LMFDB - Embedded newform 930.2.s.c.769.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (of order $6$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			769.4
Character	$\chi$	$=$	930.769
Dual form			930.2.s.c.439.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.981775 - 2.00901i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.981775 - 2.00901i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.00901 - 0.981775i) q^{10} +(0.0912000 - 0.157963i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(3.35207 + 1.93532i) q^{13} +(-0.386621 - 0.669647i) q^{14} +(-0.154263 - 2.23074i) q^{15} +1.00000 q^{16} +(5.39463 - 3.11459i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-0.298547 - 0.517099i) q^{19} +(-0.981775 + 2.00901i) q^{20} +(0.386621 - 0.669647i) q^{21} +(-0.157963 - 0.0912000i) q^{22} -3.42650i q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.07224 - 3.94479i) q^{25} +(1.93532 - 3.35207i) q^{26} -1.00000i q^{27} +(-0.669647 + 0.386621i) q^{28} -7.12532 q^{29} +(-2.23074 + 0.154263i) q^{30} +(-4.63168 + 3.08991i) q^{31} -1.00000i q^{32} -0.182400i q^{33} +(-3.11459 - 5.39463i) q^{34} +(-0.119282 - 1.72490i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.54979 - 3.20418i) q^{37} +(-0.517099 + 0.298547i) q^{38} +3.87064 q^{39} +(2.00901 + 0.981775i) q^{40} +(0.930631 - 1.61190i) q^{41} +(-0.669647 - 0.386621i) q^{42} +(-5.78617 + 3.34064i) q^{43} +(-0.0912000 + 0.157963i) q^{44} +(-1.24897 - 1.85475i) q^{45} -3.42650 q^{46} +6.17291i q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.20105 + 5.54438i) q^{49} +(-3.94479 + 3.07224i) q^{50} +(3.11459 - 5.39463i) q^{51} +(-3.35207 - 1.93532i) q^{52} +(7.49604 + 4.32784i) q^{53} -1.00000 q^{54} +(-0.227811 - 0.338306i) q^{55} +(0.386621 + 0.669647i) q^{56} +(-0.517099 - 0.298547i) q^{57} +7.12532i q^{58} +(-6.03735 - 10.4570i) q^{59} +(0.154263 + 2.23074i) q^{60} +0.975597 q^{61} +(3.08991 + 4.63168i) q^{62} -0.773241i q^{63} -1.00000 q^{64} +(7.17906 - 4.83430i) q^{65} -0.182400 q^{66} +(0.371098 + 0.214254i) q^{67} +(-5.39463 + 3.11459i) q^{68} +(-1.71325 - 2.96744i) q^{69} +(-1.72490 + 0.119282i) q^{70} +(4.02888 - 6.97823i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-9.05991 - 5.23074i) q^{73} +(-3.20418 - 5.54979i) q^{74} +(-4.63303 - 1.88017i) q^{75} +(0.298547 + 0.517099i) q^{76} -0.141039i q^{77} -3.87064i q^{78} +(3.64065 + 6.30578i) q^{79} +(0.981775 - 2.00901i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.61190 - 0.930631i) q^{82} +(6.97624 + 4.02773i) q^{83} +(-0.386621 + 0.669647i) q^{84} +(-0.960930 - 13.8957i) q^{85} +(3.34064 + 5.78617i) q^{86} +(-6.17071 + 3.56266i) q^{87} +(0.157963 + 0.0912000i) q^{88} -0.839983 q^{89} +(-1.85475 + 1.24897i) q^{90} +2.99294 q^{91} +3.42650i q^{92} +(-2.46620 + 4.99178i) q^{93} +6.17291 q^{94} +(-1.33196 + 0.0921094i) q^{95} +(-0.500000 - 0.866025i) q^{96} +9.51682i q^{97} +(5.54438 + 3.20105i) q^{98} +(-0.0912000 - 0.157963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.00000			−0.500000
$5$	0.981775	−	2.00901i	0.439063	−	0.898456i
$5$	0.981775	−	2.00901i	0.439063	−	0.898456i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.669647	−	0.386621i	0.253103	−	0.146129i	−0.368081	−	0.929794i	$-0.619985\pi$
$7$	0.669647	−	0.386621i	0.253103	−	0.146129i	0.621184	+	0.783665i	$0.286652\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.00901	−	0.981775i	−0.635304	−	0.310464i
$11$	0.0912000	−	0.157963i	0.0274978	−	0.0476277i	−0.851949	−	0.523625i	$-0.824579\pi$
$11$	0.0912000	−	0.157963i	0.0274978	−	0.0476277i	0.879447	+	0.475997i	$0.157913\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	3.35207	+	1.93532i	0.929698	+	0.536761i	0.886716	−	0.462315i	$-0.152981\pi$
$13$	3.35207	+	1.93532i	0.929698	+	0.536761i	0.0429816	+	0.999076i	$0.486314\pi$
$14$	−0.386621	−	0.669647i	−0.103329	−	0.178971i
$15$	−0.154263	−	2.23074i	−0.0398304	−	0.575975i
$16$	1.00000			0.250000
$17$	5.39463	−	3.11459i	1.30839	−	0.755400i	0.326563	−	0.945175i	$-0.394109\pi$
$17$	5.39463	−	3.11459i	1.30839	−	0.755400i	0.981828	+	0.189776i	$0.0607760\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−0.298547	−	0.517099i	−0.0684915	−	0.118631i	0.829746	−	0.558141i	$-0.188485\pi$
$19$	−0.298547	−	0.517099i	−0.0684915	−	0.118631i	−0.898237	+	0.439511i	$0.855152\pi$
$20$	−0.981775	+	2.00901i	−0.219532	+	0.449228i
$21$	0.386621	−	0.669647i	0.0843676	−	0.146129i
$22$	−0.157963	−	0.0912000i	−0.0336778	−	0.0194439i
$23$		−	3.42650i		−	0.714475i	−0.934014	−	0.357237i	$-0.883719\pi$
$23$		−	3.42650i		−	0.714475i	0.934014	−	0.357237i	$-0.116281\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.07224	−	3.94479i	−0.614447	−	0.788958i
$26$	1.93532	−	3.35207i	0.379547	−	0.657395i
$27$		−	1.00000i		−	0.192450i
$28$	−0.669647	+	0.386621i	−0.126551	+	0.0730645i
$29$	−7.12532			−1.32314			−0.661569	−	0.749884i	$-0.730109\pi$
$29$	−7.12532			−1.32314			−0.661569	+	0.749884i	$0.730109\pi$
$30$	−2.23074	+	0.154263i	−0.407276	+	0.0281644i
$31$	−4.63168	+	3.08991i	−0.831874	+	0.554964i
$31$	−4.63168	+	3.08991i	−0.831874	+	0.554964i
$32$		−	1.00000i		−	0.176777i
$33$		−	0.182400i		−	0.0317518i
$34$	−3.11459	−	5.39463i	−0.534148	−	0.925172i
$35$	−0.119282	−	1.72490i	−0.0201624	−	0.291561i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.54979	−	3.20418i	0.912381	−	0.526763i	0.0311843	−	0.999514i	$-0.490072\pi$
$37$	5.54979	−	3.20418i	0.912381	−	0.526763i	0.881196	+	0.472750i	$0.156739\pi$
$38$	−0.517099	+	0.298547i	−0.0838846	+	0.0484308i
$39$	3.87064			0.619798
$40$	2.00901	+	0.981775i	0.317652	+	0.155232i
$41$	0.930631	−	1.61190i	0.145340	−	0.251736i	−0.784160	−	0.620559i	$-0.786906\pi$
$41$	0.930631	−	1.61190i	0.145340	−	0.251736i	0.929500	+	0.368823i	$0.120239\pi$
$42$	−0.669647	−	0.386621i	−0.103329	−	0.0596569i
$43$	−5.78617	+	3.34064i	−0.882382	+	0.509444i	−0.871443	−	0.490497i	$-0.836815\pi$
$43$	−5.78617	+	3.34064i	−0.882382	+	0.509444i	−0.0109390	+	0.999940i	$0.503482\pi$
$44$	−0.0912000	+	0.157963i	−0.0137489	+	0.0238138i
$45$	−1.24897	−	1.85475i	−0.186185	−	0.276489i
$46$	−3.42650			−0.505210
$47$			6.17291i			0.900412i	0.892925	+	0.450206i	$0.148649\pi$
$47$			6.17291i			0.900412i	−0.892925	+	0.450206i	$0.851351\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−3.20105	+	5.54438i	−0.457293	+	0.792054i
$50$	−3.94479	+	3.07224i	−0.557878	+	0.434480i
$51$	3.11459	−	5.39463i	0.436130	−	0.755400i
$52$	−3.35207	−	1.93532i	−0.464849	−	0.268381i
$53$	7.49604	+	4.32784i	1.02966	+	0.594475i	0.916888	−	0.399146i	$-0.130693\pi$
$53$	7.49604	+	4.32784i	1.02966	+	0.594475i	0.112773	+	0.993621i	$0.464027\pi$
$54$	−1.00000			−0.136083
$55$	−0.227811	−	0.338306i	−0.0307181	−	0.0456172i
$56$	0.386621	+	0.669647i	0.0516644	+	0.0894853i
$57$	−0.517099	−	0.298547i	−0.0684915	−	0.0395436i
$58$			7.12532i			0.935600i
$59$	−6.03735	−	10.4570i	−0.785996	−	1.36139i	−0.928402	−	0.371577i	$-0.878817\pi$
$59$	−6.03735	−	10.4570i	−0.785996	−	1.36139i	0.142406	−	0.989808i	$-0.454516\pi$
$60$	0.154263	+	2.23074i	0.0199152	+	0.287987i
$61$	0.975597			0.124912			0.0624562	−	0.998048i	$-0.480107\pi$
$61$	0.975597			0.124912			0.0624562	+	0.998048i	$0.480107\pi$
$62$	3.08991	+	4.63168i	0.392419	+	0.588224i
$63$		−	0.773241i		−	0.0974193i
$64$	−1.00000			−0.125000
$65$	7.17906	−	4.83430i	0.890452	−	0.599621i
$66$	−0.182400			−0.0224519
$67$	0.371098	+	0.214254i	0.0453369	+	0.0261753i	0.522497	−	0.852641i	$-0.325001\pi$
$67$	0.371098	+	0.214254i	0.0453369	+	0.0261753i	−0.477160	+	0.878816i	$0.658334\pi$
$68$	−5.39463	+	3.11459i	−0.654195	+	0.377700i
$69$	−1.71325	−	2.96744i	−0.206251	−	0.357237i
$70$	−1.72490	+	0.119282i	−0.206165	+	0.0142570i
$71$	4.02888	−	6.97823i	0.478141	−	0.828164i	−0.521545	−	0.853224i	$-0.674644\pi$
$71$	4.02888	−	6.97823i	0.478141	−	0.828164i	0.999686	+	0.0250598i	$0.00797761\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−9.05991	−	5.23074i	−1.06038	−	0.612212i	−0.134844	−	0.990867i	$-0.543053\pi$
$73$	−9.05991	−	5.23074i	−1.06038	−	0.612212i	−0.925538	+	0.378655i	$0.876387\pi$
$74$	−3.20418	−	5.54979i	−0.372478	−	0.645151i
$75$	−4.63303	−	1.88017i	−0.534976	−	0.217103i
$76$	0.298547	+	0.517099i	0.0342457	+	0.0593153i
$77$		−	0.141039i		−	0.0160729i
$78$		−	3.87064i		−	0.438264i
$79$	3.64065	+	6.30578i	0.409605	+	0.709456i	0.994845	−	0.101404i	$-0.0323333\pi$
$79$	3.64065	+	6.30578i	0.409605	+	0.709456i	−0.585241	+	0.810860i	$0.699000\pi$
$80$	0.981775	−	2.00901i	0.109766	−	0.224614i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.61190	−	0.930631i	−0.178005	−	0.102771i
