LMFDB - Embedded newform 231.2.be.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(2,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	231.2
Dual form			231.2.be.a.116.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06973 - 1.18806i) q^{2} +(-0.998701 + 1.41513i) q^{3} +(-0.0580986 + 0.552771i) q^{4} +(0.161799 - 0.761203i) q^{5} +(2.74960 - 0.327297i) q^{6} +(1.95474 + 1.78298i) q^{7} +(-1.86786 + 1.35708i) q^{8} +(-1.00519 - 2.82659i) q^{9} +O(q^{10})$	\(q+(-1.06973 - 1.18806i) q^{2} +(-0.998701 + 1.41513i) q^{3} +(-0.0580986 + 0.552771i) q^{4} +(0.161799 - 0.761203i) q^{5} +(2.74960 - 0.327297i) q^{6} +(1.95474 + 1.78298i) q^{7} +(-1.86786 + 1.35708i) q^{8} +(-1.00519 - 2.82659i) q^{9} +(-1.07744 + 0.622058i) q^{10} +(0.859495 + 3.20332i) q^{11} +(-0.724221 - 0.634270i) q^{12} +(2.22198 + 0.721966i) q^{13} +(0.0272359 - 4.22965i) q^{14} +(0.915614 + 0.989181i) q^{15} +(4.69775 + 0.998538i) q^{16} +(5.18432 - 5.75778i) q^{17} +(-2.28286 + 4.21792i) q^{18} +(1.46896 - 0.154394i) q^{19} +(0.411371 + 0.133662i) q^{20} +(-4.47534 + 0.985548i) q^{21} +(2.88631 - 4.44783i) q^{22} +(6.17681 + 3.56618i) q^{23} +(-0.0550126 - 3.99859i) q^{24} +(4.01448 + 1.78736i) q^{25} +(-1.51919 - 3.41216i) q^{26} +(5.00388 + 1.40043i) q^{27} +(-1.09915 + 0.976933i) q^{28} +(-1.43650 - 1.04368i) q^{29} +(0.195743 - 2.14596i) q^{30} +(-8.26320 + 1.75640i) q^{31} +(-1.53021 - 2.65041i) q^{32} +(-5.39150 - 1.98286i) q^{33} -12.3864 q^{34} +(1.67348 - 1.19947i) q^{35} +(1.62086 - 0.391421i) q^{36} +(-6.93796 + 3.08898i) q^{37} +(-1.75483 - 1.58006i) q^{38} +(-3.24077 + 2.42337i) q^{39} +(0.730797 + 1.64140i) q^{40} +(0.788077 - 0.572571i) q^{41} +(5.95831 + 4.26270i) q^{42} -4.44203i q^{43} +(-1.82064 + 0.288996i) q^{44} +(-2.31425 + 0.307818i) q^{45} +(-2.37070 - 11.1533i) q^{46} +(4.22776 - 0.444355i) q^{47} +(-6.10471 + 5.65069i) q^{48} +(0.641986 + 6.97050i) q^{49} +(-2.17093 - 6.68144i) q^{50} +(2.97042 + 13.0868i) q^{51} +(-0.528176 + 1.18630i) q^{52} +(1.37573 + 6.47231i) q^{53} +(-3.68902 - 7.44300i) q^{54} +(2.57744 - 0.135957i) q^{55} +(-6.07082 - 0.677620i) q^{56} +(-1.24857 + 2.23297i) q^{57} +(0.296721 + 2.82311i) q^{58} +(-11.7589 - 1.23591i) q^{59} +(-0.599986 + 0.448655i) q^{60} +(1.35155 - 6.35855i) q^{61} +(10.9261 + 7.93830i) q^{62} +(3.07485 - 7.31747i) q^{63} +(1.45631 - 4.48206i) q^{64} +(0.909076 - 1.57457i) q^{65} +(3.41171 + 8.52656i) q^{66} +(5.28912 + 9.16102i) q^{67} +(2.88153 + 3.20026i) q^{68} +(-11.2154 + 5.17945i) q^{69} +(-3.21522 - 0.705085i) q^{70} +(-6.29108 + 2.04410i) q^{71} +(5.71347 + 3.91555i) q^{72} +(-6.30260 - 0.662430i) q^{73} +(11.0917 + 4.93833i) q^{74} +(-6.53861 + 3.89597i) q^{75} +0.820971i q^{76} +(-4.03136 + 7.79411i) q^{77} +(6.34587 + 1.25787i) q^{78} +(7.31961 - 6.59061i) q^{79} +(1.52018 - 