LMFDB - Embedded newform 507.2.m.a.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			79.2
Character	$\chi$	$=$	507.79
Dual form			507.2.m.a.430.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25517 - 1.18361i) q^{2} +(0.970942 + 0.239316i) q^{3} +(2.54876 + 3.69251i) q^{4} +(1.29246 + 3.40793i) q^{5} +(-1.90639 - 1.68891i) q^{6} +(0.394148 + 3.24610i) q^{7} +(-0.763417 - 6.28731i) q^{8} +(0.885456 + 0.464723i) q^{9} +O(q^{10})$	\(q+(-2.25517 - 1.18361i) q^{2} +(0.970942 + 0.239316i) q^{3} +(2.54876 + 3.69251i) q^{4} +(1.29246 + 3.40793i) q^{5} +(-1.90639 - 1.68891i) q^{6} +(0.394148 + 3.24610i) q^{7} +(-0.763417 - 6.28731i) q^{8} +(0.885456 + 0.464723i) q^{9} +(1.11893 - 9.21525i) q^{10} +(-0.642398 + 0.337157i) q^{11} +(1.59102 + 4.19517i) q^{12} +(2.54492 + 2.55409i) q^{13} +(2.95324 - 7.78705i) q^{14} +(0.439330 + 3.61821i) q^{15} +(-2.53802 + 6.69222i) q^{16} +(-0.440693 - 3.62943i) q^{17} +(-1.44681 - 2.09606i) q^{18} -0.710975 q^{19} +(-9.28967 + 13.4584i) q^{20} +(-0.394148 + 3.24610i) q^{21} +1.84778 q^{22} -3.30063 q^{23} +(0.763417 - 6.28731i) q^{24} +(-6.20101 + 5.49362i) q^{25} +(-2.71620 - 8.77210i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-10.9817 + 9.72892i) q^{28} +(-8.99537 - 4.72113i) q^{29} +(3.29177 - 8.67969i) q^{30} +(5.11524 + 4.53171i) q^{31} +(4.16328 - 3.68834i) q^{32} +(-0.704418 + 0.173623i) q^{33} +(-3.30198 + 8.70661i) q^{34} +(-10.5531 + 5.53869i) q^{35} +(0.540816 + 4.45402i) q^{36} +(-6.32329 - 5.60195i) q^{37} +(1.60337 + 0.841514i) q^{38} +(1.85974 + 3.08891i) q^{39} +(20.4400 - 10.7278i) q^{40} +(5.54253 + 1.36611i) q^{41} +(4.73098 - 6.85401i) q^{42} +(4.78027 - 4.23495i) q^{43} +(-2.88227 - 1.51273i) q^{44} +(-0.439330 + 3.61821i) q^{45} +(7.44350 + 3.90665i) q^{46} +(4.82108 - 6.98455i) q^{47} +(-4.06583 + 5.89037i) q^{48} +(-3.58524 + 0.883682i) q^{49} +(20.4866 - 5.04950i) q^{50} +(0.440693 - 3.62943i) q^{51} +(-2.94462 + 15.9069i) q^{52} +(1.34164 + 11.0494i) q^{53} +(-0.903146 - 2.38140i) q^{54} +(-1.97928 - 1.75349i) q^{55} +(20.1084 - 4.95626i) q^{56} +(-0.690315 - 0.170147i) q^{57} +(14.6982 + 21.2940i) q^{58} +(1.05351 + 2.77788i) q^{59} +(-12.2405 + 10.8442i) q^{60} +(0.747293 - 6.15451i) q^{61} +(-6.17200 - 16.2742i) q^{62} +(-1.15954 + 3.05745i) q^{63} +(0.144236 - 0.0355510i) q^{64} +(-5.41496 + 11.9740i) q^{65} +(1.79409 + 0.442203i) q^{66} +(0.703362 - 1.01900i) q^{67} +(12.2785 - 10.8778i) q^{68} +(-3.20472 - 0.789893i) q^{69} +30.3547 q^{70} +(14.2868 + 3.52139i) q^{71} +(2.24589 - 5.92191i) q^{72} +(-8.59591 + 4.51148i) q^{73} +(7.62962 + 20.1177i) q^{74} +(-7.33553 + 3.84998i) q^{75} +(-1.81210 - 2.62528i) q^{76} +(-1.34765 - 1.95240i) q^{77} +(-0.537974 - 9.16723i) q^{78} +(6.72858 - 9.74803i) q^{79} -26.0869 q^{80} +(0.568065 + 0.822984i) q^{81} +(-10.8824 - 9.64100i) q^{82} +(-2.68351 + 0.661425i) q^{83} +(-12.9909 + 6.81813i) q^{84} +(11.7993 - 6.19275i) q^{85} +(-15.7929 + 3.89259i) q^{86} +(-7.60414 - 6.73668i) q^{87} +(2.61023 + 3.78156i) q^{88} +1.20412 q^{89} +(5.27331 - 7.63970i) q^{90} +(-7.28776 + 9.26777i) q^{91} +(-8.41251 - 12.1876i) q^{92} +(3.88209 + 5.62418i) q^{93} +(-19.1393 + 10.0451i) q^{94} +(-0.918906 - 2.42295i) q^{95} +(4.92498 - 2.58483i) q^{96} +(-4.23263 + 11.1605i) q^{97} +(9.13128 + 2.25066i) q^{98} -0.725500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{13}\right)$

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 $

$2$	−2.25517	−	1.18361i	−1.59465	−	0.836936i	−0.999443	−	0.0333631i	$-0.989378\pi$
$2$	−2.25517	−	1.18361i	−1.59465	−	0.836936i	−0.595206	−	0.803573i	$-0.702929\pi$
$3$	0.970942	+	0.239316i	0.560574	+	0.138169i
$3$	0.970942	+	0.239316i	0.560574	+	0.138169i
$4$	2.54876	+	3.69251i	1.27438	+	1.84626i
$5$	1.29246	+	3.40793i	0.578005	+	1.52407i	0.830809	+	0.556557i	$0.187878\pi$
$5$	1.29246	+	3.40793i	0.578005	+	1.52407i	−0.252804	+	0.967517i	$0.581353\pi$
$6$	−1.90639	−	1.68891i	−0.778279	−	0.689495i
$7$	0.394148	+	3.24610i	0.148974	+	1.22691i	0.854963	+	0.518689i	$0.173580\pi$
$7$	0.394148	+	3.24610i	0.148974	+	1.22691i	−0.705989	+	0.708223i	$0.749497\pi$
$8$	−0.763417	−	6.28731i	−0.269909	−	2.22290i
$9$	0.885456	+	0.464723i	0.295152	+	0.154908i
$10$	1.11893	−	9.21525i	0.353838	−	2.91412i
$11$	−0.642398	+	0.337157i	−0.193690	+	0.101657i	−0.558780	−	0.829316i	$-0.688731\pi$
$11$	−0.642398	+	0.337157i	−0.193690	+	0.101657i	0.365090	+	0.930972i	$0.381038\pi$
$12$	1.59102	+	4.19517i	0.459288	+	1.21104i
$13$	2.54492	+	2.55409i	0.705834	+	0.708377i
$13$	2.54492	+	2.55409i	0.705834	+	0.708377i
$14$	2.95324	−	7.78705i	0.789286	−	2.08118i
$15$	0.439330	+	3.61821i	0.113435	+	0.934218i
$16$	−2.53802	+	6.69222i	−0.634506	+	1.67305i
$17$	−0.440693	−	3.62943i	−0.106884	−	0.880267i	−0.943247	−	0.332091i	$-0.892246\pi$
$17$	−0.440693	−	3.62943i	−0.106884	−	0.880267i	0.836363	−	0.548175i	$-0.184677\pi$
$18$	−1.44681	−	2.09606i	−0.341016	−	0.494047i
$19$	−0.710975			−0.163109			−0.0815544	−	0.996669i	$-0.525988\pi$
$19$	−0.710975			−0.163109			−0.0815544	+	0.996669i	$0.525988\pi$
$20$	−9.28967	+	13.4584i	−2.07723	+	3.00939i
$21$	−0.394148	+	3.24610i	−0.0860102	+	0.708358i
$22$	1.84778			0.393948
$23$	−3.30063			−0.688230			−0.344115	−	0.938928i	$-0.611821\pi$
$23$	−3.30063			−0.688230			−0.344115	+	0.938928i	$0.611821\pi$
$24$	0.763417	−	6.28731i	0.155832	−	1.28339i
$25$	−6.20101	+	5.49362i	−1.24020	+	1.09872i
$26$	−2.71620	−	8.77210i	−0.532691	−	1.72035i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	−10.9817	+	9.72892i	−2.07534	+	1.83859i
$29$	−8.99537	−	4.72113i	−1.67040	−	0.876693i	−0.989537	−	0.144280i	$-0.953913\pi$
$29$	−8.99537	−	4.72113i	−1.67040	−	0.876693i	−0.680861	−	0.732412i	$-0.738394\pi$
$30$	3.29177	−	8.67969i	0.600993	−	1.58469i
$31$	5.11524	+	4.53171i	0.918724	+	0.813919i	0.982923	−	0.184018i	$-0.0589106\pi$
$31$	5.11524	+	4.53171i	0.918724	+	0.813919i	−0.0641983	+	0.997937i	$0.520449\pi$
$32$	4.16328	−	3.68834i	0.735971	−	0.652013i
$33$	−0.704418	+	0.173623i	−0.122623	+	0.0302240i
$34$	−3.30198	+	8.70661i	−0.566285	+	1.49317i
$35$	−10.5531	+	5.53869i	−1.78380	+	0.936209i
$36$	0.540816	+	4.45402i	0.0901360	+	0.742337i
$37$	−6.32329	−	5.60195i	−1.03954	−	0.920954i	−0.0426001	−	0.999092i	$-0.513564\pi$
$37$	−6.32329	−	5.60195i	−1.03954	−	0.920954i	−0.996943	+	0.0781377i	$0.975103\pi$
$38$	1.60337	+	0.841514i	0.260101	+	0.136512i
$39$	1.85974	+	3.08891i	0.297796	+	0.494622i
$40$	20.4400	−	10.7278i	3.23186	−	1.69621i
$41$	5.54253	+	1.36611i	0.865598	+	0.213351i	0.647024	−	0.762470i	$-0.276013\pi$
$41$	5.54253	+	1.36611i	0.865598	+	0.213351i	0.218574	+	0.975820i	$0.429860\pi$
$42$	4.73098	−	6.85401i	0.730007	−	1.05760i
$43$	4.78027	−	4.23495i	0.728984	−	0.645824i	−0.214697	−	0.976681i	$-0.568876\pi$
$43$	4.78027	−	4.23495i	0.728984	−	0.645824i	0.943681	+	0.330857i	$0.107338\pi$
$44$	−2.88227	−	1.51273i	−0.434519	−	0.228053i
$45$	−0.439330	+	3.61821i	−0.0654915	+	0.539371i
$46$	7.44350	+	3.90665i	1.09748	+	0.576004i
$47$	4.82108	−	6.98455i	0.703227	−	1.01880i	−0.294771	−	0.955568i	$-0.595244\pi$
$47$	4.82108	−	6.98455i	0.703227	−	1.01880i	0.997999	−	0.0632330i	$-0.0201411\pi$
$48$	−4.06583	+	5.89037i	−0.586852	+	0.850201i
$49$	−3.58524	+	0.883682i	−0.512177	+	0.126240i
$50$	20.4866	−	5.04950i	2.89725	−	0.714108i
$51$	0.440693	−	3.62943i	0.0617094	−	0.508222i
$52$	−2.94462	+	15.9069i	−0.408345	+	2.20589i
$53$	1.34164	+	11.0494i	0.184288	+	1.51775i	0.732129	+	0.681166i	$0.238527\pi$
$53$	1.34164	+	11.0494i	0.184288	+	1.51775i	−0.547841	+	0.836582i	$0.684550\pi$
$54$	−0.903146	−	2.38140i	−0.122903	−	0.324067i
$55$	−1.97928	−	1.75349i	−0.266886	−	0.236441i
$56$	20.1084	−	4.95626i	2.68709	−	0.662309i
$57$	−0.690315	−	0.170147i	−0.0914345	−	0.0225366i
$58$	14.6982	+	21.2940i	1.92996	+	2.79603i
$59$	1.05351	+	2.77788i	0.137155	+	0.361649i	0.985942	−	0.167086i	$-0.0534357\pi$
$59$	1.05351	+	2.77788i	0.137155	+	0.361649i	−0.848787	+	0.528735i	$0.822666\pi$
$60$	−12.2405	+	10.8442i	−1.58025	+	1.39998i
$61$	0.747293	−	6.15451i	0.0956811	−	0.788004i	−0.863331	−	0.504638i	$-0.831626\pi$
$61$	0.747293	−	6.15451i	0.0956811	−	0.788004i	0.959012	−	0.283366i	$-0.0914511\pi$
$62$	−6.17200	−	16.2742i	−0.783845	−	2.06683i
$63$	−1.15954	+	3.05745i	−0.146088	+	0.385203i
$64$	0.144236	−	0.0355510i	0.0180295	−	0.00444388i
$65$	−5.41496	+	11.9740i	−0.671643	+	1.48519i
$66$	1.79409	+	0.442203i	0.220837	+	0.0544314i
$67$	0.703362	−	1.01900i	0.0859294	−	0.124490i	−0.777662	−	0.628683i	$-0.783594\pi$
$67$	0.703362	−	1.01900i	0.0859294	−	0.124490i	0.863591	+	0.504193i	$0.168210\pi$
$68$	12.2785	−	10.8778i	1.48899	−	1.31913i
$69$	−3.20472	−	0.789893i	−0.385803	−	0.0950920i
$70$	30.3547			3.62808
$71$	14.2868	+	3.52139i	1.69554	+	0.417912i	0.964427	−	0.264349i	$-0.0851571\pi$
$71$	14.2868	+	3.52139i	1.69554	+	0.417912i	0.731109	+	0.682261i	$0.239003\pi$
$72$	2.24589	−	5.92191i	0.264680	−	0.697904i
$73$	−8.59591	+	4.51148i	−1.00608	+	0.528029i	−0.885482	−	0.464673i	$-0.846172\pi$
$73$	−8.59591	+	4.51148i	−1.00608	+	0.528029i	−0.120593	+	0.992702i	$0.538480\pi$
$74$	7.62962	+	20.1177i	0.886925	+	2.33863i
