LMFDB - Embedded newform 490.2.p.a.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(29,490)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("490.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.p (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			239.2
Character	$\chi$	$=$	490.239
Dual form			490.2.p.a.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.781831 - 0.623490i) q^{2} +(-1.29331 + 2.68559i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.77367 - 1.36165i) q^{5} +(2.68559 - 1.29331i) q^{6} +(2.64423 - 0.0897112i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-3.66926 - 4.60111i) q^{9} +O(q^{10})$	\(q+(-0.781831 - 0.623490i) q^{2} +(-1.29331 + 2.68559i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.77367 - 1.36165i) q^{5} +(2.68559 - 1.29331i) q^{6} +(2.64423 - 0.0897112i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-3.66926 - 4.60111i) q^{9} +(0.537736 + 2.17045i) q^{10} +(2.95361 - 3.70370i) q^{11} +(-2.90604 - 0.663286i) q^{12} +(4.56905 + 3.64370i) q^{13} +(-2.12328 - 1.57851i) q^{14} +(5.95074 - 3.00231i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.258025 + 0.0588925i) q^{17} +5.88504i q^{18} +3.26667 q^{19} +(0.932832 - 2.03220i) q^{20} +(-3.17889 + 7.21734i) q^{21} +(-4.61844 + 1.05413i) q^{22} +(-8.34143 + 1.90388i) q^{23} +(1.85849 + 2.33047i) q^{24} +(1.29182 + 4.83024i) q^{25} +(-1.30042 - 5.69752i) q^{26} +(8.38407 - 1.91361i) q^{27} +(0.675858 + 2.55797i) q^{28} +(-1.42612 + 6.24822i) q^{29} +(-6.52439 - 1.36292i) q^{30} +2.52180 q^{31} +(0.974928 + 0.222521i) q^{32} +(6.12669 + 12.7222i) q^{33} +(-0.165013 - 0.206920i) q^{34} +(-4.81215 - 3.44140i) q^{35} +(3.66926 - 4.60111i) q^{36} +(1.26372 + 0.288436i) q^{37} +(-2.55398 - 2.03673i) q^{38} +(-15.6947 + 7.55816i) q^{39} +(-1.99637 + 1.00722i) q^{40} +(4.33764 + 2.08890i) q^{41} +(6.98529 - 3.66074i) q^{42} +(-1.66602 - 3.45952i) q^{43} +(4.26808 + 2.05540i) q^{44} +(0.242961 + 13.1571i) q^{45} +(7.70864 + 3.71229i) q^{46} +(7.48783 + 5.97134i) q^{47} -2.98078i q^{48} +(6.98390 - 0.474434i) q^{49} +(2.00162 - 4.58187i) q^{50} +(-0.491868 + 0.616783i) q^{51} +(-2.53563 + 5.26530i) q^{52} +(8.11159 - 1.85142i) q^{53} +(-7.74804 - 3.73126i) q^{54} +(-10.2819 + 2.54737i) q^{55} +(1.06646 - 2.42129i) q^{56} +(-4.22482 + 8.77293i) q^{57} +(5.01068 - 3.99589i) q^{58} +(0.372795 - 0.179529i) q^{59} +(4.25120 + 5.13347i) q^{60} +(1.45595 - 6.37891i) q^{61} +(-1.97162 - 1.57232i) q^{62} +(-10.1152 - 11.8372i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-3.14255 - 12.6842i) q^{65} +(3.14213 - 13.7666i) q^{66} -1.23846i q^{67} +0.264661i q^{68} +(5.67504 - 24.8640i) q^{69} +(1.61661 + 5.69092i) q^{70} +(0.298956 + 1.30981i) q^{71} +(-5.73749 + 1.30955i) q^{72} +(-8.27086 + 6.59579i) q^{73} +(-0.808179 - 1.01342i) q^{74} +(-14.6428 - 2.77772i) q^{75} +(0.726902 + 3.18477i) q^{76} +(7.47775 - 10.0584i) q^{77} +(16.9830 + 3.87627i) q^{78} +9.89077 q^{79} +(2.18882 + 0.457238i) q^{80} +(-1.77541 + 7.77857i) q^{81} +(-2.08890 - 4.33764i) q^{82} +(6.43762 - 5.13383i) q^{83} +(-7.74375 - 1.49318i) q^{84} +(-0.377460 - 0.455796i) q^{85} +(-0.854430 + 3.74350i) q^{86} +(-14.9357 - 11.9109i) q^{87} +(-2.05540 - 4.26808i) q^{88} +(3.72332 + 4.66889i) q^{89} +(8.01337 - 10.4381i) q^{90} +(12.4085 + 9.22488i) q^{91} +(-3.71229 - 7.70864i) q^{92} +(-3.26147 + 6.77252i) q^{93} +(-2.13115 - 9.33717i) q^{94} +(-5.79399 - 4.44806i) q^{95} +(-1.85849 + 2.33047i) q^{96} +10.1046i q^{97} +(-5.75604 - 3.98347i) q^{98} -27.8787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$3$	−1.29331	+	2.68559i	−0.746694	+	1.55053i	0.0856874	+	0.996322i	$0.472691\pi$
$3$	−1.29331	+	2.68559i	−0.746694	+	1.55053i	−0.832381	+	0.554204i	$0.813023\pi$
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−1.77367	−	1.36165i	−0.793210	−	0.608949i
$5$	−1.77367	−	1.36165i	−0.793210	−	0.608949i
$6$	2.68559	−	1.29331i	1.09639	−	0.527992i
$7$	2.64423	−	0.0897112i	0.999425	−	0.0339076i
$7$	2.64423	−	0.0897112i	0.999425	−	0.0339076i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$	−3.66926	−	4.60111i	−1.22309	−	1.53370i
$10$	0.537736	+	2.17045i	0.170047	+	0.686356i
$11$	2.95361	−	3.70370i	0.890545	−	1.11671i	−0.101994	−	0.994785i	$-0.532522\pi$
$11$	2.95361	−	3.70370i	0.890545	−	1.11671i	0.992539	−	0.121924i	$-0.0389063\pi$
$12$	−2.90604	−	0.663286i	−0.838903	−	0.191474i
$13$	4.56905	+	3.64370i	1.26723	+	1.01058i	0.998883	+	0.0472572i	$0.0150480\pi$
$13$	4.56905	+	3.64370i	1.26723	+	1.01058i	0.268345	+	0.963323i	$0.413523\pi$
$14$	−2.12328	−	1.57851i	−0.567469	−	0.421875i
$15$	5.95074	−	3.00231i	1.53648	−	0.775194i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.258025	+	0.0588925i	0.0625803	+	0.0142835i	0.253696	−	0.967284i	$-0.418354\pi$
$17$	0.258025	+	0.0588925i	0.0625803	+	0.0142835i	−0.191116	+	0.981567i	$0.561211\pi$
$18$			5.88504i			1.38712i
$19$	3.26667			0.749425			0.374712	−	0.927141i	$-0.377741\pi$
$19$	3.26667			0.749425			0.374712	+	0.927141i	$0.377741\pi$
$20$	0.932832	−	2.03220i	0.208588	−	0.454413i
$21$	−3.17889	+	7.21734i	−0.693690	+	1.57495i
$22$	−4.61844	+	1.05413i	−0.984655	+	0.224741i
$23$	−8.34143	+	1.90388i	−1.73931	+	0.396986i	−0.970233	−	0.242172i	$-0.922140\pi$
$23$	−8.34143	+	1.90388i	−1.73931	+	0.396986i	−0.769076	+	0.639158i	$0.779283\pi$
$24$	1.85849	+	2.33047i	0.379362	+	0.475705i
$25$	1.29182	+	4.83024i	0.258363	+	0.966048i
$26$	−1.30042	−	5.69752i	−0.255034	−	1.11737i
$27$	8.38407	−	1.91361i	1.61351	−	0.368274i
$28$	0.675858	+	2.55797i	0.127725	+	0.483411i
$29$	−1.42612	+	6.24822i	−0.264823	+	1.16027i	0.651126	+	0.758970i	$0.274297\pi$
$29$	−1.42612	+	6.24822i	−0.264823	+	1.16027i	−0.915949	+	0.401295i	$0.868560\pi$
$30$	−6.52439	−	1.36292i	−1.19119	−	0.248835i
$31$	2.52180			0.452929			0.226464	−	0.974019i	$-0.427283\pi$
$31$	2.52180			0.452929			0.226464	+	0.974019i	$0.427283\pi$
$32$	0.974928	+	0.222521i	0.172345	+	0.0393365i
$33$	6.12669	+	12.7222i	1.06652	+	2.21465i
$34$	−0.165013	−	0.206920i	−0.0282995	−	0.0354865i
$35$	−4.81215	−	3.44140i	−0.813402	−	0.581703i
$36$	3.66926	−	4.60111i	0.611544	−	0.766852i
$37$	1.26372	+	0.288436i	0.207754	+	0.0474185i	0.325131	−	0.945669i	$-0.394591\pi$
$37$	1.26372	+	0.288436i	0.207754	+	0.0474185i	−0.117377	+	0.993087i	$0.537449\pi$
$38$	−2.55398	−	2.03673i	−0.414311	−	0.330402i
$39$	−15.6947	+	7.55816i	−2.51316	+	1.21027i
$40$	−1.99637	+	1.00722i	−0.315654	+	0.159256i
$41$	4.33764	+	2.08890i	0.677426	+	0.326231i	0.740768	−	0.671761i	$-0.234462\pi$
$41$	4.33764	+	2.08890i	0.677426	+	0.326231i	−0.0633424	+	0.997992i	$0.520176\pi$
$42$	6.98529	−	3.66074i	1.07785	−	0.564865i
$43$	−1.66602	−	3.45952i	−0.254065	−	0.527571i	0.734456	−	0.678657i	$-0.237438\pi$
$43$	−1.66602	−	3.45952i	−0.254065	−	0.527571i	−0.988521	+	0.151085i	$0.951723\pi$
$44$	4.26808	+	2.05540i	0.643438	+	0.309863i
$45$	0.242961	+	13.1571i	0.0362185	+	1.96135i
$46$	7.70864	+	3.71229i	1.13658	+	0.547347i
$47$	7.48783	+	5.97134i	1.09221	+	0.871010i	0.992284	−	0.123985i	$-0.0395675\pi$
$47$	7.48783	+	5.97134i	1.09221	+	0.871010i	0.0999276	+	0.994995i	$0.468139\pi$
$48$		−	2.98078i		−	0.430238i
$49$	6.98390	−	0.474434i	0.997701	−	0.0677763i
$50$	2.00162	−	4.58187i	0.283072	−	0.647974i
$51$	−0.491868	+	0.616783i	−0.0688753	+	0.0863669i
$52$	−2.53563	+	5.26530i	−0.351629	+	0.730165i
$53$	8.11159	−	1.85142i	1.11421	−	0.254312i	0.374495	−	0.927229i	$-0.377816\pi$
$53$	8.11159	−	1.85142i	1.11421	−	0.254312i	0.739718	+	0.672917i	$0.234959\pi$
$54$	−7.74804	−	3.73126i	−1.05438	−	0.507760i
$55$	−10.2819	+	2.54737i	−1.38641	+	0.343488i
$56$	1.06646	−	2.42129i	0.142512	−	0.323559i
$57$	−4.22482	+	8.77293i	−0.559591	+	1.16200i
$58$	5.01068	−	3.99589i	0.657935	−	0.524686i
$59$	0.372795	−	0.179529i	0.0485338	−	0.0233727i	−0.409459	−	0.912328i	$-0.634283\pi$
$59$	0.372795	−	0.179529i	0.0485338	−	0.0233727i	0.457993	+	0.888956i	$0.348568\pi$
$60$	4.25120	+	5.13347i	0.548828	+	0.662728i
$61$	1.45595	−	6.37891i	0.186415	−	0.816736i	−0.792072	−	0.610427i	$-0.790998\pi$
$61$	1.45595	−	6.37891i	0.186415	−	0.816736i	0.978487	−	0.206309i	$-0.0661452\pi$
$62$	−1.97162	−	1.57232i	−0.250396	−	0.199684i
$63$	−10.1152	−	11.8372i	−1.27439	−	1.49135i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−3.14255	−	12.6842i	−0.389786	−	1.57328i
$66$	3.14213	−	13.7666i	0.386769	−	1.69455i
$67$		−	1.23846i		−	0.151303i	−0.997134	−	0.0756513i	$-0.975896\pi$
$67$		−	1.23846i		−	0.151303i	0.997134	−	0.0756513i	$-0.0241036\pi$
$68$			0.264661i			0.0320948i
$69$	5.67504	−	24.8640i	0.683194	−	2.99327i
$70$	1.61661	+	5.69092i	0.193222	+	0.680195i
$71$	0.298956	+	1.30981i	0.0354795	+	0.155446i	0.989565	−	0.144090i	$-0.0460254\pi$
$71$	0.298956	+	1.30981i	0.0354795	+	0.155446i	−0.954085	+	0.299536i	$0.903168\pi$
$72$	−5.73749	+	1.30955i	−0.676170	+	0.154331i
$73$	−8.27086	+	6.59579i	−0.968031	+	0.771979i	−0.973660	−	0.228005i	$-0.926780\pi$
$73$	−8.27086	+	6.59579i	−0.968031	+	0.771979i	0.00562880	+	0.999984i	$0.498208\pi$
$74$	−0.808179	−	1.01342i	−0.0939489	−	0.117808i
$75$	−14.6428	−	2.77772i	−1.69080	−	0.320743i
