LMFDB - Embedded newform 690.2.i.e.323.3

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			323.3
Character	$\chi$	$=$	690.323
Dual form			690.2.i.e.47.3

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	−0.545897	−	0.837852i	$-0.683811\pi$
$7$	0.772441	−	0.772441i	0.291955	−	0.291955i	0.837852	+	0.545897i	$0.183811\pi$
$8$	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	$0.0659639\pi$
$11$			1.36480i			0.411503i	−0.978604	+	0.205752i	$0.934036\pi$
$12$	−1.60960	−	0.639676i	−0.464652	−	0.184658i
$13$	0.808313	+	0.808313i	0.224186	+	0.224186i	0.810258	−	0.586073i	$-0.199327\pi$
$13$	0.808313	+	0.808313i	0.224186	+	0.224186i	−0.586073	+	0.810258i	$0.699327\pi$
$14$	−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	0.951965	−	0.306207i	$-0.0990599\pi$
$17$	2.66253	+	2.66253i	0.645758	+	0.645758i	−0.306207	+	0.951965i	$0.599060\pi$
$18$	0.0865397	+	2.99875i	0.0203976	+	0.706813i
$19$			1.89614i			0.435004i	0.976060	+	0.217502i	$0.0697908\pi$
$19$			1.89614i			0.435004i	−0.976060	+	0.217502i	$0.930209\pi$
$20$	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	−0.176277	+	0.984341i	$0.556405\pi$
$37$	−7.05976	+	7.05976i	−1.16062	+	1.16062i	−0.984341	+	0.176277i	$0.943595\pi$
$38$	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	$0.190627\pi$
$41$			7.21905i			1.12743i	−0.825971	+	0.563713i	$0.809373\pi$
$42$	0.698779	−	1.75832i	0.107824	−	0.271315i
$43$	4.99514	+	4.99514i	0.761751	+	0.761751i	0.976639	−	0.214888i	$-0.0689386\pi$
$43$	4.99514	+	4.99514i	0.761751	+	0.761751i	−0.214888	+	0.976639i	$0.568939\pi$
$44$	−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	0.997944	+	0.0640872i	$0.0204136\pi$
$47$	7.28092	+	7.28092i	1.06203	+	1.06203i	0.0640872	+	0.997944i	$0.479586\pi$
$48$	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	−0.804027	−	0.594593i	$-0.797313\pi$
$53$	−1.52470	+	1.52470i	−0.209433	+	0.209433i	0.594593	+	0.804027i	$0.297313\pi$
$54$	−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	−0.0135013	−	0.999909i	$-0.504298\pi$
$67$	8.07409	−	8.07409i	0.986408	−	0.986408i	0.999909	+	0.0135013i	$0.00429772\pi$
$68$	−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	$0.0541730\pi$
$71$			2.85426i			0.338738i	−0.985553	+	0.169369i	$0.945827\pi$
$72$	−2.99875	+	0.0865397i	−0.353406	+	0.0101988i
$73$	8.07529	+	8.07529i	0.945142	+	0.945142i	0.998572	−	0.0534300i	$-0.0170154\pi$
$73$	8.07529	+	8.07529i	0.945142	+	0.945142i	−0.0534300	+	0.998572i	$0.517015\pi$
$74$	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	$-0.918770\pi$
$79$		−	4.48733i		−	0.504864i	0.967615	−	0.252432i	$-0.0812304\pi$
$80$	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	−0.759590	−	0.650403i	$-0.774600\pi$
$83$	−0.994740	+	0.994740i	−0.109187	+	0.109187i	0.650403	+	0.759590i	$0.274600\pi$
$84$	−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	−0.722912	−	0.690940i	$-0.757197\pi$
$97$	−0.314895	+	0.314895i	−0.0319728	+	0.0319728i	0.690940	+	0.722912i	$0.257197\pi$
$98$	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	$0.0975751\pi$
$101$			6.06536i			0.603526i	−0.953383	+	0.301763i	$0.902425\pi$
$102$	6.06077	+	2.40862i	0.600105	+	0.238489i
$103$	−6.59635	−	6.59635i	−0.649958	−	0.649958i	0.303025	−	0.952983i	$-0.402003\pi$
