LMFDB - Embedded newform 390.2.bn.c.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	390.97
Dual form			390.2.bn.c.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.65293 - 1.50593i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-1.08688 + 0.627513i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.65293 - 1.50593i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-1.08688 + 0.627513i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.13064 - 0.678517i) q^{10} +(-1.61087 + 0.431631i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.26841 - 1.52233i) q^{13} -1.25503i q^{14} +(1.02680 - 1.98637i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.62805 - 1.24008i) q^{17} -1.00000i q^{18} +(1.68516 - 6.28910i) q^{19} +(-0.477706 + 2.18444i) q^{20} +(-0.887437 - 0.887437i) q^{21} +(0.431631 - 1.61087i) q^{22} +(-4.73471 + 1.26866i) q^{23} +(0.258819 + 0.965926i) q^{24} +(0.464364 + 4.97839i) q^{25} +(2.95258 - 2.06936i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.08688 + 0.627513i) q^{28} +(-6.16323 - 3.55834i) q^{29} +(1.20685 + 1.88242i) q^{30} +(4.97092 - 4.97092i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.833847 - 1.44427i) q^{33} +(3.38797 - 3.38797i) q^{34} +(2.74153 + 0.599533i) q^{35} +(0.866025 + 0.500000i) q^{36} +(8.89318 + 5.13448i) q^{37} +(4.60394 + 4.60394i) q^{38} +(0.624535 - 3.55105i) q^{39} +(-1.65293 - 1.50593i) q^{40} +(0.614688 + 2.29405i) q^{41} +(1.21226 - 0.324825i) q^{42} +(-1.65466 + 6.17528i) q^{43} +(1.17924 + 1.17924i) q^{44} +(2.18444 + 0.477706i) q^{45} +(1.26866 - 4.73471i) q^{46} -3.93547i q^{47} +(-0.965926 - 0.258819i) q^{48} +(-2.71245 + 4.69811i) q^{49} +(-4.54359 - 2.08704i) q^{50} -4.79131i q^{51} +(0.315825 + 3.59169i) q^{52} +(-2.76048 + 2.76048i) q^{53} +(0.965926 - 0.258819i) q^{54} +(3.31266 + 1.71240i) q^{55} +(-1.08688 + 0.627513i) q^{56} +6.51095 q^{57} +(6.16323 - 3.55834i) q^{58} +(-7.25043 - 1.94275i) q^{59} +(-2.23365 + 0.103947i) q^{60} +(-4.86857 - 8.43262i) q^{61} +(1.81948 + 6.79040i) q^{62} +(0.627513 - 1.08688i) q^{63} +1.00000 q^{64} +(3.10993 + 7.43830i) q^{65} +1.66769 q^{66} +(0.931803 - 1.61393i) q^{67} +(1.24008 + 4.62805i) q^{68} +(-2.45087 - 4.24503i) q^{69} +(-1.88998 + 2.07447i) q^{70} +(1.32703 + 0.355575i) q^{71} +(-0.866025 + 0.500000i) q^{72} -10.6790 q^{73} +(-8.89318 + 5.13448i) q^{74} +(-4.68857 + 1.73704i) q^{75} +(-6.28910 + 1.68516i) q^{76} +(1.47997 - 1.47997i) q^{77} +(2.76303 + 2.31639i) q^{78} +8.54874i q^{79} +(2.13064 - 0.678517i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.29405 - 0.614688i) q^{82} +3.67899i q^{83} +(-0.324825 + 1.21226i) q^{84} +(5.78237 + 9.01928i) q^{85} +(-4.52062 - 4.52062i) q^{86} +(1.84193 - 6.87419i) q^{87} +(-1.61087 + 0.431631i) q^{88} +(1.32475 + 4.94404i) q^{89} +(-1.50593 + 1.65293i) q^{90} +(4.50767 - 0.396369i) q^{91} +(3.46605 + 3.46605i) q^{92} +(6.08811 + 3.51497i) q^{93} +(3.40821 + 1.96773i) q^{94} +(-12.2564 + 7.85772i) q^{95} +(0.707107 - 0.707107i) q^{96} +(7.29623 + 12.6374i) q^{97} +(-2.71245 - 4.69811i) q^{98} +(1.17924 - 1.17924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.65293	−	1.50593i	−0.739213	−	0.673471i
$5$	−1.65293	−	1.50593i	−0.739213	−	0.673471i
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	−1.08688	+	0.627513i	−0.410804	+	0.237178i	−0.691135	−	0.722726i	$-0.742889\pi$
$7$	−1.08688	+	0.627513i	−0.410804	+	0.237178i	0.280331	+	0.959903i	$0.409556\pi$
$8$	1.00000			0.353553
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	2.13064	−	0.678517i	0.673767	−	0.214566i
$11$	−1.61087	+	0.431631i	−0.485695	+	0.130142i	−0.493353	−	0.869829i	$-0.664229\pi$
$11$	−1.61087	+	0.431631i	−0.485695	+	0.130142i	0.00765795	+	0.999971i	$0.497562\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−3.26841	−	1.52233i	−0.906494	−	0.422219i
$13$	−3.26841	−	1.52233i	−0.906494	−	0.422219i
$14$		−	1.25503i		−	0.335420i
$15$	1.02680	−	1.98637i	0.265120	−	0.512879i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.62805	−	1.24008i	−1.12247	−	0.300764i	−0.350585	−	0.936531i	$-0.614017\pi$
$17$	−4.62805	−	1.24008i	−1.12247	−	0.300764i	−0.771881	+	0.635767i	$0.780684\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.68516	−	6.28910i	0.386602	−	1.44282i	−0.449024	−	0.893520i	$-0.648228\pi$
$19$	1.68516	−	6.28910i	0.386602	−	1.44282i	0.835626	−	0.549299i	$-0.185105\pi$
$20$	−0.477706	+	2.18444i	−0.106818	+	0.488457i
$21$	−0.887437	−	0.887437i	−0.193655	−	0.193655i
$22$	0.431631	−	1.61087i	0.0920241	−	0.343439i
$23$	−4.73471	+	1.26866i	−0.987256	+	0.264535i	−0.716098	−	0.698000i	$-0.754073\pi$
$23$	−4.73471	+	1.26866i	−0.987256	+	0.264535i	−0.271159	+	0.962535i	$0.587407\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	0.464364	+	4.97839i	0.0928729	+	0.995678i
$26$	2.95258	−	2.06936i	0.579049	−	0.405835i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.08688	+	0.627513i	0.205402	+	0.118589i
$29$	−6.16323	−	3.55834i	−1.14448	−	0.660767i	−0.196946	−	0.980414i	$-0.563102\pi$
$29$	−6.16323	−	3.55834i	−1.14448	−	0.660767i	−0.947537	+	0.319647i	$0.896436\pi$
$30$	1.20685	+	1.88242i	0.220339	+	0.343682i
$31$	4.97092	−	4.97092i	0.892803	−	0.892803i	−0.101983	−	0.994786i	$-0.532519\pi$
$31$	4.97092	−	4.97092i	0.892803	−	0.892803i	0.994786	+	0.101983i	$0.0325186\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.833847	−	1.44427i	−0.145154	−	0.251414i
$34$	3.38797	−	3.38797i	0.581031	−	0.581031i
$35$	2.74153	+	0.599533i	0.463404	+	0.101340i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	8.89318	+	5.13448i	1.46203	+	0.844103i	0.999105	−	0.0422940i	$-0.0134666\pi$
$37$	8.89318	+	5.13448i	1.46203	+	0.844103i	0.462925	+	0.886397i	$0.346800\pi$
$38$	4.60394	+	4.60394i	0.746858	+	0.746858i
$39$	0.624535	−	3.55105i	0.100006	−	0.568623i
$40$	−1.65293	−	1.50593i	−0.261351	−	0.238108i
$41$	0.614688	+	2.29405i	0.0959981	+	0.358270i	0.997169	−	0.0751944i	$-0.0239577\pi$
$41$	0.614688	+	2.29405i	0.0959981	+	0.358270i	−0.901171	+	0.433464i	$0.857291\pi$
$42$	1.21226	−	0.324825i	0.187056	−	0.0501215i
$43$	−1.65466	+	6.17528i	−0.252334	+	0.941721i	0.717221	+	0.696846i	$0.245414\pi$
$43$	−1.65466	+	6.17528i	−0.252334	+	0.941721i	−0.969554	+	0.244876i	$0.921253\pi$
$44$	1.17924	+	1.17924i	0.177777	+	0.177777i
$45$	2.18444	+	0.477706i	0.325638	+	0.0712122i
$46$	1.26866	−	4.73471i	0.187054	−	0.698096i
$47$		−	3.93547i		−	0.574047i	−0.957924	−	0.287023i	$-0.907334\pi$
$47$		−	3.93547i		−	0.574047i	0.957924	−	0.287023i	$-0.0926658\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$	−2.71245	+	4.69811i	−0.387494	+	0.671159i
$50$	−4.54359	−	2.08704i	−0.642561	−	0.295153i
$51$		−	4.79131i		−	0.670917i
$52$	0.315825	+	3.59169i	0.0437971	+	0.498078i
$53$	−2.76048	+	2.76048i	−0.379181	+	0.379181i	−0.870807	−	0.491626i	$-0.836403\pi$
$53$	−2.76048	+	2.76048i	−0.379181	+	0.379181i	0.491626	+	0.870807i	$0.336403\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	3.31266	+	1.71240i	0.446679	+	0.230899i
$56$	−1.08688	+	0.627513i	−0.145241	+	0.0838549i
$57$	6.51095			0.862397
$58$	6.16323	−	3.55834i	0.809271	−	0.467233i
$59$	−7.25043	−	1.94275i	−0.943925	−	0.252924i	−0.246143	−	0.969234i	$-0.579163\pi$
$59$	−7.25043	−	1.94275i	−0.943925	−	0.252924i	−0.697783	+	0.716310i	$0.745830\pi$
$60$	−2.23365	+	0.103947i	−0.288363	+	0.0134196i
$61$	−4.86857	−	8.43262i	−0.623357	−	1.07969i	−0.988856	−	0.148874i	$-0.952435\pi$
$61$	−4.86857	−	8.43262i	−0.623357	−	1.07969i	0.365499	−	0.930812i	$-0.380898\pi$
$62$	1.81948	+	6.79040i	0.231075	+	0.862382i
$63$	0.627513	−	1.08688i	0.0790592	−	0.136935i
$64$	1.00000			0.125000
$65$	3.10993	+	7.43830i	0.385740	+	0.922608i
$66$	1.66769			0.205279
$67$	0.931803	−	1.61393i	0.113838	−	0.197173i	−0.803477	−	0.595336i	$-0.797019\pi$
$67$	0.931803	−	1.61393i	0.113838	−	0.197173i	0.917315	+	0.398163i	$0.130352\pi$
$68$	1.24008	+	4.62805i	0.150382	+	0.561233i
$69$	−2.45087	−	4.24503i	−0.295050	−	0.511041i
$70$	−1.88998	+	2.07447i	−0.225896	+	0.247947i
$71$	1.32703	+	0.355575i	0.157489	+	0.0421990i	0.336702	−	0.941611i	$-0.390688\pi$
$71$	1.32703	+	0.355575i	0.157489	+	0.0421990i	−0.179213	+	0.983810i	$0.557355\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−10.6790			−1.24988			−0.624941	−	0.780672i	$-0.714877\pi$
$73$	−10.6790			−1.24988			−0.624941	+	0.780672i	$0.714877\pi$
$74$	−8.89318	+	5.13448i	−1.03381	+	0.596871i
$75$	−4.68857	+	1.73704i	−0.541389	+	0.200577i
$76$	−6.28910	+	1.68516i	−0.721409	+	0.193301i
$77$	1.47997	−	1.47997i	0.168659	−	0.168659i
$78$	2.76303	+	2.31639i	0.312852	+	0.262279i
$79$			8.54874i			0.961809i	0.876773	+	0.480904i	$0.159692\pi$
$79$			8.54874i			0.961809i	−0.876773	+	0.480904i	$0.840308\pi$
$80$	2.13064	−	0.678517i	0.238212	−	0.0758605i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.29405	−	0.614688i	−0.253335	−	0.0678809i
$83$			3.67899i			0.403822i	0.979404	+	0.201911i	$0.0647152\pi$
