LMFDB - Embedded newform 690.2.i.f.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.01467 - 1.40373i) q^{3} -1.00000i q^{4} +(-2.22721 + 0.198845i) q^{5} +(-1.71006 - 0.275105i) q^{6} +(0.787190 + 0.787190i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.940895 + 2.84863i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.01467 - 1.40373i) q^{3} -1.00000i q^{4} +(-2.22721 + 0.198845i) q^{5} +(-1.71006 - 0.275105i) q^{6} +(0.787190 + 0.787190i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.940895 + 2.84863i) q^{9} +(-1.43427 + 1.71548i) q^{10} +0.307245i q^{11} +(-1.40373 + 1.01467i) q^{12} +(-4.92204 + 4.92204i) q^{13} +1.11326 q^{14} +(2.53900 + 2.92463i) q^{15} -1.00000 q^{16} +(-0.790416 + 0.790416i) q^{17} +(1.34897 + 2.67960i) q^{18} -0.691928i q^{19} +(0.198845 + 2.22721i) q^{20} +(0.306263 - 1.90374i) q^{21} +(0.217255 + 0.217255i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-0.275105 + 1.71006i) q^{24} +(4.92092 - 0.885741i) q^{25} +6.96081i q^{26} +(4.95340 - 1.56966i) q^{27} +(0.787190 - 0.787190i) q^{28} -6.67517 q^{29} +(3.86337 + 0.272679i) q^{30} +4.52557 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.431287 - 0.311752i) q^{33} +1.11782i q^{34} +(-1.90977 - 1.59671i) q^{35} +(2.84863 + 0.940895i) q^{36} +(1.77676 + 1.77676i) q^{37} +(-0.489267 - 0.489267i) q^{38} +(11.9034 + 1.91496i) q^{39} +(1.71548 + 1.43427i) q^{40} +0.596103i q^{41} +(-1.12959 - 1.56271i) q^{42} +(-6.70489 + 6.70489i) q^{43} +0.307245 q^{44} +(1.52913 - 6.53160i) q^{45} +1.00000 q^{46} +(-6.88967 + 6.88967i) q^{47} +(1.01467 + 1.40373i) q^{48} -5.76066i q^{49} +(2.85330 - 4.10593i) q^{50} +(1.91154 + 0.307518i) q^{51} +(4.92204 + 4.92204i) q^{52} +(5.94467 + 5.94467i) q^{53} +(2.39267 - 4.61250i) q^{54} +(-0.0610942 - 0.684298i) q^{55} -1.11326i q^{56} +(-0.971277 + 0.702077i) q^{57} +(-4.72006 + 4.72006i) q^{58} -6.38319 q^{59} +(2.92463 - 2.53900i) q^{60} -9.95861 q^{61} +(3.20006 - 3.20006i) q^{62} +(-2.98308 + 1.50175i) q^{63} +1.00000i q^{64} +(9.98368 - 11.9411i) q^{65} +(0.0845247 - 0.525408i) q^{66} +(2.19342 + 2.19342i) q^{67} +(0.790416 + 0.790416i) q^{68} +(0.275105 - 1.71006i) q^{69} +(-2.47945 + 0.221366i) q^{70} +4.55564i q^{71} +(2.67960 - 1.34897i) q^{72} +(-4.90914 + 4.90914i) q^{73} +2.51272 q^{74} +(-6.23644 - 6.00889i) q^{75} -0.691928 q^{76} +(-0.241860 + 0.241860i) q^{77} +(9.77108 - 7.06292i) q^{78} -15.7352i q^{79} +(2.22721 - 0.198845i) q^{80} +(-7.22943 - 5.36053i) q^{81} +(0.421508 + 0.421508i) q^{82} +(-6.65861 - 6.65861i) q^{83} +(-1.90374 - 0.306263i) q^{84} +(1.60325 - 1.91759i) q^{85} +9.48214i q^{86} +(6.77309 + 9.37012i) q^{87} +(0.217255 - 0.217255i) q^{88} +11.5425 q^{89} +(-3.53728 - 5.69980i) q^{90} -7.74916 q^{91} +(0.707107 - 0.707107i) q^{92} +(-4.59195 - 6.35266i) q^{93} +9.74347i q^{94} +(0.137587 + 1.54107i) q^{95} +(1.71006 + 0.275105i) q^{96} +(-12.8277 - 12.8277i) q^{97} +(-4.07340 - 4.07340i) q^{98} +(-0.875228 - 0.289085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.01467	−	1.40373i	−0.585819	−	0.810442i
$3$	−1.01467	−	1.40373i	−0.585819	−	0.810442i
$4$		−	1.00000i		−	0.500000i
$5$	−2.22721	+	0.198845i	−0.996038	+	0.0889264i
$5$	−2.22721	+	0.198845i	−0.996038	+	0.0889264i
$6$	−1.71006	−	0.275105i	−0.698130	−	0.112311i
$7$	0.787190	+	0.787190i	0.297530	+	0.297530i	0.840046	−	0.542516i	$-0.182528\pi$
$7$	0.787190	+	0.787190i	0.297530	+	0.297530i	−0.542516	+	0.840046i	$0.682528\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.940895	+	2.84863i	−0.313632	+	0.949545i
$10$	−1.43427	+	1.71548i	−0.453556	+	0.542482i
$11$			0.307245i			0.0926378i	0.998927	+	0.0463189i	$0.0147490\pi$
$11$			0.307245i			0.0926378i	−0.998927	+	0.0463189i	$0.985251\pi$
$12$	−1.40373	+	1.01467i	−0.405221	+	0.292910i
$13$	−4.92204	+	4.92204i	−1.36513	+	1.36513i	−0.497885	+	0.867243i	$0.665890\pi$
$13$	−4.92204	+	4.92204i	−1.36513	+	1.36513i	−0.867243	+	0.497885i	$0.834110\pi$
$14$	1.11326			0.297530
$15$	2.53900	+	2.92463i	0.655568	+	0.755136i
$16$	−1.00000			−0.250000
$17$	−0.790416	+	0.790416i	−0.191704	+	0.191704i	−0.796432	−	0.604728i	$-0.793282\pi$
$17$	−0.790416	+	0.790416i	−0.191704	+	0.191704i	0.604728	+	0.796432i	$0.293282\pi$
$18$	1.34897	+	2.67960i	0.317956	+	0.631588i
$19$		−	0.691928i		−	0.158739i	−0.996845	−	0.0793696i	$-0.974709\pi$
$19$		−	0.691928i		−	0.158739i	0.996845	−	0.0793696i	$-0.0252907\pi$
$20$	0.198845	+	2.22721i	0.0444632	+	0.498019i
$21$	0.306263	−	1.90374i	0.0668320	−	0.415430i
$22$	0.217255	+	0.217255i	0.0463189	+	0.0463189i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	−0.275105	+	1.71006i	−0.0561557	+	0.349065i
$25$	4.92092	−	0.885741i	0.984184	−	0.177148i
$26$			6.96081i			1.36513i
$27$	4.95340	−	1.56966i	0.953282	−	0.302081i
$28$	0.787190	−	0.787190i	0.148765	−	0.148765i
$29$	−6.67517			−1.23955			−0.619774	−	0.784780i	$-0.712776\pi$
$29$	−6.67517			−1.23955			−0.619774	+	0.784780i	$0.712776\pi$
$30$	3.86337	+	0.272679i	0.705352	+	0.0497841i
$31$	4.52557			0.812817			0.406408	−	0.913692i	$-0.366781\pi$
$31$	4.52557			0.812817			0.406408	+	0.913692i	$0.366781\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.431287	−	0.311752i	0.0750775	−	0.0542690i
$34$			1.11782i			0.191704i
$35$	−1.90977	−	1.59671i	−0.322810	−	0.269893i
$36$	2.84863	+	0.940895i	0.474772	+	0.156816i
$37$	1.77676	+	1.77676i	0.292098	+	0.292098i	0.837909	−	0.545811i	$-0.183778\pi$
$37$	1.77676	+	1.77676i	0.292098	+	0.292098i	−0.545811	+	0.837909i	$0.683778\pi$
$38$	−0.489267	−	0.489267i	−0.0793696	−	0.0793696i
$39$	11.9034	+	1.91496i	1.90607	+	0.306639i
$40$	1.71548	+	1.43427i	0.271241	+	0.226778i
$41$			0.596103i			0.0930956i	0.998916	+	0.0465478i	$0.0148220\pi$
$41$			0.596103i			0.0930956i	−0.998916	+	0.0465478i	$0.985178\pi$
$42$	−1.12959	−	1.56271i	−0.174299	−	0.241131i
$43$	−6.70489	+	6.70489i	−1.02249	+	1.02249i	−0.0227444	+	0.999741i	$0.507240\pi$
$43$	−6.70489	+	6.70489i	−1.02249	+	1.02249i	−0.999741	+	0.0227444i	$0.992760\pi$
$44$	0.307245			0.0463189
$45$	1.52913	−	6.53160i	0.227950	−	0.973673i
$46$	1.00000			0.147442
$47$	−6.88967	+	6.88967i	−1.00496	+	1.00496i	−0.00497448	+	0.999988i	$0.501583\pi$
$47$	−6.88967	+	6.88967i	−1.00496	+	1.00496i	−0.999988	+	0.00497448i	$0.998417\pi$
$48$	1.01467	+	1.40373i	0.146455	+	0.202610i
$49$		−	5.76066i		−	0.822952i
$50$	2.85330	−	4.10593i	0.403518	−	0.580666i
$51$	1.91154	+	0.307518i	0.267669	+	0.0430611i
$52$	4.92204	+	4.92204i	0.682564	+	0.682564i
$53$	5.94467	+	5.94467i	0.816563	+	0.816563i	0.985608	−	0.169045i	$-0.0540683\pi$
$53$	5.94467	+	5.94467i	0.816563	+	0.816563i	−0.169045	+	0.985608i	$0.554068\pi$
$54$	2.39267	−	4.61250i	0.325601	−	0.627682i
$55$	−0.0610942	−	0.684298i	−0.00823794	−	0.0922707i
$56$		−	1.11326i		−	0.148765i
$57$	−0.971277	+	0.702077i	−0.128649	+	0.0929924i
$58$	−4.72006	+	4.72006i	−0.619774	+	0.619774i
$59$	−6.38319			−0.831021			−0.415510	−	0.909588i	$-0.636397\pi$
$59$	−6.38319			−0.831021			−0.415510	+	0.909588i	$0.636397\pi$
$60$	2.92463	−	2.53900i	0.377568	−	0.327784i
$61$	−9.95861			−1.27507			−0.637535	−	0.770422i	$-0.720046\pi$
$61$	−9.95861			−1.27507			−0.637535	+	0.770422i	$0.720046\pi$
$62$	3.20006	−	3.20006i	0.406408	−	0.406408i
$63$	−2.98308	+	1.50175i	−0.375833	+	0.189203i
$64$			1.00000i			0.125000i
$65$	9.98368	−	11.9411i	1.23832	−	1.48112i
$66$	0.0845247	−	0.525408i	0.0104043	−	0.0646732i
$67$	2.19342	+	2.19342i	0.267969	+	0.267969i	0.828281	−	0.560312i	$-0.189319\pi$
$67$	2.19342	+	2.19342i	0.267969	+	0.267969i	−0.560312	+	0.828281i	$0.689319\pi$
$68$	0.790416	+	0.790416i	0.0958521	+	0.0958521i
$69$	0.275105	−	1.71006i	0.0331188	−	0.205867i
$70$	−2.47945	+	0.221366i	−0.296351	+	0.0264583i
$71$			4.55564i			0.540655i	0.962768	+	0.270327i	$0.0871320\pi$
$71$			4.55564i			0.540655i	−0.962768	+	0.270327i	$0.912868\pi$
$72$	2.67960	−	1.34897i	0.315794	−	0.158978i
$73$	−4.90914	+	4.90914i	−0.574571	+	0.574571i	−0.933403	−	0.358831i	$-0.883175\pi$
$73$	−4.90914	+	4.90914i	−0.574571	+	0.574571i	0.358831	+	0.933403i	$0.383175\pi$
$74$	2.51272			0.292098
$75$	−6.23644	−	6.00889i	−0.720122	−	0.693847i
$76$	−0.691928			−0.0793696
$77$	−0.241860	+	0.241860i	−0.0275625	+	0.0275625i
$78$	9.77108	−	7.06292i	1.10636	−	0.799718i
$79$		−	15.7352i		−	1.77035i	−0.465255	−	0.885177i	$-0.654037\pi$
$79$		−	15.7352i		−	1.77035i	0.465255	−	0.885177i	$-0.345963\pi$
$80$	2.22721	−	0.198845i	0.249010	−	0.0222316i
$81$	−7.22943	−	5.36053i	−0.803270	−	0.595615i
$82$	0.421508	+	0.421508i	0.0465478	+	0.0465478i
