LMFDB - Embedded newform 175.2.x.a.108.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			108.4
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0935941 - 1.78588i) q^{2} +(0.279642 + 0.226450i) q^{3} +(-1.19157 + 0.125239i) q^{4} +(1.07995 + 1.95799i) q^{5} +(0.378240 - 0.520602i) q^{6} +(-0.314872 - 2.62695i) q^{7} +(-0.224327 - 1.41635i) q^{8} +(-0.596815 - 2.80779i) q^{9} +(3.39566 - 2.11192i) q^{10} +(4.12989 + 0.877836i) q^{11} +(-0.361574 - 0.234809i) q^{12} +(0.268631 + 0.527217i) q^{13} +(-4.66195 + 0.808191i) q^{14} +(-0.141386 + 0.792089i) q^{15} +(-4.85234 + 1.03140i) q^{16} +(-0.811348 - 0.311447i) q^{17} +(-4.95853 + 1.32863i) q^{18} +(-0.667317 + 6.34910i) q^{19} +(-1.53205 - 2.19783i) q^{20} +(0.506820 - 0.805908i) q^{21} +(1.18118 - 7.45766i) q^{22} +(-1.61819 + 0.0848056i) q^{23} +(0.258000 - 0.446869i) q^{24} +(-2.66742 + 4.22905i) q^{25} +(0.916406 - 0.529087i) q^{26} +(0.959010 - 1.88216i) q^{27} +(0.704189 + 3.09076i) q^{28} +(-0.996818 - 1.37200i) q^{29} +(1.42781 + 0.178365i) q^{30} +(3.65980 + 8.22005i) q^{31} +(1.55381 + 5.79889i) q^{32} +(0.956106 + 1.18069i) q^{33} +(-0.480271 + 1.47812i) q^{34} +(4.80348 - 3.45348i) q^{35} +(1.06279 + 3.27094i) q^{36} +(-2.37321 + 3.65442i) q^{37} +(11.4012 + 0.597511i) q^{38} +(-0.0442678 + 0.208263i) q^{39} +(2.53093 - 1.96881i) q^{40} +(-5.70437 - 1.85346i) q^{41} +(-1.48669 - 0.829693i) q^{42} +(3.73281 + 3.73281i) q^{43} +(-5.03100 - 0.528779i) q^{44} +(4.85309 - 4.20083i) q^{45} +(0.302906 + 2.88195i) q^{46} +(-3.45442 - 8.99906i) q^{47} +(-1.59048 - 0.810389i) q^{48} +(-6.80171 + 1.65430i) q^{49} +(7.80224 + 4.36789i) q^{50} +(-0.156360 - 0.270823i) q^{51} +(-0.386121 - 0.594574i) q^{52} +(5.33703 - 6.59068i) q^{53} +(-3.45108 - 1.53652i) q^{54} +(2.74128 + 9.03429i) q^{55} +(-3.65004 + 1.03526i) q^{56} +(-1.62436 + 1.62436i) q^{57} +(-2.35694 + 1.90861i) q^{58} +(4.53398 + 5.03550i) q^{59} +(0.0692713 - 0.961538i) q^{60} +(-0.917861 - 0.826446i) q^{61} +(14.3375 - 7.30532i) q^{62} +(-7.18801 + 2.45190i) q^{63} +(0.774814 - 0.251752i) q^{64} +(-0.742177 + 1.09534i) q^{65} +(2.01909 - 1.81800i) q^{66} +(-4.10789 + 10.7014i) q^{67} +(1.00578 + 0.269499i) q^{68} +(-0.471717 - 0.342723i) q^{69} +(-6.61709 - 8.25523i) q^{70} +(-11.3299 + 8.23164i) q^{71} +(-3.84293 + 1.47516i) q^{72} +(2.92452 - 1.89921i) q^{73} +(6.74848 + 3.89623i) q^{74} +(-1.70359 + 0.578583i) q^{75} -7.64897i q^{76} +(1.00564 - 11.1254i) q^{77} +(0.376077 + 0.0595648i) q^{78} +(5.74668 - 12.9073i) q^{79} +(-7.25974 - 8.38696i) q^{80} +(-7.17266 + 3.19347i) q^{81} +(-2.77617 + 10.3608i) q^{82} +(3.01586 - 0.477665i) q^{83} +(-0.502981 + 1.02377i) q^{84} +(-0.266404 - 1.92496i) q^{85} +(6.31698 - 7.01572i) q^{86} +(0.0319372 - 0.609399i) q^{87} +(0.316873 - 6.04629i) q^{88} +(11.4094 - 12.6715i) q^{89} +(-7.95640 - 8.27388i) q^{90} +(1.30039 - 0.871684i) q^{91} +(1.91756 - 0.303712i) q^{92} +(-0.837993 + 3.12743i) q^{93} +(-15.7479 + 7.01144i) q^{94} +(-13.1521 + 5.55010i) q^{95} +(-0.878647 + 1.97347i) q^{96} +(-11.5748 - 1.83327i) q^{97} +(3.59099 + 11.9922i) q^{98} -12.1198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.0935941	−	1.78588i	−0.0661810	−	1.26281i	−0.806776	−	0.590857i	$-0.798790\pi$
$2$	−0.0935941	−	1.78588i	−0.0661810	−	1.26281i	0.740595	−	0.671952i	$-0.234544\pi$
$3$	0.279642	+	0.226450i	0.161451	+	0.130741i	0.706642	−	0.707572i	$-0.250209\pi$
$3$	0.279642	+	0.226450i	0.161451	+	0.130741i	−0.545190	+	0.838312i	$0.683543\pi$
$4$	−1.19157	+	0.125239i	−0.595785	+	0.0626196i
$5$	1.07995	+	1.95799i	0.482968	+	0.875638i
$5$	1.07995	+	1.95799i	0.482968	+	0.875638i
$6$	0.378240	−	0.520602i	0.154416	−	0.212535i
$7$	−0.314872	−	2.62695i	−0.119010	−	0.992893i
$7$	−0.314872	−	2.62695i	−0.119010	−	0.992893i
$8$	−0.224327	−	1.41635i	−0.0793117	−	0.500755i
$9$	−0.596815	−	2.80779i	−0.198938	−	0.935931i
$10$	3.39566	−	2.11192i	1.07380	−	0.667847i
$11$	4.12989	+	0.877836i	1.24521	+	0.264678i	0.782960	−	0.622072i	$-0.213709\pi$
$11$	4.12989	+	0.877836i	1.24521	+	0.264678i	0.462250	+	0.886750i	$0.347042\pi$
$12$	−0.361574	−	0.234809i	−0.104377	−	0.0677834i
$13$	0.268631	+	0.527217i	0.0745047	+	0.146224i	0.925254	−	0.379348i	$-0.123852\pi$
$13$	0.268631	+	0.527217i	0.0745047	+	0.146224i	−0.850749	+	0.525571i	$0.823852\pi$
$14$	−4.66195	+	0.808191i	−1.24596	+	0.215998i
$15$	−0.141386	+	0.792089i	−0.0365058	+	0.204517i
$16$	−4.85234	+	1.03140i	−1.21308	+	0.257849i
$17$	−0.811348	−	0.311447i	−0.196781	−	0.0755371i	0.257982	−	0.966150i	$-0.416943\pi$
$17$	−0.811348	−	0.311447i	−0.196781	−	0.0755371i	−0.454763	+	0.890613i	$0.650276\pi$
$18$	−4.95853	+	1.32863i	−1.16874	+	0.313162i
$19$	−0.667317	+	6.34910i	−0.153093	+	1.45658i	0.600702	+	0.799473i	$0.294888\pi$
$19$	−0.667317	+	6.34910i	−0.153093	+	1.45658i	−0.753795	+	0.657110i	$0.771779\pi$
$20$	−1.53205	−	2.19783i	−0.342577	−	0.491449i
$21$	0.506820	−	0.805908i	0.110597	−	0.175863i
$22$	1.18118	−	7.45766i	0.251828	−	1.58998i
$23$	−1.61819	+	0.0848056i	−0.337415	+	0.0176832i	−0.220291	−	0.975434i	$-0.570701\pi$
$23$	−1.61819	+	0.0848056i	−0.337415	+	0.0176832i	−0.117124	+	0.993117i	$0.537367\pi$
$24$	0.258000	−	0.446869i	0.0526640	−	0.0912168i
$25$	−2.66742	+	4.22905i	−0.533485	+	0.845810i
$26$	0.916406	−	0.529087i	0.179722	−	0.103762i
$27$	0.959010	−	1.88216i	0.184562	−	0.362223i
$28$	0.704189	+	3.09076i	0.133079	+	0.584099i
$29$	−0.996818	−	1.37200i	−0.185104	−	0.254774i	0.706373	−	0.707840i	$-0.250330\pi$
$29$	−0.996818	−	1.37200i	−0.185104	−	0.254774i	−0.891477	+	0.453066i	$0.850330\pi$
$30$	1.42781	+	0.178365i	0.260681	+	0.0325648i
$31$	3.65980	+	8.22005i	0.657320	+	1.47636i	0.866853	+	0.498563i	$0.166139\pi$
$31$	3.65980	+	8.22005i	0.657320	+	1.47636i	−0.209534	+	0.977801i	$0.567195\pi$
$32$	1.55381	+	5.79889i	0.274677	+	1.02511i
$33$	0.956106	+	1.18069i	0.166437	+	0.205532i
$34$	−0.480271	+	1.47812i	−0.0823657	+	0.253496i
$35$	4.80348	−	3.45348i	0.811937	−	0.583745i
$36$	1.06279	+	3.27094i	0.177132	+	0.545157i
$37$	−2.37321	+	3.65442i	−0.390153	+	0.600782i	−0.978105	−	0.208113i	$-0.933268\pi$
$37$	−2.37321	+	3.65442i	−0.390153	+	0.600782i	0.587952	+	0.808896i	$0.299934\pi$
$38$	11.4012	+	0.597511i	1.84952	+	0.0969291i
$39$	−0.0442678	+	0.208263i	−0.00708851	+	0.0333488i
$40$	2.53093	−	1.96881i	0.400175	−	0.311297i
$41$	−5.70437	−	1.85346i	−0.890873	−	0.289462i	−0.172408	−	0.985026i	$-0.555155\pi$
$41$	−5.70437	−	1.85346i	−0.890873	−	0.289462i	−0.718465	+	0.695563i	$0.755155\pi$
$42$	−1.48669	−	0.829693i	−0.229401	−	0.128024i
$43$	3.73281	+	3.73281i	0.569248	+	0.569248i	0.931918	−	0.362670i	$-0.118135\pi$
$43$	3.73281	+	3.73281i	0.569248	+	0.569248i	−0.362670	+	0.931918i	$0.618135\pi$
$44$	−5.03100	−	0.528779i	−0.758452	−	0.0797165i
$45$	4.85309	−	4.20083i	0.723456	−	0.626222i
$46$	0.302906	+	2.88195i	0.0446610	+	0.424921i
$47$	−3.45442	−	8.99906i	−0.503878	−	1.31265i	−0.915875	−	0.401463i	$-0.868502\pi$
$47$	−3.45442	−	8.99906i	−0.503878	−	1.31265i	0.411997	−	0.911185i	$-0.364831\pi$
$48$	−1.59048	−	0.810389i	−0.229566	−	0.116970i
$49$	−6.80171	+	1.65430i	−0.971673	+	0.236329i
$50$	7.80224	+	4.36789i	1.10340	+	0.617713i
$51$	−0.156360	−	0.270823i	−0.0218948	−	0.0379228i
$52$	−0.386121	−	0.594574i	−0.0535453	−	0.0824525i
$53$	5.33703	−	6.59068i	0.733098	−	0.905300i	−0.265166	−	0.964203i	$-0.585427\pi$
$53$	5.33703	−	6.59068i	0.733098	−	0.905300i	0.998264	+	0.0589026i	$0.0187601\pi$
$54$	−3.45108	−	1.53652i	−0.469632	−	0.209094i
$55$	2.74128	+	9.03429i	0.369634	+	1.21818i
$56$	−3.65004	+	1.03526i	−0.487757	+	0.138343i
$57$	−1.62436	+	1.62436i	−0.215152	+	0.215152i
$58$	−2.35694	+	1.90861i	−0.309481	+	0.250613i
$59$	4.53398	+	5.03550i	0.590274	+	0.655566i	0.962087	−	0.272742i	$-0.0879305\pi$
$59$	4.53398	+	5.03550i	0.590274	+	0.655566i	−0.371813	+	0.928308i	$0.621264\pi$
$60$	0.0692713	−	0.961538i	0.00894289	−	0.124134i
$61$	−0.917861	−	0.826446i	−0.117520	−	0.105816i	0.608276	−	0.793726i	$-0.291862\pi$
$61$	−0.917861	−	0.826446i	−0.117520	−	0.105816i	−0.725796	+	0.687910i	$0.758528\pi$
$62$	14.3375	−	7.30532i	1.82086	−	0.927777i
$63$	−7.18801	+	2.45190i	−0.905604	+	0.308910i
$64$	0.774814	−	0.251752i	0.0968517	−	0.0314690i
$65$	−0.742177	+	1.09534i	−0.0920557	+	0.135861i
$66$	2.01909	−	1.81800i	0.248533	−	0.223780i
$67$	−4.10789	+	10.7014i	−0.501859	+	1.30739i	0.415596	+	0.909549i	$0.363573\pi$
$67$	−4.10789	+	10.7014i	−0.501859	+	1.30739i	−0.917455	+	0.397838i	$0.869760\pi$
$68$	1.00578	+	0.269499i	0.121969	+	0.0326815i
$69$	−0.471717	−	0.342723i	−0.0567881	−	0.0412590i
$70$	−6.61709	−	8.25523i	−0.790894	−	0.986689i
$71$	−11.3299	+	8.23164i	−1.34461	+	0.976915i	−0.345348	+	0.938475i	$0.612239\pi$
$71$	−11.3299	+	8.23164i	−1.34461	+	0.976915i	−0.999261	+	0.0384406i	$0.987761\pi$
$72$	−3.84293	+	1.47516i	−0.452894	+	0.173850i
$73$	2.92452	−	1.89921i	0.342289	−	0.222285i	−0.362033	−	0.932165i	$-0.617917\pi$
$73$	2.92452	−	1.89921i	0.342289	−	0.222285i	0.704323	+	0.709880i	$0.251251\pi$
$74$	6.74848	+	3.89623i	0.784494	+	0.452928i
$75$	−1.70359	+	0.578583i	−0.196714	+	0.0668090i
$76$		−	7.64897i		−	0.877397i
$77$	1.00564	−	11.1254i	0.114604	−	1.26786i
$78$	0.376077	+	0.0595648i	0.0425823	+	0.00674438i
$79$	5.74668	−	12.9073i	0.646552	−	1.45218i	−0.231123	−	0.972924i	$-0.574240\pi$
$79$	5.74668	−	12.9073i	0.646552	−	1.45218i	0.877675	−	0.479255i	$-0.159093\pi$
$80$	−7.25974	−	8.38696i	−0.811663	−	0.937691i
