LMFDB - Embedded newform 175.2.x.a.122.8

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			122.8
Character	$\chi$	$=$	175.122
Dual form			175.2.x.a.33.8

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{20}\right)$

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	0.240133	−	0.970740i	$-0.422809\pi$
$2$	−0.776420	−	0.504213i	−0.549012	−	0.356532i	−0.789144	+	0.614208i	$0.789476\pi$
$3$	−1.23327	−	0.473408i	−0.712029	−	0.273322i	−0.0247269	−	0.999694i	$-0.507872\pi$
$3$	−1.23327	−	0.473408i	−0.712029	−	0.273322i	−0.687302	+	0.726372i	$0.741205\pi$
$4$	−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	0.658514	−	0.752569i	$-0.271185\pi$
$11$	−0.526566	−	0.584810i	−0.158765	−	0.176327i	−0.817279	+	0.576242i	$0.804519\pi$
$12$	0.0790188	+	1.50777i	0.0228108	+	0.435255i
$13$	−0.371838	+	0.729773i	−0.103129	+	0.202403i	−0.936805	−	0.349851i	$-0.886232\pi$
$13$	−0.371838	+	0.729773i	−0.103129	+	0.202403i	0.833676	+	0.552254i	$0.186232\pi$
$14$	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	−0.972876	−	0.231328i	$-0.925693\pi$
$17$	−5.77821	−	4.67910i	−1.40142	−	1.13485i	−0.428545	−	0.903520i	$-0.640974\pi$
$18$	0.300692	+	1.12220i	0.0708737	+	0.264504i
$19$	−1.68154	−	0.748668i	−0.385771	−	0.171756i	0.204682	−	0.978829i	$-0.434384\pi$
$19$	−1.68154	−	0.748668i	−0.385771	−	0.171756i	−0.590453	+	0.807072i	$0.701051\pi$
$20$	−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	−0.990794	−	0.135381i	$-0.956774\pi$
$23$	−2.22587	+	3.42753i	−0.464125	+	0.714690i	0.526669	+	0.850071i	$0.323441\pi$
$24$	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	0.111266	−	0.993791i	$-0.464509\pi$
$29$	5.50382	−	7.57536i	1.02203	−	1.40671i	0.910768	−	0.412919i	$-0.135491\pi$
$30$	2.40957	+	1.29311i	0.439925	+	0.236088i
$31$	4.69555	−	0.493522i	0.843345	−	0.0886392i	0.327005	−	0.945023i	$-0.393961\pi$
$31$	4.69555	−	0.493522i	0.843345	−	0.0886392i	0.516340	+	0.856383i	$0.327294\pi$
$32$	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	0.494766	−	0.869027i	$-0.335254\pi$
$37$	6.55514	−	0.343540i	1.07766	−	0.0564777i	0.582893	+	0.812549i	$0.301921\pi$
$38$	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	−0.491096	−	0.871106i	$-0.663404\pi$
$41$	−2.40999	+	0.783055i	−0.376378	+	0.122293i	0.114718	+	0.993398i	$0.463404\pi$
$42$	−1.80225	−	2.68724i	−0.278094	−	0.414651i
$43$	1.79811	−	1.79811i	0.274209	−	0.274209i	−0.556583	−	0.830792i	$-0.687888\pi$
$43$	1.79811	−	1.79811i	0.274209	−	0.274209i	0.830792	+	0.556583i	$0.187888\pi$
$44$	−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	−0.950149	−	0.311797i	$-0.899069\pi$
$47$	−7.25044	−	8.95355i	−1.05759	−	1.30601i	−0.107437	−	0.994212i	$-0.534264\pi$
$48$	−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	−0.512493	−	0.858691i	$-0.671278\pi$
$53$	3.22465	−	8.40051i	0.442940	−	1.15390i	0.955433	−	0.295207i	$-0.0953887\pi$
$54$	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	−0.586401	−	0.810021i	$-0.699456\pi$
$59$	−11.1497	−	2.36995i	−1.45157	−	0.308541i	−0.865169	+	0.501480i	$0.832789\pi$
$60$	1.62539	+	2.95908i	0.209837	+	0.382015i
$61$	1.75779	+	8.26975i	0.225062	+	1.05883i	0.935022	+	0.354591i	$0.115380\pi$
$61$	1.75779	+	8.26975i	0.225062	+	1.05883i	−0.709959	+	0.704243i	$0.751287\pi$
$62$	−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	−0.740828	−	0.671694i	$-0.765567\pi$
$67$	0.574734	−	0.709737i	0.0702149	−	0.0867082i	0.811043	+	0.584986i	$0.198900\pi$
$68$	−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	0.632384	−	0.774655i	$-0.282076\pi$
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	−0.541323	+	0.840815i	$0.682076\pi$
$72$	2.83768	−	2.29791i	0.334424	−	0.270811i
$73$	0.194220	−	3.70594i	0.0227317	−	0.433747i	−0.963430	−	0.267961i	$-0.913650\pi$
$73$	0.194220	−	3.70594i	0.0227317	−	0.433747i	0.986162	−	0.165787i	$-0.0530164\pi$
$74$	−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	0.374142	−	0.927371i	$-0.377937\pi$
$79$	4.86448	+	0.511278i	0.547297	+	0.0575232i	0.173155	+	0.984895i	$0.444604\pi$
