LMFDB - Embedded newform 175.2.x.a.33.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			33.8
Character	$\chi$	$=$	175.33
Dual form			175.2.x.a.122.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.776420 + 0.504213i) q^{2} +(-1.23327 + 0.473408i) q^{3} +(-0.464876 + 1.04413i) q^{4} +(2.01352 + 0.972487i) q^{5} +(0.718837 - 0.989394i) q^{6} +(-2.64389 + 0.0993238i) q^{7} +(-0.455170 - 2.87383i) q^{8} +(-0.932596 + 0.839713i) q^{9} +(-2.05368 + 0.260185i) q^{10} +(-0.526566 + 0.584810i) q^{11} +(0.0790188 - 1.50777i) q^{12} +(-0.371838 - 0.729773i) q^{13} +(2.00269 - 1.41020i) q^{14} +(-2.94360 - 0.246122i) q^{15} +(0.272873 + 0.303056i) q^{16} +(-5.77821 + 4.67910i) q^{17} +(0.300692 - 1.12220i) q^{18} +(-1.68154 + 0.748668i) q^{19} +(-1.95144 + 1.65029i) q^{20} +(3.21360 - 1.37413i) q^{21} +(0.113967 - 0.719560i) q^{22} +(-2.22587 - 3.42753i) q^{23} +(1.92184 + 3.32873i) q^{24} +(3.10854 + 3.91625i) q^{25} +(0.656664 + 0.379125i) q^{26} +(2.55179 - 5.00818i) q^{27} +(1.12537 - 2.80673i) q^{28} +(5.50382 + 7.57536i) q^{29} +(2.40957 - 1.29311i) q^{30} +(4.69555 + 0.493522i) q^{31} +(5.25635 + 1.40844i) q^{32} +(0.372543 - 0.970509i) q^{33} +(2.12705 - 6.54639i) q^{34} +(-5.42011 - 2.37115i) q^{35} +(-0.443227 - 1.36411i) q^{36} +(6.55514 + 0.343540i) q^{37} +(0.928090 - 1.42913i) q^{38} +(0.804057 + 0.723976i) q^{39} +(1.87827 - 6.22917i) q^{40} +(-2.40999 - 0.783055i) q^{41} +(-1.80225 + 2.68724i) q^{42} +(1.79811 + 1.79811i) q^{43} +(-0.365830 - 0.821667i) q^{44} +(-2.69441 + 0.783843i) q^{45} +(3.45641 + 1.53889i) q^{46} +(-7.25044 + 8.95355i) q^{47} +(-0.479996 - 0.244570i) q^{48} +(6.98027 - 0.525202i) q^{49} +(-4.38815 - 1.47329i) q^{50} +(4.91096 - 8.50604i) q^{51} +(0.934836 - 0.0489927i) q^{52} +(3.22465 + 8.40051i) q^{53} +(0.543925 + 5.17510i) q^{54} +(-1.62897 + 0.665450i) q^{55} +(1.48886 + 7.55288i) q^{56} +(1.71936 - 1.71936i) q^{57} +(-8.09287 - 3.10656i) q^{58} +(-11.1497 + 2.36995i) q^{59} +(1.62539 - 2.95908i) q^{60} +(1.75779 - 8.26975i) q^{61} +(-3.89456 + 1.98438i) q^{62} +(2.38227 - 2.31273i) q^{63} +(-5.56698 + 1.80882i) q^{64} +(-0.0390087 - 1.83102i) q^{65} +(0.200093 + 0.941364i) q^{66} +(0.574734 + 0.709737i) q^{67} +(-2.19943 - 8.20839i) q^{68} +(4.36771 + 3.17333i) q^{69} +(5.40385 - 0.891880i) q^{70} +(0.767293 - 0.557471i) q^{71} +(2.83768 + 2.29791i) q^{72} +(0.194220 + 3.70594i) q^{73} +(-5.26276 + 3.03846i) q^{74} +(-5.68765 - 3.35818i) q^{75} -2.10378i q^{76} +(1.33409 - 1.59847i) q^{77} +(-0.989324 - 0.156693i) q^{78} +(4.86448 - 0.511278i) q^{79} +(0.254718 + 0.875576i) q^{80} +(-0.382611 + 3.64030i) q^{81} +(2.26599 - 0.607171i) q^{82} +(5.14074 - 0.814213i) q^{83} +(-0.0591594 + 3.99422i) q^{84} +(-16.1849 + 3.80224i) q^{85} +(-2.30272 - 0.489458i) q^{86} +(-10.3739 - 6.73691i) q^{87} +(1.92032 + 1.24707i) q^{88} +(0.565582 + 0.120218i) q^{89} +(1.69677 - 1.96715i) q^{90} +(1.05558 + 1.89250i) q^{91} +(4.61354 - 0.730712i) q^{92} +(-6.02451 + 1.61426i) q^{93} +(1.11489 - 10.6075i) q^{94} +(-4.11388 - 0.127813i) q^{95} +(-7.14926 + 0.751418i) q^{96} +(-10.5745 - 1.67483i) q^{97} +(-5.15481 + 3.92732i) q^{98} -0.987555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$	−0.776420	+	0.504213i	−0.549012	+	0.356532i	−0.789144	−	0.614208i	$-0.789476\pi$
$2$	−0.776420	+	0.504213i	−0.549012	+	0.356532i	0.240133	+	0.970740i	$0.422809\pi$
$3$	−1.23327	+	0.473408i	−0.712029	+	0.273322i	−0.687302	−	0.726372i	$-0.741205\pi$
$3$	−1.23327	+	0.473408i	−0.712029	+	0.273322i	−0.0247269	+	0.999694i	$0.507872\pi$
$4$	−0.464876	+	1.04413i	−0.232438	+	0.522064i
$5$	2.01352	+	0.972487i	0.900474	+	0.434909i
$5$	2.01352	+	0.972487i	0.900474	+	0.434909i
$6$	0.718837	−	0.989394i	0.293464	−	0.403918i
$7$	−2.64389	+	0.0993238i	−0.999295	+	0.0375409i
$7$	−2.64389	+	0.0993238i	−0.999295	+	0.0375409i
$8$	−0.455170	−	2.87383i	−0.160927	−	1.01605i
$9$	−0.932596	+	0.839713i	−0.310865	+	0.279904i
$10$	−2.05368	+	0.260185i	−0.649430	+	0.0822778i
$11$	−0.526566	+	0.584810i	−0.158765	+	0.176327i	−0.817279	−	0.576242i	$-0.804519\pi$
$11$	−0.526566	+	0.584810i	−0.158765	+	0.176327i	0.658514	+	0.752569i	$0.271185\pi$
$12$	0.0790188	−	1.50777i	0.0228108	−	0.435255i
$13$	−0.371838	−	0.729773i	−0.103129	−	0.202403i	0.833676	−	0.552254i	$-0.186232\pi$
$13$	−0.371838	−	0.729773i	−0.103129	−	0.202403i	−0.936805	+	0.349851i	$0.886232\pi$
$14$	2.00269	−	1.41020i	0.535240	−	0.376892i
$15$	−2.94360	−	0.246122i	−0.760034	−	0.0635484i
$16$	0.272873	+	0.303056i	0.0682183	+	0.0757641i
$17$	−5.77821	+	4.67910i	−1.40142	+	1.13485i	−0.428545	+	0.903520i	$0.640974\pi$
$17$	−5.77821	+	4.67910i	−1.40142	+	1.13485i	−0.972876	+	0.231328i	$0.925693\pi$
$18$	0.300692	−	1.12220i	0.0708737	−	0.264504i
$19$	−1.68154	+	0.748668i	−0.385771	+	0.171756i	−0.590453	−	0.807072i	$-0.701051\pi$
$19$	−1.68154	+	0.748668i	−0.385771	+	0.171756i	0.204682	+	0.978829i	$0.434384\pi$
$20$	−1.95144	+	1.65029i	−0.436355	+	0.369016i
$21$	3.21360	−	1.37413i	0.701266	−	0.299860i
$22$	0.113967	−	0.719560i	0.0242979	−	0.153411i
$23$	−2.22587	−	3.42753i	−0.464125	−	0.714690i	0.526669	−	0.850071i	$-0.323441\pi$
$23$	−2.22587	−	3.42753i	−0.464125	−	0.714690i	−0.990794	+	0.135381i	$0.956774\pi$
$24$	1.92184	+	3.32873i	0.392294	+	0.679474i
$25$	3.10854	+	3.91625i	0.621707	+	0.783250i
$26$	0.656664	+	0.379125i	0.128782	+	0.0743525i
$27$	2.55179	−	5.00818i	0.491093	−	0.963824i
$28$	1.12537	−	2.80673i	0.212675	−	0.530422i
$29$	5.50382	+	7.57536i	1.02203	+	1.40671i	0.910768	+	0.412919i	$0.135491\pi$
$29$	5.50382	+	7.57536i	1.02203	+	1.40671i	0.111266	+	0.993791i	$0.464509\pi$
$30$	2.40957	−	1.29311i	0.439925	−	0.236088i
$31$	4.69555	+	0.493522i	0.843345	+	0.0886392i	0.516340	−	0.856383i	$-0.327294\pi$
$31$	4.69555	+	0.493522i	0.843345	+	0.0886392i	0.327005	+	0.945023i	$0.393961\pi$
$32$	5.25635	+	1.40844i	0.929201	+	0.248979i
$33$	0.372543	−	0.970509i	0.0648515	−	0.168944i
$34$	2.12705	−	6.54639i	0.364786	−	1.12270i
$35$	−5.42011	−	2.37115i	−0.916166	−	0.400798i
$36$	−0.443227	−	1.36411i	−0.0738712	−	0.227352i
$37$	6.55514	+	0.343540i	1.07766	+	0.0564777i	0.582893	−	0.812549i	$-0.301921\pi$
$37$	6.55514	+	0.343540i	1.07766	+	0.0564777i	0.494766	+	0.869027i	$0.335254\pi$
$38$	0.928090	−	1.42913i	0.150556	−	0.231836i
$39$	0.804057	+	0.723976i	0.128752	+	0.115929i
$40$	1.87827	−	6.22917i	0.296981	−	0.984918i
$41$	−2.40999	−	0.783055i	−0.376378	−	0.122293i	0.114718	−	0.993398i	$-0.463404\pi$
$41$	−2.40999	−	0.783055i	−0.376378	−	0.122293i	−0.491096	+	0.871106i	$0.663404\pi$
$42$	−1.80225	+	2.68724i	−0.278094	+	0.414651i
$43$	1.79811	+	1.79811i	0.274209	+	0.274209i	0.830792	−	0.556583i	$-0.187888\pi$
$43$	1.79811	+	1.79811i	0.274209	+	0.274209i	−0.556583	+	0.830792i	$0.687888\pi$
$44$	−0.365830	−	0.821667i	−0.0551509	−	0.123871i
$45$	−2.69441	+	0.783843i	−0.401659	+	0.116848i
$46$	3.45641	+	1.53889i	0.509620	+	0.226898i
$47$	−7.25044	+	8.95355i	−1.05759	+	1.30601i	−0.107437	+	0.994212i	$0.534264\pi$
$47$	−7.25044	+	8.95355i	−1.05759	+	1.30601i	−0.950149	+	0.311797i	$0.899069\pi$
$48$	−0.479996	−	0.244570i	−0.0692814	−	0.0353006i
$49$	6.98027	−	0.525202i	0.997181	−	0.0750288i
$50$	−4.38815	−	1.47329i	−0.620579	−	0.208354i
$51$	4.91096	−	8.50604i	0.687673	−	1.19108i
$52$	0.934836	−	0.0489927i	0.129638	−	0.00679406i
$53$	3.22465	+	8.40051i	0.442940	+	1.15390i	0.955433	+	0.295207i	$0.0953887\pi$
$53$	3.22465	+	8.40051i	0.442940	+	1.15390i	−0.512493	+	0.858691i	$0.671278\pi$
$54$	0.543925	+	5.17510i	0.0740188	+	0.704241i
$55$	−1.62897	+	0.665450i	−0.219650	+	0.0897292i
$56$	1.48886	+	7.55288i	0.198957	+	1.00930i
$57$	1.71936	−	1.71936i	0.227735	−	0.227735i
$58$	−8.09287	−	3.10656i	−1.06265	−	0.407912i
$59$	−11.1497	+	2.36995i	−1.45157	+	0.308541i	−0.865169	−	0.501480i	$-0.832789\pi$
$59$	−11.1497	+	2.36995i	−1.45157	+	0.308541i	−0.586401	+	0.810021i	$0.699456\pi$
$60$	1.62539	−	2.95908i	0.209837	−	0.382015i
$61$	1.75779	−	8.26975i	0.225062	−	1.05883i	−0.709959	−	0.704243i	$-0.751287\pi$
$61$	1.75779	−	8.26975i	0.225062	−	1.05883i	0.935022	−	0.354591i	$-0.115380\pi$
$62$	−3.89456	+	1.98438i	−0.494609	+	0.252016i
$63$	2.38227	−	2.31273i	0.300138	−	0.291377i
$64$	−5.56698	+	1.80882i	−0.695872	+	0.226103i
$65$	−0.0390087	−	1.83102i	−0.00483844	−	0.227110i
$66$	0.200093	+	0.941364i	0.0246298	+	0.115874i
$67$	0.574734	+	0.709737i	0.0702149	+	0.0867082i	0.811043	−	0.584986i	$-0.198900\pi$
$67$	0.574734	+	0.709737i	0.0702149	+	0.0867082i	−0.740828	+	0.671694i	$0.765567\pi$
$68$	−2.19943	−	8.20839i	−0.266720	−	0.995414i
$69$	4.36771	+	3.17333i	0.525811	+	0.382024i
$70$	5.40385	−	0.891880i	0.645884	−	0.106600i
$71$	0.767293	−	0.557471i	0.0910610	−	0.0661597i	−0.541323	−	0.840815i	$-0.682076\pi$
$71$	0.767293	−	0.557471i	0.0910610	−	0.0661597i	0.632384	+	0.774655i	$0.282076\pi$
$72$	2.83768	+	2.29791i	0.334424	+	0.270811i
$73$	0.194220	+	3.70594i	0.0227317	+	0.433747i	0.986162	+	0.165787i	$0.0530164\pi$
$73$	0.194220	+	3.70594i	0.0227317	+	0.433747i	−0.963430	+	0.267961i	$0.913650\pi$
$74$	−5.26276	+	3.03846i	−0.611783	+	0.353213i
$75$	−5.68765	−	3.35818i	−0.656753	−	0.387770i
$76$		−	2.10378i		−	0.241320i
$77$	1.33409	−	1.59847i	0.152034	−	0.182163i
$78$	−0.989324	−	0.156693i	−0.112019	−	0.0177420i
$79$	4.86448	−	0.511278i	0.547297	−	0.0575232i	0.173155	−	0.984895i	$-0.444604\pi$
$79$	4.86448	−	0.511278i	0.547297	−	0.0575232i	0.374142	+	0.927371i	$0.377937\pi$
$80$	0.254718	+	0.875576i	0.0284783	+	0.0978924i