$81$	−7.17266	+	3.19347i	−0.796962	+	0.354830i
$82$	−2.77617	+	10.3608i	−0.306577	+	1.14416i
$83$	3.01586	−	0.477665i	0.331033	−	0.0524305i	0.0112944	−	0.999936i	$-0.496405\pi$
$83$	3.01586	−	0.477665i	0.331033	−	0.0524305i	0.319739	+	0.947506i	$0.396405\pi$
$84$	−0.502981	+	1.02377i	−0.0548797	+	0.111702i
$85$	−0.266404	−	1.92496i	−0.0288956	−	0.208791i
$86$	6.31698	−	7.01572i	0.681178	−	0.756525i
$87$	0.0319372	−	0.609399i	0.00342403	−	0.0653344i
$88$	0.316873	−	6.04629i	0.0337787	−	0.644537i
$89$	11.4094	−	12.6715i	1.20940	−	1.34317i	0.286523	−	0.958073i	$-0.407500\pi$
$89$	11.4094	−	12.6715i	1.20940	−	1.34317i	0.922875	−	0.385100i	$-0.125833\pi$
$90$	−7.95640	−	8.27388i	−0.838678	−	0.872143i
$91$	1.30039	−	0.871684i	0.136318	−	0.0913774i
$92$	1.91756	−	0.303712i	0.199920	−	0.0316642i
$93$	−0.837993	+	3.12743i	−0.0868958	+	0.324300i
$94$	−15.7479	+	7.01144i	−1.62428	+	0.723174i
$95$	−13.1521	+	5.55010i	−1.34938	+	0.569428i
$96$	−0.878647	+	1.97347i	−0.0896765	+	0.201417i
$97$	−11.5748	−	1.83327i	−1.17524	−	0.186140i	−0.461884	−	0.886940i	$-0.652826\pi$
$97$	−11.5748	−	1.83327i	−1.17524	−	0.186140i	−0.713358	+	0.700800i	$0.752826\pi$
$98$	3.59099	+	11.9922i	0.362745	+	1.21140i
$99$		−	12.1198i		−	1.21809i
$100$	2.64878	−	5.37328i	0.264878	−	0.537328i
$101$	3.84878	+	2.22209i	0.382967	+	0.221106i	0.679109	−	0.734038i	$-0.262367\pi$
$101$	3.84878	+	2.22209i	0.382967	+	0.221106i	−0.296141	+	0.955144i	$0.595700\pi$
$102$	−0.469024	+	0.304588i	−0.0464403	+	0.0301587i
$103$	−1.95677	+	0.751133i	−0.192806	+	0.0740114i	−0.452855	−	0.891584i	$-0.649595\pi$
$103$	−1.95677	+	0.751133i	−0.192806	+	0.0740114i	0.260049	+	0.965595i	$0.416261\pi$
$104$	0.686462	−	0.498744i	0.0673131	−	0.0489058i
$105$	2.12530	+	0.122008i	0.207408	+	0.0119068i
$106$	−12.2697	−	8.91446i	−1.19174	−	0.865849i
$107$	3.97800	+	1.06590i	0.384568	+	0.103045i	0.445923	−	0.895071i	$-0.352876\pi$
$107$	3.97800	+	1.06590i	0.384568	+	0.103045i	−0.0613552	+	0.998116i	$0.519542\pi$
$108$	−0.907008	+	2.36284i	−0.0872769	+	0.227364i
$109$	8.87403	−	7.99021i	0.849977	−	0.765323i	−0.123925	−	0.992292i	$-0.539548\pi$
$109$	8.87403	−	7.99021i	0.849977	−	0.765323i	0.973902	+	0.226968i	$0.0728814\pi$
$110$	15.8776	−	5.74116i	1.51387	−	0.547398i
$111$	−1.49119	+	0.484517i	−0.141537	+	0.0459883i
$112$	4.23729	+	12.4221i	0.400386	+	1.17378i
$113$	−3.18186	+	1.62124i	−0.299324	+	0.152513i	−0.597202	−	0.802091i	$-0.703721\pi$
$113$	−3.18186	+	1.62124i	−0.299324	+	0.152513i	0.297878	+	0.954604i	$0.403721\pi$
$114$	3.05295	+	2.74889i	0.285935	+	0.257457i
$115$	−1.91361	−	3.07680i	−0.178445	−	0.286913i
$116$	1.35961	+	1.51000i	0.126236	+	0.140200i
$117$	1.31999	−	1.06891i	0.122034	−	0.0988208i
$118$	8.56845	−	8.56845i	0.788789	−	0.788789i
$119$	−0.562685	+	2.22943i	−0.0515813	+	0.204372i
$120$	1.15359	+	0.0225650i	0.105308	+	0.00205989i
$121$	6.23643	+	2.77664i	0.566948	+	0.252421i
$122$	−1.39003	+	1.71654i	−0.125847	+	0.155408i
$123$	−1.17547	−	1.81006i	−0.105988	−	0.163207i
$124$	−5.39038	−	9.33642i	−0.484071	−	0.838435i
$125$	−11.1611	−	0.655624i	−0.998279	−	0.0586408i
$126$	5.05155	+	12.6074i	0.450028	+	1.12316i
$127$	−2.93160	−	1.49373i	−0.260138	−	0.132547i	0.319058	−	0.947735i	$-0.396633\pi$
$127$	−2.93160	−	1.49373i	−0.260138	−	0.132547i	−0.579196	+	0.815188i	$0.696633\pi$
$128$	3.78077	+	9.84925i	0.334176	+	0.870559i
$129$	0.198557	+	1.88914i	0.0174820	+	0.166330i
$130$	2.02562	+	1.22292i	0.177658	+	0.107257i
$131$	−3.66772	−	0.385493i	−0.320450	−	0.0336806i	−0.0570620	−	0.998371i	$-0.518173\pi$
$131$	−3.66772	−	0.385493i	−0.320450	−	0.0336806i	−0.263388	+	0.964690i	$0.584840\pi$
$132$	−1.28714	−	1.28714i	−0.112031	−	0.112031i
$133$	16.8889	−	0.246144i	1.46445	−	0.0213434i
$134$	19.4960	+	6.33462i	1.68419	+	0.547228i
$135$	4.72093	−	0.154910i	0.406313	−	0.0133326i
$136$	−0.259110	+	1.21902i	−0.0222185	+	0.104530i
$137$	−1.00746	−	0.0527989i	−0.0860734	−	0.00451092i	0.00925064	−	0.999957i	$-0.497055\pi$
$137$	−1.00746	−	0.0527989i	−0.0860734	−	0.00451092i	−0.0953240	+	0.995446i	$0.530389\pi$
$138$	−0.567912	+	0.874508i	−0.0483439	+	0.0744431i
$139$	3.10037	+	9.54195i	0.262970	+	0.809337i	0.992154	+	0.125020i	$0.0398996\pi$
$139$	3.10037	+	9.54195i	0.262970	+	0.809337i	−0.729185	+	0.684317i	$0.760100\pi$
$140$	−5.29118	+	4.71665i	−0.447186	+	0.398630i
$141$	1.07183	−	3.29877i	0.0902647	−	0.277806i
$142$	15.7611	+	19.4634i	1.32265	+	1.63333i
$143$	0.646606	+	2.41316i	0.0540719	+	0.201799i
$144$	5.79190	+	13.0088i	0.482658	+	1.08407i
$145$	1.60985	−	3.43345i	0.133691	−	0.285132i
$146$	−3.66548	−	5.04510i	−0.303357	−	0.417535i
$147$	−2.27666	−	1.07763i	−0.187776	−	0.0888816i
$148$	2.37017	−	4.65171i	0.194827	−	0.382369i
$149$	6.19698	−	3.57783i	0.507676	−	0.293107i	−0.224202	−	0.974543i	$-0.571977\pi$
$149$	6.19698	−	3.57783i	0.507676	−	0.293107i	0.731878	+	0.681436i	$0.238644\pi$
$150$	1.19273	+	2.98826i	0.0973857	+	0.243990i
$151$	12.2345	−	21.1907i	0.995627	−	1.72448i	0.416908	−	0.908949i	$-0.363114\pi$
$151$	12.2345	−	21.1907i	0.995627	−	1.72448i	0.578718	−	0.815527i	$-0.303553\pi$
$152$	9.14223	−	0.479124i	0.741532	−	0.0388621i
$153$	−0.390255	+	2.46397i	−0.0315502	+	0.199200i
$154$	−19.9628	−	0.754685i	−1.60865	−	0.0608142i
$155$	−12.1423	+	16.0431i	−0.975297	+	1.28861i
$156$	0.0266654	−	0.253705i	0.00213494	−	0.0203126i
$157$	−19.3989	+	5.19791i	−1.54820	+	0.414838i	−0.928904	−	0.370321i	$-0.879248\pi$
$157$	−19.3989	+	5.19791i	−1.54820	+	0.414838i	−0.619294	+	0.785159i	$0.712581\pi$
$158$	−23.5887	−	9.05485i	−1.87662	−	0.720365i
$159$	2.98492	−	0.634464i	0.236719	−	0.0503162i
$160$	−9.67612	+	9.30484i	−0.764964	+	0.735612i
$161$	0.732301	+	4.22419i	0.0577134	+	0.332913i
$162$	6.37449	+	12.5106i	0.500827	+	0.982928i
$163$	−13.5326	−	8.78818i	−1.05996	−	0.688343i	−0.107867	−	0.994165i	$-0.534402\pi$
$163$	−13.5326	−	8.78818i	−1.05996	−	0.688343i	−0.952089	+	0.305822i	$0.901069\pi$
$164$	7.02929	+	1.49412i	0.548895	+	0.116671i
$165$	−1.27924	+	3.14713i	−0.0995883	+	0.245004i
$166$	−1.13532	−	5.34126i	−0.0881179	−	0.414562i
$167$	1.58959	+	10.0363i	0.123006	+	0.776630i	0.969655	+	0.244478i	$0.0786165\pi$
$167$	1.58959	+	10.0363i	0.123006	+	0.776630i	−0.846649	+	0.532152i	$0.821383\pi$
$168$	−1.25514	−	0.537046i	−0.0968361	−	0.0414340i
$169$	7.43541	−	10.2340i	0.571955	−	0.787228i
$170$	−3.41281	+	0.655931i	−0.261750	+	0.0503076i
$171$	18.2252	−	1.91555i	1.39372	−	0.146486i
$172$	−4.91540	−	3.98041i	−0.374795	−	0.303503i
$173$	−0.175568	−	3.35004i	−0.0133482	−	0.254699i	−0.997150	−	0.0754409i	$-0.975964\pi$
$173$	−0.175568	−	3.35004i	−0.0133482	−	0.254699i	0.983802	−	0.179258i	$-0.0573698\pi$
$174$	−1.09130			−0.0827315
$175$	11.9494	+	5.67557i	0.903289	+	0.429033i
$176$	−20.9450			−1.57879
$177$	0.127605	+	2.43485i	0.00959140	+	0.183015i
$178$	−23.6976	−	19.1899i	−1.77621	−	1.43835i
$179$	−2.88851	+	0.303595i	−0.215897	+	0.0226917i	−0.211860	−	0.977300i	$-0.567952\pi$
$179$	−2.88851	+	0.303595i	−0.215897	+	0.0226917i	−0.00403785	+	0.999992i	$0.501285\pi$
$180$	−5.25669	+	5.61338i	−0.391811	+	0.418397i
$181$	4.64922	−	6.39910i	0.345574	−	0.475641i	−0.600485	−	0.799636i	$-0.705026\pi$
$181$	4.64922	−	6.39910i	0.345574	−	0.475641i	0.946059	+	0.323994i	$0.105026\pi$
$182$	−1.67843	−	2.24076i	−0.124414	−	0.166096i
$183$	−0.0695242	−	0.438958i	−0.00513937	−	0.0324487i
$184$	0.483118	+	2.27289i	0.0356159	+	0.167560i
$185$	−9.71824	−	0.700124i	−0.714499	−	0.0514741i
$186$	5.66366	+	1.20385i	0.415279	+	0.0882704i
$187$	−3.07738	−	1.99847i	−0.225040	−	0.146143i
$188$	5.24321	+	10.2904i	0.382401	+	0.750504i
$189$	−5.24631	−	1.92663i	−0.381613	−	0.140142i
$190$	11.1428	+	22.9687i	0.808382	+	1.66632i
$191$	14.2348	−	3.02570i	1.03000	−	0.218932i	0.338237	−	0.941061i	$-0.390170\pi$
$191$	14.2348	−	3.02570i	1.03000	−	0.218932i	0.691758	+	0.722129i	$0.256836\pi$
$192$	0.273680	+	0.105056i	0.0197511	+	0.00758175i
$193$	0.600403	−	0.160877i	0.0432179	−	0.0115802i	−0.237145	−	0.971474i	$-0.576212\pi$
$193$	0.600403	−	0.160877i	0.0432179	−	0.0115802i	0.280363	+	0.959894i	$0.409545\pi$
$194$	−2.19067	+	20.8428i	−0.157281	+	1.49643i
$195$	−0.455584	+	0.138238i	−0.0326250	+	0.00989943i
$196$	7.89754	−	2.82306i	0.564110	−	0.201647i
$197$	3.81776	−	24.1044i	0.272004	−	1.71736i	−0.352048	−	0.935982i	$-0.614515\pi$
$197$	3.81776	−	24.1044i	0.272004	−	1.71736i	0.624052	−	0.781383i	$-0.285485\pi$
$198$	−21.6445	+	1.13434i	−1.53821	+	0.0806141i
$199$	−4.29215	+	7.43422i	−0.304262	+	0.526998i	−0.977097	−	0.212795i	$-0.931743\pi$
$199$	−4.29215	+	7.43422i	−0.304262	+	0.526998i	0.672835	+	0.739793i	$0.265077\pi$
$200$	6.58818	+	2.82931i	0.465855	+	0.200062i
$201$	−3.57207	+	2.06234i	−0.251955	+	0.145466i
$202$	3.60817	−	7.08143i	0.253870	−	0.498248i
$203$	−3.29031	+	3.05059i	−0.230934	+	0.214110i
$204$	0.220231	+	0.303123i	0.0154193	+	0.0212228i
$205$	−2.53137	−	13.1707i	−0.176799	−	0.919883i
$206$	1.52458	+	3.42426i	0.106222	+	0.238579i
$207$	1.20387	+	4.49292i	0.0836751	+	0.312280i
$208$	−1.84726	−	2.28117i	−0.128084	−	0.158171i
$209$	−8.32941	+	25.6353i	−0.576158	+	1.77323i
$210$	0.0189771	−	3.80695i	0.00130954	−	0.262704i
$211$	1.28435	+	3.95282i	0.0884183	+	0.272123i	0.985483	−	0.169777i	$-0.0543046\pi$
$211$	1.28435	+	3.95282i	0.0884183	+	0.272123i	−0.897064	+	0.441900i	$0.854305\pi$
$212$	−5.53404	+	8.52167i	−0.380079	+	0.585271i
$213$	−5.03236	−	0.263735i	−0.344812	−	0.0180708i
$214$	1.53126	−	7.20400i	0.104675	−	0.492455i