3.41438i) q^{80} +(-6.97917 + 5.68253i) q^{81} +(-1.52328 - 0.323783i) q^{82} +(-2.71004 - 8.34064i) q^{83} +(-0.284771 - 2.53110i) q^{84} +(-3.54402 - 4.87793i) q^{85} +(-5.27740 + 4.75179i) q^{86} +(2.91159 - 0.990517i) q^{87} +(-5.95259 - 4.81696i) q^{88} +(0.817282 + 0.471858i) q^{89} +(2.84133 + 2.42018i) q^{90} +(3.05614 + 5.37299i) q^{91} +(-2.33015 + 3.20717i) q^{92} +(5.76693 - 13.4476i) q^{93} +(-5.05049 - 4.54748i) q^{94} +(0.120151 - 1.14316i) q^{95} +(5.27890 + 0.481511i) q^{96} +(3.59669 - 11.0695i) q^{97} +(7.59461 - 8.21930i) q^{98} +(8.19050 - 5.64939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.06973	−	1.18806i	−0.756416	−	0.840085i	0.234841	−	0.972034i	$-0.424543\pi$
$2$	−1.06973	−	1.18806i	−0.756416	−	0.840085i	−0.991257	+	0.131949i	$0.957877\pi$
$3$	−0.998701	+	1.41513i	−0.576600	+	0.817026i
$3$	−0.998701	+	1.41513i	−0.576600	+	0.817026i
$4$	−0.0580986	+	0.552771i	−0.0290493	+	0.276386i
$5$	0.161799	−	0.761203i	0.0723586	−	0.340420i	−0.927045	−	0.374950i	$-0.877660\pi$
$5$	0.161799	−	0.761203i	0.0723586	−	0.340420i	0.999404	+	0.0345294i	$0.0109932\pi$
$6$	2.74960	−	0.327297i	1.12252	−	0.133619i
$7$	1.95474	+	1.78298i	0.738821	+	0.673902i
$7$	1.95474	+	1.78298i	0.738821	+	0.673902i
$8$	−1.86786	+	1.35708i	−0.660389	+	0.479801i
$9$	−1.00519	−	2.82659i	−0.335064	−	0.942195i
$10$	−1.07744	+	0.622058i	−0.340715	+	0.196712i
$11$	0.859495	+	3.20332i	0.259147	+	0.965838i
$11$	0.859495	+	3.20332i	0.259147	+	0.965838i
$12$	−0.724221	−	0.634270i	−0.209064	−	0.183098i
$13$	2.22198	+	0.721966i	0.616267	+	0.200237i	0.600482	−	0.799638i	$-0.294975\pi$
$13$	2.22198	+	0.721966i	0.616267	+	0.200237i	0.0157847	+	0.999875i	$0.494975\pi$
$14$	0.0272359	−	4.22965i	0.00727910	−	1.13042i
$15$	0.915614	+	0.989181i	0.236411	+	0.255405i
$16$	4.69775	+	0.998538i	1.17444	+	0.249634i
$17$	5.18432	−	5.75778i	1.25738	−	1.39647i	0.374261	−	0.927324i	$-0.377897\pi$
$17$	5.18432	−	5.75778i	1.25738	−	1.39647i	0.883123	−	0.469142i	$-0.155437\pi$
$18$	−2.28286	+	4.21792i	−0.538076	+	0.994174i
$19$	1.46896	−	0.154394i	0.337003	−	0.0354205i	0.0654845	−	0.997854i	$-0.479141\pi$
$19$	1.46896	−	0.154394i	0.337003	−	0.0354205i	0.271519	+	0.962433i	$0.412474\pi$
$20$	0.411371	+	0.133662i	0.0919853	+	0.0298878i
$21$	−4.47534	+	0.985548i	−0.976600	+	0.215064i
$22$	2.88631	−	4.44783i	0.615363	−	0.948281i
$23$	6.17681	+	3.56618i	1.28795	+	0.743600i	0.978289	−	0.207246i	$-0.0664499\pi$
$23$	6.17681	+	3.56618i	1.28795	+	0.743600i	0.309665	+	0.950846i	$0.399783\pi$
$24$	−0.0550126	−	3.99859i	−0.0112294	−	0.816209i
$25$	4.01448	+	1.78736i	0.802895	+	0.357472i
$26$	−1.51919	−	3.41216i	−0.297938	−	0.669179i
$27$	5.00388	+	1.40043i	0.962997	+	0.269514i
$28$	−1.09915	+	0.976933i	−0.207719	+	0.184623i
$29$	−1.43650	−	1.04368i	−0.266752	−	0.193807i	0.446366	−	0.894850i	$-0.352718\pi$
