LMFDB - Embedded newform 930.2.br.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-0.361945 - 1.69381i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.867646 + 1.49906i) q^{6} +(0.291242 + 2.77098i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.73799 + 1.22613i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.361945 - 1.69381i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.867646 + 1.49906i) q^{6} +(0.291242 + 2.77098i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.73799 + 1.22613i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(0.845000 + 0.376218i) q^{11} +(-1.28842 - 1.15758i) q^{12} +(0.183685 + 0.864168i) q^{13} +(-1.13327 - 2.54536i) q^{14} +(-1.16036 - 1.28591i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.74748 + 3.00417i) q^{17} +(2.22509 - 2.01221i) q^{18} +(-4.78556 - 1.01720i) q^{19} +(0.406737 - 0.913545i) q^{20} +(4.58810 - 1.49625i) q^{21} +(-0.919901 - 0.0966854i) q^{22} +(-4.70119 - 3.41562i) q^{23} +(1.58307 + 0.702778i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.441737 - 0.765111i) q^{26} +(3.06784 + 4.19385i) q^{27} +(1.86436 + 2.07058i) q^{28} +(-2.07551 - 6.38777i) q^{29} +(1.50094 + 0.864404i) q^{30} +(-5.55740 - 0.339510i) q^{31} +1.00000i q^{32} +(0.331399 - 1.56744i) q^{33} +(5.48890 - 4.94222i) q^{34} +(1.63771 + 2.25412i) q^{35} +(-1.49438 + 2.60131i) q^{36} +(-5.69551 - 3.28830i) q^{37} +(4.86567 - 0.511403i) q^{38} +(1.39725 - 0.623908i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-5.51083 - 4.96197i) q^{41} +(-3.90118 + 2.84082i) q^{42} +(-0.327905 + 1.54267i) q^{43} +(0.904755 - 0.192312i) q^{44} +(-1.75811 + 2.43086i) q^{45} +(5.52658 + 1.79570i) q^{46} +(8.09135 + 2.62904i) q^{47} +(-1.72276 - 0.179187i) q^{48} +(-0.746472 + 0.158668i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(7.53071 + 10.3416i) q^{51} +(0.656549 + 0.591160i) q^{52} +(-1.16801 + 11.1129i) q^{53} +(-4.21366 - 3.04058i) q^{54} +(0.919901 - 0.0966854i) q^{55} +(-2.41296 - 1.39312i) q^{56} +(0.00915890 + 8.47400i) q^{57} +(3.94786 + 5.43376i) q^{58} +(-10.2224 + 9.20431i) q^{59} +(-1.69459 - 0.358282i) q^{60} -3.49140i q^{61} +(5.39032 - 1.39444i) q^{62} +(-4.19500 - 7.22982i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.591160 + 0.656549i) q^{65} +(0.169186 + 1.59313i) q^{66} +(-1.98219 - 3.43326i) q^{67} +(-3.69302 + 6.39650i) q^{68} +(-4.08384 + 9.19919i) q^{69} +(-2.25412 - 1.63771i) q^{70} +(15.9627 + 1.67775i) q^{71} +(0.617390 - 2.93578i) q^{72} +(-0.0562466 + 0.126332i) q^{73} +(6.43289 + 1.36735i) q^{74} +(-1.64786 - 0.533452i) q^{75} +(-4.46950 + 1.98995i) q^{76} +(-0.796394 + 2.45105i) q^{77} +(-1.13607 + 1.02515i) q^{78} +(-4.01236 - 9.01191i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(5.99320 - 6.71428i) q^{81} +(6.77444 + 3.01618i) q^{82} +(-11.6516 + 12.9404i) q^{83} +(2.83238 - 3.90731i) q^{84} +(-4.34140 + 5.97543i) q^{85} +(-0.164855 - 1.56850i) q^{86} +(-10.0685 + 5.82755i) q^{87} +(-0.801045 + 0.462484i) q^{88} +(9.03934 - 6.56747i) q^{89} +(0.920881 - 2.85517i) q^{90} +(-2.34110 + 0.760668i) q^{91} -5.81099 q^{92} +(1.43641 + 9.53608i) q^{93} -8.50775 q^{94} +(-4.65302 + 1.51186i) q^{95} +(1.69381 - 0.361945i) q^{96} +(-10.3557 + 7.52384i) q^{97} +(0.660906 - 0.381574i) q^{98} +(-2.77490 + 0.00599835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	−0.361945	−	1.69381i	−0.208969	−	0.977922i
$3$	−0.361945	−	1.69381i	−0.208969	−	0.977922i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.867646	+	1.49906i	0.354215	+	0.611990i
$7$	0.291242	+	2.77098i	0.110079	+	1.04733i	0.900526	+	0.434802i	$0.143182\pi$
$7$	0.291242	+	2.77098i	0.110079	+	1.04733i	−0.790447	+	0.612530i	$0.790152\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−2.73799	+	1.22613i	−0.912664	+	0.408710i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	0.845000	+	0.376218i	0.254777	+	0.113434i	0.530151	−	0.847903i	$-0.322135\pi$
$11$	0.845000	+	0.376218i	0.254777	+	0.113434i	−0.275374	+	0.961337i	$0.588802\pi$
$12$	−1.28842	−	1.15758i	−0.371934	−	0.334164i
$13$	0.183685	+	0.864168i	0.0509449	+	0.239677i	0.996251	−	0.0865068i	$-0.0275704\pi$
$13$	0.183685	+	0.864168i	0.0509449	+	0.239677i	−0.945306	+	0.326184i	$0.894237\pi$
$14$	−1.13327	−	2.54536i	−0.302878	−	0.680276i
$15$	−1.16036	−	1.28591i	−0.299603	−	0.332021i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−6.74748	+	3.00417i	−1.63650	+	0.728619i	−0.999121	−	0.0419276i	$-0.986650\pi$
$17$	−6.74748	+	3.00417i	−1.63650	+	0.728619i	−0.637384	+	0.770546i	$0.719983\pi$
$18$	2.22509	−	2.01221i	0.524459	−	0.474282i
$19$	−4.78556	−	1.01720i	−1.09788	−	0.233362i	−0.376858	−	0.926271i	$-0.622995\pi$
$19$	−4.78556	−	1.01720i	−1.09788	−	0.233362i	−0.721025	+	0.692909i	$0.756329\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	4.58810	−	1.49625i	1.00121	−	0.326508i
$22$	−0.919901	−	0.0966854i	−0.196123	−	0.0206134i
$23$	−4.70119	−	3.41562i	−0.980266	−	0.712205i	−0.0224980	−	0.999747i	$-0.507162\pi$
$23$	−4.70119	−	3.41562i	−0.980266	−	0.712205i	−0.957768	+	0.287542i	$0.907162\pi$
$24$	1.58307	+	0.702778i	0.323142	+	0.143454i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.441737	−	0.765111i	−0.0866318	−	0.150051i
$27$	3.06784	+	4.19385i	0.590405	+	0.807107i
$28$	1.86436	+	2.07058i	0.352331	+	0.391303i
$29$	−2.07551	−	6.38777i	−0.385413	−	1.18618i	−0.936180	−	0.351521i	$-0.885665\pi$
$29$	−2.07551	−	6.38777i	−0.385413	−	1.18618i	0.550767	−	0.834659i	$-0.314335\pi$
$30$	1.50094	+	0.864404i	0.274032	+	0.157818i
$31$	−5.55740	−	0.339510i	−0.998139	−	0.0609778i
$31$	−5.55740	−	0.339510i	−0.998139	−	0.0609778i
$32$			1.00000i			0.176777i
$33$	0.331399	−	1.56744i	0.0576892	−	0.272856i
$34$	5.48890	−	4.94222i	0.941338	−	0.847584i
$35$	1.63771	+	2.25412i	0.276824	+	0.381015i
$36$	−1.49438	+	2.60131i	−0.249063	+	0.433552i
$37$	−5.69551	−	3.28830i	−0.936335	−	0.540594i	−0.0475258	−	0.998870i	$-0.515134\pi$
$37$	−5.69551	−	3.28830i	−0.936335	−	0.540594i	−0.888810	+	0.458276i	$0.848467\pi$
$38$	4.86567	−	0.511403i	0.789316	−	0.0829604i
$39$	1.39725	−	0.623908i	0.223740	−	0.0999052i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−5.51083	−	4.96197i	−0.860647	−	0.774930i	0.115210	−	0.993341i	$-0.463246\pi$
$41$	−5.51083	−	4.96197i	−0.860647	−	0.774930i	−0.975857	+	0.218411i	$0.929913\pi$
$42$	−3.90118	+	2.84082i	−0.601965	+	0.438348i
$43$	−0.327905	+	1.54267i	−0.0500050	+	0.235255i	−0.996052	−	0.0887753i	$-0.971705\pi$
$43$	−0.327905	+	1.54267i	−0.0500050	+	0.235255i	0.946047	+	0.324030i	$0.105038\pi$
$44$	0.904755	−	0.192312i	0.136397	−	0.0289921i
$45$	−1.75811	+	2.43086i	−0.262083	+	0.362371i
$46$	5.52658	+	1.79570i	0.814850	+	0.264761i
$47$	8.09135	+	2.62904i	1.18025	+	0.383485i	0.832458	−	0.554088i	$-0.186933\pi$
$47$	8.09135	+	2.62904i	1.18025	+	0.383485i	0.347787	+	0.937573i	$0.386933\pi$
$48$	−1.72276	−	0.179187i	−0.248659	−	0.0258634i
$49$	−0.746472	+	0.158668i	−0.106639	+	0.0226668i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	7.53071	+	10.3416i	1.05451	+	1.44812i
$52$	0.656549	+	0.591160i	0.0910470	+	0.0819791i
$53$	−1.16801	+	11.1129i	−0.160438	+	1.52647i	0.557391	+	0.830250i	$0.311803\pi$
$53$	−1.16801	+	11.1129i	−0.160438	+	1.52647i	−0.717829	+	0.696219i	$0.754864\pi$
$54$	−4.21366	−	3.04058i	−0.573406	−	0.413770i
$55$	0.919901	−	0.0966854i	0.124039	−	0.0130371i
$56$	−2.41296	−	1.39312i	−0.322445	−	0.186164i
$57$	0.00915890	+	8.47400i	0.00121313	+	1.12241i
$58$	3.94786	+	5.43376i	0.518380	+	0.713488i
$59$	−10.2224	+	9.20431i	−1.33085	+	1.19830i	−0.367505	+	0.930022i	$0.619788\pi$
$59$	−10.2224	+	9.20431i	−1.33085	+	1.19830i	−0.963341	+	0.268278i	$0.913545\pi$
$60$	−1.69459	−	0.358282i	−0.218771	−	0.0462540i
$61$		−	3.49140i		−	0.447028i	−0.974701	−	0.223514i	$-0.928247\pi$
$61$		−	3.49140i		−	0.447028i	0.974701	−	0.223514i	$-0.0717528\pi$
$62$	5.39032	−	1.39444i	0.684571	−	0.177094i
$63$	−4.19500	−	7.22982i	−0.528521	−	0.910872i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.591160	+	0.656549i	0.0733243	+	0.0814349i
$66$	0.169186	+	1.59313i	0.0208254	+	0.196101i
$67$	−1.98219	−	3.43326i	−0.242164	−	0.419440i	0.719167	−	0.694838i	$-0.244524\pi$
$67$	−1.98219	−	3.43326i	−0.242164	−	0.419440i	−0.961330	+	0.275398i	$0.911190\pi$
$68$	−3.69302	+	6.39650i	−0.447844	+	0.775689i
$69$	−4.08384	+	9.19919i	−0.491636	+	1.10745i
$70$	−2.25412	−	1.63771i	−0.269419	−	0.195744i
$71$	15.9627	+	1.67775i	1.89443	+	0.199112i	0.979069	−	0.203526i	$-0.0652402\pi$
$71$	15.9627	+	1.67775i	1.89443	+	0.199112i	0.915359	+	0.402639i	$0.131907\pi$
$72$	0.617390	−	2.93578i	0.0727602	−	0.345985i
$73$	−0.0562466	+	0.126332i	−0.00658317	+	0.0147860i	−0.916807	−	0.399330i	$-0.869243\pi$
$73$	−0.0562466	+	0.126332i	−0.00658317	+	0.0147860i	0.910224	+	0.414116i	$0.135909\pi$
$74$	6.43289	+	1.36735i	0.747808	+	0.158952i
$75$	−1.64786	−	0.533452i	−0.190278	−	0.0615978i
$76$	−4.46950	+	1.98995i	−0.512686	+	0.228263i
$77$	−0.796394	+	2.45105i	−0.0907575	+	0.279323i
$78$	−1.13607	+	1.02515i	−0.128635	+	0.116075i
$79$	−4.01236	−	9.01191i	−0.451426	−	1.01392i	−0.985685	−	0.168599i	$-0.946076\pi$
$79$	−4.01236	−	9.01191i	−0.451426	−	1.01392i	0.534259	−	0.845321i	$-0.320591\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	5.99320	−	6.71428i	0.665912	−	0.746031i