$215$	−3.27755	+	11.3400i	−0.223527	+	0.773383i
$216$	−2.88093	−	0.936071i	−0.196023	−	0.0636916i
$217$	20.4413	−	12.2024i	1.38764	−	0.828351i
$218$	−15.1001	−	15.1001i	−1.02271	−	1.02271i
$219$	1.24789	+	0.131159i	0.0843249	+	0.00886290i
$220$	−4.39788	−	10.4217i	−0.296505	−	0.702630i
$221$	−0.0537525	−	0.511421i	−0.00361578	−	0.0344019i
$222$	1.00486	+	2.61774i	0.0674416	+	0.175691i
$223$	11.3328	+	5.77436i	0.758902	+	0.386680i	0.790215	−	0.612830i	$-0.209969\pi$
$223$	11.3328	+	5.77436i	0.758902	+	0.386680i	−0.0313132	+	0.999510i	$0.509969\pi$
$224$	14.7441	−	5.90768i	0.985134	−	0.394723i
$225$	13.4663	+	4.96561i	0.897750	+	0.331041i
$226$	3.19314	+	5.53069i	0.212405	+	0.367896i
$227$	3.81371	+	5.87260i	0.253125	+	0.389778i	0.942275	−	0.334841i	$-0.108682\pi$
$227$	3.81371	+	5.87260i	0.253125	+	0.389778i	−0.689150	+	0.724619i	$0.742016\pi$
$228$	1.73211	−	2.13897i	0.114712	−	0.141657i
$229$	−13.5136	−	6.01664i	−0.893003	−	0.397591i	−0.0916563	−	0.995791i	$-0.529216\pi$
$229$	−13.5136	−	6.01664i	−0.893003	−	0.397591i	−0.801347	+	0.598200i	$0.795883\pi$
$230$	−5.31570	+	3.70545i	−0.350507	+	0.244330i
$231$	2.80057	−	2.88341i	0.184264	−	0.189714i
$232$	−1.71962	+	1.71962i	−0.112899	+	0.112899i
$233$	1.98260	−	1.60547i	0.129884	−	0.105178i	−0.562177	−	0.827017i	$-0.690036\pi$
$233$	1.98260	−	1.60547i	0.129884	−	0.105178i	0.692061	+	0.721839i	$0.256703\pi$
$234$	−2.03249	−	2.25731i	−0.132868	−	0.147565i
$235$	13.8894	−	16.4822i	0.906048	−	1.07518i
$236$	−6.03320	−	5.43232i	−0.392728	−	0.353614i
$237$	4.52986	−	2.30808i	0.294246	−	0.149926i
$238$	4.03417	+	0.796227i	0.261496	+	0.0516118i
$239$	−0.945911	+	0.307345i	−0.0611859	+	0.0198805i	−0.339450	−	0.940624i	$-0.610241\pi$
$239$	−0.945911	+	0.307345i	−0.0611859	+	0.0198805i	0.278264	+	0.960505i	$0.410241\pi$
$240$	−0.130903	−	3.98931i	−0.00844977	−	0.257509i
$241$	−3.98537	+	3.58844i	−0.256720	+	0.231152i	−0.787434	−	0.616399i	$-0.788591\pi$
$241$	−3.98537	+	3.58844i	−0.256720	+	0.231152i	0.530713	+	0.847551i	$0.321924\pi$
$242$	4.37505	−	11.3974i	0.281239	−	0.732653i
$243$	−8.85021	−	2.37141i	−0.567741	−	0.152126i
$244$	1.19720	+	0.869816i	0.0766428	+	0.0556843i
$245$	−10.5846	−	11.5311i	−0.676225	−	0.736695i
$246$	−3.12253	+	2.26865i	−0.199086	+	0.144644i
$247$	−3.52661	+	1.35374i	−0.224393	+	0.0861364i
$248$	10.8215	−	7.02754i	0.687163	−	0.446249i
$249$	0.951527	+	0.549365i	0.0603006	+	0.0348146i
$250$	−0.126253	+	19.9938i	−0.00798496	+	1.26452i
$251$		−	15.5071i		−	0.978800i	−0.872059	−	0.489400i	$-0.837216\pi$
$251$		−	15.5071i		−	0.978800i	0.872059	−	0.489400i	$-0.162784\pi$
$252$	8.25794	−	3.82183i	0.520202	−	0.240753i
$253$	−6.75739	−	1.07026i	−0.424833	−	0.0672870i
$254$	−2.39324	+	5.37530i	−0.150165	+	0.337277i
$255$	0.361408	−	0.598626i	0.0226322	−	0.0374874i
$256$	18.7242	−	8.33657i	1.17027	−	0.521036i
$257$	4.03975	−	15.0766i	0.251993	−	0.940449i	−0.717746	−	0.696305i	$-0.754826\pi$
$257$	4.03975	−	15.0766i	0.251993	−	0.940449i	0.969739	−	0.244145i	$-0.0785072\pi$
$258$	3.35520	−	0.531412i	0.208886	−	0.0330842i
$259$	10.3472	+	5.08362i	0.642945	+	0.315881i
$260$	0.747177	−	1.39813i	0.0463379	−	0.0867082i
$261$	−3.25738	+	3.61769i	−0.201627	+	0.223929i
$262$	−0.345168	+	6.58619i	−0.0213245	+	0.406896i
$263$	0.215114	−	4.10463i	0.0132645	−	0.253102i	−0.983946	−	0.178465i	$-0.942887\pi$
$263$	0.215114	−	4.10463i	0.0132645	−	0.253102i	0.997211	−	0.0746370i	$-0.0237798\pi$
$264$	1.45779	−	1.61904i	0.0897208	−	0.0996451i
$265$	18.6682	+	3.33224i	1.14678	+	0.204698i
$266$	−2.02028	−	30.1385i	−0.123872	−	1.84791i
$267$	6.06001	−	0.959811i	0.370866	−	0.0587395i
$268$	3.55461	−	13.2660i	0.217132	−	0.810349i
$269$	−10.7761	+	4.79784i	−0.657032	+	0.292529i	−0.708044	−	0.706169i	$-0.750422\pi$
$269$	−10.7761	+	4.79784i	−0.657032	+	0.292529i	0.0510119	+	0.998698i	$0.483755\pi$
$270$	−0.718503	−	8.41653i	−0.0437267	−	0.512214i
$271$	−2.73943	+	6.15287i	−0.166409	+	0.373760i	−0.977431	−	0.211255i	$-0.932245\pi$
$271$	−2.73943	+	6.15287i	−0.166409	+	0.373760i	0.811022	+	0.585015i	$0.198912\pi$
$272$	4.25816	+	0.674426i	0.258189	+	0.0408931i
$273$	0.561036	+	0.0507128i	0.0339554	+	0.00306928i
$274$			1.80415i			0.108993i
$275$	−14.7286	+	15.1240i	−0.888167	+	0.912009i
$276$	0.605007	+	0.349301i	0.0364171	+	0.0210254i
$277$	−25.5422	+	16.5873i	−1.53468	+	0.996635i	−0.547543	+	0.836778i	$0.684437\pi$
$277$	−25.5422	+	16.5873i	−1.53468	+	0.996635i	−0.987140	+	0.159857i	$0.948897\pi$
$278$	16.7506	−	6.42996i	1.00464	−	0.385643i
$279$	20.8960	−	15.1818i	1.25101	−	0.908911i
$280$	−5.96889	−	6.02869i	−0.356709	−	0.360283i
$281$	3.78178	+	2.74762i	0.225602	+	0.163909i	0.694845	−	0.719160i	$-0.255473\pi$
$281$	3.78178	+	2.74762i	0.225602	+	0.163909i	−0.469243	+	0.883069i	$0.655473\pi$
$282$	−5.99152	−	1.60542i	−0.356790	−	0.0956016i
$283$	−2.00715	+	5.22881i	−0.119313	+	0.310821i	−0.980211	−	0.197957i	$-0.936569\pi$
$283$	−2.00715	+	5.22881i	−0.119313	+	0.310821i	0.860898	+	0.508778i	$0.169903\pi$
$284$	12.4694	−	11.2275i	0.739924	−	0.666231i
$285$	−4.93470	−	1.42625i	−0.292306	−	0.0844838i
$286$	4.24911	−	1.38062i	0.251255	−	0.0816377i
$287$	−3.07280	+	15.5687i	−0.181382	+	0.918991i
$288$	15.3547	−	7.82364i	0.904787	−	0.461012i
$289$	−12.0722	−	10.8698i	−0.710128	−	0.639402i
$290$	−6.28241	−	2.55365i	−0.368916	−	0.149956i
$291$	−2.82166	−	3.13377i	−0.165408	−	0.183705i
$292$	−3.24692	+	2.62930i	−0.190012	+	0.153868i
$293$	−7.38400	+	7.38400i	−0.431378	+	0.431378i	−0.889097	−	0.457719i	$-0.848667\pi$
$293$	−7.38400	+	7.38400i	−0.431378	+	0.431378i	0.457719	+	0.889097i	$0.348667\pi$
$294$	−1.71144	+	4.16671i	−0.0998133	+	0.243007i
$295$	−4.96297	+	14.3155i	−0.288955	+	0.833483i
$296$	5.70830	+	2.54150i	0.331788	+	0.147722i
$297$	5.61284	−	6.93128i	0.325690	−	0.402194i
$298$	−6.96958	−	10.7322i	−0.403737	−	0.621700i
$299$	−0.479406	−	0.830355i	−0.0277247	−	0.0480207i
$300$	1.95749	−	0.902779i	0.113016	−	0.0521219i
$301$	8.63053	−	10.9812i	0.497456	−	0.632948i
$302$	−38.9892	−	19.8660i	−2.24358	−	1.14316i
$303$	0.573087	+	1.49294i	0.0329230	+	0.0857674i
$304$	−3.31039	−	31.4962i	−0.189864	−	1.80643i
$305$	0.626927	−	2.68968i	0.0358977	−	0.154011i
$306$	4.43689	+	0.466336i	0.253640	+	0.0266587i
$307$	19.4310	+	19.4310i	1.10899	+	1.10899i	0.993284	+	0.115702i	$0.0369117\pi$
$307$	19.4310	+	19.4310i	1.10899	+	1.10899i	0.115702	+	0.993284i	$0.463088\pi$
$308$	0.195044	+	13.3827i	0.0111137	+	0.762549i
$309$	−0.717289	−	0.233061i	−0.0408051	−	0.0132584i
$310$	29.7875	+	20.1833i	1.69182	+	1.14633i
$311$	3.11924	−	14.6749i	0.176876	−	0.832135i	−0.796808	−	0.604232i	$-0.793480\pi$
$311$	3.11924	−	14.6749i	0.176876	−	0.832135i	0.973684	−	0.227902i	$-0.0731867\pi$
$312$	0.304904	+	0.0159793i	0.0172618	+	0.000904652i
$313$	−16.6103	+	25.5775i	−0.938867	+	1.44573i	−0.0441858	+	0.999023i	$0.514069\pi$
$313$	−16.6103	+	25.5775i	−0.938867	+	1.44573i	−0.894681	+	0.446705i	$0.852597\pi$
$314$	11.0985	+	34.1576i	0.626323	+	1.92762i
$315$	−12.5635	−	11.4261i	−0.707871	−	0.643788i
$316$	−5.23108	+	16.0996i	−0.294271	+	0.905674i
$317$	−15.9146	−	19.6529i	−0.893852	−	1.10382i	−0.994058	−	0.108849i	$-0.965283\pi$
$317$	−15.9146	−	19.6529i	−0.893852	−	1.10382i	0.100206	−	0.994967i	$-0.468050\pi$
$318$	−1.41245	−	5.27133i	−0.0792061	−	0.295601i
$319$	−2.91236	−	6.54127i	−0.163061	−	0.366241i
$320$	1.32969	+	1.24520i	0.0743317	+	0.0696085i
$321$	0.871043	+	1.19889i	0.0486169	+	0.0669154i
$322$	7.47537	−	1.70316i	0.416586	−	0.0949136i
$323$	2.51883	−	4.94349i	0.140152	−	0.275063i
$324$	8.14678	−	4.70355i	0.452599	−	0.261308i
$325$	−2.94618	−	0.270259i	−0.163425	−	0.0149913i
$326$	−14.4281	+	24.9902i	−0.799097	+	1.38408i
$327$	4.29093	−	0.224878i	0.237289	−	0.0124358i
$328$	−1.34550	+	8.49516i	−0.0742928	+	0.469066i
$329$	−22.5524	+	11.9081i	−1.24335	+	0.656516i
$330$	5.74013	+	1.99001i	0.315984	+	0.109546i
$331$	0.691950	−	6.58346i	0.0380330	−	0.361860i	−0.958909	−	0.283714i	$-0.908433\pi$
$331$	0.691950	−	6.58346i	0.0380330	−	0.361860i	0.996942	−	0.0781459i	$-0.0249000\pi$
$332$	−3.53378	+	0.946875i	−0.193942	+	0.0519665i
$333$	11.6772	+	4.48246i	0.639907	+	0.245637i
$334$	17.7748	−	3.77815i	0.972595	−	0.206731i
$335$	−25.3896	+	3.51379i	−1.38718	+	0.191979i
$336$	−1.62805	+	4.43327i	−0.0888175	+	0.241855i
$337$	2.24236	+	4.40088i	0.122149	+	0.239731i	0.943982	−	0.329998i	$-0.107048\pi$
$337$	2.24236	+	4.40088i	0.122149	+	0.239731i	−0.821833	+	0.569729i	$0.807048\pi$
$338$	−18.9726	−	12.3209i	−1.03197	−	0.670170i
$339$	−1.25691	−	0.267165i	−0.0682660	−	0.0145104i
$340$	0.558519	+	2.26036i	0.0302900	+	0.122585i
$341$	7.89874	+	37.1606i	0.427741	+	2.01236i
$342$	−5.12671	−	32.3688i	−0.277221	−	1.75030i
$343$	6.48744	+	17.3468i	0.350289	+	0.936642i
$344$	4.44958	−	6.12432i	0.239905	−	0.330201i
$345$	0.161616	−	1.29374i	0.00870112	−	0.0696526i
$346$	−5.96635	+	0.627089i	−0.320753	+	0.0337125i
$347$	20.0098	+	16.2036i	1.07418	+	0.869857i	0.991934	−	0.126755i	$-0.0404561\pi$
$347$	20.0098	+	16.2036i	1.07418	+	0.869857i	0.0822499	+	0.996612i	$0.473789\pi$
$348$	0.0382651	+	0.730141i	0.00205122	+	0.0391397i
$349$	−23.8148			−1.27478			−0.637389	−	0.770543i	$-0.719985\pi$
$349$	−23.8148			−1.27478			−0.637389	+	0.770543i	$0.719985\pi$
$350$	9.01751	−	21.8714i	0.482006	−	1.16908i
$351$	1.24993			0.0667163
$352$	1.32659	+	25.3128i	0.0707073	+	1.34918i
$353$	24.6090	+	19.9280i	1.30980	+	1.06066i	0.993716	+	0.111929i	$0.0357031\pi$