$29$	−1.43650	−	1.04368i	−0.266752	−	0.193807i	−0.713118	+	0.701044i	$0.752718\pi$
$30$	0.195743	−	2.14596i	0.0357376	−	0.391798i
$31$	−8.26320	+	1.75640i	−1.48411	+	0.315458i	−0.877515	−	0.479549i	$-0.840800\pi$
$31$	−8.26320	+	1.75640i	−1.48411	+	0.315458i	−0.606600	+	0.795007i	$0.707467\pi$
$32$	−1.53021	−	2.65041i	−0.270506	−	0.468530i
$33$	−5.39150	−	1.98286i	−0.938539	−	0.345172i
$34$	−12.3864			−2.12425
$35$	1.67348	−	1.19947i	0.282870	−	0.202747i
$36$	1.62086	−	0.391421i	0.270143	−	0.0652368i
$37$	−6.93796	+	3.08898i	−1.14059	+	0.507825i	−0.888044	−	0.459759i	$-0.847936\pi$
$37$	−6.93796	+	3.08898i	−1.14059	+	0.507825i	−0.252550	+	0.967584i	$0.581269\pi$
$38$	−1.75483	−	1.58006i	−0.284671	−	0.256319i
$39$	−3.24077	+	2.42337i	−0.518939	+	0.388049i
$40$	0.730797	+	1.64140i	0.115549	+	0.259528i
$41$	0.788077	−	0.572571i	0.123077	−	0.0894206i	−0.524544	−	0.851383i	$-0.675764\pi$
$41$	0.788077	−	0.572571i	0.123077	−	0.0894206i	0.647621	+	0.761963i	$0.275764\pi$
$42$	5.95831	+	4.26270i	0.919388	+	0.657749i
$43$		−	4.44203i		−	0.677403i	−0.940894	−	0.338702i	$-0.890012\pi$
$43$		−	4.44203i		−	0.677403i	0.940894	−	0.338702i	$-0.109988\pi$
$44$	−1.82064	+	0.288996i	−0.274472	+	0.0435677i
$45$	−2.31425	+	0.307818i	−0.344987	+	0.0458868i
$46$	−2.37070	−	11.1533i	−0.349541	−	1.64446i
$47$	4.22776	−	0.444355i	0.616682	−	0.0648158i	0.208963	−	0.977924i	$-0.432991\pi$
$47$	4.22776	−	0.444355i	0.616682	−	0.0648158i	0.407718	+	0.913108i	$0.366324\pi$
$48$	−6.10471	+	5.65069i	−0.881139	+	0.815607i
$49$	0.641986	+	6.97050i	0.0917123	+	0.995786i
$50$	−2.17093	−	6.68144i	−0.307016	−	0.944898i
$51$	2.97042	+	13.0868i	0.415942	+	1.83252i
$52$	−0.528176	+	1.18630i	−0.0732448	+	0.164511i
$53$	1.37573	+	6.47231i	0.188971	+	0.889040i	0.965792	+	0.259318i	$0.0834978\pi$
$53$	1.37573	+	6.47231i	0.188971	+	0.889040i	−0.776821	+	0.629722i	$0.783169\pi$
$54$	−3.68902	−	7.44300i	−0.502012	−	1.01286i
$55$	2.57744	−	0.135957i	0.347542	−	0.0183324i
$56$	−6.07082	−	0.677620i	−0.811248	−	0.0905507i
$57$	−1.24857	+	2.23297i	−0.165377	+	0.295764i
$58$	0.296721	+	2.82311i	0.0389614	+	0.370693i
$59$	−11.7589	−	1.23591i	−1.53088	−	0.160902i	−0.698701	−	0.715413i	$-0.746238\pi$
$59$	−11.7589	−	1.23591i	−1.53088	−	0.160902i	−0.832176	+	0.554512i	$0.812905\pi$
$60$	−0.599986	+	0.448655i	−0.0774579	+	0.0579211i
$61$	1.35155	−	6.35855i	0.173049	−	0.814129i	−0.802897	−	0.596117i	$-0.796709\pi$
$61$	1.35155	−	6.35855i	0.173049	−	0.814129i	0.975946	−	0.218012i	$-0.0699573\pi$
$62$	10.9261	+	7.93830i	1.38762	+	1.00817i
$63$	3.07485	−	7.31747i	0.387395	−	0.921914i
$64$	1.45631	−	4.48206i	0.182039	−	0.560258i
$65$	0.909076	−	1.57457i	0.112757	−	0.195301i
$66$	3.41171	+	8.52656i	0.419952	+	1.04955i
$67$	5.28912	+	9.16102i	0.646168	+	1.11920i	0.984030	+	0.178001i	$0.0569630\pi$