$75$	−7.33553	+	3.84998i	−0.847034	+	0.444558i
$76$	−1.81210	−	2.62528i	−0.207862	−	0.301141i
$77$	−1.34765	−	1.95240i	−0.153578	−	0.222497i
$78$	−0.537974	−	9.16723i	−0.0609136	−	1.03798i
$79$	6.72858	−	9.74803i	0.757025	−	1.09674i	−0.235160	−	0.971957i	$-0.575561\pi$
$79$	6.72858	−	9.74803i	0.757025	−	1.09674i	0.992184	−	0.124783i	$-0.0398234\pi$
$80$	−26.0869			−2.91661
$81$	0.568065	+	0.822984i	0.0631183	+	0.0914427i
$82$	−10.8824	−	9.64100i	−1.20176	−	1.06467i
$83$	−2.68351	+	0.661425i	−0.294553	+	0.0726009i	−0.383823	−	0.923407i	$-0.625393\pi$
$83$	−2.68351	+	0.661425i	−0.294553	+	0.0726009i	0.0892699	+	0.996007i	$0.471547\pi$
$84$	−12.9909	+	6.81813i	−1.41742	+	0.743919i
$85$	11.7993	−	6.19275i	1.27981	−	0.671698i
$86$	−15.7929	+	3.89259i	−1.70299	+	0.419749i
$87$	−7.60414	−	6.73668i	−0.815249	−	0.722248i
$88$	2.61023	+	3.78156i	0.278251	+	0.403116i
$89$	1.20412			0.127636			0.0638182	−	0.997962i	$-0.479672\pi$
$89$	1.20412			0.127636			0.0638182	+	0.997962i	$0.479672\pi$
$90$	5.27331	−	7.63970i	0.555855	−	0.805295i
$91$	−7.28776	+	9.26777i	−0.763965	+	0.971526i
$92$	−8.41251	−	12.1876i	−0.877065	−	1.27065i
$93$	3.88209	+	5.62418i	0.402554	+	0.583201i
$94$	−19.1393	+	10.0451i	−1.97407	+	1.03607i
$95$	−0.918906	−	2.42295i	−0.0942777	−	0.248590i
$96$	4.92498	−	2.58483i	0.502654	−	0.263813i
$97$	−4.23263	+	11.1605i	−0.429759	+	1.13318i	0.528915	+	0.848675i	$0.322599\pi$
$97$	−4.23263	+	11.1605i	−0.429759	+	1.13318i	−0.958674	+	0.284506i	$0.908170\pi$
$98$	9.13128	+	2.25066i	0.922398	+	0.227351i
$99$	−0.725500			−0.0729155
$100$	−36.0901	−	8.89541i	−3.60901	−	0.889541i
$101$	12.9554	−	11.4775i	1.28911	−	1.14205i	0.307421	−	0.951574i	$-0.400534\pi$
$101$	12.9554	−	11.4775i	1.28911	−	1.14205i	0.981691	−	0.190480i	$-0.0610045\pi$
$102$	−5.28966	+	7.66340i	−0.523755	+	0.758789i
$103$	−4.80409	−	1.18410i	−0.473361	−	0.116673i	−0.00458373	−	0.999989i	$-0.501459\pi$
$103$	−4.80409	−	1.18410i	−0.473361	−	0.116673i	−0.468777	+	0.883317i	$0.655305\pi$
$104$	14.1155	−	17.9505i	1.38414	−	1.76020i
$105$	−11.5719	+	2.85222i	−1.12930	+	0.278349i
$106$	10.0525	−	26.5062i	0.976384	−	2.57451i
$107$	5.40745	+	14.2583i	0.522758	+	1.37840i	0.893249	+	0.449563i	$0.148420\pi$
$107$	5.40745	+	14.2583i	0.522758	+	1.37840i	−0.370491	+	0.928836i	$0.620811\pi$
$108$	−0.540816	+	4.45402i	−0.0520401	+	0.428589i
$109$	5.71375	−	5.06194i	0.547278	−	0.484846i	−0.343583	−	0.939122i	$-0.611641\pi$
$109$	5.71375	−	5.06194i	0.547278	−	0.484846i	0.890861	+	0.454276i	$0.150102\pi$
$110$	2.38818	+	6.29712i	0.227704	+	0.600406i
$111$	−4.79891	−	6.95243i	−0.455493	−	0.659895i
$112$	−22.7240	−	5.60096i	−2.14722	−	0.529241i
$113$	−5.23223	+	1.28963i	−0.492206	+	0.121318i	−0.477604	−	0.878575i	$-0.658495\pi$
$113$	−5.23223	+	1.28963i	−0.492206	+	0.121318i	−0.0146028	+	0.999893i	$0.504648\pi$
$114$	1.35539	+	1.20077i	0.126944	+	0.112463i
$115$	−4.26593	−	11.2483i	−0.397800	−	1.04891i
$116$	−5.49417	−	45.2485i	−0.510120	−	4.20122i
$117$	1.06647	+	3.44422i	0.0985953	+	0.318418i
$118$	0.912067	−	7.51155i	0.0839626	−	0.691494i
$119$	11.6078	−	2.86107i	1.06409	−	0.262274i
$120$	22.4134	−	5.52441i	2.04606	−	0.504307i
$121$	−5.94971	+	8.61964i	−0.540883	+	0.783604i
$122$	−8.96980	+	12.9950i	−0.812087	+	1.17651i
$123$	5.05454	+	2.65283i	0.455753	+	0.239198i
$124$	−3.69588	+	30.4383i	−0.331900	+	2.73344i
$125$	−10.5999	−	5.56328i	−0.948088	−	0.497595i
$126$	6.23378	−	5.52265i	0.555349	−	0.491997i
$127$	−0.411609	+	0.596318i	−0.0365244	+	0.0529147i	−0.840821	−	0.541314i	$-0.817927\pi$
$127$	−0.411609	+	0.596318i	−0.0365244	+	0.0529147i	0.804296	+	0.594228i	$0.202543\pi$
$128$	−11.1683	−	2.75273i	−0.987145	−	0.243309i
$129$	5.65485	−	2.96790i	0.497882	−	0.261309i
$130$	26.3842	−	20.5942i	2.31404	−	1.80623i
$131$	5.35507	+	2.81056i	0.467875	+	0.245560i	0.682148	−	0.731214i	$-0.261046\pi$
$131$	5.35507	+	2.81056i	0.467875	+	0.245560i	−0.214273	+	0.976774i	$0.568738\pi$
$132$	−2.43650	−	2.15855i	−0.212070	−	0.187878i
$133$	−0.280229	−	2.30790i	−0.0242990	−	0.200120i
$134$	−2.79230	+	1.46551i	−0.241218	+	0.126601i
$135$	−1.29246	+	3.40793i	−0.111237	+	0.293308i
$136$	−22.4829	+	5.54155i	−1.92790	+	0.475184i
$137$	−11.2632	+	9.97832i	−0.962279	+	0.852505i	−0.989116	−	0.147135i	$-0.952995\pi$
$137$	−11.2632	+	9.97832i	−0.962279	+	0.852505i	0.0268371	+	0.999640i	$0.491456\pi$
$138$	6.29229	+	5.57448i	0.535635	+	0.474531i
$139$	7.19409	−	18.9693i	0.610195	−	1.60895i	−0.171426	−	0.985197i	$-0.554837\pi$
$139$	7.19409	−	18.9693i	0.610195	−	1.60895i	0.781620	−	0.623754i	$-0.214393\pi$
$140$	−47.3489	−	24.8506i	−4.00171	−	2.10026i
$141$	6.35250	−	5.62783i	0.534977	−	0.473949i
$142$	−28.0514	−	24.8513i	−2.35402	−	2.08548i
$143$	−2.49598	−	0.782706i	−0.208724	−	0.0654531i
$144$	−5.35734	+	4.74619i	−0.446445	+	0.395516i
$145$	4.46317	−	36.7575i	0.370646	−	3.05254i
$146$	24.7251			2.04626
$147$	−3.69254			−0.304555
$148$	4.56872	−	37.6268i	0.375547	−	3.09291i
$149$	−5.79777	+	8.39952i	−0.474972	+	0.688115i	−0.985100	−	0.171983i	$-0.944983\pi$
$149$	−5.79777	+	8.39952i	−0.474972	+	0.688115i	0.510128	+	0.860098i	$0.329598\pi$
$150$	21.0998			1.72279
$151$	6.25164	+	9.05706i	0.508751	+	0.737053i	0.990236	−	0.139401i	$-0.0445178\pi$
$151$	6.25164	+	9.05706i	0.508751	+	0.737053i	−0.481485	+	0.876454i	$0.659902\pi$
$152$	0.542770	+	4.47012i	0.0440245	+	0.362574i
$153$	1.29647	−	3.41850i	0.104813	−	0.276370i
$154$	0.728300	+	5.99809i	0.0586881	+	0.483340i
$155$	−8.83252	+	23.2895i	−0.709445	+	1.87065i
$156$	−6.66583	+	14.7400i	−0.533693	+	1.18014i
$157$	2.58852	+	6.82537i	0.206586	+	0.544723i	0.997762	−	0.0668655i	$-0.0212999\pi$
$157$	2.58852	+	6.82537i	0.206586	+	0.544723i	−0.791176	+	0.611589i	$0.790531\pi$
$158$	−26.7120	+	14.0195i	−2.12509	+	1.11533i
$159$	−1.34164	+	11.0494i	−0.106399	+	0.876272i
$160$	17.9505	+	9.42115i	1.41911	+	0.744807i
$161$	−1.30094	−	10.7142i	−0.102528	−	0.844397i
$162$	−0.306996	−	2.52834i	−0.0241199	−	0.198645i
$163$	−7.23954	−	6.41367i	−0.567045	−	0.502358i	0.330188	−	0.943915i	$-0.392888\pi$
$163$	−7.23954	−	6.41367i	−0.567045	−	0.502358i	−0.897233	+	0.441557i	$0.854426\pi$
$164$	9.08218	+	23.9477i	0.709199	+	1.87000i
$165$	−1.50213	−	2.17621i	−0.116941	−	0.169418i
$166$	6.83465	+	1.68459i	0.530471	+	0.130749i
$167$	−11.8927	−	6.24176i	−0.920283	−	0.483002i	−0.0630963	−	0.998007i	$-0.520098\pi$
$167$	−11.8927	−	6.24176i	−0.920283	−	0.483002i	−0.857187	+	0.515006i	$0.827790\pi$
$168$	20.7102			1.59782
$169$	−0.0467478	+	12.9999i	−0.00359598	+	0.999994i
$170$	−33.9392			−2.60302
$171$	−0.629537	−	0.330406i	−0.0481419	−	0.0252668i
$172$	27.8213	+	6.85735i	2.12136	+	0.522868i
$173$	10.1199	+	14.6612i	0.769399	+	1.11467i	0.990242	+	0.139358i	$0.0445038\pi$
$173$	10.1199	+	14.6612i	0.769399	+	1.11467i	−0.220843	+	0.975309i	$0.570881\pi$
$174$	9.17508	+	24.1927i	0.695561	+	1.83404i
$175$	−20.2770	−	17.9638i	−1.53279	−	1.35794i
$176$	−0.625904	−	5.15478i	−0.0471793	−	0.388556i
$177$	0.358108	+	2.94928i	0.0269170	+	0.221682i
$178$	−2.71550	−	1.42520i	−0.203535	−	0.106823i
$179$	−1.26998	+	10.4592i	−0.0949226	+	0.781758i	0.865054	+	0.501679i	$0.167284\pi$
$179$	−1.26998	+	10.4592i	−0.0949226	+	0.781758i	−0.959977	+	0.280080i	$0.909639\pi$
$180$	−14.4800	+	7.59971i	−1.07928	+	0.566449i
$181$	2.30902	+	6.08839i	0.171628	+	0.452547i	0.993038	−	0.117791i	$-0.0375814\pi$
$181$	2.30902	+	6.08839i	0.171628	+	0.452547i	−0.821410	+	0.570338i	$0.806812\pi$
$182$	27.4046	−	12.2746i	2.03136	−	0.909853i
$183$	2.19845	−	5.79683i	0.162514	−	0.428514i
$184$	2.51976	+	20.7521i	0.185759	+	1.52987i
$185$	10.9185	−	28.7896i	0.802742	−	2.11666i
$186$	−2.09798	−	17.2784i	−0.153831	−	1.26691i
$187$	1.50679	+	2.18296i	0.110187	+	0.159634i
$188$	38.0783			2.77714
$189$	−1.85754	+	2.69111i	−0.135116	+	0.195750i
$190$	−0.795534	+	6.55181i	−0.0577141	+	0.475318i
$191$	14.9054			1.07852			0.539259	−	0.842140i	$-0.318704\pi$
$191$	14.9054			1.07852			0.539259	+	0.842140i	$0.318704\pi$
$192$	0.148553			0.0107209
$193$	−0.782273	+	6.44260i	−0.0563093	+	0.463748i	0.937094	+	0.349077i	$0.113505\pi$
$193$	−0.782273	+	6.44260i	−0.0563093	+	0.463748i	−0.993403	+	0.114672i	$0.963418\pi$
$194$	22.7550	−	20.1592i	1.63372	−	1.44735i
$195$	−8.12317	+	10.3302i	−0.581713	+	0.739758i
$196$	−12.4009	−	10.9863i	−0.885780	−	0.784732i
$197$	4.30607	−	3.81485i	0.306795	−	0.271797i	−0.495650	−	0.868522i	$-0.665070\pi$
$197$	4.30607	−	3.81485i	0.306795	−	0.271797i	0.802446	+	0.596725i	$0.203532\pi$
$198$	1.63613	+	0.858707i	0.116275	+	0.0610256i
$199$	6.04530	−	15.9401i	0.428540	−	1.12997i	−0.530746	−	0.847531i	$-0.678088\pi$
$199$	6.04530	−	15.9401i	0.428540	−	1.12997i	0.959286	−	0.282436i	$-0.0911425\pi$
$200$	39.2740	+	34.7937i	2.77709	+	2.46029i
$201$	0.926786	−	0.821060i	0.0653704	−	0.0579131i
$202$	−42.8016	+	10.5496i	−3.01151	+	0.742270i
$203$	11.7798	−	31.0607i	0.826778	−	2.18004i
$204$	14.5249	−	7.62328i	1.01695	−	0.533736i
$205$	2.50788	+	20.6542i	0.175158	+	1.44255i
$206$	9.43254	+	8.35650i	0.657196	+	0.582225i
$207$	−2.92257	−	1.53388i	−0.203132	−	0.106612i
$208$	−23.5516	+	10.5488i	−1.63301	+	0.731430i
