LMFDB - Embedded newform 361.2.e.m.245.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,24,0,0,0,30,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			245.1
Character	$\chi$	$=$	361.245
Dual form			361.2.e.m.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.330298 + 1.87322i) q^{2} +(1.45710 + 1.22265i) q^{3} +(-1.52045 - 0.553400i) q^{4} +(3.04091 - 1.10680i) q^{5} +(-2.77157 + 2.32563i) q^{6} +(-0.118034 - 0.204441i) q^{7} +(-0.363271 + 0.629204i) q^{8} +(0.107320 + 0.608645i) q^{9} +(1.06887 + 6.06185i) q^{10} +(0.690983 - 1.19682i) q^{11} +(-1.53884 - 2.66535i) q^{12} +(-0.556564 + 0.467013i) q^{13} +(0.421948 - 0.153577i) q^{14} +(5.78415 + 2.10526i) q^{15} +(-3.53762 - 2.96842i) q^{16} +(-1.12387 + 6.37381i) q^{17} -1.17557 q^{18} -5.23607 q^{20} +(0.0779729 - 0.442206i) q^{21} +(2.01367 + 1.68967i) q^{22} +(0.358931 + 0.130640i) q^{23} +(-1.29862 + 0.472660i) q^{24} +(4.19190 - 3.51742i) q^{25} +(-0.690983 - 1.19682i) q^{26} +(2.26538 - 3.92376i) q^{27} +(0.0663277 + 0.376163i) q^{28} +(-0.738570 - 4.18864i) q^{29} +(-5.85410 + 10.1396i) q^{30} +(-0.951057 - 1.64728i) q^{31} +(5.61582 - 4.71224i) q^{32} +(2.47013 - 0.899053i) q^{33} +(-11.5683 - 4.21052i) q^{34} +(-0.585206 - 0.491046i) q^{35} +(0.173648 - 0.984808i) q^{36} -6.60440 q^{37} -1.38197 q^{39} +(-0.408271 + 2.31542i) q^{40} +(-1.66969 - 1.40104i) q^{41} +(0.802593 + 0.292120i) q^{42} +(-8.76380 + 3.18976i) q^{43} +(-1.71293 + 1.43732i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-0.363271 + 0.629204i) q^{46} +(-1.99212 - 11.2978i) q^{47} +(-1.52533 - 8.65057i) q^{48} +(3.47214 - 6.01392i) q^{49} +(5.20431 + 9.01413i) q^{50} +(-9.43057 + 7.91319i) q^{51} +(1.10467 - 0.402069i) q^{52} +(4.67948 + 1.70319i) q^{53} +(6.60180 + 5.53957i) q^{54} +(0.776578 - 4.40419i) q^{55} +0.171513 q^{56} +8.09017 q^{58} +(1.52533 - 8.65057i) q^{59} +(-7.62949 - 6.40190i) q^{60} +(8.90090 + 3.23966i) q^{61} +(3.39984 - 1.23744i) q^{62} +(0.111764 - 0.0937814i) q^{63} +(2.35410 + 4.07742i) q^{64} +(-1.17557 + 2.03615i) q^{65} +(0.868241 + 4.92404i) q^{66} +(2.26390 + 12.8392i) q^{67} +(5.23607 - 9.06914i) q^{68} +(0.363271 + 0.629204i) q^{69} +(1.11313 - 0.934025i) q^{70} +(-9.52013 + 3.46504i) q^{71} +(-0.421948 - 0.153577i) q^{72} +(6.89440 + 5.78509i) q^{73} +(2.18142 - 12.3715i) q^{74} +10.4086 q^{75} -0.326238 q^{77} +(0.456461 - 2.58872i) q^{78} +(-3.60216 - 3.02257i) q^{79} +(-14.0430 - 5.11124i) q^{80} +(9.84059 - 3.58168i) q^{81} +(3.17594 - 2.66493i) q^{82} +(1.61803 + 2.80252i) q^{83} +(-0.363271 + 0.629204i) q^{84} +(3.63693 + 20.6261i) q^{85} +(-3.08044 - 17.4701i) q^{86} +(4.04508 - 7.00629i) q^{87} +(0.502029 + 0.869539i) q^{88} +(5.69703 - 4.78037i) q^{89} +(-3.57480 + 1.30112i) q^{90} +(0.161170 + 0.0586610i) q^{91} +(-0.473442 - 0.397265i) q^{92} +(0.628265 - 3.56307i) q^{93} +21.8213 q^{94} +13.9443 q^{96} +(-0.768353 + 4.35755i) q^{97} +(10.1185 + 8.49045i) q^{98} +(0.802593 + 0.292120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) $ 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.330298	+	1.87322i	−0.233556	+	1.32456i	0.612077	+	0.790798i	$0.290334\pi$
$2$	−0.330298	+	1.87322i	−0.233556	+	1.32456i	−0.845633	+	0.533765i	$0.820777\pi$
$3$	1.45710	+	1.22265i	0.841259	+	0.705900i	0.957847	−	0.287280i	$-0.0927511\pi$
$3$	1.45710	+	1.22265i	0.841259	+	0.705900i	−0.116588	+	0.993180i	$0.537196\pi$
$4$	−1.52045	−	0.553400i	−0.760227	−	0.276700i
$5$	3.04091	−	1.10680i	1.35994	−	0.494976i	0.443901	−	0.896076i	$-0.353594\pi$
$5$	3.04091	−	1.10680i	1.35994	−	0.494976i	0.916035	+	0.401099i	$0.131372\pi$
$6$	−2.77157	+	2.32563i	−1.13149	+	0.949433i
$7$	−0.118034	−	0.204441i	−0.0446127	−	0.0772714i	0.842857	−	0.538138i	$-0.180872\pi$
$7$	−0.118034	−	0.204441i	−0.0446127	−	0.0772714i	−0.887469	+	0.460866i	$0.847539\pi$
$8$	−0.363271	+	0.629204i	−0.128436	+	0.222457i
$9$	0.107320	+	0.608645i	0.0357735	+	0.202882i
$10$	1.06887	+	6.06185i	0.338006	+	1.91693i
$11$	0.690983	−	1.19682i	0.208339	−	0.360854i	−0.742852	−	0.669455i	$-0.766528\pi$
$11$	0.690983	−	1.19682i	0.208339	−	0.360854i	0.951191	+	0.308601i	$0.0998609\pi$
$12$	−1.53884	−	2.66535i	−0.444225	−	0.769421i
$13$	−0.556564	+	0.467013i	−0.154363	+	0.129526i	−0.716698	−	0.697383i	$-0.754348\pi$
$13$	−0.556564	+	0.467013i	−0.154363	+	0.129526i	0.562335	+	0.826909i	$0.309903\pi$
$14$	0.421948	−	0.153577i	0.112770	−	0.0410451i
$15$	5.78415	+	2.10526i	1.49346	+	0.543576i
$16$	−3.53762	−	2.96842i	−0.884405	−	0.742104i
$17$	−1.12387	+	6.37381i	−0.272580	+	1.54588i	0.473967	+	0.880543i	$0.342822\pi$
$17$	−1.12387	+	6.37381i	−0.272580	+	1.54588i	−0.746547	+	0.665333i	$0.768289\pi$
$18$	−1.17557			−0.277085
$19$		0			0
$19$		0			0
$20$	−5.23607			−1.17082
$21$	0.0779729	−	0.442206i	0.0170151	−	0.0964973i
$22$	2.01367	+	1.68967i	0.429315	+	0.360238i
$23$	0.358931	+	0.130640i	0.0748422	+	0.0272403i	0.379170	−	0.925327i	$-0.376210\pi$
$23$	0.358931	+	0.130640i	0.0748422	+	0.0272403i	−0.304328	+	0.952567i	$0.598432\pi$
$24$	−1.29862	+	0.472660i	−0.265080	+	0.0964814i
$25$	4.19190	−	3.51742i	0.838380	−	0.703484i
$26$	−0.690983	−	1.19682i	−0.135513	−	0.234715i
$27$	2.26538	−	3.92376i	0.435973	−	0.755128i
$28$	0.0663277	+	0.376163i	0.0125348	+	0.0710881i
$29$	−0.738570	−	4.18864i	−0.137149	−	0.777810i	−0.973339	−	0.229371i	$-0.926333\pi$
$29$	−0.738570	−	4.18864i	−0.137149	−	0.777810i	0.836190	−	0.548440i	$-0.184778\pi$
$30$	−5.85410	+	10.1396i	−1.06881	+	1.85123i
$31$	−0.951057	−	1.64728i	−0.170815	−	0.295860i	0.767890	−	0.640582i	$-0.221307\pi$
$31$	−0.951057	−	1.64728i	−0.170815	−	0.295860i	−0.938705	+	0.344722i	$0.887973\pi$
$32$	5.61582	−	4.71224i	0.992747	−	0.833013i
$33$	2.47013	−	0.899053i	0.429994	−	0.156505i
$34$	−11.5683	−	4.21052i	−1.98395	−	0.722098i
$35$	−0.585206	−	0.491046i	−0.0989178	−	0.0830019i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$	−6.60440			−1.08576			−0.542878	−	0.839812i	$-0.682665\pi$
$37$	−6.60440			−1.08576			−0.542878	+	0.839812i	$0.682665\pi$
$38$		0			0
$39$	−1.38197			−0.221292
$40$	−0.408271	+	2.31542i	−0.0645534	+	0.366100i
$41$	−1.66969	−	1.40104i	−0.260762	−	0.218805i	0.503028	−	0.864270i	$-0.332219\pi$
$41$	−1.66969	−	1.40104i	−0.260762	−	0.218805i	−0.763790	+	0.645465i	$0.776664\pi$
$42$	0.802593	+	0.292120i	0.123843	+	0.0450751i
$43$	−8.76380	+	3.18976i	−1.33647	+	0.486434i	−0.908698	−	0.417454i	$-0.862922\pi$
$43$	−8.76380	+	3.18976i	−1.33647	+	0.486434i	−0.427769	+	0.903888i	$0.640700\pi$
$44$	−1.71293	+	1.43732i	−0.258234	+	0.216684i
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	−0.363271	+	0.629204i	−0.0535614	+	0.0927711i
$47$	−1.99212	−	11.2978i	−0.290580	−	1.64796i	−0.684644	−	0.728878i	$-0.740042\pi$
$47$	−1.99212	−	11.2978i	−0.290580	−	1.64796i	0.394064	−	0.919083i	$-0.371069\pi$
$48$	−1.52533	−	8.65057i	−0.220162	−	1.24860i
$49$	3.47214	−	6.01392i	0.496019	−	0.859131i
$50$	5.20431	+	9.01413i	0.736001	+	1.27479i
$51$	−9.43057	+	7.91319i	−1.32054	+	1.10807i
$52$	1.10467	−	0.402069i	0.153191	−	0.0557569i
$53$	4.67948	+	1.70319i	0.642776	+	0.233951i	0.642782	−	0.766049i	$-0.277780\pi$
$53$	4.67948	+	1.70319i	0.642776	+	0.233951i	−6.71574e−6		1.00000i	$0.500002\pi$
$54$	6.60180	+	5.53957i	0.898391	+	0.753839i
$55$	0.776578	−	4.40419i	0.104714	−	0.593861i
$56$	0.171513			0.0229194
$57$		0			0
$58$	8.09017			1.06229
$59$	1.52533	−	8.65057i	0.198581	−	1.12621i	−0.708645	−	0.705565i	$-0.750693\pi$
$59$	1.52533	−	8.65057i	0.198581	−	1.12621i	0.907226	−	0.420644i	$-0.138196\pi$
$60$	−7.62949	−	6.40190i	−0.984963	−	0.826482i
$61$	8.90090	+	3.23966i	1.13964	+	0.414796i	0.841784	−	0.539814i	$-0.181505\pi$
$61$	8.90090	+	3.23966i	1.13964	+	0.414796i	0.297859	+	0.954610i	$0.403728\pi$
$62$	3.39984	−	1.23744i	0.431780	−	0.157155i
$63$	0.111764	−	0.0937814i	0.0140810	−	0.0118154i
$64$	2.35410	+	4.07742i	0.294263	+	0.509678i
$65$	−1.17557	+	2.03615i	−0.145812	+	0.252553i
$66$	0.868241	+	4.92404i	0.106873	+	0.606107i
$67$	2.26390	+	12.8392i	0.276579	+	1.56856i	0.733900	+	0.679257i	$0.237698\pi$
$67$	2.26390	+	12.8392i	0.276579	+	1.56856i	−0.457321	+	0.889302i	$0.651191\pi$
$68$	5.23607	−	9.06914i	0.634967	−	1.09979i
$69$	0.363271	+	0.629204i	0.0437327	+	0.0757473i
$70$	1.11313	−	0.934025i	0.133044	−	0.111637i
$71$	−9.52013	+	3.46504i	−1.12983	+	0.411225i	−0.838231	−	0.545315i	$-0.816410\pi$
$71$	−9.52013	+	3.46504i	−1.12983	+	0.411225i	−0.291600	+	0.956540i	$0.594188\pi$
$72$	−0.421948	−	0.153577i	−0.0497271	−	0.0180992i
$73$	6.89440	+	5.78509i	0.806928	+	0.677093i	0.949873	−	0.312637i	$-0.101212\pi$
$73$	6.89440	+	5.78509i	0.806928	+	0.677093i	−0.142944	+	0.989731i	$0.545657\pi$
$74$	2.18142	−	12.3715i	0.253585	−	1.43815i
$75$	10.4086			1.20188
$76$		0			0
$77$	−0.326238			−0.0371783
$78$	0.456461	−	2.58872i	0.0516841	−	0.293115i
$79$	−3.60216	−	3.02257i	−0.405274	−	0.340066i	0.417254	−	0.908790i	$-0.362993\pi$
