29} +(6.68448 - 7.40340i) q^{30} +9.22182 q^{31} +(1.72580 - 5.38717i) q^{32} +(-2.74225 - 10.2342i) q^{33} +(-0.697682 + 6.07389i) q^{34} +(0.361331 - 0.0602971i) q^{35} +(4.03912 + 13.2986i) q^{36} +(0.405598 - 1.51371i) q^{37} +(1.80668 + 2.27559i) q^{38} +(-3.85597 + 10.6991i) q^{39} +(5.95005 - 2.14404i) q^{40} +(7.36261 - 4.25081i) q^{41} +(-0.268461 + 0.679697i) q^{42} +(-0.817373 - 3.05048i) q^{43} +(1.52326 - 6.54312i) q^{44} +(-9.02930 + 12.6464i) q^{45} +(1.31738 + 0.976680i) q^{46} +(-4.21757 + 4.21757i) q^{47} +(-2.45290 + 12.3762i) q^{48} +(6.03893 - 3.48658i) q^{49} +(5.95672 + 3.81018i) q^{50} -13.6362i q^{51} +(-5.35252 + 4.83224i) q^{52} +(-8.62782 - 8.62782i) q^{53} +(-7.00982 - 16.1620i) q^{54} +(6.83618 - 3.11167i) q^{55} +(-0.353178 + 0.299964i) q^{56} +(-4.58246 - 4.58246i) q^{57} +(-1.07222 + 0.159237i) q^{58} +(-1.72021 - 0.993165i) q^{59} +(-12.6385 + 6.26522i) q^{60} +(0.793873 - 1.37503i) q^{61} +(-12.1298 - 4.79091i) q^{62} +(0.294658 - 1.09968i) q^{63} +(-5.06874 + 6.18934i) q^{64} +(-7.93119 - 1.44781i) q^{65} +(-1.70990 + 14.8861i) q^{66} +(-5.45208 - 1.46088i) q^{67} +(4.07319 - 7.62673i) q^{68} +(-3.16765 - 1.82884i) q^{69} +(-0.506596 - 0.108408i) q^{70} +(-4.47121 + 7.74436i) q^{71} +(1.59612 - 19.5905i) q^{72} +(-9.06992 + 9.06992i) q^{73} +(-1.31990 + 1.78032i) q^{74} +(-14.1688 - 6.92654i) q^{75} +(-1.19417 - 3.93177i) q^{76} +(-0.389122 + 0.389122i) q^{77} +(10.6303 - 12.0697i) q^{78} +6.33294 q^{79} +(-8.94016 - 0.271036i) q^{80} +(9.22218 + 15.9733i) q^{81} +(-11.8927 + 1.76621i) q^{82} +(-6.74106 - 6.74106i) q^{83} +(0.706231 - 0.754557i) q^{84} +(9.53496 - 1.59115i) q^{85} +(-0.509663 + 4.43703i) q^{86} +(2.33531 - 0.625743i) q^{87} +(-5.40287 + 7.81502i) q^{88} +(3.93581 + 6.81702i) q^{89} +(18.4466 - 11.9434i) q^{90} +(0.581385 - 0.104407i) q^{91} +(-1.22538 - 1.96906i) q^{92} +(28.0967 + 7.52850i) q^{93} +(7.73862 - 3.35640i) q^{94} +(2.66953 - 3.73894i) q^{95} +(9.65607 - 15.0045i) q^{96} +(14.4151 - 3.86251i) q^{97} +(-9.75455 + 1.44867i) q^{98} -23.3429i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.31533	−	0.519519i	−0.930081	−	0.367355i
$2$	−1.31533	−	0.519519i	−0.930081	−	0.367355i
$3$	3.04677	+	0.816378i	1.75905	+	0.471336i	0.986520	−	0.163641i	$-0.0523239\pi$
$3$	3.04677	+	0.816378i	1.75905	+	0.471336i	0.772531	+	0.634977i	$0.218991\pi$
$4$	1.46020	+	1.36668i	0.730100	+	0.683340i
$5$	−0.215330	+	2.22568i	−0.0962985	+	0.995353i
$5$	−0.215330	+	2.22568i	−0.0962985	+	0.995353i
$6$	−3.58339	−	2.65666i	−1.46291	−	1.08458i
$7$	−0.0424015	−	0.158244i	−0.0160262	−	0.0598108i	0.957450	−	0.288600i	$-0.0931899\pi$
$7$	−0.0424015	−	0.158244i	−0.0160262	−	0.0598108i	−0.973476	+	0.228790i	$0.926523\pi$
$8$	−1.21063	−	2.55624i	−0.428023	−	0.903768i
$9$	6.01823	+	3.47463i	2.00608	+	1.15821i
$10$	1.43951	−	2.81564i	0.455213	−	0.890382i
$11$	−1.67952	−	2.90902i	−0.506395	−	0.877102i	−0.999973	−	0.00740021i	$-0.997644\pi$
$11$	−1.67952	−	2.90902i	−0.506395	−	0.877102i	0.493578	−	0.869702i	$-0.335689\pi$
$12$	3.33316	+	5.35603i	0.962200	+	1.54615i
$13$	−0.302905	+	3.59281i	−0.0840109	+	0.996465i
$13$	−0.302905	+	3.59281i	−0.0840109	+	0.996465i
$14$	−0.0264389	+	0.230172i	−0.00706610	+	0.0615162i
$15$	−2.47305	+	6.60532i	−0.638540	+	1.70549i
$16$	0.264369	+	3.99125i	0.0660923	+	0.997814i
$17$	−1.11891	−	4.17582i	−0.271375	−	1.01279i	−0.958232	−	0.285993i	$-0.907677\pi$
$17$	−1.11891	−	4.17582i	−0.271375	−	1.01279i	0.686857	−	0.726793i	$-0.258990\pi$
$18$	−6.11084	−	7.69687i	−1.44034	−	1.81417i
$19$	−1.77930	−	1.02728i	−0.408199	−	0.235674i	0.281816	−	0.959468i	$-0.409063\pi$
$19$	−1.77930	−	1.02728i	−0.408199	−	0.235674i	−0.690016	+	0.723794i	$0.742396\pi$
$20$	−3.35621	+	2.95565i	−0.750472	+	0.660902i
$21$		−	0.516749i		−	0.112764i
$22$	0.697841	+	4.69887i	0.148780	+	1.00180i
$23$	−1.12010	−	0.300129i	−0.233556	−	0.0625812i	0.140143	−	0.990131i	$-0.455244\pi$
$23$	−1.12010	−	0.300129i	−0.233556	−	0.0625812i	−0.373699	+	0.927550i	$0.621911\pi$
$24$	−1.60165	−	8.77660i	−0.326936	−	1.79152i
$25$	−4.90727	−	0.958509i	−0.981453	−	0.191702i
$26$	2.26495	−	4.56837i	0.444194	−	0.895931i
$27$	8.80836	+	8.80836i	1.69517	+	1.69517i
$28$	0.154355	−	0.289018i	0.0291703	−	0.0546192i
$29$	0.663797	−	0.383243i	0.123264	−	0.0711665i	−0.437100	−	0.899413i	$-0.643994\pi$
$29$	0.663797	−	0.383243i	0.123264	−	0.0711665i	0.560364	+	0.828246i	$0.310661\pi$
$30$	6.68448	−	7.40340i	1.22041	−	1.35167i
$31$	9.22182			1.65629			0.828144	−	0.560515i	$-0.189397\pi$
$31$	9.22182			1.65629			0.828144	+	0.560515i	$0.189397\pi$
$32$	1.72580	−	5.38717i	0.305081	−	0.952326i
$33$	−2.74225	−	10.2342i	−0.477365	−	1.78155i
$34$	−0.697682	+	6.07389i	−0.119652	+	1.04166i
$35$	0.361331	−	0.0602971i	0.0610761	−	0.0101921i
$36$	4.03912	+	13.2986i	0.673186	+	2.21644i
$37$	0.405598	−	1.51371i	0.0666799	−	0.248853i	−0.924538	−	0.381089i	$-0.875549\pi$
$37$	0.405598	−	1.51371i	0.0666799	−	0.248853i	0.991218	+	0.132236i	$0.0422158\pi$
$38$	1.80668	+	2.27559i	0.293082	+	0.369150i
$39$	−3.85597	+	10.6991i	−0.617449	+	1.71323i
$40$	5.95005	−	2.14404i	0.940785	−	0.339003i
$41$	7.36261	−	4.25081i	1.14985	−	0.663864i	0.200997	−	0.979592i	$-0.435582\pi$
$41$	7.36261	−	4.25081i	1.14985	−	0.663864i	0.948850	+	0.315727i	$0.102249\pi$
$42$	−0.268461	+	0.679697i	−0.0414244	+	0.104880i
$43$	−0.817373	−	3.05048i	−0.124648	−	0.465193i	0.875179	−	0.483800i	$-0.160744\pi$
$43$	−0.817373	−	3.05048i	−0.124648	−	0.465193i	−0.999827	+	0.0186065i	$0.994077\pi$
$44$	1.52326	−	6.54312i	0.229640	−	0.986412i
$45$	−9.02930	+	12.6464i	−1.34601	+	1.88522i
$46$	1.31738	+	0.976680i	0.194237	+	0.144004i
$47$	−4.21757	+	4.21757i	−0.615196	+	0.615196i	−0.944295	−	0.329099i	$-0.893255\pi$
$47$	−4.21757	+	4.21757i	−0.615196	+	0.615196i	0.329099	+	0.944295i	$0.393255\pi$
$48$	−2.45290	+	12.3762i	−0.354046	+	1.78636i
$49$	6.03893	−	3.48658i	0.862705	−	0.498083i
$50$	5.95672	+	3.81018i	0.842408	+	0.538840i
$51$		−	13.6362i		−	1.90945i
$52$	−5.35252	+	4.83224i	−0.742261	+	0.670111i
$53$	−8.62782	−	8.62782i	−1.18512	−	1.18512i	−0.978400	−	0.206723i	$-0.933720\pi$
$53$	−8.62782	−	8.62782i	−1.18512	−	1.18512i	−0.206723	−	0.978400i	$-0.566280\pi$
$54$	−7.00982	−	16.1620i	−0.953915	−	2.19937i
$55$	6.83618	−	3.11167i	0.921791	−	0.419578i
$56$	−0.353178	+	0.299964i	−0.0471954	+	0.0400844i
$57$	−4.58246	−	4.58246i	−0.606962	−	0.606962i
$58$	−1.07222	+	0.159237i	−0.140789	+	0.0209089i
$59$	−1.72021	−	0.993165i	−0.223953	−	0.129299i	0.383827	−	0.923405i	$-0.374606\pi$
$59$	−1.72021	−	0.993165i	−0.223953	−	0.129299i	−0.607779	+	0.794106i	$0.707939\pi$
$60$	−12.6385	+	6.26522i	−1.63163	+	0.808836i
$61$	0.793873	−	1.37503i	0.101645	−	0.176054i	−0.810718	−	0.585438i	$-0.800923\pi$
$61$	0.793873	−	1.37503i	0.101645	−	0.176054i	0.912363	+	0.409383i	$0.134256\pi$
$62$	−12.1298	−	4.79091i	−1.54048	−	0.608446i
$63$	0.294658	−	1.09968i	0.0371235	−	0.138547i
$64$	−5.06874	+	6.18934i	−0.633592	+	0.773667i
$65$	−7.93119	−	1.44781i	−0.983744	−	0.179578i
$66$	−1.70990	+	14.8861i	−0.210474	+	1.83235i
$67$	−5.45208	−	1.46088i	−0.666077	−	0.178475i	−0.0900900	−	0.995934i	$-0.528715\pi$
$67$	−5.45208	−	1.46088i	−0.666077	−	0.178475i	−0.575987	+	0.817459i	$0.695382\pi$
$68$	4.07319	−	7.62673i	0.493946	−	0.924877i
$69$	−3.16765	−	1.82884i	−0.381340	−	0.220167i
$70$	−0.506596	−	0.108408i	−0.0605498	−	0.0129572i
$71$	−4.47121	+	7.74436i	−0.530635	+	0.919086i	0.468726	+	0.883343i	$0.344713\pi$
$71$	−4.47121	+	7.74436i	−0.530635	+	0.919086i	−0.999361	+	0.0357428i	$0.988620\pi$
$72$	1.59612	−	19.5905i	0.188104	−	2.30877i
$73$	−9.06992	+	9.06992i	−1.06155	+	1.06155i	−0.0635775	+	0.997977i	$0.520251\pi$
$73$	−9.06992	+	9.06992i	−1.06155	+	1.06155i	−0.997977	+	0.0635775i	$0.979749\pi$
$74$	−1.31990	+	1.78032i	−0.153435	+	0.206958i
$75$	−14.1688	−	6.92654i	−1.63607	−	0.799808i
$76$	−1.19417	−	3.93177i	−0.136981	−	0.451005i
$77$	−0.389122	+	0.389122i	−0.0443445	+	0.0443445i
$78$	10.6303	−	12.0697i	1.20364	−	1.36662i
$79$	6.33294			0.712512			0.356256	−	0.934388i	$-0.384053\pi$
$79$	6.33294			0.712512			0.356256	+	0.934388i	$0.384053\pi$
$80$	−8.94016	−	0.271036i	−0.999541	−	0.0303028i
$81$	9.22218	+	15.9733i	1.02469	+	1.77481i
$82$	−11.8927	+	1.76621i	−1.31332	+	0.195045i
$83$	−6.74106	−	6.74106i	−0.739928	−	0.739928i	0.232636	−	0.972564i	$-0.425265\pi$
$83$	−6.74106	−	6.74106i	−0.739928	−	0.739928i	−0.972564	+	0.232636i	$0.925265\pi$
$84$	0.706231	−	0.754557i	0.0770561	−	0.0823289i
$85$	9.53496	−	1.59115i	1.03421	−	0.172584i
$86$	−0.509663	+	4.43703i	−0.0549584	+	0.478457i
$87$	2.33531	−	0.625743i	0.250371	−	0.0670867i
$88$	−5.40287	+	7.81502i	−0.575948	+	0.833084i
$89$	3.93581	+	6.81702i	0.417195	+	0.722603i	0.995656	−	0.0931070i	$-0.0296799\pi$
$89$	3.93581	+	6.81702i	0.417195	+	0.722603i	−0.578461	+	0.815710i	$0.696347\pi$
$90$	18.4466	−	11.9434i	1.94444	−	1.25894i
$91$	0.581385	−	0.104407i	0.0609457	−	0.0109448i
$92$	−1.22538	−	1.96906i	−0.127755	−	0.205289i
$93$	28.0967	+	7.52850i	2.91350	+	0.780669i