$83$			3.67899i			0.403822i	−0.979404	+	0.201911i	$0.935285\pi$
$84$	−0.324825	+	1.21226i	−0.0354413	+	0.132269i
$85$	5.78237	+	9.01928i	0.627186	+	0.978278i
$86$	−4.52062	−	4.52062i	−0.487471	−	0.487471i
$87$	1.84193	−	6.87419i	0.197476	−	0.736990i
$88$	−1.61087	+	0.431631i	−0.171719	+	0.0460120i
$89$	1.32475	+	4.94404i	0.140423	+	0.524067i	0.999917	+	0.0129199i	$0.00411265\pi$
$89$	1.32475	+	4.94404i	0.140423	+	0.524067i	−0.859493	+	0.511147i	$0.829221\pi$
$90$	−1.50593	+	1.65293i	−0.158739	+	0.174234i
$91$	4.50767	−	0.396369i	0.472532	−	0.0415507i
$92$	3.46605	+	3.46605i	0.361361	+	0.361361i
$93$	6.08811	+	3.51497i	0.631307	+	0.364485i
$94$	3.40821	+	1.96773i	0.351530	+	0.202956i
$95$	−12.2564	+	7.85772i	−1.25748	+	0.806185i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	7.29623	+	12.6374i	0.740820	+	1.28314i	0.952122	+	0.305717i	$0.0988961\pi$
$97$	7.29623	+	12.6374i	0.740820	+	1.28314i	−0.211303	+	0.977421i	$0.567771\pi$
$98$	−2.71245	−	4.69811i	−0.273999	−	0.474581i
$99$	1.17924	−	1.17924i	0.118518	−	0.118518i
$100$	4.07923	−	2.89135i	0.407923	−	0.289135i
$101$	15.1633	+	8.75455i	1.50881	+	0.871110i	0.999947	+	0.0102612i	$0.00326631\pi$
$101$	15.1633	+	8.75455i	1.50881	+	0.871110i	0.508860	+	0.860849i	$0.330067\pi$
$102$	4.14939	+	2.39565i	0.410851	+	0.237205i
$103$	−6.26904	−	6.26904i	−0.617707	−	0.617707i	0.327236	−	0.944943i	$-0.393883\pi$
$103$	−6.26904	−	6.26904i	−0.617707	−	0.617707i	−0.944943	+	0.327236i	$0.893883\pi$
$104$	−3.26841	−	1.52233i	−0.320494	−	0.149277i
$105$	0.130457	+	2.80329i	0.0127313	+	0.273573i
$106$	−1.01041	−	3.77088i	−0.0981393	−	0.366261i
$107$	−1.08258	+	0.290076i	−0.104657	+	0.0280427i	−0.310767	−	0.950486i	$-0.600586\pi$
$107$	−1.08258	+	0.290076i	−0.104657	+	0.0280427i	0.206111	+	0.978529i	$0.433919\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−13.1086	−	13.1086i	−1.25557	−	1.25557i	−0.953185	−	0.302388i	$-0.902216\pi$
$109$	−13.1086	−	13.1086i	−1.25557	−	1.25557i	−0.302388	−	0.953185i	$-0.597784\pi$
$110$	−3.13931	+	2.01265i	−0.299321	+	0.191899i
$111$	−2.65780	+	9.91906i	−0.252267	+	0.941475i
$112$		−	1.25503i		−	0.118589i
$113$	7.44692	+	1.99540i	0.700548	+	0.187711i	0.591476	−	0.806323i	$-0.298546\pi$
$113$	7.44692	+	1.99540i	0.700548	+	0.187711i	0.109072	+	0.994034i	$0.465212\pi$
$114$	−3.25548	+	5.63865i	−0.304903	+	0.528108i
$115$	9.73667	+	5.03312i	0.907949	+	0.469341i
$116$			7.11668i			0.660767i
$117$	3.59169	−	0.315825i	0.332052	−	0.0291980i
$118$	5.30768	−	5.30768i	0.488612	−	0.488612i
$119$	5.80832	−	1.55633i	0.532448	−	0.142669i
$120$	1.02680	−	1.98637i	0.0937340	−	0.181330i
$121$	−7.11768	+	4.10940i	−0.647062	+	0.373582i
$122$	9.73715			0.881560
$123$	−2.05678	+	1.18749i	−0.185454	+	0.107072i
$124$	−6.79040	−	1.81948i	−0.609796	−	0.163394i
$125$	6.72953	−	8.92824i	0.601908	−	0.798566i
$126$	0.627513	+	1.08688i	0.0559033	+	0.0968274i
$127$	−2.58704	−	9.65497i	−0.229563	−	0.856740i	−0.980525	−	0.196395i	$-0.937077\pi$
$127$	−2.58704	−	9.65497i	−0.229563	−	0.856740i	0.750962	−	0.660345i	$-0.229590\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−6.39312			−0.562883
$130$	−7.99672	−	1.02587i	−0.701359	−	0.0899748i
$131$	7.04662			0.615666			0.307833	−	0.951440i	$-0.400396\pi$
$131$	7.04662			0.615666			0.307833	+	0.951440i	$0.400396\pi$
$132$	−0.833847	+	1.44427i	−0.0725771	+	0.125707i
$133$	2.11492	+	7.89298i	0.183387	+	0.684408i
$134$	0.931803	+	1.61393i	0.0804955	+	0.139422i
$135$	0.103947	+	2.23365i	0.00894637	+	0.192242i
$136$	−4.62805	−	1.24008i	−0.396852	−	0.106336i
$137$	−3.31620	+	1.91461i	−0.283322	+	0.163576i	−0.634926	−	0.772573i	$-0.718970\pi$
$137$	−3.31620	+	1.91461i	−0.283322	+	0.163576i	0.351604	+	0.936149i	$0.385636\pi$
$138$	4.90174			0.417264
$139$	13.7399	−	7.93271i	1.16540	−	0.672844i	0.212807	−	0.977094i	$-0.431739\pi$
$139$	13.7399	−	7.93271i	1.16540	−	0.672844i	0.952592	+	0.304251i	$0.0984060\pi$
$140$	−0.851556	−	2.67400i	−0.0719696	−	0.225995i
$141$	3.80137	−	1.01857i	0.320133	−	0.0857794i
$142$	−0.971450	+	0.971450i	−0.0815223	+	0.0815223i
$143$	5.92207	+	1.04153i	0.495228	+	0.0870974i
$144$		−	1.00000i		−	0.0833333i
$145$	4.82879	+	15.1631i	0.401009	+	1.25922i
$146$	5.33950	−	9.24828i	0.441900	−	0.765393i
$147$	−5.24006	−	1.40407i	−0.432193	−	0.115806i
$148$		−	10.2690i		−	0.844103i
$149$	2.04976	−	7.64982i	0.167923	−	0.626698i	−0.829726	−	0.558171i	$-0.811503\pi$
$149$	2.04976	−	7.64982i	0.167923	−	0.626698i	0.997649	−	0.0685269i	$-0.0218299\pi$
$150$	0.839961	−	4.92894i	0.0685825	−	0.402446i
$151$	−11.2421	−	11.2421i	−0.914868	−	0.914868i	0.0817826	−	0.996650i	$-0.473939\pi$
$151$	−11.2421	−	11.2421i	−0.914868	−	0.914868i	−0.996650	+	0.0817826i	$0.973939\pi$
$152$	1.68516	−	6.28910i	0.136684	−	0.510113i
$153$	4.62805	−	1.24008i	0.374156	−	0.100255i
$154$	0.541708	+	2.02168i	0.0436521	+	0.162912i
$155$	−15.7024	+	0.730744i	−1.26125	+	0.0586948i
$156$	−3.38757	+	1.23466i	−0.271222	+	0.0988521i
$157$	2.01620	+	2.01620i	0.160911	+	0.160911i	0.782970	−	0.622059i	$-0.213704\pi$
$157$	2.01620	+	2.01620i	0.160911	+	0.160911i	−0.622059	+	0.782970i	$0.713704\pi$
$158$	−7.40343	−	4.27437i	−0.588985	−	0.340051i
$159$	−3.38088	−	1.95195i	−0.268121	−	0.154800i
$160$	−0.477706	+	2.18444i	−0.0377660	+	0.172695i
$161$	4.34998	−	4.34998i	0.342827	−	0.342827i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−2.07507	−	3.59412i	−0.162532	−	0.281513i	0.773244	−	0.634108i	$-0.218633\pi$
$163$	−2.07507	−	3.59412i	−0.162532	−	0.281513i	−0.935776	+	0.352595i	$0.885299\pi$
$164$	1.67936	−	1.67936i	0.131136	−	0.131136i
$165$	−0.796667	+	3.64299i	−0.0620205	+	0.283606i
$166$	−3.18610	−	1.83950i	−0.247289	−	0.142773i
$167$	−4.66946	−	2.69591i	−0.361334	−	0.208616i	0.308332	−	0.951279i	$-0.400229\pi$
$167$	−4.66946	−	2.69591i	−0.361334	−	0.208616i	−0.669666	+	0.742663i	$0.733563\pi$
$168$	−0.887437	−	0.887437i	−0.0684673	−	0.0684673i
$169$	8.36500	+	9.95122i	0.643462	+	0.765478i
$170$	−10.7021	+	0.498044i	−0.820814	+	0.0381982i
$171$	1.68516	+	6.28910i	0.128867	+	0.480939i
$172$	6.17528	−	1.65466i	0.470861	−	0.126167i
$173$	−1.90699	+	7.11700i	−0.144986	+	0.541096i	0.854770	+	0.519007i	$0.173698\pi$
$173$	−1.90699	+	7.11700i	−0.144986	+	0.541096i	−0.999756	+	0.0220885i	$0.992968\pi$
$174$	5.03225	+	5.03225i	0.381494	+	0.381494i
$175$	−3.62871	−	5.11954i	−0.274305	−	0.387001i
$176$	0.431631	−	1.61087i	0.0325354	−	0.121424i
$177$		−	7.50620i		−	0.564200i
$178$	−4.94404	−	1.32475i	−0.370571	−	0.0992943i
$179$	1.48610	−	2.57401i	0.111077	−	0.192390i	−0.805128	−	0.593101i	$-0.797903\pi$
$179$	1.48610	−	2.57401i	0.111077	−	0.192390i	0.916205	+	0.400711i	$0.131237\pi$
$180$	−0.678517	−	2.13064i	−0.0505737	−	0.158808i
$181$			8.57582i			0.637436i	0.947850	+	0.318718i	$0.103252\pi$
$181$			8.57582i			0.637436i	−0.947850	+	0.318718i	$0.896748\pi$
$182$	−1.91057	+	4.10194i	−0.141621	+	0.304056i
$183$	6.88520	−	6.88520i	0.508969	−	0.508969i
$184$	−4.73471	+	1.26866i	−0.349048	+	0.0935271i
$185$	−6.96766	−	21.8794i	−0.512273	−	1.60861i
$186$	−6.08811	+	3.51497i	−0.446402	+	0.257730i
$187$	7.99044			0.584319
$188$	−3.40821	+	1.96773i	−0.248570	+	0.143512i
$189$	1.21226	+	0.324825i	0.0881791	+	0.0236275i
$190$	−0.676797	−	14.5432i	−0.0491000	−	1.05507i
$191$	−11.4751	−	19.8754i	−0.830308	−	1.43814i	−0.897794	−	0.440415i	$-0.854831\pi$
$191$	−11.4751	−	19.8754i	−0.830308	−	1.43814i	0.0674864	−	0.997720i	$-0.478502\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	−4.49255	+	7.78132i	−0.323381	+	0.560112i	−0.981183	−	0.193079i	$-0.938153\pi$
$193$	−4.49255	+	7.78132i	−0.323381	+	0.560112i	0.657803	+	0.753190i	$0.271486\pi$
$194$	−14.5925			−1.04768
$195$	−6.37994	+	4.92914i	−0.456877	+	0.352983i
$196$	5.42491			0.387494
$197$	12.6889	−	21.9778i	0.904047	−	1.56585i	0.0818546	−	0.996644i	$-0.473916\pi$
$197$	12.6889	−	21.9778i	0.904047	−	1.56585i	0.822192	−	0.569210i	$-0.192751\pi$
$198$	0.431631	+	1.61087i	0.0306747	+	0.114480i
$199$	−12.6150	−	21.8497i	−0.894250	−	1.54889i	−0.834730	−	0.550660i	$-0.814376\pi$
$199$	−12.6150	−	21.8497i	−0.894250	−	1.54889i	−0.0595206	−	0.998227i	$-0.518957\pi$
$200$	0.464364	+	4.97839i	0.0328355	+	0.352025i
$201$	1.80011	+	0.482337i	0.126970	+	0.0340214i
$202$	−15.1633	+	8.75455i	−1.06689	+	0.615968i
$203$	8.93162			0.626877
$204$	−4.14939	+	2.39565i	−0.290516	+	0.167729i
$205$	2.43863	−	4.71757i	0.170321	−	0.329490i
$206$	8.56367	−	2.29463i	0.596659	−	0.159874i
$207$	3.46605	−	3.46605i	0.240907	−	0.240907i
$208$	2.95258	−	2.06936i	0.204725	−	0.143484i
$209$			10.8583i			0.751083i
$210$	−2.49295	−	1.28867i	−0.172030	−	0.0889264i
$211$	−1.45207	+	2.51505i	−0.0999644	+	0.173143i	−0.911670	−	0.410924i	$-0.865206\pi$
$211$	−1.45207	+	2.51505i	−0.0999644	+	0.173143i	0.811705	+	0.584067i	$0.198540\pi$
$212$	3.77088	+	1.01041i	0.258985	+	0.0693949i
$213$			1.37384i			0.0941338i
$214$	0.290076	−	1.08258i	0.0198292	−	0.0740034i