$82$	6.77444	+	3.01618i	0.748112	+	0.333081i
$83$	−11.6516	+	12.9404i	−1.27893	+	1.42040i	−0.420642	+	0.907227i	$0.638195\pi$
$83$	−11.6516	+	12.9404i	−1.27893	+	1.42040i	−0.858288	+	0.513169i	$0.828472\pi$
$84$	2.83238	−	3.90731i	0.309038	−	0.426322i
$85$	−4.34140	+	5.97543i	−0.470891	+	0.648126i
$86$	−0.164855	−	1.56850i	−0.0177768	−	0.169135i
$87$	−10.0685	+	5.82755i	−1.07945	+	0.624779i
$88$	−0.801045	+	0.462484i	−0.0853917	+	0.0493009i
$89$	9.03934	−	6.56747i	0.958168	−	0.696150i	0.00544383	−	0.999985i	$-0.498267\pi$
$89$	9.03934	−	6.56747i	0.958168	−	0.696150i	0.952725	+	0.303835i	$0.0982672\pi$
$90$	0.920881	−	2.85517i	0.0970694	−	0.300961i
$91$	−2.34110	+	0.760668i	−0.245414	+	0.0797397i
$92$	−5.81099			−0.605838
$93$	1.43641	+	9.53608i	0.148948	+	0.988845i
$94$	−8.50775			−0.877508
$95$	−4.65302	+	1.51186i	−0.477389	+	0.155113i
$96$	1.69381	−	0.361945i	0.172874	−	0.0369408i
$97$	−10.3557	+	7.52384i	−1.05146	+	0.763930i	−0.972489	−	0.232947i	$-0.925163\pi$
$97$	−10.3557	+	7.52384i	−1.05146	+	0.763930i	−0.0789699	+	0.996877i	$0.525163\pi$
$98$	0.660906	−	0.381574i	0.0667616	−	0.0385448i
$99$	−2.77490	+	0.00599835i	−0.278888	+	0.000602857i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−4.82213	+	6.63709i	−0.479820	+	0.660416i	−0.978470	−	0.206388i	$-0.933829\pi$
$101$	−4.82213	+	6.63709i	−0.479820	+	0.660416i	0.498650	+	0.866803i	$0.333829\pi$
$102$	−10.3579	−	7.50834i	−1.02558	−	0.743437i
$103$	8.42184	−	9.35340i	0.829828	−	0.921618i	−0.168112	−	0.985768i	$-0.553767\pi$
$103$	8.42184	−	9.35340i	0.829828	−	0.921618i	0.997940	+	0.0641501i	$0.0204336\pi$
$104$	−0.807094	−	0.359341i	−0.0791421	−	0.0352363i
$105$	3.22529	−	3.58984i	0.314756	−	0.350333i
$106$	−2.32322	−	10.9299i	−0.225651	−	1.06161i
$107$	3.22774	+	7.24962i	0.312037	+	0.700847i	0.999682	−	0.0251998i	$-0.00802220\pi$
$107$	3.22774	+	7.24962i	0.312037	+	0.700847i	−0.687645	+	0.726047i	$0.741356\pi$
$108$	4.94702	+	1.58967i	0.476027	+	0.152966i
$109$	1.05510	−	3.24726i	0.101060	−	0.311031i	−0.887725	−	0.460373i	$-0.847716\pi$
$109$	1.05510	−	3.24726i	0.101060	−	0.311031i	0.988786	+	0.149342i	$0.0477156\pi$
$110$	−0.845000	+	0.376218i	−0.0805676	+	0.0358710i
$111$	−3.50831	+	10.8373i	−0.332994	+	1.02863i
$112$	2.72536	+	0.579292i	0.257522	+	0.0547380i
$113$	3.50016	−	7.86150i	0.329268	−	0.739548i	−0.670730	−	0.741702i	$-0.734019\pi$
$113$	3.50016	−	7.86150i	0.329268	−	0.739548i	0.999998	+	0.00215411i	$0.000685676\pi$
$114$	−2.62732	−	8.05643i	−0.246071	−	0.754553i
$115$	−5.77916	−	0.607414i	−0.538909	−	0.0566417i
$116$	−5.43376	−	3.94786i	−0.504512	−	0.366550i
$117$	−1.56251	−	2.14086i	−0.144454	−	0.197923i
$118$	6.87782	−	11.9127i	0.633154	−	1.09666i
$119$	−10.2896	−	17.8222i	−0.943250	−	1.63376i
$120$	1.72237	−	0.182910i	0.157230	−	0.0166973i
$121$	−6.78795	−	7.53878i	−0.617087	−	0.685344i
$122$	1.07890	+	3.32052i	0.0976792	+	0.300626i
$123$	−6.41003	+	11.1303i	−0.577973	+	1.00358i
$124$	−4.69559	+	2.99189i	−0.421677	+	0.268680i
$125$		−	1.00000i		−	0.0894427i
$126$	6.22382	+	5.57964i	0.554462	+	0.497074i
$127$	−14.8583	+	13.3785i	−1.31846	+	1.18715i	−0.350357	+	0.936616i	$0.613940\pi$
$127$	−14.8583	+	13.3785i	−1.31846	+	1.18715i	−0.968108	+	0.250535i	$0.919393\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	2.73168	−	0.00295246i	0.240511	−	0.000259950i
$130$	−0.765111	−	0.441737i	−0.0671047	−	0.0387429i
$131$	11.3786	−	1.19594i	0.994151	−	0.104489i	0.406540	−	0.913633i	$-0.366735\pi$
$131$	11.3786	−	1.19594i	0.994151	−	0.104489i	0.587611	+	0.809144i	$0.300069\pi$
$132$	−0.653211	−	1.46288i	−0.0568547	−	0.127327i
$133$	1.42489	−	13.5569i	0.123554	−	1.17554i
$134$	2.94611	+	2.65269i	0.254506	+	0.229158i
$135$	4.75375	+	2.09806i	0.409138	+	0.180572i
$136$	1.53564	−	7.22464i	0.131680	−	0.619507i
$137$	3.33398	−	0.708659i	0.284841	−	0.0605448i	−0.0632755	−	0.997996i	$-0.520155\pi$
$137$	3.33398	−	0.708659i	0.284841	−	0.0605448i	0.348117	+	0.937451i	$0.386821\pi$
$138$	1.04125	−	10.0109i	0.0886373	−	0.852187i
$139$	14.6737	+	4.76776i	1.24460	+	0.404396i	0.855984	−	0.517002i	$-0.172952\pi$
$139$	14.6737	+	4.76776i	1.24460	+	0.404396i	0.388619	+	0.921398i	$0.372952\pi$
$140$	2.64987	+	0.860996i	0.223955	+	0.0727675i
$141$	1.52448	−	14.6568i	0.128384	−	1.23432i
$142$	−15.6999	+	3.33712i	−1.31751	+	0.280045i
$143$	−0.169902	+	0.799328i	−0.0142079	+	0.0668431i
$144$	0.320034	+	2.98288i	0.0266695	+	0.248573i
$145$	−4.99133	−	4.49422i	−0.414508	−	0.373224i
$146$	0.0144550	−	0.137530i	0.00119630	−	0.0113821i
$147$	0.538934	+	1.20695i	0.0444506	+	0.0995479i
$148$	−6.54058	+	0.687442i	−0.537632	+	0.0565074i
$149$	−4.03223	−	2.32801i	−0.330334	−	0.190718i	0.325656	−	0.945488i	$-0.394415\pi$
$149$	−4.03223	−	2.32801i	−0.330334	−	0.190718i	−0.655989	+	0.754770i	$0.727748\pi$
$150$	1.73205	−	0.00187204i	0.141421	−	0.000152851i
$151$	1.96190	+	2.70032i	0.159657	+	0.219749i	0.881350	−	0.472465i	$-0.156636\pi$
$151$	1.96190	+	2.70032i	0.159657	+	0.219749i	−0.721693	+	0.692214i	$0.756636\pi$
$152$	3.63581	−	3.27370i	0.294904	−	0.265532i
$153$	14.7910	−	16.4987i	1.19578	−	1.33384i
$154$		−	2.57718i		−	0.207675i
$155$	−4.98261	+	2.48468i	−0.400213	+	0.199574i
$156$	0.763678	−	1.32604i	0.0611432	−	0.106168i
$157$	0.509494	+	1.56806i	0.0406621	+	0.125145i	0.969327	−	0.245775i	$-0.0790424\pi$
$157$	0.509494	+	1.56806i	0.0406621	+	0.125145i	−0.928665	+	0.370920i	$0.879042\pi$
$158$	6.60082	+	7.33095i	0.525133	+	0.583219i
$159$	19.2459	−	2.04385i	1.52630	−	0.162088i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	8.09542	−	14.0217i	0.638008	−	1.10506i
$162$	−3.62505	+	8.23766i	−0.284811	+	0.647212i
$163$	6.11668	+	4.44403i	0.479095	+	0.348083i	0.800975	−	0.598697i	$-0.204315\pi$
$163$	6.11668	+	4.44403i	0.479095	+	0.348083i	−0.321880	+	0.946780i	$0.604315\pi$
$164$	−7.37493	−	0.775136i	−0.575885	−	0.0605280i
$165$	−0.496720	−	1.52314i	−0.0386696	−	0.118577i
$166$	7.08253	−	15.9076i	0.549711	−	1.23467i
$167$	10.1126	+	2.14950i	0.782536	+	0.166333i	0.581821	−	0.813317i	$-0.302340\pi$
$167$	10.1126	+	2.14950i	0.782536	+	0.166333i	0.200715	+	0.979650i	$0.435674\pi$
$168$	−1.48633	+	4.59133i	−0.114673	+	0.354229i
$169$	11.1630	−	4.97011i	0.858696	−	0.382316i
$170$	2.28241	−	7.02454i	0.175053	−	0.538758i
$171$	14.3500	−	3.08263i	1.09738	−	0.235735i
$172$	0.641479	+	1.44078i	0.0489123	+	0.109859i
$173$	−1.98292	−	9.32891i	−0.150759	−	0.709264i	−0.986976	−	0.160866i	$-0.948571\pi$
$173$	−1.98292	−	9.32891i	−0.150759	−	0.709264i	0.836218	−	0.548398i	$-0.184762\pi$
$174$	7.77486	−	8.65365i	0.589411	−	0.656032i
$175$	2.54536	+	1.13327i	0.192411	+	0.0856669i
$176$	0.618924	−	0.687385i	0.0466532	−	0.0518136i
$177$	19.2903	+	13.9834i	1.44995	+	1.05106i
$178$	−6.56747	+	9.03934i	−0.492252	+	0.677527i
$179$	1.46336	+	13.9230i	0.109377	+	1.04065i	0.902235	+	0.431245i	$0.141926\pi$
$179$	1.46336	+	13.9230i	0.109377	+	1.04065i	−0.792858	+	0.609407i	$0.791408\pi$
$180$	0.00648493	+	2.99999i	0.000483358	+	0.223606i
$181$	2.85024	−	1.64559i	0.211856	−	0.122315i	−0.390317	−	0.920680i	$-0.627635\pi$
$181$	2.85024	−	1.64559i	0.211856	−	0.122315i	0.602174	+	0.798365i	$0.294301\pi$
$182$	1.99145	−	1.44688i	0.147616	−	0.107250i
$183$	−5.91377	+	1.26369i	−0.437159	+	0.0934149i
$184$	5.52658	−	1.79570i	0.407425	−	0.132380i
$185$	−6.57660			−0.483522
$186$	−4.31291	−	8.62547i	−0.316238	−	0.632450i
$187$	−6.83185			−0.499594
$188$	8.09135	−	2.62904i	0.590123	−	0.191742i
$189$	−10.7276	+	9.72234i	−0.780317	+	0.707196i
$190$	3.95809	−	2.87572i	0.287150	−	0.208627i
$191$	−3.37768	+	1.95011i	−0.244401	+	0.141105i	−0.617198	−	0.786808i	$-0.711732\pi$
$191$	−3.37768	+	1.95011i	−0.244401	+	0.141105i	0.372797	+	0.927913i	$0.378399\pi$
$192$	−1.49906	+	0.867646i	−0.108186	+	0.0626170i
$193$	0.105901	+	1.00758i	0.00762289	+	0.0725270i	0.997672	−	0.0681955i	$-0.0217242\pi$
$193$	0.105901	+	1.00758i	0.00762289	+	0.0725270i	−0.990049	+	0.140722i	$0.955057\pi$
$194$	7.52384	−	10.3557i	0.540180	−	0.743494i
$195$	0.898104	−	1.23895i	0.0643145	−	0.0887229i
$196$	−0.510646	+	0.567130i	−0.0364747	+	0.0405093i
$197$	−19.3727	−	8.62529i	−1.38025	−	0.614526i	−0.423621	−	0.905839i	$-0.639241\pi$
$197$	−19.3727	−	8.62529i	−1.38025	−	0.614526i	−0.956628	+	0.291313i	$0.905908\pi$
$198$	2.63723	−	0.863195i	0.187420	−	0.0613446i
$199$	4.41254	+	20.7594i	0.312797	+	1.47159i	0.800896	+	0.598804i	$0.204357\pi$
$199$	4.41254	+	20.7594i	0.312797	+	1.47159i	−0.488099	+	0.872788i	$0.662310\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−5.09785	+	4.60011i	−0.359575	+	0.324467i
$202$	2.53514	−	7.80237i	0.178372	−	0.548973i
$203$	17.0959	−	7.61159i	1.19990	−	0.534229i
$204$	12.1711	+	3.94010i	0.852149	+	0.275862i
$205$	−7.25351	−	1.54178i	−0.506607	−	0.107683i
$206$	−5.11929	+	11.4981i	−0.356678	+	0.801111i
$207$	17.0598	+	3.58765i	1.18574	+	0.249359i
$208$	0.878634	+	0.0923482i	0.0609223	+	0.00640320i
$209$	−3.66111	−	2.65995i	−0.253244	−	0.183993i
$210$	−1.95811	+	4.41081i	−0.135122	+	0.304375i
$211$	3.81192	−	6.60243i	0.262423	−	0.454530i	−0.704462	−	0.709741i	$-0.748812\pi$
$211$	3.81192	−	6.60243i	0.262423	−	0.454530i	0.966885	+	0.255211i	$0.0821451\pi$
$212$	5.58704	+	9.67704i	0.383720	+	0.664622i
$213$	−2.93583	−	27.6451i	−0.201160	−	1.89421i
$214$	−5.31002	−	5.89737i	−0.362985	−	0.403136i
