LMFDB - Embedded newform 930.2.s.c.439.5

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			439.5
Character	$\chi$	$=$	930.439
Dual form			930.2.s.c.769.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(1.24897 + 1.85475i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(1.24897 + 1.85475i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.85475 - 1.24897i) 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} +(-1.24897 - 1.85475i) q^{20} +(0.386621 + 0.669647i) q^{21} +(0.157963 - 0.0912000i) q^{22} -3.42650i q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.88017 + 4.63303i) 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} +(-1.85475 + 1.24897i) 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} +(-0.981775 + 2.00901i) q^{45} -3.42650 q^{46} +6.17291i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.20105 - 5.54438i) q^{49} +(4.63303 + 1.88017i) q^{50} +(3.11459 + 5.39463i) q^{51} +(3.35207 - 1.93532i) q^{52} +(-7.49604 + 4.32784i) q^{53} -1.00000 q^{54} +(-0.179076 + 0.366443i) 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} +(-7.77615 - 3.80010i) 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} +(3.94479 - 3.07224i) q^{75} +(0.298547 - 0.517099i) q^{76} -0.141039i q^{77} -3.87064i q^{78} +(3.64065 - 6.30578i) q^{79} +(1.24897 + 1.85475i) 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} +(2.00901 + 0.981775i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	1.24897	+	1.85475i	0.558554	+	0.829468i
$5$	1.24897	+	1.85475i	0.558554	+	0.829468i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.669647	−	0.386621i	−0.253103	−	0.146129i	0.368081	−	0.929794i	$-0.380015\pi$
$7$	−0.669647	−	0.386621i	−0.253103	−	0.146129i	−0.621184	+	0.783665i	$0.713348\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.85475	−	1.24897i	0.586522	−	0.394958i
$11$	0.0912000	+	0.157963i	0.0274978	+	0.0476277i	0.879447	−	0.475997i	$-0.157913\pi$
$11$	0.0912000	+	0.157963i	0.0274978	+	0.0476277i	−0.851949	+	0.523625i	$0.824579\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−3.35207	+	1.93532i	−0.929698	+	0.536761i	−0.886716	−	0.462315i	$-0.847019\pi$
$13$	−3.35207	+	1.93532i	−0.929698	+	0.536761i	−0.0429816	+	0.999076i	$0.513686\pi$
$14$	−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	$-0.605891\pi$
$17$	−5.39463	−	3.11459i	−1.30839	−	0.755400i	−0.981828	+	0.189776i	$0.939224\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−0.298547	+	0.517099i	−0.0684915	+	0.118631i	−0.898237	−	0.439511i	$-0.855152\pi$
$19$	−0.298547	+	0.517099i	−0.0684915	+	0.118631i	0.829746	+	0.558141i	$0.188485\pi$
$20$	−1.24897	−	1.85475i	−0.279277	−	0.414734i
$21$	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
$25$	−1.88017	+	4.63303i	−0.376034	+	0.926606i
$26$	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	$-0.509928\pi$
$37$	−5.54979	−	3.20418i	−0.912381	−	0.526763i	−0.881196	+	0.472750i	$0.843261\pi$
$38$	0.517099	+	0.298547i	0.0838846	+	0.0484308i
$39$	3.87064			0.619798
$40$	−1.85475	+	1.24897i	−0.293261	+	0.197479i
$41$	0.930631	+	1.61190i	0.145340	+	0.251736i	0.929500	−	0.368823i	$-0.120239\pi$
$41$	0.930631	+	1.61190i	0.145340	+	0.251736i	−0.784160	+	0.620559i	$0.786906\pi$
$42$	0.669647	−	0.386621i	0.103329	−	0.0596569i
$43$	5.78617	+	3.34064i	0.882382	+	0.509444i	0.871443	−	0.490497i	$-0.163185\pi$
$43$	5.78617	+	3.34064i	0.882382	+	0.509444i	0.0109390	+	0.999940i	$0.496518\pi$
$44$	−0.0912000	−	0.157963i	−0.0137489	−	0.0238138i
$45$	−0.981775	+	2.00901i	−0.146354	+	0.299485i
$46$	−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
$50$	4.63303	+	1.88017i	0.655209	+	0.265896i
$51$	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	$-0.869307\pi$
$53$	−7.49604	+	4.32784i	−1.02966	+	0.594475i	−0.112773	+	0.993621i	$0.535973\pi$
$54$	−1.00000			−0.136083
$55$	−0.179076	+	0.366443i	−0.0241466	+	0.0494112i
$56$	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	0.142406	+	0.989808i	$0.454516\pi$
$59$	−6.03735	+	10.4570i	−0.785996	+	1.36139i	−0.928402	+	0.371577i	$0.878817\pi$
$60$	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
$65$	−7.77615	−	3.80010i	−0.964513	−	0.471344i
$66$	−0.182400			−0.0224519
$67$	−0.371098	+	0.214254i	−0.0453369	+	0.0261753i	−0.522497	−	0.852641i	$-0.674999\pi$
$67$	−0.371098	+	0.214254i	−0.0453369	+	0.0261753i	0.477160	+	0.878816i	$0.341666\pi$
$68$	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	0.999686	−	0.0250598i	$-0.00797761\pi$
$71$	4.02888	+	6.97823i	0.478141	+	0.828164i	−0.521545	+	0.853224i	$0.674644\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	9.05991	−	5.23074i	1.06038	−	0.612212i	0.134844	−	0.990867i	$-0.456947\pi$
$73$	9.05991	−	5.23074i	1.06038	−	0.612212i	0.925538	+	0.378655i	$0.123613\pi$
$74$	−3.20418	+	5.54979i	−0.372478	+	0.645151i