$215$	12.0346	−	7.71551i	0.820751	−	0.526194i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−2.28350	+	8.52213i	−0.155014	+	0.578520i
$218$	17.9066	−	4.79807i	1.21279	−	0.324966i
$219$	−2.76393	−	10.3151i	−0.186769	−	0.697031i
$220$	−0.173353	−	3.72505i	−0.0116874	−	0.251143i
$221$	13.2385	+	11.0985i	0.890520	+	0.746568i
$222$	−7.26125	−	7.26125i	−0.487343	−	0.487343i
$223$	−3.91894	−	2.26260i	−0.262432	−	0.151515i	0.363012	−	0.931785i	$-0.381749\pi$
$223$	−3.91894	−	2.26260i	−0.262432	−	0.151515i	−0.625443	+	0.780270i	$0.715082\pi$
$224$	1.08688	+	0.627513i	0.0726205	+	0.0419275i
$225$	−2.89135	−	4.07923i	−0.192756	−	0.271949i
$226$	−5.45153	+	5.45153i	−0.362630	+	0.362630i
$227$	−11.6902	−	20.2480i	−0.775907	−	1.34391i	−0.934284	−	0.356531i	$-0.883959\pi$
$227$	−11.6902	−	20.2480i	−0.775907	−	1.34391i	0.158377	−	0.987379i	$-0.449374\pi$
$228$	−3.25548	−	5.63865i	−0.215599	−	0.373429i
$229$	9.49103	−	9.49103i	0.627185	−	0.627185i	−0.320174	−	0.947359i	$-0.603741\pi$
$229$	9.49103	−	9.49103i	0.627185	−	0.627185i	0.947359	+	0.320174i	$0.103741\pi$
$230$	−9.22715	+	5.91564i	−0.608420	+	0.390066i
$231$	1.81259	+	1.04650i	0.119260	+	0.0688546i
$232$	−6.16323	−	3.55834i	−0.404636	−	0.233616i
$233$	8.47713	+	8.47713i	0.555355	+	0.555355i	0.927981	−	0.372626i	$-0.121543\pi$
$233$	8.47713	+	8.47713i	0.555355	+	0.555355i	−0.372626	+	0.927981i	$0.621543\pi$
$234$	−1.52233	+	3.26841i	−0.0995181	+	0.213663i
$235$	−5.92653	+	6.50506i	−0.386604	+	0.424343i
$236$	1.94275	+	7.25043i	0.126462	+	0.471963i
$237$	−8.25745	+	2.21258i	−0.536379	+	0.143722i
$238$	−1.55633	+	5.80832i	−0.100882	+	0.376497i
$239$	14.9221	+	14.9221i	0.965231	+	0.965231i	0.999416	−	0.0341841i	$-0.0108833\pi$
$239$	14.9221	+	14.9221i	0.965231	+	0.965231i	−0.0341841	+	0.999416i	$0.510883\pi$
$240$	1.20685	+	1.88242i	0.0779016	+	0.121510i
$241$	−1.80748	+	6.74561i	−0.116430	+	0.434523i	−0.999390	−	0.0349257i	$-0.988881\pi$
$241$	−1.80748	+	6.74561i	−0.116430	+	0.434523i	0.882960	+	0.469448i	$0.155547\pi$
$242$		−	8.21879i		−	0.528324i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−4.86857	+	8.43262i	−0.311679	+	0.539843i
$245$	11.5585	−	3.68089i	0.738446	−	0.235164i
$246$		−	2.37497i		−	0.151423i
$247$	−15.0819	+	17.9900i	−0.959638	+	1.14467i
$248$	4.97092	−	4.97092i	0.315654	−	0.315654i
$249$	−3.55363	+	0.952193i	−0.225202	+	0.0603428i
$250$	4.36731	+	10.2921i	0.276213	+	0.650927i
$251$	3.65199	−	2.10848i	0.230512	−	0.133086i	−0.380296	−	0.924865i	$-0.624178\pi$
$251$	3.65199	−	2.10848i	0.230512	−	0.133086i	0.610808	+	0.791779i	$0.290845\pi$
$252$	−1.25503			−0.0790592
$253$	7.07941	−	4.08730i	0.445079	−	0.256966i
$254$	9.65497	+	2.58704i	0.605807	+	0.162325i
$255$	−7.21536	+	7.91970i	−0.451844	+	0.495951i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.15318	−	11.7678i	−0.196690	−	0.734057i	−0.991823	−	0.127622i	$-0.959266\pi$
$257$	−3.15318	−	11.7678i	−0.196690	−	0.734057i	0.795133	−	0.606435i	$-0.207401\pi$
$258$	3.19656	−	5.53661i	0.199009	−	0.344694i
$259$	−12.8878			−0.800810
$260$	4.88679	−	6.41243i	0.303066	−	0.397682i
$261$	7.11668			0.440511
$262$	−3.52331	+	6.10255i	−0.217671	+	0.377017i
$263$	−4.34325	−	16.2092i	−0.267816	−	0.999504i	−0.960504	−	0.278267i	$-0.910240\pi$
$263$	−4.34325	−	16.2092i	−0.267816	−	0.999504i	0.692688	−	0.721238i	$-0.256427\pi$
$264$	−0.833847	−	1.44427i	−0.0513198	−	0.0888884i
$265$	8.71996	−	0.405801i	0.535663	−	0.0249282i
$266$	−7.89298	−	2.11492i	−0.483950	−	0.129674i
$267$	−4.43270	+	2.55922i	−0.271277	+	0.156622i
$268$	−1.86361			−0.113838
$269$	−4.39441	+	2.53712i	−0.267932	+	0.154691i	−0.627948	−	0.778256i	$-0.716105\pi$
$269$	−4.39441	+	2.53712i	−0.267932	+	0.154691i	0.360015	+	0.932946i	$0.382771\pi$
$270$	−1.98637	−	1.02680i	−0.120887	−	0.0624893i
$271$	29.9794	−	8.03296i	1.82112	−	0.487968i	0.824193	−	0.566309i	$-0.191629\pi$
$271$	29.9794	−	8.03296i	1.82112	−	0.487968i	0.996927	+	0.0783409i	$0.0249623\pi$
$272$	3.38797	−	3.38797i	0.205426	−	0.205426i
$273$	1.54953	+	4.25148i	0.0937820	+	0.257312i
$274$		−	3.82922i		−	0.231332i
$275$	−2.89686	−	7.81910i	−0.174687	−	0.471510i
$276$	−2.45087	+	4.24503i	−0.147525	+	0.255521i
$277$	−26.7296	−	7.16219i	−1.60603	−	0.430334i	−0.659172	−	0.751992i	$-0.729093\pi$
$277$	−26.7296	−	7.16219i	−1.60603	−	0.430334i	−0.946856	+	0.321658i	$0.895760\pi$
$278$			15.8654i			0.951545i
$279$	−1.81948	+	6.79040i	−0.108930	+	0.406531i
$280$	2.74153	+	0.599533i	0.163838	+	0.0358290i
$281$	−6.36885	−	6.36885i	−0.379933	−	0.379933i	0.491145	−	0.871078i	$-0.336579\pi$
$281$	−6.36885	−	6.36885i	−0.379933	−	0.379933i	−0.871078	+	0.491145i	$0.836579\pi$
$282$	−1.01857	+	3.80137i	−0.0606552	+	0.226368i
$283$	19.6869	−	5.27508i	1.17026	−	0.313571i	0.379206	−	0.925312i	$-0.376197\pi$
$283$	19.6869	−	5.27508i	1.17026	−	0.313571i	0.791058	+	0.611741i	$0.209531\pi$
$284$	−0.355575	−	1.32703i	−0.0210995	−	0.0787445i
$285$	−10.7622	−	9.80503i	−0.637495	−	0.580800i
$286$	−3.86303	+	4.60789i	−0.228426	+	0.272470i
$287$	−2.10764	−	2.10764i	−0.124410	−	0.124410i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	5.15859	+	2.97832i	0.303447	+	0.175195i
$290$	−15.5460	−	3.39968i	−0.912892	−	0.199636i
$291$	−10.3184	+	10.3184i	−0.604877	+	0.604877i
$292$	5.33950	+	9.24828i	0.312470	+	0.541215i
$293$	−11.6908	−	20.2491i	−0.682986	−	1.18297i	−0.974065	−	0.226267i	$-0.927348\pi$
$293$	−11.6908	−	20.2491i	−0.682986	−	1.18297i	0.291080	−	0.956699i	$-0.405985\pi$
$294$	3.83599	−	3.83599i	0.223720	−	0.223720i
$295$	9.05882	+	14.1298i	0.527425	+	0.822671i
$296$	8.89318	+	5.13448i	0.516906	+	0.298436i
$297$	1.44427	+	0.833847i	0.0838048	+	0.0483847i
$298$	5.60006	+	5.60006i	0.324403	+	0.324403i
$299$	17.4063	+	3.06131i	1.00663	+	0.177040i
$300$	3.84861	+	3.19190i	0.222200	+	0.184284i
$301$	−2.07664	−	7.75014i	−0.119696	−	0.446710i
$302$	15.3570	−	4.11489i	0.883694	−	0.236785i
$303$	−4.53169	+	16.9125i	−0.260339	+	0.971597i
$304$	4.60394	+	4.60394i	0.264054	+	0.264054i
$305$	−4.65149	+	21.2703i	−0.266344	+	1.21793i
$306$	−1.24008	+	4.62805i	−0.0708908	+	0.264568i
$307$			15.1164i			0.862739i	0.902175	+	0.431370i	$0.141969\pi$
$307$			15.1164i			0.862739i	−0.902175	+	0.431370i	$0.858031\pi$
$308$	−2.02168	−	0.541708i	−0.115196	−	0.0308667i
$309$	4.43288	−	7.67797i	0.252178	−	0.436785i
$310$	7.21837	−	13.9641i	0.409976	−	0.793106i
$311$			32.3149i			1.83241i	0.400711	+	0.916205i	$0.368763\pi$
$311$			32.3149i			1.83241i	−0.400711	+	0.916205i	$0.631237\pi$
$312$	0.624535	−	3.55105i	0.0353573	−	0.201039i
$313$	−18.4185	+	18.4185i	−1.04107	+	1.04107i	−0.0419546	+	0.999120i	$0.513358\pi$
$313$	−18.4185	+	18.4185i	−1.04107	+	1.04107i	−0.999120	+	0.0419546i	$0.986642\pi$
$314$	−2.75418	+	0.737982i	−0.155428	+	0.0416467i
$315$	−2.67400	+	0.851556i	−0.150663	+	0.0479798i
$316$	7.40343	−	4.27437i	0.416475	−	0.240452i
$317$	14.4575			0.812015			0.406008	−	0.913870i	$-0.366921\pi$
$317$	14.4575			0.812015			0.406008	+	0.913870i	$0.366921\pi$
$318$	3.38088	−	1.95195i	0.189590	−	0.109460i
$319$	11.4640	+	3.07178i	0.641863	+	0.171987i
$320$	−1.65293	−	1.50593i	−0.0924017	−	0.0841839i
$321$	−0.560383	−	0.970612i	−0.0312775	−	0.0541743i
$322$	1.59220	+	5.94219i	0.0887301	+	0.331145i
$323$	−15.5980	+	27.0165i	−0.867896	+	1.50324i
$324$	−1.00000			−0.0555556
$325$	6.06104	−	16.9783i	0.336206	−	0.941789i
$326$	4.15014			0.229855
$327$	9.26915	−	16.0546i	0.512585	−	0.887824i
$328$	0.614688	+	2.29405i	0.0339404	+	0.126667i
$329$	2.46956	+	4.27740i	0.136151	+	0.235821i
$330$	−2.75658	−	2.51143i	−0.151745	−	0.138250i
$331$	−4.05566	−	1.08671i	−0.222919	−	0.0597310i	0.145631	−	0.989339i	$-0.453479\pi$
$331$	−4.05566	−	1.08671i	−0.222919	−	0.0597310i	−0.368550	+	0.929608i	$0.620146\pi$
$332$	3.18610	−	1.83950i	0.174860	−	0.100955i
$333$	−10.2690			−0.562736
$334$	4.66946	−	2.69591i	0.255501	−	0.147514i
$335$	−3.97067	+	1.26449i	−0.216941	+	0.0690864i
$336$	1.21226	−	0.324825i	0.0661343	−	0.0177206i
$337$	−4.57923	+	4.57923i	−0.249447	+	0.249447i	−0.820744	−	0.571297i	$-0.806441\pi$
$337$	−4.57923	+	4.57923i	−0.249447	+	0.249447i	0.571297	+	0.820744i	$0.306441\pi$
$338$	−12.8005	+	2.26869i	−0.696256	+	0.123401i
$339$			7.70962i			0.418729i
$340$	4.91974	−	9.51732i	0.266810	−	0.516149i
$341$	−5.86190	+	10.1531i	−0.317440	+	0.549821i
$342$	−6.28910	−	1.68516i	−0.340076	−	0.0911230i
$343$		−	15.5936i		−	0.841974i
$344$	−1.65466	+	6.17528i	−0.0892134	+	0.332949i
$345$	−2.34159	+	10.7076i	−0.126067	+	0.576476i
$346$	−5.21001	−	5.21001i	−0.280092	−	0.280092i
$347$	0.0269053	−	0.100412i	0.00144435	−	0.00539040i	−0.965200	−	0.261513i	$-0.915778\pi$
$347$	0.0269053	−	0.100412i	0.00144435	−	0.00539040i	0.966644	+	0.256123i	$0.0824452\pi$
$348$	−6.87419	+	1.84193i	−0.368495	+	0.0987379i
$349$	4.45057	+	16.6097i	0.238233	+	0.889099i	0.976665	+	0.214770i	$0.0689003\pi$
$349$	4.45057	+	16.6097i	0.238233	+	0.889099i	−0.738431	+	0.674329i	$0.764433\pi$
$350$	6.24801	−	0.582789i	0.333970	−	0.0311514i