$67$	5.28912	+	9.16102i	0.646168	+	1.11920i	−0.337862	+	0.941196i	$0.609704\pi$
$68$	2.88153	+	3.20026i	0.349437	+	0.388089i
$69$	−11.2154	+	5.17945i	−1.35018	+	0.623532i
$70$	−3.21522	−	0.705085i	−0.384292	−	0.0842737i
$71$	−6.29108	+	2.04410i	−0.746614	+	0.242590i	−0.657524	−	0.753434i	$-0.728396\pi$
$71$	−6.29108	+	2.04410i	−0.746614	+	0.242590i	−0.0890905	+	0.996024i	$0.528396\pi$
$72$	5.71347	+	3.91555i	0.673339	+	0.461451i
$73$	−6.30260	−	0.662430i	−0.737664	−	0.0775316i	−0.271758	−	0.962366i	$-0.587605\pi$
$73$	−6.30260	−	0.662430i	−0.737664	−	0.0775316i	−0.465906	+	0.884834i	$0.654272\pi$
$74$	11.0917	+	4.93833i	1.28938	+	0.574069i
$75$	−6.53861	+	3.89597i	−0.755014	+	0.449868i
$76$			0.820971i			0.0941718i
$77$	−4.03136	+	7.79411i	−0.459416	+	0.888221i
$78$	6.34587	+	1.25787i	0.718528	+	0.142426i
$79$	7.31961	−	6.59061i	0.823521	−	0.741501i	−0.145267	−	0.989392i	$-0.546404\pi$
$79$	7.31961	−	6.59061i	0.823521	−	0.741501i	0.968788	+	0.247891i	$0.0797375\pi$
$80$	1.52018	−	3.41438i	0.169961	−	0.381739i
$81$	−6.97917	+	5.68253i	−0.775464	+	0.631392i
$82$	−1.52328	−	0.323783i	−0.168218	−	0.0357559i
$83$	−2.71004	−	8.34064i	−0.297465	−	0.915504i	−0.982382	−	0.186883i	$-0.940161\pi$
$83$	−2.71004	−	8.34064i	−0.297465	−	0.915504i	0.684917	−	0.728621i	$-0.259839\pi$
$84$	−0.284771	−	2.53110i	−0.0310711	−	0.276166i
$85$	−3.54402	−	4.87793i	−0.384403	−	0.529085i
$86$	−5.27740	+	4.75179i	−0.569076	+	0.512399i
$87$	2.91159	−	0.990517i	0.312155	−	0.106195i
$88$	−5.95259	−	4.81696i	−0.634548	−	0.513490i
$89$	0.817282	+	0.471858i	0.0866317	+	0.0500168i	0.542690	−	0.839933i	$-0.317406\pi$
$89$	0.817282	+	0.471858i	0.0866317	+	0.0500168i	−0.456058	+	0.889950i	$0.650739\pi$
$90$	2.84133	+	2.42018i	0.299503	+	0.255109i
$91$	3.05614	+	5.37299i	0.320371	+	0.563243i
$92$	−2.33015	+	3.20717i	−0.242935	+	0.334371i
$93$	5.76693	−	13.4476i	0.598003	−	1.39445i
$94$	−5.05049	−	4.54748i	−0.520919	−	0.469037i
$95$	0.120151	−	1.14316i	0.0123272	−	0.117286i
$96$	5.27890	+	0.481511i	0.538776	+	0.0491441i
$97$	3.59669	−	11.0695i	0.365189	−	1.12394i	−0.584674	−	0.811269i	$-0.698777\pi$
$97$	3.59669	−	11.0695i	0.365189	−	1.12394i	0.949863	−	0.312667i	$-0.101223\pi$
$98$	7.59461	−	8.21930i	0.767172	−	0.830274i
$99$	8.19050	−	5.64939i	0.823177	−	0.567785i
$100$	−1.22124	+	2.11524i	−0.122124	+	0.211524i
$101$	2.49048	−	0.529368i	0.247812	−	0.0526741i	−0.0823308	−	0.996605i	$-0.526236\pi$
$101$	2.49048	−	0.529368i	0.247812	−	0.0526741i	0.330143	+	0.943931i	$0.392903\pi$
$102$	12.3703	−	17.5284i	1.22485	−	1.73557i
$103$	10.0675	−	4.48234i	0.991981	−	0.441658i	0.154422	−	0.988005i	$-0.450649\pi$
$103$	10.0675	−	4.48234i	0.991981	−	0.441658i	0.837559	+	0.546347i	$0.183982\pi$
$104$	−5.13012	+	1.66688i	−0.503050	+	0.163451i
$105$	0.0260971	+	3.56611i	0.00254681	+	0.348016i
$106$	6.21782	−	8.55810i	0.603928	−	0.831236i