$75$	3.94479	−	3.07224i	0.455505	−	0.354751i
$76$	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	−0.585241	−	0.810860i	$-0.699000\pi$
$79$	3.64065	−	6.30578i	0.409605	−	0.709456i	0.994845	+	0.101404i	$0.0323333\pi$
$80$	1.24897	+	1.85475i	0.139639	+	0.207367i
$81$	−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	$-0.812433\pi$
$83$	−6.97624	+	4.02773i	−0.765742	+	0.442101i	0.0656117	+	0.997845i	$0.479100\pi$
$84$	−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	$0.514176\pi$
$90$	2.00901	+	0.981775i	0.211768	+	0.103488i
$91$	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
$100$	1.88017	−	4.63303i	0.188017	−	0.463303i
$101$	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	$-0.509339\pi$
$103$	8.33883	−	4.81443i	0.821650	−	0.474380i	0.850985	+	0.525190i	$0.176006\pi$
$104$	−1.93532	−	3.35207i	−0.189774	−	0.328698i
$105$	−0.759149	+	1.55345i	−0.0740854	+	0.151601i
$106$	4.32784	+	7.49604i	0.420357	+	0.728080i
$107$	6.18652	+	3.57179i	0.598073	+	0.345298i	0.768283	−	0.640110i	$-0.221111\pi$
$107$	6.18652	+	3.57179i	0.598073	+	0.345298i	−0.170210	+	0.985408i	$0.554445\pi$
$108$			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	$0.777698\pi$
$110$	0.366443	+	0.179076i	0.0349390	+	0.0170742i
$111$	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	$-0.899432\pi$
$113$	−12.2956	+	7.09885i	−1.15667	+	0.667804i	−0.206167	+	0.978517i	$0.566099\pi$
$114$	−0.298547	−	0.517099i	−0.0279615	−	0.0484308i
$115$	6.35529	−	4.27958i	0.592634	−	0.399073i
$116$	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	$-0.512019\pi$
$127$	−10.3908	−	5.99913i	−0.922034	−	0.532337i	−0.884283	+	0.466951i	$0.845353\pi$
$128$			1.00000i			0.0883883i
$129$	−3.34064	−	5.78617i	−0.294127	−	0.509444i
$130$	−3.80010	+	7.77615i	−0.333291	+	0.682014i
$131$	4.14488	−	7.17915i	0.362140	−	0.627245i	−0.626173	−	0.779684i	$-0.715379\pi$
$131$	4.14488	−	7.17915i	0.362140	−	0.627245i	0.988313	+	0.152439i	$0.0487128\pi$
$132$			0.182400i			0.0158759i
$133$	0.399843	−	0.230849i	0.0346707	−	0.0200172i
$134$	0.214254	+	0.371098i	0.0185087	+	0.0320580i
$135$	1.85475	−	1.24897i	0.159631	−	0.107494i
$136$	3.11459	−	5.39463i	0.267074	−	0.462586i
$137$	−11.1202	+	6.42025i	−0.950063	+	0.548519i	−0.893100	−	0.449857i	$-0.851475\pi$
$137$	−11.1202	+	6.42025i	−0.950063	+	0.548519i	−0.0569622	+	0.998376i	$0.518141\pi$
$138$	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
$145$	−8.89928	−	13.2157i	−0.739045	−	1.09750i
$146$	−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	−0.483965	−	0.875087i	$-0.660804\pi$
$149$	6.29694	−	10.9066i	0.515865	−	0.893505i	0.999830	−	0.0184175i	$-0.00586282\pi$
$150$	−3.07224	−	3.94479i	−0.250847	−	0.322091i
$151$	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
$155$	−0.0538076	−	12.4498i	−0.00432193	−	0.999991i
$156$	−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
$160$	1.85475	−	1.24897i	0.146631	−	0.0987394i
$161$	−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
$165$	0.338306	−	0.227811i	0.0263371	−	0.0177351i
$166$	4.02773	+	6.97624i	0.312613	+	0.541461i
$167$	0.608695	+	0.351430i	0.0471022	+	0.0271945i	0.523366	−	0.852108i	$-0.324676\pi$
$167$	0.608695	+	0.351430i	0.0471022	+	0.0271945i	−0.476264	+	0.879302i	$0.658009\pi$
$168$	−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	$-0.756760\pi$
$173$	−6.36230	+	3.67328i	−0.483717	+	0.279274i	0.238247	+	0.971205i	$0.423427\pi$
$174$	3.56266	−	6.17071i	0.270084	−	0.467800i
$175$	3.05028	−	2.37558i	0.230579	−	0.179577i
$176$	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	−0.875053	−	0.484027i	$-0.839174\pi$
$179$	−0.245463	+	0.425154i	−0.0183467	+	0.0317775i	0.856706	+	0.515805i	$0.172507\pi$
$180$	0.981775	−	2.00901i	0.0731772	−	0.149743i
$181$	8.47857	+	14.6853i	0.630207	+	1.09155i	0.987509	+	0.157562i	$0.0503633\pi$
$181$	8.47857	+	14.6853i	0.630207	+	1.09155i	−0.357302	+	0.933989i	$0.616303\pi$
$182$		−	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	0.630166	−	0.776461i	$-0.282987\pi$
$191$	−4.93870	−	8.55408i	−0.357352	−	0.618952i	−0.987518	+	0.157509i	$0.949654\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−7.56580	−	4.36812i	−0.544598	−	0.314424i	0.202342	−	0.979315i	$-0.435145\pi$
$193$	−7.56580	−	4.36812i	−0.544598	−	0.314424i	−0.746941	+	0.664891i	$0.768478\pi$
$194$	9.51682			0.683268
$195$	4.83430	+	7.17906i	0.346191	+	0.514103i
$196$	3.20105	+	5.54438i	0.228646	+	0.396027i
$197$	−1.14893	+	0.663337i	−0.0818582	+	0.0472608i	−0.540370	−	0.841427i	$-0.681716\pi$
$197$	−1.14893	+	0.663337i	−0.0818582	+	0.0472608i	0.458512	+	0.888688i	$0.348383\pi$
$198$	0.157963	+	0.0912000i	0.0112259	+	0.00648130i
$199$	−12.3167	−	21.3331i	−0.873107	−	1.51226i	−0.858766	−	0.512368i	$-0.828768\pi$