$351$	1.23466	+	3.38757i	0.0659014	+	0.180815i
$352$	1.17924	+	1.17924i	0.0628536	+	0.0628536i
$353$	−25.7934	−	14.8918i	−1.37284	−	0.792612i	−0.381559	−	0.924345i	$-0.624613\pi$
$353$	−25.7934	−	14.8918i	−1.37284	−	0.792612i	−0.991285	+	0.131733i	$0.957946\pi$
$354$	6.50056	+	3.75310i	0.345501	+	0.199475i
$355$	−1.65801	−	2.58615i	−0.0879981	−	0.137258i
$356$	3.61929	−	3.61929i	0.191822	−	0.191822i
$357$	3.00661	+	5.20760i	0.159127	+	0.275615i
$358$	1.48610	+	2.57401i	0.0785430	+	0.136041i
$359$	−1.63445	+	1.63445i	−0.0862629	+	0.0862629i	−0.748922	−	0.662659i	$-0.769428\pi$
$359$	−1.63445	+	1.63445i	−0.0862629	+	0.0862629i	0.662659	+	0.748922i	$0.269428\pi$
$360$	2.18444	+	0.477706i	0.115130	+	0.0251773i
$361$	−20.2585	−	11.6963i	−1.06624	−	0.615593i
$362$	−7.42688	−	4.28791i	−0.390348	−	0.225368i
$363$	−5.81157	−	5.81157i	−0.305028	−	0.305028i
$364$	−2.59710	−	3.70557i	−0.136125	−	0.194225i
$365$	17.6516	+	16.0818i	0.923929	+	0.841759i
$366$	2.52016	+	9.40536i	0.131731	+	0.491626i
$367$	−6.33667	+	1.69791i	−0.330772	+	0.0886300i	−0.420383	−	0.907347i	$-0.638104\pi$
$367$	−6.33667	+	1.69791i	−0.330772	+	0.0886300i	0.0896112	+	0.995977i	$0.471438\pi$
$368$	1.26866	−	4.73471i	0.0661336	−	0.246814i
$369$	−1.67936	−	1.67936i	−0.0874239	−	0.0874239i
$370$	22.4320	+	4.90554i	1.16618	+	0.255027i
$371$	1.26809	−	4.73256i	0.0658357	−	0.245702i
$372$		−	7.02994i		−	0.364485i
$373$	−2.56928	−	0.688437i	−0.133032	−	0.0356459i	0.191689	−	0.981456i	$-0.438604\pi$
$373$	−2.56928	−	0.688437i	−0.133032	−	0.0356459i	−0.324721	+	0.945810i	$0.605270\pi$
$374$	−3.99522	+	6.91992i	−0.206588	+	0.357821i
$375$	10.3657	+	4.18943i	0.535285	+	0.216341i
$376$		−	3.93547i		−	0.202956i
$377$	14.7270	+	21.0126i	0.758477	+	1.08220i
$378$	−0.887437	+	0.887437i	−0.0456449	+	0.0456449i
$379$	11.2762	−	3.02144i	0.579219	−	0.155201i	0.0426975	−	0.999088i	$-0.486405\pi$
$379$	11.2762	−	3.02144i	0.579219	−	0.155201i	0.536521	+	0.843887i	$0.319738\pi$
$380$	12.9332	+	6.68548i	0.663458	+	0.342958i
$381$	8.65641	−	4.99778i	0.443481	−	0.256044i
$382$	22.9502			1.17423
$383$	−10.7158	+	6.18679i	−0.547553	+	0.316130i	−0.748135	−	0.663547i	$-0.769050\pi$
$383$	−10.7158	+	6.18679i	−0.547553	+	0.316130i	0.200581	+	0.979677i	$0.435717\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−4.67503	+	0.217562i	−0.238262	+	0.0110880i
$386$	−4.49255	−	7.78132i	−0.228665	−	0.396059i
$387$	−1.65466	−	6.17528i	−0.0841112	−	0.313907i
$388$	7.29623	−	12.6374i	0.370410	−	0.641569i
$389$	2.84284			0.144138			0.0720689	−	0.997400i	$-0.477040\pi$
$389$	2.84284			0.144138			0.0720689	+	0.997400i	$0.477040\pi$
$390$	−1.07879	−	7.98976i	−0.0546267	−	0.404577i
$391$	23.4857			1.18772
$392$	−2.71245	+	4.69811i	−0.137000	+	0.237290i
$393$	1.82380	+	6.80651i	0.0919985	+	0.343343i
$394$	12.6889	+	21.9778i	0.639257	+	1.10723i
$395$	12.8738	−	14.1305i	0.647750	−	0.710982i
$396$	−1.61087	−	0.431631i	−0.0809492	−	0.0216903i
$397$	−19.4123	+	11.2077i	−0.974277	+	0.562499i	−0.900537	−	0.434778i	$-0.856827\pi$
$397$	−19.4123	+	11.2077i	−0.974277	+	0.562499i	−0.0737396	+	0.997278i	$0.523493\pi$
$398$	25.2299			1.26466
$399$	−7.07665	+	4.08571i	−0.354276	+	0.204541i
$400$	−4.54359	−	2.08704i	−0.227180	−	0.104352i
$401$	−33.8471	+	9.06930i	−1.69024	+	0.452899i	−0.970453	−	0.241292i	$-0.922429\pi$
$401$	−33.8471	+	9.06930i	−1.69024	+	0.452899i	−0.719791	+	0.694191i	$0.755762\pi$
$402$	−1.31777	+	1.31777i	−0.0657243	+	0.0657243i
$403$	−23.8144	+	8.67960i	−1.18628	+	0.432362i
$404$		−	17.5091i		−	0.871110i
$405$	−2.13064	+	0.678517i	−0.105872	+	0.0337158i
$406$	−4.46581	+	7.73501i	−0.221634	+	0.383882i
$407$	−16.5420	−	4.43240i	−0.819954	−	0.219706i
$408$		−	4.79131i		−	0.237205i
$409$	4.62665	−	17.2669i	0.228773	−	0.853793i	−0.752084	−	0.659067i	$-0.770951\pi$
$409$	4.62665	−	17.2669i	0.228773	−	0.853793i	0.980858	−	0.194727i	$-0.0623819\pi$
$410$	2.86622	+	4.47070i	0.141553	+	0.220792i
$411$	−2.70767	−	2.70767i	−0.133559	−	0.133559i
$412$	−2.29463	+	8.56367i	−0.113048	+	0.421902i
$413$	9.09947	−	2.43820i	0.447756	−	0.119976i
$414$	1.26866	+	4.73471i	0.0623514	+	0.232699i
$415$	5.54030	−	6.08112i	0.271962	−	0.298511i
$416$	0.315825	+	3.59169i	0.0154846	+	0.176097i
$417$	11.2185	+	11.2185i	0.549374	+	0.549374i
$418$	−9.40355	−	5.42914i	−0.459943	−	0.265548i
$419$	5.50409	+	3.17779i	0.268893	+	0.155245i	0.628384	−	0.777903i	$-0.283717\pi$
$419$	5.50409	+	3.17779i	0.268893	+	0.155245i	−0.359492	+	0.933148i	$0.617050\pi$
$420$	2.36249	−	1.51462i	0.115278	−	0.0739061i
$421$	−10.3731	+	10.3731i	−0.505556	+	0.505556i	−0.913159	−	0.407603i	$-0.866365\pi$
$421$	−10.3731	+	10.3731i	−0.505556	+	0.505556i	0.407603	+	0.913159i	$0.366365\pi$
$422$	−1.45207	−	2.51505i	−0.0706855	−	0.122431i
$423$	1.96773	+	3.40821i	0.0956745	+	0.165713i
$424$	−2.76048	+	2.76048i	−0.134061	+	0.134061i
$425$	4.02451	−	23.6161i	0.195217	−	1.14555i
$426$	−1.18978	−	0.686919i	−0.0576450	−	0.0332813i
$427$	10.5832	+	6.11019i	0.512155	+	0.295693i
$428$	0.792501	+	0.792501i	0.0383070	+	0.0383070i
$429$	0.526700	+	5.98985i	0.0254293	+	0.289193i
$430$	0.664548	+	14.2800i	0.0320474	+	0.688643i
$431$	−5.58701	−	20.8510i	−0.269117	−	1.00436i	−0.959682	−	0.281088i	$-0.909305\pi$
$431$	−5.58701	−	20.8510i	−0.269117	−	1.00436i	0.690565	−	0.723270i	$-0.257362\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	1.78395	−	6.65778i	0.0857310	−	0.319952i	−0.909721	−	0.415221i	$-0.863704\pi$
$433$	1.78395	−	6.65778i	0.0857310	−	0.319952i	0.995452	+	0.0952684i	$0.0303709\pi$
$434$	−6.23863	−	6.23863i	−0.299464	−	0.299464i
$435$	−13.3966	+	8.58874i	−0.642318	+	0.411799i
$436$	−4.79807	+	17.9066i	−0.229786	+	0.857572i
$437$			31.9150i			1.52670i
$438$	10.3151	+	2.76393i	0.492875	+	0.132066i
$439$	−7.70318	+	13.3423i	−0.367653	+	0.636793i	−0.989198	−	0.146585i	$-0.953172\pi$
$439$	−7.70318	+	13.3423i	−0.367653	+	0.636793i	0.621545	+	0.783378i	$0.286505\pi$
$440$	3.31266	+	1.71240i	0.157925	+	0.0816353i
$441$		−	5.42491i		−	0.258329i
$442$	−16.2309	+	5.91565i	−0.772024	+	0.281379i
$443$	18.8974	−	18.8974i	0.897842	−	0.897842i	−0.0974031	−	0.995245i	$-0.531054\pi$
$443$	18.8974	−	18.8974i	0.897842	−	0.897842i	0.995245	+	0.0974031i	$0.0310536\pi$
$444$	9.91906	−	2.65780i	0.470738	−	0.126134i
$445$	5.25564	−	10.1671i	0.249141	−	0.481969i
$446$	3.91894	−	2.26260i	0.185567	−	0.107137i
$447$	7.91968			0.374588
$448$	−1.08688	+	0.627513i	−0.0513505	+	0.0296472i
$449$	15.8997	+	4.26032i	0.750354	+	0.201057i	0.613675	−	0.789559i	$-0.289690\pi$
$449$	15.8997	+	4.26032i	0.750354	+	0.201057i	0.136679	+	0.990615i	$0.456357\pi$
$450$	4.97839	−	0.464364i	0.234684	−	0.0218903i
$451$	−1.98036	−	3.43009i	−0.0932516	−	0.161517i
$452$	−1.99540	−	7.44692i	−0.0938556	−	0.350274i
$453$	7.94935	−	13.7687i	0.373493	−	0.646909i
$454$	23.3804			1.09730
$455$	−8.04777	−	6.13305i	−0.377285	−	0.287522i
$456$	6.51095			0.304903
$457$	8.73356	−	15.1270i	0.408539	−	0.707610i	−0.586187	−	0.810176i	$-0.699372\pi$
$457$	8.73356	−	15.1270i	0.408539	−	0.707610i	0.994726	+	0.102565i	$0.0327051\pi$
$458$	3.47396	+	12.9650i	0.162327	+	0.605814i
$459$	2.39565	+	4.14939i	0.111820	+	0.193677i
$460$	−0.509523	−	10.9488i	−0.0237566	−	0.510489i
$461$	−10.3366	−	2.76968i	−0.481423	−	0.128997i	0.00994207	−	0.999951i	$-0.496835\pi$
$461$	−10.3366	−	2.76968i	−0.481423	−	0.128997i	−0.491365	+	0.870954i	$0.663502\pi$
$462$	−1.81259	+	1.04650i	−0.0843294	+	0.0486876i
$463$	−26.0675			−1.21146			−0.605729	−	0.795671i	$-0.707118\pi$
$463$	−26.0675			−1.21146			−0.605729	+	0.795671i	$0.707118\pi$
$464$	6.16323	−	3.55834i	0.286121	−	0.165192i
$465$	−4.76993	−	14.9783i	−0.221200	−	0.694600i
$466$	−11.5800	+	3.10284i	−0.536432	+	0.143737i
$467$	−11.2734	+	11.2734i	−0.521672	+	0.521672i	−0.918076	−	0.396404i	$-0.870258\pi$
$467$	−11.2734	+	11.2734i	−0.521672	+	0.521672i	0.396404	+	0.918076i	$0.370258\pi$
$468$	−2.06936	−	2.95258i	−0.0956561	−	0.136483i
$469$			2.33887i			0.107999i
$470$	−2.67028	−	8.38505i	−0.123171	−	0.386774i
$471$	−1.42567	+	2.46933i	−0.0656915	+	0.113781i
$472$	−7.25043	−	1.94275i	−0.333728	−	0.0894221i
$473$		−	10.6618i		−	0.490229i
$474$	2.21258	−	8.25745i	0.101627	−	0.379277i
$475$	32.0921	+	5.46894i	1.47249	+	0.250932i
$476$	−4.25199	−	4.25199i	−0.194889	−	0.194889i
$477$	1.01041	−	3.77088i	0.0462633	−	0.172657i
$478$	−20.3840	+	5.46187i	−0.932342	+	0.249820i
$479$	5.77188	+	21.5410i	0.263724	+	0.984232i	0.963027	+	0.269406i	$0.0868273\pi$
$479$	5.77188	+	21.5410i	0.263724	+	0.984232i	−0.699303	+	0.714826i	$0.746506\pi$
$480$	−2.23365	+	0.103947i	−0.101952	+	0.00474453i
$481$	−21.2502	−	30.3200i	−0.968924	−	1.38247i
$482$	−4.93813	−	4.93813i	−0.224925	−	0.224925i
$483$	5.32762	+	3.07590i	0.242415	+	0.139958i
$484$	7.11768	+	4.10940i	0.323531	+	0.186791i
$485$	6.97090	−	31.8764i	0.316532	−	1.44743i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−12.1814	−	21.0987i	−0.551990	−	0.956075i	−0.998131	−	0.0611119i	$-0.980535\pi$
