LMFDB - Embedded newform 690.2.i.f.47.16

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			47.16
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.73145 + 0.0456124i) q^{3} -1.00000i q^{4} +(-1.54063 + 1.62063i) q^{5} +(1.25657 - 1.19207i) q^{6} +(0.528026 + 0.528026i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99584 + 0.157951i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.73145 + 0.0456124i) q^{3} -1.00000i q^{4} +(-1.54063 + 1.62063i) q^{5} +(1.25657 - 1.19207i) q^{6} +(0.528026 + 0.528026i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99584 + 0.157951i) q^{9} +(0.0565714 + 2.23535i) q^{10} +4.60712i q^{11} +(0.0456124 - 1.73145i) q^{12} +(4.73992 - 4.73992i) q^{13} +0.746742 q^{14} +(-2.74145 + 2.73578i) q^{15} -1.00000 q^{16} +(3.32957 - 3.32957i) q^{17} +(2.23007 - 2.00669i) q^{18} +5.21085i q^{19} +(1.62063 + 1.54063i) q^{20} +(0.890166 + 0.938335i) q^{21} +(3.25773 + 3.25773i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.19207 - 1.25657i) q^{24} +(-0.252914 - 4.99360i) q^{25} -6.70326i q^{26} +(5.17994 + 0.410132i) q^{27} +(0.528026 - 0.528026i) q^{28} -2.50593 q^{29} +(-0.00400919 + 3.87298i) q^{30} +3.91972 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.210142 + 7.97700i) q^{33} -4.70873i q^{34} +(-1.66923 + 0.0422442i) q^{35} +(0.157951 - 2.99584i) q^{36} +(-7.08238 - 7.08238i) q^{37} +(3.68463 + 3.68463i) q^{38} +(8.42313 - 7.99073i) q^{39} +(2.23535 - 0.0565714i) q^{40} +4.23059i q^{41} +(1.29295 + 0.0340607i) q^{42} +(-7.82352 + 7.82352i) q^{43} +4.60712 q^{44} +(-4.87146 + 4.61182i) q^{45} +1.00000 q^{46} +(2.42130 - 2.42130i) q^{47} +(-1.73145 - 0.0456124i) q^{48} -6.44238i q^{49} +(-3.70985 - 3.35217i) q^{50} +(5.91686 - 5.61312i) q^{51} +(-4.73992 - 4.73992i) q^{52} +(1.66113 + 1.66113i) q^{53} +(3.95278 - 3.37276i) q^{54} +(-7.46646 - 7.09787i) q^{55} -0.746742i q^{56} +(-0.237680 + 9.02233i) q^{57} +(-1.77196 + 1.77196i) q^{58} -12.7399 q^{59} +(2.73578 + 2.74145i) q^{60} -1.51016 q^{61} +(2.77166 - 2.77166i) q^{62} +(1.49848 + 1.66528i) q^{63} +1.00000i q^{64} +(0.379213 + 14.9841i) q^{65} +(5.49200 + 5.78918i) q^{66} +(-5.25010 - 5.25010i) q^{67} +(-3.32957 - 3.32957i) q^{68} +(1.19207 + 1.25657i) q^{69} +(-1.15045 + 1.21020i) q^{70} +10.9186i q^{71} +(-2.00669 - 2.23007i) q^{72} +(-5.55728 + 5.55728i) q^{73} -10.0160 q^{74} +(-0.210138 - 8.65770i) q^{75} +5.21085 q^{76} +(-2.43268 + 2.43268i) q^{77} +(0.305752 - 11.6064i) q^{78} -6.67082i q^{79} +(1.54063 - 1.62063i) q^{80} +(8.95010 + 0.946393i) q^{81} +(2.99148 + 2.99148i) q^{82} +(-9.68331 - 9.68331i) q^{83} +(0.938335 - 0.890166i) q^{84} +(0.266380 + 10.5257i) q^{85} +11.0641i q^{86} +(-4.33889 - 0.114301i) q^{87} +(3.25773 - 3.25773i) q^{88} -9.07840 q^{89} +(-0.183598 + 6.70569i) q^{90} +5.00560 q^{91} +(0.707107 - 0.707107i) q^{92} +(6.78680 + 0.178788i) q^{93} -3.42424i q^{94} +(-8.44489 - 8.02800i) q^{95} +(-1.25657 + 1.19207i) q^{96} +(5.69526 + 5.69526i) q^{97} +(-4.55545 - 4.55545i) q^{98} +(-0.727700 + 13.8022i) 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
$3$	1.73145	+	0.0456124i	0.999653	+	0.0263343i
$3$	1.73145	+	0.0456124i	0.999653	+	0.0263343i
$4$		−	1.00000i		−	0.500000i
$5$	−1.54063	+	1.62063i	−0.688991	+	0.724770i
$5$	−1.54063	+	1.62063i	−0.688991	+	0.724770i
$6$	1.25657	−	1.19207i	0.512994	−	0.486659i
$7$	0.528026	+	0.528026i	0.199575	+	0.199575i	0.799818	−	0.600243i	$-0.204929\pi$
$7$	0.528026	+	0.528026i	0.199575	+	0.199575i	−0.600243	+	0.799818i	$0.704929\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.99584	+	0.157951i	0.998613	+	0.0526504i
$10$	0.0565714	+	2.23535i	0.0178895	+	0.706880i
$11$			4.60712i			1.38910i	0.719445	+	0.694549i	$0.244396\pi$
$11$			4.60712i			1.38910i	−0.719445	+	0.694549i	$0.755604\pi$
$12$	0.0456124	−	1.73145i	0.0131672	−	0.499827i
$13$	4.73992	−	4.73992i	1.31462	−	1.31462i	0.396645	−	0.917972i	$-0.370174\pi$
$13$	4.73992	−	4.73992i	1.31462	−	1.31462i	0.917972	−	0.396645i	$-0.129826\pi$
$14$	0.746742			0.199575
$15$	−2.74145	+	2.73578i	−0.707838	+	0.706374i
$16$	−1.00000			−0.250000
$17$	3.32957	−	3.32957i	0.807541	−	0.807541i	−0.176721	−	0.984261i	$-0.556549\pi$
$17$	3.32957	−	3.32957i	0.807541	−	0.807541i	0.984261	+	0.176721i	$0.0565489\pi$
$18$	2.23007	−	2.00669i	0.525632	−	0.472981i
$19$			5.21085i			1.19545i	0.801700	+	0.597726i	$0.203929\pi$
$19$			5.21085i			1.19545i	−0.801700	+	0.597726i	$0.796071\pi$
$20$	1.62063	+	1.54063i	0.362385	+	0.344495i
$21$	0.890166	+	0.938335i	0.194250	+	0.204762i
$22$	3.25773	+	3.25773i	0.694549	+	0.694549i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	−1.19207	−	1.25657i	−0.243330	−	0.256497i
$25$	−0.252914	−	4.99360i	−0.0505828	−	0.998720i
$26$		−	6.70326i		−	1.31462i
$27$	5.17994	+	0.410132i	0.996880	+	0.0789300i
$28$	0.528026	−	0.528026i	0.0997876	−	0.0997876i
$29$	−2.50593			−0.465339			−0.232669	−	0.972556i	$-0.574746\pi$
$29$	−2.50593			−0.465339			−0.232669	+	0.972556i	$0.574746\pi$
$30$	−0.00400919	+	3.87298i	−0.000731975	+	0.707106i
$31$	3.91972			0.704003			0.352001	−	0.935999i	$-0.385501\pi$
$31$	3.91972			0.704003			0.352001	+	0.935999i	$0.385501\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.210142	+	7.97700i	−0.0365810	+	1.38862i
$34$		−	4.70873i		−	0.807541i
$35$	−1.66923	+	0.0422442i	−0.282151	+	0.00714058i
$36$	0.157951	−	2.99584i	0.0263252	−	0.499307i
$37$	−7.08238	−	7.08238i	−1.16434	−	1.16434i	−0.983516	−	0.180820i	$-0.942125\pi$
$37$	−7.08238	−	7.08238i	−1.16434	−	1.16434i	−0.180820	−	0.983516i	$-0.557875\pi$
$38$	3.68463	+	3.68463i	0.597726	+	0.597726i
$39$	8.42313	−	7.99073i	1.34878	−	1.27954i
$40$	2.23535	−	0.0565714i	0.353440	−	0.00894473i
$41$			4.23059i			0.660707i	0.943857	+	0.330353i	$0.107168\pi$
$41$			4.23059i			0.660707i	−0.943857	+	0.330353i	$0.892832\pi$
$42$	1.29295	+	0.0340607i	0.199506	+	0.00525568i
$43$	−7.82352	+	7.82352i	−1.19308	+	1.19308i	−0.216877	+	0.976199i	$0.569587\pi$
$43$	−7.82352	+	7.82352i	−1.19308	+	1.19308i	−0.976199	+	0.216877i	$0.930413\pi$
$44$	4.60712			0.694549
$45$	−4.87146	+	4.61182i	−0.726195	+	0.687489i
$46$	1.00000			0.147442
$47$	2.42130	−	2.42130i	0.353184	−	0.353184i	−0.508109	−	0.861293i	$-0.669655\pi$
$47$	2.42130	−	2.42130i	0.353184	−	0.353184i	0.861293	+	0.508109i	$0.169655\pi$
$48$	−1.73145	−	0.0456124i	−0.249913	−	0.00658358i
$49$		−	6.44238i		−	0.920340i
$50$	−3.70985	−	3.35217i	−0.524651	−	0.474069i
$51$	5.91686	−	5.61312i	0.828527	−	0.785994i
$52$	−4.73992	−	4.73992i	−0.657308	−	0.657308i
$53$	1.66113	+	1.66113i	0.228173	+	0.228173i	0.811929	−	0.583756i	$-0.198418\pi$
$53$	1.66113	+	1.66113i	0.228173	+	0.228173i	−0.583756	+	0.811929i	$0.698418\pi$
$54$	3.95278	−	3.37276i	0.537905	−	0.458975i
$55$	−7.46646	−	7.09787i	−1.00678	−	0.957077i
$56$		−	0.746742i		−	0.0997876i
$57$	−0.237680	+	9.02233i	−0.0314814	+	1.19504i
$58$	−1.77196	+	1.77196i	−0.232669	+	0.232669i
$59$	−12.7399			−1.65860			−0.829299	−	0.558806i	$-0.811260\pi$
$59$	−12.7399			−1.65860			−0.829299	+	0.558806i	$0.811260\pi$
$60$	2.73578	+	2.74145i	0.353187	+	0.353919i
$61$	−1.51016			−0.193356			−0.0966778	−	0.995316i	$-0.530822\pi$
$61$	−1.51016			−0.193356			−0.0966778	+	0.995316i	$0.530822\pi$
$62$	2.77166	−	2.77166i	0.352001	−	0.352001i
$63$	1.49848	+	1.66528i	0.188791	+	0.209806i
$64$			1.00000i			0.125000i
$65$	0.379213	+	14.9841i	0.0470356	+	1.85855i
$66$	5.49200	+	5.78918i	0.676018	+	0.712599i
$67$	−5.25010	−	5.25010i	−0.641402	−	0.641402i	0.309498	−	0.950900i	$-0.399839\pi$
$67$	−5.25010	−	5.25010i	−0.641402	−	0.641402i	−0.950900	+	0.309498i	$0.899839\pi$
$68$	−3.32957	−	3.32957i	−0.403770	−	0.403770i
$69$	1.19207	+	1.25657i	0.143508	+	0.151274i
$70$	−1.15045	+	1.21020i	−0.137505	+	0.144646i
$71$			10.9186i			1.29580i	0.761727	+	0.647898i	$0.224352\pi$
$71$			10.9186i			1.29580i	−0.761727	+	0.647898i	$0.775648\pi$
$72$	−2.00669	−	2.23007i	−0.236491	−	0.262816i
$73$	−5.55728	+	5.55728i	−0.650430	+	0.650430i	−0.953097	−	0.302667i	$-0.902123\pi$
$73$	−5.55728	+	5.55728i	−0.650430	+	0.650430i	0.302667	+	0.953097i	$0.402123\pi$
$74$	−10.0160			−1.16434
$75$	−0.210138	−	8.65770i	−0.0242647	−	0.999706i
$76$	5.21085			0.597726
$77$	−2.43268	+	2.43268i	−0.277230	+	0.277230i
$78$	0.305752	−	11.6064i	0.0346196	−	1.31416i
$79$		−	6.67082i		−	0.750526i	−0.926918	−	0.375263i	$-0.877552\pi$
$79$		−	6.67082i		−	0.750526i	0.926918	−	0.375263i	$-0.122448\pi$
$80$	1.54063	−	1.62063i	0.172248	−	0.181192i
$81$	8.95010	+	0.946393i	0.994456	+	0.105155i