$76$	0.726902	+	3.18477i	0.0833814	+	0.365318i
$77$	7.47775	−	10.0584i	0.852168	−	1.14626i
$78$	16.9830	+	3.87627i	1.92295	+	0.438901i
$79$	9.89077			1.11280			0.556400	−	0.830915i	$-0.312182\pi$
$79$	9.89077			1.11280			0.556400	+	0.830915i	$0.312182\pi$
$80$	2.18882	+	0.457238i	0.244718	+	0.0511207i
$81$	−1.77541	+	7.77857i	−0.197268	+	0.864285i
$82$	−2.08890	−	4.33764i	−0.230680	−	0.479012i
$83$	6.43762	−	5.13383i	0.706621	−	0.563511i	−0.202885	−	0.979203i	$-0.565032\pi$
$83$	6.43762	−	5.13383i	0.706621	−	0.563511i	0.909506	+	0.415691i	$0.136460\pi$
$84$	−7.74375	−	1.49318i	−0.844913	−	0.162919i
$85$	−0.377460	−	0.455796i	−0.0409413	−	0.0494380i
$86$	−0.854430	+	3.74350i	−0.0921356	+	0.403672i
$87$	−14.9357	−	11.9109i	−1.60128	−	1.27698i
$88$	−2.05540	−	4.26808i	−0.219106	−	0.454979i
$89$	3.72332	+	4.66889i	0.394671	+	0.494902i	0.938975	−	0.343987i	$-0.111778\pi$
$89$	3.72332	+	4.66889i	0.394671	+	0.494902i	−0.544304	+	0.838888i	$0.683206\pi$
$90$	8.01337	−	10.4381i	0.844684	−	1.10028i
$91$	12.4085	+	9.22488i	1.30077	+	0.967030i
$92$	−3.71229	−	7.70864i	−0.387033	−	0.803682i
$93$	−3.26147	+	6.77252i	−0.338199	+	0.702277i
$94$	−2.13115	−	9.33717i	−0.219811	−	0.963055i
$95$	−5.79399	−	4.44806i	−0.594451	−	0.456361i
$96$	−1.85849	+	2.33047i	−0.189681	+	0.237852i
$97$			10.1046i			1.02597i	0.858397	+	0.512986i	$0.171461\pi$
$97$			10.1046i			1.02597i	−0.858397	+	0.512986i	$0.828539\pi$
$98$	−5.75604	−	3.98347i	−0.581448	−	0.402391i
$99$	−27.8787			−2.80192
$100$	−4.42168	+	2.33426i	−0.442168	+	0.233426i
$101$	8.58484	+	4.13424i	0.854224	+	0.411372i	0.809144	−	0.587611i	$-0.199931\pi$
$101$	8.58484	+	4.13424i	0.854224	+	0.411372i	0.0450801	+	0.998983i	$0.485646\pi$
$102$	0.769116	−	0.175546i	0.0761538	−	0.0173816i
$103$	−3.86741	+	8.03076i	−0.381067	+	0.791294i	0.618916	+	0.785457i	$0.287572\pi$
$103$	−3.86741	+	8.03076i	−0.381067	+	0.791294i	−0.999983	+	0.00583690i	$0.998142\pi$
$104$	5.26530	−	2.53563i	0.516305	−	0.248639i
$105$	15.4658	−	8.47265i	1.50931	−	0.826846i
$106$	−7.49623	−	3.61000i	−0.728099	−	0.350634i
$107$	7.66171	−	6.11001i	0.740686	−	0.590677i	−0.178761	−	0.983893i	$-0.557209\pi$
$107$	7.66171	−	6.11001i	0.740686	−	0.590677i	0.919446	+	0.393215i	$0.128637\pi$
$108$	3.73126	+	7.74804i	0.359041	+	0.745556i
$109$	−0.480100	+	0.602026i	−0.0459852	+	0.0576636i	−0.804292	−	0.594234i	$-0.797455\pi$
$109$	−0.480100	+	0.602026i	−0.0459852	+	0.0576636i	0.758307	+	0.651898i	$0.226027\pi$
$110$	9.62695	+	4.41903i	0.917894	+	0.421338i
$111$	−2.40900	+	3.02079i	−0.228652	+	0.286721i
$112$	−2.34344	+	1.22812i	−0.221435	+	0.116046i
$113$	−11.5225	+	9.18889i	−1.08395	+	0.864418i	−0.991345	−	0.131285i	$-0.958090\pi$
$113$	−11.5225	+	9.18889i	−1.08395	+	0.864418i	−0.0926012	+	0.995703i	$0.529518\pi$
$114$	8.77293	−	4.22482i	0.821660	−	0.395691i
$115$	17.3874	+	7.98127i	1.62138	+	0.744257i
$116$	−6.40890			−0.595052
$117$		−	34.3924i		−	3.17958i
$118$	−0.403398	−	0.0920729i	−0.0371358	−	0.00847600i
$119$	0.687561	+	0.132578i	0.0630286	+	0.0121534i
$120$	−0.123060	−	6.66409i	−0.0112338	−	0.608345i
$121$	−2.54591	−	11.1544i	−0.231446	−	1.01403i
$122$	−5.11549	+	4.07947i	−0.463135	+	0.369338i
$123$	−11.2198	+	8.94753i	−1.01166	+	0.806771i
$124$	0.561153	+	2.45857i	0.0503930	+	0.220786i
$125$	4.28584	−	10.3263i	0.383337	−	0.923608i
$126$	0.527954	+	15.5614i	0.0470339	+	1.38632i
$127$	−3.85366	−	0.879572i	−0.341957	−	0.0780494i	0.0480939	−	0.998843i	$-0.484685\pi$
$127$	−3.85366	−	0.879572i	−0.341957	−	0.0780494i	−0.390051	+	0.920793i	$0.627542\pi$
$128$			1.00000i			0.0883883i
$129$	11.4455			1.00772
$130$	−5.45151	+	11.8762i	−0.478129	+	1.04161i
$131$	−20.0551	+	9.65803i	−1.75222	+	0.843826i	−0.774896	+	0.632088i	$0.782198\pi$
$131$	−20.0551	+	9.65803i	−1.75222	+	0.843826i	−0.977327	+	0.211738i	$0.932088\pi$
$132$	−11.0399	+	8.80404i	−0.960902	+	0.766294i
$133$	8.63782	−	0.293057i	0.748994	−	0.0254112i
$134$	−0.772170	+	0.968271i	−0.0667053	+	0.0836459i
$135$	−17.4762	−	8.02206i	−1.50412	−	0.690429i
$136$	0.165013	−	0.206920i	0.0141498	−	0.0177432i
$137$	0.967783	+	2.00962i	0.0826833	+	0.171694i	0.938211	−	0.346063i	$-0.112482\pi$
$137$	0.967783	+	2.00962i	0.0826833	+	0.171694i	−0.855528	+	0.517756i	$0.826767\pi$
$138$	−19.9394	+	15.9011i	−1.69735	+	1.35359i
$139$	−6.98718	−	3.36485i	−0.592645	−	0.285403i	0.113423	−	0.993547i	$-0.463819\pi$
$139$	−6.98718	−	3.36485i	−0.592645	−	0.285403i	−0.706068	+	0.708144i	$0.749533\pi$
$140$	2.28431	−	5.45728i	0.193060	−	0.461224i
$141$	−25.7207	+	12.3864i	−2.16607	+	1.04312i
$142$	0.582921	−	1.21045i	0.0489176	−	0.101579i
$143$	26.9904	−	6.16037i	2.25705	−	0.515156i
$144$	5.30224	+	2.55342i	0.441853	+	0.212785i
$145$	11.0374	−	9.14041i	0.916602	−	0.759070i
$146$	10.5788			0.875510
$147$	−7.75823	+	19.3695i	−0.639888	+	1.59757i
$148$			1.29622i			0.106548i
$149$	1.05280	−	1.32017i	0.0862485	−	0.108152i	−0.736835	−	0.676073i	$-0.763680\pi$
$149$	1.05280	−	1.32017i	0.0862485	−	0.108152i	0.823083	+	0.567921i	$0.192252\pi$
$150$	9.71629	+	11.3013i	0.793332	+	0.922749i
$151$	−2.53351	−	11.1000i	−0.206174	−	0.903307i	−0.967086	−	0.254451i	$-0.918105\pi$
$151$	−2.53351	−	11.1000i	−0.206174	−	0.903307i	0.760912	−	0.648856i	$-0.224752\pi$
$152$	1.41735	−	2.94317i	0.114963	−	0.238722i
$153$	−0.675791	−	1.40329i	−0.0546345	−	0.113450i
$154$	−12.1177	+	3.20169i	−0.976469	+	0.257999i
$155$	−4.47284	−	3.43381i	−0.359267	−	0.275810i
$156$	−10.8611	−	13.6193i	−0.869581	−	1.09042i
$157$	−6.34446	−	13.1744i	−0.506343	−	1.05143i	−0.984860	−	0.173353i	$-0.944540\pi$
$157$	−6.34446	−	13.1744i	−0.506343	−	1.05143i	0.478517	−	0.878078i	$-0.341175\pi$
$158$	−7.73292	−	6.16680i	−0.615198	−	0.490604i
$159$	−5.51867	+	24.1789i	−0.437659	+	1.91751i
$160$	−1.42621	−	1.72219i	−0.112751	−	0.136151i
$161$	−21.8859	+	5.78261i	−1.72485	+	0.455734i
$162$	6.23793	−	4.97458i	0.490098	−	0.390840i
$163$	−7.10836	−	14.7607i	−0.556770	−	1.15615i	−0.969455	−	0.245271i	$-0.921123\pi$
$163$	−7.10836	−	14.7607i	−0.556770	−	1.15615i	0.412684	−	0.910874i	$-0.364591\pi$
$164$	−1.07131	+	4.69371i	−0.0836552	+	0.366517i
$165$	6.45647	−	30.9074i	0.502635	−	2.40614i
$166$	−8.23403			−0.639085
$167$	−14.3788	−	3.28188i	−1.11267	−	0.253959i	−0.373600	−	0.927590i	$-0.621877\pi$
$167$	−14.3788	−	3.28188i	−1.11267	−	0.253959i	−0.739068	+	0.673631i	$0.764734\pi$
$168$	5.12333	+	5.99556i	0.395274	+	0.462568i
$169$	4.70694	+	20.6224i	0.362072	+	1.58634i
$170$	0.0109264	+	0.591698i	0.000838015	+	0.0453812i
$171$	−11.9863	−	15.0303i	−0.916613	−	1.14940i
$172$	3.00206	−	2.39406i	0.228905	−	0.182545i
$173$	14.7368	−	3.36358i	1.12042	−	0.255728i	0.378093	−	0.925768i	$-0.376580\pi$
$173$	14.7368	−	3.36358i	1.12042	−	0.255728i	0.742325	+	0.670040i	$0.233723\pi$
$174$	4.25093	+	18.6246i	0.322263	+	1.41192i
$175$	3.84919	+	12.6564i	0.290971	+	0.956732i
$176$	−1.05413	+	4.61844i	−0.0794580	+	0.348128i
$177$			1.23336i			0.0927052i
$178$		−	5.97174i		−	0.447601i
$179$	3.78794	−	16.5961i	0.283124	−	1.24045i	−0.610639	−	0.791909i	$-0.709087\pi$
$179$	3.78794	−	16.5961i	0.283124	−	1.24045i	0.893763	−	0.448539i	$-0.148055\pi$
$180$	−12.7732	+	3.16460i	−0.952056	+	0.235876i
$181$	4.90742	+	6.15371i	0.364766	+	0.457402i	0.930017	−	0.367517i	$-0.119792\pi$
$181$	4.90742	+	6.15371i	0.364766	+	0.457402i	−0.565251	+	0.824919i	$0.691221\pi$
$182$	−3.94974	−	14.9489i	−0.292774	−	1.10808i
$183$	15.2482	+	12.1600i	1.12718	+	0.898893i
$184$	−1.90388	+	8.34143i	−0.140356	+	0.614939i
$185$	−1.84867	−	2.23233i	−0.135917	−	0.164124i
$186$	6.77252	−	3.26147i	0.496585	−	0.239143i
$187$	0.980225	−	0.781703i	0.0716811	−	0.0571638i
$188$	−4.15543	+	8.62884i	−0.303066	+	0.629323i
$189$	21.9977	−	5.81217i	1.60010	−	0.422773i
$190$	1.75661	+	7.09013i	0.127438	+	0.514372i
$191$	−14.4054	−	6.93728i	−1.04234	−	0.501964i	−0.167244	−	0.985916i	$-0.553487\pi$
$191$	−14.4054	−	6.93728i	−1.04234	−	0.501964i	−0.875095	+	0.483952i	$0.839201\pi$
$192$	2.90604	−	0.663286i	0.209726	−	0.0478685i
$193$	0.0699499	−	0.145252i	0.00503510	−	0.0104555i	−0.898436	−	0.439104i	$-0.855296\pi$
$193$	0.0699499	−	0.145252i	0.00503510	−	0.0104555i	0.903471	+	0.428649i	$0.141010\pi$
$194$	6.30015	−	7.90013i	0.452324	−	0.567197i
$195$	38.1288	+	7.96498i	2.73046	+	0.570384i
$196$	2.01660	+	6.70323i	0.144043	+	0.478802i
$197$			5.24342i			0.373578i	0.982400	+	0.186789i	$0.0598081\pi$
$197$			5.24342i			0.373578i	−0.982400	+	0.186789i	$0.940192\pi$
$198$	21.7965	+	17.3821i	1.54901	+	1.23529i
$199$	15.5880	+	7.50680i	1.10501	+	0.532143i	0.895229	−	0.445606i	$-0.147012\pi$
$199$	15.5880	+	7.50680i	1.10501	+	0.532143i	0.209778	+	0.977749i	$0.432726\pi$
$200$	4.91239	+	0.931876i	0.347359	+	0.0658936i
$201$	3.32601	+	1.60172i	0.234598	+	0.112977i
$202$	−4.13424	−	8.58484i	−0.290884	−	0.604027i
$203$	−3.21044	+	16.6497i	−0.225329	+	1.16858i
$204$	−0.710770	−	0.342289i	−0.0497638	−	0.0239650i
$205$	−4.84920	−	9.61137i	−0.338683	−	0.671287i
$206$	8.03076	−	3.86741i	0.559530	−	0.269455i
$207$	39.3669	+	31.3940i	2.73619	+	2.18204i
$208$	−5.69752	−	1.30042i	−0.395052	−	0.0901680i
$209$	9.64845	−	12.0988i	0.667397	−	0.836889i