$81$	−0.382611	+	3.64030i	−0.0425124	+	0.404478i
$82$	2.26599	−	0.607171i	0.250237	−	0.0670509i
$83$	5.14074	−	0.814213i	0.564269	−	0.0893715i	0.132218	−	0.991221i	$-0.457790\pi$
$83$	5.14074	−	0.814213i	0.564269	−	0.0893715i	0.432051	+	0.901849i	$0.357790\pi$
$84$	−0.0591594	+	3.99422i	−0.00645482	+	0.435805i
$85$	−16.1849	+	3.80224i	−1.75550	+	0.412410i
$86$	−2.30272	−	0.489458i	−0.248309	−	0.0527796i
$87$	−10.3739	−	6.73691i	−1.11220	−	0.722273i
$88$	1.92032	+	1.24707i	0.204707	+	0.132938i
$89$	0.565582	+	0.120218i	0.0599516	+	0.0127431i	0.237790	−	0.971317i	$-0.423577\pi$
$89$	0.565582	+	0.120218i	0.0599516	+	0.0127431i	−0.177838	+	0.984060i	$0.556910\pi$
$90$	1.69677	−	1.96715i	0.178855	−	0.207356i
$91$	1.05558	+	1.89250i	0.110655	+	0.198388i
$92$	4.61354	−	0.730712i	0.480994	−	0.0761820i
$93$	−6.02451	+	1.61426i	−0.624713	+	0.167391i
$94$	1.11489	−	10.6075i	0.114992	−	1.09408i
$95$	−4.11388	−	0.127813i	−0.422075	−	0.0131133i
$96$	−7.14926	+	0.751418i	−0.729669	+	0.0766913i
$97$	−10.5745	−	1.67483i	−1.07368	−	0.170054i	−0.405529	−	0.914082i	$-0.632913\pi$
$97$	−10.5745	−	1.67483i	−1.07368	−	0.170054i	−0.668148	+	0.744029i	$0.732913\pi$
$98$	−5.15481	+	3.92732i	−0.520714	+	0.396719i
$99$		−	0.987555i		−	0.0992530i
$100$	−5.53415	+	1.42514i	−0.553415	+	0.142514i
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	−0.746950	−	0.664880i	$-0.768483\pi$
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	0.202328	+	0.979318i	$0.435149\pi$
$102$	0.475885	+	9.08043i	0.0471197	+	0.899097i
$103$	7.69483	+	6.23115i	0.758194	+	0.613974i	0.928463	−	0.371424i	$-0.121130\pi$
$103$	7.69483	+	6.23115i	0.758194	+	0.613974i	−0.170269	+	0.985398i	$0.554464\pi$
$104$	−1.92800	+	1.40077i	−0.189056	+	0.137357i
$105$	7.80698	+	0.358349i	0.761884	+	0.0349713i
$106$	−6.73933	−	4.89641i	−0.654582	−	0.475581i
$107$	1.40885	+	5.25791i	0.136199	+	0.508302i	0.999990	+	0.00445150i	$0.00141696\pi$
$107$	1.40885	+	5.25791i	0.136199	+	0.508302i	−0.863791	+	0.503850i	$0.831916\pi$
$108$	4.04291	+	4.99258i	0.389030	+	0.480412i
$109$	−3.40888	−	16.0375i	−0.326512	−	1.53612i	−0.768945	−	0.639315i	$-0.779218\pi$
$109$	−3.40888	−	16.0375i	−0.326512	−	1.53612i	0.442434	−	0.896801i	$-0.354115\pi$
$110$	0.929237	−	1.33802i	0.0885993	−	0.127575i
$111$	−8.24689	+	2.67958i	−0.782760	+	0.254334i
$112$	−0.751546	−	0.774144i	−0.0710145	−	0.0731497i
$113$	8.36368	−	4.26151i	0.786789	−	0.400889i	−0.0139501	−	0.999903i	$-0.504441\pi$
$113$	8.36368	−	4.26151i	0.786789	−	0.400889i	0.800739	+	0.599014i	$0.204441\pi$
$114$	−0.468022	+	2.20187i	−0.0438343	+	0.206224i
$115$	−1.14860	−	9.06603i	−0.107107	−	0.845412i
$116$	−10.4682	+	2.22509i	−0.971952	+	0.206595i
$117$	0.959574	+	0.368346i	0.0887127	+	0.0340536i
$118$	7.46191	−	7.46191i	0.686924	−	0.686924i
$119$	14.8122	−	12.9449i	1.35783	−	1.18666i
$120$	0.632525	+	8.57143i	0.0577414	+	0.782461i
$121$	1.08508	+	10.3239i	0.0986438	+	0.938533i
$122$	2.80493	+	7.30710i	0.253947	+	0.661554i
$123$	3.34288	−	0.175193i	0.301417	−	0.0157966i
$124$	−2.69815	+	4.67333i	−0.242301	+	0.419678i
$125$	2.45061	+	10.9085i	0.219189	+	0.975682i
$126$	−0.683534	+	2.99683i	−0.0608940	+	0.266979i
$127$	2.59888	+	1.32420i	0.230613	+	0.117503i	0.565480	−	0.824762i	$-0.308691\pi$
$127$	2.59888	+	1.32420i	0.230613	+	0.117503i	−0.334866	+	0.942266i	$0.608691\pi$
$128$	−3.43896	+	4.24676i	−0.303964	+	0.375365i
$129$	−3.06879	−	1.36632i	−0.270192	−	0.120297i
$130$	0.953512	+	1.40197i	0.0836285	+	0.122961i
$131$	−2.73808	−	6.14983i	−0.239227	−	0.537313i	0.753535	−	0.657408i	$-0.228347\pi$
$131$	−2.73808	−	6.14983i	−0.239227	−	0.537313i	−0.992763	+	0.120094i	$0.961680\pi$
$132$	0.840150	+	0.840150i	0.0731256	+	0.0731256i
$133$	4.37143	−	2.14641i	0.379051	−	0.186117i
$134$	−0.804093	−	0.261266i	−0.0694631	−	0.0225699i
$135$	10.0085	−	7.60249i	0.861393	−	0.654318i
$136$	16.0770	+	14.4758i	1.37859	+	1.24129i
$137$	10.6079	−	16.3347i	0.906294	−	1.39557i	−0.0121099	−	0.999927i	$-0.503855\pi$
$137$	10.6079	−	16.3347i	0.906294	−	1.39557i	0.918404	−	0.395644i	$-0.129479\pi$
$138$	−4.99121	−	0.261578i	−0.424880	−	0.0222670i
$139$	−0.317252	−	0.976401i	−0.0269090	−	0.0828172i	0.936700	−	0.350133i	$-0.113863\pi$
$139$	−0.317252	−	0.976401i	−0.0269090	−	0.0828172i	−0.963609	+	0.267315i	$0.913863\pi$
$140$	4.99547	−	4.55700i	0.422194	−	0.385137i
$141$	4.70307	−	14.4746i	0.396070	−	1.21898i
$142$	−0.314658	+	0.819711i	−0.0264055	+	0.0687886i
$143$	0.622576	+	0.166819i	0.0520624	+	0.0139501i
$144$	−0.508961	−	0.0534939i	−0.0424134	−	0.00445783i
$145$	3.71512	+	20.6055i	0.308524	+	1.71120i
$146$	−2.01938	−	2.77944i	−0.167125	−	0.230028i
$147$	−8.35992	+	3.95223i	−0.689515	+	0.325974i
$148$	−3.40603	+	6.68471i	−0.279974	+	0.549480i
$149$	−9.86165	−	5.69362i	−0.807897	−	0.466440i	0.0383277	−	0.999265i	$-0.487797\pi$
$149$	−9.86165	−	5.69362i	−0.807897	−	0.466440i	−0.846225	+	0.532825i	$0.821130\pi$
$150$	6.10924	−	0.260425i	0.498818	−	0.0212636i
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	0.547136	−	0.837043i	$-0.315718\pi$
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	−0.998469	+	0.0553124i	$0.982385\pi$
$152$	2.91693	+	4.49168i	0.236595	+	0.364324i
$153$	1.45963	−	9.21574i	0.118004	−	0.745049i
$154$	−0.229846	+	1.91375i	−0.0185216	+	0.154215i
$155$	8.97464	+	5.56008i	0.720861	+	0.446596i
$156$	−1.12971	+	0.502980i	−0.0904493	+	0.0402706i
$157$	4.31493	−	16.1035i	0.344369	−	1.28520i	−0.548979	−	0.835836i	$-0.684983\pi$
$157$	4.31493	−	16.1035i	0.344369	−	1.28520i	0.893348	−	0.449365i	$-0.148350\pi$
$158$	−3.51909	+	2.84970i	−0.279964	+	0.226710i
$159$	−7.95373	−	8.83352i	−0.630772	−	0.700543i
$160$	9.21409	+	7.94765i	0.728438	+	0.628317i
$161$	6.22537	+	8.84092i	0.490628	+	0.696762i
$162$	−1.53842	−	3.01932i	−0.120870	−	0.237220i
$163$	−1.07656	+	20.5419i	−0.0843225	+	1.60897i	0.549503	+	0.835492i	$0.314817\pi$
$163$	−1.07656	+	20.5419i	−0.0843225	+	1.60897i	−0.633825	+	0.773476i	$0.718516\pi$
$164$	1.93796	−	2.15232i	0.151329	−	0.168068i
$165$	1.69393	−	1.59185i	0.131872	−	0.123925i
$166$	−3.58084	+	3.22420i	−0.277927	+	0.250246i
$167$	−0.739956	−	4.67190i	−0.0572595	−	0.361522i	−0.999636	−	0.0269687i	$-0.991415\pi$
$167$	−0.739956	−	4.67190i	−0.0572595	−	0.361522i	0.942377	−	0.334553i	$-0.108585\pi$
$168$	−5.41176	−	8.60990i	−0.417526	−	0.664268i
$169$	7.24690	−	9.97451i	0.557454	−	0.767270i
$170$	10.6491	−	11.1128i	0.816752	−	0.852311i
$171$	0.939527	−	2.11021i	0.0718475	−	0.161372i
$172$	−2.71336	+	1.04156i	−0.206892	+	0.0794182i
$173$	−4.23292	+	2.74889i	−0.321823	+	0.208994i	−0.695432	−	0.718592i	$-0.744787\pi$
$173$	−4.23292	+	2.74889i	−0.321823	+	0.208994i	0.373609	+	0.927586i	$0.378120\pi$
$174$	11.4514			0.868126
$175$	−8.60760	−	10.0454i	−0.650673	−	0.759358i
$176$	−0.320916			−0.0241900
$177$	12.6287	−	8.20115i	0.949228	−	0.616436i
$178$	−0.499745	+	0.191834i	−0.0374575	+	0.0143786i
$179$	−1.46827	+	3.29779i	−0.109744	+	0.246488i	−0.960066	−	0.279774i	$-0.909740\pi$
$179$	−1.46827	+	3.29779i	−0.109744	+	0.246488i	0.850322	+	0.526263i	$0.176407\pi$
$180$	0.434135	−	3.17770i	0.0323585	−	0.236852i
$181$	−7.29441	+	10.0399i	−0.542189	+	0.746259i	−0.988927	−	0.148406i	$-0.952586\pi$
$181$	−7.29441	+	10.0399i	−0.542189	+	0.746259i	0.446737	+	0.894665i	$0.352586\pi$
$182$	−1.77380	−	0.937141i	−0.131483	−	0.0694655i
$183$	1.74714	+	11.0310i	0.129152	+	0.815434i
$184$	−8.83701	+	7.95688i	−0.651473	+	0.586589i
$185$	12.8648	+	7.06652i	0.945841	+	0.519541i
$186$	3.86362	−	4.29099i	0.283294	−	0.314630i
$187$	0.306219	−	5.84301i	0.0223930	−	0.427283i
$188$	−5.97810	−	11.7327i	−0.435998	−	0.855694i
$189$	−6.24922	+	13.4945i	−0.454564	+	0.981581i
$190$	3.25854	−	1.97504i	0.236400	−	0.143284i
$191$	15.5218	+	17.2388i	1.12312	+	1.24735i	0.965655	+	0.259828i	$0.0836660\pi$
$191$	15.5218	+	17.2388i	1.12312	+	1.24735i	0.157467	+	0.987524i	$0.449667\pi$
$192$	6.00927	−	4.86621i	0.433682	−	0.351189i
$193$	−3.86831	+	14.4367i	−0.278447	+	1.03918i	0.675049	+	0.737773i	$0.264123\pi$
$193$	−3.86831	+	14.4367i	−0.278447	+	1.03918i	−0.953496	+	0.301406i	$0.902544\pi$
$194$	9.05472	−	4.03142i	0.650091	−	0.289439i
$195$	0.914928	+	2.23968i	0.0655194	+	0.160387i
$196$	−2.69658	+	7.53245i	−0.192613	+	0.538032i
$197$	−0.235850	+	1.48910i	−0.0168036	+	0.106094i	−0.994665	−	0.103162i	$-0.967104\pi$
$197$	−0.235850	+	1.48910i	−0.0168036	+	0.106094i	0.977861	+	0.209256i	$0.0671040\pi$
$198$	0.497938	+	0.766758i	0.0353869	+	0.0544911i
$199$	−1.75472	−	3.03927i	−0.124389	−	0.215448i	0.797105	−	0.603841i	$-0.206364\pi$
$199$	−1.75472	−	3.03927i	−0.124389	−	0.215448i	−0.921494	+	0.388393i	$0.873030\pi$
$200$	9.83973	−	10.7160i	0.695774	−	0.757734i
$201$	−1.04480	−	0.603214i	−0.0736943	−	0.0425474i
$202$	2.65630	−	5.21329i	0.186897	−	0.366806i
$203$	−15.3039	−	19.4817i	−1.07412	−	1.36735i
$204$	6.59841	+	9.08193i	0.461981	+	0.635863i
$205$	−4.09106	−	3.92039i	−0.285732	−	0.273812i
$206$	−9.11625	−	0.958157i	−0.635159	−	0.0667579i
$207$	4.95398	+	1.32741i	0.344325	+	0.0922616i
$208$	0.119698	−	0.311823i	0.00829955	−	0.0216211i
$209$	0.447610	−	1.37760i	0.0309619	−	0.0952908i
$210$	−6.24218	+	3.65815i	−0.430751	+	0.252437i
$211$	−6.16756	−	18.9818i	−0.424593	−	1.30676i	−0.903384	−	0.428833i	$-0.858925\pi$
$211$	−6.16756	−	18.9818i	−0.424593	−	1.30676i	0.478791	−	0.877929i	$-0.341075\pi$
$212$	−10.2703	−	0.538243i	−0.705366	−	0.0369666i
$213$	−0.682368	+	1.05076i	−0.0467551	+	0.0719966i