$83$	−6.65861	−	6.65861i	−0.730878	−	0.730878i	0.239916	−	0.970794i	$-0.422880\pi$
$83$	−6.65861	−	6.65861i	−0.730878	−	0.730878i	−0.970794	+	0.239916i	$0.922880\pi$
$84$	−1.90374	−	0.306263i	−0.207715	−	0.0334160i
$85$	1.60325	−	1.91759i	0.173897	−	0.207992i
$86$			9.48214i			1.02249i
$87$	6.77309	+	9.37012i	0.726151	+	1.00458i
$88$	0.217255	−	0.217255i	0.0231594	−	0.0231594i
$89$	11.5425			1.22351			0.611753	−	0.791049i	$-0.290465\pi$
$89$	11.5425			1.22351			0.611753	+	0.791049i	$0.290465\pi$
$90$	−3.53728	−	5.69980i	−0.372862	−	0.600811i
$91$	−7.74916			−0.812333
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	−4.59195	−	6.35266i	−0.476163	−	0.658740i
$94$			9.74347i			1.00496i
$95$	0.137587	+	1.54107i	0.0141161	+	0.158110i
$96$	1.71006	+	0.275105i	0.174533	+	0.0280778i
$97$	−12.8277	−	12.8277i	−1.30246	−	1.30246i	−0.926731	−	0.375726i	$-0.877394\pi$
$97$	−12.8277	−	12.8277i	−1.30246	−	1.30246i	−0.375726	−	0.926731i	$-0.622606\pi$
$98$	−4.07340	−	4.07340i	−0.411476	−	0.411476i
$99$	−0.875228	−	0.289085i	−0.0879637	−	0.0290541i
$100$	−0.885741	−	4.92092i	−0.0885741	−	0.492092i
$101$		−	0.435698i		−	0.0433536i	−0.999765	−	0.0216768i	$-0.993100\pi$
$101$		−	0.435698i		−	0.0433536i	0.999765	−	0.0216768i	$-0.00690048\pi$
$102$	1.56911	−	1.13421i	0.155365	−	0.112304i
$103$	−2.47087	+	2.47087i	−0.243463	+	0.243463i	−0.818281	−	0.574818i	$-0.805073\pi$
$103$	−2.47087	+	2.47087i	−0.243463	+	0.243463i	0.574818	+	0.818281i	$0.305073\pi$
$104$	6.96081			0.682564
$105$	−0.303561	+	4.30092i	−0.0296245	+	0.419727i
$106$	8.40703			0.816563
$107$	−9.00580	+	9.00580i	−0.870623	+	0.870623i	−0.992540	−	0.121917i	$-0.961096\pi$
$107$	−9.00580	+	9.00580i	−0.870623	+	0.870623i	0.121917	+	0.992540i	$0.461096\pi$
$108$	−1.56966	−	4.95340i	−0.151041	−	0.476641i
$109$			4.71540i			0.451654i	0.974167	+	0.225827i	$0.0725084\pi$
$109$			4.71540i			0.451654i	−0.974167	+	0.225827i	$0.927492\pi$
$110$	−0.527072	−	0.440672i	−0.0502543	−	0.0420164i
$111$	0.691264	−	4.29692i	0.0656118	−	0.407845i
$112$	−0.787190	−	0.787190i	−0.0743825	−	0.0743825i
$113$	−9.74177	−	9.74177i	−0.916428	−	0.916428i	0.0803391	−	0.996768i	$-0.474400\pi$
$113$	−9.74177	−	9.74177i	−0.916428	−	0.916428i	−0.996768	+	0.0803391i	$0.974400\pi$
$114$	−0.190353	+	1.18324i	−0.0178282	+	0.110821i
$115$	−1.71548	−	1.43427i	−0.159969	−	0.133746i
$116$			6.67517i			0.619774i
$117$	−9.38996	−	18.6522i	−0.868102	−	1.72440i
$118$	−4.51360	+	4.51360i	−0.415510	+	0.415510i
$119$	−1.24442			−0.114075
$120$	0.272679	−	3.86337i	0.0248921	−	0.352676i
$121$	10.9056			0.991418
$122$	−7.04180	+	7.04180i	−0.637535	+	0.637535i
$123$	0.836765	−	0.604847i	0.0754486	−	0.0545372i
$124$		−	4.52557i		−	0.406408i
$125$	−10.7838	+	2.95123i	−0.964532	+	0.263966i
$126$	−1.04746	+	3.17126i	−0.0933149	+	0.282518i
$127$	13.7618	+	13.7618i	1.22116	+	1.22116i	0.967219	+	0.253945i	$0.0817282\pi$
$127$	13.7618	+	13.7618i	1.22116	+	1.22116i	0.253945	+	0.967219i	$0.418272\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	16.2151	+	2.60859i	1.42766	+	0.229673i
$130$	−1.38413	−	15.5032i	−0.121396	−	1.35972i
$131$			9.08484i			0.793746i	0.917874	+	0.396873i	$0.129905\pi$
$131$			9.08484i			0.793746i	−0.917874	+	0.396873i	$0.870095\pi$
$132$	−0.311752	−	0.431287i	−0.0271345	−	0.0375388i
$133$	0.544679	−	0.544679i	0.0472297	−	0.0472297i
$134$	3.10197			0.267969
$135$	−10.7201	+	4.48092i	−0.922643	+	0.385656i
$136$	1.11782			0.0958521
$137$	−6.12207	+	6.12207i	−0.523044	+	0.523044i	−0.918489	−	0.395445i	$-0.870590\pi$
$137$	−6.12207	+	6.12207i	−0.523044	+	0.523044i	0.395445	+	0.918489i	$0.370590\pi$
$138$	−1.01467	−	1.40373i	−0.0863743	−	0.119493i
$139$		−	1.70991i		−	0.145033i	−0.997367	−	0.0725164i	$-0.976897\pi$
$139$		−	1.70991i		−	0.145033i	0.997367	−	0.0725164i	$-0.0231030\pi$
$140$	−1.59671	+	1.90977i	−0.134946	+	0.161405i
$141$	16.6620	+	2.68048i	1.40319	+	0.225737i
$142$	3.22132	+	3.22132i	0.270327	+	0.270327i
$143$	−1.51227	−	1.51227i	−0.126462	−	0.126462i
$144$	0.940895	−	2.84863i	0.0784080	−	0.237386i
$145$	14.8670	−	1.32733i	1.23464	−	0.110229i
$146$			6.94257i			0.574571i
$147$	−8.08639	+	5.84516i	−0.666955	+	0.482101i
$148$	1.77676	−	1.77676i	0.146049	−	0.146049i
$149$	4.44032			0.363765			0.181883	−	0.983320i	$-0.441781\pi$
$149$	4.44032			0.363765			0.181883	+	0.983320i	$0.441781\pi$
$150$	−8.65876	+	0.160901i	−0.706985	+	0.0131375i
$151$	−18.8511			−1.53408			−0.767040	−	0.641599i	$-0.778271\pi$
$151$	−18.8511			−1.53408			−0.767040	+	0.641599i	$0.778271\pi$
$152$	−0.489267	+	0.489267i	−0.0396848	+	0.0396848i
$153$	−1.50791	−	2.99531i	−0.121907	−	0.242156i
$154$			0.342042i			0.0275625i
$155$	−10.0794	+	0.899889i	−0.809596	+	0.0722808i
$156$	1.91496	−	11.9034i	0.153319	−	0.953037i
$157$	−9.78600	−	9.78600i	−0.781007	−	0.781007i	0.198993	−	0.980001i	$-0.436233\pi$
$157$	−9.78600	−	9.78600i	−0.781007	−	0.781007i	−0.980001	+	0.198993i	$0.936233\pi$
$158$	−11.1265	−	11.1265i	−0.885177	−	0.885177i
$159$	2.31282	−	14.3766i	0.183419	−	1.14014i
$160$	1.43427	−	1.71548i	0.113389	−	0.135621i
$161$			1.11326i			0.0877368i
$162$	−8.90245	+	1.32151i	−0.699443	+	0.103828i
$163$	9.24359	−	9.24359i	0.724014	−	0.724014i	−0.245406	−	0.969420i	$-0.578921\pi$
$163$	9.24359	−	9.24359i	0.724014	−	0.724014i	0.969420	+	0.245406i	$0.0789214\pi$
$164$	0.596103			0.0465478
$165$	−0.898577	+	0.780095i	−0.0699541	+	0.0607303i
$166$	−9.41670			−0.730878
$167$	−7.44173	+	7.44173i	−0.575858	+	0.575858i	−0.933759	−	0.357901i	$-0.883492\pi$
$167$	−7.44173	+	7.44173i	−0.575858	+	0.575858i	0.357901	+	0.933759i	$0.383492\pi$
$168$	−1.56271	+	1.12959i	−0.120565	+	0.0871494i
$169$		−	35.4529i		−	2.72715i
$170$	−0.222273	−	2.48961i	−0.0170476	−	0.190945i
$171$	1.97105	+	0.651032i	0.150730	+	0.0497856i
$172$	6.70489	+	6.70489i	0.511243	+	0.511243i
$173$	9.04703	+	9.04703i	0.687833	+	0.687833i	0.961753	−	0.273920i	$-0.0883202\pi$
$173$	9.04703	+	9.04703i	0.687833	+	0.687833i	−0.273920	+	0.961753i	$0.588320\pi$
$174$	11.4150	+	1.83638i	0.865367	+	0.139215i
$175$	4.57095	+	3.17646i	0.345531	+	0.240117i
$176$		−	0.307245i		−	0.0231594i
$177$	6.47682	+	8.96025i	0.486828	+	0.673494i
$178$	8.16181	−	8.16181i	0.611753	−	0.611753i
$179$	11.2260			0.839068			0.419534	−	0.907740i	$-0.362193\pi$
$179$	11.2260			0.839068			0.419534	+	0.907740i	$0.362193\pi$
$180$	−6.53160	−	1.52913i	−0.486836	−	0.113975i
$181$	−8.65815			−0.643555			−0.321778	−	0.946815i	$-0.604280\pi$
$181$	−8.65815			−0.643555			−0.321778	+	0.946815i	$0.604280\pi$
$182$	−5.47949	+	5.47949i	−0.406167	+	0.406167i
$183$	10.1047	+	13.9792i	0.746960	+	1.03337i
$184$		−	1.00000i		−	0.0737210i
$185$	−4.31053	−	3.60392i	−0.316916	−	0.264966i
$186$	−7.73901	−	1.24501i	−0.567452	−	0.0912885i
$187$	−0.242851	−	0.242851i	−0.0177590	−	0.0177590i
$188$	6.88967	+	6.88967i	0.502481	+	0.502481i
$189$	5.13489	+	2.66365i	0.373508	+	0.193752i
$190$	1.18699	+	0.992411i	0.0861132	+	0.0719971i
$191$			18.1677i			1.31457i	0.753643	+	0.657284i	$0.228295\pi$
$191$			18.1677i			1.31457i	−0.753643	+	0.657284i	$0.771705\pi$
$192$	1.40373	−	1.01467i	0.101305	−	0.0732274i
$193$	6.41622	−	6.41622i	0.461850	−	0.461850i	−0.437412	−	0.899261i	$-0.644105\pi$
$193$	6.41622	−	6.41622i	0.461850	−	0.461850i	0.899261	+	0.437412i	$0.144105\pi$
$194$	−18.1411			−1.30246
$195$	−26.8922	−	1.89807i	−1.92579	−	0.135923i
$196$	−5.76066			−0.411476
$197$	14.6739	−	14.6739i	1.04547	−	1.04547i	0.0465587	−	0.998916i	$-0.485175\pi$
$197$	14.6739	−	14.6739i	1.04547	−	1.04547i	0.998916	−	0.0465587i	$-0.0148255\pi$
$198$	−0.823293	+	0.414465i	−0.0585089	+	0.0294548i
$199$		−	2.60795i		−	0.184873i	−0.995719	−	0.0924363i	$-0.970535\pi$
$199$		−	2.60795i		−	0.184873i	0.995719	−	0.0924363i	$-0.0294655\pi$
$200$	−4.10593	−	2.85330i	−0.290333	−	0.201759i
$201$	0.853368	−	5.30456i	0.0601919	−	0.374155i
$202$	−0.308085	−	0.308085i	−0.0216768	−	0.0216768i
$203$	−5.25463	−	5.25463i	−0.368803	−	0.368803i
$204$	0.307518	−	1.91154i	0.0215305	−	0.133834i
$205$	−0.118532	−	1.32765i	−0.00827865	−	0.0927268i
$206$			3.49434i			0.243463i
$207$	−2.67960	+	1.34897i	−0.186245	+	0.0937602i
$208$	4.92204	−	4.92204i	0.341282	−	0.341282i
$209$	0.212591			0.0147052
$210$	2.82656	+	3.25586i	0.195051	+	0.224676i
$211$	24.9846			1.72001			0.860004	−	0.510287i	$-0.170461\pi$
$211$	24.9846			1.72001			0.860004	+	0.510287i	$0.170461\pi$
$212$	5.94467	−	5.94467i	0.408282	−	0.408282i
$213$	6.39487	−	4.62246i	0.438169	−	0.316726i
$214$			12.7361i			0.870623i