$80$	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	0.432051	−	0.901849i	$-0.357790\pi$
$83$	5.14074	+	0.814213i	0.564269	+	0.0893715i	0.132218	+	0.991221i	$0.457790\pi$
$84$	−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	−0.177838	−	0.984060i	$-0.556910\pi$
$89$	0.565582	−	0.120218i	0.0599516	−	0.0127431i	0.237790	+	0.971317i	$0.423577\pi$
$90$	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	−0.668148	−	0.744029i	$-0.732913\pi$
$97$	−10.5745	+	1.67483i	−1.07368	+	0.170054i	−0.405529	+	0.914082i	$0.632913\pi$
$98$	−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	0.202328	−	0.979318i	$-0.435149\pi$
$101$	−5.47339	−	3.16006i	−0.544622	−	0.314438i	−0.746950	+	0.664880i	$0.768483\pi$
$102$	0.475885	−	9.08043i	0.0471197	−	0.899097i
$103$	7.69483	−	6.23115i	0.758194	−	0.613974i	−0.170269	−	0.985398i	$-0.554464\pi$
$103$	7.69483	−	6.23115i	0.758194	−	0.613974i	0.928463	+	0.371424i	$0.121130\pi$
$104$	−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	−0.863791	−	0.503850i	$-0.831916\pi$
$107$	1.40885	−	5.25791i	0.136199	−	0.508302i	0.999990	−	0.00445150i	$-0.00141696\pi$
$108$	4.04291	−	4.99258i	0.389030	−	0.480412i
$109$	−3.40888	+	16.0375i	−0.326512	+	1.53612i	0.442434	+	0.896801i	$0.354115\pi$
$109$	−3.40888	+	16.0375i	−0.326512	+	1.53612i	−0.768945	+	0.639315i	$0.779218\pi$
$110$	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	0.800739	−	0.599014i	$-0.204441\pi$
$113$	8.36368	+	4.26151i	0.786789	+	0.400889i	−0.0139501	+	0.999903i	$0.504441\pi$
$114$	−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	−0.334866	−	0.942266i	$-0.608691\pi$
$127$	2.59888	−	1.32420i	0.230613	−	0.117503i	0.565480	+	0.824762i	$0.308691\pi$
$128$	−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	−0.992763	−	0.120094i	$-0.961680\pi$
$131$	−2.73808	+	6.14983i	−0.239227	+	0.537313i	0.753535	+	0.657408i	$0.228347\pi$
$132$	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	0.918404	+	0.395644i	$0.129479\pi$
$137$	10.6079	+	16.3347i	0.906294	+	1.39557i	−0.0121099	+	0.999927i	$0.503855\pi$
$138$	−4.99121	+	0.261578i	−0.424880	+	0.0222670i
$139$	−0.317252	+	0.976401i	−0.0269090	+	0.0828172i	−0.963609	−	0.267315i	$-0.913863\pi$
$139$	−0.317252	+	0.976401i	−0.0269090	+	0.0828172i	0.936700	+	0.350133i	$0.113863\pi$
$140$	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	−0.846225	−	0.532825i	$-0.821130\pi$
$149$	−9.86165	+	5.69362i	−0.807897	+	0.466440i	0.0383277	+	0.999265i	$0.487797\pi$
$150$	6.10924	+	0.260425i	0.498818	+	0.0212636i
$151$	−5.54607	+	9.60607i	−0.451333	+	0.781731i	−0.998469	−	0.0553124i	$-0.982385\pi$
$151$	−5.54607	+	9.60607i	−0.451333	+	0.781731i	0.547136	+	0.837043i	$0.315718\pi$
$152$	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	0.893348	+	0.449365i	$0.148350\pi$
$157$	4.31493	+	16.1035i	0.344369	+	1.28520i	−0.548979	+	0.835836i	$0.684983\pi$
$158$	−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	−0.633825	−	0.773476i	$-0.718516\pi$
$163$	−1.07656	−	20.5419i	−0.0843225	−	1.60897i	0.549503	−	0.835492i	$-0.314817\pi$
$164$	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	0.942377	+	0.334553i	$0.108585\pi$
$167$	−0.739956	+	4.67190i	−0.0572595	+	0.361522i	−0.999636	+	0.0269687i	$0.991415\pi$
$168$	−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	0.373609	−	0.927586i	$-0.378120\pi$
$173$	−4.23292	−	2.74889i	−0.321823	−	0.208994i	−0.695432	+	0.718592i	$0.744787\pi$
$174$	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	0.850322	−	0.526263i	$-0.176407\pi$
$179$	−1.46827	−	3.29779i	−0.109744	−	0.246488i	−0.960066	+	0.279774i	$0.909740\pi$
$180$	0.434135	+	3.17770i	0.0323585	+	0.236852i
$181$	−7.29441	−	10.0399i	−0.542189	−	0.746259i	0.446737	−	0.894665i	$-0.352586\pi$
$181$	−7.29441	−	10.0399i	−0.542189	−	0.746259i	−0.988927	+	0.148406i	$0.952586\pi$
$182$	−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	0.157467	−	0.987524i	$-0.449667\pi$
$191$	15.5218	−	17.2388i	1.12312	−	1.24735i	0.965655	−	0.259828i	$-0.0836660\pi$
$192$	6.00927	+	4.86621i	0.433682	+	0.351189i
$193$	−3.86831	−	14.4367i	−0.278447	−	1.03918i	−0.953496	−	0.301406i	$-0.902544\pi$