$199$	−12.3167	−	21.3331i	−0.873107	−	1.51226i	−0.0143404	−	0.999897i	$-0.504565\pi$
$200$	−4.63303	−	1.88017i	−0.327605	−	0.132948i
$201$	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
$205$	−1.82734	+	3.73929i	−0.127627	+	0.261163i
$206$	−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
$210$	1.55345	+	0.759149i	0.107198	+	0.0523863i
$211$	8.11534	−	14.0562i	0.558683	−	0.967667i	−0.438924	−	0.898524i	$-0.644640\pi$
$211$	8.11534	−	14.0562i	0.558683	−	0.967667i	0.997607	−	0.0691431i	$-0.0220265\pi$
$212$	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
$220$	0.179076	−	0.366443i	0.0120733	−	0.0247056i
$221$	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	$-0.100175\pi$
$223$	17.2965	+	9.98614i	1.15826	+	0.668722i	0.207373	+	0.978262i	$0.433508\pi$
$224$	−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	$-0.948957\pi$
$227$	−20.2265	+	11.6778i	−1.34248	+	0.775080i	−0.355307	+	0.934750i	$0.615624\pi$
$228$	−0.517099	+	0.298547i	−0.0342457	+	0.0197718i
$229$	6.66108	−	11.5373i	0.440176	−	0.762408i	−0.557526	−	0.830160i	$-0.688249\pi$
$229$	6.66108	−	11.5373i	0.440176	−	0.762408i	0.997702	+	0.0677518i	$0.0215826\pi$
$230$	−4.27958	−	6.35529i	−0.282187	−	0.419055i
$231$	−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
$235$	−11.4492	+	7.70975i	−0.746863	+	0.502929i
$236$	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	0.675680	−	0.737195i	$-0.263850\pi$
$239$	−4.64700	−	8.04884i	−0.300589	−	0.520636i	−0.976270	+	0.216559i	$0.930517\pi$
$240$	−0.154263	−	2.23074i	−0.00995761	−	0.143994i
$241$	−4.18140	+	7.24239i	−0.269347	+	0.466523i	−0.968693	−	0.248260i	$-0.920141\pi$
$241$	−4.18140	+	7.24239i	−0.269347	+	0.466523i	0.699346	+	0.714783i	$0.253475\pi$
$242$	−9.49747	−	5.48337i	−0.610520	−	0.352484i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−0.975597			−0.0624562
$245$	6.28542	−	12.8619i	0.401561	−	0.821715i
$246$	−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	0.420690	+	0.907205i	$0.361788\pi$
$251$	−9.11474	+	15.7872i	−0.575317	+	0.996479i	−0.996007	+	0.0892742i	$0.971545\pi$
$252$			0.773241i			0.0487096i
$253$	0.541261	−	0.312497i	0.0340288	−	0.0196465i
$254$	−5.99913	+	10.3908i	−0.376419	+	0.651977i
$255$	−6.11566	+	12.5145i	−0.382977	+	0.783688i
$256$	1.00000			0.0625000
$257$	−1.29328	+	0.746676i	−0.0806727	+	0.0465764i	−0.539794	−	0.841797i	$-0.681498\pi$
$257$	−1.29328	+	0.746676i	−0.0806727	+	0.0465764i	0.459121	+	0.888374i	$0.348164\pi$
$258$	−5.78617	+	3.34064i	−0.360231	+	0.207979i
$259$	2.47760	+	4.29133i	0.153951	+	0.266650i
$260$	7.77615	+	3.80010i	0.482256	+	0.235672i
$261$	−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
$265$	−17.3894	−	8.49794i	−1.06822	−	0.522024i
$266$	−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	0.996335	−	0.0855341i	$-0.0272596\pi$
$269$	6.95564	+	12.0475i	0.424093	+	0.734551i	−0.572242	+	0.820085i	$0.693926\pi$
$270$	−1.24897	−	1.85475i	−0.0760096	−	0.112876i
$271$	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
$285$	1.19957	+	0.586213i	0.0710563	+	0.0347242i
$286$	−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
$290$	−13.2157	+	8.89928i	−0.776050	+	0.522583i
$291$	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	$-0.413329\pi$
$293$	−7.37274	−	4.25665i	−0.430720	−	0.248676i	−0.699653	+	0.714482i	$0.746662\pi$
$294$	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
$300$	−3.94479	+	3.07224i	−0.227753	+	0.177376i
$301$	−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
$305$	1.21849	+	1.80949i	0.0697704	+	0.103611i
$306$	−6.22919			−0.356099
$307$	18.6892	+	10.7902i	1.06665	+	0.615830i	0.927264	−	0.374408i	$-0.122154\pi$
$307$	18.6892	+	10.7902i	1.06665	+	0.615830i	0.139385	+	0.990238i	$0.455487\pi$
$308$			0.141039i			0.00803646i
$309$	−9.62886			−0.547766
$310$	−12.4498	+	0.0538076i	−0.707100	+	0.00305606i
$311$	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	$-0.225655\pi$
$313$	10.1694	+	5.87130i	0.574808	+	0.331866i	−0.184259	+	0.982878i	$0.558989\pi$
$314$	−14.4319			−0.814442
$315$	1.43417	−	0.965752i	0.0808062	−	0.0544140i
$316$	−3.64065	+	6.30578i	−0.204802	+	0.354728i
$317$	21.7925	+	12.5819i	1.22399	+	0.706672i	0.965766	−	0.259413i	$-0.0835291\pi$
$317$	21.7925	+	12.5819i	1.22399	+	0.706672i	0.258225	+	0.966085i	$0.416862\pi$
$318$		−	8.65569i		−	0.485387i
$319$	−0.649829	−	1.12554i	−0.0363834	−	0.0630180i
$320$	−1.24897	−	1.85475i	−0.0698193	−	0.103683i
$321$	−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
$330$	−0.227811	−	0.338306i	−0.0125406	−	0.0186231i
$331$	−16.4267	−	28.4518i	−0.902891	−	1.56385i	−0.823724	−	0.566991i	$-0.808107\pi$
$331$	−16.4267	−	28.4518i	−0.902891	−	1.56385i	−0.0791671	−	0.996861i	$-0.525226\pi$
$332$	6.97624	−	4.02773i	0.382871	−	0.221051i
$333$		−	6.40835i		−	0.351175i