$94$	7.73862	−	3.35640i	0.798178	−	0.346186i
$95$	2.66953	−	3.73894i	0.273888	−	0.383607i
$96$	9.65607	−	15.0045i	0.985519	−	1.53139i
$97$	14.4151	−	3.86251i	1.46363	−	0.392179i	0.562889	−	0.826533i	$-0.309690\pi$
$97$	14.4151	−	3.86251i	1.46363	−	0.392179i	0.900742	+	0.434354i	$0.143023\pi$
$98$	−9.75455	+	1.44867i	−0.985359	+	0.146338i
$99$		−	23.3429i		−	2.34604i
$100$	−5.85561	−	8.10628i	−0.585561	−	0.810628i
$101$	−3.12177	−	5.40707i	−0.310628	−	0.538024i	0.667870	−	0.744278i	$-0.267206\pi$
$101$	−3.12177	−	5.40707i	−0.310628	−	0.538024i	−0.978499	+	0.206254i	$0.933873\pi$
$102$	−7.08427	+	17.9361i	−0.701447	+	1.77594i
$103$	−9.83374	+	9.83374i	−0.968947	+	0.968947i	−0.999532	−	0.0305847i	$-0.990263\pi$
$103$	−9.83374	+	9.83374i	−0.968947	+	0.968947i	0.0305847	+	0.999532i	$0.490263\pi$
$104$	9.55078	−	3.57527i	0.936531	−	0.350584i
$105$	1.15012	+	0.111272i	0.112240	+	0.0108590i
$106$	6.86614	+	15.8308i	0.666898	+	1.53762i
$107$	−4.00736	+	14.9557i	−0.387406	+	1.44582i	0.446933	+	0.894568i	$0.352516\pi$
$107$	−4.00736	+	14.9557i	−0.387406	+	1.44582i	−0.834339	+	0.551252i	$0.814150\pi$
$108$	0.823756	+	24.9002i	0.0792659	+	2.39602i
$109$	−10.1909			−0.976116			−0.488058	−	0.872811i	$-0.662294\pi$
$109$	−10.1909			−0.976116			−0.488058	+	0.872811i	$0.662294\pi$
$110$	−10.6084	+	0.541360i	−1.01147	+	0.0516166i
$111$	2.47152	−	4.28080i	0.234587	−	0.406316i
$112$	0.620384	−	0.211070i	0.0586208	−	0.0199442i
$113$	−6.35536	+	1.70291i	−0.597862	+	0.160197i	−0.545044	−	0.838408i	$-0.683487\pi$
$113$	−6.35536	+	1.70291i	−0.597862	+	0.160197i	−0.0528180	+	0.998604i	$0.516820\pi$
$114$	3.64679	+	8.40814i	0.341553	+	0.787494i
$115$	0.909180	−	2.42834i	0.0847815	−	0.226444i
$116$	1.49305	+	0.347586i	0.138626	+	0.0322726i
$117$	−14.3066	+	20.5698i	−1.32265	+	1.90168i
$118$	1.74668	+	2.20003i	0.160795	+	0.202529i
$119$	−0.613357	+	0.354122i	−0.0562264	+	0.0324623i
$120$	19.8788	−	1.67490i	1.81467	−	0.152897i
$121$	−0.141592	+	0.245244i	−0.0128720	+	0.0222949i
$122$	−1.75856	+	1.39619i	−0.159213	+	0.126405i
$123$	25.9024	−	6.94053i	2.33554	−	0.625807i
$124$	13.4657	+	12.6033i	1.20926	+	1.13181i
$125$	3.19001	−	10.7156i	0.285323	−	0.958431i
$126$	−0.958879	+	1.29336i	−0.0854237	+	0.115222i
$127$	3.88958	−	14.5161i	0.345144	−	1.28810i	−0.547299	−	0.836937i	$-0.684344\pi$
$127$	3.88958	−	14.5161i	0.345144	−	1.28810i	0.892444	−	0.451159i	$-0.148989\pi$
$128$	9.88255	−	5.50773i	0.873503	−	0.486820i
$129$		−	9.96137i		−	0.877050i
$130$	9.68000	+	6.02475i	0.848992	+	0.528406i
$131$			2.19741i			0.191988i	0.995382	+	0.0959942i	$0.0306030\pi$
$131$			2.19741i			0.191988i	−0.995382	+	0.0959942i	$0.969397\pi$
$132$	9.98267	−	18.6918i	0.868880	−	1.62691i
$133$	−0.0871163	+	0.325122i	−0.00755394	+	0.0281917i
$134$	6.41234	+	4.75400i	0.553942	+	0.410683i
$135$	−21.5013	+	17.7079i	−1.85053	+	1.52405i
$136$	−9.31982	+	7.91559i	−0.799168	+	0.678756i
$137$	5.05134	−	1.35350i	0.431565	−	0.115637i	−0.0364958	−	0.999334i	$-0.511620\pi$
$137$	5.05134	−	1.35350i	0.431565	−	0.115637i	0.468061	+	0.883696i	$0.344953\pi$
$138$	3.21640	+	4.05119i	0.273798	+	0.344861i
$139$	−2.09826	+	3.63429i	−0.177972	+	0.308257i	−0.941186	−	0.337890i	$-0.890287\pi$
$139$	−2.09826	+	3.63429i	−0.177972	+	0.308257i	0.763214	+	0.646146i	$0.223620\pi$
$140$	0.610023	+	0.405778i	0.0515563	+	0.0342945i
$141$	−16.2931	+	9.40682i	−1.37213	+	0.792197i
$142$	9.90447	−	7.86353i	0.831164	−	0.659893i
$143$	10.9603	−	5.15304i	0.916544	−	0.430919i
$144$	−12.2771	+	24.9389i	−1.02309	+	2.07824i
$145$	0.710040	+	1.55992i	0.0589656	+	0.129544i
$146$	16.6420	−	7.21797i	1.37730	−	0.597364i
$147$	21.2456	−	5.69274i	1.75231	−	0.469529i
$148$	2.66101	−	1.65600i	0.218734	−	0.136122i
$149$	−0.0288765	+	0.0500155i	−0.00236565	+	0.00409743i	−0.867206	−	0.497950i	$-0.834086\pi$
$149$	−0.0288765	+	0.0500155i	−0.00236565	+	0.00409743i	0.864840	+	0.502047i	$0.167420\pi$
$150$	15.0382	+	16.4717i	1.22786	+	1.34490i
$151$	−15.6443			−1.27311			−0.636557	−	0.771230i	$-0.719642\pi$
$151$	−15.6443			−1.27311			−0.636557	+	0.771230i	$0.719642\pi$
$152$	−0.471895	+	5.79198i	−0.0382757	+	0.469791i
$153$	7.77558	−	29.0189i	0.628618	−	2.34604i
$154$	0.713980	−	0.309668i	0.0575342	−	0.0249538i
$155$	−1.98573	+	20.5248i	−0.159498	+	1.64859i
$156$	−20.2528	+	10.3530i	−1.62152	+	0.828905i
$157$	−7.76316	+	7.76316i	−0.619568	+	0.619568i	−0.945420	−	0.325853i	$-0.894349\pi$
$157$	−7.76316	+	7.76316i	−0.619568	+	0.619568i	0.325853	+	0.945420i	$0.394349\pi$
$158$	−8.32992	−	3.29008i	−0.662693	−	0.261745i
$159$	−19.2434	−	33.3305i	−1.52610	−	2.64328i
$160$	11.6185	+	5.00109i	0.918522	+	0.395371i
$161$			0.189975i			0.0149721i
$162$	−3.83181	−	25.8013i	−0.301055	−	2.02714i
$163$	6.34860	−	1.70110i	0.497261	−	0.133241i	−0.00146753	−	0.999999i	$-0.500467\pi$
$163$	6.34860	−	1.70110i	0.497261	−	0.133241i	0.498729	+	0.866758i	$0.333800\pi$
$164$	16.5604	+	3.85531i	1.29315	+	0.301049i
$165$	23.3685	−	3.89963i	1.81924	−	0.303586i
$166$	5.36463	+	12.3688i	0.416376	+	0.960009i
$167$	17.0827	+	4.57729i	1.32190	+	0.354201i	0.849688	−	0.527285i	$-0.176790\pi$
$167$	17.0827	+	4.57729i	1.32190	+	0.354201i	0.472209	+	0.881487i	$0.343457\pi$
$168$	−1.32094	+	0.625593i	−0.101912	+	0.0482656i
$169$	−12.8165	−	2.17656i	−0.985884	−	0.167428i
$170$	−13.3683	−	2.86071i	−1.02530	−	0.219406i
$171$	−7.13882	−	12.3648i	−0.545919	−	0.945560i
$172$	2.97550	−	5.57139i	0.226880	−	0.424815i
$173$	−2.61845	+	0.701612i	−0.199077	+	0.0533426i	−0.356980	−	0.934112i	$-0.616193\pi$
$173$	−2.61845	+	0.701612i	−0.199077	+	0.0533426i	0.157903	+	0.987455i	$0.449527\pi$
$174$	−3.39679	−	0.390175i	−0.257510	−	0.0295791i
$175$	0.0563965	+	0.817190i	0.00426318	+	0.0617737i
$176$	11.1666	−	7.47246i	0.841715	−	0.563258i
$177$	−4.43028	−	4.43028i	−0.333001	−	0.333001i
$178$	−1.63533	−	11.0114i	−0.122573	−	0.825338i
$179$	9.55658	+	16.5525i	0.714292	+	1.23719i	0.963232	+	0.268671i	$0.0865845\pi$
$179$	9.55658	+	16.5525i	0.714292	+	1.23719i	−0.248940	+	0.968519i	$0.580082\pi$
$180$	−30.4682	+	6.12617i	−2.27097	+	0.456617i
$181$	−9.00568			−0.669387			−0.334693	−	0.942327i	$-0.608633\pi$
$181$	−9.00568			−0.669387			−0.334693	+	0.942327i	$0.608633\pi$
$182$	−0.818956	−	0.164710i	−0.0607051	−	0.0122091i
$183$	3.54129	−	3.54129i	0.261780	−	0.261780i
$184$	0.588823	+	3.22658i	0.0434086	+	0.237867i
$185$	3.28169	+	1.22868i	0.241275	+	0.0903341i
$186$	−33.0454	−	24.4993i	−2.42300	−	1.79637i
$187$	−10.2683	+	10.2683i	−0.750894	+	0.750894i
$188$	−11.9226	+	0.394426i	−0.869543	+	0.0287665i
$189$	1.02039	−	1.76736i	0.0742222	−	0.128557i
$190$	−5.45377	+	3.53108i	−0.395658	+	0.256172i
$191$	−0.478629	−	0.276336i	−0.0346323	−	0.0199950i	0.482584	−	0.875850i	$-0.339698\pi$
$191$	−0.478629	−	0.276336i	−0.0346323	−	0.0199950i	−0.517216	+	0.855855i	$0.673032\pi$
$192$	−20.4961	+	14.7195i	−1.47918	+	1.06229i
$193$	10.7568	+	2.88227i	0.774289	+	0.207470i	0.624265	−	0.781212i	$-0.285398\pi$
$193$	10.7568	+	2.88227i	0.774289	+	0.207470i	0.150023	+	0.988682i	$0.452065\pi$
$194$	−20.9673	−	2.40842i	−1.50536	−	0.172915i
$195$	−22.9825	−	10.8860i	−1.64581	−	0.779562i
$196$	13.5831	+	3.16219i	0.970221	+	0.225871i
$197$	1.03819	−	3.87460i	0.0739683	−	0.276054i	−0.919029	−	0.394190i	$-0.871025\pi$
$197$	1.03819	−	3.87460i	0.0739683	−	0.276054i	0.992997	+	0.118136i	$0.0376920\pi$
$198$	−12.1271	+	30.7036i	−0.861832	+	2.18201i
$199$	1.12144	−	1.94240i	0.0794970	−	0.137693i	−0.823536	−	0.567264i	$-0.808002\pi$
$199$	1.12144	−	1.94240i	0.0794970	−	0.137693i	0.903033	+	0.429571i	$0.141335\pi$
$200$	3.49072	+	13.7046i	0.246831	+	0.969059i
$201$	−15.4186	−	8.90191i	−1.08754	−	0.627893i
$202$	1.29710	+	8.73392i	0.0912634	+	0.614516i
$203$	−0.0887921	−	0.0887921i	−0.00623198	−	0.00623198i
$204$	18.6363	−	19.9116i	1.30480	−	1.39409i
$205$	7.87553	+	17.3021i	0.550051	+	1.20843i
$206$	18.0435	−	7.82583i	1.25715	−	0.545251i
$207$	−5.69816	−	5.69816i	−0.396049	−	0.396049i
$208$	−14.4199	−	0.259146i	−0.999839	−	0.0179685i
$209$			6.90135i			0.477377i
$210$	−1.45498	−	0.743866i	−0.100403	−	0.0513316i
$211$	12.8705	−	7.43079i	0.886042	−	0.511557i	0.0133964	−	0.999910i	$-0.495736\pi$
$211$	12.8705	−	7.43079i	0.886042	−	0.511557i	0.872646	+	0.488354i	$0.162402\pi$
$212$	−0.806872	−	24.3898i	−0.0554162	−	1.67510i
$213$	−19.9450	+	19.9450i	−1.36661	+	1.36661i
$214$	13.0408	−	17.5898i	0.891449	−	1.20241i
$215$	6.96538	−	1.16235i	0.475035	−	0.0792715i
$216$	11.8526	−	33.1800i	0.806468	−	2.25761i
$217$	−0.391019	−	1.45930i	−0.0265441	−	0.0990639i
$218$	13.4045	+	5.29439i	0.907866	+	0.358581i
$219$	−35.0384	+	20.2294i	−2.36768	+	1.36698i
$220$	14.2349	+	4.79921i	0.959714	+	0.323563i
$221$	15.3418	−	2.75514i	1.03200	−	0.185331i
$222$	−5.47483	+	4.34668i	−0.367447	+	0.291730i
$223$	0.369164	−	1.37774i	0.0247210	−	0.0922602i	−0.952463	−	0.304654i	$-0.901459\pi$
$223$	0.369164	−	1.37774i	0.0247210	−	0.0922602i	0.977184	+	0.212394i	$0.0681259\pi$
$224$	−0.925666	−	0.0446740i	−0.0618487	−	0.00298491i
$225$	−26.2026	−	22.8194i	−1.74684	−	1.52130i
$226$	9.24411	+	1.06183i	0.614909	+	0.0706320i