$215$	0.487361	+	1.49994i	0.0332378	+	0.102295i
$216$	−5.19613	+	0.0168483i	−0.353552	+	0.00114638i
$217$	−0.677773	−	15.4983i	−0.0460102	−	1.05210i
$218$			3.41437i			0.231250i
$219$	0.234341	+	0.0495460i	0.0158353	+	0.00334801i
$220$	0.687385	−	0.618924i	0.0463435	−	0.0417279i
$221$	−3.83552	−	5.27914i	−0.258005	−	0.355113i
$222$	−0.0123117	−	11.3910i	−0.000826305	−	0.764514i
$223$	−8.06226	−	4.65475i	−0.539889	−	0.311705i	0.205145	−	0.978732i	$-0.434233\pi$
$223$	−8.06226	−	4.65475i	−0.539889	−	0.311705i	−0.745034	+	0.667027i	$0.767567\pi$
$224$	−2.77098	+	0.291242i	−0.185144	+	0.0194594i
$225$	−0.307135	+	2.98424i	−0.0204757	+	0.198949i
$226$	−0.899518	+	8.55834i	−0.0598350	+	0.569292i
$227$	15.2356	+	13.7182i	1.01122	+	0.910509i	0.995998	−	0.0893754i	$-0.0284871\pi$
$227$	15.2356	+	13.7182i	1.01122	+	0.910509i	0.0152243	+	0.999884i	$0.495154\pi$
$228$	4.98830	+	6.85023i	0.330359	+	0.453668i
$229$	0.0125672	−	0.0591241i	0.000830466	−	0.00390703i	−0.977730	−	0.209865i	$-0.932698\pi$
$229$	0.0125672	−	0.0591241i	0.000830466	−	0.00390703i	0.978561	+	0.205958i	$0.0660310\pi$
$230$	5.68401	−	1.20817i	0.374792	−	0.0796646i
$231$	4.43986	+	0.461797i	0.292122	+	0.0303840i
$232$	6.38777	+	2.07551i	0.419378	+	0.136264i
$233$	9.38457	+	3.04923i	0.614804	+	0.199762i	0.599832	−	0.800126i	$-0.295234\pi$
$233$	9.38457	+	3.04923i	0.614804	+	0.199762i	0.0149720	+	0.999888i	$0.495234\pi$
$234$	2.14760	+	1.55324i	0.140393	+	0.101539i
$235$	8.32184	−	1.76886i	0.542857	−	0.115388i
$236$	−2.85996	+	13.4550i	−0.186167	+	0.875848i
$237$	−13.8122	+	10.0580i	−0.897201	+	0.653337i
$238$	15.2934	+	13.7702i	0.991324	+	0.892592i
$239$	−1.38664	+	13.1930i	−0.0896940	+	0.853381i	0.853490	+	0.521110i	$0.174482\pi$
$239$	−1.38664	+	13.1930i	−0.0896940	+	0.853381i	−0.943184	+	0.332272i	$0.892185\pi$
$240$	−1.58154	+	0.706198i	−0.102088	+	0.0455849i
$241$	−6.31188	+	0.663406i	−0.406584	+	0.0427337i	−0.305613	−	0.952156i	$-0.598862\pi$
$241$	−6.31188	+	0.663406i	−0.406584	+	0.0427337i	−0.100971	+	0.994889i	$0.532195\pi$
$242$	8.78534	+	5.07222i	0.564743	+	0.326054i
$243$	−13.5419	−	7.72116i	−0.868715	−	0.495313i
$244$	−2.05219	−	2.82460i	−0.131378	−	0.180827i
$245$	−0.567130	+	0.510646i	−0.0362326	+	0.0326240i
$246$	2.65686	−	12.5663i	0.169395	−	0.801199i
$247$		−	4.32237i		−	0.275026i
$248$	3.54123	−	4.29647i	0.224868	−	0.272826i
$249$	26.1359	+	15.0519i	1.65629	+	0.953876i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−9.74401	−	10.8218i	−0.615036	−	0.683067i	0.352496	−	0.935813i	$-0.385333\pi$
$251$	−9.74401	−	10.8218i	−0.615036	−	0.683067i	−0.967533	+	0.252746i	$0.918666\pi$
$252$	−7.64341	−	3.38329i	−0.481490	−	0.213127i
$253$	−2.68749	−	4.65487i	−0.168961	−	0.292649i
$254$	9.99694	−	17.3152i	0.627264	−	1.08645i
$255$	11.6926	+	5.19074i	0.732219	+	0.325057i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−2.13610	−	0.224513i	−0.133246	−	0.0140047i	0.0376705	−	0.999290i	$-0.488006\pi$
$257$	−2.13610	−	0.224513i	−0.133246	−	0.0140047i	−0.170917	+	0.985285i	$0.554673\pi$
$258$	−2.59707	+	0.846942i	−0.161686	+	0.0527283i
$259$	7.45305	−	16.7398i	0.463110	−	1.04016i
$260$	0.864168	+	0.183685i	0.0535934	+	0.0113916i
$261$	13.5150	+	14.9448i	0.836557	+	0.925061i
$262$	−10.4521	+	4.65358i	−0.645733	+	0.287499i
$263$	3.56123	−	10.9603i	0.219595	−	0.675843i	−0.779201	−	0.626774i	$-0.784375\pi$
$263$	3.56123	−	10.9603i	0.219595	−	0.675843i	0.998795	−	0.0490685i	$-0.0156253\pi$
$264$	1.07329	+	1.18943i	0.0660567	+	0.0732041i
$265$	4.54491	+	10.2080i	0.279191	+	0.627074i
$266$	2.83417	+	13.3337i	0.173774	+	0.817543i
$267$	−14.3958	−	12.9339i	−0.881008	−	0.791541i
$268$	−3.62165	−	1.61246i	−0.221227	−	0.0984968i
$269$	4.26026	−	4.73150i	0.259753	−	0.288485i	−0.599136	−	0.800648i	$-0.704489\pi$
$269$	4.26026	−	4.73150i	0.259753	−	0.288485i	0.858888	+	0.512163i	$0.171156\pi$
$270$	−5.16942	−	0.526387i	−0.314601	−	0.0320349i
$271$	−16.8821	+	23.2362i	−1.02551	+	1.41150i	−0.117250	+	0.993102i	$0.537408\pi$
$271$	−16.8821	+	23.2362i	−1.02551	+	1.41150i	−0.908264	+	0.418396i	$0.862592\pi$
$272$	0.772051	+	7.34558i	0.0468125	+	0.445391i
$273$	2.13577	+	3.69005i	0.129263	+	0.223332i
$274$	−2.95181	+	1.70423i	−0.178326	+	0.102956i
$275$	0.748315	−	0.543682i	0.0451251	−	0.0327853i
$276$	2.10326	+	9.84272i	0.126601	+	0.592462i
$277$	−5.59089	+	1.81659i	−0.335924	+	0.109148i	−0.472122	−	0.881533i	$-0.656512\pi$
$277$	−5.59089	+	1.81659i	−0.335924	+	0.109148i	0.136198	+	0.990682i	$0.456512\pi$
$278$	−15.4288			−0.925358
$279$	15.6324	−	5.88453i	0.935888	−	0.352298i
$280$	−2.78624			−0.166510
$281$	−16.7567	+	5.44459i	−0.999623	+	0.324797i	−0.762715	−	0.646735i	$-0.776134\pi$
$281$	−16.7567	+	5.44459i	−0.999623	+	0.324797i	−0.236908	+	0.971532i	$0.576134\pi$
$282$	3.07933	+	14.4105i	0.183372	+	0.858134i
$283$	−1.62710	+	1.18216i	−0.0967211	+	0.0702720i	−0.635095	−	0.772434i	$-0.719039\pi$
$283$	−1.62710	+	1.18216i	−0.0967211	+	0.0702720i	0.538374	+	0.842706i	$0.319039\pi$
$284$	13.9003	−	8.02533i	0.824830	−	0.476216i
$285$	4.24493	+	7.33412i	0.251448	+	0.434436i
$286$	−0.0854191	−	0.812708i	−0.00505094	−	0.0480565i
$287$	12.1445	−	16.7155i	0.716870	−	0.986687i
$288$	−1.22613	−	2.73799i	−0.0722505	−	0.161338i
$289$	25.1282	−	27.9077i	1.47813	−	1.64163i
$290$	6.13583	+	2.73185i	0.360308	+	0.160420i
$291$	16.4921	+	14.8173i	0.966786	+	0.868608i
$292$	0.0287516	+	0.135266i	0.00168256	+	0.00791582i
$293$	−10.7509	−	24.1470i	−0.628076	−	1.41068i	−0.894606	−	0.446855i	$-0.852544\pi$
$293$	−10.7509	−	24.1470i	−0.628076	−	1.41068i	0.266531	−	0.963826i	$-0.414123\pi$
$294$	−0.885526	−	0.981342i	−0.0516450	−	0.0572330i
$295$	−4.25072	+	13.0824i	−0.247487	+	0.761686i
$296$	6.00803	−	2.67495i	0.349209	−	0.155478i
$297$	1.01452	+	4.69798i	0.0588683	+	0.272604i
$298$	4.55428	+	0.968042i	0.263822	+	0.0560771i
$299$	2.08813	−	4.69002i	0.120760	−	0.271231i
$300$	−1.64670	+	0.537013i	−0.0950722	+	0.0310045i
$301$	−4.37021	−	0.459327i	−0.251895	−	0.0264752i
$302$	−2.70032	−	1.96190i	−0.155386	−	0.112894i
$303$	12.9873	+	5.76552i	0.746102	+	0.331220i
$304$	−2.44624	+	4.23700i	−0.140301	+	0.243009i
$305$	−1.74570	−	3.02364i	−0.0999585	−	0.173133i
$306$	−8.96874	+	20.2619i	−0.512709	+	1.15829i
$307$	−1.96862	−	2.18638i	−0.112355	−	0.124783i	0.684344	−	0.729160i	$-0.260089\pi$
$307$	−1.96862	−	2.18638i	−0.112355	−	0.124783i	−0.796699	+	0.604377i	$0.793422\pi$
$308$	0.796394	+	2.45105i	0.0453787	+	0.139661i
$309$	−18.8911	−	10.8796i	−1.07468	−	0.618918i
$310$	3.97093	−	3.90278i	0.225534	−	0.221663i
$311$		−	23.9581i		−	1.35854i	−0.733888	−	0.679270i	$-0.762296\pi$
$311$		−	23.9581i		−	1.35854i	0.733888	−	0.679270i	$-0.237704\pi$
$312$	−0.316533	+	1.49713i	−0.0179202	+	0.0847581i
$313$	14.5108	−	13.0656i	0.820200	−	0.738511i	−0.147920	−	0.988999i	$-0.547258\pi$
$313$	14.5108	−	13.0656i	0.820200	−	0.738511i	0.968120	+	0.250488i	$0.0805912\pi$
$314$	−0.969116	−	1.33387i	−0.0546904	−	0.0752748i
$315$	−7.24789	−	4.16371i	−0.408372	−	0.234598i
$316$	−8.54314	−	4.93238i	−0.480589	−	0.277468i
$317$	11.5957	−	1.21876i	0.651279	−	0.0684522i	0.226873	−	0.973924i	$-0.427150\pi$
$317$	11.5957	−	1.21876i	0.651279	−	0.0684522i	0.424406	+	0.905472i	$0.360483\pi$
$318$	−17.6723	+	7.89112i	−0.991014	+	0.442512i
$319$	0.649388	−	6.17851i	0.0363587	−	0.345930i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	11.1112	−	8.09114i	0.620168	−	0.451603i
$322$	−3.36626	+	15.8370i	−0.187595	+	0.882563i
$323$	35.3463	−	7.51309i	1.96672	−	0.418040i
$324$	0.902051	−	8.95468i	0.0501139	−	0.497482i
$325$	0.840234	+	0.273009i	0.0466078	+	0.0151438i
$326$	−7.19059	−	2.33636i	−0.398250	−	0.129399i
$327$	−5.88213	−	0.611810i	−0.325283	−	0.0338332i
$328$	7.25351	−	1.54178i	0.400508	−	0.0851306i
$329$	−4.92848	+	23.1867i	−0.271716	+	1.27832i
$330$	0.943086	+	1.29510i	0.0519152	+	0.0712929i
$331$	−25.6351	−	23.0820i	−1.40903	−	1.26870i	−0.917440	−	0.397874i	$-0.869748\pi$
$331$	−25.6351	−	23.0820i	−1.40903	−	1.26870i	−0.491593	−	0.870825i	$-0.663585\pi$
$332$	−1.82016	+	17.3177i	−0.0998942	+	0.950430i
$333$	19.6261	+	2.01991i	1.07551	+	0.110690i
$334$	−10.2819	+	1.08067i	−0.562599	+	0.0591316i
$335$	−3.43326	−	1.98219i	−0.187579	−	0.108299i
$336$	−0.00521596	−	4.82591i	−0.000284554	−	0.263275i
$337$	−20.8966	−	28.7617i	−1.13831	−	1.56675i	−0.771221	−	0.636567i	$-0.780354\pi$
$337$	−20.8966	−	28.7617i	−1.13831	−	1.56675i	−0.367091	−	0.930185i	$-0.619646\pi$
$338$	−9.08084	+	8.17642i	−0.493932	+	0.444739i
$339$	−14.5828	−	3.08319i	−0.792027	−	0.167456i
$340$			7.38604i			0.400564i
$341$	−4.56828	−	2.37768i	−0.247386	−	0.128759i
$342$	−12.6951	+	7.36617i	−0.686473	+	0.398317i
$343$	5.36991	+	16.5269i	0.289948	+	0.892367i
$344$	−1.05531	−	1.17204i	−0.0568985	−	0.0631921i
$345$	1.06289	+	10.0087i	0.0572241	+	0.538848i
$346$	4.76866	+	8.25956i	0.256365	+	0.444037i
$347$	0.0955823	−	0.165553i	0.00513113	−	0.00888737i	−0.863448	−	0.504437i	$-0.831700\pi$
$347$	0.0955823	−	0.165553i	0.00513113	−	0.00888737i	0.868580	+	0.495550i	$0.165033\pi$
$348$	−4.72021	+	10.6327i	−0.253030	+	0.569971i
$349$	10.5179	+	7.64173i	0.563012	+	0.409052i	0.832560	−	0.553935i	$-0.186874\pi$
$349$	10.5179	+	7.64173i	0.563012	+	0.409052i	−0.269548	+	0.962987i	$0.586874\pi$
$350$	−2.77098	−	0.291242i	−0.148115	−	0.0155675i
