LMFDB - Embedded newform 690.2.i.e.47.3

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			47.3
Character	$\chi$	$=$	690.47
Dual form			690.2.i.e.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.639676 - 1.60960i) q^{3} -1.00000i q^{4} +(-1.63199 + 1.52859i) q^{5} +(1.59048 + 0.685841i) q^{6} +(0.772441 + 0.772441i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.18163 + 2.05924i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.639676 - 1.60960i) q^{3} -1.00000i q^{4} +(-1.63199 + 1.52859i) q^{5} +(1.59048 + 0.685841i) q^{6} +(0.772441 + 0.772441i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.18163 + 2.05924i) q^{9} +(0.0731134 - 2.23487i) q^{10} -1.36480i q^{11} +(-1.60960 + 0.639676i) q^{12} +(0.808313 - 0.808313i) q^{13} -1.09240 q^{14} +(3.50437 + 1.64905i) q^{15} -1.00000 q^{16} +(2.66253 - 2.66253i) q^{17} +(0.0865397 - 2.99875i) q^{18} -1.89614i q^{19} +(1.52859 + 1.63199i) q^{20} +(0.749210 - 1.73743i) q^{21} +(0.965061 + 0.965061i) q^{22} +(0.707107 + 0.707107i) q^{23} +(0.685841 - 1.59048i) q^{24} +(0.326798 - 4.98931i) q^{25} +1.14313i q^{26} +(4.71010 + 2.19431i) q^{27} +(0.772441 - 0.772441i) q^{28} -1.81701 q^{29} +(-3.64402 + 1.31191i) q^{30} -5.22750 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.19679 + 0.873030i) q^{33} +3.76538i q^{34} +(-2.44137 - 0.0798687i) q^{35} +(2.05924 + 2.18163i) q^{36} +(-7.05976 - 7.05976i) q^{37} +(1.34077 + 1.34077i) q^{38} +(-1.81812 - 0.784003i) q^{39} +(-2.23487 - 0.0731134i) q^{40} -7.21905i q^{41} +(0.698779 + 1.75832i) q^{42} +(4.99514 - 4.99514i) q^{43} -1.36480 q^{44} +(0.412654 - 6.69550i) q^{45} -1.00000 q^{46} +(7.28092 - 7.28092i) q^{47} +(0.639676 + 1.60960i) q^{48} -5.80667i q^{49} +(3.29689 + 3.75906i) q^{50} +(-5.98876 - 2.58245i) q^{51} +(-0.808313 - 0.808313i) q^{52} +(-1.52470 - 1.52470i) q^{53} +(-4.88215 + 1.77893i) q^{54} +(2.08623 + 2.22735i) q^{55} +1.09240i q^{56} +(-3.05202 + 1.21291i) q^{57} +(1.28482 - 1.28482i) q^{58} -5.33984 q^{59} +(1.64905 - 3.50437i) q^{60} -12.6521 q^{61} +(3.69640 - 3.69640i) q^{62} +(-3.27582 - 0.0945356i) q^{63} +1.00000i q^{64} +(-0.0835778 + 2.55474i) q^{65} +(0.936037 - 2.17069i) q^{66} +(8.07409 + 8.07409i) q^{67} +(-2.66253 - 2.66253i) q^{68} +(0.685841 - 1.59048i) q^{69} +(1.78278 - 1.66983i) q^{70} -2.85426i q^{71} +(-2.99875 - 0.0865397i) q^{72} +(8.07529 - 8.07529i) q^{73} +9.98401 q^{74} +(-8.23984 + 2.66552i) q^{75} -1.89614 q^{76} +(1.05423 - 1.05423i) q^{77} +(1.83998 - 0.731230i) q^{78} +4.48733i q^{79} +(1.63199 - 1.52859i) q^{80} +(0.519022 - 8.98502i) q^{81} +(5.10464 + 5.10464i) q^{82} +(-0.994740 - 0.994740i) q^{83} +(-1.73743 - 0.749210i) q^{84} +(-0.275300 + 8.41515i) q^{85} +7.06419i q^{86} +(1.16230 + 2.92466i) q^{87} +(0.965061 - 0.965061i) q^{88} +3.62956 q^{89} +(4.44264 + 5.02622i) q^{90} +1.24875 q^{91} +(0.707107 - 0.707107i) q^{92} +(3.34390 + 8.41418i) q^{93} +10.2968i q^{94} +(2.89842 + 3.09448i) q^{95} +(-1.59048 - 0.685841i) q^{96} +(-0.314895 - 0.314895i) q^{97} +(4.10594 + 4.10594i) q^{98} +(2.81046 + 2.97749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * 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
$3$	−0.639676	−	1.60960i	−0.369317	−	0.929304i
$3$	−0.639676	−	1.60960i	−0.369317	−	0.929304i
$4$		−	1.00000i		−	0.500000i
$5$	−1.63199	+	1.52859i	−0.729849	+	0.683608i
$5$	−1.63199	+	1.52859i	−0.729849	+	0.683608i
$6$	1.59048	+	0.685841i	0.649310	+	0.279993i
$7$	0.772441	+	0.772441i	0.291955	+	0.291955i	0.837852	−	0.545897i	$-0.183811\pi$
$7$	0.772441	+	0.772441i	0.291955	+	0.291955i	−0.545897	+	0.837852i	$0.683811\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.18163	+	2.05924i	−0.727210	+	0.686415i
$10$	0.0731134	−	2.23487i	0.0231205	−	0.706729i
$11$		−	1.36480i		−	0.411503i	−0.978604	−	0.205752i	$-0.934036\pi$
$11$		−	1.36480i		−	0.411503i	0.978604	−	0.205752i	$-0.0659639\pi$
$12$	−1.60960	+	0.639676i	−0.464652	+	0.184658i
$13$	0.808313	−	0.808313i	0.224186	−	0.224186i	−0.586073	−	0.810258i	$-0.699327\pi$
$13$	0.808313	−	0.808313i	0.224186	−	0.224186i	0.810258	+	0.586073i	$0.199327\pi$
$14$	−1.09240			−0.291955
$15$	3.50437	+	1.64905i	0.904825	+	0.425783i
$16$	−1.00000			−0.250000
$17$	2.66253	−	2.66253i	0.645758	−	0.645758i	−0.306207	−	0.951965i	$-0.599060\pi$
$17$	2.66253	−	2.66253i	0.645758	−	0.645758i	0.951965	+	0.306207i	$0.0990599\pi$
$18$	0.0865397	−	2.99875i	0.0203976	−	0.706813i
$19$		−	1.89614i		−	0.435004i	−0.976060	−	0.217502i	$-0.930209\pi$
$19$		−	1.89614i		−	0.435004i	0.976060	−	0.217502i	$-0.0697908\pi$
$20$	1.52859	+	1.63199i	0.341804	+	0.364925i
$21$	0.749210	−	1.73743i	0.163491	−	0.379139i
$22$	0.965061	+	0.965061i	0.205752	+	0.205752i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	0.685841	−	1.59048i	0.139997	−	0.324655i
$25$	0.326798	−	4.98931i	0.0653596	−	0.997862i
$26$			1.14313i			0.224186i
$27$	4.71010	+	2.19431i	0.906459	+	0.422294i
$28$	0.772441	−	0.772441i	0.145978	−	0.145978i
$29$	−1.81701			−0.337410			−0.168705	−	0.985667i	$-0.553959\pi$
$29$	−1.81701			−0.337410			−0.168705	+	0.985667i	$0.553959\pi$
$30$	−3.64402	+	1.31191i	−0.665304	+	0.239521i
$31$	−5.22750			−0.938886			−0.469443	−	0.882963i	$-0.655545\pi$
$31$	−5.22750			−0.938886			−0.469443	+	0.882963i	$0.655545\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−2.19679	+	0.873030i	−0.382411	+	0.151975i
$34$			3.76538i			0.645758i
$35$	−2.44137	−	0.0798687i	−0.412666	−	0.0135003i
$36$	2.05924	+	2.18163i	0.343207	+	0.363605i
$37$	−7.05976	−	7.05976i	−1.16062	−	1.16062i	−0.984341	−	0.176277i	$-0.943595\pi$
$37$	−7.05976	−	7.05976i	−1.16062	−	1.16062i	−0.176277	−	0.984341i	$-0.556405\pi$
$38$	1.34077	+	1.34077i	0.217502	+	0.217502i
$39$	−1.81812	−	0.784003i	−0.291132	−	0.125541i
$40$	−2.23487	−	0.0731134i	−0.353364	−	0.0115602i
$41$		−	7.21905i		−	1.12743i	−0.825971	−	0.563713i	$-0.809373\pi$
$41$		−	7.21905i		−	1.12743i	0.825971	−	0.563713i	$-0.190627\pi$
$42$	0.698779	+	1.75832i	0.107824	+	0.271315i
$43$	4.99514	−	4.99514i	0.761751	−	0.761751i	−0.214888	−	0.976639i	$-0.568939\pi$
$43$	4.99514	−	4.99514i	0.761751	−	0.761751i	0.976639	+	0.214888i	$0.0689386\pi$
$44$	−1.36480			−0.205752
$45$	0.412654	−	6.69550i	0.0615148	−	0.998106i
$46$	−1.00000			−0.147442
$47$	7.28092	−	7.28092i	1.06203	−	1.06203i	0.0640872	−	0.997944i	$-0.479586\pi$
$47$	7.28092	−	7.28092i	1.06203	−	1.06203i	0.997944	−	0.0640872i	$-0.0204136\pi$
$48$	0.639676	+	1.60960i	0.0923292	+	0.232326i
$49$		−	5.80667i		−	0.829524i
$50$	3.29689	+	3.75906i	0.466251	+	0.531611i
$51$	−5.98876	−	2.58245i	−0.838595	−	0.361616i
$52$	−0.808313	−	0.808313i	−0.112093	−	0.112093i
$53$	−1.52470	−	1.52470i	−0.209433	−	0.209433i	0.594593	−	0.804027i	$-0.297313\pi$
$53$	−1.52470	−	1.52470i	−0.209433	−	0.209433i	−0.804027	+	0.594593i	$0.797313\pi$
$54$	−4.88215	+	1.77893i	−0.664377	+	0.242082i
$55$	2.08623	+	2.22735i	0.281307	+	0.300335i
$56$			1.09240i			0.145978i
$57$	−3.05202	+	1.21291i	−0.404250	+	0.160654i
$58$	1.28482	−	1.28482i	0.168705	−	0.168705i
$59$	−5.33984			−0.695188			−0.347594	−	0.937645i	$-0.613001\pi$
$59$	−5.33984			−0.695188			−0.347594	+	0.937645i	$0.613001\pi$
$60$	1.64905	−	3.50437i	0.212892	−	0.452413i
$61$	−12.6521			−1.61994			−0.809969	−	0.586472i	$-0.800516\pi$
$61$	−12.6521			−1.61994			−0.809969	+	0.586472i	$0.800516\pi$
$62$	3.69640	−	3.69640i	0.469443	−	0.469443i
$63$	−3.27582	−	0.0945356i	−0.412715	−	0.0119104i
$64$			1.00000i			0.125000i
$65$	−0.0835778	+	2.55474i	−0.0103666	+	0.316877i
$66$	0.936037	−	2.17069i	0.115218	−	0.267193i
$67$	8.07409	+	8.07409i	0.986408	+	0.986408i	0.999909	−	0.0135013i	$-0.00429772\pi$
$67$	8.07409	+	8.07409i	0.986408	+	0.986408i	−0.0135013	+	0.999909i	$0.504298\pi$
$68$	−2.66253	−	2.66253i	−0.322879	−	0.322879i
$69$	0.685841	−	1.59048i	0.0825655	−	0.191471i
$70$	1.78278	−	1.66983i	0.213083	−	0.199583i
$71$		−	2.85426i		−	0.338738i	−0.985553	−	0.169369i	$-0.945827\pi$
$71$		−	2.85426i		−	0.338738i	0.985553	−	0.169369i	$-0.0541730\pi$
$72$	−2.99875	−	0.0865397i	−0.353406	−	0.0101988i
$73$	8.07529	−	8.07529i	0.945142	−	0.945142i	−0.0534300	−	0.998572i	$-0.517015\pi$
$73$	8.07529	−	8.07529i	0.945142	−	0.945142i	0.998572	+	0.0534300i	$0.0170154\pi$
$74$	9.98401			1.16062
$75$	−8.23984	+	2.66552i	−0.951455	+	0.307788i
$76$	−1.89614			−0.217502
$77$	1.05423	−	1.05423i	0.120140	−	0.120140i
$78$	1.83998	−	0.731230i	0.208336	−	0.0827955i
$79$			4.48733i			0.504864i	0.967615	+	0.252432i	$0.0812304\pi$
$79$			4.48733i			0.504864i	−0.967615	+	0.252432i	$0.918770\pi$