$79$	−3.60216	−	3.02257i	−0.405274	−	0.340066i	−0.822528	+	0.568724i	$0.807437\pi$
$80$	−14.0430	−	5.11124i	−1.57006	−	0.571454i
$81$	9.84059	−	3.58168i	1.09340	−	0.397965i
$82$	3.17594	−	2.66493i	0.350724	−	0.294292i
$83$	1.61803	+	2.80252i	0.177602	+	0.307616i	0.941059	−	0.338243i	$-0.109833\pi$
$83$	1.61803	+	2.80252i	0.177602	+	0.307616i	−0.763456	+	0.645859i	$0.776499\pi$
$84$	−0.363271	+	0.629204i	−0.0396361	+	0.0686518i
$85$	3.63693	+	20.6261i	0.394481	+	2.23721i
$86$	−3.08044	−	17.4701i	−0.332173	−	1.88384i
$87$	4.04508	−	7.00629i	0.433679	−	0.751153i
$88$	0.502029	+	0.869539i	0.0535164	+	0.0926932i
$89$	5.69703	−	4.78037i	0.603884	−	0.506718i	−0.288808	−	0.957387i	$-0.593259\pi$
$89$	5.69703	−	4.78037i	0.603884	−	0.506718i	0.892691	+	0.450669i	$0.148814\pi$
$90$	−3.57480	+	1.30112i	−0.376817	+	0.137150i
$91$	0.161170	+	0.0586610i	0.0168952	+	0.00614935i
$92$	−0.473442	−	0.397265i	−0.0493597	−	0.0414177i
$93$	0.628265	−	3.56307i	0.0651480	−	0.369473i
$94$	21.8213			2.25070
$95$		0			0
$96$	13.9443			1.42318
$97$	−0.768353	+	4.35755i	−0.0780144	+	0.442442i	0.920632	+	0.390431i	$0.127674\pi$
$97$	−0.768353	+	4.35755i	−0.0780144	+	0.442442i	−0.998647	+	0.0520105i	$0.983437\pi$
$98$	10.1185	+	8.49045i	1.02212	+	0.857665i
$99$	0.802593	+	0.292120i	0.0806637	+	0.0293592i
$100$	−8.32013	+	3.02828i	−0.832013	+	0.302828i
$101$	3.02149	−	2.53533i	0.300649	−	0.252275i	−0.479965	−	0.877288i	$-0.659351\pi$
$101$	3.02149	−	2.53533i	0.300649	−	0.252275i	0.780614	+	0.625013i	$0.214906\pi$
$102$	−11.7082	−	20.2792i	−1.15928	−	2.00794i
$103$	−5.56758	+	9.64333i	−0.548590	+	0.950186i	0.449781	+	0.893139i	$0.351502\pi$
$103$	−5.56758	+	9.64333i	−0.548590	+	0.950186i	−0.998371	+	0.0570473i	$0.981831\pi$
$104$	−0.0916626	−	0.519845i	−0.00898826	−	0.0509750i
$105$	−0.252326	−	1.43101i	−0.0246245	−	0.139652i
$106$	−4.73607	+	8.20311i	−0.460008	+	0.796757i
$107$	−2.99193	−	5.18217i	−0.289240	−	0.500979i	0.684388	−	0.729118i	$-0.260069\pi$
$107$	−2.99193	−	5.18217i	−0.289240	−	0.500979i	−0.973629	+	0.228139i	$0.926736\pi$
$108$	−5.61582	+	4.71224i	−0.540383	+	0.453435i
$109$	2.89208	−	1.05263i	0.277011	−	0.100824i	−0.199779	−	0.979841i	$-0.564022\pi$
$109$	2.89208	−	1.05263i	0.277011	−	0.100824i	0.476790	+	0.879017i	$0.341800\pi$
$110$	7.99350	+	2.90940i	0.762151	+	0.277400i
$111$	−9.62328	−	8.07489i	−0.913402	−	0.766435i
$112$	−0.189306	+	1.07361i	−0.0178877	+	0.101446i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	1.23607			0.115264
$116$	−1.19503	+	6.77736i	−0.110956	+	0.629262i
$117$	−0.343975	−	0.288630i	−0.0318005	−	0.0266838i
$118$	15.7006	+	5.71454i	1.44536	+	0.526066i
$119$	1.43572	−	0.522560i	0.131612	−	0.0479030i
$120$	−3.42585	+	2.87463i	−0.312736	+	0.262417i
$121$	4.54508	+	7.87232i	0.413190	+	0.715665i
$122$	−9.00854	+	15.6032i	−0.815595	+	1.41265i
$123$	−0.719928	−	4.08291i	−0.0649137	−	0.368144i
$124$	0.534434	+	3.03093i	0.0479936	+	0.272185i
$125$	0.763932	−	1.32317i	0.0683282	−	0.118348i
$126$	0.138757	+	0.240335i	0.0123615	+	0.0214107i
$127$	9.56196	−	8.02343i	0.848486	−	0.711965i	−0.110969	−	0.993824i	$-0.535396\pi$
$127$	9.56196	−	8.02343i	0.848486	−	0.711965i	0.959456	+	0.281859i	$0.0909511\pi$
$128$	5.36220	−	1.95168i	0.473956	−	0.172506i
$129$	−16.6697	−	6.06729i	−1.46769	−	0.534195i
$130$	−3.42585	−	2.87463i	−0.300467	−	0.252122i
$131$	1.05755	−	5.99765i	0.0923983	−	0.524017i	−0.903115	−	0.429398i	$-0.858726\pi$
$131$	1.05755	−	5.99765i	0.0923983	−	0.524017i	0.995514	−	0.0946187i	$-0.0301632\pi$
$132$	−4.25325			−0.370198
$133$		0			0
$134$	−24.7984			−2.14225
$135$	2.54601	−	14.4391i	0.219125	−	1.24272i
$136$	−3.60216	−	3.02257i	−0.308882	−	0.259183i
$137$	−8.18303	−	2.97838i	−0.699124	−	0.254460i	−0.0320871	−	0.999485i	$-0.510215\pi$
$137$	−8.18303	−	2.97838i	−0.699124	−	0.254460i	−0.667037	+	0.745025i	$0.732438\pi$
$138$	−1.29862	+	0.472660i	−0.110546	+	0.0402355i
$139$	−9.26161	+	7.77141i	−0.785559	+	0.659163i	−0.944642	−	0.328103i	$-0.893591\pi$
$139$	−9.26161	+	7.77141i	−0.785559	+	0.659163i	0.159083	+	0.987265i	$0.449146\pi$
$140$	0.618034	+	1.07047i	0.0522334	+	0.0904709i
$141$	10.9106	−	18.8978i	0.918842	−	1.59148i
$142$	−3.34629	−	18.9777i	−0.280814	−	1.59258i
$143$	0.174353	+	0.988803i	0.0145801	+	0.0826879i
$144$	1.42705	−	2.47172i	0.118921	−	0.205977i
$145$	−6.88191	−	11.9198i	−0.571511	−	0.989887i
$146$	−13.1139	+	11.0039i	−1.08532	+	0.910689i
$147$	12.4122	−	4.51767i	1.02374	−	0.372611i
$148$	10.0417	+	3.65487i	0.825421	+	0.300429i
$149$	4.62265	+	3.87886i	0.378702	+	0.317769i	0.812193	−	0.583389i	$-0.198274\pi$
$149$	4.62265	+	3.87886i	0.378702	+	0.317769i	−0.433490	+	0.901158i	$0.642718\pi$
$150$	−3.43795	+	19.4976i	−0.280708	+	1.59197i
$151$	−17.2905			−1.40708			−0.703542	−	0.710654i	$-0.748399\pi$
$151$	−17.2905			−1.40708			−0.703542	+	0.710654i	$0.748399\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	0.107756	−	0.611114i	0.00868322	−	0.0492450i
$155$	−4.71528	−	3.95659i	−0.378741	−	0.317801i
$156$	2.10122	+	0.764780i	0.168232	+	0.0612314i
$157$	4.28717	−	1.56040i	0.342153	−	0.124534i	−0.165228	−	0.986255i	$-0.552836\pi$
$157$	4.28717	−	1.56040i	0.342153	−	0.124534i	0.507381	+	0.861722i	$0.330614\pi$
$158$	6.85171	−	5.74927i	0.545093	−	0.457387i
$159$	4.73607	+	8.20311i	0.375595	+	0.650549i
$160$	11.8617	−	20.5451i	0.937750	−	1.62423i
$161$	−0.0156578	−	0.0888001i	−0.00123401	−	0.00699843i
$162$	3.45893	+	19.6166i	0.271759	+	1.54122i
$163$	−7.73607	+	13.3993i	−0.605936	+	1.04951i	0.385967	+	0.922512i	$0.373868\pi$
$163$	−7.73607	+	13.3993i	−0.605936	+	1.04951i	−0.991903	+	0.126999i	$0.959466\pi$
$164$	1.76336	+	3.05422i	0.137695	+	0.238495i
$165$	6.51636	−	5.46788i	0.507298	−	0.425674i
$166$	−5.78415	+	2.10526i	−0.448937	+	0.163400i
$167$	−1.52662	−	0.555645i	−0.118134	−	0.0429971i	0.282277	−	0.959333i	$-0.408910\pi$
$167$	−1.52662	−	0.555645i	−0.118134	−	0.0429971i	−0.400411	+	0.916336i	$0.631133\pi$
$168$	0.249913	+	0.209702i	0.0192812	+	0.0161788i
$169$	−2.16576	+	12.2827i	−0.166597	+	0.944820i
$170$	−39.8384			−3.05546
$171$		0			0
$172$	15.0902			1.15061
$173$	−2.89471	+	16.4167i	−0.220081	+	1.24814i	0.651788	+	0.758401i	$0.274019\pi$
$173$	−2.89471	+	16.4167i	−0.220081	+	1.24814i	−0.871869	+	0.489740i	$0.837092\pi$
$174$	11.7882	+	9.89148i	0.893662	+	0.749871i
$175$	−1.21389	−	0.441820i	−0.0917616	−	0.0333985i
$176$	−5.99709	+	2.18276i	−0.452047	+	0.164532i
$177$	12.7992	−	10.7398i	0.962049	−	0.807255i
$178$	7.07295	+	12.2507i	0.530140	+	0.918229i
$179$	4.33901	−	7.51539i	0.324313	−	0.561726i	−0.657060	−	0.753838i	$-0.728200\pi$
$179$	4.33901	−	7.51539i	0.324313	−	0.561726i	0.981373	+	0.192112i	$0.0615336\pi$
$180$	−0.561937	−	3.18690i	−0.0418843	−	0.237538i
$181$	−1.00930	−	5.72404i	−0.0750208	−	0.425464i	−0.999067	−	0.0431838i	$-0.986250\pi$
$181$	−1.00930	−	5.72404i	−0.0750208	−	0.425464i	0.924046	−	0.382281i	$-0.124861\pi$
$182$	−0.163119	+	0.282530i	−0.0120912	+	0.0209425i
$183$	9.00854	+	15.6032i	0.665930	+	1.15342i
$184$	−0.212588	+	0.178383i	−0.0156722	+	0.0131506i
$185$	−20.0834	+	7.30975i	−1.47656	+	0.537423i
$186$	6.46688	+	2.35375i	0.474175	+	0.172585i
$187$	6.85171	+	5.74927i	0.501047	+	0.420428i
$188$	−3.22331	+	18.2803i	−0.235084	+	1.33323i
$189$	−1.06957			−0.0777997
$190$		0			0
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	−1.55511	+	8.81948i	−0.112231	+	0.636491i
$193$	6.51636	+	5.46788i	0.469058	+	0.393586i	0.846451	−	0.532467i	$-0.178735\pi$
$193$	6.51636	+	5.46788i	0.469058	+	0.393586i	−0.377393	+	0.926053i	$0.623179\pi$
$194$	−7.90884	−	2.87858i	−0.567821	−	0.206670i
$195$	−4.20243	+	1.52956i	−0.300942	+	0.109534i
$196$	−8.60733	+	7.22241i	−0.614809	+	0.515886i
$197$	−5.73607	−	9.93516i	−0.408678	−	0.707851i	0.586064	−	0.810265i	$-0.300677\pi$
$197$	−5.73607	−	9.93516i	−0.408678	−	0.707851i	−0.994742	+	0.102414i	$0.967343\pi$
$198$	−0.812299	+	1.40694i	−0.0577276	+	0.0999871i
$199$	−0.183325	−	1.03969i	−0.0129956	−	0.0737016i	0.977620	−	0.210377i	$-0.0674693\pi$
$199$	−0.183325	−	1.03969i	−0.0129956	−	0.0737016i	−0.990616	+	0.136676i	$0.956358\pi$
$200$	0.690380	+	3.91534i	0.0488172	+	0.276856i
$201$	−12.3992	+	21.4760i	−0.874571	+	1.51480i
$202$	3.75123	+	6.49731i	0.263935	+	0.457149i
$203$	−0.769152	+	0.645395i	−0.0539839	+	0.0452979i
$204$	18.7179	−	6.81276i	1.31052	−	0.476989i
$205$	−6.62805	−	2.41241i	−0.462923	−	0.168490i
$206$	−16.2251	−	13.6145i	−1.13046	−	0.948564i
$207$	−0.0409928	+	0.232482i	−0.00284919	+	0.0161586i
$208$	3.35520			0.232641
$209$		0			0
$210$	2.76393			0.190729
$211$	0.107756	−	0.611114i	0.00741822	−	0.0420708i	−0.980874	−	0.194644i	$-0.937645\pi$
$211$	0.107756	−	0.611114i	0.00741822	−	0.0420708i	0.988292	+	0.152573i	$0.0487560\pi$
$212$	−6.17239	−	5.17925i	−0.423921	−	0.355712i
$213$	−18.1084	−	6.59090i	−1.24076	−	0.451601i
$214$	10.6955	−	3.89286i	0.731133	−	0.266111i
$215$	−23.1195	+	19.3995i	−1.57674	+	1.32304i