$487$	−12.1814	−	21.0987i	−0.551990	−	0.956075i	0.446141	−	0.894963i	$-0.352798\pi$
$488$	−4.86857	−	8.43262i	−0.220390	−	0.381727i
$489$	2.93459	−	2.93459i	0.132707	−	0.132707i
$490$	−2.59151	+	11.8504i	−0.117073	+	0.535347i
$491$	33.1654	+	19.1480i	1.49673	+	0.864139i	0.999993	−	0.00376002i	$-0.00119685\pi$
$491$	33.1654	+	19.1480i	1.49673	+	0.864139i	0.496740	+	0.867899i	$0.334530\pi$
$492$	2.05678	+	1.18749i	0.0927270	+	0.0535360i
$493$	24.1111	+	24.1111i	1.08591	+	1.08591i
$494$	−8.03883	−	22.0563i	−0.361684	−	0.992360i
$495$	−3.72505	+	0.173353i	−0.167428	+	0.00779162i
$496$	1.81948	+	6.79040i	0.0816972	+	0.304898i
$497$	−1.66545	+	0.446256i	−0.0747057	+	0.0200173i
$498$	0.952193	−	3.55363i	0.0426688	−	0.159242i
$499$	9.21088	+	9.21088i	0.412335	+	0.412335i	0.882551	−	0.470216i	$-0.155824\pi$
$499$	9.21088	+	9.21088i	0.412335	+	0.412335i	−0.470216	+	0.882551i	$0.655824\pi$
$500$	−11.0968	−	1.36383i	−0.496266	−	0.0609922i
$501$	1.39551	−	5.20810i	0.0623467	−	0.232681i
$502$			4.21696i			0.188212i
$503$	22.5099	+	6.03151i	1.00367	+	0.268932i	0.722981	−	0.690868i	$-0.242771\pi$
$503$	22.5099	+	6.03151i	1.00367	+	0.268932i	0.280686	+	0.959800i	$0.409438\pi$
$504$	0.627513	−	1.08688i	0.0279516	−	0.0484137i
$505$	−11.8802	−	37.3055i	−0.528663	−	1.66008i
$506$			8.17460i			0.363405i
$507$	−7.44712	+	10.6555i	−0.330738	+	0.473229i
$508$	−7.06793	+	7.06793i	−0.313589	+	0.313589i
$509$	−6.05234	+	1.62172i	−0.268265	+	0.0718815i	−0.390444	−	0.920627i	$-0.627679\pi$
$509$	−6.05234	+	1.62172i	−0.268265	+	0.0718815i	0.122179	+	0.992508i	$0.461012\pi$
$510$	−3.25098	−	10.2085i	−0.143956	−	0.452042i
$511$	11.6068	−	6.70121i	0.513456	−	0.296444i
$512$	1.00000			0.0441942
$513$	−5.63865	+	3.25548i	−0.248953	+	0.143733i
$514$	11.7678	+	3.15318i	0.519057	+	0.139081i
$515$	0.921573	+	19.8030i	0.0406093	+	0.872625i
$516$	3.19656	+	5.53661i	0.140721	+	0.243735i
$517$	1.69867	+	6.33952i	0.0747074	+	0.278812i
$518$	6.44391	−	11.1612i	0.283129	−	0.490394i
$519$	−7.36806			−0.323422
$520$	3.10993	+	7.43830i	0.136380	+	0.326191i
$521$	−27.8634			−1.22072			−0.610358	−	0.792126i	$-0.708974\pi$
$521$	−27.8634			−1.22072			−0.610358	+	0.792126i	$0.708974\pi$
$522$	−3.55834	+	6.16323i	−0.155744	+	0.269757i
$523$	−8.79109	−	32.8088i	−0.384408	−	1.43463i	−0.839099	−	0.543979i	$-0.816917\pi$
$523$	−8.79109	−	32.8088i	−0.384408	−	1.43463i	0.454691	−	0.890649i	$-0.349750\pi$
$524$	−3.52331	−	6.10255i	−0.153916	−	0.266591i
$525$	4.00591	−	4.83010i	0.174832	−	0.210803i
$526$	16.2092	+	4.34325i	0.706756	+	0.189375i
$527$	−29.1700	+	16.8413i	−1.27067	+	0.733619i
$528$	1.66769			0.0725771
$529$	0.889431	−	0.513513i	0.0386709	−	0.0223267i
$530$	−4.00855	+	7.75461i	−0.174120	+	0.336839i
$531$	7.25043	−	1.94275i	0.314642	−	0.0843080i
$532$	5.77806	−	5.77806i	0.250511	−	0.250511i
$533$	1.48325	−	8.43364i	0.0642468	−	0.365301i
$534$		−	5.11845i		−	0.221497i
$535$	2.22626	+	1.15081i	0.0962495	+	0.0497537i
$536$	0.931803	−	1.61393i	0.0402478	−	0.0697112i
$537$	2.87093	+	0.769264i	0.123890	+	0.0331962i
$538$		−	5.07423i		−	0.218766i
$539$	2.34156	−	8.73882i	0.100858	−	0.376408i
$540$	1.88242	−	1.20685i	0.0810067	−	0.0519344i
$541$	−14.8357	−	14.8357i	−0.637838	−	0.637838i	0.312184	−	0.950022i	$-0.398939\pi$
$541$	−14.8357	−	14.8357i	−0.637838	−	0.637838i	−0.950022	+	0.312184i	$0.898939\pi$
$542$	−8.03296	+	29.9794i	−0.345045	+	1.28773i
$543$	−8.28361	+	2.21959i	−0.355484	+	0.0952515i
$544$	1.24008	+	4.62805i	0.0531681	+	0.198426i
$545$	1.92701	+	41.4081i	0.0825440	+	1.77373i
$546$	−4.45666	−	0.783807i	−0.190727	−	0.0335439i
$547$	−9.75842	−	9.75842i	−0.417240	−	0.417240i	0.467011	−	0.884251i	$-0.345331\pi$
$547$	−9.75842	−	9.75842i	−0.417240	−	0.417240i	−0.884251	+	0.467011i	$0.845331\pi$
$548$	3.31620	+	1.91461i	0.141661	+	0.0817881i
$549$	8.43262	+	4.86857i	0.359895	+	0.207786i
$550$	8.21997	+	1.40080i	0.350501	+	0.0597302i
$551$	−32.7648	+	32.7648i	−1.39583	+	1.39583i
$552$	−2.45087	−	4.24503i	−0.104316	−	0.180680i
$553$	−5.36445	−	9.29149i	−0.228119	−	0.395114i
$554$	19.5675	−	19.5675i	0.831341	−	0.831341i
$555$	19.3305	−	12.3931i	0.820536	−	0.526056i
$556$	−13.7399	−	7.93271i	−0.582700	−	0.336422i
$557$	−19.6827	−	11.3638i	−0.833982	−	0.481499i	0.0212324	−	0.999775i	$-0.493241\pi$
$557$	−19.6827	−	11.3638i	−0.833982	−	0.481499i	−0.855214	+	0.518275i	$0.826574\pi$
$558$	−4.97092	−	4.97092i	−0.210436	−	0.210436i
$559$	14.8089	−	17.6644i	0.626352	−	0.747124i
$560$	−1.88998	+	2.07447i	−0.0798662	+	0.0876624i
$561$	2.06808	+	7.71817i	0.0873143	+	0.325861i
$562$	8.70000	−	2.33116i	0.366988	−	0.0983340i
$563$	8.79167	−	32.8109i	0.370525	−	1.38282i	−0.489250	−	0.872143i	$-0.662730\pi$
$563$	8.79167	−	32.8109i	0.370525	−	1.38282i	0.859775	−	0.510673i	$-0.170604\pi$
$564$	−2.78280	−	2.78280i	−0.117177	−	0.117177i
$565$	−9.30433	−	14.5128i	−0.391436	−	0.610557i
$566$	−5.27508	+	19.6869i	−0.221728	+	0.827501i
$567$			1.25503i			0.0527061i
$568$	1.32703	+	0.355575i	0.0556808	+	0.0149196i
$569$	−3.96963	+	6.87559i	−0.166415	+	0.288240i	−0.937157	−	0.348908i	$-0.886553\pi$
$569$	−3.96963	+	6.87559i	−0.166415	+	0.288240i	0.770742	+	0.637148i	$0.219886\pi$
$570$	13.8725	−	4.41779i	0.581054	−	0.185041i
$571$			4.89604i			0.204893i	0.994739	+	0.102446i	$0.0326670\pi$
$571$			4.89604i			0.204893i	−0.994739	+	0.102446i	$0.967333\pi$
$572$	−2.05904	−	5.64943i	−0.0860928	−	0.236214i
$573$	16.2282	−	16.2282i	0.677944	−	0.677944i
$574$	2.87909	−	0.771449i	0.120171	−	0.0321997i
$575$	−8.51453	−	22.9821i	−0.355081	−	0.958421i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	5.23478			0.217927			0.108963	−	0.994046i	$-0.465247\pi$
$577$	5.23478			0.217927			0.108963	+	0.994046i	$0.465247\pi$
$578$	−5.15859	+	2.97832i	−0.214569	+	0.123882i
$579$	−8.67893	−	2.32551i	−0.360684	−	0.0966450i
$580$	10.7172	−	11.7634i	0.445008	−	0.488448i
$581$	−2.30862	−	3.99864i	−0.0957775	−	0.165892i
$582$	−3.77681	−	14.0952i	−0.156554	−	0.584266i
$583$	3.25526	−	5.63828i	0.134819	−	0.233514i
$584$	−10.6790			−0.441900
$585$	−6.41243	−	4.88679i	−0.265121	−	0.202044i
$586$	23.3817			0.965887
$587$	−2.80055	+	4.85069i	−0.115591	+	0.200210i	−0.918016	−	0.396544i	$-0.870210\pi$
$587$	−2.80055	+	4.85069i	−0.115591	+	0.200210i	0.802425	+	0.596753i	$0.203543\pi$
$588$	1.40407	+	5.24006i	0.0579029	+	0.216096i
$589$	−22.8858	−	39.6394i	−0.942994	−	1.63331i
$590$	−16.7662	+	0.780250i	−0.690254	+	0.0321224i
$591$	24.5131	+	6.56826i	1.00833	+	0.270182i
$592$	−8.89318	+	5.13448i	−0.365508	+	0.211026i
$593$	3.71798			0.152679			0.0763396	−	0.997082i	$-0.475677\pi$
$593$	3.71798			0.152679			0.0763396	+	0.997082i	$0.475677\pi$
$594$	−1.44427	+	0.833847i	−0.0592590	+	0.0342132i
$595$	−11.9445	−	6.17440i	−0.489676	−	0.253126i
$596$	−7.64982	+	2.04976i	−0.313349	+	0.0839616i
$597$	17.8402	−	17.8402i	0.730152	−	0.730152i
$598$	−11.3543	+	13.5437i	−0.464313	+	0.553841i
$599$			25.7525i			1.05222i	0.850416	+	0.526110i	$0.176350\pi$
$599$			25.7525i			1.05222i	−0.850416	+	0.526110i	$0.823650\pi$
$600$	−4.68857	+	1.73704i	−0.191410	+	0.0709145i
$601$	−21.0389	+	36.4405i	−0.858195	+	1.48644i	0.0154540	+	0.999881i	$0.495081\pi$
$601$	−21.0389	+	36.4405i	−0.858195	+	1.48644i	−0.873649	+	0.486557i	$0.838253\pi$
$602$	7.75014	+	2.07664i	0.315872	+	0.0846377i
$603$			1.86361i			0.0758919i
$604$	−4.11489	+	15.3570i	−0.167432	+	0.624866i
$605$	17.9535	+	3.92617i	0.729914	+	0.159621i
$606$	−12.3808	−	12.3808i	−0.502936	−	0.502936i
$607$	−9.23125	+	34.4515i	−0.374685	+	1.39834i	0.479120	+	0.877750i	$0.340956\pi$
$607$	−9.23125	+	34.4515i	−0.374685	+	1.39834i	−0.853805	+	0.520593i	$0.825711\pi$
$608$	−6.28910	+	1.68516i	−0.255057	+	0.0683422i
$609$	2.31167	+	8.62728i	0.0936737	+	0.349595i
$610$	−16.0948	−	14.6634i	−0.651661	−	0.593705i
$611$	−5.99109	+	12.8627i	−0.242374	+	0.520370i
$612$	−3.38797	−	3.38797i	−0.136950	−	0.136950i
$613$	21.5921	+	12.4662i	0.872096	+	0.503505i	0.868044	−	0.496487i	$-0.165377\pi$
$613$	21.5921	+	12.4662i	0.872096	+	0.503505i	0.00405171	+	0.999992i	$0.498710\pi$
$614$	−13.0912	−	7.55821i	−0.528318	−	0.305024i
$615$	5.18799	+	1.13454i	0.209200	+	0.0457490i
$616$	1.47997	−	1.47997i	0.0596299	−	0.0596299i
$617$	17.9249	+	31.0469i	0.721631	+	1.24990i	0.960346	+	0.278811i	$0.0899404\pi$
$617$	17.9249	+	31.0469i	0.721631	+	1.24990i	−0.238715	+	0.971090i	$0.576726\pi$
$618$	4.43288	+	7.67797i	0.178317	+	0.308853i
$619$	−11.9813	+	11.9813i	−0.481570	+	0.481570i	−0.905633	−	0.424063i	$-0.860604\pi$
$619$	−11.9813	+	11.9813i	−0.481570	+	0.481570i	0.424063	+	0.905633i	$0.360604\pi$
$620$	8.48406	+	13.2333i	0.340728	+	0.531463i
$621$	4.24503	+	2.45087i	0.170347	+	0.0983500i
$622$	−27.9855	−	16.1574i	−1.12212	−	0.647855i
$623$	−4.54230	−	4.54230i	−0.181983	−	0.181983i
$624$	2.76303	+	2.31639i	0.110610	+	0.0927297i
$625$	−24.5687	+	4.62357i	−0.982749	+	0.184943i
$626$	−6.74163	−	25.1601i	−0.269450	−	1.00560i
$627$	−10.4883	+	2.81033i	−0.418862	+	0.112234i