$80$	1.63199	−	1.52859i	0.182462	−	0.170902i
$81$	0.519022	−	8.98502i	0.0576691	−	0.998336i
$82$	5.10464	+	5.10464i	0.563713	+	0.563713i
$83$	−0.994740	−	0.994740i	−0.109187	−	0.109187i	0.650403	−	0.759590i	$-0.274600\pi$
$83$	−0.994740	−	0.994740i	−0.109187	−	0.109187i	−0.759590	+	0.650403i	$0.774600\pi$
$84$	−1.73743	−	0.749210i	−0.189569	−	0.0817455i
$85$	−0.275300	+	8.41515i	−0.0298605	+	0.912752i
$86$			7.06419i			0.761751i
$87$	1.16230	+	2.92466i	0.124611	+	0.313557i
$88$	0.965061	−	0.965061i	0.102876	−	0.102876i
$89$	3.62956			0.384733			0.192367	−	0.981323i	$-0.438384\pi$
$89$	3.62956			0.384733			0.192367	+	0.981323i	$0.438384\pi$
$90$	4.44264	+	5.02622i	0.468296	+	0.529810i
$91$	1.24875			0.130904
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	3.34390	+	8.41418i	0.346746	+	0.872510i
$94$			10.2968i			1.06203i
$95$	2.89842	+	3.09448i	0.297372	+	0.317487i
$96$	−1.59048	−	0.685841i	−0.162328	−	0.0699983i
$97$	−0.314895	−	0.314895i	−0.0319728	−	0.0319728i	0.690940	−	0.722912i	$-0.257197\pi$
$97$	−0.314895	−	0.314895i	−0.0319728	−	0.0319728i	−0.722912	+	0.690940i	$0.757197\pi$
$98$	4.10594	+	4.10594i	0.414762	+	0.414762i
$99$	2.81046	+	2.97749i	0.282462	+	0.299249i
$100$	−4.98931	−	0.326798i	−0.498931	−	0.0326798i
$101$		−	6.06536i		−	0.603526i	−0.953383	−	0.301763i	$-0.902425\pi$
$101$		−	6.06536i		−	0.603526i	0.953383	−	0.301763i	$-0.0975751\pi$
$102$	6.06077	−	2.40862i	0.600105	−	0.238489i
$103$	−6.59635	+	6.59635i	−0.649958	+	0.649958i	−0.952983	−	0.303025i	$-0.902003\pi$
$103$	−6.59635	+	6.59635i	−0.649958	+	0.649958i	0.303025	+	0.952983i	$0.402003\pi$
$104$	1.14313			0.112093
$105$	1.43313	+	3.98071i	0.139859	+	0.388478i
$106$	2.15625			0.209433
$107$	4.92750	−	4.92750i	0.476360	−	0.476360i	−0.427606	−	0.903965i	$-0.640643\pi$
$107$	4.92750	−	4.92750i	0.476360	−	0.476360i	0.903965	+	0.427606i	$0.140643\pi$
$108$	2.19431	−	4.71010i	0.211147	−	0.453229i
$109$		−	3.61827i		−	0.346568i	−0.984872	−	0.173284i	$-0.944562\pi$
$109$		−	3.61827i		−	0.346568i	0.984872	−	0.173284i	$-0.0554378\pi$
$110$	−3.05016	−	0.0997852i	−0.290821	−	0.00951415i
$111$	−6.84744	+	15.8794i	−0.649930	+	1.50720i
$112$	−0.772441	−	0.772441i	−0.0729888	−	0.0729888i
$113$	14.6555	+	14.6555i	1.37868	+	1.37868i	0.846858	+	0.531820i	$0.178492\pi$
$113$	14.6555	+	14.6555i	1.37868	+	1.37868i	0.531820	+	0.846858i	$0.321508\pi$
$114$	1.30045	−	3.01576i	0.121798	−	0.282452i
$115$	−2.23487	−	0.0731134i	−0.208403	−	0.00681786i
$116$			1.81701i			0.168705i
$117$	−0.0989258	+	3.42795i	−0.00914570	+	0.316914i
$118$	3.77584	−	3.77584i	0.347594	−	0.347594i
$119$	4.11329			0.377065
$120$	1.31191	+	3.64402i	0.119760	+	0.332652i
$121$	9.13732			0.830665
$122$	8.94641	−	8.94641i	0.809969	−	0.809969i
$123$	−11.6198	+	4.61785i	−1.04772	+	0.416377i
$124$			5.22750i			0.469443i
$125$	7.09330	+	8.64206i	0.634444	+	0.772969i
$126$	2.38320	−	2.24951i	0.212313	−	0.200402i
$127$	−4.60108	−	4.60108i	−0.408280	−	0.408280i	0.472859	−	0.881138i	$-0.343222\pi$
$127$	−4.60108	−	4.60108i	−0.408280	−	0.408280i	−0.881138	+	0.472859i	$0.843222\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−11.2354	−	4.84491i	−0.989225	−	0.426570i
$130$	−1.74738	−	1.86557i	−0.153255	−	0.163622i
$131$			5.27382i			0.460776i	0.973099	+	0.230388i	$0.0739995\pi$
$131$			5.27382i			0.460776i	−0.973099	+	0.230388i	$0.926000\pi$
$132$	0.873030	+	2.19679i	0.0759875	+	0.191206i
$133$	1.46465	−	1.46465i	0.127002	−	0.127002i
$134$	−11.4185			−0.986408
$135$	−11.0410	+	3.61874i	−0.950262	+	0.311451i
$136$	3.76538			0.322879
$137$	15.1645	−	15.1645i	1.29559	−	1.29559i	0.364316	−	0.931275i	$-0.381303\pi$
$137$	15.1645	−	15.1645i	1.29559	−	1.29559i	0.931275	−	0.364316i	$-0.118697\pi$
$138$	0.639676	+	1.60960i	0.0544528	+	0.137018i
$139$			5.03496i			0.427060i	0.976937	+	0.213530i	$0.0684961\pi$
$139$			5.03496i			0.427060i	−0.976937	+	0.213530i	$0.931504\pi$
$140$	−0.0798687	+	2.44137i	−0.00675014	+	0.206333i
$141$	−16.3768	−	7.06195i	−1.37918	−	0.594724i
$142$	2.01827	+	2.01827i	0.169369	+	0.169369i
$143$	−1.10319	−	1.10319i	−0.0922531	−	0.0922531i
$144$	2.18163	−	2.05924i	0.181803	−	0.171604i
$145$	2.96535	−	2.77747i	0.246259	−	0.230657i
$146$			11.4202i			0.945142i
$147$	−9.34642	+	3.71439i	−0.770880	+	0.306357i
$148$	−7.05976	+	7.05976i	−0.580309	+	0.580309i
$149$	−8.21557			−0.673046			−0.336523	−	0.941675i	$-0.609251\pi$
$149$	−8.21557			−0.673046			−0.336523	+	0.941675i	$0.609251\pi$
$150$	3.94164	−	7.71126i	0.321833	−	0.629622i
$151$	−1.65202			−0.134439			−0.0672196	−	0.997738i	$-0.521413\pi$
$151$	−1.65202			−0.134439			−0.0672196	+	0.997738i	$0.521413\pi$
$152$	1.34077	−	1.34077i	0.108751	−	0.108751i
$153$	−0.325855	+	11.2915i	−0.0263438	+	0.912860i
$154$			1.49090i			0.120140i
$155$	8.53123	−	7.99072i	0.685245	−	0.641830i
$156$	−0.784003	+	1.81812i	−0.0627705	+	0.145566i
$157$	−5.93938	−	5.93938i	−0.474014	−	0.474014i	0.429197	−	0.903211i	$-0.358797\pi$
$157$	−5.93938	−	5.93938i	−0.474014	−	0.474014i	−0.903211	+	0.429197i	$0.858797\pi$
$158$	−3.17302	−	3.17302i	−0.252432	−	0.252432i
$159$	−1.47884	+	3.42947i	−0.117280	+	0.271975i
$160$	−0.0731134	+	2.23487i	−0.00578012	+	0.176682i
$161$			1.09240i			0.0860929i
$162$	5.98637	+	6.72037i	0.470333	+	0.528002i
$163$	−6.31993	+	6.31993i	−0.495015	+	0.495015i	−0.909882	−	0.414867i	$-0.863828\pi$
$163$	−6.31993	+	6.31993i	−0.495015	+	0.495015i	0.414867	+	0.909882i	$0.363828\pi$
$164$	−7.21905			−0.563713
$165$	2.25063	−	4.78277i	0.175211	−	0.372338i
$166$	1.40677			0.109187
$167$	−8.62159	+	8.62159i	−0.667159	+	0.667159i	−0.957057	−	0.289899i	$-0.906378\pi$
$167$	−8.62159	+	8.62159i	−0.667159	+	0.667159i	0.289899	+	0.957057i	$0.406378\pi$
$168$	1.75832	−	0.698779i	0.135657	−	0.0539120i
$169$			11.6933i			0.899482i
$170$	−5.75575	−	6.14508i	−0.441446	−	0.471306i
$171$	3.90461	+	4.13667i	0.298593	+	0.316339i
$172$	−4.99514	−	4.99514i	−0.380875	−	0.380875i
$173$	−3.38026	−	3.38026i	−0.256996	−	0.256996i	0.566835	−	0.823831i	$-0.308168\pi$
$173$	−3.38026	−	3.38026i	−0.256996	−	0.256996i	−0.823831	+	0.566835i	$0.808168\pi$
$174$	−2.88992	−	1.24618i	−0.219084	−	0.0944727i
$175$	4.10638	−	3.60151i	0.310413	−	0.272249i
$176$			1.36480i			0.102876i
$177$	3.41577	+	8.59501i	0.256745	+	0.646041i
$178$	−2.56649	+	2.56649i	−0.192367	+	0.192367i
$179$	−17.4987			−1.30792			−0.653958	−	0.756531i	$-0.726893\pi$
$179$	−17.4987			−1.30792			−0.653958	+	0.756531i	$0.726893\pi$
$180$	−6.69550	−	0.412654i	−0.499053	−	0.0307574i
$181$	14.3176			1.06422			0.532109	−	0.846676i	$-0.321400\pi$
$181$	14.3176			1.06422			0.532109	+	0.846676i	$0.321400\pi$
$182$	−0.882998	+	0.882998i	−0.0654521	+	0.0654521i
$183$	8.09326	+	20.3649i	0.598271	+	1.50542i
$184$			1.00000i			0.0737210i
$185$	22.3130	+	0.729964i	1.64048	+	0.0536680i
$186$	−8.31422	−	3.58523i	−0.609628	−	0.262882i
$187$	−3.63382	−	3.63382i	−0.265732	−	0.265732i
$188$	−7.28092	−	7.28092i	−0.531016	−	0.531016i
$189$	1.94330	+	5.33324i	0.141354	+	0.387936i
$190$	−4.23762	−	0.138633i	−0.307430	−	0.0100575i
$191$		−	3.47708i		−	0.251593i	−0.992056	−	0.125796i	$-0.959851\pi$
$191$		−	3.47708i		−	0.251593i	0.992056	−	0.125796i	$-0.0401486\pi$
$192$	1.60960	−	0.639676i	0.116163	−	0.0461646i
$193$	−10.8007	+	10.8007i	−0.777450	+	0.777450i	−0.979397	−	0.201946i	$-0.935273\pi$
$193$	−10.8007	+	10.8007i	−0.777450	+	0.777450i	0.201946	+	0.979397i	$0.435273\pi$
$194$	0.445329			0.0319728
$195$	4.16558	−	1.49968i	0.298303	−	0.107394i
$196$	−5.80667			−0.414762
$197$	−3.69180	+	3.69180i	−0.263030	+	0.263030i	−0.826284	−	0.563254i	$-0.809549\pi$
$197$	−3.69180	+	3.69180i	−0.263030	+	0.263030i	0.563254	+	0.826284i	$0.309549\pi$
$198$	−4.09270	−	0.118110i	−0.290856	−	0.00839368i
$199$			5.69788i			0.403912i	0.979395	+	0.201956i	$0.0647298\pi$
$199$			5.69788i			0.403912i	−0.979395	+	0.201956i	$0.935270\pi$
$200$	3.75906	−	3.29689i	0.265805	−	0.233126i
$201$	7.83127	−	18.1609i	0.552375	−	1.28097i
$202$	4.28886	+	4.28886i	0.301763	+	0.301763i
$203$	−1.40353	−	1.40353i	−0.0985087	−	0.0985087i
$204$	−2.58245	+	5.98876i	−0.180808	+	0.419297i
$205$	11.0350	+	11.7814i	0.770717	+	0.822851i
$206$		−	9.32865i		−	0.649958i
$207$	−2.99875	−	0.0865397i	−0.208428	−	0.00601492i
$208$	−0.808313	+	0.808313i	−0.0560464	+	0.0560464i
$209$	−2.58785			−0.179005
$210$	−3.82816	−	1.80142i	−0.264168	−	0.124310i
$211$	3.16715			0.218035			0.109018	−	0.994040i	$-0.465229\pi$
$211$	3.16715			0.218035			0.109018	+	0.994040i	$0.465229\pi$