$210$	−17.3743	−	3.01858i	−1.19894	−	0.208301i
$211$	2.38262	+	2.98771i	0.164026	+	0.205683i	0.857051	−	0.515231i	$-0.172294\pi$
$211$	2.38262	+	2.98771i	0.164026	+	0.205683i	−0.693025	+	0.720914i	$0.743722\pi$
$212$	3.61000	+	7.49623i	0.247936	+	0.514844i
$213$	−3.90426	−	0.891122i	−0.267515	−	0.0610587i
$214$	−9.79970			−0.669894
$215$	−1.75569	+	8.40458i	−0.119737	+	0.573187i
$216$	1.91361	−	8.38407i	0.130205	−	0.570463i
$217$	6.66822	−	0.226234i	0.452668	−	0.0153577i
$218$	0.750714	−	0.171346i	0.0508448	−	0.0116050i
$219$	−7.01679	−	30.7426i	−0.474150	−	2.07739i
$220$	−4.77144	−	9.45724i	−0.321690	−	0.637607i
$221$	0.964344	+	1.20925i	0.0648688	+	0.0813429i
$222$	3.76687	−	0.859763i	0.252816	−	0.0577035i
$223$	7.87948	−	1.79844i	0.527649	−	0.120432i	0.0496060	−	0.998769i	$-0.484203\pi$
$223$	7.87948	−	1.79844i	0.527649	−	0.120432i	0.478043	+	0.878336i	$0.341346\pi$
$224$	2.59790	+	0.500935i	0.173579	+	0.0334701i
$225$	17.4845	−	23.6672i	1.16563	−	1.57781i
$226$	14.7378			0.980346
$227$		−	8.96071i		−	0.594743i	−0.954762	−	0.297371i	$-0.903890\pi$
$227$		−	8.96071i		−	0.594743i	0.954762	−	0.297371i	$-0.0961100\pi$
$228$	−9.49308	−	2.16673i	−0.628695	−	0.143495i
$229$	11.2599	−	5.42248i	0.744074	−	0.358327i	−0.0231281	−	0.999733i	$-0.507363\pi$
$229$	11.2599	−	5.42248i	0.744074	−	0.358327i	0.767202	+	0.641405i	$0.221648\pi$
$230$	−8.61776	−	17.0809i	−0.568238	−	1.12628i
$231$	17.3417	+	33.0908i	1.14100	+	2.17722i
$232$	5.01068	+	3.99589i	0.328967	+	0.262343i
$233$	15.7572	+	3.59647i	1.03229	+	0.235613i	0.704922	−	0.709285i	$-0.250982\pi$
$233$	15.7572	+	3.59647i	1.03229	+	0.235613i	0.327365	+	0.944898i	$0.393839\pi$
$234$	−21.4433	+	26.8891i	−1.40179	+	1.75779i
$235$	−5.15006	−	20.7870i	−0.335953	−	1.35599i
$236$	0.257982	+	0.323500i	0.0167932	+	0.0210580i
$237$	−12.7919	+	26.5626i	−0.830920	+	1.72542i
$238$	−0.454896	−	0.532341i	−0.0294865	−	0.0345065i
$239$	25.6531	−	12.3539i	1.65936	−	0.799105i	0.660526	−	0.750803i	$-0.270333\pi$
$239$	25.6531	−	12.3539i	1.65936	−	0.799105i	0.998833	−	0.0483015i	$-0.0153808\pi$
$240$	−4.05878	+	5.28692i	−0.261993	+	0.341269i
$241$	−0.555229	−	2.43262i	−0.0357654	−	0.156699i	0.953892	−	0.300151i	$-0.0970369\pi$
$241$	−0.555229	−	2.43262i	−0.0357654	−	0.156699i	−0.989657	+	0.143452i	$0.954180\pi$
$242$	−4.96415	+	10.3082i	−0.319108	+	0.662634i
$243$	1.57661	+	1.25731i	0.101140	+	0.0806562i
$244$	6.54296			0.418870
$245$	−13.0332	−	8.66815i	−0.832658	−	0.553788i
$246$	14.3507			0.914968
$247$	14.9256	+	11.9028i	0.949692	+	0.757354i
$248$	1.09417	−	2.27206i	0.0694797	−	0.144276i
$249$	5.46151	+	23.9285i	0.346109	+	1.51640i
$250$	−9.78912	+	5.40121i	−0.619118	+	0.341603i
$251$	−24.5531	+	11.8241i	−1.54978	+	0.746334i	−0.996252	−	0.0864987i	$-0.972432\pi$
$251$	−24.5531	+	11.8241i	−1.54978	+	0.746334i	−0.553526	+	0.832832i	$0.686718\pi$
$252$	9.28961	−	12.4956i	0.585190	−	0.787147i
$253$	−17.5859	+	36.5175i	−1.10562	+	2.29584i
$254$	2.46451	+	3.09039i	0.154637	+	0.193908i
$255$	1.71225	−	0.424218i	0.107226	−	0.0265655i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−24.3944	−	5.56786i	−1.52168	−	0.347314i	−0.621705	−	0.783252i	$-0.713560\pi$
$257$	−24.3944	−	5.56786i	−1.52168	−	0.347314i	−0.899977	+	0.435938i	$0.856417\pi$
$258$	−8.94847	−	7.13616i	−0.557107	−	0.444278i
$259$	3.36744	+	0.649320i	0.209243	+	0.0403468i
$260$	11.6669	−	5.88626i	0.723549	−	0.365050i
$261$	33.9816	−	16.3647i	2.10341	−	1.01295i
$262$	21.7014	+	4.95320i	1.34072	+	0.306010i
$263$		−	28.7740i		−	1.77428i	−0.461500	−	0.887140i	$-0.652689\pi$
$263$		−	28.7740i		−	1.77428i	0.461500	−	0.887140i	$-0.347311\pi$
$264$	14.1206			0.869062
$265$	−16.9083	−	7.76134i	−1.03867	−	0.476776i
$266$	−6.93604	−	5.15647i	−0.425276	−	0.316164i
$267$	−17.3541	+	3.96097i	−1.06206	+	0.242407i
$268$	1.20741	−	0.275584i	0.0737545	−	0.0168340i
$269$	13.3930	+	16.7943i	0.816587	+	1.02397i	0.999168	+	0.0407768i	$0.0129833\pi$
$269$	13.3930	+	16.7943i	0.816587	+	1.02397i	−0.182581	+	0.983191i	$0.558445\pi$
$270$	8.66180	+	17.1682i	0.527141	+	1.04482i
$271$	−5.14565	−	22.5446i	−0.312576	−	1.36949i	−0.850270	−	0.526346i	$-0.823562\pi$
$271$	−5.14565	−	22.5446i	−0.312576	−	1.36949i	0.537694	−	0.843140i	$-0.319296\pi$
$272$	−0.258025	+	0.0588925i	−0.0156451	+	0.00357088i
$273$	−40.8223	+	21.3935i	−2.47068	+	1.29479i
$274$	0.496335	−	2.17459i	0.0299847	−	0.131372i
$275$	21.7053	+	9.48212i	1.30888	+	0.571793i
$276$	25.5034			1.53512
$277$	−7.43928	−	1.69797i	−0.446983	−	0.102021i	−0.00689637	−	0.999976i	$-0.502195\pi$
$277$	−7.43928	−	1.69797i	−0.446983	−	0.102021i	−0.440087	+	0.897955i	$0.645052\pi$
$278$	3.36485	+	6.98718i	0.201810	+	0.419064i
$279$	−9.25315	−	11.6031i	−0.553972	−	0.694658i
$280$	−5.18851	+	2.84243i	−0.310073	+	0.169868i
$281$	−4.11786	+	5.16363i	−0.245651	+	0.308036i	−0.889336	−	0.457254i	$-0.848833\pi$
$281$	−4.11786	+	5.16363i	−0.245651	+	0.308036i	0.643685	+	0.765290i	$0.277405\pi$
$282$	27.8320	+	6.35248i	1.65737	+	0.378285i
$283$	−5.28638	−	4.21575i	−0.314243	−	0.250600i	0.453648	−	0.891181i	$-0.350122\pi$
$283$	−5.28638	−	4.21575i	−0.314243	−	0.250600i	−0.767891	+	0.640581i	$0.778694\pi$
$284$	−1.21045	+	0.582921i	−0.0718269	+	0.0345900i
$285$	19.4391	−	9.80756i	1.15147	−	0.580950i
$286$	−24.9428	−	12.0118i	−1.47490	−	0.710275i
$287$	11.6571	+	5.13439i	0.688098	+	0.303074i
$288$	−2.55342	−	5.30224i	−0.150462	−	0.312438i
$289$	−15.2534	−	7.34563i	−0.897257	−	0.432096i
$290$	−14.3283	+	0.264588i	−0.841387	+	0.0155372i
$291$	−27.1369	−	13.0685i	−1.59080	−	0.766087i
$292$	−8.27086	−	6.59579i	−0.484016	−	0.385990i
$293$		−	20.7688i		−	1.21333i	−0.794958	−	0.606664i	$-0.792507\pi$
$293$		−	20.7688i		−	1.21333i	0.794958	−	0.606664i	$-0.207493\pi$
$294$	18.1423	−	10.3065i	1.05808	−	0.601087i
$295$	−0.905672	−	0.189192i	−0.0527303	−	0.0110152i
$296$	0.808179	−	1.01342i	0.0469744	−	0.0589041i
$297$	17.6758	−	36.7041i	1.02565	−	2.12979i
$298$	−1.64622	+	0.375739i	−0.0953629	+	0.0217660i
$299$	−45.0496	−	21.6948i	−2.60529	−	1.25464i
$300$	−0.550247	−	14.8937i	−0.0317685	−	0.859890i
$301$	−4.71569	−	8.99830i	−0.271808	−	0.518653i
$302$	−4.93997	+	10.2580i	−0.284264	+	0.590279i
$303$	−22.2058	+	17.7085i	−1.27569	+	1.01733i
$304$	−2.94317	+	1.41735i	−0.168802	+	0.0812908i
$305$	−11.2682	+	9.33160i	−0.645216	+	0.534326i
$306$	−0.346585	+	1.51849i	−0.0198130	+	0.0868062i
$307$	−9.66286	−	7.70588i	−0.551489	−	0.439798i	0.307680	−	0.951490i	$-0.400447\pi$
$307$	−9.66286	−	7.70588i	−0.551489	−	0.439798i	−0.859169	+	0.511692i	$0.829019\pi$
$308$	11.4702	+	5.05206i	0.653574	+	0.287868i
$309$	−16.5656	−	20.7726i	−0.942382	−	1.18171i
$310$	1.35606	+	5.47343i	0.0770192	+	0.310870i
$311$	−0.767270	+	3.36163i	−0.0435079	+	0.190621i	−0.992012	−	0.126145i	$-0.959740\pi$
$311$	−0.767270	+	3.36163i	−0.0435079	+	0.190621i	0.948504	+	0.316765i	$0.102597\pi$
$312$			17.4198i			0.986201i
$313$		−	3.74325i		−	0.211581i	−0.994388	−	0.105790i	$-0.966263\pi$
$313$		−	3.74325i		−	0.211581i	0.994388	−	0.105790i	$-0.0337373\pi$
$314$	−3.25381	+	14.2559i	−0.183623	+	0.804505i
$315$	1.82278	+	34.7686i	0.102702	+	1.95899i
$316$	2.20090	+	9.64279i	0.123811	+	0.542449i
$317$	17.1388	−	3.91183i	0.962613	−	0.219710i	0.287793	−	0.957693i	$-0.407078\pi$
$317$	17.1388	−	3.91183i	0.962613	−	0.219710i	0.674820	+	0.737982i	$0.264221\pi$
$318$	19.3899	−	15.4630i	1.08733	−	0.867120i
$319$	18.9294	+	23.7367i	1.05984	+	1.32900i
$320$	0.0412845	+	2.23569i	0.00230787	+	0.124979i
$321$	6.50000	+	28.4784i	0.362795	+	1.58951i
$322$	20.7165	+	9.12459i	1.15448	+	0.508494i
$323$	0.842882	+	0.192382i	0.0468992	+	0.0107044i
$324$	−7.97861			−0.443256
$325$	−11.6976	+	26.7766i	−0.648864	+	1.48530i
$326$	−3.64558	+	15.9724i	−0.201910	+	0.884627i
$327$	−0.995876	−	2.06796i	−0.0550721	−	0.114358i
$328$	3.76406	−	3.00174i	0.207836	−	0.165743i
$329$	20.3352	+	15.1179i	1.12112	+	0.833475i
$330$	−24.3183	+	20.1389i	−1.33868	+	1.10861i
$331$	−3.01660	+	13.2166i	−0.165807	+	0.726450i	0.821835	+	0.569725i	$0.192950\pi$
$331$	−3.01660	+	13.2166i	−0.165807	+	0.726450i	−0.987642	+	0.156724i	$0.949907\pi$
$332$	6.43762	+	5.13383i	0.353310	+	0.281756i
$333$	−3.30980	−	6.87286i	−0.181376	−	0.376630i
$334$	9.19561	+	11.5309i	0.503162	+	0.630945i
$335$	−1.68636	+	2.19663i	−0.0921355	+	0.120015i
$336$	−0.267409	−	7.88187i	−0.0145884	−	0.429991i
$337$	−10.3525	−	21.4971i	−0.563935	−	1.17102i	−0.966746	−	0.255740i	$-0.917681\pi$
$337$	−10.3525	−	21.4971i	−0.563935	−	1.17102i	0.402811	−	0.915283i	$-0.368033\pi$
$338$	9.17785	−	19.0580i	0.499209	−	1.03662i
$339$	−9.77539	−	42.8288i	−0.530927	−	2.32614i
$340$	0.360375	−	0.469421i	0.0195441	−	0.0254579i
$341$	7.44840	−	9.34000i	0.403353	−	0.505789i
$342$			19.2245i			1.03954i
$343$	18.4245	−	1.88105i	0.994829	−	0.101567i
$344$	−3.83977			−0.207027
$345$	−43.9217	+	36.3731i	−2.36466	+	1.95826i
$346$	−13.6188	−	6.55849i	−0.732154	−	0.352587i
$347$	−11.6241	+	2.65313i	−0.624015	+	0.142427i	−0.522825	−	0.852440i	$-0.675122\pi$
$347$	−11.6241	+	2.65313i	−0.624015	+	0.142427i	−0.101190	+	0.994867i	$0.532265\pi$
$348$	8.28871	−	17.2117i	0.444322	−	0.922643i