$103$	−6.59635	−	6.59635i	−0.649958	−	0.649958i	−0.952983	+	0.303025i	$0.902003\pi$
$104$	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	0.903965	−	0.427606i	$-0.140643\pi$
$107$	4.92750	+	4.92750i	0.476360	+	0.476360i	−0.427606	+	0.903965i	$0.640643\pi$
$108$	2.19431	+	4.71010i	0.211147	+	0.453229i
$109$			3.61827i			0.346568i	0.984872	+	0.173284i	$0.0554378\pi$
$109$			3.61827i			0.346568i	−0.984872	+	0.173284i	$0.944562\pi$
$110$	−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	0.531820	−	0.846858i	$-0.321508\pi$
$113$	14.6555	−	14.6555i	1.37868	−	1.37868i	0.846858	−	0.531820i	$-0.178492\pi$
$114$	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	−0.881138	−	0.472859i	$-0.843222\pi$
$127$	−4.60108	+	4.60108i	−0.408280	+	0.408280i	0.472859	+	0.881138i	$0.343222\pi$
$128$	−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	$-0.926000\pi$
$131$		−	5.27382i		−	0.460776i	0.973099	−	0.230388i	$-0.0739995\pi$
$132$	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	0.931275	+	0.364316i	$0.118697\pi$
$137$	15.1645	+	15.1645i	1.29559	+	1.29559i	0.364316	+	0.931275i	$0.381303\pi$
$138$	0.639676	−	1.60960i	0.0544528	−	0.137018i
$139$		−	5.03496i		−	0.427060i	−0.976937	−	0.213530i	$-0.931504\pi$
$139$		−	5.03496i		−	0.427060i	0.976937	−	0.213530i	$-0.0684961\pi$
$140$	−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	−0.903211	−	0.429197i	$-0.858797\pi$
$157$	−5.93938	+	5.93938i	−0.474014	+	0.474014i	0.429197	+	0.903211i	$0.358797\pi$
$158$	−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	0.414867	−	0.909882i	$-0.363828\pi$
$163$	−6.31993	−	6.31993i	−0.495015	−	0.495015i	−0.909882	+	0.414867i	$0.863828\pi$
$164$	−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	0.289899	−	0.957057i	$-0.406378\pi$
$167$	−8.62159	−	8.62159i	−0.667159	−	0.667159i	−0.957057	+	0.289899i	$0.906378\pi$
$168$	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	−0.823831	−	0.566835i	$-0.808168\pi$
$173$	−3.38026	+	3.38026i	−0.256996	+	0.256996i	0.566835	+	0.823831i	$0.308168\pi$
$174$	−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	$0.0401486\pi$
$191$			3.47708i			0.251593i	−0.992056	+	0.125796i	$0.959851\pi$
$192$	1.60960	+	0.639676i	0.116163	+	0.0461646i
$193$	−10.8007	−	10.8007i	−0.777450	−	0.777450i	0.201946	−	0.979397i	$-0.435273\pi$
$193$	−10.8007	−	10.8007i	−0.777450	−	0.777450i	−0.979397	+	0.201946i	$0.935273\pi$
$194$	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	0.563254	−	0.826284i	$-0.309549\pi$
$197$	−3.69180	−	3.69180i	−0.263030	−	0.263030i	−0.826284	+	0.563254i	$0.809549\pi$
$198$	−4.09270	+	0.118110i	−0.290856	+	0.00839368i
$199$		−	5.69788i		−	0.403912i	−0.979395	−	0.201956i	$-0.935270\pi$
$199$		−	5.69788i		−	0.403912i	0.979395	−	0.201956i	$-0.0647298\pi$
$200$	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	0.799148	−	0.601134i	$-0.205284\pi$
$223$	2.95699	+	2.95699i	0.198015	+	0.198015i	−0.601134	+	0.799148i	$0.705284\pi$
$224$	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	0.500713	−	0.865614i	$-0.333071\pi$
$227$	−5.49778	−	5.49778i	−0.364901	−	0.364901i	−0.865614	+	0.500713i	$0.833071\pi$
$228$	1.21291	−	3.05202i	0.0803271	−	0.202125i
$229$			16.0987i			1.06383i	0.846798	+	0.531915i	$0.178528\pi$