$212$	−1.52470	+	1.52470i	−0.104717	+	0.104717i
$213$	−4.59422	+	1.82580i	−0.314791	+	0.125102i
$214$			6.96854i			0.476360i
$215$	−0.516486	+	15.7876i	−0.0352241	+	1.07670i
$216$	1.77893	+	4.88215i	0.121041	+	0.332188i
$217$	−4.03793	−	4.03793i	−0.274113	−	0.274113i
$218$	2.55851	+	2.55851i	0.173284	+	0.173284i
$219$	−18.1636	−	7.83243i	−1.22738	−	0.529267i
$220$	2.22735	−	2.08623i	0.150168	−	0.140653i
$221$		−	4.30431i		−	0.289539i
$222$	−6.38653	−	16.0703i	−0.428636	−	1.07857i
$223$	2.95699	−	2.95699i	0.198015	−	0.198015i	−0.601134	−	0.799148i	$-0.705284\pi$
$223$	2.95699	−	2.95699i	0.198015	−	0.198015i	0.799148	+	0.601134i	$0.205284\pi$
$224$	1.09240			0.0729888
$225$	9.56126	+	11.5578i	0.637417	+	0.770519i
$226$	−20.7261			−1.37868
$227$	−5.49778	+	5.49778i	−0.364901	+	0.364901i	−0.865614	−	0.500713i	$-0.833071\pi$
$227$	−5.49778	+	5.49778i	−0.364901	+	0.364901i	0.500713	+	0.865614i	$0.333071\pi$
$228$	1.21291	+	3.05202i	0.0803271	+	0.202125i
$229$		−	16.0987i		−	1.06383i	−0.846798	−	0.531915i	$-0.821472\pi$
$229$		−	16.0987i		−	1.06383i	0.846798	−	0.531915i	$-0.178528\pi$
$230$	1.63199	−	1.52859i	0.107610	−	0.100793i
$231$	−2.37125	−	1.02252i	−0.156017	−	0.0672771i
$232$	−1.28482	−	1.28482i	−0.0843526	−	0.0843526i
$233$	−0.479523	−	0.479523i	−0.0314146	−	0.0314146i	0.691225	−	0.722640i	$-0.257071\pi$
$233$	−0.479523	−	0.479523i	−0.0314146	−	0.0314146i	−0.722640	+	0.691225i	$0.757071\pi$
$234$	−2.35398	−	2.49388i	−0.153884	−	0.163030i
$235$	−0.752832	+	23.0120i	−0.0491093	+	1.50114i
$236$			5.33984i			0.347594i
$237$	7.22281	−	2.87043i	0.469172	−	0.186455i
$238$	−2.90854	+	2.90854i	−0.188532	+	0.188532i
$239$	−16.4726			−1.06553			−0.532763	−	0.846265i	$-0.678846\pi$
$239$	−16.4726			−1.06553			−0.532763	+	0.846265i	$0.678846\pi$
$240$	−3.50437	−	1.64905i	−0.226206	−	0.106446i
$241$	−0.756022			−0.0486996			−0.0243498	−	0.999703i	$-0.507752\pi$
$241$	−0.756022			−0.0486996			−0.0243498	+	0.999703i	$0.507752\pi$
$242$	−6.46106	+	6.46106i	−0.415333	+	0.415333i
$243$	−14.7943	+	4.91208i	−0.949055	+	0.315110i
$244$			12.6521i			0.809969i
$245$	8.87604	+	9.47644i	0.567070	+	0.605428i
$246$	4.95112	−	11.4817i	0.315672	−	0.732049i
$247$	−1.53267	−	1.53267i	−0.0975215	−	0.0975215i
$248$	−3.69640	−	3.69640i	−0.234722	−	0.234722i
$249$	−0.964824	+	2.23745i	−0.0611432	+	0.141792i
$250$	−11.1266	−	1.09514i	−0.703706	−	0.0692625i
$251$		−	18.7709i		−	1.18481i	−0.805641	−	0.592404i	$-0.798179\pi$
$251$		−	18.7709i		−	1.18481i	0.805641	−	0.592404i	$-0.201821\pi$
$252$	−0.0945356	+	3.27582i	−0.00595518	+	0.206358i
$253$	0.965061	−	0.965061i	0.0606728	−	0.0606728i
$254$	6.50691			0.408280
$255$	13.7211	−	4.93985i	0.859251	−	0.309345i
$256$	1.00000			0.0625000
$257$	8.02496	−	8.02496i	0.500584	−	0.500584i	−0.411036	−	0.911619i	$-0.634833\pi$
$257$	8.02496	−	8.02496i	0.500584	−	0.500584i	0.911619	+	0.411036i	$0.134833\pi$
$258$	11.3705	−	4.51879i	0.707898	−	0.281327i
$259$		−	10.9065i		−	0.677696i
$260$	2.55474	+	0.0835778i	0.158438	+	0.00518328i
$261$	3.96405	−	3.74167i	0.245368	−	0.231604i
$262$	−3.72915	−	3.72915i	−0.230388	−	0.230388i
$263$	11.1699	+	11.1699i	0.688763	+	0.688763i	0.961959	−	0.273195i	$-0.0880806\pi$
$263$	11.1699	+	11.1699i	0.688763	+	0.688763i	−0.273195	+	0.961959i	$0.588081\pi$
$264$	−2.17069	−	0.936037i	−0.133597	−	0.0576091i
$265$	4.81894	+	0.157651i	0.296025	+	0.00968440i
$266$			2.07133i			0.127002i
$267$	−2.32174	−	5.84215i	−0.142088	−	0.357534i
$268$	8.07409	−	8.07409i	0.493204	−	0.493204i
$269$	−14.1462			−0.862509			−0.431255	−	0.902230i	$-0.641929\pi$
$269$	−14.1462			−0.862509			−0.431255	+	0.902230i	$0.641929\pi$
$270$	5.24836	−	10.3660i	0.319405	−	0.630857i
$271$	22.7957			1.38474			0.692370	−	0.721543i	$-0.256567\pi$
$271$	22.7957			1.38474			0.692370	+	0.721543i	$0.256567\pi$
$272$	−2.66253	+	2.66253i	−0.161440	+	0.161440i
$273$	−0.798793	−	2.00998i	−0.0483452	−	0.121650i
$274$			21.4459i			1.29559i
$275$	−6.80942	−	0.446014i	−0.410623	−	0.0268957i
$276$	−1.59048	−	0.685841i	−0.0957356	−	0.0412828i
$277$	−22.2098	−	22.2098i	−1.33446	−	1.33446i	−0.901334	−	0.433125i	$-0.857411\pi$
$277$	−22.2098	−	22.2098i	−1.33446	−	1.33446i	−0.433125	−	0.901334i	$-0.642589\pi$
$278$	−3.56026	−	3.56026i	−0.213530	−	0.213530i
$279$	11.4045	−	10.7647i	0.682768	−	0.644465i
$280$	−1.66983	−	1.78278i	−0.0997915	−	0.106542i
$281$			7.10907i			0.424091i	0.977260	+	0.212046i	$0.0680126\pi$
$281$			7.10907i			0.424091i	−0.977260	+	0.212046i	$0.931987\pi$
$282$	16.5737	−	6.58660i	0.986950	−	0.392226i
$283$	16.7996	−	16.7996i	0.998634	−	0.998634i	−0.00136548	−	0.999999i	$-0.500435\pi$
$283$	16.7996	−	16.7996i	0.998634	−	0.998634i	0.999999	+	0.00136548i	$0.000434647\pi$
$284$	−2.85426			−0.169369
$285$	3.12683	−	6.64477i	0.185217	−	0.393602i
$286$	1.56014			0.0922531
$287$	5.57628	−	5.57628i	0.329158	−	0.329158i
$288$	−0.0865397	+	2.99875i	−0.00509940	+	0.176703i
$289$			2.82188i			0.165993i
$290$	−0.132848	+	4.06079i	−0.00780109	+	0.238458i
$291$	−0.305425	+	0.708287i	−0.0179043	+	0.0415205i
$292$	−8.07529	−	8.07529i	−0.472571	−	0.472571i
$293$	23.0811	+	23.0811i	1.34841	+	1.34841i	0.887388	+	0.461023i	$0.152517\pi$
$293$	23.0811	+	23.0811i	1.34841	+	1.34841i	0.461023	+	0.887388i	$0.347483\pi$
$294$	3.98245	−	9.23539i	0.232261	−	0.538619i
$295$	8.71458	−	8.16245i	0.507382	−	0.475236i
$296$		−	9.98401i		−	0.580309i
$297$	2.99479	−	6.42835i	0.173775	−	0.373011i
$298$	5.80929	−	5.80929i	0.336523	−	0.336523i
$299$	1.14313			0.0661087
$300$	2.66552	+	8.23984i	0.153894	+	0.475727i
$301$	7.71689			0.444794
$302$	1.16815	−	1.16815i	0.0672196	−	0.0672196i
$303$	−9.76281	+	3.87986i	−0.560859	+	0.222892i
$304$			1.89614i			0.108751i
$305$	20.6482	−	19.3400i	1.18231	−	1.10740i
$306$	−7.75385	−	8.21468i	−0.443258	−	0.469602i
$307$	8.15376	+	8.15376i	0.465360	+	0.465360i	0.900407	−	0.435048i	$-0.143268\pi$
$307$	8.15376	+	8.15376i	0.465360	+	0.465360i	−0.435048	+	0.900407i	$0.643268\pi$
$308$	−1.05423	−	1.05423i	−0.0600702	−	0.0600702i
$309$	14.8370	+	6.39797i	0.844048	+	0.363968i
$310$	−0.382200	+	11.6828i	−0.0217075	+	0.663538i
$311$			13.6217i			0.772419i	0.922411	+	0.386209i	$0.126216\pi$
$311$			13.6217i			0.772419i	−0.922411	+	0.386209i	$0.873784\pi$
$312$	−0.731230	−	1.83998i	−0.0413978	−	0.104168i
$313$	19.4239	−	19.4239i	1.09791	−	1.09791i	0.103251	−	0.994655i	$-0.467076\pi$
$313$	19.4239	−	19.4239i	1.09791	−	1.09791i	0.994655	−	0.103251i	$-0.0329245\pi$
$314$	8.39956			0.474014
$315$	5.49063	−	4.85313i	0.309362	−	0.273443i
$316$	4.48733			0.252432
$317$	−6.12789	+	6.12789i	−0.344177	+	0.344177i	−0.857935	−	0.513758i	$-0.828253\pi$
$317$	−6.12789	+	6.12789i	−0.344177	+	0.344177i	0.513758	+	0.857935i	$0.328253\pi$
$318$	−1.37930	−	3.47070i	−0.0773473	−	0.194627i
$319$			2.47986i			0.138845i
$320$	−1.52859	−	1.63199i	−0.0854510	−	0.0912311i
$321$	−11.0833	−	4.77931i	−0.618610	−	0.266755i
$322$	−0.772441	−	0.772441i	−0.0430464	−	0.0430464i
$323$	−5.04852	−	5.04852i	−0.280907	−	0.280907i
$324$	−8.98502	−	0.519022i	−0.499168	−	0.0288346i
$325$	−3.76877	−	4.29708i	−0.209054	−	0.238359i
$326$		−	8.93774i		−	0.495015i
$327$	−5.82398	+	2.31452i	−0.322067	+	0.127993i
$328$	5.10464	−	5.10464i	0.281856	−	0.281856i
$329$	11.2482			0.620131
$330$	1.79050	+	4.97337i	0.0985636	+	0.273775i
$331$	20.0224			1.10053			0.550266	−	0.834990i	$-0.314526\pi$
$331$	20.0224			1.10053			0.550266	+	0.834990i	$0.314526\pi$
$332$	−0.994740	+	0.994740i	−0.0545934	+	0.0545934i
$333$	29.9396	+	0.864013i	1.64068	+	0.0473476i
$334$		−	12.1928i		−	0.667159i
$335$	−25.5189	−	0.834844i	−1.39425	−	0.0456124i
$336$	−0.749210	+	1.73743i	−0.0408727	+	0.0947847i
$337$	−25.7245	−	25.7245i	−1.40130	−	1.40130i	−0.795974	−	0.605331i	$-0.793041\pi$
$337$	−25.7245	−	25.7245i	−1.40130	−	1.40130i	−0.605331	−	0.795974i	$-0.706959\pi$
$338$	−8.26838	−	8.26838i	−0.449741	−	0.449741i
$339$	14.2148	−	32.9644i	0.772041	−	1.79038i
$340$	8.41515	+	0.275300i	0.456376	+	0.0149302i
$341$			7.13450i			0.386355i
$342$	−5.68604	−	0.164091i	−0.307466	−	0.00887303i
$343$	9.89239	−	9.89239i	0.534139	−	0.534139i
$344$	7.06419			0.380875
$345$	1.31191	+	3.64402i	0.0706309	+	0.196188i
$346$	4.78041			0.256996
$347$	−19.5787	+	19.5787i	−1.05104	+	1.05104i	−0.0524136	+	0.998625i	$0.516691\pi$
$347$	−19.5787	+	19.5787i	−1.05104	+	1.05104i	−0.998625	+	0.0524136i	$0.983309\pi$
$348$	2.92466	−	1.16230i	0.156778	−	0.0623057i
$349$		−	1.90866i		−	0.102168i	−0.998694	−	0.0510840i	$-0.983732\pi$