$349$	−16.1372	+	7.77126i	−0.863804	+	0.415986i	−0.812683	−	0.582706i	$-0.801994\pi$
$349$	−16.1372	+	7.77126i	−0.863804	+	0.415986i	−0.0511212	+	0.998692i	$0.516279\pi$
$350$	4.88171	−	12.2951i	0.260938	−	0.657200i
$351$	45.2799	+	21.8056i	2.41686	+	1.16390i
$352$	3.70370	−	2.95361i	0.197408	−	0.157428i
$353$	8.22487	+	17.0791i	0.437766	+	0.909030i	0.996804	+	0.0798878i	$0.0254562\pi$
$353$	8.22487	+	17.0791i	0.437766	+	0.909030i	−0.559038	+	0.829142i	$0.688829\pi$
$354$	0.768989	−	0.964281i	0.0408713	−	0.0512510i
$355$	1.25326	−	2.73025i	0.0665159	−	0.144907i
$356$	−3.72332	+	4.66889i	−0.197335	+	0.247451i
$357$	−1.24528	+	1.67504i	−0.0659072	+	0.0886526i
$358$	−13.3090	+	10.6136i	−0.703403	+	0.560945i
$359$	−3.62629	+	1.74633i	−0.191388	+	0.0921678i	−0.527124	−	0.849789i	$-0.676730\pi$
$359$	−3.62629	+	1.74633i	−0.191388	+	0.0921678i	0.335735	+	0.941956i	$0.391015\pi$
$360$	11.9596	+	5.48976i	0.630325	+	0.289336i
$361$	−8.32888			−0.438362
$362$		−	7.87090i		−	0.413685i
$363$	33.2487	+	7.58879i	1.74510	+	0.398308i
$364$	−6.23244	+	14.1501i	−0.326669	+	0.741668i
$365$	23.6509	−	0.436741i	1.23795	−	0.0228601i
$366$	−4.33985	−	19.0141i	−0.226848	−	0.993885i
$367$	−14.2449	+	11.3600i	−0.743580	+	0.592985i	−0.920271	−	0.391281i	$-0.872032\pi$
$367$	−14.2449	+	11.3600i	−0.743580	+	0.592985i	0.176691	+	0.984266i	$0.443461\pi$
$368$	6.68931	−	5.33455i	0.348704	−	0.278083i
$369$	−6.30470	−	27.6227i	−0.328210	−	1.43798i
$370$	0.0535137	+	2.89794i	0.00278204	+	0.150657i
$371$	21.2828	−	5.62327i	1.10495	−	0.291946i
$372$	−7.32846	−	1.67267i	−0.379963	−	0.0867241i
$373$			2.71853i			0.140760i	0.997520	+	0.0703800i	$0.0224212\pi$
$373$			2.71853i			0.140760i	−0.997520	+	0.0703800i	$0.977579\pi$
$374$	−1.25375			−0.0648301
$375$	22.1892	+	24.8651i	1.14584	+	1.28403i
$376$	8.62884	−	4.15543i	0.444998	−	0.214300i
$377$	−29.2826	+	23.3521i	−1.50813	+	1.20270i
$378$	−20.8223	−	9.17122i	−1.07099	−	0.471717i
$379$	−2.98042	+	3.73733i	−0.153094	+	0.191974i	−0.852464	−	0.522786i	$-0.824893\pi$
$379$	−2.98042	+	3.73733i	−0.153094	+	0.191974i	0.699370	+	0.714760i	$0.253464\pi$
$380$	3.04725	−	6.63851i	0.156321	−	0.340548i
$381$	7.34614	−	9.21177i	0.376354	−	0.471934i
$382$	6.93728	+	14.4054i	0.354942	+	0.737045i
$383$	8.00373	−	6.38276i	0.408971	−	0.326144i	−0.397301	−	0.917688i	$-0.630053\pi$
$383$	8.00373	−	6.38276i	0.408971	−	0.326144i	0.806272	+	0.591545i	$0.201482\pi$
$384$	−2.68559	−	1.29331i	−0.137048	−	0.0659990i
$385$	−26.9591	+	7.65824i	−1.37396	+	0.390300i
$386$	−0.145252	+	0.0699499i	−0.00739316	+	0.00356036i
$387$	−9.80457	+	20.3594i	−0.498395	+	1.03493i
$388$	−9.85130	+	2.24850i	−0.500124	+	0.114150i
$389$	16.3769	+	7.88669i	0.830341	+	0.399871i	0.800243	−	0.599676i	$-0.204704\pi$
$389$	16.3769	+	7.88669i	0.830341	+	0.399871i	0.0300980	+	0.999547i	$0.490418\pi$
$390$	−24.8442	−	30.0002i	−1.25803	−	1.51912i
$391$	−2.26442			−0.114517
$392$	2.60275	−	6.49813i	0.131459	−	0.328205i
$393$		−	66.3506i		−	3.34695i
$394$	3.26922	−	4.09947i	0.164701	−	0.206528i
$395$	−17.5430	−	13.4678i	−0.882683	−	0.677637i
$396$	−6.20360	−	27.1797i	−0.311743	−	1.36583i
$397$	1.09241	−	2.26841i	0.0548265	−	0.113848i	−0.871756	−	0.489941i	$-0.837018\pi$
$397$	1.09241	−	2.26841i	0.0548265	−	0.113848i	0.926582	+	0.376093i	$0.122733\pi$
$398$	−7.50680	−	15.5880i	−0.376282	−	0.781358i
$399$	−10.3844	+	23.5766i	−0.519868	+	1.18031i
$400$	−3.25965	−	3.79140i	−0.162982	−	0.189570i
$401$	10.0707	+	12.6283i	0.502907	+	0.630625i	0.966882	−	0.255223i	$-0.0821489\pi$
$401$	10.0707	+	12.6283i	0.502907	+	0.630625i	−0.463976	+	0.885848i	$0.653577\pi$
$402$	−1.60172	−	3.32601i	−0.0798866	−	0.165886i
$403$	11.5222	+	9.18868i	0.573963	+	0.457721i
$404$	−2.12028	+	9.28956i	−0.105488	+	0.462173i
$405$	13.7407	−	11.3791i	0.682780	−	0.565434i
$406$	12.8909	−	11.0156i	0.639766	−	0.546693i
$407$	4.80081	−	3.82852i	0.237967	−	0.189773i
$408$	0.342289	+	0.710770i	0.0169458	+	0.0351883i
$409$	−1.60293	+	7.02288i	−0.0792597	+	0.347259i	−0.998972	−	0.0453339i	$-0.985565\pi$
$409$	−1.60293	+	7.02288i	−0.0792597	+	0.347259i	0.919712	+	0.392593i	$0.128422\pi$
$410$	−2.20133	+	10.5379i	−0.108716	+	0.520430i
$411$	−6.64866			−0.327954
$412$	−8.68999	−	1.98343i	−0.428125	−	0.0977168i
$413$	0.969651	−	0.508159i	0.0477134	−	0.0250049i
$414$	−11.2044	−	49.0897i	−0.550666	−	2.41263i
$415$	−18.4087	+	0.339937i	−0.903648	+	0.0166869i
$416$	3.64370	+	4.56905i	0.178647	+	0.224016i
$417$	18.0732	−	14.4129i	0.885049	−	0.705803i
$418$	−15.0869	+	3.44349i	−0.737925	+	0.168427i
$419$	3.98598	+	17.4637i	0.194728	+	0.853159i	0.974014	+	0.226490i	$0.0727250\pi$
$419$	3.98598	+	17.4637i	0.194728	+	0.853159i	−0.779286	+	0.626669i	$0.784418\pi$
$420$	11.7017	+	13.1927i	0.570984	+	0.643737i
$421$	5.21785	−	22.8609i	0.254303	−	1.11417i	−0.672936	−	0.739701i	$-0.734967\pi$
$421$	5.21785	−	22.8609i	0.254303	−	1.11417i	0.927238	−	0.374471i	$-0.122176\pi$
$422$		−	3.82143i		−	0.186024i
$423$		−	56.3628i		−	2.74045i
$424$	1.85142	−	8.11159i	0.0899128	−	0.393934i
$425$	0.0488559	+	1.32240i	0.00236986	+	0.0641459i
$426$	2.49687	+	3.13097i	0.120974	+	0.151696i
$427$	3.27759	−	16.9979i	0.158614	−	0.822588i
$428$	7.66171	+	6.11001i	0.370343	+	0.295339i
$429$	−18.3627	+	80.4523i	−0.886560	+	3.88427i
$430$	6.61282	−	5.47631i	0.318899	−	0.264091i
$431$	−33.1128	+	15.9463i	−1.59499	+	0.768106i	−0.999381	−	0.0351701i	$-0.988803\pi$
$431$	−33.1128	+	15.9463i	−1.59499	+	0.768106i	−0.595607	+	0.803276i	$0.703088\pi$
$432$	−6.72350	+	5.36181i	−0.323485	+	0.257970i
$433$	−8.72997	+	18.1280i	−0.419535	+	0.871174i	0.578908	+	0.815393i	$0.303479\pi$
$433$	−8.72997	+	18.1280i	−0.419535	+	0.871174i	−0.998443	+	0.0557811i	$0.982235\pi$
$434$	−5.35448	−	3.98069i	−0.257023	−	0.191079i
$435$	10.2727	+	41.4632i	0.492537	+	1.98801i
$436$	−0.693764	−	0.334099i	−0.0332253	−	0.0160005i
$437$	−27.2487	+	6.21934i	−1.30348	+	0.297511i
$438$	−13.6817	+	28.4104i	−0.653738	+	1.35750i
$439$	−1.97527	+	2.47691i	−0.0942744	+	0.118216i	−0.826731	−	0.562597i	$-0.809802\pi$
$439$	−1.97527	+	2.47691i	−0.0942744	+	0.118216i	0.732457	+	0.680814i	$0.238374\pi$
$440$	−2.16603	+	10.3689i	−0.103262	+	0.494318i
$441$	−27.8087	−	30.3929i	−1.32422	−	1.44728i
$442$		−	1.54669i		−	0.0735684i
$443$	−17.1710	−	13.6934i	−0.815817	−	0.650592i	0.123995	−	0.992283i	$-0.460429\pi$
$443$	−17.1710	−	13.6934i	−0.815817	−	0.650592i	−0.939813	+	0.341690i	$0.889001\pi$
$444$	−3.48111	−	1.67641i	−0.165206	−	0.0795591i
$445$	−0.246540	−	13.3509i	−0.0116871	−	0.632895i
$446$	−7.28173	−	3.50670i	−0.344800	−	0.166047i
$447$	2.18383	+	4.53477i	0.103292	+	0.214487i
$448$	−1.71879	−	2.01141i	−0.0812052	−	0.0950301i
$449$	−3.57766	−	1.72291i	−0.168840	−	0.0813093i	0.347555	−	0.937660i	$-0.387012\pi$
$449$	−3.57766	−	1.72291i	−0.168840	−	0.0813093i	−0.516395	+	0.856350i	$0.672726\pi$
$450$	−28.4262	+	7.60239i	−1.34002	+	0.358380i
$451$	20.5483	−	9.89556i	0.967583	−	0.465964i
$452$	−11.5225	−	9.18889i	−0.541973	−	0.432209i
$453$	33.0867	+	7.55183i	1.55455	+	0.354816i
$454$	−5.58691	+	7.00576i	−0.262207	+	0.328797i
$455$	−9.44754	−	33.2580i	−0.442908	−	1.55916i
$456$	6.07105	+	7.61286i	0.284303	+	0.356505i
$457$	3.21298	+	6.67182i	0.150297	+	0.312095i	0.962501	−	0.271279i	$-0.0874466\pi$
$457$	3.21298	+	6.67182i	0.150297	+	0.312095i	−0.812204	+	0.583374i	$0.801732\pi$
$458$	−12.1842	−	2.78096i	−0.569330	−	0.129946i
$459$	2.27600			0.106234
$460$	−3.91210	+	18.7274i	−0.182403	+	0.873171i
$461$	2.15998	−	9.46348i	0.100600	−	0.440758i	−0.899393	−	0.437140i	$-0.855991\pi$
$461$	2.15998	−	9.46348i	0.100600	−	0.440758i	0.999993	−	0.00361768i	$-0.00115155\pi$
$462$	7.07349	−	36.6838i	0.329089	−	1.70669i
$463$	−19.5173	+	4.45470i	−0.907047	+	0.207028i	−0.650502	−	0.759505i	$-0.725441\pi$
$463$	−19.5173	+	4.45470i	−0.907047	+	0.207028i	−0.256545	+	0.966532i	$0.582584\pi$
$464$	−1.42612	−	6.24822i	−0.0662057	−	0.290066i
$465$	15.0066	−	7.57123i	0.695913	−	0.351107i
$466$	−10.0771	−	12.6363i	−0.466812	−	0.585364i
$467$	12.3621	−	2.82157i	0.572051	−	0.130567i	0.0732963	−	0.997310i	$-0.476648\pi$
$467$	12.3621	−	2.82157i	0.572051	−	0.130567i	0.498754	+	0.866743i	$0.333791\pi$
$468$	33.5301	−	7.65303i	1.54993	−	0.353762i
$469$	−0.111104	−	3.27479i	−0.00513031	−	0.151216i
$470$	−8.93400	+	19.4629i	−0.412095	+	0.897758i
$471$	43.5864			2.00836
$472$		−	0.413772i		−	0.0190454i
$473$	−17.7338	−	4.04762i	−0.815400	−	0.186110i
$474$	26.5626	−	12.7919i	1.22006	−	0.587549i
$475$	4.21993	+	15.7788i	0.193624	+	0.723980i
$476$	0.0237430	+	0.699824i	0.00108826	+	0.0320764i
$477$	−38.2821	−	30.5290i	−1.75282	−	1.39783i
$478$	−27.7589	−	6.33578i	−1.26966	−	0.289792i
$479$	−15.9619	+	20.0156i	−0.729318	+	0.914536i	−0.998825	−	0.0484621i	$-0.984568\pi$
$479$	−15.9619	+	20.0156i	−0.729318	+	0.914536i	0.269507	+	0.962999i	$0.413139\pi$
$480$	6.46962	−	1.60287i	0.295297	−	0.0731608i
$481$	4.72303	+	5.92249i	0.215352	+	0.270042i
$482$	−1.08262	+	2.24808i	−0.0493118	+	0.102397i
$483$	12.7755	−	66.2552i	0.581307	−	3.01471i
$484$	10.3082	−	4.96415i	0.468553	−	0.225643i
$485$	13.7590	−	17.9223i	0.624764	−	0.813811i