$216$	1.64590	+	2.85078i	0.111989	+	0.193971i
$217$	−0.224514	+	0.388870i	−0.0152410	+	0.0263982i
$218$	1.01655	+	5.76517i	0.0688497	+	0.390466i
$219$	2.97269	+	16.8589i	0.200876	+	1.13922i
$220$	−3.61803	+	6.26662i	−0.243928	+	0.422495i
$221$	−2.35114	−	4.07230i	−0.158155	−	0.273932i
$222$	18.3046	−	15.3594i	1.22852	−	1.03085i
$223$	15.3043	−	5.57030i	1.02485	−	0.373015i	0.225732	−	0.974189i	$-0.427522\pi$
$223$	15.3043	−	5.57030i	1.02485	−	0.373015i	0.799118	+	0.601174i	$0.205300\pi$
$224$	−1.62623	−	0.591900i	−0.108657	−	0.0395480i
$225$	2.59074	+	2.17389i	0.172716	+	0.144926i
$226$		0			0
$227$	15.7314			1.04413			0.522066	−	0.852905i	$-0.325161\pi$
$227$	15.7314			1.04413			0.522066	+	0.852905i	$0.325161\pi$
$228$		0			0
$229$	−7.09017			−0.468532			−0.234266	−	0.972173i	$-0.575269\pi$
$229$	−7.09017			−0.468532			−0.234266	+	0.972173i	$0.575269\pi$
$230$	−0.408271	+	2.31542i	−0.0269206	+	0.152674i
$231$	−0.475362	−	0.398876i	−0.0312765	−	0.0262441i
$232$	2.90381	+	1.05690i	0.190644	+	0.0693889i
$233$	−4.25480	+	1.54862i	−0.278741	+	0.101454i	−0.477608	−	0.878573i	$-0.658496\pi$
$233$	−4.25480	+	1.54862i	−0.278741	+	0.101454i	0.198867	+	0.980027i	$0.436274\pi$
$234$	0.654280	−	0.549006i	0.0427716	−	0.0358897i
$235$	−18.5623	−	32.1509i	−1.21087	−	2.09729i
$236$	−7.10642	+	12.3087i	−0.462589	+	0.801227i
$237$	−1.55316	−	8.80839i	−0.100888	−	0.572166i
$238$	0.504651	+	2.86202i	0.0327117	+	0.185517i
$239$	4.57295	−	7.92058i	0.295799	−	0.512340i	−0.679371	−	0.733795i	$-0.737747\pi$
$239$	4.57295	−	7.92058i	0.295799	−	0.512340i	0.975171	+	0.221455i	$0.0710806\pi$
$240$	−14.2128	−	24.6174i	−0.917435	−	1.58904i
$241$	−20.7936	+	17.4479i	−1.33943	+	1.12392i	−0.357663	+	0.933851i	$0.616426\pi$
$241$	−20.7936	+	17.4479i	−1.33943	+	1.12392i	−0.981771	+	0.190068i	$0.939129\pi$
$242$	−16.2478	+	5.91371i	−1.04445	+	0.380148i
$243$	5.94532	+	2.16392i	0.381393	+	0.138816i
$244$	−11.7406	−	9.85152i	−0.751614	−	0.630679i
$245$	3.90225	−	22.1307i	0.249305	−	1.41388i
$246$	7.88597			0.502791
$247$		0			0
$248$	1.38197			0.0877549
$249$	−1.06887	+	6.06185i	−0.0677368	+	0.384154i
$250$	2.22626	+	1.86805i	0.140801	+	0.118146i
$251$	15.4264	+	5.61474i	0.973704	+	0.354399i	0.779389	−	0.626540i	$-0.215529\pi$
$251$	15.4264	+	5.61474i	0.973704	+	0.354399i	0.194315	+	0.980939i	$0.437752\pi$
$252$	−0.221831	+	0.0807400i	−0.0139741	+	0.00508614i
$253$	0.404367	−	0.339304i	0.0254224	−	0.0213319i
$254$	11.8713	+	20.5617i	0.744873	+	1.29016i
$255$	−19.9192	+	34.5010i	−1.24739	+	2.16054i
$256$	3.51994	+	19.9626i	0.219996	+	1.24766i
$257$	−1.88541	−	10.6927i	−0.117609	−	0.666992i	−0.985425	−	0.170108i	$-0.945588\pi$
$257$	−1.88541	−	10.6927i	−0.117609	−	0.666992i	0.867817	−	0.496884i	$-0.165523\pi$
$258$	16.8713	−	29.2220i	1.05036	−	1.81928i
$259$	0.779543	+	1.35021i	0.0484385	+	0.0838979i
$260$	2.91421	−	2.44531i	0.180731	−	0.151652i
$261$	2.47013	−	0.899053i	0.152897	−	0.0556500i
$262$	10.8856	+	3.96203i	0.672513	+	0.244775i
$263$	−18.2997	−	15.3553i	−1.12841	−	0.946846i	−0.129409	−	0.991591i	$-0.541308\pi$
$263$	−18.2997	−	15.3553i	−1.12841	−	0.946846i	−0.998998	+	0.0447455i	$0.985752\pi$
$264$	−0.331639	+	1.88082i	−0.0204109	+	0.115756i
$265$	16.1150			0.989934
$266$		0			0
$267$	14.1459			0.865715
$268$	3.66307	−	20.7743i	0.223757	−	1.26899i
$269$	19.7617	+	16.5820i	1.20489	+	1.01102i	0.999477	+	0.0323483i	$0.0102986\pi$
$269$	19.7617	+	16.5820i	1.20489	+	1.01102i	0.205414	+	0.978675i	$0.434146\pi$
$270$	26.2067	+	9.53844i	1.59489	+	0.580491i
$271$	18.1084	−	6.59090i	1.10000	−	0.400369i	0.272686	−	0.962103i	$-0.412088\pi$
$271$	18.1084	−	6.59090i	1.10000	−	0.400369i	0.827318	+	0.561734i	$0.189866\pi$
$272$	22.8960	−	19.2120i	1.38827	−	1.16490i
$273$	0.163119	+	0.282530i	0.00987241	+	0.0170995i
$274$	8.28199	−	14.3448i	0.500334	−	0.866603i
$275$	−1.31318	−	7.44742i	−0.0791878	−	0.449096i
$276$	−0.204136	−	1.15771i	−0.0122875	−	0.0696860i
$277$	7.38197	−	12.7859i	0.443539	−	0.768233i	−0.554410	−	0.832244i	$-0.687056\pi$
$277$	7.38197	−	12.7859i	0.443539	−	0.768233i	0.997949	+	0.0640111i	$0.0203893\pi$
$278$	−11.4984	−	19.9159i	−0.689630	−	1.19447i
$279$	0.900539	−	0.755642i	0.0539139	−	0.0452391i
$280$	0.521557	−	0.189831i	0.0311690	−	0.0113446i
$281$	14.7212	+	5.35806i	0.878191	+	0.319635i	0.741479	−	0.670976i	$-0.234124\pi$
$281$	14.7212	+	5.35806i	0.878191	+	0.319635i	0.136711	+	0.990611i	$0.456347\pi$
$282$	31.7959	+	26.6799i	1.89342	+	1.58877i
$283$	−2.09944	+	11.9065i	−0.124799	+	0.707768i	0.856629	+	0.515933i	$0.172555\pi$
$283$	−2.09944	+	11.9065i	−0.124799	+	0.707768i	−0.981427	+	0.191834i	$0.938556\pi$
$284$	16.3925			0.972714
$285$		0			0
$286$	−1.90983			−0.112931
$287$	−0.0893490	+	0.506723i	−0.00527410	+	0.0299109i
$288$	3.47077	+	2.91232i	0.204517	+	0.171610i
$289$	−23.3876	−	8.51238i	−1.37574	−	0.500728i
$290$	24.6015	−	8.95420i	1.44465	−	0.525809i
$291$	−6.44734	+	5.40996i	−0.377950	+	0.317138i
$292$	−7.28115	−	12.6113i	−0.426097	−	0.738022i
$293$	7.64121	−	13.2350i	0.446404	−	0.773195i	−0.551745	−	0.834013i	$-0.686038\pi$
$293$	7.64121	−	13.2350i	0.446404	−	0.773195i	0.998149	+	0.0608184i	$0.0193710\pi$
$294$	4.36284	+	24.7429i	0.254446	+	1.44304i
$295$	−4.93607	−	27.9938i	−0.287389	−	1.62986i
$296$	2.39919	−	4.15551i	0.139450	−	0.241534i
$297$	−3.13068	−	5.42250i	−0.181661	−	0.314646i
$298$	−8.79280	+	7.37804i	−0.509353	+	0.427398i
$299$	−0.260778	+	0.0949156i	−0.0150812	+	0.00548911i
$300$	−15.8258	−	5.76013i	−0.913705	−	0.332561i
$301$	1.68654	+	1.41518i	0.0972107	+	0.0815695i
$302$	5.71104	−	32.3889i	0.328633	−	1.86377i
$303$	7.50245			0.431005
$304$		0			0
$305$	30.6525			1.75516
$306$	1.32119	−	7.49286i	0.0755276	−	0.428338i
$307$	−21.1686	−	17.7626i	−1.20816	−	1.01376i	−0.999359	−	0.0358039i	$-0.988601\pi$
$307$	−21.1686	−	17.7626i	−1.20816	−	1.01376i	−0.208797	−	0.977959i	$-0.566955\pi$
$308$	0.496030	+	0.180540i	0.0282639	+	0.0102872i
$309$	−19.9030	+	7.24410i	−1.13224	+	0.412103i
$310$	8.96900	−	7.52589i	0.509405	−	0.427442i
$311$	7.23607	+	12.5332i	0.410320	+	0.710695i	0.994925	−	0.100624i	$-0.0320838\pi$
$311$	7.23607	+	12.5332i	0.410320	+	0.710695i	−0.584605	+	0.811318i	$0.698750\pi$
$312$	0.502029	−	0.869539i	0.0284218	−	0.0492279i
$313$	0.934569	+	5.30020i	0.0528249	+	0.299585i	0.999762	−	0.0218351i	$-0.00695090\pi$
$313$	0.934569	+	5.30020i	0.0528249	+	0.299585i	−0.946937	+	0.321420i	$0.895840\pi$
$314$	1.50692	+	8.54618i	0.0850406	+	0.482289i
$315$	0.236068	−	0.408882i	0.0133009	−	0.0230379i
$316$	3.80423	+	6.58911i	0.214004	+	0.370667i
$317$	24.0016	−	20.1397i	1.34806	−	1.13116i	0.368590	−	0.929592i	$-0.379841\pi$
$317$	24.0016	−	20.1397i	1.34806	−	1.13116i	0.979475	−	0.201568i	$-0.0646037\pi$
$318$	−16.9305	+	6.16220i	−0.949416	+	0.345559i
$319$	−5.52337	−	2.01034i	−0.309250	−	0.112558i
$320$	11.6715	+	9.79356i	0.652457	+	0.547476i
$321$	1.97646	−	11.2090i	0.110315	−	0.625628i
$322$	0.171513			0.00955807
$323$		0			0
$324$	−16.9443			−0.941348
$325$	−0.690380	+	3.91534i	−0.0382954	+	0.217184i
$326$	−22.5445	−	18.9171i	−1.24862	−	1.04772i
$327$	5.50106	+	2.00222i	0.304209	+	0.110723i
$328$	1.48809	−	0.541620i	0.0821660	−	0.0299060i
$329$	−2.07460	+	1.74080i	−0.114377	+	0.0959734i
$330$	8.09017	+	14.0126i	0.445349	+	0.771367i
$331$	−10.1311	+	17.5476i	−0.556856	+	0.964503i	0.440901	+	0.897556i	$0.354659\pi$
$331$	−10.1311	+	17.5476i	−0.556856	+	0.964503i	−0.997757	+	0.0669469i	$0.978674\pi$
$332$	−0.909234	−	5.15652i	−0.0499007	−	0.283001i
$333$	−0.708787	−	4.01973i	−0.0388413	−	0.220280i
$334$	1.54508	−	2.67617i	0.0845433	−	0.146433i
$335$	21.0948	+	36.5372i	1.15253	+	1.99624i
$336$	−1.58849	+	1.33290i	−0.0866592	+	0.0727157i
$337$	0.521557	−	0.189831i	0.0284110	−	0.0103408i	−0.327776	−	0.944756i	$-0.606299\pi$
$337$	0.521557	−	0.189831i	0.0284110	−	0.0103408i	0.356187	+	0.934415i	$0.384077\pi$
$338$	−22.2927	−	8.11388i	−1.21256	−	0.441337i
$339$		0			0
$340$	5.88468	−	33.3737i	0.319142	−	1.80994i
$341$	−2.62866			−0.142350
$342$		0			0
$343$	−3.29180			−0.177740
$344$	1.17662	−	6.67297i	0.0634393	−	0.359782i
$345$	1.80108	+	1.51128i	0.0969668	+	0.0813648i
$346$	−29.7960	−	10.8448i	−1.60184	−	0.583022i
$347$	−27.0940	+	9.86140i	−1.45448	+	0.529388i	−0.943839	−	0.330405i	$-0.892815\pi$
$347$	−27.0940	+	9.86140i	−1.45448	+	0.529388i	−0.510642	+	0.859793i	$0.670592\pi$
$348$	−10.0277	+	8.41420i	−0.537539	+	0.451048i
$349$	−6.80902	−	11.7936i	−0.364478	−	0.631295i	0.624214	−	0.781253i	$-0.285419\pi$
$349$	−6.80902	−	11.7936i	−0.364478	−	0.631295i	−0.988692	+	0.149958i	$0.952086\pi$
$350$	1.22857	−	2.12795i	0.0656699	−	0.113744i
$351$	0.571614	+	3.24179i	0.0305105	+	0.173034i
$352$	−1.75925	−	9.97719i	−0.0937682	−	0.531786i
$353$	−12.6910	+	21.9814i	−0.675473	+	1.16995i	0.300858	+	0.953669i	$0.402727\pi$
$353$	−12.6910	+	21.9814i	−0.675473	+	1.16995i	−0.976330	+	0.216284i	$0.930606\pi$
$354$	15.8904	+	27.5231i	0.844568	+	1.46283i
