LMFDB - Embedded newform 125.2.h.a.4.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [125,2,Mod(4,125)] 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("125.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(125, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	125.4
Dual form			125.2.h.a.94.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.31243 + 0.145486i) q^{2} +(0.181456 + 0.0853865i) q^{3} +(3.34195 + 0.422186i) q^{4} +(-2.20265 - 0.385146i) q^{5} +(0.407181 + 0.223850i) q^{6} +(-1.85539 + 2.55372i) q^{7} +(3.11468 + 0.594156i) q^{8} +(-1.88664 - 2.28055i) q^{9} +(-5.03744 - 1.21108i) q^{10} +(0.184936 - 2.93947i) q^{11} +(0.570366 + 0.361965i) q^{12} +(3.92872 - 3.25012i) q^{13} +(-4.66199 + 5.63538i) q^{14} +(-0.366797 - 0.257963i) q^{15} +(0.590674 + 0.151659i) q^{16} +(0.718412 + 5.68682i) q^{17} +(-4.03093 - 5.54810i) q^{18} +(3.01177 + 6.40035i) q^{19} +(-7.19853 - 2.21707i) q^{20} +(-0.554724 + 0.304962i) q^{21} +(0.855302 - 6.77042i) q^{22} +(-0.236444 + 0.597190i) q^{23} +(0.514442 + 0.373764i) q^{24} +(4.70332 + 1.69668i) q^{25} +(9.55775 - 6.94411i) q^{26} +(-0.297230 - 1.15764i) q^{27} +(-7.27875 + 7.75108i) q^{28} +(-4.29958 - 4.03757i) q^{29} +(-0.810662 - 0.649887i) q^{30} +(-1.08791 + 0.137435i) q^{31} +(-4.68747 - 1.52305i) q^{32} +(0.284549 - 0.517592i) q^{33} +(0.833928 + 13.2549i) q^{34} +(5.07032 - 4.91036i) q^{35} +(-5.34222 - 8.41800i) q^{36} +(0.403881 - 1.57301i) q^{37} +(6.03336 + 15.2385i) q^{38} +(0.990405 - 0.254293i) q^{39} +(-6.63170 - 2.50832i) q^{40} +(-0.509919 + 0.201891i) q^{41} +(-1.32713 + 0.624499i) q^{42} +(1.97802 - 0.642698i) q^{43} +(1.85905 - 9.74547i) q^{44} +(3.27725 + 5.74989i) q^{45} +(-0.633644 + 1.34656i) q^{46} +(5.83382 - 1.11286i) q^{47} +(0.0942314 + 0.0779550i) q^{48} +(-0.915913 - 2.81889i) q^{49} +(10.6293 + 4.60773i) q^{50} +(-0.355218 + 1.09325i) q^{51} +(14.5017 - 9.20308i) q^{52} +(-0.538682 - 0.979859i) q^{53} +(-0.518906 - 2.72020i) q^{54} +(-1.53947 + 6.40339i) q^{55} +(-7.29624 + 6.85162i) q^{56} +1.41854i q^{57} +(-9.35507 - 9.96214i) q^{58} +(-2.76004 + 4.34912i) q^{59} +(-1.11691 - 1.01696i) q^{60} +(-10.0347 - 3.97303i) q^{61} +(-2.53571 + 0.159533i) q^{62} +(9.32434 - 0.586638i) q^{63} +(-11.7519 - 4.65290i) q^{64} +(-9.90537 + 5.64574i) q^{65} +(0.733302 - 1.15550i) q^{66} +(3.99910 + 4.25861i) q^{67} +19.3083i q^{68} +(-0.0938961 + 0.0881743i) q^{69} +(12.4392 - 10.6172i) q^{70} +(-1.52033 - 7.96986i) q^{71} +(-4.52126 - 8.22414i) q^{72} +(-1.03124 + 0.654444i) q^{73} +(1.16280 - 3.57872i) q^{74} +(0.708571 + 0.709473i) q^{75} +(7.36305 + 22.6612i) q^{76} +(7.16346 + 5.92613i) q^{77} +(2.32724 - 0.443945i) q^{78} +(2.97692 - 6.32628i) q^{79} +(-1.24264 - 0.561548i) q^{80} +(-1.61891 + 8.48663i) q^{81} +(-1.20853 + 0.392674i) q^{82} +(15.5649 - 7.32429i) q^{83} +(-1.98261 + 0.784970i) q^{84} +(0.607847 - 12.8028i) q^{85} +(4.66754 - 1.19842i) q^{86} +(-0.435428 - 1.09977i) q^{87} +(2.32252 - 9.04561i) q^{88} +(-7.70549 - 12.1419i) q^{89} +(6.74190 + 13.7730i) q^{90} +(1.01060 + 16.0631i) q^{91} +(-1.04231 + 1.89595i) q^{92} +(-0.209142 - 0.0679544i) q^{93} +(13.6522 - 1.72468i) q^{94} +(-4.16881 - 15.2577i) q^{95} +(-0.720519 - 0.676613i) q^{96} +(-4.25297 + 4.52896i) q^{97} +(-1.70788 - 6.65174i) q^{98} +(-7.05252 + 5.12395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18}+ \cdots + 45 q^{99}+O(q^{100}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{50}\right)$

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 $

$2$	2.31243	+	0.145486i	1.63514	+	0.102874i	0.853580	−	0.520961i	$-0.174426\pi$
$2$	2.31243	+	0.145486i	1.63514	+	0.102874i	0.781556	+	0.623835i	$0.214426\pi$
$3$	0.181456	+	0.0853865i	0.104763	+	0.0492979i	0.477447	−	0.878661i	$-0.341562\pi$
$3$	0.181456	+	0.0853865i	0.104763	+	0.0492979i	−0.372683	+	0.927959i	$0.621562\pi$
$4$	3.34195	+	0.422186i	1.67097	+	0.211093i
$5$	−2.20265	−	0.385146i	−0.985055	−	0.172243i
$5$	−2.20265	−	0.385146i	−0.985055	−	0.172243i
$6$	0.407181	+	0.223850i	0.166231	+	0.0913863i
$7$	−1.85539	+	2.55372i	−0.701270	+	0.965216i	0.298671	+	0.954356i	$0.403457\pi$
$7$	−1.85539	+	2.55372i	−0.701270	+	0.965216i	−0.999941	+	0.0108597i	$0.996543\pi$
$8$	3.11468	+	0.594156i	1.10120	+	0.210066i
$9$	−1.88664	−	2.28055i	−0.628879	−	0.760184i
$10$	−5.03744	−	1.21108i	−1.59298	−	0.382977i
$11$	0.184936	−	2.93947i	0.0557602	−	0.886283i	−0.866370	−	0.499403i	$-0.833553\pi$
$11$	0.184936	−	2.93947i	0.0557602	−	0.886283i	0.922130	−	0.386880i	$-0.126447\pi$
$12$	0.570366	+	0.361965i	0.164650	+	0.104490i
$13$	3.92872	−	3.25012i	1.08963	−	0.901422i	0.0940728	−	0.995565i	$-0.470011\pi$
$13$	3.92872	−	3.25012i	1.08963	−	0.901422i	0.995559	+	0.0941438i	$0.0300113\pi$
$14$	−4.66199	+	5.63538i	−1.24597	+	1.50612i
$15$	−0.366797	−	0.257963i	−0.0947065	−	0.0666059i
$16$	0.590674	+	0.151659i	0.147668	+	0.0379148i
$17$	0.718412	+	5.68682i	0.174241	+	1.37926i	0.800356	+	0.599525i	$0.204644\pi$
$17$	0.718412	+	5.68682i	0.174241	+	1.37926i	−0.626115	+	0.779731i	$0.715356\pi$
$18$	−4.03093	−	5.54810i	−0.950100	−	1.30770i
$19$	3.01177	+	6.40035i	0.690949	+	1.46834i	0.874347	+	0.485302i	$0.161290\pi$
$19$	3.01177	+	6.40035i	0.690949	+	1.46834i	−0.183398	+	0.983039i	$0.558710\pi$
$20$	−7.19853	−	2.21707i	−1.60964	−	0.495751i
$21$	−0.554724	+	0.304962i	−0.121051	+	0.0665482i
$22$	0.855302	−	6.77042i	0.182351	−	1.44346i
$23$	−0.236444	+	0.597190i	−0.0493020	+	0.124523i	−0.952341	−	0.305037i	$-0.901331\pi$
$23$	−0.236444	+	0.597190i	−0.0493020	+	0.124523i	0.903038	+	0.429560i	$0.141331\pi$
$24$	0.514442	+	0.373764i	0.105010	+	0.0762943i
$25$	4.70332	+	1.69668i	0.940665	+	0.339337i
$26$	9.55775	−	6.94411i	1.87443	−	1.36185i
$27$	−0.297230	−	1.15764i	−0.0572020	−	0.222787i
$28$	−7.27875	+	7.75108i	−1.37555	+	1.46482i
$29$	−4.29958	−	4.03757i	−0.798412	−	0.749758i	0.173568	−	0.984822i	$-0.444470\pi$
$29$	−4.29958	−	4.03757i	−0.798412	−	0.749758i	−0.971980	+	0.235063i	$0.924470\pi$
$30$	−0.810662	−	0.649887i	−0.148006	−	0.118653i
$31$	−1.08791	+	0.137435i	−0.195394	+	0.0246840i	−0.222421	−	0.974951i	$-0.571396\pi$
$31$	−1.08791	+	0.137435i	−0.195394	+	0.0246840i	0.0270270	+	0.999635i	$0.491396\pi$
$32$	−4.68747	−	1.52305i	−0.828635	−	0.269240i
$33$	0.284549	−	0.517592i	0.0495336	−	0.0901012i
$34$	0.833928	+	13.2549i	0.143017	+	2.27320i
$35$	5.07032	−	4.91036i	0.857041	−	0.830002i
$36$	−5.34222	−	8.41800i	−0.890370	−	1.40300i
$37$	0.403881	−	1.57301i	0.0663975	−	0.258601i	−0.926715	−	0.375765i	$-0.877380\pi$
$37$	0.403881	−	1.57301i	0.0663975	−	0.258601i	0.993113	+	0.117163i	$0.0373801\pi$
$38$	6.03336	+	15.2385i	0.978741	+	2.47202i
$39$	0.990405	−	0.254293i	0.158592	−	0.0407194i
$40$	−6.63170	−	2.50832i	−1.04856	−	0.396601i
$41$	−0.509919	+	0.201891i	−0.0796360	+	0.0315301i	−0.407605	−	0.913158i	$-0.633636\pi$
$41$	−0.509919	+	0.201891i	−0.0796360	+	0.0315301i	0.327969	+	0.944689i	$0.393636\pi$
$42$	−1.32713	+	0.624499i	−0.204780	+	0.0963623i
$43$	1.97802	−	0.642698i	0.301645	−	0.0980106i	−0.154284	−	0.988027i	$-0.549307\pi$
$43$	1.97802	−	0.642698i	0.301645	−	0.0980106i	0.455929	+	0.890016i	$0.349307\pi$
$44$	1.85905	−	9.74547i	0.280262	−	1.46919i
$45$	3.27725	+	5.74989i	0.488544	+	0.857142i
$46$	−0.633644	+	1.34656i	−0.0934257	+	0.198540i
$47$	5.83382	−	1.11286i	0.850950	−	0.162327i	0.256584	−	0.966522i	$-0.417403\pi$
$47$	5.83382	−	1.11286i	0.850950	−	0.162327i	0.594366	+	0.804194i	$0.297403\pi$
$48$	0.0942314	+	0.0779550i	0.0136011	+	0.0112518i
$49$	−0.915913	−	2.81889i	−0.130845	−	0.402698i
$50$	10.6293	+	4.60773i	1.50321	+	0.651632i
$51$	−0.355218	+	1.09325i	−0.0497404	+	0.153085i
$52$	14.5017	−	9.20308i	2.01103	−	1.27624i
$53$	−0.538682	−	0.979859i	−0.0739937	−	0.134594i	0.836722	−	0.547628i	$-0.184469\pi$
$53$	−0.538682	−	0.979859i	−0.0739937	−	0.134594i	−0.910716	+	0.413034i	$0.864469\pi$
$54$	−0.518906	−	2.72020i	−0.0706141	−	0.370172i
$55$	−1.53947	+	6.40339i	−0.207583	+	0.863433i
$56$	−7.29624	+	6.85162i	−0.975001	+	0.915587i
$57$			1.41854i			0.187891i
$58$	−9.35507	−	9.96214i	−1.22838	−	1.30809i
$59$	−2.76004	+	4.34912i	−0.359326	+	0.566208i	−0.975114	−	0.221705i	$-0.928838\pi$
$59$	−2.76004	+	4.34912i	−0.359326	+	0.566208i	0.615788	+	0.787912i	$0.288838\pi$
$60$	−1.11691	−	1.01696i	−0.144192	−	0.131289i
$61$	−10.0347	−	3.97303i	−1.28482	−	0.508695i	−0.376282	−	0.926505i	$-0.622798\pi$
$61$	−10.0347	−	3.97303i	−1.28482	−	0.508695i	−0.908534	+	0.417810i	$0.862798\pi$
$62$	−2.53571	+	0.159533i	−0.322036	+	0.0202608i
$63$	9.32434	−	0.586638i	1.17476	−	0.0739094i
$64$	−11.7519	−	4.65290i	−1.46899	−	0.581613i
$65$	−9.90537	+	5.64574i	−1.22861	+	0.700268i
$66$	0.733302	−	1.15550i	0.0902632	−	0.142232i
$67$	3.99910	+	4.25861i	0.488567	+	0.520271i	0.925257	−	0.379341i	$-0.123849\pi$
$67$	3.99910	+	4.25861i	0.488567	+	0.520271i	−0.436690	+	0.899612i	$0.643849\pi$
$68$			19.3083i			2.34148i
$69$	−0.0938961	+	0.0881743i	−0.0113038	+	0.0106149i
$70$	12.4392	−	10.6172i	1.48676	−	1.26900i
$71$	−1.52033	−	7.96986i	−0.180430	−	0.945848i	−0.951163	−	0.308690i	$-0.900110\pi$
$71$	−1.52033	−	7.96986i	−0.180430	−	0.945848i	0.770733	−	0.637159i	$-0.219890\pi$
$72$	−4.52126	−	8.22414i	−0.532835	−	0.969224i
$73$	−1.03124	+	0.654444i	−0.120697	+	0.0765968i	−0.594805	−	0.803870i	$-0.702771\pi$
$73$	−1.03124	+	0.654444i	−0.120697	+	0.0765968i	0.474108	+	0.880467i	$0.342771\pi$