$227$	5.00768	+	18.6889i	0.332371	+	1.24043i	0.906691	+	0.421796i	$0.138600\pi$
$227$	5.00768	+	18.6889i	0.332371	+	1.24043i	−0.574320	+	0.818631i	$0.694733\pi$
$228$	−0.428551	−	12.9541i	−0.0283815	−	0.857904i
$229$	−7.01559			−0.463603			−0.231802	−	0.972763i	$-0.574462\pi$
$229$	−7.01559			−0.463603			−0.231802	+	0.972763i	$0.574462\pi$
$230$	−2.45744	+	2.72174i	−0.162039	+	0.179467i
$231$	−1.50323	+	0.867892i	−0.0989055	+	0.0571031i
$232$	−1.78328	−	1.23286i	−0.117078	−	0.0809411i
$233$	2.28199	+	2.28199i	0.149498	+	0.149498i	0.777894	−	0.628396i	$-0.216288\pi$
$233$	2.28199	+	2.28199i	0.149498	+	0.149498i	−0.628396	+	0.777894i	$0.716288\pi$
$234$	29.5044	−	19.6236i	1.92876	−	1.28284i
$235$	−8.47878	−	10.2951i	−0.553095	−	0.671579i
$236$	−1.15452	−	3.80120i	−0.0751525	−	0.247437i
$237$	19.2950	+	5.17008i	1.25334	+	0.335832i
$238$	0.990742	−	0.147138i	0.0642203	−	0.00953751i
$239$			21.3250i			1.37940i	0.724095	+	0.689700i	$0.242258\pi$
$239$			21.3250i			1.37940i	−0.724095	+	0.689700i	$0.757742\pi$
$240$	−27.0173	−	8.12434i	−1.74396	−	0.524424i
$241$	−6.14607	−	3.54844i	−0.395903	−	0.228575i	0.288812	−	0.957386i	$-0.406740\pi$
$241$	−6.14607	−	3.54844i	−0.395903	−	0.228575i	−0.684715	+	0.728811i	$0.740073\pi$
$242$	0.313649	−	0.249018i	0.0201621	−	0.0160075i
$243$	5.38532	+	20.0983i	0.345468	+	1.28930i
$244$	3.03844	−	0.922846i	0.194516	−	0.0590792i
$245$	6.45963	+	14.1915i	0.412691	+	0.906660i
$246$	−37.6760	−	4.32769i	−2.40214	−	0.275923i
$247$	4.22977	−	6.08151i	0.269134	−	0.386957i
$248$	−11.1642	−	23.5732i	−0.708930	−	1.49690i
$249$	−15.0352	−	26.0417i	−0.952816	−	1.65032i
$250$	−9.76288	+	12.4373i	−0.617459	+	0.786603i
$251$	5.22758	+	3.01814i	0.329962	+	0.190504i	0.655824	−	0.754914i	$-0.272321\pi$
$251$	5.22758	+	3.01814i	0.329962	+	0.190504i	−0.325862	+	0.945417i	$0.605655\pi$
$252$	1.93317	−	1.20305i	0.121778	−	0.0757850i
$253$	1.00815	+	3.76245i	0.0633816	+	0.236543i
$254$	−12.6575	+	17.0728i	−0.794201	+	1.07124i
$255$	30.3498	+	2.93628i	1.90058	+	0.183877i
$256$	−15.8602	+	2.11033i	−0.991264	+	0.131896i
$257$	19.3375	+	5.18147i	1.20624	+	0.323211i	0.805286	−	0.592886i	$-0.202012\pi$
$257$	19.3375	+	5.18147i	1.20624	+	0.323211i	0.400955	+	0.916098i	$0.368678\pi$
$258$	−5.17512	+	13.1025i	−0.322189	+	0.815727i
$259$	−0.256734			−0.0159527
$260$	−9.60244	−	12.9535i	−0.595518	−	0.803342i
$261$	5.32651			0.329703
$262$	1.14159	−	2.89032i	0.0705280	−	0.178565i
$263$	−16.9714	−	4.54747i	−1.04650	−	0.280409i	−0.305696	−	0.952129i	$-0.598889\pi$
$263$	−16.9714	−	4.54747i	−1.04650	−	0.280409i	−0.740805	+	0.671720i	$0.765556\pi$
$264$	−22.8413	+	19.3997i	−1.40578	+	1.19397i
$265$	21.0606	−	17.3449i	1.29374	−	1.06549i
$266$	0.283494	−	0.382386i	0.0173821	−	0.0234456i
$267$	6.42622	+	23.9830i	0.393278	+	1.46773i
$268$	−5.96457	−	9.58442i	−0.364344	−	0.585462i
$269$	5.65892	+	3.26718i	0.345031	+	0.199204i	0.662494	−	0.749067i	$-0.269498\pi$
$269$	5.65892	+	3.26718i	0.345031	+	0.199204i	−0.317464	+	0.948270i	$0.602831\pi$
$270$	37.4809	−	12.1214i	2.28101	−	0.737685i
$271$	−1.38207	−	2.39382i	−0.0839550	−	0.145414i	0.820990	−	0.570942i	$-0.193422\pi$
$271$	−1.38207	−	2.39382i	−0.0839550	−	0.145414i	−0.904945	+	0.425528i	$0.860089\pi$
$272$	16.3710	−	5.56981i	0.992636	−	0.337719i
$273$	1.85658	+	0.156526i	0.112365	+	0.00947339i
$274$	−7.34736	−	0.843960i	−0.443870	−	0.0509855i
$275$	5.45354	+	15.8852i	0.328861	+	0.957911i
$276$	−2.12596	−	6.99965i	−0.127968	−	0.421329i
$277$	5.26392	+	19.6452i	0.316278	+	1.18037i	0.922794	+	0.385295i	$0.125900\pi$
$277$	5.26392	+	19.6452i	0.316278	+	1.18037i	−0.606515	+	0.795072i	$0.707433\pi$
$278$	4.64799	−	3.69022i	0.278768	−	0.221324i
$279$	55.4990	+	32.0424i	3.32264	+	1.91833i
$280$	−0.591573	−	0.850652i	−0.0353533	−	0.0508362i
$281$		−	2.39574i		−	0.142918i	−0.997444	−	0.0714588i	$-0.977235\pi$
$281$		−	2.39574i		−	0.142918i	0.997444	−	0.0714588i	$-0.0227654\pi$
$282$	26.3178	−	3.90853i	1.56721	−	0.232749i
$283$	−1.46412	−	0.392310i	−0.0870329	−	0.0233204i	0.215040	−	0.976605i	$-0.431012\pi$
$283$	−1.46412	−	0.392310i	−0.0870329	−	0.0233204i	−0.302073	+	0.953285i	$0.597679\pi$
$284$	−17.1129	+	5.19760i	−1.01547	+	0.308421i
$285$	11.1858	−	9.21233i	0.662590	−	0.545691i
$286$	−17.0935	+	1.08389i	−1.01076	+	0.0640919i
$287$	−0.984852	−	0.984852i	−0.0581340	−	0.0581340i
$288$	29.1047	−	26.4247i	1.71501	−	1.55709i
$289$	−1.46312	+	0.844730i	−0.0860656	+	0.0496900i
$290$	−0.123531	−	2.42069i	−0.00725397	−	0.142148i
$291$	47.0727			2.75945
$292$	−25.6396	+	0.848217i	−1.50044	+	0.0496382i
$293$	3.72018	+	13.8839i	0.217335	+	0.811106i	0.985331	+	0.170652i	$0.0545873\pi$
$293$	3.72018	+	13.8839i	0.217335	+	0.811106i	−0.767996	+	0.640455i	$0.778746\pi$
$294$	−30.9025	−	3.54964i	−1.80227	−	0.207019i
$295$	2.58088	−	3.61478i	0.150264	−	0.210460i
$296$	−4.36044	+	0.795743i	−0.253446	+	0.0462516i
$297$	10.8298	−	40.4175i	0.628411	−	2.34526i
$298$	0.0639662	−	0.0507852i	0.00370546	−	0.00294191i
$299$	1.41759	−	3.93338i	0.0819812	−	0.227473i
$300$	−11.2229	−	29.4783i	−0.647954	−	1.70193i
$301$	−0.448063	+	0.258689i	−0.0258259	+	0.0149106i
$302$	20.5774	+	8.12750i	1.18410	+	0.467685i
$303$	−5.09710	−	19.0226i	−0.292821	−	1.09282i
$304$	3.62974	−	7.37322i	0.208180	−	0.422883i
$305$	2.88942	+	2.06299i	0.165448	+	0.118126i
$306$	−25.3033	+	34.1299i	−1.44649	+	1.95108i
$307$	7.62821	−	7.62821i	0.435365	−	0.435365i	−0.455084	−	0.890449i	$-0.650391\pi$
$307$	7.62821	−	7.62821i	0.435365	−	0.435365i	0.890449	+	0.455084i	$0.150391\pi$
$308$	−1.10000	+	0.0363906i	−0.0626783	+	0.00207354i
$309$	−37.9892	+	21.9331i	−2.16113	+	1.24773i
$310$	13.2749	−	25.9653i	0.753965	−	1.47473i
$311$		−	16.0897i		−	0.912363i	−0.889887	−	0.456181i	$-0.849217\pi$
$311$		−	16.0897i		−	0.912363i	0.889887	−	0.456181i	$-0.150783\pi$
$312$	32.0178	−	3.09595i	1.81265	−	0.175274i
$313$	11.6193	+	11.6193i	0.656759	+	0.656759i	0.954612	−	0.297853i	$-0.0962704\pi$
$313$	11.6193	+	11.6193i	0.656759	+	0.656759i	−0.297853	+	0.954612i	$0.596270\pi$
$314$	14.2442	−	6.17803i	0.803849	−	0.348646i
$315$	2.38408	+	0.892608i	0.134328	+	0.0502928i
$316$	9.24736	+	8.65511i	0.520205	+	0.486888i
$317$	−5.28001	−	5.28001i	−0.296555	−	0.296555i	0.543108	−	0.839663i	$-0.317247\pi$
$317$	−5.28001	−	5.28001i	−0.296555	−	0.296555i	−0.839663	+	0.543108i	$0.817247\pi$
$318$	7.99561	+	53.8380i	0.448372	+	3.01909i
$319$	−2.22972	−	1.28733i	−0.124841	−	0.0720767i
$320$	−12.6840	−	12.6141i	−0.709058	−	0.705150i
$321$	−24.4190	+	42.2949i	−1.36293	+	2.36067i
$322$	0.0986955	−	0.249880i	0.00550009	−	0.0139253i
$323$	−2.29886	+	8.57947i	−0.127912	+	0.477375i
$324$	−8.36414	+	35.9279i	−0.464675	+	1.99600i
$325$	4.93017	−	17.3405i	0.273477	−	0.961879i
$326$	−9.23428	−	1.06070i	−0.511440	−	0.0587469i
$327$	−31.0494	−	8.31967i	−1.71704	−	0.460079i
$328$	−19.7795	−	13.6744i	−1.09214	−	0.755045i
$329$	0.846238	+	0.488576i	0.0466546	+	0.0269361i
$330$	−32.7633	−	7.01109i	−1.80356	−	0.385948i
$331$	−10.3898	+	17.9957i	−0.571078	+	0.989136i	0.425378	+	0.905016i	$0.360141\pi$
$331$	−10.3898	+	17.9957i	−0.571078	+	0.989136i	−0.996456	+	0.0841198i	$0.973192\pi$
$332$	−0.630422	−	19.0562i	−0.0345989	−	1.04584i
$333$	7.70056	−	7.70056i	0.421988	−	0.421988i
$334$	−20.0914	−	14.8954i	−1.09935	−	0.815042i
$335$	4.42544	−	11.8200i	0.241788	−	0.645795i
$336$	2.06248	−	0.136613i	0.112517	−	0.00745283i
$337$	−21.7455	+	21.7455i	−1.18455	+	1.18455i	−0.206004	+	0.978551i	$0.566046\pi$
$337$	−21.7455	+	21.7455i	−1.18455	+	1.18455i	−0.978551	+	0.206004i	$0.933954\pi$
$338$	15.7272	+	9.52131i	0.855447	+	0.517891i
$339$	−20.7535			−1.12718
$340$	16.0975	+	10.7079i	0.873012	+	0.580715i
$341$	−15.4883	−	26.8265i	−0.838736	−	1.45273i
$342$	2.96618	+	19.9726i	0.160393	+	1.07999i
$343$	−1.61869	−	1.61869i	−0.0874012	−	0.0874012i
$344$	−6.80821	+	5.78241i	−0.367074	+	0.311767i
$345$	4.75251	−	6.65636i	0.255866	−	0.358366i
$346$	3.80863	+	0.437482i	0.204753	+	0.0235192i
$347$	−33.8608	+	9.07296i	−1.81774	+	0.487062i	−0.996505	−	0.0835278i	$-0.973381\pi$
$347$	−33.8608	+	9.07296i	−1.81774	+	0.487062i	−0.821235	+	0.570590i	$0.806715\pi$
$348$	4.26520	+	2.27791i	0.228639	+	0.122109i
$349$	8.33710	+	14.4403i	0.446275	+	0.772971i	0.998140	−	0.0609628i	$-0.0194171\pi$
$349$	8.33710	+	14.4403i	0.446275	+	0.772971i	−0.551865	+	0.833933i	$0.686084\pi$
$350$	0.350365	−	1.10418i	0.0187278	−	0.0590206i
$351$	−34.3148	+	28.9786i	−1.83159	+	1.54676i
$352$	−18.5699	+	4.02750i	−0.989779	+	0.214666i
$353$	−6.02155	−	1.61347i	−0.320495	−	0.0858762i	0.0949852	−	0.995479i	$-0.469720\pi$
$353$	−6.02155	−	1.61347i	−0.320495	−	0.0858762i	−0.415480	+	0.909602i	$0.636386\pi$
$354$	3.52568	+	8.12891i	0.187388	+	0.432047i
$355$	−16.2736	−	11.6191i	−0.863715	−	0.616675i
$356$	−3.56962	+	15.3332i	−0.189190	+	0.812659i
$357$	−2.15785	+	0.578195i	−0.114206	+	0.0306013i
$358$	−3.97075	−	26.7368i	−0.209861	−	1.41309i
$359$		−	15.1568i		−	0.799944i	−0.916527	−	0.399972i	$-0.869020\pi$
$359$		−	15.1568i		−	0.799944i	0.916527	−	0.399972i	$-0.130980\pi$