$355$	−25.1147	+	21.0738i	−1.33295	+	1.11848i
$356$	−11.3075	+	4.11560i	−0.599298	+	0.218127i
$357$	2.73091	+	0.993969i	0.144535	+	0.0526064i
$358$	12.6448	+	10.6102i	0.668297	+	0.560768i
$359$	−6.14401	+	34.8444i	−0.324269	+	1.83902i	0.190497	+	0.981688i	$0.438990\pi$
$359$	−6.14401	+	34.8444i	−0.324269	+	1.83902i	−0.514765	+	0.857331i	$0.672121\pi$
$360$	−1.45309			−0.0765843
$361$		0			0
$362$	11.0557			0.581076
$363$	−3.00247	+	17.0278i	−0.157589	+	0.893730i
$364$	−0.212588	−	0.178383i	−0.0111427	−	0.00934981i
$365$	27.3682	+	9.96120i	1.43252	+	0.521393i
$366$	−32.2037	+	11.7212i	−1.68332	+	0.612677i
$367$	9.59690	−	8.05276i	0.500954	−	0.420350i	−0.356979	−	0.934113i	$-0.616193\pi$
$367$	9.59690	−	8.05276i	0.500954	−	0.420350i	0.857933	+	0.513762i	$0.171749\pi$
$368$	−0.881966	−	1.52761i	−0.0459757	−	0.0796322i
$369$	0.673542	−	1.16661i	0.0350632	−	0.0607312i
$370$	−7.05923	−	40.0349i	−0.366992	−	2.08131i
$371$	−0.204136	−	1.15771i	−0.0105982	−	0.0601054i
$372$	−2.92705	+	5.06980i	−0.151761	+	0.262857i
$373$	18.3803	+	31.8357i	0.951698	+	1.64839i	0.741749	+	0.670677i	$0.233996\pi$
$373$	18.3803	+	31.8357i	0.951698	+	1.64839i	0.209949	+	0.977712i	$0.432670\pi$
$374$	−13.0327	+	10.9358i	−0.673906	+	0.565474i
$375$	2.73091	−	0.993969i	0.141023	−	0.0513283i
$376$	7.83233	+	2.85074i	0.403922	+	0.147015i
$377$	2.36721	+	1.98632i	0.121917	+	0.102301i
$378$	0.353277	−	2.00353i	0.0181706	−	0.103051i
$379$	−21.3723			−1.09782			−0.548910	−	0.835882i	$-0.684957\pi$
$379$	−21.3723			−1.09782			−0.548910	+	0.835882i	$0.684957\pi$
$380$		0			0
$381$	23.7426			1.21637
$382$	5.61507	−	31.8447i	0.287292	−	1.62931i
$383$	−8.66142	−	7.26779i	−0.442578	−	0.371367i	0.394095	−	0.919070i	$-0.371058\pi$
$383$	−8.66142	−	7.26779i	−0.442578	−	0.371367i	−0.836673	+	0.547703i	$0.815502\pi$
$384$	10.1995	+	3.71232i	0.520492	+	0.189444i
$385$	−0.992060	+	0.361080i	−0.0505601	+	0.0184024i
$386$	−12.3949	+	10.4005i	−0.630882	+	0.529373i
$387$	−2.88197	−	4.99171i	−0.146499	−	0.253743i
$388$	3.57971	−	6.20024i	0.181732	−	0.314770i
$389$	0.331639	+	1.88082i	0.0168147	+	0.0953611i	0.992060	−	0.125764i	$-0.0401382\pi$
$389$	0.331639	+	1.88082i	0.0168147	+	0.0953611i	−0.975245	+	0.221125i	$0.929027\pi$
$390$	−1.47714	−	8.37728i	−0.0747979	−	0.424200i
$391$	−1.23607	+	2.14093i	−0.0625106	+	0.108272i
$392$	2.52265	+	4.36937i	0.127413	+	0.220686i
$393$	8.87401	−	7.44617i	0.447634	−	0.375610i
$394$	20.5053	−	7.46332i	1.03304	−	0.375997i
$395$	−14.2992	−	5.20449i	−0.719471	−	0.261866i
$396$	−1.05865	−	0.888311i	−0.0531990	−	0.0446393i
$397$	0.224318	−	1.27217i	0.0112582	−	0.0638484i	−0.978661	−	0.205481i	$-0.934124\pi$
$397$	0.224318	−	1.27217i	0.0112582	−	0.0638484i	0.989919	+	0.141633i	$0.0452352\pi$
$398$	2.00811			0.100658
$399$		0			0
$400$	−25.2705			−1.26353
$401$	0.816543	−	4.63084i	0.0407762	−	0.231253i	−0.957608	−	0.288074i	$-0.906985\pi$
$401$	0.816543	−	4.63084i	0.0407762	−	0.231253i	0.998384	+	0.0568205i	$0.0180963\pi$
$402$	−36.1338	−	30.3198i	−1.80219	−	1.51222i
$403$	1.29862	+	0.472660i	0.0646890	+	0.0235449i
$404$	−5.99709	+	2.18276i	−0.298366	+	0.108596i
$405$	25.9601	−	21.7831i	1.28997	−	1.08241i
$406$	−0.954915	−	1.65396i	−0.0473916	−	0.0820847i
$407$	−4.56352	+	7.90426i	−0.226206	+	0.391799i
$408$	−1.55316	−	8.80839i	−0.0768927	−	0.436080i
$409$	−4.17909	−	23.7008i	−0.206643	−	1.17193i	−0.894834	−	0.446400i	$-0.852706\pi$
$409$	−4.17909	−	23.7008i	−0.206643	−	1.17193i	0.688191	−	0.725530i	$-0.258405\pi$
$410$	6.70820	−	11.6190i	0.331295	−	0.573819i
$411$	−8.28199	−	14.3448i	−0.408521	−	0.707579i
$412$	13.8019	−	11.5812i	0.679970	−	0.570562i
$413$	−1.94857	+	0.709222i	−0.0958829	+	0.0348985i
$414$	−0.421948	−	0.153577i	−0.0207376	−	0.00754788i
$415$	8.02212	+	6.73136i	0.393790	+	0.330429i
$416$	−0.924892	+	5.24532i	−0.0453465	+	0.257173i
$417$	−22.9969			−1.12616
$418$		0			0
$419$	−6.58359			−0.321630			−0.160815	−	0.986985i	$-0.551412\pi$
$419$	−6.58359			−0.321630			−0.160815	+	0.986985i	$0.551412\pi$
$420$	−0.408271	+	2.31542i	−0.0199216	+	0.112981i
$421$	24.8209	+	20.8272i	1.20970	+	1.01506i	0.999299	+	0.0374421i	$0.0119210\pi$
$421$	24.8209	+	20.8272i	1.20970	+	1.01506i	0.210400	+	0.977615i	$0.432523\pi$
$422$	1.10916	+	0.403700i	0.0539929	+	0.0196518i
$423$	6.66258	−	2.42498i	0.323946	−	0.117907i
$424$	−2.77157	+	2.32563i	−0.134600	+	0.112942i
$425$	17.7082	+	30.6715i	0.858974	+	1.48779i
$426$	18.3273	−	31.7439i	0.887963	−	1.53800i
$427$	−0.388289	−	2.20210i	−0.0187906	−	0.106567i
$428$	1.68128	+	9.53499i	0.0812675	+	0.460891i
$429$	−0.954915	+	1.65396i	−0.0461037	+	0.0798540i
$430$	−28.7032	−	49.7154i	−1.38419	−	2.39749i
$431$	9.56196	−	8.02343i	0.460583	−	0.386475i	−0.382762	−	0.923847i	$-0.625027\pi$
$431$	9.56196	−	8.02343i	0.460583	−	0.386475i	0.843346	+	0.537372i	$0.180583\pi$
$432$	−19.6614	+	7.15617i	−0.945960	+	0.344301i
$433$	−17.7744	−	6.46936i	−0.854184	−	0.310897i	−0.122439	−	0.992476i	$-0.539071\pi$
$433$	−17.7744	−	6.46936i	−0.854184	−	0.310897i	−0.731745	+	0.681579i	$0.761294\pi$
$434$	−0.654280	−	0.549006i	−0.0314064	−	0.0263531i
$435$	4.54617	−	25.7826i	0.217972	−	1.23618i
$436$	−4.97980			−0.238489
$437$		0			0
$438$	−32.5623			−1.55589
$439$	−1.03909	+	5.89295i	−0.0495928	+	0.281255i	−0.999512	−	0.0312412i	$-0.990054\pi$
$439$	−1.03909	+	5.89295i	−0.0495928	+	0.281255i	0.949919	+	0.312496i	$0.101165\pi$
$440$	2.48903	+	2.08854i	0.118660	+	0.0995674i
$441$	4.03297	+	1.46788i	0.192046	+	0.0698991i
$442$	8.40487	−	3.05912i	0.399779	−	0.145508i
$443$	11.6288	−	9.75773i	0.552502	−	0.463604i	−0.323285	−	0.946301i	$-0.604787\pi$
$443$	11.6288	−	9.75773i	0.552502	−	0.463604i	0.875787	+	0.482698i	$0.160343\pi$
$444$	10.1631	+	17.6030i	0.482320	+	0.835403i
$445$	12.0332	−	20.8421i	0.570429	−	0.988013i
$446$	5.37940	+	30.5081i	0.254722	+	1.44460i
$447$	1.99317	+	11.3038i	0.0942736	+	0.534652i
$448$	0.555728	−	0.962549i	0.0262557	−	0.0454762i
$449$	−12.1190	−	20.9907i	−0.571930	−	0.990612i	−0.996368	−	0.0851545i	$-0.972862\pi$
$449$	−12.1190	−	20.9907i	−0.571930	−	0.990612i	0.424438	−	0.905457i	$-0.360472\pi$
$450$	−4.92787	+	4.13498i	−0.232302	+	0.194925i
$451$	−2.83052	+	1.03022i	−0.133284	+	0.0485113i
$452$		0			0
$453$	−25.1941	−	21.1403i	−1.18372	−	0.993260i
$454$	−5.19607	+	29.4684i	−0.243864	+	1.38302i
$455$	0.555029			0.0260202
$456$		0			0
$457$	6.29180			0.294318			0.147159	−	0.989113i	$-0.452987\pi$
$457$	6.29180			0.294318			0.147159	+	0.989113i	$0.452987\pi$
$458$	2.34187	−	13.2814i	0.109429	−	0.620600i
$459$	22.4633	+	18.8489i	1.04850	+	0.879793i
$460$	−1.87939	−	0.684040i	−0.0876268	−	0.0318935i
$461$	11.1068	−	4.04256i	0.517297	−	0.188281i	−0.0701603	−	0.997536i	$-0.522351\pi$
$461$	11.1068	−	4.04256i	0.517297	−	0.188281i	0.587458	+	0.809255i	$0.300129\pi$
$462$	0.904193	−	0.758708i	0.0420669	−	0.0352983i
$463$	−5.07295	−	8.78661i	−0.235760	−	0.408348i	0.723733	−	0.690080i	$-0.242425\pi$
$463$	−5.07295	−	8.78661i	−0.235760	−	0.408348i	−0.959493	+	0.281732i	$0.909091\pi$
$464$	−9.82084	+	17.0102i	−0.455921	+	0.789678i
$465$	−2.03311	−	11.5303i	−0.0942831	−	0.534706i
$466$	−1.49555	−	8.48167i	−0.0692799	−	0.392906i
$467$	−2.11803	+	3.66854i	−0.0980109	+	0.169760i	−0.910861	−	0.412713i	$-0.864581\pi$
$467$	−2.11803	+	3.66854i	−0.0980109	+	0.169760i	0.812850	+	0.582473i	$0.197915\pi$
$468$	0.363271	+	0.629204i	0.0167922	+	0.0290850i
$469$	2.35764	−	1.97830i	0.108866	−	0.0913493i
$470$	66.3566	−	24.1518i	3.06080	−	1.11404i
$471$	8.15467	+	2.96806i	0.375747	+	0.136761i
$472$	4.88887	+	4.10225i	0.225028	+	0.188821i
$473$	−2.23807	+	12.6927i	−0.102907	+	0.583613i
$474$	17.0130			0.781434
$475$		0			0
$476$	−2.47214			−0.113310
$477$	−0.534434	+	3.03093i	−0.0244701	+	0.138777i
$478$	13.3265	+	11.1823i	0.609541	+	0.511465i
$479$	14.9503	+	5.44148i	0.683099	+	0.248628i	0.660178	−	0.751110i	$-0.270481\pi$
$479$	14.9503	+	5.44148i	0.683099	+	0.248628i	0.0229214	+	0.999737i	$0.492703\pi$
$480$	42.4033	−	15.4335i	1.93544	−	0.704441i
$481$	3.67577	−	3.08434i	0.167601	−	0.140634i
$482$	−25.8156	−	44.7139i	−1.17587	−	2.03666i
$483$	0.0857567	−	0.148535i	0.00390207	−	0.00675858i
$484$	−2.55405	−	14.4848i	−0.116093	−	0.658398i
$485$	2.48644	+	14.1013i	0.112904	+	0.640308i
$486$	−6.01722	+	10.4221i	−0.272947	+	0.472758i
$487$	−8.33499	−	14.4366i	−0.377695	−	0.654186i	0.613032	−	0.790058i	$-0.289950\pi$
$487$	−8.33499	−	14.4366i	−0.377695	−	0.654186i	−0.990726	+	0.135872i	$0.956616\pi$
$488$	−5.27185	+	4.42361i	−0.238645	+	0.200247i
$489$	−27.6549	+	10.0656i	−1.25060	+	0.455181i
$490$	40.1667	+	14.6195i	1.81455	+	0.660441i
$491$	13.2300	+	11.1013i	0.597061	+	0.500993i	0.890499	−	0.454985i	$-0.150355\pi$
$491$	13.2300	+	11.1013i	0.597061	+	0.500993i	−0.293439	+	0.955978i	$0.594800\pi$
$492$	−1.16487	+	6.60629i	−0.0525163	+	0.297835i
$493$	27.5276			1.23978
$494$		0			0
$495$	2.76393			0.124230
