LMFDB - Embedded newform 558.2.bd.a.383.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(65,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.65"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.bd (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			383.23
Character	$\chi$	$=$	558.383
Dual form			558.2.bd.a.389.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.743145 + 0.669131i) q^{2} +(-0.357311 - 1.69479i) q^{3} +(0.104528 + 0.994522i) q^{4} +1.56835i q^{5} +(0.868505 - 1.49857i) q^{6} +(0.0575765 - 0.0418318i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.74466 + 1.21114i) q^{9} +(-1.04943 + 1.16551i) q^{10} +(0.610038 + 5.80412i) q^{11} +(1.64816 - 0.532508i) q^{12} +(2.03396 + 0.660873i) q^{13} +(0.0707786 + 0.00743914i) q^{14} +(2.65803 - 0.560387i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-0.552343 + 0.245919i) q^{17} +(-2.85009 - 0.936485i) q^{18} +(6.86216 + 1.45860i) q^{19} +(-1.55976 + 0.163937i) q^{20} +(-0.0914690 - 0.0826335i) q^{21} +(-3.43037 + 4.72150i) q^{22} +(-2.52696 + 1.12507i) q^{23} +(1.58114 + 0.707105i) q^{24} +2.54029 q^{25} +(1.06931 + 1.85211i) q^{26} +(3.03332 + 4.21888i) q^{27} +(0.0476210 + 0.0528885i) q^{28} +(4.38699 - 4.87225i) q^{29} +(2.35027 + 1.36212i) q^{30} +(-4.96204 - 2.52550i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(9.61882 - 3.10776i) q^{33} +(-0.575023 - 0.186836i) q^{34} +(0.0656068 + 0.0903000i) q^{35} +(-1.49140 - 2.60302i) q^{36} +(-4.86239 - 2.80730i) q^{37} +(4.12359 + 5.67563i) q^{38} +(0.393289 - 3.68328i) q^{39} +(-1.26882 - 0.921852i) q^{40} +(0.835596 - 0.271502i) q^{41} +(-0.0126822 - 0.122613i) q^{42} +(-1.49673 + 0.486317i) q^{43} +(-5.70856 + 1.21339i) q^{44} +(-1.89948 - 4.30458i) q^{45} +(-2.63071 - 0.854771i) q^{46} +(0.787769 + 3.70616i) q^{47} +(0.701870 + 1.58347i) q^{48} +(-2.16155 + 6.65258i) q^{49} +(1.88780 + 1.69978i) q^{50} +(0.614140 + 0.848239i) q^{51} +(-0.444646 + 2.09189i) q^{52} +(-0.596147 + 5.67196i) q^{53} +(-0.568784 + 5.16493i) q^{54} +(-9.10288 + 0.956751i) q^{55} +0.0711685i q^{56} +(0.0201002 - 12.1511i) q^{57} +(6.52034 - 0.685316i) q^{58} +(1.34402 + 6.32310i) q^{59} +(0.835157 + 2.58489i) q^{60} +(9.71142 - 5.60689i) q^{61} +(-1.99762 - 5.19707i) q^{62} +(-0.107364 + 0.184547i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.03648 + 3.18995i) q^{65} +(9.22768 + 4.12673i) q^{66} -10.9248 q^{67} +(-0.302307 - 0.523612i) q^{68} +(2.80968 + 3.88067i) q^{69} +(-0.0116672 + 0.111006i) q^{70} +(-4.95717 - 0.521020i) q^{71} +(0.633440 - 2.93236i) q^{72} +(4.35802 - 9.78828i) q^{73} +(-1.73501 - 5.33980i) q^{74} +(-0.907671 - 4.30526i) q^{75} +(-0.733316 + 6.97704i) q^{76} +(0.277921 + 0.308662i) q^{77} +(2.75686 - 2.47405i) q^{78} +(6.55101 - 9.01670i) q^{79} +(-0.326078 - 1.53408i) q^{80} +(6.06630 - 6.64831i) q^{81} +(0.802639 + 0.357358i) q^{82} +(-11.5896 - 2.46344i) q^{83} +(0.0726197 - 0.0996055i) q^{84} +(-0.385686 - 0.866266i) q^{85} +(-1.43770 - 0.640103i) q^{86} +(-9.82498 - 5.69415i) q^{87} +(-5.05420 - 2.91805i) q^{88} +(7.90469 - 5.74310i) q^{89} +(1.46873 - 4.46993i) q^{90} +(0.144754 - 0.0470333i) q^{91} +(-1.38305 - 2.39551i) q^{92} +(-2.50722 + 9.31203i) q^{93} +(-1.89448 + 3.28134i) q^{94} +(-2.28759 + 10.7623i) q^{95} +(-0.537957 + 1.64639i) q^{96} +(-16.6947 - 7.43298i) q^{97} +(-6.05779 + 3.49747i) q^{98} +(-8.70393 - 15.1915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} + 4 q^{9} - 16 q^{15} + 32 q^{16} + 16 q^{18} - 4 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} - 268 q^{25} + 12 q^{26} - 18 q^{28} + 18 q^{30} + 22 q^{31} + 60 q^{33} - 4 q^{36}+ \cdots - 138 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 + 4 * q^9 - 16 * q^15 + 32 * q^16 + 16 * q^18 - 4 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 - 268 * q^25 + 12 * q^26 - 18 * q^28 + 18 * q^30 + 22 * q^31 + 60 * q^33 - 4 * q^36 + 72 * q^37 + 8 * q^39 + 6 * q^42 + 10 * q^43 - 24 * q^45 - 54 * q^47 + 10 * q^48 - 60 * q^49 + 28 * q^51 + 90 * q^53 - 96 * q^57 - 18 * q^58 + 6 * q^59 - 10 * q^60 - 42 * q^61 + 90 * q^62 + 124 * q^63 + 64 * q^64 + 120 * q^65 - 12 * q^66 - 16 * q^67 - 24 * q^69 - 6 * q^70 + 6 * q^71 + 8 * q^72 + 42 * q^73 - 48 * q^74 - 6 * q^76 - 90 * q^77 + 20 * q^78 - 10 * q^79 - 6 * q^80 + 8 * q^81 + 174 * q^83 - 2 * q^84 - 96 * q^86 + 100 * q^87 + 36 * q^89 - 176 * q^90 - 10 * q^91 + 18 * q^92 - 92 * q^93 - 150 * q^95 - 18 * q^97 + 48 * q^98 - 138 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.743145	+	0.669131i	0.525483	+	0.473147i
$2$	0.743145	+	0.669131i	0.525483	+	0.473147i
$3$	−0.357311	−	1.69479i	−0.206293	−	0.978490i
$3$	−0.357311	−	1.69479i	−0.206293	−	0.978490i
$4$	0.104528	+	0.994522i	0.0522642	+	0.497261i
$5$			1.56835i			0.701386i	0.936490	+	0.350693i	$0.114054\pi$
$5$			1.56835i			0.701386i	−0.936490	+	0.350693i	$0.885946\pi$
$6$	0.868505	−	1.49857i	0.354566	−	0.611787i
$7$	0.0575765	−	0.0418318i	0.0217619	−	0.0158109i	−0.576851	−	0.816849i	$-0.695719\pi$
$7$	0.0575765	−	0.0418318i	0.0217619	−	0.0158109i	0.598613	+	0.801038i	$0.295719\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−2.74466	+	1.21114i	−0.914886	+	0.403712i
$10$	−1.04943	+	1.16551i	−0.331859	+	0.368566i
$11$	0.610038	+	5.80412i	0.183933	+	1.75001i	0.564663	+	0.825322i	$0.309006\pi$
$11$	0.610038	+	5.80412i	0.183933	+	1.75001i	−0.380729	+	0.924687i	$0.624327\pi$
$12$	1.64816	−	0.532508i	0.475783	−	0.153722i
$13$	2.03396	+	0.660873i	0.564118	+	0.183293i	0.577173	−	0.816622i	$-0.304156\pi$
$13$	2.03396	+	0.660873i	0.564118	+	0.183293i	−0.0130552	+	0.999915i	$0.504156\pi$
$14$	0.0707786	+	0.00743914i	0.0189164	+	0.00198819i
$15$	2.65803	−	0.560387i	0.686300	−	0.144691i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	−0.552343	+	0.245919i	−0.133963	+	0.0596441i	−0.472623	−	0.881265i	$-0.656693\pi$
$17$	−0.552343	+	0.245919i	−0.133963	+	0.0596441i	0.338660	+	0.940909i	$0.390026\pi$
$18$	−2.85009	−	0.936485i	−0.671772	−	0.220732i
$19$	6.86216	+	1.45860i	1.57429	+	0.334625i	0.910569	−	0.413356i	$-0.135644\pi$
$19$	6.86216	+	1.45860i	1.57429	+	0.334625i	0.663719	+	0.747982i	$0.268977\pi$
$20$	−1.55976	+	0.163937i	−0.348772	+	0.0366574i
$21$	−0.0914690	−	0.0826335i	−0.0199602	−	0.0180321i
$22$	−3.43037	+	4.72150i	−0.731357	+	1.00663i
$23$	−2.52696	+	1.12507i	−0.526907	+	0.234594i	−0.652910	−	0.757436i	$-0.726452\pi$
$23$	−2.52696	+	1.12507i	−0.526907	+	0.234594i	0.126003	+	0.992030i	$0.459785\pi$
$24$	1.58114	+	0.707105i	0.322749	+	0.144337i
$25$	2.54029			0.508057
$26$	1.06931	+	1.85211i	0.209710	+	0.363228i
$27$	3.03332	+	4.21888i	0.583763	+	0.811924i
$28$	0.0476210	+	0.0528885i	0.00899953	+	0.00999499i
$29$	4.38699	−	4.87225i	0.814644	−	0.904754i	−0.182270	−	0.983248i	$-0.558345\pi$
$29$	4.38699	−	4.87225i	0.814644	−	0.904754i	0.996915	+	0.0784944i	$0.0250113\pi$
$30$	2.35027	+	1.36212i	0.429099	+	0.248688i
$31$	−4.96204	−	2.52550i	−0.891209	−	0.453594i
$31$	−4.96204	−	2.52550i	−0.891209	−	0.453594i
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	9.61882	−	3.10776i	1.67442	−	0.540992i
$34$	−0.575023	−	0.186836i	−0.0986156	−	0.0320422i
$35$	0.0656068	+	0.0903000i	0.0110896	+	0.0152635i
$36$	−1.49140	−	2.60302i	−0.248566	−	0.433837i
$37$	−4.86239	−	2.80730i	−0.799372	−	0.461517i	0.0438798	−	0.999037i	$-0.486028\pi$
$37$	−4.86239	−	2.80730i	−0.799372	−	0.461517i	−0.843251	+	0.537519i	$0.819361\pi$
$38$	4.12359	+	5.67563i	0.668935	+	0.920709i
$39$	0.393289	−	3.68328i	0.0629767	−	0.589796i
$40$	−1.26882	−	0.921852i	−0.200618	−	0.145758i
$41$	0.835596	−	0.271502i	0.130498	−	0.0424014i	−0.243040	−	0.970016i	$-0.578145\pi$
$41$	0.835596	−	0.271502i	0.130498	−	0.0424014i	0.373538	+	0.927615i	$0.378145\pi$
$42$	−0.0126822	−	0.122613i	−0.00195690	−	0.0189197i
$43$	−1.49673	+	0.486317i	−0.228249	+	0.0741626i	−0.420909	−	0.907103i	$-0.638289\pi$
$43$	−1.49673	+	0.486317i	−0.228249	+	0.0741626i	0.192660	+	0.981266i	$0.438289\pi$
$44$	−5.70856	+	1.21339i	−0.860598	+	0.182926i
$45$	−1.89948	−	4.30458i	−0.283158	−	0.641689i
$46$	−2.63071	−	0.854771i	−0.387878	−	0.126029i
$47$	0.787769	+	3.70616i	0.114908	+	0.540599i	0.997513	+	0.0704840i	$0.0224544\pi$
$47$	0.787769	+	3.70616i	0.114908	+	0.540599i	−0.882605	+	0.470115i	$0.844212\pi$
$48$	0.701870	+	1.58347i	0.101306	+	0.228554i
$49$	−2.16155	+	6.65258i	−0.308793	+	0.950368i
$50$	1.88780	+	1.69978i	0.266975	+	0.240386i
$51$	0.614140	+	0.848239i	0.0859968	+	0.118777i
$52$	−0.444646	+	2.09189i	−0.0616613	+	0.290094i
$53$	−0.596147	+	5.67196i	−0.0818871	+	0.779104i	0.874110	+	0.485728i	$0.161445\pi$
$53$	−0.596147	+	5.67196i	−0.0818871	+	0.779104i	−0.955997	+	0.293376i	$0.905221\pi$
$54$	−0.568784	+	5.16493i	−0.0774017	+	0.702858i
$55$	−9.10288	+	0.956751i	−1.22743	+	0.129008i
$56$			0.0711685i			0.00951029i
$57$	0.0201002	−	12.1511i	0.00266234	−	1.60946i
$58$	6.52034	−	0.685316i	0.856163	−	0.0899864i
$59$	1.34402	+	6.32310i	0.174976	+	0.823197i	0.974821	+	0.222990i	$0.0715818\pi$
$59$	1.34402	+	6.32310i	0.174976	+	0.823197i	−0.799845	+	0.600207i	$0.795085\pi$
$60$	0.835157	+	2.58489i	0.107818	+	0.333708i
$61$	9.71142	−	5.60689i	1.24342	−	0.717889i	0.273631	−	0.961835i	$-0.411775\pi$
$61$	9.71142	−	5.60689i	1.24342	−	0.717889i	0.969789	+	0.243946i	$0.0784420\pi$
$62$	−1.99762	−	5.19707i	−0.253698	−	0.660028i
$63$	−0.107364	+	0.184547i	−0.0135266	+	0.0232507i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−1.03648	+	3.18995i	−0.128559	+	0.395665i
$66$	9.22768	+	4.12673i	1.13585	+	0.507965i
$67$	−10.9248			−1.33468			−0.667340	−	0.744753i	$-0.732567\pi$
$67$	−10.9248			−1.33468			−0.667340	+	0.744753i	$0.732567\pi$