$360$	43.2585	+	7.77087i	2.27992	+	0.409561i
$361$	−7.38939	−	12.7988i	−0.388916	−	0.673621i
$362$	11.8455	+	4.67862i	0.622584	+	0.245903i
$363$	−0.631608	+	0.631608i	−0.0331508	+	0.0331508i
$364$	0.991629	+	0.642112i	0.0519755	+	0.0336558i
$365$	−18.2337	−	22.1397i	−0.954395	−	1.15885i
$366$	−6.49774	+	2.81821i	−0.339642	+	0.147310i
$367$	7.93725	−	29.6222i	0.414321	−	1.54627i	−0.371871	−	0.928284i	$-0.621284\pi$
$367$	7.93725	−	29.6222i	0.414321	−	1.54627i	0.786192	−	0.617982i	$-0.212050\pi$
$368$	0.901772	−	4.54993i	0.0470081	−	0.237182i
$369$	59.0799			3.07557
$370$	−3.67820	−	3.32102i	−0.191220	−	0.172652i
$371$	−0.999472	+	1.73114i	−0.0518900	+	0.0898761i
$372$	30.7378	+	49.3924i	1.59368	+	2.56087i
$373$	−13.9598	+	3.74051i	−0.722810	+	0.193676i	−0.601425	−	0.798929i	$-0.705400\pi$
$373$	−13.9598	+	3.74051i	−0.722810	+	0.193676i	−0.121385	+	0.992606i	$0.538734\pi$
$374$	18.8408	−	8.17167i	0.974236	−	0.422547i
$375$	18.4672	−	30.0436i	0.953642	−	1.55145i
$376$	15.8871	+	5.67520i	0.819313	+	0.292676i
$377$	1.17585	+	2.50098i	0.0605594	+	0.128807i
$378$	−2.26033	+	1.79456i	−0.116259	+	0.0923021i
$379$	13.2319	−	7.63943i	0.679676	−	0.392411i	−0.120057	−	0.992767i	$-0.538308\pi$
$379$	13.2319	−	7.63943i	0.679676	−	0.392411i	0.799733	+	0.600356i	$0.204974\pi$
$380$	9.00798	−	1.81121i	0.462100	−	0.0929132i
$381$	23.7013	−	41.0518i	1.21425	−	2.10315i
$382$	0.485994	+	0.612131i	0.0248656	+	0.0313193i
$383$	−1.98917	+	0.532995i	−0.101642	+	0.0272348i	−0.309281	−	0.950971i	$-0.600088\pi$
$383$	−1.98917	+	0.532995i	−0.101642	+	0.0272348i	0.207640	+	0.978205i	$0.433422\pi$
$384$	34.6062	−	8.71287i	1.76599	−	0.444627i
$385$	−0.782269	−	0.949848i	−0.0398681	−	0.0484087i
$386$	−12.6513	−	9.37948i	−0.643936	−	0.477403i
$387$	5.68013	−	21.1985i	0.288737	−	1.07758i
$388$	26.3277	+	14.0608i	1.33659	+	0.713828i
$389$			30.7357i			1.55836i	0.626799	+	0.779181i	$0.284365\pi$
$389$			30.7357i			1.55836i	−0.626799	+	0.779181i	$0.715635\pi$
$390$	24.5742	+	26.2586i	1.24436	+	1.32965i
$391$			5.01314i			0.253525i
$392$	−16.2235	−	11.2160i	−0.819409	−	0.566494i
$393$	−1.79392	+	6.69498i	−0.0904911	+	0.337717i
$394$	−3.37850	+	4.55702i	−0.170206	+	0.229579i
$395$	−1.36367	+	14.0951i	−0.0686138	+	0.709200i
$396$	31.9022	−	34.0852i	1.60315	−	1.71285i
$397$	−8.35399	+	2.23844i	−0.419275	+	0.112344i	−0.462287	−	0.886730i	$-0.652971\pi$
$397$	−8.35399	+	2.23844i	−0.419275	+	0.112344i	0.0430126	+	0.999075i	$0.486304\pi$
$398$	−2.48418	+	1.97229i	−0.124521	+	0.0988618i
$399$	−0.530846	+	0.919452i	−0.0265755	+	0.0460302i
$400$	2.52832	−	19.8395i	0.126416	−	0.991977i
$401$	−14.1843	+	8.18931i	−0.708330	+	0.408955i	−0.810442	−	0.585818i	$-0.800773\pi$
$401$	−14.1843	+	8.18931i	−0.708330	+	0.408955i	0.102112	+	0.994773i	$0.467440\pi$
$402$	15.6558	+	19.7192i	0.780842	+	0.983505i
$403$	−2.79334	+	33.1322i	−0.139146	+	1.65043i
$404$	2.83132	−	12.1619i	0.140864	−	0.605076i
$405$	−37.5371	+	17.0860i	−1.86524	+	0.849013i
$406$	0.0706620	+	0.162920i	0.00350689	+	0.00808560i
$407$	−5.08463	+	1.36242i	−0.252036	+	0.0675327i
$408$	−34.8574	+	16.5084i	−1.72570	+	0.817290i
$409$	8.64649	−	14.9762i	0.427541	−	0.740523i	−0.569113	−	0.822260i	$-0.692713\pi$
$409$	8.64649	−	14.9762i	0.427541	−	0.740523i	0.996654	+	0.0817363i	$0.0260465\pi$
$410$	−1.37016	−	26.8495i	−0.0676674	−	1.32600i
$411$	16.4952			0.813648
$412$	−27.7988	+	0.919649i	−1.36955	+	0.0453079i
$413$	−0.0842233	+	0.314326i	−0.00414436	+	0.0154670i
$414$	4.53467	+	10.4553i	0.222867	+	0.513849i
$415$	16.4550	−	13.5519i	0.807743	−	0.665235i
$416$	18.8323	+	7.83226i	0.923330	+	0.384008i
$417$	−9.35986	+	9.35986i	−0.458354	+	0.458354i
$418$	3.58538	−	9.07758i	0.175367	−	0.443999i
$419$	7.42077	+	12.8531i	0.362528	+	0.627917i	0.988376	−	0.152028i	$-0.0485803\pi$
$419$	7.42077	+	12.8531i	0.362528	+	0.627917i	−0.625848	+	0.779945i	$0.715247\pi$
$420$	1.52733	+	1.73432i	0.0745259	+	0.0846262i
$421$		−	23.5194i		−	1.14627i	−0.819462	−	0.573134i	$-0.805728\pi$
$421$		−	23.5194i		−	1.14627i	0.819462	−	0.573134i	$-0.194272\pi$
$422$	−20.7894	+	3.08749i	−1.01201	+	0.150297i
$423$	−40.0368	+	10.7278i	−1.94666	+	0.521605i
$424$	−11.6097	+	32.4999i	−0.563815	+	1.57834i
$425$	1.48822	+	21.5644i	0.0721891	+	1.04603i
$426$	36.5962	−	15.8725i	1.77309	−	0.769027i
$427$	−0.251252	−	0.0673227i	−0.0121589	−	0.00325798i
$428$	−26.2912	+	16.3615i	−1.27083	+	0.790863i
$429$	37.6002	−	6.75237i	1.81536	−	0.326008i
$430$	−9.76565	−	2.08977i	−0.470941	−	0.100778i
$431$	13.4711	+	23.3326i	0.648879	+	1.12389i	0.983391	+	0.181500i	$0.0580951\pi$
$431$	13.4711	+	23.3326i	0.648879	+	1.12389i	−0.334512	+	0.942391i	$0.608572\pi$
$432$	−32.8277	+	37.4851i	−1.57943	+	1.80350i
$433$	23.7791	−	6.37160i	1.14275	−	0.306200i	0.362695	−	0.931908i	$-0.381857\pi$
$433$	23.7791	−	6.37160i	1.14275	−	0.306200i	0.780057	+	0.625708i	$0.215190\pi$
$434$	−0.243815	+	2.12261i	−0.0117035	+	0.101888i
$435$	0.889840	+	5.33237i	0.0426646	+	0.255668i
$436$	−14.8808	−	13.9278i	−0.712662	−	0.667019i
$437$	1.68467	+	1.68467i	0.0805887	+	0.0805887i
$438$	56.5968	−	8.40532i	2.70430	−	0.401622i
$439$	−0.831387	−	1.44000i	−0.0396799	−	0.0687276i	0.845503	−	0.533970i	$-0.179300\pi$
$439$	−0.831387	−	1.44000i	−0.0396799	−	0.0687276i	−0.885183	+	0.465242i	$0.845967\pi$
$440$	−16.2303	−	13.7078i	−0.773749	−	0.653496i
$441$	48.4583			2.30754
$442$	−21.6110	−	4.34645i	−1.02793	−	0.206740i
$443$	18.5752	−	18.5752i	0.882532	−	0.882532i	−0.111259	−	0.993791i	$-0.535488\pi$
$443$	18.5752	−	18.5752i	0.882532	−	0.882532i	0.993791	+	0.111259i	$0.0354884\pi$
$444$	9.45941	−	2.87305i	0.448924	−	0.136349i
$445$	−16.0200	+	7.29193i	−0.759420	+	0.345671i
$446$	−1.20133	+	1.62040i	−0.0568848	+	0.0767280i
$447$	−0.128812	+	0.128812i	−0.00609257	+	0.00609257i
$448$	1.19435	+	0.539662i	0.0564277	+	0.0254966i
$449$	−11.2483	+	19.4826i	−0.530838	+	0.919439i	0.468514	+	0.883456i	$0.344790\pi$
$449$	−11.2483	+	19.4826i	−0.530838	+	0.919439i	−0.999352	+	0.0359829i	$0.988544\pi$
$450$	22.6100	+	43.6279i	1.06585	+	2.05664i
$451$	−24.7313	−	14.2787i	−1.16455	−	0.672355i
$452$	−11.6074	−	6.19915i	−0.545968	−	0.291584i
$453$	−47.6645	−	12.7717i	−2.23947	−	0.600065i
$454$	3.12248	−	27.1837i	0.146545	−	1.27580i
$455$	0.107187	+	1.31646i	0.00502499	+	0.0617164i
$456$	−6.16620	+	17.2616i	−0.288759	+	0.808346i
$457$	3.04489	−	11.3637i	0.142434	−	0.531571i	−0.857422	−	0.514614i	$-0.827935\pi$
$457$	3.04489	−	11.3637i	0.142434	−	0.531571i	0.999856	−	0.0169575i	$-0.00539801\pi$
$458$	9.22783	+	3.64473i	0.431188	+	0.170307i
$459$	26.9264	−	46.6379i	1.25682	−	2.17687i
$460$	4.64636	−	2.30331i	0.216637	−	0.107392i
$461$	−0.245659	−	0.141831i	−0.0114415	−	0.00660574i	0.494268	−	0.869309i	$-0.335436\pi$
$461$	−0.245659	−	0.141831i	−0.0114415	−	0.00660574i	−0.505710	+	0.862704i	$0.668769\pi$
$462$	2.42814	−	0.360609i	0.112967	−	0.0167770i
$463$	9.78891	+	9.78891i	0.454929	+	0.454929i	0.896987	−	0.442058i	$-0.145751\pi$
$463$	9.78891	+	9.78891i	0.454929	+	0.454929i	−0.442058	+	0.896987i	$0.645751\pi$
$464$	1.70511	+	2.54806i	0.0791577	+	0.118291i
$465$	−22.8061	+	60.9131i	−1.05761	+	2.82478i
$466$	−1.81604	−	4.18712i	−0.0841266	−	0.193965i
$467$	−7.98810	−	7.98810i	−0.369645	−	0.369645i	0.497703	−	0.867348i	$-0.334177\pi$
$467$	−7.98810	−	7.98810i	−0.369645	−	0.369645i	−0.867348	+	0.497703i	$0.834177\pi$
$468$	−49.0029	+	10.4835i	−2.26516	+	0.484601i
$469$			0.924704i			0.0426989i
$470$	5.80391	+	17.9464i	0.267714	+	0.827805i
$471$	−29.9902	+	17.3148i	−1.38188	+	0.797826i
$472$	−0.456224	+	5.59963i	−0.0209994	+	0.257744i
$473$	−7.50110	+	7.50110i	−0.344901	+	0.344901i
$474$	−22.6934	−	16.8245i	−1.04234	−	0.772774i
$475$	7.74684	+	6.74661i	0.355449	+	0.309556i
$476$	−1.37960	−	0.321174i	−0.0632337	−	0.0147210i
$477$	−21.9457	−	81.9027i	−1.00483	−	3.75006i
$478$	11.0787	−	28.0495i	0.506730	−	1.28295i
$479$	2.34517	−	1.35398i	0.107154	−	0.0618651i	−0.445466	−	0.895299i	$-0.646962\pi$
$479$	2.34517	−	1.35398i	0.107154	−	0.0618651i	0.552619	+	0.833434i	$0.313628\pi$
$480$	31.3160	+	24.7222i	1.42937	+	1.12841i
$481$	5.31561	+	1.91575i	0.242371	+	0.0873505i
$482$	6.24065	+	7.86037i	0.284254	+	0.358030i
$483$	−0.155091	+	0.578809i	−0.00705690	+	0.0263367i
$484$	−0.541922	+	0.164595i	−0.0246328	+	0.00748157i
$485$	5.49270	+	32.9150i	0.249411	+	1.49459i
$486$	3.35795	−	29.2337i	0.152320	−	1.32607i
$487$	−2.51813	−	9.39781i	−0.114108	−	0.425855i	0.885111	−	0.465380i	$-0.154082\pi$
$487$	−2.51813	−	9.39781i	−0.114108	−	0.425855i	−0.999219	+	0.0395247i	$0.987416\pi$
$488$	−4.47599	−	0.364676i	−0.202619	−	0.0165081i
$489$	20.7314			0.937509
$490$	−1.12383	−	22.0224i	−0.0507694	−	0.994871i
$491$	−1.40495	+	0.811148i	−0.0634045	+	0.0366066i	−0.531367	−	0.847142i	$-0.678322\pi$
$491$	−1.40495	+	0.811148i	−0.0634045	+	0.0366066i	0.467963	+	0.883748i	$0.344988\pi$
$492$	47.3082	+	25.2658i	2.13282	+	1.13907i
$493$	−2.34309	−	2.34309i	−0.105527	−	0.105527i
$494$	−8.72302	+	5.80176i	−0.392467	+	0.261034i
$495$	51.9536	+	5.02641i	2.33514	+	0.225921i