$82$	2.99148	+	2.99148i	0.330353	+	0.330353i
$83$	−9.68331	−	9.68331i	−1.06288	−	1.06288i	−0.997886	−	0.0649958i	$-0.979297\pi$
$83$	−9.68331	−	9.68331i	−1.06288	−	1.06288i	−0.0649958	−	0.997886i	$-0.520703\pi$
$84$	0.938335	−	0.890166i	0.102381	−	0.0971251i
$85$	0.266380	+	10.5257i	0.0288929	+	1.14167i
$86$			11.0641i			1.19308i
$87$	−4.33889	−	0.114301i	−0.465178	−	0.0122544i
$88$	3.25773	−	3.25773i	0.347275	−	0.347275i
$89$	−9.07840			−0.962309			−0.481154	−	0.876636i	$-0.659782\pi$
$89$	−9.07840			−0.962309			−0.481154	+	0.876636i	$0.659782\pi$
$90$	−0.183598	+	6.70569i	−0.0193529	+	0.706842i
$91$	5.00560			0.524730
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	6.78680	+	0.178788i	0.703759	+	0.0185394i
$94$		−	3.42424i		−	0.353184i
$95$	−8.44489	−	8.02800i	−0.866428	−	0.823656i
$96$	−1.25657	+	1.19207i	−0.128248	+	0.121665i
$97$	5.69526	+	5.69526i	0.578266	+	0.578266i	0.934425	−	0.356159i	$-0.115914\pi$
$97$	5.69526	+	5.69526i	0.578266	+	0.578266i	−0.356159	+	0.934425i	$0.615914\pi$
$98$	−4.55545	−	4.55545i	−0.460170	−	0.460170i
$99$	−0.727700	+	13.8022i	−0.0731366	+	1.38717i
$100$	−4.99360	+	0.252914i	−0.499360	+	0.0252914i
$101$		−	7.99014i		−	0.795049i	−0.917592	−	0.397524i	$-0.869869\pi$
$101$		−	7.99014i		−	0.795049i	0.917592	−	0.397524i	$-0.130131\pi$
$102$	0.214777	−	8.15293i	0.0212660	−	0.807260i
$103$	8.37328	−	8.37328i	0.825044	−	0.825044i	−0.161783	−	0.986826i	$-0.551724\pi$
$103$	8.37328	−	8.37328i	0.825044	−	0.825044i	0.986826	+	0.161783i	$0.0517244\pi$
$104$	−6.70326			−0.657308
$105$	−2.89212	−	0.00299383i	−0.282242	−	0.000292168i
$106$	2.34919			0.228173
$107$	10.8290	−	10.8290i	1.04688	−	1.04688i	0.0480314	−	0.998846i	$-0.484705\pi$
$107$	10.8290	−	10.8290i	1.04688	−	1.04688i	0.998846	−	0.0480314i	$-0.0152948\pi$
$108$	0.410132	−	5.17994i	0.0394650	−	0.498440i
$109$		−	5.81042i		−	0.556538i	−0.960503	−	0.278269i	$-0.910239\pi$
$109$		−	5.81042i		−	0.556538i	0.960503	−	0.278269i	$-0.0897606\pi$
$110$	−10.2985	+	0.260631i	−0.981927	+	0.0248502i
$111$	−11.9397	−	12.5858i	−1.13327	−	1.19459i
$112$	−0.528026	−	0.528026i	−0.0498938	−	0.0498938i
$113$	−0.624299	−	0.624299i	−0.0587291	−	0.0587291i	0.677132	−	0.735861i	$-0.263222\pi$
$113$	−0.624299	−	0.624299i	−0.0587291	−	0.0587291i	−0.735861	+	0.677132i	$0.763222\pi$
$114$	6.21169	+	6.54782i	0.581778	+	0.613259i
$115$	−2.23535	+	0.0565714i	−0.208448	+	0.00527531i
$116$			2.50593i			0.232669i
$117$	14.9487	−	13.4514i	1.38201	−	1.24358i
$118$	−9.00849	+	9.00849i	−0.829299	+	0.829299i
$119$	3.51621			0.322330
$120$	3.87298	+	0.00400919i	0.353553	+	0.000365988i
$121$	−10.2255			−0.929595
$122$	−1.06784	+	1.06784i	−0.0966778	+	0.0966778i
$123$	−0.192967	+	7.32505i	−0.0173993	+	0.660478i
$124$		−	3.91972i		−	0.352001i
$125$	8.48245	+	7.28341i	0.758693	+	0.651448i
$126$	2.23712	+	0.117949i	0.199298	+	0.0105077i
$127$	11.0353	+	11.0353i	0.979224	+	0.979224i	0.999789	−	0.0205641i	$-0.00654623\pi$
$127$	11.0353	+	11.0353i	0.979224	+	0.979224i	−0.0205641	+	0.999789i	$0.506546\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−13.9029	+	13.1892i	−1.22408	+	1.16124i
$130$	10.8635	+	10.3272i	0.952795	+	0.905759i
$131$		−	9.85239i		−	0.860807i	−0.902637	−	0.430404i	$-0.858371\pi$
$131$		−	9.85239i		−	0.860807i	0.902637	−	0.430404i	$-0.141629\pi$
$132$	7.97700	+	0.210142i	0.694309	+	0.0182905i
$133$	−2.75147	+	2.75147i	−0.238582	+	0.238582i
$134$	−7.42476			−0.641402
$135$	−8.64505	+	7.76293i	−0.744048	+	0.668127i
$136$	−4.70873			−0.403770
$137$	−7.59469	+	7.59469i	−0.648858	+	0.648858i	−0.952717	−	0.303859i	$-0.901725\pi$
$137$	−7.59469	+	7.59469i	−0.648858	+	0.648858i	0.303859	+	0.952717i	$0.401725\pi$
$138$	1.73145	+	0.0456124i	0.147391	+	0.00388279i
$139$			14.6607i			1.24350i	0.783214	+	0.621752i	$0.213579\pi$
$139$			14.6607i			1.24350i	−0.783214	+	0.621752i	$0.786421\pi$
$140$	0.0422442	+	1.66923i	0.00357029	+	0.141076i
$141$	4.30281	−	4.08193i	0.362362	−	0.343760i
$142$	7.72060	+	7.72060i	0.647898	+	0.647898i
$143$	21.8374	+	21.8374i	1.82613	+	1.82613i
$144$	−2.99584	−	0.157951i	−0.249653	−	0.0131626i
$145$	3.86071	−	4.06119i	0.320614	−	0.337264i
$146$			7.85918i			0.650430i
$147$	0.293852	−	11.1547i	0.0242365	−	0.920020i
$148$	−7.08238	+	7.08238i	−0.582168	+	0.582168i
$149$	−5.81897			−0.476708			−0.238354	−	0.971178i	$-0.576608\pi$
$149$	−5.81897			−0.476708			−0.238354	+	0.971178i	$0.576608\pi$
$150$	−6.27051	−	5.97333i	−0.511985	−	0.487720i
$151$	2.78052			0.226276			0.113138	−	0.993579i	$-0.463910\pi$
$151$	2.78052			0.226276			0.113138	+	0.993579i	$0.463910\pi$
$152$	3.68463	−	3.68463i	0.298863	−	0.298863i
$153$	10.5008	−	9.44896i	0.848938	−	0.763903i
$154$			3.44033i			0.277230i
$155$	−6.03884	+	6.35244i	−0.485052	+	0.510240i
$156$	−7.99073	−	8.42313i	−0.639771	−	0.674390i
$157$	−6.33516	−	6.33516i	−0.505601	−	0.505601i	0.407572	−	0.913173i	$-0.366375\pi$
$157$	−6.33516	−	6.33516i	−0.505601	−	0.505601i	−0.913173	+	0.407572i	$0.866375\pi$
$158$	−4.71698	−	4.71698i	−0.375263	−	0.375263i
$159$	2.80039	+	2.95192i	0.222085	+	0.234103i
$160$	−0.0565714	−	2.23535i	−0.00447236	−	0.176720i
$161$			0.746742i			0.0588515i
$162$	6.99788	−	5.65948i	0.549805	−	0.444651i
$163$	−3.13303	+	3.13303i	−0.245398	+	0.245398i	−0.819079	−	0.573681i	$-0.805515\pi$
$163$	−3.13303	+	3.13303i	−0.245398	+	0.245398i	0.573681	+	0.819079i	$0.305515\pi$
$164$	4.23059			0.330353
$165$	−12.6040	−	12.6302i	−0.981224	−	0.983257i
$166$	−13.6943			−1.06288
$167$	5.90660	−	5.90660i	0.457067	−	0.457067i	−0.440625	−	0.897691i	$-0.645243\pi$
$167$	5.90660	−	5.90660i	0.457067	−	0.457067i	0.897691	+	0.440625i	$0.145243\pi$
$168$	0.0340607	−	1.29295i	0.00262784	−	0.0997529i
$169$		−	31.9337i		−	2.45644i
$170$	7.63113	+	7.25441i	0.585281	+	0.556388i
$171$	−0.823061	+	15.6109i	−0.0629410	+	1.19379i
$172$	7.82352	+	7.82352i	0.596538	+	0.596538i
$173$	−10.1099	−	10.1099i	−0.768643	−	0.768643i	0.209225	−	0.977868i	$-0.432906\pi$
$173$	−10.1099	−	10.1099i	−0.768643	−	0.768643i	−0.977868	+	0.209225i	$0.932906\pi$
$174$	−3.14888	+	2.98723i	−0.238716	+	0.226462i
$175$	2.50321	−	2.77030i	0.189225	−	0.209415i
$176$		−	4.60712i		−	0.347275i
$177$	−22.0585	−	0.581099i	−1.65802	−	0.0436781i
$178$	−6.41940	+	6.41940i	−0.481154	+	0.481154i
$179$	−10.7084			−0.800386			−0.400193	−	0.916431i	$-0.631057\pi$
$179$	−10.7084			−0.800386			−0.400193	+	0.916431i	$0.631057\pi$
$180$	4.61182	+	4.87146i	0.343744	+	0.363097i
$181$	19.3288			1.43670			0.718349	−	0.695683i	$-0.244898\pi$
$181$	19.3288			1.43670			0.718349	+	0.695683i	$0.244898\pi$
$182$	3.53949	−	3.53949i	0.262365	−	0.262365i
$183$	−2.61476	−	0.0688818i	−0.193288	−	0.00509189i
$184$		−	1.00000i		−	0.0737210i
$185$	22.3893	−	0.566619i	1.64609	−	0.0416587i
$186$	4.92542	−	4.67257i	0.361149	−	0.342610i
$187$	15.3397	+	15.3397i	1.12175	+	1.12175i
$188$	−2.42130	−	2.42130i	−0.176592	−	0.176592i
$189$	2.51858	+	2.95170i	0.183200	+	0.214705i
$190$	−11.6481	+	0.294785i	−0.845042	+	0.0213860i
$191$		−	16.3310i		−	1.18167i	−0.806792	−	0.590835i	$-0.798798\pi$
$191$		−	16.3310i		−	1.18167i	0.806792	−	0.590835i	$-0.201202\pi$
$192$	−0.0456124	+	1.73145i	−0.00329179	+	0.124957i
$193$	−4.44978	+	4.44978i	−0.320302	+	0.320302i	−0.848883	−	0.528581i	$-0.822724\pi$
$193$	−4.44978	+	4.44978i	−0.320302	+	0.320302i	0.528581	+	0.848883i	$0.322724\pi$
$194$	8.05432			0.578266
$195$	−0.0268747	+	25.9616i	−0.00192453	+	1.85915i
$196$	−6.44238			−0.460170
$197$	−19.0107	+	19.0107i	−1.35446	+	1.35446i	−0.473858	+	0.880601i	$0.657139\pi$
$197$	−19.0107	+	19.0107i	−1.35446	+	1.35446i	−0.880601	+	0.473858i	$0.842861\pi$
$198$	9.24506	+	10.2742i	0.657018	+	0.730154i
$199$			19.6455i			1.39263i	0.717737	+	0.696315i	$0.245178\pi$
$199$			19.6455i			1.39263i	−0.717737	+	0.696315i	$0.754822\pi$
$200$	−3.35217	+	3.70985i	−0.237034	+	0.262326i
$201$	−8.85081	−	9.32975i	−0.624288	−	0.658070i
$202$	−5.64988	−	5.64988i	−0.397524	−	0.397524i
$203$	−1.32319	−	1.32319i	−0.0928701	−	0.0928701i
$204$	−5.61312	−	5.91686i	−0.392997	−	0.414263i
$205$	−6.85624	−	6.51777i	−0.478860	−	0.455221i
$206$		−	11.8416i		−	0.825044i
$207$	2.00669	+	2.23007i	0.139475	+	0.155000i
$208$	−4.73992	+	4.73992i	−0.328654	+	0.328654i
$209$	−24.0070			−1.66060
$210$	−2.04715	+	2.04292i	−0.141267	+	0.140975i
$211$	−4.38087			−0.301592			−0.150796	−	0.988565i	$-0.548184\pi$
$211$	−4.38087			−0.301592			−0.150796	+	0.988565i	$0.548184\pi$
$212$	1.66113	−	1.66113i	0.114087	−	0.114087i