$68$	−0.302307	−	0.523612i	−0.0366602	−	0.0634973i
$69$	2.80968	+	3.88067i	0.338245	+	0.467178i
$70$	−0.0116672	+	0.111006i	−0.00139449	+	0.0132677i
$71$	−4.95717	−	0.521020i	−0.588308	−	0.0618336i	−0.194302	−	0.980942i	$-0.562244\pi$
$71$	−4.95717	−	0.521020i	−0.588308	−	0.0618336i	−0.394006	+	0.919108i	$0.628911\pi$
$72$	0.633440	−	2.93236i	0.0746516	−	0.345582i
$73$	4.35802	−	9.78828i	0.510068	−	1.14563i	−0.456617	−	0.889663i	$-0.650939\pi$
$73$	4.35802	−	9.78828i	0.510068	−	1.14563i	0.966685	−	0.255968i	$-0.0823943\pi$
$74$	−1.73501	−	5.33980i	−0.201691	−	0.620740i
$75$	−0.907671	−	4.30526i	−0.104809	−	0.497129i
$76$	−0.733316	+	6.97704i	−0.0841171	+	0.800321i
$77$	0.277921	+	0.308662i	0.0316720	+	0.0351753i
$78$	2.75686	−	2.47405i	0.312153	−	0.280131i
$79$	6.55101	−	9.01670i	0.737047	−	1.01446i	−0.261736	−	0.965139i	$-0.584295\pi$
$79$	6.55101	−	9.01670i	0.737047	−	1.01446i	0.998783	−	0.0493184i	$-0.0157049\pi$
$80$	−0.326078	−	1.53408i	−0.0364566	−	0.171515i
$81$	6.06630	−	6.64831i	0.674033	−	0.738701i
$82$	0.802639	+	0.357358i	0.0886367	+	0.0394636i
$83$	−11.5896	−	2.46344i	−1.27212	−	0.270398i	−0.478110	−	0.878300i	$-0.658678\pi$
$83$	−11.5896	−	2.46344i	−1.27212	−	0.270398i	−0.794012	+	0.607902i	$0.792011\pi$
$84$	0.0726197	−	0.0996055i	0.00792346	−	0.0108679i
$85$	−0.385686	−	0.866266i	−0.0418336	−	0.0939597i
$86$	−1.43770	−	0.640103i	−0.155031	−	0.0690241i
$87$	−9.82498	−	5.69415i	−1.05335	−	0.610477i
$88$	−5.05420	−	2.91805i	−0.538780	−	0.311065i
$89$	7.90469	−	5.74310i	0.837896	−	0.608767i	−0.0838863	−	0.996475i	$-0.526733\pi$
$89$	7.90469	−	5.74310i	0.837896	−	0.608767i	0.921782	+	0.387708i	$0.126733\pi$
$90$	1.46873	−	4.46993i	0.154818	−	0.471172i
$91$	0.144754	−	0.0470333i	0.0151743	−	0.00493043i
$92$	−1.38305	−	2.39551i	−0.144193	−	0.249749i
$93$	−2.50722	+	9.31203i	−0.259987	+	0.965612i
$94$	−1.89448	+	3.28134i	−0.195401	+	0.338444i
$95$	−2.28759	+	10.7623i	−0.234702	+	1.10418i
$96$	−0.537957	+	1.64639i	−0.0549050	+	0.168034i
$97$	−16.6947	−	7.43298i	−1.69509	−	0.754705i	−0.999336	−	0.0364289i	$-0.988402\pi$
$97$	−16.6947	−	7.43298i	−1.69509	−	0.754705i	−0.695758	−	0.718276i	$-0.744932\pi$
$98$	−6.05779	+	3.49747i	−0.611929	+	0.353298i
$99$	−8.70393	−	15.1915i	−0.874778	−	1.52680i
$100$	0.265532	+	2.52637i	0.0265532	+	0.252637i
$101$	10.4252	+	1.09574i	1.03735	+	0.109030i	0.607862	−	0.794043i	$-0.292027\pi$
$101$	10.4252	+	1.09574i	1.03735	+	0.109030i	0.429488	+	0.903073i	$0.358694\pi$
$102$	−0.111187	+	1.04130i	−0.0110092	+	0.103104i
$103$	1.38799	+	4.27181i	0.136763	+	0.420914i	0.995860	−	0.0908993i	$-0.0289741\pi$
$103$	1.38799	+	4.27181i	0.136763	+	0.420914i	−0.859097	+	0.511813i	$0.828974\pi$
$104$	−1.73019	+	1.25705i	−0.169659	+	0.123264i
$105$	0.129598	−	0.143455i	0.0126475	−	0.0139998i
$106$	−4.23831	+	3.81619i	−0.411661	+	0.370661i
$107$	−3.05798	−	6.86834i	−0.295626	−	0.663987i	0.703272	−	0.710921i	$-0.251722\pi$
$107$	−3.05798	−	6.86834i	−0.295626	−	0.663987i	−0.998898	+	0.0469338i	$0.985055\pi$
$108$	−3.87870	+	3.45770i	−0.373228	+	0.332717i
$109$	5.85225	−	18.0114i	0.560544	−	1.72518i	−0.120291	−	0.992739i	$-0.538383\pi$
$109$	5.85225	−	18.0114i	0.560544	−	1.72518i	0.680835	−	0.732437i	$-0.261617\pi$
$110$	−7.40495	−	5.38001i	−0.706034	−	0.512964i
$111$	−3.02042	+	9.24383i	−0.286685	+	0.877385i
$112$	−0.0476210	+	0.0528885i	−0.00449976	+	0.00499749i
$113$	3.38345	+	4.65693i	0.318289	+	0.438087i	0.937944	−	0.346788i	$-0.112728\pi$
$113$	3.38345	+	4.65693i	0.318289	+	0.438087i	−0.619655	+	0.784874i	$0.712728\pi$
$114$	8.14563	−	9.01660i	0.762908	−	0.844482i
$115$	−1.76451	−	3.96314i	−0.164541	−	0.369565i
$116$	5.30412	+	3.85367i	0.492476	+	0.357804i
$117$	−6.38292	+	0.649529i	−0.590101	+	0.0600490i
$118$	−3.23218	+	5.59830i	−0.297546	+	0.515365i
$119$	−0.0215148	+	0.0372647i	−0.00197226	+	0.00341605i
$120$	−1.10899	+	2.47978i	−0.101236	+	0.226372i
$121$	−22.5561	+	4.79444i	−2.05055	+	0.435858i
$122$	10.9687	+	2.33148i	0.993062	+	0.211082i
$123$	−0.758707	−	1.31915i	−0.0684103	−	0.118944i
$124$	1.99299	−	5.19884i	0.178976	−	0.466870i
$125$			11.8258i			1.05773i
$126$	−0.203273	+	0.0653047i	−0.0181090	+	0.00581780i
$127$	8.15952	−	7.34687i	0.724041	−	0.651929i	−0.222345	−	0.974968i	$-0.571371\pi$
$127$	8.15952	−	7.34687i	0.724041	−	0.651929i	0.946386	+	0.323039i	$0.104704\pi$
$128$	0.406737	−	0.913545i	0.0359508	−	0.0807468i
$129$	1.35900	+	2.36288i	0.119654	+	0.208040i
$130$	−2.90475	+	1.67706i	−0.254763	+	0.147088i
$131$	−1.45091	+	3.25880i	−0.126767	+	0.284722i	−0.965768	−	0.259407i	$-0.916473\pi$
$131$	−1.45091	+	3.25880i	−0.126767	+	0.284722i	0.839002	+	0.544129i	$0.183140\pi$
$132$	4.09618	+	9.24128i	0.356527	+	0.804350i
$133$	0.456115	−	0.203076i	0.0395502	−	0.0176089i
$134$	−8.11873	−	7.31014i	−0.701352	−	0.631500i
$135$	−6.61667	+	4.75730i	−0.569472	+	0.409444i
$136$	0.125706	−	0.591403i	0.0107792	−	0.0507123i
$137$	−3.79105	−	4.21039i	−0.323891	−	0.359718i	0.559106	−	0.829096i	$-0.311145\pi$
$137$	−3.79105	−	4.21039i	−0.323891	−	0.359718i	−0.882997	+	0.469379i	$0.844478\pi$
$138$	−0.508679	+	4.76394i	−0.0433016	+	0.405534i
$139$	0.508634	−	0.457976i	0.0431417	−	0.0388450i	−0.647278	−	0.762254i	$-0.724093\pi$
$139$	0.508634	−	0.457976i	0.0431417	−	0.0388450i	0.690420	+	0.723409i	$0.257426\pi$
$140$	−0.0829476	+	0.0746863i	−0.00701035	+	0.00631215i
$141$	5.99971	−	2.65936i	0.505266	−	0.223958i
$142$	−3.33526	−	3.70419i	−0.279889	−	0.310848i
$143$	−2.59499	+	12.2085i	−0.217004	+	1.02093i
$144$	2.43287	−	1.75532i	0.202739	−	0.146276i
$145$	7.64138	+	6.88033i	0.634582	+	0.571380i
$146$	9.78828	−	4.35802i	0.810084	−	0.360673i
$147$	12.0471	+	1.28635i	0.993628	+	0.106097i
$148$	2.28366	−	5.12919i	0.187716	−	0.421617i
$149$	13.0059	−	7.50894i	1.06548	−	0.615156i	0.138539	−	0.990357i	$-0.455760\pi$
$149$	13.0059	−	7.50894i	1.06548	−	0.615156i	0.926944	+	0.375201i	$0.122426\pi$
$150$	2.20625	−	3.80678i	0.180140	−	0.310823i
$151$	−0.226052	+	0.507720i	−0.0183958	+	0.0413177i	−0.922510	−	0.385974i	$-0.873866\pi$
$151$	−0.226052	+	0.507720i	−0.0183958	+	0.0413177i	0.904114	+	0.427291i	$0.140532\pi$
$152$	−5.21351	+	4.69427i	−0.422871	+	0.380755i
$153$	1.21815	−	1.34393i	0.0984817	−	0.108650i
$154$			0.415346i			0.0334695i
$155$	3.96087	−	7.78220i	0.318144	−	0.625082i
$156$	3.70421	+	0.00612744i	0.296574	+	0.000490588i
$157$	−11.0618	−	2.35125i	−0.882825	−	0.187650i	−0.255875	−	0.966710i	$-0.582364\pi$
$157$	−11.0618	−	2.35125i	−0.882825	−	0.187650i	−0.626950	+	0.779060i	$0.715697\pi$
$158$	10.9017	−	2.31723i	0.867293	−	0.184349i
$159$	9.82582	−	1.01630i	0.779238	−	0.0805982i
$160$	0.784174	−	1.35823i	0.0619944	−	0.107377i
$161$	−0.0984295	+	0.170485i	−0.00775733	+	0.0134361i
$162$	8.95673	−	0.881512i	0.703707	−	0.0692581i
$163$	9.30747	+	6.76228i	0.729018	+	0.529662i	0.889253	−	0.457417i	$-0.151225\pi$
$163$	9.30747	+	6.76228i	0.729018	+	0.529662i	−0.160235	+	0.987079i	$0.551225\pi$
$164$	0.357358	+	0.802639i	0.0279050	+	0.0626756i
$165$	4.87405	+	15.0857i	0.379444	+	1.17442i
$166$	−6.96438	−	9.58564i	−0.540541	−	0.743990i
$167$	5.86916	−	6.51837i	0.454170	−	0.504406i	−0.471956	−	0.881622i	$-0.656452\pi$
$167$	5.86916	−	6.51837i	0.454170	−	0.504406i	0.926125	+	0.377216i	$0.123118\pi$
$168$	0.120616	−	0.0254293i	0.00930573	−	0.00196191i
$169$	−6.81699	−	4.95284i	−0.524384	−	0.380987i
$170$	0.293024	−	0.901836i	0.0224739	−	0.0691676i
$171$	−20.6009	+	4.30766i	−1.57539	+	0.329415i
$172$	−0.640103	−	1.43770i	−0.0488074	−	0.109623i
$173$	−3.61619	+	3.25603i	−0.274934	+	0.247552i	−0.795050	−	0.606544i	$-0.792555\pi$
$173$	−3.61619	+	3.25603i	−0.274934	+	0.247552i	0.520116	+	0.854096i	$0.325889\pi$
$174$	−3.49126	−	10.8058i	−0.264672	−	0.819183i
$175$	0.146261	−	0.106265i	0.0110563	−	0.00803286i
$176$	−1.80345	−	5.55045i	−0.135940	−	0.418381i
$177$	10.2361	−	4.53714i	0.769394	−	0.341032i
$178$	9.71721	+	1.02132i	0.728336	+	0.0765512i
$179$	−1.28822	−	12.2566i	−0.0962858	−	0.916098i	−0.930903	−	0.365267i	$-0.880978\pi$
$179$	−1.28822	−	12.2566i	−0.0962858	−	0.916098i	0.834617	−	0.550831i	$-0.185689\pi$
$180$	4.08245	−	2.33903i	0.304288	−	0.174341i
$181$	15.2774	−	8.82041i	1.13556	−	0.655616i	0.190233	−	0.981739i	$-0.439076\pi$
$181$	15.2774	−	8.82041i	1.13556	−	0.655616i	0.945327	+	0.326123i	$0.105742\pi$
$182$	0.139044	+	0.0619065i	0.0103067	+	0.00458882i
$183$	−12.9725	−	14.4555i	−0.958956	−	1.06858i
$184$	0.575104	−	2.70565i	0.0423972	−	0.199463i
$185$	4.40282	−	7.62591i	0.323702	−	0.560668i
$186$	−8.09419	+	5.24253i	−0.593495	+	0.384401i
$187$	−1.76429	−	3.05585i	−0.129018	−	0.223466i
$188$	−3.60352	+	1.17085i	−0.262813	+	0.0853932i
$189$	0.351132	+	0.116019i	0.0255411	+	0.00843915i
$190$	−8.90137	+	6.46722i	−0.645773	+	0.469182i
$191$	13.2324	+	7.63970i	0.957459	+	0.552789i	0.895390	−	0.445282i	$-0.146897\pi$
$191$	13.2324	+	7.63970i	0.957459	+	0.552789i	0.0620691	+	0.998072i	$0.480230\pi$
$192$	−1.50143	+	0.863543i	−0.108356	+	0.0623208i
$193$	15.6317	+	6.95968i	1.12519	+	0.500968i	0.883053	−	0.469273i	$-0.155484\pi$
$193$	15.6317	+	6.95968i	1.12519	+	0.500968i	0.242140	+	0.970241i	$0.422151\pi$
$194$	−7.43298	−	16.6947i	−0.533657	−	1.19861i
$195$	5.77666	+	0.616814i	0.413675	+	0.0441710i
$196$	−6.84208	−	1.45433i	−0.488720	−	0.103881i
$197$	7.31315	+	3.25603i	0.521041	+	0.231982i	0.650367	−	0.759620i	$-0.274615\pi$
$197$	7.31315	+	3.25603i	0.521041	+	0.231982i	−0.129327	+	0.991602i	$0.541282\pi$
$198$	3.69681	−	17.1135i	0.262721	−	1.21621i
$199$	1.55324	+	7.30743i	0.110106	+	0.518010i	0.998287	+	0.0585144i	$0.0186364\pi$
$199$	1.55324	+	7.30743i	0.110106	+	0.518010i	−0.888180	+	0.459495i	$0.848030\pi$