$496$	−1.52533	+	8.65057i	−0.0684893	+	0.388422i
$497$	1.83209	+	1.53731i	0.0821807	+	0.0689578i
$498$	−11.0021	−	4.00444i	−0.493016	−	0.179443i
$499$	−28.6344	+	10.4221i	−1.28185	+	0.466557i	−0.891045	−	0.453915i	$-0.850027\pi$
$499$	−28.6344	+	10.4221i	−1.28185	+	0.466557i	−0.390809	+	0.920472i	$0.627805\pi$
$500$	−1.89377	+	1.58906i	−0.0846918	+	0.0710649i
$501$	−1.54508	−	2.67617i	−0.0690293	−	0.119562i
$502$	−15.6129	+	27.0424i	−0.696839	+	1.20696i
$503$	3.57659	+	20.2838i	0.159472	+	0.904412i	0.954582	+	0.297947i	$0.0963018\pi$
$503$	3.57659	+	20.2838i	0.159472	+	0.904412i	−0.795110	+	0.606465i	$0.792587\pi$
$504$	0.0184069	+	0.104391i	0.000819909	+	0.00464993i
$505$	6.38197	−	11.0539i	0.283994	−	0.491892i
$506$	0.502029	+	0.869539i	0.0223179	+	0.0386557i
$507$	−18.1732	+	15.2491i	−0.807100	+	0.677237i
$508$	−18.9787	+	6.90768i	−0.842043	+	0.306479i
$509$	17.0917	+	6.22086i	0.757575	+	0.275735i	0.691790	−	0.722099i	$-0.256822\pi$
$509$	17.0917	+	6.22086i	0.757575	+	0.275735i	0.0657856	+	0.997834i	$0.479045\pi$
$510$	−58.0486	−	48.7086i	−2.57044	−	2.15685i
$511$	0.368935	−	2.09233i	0.0163207	−	0.0925594i
$512$	−27.1441			−1.19961
$513$		0			0
$514$	20.6525			0.910942
$515$	−6.25726	+	35.4867i	−0.275728	+	1.56373i
$516$	21.9879	+	18.4501i	0.967965	+	0.812219i
$517$	−14.8980	−	5.42242i	−0.655213	−	0.238478i
$518$	−2.78671	+	1.01428i	−0.122441	+	0.0445649i
$519$	−24.2899	+	20.3816i	−1.06621	+	0.894655i
$520$	−0.854102	−	1.47935i	−0.0374548	−	0.0648737i
$521$	−10.9106	+	18.8978i	−0.478004	+	0.827928i	−0.999682	−	0.0252149i	$-0.991973\pi$
$521$	−10.9106	+	18.8978i	−0.478004	+	0.827928i	0.521678	+	0.853143i	$0.325306\pi$
$522$	0.868241	+	4.92404i	0.0380019	+	0.215519i
$523$	5.97516	+	33.8868i	0.261275	+	1.48177i	0.779436	+	0.626482i	$0.215506\pi$
$523$	5.97516	+	33.8868i	0.261275	+	1.48177i	−0.518160	+	0.855284i	$0.673383\pi$
$524$	−4.92705	+	8.53390i	−0.215239	+	0.372805i
$525$	−1.22857	−	2.12795i	−0.0536192	−	0.0928712i
$526$	34.8081	−	29.2074i	1.51770	−	1.27350i
$527$	11.5683	−	4.21052i	0.503923	−	0.183413i
$528$	−11.4071	−	4.15186i	−0.496432	−	0.180686i
$529$	−17.5073	−	14.6903i	−0.761185	−	0.638710i
$530$	−5.32275	+	30.1868i	−0.231205	+	1.31123i
$531$	5.42882			0.235591
$532$		0			0
$533$	1.58359			0.0685930
$534$	−4.67237	+	26.4983i	−0.202193	+	1.14669i
$535$	−14.8338	−	12.4470i	−0.641321	−	0.538132i
$536$	−8.90090	−	3.23966i	−0.384460	−	0.139932i
$537$	15.5111	−	5.64558i	0.669354	−	0.243625i
$538$	−37.5889	+	31.5409i	−1.62057	+	1.35982i
$539$	−4.79837	−	8.31103i	−0.206681	−	0.357981i
$540$	−11.8617	+	20.5451i	−0.510447	+	0.884119i
$541$	1.16487	+	6.60629i	0.0500816	+	0.284027i	0.999555	−	0.0298199i	$-0.00949337\pi$
$541$	1.16487	+	6.60629i	0.0500816	+	0.284027i	−0.949474	+	0.313847i	$0.898382\pi$
$542$	6.36502	+	36.0978i	0.273401	+	1.55053i
$543$	5.52786	−	9.57454i	0.237223	−	0.410883i
$544$	23.7234	+	41.0902i	1.01713	+	1.76173i
$545$	7.62949	−	6.40190i	0.326811	−	0.274227i
$546$	−0.583118	+	0.212238i	−0.0249552	+	0.00908293i
$547$	19.4622	+	7.08366i	0.832144	+	0.302876i	0.722738	−	0.691122i	$-0.242883\pi$
$547$	19.4622	+	7.08366i	0.832144	+	0.302876i	0.109405	+	0.993997i	$0.465105\pi$
$548$	10.7937	+	9.05699i	0.461084	+	0.386895i
$549$	−1.01655	+	5.76517i	−0.0433855	+	0.246051i
$550$	14.3844			0.613351
$551$		0			0
$552$	−0.527864			−0.0224674
$553$	−0.192760	+	1.09319i	−0.00819697	+	0.0464873i
$554$	21.5126	+	18.0512i	0.913982	+	0.766922i
$555$	−38.2008	−	13.9040i	−1.62153	−	0.590190i
$556$	18.3826	−	6.69070i	0.779594	−	0.283749i
$557$	−30.1520	+	25.3006i	−1.27758	+	1.07202i	−0.284010	+	0.958821i	$0.591665\pi$
$557$	−30.1520	+	25.3006i	−1.27758	+	1.07202i	−0.993572	+	0.113198i	$0.963891\pi$
$558$	1.11803	+	1.93649i	0.0473302	+	0.0819782i
$559$	3.38795	−	5.86811i	0.143295	−	0.248195i
$560$	0.612607	+	3.47427i	0.0258874	+	0.146815i
$561$	2.95428	+	16.7546i	0.124730	+	0.707378i
$562$	−14.8992	+	25.8061i	−0.628484	+	1.08857i
$563$	−10.8576	−	18.8060i	−0.457595	−	0.792578i	0.541238	−	0.840869i	$-0.317956\pi$
$563$	−10.8576	−	18.8060i	−0.457595	−	0.792578i	−0.998833	+	0.0482911i	$0.984622\pi$
$564$	−27.0472	+	22.6953i	−1.13889	+	0.955644i
$565$		0			0
$566$	−21.6100	−	7.86539i	−0.908336	−	0.330607i
$567$	−1.89377	−	1.58906i	−0.0795307	−	0.0667342i
$568$	1.27817	−	7.24885i	0.0536308	−	0.304155i
$569$	25.4540			1.06709			0.533544	−	0.845772i	$-0.320860\pi$
$569$	25.4540			1.06709			0.533544	+	0.845772i	$0.320860\pi$
$570$		0			0
$571$	−46.1033			−1.92936			−0.964682	−	0.263417i	$-0.915150\pi$
$571$	−46.1033			−1.92936			−0.964682	+	0.263417i	$0.915150\pi$
$572$	0.282109	−	1.59992i	0.0117956	−	0.0668959i
$573$	−24.7708	−	20.7851i	−1.03481	−	0.868311i
$574$	−0.919690	−	0.334740i	−0.0383871	−	0.0139718i
$575$	1.96412	−	0.714880i	0.0819094	−	0.0298126i
$576$	−2.22906	+	1.87040i	−0.0928775	+	0.0779334i
$577$	7.64590	+	13.2431i	0.318303	+	0.551317i	0.980134	−	0.198336i	$-0.0635538\pi$
$577$	7.64590	+	13.2431i	0.318303	+	0.551317i	−0.661831	+	0.749653i	$0.730220\pi$
$578$	23.6704	−	40.9984i	0.984559	−	1.70531i
$579$	2.80969	+	15.9345i	0.116767	+	0.662216i
$580$	3.86720	+	21.9320i	0.160577	+	0.910676i
$581$	0.381966	−	0.661585i	0.0158466	−	0.0274472i
$582$	−8.00448	−	13.8642i	−0.331796	−	0.574688i
$583$	5.27185	−	4.42361i	0.218338	−	0.183207i
$584$	−6.14454	+	2.23643i	−0.254263	+	0.0925441i
$585$	−1.36545	−	0.496984i	−0.0564545	−	0.0205478i
$586$	22.2681	+	18.6851i	0.919885	+	0.771875i
$587$	2.92070	−	16.5641i	0.120550	−	0.683675i	−0.863301	−	0.504689i	$-0.831607\pi$
$587$	2.92070	−	16.5641i	0.120550	−	0.683675i	0.983852	−	0.178986i	$-0.0572817\pi$
$588$	−21.3723			−0.881378
$589$		0			0
$590$	54.0689			2.22598
$591$	3.78923	−	21.4898i	0.155868	−	0.883972i
$592$	23.3638	+	19.6046i	0.960248	+	0.805744i
$593$	−16.2490	−	5.91414i	−0.667265	−	0.242865i	−0.0138953	−	0.999903i	$-0.504423\pi$
$593$	−16.2490	−	5.91414i	−0.667265	−	0.242865i	−0.653370	+	0.757039i	$0.726645\pi$
$594$	11.1916	−	4.07340i	0.459196	−	0.167134i
$595$	3.78753	−	3.17812i	0.155274	−	0.130290i
$596$	−4.88197	−	8.45581i	−0.199973	−	0.346364i
$597$	1.00406	−	1.73908i	0.0410933	−	0.0711757i
$598$	−0.0916626	−	0.519845i	−0.00374836	−	0.0212580i
$599$	0.846326	+	4.79975i	0.0345799	+	0.196113i	0.997204	−	0.0747290i	$-0.0238092\pi$
$599$	0.846326	+	4.79975i	0.0345799	+	0.196113i	−0.962624	+	0.270842i	$0.912698\pi$
$600$	−3.78115	+	6.54915i	−0.154365	+	0.267368i
$601$	4.87380	+	8.44166i	0.198806	+	0.344343i	0.948142	−	0.317848i	$-0.102960\pi$
$601$	4.87380	+	8.44166i	0.198806	+	0.344343i	−0.749335	+	0.662191i	$0.769627\pi$
$602$	−3.20800	+	2.69183i	−0.130748	+	0.109711i
$603$	−7.57155	+	2.75582i	−0.308338	+	0.112226i
$604$	26.2895	+	9.56858i	1.06970	+	0.389340i
$605$	22.5343	+	18.9085i	0.916149	+	0.768740i
$606$	−2.47805	+	14.0537i	−0.100664	+	0.570893i
$607$	−27.9767			−1.13554			−0.567769	−	0.823188i	$-0.692193\pi$
$607$	−27.9767			−1.13554			−0.567769	+	0.823188i	$0.692193\pi$
$608$		0			0
$609$	−1.90983			−0.0773902
$610$	−10.1245	+	57.4187i	−0.409928	+	2.32482i
$611$	6.38498	+	5.35763i	0.258308	+	0.216747i
$612$	6.08182	+	2.21360i	0.245843	+	0.0894795i
$613$	31.4535	−	11.4481i	1.27040	−	0.462386i	0.383151	−	0.923686i	$-0.374839\pi$
$613$	31.4535	−	11.4481i	1.27040	−	0.462386i	0.887245	+	0.461299i	$0.152617\pi$
$614$	40.2651	−	33.7864i	1.62497	−	1.36351i
$615$	−6.70820	−	11.6190i	−0.270501	−	0.468521i
$616$	0.118513	−	0.205270i	0.00477502	−	0.00827058i
$617$	−2.82534	−	16.0233i	−0.113744	−	0.645075i	−0.987364	−	0.158466i	$-0.949345\pi$
$617$	−2.82534	−	16.0233i	−0.113744	−	0.645075i	0.873620	−	0.486608i	$-0.161766\pi$
$618$	−6.99583	−	39.6753i	−0.281414	−	1.59598i
$619$	17.3885	−	30.1178i	0.698905	−	1.21054i	−0.269942	−	0.962877i	$-0.587005\pi$
$619$	17.3885	−	30.1178i	0.698905	−	1.21054i	0.968847	−	0.247662i	$-0.0796621\pi$
$620$	4.97980	+	8.62526i	0.199993	+	0.346399i
$621$	1.32572	−	1.11241i	0.0531992	−	0.0446394i
$622$	−25.8675	+	9.41501i	−1.03719	+	0.377507i
$623$	−1.64975	−	0.600458i	−0.0660957	−	0.0240569i
$624$	4.88887	+	4.10225i	0.195711	+	0.164221i
$625$	−3.89257	+	22.0759i	−0.155703	+	0.883034i
$626$	−10.2371			−0.409157
$627$		0			0
$628$	−7.38197			−0.294573
$629$	7.42251	−	42.0952i	0.295955	−	1.67844i
$630$	0.687951	+	0.577259i	0.0274086	+	0.0229986i
$631$	23.4923	+	8.55050i	0.935214	+	0.340390i	0.764274	−	0.644891i	$-0.223097\pi$
$631$	23.4923	+	8.55050i	0.935214	+	0.340390i	0.170940	+	0.985281i	$0.445320\pi$
$632$	3.21037	−	1.16848i	0.127702	−	0.0464797i
$633$	0.904193	−	0.758708i	0.0359384	−	0.0301559i
$634$	29.7984	+	51.6123i	1.18344	+	2.04979i
$635$	20.1967	−	34.9817i	0.801482	−	1.38821i
$636$	−2.66137	−	15.0934i	−0.105530	−	0.598492i
$637$	0.876109	+	4.96866i	0.0347127	+	0.196865i
$638$	5.59017	−	9.68246i	0.221317	−	0.383332i
$639$	−3.13068	−	5.42250i	−0.123848	−	0.214511i
$640$	14.1459	−	11.8698i	0.559164	−	0.469194i