$213$	−0.498023	+	18.9050i	−0.0341239	+	1.29535i
$214$		−	15.3145i		−	1.04688i
$215$	−0.625914	−	24.7322i	−0.0426870	−	1.68672i
$216$	−3.37276	−	3.95278i	−0.229488	−	0.268953i
$217$	2.06972	+	2.06972i	0.140501	+	0.140501i
$218$	−4.10859	−	4.10859i	−0.278269	−	0.278269i
$219$	−9.87563	+	9.36867i	−0.667333	+	0.633076i
$220$	−7.09787	+	7.46646i	−0.478538	+	0.503388i
$221$		−	31.5638i		−	2.12321i
$222$	−17.3422	−	0.456854i	−1.16393	−	0.0306620i
$223$	8.23185	−	8.23185i	0.551245	−	0.551245i	−0.375555	−	0.926800i	$-0.622548\pi$
$223$	8.23185	−	8.23185i	0.551245	−	0.551245i	0.926800	+	0.375555i	$0.122548\pi$
$224$	−0.746742			−0.0498938
$225$	0.0310551	−	15.0000i	0.00207034	−	0.999998i
$226$	−0.882892			−0.0587291
$227$	−4.42457	+	4.42457i	−0.293669	+	0.293669i	−0.838528	−	0.544859i	$-0.816583\pi$
$227$	−4.42457	+	4.42457i	−0.293669	+	0.293669i	0.544859	+	0.838528i	$0.316583\pi$
$228$	9.02233	+	0.237680i	0.597519	+	0.0157407i
$229$			0.539521i			0.0356526i	0.999841	+	0.0178263i	$0.00567458\pi$
$229$			0.539521i			0.0356526i	−0.999841	+	0.0178263i	$0.994325\pi$
$230$	−1.54063	+	1.62063i	−0.101586	+	0.106861i
$231$	−4.32302	+	4.10110i	−0.284434	+	0.269833i
$232$	1.77196	+	1.77196i	0.116335	+	0.116335i
$233$	5.01691	+	5.01691i	0.328669	+	0.328669i	0.852080	−	0.523411i	$-0.175341\pi$
$233$	5.01691	+	5.01691i	0.328669	+	0.328669i	−0.523411	+	0.852080i	$0.675341\pi$
$234$	1.05879	−	20.0819i	0.0692151	−	1.31279i
$235$	0.193714	+	7.65439i	0.0126365	+	0.499317i
$236$			12.7399i			0.829299i
$237$	0.304272	−	11.5502i	0.0197646	−	0.750265i
$238$	2.48633	−	2.48633i	0.161165	−	0.161165i
$239$	−3.23606			−0.209324			−0.104662	−	0.994508i	$-0.533376\pi$
$239$	−3.23606			−0.209324			−0.104662	+	0.994508i	$0.533376\pi$
$240$	2.74145	−	2.73578i	0.176960	−	0.176594i
$241$	2.49371			0.160634			0.0803171	−	0.996769i	$-0.474407\pi$
$241$	2.49371			0.160634			0.0803171	+	0.996769i	$0.474407\pi$
$242$	−7.23056	+	7.23056i	−0.464798	+	0.464798i
$243$	15.4535	+	2.04687i	0.991342	+	0.131307i
$244$			1.51016i			0.0966778i
$245$	10.4407	+	9.92532i	0.667034	+	0.634106i
$246$	5.04315	+	5.31604i	0.321539	+	0.338939i
$247$	24.6990	+	24.6990i	1.57156	+	1.57156i
$248$	−2.77166	−	2.77166i	−0.176001	−	0.176001i
$249$	−16.3245	−	17.2078i	−1.03452	−	1.09050i
$250$	11.1481	−	0.847847i	0.705071	−	0.0536226i
$251$			5.39309i			0.340409i	0.985409	+	0.170205i	$0.0544428\pi$
$251$			5.39309i			0.340409i	−0.985409	+	0.170205i	$0.945557\pi$
$252$	1.66528	−	1.49848i	0.104903	−	0.0943953i
$253$	−3.25773	+	3.25773i	−0.204811	+	0.204811i
$254$	15.6063			0.979224
$255$	−0.0188782	+	18.2368i	−0.00118220	+	1.14203i
$256$	1.00000			0.0625000
$257$	0.454641	−	0.454641i	0.0283597	−	0.0283597i	−0.692785	−	0.721144i	$-0.743616\pi$
$257$	0.454641	−	0.454641i	0.0283597	−	0.0283597i	0.721144	+	0.692785i	$0.243616\pi$
$258$	−0.504662	+	19.1570i	−0.0314189	+	1.19266i
$259$		−	7.47937i		−	0.464745i
$260$	14.9841	−	0.379213i	0.929277	−	0.0235178i
$261$	−7.50735	−	0.395814i	−0.464693	−	0.0245003i
$262$	−6.96669	−	6.96669i	−0.430404	−	0.430404i
$263$	−10.1010	−	10.1010i	−0.622853	−	0.622853i	0.323407	−	0.946260i	$-0.395172\pi$
$263$	−10.1010	−	10.1010i	−0.622853	−	0.622853i	−0.946260	+	0.323407i	$0.895172\pi$
$264$	5.78918	−	5.49200i	0.356300	−	0.338009i
$265$	−5.25126	+	0.132897i	−0.322582	+	0.00816379i
$266$			3.89116i			0.238582i
$267$	−15.7188	−	0.414088i	−0.961975	−	0.0253418i
$268$	−5.25010	+	5.25010i	−0.320701	+	0.320701i
$269$	−23.4948			−1.43250			−0.716252	−	0.697842i	$-0.754144\pi$
$269$	−23.4948			−1.43250			−0.716252	+	0.697842i	$0.754144\pi$
$270$	−0.623753	+	11.6022i	−0.0379604	+	0.706087i
$271$	−6.16572			−0.374541			−0.187270	−	0.982308i	$-0.559964\pi$
$271$	−6.16572			−0.374541			−0.187270	+	0.982308i	$0.559964\pi$
$272$	−3.32957	+	3.32957i	−0.201885	+	0.201885i
$273$	8.66695	+	0.228318i	0.524548	+	0.0138184i
$274$			10.7405i			0.648858i
$275$	23.0061	−	1.16521i	1.38732	−	0.0702645i
$276$	1.25657	−	1.19207i	0.0756368	−	0.0717540i
$277$	16.3851	+	16.3851i	0.984482	+	0.984482i	0.999881	−	0.0153991i	$-0.00490187\pi$
$277$	16.3851	+	16.3851i	0.984482	+	0.984482i	−0.0153991	+	0.999881i	$0.504902\pi$
$278$	10.3667	+	10.3667i	0.621752	+	0.621752i
$279$	11.7429	+	0.619125i	0.703026	+	0.0370660i
$280$	1.21020	+	1.15045i	0.0723230	+	0.0687527i
$281$		−	0.344451i		−	0.0205482i	−0.999947	−	0.0102741i	$-0.996730\pi$
$281$		−	0.344451i		−	0.0205482i	0.999947	−	0.0102741i	$-0.00327041\pi$
$282$	0.156188	−	5.92890i	0.00930086	−	0.353061i
$283$	−1.89935	+	1.89935i	−0.112905	+	0.112905i	−0.761302	−	0.648397i	$-0.775440\pi$
$283$	−1.89935	+	1.89935i	−0.112905	+	0.112905i	0.648397	+	0.761302i	$0.275440\pi$
$284$	10.9186			0.647898
$285$	−14.2557	−	14.2853i	−0.844437	−	0.846187i
$286$	30.8827			1.82613
$287$	−2.23386	+	2.23386i	−0.131861	+	0.131861i
$288$	−2.23007	+	2.00669i	−0.131408	+	0.118245i
$289$		−	5.17214i		−	0.304243i
$290$	−0.141764	−	5.60163i	−0.00832466	−	0.328939i
$291$	9.60129	+	10.1208i	0.562838	+	0.593294i
$292$	5.55728	+	5.55728i	0.325215	+	0.325215i
$293$	−0.184488	−	0.184488i	−0.0107779	−	0.0107779i	0.701697	−	0.712475i	$-0.252426\pi$
$293$	−0.184488	−	0.184488i	−0.0107779	−	0.0107779i	−0.712475	+	0.701697i	$0.752426\pi$
$294$	−7.67975	−	8.09532i	−0.447892	−	0.472128i
$295$	19.6275	−	20.6468i	1.14276	−	1.20210i
$296$			10.0160i			0.582168i
$297$	−1.88953	+	23.8646i	−0.109642	+	1.38477i
$298$	−4.11463	+	4.11463i	−0.238354	+	0.238354i
$299$	6.70326			0.387659
$300$	−8.65770	+	0.210138i	−0.499853	+	0.0121323i
$301$	−8.26205			−0.476217
$302$	1.96613	−	1.96613i	0.113138	−	0.113138i
$303$	0.364450	−	13.8345i	0.0209371	−	0.794773i
$304$		−	5.21085i		−	0.298863i
$305$	2.32659	−	2.44741i	0.133220	−	0.140138i
$306$	0.743750	−	14.1066i	0.0425173	−	0.806420i
$307$	−5.11094	−	5.11094i	−0.291697	−	0.291697i	0.546054	−	0.837750i	$-0.316130\pi$
$307$	−5.11094	−	5.11094i	−0.291697	−	0.291697i	−0.837750	+	0.546054i	$0.816130\pi$
$308$	2.43268	+	2.43268i	0.138615	+	0.138615i
$309$	14.8798	−	14.1160i	0.846484	−	0.803031i
$310$	0.221744	+	8.76196i	0.0125942	+	0.497646i
$311$			13.3425i			0.756584i	0.925686	+	0.378292i	$0.123489\pi$
$311$			13.3425i			0.756584i	−0.925686	+	0.378292i	$0.876511\pi$
$312$	−11.6064	−	0.305752i	−0.657081	−	0.0173098i
$313$	5.87924	−	5.87924i	0.332314	−	0.332314i	−0.521151	−	0.853465i	$-0.674497\pi$
$313$	5.87924	−	5.87924i	0.332314	−	0.332314i	0.853465	+	0.521151i	$0.174497\pi$
$314$	−8.95927			−0.505601
$315$	−5.00742	−	0.137100i	−0.282136	−	0.00772471i
$316$	−6.67082			−0.375263
$317$	15.0768	−	15.0768i	0.846797	−	0.846797i	−0.142935	−	0.989732i	$-0.545654\pi$
$317$	15.0768	−	15.0768i	0.846797	−	0.846797i	0.989732	+	0.142935i	$0.0456540\pi$
$318$	4.06750	+	0.107152i	0.228094	+	0.00600879i
$319$		−	11.5451i		−	0.646402i
$320$	−1.62063	−	1.54063i	−0.0905962	−	0.0861239i
$321$	19.2438	−	18.2559i	1.07408	−	1.01895i
$322$	0.528026	+	0.528026i	0.0294257	+	0.0294257i
$323$	17.3499	+	17.3499i	0.965376	+	0.965376i
$324$	0.946393	−	8.95010i	0.0525774	−	0.497228i
$325$	−24.8680	−	22.4705i	−1.37943	−	1.24644i
$326$			4.43077i			0.245398i
$327$	0.265027	−	10.0605i	0.0146561	−	0.556345i
$328$	2.99148	−	2.99148i	0.165177	−	0.165177i
$329$	2.55702			0.140973
$330$	−17.8433	−	0.0184708i	−0.982241	−	0.00101679i
$331$	18.7391			1.02999			0.514996	−	0.857192i	$-0.327793\pi$
$331$	18.7391			1.02999			0.514996	+	0.857192i	$0.327793\pi$
$332$	−9.68331	+	9.68331i	−0.531441	+	0.531441i
$333$	−20.0990	−	22.3363i	−1.10142	−	1.22402i
$334$		−	8.35320i		−	0.457067i
$335$	16.5970	−	0.420029i	0.906788	−	0.0229487i
$336$	−0.890166	−	0.938335i	−0.0485626	−	0.0511904i
$337$	11.5783	+	11.5783i	0.630712	+	0.630712i	0.948247	−	0.317535i	$-0.102855\pi$
$337$	11.5783	+	11.5783i	0.630712	+	0.630712i	−0.317535	+	0.948247i	$0.602855\pi$
$338$	−22.5805	−	22.5805i	−1.22822	−	1.22822i
$339$	−1.05247	−	1.10942i	−0.0571621	−	0.0602553i
$340$	10.5257	−	0.266380i	0.570835	−	0.0144465i
$341$			18.0586i			0.977929i
$342$	10.4566	+	11.6206i	0.565426	+	0.628367i
$343$	7.09793	−	7.09793i	0.383252	−	0.383252i
$344$	11.0641			0.596538
$345$	−3.87298	−	0.00400919i	−0.208514	−	0.000215848i
$346$	−14.2976			−0.768643
$347$	9.53609	−	9.53609i	0.511924	−	0.511924i	−0.403191	−	0.915116i	$-0.632099\pi$
$347$	9.53609	−	9.53609i	0.511924	−	0.511924i	0.915116	+	0.403191i	$0.132099\pi$
$348$	−0.114301	+	4.33889i	−0.00612720	+	0.232589i
$349$		−	22.7071i		−	1.21549i	−0.794134	−	0.607743i	$-0.792075\pi$
$349$		−	22.7071i		−	1.21549i	0.794134	−	0.607743i	$-0.207925\pi$