$74$	1.16280	−	3.57872i	0.135172	−	0.416018i
$75$	0.708571	+	0.709473i	0.0818187	+	0.0819229i
$76$	7.36305	+	22.6612i	0.844600	+	2.59941i
$77$	7.16346	+	5.92613i	0.816352	+	0.675345i
$78$	2.32724	−	0.443945i	0.263508	−	0.0502669i
$79$	2.97692	−	6.32628i	0.334930	−	0.711762i	−0.664437	−	0.747344i	$-0.731329\pi$
$79$	2.97692	−	6.32628i	0.334930	−	0.711762i	0.999367	+	0.0355821i	$0.0113285\pi$
$80$	−1.24264	−	0.561548i	−0.138931	−	0.0627830i
$81$	−1.61891	+	8.48663i	−0.179879	+	0.942959i
$82$	−1.20853	+	0.392674i	−0.133459	+	0.0433636i
$83$	15.5649	−	7.32429i	1.70847	−	0.803946i	0.713858	−	0.700290i	$-0.246946\pi$
$83$	15.5649	−	7.32429i	1.70847	−	0.803946i	0.994613	−	0.103656i	$-0.0330540\pi$
$84$	−1.98261	+	0.784970i	−0.216320	+	0.0856473i
$85$	0.607847	−	12.8028i	0.0659303	−	1.38865i
$86$	4.66754	−	1.19842i	0.503314	−	0.129229i
$87$	−0.435428	−	1.09977i	−0.0466828	−	0.117907i
$88$	2.32252	−	9.04561i	0.247581	−	0.964265i
$89$	−7.70549	−	12.1419i	−0.816781	−	1.28704i	−0.954990	−	0.296637i	$-0.904135\pi$
$89$	−7.70549	−	12.1419i	−0.816781	−	1.28704i	0.138210	−	0.990403i	$-0.455865\pi$
$90$	6.74190	+	13.7730i	0.710658	+	1.45180i
$91$	1.01060	+	16.0631i	0.105940	+	1.68387i
$92$	−1.04231	+	1.89595i	−0.108668	+	0.197667i
$93$	−0.209142	−	0.0679544i	−0.0216870	−	0.00704655i
$94$	13.6522	−	1.72468i	1.40812	−	0.177887i
$95$	−4.16881	−	15.2577i	−0.427711	−	1.56541i
$96$	−0.720519	−	0.676613i	−0.0735377	−	0.0690565i
$97$	−4.25297	+	4.52896i	−0.431824	+	0.459846i	−0.907671	−	0.419682i	$-0.862142\pi$
$97$	−4.25297	+	4.52896i	−0.431824	+	0.459846i	0.475847	+	0.879528i	$0.342142\pi$
$98$	−1.70788	−	6.65174i	−0.172522	−	0.671927i
$99$	−7.05252	+	5.12395i	−0.708805	+	0.514977i
$100$	15.0019	+	7.65591i	1.50019	+	0.765591i
$101$	−10.1866	−	7.40103i	−1.01361	−	0.736430i	−0.0486458	−	0.998816i	$-0.515491\pi$
$101$	−10.1866	−	7.40103i	−1.01361	−	0.736430i	−0.964963	+	0.262386i	$0.915491\pi$
$102$	−0.980469	+	2.47638i	−0.0970809	+	0.245198i
$103$	−1.73224	+	13.7121i	−0.170683	+	1.35109i	0.641245	+	0.767336i	$0.278418\pi$
$103$	−1.73224	+	13.7121i	−0.170683	+	1.35109i	−0.811928	+	0.583757i	$0.801582\pi$
$104$	14.1678	−	7.78880i	1.38926	−	0.763755i
$105$	1.33932	−	0.458074i	0.130704	−	0.0447035i
$106$	−1.10311	−	2.34423i	−0.107144	−	0.227692i
$107$	6.43545	+	8.85764i	0.622139	+	0.856301i	0.997506	−	0.0705753i	$-0.0224835\pi$
$107$	6.43545	+	8.85764i	0.622139	+	0.856301i	−0.375368	+	0.926876i	$0.622484\pi$
$108$	−0.504591	−	3.99425i	−0.0485542	−	0.384346i
$109$	13.9676	+	3.58627i	1.33785	+	0.343502i	0.848782	−	0.528743i	$-0.177336\pi$
$109$	13.9676	+	3.58627i	1.33785	+	0.343502i	0.489070	+	0.872245i	$0.337336\pi$
$110$	−4.49153	+	14.5834i	−0.428251	+	1.39048i
$111$	0.207600	−	0.250946i	0.0197045	−	0.0238187i
$112$	−1.48322	+	1.22703i	−0.140151	+	0.115943i
$113$	−9.52408	−	6.04417i	−0.895951	−	0.568587i	0.00621349	−	0.999981i	$-0.498022\pi$
$113$	−9.52408	−	6.04417i	−0.895951	−	0.568587i	−0.902164	+	0.431393i	$0.858022\pi$
$114$	−0.206378	+	3.28029i	−0.0193291	+	0.307227i
$115$	0.750809	−	1.22433i	0.0700133	−	0.114170i
$116$	−12.6644	−	15.3086i	−1.17586	−	1.42137i
$117$	−14.8241	−	2.82786i	−1.37049	−	0.261435i
$118$	−7.01514	+	9.65551i	−0.645796	+	0.888861i
$119$	−15.8555	−	8.71663i	−1.45347	−	0.799052i
$120$	−0.989182	−	1.02141i	−0.0902996	−	0.0932413i
$121$	2.30699	+	0.291440i	0.209726	+	0.0264946i
$122$	−22.6266	−	10.6473i	−2.04852	−	0.963960i
$123$	−0.109766	−	0.00690592i	−0.00989731	−	0.000622686i
$124$	−3.69376			−0.331709
$125$	−9.70630	−	5.54867i	−0.868158	−	0.496288i
$126$	21.6472			1.92849
$127$	−4.01527	−	0.252619i	−0.356297	−	0.0224163i	−0.116367	−	0.993206i	$-0.537125\pi$
$127$	−4.01527	−	0.252619i	−0.356297	−	0.0224163i	−0.239931	+	0.970790i	$0.577125\pi$
$128$	−17.5793	−	8.27218i	−1.55380	−	0.731164i
$129$	0.413801	+	0.0522752i	0.0364331	+	0.00460257i
$130$	−23.7269	+	11.6143i	−2.08098	+	1.01864i
$131$	3.61912	+	1.98963i	0.316204	+	0.173835i	0.631950	−	0.775009i	$-0.282255\pi$
$131$	3.61912	+	1.98963i	0.316204	+	0.173835i	−0.315746	+	0.948844i	$0.602255\pi$
$132$	1.16947	−	1.60963i	0.101789	−	0.140101i
$133$	−21.9327	−	4.18389i	−1.90181	−	0.362789i
$134$	8.62807	+	10.4295i	0.745352	+	0.900976i
$135$	0.208835	+	2.66434i	0.0179737	+	0.229310i
$136$	−1.14124	+	18.1394i	−0.0978603	+	1.55544i
$137$	−9.89164	−	6.27743i	−0.845100	−	0.536317i	0.0413482	−	0.999145i	$-0.486835\pi$
$137$	−9.89164	−	6.27743i	−0.845100	−	0.536317i	−0.886448	+	0.462828i	$0.846835\pi$
$138$	−0.229956	+	0.190237i	−0.0195752	+	0.0161940i
$139$	−1.26457	+	1.52860i	−0.107259	+	0.129654i	−0.821411	−	0.570337i	$-0.806813\pi$
$139$	−1.26457	+	1.52860i	−0.107259	+	0.129654i	0.714152	+	0.699991i	$0.246813\pi$
$140$	19.0178	−	14.2695i	1.60730	−	1.20600i
$141$	1.15360	+	0.296195i	0.0971509	+	0.0249441i
$142$	−2.35616	−	18.6509i	−0.197725	−	1.56515i
$143$	−8.82707	−	12.1494i	−0.738157	−	1.01599i
$144$	−0.768520	−	1.63319i	−0.0640433	−	0.136099i
$145$	7.91541	+	10.5493i	0.657339	+	0.876073i
$146$	−2.47988	+	1.36333i	−0.205236	+	0.112830i
$147$	0.0744977	−	0.589710i	0.00614446	−	0.0486384i
$148$	2.01385	−	5.08641i	0.165537	−	0.418100i
$149$	9.30708	+	6.76199i	0.762466	+	0.553964i	0.899666	−	0.436580i	$-0.143810\pi$
$149$	9.30708	+	6.76199i	0.762466	+	0.553964i	−0.137200	+	0.990543i	$0.543810\pi$
$150$	1.53530	+	1.74370i	0.125357	+	0.142372i
$151$	−4.69413	+	3.41049i	−0.382003	+	0.277541i	−0.762171	−	0.647376i	$-0.775866\pi$
$151$	−4.69413	+	3.41049i	−0.382003	+	0.277541i	0.380168	+	0.924918i	$0.375866\pi$
$152$	5.57790	+	21.7245i	0.452427	+	1.76209i
$153$	11.6137	−	12.3673i	0.938912	−	0.999840i
$154$	15.7028	+	14.7459i	1.26537	+	1.18826i
$155$	2.44921	+	0.116283i	0.196726	+	0.00934010i
$156$	3.41724	−	0.431698i	0.273598	−	0.0345635i
$157$	7.18476	+	2.33447i	0.573406	+	0.186311i	0.581345	−	0.813658i	$-0.302527\pi$
$157$	7.18476	+	2.33447i	0.573406	+	0.186311i	−0.00793827	+	0.999968i	$0.502527\pi$
$158$	7.80432	−	14.1960i	0.620878	−	1.12937i
$159$	−0.0140801	−	0.223797i	−0.00111663	−	0.0177483i
$160$	9.73825	+	5.16011i	0.769876	+	0.407942i
$161$	−1.08636	−	1.71183i	−0.0856173	−	0.134911i
$162$	−4.97831	+	19.3892i	−0.391133	+	1.52336i
$163$	6.43065	+	16.2420i	0.503687	+	1.27217i	0.929989	+	0.367587i	$0.119816\pi$
$163$	6.43065	+	16.2420i	0.503687	+	1.27217i	−0.426302	+	0.904581i	$0.640184\pi$
$164$	−1.78936	+	0.459429i	−0.139725	+	0.0358754i
$165$	−0.826109	+	1.03048i	−0.0643125	+	0.0802228i
$166$	37.0584	−	14.6725i	2.87629	−	1.13880i
$167$	−15.4022	+	7.24774i	−1.19186	+	0.560847i	−0.916322	−	0.400443i	$-0.868856\pi$
$167$	−15.4022	+	7.24774i	−1.19186	+	0.560847i	−0.275538	+	0.961290i	$0.588856\pi$
$168$	−1.90898	+	0.620265i	−0.147281	+	0.0478545i
$169$	2.43561	−	12.7679i	0.187355	−	0.982147i
$170$	3.26823	−	29.5171i	0.250661	−	2.26386i
$171$	8.91420	−	18.9436i	0.681686	−	1.44866i
$172$	6.88178	−	1.31277i	0.524731	−	0.100098i
$173$	9.70215	+	8.02631i	0.737640	+	0.610229i	0.928476	−	0.371393i	$-0.121120\pi$
$173$	9.70215	+	8.02631i	0.737640	+	0.610229i	−0.190835	+	0.981622i	$0.561120\pi$
$174$	−0.846898	−	2.60648i	−0.0642031	−	0.197597i
$175$	−13.0593	+	8.86298i	−0.987194	+	0.669978i
$176$	0.555034	−	1.70822i	0.0418373	−	0.128762i
$177$	−0.872181	+	0.553503i	−0.0655571	+	0.0416038i
$178$	−16.0519	−	29.1984i	−1.20314	−	2.18851i
$179$	2.86030	+	14.9942i	0.213789	+	1.12072i	0.913669	+	0.406460i	$0.133237\pi$
$179$	2.86030	+	14.9942i	0.213789	+	1.12072i	−0.699880	+	0.714261i	$0.746763\pi$
$180$	8.52488	+	20.5994i	0.635407	+	1.53539i
$181$	−14.4369	+	13.5571i	−1.07308	+	1.00769i	−0.0731368	+	0.997322i	$0.523301\pi$
$181$	−14.4369	+	13.5571i	−1.07308	+	1.00769i	−0.999946	+	0.0103701i	$0.996699\pi$
$182$			37.2918i			2.76426i
$183$	−1.48162	−	1.57776i	−0.109524	−	0.116631i
$184$	−1.09127	+	1.71957i	−0.0804496	+	0.126768i
$185$	−1.49545	+	3.30924i	−0.109947	+	0.243300i
$186$	−0.473741	−	0.187567i	−0.0347364	−	0.0137531i
$187$	16.8491	−	1.06005i	1.23213	−	0.0775189i
$188$	19.9662	−	1.25616i	1.45618	−	0.0916152i
$189$	3.50776	+	1.38882i	0.255152	+	0.101022i
$190$	−7.42032	−	35.8889i	−0.538326	−	2.60365i
$191$	0.135716	−	0.213854i	0.00982003	−	0.0154739i	−0.839382	−	0.543541i	$-0.817083\pi$
$191$	0.135716	−	0.213854i	0.00982003	−	0.0154739i	0.849202	+	0.528067i	$0.177083\pi$
$192$	−1.73515	−	1.84775i	−0.125224	−	0.133350i
$193$		−	4.44244i		−	0.319774i	−0.987135	−	0.159887i	$-0.948887\pi$
$193$		−	4.44244i		−	0.319774i	0.987135	−	0.159887i	$-0.0511130\pi$
$194$	−10.4936	+	9.85416i	−0.753398	+	0.707487i
$195$	−2.27945	+	0.178667i	−0.163235	+	0.0127946i
$196$	−1.87084	−	9.80726i	−0.133631	−	0.700519i
$197$	−2.61419	−	4.75520i	−0.186254	−	0.338794i	0.766651	−	0.642064i	$-0.221922\pi$
$197$	−2.61419	−	4.75520i	−0.186254	−	0.338794i	−0.952905	+	0.303270i	$0.901922\pi$
$198$	−17.0539	+	10.8228i	−1.21197	+	0.769140i
$199$	4.56275	−	14.0427i	0.323445	−	0.995461i	−0.648693	−	0.761050i	$-0.724684\pi$
$199$	4.56275	−	14.0427i	0.323445	−	0.995461i	0.972138	−	0.234411i	$-0.0753160\pi$
$200$	13.6412	+	8.07913i	0.964581	+	0.571281i
$201$	0.362031	+	1.11422i	0.0255357	+	0.0785908i
$202$	−22.4792	−	18.5964i	−1.58163	−	1.30844i
$203$	18.2882	−	3.48866i	1.28358	−	0.244856i
$204$	−1.64867	+	3.50361i	−0.115430	+	0.245302i
$205$	1.20093	−	0.248302i	0.0838766	−	0.0173422i
$206$	−6.00061	+	31.4563i	−0.418082	+	2.19166i
$207$	1.80801	−	0.587457i	0.125665	−	0.0408311i