$334$	0.351430	−	0.608695i	0.0192294	−	0.0333063i
$335$	−0.860875	−	0.420698i	−0.0470347	−	0.0229852i
$336$	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	$-0.0339505\pi$
$347$	26.0657	+	15.0491i	1.39928	+	0.807876i	0.404964	+	0.914332i	$0.367284\pi$
$348$	−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	$0.423706\pi$
$350$	−2.37558	−	3.05028i	−0.126980	−	0.163044i
$351$	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	$-0.436477\pi$
$353$	−10.3613	−	5.98210i	−0.551476	−	0.318395i	−0.749717	+	0.661758i	$0.769810\pi$
$354$	−6.03735	−	10.4570i	−0.320882	−	0.555783i
$355$	−7.91091	+	16.1881i	−0.419868	+	0.859177i
$356$	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	0.787685	−	0.616079i	$-0.211280\pi$
$359$	−2.64689	−	4.58455i	−0.139697	−	0.241963i	−0.927382	+	0.374116i	$0.877946\pi$
$360$	−2.00901	−	0.981775i	−0.105884	−	0.0517441i
$361$	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
$365$	21.0172	+	10.2708i	1.10009	+	0.537599i
$366$	−0.487799	+	0.844892i	−0.0254976	+	0.0441632i
$367$	19.4298	−	11.2178i	1.01423	−	0.585564i	0.101801	−	0.994805i	$-0.467540\pi$
$367$	19.4298	−	11.2178i	1.01423	−	0.585564i	0.912427	+	0.409240i	$0.134206\pi$
$368$		−	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
$375$	10.6251	+	3.47947i	0.548679	+	0.179679i
$376$	−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	−0.388787	−	0.921327i	$-0.627106\pi$
$379$	11.7489	−	20.3497i	0.603499	−	1.04529i	0.992287	−	0.123964i	$-0.0395607\pi$
$380$	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	$-0.617318\pi$
$383$	5.23407	−	3.02189i	0.267449	−	0.154412i	0.627728	+	0.778433i	$0.283985\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	0.261592	−	0.176153i	0.0133320	−	0.00897760i
$386$	−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	−0.772912	−	0.634513i	$-0.781201\pi$
$389$	3.21583	−	5.56997i	0.163049	−	0.282409i	0.935961	+	0.352105i	$0.114534\pi$
$390$	7.17906	−	4.83430i	0.363526	−	0.244794i
$391$	−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	$-0.660456\pi$
$397$	−29.5449	−	17.0578i	−1.48282	−	0.856105i	−0.999810	+	0.0195106i	$0.993789\pi$
$398$	−21.3331	+	12.3167i	−1.06933	+	0.617380i
$399$	−0.461698			−0.0231138
$400$	−1.88017	+	4.63303i	−0.0940085	+	0.231651i
$401$	−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	0.477238	+	0.878774i	$0.341638\pi$
$409$	−10.5653	+	18.2997i	−0.522422	+	0.904861i	−0.999660	+	0.0260870i	$0.991695\pi$
$410$	3.73929	+	1.82734i	0.184670	+	0.0902459i
$411$	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
$415$	−16.1835	−	7.90866i	−0.794417	−	0.388221i
$416$	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	$0.688587\pi$
$420$	0.759149	−	1.55345i	0.0370427	−	0.0758006i
$421$	−6.83483	−	11.8383i	−0.333109	−	0.576962i	0.650010	−	0.759925i	$-0.274765\pi$
$421$	−6.83483	−	11.8383i	−0.333109	−	0.576962i	−0.983120	+	0.182963i	$0.941431\pi$
$422$	−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
$425$	24.5728	−	19.1375i	1.19196	−	0.928307i
$426$	−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	−0.997573	−	0.0696289i	$-0.977818\pi$
$431$	−9.10321	+	15.7672i	−0.438486	+	0.759480i	0.559087	+	0.829109i	$0.311152\pi$
$432$		−	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	0.907429	−	0.420206i	$-0.138042\pi$
$439$	1.88163	+	3.25908i	0.0898052	+	0.155547i	−0.817623	+	0.575753i	$0.804709\pi$
$440$	−0.366443	−	0.179076i	−0.0174695	−	0.00853710i
$441$	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	$-0.443727\pi$
$443$	23.4960	−	13.5654i	1.11633	−	0.644512i	0.940461	+	0.339903i	$0.110394\pi$
$444$	−3.20418	−	5.54979i	−0.152063	−	0.263382i
$445$	−1.04911	−	1.55796i	−0.0497326	−	0.0738542i
$446$	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
$455$	3.73808	+	5.55114i	0.175244	+	0.260242i
$456$	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
$460$	−6.35529	+	4.27958i	−0.296317	+	0.199536i
$461$	−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
$465$	−6.17829	+	10.8087i	−0.286511	+	0.501243i
$466$	−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
$470$	7.70975	+	11.4492i	0.355624	+	0.528112i
$471$	−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
$475$	−1.83442	−	2.35541i	−0.0841688	−	0.108074i
$476$	−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	−0.0469010	+	0.998900i	$0.514935\pi$
$479$	−19.4463	+	33.6819i	−0.888523	+	1.53897i	−0.841622	+	0.540067i	$0.818399\pi$
$480$	−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
$485$	−17.6513	+	11.8862i	−0.801504	+	0.539724i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−1.68240	+	0.971337i	−0.0762370	+	0.0440155i	−0.537634	−	0.843178i	$-0.680682\pi$
$487$	−1.68240	+	0.971337i	−0.0762370	+	0.0440155i	0.461397	+	0.887194i	$0.347348\pi$
$488$			0.975597i			0.0441632i