$353$	24.6090	+	19.9280i	1.30980	+	1.06066i	0.316089	+	0.948730i	$0.397630\pi$
$354$	4.33642	−	0.455776i	0.230478	−	0.0242242i
$355$	−28.3531	−	13.2940i	−1.50483	−	0.705572i
$356$	−12.0082	+	16.5279i	−0.636433	+	0.875975i
$357$	−0.662205	+	0.496024i	−0.0350476	+	0.0262524i
$358$	0.812532	+	5.13013i	0.0429437	+	0.271136i
$359$	−2.63745	−	12.4082i	−0.139199	−	0.654881i	−0.991313	−	0.131524i	$-0.958013\pi$
$359$	−2.63745	−	12.4082i	−0.139199	−	0.654881i	0.852114	−	0.523357i	$-0.175320\pi$
$360$	−7.03851	−	5.93131i	−0.370962	−	0.312607i
$361$	−21.2809	−	4.52340i	−1.12005	−	0.238073i
$362$	−11.8632	−	7.70404i	−0.623515	−	0.404915i
$363$	1.11520	+	2.18870i	0.0585328	+	0.114877i
$364$	−1.44034	+	1.20153i	−0.0754941	+	0.0629775i
$365$	6.87696	+	3.67513i	0.359956	+	0.192365i
$366$	−0.777421	+	0.165246i	−0.0406364	+	0.00863754i
$367$	−7.32836	−	2.81310i	−0.382538	−	0.146842i	0.159497	−	0.987198i	$-0.449013\pi$
$367$	−7.32836	−	2.81310i	−0.382538	−	0.146842i	−0.542035	+	0.840356i	$0.682346\pi$
$368$	7.76452	−	2.08050i	0.404754	−	0.108453i
$369$	−1.79969	+	17.1229i	−0.0936879	+	0.891381i
$370$	−0.340769	+	17.4212i	−0.0177157	+	0.905683i
$371$	−18.9939	−	11.9449i	−0.986112	−	0.620147i
$372$	0.606851	−	3.83151i	0.0314638	−	0.198654i
$373$	3.64111	−	0.190823i	0.188530	−	0.00988042i	0.0421626	−	0.999111i	$-0.486575\pi$
$373$	3.64111	−	0.190823i	0.188530	−	0.00988042i	0.146367	+	0.989230i	$0.453242\pi$
$374$	−3.28101	+	5.68288i	−0.169657	+	0.293855i
$375$	−2.97265	−	2.71077i	−0.153507	−	0.139983i
$376$	−11.9709	+	6.91139i	−0.617351	+	0.356428i
$377$	0.455567	−	0.894102i	0.0234629	−	0.0460486i
$378$	−2.94971	+	9.54961i	−0.151717	+	0.491179i
$379$	12.1944	+	16.7841i	0.626384	+	0.862143i	0.997798	−	0.0663239i	$-0.0211271\pi$
$379$	12.1944	+	16.7841i	0.626384	+	0.862143i	−0.371414	+	0.928467i	$0.621127\pi$
$380$	14.9766	−	8.26049i	0.768283	−	0.423754i
$381$	−0.481546	−	1.08157i	−0.0246703	−	0.0554105i
$382$	−6.73584	−	25.1385i	−0.344636	−	1.28620i
$383$	−12.2271	−	15.0992i	−0.624775	−	0.771533i	0.362253	−	0.932080i	$-0.382008\pi$
$383$	−12.2271	−	15.0992i	−0.624775	−	0.771533i	−0.987028	+	0.160546i	$0.948674\pi$
$384$	−1.17310	+	3.61042i	−0.0598643	+	0.184243i
$385$	22.8695	−	10.0458i	1.16554	−	0.511984i
$386$	−0.343502	−	1.05719i	−0.0174838	−	0.0538096i
$387$	8.25315	−	12.7087i	0.419531	−	0.646022i
$388$	14.0218	+	0.734850i	0.711848	+	0.0373064i
$389$	3.18105	−	14.9656i	0.161285	−	0.758788i	−0.820930	−	0.571029i	$-0.806544\pi$
$389$	3.18105	−	14.9656i	0.161285	−	0.758788i	0.982215	−	0.187759i	$-0.0601224\pi$
$390$	0.289517	+	0.800681i	0.0146603	+	0.0405440i
$391$	1.33933	+	0.435173i	0.0677326	+	0.0220077i
$392$	3.86888	+	9.26248i	0.195408	+	0.467826i
$393$	−0.938353	−	0.938353i	−0.0473337	−	0.0473337i
$394$	−43.4049	−	4.56204i	−2.18671	−	0.229832i
$395$	31.4784	−	2.68725i	1.58385	−	0.135210i
$396$	1.51787	+	14.4416i	0.0762760	+	0.725717i
$397$	10.4769	+	27.2933i	0.525822	+	1.36981i	0.897321	+	0.441379i	$0.145511\pi$
$397$	10.4769	+	27.2933i	0.525822	+	1.36981i	−0.371499	+	0.928434i	$0.621156\pi$
$398$	13.6784	+	6.96947i	0.685634	+	0.349348i
$399$	4.77858	+	3.75565i	0.239228	+	0.188017i
$400$	8.58141	−	23.2719i	0.429071	−	1.16360i
$401$	10.9327	+	18.9359i	0.545952	+	0.945616i	0.998546	+	0.0538996i	$0.0171651\pi$
$401$	10.9327	+	18.9359i	0.545952	+	0.945616i	−0.452595	+	0.891716i	$0.649502\pi$
$402$	4.01742	+	6.18628i	0.200371	+	0.308544i
$403$	−3.35062	+	4.13767i	−0.166906	+	0.206112i
$404$	−4.86438	−	2.16576i	−0.242012	−	0.107751i
$405$	−13.9989	−	10.5952i	−0.695610	−	0.526479i
$406$	5.75595	+	5.59059i	0.285663	+	0.277456i
$407$	−13.0091	+	13.0091i	−0.644836	+	0.644836i
$408$	−0.348504	+	0.282213i	−0.0172535	+	0.0139716i
$409$	20.5599	+	22.8341i	1.01662	+	1.12907i	0.991594	+	0.129385i	$0.0413002\pi$
$409$	20.5599	+	22.8341i	1.01662	+	1.12907i	0.0250261	+	0.999687i	$0.492033\pi$
$410$	−23.2844	+	5.75343i	−1.14994	+	0.284142i
$411$	−0.269773	−	0.242904i	−0.0133069	−	0.0119816i
$412$	2.23756	−	1.14009i	0.110237	−	0.0561683i
$413$	11.8004	−	13.4961i	0.580658	−	0.664098i
$414$	7.91115	−	2.57049i	0.388812	−	0.126333i
$415$	4.19223	+	5.38915i	0.205789	+	0.264543i
$416$	−2.63987	+	2.37695i	−0.129431	+	0.116540i
$417$	−1.29378	+	3.37041i	−0.0633566	+	0.165049i
$418$	46.5612	+	12.4760i	2.27738	+	0.610223i
$419$	−8.60424	−	6.25134i	−0.420345	−	0.305398i	0.357432	−	0.933939i	$-0.383652\pi$
$419$	−8.60424	−	6.25134i	−0.420345	−	0.305398i	−0.777776	+	0.628541i	$0.783652\pi$
$420$	−2.54772	+	0.120789i	−0.124316	+	0.00589389i
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	−0.0812007	−	0.996698i	$-0.525875\pi$
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	0.922824	+	0.385223i	$0.125875\pi$
$422$	6.93906	−	2.66366i	0.337788	−	0.129665i
$423$	−23.2059	+	15.0701i	−1.12831	+	0.732731i
$424$	−10.5319	−	6.08062i	−0.511476	−	0.295301i
$425$	3.48133	−	2.60047i	0.168869	−	0.126141i
$426$			9.01188i			0.436627i
$427$	−1.88202	+	2.67140i	−0.0910774	+	0.129278i
$428$	−4.87356	−	0.771896i	−0.235572	−	0.0373110i
$429$	−0.365642	+	0.821246i	−0.0176534	+	0.0396501i
$430$	20.5587	+	4.79195i	0.991429	+	0.231088i
$431$	−7.00187	+	3.11743i	−0.337268	+	0.150161i	−0.568381	−	0.822765i	$-0.692430\pi$
$431$	−7.00187	+	3.11743i	−0.337268	+	0.150161i	0.231113	+	0.972927i	$0.425763\pi$
$432$	−2.71219	+	10.1220i	−0.130490	+	0.486996i
$433$	20.2759	−	3.21139i	0.974399	−	0.154330i	0.351121	−	0.936330i	$-0.385801\pi$
$433$	20.2759	−	3.21139i	0.974399	−	0.154330i	0.623278	+	0.782000i	$0.285801\pi$
$434$	−23.7052	−	35.3636i	−1.13788	−	1.69751i
$435$	1.22768	−	0.595586i	0.0588630	−	0.0285562i
$436$	−9.57334	+	10.6323i	−0.458480	+	0.509194i
$437$	0.541405	−	10.3306i	0.0258989	−	0.494180i
$438$	0.117439	−	2.24087i	0.00561145	−	0.107073i
$439$	8.37290	−	9.29905i	0.399617	−	0.443820i	−0.509431	−	0.860512i	$-0.670144\pi$
$439$	8.37290	−	9.29905i	0.399617	−	0.443820i	0.909048	+	0.416692i	$0.136811\pi$
$440$	12.1808	−	5.90925i	0.580695	−	0.281712i
$441$	8.70430	+	18.1105i	0.414491	+	0.862404i
$442$	−0.908306	+	0.143862i	−0.0432037	+	0.00684280i
$443$	−9.05910	+	33.8090i	−0.430411	+	1.60632i	0.321405	+	0.946942i	$0.395845\pi$
$443$	−9.05910	+	33.8090i	−0.430411	+	1.60632i	−0.751816	+	0.659373i	$0.770822\pi$
$444$	1.71618	−	0.764091i	0.0814462	−	0.0362622i
$445$	37.1322	+	8.65500i	1.76023	+	0.410286i
$446$	9.25164	−	20.7795i	0.438078	−	0.983939i
$447$	2.54313	+	0.402793i	0.120286	+	0.0190514i
$448$	−0.905307	−	1.95613i	−0.0427717	−	0.0924182i
$449$			4.28525i			0.202233i	0.994875	+	0.101117i	$0.0322416\pi$
$449$			4.28525i			0.202233i	−0.994875	+	0.101117i	$0.967758\pi$
$450$	7.60764	−	24.5139i	0.358627	−	1.15560i
$451$	−21.9314	−	12.6621i	−1.03271	−	0.596235i
$452$	3.58837	−	2.33031i	0.168783	−	0.109609i
$453$	8.21990	−	3.15532i	0.386205	−	0.148250i
$454$	10.1308	−	7.36048i	0.475464	−	0.345445i
$455$	3.11110	+	1.60477i	0.145851	+	0.0752327i
$456$	2.66505	+	1.93627i	0.124802	+	0.0906742i
$457$	17.0829	+	4.57736i	0.799107	+	0.214120i	0.635192	−	0.772355i	$-0.280921\pi$
$457$	17.0829	+	4.57736i	0.799107	+	0.214120i	0.163915	+	0.986474i	$0.447588\pi$
$458$	−9.48021	+	24.6968i	−0.442981	+	1.15401i
$459$	−1.36429	+	1.22841i	−0.0636794	+	0.0573372i
$460$	2.66553	+	3.42657i	0.124281	+	0.159765i
$461$	−23.7965	+	7.73195i	−1.10831	+	0.360113i	−0.805297	−	0.592872i	$-0.797994\pi$
$461$	−23.7965	+	7.73195i	−1.10831	+	0.360113i	−0.303017	+	0.952985i	$0.597994\pi$
$462$	−5.41154	−	4.73161i	−0.251768	−	0.220135i
$463$	24.3244	−	12.3939i	1.13045	−	0.575994i	0.214277	−	0.976773i	$-0.431260\pi$
$463$	24.3244	−	12.3939i	1.13045	−	0.575994i	0.916175	+	0.400779i	$0.131260\pi$
$464$	6.25198	+	5.62931i	0.290241	+	0.261334i
$465$	−7.02846	+	1.73669i	−0.325937	+	0.0805369i
$466$	−3.05275	−	3.39042i	−0.141416	−	0.157058i
$467$	−5.50117	+	4.45476i	−0.254564	+	0.206142i	−0.748104	−	0.663581i	$-0.769036\pi$
$467$	−5.50117	+	4.45476i	−0.254564	+	0.206142i	0.493541	+	0.869723i	$0.335702\pi$
$468$	−1.43900	+	1.43900i	−0.0665177	+	0.0665177i
$469$	29.4056	+	7.42165i	1.35782	+	0.342700i
$470$	−30.7353	−	23.2623i	−1.41771	−	1.07301i
$471$	−6.60180	−	2.93931i	−0.304195	−	0.135436i
$472$	6.11492	−	7.55129i	0.281462	−	0.347576i
$473$	12.1393	+	18.6929i	0.558166	+	0.859500i
$474$	−4.54592	−	7.87377i	−0.208801	−	0.361654i
$475$	−25.0706	−	19.7578i	−1.15032	−	0.906552i
$476$	0.391267	−	2.72700i	0.0179337	−	0.124992i
$477$	−21.6905	−	11.0519i	−0.993140	−	0.506030i
$478$	0.637414	+	1.66052i	0.0291546	+	0.0759504i
$479$	−3.94813	−	37.5639i	−0.180394	−	1.71634i	−0.592809	−	0.805343i	$-0.701981\pi$
$479$	−3.94813	−	37.5639i	−0.180394	−	1.71634i	0.412415	−	0.910996i	$-0.364685\pi$
$480$	−4.81293	+	0.410870i	−0.219679	+	0.0187536i
$481$	−2.56419	−	0.269507i	−0.116917	−	0.0122885i
$482$	6.78154	+	6.78154i	0.308891	+	0.308891i
$483$	−0.751784	+	1.34709i	−0.0342074	+	0.0612947i
$484$	−7.77889	−	2.52751i	−0.353586	−	0.114887i
$485$	−8.91067	−	24.6431i	−0.404612	−	1.11899i
$486$	−3.40672	+	16.0274i	−0.154532	+	0.727017i
$487$	−13.1253	−	0.687869i	−0.594765	−	0.0311703i	−0.247421	−	0.968908i	$-0.579583\pi$
$487$	−13.1253	−	0.687869i	−0.594765	−	0.0311703i	−0.347344	+	0.937738i	$0.612916\pi$
$488$	−0.964633	+	1.48540i	−0.0436669	+	0.0672411i
$489$	−1.79421	−	5.52200i	−0.0811368	−	0.249713i
$490$	−19.6025	+	19.9821i	−0.885552	+	0.902699i
$491$	−7.21929	+	22.2187i	−0.325802	+	1.00272i	0.645275	+	0.763950i	$0.276743\pi$