$193$	−3.86831	−	14.4367i	−0.278447	−	1.03918i	0.675049	−	0.737773i	$-0.264123\pi$
$194$	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	0.977861	−	0.209256i	$-0.0671040\pi$
$197$	−0.235850	−	1.48910i	−0.0168036	−	0.106094i	−0.994665	+	0.103162i	$0.967104\pi$
$198$	0.497938	−	0.766758i	0.0353869	−	0.0544911i
$199$	−1.75472	+	3.03927i	−0.124389	+	0.215448i	−0.921494	−	0.388393i	$-0.873030\pi$
$199$	−1.75472	+	3.03927i	−0.124389	+	0.215448i	0.797105	+	0.603841i	$0.206364\pi$
$200$	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	0.478791	+	0.877929i	$0.341075\pi$
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	−0.903384	+	0.428833i	$0.858925\pi$
$212$	−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	−0.172777	−	0.984961i	$-0.555274\pi$
$223$	7.80285	−	3.97575i	0.522518	−	0.266236i	0.695294	+	0.718725i	$0.255274\pi$
$224$	−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	−0.261487	−	0.965207i	$-0.584213\pi$
$227$	−9.37790	−	0.491475i	−0.622433	−	0.0326203i	−0.360946	+	0.932587i	$0.617546\pi$
$228$	0.995946	−	2.59453i	0.0659581	−	0.171827i
$229$	0.899141	−	8.55475i	0.0594169	−	0.565314i	−0.923800	−	0.382875i	$-0.874934\pi$
$229$	0.899141	−	8.55475i	0.0594169	−	0.565314i	0.983217	−	0.182439i	$-0.0583993\pi$
$230$	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	−0.442060	−	0.896986i	$-0.645752\pi$
$233$	−2.60064	+	0.998293i	−0.170374	+	0.0654004i	0.271686	+	0.962386i	$0.412419\pi$
$234$	−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	−0.0413782	−	0.999144i	$-0.513175\pi$
$239$	−10.2364	−	3.32600i	−0.662136	−	0.215141i	−0.620757	+	0.784003i	$0.713175\pi$
$240$	−0.728640	+	0.959236i	−0.0470335	+	0.0619184i
$241$	−2.19409	+	10.3224i	−0.141334	+	0.664922i	0.849247	+	0.527995i	$0.177056\pi$
$241$	−2.19409	+	10.3224i	−0.141334	+	0.664922i	−0.990581	+	0.136927i	$0.956277\pi$
$242$	−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	$-0.630461\pi$
$251$		−	29.0617i		−	1.83436i	0.398477	−	0.917178i	$-0.369539\pi$
$252$	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	0.771571	−	0.636143i	$-0.219471\pi$
$257$	17.9822	+	4.81832i	1.12170	+	0.300559i	0.350129	+	0.936701i	$0.386138\pi$
$258$	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	−0.954739	−	0.297444i	$-0.903866\pi$
$263$	−17.3742	+	11.2829i	−1.07134	+	0.695735i	−0.116599	+	0.993179i	$0.537199\pi$
$264$	−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	0.997852	−	0.0655149i	$-0.0208690\pi$
$269$	0.134230	+	1.27711i	0.00818414	+	0.0778669i	−0.989667	+	0.143382i	$0.954202\pi$
$270$	−3.93751	−	10.9491i	−0.239629	−	0.666343i
$271$	12.3405	+	1.29704i	0.749631	+	0.0787894i	0.471636	−	0.881793i	$-0.343664\pi$
$271$	12.3405	+	1.29704i	0.749631	+	0.0787894i	0.277995	+	0.960583i	$0.410330\pi$
$272$	−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	−0.996013	−	0.0892027i	$-0.971568\pi$
$277$	0.0643756	−	1.22836i	0.00386795	−	0.0738049i	0.999881	+	0.0153977i	$0.00490145\pi$
$278$	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	−0.544440	−	0.838800i	$-0.683258\pi$
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	0.629505	+	0.776996i	$0.283258\pi$
$282$	3.64670	−	13.6097i	0.217158	−	0.810445i
$283$	9.48873	−	11.7176i	0.564046	−	0.696539i	−0.412717	−	0.910859i	$-0.635420\pi$
$283$	9.48873	−	11.7176i	0.564046	−	0.696539i	0.976764	+	0.214320i	$0.0687535\pi$
$284$	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	0.622454	−	0.782657i	$-0.286136\pi$
$293$	−2.74224	−	2.74224i	−0.160203	−	0.160203i	−0.782657	+	0.622454i	$0.786136\pi$
$294$	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	−0.138889	+	0.990308i	$0.544353\pi$
$307$	−19.7851	+	19.7851i	−1.12920	+	1.12920i	−0.990308	+	0.138889i	$0.955647\pi$
$308$	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	−0.0888962	−	0.996041i	$-0.528334\pi$
$311$	15.7376	−	14.1702i	0.892396	−	0.803517i	0.981292	+	0.192524i	$0.0616673\pi$
$312$	1.71460	+	2.64026i	0.0970703	+	0.149475i
$313$	4.79892	−	0.251501i	0.271251	−	0.0142157i	0.0837745	−	0.996485i	$-0.473302\pi$