$486$	−0.448727	−	1.96600i	−0.0203547	−	0.0891797i
$487$	−6.54843	+	13.5980i	−0.296738	+	0.616182i	−0.995024	−	0.0996363i	$-0.968232\pi$
$487$	−6.54843	+	13.5980i	−0.296738	+	0.616182i	0.698286	+	0.715819i	$0.253946\pi$
$488$	−5.11549	−	4.07947i	−0.231567	−	0.184669i
$489$	48.8344			2.20837
$490$	4.78523	+	14.9031i	0.216175	+	0.673252i
$491$	24.8698			1.12236			0.561178	−	0.827695i	$-0.310348\pi$
$491$	24.8698			1.12236			0.561178	+	0.827695i	$0.310348\pi$
$492$	−11.2198	−	8.94753i	−0.505830	−	0.403386i
$493$	−0.735947	+	1.52821i	−0.0331454	+	0.0688271i
$494$	−4.24804	−	18.6119i	−0.191128	−	0.837389i
$495$	49.4477	+	37.9611i	2.22251	+	1.70622i
$496$	−2.27206	+	1.09417i	−0.102019	+	0.0491296i
$497$	0.908013	+	3.43662i	0.0407300	+	0.154154i
$498$	10.6492	−	22.1132i	0.477201	−	0.990917i
$499$	−21.0928	−	26.4495i	−0.944244	−	1.18404i	−0.982779	−	0.184787i	$-0.940841\pi$
$499$	−21.0928	−	26.4495i	−0.944244	−	1.18404i	0.0385349	−	0.999257i	$-0.487731\pi$
$500$	11.0210	+	1.88058i	0.492876	+	0.0841020i
$501$	27.4101	−	34.3712i	1.22459	−	1.53559i
$502$	26.5686	+	6.06411i	1.18582	+	0.270655i
$503$	−31.8070	−	25.3652i	−1.41820	−	1.13098i	−0.971706	−	0.236193i	$-0.924100\pi$
$503$	−31.8070	−	25.3652i	−1.41820	−	1.13098i	−0.446496	−	0.894786i	$-0.647328\pi$
$504$	−15.0538	+	3.97746i	−0.670548	+	0.177170i
$505$	−9.59729	−	19.0223i	−0.427074	−	0.846483i
$506$	36.5175	−	17.5859i	1.62340	−	0.781789i
$507$	−61.4709	−	14.0303i	−2.73002	−	0.623109i
$508$		−	3.95276i		−	0.175375i
$509$	−1.94823			−0.0863536			−0.0431768	−	0.999067i	$-0.513748\pi$
$509$	−1.94823			−0.0863536			−0.0431768	+	0.999067i	$0.513748\pi$
$510$	−1.60319	−	0.735907i	−0.0709904	−	0.0325865i
$511$	−21.2783	+	18.1828i	−0.941298	+	0.804359i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$	27.3880	−	6.25112i	1.20921	−	0.275994i
$514$	15.6008	+	19.5628i	0.688122	+	0.862878i
$515$	17.7946	−	8.97786i	0.784124	−	0.395612i
$516$	2.54687	+	11.1586i	0.112120	+	0.491228i
$517$	44.2322	−	10.0957i	1.94533	−	0.444009i
$518$	−2.22793	−	2.60722i	−0.0978894	−	0.114555i
$519$	−10.0261	+	43.9271i	−0.440096	+	1.92819i
$520$	−12.7915	−	2.67212i	−0.560947	−	0.117180i
$521$	−16.0538			−0.703330			−0.351665	−	0.936126i	$-0.614384\pi$
$521$	−16.0538			−0.703330			−0.351665	+	0.936126i	$0.614384\pi$
$522$	−36.7710	−	8.39275i	−1.60943	−	0.367341i
$523$	−6.15167	−	12.7741i	−0.268994	−	0.558572i	0.722092	−	0.691797i	$-0.243181\pi$
$523$	−6.15167	−	12.7741i	−0.268994	−	0.558572i	−0.991086	+	0.133226i	$0.957466\pi$
$524$	−13.8786	−	17.4032i	−0.606288	−	0.760261i
$525$	−38.9680	−	6.03130i	−1.70070	−	0.263228i
$526$	−17.9403	+	22.4964i	−0.782234	+	0.980890i
$527$	0.650687	+	0.148515i	0.0283444	+	0.00646942i
$528$	−11.0399	−	8.80404i	−0.480451	−	0.383147i
$529$	45.2325	−	21.7828i	1.96663	−	0.947079i
$530$	8.38030	+	16.6102i	0.364017	+	0.721501i
$531$	−2.19392	−	1.05654i	−0.0952079	−	0.0458497i
$532$	2.20780	+	8.35604i	0.0957205	+	0.362280i
$533$	12.2076	+	25.3493i	0.528770	+	1.09800i
$534$	16.0376	+	7.72332i	0.694016	+	0.334221i
$535$	−21.9091	+	0.404575i	−0.947211	+	0.0174913i
$536$	−1.11582	−	0.537350i	−0.0481960	−	0.0232100i
$537$	39.6712	+	31.6367i	1.71194	+	1.36523i
$538$		−	21.4807i		−	0.926100i
$539$	18.8705	−	27.2676i	0.812811	−	1.17450i
$540$	3.93210	−	18.8231i	0.169211	−	0.810019i
$541$	−9.33920	+	11.7110i	−0.401523	+	0.503495i	−0.940953	−	0.338536i	$-0.890068\pi$
$541$	−9.33920	+	11.7110i	−0.401523	+	0.503495i	0.539430	+	0.842030i	$0.318640\pi$
$542$	−10.0333	+	20.8343i	−0.430966	+	0.894911i
$543$	−22.8732	+	5.22065i	−0.981582	+	0.224040i
$544$	0.238451	+	0.114832i	0.0102235	+	0.00492338i
$545$	1.67129	−	0.414068i	0.0715901	−	0.0177367i
$546$	45.2548	+	8.72617i	1.93673	+	0.373446i
$547$	9.10464	−	18.9060i	0.389286	−	0.808362i	−0.610579	−	0.791955i	$-0.709063\pi$
$547$	9.10464	−	18.9060i	0.389286	−	0.808362i	0.999865	−	0.0164062i	$-0.00522250\pi$
$548$	−1.74388	+	1.39070i	−0.0744950	+	0.0594078i
$549$	−34.6924	+	16.7070i	−1.48063	+	0.713036i
$550$	−11.0579	−	20.9464i	−0.471509	−	0.893159i
$551$	−4.65864	+	20.4109i	−0.198465	+	0.869532i
$552$	−19.9394	−	15.9011i	−0.848675	−	0.676796i
$553$	26.1535	−	0.887313i	1.11216	−	0.0377324i
$554$	4.75760	+	5.96584i	0.202131	+	0.253464i
$555$	8.38604	−	2.07767i	0.355968	−	0.0881923i
$556$	1.72569	−	7.56075i	0.0731856	−	0.320647i
$557$		−	27.6478i		−	1.17147i	−0.810501	−	0.585737i	$-0.800805\pi$
$557$		−	27.6478i		−	1.17147i	0.810501	−	0.585737i	$-0.199195\pi$
$558$			14.8409i			0.628265i
$559$	4.99332	−	21.8772i	0.211195	−	0.925306i
$560$	5.82876	+	1.01268i	0.246310	+	0.0427935i
$561$	0.831597	+	3.64347i	0.0351101	+	0.153827i
$562$	6.43894	−	1.46965i	0.271610	−	0.0619933i
$563$	−0.948374	+	0.756303i	−0.0399692	+	0.0318744i	−0.643271	−	0.765639i	$-0.722423\pi$
$563$	−0.948374	+	0.756303i	−0.0399692	+	0.0318744i	0.603301	+	0.797513i	$0.293852\pi$
$564$	−17.7993	−	22.3196i	−0.749484	−	0.939823i
$565$	32.9492	−	0.608444i	1.38618	−	0.0255974i
$566$	1.50458	+	6.59201i	0.0632424	+	0.277083i
$567$	−3.99676	+	20.7276i	−0.167848	+	0.870477i
$568$	1.30981	+	0.298956i	0.0549585	+	0.0125439i
$569$	−35.1748			−1.47461			−0.737303	−	0.675562i	$-0.763901\pi$
$569$	−35.1748			−1.47461			−0.737303	+	0.675562i	$0.763901\pi$
$570$	−21.3130	−	4.45222i	−0.892704	−	0.186483i
$571$	1.49805	−	6.56338i	0.0626914	−	0.274669i	−0.933861	−	0.357637i	$-0.883583\pi$
$571$	1.49805	−	6.56338i	0.0626914	−	0.274669i	0.996552	+	0.0829676i	$0.0264398\pi$
$572$	12.0118	+	24.9428i	0.502240	+	1.04291i
$573$	37.2614	−	29.7149i	1.55662	−	1.24136i
$574$	−5.91266	−	11.2823i	−0.246790	−	0.470915i
$575$	−19.9718	−	37.8317i	−0.832881	−	1.57769i
$576$	−1.30955	+	5.73749i	−0.0545644	+	0.239062i
$577$	34.7207	+	27.6888i	1.44544	+	1.15270i	0.960544	+	0.278129i	$0.0897142\pi$
$577$	34.7207	+	27.6888i	1.44544	+	1.15270i	0.484897	+	0.874571i	$0.338857\pi$
$578$	7.34563	+	15.2534i	0.305538	+	0.634456i
$579$	0.299621	+	0.375713i	0.0124518	+	0.0156141i
$580$	11.3673	+	8.72669i	0.472001	+	0.362356i
$581$	16.5620	−	14.1526i	0.687107	−	0.587147i
$582$	13.0685	+	27.1369i	0.541705	+	1.12486i
$583$	17.1013	−	35.5113i	0.708265	−	1.47073i
$584$	2.35401	+	10.3136i	0.0974097	+	0.426780i
$585$	−46.8305	+	61.0008i	−1.93620	+	2.52207i
$586$	−12.9492	+	16.2377i	−0.534924	+	0.670774i
$587$			14.9100i			0.615401i	0.951483	+	0.307701i	$0.0995595\pi$
$587$			14.9100i			0.615401i	−0.951483	+	0.307701i	$0.900440\pi$
$588$	−20.6102	−	3.25360i	−0.849951	−	0.134176i
$589$	8.23788			0.339436
$590$	0.590124	+	0.712594i	0.0242950	+	0.0293370i
$591$	−14.0817	−	6.78137i	−0.579242	−	0.278948i
$592$	−1.26372	+	0.288436i	−0.0519385	+	0.0118546i
$593$	−20.1638	+	41.8705i	−0.828028	+	1.71942i	−0.144485	+	0.989507i	$0.546152\pi$
$593$	−20.1638	+	41.8705i	−0.828028	+	1.71942i	−0.683543	+	0.729910i	$0.739562\pi$
$594$	−36.7041	+	17.6758i	−1.50599	+	0.725246i
$595$	−1.03898	−	1.17137i	−0.0425941	−	0.0480214i
$596$	1.52134	+	0.732637i	0.0623163	+	0.0300100i
$597$	−40.3204	+	32.1544i	−1.65020	+	1.31599i
$598$	21.6948	+	45.0496i	0.887164	+	1.84222i
$599$	1.88084	−	2.35850i	0.0768491	−	0.0963658i	−0.741921	−	0.670488i	$-0.766085\pi$
$599$	1.88084	−	2.35850i	0.0768491	−	0.0963658i	0.818770	+	0.574122i	$0.194656\pi$
$600$	−8.85589	+	11.9875i	−0.361540	+	0.489386i
$601$	1.80662	−	2.26543i	0.0736936	−	0.0924088i	−0.743618	−	0.668604i	$-0.766892\pi$
$601$	1.80662	−	2.26543i	0.0736936	−	0.0924088i	0.817312	+	0.576196i	$0.195463\pi$
$602$	−1.92348	+	9.97533i	−0.0783950	+	0.406564i
$603$	−5.69832	+	4.54426i	−0.232053	+	0.185056i
$604$	10.2580	−	4.93997i	0.417391	−	0.201005i
$605$	−10.6727	+	23.2508i	−0.433908	+	0.945279i
$606$	28.4022			1.15376
$607$		−	32.7068i		−	1.32753i	−0.747941	−	0.663765i	$-0.768958\pi$
$607$		−	32.7068i		−	1.32753i	0.747941	−	0.663765i	$-0.231042\pi$
$608$	3.18477	+	0.726902i	0.129159	+	0.0294798i
$609$	−40.5621	−	30.1551i	−1.64366	−	1.22195i
$610$	14.6280	−	0.270123i	0.592271	−	0.0109369i
$611$	12.4545	+	54.5668i	0.503855	+	2.20753i
$612$	1.21773	−	0.971110i	0.0492240	−	0.0392548i
$613$	−25.7706	+	20.5513i	−1.04086	+	0.830061i	−0.985716	−	0.168418i	$-0.946134\pi$
$613$	−25.7706	+	20.5513i	−1.04086	+	0.830061i	−0.0551474	+	0.998478i	$0.517563\pi$
$614$	2.75019	+	12.0494i	0.110989	+	0.486274i
$615$	32.0837	−	0.592462i	1.29374	−	0.0238904i
$616$	−5.81785	−	11.1014i	−0.234408	−	0.447288i
$617$	−1.19620	−	0.273025i	−0.0481573	−	0.0109916i	0.198374	−	0.980126i	$-0.436434\pi$
$617$	−1.19620	−	0.273025i	−0.0481573	−	0.0109916i	−0.246532	+	0.969135i	$0.579291\pi$
$618$			26.5691i			1.06877i
$619$	20.8451			0.837837			0.418919	−	0.908024i	$-0.362409\pi$
$619$	20.8451			0.837837			0.418919	+	0.908024i	$0.362409\pi$
$620$	2.35242	−	5.12479i	0.0944753	−	0.205817i
$621$	−66.2919	+	31.9245i	−2.66020	+	1.28109i
$622$	2.69582	−	2.14984i	0.108092	−	0.0862009i
$623$	10.2642	+	12.0116i	0.411225	+	0.481235i
$624$	10.8611	−	13.6193i	0.434790	−	0.545210i
$625$	−21.6624	+	12.4796i	−0.866497	+	0.499182i
$626$	−2.33388	+	2.92659i	−0.0932804	+	0.116970i
$627$	20.0139	+	41.5592i	0.799277	+	1.65972i
$628$	11.4323	−	9.11697i	0.456199	−	0.363807i