$489$	0.932193	−	1.61461i	0.0421552	−	0.0730150i
$490$	−12.8619	−	6.28542i	−0.581040	−	0.283946i
$491$	14.8550	+	25.7295i	0.670395	+	1.16116i	0.977792	+	0.209576i	$0.0672085\pi$
$491$	14.8550	+	25.7295i	0.670395	+	1.16116i	−0.307398	+	0.951581i	$0.599458\pi$
$492$			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	−0.907287	−	0.420512i	$-0.861850\pi$
$499$	−1.99859	+	3.46166i	−0.0894693	+	0.154965i	0.817818	+	0.575477i	$0.195184\pi$
$500$	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	$-0.508091\pi$
$503$	−20.2717	−	11.7039i	−0.903871	−	0.521850i	−0.878454	+	0.477827i	$0.841425\pi$
$504$	0.773241			0.0344429
$505$	14.6838	+	21.8059i	0.653422	+	0.970349i
$506$	−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	0.947629	+	0.319372i	$0.103472\pi$
$509$	16.9298	+	29.3232i	0.750399	+	1.29973i	−0.197230	+	0.980357i	$0.563195\pi$
$510$	12.5145	+	6.11566i	0.554151	+	0.270806i
$511$	−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
$515$	19.3445	+	9.45337i	0.852419	+	0.416565i
$516$	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
$520$	3.80010	−	7.77615i	0.166645	−	0.341007i
$521$	−9.26685	+	16.0507i	−0.405988	+	0.703192i	−0.994436	−	0.105343i	$-0.966406\pi$
$521$	−9.26685	+	16.0507i	−0.405988	+	0.703192i	0.588448	+	0.808535i	$0.299739\pi$
$522$	−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
$530$	−8.49794	+	17.3894i	−0.369127	+	0.755345i
$531$	−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
$540$	−1.85475	+	1.24897i	−0.0798156	+	0.0537469i
$541$	−4.65254	+	8.05844i	−0.200028	+	0.346459i	−0.948537	−	0.316665i	$-0.897437\pi$
$541$	−4.65254	+	8.05844i	−0.200028	+	0.346459i	0.748509	+	0.663125i	$0.230770\pi$
$542$		−	16.6543i		−	0.715362i
$543$		−	16.9571i		−	0.727700i
$544$	−3.11459	+	5.39463i	−0.133537	+	0.231293i
$545$	−19.9736	−	29.6613i	−0.855575	−	1.27055i
$546$	−1.49647	+	2.59196i	−0.0640430	+	0.110926i
$547$	−0.685180	+	0.395589i	−0.0292962	+	0.0169141i	−0.514577	−	0.857444i	$-0.672051\pi$
$547$	−0.685180	+	0.395589i	−0.0292962	+	0.0169141i	0.485280	+	0.874359i	$0.338718\pi$
$548$	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
$555$	−6.29156	+	12.8744i	−0.267062	+	0.546489i
$556$	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	0.651389	−	0.758744i	$-0.274186\pi$
$563$	38.7751	−	22.3868i	1.63418	−	0.943492i	0.982786	−	0.184748i	$-0.0591468\pi$
$564$	−3.08646	+	5.34590i	−0.129963	+	0.225103i
$565$	−28.5233	−	13.9390i	−1.19999	−	0.586416i
$566$	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	−0.988785	−	0.149344i	$-0.952284\pi$
$569$	−14.8782	−	25.7699i	−0.623728	−	1.08033i	0.365057	−	0.930985i	$-0.381049\pi$
$570$	0.586213	−	1.19957i	0.0245537	−	0.0502444i
$571$	−5.85732	−	10.1452i	−0.245121	−	0.424562i	0.717045	−	0.697027i	$-0.245494\pi$
$571$	−5.85732	−	10.1452i	−0.245121	−	0.424562i	−0.962166	+	0.272465i	$0.912161\pi$
$572$	0.611418	+	0.353002i	0.0255647	+	0.0147598i
$573$			9.87740i			0.412634i
$574$	−1.43920			−0.0600712
$575$	15.8751	+	6.44240i	0.662036	+	0.268667i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−26.0152	−	15.0199i	−1.08303	−	0.625286i	−0.151316	−	0.988485i	$-0.548351\pi$
$577$	−26.0152	−	15.0199i	−1.08303	−	0.625286i	−0.931712	+	0.363199i	$0.881685\pi$
$578$	18.8817	−	10.9014i	0.785377	−	0.453438i
$579$	4.36812	+	7.56580i	0.181533	+	0.314424i
$580$	8.89928	+	13.2157i	0.369522	+	0.548750i
$581$	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
$595$	−4.72888	+	9.67672i	−0.193865	+	0.396707i
$596$	−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	0.987464	−	0.157843i	$-0.0504541\pi$
$599$	8.73826	+	15.1351i	0.357036	+	0.618404i	−0.630428	+	0.776247i	$0.717121\pi$
$600$	3.07224	+	3.94479i	0.125424	+	0.161045i
$601$	−12.7413	+	22.0685i	−0.519728	+	0.900195i	0.480009	+	0.877263i	$0.340633\pi$
$601$	−12.7413	+	22.0685i	−0.519728	+	0.900195i	−0.999737	+	0.0229313i	$0.992700\pi$
$602$	−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	$-0.921832\pi$
$607$	−30.6602	+	17.7016i	−1.24446	+	0.718488i	−0.274459	+	0.961599i	$0.588499\pi$
$608$	0.517099	+	0.298547i	0.0209711	+	0.0121077i
$609$	−2.75480	−	4.77145i	−0.111630	−	0.193349i
$610$	1.80949	−	1.21849i	0.0732639	−	0.0493351i
$611$	−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	$-0.363255\pi$
$613$	−4.02516	−	2.32392i	−0.162574	−	0.0938624i	−0.579080	+	0.815271i	$0.696588\pi$
$614$	10.7902	−	18.6892i	0.435458	−	0.754235i
$615$	3.45217	−	2.32465i	0.139205	−	0.0937390i
$616$	0.141039			0.00568263
$617$	−33.5728	−	19.3833i	−1.35159	−	0.780341i	−0.363119	−	0.931743i	$-0.618288\pi$
$617$	−33.5728	−	19.3833i	−1.35159	−	0.780341i	−0.988472	+	0.151401i	$0.951621\pi$
$618$			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	$0.675223\pi$
$620$	0.0538076	+	12.4498i	0.00216096	+	0.499995i
$621$	−3.42650			−0.137501