$209$	0.456729	−	0.239710i	0.0315926	−	0.0165811i
$210$	29.4726	+	7.26435i	2.03380	+	0.501288i
$211$	6.63556	−	9.61327i	0.456811	−	0.661805i	−0.525123	−	0.851026i	$-0.675981\pi$
$211$	6.63556	−	9.61327i	0.456811	−	0.661805i	0.981935	+	0.189221i	$0.0605962\pi$
$212$	−37.3804	+	33.1162i	−2.56730	+	2.27443i
$213$	13.0290	+	6.83813i	0.892730	+	0.468541i
$214$	4.68144	−	38.5552i	0.320017	−	2.63558i
$215$	20.6107	+	10.8173i	1.40564	+	0.737737i
$216$	3.59783	−	5.21236i	0.244801	−	0.354656i
$217$	−12.6942	+	18.3908i	−0.861740	+	1.24845i
$218$	−18.8769	+	4.65273i	−1.27850	+	0.315122i
$219$	−9.42580	+	2.32325i	−0.636936	+	0.156991i
$220$	1.43008	−	11.7777i	0.0964157	−	0.794055i
$221$	8.14837	−	10.3622i	0.548119	−	0.697036i
$222$	2.59345	+	21.3590i	0.174061	+	1.43352i
$223$	1.24352	+	3.27889i	0.0832722	+	0.219571i	0.970185	−	0.242367i	$-0.0779237\pi$
$223$	1.24352	+	3.27889i	0.0832722	+	0.219571i	−0.886913	+	0.461937i	$0.847154\pi$
$224$	13.6137	+	12.0607i	0.909603	+	0.805838i
$225$	−8.04373	+	1.98260i	−0.536249	+	0.132173i
$226$	13.3260	+	3.28456i	0.886432	+	0.218486i
$227$	6.83202	+	9.89788i	0.453457	+	0.656946i	0.981320	−	0.192384i	$-0.0616219\pi$
$227$	6.83202	+	9.89788i	0.453457	+	0.656946i	−0.527863	+	0.849330i	$0.677007\pi$
$228$	−1.13117	−	2.98266i	−0.0749138	−	0.197532i
$229$	−8.27182	+	7.32820i	−0.546617	+	0.484261i	−0.890645	−	0.454699i	$-0.849747\pi$
$229$	−8.27182	+	7.32820i	−0.546617	+	0.484261i	0.344028	+	0.938959i	$0.388209\pi$
$230$	−3.69319	+	30.4162i	−0.243522	+	2.00558i
$231$	−0.841245	−	2.21818i	−0.0553499	−	0.145946i
$232$	−22.8160	+	60.1609i	−1.49794	+	3.94975i
$233$	2.73799	−	0.674853i	0.179371	−	0.0442111i	−0.148607	−	0.988896i	$-0.547479\pi$
$233$	2.73799	−	0.674853i	0.179371	−	0.0442111i	0.327978	+	0.944685i	$0.393633\pi$
$234$	1.67152	−	9.02960i	0.109271	−	0.590283i
$235$	30.0339	+	7.40270i	1.95920	+	0.482899i
$236$	−7.57221	+	10.9702i	−0.492909	+	0.714102i
$237$	8.86592	−	7.85452i	0.575903	−	0.510206i
$238$	−29.5640	−	7.28688i	−1.91635	−	0.472338i
$239$	−6.18497			−0.400073			−0.200036	−	0.979788i	$-0.564106\pi$
$239$	−6.18497			−0.400073			−0.200036	+	0.979788i	$0.564106\pi$
$240$	−25.3289	−	6.24301i	−1.63497	−	0.402985i
$241$	−0.137415	+	0.362334i	−0.00885169	+	0.0233400i	−0.939369	−	0.342907i	$-0.888588\pi$
$241$	−0.137415	+	0.362334i	−0.00885169	+	0.0233400i	0.930518	+	0.366247i	$0.119358\pi$
$242$	23.6199	−	12.3967i	1.51835	−	0.796889i
$243$	0.354605	+	0.935016i	0.0227479	+	0.0599813i
$244$	24.6303	−	12.9270i	1.57679	−	0.827564i
$245$	−7.64531	−	11.0761i	−0.488441	−	0.707629i
$246$	−8.25897	−	11.9652i	−0.526573	−	0.762872i
$247$	−1.80937	−	1.81589i	−0.115128	−	0.115543i
$248$	24.5872	−	35.6207i	1.56129	−	2.26192i
$249$	−2.76382			−0.175150
$250$	17.3200	+	25.0923i	1.09541	+	1.58698i
$251$	1.09793	+	0.972677i	0.0693004	+	0.0613948i	0.697062	−	0.717011i	$-0.254490\pi$
$251$	1.09793	+	0.972677i	0.0693004	+	0.0613948i	−0.627762	+	0.778406i	$0.716029\pi$
$252$	−14.2451	+	3.51109i	−0.897354	+	0.221178i
$253$	2.12032	−	1.11283i	0.133303	−	0.0699630i
$254$	1.63406	−	0.857618i	0.102530	−	0.0538118i
$255$	12.9384	−	3.18904i	0.810237	−	0.199705i
$256$	21.7059	+	19.2297i	1.35662	+	1.20186i
$257$	−3.59816	−	5.21283i	−0.224447	−	0.325168i	0.694541	−	0.719453i	$-0.255607\pi$
$257$	−3.59816	−	5.21283i	−0.224447	−	0.325168i	−0.918988	+	0.394286i	$0.870992\pi$
$258$	−16.2655			−1.01265
$259$	15.6922	−	22.7341i	0.975065	−	1.41263i
$260$	−58.0155	+	10.5240i	−3.59797	+	0.652668i
$261$	−5.77098	−	8.36071i	−0.357215	−	0.517515i
$262$	−8.75002	−	12.6766i	−0.540578	−	0.783163i
$263$	1.38793	−	0.728442i	0.0855834	−	0.0449176i	−0.421388	−	0.906880i	$-0.638457\pi$
$263$	1.38793	−	0.728442i	0.0855834	−	0.0449176i	0.506972	+	0.861963i	$0.330765\pi$
$264$	1.62939	+	4.29635i	0.100282	+	0.264422i
$265$	−35.9215	+	18.8531i	−2.20664	+	1.15813i
$266$	−2.09968	+	5.53639i	−0.128739	+	0.339458i
$267$	1.16913	+	0.288164i	0.0715496	+	0.0176354i
$268$	5.55535			0.339347
$269$	−8.60939	−	2.12202i	−0.524924	−	0.129382i	−0.0320555	−	0.999486i	$-0.510205\pi$
$269$	−8.60939	−	2.12202i	−0.524924	−	0.129382i	−0.492868	+	0.870104i	$0.664051\pi$
$270$	6.94837	−	6.15572i	0.422865	−	0.374625i
$271$	8.18997	−	11.8652i	0.497505	−	0.720761i	−0.491131	−	0.871085i	$-0.663417\pi$
$271$	8.18997	−	11.8652i	0.497505	−	0.720761i	0.988637	+	0.150325i	$0.0480319\pi$
$272$	25.4075	+	6.26238i	1.54055	+	0.379712i
$273$	−9.29392	+	7.25439i	−0.562493	+	0.439056i
$274$	37.2109	−	9.17165i	2.24799	−	0.554080i
$275$	2.13131	−	5.61980i	0.128523	−	0.338887i
$276$	−5.25137	−	13.8467i	−0.316095	−	0.833475i
$277$	3.44479	−	28.3704i	0.206977	−	1.70461i	−0.405477	−	0.914105i	$-0.632894\pi$
$277$	3.44479	−	28.3704i	0.206977	−	1.70461i	0.612454	−	0.790506i	$-0.290182\pi$
$278$	−38.6761	+	34.2640i	−2.31964	+	2.05502i
$279$	2.42333	+	6.38980i	0.145081	+	0.382547i
$280$	42.8798	+	62.1222i	2.56256	+	3.71251i
$281$	−29.9984	−	7.39395i	−1.78956	−	0.441086i	−0.801866	−	0.597504i	$-0.796159\pi$
$281$	−29.9984	−	7.39395i	−1.78956	−	0.441086i	−0.987691	+	0.156418i	$0.950005\pi$
$282$	−20.9871	+	5.17286i	−1.24977	+	0.308040i
$283$	10.6218	+	9.41011i	0.631402	+	0.559373i	0.916955	−	0.398990i	$-0.130639\pi$
$283$	10.6218	+	9.41011i	0.631402	+	0.559373i	−0.285554	+	0.958363i	$0.592178\pi$
$284$	23.4109	+	61.7295i	1.38918	+	3.66297i
$285$	−0.312353	−	2.57246i	−0.0185022	−	0.152379i
$286$	4.70246	+	4.71940i	0.278062	+	0.279064i
$287$	−2.24996	+	18.5301i	−0.132811	+	1.09380i
$288$	5.40046	−	1.33109i	0.318225	−	0.0784354i
$289$	3.52744	−	0.869435i	0.207496	−	0.0511432i
$290$	−53.5716	+	77.6119i	−3.14584	+	4.55753i
$291$	−6.78053	+	9.82330i	−0.397482	+	0.575852i
$292$	−38.5676	−	20.2418i	−2.25700	−	1.18456i
$293$	3.83531	−	31.5866i	0.224061	−	1.84531i	−0.254271	−	0.967133i	$-0.581836\pi$
$293$	3.83531	−	31.5866i	0.224061	−	1.84531i	0.478333	−	0.878179i	$-0.341241\pi$
$294$	8.32732	+	4.37051i	0.485659	+	0.254894i
$295$	−8.10521	+	7.18059i	−0.471904	+	0.418070i
$296$	−30.3939	+	44.0331i	−1.76661	+	2.55937i
$297$	−0.704418	−	0.173623i	−0.0408745	−	0.0100747i
$298$	23.0167	−	12.0801i	1.33332	−	0.699781i
$299$	−8.39985	−	8.43011i	−0.485776	−	0.487526i
$300$	−32.9126	−	17.2739i	−1.90021	−	0.997306i
$301$	15.6312	+	13.8481i	0.900969	+	0.798188i
$302$	−3.37853	−	27.8247i	−0.194413	−	1.60113i
$303$	15.3257	−	8.04355i	0.880439	−	0.462090i
$304$	1.80447	−	4.75800i	0.103494	−	0.272890i
$305$	21.9400	−	5.40773i	1.25628	−	0.309646i
$306$	−6.96992	+	6.17481i	−0.398444	+	0.352991i
$307$	−17.9533	−	15.9053i	−1.02465	−	0.907761i	−0.0288746	−	0.999583i	$-0.509192\pi$
$307$	−17.9533	−	15.9053i	−1.02465	−	0.907761i	−0.995775	+	0.0918224i	$0.970731\pi$
$308$	3.77444	−	9.95239i	0.215069	−	0.567090i
$309$	−4.38111	−	2.29939i	−0.249233	−	0.130808i
$310$	47.4844	−	42.0675i	2.69693	−	2.38928i
$311$	−13.4912	−	11.9521i	−0.765014	−	0.677743i	0.187491	−	0.982266i	$-0.439964\pi$
$311$	−13.4912	−	11.9521i	−0.765014	−	0.677743i	−0.952505	+	0.304523i	$0.901503\pi$
$312$	18.0012	−	14.0509i	1.01912	−	0.795474i
$313$	12.0160	−	10.6453i	0.679186	−	0.601707i	−0.251354	−	0.967895i	$-0.580876\pi$
$313$	12.0160	−	10.6453i	0.679186	−	0.601707i	0.930541	+	0.366189i	$0.119337\pi$
$314$	2.24099	−	18.4562i	0.126466	−	1.04154i
$315$	−11.9182			−0.671517
$316$	53.1442			2.98960
$317$	3.08155	−	25.3788i	0.173077	−	1.42542i	−0.604487	−	0.796615i	$-0.706622\pi$
$317$	3.08155	−	25.3788i	0.173077	−	1.42542i	0.777565	−	0.628803i	$-0.216455\pi$
$318$	16.1037	−	23.3303i	0.903053	−	1.30830i
$319$	7.37037			0.412662
$320$	0.307575	+	0.445599i	0.0171940	+	0.0249097i
$321$	1.83809	+	15.1380i	0.102592	+	0.844923i
$322$	−9.74755	+	25.7022i	−0.543210	+	1.43233i
$323$	0.313322	+	2.58044i	0.0174337	+	0.143579i
$324$	−1.59102	+	4.19517i	−0.0883899	+	0.233065i
$325$	−29.8123	−	1.85711i	−1.65369	−	0.103014i
$326$	8.73516	+	23.0327i	0.483796	+	1.27566i
$327$	6.75912	−	3.54746i	0.373780	−	0.196175i
$328$	4.35790	−	35.8905i	0.240625	−	1.98172i
$329$	24.5728	+	12.8968i	1.35474	+	0.711023i
$330$	0.811786	+	6.68566i	0.0446874	+	0.368034i
$331$	0.187861	+	1.54718i	0.0103258	+	0.0850406i	0.996961	−	0.0779058i	$-0.0248233\pi$
$331$	0.187861	+	1.54718i	0.0103258	+	0.0850406i	−0.986635	+	0.162946i	$0.947900\pi$
$332$	−9.28193	−	8.22307i	−0.509412	−	0.451300i
$333$	−2.99564	−	7.89886i	−0.164160	−	0.432855i
$334$	19.4323	+	28.1525i	1.06329	+	1.54044i
$335$	4.38174	+	1.08000i	0.239400	+	0.0590068i
$336$	−20.7233	−	10.8764i	−1.13055	−	0.593357i
$337$	−23.0370			−1.25490			−0.627452	−	0.778655i	$-0.715902\pi$
$337$	−23.0370			−1.25490			−0.627452	+	0.778655i	$0.715902\pi$
$338$	15.4922	−	29.2617i	0.842665	−	1.59163i
$339$	−5.38882			−0.292680
$340$	52.9403	+	27.7852i	2.87109	+	1.50686i
$341$	−4.81392	−	1.18652i	−0.260688	−	0.0642539i
$342$	1.02864	+	1.49025i	0.0556227	+	0.0805834i
$343$	3.83513	+	10.1124i	0.207077	+	0.546018i
$344$	−30.2758	−	26.8220i	−1.63236	−	1.44615i
$345$	−1.45007	−	11.9424i	−0.0780691	−	0.642957i
$346$	−5.46902	−	45.0414i	−0.294016	−	2.42144i
$347$	16.9803	+	8.91197i	0.911552	+	0.478420i	0.854206	−	0.519935i	$-0.174044\pi$