$83$	6.97624	+	4.02773i	0.765742	+	0.442101i	0.831353	−	0.555744i	$-0.187567\pi$
$83$	6.97624	+	4.02773i	0.765742	+	0.442101i	−0.0656117	+	0.997845i	$0.520900\pi$
$84$	−0.386621	+	0.669647i	−0.0421838	+	0.0730645i
$85$	−0.960930	−	13.8957i	−0.104228	−	1.50720i
$86$	3.34064	+	5.78617i	0.360231	+	0.623938i
$87$	−6.17071	+	3.56266i	−0.661569	+	0.381957i
$88$	0.157963	+	0.0912000i	0.0168389	+	0.00972196i
$89$	−0.839983			−0.0890380			−0.0445190	−	0.999009i	$-0.514176\pi$
$89$	−0.839983			−0.0890380			−0.0445190	+	0.999009i	$0.514176\pi$
$90$	−1.85475	+	1.24897i	−0.195507	+	0.131653i
$91$	2.99294			0.313745
$92$			3.42650i			0.357237i
$93$	−2.46620	+	4.99178i	−0.255733	+	0.517624i
$94$	6.17291			0.636687
$95$	−1.33196	+	0.0921094i	−0.136657	+	0.00945022i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			9.51682i			0.966287i	0.875541	+	0.483143i	$0.160505\pi$
$97$			9.51682i			0.966287i	−0.875541	+	0.483143i	$0.839495\pi$
$98$	5.54438	+	3.20105i	0.560067	+	0.323355i
$99$	−0.0912000	−	0.157963i	−0.00916595	−	0.0158759i
$100$	3.07224	+	3.94479i	0.307224	+	0.394479i
$101$	11.7568			1.16985			0.584923	−	0.811089i	$-0.301125\pi$
$101$	11.7568			1.16985			0.584923	+	0.811089i	$0.301125\pi$
$102$	−5.39463	−	3.11459i	−0.534148	−	0.308391i
$103$	−8.33883	−	4.81443i	−0.821650	−	0.474380i	0.0293353	−	0.999570i	$-0.490661\pi$
$103$	−8.33883	−	4.81443i	−0.821650	−	0.474380i	−0.850985	+	0.525190i	$0.823994\pi$
$104$	−1.93532	+	3.35207i	−0.189774	+	0.328698i
$105$	−0.965752	−	1.43417i	−0.0942477	−	0.139960i
$106$	4.32784	−	7.49604i	0.420357	−	0.728080i
$107$	−6.18652	+	3.57179i	−0.598073	+	0.345298i	−0.768283	−	0.640110i	$-0.778889\pi$
$107$	−6.18652	+	3.57179i	−0.598073	+	0.345298i	0.170210	+	0.985408i	$0.445555\pi$
$108$			1.00000i			0.0962250i
$109$	−15.9921			−1.53177			−0.765883	−	0.642979i	$-0.777698\pi$
$109$	−15.9921			−1.53177			−0.765883	+	0.642979i	$0.777698\pi$
$110$	−0.338306	+	0.227811i	−0.0322562	+	0.0217210i
$111$	3.20418	−	5.54979i	0.304127	−	0.526763i
$112$	0.669647	−	0.386621i	0.0632757	−	0.0365322i
$113$	12.2956	+	7.09885i	1.15667	+	0.667804i	0.950504	−	0.310713i	$-0.100568\pi$
$113$	12.2956	+	7.09885i	1.15667	+	0.667804i	0.206167	+	0.978517i	$0.433901\pi$
$114$	−0.298547	+	0.517099i	−0.0279615	+	0.0484308i
$115$	−6.88387	−	3.36405i	−0.641924	−	0.313700i
$116$	7.12532			0.661569
$117$	3.35207	−	1.93532i	0.309899	−	0.178920i
$118$	−10.4570	+	6.03735i	−0.962645	+	0.555783i
$119$	2.40833	−	4.17135i	0.220771	−	0.382387i
$120$	2.23074	−	0.154263i	0.203638	−	0.0140822i
$121$	5.48337	+	9.49747i	0.498488	+	0.863406i
$122$		−	0.975597i		−	0.0883264i
$123$		−	1.86126i		−	0.167824i
$124$	4.63168	−	3.08991i	0.415937	−	0.277482i
$125$	−10.9414	+	2.29925i	−0.978625	+	0.205652i
$126$	−0.773241			−0.0688858
$127$	10.3908	−	5.99913i	0.922034	−	0.532337i	0.0377506	−	0.999287i	$-0.487981\pi$
$127$	10.3908	−	5.99913i	0.922034	−	0.532337i	0.884283	+	0.466951i	$0.154647\pi$
$128$			1.00000i			0.0883883i
$129$	−3.34064	+	5.78617i	−0.294127	+	0.509444i
$130$	−4.83430	−	7.17906i	−0.423996	−	0.629645i
$131$	4.14488	+	7.17915i	0.362140	+	0.627245i	0.988313	−	0.152439i	$-0.0487128\pi$
$131$	4.14488	+	7.17915i	0.362140	+	0.627245i	−0.626173	+	0.779684i	$0.715379\pi$
$132$			0.182400i			0.0158759i
$133$	−0.399843	−	0.230849i	−0.0346707	−	0.0200172i
$134$	0.214254	−	0.371098i	0.0185087	−	0.0320580i
$135$	−2.00901	−	0.981775i	−0.172908	−	0.0844977i
$136$	3.11459	+	5.39463i	0.267074	+	0.462586i
$137$	11.1202	+	6.42025i	0.950063	+	0.548519i	0.893100	−	0.449857i	$-0.148525\pi$
$137$	11.1202	+	6.42025i	0.950063	+	0.548519i	0.0569622	+	0.998376i	$0.481859\pi$
$138$	−2.96744	+	1.71325i	−0.252605	+	0.145842i
$139$	−3.85068			−0.326611			−0.163305	−	0.986576i	$-0.552216\pi$
$139$	−3.85068			−0.326611			−0.163305	+	0.986576i	$0.552216\pi$
$140$	0.119282	+	1.72490i	0.0100812	+	0.145781i
$141$	3.08646	+	5.34590i	0.259926	+	0.450206i
$142$	−6.97823	−	4.02888i	−0.585600	−	0.338096i
$143$	0.611418	−	0.353002i	0.0511294	−	0.0295195i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−6.99546	+	14.3148i	−0.580941	+	1.18878i
$146$	−5.23074	+	9.05991i	−0.432899	+	0.749803i
$147$			6.40210i			0.528036i
$148$	−5.54979	+	3.20418i	−0.456190	+	0.263382i
$149$	6.29694	+	10.9066i	0.515865	+	0.893505i	0.999830	+	0.0184175i	$0.00586282\pi$
$149$	6.29694	+	10.9066i	0.515865	+	0.893505i	−0.483965	+	0.875087i	$0.660804\pi$
$150$	−1.88017	+	4.63303i	−0.153515	+	0.378285i
$151$	12.8986			1.04967			0.524835	−	0.851204i	$-0.324127\pi$
$151$	12.8986			1.04967			0.524835	+	0.851204i	$0.324127\pi$
$152$	0.517099	−	0.298547i	0.0419423	−	0.0242154i
$153$		−	6.22919i		−	0.503600i
$154$	−0.141039			−0.0113653
$155$	1.66039	+	12.3387i	0.133366	+	0.991067i
$156$	−3.87064			−0.309899
$157$		−	14.4319i		−	1.15179i	−0.817522	−	0.575897i	$-0.804653\pi$
$157$		−	14.4319i		−	1.15179i	0.817522	−	0.575897i	$-0.195347\pi$
$158$	6.30578	−	3.64065i	0.501661	−	0.289634i
$159$	8.65569			0.686441
$160$	−2.00901	−	0.981775i	−0.158826	−	0.0776161i
$161$	−1.32476	−	2.29455i	−0.104405	−	0.180835i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$			1.86439i			0.146030i	0.997331	+	0.0730150i	$0.0232621\pi$
$163$			1.86439i			0.146030i	−0.997331	+	0.0730150i	$0.976738\pi$
$164$	−0.930631	+	1.61190i	−0.0726700	+	0.125868i
$165$	−0.366443	−	0.179076i	−0.0285276	−	0.0139410i
$166$	4.02773	−	6.97624i	0.312613	−	0.541461i
$167$	−0.608695	+	0.351430i	−0.0471022	+	0.0271945i	−0.523366	−	0.852108i	$-0.675324\pi$
$167$	−0.608695	+	0.351430i	−0.0471022	+	0.0271945i	0.476264	+	0.879302i	$0.341991\pi$
$168$	0.669647	+	0.386621i	0.0516644	+	0.0298284i
$169$	0.990925	+	1.71633i	0.0762250	+	0.132026i
$170$	−13.8957	+	0.960930i	−1.06575	+	0.0737000i
$171$	−0.597095			−0.0456610
$172$	5.78617	−	3.34064i	0.441191	−	0.254722i
$173$	6.36230	+	3.67328i	0.483717	+	0.279274i	0.721964	−	0.691930i	$-0.243240\pi$
$173$	6.36230	+	3.67328i	0.483717	+	0.279274i	−0.238247	+	0.971205i	$0.576573\pi$
$174$	3.56266	+	6.17071i	0.270084	+	0.467800i
$175$	−3.58245	−	1.45383i	−0.270808	−	0.109899i
$176$	0.0912000	−	0.157963i	0.00687446	−	0.0119069i
$177$	−10.4570	−	6.03735i	−0.785996	−	0.453795i
$178$			0.839983i			0.0629594i
$179$	−0.245463	−	0.425154i	−0.0183467	−	0.0317775i	0.856706	−	0.515805i	$-0.172507\pi$
$179$	−0.245463	−	0.425154i	−0.0183467	−	0.0317775i	−0.875053	+	0.484027i	$0.839174\pi$
$180$	1.24897	+	1.85475i	0.0930924	+	0.138245i
$181$	8.47857	−	14.6853i	0.630207	−	1.09155i	−0.357302	−	0.933989i	$-0.616303\pi$
$181$	8.47857	−	14.6853i	0.630207	−	1.09155i	0.987509	−	0.157562i	$-0.0503633\pi$
$182$		−	2.99294i		−	0.221851i
$183$	0.844892	−	0.487799i	0.0624562	−	0.0360591i
$184$	3.42650			0.252605
$185$	−0.988569	−	14.2954i	−0.0726810	−	1.05102i
$186$	4.99178	+	2.46620i	0.366015	+	0.180830i
$187$		−	1.13620i		−	0.0830875i
$188$		−	6.17291i		−	0.450206i
$189$	−0.386621	−	0.669647i	−0.0281225	−	0.0487096i
$190$	0.0921094	+	1.33196i	0.00668232	+	0.0966308i
$191$	−4.93870	+	8.55408i	−0.357352	+	0.618952i	−0.987518	−	0.157509i	$-0.949654\pi$
$191$	−4.93870	+	8.55408i	−0.357352	+	0.618952i	0.630166	+	0.776461i	$0.282987\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	7.56580	−	4.36812i	0.544598	−	0.314424i	−0.202342	−	0.979315i	$-0.564855\pi$
$193$	7.56580	−	4.36812i	0.544598	−	0.314424i	0.746941	+	0.664891i	$0.231522\pi$
$194$	9.51682			0.683268
$195$	3.80010	−	7.77615i	0.272131	−	0.556862i
$196$	3.20105	−	5.54438i	0.228646	−	0.396027i
$197$	1.14893	+	0.663337i	0.0818582	+	0.0472608i	0.540370	−	0.841427i	$-0.318284\pi$
$197$	1.14893	+	0.663337i	0.0818582	+	0.0472608i	−0.458512	+	0.888688i	$0.651617\pi$
$198$	−0.157963	+	0.0912000i	−0.0112259	+	0.00648130i
$199$	−12.3167	+	21.3331i	−0.873107	+	1.51226i	−0.0143404	+	0.999897i	$0.504565\pi$
$199$	−12.3167	+	21.3331i	−0.873107	+	1.51226i	−0.858766	+	0.512368i	$0.828768\pi$
$200$	3.94479	−	3.07224i	0.278939	−	0.217240i
$201$	0.428507			0.0302246
$202$		−	11.7568i		−	0.827206i
$203$	−4.77145	+	2.75480i	−0.334890	+	0.193349i
$204$	−3.11459	+	5.39463i	−0.218065	+	0.377700i
$205$	−2.32465	−	3.45217i	−0.162361	−	0.241110i
$206$	−4.81443	+	8.33883i	−0.335437	+	0.580994i
$207$	−2.96744	−	1.71325i	−0.206251	−	0.119079i
$208$	3.35207	+	1.93532i	0.232424	+	0.134190i
$209$	−0.108910			−0.00753347
$210$	−1.43417	+	0.965752i	−0.0989669	+	0.0666432i
$211$	8.11534	+	14.0562i	0.558683	+	0.967667i	0.997607	+	0.0691431i	$0.0220265\pi$
$211$	8.11534	+	14.0562i	0.558683	+	0.967667i	−0.438924	+	0.898524i	$0.644640\pi$
$212$	−7.49604	−	4.32784i	−0.514830	−	0.297238i