$215$	13.5999	−	16.2664i	0.927509	−	1.10936i
$216$	−4.61250	−	2.39267i	−0.313841	−	0.162800i
$217$	3.56249	+	3.56249i	0.241837	+	0.241837i
$218$	3.33429	+	3.33429i	0.225827	+	0.225827i
$219$	11.8722	+	1.90994i	0.802252	+	0.129062i
$220$	−0.684298	+	0.0610942i	−0.0461354	+	0.00411897i
$221$		−	7.78092i		−	0.523401i
$222$	−2.54958	−	3.52718i	−0.171117	−	0.236729i
$223$	2.06860	−	2.06860i	0.138524	−	0.138524i	−0.634444	−	0.772968i	$-0.718771\pi$
$223$	2.06860	−	2.06860i	0.138524	−	0.138524i	0.772968	+	0.634444i	$0.218771\pi$
$224$	−1.11326			−0.0743825
$225$	−2.10692	+	14.8513i	−0.140461	+	0.990086i
$226$	−13.7769			−0.916428
$227$	−14.8927	+	14.8927i	−0.988463	+	0.988463i	−0.999934	−	0.0114717i	$-0.996348\pi$
$227$	−14.8927	+	14.8927i	−0.988463	+	0.988463i	0.0114717	+	0.999934i	$0.496348\pi$
$228$	0.702077	+	0.971277i	0.0464962	+	0.0643244i
$229$			4.61161i			0.304743i	0.988323	+	0.152372i	$0.0486911\pi$
$229$			4.61161i			0.304743i	−0.988323	+	0.152372i	$0.951309\pi$
$230$	−2.22721	+	0.198845i	−0.146858	+	0.0131115i
$231$	0.584913	+	0.0940976i	0.0384845	+	0.00619116i
$232$	4.72006	+	4.72006i	0.309887	+	0.309887i
$233$	−3.47172	−	3.47172i	−0.227440	−	0.227440i	0.584182	−	0.811622i	$-0.301415\pi$
$233$	−3.47172	−	3.47172i	−0.227440	−	0.227440i	−0.811622	+	0.584182i	$0.801415\pi$
$234$	−19.8288	−	6.54940i	−1.29625	−	0.428148i
$235$	13.9748	−	16.7147i	0.911613	−	1.09035i
$236$			6.38319i			0.415510i
$237$	−22.0880	+	15.9661i	−1.43477	+	1.03711i
$238$	−0.879935	+	0.879935i	−0.0570377	+	0.0570377i
$239$	20.2807			1.31185			0.655924	−	0.754827i	$-0.272279\pi$
$239$	20.2807			1.31185			0.655924	+	0.754827i	$0.272279\pi$
$240$	−2.53900	−	2.92463i	−0.163892	−	0.188784i
$241$	6.16685			0.397242			0.198621	−	0.980076i	$-0.436354\pi$
$241$	6.16685			0.397242			0.198621	+	0.980076i	$0.436354\pi$
$242$	7.71142	−	7.71142i	0.495709	−	0.495709i
$243$	−0.189246	+	15.5873i	−0.0121401	+	0.999926i
$244$			9.95861i			0.637535i
$245$	1.14548	+	12.8302i	0.0731821	+	0.819691i
$246$	0.163991	−	1.01937i	0.0104557	−	0.0649929i
$247$	3.40570	+	3.40570i	0.216699	+	0.216699i
$248$	−3.20006	−	3.20006i	−0.203204	−	0.203204i
$249$	−2.59059	+	16.1032i	−0.164172	+	1.02050i
$250$	−5.53846	+	9.71213i	−0.350283	+	0.614249i
$251$		−	6.43760i		−	0.406338i	−0.979144	−	0.203169i	$-0.934876\pi$
$251$		−	6.43760i		−	0.406338i	0.979144	−	0.203169i	$-0.0651240\pi$
$252$	1.50175	+	2.98308i	0.0946016	+	0.187916i
$253$	−0.217255	+	0.217255i	−0.0136587	+	0.0136587i
$254$	19.4621			1.22116
$255$	−4.31855	−	0.304805i	−0.270438	−	0.0190876i
$256$	1.00000			0.0625000
$257$	8.53147	−	8.53147i	0.532178	−	0.532178i	−0.389042	−	0.921220i	$-0.627194\pi$
$257$	8.53147	−	8.53147i	0.532178	−	0.532178i	0.921220	+	0.389042i	$0.127194\pi$
$258$	13.3103	−	9.62123i	0.828665	−	0.598992i
$259$			2.79730i			0.173816i
$260$	−11.9411	−	9.98368i	−0.740558	−	0.619162i
$261$	6.28064	−	19.0151i	0.388762	−	1.17701i
$262$	6.42395	+	6.42395i	0.396873	+	0.396873i
$263$	4.18176	+	4.18176i	0.257858	+	0.257858i	0.824183	−	0.566324i	$-0.191635\pi$
$263$	4.18176	+	4.18176i	0.257858	+	0.257858i	−0.566324	+	0.824183i	$0.691635\pi$
$264$	−0.525408	−	0.0845247i	−0.0323366	−	0.00520213i
$265$	−14.4221	−	12.0580i	−0.885942	−	0.740714i
$266$		−	0.770292i		−	0.0472297i
$267$	−11.7118	−	16.2026i	−0.716754	−	0.991581i
$268$	2.19342	−	2.19342i	0.133985	−	0.133985i
$269$	−4.70169			−0.286667			−0.143334	−	0.989674i	$-0.545782\pi$
$269$	−4.70169			−0.286667			−0.143334	+	0.989674i	$0.545782\pi$
$270$	−4.41179	+	10.7488i	−0.268493	+	0.654149i
$271$	2.81014			0.170704			0.0853521	−	0.996351i	$-0.472799\pi$
$271$	2.81014			0.170704			0.0853521	+	0.996351i	$0.472799\pi$
$272$	0.790416	−	0.790416i	0.0479260	−	0.0479260i
$273$	7.86283	+	10.8777i	0.475880	+	0.658349i
$274$			8.65792i			0.523044i
$275$	0.272139	+	1.51193i	0.0164106	+	0.0911726i
$276$	−1.71006	−	0.275105i	−0.102934	−	0.0165594i
$277$	−7.56846	−	7.56846i	−0.454744	−	0.454744i	0.442181	−	0.896926i	$-0.354205\pi$
$277$	−7.56846	−	7.56846i	−0.454744	−	0.454744i	−0.896926	+	0.442181i	$0.854205\pi$
$278$	−1.20909	−	1.20909i	−0.0725164	−	0.0725164i
$279$	−4.25809	+	12.8917i	−0.254925	+	0.771806i
$280$	0.221366	+	2.47945i	0.0132291	+	0.148176i
$281$		−	6.92797i		−	0.413288i	−0.978416	−	0.206644i	$-0.933746\pi$
$281$		−	6.92797i		−	0.413288i	0.978416	−	0.206644i	$-0.0662542\pi$
$282$	13.6772	−	9.88639i	0.814463	−	0.588726i
$283$	−12.5993	+	12.5993i	−0.748951	+	0.748951i	−0.974282	−	0.225331i	$-0.927654\pi$
$283$	−12.5993	+	12.5993i	−0.748951	+	0.748951i	0.225331	+	0.974282i	$0.427654\pi$
$284$	4.55564			0.270327
$285$	2.02363	−	1.75681i	0.119870	−	0.104064i
$286$	−2.13867			−0.126462
$287$	−0.469246	+	0.469246i	−0.0276987	+	0.0276987i
$288$	−1.34897	−	2.67960i	−0.0794891	−	0.157897i
$289$			15.7505i			0.926499i
$290$	9.57400	−	11.4511i	0.562205	−	0.672433i
$291$	−4.99072	+	31.0225i	−0.292561	+	1.81857i
$292$	4.90914	+	4.90914i	0.287286	+	0.287286i
$293$	4.71078	+	4.71078i	0.275207	+	0.275207i	0.831192	−	0.555985i	$-0.187659\pi$
$293$	4.71078	+	4.71078i	0.275207	+	0.275207i	−0.555985	+	0.831192i	$0.687659\pi$
$294$	−1.58479	+	9.85110i	−0.0924268	+	0.574528i
$295$	14.2167	−	1.26927i	0.827728	−	0.0738997i
$296$		−	2.51272i		−	0.146049i
$297$	0.482270	+	1.52191i	0.0279841	+	0.0883099i
$298$	3.13978	−	3.13978i	0.181883	−	0.181883i
$299$	−6.96081			−0.402554
$300$	−6.00889	+	6.23644i	−0.346924	+	0.360061i
$301$	−10.5560			−0.608440
$302$	−13.3297	+	13.3297i	−0.767040	+	0.767040i
$303$	−0.611601	+	0.442089i	−0.0351356	+	0.0253974i
$304$			0.691928i			0.0396848i
$305$	22.1799	−	1.98022i	1.27002	−	0.113387i
$306$	−3.18425	−	1.05175i	−0.182032	−	0.0601245i
$307$	6.16188	+	6.16188i	0.351677	+	0.351677i	0.860733	−	0.509056i	$-0.170006\pi$
$307$	6.16188	+	6.16188i	0.351677	+	0.351677i	−0.509056	+	0.860733i	$0.670006\pi$
$308$	0.241860	+	0.241860i	0.0137813	+	0.0137813i
$309$	5.97555	+	0.961313i	0.339937	+	0.0546872i
$310$	−6.49089	+	7.76352i	−0.368658	+	0.440939i
$311$			6.56745i			0.372406i	0.982511	+	0.186203i	$0.0596182\pi$
$311$			6.56745i			0.372406i	−0.982511	+	0.186203i	$0.940382\pi$
$312$	−7.06292	−	9.77108i	−0.399859	−	0.553178i
$313$	5.15434	−	5.15434i	0.291341	−	0.291341i	−0.546269	−	0.837610i	$-0.683952\pi$
$313$	5.15434	−	5.15434i	0.291341	−	0.291341i	0.837610	+	0.546269i	$0.183952\pi$
$314$	−13.8395			−0.781007
$315$	6.34533	−	3.93789i	0.357519	−	0.221875i
$316$	−15.7352			−0.885177
$317$	18.9615	−	18.9615i	1.06498	−	1.06498i	0.0672456	−	0.997736i	$-0.478579\pi$
$317$	18.9615	−	18.9615i	1.06498	−	1.06498i	0.997736	−	0.0672456i	$-0.0214211\pi$
$318$	−8.53035	−	11.8012i	−0.478358	−	0.661777i
$319$		−	2.05091i		−	0.114829i
$320$	−0.198845	−	2.22721i	−0.0111158	−	0.124505i
$321$	21.7796	+	3.50378i	1.21562	+	0.195562i
$322$	0.787190	+	0.787190i	0.0438684	+	0.0438684i
$323$	0.546911	+	0.546911i	0.0304309	+	0.0304309i
$324$	−5.36053	+	7.22943i	−0.297807	+	0.401635i
$325$	−19.8613	+	28.5806i	−1.10171	+	1.58537i
$326$		−	13.0724i		−	0.724014i
$327$	6.61914	−	4.78457i	0.366039	−	0.264587i
$328$	0.421508	−	0.421508i	0.0232739	−	0.0232739i
$329$	−10.8470			−0.598013
$330$	−0.0837792	+	1.18700i	−0.00461189	+	0.0653422i
$331$	−0.116417			−0.00639884			−0.00319942	−	0.999995i	$-0.501018\pi$
$331$	−0.116417			−0.00639884			−0.00319942	+	0.999995i	$0.501018\pi$
$332$	−6.65861	+	6.65861i	−0.365439	+	0.365439i
$333$	−6.73310	+	3.38960i	−0.368971	+	0.185749i
$334$			10.5242i			0.575858i
$335$	−5.32136	−	4.44906i	−0.290737	−	0.243078i
$336$	−0.306263	+	1.90374i	−0.0167080	+	0.103857i
$337$	8.19544	+	8.19544i	0.446434	+	0.446434i	0.894167	−	0.447733i	$-0.147769\pi$
$337$	8.19544	+	8.19544i	0.446434	+	0.446434i	−0.447733	+	0.894167i	$0.647769\pi$
$338$	−25.0690	−	25.0690i	−1.36357	−	1.36357i
$339$	−3.79011	+	23.5594i	−0.205851	+	1.27957i
$340$	−1.91759	−	1.60325i	−0.103996	−	0.0869485i
$341$			1.39046i			0.0752975i
$342$	1.85409	−	0.933393i	0.100258	−	0.0504721i
$343$	10.0451	−	10.0451i	0.542383	−	0.542383i
$344$	9.48214			0.511243
$345$	−0.272679	+	3.86337i	−0.0146805	+	0.207997i
$346$	12.7944			0.687833
$347$	4.19660	−	4.19660i	0.225285	−	0.225285i	−0.585435	−	0.810720i	$-0.699076\pi$
$347$	4.19660	−	4.19660i	0.225285	−	0.225285i	0.810720	+	0.585435i	$0.199076\pi$
$348$	9.37012	−	6.77309i	0.502291	−	0.363076i
$349$		−	5.51143i		−	0.295020i	−0.989061	−	0.147510i	$-0.952874\pi$
$349$		−	5.51143i		−	0.295020i	0.989061	−	0.147510i	$-0.0471259\pi$
$350$	5.47824	−	0.986056i	0.292824	−	0.0527069i