$347$	16.9803	+	8.91197i	0.911552	+	0.478420i	0.0573464	+	0.998354i	$0.481736\pi$
$348$	5.49417	−	45.2485i	0.294518	−	2.42558i
$349$	18.2033	−	9.55385i	0.974402	−	0.511406i	0.0991501	−	0.995072i	$-0.468388\pi$
$349$	18.2033	−	9.55385i	0.974402	−	0.511406i	0.875252	+	0.483667i	$0.160695\pi$
$350$	24.4660	+	64.5115i	1.30776	+	3.44828i
$351$	0.211226	+	3.59936i	0.0112744	+	0.192120i
$352$	−1.43093	+	3.77306i	−0.0762690	+	0.201105i
$353$	1.89524	+	15.6087i	0.100874	+	0.830768i	0.952061	+	0.305907i	$0.0989597\pi$
$353$	1.89524	+	15.6087i	0.100874	+	0.830768i	−0.851188	+	0.524861i	$0.824117\pi$
$354$	2.68319	−	7.07500i	0.142610	−	0.376032i
$355$	6.46449	+	53.2398i	0.343099	+	2.82568i
$356$	3.06901	+	4.44622i	0.162657	+	0.235649i
$357$	11.9552			0.632737
$358$	15.2436	−	22.0842i	0.805650	−	1.16719i
$359$	3.45971	−	28.4932i	0.182596	−	1.50382i	−0.556857	−	0.830608i	$-0.687993\pi$
$359$	3.45971	−	28.4932i	0.182596	−	1.50382i	0.739454	−	0.673207i	$-0.235084\pi$
$360$	23.0842			1.21664
$361$	−18.4945			−0.973396
$362$	1.99901	−	16.4634i	0.105066	−	0.865295i
$363$	−7.83964	+	6.94531i	−0.411474	+	0.364534i
$364$	−52.7961	−	3.28886i	−2.76727	−	0.172383i
$365$	−26.4847	−	23.4634i	−1.38627	−	1.22813i
$366$	−11.8191	+	10.4708i	−0.617792	+	0.547316i
$367$	9.00648	+	4.72697i	0.470135	+	0.246746i	0.683115	−	0.730311i	$-0.260625\pi$
$367$	9.00648	+	4.72697i	0.470135	+	0.246746i	−0.212980	+	0.977056i	$0.568317\pi$
$368$	8.37709	−	22.0886i	0.436686	−	1.15145i
$369$	4.27280	+	3.78537i	0.222433	+	0.197059i
$370$	−58.6987	+	52.0025i	−3.05160	+	2.70348i
$371$	−35.3386	+	8.71018i	−1.83469	+	0.452210i
$372$	−10.8728	+	28.6693i	−0.563731	+	1.48644i
$373$	4.38560	−	2.30174i	0.227078	−	0.119180i	−0.347348	−	0.937736i	$-0.612918\pi$
$373$	4.38560	−	2.30174i	0.227078	−	0.119180i	0.574426	+	0.818557i	$0.305225\pi$
$374$	−0.814304	−	6.70640i	−0.0421067	−	0.346780i
$375$	−8.96055	−	7.93835i	−0.462721	−	0.409935i
$376$	−47.5945	−	24.9795i	−2.45450	−	1.28822i
$377$	−10.8343	−	34.9899i	−0.557995	−	1.80207i
$378$	7.37430	−	3.87033i	0.379293	−	0.199068i
$379$	11.6033	+	2.85995i	0.596021	+	0.146906i	0.525775	−	0.850624i	$-0.323775\pi$
$379$	11.6033	+	2.85995i	0.596021	+	0.146906i	0.0702461	+	0.997530i	$0.477622\pi$
$380$	6.60472	−	9.56859i	0.338815	−	0.490858i
$381$	−0.542356	+	0.480486i	−0.0277858	+	0.0246160i
$382$	−33.6143	−	17.6422i	−1.71986	−	0.902651i
$383$	0.155510	−	1.28074i	0.00794619	−	0.0654428i	−0.988196	−	0.153193i	$-0.951045\pi$
$383$	0.155510	−	1.28074i	0.00794619	−	0.0654428i	0.996143	+	0.0877498i	$0.0279676\pi$
$384$	−10.1850	−	5.34549i	−0.519750	−	0.272786i
$385$	4.91188	−	7.11608i	0.250333	−	0.362669i
$386$	9.38967	−	13.6033i	0.477921	−	0.692389i
$387$	6.20080	−	1.52836i	0.315204	−	0.0776909i
$388$	−51.9984	+	12.8164i	−2.63982	+	0.650657i
$389$	−0.225561	+	1.85766i	−0.0114364	+	0.0941873i	−0.997309	−	0.0733073i	$-0.976645\pi$
$389$	−0.225561	+	1.85766i	−0.0114364	+	0.0941873i	0.985873	+	0.167495i	$0.0535677\pi$
$390$	30.5460	−	13.6817i	1.54676	−	0.692797i
$391$	1.45457	+	11.9794i	0.0735606	+	0.605826i
$392$	8.29302	+	21.8669i	0.418861	+	1.10444i
$393$	4.52685	+	4.01044i	0.228350	+	0.202300i
$394$	−14.2262	+	3.50645i	−0.716707	+	0.176652i
$395$	41.9171	+	10.3316i	2.10908	+	0.519841i
$396$	−1.84912	−	2.67892i	−0.0929219	−	0.134621i
$397$	−6.11963	−	16.1361i	−0.307135	−	0.809849i	−0.996356	−	0.0852972i	$-0.972816\pi$
$397$	−6.11963	−	16.1361i	−0.307135	−	0.809849i	0.689220	−	0.724552i	$-0.257953\pi$
$398$	−32.5001	+	28.7925i	−1.62908	+	1.44324i
$399$	0.280229	−	2.30790i	0.0140290	−	0.115539i
$400$	−21.0262	−	55.4415i	−1.05131	−	2.77207i
$401$	2.52954	−	6.66985i	0.126319	−	0.333076i	−0.856906	−	0.515473i	$-0.827616\pi$
$401$	2.52954	−	6.66985i	0.126319	−	0.333076i	0.983225	+	0.182397i	$0.0583855\pi$
$402$	−3.06188	+	0.754685i	−0.152712	+	0.0376402i
$403$	1.44350	+	24.5976i	0.0719058	+	1.22530i
$404$	75.4010	+	18.5847i	3.75134	+	0.924622i
$405$	−2.07047	+	2.99960i	−0.102883	+	0.149051i
$406$	−63.3291	+	56.1047i	−3.14297	+	2.78443i
$407$	5.95081	+	1.46674i	0.294970	+	0.0727037i
$408$	−23.1558			−1.14638
$409$	25.4783	+	6.27985i	1.25982	+	0.310518i	0.812028	−	0.583618i	$-0.198363\pi$
$409$	25.4783	+	6.27985i	1.25982	+	0.310518i	0.447795	+	0.894136i	$0.352210\pi$
$410$	18.7908	−	49.5472i	0.928010	−	2.44696i
$411$	−13.3239	+	6.99291i	−0.657218	+	0.344935i
$412$	−7.87214	−	20.7571i	−0.387833	−	1.02263i
$413$	−8.60205	+	4.51470i	−0.423279	+	0.222154i
$414$	4.77538	+	6.91834i	0.234697	+	0.340018i
$415$	−5.72242	−	8.29035i	−0.280902	−	0.406957i
$416$	20.0156	+	1.24684i	0.981344	+	0.0611315i
$417$	11.5247	−	16.6964i	0.564366	−	0.817626i
$418$	−1.31373			−0.0642564
$419$	−21.9375	−	31.7820i	−1.07172	−	1.55265i	−0.809026	−	0.587773i	$-0.800005\pi$
$419$	−21.9375	−	31.7820i	−1.07172	−	1.55265i	−0.262693	−	0.964880i	$-0.584610\pi$
$420$	−40.0259	−	35.4598i	−1.95306	−	1.73026i
$421$	−6.21702	+	1.53236i	−0.302999	+	0.0746825i	−0.387884	−	0.921708i	$-0.626794\pi$
$421$	−6.21702	+	1.53236i	−0.302999	+	0.0746825i	0.0848851	+	0.996391i	$0.472948\pi$
$422$	−26.3427	+	13.8257i	−1.28234	+	0.673025i
$423$	7.51474	−	3.94404i	0.365379	−	0.191766i
$424$	68.4466	−	16.8706i	3.32406	−	0.819307i
$425$	22.6715	+	20.0852i	1.09973	+	0.974273i
$426$	−21.2889	−	30.8423i	−1.03145	−	1.49432i
$427$	20.2727			0.981066
$428$	−38.8665	+	56.3079i	−1.87869	+	2.72175i
$429$	−2.23614	−	1.35729i	−0.107962	−	0.0655305i
$430$	−33.6773	−	48.7900i	−1.62406	−	2.35286i
$431$	19.6705	+	28.4977i	0.947495	+	1.37268i	0.927881	+	0.372877i	$0.121629\pi$
$431$	19.6705	+	28.4977i	0.947495	+	1.37268i	0.0196145	+	0.999808i	$0.493756\pi$
$432$	−6.33750	+	3.32618i	−0.304913	+	0.160031i
$433$	0.755734	+	1.99271i	0.0363182	+	0.0957633i	0.951949	−	0.306258i	$-0.0990770\pi$
$433$	0.755734	+	1.99271i	0.0363182	+	0.0957633i	−0.915630	+	0.402021i	$0.868308\pi$
$434$	50.3951	−	26.4494i	2.41904	−	1.26961i
$435$	13.1301	−	34.6213i	0.629541	−	1.65996i
$436$	33.2542	+	8.19644i	1.59259	+	0.392538i
$437$	2.34667			0.112256
$438$	24.0066	+	5.91710i	1.14708	+	0.282730i
$439$	−2.42324	+	2.14680i	−0.115655	+	0.102461i	−0.718968	−	0.695043i	$-0.755385\pi$
$439$	−2.42324	+	2.14680i	−0.115655	+	0.102461i	0.603313	+	0.797504i	$0.293847\pi$
$440$	−9.51371	+	13.7830i	−0.453548	+	0.657078i
$441$	−3.58524	−	0.883682i	−0.170726	−	0.0420801i
$442$	−30.6408	+	13.7241i	−1.45743	+	0.652788i
$443$	26.0480	−	6.42025i	1.23758	−	0.305035i	0.434369	−	0.900735i	$-0.356971\pi$
$443$	26.0480	−	6.42025i	1.23758	−	0.305035i	0.803207	+	0.595700i	$0.203125\pi$
$444$	13.4407	−	35.4401i	0.637865	−	1.68191i
$445$	1.55627	+	4.10356i	0.0737745	+	0.194527i
$446$	1.07656	−	8.86631i	0.0509768	−	0.419832i
$447$	−7.63943	+	6.76794i	−0.361333	+	0.320113i
$448$	0.172253	+	0.454193i	0.00813818	+	0.0214586i
$449$	9.33541	+	13.5247i	0.440565	+	0.638269i	0.978871	−	0.204481i	$-0.0655507\pi$
$449$	9.33541	+	13.5247i	0.440565	+	0.638269i	−0.538305	+	0.842750i	$0.680935\pi$
$450$	20.4866	+	5.04950i	0.965749	+	0.238036i
$451$	−4.02111	+	0.991114i	−0.189346	+	0.0466697i
$452$	−18.0976	−	16.0331i	−0.851241	−	0.754134i
$453$	3.90248	+	10.2900i	0.183354	+	0.483466i
$454$	−3.69218	−	30.4079i	−0.173283	−	1.42711i
$455$	−41.0031	−	12.8580i	−1.92225	−	0.602792i
$456$	−0.542770	+	4.47012i	−0.0254176	+	0.209332i
$457$	−35.3643	+	8.71651i	−1.65427	+	0.407741i	−0.952470	−	0.304632i	$-0.901467\pi$
$457$	−35.3643	+	8.71651i	−1.65427	+	0.407741i	−0.701801	+	0.712373i	$0.747620\pi$
$458$	27.3281	−	6.73577i	1.27696	−	0.314742i
$459$	2.07690	−	3.00890i	0.0969412	−	0.140444i
$460$	30.6618	−	44.4213i	1.42961	−	2.07115i
$461$	−23.3332	−	12.2462i	−1.08673	−	0.570362i	−0.176435	−	0.984312i	$-0.556457\pi$
$461$	−23.3332	−	12.2462i	−1.08673	−	0.570362i	−0.910300	+	0.413950i	$0.864149\pi$
$462$	−0.728300	+	5.99809i	−0.0338836	+	0.279056i
$463$	−2.14546	−	1.12602i	−0.0997078	−	0.0523307i	0.414132	−	0.910217i	$-0.364085\pi$
$463$	−2.14546	−	1.12602i	−0.0997078	−	0.0523307i	−0.513840	+	0.857886i	$0.671777\pi$
$464$	54.4253	−	48.2166i	2.52663	−	2.23840i
$465$	−14.1494	+	20.4989i	−0.656163	+	0.950616i
$466$	−6.97340	−	1.71879i	−0.323036	−	0.0796213i
$467$	8.09072	−	4.24634i	0.374394	−	0.196497i	−0.267022	−	0.963690i	$-0.586040\pi$
$467$	8.09072	−	4.24634i	0.374394	−	0.196497i	0.641416	+	0.767193i	$0.278347\pi$
$468$	−9.99964	+	12.7164i	−0.462233	+	0.587817i
$469$	3.58500	+	1.88155i	0.165540	+	0.0868820i
$470$	−58.9699	−	52.2427i	−2.72008	−	2.40978i
$471$	0.879885	+	7.24651i	0.0405430	+	0.333901i
$472$	16.6611	−	8.74443i	0.766890	−	0.402495i
$473$	−1.64300	+	4.33222i	−0.0755450	+	0.199196i
$474$	−29.2909	+	7.21955i	−1.34537	+	0.331605i
$475$	4.40876	−	3.90582i	0.202288	−	0.179211i
$476$	40.1500	+	35.5698i	1.84027	+	1.63034i
$477$	−3.94694	+	10.4072i	−0.180718	+	0.476514i
$478$	13.9482	+	7.32058i	0.637976	+	0.334835i
$479$	−5.70827	+	5.05708i	−0.260817	+	0.231064i	−0.783390	−	0.621531i	$-0.786511\pi$
$479$	−5.70827	+	5.05708i	−0.260817	+	0.231064i	0.522572	+	0.852595i	$0.324973\pi$
$480$	15.1743	+	13.4432i	0.692607	+	0.613596i
$481$	−1.78441	−	30.4068i	−0.0813619	−	1.38643i
$482$	0.738756	−	0.654481i	0.0336494	−	0.0298108i