$628$	0.737982	−	2.75418i	0.0294487	−	0.109904i
$629$	−34.7909	−	34.7909i	−1.38720	−	1.38720i
$630$	0.599533	−	2.74153i	0.0238860	−	0.109225i
$631$	0.678114	−	2.53076i	0.0269953	−	0.100748i	−0.951114	−	0.308841i	$-0.900059\pi$
$631$	0.678114	−	2.53076i	0.0269953	−	0.100748i	0.978109	+	0.208093i	$0.0667257\pi$
$632$			8.54874i			0.340051i
$633$	−2.80518	−	0.751645i	−0.111496	−	0.0298752i
$634$	−7.22876	+	12.5206i	−0.287091	+	0.497256i
$635$	−10.2635	+	19.8549i	−0.407294	+	0.787918i
$636$			3.90391i			0.154800i
$637$	16.0175	−	11.2261i	0.634637	−	0.444794i
$638$	−8.39226	+	8.39226i	−0.332253	+	0.332253i
$639$	−1.32703	+	0.355575i	−0.0524963	+	0.0140663i
$640$	2.13064	−	0.678517i	0.0842208	−	0.0268207i
$641$	−10.5572	+	6.09522i	−0.416986	+	0.240747i	−0.693787	−	0.720180i	$-0.744059\pi$
$641$	−10.5572	+	6.09522i	−0.416986	+	0.240747i	0.276801	+	0.960927i	$0.410726\pi$
$642$	1.12077			0.0442331
$643$	30.1333	−	17.3974i	1.18834	−	0.686088i	0.230411	−	0.973093i	$-0.425993\pi$
$643$	30.1333	−	17.3974i	1.18834	−	0.686088i	0.957929	+	0.287005i	$0.0926596\pi$
$644$	−5.94219	−	1.59220i	−0.234155	−	0.0627417i
$645$	10.5674	+	9.62758i	0.416091	+	0.379085i
$646$	−15.5980	−	27.0165i	−0.613695	−	1.06295i
$647$	−6.70240	−	25.0137i	−0.263498	−	0.983389i	−0.963163	−	0.268918i	$-0.913334\pi$
$647$	−6.70240	−	25.0137i	−0.263498	−	0.983389i	0.699665	−	0.714471i	$-0.253333\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	12.5180			0.491376
$650$	11.6731	+	13.7382i	0.457859	+	0.538856i
$651$	−8.82276			−0.345791
$652$	−2.07507	+	3.59412i	−0.0812659	+	0.140757i
$653$	3.14838	+	11.7499i	0.123206	+	0.459810i	0.999769	−	0.0214759i	$-0.00683651\pi$
$653$	3.14838	+	11.7499i	0.123206	+	0.459810i	−0.876564	+	0.481286i	$0.840170\pi$
$654$	9.26915	+	16.0546i	0.362453	+	0.627786i
$655$	−11.6476	−	10.6117i	−0.455109	−	0.414633i
$656$	−2.29405	−	0.614688i	−0.0895674	−	0.0239995i
$657$	9.24828	−	5.33950i	0.360810	−	0.208314i
$658$	−4.93911			−0.192547
$659$	4.99063	−	2.88134i	0.194407	−	0.112241i	−0.399637	−	0.916674i	$-0.630864\pi$
$659$	4.99063	−	2.88134i	0.194407	−	0.112241i	0.594044	+	0.804432i	$0.297530\pi$
$660$	3.55325	−	1.13156i	0.138310	−	0.0440459i
$661$	21.4446	−	5.74606i	0.834098	−	0.223496i	0.183597	−	0.983002i	$-0.441226\pi$
$661$	21.4446	−	5.74606i	0.834098	−	0.223496i	0.650501	+	0.759506i	$0.274559\pi$
$662$	2.96895	−	2.96895i	0.115392	−	0.115392i
$663$	−7.29397	+	15.6600i	−0.283274	+	0.608182i
$664$			3.67899i			0.142773i
$665$	8.39044	−	16.2315i	0.325367	−	0.629429i
$666$	5.13448	−	8.89318i	0.198957	−	0.344604i
$667$	33.6955	+	9.02867i	1.30469	+	0.349591i
$668$			5.39183i			0.208616i
$669$	1.17121	−	4.37101i	0.0452816	−	0.168993i
$670$	0.890256	−	4.07094i	0.0343936	−	0.157274i
$671$	11.4824	+	11.4824i	0.443274	+	0.443274i
$672$	−0.324825	+	1.21226i	−0.0125304	+	0.0467640i
$673$	−40.6294	+	10.8866i	−1.56615	+	0.419649i	−0.934604	−	0.355690i	$-0.884246\pi$
$673$	−40.6294	+	10.8866i	−1.56615	+	0.419649i	−0.631546	+	0.775338i	$0.717579\pi$
$674$	−1.67612	−	6.25535i	−0.0645615	−	0.240947i
$675$	3.19190	−	3.84861i	0.122856	−	0.148133i
$676$	4.43551	−	12.2199i	0.170596	−	0.469997i
$677$	−30.1855	−	30.1855i	−1.16012	−	1.16012i	−0.984448	−	0.175676i	$-0.943789\pi$
$677$	−30.1855	−	30.1855i	−1.16012	−	1.16012i	−0.175676	−	0.984448i	$-0.556211\pi$
$678$	−6.67673	−	3.85481i	−0.256418	−	0.148043i
$679$	−15.8603	−	9.15696i	−0.608663	−	0.351412i
$680$	5.78237	+	9.01928i	0.221744	+	0.345873i
$681$	16.5325	−	16.5325i	0.633525	−	0.633525i
$682$	−5.86190	−	10.1531i	−0.224464	−	0.388783i
$683$	−9.77230	−	16.9261i	−0.373927	−	0.647660i	0.616239	−	0.787559i	$-0.288655\pi$
$683$	−9.77230	−	16.9261i	−0.373927	−	0.647660i	−0.990166	+	0.139899i	$0.955322\pi$
$684$	4.60394	−	4.60394i	0.176036	−	0.176036i
$685$	8.36472	+	1.82924i	0.319599	+	0.0698917i
$686$	13.5044	+	7.79679i	0.515602	+	0.297683i
$687$	11.6241	+	6.71117i	0.443487	+	0.256047i
$688$	−4.52062	−	4.52062i	−0.172347	−	0.172347i
$689$	13.2247	−	4.82001i	0.503823	−	0.183628i
$690$	−8.10224	−	7.38166i	−0.308447	−	0.281015i
$691$	−3.95977	−	14.7781i	−0.150637	−	0.562184i	−0.999440	−	0.0334744i	$-0.989343\pi$
$691$	−3.95977	−	14.7781i	−0.150637	−	0.562184i	0.848803	−	0.528709i	$-0.177324\pi$
$692$	7.11700	−	1.90699i	0.270548	−	0.0724931i
$693$	−0.541708	+	2.02168i	−0.0205778	+	0.0767974i
$694$	0.0735068	+	0.0735068i	0.00279028	+	0.00279028i
$695$	−34.6571	−	7.57900i	−1.31462	−	0.287488i
$696$	1.84193	−	6.87419i	0.0698183	−	0.260565i
$697$		−	11.3792i		−	0.431019i
$698$	−16.6097	−	4.45057i	−0.628688	−	0.168456i
$699$	−5.99424	+	10.3823i	−0.226723	+	0.392695i
$700$	−2.61929	+	5.70233i	−0.0990000	+	0.215528i
$701$			25.6806i			0.969944i	0.874530	+	0.484972i	$0.161170\pi$
$701$			25.6806i			0.969944i	−0.874530	+	0.484972i	$0.838830\pi$
$702$	−3.55105	−	0.624535i	−0.134026	−	0.0235715i
$703$	47.2777	−	47.2777i	1.78311	−	1.78311i
$704$	−1.61087	+	0.431631i	−0.0607119	+	0.0162677i
$705$	−7.81730	−	4.04095i	−0.294417	−	0.152191i
$706$	25.7934	−	14.8918i	0.970747	−	0.560461i
$707$	−21.9744			−0.826432
$708$	−6.50056	+	3.75310i	−0.244306	+	0.141050i
$709$	2.34589	+	0.628580i	0.0881018	+	0.0236068i	0.302601	−	0.953117i	$-0.402145\pi$
$709$	2.34589	+	0.628580i	0.0881018	+	0.0236068i	−0.214499	+	0.976724i	$0.568812\pi$
$710$	3.06867	−	0.142807i	0.115165	−	0.00535945i
$711$	−4.27437	−	7.40343i	−0.160301	−	0.277650i
$712$	1.32475	+	4.94404i	0.0496472	+	0.185286i
$713$	−17.2295	+	29.8423i	−0.645248	+	1.11760i
$714$	−6.01322			−0.225039
$715$	−8.22030	−	10.6398i	−0.307422	−	0.397906i
$716$	−2.97221			−0.111077
$717$	−10.5515	+	18.2758i	−0.394054	+	0.682522i
$718$	−0.598250	−	2.23270i	−0.0223265	−	0.0833236i
$719$	22.0098	+	38.1221i	0.820827	+	1.42171i	0.905067	+	0.425268i	$0.139820\pi$
$719$	22.0098	+	38.1221i	0.820827	+	1.42171i	−0.0842403	+	0.996445i	$0.526846\pi$
$720$	−1.50593	+	1.65293i	−0.0561226	+	0.0616011i
$721$	10.7476	+	2.87982i	0.400262	+	0.107250i
$722$	20.2585	−	11.6963i	0.753944	−	0.435290i
$723$	−6.98356			−0.259722
$724$	7.42688	−	4.28791i	0.276018	−	0.159359i
$725$	14.8528	−	32.3353i	0.551620	−	1.20090i
$726$	7.93875	−	2.12718i	0.294634	−	0.0789471i
$727$	26.8208	−	26.8208i	0.994730	−	0.994730i	−0.00525659	−	0.999986i	$-0.501673\pi$
$727$	26.8208	−	26.8208i	0.994730	−	0.994730i	0.999986	+	0.00525659i	$0.00167323\pi$
$728$	4.50767	−	0.396369i	0.167065	−	0.0146904i
$729$			1.00000i			0.0370370i
$730$	−22.7531	+	7.24588i	−0.842129	+	0.268182i
$731$	15.3157	−	26.5276i	0.566472	−	0.981158i
$732$	−9.40536	−	2.52016i	−0.347632	−	0.0931478i
$733$			12.0371i			0.444602i	0.974978	+	0.222301i	$0.0713567\pi$
$733$			12.0371i			0.444602i	−0.974978	+	0.222301i	$0.928643\pi$
$734$	1.69791	−	6.33667i	0.0626709	−	0.233891i
$735$	6.54703	+	10.2120i	0.241491	+	0.376675i
$736$	3.46605	+	3.46605i	0.127760	+	0.127760i
$737$	−0.804391	+	3.00203i	−0.0296301	+	0.110581i
$738$	2.29405	−	0.614688i	0.0844450	−	0.0226270i
$739$	3.43048	+	12.8027i	0.126192	+	0.470956i	0.999879	−	0.0155321i	$-0.00494422\pi$
$739$	3.43048	+	12.8027i	0.126192	+	0.470956i	−0.873687	+	0.486488i	$0.838278\pi$
$740$	−15.4643	+	16.9739i	−0.568479	+	0.623973i
$741$	−21.2805	−	9.91184i	−0.781757	−	0.364121i
$742$	3.46447	+	3.46447i	0.127185	+	0.127185i
$743$	28.4291	+	16.4135i	1.04296	+	0.602154i	0.920671	−	0.390340i	$-0.127643\pi$
$743$	28.4291	+	16.4135i	1.04296	+	0.602154i	0.122291	+	0.992494i	$0.460976\pi$
$744$	6.08811	+	3.51497i	0.223201	+	0.128865i
$745$	−14.9082	+	9.55783i	−0.546194	+	0.350172i
$746$	1.88084	−	1.88084i	0.0688626	−	0.0688626i
$747$	−1.83950	−	3.18610i	−0.0673037	−	0.116573i
$748$	−3.99522	−	6.91992i	−0.146080	−	0.253017i
$749$	0.994610	−	0.994610i	0.0363422	−	0.0363422i
$750$	−8.81103	+	6.88228i	−0.321733	+	0.251305i
$751$	35.6504	+	20.5828i	1.30090	+	0.751076i	0.980559	−	0.196225i	$-0.0628683\pi$
$751$	35.6504	+	20.5828i	1.30090	+	0.751076i	0.320344	+	0.947301i	$0.396202\pi$
$752$	3.40821	+	1.96773i	0.124285	+	0.0717559i
$753$	2.98184	+	2.98184i	0.108664	+	0.108664i
$754$	−25.5609	+	2.24763i	−0.930874	+	0.0818537i
$755$	1.65263	+	35.5121i	0.0601453	+	1.29242i
$756$	−0.324825	−	1.21226i	−0.0118138	−	0.0440895i
$757$	12.4836	−	3.34498i	0.453725	−	0.121575i	−0.0247168	−	0.999694i	$-0.507868\pi$
$757$	12.4836	−	3.34498i	0.453725	−	0.121575i	0.478442	+	0.878119i	$0.341202\pi$
$758$	−3.02144	+	11.2762i	−0.109744	+	0.409569i
$759$	5.78032	+	5.78032i	0.209812	+	0.209812i
$760$	−12.2564	+	7.85772i	−0.444586	+	0.285030i
$761$	6.49514	−	24.2402i	0.235449	−	0.878707i	−0.742497	−	0.669849i	$-0.766359\pi$
$761$	6.49514	−	24.2402i	0.235449	−	0.878707i	0.977946	−	0.208858i	$-0.0669745\pi$
$762$			9.99556i			0.362101i
$763$	22.4733	+	6.02170i	0.813588	+	0.218000i
$764$	−11.4751	+	19.8754i	−0.415154	+	0.719068i
$765$	−9.51732	−	4.91974i	−0.344099	−	0.177873i
$766$		−	12.3736i		−	0.447075i