$351$	−16.6549	+	32.1067i	−0.888973	+	1.71373i
$352$	−0.217255	−	0.217255i	−0.0115797	−	0.0115797i
$353$	−2.34200	−	2.34200i	−0.124652	−	0.124652i	0.642029	−	0.766681i	$-0.278093\pi$
$353$	−2.34200	−	2.34200i	−0.124652	−	0.124652i	−0.766681	+	0.642029i	$0.778093\pi$
$354$	10.9157	+	1.75605i	0.580161	+	0.0933330i
$355$	−0.905868	−	10.1464i	−0.0480785	−	0.538513i
$356$		−	11.5425i		−	0.611753i
$357$	1.26267	+	1.74682i	0.0668276	+	0.0924515i
$358$	7.93796	−	7.93796i	0.419534	−	0.419534i
$359$	−12.4668			−0.657974			−0.328987	−	0.944334i	$-0.606707\pi$
$359$	−12.4668			−0.657974			−0.328987	+	0.944334i	$0.606707\pi$
$360$	−5.69980	+	3.53728i	−0.300406	+	0.186431i
$361$	18.5212			0.974802
$362$	−6.12224	+	6.12224i	−0.321778	+	0.321778i
$363$	−11.0656	−	15.3085i	−0.580792	−	0.803487i
$364$			7.74916i			0.406167i
$365$	9.95752	−	11.9098i	0.521201	−	0.623390i
$366$	17.0299	+	2.73967i	0.890165	+	0.143205i
$367$	3.53418	+	3.53418i	0.184483	+	0.184483i	0.793306	−	0.608823i	$-0.208358\pi$
$367$	3.53418	+	3.53418i	0.184483	+	0.184483i	−0.608823	+	0.793306i	$0.708358\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	−1.69808	−	0.560870i	−0.0883984	−	0.0291977i
$370$	−5.59636	+	0.499644i	−0.290941	+	0.0259752i
$371$			9.35918i			0.485904i
$372$	−6.35266	+	4.59195i	−0.329370	+	0.238082i
$373$	−17.4340	+	17.4340i	−0.902700	+	0.902700i	−0.995669	−	0.0929686i	$-0.970364\pi$
$373$	−17.4340	+	17.4340i	−0.902700	+	0.902700i	0.0929686	+	0.995669i	$0.470364\pi$
$374$	−0.343444			−0.0177590
$375$	15.0847	+	12.1430i	0.778971	+	0.627060i
$376$	9.74347			0.502481
$377$	32.8555	−	32.8555i	1.69214	−	1.69214i
$378$	5.51440	−	1.74743i	0.283630	−	0.0898782i
$379$		−	27.9253i		−	1.43443i	−0.696853	−	0.717214i	$-0.745417\pi$
$379$		−	27.9253i		−	1.43443i	0.696853	−	0.717214i	$-0.254583\pi$
$380$	1.54107	−	0.137587i	0.0790551	−	0.00705805i
$381$	5.35414	−	33.2815i	0.274301	−	1.70506i
$382$	12.8465	+	12.8465i	0.657284	+	0.657284i
$383$	−10.0383	−	10.0383i	−0.512932	−	0.512932i	0.402492	−	0.915424i	$-0.368144\pi$
$383$	−10.0383	−	10.0383i	−0.512932	−	0.512932i	−0.915424	+	0.402492i	$0.868144\pi$
$384$	0.275105	−	1.71006i	0.0140389	−	0.0872663i
$385$	0.490580	−	0.586766i	0.0250023	−	0.0299044i
$386$		−	9.07391i		−	0.461850i
$387$	−12.7912	−	25.4084i	−0.650212	−	1.29158i
$388$	−12.8277	+	12.8277i	−0.651228	+	0.651228i
$389$	20.3937			1.03400			0.517000	−	0.855985i	$-0.327049\pi$
$389$	20.3937			1.03400			0.517000	+	0.855985i	$0.327049\pi$
$390$	−20.3578	+	17.6735i	−1.03086	+	0.894934i
$391$	−1.11782			−0.0565305
$392$	−4.07340	+	4.07340i	−0.205738	+	0.205738i
$393$	12.7526	−	9.21810i	0.643285	−	0.464992i
$394$		−	20.7521i		−	1.04547i
$395$	3.12888	+	35.0457i	0.157431	+	1.76334i
$396$	−0.289085	+	0.875228i	−0.0145271	+	0.0439818i
$397$	11.8044	+	11.8044i	0.592447	+	0.592447i	0.938292	−	0.345845i	$-0.112408\pi$
$397$	11.8044	+	11.8044i	0.592447	+	0.592447i	−0.345845	+	0.938292i	$0.612408\pi$
$398$	−1.84410	−	1.84410i	−0.0924363	−	0.0924363i
$399$	−1.31725	−	0.211912i	−0.0659449	−	0.0106089i
$400$	−4.92092	+	0.885741i	−0.246046	+	0.0442870i
$401$		−	8.66485i		−	0.432702i	−0.976316	−	0.216351i	$-0.930584\pi$
$401$		−	8.66485i		−	0.432702i	0.976316	−	0.216351i	$-0.0694156\pi$
$402$	−3.14747	−	4.35431i	−0.156981	−	0.217173i
$403$	−22.2750	+	22.2750i	−1.10960	+	1.10960i
$404$	−0.435698			−0.0216768
$405$	17.1674	+	10.5015i	0.853054	+	0.521823i
$406$	−7.43117			−0.368803
$407$	−0.545901	+	0.545901i	−0.0270593	+	0.0270593i
$408$	−1.13421	−	1.56911i	−0.0561520	−	0.0776825i
$409$			22.5197i			1.11353i	0.830670	+	0.556765i	$0.187957\pi$
$409$			22.5197i			1.11353i	−0.830670	+	0.556765i	$0.812043\pi$
$410$	−1.02260	−	0.854972i	−0.0505027	−	0.0422241i
$411$	14.8056	+	2.38184i	0.730306	+	0.117488i
$412$	2.47087	+	2.47087i	0.121731	+	0.121731i
$413$	−5.02479	−	5.02479i	−0.247254	−	0.247254i
$414$	−0.940895	+	2.84863i	−0.0462425	+	0.140003i
$415$	16.1542	+	13.5061i	0.792977	+	0.662988i
$416$		−	6.96081i		−	0.341282i
$417$	−2.40025	+	1.73499i	−0.117541	+	0.0849630i
$418$	0.150325	−	0.150325i	0.00735262	−	0.00735262i
$419$	−19.7745			−0.966048			−0.483024	−	0.875607i	$-0.660462\pi$
$419$	−19.7745			−0.966048			−0.483024	+	0.875607i	$0.660462\pi$
$420$	4.30092	+	0.303561i	0.209863	+	0.0148123i
$421$	−3.54002			−0.172530			−0.0862649	−	0.996272i	$-0.527493\pi$
$421$	−3.54002			−0.172530			−0.0862649	+	0.996272i	$0.527493\pi$
$422$	17.6667	−	17.6667i	0.860004	−	0.860004i
$423$	−13.1437	−	26.1086i	−0.639068	−	1.26944i
$424$		−	8.40703i		−	0.408282i
$425$	−3.18947	+	4.58968i	−0.154712	+	0.222632i
$426$	1.25328	−	7.79043i	0.0607217	−	0.377448i
$427$	−7.83932	−	7.83932i	−0.379371	−	0.379371i
$428$	9.00580	+	9.00580i	0.435312	+	0.435312i
$429$	−0.588361	+	3.65727i	−0.0284063	+	0.176574i
$430$	−1.88548	−	21.1187i	−0.0909260	−	1.01843i
$431$		−	6.98806i		−	0.336603i	−0.985736	−	0.168302i	$-0.946172\pi$
$431$		−	6.98806i		−	0.336603i	0.985736	−	0.168302i	$-0.0538282\pi$
$432$	−4.95340	+	1.56966i	−0.238321	+	0.0755203i
$433$	−22.0257	+	22.0257i	−1.05849	+	1.05849i	−0.0603055	+	0.998180i	$0.519207\pi$
$433$	−22.0257	+	22.0257i	−1.05849	+	1.05849i	−0.998180	+	0.0603055i	$0.980793\pi$
$434$	5.03812			0.241837
$435$	−16.9483	−	19.5224i	−0.812608	−	0.936028i
$436$	4.71540			0.225827
$437$	0.489267	−	0.489267i	0.0234048	−	0.0234048i
$438$	9.74547	−	7.04441i	0.465657	−	0.336595i
$439$			12.4962i			0.596410i	0.954502	+	0.298205i	$0.0963879\pi$
$439$			12.4962i			0.596410i	−0.954502	+	0.298205i	$0.903612\pi$
$440$	−0.440672	+	0.527072i	−0.0210082	+	0.0251272i
$441$	16.4100	+	5.42018i	0.781429	+	0.258104i
$442$	−5.50194	−	5.50194i	−0.261701	−	0.261701i
$443$	−3.45517	−	3.45517i	−0.164160	−	0.164160i	0.620247	−	0.784407i	$-0.287033\pi$
$443$	−3.45517	−	3.45517i	−0.164160	−	0.164160i	−0.784407	+	0.620247i	$0.787033\pi$
$444$	−4.29692	−	0.691264i	−0.203923	−	0.0328059i
$445$	−25.7076	+	2.29518i	−1.21866	+	0.108802i
$446$		−	2.92545i		−	0.138524i
$447$	−4.50546	−	6.23300i	−0.213101	−	0.294811i
$448$	−0.787190	+	0.787190i	−0.0371913	+	0.0371913i
$449$	−5.44836			−0.257124			−0.128562	−	0.991701i	$-0.541036\pi$
$449$	−5.44836			−0.257124			−0.128562	+	0.991701i	$0.541036\pi$
$450$	9.01163	+	11.9913i	0.424812	+	0.565274i
$451$	−0.183149			−0.00862417
$452$	−9.74177	+	9.74177i	−0.458214	+	0.458214i
$453$	19.1276	+	26.4618i	0.898694	+	1.24328i
$454$			21.0614i			0.988463i
$455$	17.2590	−	1.54089i	0.809115	−	0.0722378i
$456$	1.18324	+	0.190353i	0.0554103	+	0.00891410i
$457$	−9.46760	−	9.46760i	−0.442876	−	0.442876i	0.450102	−	0.892977i	$-0.351388\pi$
$457$	−9.46760	−	9.46760i	−0.442876	−	0.442876i	−0.892977	+	0.450102i	$0.851388\pi$
$458$	3.26090	+	3.26090i	0.152372	+	0.152372i
$459$	−2.67456	+	5.15593i	−0.124838	+	0.240658i
$460$	−1.43427	+	1.71548i	−0.0668732	+	0.0799847i
$461$			29.8517i			1.39033i	0.718849	+	0.695166i	$0.244669\pi$
$461$			29.8517i			1.39033i	−0.718849	+	0.695166i	$0.755331\pi$
$462$	0.480133	−	0.347059i	0.0223378	−	0.0161466i
$463$	−17.9865	+	17.9865i	−0.835905	+	0.835905i	−0.988317	−	0.152412i	$-0.951296\pi$
$463$	−17.9865	+	17.9865i	−0.835905	+	0.835905i	0.152412	+	0.988317i	$0.451296\pi$
$464$	6.67517			0.309887
$465$	11.4904	+	13.2356i	0.532856	+	0.613787i
$466$	−4.90975			−0.227440
$467$	3.58351	−	3.58351i	0.165825	−	0.165825i	−0.619317	−	0.785141i	$-0.712590\pi$
$467$	3.58351	−	3.58351i	0.165825	−	0.165825i	0.785141	+	0.619317i	$0.212590\pi$
$468$	−18.6522	+	9.38996i	−0.862199	+	0.434051i
$469$			3.45328i			0.159458i
$470$	−1.93744	−	21.7007i	−0.0893677	−	1.00098i
$471$	−3.80732	+	23.6664i	−0.175432	+	1.09049i
$472$	4.51360	+	4.51360i	0.207755	+	0.207755i
$473$	−2.06004	−	2.06004i	−0.0947208	−	0.0947208i
$474$	−4.32885	+	26.9083i	−0.198831	+	1.23594i
$475$	−0.612869	−	3.40492i	−0.0281203	−	0.156229i
$476$			1.24442i			0.0570377i
$477$	−22.5275	+	11.3409i	−1.03146	+	0.519263i
$478$	14.3406	−	14.3406i	0.655924	−	0.655924i
$479$	39.2172			1.79188			0.895939	−	0.444177i	$-0.146504\pi$
$479$	39.2172			1.79188			0.895939	+	0.444177i	$0.146504\pi$
$480$	−3.86337	−	0.272679i	−0.176338	−	0.0124460i
$481$	−17.4906			−0.797503
$482$	4.36062	−	4.36062i	0.198621	−	0.198621i
$483$	1.56271	−	1.12959i	0.0711056	−	0.0513979i
$484$		−	10.9056i		−	0.495709i
$485$	31.1207	+	26.0193i	1.41312	+	1.18147i
$486$	10.8881	+	11.1557i	0.493893	+	0.506033i
$487$	18.9608	+	18.9608i	0.859194	+	0.859194i	0.991243	−	0.132049i	$-0.0421556\pi$
$487$	18.9608	+	18.9608i	0.859194	+	0.859194i	−0.132049	+	0.991243i	$0.542156\pi$