$213$		−	8.05777i		−	0.552109i
$214$	3.57179	+	6.18652i	0.244162	+	0.422902i
$215$	1.03067	+	14.9042i	0.0702913	+	1.01646i
$216$	1.00000			0.0680414
$217$	−1.90697	+	3.85985i	−0.129453	+	0.262024i
$218$			15.9921i			1.08312i
$219$	−10.4615			−0.706921
$220$	0.227811	+	0.338306i	0.0153590	+	0.0228086i
$221$	24.1109			1.62188
$222$	−5.54979	−	3.20418i	−0.372478	−	0.215050i
$223$	−17.2965	+	9.98614i	−1.15826	+	0.668722i	−0.950886	−	0.309540i	$-0.899825\pi$
$223$	−17.2965	+	9.98614i	−1.15826	+	0.668722i	−0.207373	+	0.978262i	$0.566492\pi$
$224$	−0.386621	−	0.669647i	−0.0258322	−	0.0447427i
$225$	−4.95241	+	0.688239i	−0.330160	+	0.0458826i
$226$	7.09885	−	12.2956i	0.472209	−	0.817889i
$227$	20.2265	+	11.6778i	1.34248	+	0.775080i	0.987171	−	0.159670i	$-0.0510429\pi$
$227$	20.2265	+	11.6778i	1.34248	+	0.775080i	0.355307	+	0.934750i	$0.384376\pi$
$228$	0.517099	+	0.298547i	0.0342457	+	0.0197718i
$229$	6.66108	+	11.5373i	0.440176	+	0.762408i	0.997702	−	0.0677518i	$-0.0215826\pi$
$229$	6.66108	+	11.5373i	0.440176	+	0.762408i	−0.557526	+	0.830160i	$0.688249\pi$
$230$	−3.36405	+	6.88387i	−0.221819	+	0.453909i
$231$	−0.0705196	−	0.122144i	−0.00463985	−	0.00803646i
$232$		−	7.12532i		−	0.467800i
$233$		−	10.6233i		−	0.695957i	−0.937503	−	0.347978i	$-0.886868\pi$
$233$		−	10.6233i		−	0.695957i	0.937503	−	0.347978i	$-0.113132\pi$
$234$	−1.93532	−	3.35207i	−0.126516	−	0.219132i
$235$	12.4014	+	6.06041i	0.808980	+	0.395338i
$236$	6.03735	+	10.4570i	0.392998	+	0.680693i
$237$	6.30578	+	3.64065i	0.409605	+	0.236485i
$238$	−4.17135	−	2.40833i	−0.270389	−	0.156109i
$239$	−4.64700	+	8.04884i	−0.300589	+	0.520636i	−0.976270	−	0.216559i	$-0.930517\pi$
$239$	−4.64700	+	8.04884i	−0.300589	+	0.520636i	0.675680	+	0.737195i	$0.263850\pi$
$240$	−0.154263	−	2.23074i	−0.00995761	−	0.143994i
$241$	−4.18140	−	7.24239i	−0.269347	−	0.466523i	0.699346	−	0.714783i	$-0.253475\pi$
$241$	−4.18140	−	7.24239i	−0.269347	−	0.466523i	−0.968693	+	0.248260i	$0.920141\pi$
$242$	9.49747	−	5.48337i	0.610520	−	0.352484i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.975597			−0.0624562
$245$	7.99600	+	11.8743i	0.510846	+	0.758619i
$246$	−1.86126			−0.118670
$247$		−	2.31114i		−	0.147054i
$248$	−3.08991	−	4.63168i	−0.196209	−	0.294112i
$249$	8.05547			0.510495
$250$	2.29925	+	10.9414i	0.145418	+	0.691993i
$251$	−9.11474	−	15.7872i	−0.575317	−	0.996479i	−0.996007	−	0.0892742i	$-0.971545\pi$
$251$	−9.11474	−	15.7872i	−0.575317	−	0.996479i	0.420690	−	0.907205i	$-0.361788\pi$
$252$			0.773241i			0.0487096i
$253$	−0.541261	−	0.312497i	−0.0340288	−	0.0196465i
$254$	−5.99913	−	10.3908i	−0.376419	−	0.651977i
$255$	−7.78004	−	11.5536i	−0.487205	−	0.723512i
$256$	1.00000			0.0625000
$257$	1.29328	+	0.746676i	0.0806727	+	0.0465764i	0.539794	−	0.841797i	$-0.318502\pi$
$257$	1.29328	+	0.746676i	0.0806727	+	0.0465764i	−0.459121	+	0.888374i	$0.651836\pi$
$258$	5.78617	+	3.34064i	0.360231	+	0.207979i
$259$	2.47760	−	4.29133i	0.153951	−	0.266650i
$260$	−7.17906	+	4.83430i	−0.445226	+	0.299810i
$261$	−3.56266	+	6.17071i	−0.220523	+	0.381957i
$262$	7.17915	−	4.14488i	0.443529	−	0.256072i
$263$		−	21.7443i		−	1.34081i	−0.741996	−	0.670404i	$-0.766121\pi$
$263$		−	21.7443i		−	1.34081i	0.741996	−	0.670404i	$-0.233879\pi$
$264$	0.182400			0.0112259
$265$	16.0541	−	10.8107i	0.986196	−	0.664093i
$266$	−0.230849	+	0.399843i	−0.0141543	+	0.0245159i
$267$	−0.727447	+	0.419992i	−0.0445190	+	0.0257031i
$268$	−0.371098	−	0.214254i	−0.0226684	−	0.0130876i
$269$	6.95564	−	12.0475i	0.424093	−	0.734551i	−0.572242	−	0.820085i	$-0.693926\pi$
$269$	6.95564	−	12.0475i	0.424093	−	0.734551i	0.996335	+	0.0855341i	$0.0272596\pi$
$270$	−0.981775	+	2.00901i	−0.0597489	+	0.122264i
$271$	16.6543			1.01168			0.505838	−	0.862629i	$-0.331184\pi$
$271$	16.6543			1.01168			0.505838	+	0.862629i	$0.331184\pi$
$272$	5.39463	−	3.11459i	0.327098	−	0.188850i
$273$	2.59196	−	1.49647i	0.156873	−	0.0905705i
$274$	6.42025	−	11.1202i	0.387861	−	0.671796i
$275$	−0.903319	+	0.125535i	−0.0544722	+	0.00757004i
$276$	1.71325	+	2.96744i	0.103126	+	0.178619i
$277$			15.3671i			0.923321i	0.887057	+	0.461660i	$0.152746\pi$
$277$			15.3671i			0.923321i	−0.887057	+	0.461660i	$0.847254\pi$
$278$			3.85068i			0.230949i
$279$	0.360101	+	5.55611i	0.0215587	+	0.332635i
$280$	1.72490	−	0.119282i	0.103083	−	0.00712848i
$281$	17.4465			1.04077			0.520384	−	0.853932i	$-0.325789\pi$
$281$	17.4465			1.04077			0.520384	+	0.853932i	$0.325789\pi$
$282$	5.34590	−	3.08646i	0.318344	−	0.183796i
$283$			28.9290i			1.71965i	0.510588	+	0.859826i	$0.329428\pi$
$283$			28.9290i			1.71965i	−0.510588	+	0.859826i	$0.670572\pi$
$284$	−4.02888	+	6.97823i	−0.239070	+	0.414082i
$285$	−1.10746	+	0.745751i	−0.0656002	+	0.0441745i
$286$	−0.353002	−	0.611418i	−0.0208735	−	0.0361539i
$287$		−	1.43920i		−	0.0849536i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	10.9014	−	18.8817i	0.641258	−	1.11069i
$290$	14.3148	+	6.99546i	0.840596	+	0.410787i
$291$	4.75841	+	8.24181i	0.278943	+	0.483143i
$292$	9.05991	+	5.23074i	0.530191	+	0.306106i
$293$	7.37274	−	4.25665i	0.430720	−	0.248676i	−0.268933	−	0.963159i	$-0.586671\pi$
$293$	7.37274	−	4.25665i	0.430720	−	0.248676i	0.699653	+	0.714482i	$0.253338\pi$
$294$	6.40210			0.373378
$295$	−26.9355	+	1.86267i	−1.56825	+	0.108449i
$296$	3.20418	+	5.54979i	0.186239	+	0.322575i
$297$	−0.157963	−	0.0912000i	−0.00916595	−	0.00529196i
$298$	10.9066	−	6.29694i	0.631803	−	0.364772i
$299$	6.63137	−	11.4859i	0.383502	−	0.664245i
$300$	4.63303	+	1.88017i	0.267488	+	0.108552i
$301$	−2.58312	+	4.47410i	−0.148889	+	0.257883i
$302$		−	12.8986i		−	0.742229i
$303$	10.1817	−	5.87840i	0.584923	−	0.337705i
$304$	−0.298547	−	0.517099i	−0.0171229	−	0.0296577i
$305$	0.957817	−	1.95998i	0.0548444	−	0.112228i
$306$	−6.22919			−0.356099
$307$	−18.6892	+	10.7902i	−1.06665	+	0.615830i	−0.927264	−	0.374408i	$-0.877846\pi$
$307$	−18.6892	+	10.7902i	−1.06665	+	0.615830i	−0.139385	+	0.990238i	$0.544513\pi$
$308$			0.141039i			0.00803646i
$309$	−9.62886			−0.547766
$310$	12.3387	−	1.66039i	0.700790	−	0.0943039i
$311$	7.50012			0.425293			0.212646	−	0.977129i	$-0.431792\pi$
$311$	7.50012			0.425293			0.212646	+	0.977129i	$0.431792\pi$
$312$			3.87064i			0.219132i
$313$	−10.1694	+	5.87130i	−0.574808	+	0.331866i	−0.759067	−	0.651012i	$-0.774345\pi$
$313$	−10.1694	+	5.87130i	−0.574808	+	0.331866i	0.184259	+	0.982878i	$0.441011\pi$
$314$	−14.4319			−0.814442
$315$	−1.55345	−	0.759149i	−0.0875269	−	0.0427732i
$316$	−3.64065	−	6.30578i	−0.204802	−	0.354728i
$317$	−21.7925	+	12.5819i	−1.22399	+	0.706672i	−0.965766	−	0.259413i	$-0.916471\pi$
$317$	−21.7925	+	12.5819i	−1.22399	+	0.706672i	−0.258225	+	0.966085i	$0.583138\pi$
$318$		−	8.65569i		−	0.485387i
$319$	−0.649829	+	1.12554i	−0.0363834	+	0.0630180i
$320$	−0.981775	+	2.00901i	−0.0548829	+	0.112307i
$321$	−3.57179	+	6.18652i	−0.199358	+	0.345298i
$322$	−2.29455	+	1.32476i	−0.127870	+	0.0738258i
$323$	−3.22111	−	1.85971i	−0.179227	−	0.103477i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−2.66393	−	19.1690i	−0.147768	−	1.06330i
$326$	1.86439			0.103259
$327$	−13.8496	+	7.99606i	−0.765883	+	0.442183i
$328$	1.61190	+	0.930631i	0.0890023	+	0.0513855i
$329$	2.38658	+	4.13367i	0.131576	+	0.227897i
$330$	−0.179076	+	0.366443i	−0.00985780	+	0.0201720i
$331$	−16.4267	+	28.4518i	−0.902891	+	1.56385i	−0.0791671	+	0.996861i	$0.525226\pi$
$331$	−16.4267	+	28.4518i	−0.902891	+	1.56385i	−0.823724	+	0.566991i	$0.808107\pi$
$332$	−6.97624	−	4.02773i	−0.382871	−	0.221051i
$333$		−	6.40835i		−	0.351175i
$334$	0.351430	+	0.608695i	0.0192294	+	0.0333063i
$335$	0.794773	−	0.535191i	0.0434231	−	0.0292406i
$336$	0.386621	−	0.669647i	0.0210919	−	0.0365322i
$337$			12.7086i			0.692281i	0.938183	+	0.346140i	$0.112508\pi$
$337$			12.7086i			0.692281i	−0.938183	+	0.346140i	$0.887492\pi$
$338$	1.71633	−	0.990925i	0.0933562	−	0.0538992i
$339$	14.1977			0.771114
$340$	0.960930	+	13.8957i	0.0521138	+	0.753600i
$341$	0.0656824	+	1.01343i	0.00355690	+	0.0548805i
$342$			0.597095i			0.0322872i
$343$			10.3631i			0.559553i
$344$	−3.34064	−	5.78617i	−0.180115	−	0.311969i
$345$	−7.64363	+	0.528581i	−0.411519	+	0.0284578i
$346$	3.67328	−	6.36230i	0.197477	−	0.342040i
$347$	−26.0657	+	15.0491i	−1.39928	+	0.807876i	−0.994317	−	0.106457i	$-0.966049\pi$
$347$	−26.0657	+	15.0491i	−1.39928	+	0.807876i	−0.404964	+	0.914332i	$0.632716\pi$
$348$	6.17071	−	3.56266i	0.330785	−	0.190979i
$349$	8.86982			0.474790			0.237395	−	0.971413i	$-0.423706\pi$
$349$	8.86982			0.474790			0.237395	+	0.971413i	$0.423706\pi$
$350$	−1.45383	+	3.58245i	−0.0777102	+	0.191490i