$214$	−3.74497	−	3.37199i	−0.256001	−	0.230504i
$215$	1.87189	+	5.36917i	0.127662	+	0.366175i
$216$	−15.5542	−	5.05385i	−1.05833	−	0.343871i
$217$	−12.4635	−	0.838436i	−0.846079	−	0.0569168i
$218$	10.7331	+	10.7331i	0.726934	+	0.726934i
$219$	−1.99395	−	4.47848i	−0.134738	−	0.302627i
$220$	0.0624546	−	2.01021i	0.00421069	−	0.135528i
$221$	5.56324	+	2.47691i	0.374224	+	0.166615i
$222$	5.05197	−	6.23867i	0.339066	−	0.418712i
$223$	7.80285	+	3.97575i	0.522518	+	0.266236i	0.695294	−	0.718725i	$-0.255274\pi$
$223$	7.80285	+	3.97575i	0.522518	+	0.266236i	−0.172777	+	0.984961i	$0.555274\pi$
$224$	−14.0371	−	3.20166i	−0.937893	−	0.213920i
$225$	−6.18753	−	1.04200i	−0.412502	−	0.0694664i
$226$	−4.34502	+	7.52579i	−0.289026	+	0.500608i
$227$	−9.37790	+	0.491475i	−0.622433	+	0.0326203i	−0.360946	−	0.932587i	$-0.617546\pi$
$227$	−9.37790	+	0.491475i	−0.622433	+	0.0326203i	−0.261487	+	0.965207i	$0.584213\pi$
$228$	0.995946	+	2.59453i	0.0659581	+	0.171827i
$229$	0.899141	+	8.55475i	0.0594169	+	0.565314i	0.983217	+	0.182439i	$0.0583993\pi$
$229$	0.899141	+	8.55475i	0.0594169	+	0.565314i	−0.923800	+	0.382875i	$0.874934\pi$
$230$	5.46301	+	6.45991i	0.360220	+	0.425954i
$231$	−0.888568	+	2.60292i	−0.0584635	+	0.171259i
$232$	19.2651	−	19.2651i	1.26482	−	1.26482i
$233$	−2.60064	−	0.998293i	−0.170374	−	0.0654004i	0.271686	−	0.962386i	$-0.412419\pi$
$233$	−2.60064	−	0.998293i	−0.170374	−	0.0654004i	−0.442060	+	0.896986i	$0.645752\pi$
$234$	−0.930758	+	0.197839i	−0.0608455	+	0.0129331i
$235$	−23.3061	+	10.9772i	−1.52032	+	0.716074i
$236$	2.70871	−	12.7435i	0.176322	−	0.829529i
$237$	−5.75718	+	2.93343i	−0.373969	+	0.190547i
$238$	−4.97347	+	17.5192i	−0.322382	+	1.13560i
$239$	−10.2364	+	3.32600i	−0.662136	+	0.215141i	−0.620757	−	0.784003i	$-0.713175\pi$
$239$	−10.2364	+	3.32600i	−0.662136	+	0.215141i	−0.0413782	+	0.999144i	$0.513175\pi$
$240$	−0.728640	−	0.959236i	−0.0470335	−	0.0619184i
$241$	−2.19409	−	10.3224i	−0.141334	−	0.664922i	−0.990581	−	0.136927i	$-0.956277\pi$
$241$	−2.19409	−	10.3224i	−0.141334	−	0.664922i	0.849247	−	0.527995i	$-0.177056\pi$
$242$	−6.04790	−	7.46854i	−0.388774	−	0.480096i
$243$	3.11283	+	11.6172i	0.199688	+	0.745247i
$244$	7.81753	+	5.67977i	0.500466	+	0.363610i
$245$	14.5657	+	5.73072i	0.930567	+	0.366122i
$246$	−2.50714	+	1.82155i	−0.159850	+	0.116137i
$247$	1.17162	+	0.948757i	0.0745482	+	0.0603680i
$248$	−0.718975	−	13.7189i	−0.0456550	−	0.871148i
$249$	−5.95446	+	3.43781i	−0.377349	+	0.217862i
$250$	−7.40289	−	7.23392i	−0.468200	−	0.457513i
$251$			29.0617i			1.83436i	0.398477	+	0.917178i	$0.369539\pi$
$251$			29.0617i			1.83436i	−0.398477	+	0.917178i	$0.630461\pi$
$252$	1.30733	+	3.56254i	0.0823541	+	0.224419i
$253$	3.17652	+	0.503111i	0.199706	+	0.0316303i
$254$	−2.68550	+	0.282257i	−0.168503	+	0.0177104i
$255$	18.1603	−	12.3512i	1.13725	−	0.773465i
$256$	1.75251	−	16.6740i	0.109532	−	1.04213i
$257$	17.9822	−	4.81832i	1.12170	−	0.300559i	0.350129	−	0.936701i	$-0.386138\pi$
$257$	17.9822	−	4.81832i	1.12170	−	0.300559i	0.771571	+	0.636143i	$0.219471\pi$
$258$	3.07159	−	0.486492i	0.191229	−	0.0302876i
$259$	−17.3652	−	0.257200i	−1.07902	−	0.0159816i
$260$	1.92996	+	0.810468i	0.119691	+	0.0502631i
$261$	−11.4940	−	2.44312i	−0.711459	−	0.151225i
$262$	5.22673	+	3.39428i	0.322908	+	0.209699i
$263$	−17.3742	−	11.2829i	−1.07134	−	0.695735i	−0.116599	−	0.993179i	$-0.537199\pi$
$263$	−17.3742	−	11.2829i	−1.07134	−	0.695735i	−0.954739	+	0.297444i	$0.903866\pi$
$264$	−2.95865	−	0.628881i	−0.182092	−	0.0387049i
$265$	−1.67648	+	20.0505i	−0.102985	+	1.23169i
$266$	−2.31182	+	3.87065i	−0.141747	+	0.237325i
$267$	−0.754428	+	0.119490i	−0.0461702	+	0.00731265i
$268$	−1.00824	+	0.270156i	−0.0615879	+	0.0165024i
$269$	0.134230	−	1.27711i	0.00818414	−	0.0778669i	−0.989667	−	0.143382i	$-0.954202\pi$
$269$	0.134230	−	1.27711i	0.00818414	−	0.0778669i	0.997852	+	0.0655149i	$0.0208690\pi$
$270$	−3.93751	+	10.9491i	−0.239629	+	0.666343i
$271$	12.3405	−	1.29704i	0.749631	−	0.0787894i	0.277995	−	0.960583i	$-0.410330\pi$
$271$	12.3405	−	1.29704i	0.749631	−	0.0787894i	0.471636	+	0.881793i	$0.343664\pi$
$272$	−2.99475	−	0.474322i	−0.181583	−	0.0287600i
$273$	−2.19774	−	1.83425i	−0.133013	−	0.111014i
$274$			18.0313i			1.08931i
$275$	−3.92711	−	0.244256i	−0.236814	−	0.0147292i
$276$	−5.34381	+	3.08525i	−0.321660	+	0.185710i
$277$	0.0643756	+	1.22836i	0.00386795	+	0.0738049i	0.999881	−	0.0153977i	$-0.00490145\pi$
$277$	0.0643756	+	1.22836i	0.00386795	+	0.0738049i	−0.996013	+	0.0892027i	$0.971568\pi$
$278$	0.738635	+	0.598135i	0.0443004	+	0.0358737i
$279$	−4.79347	+	3.48266i	−0.286977	+	0.208501i
$280$	−4.34723	+	16.6558i	−0.259797	+	0.995373i
$281$	1.42595	+	1.03602i	0.0850652	+	0.0618035i	0.629505	−	0.776996i	$-0.283258\pi$
$281$	1.42595	+	1.03602i	0.0850652	+	0.0618035i	−0.544440	+	0.838800i	$0.683258\pi$
$282$	3.64670	+	13.6097i	0.217158	+	0.810445i
$283$	9.48873	+	11.7176i	0.564046	+	0.696539i	0.976764	−	0.214320i	$-0.0687535\pi$
$283$	9.48873	+	11.7176i	0.564046	+	0.696539i	−0.412717	+	0.910859i	$0.635420\pi$
$284$	0.225375	+	1.06031i	0.0133736	+	0.0629177i
$285$	5.13403	−	1.78992i	0.304114	−	0.106025i
$286$	−0.567492	+	0.184389i	−0.0335565	+	0.0109032i
$287$	6.44953	+	1.83094i	0.380704	+	0.108077i
$288$	−6.08473	+	3.10033i	−0.358546	+	0.182689i
$289$	7.95920	−	37.4451i	0.468188	−	2.20265i
$290$	−13.2741	−	14.1253i	−0.779481	−	0.829469i
$291$	13.8341	−	2.94052i	0.810968	−	0.172377i
$292$	−3.95977	−	1.52001i	−0.231728	−	0.0889520i
$293$	−2.74224	+	2.74224i	−0.160203	+	0.160203i	−0.782657	−	0.622454i	$-0.786136\pi$
$293$	−2.74224	+	2.74224i	−0.160203	+	0.160203i	0.622454	+	0.782657i	$0.286136\pi$
$294$	4.49804	−	7.28377i	0.262331	−	0.424798i
$295$	−24.7549	−	6.07102i	−1.44129	−	0.353469i
$296$	−1.99643	−	18.9948i	−0.116040	−	1.10405i
$297$	1.58515	+	4.12945i	0.0919795	+	0.239615i
$298$	10.5276	−	0.551727i	0.609846	−	0.0319607i
$299$	−1.67366	+	2.89886i	−0.0967902	+	0.167646i
$300$	6.15043	−	4.37750i	0.355095	−	0.252735i
$301$	−4.93259	−	4.57540i	−0.284310	−	0.263722i
$302$	9.14958	+	4.66195i	0.526499	+	0.268265i
$303$	5.25416	−	6.48835i	0.301844	−	0.372746i
$304$	−0.685735	−	0.305309i	−0.0393296	−	0.0175107i
$305$	11.5816	−	14.9419i	0.663159	−	0.855571i
$306$	3.51341	+	7.89125i	0.200848	+	0.451113i
$307$	−19.7851	−	19.7851i	−1.12920	−	1.12920i	−0.990308	−	0.138889i	$-0.955647\pi$
$307$	−19.7851	−	19.7851i	−1.12920	−	1.12920i	−0.138889	−	0.990308i	$-0.544353\pi$
$308$	1.04882	+	2.13606i	0.0597622	+	0.121713i
$309$	−12.4397	−	4.04190i	−0.707669	−	0.229935i
$310$	−9.77156	+	0.208177i	−0.554987	+	0.0118236i
$311$	15.7376	+	14.1702i	0.892396	+	0.803517i	0.981292	−	0.192524i	$-0.0616673\pi$
$311$	15.7376	+	14.1702i	0.892396	+	0.803517i	−0.0888962	+	0.996041i	$0.528334\pi$
$312$	1.71460	−	2.64026i	0.0970703	−	0.149475i
$313$	4.79892	+	0.251501i	0.271251	+	0.0142157i	0.187477	−	0.982269i	$-0.439969\pi$
$313$	4.79892	+	0.251501i	0.271251	+	0.0142157i	0.0837745	+	0.996485i	$0.473302\pi$
$314$	4.76941	+	14.6787i	0.269153	+	0.828369i
$315$	7.04586	−	2.34001i	0.396989	−	0.131845i
$316$	−1.72754	+	5.31683i	−0.0971818	+	0.299095i
$317$	−10.6491	+	27.7417i	−0.598110	+	1.55813i	0.215366	+	0.976533i	$0.430905\pi$
$317$	−10.6491	+	27.7417i	−0.598110	+	1.55813i	−0.813477	+	0.581598i	$0.802428\pi$
$318$	10.6294	+	2.84814i	0.596068	+	0.159716i
$319$	−7.32827	−	0.770232i	−0.410304	−	0.0431247i
$320$	−12.9683	−	1.77171i	−0.724949	−	0.0990419i
$321$	−4.22663	−	5.81746i	−0.235908	−	0.324699i
$322$	−9.29121	−	3.72536i	−0.517779	−	0.207606i
$323$	6.21317	−	12.1940i	0.345710	−	0.678495i
$324$	−3.62308	−	2.09178i	−0.201282	−	0.116210i
$325$	1.70210	−	3.72474i	0.0944155	−	0.206611i
$326$	−9.52165	−	16.4920i	−0.527355	−	0.913406i
$327$	11.7964	+	18.1648i	0.652340	+	1.00452i
$328$	−1.15341	+	7.28234i	−0.0636864	+	0.402100i
$329$	18.2800	−	24.3923i	1.00781	−	1.34479i
$330$	−0.512573	+	2.09004i	−0.0282162	+	0.115053i
$331$	21.0153	−	9.35662i	1.15511	−	0.514286i	0.262415	−	0.964955i	$-0.415481\pi$
$331$	21.0153	−	9.35662i	1.15511	−	0.514286i	0.892691	+	0.450669i	$0.148815\pi$
$332$	−1.53966	+	5.74610i	−0.0845000	+	0.315358i
$333$	−6.40177	+	5.18405i	−0.350815	+	0.284084i
$334$	2.93015	+	3.25426i	0.160331	+	0.178065i
$335$	0.467028	+	1.98799i	0.0255165	+	0.108616i
$336$	1.29335	+	0.598940i	0.0705578	+	0.0326749i
$337$	2.42351	+	4.75641i	0.132017	+	0.259098i	0.947547	−	0.319617i	$-0.103554\pi$
$337$	2.42351	+	4.75641i	0.132017	+	0.259098i	−0.815530	+	0.578715i	$0.803554\pi$
$338$	−0.597364	+	11.3984i	−0.0324923	+	0.619991i
$339$	−8.29724	+	9.21502i	−0.450644	+	0.500491i
$340$	3.55395	−	18.6667i	0.192740	−	1.01234i
$341$	−2.76113	+	2.48613i	−0.149524	+	0.134632i
$342$	0.334529	+	2.11213i	0.0180893	+	0.114211i
$343$	−18.4029	+	2.08188i	−0.993662	+	0.112411i
$344$	4.34902	−	5.98591i	0.234484	−	0.322739i
$345$	5.70846	+	10.6371i	0.307333	+	0.572683i
$346$	1.90050	−	4.26859i	0.102171	−	0.229481i
$347$	16.0699	−	6.16865i	0.862677	−	0.331151i	0.113514	−	0.993536i	$-0.463789\pi$
$347$	16.0699	−	6.16865i	0.862677	−	0.331151i	0.749163	+	0.662386i	$0.230456\pi$
$348$	11.8568	−	7.69989i	0.635591	−	0.412758i
$349$	20.0775			1.07472			0.537362	−	0.843351i	$-0.319421\pi$
$349$	20.0775			1.07472			0.537362	+	0.843351i	$0.319421\pi$
$350$	11.7481	+	3.45936i	0.627963	+	0.184910i
$351$	−4.60369			−0.245727
$352$	−3.59148	+	2.33234i	−0.191427	+	0.124314i
$353$	−12.0284	+	4.61726i	−0.640206	+	0.245752i	−0.656747	−	0.754111i	$-0.728068\pi$