$496$	2.43797	+	36.8066i	0.109468	+	1.65267i
$497$	1.41509	+	0.379171i	0.0634753	+	0.0170082i
$498$	6.24711	+	42.0645i	0.279940	+	1.88496i
$499$		−	31.4652i		−	1.40858i	−0.709914	−	0.704289i	$-0.751266\pi$
$499$		−	31.4652i		−	1.40858i	0.709914	−	0.704289i	$-0.248734\pi$
$500$	19.3028	−	11.2872i	0.863249	−	0.504778i
$501$	48.3101	+	27.8919i	2.15834	+	1.24612i
$502$	−5.30802	−	6.68569i	−0.236909	−	0.298397i
$503$	−1.56391	−	5.83660i	−0.0697314	−	0.260241i	0.922256	−	0.386580i	$-0.126344\pi$
$503$	−1.56391	−	5.83660i	−0.0697314	−	0.260241i	−0.991987	+	0.126339i	$0.959677\pi$
$504$	−3.16777	+	0.578091i	−0.141104	+	0.0257502i
$505$	12.7066	−	5.78375i	0.565436	−	0.257374i
$506$	0.628618	−	5.47263i	0.0279455	−	0.243288i
$507$	−37.2720	−	17.0946i	−1.65531	−	0.759197i
$508$	25.5184	−	15.8806i	1.13220	−	0.704588i
$509$	−6.49123	−	11.2431i	−0.287719	−	0.498344i	0.685546	−	0.728029i	$-0.259564\pi$
$509$	−6.49123	−	11.2431i	−0.287719	−	0.498344i	−0.973265	+	0.229686i	$0.926230\pi$
$510$	−38.3946	−	19.6295i	−1.70014	−	0.869208i
$511$	1.81984	+	1.05069i	0.0805051	+	0.0464796i
$512$	21.9578	+	5.46390i	0.970408	+	0.241472i
$513$	−6.62407	−	24.7214i	−0.292460	−	1.09147i
$514$	−22.7434	−	16.8616i	−1.00317	−	0.743732i
$515$	−19.7692	−	24.0042i	−0.871136	−	1.05775i
$516$	13.6140	−	14.5456i	0.599323	−	0.640334i
$517$	19.3525	+	5.18549i	0.851122	+	0.228057i
$518$	0.337691	+	0.133378i	0.0148373	+	0.00586031i
$519$	−8.55059			−0.375329
$520$	5.90082	+	22.0268i	0.258768	+	0.965940i
$521$	25.1504			1.10186			0.550929	−	0.834552i	$-0.314274\pi$
$521$	25.1504			1.10186			0.550929	+	0.834552i	$0.314274\pi$
$522$	−7.00613	−	2.76722i	−0.306650	−	0.121118i
$523$	14.8595	+	3.98160i	0.649761	+	0.174103i	0.568621	−	0.822600i	$-0.307477\pi$
$523$	14.8595	+	3.98160i	0.649761	+	0.174103i	0.0811405	+	0.996703i	$0.474144\pi$
$524$	−3.00315	+	3.20865i	−0.131193	+	0.140171i
$525$	−0.495309	+	2.53583i	−0.0216171	+	0.110673i
$526$	19.9605	+	14.7984i	0.870320	+	0.645240i
$527$	−10.3184	−	38.5087i	−0.449476	−	1.67747i
$528$	40.1224	−	13.6506i	1.74610	−	0.594068i
$529$	−18.7540	−	10.8277i	−0.815393	−	0.470768i
$530$	−36.7126	+	11.8730i	−1.59470	+	0.515728i
$531$	−6.90175	−	11.9542i	−0.299511	−	0.518768i
$532$	−0.571546	+	0.355684i	−0.0247796	+	0.0154208i
$533$	13.0421	+	27.7400i	0.564918	+	1.20155i
$534$	4.00699	−	34.8841i	0.173400	−	1.50958i
$535$	−32.4236	−	12.1395i	−1.40179	−	0.524836i
$536$	2.86610	+	15.7054i	0.123797	+	0.678370i
$537$	15.6036	+	58.2333i	0.673343	+	2.51295i
$538$	−5.74601	−	7.23735i	−0.247728	−	0.312024i
$539$	−20.2851	−	11.7116i	−0.873739	−	0.504453i
$540$	−55.5971	−	3.52834i	−2.39252	−	0.151836i
$541$			12.5555i			0.539804i	0.962888	+	0.269902i	$0.0869913\pi$
$541$			12.5555i			0.539804i	−0.962888	+	0.269902i	$0.913009\pi$
$542$	0.574251	+	3.86668i	0.0246662	+	0.166088i
$543$	−27.4382	−	7.35204i	−1.17749	−	0.315506i
$544$	−24.4269	−	1.17888i	−1.04729	−	0.0505440i
$545$	2.19442	−	22.6817i	0.0939985	−	0.971579i
$546$	−2.36070	−	1.17041i	−0.101029	−	0.0500890i
$547$	20.8999	+	20.8999i	0.893617	+	0.893617i	0.994862	−	0.101244i	$-0.0322824\pi$
$547$	20.8999	+	20.8999i	0.893617	+	0.893617i	−0.101244	+	0.994862i	$0.532282\pi$
$548$	9.22577	+	4.92718i	0.394105	+	0.210479i
$549$	9.55542	−	5.51682i	0.407815	−	0.235452i
$550$	1.07942	−	23.7275i	0.0460267	−	1.01174i
$551$	−1.57479			−0.0670884
$552$	−0.840105	+	10.3113i	−0.0357572	+	0.438880i
$553$	−0.268526	−	1.00215i	−0.0114189	−	0.0426159i
$554$	3.28225	−	28.5747i	0.139450	−	1.21402i
$555$	8.99549	+	6.42259i	0.381837	+	0.272624i
$556$	−8.03079	+	2.43914i	−0.340581	+	0.103443i
$557$	4.74177	−	17.6965i	0.200915	−	0.749826i	−0.789741	−	0.613441i	$-0.789785\pi$
$557$	4.74177	−	17.6965i	0.200915	−	0.749826i	0.990656	−	0.136385i	$-0.0435484\pi$
$558$	−56.3531	−	70.9792i	−2.38562	−	3.00479i
$559$	11.2074	−	2.01265i	0.474021	−	0.0851262i
$560$	0.336186	+	1.42622i	0.0142065	+	0.0602689i
$561$	−39.6680	+	22.9023i	−1.67478	+	0.966937i
$562$	−1.24463	+	3.15119i	−0.0525015	+	0.132925i
$563$	−7.29035	−	27.2080i	−0.307252	−	1.14668i	−0.930990	−	0.365045i	$-0.881053\pi$
$563$	−7.29035	−	27.2080i	−0.307252	−	1.14668i	0.623738	−	0.781633i	$-0.285613\pi$
$564$	−36.6473	−	8.53161i	−1.54313	−	0.359245i
$565$	−2.42163	−	14.5117i	−0.101879	−	0.610510i
$566$	1.72199	+	1.27666i	0.0723807	+	0.0536618i
$567$	2.13665	−	2.13665i	0.0897308	−	0.0897308i
$568$	25.2094	+	2.05391i	1.05776	+	0.0861802i
$569$	−23.7981	+	13.7398i	−0.997668	+	0.576004i	−0.907557	−	0.419928i	$-0.862055\pi$
$569$	−23.7981	+	13.7398i	−0.997668	+	0.576004i	−0.0901103	+	0.995932i	$0.528722\pi$
$570$	−19.4990	+	6.30604i	−0.816725	+	0.264131i
$571$			47.3246i			1.98047i	0.139401	+	0.990236i	$0.455482\pi$
$571$			47.3246i			1.98047i	−0.139401	+	0.990236i	$0.544518\pi$
$572$	23.0467	+	7.45472i	0.963633	+	0.311698i
$573$	−1.23267	−	1.23267i	−0.0514957	−	0.0514957i
$574$	0.783759	+	1.80706i	0.0327135	+	0.0754251i
$575$	5.20893	+	2.54643i	0.217228	+	0.106194i
$576$	−52.0105	+	19.6369i	−2.16710	+	0.818204i
$577$	−28.3643	−	28.3643i	−1.18082	−	1.18082i	−0.979532	−	0.201287i	$-0.935488\pi$
$577$	−28.3643	−	28.3643i	−1.18082	−	1.18082i	−0.201287	−	0.979532i	$-0.564512\pi$
$578$	2.36334	−	0.350985i	0.0983019	−	0.0145991i
$579$	30.4203	+	17.5632i	1.26423	+	0.729901i
$580$	−1.09511	+	3.24819i	−0.0454721	+	0.134874i
$581$	−0.780904	+	1.35257i	−0.0323974	+	0.0561139i
$582$	−61.9162	−	24.4551i	−2.56651	−	1.01370i
$583$	−10.6079	+	39.5891i	−0.439333	+	1.63961i
$584$	34.1653	+	12.2046i	1.41377	+	0.505029i
$585$	−42.7012	−	36.2712i	−1.76548	−	1.49963i
$586$	2.31968	−	20.1947i	0.0958249	−	0.834234i
$587$	22.2127	+	5.95187i	0.916816	+	0.245660i	0.686224	−	0.727390i	$-0.259267\pi$
$587$	22.2127	+	5.95187i	0.916816	+	0.245660i	0.230592	+	0.973050i	$0.425934\pi$
$588$	38.8030	+	20.7234i	1.60021	+	0.854618i
$589$	−16.4084	−	9.47339i	−0.676096	−	0.390344i
$590$	−5.27266	+	3.41382i	−0.217072	+	0.140545i
$591$	6.32627	−	10.9574i	0.260228	−	0.450728i
$592$	6.14884	+	1.21867i	0.252716	+	0.0500868i
$593$	−5.59820	+	5.59820i	−0.229891	+	0.229891i	−0.812647	−	0.582756i	$-0.801974\pi$
$593$	−5.59820	+	5.59820i	−0.229891	+	0.229891i	0.582756	+	0.812647i	$0.301974\pi$
$594$	−35.2425	+	47.5362i	−1.44602	+	1.95043i
$595$	−0.656087	−	1.44139i	−0.0268969	−	0.0590911i
$596$	−0.110521	+	0.0335678i	−0.00452711	+	0.00137499i
$597$	5.00250	−	5.00250i	0.204739	−	0.204739i
$598$	−3.90806	+	4.43724i	−0.159813	+	0.181452i
$599$	13.9664			0.570653			0.285326	−	0.958430i	$-0.407898\pi$
$599$	13.9664			0.570653			0.285326	+	0.958430i	$0.407898\pi$
$600$	−0.552711	+	44.6043i	−0.0225643	+	1.82096i
$601$	−17.0086	−	29.4598i	−0.693797	−	1.20169i	−0.970585	−	0.240760i	$-0.922603\pi$
$601$	−17.0086	−	29.4598i	−0.693797	−	1.20169i	0.276788	−	0.960931i	$-0.410730\pi$
$602$	0.723746	−	0.107485i	0.0294977	−	0.00438077i
$603$	−27.7358	−	27.7358i	−1.12949	−	1.12949i
$604$	−22.8438	−	21.3807i	−0.929500	−	0.869970i
$605$	−0.515344	−	0.367945i	−0.0209517	−	0.0149591i
$606$	−3.17824	+	27.6691i	−0.129107	+	1.12398i
$607$	7.35319	−	1.97028i	0.298457	−	0.0799712i	−0.106483	−	0.994314i	$-0.533959\pi$
$607$	7.35319	−	1.97028i	0.298457	−	0.0799712i	0.404940	+	0.914343i	$0.367292\pi$
$608$	−8.60484	+	7.81252i	−0.348972	+	0.316839i
$609$	−0.198041	−	0.343017i	−0.00802501	−	0.0138997i
$610$	−2.72879	−	4.21463i	−0.110485	−	0.170645i
$611$	−13.8754	−	16.4304i	−0.561338	−	0.664704i
$612$	51.0134	−	31.7466i	2.06209	−	1.28328i
$613$	−26.7684	−	7.17258i	−1.08117	−	0.289698i	−0.326093	−	0.945338i	$-0.605732\pi$
$613$	−26.7684	−	7.17258i	−1.08117	−	0.289698i	−0.755074	+	0.655640i	$0.772399\pi$
$614$	−13.9966	+	6.07063i	−0.564858	+	0.244991i
$615$	9.86981	+	59.1449i	0.397989	+	2.38495i
$616$	1.46577	+	0.523605i	0.0590576	+	0.0210967i
$617$	32.5157	−	8.71256i	1.30903	−	0.350754i	0.464175	−	0.885744i	$-0.346351\pi$
$617$	32.5157	−	8.71256i	1.30903	−	0.350754i	0.844859	+	0.534989i	$0.179684\pi$
$618$	61.3630	−	9.11317i	2.46838	−	0.366586i
$619$			26.6411i			1.07080i	0.844599	+	0.535399i	$0.179839\pi$
$619$			26.6411i			1.07080i	−0.844599	+	0.535399i	$0.820161\pi$
$620$	−30.9504	+	27.2564i	−1.24300	+	1.09464i
$621$	−7.22257	−	12.5099i	−0.289832	−	0.502003i
$622$	−8.35890	+	21.1633i	−0.335161	+	0.848571i
$623$	0.911872	−	0.911872i	0.0365334	−	0.0365334i
$624$	−43.7224	−	12.5616i	−1.75030	−	0.502868i
$625$	23.1625	+	9.40732i	0.926501	+	0.376293i
$626$	−9.24676	−	21.3196i	−0.369575	−	0.852103i
$627$	−5.63412	+	21.0268i	−0.225005	+	0.839730i
$628$	−21.9455	+	0.726009i	−0.875722	+	0.0289709i
$629$	−6.77482			−0.270130
$630$	−2.67214	−	2.41265i	−0.106460	−	0.0961224i
$631$	18.1187	−	31.3825i	0.721295	−	1.24932i	−0.239186	−	0.970974i	$-0.576881\pi$
$631$	18.1187	−	31.3825i	0.721295	−	1.24932i	0.960481	−	0.278345i	$-0.0897860\pi$
$632$	−7.66687	−	16.1885i	−0.304972	−	0.643945i
$633$	45.2798	−	12.1327i	1.79971	−	0.482230i
$634$	4.20190	+	9.68803i	0.166879	+	0.384761i
$635$	31.4706	+	11.7827i	1.24887	+	0.467582i
$636$	17.4530	−	74.9688i	0.692055	−	2.97270i