$351$	1.93532	−	3.35207i	0.103300	−	0.178920i
$352$	−0.157963	−	0.0912000i	−0.00841946	−	0.00486098i
$353$	10.3613	−	5.98210i	0.551476	−	0.318395i	−0.198241	−	0.980153i	$-0.563523\pi$
$353$	10.3613	−	5.98210i	0.551476	−	0.318395i	0.749717	+	0.661758i	$0.230190\pi$
$354$	−6.03735	+	10.4570i	−0.320882	+	0.555783i
$355$	−10.0639	−	14.9451i	−0.534135	−	0.793205i
$356$	0.839983			0.0445190
$357$		−	4.81667i		−	0.254925i
$358$	−0.425154	+	0.245463i	−0.0224701	+	0.0129731i
$359$	−2.64689	+	4.58455i	−0.139697	+	0.241963i	−0.927382	−	0.374116i	$-0.877946\pi$
$359$	−2.64689	+	4.58455i	−0.139697	+	0.241963i	0.787685	+	0.616079i	$0.211280\pi$
$360$	1.85475	−	1.24897i	0.0977537	−	0.0658263i
$361$	9.32174	−	16.1457i	0.490618	−	0.849775i
$362$	−14.6853	−	8.47857i	−0.771843	−	0.445624i
$363$	9.49747	+	5.48337i	0.498488	+	0.287802i
$364$	−2.99294			−0.156873
$365$	−19.4034	+	13.0660i	−1.01562	+	0.683907i
$366$	−0.487799	−	0.844892i	−0.0254976	−	0.0441632i
$367$	−19.4298	−	11.2178i	−1.01423	−	0.585564i	−0.101801	−	0.994805i	$-0.532460\pi$
$367$	−19.4298	−	11.2178i	−1.01423	−	0.585564i	−0.912427	+	0.409240i	$0.865794\pi$
$368$		−	3.42650i		−	0.178619i
$369$	−0.930631	−	1.61190i	−0.0484467	−	0.0839121i
$370$	−14.2954	+	0.988569i	−0.743181	+	0.0513932i
$371$	6.69294			0.347480
$372$	2.46620	−	4.99178i	0.127866	−	0.258812i
$373$			3.89756i			0.201808i	0.994896	+	0.100904i	$0.0321735\pi$
$373$			3.89756i			0.201808i	−0.994896	+	0.100904i	$0.967826\pi$
$374$	−1.13620			−0.0587517
$375$	−8.32587	+	7.46189i	−0.429946	+	0.385331i
$376$	−6.17291			−0.318344
$377$	−23.8846	−	13.7898i	−1.23012	−	0.710209i
$378$	−0.669647	+	0.386621i	−0.0344429	+	0.0198856i
$379$	11.7489	+	20.3497i	0.603499	+	1.04529i	0.992287	+	0.123964i	$0.0395607\pi$
$379$	11.7489	+	20.3497i	0.603499	+	1.04529i	−0.388787	+	0.921327i	$0.627106\pi$
$380$	1.33196	−	0.0921094i	0.0683283	−	0.00472511i
$381$	5.99913	−	10.3908i	0.307345	−	0.532337i
$382$	8.55408	+	4.93870i	0.437665	+	0.252686i
$383$	−5.23407	−	3.02189i	−0.267449	−	0.154412i	0.360279	−	0.932845i	$-0.382682\pi$
$383$	−5.23407	−	3.02189i	−0.267449	−	0.154412i	−0.627728	+	0.778433i	$0.716015\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−0.283349	−	0.138469i	−0.0144408	−	0.00705703i
$386$	−4.36812	−	7.56580i	−0.222331	−	0.385089i
$387$			6.68129i			0.339629i
$388$		−	9.51682i		−	0.483143i
$389$	3.21583	+	5.56997i	0.163049	+	0.282409i	0.935961	−	0.352105i	$-0.114534\pi$
$389$	3.21583	+	5.56997i	0.163049	+	0.282409i	−0.772912	+	0.634513i	$0.781201\pi$
$390$	−7.77615	−	3.80010i	−0.393761	−	0.192425i
$391$	−10.6722	−	18.4847i	−0.539714	−	0.934812i
$392$	−5.54438	−	3.20105i	−0.280033	−	0.161677i
$393$	7.17915	+	4.14488i	0.362140	+	0.209082i
$394$	0.663337	−	1.14893i	0.0334185	−	0.0578825i
$395$	16.2427	−	1.12323i	0.817257	−	0.0565159i
$396$	0.0912000	+	0.157963i	0.00458297	+	0.00793794i
$397$	29.5449	−	17.0578i	1.48282	−	0.856105i	0.483008	−	0.875616i	$-0.339544\pi$
$397$	29.5449	−	17.0578i	1.48282	−	0.856105i	0.999810	+	0.0195106i	$0.00621081\pi$
$398$	21.3331	+	12.3167i	1.06933	+	0.617380i
$399$	−0.461698			−0.0231138
$400$	−3.07224	−	3.94479i	−0.153612	−	0.197239i
$401$	−36.6374			−1.82959			−0.914793	−	0.403924i	$-0.867646\pi$
$401$	−36.6374			−1.82959			−0.914793	+	0.403924i	$0.867646\pi$
$402$		−	0.428507i		−	0.0213720i
$403$	−21.5057	+	1.39382i	−1.07127	+	0.0694312i
$404$	−11.7568			−0.584923
$405$	−2.23074	+	0.154263i	−0.110846	+	0.00766537i
$406$	2.75480	+	4.77145i	0.136718	+	0.236803i
$407$		−	1.16888i		−	0.0579394i
$408$	5.39463	+	3.11459i	0.267074	+	0.154195i
$409$	−10.5653	−	18.2997i	−0.522422	−	0.904861i	−0.999660	−	0.0260870i	$-0.991695\pi$
$409$	−10.5653	−	18.2997i	−0.522422	−	0.904861i	0.477238	−	0.878774i	$-0.341638\pi$
$410$	−3.45217	+	2.32465i	−0.170490	+	0.114806i
$411$	12.8405			0.633375
$412$	8.33883	+	4.81443i	0.410825	+	0.237190i
$413$	−8.08579	−	4.66833i	−0.397876	−	0.229714i
$414$	−1.71325	+	2.96744i	−0.0842017	+	0.145842i
$415$	14.9409	−	10.0610i	0.733418	−	0.493875i
$416$	1.93532	−	3.35207i	0.0948869	−	0.164349i
$417$	−3.33479	+	1.92534i	−0.163305	+	0.0942844i
$418$			0.108910i			0.00532697i
$419$	−22.8606			−1.11681			−0.558406	−	0.829568i	$-0.688587\pi$
$419$	−22.8606			−1.11681			−0.558406	+	0.829568i	$0.688587\pi$
$420$	0.965752	+	1.43417i	0.0471239	+	0.0699802i
$421$	−6.83483	+	11.8383i	−0.333109	+	0.576962i	−0.983120	−	0.182963i	$-0.941431\pi$
$421$	−6.83483	+	11.8383i	−0.333109	+	0.576962i	0.650010	+	0.759925i	$0.274765\pi$
$422$	14.0562	−	8.11534i	0.684244	−	0.395049i
$423$	5.34590	+	3.08646i	0.259926	+	0.150069i
$424$	−4.32784	+	7.49604i	−0.210179	+	0.364040i
$425$	−28.8600	−	11.7119i	−1.39992	−	0.568112i
$426$	−8.05777			−0.390400
$427$	0.653305	−	0.377186i	0.0316157	−	0.0182533i
$428$	6.18652	−	3.57179i	0.299037	−	0.172649i
$429$	0.353002	−	0.611418i	0.0170431	−	0.0295195i
$430$	14.9042	−	1.03067i	0.718745	−	0.0497035i
$431$	−9.10321	−	15.7672i	−0.438486	−	0.759480i	0.559087	−	0.829109i	$-0.311152\pi$
$431$	−9.10321	−	15.7672i	−0.438486	−	0.759480i	−0.997573	+	0.0696289i	$0.977818\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			2.97874i			0.143149i	0.997435	+	0.0715746i	$0.0228024\pi$
$433$			2.97874i			0.143149i	−0.997435	+	0.0715746i	$0.977198\pi$
$434$	3.85985	+	1.90697i	0.185279	+	0.0915373i
$435$	1.09917	+	15.8947i	0.0527012	+	0.762094i
$436$	15.9921			0.765883
$437$	−1.77184	+	1.02297i	−0.0847586	+	0.0489354i
$438$			10.4615i			0.499869i
$439$	1.88163	−	3.25908i	0.0898052	−	0.155547i	−0.817623	−	0.575753i	$-0.804709\pi$
$439$	1.88163	−	3.25908i	0.0898052	−	0.155547i	0.907429	+	0.420206i	$0.138042\pi$
$440$	0.338306	−	0.227811i	0.0161281	−	0.0108605i
$441$	3.20105	+	5.54438i	0.152431	+	0.264018i
$442$		−	24.1109i		−	1.14684i
$443$	−23.4960	−	13.5654i	−1.11633	−	0.644512i	−0.175866	−	0.984414i	$-0.556273\pi$
$443$	−23.4960	−	13.5654i	−1.11633	−	0.644512i	−0.940461	+	0.339903i	$0.889606\pi$
$444$	−3.20418	+	5.54979i	−0.152063	+	0.263382i
$445$	−0.824674	+	1.68753i	−0.0390933	+	0.0799968i
$446$	9.98614	+	17.2965i	0.472858	+	0.819013i
$447$	10.9066	+	6.29694i	0.515865	+	0.297835i
$448$	−0.669647	+	0.386621i	−0.0316378	+	0.0182661i
$449$	−41.4038			−1.95397			−0.976983	−	0.213316i	$-0.931574\pi$
$449$	−41.4038			−1.95397			−0.976983	+	0.213316i	$0.931574\pi$
$450$	0.688239	+	4.95241i	0.0324439	+	0.233459i
$451$	−0.169747	−	0.294011i	−0.00799308	−	0.0138444i
$452$	−12.2956	−	7.09885i	−0.578335	−	0.333902i
$453$	11.1705	−	6.44928i	0.524835	−	0.303014i
$454$	11.6778	−	20.2265i	0.548064	−	0.949275i
$455$	2.93839	−	6.01284i	0.137754	−	0.281886i
$456$	0.298547	−	0.517099i	0.0139808	−	0.0242154i
$457$			24.6010i			1.15079i	0.817877	+	0.575393i	$0.195151\pi$
$457$			24.6010i			1.15079i	−0.817877	+	0.575393i	$0.804849\pi$
$458$	11.5373	−	6.66108i	0.539104	−	0.311252i
$459$	−3.11459	−	5.39463i	−0.145377	−	0.251800i
$460$	6.88387	+	3.36405i	0.320962	+	0.156850i
$461$	−5.75649			−0.268106			−0.134053	−	0.990974i	$-0.542799\pi$
$461$	−5.75649			−0.268106			−0.134053	+	0.990974i	$0.542799\pi$
$462$	−0.122144	+	0.0705196i	−0.00568263	+	0.00328087i
$463$		−	30.2945i		−	1.40791i	−0.710246	−	0.703953i	$-0.751417\pi$
$463$		−	30.2945i		−	1.40791i	0.710246	−	0.703953i	$-0.248583\pi$
$464$	−7.12532			−0.330785
$465$	7.60728	+	9.85542i	0.352779	+	0.457034i
$466$	−10.6233			−0.492116
$467$			24.8358i			1.14927i	0.818412	+	0.574633i	$0.194855\pi$
$467$			24.8358i			1.14927i	−0.818412	+	0.574633i	$0.805145\pi$
$468$	−3.35207	+	1.93532i	−0.154950	+	0.0894602i
$469$	0.331340			0.0152998
$470$	6.06041	−	12.4014i	0.279546	−	0.572036i
$471$	−7.21597	−	12.4984i	−0.332494	−	0.575897i
$472$	10.4570	−	6.03735i	0.481323	−	0.277892i
$473$			1.21867i			0.0560344i
$474$	3.64065	−	6.30578i	0.167220	−	0.289634i
$475$	−1.12264	+	2.76636i	−0.0515102	+	0.126929i
$476$	−2.40833	+	4.17135i	−0.110386	+	0.191194i
$477$	7.49604	−	4.32784i	0.343220	−	0.198158i
$478$	8.04884	+	4.64700i	0.368145	+	0.212549i
$479$	−19.4463	−	33.6819i	−0.888523	−	1.53897i	−0.841622	−	0.540067i	$-0.818399\pi$
$479$	−19.4463	−	33.6819i	−0.888523	−	1.53897i	−0.0469010	−	0.998900i	$-0.514935\pi$
$480$	−2.23074	+	0.154263i	−0.101819	+	0.00704109i
$481$	24.8044			1.13098
$482$	−7.24239	+	4.18140i	−0.329882	+	0.190457i
$483$	−2.29455	−	1.32476i	−0.104405	−	0.0602785i
$484$	−5.48337	−	9.49747i	−0.249244	−	0.431703i
$485$	19.1194	+	9.34338i	0.868166	+	0.424261i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	1.68240	+	0.971337i	0.0762370	+	0.0440155i	0.537634	−	0.843178i	$-0.319318\pi$