$107$	−0.00581425	−	0.0553189i	−0.000562084	−	0.00534788i	0.994237	−	0.107202i	$-0.0341892\pi$
$107$	−0.00581425	−	0.0553189i	−0.000562084	−	0.00534788i	−0.994799	+	0.101854i	$0.967522\pi$
$108$	−1.06484	+	2.68464i	−0.102464	+	0.258329i
$109$	−8.79781	+	5.07942i	−0.842677	+	0.486520i	−0.858173	−	0.513360i	$-0.828401\pi$
$109$	−8.79781	+	5.07942i	−0.842677	+	0.486520i	0.0154961	+	0.999880i	$0.495067\pi$
$110$	−2.91870	−	2.91672i	−0.278287	−	0.278098i
$111$	2.55764	−	12.9031i	0.242760	−	1.22471i
$112$	7.40249	+	10.3279i	0.699470	+	0.975891i
$113$	−2.18397	−	3.00598i	−0.205451	−	0.282779i	0.693841	−	0.720128i	$-0.255917\pi$
$113$	−2.18397	−	3.00598i	−0.205451	−	0.282779i	−0.899291	+	0.437350i	$0.855917\pi$
$114$	3.98854	−	0.905311i	0.373561	−	0.0847902i
$115$	3.71399	−	4.12480i	0.346331	−	0.384640i
$116$	0.660376	−	0.733422i	0.0613144	−	0.0680965i
$117$	−0.192823	−	7.00634i	−0.0178265	−	0.647736i
$118$	11.1105	+	15.2924i	1.02281	+	1.40778i
$119$	20.4000	−	2.01140i	1.87006	−	0.184385i
$120$	−3.05264	−	0.605091i	−0.278667	−	0.0552370i
$121$	−9.52254	+	5.50648i	−0.865685	+	0.500589i
$122$	−9.00014	+	5.19623i	−0.814835	+	0.470445i
$123$	0.0232106	+	1.68706i	0.00209283	+	0.152117i
$124$	−0.490806	−	4.66970i	−0.0440756	−	0.419352i
$125$	4.29718	−	5.91456i	0.384351	−	0.529014i
$126$	−11.9829	+	4.17463i	−1.06752	+	0.371906i
$127$	4.00094	−	1.29999i	0.355026	−	0.115355i	−0.126073	−	0.992021i	$-0.540237\pi$
$127$	4.00094	−	1.29999i	0.355026	−	0.115355i	0.481100	+	0.876666i	$0.340237\pi$
$128$	−12.4745	+	5.55401i	−1.10260	+	0.490909i
$129$	6.28606	+	4.43626i	0.553456	+	0.390591i
$130$	−2.84315	+	0.604330i	−0.249361	+	0.0530032i
$131$	−5.27273	+	9.13263i	−0.460680	+	0.797922i	−0.998995	−	0.0448221i	$-0.985728\pi$
$131$	−5.27273	+	9.13263i	−0.460680	+	0.797922i	0.538315	+	0.842744i	$0.319061\pi$
$132$	1.40931	−	2.86506i	0.122664	−	0.249372i
$133$	3.14672	+	2.31733i	0.272855	+	0.200938i
$134$	5.22589	−	16.0836i	0.451448	−	1.38941i
$135$	1.87564	−	3.58238i	0.161429	−	0.308322i
$136$	−1.86983	+	17.7903i	−0.160337	+	1.52550i
$137$	−6.81758	−	6.13858i	−0.582465	−	0.524454i	0.324375	−	0.945929i	$-0.394846\pi$
$137$	−6.81758	−	6.13858i	−0.582465	−	0.524454i	−0.906840	+	0.421474i	$0.861513\pi$
$138$	18.1510	+	7.78394i	1.54511	+	0.662613i
$139$	0.242449	−	0.333703i	0.0205643	−	0.0283043i	−0.798611	−	0.601847i	$-0.794432\pi$
$139$	0.242449	−	0.333703i	0.0205643	−	0.0283043i	0.819175	+	0.573543i	$0.194432\pi$
$140$	0.565804	+	0.994740i	0.0478192	+	0.0840708i
$141$	−3.59344	+	6.42661i	−0.302622	+	0.541218i
$142$	9.15829	+	5.28754i	0.768547	+	0.443721i
$143$	−0.402906	+	7.73825i	−0.0336927	+	0.647105i
$144$	−1.89969	−	14.2823i	−0.158308	−	1.19019i
$145$	−1.02688	+	0.924606i	−0.0852776	+	0.0767843i
$146$	5.95510	+	8.19649i	0.492848	+	0.678347i