$637$	10.6974	+	22.7528i	0.423846	+	0.901499i
$638$	2.26404	+	2.85165i	0.0896340	+	0.112898i
$639$	−53.8175	+	31.0715i	−2.12899	+	1.22917i
$640$	10.1304	+	23.1813i	0.400440	+	0.916323i
$641$	−0.857438	+	1.48513i	−0.0338668	+	0.0586589i	−0.882462	−	0.470384i	$-0.844116\pi$
$641$	−0.857438	+	1.48513i	−0.0338668	+	0.0586589i	0.848595	+	0.529043i	$0.177449\pi$
$642$	54.0921	−	42.9458i	2.13484	−	1.69493i
$643$	−13.2883	+	3.56058i	−0.524039	+	0.140416i	−0.511134	−	0.859501i	$-0.670774\pi$
$643$	−13.2883	+	3.56058i	−0.524039	+	0.140416i	−0.0129046	+	0.999917i	$0.504108\pi$
$644$	−0.259635	+	0.277401i	−0.0102310	+	0.0109311i
$645$	22.1708	+	2.14498i	0.872974	+	0.0844586i
$646$	7.48097	−	10.0906i	0.294335	−	0.397008i
$647$	1.11465	−	4.15992i	0.0438213	−	0.163543i	−0.940548	−	0.339662i	$-0.889687\pi$
$647$	1.11465	−	4.15992i	0.0438213	−	0.163543i	0.984369	+	0.176118i	$0.0563541\pi$
$648$	29.6669	−	42.9119i	1.16543	−	1.68574i
$649$			6.67217i			0.261906i
$650$	−15.4935	+	20.2472i	−0.607707	+	0.794161i
$651$		−	4.76537i		−	0.186770i
$652$	11.5951	+	6.19256i	0.454099	+	0.242519i
$653$	2.65151	−	9.89557i	0.103762	−	0.387243i	−0.894440	−	0.447188i	$-0.852426\pi$
$653$	2.65151	−	9.89557i	0.103762	−	0.387243i	0.998202	+	0.0599442i	$0.0190923\pi$
$654$	36.5181	+	27.0739i	1.42797	+	1.05867i
$655$	−4.89072	−	0.473168i	−0.191096	−	0.0184882i
$656$	18.9125	+	28.2623i	0.738409	+	1.10346i
$657$	−86.0995	+	23.0703i	−3.35906	+	0.900058i
$658$	−0.859261	−	1.08228i	−0.0334975	−	0.0421915i
$659$	−5.49476	+	9.51720i	−0.214045	+	0.370737i	−0.952977	−	0.303043i	$-0.901997\pi$
$659$	−5.49476	+	9.51720i	−0.214045	+	0.370737i	0.738932	+	0.673781i	$0.235331\pi$
$660$	39.4523	+	26.2431i	1.53568	+	1.02151i
$661$	−7.87543	+	4.54688i	−0.306319	+	0.176853i	−0.645278	−	0.763948i	$-0.723258\pi$
$661$	−7.87543	+	4.54688i	−0.306319	+	0.176853i	0.338959	+	0.940801i	$0.389925\pi$
$662$	23.0152	−	18.2727i	0.894513	−	0.710187i
$663$	48.9922	+	4.13048i	1.90270	+	0.160415i
$664$	−9.07083	+	25.3927i	−0.352016	+	0.985429i
$665$	−0.704858	−	0.263901i	−0.0273332	−	0.0102336i
$666$	−14.1294	+	6.12821i	−0.547503	+	0.237463i
$667$	−0.858539	+	0.230045i	−0.0332428	+	0.00890737i
$668$	18.6884	+	30.0303i	0.723078	+	1.16191i
$669$	2.24951	−	3.89627i	0.0869711	−	0.150638i
$670$	−11.9616	+	13.2481i	−0.462118	+	0.511819i
$671$	−5.33331			−0.205890
$672$	−2.78382	−	0.891805i	−0.107388	−	0.0344021i
$673$	8.78429	−	32.7834i	0.338609	−	1.26371i	−0.561293	−	0.827617i	$-0.689696\pi$
$673$	8.78429	−	32.7834i	0.338609	−	1.26371i	0.899903	−	0.436091i	$-0.143637\pi$
$674$	39.8998	−	17.3054i	1.53688	−	0.666579i
$675$	−34.7821	−	51.6679i	−1.33876	−	1.98870i
$676$	−15.7400	−	20.6943i	−0.605384	−	0.795933i
$677$	16.8240	−	16.8240i	0.646600	−	0.646600i	−0.305570	−	0.952170i	$-0.598847\pi$
$677$	16.8240	−	16.8240i	0.646600	−	0.646600i	0.952170	+	0.305570i	$0.0988469\pi$
$678$	27.2978	+	10.7818i	1.04836	+	0.414074i
$679$	−1.22244	−	2.11733i	−0.0469130	−	0.0812557i
$680$	−15.6107	−	22.4474i	−0.598643	−	0.860817i
$681$			61.0289i			2.33863i
$682$	6.43536	+	43.3322i	0.246423	+	1.65927i
$683$	1.44830	−	0.388072i	0.0554178	−	0.0148492i	−0.231004	−	0.972953i	$-0.574201\pi$
$683$	1.44830	−	0.388072i	0.0554178	−	0.0148492i	0.286421	+	0.958104i	$0.407534\pi$
$684$	6.47462	−	27.8116i	0.247563	−	1.06340i
$685$	1.92475	+	11.5341i	0.0735410	+	0.440695i
$686$	1.28818	+	2.97006i	0.0491828	+	0.113397i
$687$	−21.3749	−	5.72737i	−0.815502	−	0.218513i
$688$	11.9591	−	4.06879i	0.455938	−	0.155121i
$689$	33.6115	−	28.3847i	1.28050	−	1.08137i
$690$	−9.70923	+	6.28631i	−0.369624	+	0.239316i
$691$	−10.9649	−	18.9917i	−0.417124	−	0.722480i	0.578525	−	0.815665i	$-0.303628\pi$
$691$	−10.9649	−	18.9917i	−0.417124	−	0.722480i	−0.995649	+	0.0931851i	$0.970295\pi$
$692$	−4.78234	−	2.55409i	−0.181797	−	0.0970920i
$693$	−3.69388	+	0.989771i	−0.140319	+	0.0375983i
$694$	49.2517	+	5.65734i	1.86957	+	0.214750i
$695$	−7.63693	−	5.45262i	−0.289685	−	0.206829i
$696$	−4.42675	−	5.21206i	−0.167795	−	0.197563i
$697$	−25.9887	−	25.9887i	−0.984393	−	0.984393i
$698$	−3.46406	−	23.3251i	−0.131117	−	0.882866i
$699$	5.08973	+	8.81567i	0.192511	+	0.333439i
$700$	−1.03449	+	1.27034i	−0.0390999	+	0.0480142i
$701$	−10.0746			−0.380511			−0.190256	−	0.981735i	$-0.560932\pi$
$701$	−10.0746			−0.380511			−0.190256	+	0.981735i	$0.560932\pi$
$702$	60.1904	−	20.2893i	2.27174	−	0.765771i
$703$	−2.27668	+	2.27668i	−0.0858668	+	0.0858668i
$704$	26.5180	+	4.34992i	0.999433	+	0.163944i
$705$	−17.4281	−	38.2887i	−0.656382	−	1.44204i
$706$	7.08211	+	5.25055i	0.266539	+	0.197607i
$707$	−0.723271	+	0.723271i	−0.0272014	+	0.0272014i
$708$	−0.414319	−	12.5239i	−0.0155711	−	0.470676i
$709$	11.8760	−	20.5697i	0.446011	−	0.772513i	−0.552111	−	0.833770i	$-0.686178\pi$
$709$	11.8760	−	20.5697i	0.446011	−	0.772513i	0.998122	+	0.0612572i	$0.0195110\pi$
$710$	15.3689	+	23.7374i	0.576786	+	0.890848i
$711$	38.1131	+	22.0046i	1.42935	+	0.825237i
$712$	12.6611	−	18.3138i	0.474496	−	0.686338i
$713$	−10.3293	−	2.76774i	−0.386836	−	0.103653i
$714$	3.13868	+	0.360527i	0.117462	+	0.0134924i
$715$	9.10892	+	25.5036i	0.340654	+	0.953781i
$716$	−8.66743	+	37.2307i	−0.323917	+	1.39138i
$717$	−17.4093	+	64.9723i	−0.650161	+	2.42643i
$718$	−7.87423	+	19.9362i	−0.293864	+	0.744012i
$719$	6.07419	−	10.5208i	0.226529	−	0.392360i	−0.730248	−	0.683182i	$-0.760596\pi$
$719$	6.07419	−	10.5208i	0.226529	−	0.392360i	0.956777	+	0.290822i	$0.0939289\pi$
$720$	−52.8622	−	32.6949i	−1.97006	−	1.21847i
$721$	1.97310	+	1.13917i	0.0734821	+	0.0424249i
$722$	3.07029	+	20.6736i	0.114264	+	0.769392i
$723$	−15.8288	−	15.8288i	−0.588678	−	0.588678i
$724$	−13.1501	−	12.3079i	−0.488719	−	0.457419i
$725$	−3.62477	+	1.24442i	−0.134621	+	0.0462167i
$726$	1.15891	−	0.502642i	0.0430111	−	0.0186548i
$727$	27.0352	+	27.0352i	1.00268	+	1.00268i	0.999996	+	0.00268440i	$0.000854473\pi$
$727$	27.0352	+	27.0352i	1.00268	+	1.00268i	0.00268440	+	0.999996i	$0.499146\pi$
$728$	−0.970733	−	1.35976i	−0.0359778	−	0.0503961i
$729$			10.2981i			0.381412i
$730$	12.4814	+	38.5939i	0.461956	+	1.42842i
$731$	−11.8237	+	6.82641i	−0.437315	+	0.252484i
$732$	10.0108	−	0.331180i	0.370010	−	0.0122408i
$733$	18.5471	−	18.5471i	0.685053	−	0.685053i	−0.276082	−	0.961134i	$-0.589036\pi$
$733$	18.5471	−	18.5471i	0.685053	−	0.685053i	0.961134	+	0.276082i	$0.0890360\pi$
$734$	−25.8294	+	34.8395i	−0.953381	+	1.28595i
$735$	8.09538	+	48.5116i	0.298602	+	1.78938i
$736$	−3.54991	+	5.51619i	−0.130851	+	0.203329i
$737$	4.90716	+	18.3138i	0.180758	+	0.674596i
$738$	−77.7097	−	30.6931i	−2.86053	−	1.12983i
$739$	23.6085	−	13.6304i	0.868451	−	0.501401i	0.00161807	−	0.999999i	$-0.499485\pi$
$739$	23.6085	−	13.6304i	0.868451	−	0.501401i	0.866833	+	0.498598i	$0.166152\pi$
$740$	3.11272	+	6.27914i	0.114426	+	0.230826i
$741$	17.8519	−	15.0758i	0.655807	−	0.553825i
$742$	2.21400	−	1.75778i	0.0812784	−	0.0645300i
$743$	−8.94853	+	33.3964i	−0.328290	+	1.22519i	0.582674	+	0.812706i	$0.302007\pi$
$743$	−8.94853	+	33.3964i	−0.328290	+	1.22519i	−0.910963	+	0.412487i	$0.864660\pi$
$744$	−14.7702	−	80.9363i	−0.541501	−	2.96727i
$745$	−0.105100	−	0.0750396i	−0.00385058	−	0.00274924i
$746$	20.3050	+	2.33235i	0.743420	+	0.0853935i
$747$	−17.1466	−	63.9919i	−0.627361	−	2.34134i
$748$	−29.0273	+	0.960290i	−1.06134	+	0.0351117i
$749$	2.53657			0.0926842
$750$	−39.8987	+	29.9233i	−1.45690	+	1.09264i
$751$	−9.18463	+	5.30275i	−0.335152	+	0.193500i	−0.658126	−	0.752908i	$-0.728651\pi$
$751$	−9.18463	+	5.30275i	−0.335152	+	0.193500i	0.322974	+	0.946408i	$0.395317\pi$
$752$	−17.9484	−	15.7184i	−0.654511	−	0.573191i
$753$	13.4633	+	13.4633i	0.490628	+	0.490628i
$754$	−0.247329	−	3.90050i	−0.00900719	−	0.142048i
$755$	3.36868	−	34.8191i	0.122599	−	1.26720i
$756$	3.90539	−	1.18616i	0.142038	−	0.0431402i
$757$	16.7429	+	4.48624i	0.608530	+	0.163055i	0.549908	−	0.835225i	$-0.314663\pi$
$757$	16.7429	+	4.48624i	0.608530	+	0.163055i	0.0586216	+	0.998280i	$0.481329\pi$
$758$	−21.3731	+	3.17418i	−0.776308	+	0.115291i
$759$			12.2863i			0.445966i
$760$	−12.7895	−	2.29747i	−0.463922	−	0.0833380i
$761$	−4.45299	−	2.57093i	−0.161421	−	0.0931963i	0.417114	−	0.908854i	$-0.363042\pi$
$761$	−4.45299	−	2.57093i	−0.161421	−	0.0931963i	−0.578534	+	0.815658i	$0.696375\pi$
$762$	−52.5022	+	41.6835i	−1.90196	+	1.51003i
$763$	0.432111	+	1.61266i	0.0156435	+	0.0583822i
$764$	−0.321230	−	1.05764i	−0.0116217	−	0.0382640i
$765$	62.9122	+	23.5545i	2.27460	+	0.851616i
$766$	2.89332	+	0.332343i	0.104540	+	0.0120080i
$767$	4.08931	−	5.87955i	0.147656	−	0.212298i
$768$	−50.0452	−	6.51826i	−1.80585	−	0.235207i
$769$	−2.73010	−	4.72867i	−0.0984498	−	0.170520i	0.812593	−	0.582831i	$-0.198055\pi$
$769$	−2.73010	−	4.72867i	−0.0984498	−	0.170520i	−0.911043	+	0.412311i	$0.864722\pi$
$770$	0.535480	+	1.65577i	0.0192974	+	0.0596698i
$771$	54.6869	+	31.5735i	1.96950	+	1.13709i
$772$	11.7679	+	18.9097i	0.423536	+	0.680577i
$773$	1.64450	+	6.13736i	0.0591486	+	0.220745i	0.989173	−	0.146751i	$-0.0468816\pi$
$773$	1.64450	+	6.13736i	0.0591486	+	0.220745i	−0.930025	+	0.367497i	$0.880215\pi$