$350$	−0.188862	−	3.72893i	−0.0100951	−	0.199320i
$351$	26.4965	−	22.6085i	1.41428	−	1.20675i
$352$	−3.25773	−	3.25773i	−0.173637	−	0.173637i
$353$	20.2080	+	20.2080i	1.07556	+	1.07556i	0.996902	+	0.0786597i	$0.0250641\pi$
$353$	20.2080	+	20.2080i	1.07556	+	1.07556i	0.0786597	+	0.996902i	$0.474936\pi$
$354$	−16.0086	+	15.1868i	−0.850850	+	0.807172i
$355$	−17.6950	−	16.8215i	−0.939155	−	0.892792i
$356$			9.07840i			0.481154i
$357$	6.08813	+	0.160383i	0.322218	+	0.00848835i
$358$	−7.57201	+	7.57201i	−0.400193	+	0.400193i
$359$	9.55317			0.504197			0.252098	−	0.967702i	$-0.418879\pi$
$359$	9.55317			0.504197			0.252098	+	0.967702i	$0.418879\pi$
$360$	6.70569	+	0.183598i	0.353421	+	0.00967645i
$361$	−8.15300			−0.429105
$362$	13.6675	−	13.6675i	0.718349	−	0.718349i
$363$	−17.7050	−	0.466412i	−0.929273	−	0.0244803i
$364$		−	5.00560i		−	0.262365i
$365$	−0.444605	−	17.5680i	−0.0232717	−	0.919552i
$366$	−1.89762	+	1.80021i	−0.0991902	+	0.0940983i
$367$	−15.8937	−	15.8937i	−0.829645	−	0.829645i	0.157823	−	0.987467i	$-0.449553\pi$
$367$	−15.8937	−	15.8937i	−0.829645	−	0.829645i	−0.987467	+	0.157823i	$0.949553\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	−0.668227	+	12.6742i	−0.0347865	+	0.659790i
$370$	15.4310	−	16.2323i	0.802217	−	0.843876i
$371$			1.75424i			0.0910754i
$372$	0.178788	−	6.78680i	0.00926972	−	0.351879i
$373$	21.9117	−	21.9117i	1.13455	−	1.13455i	0.145135	−	0.989412i	$-0.453638\pi$
$373$	21.9117	−	21.9117i	1.13455	−	1.13455i	0.989412	−	0.145135i	$-0.0463617\pi$
$374$	21.6937			1.12175
$375$	14.3547	+	12.9978i	0.741275	+	0.671202i
$376$	−3.42424			−0.176592
$377$	−11.8779	+	11.8779i	−0.611742	+	0.611742i
$378$	3.86808	+	0.306263i	0.198952	+	0.0157525i
$379$			3.01254i			0.154744i	0.997002	+	0.0773719i	$0.0246529\pi$
$379$			3.01254i			0.154744i	−0.997002	+	0.0773719i	$0.975347\pi$
$380$	−8.02800	+	8.44489i	−0.411828	+	0.433214i
$381$	18.6037	+	19.6104i	0.953098	+	1.00467i
$382$	−11.5478	−	11.5478i	−0.590835	−	0.590835i
$383$	17.7386	+	17.7386i	0.906400	+	0.906400i	0.995980	−	0.0895800i	$-0.0285525\pi$
$383$	17.7386	+	17.7386i	0.906400	+	0.906400i	−0.0895800	+	0.995980i	$0.528552\pi$
$384$	1.19207	+	1.25657i	0.0608324	+	0.0641242i
$385$	−0.194624	−	7.69035i	−0.00991897	−	0.391936i
$386$			6.29293i			0.320302i
$387$	−24.6738	+	22.2023i	−1.25424	+	1.12861i
$388$	5.69526	−	5.69526i	0.289133	−	0.289133i
$389$	20.0679			1.01748			0.508742	−	0.860919i	$-0.330111\pi$
$389$	20.0679			1.01748			0.508742	+	0.860919i	$0.330111\pi$
$390$	18.3386	+	18.3766i	0.928612	+	0.930536i
$391$	4.70873			0.238131
$392$	−4.55545	+	4.55545i	−0.230085	+	0.230085i
$393$	0.449391	−	17.0589i	0.0226688	−	0.860509i
$394$			26.8853i			1.35446i
$395$	10.8110	+	10.2773i	0.543958	+	0.517105i
$396$	13.8022	+	0.727700i	0.693586	+	0.0365683i
$397$	26.1076	+	26.1076i	1.31030	+	1.31030i	0.921190	+	0.389114i	$0.127219\pi$
$397$	26.1076	+	26.1076i	1.31030	+	1.31030i	0.389114	+	0.921190i	$0.372781\pi$
$398$	13.8914	+	13.8914i	0.696315	+	0.696315i
$399$	−4.88953	+	4.63853i	−0.244783	+	0.232217i
$400$	0.252914	+	4.99360i	0.0126457	+	0.249680i
$401$		−	21.9907i		−	1.09816i	−0.835769	−	0.549082i	$-0.814978\pi$
$401$		−	21.9907i		−	1.09816i	0.835769	−	0.549082i	$-0.185022\pi$
$402$	−12.8556	−	0.338661i	−0.641179	−	0.0168909i
$403$	18.5792	−	18.5792i	0.925494	−	0.925494i
$404$	−7.99014			−0.397524
$405$	−15.3226	+	13.0468i	−0.761384	+	0.648301i
$406$	−1.87128			−0.0928701
$407$	32.6294	−	32.6294i	1.61738	−	1.61738i
$408$	−8.15293	−	0.214777i	−0.403630	−	0.0106330i
$409$		−	38.2076i		−	1.88924i	−0.328159	−	0.944622i	$-0.606428\pi$
$409$		−	38.2076i		−	1.88924i	0.328159	−	0.944622i	$-0.393572\pi$
$410$	−9.45685	+	0.239330i	−0.467041	+	0.0118197i
$411$	−13.4962	+	12.8034i	−0.665721	+	0.631546i
$412$	−8.37328	−	8.37328i	−0.412522	−	0.412522i
$413$	−6.72701	−	6.72701i	−0.331015	−	0.331015i
$414$	2.99584	+	0.157951i	0.147237	+	0.00776288i
$415$	30.6115	−	0.774704i	1.50266	−	0.0380287i
$416$			6.70326i			0.328654i
$417$	−0.668710	+	25.3843i	−0.0327469	+	1.24307i
$418$	−16.9755	+	16.9755i	−0.830300	+	0.830300i
$419$	−9.14872			−0.446944			−0.223472	−	0.974710i	$-0.571739\pi$
$419$	−9.14872			−0.446944			−0.223472	+	0.974710i	$0.571739\pi$
$420$	−0.00299383	+	2.89212i	−0.000146084	+	0.141121i
$421$	−28.4290			−1.38554			−0.692772	−	0.721157i	$-0.743611\pi$
$421$	−28.4290			−1.38554			−0.692772	+	0.721157i	$0.743611\pi$
$422$	−3.09774	+	3.09774i	−0.150796	+	0.150796i
$423$	7.63629	−	6.87139i	0.371289	−	0.334099i
$424$		−	2.34919i		−	0.114087i
$425$	−17.4687	−	15.7845i	−0.847354	−	0.765659i
$426$	13.0157	+	13.7200i	0.630612	+	0.664736i
$427$	−0.797401	−	0.797401i	−0.0385890	−	0.0385890i
$428$	−10.8290	−	10.8290i	−0.523439	−	0.523439i
$429$	36.8143	+	38.8064i	1.77741	+	1.87359i
$430$	−17.9309	−	17.0457i	−0.864706	−	0.822019i
$431$		−	11.1238i		−	0.535814i	−0.963445	−	0.267907i	$-0.913668\pi$
$431$		−	11.1238i		−	0.535814i	0.963445	−	0.267907i	$-0.0863321\pi$
$432$	−5.17994	−	0.410132i	−0.249220	−	0.0197325i
$433$	−20.0373	+	20.0373i	−0.962929	+	0.962929i	−0.999337	−	0.0364075i	$-0.988409\pi$
$433$	−20.0373	+	20.0373i	−0.962929	+	0.962929i	0.0364075	+	0.999337i	$0.488409\pi$
$434$	2.92702			0.140501
$435$	6.86986	−	6.85565i	0.329385	−	0.328703i
$436$	−5.81042			−0.278269
$437$	−3.68463	+	3.68463i	−0.176260	+	0.176260i
$438$	−0.358476	+	13.6078i	−0.0171286	+	0.650204i
$439$			13.8002i			0.658647i	0.944217	+	0.329324i	$0.106821\pi$
$439$			13.8002i			0.658647i	−0.944217	+	0.329324i	$0.893179\pi$
$440$	0.260631	+	10.2985i	0.0124251	+	0.490963i
$441$	1.01758	−	19.3003i	0.0484563	−	0.919063i
$442$	−22.3190	−	22.3190i	−1.06161	−	1.06161i
$443$	−4.08292	−	4.08292i	−0.193986	−	0.193986i	0.603430	−	0.797416i	$-0.293800\pi$
$443$	−4.08292	−	4.08292i	−0.193986	−	0.193986i	−0.797416	+	0.603430i	$0.793800\pi$
$444$	−12.5858	+	11.9397i	−0.597297	+	0.566635i
$445$	13.9865	−	14.7128i	0.663022	−	0.697452i
$446$		−	11.6416i		−	0.551245i
$447$	−10.0753	−	0.265417i	−0.476543	−	0.0125538i
$448$	−0.528026	+	0.528026i	−0.0249469	+	0.0249469i
$449$	5.80447			0.273930			0.136965	−	0.990576i	$-0.456265\pi$
$449$	5.80447			0.273930			0.136965	+	0.990576i	$0.456265\pi$
$450$	−10.5846	−	10.6285i	−0.498964	−	0.501034i
$451$	−19.4908			−0.917787
$452$	−0.624299	+	0.624299i	−0.0293645	+	0.0293645i
$453$	4.81433	+	0.126826i	0.226197	+	0.00595882i
$454$			6.25729i			0.293669i
$455$	−7.71178	+	8.11225i	−0.361534	+	0.380308i
$456$	6.54782	−	6.21169i	0.306630	−	0.290889i
$457$	−3.04689	−	3.04689i	−0.142528	−	0.142528i	0.632243	−	0.774770i	$-0.282135\pi$
$457$	−3.04689	−	3.04689i	−0.142528	−	0.142528i	−0.774770	+	0.632243i	$0.782135\pi$
$458$	0.381499	+	0.381499i	0.0178263	+	0.0178263i
$459$	18.6126	−	15.8814i	0.868760	−	0.741282i
$460$	0.0565714	+	2.23535i	0.00263766	+	0.104224i
$461$			10.8450i			0.505103i	0.967583	+	0.252551i	$0.0812697\pi$
$461$			10.8450i			0.505103i	−0.967583	+	0.252551i	$0.918730\pi$
$462$	−0.156922	+	5.95676i	−0.00730066	+	0.277133i
$463$	−0.966000	+	0.966000i	−0.0448939	+	0.0448939i	−0.729197	−	0.684303i	$-0.760106\pi$
$463$	−0.966000	+	0.966000i	−0.0448939	+	0.0448939i	0.684303	+	0.729197i	$0.260106\pi$
$464$	2.50593			0.116335
$465$	−10.7457	+	10.7235i	−0.498320	+	0.497290i
$466$	7.09498			0.328669
$467$	4.97855	−	4.97855i	0.230380	−	0.230380i	−0.582471	−	0.812851i	$-0.697914\pi$
$467$	4.97855	−	4.97855i	0.230380	−	0.230380i	0.812851	+	0.582471i	$0.197914\pi$
$468$	−13.4514	−	14.9487i	−0.621789	−	0.691004i
$469$		−	5.54438i		−	0.256016i
$470$	5.54945	+	5.27549i	0.255977	+	0.243340i
$471$	−10.6800	−	11.2580i	−0.492111	−	0.518740i
$472$	9.00849	+	9.00849i	0.414649	+	0.414649i
$473$	−36.0439	−	36.0439i	−1.65730	−	1.65730i
$474$	−7.95206	−	8.38237i	−0.365250	−	0.385015i
$475$	26.0209	−	1.31790i	1.19392	−	0.0604693i
$476$		−	3.51621i		−	0.161165i
$477$	4.71409	+	5.23884i	0.215843	+	0.239870i
$478$	−2.28824	+	2.28824i	−0.104662	+	0.104662i
$479$	−19.7275			−0.901373			−0.450686	−	0.892682i	$-0.648821\pi$
$479$	−19.7275			−0.901373			−0.450686	+	0.892682i	$0.648821\pi$
$480$	0.00400919	−	3.87298i	0.000182994	−	0.176777i
$481$	−67.1398			−3.06131
$482$	1.76332	−	1.76332i	0.0803171	−	0.0803171i
$483$	−0.0340607	+	1.29295i	−0.00154981	+	0.0588311i
$484$			10.2255i			0.464798i
$485$	−18.0042	+	0.455644i	−0.817530	+	0.0206897i
$486$	12.3746	−	9.47991i	0.561324	−	0.430018i
$487$	5.32308	+	5.32308i	0.241212	+	0.241212i	0.817351	−	0.576140i	$-0.195442\pi$