$488$	7.04180	+	7.04180i	0.318767	+	0.318767i
$489$	−22.3547	−	3.59629i	−1.01091	−	0.162630i
$490$	9.88230	+	8.26234i	0.446437	+	0.373255i
$491$		−	14.7080i		−	0.663761i	−0.943321	−	0.331880i	$-0.892317\pi$
$491$		−	14.7080i		−	0.663761i	0.943321	−	0.331880i	$-0.107683\pi$
$492$	−0.604847	−	0.836765i	−0.0272686	−	0.0377243i
$493$	5.27617	−	5.27617i	0.237627	−	0.237627i
$494$	4.81638			0.216699
$495$	2.00680	+	0.469818i	0.0901989	+	0.0211167i
$496$	−4.52557			−0.203204
$497$	−3.58616	+	3.58616i	−0.160861	+	0.160861i
$498$	9.55483	+	13.2185i	0.428162	+	0.592334i
$499$			12.6459i			0.566109i	0.959104	+	0.283055i	$0.0913477\pi$
$499$			12.6459i			0.566109i	−0.959104	+	0.283055i	$0.908652\pi$
$500$	2.95123	+	10.7838i	0.131983	+	0.482266i
$501$	17.9970	+	2.89526i	0.804048	+	0.129351i
$502$	−4.55207	−	4.55207i	−0.203169	−	0.203169i
$503$	29.2502	+	29.2502i	1.30420	+	1.30420i	0.925532	+	0.378668i	$0.123618\pi$
$503$	29.2502	+	29.2502i	1.30420	+	1.30420i	0.378668	+	0.925532i	$0.376382\pi$
$504$	3.17126	+	1.04746i	0.141259	+	0.0466574i
$505$	0.0866366	+	0.970391i	0.00385528	+	0.0431818i
$506$			0.307245i			0.0136587i
$507$	−49.7662	+	35.9730i	−2.21019	+	1.59762i
$508$	13.7618	−	13.7618i	0.610582	−	0.610582i
$509$	−17.2813			−0.765978			−0.382989	−	0.923753i	$-0.625105\pi$
$509$	−17.2813			−0.765978			−0.382989	+	0.923753i	$0.625105\pi$
$510$	−3.26920	+	2.83814i	−0.144763	+	0.125675i
$511$	−7.72886			−0.341904
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.08609	−	3.42740i	−0.0479521	−	0.151323i
$514$		−	12.0653i		−	0.532178i
$515$	5.01183	−	5.99448i	0.220848	−	0.264148i
$516$	2.60859	−	16.2151i	0.114837	−	0.713828i
$517$	−2.11682	−	2.11682i	−0.0930974	−	0.0930974i
$518$	1.97799	+	1.97799i	0.0869080	+	0.0869080i
$519$	3.51982	−	21.8793i	0.154503	−	0.960394i
$520$	−15.5032	+	1.38413i	−0.679860	+	0.0606980i
$521$			34.5203i			1.51236i	0.654363	+	0.756181i	$0.272937\pi$
$521$			34.5203i			1.51236i	−0.654363	+	0.756181i	$0.727063\pi$
$522$	−9.00464	−	17.8868i	−0.394123	−	0.782884i
$523$	29.4556	−	29.4556i	1.28800	−	1.28800i	0.352005	−	0.935998i	$-0.385500\pi$
$523$	29.4556	−	29.4556i	1.28800	−	1.28800i	0.935998	−	0.352005i	$-0.114500\pi$
$524$	9.08484			0.396873
$525$	−0.179124	−	9.63941i	−0.00781761	−	0.420698i
$526$	5.91390			0.257858
$527$	−3.57709	+	3.57709i	−0.155820	+	0.155820i
$528$	−0.431287	+	0.311752i	−0.0187694	+	0.0135672i
$529$			1.00000i			0.0434783i
$530$	−18.7242	+	1.67170i	−0.813328	+	0.0726140i
$531$	6.00591	−	18.1834i	0.260634	−	0.789091i
$532$	−0.544679	−	0.544679i	−0.0236148	−	0.0236148i
$533$	−2.93404	−	2.93404i	−0.127087	−	0.127087i
$534$	−19.7385	−	3.17541i	−0.854167	−	0.137414i
$535$	18.2670	−	21.8486i	0.789753	−	0.944595i
$536$		−	3.10197i		−	0.133985i
$537$	−11.3906	−	15.7582i	−0.491542	−	0.680016i
$538$	−3.32460	+	3.32460i	−0.143334	+	0.143334i
$539$	1.76993			0.0762364
$540$	4.48092	+	10.7201i	0.192828	+	0.461321i
$541$	−22.6506			−0.973824			−0.486912	−	0.873451i	$-0.661877\pi$
$541$	−22.6506			−0.973824			−0.486912	+	0.873451i	$0.661877\pi$
$542$	1.98707	−	1.98707i	0.0853521	−	0.0853521i
$543$	8.78515	+	12.1537i	0.377007	+	0.521564i
$544$		−	1.11782i		−	0.0479260i
$545$	−0.937637	−	10.5022i	−0.0401639	−	0.449864i
$546$	13.2516	+	2.13184i	0.567114	+	0.0912342i
$547$	0.166563	+	0.166563i	0.00712170	+	0.00712170i	0.710659	−	0.703537i	$-0.248397\pi$
$547$	0.166563	+	0.166563i	0.00712170	+	0.00712170i	−0.703537	+	0.710659i	$0.748397\pi$
$548$	6.12207	+	6.12207i	0.261522	+	0.261522i
$549$	9.37001	−	28.3684i	0.399902	−	1.21074i
$550$	1.26153	+	0.876662i	0.0537916	+	0.0373810i
$551$			4.61874i			0.196765i
$552$	−1.40373	+	1.01467i	−0.0597466	+	0.0431872i
$553$	12.3866	−	12.3866i	0.526733	−	0.526733i
$554$	−10.7034			−0.454744
$555$	−0.685167	+	9.70758i	−0.0290837	+	0.412064i
$556$	−1.70991			−0.0725164
$557$	−22.4801	+	22.4801i	−0.952511	+	0.952511i	−0.998922	−	0.0464113i	$-0.985222\pi$
$557$	−22.4801	+	22.4801i	−0.952511	+	0.952511i	0.0464113	+	0.998922i	$0.485222\pi$
$558$	6.10488	+	12.1267i	0.258440	+	0.513365i
$559$		−	66.0034i		−	2.79165i
$560$	1.90977	+	1.59671i	0.0807024	+	0.0674732i
$561$	−0.0944832	+	0.587310i	−0.00398908	+	0.0247963i
$562$	−4.89882	−	4.89882i	−0.206644	−	0.206644i
$563$	−24.7485	−	24.7485i	−1.04302	−	1.04302i	−0.999032	−	0.0439915i	$-0.985993\pi$
$563$	−24.7485	−	24.7485i	−1.04302	−	1.04302i	−0.0439915	−	0.999032i	$-0.514007\pi$
$564$	2.68048	−	16.6620i	0.112869	−	0.701595i
$565$	23.6341	+	19.7598i	0.994292	+	0.831303i
$566$			17.8181i			0.748951i
$567$	−1.47118	−	9.91070i	−0.0617837	−	0.416210i
$568$	3.22132	−	3.22132i	0.135164	−	0.135164i
$569$	−41.8001			−1.75235			−0.876176	−	0.481991i	$-0.839914\pi$
$569$	−41.8001			−1.75235			−0.876176	+	0.481991i	$0.839914\pi$
$570$	0.188674	−	2.67317i	0.00790269	−	0.111967i
$571$	−6.16454			−0.257978			−0.128989	−	0.991646i	$-0.541173\pi$
$571$	−6.16454			−0.257978			−0.128989	+	0.991646i	$0.541173\pi$
$572$	−1.51227	+	1.51227i	−0.0632312	+	0.0632312i
$573$	25.5025	−	18.4342i	1.06538	−	0.770099i
$574$			0.663614i			0.0276987i
$575$	4.10593	+	2.85330i	0.171229	+	0.118991i
$576$	−2.84863	−	0.940895i	−0.118693	−	0.0392040i
$577$	−32.6610	−	32.6610i	−1.35970	−	1.35970i	−0.874287	−	0.485410i	$-0.838670\pi$
$577$	−32.6610	−	32.6610i	−1.35970	−	1.35970i	−0.485410	−	0.874287i	$-0.661330\pi$
$578$	11.1373	+	11.1373i	0.463250	+	0.463250i
$579$	−15.5170	−	2.49628i	−0.644863	−	0.103742i
$580$	−1.32733	−	14.8670i	−0.0551143	−	0.617319i
$581$		−	10.4832i		−	0.434916i
$582$	18.4072	+	25.4652i	0.763004	+	1.05557i
$583$	−1.82647	+	1.82647i	−0.0756446	+	0.0756446i
$584$	6.94257			0.287286
$585$	24.6223	+	39.6752i	1.01801	+	1.64037i
$586$	6.66204			0.275207
$587$	22.6013	−	22.6013i	0.932856	−	0.932856i	−0.0650272	−	0.997883i	$-0.520713\pi$
$587$	22.6013	−	22.6013i	0.932856	−	0.932856i	0.997883	+	0.0650272i	$0.0207134\pi$
$588$	5.84516	+	8.08639i	0.241050	+	0.333477i
$589$		−	3.13137i		−	0.129026i
$590$	9.15522	−	10.9502i	0.376914	−	0.450814i
$591$	−35.4874	−	5.70901i	−1.45975	−	0.234837i
$592$	−1.77676	−	1.77676i	−0.0730245	−	0.0730245i
$593$	16.9395	+	16.9395i	0.695621	+	0.695621i	0.963463	−	0.267842i	$-0.0863106\pi$
$593$	16.9395	+	16.9395i	0.695621	+	0.695621i	−0.267842	+	0.963463i	$0.586311\pi$
$594$	1.41717	+	0.735134i	0.0581470	+	0.0301629i
$595$	2.77158	−	0.247447i	0.113624	−	0.0101443i
$596$		−	4.44032i		−	0.181883i
$597$	−3.66085	+	2.64620i	−0.149828	+	0.108302i
$598$	−4.92204	+	4.92204i	−0.201277	+	0.201277i
$599$	−35.0050			−1.43027			−0.715133	−	0.698988i	$-0.753634\pi$
$599$	−35.0050			−1.43027			−0.715133	+	0.698988i	$0.753634\pi$
$600$	0.160901	+	8.65876i	0.00656876	+	0.353492i
$601$	−2.10282			−0.0857759			−0.0428880	−	0.999080i	$-0.513656\pi$
$601$	−2.10282			−0.0857759			−0.0428880	+	0.999080i	$0.513656\pi$
$602$	−7.46425	+	7.46425i	−0.304220	+	0.304220i
$603$	−8.31203	+	4.18447i	−0.338492	+	0.170405i
$604$			18.8511i			0.767040i
$605$	−24.2891	+	2.16853i	−0.987490	+	0.0881633i
$606$	−0.119863	+	0.745072i	−0.00486910	+	0.0302665i
$607$	3.54626	+	3.54626i	0.143938	+	0.143938i	0.775404	−	0.631466i	$-0.217546\pi$
$607$	3.54626	+	3.54626i	0.143938	+	0.143938i	−0.631466	+	0.775404i	$0.717546\pi$
$608$	0.489267	+	0.489267i	0.0198424	+	0.0198424i
$609$	−2.04436	+	12.7078i	−0.0828415	+	0.514945i
$610$	14.2833	−	17.0838i	0.578315	−	0.691703i
$611$		−	67.8225i		−	2.74380i
$612$	−2.99531	+	1.50791i	−0.121078	+	0.0609536i
$613$	−29.6529	+	29.6529i	−1.19767	+	1.19767i	−0.222808	+	0.974862i	$0.571522\pi$
$613$	−29.6529	+	29.6529i	−1.19767	+	1.19767i	−0.974862	+	0.222808i	$0.928478\pi$
$614$	8.71421			0.351677
$615$	−1.74338	+	1.51351i	−0.0702998	+	0.0610305i
$616$	0.342042			0.0137813
$617$	32.2270	−	32.2270i	1.29741	−	1.29741i	0.367311	−	0.930098i	$-0.380279\pi$
$617$	32.2270	−	32.2270i	1.29741	−	1.29741i	0.930098	−	0.367311i	$-0.119721\pi$
$618$	4.90510	−	3.54560i	0.197312	−	0.142625i
$619$		−	17.9166i		−	0.720130i	−0.932927	−	0.360065i	$-0.882755\pi$
$619$		−	17.9166i		−	0.720130i	0.932927	−	0.360065i	$-0.117245\pi$
$620$	0.899889	+	10.0794i	0.0361404	+	0.404798i
$621$	4.61250	+	2.39267i	0.185093	+	0.0960144i
$622$	4.64389	+	4.64389i	0.186203	+	0.186203i
$623$	9.08617	+	9.08617i	0.364030	+	0.364030i
$624$	−11.9034	−	1.91496i	−0.476519	−	0.0766597i
$625$	23.4309	−	8.71732i	0.937237	−	0.348693i
$626$		−	7.28934i		−	0.291341i
$627$	−0.215710	−	0.298420i	−0.00861461	−	0.0119177i
$628$	−9.78600	+	9.78600i	−0.390504	+	0.390504i