$353$	−12.0284	+	4.61726i	−0.640206	+	0.245752i	0.0165408	+	0.999863i	$0.494735\pi$
$354$	−5.67002	+	12.7351i	−0.301358	+	0.676861i
$355$	2.08710	−	0.376297i	0.110772	−	0.0199718i
$356$	−0.388449	+	0.534654i	−0.0205878	+	0.0283366i
$357$	−12.1392	+	22.9768i	−0.642473	+	1.21606i
$358$	−0.522794	−	3.30079i	−0.0276305	−	0.174452i
$359$	−5.74355	+	5.17152i	−0.303133	+	0.272942i	−0.806633	−	0.591053i	$-0.798712\pi$
$359$	−5.74355	+	5.17152i	−0.303133	+	0.272942i	0.503499	+	0.863996i	$0.332046\pi$
$360$	3.47905	+	7.38651i	0.183362	+	0.389303i
$361$	−10.4464	+	11.6019i	−0.549812	+	0.610628i
$362$	0.601280	−	11.4731i	0.0316026	−	0.603013i
$363$	−6.22559	−	12.2184i	−0.326759	−	0.641300i
$364$	−2.46673	+	0.222382i	−0.129292	+	0.0116560i
$365$	−3.21291	+	7.65086i	−0.168171	+	0.400465i
$366$	−6.91848	−	7.68375i	−0.361635	−	0.401636i
$367$	−2.57114	+	2.08207i	−0.134212	+	0.108683i	−0.694076	−	0.719902i	$-0.744187\pi$
$367$	−2.57114	+	2.08207i	−0.134212	+	0.108683i	0.559864	+	0.828585i	$0.310854\pi$
$368$	0.431357	−	1.60984i	0.0224860	−	0.0839189i
$369$	2.90509	−	1.29343i	0.151233	−	0.0673333i
$370$	−13.5515	+	1.00003i	−0.704511	+	0.0519891i
$371$	−9.35999	−	21.8897i	−0.485946	−	1.13646i
$372$	1.11515	−	7.04080i	0.0578180	−	0.365049i
$373$	2.06888	+	3.18580i	0.107123	+	0.164955i	0.888167	−	0.459522i	$-0.151979\pi$
$373$	2.06888	+	3.18580i	0.107123	+	0.164955i	−0.781044	+	0.624476i	$0.785312\pi$
$374$	2.70837	+	4.69103i	0.140046	+	0.242567i
$375$	−8.18641	−	12.2929i	−0.422744	−	0.634805i
$376$	29.0312	+	16.7612i	1.49717	+	0.864391i
$377$	3.48176	−	6.83335i	0.179320	−	0.351935i
$378$	−1.95209	−	13.6283i	−0.100404	−	0.700966i
$379$	17.8775	+	24.6063i	0.918306	+	1.26394i	0.964250	+	0.264996i	$0.0853705\pi$
$379$	17.8775	+	24.6063i	0.918306	+	1.26394i	−0.0459436	+	0.998944i	$0.514629\pi$
$380$	2.04590	−	4.23600i	0.104952	−	0.217302i
$381$	−3.83201	−	0.402760i	−0.196320	−	0.0206340i
$382$	−20.7435	−	5.55820i	−1.06133	−	0.284382i
$383$	7.28545	−	18.9792i	0.372269	−	0.969794i	−0.611642	−	0.791135i	$-0.709491\pi$
$383$	7.28545	−	18.9792i	0.372269	−	0.969794i	0.983911	−	0.178659i	$-0.0571760\pi$
$384$	2.23072	−	6.86544i	0.113836	−	0.350350i
$385$	4.24072	−	1.92117i	0.216127	−	0.0979118i
$386$	−4.27576	−	13.1594i	−0.217630	−	0.669797i
$387$	−3.18681	−	0.167013i	−0.161994	−	0.00848977i
$388$	6.66457	−	10.2625i	0.338342	−	0.521001i
$389$	−8.29482	−	7.46869i	−0.420564	−	0.378678i	0.431502	−	0.902112i	$-0.357984\pi$
$389$	−8.29482	−	7.46869i	−0.420564	−	0.378678i	−0.852066	+	0.523434i	$0.824650\pi$
$390$	−1.83964	−	1.27761i	−0.0931539	−	0.0646943i
$391$	28.8993	+	9.38994i	1.46150	+	0.474870i
$392$	−4.68655	−	19.8211i	−0.236707	−	1.00112i
$393$	6.28817	+	6.28817i	0.317196	+	0.317196i
$394$	−0.567703	−	1.27508i	−0.0286005	−	0.0642377i
$395$	10.2920	+	3.70118i	0.517844	+	0.186226i
$396$	1.03113	+	0.459091i	0.0518165	+	0.0230702i
$397$	−7.18871	+	8.87732i	−0.360791	+	0.445540i	−0.924929	−	0.380141i	$-0.875875\pi$
$397$	−7.18871	+	8.87732i	−0.360791	+	0.445540i	0.564138	+	0.825681i	$0.309209\pi$
$398$	2.89484	+	1.47500i	0.145105	+	0.0739348i
$399$	−4.37503	+	4.71657i	−0.219025	+	0.236124i
$400$	−0.338607	+	2.01070i	−0.0169304	+	0.100535i
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	−0.229493	−	0.973310i	$-0.573707\pi$
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	0.957658	−	0.287908i	$-0.0929597\pi$
$402$	1.11535	−	0.0584530i	0.0556285	−	0.00291537i
$403$	−1.38582	−	3.61020i	−0.0690328	−	0.179837i
$404$	−0.755064	−	7.18396i	−0.0375659	−	0.357415i
$405$	−4.31054	+	6.95774i	−0.214193	+	0.345733i
$406$	21.7052	+	7.40958i	1.07721	+	0.367731i
$407$	−3.65262	+	3.65262i	−0.181054	+	0.181054i
$408$	−26.6803	−	10.2416i	−1.32087	−	0.507034i
$409$	31.5725	−	6.71095i	1.56116	−	0.331835i	0.655287	−	0.755380i	$-0.272548\pi$
$409$	31.5725	−	6.71095i	1.56116	−	0.331835i	0.905875	+	0.423545i	$0.139214\pi$
$410$	5.15309	+	0.981098i	0.254493	+	0.0484530i
$411$	−5.34941	+	25.1670i	−0.263867	+	1.24140i
$412$	−10.0833	+	5.13768i	−0.496767	+	0.253115i
$413$	29.2432	−	7.37330i	1.43896	−	0.362816i
$414$	−4.51566	+	1.46723i	−0.221933	+	0.0721103i
$415$	11.1428	+	3.35987i	0.546978	+	0.164929i
$416$	−0.926673	−	4.35966i	−0.0454339	−	0.213750i
$417$	0.853493	+	1.05398i	0.0417957	+	0.0516134i
$418$	0.347072	+	1.29529i	0.0169758	+	0.0633547i
$419$	22.7957	+	16.5620i	1.11364	+	0.809109i	0.983233	−	0.182351i	$-0.0583708\pi$
$419$	22.7957	+	16.5620i	1.11364	+	0.809109i	0.130410	+	0.991460i	$0.458371\pi$
$420$	−4.00344	+	7.98491i	−0.195348	+	0.389624i
$421$	−16.8306	+	12.2282i	−0.820274	+	0.595964i	−0.916791	−	0.399368i	$-0.869230\pi$
$421$	−16.8306	+	12.2282i	−0.820274	+	0.595964i	0.0965173	+	0.995331i	$0.469230\pi$
$422$	14.3595	+	11.6281i	0.699009	+	0.566047i
$423$	−0.756681	−	14.4383i	−0.0367911	−	0.702015i
$424$	22.6739	−	13.0908i	1.10114	−	0.635744i
$425$	−36.2863	−	8.08373i	−1.76014	−	0.392119i
$426$		−	1.15989i		−	0.0561967i
$427$	−3.82601	+	22.0389i	−0.185154	+	1.06654i
$428$	−6.14488	−	0.973254i	−0.297024	−	0.0470440i
$429$	−0.846777	+	0.0889999i	−0.0408828	+	0.00429695i
$430$	−4.16058	−	3.22490i	−0.200641	−	0.155518i
$431$	−0.259952	+	2.47328i	−0.0125215	+	0.119134i	−0.998997	−	0.0447740i	$-0.985743\pi$
$431$	−0.259952	+	2.47328i	−0.0125215	+	0.119134i	0.986476	+	0.163908i	$0.0524099\pi$
$432$	2.21408	−	0.593260i	0.106525	−	0.0285432i
$433$	9.13869	−	1.44743i	0.439178	−	0.0695589i	0.0670695	−	0.997748i	$-0.478635\pi$
$433$	9.13869	−	1.44743i	0.439178	−	0.0695589i	0.372108	+	0.928189i	$0.378635\pi$
$434$	10.0997	−	5.63329i	0.484800	−	0.270406i
$435$	−14.3366	−	23.6534i	−0.687386	−	1.13410i
$436$	18.3299	+	3.89615i	0.877845	+	0.186592i
$437$	6.30896	+	4.09709i	0.301798	+	0.195990i
$438$	3.80625	+	2.47180i	0.181869	+	0.118107i
$439$	20.7692	+	4.41462i	0.991258	+	0.210698i	0.674874	−	0.737933i	$-0.264198\pi$
$439$	20.7692	+	4.41462i	0.991258	+	0.210698i	0.316384	+	0.948631i	$0.397531\pi$
$440$	2.65385	+	4.37850i	0.126517	+	0.208737i
$441$	−6.06875	+	6.35122i	−0.288988	+	0.302439i
$442$	−5.56830	+	0.881932i	−0.264857	+	0.0419492i
$443$	22.0209	−	5.90047i	1.04624	−	0.280340i	0.305545	−	0.952178i	$-0.401161\pi$
$443$	22.0209	−	5.90047i	1.04624	−	0.280340i	0.740698	+	0.671838i	$0.234495\pi$
$444$	1.03596	−	9.85649i	0.0491644	−	0.467768i
$445$	1.02190	+	0.792084i	0.0484428	+	0.0375484i
$446$	−8.06292	+	0.847447i	−0.381790	+	0.0401278i
$447$	14.8575	+	2.35319i	0.702734	+	0.111302i
$448$	14.5388	−	5.33525i	0.686893	−	0.252067i
$449$			32.5816i			1.53762i	0.639478	+	0.768809i	$0.279150\pi$
$449$			32.5816i			1.53762i	−0.639478	+	0.768809i	$0.720850\pi$
$450$	5.32951	−	2.31081i	0.251236	−	0.108932i
$451$	1.72696	−	0.997060i	0.0813193	−	0.0469497i
$452$	0.561488	+	10.7138i	0.0264102	+	0.503936i
$453$	11.3874	+	9.22132i	0.535026	+	0.433256i
$454$	7.03338	−	5.11005i	0.330093	−	0.239827i
$455$	0.284999	+	4.83714i	0.0133609	+	0.226769i
$456$	−5.72376	−	4.15856i	−0.268040	−	0.194742i
$457$	−2.09102	−	7.80380i	−0.0978138	−	0.365046i	0.899617	−	0.436679i	$-0.143846\pi$
$457$	−2.09102	−	7.80380i	−0.0978138	−	0.365046i	−0.997431	+	0.0716332i	$0.977179\pi$
$458$	−5.01153	−	6.18872i	−0.234173	−	0.289180i
$459$	8.68897	+	40.8784i	0.405566	+	1.90804i
$460$	10.0001	+	3.01530i	0.466255	+	0.140589i
$461$	−36.2181	+	11.7680i	−1.68684	+	0.548089i	−0.986220	−	0.165441i	$-0.947095\pi$
$461$	−36.2181	+	11.7680i	−1.68684	+	0.548089i	−0.700625	+	0.713530i	$0.747095\pi$
$462$	−0.622523	−	2.46898i	−0.0289624	−	0.114868i
$463$	32.7647	−	16.6944i	1.52270	−	0.775856i	0.525514	−	0.850785i	$-0.323873\pi$
$463$	32.7647	−	16.6944i	1.52270	−	0.775856i	0.997189	+	0.0749286i	$0.0238729\pi$
$464$	−0.793916	+	3.73508i	−0.0368566	+	0.173397i
$465$	−13.7003	−	2.60841i	−0.635338	−	0.120962i
$466$	2.52254	−	0.536183i	0.116855	−	0.0248382i
$467$	−19.4390	−	7.46192i	−0.899528	−	0.345297i	−0.135726	−	0.990746i	$-0.543337\pi$
$467$	−19.4390	−	7.46192i	−0.899528	−	0.345297i	−0.763803	+	0.645450i	$0.776670\pi$
$468$	−0.830684	+	0.830684i	−0.0383984	+	0.0383984i
$469$	−1.59002	−	1.81938i	−0.0734205	−	0.0840111i
$470$	12.5605	−	20.2742i	0.579372	−	0.935178i
$471$	2.30207	+	21.9027i	0.106074	+	1.00922i
$472$	11.8858	+	30.9637i	0.547091	+	1.42522i
$473$	−1.99838	+	0.104730i	−0.0918854	+	0.00481551i
$474$	2.99091	−	5.18041i	0.137377	−	0.237944i
$475$	−8.15909	−	4.25805i	−0.374365	−	0.195373i
$476$	6.63034	+	21.4836i	0.303901	+	0.984699i
$477$	−10.0613	−	5.12650i	−0.460676	−	0.234726i
$478$	6.27071	−	7.74368i	0.286816	−	0.354188i
$479$	−1.27864	−	0.569287i	−0.0584226	−	0.0260114i	0.377317	−	0.926084i	$-0.376847\pi$
$479$	−1.27864	−	0.569287i	−0.0584226	−	0.0260114i	−0.435740	+	0.900073i	$0.643513\pi$
$480$	−15.1259	−	5.43957i	−0.690402	−	0.248281i
$481$	−2.18674	−	4.91151i	−0.0997069	−	0.223945i
$482$	6.90821	+	6.90821i	0.314660	+	0.314660i
$483$	−11.8629	−	7.95610i	−0.539782	−	0.362015i
$484$	−11.2839	−	3.66635i	−0.512903	−	0.166652i
$485$	−19.6632	−	13.6559i	−0.892860	−	0.620081i
$486$	−8.27443	−	7.45033i	−0.375336	−	0.337954i
$487$	−14.4876	+	22.3089i	−0.656494	+	1.01091i	0.340994	+	0.940066i	$0.389237\pi$
$487$	−14.4876	+	22.3089i	−0.656494	+	1.01091i	−0.997487	+	0.0708461i	$0.977430\pi$
$488$	−24.5660	−	1.28745i	−1.11205	−	0.0582801i
$489$	−8.39703	−	25.8434i	−0.379727	−	1.16868i
$490$	−14.1986	+	2.89476i	−0.641427	+	0.130772i
$491$	0.0638187	−	0.196414i	0.00288010	−	0.00886403i	−0.949606	−	0.313446i	$-0.898517\pi$