$313$	4.79892	−	0.251501i	0.271251	−	0.0142157i	0.187477	+	0.982269i	$0.439969\pi$
$314$	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	−0.813477	−	0.581598i	$-0.802428\pi$
$317$	−10.6491	−	27.7417i	−0.598110	−	1.55813i	0.215366	−	0.976533i	$-0.430905\pi$
$318$	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	0.892691	−	0.450669i	$-0.148815\pi$
$331$	21.0153	+	9.35662i	1.15511	+	0.514286i	0.262415	+	0.964955i	$0.415481\pi$
$332$	−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	−0.815530	−	0.578715i	$-0.803554\pi$
$337$	2.42351	−	4.75641i	0.132017	−	0.259098i	0.947547	+	0.319617i	$0.103554\pi$
$338$	−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	0.749163	−	0.662386i	$-0.230456\pi$
$347$	16.0699	+	6.16865i	0.862677	+	0.331151i	0.113514	+	0.993536i	$0.463789\pi$
$348$	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	0.0165408	−	0.999863i	$-0.494735\pi$
$353$	−12.0284	−	4.61726i	−0.640206	−	0.245752i	−0.656747	+	0.754111i	$0.728068\pi$
$354$	−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	0.503499	−	0.863996i	$-0.332046\pi$
$359$	−5.74355	−	5.17152i	−0.303133	−	0.272942i	−0.806633	+	0.591053i	$0.798712\pi$
$360$	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	0.559864	−	0.828585i	$-0.310854\pi$
$367$	−2.57114	−	2.08207i	−0.134212	−	0.108683i	−0.694076	+	0.719902i	$0.744187\pi$
$368$	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	−0.781044	−	0.624476i	$-0.785312\pi$
$373$	2.06888	−	3.18580i	0.107123	−	0.164955i	0.888167	+	0.459522i	$0.151979\pi$
$374$	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	−0.0459436	−	0.998944i	$-0.514629\pi$
$379$	17.8775	−	24.6063i	0.918306	−	1.26394i	0.964250	−	0.264996i	$-0.0853705\pi$
$380$	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	0.983911	+	0.178659i	$0.0571760\pi$
$383$	7.28545	+	18.9792i	0.372269	+	0.969794i	−0.611642	+	0.791135i	$0.709491\pi$
$384$	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	−0.852066	−	0.523434i	$-0.824650\pi$
$389$	−8.29482	+	7.46869i	−0.420564	+	0.378678i	0.431502	+	0.902112i	$0.357984\pi$
$390$	−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	0.564138	−	0.825681i	$-0.309209\pi$
$397$	−7.18871	−	8.87732i	−0.360791	−	0.445540i	−0.924929	+	0.380141i	$0.875875\pi$
$398$	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	0.957658	+	0.287908i	$0.0929597\pi$
$401$	14.5815	+	25.2559i	0.728165	+	1.26122i	−0.229493	+	0.973310i	$0.573707\pi$
$402$	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	0.905875	−	0.423545i	$-0.139214\pi$
$409$	31.5725	+	6.71095i	1.56116	+	0.331835i	0.655287	+	0.755380i	$0.272548\pi$
$410$	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	0.130410	−	0.991460i	$-0.458371\pi$
$419$	22.7957	−	16.5620i	1.11364	−	0.809109i	0.983233	+	0.182351i	$0.0583708\pi$
$420$	−4.00344	−	7.98491i	−0.195348	−	0.389624i
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	0.0965173	−	0.995331i	$-0.469230\pi$
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	−0.916791	+	0.399368i	$0.869230\pi$
$422$	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	0.986476	−	0.163908i	$-0.0524099\pi$
$431$	−0.259952	−	2.47328i	−0.0125215	−	0.119134i	−0.998997	+	0.0447740i	$0.985743\pi$
$432$	2.21408	+	0.593260i	0.106525	+	0.0285432i
$433$	9.13869	+	1.44743i	0.439178	+	0.0695589i	0.372108	−	0.928189i	$-0.378635\pi$
$433$	9.13869	+	1.44743i	0.439178	+	0.0695589i	0.0670695	+	0.997748i	$0.478635\pi$
$434$	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	0.316384	−	0.948631i	$-0.397531\pi$
$439$	20.7692	−	4.41462i	0.991258	−	0.210698i	0.674874	+	0.737933i	$0.264198\pi$
$440$	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	0.740698	−	0.671838i	$-0.234495\pi$
$443$	22.0209	+	5.90047i	1.04624	+	0.280340i	0.305545	+	0.952178i	$0.401161\pi$
$444$	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	$-0.720850\pi$
$449$		−	32.5816i		−	1.53762i	0.639478	−	0.768809i	$-0.279150\pi$
$450$	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	−0.997431	−	0.0716332i	$-0.977179\pi$