$491$	−7.21929	+	22.2187i	−0.325802	+	1.00272i	−0.971077	+	0.238765i	$0.923257\pi$
$492$	1.62734	+	2.00960i	0.0733662	+	0.0905997i
$493$	0.381460	+	1.42363i	0.0171801	+	0.0641170i
$494$	2.74769	+	6.17142i	0.123624	+	0.277665i
$495$	23.7304	−	13.0888i	1.06660	−	0.588296i
$496$	−26.2367	−	36.1118i	−1.17806	−	1.62147i
$497$	25.1915	+	27.1711i	1.12999	+	1.21879i
$498$	0.892043	−	1.75073i	0.0399734	−	0.0784522i
$499$	−7.78986	+	4.49748i	−0.348722	+	0.201335i	−0.664122	−	0.747624i	$-0.731195\pi$
$499$	−7.78986	+	4.49748i	−0.348722	+	0.201335i	0.315400	+	0.948959i	$0.397861\pi$
$500$	13.3814	−	0.616585i	0.598432	−	0.0275745i
$501$	−1.82819	+	3.16652i	−0.0816777	+	0.141470i
$502$	−27.6939	+	1.45137i	−1.23604	+	0.0647780i
$503$	5.63363	−	35.5693i	0.251191	−	1.58596i	−0.463228	−	0.886239i	$-0.653309\pi$
$503$	5.63363	−	35.5693i	0.251191	−	1.58596i	0.714419	−	0.699718i	$-0.246691\pi$
$504$	5.08521	+	9.63069i	0.226513	+	0.428985i
$505$	−0.194347	+	9.93559i	−0.00864831	+	0.442128i
$506$	−1.27892	+	12.1681i	−0.0568547	+	0.540937i
$507$	4.39673	−	1.17810i	0.195266	−	0.0523213i
$508$	3.68029	+	1.41273i	0.163286	+	0.0626797i
$509$	−8.98152	+	1.90908i	−0.398099	+	0.0846185i	−0.402611	−	0.915371i	$-0.631897\pi$
$509$	−8.98152	+	1.90908i	−0.398099	+	0.0846185i	0.00451185	+	0.999990i	$0.498564\pi$
$510$	−1.10290	−	0.589403i	−0.0488372	−	0.0260992i
$511$	−5.90997	−	7.08456i	−0.261442	−	0.313403i
$512$	−7.06144	−	13.8588i	−0.312074	−	0.612480i
$513$	11.3101	+	7.34485i	0.499352	+	0.324283i
$514$	−27.3030	−	5.80344i	−1.20429	−	0.255979i
$515$	−3.58392	−	3.02014i	−0.157926	−	0.133083i
$516$	−0.473189	−	2.22618i	−0.0208310	−	0.0980021i
$517$	−6.36667	−	40.1976i	−0.280006	−	1.76789i
$518$	8.11030	−	18.9547i	0.356346	−	0.832822i
$519$	0.709520	−	0.976571i	0.0311445	−	0.0428667i
$520$	1.71788	+	0.805466i	0.0753339	+	0.0353220i
$521$	−12.1370	+	1.27565i	−0.531732	+	0.0558872i	−0.366590	−	0.930383i	$-0.619475\pi$
$521$	−12.1370	+	1.27565i	−0.531732	+	0.0558872i	−0.165142	+	0.986270i	$0.552808\pi$
$522$	6.76564	+	5.47871i	0.296124	+	0.239796i
$523$	−1.06831	−	20.3847i	−0.0467141	−	0.891359i	−0.917019	−	0.398845i	$-0.869411\pi$
$523$	−1.06831	−	20.3847i	−0.0467141	−	0.891359i	0.870304	−	0.492514i	$-0.163922\pi$
$524$	4.41862			0.193028
$525$	2.05632	+	4.29306i	0.0897451	+	0.187365i
$526$	−7.35051			−0.320498
$527$	−0.409260	−	7.80915i	−0.0178277	−	0.340172i
$528$	−5.85711	−	4.74300i	−0.254898	−	0.206412i
$529$	−20.2627	+	2.12969i	−0.880985	+	0.0925953i
$530$	4.20375	−	33.6511i	0.182599	−	1.46171i
$531$	11.4327	−	15.7357i	0.496136	−	0.682873i
$532$	−20.0934	+	2.40845i	−0.871162	+	0.104419i
$533$	−0.555191	−	3.50534i	−0.0240480	−	0.151833i
$534$	−2.28129	−	10.7326i	−0.0987211	−	0.464446i
$535$	2.20901	+	8.93999i	0.0955039	+	0.386509i
$536$	16.0785	+	3.41758i	0.694484	+	0.147617i
$537$	−0.876498	−	0.569204i	−0.0378237	−	0.0245630i
$538$	9.57695	+	18.7958i	0.412892	+	0.810346i
$539$	−29.5426	+	0.861311i	−1.27249	+	0.0370993i
$540$	−5.60592	+	0.775832i	−0.241241	+	0.0333865i
$541$	17.2586	−	3.66843i	0.742006	−	0.157718i	0.178627	−	0.983917i	$-0.442835\pi$
$541$	17.2586	−	3.66843i	0.742006	−	0.157718i	0.563379	+	0.826199i	$0.309501\pi$
$542$	11.2447	+	4.31643i	0.483001	+	0.185407i
$543$	2.74919	−	0.736644i	0.117979	−	0.0316124i
$544$	0.545370	−	5.18885i	0.0233825	−	0.222470i
$545$	25.2282	+	8.74621i	1.08066	+	0.374646i
$546$	0.0380575	−	1.00669i	0.00162871	−	0.0430824i
$547$	0.468776	−	2.95974i	0.0200434	−	0.126549i	−0.975638	−	0.219388i	$-0.929594\pi$
$547$	0.468776	−	2.95974i	0.0200434	−	0.126549i	0.995681	+	0.0928385i	$0.0295940\pi$
$548$	1.20708	−	0.0632602i	0.0515637	−	0.00270234i
$549$	−1.77270	+	3.07040i	−0.0756568	+	0.131041i
$550$	28.3881	+	24.8880i	1.21047	+	1.06123i
$551$	9.37617	−	5.41333i	0.399438	−	0.230616i
$552$	−0.379595	+	0.744998i	−0.0161567	+	0.0317092i
$553$	−35.7162	−	11.0321i	−1.51881	−	0.469133i
$554$	32.0136	+	44.0629i	1.36013	+	1.87205i
$555$	−2.55909	−	2.39648i	−0.108627	−	0.101725i
$556$	−4.88933	−	10.9816i	−0.207354	−	0.465724i
$557$	−8.10705	−	30.2559i	−0.343507	−	1.28198i	−0.894347	−	0.447373i	$-0.852359\pi$
$557$	−8.10705	−	30.2559i	−0.343507	−	1.28198i	0.550841	−	0.834610i	$-0.314307\pi$
$558$	−29.0687	−	35.8968i	−1.23057	−	1.51963i
$559$	−0.965254	+	2.97075i	−0.0408259	+	0.125649i
$560$	−19.7462	+	21.7118i	−0.834430	+	0.917490i
$561$	−0.408011	−	1.25573i	−0.0172262	−	0.0530169i
$562$	4.55298	−	7.01097i	0.192056	−	0.295740i
$563$	−18.5816	−	0.973818i	−0.783119	−	0.0410415i	−0.343414	−	0.939184i	$-0.611584\pi$
$563$	−18.5816	−	0.973818i	−0.783119	−	0.0410415i	−0.439705	+	0.898142i	$0.644917\pi$
$564$	−0.864032	+	4.06495i	−0.0363823	+	0.171165i
$565$	−6.61061	−	4.47919i	−0.278110	−	0.188441i
$566$	9.52590	+	3.09515i	0.400404	+	0.130099i
$567$	10.6476	+	17.8367i	0.447155	+	0.749070i
$568$	14.2005	+	14.2005i	0.595838	+	0.595838i
$569$	−1.55796	−	0.163748i	−0.0653132	−	0.00686469i	0.0718155	−	0.997418i	$-0.477121\pi$
$569$	−1.55796	−	0.163748i	−0.0653132	−	0.00686469i	−0.137129	+	0.990553i	$0.543787\pi$
$570$	−2.08526	+	8.94628i	−0.0873418	+	0.374719i
$571$	1.38221	+	13.1509i	0.0578437	+	0.550346i	0.984617	+	0.174725i	$0.0559038\pi$
$571$	1.38221	+	13.1509i	0.0578437	+	0.550346i	−0.926773	+	0.375621i	$0.877430\pi$
$572$	−1.07270	−	2.79448i	−0.0448518	−	0.116843i
$573$	4.66582	+	2.37736i	0.194918	+	0.0993154i
$574$	28.0914	+	4.03053i	1.17251	+	0.168231i
$575$	3.95774	−	7.06961i	0.165049	−	0.294823i
$576$	−1.16929	−	2.02527i	−0.0487204	−	0.0843861i
$577$	5.05877	+	7.78982i	0.210599	+	0.324294i	0.928146	−	0.372216i	$-0.121402\pi$
$577$	5.05877	+	7.78982i	0.210599	+	0.324294i	−0.717547	+	0.696510i	$0.754735\pi$
$578$	−18.2824	+	22.5768i	−0.760446	+	0.939073i
$579$	0.204328	+	0.0909729i	0.00849160	+	0.00378070i
$580$	−1.48825	+	4.29281i	−0.0617961	+	0.178249i
$581$	−2.20441	−	7.77210i	−0.0914543	−	0.322441i
$582$	−5.33245	+	5.33245i	−0.221037	+	0.221037i
$583$	27.8269	−	22.5338i	1.15247	−	0.933254i
$584$	−3.34599	−	3.71610i	−0.138458	−	0.153773i
$585$	3.51844	+	1.43016i	0.145469	+	0.0591300i
$586$	13.8781	+	12.4959i	0.573297	+	0.516199i
$587$	11.8830	−	6.05467i	0.490462	−	0.249903i	−0.191226	−	0.981546i	$-0.561246\pi$
$587$	11.8830	−	6.05467i	0.490462	−	0.249903i	0.681688	+	0.731643i	$0.261246\pi$
$588$	2.84776	+	0.998948i	0.117440	+	0.0411959i
$589$	−54.6321	+	17.7511i	−2.25108	+	0.731419i
$590$	26.0304	+	7.52342i	1.07165	+	0.309734i
$591$	6.52603	−	5.87606i	0.268445	−	0.241709i
$592$	7.74645	−	20.1802i	0.318377	−	0.829400i
$593$	−35.2829	−	9.45404i	−1.44890	−	0.388231i	−0.553257	−	0.833011i	$-0.686615\pi$
$593$	−35.2829	−	9.45404i	−1.44890	−	0.388231i	−0.895640	+	0.444780i	$0.853282\pi$
$594$	−12.9038	−	9.37515i	−0.529449	−	0.384667i
$595$	−4.97287	+	1.30594i	−0.203868	+	0.0535385i
$596$	−6.93605	+	5.03934i	−0.284112	+	0.206419i
$597$	−2.88374	+	1.10696i	−0.118024	+	0.0453050i
$598$	−1.43805	+	0.933878i	−0.0588061	+	0.0381891i
$599$	0.214739	+	0.123980i	0.00877399	+	0.00506567i	0.504381	−	0.863481i	$-0.331721\pi$
$599$	0.214739	+	0.123980i	0.00877399	+	0.00506567i	−0.495607	+	0.868547i	$0.665054\pi$
$600$	1.20164	+	2.28308i	0.0490566	+	0.0932065i
$601$			19.3484i			0.789237i	0.918845	+	0.394618i	$0.129123\pi$
$601$			19.3484i			0.789237i	−0.918845	+	0.394618i	$0.870877\pi$
$602$	−20.4190	−	14.3853i	−0.832215	−	0.586302i
$603$	32.4991	+	5.14734i	1.32346	+	0.209616i
$604$	−11.9243	+	26.7825i	−0.485194	+	1.08976i
$605$	1.29840	+	15.2095i	0.0527876	+	0.618353i
$606$	2.61258	−	1.16320i	0.106129	−	0.0472517i
$607$	9.35079	−	34.8976i	0.379537	−	1.41645i	−0.467065	−	0.884223i	$-0.654688\pi$
$607$	9.35079	−	34.8976i	0.379537	−	1.41645i	0.846601	−	0.532227i	$-0.178645\pi$
$608$	−37.8546	+	5.99558i	−1.53521	+	0.243153i
$609$	−1.61091	+	0.107985i	−0.0652776	+	0.00437577i
$610$	−4.86212	−	0.867880i	−0.196862	−	0.0351394i
$611$	3.81650	−	4.23865i	0.154399	−	0.171477i
$612$	0.156431	−	2.98487i	0.00632333	−	0.120656i
$613$	−0.817047	+	15.5902i	−0.0330002	+	0.629681i	0.931200	+	0.364508i	$0.118763\pi$
$613$	−0.817047	+	15.5902i	−0.0330002	+	0.629681i	−0.964201	+	0.265174i	$0.914571\pi$
$614$	32.8828	−	36.5201i	1.32704	−	1.47383i
$615$	2.27463	−	4.25632i	0.0917219	−	0.171631i
$616$	−15.9831	+	1.07140i	−0.643976	+	0.0431679i
$617$	27.4606	−	4.34934i	1.10552	−	0.175098i	0.423120	−	0.906074i	$-0.360935\pi$
$617$	27.4606	−	4.34934i	1.10552	−	0.175098i	0.682403	+	0.730976i	$0.260935\pi$
$618$	−0.349086	+	1.30281i	−0.0140423	+	0.0524065i
$619$	32.8458	−	14.6239i	1.32018	−	0.587784i	0.378913	−	0.925432i	$-0.376298\pi$
$619$	32.8458	−	14.6239i	1.32018	−	0.587784i	0.941272	+	0.337648i	$0.109631\pi$
$620$	12.4592	−	20.6372i	0.500375	−	0.828808i
$621$	−1.39224	+	3.12702i	−0.0558687	+	0.125483i
$622$	−26.4995	−	4.19711i	−1.06253	−	0.168289i
$623$	−36.8798	−	25.9821i	−1.47756	−	1.04095i
$624$		−	1.05622i		−	0.0422827i
$625$	−10.7697	−	22.5613i	−0.430788	−	0.902453i
$626$	47.2331	+	27.2700i	1.88781	+	1.08993i
$627$	−8.13436	+	5.28251i	−0.324855	+	0.210963i
$628$	22.4641	−	8.62317i	0.896416	−	0.344102i
$629$	3.06365	−	2.22587i	0.122156	−	0.0887514i
$630$	−19.2298	+	23.5063i	−0.766133	+	0.936512i
$631$	23.2118	+	16.8644i	0.924048	+	0.671360i	0.944528	−	0.328430i	$-0.106520\pi$
$631$	23.2118	+	16.8644i	0.924048	+	0.671360i	−0.0204802	+	0.999790i	$0.506520\pi$
$632$	−19.5703	−	5.24385i	−0.778465	−	0.208589i
$633$	−0.535957	+	1.39622i	−0.0213024	+	0.0554946i