$351$	−3.06068	+	3.42147i	−0.163367	+	0.182625i
$352$	−0.376218	+	0.845000i	−0.0200525	+	0.0450386i
$353$	−4.26901	−	0.907407i	−0.227217	−	0.0482964i	0.0928963	−	0.995676i	$-0.470388\pi$
$353$	−4.26901	−	0.907407i	−0.227217	−	0.0482964i	−0.320113	+	0.947379i	$0.603721\pi$
$354$	−22.6673	−	7.33797i	−1.20475	−	0.390009i
$355$	14.6630	−	6.52839i	0.778232	−	0.346491i
$356$	3.45272	−	10.6264i	0.182994	−	0.563197i
$357$	−26.4631	+	23.8794i	−1.40058	+	1.26383i
$358$	−5.69418	−	12.7893i	−0.300947	−	0.675937i
$359$	−0.474726	−	2.23341i	−0.0250551	−	0.117875i	0.963843	−	0.266471i	$-0.0858578\pi$
$359$	−0.474726	−	2.23341i	−0.0250551	−	0.117875i	−0.988898	+	0.148596i	$0.952524\pi$
$360$	−0.933216	−	2.85116i	−0.0491848	−	0.150269i
$361$	4.50951	+	2.00776i	0.237343	+	0.105672i
$362$	−2.20222	+	2.44582i	−0.115746	+	0.128549i
$363$	−10.3124	+	14.2261i	−0.541261	+	0.746678i
$364$	−1.44688	+	1.99145i	−0.0758369	+	0.104381i
$365$	0.0144550	+	0.137530i	0.000756609	+	0.00719865i
$366$	5.23383	−	3.02930i	0.273577	−	0.158344i
$367$	−11.9566	+	6.90315i	−0.624130	+	0.360341i	−0.778475	−	0.627675i	$-0.784006\pi$
$367$	−11.9566	+	6.90315i	−0.624130	+	0.360341i	0.154345	+	0.988017i	$0.450673\pi$
$368$	−4.70119	+	3.41562i	−0.245067	+	0.178051i
$369$	21.1726	+	6.82884i	1.10220	+	0.355495i
$370$	6.25472	−	2.03228i	0.325168	−	0.105653i
$371$	−31.1337			−1.61638
$372$	6.76724	+	6.87055i	0.350865	+	0.356221i
$373$	6.12207			0.316989			0.158494	−	0.987360i	$-0.449336\pi$
$373$	6.12207			0.316989			0.158494	+	0.987360i	$0.449336\pi$
$374$	6.49747	−	2.11116i	0.335976	−	0.109165i
$375$	−1.69381	+	0.361945i	−0.0874680	+	0.0186907i
$376$	−6.88292	+	5.00073i	−0.354959	+	0.257893i
$377$	5.13887	−	2.96693i	0.264665	−	0.152805i
$378$	7.19818	−	12.5615i	0.370234	−	0.646094i
$379$	1.84710	+	17.5740i	0.0948793	+	0.902716i	0.933639	+	0.358215i	$0.116614\pi$
$379$	1.84710	+	17.5740i	0.0948793	+	0.902716i	−0.838760	+	0.544501i	$0.816719\pi$
$380$	−2.87572	+	3.95809i	−0.147521	+	0.203046i
$381$	28.0386	+	20.3249i	1.43646	+	1.04128i
$382$	2.60975	−	2.89842i	0.133526	−	0.148296i
$383$	−2.64967	−	1.17971i	−0.135392	−	0.0602804i	0.337922	−	0.941174i	$-0.390276\pi$
$383$	−2.64967	−	1.17971i	−0.135392	−	0.0602804i	−0.473314	+	0.880894i	$0.656943\pi$
$384$	1.15758	−	1.28842i	0.0590723	−	0.0657492i
$385$	0.535827	+	2.52087i	0.0273083	+	0.128475i
$386$	−0.412076	−	0.925537i	−0.0209741	−	0.0471086i
$387$	−0.993716	−	4.62587i	−0.0505134	−	0.235146i
$388$	−3.95552	+	12.1738i	−0.200811	+	0.618032i
$389$	−26.1465	+	11.6412i	−1.32568	+	0.590231i	−0.942736	−	0.333541i	$-0.891757\pi$
$389$	−26.1465	+	11.6412i	−1.32568	+	0.590231i	−0.382944	+	0.923771i	$0.625090\pi$
$390$	−0.471291	+	1.45584i	−0.0238648	+	0.0737192i
$391$	41.9823	+	8.92361i	2.12314	+	0.451286i
$392$	0.310401	−	0.697171i	0.0156776	−	0.0352125i
$393$	−6.14410	−	18.8403i	−0.309929	−	0.950367i
$394$	21.0899	+	2.21664i	1.06249	+	0.111673i
$395$	−7.98076	−	5.79837i	−0.401556	−	0.291747i
$396$	−2.24141	+	1.63590i	−0.112635	+	0.0822069i
$397$	−9.04272	+	15.6625i	−0.453841	+	0.786076i	−0.998621	−	0.0525034i	$-0.983280\pi$
$397$	−9.04272	+	15.6625i	−0.453841	+	0.786076i	0.544780	+	0.838579i	$0.316613\pi$
$398$	−10.6116	−	18.3798i	−0.531910	−	0.921295i
$399$	−23.4786	+	2.49336i	−1.17540	+	0.124824i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−8.50516	−	26.1762i	−0.424727	−	1.30718i	−0.903255	−	0.429104i	$-0.858829\pi$
$401$	−8.50516	−	26.1762i	−0.424727	−	1.30718i	0.478528	−	0.878072i	$-0.341171\pi$
$402$	3.42683	−	5.95029i	0.170915	−	0.296774i
$403$	−0.727416	−	4.86489i	−0.0362352	−	0.242338i
$404$			8.20390i			0.408159i
$405$	1.83313	−	8.81134i	0.0910889	−	0.437839i
$406$	−13.9071	+	12.5220i	−0.690196	+	0.621455i
$407$	−3.57558	−	4.92137i	−0.177235	−	0.243943i
$408$	−12.7930	+	0.0138270i	−0.633347	+	0.000684536i
$409$	7.85042	+	4.53244i	0.388178	+	0.224115i	0.681370	−	0.731939i	$-0.261384\pi$
$409$	7.85042	+	4.53244i	0.388178	+	0.224115i	−0.293192	+	0.956053i	$0.594718\pi$
$410$	7.37493	−	0.775136i	0.364222	−	0.0382813i
$411$	−2.40705	−	5.39064i	−0.118731	−	0.265900i
$412$	1.31562	−	12.5173i	0.0648160	−	0.616683i
$413$	−28.4822	−	25.6455i	−1.40152	−	1.26193i
$414$	−17.3335	+	1.85972i	−0.851895	+	0.0914000i
$415$	−3.62038	+	17.0325i	−0.177717	+	0.836094i
$416$	−0.864168	+	0.183685i	−0.0423693	+	0.00900588i
$417$	2.76464	−	26.5801i	0.135385	−	1.30163i
$418$	4.30389	+	1.39842i	0.210510	+	0.0683989i
$419$	2.52784	+	0.821344i	0.123493	+	0.0401253i	0.370112	−	0.928987i	$-0.379319\pi$
$419$	2.52784	+	0.821344i	0.123493	+	0.0401253i	−0.246619	+	0.969113i	$0.579319\pi$
$420$	0.499258	−	4.80002i	0.0243613	−	0.234217i
$421$	21.9362	−	4.66269i	1.06911	−	0.227246i	0.360435	−	0.932784i	$-0.382628\pi$
$421$	21.9362	−	4.66269i	1.06911	−	0.227246i	0.708671	+	0.705539i	$0.249295\pi$
$422$	−1.58508	+	7.45723i	−0.0771607	+	0.363012i
$423$	−25.3776	+	2.72277i	−1.23390	+	0.132386i
$424$	−8.30396	−	7.47692i	−0.403276	−	0.363111i
$425$	−0.772051	+	7.34558i	−0.0374500	+	0.356313i
$426$	11.3350	+	25.3848i	0.549180	+	1.22990i
$427$	9.67460	−	1.01684i	0.468187	−	0.0492084i
$428$	6.87251	+	3.96785i	0.332195	+	0.191793i
$429$	1.41541	−	0.00152980i	0.0683364	−	7.38596e-5i
$430$	−0.927017	−	1.27593i	−0.0447047	−	0.0615308i
$431$	−18.0880	+	16.2865i	−0.871266	+	0.784491i	−0.977739	−	0.209824i	$-0.932711\pi$
$431$	−18.0880	+	16.2865i	−0.871266	+	0.784491i	0.106473	+	0.994316i	$0.466044\pi$
$432$	4.93660	−	1.62171i	0.237512	−	0.0780248i
$433$			4.26954i			0.205181i	0.994724	+	0.102591i	$0.0327132\pi$
$433$			4.26954i			0.205181i	−0.994724	+	0.102591i	$0.967287\pi$
$434$	5.43385	+	14.5303i	0.260833	+	0.697479i
$435$	−5.80577	+	10.0810i	−0.278365	+	0.483349i
$436$	−1.05510	−	3.24726i	−0.0505301	−	0.155516i
$437$	19.0235	+	21.1277i	0.910015	+	1.01067i
$438$	−0.238182	+	0.0252942i	−0.0113808	+	0.00120860i
$439$	11.0448	+	19.1302i	0.527142	+	0.913036i	0.999500	+	0.0316293i	$0.0100696\pi$
$439$	11.0448	+	19.1302i	0.527142	+	0.913036i	−0.472358	+	0.881407i	$0.656597\pi$
$440$	−0.462484	+	0.801045i	−0.0220481	+	0.0381883i
$441$	1.84929	−	1.34970i	0.0880613	−	0.0642716i
$442$	5.27914	+	3.83552i	0.251103	+	0.182437i
$443$	−35.6120	−	3.74298i	−1.69198	−	0.177834i	−0.791035	−	0.611771i	$-0.790458\pi$
$443$	−35.6120	−	3.74298i	−1.69198	−	0.177834i	−0.900944	+	0.433936i	$0.857124\pi$
$444$	3.53172	+	10.8297i	0.167608	+	0.513954i
$445$	4.54457	−	10.2073i	0.215433	−	0.483871i
$446$	9.10606	+	1.93555i	0.431185	+	0.0916511i
$447$	−2.48377	+	7.67245i	−0.117478	+	0.362895i
$448$	2.54536	−	1.13327i	0.120257	−	0.0535418i
$449$	2.17626	−	6.69784i	0.102704	−	0.316091i	−0.886481	−	0.462766i	$-0.846857\pi$
$449$	2.17626	−	6.69784i	0.102704	−	0.316091i	0.989185	+	0.146675i	$0.0468571\pi$
$450$	−0.630077	−	2.93309i	−0.0297021	−	0.138267i
$451$	−2.78987	−	6.26614i	−0.131370	−	0.295061i
$452$	−1.78918	−	8.41743i	−0.0841560	−	0.395923i
$453$	3.86373	−	4.30045i	0.181534	−	0.202053i
$454$	−18.7291	−	8.33872i	−0.878999	−	0.391356i
$455$	−1.64711	+	1.82931i	−0.0772179	+	0.0857592i
$456$	−6.86100	−	4.97348i	−0.321296	−	0.232905i
$457$	−3.49698	+	4.81318i	−0.163582	+	0.225151i	−0.882937	−	0.469491i	$-0.844437\pi$
$457$	−3.49698	+	4.81318i	−0.163582	+	0.225151i	0.719355	+	0.694642i	$0.244437\pi$
$458$	0.00631822	+	0.0601139i	0.000295231	+	0.00280894i
$459$	−33.2992	−	19.0816i	−1.55427	−	0.890654i
$460$	−5.03247	+	2.90550i	−0.234640	+	0.135469i
$461$	−29.3438	+	21.3195i	−1.36668	+	0.992949i	−0.368689	+	0.929553i	$0.620193\pi$
$461$	−29.3438	+	21.3195i	−1.36668	+	0.992949i	−0.997988	+	0.0633964i	$0.979807\pi$
$462$	−4.36526	+	0.932798i	−0.203090	+	0.0433977i
$463$	−23.2521	+	7.55508i	−1.08062	+	0.351114i	−0.794615	−	0.607114i	$-0.792327\pi$
$463$	−23.2521	+	7.55508i	−1.08062	+	0.351114i	−0.286004	+	0.958228i	$0.592327\pi$
$464$	−6.71650			−0.311806
$465$	6.01200	+	7.54028i	0.278800	+	0.349672i
$466$	−9.86753			−0.457104
$467$	7.01630	−	2.27973i	0.324675	−	0.105493i	−0.142144	−	0.989846i	$-0.545400\pi$
$467$	7.01630	−	2.27973i	0.324675	−	0.105493i	0.466820	+	0.884353i	$0.345400\pi$
$468$	−2.52247	−	0.813575i	−0.116601	−	0.0376075i
$469$	8.93620	−	6.49253i	0.412635	−	0.299797i
$470$	−7.36793	+	4.25388i	−0.339857	+	0.196217i
$471$	2.47159	−	1.43054i	0.113885	−	0.0659157i
$472$	−1.43786	−	13.6803i	−0.0661826	−	0.629686i
$473$	−0.857460	+	1.18019i	−0.0394261	+	0.0542653i
$474$	10.0281	−	13.8339i	0.460607	−	0.635414i
$475$	−3.27370	+	3.63581i	−0.150208	+	0.166823i
$476$	−18.8001	−	8.37035i	−0.861702	−	0.383655i
$477$	−10.4278	−	31.8591i	−0.477458	−	1.45873i
$478$	−2.75808	−	12.9757i	−0.126152	−	0.593496i
$479$	0.583908	+	1.31148i	0.0266795	+	0.0599230i	0.926394	−	0.376556i	$-0.122892\pi$
$479$	0.583908	+	1.31148i	0.0266795	+	0.0599230i	−0.899714	+	0.436479i	$0.856225\pi$
$480$	1.28591	−	1.16036i	0.0586935	−	0.0529629i
$481$	1.79547	−	5.52589i	0.0818663	−	0.251959i
$482$	5.79795	−	2.58142i	0.264090	−	0.117580i
$483$	−26.6802	−	8.63704i	−1.21399	−	0.392999i
$484$	−9.92275	−	2.10915i	−0.451034	−	0.0958703i
$485$	−5.20636	+	11.6937i	−0.236409	+	0.530982i
$486$	15.2651	+	3.15857i	0.692439	+	0.143276i
$487$	−3.04239	−	0.319768i	−0.137864	−	0.0144901i	0.0353451	−	0.999375i	$-0.488747\pi$
$487$	−3.04239	−	0.319768i	−0.137864	−	0.0144901i	−0.173209	+	0.984885i	$0.555414\pi$