$641$	43.9643	−	16.0017i	1.73648	−	0.632029i	0.737426	−	0.675428i	$-0.236041\pi$
$641$	43.9643	−	16.0017i	1.73648	−	0.632029i	0.999058	+	0.0433991i	$0.0138187\pi$
$642$	20.3441	+	7.40466i	0.802919	+	0.292239i
$643$	−4.37274	−	3.66916i	−0.172444	−	0.144698i	0.552481	−	0.833525i	$-0.313681\pi$
$643$	−4.37274	−	3.66916i	−0.172444	−	0.144698i	−0.724925	+	0.688828i	$0.758126\pi$
$644$	−0.0253349	+	0.143682i	−0.000998336	+	0.00566184i
$645$	−57.4064			−2.26038
$646$		0			0
$647$	8.12461			0.319411			0.159706	−	0.987165i	$-0.448945\pi$
$647$	8.12461			0.319411			0.159706	+	0.987165i	$0.448945\pi$
$648$	−1.32119	+	7.49286i	−0.0519014	+	0.294347i
$649$	−9.29918	−	7.80294i	−0.365025	−	0.306292i
$650$	−7.10624	−	2.58646i	−0.278730	−	0.101449i
$651$	−0.802593	+	0.292120i	−0.0314561	+	0.0114491i
$652$	19.1775	−	16.0918i	0.751049	−	0.630205i
$653$	11.3713	+	19.6957i	0.444994	+	0.770753i	0.998052	−	0.0623904i	$-0.0198724\pi$
$653$	11.3713	+	19.6957i	0.444994	+	0.770753i	−0.553058	+	0.833143i	$0.686539\pi$
$654$	−5.56758	+	9.64333i	−0.217710	+	0.377084i
$655$	−3.42229	−	19.4088i	−0.133720	−	0.758364i
$656$	1.74787	+	9.91268i	0.0682429	+	0.387025i
$657$	−2.78115	+	4.81710i	−0.108503	+	0.187933i
$658$	−2.57565	−	4.46117i	−0.100409	−	0.173914i
$659$	−28.9797	+	24.3168i	−1.12889	+	0.947249i	−0.999019	−	0.0442824i	$-0.985900\pi$
$659$	−28.9797	+	24.3168i	−1.12889	+	0.947249i	−0.129868	+	0.991531i	$0.541455\pi$
$660$	−12.9338	+	4.70750i	−0.503446	+	0.183239i
$661$	−31.6517	−	11.5203i	−1.23111	−	0.448086i	−0.357131	−	0.934054i	$-0.616245\pi$
$661$	−31.6517	−	11.5203i	−1.23111	−	0.448086i	−0.873977	+	0.485968i	$0.838467\pi$
$662$	−29.5241	−	24.7737i	−1.14749	−	0.962857i
$663$	1.55316	−	8.80839i	0.0603196	−	0.342089i
$664$	−2.35114			−0.0912420
$665$		0			0
$666$	7.76393			0.300846
$667$	0.282109	−	1.59992i	0.0109233	−	0.0619490i
$668$	2.01367	+	1.68967i	0.0779111	+	0.0653752i
$669$	29.1105	+	10.5953i	1.12548	+	0.409640i
$670$	−75.4096	+	27.4469i	−2.91333	+	1.06036i
$671$	10.0277	−	8.41420i	0.387113	−	0.324827i
$672$	−1.64590	−	2.85078i	−0.0634919	−	0.109971i
$673$	−4.78804	+	8.29313i	−0.184565	+	0.319677i	−0.943430	−	0.331572i	$-0.892421\pi$
$673$	−4.78804	+	8.29313i	−0.184565	+	0.319677i	0.758865	+	0.651248i	$0.225754\pi$
$674$	0.183325	+	1.03969i	0.00706143	+	0.0400473i
$675$	−4.30526	−	24.4163i	−0.165709	−	0.939785i
$676$	10.0902	−	17.4767i	0.388083	−	0.672180i
$677$	−7.55545	−	13.0864i	−0.290380	−	0.502952i	0.683520	−	0.729932i	$-0.260448\pi$
$677$	−7.55545	−	13.0864i	−0.290380	−	0.502952i	−0.973899	+	0.226980i	$0.927115\pi$
$678$		0			0
$679$	0.981552	−	0.357256i	0.0376685	−	0.0137102i
$680$	−14.2992	−	5.20449i	−0.548350	−	0.199583i
$681$	22.9223	+	19.2341i	0.878386	+	0.737053i
$682$	0.868241	−	4.92404i	0.0332467	−	0.188551i
$683$	40.2219			1.53905			0.769524	−	0.638618i	$-0.220494\pi$
$683$	40.2219			1.53905			0.769524	+	0.638618i	$0.220494\pi$
$684$		0			0
$685$	−28.1803			−1.07672
$686$	1.08728	−	6.16624i	0.0415124	−	0.235428i
$687$	−10.3311	−	8.66883i	−0.394156	−	0.330736i
$688$	40.4715	+	14.7304i	1.54296	+	0.561592i
$689$	−3.39984	+	1.23744i	−0.129524	+	0.0471427i
$690$	−3.42585	+	2.87463i	−0.130420	+	0.109435i
$691$	8.15248	+	14.1205i	0.310135	+	0.537169i	0.978391	−	0.206762i	$-0.0662925\pi$
$691$	8.15248	+	14.1205i	0.310135	+	0.537169i	−0.668257	+	0.743931i	$0.732959\pi$
$692$	13.4863	−	23.3590i	0.512672	−	0.887975i
$693$	−0.0350120	−	0.198563i	−0.00133000	−	0.00754278i
$694$	−9.52343	−	54.0101i	−0.361505	−	2.05019i
$695$	−19.5623	+	33.8829i	−0.742041	+	1.28525i
$696$	2.93893	+	5.09037i	0.111400	+	0.192950i
$697$	10.8065	−	9.06771i	0.409324	−	0.343464i
$698$	24.3409	−	8.85936i	0.921316	−	0.335332i
$699$	−8.09311	−	2.94565i	−0.306110	−	0.111415i
$700$	1.60116	+	1.34354i	0.0605183	+	0.0507809i
$701$	1.51814	−	8.60983i	0.0573395	−	0.325189i	−0.942623	−	0.333859i	$-0.891649\pi$
$701$	1.51814	−	8.60983i	0.0573395	−	0.325189i	0.999962	+	0.00867079i	$0.00276003\pi$
$702$	−6.26137			−0.236320
$703$		0			0
$704$	6.50658			0.245226
$705$	12.2622	−	69.5424i	0.461821	−	2.61912i
$706$	−36.9841	−	31.0334i	−1.39192	−	1.16796i
$707$	−0.874963	−	0.318461i	−0.0329064	−	0.0119769i
$708$	−25.4041	+	9.24632i	−0.954743	+	0.347498i
$709$	−10.2776	+	8.62390i	−0.385982	+	0.323877i	−0.815045	−	0.579397i	$-0.803288\pi$
$709$	−10.2776	+	8.62390i	−0.385982	+	0.323877i	0.429063	+	0.903274i	$0.358844\pi$
$710$	−31.1803	−	54.0059i	−1.17018	−	2.02681i
$711$	1.45309	−	2.51682i	0.0544949	−	0.0943880i
$712$	0.938265	+	5.32116i	0.0351630	+	0.199419i
$713$	−0.126163	−	0.715505i	−0.00472483	−	0.0267959i
$714$	−2.76393	+	4.78727i	−0.103438	+	0.179159i
$715$	1.62460	+	2.81389i	0.0607565	+	0.105233i
$716$	−10.7563	+	9.02560i	−0.401981	+	0.337302i
$717$	16.3474	−	5.94996i	0.610505	−	0.222205i
$718$	−63.2418	−	23.0181i	−2.36016	−	0.859029i
$719$	11.1981	+	9.39629i	0.417617	+	0.350423i	0.827256	−	0.561825i	$-0.189901\pi$
$719$	11.1981	+	9.39629i	0.417617	+	0.350423i	−0.409639	+	0.912248i	$0.634345\pi$
$720$	1.60383	−	9.09575i	0.0597711	−	0.338979i
$721$	2.62866			0.0978962
$722$		0			0
$723$	−51.6312			−1.92018
$724$	−1.63309	+	9.26169i	−0.0606931	+	0.344208i
$725$	−17.8292	−	14.9605i	−0.662160	−	0.555618i
$726$	−30.9051	−	11.2485i	−1.14700	−	0.417473i
$727$	34.7163	−	12.6357i	1.28755	−	0.468632i	0.394631	−	0.918840i	$-0.370872\pi$
$727$	34.7163	−	12.6357i	1.28755	−	0.468632i	0.892924	+	0.450208i	$0.148650\pi$
$728$	−0.0954582	+	0.0800989i	−0.00353792	+	0.00296866i
$729$	−9.69098	−	16.7853i	−0.358925	−	0.621677i
$730$	−27.6992	+	47.9763i	−1.02519	+	1.77568i
$731$	−10.4815	−	59.4437i	−0.387673	−	2.19860i
$732$	−5.06223	−	28.7093i	−0.187106	−	1.06113i
$733$	−6.40983	+	11.1022i	−0.236752	+	0.410067i	−0.959781	−	0.280751i	$-0.909416\pi$
$733$	−6.40983	+	11.1022i	−0.236752	+	0.410067i	0.723028	+	0.690819i	$0.242750\pi$
$734$	11.9147	+	20.6369i	0.439780	+	0.761721i
$735$	32.7442	−	27.4757i	1.20779	−	1.01346i
$736$	2.63130	−	0.957714i	0.0969909	−	0.0353018i
$737$	16.9305	+	6.16220i	0.623643	+	0.226988i
$738$	1.96284	+	1.64702i	0.0722531	+	0.0606276i
$739$	3.38130	−	19.1763i	0.124383	−	0.705412i	−0.857289	−	0.514835i	$-0.827853\pi$
$739$	3.38130	−	19.1763i	0.124383	−	0.705412i	0.981672	−	0.190577i	$-0.0610358\pi$
$740$	34.5811			1.27123
$741$		0			0
$742$	2.23607			0.0820886
$743$	6.38343	−	36.2022i	0.234185	−	1.32813i	−0.610138	−	0.792295i	$-0.708886\pi$
$743$	6.38343	−	36.2022i	0.234185	−	1.32813i	0.844323	−	0.535835i	$-0.180003\pi$
$744$	2.01367	+	1.68967i	0.0738246	+	0.0619462i
$745$	18.3502	+	6.67892i	0.672299	+	0.244697i
$746$	−65.7061	+	23.9151i	−2.40567	+	0.875593i
$747$	−1.53209	+	1.28558i	−0.0560562	+	0.0470367i
$748$	−7.23607	−	12.5332i	−0.264577	−	0.458261i
$749$	−0.706298	+	1.22334i	−0.0258076	+	0.0447000i
$750$	0.959904	+	5.44388i	0.0350507	+	0.198783i
$751$	2.09658	+	11.8903i	0.0765052	+	0.433883i	0.998868	+	0.0475588i	$0.0151441\pi$
$751$	2.09658	+	11.8903i	0.0765052	+	0.433883i	−0.922363	+	0.386324i	$0.873745\pi$
$752$	−26.4894	+	45.8809i	−0.965967	+	1.67310i
$753$	15.6129	+	27.0424i	0.568967	+	0.985480i
$754$	−4.50270	+	3.77821i	−0.163979	+	0.137594i
$755$	−52.5789	+	19.1372i	−1.91354	+	0.696473i
$756$	1.62623	+	0.591900i	0.0591455	+	0.0215272i
$757$	−28.5509	−	23.9570i	−1.03770	−	0.870733i	−0.0459520	−	0.998944i	$-0.514632\pi$
$757$	−28.5509	−	23.9570i	−1.03770	−	0.870733i	−0.991747	+	0.128211i	$0.959077\pi$
$758$	7.05923	−	40.0349i	0.256403	−	1.45413i
$759$	1.00406			0.0364450
$760$		0			0
$761$	−23.9443			−0.867979			−0.433990	−	0.900918i	$-0.642895\pi$
$761$	−23.9443			−0.867979			−0.433990	+	0.900918i	$0.642895\pi$
$762$	−7.84216	+	44.4751i	−0.284091	+	1.61116i
$763$	−0.556564	−	0.467013i	−0.0201490	−	0.0169070i
$764$	25.8477	+	9.40780i	0.935138	+	0.340362i
$765$	−12.1636	+	4.42720i	−0.439777	+	0.160066i
$766$	16.4750	−	13.8242i	0.595266	−	0.499487i
$767$	3.19098	+	5.52694i	0.115220	+	0.199566i
$768$	−19.2784	+	33.3912i	−0.695649	+	1.20490i
$769$	5.75801	+	32.6553i	0.207639	+	1.17758i	0.893232	+	0.449595i	$0.148432\pi$
$769$	5.75801	+	32.6553i	0.207639	+	1.17758i	−0.685593	+	0.727985i	$0.740457\pi$
$770$	−0.348705	−	1.97761i	−0.0125665	−	0.0712680i
$771$	10.3262	−	17.8856i	0.371890	−	0.644133i
$772$	−6.88191	−	11.9198i	−0.247685	−	0.429004i
$773$	−9.48075	+	7.95530i	−0.340999	+	0.286132i	−0.797164	−	0.603763i	$-0.793667\pi$
$773$	−9.48075	+	7.95530i	−0.340999	+	0.286132i	0.456165	+	0.889895i	$0.349223\pi$
$774$	10.3025	−	3.74979i	0.370314	−	0.134783i
$775$	−9.78090	−	3.55996i	−0.351340	−	0.127877i
$776$	−2.46267	−	2.06642i	−0.0884045	−	0.0741802i
$777$	−0.514964	+	2.92050i	−0.0184742	+	0.104773i
$778$	−3.63271			−0.130239
$779$		0			0
$780$	7.23607			0.259093
$781$	−2.43122	+	13.7881i	−0.0869959	+	0.493378i
$782$	−3.60216	−	3.02257i	−0.128813	−	0.108087i
$783$	−18.1084	−	6.59090i	−0.647140	−	0.235540i
$784$	−30.1349	+	10.9682i	−1.07625	+	0.391722i
$785$	11.3098	−	9.49007i	0.403665	−	0.338715i