$622$		−	7.50012i		−	0.300727i
$623$	0.562492	+	0.324755i	0.0225358	+	0.0130110i
$624$	3.87064			0.154950
$625$	−17.9299	−	17.4218i	−0.717197	−	0.696871i
$626$	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
$630$	−0.965752	−	1.43417i	−0.0384765	−	0.0571386i
$631$	−3.96941	−	6.87523i	−0.158020	−	0.273698i	0.776135	−	0.630567i	$-0.217178\pi$
$631$	−3.96941	−	6.87523i	−0.158020	−	0.273698i	−0.934155	+	0.356869i	$0.883844\pi$
$632$	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
$640$	−1.85475	+	1.24897i	−0.0733153	+	0.0493697i
$641$	4.48266	+	7.76419i	0.177054	+	0.306667i	0.940870	−	0.338767i	$-0.110010\pi$
$641$	4.48266	+	7.76419i	0.177054	+	0.306667i	−0.763816	+	0.645434i	$0.776676\pi$
$642$	−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
$645$	6.55952	−	13.4228i	0.258281	−	0.528521i
$646$	−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	$0.539756\pi$
$660$	−0.338306	+	0.227811i	−0.0131685	+	0.00886755i
$661$	−13.5355	−	23.4443i	−0.526472	−	0.911876i	−0.999524	−	0.0308417i	$-0.990181\pi$
$661$	−13.5355	−	23.4443i	−0.526472	−	0.911876i	0.473052	−	0.881034i	$-0.343152\pi$
$662$	−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
$665$	0.927556	+	0.453284i	0.0359691	+	0.0175776i
$666$	−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
$670$	−0.420698	+	0.860875i	−0.0162530	+	0.0332585i
$671$	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	$-0.623927\pi$
$673$	6.01517	−	3.47286i	0.231868	−	0.133869i	0.611433	+	0.791296i	$0.290593\pi$
$674$	12.7086			0.489516
$675$	4.63303	+	1.88017i	0.178325	+	0.0723678i
$676$	−0.990925	+	1.71633i	−0.0381125	+	0.0660128i
$677$	−5.78792	+	3.34166i	−0.222448	+	0.128430i	−0.607083	−	0.794638i	$-0.707661\pi$
$677$	−5.78792	+	3.34166i	−0.222448	+	0.128430i	0.384635	+	0.923069i	$0.374327\pi$
$678$		−	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
$685$	−25.7967	−	12.6065i	−0.985640	−	0.481669i
$686$	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	−0.905970	−	0.423341i	$-0.860857\pi$
$691$	−21.5450	−	37.3170i	−0.819610	−	1.41961i	0.0863607	−	0.996264i	$-0.472476\pi$
$692$	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
$695$	−4.80937	−	7.14204i	−0.182430	−	0.270913i
$696$	−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
$700$	−3.05028	+	2.37558i	−0.115290	+	0.0897885i
$701$	−7.89296	+	13.6710i	−0.298113	+	0.516347i	−0.975704	−	0.219092i	$-0.929691\pi$
$701$	−7.89296	+	13.6710i	−0.298113	+	0.516347i	0.677591	+	0.735439i	$0.263024\pi$
$702$	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	$0.424234\pi$
$710$	16.1881	+	7.91091i	0.607530	+	0.296891i
$711$	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	−0.687200	−	0.726468i	$-0.741161\pi$
$719$	7.65650	−	13.2615i	0.285539	−	0.494569i	0.972740	+	0.231899i	$0.0744939\pi$
$720$	−0.981775	+	2.00901i	−0.0365886	+	0.0748714i
$721$	−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
$725$	13.3968	−	33.0118i	0.497545	−	1.22603i
$726$	5.48337	+	9.49747i	0.203507	+	0.352484i
$727$	−1.68725	−	0.974136i	−0.0625768	−	0.0361287i	0.468385	−	0.883524i	$-0.344836\pi$
$727$	−1.68725	−	0.974136i	−0.0625768	−	0.0361287i	−0.530962	+	0.847396i	$0.678169\pi$
$728$			2.99294i			0.110926i
$729$	−1.00000			−0.0370370
$730$	10.2708	−	21.0172i	0.380140	−	0.777882i
$731$	−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	$-0.717262\pi$
$733$	−7.42242	+	4.28533i	−0.274153	+	0.158282i	0.356620	+	0.934249i	$0.383929\pi$
$734$	−11.2178	−	19.4298i	−0.414057	−	0.717167i
$735$	−11.8743	+	7.99600i	−0.437989	+	0.294937i
$736$	−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	0.993165	+	0.116716i	$0.0372367\pi$
$739$	16.2472	+	28.1409i	0.597662	+	1.03518i	−0.395504	+	0.918464i	$0.629430\pi$
$740$	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
$750$	3.47947	−	10.6251i	0.127052	−	0.387975i
$751$	11.3158	−	19.5996i	0.412920	−	0.715199i	−0.582287	−	0.812983i	$-0.697842\pi$
$751$	11.3158	−	19.5996i	0.412920	−	0.715199i	0.995208	+	0.0977840i	$0.0311754\pi$
$752$			6.17291i			0.225103i
$753$	15.7872	−	9.11474i	0.575317	−	0.332160i
$754$	−13.7898	−	23.8846i	−0.502194	−	0.869825i
$755$	16.1099	+	23.9236i	0.586298	+	0.870667i
$756$	0.386621	−	0.669647i	0.0140613	−	0.0243548i
$757$	−13.7398	+	7.93270i	−0.499383	+	0.288319i	−0.728459	−	0.685090i	$-0.759763\pi$
$757$	−13.7398	+	7.93270i	−0.499383	+	0.288319i	0.229076	+	0.973409i	$0.426430\pi$
$758$	−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	0.130349	+	0.991468i	$0.458390\pi$
$761$	−21.8886	+	37.9122i	−0.793462	+	1.37432i	−0.923811	+	0.382849i	$0.874943\pi$
$762$	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
$765$	11.5536	−	7.78004i	0.417720	−	0.281288i
$766$	−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	−0.990038	−	0.140801i	$-0.955032\pi$