$487$	5.32308	+	5.32308i	0.241212	+	0.241212i	−0.576140	+	0.817351i	$0.695442\pi$
$488$	1.06784	+	1.06784i	0.0483389	+	0.0483389i
$489$	−5.56758	+	5.28177i	−0.251775	+	0.238850i
$490$	14.4010	−	0.364454i	0.650570	−	0.0164644i
$491$			6.35205i			0.286664i	0.989675	+	0.143332i	$0.0457817\pi$
$491$			6.35205i			0.286664i	−0.989675	+	0.143332i	$0.954218\pi$
$492$	7.32505	+	0.192967i	0.330239	+	0.00869964i
$493$	−8.34367	+	8.34367i	−0.375780	+	0.375780i
$494$	34.9297			1.57156
$495$	−21.2472	−	22.4434i	−0.954990	−	1.00876i
$496$	−3.91972			−0.176001
$497$	−5.76529	+	5.76529i	−0.258609	+	0.258609i
$498$	−23.7109	−	0.624629i	−1.06251	−	0.0279903i
$499$			26.5555i			1.18879i	0.804174	+	0.594394i	$0.202608\pi$
$499$			26.5555i			1.18879i	−0.804174	+	0.594394i	$0.797392\pi$
$500$	7.28341	−	8.48245i	0.325724	−	0.379347i
$501$	10.4964	−	9.95758i	0.468945	−	0.444872i
$502$	3.81349	+	3.81349i	0.170205	+	0.170205i
$503$	20.7736	+	20.7736i	0.926248	+	0.926248i	0.997461	−	0.0712128i	$-0.0226869\pi$
$503$	20.7736	+	20.7736i	0.926248	+	0.926248i	−0.0712128	+	0.997461i	$0.522687\pi$
$504$	0.117949	−	2.23712i	0.00525386	−	0.0996492i
$505$	12.9491	+	12.3099i	0.576227	+	0.547781i
$506$			4.60712i			0.204811i
$507$	1.45657	−	55.2915i	0.0646886	−	2.45558i
$508$	11.0353	−	11.0353i	0.489612	−	0.489612i
$509$	3.09578			0.137218			0.0686090	−	0.997644i	$-0.478144\pi$
$509$	3.09578			0.137218			0.0686090	+	0.997644i	$0.478144\pi$
$510$	12.8820	+	12.9087i	0.570426	+	0.571608i
$511$	−5.86877			−0.259619
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.13714	+	26.9919i	−0.0943570	+	1.19172i
$514$		−	0.642960i		−	0.0283597i
$515$	0.669896	+	26.4702i	0.0295192	+	1.16641i
$516$	13.1892	+	13.9029i	0.580622	+	0.612041i
$517$	11.1552	+	11.1552i	0.490607	+	0.490607i
$518$	−5.28871	−	5.28871i	−0.232373	−	0.232373i
$519$	−17.0437	−	17.9660i	−0.748134	−	0.788618i
$520$	10.3272	−	10.8635i	0.452880	−	0.476397i
$521$			7.99544i			0.350287i	0.984543	+	0.175143i	$0.0560389\pi$
$521$			7.99544i			0.350287i	−0.984543	+	0.175143i	$0.943961\pi$
$522$	−5.58838	+	5.02862i	−0.244597	+	0.220097i
$523$	−16.4846	+	16.4846i	−0.720823	+	0.720823i	−0.968773	−	0.247950i	$-0.920243\pi$
$523$	−16.4846	+	16.4846i	−0.720823	+	0.720823i	0.247950	+	0.968773i	$0.420243\pi$
$524$	−9.85239			−0.430404
$525$	4.46054	−	4.68245i	0.194674	−	0.204359i
$526$	−14.2850			−0.622853
$527$	13.0510	−	13.0510i	0.568511	−	0.568511i
$528$	0.210142	−	7.97700i	0.00914525	−	0.347154i
$529$			1.00000i			0.0434783i
$530$	−3.61923	+	3.80717i	−0.157209	+	0.165373i
$531$	−38.1668	−	2.01229i	−1.65630	−	0.0873258i
$532$	2.75147	+	2.75147i	0.119291	+	0.119291i
$533$	20.0526	+	20.0526i	0.868576	+	0.868576i
$534$	−11.4077	+	10.8221i	−0.493658	+	0.468317i
$535$	0.866363	+	34.2333i	0.0374561	+	1.48003i
$536$			7.42476i			0.320701i
$537$	−18.5411	−	0.488437i	−0.800108	−	0.0210776i
$538$	−16.6133	+	16.6133i	−0.716252	+	0.716252i
$539$	29.6808			1.27844
$540$	7.76293	+	8.64505i	0.334063	+	0.372024i
$541$	−19.2338			−0.826927			−0.413463	−	0.910521i	$-0.635681\pi$
$541$	−19.2338			−0.826927			−0.413463	+	0.910521i	$0.635681\pi$
$542$	−4.35982	+	4.35982i	−0.187270	+	0.187270i
$543$	33.4668	+	0.881633i	1.43620	+	0.0378345i
$544$			4.70873i			0.201885i
$545$	9.41658	+	8.95172i	0.403362	+	0.383450i
$546$	6.28990	−	5.96701i	0.269183	−	0.255365i
$547$	−18.7883	−	18.7883i	−0.803330	−	0.803330i	0.180284	−	0.983615i	$-0.442298\pi$
$547$	−18.7883	−	18.7883i	−0.803330	−	0.803330i	−0.983615	+	0.180284i	$0.942298\pi$
$548$	7.59469	+	7.59469i	0.324429	+	0.324429i
$549$	−4.52418	−	0.238531i	−0.193087	−	0.0101802i
$550$	15.4439	−	17.0917i	0.658528	−	0.728793i
$551$		−	13.0580i		−	0.556290i
$552$	0.0456124	−	1.73145i	0.00194139	−	0.0736954i
$553$	3.52237	−	3.52237i	0.149786	−	0.149786i
$554$	23.1720			0.984482
$555$	38.7918	+	0.0401561i	1.64662	+	0.00170453i
$556$	14.6607			0.621752
$557$	17.0441	−	17.0441i	0.722182	−	0.722182i	−0.246867	−	0.969049i	$-0.579401\pi$
$557$	17.0441	−	17.0441i	0.722182	−	0.722182i	0.969049	+	0.246867i	$0.0794012\pi$
$558$	8.74124	−	7.86566i	0.370046	−	0.332980i
$559$			74.1657i			3.13688i
$560$	1.66923	−	0.0422442i	0.0705379	−	0.00178515i
$561$	25.8603	+	27.2597i	1.09182	+	1.15091i
$562$	−0.243563	−	0.243563i	−0.0102741	−	0.0102741i
$563$	3.36582	+	3.36582i	0.141852	+	0.141852i	0.774467	−	0.632614i	$-0.218018\pi$
$563$	3.36582	+	3.36582i	0.141852	+	0.141852i	−0.632614	+	0.774467i	$0.718018\pi$
$564$	−4.08193	−	4.30281i	−0.171880	−	0.181181i
$565$	1.97357	−	0.0499465i	0.0830289	−	0.00210126i
$566$			2.68608i			0.112905i
$567$	4.22617	+	5.22561i	0.177482	+	0.219455i
$568$	7.72060	−	7.72060i	0.323949	−	0.323949i
$569$	34.6119			1.45100			0.725502	−	0.688220i	$-0.241607\pi$
$569$	34.6119			1.45100			0.725502	+	0.688220i	$0.241607\pi$
$570$	−20.1815	−	0.0208913i	−0.845312	−	0.000875042i
$571$	10.0717			0.421486			0.210743	−	0.977541i	$-0.432412\pi$
$571$	10.0717			0.421486			0.210743	+	0.977541i	$0.432412\pi$
$572$	21.8374	−	21.8374i	0.913066	−	0.913066i
$573$	0.744897	−	28.2763i	0.0311185	−	1.18126i
$574$			3.15916i			0.131861i
$575$	3.35217	−	3.70985i	0.139795	−	0.154711i
$576$	−0.157951	+	2.99584i	−0.00658130	+	0.124827i
$577$	22.9930	+	22.9930i	0.957209	+	0.957209i	0.999121	−	0.0419120i	$-0.0133449\pi$
$577$	22.9930	+	22.9930i	0.957209	+	0.957209i	−0.0419120	+	0.999121i	$0.513345\pi$
$578$	−3.65725	−	3.65725i	−0.152122	−	0.152122i
$579$	−7.90753	+	7.50160i	−0.328626	+	0.311756i
$580$	−4.06119	−	3.86071i	−0.168632	−	0.160307i
$581$		−	10.2261i		−	0.424249i
$582$	13.9457	+	0.367377i	0.578066	+	0.0152283i
$583$	−7.65301	+	7.65301i	−0.316955	+	0.316955i
$584$	7.85918			0.325215
$585$	−1.23070	+	44.9500i	−0.0508833	+	1.85845i
$586$	−0.260905			−0.0107779
$587$	−27.0582	+	27.0582i	−1.11681	+	1.11681i	−0.124605	+	0.992206i	$0.539766\pi$
$587$	−27.0582	+	27.0582i	−1.11681	+	1.11681i	−0.992206	+	0.124605i	$0.960234\pi$
$588$	−11.1547	−	0.293852i	−0.460010	−	0.0121183i
$589$			20.4251i			0.841601i
$590$	−0.720716	−	28.4782i	−0.0296714	−	1.17243i
$591$	−33.7833	+	32.0490i	−1.38966	+	1.31832i
$592$	7.08238	+	7.08238i	0.291084	+	0.291084i
$593$	−4.06419	−	4.06419i	−0.166896	−	0.166896i	0.618717	−	0.785614i	$-0.287653\pi$
$593$	−4.06419	−	4.06419i	−0.166896	−	0.166896i	−0.785614	+	0.618717i	$0.787653\pi$
$594$	15.5387	+	18.2109i	0.637562	+	0.747203i
$595$	−5.41717	+	5.69848i	−0.222082	+	0.233615i
$596$			5.81897i			0.238354i
$597$	−0.896076	+	34.0151i	−0.0366740	+	1.39215i
$598$	4.73992	−	4.73992i	0.193830	−	0.193830i
$599$	3.30686			0.135115			0.0675574	−	0.997715i	$-0.478479\pi$
$599$	3.30686			0.135115			0.0675574	+	0.997715i	$0.478479\pi$
$600$	−5.97333	+	6.27051i	−0.243860	+	0.255993i
$601$	9.16480			0.373840			0.186920	−	0.982375i	$-0.440149\pi$
$601$	9.16480			0.373840			0.186920	+	0.982375i	$0.440149\pi$
$602$	−5.84215	+	5.84215i	−0.238108	+	0.238108i
$603$	−14.8992	−	16.5577i	−0.606742	−	0.674282i
$604$		−	2.78052i		−	0.113138i
$605$	15.7538	−	16.5719i	0.640483	−	0.673743i
$606$	−9.52479	−	10.0402i	−0.386918	−	0.407855i
$607$	−22.2691	−	22.2691i	−0.903875	−	0.903875i	0.0918938	−	0.995769i	$-0.470708\pi$
$607$	−22.2691	−	22.2691i	−0.903875	−	0.903875i	−0.995769	+	0.0918938i	$0.970708\pi$
$608$	−3.68463	−	3.68463i	−0.149431	−	0.149431i
$609$	−2.23069	−	2.35140i	−0.0903922	−	0.0952835i
$610$	−0.0854316	−	3.37573i	−0.00345903	−	0.136679i
$611$		−	22.9536i		−	0.928602i
$612$	−9.44896	−	10.5008i	−0.381952	−	0.424469i
$613$	5.89129	−	5.89129i	0.237947	−	0.237947i	−0.578053	−	0.816000i	$-0.696187\pi$
$613$	5.89129	−	5.89129i	0.237947	−	0.237947i	0.816000	+	0.578053i	$0.196187\pi$
$614$	−7.22796			−0.291697
$615$	−11.5739	−	11.5979i	−0.466706	−	0.467674i
$616$	3.44033			0.138615
$617$	−21.2085	+	21.2085i	−0.853823	+	0.853823i	−0.990602	−	0.136778i	$-0.956325\pi$
$617$	−21.2085	+	21.2085i	−0.853823	+	0.853823i	0.136778	+	0.990602i	$0.456325\pi$
$618$	0.540124	−	20.5031i	0.0217270	−	0.824758i
$619$		−	6.49659i		−	0.261120i	−0.991440	−	0.130560i	$-0.958322\pi$
$619$		−	6.49659i		−	0.261120i	0.991440	−	0.130560i	$-0.0416775\pi$
$620$	6.35244	+	6.03884i	0.255120	+	0.242526i
$621$	3.37276	+	3.95278i	0.135344	+	0.158620i
$622$	9.43458	+	9.43458i	0.378292	+	0.378292i
$623$	−4.79363	−	4.79363i	−0.192053	−	0.192053i
$624$	−8.42313	+	7.99073i	−0.337195	+	0.319885i
$625$	−24.8721	+	2.52590i	−0.994883	+	0.101036i
$626$		−	8.31450i		−	0.332314i
$627$	−41.5670	−	1.09502i	−1.66002	−	0.0437308i
$628$	−6.33516	+	6.33516i	−0.252800	+	0.252800i