$774$	−18.4843	+	24.9322i	−0.664404	+	0.896169i
$775$	−45.2539	−	8.83920i	−1.62557	−	0.317514i
$776$	−27.3249	−	32.1724i	−0.980907	−	1.15492i
$777$	−0.782209	−	0.209592i	−0.0280616	−	0.00751908i
$778$	15.9678	−	40.4277i	0.572472	−	1.44940i
$779$	−17.4671			−0.625822
$780$	−18.6814	−	47.3055i	−0.668903	−	1.69381i
$781$	30.0380			1.07484
$782$	2.60442	−	6.59395i	0.0931339	−	0.235799i
$783$	9.22271	+	2.47122i	0.329593	+	0.0883141i
$784$	15.5123	+	23.1812i	0.554012	+	0.827899i
$785$	−15.6066	−	18.9499i	−0.557025	−	0.676351i
$786$	5.83777	−	7.87416i	0.208226	−	0.280862i
$787$	6.31029	+	23.5503i	0.224938	+	0.839479i	0.982429	+	0.186634i	$0.0597579\pi$
$787$	6.31029	+	23.5503i	0.224938	+	0.839479i	−0.757492	+	0.652845i	$0.773575\pi$
$788$	6.81131	−	4.23880i	0.242643	−	0.151001i
$789$	−47.9954	−	27.7101i	−1.70868	−	0.986507i
$790$	9.11634	−	17.8313i	0.324345	−	0.634408i
$791$	0.538953	+	0.933494i	0.0191630	+	0.0331912i
$792$	−59.6700	+	28.2596i	−2.12028	+	1.00416i
$793$	4.69974	+	3.26873i	0.166893	+	0.116076i
$794$	12.1512	+	1.39576i	0.431230	+	0.0495335i
$795$	78.3266	−	35.6525i	2.77796	−	1.26446i
$796$	4.29216	−	1.30363i	0.152132	−	0.0462060i
$797$	−8.06689	−	30.1060i	−0.285744	−	1.06641i	−0.948294	−	0.317393i	$-0.897193\pi$
$797$	−8.06689	−	30.1060i	−0.285744	−	1.06641i	0.662550	−	0.749017i	$-0.269474\pi$
$798$	1.17591	−	0.933601i	0.0416268	−	0.0330491i
$799$	22.3309	+	12.8928i	0.790011	+	0.456113i
$800$	−13.6326	+	24.7821i	−0.481985	+	0.876179i
$801$			54.7019i			1.93280i
$802$	22.9116	−	3.40265i	0.809036	−	0.120152i
$803$	41.6177	+	11.1514i	1.46866	+	0.393526i
$804$	−10.3481	−	34.0708i	−0.364950	−	1.20159i
$805$	−0.422822	−	0.0409073i	−0.0149025	−	0.00144179i
$806$	20.8870	−	42.1287i	0.735713	−	1.48392i
$807$	14.5742	+	14.5742i	0.513035	+	0.513035i
$808$	−10.0425	+	14.5260i	−0.353292	+	0.511022i
$809$	−15.0899	+	8.71214i	−0.530531	+	0.306302i	−0.741233	−	0.671248i	$-0.765759\pi$
$809$	−15.0899	+	8.71214i	−0.530531	+	0.306302i	0.210701	+	0.977550i	$0.432425\pi$
$810$	58.2504	−	2.97258i	2.04671	−	0.104446i
$811$	−29.7766			−1.04560			−0.522798	−	0.852457i	$-0.675112\pi$
$811$	−29.7766			−1.04560			−0.522798	+	0.852457i	$0.675112\pi$
$812$	−0.00830382	−	0.251005i	−0.000291407	−	0.00880854i
$813$	−2.25659	−	8.42171i	−0.0791420	−	0.295362i
$814$	7.39578	+	0.849522i	0.259222	+	0.0297757i
$815$	2.41906	+	14.4962i	0.0847360	+	0.507781i
$816$	54.4256	−	3.60499i	1.90528	−	0.126200i
$817$	−1.67934	+	6.26738i	−0.0587527	+	0.219268i
$818$	−19.1534	+	15.2066i	−0.669683	+	0.531687i
$819$	3.86168	+	1.39175i	0.134938	+	0.0486317i
$820$	−12.1466	+	36.0279i	−0.424178	+	1.25815i
$821$	22.7382	−	13.1279i	0.793569	−	0.458168i	−0.0476482	−	0.998864i	$-0.515173\pi$
$821$	22.7382	−	13.1279i	0.793569	−	0.458168i	0.841218	+	0.540697i	$0.181839\pi$
$822$	−21.6967	−	8.56957i	−0.756759	−	0.298898i
$823$	9.76939	+	36.4599i	0.340540	+	1.27091i	0.897737	+	0.440531i	$0.145210\pi$
$823$	9.76939	+	36.4599i	0.340540	+	1.27091i	−0.557198	+	0.830380i	$0.688123\pi$
$824$	37.0425	+	13.2324i	1.29044	+	0.460971i
$825$	3.64736	+	52.8505i	0.126985	+	1.84002i
$826$	0.274080	−	0.369687i	0.00953645	−	0.0128631i
$827$	22.3365	−	22.3365i	0.776715	−	0.776715i	−0.202556	−	0.979271i	$-0.564925\pi$
$827$	22.3365	−	22.3365i	0.776715	−	0.776715i	0.979271	+	0.202556i	$0.0649248\pi$
$828$	−0.532891	−	16.1080i	−0.0185192	−	0.559792i
$829$	5.14191	−	2.96868i	0.178586	−	0.103107i	−0.408042	−	0.912963i	$-0.633788\pi$
$829$	5.14191	−	2.96868i	0.178586	−	0.103107i	0.586628	+	0.809856i	$0.300455\pi$
$830$	−28.6842	+	9.27654i	−0.995643	+	0.321994i
$831$			64.1517i			2.22540i
$832$	−20.7017	−	20.0858i	−0.717704	−	0.696349i
$833$	−21.3164	−	21.3164i	−0.738568	−	0.738568i
$834$	17.1739	−	7.44870i	0.594685	−	0.257928i
$835$	−13.8660	+	37.0349i	−0.479852	+	1.28165i
$836$	−9.43195	+	10.0774i	−0.326211	+	0.348533i
$837$	81.2291	+	81.2291i	2.80769	+	2.80769i
$838$	−3.08333	−	20.7614i	−0.106512	−	0.717190i
$839$	−36.2372	−	20.9215i	−1.25105	−	0.722292i	−0.279729	−	0.960079i	$-0.590245\pi$
$839$	−36.2372	−	20.9215i	−1.25105	−	0.722292i	−0.971317	+	0.237787i	$0.923578\pi$
$840$	−1.10793	−	3.07468i	−0.0382273	−	0.106087i
$841$	−14.2062	+	24.6059i	−0.489871	+	0.848481i
$842$	−12.2188	+	30.9359i	−0.421087	+	1.06612i
$843$	1.95583	−	7.29924i	0.0673622	−	0.251399i
$844$	28.9490	+	6.73943i	0.996467	+	0.231981i
$845$	7.60409	−	28.0567i	0.261589	−	0.965179i
$846$	58.2350	+	6.68921i	2.00216	+	0.229980i
$847$	0.0448121	+	0.0120074i	0.00153976	+	0.000412578i
$848$	32.1549	−	36.7168i	1.10420	−	1.26086i
$849$	−4.14055	−	2.39055i	−0.142103	−	0.0820435i
$850$	9.24559	−	29.1375i	0.317121	−	0.999407i
$851$	−0.908617	+	1.57377i	−0.0311470	+	0.0539482i
$852$	−56.3823	+	1.86526i	−1.93162	+	0.0639026i
$853$	−12.3949	+	12.3949i	−0.424395	+	0.424395i	−0.886714	−	0.462319i	$-0.847018\pi$
$853$	−12.3949	+	12.3949i	−0.424395	+	0.424395i	0.462319	+	0.886714i	$0.347018\pi$
$854$	0.295504	+	0.219082i	0.0101120	+	0.00749683i
$855$	29.0572	−	13.2262i	0.993737	−	0.452326i
$856$	43.0818	−	7.86205i	1.47250	−	0.268719i
$857$	−37.7415	+	37.7415i	−1.28923	+	1.28923i	−0.353969	+	0.935257i	$0.615168\pi$
$857$	−37.7415	+	37.7415i	−1.28923	+	1.28923i	−0.935257	+	0.353969i	$0.884832\pi$
$858$	−52.9648	−	10.6524i	−1.80819	−	0.363667i
$859$	−44.0614			−1.50335			−0.751677	−	0.659531i	$-0.770755\pi$
$859$	−44.0614			−1.50335			−0.751677	+	0.659531i	$0.770755\pi$
$860$	11.7594	+	7.82218i	0.400992	+	0.266734i
$861$	−2.19660	−	3.80462i	−0.0748600	−	0.129661i
$862$	−5.59723	−	37.6886i	−0.190642	−	1.28368i
$863$	27.0922	+	27.0922i	0.922229	+	0.922229i	0.997187	−	0.0749581i	$-0.0238823\pi$
$863$	27.0922	+	27.0922i	0.922229	+	0.922229i	−0.0749581	+	0.997187i	$0.523882\pi$
$864$	62.6536	−	32.2507i	2.13152	−	1.09719i
$865$	−0.997730	−	5.97890i	−0.0339238	−	0.203289i
$866$	−34.5876	−	3.97294i	−1.17534	−	0.135006i
$867$	−5.14739	+	1.37924i	−0.174815	+	0.0468414i
$868$	1.42343	−	2.66527i	0.0483145	−	0.0904652i
$869$	−10.6363	−	18.4226i	−0.360812	−	0.624945i
$870$	1.59983	−	7.47614i	0.0542394	−	0.253465i
$871$	6.90012	−	19.1457i	0.233802	−	0.648729i
$872$	12.3375	+	26.0505i	0.417800	+	0.882182i
$873$	100.174	+	26.8416i	3.39038	+	0.908450i
$874$	−1.34068	−	3.09112i	−0.0453493	−	0.104559i
$875$	−1.83094	−	0.0504450i	−0.0618972	−	0.00170535i
$876$	−78.8103	−	18.3473i	−2.66275	−	0.619897i
$877$	11.0734	−	2.96711i	0.373922	−	0.100192i	−0.0669636	−	0.997755i	$-0.521331\pi$
$877$	11.0734	−	2.96711i	0.373922	−	0.100192i	0.440885	+	0.897563i	$0.354664\pi$
$878$	0.345441	+	2.32601i	0.0116581	+	0.0784989i
$879$			45.3381i			1.52922i
$880$	14.2268	+	26.4623i	0.479584	+	0.892044i
$881$	9.11153	+	15.7816i	0.306975	+	0.531696i	0.977699	−	0.210011i	$-0.0673498\pi$
$881$	9.11153	+	15.7816i	0.306975	+	0.531696i	−0.670724	+	0.741707i	$0.734016\pi$
$882$	−63.7387	−	25.1750i	−2.14619	−	0.847686i
$883$	22.5334	−	22.5334i	0.758309	−	0.758309i	−0.217706	−	0.976014i	$-0.569857\pi$
$883$	22.5334	−	22.5334i	0.758309	−	0.758309i	0.976014	+	0.217706i	$0.0698573\pi$
$884$	26.1676	+	16.9443i	0.880110	+	0.569900i
$885$	10.8143	−	8.90640i	0.363520	−	0.299385i
$886$	−34.0827	+	14.7824i	−1.14503	+	0.496623i
$887$	9.29347	−	34.6837i	0.312044	−	1.16457i	−0.614666	−	0.788788i	$-0.710709\pi$
$887$	9.29347	−	34.6837i	0.312044	−	1.16457i	0.926710	−	0.375777i	$-0.122624\pi$
$888$	−13.9349	−	1.13533i	−0.467624	−	0.0380991i
$889$	−2.46202			−0.0825734
$890$	24.8599	−	1.26863i	0.833306	−	0.0425245i
$891$	30.9777	−	53.6550i	1.03779	−	1.79751i
$892$	2.42198	−	1.50724i	0.0810939	−	0.0504663i
$893$	11.8369	−	3.17170i	0.396108	−	0.106137i
$894$	0.236350	−	0.102510i	0.00790473	−	0.00342845i
$895$	−38.8983	+	17.7056i	−1.30023	+	0.591833i
$896$	−1.29060	−	1.33032i	−0.0431160	−	0.0444430i
$897$	7.53018	−	10.8268i	0.251425	−	0.361496i
$898$	24.9168	−	19.7824i	0.831483	−	0.660146i
$899$	6.12142	−	3.53420i	0.204161	−	0.117872i
$900$	−7.07414	−	69.1315i	−0.235805	−	2.30438i
$901$	−26.3745	+	45.6820i	−0.878662	+	1.52189i
$902$	25.1119	+	31.6296i	0.836136	+	1.05315i
$903$	−1.57633	+	0.422377i	−0.0524570	+	0.0140558i
$904$	12.0471	+	14.1842i	0.400679	+	0.471760i
$905$	1.93919	−	20.0437i	0.0644609	−	0.666276i
$906$	56.0595	+	41.5616i	1.86245	+	1.38079i
$907$	−1.12659	+	4.20448i	−0.0374077	+	0.139607i	−0.982104	−	0.188339i	$-0.939690\pi$
$907$	−1.12659	+	4.20448i	−0.0374077	+	0.139607i	0.944696	+	0.327946i	$0.106356\pi$
$908$	−18.2296	+	34.1335i	−0.604969	+	1.13276i
$909$		−	43.3880i		−	1.43909i
$910$	0.542938	−	1.78726i	0.0179982	−	0.0592472i
$911$		−	5.66695i		−	0.187754i	−0.995584	−	0.0938772i	$-0.970074\pi$
$911$		−	5.66695i		−	0.187754i	0.995584	−	0.0938772i	$-0.0299261\pi$
$912$	17.0783	−	19.5012i	0.565519	−	0.645750i
$913$	−8.28811	+	30.9316i	−0.274296	+	1.02369i
$914$	−9.90870	+	13.3652i	−0.327751	+	0.442080i
$915$	7.11921	+	8.64430i	0.235354	+	0.285772i
$916$	−10.2442	−	9.58807i	−0.338477	−	0.316799i
$917$	0.347727	−	0.0931733i	0.0114830	−	0.00307685i
$918$	−59.6465	+	47.3556i	−1.96863	+	1.56297i