$208$	2.81350	−	1.32393i	0.195081	−	0.0917983i
$209$	19.3706	−	7.66937i	1.33989	−	0.530501i
$210$	3.16372	−	0.864414i	0.218318	−	0.0596503i
$211$	19.3302	−	4.96315i	1.33074	−	0.341677i	0.484649	−	0.874709i	$-0.338947\pi$
$211$	19.3302	−	4.96315i	1.33074	−	0.341677i	0.846095	+	0.533032i	$0.178947\pi$
$212$	−1.38656	−	3.50206i	−0.0952296	−	0.240523i
$213$	0.404646	−	1.57599i	0.0277259	−	0.107985i
$214$	13.5929	+	21.4190i	0.929191	+	1.46417i
$215$	−4.60442	+	0.653811i	−0.314019	+	0.0445895i
$216$	−0.237960	−	3.78226i	−0.0161911	−	0.257350i
$217$	1.66752	−	3.03321i	0.113199	−	0.205908i
$218$	31.7773	+	10.3251i	2.15223	+	0.699303i
$219$	−0.243005	+	0.0306986i	−0.0164207	+	0.00207442i
$220$	−7.84826	+	20.7498i	−0.529130	+	1.39895i
$221$	21.3053	+	20.0070i	1.43315	+	1.34582i
$222$	0.516571	−	0.550092i	0.0346700	−	0.0369197i
$223$	1.77206	+	6.90172i	0.118666	+	0.462173i	0.999946	−	0.0104218i	$-0.00331741\pi$
$223$	1.77206	+	6.90172i	0.118666	+	0.462173i	−0.881280	+	0.472595i	$0.843317\pi$
$224$	12.5865	−	9.14464i	0.840972	−	0.611002i
$225$	−5.00409	−	13.9272i	−0.333606	−	0.928480i
$226$	−21.1445	−	15.3623i	−1.40651	−	1.02189i
$227$	2.76391	−	6.98083i	0.183447	−	0.463334i	−0.808729	−	0.588181i	$-0.799844\pi$
$227$	2.76391	−	6.98083i	0.183447	−	0.463334i	0.992176	+	0.124847i	$0.0398442\pi$
$228$	−0.598889	+	4.74070i	−0.0396624	+	0.313960i
$229$	−5.72995	+	3.15007i	−0.378646	+	0.208162i	−0.659699	−	0.751530i	$-0.729316\pi$
$229$	−5.72995	+	3.15007i	−0.378646	+	0.208162i	0.281053	+	0.959692i	$0.409316\pi$
$230$	1.91432	−	2.72196i	0.126226	−	0.179481i
$231$	0.793838	+	1.68699i	0.0522307	+	0.110996i
$232$	−10.9928	−	15.1304i	−0.721715	−	0.993356i
$233$	1.43422	+	11.3530i	0.0939586	+	0.743759i	0.966760	+	0.255684i	$0.0823007\pi$
$233$	1.43422	+	11.3530i	0.0939586	+	0.743759i	−0.872802	+	0.488075i	$0.837699\pi$
$234$	−33.8684	−	8.69593i	−2.21405	−	0.568471i
$235$	−13.2785	+	0.204367i	−0.866192	+	0.0133315i
$236$	−11.0600	+	13.3693i	−0.719947	+	0.870267i
$237$	1.08036	−	0.893750i	0.0701768	−	0.0580553i
$238$	−35.3966	−	22.4634i	−2.29442	−	1.45608i
$239$	1.45980	−	23.2028i	0.0944265	−	1.50087i	−0.610744	−	0.791828i	$-0.709129\pi$
$239$	1.45980	−	23.2028i	0.0944265	−	1.50087i	0.705170	−	0.709038i	$-0.250871\pi$
$240$	−0.177535	−	0.208000i	−0.0114598	−	0.0134264i
$241$	0.0108362	+	0.0130987i	0.000698021	+	0.000843763i	0.770862	−	0.637002i	$-0.219826\pi$
$241$	0.0108362	+	0.0130987i	0.000698021	+	0.000843763i	−0.770164	+	0.637846i	$0.779826\pi$
$242$	5.29235	+	1.00957i	0.340205	+	0.0648976i
$243$	−3.12594	+	4.30249i	−0.200529	+	0.276005i
$244$	−31.8582	−	17.5142i	−2.03951	−	1.12123i
$245$	0.931749	+	6.56178i	0.0595273	+	0.419217i
$246$	−0.252823	−	0.0319389i	−0.0161194	−	0.00203635i
$247$	32.6343	+	15.3566i	2.07647	+	0.977114i
$248$	−3.47014	−	0.218323i	−0.220354	−	0.0138635i
$249$	3.44974			0.218618
$250$	−21.6379	−	14.2430i	−1.36850	−	0.900809i
$251$	−15.1681			−0.957405			−0.478702	−	0.877977i	$-0.658893\pi$
$251$	−15.1681			−0.957405			−0.478702	+	0.877977i	$0.658893\pi$
$252$	31.4091	+	1.97609i	1.97859	+	0.124482i
$253$	1.71169	+	0.805462i	0.107613	+	0.0506390i
$254$	−9.24828	−	1.16833i	−0.580289	−	0.0733075i
$255$	1.20348	−	2.27123i	0.0753649	−	0.142230i
$256$	−17.2953	−	9.50816i	−1.08095	−	0.594260i
$257$	2.86409	−	3.94208i	0.178657	−	0.245900i	−0.710291	−	0.703908i	$-0.751437\pi$
$257$	2.86409	−	3.94208i	0.178657	−	0.245900i	0.888948	+	0.458008i	$0.151437\pi$
$258$	0.949281	+	0.181085i	0.0590997	+	0.0112739i
$259$	3.26768	+	3.94994i	0.203044	+	0.245437i
$260$	−35.4868	+	14.6859i	−2.20080	+	0.910779i
$261$	−1.09615	+	17.4228i	−0.0678501	+	1.07845i
$262$	8.07952	+	5.12742i	0.499154	+	0.316773i
$263$	−18.0192	+	14.9067i	−1.11111	+	0.919189i	−0.997235	−	0.0743063i	$-0.976326\pi$
$263$	−18.0192	+	14.9067i	−1.11111	+	0.919189i	−0.113873	+	0.993495i	$0.536326\pi$
$264$	1.19381	−	1.44306i	0.0734738	−	0.0888145i
$265$	0.809138	+	2.36576i	0.0497050	+	0.145327i
$266$	−50.1092	−	12.8659i	−3.07239	−	0.788856i
$267$	−0.361449	−	2.86116i	−0.0221203	−	0.175100i
$268$	11.5668	+	15.9204i	0.706558	+	0.972493i
$269$	7.46089	+	15.8552i	0.454899	+	0.966709i	0.992355	+	0.123417i	$0.0393853\pi$
$269$	7.46089	+	15.8552i	0.454899	+	0.966709i	−0.537456	+	0.843292i	$0.680615\pi$
$270$	0.0952926	+	6.19150i	0.00579932	+	0.376802i
$271$	−5.98233	+	3.28881i	−0.363401	+	0.199781i	−0.652984	−	0.757372i	$-0.726483\pi$
$271$	−5.98233	+	3.28881i	−0.363401	+	0.199781i	0.289584	+	0.957153i	$0.406483\pi$
$272$	−0.438111	+	3.46801i	−0.0265644	+	0.210279i
$273$	−1.18819	+	3.00103i	−0.0719127	+	0.181631i
$274$	−21.9605	−	15.9552i	−1.32668	−	0.963890i
$275$	5.85716	−	13.5115i	0.353200	−	0.814774i
$276$	−0.351022	+	0.255032i	−0.0211290	+	0.0153511i
$277$	−3.69648	−	14.3969i	−0.222100	−	0.865023i	−0.977703	−	0.209993i	$-0.932656\pi$
$277$	−3.69648	−	14.3969i	−0.222100	−	0.865023i	0.755603	−	0.655030i	$-0.227344\pi$
$278$	−3.14661	+	3.35080i	−0.188721	+	0.200968i
$279$	2.36592	+	2.22174i	0.141644	+	0.133012i
$280$	18.7099	−	12.2816i	1.11813	−	0.733966i
$281$	22.1231	−	2.79480i	1.31976	−	0.166724i	0.566288	−	0.824208i	$-0.308379\pi$
$281$	22.1231	−	2.79480i	1.31976	−	0.166724i	0.753469	+	0.657484i	$0.228379\pi$
$282$	2.62454	+	0.852764i	0.156289	+	0.0507813i
$283$	−1.89252	+	3.44248i	−0.112499	+	0.204634i	−0.926562	−	0.376142i	$-0.877251\pi$
$283$	−1.89252	+	3.44248i	−0.112499	+	0.204634i	0.814064	+	0.580776i	$0.197251\pi$
$284$	−1.71611	−	27.2767i	−0.101832	−	1.61858i
$285$	0.546347	−	3.12455i	0.0323628	−	0.185083i
$286$	−18.6444	−	29.3789i	−1.10247	−	1.73721i
$287$	0.430523	−	1.67678i	0.0254130	−	0.0989770i
$288$	5.37015	+	13.5635i	0.316439	+	0.799234i
$289$	−15.3579	+	3.94323i	−0.903405	+	0.231955i
$290$	16.7691	+	25.5462i	0.984713	+	1.50012i
$291$	−1.15844	+	0.458658i	−0.0679088	+	0.0268870i
$292$	−3.72264	+	1.75174i	−0.217851	+	0.102513i
$293$	8.20157	−	2.66485i	0.479141	−	0.155682i	−0.0594818	−	0.998229i	$-0.518945\pi$
$293$	8.20157	−	2.66485i	0.479141	−	0.155682i	0.538623	+	0.842547i	$0.318945\pi$
$294$	0.258065	−	1.35283i	0.0150507	−	0.0788984i
$295$	7.75444	−	8.51657i	0.451481	−	0.495854i
$296$	2.19257	−	4.65945i	0.127441	−	0.270825i
$297$	−3.45780	+	0.659611i	−0.200642	+	0.0382745i
$298$	20.5382	+	16.9907i	1.18975	+	0.984244i
$299$	1.01202	+	3.11467i	0.0585264	+	0.180126i
$300$	2.06848	+	2.67017i	0.119423	+	0.154162i
$301$	−2.02872	+	6.24377i	−0.116934	+	0.359885i
$302$	−11.3510	+	7.20359i	−0.653179	+	0.414520i
$303$	−1.21648	−	2.21276i	−0.0698847	−	0.127120i
$304$	0.808304	+	4.23728i	0.0463594	+	0.243025i
$305$	20.5728	+	12.6160i	1.17800	+	0.722392i
$306$	28.6552	−	26.9090i	1.63811	−	1.53829i
$307$		−	25.6000i		−	1.46107i	−0.682877	−	0.730533i	$-0.739271\pi$
$307$		−	25.6000i		−	1.46107i	0.682877	−	0.730533i	$-0.260729\pi$
$308$	21.4380	+	22.8291i	1.22154	+	1.30081i
$309$	−1.48515	+	2.34023i	−0.0844874	+	0.133131i
$310$	5.64672	+	0.625223i	0.320712	+	0.0355103i
$311$	−6.61122	−	2.61757i	−0.374888	−	0.148429i	0.173122	−	0.984900i	$-0.444614\pi$
$311$	−6.61122	−	2.61757i	−0.374888	−	0.148429i	−0.548010	+	0.836472i	$0.684614\pi$
$312$	3.23588	−	0.203584i	0.183196	−	0.0115257i
$313$	24.4105	−	1.53578i	1.37976	−	0.0868073i	0.644507	−	0.764598i	$-0.277063\pi$
$313$	24.4105	−	1.53578i	1.37976	−	0.0868073i	0.735255	+	0.677791i	$0.237063\pi$
$314$	16.2746	+	6.44358i	0.918431	+	0.363633i
$315$	−20.7642	−	2.29908i	−1.16993	−	0.129538i
$316$	12.6196	−	19.8853i	0.709907	−	1.11863i
$317$	−4.41757	−	4.70423i	−0.248115	−	0.264216i	0.592840	−	0.805320i	$-0.298007\pi$
$317$	−4.41757	−	4.70423i	−0.248115	−	0.264216i	−0.840956	+	0.541104i	$0.818007\pi$
$318$		−	0.519564i		−	0.0291357i
$319$	−12.6635	+	11.8918i	−0.709018	+	0.665812i
$320$	24.0932	+	14.7749i	1.34685	+	0.825942i
$321$	0.411426	+	2.15677i	0.0229636	+	0.120379i
$322$	−2.26309	−	4.11654i	−0.126117	−	0.229406i
$323$	−34.2339	+	21.7255i	−1.90483	+	1.20884i
$324$	−8.99325	+	27.6784i	−0.499625	+	1.53769i
$325$	23.9925	−	8.62058i	1.33086	−	0.478184i
$326$	12.5075	+	38.4940i	0.692724	+	2.13199i
$327$	2.22828	+	1.84339i	0.123224	+	0.101940i
$328$	−1.70819	+	0.325854i	−0.0943189	+	0.0179923i
$329$	−7.98206	+	16.9627i	−0.440065	+	0.935186i
$330$	−2.06024	+	2.26273i	−0.113413	+	0.124559i
$331$	5.22674	−	27.3996i	0.287288	−	1.50602i	−0.487123	−	0.873333i	$-0.661954\pi$
$331$	5.22674	−	27.3996i	0.287288	−	1.50602i	0.774411	−	0.632683i	$-0.218046\pi$
$332$	55.1093	−	17.9061i	3.02452	−	0.982725i
$333$	−4.34931	+	2.04663i	−0.238341	+	0.112155i
$334$	−36.6710	+	14.5191i	−2.00655	+	0.794449i
$335$	−7.16842	−	10.9205i	−0.391653	−	0.596648i
$336$	−0.373911	+	0.0960040i	−0.0203985	+	0.00523745i
$337$	−6.30424	−	15.9227i	−0.343414	−	0.867364i	−0.994145	−	0.108056i	$-0.965538\pi$
$337$	−6.30424	−	15.9227i	−0.343414	−	0.867364i	0.650731	−	0.759308i	$-0.274462\pi$
$338$	7.48973	−	29.1706i	0.407388	−	1.58667i
$339$	−1.21211	−	1.90998i	−0.0658327	−	0.103736i
$340$	7.43654	−	42.5295i	0.403303	−	2.30649i
$341$	0.202792	+	3.22329i	0.0109818	+	0.174551i
$342$	23.3695	−	42.5090i	1.26368	−	2.29862i
$343$	−12.1165	−	3.93690i	−0.654231	−	0.212573i
$344$	6.54276	−	0.826543i	0.352762	−	0.0445642i
$345$	0.240780	−	0.158053i	0.0129632	−	0.00850930i
$346$	21.2678	+	19.9718i	1.14337	+	1.07369i
$347$	7.68420	−	8.18285i	0.412510	−	0.439278i	−0.488838	−	0.872375i	$-0.662579\pi$