$483$	1.30094	−	10.7142i	0.0591948	−	0.487513i
$484$	−46.9925			−2.13602
$485$	−43.5049			−1.97546
$486$	0.306996	−	2.52834i	0.0139256	−	0.114688i
$487$	4.41871	−	6.40160i	0.200231	−	0.290084i	−0.709987	−	0.704215i	$-0.751299\pi$
$487$	4.41871	−	6.40160i	0.200231	−	0.290084i	0.910217	+	0.414131i	$0.135914\pi$
$488$	−39.2658			−1.77748
$489$	−5.49428	−	7.95984i	−0.248460	−	0.359956i
$490$	4.13171	+	34.0277i	0.186651	+	1.53721i
$491$	−7.78334	+	20.5230i	−0.351257	+	0.926189i	0.636652	+	0.771152i	$0.280319\pi$
$491$	−7.78334	+	20.5230i	−0.351257	+	0.926189i	−0.987909	+	0.155037i	$0.950450\pi$
$492$	3.08720	+	25.4254i	0.139182	+	1.14626i
$493$	−13.1708	+	34.7287i	−0.593185	+	1.56410i
$494$	1.93115	+	6.23674i	0.0868867	+	0.280604i
$495$	−0.937679	−	2.47246i	−0.0421455	−	0.111129i
$496$	−43.3098	+	22.7307i	−1.94467	+	1.02064i
$497$	−5.79966	+	47.7645i	−0.260150	+	2.14253i
$498$	6.23289	+	3.27128i	0.279303	+	0.146589i
$499$	−1.65682	−	13.6452i	−0.0741697	−	0.610842i	−0.981642	−	0.190731i	$-0.938914\pi$
$499$	−1.65682	−	13.6452i	−0.0741697	−	0.610842i	0.907473	−	0.420111i	$-0.138009\pi$
$500$	−6.47420	−	53.3199i	−0.289535	−	2.38454i
$501$	−10.0533	−	8.90649i	−0.449151	−	0.397913i
$502$	−1.32475	−	3.49307i	−0.0591263	−	0.155903i
$503$	16.9523	+	24.5597i	0.755866	+	1.09506i	0.992354	+	0.123427i	$0.0393884\pi$
$503$	16.9523	+	24.5597i	0.755866	+	1.09506i	−0.236487	+	0.971635i	$0.575996\pi$
$504$	20.1084	+	4.95626i	0.895697	+	0.220770i
$505$	55.8589	+	29.3170i	2.48569	+	1.30459i
$506$	−6.09885			−0.271127
$507$	−3.15647	+	12.6110i	−0.140184	+	0.560073i
$508$	−3.25100			−0.144240
$509$	16.3374	+	8.57452i	0.724142	+	0.380059i	0.786166	−	0.618016i	$-0.212063\pi$
$509$	16.3374	+	8.57452i	0.724142	+	0.380059i	−0.0620238	+	0.998075i	$0.519755\pi$
$510$	−32.9530	−	8.12219i	−1.45918	−	0.359657i
$511$	−18.0328	−	26.1250i	−0.797724	−	1.15570i
$512$	−18.0324	−	47.5475i	−0.796926	−	2.10132i
$513$	−0.532172	−	0.471463i	−0.0234960	−	0.0208156i
$514$	1.94453	+	16.0147i	0.0857696	+	0.706376i
$515$	−2.17375	−	17.9024i	−0.0957867	−	0.788874i
$516$	25.3718	+	13.3162i	1.11693	+	0.586212i
$517$	−0.742170	+	6.11232i	−0.0326406	+	0.268820i
$518$	−62.2968	+	32.6959i	−2.73716	+	1.43657i
$519$	6.31716	+	16.6570i	0.277292	+	0.731160i
$520$	79.4180	+	24.9044i	3.48271	+	1.09213i
$521$	4.77019	−	12.5780i	0.208986	−	0.551050i	−0.789007	−	0.614385i	$-0.789404\pi$
$521$	4.77019	−	12.5780i	0.208986	−	0.551050i	0.997992	+	0.0633346i	$0.0201735\pi$
$522$	3.11878	+	25.6854i	0.136505	+	1.12422i
$523$	6.23984	−	16.4531i	0.272849	−	0.719444i	−0.726625	−	0.687034i	$-0.758912\pi$
$523$	6.23984	−	16.4531i	0.272849	−	0.719444i	0.999475	−	0.0324104i	$-0.0103184\pi$
$524$	3.27076	+	26.9371i	0.142884	+	1.17675i
$525$	−15.3887	−	22.2944i	−0.671619	−	0.973008i
$526$	−3.99221			−0.174069
$527$	14.1933	−	20.5625i	0.618269	−	0.895717i
$528$	0.625904	−	5.15478i	0.0272390	−	0.224333i
$529$	−12.1058			−0.526340
$530$	103.324			4.48810
$531$	−0.358108	+	2.94928i	−0.0155405	+	0.127988i
$532$	7.80770	−	6.91702i	0.338507	−	0.299891i
$533$	10.6161	+	17.6328i	0.459836	+	0.763760i
$534$	−2.29552	−	2.03365i	−0.0993367	−	0.0880047i
$535$	−41.6023	+	36.8564i	−1.79863	+	1.59344i
$536$	−6.94370	−	3.64434i	−0.299922	−	0.157411i
$537$	−3.73613	+	9.85136i	−0.161226	+	0.425118i
$538$	16.9040	+	14.9757i	0.728784	+	0.645647i
$539$	2.00521	−	1.77646i	0.0863706	−	0.0765177i
$540$	−15.8780	+	3.91358i	−0.683280	+	0.168413i
$541$	−13.2842	+	35.0275i	−0.571132	+	1.50595i	0.268765	+	0.963206i	$0.413385\pi$
$541$	−13.2842	+	35.0275i	−0.571132	+	1.50595i	−0.839897	+	0.542746i	$0.817385\pi$
$542$	−32.5136	+	17.0644i	−1.39658	+	0.732980i
$543$	0.784879	+	6.46406i	0.0336824	+	0.277399i
$544$	−15.2213	−	13.4849i	−0.652609	−	0.578161i
$545$	24.6356	+	12.9297i	1.05527	+	0.553849i
$546$	29.5457	−	5.35957i	1.26444	−	0.229368i
$547$	−32.4086	+	17.0093i	−1.38569	+	0.727267i	−0.982221	−	0.187726i	$-0.939888\pi$
$547$	−32.4086	+	17.0093i	−1.38569	+	0.727267i	−0.403470	+	0.914993i	$0.632196\pi$
$548$	−65.5522	−	16.1572i	−2.80025	−	0.690200i
$549$	3.52184	−	5.10226i	0.150308	−	0.217759i
$550$	−11.4581	+	10.1510i	−0.488575	+	0.432840i
$551$	6.39548	+	3.35661i	0.272457	+	0.142996i
$552$	−2.51976	+	20.7521i	−0.107248	+	0.883268i
$553$	34.2952	+	17.9995i	1.45838	+	0.765417i
$554$	−41.3480	+	59.9029i	−1.75671	+	2.54503i
$555$	17.4910	−	25.3401i	0.742452	−	1.07563i
$556$	88.3802	−	21.7838i	3.74816	−	0.923837i
$557$	37.5935	−	9.26598i	1.59289	−	0.392612i	0.659566	−	0.751647i	$-0.270740\pi$
$557$	37.5935	−	9.26598i	1.59289	−	0.392612i	0.933324	+	0.359035i	$0.116894\pi$
$558$	2.09798	−	17.2784i	0.0888144	−	0.731452i
$559$	22.9819	+	1.43162i	0.972029	+	0.0605512i
$560$	−10.2821	−	84.6809i	−0.434499	−	3.57842i
$561$	0.940587	+	2.48012i	0.0397116	+	0.104711i
$562$	58.9002	+	52.1810i	2.48455	+	2.20112i
$563$	19.2081	−	4.73438i	0.809527	−	0.199530i	0.187234	−	0.982315i	$-0.440048\pi$
$563$	19.2081	−	4.73438i	0.809527	−	0.199530i	0.622292	+	0.782785i	$0.286201\pi$
$564$	36.9718	+	9.11273i	1.55679	+	0.383715i
$565$	−11.1574	−	16.1643i	−0.469396	−	0.680037i
$566$	−12.8162	−	33.7935i	−0.538704	−	1.42045i
$567$	−2.44759	+	2.16837i	−0.102789	+	0.0910632i
$568$	11.2332	−	92.5140i	0.471336	−	3.88180i
$569$	−5.44006	−	14.3443i	−0.228059	−	0.601343i	0.771325	−	0.636442i	$-0.219594\pi$
$569$	−5.44006	−	14.3443i	−0.228059	−	0.601343i	−0.999384	+	0.0350993i	$0.988825\pi$
$570$	−2.34037	+	6.17104i	−0.0980272	+	0.258476i
$571$	1.58742	−	0.391263i	0.0664314	−	0.0163739i	−0.205960	−	0.978560i	$-0.566032\pi$
$571$	1.58742	−	0.391263i	0.0664314	−	0.0163739i	0.272391	+	0.962187i	$0.412185\pi$
$572$	−3.47150	−	11.2114i	−0.145151	−	0.468771i
$573$	14.4723	+	3.56710i	0.604589	+	0.149018i
$574$	27.0064	−	39.1255i	1.12722	−	1.63307i
$575$	20.4673	−	18.1324i	0.853544	−	0.756174i
$576$	0.144236	+	0.0355510i	0.00600984	+	0.00148129i
$577$	6.17822			0.257202			0.128601	−	0.991696i	$-0.458951\pi$
$577$	6.17822			0.257202			0.128601	+	0.991696i	$0.458951\pi$
$578$	−8.98405	−	2.21437i	−0.373687	−	0.0921056i
$579$	−2.30136	+	6.06818i	−0.0956411	+	0.252185i
$580$	147.103	−	77.2056i	6.10812	−	3.20579i
$581$	−3.20475	−	8.45024i	−0.132956	−	0.350575i
$582$	26.9182	−	14.1278i	1.11580	−	0.585615i
$583$	−4.58723	−	6.64576i	−0.189984	−	0.275239i
$584$	34.9274	+	50.6010i	1.44530	+	2.09388i
$585$	−10.3593	+	8.08597i	−0.428304	+	0.334314i
$586$	−46.0355	+	66.6939i	−1.90171	+	2.75510i
$587$	29.5012			1.21765			0.608823	−	0.793306i	$-0.291642\pi$
$587$	29.5012			1.21765			0.608823	+	0.793306i	$0.291642\pi$
$588$	−9.41138	−	13.6347i	−0.388119	−	0.562287i
$589$	−3.63681	−	3.22193i	−0.149852	−	0.132757i
$590$	26.7777	−	6.60010i	1.10242	−	0.271722i
$591$	5.09390	−	2.67349i	0.209535	−	0.109972i
$592$	53.5381	−	28.0990i	2.20040	−	1.15486i
$593$	−24.5335	+	6.04697i	−1.00747	+	0.248319i	−0.708324	−	0.705888i	$-0.750548\pi$
$593$	−24.5335	+	6.04697i	−1.00747	+	0.248319i	−0.299147	+	0.954207i	$0.596702\pi$
$594$	1.38308	+	1.22531i	0.0567486	+	0.0502749i
$595$	24.7530	+	35.8609i	1.01477	+	1.47015i
$596$	−45.7924			−1.87573
$597$	9.68436	−	14.0302i	0.396354	−	0.574219i
$598$	8.96519	+	28.9535i	0.366614	+	1.18400i
$599$	18.7912	+	27.2238i	0.767788	+	1.11233i	0.990509	+	0.137451i	$0.0438909\pi$
$599$	18.7912	+	27.2238i	0.767788	+	1.11233i	−0.222721	+	0.974882i	$0.571494\pi$
$600$	29.8061	+	43.1816i	1.21683	+	1.76288i
$601$	11.3221	−	5.94230i	0.461839	−	0.242392i	−0.217722	−	0.976011i	$-0.569863\pi$
$601$	11.3221	−	5.94230i	0.461839	−	0.242392i	0.679561	+	0.733619i	$0.262170\pi$
$602$	−18.8605	−	49.7310i	−0.768696	−	2.02688i
$603$	1.09635	−	0.575408i	0.0446467	−	0.0234324i
$604$	−17.5094	+	46.1685i	−0.712447	+	1.87857i
$605$	−37.0649	−	9.13569i	−1.50690	−	0.371418i
$606$	−44.0825			−1.79073
$607$	−26.3181	−	6.48683i	−1.06822	−	0.263292i	−0.334256	−	0.942482i	$-0.608485\pi$
$607$	−26.3181	−	6.48683i	−1.06822	−	0.263292i	−0.733963	+	0.679190i	$0.762331\pi$
$608$	−2.95999	+	2.62232i	−0.120043	+	0.106349i
$609$	18.8708	−	27.3391i	0.764683	−	1.10784i
$610$	−55.8792	−	13.7730i	−2.26248	−	0.557652i
$611$	30.1084	−	5.46164i	1.21806	−	0.220954i
$612$	15.9272	−	3.92571i	0.643821	−	0.158688i
$613$	9.10976	−	24.0205i	0.367940	−	0.970177i	−0.615370	−	0.788238i	$-0.710993\pi$
$613$	9.10976	−	24.0205i	0.367940	−	0.970177i	0.983310	−	0.181939i	$-0.0582373\pi$
$614$	21.6623	+	57.1188i	0.874219	+	2.30513i
$615$	−2.50788	+	20.6542i	−0.101127	+	0.832859i
$616$	−11.2465	+	9.96356i	−0.453136	+	0.401443i
$617$	−9.82380	−	25.9032i	−0.395491	−	1.04282i	−0.973880	−	0.227064i	$-0.927087\pi$
$617$	−9.82380	−	25.9032i	−0.395491	−	1.04282i	0.578389	−	0.815761i	$-0.303682\pi$
$618$	7.15861	+	10.3710i	0.287961	+	0.417184i
$619$	8.35069	+	2.05826i	0.335642	+	0.0827284i	0.403535	−	0.914964i	$-0.367781\pi$
$619$	8.35069	+	2.05826i	0.335642	+	0.0827284i	−0.0678925	+	0.997693i	$0.521628\pi$
$620$	−108.509	+	26.7449i	−4.35781	+	1.07410i
$621$	−2.47056	−	2.18872i	−0.0991401	−	0.0878305i
$622$	16.2783	+	42.9224i	0.652701	+	1.72103i
$623$	0.474601	+	3.90869i	0.0190145	+	0.156599i
$624$	−25.3917	+	4.60604i	−1.01648	+	0.184389i