$200$	−1.49314	+	2.05513i	−0.105581	+	0.145320i
$201$	3.90356	+	18.5153i	0.275336	+	1.30597i
$202$	7.01427	+	7.79014i	0.493522	+	0.548112i
$203$	0.0487729	−	0.464043i	0.00342319	−	0.0325694i
$204$	−0.779397	+	0.699441i	−0.0545687	+	0.0489707i
$205$	0.425809	+	1.31051i	0.0297398	+	0.0915297i
$206$	−1.82692	+	4.10332i	−0.127287	+	0.285892i
$207$	5.57301	−	6.14843i	0.387351	−	0.427345i
$208$	−2.12691	−	0.223548i	−0.147475	−	0.0155002i
$209$	−4.27970	+	40.7186i	−0.296033	+	2.81657i
$210$	0.192300	−	0.0198900i	0.0132700	−	0.00137254i
$211$	−4.74670	−	8.22152i	−0.326776	−	0.565993i	0.655094	−	0.755547i	$-0.272629\pi$
$211$	−4.74670	−	8.22152i	−0.326776	−	0.565993i	−0.981870	+	0.189554i	$0.939296\pi$
$212$	−5.70320			−0.391698
$213$	0.888228	+	8.58755i	0.0608604	+	0.588409i
$214$	2.32329	−	7.15036i	0.158817	−	0.488788i
$215$	−0.762714	−	2.34739i	−0.0520166	−	0.160091i
$216$	−5.19609	−	0.0257860i	−0.353549	−	0.00175452i
$217$	−0.391343	+	0.0621613i	−0.0265661	+	0.00421979i
$218$	16.4010	−	9.46913i	1.11082	−	0.641331i
$219$	−18.1463	−	3.88850i	−1.22621	−	0.262760i
$220$	−1.90302	−	8.95301i	−0.128302	−	0.603612i
$221$	−1.28596	+	0.135160i	−0.0865032	+	0.00909186i
$222$	−8.42993	+	4.84845i	−0.565780	+	0.325407i
$223$			2.80130i			0.187589i	0.995592	+	0.0937944i	$0.0298996\pi$
$223$			2.80130i			0.187589i	−0.995592	+	0.0937944i	$0.970100\pi$
$224$	−0.0707786	+	0.00743914i	−0.00472910	+	0.000497048i
$225$	−6.97222	+	3.07663i	−0.464814	+	0.205109i
$226$	−0.601695	+	5.72474i	−0.0400241	+	0.380804i
$227$	−2.20099	+	10.3548i	−0.146085	+	0.687275i	0.842756	+	0.538297i	$0.180932\pi$
$227$	−2.20099	+	10.3548i	−0.146085	+	0.687275i	−0.988840	+	0.148979i	$0.952401\pi$
$228$	12.0867	−	1.25015i	0.800459	−	0.0827931i
$229$	17.8596	+	16.0809i	1.18020	+	1.06266i	0.996826	+	0.0796117i	$0.0253681\pi$
$229$	17.8596	+	16.0809i	1.18020	+	1.06266i	0.183372	+	0.983044i	$0.441299\pi$
$230$	1.34058	−	4.12588i	0.0883951	−	0.272052i
$231$	0.423815	−	0.581307i	0.0278850	−	0.0382472i
$232$	1.36312	+	6.41299i	0.0894934	+	0.421033i
$233$	26.7984	+	8.70731i	1.75562	+	0.570435i	0.996731	−	0.0807869i	$-0.0257433\pi$
$233$	26.7984	+	8.70731i	1.75562	+	0.570435i	0.758887	+	0.651222i	$0.225743\pi$
$234$	−5.17806	−	3.78831i	−0.338500	−	0.247650i
$235$	−5.81255	+	1.23550i	−0.379169	+	0.0805949i
$236$	−6.14797	+	1.99760i	−0.400199	+	0.130033i
$237$	−17.6222	−	7.88086i	−1.14468	−	0.511917i
$238$	−0.0409235	+	0.0132969i	−0.00265268	+	0.000861907i
$239$	2.46147	+	1.78836i	0.159219	+	0.115680i	0.664542	−	0.747251i	$-0.268627\pi$
$239$	2.46147	+	1.78836i	0.159219	+	0.115680i	−0.505323	+	0.862930i	$0.668627\pi$
$240$	−2.48343	+	1.10078i	−0.160305	+	0.0710548i
$241$	11.7144	+	16.1235i	0.754593	+	1.03861i	0.997645	+	0.0685949i	$0.0218516\pi$
$241$	11.7144	+	16.1235i	0.754593	+	1.03861i	−0.243052	+	0.970013i	$0.578148\pi$
$242$	−19.9705	−	11.5300i	−1.28375	−	0.741176i
$243$	−13.4351	−	7.90562i	−0.861860	−	0.507146i
$244$	6.59129	+	9.07214i	0.421964	+	0.580784i
$245$	−10.4336	−	3.39007i	−0.666575	−	0.216583i
$246$	0.318857	−	1.48800i	0.0203296	−	0.0948712i
$247$	12.9934	+	7.50174i	0.826750	+	0.477324i
$248$	4.95979	−	2.52992i	0.314947	−	0.160650i
$249$	−0.0339475	+	20.5222i	−0.00215133	+	1.30054i
$250$	−7.91300	+	8.78827i	−0.500462	+	0.555819i
$251$	−12.5040	−	13.8871i	−0.789246	−	0.876546i	0.205528	−	0.978651i	$-0.434109\pi$
$251$	−12.5040	−	13.8871i	−0.789246	−	0.876546i	−0.994774	+	0.102105i	$0.967442\pi$
$252$	−0.194759	−	0.0874853i	−0.0122686	−	0.00551106i
$253$	−8.07160	−	13.9804i	−0.507457	−	0.878941i
$254$	10.9797			0.688929
$255$	−1.33033	+	0.963185i	−0.0833087	+	0.0603170i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−0.455818	+	0.627380i	−0.0284331	+	0.0391349i	−0.822997	−	0.568046i	$-0.807700\pi$
$257$	−0.455818	+	0.627380i	−0.0284331	+	0.0391349i	0.794564	+	0.607181i	$0.207700\pi$
$258$	−0.571140	+	2.66532i	−0.0355576	+	0.165935i
$259$	−0.397394	+	0.0417678i	−0.0246929	+	0.00259532i
$260$	−3.28082	−	0.697359i	−0.203468	−	0.0432484i
$261$	−6.13984	+	18.6859i	−0.380047	+	1.15663i
$262$	−3.25880	+	1.45091i	−0.201329	+	0.0896375i
$263$	7.24444	−	1.53985i	0.446712	−	0.0949515i	0.0209371	−	0.999781i	$-0.493335\pi$
$263$	7.24444	−	1.53985i	0.446712	−	0.0949515i	0.425774	+	0.904829i	$0.360002\pi$
$264$	−3.13957	+	9.60849i	−0.193227	+	0.591362i
$265$	−8.89561	−	0.934966i	−0.546453	−	0.0574345i
$266$	0.474844	+	0.154286i	0.0291146	+	0.00945989i
$267$	−12.5578	−	11.3448i	−0.768525	−	0.694288i
$268$	−1.14196	−	10.8650i	−0.0697561	−	0.663685i
$269$	8.76500	−	9.73452i	0.534411	−	0.593524i	−0.414114	−	0.910225i	$-0.635909\pi$
$269$	8.76500	−	9.73452i	0.534411	−	0.593524i	0.948525	+	0.316701i	$0.102575\pi$
$270$	−8.10040	−	0.892051i	−0.492975	−	0.0542885i
$271$	−7.32469	+	10.0816i	−0.444943	+	0.612412i	−0.971302	−	0.237851i	$-0.923557\pi$
$271$	−7.32469	+	10.0816i	−0.444943	+	0.612412i	0.526359	+	0.850263i	$0.323557\pi$
$272$	0.489144	−	0.355384i	0.0296587	−	0.0215483i
$273$	−0.131434	−	0.228522i	−0.00795474	−	0.0138308i
$274$		−	5.66563i		−	0.342273i
$275$	1.54967	+	14.7441i	0.0934486	+	0.889104i
$276$	−3.56572	+	3.19992i	−0.214631	+	0.192613i
$277$	−13.0445	−	11.7453i	−0.783768	−	0.705708i	0.176649	−	0.984274i	$-0.443474\pi$
$277$	−13.0445	−	11.7453i	−0.783768	−	0.705708i	−0.960417	+	0.278566i	$0.910141\pi$
$278$	0.684434			0.0410496
$279$	16.6778	+	0.921936i	0.998476	+	0.0551949i
$280$	−0.111617			−0.00667039
$281$	−16.3303	−	14.7039i	−0.974184	−	0.877160i	0.0182626	−	0.999833i	$-0.494187\pi$
$281$	−16.3303	−	14.7039i	−0.974184	−	0.877160i	−0.992447	+	0.122674i	$0.960853\pi$
$282$	6.23811	+	2.03830i	0.371474	+	0.121379i
$283$	−0.388369	−	3.69509i	−0.0230862	−	0.219650i	−0.999982	−	0.00593590i	$-0.998111\pi$
$283$	−0.388369	−	3.69509i	−0.0230862	−	0.219650i	0.976896	−	0.213714i	$-0.0685561\pi$
$284$		−	4.98447i		−	0.295774i
$285$	19.0572	+	0.0315241i	1.12885	+	0.00186733i
$286$	−10.0975	+	7.33629i	−0.597080	+	0.433804i
$287$	0.0367533	−	0.0505866i	0.00216948	−	0.00298603i
$288$	2.98251	+	0.323454i	0.175746	+	0.0190597i
$289$	−11.1306	+	12.3618i	−0.654742	+	0.727165i
$290$	1.07481	+	10.2262i	0.0631152	+	0.600501i
$291$	−6.63217	+	30.9501i	−0.388784	+	1.81432i
$292$	10.1902	+	3.31100i	0.596336	+	0.193761i
$293$	−18.7721	−	1.97302i	−1.09668	−	0.115265i	−0.461133	−	0.887331i	$-0.652557\pi$
$293$	−18.7721	−	1.97302i	−1.09668	−	0.115265i	−0.635543	+	0.772066i	$0.719224\pi$
$294$	8.09200	+	9.01703i	0.471935	+	0.525884i
$295$	−9.91682	+	2.10788i	−0.577379	+	0.122726i
$296$	5.12919	−	2.28366i	0.298128	−	0.132735i
$297$	−22.6365	+	20.1795i	−1.31350	+	1.17093i
$298$	14.6897	+	3.12239i	0.850952	+	0.180875i
$299$	−5.88325	+	0.618354i	−0.340237	+	0.0357604i
$300$	4.18680	−	1.35272i	0.241725	−	0.0780994i
$301$	−0.0658330	+	0.0906113i	−0.00379455	+	0.00522275i
$302$	−0.507720	+	0.226052i	−0.0292160	+	0.0130078i
$303$	−1.86800	−	18.0602i	−0.107314	−	1.03753i
$304$	−7.01547			−0.402365
$305$	8.79355	+	15.2309i	0.503517	+	0.872118i
$306$	1.80453	−	0.183629i	0.103158	−	0.0104974i
$307$	10.5314	+	11.6963i	0.601057	+	0.667541i	0.964502	−	0.264074i	$-0.0850664\pi$
$307$	10.5314	+	11.6963i	0.601057	+	0.667541i	−0.363446	+	0.931615i	$0.618400\pi$
$308$	−0.277921	+	0.308662i	−0.0158360	+	0.0175877i
$309$	6.74389	−	3.87873i	0.383646	−	0.220653i
$310$	8.15081	−	3.13297i	0.462935	−	0.177941i
$311$	−9.64079	−	5.56611i	−0.546679	−	0.315625i	0.201102	−	0.979570i	$-0.435548\pi$
$311$	−9.64079	−	5.56611i	−0.546679	−	0.315625i	−0.747782	+	0.663945i	$0.768881\pi$
$312$	2.74866	+	2.48315i	0.155612	+	0.140581i
$313$	−20.2407	−	6.57661i	−1.14407	−	0.371732i	−0.325166	−	0.945657i	$-0.605420\pi$
$313$	−20.2407	−	6.57661i	−1.14407	−	0.371732i	−0.818908	+	0.573925i	$0.805420\pi$
$314$	−6.64720	−	9.14908i	−0.375123	−	0.516313i
$315$	−0.289434	−	0.168384i	−0.0163078	−	0.00948736i
$316$	9.65207	+	5.57263i	0.542971	+	0.313485i
$317$	−8.20907	−	11.2988i	−0.461067	−	0.634604i	0.513663	−	0.857992i	$-0.328288\pi$
$317$	−8.20907	−	11.2988i	−0.461067	−	0.634604i	−0.974730	+	0.223388i	$0.928288\pi$
$318$	7.98205	+	5.81950i	0.447611	+	0.326341i
$319$	30.9554	+	22.4904i	1.73317	+	1.25922i
$320$	1.49159	−	0.484646i	0.0833823	−	0.0270925i
$321$	−10.5478	+	7.63678i	−0.588719	+	0.426244i
$322$	−0.187224	+	0.0608328i	−0.0104336	+	0.00339008i
$323$	−4.14897	+	0.881890i	−0.230855	+	0.0490697i
$324$	7.24599	+	5.33813i	0.402555	+	0.296563i
$325$	5.16683	+	1.67881i	0.286604	+	0.0931234i
$326$	2.39196	+	11.2533i	0.132478	+	0.623261i
$327$	−32.6166	−	3.48271i	−1.80370	−	0.192594i
$328$	−0.271502	+	0.835596i	−0.0149912	+	0.0461381i
$329$	0.200392	+	0.180434i	0.0110480	+	0.00994766i
$330$	−6.47215	+	14.4722i	−0.356280	+	0.796669i
$331$	1.44002	−	6.77477i	0.0791507	−	0.372375i	−0.920689	−	0.390298i	$-0.872372\pi$
$331$	1.44002	−	6.77477i	0.0791507	−	0.372375i	0.999839	+	0.0179230i	$0.00570537\pi$
$332$	1.23851	−	11.7836i	0.0679719	−	0.646709i
$333$	16.7456	+	1.81607i	0.917654	+	0.0995199i
$334$	8.72328	−	0.916853i	0.477317	−	0.0501680i
$335$		−	17.1339i		−	0.936127i
$336$	0.106651	+	0.0618102i	0.00581827	+	0.00337203i
$337$	−15.0450	+	1.58129i	−0.819552	+	0.0861384i	−0.505019	−	0.863108i	$-0.668515\pi$
$337$	−15.0450	+	1.58129i	−0.819552	+	0.0861384i	−0.314533	+	0.949247i	$0.601848\pi$
$338$	−1.75192	−	8.24213i	−0.0952919	−	0.448313i
$339$	6.68359	−	7.39823i	0.363003	−	0.401817i
$340$	0.821205	−	0.474123i	0.0445361	−	0.0257129i
$341$	11.6313	−	30.3409i	0.629870	−	1.64305i
$342$	−18.1918	−	10.5834i	−0.983700	−	0.572287i
$343$	0.307781	+	0.947251i	0.0166186	+	0.0511467i
$344$	0.486317	−	1.49673i	0.0262204	−	0.0806982i