$629$	−47.1626			−1.88050
$630$	−3.63772	+	3.44384i	−0.144930	+	0.137206i
$631$	−18.5689			−0.739217			−0.369609	−	0.929188i	$-0.620508\pi$
$631$	−18.5689			−0.739217			−0.369609	+	0.929188i	$0.620508\pi$
$632$	−4.71698	+	4.71698i	−0.187631	+	0.187631i
$633$	−7.58526	−	0.199822i	−0.301487	−	0.00794222i
$634$		−	21.3218i		−	0.846797i
$635$	−34.8855	+	0.882869i	−1.38439	+	0.0350356i
$636$	2.95192	−	2.80039i	0.117051	−	0.111043i
$637$	−30.5363	−	30.5363i	−1.20989	−	1.20989i
$638$	−8.16362	−	8.16362i	−0.323201	−	0.323201i
$639$	−1.72460	+	32.7103i	−0.0682242	+	1.29400i
$640$	−2.23535	+	0.0565714i	−0.0883601	+	0.00223618i
$641$			21.0110i			0.829884i	0.909848	+	0.414942i	$0.136198\pi$
$641$			21.0110i			0.829884i	−0.909848	+	0.414942i	$0.863802\pi$
$642$	0.698531	−	26.5163i	0.0275688	−	1.04651i
$643$	−23.8932	+	23.8932i	−0.942254	+	0.942254i	−0.998421	−	0.0561671i	$-0.982112\pi$
$643$	−23.8932	+	23.8932i	−0.942254	+	0.942254i	0.0561671	+	0.998421i	$0.482112\pi$
$644$	0.746742			0.0294257
$645$	0.0443583	−	42.8512i	0.00174661	−	1.68726i
$646$	24.5365			0.965376
$647$	1.33655	−	1.33655i	0.0525450	−	0.0525450i	−0.680346	−	0.732891i	$-0.738170\pi$
$647$	1.33655	−	1.33655i	0.0525450	−	0.0525450i	0.732891	+	0.680346i	$0.238170\pi$
$648$	−5.65948	−	6.99788i	−0.222325	−	0.274903i
$649$		−	58.6944i		−	2.30396i
$650$	−33.4734	+	1.69535i	−1.31293	+	0.0664970i
$651$	3.48920	+	3.67801i	0.136753	+	0.144153i
$652$	3.13303	+	3.13303i	0.122699	+	0.122699i
$653$	−27.6886	−	27.6886i	−1.08354	−	1.08354i	−0.996177	−	0.0873627i	$-0.972156\pi$
$653$	−27.6886	−	27.6886i	−1.08354	−	1.08354i	−0.0873627	−	0.996177i	$-0.527844\pi$
$654$	−6.92642	−	7.30122i	−0.270844	−	0.285500i
$655$	15.9671	+	15.1789i	0.623887	+	0.593088i
$656$		−	4.23059i		−	0.165177i
$657$	−17.5265	+	15.7709i	−0.683773	+	0.615282i
$658$	1.80809	−	1.80809i	0.0704867	−	0.0704867i
$659$	26.7954			1.04380			0.521901	−	0.853006i	$-0.325223\pi$
$659$	26.7954			1.04380			0.521901	+	0.853006i	$0.325223\pi$
$660$	−12.6302	+	12.6040i	−0.491629	+	0.490612i
$661$	19.6886			0.765797			0.382899	−	0.923790i	$-0.374926\pi$
$661$	19.6886			0.765797			0.382899	+	0.923790i	$0.374926\pi$
$662$	13.2505	−	13.2505i	0.514996	−	0.514996i
$663$	1.43970	−	54.6512i	0.0559134	−	2.12248i
$664$			13.6943i			0.531441i
$665$	−0.220129	−	8.69812i	−0.00853622	−	0.337299i
$666$	−30.0063	−	1.58204i	−1.16272	−	0.0613028i
$667$	−1.77196	−	1.77196i	−0.0686105	−	0.0686105i
$668$	−5.90660	−	5.90660i	−0.228533	−	0.228533i
$669$	14.6285	−	13.8776i	0.565571	−	0.536537i
$670$	11.4388	−	12.0328i	0.441920	−	0.464869i
$671$		−	6.95746i		−	0.268590i
$672$	−1.29295	−	0.0340607i	−0.0498765	−	0.00131392i
$673$	−10.7591	+	10.7591i	−0.414733	+	0.414733i	−0.883384	−	0.468651i	$-0.844740\pi$
$673$	−10.7591	+	10.7591i	−0.414733	+	0.414733i	0.468651	+	0.883384i	$0.344740\pi$
$674$	16.3742			0.630712
$675$	0.737955	−	25.9703i	0.0284039	−	0.999597i
$676$	−31.9337			−1.22822
$677$	−21.0042	+	21.0042i	−0.807257	+	0.807257i	−0.984218	−	0.176961i	$-0.943373\pi$
$677$	−21.0042	+	21.0042i	−0.807257	+	0.807257i	0.176961	+	0.984218i	$0.443373\pi$
$678$	−1.52868	−	0.0402708i	−0.0587087	−	0.00154659i
$679$			6.01450i			0.230815i
$680$	7.25441	−	7.63113i	0.278194	−	0.292641i
$681$	−7.86275	+	7.45912i	−0.301301	+	0.285834i
$682$	12.7694	+	12.7694i	0.488965	+	0.488965i
$683$	21.6555	+	21.6555i	0.828624	+	0.828624i	0.987326	−	0.158702i	$-0.0507310\pi$
$683$	21.6555	+	21.6555i	0.828624	+	0.828624i	−0.158702	+	0.987326i	$0.550731\pi$
$684$	15.6109	+	0.823061i	0.596897	+	0.0314705i
$685$	−0.607606	−	24.0088i	−0.0232154	−	0.917330i
$686$		−	10.0380i		−	0.383252i
$687$	−0.0246089	+	0.934154i	−0.000938886	+	0.0356402i
$688$	7.82352	−	7.82352i	0.298269	−	0.298269i
$689$	15.7472			0.599921
$690$	−2.74145	+	2.73578i	−0.104365	+	0.104149i
$691$	−10.1870			−0.387532			−0.193766	−	0.981048i	$-0.562070\pi$
$691$	−10.1870			−0.387532			−0.193766	+	0.981048i	$0.562070\pi$
$692$	−10.1099	+	10.1099i	−0.384321	+	0.384321i
$693$	−7.67216	+	6.90367i	−0.291441	+	0.262249i
$694$		−	13.4861i		−	0.511924i
$695$	−23.7596	−	22.5867i	−0.901255	−	0.856763i
$696$	2.98723	+	3.14888i	0.113231	+	0.119358i
$697$	14.0861	+	14.0861i	0.533548	+	0.533548i
$698$	−16.0564	−	16.0564i	−0.607743	−	0.607743i
$699$	8.45769	+	8.91536i	0.319899	+	0.337210i
$700$	−2.77030	−	2.50321i	−0.104707	−	0.0946123i
$701$			8.07940i			0.305155i	0.988292	+	0.152577i	$0.0487573\pi$
$701$			8.07940i			0.305155i	−0.988292	+	0.152577i	$0.951243\pi$
$702$	2.74922	−	34.7225i	0.103763	−	1.31052i
$703$	36.9053	−	36.9053i	1.39191	−	1.39191i
$704$	−4.60712			−0.173637
$705$	−0.0137285	+	13.2620i	−0.000517044	+	0.499477i
$706$	28.5784			1.07556
$707$	4.21900	−	4.21900i	0.158672	−	0.158672i
$708$	−0.581099	+	22.0585i	−0.0218390	+	0.829011i
$709$			3.66459i			0.137627i	0.997630	+	0.0688133i	$0.0219213\pi$
$709$			3.66459i			0.137627i	−0.997630	+	0.0688133i	$0.978079\pi$
$710$	−24.4069	+	0.617680i	−0.915973	+	0.0231811i
$711$	1.05366	−	19.9847i	0.0395155	−	0.749485i
$712$	6.41940	+	6.41940i	0.240577	+	0.240577i
$713$	2.77166	+	2.77166i	0.103800	+	0.103800i
$714$	4.41837	−	4.19155i	0.165353	−	0.156865i
$715$	−69.0337	+	1.74708i	−2.58172	+	0.0653370i
$716$			10.7084i			0.400193i
$717$	−5.60308	−	0.147605i	−0.209251	−	0.00551240i
$718$	6.75511	−	6.75511i	0.252098	−	0.252098i
$719$	2.43829			0.0909327			0.0454664	−	0.998966i	$-0.485523\pi$
$719$	2.43829			0.0909327			0.0454664	+	0.998966i	$0.485523\pi$
$720$	4.87146	−	4.61182i	0.181549	−	0.171872i
$721$	8.84262			0.329316
$722$	−5.76504	+	5.76504i	−0.214553	+	0.214553i
$723$	4.31774	+	0.113744i	0.160579	+	0.00423020i
$724$		−	19.3288i		−	0.718349i
$725$	0.633784	+	12.5136i	0.0235382	+	0.464743i
$726$	−12.8491	+	12.1895i	−0.476877	+	0.452396i
$727$	20.2113	+	20.2113i	0.749597	+	0.749597i	0.974403	−	0.224807i	$-0.0721751\pi$
$727$	20.2113	+	20.2113i	0.749597	+	0.749597i	−0.224807	+	0.974403i	$0.572175\pi$
$728$	−3.53949	−	3.53949i	−0.131182	−	0.131182i
$729$	26.6636	+	4.24892i	0.987540	+	0.157367i
$730$	−12.7369	−	12.1081i	−0.471412	−	0.448140i
$731$			52.0980i			1.92691i
$732$	−0.0688818	+	2.61476i	−0.00254594	+	0.0966442i
$733$	−27.8025	+	27.8025i	−1.02691	+	1.02691i	−0.0272828	+	0.999628i	$0.508685\pi$
$733$	−27.8025	+	27.8025i	−1.02691	+	1.02691i	−0.999628	+	0.0272828i	$0.991315\pi$
$734$	−22.4771			−0.829645
$735$	17.6249	+	17.6614i	0.650104	+	0.651452i
$736$	−1.00000			−0.0368605
$737$	24.1878	−	24.1878i	0.890970	−	0.890970i
$738$	8.48948	+	9.43449i	0.312502	+	0.347288i
$739$			4.34293i			0.159757i	0.996805	+	0.0798786i	$0.0254533\pi$
$739$			4.34293i			0.159757i	−0.996805	+	0.0798786i	$0.974547\pi$
$740$	−0.566619	−	22.3893i	−0.0208293	−	0.823047i
$741$	41.6385	+	43.8917i	1.52963	+	1.61240i
$742$	1.24043	+	1.24043i	0.0455377	+	0.0455377i
$743$	−23.1858	−	23.1858i	−0.850606	−	0.850606i	0.139601	−	0.990208i	$-0.455418\pi$
$743$	−23.1858	−	23.1858i	−0.850606	−	0.850606i	−0.990208	+	0.139601i	$0.955418\pi$
$744$	−4.67257	−	4.92542i	−0.171305	−	0.180575i
$745$	8.96488	−	9.43042i	0.328448	−	0.345504i
$746$		−	30.9879i		−	1.13455i
$747$	−27.4801	−	30.5391i	−1.00545	−	1.11737i
$748$	15.3397	−	15.3397i	0.560877	−	0.560877i
$749$	11.4360			0.417861
$750$	19.3411	−	0.959511i	0.706238	−	0.0350364i
$751$	4.73251			0.172692			0.0863459	−	0.996265i	$-0.472481\pi$
$751$	4.73251			0.172692			0.0863459	+	0.996265i	$0.472481\pi$
$752$	−2.42130	+	2.42130i	−0.0882959	+	0.0882959i
$753$	−0.245992	+	9.33787i	−0.00896445	+	0.340291i
$754$			16.7979i			0.611742i
$755$	−4.28376	+	4.50621i	−0.155902	+	0.163998i
$756$	2.95170	−	2.51858i	0.107352	−	0.0916000i
$757$	5.16180	+	5.16180i	0.187609	+	0.187609i	0.794662	−	0.607053i	$-0.207648\pi$
$757$	5.16180	+	5.16180i	0.187609	+	0.187609i	−0.607053	+	0.794662i	$0.707648\pi$
$758$	2.13019	+	2.13019i	0.0773719	+	0.0773719i
$759$	−5.78918	+	5.49200i	−0.210134	+	0.199347i
$760$	0.294785	+	11.6481i	0.0106930	+	0.422521i
$761$			17.2128i			0.623963i	0.950088	+	0.311982i	$0.100993\pi$
$761$			17.2128i			0.623963i	−0.950088	+	0.311982i	$0.899007\pi$
$762$	27.0215	+	0.711839i	0.978885	+	0.0257872i
$763$	3.06806	−	3.06806i	0.111071	−	0.111071i
$764$	−16.3310			−0.590835
$765$	−0.864512	+	31.5753i	−0.0312565	+	1.14161i
$766$	25.0862			0.906400
$767$	−60.3862	+	60.3862i	−2.18042	+	2.18042i
$768$	1.73145	+	0.0456124i	0.0624783	+	0.00164590i
$769$			41.6311i			1.50126i	0.660725	+	0.750628i	$0.270249\pi$
$769$			41.6311i			1.50126i	−0.660725	+	0.750628i	$0.729751\pi$