$629$	−2.80877			−0.111993
$630$	1.70232	−	7.27133i	0.0678219	−	0.289697i
$631$	−7.91640			−0.315147			−0.157573	−	0.987507i	$-0.550367\pi$
$631$	−7.91640			−0.315147			−0.157573	+	0.987507i	$0.550367\pi$
$632$	−11.1265	+	11.1265i	−0.442588	+	0.442588i
$633$	−25.3510	−	35.0715i	−1.00761	−	1.39397i
$634$		−	26.8156i		−	1.06498i
$635$	−33.3869	−	27.9140i	−1.32492	−	1.10773i
$636$	−14.3766	−	2.31282i	−0.570068	−	0.0917093i
$637$	28.3542	+	28.3542i	1.12343	+	1.12343i
$638$	−1.45021	−	1.45021i	−0.0574145	−	0.0574145i
$639$	−12.9773	−	4.28638i	−0.513376	−	0.169567i
$640$	−1.71548	−	1.43427i	−0.0678103	−	0.0566945i
$641$		−	27.3529i		−	1.08037i	−0.841545	−	0.540187i	$-0.818354\pi$
$641$		−	27.3529i		−	1.08037i	0.841545	−	0.540187i	$-0.181646\pi$
$642$	17.8780	−	12.9229i	0.705589	−	0.510028i
$643$	−9.00024	+	9.00024i	−0.354935	+	0.354935i	−0.861942	−	0.507007i	$-0.830752\pi$
$643$	−9.00024	+	9.00024i	−0.354935	+	0.354935i	0.507007	+	0.861942i	$0.330752\pi$
$644$	1.11326			0.0438684
$645$	−36.6330	−	2.58558i	−1.44242	−	0.101807i
$646$	0.773449			0.0304309
$647$	−15.7372	+	15.7372i	−0.618691	+	0.618691i	−0.945196	−	0.326504i	$-0.894129\pi$
$647$	−15.7372	+	15.7372i	−0.618691	+	0.618691i	0.326504	+	0.945196i	$0.394129\pi$
$648$	1.32151	+	8.90245i	0.0519138	+	0.349721i
$649$		−	1.96120i		−	0.0769839i
$650$	6.16548	+	34.2536i	0.241830	+	1.34354i
$651$	1.38601	−	8.61550i	0.0543221	−	0.337668i
$652$	−9.24359	−	9.24359i	−0.362007	−	0.362007i
$653$	−9.00813	−	9.00813i	−0.352515	−	0.352515i	0.508529	−	0.861045i	$-0.330189\pi$
$653$	−9.00813	−	9.00813i	−0.352515	−	0.352515i	−0.861045	+	0.508529i	$0.830189\pi$
$654$	1.29723	−	8.06364i	0.0507258	−	0.315313i
$655$	−1.80648	−	20.2338i	−0.0705850	−	0.790601i
$656$		−	0.596103i		−	0.0232739i
$657$	−9.36536	−	18.6033i	−0.365377	−	0.725785i
$658$	−7.66997	+	7.66997i	−0.299006	+	0.299006i
$659$	−0.859802			−0.0334931			−0.0167466	−	0.999860i	$-0.505331\pi$
$659$	−0.859802			−0.0334931			−0.0167466	+	0.999860i	$0.505331\pi$
$660$	0.780095	+	0.898577i	0.0303652	+	0.0349771i
$661$	−2.50289			−0.0973513			−0.0486757	−	0.998815i	$-0.515500\pi$
$661$	−2.50289			−0.0973513			−0.0486757	+	0.998815i	$0.515500\pi$
$662$	−0.0823190	+	0.0823190i	−0.00319942	+	0.00319942i
$663$	−10.9223	+	7.89505i	−0.424186	+	0.306619i
$664$			9.41670i			0.365439i
$665$	−1.10481	+	1.32142i	−0.0428426	+	0.0512425i
$666$	−2.36421	+	7.15783i	−0.0916113	+	0.277360i
$667$	−4.72006	−	4.72006i	−0.182762	−	0.182762i
$668$	7.44173	+	7.44173i	0.287929	+	0.287929i
$669$	−5.00270	−	0.804807i	−0.193416	−	0.0311156i
$670$	−6.90873	+	0.616812i	−0.266907	+	0.0238295i
$671$		−	3.05973i		−	0.118120i
$672$	1.12959	+	1.56271i	0.0435747	+	0.0602827i
$673$	−22.4457	+	22.4457i	−0.865220	+	0.865220i	−0.991939	−	0.126719i	$-0.959555\pi$
$673$	−22.4457	+	22.4457i	−0.865220	+	0.865220i	0.126719	+	0.991939i	$0.459555\pi$
$674$	11.5901			0.446434
$675$	22.9850	−	12.1116i	0.884692	−	0.466176i
$676$	−35.4529			−1.36357
$677$	28.5893	−	28.5893i	1.09878	−	1.09878i	0.104222	−	0.994554i	$-0.466765\pi$
$677$	28.5893	−	28.5893i	1.09878	−	1.09878i	0.994554	−	0.104222i	$-0.0332354\pi$
$678$	13.9790	+	19.3391i	0.536861	+	0.742712i
$679$		−	20.1957i		−	0.775040i
$680$	−2.48961	+	0.222273i	−0.0954723	+	0.00852378i
$681$	36.0164	+	5.79412i	1.38015	+	0.222031i
$682$	0.983202	+	0.983202i	0.0376488	+	0.0376488i
$683$	14.6754	+	14.6754i	0.561537	+	0.561537i	0.929744	−	0.368207i	$-0.120028\pi$
$683$	14.6754	+	14.6754i	0.561537	+	0.561537i	−0.368207	+	0.929744i	$0.620028\pi$
$684$	0.651032	−	1.97105i	0.0248928	−	0.0753650i
$685$	12.4178	−	14.8525i	0.474459	−	0.567484i
$686$		−	14.2059i		−	0.542383i
$687$	6.47343	−	4.67925i	0.246977	−	0.178525i
$688$	6.70489	−	6.70489i	0.255621	−	0.255621i
$689$	−58.5198			−2.22943
$690$	2.53900	+	2.92463i	0.0966582	+	0.111339i
$691$	41.2032			1.56744			0.783721	−	0.621113i	$-0.213319\pi$
$691$	41.2032			1.56744			0.783721	+	0.621113i	$0.213319\pi$
$692$	9.04703	−	9.04703i	0.343916	−	0.343916i
$693$	−0.461406	−	0.916536i	−0.0175274	−	0.0348163i
$694$		−	5.93489i		−	0.225285i
$695$	0.340008	+	3.80833i	0.0128972	+	0.144458i
$696$	1.83638	−	11.4150i	0.0696077	−	0.432683i
$697$	−0.471169	−	0.471169i	−0.0178468	−	0.0178468i
$698$	−3.89717	−	3.89717i	−0.147510	−	0.147510i
$699$	−1.35070	+	8.39599i	−0.0510882	+	0.317566i
$700$	3.17646	−	4.57095i	0.120059	−	0.172766i
$701$		−	15.0725i		−	0.569281i	−0.958634	−	0.284641i	$-0.908126\pi$
$701$		−	15.0725i		−	0.569281i	0.958634	−	0.284641i	$-0.0918743\pi$
$702$	10.9261	+	34.4797i	0.412379	+	1.30135i
$703$	1.22939	−	1.22939i	0.0463674	−	0.0463674i
$704$	−0.307245			−0.0115797
$705$	−37.6426	−	2.65684i	−1.41770	−	0.100062i
$706$	−3.31208			−0.124652
$707$	0.342978	−	0.342978i	0.0128990	−	0.0128990i
$708$	8.96025	−	6.47682i	0.336747	−	0.243414i
$709$		−	18.9496i		−	0.711666i	−0.934550	−	0.355833i	$-0.884197\pi$
$709$		−	18.9496i		−	0.711666i	0.934550	−	0.355833i	$-0.115803\pi$
$710$	−7.81511	−	6.53402i	−0.293296	−	0.245217i
$711$	44.8240	+	14.8052i	1.68103	+	0.555239i
$712$	−8.16181	−	8.16181i	−0.305877	−	0.305877i
$713$	3.20006	+	3.20006i	0.119843	+	0.119843i
$714$	2.12803	+	0.342346i	0.0796396	+	0.0128120i
$715$	3.66885	+	3.06743i	0.137207	+	0.114716i
$716$		−	11.2260i		−	0.419534i
$717$	−20.5782	−	28.4685i	−0.768506	−	1.06318i
$718$	−8.81537	+	8.81537i	−0.328987	+	0.328987i
$719$	−32.0644			−1.19580			−0.597900	−	0.801571i	$-0.703998\pi$
$719$	−32.0644			−1.19580			−0.597900	+	0.801571i	$0.703998\pi$
$720$	−1.52913	+	6.53160i	−0.0569874	+	0.243418i
$721$	−3.89010			−0.144875
$722$	13.0965	−	13.0965i	0.487401	−	0.487401i
$723$	−6.25731	−	8.65657i	−0.232712	−	0.321941i
$724$			8.65815i			0.321778i
$725$	−32.8480	+	5.91248i	−1.21994	+	0.219584i
$726$	−18.6493	−	3.00019i	−0.692139	−	0.111347i
$727$	−24.2721	−	24.2721i	−0.900201	−	0.900201i	0.0952521	−	0.995453i	$-0.469634\pi$
$727$	−24.2721	−	24.2721i	−0.900201	−	0.900201i	−0.995453	+	0.0952521i	$0.969634\pi$
$728$	5.47949	+	5.47949i	0.203083	+	0.203083i
$729$	22.0723	−	15.5503i	0.817494	−	0.575937i
$730$	−1.38050	−	15.4626i	−0.0510946	−	0.572295i
$731$		−	10.5993i		−	0.392029i
$732$	13.9792	−	10.1047i	0.516685	−	0.373480i
$733$	26.6081	−	26.6081i	0.982793	−	0.982793i	−0.0170616	−	0.999854i	$-0.505431\pi$
$733$	26.6081	−	26.6081i	0.982793	−	0.982793i	0.999854	+	0.0170616i	$0.00543113\pi$
$734$	4.99809			0.184483
$735$	16.8478	−	14.6263i	0.621441	−	0.539501i
$736$	−1.00000			−0.0368605
$737$	−0.673917	+	0.673917i	−0.0248240	+	0.0248240i
$738$	−1.59732	+	0.804127i	−0.0587981	+	0.0296003i
$739$			38.0885i			1.40111i	0.713599	+	0.700554i	$0.247064\pi$
$739$			38.0885i			1.40111i	−0.713599	+	0.700554i	$0.752936\pi$
$740$	−3.60392	+	4.31053i	−0.132483	+	0.158458i
$741$	1.32501	−	8.23632i	0.0486756	−	0.302569i
$742$	6.61794	+	6.61794i	0.242952	+	0.242952i
$743$	27.8032	+	27.8032i	1.02000	+	1.02000i	0.999796	+	0.0202029i	$0.00643121\pi$
$743$	27.8032	+	27.8032i	1.02000	+	1.02000i	0.0202029	+	0.999796i	$0.493569\pi$
$744$	−1.24501	+	7.73901i	−0.0456442	+	0.283726i
$745$	−9.88953	+	0.882938i	−0.362324	+	0.0323484i
$746$			24.6555i			0.902700i
$747$	25.2330	−	12.7029i	0.923228	−	0.464775i
$748$	−0.242851	+	0.242851i	−0.00887952	+	0.00887952i
$749$	−14.1786			−0.518073
$750$	19.2529	−	2.08012i	0.703016	−	0.0759551i
$751$	11.8305			0.431701			0.215850	−	0.976426i	$-0.430748\pi$
$751$	11.8305			0.431701			0.215850	+	0.976426i	$0.430748\pi$
$752$	6.88967	−	6.88967i	0.251241	−	0.251241i
$753$	−9.03663	+	6.53203i	−0.329313	+	0.238040i
$754$		−	46.4646i		−	1.69214i
$755$	41.9853	−	3.74846i	1.52800	−	0.136420i
$756$	2.66365	−	5.13489i	0.0968759	−	0.186754i
$757$	−9.09388	−	9.09388i	−0.330523	−	0.330523i	0.522262	−	0.852785i	$-0.325088\pi$
$757$	−9.09388	−	9.09388i	−0.330523	−	0.330523i	−0.852785	+	0.522262i	$0.825088\pi$
$758$	−19.7462	−	19.7462i	−0.717214	−	0.717214i
$759$	0.525408	+	0.0845247i	0.0190711	+	0.00306805i
$760$	0.992411	−	1.18699i	0.0359985	−	0.0430566i
$761$		−	41.4873i		−	1.50391i	−0.659213	−	0.751956i	$-0.729111\pi$
$761$		−	41.4873i		−	1.50391i	0.659213	−	0.751956i	$-0.270889\pi$
$762$	−19.7476	−	27.3195i	−0.715381	−	0.989682i
$763$	−3.71192	+	3.71192i	−0.134381	+	0.134381i
$764$	18.1677			0.657284
$765$	3.95403	+	6.37133i	0.142958	+	0.230356i
$766$	−14.1963			−0.512932
$767$	31.4183	−	31.4183i	1.13445	−	1.13445i
$768$	−1.01467	−	1.40373i	−0.0366137	−	0.0506526i
$769$			45.6787i			1.64722i	0.567159	+	0.823608i	$0.308042\pi$
$769$			45.6787i			1.64722i	−0.567159	+	0.823608i	$0.691958\pi$