$147$	−10.5053	−	6.05295i	−0.866464	−	0.499239i
$148$	−1.30441	−	4.01457i	−0.107222	−	0.329996i
$149$	−1.45739	−	0.309779i	−0.119394	−	0.0253781i	0.147827	−	0.989013i	$-0.452772\pi$
$149$	−1.45739	−	0.309779i	−0.119394	−	0.0253781i	−0.267221	+	0.963635i	$0.586105\pi$
$150$	11.6232	+	3.60060i	0.949032	+	0.293988i
$151$	6.88796	−	15.4706i	0.560534	−	1.25898i	−0.381781	−	0.924253i	$-0.624689\pi$
$151$	6.88796	−	15.4706i	0.560534	−	1.25898i	0.942315	−	0.334727i	$-0.108644\pi$
$152$	−2.53430	+	2.28189i	−0.205559	+	0.185086i
$153$	−21.4861	−	8.86626i	−1.73705	−	0.716795i
$154$	13.5723	−	3.54812i	1.09369	−	0.285916i
$155$			6.57416i			0.528049i
$156$	−1.15128	−	1.93220i	−0.0921765	−	0.154700i
$157$	−7.88901	−	3.51241i	−0.629612	−	0.280321i	0.0670183	−	0.997752i	$-0.478651\pi$
$157$	−7.88901	−	3.51241i	−0.629612	−	0.280321i	−0.696630	+	0.717431i	$0.745318\pi$
$158$	−15.6601	−	1.64594i	−1.24585	−	0.130944i
$159$	−10.5331	−	4.51706i	−0.835330	−	0.358226i
$160$	−2.26509	+	0.735971i	−0.179071	+	0.0581836i
$161$	5.71561	+	17.9841i	0.450453	+	1.41734i
$162$	14.2170	+	2.21288i	1.11700	+	0.173860i
$163$	0.386113	+	0.428822i	0.0302427	+	0.0335879i	0.758076	−	0.652166i	$-0.226139\pi$
$163$	0.386113	+	0.428822i	0.0302427	+	0.0335879i	−0.727834	+	0.685754i	$0.759473\pi$
$164$	0.270715	+	0.468892i	0.0211393	+	0.0366143i
$165$	−2.38170	+	3.78320i	−0.185415	+	0.294522i
$166$	−7.01016	+	12.1420i	−0.544094	+	0.942398i
$167$	0.0760934	−	0.234192i	0.00588829	−	0.0181223i	−0.948069	−	0.318064i	$-0.896967\pi$
$167$	0.0760934	−	0.234192i	0.00588829	−	0.0181223i	0.953957	+	0.299942i	$0.0969673\pi$
$168$	7.02186	−	7.91427i	0.541748	−	0.610600i
$169$	−6.10125	−	4.43282i	−0.469327	−	0.340986i
$170$	−2.00411	+	9.42859i	−0.153708	+	0.723140i
$171$	−1.91300	−	3.99696i	−0.146291	−	0.305655i
$172$	2.45543	+	0.258076i	0.187224	+	0.0196781i
$173$	0.397097	+	3.77813i	0.0301908	+	0.287246i	0.999192	+	0.0401902i	$0.0127964\pi$
$173$	0.397097	+	3.77813i	0.0301908	+	0.287246i	−0.969001	+	0.247056i	$0.920537\pi$
$174$	−4.29141	−	2.39955i	−0.325331	−	0.181909i
$175$	4.66042	+	10.6515i	0.352295	+	0.805180i
$176$	0.839056	+	15.9066i	0.0632462	+	1.19901i
$177$	13.4926	−	15.4061i	1.01417	−	1.15799i
$178$	−0.313679	−	1.47574i	−0.0235112	−	0.110612i
$179$	−0.155292	+	0.348791i	−0.0116070	+	0.0260699i	−0.919256	−	0.393660i	$-0.871209\pi$
$179$	−0.155292	+	0.348791i	−0.0116070	+	0.0260699i	0.907649	+	0.419730i	$0.137875\pi$
$180$	−0.0356986	−	1.29713i	−0.00266082	−	0.0966825i
$181$	−2.25037	−	6.92591i	−0.167268	−	0.514799i	0.831928	−	0.554884i	$-0.187237\pi$
$181$	−2.25037	−	6.92591i	−0.167268	−	0.514799i	−0.999196	+	0.0400846i	$0.987237\pi$
$182$	3.11418	−	9.37855i	0.230839	−	0.695184i
$183$	7.64839	+	8.26292i	0.565385	+	0.610812i
$184$	−16.3770	+	1.72130i	−1.20733	+	0.126896i
$185$	1.22879	+	5.78099i	0.0903423	+	0.425027i