$770$	−5.57552	−	5.30028i	−0.200928	−	0.191009i
$771$	0.807926	−	0.766451i	0.0290967	−	0.0276031i
$772$	4.44978	+	4.44978i	0.160151	+	0.160151i
$773$	−19.8333	−	19.8333i	−0.713355	−	0.713355i	0.253881	−	0.967235i	$-0.418293\pi$
$773$	−19.8333	−	19.8333i	−0.713355	−	0.713355i	−0.967235	+	0.253881i	$0.918293\pi$
$774$	−1.74759	+	33.1464i	−0.0628159	+	1.19142i
$775$	−0.991353	−	19.5735i	−0.0356104	−	0.703102i
$776$		−	8.05432i		−	0.289133i
$777$	0.341152	−	12.9501i	0.0122388	−	0.464584i
$778$	14.1902	−	14.1902i	0.508742	−	0.508742i
$779$	−22.0450			−0.789843
$780$	25.9616	+	0.0268747i	0.929574	+	0.000962267i
$781$	−50.3032			−1.79999
$782$	3.32957	−	3.32957i	0.119065	−	0.119065i
$783$	−12.9806	−	1.02776i	−0.463887	−	0.0367292i
$784$			6.44238i			0.230085i
$785$	20.0271	−	0.506838i	0.714798	−	0.0180898i
$786$	−11.7447	−	12.3802i	−0.418920	−	0.441589i
$787$	9.89797	+	9.89797i	0.352824	+	0.352824i	0.861159	−	0.508335i	$-0.169739\pi$
$787$	9.89797	+	9.89797i	0.352824	+	0.352824i	−0.508335	+	0.861159i	$0.669739\pi$
$788$	19.0107	+	19.0107i	0.677230	+	0.677230i
$789$	−17.0286	−	17.9501i	−0.606235	−	0.639040i
$790$	14.9116	−	0.377378i	0.530532	−	0.0134265i
$791$		−	0.659292i		−	0.0234417i
$792$	10.2742	−	9.24506i	0.365077	−	0.328509i
$793$	−7.15801	+	7.15801i	−0.254188	+	0.254188i
$794$	36.9217			1.31030
$795$	−9.09836	−	0.00941835i	−0.322685	−	0.000334034i
$796$	19.6455			0.696315
$797$	20.9341	−	20.9341i	0.741522	−	0.741522i	−0.231349	−	0.972871i	$-0.574314\pi$
$797$	20.9341	−	20.9341i	0.741522	−	0.741522i	0.972871	+	0.231349i	$0.0743138\pi$
$798$	−0.177485	+	6.73735i	−0.00628291	+	0.238500i
$799$		−	16.1238i		−	0.570420i
$800$	3.70985	+	3.35217i	0.131163	+	0.118517i
$801$	−27.1974	−	1.43394i	−0.960974	−	0.0506659i
$802$	−15.5498	−	15.5498i	−0.549082	−	0.549082i
$803$	−25.6030	−	25.6030i	−0.903512	−	0.903512i
$804$	−9.32975	+	8.85081i	−0.329035	+	0.312144i
$805$	−1.21020	−	1.15045i	−0.0426538	−	0.0405481i
$806$		−	26.2749i		−	0.925494i
$807$	−40.6801	−	1.07166i	−1.43201	−	0.0377241i
$808$	−5.64988	+	5.64988i	−0.198762	+	0.198762i
$809$	1.00481			0.0353272			0.0176636	−	0.999844i	$-0.494377\pi$
$809$	1.00481			0.0353272			0.0176636	+	0.999844i	$0.494377\pi$
$810$	−1.60920	+	20.0602i	−0.0565416	+	0.704843i
$811$	47.6896			1.67461			0.837305	−	0.546736i	$-0.184130\pi$
$811$	47.6896			1.67461			0.837305	+	0.546736i	$0.184130\pi$
$812$	−1.32319	+	1.32319i	−0.0464350	+	0.0464350i
$813$	−10.6756	−	0.281233i	−0.374411	−	0.00986328i
$814$		−	46.1449i		−	1.61738i
$815$	−0.250655	−	9.90433i	−0.00878006	−	0.346933i
$816$	−5.91686	+	5.61312i	−0.207132	+	0.196499i
$817$	−40.7672	−	40.7672i	−1.42627	−	1.42627i
$818$	−27.0169	−	27.0169i	−0.944622	−	0.944622i
$819$	14.9960	+	0.790641i	0.524002	+	0.0276272i
$820$	−6.51777	+	6.85624i	−0.227611	+	0.239430i
$821$		−	22.9888i		−	0.802315i	−0.916009	−	0.401157i	$-0.868608\pi$
$821$		−	22.9888i		−	0.802315i	0.916009	−	0.401157i	$-0.131392\pi$
$822$	−0.489901	+	18.5967i	−0.0170873	+	0.648633i
$823$	23.9384	−	23.9384i	0.834442	−	0.834442i	−0.153679	−	0.988121i	$-0.549112\pi$
$823$	23.9384	−	23.9384i	0.834442	−	0.834442i	0.988121	+	0.153679i	$0.0491122\pi$
$824$	−11.8416			−0.412522
$825$	39.8871	−	0.968131i	1.38869	−	0.0337060i
$826$	−9.51343			−0.331015
$827$	12.6490	−	12.6490i	0.439849	−	0.439849i	−0.452112	−	0.891961i	$-0.649329\pi$
$827$	12.6490	−	12.6490i	0.439849	−	0.439849i	0.891961	+	0.452112i	$0.149329\pi$
$828$	2.23007	−	2.00669i	0.0775002	−	0.0697373i
$829$			36.2001i			1.25728i	0.777696	+	0.628641i	$0.216388\pi$
$829$			36.2001i			1.25728i	−0.777696	+	0.628641i	$0.783612\pi$
$830$	21.0978	−	22.1934i	0.732316	−	0.770344i
$831$	27.6225	+	29.1173i	0.958215	+	1.01007i
$832$	4.73992	+	4.73992i	0.164327	+	0.164327i
$833$	−21.4504	−	21.4504i	−0.743211	−	0.743211i
$834$	17.4765	+	18.4222i	0.605163	+	0.637910i
$835$	0.472552	+	18.6723i	0.0163534	+	0.646183i
$836$			24.0070i			0.830300i
$837$	20.3039	+	1.60760i	0.701806	+	0.0555669i
$838$	−6.46912	+	6.46912i	−0.223472	+	0.223472i
$839$	−40.1271			−1.38534			−0.692671	−	0.721254i	$-0.743566\pi$
$839$	−40.1271			−1.38534			−0.692671	+	0.721254i	$0.743566\pi$
$840$	2.04292	+	2.04715i	0.0704874	+	0.0706335i
$841$	−22.7203			−0.783460
$842$	−20.1023	+	20.1023i	−0.692772	+	0.692772i
$843$	0.0157112	−	0.596399i	0.000541123	−	0.0205411i
$844$			4.38087i			0.150796i
$845$	51.7528	+	49.1980i	1.78035	+	1.69246i
$846$	0.540863	−	10.2585i	0.0185953	−	0.352694i
$847$	−5.39936	−	5.39936i	−0.185524	−	0.185524i
$848$	−1.66113	−	1.66113i	−0.0570433	−	0.0570433i
$849$	−3.37526	+	3.20199i	−0.115839	+	0.109892i
$850$	−23.5135	+	1.19090i	−0.806507	+	0.0408477i
$851$		−	10.0160i		−	0.343344i
$852$	18.9050	+	0.498023i	0.647674	+	0.0170620i
$853$	−32.6791	+	32.6791i	−1.11891	+	1.11891i	−0.127011	+	0.991901i	$0.540539\pi$
$853$	−32.6791	+	32.6791i	−1.11891	+	1.11891i	−0.991901	+	0.127011i	$0.959461\pi$
$854$	−1.12770			−0.0385890
$855$	−24.0315	−	25.3845i	−0.821860	−	0.868131i
$856$	−15.3145			−0.523439
$857$	38.3689	−	38.3689i	1.31066	−	1.31066i	0.389725	−	0.920931i	$-0.372570\pi$
$857$	38.3689	−	38.3689i	1.31066	−	1.31066i	0.920931	−	0.389725i	$-0.127430\pi$
$858$	53.4719	+	1.40863i	1.82550	+	0.0480900i
$859$			27.0975i			0.924554i	0.886736	+	0.462277i	$0.152967\pi$
$859$			27.0975i			0.924554i	−0.886736	+	0.462277i	$0.847033\pi$
$860$	−24.7322	+	0.625914i	−0.843362	+	0.0213435i
$861$	−3.96971	+	3.76593i	−0.135287	+	0.128342i
$862$	−7.86571	−	7.86571i	−0.267907	−	0.267907i
$863$	18.8147	+	18.8147i	0.640459	+	0.640459i	0.950668	−	0.310209i	$-0.100399\pi$
$863$	18.8147	+	18.8147i	0.640459	+	0.640459i	−0.310209	+	0.950668i	$0.600399\pi$
$864$	−3.95278	+	3.37276i	−0.134476	+	0.114744i
$865$	31.9601	−	0.808834i	1.08668	−	0.0275012i
$866$			28.3370i			0.962929i
$867$	0.235914	−	8.95530i	0.00801205	−	0.304138i
$868$	2.06972	−	2.06972i	0.0702507	−	0.0702507i
$869$	30.7333			1.04255
$870$	0.0100467	−	9.70541i	0.000340617	−	0.329044i
$871$	−49.7701			−1.68639
$872$	−4.10859	+	4.10859i	−0.139134	+	0.139134i
$873$	16.1625	+	17.9617i	0.547018	+	0.607910i
$874$			5.21085i			0.176260i
$875$	0.633123	+	8.32479i	0.0214035	+	0.281429i
$876$	9.36867	+	9.87563i	0.316538	+	0.333667i
$877$	5.03549	+	5.03549i	0.170037	+	0.170037i	0.786995	−	0.616959i	$-0.211636\pi$
$877$	5.03549	+	5.03549i	0.170037	+	0.170037i	−0.616959	+	0.786995i	$0.711636\pi$
$878$	9.75821	+	9.75821i	0.329324	+	0.329324i
$879$	−0.311016	−	0.327846i	−0.0104903	−	0.0110580i
$880$	7.46646	+	7.09787i	0.251694	+	0.239269i
$881$			32.0410i			1.07949i	0.841829	+	0.539744i	$0.181479\pi$
$881$			32.0410i			1.07949i	−0.841829	+	0.539744i	$0.818521\pi$
$882$	−12.9279	−	14.3669i	−0.435303	−	0.483760i
$883$	20.5528	−	20.5528i	0.691656	−	0.691656i	−0.270940	−	0.962596i	$-0.587335\pi$
$883$	20.5528	−	20.5528i	0.691656	−	0.691656i	0.962596	+	0.270940i	$0.0873346\pi$
$884$	−31.5638			−1.06161
$885$	34.9258	−	34.8536i	1.17402	−	1.17159i
$886$	−5.77413			−0.193986
$887$	3.65344	−	3.65344i	0.122671	−	0.122671i	−0.643106	−	0.765777i	$-0.722355\pi$
$887$	3.65344	−	3.65344i	0.122671	−	0.122671i	0.765777	+	0.643106i	$0.222355\pi$
$888$	−0.456854	+	17.3422i	−0.0153310	+	0.581966i
$889$			11.6539i			0.390858i
$890$	−0.513578	−	20.2934i	−0.0172152	−	0.680237i
$891$	−4.36014	+	41.2342i	−0.146070	+	1.38140i
$892$	−8.23185	−	8.23185i	−0.275623	−	0.275623i
$893$	12.6171	+	12.6171i	0.422214	+	0.422214i
$894$	−7.31196	+	6.93660i	−0.244548	+	0.231995i
$895$	16.4977	−	17.3545i	0.551459	−	0.580096i
$896$			0.746742i			0.0249469i
$897$	11.6064	+	0.305752i	0.387525	+	0.0102088i
$898$	4.10438	−	4.10438i	0.136965	−	0.136965i
$899$	−9.82253			−0.327600
$900$	−15.0000	−	0.0310551i	−0.499999	−	0.00103517i
$901$	11.0617			0.368518
$902$	−13.7821	+	13.7821i	−0.458894	+	0.458894i
$903$	−14.3053	−	0.376852i	−0.476051	−	0.0125408i
$904$			0.882892i			0.0293645i
$905$	−29.7785	+	31.3249i	−0.989872	+	1.04128i
$906$	3.49393	−	3.31457i	0.116078	−	0.110119i
$907$	15.6822	+	15.6822i	0.520720	+	0.520720i	0.917789	−	0.397069i	$-0.129972\pi$
$907$	15.6822	+	15.6822i	0.520720	+	0.520720i	−0.397069	+	0.917789i	$0.629972\pi$
$908$	4.42457	+	4.42457i	0.146835	+	0.146835i
$909$	1.26205	−	23.9372i	0.0418596	−	0.793946i
$910$	0.283174	+	11.1893i	0.00938713	+	0.370921i
$911$			17.1132i			0.566984i	0.958975	+	0.283492i	$0.0914930\pi$
$911$			17.1132i			0.566984i	−0.958975	+	0.283492i	$0.908507\pi$
$912$	0.237680	−	9.02233i	0.00787036	−	0.298759i