$349$		−	1.90866i		−	0.102168i	0.998694	−	0.0510840i	$-0.0162676\pi$
$350$	−0.356993	+	5.45030i	−0.0190821	+	0.291331i
$351$	5.58092	−	2.03355i	0.297887	−	0.108543i
$352$	−0.965061	−	0.965061i	−0.0514379	−	0.0514379i
$353$	−15.6064	−	15.6064i	−0.830643	−	0.830643i	0.156961	−	0.987605i	$-0.449830\pi$
$353$	−15.6064	−	15.6064i	−0.830643	−	0.830643i	−0.987605	+	0.156961i	$0.949830\pi$
$354$	−8.49290	−	3.66228i	−0.451393	−	0.194648i
$355$	4.36300	+	4.65813i	0.231564	+	0.247228i
$356$		−	3.62956i		−	0.192367i
$357$	−2.63117	−	6.62076i	−0.139256	−	0.350408i
$358$	12.3735	−	12.3735i	0.653958	−	0.653958i
$359$	−25.7394			−1.35847			−0.679237	−	0.733919i	$-0.737689\pi$
$359$	−25.7394			−1.35847			−0.679237	+	0.733919i	$0.737689\pi$
$360$	5.02622	−	4.44264i	0.264905	−	0.234148i
$361$	15.4047			0.810772
$362$	−10.1241	+	10.1241i	−0.532109	+	0.532109i
$363$	−5.84492	−	14.7074i	−0.306779	−	0.771940i
$364$		−	1.24875i		−	0.0654521i
$365$	−0.834968	+	25.5227i	−0.0437042	+	1.33592i
$366$	−20.1229	−	8.67735i	−1.05184	−	0.453572i
$367$	12.7473	+	12.7473i	0.665403	+	0.665403i	0.956648	−	0.291245i	$-0.0940695\pi$
$367$	12.7473	+	12.7473i	0.665403	+	0.665403i	−0.291245	+	0.956648i	$0.594070\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	14.8658	+	15.7493i	0.773882	+	0.819875i
$370$	−16.2938	+	15.2615i	−0.847076	+	0.793408i
$371$		−	2.35548i		−	0.122290i
$372$	8.41418	−	3.34390i	0.436255	−	0.173373i
$373$	−4.06861	+	4.06861i	−0.210664	+	0.210664i	−0.804550	−	0.593885i	$-0.797593\pi$
$373$	−4.06861	+	4.06861i	−0.210664	+	0.210664i	0.593885	+	0.804550i	$0.297593\pi$
$374$	5.13900			0.265732
$375$	9.37285	−	16.9455i	0.484012	−	0.875061i
$376$	10.2968			0.531016
$377$	−1.46871	+	1.46871i	−0.0756426	+	0.0756426i
$378$	−5.14529	−	2.39705i	−0.264645	−	0.123291i
$379$		−	24.1694i		−	1.24150i	−0.784009	−	0.620749i	$-0.786829\pi$
$379$		−	24.1694i		−	1.24150i	0.784009	−	0.620749i	$-0.213171\pi$
$380$	3.09448	−	2.89842i	0.158743	−	0.148686i
$381$	−4.46270	+	10.3491i	−0.228631	+	0.530200i
$382$	2.45867	+	2.45867i	0.125796	+	0.125796i
$383$	15.3856	+	15.3856i	0.786167	+	0.786167i	0.980863	−	0.194697i	$-0.0623722\pi$
$383$	15.3856	+	15.3856i	0.786167	+	0.786167i	−0.194697	+	0.980863i	$0.562372\pi$
$384$	−0.685841	+	1.59048i	−0.0349992	+	0.0811638i
$385$	−0.109005	+	3.33198i	−0.00555541	+	0.169813i
$386$		−	15.2745i		−	0.777450i
$387$	−0.611333	+	21.1837i	−0.0310758	+	1.07683i
$388$	−0.314895	+	0.314895i	−0.0159864	+	0.0159864i
$389$	−3.95930			−0.200744			−0.100372	−	0.994950i	$-0.532003\pi$
$389$	−3.95930			−0.200744			−0.100372	+	0.994950i	$0.532003\pi$
$390$	−1.88508	+	4.00594i	−0.0954545	+	0.202849i
$391$	3.76538			0.190424
$392$	4.10594	−	4.10594i	0.207381	−	0.207381i
$393$	8.48875	−	3.37353i	0.428201	−	0.170172i
$394$		−	5.22100i		−	0.263030i
$395$	−6.85931	−	7.32329i	−0.345129	−	0.368475i
$396$	2.97749	−	2.81046i	0.149625	−	0.141231i
$397$	−15.4078	−	15.4078i	−0.773294	−	0.773294i	0.205387	−	0.978681i	$-0.434155\pi$
$397$	−15.4078	−	15.4078i	−0.773294	−	0.773294i	−0.978681	+	0.205387i	$0.934155\pi$
$398$	−4.02901	−	4.02901i	−0.201956	−	0.201956i
$399$	−3.29441	−	1.42060i	−0.164927	−	0.0711192i
$400$	−0.326798	+	4.98931i	−0.0163399	+	0.249465i
$401$			18.2444i			0.911080i	0.890215	+	0.455540i	$0.150554\pi$
$401$			18.2444i			0.911080i	−0.890215	+	0.455540i	$0.849446\pi$
$402$	7.30413	+	18.3792i	0.364297	+	0.916672i
$403$	−4.22545	+	4.22545i	−0.210485	+	0.210485i
$404$	−6.06536			−0.301763
$405$	12.8874	+	15.4569i	0.640381	+	0.768058i
$406$	1.98490			0.0985087
$407$	−9.63517	+	9.63517i	−0.477598	+	0.477598i
$408$	−2.40862	−	6.06077i	−0.119245	−	0.300053i
$409$			24.0799i			1.19067i	0.803477	+	0.595336i	$0.202981\pi$
$409$			24.0799i			1.19067i	−0.803477	+	0.595336i	$0.797019\pi$
$410$	−16.1336	−	0.527809i	−0.796784	−	0.0260666i
$411$	−34.1092	−	14.7084i	−1.68248	−	0.725514i
$412$	6.59635	+	6.59635i	0.324979	+	0.324979i
$413$	−4.12471	−	4.12471i	−0.202964	−	0.202964i
$414$	2.18163	−	2.05924i	0.107221	−	0.101206i
$415$	3.14396	+	0.102854i	0.154331	+	0.00504891i
$416$		−	1.14313i		−	0.0560464i
$417$	8.10428	−	3.22074i	0.396868	−	0.157720i
$418$	1.82989	−	1.82989i	0.0895027	−	0.0895027i
$419$	14.3159			0.699380			0.349690	−	0.936866i	$-0.386287\pi$
$419$	14.3159			0.699380			0.349690	+	0.936866i	$0.386287\pi$
$420$	3.98071	−	1.43313i	0.194239	−	0.0699294i
$421$	13.1564			0.641205			0.320603	−	0.947214i	$-0.396115\pi$
$421$	13.1564			0.641205			0.320603	+	0.947214i	$0.396115\pi$
$422$	−2.23951	+	2.23951i	−0.109018	+	0.109018i
$423$	−0.891080	+	30.8775i	−0.0433258	+	1.50131i
$424$		−	2.15625i		−	0.104717i
$425$	−12.4141	−	14.1543i	−0.602171	−	0.686584i
$426$	1.95757	−	4.53964i	0.0948444	−	0.219946i
$427$	−9.77302	−	9.77302i	−0.472950	−	0.472950i
$428$	−4.92750	−	4.92750i	−0.238180	−	0.238180i
$429$	−1.07001	+	2.48137i	−0.0516605	+	0.119802i
$430$	−10.7983	−	11.5287i	−0.520739	−	0.555963i
$431$			15.2273i			0.733472i	0.930325	+	0.366736i	$0.119525\pi$
$431$			15.2273i			0.733472i	−0.930325	+	0.366736i	$0.880475\pi$
$432$	−4.71010	−	2.19431i	−0.226615	−	0.105574i
$433$	−14.9801	+	14.9801i	−0.719899	+	0.719899i	−0.968584	−	0.248686i	$-0.920001\pi$
$433$	−14.9801	+	14.9801i	−0.719899	+	0.719899i	0.248686	+	0.968584i	$0.420001\pi$
$434$	5.71050			0.274113
$435$	−6.36748	−	2.99635i	−0.305297	−	0.143664i
$436$	−3.61827			−0.173284
$437$	1.34077	−	1.34077i	0.0641378	−	0.0641378i
$438$	18.3819	−	7.30522i	0.878323	−	0.349057i
$439$		−	28.6098i		−	1.36547i	−0.730667	−	0.682734i	$-0.760791\pi$
$439$		−	28.6098i		−	1.36547i	0.730667	−	0.682734i	$-0.239209\pi$
$440$	−0.0997852	+	3.05016i	−0.00475707	+	0.145411i
$441$	11.9574	+	12.6680i	0.569398	+	0.603239i
$442$	3.04361	+	3.04361i	0.144770	+	0.144770i
$443$	−20.0573	−	20.0573i	−0.952950	−	0.952950i	0.0459922	−	0.998942i	$-0.485355\pi$
$443$	−20.0573	−	20.0573i	−0.952950	−	0.952950i	−0.998942	+	0.0459922i	$0.985355\pi$
$444$	15.8794	+	6.84744i	0.753601	+	0.324965i
$445$	−5.92342	+	5.54813i	−0.280797	+	0.263007i
$446$			4.18182i			0.198015i
$447$	5.25530	+	13.2238i	0.248567	+	0.625464i
$448$	−0.772441	+	0.772441i	−0.0364944	+	0.0364944i
$449$	−41.1141			−1.94030			−0.970148	−	0.242513i	$-0.922028\pi$
$449$	−41.1141			−1.94030			−0.970148	+	0.242513i	$0.922028\pi$
$450$	−14.9334	−	1.41176i	−0.703968	−	0.0665510i
$451$	−9.85257			−0.463939
$452$	14.6555	−	14.6555i	0.689339	−	0.689339i
$453$	1.05675	+	2.65909i	0.0496507	+	0.124935i
$454$		−	7.77504i		−	0.364901i
$455$	−2.03795	+	1.90883i	−0.0955404	+	0.0894872i
$456$	−3.01576	−	1.30045i	−0.141226	−	0.0608991i
$457$	−12.6446	−	12.6446i	−0.591491	−	0.591491i	0.346543	−	0.938034i	$-0.387356\pi$
$457$	−12.6446	−	12.6446i	−0.591491	−	0.591491i	−0.938034	+	0.346543i	$0.887356\pi$
$458$	11.3835	+	11.3835i	0.531915	+	0.531915i
$459$	18.3832	−	6.69837i	0.858053	−	0.312653i
$460$	−0.0731134	+	2.23487i	−0.00340893	+	0.104201i
$461$		−	19.0617i		−	0.887793i	−0.896078	−	0.443896i	$-0.853596\pi$
$461$		−	19.0617i		−	0.887793i	0.896078	−	0.443896i	$-0.146404\pi$
$462$	2.39976	−	0.953695i	0.111647	−	0.0443699i
$463$	−7.42348	+	7.42348i	−0.344998	+	0.344998i	−0.858243	−	0.513244i	$-0.828444\pi$
$463$	−7.42348	+	7.42348i	−0.344998	+	0.344998i	0.513244	+	0.858243i	$0.328444\pi$
$464$	1.81701			0.0843526
$465$	−18.3191	−	8.62041i	−0.849528	−	0.399762i
$466$	0.678148			0.0314146
$467$	23.3313	−	23.3313i	1.07964	−	1.07964i	0.0831015	−	0.996541i	$-0.473517\pi$
$467$	23.3313	−	23.3313i	1.07964	−	1.07964i	0.996541	−	0.0831015i	$-0.0264826\pi$
$468$	3.42795	+	0.0989258i	0.158457	+	0.00457285i
$469$			12.4735i			0.575974i
$470$	−15.7396	−	16.8043i	−0.726013	−	0.775123i
$471$	−5.76076	+	13.3593i	−0.265442	+	0.615565i
$472$	−3.77584	−	3.77584i	−0.173797	−	0.173797i
$473$	−6.81737	−	6.81737i	−0.313463	−	0.313463i
$474$	−3.07759	+	7.13700i	−0.141359	+	0.327813i
$475$	−9.46041	−	0.619654i	−0.434073	−	0.0284317i
$476$		−	4.11329i		−	0.188532i
$477$	6.46606	+	0.186601i	0.296060	+	0.00854388i
$478$	11.6479	−	11.6479i	0.532763	−	0.532763i
$479$	−32.6430			−1.49150			−0.745749	−	0.666227i	$-0.767908\pi$
$479$	−32.6430			−1.49150			−0.745749	+	0.666227i	$0.767908\pi$
$480$	3.64402	−	1.31191i	0.166326	−	0.0598802i
$481$	−11.4130			−0.520387
$482$	0.534588	−	0.534588i	0.0243498	−	0.0243498i
$483$	1.75832	−	0.698779i	0.0800064	−	0.0317955i
$484$		−	9.13732i		−	0.415333i
$485$	0.995254	+	0.0325595i	0.0451922	+	0.00147845i
$486$	6.98779	−	13.9345i	0.316973	−	0.632083i
$487$	17.5268	+	17.5268i	0.794213	+	0.794213i	0.982176	−	0.187963i	$-0.0601885\pi$