$770$	−0.0680135	−	0.761799i	−0.00245104	−	0.0274533i
$771$	−20.6325	−	3.31923i	−0.743060	−	0.119539i
$772$	−6.41622	−	6.41622i	−0.230925	−	0.230925i
$773$	−29.1634	−	29.1634i	−1.04894	−	1.04894i	−0.998739	−	0.0501962i	$-0.984015\pi$
$773$	−29.1634	−	29.1634i	−1.04894	−	1.04894i	−0.0501962	−	0.998739i	$-0.515985\pi$
$774$	−27.0112	−	8.92170i	−0.970896	−	0.320684i
$775$	22.2700	−	4.00848i	0.799961	−	0.143989i
$776$			18.1411i			0.651228i
$777$	3.92665	−	2.83833i	0.140868	−	0.101825i
$778$	14.4205	−	14.4205i	0.517000	−	0.517000i
$779$	0.412460			0.0147779
$780$	−1.89807	+	26.8922i	−0.0679617	+	0.962896i
$781$	−1.39970			−0.0500851
$782$	−0.790416	+	0.790416i	−0.0282652	+	0.0282652i
$783$	−33.0648	+	10.4778i	−1.18164	+	0.374444i
$784$			5.76066i			0.205738i
$785$	23.7414	+	19.8496i	0.847365	+	0.708461i
$786$	2.49929	−	15.5356i	0.0891467	−	0.554138i
$787$	24.6107	+	24.6107i	0.877277	+	0.877277i	0.993252	−	0.115975i	$-0.0369993\pi$
$787$	24.6107	+	24.6107i	0.877277	+	0.877277i	−0.115975	+	0.993252i	$0.536999\pi$
$788$	−14.6739	−	14.6739i	−0.522737	−	0.522737i
$789$	1.62695	−	10.1132i	0.0579209	−	0.360038i
$790$	26.9935	+	22.5686i	0.960386	+	0.802954i
$791$		−	15.3373i		−	0.545330i
$792$	0.414465	+	0.823293i	0.0147274	+	0.0292545i
$793$	49.0167	−	49.0167i	1.74063	−	1.74063i
$794$	16.6940			0.592447
$795$	−2.29242	+	32.4795i	−0.0813038	+	1.15193i
$796$	−2.60795			−0.0924363
$797$	−25.2336	+	25.2336i	−0.893820	+	0.893820i	−0.994880	−	0.101060i	$-0.967777\pi$
$797$	−25.2336	+	25.2336i	−0.893820	+	0.893820i	0.101060	+	0.994880i	$0.467777\pi$
$798$	−1.08128	+	0.781591i	−0.0382769	+	0.0276680i
$799$		−	10.8914i		−	0.385311i
$800$	−2.85330	+	4.10593i	−0.100880	+	0.145167i
$801$	−10.8603	+	32.8805i	−0.383731	+	1.16177i
$802$	−6.12698	−	6.12698i	−0.216351	−	0.216351i
$803$	−1.50831	−	1.50831i	−0.0532270	−	0.0532270i
$804$	−5.30456	−	0.853368i	−0.187077	−	0.0300960i
$805$	−0.221366	−	2.47945i	−0.00780212	−	0.0873892i
$806$			31.5017i			1.10960i
$807$	4.77066	+	6.59989i	0.167935	+	0.232327i
$808$	−0.308085	+	0.308085i	−0.0108384	+	0.0108384i
$809$	−2.69190			−0.0946422			−0.0473211	−	0.998880i	$-0.515068\pi$
$809$	−2.69190			−0.0946422			−0.0473211	+	0.998880i	$0.515068\pi$
$810$	19.5648	−	4.71349i	0.687438	−	0.165615i
$811$	−40.9585			−1.43825			−0.719124	−	0.694881i	$-0.755457\pi$
$811$	−40.9585			−1.43825			−0.719124	+	0.694881i	$0.755457\pi$
$812$	−5.25463	+	5.25463i	−0.184401	+	0.184401i
$813$	−2.85137	−	3.94467i	−0.100002	−	0.138346i
$814$			0.772021i			0.0270593i
$815$	−18.7494	+	22.4255i	−0.656762	+	0.785529i
$816$	−1.91154	−	0.307518i	−0.0669172	−	0.0107653i
$817$	4.63930	+	4.63930i	0.162308	+	0.162308i
$818$	15.9239	+	15.9239i	0.556765	+	0.556765i
$819$	7.29115	−	22.0745i	0.254773	−	0.771346i
$820$	−1.32765	+	0.118532i	−0.0463634	+	0.00413933i
$821$		−	43.8765i		−	1.53130i	−0.643257	−	0.765651i	$-0.722417\pi$
$821$		−	43.8765i		−	1.53130i	0.643257	−	0.765651i	$-0.277583\pi$
$822$	12.1534	−	8.78492i	0.423897	−	0.306409i
$823$	−26.3103	+	26.3103i	−0.917118	+	0.917118i	−0.996819	−	0.0797004i	$-0.974604\pi$
$823$	−26.3103	+	26.3103i	−0.917118	+	0.917118i	0.0797004	+	0.996819i	$0.474604\pi$
$824$	3.49434			0.121731
$825$	1.84620	−	1.91611i	0.0642765	−	0.0667105i
$826$	−7.10612			−0.247254
$827$	−19.6739	+	19.6739i	−0.684130	+	0.684130i	−0.960928	−	0.276798i	$-0.910727\pi$
$827$	−19.6739	+	19.6739i	−0.684130	+	0.684130i	0.276798	+	0.960928i	$0.410727\pi$
$828$	1.34897	+	2.67960i	0.0468801	+	0.0931226i
$829$			46.9364i			1.63017i	0.579343	+	0.815084i	$0.303309\pi$
$829$			46.9364i			1.63017i	−0.579343	+	0.815084i	$0.696691\pi$
$830$	20.9730	−	1.87247i	0.727982	−	0.0649943i
$831$	−2.94457	+	18.3035i	−0.102146	+	0.634942i
$832$	−4.92204	−	4.92204i	−0.170641	−	0.170641i
$833$	4.55332	+	4.55332i	0.157763	+	0.157763i
$834$	−0.470406	+	2.92406i	−0.0162888	+	0.101252i
$835$	15.0945	−	18.0540i	0.522368	−	0.624786i
$836$		−	0.212591i		−	0.00735262i
$837$	22.4170	−	7.10361i	0.774844	−	0.245537i
$838$	−13.9827	+	13.9827i	−0.483024	+	0.483024i
$839$	27.6624			0.955013			0.477507	−	0.878628i	$-0.341541\pi$
$839$	27.6624			0.955013			0.477507	+	0.878628i	$0.341541\pi$
$840$	3.25586	−	2.82656i	0.112338	−	0.0975256i
$841$	15.5580			0.536481
$842$	−2.50317	+	2.50317i	−0.0862649	+	0.0862649i
$843$	−9.72498	+	7.02960i	−0.334946	+	0.242112i
$844$		−	24.9846i		−	0.860004i
$845$	7.04965	+	78.9611i	0.242515	+	2.71634i
$846$	−27.7556	−	9.16759i	−0.954256	−	0.315188i
$847$	8.58478	+	8.58478i	0.294977	+	0.294977i
$848$	−5.94467	−	5.94467i	−0.204141	−	0.204141i
$849$	30.4701	+	4.90186i	1.04573	+	0.168231i
$850$	0.990097	+	5.50069i	0.0339600	+	0.188672i
$851$			2.51272i			0.0861350i
$852$	−4.62246	−	6.39487i	−0.158363	−	0.219085i
$853$	−11.6144	+	11.6144i	−0.397671	+	0.397671i	−0.877411	−	0.479740i	$-0.840731\pi$
$853$	−11.6144	+	11.6144i	−0.397671	+	0.397671i	0.479740	+	0.877411i	$0.340731\pi$
$854$	−11.0865			−0.379371
$855$	−4.51939	−	1.05805i	−0.154560	−	0.0361845i
$856$	12.7361			0.435312
$857$	2.96243	−	2.96243i	0.101195	−	0.101195i	−0.654697	−	0.755892i	$-0.727204\pi$
$857$	2.96243	−	2.96243i	0.101195	−	0.101195i	0.755892	+	0.654697i	$0.227204\pi$
$858$	2.17004	+	3.00211i	0.0740841	+	0.102490i
$859$			54.1769i			1.84849i	0.381797	+	0.924246i	$0.375305\pi$
$859$			54.1769i			1.84849i	−0.381797	+	0.924246i	$0.624695\pi$
$860$	−16.2664	−	13.5999i	−0.554680	−	0.463754i
$861$	1.13482	+	0.182564i	0.0386747	+	0.00622176i
$862$	−4.94131	−	4.94131i	−0.168302	−	0.168302i
$863$	23.6935	+	23.6935i	0.806536	+	0.806536i	0.984108	−	0.177572i	$-0.0568242\pi$
$863$	23.6935	+	23.6935i	0.806536	+	0.806536i	−0.177572	+	0.984108i	$0.556824\pi$
$864$	−2.39267	+	4.61250i	−0.0814001	+	0.156920i
$865$	−21.9486	−	18.3507i	−0.746274	−	0.623941i
$866$			31.1490i			1.05849i
$867$	22.1094	−	15.9815i	0.750874	−	0.542761i
$868$	3.56249	−	3.56249i	0.120919	−	0.120919i
$869$	4.83457			0.164002
$870$	−25.7887	−	1.82018i	−0.874318	−	0.0617099i
$871$	−21.5922			−0.731624
$872$	3.33429	−	3.33429i	0.112913	−	0.112913i
$873$	48.6110	−	24.4719i	1.64523	−	0.828249i
$874$		−	0.691928i		−	0.0234048i
$875$	−10.8121	−	6.16572i	−0.365515	−	0.208439i
$876$	1.90994	−	11.8722i	0.0645309	−	0.401126i
$877$	−17.6838	−	17.6838i	−0.597140	−	0.597140i	0.342410	−	0.939551i	$-0.388757\pi$
$877$	−17.6838	−	17.6838i	−0.597140	−	0.597140i	−0.939551	+	0.342410i	$0.888757\pi$
$878$	8.83613	+	8.83613i	0.298205	+	0.298205i
$879$	1.83276	−	11.3925i	0.0618176	−	0.384260i
$880$	0.0610942	+	0.684298i	0.00205949	+	0.0230677i
$881$			41.8174i			1.40886i	0.709772	+	0.704432i	$0.248798\pi$
$881$			41.8174i			1.40886i	−0.709772	+	0.704432i	$0.751202\pi$
$882$	15.4363	−	7.77099i	0.519767	−	0.261663i
$883$	−15.8834	+	15.8834i	−0.534520	+	0.534520i	−0.921914	−	0.387394i	$-0.873375\pi$
$883$	−15.8834	+	15.8834i	−0.534520	+	0.534520i	0.387394	+	0.921914i	$0.373375\pi$
$884$	−7.78092			−0.261701
$885$	−16.2069	−	18.6685i	−0.544790	−	0.627534i
$886$	−4.88635			−0.164160
$887$	26.4613	−	26.4613i	0.888484	−	0.888484i	−0.105893	−	0.994378i	$-0.533770\pi$
$887$	26.4613	−	26.4613i	0.888484	−	0.888484i	0.994378	+	0.105893i	$0.0337701\pi$
$888$	−3.52718	+	2.54958i	−0.118364	+	0.0855583i
$889$			21.6663i			0.726666i
$890$	−16.5551	+	19.8010i	−0.554929	+	0.663731i
$891$	1.64700	−	2.22120i	0.0551764	−	0.0744131i
$892$	−2.06860	−	2.06860i	−0.0692620	−	0.0692620i
$893$	4.76716	+	4.76716i	0.159527	+	0.159527i
$894$	−7.59323	−	1.22156i	−0.253956	−	0.0408550i
$895$	−25.0026	+	2.23223i	−0.835744	+	0.0746153i
$896$			1.11326i			0.0371913i
$897$	7.06292	+	9.77108i	0.235824	+	0.326247i
$898$	−3.85257	+	3.85257i	−0.128562	+	0.128562i
$899$	−30.2090			−1.00753
$900$	14.8513	+	2.10692i	0.495043	+	0.0702307i
$901$	−9.39753			−0.313077
$902$	−0.129506	+	0.129506i	−0.00431208	+	0.00431208i
$903$	10.7109	+	14.8178i	0.356436	+	0.493106i
$904$			13.7769i			0.458214i
$905$	19.2835	−	1.72163i	0.641006	−	0.0572290i
$906$	32.2366	+	5.18604i	1.07099	+	0.172295i
$907$	36.4729	+	36.4729i	1.21106	+	1.21106i	0.970677	+	0.240387i	$0.0772743\pi$
$907$	36.4729	+	36.4729i	1.21106	+	1.21106i	0.240387	+	0.970677i	$0.422726\pi$
$908$	14.8927	+	14.8927i	0.494231	+	0.494231i
$909$	1.24115	+	0.409947i	0.0411662	+	0.0135971i
$910$	11.1144	−	13.2935i	0.368438	−	0.440676i
$911$			41.2639i			1.36713i	0.729888	+	0.683567i	$0.239572\pi$
$911$			41.2639i			1.36713i	−0.729888	+	0.683567i	$0.760428\pi$
$912$	0.971277	−	0.702077i	0.0321622	−	0.0232481i