$229$			16.0987i			1.06383i	−0.846798	+	0.531915i	$0.821472\pi$
$230$	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	−0.722640	−	0.691225i	$-0.757071\pi$
$233$	−0.479523	+	0.479523i	−0.0314146	+	0.0314146i	0.691225	+	0.722640i	$0.257071\pi$
$234$	−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	$0.201821\pi$
$251$			18.7709i			1.18481i	−0.805641	+	0.592404i	$0.798179\pi$
$252$	−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	0.911619	−	0.411036i	$-0.134833\pi$
$257$	8.02496	+	8.02496i	0.500584	+	0.500584i	−0.411036	+	0.911619i	$0.634833\pi$
$258$	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	−0.273195	−	0.961959i	$-0.588081\pi$
$263$	11.1699	−	11.1699i	0.688763	−	0.688763i	0.961959	+	0.273195i	$0.0880806\pi$
$264$	−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	−0.433125	+	0.901334i	$0.642589\pi$
$277$	−22.2098	+	22.2098i	−1.33446	+	1.33446i	−0.901334	+	0.433125i	$0.857411\pi$
$278$	−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	$-0.931987\pi$
$281$		−	7.10907i		−	0.424091i	0.977260	−	0.212046i	$-0.0680126\pi$
$282$	16.5737	+	6.58660i	0.986950	+	0.392226i
$283$	16.7996	+	16.7996i	0.998634	+	0.998634i	0.999999	−	0.00136548i	$-0.000434647\pi$
$283$	16.7996	+	16.7996i	0.998634	+	0.998634i	−0.00136548	+	0.999999i	$0.500435\pi$
$284$	−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	0.461023	−	0.887388i	$-0.347483\pi$
$293$	23.0811	−	23.0811i	1.34841	−	1.34841i	0.887388	−	0.461023i	$-0.152517\pi$
$294$	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	−0.435048	−	0.900407i	$-0.643268\pi$
$307$	8.15376	−	8.15376i	0.465360	−	0.465360i	0.900407	+	0.435048i	$0.143268\pi$
$308$	−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	$-0.873784\pi$
$311$		−	13.6217i		−	0.772419i	0.922411	−	0.386209i	$-0.126216\pi$
$312$	−0.731230	+	1.83998i	−0.0413978	+	0.104168i
$313$	19.4239	+	19.4239i	1.09791	+	1.09791i	0.994655	+	0.103251i	$0.0329245\pi$
$313$	19.4239	+	19.4239i	1.09791	+	1.09791i	0.103251	+	0.994655i	$0.467076\pi$
$314$	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	0.513758	−	0.857935i	$-0.328253\pi$
$317$	−6.12789	−	6.12789i	−0.344177	−	0.344177i	−0.857935	+	0.513758i	$0.828253\pi$
$318$	−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	−0.605331	+	0.795974i	$0.706959\pi$
$337$	−25.7245	+	25.7245i	−1.40130	+	1.40130i	−0.795974	+	0.605331i	$0.793041\pi$
$338$	−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	−0.998625	−	0.0524136i	$-0.983309\pi$
$347$	−19.5787	−	19.5787i	−1.05104	−	1.05104i	−0.0524136	−	0.998625i	$-0.516691\pi$
$348$	2.92466	+	1.16230i	0.156778	+	0.0623057i
$349$			1.90866i			0.102168i	0.998694	+	0.0510840i	$0.0162676\pi$
$349$			1.90866i			0.102168i	−0.998694	+	0.0510840i	$0.983732\pi$
$350$	−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	−0.987605	−	0.156961i	$-0.949830\pi$
$353$	−15.6064	+	15.6064i	−0.830643	+	0.830643i	0.156961	+	0.987605i	$0.449830\pi$
$354$	−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	−0.291245	−	0.956648i	$-0.594070\pi$
$367$	12.7473	−	12.7473i	0.665403	−	0.665403i	0.956648	+	0.291245i	$0.0940695\pi$
$368$	−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	0.593885	−	0.804550i	$-0.297593\pi$
$373$	−4.06861	−	4.06861i	−0.210664	−	0.210664i	−0.804550	+	0.593885i	$0.797593\pi$