$769$	−10.3459	+	17.9196i	−0.373081	+	0.646196i	0.616956	+	0.786997i	$0.288365\pi$
$770$	−0.176153	−	0.261592i	−0.00634812	−	0.00942713i
$771$	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
$775$	23.0240	−	15.6491i	0.827046	−	0.562134i
$776$	−9.51682			−0.341634
$777$		−	4.95520i		−	0.177767i
$778$	−5.56997	−	3.21583i	−0.199693	−	0.115293i
$779$	−1.11135			−0.0398182
$780$	−4.83430	−	7.17906i	−0.173096	−	0.257051i
$781$	−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
$785$	26.7676	−	18.0250i	0.955377	−	0.643340i
$786$	4.14488	+	7.17915i	0.147843	+	0.256072i
$787$	32.8966	+	18.9928i	1.17264	+	0.677022i	0.954299	−	0.298852i	$-0.0966037\pi$
$787$	32.8966	+	18.9928i	1.17264	+	0.677022i	0.218336	+	0.975874i	$0.429937\pi$
$788$	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
$795$	10.8107	+	16.0541i	0.383414	+	0.569380i
$796$	12.3167	+	21.3331i	0.436553	+	0.756132i
$797$	1.01175	−	0.584137i	0.0358382	−	0.0206912i	−0.481974	−	0.876186i	$-0.660080\pi$
$797$	1.01175	−	0.584137i	0.0358382	−	0.0206912i	0.517812	+	0.855494i	$0.326747\pi$
$798$			0.461698i			0.0163439i
$799$	19.2261	−	33.3006i	0.680171	−	1.17809i
$800$	4.63303	+	1.88017i	0.163802	+	0.0664741i
$801$	−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	0.123433	−	0.992353i	$-0.460610\pi$
$809$	26.1993	−	45.3786i	0.921119	−	1.59543i	0.797687	−	0.603072i	$-0.206057\pi$
$810$	0.154263	+	2.23074i	0.00542023	+	0.0783802i
$811$	−12.9976	−	22.5125i	−0.456408	−	0.790522i	0.542360	−	0.840146i	$-0.317531\pi$
$811$	−12.9976	−	22.5125i	−0.456408	−	0.790522i	−0.998768	+	0.0496241i	$0.984198\pi$
$812$	−4.77145	−	2.75480i	−0.167445	−	0.0966744i
$813$	−14.4230	−	8.32714i	−0.505838	−	0.292045i
$814$	−1.16888			−0.0409693
$815$	−3.45796	+	2.32855i	−0.121127	+	0.0815657i
$816$	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
$820$	1.82734	−	3.73929i	0.0638135	−	0.130582i
$821$	−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	$-0.493385\pi$
$823$	−23.9449	−	13.8246i	−0.834667	−	0.481895i	−0.855448	+	0.517889i	$0.826718\pi$
$824$	4.81443	+	8.33883i	0.167719	+	0.290497i
$825$	0.845065	+	0.342943i	0.0294214	+	0.0119397i
$826$	−4.66833	−	8.08579i	−0.162432	−	0.281341i
$827$	13.7054	−	7.91284i	0.476585	−	0.275156i	−0.242407	−	0.970175i	$-0.577937\pi$
$827$	13.7054	−	7.91284i	0.476585	−	0.275156i	0.718992	+	0.695018i	$0.244604\pi$
$828$	−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	$0.253106\pi$
$830$	−7.90866	+	16.1835i	−0.274513	+	0.561738i
$831$	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	$0.298637\pi$
$840$	−1.55345	−	0.759149i	−0.0535991	−	0.0261931i
$841$	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
$850$	−19.1375	−	24.5728i	−0.656412	−	0.842841i
$851$	−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
$855$	−0.745751	−	1.10746i	−0.0255041	−	0.0378743i
$856$	−3.57179	+	6.18652i	−0.122081	+	0.211451i
$857$	16.7037	−	9.64390i	0.570588	−	0.329429i	−0.186796	−	0.982399i	$-0.559810\pi$
$857$	16.7037	−	9.64390i	0.570588	−	0.329429i	0.757384	+	0.652969i	$0.226477\pi$
$858$	0.611418	−	0.353002i	0.0208735	−	0.0120513i
$859$	−18.9369	−	32.7997i	−0.646120	−	1.11911i	−0.984042	−	0.177938i	$-0.943057\pi$
$859$	−18.9369	−	32.7997i	−0.646120	−	1.11911i	0.337922	−	0.941174i	$-0.390276\pi$
$860$	−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	$-0.670768\pi$
$863$	−0.655557	+	0.378486i	−0.0223154	+	0.0128838i	0.488801	+	0.872395i	$0.337434\pi$
$864$	−1.00000			−0.0340207
$865$	−14.7593	−	7.21266i	−0.501831	−	0.245238i
$866$	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
$875$	8.21579	+	2.69047i	0.277744	+	0.0909545i
$876$	10.4615			0.353461
$877$	−1.71623	+	0.990863i	−0.0579528	+	0.0334591i	−0.528696	−	0.848811i	$-0.677319\pi$
$877$	−1.71623	+	0.990863i	−0.0579528	+	0.0334591i	0.470744	+	0.882270i	$0.343986\pi$
$878$	3.25908	−	1.88163i	0.109989	−	0.0635019i
$879$	4.25665	+	7.37274i	0.143573	+	0.248676i
$880$	−0.179076	+	0.366443i	−0.00603664	+	0.0123528i
$881$	−25.1594	−	43.5774i	−0.847643	−	1.46816i	−0.883306	−	0.468796i	$-0.844688\pi$
$881$	−25.1594	−	43.5774i	−0.847643	−	1.46816i	0.0356635	−	0.999364i	$-0.488646\pi$
$882$	−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
$885$	24.2582	+	11.8546i	0.815430	+	0.398489i
$886$	−13.5654	−	23.4960i	−0.455739	−	0.789362i
$887$	15.3394	+	8.85623i	0.515048	+	0.297363i	0.734906	−	0.678169i	$-0.237226\pi$
$887$	15.3394	+	8.85623i	0.515048	+	0.297363i	−0.219858	+	0.975532i	$0.570559\pi$
$888$	−5.54979	+	3.20418i	−0.186239	+	0.107525i
$889$	4.63878	+	8.03459i	0.155580	+	0.269472i
$890$	−1.55796	+	1.04911i	−0.0522228	+	0.0351662i
$891$	−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
$905$	−16.6481	+	34.0670i	−0.553401	+	1.13243i
$906$	−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
$910$	5.55114	−	3.73808i	0.184019	−	0.123916i