$487$	1.68240	+	0.971337i	0.0762370	+	0.0440155i	−0.461397	+	0.887194i	$0.652652\pi$
$488$			0.975597i			0.0441632i
$489$	0.932193	+	1.61461i	0.0421552	+	0.0730150i
$490$	11.8743	−	7.99600i	0.536425	−	0.361222i
$491$	14.8550	−	25.7295i	0.670395	−	1.16116i	−0.307398	−	0.951581i	$-0.599458\pi$
$491$	14.8550	−	25.7295i	0.670395	−	1.16116i	0.977792	−	0.209576i	$-0.0672085\pi$
$492$			1.86126i			0.0839121i
$493$	−38.4385	+	22.1925i	−1.73118	+	0.999498i
$494$	−2.31114			−0.103983
$495$	−0.406887	+	0.0281375i	−0.0182882	+	0.00126469i
$496$	−4.63168	+	3.08991i	−0.207969	+	0.138741i
$497$		−	6.23060i		−	0.279481i
$498$		−	8.05547i		−	0.360974i
$499$	−1.99859	−	3.46166i	−0.0894693	−	0.154965i	0.817818	−	0.575477i	$-0.195184\pi$
$499$	−1.99859	−	3.46166i	−0.0894693	−	0.154965i	−0.907287	+	0.420512i	$0.861850\pi$
$500$	10.9414	−	2.29925i	0.489313	−	0.102826i
$501$	−0.351430	+	0.608695i	−0.0157007	+	0.0271945i
$502$	−15.7872	+	9.11474i	−0.704617	+	0.406811i
$503$	20.2717	−	11.7039i	0.903871	−	0.521850i	0.0254170	−	0.999677i	$-0.491909\pi$
$503$	20.2717	−	11.7039i	0.903871	−	0.521850i	0.878454	+	0.477827i	$0.158575\pi$
$504$	0.773241			0.0344429
$505$	11.5425	−	23.6195i	0.513636	−	1.05106i
$506$	−0.312497	+	0.541261i	−0.0138922	+	0.0240620i
$507$	1.71633	+	0.990925i	0.0762250	+	0.0440085i
$508$	−10.3908	+	5.99913i	−0.461017	+	0.266168i
$509$	16.9298	−	29.3232i	0.750399	−	1.29973i	−0.197230	−	0.980357i	$-0.563195\pi$
$509$	16.9298	−	29.3232i	0.750399	−	1.29973i	0.947629	−	0.319372i	$-0.103472\pi$
$510$	−11.5536	+	7.78004i	−0.511600	+	0.344506i
$511$	−8.08925			−0.357847
$512$		−	1.00000i		−	0.0441942i
$513$	−0.517099	+	0.298547i	−0.0228305	+	0.0131812i
$514$	0.746676	−	1.29328i	0.0329345	−	0.0570442i
$515$	−17.8591	+	12.0261i	−0.786965	+	0.529934i
$516$	3.34064	−	5.78617i	0.147064	−	0.254722i
$517$	0.975092	+	0.562970i	0.0428845	+	0.0247594i
$518$	−4.29133	−	2.47760i	−0.188550	−	0.108860i
$519$	7.34656			0.322478
$520$	4.83430	+	7.17906i	0.211998	+	0.314822i
$521$	−9.26685	−	16.0507i	−0.405988	−	0.703192i	0.588448	−	0.808535i	$-0.299739\pi$
$521$	−9.26685	−	16.0507i	−0.405988	−	0.703192i	−0.994436	+	0.105343i	$0.966406\pi$
$522$	6.17071	+	3.56266i	0.270084	+	0.155933i
$523$		−	19.2334i		−	0.841019i	−0.907288	−	0.420509i	$-0.861851\pi$
$523$		−	19.2334i		−	0.841019i	0.907288	−	0.420509i	$-0.138149\pi$
$524$	−4.14488	−	7.17915i	−0.181070	−	0.313623i
$525$	−3.82941	+	0.532175i	−0.167129	+	0.0232260i
$526$	−21.7443			−0.948095
$527$	−15.3624	+	31.0947i	−0.669197	+	1.35451i
$528$		−	0.182400i		−	0.00793794i
$529$	11.2591			0.489526
$530$	−10.8107	−	16.0541i	−0.469585	−	0.697346i
$531$	−12.0747			−0.523998
$532$	0.399843	+	0.230849i	0.0173354	+	0.0100086i
$533$	6.23908	−	3.60214i	0.270245	−	0.156026i
$534$	0.419992	+	0.727447i	0.0181748	+	0.0314797i
$535$	1.10199	+	15.9355i	0.0476430	+	0.688950i
$536$	−0.214254	+	0.371098i	−0.00925435	+	0.0160290i
$537$	−0.425154	−	0.245463i	−0.0183467	−	0.0105925i
$538$	−12.0475	−	6.95564i	−0.519406	−	0.299879i
$539$	0.583871	+	1.01130i	0.0251491	+	0.0435596i
$540$	2.00901	+	0.981775i	0.0864540	+	0.0422489i
$541$	−4.65254	−	8.05844i	−0.200028	−	0.346459i	0.748509	−	0.663125i	$-0.230770\pi$
$541$	−4.65254	−	8.05844i	−0.200028	−	0.346459i	−0.948537	+	0.316665i	$0.897437\pi$
$542$		−	16.6543i		−	0.715362i
$543$		−	16.9571i		−	0.727700i
$544$	−3.11459	−	5.39463i	−0.133537	−	0.231293i
$545$	−15.7007	+	32.1283i	−0.672542	+	1.37623i
$546$	−1.49647	−	2.59196i	−0.0640430	−	0.110926i
$547$	0.685180	+	0.395589i	0.0292962	+	0.0169141i	0.514577	−	0.857444i	$-0.327949\pi$
$547$	0.685180	+	0.395589i	0.0292962	+	0.0169141i	−0.485280	+	0.874359i	$0.661282\pi$
$548$	−11.1202	−	6.42025i	−0.475031	−	0.274259i
$549$	0.487799	−	0.844892i	0.0208187	−	0.0360591i
$550$	0.125535	+	0.903319i	0.00535283	+	0.0385177i
$551$	2.12724	+	3.68450i	0.0906237	+	0.156965i
$552$	2.96744	−	1.71325i	0.126302	−	0.0729208i
$553$	4.87589	+	2.81510i	0.207344	+	0.119710i
$554$	15.3671			0.652886
$555$	−8.00381	−	11.8859i	−0.339743	−	0.504527i
$556$	3.85068			0.163305
$557$		−	25.2701i		−	1.07073i	−0.844621	−	0.535365i	$-0.820174\pi$
$557$		−	25.2701i		−	1.07073i	0.844621	−	0.535365i	$-0.179826\pi$
$558$	5.55611	−	0.360101i	0.235209	−	0.0152443i
$559$	−25.8609			−1.09380
$560$	−0.119282	−	1.72490i	−0.00504059	−	0.0728904i
$561$	−0.568102	−	0.983981i	−0.0239853	−	0.0415437i
$562$		−	17.4465i		−	0.735934i
$563$	−38.7751	−	22.3868i	−1.63418	−	0.943492i	−0.982786	−	0.184748i	$-0.940853\pi$
$563$	−38.7751	−	22.3868i	−1.63418	−	0.943492i	−0.651389	−	0.758744i	$-0.725814\pi$
$564$	−3.08646	−	5.34590i	−0.129963	−	0.225103i
$565$	26.3331	−	17.7324i	1.10784	−	0.746010i
$566$	28.9290			1.21598
$567$	−0.669647	−	0.386621i	−0.0281225	−	0.0162365i
$568$	6.97823	+	4.02888i	0.292800	+	0.169048i
$569$	−14.8782	+	25.7699i	−0.623728	+	1.08033i	0.365057	+	0.930985i	$0.381049\pi$
$569$	−14.8782	+	25.7699i	−0.623728	+	1.08033i	−0.988785	+	0.149344i	$0.952284\pi$
$570$	0.745751	+	1.10746i	0.0312361	+	0.0463864i
$571$	−5.85732	+	10.1452i	−0.245121	+	0.424562i	−0.962166	−	0.272465i	$-0.912161\pi$
$571$	−5.85732	+	10.1452i	−0.245121	+	0.424562i	0.717045	+	0.697027i	$0.245494\pi$
$572$	−0.611418	+	0.353002i	−0.0255647	+	0.0147598i
$573$			9.87740i			0.412634i
$574$	−1.43920			−0.0600712
$575$	−13.5168	+	10.5270i	−0.563691	+	0.439007i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	26.0152	−	15.0199i	1.08303	−	0.625286i	0.151316	−	0.988485i	$-0.451649\pi$
$577$	26.0152	−	15.0199i	1.08303	−	0.625286i	0.931712	+	0.363199i	$0.118315\pi$
$578$	−18.8817	−	10.9014i	−0.785377	−	0.453438i
$579$	4.36812	−	7.56580i	0.181533	−	0.314424i
$580$	6.99546	−	14.3148i	0.290471	−	0.594391i
$581$	6.22882			0.258415
$582$	8.24181	−	4.75841i	0.341634	−	0.197242i
$583$	1.36728	−	0.789399i	0.0566269	−	0.0326936i
$584$	5.23074	−	9.05991i	0.216450	−	0.374902i
$585$	−0.597095	−	8.63439i	−0.0246868	−	0.356988i
$586$	−4.25665	−	7.37274i	−0.175841	−	0.304565i
$587$			37.1122i			1.53178i	0.642969	+	0.765892i	$0.277702\pi$
$587$			37.1122i			1.53178i	−0.642969	+	0.765892i	$0.722298\pi$
$588$		−	6.40210i		−	0.264018i
$589$	2.98057	+	1.47255i	0.122812	+	0.0606755i
$590$	1.86267	+	26.9355i	0.0766851	+	1.10892i
$591$	1.32667			0.0545721
$592$	5.54979	−	3.20418i	0.228095	−	0.131691i
$593$			11.8545i			0.486806i	0.969925	+	0.243403i	$0.0782638\pi$
$593$			11.8545i			0.486806i	−0.969925	+	0.243403i	$0.921736\pi$
$594$	−0.0912000	+	0.157963i	−0.00374198	+	0.00648130i
$595$	−6.01585	−	8.93369i	−0.246626	−	0.366246i
$596$	−6.29694	−	10.9066i	−0.257933	−	0.446752i
$597$			24.6334i			1.00818i
$598$	−11.4859	−	6.63137i	−0.469692	−	0.271177i
$599$	8.73826	−	15.1351i	0.357036	−	0.618404i	−0.630428	−	0.776247i	$-0.717121\pi$
$599$	8.73826	−	15.1351i	0.357036	−	0.618404i	0.987464	+	0.157843i	$0.0504541\pi$
$600$	1.88017	−	4.63303i	0.0767576	−	0.189143i
$601$	−12.7413	−	22.0685i	−0.519728	−	0.900195i	−0.999737	−	0.0229313i	$-0.992700\pi$
$601$	−12.7413	−	22.0685i	−0.519728	−	0.900195i	0.480009	−	0.877263i	$-0.340633\pi$
$602$	4.47410	+	2.58312i	0.182351	+	0.105280i
$603$	0.371098	−	0.214254i	0.0151123	−	0.00872509i
$604$	−12.8986			−0.524835
$605$	24.4639	−	1.69176i	0.994600	−	0.0687797i
$606$	−5.87840	−	10.1817i	−0.238794	−	0.413603i
$607$	30.6602	+	17.7016i	1.24446	+	0.718488i	0.969998	−	0.243111i	$-0.0781680\pi$
$607$	30.6602	+	17.7016i	1.24446	+	0.718488i	0.274459	+	0.961599i	$0.411501\pi$
$608$	−0.517099	+	0.298547i	−0.0209711	+	0.0121077i
$609$	−2.75480	+	4.77145i	−0.111630	+	0.193349i
$610$	−1.95998	−	0.957817i	−0.0793574	−	0.0387809i
$611$	−11.9466	+	20.6920i	−0.483306	+	0.837111i
$612$			6.22919i			0.251800i
$613$	4.02516	−	2.32392i	0.162574	−	0.0938624i	−0.416505	−	0.909133i	$-0.636745\pi$
$613$	4.02516	−	2.32392i	0.162574	−	0.0938624i	0.579080	+	0.815271i	$0.303412\pi$
$614$	10.7902	+	18.6892i	0.435458	+	0.754235i
$615$	−3.73929	−	1.82734i	−0.150783	−	0.0736855i
$616$	0.141039			0.00568263
$617$	33.5728	−	19.3833i	1.35159	−	0.780341i	0.363119	−	0.931743i	$-0.381712\pi$
$617$	33.5728	−	19.3833i	1.35159	−	0.780341i	0.988472	+	0.151401i	$0.0483786\pi$
$618$			9.62886i			0.387329i
$619$	−26.0289			−1.04619			−0.523096	−	0.852274i	$-0.675223\pi$
$619$	−26.0289			−1.04619			−0.523096	+	0.852274i	$0.675223\pi$
$620$	−1.66039	−	12.3387i	−0.0666829	−	0.495533i
$621$	−3.42650			−0.137501
$622$		−	7.50012i		−	0.300727i
$623$	−0.562492	+	0.324755i	−0.0225358	+	0.0130110i
$624$	3.87064			0.154950
$625$	−6.12273	+	24.2386i	−0.244909	+	0.969546i
$626$	5.87130	+	10.1694i	0.234664	+	0.406451i