$488$	2.82460	+	2.05219i	0.127864	+	0.0928984i
$489$	5.31345	−	11.9690i	0.240282	−	0.541257i
$490$	0.381574	−	0.660906i	0.0172378	−	0.0298567i
$491$	8.30873	+	14.3911i	0.374968	+	0.649463i	0.990322	−	0.138788i	$-0.0443205\pi$
$491$	8.30873	+	14.3911i	0.374968	+	0.649463i	−0.615355	+	0.788250i	$0.710987\pi$
$492$	1.35638	+	12.7723i	0.0611504	+	0.575820i
$493$	33.1945	+	36.8662i	1.49500	+	1.66037i
$494$	1.33569	+	4.11082i	0.0600954	+	0.184955i
$495$	−2.40013	+	1.39264i	−0.107878	+	0.0625946i
$496$	−2.04023	+	5.18049i	−0.0916088	+	0.232611i
$497$			44.7211i			2.00601i
$498$	−29.5080	−	6.23879i	−1.32228	−	0.279567i
$499$	8.82595	−	7.94692i	0.395104	−	0.355753i	−0.447503	−	0.894282i	$-0.647687\pi$
$499$	8.82595	−	7.94692i	0.395104	−	0.355753i	0.842607	+	0.538529i	$0.181020\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	−0.0193541	−	17.9068i	−0.000864678	−	0.800018i
$502$	12.6112	+	7.28110i	0.562867	+	0.324971i
$503$	16.6672	−	1.75179i	0.743152	−	0.0781084i	0.274617	−	0.961554i	$-0.411449\pi$
$503$	16.6672	−	1.75179i	0.743152	−	0.0781084i	0.468534	+	0.883445i	$0.344782\pi$
$504$	8.31481	+	0.855753i	0.370371	+	0.0381183i
$505$	−0.857541	+	8.15896i	−0.0381601	+	0.363069i
$506$	3.99439	+	3.59656i	0.177572	+	0.159887i
$507$	−12.4588	−	17.1092i	−0.553316	−	0.759846i
$508$	−4.15696	+	19.5570i	−0.184435	+	0.867700i
$509$	−6.08518	+	1.29345i	−0.269721	+	0.0573310i	−0.340787	−	0.940141i	$-0.610693\pi$
$509$	−6.08518	+	1.29345i	−0.269721	+	0.0573310i	0.0710656	+	0.997472i	$0.477360\pi$
$510$	−12.7243	−	1.32348i	−0.563444	−	0.0586047i
$511$	−0.366445	−	0.119065i	−0.0162106	−	0.00526713i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−10.4153	−	23.1905i	−0.459848	−	1.02389i
$514$	2.10093	−	0.446566i	0.0926680	−	0.0196972i
$515$	2.61683	−	12.3112i	0.115311	−	0.542496i
$516$	2.20824	−	1.60803i	0.0972122	−	0.0707895i
$517$	5.84810	+	5.26565i	0.257199	+	0.231583i
$518$	−1.91538	+	18.2236i	−0.0841570	+	0.800701i
$519$	−15.0837	+	6.73524i	−0.662101	+	0.295644i
$520$	−0.878634	+	0.0923482i	−0.0385307	+	0.00404974i
$521$	−37.4177	−	21.6031i	−1.63930	−	0.946450i	−0.981075	−	0.193629i	$-0.937974\pi$
$521$	−37.4177	−	21.6031i	−1.63930	−	0.946450i	−0.658225	−	0.752821i	$-0.728693\pi$
$522$	−17.4717	−	10.0370i	−0.764716	−	0.439308i
$523$	−0.143580	−	0.197621i	−0.00627831	−	0.00864136i	0.805866	−	0.592098i	$-0.201700\pi$
$523$	−0.143580	−	0.197621i	−0.00627831	−	0.00864136i	−0.812145	+	0.583456i	$0.801700\pi$
$524$	8.50251	−	7.65569i	0.371434	−	0.334441i
$525$	0.998261	−	4.72154i	0.0435677	−	0.206065i
$526$			11.5244i			0.502487i
$527$	38.5184	−	14.4046i	1.67789	−	0.627473i
$528$	−1.38832	−	0.799545i	−0.0604187	−	0.0347957i
$529$	3.32738	+	10.2406i	0.144669	+	0.445244i
$530$	−7.47692	−	8.30396i	−0.324777	−	0.360701i
$531$	16.7032	−	37.7354i	0.724858	−	1.63758i
$532$	−6.81581	−	11.8053i	−0.295503	−	0.511826i
$533$	3.27572	−	5.67372i	0.141887	−	0.245756i
$534$	17.6880	+	7.85231i	0.765435	+	0.339803i
$535$	6.42011	+	4.66448i	0.277566	+	0.201663i
$536$	3.94267	+	0.414391i	0.170297	+	0.0178990i
$537$	23.0532	−	7.51801i	0.994820	−	0.324426i
$538$	−2.58964	+	5.81642i	−0.111647	+	0.250764i
$539$	−0.690463	−	0.146762i	−0.0297403	−	0.00632150i
$540$	5.07907	−	1.09682i	0.218569	−	0.0471994i
$541$	−25.5692	+	11.3841i	−1.09930	+	0.489442i	−0.874531	−	0.484970i	$-0.838831\pi$
$541$	−25.5692	+	11.3841i	−1.09930	+	0.489442i	−0.224773	+	0.974411i	$0.572164\pi$
$542$	8.87544	−	27.3158i	0.381233	−	1.17331i
$543$	−3.81894	−	4.23215i	−0.163886	−	0.181619i
$544$	−3.00417	−	6.74748i	−0.128803	−	0.289296i
$545$	−0.709888	−	3.33976i	−0.0304083	−	0.143060i
$546$	−3.17153	−	2.84946i	−0.135729	−	0.121946i
$547$	−17.8077	−	7.92851i	−0.761403	−	0.338999i	−0.0109656	−	0.999940i	$-0.503491\pi$
$547$	−17.8077	−	7.92851i	−0.761403	−	0.338999i	−0.750438	+	0.660941i	$0.770157\pi$
$548$	2.28071	−	2.53298i	0.0974269	−	0.108204i
$549$	4.28092	+	9.55943i	0.182705	+	0.407986i
$550$	−0.543682	+	0.748315i	−0.0231827	+	0.0319082i
$551$	3.43484	+	32.6803i	0.146329	+	1.39223i
$552$	−5.04188	−	8.71104i	−0.214597	−	0.370767i
$553$	23.8033	−	13.7428i	1.01222	−	0.584404i
$554$	4.75589	−	3.45536i	0.202059	−	0.146804i
$555$	2.38037	+	11.1395i	0.101041	+	0.472847i
$556$	14.6737	−	4.76776i	0.622302	−	0.202198i
$557$	−9.73398			−0.412442			−0.206221	−	0.978505i	$-0.566117\pi$
$557$	−9.73398			−0.412442			−0.206221	+	0.978505i	$0.566117\pi$
$558$	−13.0489	+	10.4272i	−0.552403	+	0.441419i
$559$	−1.39336			−0.0589328
$560$	2.64987	−	0.860996i	0.111978	−	0.0363837i
$561$	2.47275	+	11.5719i	0.104400	+	0.488564i
$562$	14.2541	−	10.3562i	0.601274	−	0.436851i
$563$	9.32645	−	5.38463i	0.393063	−	0.226935i	−0.290423	−	0.956898i	$-0.593796\pi$
$563$	9.32645	−	5.38463i	0.393063	−	0.226935i	0.683487	+	0.729963i	$0.260463\pi$
$564$	−7.38172	−	12.7537i	−0.310826	−	0.537026i
$565$	−0.899518	−	8.55834i	−0.0378430	−	0.360052i
$566$	1.18216	−	1.62710i	0.0496898	−	0.0683922i
$567$	20.3506	+	14.6516i	0.854645	+	0.615308i
$568$	−10.7400	+	11.9280i	−0.450640	+	0.500486i
$569$	2.13601	+	0.951011i	0.0895460	+	0.0398685i	0.451021	−	0.892513i	$-0.351060\pi$
$569$	2.13601	+	0.951011i	0.0895460	+	0.0398685i	−0.361475	+	0.932382i	$0.617727\pi$
$570$	−6.30354	−	5.66341i	−0.264026	−	0.237214i
$571$	−2.47172	−	11.6285i	−0.103438	−	0.486639i	−0.999120	−	0.0419432i	$-0.986645\pi$
$571$	−2.47172	−	11.6285i	−0.103438	−	0.486639i	0.895682	−	0.444696i	$-0.146688\pi$
$572$	0.332379	+	0.746536i	0.0138975	+	0.0312142i
$573$	4.52564	+	5.01533i	0.189062	+	0.209518i
$574$	−6.38476	+	19.6503i	−0.266495	+	0.820187i
$575$	−5.30861	+	2.36354i	−0.221384	+	0.0985666i
$576$	2.01221	+	2.22509i	0.0838419	+	0.0927121i
$577$	34.0608	+	7.23984i	1.41797	+	0.301398i	0.852222	−	0.523181i	$-0.175255\pi$
$577$	34.0608	+	7.23984i	1.41797	+	0.301398i	0.565746	+	0.824579i	$0.308588\pi$
$578$	−15.2744	+	34.3069i	−0.635332	+	1.42698i
$579$	1.66831	−	0.544062i	0.0693328	−	0.0226105i
$580$	−6.67971	−	0.702066i	−0.277360	−	0.0291517i
$581$	−39.2511	−	28.5176i	−1.62841	−	1.18311i
$582$	−20.2638	−	8.99578i	−0.839960	−	0.372887i
$583$	−5.16783	+	8.95095i	−0.214030	+	0.370710i
$584$	−0.0691438	−	0.119761i	−0.00286119	−	0.00495573i
$585$	−2.42361	−	1.07279i	−0.100204	−	0.0443543i
$586$	17.6866	+	19.6429i	0.730625	+	0.811441i
$587$	−5.34148	−	16.4394i	−0.220467	−	0.678527i	−0.998720	−	0.0505764i	$-0.983894\pi$
$587$	−5.34148	−	16.4394i	−0.220467	−	0.678527i	0.778254	−	0.627950i	$-0.216106\pi$
$588$	1.14544	+	0.659669i	0.0472370	+	0.0272043i
$589$	26.2499	+	7.27775i	1.08161	+	0.299874i
$590$		−	13.7556i		−	0.566310i
$591$	−7.59776	+	35.9356i	−0.312530	+	1.47819i
$592$	−4.88737	+	4.40061i	−0.200870	+	0.180864i
$593$	16.8514	+	23.1939i	0.692002	+	0.952459i	0.999999	+	0.00107201i	$0.000341233\pi$
$593$	16.8514	+	23.1939i	0.692002	+	0.952459i	−0.307997	+	0.951387i	$0.599659\pi$
$594$	−2.41662	−	4.15454i	−0.0991551	−	0.170463i
$595$	−17.8222	−	10.2896i	−0.730639	−	0.421834i
$596$	−4.63052	+	0.486687i	−0.189673	+	0.0199355i
$597$	33.5653	−	14.9877i	1.37374	−	0.613407i
$598$	−0.536635	+	5.10574i	−0.0219446	+	0.208789i
$599$	−6.72850	−	6.05836i	−0.274919	−	0.247538i	0.520125	−	0.854090i	$-0.325885\pi$
$599$	−6.72850	−	6.05836i	−0.274919	−	0.247538i	−0.795044	+	0.606552i	$0.792552\pi$
$600$	1.40016	−	1.01959i	0.0571612	−	0.0416245i
$601$	−1.31179	+	6.17149i	−0.0535090	+	0.251740i	−0.996770	−	0.0803130i	$-0.974408\pi$
$601$	−1.31179	+	6.17149i	−0.0535090	+	0.251740i	0.943261	+	0.332053i	$0.107741\pi$
$602$	4.29826	−	0.913622i	0.175184	−	0.0372365i
$603$	9.63686	+	6.96981i	0.392443	+	0.283833i
$604$	3.17441	+	1.03143i	0.129165	+	0.0419683i
$605$	−9.64793	−	3.13480i	−0.392244	−	0.127448i
$606$	−14.1333	−	1.47003i	−0.574127	−	0.0597159i
$607$	−19.7584	+	4.19977i	−0.801967	+	0.170463i	−0.590622	−	0.806948i	$-0.701118\pi$
$607$	−19.7584	+	4.19977i	−0.801967	+	0.170463i	−0.211345	+	0.977412i	$0.567784\pi$
$608$	1.01720	−	4.78556i	0.0412530	−	0.194080i
$609$	−19.0804	−	26.2023i	−0.773176	−	1.06177i
$610$	2.59462	+	2.33620i	0.105053	+	0.0945901i
$611$	−0.785676	+	7.47520i	−0.0317850	+	0.302414i
$612$	2.26851	−	22.0417i	0.0916992	−	0.890982i
$613$	−22.8051	+	2.39692i	−0.921091	+	0.0968106i	−0.553191	−	0.833055i	$-0.686590\pi$
$613$	−22.8051	+	2.39692i	−0.921091	+	0.0968106i	−0.367900	+	0.929865i	$0.619923\pi$
$614$	2.54790	+	1.47103i	0.102825	+	0.0593659i
$615$	0.0138822	+	12.8441i	0.000559785	+	0.517924i
$616$	−1.51483	−	2.08499i	−0.0610343	−	0.0840065i
$617$	−31.2765	+	28.1615i	−1.25914	+	1.13374i	−0.274052	+	0.961715i	$0.588364\pi$
$617$	−31.2765	+	28.1615i	−1.25914	+	1.13374i	−0.985093	+	0.172024i	$0.944969\pi$
$618$	21.3285	+	4.50943i	0.857959	+	0.181396i
$619$			33.3033i			1.33857i	0.743004	+	0.669287i	$0.233400\pi$
$619$			33.3033i			1.33857i	−0.743004	+	0.669287i	$0.766600\pi$
$620$	−2.57056	+	4.93885i	−0.103236	+	0.198349i
$621$	−0.0979055	−	30.1946i	−0.00392881	−	1.21167i
$622$	7.40347	+	22.7855i	0.296852	+	0.913617i
$623$	20.8310	+	23.1351i	0.834574	+	0.926889i
$624$	−0.161597	−	1.52167i	−0.00646904	−	0.0609154i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−9.76311	+	16.9102i	−0.390212	+	0.675868i
$627$	−3.18034	+	7.16398i	−0.127010	+	0.286102i
$628$	1.33387	+	0.969116i	0.0532273	+	0.0386719i