$186$	−22.1457	+	7.53392i	−1.62380	+	0.552414i
$187$	22.8999	+	11.6583i	1.67461	+	0.852538i
$188$			2.36280i			0.172325i
$189$	7.28432	+	11.6593i	0.529856	+	0.848087i
$190$	−1.48667	+	1.08013i	−0.107855	+	0.0783609i
$191$	1.37524	+	3.08883i	0.0995086	+	0.223500i	0.956439	−	0.291932i	$-0.0942981\pi$
$191$	1.37524	+	3.08883i	0.0995086	+	0.223500i	−0.856930	+	0.515432i	$0.827631\pi$
$192$	4.88829	+	6.53711i	0.352782	+	0.471775i
$193$	3.82495	+	3.44400i	0.275326	+	0.247905i	0.795213	−	0.606330i	$-0.207359\pi$
$193$	3.82495	+	3.44400i	0.275326	+	0.247905i	−0.519887	+	0.854235i	$0.674026\pi$
$194$	−16.9987	+	7.56831i	−1.22044	+	0.543373i
$195$	1.32032	+	2.85898i	0.0945503	+	0.204736i
$196$	−3.89039	−	0.0501046i	−0.277885	−	0.00357890i
$197$	15.8556			1.12966			0.564832	−	0.825206i	$-0.308941\pi$
$197$	15.8556			1.12966			0.564832	+	0.825206i	$0.308941\pi$
$198$	−15.4735	−	3.68746i	−1.09965	−	0.262056i
$199$	1.94006	+	3.36029i	0.137527	+	0.238204i	0.926560	−	0.376147i	$-0.122751\pi$
$199$	1.94006	+	3.36029i	0.137527	+	0.238204i	−0.789033	+	0.614351i	$0.789418\pi$
$200$	−9.92408	+	2.10943i	−0.701739	+	0.149159i
$201$	−18.2463	−	1.66432i	−1.28699	−	0.117392i
$202$	−3.29307	−	2.39256i	−0.231700	−	0.168340i
$203$	−0.947127	−	4.60138i	−0.0664753	−	0.322953i
$204$	−7.40658	+	0.881637i	−0.518564	+	0.0617270i
$205$	−0.308333	−	0.692528i	−0.0215349	−	0.0483683i
$206$	−16.0948	−	7.16588i	−1.12138	−	0.499271i
$207$	3.87123	−	21.0440i	0.269069	−	1.46266i
$208$	9.71741	+	5.61035i	0.673781	+	0.389008i
$209$	1.75714	+	4.57286i	0.121544	+	0.316311i
$210$	4.20883	−	3.84579i	0.290437	−	0.265385i
$211$	−9.83151	−	3.19445i	−0.676829	−	0.219915i	−0.0496225	−	0.998768i	$-0.515802\pi$
$211$	−9.83151	−	3.19445i	−0.676829	−	0.219915i	−0.627207	+	0.778853i	$0.715802\pi$
$212$	−3.65763	+	0.384433i	−0.251207	+	0.0264029i
$213$	3.39024	−	10.9441i	0.232296	−	0.749881i
$214$	−0.0595024	+	0.0660841i	−0.00406750	+	0.00451742i
$215$	−3.38129	−	0.718715i	−0.230602	−	0.0490159i
$216$	−11.2471	+	4.17485i	−0.765265	+	0.284063i
$217$	−19.2840	−	11.2998i	−1.30908	−	0.767081i
$218$	15.4460	+	5.01870i	1.04613	+	0.339909i
$219$	7.23184	−	8.25744i	0.488683	−	0.557986i
$220$	−0.0745927	+	1.43264i	−0.00502904	+	0.0965883i
$221$	15.6764	−	9.05077i	1.05451	−	0.608821i
$222$	−18.0656	+	10.7642i	−1.21249	+	0.722449i
$223$	−22.8622	+	16.6104i	−1.53097	+	1.11231i	−0.575270	+	0.817963i	$0.695103\pi$
$223$	−22.8622	+	16.6104i	−1.53097	+	1.11231i	−0.955698	+	0.294350i	$0.904897\pi$
$224$	1.73445	−	7.90918i	0.115888	−	0.528455i
$225$	1.01680	−	13.1439i	0.0677868	−	0.876260i
$226$	−1.23501	+	5.81028i	−0.0821519	+	0.386494i
$227$	1.87579	−	17.8470i	0.124501	−	1.18455i	−0.736678	−	0.676243i	$-0.763607\pi$
$227$	1.87579	−	17.8470i	0.124501	−	1.18455i	0.861179	−	0.508302i	$-0.169727\pi$