$347$	7.68420	−	8.18285i	0.412510	−	0.439278i	0.901348	+	0.433096i	$0.142579\pi$
$348$	−0.990872	−	3.85919i	−0.0531163	−	0.206874i
$349$	24.8296	−	18.0398i	1.32910	−	0.965646i	0.329328	−	0.944216i	$-0.393178\pi$
$349$	24.8296	−	18.0398i	1.32910	−	0.965646i	0.999770	−	0.0214305i	$-0.00682207\pi$
$350$	−31.4883	+	18.5951i	−1.68312	+	0.993949i
$351$	−4.93019	−	3.58200i	−0.263154	−	0.191193i
$352$	−5.34384	+	13.4970i	−0.284828	+	0.719392i
$353$	−0.432941	+	3.42708i	−0.0230431	+	0.182405i	−0.999435	−	0.0336001i	$-0.989303\pi$
$353$	−0.432941	+	3.42708i	−0.0230431	+	0.182405i	0.976392	+	0.216005i	$0.0693027\pi$
$354$	−2.09739	+	1.15305i	−0.111475	+	0.0612838i
$355$	0.279196	+	18.1404i	0.0148182	+	0.962790i
$356$	−20.6252	−	43.8308i	−1.09313	−	2.32303i
$357$	−2.13278	−	2.93553i	−0.112879	−	0.155364i
$358$	4.43280	+	35.0893i	0.234281	+	1.85453i
$359$	13.9247	+	3.57526i	0.734919	+	0.188695i	0.597558	−	0.801826i	$-0.296138\pi$
$359$	13.9247	+	3.57526i	0.734919	+	0.188695i	0.137361	+	0.990521i	$0.456138\pi$
$360$	6.79125	+	19.8562i	0.357930	+	1.04652i
$361$	−19.7826	+	23.9131i	−1.04119	+	1.25858i
$362$	−35.3566	+	29.2495i	−1.85830	+	1.53732i
$363$	0.393731	+	0.249869i	0.0206655	+	0.0131147i
$364$	−3.40423	+	54.1087i	−0.178430	+	2.83607i
$365$	2.52351	−	1.04433i	0.132087	−	0.0546628i
$366$	−3.19659	−	3.86402i	−0.167089	−	0.201975i
$367$	0.598228	+	0.114118i	0.0312272	+	0.00595691i	0.202971	−	0.979185i	$-0.434940\pi$
$367$	0.598228	+	0.114118i	0.0312272	+	0.00595691i	−0.171744	+	0.985142i	$0.554940\pi$
$368$	−0.230231	+	0.316885i	−0.0120016	+	0.0165188i
$369$	1.42246	+	0.782001i	0.0740501	+	0.0407094i
$370$	−3.93957	+	7.43482i	−0.204808	+	0.386518i
$371$	3.50175	+	0.442374i	0.181802	+	0.0229669i
$372$	−0.670253	−	0.315397i	−0.0347510	−	0.0163526i
$373$	−35.7636	−	2.25005i	−1.85177	−	0.116503i	−0.902445	−	0.430805i	$-0.858230\pi$
$373$	−35.7636	−	2.25005i	−1.85177	−	0.116503i	−0.949323	+	0.314301i	$0.898230\pi$
$374$	39.1166			2.02267
$375$	−1.28748	−	1.83562i	−0.0664852	−	0.0947912i
$376$	18.8317			0.971170
$377$	−30.0144	−	1.88835i	−1.54582	−	0.0972549i
$378$	7.90940	+	3.72188i	0.406816	+	0.191433i
$379$	2.33647	+	0.295164i	0.120016	+	0.0151616i	0.185112	−	0.982717i	$-0.440735\pi$
$379$	2.33647	+	0.295164i	0.120016	+	0.0151616i	−0.0650956	+	0.997879i	$0.520735\pi$
$380$	−7.49037	−	52.7504i	−0.384248	−	2.70604i
$381$	−0.707022	−	0.388689i	−0.0362219	−	0.0199131i
$382$	0.344946	−	0.474777i	0.0176490	−	0.0242917i
$383$	21.5819	+	4.11696i	1.10278	+	0.210367i	0.706466	−	0.707747i	$-0.250288\pi$
$383$	21.5819	+	4.11696i	1.10278	+	0.210367i	0.396316	+	0.918114i	$0.370288\pi$
$384$	−2.48352	−	3.00207i	−0.126737	−	0.153199i
$385$	−13.4962	−	15.8122i	−0.687828	−	0.805862i
$386$	0.646313	−	10.2728i	0.0328964	−	0.522874i
$387$	−5.19751	−	3.29844i	−0.264205	−	0.167669i
$388$	−16.1253	+	13.3400i	−0.818637	+	0.677235i
$389$	11.8383	−	14.3100i	0.600224	−	0.725546i	−0.379658	−	0.925127i	$-0.623958\pi$
$389$	11.8383	−	14.3100i	0.600224	−	0.725546i	0.979881	+	0.199581i	$0.0639582\pi$
$390$	−5.29708	+	0.0815267i	−0.268228	+	0.00412827i
$391$	−3.56598	−	0.915587i	−0.180339	−	0.0463032i
$392$	−1.17791	−	9.32412i	−0.0594935	−	0.470939i
$393$	0.486823	+	0.670054i	0.0245570	+	0.0337998i
$394$	−5.35333	−	11.3764i	−0.269697	−	0.573135i
$395$	−8.99366	+	12.7880i	−0.452520	+	0.643436i
$396$	−25.7324	+	14.1465i	−1.29310	+	0.710889i
$397$	−4.16657	+	32.9818i	−0.209114	+	1.65531i	0.442506	+	0.896765i	$0.354089\pi$
$397$	−4.16657	+	32.9818i	−0.209114	+	1.65531i	−0.651621	+	0.758545i	$0.725911\pi$
$398$	12.5941	−	31.8090i	0.631284	−	1.59444i
$399$	−3.62257	−	2.63195i	−0.181355	−	0.131762i
$400$	2.52081	+	1.71549i	0.126041	+	0.0857745i
$401$	14.0623	−	10.2169i	0.702237	−	0.510205i	−0.178423	−	0.983954i	$-0.557100\pi$
$401$	14.0623	−	10.2169i	0.702237	−	0.510205i	0.880660	+	0.473749i	$0.157100\pi$
$402$	0.675069	+	2.62922i	0.0336694	+	0.131134i
$403$	−3.82741	+	4.07578i	−0.190657	+	0.203029i
$404$	−30.9186	−	29.0345i	−1.53826	−	1.44452i
$405$	6.83449	−	18.0696i	0.339608	−	0.897883i
$406$	42.7978	−	5.40662i	2.12402	−	0.268326i
$407$	−4.54912	−	1.47810i	−0.225492	−	0.0732667i
$408$	−1.75595	+	3.19406i	−0.0869324	+	0.158129i
$409$	−0.0966374	−	1.53601i	−0.00477841	−	0.0759507i	0.994915	−	0.100720i	$-0.0321147\pi$
$409$	−0.0966374	−	1.53601i	−0.00477841	−	0.0759507i	−0.999693	+	0.0247697i	$0.992115\pi$
$410$	2.81319	−	0.399463i	0.138934	−	0.0197281i
$411$	−1.25889	−	1.98369i	−0.0620963	−	0.0978480i
$412$	−11.5781	+	45.0938i	−0.570413	+	2.22161i
$413$	−5.98551	−	15.1177i	−0.294528	−	0.743892i
$414$	4.26636	−	1.09542i	0.209680	−	0.0538367i
$415$	−37.1050	+	10.1381i	−1.82141	+	0.497659i
$416$	−23.3659	+	9.25120i	−1.14561	+	0.453577i
$417$	−0.359984	+	0.169396i	−0.0176285	+	0.00829534i
$418$	45.9090	−	14.9167i	2.24548	−	0.729601i
$419$	−4.35734	+	22.8420i	−0.212870	+	1.11590i	0.702007	+	0.712171i	$0.252288\pi$
$419$	−4.35734	+	22.8420i	−0.212870	+	1.11590i	−0.914877	+	0.403734i	$0.867712\pi$
$420$	4.66932	−	0.965419i	0.227839	−	0.0471076i
$421$	12.1682	−	25.8586i	0.593040	−	1.26027i	−0.352818	−	0.935692i	$-0.614777\pi$
$421$	12.1682	−	25.8586i	0.593040	−	1.26027i	0.945858	−	0.324581i	$-0.105223\pi$
$422$	45.4218	−	8.66467i	2.21110	−	0.421790i
$423$	−13.5442	−	11.2048i	−0.658543	−	0.544795i
$424$	−1.09563	−	3.37200i	−0.0532085	−	0.163759i
$425$	−6.26981	+	27.9659i	−0.304130	+	1.35654i
$426$	1.16500	−	3.58550i	0.0564445	−	0.173718i
$427$	28.7643	−	18.2544i	1.39200	−	0.883393i
$428$	17.7674	+	32.3187i	0.858818	+	1.56218i
$429$	−0.564325	−	2.95829i	−0.0272458	−	0.142828i
$430$	−10.7425	+	0.842015i	−0.518051	+	0.0406056i
$431$	−6.54308	+	6.14436i	−0.315169	+	0.295963i	−0.825945	−	0.563750i	$-0.809358\pi$
$431$	−6.54308	+	6.14436i	−0.315169	+	0.295963i	0.510776	+	0.859714i	$0.329358\pi$
$432$		−	0.728863i		−	0.0350674i
$433$	−8.22836	−	8.76231i	−0.395430	−	0.421090i	0.500186	−	0.865918i	$-0.333265\pi$
$433$	−8.22836	−	8.76231i	−0.395430	−	0.421090i	−0.895616	+	0.444828i	$0.853265\pi$
$434$	4.29732	−	6.77149i	0.206278	−	0.325042i
$435$	0.535525	+	2.59010i	0.0256764	+	0.124186i
$436$	45.1649	+	17.8820i	2.16300	+	0.856394i
$437$	−4.53434	+	0.285276i	−0.216907	+	0.0136466i
$438$	−0.566398	+	0.0356347i	−0.0270635	+	0.00170269i
$439$	11.6491	+	4.61221i	0.555982	+	0.220129i	0.629276	−	0.777182i	$-0.283351\pi$
$439$	11.6491	+	4.61221i	0.555982	+	0.220129i	−0.0732948	+	0.997310i	$0.523351\pi$
$440$	−8.59958	+	19.0298i	−0.409969	+	0.907210i
$441$	−4.70063	+	7.40701i	−0.223839	+	0.352715i
$442$	46.3563	+	49.3645i	2.20494	+	2.34803i
$443$		−	1.22733i		−	0.0583120i	−0.999575	−	0.0291560i	$-0.990718\pi$
$443$		−	1.22733i		−	0.0583120i	0.999575	−	0.0291560i	$-0.00928196\pi$
$444$	0.799735	−	0.751001i	0.0379537	−	0.0356409i
$445$	12.2961	+	29.7121i	0.582890	+	1.40849i
$446$	3.09367	+	16.2176i	0.146489	+	0.767924i
$447$	1.11144	+	2.02170i	0.0525693	+	0.0956231i
$448$	33.6865	−	21.3781i	1.59154	−	1.01002i
$449$	3.15571	−	9.71228i	0.148927	−	0.458351i	−0.848568	−	0.529087i	$-0.822535\pi$
$449$	3.15571	−	9.71228i	0.148927	−	0.458351i	0.997495	+	0.0707356i	$0.0225347\pi$
$450$	−9.54540	−	32.9337i	−0.449975	−	1.55251i
$451$	0.499151	+	1.53623i	0.0235041	+	0.0723381i
$452$	−29.2772	−	24.2202i	−1.37708	−	1.13922i
$453$	−1.14299	+	0.218036i	−0.0537022	+	0.0102442i
$454$	7.40695	−	15.7406i	0.347626	−	0.738742i
$455$	3.96063	−	35.7706i	0.185677	−	1.67695i
$456$	−0.842837	+	4.41830i	−0.0394694	+	0.206906i
$457$	−16.6376	+	5.40587i	−0.778273	+	0.252876i	−0.671102	−	0.741365i	$-0.734179\pi$
$457$	−16.6376	+	5.40587i	−0.778273	+	0.252876i	−0.107170	+	0.994241i	$0.534179\pi$
$458$	−13.7084	+	6.45069i	−0.640552	+	0.301421i
$459$	6.36973	−	2.52196i	0.297314	−	0.117715i
$460$	3.02606	−	3.77468i	0.141091	−	0.175995i
$461$	12.1680	−	3.12420i	0.566719	−	0.145509i	0.0455498	−	0.998962i	$-0.485496\pi$
$461$	12.1680	−	3.12420i	0.566719	−	0.145509i	0.521169	+	0.853453i	$0.325496\pi$
$462$	1.59026	+	4.01655i	0.0739857	+	0.186867i
$463$	5.50488	−	21.4401i	0.255833	−	0.996406i	−0.702714	−	0.711473i	$-0.748029\pi$
$463$	5.50488	−	21.4401i	0.255833	−	0.996406i	0.958547	−	0.284933i	$-0.0919714\pi$
$464$	−1.92731	−	3.03696i	−0.0894732	−	0.140987i
$465$	0.434494	+	0.230230i	0.0201492	+	0.0106767i
$466$	1.66483	+	26.4617i	0.0771216	+	1.22581i
$467$	−16.0640	+	29.2203i	−0.743354	+	1.35216i	0.185846	+	0.982579i	$0.440498\pi$
$467$	−16.0640	+	29.2203i	−0.743354	+	1.35216i	−0.929200	+	0.369577i	$0.879502\pi$
$468$	−48.3476	−	15.7091i	−2.23487	−	0.726153i
$469$	−18.2952	+	2.31122i	−0.844792	+	0.106722i
$470$	−30.7353	−	1.45925i	−1.41771	−	0.0673100i
$471$	1.10438	+	1.03708i	0.0508873	+	0.0477863i
$472$	−11.1807	+	11.9062i	−0.514633	+	0.548028i
$473$	−1.52338	−	5.93319i	−0.0700453	−	0.272808i
$474$	2.62828	−	1.90956i	0.120721	−	0.0877090i
$475$	3.30599	+	35.2129i	0.151689	+	1.61568i
$476$	−49.3081	−	35.8245i	−2.26004	−	1.64201i
$477$	−1.21832	+	3.07713i	−0.0557831	+	0.140892i
$478$	6.75137	−	53.4426i	0.308800	−	2.44441i
$479$	−30.7785	+	16.9206i	−1.40630	+	0.773122i	−0.990653	−	0.136403i	$-0.956446\pi$
$479$	−30.7785	+	16.9206i	−1.40630	+	0.773122i	−0.415650	+	0.909525i	$0.636446\pi$
$480$	1.32646	+	1.76785i	0.0605442	+	0.0806907i
$481$	−3.52574	−	7.49258i	−0.160760	−	0.341632i
$482$	0.0231523	+	0.0318664i	0.00105456	+	0.00145148i
$483$	−0.0509590	−	0.403382i	−0.00231871	−	0.0183545i
$484$	7.58678	+	1.94796i	0.344854	+	0.0885434i