$374$	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	$0.213171\pi$
$379$			24.1694i			1.24150i	−0.784009	+	0.620749i	$0.786829\pi$
$380$	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	−0.194697	−	0.980863i	$-0.562372\pi$
$383$	15.3856	−	15.3856i	0.786167	−	0.786167i	0.980863	+	0.194697i	$0.0623722\pi$
$384$	−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	−0.978681	−	0.205387i	$-0.934155\pi$
$397$	−15.4078	+	15.4078i	−0.773294	+	0.773294i	0.205387	+	0.978681i	$0.434155\pi$
$398$	−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	$-0.849446\pi$
$401$		−	18.2444i		−	0.911080i	0.890215	−	0.455540i	$-0.150554\pi$
$402$	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	$-0.797019\pi$
$409$		−	24.0799i		−	1.19067i	0.803477	−	0.595336i	$-0.202981\pi$
$410$	−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	$-0.880475\pi$
$431$		−	15.2273i		−	0.733472i	0.930325	−	0.366736i	$-0.119525\pi$
$432$	−4.71010	+	2.19431i	−0.226615	+	0.105574i
$433$	−14.9801	−	14.9801i	−0.719899	−	0.719899i	0.248686	−	0.968584i	$-0.420001\pi$
$433$	−14.9801	−	14.9801i	−0.719899	−	0.719899i	−0.968584	+	0.248686i	$0.920001\pi$
$434$	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	$0.239209\pi$
$439$			28.6098i			1.36547i	−0.730667	+	0.682734i	$0.760791\pi$
$440$	−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	−0.998942	−	0.0459922i	$-0.985355\pi$
$443$	−20.0573	+	20.0573i	−0.952950	+	0.952950i	0.0459922	+	0.998942i	$0.485355\pi$
$444$	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	−0.938034	−	0.346543i	$-0.887356\pi$
$457$	−12.6446	+	12.6446i	−0.591491	+	0.591491i	0.346543	+	0.938034i	$0.387356\pi$
$458$	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	$0.146404\pi$
$461$			19.0617i			0.887793i	−0.896078	+	0.443896i	$0.853596\pi$
$462$	2.39976	+	0.953695i	0.111647	+	0.0443699i
$463$	−7.42348	−	7.42348i	−0.344998	−	0.344998i	0.513244	−	0.858243i	$-0.328444\pi$
$463$	−7.42348	−	7.42348i	−0.344998	−	0.344998i	−0.858243	+	0.513244i	$0.828444\pi$
$464$	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	0.996541	+	0.0831015i	$0.0264826\pi$
$467$	23.3313	+	23.3313i	1.07964	+	1.07964i	0.0831015	+	0.996541i	$0.473517\pi$
$468$	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	−0.187963	−	0.982176i	$-0.560188\pi$
$487$	17.5268	−	17.5268i	0.794213	−	0.794213i	0.982176	+	0.187963i	$0.0601885\pi$
$488$	−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	$-0.800114\pi$
$491$		−	26.0360i		−	1.17499i	0.809228	−	0.587495i	$-0.199886\pi$
$492$	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	$-0.847919\pi$
$499$		−	20.5426i		−	0.919612i	0.888019	−	0.459806i	$-0.152081\pi$
$500$	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	−0.728104	−	0.685467i	$-0.759598\pi$
$503$	−0.956236	+	0.956236i	−0.0426365	+	0.0426365i	0.685467	+	0.728104i	$0.259598\pi$
$504$	−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	$0.146903\pi$
$521$			20.3284i			0.890602i	−0.895381	+	0.445301i	$0.853097\pi$
$522$	−0.157244	−	5.44876i	−0.00688236	−	0.238486i
$523$	−7.42441	−	7.42441i	−0.324647	−	0.324647i	0.525900	−	0.850547i	$-0.323729\pi$
$523$	−7.42441	−	7.42441i	−0.324647	−	0.324647i	−0.850547	+	0.525900i	$0.823729\pi$