$457$	−2.09102	+	7.80380i	−0.0978138	+	0.365046i	0.899617	+	0.436679i	$0.143846\pi$
$458$	−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	−0.700625	−	0.713530i	$-0.747095\pi$
$461$	−36.2181	−	11.7680i	−1.68684	−	0.548089i	−0.986220	+	0.165441i	$0.947095\pi$
$462$	−0.622523	+	2.46898i	−0.0289624	+	0.114868i
$463$	32.7647	+	16.6944i	1.52270	+	0.775856i	0.997189	−	0.0749286i	$-0.0238729\pi$
$463$	32.7647	+	16.6944i	1.52270	+	0.775856i	0.525514	+	0.850785i	$0.323873\pi$
$464$	−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	−0.763803	−	0.645450i	$-0.776670\pi$
$467$	−19.4390	+	7.46192i	−0.899528	+	0.345297i	−0.135726	+	0.990746i	$0.543337\pi$
$468$	−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	−0.435740	−	0.900073i	$-0.643513\pi$
$479$	−1.27864	+	0.569287i	−0.0584226	+	0.0260114i	0.377317	+	0.926084i	$0.376847\pi$
$480$	−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	−0.997487	−	0.0708461i	$-0.977430\pi$
$487$	−14.4876	−	22.3089i	−0.656494	−	1.01091i	0.340994	−	0.940066i	$-0.389237\pi$
$488$	−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	0.952486	−	0.304582i	$-0.0985166\pi$
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	−0.949606	+	0.313446i	$0.898517\pi$
$492$	−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	−0.882120	−	0.471024i	$-0.843884\pi$
$499$	−20.4454	+	11.8042i	−0.915262	+	0.528427i	−0.0331413	+	0.999451i	$0.510551\pi$
$500$	−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	0.973530	−	0.228558i	$-0.0734011\pi$
$503$	−0.515396	−	3.25409i	−0.0229804	−	0.145092i	−0.996511	+	0.0834657i	$0.973401\pi$
$504$	−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	−0.913961	−	0.405802i	$-0.866992\pi$
$509$	−9.35937	+	10.3946i	−0.414847	+	0.460734i	0.499114	+	0.866536i	$0.333659\pi$
$510$	−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	0.968237	+	0.250035i	$0.0804421\pi$
$521$	11.5536	+	25.9498i	0.506172	+	1.13688i	−0.462065	+	0.886846i	$0.652891\pi$
$522$	10.1560	+	3.89852i	0.444516	+	0.170634i
$523$	−33.3009	−	21.6259i	−1.45615	−	0.945633i	−0.998400	−	0.0565510i	$-0.981990\pi$
$523$	−33.3009	−	21.6259i	−1.45615	−	0.945633i	−0.457748	−	0.889082i	$-0.651344\pi$
$524$	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	−0.761810	−	0.647801i	$-0.775689\pi$
$541$	−0.882148	+	0.979725i	−0.0379265	+	0.0421217i	0.723883	+	0.689923i	$0.242355\pi$
$542$	−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	0.947766	+	0.318968i	$0.103336\pi$
$547$	3.39018	+	21.4047i	0.144953	+	0.915200i	−0.802812	+	0.596232i	$0.796664\pi$
$548$	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	−0.0204931	−	0.999790i	$-0.506524\pi$
$557$	10.8954	−	2.91942i	0.461654	−	0.123700i	0.482147	+	0.876090i	$0.339857\pi$
$558$	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	0.777290	−	0.629143i	$-0.216594\pi$
$563$	−2.69577	−	4.15112i	−0.113613	−	0.174949i	−0.890903	+	0.454194i	$0.849927\pi$
$564$	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	−0.710031	−	0.704171i	$-0.751319\pi$
$569$	6.87878	−	15.4500i	0.288373	−	0.647697i	0.998404	+	0.0564736i	$0.0179857\pi$
$570$	−3.08367	−	3.97837i	−0.129161	−	0.166636i
$571$	26.2708	−	11.6965i	1.09940	−	0.489484i	0.224836	−	0.974397i	$-0.427815\pi$
$571$	26.2708	−	11.6965i	1.09940	−	0.489484i	0.874562	+	0.484913i	$0.161149\pi$
$572$	−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	0.266810	−	0.963749i	$-0.414030\pi$
$577$	10.3630	+	0.543104i	0.431419	+	0.0226097i	0.164609	+	0.986359i	$0.447364\pi$
$578$	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	0.536332	−	0.844007i	$-0.319809\pi$
$587$	4.08885	+	2.08337i	0.168765	+	0.0859899i	−0.367568	+	0.929997i	$0.619809\pi$
$588$	−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	−0.834466	−	0.551060i	$-0.814224\pi$
$593$	3.98715	−	14.8803i	0.163733	−	0.611059i	0.998198	−	0.0599990i	$-0.0191098\pi$
$594$	−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	0.199472	−	0.979903i	$-0.436077\pi$
$599$	−13.4466	−	7.76339i	−0.549413	−	0.317204i	−0.748885	+	0.662700i	$0.769411\pi$
$600$	−7.06201	−	17.8739i	−0.288305	−	0.729699i