$487$	17.5268	+	17.5268i	0.794213	+	0.794213i	−0.187963	+	0.982176i	$0.560188\pi$
$488$	−8.94641	−	8.94641i	−0.404985	−	0.404985i
$489$	14.2153	+	6.12986i	0.642837	+	0.277202i
$490$	−12.9772	−	0.424545i	−0.586249	−	0.0191790i
$491$			26.0360i			1.17499i	0.809228	+	0.587495i	$0.199886\pi$
$491$			26.0360i			1.17499i	−0.809228	+	0.587495i	$0.800114\pi$
$492$	4.61785	+	11.6198i	0.208189	+	0.523860i
$493$	−4.83784	+	4.83784i	−0.217886	+	0.217886i
$494$	2.16752			0.0975215
$495$	−9.13803	−	0.563191i	−0.410724	−	0.0253135i
$496$	5.22750			0.234722
$497$	2.20475	−	2.20475i	0.0988964	−	0.0988964i
$498$	−0.899879	−	2.26435i	−0.0403246	−	0.101468i
$499$			20.5426i			0.919612i	0.888019	+	0.459806i	$0.152081\pi$
$499$			20.5426i			0.919612i	−0.888019	+	0.459806i	$0.847919\pi$
$500$	8.64206	−	7.09330i	0.386484	−	0.317222i
$501$	19.3923	+	8.36230i	0.866386	+	0.373600i
$502$	13.2730	+	13.2730i	0.592404	+	0.592404i
$503$	−0.956236	−	0.956236i	−0.0426365	−	0.0426365i	0.685467	−	0.728104i	$-0.259598\pi$
$503$	−0.956236	−	0.956236i	−0.0426365	−	0.0426365i	−0.728104	+	0.685467i	$0.759598\pi$
$504$	−2.24951	−	2.38320i	−0.100201	−	0.106156i
$505$	9.27148	+	9.89862i	0.412575	+	0.440483i
$506$			1.36480i			0.0606728i
$507$	18.8215	−	7.47989i	0.835891	−	0.332194i
$508$	−4.60108	+	4.60108i	−0.204140	+	0.204140i
$509$	24.6665			1.09332			0.546662	−	0.837353i	$-0.315898\pi$
$509$	24.6665			1.09332			0.546662	+	0.837353i	$0.315898\pi$
$510$	−6.20931	+	13.1953i	−0.274953	+	0.584298i
$511$	12.4754			0.551878
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.16070	−	8.93099i	0.183700	−	0.394313i
$514$			11.3490i			0.500584i
$515$	0.682049	−	20.8483i	0.0300547	−	0.918688i
$516$	−4.84491	+	11.2354i	−0.213285	+	0.494613i
$517$	−9.93701	−	9.93701i	−0.437029	−	0.437029i
$518$	7.71206	+	7.71206i	0.338848	+	0.338848i
$519$	−3.27860	+	7.60314i	−0.143914	+	0.333741i
$520$	−1.86557	+	1.74738i	−0.0818108	+	0.0766276i
$521$		−	20.3284i		−	0.890602i	−0.895381	−	0.445301i	$-0.853097\pi$
$521$		−	20.3284i		−	0.890602i	0.895381	−	0.445301i	$-0.146903\pi$
$522$	−0.157244	+	5.44876i	−0.00688236	+	0.238486i
$523$	−7.42441	+	7.42441i	−0.324647	+	0.324647i	−0.850547	−	0.525900i	$-0.823729\pi$
$523$	−7.42441	+	7.42441i	−0.324647	+	0.324647i	0.525900	+	0.850547i	$0.323729\pi$
$524$	5.27382			0.230388
$525$	−8.42375	−	4.30583i	−0.367643	−	0.187922i
$526$	−15.7966			−0.688763
$527$	−13.9184	+	13.9184i	−0.606293	+	0.606293i
$528$	2.19679	−	0.873030i	0.0956028	−	0.0379938i
$529$			1.00000i			0.0434783i
$530$	−3.51898	+	3.29603i	−0.152855	+	0.143170i
$531$	11.6496	−	10.9960i	0.505548	−	0.477188i
$532$	−1.46465	−	1.46465i	−0.0635008	−	0.0635008i
$533$	−5.83525	−	5.83525i	−0.252753	−	0.252753i
$534$	5.77274	+	2.48930i	0.249811	+	0.107723i
$535$	−0.509493	+	15.5738i	−0.0220273	+	0.673314i
$536$			11.4185i			0.493204i
$537$	11.1935	+	28.1659i	0.483035	+	1.21545i
$538$	10.0029	−	10.0029i	0.431255	−	0.431255i
$539$	−7.92495			−0.341352
$540$	3.61874	+	11.0410i	0.155726	+	0.475131i
$541$	−7.90986			−0.340071			−0.170036	−	0.985438i	$-0.554388\pi$
$541$	−7.90986			−0.340071			−0.170036	+	0.985438i	$0.554388\pi$
$542$	−16.1190	+	16.1190i	−0.692370	+	0.692370i
$543$	−9.15862	−	23.0456i	−0.393034	−	0.988982i
$544$		−	3.76538i		−	0.161440i
$545$	5.53087	+	5.90500i	0.236917	+	0.252942i
$546$	1.98611	+	0.856442i	0.0849975	+	0.0366523i
$547$	−23.3163	−	23.3163i	−0.996934	−	0.996934i	0.00306145	−	0.999995i	$-0.499026\pi$
$547$	−23.3163	−	23.3163i	−0.996934	−	0.996934i	−0.999995	+	0.00306145i	$0.999026\pi$
$548$	−15.1645	−	15.1645i	−0.647796	−	0.647796i
$549$	27.6023	−	26.0538i	1.17804	−	1.11195i
$550$	5.13036	−	4.49961i	0.218759	−	0.191864i
$551$			3.44530i			0.146775i
$552$	1.60960	−	0.639676i	0.0685092	−	0.0272264i
$553$	−3.46620	+	3.46620i	−0.147398	+	0.147398i
$554$	31.4094			1.33446
$555$	−13.0981	−	36.3819i	−0.555984	−	1.54433i
$556$	5.03496			0.213530
$557$	−22.9466	+	22.9466i	−0.972281	+	0.972281i	−0.999626	−	0.0273453i	$-0.991295\pi$
$557$	−22.9466	+	22.9466i	−0.972281	+	0.972281i	0.0273453	+	0.999626i	$0.491295\pi$
$558$	−0.452386	+	15.6760i	−0.0191510	+	0.663616i
$559$		−	8.07526i		−	0.341547i
$560$	2.44137	+	0.0798687i	0.103167	+	0.00337507i
$561$	−3.52454	+	8.17348i	−0.148806	+	0.345084i
$562$	−5.02687	−	5.02687i	−0.212046	−	0.212046i
$563$	−21.6668	−	21.6668i	−0.913146	−	0.913146i	0.0833728	−	0.996518i	$-0.473431\pi$
$563$	−21.6668	−	21.6668i	−0.913146	−	0.913146i	−0.996518	+	0.0833728i	$0.973431\pi$
$564$	−7.06195	+	16.3768i	−0.297362	+	0.689588i
$565$	−46.3201	−	1.51535i	−1.94870	−	0.0637513i
$566$			23.7582i			0.998634i
$567$	7.34131	−	6.53948i	0.308306	−	0.274632i
$568$	2.01827	−	2.01827i	0.0846846	−	0.0846846i
$569$	38.1889			1.60096			0.800480	−	0.599359i	$-0.204578\pi$
$569$	38.1889			1.60096			0.800480	+	0.599359i	$0.204578\pi$
$570$	2.48756	+	6.90956i	0.104192	+	0.289410i
$571$	15.6401			0.654516			0.327258	−	0.944935i	$-0.393875\pi$
$571$	15.6401			0.654516			0.327258	+	0.944935i	$0.393875\pi$
$572$	−1.10319	+	1.10319i	−0.0461265	+	0.0461265i
$573$	−5.59671	+	2.22420i	−0.233806	+	0.0929174i
$574$			7.88606i			0.329158i
$575$	3.75906	−	3.29689i	0.156763	−	0.137490i
$576$	−2.05924	−	2.18163i	−0.0858019	−	0.0909013i
$577$	−13.3358	−	13.3358i	−0.555175	−	0.555175i	0.372755	−	0.927930i	$-0.378413\pi$
$577$	−13.3358	−	13.3358i	−0.555175	−	0.555175i	−0.927930	+	0.372755i	$0.878413\pi$
$578$	−1.99537	−	1.99537i	−0.0829964	−	0.0829964i
$579$	24.2937	+	10.4759i	1.00961	+	0.435362i
$580$	−2.77747	−	2.96535i	−0.115328	−	0.123129i
$581$		−	1.53676i		−	0.0637554i
$582$	−0.284866	−	0.716802i	−0.0118081	−	0.0297124i
$583$	−2.08091	+	2.08091i	−0.0861825	+	0.0861825i
$584$	11.4202			0.472571
$585$	−5.07850	−	5.74561i	−0.209970	−	0.237552i
$586$	−32.6416			−1.34841
$587$	−25.1695	+	25.1695i	−1.03886	+	1.03886i	−0.0396423	+	0.999214i	$0.512622\pi$
$587$	−25.1695	+	25.1695i	−1.03886	+	1.03886i	−0.999214	+	0.0396423i	$0.987378\pi$
$588$	3.71439	+	9.34642i	0.153179	+	0.385440i
$589$			9.91205i			0.408419i
$590$	−0.390414	+	11.9339i	−0.0160731	+	0.491309i
$591$	8.30388	+	3.58077i	0.341576	+	0.147293i
$592$	7.05976	+	7.05976i	0.290154	+	0.290154i
$593$	4.65441	+	4.65441i	0.191134	+	0.191134i	0.796186	−	0.605052i	$-0.206848\pi$
$593$	4.65441	+	4.65441i	0.191134	+	0.191134i	−0.605052	+	0.796186i	$0.706848\pi$
$594$	2.42789	+	6.66317i	0.0996176	+	0.273393i
$595$	−6.71286	+	6.28755i	−0.275200	+	0.257765i
$596$			8.21557i			0.336523i
$597$	9.17132	−	3.64480i	0.375357	−	0.149172i
$598$	−0.808313	+	0.808313i	−0.0330544	+	0.0330544i
$599$	15.7951			0.645371			0.322685	−	0.946506i	$-0.395414\pi$
$599$	15.7951			0.645371			0.322685	+	0.946506i	$0.395414\pi$
$600$	−7.71126	−	3.94164i	−0.314811	−	0.160917i
$601$	31.7249			1.29408			0.647042	−	0.762454i	$-0.276006\pi$
$601$	31.7249			1.29408			0.647042	+	0.762454i	$0.276006\pi$
$602$	−5.45667	+	5.45667i	−0.222397	+	0.222397i
$603$	−34.2412	−	0.988153i	−1.39441	−	0.0402407i
$604$			1.65202i			0.0672196i
$605$	−14.9120	+	13.9673i	−0.606260	+	0.567850i
$606$	4.15987	−	9.64683i	0.168983	−	0.391875i
$607$	25.4971	+	25.4971i	1.03490	+	1.03490i	0.999369	+	0.0355281i	$0.0113113\pi$
$607$	25.4971	+	25.4971i	1.03490	+	1.03490i	0.0355281	+	0.999369i	$0.488689\pi$
$608$	−1.34077	−	1.34077i	−0.0543754	−	0.0543754i
$609$	−1.36132	+	3.15693i	−0.0551636	+	0.127925i
$610$	−0.925039	+	28.2759i	−0.0374538	+	1.14486i
$611$		−	11.7705i		−	0.476184i
$612$	11.2915	+	0.325855i	0.456430	+	0.0131719i
$613$	−5.89927	+	5.89927i	−0.238269	+	0.238269i	−0.816133	−	0.577864i	$-0.803886\pi$
$613$	−5.89927	+	5.89927i	−0.238269	+	0.238269i	0.577864	+	0.816133i	$0.303886\pi$
$614$	−11.5312			−0.465360
$615$	11.9046	−	25.2982i	0.480039	−	1.02012i
$616$	1.49090			0.0600702
$617$	−4.82392	+	4.82392i	−0.194204	+	0.194204i	−0.797510	−	0.603306i	$-0.793850\pi$
$617$	−4.82392	+	4.82392i	−0.194204	+	0.194204i	0.603306	+	0.797510i	$0.293850\pi$
$618$	−15.0154	+	5.96731i	−0.604008	+	0.240040i
$619$			15.1098i			0.607315i	0.952781	+	0.303658i	$0.0982079\pi$
$619$			15.1098i			0.607315i	−0.952781	+	0.303658i	$0.901792\pi$
$620$	−7.99072	−	8.53123i	−0.320915	−	0.342623i
$621$	1.77893	+	4.88215i	0.0713862	+	0.195914i
$622$	−9.63203	−	9.63203i	−0.386209	−	0.386209i
$623$	2.80362	+	2.80362i	0.112325	+	0.112325i
$624$	1.81812	+	0.784003i	0.0727830	+	0.0313852i
$625$	−24.7864	−	3.26099i	−0.991456	−	0.130440i
$626$			27.4696i			1.09791i
$627$	1.65538	+	4.16541i	0.0661097	+	0.166350i