$786$	11.0172	+	19.0824i	0.392971	+	0.680646i
$787$	9.68208	−	16.7699i	0.345129	−	0.597781i	−0.640248	−	0.768168i	$-0.721169\pi$
$787$	9.68208	−	16.7699i	0.345129	−	0.597781i	0.985377	+	0.170387i	$0.0545019\pi$
$788$	3.22331	+	18.2803i	0.114826	+	0.651209i
$789$	−7.89035	−	44.7484i	−0.280904	−	1.59309i
$790$	14.4721	−	25.0665i	0.514895	−	0.891825i
$791$		0			0
$792$	−0.475362	+	0.398876i	−0.0168913	+	0.0141735i
$793$	−6.46688	+	2.35375i	−0.229646	+	0.0835842i
$794$	2.30896	+	0.840392i	0.0819419	+	0.0298244i
$795$	23.4812	+	19.7030i	0.832791	+	0.698795i
$796$	−0.296626	+	1.68225i	−0.0105136	+	0.0596259i
$797$	13.2088			0.467879			0.233940	−	0.972251i	$-0.424838\pi$
$797$	13.2088			0.467879			0.233940	+	0.972251i	$0.424838\pi$
$798$		0			0
$799$	74.2492			2.62675
$800$	6.96605	−	39.5064i	0.246287	−	1.39676i
$801$	3.52096	+	2.95443i	0.124407	+	0.104390i
$802$	8.40487	+	3.05912i	0.296786	+	0.108021i
$803$	11.6876	−	4.25394i	0.412447	−	0.150118i
$804$	30.7372	−	25.7916i	1.08402	−	0.909600i
$805$	−0.145898	−	0.252703i	−0.00514223	−	0.00890660i
$806$	−1.31433	+	2.27648i	−0.0462952	+	0.0801857i
$807$	8.52072	+	48.3234i	0.299944	+	1.70106i
$808$	0.497620	+	2.82215i	0.0175062	+	0.0992827i
$809$	17.1353	−	29.6791i	0.602443	−	1.04346i	−0.390006	−	0.920812i	$-0.627527\pi$
$809$	17.1353	−	29.6791i	0.602443	−	1.04346i	0.992450	−	0.122651i	$-0.0391394\pi$
$810$	32.2299	+	55.8239i	1.13244	+	1.96145i
$811$	17.0099	−	14.2730i	0.597298	−	0.501192i	−0.293278	−	0.956027i	$-0.594746\pi$
$811$	17.0099	−	14.2730i	0.597298	−	0.501192i	0.890576	+	0.454835i	$0.150302\pi$
$812$	1.52662	−	0.555645i	0.0535740	−	0.0194993i
$813$	34.4441	+	12.5366i	1.20801	+	0.439679i
$814$	−13.2991	−	11.1592i	−0.466132	−	0.391131i
$815$	−8.69437	+	49.3082i	−0.304551	+	1.72719i
$816$	56.8514			1.99020
$817$		0			0
$818$	45.7771			1.60056
$819$	−0.0184069	+	0.104391i	−0.000643189	+	0.00364771i
$820$	8.74262	+	7.33593i	0.305305	+	0.256182i
$821$	−9.42929	−	3.43198i	−0.329085	−	0.119777i	0.172194	−	0.985063i	$-0.444914\pi$
$821$	−9.42929	−	3.43198i	−0.329085	−	0.119777i	−0.501278	+	0.865286i	$0.667137\pi$
$822$	29.6065	−	10.7759i	1.03265	−	0.375852i
$823$	38.8548	−	32.6031i	1.35439	−	1.13647i	0.376724	−	0.926326i	$-0.377051\pi$
$823$	38.8548	−	32.6031i	1.35439	−	1.13647i	0.977670	−	0.210146i	$-0.0673938\pi$
$824$	−4.04508	−	7.00629i	−0.140917	−	0.244076i
$825$	7.19218	−	12.4572i	0.250400	−	0.433705i
$826$	−0.684916	−	3.88435i	−0.0238313	−	0.135154i
$827$	−5.15861	−	29.2559i	−0.179383	−	1.01733i	−0.932963	−	0.359973i	$-0.882786\pi$
$827$	−5.15861	−	29.2559i	−0.179383	−	1.01733i	0.753580	−	0.657356i	$-0.228325\pi$
$828$	0.190983	−	0.330792i	0.00663712	−	0.0114958i
$829$	−7.55545	−	13.0864i	−0.262412	−	0.454510i	0.704471	−	0.709733i	$-0.251185\pi$
$829$	−7.55545	−	13.0864i	−0.262412	−	0.454510i	−0.966882	+	0.255223i	$0.917851\pi$
$830$	−15.2590	+	12.8038i	−0.529647	+	0.444427i
$831$	26.3891	−	9.60484i	0.915427	−	0.333188i
$832$	−3.21442	−	1.16995i	−0.111440	−	0.0405608i
$833$	34.4293	+	28.8896i	1.19290	+	1.00097i
$834$	7.59583	−	43.0781i	0.263022	−	1.49167i
$835$	−5.25731			−0.181937
$836$		0			0
$837$	−8.61803			−0.297883
$838$	2.17455	−	12.3325i	0.0751186	−	0.426019i
$839$	−12.9825	−	10.8936i	−0.448207	−	0.376090i	0.390563	−	0.920576i	$-0.372280\pi$
$839$	−12.9825	−	10.8936i	−0.448207	−	0.376090i	−0.838770	+	0.544486i	$0.816725\pi$
$840$	0.992060	+	0.361080i	0.0342293	+	0.0124585i
$841$	10.2519	−	3.73138i	0.353513	−	0.128668i
$842$	−47.2122	+	39.6158i	−1.62704	+	1.36525i
$843$	14.8992	+	25.8061i	0.513155	+	0.888811i
$844$	−0.502029	+	0.869539i	−0.0172805	+	0.0299308i
$845$	7.00856	+	39.7475i	0.241102	+	1.36736i
$846$	2.34187	+	13.2814i	0.0805152	+	0.456625i
$847$	1.07295	−	1.85840i	0.0368670	−	0.0638555i
$848$	−11.4984	−	19.9159i	−0.394858	−	0.683914i
$849$	−17.6166	+	14.7821i	−0.604601	+	0.507320i
$850$	−63.3033	+	23.0405i	−2.17129	+	0.790284i
$851$	−2.37052	−	0.862799i	−0.0812604	−	0.0295764i
$852$	23.8855	+	20.0423i	0.818305	+	0.686639i
$853$	6.99888	−	39.6926i	0.239637	−	1.35905i	−0.592987	−	0.805212i	$-0.702052\pi$
$853$	6.99888	−	39.6926i	0.239637	−	1.35905i	0.832624	−	0.553838i	$-0.186837\pi$
$854$	4.25325			0.145543
$855$		0			0
$856$	4.34752			0.148595
$857$	−9.60844	+	54.4922i	−0.328218	+	1.86142i	0.157804	+	0.987470i	$0.449558\pi$
$857$	−9.60844	+	54.4922i	−0.328218	+	1.86142i	−0.486022	+	0.873946i	$0.661553\pi$
$858$	−2.78282	−	2.33506i	−0.0950039	−	0.0797177i
$859$	−36.5956	−	13.3197i	−1.24863	−	0.454463i	−0.368690	−	0.929553i	$-0.620194\pi$
$859$	−36.5956	−	13.3197i	−1.24863	−	0.454463i	−0.879938	+	0.475089i	$0.842416\pi$
$860$	45.8878	−	16.7018i	1.56476	−	0.569527i
$861$	−0.749738	+	0.629105i	−0.0255510	+	0.0214398i
$862$	11.8713	+	20.5617i	0.404339	+	0.700335i
$863$	16.2865	−	28.2090i	0.554398	−	0.960246i	−0.443552	−	0.896249i	$-0.646282\pi$
$863$	16.2865	−	28.2090i	0.554398	−	0.960246i	0.997950	−	0.0639969i	$-0.0203848\pi$
$864$	−5.76769	−	32.7102i	−0.196221	−	1.11282i
$865$	9.36749	+	53.1257i	0.318504	+	1.80633i
$866$	17.9894	−	31.1585i	0.611303	−	1.05881i
$867$	−23.6704	−	40.9984i	−0.803889	−	1.39238i
$868$	0.556564	−	0.467013i	0.0188910	−	0.0158514i
$869$	−6.10649	+	2.22258i	−0.207149	+	0.0753959i
$870$	46.7948	+	17.0319i	1.58649	+	0.577436i
$871$	−7.25608	−	6.08857i	−0.245863	−	0.206303i
$872$	−0.388289	+	2.20210i	−0.0131491	+	0.0745724i
$873$	−2.73466			−0.0925541
$874$		0			0
$875$	−0.360680			−0.0121932
$876$	4.80991	−	27.2783i	0.162512	−	0.921650i
$877$	−7.46709	−	6.26563i	−0.252146	−	0.211575i	0.507950	−	0.861387i	$-0.330403\pi$
$877$	−7.46709	−	6.26563i	−0.252146	−	0.211575i	−0.760096	+	0.649811i	$0.774848\pi$
$878$	−10.6955	−	3.89286i	−0.360957	−	0.131378i
$879$	27.3158	−	9.94214i	0.921340	−	0.335340i
$880$	−15.8207	+	13.2752i	−0.533316	+	0.447505i
$881$	−20.2877	−	35.1394i	−0.683511	−	1.18388i	−0.973902	−	0.226968i	$-0.927119\pi$
$881$	−20.2877	−	35.1394i	−0.683511	−	1.18388i	0.290391	−	0.956908i	$-0.406215\pi$
$882$	−4.08174	+	7.06978i	−0.137439	+	0.238052i
$883$	2.42509	+	13.7534i	0.0816109	+	0.462838i	0.998037	+	0.0626335i	$0.0199499\pi$
$883$	2.42509	+	13.7534i	0.0816109	+	0.462838i	−0.916426	+	0.400205i	$0.868939\pi$
$884$	1.32119	+	7.49286i	0.0444366	+	0.252012i
$885$	27.0344	−	46.8250i	0.908753	−	1.57401i
$886$	14.4374	+	25.0062i	0.485033	+	0.840101i
$887$	−12.6075	+	10.5790i	−0.423320	+	0.355208i	−0.829424	−	0.558619i	$-0.811331\pi$
$887$	−12.6075	+	10.5790i	−0.423320	+	0.355208i	0.406104	+	0.913827i	$0.366887\pi$
$888$	8.57662	−	3.12163i	0.287813	−	0.104755i
$889$	−2.76895	−	1.00782i	−0.0928677	−	0.0338011i
$890$	35.0673	+	29.4249i	1.17546	+	0.986326i
$891$	2.51306	−	14.2523i	0.0841907	−	0.477469i
$892$	−26.3521			−0.882332
$893$		0			0
$894$	−21.8328			−0.730199
$895$	4.87650	−	27.6560i	0.163004	−	0.924439i
$896$	−1.03193	−	0.865889i	−0.0344742	−	0.0289273i
$897$	−0.496030	−	0.180540i	−0.0165620	−	0.00602806i
$898$	43.3230	−	15.7683i	1.44571	−	0.526194i
$899$	−6.19743	+	5.20026i	−0.206696	+	0.173438i
$900$	−2.73607	−	4.73901i	−0.0912023	−	0.157967i
$901$	−16.1150	+	27.9119i	−0.536867	+	0.929881i
$902$	−0.994916	−	5.64245i	−0.0331271	−	0.187873i
$903$	0.727194	+	4.12412i	0.0241995	+	0.137242i
$904$		0			0
$905$	−9.40456	−	16.2892i	−0.312618	−	0.541471i
$906$	47.9220	−	40.2113i	1.59210	−	1.33593i
$907$	−27.2330	+	9.91199i	−0.904256	+	0.329122i	−0.751957	−	0.659212i	$-0.770890\pi$
$907$	−27.2330	+	9.91199i	−0.904256	+	0.329122i	−0.152299	+	0.988334i	$0.548668\pi$
$908$	−23.9189	−	8.70578i	−0.793778	−	0.288912i
$909$	1.86738	+	1.56692i	0.0619372	+	0.0519714i
$910$	−0.183325	+	1.03969i	−0.00607717	+	0.0344654i
$911$	25.4540			0.843329			0.421665	−	0.906752i	$-0.361446\pi$
$911$	25.4540			0.843329			0.421665	+	0.906752i	$0.361446\pi$
$912$		0			0
$913$	4.47214			0.148006
$914$	−2.07817	+	11.7859i	−0.0687398	+	0.389843i
$915$	44.6638	+	37.4774i	1.47654	+	1.23896i
$916$	10.7803	+	3.92370i	0.356191	+	0.129643i
$917$	−1.35099	+	0.491720i	−0.0446136	+	0.0162380i
$918$	−42.7277	+	35.8528i	−1.41023	+	1.18332i
$919$	23.6803	+	41.0156i	0.781142	+	1.35298i	0.931277	+	0.364313i	$0.118696\pi$
$919$	23.6803	+	41.0156i	0.781142	+	1.35298i	−0.150134	+	0.988666i	$0.547971\pi$
$920$	−0.449028	+	0.777739i	−0.0148040	+	0.0256413i
$921$	−9.12735	−	51.7638i	−0.300756	−	1.70567i
$922$	3.90402	+	22.1408i	0.128572	+	0.729168i
$923$	3.68034	−	6.37454i	0.121140	−	0.209820i
$924$	0.502029	+	0.869539i	0.0165155	+	0.0286057i
$925$	−27.6850	+	23.2304i	−0.910276	+	0.763812i
$926$	18.1348	−	6.60053i	0.595946	−	0.216907i
$927$	−6.46688	−	2.35375i	−0.212400	−	0.0773073i
$928$	−23.8855	−	20.0423i	−0.784081	−	0.657922i
$929$	2.86634	−	16.2558i	0.0940415	−	0.533336i	−0.900995	−	0.433829i	$-0.857162\pi$
$929$	2.86634	−	16.2558i	0.0940415	−	0.533336i	0.995037	−	0.0995070i	$-0.0317266\pi$
$930$	22.2703			0.730273
$931$		0			0
$932$	7.32624			0.239979