$524$	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	−0.999995	−	0.00306145i	$-0.999026\pi$
$547$	−23.3163	+	23.3163i	−0.996934	+	0.996934i	0.00306145	+	0.999995i	$0.499026\pi$
$548$	−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	0.0273453	−	0.999626i	$-0.491295\pi$
$557$	−22.9466	−	22.9466i	−0.972281	−	0.972281i	−0.999626	+	0.0273453i	$0.991295\pi$
$558$	−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	−0.996518	−	0.0833728i	$-0.973431\pi$
$563$	−21.6668	+	21.6668i	−0.913146	+	0.913146i	0.0833728	+	0.996518i	$0.473431\pi$
$564$	−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	−0.927930	−	0.372755i	$-0.878413\pi$
$577$	−13.3358	+	13.3358i	−0.555175	+	0.555175i	0.372755	+	0.927930i	$0.378413\pi$
$578$	−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	−0.999214	−	0.0396423i	$-0.987378\pi$
$587$	−25.1695	−	25.1695i	−1.03886	−	1.03886i	−0.0396423	−	0.999214i	$-0.512622\pi$
$588$	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	−0.605052	−	0.796186i	$-0.706848\pi$
$593$	4.65441	−	4.65441i	0.191134	−	0.191134i	0.796186	+	0.605052i	$0.206848\pi$
$594$	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	0.0355281	−	0.999369i	$-0.488689\pi$
$607$	25.4971	−	25.4971i	1.03490	−	1.03490i	0.999369	−	0.0355281i	$-0.0113113\pi$
$608$	−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	0.577864	−	0.816133i	$-0.303886\pi$
$613$	−5.89927	−	5.89927i	−0.238269	−	0.238269i	−0.816133	+	0.577864i	$0.803886\pi$
$614$	−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	0.603306	−	0.797510i	$-0.293850\pi$
$617$	−4.82392	−	4.82392i	−0.194204	−	0.194204i	−0.797510	+	0.603306i	$0.793850\pi$
$618$	−15.0154	−	5.96731i	−0.604008	−	0.240040i
$619$		−	15.1098i		−	0.607315i	−0.952781	−	0.303658i	$-0.901792\pi$
$619$		−	15.1098i		−	0.607315i	0.952781	−	0.303658i	$-0.0982079\pi$
$620$	−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	$-0.898862\pi$
$641$		−	15.8194i		−	0.624829i	0.949946	−	0.312414i	$-0.101138\pi$
$642$	11.2166	+	4.45760i	0.442683	+	0.175928i
$643$	−7.41965	−	7.41965i	−0.292603	−	0.292603i	0.545505	−	0.838108i	$-0.316338\pi$
$643$	−7.41965	−	7.41965i	−0.292603	−	0.292603i	−0.838108	+	0.545505i	$0.816338\pi$
$644$	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	0.919954	+	0.392027i	$0.128226\pi$
$647$	33.3718	+	33.3718i	1.31198	+	1.31198i	0.392027	+	0.919954i	$0.371774\pi$
$648$	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	−0.996418	−	0.0845653i	$-0.973050\pi$
$653$	−23.3014	+	23.3014i	−0.911853	+	0.911853i	0.0845653	+	0.996418i	$0.473050\pi$
$654$	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	0.973699	−	0.227837i	$-0.0731655\pi$
$673$	19.3493	+	19.3493i	0.745862	+	0.745862i	−0.227837	+	0.973699i	$0.573165\pi$
$674$	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	0.990101	−	0.140355i	$-0.0448245\pi$
$677$	22.1097	+	22.1097i	0.849746	+	0.849746i	−0.140355	+	0.990101i	$0.544824\pi$
$678$	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	−0.304009	−	0.952669i	$-0.598325\pi$
$683$	16.9522	−	16.9522i	0.648660	−	0.648660i	0.952669	+	0.304009i	$0.0983254\pi$
$684$	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	$0.134929\pi$
$701$			21.7801i			0.822622i	−0.911495	+	0.411311i	$0.865071\pi$