$634$	−33.6082	+	30.2610i	−1.33475	+	1.20182i
$635$	−0.241284	−	7.35319i	−0.00957506	−	0.291802i
$636$	−3.47728	+	1.12984i	−0.137883	+	0.0448009i
$637$	−2.69933	−	3.14158i	−0.106951	−	0.124474i
$638$	−11.4094	+	5.81335i	−0.451701	+	0.230153i
$639$	29.8746	+	26.8992i	1.18182	+	1.06412i
$640$	−15.2017	+	18.0394i	−0.600898	+	0.713069i
$641$	12.0398	+	13.3716i	0.475545	+	0.528146i	0.932416	−	0.361387i	$-0.117697\pi$
$641$	12.0398	+	13.3716i	0.475545	+	0.528146i	−0.456871	+	0.889533i	$0.651030\pi$
$642$	2.05955	−	1.66779i	0.0812838	−	0.0658223i
$643$	−9.47610	+	9.47610i	−0.373701	+	0.373701i	−0.868823	−	0.495122i	$-0.835123\pi$
$643$	−9.47610	+	9.47610i	−0.373701	+	0.373701i	0.495122	+	0.868823i	$0.335123\pi$
$644$	−1.40162	−	4.94171i	−0.0552317	−	0.194731i
$645$	−3.48448	+	2.42895i	−0.137201	+	0.0956397i
$646$	−9.06424	−	4.03566i	−0.356628	−	0.158781i
$647$	−8.71831	+	10.7662i	−0.342752	+	0.423264i	−0.919151	−	0.393905i	$-0.871124\pi$
$647$	−8.71831	+	10.7662i	−0.342752	+	0.423264i	0.576399	+	0.817168i	$0.304457\pi$
$648$	6.13209	+	9.44260i	0.240891	+	0.370940i
$649$	14.3045	+	24.7762i	0.561502	+	0.972549i
$650$	−0.206906	+	5.28682i	−0.00811554	+	0.207366i
$651$	8.47946	+	1.21662i	0.332336	+	0.0476832i
$652$	17.2257	+	8.77692i	0.674610	+	0.343731i
$653$	13.1540	+	34.2673i	0.514754	+	1.34098i	0.907004	+	0.421122i	$0.138364\pi$
$653$	13.1540	+	34.2673i	0.514754	+	1.34098i	−0.392249	+	0.919859i	$0.628303\pi$
$654$	−0.803212	−	7.64205i	−0.0314081	−	0.298828i
$655$	−3.20616	−	7.59765i	−0.125275	−	0.296865i
$656$	29.5912	+	3.11016i	1.15534	+	0.121431i
$657$	−7.07798	−	7.07798i	−0.276138	−	0.276138i
$658$	23.3773	+	39.1613i	0.911341	+	1.52667i
$659$	−17.1826	−	5.58297i	−0.669340	−	0.217482i	−0.0454175	−	0.998968i	$-0.514462\pi$
$659$	−17.1826	−	5.58297i	−0.669340	−	0.217482i	−0.623922	+	0.781486i	$0.714462\pi$
$660$	1.13016	−	3.91024i	0.0439912	−	0.152206i
$661$	5.47564	−	25.7609i	0.212978	−	1.00198i	−0.733619	−	0.679561i	$-0.762170\pi$
$661$	5.47564	−	25.7609i	0.212978	−	1.00198i	0.946596	−	0.322421i	$-0.104497\pi$
$662$	−11.8221	−	0.619568i	−0.459477	−	0.0240802i
$663$	0.100780	−	0.155187i	0.00391396	−	0.00602696i
$664$	−1.35308	−	4.16435i	−0.0525097	−	0.161608i
$665$	18.7210	+	32.8023i	0.725971	+	1.27202i
$666$	6.91223	−	21.2737i	0.267843	−	0.824337i
$667$	1.72939	+	2.13562i	0.0669623	+	0.0826916i
$668$	−3.15104	−	11.7598i	−0.121917	−	0.455002i
$669$	1.86153	+	4.18107i	0.0719709	+	0.161649i
$670$	8.65153	+	45.0139i	0.334238	+	1.73904i
$671$	−3.06518	−	4.21886i	−0.118330	−	0.162867i
$672$	5.46087	+	1.68677i	0.210658	+	0.0650685i
$673$	23.2205	−	45.5727i	0.895083	−	1.75670i	0.297896	−	0.954598i	$-0.403715\pi$
$673$	23.2205	−	45.5727i	0.895083	−	1.75670i	0.597187	−	0.802102i	$-0.296285\pi$
$674$	7.64957	−	4.41648i	0.294651	−	0.170117i
$675$	5.40168	+	9.07623i	0.207911	+	0.349344i
$676$	−7.57813	+	13.1257i	−0.291466	+	0.504835i
$677$	39.4906	−	2.06961i	1.51775	−	0.0795417i	0.724854	−	0.688903i	$-0.241907\pi$
$677$	39.4906	−	2.06961i	1.51775	−	0.0795417i	0.792893	+	0.609361i	$0.208574\pi$
$678$	−0.359485	+	2.26970i	−0.0138059	+	0.0871673i
$679$	−1.17132	+	30.9836i	−0.0449512	+	1.18904i
$680$	−2.66664	+	0.809141i	−0.102261	+	0.0310292i
$681$	−0.263374	+	2.50584i	−0.0100925	+	0.0960240i
$682$	65.6252	−	17.5842i	2.51292	−	0.673335i
$683$	10.1751	+	3.90584i	0.389338	+	0.149453i	0.545159	−	0.838332i	$-0.316469\pi$
$683$	10.1751	+	3.90584i	0.389338	+	0.149453i	−0.155822	+	0.987785i	$0.549802\pi$
$684$	−21.4767	+	4.56502i	−0.821183	+	0.174548i
$685$	−0.984629	−	2.02962i	−0.0376207	−	0.0775478i
$686$	30.3722	−	13.2094i	1.15962	−	0.504336i
$687$	−2.41650	−	4.74265i	−0.0921953	−	0.180943i
$688$	−21.9628	−	14.2628i	−0.837326	−	0.543766i
$689$	4.90841	+	1.04332i	0.186996	+	0.0397471i
$690$	−2.32559	−	0.167541i	−0.0885338	−	0.00637817i
$691$	−7.18035	−	33.7809i	−0.273153	−	1.28509i	−0.874080	−	0.485782i	$-0.838535\pi$
$691$	−7.18035	−	33.7809i	−0.273153	−	1.28509i	0.600927	−	0.799304i	$-0.294798\pi$
$692$	0.628759	+	3.96983i	0.0239018	+	0.150910i
$693$	−31.8381	+	3.81618i	−1.20943	+	0.144965i
$694$	27.0650	−	37.2518i	1.02737	−	1.41406i
$695$	−15.3348	+	16.3753i	−0.581681	+	0.621150i
$696$	−0.870285	+	0.0914706i	−0.0329881	+	0.00346719i
$697$	4.05097	+	3.28041i	0.153442	+	0.124255i
$698$	2.22893	+	42.5304i	0.0843661	+	1.60980i
$699$	0.917976			0.0347211
$700$	−14.9493	−	5.26632i	−0.565032	−	0.199048i
$701$	16.6461			0.628716			0.314358	−	0.949305i	$-0.398211\pi$
$701$	16.6461			0.628716			0.314358	+	0.949305i	$0.398211\pi$
$702$	−0.116986	−	2.23223i	−0.00441535	−	0.0842499i
$703$	−21.6186	−	17.5064i	−0.815360	−	0.660265i
$704$	3.42090	−	0.359551i	0.128930	−	0.0135511i
$705$	7.61647	−	1.46386i	0.286853	−	0.0551322i
$706$	33.2858	−	45.8139i	1.25273	−	1.72423i
$707$	4.62545	−	10.8102i	0.173958	−	0.406560i
$708$	−0.456990	−	2.88532i	−0.0171747	−	0.108437i
$709$	−3.91289	−	18.4087i	−0.146952	−	0.691353i	−0.988506	−	0.151181i	$-0.951692\pi$
$709$	−3.91289	−	18.4087i	−0.146952	−	0.691353i	0.841555	−	0.540172i	$-0.181641\pi$
$710$	−21.0878	+	51.8795i	−0.791412	+	1.94700i
$711$	−39.6706	−	8.43225i	−1.48776	−	0.316234i
$712$	−20.5067	−	13.3172i	−0.768519	−	0.499082i
$713$	−6.61935	−	12.9912i	−0.247897	−	0.486525i
$714$	0.947818	+	1.13620i	0.0354712	+	0.0425210i
$715$	−4.02664	+	3.87214i	−0.150588	+	0.144810i
$716$	3.40384	−	0.723509i	0.127208	−	0.0270388i
$717$	−0.334115	−	0.128255i	−0.0124777	−	0.00478976i
$718$	−21.9128	+	5.87151i	−0.817777	+	0.219123i
$719$	−4.33832	+	41.2764i	−0.161792	+	1.53935i	0.548926	+	0.835871i	$0.315037\pi$
$719$	−4.33832	+	41.2764i	−0.161792	+	1.53935i	−0.710718	+	0.703477i	$0.751630\pi$
$720$	−19.2161	+	25.3893i	−0.716143	+	0.946203i
$721$	2.58932	+	4.90382i	0.0964313	+	0.182628i
$722$	−6.08648	+	38.4285i	−0.226515	+	1.43016i
$723$	−1.92708	+	0.100994i	−0.0716688	+	0.00375601i
$724$	−4.73846	+	8.20725i	−0.176103	+	0.305020i
$725$	8.46120	−	0.555882i	0.314241	−	0.0206449i
$726$	3.80439	−	2.19646i	0.141194	−	0.0815184i
$727$	−9.01500	+	17.6929i	−0.334348	+	0.656195i	−0.995573	−	0.0939929i	$-0.970037\pi$
$727$	−9.01500	+	17.6929i	−0.334348	+	0.656195i	0.661225	+	0.750188i	$0.270037\pi$
$728$	−1.52632	−	1.64626i	−0.0565692	−	0.0610144i
$729$	11.9070	+	16.3886i	0.441001	+	0.606985i
$730$	5.91971	−	12.6254i	0.219098	−	0.467287i
$731$	−1.86603	−	4.19118i	−0.0690177	−	0.155016i
$732$	0.137818	+	0.514343i	0.00509389	+	0.0190107i
$733$	−6.23862	−	7.70405i	−0.230429	−	0.284556i	0.648797	−	0.760962i	$-0.275273\pi$
$733$	−6.23862	−	7.70405i	−0.230429	−	0.284556i	−0.879225	+	0.476406i	$0.841939\pi$
$734$	−4.33796	+	13.3509i	−0.160117	+	0.492790i
$735$	−0.348687	−	5.62146i	−0.0128615	−	0.207351i
$736$	−3.00613	−	9.25192i	−0.110807	−	0.341030i
$737$	−26.3593	+	40.5897i	−0.970956	+	1.49514i
$738$	30.7479	+	1.61143i	1.13184	+	0.0593174i
$739$	1.91774	−	9.02225i	0.0705451	−	0.331889i	−0.928696	−	0.370842i	$-0.879069\pi$
$739$	1.91774	−	9.02225i	0.0705451	−	0.331889i	0.999241	+	0.0389534i	$0.0124024\pi$
$740$	11.6677	−	0.382857i	0.428911	−	0.0140741i
$741$	−1.29274	−	0.420038i	−0.0474901	−	0.0154305i
$742$	−19.5544	+	35.0388i	−0.717866	+	1.28631i
$743$	−31.8855	−	31.8855i	−1.16976	−	1.16976i	−0.982265	−	0.187500i	$-0.939962\pi$
$743$	−31.8855	−	31.8855i	−1.16976	−	1.16976i	−0.187500	−	0.982265i	$-0.560038\pi$
$744$	4.61752	+	0.485321i	0.169286	+	0.0177927i
$745$	13.6978	+	8.26973i	0.501847	+	0.302980i
$746$	−0.681574	−	6.48474i	−0.0249542	−	0.237423i
$747$	−3.14109	−	8.18282i	−0.114927	−	0.299394i
$748$	3.91720	+	1.99592i	0.143227	+	0.0729779i
$749$	1.54751	−	10.7856i	0.0565447	−	0.394098i
$750$	−4.56289	+	5.56251i	−0.166613	+	0.203114i
$751$	−4.83420	−	8.37308i	−0.176403	−	0.305538i	0.764243	−	0.644928i	$-0.223113\pi$
$751$	−4.83420	−	8.37308i	−0.176403	−	0.305538i	−0.940646	+	0.339390i	$0.889779\pi$
$752$	26.0436	+	40.1036i	0.949712	+	1.46243i
$753$	3.51158	−	4.33644i	0.127969	−	0.158029i
$754$	−1.63940	−	0.729907i	−0.0597034	−	0.0265816i
$755$	54.7037	+	1.07004i	1.99087	+	0.0389427i
$756$	6.49264	+	1.63867i	0.236135	+	0.0595979i
$757$	−29.1640	+	29.1640i	−1.05998	+	1.05998i	−0.0619022	+	0.998082i	$0.519717\pi$
$757$	−29.1640	+	29.1640i	−1.05998	+	1.05998i	−0.998082	+	0.0619022i	$0.980283\pi$
$758$	28.8332	−	23.3486i	1.04727	−	0.848061i
$759$	−1.64729	−	1.82950i	−0.0597928	−	0.0664066i
$760$	10.8113	+	17.3829i	0.392165	+	0.630545i
$761$	−2.78122	−	2.50423i	−0.100819	−	0.0907781i	0.617180	−	0.786822i	$-0.288275\pi$
$761$	−2.78122	−	2.50423i	−0.100819	−	0.0907781i	−0.717999	+	0.696044i	$0.754942\pi$
$762$	−1.88649	+	0.961213i	−0.0683402	+	0.0348211i
$763$	−23.7840	−	20.7957i	−0.861040	−	0.752855i
$764$	−16.5829	+	5.38810i	−0.599947	+	0.194934i
$765$	−5.24588	+	1.89685i	−0.189665	+	0.0685807i
$766$	−25.8210	+	23.2493i	−0.932951	+	0.840033i
$767$	−1.43683	+	3.74308i	−0.0518811	+	0.135155i
$768$	7.12390	+	1.90884i	0.257062	+	0.0688795i
$769$	−16.8695	−	12.2564i	−0.608330	−	0.441977i	0.240496	−	0.970650i	$-0.422690\pi$
$769$	−16.8695	−	12.2564i	−0.608330	−	0.441977i	−0.848826	+	0.528673i	$0.822690\pi$
$770$	−20.0811	−	39.9019i	−0.723674	−	1.43797i
$771$	4.54376	−	3.30124i	0.163640	−	0.118891i
$772$	−0.695274	+	0.266891i	−0.0250235	+	0.00960561i
$773$	−15.9134	+	10.3343i	−0.572365	+	0.371698i	−0.798132	−	0.602483i	$-0.794178\pi$
$773$	−15.9134	+	10.3343i	−0.572365	+	0.371698i	0.225766	+	0.974181i	$0.427511\pi$
$774$	−23.4688	−	13.5497i	−0.843567	−	0.487034i