$628$	−5.93938	+	5.93938i	−0.237007	+	0.237007i
$629$	−37.5936			−1.49896
$630$	−0.450782	+	7.31414i	−0.0179596	+	0.291402i
$631$	13.3645			0.532033			0.266016	−	0.963969i	$-0.414292\pi$
$631$	13.3645			0.532033			0.266016	+	0.963969i	$0.414292\pi$
$632$	−3.17302	+	3.17302i	−0.126216	+	0.126216i
$633$	−2.02595	−	5.09784i	−0.0805241	−	0.202621i
$634$		−	8.66614i		−	0.344177i
$635$	14.5421	+	0.475742i	0.577086	+	0.0188792i
$636$	3.42947	+	1.47884i	0.135987	+	0.0586400i
$637$	−4.69361	−	4.69361i	−0.185967	−	0.185967i
$638$	−1.75353	−	1.75353i	−0.0694227	−	0.0694227i
$639$	5.87762	+	6.22694i	0.232515	+	0.246334i
$640$	2.23487	+	0.0731134i	0.0883411	+	0.00289006i
$641$			15.8194i			0.624829i	0.949946	+	0.312414i	$0.101138\pi$
$641$			15.8194i			0.624829i	−0.949946	+	0.312414i	$0.898862\pi$
$642$	11.2166	−	4.45760i	0.442683	−	0.175928i
$643$	−7.41965	+	7.41965i	−0.292603	+	0.292603i	−0.838108	−	0.545505i	$-0.816338\pi$
$643$	−7.41965	+	7.41965i	−0.292603	+	0.292603i	0.545505	+	0.838108i	$0.316338\pi$
$644$	1.09240			0.0430464
$645$	25.7421	−	9.26758i	1.01359	−	0.364911i
$646$	7.13968			0.280907
$647$	33.3718	−	33.3718i	1.31198	−	1.31198i	0.392027	−	0.919954i	$-0.371774\pi$
$647$	33.3718	−	33.3718i	1.31198	−	1.31198i	0.919954	−	0.392027i	$-0.128226\pi$
$648$	6.72037	−	5.98637i	0.264001	−	0.235167i
$649$			7.28782i			0.286072i
$650$	5.70341	+	0.373572i	0.223706	+	0.0146527i
$651$	−3.91649	+	9.08242i	−0.153499	+	0.355968i
$652$	6.31993	+	6.31993i	0.247508	+	0.247508i
$653$	−23.3014	−	23.3014i	−0.911853	−	0.911853i	0.0845653	−	0.996418i	$-0.473050\pi$
$653$	−23.3014	−	23.3014i	−0.911853	−	0.911853i	−0.996418	+	0.0845653i	$0.973050\pi$
$654$	2.48156	−	5.75479i	0.0970367	−	0.225030i
$655$	−8.06153	−	8.60684i	−0.314990	−	0.336297i
$656$			7.21905i			0.281856i
$657$	−0.988300	+	34.2463i	−0.0385572	+	1.33608i
$658$	−7.95365	+	7.95365i	−0.310066	+	0.310066i
$659$	35.6736			1.38965			0.694823	−	0.719181i	$-0.255483\pi$
$659$	35.6736			1.38965			0.694823	+	0.719181i	$0.255483\pi$
$660$	−4.78277	−	2.25063i	−0.186169	−	0.0876056i
$661$	−36.4024			−1.41589			−0.707946	−	0.706267i	$-0.750378\pi$
$661$	−36.4024			−1.41589			−0.707946	+	0.706267i	$0.750378\pi$
$662$	−14.1580	+	14.1580i	−0.550266	+	0.550266i
$663$	−6.92822	+	2.75336i	−0.269070	+	0.106932i
$664$		−	1.40677i		−	0.0545934i
$665$	−0.151442	+	4.62916i	−0.00587267	+	0.179511i
$666$	−21.7814	+	20.5595i	−0.844013	+	0.796665i
$667$	−1.28482	−	1.28482i	−0.0497485	−	0.0497485i
$668$	8.62159	+	8.62159i	0.333579	+	0.333579i
$669$	−6.65109	−	2.86806i	−0.257146	−	0.110886i
$670$	18.6349	−	17.4542i	0.719929	−	0.674316i
$671$			17.2676i			0.666610i
$672$	−0.698779	−	1.75832i	−0.0269560	−	0.0678287i
$673$	19.3493	−	19.3493i	0.745862	−	0.745862i	−0.227837	−	0.973699i	$-0.573165\pi$
$673$	19.3493	−	19.3493i	0.745862	−	0.745862i	0.973699	+	0.227837i	$0.0731655\pi$
$674$	36.3800			1.40130
$675$	12.4873	−	22.7830i	0.480637	−	0.876920i
$676$	11.6933			0.449741
$677$	22.1097	−	22.1097i	0.849746	−	0.849746i	−0.140355	−	0.990101i	$-0.544824\pi$
$677$	22.1097	−	22.1097i	0.849746	−	0.849746i	0.990101	+	0.140355i	$0.0448245\pi$
$678$	13.2580	+	33.3607i	0.509169	+	1.28121i
$679$		−	0.486476i		−	0.0186692i
$680$	−6.14508	+	5.75575i	−0.235653	+	0.220723i
$681$	12.3660	+	5.33244i	0.473868	+	0.204340i
$682$	−5.04485	−	5.04485i	−0.193177	−	0.193177i
$683$	16.9522	+	16.9522i	0.648660	+	0.648660i	0.952669	−	0.304009i	$-0.0983254\pi$
$683$	16.9522	+	16.9522i	0.648660	+	0.648660i	−0.304009	+	0.952669i	$0.598325\pi$
$684$	4.13667	−	3.90461i	0.158169	−	0.149296i
$685$	−1.56798	+	47.9288i	−0.0599094	+	1.83126i
$686$			13.9900i			0.534139i
$687$	−25.9124	+	10.2979i	−0.988622	+	0.392891i
$688$	−4.99514	+	4.99514i	−0.190438	+	0.190438i
$689$	−2.46487			−0.0939039
$690$	−3.50437	−	1.64905i	−0.133409	−	0.0627783i
$691$	−32.5197			−1.23711			−0.618553	−	0.785743i	$-0.712281\pi$
$691$	−32.5197			−1.23711			−0.618553	+	0.785743i	$0.712281\pi$
$692$	−3.38026	+	3.38026i	−0.128498	+	0.128498i
$693$	−0.129022	+	4.47085i	−0.00490115	+	0.169834i
$694$		−	27.6884i		−	1.05104i
$695$	−7.69641	−	8.21702i	−0.291942	−	0.311689i
$696$	−1.24618	+	2.88992i	−0.0472363	+	0.109542i
$697$	−19.2209	−	19.2209i	−0.728044	−	0.728044i
$698$	1.34962	+	1.34962i	0.0510840	+	0.0510840i
$699$	−0.465102	+	1.07858i	−0.0175918	+	0.0407956i
$700$	−3.60151	−	4.10638i	−0.136124	−	0.155206i
$701$		−	21.7801i		−	0.822622i	−0.911495	−	0.411311i	$-0.865071\pi$
$701$		−	21.7801i		−	0.822622i	0.911495	−	0.411311i	$-0.134929\pi$
$702$	−2.50837	+	5.38424i	−0.0946723	+	0.203215i
$703$	−13.3863	+	13.3863i	−0.504873	+	0.504873i
$704$	1.36480			0.0514379
$705$	37.5217	−	13.5084i	1.41315	−	0.508757i
$706$	22.0707			0.830643
$707$	4.68513	−	4.68513i	0.176202	−	0.176202i
$708$	8.59501	−	3.41577i	0.323020	−	0.128372i
$709$			29.7437i			1.11705i	0.829489	+	0.558523i	$0.188632\pi$
$709$			29.7437i			1.11705i	−0.829489	+	0.558523i	$0.811368\pi$
$710$	−6.37890	−	0.208684i	−0.239396	−	0.00783179i
$711$	−9.24051	−	9.78969i	−0.346546	−	0.367142i
$712$	2.56649	+	2.56649i	0.0961833	+	0.0961833i
$713$	−3.69640	−	3.69640i	−0.138431	−	0.138431i
$714$	6.54210	+	2.82106i	0.244832	+	0.105576i
$715$	3.48672	+	0.114067i	0.130396	+	0.00426587i
$716$			17.4987i			0.653958i
$717$	10.5371	+	26.5143i	0.393516	+	0.990197i
$718$	18.2005	−	18.2005i	0.679237	−	0.679237i
$719$	26.3107			0.981223			0.490611	−	0.871378i	$-0.336773\pi$
$719$	26.3107			0.981223			0.490611	+	0.871378i	$0.336773\pi$
$720$	−0.412654	+	6.69550i	−0.0153787	+	0.249527i
$721$	−10.1906			−0.379517
$722$	−10.8927	+	10.8927i	−0.405386	+	0.405386i
$723$	0.483609	+	1.21689i	0.0179856	+	0.0452568i
$724$		−	14.3176i		−	0.532109i
$725$	−0.593796	+	9.06563i	−0.0220530	+	0.336689i
$726$	14.5327	+	6.26674i	0.539359	+	0.232581i
$727$	15.9921	+	15.9921i	0.593115	+	0.593115i	0.938472	−	0.345356i	$-0.112242\pi$
$727$	15.9921	+	15.9921i	0.593115	+	0.593115i	−0.345356	+	0.938472i	$0.612242\pi$
$728$	0.882998	+	0.882998i	0.0327261	+	0.0327261i
$729$	17.3700	+	20.6708i	0.643335	+	0.765585i
$730$	−17.4568	−	18.6377i	−0.646107	−	0.689811i
$731$		−	26.5994i		−	0.983814i
$732$	20.3649	−	8.09326i	0.752708	−	0.299135i
$733$	22.3497	−	22.3497i	0.825506	−	0.825506i	−0.161386	−	0.986891i	$-0.551596\pi$
$733$	22.3497	−	22.3497i	0.825506	−	0.825506i	0.986891	+	0.161386i	$0.0515963\pi$
$734$	−18.0274			−0.665403
$735$	9.57550	−	20.3487i	0.353198	−	0.750575i
$736$	1.00000			0.0368605
$737$	11.0195	−	11.0195i	0.405910	−	0.405910i
$738$	−21.6481	−	0.624734i	−0.796878	−	0.0229968i
$739$			41.0456i			1.50989i	0.655789	+	0.754944i	$0.272336\pi$
$739$			41.0456i			1.50989i	−0.655789	+	0.754944i	$0.727664\pi$
$740$	0.729964	−	22.3130i	0.0268340	−	0.820242i
$741$	−1.48658	+	3.44740i	−0.0546108	+	0.126643i
$742$	1.66557	+	1.66557i	0.0611452	+	0.0611452i
$743$	35.7650	+	35.7650i	1.31209	+	1.31209i	0.919871	+	0.392222i	$0.128293\pi$
$743$	35.7650	+	35.7650i	1.31209	+	1.31209i	0.392222	+	0.919871i	$0.371707\pi$
$744$	−3.58523	+	8.31422i	−0.131441	+	0.304814i
$745$	13.4078	−	12.5583i	0.491222	−	0.460100i
$746$		−	5.75388i		−	0.210664i
$747$	4.21857	+	0.121742i	0.154349	+	0.00445430i
$748$	−3.63382	+	3.63382i	−0.132866	+	0.132866i
$749$	7.61241			0.278151
$750$	5.35466	+	18.6099i	0.195525	+	0.679537i
$751$	−11.1694			−0.407579			−0.203789	−	0.979015i	$-0.565326\pi$
$751$	−11.1694			−0.407579			−0.203789	+	0.979015i	$0.565326\pi$
$752$	−7.28092	+	7.28092i	−0.265508	+	0.265508i
$753$	−30.2137	+	12.0073i	−1.10105	+	0.437570i
$754$		−	2.07707i		−	0.0756426i
$755$	2.69608	−	2.52526i	0.0981203	−	0.0919037i
$756$	5.33324	−	1.94330i	0.193968	−	0.0706771i
$757$	−0.501800	−	0.501800i	−0.0182382	−	0.0182382i	0.697929	−	0.716167i	$-0.254105\pi$
$757$	−0.501800	−	0.501800i	−0.0182382	−	0.0182382i	−0.716167	+	0.697929i	$0.754105\pi$
$758$	17.0903	+	17.0903i	0.620749	+	0.620749i
$759$	−2.17069	−	0.936037i	−0.0787910	−	0.0339760i
$760$	−0.138633	+	4.23762i	−0.00502874	+	0.153715i
$761$			32.3967i			1.17438i	0.809449	+	0.587190i	$0.199766\pi$
$761$			32.3967i			1.17438i	−0.809449	+	0.587190i	$0.800234\pi$
$762$	−4.16231	−	10.4735i	−0.150785	−	0.379416i
$763$	2.79490	−	2.79490i	0.101182	−	0.101182i
$764$	−3.47708			−0.125796
$765$	−16.7283	−	18.9257i	−0.604812	−	0.684259i
$766$	−21.7585			−0.786167
$767$	−4.31626	+	4.31626i	−0.155851	+	0.155851i
$768$	−0.639676	−	1.60960i	−0.0230823	−	0.0580815i
$769$		−	27.3542i		−	0.986419i	−0.869911	−	0.493209i	$-0.835824\pi$
$769$		−	27.3542i		−	0.986419i	0.869911	−	0.493209i	$-0.164176\pi$