$345$	−6.08624	+	4.40655i	−0.327672	+	0.237241i
$346$	−4.86607			−0.261601
$347$	−17.0035	−	29.4509i	−0.912796	−	1.58101i	−0.810097	−	0.586296i	$-0.800586\pi$
$347$	−17.0035	−	29.4509i	−0.912796	−	1.58101i	−0.102699	−	0.994713i	$-0.532748\pi$
$348$	4.63596	−	10.3664i	0.248514	−	0.555695i
$349$	1.46150	−	13.9053i	0.0782324	−	0.744332i	−0.883145	−	0.469099i	$-0.844579\pi$
$349$	1.46150	−	13.9053i	0.0782324	−	0.744332i	0.961378	−	0.275232i	$-0.0887547\pi$
$350$	0.179798	+	0.0188975i	0.00961061	+	0.00101012i
$351$	3.38150	+	10.5857i	0.180491	+	0.565021i
$352$	2.37375	−	5.33154i	0.126521	−	0.284172i
$353$	7.15746	+	22.0284i	0.380953	+	1.17245i	0.939374	+	0.342895i	$0.111407\pi$
$353$	7.15746	+	22.0284i	0.380953	+	1.17245i	−0.558421	+	0.829558i	$0.688593\pi$
$354$	10.6429	+	3.47755i	0.565662	+	0.184830i
$355$	0.817140	−	7.77457i	0.0433693	−	0.412631i
$356$	6.53790	+	7.26107i	0.346508	+	0.384836i
$357$	0.0708434	+	0.0231481i	0.00374943	+	0.00122512i
$358$	7.24391	−	9.97038i	0.382852	−	0.526951i
$359$	2.74545	+	12.9163i	0.144899	+	0.681698i	0.989289	+	0.145969i	$0.0466300\pi$
$359$	2.74545	+	12.9163i	0.144899	+	0.681698i	−0.844390	+	0.535729i	$0.820037\pi$
$360$	4.59896	+	0.993454i	0.242387	+	0.0523596i
$361$	27.6044	+	12.2903i	1.45286	+	0.646857i
$362$	17.2553	+	3.66773i	0.906920	+	0.192772i
$363$	16.1851	+	36.5148i	0.849498	+	1.91653i
$364$	0.0619065	+	0.139044i	0.00324478	+	0.00728791i
$365$	15.3514	+	6.83490i	0.803530	+	0.357755i
$366$	0.0321289	−	19.4228i	0.00167940	−	1.01525i
$367$	26.1217	+	15.0814i	1.36354	+	0.787241i	0.990093	−	0.140410i	$-0.0448420\pi$
$367$	26.1217	+	15.0814i	1.36354	+	0.787241i	0.373448	+	0.927651i	$0.378175\pi$
$368$	2.23782	−	1.62587i	0.116654	−	0.0847544i
$369$	−1.96460	+	1.75720i	−0.102273	+	0.0914762i
$370$	8.37467	−	2.72109i	0.435378	−	0.141463i
$371$	0.202944	+	0.351510i	0.0105363	+	0.0182495i
$372$	−9.52309	−	1.52011i	−0.493749	−	0.0788142i
$373$	−1.05494	+	1.82720i	−0.0546225	+	0.0946090i	−0.892044	−	0.451949i	$-0.850729\pi$
$373$	−1.05494	+	1.82720i	−0.0546225	+	0.0946090i	0.837421	+	0.546558i	$0.184062\pi$
$374$	0.733635	−	3.45148i	0.0379353	−	0.178472i
$375$	20.0423	−	4.22548i	1.03498	−	0.218203i
$376$	−3.46139	−	1.54111i	−0.178507	−	0.0794766i
$377$	12.1429	−	7.01070i	0.625391	−	0.361070i
$378$	0.183310	+	0.321172i	0.00942843	+	0.0165193i
$379$	2.28576	+	21.7476i	0.117412	+	1.11710i	0.881565	+	0.472063i	$0.156491\pi$
$379$	2.28576	+	21.7476i	0.117412	+	1.11710i	−0.764153	+	0.645035i	$0.776843\pi$
$380$	−10.9424	−	1.15009i	−0.561334	−	0.0589986i
$381$	−15.3669	−	11.2036i	−0.787271	−	0.573978i
$382$	4.72159	+	14.5316i	0.241578	+	0.743500i
$383$	1.06581	−	0.774357i	0.0544604	−	0.0395678i	−0.560222	−	0.828342i	$-0.689284\pi$
$383$	1.06581	−	0.774357i	0.0544604	−	0.0395678i	0.614682	+	0.788775i	$0.289284\pi$
$384$	−1.69360	−	0.362916i	−0.0864263	−	0.0185200i
$385$	−0.484090	+	0.435876i	−0.0246715	+	0.0222143i
$386$	6.95968	+	15.6317i	0.354238	+	0.795632i
$387$	3.51901	−	3.14752i	0.178882	−	0.159997i
$388$	5.64719	−	17.3802i	0.286692	−	0.882348i
$389$	−19.6934	−	14.3081i	−0.998497	−	0.725451i	−0.0367318	−	0.999325i	$-0.511695\pi$
$389$	−19.6934	−	14.3081i	−0.998497	−	0.725451i	−0.961765	+	0.273874i	$0.911695\pi$
$390$	3.88016	+	4.32372i	0.196480	+	0.218940i
$391$	1.11907	−	1.24285i	0.0565938	−	0.0628538i
$392$	−4.11152	−	5.65902i	−0.207663	−	0.285824i
$393$	6.04142	+	1.29459i	0.304749	+	0.0653035i
$394$	3.25603	+	7.31315i	0.164036	+	0.368431i
$395$	14.1413	+	10.2743i	0.711527	+	0.516955i
$396$	14.1985	−	10.2442i	0.713500	−	0.514790i
$397$	11.0088	−	19.0678i	0.552517	−	0.956987i	−0.445575	−	0.895244i	$-0.647001\pi$
$397$	11.0088	−	19.0678i	0.552517	−	0.956987i	0.998092	−	0.0617427i	$-0.0196658\pi$
$398$	−3.73534	+	6.46980i	−0.187236	+	0.324302i
$399$	−0.507146	−	0.700461i	−0.0253891	−	0.0350669i
$400$	−2.48477	+	0.528155i	−0.124239	+	0.0264078i
$401$	−0.202612	−	0.0430666i	−0.0101180	−	0.00215064i	0.202850	−	0.979210i	$-0.434980\pi$
$401$	−0.202612	−	0.0430666i	−0.0101180	−	0.00215064i	−0.212968	+	0.977059i	$0.568313\pi$
$402$	−9.48828	+	16.3716i	−0.473232	+	0.816540i
$403$	−8.42354	−	8.41604i	−0.419606	−	0.419233i
$404$			10.4827i			0.521532i
$405$	10.4269	+	9.51406i	0.518115	+	0.472758i
$406$	0.346751	−	0.312216i	0.0172090	−	0.0154950i
$407$	13.3277	−	29.9344i	0.660628	−	1.48380i
$408$	−1.04722	−	0.00173230i	−0.0518452	−	8.57615e-5i
$409$	18.8096	−	10.8597i	0.930073	−	0.536978i	0.0432387	−	0.999065i	$-0.486232\pi$
$409$	18.8096	−	10.8597i	0.930073	−	0.536978i	0.886835	+	0.462087i	$0.152899\pi$
$410$	−0.560461	+	1.25882i	−0.0276792	+	0.0621685i
$411$	−5.78116	+	7.92947i	−0.285164	+	0.391132i
$412$	−4.10332	+	1.82692i	−0.202156	+	0.0900057i
$413$	0.341890	+	0.307840i	0.0168233	+	0.0151478i
$414$	8.25566	−	0.840100i	0.405743	−	0.0412886i
$415$	3.86354	−	18.1765i	0.189654	−	0.892250i
$416$	−1.43102	−	1.58931i	−0.0701616	−	0.0779224i
$417$	−0.957915	−	0.698390i	−0.0469093	−	0.0342003i
$418$	−30.4265	+	27.3962i	−1.48821	+	1.33999i
$419$	−28.4041	+	25.5751i	−1.38763	+	1.24943i	−0.454088	+	0.890957i	$0.650035\pi$
$419$	−28.4041	+	25.5751i	−1.38763	+	1.24943i	−0.933541	+	0.358470i	$0.883299\pi$
$420$	0.156216	+	0.113893i	0.00762256	+	0.00555740i
$421$	19.9193	+	22.1226i	0.970807	+	1.07819i	0.996912	+	0.0785310i	$0.0250230\pi$
$421$	19.9193	+	22.1226i	0.970807	+	1.07819i	−0.0261048	+	0.999659i	$0.508310\pi$
$422$	1.97379	−	9.28594i	0.0960825	−	0.452033i
$423$	−6.65082	−	9.21805i	−0.323374	−	0.448197i
$424$	−4.23831	−	3.81619i	−0.205830	−	0.185331i
$425$	−1.40311	+	0.624704i	−0.0680608	+	0.0303026i
$426$	−5.08611	+	6.97613i	−0.246423	+	0.337995i
$427$	0.324603	−	0.729071i	0.0157087	−	0.0352822i
$428$	6.51107	−	3.75917i	0.314724	−	0.181706i
$429$	21.6181	+	0.0357603i	1.04373	+	0.00172652i
$430$	1.00390	−	2.25481i	0.0484126	−	0.108736i
$431$	−17.2379	+	15.5211i	−0.830322	+	0.747626i	−0.970138	−	0.242552i	$-0.922016\pi$
$431$	−17.2379	+	15.5211i	−0.830322	+	0.747626i	0.139816	+	0.990177i	$0.455349\pi$
$432$	−3.84419	−	3.49602i	−0.184954	−	0.168203i
$433$			0.450667i			0.0216577i	0.999941	+	0.0108288i	$0.00344699\pi$
$433$			0.450667i			0.0216577i	−0.999941	+	0.0108288i	$0.996553\pi$
$434$	−0.332419	−	0.215665i	−0.0159566	−	0.0103522i
$435$	8.93040	−	15.4090i	0.428180	−	0.738804i
$436$	18.5244	+	3.93749i	0.887159	+	0.188571i
$437$	−18.9814	+	4.03462i	−0.908004	+	0.193002i
$438$	−10.8834	−	15.0320i	−0.520030	−	0.718255i
$439$	4.99330	−	8.64864i	0.238317	−	0.412777i	−0.721914	−	0.691982i	$-0.756738\pi$
$439$	4.99330	−	8.64864i	0.238317	−	0.412777i	0.960231	+	0.279205i	$0.0900709\pi$
$440$	4.57651	−	7.92675i	0.218177	−	0.377893i
$441$	−2.12445	−	20.8770i	−0.101164	−	0.994142i
$442$	−1.04610	−	0.760034i	−0.0497577	−	0.0361511i
$443$	−13.2725	−	29.8105i	−0.630594	−	1.41634i	−0.892413	−	0.451220i	$-0.850989\pi$
$443$	−13.2725	−	29.8105i	−0.630594	−	1.41634i	0.261818	−	0.965117i	$-0.415678\pi$
$444$	−9.50891	−	2.03763i	−0.451273	−	0.0967015i
$445$	9.00717	+	12.3973i	0.426981	+	0.587689i
$446$	−1.87443	+	2.08177i	−0.0887570	+	0.0985746i
$447$	−17.3732	−	19.3593i	−0.821726	−	0.915661i
$448$	−0.0575765	−	0.0418318i	−0.00272024	−	0.00197637i
$449$	5.13950	−	15.8178i	0.242548	−	0.746486i	−0.753482	−	0.657468i	$-0.771627\pi$
$449$	5.13950	−	15.8178i	0.242548	−	0.746486i	0.996030	−	0.0890176i	$-0.0283727\pi$
$450$	−7.24003	−	2.37894i	−0.341299	−	0.112144i
$451$	2.08557	+	4.68428i	0.0982058	+	0.220574i
$452$	−4.27775	+	3.85170i	−0.201208	+	0.181169i
$453$	0.941252	+	0.201697i	0.0442239	+	0.00947656i
$454$	−8.56440	+	6.22240i	−0.401947	+	0.292032i
$455$	0.0737646	+	0.227024i	0.00345814	+	0.0106431i
$456$	9.81866	+	7.15852i	0.459801	+	0.335228i
$457$	21.7416	+	2.28514i	1.01703	+	0.106894i	0.598346	−	0.801238i	$-0.295825\pi$
$457$	21.7416	+	2.28514i	1.01703	+	0.106894i	0.418684	+	0.908132i	$0.362492\pi$
$458$	2.51208	+	23.9009i	0.117382	+	1.11681i
$459$	−2.71294	−	1.58432i	−0.126629	−	0.0739496i
$460$	3.75699	−	2.16910i	0.175171	−	0.101135i
$461$	−19.9467	−	8.88083i	−0.929009	−	0.413621i	−0.114270	−	0.993450i	$-0.536453\pi$
$461$	−19.9467	−	8.88083i	−0.929009	−	0.413621i	−0.814739	+	0.579828i	$0.803120\pi$
$462$	0.703926	−	0.148408i	0.0327496	−	0.00690454i
$463$	2.36315	−	11.1178i	0.109825	−	0.516686i	−0.888502	−	0.458872i	$-0.848254\pi$
$463$	2.36315	−	11.1178i	0.109825	−	0.516686i	0.998327	−	0.0578139i	$-0.0184130\pi$
$464$	−3.27813	+	5.67789i	−0.152183	+	0.263589i
$465$	−14.6045	−	3.93219i	−0.677267	−	0.182351i
$466$	14.0887	+	24.4024i	0.652648	+	1.13042i
$467$	−2.98617	+	0.970264i	−0.138183	+	0.0448985i	−0.377292	−	0.926094i	$-0.623145\pi$
$467$	−2.98617	+	0.970264i	−0.138183	+	0.0448985i	0.239109	+	0.970993i	$0.423145\pi$
$468$	−1.31317	−	6.28006i	−0.0607012	−	0.290296i
$469$	−0.629014	+	0.457005i	−0.0290452	+	0.0211026i
$470$	−5.14628	−	2.97120i	−0.237380	−	0.137051i
$471$	−0.0324014	+	19.5875i	−0.00149298	+	0.902546i
$472$	−5.90549	−	2.62929i	−0.271822	−	0.121023i
$473$	−3.73570	−	8.39053i	−0.171768	−	0.385797i
$474$	−7.82252	−	17.6482i	−0.359300	−	0.810608i
$475$	17.4319	+	3.70526i	0.799828	+	0.170009i
$476$	−0.0393094	−	0.0175017i	−0.00180175	−	0.000802189i
$477$	−5.23330	−	16.2896i	−0.239616	−	0.745850i
$478$	0.632581	+	2.97606i	0.0289336	+	0.136122i
$479$	−22.3071	+	30.7031i	−1.01924	+	1.40286i	−0.106503	+	0.994312i	$0.533965\pi$
$479$	−22.3071	+	30.7031i	−1.01924	+	1.40286i	−0.912736	+	0.408550i	$0.866035\pi$
$480$	−2.58211	−	0.843704i	−0.117857	−	0.0385096i
$481$	−8.03462	−	8.92335i	−0.366347	−	0.406870i
$482$	−2.08323	+	19.8206i	−0.0948885	+	0.902804i
$483$	0.324107	+	0.105902i	0.0147474	+	0.00481870i