$491$	0.0638187	−	0.196414i	0.00288010	−	0.00886403i	0.952486	+	0.304582i	$0.0985166\pi$
$492$	−1.37110	+	3.57184i	−0.0618140	+	0.161031i
$493$	−67.2481	−	18.0191i	−3.02870	−	0.811538i
$494$	−1.38804	−	0.145889i	−0.0624510	−	0.00656386i
$495$	0.960385	−	1.98846i	0.0431661	−	0.0893748i
$496$	1.13172	+	1.55769i	0.0508159	+	0.0699421i
$497$	−1.97327	+	1.55010i	−0.0885131	+	0.0695315i
$498$	2.88977	−	5.67150i	0.129494	−	0.254146i
$499$	−20.4454	−	11.8042i	−0.915262	−	0.528427i	−0.0331413	−	0.999451i	$-0.510551\pi$
$499$	−20.4454	−	11.8042i	−0.915262	−	0.528427i	−0.882120	+	0.471024i	$0.843884\pi$
$500$	−12.5291	−	2.51233i	−0.560317	−	0.112355i
$501$	3.12428	+	5.41141i	0.139582	+	0.241764i
$502$	−14.6533	−	22.5641i	−0.654008	−	1.00708i
$503$	−0.515396	+	3.25409i	−0.0229804	+	0.145092i	−0.996511	−	0.0834657i	$-0.973401\pi$
$503$	−0.515396	+	3.25409i	−0.0229804	+	0.145092i	0.973530	+	0.228558i	$0.0734011\pi$
$504$	−7.73075	−	5.79357i	−0.344355	−	0.258066i
$505$	−14.0939	+	1.04005i	−0.627170	+	0.0462817i
$506$	−2.71999	+	1.21102i	−0.120918	+	0.0538363i
$507$	−4.21538	+	15.7320i	−0.187211	+	0.698682i
$508$	−2.59079	+	2.09798i	−0.114948	+	0.0930828i
$509$	−9.35937	−	10.3946i	−0.414847	−	0.460734i	0.499114	−	0.866536i	$-0.333659\pi$
$509$	−9.35937	−	10.3946i	−0.414847	−	0.460734i	−0.913961	+	0.405802i	$0.866992\pi$
$510$	−7.87240	+	18.7464i	−0.348596	+	0.830106i
$511$	−0.881584	−	9.77879i	−0.0389990	−	0.432588i
$512$	2.08486	+	4.09177i	0.0921387	+	0.180832i
$513$	−0.541471	+	10.3319i	−0.0239065	+	0.456164i
$514$	−11.5323	+	12.8079i	−0.508668	+	0.564933i
$515$	9.43400	+	20.0297i	0.415712	+	0.882613i
$516$	2.85322	−	2.56905i	0.125606	−	0.113096i
$517$	−1.41829	−	8.95476i	−0.0623765	−	0.393830i
$518$	13.6123	−	8.55605i	0.598092	−	0.375931i
$519$	3.91899	−	5.39402i	0.172024	−	0.236771i
$520$	−5.24429	+	0.945531i	−0.229977	+	0.0414643i
$521$	11.5536	−	25.9498i	0.506172	−	1.13688i	−0.462065	−	0.886846i	$-0.652891\pi$
$521$	11.5536	−	25.9498i	0.506172	−	1.13688i	0.968237	−	0.250035i	$-0.0804421\pi$
$522$	10.1560	−	3.89852i	0.444516	−	0.170634i
$523$	−33.3009	+	21.6259i	−1.45615	+	0.945633i	−0.457748	+	0.889082i	$0.651344\pi$
$523$	−33.3009	+	21.6259i	−1.45615	+	0.945633i	−0.998400	+	0.0565510i	$0.981990\pi$
$524$	7.69409			0.336118
$525$	15.3710	+	8.31374i	0.670847	+	0.362841i
$526$	19.1787			0.836229
$527$	−29.4411	+	19.1193i	−1.28247	+	0.832848i
$528$	0.395776	−	0.151924i	0.0172239	−	0.00661165i
$529$	2.56144	−	5.75310i	0.111367	−	0.250135i
$530$	−8.80809	−	16.4129i	−0.382599	−	0.712933i
$531$	8.40811	−	11.5728i	0.364881	−	0.502215i
$532$	0.208955	+	5.56215i	0.00905937	+	0.241150i
$533$	0.324675	+	2.04992i	0.0140632	+	0.0887918i
$534$	0.525505	−	0.473167i	0.0227408	−	0.0204759i
$535$	−2.27650	+	11.9570i	−0.0984215	+	0.516947i
$536$	1.77806	−	1.97474i	0.0768006	−	0.0852958i
$537$	0.249574	−	4.76216i	0.0107699	−	0.205502i
$538$	0.539718	+	1.05926i	0.0232689	+	0.0456677i
$539$	−3.36843	+	4.35869i	−0.145088	+	0.187742i
$540$	3.28527	+	13.9844i	0.141376	+	0.601791i
$541$	−0.882148	−	0.979725i	−0.0379265	−	0.0421217i	0.723883	−	0.689923i	$-0.242355\pi$
$541$	−0.882148	−	0.979725i	−0.0379265	−	0.0421217i	−0.761810	+	0.647801i	$0.775689\pi$
$542$	−8.92742	+	7.22928i	−0.383465	+	0.310524i
$543$	4.24301	−	15.8351i	0.182085	−	0.679550i
$544$	−36.9625	+	16.4568i	−1.58475	+	0.705578i
$545$	8.73243	−	35.6070i	0.374056	−	1.52524i
$546$	2.63122	+	0.316016i	0.112606	+	0.0135243i
$547$	3.39018	−	21.4047i	0.144953	−	0.915200i	−0.802812	−	0.596232i	$-0.796664\pi$
$547$	3.39018	−	21.4047i	0.144953	−	0.915200i	0.947766	−	0.318968i	$-0.103336\pi$
$548$	12.1242	+	18.6696i	0.517920	+	0.797528i
$549$	5.30491	+	9.18838i	0.226408	+	0.392150i
$550$	3.17224	−	1.79045i	0.135265	−	0.0763452i
$551$	−14.9263	−	8.61771i	−0.635882	−	0.367127i
$552$	7.13156	−	13.9965i	0.303539	−	0.595730i
$553$	−12.8104	+	1.83492i	−0.544752	+	0.0780287i
$554$	−0.669337	−	0.921263i	−0.0284374	−	0.0391407i
$555$	−19.2111	−	2.62461i	−0.815468	−	0.111408i
$556$	1.16697	+	0.122654i	0.0494906	+	0.00520167i
$557$	10.8954	+	2.91942i	0.461654	+	0.123700i	0.482147	−	0.876090i	$-0.339857\pi$
$557$	10.8954	+	2.91942i	0.461654	+	0.123700i	−0.0204931	+	0.999790i	$0.506524\pi$
$558$	1.96574	−	5.12093i	0.0832165	−	0.216786i
$559$	0.643607	−	1.98082i	0.0272217	−	0.0837797i
$560$	−0.760410	−	2.28962i	−0.0321332	−	0.0967543i
$561$	2.38847	+	7.35097i	0.100841	+	0.310358i
$562$	−1.62951	−	0.0853991i	−0.0687368	−	0.00360234i
$563$	−2.69577	+	4.15112i	−0.113613	+	0.174949i	−0.890903	−	0.454194i	$-0.849927\pi$
$563$	−2.69577	+	4.15112i	−0.113613	+	0.174949i	0.777290	+	0.629143i	$0.216594\pi$
$564$	12.9270	+	11.6395i	0.544323	+	0.490111i
$565$	20.9847	−	0.447066i	0.882833	−	0.0188082i
$566$	−13.2754	−	4.31344i	−0.558007	−	0.181307i
$567$	0.650012	−	9.66255i	0.0272979	−	0.405789i
$568$	−1.95133	−	1.95133i	−0.0818759	−	0.0818759i
$569$	6.87878	+	15.4500i	0.288373	+	0.647697i	0.998404	−	0.0564736i	$-0.0179857\pi$
$569$	6.87878	+	15.4500i	0.288373	+	0.647697i	−0.710031	+	0.704171i	$0.751319\pi$
$570$	−3.08367	+	3.97837i	−0.129161	+	0.166636i
$571$	26.2708	+	11.6965i	1.09940	+	0.489484i	0.874562	−	0.484913i	$-0.161149\pi$
$571$	26.2708	+	11.6965i	1.09940	+	0.489484i	0.224836	+	0.974397i	$0.427815\pi$
$572$	−0.463601	+	0.572499i	−0.0193841	+	0.0239374i
$573$	−27.3036	−	13.9119i	−1.14062	−	0.581177i
$574$	−5.93072	+	1.83036i	−0.247544	+	0.0763977i
$575$	6.50388	−	19.3717i	0.271230	−	0.807854i
$576$	3.67285	−	6.36156i	0.153035	−	0.265065i
$577$	10.3630	−	0.543104i	0.431419	−	0.0226097i	0.164609	−	0.986359i	$-0.447364\pi$
$577$	10.3630	−	0.543104i	0.431419	−	0.0226097i	0.266810	+	0.963749i	$0.414030\pi$
$578$	12.7006	+	33.0863i	0.528276	+	1.37621i
$579$	−2.06379	−	19.6357i	−0.0857683	−	0.816031i
$580$	−23.2419	−	5.69996i	−0.965068	−	0.236678i
$581$	−13.5107	+	2.66328i	−0.560517	+	0.110492i
$582$	−9.25840	+	9.25840i	−0.383773	+	0.383773i
$583$	−6.61070	−	2.53761i	−0.273787	−	0.105097i
$584$	10.5618	−	2.24499i	0.437052	−	0.0928983i
$585$	1.57391	+	1.67485i	0.0650732	+	0.0692464i
$586$	0.746455	−	3.51180i	0.0308358	−	0.145071i
$587$	4.08885	−	2.08337i	0.168765	−	0.0859899i	−0.367568	−	0.929997i	$-0.619809\pi$
$587$	4.08885	−	2.08337i	0.168765	−	0.0859899i	0.536332	+	0.844007i	$0.319809\pi$
$588$	−0.240310	−	10.5661i	−0.00991023	−	0.435740i
$589$	−8.26522	+	2.68553i	−0.340563	+	0.110655i
$590$	22.2813	−	7.76810i	0.917307	−	0.319808i
$591$	−0.414084	−	1.94811i	−0.0170331	−	0.0801345i
$592$	1.68461	+	2.08032i	0.0692371	+	0.0855007i
$593$	3.98715	+	14.8803i	0.163733	+	0.611059i	0.998198	+	0.0599990i	$0.0191098\pi$
$593$	3.98715	+	14.8803i	0.163733	+	0.611059i	−0.834466	+	0.551060i	$0.814224\pi$
$594$	−3.31286	−	2.40693i	−0.135928	−	0.0987577i
$595$	42.4134	−	11.6602i	1.73878	−	0.478023i
$596$	10.5293	−	7.65000i	0.431298	−	0.313356i
$597$	3.60286	+	2.91754i	0.147455	+	0.119407i
$598$	−0.162182	−	3.09462i	−0.00663211	−	0.126548i
$599$	−13.4466	+	7.76339i	−0.549413	+	0.317204i	−0.748885	−	0.662700i	$-0.769411\pi$
$599$	−13.4466	+	7.76339i	−0.549413	+	0.317204i	0.199472	+	0.979903i	$0.436077\pi$
$600$	−7.06201	+	17.8739i	−0.288305	+	0.729699i
$601$		−	41.2449i		−	1.68241i	−0.540714	−	0.841207i	$-0.681846\pi$
$601$		−	41.2449i		−	1.68241i	0.540714	−	0.841207i	$-0.318154\pi$
$602$	6.13674	+	1.06536i	0.250115	+	0.0434207i
$603$	−1.13197	−	0.179286i	−0.0460974	−	0.00730110i
$604$	12.6082	−	1.32518i	0.513021	−	0.0539207i
$605$	−7.85499	+	21.8425i	−0.319351	+	0.888026i
$606$	−0.807926	+	7.68690i	−0.0328198	+	0.312259i
$607$	10.7885	−	2.89077i	0.437891	−	0.117333i	−0.0331368	−	0.999451i	$-0.510550\pi$
$607$	10.7885	−	2.89077i	0.437891	−	0.117333i	0.471028	+	0.882118i	$0.343883\pi$
$608$	−9.89320	+	1.56693i	−0.401222	+	0.0635474i
$609$	28.0966	+	16.7812i	1.13853	+	0.680010i
$610$	−1.45827	+	17.4408i	−0.0590436	+	0.706156i
$611$	9.23005	+	1.96191i	0.373408	+	0.0793703i
$612$	8.94388	+	5.80822i	0.361535	+	0.234783i
$613$	−2.60236	−	1.68999i	−0.105108	−	0.0682580i	0.491015	−	0.871151i	$-0.336626\pi$
$613$	−2.60236	−	1.68999i	−0.105108	−	0.0682580i	−0.596123	+	0.802893i	$0.703293\pi$
$614$	25.3375	+	5.38565i	1.02254	+	0.217347i
$615$	6.90133	+	2.89815i	0.278288	+	0.116865i
$616$	−5.20098	−	3.10638i	−0.209554	−	0.125160i
$617$	45.2349	−	7.16450i	1.82109	−	0.288432i	0.849935	−	0.526888i	$-0.176641\pi$
$617$	45.2349	−	7.16450i	1.82109	−	0.288432i	0.971153	+	0.238456i	$0.0766413\pi$
$618$	11.6964	−	3.13404i	0.470498	−	0.126070i
$619$	−1.86817	+	17.7745i	−0.0750883	+	0.714417i	0.890613	+	0.454762i	$0.150276\pi$
$619$	−1.86817	+	17.7745i	−0.0750883	+	0.714417i	−0.965701	+	0.259655i	$0.916391\pi$
$620$	−9.97754	+	6.78594i	−0.400707	+	0.272530i
$621$	−22.8456	+	2.40117i	−0.916764	+	0.0963558i
$622$	−19.3638	−	3.06692i	−0.776416	−	0.122972i
$623$	−1.50728	−	0.261668i	−0.0603878	−	0.0104835i
$624$			0.441228i			0.0176633i
$625$	−5.67399	+	24.3476i	−0.226960	+	0.973904i
$626$	−3.85279	+	2.22441i	−0.153988	+	0.0889052i
$627$	0.100144	+	1.91086i	0.00399936	+	0.0763123i
$628$	14.8082	+	11.9915i	0.590913	+	0.478512i
$629$	−39.4844	+	28.6871i	−1.57435	+	1.14383i
$630$	−4.29069	+	5.36945i	−0.170945	+	0.213924i
$631$	0.0581461	+	0.0422456i	0.00231476	+	0.00168177i	0.588942	−	0.808175i	$-0.299545\pi$
$631$	0.0581461	+	0.0422456i	0.00231476	+	0.00168177i	−0.586627	+	0.809857i	$0.699545\pi$
$632$	−3.68350	−	13.7470i	−0.146522	−	0.546826i
$633$	16.5924	+	20.4899i	0.659489	+	0.814401i
$634$	−5.71961	−	26.9086i	−0.227155	−	1.06868i