$702$	−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	$-0.811368\pi$
$709$		−	29.7437i		−	1.11705i	0.829489	−	0.558523i	$-0.188632\pi$
$710$	−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	−0.345356	−	0.938472i	$-0.612242\pi$
$727$	15.9921	−	15.9921i	0.593115	−	0.593115i	0.938472	+	0.345356i	$0.112242\pi$
$728$	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	0.986891	−	0.161386i	$-0.0515963\pi$
$733$	22.3497	+	22.3497i	0.825506	+	0.825506i	−0.161386	+	0.986891i	$0.551596\pi$
$734$	−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	$-0.727664\pi$
$739$		−	41.0456i		−	1.50989i	0.655789	−	0.754944i	$-0.272336\pi$
$740$	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	0.392222	−	0.919871i	$-0.371707\pi$
$743$	35.7650	−	35.7650i	1.31209	−	1.31209i	0.919871	−	0.392222i	$-0.128293\pi$
$744$	−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	−0.716167	−	0.697929i	$-0.754105\pi$
$757$	−0.501800	+	0.501800i	−0.0182382	+	0.0182382i	0.697929	+	0.716167i	$0.254105\pi$
$758$	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	$-0.800234\pi$
$761$		−	32.3967i		−	1.17438i	0.809449	−	0.587190i	$-0.199766\pi$
$762$	−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	$0.164176\pi$
$769$			27.3542i			0.986419i	−0.869911	+	0.493209i	$0.835824\pi$
$770$	−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	−0.782710	−	0.622387i	$-0.786163\pi$
$773$	−4.45744	+	4.45744i	−0.160323	+	0.160323i	0.622387	+	0.782710i	$0.286163\pi$
$774$	−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	−0.227632	−	0.973747i	$-0.573098\pi$
$787$	20.9311	−	20.9311i	0.746115	−	0.746115i	0.973747	+	0.227632i	$0.0730984\pi$
$788$	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	0.766753	−	0.641942i	$-0.221871\pi$
$797$	3.52355	+	3.52355i	0.124811	+	0.124811i	−0.641942	+	0.766753i	$0.721871\pi$
$798$	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	$0.0718486\pi$
$821$			12.8255i			0.447614i	−0.974633	+	0.223807i	$0.928151\pi$
$822$	34.5193	+	13.7184i	1.20400	+	0.478484i
$823$	−39.8650	−	39.8650i	−1.38961	−	1.38961i	−0.826135	−	0.563473i	$-0.809465\pi$
$823$	−39.8650	−	39.8650i	−1.38961	−	1.38961i	−0.563473	−	0.826135i	$-0.690535\pi$
$824$	−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	0.922771	−	0.385349i	$-0.125919\pi$
$827$	15.4550	+	15.4550i	0.537421	+	0.537421i	−0.385349	+	0.922771i	$0.625919\pi$
$828$	−0.0865397	−	2.99875i	−0.00300746	−	0.104214i
$829$			22.1839i			0.770478i	0.922817	+	0.385239i	$0.125881\pi$
$829$			22.1839i			0.770478i	−0.922817	+	0.385239i	$0.874119\pi$
$830$	−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	0.802597	−	0.596521i	$-0.203451\pi$
$853$	6.01870	+	6.01870i	0.206076	+	0.206076i	−0.596521	+	0.802597i	$0.703451\pi$
$854$	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	0.953213	+	0.302300i	$0.0977544\pi$
$857$	36.7546	+	36.7546i	1.25551	+	1.25551i	0.302300	+	0.953213i	$0.402246\pi$
$858$	−0.997984	+	2.51120i	−0.0340706	+	0.0857311i
$859$		−	21.3618i		−	0.728856i	−0.931232	−	0.364428i	$-0.881264\pi$
$859$		−	21.3618i		−	0.728856i	0.931232	−	0.364428i	$-0.118736\pi$
$860$	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	−0.240444	−	0.970663i	$-0.577293\pi$
$863$	21.4516	−	21.4516i	0.730219	−	0.730219i	0.970663	+	0.240444i	$0.0772930\pi$