$625$	0.266388	−	2.19391i	0.0106555	−	0.0877563i
$626$	−39.6981	+	9.78470i	−1.58665	+	0.391075i
$627$	0.500824	−	0.123442i	0.0200010	−	0.00492979i
$628$	−18.6052	+	26.9543i	−0.742430	+	1.07560i
$629$	−17.5453	+	25.4187i	−0.699575	+	1.01351i
$630$	26.8777	+	14.1065i	1.07083	+	0.562017i
$631$	−0.0602121	+	0.495892i	−0.00239701	+	0.0197411i	−0.993858	−	0.110660i	$-0.964703\pi$
$631$	−0.0602121	+	0.495892i	−0.00239701	+	0.0197411i	0.991461	+	0.130401i	$0.0416266\pi$
$632$	−66.4256	−	34.8628i	−2.64227	−	1.38677i
$633$	8.74335	−	7.74594i	0.347517	−	0.307873i
$634$	−36.9880	+	53.5864i	−1.46898	+	2.12819i
$635$	−2.56420	−	0.632019i	−0.101757	−	0.0250809i
$636$	−44.2194	+	23.2082i	−1.75342	+	0.920263i
$637$	−11.3812	−	6.90812i	−0.450938	−	0.273710i
$638$	−16.6215	−	8.72362i	−0.658050	−	0.345371i
$639$	11.0139	+	9.75746i	0.435703	+	0.385999i
$640$	−5.05340	−	41.6185i	−0.199753	−	1.64512i
$641$	−37.1176	+	19.4808i	−1.46606	+	0.769447i	−0.993712	−	0.111966i	$-0.964285\pi$
$641$	−37.1176	+	19.4808i	−1.46606	+	0.769447i	−0.472347	+	0.881413i	$0.656593\pi$
$642$	13.7723	−	36.3145i	0.543548	−	1.43322i
$643$	−15.8332	+	3.90252i	−0.624398	+	0.153900i	−0.538806	−	0.842430i	$-0.681124\pi$
$643$	−15.8332	+	3.90252i	−0.624398	+	0.153900i	−0.0855924	+	0.996330i	$0.527278\pi$
$644$	36.2465	−	32.1116i	1.42831	−	1.26537i
$645$	17.4231	+	15.4355i	0.686032	+	0.607772i
$646$	2.34763	−	6.19018i	0.0923661	−	0.243549i
$647$	7.71973	+	4.05163i	0.303494	+	0.159286i	0.609595	−	0.792713i	$-0.291332\pi$
$647$	7.71973	+	4.05163i	0.303494	+	0.159286i	−0.306101	+	0.951999i	$0.599024\pi$
$648$	4.74068	−	4.19988i	0.186232	−	0.164987i
$649$	−1.61335	−	1.42931i	−0.0633297	−	0.0561052i
$650$	65.0338	+	39.4741i	2.55083	+	1.54830i
$651$	−16.7266	+	14.8184i	−0.655565	+	0.580780i
$652$	5.23073	−	43.0790i	0.204851	−	1.68710i
$653$	−29.6688			−1.16103			−0.580516	−	0.814249i	$-0.697149\pi$
$653$	−29.6688			−1.16103			−0.580516	+	0.814249i	$0.697149\pi$
$654$	−19.4418			−0.760235
$655$	−2.65699	+	21.8823i	−0.103817	+	0.855011i
$656$	−23.2094	+	33.6246i	−0.906175	+	1.31282i
$657$	−9.70789			−0.378741
$658$	−40.1512	−	58.1690i	−1.56526	−	2.26766i
$659$	−0.0833527	−	0.686472i	−0.00324696	−	0.0267411i	0.990995	−	0.133896i	$-0.0427489\pi$
$659$	−0.0833527	−	0.686472i	−0.00324696	−	0.0267411i	−0.994242	+	0.107155i	$0.965826\pi$
$660$	4.20712	−	11.0933i	0.163762	−	0.431804i
$661$	0.0620149	+	0.510739i	0.00241210	+	0.0198654i	0.993865	−	0.110598i	$-0.0352766\pi$
$661$	0.0620149	+	0.510739i	0.00241210	+	0.0198654i	−0.991453	+	0.130463i	$0.958354\pi$
$662$	1.40759	−	3.71151i	0.0547076	−	0.144252i
$663$	10.3914	−	8.11105i	0.403570	−	0.315007i
$664$	6.20722	+	16.3671i	0.240887	+	0.635167i
$665$	7.50298	−	3.93787i	0.290953	−	0.152704i
$666$	−2.59345	+	21.3590i	−0.100494	+	0.827643i
$667$	29.6904	+	15.5827i	1.14962	+	0.603366i
$668$	−7.26378	−	59.8226i	−0.281044	−	2.31461i
$669$	0.422695	+	3.48121i	0.0163423	+	0.134591i
$670$	−8.60329	−	7.62185i	−0.332374	−	0.294458i
$671$	1.59497	+	4.20560i	0.0615733	+	0.162355i
$672$	10.3318	+	14.9682i	0.398558	+	0.577410i
$673$	42.0330	+	10.3602i	1.62025	+	0.399356i	0.942038	−	0.335507i	$-0.108908\pi$
$673$	42.0330	+	10.3602i	1.62025	+	0.399356i	0.678215	+	0.734864i	$0.262754\pi$
$674$	51.9524	+	27.2667i	2.00113	+	1.05027i
$675$	−8.28446			−0.318869
$676$	−48.1215	+	32.9610i	−1.85083	+	1.26773i
$677$	−16.0717			−0.617685			−0.308842	−	0.951113i	$-0.599942\pi$
$677$	−16.0717			−0.617685			−0.308842	+	0.951113i	$0.599942\pi$
$678$	12.1527	+	6.37824i	0.466722	+	0.244955i
$679$	−37.8965	−	9.34066i	−1.45434	−	0.358462i
$680$	−47.9435	−	69.4581i	−1.83855	−	2.66360i
$681$	4.26477	+	11.2453i	0.163426	+	0.430920i
$682$	9.45185	+	8.37360i	0.361930	+	0.320642i
$683$	−2.92999	−	24.1306i	−0.112113	−	0.923332i	−0.934883	−	0.354957i	$-0.884495\pi$
$683$	−2.92999	−	24.1306i	−0.112113	−	0.923332i	0.822770	−	0.568375i	$-0.192428\pi$
$684$	−0.384507	−	3.16670i	−0.0147020	−	0.121082i
$685$	−48.5627	−	25.4876i	−1.85548	−	0.973833i
$686$	3.32022	−	27.3445i	0.126767	−	1.04402i
$687$	−9.78521	+	5.13567i	−0.373329	+	0.195938i
$688$	16.2088	+	42.7390i	0.617954	+	1.62941i
$689$	−24.8067	+	31.5464i	−0.945061	+	1.20182i
$690$	−10.8649	+	28.6485i	−0.413621	+	1.09063i
$691$	−1.21714	−	10.0241i	−0.0463023	−	0.381334i	−0.997378	−	0.0723744i	$-0.976942\pi$
$691$	−1.21714	−	10.0241i	−0.0463023	−	0.381334i	0.951075	−	0.308959i	$-0.0999807\pi$
$692$	−28.3434	+	74.7354i	−1.07746	+	2.84102i
$693$	−0.285955	−	2.35505i	−0.0108625	−	0.0894609i
$694$	−27.7454	−	40.1961i	−1.05320	−	1.52582i
$695$	73.9440			2.80486
$696$	−36.5504	+	52.9525i	−1.38544	+	2.00716i
$697$	2.51565	−	20.7183i	0.0952872	−	0.784761i
$698$	−52.3597			−1.98184
$699$	2.81993			0.106659
$700$	14.6506	−	120.658i	0.553740	−	4.56046i
$701$	6.95316	−	6.15997i	0.262617	−	0.232659i	−0.521531	−	0.853233i	$-0.674639\pi$
$701$	6.95316	−	6.15997i	0.262617	−	0.232659i	0.784148	+	0.620574i	$0.213100\pi$
$702$	3.78387	−	8.36719i	0.142813	−	0.315799i
$703$	4.49570	+	3.98284i	0.169559	+	0.150216i
$704$	−0.0806708	+	0.0714681i	−0.00304039	+	0.00269355i
$705$	27.3896	+	14.3752i	1.03155	+	0.541400i
$706$	14.2005	−	37.4436i	0.534442	−	1.40921i
$707$	42.3635	+	37.5308i	1.59324	+	1.41149i
$708$	−9.97753	+	8.83932i	−0.374978	+	0.332202i
$709$	8.96124	−	2.20875i	0.336546	−	0.0829512i	−0.0674210	−	0.997725i	$-0.521477\pi$
$709$	8.96124	−	2.20875i	0.336546	−	0.0829512i	0.403967	+	0.914773i	$0.367631\pi$
$710$	48.4365	−	127.717i	1.81779	−	4.79312i
$711$	10.4880	−	5.50453i	0.393331	−	0.206436i
$712$	−0.919245	−	7.57067i	−0.0344502	−	0.283723i
$713$	−16.8835	−	14.9575i	−0.632293	−	0.560163i
$714$	−26.9611	−	14.1503i	−1.00899	−	0.529561i
$715$	−0.558544	−	9.51775i	−0.0208884	−	0.355944i
$716$	−41.8576	+	21.9686i	−1.56429	+	0.821004i
$717$	−6.00525	−	1.48016i	−0.224270	−	0.0552776i
$718$	−41.5270	+	60.1623i	−1.54977	+	2.24524i
$719$	6.37278	−	5.64579i	0.237665	−	0.210552i	−0.535880	−	0.844294i	$-0.680020\pi$
$719$	6.37278	−	5.64579i	0.237665	−	0.210552i	0.773545	+	0.633742i	$0.218482\pi$
$720$	−23.0988	−	12.1232i	−0.860843	−	0.451805i
$721$	1.95019	−	16.0613i	0.0726289	−	0.598153i
$722$	41.7084	+	21.8902i	1.55222	+	0.814670i
$723$	−0.220134	+	0.318920i	−0.00818689	+	0.0118608i
$724$	−16.5963	+	24.0439i	−0.616797	+	0.893585i
$725$	81.7165	−	20.1413i	3.03487	−	0.748029i
$726$	25.9003	−	6.38384i	0.961249	−	0.236927i
$727$	4.25738	−	35.0627i	0.157897	−	1.30040i	−0.671191	−	0.741285i	$-0.734217\pi$
$727$	4.25738	−	35.0627i	0.157897	−	1.30040i	0.829088	−	0.559118i	$-0.188860\pi$
$728$	63.8329	+	38.7452i	2.36581	+	1.43599i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	31.9562	+	84.2615i	1.18275	+	3.11866i
$731$	−17.4771	−	15.4834i	−0.646414	−	0.572673i
$732$	27.0082	−	6.65692i	0.998251	−	0.246047i
$733$	−43.4898	−	10.7193i	−1.60633	−	0.395926i	−0.668695	−	0.743537i	$-0.733147\pi$
$733$	−43.4898	−	10.7193i	−1.60633	−	0.395926i	−0.937639	+	0.347611i	$0.886993\pi$
$734$	−14.7163	−	21.3203i	−0.543189	−	0.786946i
$735$	−4.77245	−	12.5839i	−0.176035	−	0.464165i
$736$	−13.7415	+	12.1739i	−0.506517	+	0.448735i
$737$	−0.108277	+	0.891745i	−0.00398845	+	0.0328478i
$738$	−5.15552	−	13.5940i	−0.189777	−	0.500402i
$739$	−5.71312	+	15.0642i	−0.210160	+	0.554147i	−0.998101	−	0.0616044i	$-0.980378\pi$
$739$	−5.71312	+	15.0642i	−0.210160	+	0.554147i	0.787940	+	0.615752i	$0.211148\pi$
$740$	134.135	−	33.0612i	4.93089	−	1.21535i
$741$	−1.32223	−	2.19614i	−0.0485732	−	0.0806772i
$742$	90.0041	+	22.1840i	3.30416	+	0.814401i
$743$	−10.0961	+	14.6267i	−0.370389	+	0.536601i	−0.963216	−	0.268729i	$-0.913396\pi$
$743$	−10.0961	+	14.6267i	−0.370389	+	0.536601i	0.592827	+	0.805330i	$0.298012\pi$
$744$	32.3973	−	28.7015i	1.18774	−	1.05225i
$745$	−36.1184	−	8.90238i	−1.32327	−	0.326158i
$746$	−12.6147			−0.461856
$747$	−2.68351	−	0.661425i	−0.0981844	−	0.0242003i
$748$	−4.22017	+	11.1277i	−0.154305	+	0.406868i
$749$	−44.1525	+	23.1730i	−1.61330	+	0.846723i
$750$	10.8117	+	28.5081i	0.394788	+	1.04097i
$751$	12.0130	−	6.30493i	0.438362	−	0.230070i	−0.231079	−	0.972935i	$-0.574226\pi$
$751$	12.0130	−	6.30493i	0.438362	−	0.230070i	0.669442	+	0.742865i	$0.266533\pi$
$752$	34.5061	+	49.9907i	1.25831	+	1.82297i
$753$	0.833245	+	1.20716i	0.0303651	+	0.0439915i
$754$	−16.9810	+	91.7319i	−0.618412	+	3.34068i
$755$	−22.7859	+	33.0110i	−0.829263	+	1.20139i
$756$	−14.6714			−0.533593
$757$	−24.1661	−	35.0106i	−0.878331	−	1.27248i	−0.961180	−	0.275921i	$-0.911017\pi$
$757$	−24.1661	−	35.0106i	−0.878331	−	1.27248i	0.0828491	−	0.996562i	$-0.473598\pi$
$758$	−22.7824	−	20.1834i	−0.827494	−	0.733095i
$759$	2.32503	−	0.573067i	0.0843931	−	0.0208010i
$760$	−14.5324	+	7.62717i	−0.527144	+	0.276666i
$761$	21.9273	−	11.5083i	0.794864	−	0.417177i	−0.0178492	−	0.999841i	$-0.505682\pi$
$761$	21.9273	−	11.5083i	0.794864	−	0.417177i	0.812713	+	0.582664i	$0.197990\pi$
$762$	1.79181	−	0.441643i	0.0649106	−	0.0159990i
$763$	18.6837	+	16.5523i	0.676394	+	0.599233i
$764$	37.9903	+	55.0384i	1.37444	+	1.99122i
$765$	13.3257			0.481790
$766$	−1.86660	+	2.70423i	−0.0674428	+	0.0977078i