$635$	3.94514	+	5.19368i	0.156558	+	0.206105i
$636$	12.9208	−	4.19823i	0.512344	−	0.166471i
$637$	−2.97881	−	4.89872i	−0.118025	−	0.194094i
$638$	6.07818	−	3.09699i	0.240637	−	0.122611i
$639$	−0.247459	+	1.16420i	−0.00978931	+	0.0460551i
$640$	−11.0543	+	5.20661i	−0.436962	+	0.205809i
$641$	22.8779	−	4.86285i	0.903622	−	0.192071i	0.267408	−	0.963583i	$-0.413833\pi$
$641$	22.8779	−	4.86285i	0.903622	−	0.192071i	0.636214	+	0.771513i	$0.280499\pi$
$642$	6.21488	+	2.38567i	0.245282	+	0.0941549i
$643$	20.9354	−	20.9354i	0.825611	−	0.825611i	−0.161295	−	0.986906i	$-0.551567\pi$
$643$	20.9354	−	20.9354i	0.825611	−	0.825611i	0.986906	+	0.161295i	$0.0515672\pi$
$644$	−12.1251	+	2.39015i	−0.477795	+	0.0941853i
$645$	−4.85036	−	5.73547i	−0.190983	−	0.225834i
$646$	1.32436	+	12.6005i	0.0521063	+	0.495758i
$647$	−6.98885	−	18.2066i	−0.274760	−	0.715775i	−0.999638	−	0.0268974i	$-0.991437\pi$
$647$	−6.98885	−	18.2066i	−0.274760	−	0.715775i	0.724878	−	0.688877i	$-0.241896\pi$
$648$	10.6358	−	0.557397i	0.417813	−	0.0218966i
$649$	4.48509	−	7.76840i	0.176055	−	0.304936i
$650$	0.556516	+	3.75018i	0.0218284	+	0.147094i
$651$	15.7678	−	4.86631i	0.617989	−	0.190726i
$652$	−20.9480	−	10.6735i	−0.820385	−	0.418007i
$653$	1.98821	−	2.45523i	0.0778046	−	0.0960807i	−0.736757	−	0.676157i	$-0.763644\pi$
$653$	1.98821	−	2.45523i	0.0778046	−	0.0960807i	0.814562	+	0.580077i	$0.196977\pi$
$654$	−18.3179	−	8.15563i	−0.716285	−	0.318911i
$655$	0.467447	−	15.0456i	0.0182647	−	0.587879i
$656$	−0.420313	−	0.944039i	−0.0164105	−	0.0368585i
$657$	−3.29305	−	3.29305i	−0.128474	−	0.128474i
$658$	−1.89407	+	28.1557i	−0.0738385	+	1.09762i
$659$	13.3517	+	4.33824i	0.520110	+	0.168994i	0.557295	−	0.830314i	$-0.311839\pi$
$659$	13.3517	+	4.33824i	0.520110	+	0.168994i	−0.0371852	+	0.999308i	$0.511839\pi$
$660$	0.874625	+	2.50869i	0.0340447	+	0.0976508i
$661$	−9.47098	−	8.52771i	−0.368378	−	0.331689i	0.464063	−	0.885802i	$-0.346391\pi$
$661$	−9.47098	−	8.52771i	−0.368378	−	0.331689i	−0.832442	+	0.554113i	$0.813058\pi$
$662$	−11.5990	+	17.8609i	−0.450807	+	0.694182i
$663$	−8.03356	−	0.421021i	−0.311998	−	0.0163511i
$664$	−4.67982	−	14.4030i	−0.181612	−	0.558945i
$665$	10.8893	−	0.0706832i	0.422270	−	0.00274098i
$666$	2.35660	−	7.25286i	0.0913163	−	0.281043i
$667$	13.7140	−	35.7263i	0.531009	−	1.38333i
$668$	5.22205	+	1.39924i	0.202047	+	0.0541384i
$669$	−11.5052	−	1.20924i	−0.444816	−	0.0467520i
$670$	−1.36498	−	1.30803i	−0.0527338	−	0.0505338i
$671$	3.91065	+	5.38254i	0.150969	+	0.207791i
$672$	18.8272	−	2.69676i	0.726275	−	0.104030i
$673$	−14.9409	+	29.3231i	−0.575928	+	1.13032i	0.400865	+	0.916137i	$0.368710\pi$
$673$	−14.9409	+	29.3231i	−0.575928	+	1.13032i	−0.976793	+	0.214185i	$0.931290\pi$
$674$	−4.27990	−	2.47100i	−0.164856	−	0.0951795i
$675$	27.5456	−	5.57465i	1.06023	−	0.214568i
$676$	7.04576	+	12.2036i	0.270991	+	0.469370i
$677$	−3.16813	−	4.87849i	−0.121761	−	0.187496i	0.772534	−	0.634973i	$-0.218989\pi$
$677$	−3.16813	−	4.87849i	−0.121761	−	0.187496i	−0.894295	+	0.447478i	$0.852322\pi$
$678$	1.79581	−	11.3383i	0.0689677	−	0.435445i
$679$	28.1241	+	3.37777i	1.07930	+	0.129627i
$680$	18.2939	+	44.7821i	0.701538	+	1.71731i
$681$	11.3328	−	5.04569i	0.434274	−	0.193351i
$682$	0.890256	−	3.32248i	0.0340897	−	0.127224i
$683$	13.7202	−	11.1104i	0.524989	−	0.425127i	−0.329841	−	0.944037i	$-0.606995\pi$
$683$	13.7202	−	11.1104i	0.524989	−	0.425127i	0.854829	+	0.518909i	$0.173662\pi$
$684$	1.76657	+	1.96198i	0.0675465	+	0.0750180i
$685$	37.2446	−	22.5743i	1.42304	−	0.862519i
$686$	13.2386	−	10.8954i	0.505454	−	0.415988i
$687$	−5.15877	−	10.1247i	−0.196819	−	0.386280i
$688$	−0.0542727	+	1.03558i	−0.00206913	+	0.0394813i
$689$	4.93142	−	5.47689i	0.187872	−	0.208653i
$690$	−9.79553	−	5.38058i	−0.372910	−	0.204835i
$691$	25.8993	−	23.3198i	0.985254	−	0.887127i	−0.00835918	−	0.999965i	$-0.502661\pi$
$691$	25.8993	−	23.3198i	0.985254	−	0.887127i	0.993613	+	0.112838i	$0.0359942\pi$
$692$	−0.902413	−	5.69761i	−0.0343046	−	0.216591i
$693$	0.0980878	+	2.61098i	0.00372605	+	0.0991831i
$694$	−9.36667	+	12.8921i	−0.355554	+	0.489378i
$695$	0.310744	−	2.27453i	0.0117872	−	0.0862777i
$696$	−14.6388	+	32.8794i	−0.554884	+	1.24629i
$697$	17.5894	−	6.75195i	0.666247	−	0.255748i
$698$	−15.5886	+	10.1233i	−0.590037	+	0.383174i
$699$	3.67989			0.139186
$700$	14.4901	−	4.31759i	0.547675	−	0.163190i
$701$	−5.86630			−0.221567			−0.110783	−	0.993845i	$-0.535336\pi$
$701$	−5.86630			−0.221567			−0.110783	+	0.993845i	$0.535336\pi$
$702$	3.57439	−	2.32124i	0.134907	−	0.0876095i
$703$	−11.2799	+	4.32995i	−0.425430	+	0.163307i
$704$	1.87356	−	4.20809i	0.0706125	−	0.158598i
$705$	23.5460	−	24.5711i	0.886795	−	0.925403i
$706$	7.01099	−	9.64980i	0.263862	−	0.363175i
$707$	14.1571	−	8.89848i	0.532434	−	0.334662i
$708$	2.69229	+	16.9985i	0.101183	+	0.638841i
$709$	−7.00111	+	6.30382i	−0.262932	+	0.236745i	−0.790043	−	0.613051i	$-0.789942\pi$
$709$	−7.00111	+	6.30382i	−0.262932	+	0.236745i	0.527111	+	0.849796i	$0.323275\pi$
$710$	−1.43073	+	1.34451i	−0.0536943	+	0.0504584i
$711$	−4.10727	+	4.56158i	−0.154035	+	0.171073i
$712$	0.0880508	−	1.68011i	0.00329984	−	0.0629648i
$713$	−8.76010	−	17.1927i	−0.328068	−	0.643870i
$714$	−2.16009	−	23.9604i	−0.0808393	−	0.896694i
$715$	1.09134	+	0.941340i	0.0408138	+	0.0352041i
$716$	−2.76075	−	3.06613i	−0.103174	−	0.114587i
$717$	11.0496	−	8.94783i	0.412657	−	0.334163i
$718$	1.85186	−	6.91124i	0.0691109	−	0.257925i
$719$	−38.4705	+	17.1281i	−1.43471	+	0.638772i	−0.969201	−	0.246273i	$-0.920794\pi$
$719$	−38.4705	+	17.1281i	−1.43471	+	0.638772i	−0.465505	+	0.885045i	$0.654127\pi$
$720$	−0.972781	−	0.602669i	−0.0362534	−	0.0224601i
$721$	−20.9632	−	15.7102i	−0.780709	−	0.585078i
$722$	2.26097	−	14.2752i	0.0841445	−	0.531267i
$723$	7.59259	+	11.6916i	0.282372	+	0.434814i
$724$	−7.09194	−	12.2836i	−0.263570	−	0.456517i
$725$	−12.5582	+	45.1026i	−0.466398	+	1.67507i
$726$	10.9944	+	6.34760i	0.408039	+	0.235581i
$727$	−5.76081	+	11.3062i	−0.213657	+	0.419325i	−0.972816	−	0.231580i	$-0.925610\pi$
$727$	−5.76081	+	11.3062i	−0.213657	+	0.419325i	0.759159	+	0.650905i	$0.225610\pi$
$728$	4.95827	−	3.89498i	0.183766	−	0.144357i
$729$	−15.7932	−	21.7374i	−0.584932	−	0.805090i
$730$	−1.36310	−	7.56028i	−0.0504505	−	0.279818i
$731$	−18.8034	−	1.97632i	−0.695469	−	0.0730967i
$732$	−12.3300	−	3.30381i	−0.455729	−	0.122112i
$733$	16.9027	−	44.0331i	0.624316	−	1.62640i	−0.146404	−	0.989225i	$-0.546770\pi$
$733$	16.9027	−	44.0331i	0.624316	−	1.62640i	0.770720	−	0.637174i	$-0.219897\pi$
$734$	0.946479	−	2.91296i	0.0349352	−	0.107519i
$735$	−20.6764	−	0.172015i	−0.762659	−	0.00634487i
$736$	−6.87248	−	21.1513i	−0.253323	−	0.779648i
$737$	−0.717696	−	0.0376129i	−0.0264367	−	0.00138549i
$738$	−1.60341	+	2.46903i	−0.0590222	+	0.0908862i
$739$	33.3478	+	30.0265i	1.22672	+	1.10454i	0.991159	+	0.132683i	$0.0423591\pi$
$739$	33.3478	+	30.0265i	1.22672	+	1.10454i	0.235560	+	0.971860i	$0.424308\pi$
$740$	−13.3589	+	10.1475i	−0.491083	+	0.373029i
$741$	−1.89407	−	0.615420i	−0.0695804	−	0.0226080i
$742$	18.3044	+	12.2762i	0.671974	+	0.450673i
$743$	11.1530	+	11.1530i	0.409164	+	0.409164i	0.881447	−	0.472283i	$-0.156570\pi$
$743$	11.1530	+	11.1530i	0.409164	+	0.409164i	−0.472283	+	0.881447i	$0.656570\pi$
$744$	7.38130	+	16.5787i	0.270612	+	0.607804i
$745$	−14.3197	−	21.0546i	−0.524632	−	0.771379i
$746$	−3.21265	−	1.43036i	−0.117623	−	0.0523693i
$747$	−4.11053	+	5.07608i	−0.150396	+	0.185724i
$748$	5.95850	+	3.03601i	0.217864	+	0.111007i
$749$	−4.24708	−	13.7614i	−0.155185	−	0.502830i
$750$	12.5544	+	5.41679i	0.458420	+	0.197793i
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	0.132996	+	0.991117i	$0.457540\pi$
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	−0.924830	+	0.380380i	$0.875793\pi$
$752$	−4.69188	+	0.245891i	−0.171095	+	0.00896672i
$753$	−13.7580	−	35.8409i	−0.501370	−	1.30611i
$754$	0.742151	+	7.06110i	0.0270276	+	0.257150i
$755$	−1.82535	−	24.7355i	−0.0664311	−	0.900217i
$756$	−11.1849	−	12.7983i	−0.406790	−	0.465468i
$757$	−35.7542	+	35.7542i	−1.29951	+	1.29951i	−0.370793	+	0.928716i	$0.620914\pi$
$757$	−35.7542	+	35.7542i	−1.29951	+	1.29951i	−0.928716	+	0.370793i	$0.879086\pi$
$758$	−26.2873	−	10.0907i	−0.954796	−	0.366512i
$759$	−4.15568	+	0.883317i	−0.150842	+	0.0320624i
$760$	1.50520	+	11.8808i	0.0545995	+	0.430961i
$761$	−0.918515	+	4.32127i	−0.0332961	+	0.156646i	−0.991655	−	0.128921i	$-0.958849\pi$
$761$	−0.918515	+	4.32127i	−0.0332961	+	0.156646i	0.958359	+	0.285567i	$0.0921820\pi$
$762$	3.17832	−	1.61944i	0.115138	−	0.0586660i
$763$	10.6056	+	42.0628i	0.383949	+	1.52278i
$764$	−25.2152	+	8.19292i	−0.912255	+	0.296409i
$765$	11.9012	−	17.1366i	0.430288	−	0.619576i
$766$	3.91301	+	18.4093i	0.141383	+	0.665154i
$767$	5.87541	+	7.25553i	0.212149	+	0.261982i
$768$	5.73230	+	21.3932i	0.206847	+	0.771962i
$769$	−29.9959	−	21.7933i	−1.08168	−	0.785888i	−0.103706	−	0.994608i	$-0.533070\pi$
$769$	−29.9959	−	21.7933i	−1.08168	−	0.785888i	−0.977975	+	0.208720i	$0.933070\pi$
$770$	−2.32390	+	3.62986i	−0.0837476	+	0.130811i
$771$	−19.8959	+	14.4552i	−0.716533	+	0.520592i
$772$	−13.2755	−	10.7503i	−0.477797	−	0.386912i
$773$	0.340031	+	6.48817i	0.0122301	+	0.233363i	0.997904	+	0.0647042i	$0.0206104\pi$
$773$	0.340031	+	6.48817i	0.0122301	+	0.233363i	−0.985674	+	0.168659i	$0.946056\pi$
$774$	2.55851	−	1.47716i	0.0919638	−	0.0530953i
$775$	12.6635	+	19.9231i	0.454888	+	0.715658i