$627$	−0.0943189	+	0.0544551i	−0.00376674	+	0.00217473i
$628$			14.4319i			0.575897i
$629$	19.9594	−	34.5707i	0.795834	−	1.37842i
$630$	−0.759149	+	1.55345i	−0.0302452	+	0.0618909i
$631$	−3.96941	+	6.87523i	−0.158020	+	0.273698i	−0.934155	−	0.356869i	$-0.883844\pi$
$631$	−3.96941	+	6.87523i	−0.158020	+	0.273698i	0.776135	+	0.630567i	$0.217178\pi$
$632$	−6.30578	+	3.64065i	−0.250831	+	0.144817i
$633$	14.0562	+	8.11534i	0.558683	+	0.322556i
$634$	12.5819	+	21.7925i	0.499692	+	0.865493i
$635$	−1.85088	−	26.7650i	−0.0734500	−	1.06214i
$636$	−8.65569			−0.343220
$637$	−21.4603	+	12.3901i	−0.850288	+	0.490914i
$638$	1.12554	+	0.649829i	0.0445604	+	0.0257270i
$639$	−4.02888	−	6.97823i	−0.159380	−	0.276055i
$640$	2.00901	+	0.981775i	0.0794131	+	0.0388081i
$641$	4.48266	−	7.76419i	0.177054	−	0.306667i	−0.763816	−	0.645434i	$-0.776676\pi$
$641$	4.48266	−	7.76419i	0.177054	−	0.306667i	0.940870	+	0.338767i	$0.110010\pi$
$642$	6.18652	+	3.57179i	0.244162	+	0.140967i
$643$			3.96229i			0.156257i	0.996943	+	0.0781287i	$0.0248945\pi$
$643$			3.96229i			0.156257i	−0.996943	+	0.0781287i	$0.975106\pi$
$644$	1.32476	+	2.29455i	0.0522027	+	0.0904177i
$645$	8.34470	+	12.3921i	0.328572	+	0.487938i
$646$	−1.85971	+	3.22111i	−0.0731692	+	0.126733i
$647$		−	4.25345i		−	0.167220i	−0.996499	−	0.0836102i	$-0.973355\pi$
$647$		−	4.25345i		−	0.167220i	0.996499	−	0.0836102i	$-0.0266451\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−2.20243			−0.0864528
$650$	−19.1690	+	2.66393i	−0.751869	+	0.104488i
$651$	0.278445	+	4.29621i	0.0109131	+	0.168382i
$652$		−	1.86439i		−	0.0730150i
$653$		−	22.0646i		−	0.863455i	−0.902004	−	0.431727i	$-0.857904\pi$
$653$		−	22.0646i		−	0.863455i	0.902004	−	0.431727i	$-0.142096\pi$
$654$	7.99606	+	13.8496i	0.312671	+	0.541561i
$655$	18.4923	−	1.27880i	0.722555	−	0.0499669i
$656$	0.930631	−	1.61190i	0.0363350	−	0.0629341i
$657$	−9.05991	+	5.23074i	−0.353461	+	0.204071i
$658$	4.13367	−	2.38658i	0.161147	−	0.0930384i
$659$	−6.39574			−0.249143			−0.124571	−	0.992211i	$-0.539756\pi$
$659$	−6.39574			−0.249143			−0.124571	+	0.992211i	$0.539756\pi$
$660$	0.366443	+	0.179076i	0.0142638	+	0.00697052i
$661$	−13.5355	+	23.4443i	−0.526472	+	0.911876i	0.473052	+	0.881034i	$0.343152\pi$
$661$	−13.5355	+	23.4443i	−0.526472	+	0.911876i	−0.999524	+	0.0308417i	$0.990181\pi$
$662$	28.4518	+	16.4267i	1.10581	+	0.638440i
$663$	20.8807	−	12.0555i	0.810938	−	0.468196i
$664$	−4.02773	+	6.97624i	−0.156306	+	0.270731i
$665$	−0.856334	+	0.576645i	−0.0332072	+	0.0223614i
$666$	−6.40835			−0.248319
$667$			24.4149i			0.945349i
$668$	0.608695	−	0.351430i	0.0235511	−	0.0135972i
$669$	−9.98614	+	17.2965i	−0.386087	+	0.668722i
$670$	−0.535191	−	0.794773i	−0.0206762	−	0.0307048i
$671$	0.0889745	−	0.154108i	0.00343482	−	0.00594929i
$672$	−0.669647	−	0.386621i	−0.0258322	−	0.0149142i
$673$	−6.01517	−	3.47286i	−0.231868	−	0.133869i	0.379566	−	0.925165i	$-0.376073\pi$
$673$	−6.01517	−	3.47286i	−0.231868	−	0.133869i	−0.611433	+	0.791296i	$0.709407\pi$
$674$	12.7086			0.489516
$675$	−3.94479	+	3.07224i	−0.151835	+	0.118250i
$676$	−0.990925	−	1.71633i	−0.0381125	−	0.0660128i
$677$	5.78792	+	3.34166i	0.222448	+	0.128430i	0.607083	−	0.794638i	$-0.292339\pi$
$677$	5.78792	+	3.34166i	0.222448	+	0.128430i	−0.384635	+	0.923069i	$0.625673\pi$
$678$		−	14.1977i		−	0.545260i
$679$	3.67940	+	6.37291i	0.141202	+	0.244570i
$680$	13.8957	−	0.960930i	0.532876	−	0.0368500i
$681$	23.3555			0.894985
$682$	1.01343	−	0.0656824i	0.0388064	−	0.00251511i
$683$			5.17502i			0.198017i	0.995087	+	0.0990083i	$0.0315671\pi$
$683$			5.17502i			0.198017i	−0.995087	+	0.0990083i	$0.968433\pi$
$684$	0.597095			0.0228305
$685$	23.8159	−	16.0373i	0.909958	−	0.612755i
$686$	10.3631			0.395663
$687$	11.5373	+	6.66108i	0.440176	+	0.254136i
$688$	−5.78617	+	3.34064i	−0.220596	+	0.127361i
$689$	16.7515	+	29.0145i	0.638182	+	1.10536i
$690$	0.528581	+	7.64363i	0.0201227	+	0.290988i
$691$	−21.5450	+	37.3170i	−0.819610	+	1.41961i	0.0863607	+	0.996264i	$0.472476\pi$
$691$	−21.5450	+	37.3170i	−0.819610	+	1.41961i	−0.905970	+	0.423341i	$0.860857\pi$
$692$	−6.36230	−	3.67328i	−0.241858	−	0.139637i
$693$	−0.122144	−	0.0705196i	−0.00463985	−	0.00267882i
$694$	15.0491	+	26.0657i	0.571254	+	0.989442i
$695$	−3.78051	+	7.73606i	−0.143403	+	0.293445i
$696$	−3.56266	−	6.17071i	−0.135042	−	0.233900i
$697$		−	11.5941i		−	0.439160i
$698$		−	8.86982i		−	0.335727i
$699$	−5.31166	−	9.20007i	−0.200905	−	0.347978i
$700$	3.58245	+	1.45383i	0.135404	+	0.0549494i
$701$	−7.89296	−	13.6710i	−0.298113	−	0.516347i	0.677591	−	0.735439i	$-0.263024\pi$
$701$	−7.89296	−	13.6710i	−0.298113	−	0.516347i	−0.975704	+	0.219092i	$0.929691\pi$
$702$	−3.35207	−	1.93532i	−0.126516	−	0.0730439i
$703$	−3.31375	−	1.91320i	−0.124981	−	0.0721576i
$704$	−0.0912000	+	0.157963i	−0.00343723	+	0.00595346i
$705$	13.7702	−	0.952249i	0.518614	−	0.0358638i
$706$	−5.98210	−	10.3613i	−0.225139	−	0.389953i
$707$	7.87290	−	4.54542i	0.296091	−	0.170948i
$708$	10.4570	+	6.03735i	0.392998	+	0.226898i
$709$	12.5564			0.471567			0.235783	−	0.971806i	$-0.424234\pi$
$709$	12.5564			0.471567			0.235783	+	0.971806i	$0.424234\pi$
$710$	−14.9451	+	10.0639i	−0.560880	+	0.377690i
$711$	7.28129			0.273070
$712$		−	0.839983i		−	0.0314797i
$713$	10.5876	+	15.8705i	0.396508	+	0.594353i
$714$	−4.81667			−0.180259
$715$	−0.108910	−	1.57491i	−0.00407301	−	0.0588984i
$716$	0.245463	+	0.425154i	0.00917337	+	0.0158887i
$717$			9.29400i			0.347091i
$718$	4.58455	+	2.64689i	0.171094	+	0.0987810i
$719$	7.65650	+	13.2615i	0.285539	+	0.494569i	0.972740	−	0.231899i	$-0.0744939\pi$
$719$	7.65650	+	13.2615i	0.285539	+	0.494569i	−0.687200	+	0.726468i	$0.741161\pi$
$720$	−1.24897	−	1.85475i	−0.0465462	−	0.0691223i
$721$	−7.44543			−0.277282
$722$	−16.1457	−	9.32174i	−0.600882	−	0.346919i
$723$	−7.24239	−	4.18140i	−0.269347	−	0.155508i
$724$	−8.47857	+	14.6853i	−0.315103	+	0.545775i
$725$	21.8907	+	28.1079i	0.812999	+	1.04390i
$726$	5.48337	−	9.49747i	0.203507	−	0.352484i
$727$	1.68725	−	0.974136i	0.0625768	−	0.0361287i	−0.468385	−	0.883524i	$-0.655164\pi$
$727$	1.68725	−	0.974136i	0.0625768	−	0.0361287i	0.530962	+	0.847396i	$0.321831\pi$
$728$			2.99294i			0.110926i
$729$	−1.00000			−0.0370370
$730$	13.0660	+	19.4034i	0.483595	+	0.718152i
$731$	−20.8095	+	36.0431i	−0.769667	+	1.33310i
$732$	−0.844892	+	0.487799i	−0.0312281	+	0.0180296i
$733$	7.42242	+	4.28533i	0.274153	+	0.158282i	0.630774	−	0.775967i	$-0.282738\pi$
$733$	7.42242	+	4.28533i	0.274153	+	0.158282i	−0.356620	+	0.934249i	$0.616071\pi$
$734$	−11.2178	+	19.4298i	−0.414057	+	0.717167i
$735$	12.8619	+	6.28542i	0.474417	+	0.231841i
$736$	−3.42650			−0.126302
$737$	0.0676884	−	0.0390799i	0.00249333	−	0.00143953i
$738$	−1.61190	+	0.930631i	−0.0593348	+	0.0342570i
$739$	16.2472	−	28.1409i	0.597662	−	1.03518i	−0.395504	−	0.918464i	$-0.629430\pi$
$739$	16.2472	−	28.1409i	0.597662	−	1.03518i	0.993165	−	0.116716i	$-0.0372367\pi$
$740$	0.988569	+	14.2954i	0.0363405	+	0.525508i
$741$	−1.15557	−	2.00150i	−0.0424509	−	0.0735271i
$742$		−	6.69294i		−	0.245705i
$743$		−	39.0832i		−	1.43383i	−0.697163	−	0.716913i	$-0.745555\pi$
$743$		−	39.0832i		−	1.43383i	0.697163	−	0.716913i	$-0.254445\pi$
$744$	−4.99178	−	2.46620i	−0.183008	−	0.0904152i
$745$	28.0937	−	1.94276i	1.02927	−	0.0711773i
$746$	3.89756			0.142700
$747$	6.97624	−	4.02773i	0.255247	−	0.147367i
$748$			1.13620i			0.0415437i
$749$	−2.76186	+	4.78367i	−0.100916	+	0.174792i
$750$	7.46189	+	8.32587i	0.272470	+	0.304018i
$751$	11.3158	+	19.5996i	0.412920	+	0.715199i	0.995208	−	0.0977840i	$-0.0311754\pi$
$751$	11.3158	+	19.5996i	0.412920	+	0.715199i	−0.582287	+	0.812983i	$0.697842\pi$
$752$			6.17291i			0.225103i
$753$	−15.7872	−	9.11474i	−0.575317	−	0.332160i
$754$	−13.7898	+	23.8846i	−0.502194	+	0.869825i
$755$	12.6635	−	25.9133i	0.460871	−	0.943082i
$756$	0.386621	+	0.669647i	0.0140613	+	0.0243548i
$757$	13.7398	+	7.93270i	0.499383	+	0.288319i	0.728459	−	0.685090i	$-0.240237\pi$
$757$	13.7398	+	7.93270i	0.499383	+	0.288319i	−0.229076	+	0.973409i	$0.573570\pi$
$758$	20.3497	−	11.7489i	0.739133	−	0.426738i
$759$	−0.624994			−0.0226858
$760$	−0.0921094	−	1.33196i	−0.00334116	−	0.0483154i
$761$	−21.8886	−	37.9122i	−0.793462	−	1.37432i	−0.923811	−	0.382849i	$-0.874943\pi$
$761$	−21.8886	−	37.9122i	−0.793462	−	1.37432i	0.130349	−	0.991468i	$-0.458390\pi$
$762$	−10.3908	−	5.99913i	−0.376419	−	0.217326i
$763$	−10.7091	+	6.18288i	−0.387694	+	0.223835i
$764$	4.93870	−	8.55408i	0.178676	−	0.309476i
$765$	−12.5145	−	6.11566i	−0.452462	−	0.221112i
$766$	−3.02189	+	5.23407i	−0.109185	+	0.189115i