$629$	48.3089	+	5.07747i	1.92620	+	0.202452i
$630$	8.17981	+	1.72020i	0.325891	+	0.0685344i
$631$	16.1310	−	36.2308i	0.642164	−	1.44232i	−0.239712	−	0.970844i	$-0.577053\pi$
$631$	16.1310	−	36.2308i	0.642164	−	1.44232i	0.881876	−	0.471481i	$-0.156280\pi$
$632$	9.64920	+	2.05100i	0.383825	+	0.0815844i
$633$	−12.5630	−	4.06695i	−0.499333	−	0.161647i
$634$	−10.6515	+	4.74237i	−0.423027	+	0.188344i
$635$	−6.17845	+	19.0153i	−0.245184	+	0.754599i
$636$	14.3689	−	12.9659i	0.569763	−	0.514133i
$637$	−0.274231	−	0.615933i	−0.0108654	−	0.0244041i
$638$	1.29166	+	6.07679i	0.0511374	+	0.240582i
$639$	−45.7630	+	14.9787i	−1.81036	+	0.592550i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	24.4509	−	27.1554i	0.965751	−	1.07258i	−0.0315752	−	0.999501i	$-0.510052\pi$
$641$	24.4509	−	27.1554i	0.965751	−	1.07258i	0.997327	−	0.0730741i	$-0.0232810\pi$
$642$	−8.06710	+	11.1287i	−0.318383	+	0.439214i
$643$	−2.53221	+	3.48529i	−0.0998607	+	0.137447i	−0.856023	−	0.516937i	$-0.827072\pi$
$643$	−2.53221	+	3.48529i	−0.0998607	+	0.137447i	0.756162	+	0.654384i	$0.227072\pi$
$644$	−1.69240	−	16.1021i	−0.0666900	−	0.634513i
$645$	2.36422	−	1.36839i	0.0930913	−	0.0538805i
$646$	−31.2947	+	18.0680i	−1.23127	+	0.710876i
$647$	22.6948	−	16.4887i	0.892224	−	0.648239i	−0.0442327	−	0.999021i	$-0.514084\pi$
$647$	22.6948	−	16.4887i	0.892224	−	0.648239i	0.936457	+	0.350782i	$0.114084\pi$
$648$	1.90925	+	8.79516i	0.0750023	+	0.345506i
$649$	−12.1008	+	3.93178i	−0.474997	+	0.154336i
$650$	−0.883474			−0.0346527
$651$	−26.0059	+	6.75755i	−1.01925	+	0.264849i
$652$	7.56063			0.296097
$653$	21.2549	−	6.90613i	0.831768	−	0.270258i	0.137978	−	0.990435i	$-0.455940\pi$
$653$	21.2549	−	6.90613i	0.831768	−	0.270258i	0.693790	+	0.720177i	$0.255940\pi$
$654$	5.78330	−	1.23581i	0.226145	−	0.0483241i
$655$	9.25617	−	6.72500i	0.361668	−	0.262768i
$656$	−6.42206	+	3.70778i	−0.250739	+	0.144764i
$657$	−0.000896786	−	0.414862i	−3.49869e−5	−	0.0161853i
$658$	−2.47781	−	23.5748i	−0.0965952	−	0.919042i
$659$	−11.1144	+	15.2977i	−0.432955	+	0.595912i	−0.968628	−	0.248513i	$-0.920058\pi$
$659$	−11.1144	+	15.2977i	−0.432955	+	0.595912i	0.535673	+	0.844426i	$0.320058\pi$
$660$	−1.29714	−	0.940284i	−0.0504909	−	0.0366005i
$661$	−5.96530	+	6.62514i	−0.232023	+	0.257688i	−0.847902	−	0.530153i	$-0.822134\pi$
$661$	−5.96530	+	6.62514i	−0.232023	+	0.257688i	0.615879	+	0.787841i	$0.288801\pi$
$662$	31.5132	+	14.0306i	1.22479	+	0.545313i
$663$	−7.55362	+	8.40740i	−0.293358	+	0.326516i
$664$	−3.62038	−	17.0325i	−0.140498	−	0.660990i
$665$	−5.54448	−	12.4531i	−0.215006	−	0.482910i
$666$	−19.2898	+	4.14377i	−0.747463	+	0.160568i
$667$	−12.0608	+	37.1193i	−0.466996	+	1.43726i
$668$	9.44470	−	4.20505i	0.365426	−	0.162698i
$669$	−4.96617	+	15.3407i	−0.192003	+	0.593106i
$670$	3.87776	+	0.824243i	0.149811	+	0.0318433i
$671$	1.31353	−	2.95023i	0.0507082	−	0.113892i
$672$	1.49625	+	4.58810i	0.0577191	+	0.176990i
$673$	−24.5319	−	2.57841i	−0.945636	−	0.0993903i	−0.380858	−	0.924634i	$-0.624371\pi$
$673$	−24.5319	−	2.57841i	−0.945636	−	0.0993903i	−0.564778	+	0.825243i	$0.691038\pi$
$674$	28.7617	+	20.8966i	1.10786	+	0.804908i
$675$	5.16590	−	0.559899i	0.198836	−	0.0215505i
$676$	6.10974	−	10.5824i	0.234990	−	0.407014i
$677$	7.16529	+	12.4107i	0.275385	+	0.476980i	0.970232	−	0.242177i	$-0.0778615\pi$
$677$	7.16529	+	12.4107i	0.275385	+	0.476980i	−0.694847	+	0.719157i	$0.744528\pi$
$678$	14.8218	−	1.57403i	0.569227	−	0.0604503i
$679$	−23.8644	−	26.5041i	−0.915832	−	1.01713i
$680$	−2.28241	−	7.02454i	−0.0875265	−	0.269379i
$681$	17.7216	−	30.7715i	0.679093	−	1.17916i
$682$	5.07943	+	0.849635i	0.194502	+	0.0325342i
$683$		−	28.7786i		−	1.10118i	−0.834775	−	0.550591i	$-0.814402\pi$
$683$		−	28.7786i		−	1.10118i	0.834775	−	0.550591i	$-0.185598\pi$
$684$	9.79751	−	10.9286i	0.374617	−	0.417867i
$685$	2.53298	−	2.28071i	0.0967802	−	0.0871413i
$686$	−10.2142	−	14.0586i	−0.389979	−	0.536760i
$687$	−0.104694		0.000113155i	−0.00399432		4.31715e-6i
$688$	1.36584	+	0.788567i	0.0520721	+	0.0300639i
$689$	−9.81793	+	1.03191i	−0.374033	+	0.0393125i
$690$	−4.10371	−	9.19034i	−0.156226	−	0.349870i
$691$	−4.08844	+	38.8989i	−0.155532	+	1.47978i	0.586789	+	0.809740i	$0.300392\pi$
$691$	−4.08844	+	38.8989i	−0.155532	+	1.47978i	−0.742321	+	0.670045i	$0.766275\pi$
$692$	−7.08761	−	6.38172i	−0.269431	−	0.242596i
$693$	−0.824787	−	7.68743i	−0.0313311	−	0.292021i
$694$	−0.0397453	+	0.186987i	−0.00150871	+	0.00709793i
$695$	15.0916	−	3.20783i	0.572459	−	0.121680i
$696$	1.20351	−	11.5709i	0.0456189	−	0.438594i
$697$	52.0908	+	16.9253i	1.97308	+	0.641093i
$698$	−12.3646	−	4.01749i	−0.468006	−	0.152064i
$699$	1.76813	−	16.9994i	0.0668768	−	0.642974i
$700$	2.72536	−	0.579292i	0.103009	−	0.0218952i
$701$	−7.16738	+	33.7199i	−0.270708	+	1.27358i	0.607122	+	0.794609i	$0.292324\pi$
$701$	−7.16738	+	33.7199i	−0.270708	+	1.27358i	−0.877830	+	0.478973i	$0.841009\pi$
$702$	1.85358	−	4.19981i	0.0699590	−	0.158512i
$703$	23.9113	+	21.5298i	0.901832	+	0.812013i
$704$	0.0966854	−	0.919901i	0.00364397	−	0.0346701i
$705$	−6.00816	−	13.4554i	−0.226280	−	0.506759i
$706$	4.34048	−	0.456202i	0.163356	−	0.0171694i
$707$	−19.7957	−	11.4290i	−0.744492	−	0.429833i
$708$	23.8254	−	0.0257511i	0.895415	−	0.000967785i
$709$	15.7121	+	21.6259i	0.590082	+	0.812178i	0.994755	−	0.102284i	$-0.0326149\pi$
$709$	15.7121	+	21.6259i	0.590082	+	0.812178i	−0.404674	+	0.914461i	$0.632615\pi$
$710$	−11.9280	+	10.7400i	−0.447649	+	0.403065i
$711$	22.0356	+	19.7549i	0.826400	+	0.740865i
$712$			11.1732i			0.418735i
$713$	24.9668	+	20.5781i	0.935013	+	0.770654i
$714$	17.7888	−	30.8882i	0.665730	−	1.15596i
$715$	0.252524	+	0.777189i	0.00944386	+	0.0290652i
$716$	9.36760	+	10.4038i	0.350084	+	0.388807i
$717$	22.8483	−	2.42642i	0.853284	−	0.0906163i
$718$	1.14165	+	1.97740i	0.0426061	+	0.0737960i
$719$	14.9203	−	25.8428i	0.556435	−	0.963773i	−0.441356	−	0.897332i	$-0.645502\pi$
$719$	14.9203	−	25.8428i	0.556435	−	0.963773i	0.997790	−	0.0664407i	$-0.0211643\pi$
$720$	1.76860	+	2.42323i	0.0659118	+	0.0903086i
$721$	28.3709	+	20.6126i	1.05659	+	0.767655i
$722$	−4.90924	−	0.515981i	−0.182703	−	0.0192028i
$723$	3.40824	+	10.4510i	0.126754	+	0.388678i
$724$	1.33864	−	3.00663i	0.0497501	−	0.111741i
$725$	−6.56973	−	1.39644i	−0.243994	−	0.0518625i
$726$	5.41157	−	16.7166i	0.200842	−	0.620410i
$727$	29.9011	−	13.3128i	1.10897	−	0.493745i	0.231237	−	0.972897i	$-0.425723\pi$
$727$	29.9011	−	13.3128i	1.10897	−	0.493745i	0.877732	+	0.479153i	$0.159056\pi$
$728$	0.760668	−	2.34110i	0.0281922	−	0.0867668i
$729$	−8.17676	+	25.7321i	−0.302843	+	0.953040i
$730$	−0.0562466	−	0.126332i	−0.00208178	−	0.00467576i
$731$	−2.42192	−	11.3942i	−0.0895778	−	0.421431i
$732$	−4.04156	+	4.49838i	−0.149380	+	0.166265i
$733$	36.6446	+	16.3152i	1.35350	+	0.602616i	0.949967	−	0.312350i	$-0.101116\pi$
$733$	36.6446	+	16.3152i	1.35350	+	0.602616i	0.403531	+	0.914966i	$0.367783\pi$
$734$	9.23822	−	10.2601i	0.340989	−	0.378706i
$735$	1.07021	+	0.775786i	0.0394752	+	0.0286153i
$736$	3.41562	−	4.70119i	0.125901	−	0.173288i
$737$	−0.383299	−	3.64684i	−0.0141190	−	0.134333i
$738$	−22.2466	+	0.0480894i	−0.818909	+	0.00177019i
$739$	−0.0469575	+	0.0271109i	−0.00172736	+	0.000997292i	−0.500863	−	0.865526i	$-0.666984\pi$
$739$	−0.0469575	+	0.0271109i	−0.00172736	+	0.000997292i	0.499136	+	0.866524i	$0.333651\pi$
$740$	−5.32058	+	3.86563i	−0.195589	+	0.142103i
$741$	−7.32128	+	1.56446i	−0.268954	+	0.0574718i
$742$	29.6099	−	9.62084i	1.08701	−	0.353192i
$743$	16.6969			0.612549			0.306275	−	0.951943i	$-0.400917\pi$
$743$	16.6969			0.612549			0.306275	+	0.951943i	$0.400917\pi$
$744$	−8.55915	−	4.44309i	−0.313794	−	0.162891i
$745$	−4.65602			−0.170583
$746$	−5.82243	+	1.89182i	−0.213174	+	0.0692645i
$747$	16.0354	−	49.7172i	0.586703	−	1.81906i
$748$	−5.52708	+	4.01566i	−0.202090	+	0.146827i
$749$	−19.1485	+	11.0554i	−0.699671	+	0.403955i
$750$	1.49906	−	0.867646i	0.0547380	−	0.0316820i
$751$	1.99349	+	18.9668i	0.0727433	+	0.692107i	0.968745	+	0.248057i	$0.0797920\pi$
$751$	1.99349	+	18.9668i	0.0727433	+	0.692107i	−0.896002	+	0.444050i	$0.853541\pi$
$752$	5.00073	−	6.88292i	0.182358	−	0.250994i
$753$	−14.8033	+	20.4214i	−0.539463	+	0.744197i
$754$	−3.97053	+	4.40971i	−0.144598	+	0.160592i
$755$	3.04921	+	1.35760i	0.110972	+	0.0494080i
$756$	−2.96416	+	14.1711i	−0.107805	+	0.515396i
$757$	−6.41489	−	30.1797i	−0.233153	−	1.09690i	−0.926500	−	0.376295i	$-0.877198\pi$
$757$	−6.41489	−	30.1797i	−0.233153	−	1.09690i	0.693347	−	0.720604i	$-0.256135\pi$
$758$	−7.18736	−	16.1431i	−0.261057	−	0.586343i
$759$	−6.91175	+	6.23690i	−0.250880	+	0.226385i
$760$	1.51186	−	4.65302i	0.0548408	−	0.168783i
$761$	3.44955	−	1.53584i	0.125046	−	0.0556741i	−0.343260	−	0.939240i	$-0.611531\pi$
$761$	3.44955	−	1.53584i	0.125046	−	0.0556741i	0.468306	+	0.883566i	$0.344864\pi$
$762$	−32.9470	−	10.6658i	−1.19354	−	0.386380i
$763$	9.30538	+	1.97792i	0.336877	+	0.0716055i
$764$	−1.58636	+	3.56302i	−0.0573925	+	0.128906i
$765$	4.56007	−	21.6838i	0.164870	−	0.783980i
$766$	2.88454	+	0.303177i	0.104223	+	0.0109542i
$767$	−9.83178	−	7.14320i	−0.355005	−	0.257926i
$768$	−0.702778	+	1.58307i	−0.0253593	+	0.0571240i
$769$	−7.61362	+	13.1872i	−0.274554	+	0.475542i	−0.970023	−	0.243015i	$-0.921864\pi$