$767$	20.7399	+	17.3873i	0.748873	+	0.627818i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−1.47911	+	0.396327i	−0.0533382	+	0.0142919i	−0.285389	−	0.958412i	$-0.592123\pi$
$769$	−1.47911	+	0.396327i	−0.0533382	+	0.0142919i	0.232051	+	0.972704i	$0.425456\pi$
$770$	2.14910	−	4.15748i	0.0774482	−	0.149825i
$771$	10.5507	−	6.09148i	0.379976	−	0.219379i
$772$	8.98509			0.323381
$773$	19.8283	−	11.4479i	0.713176	−	0.411752i	−0.0990599	−	0.995081i	$-0.531584\pi$
$773$	19.8283	−	11.4479i	0.713176	−	0.411752i	0.812236	+	0.583329i	$0.198250\pi$
$774$	6.17528	+	1.65466i	0.221966	+	0.0594756i
$775$	27.0555	+	22.4389i	0.971862	+	0.806028i
$776$	7.29623	+	12.6374i	0.261919	+	0.453658i
$777$	−3.33561	−	12.4487i	−0.119664	−	0.446594i
$778$	−1.42142	+	2.46197i	−0.0509604	+	0.0882660i
$779$	15.4633			0.554031
$780$	7.45873	+	3.06062i	0.267065	+	0.109588i
$781$	−2.29114			−0.0819835
$782$	−11.7429	+	20.3392i	−0.419924	+	0.727330i
$783$	1.84193	+	6.87419i	0.0658253	+	0.245663i
$784$	−2.71245	−	4.69811i	−0.0968734	−	0.167790i
$785$	−0.296390	−	6.36890i	−0.0105786	−	0.227316i
$786$	−6.80651	−	1.82380i	−0.242780	−	0.0650528i
$787$	2.23919	−	1.29280i	0.0798184	−	0.0460832i	−0.459560	−	0.888147i	$-0.651993\pi$
$787$	2.23919	−	1.29280i	0.0798184	−	0.0460832i	0.539378	+	0.842064i	$0.318659\pi$
$788$	−25.3778			−0.904047
$789$	14.5328	−	8.39052i	0.517382	−	0.298710i
$790$	5.80046	+	18.2143i	0.206371	+	0.648035i
$791$	−9.34608	+	2.50427i	−0.332308	+	0.0890418i
$792$	1.17924	−	1.17924i	0.0419024	−	0.0419024i
$793$	3.07524	+	34.9728i	0.109205	+	1.24192i
$794$		−	22.4154i		−	0.795494i
$795$	2.64887	+	8.31781i	0.0939456	+	0.295002i
$796$	−12.6150	+	21.8497i	−0.447125	+	0.774443i
$797$	45.3134	+	12.1417i	1.60508	+	0.430080i	0.946572	−	0.322492i	$-0.104520\pi$
$797$	45.3134	+	12.1417i	1.60508	+	0.430080i	0.658510	+	0.752572i	$0.271187\pi$
$798$		−	8.17142i		−	0.289265i
$799$	−4.88030	+	18.2135i	−0.172653	+	0.644348i
$800$	4.07923	−	2.89135i	0.144223	−	0.102225i
$801$	−3.61929	−	3.61929i	−0.127881	−	0.127881i
$802$	9.06930	−	33.8471i	0.320248	−	1.19518i
$803$	17.2025	−	4.60939i	0.607062	−	0.162662i
$804$	−0.482337	−	1.80011i	−0.0170107	−	0.0634848i
$805$	−13.7410	+	0.639464i	−0.484306	+	0.0225382i
$806$	4.39044	−	24.9637i	0.154647	−	0.879308i
$807$	−3.58802	−	3.58802i	−0.126304	−	0.126304i
$808$	15.1633	+	8.75455i	0.533444	+	0.307984i
$809$	−16.8126	−	9.70675i	−0.591099	−	0.341271i	0.174433	−	0.984669i	$-0.444191\pi$
$809$	−16.8126	−	9.70675i	−0.591099	−	0.341271i	−0.765532	+	0.643398i	$0.777524\pi$
$810$	0.477706	−	2.18444i	0.0167849	−	0.0767536i
$811$	−3.18239	+	3.18239i	−0.111749	+	0.111749i	−0.760770	−	0.649021i	$-0.775179\pi$
$811$	−3.18239	+	3.18239i	−0.111749	+	0.111749i	0.649021	+	0.760770i	$0.275179\pi$
$812$	−4.46581	−	7.73501i	−0.156719	−	0.271446i
$813$	15.5185	+	26.8788i	0.544257	+	0.942681i
$814$	12.1096	−	12.1096i	0.424440	−	0.424440i
$815$	−1.98254	+	9.06574i	−0.0694455	+	0.317559i
$816$	4.14939	+	2.39565i	0.145258	+	0.0838647i
$817$	36.0486	+	20.8127i	1.26118	+	0.728143i
$818$	12.6403	+	12.6403i	0.441956	+	0.441956i
$819$	−3.70557	+	2.59710i	−0.129483	+	0.0907500i
$820$	−5.30485	+	0.246872i	−0.185254	+	0.00862115i
$821$	2.04795	+	7.64305i	0.0714739	+	0.266744i	0.992411	−	0.122968i	$-0.0392412\pi$
$821$	2.04795	+	7.64305i	0.0714739	+	0.266744i	−0.920937	+	0.389712i	$0.872575\pi$
$822$	3.69874	−	0.991075i	0.129008	−	0.0345677i
$823$	−7.74804	+	28.9161i	−0.270080	+	1.00795i	0.688988	+	0.724773i	$0.258055\pi$
$823$	−7.74804	+	28.9161i	−0.270080	+	1.00795i	−0.959067	+	0.283178i	$0.908611\pi$
$824$	−6.26904	−	6.26904i	−0.218392	−	0.218392i
$825$	6.80291	−	4.82188i	0.236847	−	0.167876i
$826$	−2.43820	+	9.09947i	−0.0848357	+	0.316611i
$827$			52.9999i			1.84299i	0.388394	+	0.921493i	$0.373030\pi$
$827$			52.9999i			1.84299i	−0.388394	+	0.921493i	$0.626970\pi$
$828$	−4.73471	−	1.26866i	−0.164543	−	0.0440891i
$829$	6.62400	−	11.4731i	0.230061	−	0.398478i	−0.727765	−	0.685827i	$-0.759441\pi$
$829$	6.62400	−	11.4731i	0.230061	−	0.398478i	0.957826	+	0.287349i	$0.0927740\pi$
$830$	2.49626	+	7.83860i	0.0866464	+	0.272082i
$831$		−	27.6726i		−	0.959950i
$832$	−3.26841	−	1.52233i	−0.113312	−	0.0527774i
$833$	18.3794	−	18.3794i	0.636809	−	0.636809i
$834$	−15.3248	+	4.10627i	−0.530655	+	0.142189i
$835$	3.65845	+	11.4880i	0.126606	+	0.397560i
$836$	9.40355	−	5.42914i	0.325229	−	0.187771i
$837$	−7.02994			−0.242990
$838$	−5.50409	+	3.17779i	−0.190136	+	0.109775i
$839$	−20.7102	−	5.54929i	−0.714997	−	0.191583i	−0.117059	−	0.993125i	$-0.537347\pi$
$839$	−20.7102	−	5.54929i	−0.714997	−	0.191583i	−0.597938	+	0.801542i	$0.704013\pi$
$840$	0.130457	+	2.80329i	0.00450118	+	0.0967227i
$841$	10.8236	+	18.7470i	0.373227	+	0.646447i
$842$	−3.79683	−	14.1700i	−0.130848	−	0.488330i
$843$	4.50345	−	7.80021i	0.155107	−	0.268654i
$844$	2.90413			0.0999644
$845$	1.15904	−	29.0458i	0.0398723	−	0.999205i
$846$	−3.93547			−0.135304
$847$	5.15740	−	8.93288i	0.177210	−	0.306937i
$848$	−1.01041	−	3.77088i	−0.0346975	−	0.129493i
$849$	10.1907	+	17.6508i	0.349743	+	0.605773i
$850$	18.4399	+	15.2934i	0.632482	+	0.524558i
$851$	−48.6206	−	13.0279i	−1.66669	−	0.446589i
$852$	1.18978	−	0.686919i	0.0407611	−	0.0235335i
$853$	−21.3327			−0.730419			−0.365210	−	0.930925i	$-0.619003\pi$
$853$	−21.3327			−0.730419			−0.365210	+	0.930925i	$0.619003\pi$
$854$	−10.5832	+	6.11019i	−0.362148	+	0.209086i
$855$	6.68548	−	12.9332i	0.228638	−	0.442305i
$856$	−1.08258	+	0.290076i	−0.0370017	+	0.00991458i
$857$	24.2701	−	24.2701i	0.829051	−	0.829051i	−0.158334	−	0.987386i	$-0.550612\pi$
$857$	24.2701	−	24.2701i	0.829051	−	0.829051i	0.987386	+	0.158334i	$0.0506123\pi$
$858$	−5.45071	−	2.53879i	−0.186084	−	0.0866728i
$859$			22.1224i			0.754807i	0.926049	+	0.377403i	$0.123183\pi$
$859$			22.1224i			0.754807i	−0.926049	+	0.377403i	$0.876817\pi$
$860$	−12.6991	−	6.56448i	−0.433036	−	0.223847i
$861$	1.49032	−	2.58132i	0.0507901	−	0.0879711i
$862$	20.8510	+	5.58701i	0.710188	+	0.190294i
$863$			35.7630i			1.21739i	0.793406	+	0.608693i	$0.208306\pi$
$863$			35.7630i			1.21739i	−0.793406	+	0.608693i	$0.791694\pi$
$864$	−0.258819	+	0.965926i	−0.00880520	+	0.0328615i
$865$	13.8698	−	8.89212i	0.471588	−	0.302341i
$866$	4.87383	+	4.87383i	0.165620	+	0.165620i
$867$	−1.54169	+	5.75366i	−0.0523585	+	0.195405i
$868$	8.52213	−	2.28350i	0.289260	−	0.0775070i
$869$	−3.68990	−	13.7709i	−0.125171	−	0.467146i
$870$	−0.739761	−	15.8962i	−0.0250802	−	0.538931i
$871$	−5.50245	+	3.85647i	−0.186444	+	0.130672i
$872$	−13.1086	−	13.1086i	−0.443912	−	0.443912i
$873$	−12.6374	−	7.29623i	−0.427713	−	0.246940i
$874$	−27.6392	−	15.9575i	−0.934909	−	0.539770i
$875$	−1.71164	+	13.9268i	−0.0578640	+	0.470813i
$876$	−7.55119	+	7.55119i	−0.255131	+	0.255131i
$877$	−4.87120	−	8.43716i	−0.164489	−	0.284903i	0.771985	−	0.635641i	$-0.219264\pi$
$877$	−4.87120	−	8.43716i	−0.164489	−	0.284903i	−0.936474	+	0.350738i	$0.885931\pi$
$878$	−7.70318	−	13.3423i	−0.259970	−	0.450281i
$879$	16.5333	−	16.5333i	0.557655	−	0.557655i
$880$	−3.13931	+	2.01265i	−0.105826	+	0.0678465i
$881$	3.83408	+	2.21361i	0.129174	+	0.0745784i	0.563194	−	0.826324i	$-0.309572\pi$
$881$	3.83408	+	2.21361i	0.129174	+	0.0745784i	−0.434021	+	0.900903i	$0.642906\pi$
$882$	4.69811	+	2.71245i	0.158194	+	0.0913331i
$883$	−8.13776	−	8.13776i	−0.273858	−	0.273858i	0.556793	−	0.830651i	$-0.312031\pi$
$883$	−8.13776	−	8.13776i	−0.273858	−	0.273858i	−0.830651	+	0.556793i	$0.812031\pi$
$884$	2.99234	−	17.0142i	0.100643	−	0.572249i
$885$	−11.3038	+	12.4072i	−0.379973	+	0.417064i
$886$	6.91692	+	25.8143i	0.232379	+	0.867249i
$887$	32.1340	−	8.61028i	1.07895	−	0.289105i	0.324787	−	0.945787i	$-0.394707\pi$
$887$	32.1340	−	8.61028i	1.07895	−	0.289105i	0.754167	+	0.656682i	$0.228041\pi$
$888$	−2.65780	+	9.91906i	−0.0891900	+	0.332862i
$889$	8.87043	+	8.87043i	0.297505	+	0.297505i
$890$	6.17718	+	9.63509i	0.207059	+	0.322969i
$891$	−0.431631	+	1.61087i	−0.0144602	+	0.0539662i
$892$			4.52521i			0.151515i
$893$	−24.7505	−	6.63189i	−0.828245	−	0.221928i
$894$	−3.95984	+	6.85864i	−0.132437	+	0.229387i
$895$	−6.33270	+	2.01669i	−0.211679	+	0.0674106i
$896$		−	1.25503i		−	0.0419275i
$897$	1.54809	+	17.6055i	0.0516893	+	0.587832i
$898$	−11.6394	+	11.6394i	−0.388412	+	0.388412i
$899$	−48.3251	+	12.9487i	−1.61173	+	0.431863i
$900$	−2.08704	+	4.54359i	−0.0695681	+	0.151453i
$901$	16.1988	−	9.35241i	0.539662	−	0.311574i
$902$	3.96073			0.131878
$903$	6.94858	−	4.01177i	0.231234	−	0.133503i
$904$	7.44692	+	1.99540i	0.247681	+	0.0663659i
$905$	12.9146	−	14.1752i	0.429295	−	0.471201i
$906$	7.94935	+	13.7687i	0.264100	+	0.457434i
$907$	−7.16492	−	26.7398i	−0.237907	−	0.887882i	−0.976817	−	0.214077i	$-0.931326\pi$
$907$	−7.16492	−	26.7398i	−0.237907	−	0.887882i	0.738910	−	0.673805i	$-0.235341\pi$
$908$	−11.6902	+	20.2480i	−0.387953	+	0.671955i
$909$	−17.5091			−0.580740
$910$	9.33526	−	3.90305i	0.309461	−	0.129385i
$911$	54.7622			1.81435			0.907177	−	0.420749i	$-0.138233\pi$