$775$	−44.5252	−	6.44887i	−1.59939	−	0.231650i
$776$			16.8052i			0.603271i
$777$	1.74233	+	3.76472i	0.0625059	+	0.135058i
$778$	−27.0246	−	4.28028i	−0.968879	−	0.153455i
$779$	15.5744	−	34.9807i	0.558012	−	1.25332i
$780$	0.525548	−	0.221777i	0.0188176	−	0.00794090i
$781$	−54.0172	+	24.0500i	−1.93289	+	0.860577i
$782$	0.651815	−	2.43261i	0.0233089	−	0.0869898i
$783$	−3.53829	+	0.560410i	−0.126448	+	0.0200274i
$784$	31.2980	−	15.0425i	1.11778	−	0.537232i
$785$	−31.1272	−	32.3692i	−1.11098	−	1.15531i
$786$	−1.58796	+	1.76361i	−0.0566408	+	0.0629060i
$787$	0.910595	−	17.3752i	0.0324592	−	0.619359i	−0.933170	−	0.359435i	$-0.882969\pi$
$787$	0.910595	−	17.3752i	0.0324592	−	0.619359i	0.965629	−	0.259923i	$-0.0836973\pi$
$788$	−1.53032	+	29.2002i	−0.0545153	+	1.04021i
$789$	0.989646	−	1.09911i	0.0352323	−	0.0391295i
$790$	−7.74529	−	55.9651i	−0.275565	−	1.99115i
$791$	5.26079	+	7.84810i	0.187052	+	0.279046i
$792$	−17.1658	+	2.71880i	−0.609962	+	0.0966084i
$793$	0.189151	−	0.705921i	0.00671694	−	0.0250680i
$794$	47.7621	−	21.2651i	1.69501	−	0.754668i
$795$	4.46583	+	5.15924i	0.158387	+	0.182979i
$796$	4.18334	−	9.39594i	0.148275	−	0.333030i
$797$	−1.32890	−	0.210477i	−0.0470720	−	0.00745547i	0.132854	−	0.991136i	$-0.457586\pi$
$797$	−1.32890	−	0.210477i	−0.0470720	−	0.00745547i	−0.179926	+	0.983680i	$0.557586\pi$
$798$	6.25989	−	8.88548i	0.221598	−	0.314543i
$799$			8.37724i			0.296365i
$800$	−28.6685	−	8.89696i	−1.01358	−	0.314555i
$801$	−42.3882	−	24.4728i	−1.49771	−	0.864705i
$802$	32.7941	−	21.2968i	1.15800	−	0.752015i
$803$	13.7452	−	5.27627i	0.485056	−	0.186196i
$804$	3.99809	−	2.90479i	0.141002	−	0.102444i
$805$	−7.48006	+	5.99574i	−0.263638	+	0.211322i
$806$	7.70298	+	5.59655i	0.271326	+	0.197130i
$807$	−4.09993	−	1.09857i	−0.144324	−	0.0386716i
$808$	2.28387	−	5.94968i	0.0803462	−	0.209309i
$809$	−10.7064	+	9.64006i	−0.376416	+	0.338927i	−0.835524	−	0.549454i	$-0.814836\pi$
$809$	−10.7064	+	9.64006i	−0.376416	+	0.338927i	0.459108	+	0.888380i	$0.348169\pi$
$810$	−17.6115	+	25.9920i	−0.618806	+	0.913266i
$811$	6.31358	−	2.05141i	0.221700	−	0.0720346i	−0.196061	−	0.980592i	$-0.562815\pi$
$811$	6.31358	−	2.05141i	0.221700	−	0.0720346i	0.417761	+	0.908557i	$0.362815\pi$
$812$	3.53858	−	4.04707i	0.124180	−	0.142024i
$813$	−2.15938	+	1.10026i	−0.0757326	+	0.0385877i
$814$	24.4502	+	22.0151i	0.856980	+	0.771628i
$815$	2.59262	−	35.9874i	0.0908154	−	1.26059i
$816$	1.03804	+	1.15286i	0.0363386	+	0.0403581i
$817$	−26.1909	+	21.2090i	−0.916304	+	0.742008i
$818$	38.8546	−	38.8546i	1.35852	−	1.35852i
$819$	−3.22360	−	3.13099i	−0.112642	−	0.109406i
$820$	4.66580	+	15.3768i	0.162937	+	0.536982i
$821$	18.0995	+	8.05844i	0.631678	+	0.281241i	0.697494	−	0.716590i	$-0.254298\pi$
$821$	18.0995	+	8.05844i	0.631678	+	0.281241i	−0.0658157	+	0.997832i	$0.520965\pi$
$822$	−0.408550	+	0.504517i	−0.0142498	+	0.0175970i
$823$	−12.5518	−	19.3281i	−0.437528	−	0.673734i	0.549278	−	0.835640i	$-0.314903\pi$
$823$	−12.5518	−	19.3281i	−0.437528	−	0.673734i	−0.986806	+	0.161905i	$0.948236\pi$
$824$	1.50282	+	2.60297i	0.0523533	+	0.0906786i
$825$	−7.54355	+	0.894013i	−0.262633	+	0.0311255i
$826$	−25.2068	−	19.8109i	−0.877058	−	0.689309i
$827$	35.9571	+	18.3211i	1.25035	+	0.637086i	0.948653	−	0.316317i	$-0.102446\pi$
$827$	35.9571	+	18.3211i	1.25035	+	0.637086i	0.301698	+	0.953403i	$0.402446\pi$
$828$	−1.99719	−	5.20286i	−0.0694072	−	0.180812i
$829$	1.29555	+	12.3263i	0.0449962	+	0.428110i	0.993711	+	0.111976i	$0.0357181\pi$
$829$	1.29555	+	12.3263i	0.0449962	+	0.428110i	−0.948715	+	0.316133i	$0.897615\pi$
$830$	9.23202	−	7.99122i	0.320448	−	0.277379i
$831$	−10.8989	−	1.14552i	−0.378078	−	0.0397376i
$832$	0.340867	+	0.340867i	0.0118174	+	0.0118174i
$833$	6.03378	+	0.776159i	0.209058	+	0.0268923i
$834$	6.14024	+	1.99508i	0.212619	+	0.0690841i
$835$	−17.9342	+	13.9510i	−0.620639	+	0.482796i
$836$	6.71454	−	31.5894i	0.232227	−	1.09254i
$837$	18.9813	+	0.994766i	0.656089	+	0.0343841i
$838$	−10.3589	+	15.9512i	−0.357841	+	0.551027i
$839$	8.58250	+	26.4142i	0.296301	+	0.911920i	0.982781	+	0.184772i	$0.0591547\pi$
$839$	8.58250	+	26.4142i	0.296301	+	0.911920i	−0.686481	+	0.727148i	$0.740845\pi$
$840$	−0.303956	−	3.03753i	−0.0104875	−	0.104805i
$841$	8.07275	−	24.8454i	0.278371	−	0.856737i
$842$	−24.0227	−	29.6655i	−0.827875	−	1.02234i
$843$	0.435346	+	1.62473i	0.0149941	+	0.0559588i
$844$	−2.02544	−	4.54921i	−0.0697185	−	0.156590i
$845$	28.0678	+	3.50628i	0.965563	+	0.120620i
$846$	29.0853	+	40.0324i	0.999972	+	1.37634i
$847$	5.33040	−	17.2571i	0.183155	−	0.592959i
$848$	−19.0995	+	37.4848i	−0.655879	+	1.28723i
$849$	−1.74535	+	1.00768i	−0.0599002	+	0.0345834i
$850$	−4.96996	−	5.97386i	−0.170468	−	0.204902i
$851$	3.53038	−	6.11479i	0.121020	−	0.209612i
$852$	6.02944	−	0.315990i	0.206565	−	0.0108256i
$853$	4.31272	−	27.2295i	0.147665	−	0.932319i	−0.796928	−	0.604074i	$-0.793543\pi$
$853$	4.31272	−	27.2295i	0.147665	−	0.932319i	0.944593	−	0.328245i	$-0.106457\pi$
$854$	4.94695	+	3.11104i	0.169281	+	0.106458i
$855$	23.4329	+	33.6160i	0.801388	+	1.14964i
$856$	0.617313	−	5.87334i	0.0210993	−	0.200747i
$857$	6.73593	−	1.80489i	0.230095	−	0.0616538i	−0.141929	−	0.989877i	$-0.545331\pi$
$857$	6.73593	−	1.80489i	0.230095	−	0.0616538i	0.372024	+	0.928223i	$0.378664\pi$
$858$	1.50087	+	0.576130i	0.0512389	+	0.0196688i
$859$	7.73489	−	1.64410i	0.263911	−	0.0560961i	−0.0740555	−	0.997254i	$-0.523594\pi$
$859$	7.73489	−	1.64410i	0.263911	−	0.0560961i	0.337967	+	0.941158i	$0.390261\pi$
$860$	2.48521	−	13.9229i	0.0847451	−	0.474768i
$861$	−4.38481	+	3.65782i	−0.149434	+	0.124658i
$862$	6.22270	+	12.2127i	0.211946	+	0.415968i
$863$	−12.5140	−	8.12671i	−0.425983	−	0.276637i	0.313791	−	0.949492i	$-0.398401\pi$
$863$	−12.5140	−	8.12671i	−0.425983	−	0.276637i	−0.739774	+	0.672856i	$0.765068\pi$
$864$	12.4046	+	2.63667i	0.422012	+	0.0897015i
$865$	6.36974	−	3.96164i	0.216578	−	0.134700i
$866$	−7.63288	−	35.9099i	−0.259376	−	1.22027i
$867$	−0.914417	−	5.77340i	−0.0310552	−	0.196075i
$868$	−22.8290	+	17.1000i	−0.774867	+	0.580413i
$869$	35.0636	−	48.2610i	1.18945	−	1.63714i
$870$	−1.17855	−	2.13676i	−0.0399566	−	0.0724428i
$871$	−6.74548	+	0.708979i	−0.228562	+	0.0240228i
$872$	−13.3076	−	10.7763i	−0.450652	−	0.364931i
$873$	1.76057	+	33.5937i	0.0595864	+	1.13698i
$874$	−18.4999			−0.625770
$875$	1.79203	+	29.5261i	0.0605815	+	0.998163i
$876$	−1.50338			−0.0507945
$877$	−1.51186	−	28.8481i	−0.0510520	−	0.974131i	−0.897322	−	0.441376i	$-0.854490\pi$
$877$	−1.51186	−	28.8481i	−0.0510520	−	0.974131i	0.846270	−	0.532754i	$-0.178843\pi$
$878$	−17.3907	−	14.0827i	−0.586907	−	0.475268i
$879$	−3.73698	+	0.392773i	−0.126045	+	0.0132479i
$880$	−22.6196	−	41.0101i	−0.762505	−	1.38245i
$881$	−26.6392	+	36.6657i	−0.897498	+	1.23530i	0.0737612	+	0.997276i	$0.476500\pi$
$881$	−26.6392	+	36.6657i	−0.897498	+	1.23530i	−0.971259	+	0.238024i	$0.923500\pi$
$882$	31.5285	−	17.2399i	1.06162	−	0.580497i
$883$	−0.361222	−	2.28067i	−0.0121561	−	0.0767506i	0.980865	−	0.194692i	$-0.0623706\pi$
$883$	−0.361222	−	2.28067i	−0.0121561	−	0.0767506i	−0.993021	+	0.117941i	$0.962371\pi$
$884$	0.128100	+	0.602662i	0.00430846	+	0.0202697i
$885$	−4.62961	+	2.87937i	−0.155622	+	0.0967889i
$886$	61.2268	+	13.0142i	2.05695	+	0.437219i
$887$	31.9982	+	20.7799i	1.07440	+	0.697720i	0.955442	−	0.295180i	$-0.0953795\pi$
$887$	31.9982	+	20.7799i	1.07440	+	0.697720i	0.118953	+	0.992900i	$0.462046\pi$
$888$	1.02076	+	2.00335i	0.0342544	+	0.0672281i
$889$	−3.00086	+	8.17150i	−0.100646	+	0.274063i
$890$	11.9815	−	67.1237i	0.401619	−	2.24999i
$891$	−32.4257	+	6.89229i	−1.08630	+	0.230900i
$892$	−14.2270	−	5.46125i	−0.476356	−	0.182856i
$893$	59.4411	−	15.9272i	1.98912	−	0.532983i
$894$	0.481318	−	4.57944i	0.0160977	−	0.153159i
$895$	−3.71388	−	5.32780i	−0.124141	−	0.178089i
$896$	24.6830	−	13.0331i	0.824601	−	0.435407i
$897$	0.0539716	−	0.340763i	0.00180206	−	0.0113778i
$898$	7.65295	−	0.401074i	0.255382	−	0.0133840i
$899$	7.62977	−	13.2152i	0.254467	−	0.440750i
$900$	−16.6679	−	4.23038i	−0.555596	−	0.141013i
$901$	−6.38284	+	3.68513i	−0.212643	+	0.122770i
$902$	−20.5604	+	40.3520i	−0.684586	+	1.34357i
$903$	4.90016	−	1.11644i	0.163067	−	0.0371527i
$904$	3.01002	+	4.14293i	0.100112	+	0.137792i
$905$	17.5503	+	2.19241i	0.583391	+	0.0728782i
$906$	−6.40437	−	14.3845i	−0.212771	−	0.477891i
$907$	8.92281	+	33.3004i	0.296277	+	1.10572i	0.940198	+	0.340629i	$0.110640\pi$
$907$	8.92281	+	33.3004i	0.296277	+	1.10572i	−0.643921	+	0.765092i	$0.722693\pi$
$908$	−5.27979	−	6.52000i	−0.175216	−	0.216374i
$909$	3.94217	−	12.1327i	0.130753	−	0.402418i
$910$	2.57475	−	5.70625i	0.0853520	−	0.189160i
$911$	5.06918	+	15.6013i	0.167949	+	0.516895i	0.999242	−	0.0389409i	$-0.0123984\pi$
$911$	5.06918	+	15.6013i	0.167949	+	0.516895i	−0.831292	+	0.555836i	$0.812398\pi$
$912$	6.20659	−	9.55731i	0.205521	−	0.316474i
$913$	12.8745	+	0.674723i	0.426083	+	0.0223301i
$914$	6.57576	−	30.9365i	0.217507	−	1.02329i
$915$	0.784392	−	0.610180i	0.0259312	−	0.0201719i
$916$	16.8559	+	5.47682i	0.556935	+	0.180959i
$917$	0.142192	+	9.75628i	0.00469558	+	0.322181i
$918$	2.32148	+	2.32148i	0.0766203	+	0.0766203i
$919$	−0.795668	−	0.0836281i	−0.0262467	−	0.00275864i	0.0913960	−	0.995815i	$-0.470867\pi$
$919$	−0.795668	−	0.0836281i	−0.0262467	−	0.00275864i	−0.117643	+	0.993056i	$0.537534\pi$
$920$	−3.92855	+	3.40054i	−0.129520	+	0.112113i
$921$	1.03358	+	9.83387i	0.0340577	+	0.324037i