$767$	−4.41385	+	9.76025i	−0.159375	+	0.352422i
$768$	16.4732	+	23.8655i	0.594424	+	0.861172i
$769$	−27.6827	−	40.1053i	−0.998263	−	1.44623i	−0.892075	−	0.451888i	$-0.850751\pi$
$769$	−27.6827	−	40.1053i	−0.998263	−	1.44623i	−0.106189	−	0.994346i	$-0.533865\pi$
$770$	−19.4998	+	10.2343i	−0.702724	+	0.368818i
$771$	−2.24609	−	5.92245i	−0.0808910	−	0.213292i
$772$	−25.7832	+	13.5321i	−0.927958	+	0.487030i
$773$	7.82969	−	20.6452i	0.281614	−	0.742556i	−0.717335	−	0.696728i	$-0.754638\pi$
$773$	7.82969	−	20.6452i	0.281614	−	0.742556i	0.998949	−	0.0458274i	$-0.0145924\pi$
$774$	−15.7929	−	3.89259i	−0.567663	−	0.139916i
$775$	−56.6151			−2.03368
$776$	73.4010	+	18.0917i	2.63494	+	0.649455i
$777$	20.6768	−	18.3181i	0.741777	−	0.657157i
$778$	2.70742	−	3.92238i	0.0970658	−	0.140624i
$779$	−3.94060	−	0.971271i	−0.141187	−	0.0347994i
$780$	−58.8482	−	3.66587i	−2.10710	−	0.131259i
$781$	−10.3651	+	2.55477i	−0.370892	+	0.0914168i
$782$	10.8986	−	28.7373i	0.389734	−	1.02764i
$783$	−3.60244	−	9.49885i	−0.128741	−	0.339461i
$784$	3.18563	−	26.2360i	0.113773	−	0.937001i
$785$	−19.9148	+	17.6430i	−0.710791	+	0.629706i
$786$	−5.46206	−	14.4023i	−0.194825	−	0.513712i
$787$	−5.99231	−	8.68135i	−0.213603	−	0.309457i	0.701507	−	0.712663i	$-0.252511\pi$
$787$	−5.99231	−	8.68135i	−0.213603	−	0.309457i	−0.915109	+	0.403206i	$0.867896\pi$
$788$	25.0615	+	6.17711i	0.892779	+	0.220050i
$789$	1.52193	−	0.375121i	0.0541820	−	0.0133547i
$790$	−82.3017	−	72.9130i	−2.92816	−	2.59413i
$791$	−6.24854	−	16.4760i	−0.222172	−	0.585821i
$792$	0.553859	+	4.56144i	0.0196805	+	0.162084i
$793$	17.6210	−	13.7541i	0.625739	−	0.488422i
$794$	−5.29801	+	43.6330i	−0.188019	+	1.54848i
$795$	−39.3895	+	9.70865i	−1.39700	+	0.344330i
$796$	74.2672	−	18.3052i	2.63233	−	0.648811i
$797$	7.45561	−	10.8013i	0.264091	−	0.382602i	−0.668396	−	0.743806i	$-0.733019\pi$
$797$	7.45561	−	10.8013i	0.264091	−	0.382602i	0.932487	+	0.361204i	$0.117634\pi$
$798$	−3.36361	+	4.87303i	−0.119070	+	0.172503i
$799$	−27.4746	−	14.4198i	−0.971980	−	0.510135i
$800$	−5.55419	+	45.7429i	−0.196370	+	1.61726i
$801$	1.06619	+	0.559582i	0.0376721	+	0.0197719i
$802$	−13.5990	+	12.0477i	−0.480199	+	0.425419i
$803$	4.00092	−	5.79634i	0.141190	−	0.204548i
$804$	5.39393	+	1.32948i	0.190229	+	0.0468873i
$805$	34.8319	−	18.2812i	1.22766	−	0.644327i
$806$	25.8586	−	57.1805i	0.910830	−	2.01410i
$807$	−7.85138	−	4.12072i	−0.276382	−	0.145056i
$808$	−82.0530	−	72.6926i	−2.88661	−	2.55732i
$809$	−1.70658	−	14.0550i	−0.0600002	−	0.494146i	−0.991471	−	0.130329i	$-0.958397\pi$
$809$	−1.70658	−	14.0550i	−0.0600002	−	0.494146i	0.931471	−	0.363817i	$-0.118527\pi$
$810$	8.21963	−	4.31399i	0.288808	−	0.151578i
$811$	−6.13010	+	16.1638i	−0.215257	+	0.567586i	−0.998536	−	0.0540838i	$-0.982776\pi$
$811$	−6.13010	+	16.1638i	−0.215257	+	0.567586i	0.783279	+	0.621670i	$0.213545\pi$
$812$	144.716	−	35.6693i	5.07853	−	1.25175i
$813$	10.7915	−	9.56045i	0.378475	−	0.335300i
$814$	−11.6841	−	10.3512i	−0.409526	−	0.362808i
$815$	12.5006	−	32.9613i	0.437876	−	1.15458i
$816$	23.1705	+	12.1608i	0.811129	+	0.425713i
$817$	−3.39865	+	3.01094i	−0.118904	+	0.105340i
$818$	−50.0252	−	44.3185i	−1.74909	−	1.54956i
$819$	−10.7599	+	4.81941i	−0.375983	+	0.168404i
$820$	−69.8740	+	61.9030i	−2.44011	+	2.16174i
$821$	−3.25228	+	26.7849i	−0.113505	+	0.934800i	0.819038	+	0.573740i	$0.194508\pi$
$821$	−3.25228	+	26.7849i	−0.113505	+	0.934800i	−0.932543	+	0.361060i	$0.882415\pi$
$822$	38.3245			1.33672
$823$	−8.70338			−0.303381			−0.151690	−	0.988428i	$-0.548472\pi$
$823$	−8.70338			−0.303381			−0.151690	+	0.988428i	$0.548472\pi$
$824$	−3.77728	+	31.1087i	−0.131588	+	1.08372i
$825$	3.41428	−	4.94644i	0.118870	−	0.172213i
$826$	24.7427			0.860910
$827$	−27.8751	−	40.3840i	−0.969310	−	1.40429i	−0.913952	−	0.405822i	$-0.866985\pi$
$827$	−27.8751	−	40.3840i	−0.969310	−	1.40429i	−0.0553584	−	0.998467i	$-0.517630\pi$
$828$	−1.78504	−	14.7011i	−0.0620343	−	0.510898i
$829$	−10.8392	+	28.5807i	−0.376462	+	0.992647i	0.604182	+	0.796846i	$0.293500\pi$
$829$	−10.8392	+	28.5807i	−0.376462	+	0.992647i	−0.980644	+	0.195801i	$0.937269\pi$
$830$	3.09253	+	25.4693i	0.107343	+	0.884052i
$831$	10.1342	−	26.7216i	0.351550	−	0.926962i
$832$	0.457870	+	0.277918i	0.0158738	+	0.00963506i
$833$	4.78726	+	12.6230i	0.165869	+	0.437360i
$834$	−45.7521	+	24.0126i	−1.58427	+	0.831487i
$835$	5.90071	−	48.5967i	0.204202	−	1.68176i
$836$	2.04922	+	1.07551i	0.0708738	+	0.0371975i
$837$	0.823735	+	6.78407i	0.0284724	+	0.234492i
$838$	11.8556	+	97.6394i	0.409544	+	3.37290i
$839$	5.82040	+	5.15642i	0.200943	+	0.178020i	0.757593	−	0.652727i	$-0.226375\pi$
$839$	5.82040	+	5.15642i	0.200943	+	0.178020i	−0.556650	+	0.830747i	$0.687914\pi$
$840$	26.7670	+	70.5788i	0.923550	+	2.43520i
$841$	42.1537	+	61.0702i	1.45358	+	2.10587i
$842$	15.8342	+	3.90277i	0.545681	+	0.134498i
$843$	−27.3573	−	14.3582i	−0.942234	−	0.494522i
$844$	52.4096			1.80401
$845$	−44.3633	+	16.6425i	−1.52614	+	0.572521i
$846$	−21.6152			−0.743147
$847$	−30.3253	−	15.9160i	−1.04199	−	0.546879i
$848$	−77.3499	−	19.0650i	−2.65621	−	0.654696i
$849$	8.06118	+	11.6786i	0.276659	+	0.400810i
$850$	−27.3552	−	72.1296i	−0.938274	−	2.47403i
$851$	20.8709	+	18.4900i	0.715444	+	0.633828i
$852$	7.95779	+	65.5383i	0.272630	+	2.24531i
$853$	3.83870	+	31.6145i	0.131434	+	1.08246i	0.897908	+	0.440184i	$0.145087\pi$
$853$	3.83870	+	31.6145i	0.131434	+	1.08246i	−0.766473	+	0.642276i	$0.777990\pi$
$854$	−45.7185	−	23.9949i	−1.56446	−	0.821090i
$855$	0.312353	−	2.57246i	0.0106822	−	0.0879762i
$856$	85.5180	−	44.8833i	2.92294	−	1.53408i
$857$	−9.71345	−	25.6123i	−0.331805	−	0.874898i	−0.992276	−	0.124047i	$-0.960413\pi$
$857$	−9.71345	−	25.6123i	−0.331805	−	0.874898i	0.660471	−	0.750851i	$-0.270357\pi$
$858$	3.43639	+	5.70763i	0.117316	+	0.194855i
$859$	−6.85888	+	18.0854i	−0.234022	+	0.617065i	−0.999656	−	0.0262109i	$-0.991656\pi$
$859$	−6.85888	+	18.0854i	−0.234022	+	0.617065i	0.765635	+	0.643276i	$0.222425\pi$
$860$	12.5886	+	103.676i	0.429266	+	3.53533i
$861$	−6.61912	+	17.4532i	−0.225579	+	0.594803i
$862$	−10.6304	−	87.5494i	−0.362073	−	2.98194i
$863$	−6.44498	−	9.33717i	−0.219390	−	0.317841i	0.697799	−	0.716293i	$-0.254163\pi$
$863$	−6.44498	−	9.33717i	−0.219390	−	0.317841i	−0.917189	+	0.398453i	$0.869547\pi$
$864$	5.56208			0.189226
$865$	−36.8847	+	53.4368i	−1.25412	+	1.81691i
$866$	0.654269	−	5.38839i	0.0222330	−	0.183105i
$867$	3.63300			0.123383
$868$	−100.263			−3.40314
$869$	−1.03582	+	8.53071i	−0.0351376	+	0.289384i
$870$	−70.5887	+	62.5361i	−2.39318	+	2.12017i
$871$	4.39261	−	0.796815i	0.148838	−	0.0269991i
$872$	−36.1880	−	32.0597i	−1.22548	−	1.08568i
$873$	−8.93437	+	7.91516i	−0.302383	+	0.267888i
$874$	−5.29214	−	2.77753i	−0.179009	−	0.0939514i
$875$	13.8810	−	36.6013i	0.469264	−	1.23735i
$876$	−32.6027	−	28.8835i	−1.10154	−	0.975882i
$877$	39.2096	−	34.7366i	1.32401	−	1.17297i	0.352546	−	0.935794i	$-0.385316\pi$
$877$	39.2096	−	34.7366i	1.32401	−	1.17297i	0.971466	−	0.237178i	$-0.0762226\pi$
$878$	8.00581	−	1.97325i	0.270183	−	0.0665941i
$879$	11.2830	−	29.7509i	0.380568	−	1.00347i
$880$	16.7582	−	8.79538i	0.564919	−	0.296492i
$881$	1.89353	+	15.5946i	0.0637946	+	0.525396i	0.989217	+	0.146458i	$0.0467874\pi$
$881$	1.89353	+	15.5946i	0.0637946	+	0.525396i	−0.925422	+	0.378937i	$0.876290\pi$
$882$	7.03941	+	6.23637i	0.237029	+	0.209990i
$883$	47.9989	+	25.1918i	1.61529	+	0.847770i	0.998142	+	0.0609232i	$0.0194045\pi$
$883$	47.9989	+	25.1918i	1.61529	+	0.847770i	0.617148	+	0.786847i	$0.288288\pi$
$884$	59.0307	+	3.67724i	1.98542	+	0.123679i
$885$	−9.58812	+	5.03223i	−0.322301	+	0.169157i
$886$	−66.3418	−	16.3518i	−2.22880	−	0.549349i
$887$	−20.9134	+	30.2983i	−0.702203	+	1.01732i	0.295868	+	0.955229i	$0.404391\pi$
$887$	−20.9134	+	30.2983i	−0.702203	+	1.01732i	−0.998071	+	0.0620875i	$0.980224\pi$
$888$	−40.0485	+	35.4799i	−1.34394	+	1.19063i
$889$	−2.09794	−	1.10109i	−0.0703628	−	0.0369293i
$890$	1.34733	−	11.0963i	0.0451626	−	0.371947i
$891$	−0.642398	−	0.337157i	−0.0215212	−	0.0112952i
$892$	−8.93792	+	12.9488i	−0.299264	+	0.433558i
$893$	−3.42767	+	4.96584i	−0.114703	+	0.166175i
$894$	25.2388	−	6.22081i	0.844113	−	0.208055i
$895$	−37.2857	+	9.19010i	−1.24632	+	0.307191i
$896$	4.53370	−	37.3384i	0.151460	−	1.24739i
$897$	−6.13831	−	10.1954i	−0.204952	−	0.340413i
$898$	−5.04508	−	41.5499i	−0.168356	−	1.38654i
$899$	−24.6187	−	64.9141i	−0.821079	−	2.16501i
$900$	−27.8223	−	24.6484i	−0.927410	−	0.821613i
$901$	39.5117	−	9.73876i	1.31633	−	0.324445i
$902$	10.2414	+	2.52427i	0.341001	+	0.0840491i
$903$	11.8629	+	17.1864i	0.394774	+	0.571929i
$904$	12.1027	+	31.9121i	0.402529	+	1.06138i
$905$	−17.7645	+	15.7380i	−0.590513	+	0.523149i
$906$	3.37853	−	27.8247i	0.112244	−	0.924415i
$907$	7.11487	+	18.7604i	0.236245	+	0.622927i	0.999738	−	0.0228889i	$-0.00728639\pi$
$907$	7.11487	+	18.7604i	0.236245	+	0.622927i	−0.763493	+	0.645816i	$0.776517\pi$
$908$	−19.1349	+	50.4546i	−0.635014	+	1.67439i
$909$	16.8053	−	4.14214i	0.557397	−	0.137386i
$910$	77.2503	+	77.5286i	2.56082	+	2.57005i
$911$	−50.5937	−	12.4702i	−1.67625	−	0.413157i	−0.717303	−	0.696761i	$-0.754624\pi$