$769$	−7.61362	+	13.1872i	−0.274554	+	0.475542i	0.695468	+	0.718557i	$0.255197\pi$
$770$	−1.28859	−	2.23191i	−0.0464376	−	0.0804323i
$771$	0.392867	+	3.69941i	0.0141487	+	0.133231i
$772$	0.677914	+	0.752900i	0.0243987	+	0.0270975i
$773$	9.03296	+	27.8006i	0.324893	+	0.999918i	0.971489	+	0.237085i	$0.0761920\pi$
$773$	9.03296	+	27.8006i	0.324893	+	0.999918i	−0.646596	+	0.762833i	$0.723808\pi$
$774$	2.37455	+	4.09239i	0.0853516	+	0.147098i
$775$	−3.07273	+	4.64310i	−0.110376	+	0.166785i
$776$		−	12.8003i		−	0.459505i
$777$	−31.0517	−	6.56517i	−1.11397	−	0.235524i
$778$	21.2695	−	19.1511i	0.762548	−	0.686601i
$779$	21.3251	+	29.3514i	0.764050	+	1.05162i
$780$	−0.00165390	−	1.53022i	−5.92191e−5	−	0.0547907i
$781$	12.8573	+	7.42317i	0.460071	+	0.265622i
$782$	−42.6851	+	4.48638i	−1.52642	+	0.160433i
$783$	20.4220	−	28.3010i	0.729824	−	1.01140i
$784$	−0.0797708	+	0.758968i	−0.00284896	+	0.0271060i
$785$	1.22527	+	1.10323i	0.0437316	+	0.0393761i
$786$	11.6654	+	16.0196i	0.416090	+	0.571399i
$787$	−0.353229	+	1.66181i	−0.0125912	+	0.0592371i	−0.983995	−	0.178198i	$-0.942973\pi$
$787$	−0.353229	+	1.66181i	−0.0125912	+	0.0592371i	0.971403	+	0.237435i	$0.0763066\pi$
$788$	−20.7427	+	4.40899i	−0.738927	+	0.157064i
$789$	−19.8537	−	2.06501i	−0.706810	−	0.0735165i
$790$	9.38195	+	3.04838i	0.333795	+	0.108457i
$791$	22.8034	+	7.40929i	0.810797	+	0.263444i
$792$	1.62619	−	2.24846i	0.0577842	−	0.0798957i
$793$	3.01716	−	0.641317i	0.107142	−	0.0227738i
$794$	3.76017	−	17.6902i	0.133444	−	0.627803i
$795$	15.6455	−	11.3930i	0.554888	−	0.404067i
$796$	15.7719	+	14.2010i	0.559019	+	0.503343i
$797$	1.01203	−	9.62878i	0.0358478	−	0.341069i	−0.961868	−	0.273515i	$-0.911814\pi$
$797$	1.01203	−	9.62878i	0.0358478	−	0.341069i	0.997716	−	0.0675542i	$-0.0215195\pi$
$798$	21.5590	−	9.62662i	0.763181	−	0.340779i
$799$	−62.4943	+	6.56842i	−2.21089	+	0.232374i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−16.6971	+	29.0651i	−0.589962	+	1.02696i
$802$	16.1778	+	22.2668i	0.571257	+	0.786268i
$803$	−0.0950568	+	0.0855895i	−0.00335448	+	0.00302039i
$804$	−1.42037	+	6.71801i	−0.0500926	+	0.236926i
$805$		−	16.1908i		−	0.570652i
$806$	2.19515	+	4.40201i	0.0773208	+	0.155054i
$807$	−9.55624	−	5.50354i	−0.336396	−	0.193734i
$808$	−2.53514	−	7.80237i	−0.0891861	−	0.274486i
$809$	26.2737	+	29.1799i	0.923733	+	1.02591i	0.999585	+	0.0287900i	$0.00916541\pi$
$809$	26.2737	+	29.1799i	0.923733	+	1.02591i	−0.0758529	+	0.997119i	$0.524168\pi$
$810$	0.979444	+	8.94655i	0.0344141	+	0.314350i
$811$	−18.8218	−	32.6003i	−0.660923	−	1.14475i	−0.980373	−	0.197150i	$-0.936831\pi$
$811$	−18.8218	−	32.6003i	−0.660923	−	1.14475i	0.319450	−	0.947603i	$-0.396502\pi$
$812$	9.35690	−	16.2066i	0.328363	−	0.568741i
$813$	45.4681	+	20.1849i	1.59464	+	0.707914i
$814$	4.92137	+	3.57558i	0.172494	+	0.125324i
$815$	7.51922	+	0.790301i	0.263387	+	0.0276831i
$816$	12.1626	−	3.96640i	0.425775	−	0.138852i
$817$	3.13842	−	7.04900i	0.109799	−	0.246613i
$818$	−8.86679	−	1.88469i	−0.310020	−	0.0658968i
$819$	5.47722	−	4.95319i	0.191390	−	0.173079i
$820$	−6.77444	+	3.01618i	−0.236574	+	0.105329i
$821$	10.1363	−	31.1964i	0.353761	−	1.08876i	−0.602964	−	0.797768i	$-0.706014\pi$
$821$	10.1363	−	31.1964i	0.353761	−	1.08876i	0.956725	−	0.290995i	$-0.0939863\pi$
$822$	3.95504	+	4.38298i	0.137948	+	0.152874i
$823$	−20.8916	−	46.9232i	−0.728234	−	1.63564i	−0.771223	−	0.636565i	$-0.780355\pi$
$823$	−20.8916	−	46.9232i	−0.728234	−	1.63564i	0.0429896	−	0.999076i	$-0.486312\pi$
$824$	2.61683	+	12.3112i	0.0911615	+	0.428881i
$825$	−1.19174	−	1.07072i	−0.0414912	−	0.0372777i
$826$	35.0130	+	15.5888i	1.21826	+	0.542404i
$827$	34.5516	−	38.3734i	1.20148	−	1.33437i	0.273437	−	0.961890i	$-0.411839\pi$
$827$	34.5516	−	38.3734i	1.20148	−	1.33437i	0.928039	−	0.372484i	$-0.121494\pi$
$828$	15.9105	−	7.12504i	0.552926	−	0.247612i
$829$	−3.57945	+	4.92670i	−0.124320	+	0.171111i	−0.866640	−	0.498934i	$-0.833725\pi$
$829$	−3.57945	+	4.92670i	−0.124320	+	0.171111i	0.742321	+	0.670045i	$0.233725\pi$
$830$	−1.82016	−	17.3177i	−0.0631787	−	0.601105i
$831$	5.10055	+	8.81240i	0.176936	+	0.305699i
$832$	0.765111	−	0.441737i	0.0265255	−	0.0153145i
$833$	4.56014	−	3.31314i	0.158000	−	0.114793i
$834$	5.58437	+	26.1335i	0.193371	+	0.904928i
$835$	9.83251	−	3.19478i	0.340268	−	0.110560i
$836$	−4.52538			−0.156513
$837$	−15.6254	−	24.3485i	−0.540091	−	0.841607i
$838$	−2.65793			−0.0918165
$839$	6.27679	−	2.03945i	0.216699	−	0.0704098i	−0.198656	−	0.980069i	$-0.563658\pi$
$839$	6.27679	−	2.03945i	0.216699	−	0.0704098i	0.415355	+	0.909660i	$0.363658\pi$
$840$	1.00847	+	4.71937i	0.0347954	+	0.162834i
$841$	−13.0344	+	9.47004i	−0.449462	+	0.326553i
$842$	−19.4217	+	11.2131i	−0.669317	+	0.386431i
$843$	15.2871	+	26.4121i	0.526517	+	0.909681i
$844$	−0.796907	−	7.58207i	−0.0274307	−	0.260985i
$845$	7.18243	−	9.88576i	0.247083	−	0.340081i
$846$	23.2942	−	10.4316i	0.800870	−	0.358647i
$847$	18.9129	−	21.0049i	0.649854	−	0.721736i
$848$	10.2080	+	4.54491i	0.350545	+	0.156073i
$849$	2.59127	+	2.32813i	0.0889323	+	0.0799011i
$850$	−1.53564	−	7.22464i	−0.0526721	−	0.247803i
$851$	15.5441	+	34.9126i	0.532844	+	1.19679i
$852$	−18.6245	−	20.6397i	−0.638066	−	0.707106i
$853$	−3.46859	+	10.6752i	−0.118762	+	0.365512i	−0.992713	−	0.120502i	$-0.961550\pi$
$853$	−3.46859	+	10.6752i	−0.118762	+	0.365512i	0.873951	+	0.486014i	$0.161550\pi$
$854$	−8.88687	+	3.95669i	−0.304102	+	0.135395i
$855$	10.8862	−	9.84466i	0.372300	−	0.336680i
$856$	−7.76228	−	1.64992i	−0.265309	−	0.0563932i
$857$	3.47886	−	7.81365i	0.118836	−	0.266909i	−0.844327	−	0.535828i	$-0.820000\pi$
$857$	3.47886	−	7.81365i	0.118836	−	0.266909i	0.963163	+	0.268919i	$0.0866663\pi$
$858$	−1.34566	+	0.438839i	−0.0459400	+	0.0149817i
$859$	−4.30710	−	0.452695i	−0.146956	−	0.0154457i	0.0307646	−	0.999527i	$-0.490206\pi$
$859$	−4.30710	−	0.452695i	−0.146956	−	0.0154457i	−0.177721	+	0.984081i	$0.556872\pi$
$860$	1.27593	+	0.927017i	0.0435088	+	0.0316110i
$861$	−32.7086	−	14.5205i	−1.11471	−	0.494856i
$862$	12.1699	−	21.0788i	0.414507	−	0.717948i
$863$	3.06869	+	5.31513i	0.104460	+	0.180929i	0.913517	−	0.406800i	$-0.133355\pi$
$863$	3.06869	+	5.31513i	0.104460	+	0.180929i	−0.809058	+	0.587729i	$0.800022\pi$
$864$	−4.19385	+	3.06784i	−0.142678	+	0.104370i
$865$	−6.38172	−	7.08761i	−0.216985	−	0.240986i
$866$	−1.31936	−	4.06058i	−0.0448337	−	0.137984i
$867$	−56.3654	−	32.4614i	−1.91427	−	1.10245i
$868$	−9.65802	−	12.1400i	−0.327815	−	0.412059i
$869$		−	9.12459i		−	0.309531i
$870$	2.40640	−	11.3817i	0.0815847	−	0.385876i
$871$	2.60282	−	2.34359i	0.0881931	−	0.0794094i
$872$	2.00692	+	2.76229i	0.0679628	+	0.0935428i
$873$	19.1285	−	33.2976i	0.647403	−	1.12695i
$874$	−24.6212	−	14.2151i	−0.832824	−	0.480831i
$875$	2.77098	−	0.291242i	0.0936762	−	0.00984577i
$876$	0.218708	−	0.0976585i	0.00738946	−	0.00329957i
$877$	4.16549	−	39.6320i	0.140659	−	1.33828i	−0.665420	−	0.746469i	$-0.731748\pi$
$877$	4.16549	−	39.6320i	0.140659	−	1.33828i	0.806079	−	0.591808i	$-0.201586\pi$
$878$	−16.4158	−	14.7809i	−0.554008	−	0.498831i
$879$	−37.0092	+	26.9499i	−1.24829	+	0.908998i
$880$	0.192312	−	0.904755i	0.00648282	−	0.0304993i
$881$	29.4918	−	6.26867i	0.993602	−	0.211197i	0.317703	−	0.948190i	$-0.397089\pi$
$881$	29.4918	−	6.26867i	0.993602	−	0.211197i	0.675900	+	0.736994i	$0.263755\pi$
$882$	−1.34170	+	1.85511i	−0.0451773	+	0.0624647i
$883$	−39.8780	−	12.9572i	−1.34200	−	0.436043i	−0.452008	−	0.892014i	$-0.649292\pi$
$883$	−39.8780	−	12.9572i	−1.34200	−	0.436043i	−0.889995	+	0.455971i	$0.849292\pi$
$884$	−6.20600	−	2.01645i	−0.208730	−	0.0678206i
$885$	23.6976	+	2.46483i	0.796587	+	0.0828542i
$886$	35.0257	−	7.44494i	1.17671	−	0.250118i
$887$	−4.36149	+	20.5192i	−0.146444	+	0.688967i	0.842258	+	0.539075i	$0.181226\pi$
$887$	−4.36149	+	20.5192i	−0.146444	+	0.688967i	−0.988702	+	0.149892i	$0.952107\pi$
$888$	−6.70543	−	9.20828i	−0.225019	−	0.309010i
$889$	−41.3990	−	37.2758i	−1.38848	−	1.25019i
$890$	−1.16792	+	11.1120i	−0.0391488	+	0.372476i
$891$	7.59029	−	3.41881i	0.254284	−	0.114534i
$892$	−9.25850	+	0.973108i	−0.309998	+	0.0325821i
$893$	−36.0474	−	20.8120i	−1.20628	−	0.696446i
$894$	−0.00871626	−	8.06446i	−0.000291515	−	0.269716i
$895$	8.22880	+	11.3260i	0.275058	+	0.378585i
$896$	−2.07058	+	1.86436i	−0.0691733	+	0.0622839i
$897$	−8.69979	−	1.83937i	−0.290477	−	0.0614148i
$898$			7.04253i			0.235012i
$899$	9.36575	+	36.2041i	0.312365	+	1.20747i
$900$	1.50561	+	2.59483i	0.0501871	+	0.0864943i
$901$	−25.5038	−	78.4928i	−0.849656	−	2.61497i
$902$	4.58966	+	5.09734i	0.152819	+	0.169723i
$903$	0.803759	+	7.56856i	0.0267474	+	0.251866i
$904$	4.30274	+	7.45257i	0.143107	+	0.247869i
$905$	1.64559	−	2.85024i	0.0547011	−	0.0947451i
$906$	−2.34572	+	5.28393i	−0.0779312	+	0.175547i
$907$	5.43443	+	3.94835i	0.180447	+	0.131103i	0.674342	−	0.738419i	$-0.264427\pi$
$907$	5.43443	+	3.94835i	0.180447	+	0.131103i	−0.493895	+	0.869522i	$0.664427\pi$
$908$	20.3892	+	2.14299i	0.676640	+	0.0711177i
$909$	5.06501	−	24.0849i	0.167996	−	0.798845i
$910$	1.00121	−	2.24876i	0.0331899	−	0.0745456i
$911$	−55.9192	−	11.8860i	−1.85269	−	0.393800i	−0.859578	−	0.511005i	$-0.829273\pi$
$911$	−55.9192	−	11.8860i	−1.85269	−	0.393800i	−0.993108	+	0.117205i	$0.962607\pi$
$912$	8.06209	+	2.60990i	0.266962	+	0.0864224i
$913$	−14.7140	+	6.55111i	−0.486963	+	0.216810i