$485$	11.1121	−	8.33769i	0.504575	−	0.378595i
$486$	−7.85448	+	9.49443i	−0.356286	+	0.430676i
$487$	2.85874	−	2.36495i	0.129542	−	0.107166i	−0.570397	−	0.821369i	$-0.693211\pi$
$487$	2.85874	−	2.36495i	0.129542	−	0.107166i	0.699939	+	0.714203i	$0.253211\pi$
$488$	−28.8944	−	18.3369i	−1.30799	−	0.830073i
$489$	−0.219968	+	3.49628i	−0.00994728	+	0.158107i
$490$	1.19996	+	15.3092i	0.0542087	+	0.691601i
$491$	4.64041	+	5.60929i	0.209419	+	0.253144i	0.864756	−	0.502193i	$-0.167473\pi$
$491$	4.64041	+	5.60929i	0.209419	+	0.253144i	−0.655337	+	0.755337i	$0.727473\pi$
$492$	−0.363918	−	0.0694211i	−0.0164067	−	0.00312974i
$493$	19.8721	−	27.3516i	0.894993	−	1.23185i
$494$	73.2305	+	40.2588i	3.29480	+	1.81133i
$495$	17.5077	−	8.57002i	0.786912	−	0.385194i
$496$	−0.663442	−	0.0838123i	−0.0297894	−	0.00376328i
$497$	23.1736	+	10.9047i	1.03948	+	0.489141i
$498$	7.97728	+	0.501888i	0.357471	+	0.0224901i
$499$	−38.7682			−1.73550			−0.867752	−	0.496998i	$-0.834436\pi$
$499$	−38.7682			−1.73550			−0.867752	+	0.496998i	$0.834436\pi$
$500$	−30.0954	−	22.6412i	−1.34591	−	1.01255i
$501$	−3.41368			−0.152512
$502$	−35.0753	−	2.20675i	−1.56549	−	0.0984921i
$503$	9.67394	+	4.55221i	0.431339	+	0.202973i	0.629177	−	0.777262i	$-0.283392\pi$
$503$	9.67394	+	4.55221i	0.431339	+	0.202973i	−0.197838	+	0.980235i	$0.563392\pi$
$504$	29.3908	+	3.71293i	1.30917	+	0.165387i
$505$	19.5871	+	20.2252i	0.871615	+	0.900010i
$506$	3.84099	+	2.11160i	0.170753	+	0.0938722i
$507$	1.53216	−	2.10884i	0.0680457	−	0.0936569i
$508$	−13.3122	−	2.53943i	−0.590631	−	0.112669i
$509$	−20.3553	−	24.6054i	−0.902234	−	1.09061i	−0.995480	−	0.0949706i	$-0.969724\pi$
$509$	−20.3553	−	24.6054i	−0.902234	−	1.09061i	0.0932460	−	0.995643i	$-0.470276\pi$
$510$	3.11340	−	5.07698i	0.137864	−	0.224812i
$511$	0.242079	−	3.84774i	0.0107090	−	0.170214i
$512$	−5.80310	−	3.68276i	−0.256463	−	0.162757i
$513$	6.51408	−	5.38892i	0.287604	−	0.237927i
$514$	7.19653	−	8.69911i	0.317425	−	0.383701i
$515$	9.09668	−	29.5358i	0.400848	−	1.30150i
$516$	1.36083	+	0.349402i	0.0599072	+	0.0153816i
$517$	−2.19234	−	17.3541i	−0.0964189	−	0.763234i
$518$	6.98162	+	9.60937i	0.306755	+	0.422212i
$519$	1.07517	+	2.28485i	0.0471947	+	0.100294i
$520$	−34.2065	+	11.6993i	−1.50005	+	0.513049i
$521$	12.2036	−	6.70899i	0.534650	−	0.293926i	−0.191465	−	0.981499i	$-0.561324\pi$
$521$	12.2036	−	6.70899i	0.534650	−	0.293926i	0.726115	+	0.687573i	$0.241324\pi$
$522$	−5.06956	+	40.1297i	−0.221888	+	1.75643i
$523$	−11.4931	+	29.0283i	−0.502558	+	1.26932i	0.428201	+	0.903684i	$0.359148\pi$
$523$	−11.4931	+	29.0283i	−0.502558	+	1.26932i	−0.930759	+	0.365633i	$0.880852\pi$
$524$	11.2549	+	8.17718i	0.491674	+	0.357222i
$525$	−3.12647	+	0.493144i	−0.136450	+	0.0215226i
$526$	−43.8368	+	31.8493i	−1.91137	+	1.38870i
$527$	−1.56313	−	6.08801i	−0.0680912	−	0.265198i
$528$	0.246573	−	0.262574i	0.0107307	−	0.0114270i
$529$	16.4655	+	15.4622i	0.715893	+	0.672269i
$530$	1.52689	+	5.58837i	0.0663240	+	0.242743i
$531$	15.1256	−	1.91081i	0.656395	−	0.0829219i
$532$	−71.5316	−	23.2420i	−3.10129	−	1.00767i
$533$	−1.34716	+	2.45047i	−0.0583519	+	0.106142i
$534$	−0.419567	−	6.66883i	−0.0181565	−	0.288589i
$535$	−10.7636	−	21.9889i	−0.465349	−	0.950662i
$536$	9.92561	+	15.6403i	0.428721	+	0.675556i
$537$	−0.761287	+	2.96502i	−0.0328520	+	0.127950i
$538$	14.9461	+	37.7495i	0.644372	+	1.62750i
$539$	−8.45542	+	2.17098i	−0.364201	+	0.0935109i
$540$	−0.426933	+	8.99226i	−0.0183723	+	0.386965i
$541$	20.8098	−	8.23918i	0.894683	−	0.354230i	0.124625	−	0.992204i	$-0.460227\pi$
$541$	20.8098	−	8.23918i	0.894683	−	0.354230i	0.770058	+	0.637974i	$0.220227\pi$
$542$	−14.3122	+	6.73481i	−0.614762	+	0.289285i
$543$	−3.77724	+	1.22730i	−0.162097	+	0.0526685i
$544$	5.29378	−	27.7510i	0.226969	−	1.18981i
$545$	−29.3845	−	13.2789i	−1.25869	−	0.568803i
$546$	−3.18422	+	6.76681i	−0.136272	+	0.289593i
$547$	−24.6313	+	4.69868i	−1.05316	+	0.200901i	−0.684762	−	0.728767i	$-0.740094\pi$
$547$	−24.6313	+	4.69868i	−1.05316	+	0.200901i	−0.368398	+	0.929668i	$0.620094\pi$
$548$	−30.4071	−	25.1549i	−1.29893	−	1.07457i
$549$	9.87119	+	30.3804i	0.421292	+	1.29660i
$550$	15.5100	−	30.3923i	0.661350	−	1.29593i
$551$	12.8925	−	39.6791i	0.549239	−	1.69038i
$552$	−0.344845	+	0.218845i	−0.0146776	+	0.00931468i
$553$	10.6322	+	19.3399i	0.452128	+	0.822418i
$554$	−6.45333	−	33.8295i	−0.274176	−	1.43728i
$555$	−0.553921	+	0.472789i	−0.0235127	+	0.0200688i
$556$	−4.87146	+	4.57461i	−0.206596	+	0.194007i
$557$			39.8943i			1.69038i	0.534469	+	0.845188i	$0.320512\pi$
$557$			39.8943i			1.69038i	−0.534469	+	0.845188i	$0.679488\pi$
$558$	5.14779	+	5.48184i	0.217923	+	0.232065i
$559$	5.68225	−	8.95379i	0.240334	−	0.378705i
$560$	3.73961	−	2.13146i	0.158027	−	0.0900705i
$561$	3.14788	+	1.24633i	0.132903	+	0.0526202i
$562$	51.5649	−	3.24419i	2.17513	−	0.136848i
$563$	−0.830727	+	0.0522649i	−0.0350110	+	0.00220270i	−0.0802863	−	0.996772i	$-0.525583\pi$
$563$	−0.830727	+	0.0522649i	−0.0350110	+	0.00220270i	0.0452754	+	0.998975i	$0.485583\pi$
$564$	3.73023	+	1.47690i	0.157071	+	0.0621888i
$565$	18.6503	+	16.9813i	0.784625	+	0.714411i
$566$	−4.87715	+	7.68516i	−0.205002	+	0.323031i
$567$	−18.6688	−	19.8802i	−0.784015	−	0.834892i
$568$		−	25.7268i		−	1.07947i
$569$	5.52941	−	5.19246i	0.231805	−	0.217679i	−0.559937	−	0.828535i	$-0.689175\pi$
$569$	5.52941	−	5.19246i	0.231805	−	0.217679i	0.791742	+	0.610856i	$0.209175\pi$
$570$	1.71797	−	7.14583i	0.0719578	−	0.299306i
$571$	−5.37204	−	28.1612i	−0.224813	−	1.17851i	−0.898324	−	0.439333i	$-0.855215\pi$
$571$	−5.37204	−	28.1612i	−0.224813	−	1.17851i	0.673512	−	0.739177i	$-0.264785\pi$
$572$	−24.3703	−	44.3294i	−1.01897	−	1.85350i
$573$	0.0428866	−	0.0272166i	0.00179161	−	0.00113699i
$574$	1.23950	−	3.81480i	0.0517359	−	0.159227i
$575$	−2.12532	+	2.40761i	−0.0886318	+	0.100404i
$576$	11.5604	+	35.5791i	0.481681	+	1.48246i
$577$	2.62087	+	2.16818i	0.109108	+	0.0902624i	0.690379	−	0.723448i	$-0.257444\pi$
$577$	2.62087	+	2.16818i	0.109108	+	0.0902624i	−0.581270	+	0.813711i	$0.697444\pi$
$578$	−36.0877	+	6.88410i	−1.50105	+	0.286341i
$579$	0.379325	−	0.806106i	0.0157642	−	0.0335006i
$580$	21.9991	+	38.5970i	0.913462	+	1.60266i
$581$	−10.1747	+	53.3379i	−0.422119	+	2.21283i
$582$	−2.74554	+	0.892079i	−0.113806	+	0.0369779i
$583$	−2.97989	+	1.40223i	−0.123414	+	0.0580744i
$584$	−3.60081	+	1.42566i	−0.149003	+	0.0589944i
$585$	31.5632	+	11.9382i	1.30498	+	0.493585i
$586$	19.3533	−	4.96908i	0.799476	−	0.205271i
$587$	−5.71508	−	14.4346i	−0.235887	−	0.595782i	0.762821	−	0.646610i	$-0.223814\pi$
$587$	−5.71508	−	14.4346i	−0.235887	−	0.595782i	−0.998707	+	0.0508284i	$0.983814\pi$
$588$	0.497935	−	1.93933i	0.0205345	−	0.0799765i
$589$	−4.15617	−	6.54907i	−0.171252	−	0.269850i
$590$	19.1707	−	18.5658i	0.789244	−	0.764343i
$591$	−0.0683300	−	1.08607i	−0.00281072	−	0.0446752i
$592$	0.477123	−	0.867884i	0.0196096	−	0.0356698i
$593$	−25.5633	−	8.30604i	−1.04976	−	0.341088i	−0.267186	−	0.963645i	$-0.586094\pi$
$593$	−25.5633	−	8.30604i	−1.04976	−	0.341088i	−0.782575	+	0.622557i	$0.786094\pi$
$594$	−8.09190	+	1.02224i	−0.332015	+	0.0419432i
$595$	31.5669	+	25.3063i	1.29412	+	1.03746i
$596$	28.2489	+	26.5275i	1.15712	+	1.08661i
$597$	2.02699	−	2.15853i	0.0829593	−	0.0883427i
$598$	1.88708	+	7.34969i	0.0771684	+	0.300551i
$599$	−26.2953	+	19.1047i	−1.07440	+	0.780596i	−0.976698	−	0.214620i	$-0.931149\pi$
$599$	−26.2953	+	19.1047i	−1.07440	+	0.780596i	−0.0977004	+	0.995216i	$0.531149\pi$
$600$	1.78543	+	2.63078i	0.0728899	+	0.107401i
$601$	−21.9302	−	15.9332i	−0.894551	−	0.649929i	0.0425098	−	0.999096i	$-0.486465\pi$
$601$	−21.9302	−	15.9332i	−0.894551	−	0.649929i	−0.937061	+	0.349167i	$0.886465\pi$
$602$	−5.59967	+	14.1431i	−0.228225	+	0.576432i
$603$	2.16713	−	17.1546i	0.0882523	−	0.698589i
$604$	−17.1274	+	9.41587i	−0.696904	+	0.383126i
$605$	−4.96923	−	1.53047i	−0.202028	−	0.0622224i
$606$	−2.49109	−	5.29384i	−0.101194	−	0.215047i
$607$	−4.78199	−	6.58184i	−0.194095	−	0.267149i	0.700866	−	0.713293i	$-0.252797\pi$
$607$	−4.78199	−	6.58184i	−0.194095	−	0.267149i	−0.894961	+	0.446144i	$0.852797\pi$
$608$	−4.36954	−	34.5885i	−0.177208	−	1.40275i
$609$	3.61638	+	0.928530i	0.146543	+	0.0376259i
$610$	45.7378	+	32.1668i	1.85187	+	1.30240i
$611$	19.3025	−	23.3328i	0.780897	−	0.943942i
$612$	44.0337	−	36.4278i	1.77996	−	1.47251i
$613$	−4.22108	−	2.67878i	−0.170488	−	0.108195i	0.447845	−	0.894111i	$-0.352192\pi$
$613$	−4.22108	−	2.67878i	−0.170488	−	0.108195i	−0.618333	+	0.785916i	$0.712192\pi$
$614$	3.72443	−	59.1982i	0.150306	−	2.38904i
$615$	0.239117	+	0.0574874i	0.00964213	+	0.00231812i
$616$	18.7908	+	22.7142i	0.757103	+	0.915180i
$617$	12.0219	+	2.29331i	0.483985	+	0.0923250i	0.423598	−	0.905850i	$-0.360767\pi$
$617$	12.0219	+	2.29331i	0.483985	+	0.0923250i	0.0603863	+	0.998175i	$0.480767\pi$
$618$	−3.77479	+	5.19555i	−0.151844	+	0.208996i
$619$	14.9067	+	8.19504i	0.599152	+	0.329386i	0.752304	−	0.658816i	$-0.228943\pi$
$619$	14.9067	+	8.19504i	0.599152	+	0.329386i	−0.153152	+	0.988203i	$0.548943\pi$
$620$	8.13605	+	1.42264i	0.326752	+	0.0571345i
$621$	0.761607	+	0.0962134i	0.0305622	+	0.00386091i
$622$	−14.9072	−	7.01479i	−0.597724	−	0.281267i
$623$	45.3037	+	2.85027i	1.81506	+	0.114194i
$624$	0.623572			0.0249629
$625$	19.2425	+	15.9601i	0.769701	+	0.638404i
$626$	56.6710			2.26503
$627$	4.16977	+	0.262339i	0.166524	+	0.0104768i