$933$	−4.78012	+	27.1094i	−0.156494	+	0.887523i
$934$	−6.17239	−	5.17925i	−0.201967	−	0.169470i
$935$	27.1987	+	9.89952i	0.889493	+	0.323749i
$936$	0.306563	−	0.111580i	0.0100203	−	0.00364710i
$937$	−13.1772	+	11.0570i	−0.430481	+	0.361216i	−0.832133	−	0.554576i	$-0.812880\pi$
$937$	−13.1772	+	11.0570i	−0.430481	+	0.361216i	0.401652	+	0.915792i	$0.368436\pi$
$938$	2.92705	+	5.06980i	0.0955716	+	0.165535i
$939$	−5.11855	+	8.86560i	−0.167038	+	0.289318i
$940$	10.4309	+	59.1563i	0.340217	+	1.92947i
$941$	4.82831	+	27.3827i	0.157399	+	0.892651i	0.956560	+	0.291535i	$0.0941660\pi$
$941$	4.82831	+	27.3827i	0.157399	+	0.892651i	−0.799162	+	0.601116i	$0.794723\pi$
$942$	−8.25329	+	14.2951i	−0.268907	+	0.465760i
$943$	−0.416272	−	0.721004i	−0.0135557	−	0.0234791i
$944$	−31.0745	+	26.0746i	−1.01139	+	0.848657i
$945$	−3.25246	+	1.18380i	−0.105803	+	0.0385090i
$946$	−23.0370	−	8.38478i	−0.748998	−	0.272613i
$947$	−21.5874	−	18.1140i	−0.701496	−	0.588625i	0.220703	−	0.975341i	$-0.429165\pi$
$947$	−21.5874	−	18.1140i	−0.701496	−	0.588625i	−0.922199	+	0.386716i	$0.873609\pi$
$948$	−2.51306	+	14.2523i	−0.0816204	+	0.462892i
$949$	−6.53888			−0.212261
$950$		0			0
$951$	59.5967			1.93256
$952$	−0.192760	+	1.09319i	−0.00624737	+	0.0354306i
$953$	−15.6531	−	13.1345i	−0.507055	−	0.425470i	0.353036	−	0.935610i	$-0.385149\pi$
$953$	−15.6531	−	13.1345i	−0.507055	−	0.425470i	−0.860091	+	0.510140i	$0.829594\pi$
$954$	−5.50106	−	2.00222i	−0.178103	−	0.0648243i
$955$	−51.6955	+	18.8156i	−1.67283	+	0.608859i
$956$	−11.3362	+	9.51221i	−0.366639	+	0.307647i
$957$	−5.59017	−	9.68246i	−0.180705	−	0.312989i
$958$	−15.1311	+	26.2079i	−0.488865	+	0.846739i
$959$	0.356973	+	2.02450i	0.0115273	+	0.0653744i
$960$	5.03245	+	28.5404i	0.162422	+	0.921139i
$961$	13.6910	−	23.7135i	0.441645	−	0.764951i
$962$	4.56352	+	7.90426i	0.147134	+	0.254843i
$963$	2.83300	−	2.37717i	0.0912923	−	0.0766033i
$964$	41.2714	−	15.0216i	1.32926	−	0.483812i
$965$	25.8675	+	9.41501i	0.832705	+	0.303080i
$966$	0.249913	+	0.209702i	0.00804081	+	0.00674704i
$967$	3.52363	−	19.9835i	0.113312	−	0.642627i	−0.874260	−	0.485459i	$-0.838653\pi$
$967$	3.52363	−	19.9835i	0.113312	−	0.642627i	0.987572	−	0.157168i	$-0.0502363\pi$
$968$	−6.60440			−0.212273
$969$		0			0
$970$	−27.2361			−0.874497
$971$	−7.75281	+	43.9684i	−0.248800	+	1.41101i	0.562701	+	0.826661i	$0.309762\pi$
$971$	−7.75281	+	43.9684i	−0.248800	+	1.41101i	−0.811501	+	0.584352i	$0.801349\pi$
$972$	−7.84208	−	6.58029i	−0.251535	−	0.211063i
$973$	2.68198	+	0.976160i	0.0859803	+	0.0312943i
$974$	29.7960	−	10.8448i	0.954724	−	0.347491i
$975$	−5.79306	+	4.86096i	−0.185526	+	0.155675i
$976$	−21.8713	−	37.8822i	−0.700084	−	1.21258i
$977$	−4.78804	+	8.29313i	−0.153183	+	0.265321i	−0.932396	−	0.361439i	$-0.882286\pi$
$977$	−4.78804	+	8.29313i	−0.153183	+	0.265321i	0.779213	+	0.626759i	$0.215619\pi$
$978$	−9.72060	−	55.1283i	−0.310831	−	1.76281i
$979$	−1.78469	−	10.1215i	−0.0570388	−	0.323483i
$980$	−18.1803	+	31.4893i	−0.580750	+	1.00589i
$981$	0.951057	+	1.64728i	0.0303649	+	0.0525935i
$982$	−25.1649	+	21.1159i	−0.803045	+	0.673834i
$983$	36.8527	−	13.4133i	1.17542	−	0.427817i	0.320837	−	0.947134i	$-0.396036\pi$
$983$	36.8527	−	13.4133i	1.17542	−	0.427817i	0.854582	+	0.519317i	$0.173814\pi$
$984$	2.83052	+	1.03022i	0.0902335	+	0.0328423i
$985$	−28.4391	−	23.8632i	−0.906145	−	0.760346i
$986$	−9.09234	+	51.5652i	−0.289559	+	1.64217i
$987$	−5.15131			−0.163968
$988$		0			0
$989$	−3.56231			−0.113275
$990$	−0.912922	+	5.17744i	−0.0290146	+	0.164550i
$991$	42.3874	+	35.5672i	1.34648	+	1.12983i	0.979910	+	0.199440i	$0.0639122\pi$
$991$	42.3874	+	35.5672i	1.34648	+	1.12983i	0.366569	+	0.930391i	$0.380532\pi$
$992$	−13.1033	−	4.76922i	−0.416031	−	0.151423i
$993$	−36.2167	+	13.1818i	−1.14930	+	0.418312i
$994$	−3.48485	+	2.92414i	−0.110533	+	0.0927480i
$995$	−1.70820	−	2.95870i	−0.0541537	−	0.0937970i
$996$	4.97980	−	8.62526i	0.157791	−	0.273302i
$997$	−5.75203	−	32.6214i	−0.182169	−	1.03313i	−0.929540	−	0.368722i	$-0.879795\pi$
$997$	−5.75203	−	32.6214i	−0.182169	−	1.03313i	0.747371	−	0.664407i	$-0.231316\pi$
$998$	−10.0649	−	57.0809i	−0.318599	−	1.80686i
$999$	−14.9615	+	25.9141i	−0.473361	+	0.819885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.m.245.1		24
19.2	odd	18		361.2.c.j.68.1		8
19.3	odd	18		361.2.a.i.1.4	yes	4
19.4	even	9	inner	361.2.e.m.234.1		24
19.5	even	9		361.2.c.j.292.4		8
19.6	even	9	inner	361.2.e.m.99.4		24
19.7	even	3	inner	361.2.e.m.54.1		24
19.8	odd	6	inner	361.2.e.m.62.1		24
19.9	even	9	inner	361.2.e.m.28.1		24
19.10	odd	18	inner	361.2.e.m.28.4		24
19.11	even	3	inner	361.2.e.m.62.4		24
19.12	odd	6	inner	361.2.e.m.54.4		24
19.13	odd	18	inner	361.2.e.m.99.1		24
19.14	odd	18		361.2.c.j.292.1		8
19.15	odd	18	inner	361.2.e.m.234.4		24
19.16	even	9		361.2.a.i.1.1	✓	4
19.17	even	9		361.2.c.j.68.4		8
19.18	odd	2	inner	361.2.e.m.245.4		24
57.35	odd	18		3249.2.a.bc.1.4		4
57.41	even	18		3249.2.a.bc.1.1		4
76.3	even	18		5776.2.a.bu.1.4		4
76.35	odd	18		5776.2.a.bu.1.1		4
95.54	even	18		9025.2.a.bj.1.4		4
95.79	odd	18		9025.2.a.bj.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.i.1.1	✓	4	19.16	even	9
361.2.a.i.1.4	yes	4	19.3	odd	18
361.2.c.j.68.1		8	19.2	odd	18
361.2.c.j.68.4		8	19.17	even	9
361.2.c.j.292.1		8	19.14	odd	18
361.2.c.j.292.4		8	19.5	even	9
361.2.e.m.28.1		24	19.9	even	9	inner
361.2.e.m.28.4		24	19.10	odd	18	inner
361.2.e.m.54.1		24	19.7	even	3	inner
361.2.e.m.54.4		24	19.12	odd	6	inner
361.2.e.m.62.1		24	19.8	odd	6	inner
361.2.e.m.62.4		24	19.11	even	3	inner
361.2.e.m.99.1		24	19.13	odd	18	inner
361.2.e.m.99.4		24	19.6	even	9	inner
361.2.e.m.234.1		24	19.4	even	9	inner
361.2.e.m.234.4		24	19.15	odd	18	inner
361.2.e.m.245.1		24	1.1	even	1	trivial
361.2.e.m.245.4		24	19.18	odd	2	inner
3249.2.a.bc.1.1		4	57.41	even	18
3249.2.a.bc.1.4		4	57.35	odd	18
5776.2.a.bu.1.1		4	76.35	odd	18
5776.2.a.bu.1.4		4	76.3	even	18
9025.2.a.bj.1.1		4	95.79	odd	18
9025.2.a.bj.1.4		4	95.54	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.330298 + 1.87322i) q^{2} +(1.45710 + 1.22265i) q^{3} +(-1.52045 - 0.553400i) q^{4} +(3.04091 - 1.10680i) q^{5} +(-2.77157 + 2.32563i) q^{6} +(-0.118034 - 0.204441i) q^{7} +(-0.363271 + 0.629204i) q^{8} +(0.107320 + 0.608645i) q^{9} +(1.06887 + 6.06185i) q^{10} +(0.690983 - 1.19682i) q^{11} +(-1.53884 - 2.66535i) q^{12} +(-0.556564 + 0.467013i) q^{13} +(0.421948 - 0.153577i) q^{14} +(5.78415 + 2.10526i) q^{15} +(-3.53762 - 2.96842i) q^{16} +(-1.12387 + 6.37381i) q^{17} -1.17557 q^{18} -5.23607 q^{20} +(0.0779729 - 0.442206i) q^{21} +(2.01367 + 1.68967i) q^{22} +(0.358931 + 0.130640i) q^{23} +(-1.29862 + 0.472660i) q^{24} +(4.19190 - 3.51742i) q^{25} +(-0.690983 - 1.19682i) q^{26} +(2.26538 - 3.92376i) q^{27} +(0.0663277 + 0.376163i) q^{28} +(-0.738570 - 4.18864i) q^{29} +(-5.85410 + 10.1396i) q^{30} +(-0.951057 - 1.64728i) q^{31} +(5.61582 - 4.71224i) q^{32} +(2.47013 - 0.899053i) q^{33} +(-11.5683 - 4.21052i) q^{34} +(-0.585206 - 0.491046i) q^{35} +(0.173648 - 0.984808i) q^{36} -6.60440 q^{37} -1.38197 q^{39} +(-0.408271 + 2.31542i) q^{40} +(-1.66969 - 1.40104i) q^{41} +(0.802593 + 0.292120i) q^{42} +(-8.76380 + 3.18976i) q^{43} +(-1.71293 + 1.43732i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-0.363271 + 0.629204i) q^{46} +(-1.99212 - 11.2978i) q^{47} +(-1.52533 - 8.65057i) q^{48} +(3.47214 - 6.01392i) q^{49} +(5.20431 + 9.01413i) q^{50} +(-9.43057 + 7.91319i) q^{51} +(1.10467 - 0.402069i) q^{52} +(4.67948 + 1.70319i) q^{53} +(6.60180 + 5.53957i) q^{54} +(0.776578 - 4.40419i) q^{55} +0.171513 q^{56} +8.09017 q^{58} +(1.52533 - 8.65057i) q^{59} +(-7.62949 - 6.40190i) q^{60} +(8.90090 + 3.23966i) q^{61} +(3.39984 - 1.23744i) q^{62} +(0.111764 - 0.0937814i) q^{63} +(2.35410 + 4.07742i) q^{64} +(-1.17557 + 2.03615i) q^{65} +(0.868241 + 4.92404i) q^{66} +(2.26390 + 12.8392i) q^{67} +(5.23607 - 9.06914i) q^{68} +(0.363271 + 0.629204i) q^{69} +(1.11313 - 0.934025i) q^{70} +(-9.52013 + 3.46504i) q^{71} +(-0.421948 - 0.153577i) q^{72} +(6.89440 + 5.78509i) q^{73} +(2.18142 - 12.3715i) q^{74} +10.4086 q^{75} -0.326238 q^{77} +(0.456461 - 2.58872i) q^{78} +(-3.60216 - 3.02257i) q^{79} +(-14.0430 - 5.11124i) q^{80} +(9.84059 - 3.58168i) q^{81} +(3.17594 - 2.66493i) q^{82} +(1.61803 + 2.80252i) q^{83} +(-0.363271 + 0.629204i) q^{84} +(3.63693 + 20.6261i) q^{85} +(-3.08044 - 17.4701i) q^{86} +(4.04508 - 7.00629i) q^{87} +(0.502029 + 0.869539i) q^{88} +(5.69703 - 4.78037i) q^{89} +(-3.57480 + 1.30112i) q^{90} +(0.161170 + 0.0586610i) q^{91} +(-0.473442 - 0.397265i) q^{92} +(0.628265 - 3.56307i) q^{93} +21.8213 q^{94} +13.9443 q^{96} +(-0.768353 + 4.35755i) q^{97} +(10.1185 + 8.49045i) q^{98} +(0.802593 + 0.292120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) \) 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Introduction

L-functions

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