$919$	29.0439	−	50.3054i	0.958069	−	1.65942i	0.230884	−	0.972981i	$-0.425838\pi$
$919$	29.0439	−	50.3054i	0.958069	−	1.65942i	0.727184	−	0.686442i	$-0.240829\pi$
$920$	−7.30812	+	0.615750i	−0.240941	+	0.0203007i
$921$	29.4689	−	17.0139i	0.971032	−	0.560626i
$922$	0.249439	+	0.314180i	0.00821485	+	0.0103470i
$923$	−26.4696	−	18.4100i	−0.871258	−	0.605972i
$924$	−3.38115	−	0.787143i	−0.111232	−	0.0258951i
$925$	−3.44128	+	7.03942i	−0.113149	+	0.231455i
$926$	−7.79015	−	17.9612i	−0.256000	−	0.590241i
$927$	−93.3503	+	25.0131i	−3.06603	+	0.821539i
$928$	−0.919018	−	4.23739i	−0.0301682	−	0.139099i
$929$	−18.9298	+	32.7874i	−0.621068	+	1.07572i	0.368219	+	0.929739i	$0.379968\pi$
$929$	−18.9298	+	32.7874i	−0.621068	+	1.07572i	−0.989287	+	0.145982i	$0.953366\pi$
$930$	61.6431	−	68.2728i	2.02136	−	2.23875i
$931$	−14.3268			−0.469541
$932$	0.213412	+	6.45093i	0.00699053	+	0.211307i
$933$	13.1353	−	49.0215i	0.430030	−	1.60489i
$934$	6.35704	+	14.6570i	0.208009	+	0.479591i
$935$	−20.6429	−	25.0650i	−0.675094	−	0.819714i
$936$	69.9015	+	11.6686i	2.28480	+	0.381401i
$937$	15.3936	−	15.3936i	0.502888	−	0.502888i	−0.409446	−	0.912334i	$-0.634278\pi$
$937$	15.3936	−	15.3936i	0.502888	−	0.502888i	0.912334	+	0.409446i	$0.134278\pi$
$938$	0.480401	−	1.21629i	0.0156857	−	0.0397134i
$939$	25.9154	+	44.8869i	0.845718	+	1.46483i
$940$	1.68942	−	26.6207i	0.0551029	−	0.868272i
$941$		−	45.4266i		−	1.48087i	−0.672131	−	0.740433i	$-0.734621\pi$
$941$		−	45.4266i		−	1.48087i	0.672131	−	0.740433i	$-0.265379\pi$
$942$	48.4425	−	7.19431i	1.57834	−	0.234403i
$943$	−9.52262	+	2.55158i	−0.310099	+	0.0830909i
$944$	3.50920	−	7.12837i	0.114215	−	0.232009i
$945$	3.71385	+	2.65162i	0.120812	+	0.0862571i
$946$	13.7634	−	5.96948i	0.447487	−	0.194084i
$947$	−37.2065	−	9.96946i	−1.20905	−	0.323964i	−0.402661	−	0.915349i	$-0.631915\pi$
$947$	−37.2065	−	9.96946i	−1.20905	−	0.323964i	−0.806389	+	0.591385i	$0.798581\pi$
$948$	21.1087	+	33.9194i	0.685579	+	1.10165i
$949$	−29.8391	−	35.3338i	−0.968620	−	1.14698i
$950$	−6.68468	−	12.8987i	−0.216880	−	0.418488i
$951$	−11.7765	−	20.3974i	−0.381878	−	0.661432i
$952$	1.64777	+	1.13918i	0.0534046	+	0.0369210i
$953$	−28.8611	+	7.73331i	−0.934903	+	0.250506i	−0.693944	−	0.720029i	$-0.744128\pi$
$953$	−28.8611	+	7.73331i	−0.934903	+	0.250506i	−0.240959	+	0.970535i	$0.577462\pi$
$954$	−13.6840	+	119.130i	−0.443036	+	3.85699i
$955$	0.718098	−	1.00577i	0.0232371	−	0.0325459i
$956$	−29.1445	+	31.1388i	−0.942599	+	1.00710i
$957$	−5.74250	−	5.74250i	−0.185629	−	0.185629i
$958$	−3.78810	+	0.562580i	−0.122388	+	0.0181761i
$959$	−0.428368	−	0.741955i	−0.0138327	−	0.0239590i
$960$	−28.3473	−	48.7872i	−0.914906	−	1.57460i
$961$	54.0420			1.74329
$962$	−5.99653	−	5.28140i	−0.193336	−	0.170279i
$963$	−76.0826	+	76.0826i	−2.45173	+	2.45173i
$964$	−4.12492	−	13.5811i	−0.132855	−	0.437419i
$965$	−8.73124	+	23.3204i	−0.281069	+	0.750711i
$966$	0.504699	−	0.680753i	0.0162384	−	0.0219029i
$967$	2.15476	−	2.15476i	0.0692926	−	0.0692926i	−0.671611	−	0.740904i	$-0.734397\pi$
$967$	2.15476	−	2.15476i	0.0692926	−	0.0692926i	0.740904	+	0.671611i	$0.234397\pi$
$968$	0.798317	+	0.0650420i	0.0256589	+	0.00209053i
$969$	−14.0082	+	24.2629i	−0.450008	+	0.779437i
$970$	9.87526	−	46.1478i	0.317075	−	1.48172i
$971$	32.1864	+	18.5828i	1.03291	+	0.596352i	0.917818	−	0.397003i	$-0.129950\pi$
$971$	32.1864	+	18.5828i	1.03291	+	0.596352i	0.115094	+	0.993355i	$0.463283\pi$
$972$	−19.6043	+	36.7075i	−0.628807	+	1.17739i
$973$	0.664075	+	0.177938i	0.0212893	+	0.00570445i
$974$	−1.57015	+	13.6695i	−0.0503110	+	0.437998i
$975$	29.1775	−	48.8076i	0.934428	−	1.56309i
$976$	5.69796	+	2.80503i	0.182387	+	0.0897869i
$977$	9.05993	−	33.8121i	0.289853	−	1.08175i	−0.655367	−	0.755311i	$-0.727486\pi$
$977$	9.05993	−	33.8121i	0.289853	−	1.08175i	0.945220	−	0.326435i	$-0.105847\pi$
$978$	−27.2688	−	10.7704i	−0.871959	−	0.344399i
$979$	13.2206	−	22.8987i	0.422531	−	0.731845i
$980$	−9.96285	+	29.5507i	−0.318252	+	0.943961i
$981$	−61.3315	−	35.4097i	−1.95816	−	1.13055i
$982$	2.26938	−	0.337032i	0.0724189	−	0.0107551i
$983$	−0.544366	−	0.544366i	−0.0173626	−	0.0173626i	0.698372	−	0.715735i	$-0.253908\pi$
$983$	−0.544366	−	0.544366i	−0.0173626	−	0.0173626i	−0.715735	+	0.698372i	$0.753908\pi$
$984$	−49.1000	−	57.8104i	−1.56525	−	1.84293i
$985$	8.40004	+	3.14500i	0.267648	+	0.100208i
$986$	1.86466	+	4.29921i	0.0593829	+	0.136915i
$987$	2.17943	+	2.17943i	0.0693719	+	0.0693719i
$988$	14.4878	−	3.09947i	0.460918	−	0.0986073i
$989$			3.66214i			0.116449i
$990$	−65.7250	−	33.6023i	−2.08888	−	1.06795i
$991$	36.3606	−	20.9928i	1.15503	−	0.666858i	0.204923	−	0.978778i	$-0.434306\pi$
$991$	36.3606	−	20.9928i	1.15503	−	0.666858i	0.950108	+	0.311920i	$0.100972\pi$
$992$	15.9150	−	49.6795i	0.505302	−	1.57733i
$993$	−46.3468	+	46.3468i	−1.47077	+	1.47077i
$994$	−1.66432	−	1.23390i	−0.0527891	−	0.0391370i
$995$	4.08166	+	2.91422i	0.129397	+	0.0923871i
$996$	13.6363	−	58.5744i	0.432083	−	1.85600i
$997$	0.338676	+	1.26396i	0.0107260	+	0.0400299i	0.971081	−	0.238749i	$-0.0767372\pi$
$997$	0.338676	+	1.26396i	0.0107260	+	0.0400299i	−0.960355	+	0.278778i	$0.910070\pi$
$998$	−16.3468	+	41.3873i	−0.517448	+	1.31009i
$999$	16.9060	−	9.76067i	0.534881	−	0.308814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.c.23.6	✓	144
4.3	odd	2	inner	260.2.bg.c.23.35	yes	144
5.2	odd	4	inner	260.2.bg.c.127.24	yes	144
13.4	even	6	inner	260.2.bg.c.43.19	yes	144
20.7	even	4	inner	260.2.bg.c.127.19	yes	144
52.43	odd	6	inner	260.2.bg.c.43.24	yes	144
65.17	odd	12	inner	260.2.bg.c.147.35	yes	144
260.147	even	12	inner	260.2.bg.c.147.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.6	✓	144	1.1	even	1	trivial
260.2.bg.c.23.35	yes	144	4.3	odd	2	inner
260.2.bg.c.43.19	yes	144	13.4	even	6	inner
260.2.bg.c.43.24	yes	144	52.43	odd	6	inner
260.2.bg.c.127.19	yes	144	20.7	even	4	inner
260.2.bg.c.127.24	yes	144	5.2	odd	4	inner
260.2.bg.c.147.6	yes	144	260.147	even	12	inner
260.2.bg.c.147.35	yes	144	65.17	odd	12	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31533 - 0.519519i) q^{2} +(3.04677 + 0.816378i) q^{3} +(1.46020 + 1.36668i) q^{4} +(-0.215330 + 2.22568i) q^{5} +(-3.58339 - 2.65666i) q^{6} +(-0.0424015 - 0.158244i) q^{7} +(-1.21063 - 2.55624i) q^{8} +(6.01823 + 3.47463i) q^{9} +(1.43951 - 2.81564i) q^{10} +(-1.67952 - 2.90902i) q^{11} +(3.33316 + 5.35603i) q^{12} +(-0.302905 + 3.59281i) q^{13} +(-0.0264389 + 0.230172i) q^{14} +(-2.47305 + 6.60532i) q^{15} +(0.264369 + 3.99125i) q^{16} +(-1.11891 - 4.17582i) q^{17} +(-6.11084 - 7.69687i) q^{18} +(-1.77930 - 1.02728i) q^{19} +(-3.35621 + 2.95565i) q^{20} -0.516749i q^{21} +(0.697841 + 4.69887i) q^{22} +(-1.12010 - 0.300129i) q^{23} +(-1.60165 - 8.77660i) q^{24} +(-4.90727 - 0.958509i) q^{25} +(2.26495 - 4.56837i) q^{26} +(8.80836 + 8.80836i) q^{27} +(0.154355 - 0.289018i) q^{28} +(0.663797 - 0.383243i) q^{29} +(6.68448 - 7.40340i) q^{30} +9.22182 q^{31} +(1.72580 - 5.38717i) q^{32} +(-2.74225 - 10.2342i) q^{33} +(-0.697682 + 6.07389i) q^{34} +(0.361331 - 0.0602971i) q^{35} +(4.03912 + 13.2986i) q^{36} +(0.405598 - 1.51371i) q^{37} +(1.80668 + 2.27559i) q^{38} +(-3.85597 + 10.6991i) q^{39} +(5.95005 - 2.14404i) q^{40} +(7.36261 - 4.25081i) q^{41} +(-0.268461 + 0.679697i) q^{42} +(-0.817373 - 3.05048i) q^{43} +(1.52326 - 6.54312i) q^{44} +(-9.02930 + 12.6464i) q^{45} +(1.31738 + 0.976680i) q^{46} +(-4.21757 + 4.21757i) q^{47} +(-2.45290 + 12.3762i) q^{48} +(6.03893 - 3.48658i) q^{49} +(5.95672 + 3.81018i) q^{50} -13.6362i q^{51} +(-5.35252 + 4.83224i) q^{52} +(-8.62782 - 8.62782i) q^{53} +(-7.00982 - 16.1620i) q^{54} +(6.83618 - 3.11167i) q^{55} +(-0.353178 + 0.299964i) q^{56} +(-4.58246 - 4.58246i) q^{57} +(-1.07222 + 0.159237i) q^{58} +(-1.72021 - 0.993165i) q^{59} +(-12.6385 + 6.26522i) q^{60} +(0.793873 - 1.37503i) q^{61} +(-12.1298 - 4.79091i) q^{62} +(0.294658 - 1.09968i) q^{63} +(-5.06874 + 6.18934i) q^{64} +(-7.93119 - 1.44781i) q^{65} +(-1.70990 + 14.8861i) q^{66} +(-5.45208 - 1.46088i) q^{67} +(4.07319 - 7.62673i) q^{68} +(-3.16765 - 1.82884i) q^{69} +(-0.506596 - 0.108408i) q^{70} +(-4.47121 + 7.74436i) q^{71} +(1.59612 - 19.5905i) q^{72} +(-9.06992 + 9.06992i) q^{73} +(-1.31990 + 1.78032i) q^{74} +(-14.1688 - 6.92654i) q^{75} +(-1.19417 - 3.93177i) q^{76} +(-0.389122 + 0.389122i) q^{77} +(10.6303 - 12.0697i) q^{78} +6.33294 q^{79} +(-8.94016 - 0.271036i) q^{80} +(9.22218 + 15.9733i) q^{81} +(-11.8927 + 1.76621i) q^{82} +(-6.74106 - 6.74106i) q^{83} +(0.706231 - 0.754557i) q^{84} +(9.53496 - 1.59115i) q^{85} +(-0.509663 + 4.43703i) q^{86} +(2.33531 - 0.625743i) q^{87} +(-5.40287 + 7.81502i) q^{88} +(3.93581 + 6.81702i) q^{89} +(18.4466 - 11.9434i) q^{90} +(0.581385 - 0.104407i) q^{91} +(-1.22538 - 1.96906i) q^{92} +(28.0967 + 7.52850i) q^{93} +(7.73862 - 3.35640i) q^{94} +(2.66953 - 3.73894i) q^{95} +(9.65607 - 15.0045i) q^{96} +(14.4151 - 3.86251i) q^{97} +(-9.75455 + 1.44867i) q^{98} -23.3429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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