$628$	23.0255	+	10.8350i	0.918818	+	0.432363i
$629$	9.23558	+	1.16673i	0.368247	+	0.0465204i
$630$	−47.6813	−	8.33735i	−1.89967	−	0.332168i
$631$	−32.1717	−	17.6866i	−1.28074	−	0.704091i	−0.311506	−	0.950244i	$-0.600833\pi$
$631$	−32.1717	−	17.6866i	−1.28074	−	0.704091i	−0.969231	+	0.246153i	$0.920833\pi$
$632$	13.0309	−	17.9356i	0.518343	−	0.713438i
$633$	3.93135	+	0.749946i	0.156257	+	0.0298077i
$634$	−9.53093	−	11.5209i	−0.378521	−	0.457554i
$635$	8.74693	+	2.10290i	0.347111	+	0.0834509i
$636$	0.0474290	−	0.753862i	0.00188068	−	0.0298926i
$637$	−12.7601	−	8.09781i	−0.505574	−	0.320847i
$638$	−31.0135	+	25.6566i	−1.22784	+	1.01575i
$639$	−15.3074	+	18.5034i	−0.605550	+	0.731984i
$640$	35.5350	+	24.9913i	1.40464	+	0.987868i
$641$	0.889985	+	0.228509i	0.0351523	+	0.00902557i	0.266225	−	0.963911i	$-0.414224\pi$
$641$	0.889985	+	0.228509i	0.0351523	+	0.00902557i	−0.231073	+	0.972936i	$0.574224\pi$
$642$	0.637615	+	5.04724i	0.0251646	+	0.199199i
$643$	1.25853	+	1.73222i	0.0496315	+	0.0683119i	0.833111	−	0.553105i	$-0.186557\pi$
$643$	1.25853	+	1.73222i	0.0496315	+	0.0683119i	−0.783480	+	0.621417i	$0.786557\pi$
$644$	−2.90785	−	6.17950i	−0.114585	−	0.243506i
$645$	−0.891324	−	0.274518i	−0.0350959	−	0.0108091i
$646$	−82.3244	+	45.2582i	−3.23901	+	1.78066i
$647$	1.16955	−	9.25792i	0.0459796	−	0.363966i	−0.952292	−	0.305190i	$-0.901280\pi$
$647$	1.16955	−	9.25792i	0.0459796	−	0.363966i	0.998271	−	0.0587765i	$-0.0187199\pi$
$648$	−10.0848	+	25.4712i	−0.396167	+	1.00060i
$649$	12.2737	+	8.91735i	0.481784	+	0.350037i
$650$	56.7352	−	16.4439i	2.22534	−	0.644984i
$651$	0.561576	−	0.408009i	0.0220099	−	0.0159911i
$652$	14.6337	+	56.9947i	0.573102	+	2.23208i
$653$	−15.4231	+	16.4239i	−0.603552	+	0.642717i	−0.956088	−	0.293081i	$-0.905319\pi$
$653$	−15.4231	+	16.4239i	−0.603552	+	0.642717i	0.352536	+	0.935798i	$0.385319\pi$
$654$	4.88455	+	4.58690i	0.191001	+	0.179362i
$655$	−7.20536	−	5.77635i	−0.281537	−	0.225701i
$656$	−0.331814	+	0.0419179i	−0.0129552	+	0.00163662i
$657$	3.43806	+	1.11709i	0.134132	+	0.0435820i
$658$	−20.9258	+	38.0639i	−0.815773	+	1.48389i
$659$	2.07653	+	33.0054i	0.0808900	+	1.28571i	0.803855	+	0.594825i	$0.202779\pi$
$659$	2.07653	+	33.0054i	0.0808900	+	1.28571i	−0.722965	+	0.690884i	$0.757221\pi$
$660$	−3.19587	+	3.09504i	−0.124399	+	0.120474i
$661$	−8.15327	−	12.8475i	−0.317125	−	0.499709i	0.647950	−	0.761683i	$-0.275627\pi$
$661$	−8.15327	−	12.8475i	−0.317125	−	0.499709i	−0.965075	+	0.261974i	$0.915627\pi$
$662$	16.0727	−	62.5992i	0.624685	−	2.43299i
$663$	2.15764	+	5.44957i	0.0837957	+	0.211644i
$664$	52.8314	−	13.5648i	2.05026	−	0.526417i
$665$	46.6987	+	17.6629i	1.81090	+	0.684939i
$666$	−10.3552	+	4.09993i	−0.401257	+	0.158869i
$667$	3.42781	−	1.61300i	0.132725	−	0.0624558i
$668$	−54.5333	+	17.7189i	−2.10996	+	0.685567i
$669$	−0.267763	+	1.40366i	−0.0103523	+	0.0542688i
$670$	−14.9877	−	26.2957i	−0.579026	−	1.01589i
$671$	−13.5344	+	28.7620i	−0.522489	+	1.11035i
$672$	3.06472	−	0.584627i	0.118224	−	0.0225525i
$673$	10.4043	+	8.60722i	0.401058	+	0.331784i	0.815987	−	0.578070i	$-0.196194\pi$
$673$	10.4043	+	8.60722i	0.401058	+	0.331784i	−0.414930	+	0.909854i	$0.636194\pi$
$674$	−12.2616	−	37.7373i	−0.472299	−	1.45359i
$675$	0.566172	−	5.94905i	0.0217920	−	0.228979i
$676$	13.5301	−	41.6414i	0.520389	−	1.60159i
$677$	6.13109	−	3.89091i	0.235637	−	0.149540i	−0.412766	−	0.910837i	$-0.635437\pi$
$677$	6.13109	−	3.89091i	0.235637	−	0.149540i	0.648403	+	0.761297i	$0.275437\pi$
$678$	−2.52504	−	4.59304i	−0.0969737	−	0.176394i
$679$	−3.67478	−	19.2639i	−0.141025	−	0.739280i
$680$	9.50008	−	39.5153i	0.364312	−	1.51534i
$681$	1.09759	−	1.03071i	0.0420599	−	0.0394969i
$682$			7.48314i			0.286544i
$683$	0.208465	+	0.221993i	0.00797671	+	0.00849433i	0.732945	−	0.680288i	$-0.238145\pi$
$683$	0.208465	+	0.221993i	0.00797671	+	0.00849433i	−0.724968	+	0.688783i	$0.758145\pi$
$684$	37.7885	−	59.5452i	1.44488	−	2.27677i
$685$	19.3701	+	17.6367i	0.740093	+	0.673863i
$686$	−27.4459	−	10.8666i	−1.04789	−	0.414888i
$687$	−1.30870	+	0.0823367i	−0.0499302	+	0.00314134i
$688$	1.26584	−	0.0796397i	0.0482596	−	0.00303623i
$689$	−5.30099	−	2.09881i	−0.201952	−	0.0799584i
$690$	0.579782	−	0.330457i	0.0220719	−	0.0125803i
$691$	3.80347	−	5.99331i	0.144691	−	0.227996i	−0.764251	−	0.644919i	$-0.776891\pi$
$691$	3.80347	−	5.99331i	0.144691	−	0.227996i	0.908942	+	0.416922i	$0.136891\pi$
$692$	29.0355	+	30.9196i	1.10376	+	1.17539i
$693$		−	27.5171i		−	1.04529i
$694$	18.9597	−	17.8043i	0.719700	−	0.675843i
$695$	3.37413	−	2.87992i	0.127988	−	0.109242i
$696$	−0.702785	−	3.68413i	−0.0266390	−	0.139646i
$697$	−1.51445	−	2.75478i	−0.0573639	−	0.104345i
$698$	60.0413	−	38.1034i	2.27260	−	1.44223i
$699$	−0.709146	+	2.18253i	−0.0268224	+	0.0825507i
$700$	−47.3855	+	24.1061i	−1.79100	+	0.911126i
$701$	−1.66708	−	5.13075i	−0.0629648	−	0.193786i	0.914626	−	0.404302i	$-0.132486\pi$
$701$	−1.66708	−	5.13075i	−0.0629648	−	0.193786i	−0.977590	+	0.210516i	$0.932486\pi$
$702$	−10.8796	−	9.00040i	−0.410624	−	0.339698i
$703$	11.2842	−	2.15258i	0.425592	−	0.0811860i
$704$	−15.8504	+	33.6838i	−0.597384	+	1.26951i
$705$	−2.42690	−	1.09672i	−0.0914025	−	0.0413048i
$706$	−1.49974	+	7.86190i	−0.0564433	+	0.295886i
$707$	37.8003	−	12.2821i	1.42163	−	0.461915i
$708$	−3.14846	+	1.48155i	−0.118326	+	0.0556802i
$709$	21.5387	−	8.52777i	0.808903	−	0.320267i	0.0729806	−	0.997333i	$-0.476749\pi$
$709$	21.5387	−	8.52777i	0.808903	−	0.320267i	0.735922	+	0.677066i	$0.236749\pi$
$710$	−1.99354	+	41.9890i	−0.0748164	+	1.57582i
$711$	−20.0438	+	5.14637i	−0.751701	+	0.193004i
$712$	−16.7859	−	42.3964i	−0.629079	−	1.58887i
$713$	0.175155	−	0.682184i	0.00655961	−	0.0255480i
$714$	−4.50484	−	7.09849i	−0.168589	−	0.265654i
$715$	14.7636	+	30.1606i	0.552129	+	1.12794i
$716$	3.22862	+	51.3175i	0.120659	+	1.91782i
$717$	2.24610	−	4.08564i	0.0838821	−	0.152581i
$718$	31.6798	+	10.2934i	1.18228	+	0.384146i
$719$	−39.0560	+	4.93392i	−1.45654	+	0.184004i	−0.813384	−	0.581728i	$-0.802377\pi$
$719$	−39.0560	+	4.93392i	−1.45654	+	0.184004i	−0.643160	+	0.765732i	$0.722377\pi$
$720$	1.06376	+	3.89333i	0.0396441	+	0.145096i
$721$	−31.8029	−	29.8649i	−1.18440	−	1.11223i
$722$	−49.2249	+	52.4192i	−1.83196	+	1.95084i
$723$	0.000847836		0.00330210i	3.15314e−5		0.000122807i
$724$	−53.9708	+	39.2121i	−2.00581	+	1.45731i
$725$	−13.3718	−	26.2850i	−0.496617	−	0.976202i
$726$	0.874123	+	0.635087i	0.0324417	+	0.0235703i
$727$	−16.5358	+	41.7648i	−0.613280	+	1.54897i	0.207809	+	0.978169i	$0.433367\pi$
$727$	−16.5358	+	41.7648i	−0.613280	+	1.54897i	−0.821089	+	0.570800i	$0.806633\pi$
$728$	−6.39628	+	50.6318i	−0.237062	+	1.87654i
$729$	21.7784	−	11.9728i	0.806607	−	0.443436i
$730$	5.98739	−	2.04781i	0.221603	−	0.0757929i
$731$	5.07594	+	10.7869i	0.187741	+	0.398969i
$732$	−4.28537	−	5.89831i	−0.158392	−	0.218008i
$733$	−5.87328	−	46.4918i	−0.216935	−	1.71721i	−0.605545	−	0.795811i	$-0.707045\pi$
$733$	−5.87328	−	46.4918i	−0.216935	−	1.71721i	0.388610	−	0.921402i	$-0.372955\pi$
$734$	1.36676	+	0.350924i	0.0504480	+	0.0129528i
$735$	−0.391217	+	1.27023i	−0.0144302	+	0.0468532i
$736$	2.01788	−	2.43919i	0.0743799	−	0.0899098i
$737$	13.2576	−	10.9677i	0.488350	−	0.403999i
$738$	3.17556	+	2.01527i	0.116894	+	0.0741832i
$739$	2.26933	−	36.0700i	0.0834787	−	1.32686i	−0.703861	−	0.710337i	$-0.748542\pi$
$739$	2.26933	−	36.0700i	0.0834787	−	1.32686i	0.787340	−	0.616519i	$-0.211458\pi$
$740$	−6.39482	+	10.4279i	−0.235078	+	0.383339i
$741$	4.61044	+	5.57306i	0.169369	+	0.204732i
$742$	8.03320	+	1.53242i	0.294908	+	0.0562567i
$743$	−8.94193	+	12.3075i	−0.328048	+	0.451519i	−0.940903	−	0.338676i	$-0.890021\pi$
$743$	−8.94193	+	12.3075i	−0.328048	+	0.451519i	0.612855	+	0.790195i	$0.290021\pi$
$744$	−0.611035	−	0.335919i	−0.0224016	−	0.0123154i
$745$	−17.8959	−	18.4789i	−0.655654	−	0.677014i
$746$	−82.3735	−	10.4062i	−3.01591	−	0.380998i
$747$	−46.0688	−	21.6783i	−1.68557	−	0.793168i
$748$	56.7563	+	3.57080i	2.07522	+	0.130561i
$749$	−34.5602			−1.26280
$750$	−2.71016	−	4.43207i	−0.0989609	−	0.161836i
$751$	−16.8017			−0.613104			−0.306552	−	0.951854i	$-0.599175\pi$
$751$	−16.8017			−0.613104			−0.306552	+	0.951854i	$0.599175\pi$
$752$	3.61466	+	0.227415i	0.131813	+	0.00829298i
$753$	−2.75234	−	1.29515i	−0.100301	−	0.0471981i
$754$	−69.1316	−	8.73336i	−2.51763	−	0.318050i
$755$	11.6531	−	5.70418i	0.424098	−	0.207596i
$756$	11.1364	+	6.12229i	0.405027	+	0.222665i
$757$	5.68912	−	7.83041i	0.206775	−	0.284601i	−0.693016	−	0.720922i	$-0.743719\pi$
$757$	5.68912	−	7.83041i	0.206775	−	0.284601i	0.899791	+	0.436321i	$0.143719\pi$
$758$	5.35998	+	1.02247i	0.194683	+	0.0371378i
$759$	0.241821	+	0.292311i	0.00877754	+	0.0106102i
$760$	−3.91905	−	49.9997i	−0.142159	−	1.81368i
$761$	−0.179454	+	2.85234i	−0.00650519	+	0.103397i	−0.999939	−	0.0110077i	$-0.996496\pi$
$761$	−0.179454	+	2.85234i	−0.00650519	+	0.103397i	0.993434	+	0.114405i	$0.0364961\pi$
$762$	−1.57839	−	1.00168i	−0.0571791	−	0.0362870i
$763$	−35.0736	+	29.0154i	−1.26975	+	1.05043i
$764$	0.543840	−	0.657390i	0.0196754	−	0.0237835i
$765$	−30.3441	+	22.7679i	−1.09709	+	0.823176i
$766$	49.3076	+	12.6600i	1.78156	+	0.457426i
$767$	3.29176	+	26.0570i	0.118859	+	0.940862i
$768$	−2.32646	−	3.20209i	−0.0839488	−	0.115546i
$769$	−16.1173	−	34.2509i	−0.581203	−	1.23512i	−0.951912	−	0.306371i	$-0.900885\pi$