$767$		−	46.7368i		−	1.68757i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−10.3459	−	17.9196i	−0.373081	−	0.646196i	0.616956	−	0.786997i	$-0.288365\pi$
$769$	−10.3459	−	17.9196i	−0.373081	−	0.646196i	−0.990038	+	0.140801i	$0.955032\pi$
$770$	−0.138469	+	0.283349i	−0.00499007	+	0.0102112i
$771$	1.49335			0.0537818
$772$	−7.56580	+	4.36812i	−0.272299	+	0.157212i
$773$			4.79978i			0.172636i	0.996268	+	0.0863180i	$0.0275101\pi$
$773$			4.79978i			0.172636i	−0.996268	+	0.0863180i	$0.972490\pi$
$774$	6.68129			0.240154
$775$	26.4187	+	8.77807i	0.948986	+	0.315318i
$776$	−9.51682			−0.341634
$777$		−	4.95520i		−	0.177767i
$778$	5.56997	−	3.21583i	0.199693	−	0.115293i
$779$	−1.11135			−0.0398182
$780$	−3.80010	+	7.77615i	−0.136065	+	0.278431i
$781$	−0.734869	−	1.27283i	−0.0262957	−	0.0455454i
$782$	−18.4847	+	10.6722i	−0.661012	+	0.381635i
$783$			7.12532i			0.254638i
$784$	−3.20105	+	5.54438i	−0.114323	+	0.198014i
$785$	−28.9939	−	14.1689i	−1.03484	−	0.505711i
$786$	4.14488	−	7.17915i	0.147843	−	0.256072i
$787$	−32.8966	+	18.9928i	−1.17264	+	0.677022i	−0.954299	−	0.298852i	$-0.903396\pi$
$787$	−32.8966	+	18.9928i	−1.17264	+	0.677022i	−0.218336	+	0.975874i	$0.570063\pi$
$788$	−1.14893	−	0.663337i	−0.0409291	−	0.0236304i
$789$	−10.8721	−	18.8311i	−0.387058	−	0.670404i
$790$	−1.12323	−	16.2427i	−0.0399628	−	0.577888i
$791$	10.9783			0.390342
$792$	0.157963	−	0.0912000i	0.00561297	−	0.00324065i
$793$	3.27027	+	1.88809i	0.116131	+	0.0670481i
$794$	−17.0578	−	29.5449i	−0.605358	−	1.04851i
$795$	8.49794	−	17.3894i	0.301391	−	0.616737i
$796$	12.3167	−	21.3331i	0.436553	−	0.756132i
$797$	−1.01175	−	0.584137i	−0.0358382	−	0.0206912i	0.481974	−	0.876186i	$-0.339920\pi$
$797$	−1.01175	−	0.584137i	−0.0358382	−	0.0206912i	−0.517812	+	0.855494i	$0.673253\pi$
$798$			0.461698i			0.0163439i
$799$	19.2261	+	33.3006i	0.680171	+	1.17809i
$800$	−3.94479	+	3.07224i	−0.139469	+	0.108620i
$801$	−0.419992	+	0.727447i	−0.0148397	+	0.0257031i
$802$			36.6374i			1.29371i
$803$	−1.65253	+	0.954087i	−0.0583164	+	0.0336690i
$804$	−0.428507			−0.0151123
$805$	−5.91037	+	0.408721i	−0.208313	+	0.0144055i
$806$	1.39382	+	21.5057i	0.0490952	+	0.757506i
$807$		−	13.9113i		−	0.489700i
$808$			11.7568i			0.413603i
$809$	26.1993	+	45.3786i	0.921119	+	1.59543i	0.797687	+	0.603072i	$0.206057\pi$
$809$	26.1993	+	45.3786i	0.921119	+	1.59543i	0.123433	+	0.992353i	$0.460610\pi$
$810$	0.154263	+	2.23074i	0.00542023	+	0.0783802i
$811$	−12.9976	+	22.5125i	−0.456408	+	0.790522i	−0.998768	−	0.0496241i	$-0.984198\pi$
$811$	−12.9976	+	22.5125i	−0.456408	+	0.790522i	0.542360	+	0.840146i	$0.317531\pi$
$812$	4.77145	−	2.75480i	0.167445	−	0.0966744i
$813$	14.4230	−	8.32714i	0.505838	−	0.292045i
$814$	−1.16888			−0.0409693
$815$	3.74557	+	1.83041i	0.131202	+	0.0641164i
$816$	3.11459	−	5.39463i	0.109033	−	0.188850i
$817$	3.45489	+	1.99468i	0.120871	+	0.0697851i
$818$	−18.2997	+	10.5653i	−0.639833	+	0.369408i
$819$	1.49647	−	2.59196i	0.0522909	−	0.0905705i
$820$	2.32465	+	3.45217i	0.0811803	+	0.120555i
$821$	−34.7207			−1.21176			−0.605880	−	0.795556i	$-0.707179\pi$
$821$	−34.7207			−1.21176			−0.605880	+	0.795556i	$0.707179\pi$
$822$		−	12.8405i		−	0.447864i
$823$	23.9449	−	13.8246i	0.834667	−	0.481895i	−0.0207808	−	0.999784i	$-0.506615\pi$
$823$	23.9449	−	13.8246i	0.834667	−	0.481895i	0.855448	+	0.517889i	$0.173282\pi$
$824$	4.81443	−	8.33883i	0.167719	−	0.290497i
$825$	−0.719530	+	0.560376i	−0.0250508	+	0.0195098i
$826$	−4.66833	+	8.08579i	−0.162432	+	0.281341i
$827$	−13.7054	−	7.91284i	−0.476585	−	0.275156i	0.242407	−	0.970175i	$-0.422063\pi$
$827$	−13.7054	−	7.91284i	−0.476585	−	0.275156i	−0.718992	+	0.695018i	$0.755396\pi$
$828$	2.96744	+	1.71325i	0.103126	+	0.0595396i
$829$	40.3193			1.40035			0.700173	−	0.713973i	$-0.253106\pi$
$829$	40.3193			1.40035			0.700173	+	0.713973i	$0.253106\pi$
$830$	−10.0610	−	14.9409i	−0.349222	−	0.518605i
$831$	7.68356	+	13.3083i	0.266540	+	0.461660i
$832$	−3.35207	−	1.93532i	−0.116212	−	0.0670951i
$833$			39.8799i			1.38176i
$834$	1.92534	+	3.33479i	0.0666691	+	0.115474i
$835$	0.108425	+	1.56790i	0.00375220	+	0.0542593i
$836$	0.108910			0.00376674
$837$	3.08991	+	4.63168i	0.106803	+	0.160094i
$838$			22.8606i			0.789706i
$839$	34.2514			1.18249			0.591245	−	0.806492i	$-0.298637\pi$
$839$	34.2514			1.18249			0.591245	+	0.806492i	$0.298637\pi$
$840$	1.43417	−	0.965752i	0.0494835	−	0.0333216i
$841$	21.7701			0.750695
$842$	11.8383	+	6.83483i	0.407974	+	0.235544i
$843$	15.1091	−	8.72323i	0.520384	−	0.300444i
$844$	−8.11534	−	14.0562i	−0.279342	−	0.483834i
$845$	4.42099	−	0.305725i	0.152087	−	0.0105173i
$846$	3.08646	−	5.34590i	0.106115	−	0.183796i
$847$	7.34384	+	4.23997i	0.252337	+	0.145687i
$848$	7.49604	+	4.32784i	0.257415	+	0.148619i
$849$	14.4645	+	25.0533i	0.496421	+	0.859826i
$850$	−11.7119	+	28.8600i	−0.401716	+	0.989890i
$851$	−10.9791	−	19.0164i	−0.376359	−	0.651873i
$852$			8.05777i			0.276055i
$853$			32.9827i			1.12931i	0.825328	+	0.564654i	$0.190990\pi$
$853$			32.9827i			1.12931i	−0.825328	+	0.564654i	$0.809010\pi$
$854$	−0.377186	−	0.653305i	−0.0129070	−	0.0223557i
$855$	−0.586213	+	1.19957i	−0.0200481	+	0.0410244i
$856$	−3.57179	−	6.18652i	−0.122081	−	0.211451i
$857$	−16.7037	−	9.64390i	−0.570588	−	0.329429i	0.186796	−	0.982399i	$-0.440190\pi$
$857$	−16.7037	−	9.64390i	−0.570588	−	0.329429i	−0.757384	+	0.652969i	$0.773523\pi$
$858$	−0.611418	−	0.353002i	−0.0208735	−	0.0120513i
$859$	−18.9369	+	32.7997i	−0.646120	+	1.11911i	0.337922	+	0.941174i	$0.390276\pi$
$859$	−18.9369	+	32.7997i	−0.646120	+	1.11911i	−0.984042	+	0.177938i	$0.943057\pi$
$860$	−1.03067	−	14.9042i	−0.0351456	−	0.508230i
$861$	−0.719602	−	1.24639i	−0.0245240	−	0.0424768i
$862$	−15.7672	+	9.10321i	−0.537034	+	0.310057i
$863$	0.655557	+	0.378486i	0.0223154	+	0.0128838i	0.511116	−	0.859512i	$-0.329232\pi$
$863$	0.655557	+	0.378486i	0.0223154	+	0.0128838i	−0.488801	+	0.872395i	$0.662566\pi$
$864$	−1.00000			−0.0340207
$865$	13.6260	−	9.17559i	0.463298	−	0.311980i
$866$	2.97874			0.101222
$867$		−	21.8028i		−	0.740461i
$868$	1.90697	−	3.85985i	0.0647266	−	0.131012i
$869$	1.32811			0.0450530
$870$	15.8947	−	1.09917i	0.538882	−	0.0372653i
$871$	0.829299	+	1.43639i	0.0280997	+	0.0486702i
$872$		−	15.9921i		−	0.541561i
$873$	8.24181	+	4.75841i	0.278943	+	0.161048i
$874$	1.02297	+	1.77184i	0.0346026	+	0.0599334i
$875$	−6.43791	+	5.76985i	−0.217641	+	0.195056i
$876$	10.4615			0.353461
$877$	1.71623	+	0.990863i	0.0579528	+	0.0334591i	0.528696	−	0.848811i	$-0.322681\pi$
$877$	1.71623	+	0.990863i	0.0579528	+	0.0334591i	−0.470744	+	0.882270i	$0.656014\pi$
$878$	−3.25908	−	1.88163i	−0.109989	−	0.0635019i
$879$	4.25665	−	7.37274i	0.143573	−	0.248676i
$880$	−0.227811	−	0.338306i	−0.00767952	−	0.0114043i
$881$	−25.1594	+	43.5774i	−0.847643	+	1.46816i	0.0356635	+	0.999364i	$0.488646\pi$
$881$	−25.1594	+	43.5774i	−0.847643	+	1.46816i	−0.883306	+	0.468796i	$0.844688\pi$
$882$	5.54438	−	3.20105i	0.186689	−	0.107785i
$883$		−	11.1079i		−	0.373809i	−0.982378	−	0.186905i	$-0.940154\pi$
$883$		−	11.1079i		−	0.373809i	0.982378	−	0.186905i	$-0.0598456\pi$
$884$	−24.1109			−0.810938
$885$	−22.3955	+	15.0809i	−0.752817	+	0.506939i
$886$	−13.5654	+	23.4960i	−0.455739	+	0.789362i
$887$	−15.3394	+	8.85623i	−0.515048	+	0.297363i	−0.734906	−	0.678169i	$-0.762774\pi$
$887$	−15.3394	+	8.85623i	−0.515048	+	0.297363i	0.219858	+	0.975532i	$0.429441\pi$
$888$	5.54979	+	3.20418i	0.186239	+	0.107525i
$889$	4.63878	−	8.03459i	0.155580	−	0.269472i
$890$	1.68753	+	0.824674i	0.0565663	+	0.0276432i
$891$	−0.182400			−0.00611063
$892$	17.2965	−	9.98614i	0.579130	−	0.334361i
$893$	3.19201	−	1.84291i	0.106816	−	0.0616705i
$894$	6.29694	−	10.9066i	0.210601	−	0.364772i
$895$	−1.09513	+	0.0757314i	−0.0366060	+	0.00253142i
$896$	0.386621	+	0.669647i	0.0129161	+	0.0223713i
$897$		−	13.2627i		−	0.442830i
$898$			41.4038i			1.38166i
$899$	33.0022	−	22.0166i	1.10068	−	0.734294i
$900$	4.95241	−	0.688239i	0.165080	−	0.0229413i
$901$	53.9179			1.79627
$902$	−0.294011	+	0.169747i	−0.00978948	+	0.00565196i
$903$			5.16625i			0.171922i
$904$	−7.09885	+	12.2956i	−0.236104	+	0.408945i
$905$	−21.1789	−	31.4512i	−0.704010	−	1.04547i
$906$	−6.44928	−	11.1705i	−0.214263	−	0.371114i
$907$		−	0.154060i		−	0.00511547i	−0.999997	−	0.00255774i	$-0.999186\pi$
$907$		−	0.154060i		−	0.00511547i	0.999997	−	0.00255774i	$-0.000814153\pi$
$908$	−20.2265	−	11.6778i	−0.671239	−	0.387540i
$909$	5.87840	−	10.1817i	0.194974	−	0.337705i
$910$	−6.01284	−	2.93839i	−0.199324	−	0.0974068i