$629$	0.309085	+	0.148847i	0.0123240	+	0.00593493i
$630$	20.2528	−	28.3197i	0.806890	−	1.12828i
$631$	28.9376	−	13.9356i	1.15199	−	0.554769i	0.242359	−	0.970187i	$-0.422079\pi$
$631$	28.9376	−	13.9356i	1.15199	−	0.554769i	0.909631	+	0.415418i	$0.136365\pi$
$632$	4.29145	−	8.91128i	0.170705	−	0.354472i
$633$	−11.1052	+	2.53470i	−0.441394	+	0.100745i
$634$	−15.8387	−	7.62750i	−0.629034	−	0.302927i
$635$	5.63745	+	6.80740i	0.223715	+	0.270144i
$636$	−24.8007			−0.983410
$637$	33.6385	+	23.2795i	1.33281	+	0.922368i
$638$		−	30.3604i		−	1.20198i
$639$	4.92964	−	6.18158i	0.195014	−	0.244539i
$640$	1.36165	−	1.77367i	0.0538240	−	0.0701105i
$641$	2.04832	+	8.97430i	0.0809040	+	0.354463i	0.999135	−	0.0415815i	$-0.0132396\pi$
$641$	2.04832	+	8.97430i	0.0809040	+	0.354463i	−0.918231	+	0.396045i	$0.870382\pi$
$642$	12.6741	−	26.3180i	0.500205	−	1.03869i
$643$	3.61926	+	7.51548i	0.142730	+	0.296382i	0.960063	−	0.279784i	$-0.0902628\pi$
$643$	3.61926	+	7.51548i	0.142730	+	0.296382i	−0.817333	+	0.576165i	$0.804548\pi$
$644$	−10.5077	−	20.0504i	−0.414061	−	0.790096i
$645$	−20.3006	−	15.5848i	−0.799335	−	0.613651i
$646$	−0.539043	−	0.675939i	−0.0212084	−	0.0265945i
$647$	−7.55590	−	15.6900i	−0.297053	−	0.616837i	0.698009	−	0.716089i	$-0.254069\pi$
$647$	−7.55590	−	15.6900i	−0.297053	−	0.616837i	−0.995062	+	0.0992514i	$0.968355\pi$
$648$	6.23793	+	4.97458i	0.245049	+	0.195420i
$649$	0.436169	−	1.91098i	0.0171211	−	0.0750126i
$650$	25.8405	−	13.6415i	1.01355	−	0.535063i
$651$	−8.01651	+	18.2007i	−0.314192	+	0.713341i
$652$	12.8088	−	10.2147i	0.501633	−	0.400039i
$653$	12.0470	+	25.0158i	0.471435	+	0.978945i	0.992131	+	0.125203i	$0.0399581\pi$
$653$	12.0470	+	25.0158i	0.471435	+	0.978945i	−0.520696	+	0.853742i	$0.674328\pi$
$654$	−0.510743	+	2.23771i	−0.0199717	+	0.0875015i
$655$	48.7220	+	10.1779i	1.90373	+	0.397683i
$656$	−4.81442			−0.187971
$657$	60.6960	+	13.8535i	2.36798	+	0.540475i
$658$	−6.47289	−	24.4984i	−0.252340	−	0.955048i
$659$	−3.26540	−	14.3066i	−0.127202	−	0.557307i	−0.997858	−	0.0654156i	$-0.979163\pi$
$659$	−3.26540	−	14.3066i	−0.127202	−	0.557307i	0.870656	−	0.491892i	$-0.163694\pi$
$660$	31.5692	−	0.582961i	1.22883	−	0.0226917i
$661$	−0.935128	−	1.17261i	−0.0363723	−	0.0456094i	0.763313	−	0.646029i	$-0.223572\pi$
$661$	−0.935128	−	1.17261i	−0.0363723	−	0.0456094i	−0.799685	+	0.600420i	$0.795000\pi$
$662$	10.5989	−	8.45233i	0.411937	−	0.328509i
$663$	−4.49474	+	1.02590i	−0.174561	+	0.0398425i
$664$	−1.83224	−	8.02759i	−0.0711049	−	0.311531i
$665$	−15.7197	−	11.2419i	−0.609583	−	0.435942i
$666$	−1.69746	+	7.43704i	−0.0657751	+	0.288180i
$667$		−	54.8343i		−	2.12319i
$668$		−	14.7486i		−	0.570641i
$669$	−5.36075	+	23.4870i	−0.207259	+	0.908059i
$670$	2.68802	−	0.665968i	0.103847	−	0.0257286i
$671$	−19.3253	−	24.2332i	−0.746046	−	0.935512i
$672$	−4.70519	+	6.32902i	−0.181507	+	0.244147i
$673$	−16.0872	−	12.8292i	−0.620118	−	0.494527i	0.262305	−	0.964985i	$-0.415517\pi$
$673$	−16.0872	−	12.8292i	−0.620118	−	0.494527i	−0.882423	+	0.470458i	$0.844089\pi$
$674$	−5.30935	+	23.2618i	−0.204509	+	0.896011i
$675$	20.0739	+	38.0250i	0.772643	+	1.46358i
$676$	−19.0580	+	9.17785i	−0.733000	+	0.352994i
$677$	−8.34613	+	6.65582i	−0.320768	+	0.255804i	−0.770614	−	0.637302i	$-0.780050\pi$
$677$	−8.34613	+	6.65582i	−0.320768	+	0.255804i	0.449846	+	0.893106i	$0.351479\pi$
$678$	−19.0606	+	39.5798i	−0.732018	+	1.52005i
$679$	0.906500	+	26.7190i	0.0347883	+	1.02538i
$680$	−0.574432	+	0.142318i	−0.0220285	+	0.00545763i
$681$	24.0648	+	11.5890i	0.922164	+	0.444091i
$682$	−11.6468	+	2.65830i	−0.445979	+	0.101792i
$683$	1.68014	−	3.48885i	0.0642889	−	0.133497i	−0.866348	−	0.499440i	$-0.833539\pi$
$683$	1.68014	−	3.48885i	0.0642889	−	0.133497i	0.930637	+	0.365943i	$0.119253\pi$
$684$	11.9863	−	15.0303i	0.458306	−	0.574698i
$685$	1.01987	−	4.88219i	0.0389674	−	0.186539i
$686$	−15.5777	−	10.0168i	−0.594758	−	0.382444i
$687$			37.2524i			1.42127i
$688$	3.00206	+	2.39406i	0.114452	+	0.0912727i
$689$	43.8083	+	21.0970i	1.66896	+	0.803730i
$690$	57.0176	−	1.05289i	2.17062	−	0.0400830i
$691$	−11.1930	−	5.39026i	−0.425801	−	0.205055i	0.208695	−	0.977981i	$-0.433078\pi$
$691$	−11.1930	−	5.39026i	−0.425801	−	0.205055i	−0.634497	+	0.772926i	$0.718793\pi$
$692$	6.55849	+	13.6188i	0.249316	+	0.517711i
$693$	−73.7177	+	2.50103i	−2.80031	+	0.0950064i
$694$	10.7423	+	5.17322i	0.407772	+	0.196373i
$695$	7.81122	+	15.4822i	0.296296	+	0.587275i
$696$	−17.2117	+	8.28871i	−0.652407	+	0.314183i
$697$	0.996200	+	0.794443i	0.0377338	+	0.0300917i
$698$	17.4619	+	3.98556i	0.660941	+	0.150856i
$699$	−30.0376	+	37.6659i	−1.13613	+	1.42466i
$700$	−11.4825	+	6.56899i	−0.433999	+	0.248284i
$701$	31.7586	+	39.8241i	1.19951	+	1.50413i	0.813424	+	0.581671i	$0.197601\pi$
$701$	31.7586	+	39.8241i	1.19951	+	1.50413i	0.386083	+	0.922464i	$0.373828\pi$
$702$	−21.8056	−	45.2799i	−0.823000	−	1.70898i
$703$	4.12815	+	0.942223i	0.155696	+	0.0355366i
$704$	−4.73721			−0.178541
$705$	62.4860	+	13.0531i	2.35336	+	0.491609i
$706$	4.21819	−	18.4811i	0.158754	−	0.695546i
$707$	23.0712	+	10.1617i	0.867681	+	0.382171i
$708$	−1.20244	+	0.274449i	−0.0451904	+	0.0103144i
$709$	−10.8468	−	47.5228i	−0.407359	−	1.78476i	−0.596292	−	0.802768i	$-0.703360\pi$
$709$	−10.8468	−	47.5228i	−0.407359	−	1.78476i	0.188933	−	0.981990i	$-0.439497\pi$
$710$	−2.68212	+	1.35320i	−0.100658	+	0.0507848i
$711$	−36.2919	−	45.5086i	−1.36105	−	1.70670i
$712$	5.82201	−	1.32884i	0.218189	−	0.0498003i
$713$	−21.0354	+	4.80120i	−0.787783	+	0.179806i
$714$	2.01797	−	0.533181i	0.0755206	−	0.0199538i
$715$	−56.2603	−	25.8250i	−2.10402	−	0.965799i
$716$	17.0229			0.636174
$717$			84.8710i			3.16956i
$718$	3.92397	+	0.895620i	0.146441	+	0.0334243i
$719$	−4.62372	+	2.22667i	−0.172436	+	0.0830407i	−0.518110	−	0.855314i	$-0.673364\pi$
$719$	−4.62372	+	2.22667i	−0.172436	+	0.0830407i	0.345675	+	0.938354i	$0.387650\pi$
$720$	−5.92756	−	11.7487i	−0.220907	−	0.437849i
$721$	−9.50587	+	21.5821i	−0.354017	+	0.803760i
$722$	6.51178	+	5.19297i	0.242344	+	0.193263i
$723$	7.25110	+	1.65502i	0.269671	+	0.0615507i
$724$	−4.90742	+	6.15371i	−0.182383	+	0.228701i
$725$	−32.0227	+	1.18307i	−1.18929	+	0.0439382i
$726$	−21.2633	−	26.6634i	−0.789156	−	0.989570i
$727$	18.5742	−	38.5696i	0.688877	−	1.43047i	−0.203453	−	0.979085i	$-0.565216\pi$
$727$	18.5742	−	38.5696i	0.688877	−	1.43047i	0.892330	−	0.451383i	$-0.149069\pi$
$728$	13.6952	−	7.17715i	0.507577	−	0.266003i
$729$	−26.9811	+	12.9934i	−0.999300	+	0.481237i
$730$	−18.7634	−	14.4047i	−0.694463	−	0.533141i
$731$	−0.226134	−	0.990758i	−0.00836387	−	0.0366445i
$732$	−8.46209	+	17.5717i	−0.312768	+	0.649469i
$733$	−11.2605	−	8.97997i	−0.415917	−	0.331683i	0.393071	−	0.919508i	$-0.371413\pi$
$733$	−11.2605	−	8.97997i	−0.415917	−	0.331683i	−0.808988	+	0.587826i	$0.799984\pi$
$734$	18.2200			0.672511
$735$	40.1350	−	23.7911i	1.48040	−	0.877548i
$736$	−8.55595			−0.315377
$737$	−4.58691	−	3.65794i	−0.168961	−	0.134742i
$738$	−12.2933	+	25.5272i	−0.452521	+	0.939670i
$739$	−3.28005	−	14.3708i	−0.120659	−	0.528640i	−0.998743	−	0.0501333i	$-0.984035\pi$
$739$	−3.28005	−	14.3708i	−0.120659	−	0.528640i	0.878084	−	0.478507i	$-0.158822\pi$
$740$	1.76500	−	2.29906i	0.0648825	−	0.0845153i
$741$	−51.2693	+	24.6900i	−1.88343	+	0.907010i
$742$	−20.1456	−	8.87316i	−0.739569	−	0.325744i
$743$	−1.99816	+	4.14922i	−0.0733053	+	0.152220i	−0.934401	−	0.356223i	$-0.884064\pi$
$743$	−1.99816	+	4.14922i	−0.0733053	+	0.152220i	0.861096	+	0.508443i	$0.169779\pi$
$744$	4.68673	+	5.87697i	0.171824	+	0.215460i
$745$	−3.66492	+	0.907998i	−0.134272	+	0.0332665i
$746$	1.69497	−	2.12543i	0.0620574	−	0.0778175i
$747$	−47.2427	−	10.7828i	−1.72852	−	0.394523i
$748$	0.980225	+	0.781703i	0.0358406	+	0.0285819i
$749$	19.7112	−	16.8436i	0.720231	−	0.615452i
$750$	−1.84506	−	33.2750i	−0.0673720	−	1.21503i
$751$	8.47073	−	4.07929i	0.309101	−	0.148855i	−0.272902	−	0.962042i	$-0.587983\pi$
$751$	8.47073	−	4.07929i	0.309101	−	0.148855i	0.582003	+	0.813187i	$0.302269\pi$
$752$	−9.33717	−	2.13115i	−0.340491	−	0.0777149i
$753$		−	81.2318i		−	2.96025i
$754$	37.4539			1.36399
$755$	−10.6207	+	23.1375i	−0.386528	+	0.842061i
$756$	10.5614	+	20.1529i	0.384114	+	0.732953i
$757$	−34.2136	+	7.80904i	−1.24352	+	0.283824i	−0.793154	−	0.609022i	$-0.791562\pi$
$757$	−34.2136	+	7.80904i	−1.24352	+	0.283824i	−0.450362	+	0.892846i	$0.648705\pi$
$758$	4.66038	−	1.06370i	0.169272	−	0.0386353i
$759$	−75.3270	−	94.4570i	−2.73420	−	3.42857i
$760$	−6.52148	+	3.29027i	−0.236559	+	0.119351i
$761$	−5.48020	−	24.0103i	−0.198657	−	0.870374i	−0.971737	−	0.236065i	$-0.924142\pi$
$761$	−5.48020	−	24.0103i	−0.198657	−	0.870374i	0.773080	−	0.634309i	$-0.218715\pi$
$762$	−11.4869	+	2.62181i	−0.416126	+	0.0949781i
$763$	−1.21549	+	1.63497i	−0.0440035	+	0.0591897i
$764$	3.55784	−	15.5879i	0.128718	−	0.563951i
$765$	−0.712166	+	3.40917i	−0.0257484	+	0.123259i
$766$	−10.2372			−0.369883
$767$	2.35747	+	0.538077i	0.0851234	+	0.0194289i
$768$	1.29331	+	2.68559i	0.0466684	+	0.0969079i
$769$	−1.54747	−	1.94046i	−0.0558031	−	0.0699749i	0.753147	−	0.657853i	$-0.228535\pi$