$601$			41.2449i			1.68241i	0.540714	+	0.841207i	$0.318154\pi$
$601$			41.2449i			1.68241i	−0.540714	+	0.841207i	$0.681846\pi$
$602$	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	0.471028	−	0.882118i	$-0.343883\pi$
$607$	10.7885	+	2.89077i	0.437891	+	0.117333i	−0.0331368	+	0.999451i	$0.510550\pi$
$608$	−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	−0.596123	−	0.802893i	$-0.703293\pi$
$613$	−2.60236	+	1.68999i	−0.105108	+	0.0682580i	0.491015	+	0.871151i	$0.336626\pi$
$614$	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	0.971153	−	0.238456i	$-0.0766413\pi$
$617$	45.2349	+	7.16450i	1.82109	+	0.288432i	0.849935	+	0.526888i	$0.176641\pi$
$618$	11.6964	+	3.13404i	0.470498	+	0.126070i
$619$	−1.86817	−	17.7745i	−0.0750883	−	0.714417i	−0.965701	−	0.259655i	$-0.916391\pi$
$619$	−1.86817	−	17.7745i	−0.0750883	−	0.714417i	0.890613	−	0.454762i	$-0.150276\pi$
$620$	−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	−0.586627	−	0.809857i	$-0.699545\pi$
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	0.588942	+	0.808175i	$0.299545\pi$
$632$	−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	0.636214	−	0.771513i	$-0.280499\pi$
$641$	22.8779	+	4.86285i	0.903622	+	0.192071i	0.267408	+	0.963583i	$0.413833\pi$
$642$	6.21488	−	2.38567i	0.245282	−	0.0941549i
$643$	20.9354	+	20.9354i	0.825611	+	0.825611i	0.986906	−	0.161295i	$-0.0515672\pi$
$643$	20.9354	+	20.9354i	0.825611	+	0.825611i	−0.161295	+	0.986906i	$0.551567\pi$
$644$	−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	0.724878	+	0.688877i	$0.241896\pi$
$647$	−6.98885	+	18.2066i	−0.274760	+	0.715775i	−0.999638	+	0.0268974i	$0.991437\pi$
$648$	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	0.814562	−	0.580077i	$-0.196977\pi$
$653$	1.98821	+	2.45523i	0.0778046	+	0.0960807i	−0.736757	+	0.676157i	$0.763644\pi$
$654$	−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	−0.0371852	−	0.999308i	$-0.511839\pi$
$659$	13.3517	−	4.33824i	0.520110	−	0.168994i	0.557295	+	0.830314i	$0.311839\pi$
$660$	0.874625	−	2.50869i	0.0340447	−	0.0976508i
$661$	−9.47098	+	8.52771i	−0.368378	+	0.331689i	−0.832442	−	0.554113i	$-0.813058\pi$
$661$	−9.47098	+	8.52771i	−0.368378	+	0.331689i	0.464063	+	0.885802i	$0.346391\pi$
$662$	−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	−0.976793	−	0.214185i	$-0.931290\pi$
$673$	−14.9409	−	29.3231i	−0.575928	−	1.13032i	0.400865	−	0.916137i	$-0.368710\pi$
$674$	−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	−0.894295	−	0.447478i	$-0.852322\pi$
$677$	−3.16813	+	4.87849i	−0.121761	+	0.187496i	0.772534	+	0.634973i	$0.218989\pi$
$678$	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	0.854829	−	0.518909i	$-0.173662\pi$
$683$	13.7202	+	11.1104i	0.524989	+	0.425127i	−0.329841	+	0.944037i	$0.606995\pi$
$684$	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	0.993613	−	0.112838i	$-0.0359942\pi$
$691$	25.8993	+	23.3198i	0.985254	+	0.887127i	−0.00835918	+	0.999965i	$0.502661\pi$
$692$	−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	0.527111	−	0.849796i	$-0.323275\pi$
$709$	−7.00111	−	6.30382i	−0.262932	−	0.236745i	−0.790043	+	0.613051i	$0.789942\pi$
$710$	−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	−0.465505	−	0.885045i	$-0.654127\pi$
$719$	−38.4705	−	17.1281i	−1.43471	−	0.638772i	−0.969201	+	0.246273i	$0.920794\pi$
$720$	−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	0.759159	−	0.650905i	$-0.225610\pi$
$727$	−5.76081	−	11.3062i	−0.213657	−	0.419325i	−0.972816	+	0.231580i	$0.925610\pi$
$728$	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	0.770720	+	0.637174i	$0.219897\pi$
$733$	16.9027	+	44.0331i	0.624316	+	1.62640i	−0.146404	+	0.989225i	$0.546770\pi$
$734$	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	0.235560	−	0.971860i	$-0.424308\pi$
$739$	33.3478	−	30.0265i	1.22672	−	1.10454i	0.991159	−	0.132683i	$-0.0423591\pi$
$740$	−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	−0.472283	−	0.881447i	$-0.656570\pi$
$743$	11.1530	−	11.1530i	0.409164	−	0.409164i	0.881447	+	0.472283i	$0.156570\pi$