$770$	−2.27899	−	2.43314i	−0.0821290	−	0.0876844i
$771$	−18.0504	−	7.78362i	−0.650068	−	0.280320i
$772$	10.8007	+	10.8007i	0.388725	+	0.388725i
$773$	−4.45744	−	4.45744i	−0.160323	−	0.160323i	0.622387	−	0.782710i	$-0.286163\pi$
$773$	−4.45744	−	4.45744i	−0.160323	−	0.160323i	−0.782710	+	0.622387i	$0.786163\pi$
$774$	−14.5469	−	15.4114i	−0.522877	−	0.553953i
$775$	−1.70834	+	26.0816i	−0.0613652	+	0.936879i
$776$		−	0.445329i		−	0.0159864i
$777$	−17.5551	+	6.97662i	−0.629786	+	0.250285i
$778$	2.79965	−	2.79965i	0.100372	−	0.100372i
$779$	−13.6883			−0.490434
$780$	−1.49968	−	4.16558i	−0.0536971	−	0.149152i
$781$	−3.89550			−0.139392
$782$	−2.66253	+	2.66253i	−0.0952118	+	0.0952118i
$783$	−8.55830	−	3.98708i	−0.305849	−	0.142487i
$784$			5.80667i			0.207381i
$785$	18.7719	+	0.614120i	0.669999	+	0.0219189i
$786$	−3.61700	+	8.38790i	−0.129014	+	0.299186i
$787$	20.9311	+	20.9311i	0.746115	+	0.746115i	0.973747	−	0.227632i	$-0.0730984\pi$
$787$	20.9311	+	20.9311i	0.746115	+	0.746115i	−0.227632	+	0.973747i	$0.573098\pi$
$788$	3.69180	+	3.69180i	0.131515	+	0.131515i
$789$	10.8339	−	25.1241i	0.385698	−	0.894442i
$790$	10.0286	+	0.328084i	0.356802	+	0.0116727i
$791$			22.6411i			0.805024i
$792$	−0.118110	+	4.09270i	−0.00419684	+	0.145428i
$793$	−10.2269	+	10.2269i	−0.363167	+	0.363167i
$794$	21.7899			0.773294
$795$	−2.82880	−	7.85742i	−0.100327	−	0.278674i
$796$	5.69788			0.201956
$797$	3.52355	−	3.52355i	0.124811	−	0.124811i	−0.641942	−	0.766753i	$-0.721871\pi$
$797$	3.52355	−	3.52355i	0.124811	−	0.124811i	0.766753	+	0.641942i	$0.221871\pi$
$798$	3.33402	−	1.32498i	0.118023	−	0.0469038i
$799$		−	38.7713i		−	1.37163i
$800$	−3.29689	−	3.75906i	−0.116563	−	0.132903i
$801$	−7.91837	+	7.47416i	−0.279782	+	0.264087i
$802$	−12.9007	−	12.9007i	−0.455540	−	0.455540i
$803$	−11.0212	−	11.0212i	−0.388929	−	0.388929i
$804$	−18.1609	−	7.83127i	−0.640485	−	0.276188i
$805$	−1.66983	−	1.78278i	−0.0588538	−	0.0628348i
$806$		−	5.97569i		−	0.210485i
$807$	9.04898	+	22.7697i	0.318539	+	0.801533i
$808$	4.28886	−	4.28886i	0.150881	−	0.150881i
$809$	28.9862			1.01910			0.509550	−	0.860441i	$-0.329812\pi$
$809$	28.9862			1.01910			0.509550	+	0.860441i	$0.329812\pi$
$810$	−20.0424	−	1.81687i	−0.704219	−	0.0638384i
$811$	33.5131			1.17680			0.588402	−	0.808569i	$-0.299757\pi$
$811$	33.5131			1.17680			0.588402	+	0.808569i	$0.299757\pi$
$812$	−1.40353	+	1.40353i	−0.0492544	+	0.0492544i
$813$	−14.5818	−	36.6920i	−0.511408	−	1.28684i
$814$		−	13.6262i		−	0.477598i
$815$	0.653468	−	19.9747i	0.0228900	−	0.699683i
$816$	5.98876	+	2.58245i	0.209649	+	0.0904040i
$817$	−9.47146	−	9.47146i	−0.331364	−	0.331364i
$818$	−17.0270	−	17.0270i	−0.595336	−	0.595336i
$819$	−2.72430	+	2.57148i	−0.0951949	+	0.0898546i
$820$	11.7814	−	11.0350i	0.411425	−	0.385359i
$821$		−	12.8255i		−	0.447614i	−0.974633	−	0.223807i	$-0.928151\pi$
$821$		−	12.8255i		−	0.447614i	0.974633	−	0.223807i	$-0.0718486\pi$
$822$	34.5193	−	13.7184i	1.20400	−	0.478484i
$823$	−39.8650	+	39.8650i	−1.38961	+	1.38961i	−0.563473	+	0.826135i	$0.690535\pi$
$823$	−39.8650	+	39.8650i	−1.38961	+	1.38961i	−0.826135	+	0.563473i	$0.809465\pi$
$824$	−9.32865			−0.324979
$825$	3.63791	+	11.2457i	0.126656	+	0.391527i
$826$	5.83322			0.202964
$827$	15.4550	−	15.4550i	0.537421	−	0.537421i	−0.385349	−	0.922771i	$-0.625919\pi$
$827$	15.4550	−	15.4550i	0.537421	−	0.537421i	0.922771	+	0.385349i	$0.125919\pi$
$828$	−0.0865397	+	2.99875i	−0.00300746	+	0.104214i
$829$		−	22.1839i		−	0.770478i	−0.922817	−	0.385239i	$-0.874119\pi$
$829$		−	22.1839i		−	0.770478i	0.922817	−	0.385239i	$-0.125881\pi$
$830$	−2.29585	+	2.15039i	−0.0796900	+	0.0746411i
$831$	−21.5419	+	49.9560i	−0.747279	+	1.73296i
$832$	0.808313	+	0.808313i	0.0280232	+	0.0280232i
$833$	−15.4604	−	15.4604i	−0.535672	−	0.535672i
$834$	−3.45318	+	8.00800i	−0.119574	+	0.277294i
$835$	0.891454	−	27.2493i	0.0308500	−	0.943000i
$836$			2.58785i			0.0895027i
$837$	−24.6220	−	11.4707i	−0.851062	−	0.396486i
$838$	−10.1229	+	10.1229i	−0.349690	+	0.349690i
$839$	26.4989			0.914842			0.457421	−	0.889250i	$-0.348773\pi$
$839$	26.4989			0.914842			0.457421	+	0.889250i	$0.348773\pi$
$840$	−1.80142	+	3.82816i	−0.0621548	+	0.132084i
$841$	−25.6985			−0.886154
$842$	−9.30300	+	9.30300i	−0.320603	+	0.320603i
$843$	11.4428	−	4.54750i	0.394110	−	0.156624i
$844$		−	3.16715i		−	0.109018i
$845$	−17.8743	−	19.0833i	−0.614893	−	0.656486i
$846$	−21.2036	−	22.4638i	−0.728994	−	0.772320i
$847$	7.05803	+	7.05803i	0.242517	+	0.242517i
$848$	1.52470	+	1.52470i	0.0523584	+	0.0523584i
$849$	−37.7870	−	16.2944i	−1.29685	−	0.559222i
$850$	18.7867	+	1.23052i	0.644377	+	0.0422065i
$851$		−	9.98401i		−	0.342247i
$852$	1.82580	+	4.59422i	0.0625509	+	0.157395i
$853$	6.01870	−	6.01870i	0.206076	−	0.206076i	−0.596521	−	0.802597i	$-0.703451\pi$
$853$	6.01870	−	6.01870i	0.206076	−	0.206076i	0.802597	+	0.596521i	$0.203451\pi$
$854$	13.8211			0.472950
$855$	−12.6956	−	0.782448i	−0.434180	−	0.0267592i
$856$	6.96854			0.238180
$857$	36.7546	−	36.7546i	1.25551	−	1.25551i	0.302300	−	0.953213i	$-0.402246\pi$
$857$	36.7546	−	36.7546i	1.25551	−	1.25551i	0.953213	−	0.302300i	$-0.0977544\pi$
$858$	−0.997984	−	2.51120i	−0.0340706	−	0.0857311i
$859$			21.3618i			0.728856i	0.931232	+	0.364428i	$0.118736\pi$
$859$			21.3618i			0.728856i	−0.931232	+	0.364428i	$0.881264\pi$
$860$	15.7876	+	0.516486i	0.538351	+	0.0176120i
$861$	−12.5426	−	5.40858i	−0.427451	−	0.184324i
$862$	−10.7673	−	10.7673i	−0.366736	−	0.366736i
$863$	21.4516	+	21.4516i	0.730219	+	0.730219i	0.970663	−	0.240444i	$-0.0772930\pi$
$863$	21.4516	+	21.4516i	0.730219	+	0.730219i	−0.240444	+	0.970663i	$0.577293\pi$
$864$	4.88215	−	1.77893i	0.166094	−	0.0605206i
$865$	10.6836	+	0.349512i	0.363253	+	0.0118838i
$866$		−	21.1851i		−	0.719899i
$867$	4.54210	−	1.80509i	0.154258	−	0.0613039i
$868$	−4.03793	+	4.03793i	−0.137056	+	0.137056i
$869$	6.12431			0.207753
$870$	6.62123	−	2.38375i	0.224481	−	0.0808169i
$871$	13.0528			0.442277
$872$	2.55851	−	2.55851i	0.0866420	−	0.0866420i
$873$	1.33543	+	0.0385387i	0.0451975	+	0.00130434i
$874$			1.89614i			0.0641378i
$875$	−1.19632	+	12.1546i	−0.0404431	+	0.410901i
$876$	−7.83243	+	18.1636i	−0.264633	+	0.613690i
$877$	36.4976	+	36.4976i	1.23244	+	1.23244i	0.963025	+	0.269411i	$0.0868291\pi$
$877$	36.4976	+	36.4976i	1.23244	+	1.23244i	0.269411	+	0.963025i	$0.413171\pi$
$878$	20.2302	+	20.2302i	0.682734	+	0.682734i
$879$	22.3869	−	51.9157i	0.755092	−	1.75107i
$880$	−2.08623	−	2.22735i	−0.0703267	−	0.0750838i
$881$		−	33.8871i		−	1.14169i	−0.821060	−	0.570843i	$-0.806617\pi$
$881$		−	33.8871i		−	1.14169i	0.821060	−	0.570843i	$-0.193383\pi$
$882$	−17.4128	−	0.502507i	−0.586318	−	0.0169203i
$883$	−6.74287	+	6.74287i	−0.226916	+	0.226916i	−0.811403	−	0.584487i	$-0.801296\pi$
$883$	−6.74287	+	6.74287i	−0.226916	+	0.226916i	0.584487	+	0.811403i	$0.301296\pi$
$884$	−4.30431			−0.144770
$885$	−18.7128	−	8.80568i	−0.629024	−	0.296000i
$886$	28.3653			0.952950
$887$	1.20348	−	1.20348i	0.0404088	−	0.0404088i	−0.686614	−	0.727022i	$-0.740904\pi$
$887$	1.20348	−	1.20348i	0.0404088	−	0.0404088i	0.727022	+	0.686614i	$0.240904\pi$
$888$	−16.0703	+	6.38653i	−0.539283	+	0.214318i
$889$		−	7.10812i		−	0.238399i
$890$	0.265370	−	8.11161i	0.00889521	−	0.271902i
$891$	−12.2628	−	0.708362i	−0.410818	−	0.0237310i
$892$	−2.95699	−	2.95699i	−0.0990074	−	0.0990074i
$893$	−13.8056	−	13.8056i	−0.461988	−	0.461988i
$894$	−13.0667	−	5.63458i	−0.437016	−	0.188448i
$895$	28.5578	−	26.7484i	0.954581	−	0.894102i
$896$		−	1.09240i		−	0.0364944i
$897$	−0.731230	−	1.83998i	−0.0244151	−	0.0614351i
$898$	29.0721	−	29.0721i	0.970148	−	0.970148i
$899$	9.49842			0.316790
$900$	11.5578	−	9.56126i	0.385259	−	0.318709i
$901$	−8.11911			−0.270487
$902$	6.96682	−	6.96682i	0.231970	−	0.231970i
$903$	−4.93631	−	12.4211i	−0.164270	−	0.413349i
$904$			20.7261i			0.689339i
$905$	−23.3662	+	21.8858i	−0.776719	+	0.727508i
$906$	−2.62750	−	1.13302i	−0.0872927	−	0.0376421i
$907$	31.5222	+	31.5222i	1.04668	+	1.04668i	0.998856	+	0.0478228i	$0.0152283\pi$
$907$	31.5222	+	31.5222i	1.04668	+	1.04668i	0.0478228	+	0.998856i	$0.484772\pi$
$908$	5.49778	+	5.49778i	0.182450	+	0.182450i
$909$	12.4901	+	13.2324i	0.414269	+	0.438890i
$910$	0.0913001	−	2.79079i	0.00302657	−	0.0925138i
$911$		−	16.8038i		−	0.556735i	−0.960475	−	0.278367i	$-0.910207\pi$
$911$		−	16.8038i		−	0.556735i	0.960475	−	0.278367i	$-0.0897933\pi$
$912$	3.05202	−	1.21291i	0.101063	−	0.0401635i