$911$	54.7622			1.81435			0.907177	+	0.420749i	$0.138233\pi$
$912$	−3.25548	+	5.63865i	−0.107800	+	0.186714i
$913$	−1.58797	−	5.92638i	−0.0525541	−	0.196134i
$914$	8.73356	+	15.1270i	0.288881	+	0.500356i
$915$	−21.7494	+	1.01215i	−0.719013	+	0.0334607i
$916$	−12.9650	−	3.47396i	−0.428375	−	0.114783i
$917$	−7.65886	+	4.42184i	−0.252918	+	0.146022i
$918$	−4.79131			−0.158137
$919$	−15.8534	+	9.15294i	−0.522954	+	0.301928i	−0.738142	−	0.674645i	$-0.764297\pi$
$919$	−15.8534	+	9.15294i	−0.522954	+	0.301928i	0.215188	+	0.976573i	$0.430963\pi$
$920$	9.73667	+	5.03312i	0.321009	+	0.165937i
$921$	−14.6013	+	3.91241i	−0.481130	+	0.128918i
$922$	7.56691	−	7.56691i	0.249203	−	0.249203i
$923$	−3.79596	−	3.18234i	−0.124945	−	0.104748i
$924$		−	2.09300i		−	0.0688546i
$925$	−21.4318	+	46.6580i	−0.704672	+	1.53411i
$926$	13.0337	−	22.5751i	0.428315	−	0.741863i
$927$	8.56367	+	2.29463i	0.281268	+	0.0753654i
$928$			7.11668i			0.233616i
$929$	−8.75599	+	32.6778i	−0.287275	+	1.07212i	0.659886	+	0.751365i	$0.270604\pi$
$929$	−8.75599	+	32.6778i	−0.287275	+	1.07212i	−0.947161	+	0.320758i	$0.896062\pi$
$930$	15.3565	+	3.35824i	0.503560	+	0.110121i
$931$	24.9760	+	24.9760i	0.818554	+	0.818554i
$932$	3.10284	−	11.5800i	0.101637	−	0.379315i
$933$	−31.2138	+	8.36371i	−1.02189	+	0.273816i
$934$	−4.12636	−	15.3998i	−0.135019	−	0.503897i
$935$	−13.2076	−	12.0330i	−0.431936	−	0.393522i
$936$	3.59169	−	0.315825i	0.117398	−	0.0103231i
$937$	−24.2014	−	24.2014i	−0.790626	−	0.790626i	0.190970	−	0.981596i	$-0.438837\pi$
$937$	−24.2014	−	24.2014i	−0.790626	−	0.790626i	−0.981596	+	0.190970i	$0.938837\pi$
$938$	−2.02552	−	1.16944i	−0.0661357	−	0.0381835i
$939$	−22.5579	−	13.0238i	−0.736151	−	0.425017i
$940$	8.59681	+	1.88000i	0.280397	+	0.0613187i
$941$	−18.5270	+	18.5270i	−0.603962	+	0.603962i	−0.941362	−	0.337399i	$-0.890453\pi$
$941$	−18.5270	+	18.5270i	−0.603962	+	0.603962i	0.337399	+	0.941362i	$0.390453\pi$
$942$	−1.42567	−	2.46933i	−0.0464509	−	0.0804553i
$943$	−5.82074	−	10.0818i	−0.189549	−	0.328309i
$944$	5.30768	−	5.30768i	0.172750	−	0.172750i
$945$	−1.51462	−	2.36249i	−0.0492707	−	0.0768519i
$946$	9.23337	+	5.33089i	0.300203	+	0.173322i
$947$	−42.3100	−	24.4277i	−1.37489	−	0.793793i	−0.383351	−	0.923603i	$-0.625230\pi$
$947$	−42.3100	−	24.4277i	−1.37489	−	0.793793i	−0.991539	+	0.129809i	$0.958564\pi$
$948$	6.04487	+	6.04487i	0.196328	+	0.196328i
$949$	34.9033	+	16.2570i	1.13301	+	0.527724i
$950$	−20.7823	+	25.0581i	−0.674267	+	0.812993i
$951$	3.74188	+	13.9649i	0.121339	+	0.452843i
$952$	5.80832	−	1.55633i	0.188249	−	0.0504411i
$953$	−0.644227	+	2.40429i	−0.0208686	+	0.0778825i	−0.975575	−	0.219667i	$-0.929503\pi$
$953$	−0.644227	+	2.40429i	−0.0208686	+	0.0778825i	0.954706	+	0.297550i	$0.0961695\pi$
$954$	2.76048	+	2.76048i	0.0893738	+	0.0893738i
$955$	−10.9634	+	50.1334i	−0.354768	+	1.62228i
$956$	5.46187	−	20.3840i	0.176650	−	0.659265i
$957$			11.8685i			0.383653i
$958$	−21.5410	−	5.77188i	−0.695957	−	0.186481i
$959$	2.40288	−	4.16192i	0.0775932	−	0.134395i
$960$	1.02680	−	1.98637i	0.0331400	−	0.0641099i
$961$		−	18.4201i		−	0.594196i
$962$	36.8830	−	3.24320i	1.18915	−	0.104565i
$963$	0.792501	−	0.792501i	0.0255380	−	0.0255380i
$964$	6.74561	−	1.80748i	0.217261	−	0.0582150i
$965$	19.1440	−	6.09654i	0.616266	−	0.196254i
$966$	−5.32762	+	3.07590i	−0.171413	+	0.0989656i
$967$	−39.1521			−1.25905			−0.629523	−	0.776982i	$-0.716749\pi$
$967$	−39.1521			−1.25905			−0.629523	+	0.776982i	$0.716749\pi$
$968$	−7.11768	+	4.10940i	−0.228771	+	0.132081i
$969$	−30.1330	−	8.07412i	−0.968012	−	0.259378i
$970$	24.1203	+	21.9752i	0.774457	+	0.705581i
$971$	−14.5620	−	25.2222i	−0.467318	−	0.809418i	0.531985	−	0.846754i	$-0.321446\pi$
$971$	−14.5620	−	25.2222i	−0.467318	−	0.809418i	−0.999303	+	0.0373354i	$0.988113\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−9.95576	+	17.2439i	−0.319167	+	0.552813i
$974$	24.3627			0.780632
$975$	17.9685	+	1.46020i	0.575453	+	0.0467637i
$976$	9.73715			0.311679
$977$	27.6011	−	47.8066i	0.883039	−	1.52947i	0.0350931	−	0.999384i	$-0.488827\pi$
$977$	27.6011	−	47.8066i	0.883039	−	1.52947i	0.847945	−	0.530084i	$-0.177839\pi$
$978$	1.07413	+	4.00872i	0.0343470	+	0.128185i
$979$	−4.26800	−	7.39240i	−0.136406	−	0.236262i
$980$	−8.96700	−	8.16952i	−0.286440	−	0.260966i
$981$	17.9066	+	4.79807i	0.571715	+	0.153190i
$982$	−33.1654	+	19.1480i	−1.05835	+	0.611039i
$983$	45.1532			1.44016			0.720081	−	0.693890i	$-0.244105\pi$
$983$	45.1532			1.44016			0.720081	+	0.693890i	$0.244105\pi$
$984$	−2.05678	+	1.18749i	−0.0655679	+	0.0378556i
$985$	−54.0709	+	17.2193i	−1.72284	+	0.548651i
$986$	−32.9363	+	8.82527i	−1.04891	+	0.281054i
$987$	−3.49248	+	3.49248i	−0.111167	+	0.111167i
$988$	23.1207	+	4.06632i	0.735568	+	0.129367i
$989$		−	31.3374i		−	0.996471i
$990$	1.71240	−	3.31266i	0.0544235	−	0.105283i
$991$	−30.2300	+	52.3598i	−0.960286	+	1.66326i	−0.238508	+	0.971140i	$0.576658\pi$
$991$	−30.2300	+	52.3598i	−0.960286	+	1.66326i	−0.721778	+	0.692125i	$0.756675\pi$
$992$	−6.79040	−	1.81948i	−0.215595	−	0.0577686i
$993$		−	4.19873i		−	0.133243i
$994$	0.446256	−	1.66545i	0.0141544	−	0.0528249i
$995$	−12.0525	+	55.1133i	−0.382089	+	1.74721i
$996$	2.60144	+	2.60144i	0.0824298	+	0.0824298i
$997$	−5.50966	+	20.5623i	−0.174493	+	0.651216i	0.822145	+	0.569278i	$0.192777\pi$
$997$	−5.50966	+	20.5623i	−0.174493	+	0.651216i	−0.996638	+	0.0819371i	$0.973889\pi$
$998$	−12.5823	+	3.37141i	−0.398285	+	0.106720i
$999$	−2.65780	−	9.91906i	−0.0840892	−	0.313825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.c.97.5	yes	32
5.3	odd	4		390.2.bd.c.253.3	yes	32
13.11	odd	12		390.2.bd.c.37.3	✓	32
65.63	even	12	inner	390.2.bn.c.193.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.37.3	✓	32	13.11	odd	12
390.2.bd.c.253.3	yes	32	5.3	odd	4
390.2.bn.c.97.5	yes	32	1.1	even	1	trivial
390.2.bn.c.193.5	yes	32	65.63	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.65293 - 1.50593i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-1.08688 + 0.627513i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.65293 - 1.50593i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-1.08688 + 0.627513i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.13064 - 0.678517i) q^{10} +(-1.61087 + 0.431631i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.26841 - 1.52233i) q^{13} -1.25503i q^{14} +(1.02680 - 1.98637i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.62805 - 1.24008i) q^{17} -1.00000i q^{18} +(1.68516 - 6.28910i) q^{19} +(-0.477706 + 2.18444i) q^{20} +(-0.887437 - 0.887437i) q^{21} +(0.431631 - 1.61087i) q^{22} +(-4.73471 + 1.26866i) q^{23} +(0.258819 + 0.965926i) q^{24} +(0.464364 + 4.97839i) q^{25} +(2.95258 - 2.06936i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.08688 + 0.627513i) q^{28} +(-6.16323 - 3.55834i) q^{29} +(1.20685 + 1.88242i) q^{30} +(4.97092 - 4.97092i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.833847 - 1.44427i) q^{33} +(3.38797 - 3.38797i) q^{34} +(2.74153 + 0.599533i) q^{35} +(0.866025 + 0.500000i) q^{36} +(8.89318 + 5.13448i) q^{37} +(4.60394 + 4.60394i) q^{38} +(0.624535 - 3.55105i) q^{39} +(-1.65293 - 1.50593i) q^{40} +(0.614688 + 2.29405i) q^{41} +(1.21226 - 0.324825i) q^{42} +(-1.65466 + 6.17528i) q^{43} +(1.17924 + 1.17924i) q^{44} +(2.18444 + 0.477706i) q^{45} +(1.26866 - 4.73471i) q^{46} -3.93547i q^{47} +(-0.965926 - 0.258819i) q^{48} +(-2.71245 + 4.69811i) q^{49} +(-4.54359 - 2.08704i) q^{50} -4.79131i q^{51} +(0.315825 + 3.59169i) q^{52} +(-2.76048 + 2.76048i) q^{53} +(0.965926 - 0.258819i) q^{54} +(3.31266 + 1.71240i) q^{55} +(-1.08688 + 0.627513i) q^{56} +6.51095 q^{57} +(6.16323 - 3.55834i) q^{58} +(-7.25043 - 1.94275i) q^{59} +(-2.23365 + 0.103947i) q^{60} +(-4.86857 - 8.43262i) q^{61} +(1.81948 + 6.79040i) q^{62} +(0.627513 - 1.08688i) q^{63} +1.00000 q^{64} +(3.10993 + 7.43830i) q^{65} +1.66769 q^{66} +(0.931803 - 1.61393i) q^{67} +(1.24008 + 4.62805i) q^{68} +(-2.45087 - 4.24503i) q^{69} +(-1.88998 + 2.07447i) q^{70} +(1.32703 + 0.355575i) q^{71} +(-0.866025 + 0.500000i) q^{72} -10.6790 q^{73} +(-8.89318 + 5.13448i) q^{74} +(-4.68857 + 1.73704i) q^{75} +(-6.28910 + 1.68516i) q^{76} +(1.47997 - 1.47997i) q^{77} +(2.76303 + 2.31639i) q^{78} +8.54874i q^{79} +(2.13064 - 0.678517i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.29405 - 0.614688i) q^{82} +3.67899i q^{83} +(-0.324825 + 1.21226i) q^{84} +(5.78237 + 9.01928i) q^{85} +(-4.52062 - 4.52062i) q^{86} +(1.84193 - 6.87419i) q^{87} +(-1.61087 + 0.431631i) q^{88} +(1.32475 + 4.94404i) q^{89} +(-1.50593 + 1.65293i) q^{90} +(4.50767 - 0.396369i) q^{91} +(3.46605 + 3.46605i) q^{92} +(6.08811 + 3.51497i) q^{93} +(3.40821 + 1.96773i) q^{94} +(-12.2564 + 7.85772i) q^{95} +(0.707107 - 0.707107i) q^{96} +(7.29623 + 12.6374i) q^{97} +(-2.71245 - 4.69811i) q^{98} +(1.17924 - 1.17924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

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