$911$	−5.64684	−	9.78062i	−0.187088	−	0.324046i	0.757190	−	0.653195i	$-0.226572\pi$
$911$	−5.64684	−	9.78062i	−0.187088	−	0.324046i	−0.944278	+	0.329148i	$0.893238\pi$
$912$	−0.517099	−	0.298547i	−0.0171229	−	0.00988589i
$913$	1.27247	−	0.734659i	0.0421125	−	0.0243137i
$914$	24.6010			0.813729
$915$	−0.150498	−	2.17630i	−0.00497531	−	0.0719464i
$916$	−6.66108	−	11.5373i	−0.220088	−	0.381204i
$917$	5.55122	+	3.20500i	0.183317	+	0.105838i
$918$	−5.39463	+	3.11459i	−0.178049	+	0.102797i
$919$	−1.62927	+	2.82198i	−0.0537446	+	0.0930884i	−0.891646	−	0.452733i	$-0.850449\pi$
$919$	−1.62927	+	2.82198i	−0.0537446	+	0.0930884i	0.837901	+	0.545822i	$0.183782\pi$
$920$	3.36405	−	6.88387i	0.110910	−	0.226955i
$921$	−10.7902	+	18.6892i	−0.355550	+	0.615830i
$922$			5.75649i			0.189580i
$923$	27.0102	−	15.5944i	0.889052	−	0.513295i
$924$	0.0705196	+	0.122144i	0.00231993	+	0.00401823i
$925$	−29.6901	−	12.0488i	−0.976204	−	0.396162i
$926$	−30.2945			−0.995540
$927$	−8.33883	+	4.81443i	−0.273883	+	0.158127i
$928$			7.12532i			0.233900i
$929$	5.49130			0.180164			0.0900819	−	0.995934i	$-0.471287\pi$
$929$	5.49130			0.180164			0.0900819	+	0.995934i	$0.471287\pi$
$930$	9.85542	−	7.60728i	0.323172	−	0.249453i
$931$	3.82266			0.125283
$932$			10.6233i			0.347978i
$933$	6.49529	−	3.75006i	0.212646	−	0.122771i
$934$	24.8358			0.812653
$935$	−2.28264	−	1.11550i	−0.0746504	−	0.0364806i
$936$	1.93532	+	3.35207i	0.0632579	+	0.109566i
$937$	39.2023	−	22.6335i	1.28068	−	0.739403i	0.303710	−	0.952764i	$-0.401775\pi$
$937$	39.2023	−	22.6335i	1.28068	−	0.739403i	0.976973	+	0.213362i	$0.0684412\pi$
$938$		−	0.331340i		−	0.0108186i
$939$	−5.87130	+	10.1694i	−0.191603	+	0.331866i
$940$	−12.4014	−	6.06041i	−0.404490	−	0.197669i
$941$	−0.692766	+	1.19991i	−0.0225835	+	0.0391158i	−0.877096	−	0.480315i	$-0.840523\pi$
$941$	−0.692766	+	1.19991i	−0.0225835	+	0.0391158i	0.854513	+	0.519430i	$0.173856\pi$
$942$	−12.4984	+	7.21597i	−0.407221	+	0.235109i
$943$	−5.52318	−	3.18881i	−0.179859	−	0.103842i
$944$	−6.03735	−	10.4570i	−0.196499	−	0.340346i
$945$	−1.72490	+	0.119282i	−0.0561110	+	0.00388025i
$946$	1.21867			0.0396223
$947$	11.0470	−	6.37797i	0.358978	−	0.207256i	−0.309654	−	0.950849i	$-0.600213\pi$
$947$	11.0470	−	6.37797i	0.358978	−	0.207256i	0.668633	+	0.743593i	$0.266880\pi$
$948$	−6.30578	−	3.64065i	−0.204802	−	0.118243i
$949$	−20.2463	−	35.0676i	−0.657223	−	1.13834i
$950$	2.76636	+	1.12264i	0.0897525	+	0.0364232i
$951$	−12.5819	+	21.7925i	−0.407997	+	0.706672i
$952$	4.17135	+	2.40833i	0.135194	+	0.0780545i
$953$		−	34.8545i		−	1.12905i	−0.825417	−	0.564524i	$-0.809060\pi$
$953$		−	34.8545i		−	1.12905i	0.825417	−	0.564524i	$-0.190940\pi$
$954$	−4.32784	−	7.49604i	−0.140119	−	0.242693i
$955$	12.3365	+	18.3201i	0.399201	+	0.592824i
$956$	4.64700	−	8.04884i	0.150295	−	0.260318i
$957$			1.29966i			0.0420120i
$958$	−33.6819	+	19.4463i	−1.08821	+	0.628281i
$959$	9.92881			0.320618
$960$	0.154263	+	2.23074i	0.00497880	+	0.0719968i
$961$	11.9049	−	28.6229i	0.384029	−	0.923321i
$962$		−	24.8044i		−	0.799726i
$963$			7.14358i			0.230199i
$964$	4.18140	+	7.24239i	0.134674	+	0.233262i
$965$	−1.34767	−	19.4883i	−0.0433832	−	0.627350i
$966$	−1.32476	+	2.29455i	−0.0426233	+	0.0738258i
$967$	38.4657	−	22.2082i	1.23697	−	0.714168i	0.268500	−	0.963280i	$-0.413472\pi$
$967$	38.4657	−	22.2082i	1.23697	−	0.714168i	0.968475	+	0.249112i	$0.0801387\pi$
$968$	−9.49747	+	5.48337i	−0.305260	+	0.176242i
$969$	−3.71941			−0.119485
$970$	9.34338	−	19.1194i	0.299998	−	0.613886i
$971$	3.59816	−	6.23220i	0.115470	−	0.200001i	−0.802497	−	0.596656i	$-0.796496\pi$
$971$	3.59816	−	6.23220i	0.115470	−	0.200001i	0.917968	+	0.396655i	$0.129829\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−2.57860	+	1.48875i	−0.0826661	+	0.0477273i
$974$	0.971337	−	1.68240i	0.0311236	−	0.0539077i
$975$	−11.8915	−	15.2689i	−0.380833	−	0.488995i
$976$	0.975597			0.0312281
$977$			42.7392i			1.36735i	0.729788	+	0.683673i	$0.239619\pi$
$977$			42.7392i			1.36735i	−0.729788	+	0.683673i	$0.760381\pi$
$978$	1.61461	−	0.932193i	0.0516294	−	0.0298082i
$979$	−0.0766065	+	0.132686i	−0.00244835	+	0.00424067i
$980$	−7.99600	−	11.8743i	−0.255423	−	0.379310i
$981$	−7.99606	+	13.8496i	−0.255294	+	0.442183i
$982$	−25.7295	−	14.8550i	−0.821062	−	0.474041i
$983$	−0.451740	−	0.260812i	−0.0144083	−	0.00831862i	0.492779	−	0.870155i	$-0.335981\pi$
$983$	−0.451740	−	0.260812i	−0.0144083	−	0.00831862i	−0.507187	+	0.861836i	$0.669315\pi$
$984$	1.86126			0.0593348
$985$	2.46065	−	1.65697i	0.0784027	−	0.0527955i
$986$	22.1925	+	38.4385i	0.706752	+	1.22413i
$987$	4.13367	+	2.38658i	0.131576	+	0.0759655i
$988$			2.31114i			0.0735271i
$989$	11.4467	+	19.8263i	0.363985	+	0.630440i
$990$	0.0281375	+	0.406887i	0.000894268	+	0.0129317i
$991$	−61.1300			−1.94186			−0.970930	−	0.239365i	$-0.923061\pi$
$991$	−61.1300			−1.94186			−0.970930	+	0.239365i	$0.923061\pi$
$992$	3.08991	+	4.63168i	0.0981047	+	0.147056i
$993$			32.8533i			1.04257i
$994$	−6.23060			−0.197623
$995$	30.7662	+	45.6887i	0.975355	+	1.44843i
$996$	−8.05547			−0.255247
$997$	−16.8876	−	9.75004i	−0.534834	−	0.308787i	0.208148	−	0.978097i	$-0.433256\pi$
$997$	−16.8876	−	9.75004i	−0.534834	−	0.308787i	−0.742983	+	0.669310i	$0.766590\pi$
$998$	−3.46166	+	1.99859i	−0.109577	+	0.0632643i
$999$	−3.20418	−	5.54979i	−0.101376	−	0.175588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.c.769.4	yes	24
5.4	even	2	inner	930.2.s.c.769.11	yes	24
31.5	even	3	inner	930.2.s.c.439.5	✓	24
155.129	even	6	inner	930.2.s.c.439.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.c.439.5	✓	24	31.5	even	3	inner
930.2.s.c.439.10	yes	24	155.129	even	6	inner
930.2.s.c.769.4	yes	24	1.1	even	1	trivial
930.2.s.c.769.11	yes	24	5.4	even	2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.981775 - 2.00901i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.981775 - 2.00901i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.00901 - 0.981775i) q^{10} +(0.0912000 - 0.157963i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(3.35207 + 1.93532i) q^{13} +(-0.386621 - 0.669647i) q^{14} +(-0.154263 - 2.23074i) q^{15} +1.00000 q^{16} +(5.39463 - 3.11459i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-0.298547 - 0.517099i) q^{19} +(-0.981775 + 2.00901i) q^{20} +(0.386621 - 0.669647i) q^{21} +(-0.157963 - 0.0912000i) q^{22} -3.42650i q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.07224 - 3.94479i) q^{25} +(1.93532 - 3.35207i) q^{26} -1.00000i q^{27} +(-0.669647 + 0.386621i) q^{28} -7.12532 q^{29} +(-2.23074 + 0.154263i) q^{30} +(-4.63168 + 3.08991i) q^{31} -1.00000i q^{32} -0.182400i q^{33} +(-3.11459 - 5.39463i) q^{34} +(-0.119282 - 1.72490i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.54979 - 3.20418i) q^{37} +(-0.517099 + 0.298547i) q^{38} +3.87064 q^{39} +(2.00901 + 0.981775i) q^{40} +(0.930631 - 1.61190i) q^{41} +(-0.669647 - 0.386621i) q^{42} +(-5.78617 + 3.34064i) q^{43} +(-0.0912000 + 0.157963i) q^{44} +(-1.24897 - 1.85475i) q^{45} -3.42650 q^{46} +6.17291i q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.20105 + 5.54438i) q^{49} +(-3.94479 + 3.07224i) q^{50} +(3.11459 - 5.39463i) q^{51} +(-3.35207 - 1.93532i) q^{52} +(7.49604 + 4.32784i) q^{53} -1.00000 q^{54} +(-0.227811 - 0.338306i) q^{55} +(0.386621 + 0.669647i) q^{56} +(-0.517099 - 0.298547i) q^{57} +7.12532i q^{58} +(-6.03735 - 10.4570i) q^{59} +(0.154263 + 2.23074i) q^{60} +0.975597 q^{61} +(3.08991 + 4.63168i) q^{62} -0.773241i q^{63} -1.00000 q^{64} +(7.17906 - 4.83430i) q^{65} -0.182400 q^{66} +(0.371098 + 0.214254i) q^{67} +(-5.39463 + 3.11459i) q^{68} +(-1.71325 - 2.96744i) q^{69} +(-1.72490 + 0.119282i) q^{70} +(4.02888 - 6.97823i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-9.05991 - 5.23074i) q^{73} +(-3.20418 - 5.54979i) q^{74} +(-4.63303 - 1.88017i) q^{75} +(0.298547 + 0.517099i) q^{76} -0.141039i q^{77} -3.87064i q^{78} +(3.64065 + 6.30578i) q^{79} +(0.981775 - 2.00901i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.61190 - 0.930631i) q^{82} +(6.97624 + 4.02773i) q^{83} +(-0.386621 + 0.669647i) q^{84} +(-0.960930 - 13.8957i) q^{85} +(3.34064 + 5.78617i) q^{86} +(-6.17071 + 3.56266i) q^{87} +(0.157963 + 0.0912000i) q^{88} -0.839983 q^{89} +(-1.85475 + 1.24897i) q^{90} +2.99294 q^{91} +3.42650i q^{92} +(-2.46620 + 4.99178i) q^{93} +6.17291 q^{94} +(-1.33196 + 0.0921094i) q^{95} +(-0.500000 - 0.866025i) q^{96} +9.51682i q^{97} +(5.54438 + 3.20105i) q^{98} +(-0.0912000 - 0.157963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

Introduction

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