$913$	−1.35762	+	1.35762i	−0.0449308	+	0.0449308i
$914$	17.8822			0.591491
$915$	−44.3378	−	20.8640i	−1.46576	−	0.689743i
$916$	−16.0987			−0.531915
$917$	−4.07371	+	4.07371i	−0.134526	+	0.134526i
$918$	−8.26241	+	17.7353i	−0.272700	+	0.585353i
$919$		−	22.6628i		−	0.747578i	−0.927514	−	0.373789i	$-0.878058\pi$
$919$		−	22.6628i		−	0.747578i	0.927514	−	0.373789i	$-0.121942\pi$
$920$	−1.52859	−	1.63199i	−0.0503963	−	0.0538052i
$921$	7.90854	−	18.3401i	0.260595	−	0.604326i
$922$	13.4787	+	13.4787i	0.443896	+	0.443896i
$923$	−2.30713	−	2.30713i	−0.0759402	−	0.0759402i
$924$	−1.02252	+	2.37125i	−0.0336385	+	0.0780084i
$925$	−37.5304	+	32.9162i	−1.23399	+	1.08228i
$926$		−	10.4984i		−	0.344998i
$927$	0.807298	−	27.9743i	0.0265152	−	0.918796i
$928$	−1.28482	+	1.28482i	−0.0421763	+	0.0421763i
$929$	−45.8275			−1.50355			−0.751776	−	0.659418i	$-0.770803\pi$
$929$	−45.8275			−1.50355			−0.751776	+	0.659418i	$0.770803\pi$
$930$	19.0491	−	6.85800i	0.624645	−	0.224883i
$931$	−11.0102			−0.360846
$932$	−0.479523	+	0.479523i	−0.0157073	+	0.0157073i
$933$	21.9256	−	8.71350i	0.717811	−	0.285267i
$934$			32.9954i			1.07964i
$935$	11.4850	+	0.375730i	0.375600	+	0.0122877i
$936$	−2.49388	+	2.35398i	−0.0815150	+	0.0769422i
$937$	27.6873	+	27.6873i	0.904504	+	0.904504i	0.995822	−	0.0913178i	$-0.0291079\pi$
$937$	27.6873	+	27.6873i	0.904504	+	0.904504i	−0.0913178	+	0.995822i	$0.529108\pi$
$938$	−8.82011	−	8.82011i	−0.287987	−	0.287987i
$939$	−43.6898	−	18.8398i	−1.42576	−	0.614813i
$940$	23.0120	+	0.752832i	0.750568	+	0.0245547i
$941$		−	5.46459i		−	0.178141i	−0.996025	−	0.0890703i	$-0.971610\pi$
$941$		−	5.46459i		−	0.178141i	0.996025	−	0.0890703i	$-0.0283896\pi$
$942$	−5.37299	−	13.5199i	−0.175062	−	0.440503i
$943$	5.10464	−	5.10464i	0.166230	−	0.166230i
$944$	5.33984			0.173797
$945$	−11.3238	−	5.73329i	−0.368364	−	0.186504i
$946$	9.64122			0.313463
$947$	−19.0051	+	19.0051i	−0.617583	+	0.617583i	−0.944911	−	0.327327i	$-0.893852\pi$
$947$	−19.0051	+	19.0051i	−0.617583	+	0.617583i	0.327327	+	0.944911i	$0.393852\pi$
$948$	−2.87043	−	7.22281i	−0.0932274	−	0.234586i
$949$		−	13.0547i		−	0.423774i
$950$	7.12768	−	6.25136i	0.231253	−	0.202821i
$951$	13.7833	+	5.94360i	0.446955	+	0.192734i
$952$	2.90854	+	2.90854i	0.0942662	+	0.0942662i
$953$	−30.5368	−	30.5368i	−0.989184	−	0.989184i	0.0107585	−	0.999942i	$-0.496575\pi$
$953$	−30.5368	−	30.5368i	−0.989184	−	0.989184i	−0.999942	+	0.0107585i	$0.996575\pi$
$954$	−4.70414	+	4.44024i	−0.152302	+	0.143758i
$955$	5.31505	+	5.67457i	0.171991	+	0.183625i
$956$			16.4726i			0.532763i
$957$	3.99158	−	1.58631i	0.129030	−	0.0512780i
$958$	23.0821	−	23.0821i	0.745749	−	0.745749i
$959$	23.4274			0.756509
$960$	−1.64905	+	3.50437i	−0.0532229	+	0.113103i
$961$	−3.67328			−0.118493
$962$	8.07020	−	8.07020i	0.260194	−	0.260194i
$963$	−0.603055	+	20.8969i	−0.0194332	+	0.673394i
$964$			0.756022i			0.0243498i
$965$	1.11677	−	34.1365i	0.0359500	−	1.09889i
$966$	−0.749210	+	1.73743i	−0.0241054	+	0.0559010i
$967$	−21.6343	−	21.6343i	−0.695713	−	0.695713i	0.267770	−	0.963483i	$-0.413713\pi$
$967$	−21.6343	−	21.6343i	−0.695713	−	0.695713i	−0.963483	+	0.267770i	$0.913713\pi$
$968$	6.46106	+	6.46106i	0.207666	+	0.207666i
$969$	−4.89669	+	11.3555i	−0.157304	+	0.364792i
$970$	−0.726774	+	0.680728i	−0.0233353	+	0.0218569i
$971$		−	36.5285i		−	1.17225i	−0.810219	−	0.586127i	$-0.800652\pi$
$971$		−	36.5285i		−	1.17225i	0.810219	−	0.586127i	$-0.199348\pi$
$972$	4.91208	+	14.7943i	0.157555	+	0.474528i
$973$	−3.88921	+	3.88921i	−0.124682	+	0.124682i
$974$	−24.7866			−0.794213
$975$	−4.50579	+	8.81495i	−0.144301	+	0.282304i
$976$	12.6521			0.404985
$977$	−28.9803	+	28.9803i	−0.927161	+	0.927161i	−0.997522	−	0.0703611i	$-0.977585\pi$
$977$	−28.9803	+	28.9803i	−0.927161	+	0.927161i	0.0703611	+	0.997522i	$0.477585\pi$
$978$	−14.3862	+	5.71725i	−0.460020	+	0.182818i
$979$		−	4.95364i		−	0.158319i
$980$	9.47644	−	8.87604i	0.302714	−	0.283535i
$981$	7.45091	+	7.89374i	0.237889	+	0.252028i
$982$	−18.4103	−	18.4103i	−0.587495	−	0.587495i
$983$	15.7918	+	15.7918i	0.503679	+	0.503679i	0.912579	−	0.408900i	$-0.134088\pi$
$983$	15.7918	+	15.7918i	0.503679	+	0.503679i	−0.408900	+	0.912579i	$0.634088\pi$
$984$	−11.4817	−	4.95112i	−0.366024	−	0.157836i
$985$	0.381724	−	11.6683i	0.0121628	−	0.371782i
$986$		−	6.84175i		−	0.217886i
$987$	−7.19517	−	18.1050i	−0.229025	−	0.576290i
$988$	−1.53267	+	1.53267i	−0.0487608	+	0.0487608i
$989$	7.06419			0.224628
$990$	6.85980	−	6.06333i	0.218019	−	0.192705i
$991$	38.9898			1.23855			0.619276	−	0.785173i	$-0.287426\pi$
$991$	38.9898			1.23855			0.619276	+	0.785173i	$0.287426\pi$
$992$	−3.69640	+	3.69640i	−0.117361	+	0.117361i
$993$	−12.8078	−	32.2281i	−0.406445	−	1.02273i
$994$			3.11798i			0.0988964i
$995$	−8.70975	−	9.29890i	−0.276118	−	0.294795i
$996$	2.23745	+	0.964824i	0.0708962	+	0.0305716i
$997$	−25.2701	−	25.2701i	−0.800311	−	0.800311i	0.182833	−	0.983144i	$-0.441473\pi$
$997$	−25.2701	−	25.2701i	−0.800311	−	0.800311i	−0.983144	+	0.182833i	$0.941473\pi$
$998$	−14.5258	−	14.5258i	−0.459806	−	0.459806i
$999$	−17.7609	−	48.7434i	−0.561930	−	1.54217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.e.47.3	✓	32
3.2	odd	2	inner	690.2.i.e.47.15	yes	32
5.3	odd	4	inner	690.2.i.e.323.15	yes	32
15.8	even	4	inner	690.2.i.e.323.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.3	✓	32	1.1	even	1	trivial
690.2.i.e.47.15	yes	32	3.2	odd	2	inner
690.2.i.e.323.3	yes	32	15.8	even	4	inner
690.2.i.e.323.15	yes	32	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.639676 - 1.60960i) q^{3} -1.00000i q^{4} +(-1.63199 + 1.52859i) q^{5} +(1.59048 + 0.685841i) q^{6} +(0.772441 + 0.772441i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.18163 + 2.05924i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.639676 - 1.60960i) q^{3} -1.00000i q^{4} +(-1.63199 + 1.52859i) q^{5} +(1.59048 + 0.685841i) q^{6} +(0.772441 + 0.772441i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.18163 + 2.05924i) q^{9} +(0.0731134 - 2.23487i) q^{10} -1.36480i q^{11} +(-1.60960 + 0.639676i) q^{12} +(0.808313 - 0.808313i) q^{13} -1.09240 q^{14} +(3.50437 + 1.64905i) q^{15} -1.00000 q^{16} +(2.66253 - 2.66253i) q^{17} +(0.0865397 - 2.99875i) q^{18} -1.89614i q^{19} +(1.52859 + 1.63199i) q^{20} +(0.749210 - 1.73743i) q^{21} +(0.965061 + 0.965061i) q^{22} +(0.707107 + 0.707107i) q^{23} +(0.685841 - 1.59048i) q^{24} +(0.326798 - 4.98931i) q^{25} +1.14313i q^{26} +(4.71010 + 2.19431i) q^{27} +(0.772441 - 0.772441i) q^{28} -1.81701 q^{29} +(-3.64402 + 1.31191i) q^{30} -5.22750 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.19679 + 0.873030i) q^{33} +3.76538i q^{34} +(-2.44137 - 0.0798687i) q^{35} +(2.05924 + 2.18163i) q^{36} +(-7.05976 - 7.05976i) q^{37} +(1.34077 + 1.34077i) q^{38} +(-1.81812 - 0.784003i) q^{39} +(-2.23487 - 0.0731134i) q^{40} -7.21905i q^{41} +(0.698779 + 1.75832i) q^{42} +(4.99514 - 4.99514i) q^{43} -1.36480 q^{44} +(0.412654 - 6.69550i) q^{45} -1.00000 q^{46} +(7.28092 - 7.28092i) q^{47} +(0.639676 + 1.60960i) q^{48} -5.80667i q^{49} +(3.29689 + 3.75906i) q^{50} +(-5.98876 - 2.58245i) q^{51} +(-0.808313 - 0.808313i) q^{52} +(-1.52470 - 1.52470i) q^{53} +(-4.88215 + 1.77893i) q^{54} +(2.08623 + 2.22735i) q^{55} +1.09240i q^{56} +(-3.05202 + 1.21291i) q^{57} +(1.28482 - 1.28482i) q^{58} -5.33984 q^{59} +(1.64905 - 3.50437i) q^{60} -12.6521 q^{61} +(3.69640 - 3.69640i) q^{62} +(-3.27582 - 0.0945356i) q^{63} +1.00000i q^{64} +(-0.0835778 + 2.55474i) q^{65} +(0.936037 - 2.17069i) q^{66} +(8.07409 + 8.07409i) q^{67} +(-2.66253 - 2.66253i) q^{68} +(0.685841 - 1.59048i) q^{69} +(1.78278 - 1.66983i) q^{70} -2.85426i q^{71} +(-2.99875 - 0.0865397i) q^{72} +(8.07529 - 8.07529i) q^{73} +9.98401 q^{74} +(-8.23984 + 2.66552i) q^{75} -1.89614 q^{76} +(1.05423 - 1.05423i) q^{77} +(1.83998 - 0.731230i) q^{78} +4.48733i q^{79} +(1.63199 - 1.52859i) q^{80} +(0.519022 - 8.98502i) q^{81} +(5.10464 + 5.10464i) q^{82} +(-0.994740 - 0.994740i) q^{83} +(-1.73743 - 0.749210i) q^{84} +(-0.275300 + 8.41515i) q^{85} +7.06419i q^{86} +(1.16230 + 2.92466i) q^{87} +(0.965061 - 0.965061i) q^{88} +3.62956 q^{89} +(4.44264 + 5.02622i) q^{90} +1.24875 q^{91} +(0.707107 - 0.707107i) q^{92} +(3.34390 + 8.41418i) q^{93} +10.2968i q^{94} +(2.89842 + 3.09448i) q^{95} +(-1.59048 - 0.685841i) q^{96} +(-0.314895 - 0.314895i) q^{97} +(4.10594 + 4.10594i) q^{98} +(2.81046 + 2.97749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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