$913$	44.6122	−	44.6122i	1.47645	−	1.47645i
$914$	−4.30896			−0.142528
$915$	4.14001	−	4.13145i	0.136864	−	0.136581i
$916$	0.539521			0.0178263
$917$	5.20232	−	5.20232i	0.171796	−	0.171796i
$918$	1.93120	−	24.3909i	0.0637391	−	0.805021i
$919$		−	38.6421i		−	1.27469i	−0.770580	−	0.637343i	$-0.780033\pi$
$919$		−	38.6421i		−	1.27469i	0.770580	−	0.637343i	$-0.219967\pi$
$920$	1.62063	+	1.54063i	0.0534307	+	0.0507931i
$921$	−8.61622	−	9.08246i	−0.283914	−	0.299277i
$922$	7.66859	+	7.66859i	0.252551	+	0.252551i
$923$	51.7532	+	51.7532i	1.70348	+	1.70348i
$924$	4.10110	+	4.32302i	0.134916	+	0.142217i
$925$	−33.5753	+	37.1578i	−1.10395	+	1.22174i
$926$			1.36613i			0.0448939i
$927$	26.4076	−	23.7624i	0.867338	−	0.780460i
$928$	1.77196	−	1.77196i	0.0581674	−	0.0581674i
$929$	4.79606			0.157354			0.0786768	−	0.996900i	$-0.474930\pi$
$929$	4.79606			0.157354			0.0786768	+	0.996900i	$0.474930\pi$
$930$	−0.0157149	+	15.1810i	−0.000515313	+	0.497805i
$931$	33.5703			1.10022
$932$	5.01691	−	5.01691i	0.164334	−	0.164334i
$933$	−0.608584	+	23.1019i	−0.0199241	+	0.756322i
$934$		−	7.04073i		−	0.230380i
$935$	−48.4930	+	1.22724i	−1.58589	+	0.0401351i
$936$	−20.0819	−	1.05879i	−0.656397	−	0.0346076i
$937$	9.71119	+	9.71119i	0.317251	+	0.317251i	0.847710	−	0.530460i	$-0.177981\pi$
$937$	9.71119	+	9.71119i	0.317251	+	0.317251i	−0.530460	+	0.847710i	$0.677981\pi$
$938$	−3.92047	−	3.92047i	−0.128008	−	0.128008i
$939$	10.4478	−	9.91144i	0.340950	−	0.323448i
$940$	7.65439	−	0.193714i	0.249659	−	0.00631826i
$941$			6.87914i			0.224254i	0.993694	+	0.112127i	$0.0357663\pi$
$941$			6.87914i			0.224254i	−0.993694	+	0.112127i	$0.964234\pi$
$942$	−15.5125	−	0.408654i	−0.505425	−	0.0133147i
$943$	−2.99148	+	2.99148i	−0.0974159	+	0.0974159i
$944$	12.7399			0.414649
$945$	−8.66384	−	0.465782i	−0.281835	−	0.0151519i
$946$	−50.9738			−1.65730
$947$	7.17276	−	7.17276i	0.233083	−	0.233083i	−0.580895	−	0.813978i	$-0.697297\pi$
$947$	7.17276	−	7.17276i	0.233083	−	0.233083i	0.813978	+	0.580895i	$0.197297\pi$
$948$	−11.5502	−	0.304272i	−0.375133	−	0.00988230i
$949$			52.6821i			1.71013i
$950$	17.4677	−	19.3315i	0.566726	−	0.627195i
$951$	26.7924	−	25.4170i	0.868803	−	0.824204i
$952$	−2.48633	−	2.48633i	−0.0805825	−	0.0805825i
$953$	1.36152	+	1.36152i	0.0441038	+	0.0441038i	0.728815	−	0.684711i	$-0.240072\pi$
$953$	1.36152	+	1.36152i	0.0441038	+	0.0441038i	−0.684711	+	0.728815i	$0.740072\pi$
$954$	7.03779	+	0.371057i	0.227857	+	0.0120134i
$955$	26.4666	+	25.1601i	0.856439	+	0.814160i
$956$			3.23606i			0.104662i
$957$	0.526600	−	19.9898i	0.0170226	−	0.646178i
$958$	−13.9494	+	13.9494i	−0.450686	+	0.450686i
$959$	−8.02039			−0.258992
$960$	−2.73578	−	2.74145i	−0.0882968	−	0.0884798i
$961$	−15.6358			−0.504380
$962$	−47.4750	+	47.4750i	−1.53066	+	1.53066i
$963$	34.1523	−	30.7314i	1.10054	−	0.990307i
$964$		−	2.49371i		−	0.0803171i
$965$	−0.356000	−	14.0669i	−0.0114601	−	0.452830i
$966$	0.890166	+	0.938335i	0.0286406	+	0.0301904i
$967$	−3.08307	−	3.08307i	−0.0991448	−	0.0991448i	0.655795	−	0.754939i	$-0.272334\pi$
$967$	−3.08307	−	3.08307i	−0.0991448	−	0.0991448i	−0.754939	+	0.655795i	$0.772334\pi$
$968$	7.23056	+	7.23056i	0.232399	+	0.232399i
$969$	29.2492	+	30.8319i	0.939619	+	0.990464i
$970$	−12.4087	+	13.0531i	−0.398420	+	0.419110i
$971$			34.8356i			1.11793i	0.829192	+	0.558965i	$0.188801\pi$
$971$			34.8356i			1.11793i	−0.829192	+	0.558965i	$0.811199\pi$
$972$	2.04687	−	15.4535i	0.0656533	−	0.495671i
$973$	−7.74123	+	7.74123i	−0.248173	+	0.248173i
$974$	7.52797			0.241212
$975$	−42.0329	−	40.0408i	−1.34613	−	1.28233i
$976$	1.51016			0.0483389
$977$	34.9877	−	34.9877i	1.11936	−	1.11936i	0.127521	−	0.991836i	$-0.459298\pi$
$977$	34.9877	−	34.9877i	1.11936	−	1.11936i	0.991836	−	0.127521i	$-0.0407020\pi$
$978$	−0.202098	+	7.67165i	−0.00646238	+	0.245312i
$979$		−	41.8253i		−	1.33674i
$980$	9.92532	−	10.4407i	0.317053	−	0.333517i
$981$	0.917764	−	17.4071i	0.0293019	−	0.555766i
$982$	4.49158	+	4.49158i	0.143332	+	0.143332i
$983$	−2.48551	−	2.48551i	−0.0792755	−	0.0792755i	0.666357	−	0.745633i	$-0.267853\pi$
$983$	−2.48551	−	2.48551i	−0.0792755	−	0.0792755i	−0.745633	+	0.666357i	$0.767853\pi$
$984$	5.31604	−	5.04315i	0.169469	−	0.160770i
$985$	−1.52094	−	60.0980i	−0.0484611	−	1.91488i
$986$			11.7997i			0.375780i
$987$	4.42736	+	0.116632i	0.140924	+	0.00371244i
$988$	24.6990	−	24.6990i	0.785781	−	0.785781i
$989$	−11.0641			−0.351819
$990$	−30.8939	−	0.845857i	−0.981873	−	0.0268831i
$991$	35.3250			1.12214			0.561068	−	0.827770i	$-0.310391\pi$
$991$	35.3250			1.12214			0.561068	+	0.827770i	$0.310391\pi$
$992$	−2.77166	+	2.77166i	−0.0880003	+	0.0880003i
$993$	32.4458	+	0.854734i	1.02964	+	0.0271242i
$994$			8.15336i			0.258609i
$995$	−31.8381	−	30.2664i	−1.00934	−	0.959509i
$996$	−17.2078	+	16.3245i	−0.545252	+	0.517261i
$997$	−26.5260	−	26.5260i	−0.840088	−	0.840088i	0.148782	−	0.988870i	$-0.452465\pi$
$997$	−26.5260	−	26.5260i	−0.840088	−	0.840088i	−0.988870	+	0.148782i	$0.952465\pi$
$998$	18.7776	+	18.7776i	0.594394	+	0.594394i
$999$	−33.7816	−	39.5910i	−1.06880	−	1.25260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.47.16	yes	32
3.2	odd	2	inner	690.2.i.f.47.5	✓	32
5.3	odd	4	inner	690.2.i.f.323.5	yes	32
15.8	even	4	inner	690.2.i.f.323.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.5	✓	32	3.2	odd	2	inner
690.2.i.f.47.16	yes	32	1.1	even	1	trivial
690.2.i.f.323.5	yes	32	5.3	odd	4	inner
690.2.i.f.323.16	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.73145 + 0.0456124i) q^{3} -1.00000i q^{4} +(-1.54063 + 1.62063i) q^{5} +(1.25657 - 1.19207i) q^{6} +(0.528026 + 0.528026i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99584 + 0.157951i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.73145 + 0.0456124i) q^{3} -1.00000i q^{4} +(-1.54063 + 1.62063i) q^{5} +(1.25657 - 1.19207i) q^{6} +(0.528026 + 0.528026i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99584 + 0.157951i) q^{9} +(0.0565714 + 2.23535i) q^{10} +4.60712i q^{11} +(0.0456124 - 1.73145i) q^{12} +(4.73992 - 4.73992i) q^{13} +0.746742 q^{14} +(-2.74145 + 2.73578i) q^{15} -1.00000 q^{16} +(3.32957 - 3.32957i) q^{17} +(2.23007 - 2.00669i) q^{18} +5.21085i q^{19} +(1.62063 + 1.54063i) q^{20} +(0.890166 + 0.938335i) q^{21} +(3.25773 + 3.25773i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.19207 - 1.25657i) q^{24} +(-0.252914 - 4.99360i) q^{25} -6.70326i q^{26} +(5.17994 + 0.410132i) q^{27} +(0.528026 - 0.528026i) q^{28} -2.50593 q^{29} +(-0.00400919 + 3.87298i) q^{30} +3.91972 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.210142 + 7.97700i) q^{33} -4.70873i q^{34} +(-1.66923 + 0.0422442i) q^{35} +(0.157951 - 2.99584i) q^{36} +(-7.08238 - 7.08238i) q^{37} +(3.68463 + 3.68463i) q^{38} +(8.42313 - 7.99073i) q^{39} +(2.23535 - 0.0565714i) q^{40} +4.23059i q^{41} +(1.29295 + 0.0340607i) q^{42} +(-7.82352 + 7.82352i) q^{43} +4.60712 q^{44} +(-4.87146 + 4.61182i) q^{45} +1.00000 q^{46} +(2.42130 - 2.42130i) q^{47} +(-1.73145 - 0.0456124i) q^{48} -6.44238i q^{49} +(-3.70985 - 3.35217i) q^{50} +(5.91686 - 5.61312i) q^{51} +(-4.73992 - 4.73992i) q^{52} +(1.66113 + 1.66113i) q^{53} +(3.95278 - 3.37276i) q^{54} +(-7.46646 - 7.09787i) q^{55} -0.746742i q^{56} +(-0.237680 + 9.02233i) q^{57} +(-1.77196 + 1.77196i) q^{58} -12.7399 q^{59} +(2.73578 + 2.74145i) q^{60} -1.51016 q^{61} +(2.77166 - 2.77166i) q^{62} +(1.49848 + 1.66528i) q^{63} +1.00000i q^{64} +(0.379213 + 14.9841i) q^{65} +(5.49200 + 5.78918i) q^{66} +(-5.25010 - 5.25010i) q^{67} +(-3.32957 - 3.32957i) q^{68} +(1.19207 + 1.25657i) q^{69} +(-1.15045 + 1.21020i) q^{70} +10.9186i q^{71} +(-2.00669 - 2.23007i) q^{72} +(-5.55728 + 5.55728i) q^{73} -10.0160 q^{74} +(-0.210138 - 8.65770i) q^{75} +5.21085 q^{76} +(-2.43268 + 2.43268i) q^{77} +(0.305752 - 11.6064i) q^{78} -6.67082i q^{79} +(1.54063 - 1.62063i) q^{80} +(8.95010 + 0.946393i) q^{81} +(2.99148 + 2.99148i) q^{82} +(-9.68331 - 9.68331i) q^{83} +(0.938335 - 0.890166i) q^{84} +(0.266380 + 10.5257i) q^{85} +11.0641i q^{86} +(-4.33889 - 0.114301i) q^{87} +(3.25773 - 3.25773i) q^{88} -9.07840 q^{89} +(-0.183598 + 6.70569i) q^{90} +5.00560 q^{91} +(0.707107 - 0.707107i) q^{92} +(6.78680 + 0.178788i) q^{93} -3.42424i q^{94} +(-8.44489 - 8.02800i) q^{95} +(-1.25657 + 1.19207i) q^{96} +(5.69526 + 5.69526i) q^{97} +(-4.55545 - 4.55545i) q^{98} +(-0.727700 + 13.8022i) 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

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