$744$	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	−0.924830	−	0.380380i	$-0.875793\pi$
$751$	−21.6997	−	37.5850i	−0.791834	−	1.37150i	0.132996	−	0.991117i	$-0.457540\pi$
$752$	−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	−0.928716	−	0.370793i	$-0.879086\pi$
$757$	−35.7542	−	35.7542i	−1.29951	−	1.29951i	−0.370793	−	0.928716i	$-0.620914\pi$
$758$	−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	0.958359	−	0.285567i	$-0.0921820\pi$
$761$	−0.918515	−	4.32127i	−0.0332961	−	0.156646i	−0.991655	+	0.128921i	$0.958849\pi$
$762$	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	−0.977975	−	0.208720i	$-0.933070\pi$
$769$	−29.9959	+	21.7933i	−1.08168	+	0.785888i	−0.103706	+	0.994608i	$0.533070\pi$
$770$	−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	−0.985674	−	0.168659i	$-0.946056\pi$
$773$	0.340031	−	6.48817i	0.0122301	−	0.233363i	0.997904	−	0.0647042i	$-0.0206104\pi$
$774$	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	−0.433593	−	0.901109i	$-0.642754\pi$
$787$	5.98249	−	3.88508i	0.213253	−	0.138488i	0.646846	+	0.762621i	$0.276088\pi$
$788$	−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	0.391154	−	0.920325i	$-0.372076\pi$
$797$	29.5739	−	4.68404i	1.04756	−	0.165917i	0.656406	+	0.754408i	$0.272076\pi$
$798$	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	−0.985276	−	0.170970i	$-0.945310\pi$
$809$	−0.444905	+	2.09311i	−0.0156420	+	0.0735900i	0.969634	+	0.244560i	$0.0786434\pi$
$810$	−0.161392	+	7.57556i	−0.00567075	+	0.266178i
$811$	−11.1135	−	3.61100i	−0.390248	−	0.126799i	0.107319	−	0.994225i	$-0.465773\pi$
$811$	−11.1135	−	3.61100i	−0.390248	−	0.126799i	−0.497567	+	0.867425i	$0.665773\pi$
$812$	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	0.835892	+	0.548894i	$0.184951\pi$
$821$	−2.74655	+	26.1317i	−0.0958552	+	0.912001i	−0.931747	+	0.363107i	$0.881716\pi$
$822$	−8.53614	+	22.2374i	−0.297732	+	0.775618i
$823$	−19.4457	−	1.01911i	−0.677835	−	0.0355239i	−0.289688	−	0.957121i	$-0.593552\pi$
$823$	−19.4457	−	1.01911i	−0.677835	−	0.0355239i	−0.388147	+	0.921597i	$0.626885\pi$
$824$	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	−0.700104	−	0.714041i	$-0.746863\pi$
$827$	−15.3550	+	7.82374i	−0.533944	+	0.272058i	0.166160	+	0.986099i	$0.446863\pi$
$828$	−3.68898	−	4.55551i	−0.128201	−	0.158315i
$829$	−37.9342	+	16.8894i	−1.31751	+	0.586592i	−0.940555	−	0.339640i	$-0.889695\pi$
$829$	−37.9342	+	16.8894i	−1.31751	+	0.586592i	−0.376952	+	0.926233i	$0.623028\pi$
$830$	−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	−0.501666	−	0.865061i	$-0.667280\pi$
$839$	11.9529	−	36.7873i	0.412660	−	1.27004i	0.914327	−	0.404977i	$-0.132720\pi$
$840$	−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	−0.946677	−	0.322184i	$-0.895583\pi$
$853$	−4.26100	−	26.9029i	−0.145894	−	0.921138i	0.800783	−	0.598954i	$-0.204417\pi$
$854$	−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	0.899343	+	0.437244i	$0.144045\pi$
$857$	9.92732	+	37.0493i	0.339111	+	1.26558i	−0.560232	+	0.828336i	$0.689288\pi$
$858$	0.612580	+	0.496057i	0.0209131	+	0.0169351i
$859$	0.603007	−	0.669707i	0.0205743	−	0.0228501i	−0.732770	−	0.680477i	$-0.761773\pi$
$859$	0.603007	−	0.669707i	0.0205743	−	0.0228501i	0.753344	+	0.657626i	$0.228439\pi$
$860$	−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	0.999477	−	0.0323256i	$-0.0102914\pi$
$863$	0.0615826	+	1.17507i	0.00209629	+	0.0399997i	−0.997381	+	0.0723253i	$0.976958\pi$
$864$	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	0.976028	−	0.217646i	$-0.0698378\pi$
$877$	34.7725	+	22.5815i	1.17418	+	0.762524i	0.198157	+	0.980170i	$0.436504\pi$
$878$	−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	−0.999966	−	0.00827221i	$-0.997367\pi$
$881$	−20.7423	−	28.5494i	−0.698827	−	0.961852i	0.301139	−	0.953580i	$-0.402633\pi$
$882$	1.50953	+	7.99116i	0.0508285	+	0.269076i
$883$	−2.01591	+	12.7280i	−0.0678407	+	0.428330i	0.930269	+	0.366877i	$0.119573\pi$
$883$	−2.01591	+	12.7280i	−0.0678407	+	0.428330i	−0.998110	+	0.0614522i	$0.980427\pi$
$884$	−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	−0.678289	−	0.734796i	$-0.737278\pi$