$769$	−16.1173	−	34.2509i	−0.581203	−	1.23512i	0.370709	−	0.928749i	$-0.379115\pi$
$770$	−28.9085	−	38.5280i	−1.04179	−	1.38845i
$771$	0.856306	−	0.470758i	0.0308391	−	0.0169539i
$772$	1.87554	−	14.8464i	0.0675020	−	0.534334i
$773$	1.30006	−	3.28356i	0.0467597	−	0.118102i	−0.904520	−	0.426432i	$-0.859770\pi$
$773$	1.30006	−	3.28356i	0.0467597	−	0.118102i	0.951279	+	0.308331i	$0.0997703\pi$
$774$	−11.5390	−	8.38359i	−0.414762	−	0.301342i
$775$	−5.34997	−	1.19944i	−0.192177	−	0.0430850i
$776$	−15.9375	+	11.5793i	−0.572124	+	0.415673i
$777$	0.255666	+	0.995755i	0.00917198	+	0.0357225i
$778$	29.4571	−	31.3686i	1.05609	−	1.12462i
$779$	−2.82794	−	2.65561i	−0.101321	−	0.0951470i
$780$	−7.69325	−	0.365259i	−0.275462	−	0.0130784i
$781$	−23.7083	+	2.99506i	−0.848350	+	0.107172i
$782$	−8.11287	−	2.63603i	−0.290116	−	0.0942643i
$783$	−3.39607	+	6.17744i	−0.121366	+	0.220764i
$784$	−0.113495	−	1.80395i	−0.00405339	−	0.0644268i
$785$	−14.9264	−	7.90920i	−0.532746	−	0.282291i
$786$	1.02826	+	1.62028i	0.0366769	+	0.0577935i
$787$	−5.78223	+	22.5203i	−0.206114	+	0.802762i	0.778446	+	0.627712i	$0.216009\pi$
$787$	−5.78223	+	22.5203i	−0.206114	+	0.802762i	−0.984560	+	0.175049i	$0.943991\pi$
$788$	−6.72892	−	16.9953i	−0.239708	−	0.605433i
$789$	−4.54251	+	1.16632i	−0.161718	+	0.0415220i
$790$	−22.6577	+	28.2630i	−0.806125	+	1.00555i
$791$	33.1060	−	13.1076i	1.17711	−	0.466052i
$792$	−25.0107	+	11.7692i	−0.888718	+	0.418199i
$793$	−52.3365	+	17.0052i	−1.85852	+	0.603871i
$794$	−14.4333	+	75.6621i	−0.512219	+	2.68515i
$795$	−0.0551811	+	0.498369i	−0.00195707	+	0.0176753i
$796$	21.1771	−	45.0036i	0.750603	−	1.59511i
$797$	16.5487	−	3.15684i	0.586186	−	0.111821i	0.114247	−	0.993452i	$-0.463554\pi$
$797$	16.5487	−	3.15684i	0.586186	−	0.111821i	0.471939	+	0.881631i	$0.343554\pi$
$798$	−7.99403	−	6.61323i	−0.282985	−	0.234106i
$799$	10.5197	+	32.3764i	0.372161	+	1.14539i
$800$	−19.4625	−	15.1166i	−0.688105	−	0.534451i
$801$	−13.1528	+	40.4802i	−0.464731	+	1.43030i
$802$	34.0045	−	21.5799i	1.20074	−	0.762013i
$803$	1.73300	+	3.15232i	0.0611564	+	0.111243i
$804$	0.739481	+	3.87650i	0.0260795	+	0.136714i
$805$	1.73357	+	4.18897i	0.0611002	+	0.147642i
$806$	−9.44360	+	8.86813i	−0.332637	+	0.312366i
$807$			3.51407i			0.123701i
$808$	−27.3307	−	29.1043i	−0.961491	−	1.02388i
$809$	−15.1657	+	23.8974i	−0.533199	+	0.840187i	−0.999000	−	0.0447020i	$-0.985766\pi$
$809$	−15.1657	+	23.8974i	−0.533199	+	0.840187i	0.465801	+	0.884889i	$0.345766\pi$
$810$	18.4332	−	40.7903i	0.647675	−	1.43322i
$811$	45.2141	+	17.9015i	1.58768	+	0.628608i	0.985488	−	0.169743i	$-0.0542936\pi$
$811$	45.2141	+	17.9015i	1.58768	+	0.628608i	0.602193	+	0.798350i	$0.294294\pi$
$812$	62.5911	−	3.93790i	2.19652	−	0.138193i
$813$	−1.36635	+	0.0859633i	−0.0479199	+	0.00301486i
$814$	−10.3045	−	4.07984i	−0.361172	−	0.142998i
$815$	−7.90893	−	38.2521i	−0.277038	−	1.33991i
$816$	−0.375619	+	0.591881i	−0.0131493	+	0.0207200i
$817$	10.0708	+	10.7244i	0.352334	+	0.375198i
$818$		−	3.56597i		−	0.124681i
$819$	34.7261	−	32.6100i	1.21343	−	1.13948i
$820$	4.11827	−	0.322796i	0.143816	−	0.0112725i
$821$	0.581105	+	3.04626i	0.0202807	+	0.106315i	0.990988	−	0.133949i	$-0.0427659\pi$
$821$	0.581105	+	3.04626i	0.0202807	+	0.106315i	−0.970708	+	0.240264i	$0.922766\pi$
$822$	−2.62249	−	4.77029i	−0.0914698	−	0.166383i
$823$	47.3721	−	30.0633i	1.65129	−	1.04794i	0.713546	−	0.700608i	$-0.247088\pi$
$823$	47.3721	−	30.0633i	1.65129	−	1.04794i	0.937742	−	0.347332i	$-0.112912\pi$
$824$	−13.5425	+	41.6795i	−0.471775	+	1.45198i
$825$	2.21651	−	1.95161i	0.0771691	−	0.0679465i
$826$	−11.6417	−	35.8294i	−0.405066	−	1.24666i
$827$	33.4490	+	27.6714i	1.16313	+	0.962228i	0.999704	−	0.0243266i	$-0.00774415\pi$
$827$	33.4490	+	27.6714i	1.16313	+	0.962228i	0.163430	+	0.986555i	$0.447744\pi$
$828$	6.29028	−	1.19994i	0.218602	−	0.0417006i
$829$	12.0896	−	25.6917i	0.419889	−	0.892310i	−0.577239	−	0.816575i	$-0.695870\pi$
$829$	12.0896	−	25.6917i	0.419889	−	0.892310i	0.997128	−	0.0757347i	$-0.0241302\pi$
$830$	−87.2777	+	18.0454i	−3.02945	+	0.626364i
$831$	0.558550	−	2.92802i	0.0193759	−	0.101572i
$832$	−61.2924	+	19.9151i	−2.12493	+	0.690432i
$833$	15.3725	−	7.23375i	0.532626	−	0.250635i
$834$	−0.857083	+	0.339343i	−0.0296784	+	0.0117505i
$835$	36.7171	−	10.0321i	1.27065	−	0.347175i
$836$	67.9734	−	17.4526i	2.35091	−	0.603611i
$837$	0.482459	+	1.21855i	0.0166762	+	0.0421193i
$838$	−13.3992	+	52.1866i	−0.462869	+	1.80276i
$839$	5.16710	+	8.14205i	0.178388	+	0.281095i	0.921742	−	0.387804i	$-0.126766\pi$
$839$	5.16710	+	8.14205i	0.178388	+	0.281095i	−0.743354	+	0.668898i	$0.766766\pi$
$840$	4.44371	−	0.630990i	0.153322	−	0.0217712i
$841$	0.363454	+	5.77694i	0.0125329	+	0.199205i
$842$	31.9001	−	58.0261i	1.09935	−	1.99971i
$843$	4.25301	+	1.38189i	0.146481	+	0.0475947i
$844$	66.6958	−	8.42564i	2.29576	−	0.290022i
$845$	−10.2823	+	27.1852i	−0.353722	+	0.935198i
$846$	−29.6900	−	27.8808i	−1.02076	−	0.958560i
$847$	−5.02461	+	5.35067i	−0.172648	+	0.183851i
$848$	−0.169581	−	0.660473i	−0.00582342	−	0.0226807i
$849$	−0.637349	+	0.463061i	−0.0218738	+	0.0158922i
$850$	−18.5671	+	63.7570i	−0.636848	+	2.18685i
$851$	0.843891	+	0.613123i	0.0289282	+	0.0210176i
$852$	2.01767	−	5.09604i	0.0691241	−	0.174588i
$853$	−2.00361	+	15.8602i	−0.0686024	+	0.543044i	0.919935	+	0.392070i	$0.128241\pi$
$853$	−2.00361	+	15.8602i	−0.0686024	+	0.543044i	−0.988538	+	0.150974i	$0.951759\pi$
$854$	69.1714	−	38.0273i	2.36700	−	1.30127i
$855$	−26.9309	+	38.2929i	−0.921018	+	1.30959i
$856$	14.7815	+	31.4124i	0.505222	+	1.07365i
$857$	−28.3327	−	38.9966i	−0.967825	−	1.33210i	−0.943138	−	0.332402i	$-0.892141\pi$
$857$	−28.3327	−	38.9966i	−0.967825	−	1.33210i	−0.0246876	−	0.999695i	$-0.507859\pi$
$858$	−0.874572	−	6.92295i	−0.0298574	−	0.236346i
$859$	−7.19890	−	1.84836i	−0.245623	−	0.0630653i	0.123871	−	0.992298i	$-0.460469\pi$
$859$	−7.19890	−	1.84836i	−0.245623	−	0.0630653i	−0.369494	+	0.929233i	$0.620469\pi$
$860$	−15.6638	+	0.241079i	−0.534130	+	0.00822073i
$861$	0.221295	−	0.267500i	0.00754172	−	0.00911637i
$862$	−16.0243	+	13.2565i	−0.545791	+	0.451518i
$863$	23.2852	+	14.7772i	0.792638	+	0.503023i	0.869449	−	0.494022i	$-0.164474\pi$
$863$	23.2852	+	14.7772i	0.792638	+	0.503023i	−0.0768112	+	0.997046i	$0.524474\pi$
$864$	−0.369880	+	5.87908i	−0.0125836	+	0.200010i
$865$	−18.2791	−	21.4159i	−0.621509	−	0.728162i
$866$	−17.7527	−	21.4594i	−0.603262	−	0.729219i
$867$	−3.12347	−	0.595834i	−0.106079	−	0.0202356i
$868$	6.85335	−	9.43283i	0.232618	−	0.320171i
$869$	−18.0454	−	9.92053i	−0.612147	−	0.336531i
$870$	0.861541	+	6.06735i	0.0292090	+	0.205702i
$871$	29.5523	+	3.73333i	1.00134	+	0.126499i
$872$	41.3737	+	19.4690i	1.40109	+	0.659303i
$873$	18.3523	+	1.15463i	0.621133	+	0.0390784i
$874$	−10.5269			−0.356076
$875$	32.1787	−	14.4923i	1.08784	−	0.489928i
$876$	−0.825069			−0.0278765
$877$	16.5522	+	1.04138i	0.558928	+	0.0351648i	0.339743	−	0.940518i	$-0.389660\pi$
$877$	16.5522	+	1.04138i	0.558928	+	0.0351648i	0.219185	+	0.975683i	$0.429660\pi$
$878$	26.2668	+	12.3602i	0.886460	+	0.417136i
$879$	1.71576	+	0.216751i	0.0578713	+	0.00731084i
$880$	−1.88046	+	3.54884i	−0.0633903	+	0.119631i
$881$	1.92795	+	1.05990i	0.0649544	+	0.0357090i	0.513900	−	0.857850i	$-0.328200\pi$
$881$	1.92795	+	1.05990i	0.0649544	+	0.0357090i	−0.448945	+	0.893559i	$0.648200\pi$
$882$	−11.9475	+	16.4443i	−0.402293	+	0.553709i
$883$	16.8422	+	3.21282i	0.566785	+	0.108120i	0.462806	−	0.886459i	$-0.346843\pi$
$883$	16.8422	+	3.21282i	0.566785	+	0.108120i	0.103979	+	0.994579i	$0.466843\pi$
$884$	62.7545	+	75.8571i	2.11066	+	2.55135i
$885$	2.13429	−	0.883255i	0.0717433	−	0.0296903i
$886$	0.178559	−	2.83811i	0.00599880	−	0.0953481i
$887$	22.7218	+	14.4197i	0.762925	+	0.484167i	0.859485	−	0.511160i	$-0.170784\pi$
$887$	22.7218	+	14.4197i	0.762925	+	0.484167i	−0.0965607	+	0.995327i	$0.530784\pi$
$888$	0.795708	−	0.658267i	0.0267022	−	0.0220900i
$889$	8.09500	−	9.78517i	0.271497	−	0.328184i
$890$	24.1112	+	70.4961i	0.808208	+	2.36304i
$891$	24.6468	+	6.32822i	0.825699	+	0.212003i
$892$	3.00832	+	23.8133i	0.100726	+	0.797329i
$893$	24.6929	+	33.9868i	0.826315	+	1.13732i
$894$	2.27600	+	4.83674i	0.0761208	+	0.161765i
$895$	−0.525270	−	34.1287i	−0.0175578	−	1.14079i
$896$	53.7412	−	29.5445i	1.79537	−	0.987011i
$897$	−0.0823145	+	0.651586i	−0.00274840	+	0.0217558i
$898$	8.71037	−	21.9999i	0.290669	−	0.734146i
$899$	5.23245	+	3.80160i	0.174512	+	0.126790i
$900$	−10.8435	−	48.6566i	−0.361451	−	1.62189i
$901$	5.18528	−	3.76733i	0.172747	−	0.125508i
$902$	0.930753	+	3.62504i	0.0309907	+	0.120701i
$903$	−0.901257	+	0.959741i	−0.0299920	+	0.0319382i
$904$	−26.0733	−	24.4844i	−0.867184	−	0.814340i
$905$	37.0208	−	24.3013i	1.23061	−	0.807801i
$906$	−2.67480	+	0.337906i	−0.0888642	+	0.0112262i
$907$	23.1817	+	7.53219i	0.769736	+	0.250102i	0.667452	−	0.744653i	$-0.267385\pi$
$907$	23.1817	+	7.53219i	0.769736	+	0.250102i	0.102284	+	0.994755i	$0.467385\pi$
$908$	12.1840	−	22.1627i	0.404341	−	0.735494i
$909$	2.34006	+	37.1942i	0.0776150	+	1.23365i
$910$	14.3628	−	82.1409i	0.476123	−	2.72294i
$911$	−3.80728	−	5.99931i	−0.126141	−	0.198766i	0.775388	−	0.631485i	$-0.217554\pi$
$911$	−3.80728	−	5.99931i	−0.126141	−	0.198766i	−0.901529	+	0.432719i	$0.857554\pi$
$912$	−0.215135	+	0.837897i	−0.00712384	+	0.0277455i
$913$	−18.6510	−	47.1071i	−0.617259	−	1.55902i