$769$	−1.54747	−	1.94046i	−0.0558031	−	0.0699749i	−0.808950	+	0.587878i	$0.799964\pi$
$770$	25.8523	+	10.8213i	0.931653	+	0.389972i
$771$	46.5026	−	58.3124i	1.67475	−	2.10007i
$772$	0.157176	+	0.0358744i	0.00565689	+	0.00129115i
$773$	2.86029	+	2.28100i	0.102877	+	0.0820420i	0.673578	−	0.739116i	$-0.264757\pi$
$773$	2.86029	+	2.28100i	0.102877	+	0.0820420i	−0.570700	+	0.821159i	$0.693328\pi$
$774$	20.3594	−	9.80457i	0.731804	−	0.352418i
$775$	3.25770	+	12.1809i	0.117020	+	0.437551i
$776$	9.10397	+	4.38424i	0.326814	+	0.157385i
$777$	−6.09896	+	8.20379i	−0.218799	+	0.294309i
$778$	−7.88669	−	16.3769i	−0.282752	−	0.587140i
$779$	14.1696	+	6.82373i	0.507680	+	0.244486i
$780$	0.719167	+	38.9452i	0.0257503	+	1.39446i
$781$	5.73415	+	2.76142i	0.205184	+	0.0988115i
$782$	1.77040	+	1.41184i	0.0633093	+	0.0504875i
$783$			55.1145i			1.96963i
$784$	−6.08643	+	3.45765i	−0.217373	+	0.123488i
$785$	−6.68595	+	32.0060i	−0.238632	+	1.14234i
$786$	−41.3689	+	51.8750i	−1.47558	+	1.85032i
$787$	13.8384	−	28.7356i	0.493284	−	1.02431i	−0.494600	−	0.869121i	$-0.664685\pi$
$787$	13.8384	−	28.7356i	0.493284	−	1.02431i	0.987884	−	0.155194i	$-0.0496003\pi$
$788$	−5.11195	+	1.16677i	−0.182106	+	0.0415645i
$789$	77.2751	+	37.2137i	2.75107	+	1.32484i
$790$	5.31863	+	21.4674i	0.189228	+	0.763776i
$791$	−29.6438	+	25.3312i	−1.05401	+	0.900675i
$792$	−12.0961	+	25.1179i	−0.429817	+	0.892524i
$793$	29.8951	−	23.8406i	1.06161	−	0.846604i
$794$	−2.26841	+	1.09241i	−0.0805030	+	0.0387682i
$795$	42.7114	−	35.3708i	1.51482	−	1.25447i
$796$	−3.84993	+	16.8676i	−0.136457	+	0.597858i
$797$	−1.66269	−	1.32595i	−0.0588955	−	0.0469676i	0.593600	−	0.804760i	$-0.297706\pi$
$797$	−1.66269	−	1.32595i	−0.0588955	−	0.0469676i	−0.652495	+	0.757793i	$0.726278\pi$
$798$	22.8186	−	11.9584i	0.807770	−	0.423324i
$799$	1.58038	+	1.98173i	0.0559098	+	0.0701087i
$800$	0.184598	+	4.99659i	0.00652653	+	0.176656i
$801$	7.82026	−	34.2628i	0.276315	−	1.21062i
$802$		−	16.1521i		−	0.570352i
$803$			50.1142i			1.76849i
$804$	−0.821456	+	3.59903i	−0.0289705	+	0.126928i
$805$	46.6922	+	19.5445i	1.64568	+	0.688852i
$806$	−3.27940	−	14.3680i	−0.115512	−	0.506091i
$807$	−62.4240	+	14.2479i	−2.19743	+	0.501549i
$808$	7.44965	−	5.94090i	0.262078	−	0.209000i
$809$	4.87717	+	6.11578i	0.171472	+	0.215019i	0.860140	−	0.510057i	$-0.170376\pi$
$809$	4.87717	+	6.11578i	0.171472	+	0.215019i	−0.688668	+	0.725077i	$0.741804\pi$
$810$	−17.8377	+	0.329393i	−0.626752	+	0.0115737i
$811$	2.27272	+	9.95743i	0.0798059	+	0.349653i	0.999028	−	0.0440877i	$-0.0140381\pi$
$811$	2.27272	+	9.95743i	0.0798059	+	0.349653i	−0.919222	+	0.393740i	$0.871181\pi$
$812$	−16.9466	+	0.574950i	−0.594710	+	0.0201768i
$813$	67.2004	+	15.3381i	2.35682	+	0.537929i
$814$	−6.14046			−0.215223
$815$	−7.49098	+	35.8597i	−0.262397	+	1.25611i
$816$	0.175546	−	0.769116i	0.00614533	−	0.0269244i
$817$	−5.44232	−	11.3011i	−0.190403	−	0.395375i
$818$	5.63192	−	4.49130i	0.196915	−	0.157035i
$819$	−3.08539	−	90.9415i	−0.107812	−	3.17775i
$820$	8.29134	−	6.86635i	0.289546	−	0.239783i
$821$	9.01993	−	39.5189i	0.314798	−	1.37922i	−0.531748	−	0.846902i	$-0.678465\pi$
$821$	9.01993	−	39.5189i	0.314798	−	1.37922i	0.846546	−	0.532316i	$-0.178678\pi$
$822$	5.19813	+	4.14537i	0.181306	+	0.144586i
$823$	7.59655	+	15.7744i	0.264799	+	0.549861i	0.990396	−	0.138259i	$-0.0441506\pi$
$823$	7.59655	+	15.7744i	0.264799	+	0.549861i	−0.725597	+	0.688120i	$0.758436\pi$
$824$	5.55746	+	6.96883i	0.193603	+	0.242771i
$825$	−53.5368	+	46.0282i	−1.86391	+	1.60249i
$826$	−1.07494	−	0.207273i	−0.0374018	−	0.00721194i
$827$	7.73933	+	16.0709i	0.269123	+	0.558839i	0.991107	−	0.133071i	$-0.0424837\pi$
$827$	7.73933	+	16.0709i	0.269123	+	0.558839i	−0.721984	+	0.691910i	$0.756769\pi$
$828$	−21.8470	+	45.3657i	−0.759235	+	1.57657i
$829$	−10.1059	−	44.2768i	−0.350992	−	1.53780i	−0.774895	−	0.632090i	$-0.782197\pi$
$829$	−10.1059	−	44.2768i	−0.350992	−	1.53780i	0.423903	−	0.905708i	$-0.360660\pi$
$830$	14.6045	+	11.2119i	0.506928	+	0.389170i
$831$	14.1814	−	17.7829i	0.491946	−	0.616880i
$832$		−	5.84404i		−	0.202606i
$833$	1.82996	+	0.288884i	0.0634045	+	0.0100092i
$834$	−23.1165			−0.800459
$835$	21.0346	+	25.3999i	0.727931	+	0.879000i
$836$	13.9424	+	6.71431i	0.482208	+	0.232219i
$837$	21.1429	−	4.82574i	0.730807	−	0.166802i
$838$	7.77209	−	16.1389i	0.268482	−	0.557509i
$839$	13.7573	−	6.62519i	0.474956	−	0.228727i	−0.181062	−	0.983472i	$-0.557954\pi$
$839$	13.7573	−	6.62519i	0.474956	−	0.228727i	0.656019	+	0.754745i	$0.272239\pi$
$840$	−0.923242	−	17.6103i	−0.0318549	−	0.607615i
$841$	−10.8783	−	5.23874i	−0.375115	−	0.180646i
$842$	−18.3330	+	14.6201i	−0.631798	+	0.503842i
$843$	−8.54172	−	17.7371i	−0.294192	−	0.610897i
$844$	−2.38262	+	2.98771i	−0.0820132	+	0.102841i
$845$	19.7320	−	42.9866i	0.678801	−	1.47878i
$846$	−35.1416	+	44.0662i	−1.20819	+	1.51503i
$847$	−7.73264	−	29.2663i	−0.265697	−	1.00560i
$848$	−6.50499	+	5.18756i	−0.223382	+	0.178141i
$849$	18.1587	−	8.74477i	0.623205	−	0.300120i
$850$	0.786307	−	1.06436i	0.0269701	−	0.0365071i
$851$	−11.0904			−0.380173
$852$		−	4.00466i		−	0.137198i
$853$	0.252090	+	0.0575379i	0.00863140	+	0.00197006i	0.226834	−	0.973933i	$-0.427162\pi$
$853$	0.252090	+	0.0575379i	0.00863140	+	0.00197006i	−0.218203	+	0.975903i	$0.570020\pi$
$854$	−13.1606	+	11.2460i	−0.450345	+	0.384829i
$855$	0.793672	+	42.9799i	0.0271430	+	1.46988i
$856$	−2.18064	−	9.55400i	−0.0745327	−	0.326549i
$857$	10.8108	−	8.62133i	0.369290	−	0.294499i	−0.421207	−	0.906964i	$-0.638394\pi$
$857$	10.8108	−	8.62133i	0.369290	−	0.294499i	0.790497	+	0.612465i	$0.209822\pi$
$858$	64.5177	−	51.4512i	2.20260	−	1.75651i
$859$	6.19084	+	27.1239i	0.211229	+	0.925454i	0.963733	+	0.266867i	$0.0859884\pi$
$859$	6.19084	+	27.1239i	0.211229	+	0.925454i	−0.752505	+	0.658587i	$0.771154\pi$
$860$	−8.58453	+	0.158523i	−0.292730	+	0.00540559i
$861$	−28.8652	+	24.6659i	−0.983722	+	0.840610i
$862$	35.8310	+	8.17819i	1.22041	+	0.278550i
$863$		−	27.1028i		−	0.922590i	−0.887247	−	0.461295i	$-0.847385\pi$
$863$		−	27.1028i		−	0.922590i	0.887247	−	0.461295i	$-0.152615\pi$
$864$	8.59968			0.292567
$865$	−30.7182	−	14.1005i	−1.04445	−	0.479431i
$866$	18.1280	−	8.72997i	0.616013	−	0.296656i
$867$	39.4547	−	31.4641i	1.33995	−	1.06858i
$868$	1.70438	+	6.45069i	0.0578504	+	0.218951i
$869$	29.2134	−	36.6325i	0.990998	−	1.24267i
$870$	17.8204	−	38.8221i	0.604168	−	1.31619i
$871$	4.51259	−	5.65861i	0.152903	−	0.191735i
$872$	0.334099	+	0.693764i	0.0113140	+	0.0234938i
$873$	46.4926	−	37.0766i	1.57354	−	1.25485i
$874$	25.1816	+	12.1268i	0.851780	+	0.410195i
$875$	10.4064	−	27.6895i	0.351799	−	0.936075i
$876$	28.4104	−	13.6817i	0.959898	−	0.462263i
$877$	−18.2089	+	37.8111i	−0.614870	+	1.27679i	0.328329	+	0.944564i	$0.393515\pi$
$877$	−18.2089	+	37.8111i	−0.614870	+	1.27679i	−0.943199	+	0.332228i	$0.892200\pi$
$878$	3.08865	−	0.704965i	0.104237	−	0.0237914i
$879$	55.7765	+	26.8606i	1.88130	+	0.905984i
$880$	8.15838	−	6.75624i	0.275019	−	0.227753i
$881$	−57.6945			−1.94378			−0.971889	−	0.235441i	$-0.924346\pi$
$881$	−57.6945			−1.94378			−0.971889	+	0.235441i	$0.924346\pi$
$882$	2.79207	+	41.1006i	0.0940137	+	1.38393i
$883$			25.8043i			0.868383i	0.900820	+	0.434192i	$0.142966\pi$
$883$			25.8043i			0.868383i	−0.900820	+	0.434192i	$0.857034\pi$
$884$	−0.964344	+	1.20925i	−0.0324344	+	0.0406714i
$885$	1.67941	−	2.18758i	0.0564527	−	0.0735346i
$886$	4.88711	+	21.4118i	0.164186	+	0.719345i
$887$	−6.18582	+	12.8450i	−0.207700	+	0.431293i	−0.978631	−	0.205626i	$-0.934077\pi$
$887$	−6.18582	+	12.8450i	−0.207700	+	0.431293i	0.770931	+	0.636919i	$0.219791\pi$
$888$	1.67641	+	3.48111i	0.0562568	+	0.116818i
$889$	−10.2689	−	1.98007i	−0.344406	−	0.0664095i
$890$	−8.13142	+	10.5919i	−0.272566	+	0.355041i
$891$	23.5657	+	29.5504i	0.789479	+	0.989976i
$892$	3.50670	+	7.28173i	0.117413	+	0.243810i
$893$	24.4602	+	19.5064i	0.818531	+	0.652756i
$894$	1.11999	−	4.90702i	0.0374582	−	0.164115i
$895$	−29.3166	+	24.2781i	−0.979946	+	0.811527i
$896$	0.0897112	+	2.64423i	0.00299704	+	0.0883375i
$897$	116.526	−	92.9267i	3.89070	−	3.10273i
$898$	1.72291	+	3.57766i	0.0574943	+	0.119388i
$899$	−3.59638	+	15.7568i	−0.119946	+	0.525517i
$900$	26.9645	+	11.7796i	0.898816	+	0.392655i
$901$	2.20203			0.0733602
$902$	−22.2351	−	5.07502i	−0.740348	−	0.168980i
$903$	30.2646	−	1.02679i	1.00714	−	0.0341695i
$904$	3.27948	+	14.3683i	0.109074	+	0.477883i
$905$	−0.324946	−	17.5969i	−0.0108016	−	0.584939i
$906$	−21.1597	−	26.5335i	−0.702986	−	0.881516i
$907$	18.3917	−	14.6669i	0.610685	−	0.487005i	−0.268631	−	0.963243i	$-0.586571\pi$
$907$	18.3917	−	14.6669i	0.610685	−	0.487005i	0.879317	+	0.476238i	$0.158000\pi$
$908$	8.73604	−	1.99394i	0.289916	−	0.0661714i
$909$	−12.4779	−	54.6695i	−0.413867	−	1.81327i
$910$	−13.3496	+	31.8926i	−0.442535	+	1.05723i
$911$	5.12246	−	22.4430i	0.169715	−	0.743569i	−0.816398	−	0.577490i	$-0.804032\pi$
$911$	5.12246	−	22.4430i	0.169715	−	0.743569i	0.986113	−	0.166079i	$-0.0531106\pi$
$912$		−	9.73721i		−	0.322431i
$913$		−	39.0064i		−	1.29092i
$914$	1.64780	−	7.21950i	0.0545045	−	0.238800i