$922$	16.0356	+	41.7741i	0.528103	+	1.37576i
$923$	−7.38341	−	3.76204i	−0.243028	−	0.123829i
$924$	−2.97596	+	3.78653i	−0.0979019	+	0.124568i
$925$	−9.12436	−	19.7843i	−0.300007	−	0.650503i
$926$	−24.4107	−	42.2806i	−0.802185	−	1.38943i
$927$	3.27686	+	5.04592i	0.107626	+	0.165730i
$928$	6.40723	−	7.91227i	0.210328	−	0.259733i
$929$	28.9365	+	12.8834i	0.949377	+	0.422690i	0.822205	−	0.569191i	$-0.192743\pi$
$929$	28.9365	+	12.8834i	0.949377	+	0.422690i	0.127172	+	0.991881i	$0.459410\pi$
$930$	3.75934	+	12.3895i	0.123274	+	0.406266i
$931$	−5.96444	−	44.2887i	−0.195476	−	1.45150i
$932$	−2.16134	+	2.16134i	−0.0707969	+	0.0707969i
$933$	4.19538	−	3.39736i	0.137351	−	0.111224i
$934$	8.47055	+	9.40750i	0.277165	+	0.307823i
$935$	0.589574	−	8.18372i	0.0192811	−	0.267636i
$936$	−1.81006	−	1.62979i	−0.0591637	−	0.0532712i
$937$	−17.1761	+	8.75168i	−0.561120	+	0.285905i	−0.711457	−	0.702730i	$-0.751964\pi$
$937$	−17.1761	+	8.75168i	−0.561120	+	0.285905i	0.150337	+	0.988635i	$0.451964\pi$
$938$	10.5020	−	53.2095i	0.342902	−	1.73735i
$939$	−10.4370	+	3.39117i	−0.340597	+	0.110667i
$940$	−14.4860	+	21.3792i	−0.472483	+	0.697314i
$941$	38.3796	−	34.5572i	1.25114	−	1.12653i	0.264368	−	0.964422i	$-0.414837\pi$
$941$	38.3796	−	34.5572i	1.25114	−	1.12653i	0.986773	−	0.162110i	$-0.0518299\pi$
$942$	−4.63137	+	12.0651i	−0.150898	+	0.393103i
$943$	9.38792	+	2.51549i	0.305713	+	0.0819155i
$944$	−27.1940	−	19.7576i	−0.885089	−	0.643055i
$945$	−1.89343	−	12.3529i	−0.0615933	−	0.401839i
$946$	32.2471	−	23.4289i	1.04844	−	0.761739i
$947$	−44.5560	+	17.1035i	−1.44788	+	0.555788i	−0.950218	−	0.311585i	$-0.899140\pi$
$947$	−44.5560	+	17.1035i	−1.44788	+	0.555788i	−0.497659	+	0.867373i	$0.665807\pi$
$948$	−5.10858	+	3.31755i	−0.165919	+	0.107749i
$949$	1.78691	+	1.03167i	0.0580056	+	0.0334895i
$950$	−32.9387	+	46.6224i	−1.06867	+	1.51263i
$951$		−	9.09962i		−	0.295076i
$952$	3.28388	+	0.296835i	0.106431	+	0.00962046i
$953$	1.41848	+	0.224666i	0.0459492	+	0.00727764i	0.179367	−	0.983782i	$-0.442595\pi$
$953$	1.41848	+	0.224666i	0.0459492	+	0.00727764i	−0.133418	+	0.991060i	$0.542595\pi$
$954$	−17.7072	+	39.7711i	−0.573292	+	1.28764i
$955$	21.2972	+	24.6040i	0.689160	+	0.796166i
$956$	1.08863	−	0.484689i	0.0352088	−	0.0156760i
$957$	0.666849	−	2.48872i	0.0215562	−	0.0804488i
$958$	−66.7152	+	10.5666i	−2.15547	+	0.341393i
$959$	0.178522	+	2.66318i	0.00576477	+	0.0859985i
$960$	0.0898621	+	0.649316i	0.00290029	+	0.0209566i
$961$	−33.4320	+	37.1300i	−1.07845	+	1.19774i
$962$	−0.241315	+	4.60456i	−0.00778030	+	0.148457i
$963$	0.618702	−	11.8055i	0.0199374	−	0.380428i
$964$	4.29944	−	4.77501i	0.138476	−	0.153793i
$965$	0.963400	+	1.00184i	0.0310129	+	0.0322504i
$966$	2.47611	+	1.21652i	0.0796675	+	0.0391408i
$967$	7.29472	−	1.15537i	0.234582	−	0.0371542i	−0.0380364	−	0.999276i	$-0.512110\pi$
$967$	7.29472	−	1.15537i	0.234582	−	0.0371542i	0.272619	+	0.962122i	$0.412110\pi$
$968$	2.53368	−	9.45583i	0.0814356	−	0.303922i
$969$	1.82382	−	0.812019i	0.0585897	−	0.0260858i
$970$	−43.1757	+	18.2198i	−1.38629	+	0.585004i
$971$	−12.4406	+	27.9420i	−0.399237	+	0.896701i	0.596338	+	0.802733i	$0.296622\pi$
$971$	−12.4406	+	27.9420i	−0.399237	+	0.896701i	−0.995575	+	0.0939680i	$0.970045\pi$
$972$	10.8426	+	1.71731i	0.347778	+	0.0550826i
$973$	24.0900	−	11.1490i	0.772289	−	0.357420i
$974$			23.5047i			0.753138i
$975$	−0.762675	−	0.742737i	−0.0244252	−	0.0237866i
$976$	5.30617	+	3.06352i	0.169846	+	0.0980608i
$977$	32.4748	−	21.0894i	1.03896	−	0.674708i	0.0919010	−	0.995768i	$-0.470706\pi$
$977$	32.4748	−	21.0894i	1.03896	−	0.674708i	0.947059	+	0.321060i	$0.104039\pi$
$978$	−9.69371	+	3.72107i	−0.309971	+	0.118987i
$979$	58.2432	−	42.3162i	1.86146	−	1.35243i
$980$	14.0564	+	12.4145i	0.449017	+	0.396567i
$981$	−27.7310	−	20.1478i	−0.885383	−	0.643268i
$982$	40.3556	+	10.8133i	1.28780	+	0.345065i
$983$	−19.1270	+	49.8274i	−0.610055	+	1.58925i	0.185018	+	0.982735i	$0.440766\pi$
$983$	−19.1270	+	49.8274i	−0.610055	+	1.58925i	−0.795073	+	0.606514i	$0.792568\pi$
$984$	−2.29998	+	2.07091i	−0.0733208	+	0.0660183i
$985$	51.3190	−	18.5564i	1.63516	−	0.591255i
$986$	2.50673	−	0.814485i	0.0798305	−	0.0259385i
$987$	−9.00318	−	1.77696i	−0.286574	−	0.0565614i
$988$	4.03267	−	2.05475i	0.128296	−	0.0653702i
$989$	−6.35694	−	5.72382i	−0.202139	−	0.182007i
$990$	−25.5960	−	41.1547i	−0.813494	−	1.30798i
$991$	12.2468	+	13.6014i	0.389032	+	0.432063i	0.905568	−	0.424202i	$-0.139445\pi$
$991$	12.2468	+	13.6014i	0.389032	+	0.432063i	−0.516536	+	0.856266i	$0.672779\pi$
$992$	−41.9805	+	33.9952i	−1.33288	+	1.07935i
$993$	1.68432	−	1.68432i	0.0534503	−	0.0534503i
$994$	46.1666	−	47.5322i	1.46431	−	1.50763i
$995$	−19.1914	−	0.375396i	−0.608408	−	0.0119008i
$996$	−1.20261	−	0.535438i	−0.0381063	−	0.0169660i
$997$	−27.3105	+	33.7256i	−0.864931	+	1.06810i	0.132110	+	0.991235i	$0.457825\pi$
$997$	−27.3105	+	33.7256i	−0.864931	+	1.06810i	−0.997041	+	0.0768658i	$0.975509\pi$
$998$	8.76105	+	13.4908i	0.277326	+	0.427045i
$999$	4.60228	+	7.97139i	0.145610	+	0.252203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.4	yes	288
5.2	odd	4		875.2.bb.b.857.15		288
5.3	odd	4		875.2.bb.a.857.4		288
5.4	even	2		875.2.bb.c.143.15		288
7.5	odd	6	inner	175.2.x.a.33.4	✓	288
25.3	odd	20		875.2.bb.c.507.15		288
25.4	even	10		875.2.bb.a.493.15		288
25.21	even	5		875.2.bb.b.493.4		288
25.22	odd	20	inner	175.2.x.a.122.4	yes	288
35.12	even	12		875.2.bb.b.607.4		288
35.19	odd	6		875.2.bb.c.768.15		288
35.33	even	12		875.2.bb.a.607.15		288
175.47	even	60	inner	175.2.x.a.47.4	yes	288
175.54	odd	30		875.2.bb.a.243.4		288
175.96	odd	30		875.2.bb.b.243.15		288
175.103	even	60		875.2.bb.c.257.15		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.4	✓	288	7.5	odd	6	inner
175.2.x.a.47.4	yes	288	175.47	even	60	inner
175.2.x.a.108.4	yes	288	1.1	even	1	trivial
175.2.x.a.122.4	yes	288	25.22	odd	20	inner
875.2.bb.a.243.4		288	175.54	odd	30
875.2.bb.a.493.15		288	25.4	even	10
875.2.bb.a.607.15		288	35.33	even	12
875.2.bb.a.857.4		288	5.3	odd	4
875.2.bb.b.243.15		288	175.96	odd	30
875.2.bb.b.493.4		288	25.21	even	5
875.2.bb.b.607.4		288	35.12	even	12
875.2.bb.b.857.15		288	5.2	odd	4
875.2.bb.c.143.15		288	5.4	even	2
875.2.bb.c.257.15		288	175.103	even	60
875.2.bb.c.507.15		288	25.3	odd	20
875.2.bb.c.768.15		288	35.19	odd	6

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0935941 - 1.78588i) q^{2} +(0.279642 + 0.226450i) q^{3} +(-1.19157 + 0.125239i) q^{4} +(1.07995 + 1.95799i) q^{5} +(0.378240 - 0.520602i) q^{6} +(-0.314872 - 2.62695i) q^{7} +(-0.224327 - 1.41635i) q^{8} +(-0.596815 - 2.80779i) q^{9} +(3.39566 - 2.11192i) q^{10} +(4.12989 + 0.877836i) q^{11} +(-0.361574 - 0.234809i) q^{12} +(0.268631 + 0.527217i) q^{13} +(-4.66195 + 0.808191i) q^{14} +(-0.141386 + 0.792089i) q^{15} +(-4.85234 + 1.03140i) q^{16} +(-0.811348 - 0.311447i) q^{17} +(-4.95853 + 1.32863i) q^{18} +(-0.667317 + 6.34910i) q^{19} +(-1.53205 - 2.19783i) q^{20} +(0.506820 - 0.805908i) q^{21} +(1.18118 - 7.45766i) q^{22} +(-1.61819 + 0.0848056i) q^{23} +(0.258000 - 0.446869i) q^{24} +(-2.66742 + 4.22905i) q^{25} +(0.916406 - 0.529087i) q^{26} +(0.959010 - 1.88216i) q^{27} +(0.704189 + 3.09076i) q^{28} +(-0.996818 - 1.37200i) q^{29} +(1.42781 + 0.178365i) q^{30} +(3.65980 + 8.22005i) q^{31} +(1.55381 + 5.79889i) q^{32} +(0.956106 + 1.18069i) q^{33} +(-0.480271 + 1.47812i) q^{34} +(4.80348 - 3.45348i) q^{35} +(1.06279 + 3.27094i) q^{36} +(-2.37321 + 3.65442i) q^{37} +(11.4012 + 0.597511i) q^{38} +(-0.0442678 + 0.208263i) q^{39} +(2.53093 - 1.96881i) q^{40} +(-5.70437 - 1.85346i) q^{41} +(-1.48669 - 0.829693i) q^{42} +(3.73281 + 3.73281i) q^{43} +(-5.03100 - 0.528779i) q^{44} +(4.85309 - 4.20083i) q^{45} +(0.302906 + 2.88195i) q^{46} +(-3.45442 - 8.99906i) q^{47} +(-1.59048 - 0.810389i) q^{48} +(-6.80171 + 1.65430i) q^{49} +(7.80224 + 4.36789i) q^{50} +(-0.156360 - 0.270823i) q^{51} +(-0.386121 - 0.594574i) q^{52} +(5.33703 - 6.59068i) q^{53} +(-3.45108 - 1.53652i) q^{54} +(2.74128 + 9.03429i) q^{55} +(-3.65004 + 1.03526i) q^{56} +(-1.62436 + 1.62436i) q^{57} +(-2.35694 + 1.90861i) q^{58} +(4.53398 + 5.03550i) q^{59} +(0.0692713 - 0.961538i) q^{60} +(-0.917861 - 0.826446i) q^{61} +(14.3375 - 7.30532i) q^{62} +(-7.18801 + 2.45190i) q^{63} +(0.774814 - 0.251752i) q^{64} +(-0.742177 + 1.09534i) q^{65} +(2.01909 - 1.81800i) q^{66} +(-4.10789 + 10.7014i) q^{67} +(1.00578 + 0.269499i) q^{68} +(-0.471717 - 0.342723i) q^{69} +(-6.61709 - 8.25523i) q^{70} +(-11.3299 + 8.23164i) q^{71} +(-3.84293 + 1.47516i) q^{72} +(2.92452 - 1.89921i) q^{73} +(6.74848 + 3.89623i) q^{74} +(-1.70359 + 0.578583i) q^{75} -7.64897i q^{76} +(1.00564 - 11.1254i) q^{77} +(0.376077 + 0.0595648i) q^{78} +(5.74668 - 12.9073i) q^{79} +(-7.25974 - 8.38696i) q^{80} +(-7.17266 + 3.19347i) q^{81} +(-2.77617 + 10.3608i) q^{82} +(3.01586 - 0.477665i) q^{83} +(-0.502981 + 1.02377i) q^{84} +(-0.266404 - 1.92496i) q^{85} +(6.31698 - 7.01572i) q^{86} +(0.0319372 - 0.609399i) q^{87} +(0.316873 - 6.04629i) q^{88} +(11.4094 - 12.6715i) q^{89} +(-7.95640 - 8.27388i) q^{90} +(1.30039 - 0.871684i) q^{91} +(1.91756 - 0.303712i) q^{92} +(-0.837993 + 3.12743i) q^{93} +(-15.7479 + 7.01144i) q^{94} +(-13.1521 + 5.55010i) q^{95} +(-0.878647 + 1.97347i) q^{96} +(-11.5748 - 1.83327i) q^{97} +(3.59099 + 11.9922i) q^{98} -12.1198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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