$776$			31.1516i			1.11828i
$777$	21.5377	−	7.90361i	0.772661	−	0.283540i
$778$	10.2061	+	1.61648i	0.365905	+	0.0579537i
$779$	4.63874	−	0.487552i	0.166200	−	0.0174683i
$780$	−2.76384	−	0.0858690i	−0.0989613	−	0.00307460i
$781$	−0.0780153	+	0.742266i	−0.00279161	+	0.0265604i
$782$	−27.1725	+	7.28085i	−0.971687	+	0.260363i
$783$	51.9834	−	8.23336i	1.85773	−	0.294236i
$784$	2.06389	+	1.97210i	0.0737105	+	0.0704322i
$785$	24.3487	−	28.2286i	0.869041	−	1.00752i
$786$	−8.05284	−	1.71168i	−0.287235	−	0.0610538i
$787$	5.98249	+	3.88508i	0.213253	+	0.138488i	0.646846	−	0.762621i	$-0.276088\pi$
$787$	5.98249	+	3.88508i	0.213253	+	0.138488i	−0.433593	+	0.901109i	$0.642754\pi$
$788$	−1.44517	−	0.938503i	−0.0514820	−	0.0334328i
$789$	26.7685	+	5.68981i	0.952983	+	0.202563i
$790$	−9.85706	+	2.31567i	−0.350698	+	0.0823877i
$791$	−21.6893	+	12.0977i	−0.771184	+	0.430143i
$792$	−2.83807	+	0.449506i	−0.100846	+	0.0159725i
$793$	−6.68866	+	1.79222i	−0.237521	+	0.0636436i
$794$	1.10540	−	10.5172i	0.0392291	−	0.373240i
$795$	−7.42453	−	25.5214i	−0.263321	−	0.905150i
$796$	3.98912	−	0.419273i	0.141391	−	0.0148607i
$797$	29.5739	+	4.68404i	1.04756	+	0.165917i	0.656406	−	0.754408i	$-0.272076\pi$
$797$	29.5739	+	4.68404i	1.04756	+	0.165917i	0.391154	+	0.920325i	$0.372076\pi$
$798$	1.01870	−	5.86799i	0.0360616	−	0.207724i
$799$		−	85.6610i		−	3.03047i
$800$	10.8238	+	24.9634i	0.382679	+	0.882588i
$801$	−0.628409	+	0.362812i	−0.0222037	+	0.0128193i
$802$	1.41298	+	26.9613i	0.0498942	+	0.952038i
$803$	−2.26954	−	1.83784i	−0.0800903	−	0.0648559i
$804$	1.11553	−	0.810483i	0.0393418	−	0.0285835i
$805$	3.93723	+	23.8555i	0.138769	+	0.840795i
$806$	2.89629	+	2.10428i	0.102017	+	0.0741200i
$807$	0.439053	+	1.63857i	0.0154554	+	0.0576803i
$808$	11.5728	+	14.2912i	0.407130	+	0.502764i
$809$	−0.444905	−	2.09311i	−0.0156420	−	0.0735900i	0.969634	−	0.244560i	$-0.0786434\pi$
$809$	−0.444905	−	2.09311i	−0.0156420	−	0.0735900i	−0.985276	+	0.170970i	$0.945310\pi$
$810$	−0.161392	−	7.57556i	−0.00567075	−	0.266178i
$811$	−11.1135	+	3.61100i	−0.390248	+	0.126799i	−0.497567	−	0.867425i	$-0.665773\pi$
$811$	−11.1135	+	3.61100i	−0.390248	+	0.126799i	0.107319	+	0.994225i	$0.465773\pi$
$812$	27.4559	−	6.92264i	0.963512	−	0.242937i
$813$	−14.6051	+	7.44168i	−0.512224	+	0.260991i
$814$	0.994268	−	4.67766i	0.0348491	−	0.163952i
$815$	−22.1444	+	40.3147i	−0.775686	+	1.41216i
$816$	3.91788	−	0.832771i	0.137153	−	0.0291528i
$817$	−4.36978	−	1.67740i	−0.152879	−	0.0586848i
$818$	−21.1298	+	21.1298i	−0.738786	+	0.738786i
$819$	−2.57359	−	0.878557i	−0.0899286	−	0.0306993i
$820$	5.99523	−	2.44910i	0.209362	−	0.0855265i
$821$	−2.74655	−	26.1317i	−0.0958552	−	0.912001i	−0.931747	−	0.363107i	$-0.881716\pi$
$821$	−2.74655	−	26.1317i	−0.0958552	−	0.912001i	0.835892	−	0.548894i	$-0.184951\pi$
$822$	−8.53614	−	22.2374i	−0.297732	−	0.775618i
$823$	−19.4457	+	1.01911i	−0.677835	+	0.0355239i	−0.388147	−	0.921597i	$-0.626885\pi$
$823$	−19.4457	+	1.01911i	−0.677835	+	0.0355239i	−0.289688	+	0.957121i	$0.593552\pi$
$824$	14.4048	−	24.9499i	0.501816	−	0.869171i
$825$	4.95882	−	1.55789i	0.172644	−	0.0542388i
$826$	−18.9873	+	20.4696i	−0.660652	+	0.712228i
$827$	−15.3550	−	7.82374i	−0.533944	−	0.272058i	0.166160	−	0.986099i	$-0.446863\pi$
$827$	−15.3550	−	7.82374i	−0.533944	−	0.272058i	−0.700104	+	0.714041i	$0.746863\pi$
$828$	−3.68898	+	4.55551i	−0.128201	+	0.158315i
$829$	−37.9342	−	16.8894i	−1.31751	−	0.586592i	−0.376952	−	0.926233i	$-0.623028\pi$
$829$	−37.9342	−	16.8894i	−1.31751	−	0.586592i	−0.940555	+	0.339640i	$0.889695\pi$
$830$	−10.3456	+	3.00968i	−0.359100	+	0.104467i
$831$	−0.660907	−	1.48442i	−0.0229266	−	0.0514940i
$832$	3.39004	+	3.39004i	0.117529	+	0.117529i
$833$	−37.8760	+	35.6961i	−1.31232	+	1.23680i
$834$	−1.19410	−	0.387986i	−0.0413482	−	0.0134348i
$835$	3.05344	−	10.1266i	0.105669	−	0.350444i
$836$	1.23031	+	1.10778i	0.0425512	+	0.0383133i
$837$	14.4537	−	22.2568i	0.499594	−	0.769307i
$838$	−26.0498	−	1.36521i	−0.899877	−	0.0471605i
$839$	11.9529	+	36.7873i	0.412660	+	1.27004i	0.914327	+	0.404977i	$0.132720\pi$
$839$	11.9529	+	36.7873i	0.412660	+	1.27004i	−0.501666	+	0.865061i	$0.667280\pi$
$840$	−2.52367	−	22.5991i	−0.0870750	−	0.779742i
$841$	−18.1325	+	55.8062i	−0.625260	+	1.92435i
$842$	6.90203	−	17.9804i	0.237860	−	0.619645i
$843$	−2.24904	−	0.602629i	−0.0774612	−	0.0207557i
$844$	22.6866	+	2.38446i	0.780905	+	0.0820765i
$845$	24.2919	−	13.0364i	0.835666	−	0.448464i
$846$	7.86749	+	10.8287i	0.270490	+	0.372298i
$847$	−3.89424	−	27.1873i	−0.133808	−	0.934168i
$848$	−1.66591	+	3.26953i	−0.0572075	+	0.112276i
$849$	−17.2494	−	9.95893i	−0.591997	−	0.341789i
$850$	32.2493	−	12.0196i	1.10614	−	0.412270i
$851$	−13.4134	−	23.2326i	−0.459804	−	0.796404i
$852$	−0.779907	−	1.20095i	−0.0267192	−	0.0411439i
$853$	−4.26100	+	26.9029i	−0.145894	+	0.921138i	0.800783	+	0.598954i	$0.204417\pi$
$853$	−4.26100	+	26.9029i	−0.145894	+	0.921138i	−0.946677	+	0.322184i	$0.895583\pi$
$854$	−8.14170	−	19.0406i	−0.278603	−	0.651554i
$855$	3.94391	−	3.33528i	0.134879	−	0.114064i
$856$	14.4691	−	6.44206i	0.494543	−	0.220185i
$857$	9.92732	−	37.0493i	0.339111	−	1.26558i	−0.560232	−	0.828336i	$-0.689288\pi$
$857$	9.92732	−	37.0493i	0.339111	−	1.26558i	0.899343	−	0.437244i	$-0.144045\pi$
$858$	0.612580	−	0.496057i	0.0209131	−	0.0169351i
$859$	0.603007	+	0.669707i	0.0205743	+	0.0228501i	0.753344	−	0.657626i	$-0.228439\pi$
$859$	0.603007	+	0.669707i	0.0205743	+	0.0228501i	−0.732770	+	0.680477i	$0.761773\pi$
$860$	−6.47631	−	0.541501i	−0.220840	−	0.0184650i
$861$	−8.82079	+	0.795217i	−0.300612	+	0.0271009i
$862$	−1.04523	−	2.05137i	−0.0356006	−	0.0698701i
$863$	0.0615826	−	1.17507i	0.00209629	−	0.0399997i	−0.997381	−	0.0723253i	$-0.976958\pi$
$863$	0.0615826	−	1.17507i	0.00209629	−	0.0399997i	0.999477	+	0.0323256i	$0.0102914\pi$
$864$	20.4668	−	22.7307i	0.696296	−	0.773315i
$865$	−11.1963	+	1.41849i	−0.380687	+	0.0482301i
$866$	−6.36565	+	5.73166i	−0.216314	+	0.194770i
$867$	7.91096	+	49.9479i	0.268670	+	1.69632i
$868$	6.66943	−	12.6237i	0.226375	−	0.428478i
$869$	−2.26247	+	3.11402i	−0.0767490	+	0.105636i
$870$	23.0576	+	11.1363i	0.781725	+	0.377556i
$871$	0.304239	−	0.683332i	0.0103087	−	0.0231538i
$872$	−44.5375	+	17.0964i	−1.50823	+	0.578956i
$873$	11.2681	−	7.31759i	0.381367	−	0.247663i
$874$	−6.96421			−0.235568
$875$	−7.56259	−	28.5973i	−0.255662	−	0.966766i
$876$	5.60304			0.189309
$877$	34.7725	−	22.5815i	1.17418	−	0.762524i	0.198157	−	0.980170i	$-0.436504\pi$
$877$	34.7725	−	22.5815i	1.17418	−	0.762524i	0.976028	+	0.217646i	$0.0698378\pi$
$878$	−18.3515	+	7.04448i	−0.619333	+	0.237740i
$879$	2.08372	−	4.68011i	0.0702821	−	0.157856i
$880$	−0.646171	−	0.312087i	−0.0217824	−	0.0105204i
$881$	−20.7423	+	28.5494i	−0.698827	+	0.961852i	0.301139	+	0.953580i	$0.402633\pi$
$881$	−20.7423	+	28.5494i	−0.698827	+	0.961852i	−0.999966	+	0.00827221i	$0.997367\pi$
$882$	1.50953	−	7.99116i	0.0508285	−	0.269076i
$883$	−2.01591	−	12.7280i	−0.0678407	−	0.428330i	−0.998110	−	0.0614522i	$-0.980427\pi$
$883$	−2.01591	−	12.7280i	−0.0678407	−	0.428330i	0.930269	−	0.366877i	$-0.119573\pi$
$884$	−5.17243	+	4.65728i	−0.173968	+	0.156641i
$885$	33.4036	−	4.23198i	1.12285	−	0.142256i
$886$	−14.1223	+	15.6845i	−0.474450	+	0.526930i
$887$	−2.39817	+	45.7599i	−0.0805228	+	1.53647i	0.597766	+	0.801671i	$0.296055\pi$
$887$	−2.39817	+	45.7599i	−0.0805228	+	1.53647i	−0.678289	+	0.734796i	$0.737278\pi$
$888$	11.4544	+	22.4805i	0.384384	+	0.754397i
$889$	−7.00267	−	3.24289i	−0.234862	−	0.108763i
$890$	−1.19280	−	0.0997335i	−0.0399829	−	0.00334307i
$891$	−1.92742	−	2.14061i	−0.0645709	−	0.0717132i
$892$	−7.77856	+	6.29895i	−0.260445	+	0.210904i
$893$	5.48864	−	20.4839i	0.183670	−	0.685467i
$894$	−12.7221	+	5.66427i	−0.425492	+	0.189441i
$895$	−6.16345	+	5.21230i	−0.206022	+	0.174228i
$896$	8.67042	−	11.5695i	0.289658	−	0.386511i
$897$	0.691729	−	4.36740i	0.0230961	−	0.145823i
$898$	−16.4280	−	25.2970i	−0.548211	−	0.844171i
$899$	22.1049	+	38.2867i	0.737238	+	1.27693i
$900$	3.96441	−	5.97618i	0.132147	−	0.199206i
$901$	−57.9395	−	33.4514i	−1.93025	−	1.11443i
$902$	−0.838114	+	1.64489i	−0.0279062	+	0.0547689i
$903$	8.24925	+	3.30758i	0.274518	+	0.110069i
$904$	−16.0538	−	22.0961i	−0.533940	−	0.734905i
$905$	−24.4511	+	13.1218i	−0.812783	+	0.436184i
$906$	−13.4909	−	1.41795i	−0.448205	−	0.0471083i
$907$	19.0139	+	5.09475i	0.631345	+	0.169168i	0.560280	−	0.828303i	$-0.310693\pi$
$907$	19.0139	+	5.09475i	0.631345	+	0.169168i	0.0710652	+	0.997472i	$0.477360\pi$
$908$	3.84640	−	10.0202i	0.127647	−	0.332532i
$909$	2.45091	−	7.54313i	0.0812916	−	0.250190i
$910$	−2.66023	−	3.61195i	−0.0881857	−	0.119735i
$911$	10.8138	+	33.2815i	0.358278	+	1.10267i	0.954085	+	0.299537i	$0.0968323\pi$
$911$	10.8138	+	33.2815i	0.358278	+	1.10267i	−0.595807	+	0.803128i	$0.703168\pi$
$912$	0.990232	+	0.0518959i	0.0327899	+	0.00171844i
$913$	−2.23078	+	3.43509i	−0.0738279	+	0.113685i
$914$	5.55829	+	5.00470i	0.183852	+	0.165541i
$915$	−7.20960	+	23.9102i	−0.238342	+	0.790447i
$916$	−9.35025	−	3.03808i	−0.308941	−	0.100381i
$917$	7.85000	+	15.9875i	0.259230	+	0.527954i
$918$	−27.3577	−	27.3577i	−0.902939	−	0.902939i
$919$	14.7750	+	33.1853i	0.487384	+	1.09468i	0.975117	+	0.221689i	$0.0711571\pi$
$919$	14.7750	+	33.1853i	0.487384	+	1.09468i	−0.487734	+	0.872992i	$0.662176\pi$
$920$	−25.5315	+	7.42746i	−0.841747	+	0.244876i
$921$	33.7668	+	15.0340i	1.11266	+	0.495386i
$922$	22.1869	−	27.3985i	0.730686	−	0.902322i