$911$	−50.5937	−	12.4702i	−1.67625	−	0.413157i	−0.958942	+	0.283604i	$0.908470\pi$
$912$	2.89070	−	4.18790i	0.0957206	−	0.138675i
$913$	1.50088	−	1.32966i	0.0496718	−	0.0440053i
$914$	90.0695	+	22.2001i	2.97924	+	0.734315i
$915$	22.5966			0.747022
$916$	−48.1423	−	11.8660i	−1.59067	−	0.392064i
$917$	−7.01267	+	18.4909i	−0.231579	+	0.610623i
$918$	−8.24512	+	4.32737i	−0.272130	+	0.142825i
$919$	−16.9129	−	44.5957i	−0.557905	−	1.47108i	−0.856222	−	0.516609i	$-0.827194\pi$
$919$	−16.9129	−	44.5957i	−0.557905	−	1.47108i	0.298316	−	0.954467i	$-0.403575\pi$
$920$	−67.4651	+	35.4084i	−2.22426	+	1.16738i
$921$	−13.6253	−	19.7396i	−0.448967	−	0.650441i
$922$	38.1257	+	55.2346i	1.25560	+	1.81906i
$923$	27.3649	+	45.4515i	0.900728	+	1.49606i
$924$	6.04653	−	8.75991i	0.198916	−	0.288180i
$925$	69.9857			2.30112
$926$	3.50561	+	5.07875i	0.115201	+	0.166898i
$927$	−3.70353	−	3.28104i	−0.121640	−	0.107763i
$928$	−54.8634	+	13.5226i	−1.80098	+	0.443901i
$929$	4.57527	−	2.40129i	0.150110	−	0.0787836i	−0.387996	−	0.921661i	$-0.626833\pi$
$929$	4.57527	−	2.40129i	0.150110	−	0.0787836i	0.538105	+	0.842878i	$0.319140\pi$
$930$	56.1720	−	29.4814i	1.84195	−	0.966732i
$931$	2.54902	−	0.628276i	0.0835406	−	0.0205909i
$932$	9.47036	+	8.39001i	0.310212	+	0.274824i
$933$	−10.2388	−	14.8335i	−0.335203	−	0.485626i
$934$	−23.2720			−0.761482
$935$	−5.49192	+	7.95642i	−0.179605	+	0.260203i
$936$	20.8407	−	9.33461i	0.681200	−	0.305111i
$937$	−15.8592	−	22.9760i	−0.518097	−	0.750593i	0.473382	−	0.880857i	$-0.343033\pi$
$937$	−15.8592	−	22.9760i	−0.518097	−	0.750593i	−0.991479	+	0.130264i	$0.958418\pi$
$938$	−5.85777	−	8.48645i	−0.191263	−	0.277092i
$939$	14.2145	−	7.46032i	0.463871	−	0.243458i
$940$	49.2146	+	129.768i	1.60520	+	4.23257i
$941$	−2.92966	+	1.53760i	−0.0955040	+	0.0501244i	−0.511799	−	0.859105i	$-0.671021\pi$
$941$	−2.92966	+	1.53760i	−0.0955040	+	0.0501244i	0.416295	+	0.909230i	$0.363328\pi$
$942$	6.59272	−	17.3836i	0.214802	−	0.566387i
$943$	−18.2939	−	4.50903i	−0.595730	−	0.146834i
$944$	−21.2640			−0.692085
$945$	−11.5719	−	2.85222i	−0.376435	−	0.0927828i
$946$	8.83289	−	7.82526i	0.287182	−	0.254421i
$947$	17.7459	−	25.7093i	0.576663	−	0.835441i	−0.420761	−	0.907172i	$-0.638237\pi$
$947$	17.7459	−	25.7093i	0.576663	−	0.835441i	0.997424	+	0.0717308i	$0.0228522\pi$
$948$	51.6000	+	12.7182i	1.67589	+	0.413070i
$949$	−33.3987	−	10.4734i	−1.08417	−	0.339980i
$950$	−14.5655	+	3.59007i	−0.472567	+	0.116477i
$951$	9.06556	−	23.9039i	0.293971	−	0.775138i
$952$	−26.8500	−	70.7977i	−0.870215	−	2.29457i
$953$	1.36963	−	11.2800i	0.0443668	−	0.365394i	−0.953569	−	0.301175i	$-0.902621\pi$
$953$	1.36963	−	11.2800i	0.0443668	−	0.365394i	0.997936	−	0.0642190i	$-0.0204556\pi$
$954$	21.2191	−	18.7985i	0.686994	−	0.608623i
$955$	19.2646	+	50.7967i	0.623389	+	1.64374i
$956$	−15.7640	−	22.8381i	−0.509844	−	0.738637i
$957$	7.15620	+	1.76385i	0.231327	+	0.0570170i
$958$	18.8587	−	4.64826i	0.609298	−	0.150179i
$959$	−36.8300	−	32.6285i	−1.18930	−	1.05363i
$960$	0.191998	+	0.506258i	0.00619672	+	0.0163394i
$961$	1.89268	+	15.5876i	0.0610541	+	0.502826i
$962$	−31.9655	+	70.6846i	−1.03061	+	2.27896i
$963$	−1.83809	+	15.1380i	−0.0592316	+	0.487816i
$964$	−1.68816	+	0.416094i	−0.0543720	+	0.0134015i
$965$	−22.9670	+	5.66086i	−0.739334	+	0.182230i
$966$	−15.6152	+	22.6226i	−0.502412	+	0.727870i
$967$	−4.41904	+	6.40208i	−0.142107	+	0.205877i	−0.887574	−	0.460665i	$-0.847611\pi$
$967$	−4.41904	+	6.40208i	−0.142107	+	0.205877i	0.745467	+	0.666542i	$0.232226\pi$
$968$	58.7365	+	30.8273i	1.88786	+	0.990826i
$969$	−0.313322	+	2.58044i	−0.0100653	+	0.0828955i
$970$	98.1111	+	51.4927i	3.15016	+	1.65333i
$971$	28.4644	−	25.2173i	0.913466	−	0.809260i	−0.0686297	−	0.997642i	$-0.521863\pi$
$971$	28.4644	−	25.2173i	0.913466	−	0.809260i	0.982096	+	0.188382i	$0.0603242\pi$
$972$	−2.54876	+	3.69251i	−0.0817514	+	0.118437i
$973$	64.4117	+	15.8761i	2.06494	+	0.508963i
$974$	−17.5419	+	9.20672i	−0.562080	+	0.295002i
$975$	−28.5015	−	8.93769i	−0.912780	−	0.286235i
$976$	39.2907	+	20.6213i	1.25766	+	0.660073i
$977$	8.66143	+	7.67336i	0.277104	+	0.245493i	0.790215	−	0.612829i	$-0.209969\pi$
$977$	8.66143	+	7.67336i	0.277104	+	0.245493i	−0.513111	+	0.858322i	$0.671507\pi$
$978$	2.96924	+	24.4539i	0.0949458	+	0.781949i
$979$	−0.773524	+	0.405977i	−0.0247219	+	0.0129751i
$980$	21.4127	−	56.4608i	0.684005	−	1.80357i
$981$	7.41168	−	1.82681i	0.236637	−	0.0583257i
$982$	41.8439	−	37.0705i	1.33529	−	1.18297i
$983$	28.6148	+	25.3505i	0.912670	+	0.808555i	0.981969	−	0.189041i	$-0.0605378\pi$
$983$	28.6148	+	25.3505i	0.912670	+	0.808555i	−0.0692992	+	0.997596i	$0.522076\pi$
$984$	12.8204	−	33.8047i	0.408700	−	1.07765i
$985$	18.5662	+	9.74428i	0.591568	+	0.310479i
$986$	70.8076	−	62.7301i	2.25497	−	1.99773i
$987$	20.7723	+	18.4027i	0.661191	+	0.585764i
$988$	2.09355	−	11.3094i	0.0666047	−	0.359800i
$989$	−15.7779	+	13.9780i	−0.501709	+	0.444475i
$990$	−0.811786	+	6.68566i	−0.0258003	+	0.212484i
$991$	−12.8882			−0.409408			−0.204704	−	0.978824i	$-0.565623\pi$
$991$	−12.8882			−0.409408			−0.204704	+	0.978824i	$0.565623\pi$
$992$	38.0107			1.20684
$993$	−0.187861	+	1.54718i	−0.00596160	+	0.0490982i
$994$	69.6136	−	100.853i	2.20801	−	3.19885i
$995$	62.1363			1.96985
$996$	−7.04430	−	10.2054i	−0.223207	−	0.323372i
$997$	4.81413	+	39.6479i	0.152465	+	1.25566i	0.845192	+	0.534463i	$0.179486\pi$
$997$	4.81413	+	39.6479i	0.152465	+	1.25566i	−0.692727	+	0.721200i	$0.743591\pi$
$998$	−12.4141	+	32.7333i	−0.392961	+	1.03615i
$999$	−1.01827	−	8.38624i	−0.0322167	−	0.265329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.79.2	✓	180
169.92	even	13	inner	507.2.m.a.430.2	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.79.2	✓	180	1.1	even	1	trivial
507.2.m.a.430.2	yes	180	169.92	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25517 - 1.18361i) q^{2} +(0.970942 + 0.239316i) q^{3} +(2.54876 + 3.69251i) q^{4} +(1.29246 + 3.40793i) q^{5} +(-1.90639 - 1.68891i) q^{6} +(0.394148 + 3.24610i) q^{7} +(-0.763417 - 6.28731i) q^{8} +(0.885456 + 0.464723i) q^{9} +O(q^{10})\)	\(q+(-2.25517 - 1.18361i) q^{2} +(0.970942 + 0.239316i) q^{3} +(2.54876 + 3.69251i) q^{4} +(1.29246 + 3.40793i) q^{5} +(-1.90639 - 1.68891i) q^{6} +(0.394148 + 3.24610i) q^{7} +(-0.763417 - 6.28731i) q^{8} +(0.885456 + 0.464723i) q^{9} +(1.11893 - 9.21525i) q^{10} +(-0.642398 + 0.337157i) q^{11} +(1.59102 + 4.19517i) q^{12} +(2.54492 + 2.55409i) q^{13} +(2.95324 - 7.78705i) q^{14} +(0.439330 + 3.61821i) q^{15} +(-2.53802 + 6.69222i) q^{16} +(-0.440693 - 3.62943i) q^{17} +(-1.44681 - 2.09606i) q^{18} -0.710975 q^{19} +(-9.28967 + 13.4584i) q^{20} +(-0.394148 + 3.24610i) q^{21} +1.84778 q^{22} -3.30063 q^{23} +(0.763417 - 6.28731i) q^{24} +(-6.20101 + 5.49362i) q^{25} +(-2.71620 - 8.77210i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-10.9817 + 9.72892i) q^{28} +(-8.99537 - 4.72113i) q^{29} +(3.29177 - 8.67969i) q^{30} +(5.11524 + 4.53171i) q^{31} +(4.16328 - 3.68834i) q^{32} +(-0.704418 + 0.173623i) q^{33} +(-3.30198 + 8.70661i) q^{34} +(-10.5531 + 5.53869i) q^{35} +(0.540816 + 4.45402i) q^{36} +(-6.32329 - 5.60195i) q^{37} +(1.60337 + 0.841514i) q^{38} +(1.85974 + 3.08891i) q^{39} +(20.4400 - 10.7278i) q^{40} +(5.54253 + 1.36611i) q^{41} +(4.73098 - 6.85401i) q^{42} +(4.78027 - 4.23495i) q^{43} +(-2.88227 - 1.51273i) q^{44} +(-0.439330 + 3.61821i) q^{45} +(7.44350 + 3.90665i) q^{46} +(4.82108 - 6.98455i) q^{47} +(-4.06583 + 5.89037i) q^{48} +(-3.58524 + 0.883682i) q^{49} +(20.4866 - 5.04950i) q^{50} +(0.440693 - 3.62943i) q^{51} +(-2.94462 + 15.9069i) q^{52} +(1.34164 + 11.0494i) q^{53} +(-0.903146 - 2.38140i) q^{54} +(-1.97928 - 1.75349i) q^{55} +(20.1084 - 4.95626i) q^{56} +(-0.690315 - 0.170147i) q^{57} +(14.6982 + 21.2940i) q^{58} +(1.05351 + 2.77788i) q^{59} +(-12.2405 + 10.8442i) q^{60} +(0.747293 - 6.15451i) q^{61} +(-6.17200 - 16.2742i) q^{62} +(-1.15954 + 3.05745i) q^{63} +(0.144236 - 0.0355510i) q^{64} +(-5.41496 + 11.9740i) q^{65} +(1.79409 + 0.442203i) q^{66} +(0.703362 - 1.01900i) q^{67} +(12.2785 - 10.8778i) q^{68} +(-3.20472 - 0.789893i) q^{69} +30.3547 q^{70} +(14.2868 + 3.52139i) q^{71} +(2.24589 - 5.92191i) q^{72} +(-8.59591 + 4.51148i) q^{73} +(7.62962 + 20.1177i) q^{74} +(-7.33553 + 3.84998i) q^{75} +(-1.81210 - 2.62528i) q^{76} +(-1.34765 - 1.95240i) q^{77} +(-0.537974 - 9.16723i) q^{78} +(6.72858 - 9.74803i) q^{79} -26.0869 q^{80} +(0.568065 + 0.822984i) q^{81} +(-10.8824 - 9.64100i) q^{82} +(-2.68351 + 0.661425i) q^{83} +(-12.9909 + 6.81813i) q^{84} +(11.7993 - 6.19275i) q^{85} +(-15.7929 + 3.89259i) q^{86} +(-7.60414 - 6.73668i) q^{87} +(2.61023 + 3.78156i) q^{88} +1.20412 q^{89} +(5.27331 - 7.63970i) q^{90} +(-7.28776 + 9.26777i) q^{91} +(-8.41251 - 12.1876i) q^{92} +(3.88209 + 5.62418i) q^{93} +(-19.1393 + 10.0451i) q^{94} +(-0.918906 - 2.42295i) q^{95} +(4.92498 - 2.58483i) q^{96} +(-4.23263 + 11.1605i) q^{97} +(9.13128 + 2.25066i) q^{98} -0.725500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

L-functions

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