$911$	−5.64684	+	9.78062i	−0.187088	+	0.324046i	−0.944278	−	0.329148i	$-0.893238\pi$
$911$	−5.64684	+	9.78062i	−0.187088	+	0.324046i	0.757190	+	0.653195i	$0.226572\pi$
$912$	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	0.837901	−	0.545822i	$-0.183782\pi$
$919$	−1.62927	−	2.82198i	−0.0537446	−	0.0930884i	−0.891646	+	0.452733i	$0.850449\pi$
$920$	4.27958	+	6.35529i	0.141094	+	0.209528i
$921$	−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
$925$	25.2796	−	19.6880i	0.831188	−	0.647336i
$926$	−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	$0.471287\pi$
$930$	10.8087	+	6.17829i	0.354432	+	0.202594i
$931$	3.82266			0.125283
$932$			10.6233i			0.347978i
$933$	−6.49529	−	3.75006i	−0.212646	−	0.122771i
$934$	24.8358			0.812653
$935$	2.10737	−	1.41908i	0.0689184	−	0.0464089i
$936$	1.93532	−	3.35207i	0.0632579	−	0.109566i
$937$	−39.2023	−	22.6335i	−1.28068	−	0.739403i	−0.303710	−	0.952764i	$-0.598225\pi$
$937$	−39.2023	−	22.6335i	−1.28068	−	0.739403i	−0.976973	+	0.213362i	$0.931559\pi$
$938$		−	0.331340i		−	0.0108186i
$939$	−5.87130	−	10.1694i	−0.191603	−	0.331866i
$940$	11.4492	−	7.70975i	0.373431	−	0.251464i
$941$	−0.692766	−	1.19991i	−0.0225835	−	0.0391158i	0.854513	−	0.519430i	$-0.173856\pi$
$941$	−0.692766	−	1.19991i	−0.0225835	−	0.0391158i	−0.877096	+	0.480315i	$0.840523\pi$
$942$	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	$-0.399787\pi$
$947$	−11.0470	−	6.37797i	−0.358978	−	0.207256i	−0.668633	+	0.743593i	$0.733120\pi$
$948$	6.30578	−	3.64065i	0.204802	−	0.118243i
$949$	−20.2463	+	35.0676i	−0.657223	+	1.13834i
$950$	−2.35541	+	1.83442i	−0.0764197	+	0.0595163i
$951$	−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
$955$	9.69739	−	19.8438i	0.313800	−	0.642130i
$956$	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	$-0.586528\pi$
$967$	−38.4657	−	22.2082i	−1.23697	−	0.714168i	−0.968475	+	0.249112i	$0.919861\pi$
$968$	9.49747	+	5.48337i	0.305260	+	0.176242i
$969$	−3.71941			−0.119485
$970$	11.8862	+	17.6513i	0.381642	+	0.566749i
$971$	3.59816	+	6.23220i	0.115470	+	0.200001i	0.917968	−	0.396655i	$-0.129829\pi$
$971$	3.59816	+	6.23220i	0.115470	+	0.200001i	−0.802497	+	0.596656i	$0.796496\pi$
$972$	−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
$975$	−7.27746	+	17.9328i	−0.233065	+	0.574309i
$976$	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
$980$	−6.28542	+	12.8619i	−0.200780	+	0.410857i
$981$	−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	$-0.664019\pi$
$983$	0.451740	−	0.260812i	0.0144083	−	0.00831862i	0.507187	+	0.861836i	$0.330685\pi$
$984$	1.86126			0.0593348
$985$	−2.66530	−	1.30250i	−0.0849236	−	0.0415010i
$986$	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
$995$	24.1844	−	49.4887i	0.766698	−	1.56890i
$996$	−8.05547			−0.255247
$997$	16.8876	−	9.75004i	0.534834	−	0.308787i	−0.208148	−	0.978097i	$-0.566744\pi$
$997$	16.8876	−	9.75004i	0.534834	−	0.308787i	0.742983	+	0.669310i	$0.233410\pi$
$998$	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.439.5	✓	24
5.4	even	2	inner	930.2.s.c.439.10	yes	24
31.25	even	3	inner	930.2.s.c.769.4	yes	24
155.149	even	6	inner	930.2.s.c.769.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.c.439.5	✓	24	1.1	even	1	trivial
930.2.s.c.439.10	yes	24	5.4	even	2	inner
930.2.s.c.769.4	yes	24	31.25	even	3	inner
930.2.s.c.769.11	yes	24	155.149	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(1.24897 + 1.85475i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(1.24897 + 1.85475i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.669647 - 0.386621i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.85475 - 1.24897i) 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} +(-1.24897 - 1.85475i) q^{20} +(0.386621 + 0.669647i) q^{21} +(0.157963 - 0.0912000i) q^{22} -3.42650i q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.88017 + 4.63303i) 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} +(-1.85475 + 1.24897i) 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} +(-0.981775 + 2.00901i) q^{45} -3.42650 q^{46} +6.17291i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.20105 - 5.54438i) q^{49} +(4.63303 + 1.88017i) q^{50} +(3.11459 + 5.39463i) q^{51} +(3.35207 - 1.93532i) q^{52} +(-7.49604 + 4.32784i) q^{53} -1.00000 q^{54} +(-0.179076 + 0.366443i) 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} +(-7.77615 - 3.80010i) 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} +(3.94479 - 3.07224i) q^{75} +(0.298547 - 0.517099i) q^{76} -0.141039i q^{77} -3.87064i q^{78} +(3.64065 - 6.30578i) q^{79} +(1.24897 + 1.85475i) 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} +(2.00901 + 0.981775i) 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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