$913$	2.04582	−	2.04582i	0.0677069	−	0.0677069i
$914$	−13.3892			−0.442876
$915$	−25.2849	−	29.1252i	−0.835895	−	0.962851i
$916$	4.61161			0.152372
$917$	−7.15150	+	7.15150i	−0.236163	+	0.236163i
$918$	1.75459	+	5.53700i	0.0579102	+	0.182748i
$919$			9.49797i			0.313309i	0.987653	+	0.156655i	$0.0500710\pi$
$919$			9.49797i			0.313309i	−0.987653	+	0.156655i	$0.949929\pi$
$920$	0.198845	+	2.22721i	0.00655574	+	0.0734289i
$921$	2.39733	−	14.9018i	0.0789946	−	0.491033i
$922$	21.1083	+	21.1083i	0.695166	+	0.695166i
$923$	−22.4230	−	22.4230i	−0.738063	−	0.738063i
$924$	0.0940976	−	0.584913i	0.00309558	−	0.0192422i
$925$	10.3171	+	7.16956i	0.339223	+	0.235734i
$926$			25.4368i			0.835905i
$927$	−4.71378	−	9.36345i	−0.154821	−	0.307536i
$928$	4.72006	−	4.72006i	0.154944	−	0.154944i
$929$	−54.3893			−1.78446			−0.892228	−	0.451585i	$-0.850859\pi$
$929$	−54.3893			−1.78446			−0.892228	+	0.451585i	$0.850859\pi$
$930$	17.4840	+	1.23403i	0.573322	+	0.0404654i
$931$	−3.98596			−0.130635
$932$	−3.47172	+	3.47172i	−0.113720	+	0.113720i
$933$	9.21890	−	6.66378i	0.301813	−	0.218162i
$934$		−	5.06784i		−	0.165825i
$935$	0.589170	+	0.492591i	0.0192679	+	0.0161094i
$936$	−6.54940	+	19.8288i	−0.214074	+	0.648125i
$937$	−1.83354	−	1.83354i	−0.0598992	−	0.0598992i	0.676523	−	0.736422i	$-0.263486\pi$
$937$	−1.83354	−	1.83354i	−0.0598992	−	0.0598992i	−0.736422	+	0.676523i	$0.763486\pi$
$938$	2.44184	+	2.44184i	0.0797288	+	0.0797288i
$939$	−12.4652	−	2.00534i	−0.406788	−	0.0654417i
$940$	−16.7147	−	13.9748i	−0.545174	−	0.455806i
$941$		−	24.0075i		−	0.782621i	−0.920259	−	0.391310i	$-0.872022\pi$
$941$		−	24.0075i		−	0.782621i	0.920259	−	0.391310i	$-0.127978\pi$
$942$	14.0425	+	19.4269i	0.457529	+	0.632961i
$943$	−0.421508	+	0.421508i	−0.0137262	+	0.0137262i
$944$	6.38319			0.207755
$945$	−11.9661	−	4.91145i	−0.389258	−	0.159770i
$946$	−2.91334			−0.0947208
$947$	−4.17084	+	4.17084i	−0.135534	+	0.135534i	−0.771619	−	0.636085i	$-0.780553\pi$
$947$	−4.17084	+	4.17084i	−0.135534	+	0.135534i	0.636085	+	0.771619i	$0.280553\pi$
$948$	15.9661	+	22.0880i	0.518554	+	0.717384i
$949$		−	48.3260i		−	1.56873i
$950$	−2.84101	−	1.97428i	−0.0921744	−	0.0640541i
$951$	−45.8563	−	7.37711i	−1.48699	−	0.239219i
$952$	0.879935	+	0.879935i	0.0285189	+	0.0285189i
$953$	−4.40507	−	4.40507i	−0.142694	−	0.142694i	0.632151	−	0.774845i	$-0.282172\pi$
$953$	−4.40507	−	4.40507i	−0.142694	−	0.142694i	−0.774845	+	0.632151i	$0.782172\pi$
$954$	−7.91014	+	23.9486i	−0.256100	+	0.775363i
$955$	−3.61256	−	40.4632i	−0.116900	−	1.30936i
$956$		−	20.2807i		−	0.655924i
$957$	−2.87892	+	2.08100i	−0.0930622	+	0.0672690i
$958$	27.7307	−	27.7307i	0.895939	−	0.895939i
$959$	−9.63848			−0.311243
$960$	−2.92463	+	2.53900i	−0.0943920	+	0.0819460i
$961$	−10.5192			−0.339329
$962$	−12.3677	+	12.3677i	−0.398751	+	0.398751i
$963$	−17.1807	−	34.1277i	−0.553640	−	1.09975i
$964$		−	6.16685i		−	0.198621i
$965$	−13.0144	+	15.5661i	−0.418949	+	0.501091i
$966$	0.306263	−	1.90374i	0.00985384	−	0.0612517i
$967$	30.9294	+	30.9294i	0.994624	+	0.994624i	0.999986	−	0.00536164i	$-0.00170667\pi$
$967$	30.9294	+	30.9294i	0.994624	+	0.994624i	−0.00536164	+	0.999986i	$0.501707\pi$
$968$	−7.71142	−	7.71142i	−0.247855	−	0.247855i
$969$	0.212780	−	1.32265i	0.00683548	−	0.0424895i
$970$	40.4041	−	3.60728i	1.29730	−	0.115823i
$971$		−	57.5128i		−	1.84568i	−0.385189	−	0.922838i	$-0.625864\pi$
$971$		−	57.5128i		−	1.84568i	0.385189	−	0.922838i	$-0.374136\pi$
$972$	15.5873	+	0.189246i	0.499963	+	0.00607006i
$973$	1.34603	−	1.34603i	0.0431516	−	0.0431516i
$974$	26.8146			0.859194
$975$	60.2720	−	1.12000i	1.93025	−	0.0358688i
$976$	9.95861			0.318767
$977$	−36.8392	+	36.8392i	−1.17859	+	1.17859i	−0.198487	+	0.980103i	$0.563603\pi$
$977$	−36.8392	+	36.8392i	−1.17859	+	1.17859i	−0.980103	+	0.198487i	$0.936397\pi$
$978$	−18.3501	+	13.2642i	−0.586771	+	0.424141i
$979$			3.54638i			0.113343i
$980$	12.8302	−	1.14548i	0.409846	−	0.0365911i
$981$	−13.4325	−	4.43670i	−0.428865	−	0.141653i
$982$	−10.4001	−	10.4001i	−0.331880	−	0.331880i
$983$	36.6462	+	36.6462i	1.16883	+	1.16883i	0.982484	+	0.186349i	$0.0596657\pi$
$983$	36.6462	+	36.6462i	1.16883	+	1.16883i	0.186349	+	0.982484i	$0.440334\pi$
$984$	−1.01937	−	0.163991i	−0.0324964	−	0.00522784i
$985$	−29.7641	+	35.5998i	−0.948362	+	1.13430i
$986$		−	7.46163i		−	0.237627i
$987$	11.0061	+	15.2262i	0.350327	+	0.484655i
$988$	3.40570	−	3.40570i	0.108350	−	0.108350i
$989$	−9.48214			−0.301515
$990$	1.75123	−	1.08681i	0.0556578	−	0.0345411i
$991$	18.6888			0.593669			0.296834	−	0.954929i	$-0.404069\pi$
$991$	18.6888			0.593669			0.296834	+	0.954929i	$0.404069\pi$
$992$	−3.20006	+	3.20006i	−0.101602	+	0.101602i
$993$	0.118124	+	0.163417i	0.00374856	+	0.00518588i
$994$			5.07159i			0.160861i
$995$	0.518579	+	5.80845i	0.0164401	+	0.184140i
$996$	16.1032	+	2.59059i	0.510248	+	0.0820859i
$997$	6.75334	+	6.75334i	0.213881	+	0.213881i	0.805914	−	0.592033i	$-0.201675\pi$
$997$	6.75334	+	6.75334i	0.213881	+	0.213881i	−0.592033	+	0.805914i	$0.701675\pi$
$998$	8.94201	+	8.94201i	0.283055	+	0.283055i
$999$	11.5899	+	6.01211i	0.366689	+	0.190215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.47.10	yes	32
3.2	odd	2	inner	690.2.i.f.47.8	✓	32
5.3	odd	4	inner	690.2.i.f.323.8	yes	32
15.8	even	4	inner	690.2.i.f.323.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.8	✓	32	3.2	odd	2	inner
690.2.i.f.47.10	yes	32	1.1	even	1	trivial
690.2.i.f.323.8	yes	32	5.3	odd	4	inner
690.2.i.f.323.10	yes	32	15.8	even	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.01467 - 1.40373i) q^{3} -1.00000i q^{4} +(-2.22721 + 0.198845i) q^{5} +(-1.71006 - 0.275105i) q^{6} +(0.787190 + 0.787190i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.940895 + 2.84863i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.01467 - 1.40373i) q^{3} -1.00000i q^{4} +(-2.22721 + 0.198845i) q^{5} +(-1.71006 - 0.275105i) q^{6} +(0.787190 + 0.787190i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.940895 + 2.84863i) q^{9} +(-1.43427 + 1.71548i) q^{10} +0.307245i q^{11} +(-1.40373 + 1.01467i) q^{12} +(-4.92204 + 4.92204i) q^{13} +1.11326 q^{14} +(2.53900 + 2.92463i) q^{15} -1.00000 q^{16} +(-0.790416 + 0.790416i) q^{17} +(1.34897 + 2.67960i) q^{18} -0.691928i q^{19} +(0.198845 + 2.22721i) q^{20} +(0.306263 - 1.90374i) q^{21} +(0.217255 + 0.217255i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-0.275105 + 1.71006i) q^{24} +(4.92092 - 0.885741i) q^{25} +6.96081i q^{26} +(4.95340 - 1.56966i) q^{27} +(0.787190 - 0.787190i) q^{28} -6.67517 q^{29} +(3.86337 + 0.272679i) q^{30} +4.52557 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.431287 - 0.311752i) q^{33} +1.11782i q^{34} +(-1.90977 - 1.59671i) q^{35} +(2.84863 + 0.940895i) q^{36} +(1.77676 + 1.77676i) q^{37} +(-0.489267 - 0.489267i) q^{38} +(11.9034 + 1.91496i) q^{39} +(1.71548 + 1.43427i) q^{40} +0.596103i q^{41} +(-1.12959 - 1.56271i) q^{42} +(-6.70489 + 6.70489i) q^{43} +0.307245 q^{44} +(1.52913 - 6.53160i) q^{45} +1.00000 q^{46} +(-6.88967 + 6.88967i) q^{47} +(1.01467 + 1.40373i) q^{48} -5.76066i q^{49} +(2.85330 - 4.10593i) q^{50} +(1.91154 + 0.307518i) q^{51} +(4.92204 + 4.92204i) q^{52} +(5.94467 + 5.94467i) q^{53} +(2.39267 - 4.61250i) q^{54} +(-0.0610942 - 0.684298i) q^{55} -1.11326i q^{56} +(-0.971277 + 0.702077i) q^{57} +(-4.72006 + 4.72006i) q^{58} -6.38319 q^{59} +(2.92463 - 2.53900i) q^{60} -9.95861 q^{61} +(3.20006 - 3.20006i) q^{62} +(-2.98308 + 1.50175i) q^{63} +1.00000i q^{64} +(9.98368 - 11.9411i) q^{65} +(0.0845247 - 0.525408i) q^{66} +(2.19342 + 2.19342i) q^{67} +(0.790416 + 0.790416i) q^{68} +(0.275105 - 1.71006i) q^{69} +(-2.47945 + 0.221366i) q^{70} +4.55564i q^{71} +(2.67960 - 1.34897i) q^{72} +(-4.90914 + 4.90914i) q^{73} +2.51272 q^{74} +(-6.23644 - 6.00889i) q^{75} -0.691928 q^{76} +(-0.241860 + 0.241860i) q^{77} +(9.77108 - 7.06292i) q^{78} -15.7352i q^{79} +(2.22721 - 0.198845i) q^{80} +(-7.22943 - 5.36053i) q^{81} +(0.421508 + 0.421508i) q^{82} +(-6.65861 - 6.65861i) q^{83} +(-1.90374 - 0.306263i) q^{84} +(1.60325 - 1.91759i) q^{85} +9.48214i q^{86} +(6.77309 + 9.37012i) q^{87} +(0.217255 - 0.217255i) q^{88} +11.5425 q^{89} +(-3.53728 - 5.69980i) q^{90} -7.74916 q^{91} +(0.707107 - 0.707107i) q^{92} +(-4.59195 - 6.35266i) q^{93} +9.74347i q^{94} +(0.137587 + 1.54107i) q^{95} +(1.71006 + 0.275105i) q^{96} +(-12.8277 - 12.8277i) q^{97} +(-4.07340 - 4.07340i) q^{98} +(-0.875228 - 0.289085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more