$484$	−7.12592	−	21.9313i	−0.323906	−	0.996879i
$485$	11.6575	−	26.1832i	0.529340	−	1.18892i
$486$	−4.69431	−	14.8648i	−0.212938	−	0.674283i
$487$	−1.19534	−	0.125635i	−0.0541660	−	0.00569308i	0.0774067	−	0.997000i	$-0.475336\pi$
$487$	−1.19534	−	0.125635i	−0.0541660	−	0.00569308i	−0.131573	+	0.991307i	$0.542003\pi$
$488$	−1.17216	+	11.1523i	−0.0530612	+	0.504843i
$489$	8.13501	−	18.1905i	0.367878	−	0.822602i
$490$	−5.48524	−	9.50072i	−0.247798	−	0.429199i
$491$	−24.5139			−1.10630			−0.553149	−	0.833082i	$-0.686574\pi$
$491$	−24.5139			−1.10630			−0.553149	+	0.833082i	$0.686574\pi$
$492$	1.23262	−	0.892440i	0.0555708	−	0.0402343i
$493$	−1.22495	+	3.77000i	−0.0551688	+	0.169792i
$494$	4.63633	+	14.2692i	0.208598	+	0.642000i
$495$	23.8255	−	13.6508i	1.07088	−	0.613557i
$496$	5.37869	+	1.43865i	0.241510	+	0.0645972i
$497$	−0.307212	+	0.177369i	−0.0137803	+	0.00795608i
$498$	−13.7573	+	15.2282i	−0.616477	+	0.682394i
$499$	−4.27943	−	20.1331i	−0.191574	−	0.901283i	−0.963943	−	0.266109i	$-0.914262\pi$
$499$	−4.27943	−	20.1331i	−0.191574	−	0.901283i	0.772369	−	0.635174i	$-0.219072\pi$
$500$	−11.7610	+	1.23613i	−0.525968	+	0.0552815i
$501$	−13.1444	−	7.61795i	−0.587249	−	0.340345i
$502$		−	18.6869i		−	0.834039i
$503$	32.4263	−	3.40814i	1.44582	−	0.151962i	0.651124	−	0.758971i	$-0.274298\pi$
$503$	32.4263	−	3.40814i	1.44582	−	0.151962i	0.794695	+	0.607010i	$0.207631\pi$
$504$	−0.0861948	−	0.195333i	−0.00383942	−	0.00870083i
$505$	−1.71850	+	16.3504i	−0.0764721	+	0.727583i
$506$	3.35636	−	15.7904i	0.149208	−	0.701970i
$507$	−5.95826	+	13.3231i	−0.264615	+	0.591700i
$508$	8.15952	+	7.34687i	0.362020	+	0.325965i
$509$	2.36817	−	7.28849i	0.104967	−	0.323057i	−0.884755	−	0.466056i	$-0.845675\pi$
$509$	2.36817	−	7.28849i	0.104967	−	0.323057i	0.989723	+	0.142999i	$0.0456746\pi$
$510$	−1.63313	−	0.174380i	−0.0723161	−	0.00772169i
$511$	−0.158542	−	0.745879i	−0.00701346	−	0.0329958i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	14.6615	+	33.3751i	0.647321	+	1.47354i
$514$	−0.758538	+	0.161232i	−0.0334577	+	0.00711165i
$515$	−6.69968	+	2.17686i	−0.295223	+	0.0959238i
$516$	−2.20788	+	1.59855i	−0.0971967	+	0.0703722i
$517$	−21.0304	+	6.83321i	−0.924918	+	0.300524i
$518$	−0.323269	−	0.234869i	−0.0142036	−	0.0103195i
$519$	6.81041	+	4.96529i	0.298944	+	0.217952i
$520$	−1.97150	−	2.71353i	−0.0864559	−	0.118996i
$521$	−4.21515	−	2.43362i	−0.184669	−	0.106619i	0.404815	−	0.914398i	$-0.367336\pi$
$521$	−4.21515	−	2.43362i	−0.184669	−	0.106619i	−0.589485	+	0.807780i	$0.700669\pi$
$522$	−17.0661	+	9.77798i	−0.746963	+	0.427971i
$523$	7.04081	+	9.69084i	0.307873	+	0.423751i	0.934716	−	0.355394i	$-0.115653\pi$
$523$	7.04081	+	9.69084i	0.307873	+	0.423751i	−0.626843	+	0.779145i	$0.715653\pi$
$524$	−3.39261	−	1.10232i	−0.148207	−	0.0481553i
$525$	−0.232357	−	0.209913i	−0.0101409	−	0.00916134i
$526$	6.41403	+	3.70314i	0.279665	+	0.161465i
$527$	3.36182	+	0.174684i	0.146443	+	0.00760937i
$528$	−8.76249	+	5.03972i	−0.381338	+	0.219326i
$529$	−10.2703	+	11.4063i	−0.446534	+	0.495927i
$530$	−5.98511	−	6.64714i	−0.259977	−	0.288733i
$531$	−11.3470	−	15.7270i	−0.492418	−	0.682492i
$532$	0.249640	+	0.432390i	0.0108233	+	0.0187465i
$533$	1.87899			0.0813883
$534$	−1.74113	−	16.8336i	−0.0753463	−	0.728461i
$535$	10.7719	−	4.79598i	0.465712	−	0.207348i
$536$	6.42146	−	8.83838i	0.277365	−	0.381760i
$537$	−20.3121	+	6.56266i	−0.876530	+	0.283200i
$538$	13.0273	−	1.36923i	0.561648	−	0.0590316i
$539$	−39.9310	−	8.48760i	−1.71995	−	0.365587i
$540$	−5.42287	−	6.08315i	−0.233363	−	0.261777i
$541$	34.4192	−	15.3244i	1.47980	−	0.658847i	0.501330	−	0.865256i	$-0.332844\pi$
$541$	34.4192	−	15.3244i	1.47980	−	0.658847i	0.978466	+	0.206409i	$0.0661778\pi$
$542$	−12.1892	+	2.59089i	−0.523570	+	0.111288i
$543$	−20.4076	−	22.7404i	−0.875772	−	0.975885i
$544$	0.601303	+	0.0631995i	0.0257806	+	0.00270965i
$545$	28.2481	+	9.17836i	1.21001	+	0.393158i
$546$	0.0552369	−	0.257772i	0.00236392	−	0.0110316i
$547$	0.264995	+	2.52126i	0.0113304	+	0.107801i	0.998725	−	0.0504742i	$-0.0160733\pi$
$547$	0.264995	+	2.52126i	0.0113304	+	0.107801i	−0.987395	+	0.158275i	$0.949407\pi$
$548$	3.79105	−	4.21039i	0.161946	−	0.179859i
$549$	−19.8638	+	27.1508i	−0.847767	+	1.15877i
$550$	−8.71412	+	11.9940i	−0.371571	+	0.511424i
$551$	37.2109	−	27.0353i	1.58524	−	1.15174i
$552$	−4.79101	−	0.00792522i	−0.203919	−	0.000337320i
$553$		−	0.793191i		−	0.0337299i
$554$	−1.83480	−	17.4569i	−0.0779531	−	0.741674i
$555$	−14.4975	−	4.73706i	−0.615386	−	0.201077i
$556$	0.508634	+	0.457976i	0.0215709	+	0.0194225i
$557$	42.6518			1.80722			0.903608	−	0.428361i	$-0.140909\pi$
$557$	42.6518			1.80722			0.903608	+	0.428361i	$0.140909\pi$
$558$	11.7771	+	11.8448i	0.498566	+	0.501429i
$559$	−3.36568			−0.142353
$560$	−0.0829476	−	0.0746863i	−0.00350517	−	0.00315607i
$561$	−4.54863	+	4.08200i	−0.192043	+	0.172342i
$562$	−2.29697	−	21.8542i	−0.0968919	−	0.921864i
$563$		−	30.6074i		−	1.28995i	−0.764205	−	0.644973i	$-0.776868\pi$
$563$		−	30.6074i		−	1.28995i	0.764205	−	0.644973i	$-0.223132\pi$
$564$	3.27193	+	5.68886i	0.137773	+	0.239544i
$565$	−7.30368	+	5.30643i	−0.307268	+	0.223243i
$566$	2.18388	−	3.00585i	0.0917954	−	0.126345i
$567$	0.0711656	−	0.636551i	0.00298868	−	0.0267326i
$568$	3.33526	−	3.70419i	0.139945	−	0.155424i
$569$	−3.62372	−	34.4774i	−0.151914	−	1.44537i	−0.759187	−	0.650873i	$-0.774403\pi$
$569$	−3.62372	−	34.4774i	−0.151914	−	1.44537i	0.607273	−	0.794494i	$-0.292264\pi$
$570$	14.1412	+	12.7752i	0.592308	+	0.535094i
$571$	13.8247	+	4.49190i	0.578544	+	0.187980i	0.583648	−	0.812007i	$-0.301625\pi$
$571$	13.8247	+	4.49190i	0.578544	+	0.187980i	−0.00510427	+	0.999987i	$0.501625\pi$
$572$	−12.4129	−	1.30464i	−0.519008	−	0.0545499i
$573$	8.21967	−	25.1559i	0.343381	−	1.05090i
$574$	0.0611621	−	0.0130004i	0.00255286	−	0.000542626i
$575$	−6.41919	+	2.85801i	−0.267699	+	0.119187i
$576$	2.00001	+	2.23606i	0.0833335	+	0.0931693i
$577$	−19.8244	−	4.21380i	−0.825299	−	0.175423i	−0.224145	−	0.974556i	$-0.571959\pi$
$577$	−19.8244	−	4.21380i	−0.825299	−	0.175423i	−0.601154	+	0.799133i	$0.705292\pi$
$578$	−16.5433	+	1.73877i	−0.688111	+	0.0723234i
$579$	6.20985	−	28.9793i	0.258073	−	1.20434i
$580$	−6.04390	+	8.31871i	−0.250959	+	0.345416i
$581$	−0.770339	+	0.342977i	−0.0319590	+	0.0142291i
$582$	−25.6383	+	18.5626i	−1.06274	+	0.769444i
$583$	−33.2844			−1.37850
$584$	5.35730	+	9.27912i	0.221687	+	0.383973i
$585$	−1.01869	−	10.0106i	−0.0421176	−	0.413889i
$586$	−12.6302	−	14.0272i	−0.521747	−	0.579459i
$587$	−8.52102	+	9.46355i	−0.351700	+	0.390603i	−0.892873	−	0.450309i	$-0.851314\pi$
$587$	−8.52102	+	9.46355i	−0.351700	+	0.390603i	0.541173	+	0.840911i	$0.317981\pi$
$588$	−0.0200414	+	12.1156i	−0.000826493	+	0.499638i
$589$	−30.3666	−	24.5680i	−1.25124	−	1.01231i
$590$	−8.78008	−	5.06918i	−0.361470	−	0.208695i
$591$	2.90523	−	13.5577i	0.119505	−	0.557690i
$592$	5.33980	+	1.73501i	0.219465	+	0.0713084i
$593$	−4.30181	−	5.92093i	−0.176654	−	0.243143i	0.711504	−	0.702683i	$-0.248015\pi$
$593$	−4.30181	−	5.92093i	−0.176654	−	0.243143i	−0.888157	+	0.459539i	$0.848015\pi$
$594$	−30.3249	−	0.150490i	−1.24424	−	0.00617467i
$595$	−0.0584440	−	0.0337426i	−0.00239597	−	0.00138331i
$596$	8.82729	+	12.1497i	0.361580	+	0.497672i
$597$	11.8296	−	5.24345i	0.484153	−	0.214600i
$598$	−4.78587	−	3.47713i	−0.195709	−	0.142191i
$599$	−24.2519	+	7.87991i	−0.990905	+	0.321965i	−0.759226	−	0.650828i	$-0.774422\pi$
$599$	−24.2519	+	7.87991i	−0.990905	+	0.321965i	−0.231680	+	0.972792i	$0.574422\pi$
$600$	4.01655	+	1.79625i	0.163975	+	0.0733315i
$601$	−5.61421	+	1.82417i	−0.229009	+	0.0744094i	−0.421273	−	0.906934i	$-0.638417\pi$
$601$	−5.61421	+	1.82417i	−0.229009	+	0.0744094i	0.192265	+	0.981343i	$0.438417\pi$
$602$	−0.109554	+	0.0232865i	−0.00446510	+	0.000949086i
$603$	29.9849	−	13.2315i	1.22108	−	0.538827i
$604$	−0.528568	−	0.171742i	−0.0215071	−	0.00698808i
$605$	−7.51935	−	35.3757i	−0.305705	−	1.43823i
$606$	10.6964	−	14.6712i	0.434512	−	0.595979i
$607$	−1.08705	+	3.34559i	−0.0441219	+	0.135793i	−0.970691	−	0.240332i	$-0.922744\pi$
$607$	−1.08705	+	3.34559i	−0.0441219	+	0.135793i	0.926569	+	0.376125i	$0.122744\pi$
$608$	−5.21351	−	4.69427i	−0.211436	−	0.190378i
$609$	−0.803885	+	0.0831475i	−0.0325751	+	0.00336931i
$610$	−3.65656	+	17.2028i	−0.148050	+	0.696520i
$611$	−0.847013	+	8.05879i	−0.0342665	+	0.326024i
$612$	1.46390	+	1.07100i	0.0591745	+	0.0432926i
$613$	−44.7989	+	4.70855i	−1.80941	+	0.190177i	−0.948114	−	0.317930i	$-0.897012\pi$
$613$	−44.7989	+	4.70855i	−1.80941	+	0.190177i	−0.861294	+	0.508106i	$0.830346\pi$
$614$			15.7389i			0.635169i
$615$	2.06889	−	1.18992i	0.0834258	−	0.0479821i
$616$	−0.413071	+	0.0434155i	−0.0166431	+	0.00174926i
$617$	4.24135	+	19.9540i	0.170750	+	0.803317i	0.977251	+	0.212084i	$0.0680252\pi$
$617$	4.24135	+	19.9540i	0.170750	+	0.803317i	−0.806501	+	0.591233i	$0.798642\pi$
$618$	7.60706	+	1.63009i	0.306001	+	0.0655717i
$619$	−11.7811	+	6.80182i	−0.473523	+	0.273388i	−0.717713	−	0.696339i	$-0.754811\pi$
$619$	−11.7811	+	6.80182i	−0.473523	+	0.273388i	0.244191	+	0.969727i	$0.421478\pi$
$620$	8.15359	+	3.12571i	0.327456	+	0.125531i
$621$	−12.4116	−	7.24821i	−0.498061	−	0.290861i
$622$	−3.44005	−	10.5874i	−0.137933	−	0.424515i
$623$	0.214881	−	0.661335i	0.00860902	−	0.0264958i
$624$	0.381101	+	3.68456i	0.0152563	+	0.147500i
$625$	−5.84552			−0.233821
$626$	−10.6412	−	18.4311i	−0.425307	−	0.736654i
$627$	70.5389	−	7.29599i	2.81705	−	0.291374i
$628$	1.18210	−	11.2469i	0.0471710	−	0.448802i
$629$	3.37607	+	0.354840i	0.134613	+	0.0141484i
$630$	−0.102420	−	0.318803i	−0.00408053	−	0.0127014i