$914$	1.83847	−	5.65823i	0.0608112	−	0.187158i
$915$	−4.48963	+	4.05128i	−0.148423	+	0.133931i
$916$	−0.0245852	−	0.0552193i	−0.000812318	−	0.00182450i
$917$	6.62783	+	31.1815i	0.218870	+	1.02970i
$918$	37.5660	+	7.85767i	1.23986	+	0.259342i
$919$	10.6209	+	4.72871i	0.350350	+	0.155986i	0.574364	−	0.818600i	$-0.305249\pi$
$919$	10.6209	+	4.72871i	0.350350	+	0.155986i	−0.224014	+	0.974586i	$0.571916\pi$
$920$	3.88831	−	4.31841i	0.128194	−	0.142374i
$921$	−2.99078	+	4.12582i	−0.0985494	+	0.135950i
$922$	21.3195	−	29.3438i	0.702121	−	0.966387i
$923$	1.48225	+	14.1027i	0.0487889	+	0.464195i
$924$	3.86336	−	2.23608i	0.127095	−	0.0735618i
$925$	−5.69551	+	3.28830i	−0.187267	+	0.108119i
$926$	19.7795	−	14.3706i	0.649993	−	0.472248i
$927$	−11.5904	+	35.9358i	−0.380680	+	1.18029i
$928$	6.38777	−	2.07551i	0.209689	−	0.0681321i
$929$	37.1077			1.21746			0.608732	−	0.793376i	$-0.291678\pi$
$929$	37.1077			1.21746			0.608732	+	0.793376i	$0.291678\pi$
$930$	−8.04783	−	5.31342i	−0.263899	−	0.174234i
$931$	3.73368			0.122367
$932$	9.38457	−	3.04923i	0.307402	−	0.0998810i
$933$	−40.5805	+	8.67151i	−1.32855	+	0.283893i
$934$	−5.96842	+	4.33631i	−0.195293	+	0.141888i
$935$	−5.91655	+	3.41592i	−0.193492	+	0.111713i
$936$	2.65042	−	0.00572927i	0.0866316	−	0.000187267i
$937$	1.82364	+	17.3507i	0.0595756	+	0.566824i	0.983072	+	0.183218i	$0.0586513\pi$
$937$	1.82364	+	17.3507i	0.0595756	+	0.566824i	−0.923497	+	0.383606i	$0.874682\pi$
$938$	−6.49253	+	8.93620i	−0.211989	+	0.291777i
$939$	−27.3828	−	19.8496i	−0.893602	−	0.647766i
$940$	5.69280	−	6.32249i	0.185679	−	0.206217i
$941$	33.6825	+	14.9964i	1.09802	+	0.488869i	0.874104	−	0.485740i	$-0.161450\pi$
$941$	33.6825	+	14.9964i	1.09802	+	0.488869i	0.223915	+	0.974609i	$0.428116\pi$
$942$	−1.90856	+	2.12429i	−0.0621844	+	0.0692130i
$943$	8.95927	+	42.1501i	0.291754	+	1.37259i
$944$	5.59492	+	12.5664i	0.182099	+	0.409001i
$945$	−4.42920	+	13.7836i	−0.144082	+	0.448380i
$946$	0.450794	−	1.38740i	0.0146566	−	0.0451083i
$947$	31.6902	−	14.1094i	1.02979	−	0.458493i	0.178919	−	0.983864i	$-0.442740\pi$
$947$	31.6902	−	14.1094i	1.02979	−	0.458493i	0.850874	+	0.525370i	$0.176073\pi$
$948$	−5.26238	+	16.2557i	−0.170914	+	0.527961i
$949$	−0.119504	−	0.0254013i	−0.00387926	−	0.000824561i
$950$	1.98995	−	4.46950i	0.0645624	−	0.145010i
$951$	−6.26134	−	19.1998i	−0.203038	−	0.622596i
$952$	20.4666	+	2.15112i	0.663325	+	0.0697183i
$953$	2.11251	+	1.53483i	0.0684309	+	0.0497180i	0.621475	−	0.783434i	$-0.286534\pi$
$953$	2.11251	+	1.53483i	0.0684309	+	0.0497180i	−0.553044	+	0.833152i	$0.686534\pi$
$954$	19.7625	+	27.0774i	0.639833	+	0.876663i
$955$	−1.95011	+	3.37768i	−0.0631039	+	0.109299i
$956$	6.63281	+	11.4884i	0.214520	+	0.371560i
$957$	−10.7003	+	1.13634i	−0.345891	+	0.0367326i
$958$	−0.960600	−	1.06685i	−0.0310356	−	0.0344685i
$959$	2.93467	+	9.03200i	0.0947655	+	0.291658i
$960$	−0.864404	+	1.50094i	−0.0278985	+	0.0484425i
$961$	30.7695	+	3.77359i	0.992563	+	0.121729i
$962$			5.81026i			0.187330i
$963$	−17.7265	−	15.8918i	−0.571229	−	0.512105i
$964$	−4.71648	+	4.24674i	−0.151908	+	0.136778i
$965$	0.595501	+	0.819637i	0.0191699	+	0.0263850i
$966$	28.0433	−	0.0303099i	0.902279	−	0.000975205i
$967$	−9.56049	−	5.51975i	−0.307445	−	0.177503i	0.338338	−	0.941025i	$-0.390135\pi$
$967$	−9.56049	−	5.51975i	−0.307445	−	0.177503i	−0.645782	+	0.763521i	$0.723469\pi$
$968$	10.0889	−	1.06038i	0.324268	−	0.0340820i
$969$	−25.5192	−	57.1507i	−0.819794	−	1.83594i
$970$	1.33800	−	12.7302i	0.0429605	−	0.408742i
$971$	−13.5074	−	12.1621i	−0.433473	−	0.390301i	0.423304	−	0.905988i	$-0.360870\pi$
$971$	−13.5074	−	12.1621i	−0.433473	−	0.390301i	−0.856777	+	0.515687i	$0.827537\pi$
$972$	−15.4940	+	1.71319i	−0.496971	+	0.0549507i
$973$	−8.93779	+	42.0490i	−0.286532	+	1.34803i
$974$	2.99230	−	0.636033i	0.0958795	−	0.0203798i
$975$	0.158307	−	1.52201i	0.00506988	−	0.0487434i
$976$	−3.32052	−	1.07890i	−0.106287	−	0.0345348i
$977$	7.22746	+	2.34834i	0.231227	+	0.0751301i	0.422339	−	0.906438i	$-0.361209\pi$
$977$	7.22746	+	2.34834i	0.231227	+	0.0751301i	−0.191112	+	0.981568i	$0.561209\pi$
$978$	−1.35477	+	13.0251i	−0.0433206	+	0.416498i
$979$	10.1090	−	2.14874i	0.323087	−	0.0686742i
$980$	−0.158668	+	0.746472i	−0.00506845	+	0.0238452i
$981$	1.09272	+	10.1847i	0.0348877	+	0.325171i
$982$	−12.3492	−	11.1192i	−0.394078	−	0.354829i
$983$	−4.09269	+	38.9394i	−0.130537	+	1.24197i	0.711552	+	0.702634i	$0.247993\pi$
$983$	−4.09269	+	38.9394i	−0.130537	+	1.24197i	−0.842088	+	0.539340i	$0.818674\pi$
$984$	−5.23685	−	11.7280i	−0.166945	−	0.373876i
$985$	−21.0899	+	2.21664i	−0.671980	+	0.0706280i
$986$	−42.9621	−	24.8042i	−1.36819	−	0.789926i
$987$	41.0577	−	0.0443761i	1.30688	−	0.00141251i
$988$	−2.54063	−	3.49687i	−0.0808281	−	0.111250i
$989$	6.81071	−	6.13239i	0.216568	−	0.194999i
$990$	1.85231	−	2.06616i	0.0588703	−	0.0656670i
$991$			43.9720i			1.39682i	0.715700	+	0.698408i	$0.246108\pi$
$991$			43.9720i			1.39682i	−0.715700	+	0.698408i	$0.753892\pi$
$992$	0.339510	−	5.55740i	0.0107795	−	0.176448i
$993$	−29.8180	+	51.7754i	−0.946245	+	1.64304i
$994$	−13.8196	−	42.5322i	−0.438330	−	1.34904i
$995$	14.2010	+	15.7719i	0.450204	+	0.500002i
$996$	29.9916	−	3.18503i	0.950322	−	0.100921i
$997$	−13.3473	−	23.1182i	−0.422714	−	0.732162i	0.573490	−	0.819213i	$-0.305589\pi$
$997$	−13.3473	−	23.1182i	−0.422714	−	0.732162i	−0.996204	+	0.0870504i	$0.972256\pi$
$998$	−5.93824	+	10.2853i	−0.187972	+	0.325577i
$999$	−3.68223	−	33.9741i	−0.116501	−	1.07489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.5	✓	176
3.2	odd	2	inner	930.2.br.a.11.22	yes	176
31.17	odd	30	inner	930.2.br.a.761.22	yes	176
93.17	even	30	inner	930.2.br.a.761.5	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.5	✓	176	1.1	even	1	trivial
930.2.br.a.11.22	yes	176	3.2	odd	2	inner
930.2.br.a.761.5	yes	176	93.17	even	30	inner
930.2.br.a.761.22	yes	176	31.17	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.361945 - 1.69381i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.867646 + 1.49906i) q^{6} +(0.291242 + 2.77098i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.73799 + 1.22613i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.361945 - 1.69381i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.867646 + 1.49906i) q^{6} +(0.291242 + 2.77098i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.73799 + 1.22613i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(0.845000 + 0.376218i) q^{11} +(-1.28842 - 1.15758i) q^{12} +(0.183685 + 0.864168i) q^{13} +(-1.13327 - 2.54536i) q^{14} +(-1.16036 - 1.28591i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.74748 + 3.00417i) q^{17} +(2.22509 - 2.01221i) q^{18} +(-4.78556 - 1.01720i) q^{19} +(0.406737 - 0.913545i) q^{20} +(4.58810 - 1.49625i) q^{21} +(-0.919901 - 0.0966854i) q^{22} +(-4.70119 - 3.41562i) q^{23} +(1.58307 + 0.702778i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.441737 - 0.765111i) q^{26} +(3.06784 + 4.19385i) q^{27} +(1.86436 + 2.07058i) q^{28} +(-2.07551 - 6.38777i) q^{29} +(1.50094 + 0.864404i) q^{30} +(-5.55740 - 0.339510i) q^{31} +1.00000i q^{32} +(0.331399 - 1.56744i) q^{33} +(5.48890 - 4.94222i) q^{34} +(1.63771 + 2.25412i) q^{35} +(-1.49438 + 2.60131i) q^{36} +(-5.69551 - 3.28830i) q^{37} +(4.86567 - 0.511403i) q^{38} +(1.39725 - 0.623908i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-5.51083 - 4.96197i) q^{41} +(-3.90118 + 2.84082i) q^{42} +(-0.327905 + 1.54267i) q^{43} +(0.904755 - 0.192312i) q^{44} +(-1.75811 + 2.43086i) q^{45} +(5.52658 + 1.79570i) q^{46} +(8.09135 + 2.62904i) q^{47} +(-1.72276 - 0.179187i) q^{48} +(-0.746472 + 0.158668i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(7.53071 + 10.3416i) q^{51} +(0.656549 + 0.591160i) q^{52} +(-1.16801 + 11.1129i) q^{53} +(-4.21366 - 3.04058i) q^{54} +(0.919901 - 0.0966854i) q^{55} +(-2.41296 - 1.39312i) q^{56} +(0.00915890 + 8.47400i) q^{57} +(3.94786 + 5.43376i) q^{58} +(-10.2224 + 9.20431i) q^{59} +(-1.69459 - 0.358282i) q^{60} -3.49140i q^{61} +(5.39032 - 1.39444i) q^{62} +(-4.19500 - 7.22982i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.591160 + 0.656549i) q^{65} +(0.169186 + 1.59313i) q^{66} +(-1.98219 - 3.43326i) q^{67} +(-3.69302 + 6.39650i) q^{68} +(-4.08384 + 9.19919i) q^{69} +(-2.25412 - 1.63771i) q^{70} +(15.9627 + 1.67775i) q^{71} +(0.617390 - 2.93578i) q^{72} +(-0.0562466 + 0.126332i) q^{73} +(6.43289 + 1.36735i) q^{74} +(-1.64786 - 0.533452i) q^{75} +(-4.46950 + 1.98995i) q^{76} +(-0.796394 + 2.45105i) q^{77} +(-1.13607 + 1.02515i) q^{78} +(-4.01236 - 9.01191i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(5.99320 - 6.71428i) q^{81} +(6.77444 + 3.01618i) q^{82} +(-11.6516 + 12.9404i) q^{83} +(2.83238 - 3.90731i) q^{84} +(-4.34140 + 5.97543i) q^{85} +(-0.164855 - 1.56850i) q^{86} +(-10.0685 + 5.82755i) q^{87} +(-0.801045 + 0.462484i) q^{88} +(9.03934 - 6.56747i) q^{89} +(0.920881 - 2.85517i) q^{90} +(-2.34110 + 0.760668i) q^{91} -5.81099 q^{92} +(1.43641 + 9.53608i) q^{93} -8.50775 q^{94} +(-4.65302 + 1.51186i) q^{95} +(1.69381 - 0.361945i) q^{96} +(-10.3557 + 7.52384i) q^{97} +(0.660906 - 0.381574i) q^{98} +(-2.77490 + 0.00599835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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