$915$	−10.4875	−	42.3305i	−0.346707	−	1.39940i
$916$	7.79208	+	9.77096i	0.257458	+	0.322842i
$917$	−52.1639	+	27.3372i	−1.72260	+	0.902755i
$918$	−1.77945	−	1.41906i	−0.0587305	−	0.0468360i
$919$	−12.1314	+	53.1512i	−0.400179	+	1.75330i	0.226492	+	0.974013i	$0.427274\pi$
$919$	−12.1314	+	53.1512i	−0.400179	+	1.75330i	−0.626671	+	0.779284i	$0.715583\pi$
$920$	14.7350	−	12.2025i	0.485798	−	0.402306i
$921$	33.1919	−	15.9844i	1.09371	−	0.526703i
$922$	−7.58912	+	6.05212i	−0.249934	+	0.199316i
$923$	−3.40661	+	7.07391i	−0.112130	+	0.232840i
$924$	−28.4023	+	24.2703i	−0.934366	+	0.798435i
$925$	0.239280	+	6.47667i	0.00786746	+	0.212952i
$926$	18.0367	+	8.68603i	0.592723	+	0.285441i
$927$	51.1410	−	11.6726i	1.67969	−	0.383378i
$928$	−2.78072	+	5.77422i	−0.0912816	+	0.189548i
$929$	−16.4417	+	20.6173i	−0.539436	+	0.676431i	−0.974608	−	0.223916i	$-0.928116\pi$
$929$	−16.4417	+	20.6173i	−0.539436	+	0.676431i	0.435173	+	0.900347i	$0.356687\pi$
$930$	−16.4532	−	3.43702i	−0.539522	−	0.112704i
$931$	22.8141	−	1.54982i	0.747702	−	0.0507932i
$932$			16.1624i			0.529417i
$933$	−8.03564	−	6.40821i	−0.263075	−	0.209795i
$934$	−11.4243	−	5.50166i	−0.373815	−	0.180020i
$935$	−2.80300	+	0.0517606i	−0.0916680	+	0.00169275i
$936$	−30.9865	−	14.9223i	−1.01283	−	0.487751i
$937$	−11.6739	−	24.2410i	−0.381368	−	0.791920i	−0.999981	−	0.00622330i	$-0.998019\pi$
$937$	−11.6739	−	24.2410i	−0.381368	−	0.791920i	0.618612	−	0.785697i	$-0.287695\pi$
$938$	−1.95493	+	2.62960i	−0.0638307	+	0.0858596i
$939$	10.0528	+	4.84118i	0.328061	+	0.157986i
$940$	19.1198	−	9.64648i	0.623620	−	0.314633i
$941$	−40.2456	+	19.3812i	−1.31197	+	0.631811i	−0.953405	−	0.301695i	$-0.902448\pi$
$941$	−40.2456	+	19.3812i	−1.31197	+	0.631811i	−0.358564	+	0.933505i	$0.616733\pi$
$942$	−34.0772	−	27.1757i	−1.11030	−	0.885431i
$943$	−40.1592	−	9.16607i	−1.30776	−	0.298488i
$944$	−0.257982	+	0.323500i	−0.00839661	+	0.0105290i
$945$	−46.9309	−	19.6443i	−1.52666	−	0.639031i
$946$	11.3412	+	14.2214i	0.368733	+	0.462377i
$947$	8.93211	+	18.5477i	0.290254	+	0.602720i	0.994202	−	0.107533i	$-0.0342951\pi$
$947$	8.93211	+	18.5477i	0.290254	+	0.602720i	−0.703947	+	0.710252i	$0.748581\pi$
$948$	−28.7430	−	6.56041i	−0.933530	−	0.213072i
$949$	−61.8231			−2.00686
$950$	6.53863	−	14.9674i	0.212141	−	0.485608i
$951$	−11.6603	+	51.0871i	−0.378111	+	1.65661i
$952$	0.417770	−	0.561948i	0.0135400	−	0.0182128i
$953$	−17.6704	+	4.03315i	−0.572400	+	0.130647i	−0.498917	−	0.866650i	$-0.666269\pi$
$953$	−17.6704	+	4.03315i	−0.572400	+	0.130647i	−0.0734831	+	0.997296i	$0.523412\pi$
$954$	10.8957	+	47.7371i	0.352760	+	1.54554i
$955$	16.1043	+	31.9196i	0.521123	+	1.03289i
$956$	17.7525	+	22.2609i	0.574156	+	0.719969i
$957$	−88.2286	+	20.1376i	−2.85202	+	0.650956i
$958$	24.9591	−	5.69674i	0.806390	−	0.184053i
$959$	2.73933	+	5.22708i	0.0884574	+	0.168791i
$960$	−6.05753	−	2.78057i	−0.195506	−	0.0897424i
$961$	−24.6405			−0.794856
$962$		−	7.57515i		−	0.244233i
$963$	−56.2257	−	12.8332i	−1.81185	−	0.413542i
$964$	2.24808	−	1.08262i	0.0724057	−	0.0348687i
$965$	−0.321851	+	0.162383i	−0.0103608	+	0.00522729i
$966$	−51.2977	+	43.8350i	−1.65048	+	1.41037i
$967$	22.6123	+	18.0327i	0.727161	+	0.579892i	0.915551	−	0.402203i	$-0.131755\pi$
$967$	22.6123	+	18.0327i	0.727161	+	0.579892i	−0.188389	+	0.982094i	$0.560327\pi$
$968$	−11.1544	−	2.54591i	−0.358514	−	0.0818286i
$969$	−1.60677	+	2.01482i	−0.0516169	+	0.0647255i
$970$	−21.9316	+	5.43364i	−0.704181	+	0.174464i
$971$	12.0759	+	15.1427i	0.387535	+	0.485954i	0.936885	−	0.349639i	$-0.113696\pi$
$971$	12.0759	+	15.1427i	0.387535	+	0.485954i	−0.549349	+	0.835593i	$0.685124\pi$
$972$	−0.874954	+	1.81686i	−0.0280642	+	0.0582758i
$973$	−18.7776	−	8.27061i	−0.601982	−	0.265144i
$974$	13.5980	−	6.54843i	0.435707	−	0.209825i
$975$	−56.7824	−	66.0453i	−1.81849	−	2.11514i
$976$	1.45595	+	6.37891i	0.0466037	+	0.204184i
$977$	9.92625	−	20.6121i	0.317569	−	0.659439i	−0.679684	−	0.733505i	$-0.737883\pi$
$977$	9.92625	−	20.6121i	0.317569	−	0.659439i	0.997253	+	0.0740661i	$0.0235976\pi$
$978$	−38.1803	−	30.4478i	−1.22087	−	0.973612i
$979$	28.2894			0.904133
$980$	5.55067	−	14.6352i	0.177310	−	0.467505i
$981$	4.53160			0.144683
$982$	−19.4440	−	15.5060i	−0.620482	−	0.494818i
$983$	−6.91158	+	14.3520i	−0.220445	+	0.457759i	−0.981635	−	0.190770i	$-0.938901\pi$
$983$	−6.91158	+	14.3520i	−0.220445	+	0.457759i	0.761190	+	0.648530i	$0.224616\pi$
$984$	3.19334	+	13.9909i	0.101800	+	0.446014i
$985$	7.13970	−	9.30010i	0.227490	−	0.296326i
$986$	1.52821	−	0.735947i	0.0486681	−	0.0234373i
$987$	−66.9001	+	35.0600i	−2.12946	+	1.11597i
$988$	−8.28307	+	17.2000i	−0.263520	+	0.547204i
$989$	20.4835	+	25.6854i	0.651336	+	0.816750i
$990$	−14.9914	−	60.5093i	−0.476458	−	1.92311i
$991$	7.08120	−	8.87954i	0.224942	−	0.282068i	−0.656535	−	0.754296i	$-0.727979\pi$
$991$	7.08120	−	8.87954i	0.224942	−	0.282068i	0.881477	+	0.472228i	$0.156550\pi$
$992$	2.45857	+	0.561153i	0.0780598	+	0.0178166i
$993$	−31.5929	−	25.1945i	−1.00257	−	0.799524i
$994$	1.43279	−	3.25300i	0.0454452	−	0.103179i
$995$	−17.4264	−	34.5401i	−0.552454	−	1.09499i
$996$	−22.1132	+	10.6492i	−0.700684	+	0.337432i
$997$	8.89174	+	2.02948i	0.281604	+	0.0642743i	0.360990	−	0.932570i	$-0.382439\pi$
$997$	8.89174	+	2.02948i	0.281604	+	0.0642743i	−0.0793859	+	0.996844i	$0.525296\pi$
$998$			33.8302i			1.07088i
$999$	11.1471			0.352677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.p.a.239.2	✓	168
5.4	even	2	inner	490.2.p.a.239.27	yes	168
49.8	even	7	inner	490.2.p.a.449.27	yes	168
245.204	even	14	inner	490.2.p.a.449.2	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.p.a.239.2	✓	168	1.1	even	1	trivial
490.2.p.a.239.27	yes	168	5.4	even	2	inner
490.2.p.a.449.2	yes	168	245.204	even	14	inner
490.2.p.a.449.27	yes	168	49.8	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.781831 - 0.623490i) q^{2} +(-1.29331 + 2.68559i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.77367 - 1.36165i) q^{5} +(2.68559 - 1.29331i) q^{6} +(2.64423 - 0.0897112i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-3.66926 - 4.60111i) q^{9} +O(q^{10})\)	\(q+(-0.781831 - 0.623490i) q^{2} +(-1.29331 + 2.68559i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.77367 - 1.36165i) q^{5} +(2.68559 - 1.29331i) q^{6} +(2.64423 - 0.0897112i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-3.66926 - 4.60111i) q^{9} +(0.537736 + 2.17045i) q^{10} +(2.95361 - 3.70370i) q^{11} +(-2.90604 - 0.663286i) q^{12} +(4.56905 + 3.64370i) q^{13} +(-2.12328 - 1.57851i) q^{14} +(5.95074 - 3.00231i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.258025 + 0.0588925i) q^{17} +5.88504i q^{18} +3.26667 q^{19} +(0.932832 - 2.03220i) q^{20} +(-3.17889 + 7.21734i) q^{21} +(-4.61844 + 1.05413i) q^{22} +(-8.34143 + 1.90388i) q^{23} +(1.85849 + 2.33047i) q^{24} +(1.29182 + 4.83024i) q^{25} +(-1.30042 - 5.69752i) q^{26} +(8.38407 - 1.91361i) q^{27} +(0.675858 + 2.55797i) q^{28} +(-1.42612 + 6.24822i) q^{29} +(-6.52439 - 1.36292i) q^{30} +2.52180 q^{31} +(0.974928 + 0.222521i) q^{32} +(6.12669 + 12.7222i) q^{33} +(-0.165013 - 0.206920i) q^{34} +(-4.81215 - 3.44140i) q^{35} +(3.66926 - 4.60111i) q^{36} +(1.26372 + 0.288436i) q^{37} +(-2.55398 - 2.03673i) q^{38} +(-15.6947 + 7.55816i) q^{39} +(-1.99637 + 1.00722i) q^{40} +(4.33764 + 2.08890i) q^{41} +(6.98529 - 3.66074i) q^{42} +(-1.66602 - 3.45952i) q^{43} +(4.26808 + 2.05540i) q^{44} +(0.242961 + 13.1571i) q^{45} +(7.70864 + 3.71229i) q^{46} +(7.48783 + 5.97134i) q^{47} -2.98078i q^{48} +(6.98390 - 0.474434i) q^{49} +(2.00162 - 4.58187i) q^{50} +(-0.491868 + 0.616783i) q^{51} +(-2.53563 + 5.26530i) q^{52} +(8.11159 - 1.85142i) q^{53} +(-7.74804 - 3.73126i) q^{54} +(-10.2819 + 2.54737i) q^{55} +(1.06646 - 2.42129i) q^{56} +(-4.22482 + 8.77293i) q^{57} +(5.01068 - 3.99589i) q^{58} +(0.372795 - 0.179529i) q^{59} +(4.25120 + 5.13347i) q^{60} +(1.45595 - 6.37891i) q^{61} +(-1.97162 - 1.57232i) q^{62} +(-10.1152 - 11.8372i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-3.14255 - 12.6842i) q^{65} +(3.14213 - 13.7666i) q^{66} -1.23846i q^{67} +0.264661i q^{68} +(5.67504 - 24.8640i) q^{69} +(1.61661 + 5.69092i) q^{70} +(0.298956 + 1.30981i) q^{71} +(-5.73749 + 1.30955i) q^{72} +(-8.27086 + 6.59579i) q^{73} +(-0.808179 - 1.01342i) q^{74} +(-14.6428 - 2.77772i) q^{75} +(0.726902 + 3.18477i) q^{76} +(7.47775 - 10.0584i) q^{77} +(16.9830 + 3.87627i) q^{78} +9.89077 q^{79} +(2.18882 + 0.457238i) q^{80} +(-1.77541 + 7.77857i) q^{81} +(-2.08890 - 4.33764i) q^{82} +(6.43762 - 5.13383i) q^{83} +(-7.74375 - 1.49318i) q^{84} +(-0.377460 - 0.455796i) q^{85} +(-0.854430 + 3.74350i) q^{86} +(-14.9357 - 11.9109i) q^{87} +(-2.05540 - 4.26808i) q^{88} +(3.72332 + 4.66889i) q^{89} +(8.01337 - 10.4381i) q^{90} +(12.4085 + 9.22488i) q^{91} +(-3.71229 - 7.70864i) q^{92} +(-3.26147 + 6.77252i) q^{93} +(-2.13115 - 9.33717i) q^{94} +(-5.79399 - 4.44806i) q^{95} +(-1.85849 + 2.33047i) q^{96} +10.1046i q^{97} +(-5.75604 - 3.98347i) q^{98} -27.8787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Introduction

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