$631$	−9.04762	+	20.3213i	−0.360180	+	0.808977i	0.639028	+	0.769184i	$0.279337\pi$
$631$	−9.04762	+	20.3213i	−0.360180	+	0.808977i	−0.999208	+	0.0397939i	$0.987330\pi$
$632$	3.44407	+	10.5998i	0.136998	+	0.421636i
$633$	−12.2377	+	10.9823i	−0.486407	+	0.436508i
$634$	1.45985	−	13.8896i	0.0579782	−	0.551626i
$635$	11.5224	+	12.7970i	0.457254	+	0.507832i
$636$	2.03782	+	9.66576i	0.0808046	+	0.383272i
$637$	−8.79301	+	12.1025i	−0.348392	+	0.479520i
$638$	7.95531	+	37.4268i	0.314954	+	1.48174i
$639$	14.2368	−	4.57379i	0.563198	−	0.180936i
$640$	1.43276	+	0.637904i	0.0566347	+	0.0252154i
$641$	42.2143	+	8.97293i	1.66737	+	0.354409i	0.942429	−	0.334406i	$-0.108536\pi$
$641$	42.2143	+	8.97293i	1.66737	+	0.354409i	0.724936	+	0.688816i	$0.241869\pi$
$642$	−12.9485	−	1.38260i	−0.511038	−	0.0545671i
$643$	0.641454	+	1.44073i	0.0252965	+	0.0568168i	0.925752	−	0.378132i	$-0.123433\pi$
$643$	0.641454	+	1.44073i	0.0252965	+	0.0568168i	−0.900455	+	0.434948i	$0.856767\pi$
$644$	−0.179840	−	0.0800698i	−0.00708668	−	0.00315519i
$645$	−3.70582	+	2.13139i	−0.145917	+	0.0839234i
$646$	−3.67338	−	2.12083i	−0.144527	−	0.0834429i
$647$	−31.8550	+	23.1440i	−1.25235	+	0.909886i	−0.998356	−	0.0573202i	$-0.981744\pi$
$647$	−31.8550	+	23.1440i	−1.25235	+	0.909886i	−0.253994	+	0.967206i	$0.581744\pi$
$648$	1.81292	+	8.81552i	0.0712180	+	0.346306i
$649$	−35.8801	+	11.6582i	−1.40842	+	0.457623i
$650$	2.71636	+	4.70488i	0.106545	+	0.184541i
$651$	0.245182	+	0.641036i	0.00960943	+	0.0251242i
$652$	−5.75233	+	9.96334i	−0.225279	+	0.390194i
$653$	1.90714	−	8.97241i	0.0746323	−	0.351118i	−0.924948	−	0.380094i	$-0.875892\pi$
$653$	1.90714	−	8.97241i	0.0746323	−	0.351118i	0.999580	+	0.0289767i	$0.00922486\pi$
$654$	−21.9085	−	24.4129i	−0.856690	−	0.954622i
$655$	−5.11092	−	2.27553i	−0.199700	−	0.0889123i
$656$	−0.760888	+	0.439299i	−0.0297077	+	0.0171517i
$657$	−0.106343	+	32.1436i	−0.00414885	+	1.25404i
$658$	0.0281866	+	0.268177i	0.00109883	+	0.0104546i
$659$	−25.0660	−	2.63454i	−0.976432	−	0.102627i	−0.397149	−	0.917754i	$-0.630000\pi$
$659$	−25.0660	−	2.63454i	−0.976432	−	0.102627i	−0.579282	+	0.815127i	$0.696667\pi$
$660$	−14.4935	+	6.42423i	−0.564160	+	0.250063i
$661$	−8.43886	−	25.9721i	−0.328234	−	1.01020i	−0.969960	−	0.243265i	$-0.921781\pi$
$661$	−8.43886	−	25.9721i	−0.328234	−	1.01020i	0.641726	−	0.766934i	$-0.278219\pi$
$662$	5.60335	−	4.07107i	0.217780	−	0.158227i
$663$	0.688557	+	2.13115i	0.0267413	+	0.0827670i
$664$	8.80516	−	7.92820i	0.341706	−	0.307674i
$665$	0.318493	+	0.715348i	0.0123506	+	0.0277400i
$666$	11.2292	+	12.5546i	0.435124	+	0.486481i
$667$	−5.60410	+	17.2476i	−0.216992	+	0.667832i
$668$	7.09615	+	5.15566i	0.274558	+	0.199478i
$669$	4.74762	−	1.00093i	0.183554	−	0.0386983i
$670$	11.4648	−	12.7330i	0.442925	−	0.491919i
$671$	38.4674	+	52.9458i	1.48502	+	2.04395i
$672$	0.0378978	+	0.117297i	0.00146194	+	0.00452484i
$673$	−12.0377	−	27.0372i	−0.464021	−	1.04221i	−0.982354	−	0.187030i	$-0.940114\pi$
$673$	−12.0377	−	27.0372i	−0.464021	−	1.04221i	0.518333	−	0.855179i	$-0.326553\pi$
$674$	−12.2387	−	8.89193i	−0.471417	−	0.342504i
$675$	7.70551	+	10.7172i	0.296585	+	0.412504i
$676$	4.21313	−	7.29736i	0.162044	−	0.280668i
$677$	23.0337	−	39.8955i	0.885255	−	1.53331i	0.0398346	−	0.999206i	$-0.487317\pi$
$677$	23.0337	−	39.8955i	0.885255	−	1.53331i	0.845421	−	0.534101i	$-0.179350\pi$
$678$	9.91726	−	1.02576i	0.380870	−	0.0393942i
$679$	−1.27216	+	0.270406i	−0.0488210	+	0.0103772i
$680$	0.927525	+	0.197151i	0.0355689	+	0.00756041i
$681$	18.3358	+	0.0303308i	0.702628	+	0.00116228i
$682$	28.9458	−	14.7649i	1.10839	−	0.565375i
$683$			37.0776i			1.41874i	0.704838	+	0.709368i	$0.251020\pi$
$683$			37.0776i			1.41874i	−0.704838	+	0.709368i	$0.748980\pi$
$684$	−6.43744	−	20.0377i	−0.246142	−	0.766162i
$685$	6.60335	−	5.94568i	0.252301	−	0.227173i
$686$	−0.405109	+	0.909890i	−0.0154671	+	0.0347398i
$687$	20.8724	−	36.0143i	0.796331	−	1.37403i
$688$	1.36291	−	0.786877i	0.0519605	−	0.0299994i
$689$	−4.96098	+	11.1425i	−0.188998	+	0.424497i
$690$	−7.47151	−	0.797786i	−0.284436	−	0.0303712i
$691$	34.3935	−	15.3130i	1.30839	−	0.582534i	0.370298	−	0.928913i	$-0.379256\pi$
$691$	34.3935	−	15.3130i	1.30839	−	0.582534i	0.938095	+	0.346379i	$0.112589\pi$
$692$	−3.61619	−	3.25603i	−0.137467	−	0.123776i
$693$	−1.13663	−	0.510572i	−0.0431770	−	0.0193950i
$694$	7.07045	−	33.2639i	0.268391	−	1.26268i
$695$	0.718265	+	0.797714i	0.0272453	+	0.0302590i
$696$	10.3816	−	4.60164i	0.393515	−	0.174425i
$697$	−0.394768	+	0.355451i	−0.0149529	+	0.0134637i
$698$	10.3905	−	9.35569i	0.393288	−	0.354118i
$699$	5.18177	−	48.5289i	0.195993	−	1.83553i
$700$	0.120971	+	0.134352i	0.00457227	+	0.00507803i
$701$	−1.99952	+	9.40701i	−0.0755209	+	0.355298i	−0.999641	−	0.0268049i	$-0.991467\pi$
$701$	−1.99952	+	9.40701i	−0.0755209	+	0.355298i	0.924120	+	0.382103i	$0.124800\pi$
$702$	−4.57024	+	10.1293i	−0.172493	+	0.382308i
$703$	−29.2718	−	26.3564i	−1.10401	−	0.994052i
$704$	5.33154	−	2.37375i	0.200940	−	0.0894642i
$705$	4.17080	+	9.40962i	0.157081	+	0.354387i
$706$	−9.42084	+	21.1596i	−0.354558	+	0.796350i
$707$	0.646086	−	0.373018i	0.0242986	−	0.0140288i
$708$	5.58225	+	9.70579i	0.209794	+	0.364766i
$709$	−3.63409	+	8.16229i	−0.136481	+	0.306541i	−0.968837	−	0.247701i	$-0.920325\pi$
$709$	−3.63409	+	8.16229i	−0.136481	+	0.306541i	0.832356	+	0.554242i	$0.186992\pi$
$710$	5.80945	−	5.23085i	0.218025	−	0.196310i
$711$	−7.05985	+	32.6819i	−0.264765	+	1.22567i
$712$			9.77074i			0.366174i
$713$	15.3802	+	0.799176i	0.575994	+	0.0299294i
$714$	0.0371579	+	0.0646059i	0.00139060	+	0.00241781i
$715$	−19.1472	−	4.06985i	−0.716063	−	0.152204i
$716$	12.0548	−	2.56232i	0.450507	−	0.0957583i
$717$	2.15140	−	4.81069i	0.0803455	−	0.179658i
$718$	−6.60245	+	11.4358i	−0.246401	+	0.426779i
$719$	−2.10249	+	3.64162i	−0.0784096	+	0.135809i	−0.902564	−	0.430556i	$-0.858318\pi$
$719$	−2.10249	+	3.64162i	−0.0784096	+	0.135809i	0.824154	+	0.566365i	$0.191651\pi$
$720$	2.75295	+	3.81559i	0.102596	+	0.142199i
$721$	0.258613	+	0.187894i	0.00963126	+	0.00699752i
$722$	12.2903	+	27.6044i	0.457397	+	1.02733i
$723$	23.1404	−	25.6147i	0.860600	−	0.952620i
$724$	10.3690	+	14.2717i	0.385361	+	0.530405i
$725$	11.1442	−	12.3769i	0.413886	−	0.459667i
$726$	−12.4053	+	37.9657i	−0.460403	+	1.40904i
$727$	−24.5682	−	17.8499i	−0.911186	−	0.662015i	0.0301288	−	0.999546i	$-0.490408\pi$
$727$	−24.5682	−	17.8499i	−0.911186	−	0.662015i	−0.941314	+	0.337531i	$0.890408\pi$
$728$	−0.0470333	+	0.144754i	−0.00174317	+	0.00536493i
$729$	−8.59791	+	25.5945i	−0.318441	+	0.947943i
$730$	6.83490	+	15.3514i	0.252971	+	0.568182i
$731$	0.707113	−	0.636688i	0.0261535	−	0.0235488i
$732$	13.0203	−	14.4125i	0.481243	−	0.532700i
$733$	−41.9934	+	30.5100i	−1.55106	+	1.12691i	−0.608172	+	0.793805i	$0.708097\pi$
$733$	−41.9934	+	30.5100i	−1.55106	+	1.12691i	−0.942889	+	0.333106i	$0.891903\pi$
$734$	9.32080	+	28.6865i	0.344037	+	1.05884i
$735$	−2.01745	+	18.8940i	−0.0744147	+	0.696917i
$736$	2.75094	+	0.289136i	0.101401	+	0.0106577i
$737$	−6.66456	−	63.4091i	−0.245492	−	2.33570i
$738$	−2.63578	−	0.00872015i	−0.0970244	−	0.000320993i
$739$	26.1701	−	15.1093i	0.962683	−	0.555805i	0.0656853	−	0.997840i	$-0.479077\pi$
$739$	26.1701	−	15.1093i	0.962683	−	0.555805i	0.896998	+	0.442035i	$0.145743\pi$
$740$	8.04436	+	3.58158i	0.295717	+	0.131661i
$741$	8.07123	−	24.7016i	0.296504	−	0.907436i
$742$	−0.0843890	+	0.397019i	−0.00309802	+	0.0145750i
$743$	−4.10123	+	7.10355i	−0.150460	+	0.260604i	−0.931397	−	0.364006i	$-0.881409\pi$
$743$	−4.10123	+	7.10355i	−0.150460	+	0.260604i	0.780937	+	0.624610i	$0.214742\pi$
$744$	−6.05988	−	7.50186i	−0.222166	−	0.275031i
$745$	11.7766	+	20.3977i	0.431462	+	0.747315i
$746$	−2.00661	+	0.651986i	−0.0734671	+	0.0238709i
$747$	34.7930	−	7.27526i	1.27301	−	0.266188i
$748$	2.85469	−	2.07405i	0.104378	−	0.0758348i
$749$	−0.463383	−	0.267534i	−0.0169316	−	0.00977549i
$750$	17.7217	+	10.2708i	0.647106	+	0.375035i
$751$	48.4130	+	21.5549i	1.76662	+	0.786548i	0.987088	+	0.160181i	$0.0512078\pi$
$751$	48.4130	+	21.5549i	1.76662	+	0.786548i	0.779528	+	0.626367i	$0.215459\pi$
$752$	−1.54111	−	3.46139i	−0.0561985	−	0.126224i
$753$	−19.0680	+	26.1537i	−0.694876	+	0.953095i
$754$	13.7150	+	2.91521i	0.499471	+	0.106166i
$755$	−0.796282	−	0.354527i	−0.0289797	−	0.0129026i
$756$	−0.0786804	+	0.361335i	−0.00286158	+	0.0131416i
$757$	−0.303731	−	1.42894i	−0.0110393	−	0.0519357i	0.972283	−	0.233806i	$-0.0751182\pi$
$757$	−0.303731	−	1.42894i	−0.0110393	−	0.0519357i	−0.983322	+	0.181871i	$0.941785\pi$
$758$	−12.8533	+	17.6911i	−0.466853	+	0.642569i
$759$	−20.8099	+	18.6751i	−0.755351	+	0.677862i
$760$	−7.36224	−	8.17660i	−0.267057	−	0.296596i
$761$	−1.76824	+	16.8236i	−0.0640985	+	0.609857i	0.914572	+	0.404422i	$0.132527\pi$
$761$	−1.76824	+	16.8236i	−0.0640985	+	0.609857i	−0.978671	+	0.205434i	$0.934139\pi$
$762$	−3.92317	−	18.6084i	−0.142121	−	0.674110i
$763$	−0.416496	−	1.28184i	−0.0150782	−	0.0464058i
$764$	−6.21469	+	13.9584i	−0.224840	+	0.504998i
$765$	2.10774	+	1.91049i	0.0762056	+	0.0690737i
$766$	1.31020	+	0.137707i	0.0473394	+	0.00497557i
$767$	−1.44509	+	13.7491i	−0.0521793	+	0.496452i
$768$	−1.01575	−	1.40294i	−0.0366529	−	0.0506243i
$769$	8.69817	+	15.0657i	0.313664	+	0.543282i	0.979153	−	0.203126i	$-0.0651101\pi$
$769$	8.69817	+	15.0657i	0.313664	+	0.543282i	−0.665489	+	0.746408i	$0.731777\pi$
$770$	−0.651407			−0.0234751
$771$	1.22615	+	0.548348i	0.0441586	+	0.0197483i
$772$	−5.28759	+	16.2735i	−0.190305	+	0.585698i
$773$	10.1801	+	31.3312i	0.366153	+	1.12690i	0.949256	+	0.314505i	$0.101839\pi$
$773$	10.1801	+	31.3312i	0.366153	+	1.12690i	−0.583102	+	0.812399i	$0.698161\pi$