$887$	−2.39817	−	45.7599i	−0.0805228	−	1.53647i	0.597766	−	0.801671i	$-0.296055\pi$
$888$	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	0.0710652	−	0.997472i	$-0.477360\pi$
$907$	19.0139	−	5.09475i	0.631345	−	0.169168i	0.560280	+	0.828303i	$0.310693\pi$
$908$	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	−0.595807	−	0.803128i	$-0.703168\pi$
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	0.954085	−	0.299537i	$-0.0968323\pi$
$912$	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	−0.487734	−	0.872992i	$-0.662176\pi$
$919$	14.7750	−	33.1853i	0.487384	−	1.09468i	0.975117	−	0.221689i	$-0.0711571\pi$
$920$	−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	−0.998715	−	0.0506867i	$-0.983859\pi$
$929$	−0.343990	+	3.27285i	−0.0112860	+	0.107379i	0.987429	+	0.158065i	$0.0505257\pi$
$930$	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	0.301811	−	0.953368i	$-0.402409\pi$
$937$	−8.94070	−	4.55551i	−0.292080	−	0.148822i	−0.593891	+	0.804546i	$0.702409\pi$
$938$	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	0.896922	+	0.442188i	$0.145798\pi$
$941$	−3.13847	+	14.7653i	−0.102311	+	0.481336i	−0.999233	+	0.0391481i	$0.987536\pi$
$942$	−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	−0.482036	+	0.876151i	$0.660103\pi$
$947$	−44.2910	+	35.8661i	−1.43926	+	1.16549i	−0.957226	+	0.289341i	$0.906564\pi$
$948$	−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	−0.406324	−	0.913729i	$-0.633190\pi$
$953$	−15.7565	+	2.49558i	−0.510403	+	0.0808399i	−0.104079	+	0.994569i	$0.533190\pi$
$954$	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	0.625743	−	0.780030i	$-0.284796\pi$
$967$	30.4690	+	4.82581i	0.979817	+	0.155188i	0.354074	+	0.935217i	$0.384796\pi$
$968$	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	0.0399446	−	0.999202i	$-0.487282\pi$
$971$	−4.01132	−	0.421607i	−0.128729	−	0.0135300i	−0.168674	+	0.985672i	$0.553949\pi$
$972$	−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	0.897999	+	0.439998i	$0.145021\pi$
$977$	−1.28382	+	24.4967i	−0.0410730	+	0.783719i	−0.939072	+	0.343721i	$0.888312\pi$
$978$	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	−0.0739487	−	0.997262i	$-0.523560\pi$
$983$	28.7473	−	35.4999i	0.916896	−	1.13227i	0.990844	−	0.135010i	$-0.0431066\pi$
$984$	−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	−0.569836	−	0.821758i	$-0.692993\pi$
$991$	−44.8481	−	9.53276i	−1.42465	−	0.302818i	−0.854810	+	0.518940i	$0.826327\pi$
$992$	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	−0.741170	−	0.671317i	$-0.765729\pi$
$997$	8.17250	−	21.2901i	0.258826	−	0.674264i	0.999996	−	0.00294638i	$-0.000937862\pi$
$998$	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.122.8	yes	288
5.2	odd	4		875.2.bb.a.493.11		288
5.3	odd	4		875.2.bb.b.493.8		288
5.4	even	2		875.2.bb.c.507.11		288
7.5	odd	6	inner	175.2.x.a.47.8	yes	288
25.6	even	5		875.2.bb.b.857.11		288
25.8	odd	20	inner	175.2.x.a.108.8	yes	288
25.17	odd	20		875.2.bb.c.143.11		288
25.19	even	10		875.2.bb.a.857.8		288
35.12	even	12		875.2.bb.a.243.8		288
35.19	odd	6		875.2.bb.c.257.11		288
35.33	even	12		875.2.bb.b.243.11		288
175.19	odd	30		875.2.bb.a.607.11		288
175.33	even	60	inner	175.2.x.a.33.8	✓	288
175.117	even	60		875.2.bb.c.768.11		288
175.131	odd	30		875.2.bb.b.607.8		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	175.33	even	60	inner
175.2.x.a.47.8	yes	288	7.5	odd	6	inner
175.2.x.a.108.8	yes	288	25.8	odd	20	inner
175.2.x.a.122.8	yes	288	1.1	even	1	trivial
875.2.bb.a.243.8		288	35.12	even	12
875.2.bb.a.493.11		288	5.2	odd	4
875.2.bb.a.607.11		288	175.19	odd	30
875.2.bb.a.857.8		288	25.19	even	10
875.2.bb.b.243.11		288	35.33	even	12
875.2.bb.b.493.8		288	5.3	odd	4
875.2.bb.b.607.8		288	175.131	odd	30
875.2.bb.b.857.11		288	25.6	even	5
875.2.bb.c.143.11		288	25.17	odd	20
875.2.bb.c.257.11		288	35.19	odd	6
875.2.bb.c.507.11		288	5.4	even	2
875.2.bb.c.768.11		288	175.117	even	60

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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