$914$	−39.2597	+	10.0802i	−1.29860	+	0.333423i
$915$	2.65581	+	4.04589i	0.0877984	+	0.133753i
$916$	−20.4791	+	8.10825i	−0.676649	+	0.267904i
$917$	−11.7958	+	5.55070i	−0.389533	+	0.183300i
$918$	15.0965	−	4.90515i	0.498258	−	0.161894i
$919$	−4.06737	+	21.3219i	−0.134170	+	0.703344i	0.850093	+	0.526633i	$0.176546\pi$
$919$	−4.06737	+	21.3219i	−0.134170	+	0.703344i	−0.984263	+	0.176711i	$0.943454\pi$
$920$	3.06597	−	3.36731i	0.101082	−	0.111017i
$921$	2.18589	−	4.64526i	0.0720276	−	0.153066i
$922$	28.5921	−	5.45424i	0.941632	−	0.179626i
$923$	−31.8760	−	26.3701i	−1.04921	−	0.867982i
$924$	1.94074	+	5.97298i	0.0638457	+	0.196497i
$925$	4.56848	−	6.71312i	0.150211	−	0.220726i
$926$	15.8489	−	48.7779i	0.520827	−	1.60294i
$927$	34.5393	−	21.9193i	1.13442	−	0.719924i
$928$	14.0047	+	25.4745i	0.459727	+	0.836240i
$929$	8.86540	+	46.4740i	0.290864	+	1.52476i	0.764837	+	0.644224i	$0.222820\pi$
$929$	8.86540	+	46.4740i	0.290864	+	1.52476i	−0.473973	+	0.880540i	$0.657180\pi$
$930$	0.971244	+	0.595604i	0.0318483	+	0.0195306i
$931$	15.2833	−	14.3520i	0.500892	−	0.470368i
$932$			38.5466i			1.26264i
$933$	−0.976138	−	1.03948i	−0.0319573	−	0.0340311i
$934$	−41.3981	+	65.2330i	−1.35459	+	2.13449i
$935$	−37.5209	−	4.15443i	−1.22706	−	0.135865i
$936$	−44.4922	−	17.6157i	−1.45427	−	0.575788i
$937$	−47.6982	+	3.00092i	−1.55823	+	0.0980357i	−0.818358	−	0.574709i	$-0.805115\pi$
$937$	−47.6982	+	3.00092i	−1.55823	+	0.0980357i	−0.739875	+	0.672744i	$0.765115\pi$
$938$	−42.6426	+	2.68284i	−1.39233	+	0.0875980i
$939$	4.56055	+	1.80565i	0.148828	+	0.0589252i
$940$	−44.4622	−	4.92300i	−1.45020	−	0.160571i
$941$	−4.67561	+	7.36759i	−0.152421	+	0.240176i	−0.911955	−	0.410291i	$-0.865427\pi$
$941$	−4.67561	+	7.36759i	−0.152421	+	0.240176i	0.759534	+	0.650468i	$0.225427\pi$
$942$	2.40293	+	2.55886i	0.0782916	+	0.0833721i
$943$		−	0.352255i		−	0.0114710i
$944$	−2.28987	+	2.15033i	−0.0745288	+	0.0699872i
$945$	−7.19146	−	4.41008i	−0.233938	−	0.143460i
$946$	−2.65953	−	13.9417i	−0.0864687	−	0.453285i
$947$	−10.9390	−	19.8980i	−0.355471	−	0.646599i	0.636753	−	0.771068i	$-0.280277\pi$
$947$	−10.9390	−	19.8980i	−0.355471	−	0.646599i	−0.992224	+	0.124469i	$0.960277\pi$
$948$	3.98783	−	2.53075i	0.129519	−	0.0821950i
$949$	−1.92443	+	5.92278i	−0.0624695	+	0.192261i
$950$	2.52189	+	81.9085i	0.0818208	+	2.65746i
$951$	−0.399914	−	1.23081i	−0.0129681	−	0.0399117i
$952$	−44.2057	−	36.5701i	−1.43271	−	1.18524i
$953$	−29.6806	+	5.66189i	−0.961450	+	0.183406i	−0.644133	−	0.764913i	$-0.722782\pi$
$953$	−29.6806	+	5.66189i	−0.961450	+	0.183406i	−0.317317	+	0.948320i	$0.602782\pi$
$954$	−3.26497	+	6.93841i	−0.105707	+	0.224639i
$955$	−0.381299	+	0.418774i	−0.0123385	+	0.0135512i
$956$	14.6745	−	76.9263i	0.474607	−	2.48798i
$957$	−3.31325	+	1.07654i	−0.107102	+	0.0347996i
$958$	−73.6348	+	34.6499i	−2.37903	+	1.11949i
$959$	34.3836	−	13.6134i	1.11030	−	0.439601i
$960$	3.11027	+	4.73823i	0.100384	+	0.152926i
$961$	−28.8614	+	7.41035i	−0.931014	+	0.239044i
$962$	−7.06297	−	17.8390i	−0.227719	−	0.575154i
$963$	8.05895	−	31.3875i	0.259696	−	1.01145i
$964$	0.0306839	+	0.0483501i	0.000988263	+	0.00155725i
$965$	−1.71099	+	9.78514i	−0.0550787	+	0.314995i
$966$	−0.0591528	−	0.940207i	−0.00190321	−	0.0302507i
$967$	−6.08537	+	11.0692i	−0.195692	+	0.355963i	−0.955888	−	0.293731i	$-0.905103\pi$
$967$	−6.08537	+	11.0692i	−0.195692	+	0.355963i	0.760196	+	0.649694i	$0.225103\pi$
$968$	7.01235	+	2.27845i	0.225386	+	0.0732322i
$969$	−8.06700	+	1.01910i	−0.259149	+	0.0327382i
$970$	26.9090	−	17.6637i	0.863997	−	0.567147i
$971$	0.426996	+	0.400975i	0.0137029	+	0.0128679i	0.691368	−	0.722502i	$-0.257008\pi$
$971$	0.426996	+	0.400975i	0.0137029	+	0.0128679i	−0.677665	+	0.735370i	$0.737008\pi$
$972$	−12.2632	+	13.0590i	−0.393342	+	0.418866i
$973$	−1.55735	−	6.06549i	−0.0499264	−	0.194451i
$974$	6.95470	−	5.05289i	0.222843	−	0.161905i
$975$	5.08965	+	0.484383i	0.162999	+	0.0155127i
$976$	−5.32471	−	3.86863i	−0.170440	−	0.123832i
$977$	−13.7577	+	34.7480i	−0.440148	+	1.11169i	0.525260	+	0.850942i	$0.323968\pi$
$977$	−13.7577	+	34.7480i	−0.440148	+	1.11169i	−0.965408	+	0.260745i	$0.916032\pi$
$978$	−1.01732	+	8.05292i	−0.0325303	+	0.257504i
$979$	−37.1158	+	20.4046i	−1.18623	+	0.652133i
$980$	0.343563	+	22.3225i	0.0109747	+	0.713066i
$981$	−18.1731	−	38.6198i	−0.580222	−	1.23304i
$982$	9.91456	+	13.6462i	0.316386	+	0.435468i
$983$	3.80408	+	30.1124i	0.121331	+	0.960437i	0.928814	+	0.370546i	$0.120829\pi$
$983$	3.80408	+	30.1124i	0.121331	+	0.960437i	−0.807483	+	0.589891i	$0.799171\pi$
$984$	−0.337784	−	0.0867281i	−0.0107682	−	0.00276479i
$985$	3.92670	+	11.4809i	0.125115	+	0.365811i
$986$	49.9321	−	60.3575i	1.59016	−	1.92218i
$987$	−2.89678	+	2.39642i	−0.0922055	+	0.0762790i
$988$	102.579	+	65.0985i	3.26347	+	2.07106i
$989$	−0.0838789	+	1.33322i	−0.00266719	+	0.0423938i
$990$	41.7322	−	17.2705i	1.32634	−	0.548892i
$991$	2.21631	+	2.67905i	0.0704033	+	0.0851029i	0.804539	−	0.593900i	$-0.202412\pi$
$991$	2.21631	+	2.67905i	0.0704033	+	0.0851029i	−0.734136	+	0.679003i	$0.762412\pi$
$992$	5.30886	+	1.01272i	0.168556	+	0.0321539i
$993$	3.28797	−	4.52551i	0.104341	−	0.143613i
$994$	52.0009	+	28.5877i	1.64937	+	0.906748i
$995$	−15.4586	+	29.1738i	−0.490072	+	0.924872i
$996$	11.5288	+	1.45643i	0.365305	+	0.0461488i
$997$	−19.1296	−	9.00171i	−0.605841	−	0.285087i	0.0982894	−	0.995158i	$-0.468663\pi$
$997$	−19.1296	−	9.00171i	−0.605841	−	0.285087i	−0.704130	+	0.710071i	$0.748663\pi$
$998$	−89.6489	−	5.64023i	−2.83778	−	0.178538i
$999$	−1.94102			−0.0614112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.4.12	✓	240
5.2	odd	4		625.2.g.b.226.3		480
5.3	odd	4		625.2.g.b.226.22		480
5.4	even	2		625.2.h.a.399.1		240
125.17	odd	100		625.2.g.b.401.3		480
125.31	even	25		625.2.h.a.224.1		240
125.94	even	50	inner	125.2.h.a.94.12	yes	240
125.108	odd	100		625.2.g.b.401.22		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.4.12	✓	240	1.1	even	1	trivial
125.2.h.a.94.12	yes	240	125.94	even	50	inner
625.2.g.b.226.3		480	5.2	odd	4
625.2.g.b.226.22		480	5.3	odd	4
625.2.g.b.401.3		480	125.17	odd	100
625.2.g.b.401.22		480	125.108	odd	100
625.2.h.a.224.1		240	125.31	even	25
625.2.h.a.399.1		240	5.4	even	2

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.31243 + 0.145486i) q^{2} +(0.181456 + 0.0853865i) q^{3} +(3.34195 + 0.422186i) q^{4} +(-2.20265 - 0.385146i) q^{5} +(0.407181 + 0.223850i) q^{6} +(-1.85539 + 2.55372i) q^{7} +(3.11468 + 0.594156i) q^{8} +(-1.88664 - 2.28055i) q^{9} +(-5.03744 - 1.21108i) q^{10} +(0.184936 - 2.93947i) q^{11} +(0.570366 + 0.361965i) q^{12} +(3.92872 - 3.25012i) q^{13} +(-4.66199 + 5.63538i) q^{14} +(-0.366797 - 0.257963i) q^{15} +(0.590674 + 0.151659i) q^{16} +(0.718412 + 5.68682i) q^{17} +(-4.03093 - 5.54810i) q^{18} +(3.01177 + 6.40035i) q^{19} +(-7.19853 - 2.21707i) q^{20} +(-0.554724 + 0.304962i) q^{21} +(0.855302 - 6.77042i) q^{22} +(-0.236444 + 0.597190i) q^{23} +(0.514442 + 0.373764i) q^{24} +(4.70332 + 1.69668i) q^{25} +(9.55775 - 6.94411i) q^{26} +(-0.297230 - 1.15764i) q^{27} +(-7.27875 + 7.75108i) q^{28} +(-4.29958 - 4.03757i) q^{29} +(-0.810662 - 0.649887i) q^{30} +(-1.08791 + 0.137435i) q^{31} +(-4.68747 - 1.52305i) q^{32} +(0.284549 - 0.517592i) q^{33} +(0.833928 + 13.2549i) q^{34} +(5.07032 - 4.91036i) q^{35} +(-5.34222 - 8.41800i) q^{36} +(0.403881 - 1.57301i) q^{37} +(6.03336 + 15.2385i) q^{38} +(0.990405 - 0.254293i) q^{39} +(-6.63170 - 2.50832i) q^{40} +(-0.509919 + 0.201891i) q^{41} +(-1.32713 + 0.624499i) q^{42} +(1.97802 - 0.642698i) q^{43} +(1.85905 - 9.74547i) q^{44} +(3.27725 + 5.74989i) q^{45} +(-0.633644 + 1.34656i) q^{46} +(5.83382 - 1.11286i) q^{47} +(0.0942314 + 0.0779550i) q^{48} +(-0.915913 - 2.81889i) q^{49} +(10.6293 + 4.60773i) q^{50} +(-0.355218 + 1.09325i) q^{51} +(14.5017 - 9.20308i) q^{52} +(-0.538682 - 0.979859i) q^{53} +(-0.518906 - 2.72020i) q^{54} +(-1.53947 + 6.40339i) q^{55} +(-7.29624 + 6.85162i) q^{56} +1.41854i q^{57} +(-9.35507 - 9.96214i) q^{58} +(-2.76004 + 4.34912i) q^{59} +(-1.11691 - 1.01696i) q^{60} +(-10.0347 - 3.97303i) q^{61} +(-2.53571 + 0.159533i) q^{62} +(9.32434 - 0.586638i) q^{63} +(-11.7519 - 4.65290i) q^{64} +(-9.90537 + 5.64574i) q^{65} +(0.733302 - 1.15550i) q^{66} +(3.99910 + 4.25861i) q^{67} +19.3083i q^{68} +(-0.0938961 + 0.0881743i) q^{69} +(12.4392 - 10.6172i) q^{70} +(-1.52033 - 7.96986i) q^{71} +(-4.52126 - 8.22414i) q^{72} +(-1.03124 + 0.654444i) q^{73} +(1.16280 - 3.57872i) q^{74} +(0.708571 + 0.709473i) q^{75} +(7.36305 + 22.6612i) q^{76} +(7.16346 + 5.92613i) q^{77} +(2.32724 - 0.443945i) q^{78} +(2.97692 - 6.32628i) q^{79} +(-1.24264 - 0.561548i) q^{80} +(-1.61891 + 8.48663i) q^{81} +(-1.20853 + 0.392674i) q^{82} +(15.5649 - 7.32429i) q^{83} +(-1.98261 + 0.784970i) q^{84} +(0.607847 - 12.8028i) q^{85} +(4.66754 - 1.19842i) q^{86} +(-0.435428 - 1.09977i) q^{87} +(2.32252 - 9.04561i) q^{88} +(-7.70549 - 12.1419i) q^{89} +(6.74190 + 13.7730i) q^{90} +(1.01060 + 16.0631i) q^{91} +(-1.04231 + 1.89595i) q^{92} +(-0.209142 - 0.0679544i) q^{93} +(13.6522 - 1.72468i) q^{94} +(-4.16881 - 15.2577i) q^{95} +(-0.720519 - 0.676613i) q^{96} +(-4.25297 + 4.52896i) q^{97} +(-1.70788 - 6.65174i) q^{98} +(-7.05252 + 5.12395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18}+ \cdots + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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