$774$	4.72124	+	0.0156196i	0.169701	+	0.000561436i
$775$	−12.6050	−	6.41550i	−0.452785	−	0.230452i
$776$	15.8263	−	9.13734i	0.568132	−	0.328011i
$777$	0.212781	+	0.658577i	0.00763347	+	0.0236263i
$778$	−5.06108	−	23.8105i	−0.181448	−	0.853648i
$779$	6.13001	−	0.644290i	0.219630	−	0.0230841i
$780$	−0.00960996	+	5.80949i	−0.000344092	+	0.208013i
$781$		−	29.0899i		−	1.04092i
$782$	1.66326	−	0.174816i	0.0594781	−	0.00625140i
$783$	33.8626	+	3.72909i	1.21015	+	0.133267i
$784$	0.731170	−	6.95662i	0.0261132	−	0.248451i
$785$	3.68758	−	17.3487i	0.131615	−	0.619201i
$786$	3.62340	+	5.00456i	0.129242	+	0.178507i
$787$	15.8379	+	14.2605i	0.564561	+	0.508333i	0.901260	−	0.433279i	$-0.142644\pi$
$787$	15.8379	+	14.2605i	0.564561	+	0.508333i	−0.336699	+	0.941612i	$0.609310\pi$
$788$	−2.47376	+	7.61344i	−0.0881239	+	0.271218i
$789$	−5.19825	−	11.7276i	−0.185063	−	0.417515i
$790$	3.63422	+	17.0977i	0.129300	+	0.608307i
$791$	0.389615	+	0.126594i	0.0138531	+	0.00450115i
$792$	17.4062	+	1.88771i	0.618503	+	0.0670768i
$793$	23.4580	−	4.98616i	0.833020	−	0.177064i
$794$	20.9400	−	6.80382i	0.743133	−	0.241459i
$795$	1.59392	+	15.4103i	0.0565305	+	0.546547i
$796$	−7.10504	+	2.30857i	−0.251831	+	0.0818250i
$797$	−32.8944	−	23.8992i	−1.16518	−	0.846552i	−0.174756	−	0.984612i	$-0.555914\pi$
$797$	−32.8944	−	23.8992i	−1.16518	−	0.846552i	−0.990424	+	0.138059i	$0.955914\pi$
$798$	0.0918166	−	0.859891i	0.00325027	−	0.0304398i
$799$	−1.34653	−	1.85335i	−0.0476370	−	0.0655667i
$800$	−2.19995	−	1.27014i	−0.0777800	−	0.0449063i
$801$	−14.7400	+	25.3365i	−0.520813	+	0.895221i
$802$	−0.121753	−	0.167579i	−0.00429925	−	0.00591741i
$803$	59.4709	+	19.3233i	2.09868	+	0.681904i
$804$	−18.0059	+	5.81756i	−0.635019	+	0.205169i
$805$	−0.267380	−	0.154372i	−0.00942389	−	0.00544089i
$806$	−0.628479	−	11.8908i	−0.0221372	−	0.418835i
$807$	−19.6298	−	11.3766i	−0.691003	−	0.400476i
$808$	−7.01427	+	7.79014i	−0.246761	+	0.274056i
$809$	−15.9733	−	17.7401i	−0.561591	−	0.623710i	0.393749	−	0.919218i	$-0.371178\pi$
$809$	−15.9733	−	17.7401i	−0.561591	−	0.623710i	−0.955340	+	0.295508i	$0.904511\pi$
$810$	1.38252	+	14.0473i	0.0485767	+	0.493570i
$811$	10.8836	+	18.8509i	0.382174	+	0.661946i	0.991373	−	0.131072i	$-0.0418420\pi$
$811$	10.8836	+	18.8509i	0.382174	+	0.661946i	−0.609198	+	0.793018i	$0.708509\pi$
$812$	0.466599			0.0163744
$813$	19.7034	+	8.81159i	0.691028	+	0.309036i
$814$	29.9344	−	13.3277i	1.04920	−	0.467135i
$815$	−10.6056	+	14.5974i	−0.371498	+	0.511323i
$816$	−0.777079	−	0.702016i	−0.0272032	−	0.0245755i
$817$	−10.9801	+	1.15406i	−0.384147	+	0.0403754i
$818$	21.2448	+	4.51572i	0.742807	+	0.157889i
$819$	−0.340336	+	0.304407i	−0.0118923	+	0.0106368i
$820$	−1.25882	+	0.560461i	−0.0439598	+	0.0195722i
$821$	−30.6716	+	6.51945i	−1.07045	+	0.227530i	−0.709248	−	0.704959i	$-0.750965\pi$
$821$	−30.6716	+	6.51945i	−1.07045	+	0.227530i	−0.361198	+	0.932489i	$0.617632\pi$
$822$	−9.60209	+	2.02439i	−0.334911	+	0.0706087i
$823$	37.9501	+	3.98872i	1.32286	+	0.139038i	0.739488	−	0.673169i	$-0.235067\pi$
$823$	37.9501	+	3.98872i	1.32286	+	0.139038i	0.583369	+	0.812207i	$0.301734\pi$
$824$	−4.27181	−	1.38799i	−0.148815	−	0.0483531i
$825$	24.4346	−	7.89461i	0.850702	−	0.274855i
$826$	0.0480893	+	0.457539i	0.00167324	+	0.0159198i
$827$	28.7120	−	31.8879i	0.998414	−	1.10885i	0.00435724	−	0.999991i	$-0.498613\pi$
$827$	28.7120	−	31.8879i	0.998414	−	1.10885i	0.994057	−	0.108861i	$-0.0347203\pi$
$828$	6.69729	+	4.89980i	0.232747	+	0.170280i
$829$	−22.4905	+	30.9555i	−0.781127	+	1.07513i	0.214029	+	0.976827i	$0.431341\pi$
$829$	−22.4905	+	30.9555i	−0.781127	+	1.07513i	−0.995157	+	0.0983022i	$0.968659\pi$
$830$	15.0336	−	10.9226i	0.521825	−	0.379128i
$831$	−15.2450	+	26.3045i	−0.528842	+	0.912492i
$832$		−	2.13863i		−	0.0741436i
$833$	−0.442076	−	4.20607i	−0.0153170	−	0.145732i
$834$	−0.244555	−	1.15997i	−0.00846826	−	0.0401666i
$835$	10.2231	+	9.20489i	0.353784	+	0.318548i
$836$	−40.9429			−1.41604
$837$	−4.39667	−	28.5949i	−0.151971	−	0.988385i
$838$	−38.2214			−1.32034
$839$	−6.51452	−	5.86570i	−0.224906	−	0.202506i	0.548972	−	0.835841i	$-0.315019\pi$
$839$	−6.51452	−	5.86570i	−0.224906	−	0.202506i	−0.773878	+	0.633334i	$0.781686\pi$
$840$	0.0398819	+	0.189168i	0.00137606	+	0.00652691i
$841$	−1.46178	−	13.9079i	−0.0504063	−	0.479583i
$842$			29.7689i			1.02590i
$843$	−19.0851	+	32.9304i	−0.657324	+	1.13418i
$844$	7.68032	−	5.58008i	0.264367	−	0.192074i
$845$	7.76777	−	10.6914i	0.267219	−	0.367796i
$846$	1.22556	−	11.3006i	0.0421355	−	0.388523i
$847$	−1.09814	+	1.21961i	−0.0377325	+	0.0419062i
$848$	−0.596147	−	5.67196i	−0.0204718	−	0.194776i
$849$	−6.12365	+	1.97850i	−0.210163	+	0.0679019i
$850$	−1.46072	−	0.474617i	−0.0501024	−	0.0162792i
$851$	15.4455	+	1.62338i	0.529463	+	0.0556488i
$852$	−8.44766	+	1.78101i	−0.289412	+	0.0610163i
$853$	−31.5774	+	6.71198i	−1.08119	+	0.229814i	−0.713868	−	0.700280i	$-0.753058\pi$
$853$	−31.5774	+	6.71198i	−1.08119	+	0.229814i	−0.367321	+	0.930094i	$0.619725\pi$
$854$	0.729071	−	0.324603i	0.0249483	−	0.0111077i
$855$	−6.75591	−	32.3093i	−0.231047	−	1.10495i
$856$	7.35404	+	1.56315i	0.251356	+	0.0534273i
$857$	−6.12784	+	0.644062i	−0.209323	+	0.0220007i	−0.208610	−	0.977999i	$-0.566894\pi$
$857$	−6.12784	+	0.644062i	−0.209323	+	0.0220007i	−0.000713490		1.00000i	$0.500227\pi$
$858$	16.0415	+	14.4919i	0.547646	+	0.494746i
$859$	−24.2315	+	33.3518i	−0.826769	+	1.13795i	0.161747	+	0.986832i	$0.448287\pi$
$859$	−24.2315	+	33.3518i	−0.826769	+	1.13795i	−0.988516	+	0.151118i	$0.951713\pi$
$860$	2.25481	−	1.00390i	0.0768883	−	0.0342329i
$861$	−0.0988663	−	0.0442142i	−0.00336935	−	0.00150682i
$862$	−23.1959			−0.790057
$863$	3.64666	+	6.31621i	0.124134	+	0.215006i	0.921394	−	0.388630i	$-0.127051\pi$
$863$	3.64666	+	6.31621i	0.124134	+	0.215006i	−0.797260	+	0.603636i	$0.793718\pi$
$864$	−0.517494	−	5.17032i	−0.0176055	−	0.175898i
$865$	−5.10659	−	5.67145i	−0.173629	−	0.192835i
$866$	−0.301555	+	0.334911i	−0.0102473	+	0.0113807i
$867$	24.9278	+	14.4471i	0.846592	+	0.490649i
$868$	−0.102727	−	0.382702i	−0.00348679	−	0.0129897i
$869$	56.3304	+	32.5224i	1.91088	+	1.10325i
$870$	16.9472	−	5.47550i	0.574564	−	0.185637i
$871$	−22.2206	−	7.21992i	−0.752918	−	0.244638i
$872$	11.1316	+	15.3214i	0.376965	+	0.518847i
$873$	54.8237	+	0.181378i	1.85550	+	0.00613870i
$874$	−16.8056	−	9.70274i	−0.568459	−	0.328200i
$875$	0.494694	+	0.680888i	0.0167237	+	0.0230182i
$876$	1.97039	−	18.4533i	0.0665734	−	0.623481i
$877$	−15.4713	−	11.2405i	−0.522428	−	0.379566i	0.295090	−	0.955470i	$-0.404650\pi$
$877$	−15.4713	−	11.2405i	−0.522428	−	0.379566i	−0.817518	+	0.575903i	$0.804650\pi$
$878$	9.49781	−	3.08603i	0.320536	−	0.104148i
$879$	3.36359	+	32.5198i	0.113451	+	1.09687i
$880$	8.70504	−	2.82844i	0.293447	−	0.0953467i
$881$	−56.3642	+	11.9806i	−1.89896	+	0.403636i	−0.999447	−	0.0332608i	$-0.989411\pi$
$881$	−56.3642	+	11.9806i	−1.89896	+	0.403636i	−0.899512	+	0.436897i	$0.856077\pi$
$882$	12.3907	−	16.9362i	0.417215	−	0.570270i
$883$	−44.6430	−	14.5054i	−1.50236	−	0.488145i	−0.561652	−	0.827374i	$-0.689834\pi$
$883$	−44.6430	−	14.5054i	−1.50236	−	0.488145i	−0.940704	+	0.339229i	$0.889834\pi$
$884$	−0.268839	−	1.26479i	−0.00904205	−	0.0425395i
$885$	7.11582	+	16.0538i	0.239196	+	0.539643i
$886$	10.0837	−	31.0345i	0.338769	−	1.04262i
$887$	27.0875	+	24.3897i	0.909510	+	0.818926i	0.983977	−	0.178297i	$-0.0570588\pi$
$887$	27.0875	+	24.3897i	0.909510	+	0.818926i	−0.0744667	+	0.997223i	$0.523725\pi$
$888$	−5.70306	−	7.87695i	−0.191382	−	0.264333i
$889$	0.162464	−	0.764335i	0.00544888	−	0.0256350i
$890$	−1.60179	+	15.2400i	−0.0536920	+	0.510845i
$891$	42.2883	+	31.1538i	1.41671	+	1.04369i
$892$	−2.78595	+	0.292815i	−0.0932805	+	0.00980418i
$893$			26.5813i			0.889510i
$894$	0.0430281	−	26.0117i	0.00143908	−	0.869961i
$895$	19.2225	−	2.02037i	0.642539	−	0.0675335i
$896$	−0.0147968	−	0.0696133i	−0.000494325	−	0.00232562i
$897$	3.15013	+	9.74995i	0.105180	+	0.325541i
$898$	14.4035	−	8.31589i	0.480652	−	0.277505i
$899$	−34.0733	+	13.0969i	−1.13641	+	0.436807i
$900$	−3.78857	−	6.61243i	−0.126286	−	0.220414i
$901$	−1.06557	−	3.27947i	−0.0354991	−	0.109255i
$902$	−1.58451	+	4.87662i	−0.0527584	+	0.162374i
$903$	0.177090	+	0.0791970i	0.00589320	+	0.00263551i
$904$	−5.75628			−0.191451
$905$	13.8335	+	23.9603i	0.459840	+	0.796467i
$906$	0.564525	+	0.779711i	0.0187551	+	0.0259042i
$907$	−0.414420	+	3.94295i	−0.0137606	+	0.130923i	−0.999245	−	0.0388401i	$-0.987634\pi$
$907$	−0.414420	+	3.94295i	−0.0137606	+	0.130923i	0.985485	+	0.169763i	$0.0543004\pi$
$908$	−10.5282	−	1.10656i	−0.349390	−	0.0367224i
$909$	−29.9408	+	9.61896i	−0.993074	+	0.319041i
$910$	−0.0970910	+	0.218070i	−0.00321853	+	0.00722895i
$911$	2.00550	+	6.17231i	0.0664453	+	0.204498i	0.978767	−	0.204977i	$-0.0657120\pi$
$911$	2.00550	+	6.17231i	0.0664453	+	0.204498i	−0.912321	+	0.409475i	$0.865712\pi$
$912$	2.50670	+	11.8898i	0.0830052	+	0.393710i
$913$	7.22804	−	68.7702i	0.239213	−	2.27596i
$914$	14.6281	+	16.2462i	0.483855	+	0.537375i
$915$	22.6712	−	20.3454i	0.749486	−	0.672599i
$916$	−14.1260	+	19.4427i	−0.466735	+	0.642405i
$917$	0.0527830	+	0.248324i	0.00174305	+	0.00820039i
$918$	−0.955990	−	2.99269i	−0.0315524	−	0.0987734i
$919$	−38.0347	−	16.9342i	−1.25465	−	0.558606i	−0.331649	−	0.943403i	$-0.607605\pi$
$919$	−38.0347	−	16.9342i	−1.25465	−	0.558606i	−0.923001	+	0.384796i	$0.874272\pi$
$920$	4.24340	+	0.901963i	0.139901	+	0.0297368i
$921$	16.0598	−	22.0277i	0.529188	−	0.725837i
$922$	−8.88083	−	19.9467i	−0.292474	−	0.656908i
$923$	−9.73834	−	4.33579i	−0.320541	−	0.142714i