$864$	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	0.269411	−	0.963025i	$-0.413171\pi$
$877$	36.4976	−	36.4976i	1.23244	−	1.23244i	0.963025	−	0.269411i	$-0.0868291\pi$
$878$	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	$0.193383\pi$
$881$			33.8871i			1.14169i	−0.821060	+	0.570843i	$0.806617\pi$
$882$	−17.4128	+	0.502507i	−0.586318	+	0.0169203i
$883$	−6.74287	−	6.74287i	−0.226916	−	0.226916i	0.584487	−	0.811403i	$-0.301296\pi$
$883$	−6.74287	−	6.74287i	−0.226916	−	0.226916i	−0.811403	+	0.584487i	$0.801296\pi$
$884$	−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	0.727022	−	0.686614i	$-0.240904\pi$
$887$	1.20348	+	1.20348i	0.0404088	+	0.0404088i	−0.686614	+	0.727022i	$0.740904\pi$
$888$	−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	0.0478228	−	0.998856i	$-0.484772\pi$
$907$	31.5222	−	31.5222i	1.04668	−	1.04668i	0.998856	−	0.0478228i	$-0.0152283\pi$
$908$	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	$0.0897933\pi$
$911$			16.8038i			0.556735i	−0.960475	+	0.278367i	$0.910207\pi$
$912$	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	$0.121942\pi$
$919$			22.6628i			0.747578i	−0.927514	+	0.373789i	$0.878058\pi$
$920$	−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	−0.0913178	−	0.995822i	$-0.529108\pi$
$937$	27.6873	−	27.6873i	0.904504	−	0.904504i	0.995822	+	0.0913178i	$0.0291079\pi$
$938$	−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	$0.0283896\pi$
$941$			5.46459i			0.178141i	−0.996025	+	0.0890703i	$0.971610\pi$
$942$	−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	0.327327	−	0.944911i	$-0.393852\pi$
$947$	−19.0051	−	19.0051i	−0.617583	−	0.617583i	−0.944911	+	0.327327i	$0.893852\pi$
$948$	−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	−0.999942	−	0.0107585i	$-0.996575\pi$
$953$	−30.5368	+	30.5368i	−0.989184	+	0.989184i	0.0107585	+	0.999942i	$0.496575\pi$
$954$	−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	−0.963483	−	0.267770i	$-0.913713\pi$
$967$	−21.6343	+	21.6343i	−0.695713	+	0.695713i	0.267770	+	0.963483i	$0.413713\pi$
$968$	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	$0.199348\pi$
$971$			36.5285i			1.17225i	−0.810219	+	0.586127i	$0.800652\pi$
$972$	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	0.0703611	−	0.997522i	$-0.477585\pi$
$977$	−28.9803	−	28.9803i	−0.927161	−	0.927161i	−0.997522	+	0.0703611i	$0.977585\pi$
$978$	−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	−0.408900	−	0.912579i	$-0.634088\pi$
$983$	15.7918	−	15.7918i	0.503679	−	0.503679i	0.912579	+	0.408900i	$0.134088\pi$
$984$	−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	−0.983144	−	0.182833i	$-0.941473\pi$
$997$	−25.2701	+	25.2701i	−0.800311	+	0.800311i	0.182833	+	0.983144i	$0.441473\pi$
$998$	−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.323.3	yes	32
3.2	odd	2	inner	690.2.i.e.323.15	yes	32
5.2	odd	4	inner	690.2.i.e.47.15	yes	32
15.2	even	4	inner	690.2.i.e.47.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.3	✓	32	15.2	even	4	inner
690.2.i.e.47.15	yes	32	5.2	odd	4	inner
690.2.i.e.323.3	yes	32	1.1	even	1	trivial
690.2.i.e.323.15	yes	32	3.2	odd	2	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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