$923$	−0.692136	−	0.352661i	−0.0227819	−	0.0116080i
$924$	−2.30471	−	2.13781i	−0.0758193	−	0.0703289i
$925$	19.0315	+	26.7395i	0.625752	+	0.879188i
$926$	−17.0216	+	29.4823i	−0.559364	+	0.968847i
$927$	−12.4085	+	0.650304i	−0.407550	+	0.0213588i
$928$	18.2606	+	47.5706i	0.599434	+	1.56158i
$929$	−0.343990	−	3.27285i	−0.0112860	−	0.107379i	0.987429	−	0.158065i	$-0.0505257\pi$
$929$	−0.343990	−	3.27285i	−0.0112860	−	0.107379i	−0.998715	+	0.0506867i	$0.983859\pi$
$930$	11.9524	−	4.88267i	0.391935	−	0.160109i
$931$	−11.3444	+	6.10905i	−0.371797	+	0.200216i
$932$	2.25132	−	2.25132i	0.0737446	−	0.0737446i
$933$	−26.1169	−	10.0254i	−0.855030	−	0.328215i
$934$	18.8552	−	4.00780i	0.616961	−	0.131139i
$935$	6.29883	−	11.4672i	0.205994	−	0.375018i
$936$	0.621795	−	2.92532i	0.0203240	−	0.0956170i
$937$	−8.94070	+	4.55551i	−0.292080	+	0.148822i	−0.593891	−	0.804546i	$-0.702409\pi$
$937$	−8.94070	+	4.55551i	−0.292080	+	0.148822i	0.301811	+	0.953368i	$0.402409\pi$
$938$	2.15188	+	0.610891i	0.0702614	+	0.0199463i
$939$	−6.03743	+	1.96168i	−0.197024	+	0.0640170i
$940$	−0.627150	−	29.4376i	−0.0204554	−	0.960150i
$941$	−3.13847	−	14.7653i	−0.102311	−	0.481336i	−0.999233	−	0.0391481i	$-0.987536\pi$
$941$	−3.13847	−	14.7653i	−0.102311	−	0.481336i	0.896922	−	0.442188i	$-0.145798\pi$
$942$	−12.8310	−	15.8450i	−0.418057	−	0.516257i
$943$	2.68038	+	10.0033i	0.0872851	+	0.325752i
$944$	−3.76069	−	2.73230i	−0.122400	−	0.0889288i
$945$	−25.7062	+	21.0942i	−0.836222	+	0.686194i
$946$	1.49877	−	1.08892i	0.0487293	−	0.0354039i
$947$	−44.2910	−	35.8661i	−1.43926	−	1.16549i	−0.957226	−	0.289341i	$-0.906564\pi$
$947$	−44.2910	−	35.8661i	−1.43926	−	1.16549i	−0.482036	−	0.876151i	$-0.660103\pi$
$948$	−0.386503	−	7.37491i	−0.0125530	−	0.239526i
$949$	2.63228	−	1.51975i	0.0854473	−	0.0493330i
$950$	8.48185	−	0.807884i	0.275187	−	0.0262112i
$951$		−	39.2544i		−	1.27291i
$952$	−43.9436	−	36.6756i	−1.42422	−	1.18866i
$953$	−15.7565	−	2.49558i	−0.510403	−	0.0808399i	−0.104079	−	0.994569i	$-0.533190\pi$
$953$	−15.7565	−	2.49558i	−0.510403	−	0.0808399i	−0.406324	+	0.913729i	$0.633190\pi$
$954$	10.3967	−	1.09273i	0.336604	−	0.0353785i
$955$	14.4891	+	49.8054i	0.468856	+	1.61167i
$956$	1.28587	−	12.2343i	0.0415881	−	0.395684i
$957$	9.40237	−	2.51936i	0.303935	−	0.0814392i
$958$	1.27980	−	0.202701i	0.0413486	−	0.00654897i
$959$	−26.4237	+	44.2408i	−0.853264	+	1.42861i
$960$	16.8321	−	3.95428i	0.543255	−	0.127624i
$961$	−8.51796	−	1.81055i	−0.274773	−	0.0584048i
$962$	4.17428	+	2.71081i	0.134584	+	0.0873999i
$963$	−5.72903	−	3.72047i	−0.184615	−	0.119891i
$964$	11.7979	+	2.50771i	0.379984	+	0.0807680i
$965$	−21.8285	+	25.3068i	−0.702684	+	0.814655i
$966$	13.2222	+	0.195837i	0.425417	+	0.00630096i
$967$	30.4690	−	4.82581i	0.979817	−	0.155188i	0.354074	−	0.935217i	$-0.384796\pi$
$967$	30.4690	−	4.82581i	0.979817	−	0.155188i	0.625743	+	0.780030i	$0.284796\pi$
$968$	29.1751	−	7.81746i	0.937725	−	0.251263i
$969$	−1.88976	+	17.9799i	−0.0607080	+	0.577598i
$970$	22.1524	+	0.688246i	0.711270	+	0.0220983i
$971$	−4.01132	+	0.421607i	−0.128729	+	0.0135300i	−0.168674	−	0.985672i	$-0.553949\pi$
$971$	−4.01132	+	0.421607i	−0.128729	+	0.0135300i	0.0399446	+	0.999202i	$0.487282\pi$
$972$	−13.5770	−	2.15038i	−0.435482	−	0.0689736i
$973$	0.935758	+	2.54998i	0.0299990	+	0.0817487i
$974$		−	24.6259i		−	0.789064i
$975$	−0.335829	+	5.39939i	−0.0107551	+	0.172919i
$976$	2.98586	−	1.72388i	0.0955749	−	0.0551802i
$977$	−1.28382	−	24.4967i	−0.0410730	−	0.783719i	−0.939072	−	0.343721i	$-0.888312\pi$
$977$	−1.28382	−	24.4967i	−0.0410730	−	0.783719i	0.897999	−	0.439998i	$-0.145021\pi$
$978$	19.5502	+	15.8314i	0.625146	+	0.506233i
$979$	−0.368121	+	0.267456i	−0.0117652	+	0.00854792i
$980$	−12.7548	+	12.5444i	−0.407438	+	0.400715i
$981$	16.6460	+	12.0940i	0.531467	+	0.386133i
$982$	0.0494843	+	0.184678i	0.00157911	+	0.00589331i
$983$	28.7473	+	35.4999i	0.916896	+	1.13227i	0.990844	+	0.135010i	$0.0431066\pi$
$983$	28.7473	+	35.4999i	0.916896	+	1.13227i	−0.0739487	+	0.997262i	$0.523560\pi$
$984$	−2.02505	−	9.52713i	−0.0645563	−	0.303714i
$985$	−1.92302	+	2.76897i	−0.0612724	+	0.0882266i
$986$	61.2982	−	19.9170i	1.95213	−	0.634286i
$987$	−10.9967	+	38.7362i	−0.350029	+	1.23299i
$988$	−1.53528	+	0.782265i	−0.0488438	+	0.0248872i
$989$	2.16073	−	10.1654i	0.0687072	−	0.323242i
$990$	0.256947	+	2.02812i	0.00816632	+	0.0644579i
$991$	−44.8481	+	9.53276i	−1.42465	+	0.302818i	−0.854810	−	0.518940i	$-0.826327\pi$
$991$	−44.8481	+	9.53276i	−1.42465	+	0.302818i	−0.569836	+	0.821758i	$0.692993\pi$
$992$	23.9864	+	9.20750i	0.761568	+	0.292339i
$993$	−21.4880	+	21.4880i	−0.681902	+	0.681902i
$994$	0.750502	−	2.19848i	0.0238045	−	0.0697314i
$995$	−0.577522	−	7.82608i	−0.0183087	−	0.248103i
$996$	−0.821430	−	7.81538i	−0.0260280	−	0.247640i
$997$	8.17250	+	21.2901i	0.258826	+	0.674264i	0.999996	+	0.00294638i	$0.000937862\pi$
$997$	8.17250	+	21.2901i	0.258826	+	0.674264i	−0.741170	+	0.671317i	$0.765729\pi$
$998$	21.8260	−	1.14385i	0.690891	−	0.0362080i
$999$	18.4479	−	31.9527i	0.583665	−	1.01094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.33.8	✓	288
5.2	odd	4		875.2.bb.b.607.8		288
5.3	odd	4		875.2.bb.a.607.11		288
5.4	even	2		875.2.bb.c.768.11		288
7.3	odd	6	inner	175.2.x.a.108.8	yes	288
25.3	odd	20		875.2.bb.c.257.11		288
25.4	even	10		875.2.bb.a.243.8		288
25.21	even	5		875.2.bb.b.243.11		288
25.22	odd	20	inner	175.2.x.a.47.8	yes	288
35.3	even	12		875.2.bb.a.857.8		288
35.17	even	12		875.2.bb.b.857.11		288
35.24	odd	6		875.2.bb.c.143.11		288
175.3	even	60		875.2.bb.c.507.11		288
175.122	even	60	inner	175.2.x.a.122.8	yes	288
175.129	odd	30		875.2.bb.a.493.11		288
175.171	odd	30		875.2.bb.b.493.8		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	1.1	even	1	trivial
175.2.x.a.47.8	yes	288	25.22	odd	20	inner
175.2.x.a.108.8	yes	288	7.3	odd	6	inner
175.2.x.a.122.8	yes	288	175.122	even	60	inner
875.2.bb.a.243.8		288	25.4	even	10
875.2.bb.a.493.11		288	175.129	odd	30
875.2.bb.a.607.11		288	5.3	odd	4
875.2.bb.a.857.8		288	35.3	even	12
875.2.bb.b.243.11		288	25.21	even	5
875.2.bb.b.493.8		288	175.171	odd	30
875.2.bb.b.607.8		288	5.2	odd	4
875.2.bb.b.857.11		288	35.17	even	12
875.2.bb.c.143.11		288	35.24	odd	6
875.2.bb.c.257.11		288	25.3	odd	20
875.2.bb.c.507.11		288	175.3	even	60
875.2.bb.c.768.11		288	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.776420 + 0.504213i) q^{2} +(-1.23327 + 0.473408i) q^{3} +(-0.464876 + 1.04413i) q^{4} +(2.01352 + 0.972487i) q^{5} +(0.718837 - 0.989394i) q^{6} +(-2.64389 + 0.0993238i) q^{7} +(-0.455170 - 2.87383i) q^{8} +(-0.932596 + 0.839713i) q^{9} +(-2.05368 + 0.260185i) q^{10} +(-0.526566 + 0.584810i) q^{11} +(0.0790188 - 1.50777i) q^{12} +(-0.371838 - 0.729773i) q^{13} +(2.00269 - 1.41020i) q^{14} +(-2.94360 - 0.246122i) q^{15} +(0.272873 + 0.303056i) q^{16} +(-5.77821 + 4.67910i) q^{17} +(0.300692 - 1.12220i) q^{18} +(-1.68154 + 0.748668i) q^{19} +(-1.95144 + 1.65029i) q^{20} +(3.21360 - 1.37413i) q^{21} +(0.113967 - 0.719560i) q^{22} +(-2.22587 - 3.42753i) q^{23} +(1.92184 + 3.32873i) q^{24} +(3.10854 + 3.91625i) q^{25} +(0.656664 + 0.379125i) q^{26} +(2.55179 - 5.00818i) q^{27} +(1.12537 - 2.80673i) q^{28} +(5.50382 + 7.57536i) q^{29} +(2.40957 - 1.29311i) q^{30} +(4.69555 + 0.493522i) q^{31} +(5.25635 + 1.40844i) q^{32} +(0.372543 - 0.970509i) q^{33} +(2.12705 - 6.54639i) q^{34} +(-5.42011 - 2.37115i) q^{35} +(-0.443227 - 1.36411i) q^{36} +(6.55514 + 0.343540i) q^{37} +(0.928090 - 1.42913i) q^{38} +(0.804057 + 0.723976i) q^{39} +(1.87827 - 6.22917i) q^{40} +(-2.40999 - 0.783055i) q^{41} +(-1.80225 + 2.68724i) q^{42} +(1.79811 + 1.79811i) q^{43} +(-0.365830 - 0.821667i) q^{44} +(-2.69441 + 0.783843i) q^{45} +(3.45641 + 1.53889i) q^{46} +(-7.25044 + 8.95355i) q^{47} +(-0.479996 - 0.244570i) q^{48} +(6.98027 - 0.525202i) q^{49} +(-4.38815 - 1.47329i) q^{50} +(4.91096 - 8.50604i) q^{51} +(0.934836 - 0.0489927i) q^{52} +(3.22465 + 8.40051i) q^{53} +(0.543925 + 5.17510i) q^{54} +(-1.62897 + 0.665450i) q^{55} +(1.48886 + 7.55288i) q^{56} +(1.71936 - 1.71936i) q^{57} +(-8.09287 - 3.10656i) q^{58} +(-11.1497 + 2.36995i) q^{59} +(1.62539 - 2.95908i) q^{60} +(1.75779 - 8.26975i) q^{61} +(-3.89456 + 1.98438i) q^{62} +(2.38227 - 2.31273i) q^{63} +(-5.56698 + 1.80882i) q^{64} +(-0.0390087 - 1.83102i) q^{65} +(0.200093 + 0.941364i) q^{66} +(0.574734 + 0.709737i) q^{67} +(-2.19943 - 8.20839i) q^{68} +(4.36771 + 3.17333i) q^{69} +(5.40385 - 0.891880i) q^{70} +(0.767293 - 0.557471i) q^{71} +(2.83768 + 2.29791i) q^{72} +(0.194220 + 3.70594i) q^{73} +(-5.26276 + 3.03846i) q^{74} +(-5.68765 - 3.35818i) q^{75} -2.10378i q^{76} +(1.33409 - 1.59847i) q^{77} +(-0.989324 - 0.156693i) q^{78} +(4.86448 - 0.511278i) q^{79} +(0.254718 + 0.875576i) q^{80} +(-0.382611 + 3.64030i) q^{81} +(2.26599 - 0.607171i) q^{82} +(5.14074 - 0.814213i) q^{83} +(-0.0591594 + 3.99422i) q^{84} +(-16.1849 + 3.80224i) q^{85} +(-2.30272 - 0.489458i) q^{86} +(-10.3739 - 6.73691i) q^{87} +(1.92032 + 1.24707i) q^{88} +(0.565582 + 0.120218i) q^{89} +(1.69677 - 1.96715i) q^{90} +(1.05558 + 1.89250i) q^{91} +(4.61354 - 0.730712i) q^{92} +(-6.02451 + 1.61426i) q^{93} +(1.11489 - 10.6075i) q^{94} +(-4.11388 - 0.127813i) q^{95} +(-7.14926 + 0.751418i) q^{96} +(-10.5745 - 1.67483i) q^{97} +(-5.15481 + 3.92732i) q^{98} -0.987555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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