$924$	0.622423	+	0.360730i	0.0204762	+	0.0118672i
$925$	−12.3519	−	7.13135i	−0.406126	−	0.234477i
$926$	9.19539	−	6.68085i	0.302179	−	0.219546i
$927$	−8.98331	−	10.0436i	−0.295051	−	0.329875i
$928$	−6.23537	+	2.02600i	−0.204686	+	0.0665066i
$929$	5.88743	+	10.1973i	0.193160	+	0.334563i	0.946296	−	0.323302i	$-0.104793\pi$
$929$	5.88743	+	10.1973i	0.193160	+	0.334563i	−0.753136	+	0.657865i	$0.771460\pi$
$930$	−8.22211	−	12.6945i	−0.269613	−	0.416269i
$931$	−24.5364	+	42.4982i	−0.804147	+	1.39282i
$932$	−5.85842	+	27.5617i	−0.191899	+	0.902814i
$933$	−5.98866	+	18.3280i	−0.196060	+	0.600032i
$934$	−2.86839	−	1.27709i	−0.0938565	−	0.0417876i
$935$	4.79263	−	2.76703i	0.156736	−	0.0904914i
$936$	3.22631	−	5.54568i	0.105455	−	0.181266i
$937$	−1.03424	−	9.84015i	−0.0337872	−	0.321464i	−0.998341	−	0.0575776i	$-0.981662\pi$
$937$	−1.03424	−	9.84015i	−0.0337872	−	0.321464i	0.964554	−	0.263886i	$-0.0850043\pi$
$938$	−0.773245	−	0.0812713i	−0.0252473	−	0.00265360i
$939$	−3.91378	+	36.6538i	−0.127721	+	1.19615i
$940$	−1.83630	−	5.65156i	−0.0598937	−	0.184334i
$941$	1.87859	−	1.36488i	0.0612404	−	0.0444938i	−0.556744	−	0.830684i	$-0.687950\pi$
$941$	1.87859	−	1.36488i	0.0612404	−	0.0444938i	0.617984	+	0.786190i	$0.287950\pi$
$942$	−13.1307	+	14.5347i	−0.427821	+	0.473566i
$943$	−1.80606	+	1.62618i	−0.0588132	+	0.0529557i
$944$	−2.62929	−	5.90549i	−0.0855762	−	0.192207i
$945$	−0.181958	+	0.550696i	−0.00591911	+	0.0179142i
$946$	2.83819	−	8.73505i	0.0922775	−	0.284001i
$947$	−34.7893	−	25.2759i	−1.13050	−	0.821357i	−0.144734	−	0.989471i	$-0.546233\pi$
$947$	−34.7893	−	25.2759i	−1.13050	−	0.821357i	−0.985768	+	0.168113i	$0.946233\pi$
$948$	5.99567	−	18.3494i	0.194730	−	0.595962i
$949$	15.3328	−	17.0288i	0.497725	−	0.552780i
$950$	10.4751	+	14.4177i	0.339857	+	0.467773i
$951$	−16.2160	+	17.9499i	−0.525839	+	0.582064i
$952$	−0.0175017	−	0.0393094i	−0.000567233	−	0.00127403i
$953$	−4.51817	−	3.28264i	−0.146358	−	0.106335i	0.512197	−	0.858868i	$-0.328832\pi$
$953$	−4.51817	−	3.28264i	−0.146358	−	0.106335i	−0.658555	+	0.752533i	$0.728832\pi$
$954$	7.01078	−	15.6073i	0.226982	−	0.505305i
$955$	−11.9817	+	20.7529i	−0.387719	+	0.671549i
$956$	−1.52127	+	2.63492i	−0.0492015	+	0.0852194i
$957$	27.0559	−	60.4990i	0.874593	−	1.95566i
$958$	−37.1218	+	7.89049i	−1.19935	+	0.254930i
$959$	−0.394404	−	0.0838331i	−0.0127360	−	0.00270711i
$960$	−1.35434	−	2.35477i	−0.0437110	−	0.0759997i
$961$	18.2437	+	25.0633i	0.588506	+	0.808493i
$962$		−	12.0075i		−	0.387139i
$963$	16.7116	+	15.1476i	0.538524	+	0.488125i
$964$	−14.8107	+	13.3356i	−0.477021	+	0.429512i
$965$	−10.9152	+	24.5159i	−0.351372	+	0.789195i
$966$	0.169996	+	0.295570i	0.00546954	+	0.00950981i
$967$	15.6032	−	9.00851i	0.501765	−	0.289694i	−0.227677	−	0.973737i	$-0.573113\pi$
$967$	15.6032	−	9.00851i	0.501765	−	0.289694i	0.729442	+	0.684043i	$0.239780\pi$
$968$	9.37934	−	21.0663i	0.301463	−	0.677098i
$969$	2.97709	+	6.71654i	0.0956380	+	0.215766i
$970$	26.1832	−	11.6575i	0.840691	−	0.374300i
$971$	19.2450	+	17.3282i	0.617600	+	0.556089i	0.917427	−	0.397904i	$-0.130262\pi$
$971$	19.2450	+	17.3282i	0.617600	+	0.556089i	−0.299827	+	0.953994i	$0.596929\pi$
$972$	6.45796	−	14.1878i	0.207139	−	0.455075i
$973$	0.0101274	−	0.0476457i	0.000324670	−	0.00152745i
$974$	−0.804244	−	0.893203i	−0.0257696	−	0.0286201i
$975$	0.999067	−	9.35657i	0.0319957	−	0.299650i
$976$	−8.33346	+	7.50348i	−0.266748	+	0.240181i
$977$	−25.2482	+	22.7336i	−0.807761	+	0.727311i	−0.965566	−	0.260159i	$-0.916225\pi$
$977$	−25.2482	+	22.7336i	−0.807761	+	0.727311i	0.157805	+	0.987470i	$0.449558\pi$
$978$	18.2173	−	8.07478i	0.582525	−	0.258203i
$979$	38.1558	+	42.3763i	1.21946	+	1.35435i
$980$	2.28089	−	10.7308i	0.0728605	−	0.342782i
$981$	5.75180	+	56.5229i	0.183641	+	1.80464i
$982$	−18.2174	−	16.4030i	−0.581341	−	0.523442i
$983$	−23.9456	+	10.6613i	−0.763745	+	0.340041i	−0.751369	−	0.659882i	$-0.770606\pi$
$983$	−23.9456	+	10.6613i	−0.763745	+	0.340041i	−0.0123758	+	0.999923i	$0.503939\pi$
$984$	1.51317	+	0.161572i	0.0482382	+	0.00515073i
$985$	−5.10658	+	11.4696i	−0.162709	+	0.365451i
$986$	−3.43293	+	1.98201i	−0.109327	+	0.0631199i
$987$	0.234197	−	0.404095i	0.00745456	−	0.0128625i
$988$	−6.10247	+	13.7064i	−0.194145	+	0.436058i
$989$	3.23503	−	2.91283i	0.102868	−	0.0926226i
$990$	26.8400	+	5.79789i	0.853031	+	0.184269i
$991$			9.03761i			0.287089i	0.989644	+	0.143545i	$0.0458501\pi$
$991$			9.03761i			0.287089i	−0.989644	+	0.143545i	$0.954150\pi$
$992$	3.03450	+	4.66817i	0.0963455	+	0.148215i
$993$	−11.9964	−	0.0198442i	−0.380693	−	0.000629737i
$994$	−0.346986	−	0.0737541i	−0.0110057	−	0.00233934i
$995$	−11.4606	+	2.43602i	−0.363325	+	0.0772271i
$996$	−20.4133	+	2.11139i	−0.646821	+	0.0669020i
$997$	8.02513	−	13.8999i	0.254158	−	0.440215i	−0.710508	−	0.703689i	$-0.751535\pi$
$997$	8.02513	−	13.8999i	0.254158	−	0.440215i	0.964667	+	0.263474i	$0.0848682\pi$
$998$	10.2915	−	17.8253i	0.325771	−	0.564251i
$999$	−2.90552	−	29.0293i	−0.0919267	−	0.918446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.bd.a.383.23	✓	256
9.2	odd	6		558.2.bh.a.11.15	yes	256
31.17	odd	30		558.2.bh.a.203.15	yes	256
279.110	even	30	inner	558.2.bd.a.389.23	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.bd.a.383.23	✓	256	1.1	even	1	trivial
558.2.bd.a.389.23	yes	256	279.110	even	30	inner
558.2.bh.a.11.15	yes	256	9.2	odd	6
558.2.bh.a.203.15	yes	256	31.17	odd	30

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.bd (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.743145 + 0.669131i) q^{2} +(-0.357311 - 1.69479i) q^{3} +(0.104528 + 0.994522i) q^{4} +1.56835i q^{5} +(0.868505 - 1.49857i) q^{6} +(0.0575765 - 0.0418318i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.74466 + 1.21114i) q^{9} +(-1.04943 + 1.16551i) q^{10} +(0.610038 + 5.80412i) q^{11} +(1.64816 - 0.532508i) q^{12} +(2.03396 + 0.660873i) q^{13} +(0.0707786 + 0.00743914i) q^{14} +(2.65803 - 0.560387i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-0.552343 + 0.245919i) q^{17} +(-2.85009 - 0.936485i) q^{18} +(6.86216 + 1.45860i) q^{19} +(-1.55976 + 0.163937i) q^{20} +(-0.0914690 - 0.0826335i) q^{21} +(-3.43037 + 4.72150i) q^{22} +(-2.52696 + 1.12507i) q^{23} +(1.58114 + 0.707105i) q^{24} +2.54029 q^{25} +(1.06931 + 1.85211i) q^{26} +(3.03332 + 4.21888i) q^{27} +(0.0476210 + 0.0528885i) q^{28} +(4.38699 - 4.87225i) q^{29} +(2.35027 + 1.36212i) q^{30} +(-4.96204 - 2.52550i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(9.61882 - 3.10776i) q^{33} +(-0.575023 - 0.186836i) q^{34} +(0.0656068 + 0.0903000i) q^{35} +(-1.49140 - 2.60302i) q^{36} +(-4.86239 - 2.80730i) q^{37} +(4.12359 + 5.67563i) q^{38} +(0.393289 - 3.68328i) q^{39} +(-1.26882 - 0.921852i) q^{40} +(0.835596 - 0.271502i) q^{41} +(-0.0126822 - 0.122613i) q^{42} +(-1.49673 + 0.486317i) q^{43} +(-5.70856 + 1.21339i) q^{44} +(-1.89948 - 4.30458i) q^{45} +(-2.63071 - 0.854771i) q^{46} +(0.787769 + 3.70616i) q^{47} +(0.701870 + 1.58347i) q^{48} +(-2.16155 + 6.65258i) q^{49} +(1.88780 + 1.69978i) q^{50} +(0.614140 + 0.848239i) q^{51} +(-0.444646 + 2.09189i) q^{52} +(-0.596147 + 5.67196i) q^{53} +(-0.568784 + 5.16493i) q^{54} +(-9.10288 + 0.956751i) q^{55} +0.0711685i q^{56} +(0.0201002 - 12.1511i) q^{57} +(6.52034 - 0.685316i) q^{58} +(1.34402 + 6.32310i) q^{59} +(0.835157 + 2.58489i) q^{60} +(9.71142 - 5.60689i) q^{61} +(-1.99762 - 5.19707i) q^{62} +(-0.107364 + 0.184547i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.03648 + 3.18995i) q^{65} +(9.22768 + 4.12673i) q^{66} -10.9248 q^{67} +(-0.302307 - 0.523612i) q^{68} +(2.80968 + 3.88067i) q^{69} +(-0.0116672 + 0.111006i) q^{70} +(-4.95717 - 0.521020i) q^{71} +(0.633440 - 2.93236i) q^{72} +(4.35802 - 9.78828i) q^{73} +(-1.73501 - 5.33980i) q^{74} +(-0.907671 - 4.30526i) q^{75} +(-0.733316 + 6.97704i) q^{76} +(0.277921 + 0.308662i) q^{77} +(2.75686 - 2.47405i) q^{78} +(6.55101 - 9.01670i) q^{79} +(-0.326078 - 1.53408i) q^{80} +(6.06630 - 6.64831i) q^{81} +(0.802639 + 0.357358i) q^{82} +(-11.5896 - 2.46344i) q^{83} +(0.0726197 - 0.0996055i) q^{84} +(-0.385686 - 0.866266i) q^{85} +(-1.43770 - 0.640103i) q^{86} +(-9.82498 - 5.69415i) q^{87} +(-5.05420 - 2.91805i) q^{88} +(7.90469 - 5.74310i) q^{89} +(1.46873 - 4.46993i) q^{90} +(0.144754 - 0.0470333i) q^{91} +(-1.38305 - 2.39551i) q^{92} +(-2.50722 + 9.31203i) q^{93} +(-1.89448 + 3.28134i) q^{94} +(-2.28759 + 10.7623i) q^{95} +(-0.537957 + 1.64639i) q^{96} +(-16.6947 - 7.43298i) q^{97} +(-6.05779 + 3.49747i) q^{98} +(-8.70393 - 15.1915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} + 4 q^{9} - 16 q^{15} + 32 q^{16} + 16 q^{18} - 4 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} - 268 q^{25} + 12 q^{26} - 18 q^{28} + 18 q^{30} + 22 q^{31} + 60 q^{33} - 4 q^{36}+ \cdots - 138 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 + 4 * q^9 - 16 * q^15 + 32 * q^16 + 16 * q^18 - 4 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 - 268 * q^25 + 12 * q^26 - 18 * q^28 + 18 * q^30 + 22 * q^31 + 60 * q^33 - 4 * q^36 + 72 * q^37 + 8 * q^39 + 6 * q^42 + 10 * q^43 - 24 * q^45 - 54 * q^47 + 10 * q^48 - 60 * q^49 + 28 * q^51 + 90 * q^53 - 96 * q^57 - 18 * q^58 + 6 * q^59 - 10 * q^60 - 42 * q^61 + 90 * q^62 + 124 * q^63 + 64 * q^64 + 120 * q^65 - 12 * q^66 - 16 * q^67 - 24 * q^69 - 6 * q^70 + 6 * q^71 + 8 * q^72 + 42 * q^73 - 48 * q^74 - 6 * q^76 - 90 * q^77 + 20 * q^78 - 10 * q^79 - 6 * q^80 + 8 * q^81 + 174 * q^83 - 2 * q^84 - 96 * q^86 + 100 * q^87 + 36 * q^89 - 176 * q^90 - 10 * q^91 + 18 * q^92 - 92 * q^93 - 150 * q^95 - 18 * q^97 + 48 * q^98 - 138 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more