$228$	−1.16178	−	0.819904i	−0.0769409	−	0.0542995i
$229$	0.894728	+	0.993696i	0.0591253	+	0.0656653i	0.771982	−	0.635645i	$-0.219266\pi$
$229$	0.894728	+	0.993696i	0.0591253	+	0.0656653i	−0.712857	+	0.701310i	$0.752599\pi$
$230$	−8.87349			−0.585101
$231$	−7.00356	−	13.4889i	−0.460800	−	0.887504i
$232$	4.09956			0.269149
$233$	3.03546	+	3.37122i	0.198859	+	0.220856i	0.834324	−	0.551274i	$-0.185858\pi$
$233$	3.03546	+	3.37122i	0.198859	+	0.220856i	−0.635465	+	0.772130i	$0.719191\pi$
$234$	−8.11768	+	7.72400i	−0.530669	+	0.504934i
$235$	0.345801	−	3.29008i	0.0225576	−	0.214621i
$236$	1.36635	−	6.42817i	0.0889418	−	0.418438i
$237$	2.01647	+	16.9403i	0.130984	+	1.10039i
$238$	−24.2122	−	22.0847i	−1.56944	−	1.43154i
$239$	−21.8507	+	15.8754i	−1.41340	+	1.02690i	−0.420585	+	0.907253i	$0.638175\pi$
$239$	−21.8507	+	15.8754i	−1.41340	+	1.02690i	−0.992817	+	0.119643i	$0.961825\pi$
$240$	3.31359	+	5.56120i	0.213891	+	0.358974i
$241$	16.5002	−	9.52637i	1.06287	−	0.613648i	0.136644	−	0.990620i	$-0.456368\pi$
$241$	16.5002	−	9.52637i	1.06287	−	0.613648i	0.926224	+	0.376973i	$0.123035\pi$
$242$	16.7286	+	5.42288i	1.07536	+	0.348596i
$243$	−1.07142	−	15.5516i	−0.0687315	−	0.997635i
$244$	3.43630	+	1.11652i	0.219987	+	0.0714780i
$245$	5.40984	+	0.639136i	0.345622	+	0.0408329i
$246$	1.97950	−	1.83228i	0.126208	−	0.116822i
$247$	3.37548	+	0.717480i	0.214777	+	0.0456522i
$248$	13.0510	−	14.4946i	0.828736	−	0.920405i
$249$	14.5096	+	4.49474i	0.919510	+	0.284843i
$250$	−11.6237	+	1.22170i	−0.735147	+	0.0772670i
$251$	−1.85771	−	0.603606i	−0.117258	−	0.0380993i	0.249801	−	0.968297i	$-0.419635\pi$
$251$	−1.85771	−	0.603606i	−0.117258	−	0.0380993i	−0.367058	+	0.930198i	$0.619635\pi$
$252$	3.86624	+	2.12482i	0.243550	+	0.133851i
$253$	−6.11469	+	22.8514i	−0.384427	+	1.43666i
$254$	−5.82441	−	3.36272i	−0.365456	−	0.210996i
$255$	10.4423	−	0.143665i	0.653923	−	0.00899668i
$256$	11.3323	+	5.04547i	0.708270	+	0.315342i
$257$	2.41318	+	5.42010i	0.150530	+	0.338096i	0.973033	−	0.230664i	$-0.0740899\pi$
$257$	2.41318	+	5.42010i	0.150530	+	0.338096i	−0.822503	+	0.568760i	$0.807423\pi$
$258$	−1.45386	−	12.2138i	−0.0905137	−	0.760400i
$259$	−19.0695	−	6.33209i	−1.18492	−	0.393457i
$260$	0.817559	+	0.593991i	0.0507028	+	0.0368378i
$261$	−1.50609	+	5.10951i	−0.0932247	+	0.316270i
$262$	16.4905	−	3.50517i	1.01879	−	0.216550i
$263$	−3.85973	−	6.68525i	−0.238001	−	0.412230i	0.722140	−	0.691747i	$-0.243159\pi$
$263$	−3.85973	−	6.68525i	−0.238001	−	0.412230i	−0.960141	+	0.279517i	$0.909826\pi$
$264$	12.7615	−	3.61299i	0.785415	−	0.222364i
$265$	5.14933			0.316321
$266$	−0.613026	−	6.21741i	−0.0375870	−	0.381214i
$267$	−1.48396	+	0.685316i	−0.0908170	+	0.0419407i
$268$	−5.37124	+	2.39143i	−0.328100	+	0.146080i
$269$	−5.20189	−	4.68380i	−0.317165	−	0.285576i	0.495136	−	0.868816i	$-0.335118\pi$
$269$	−5.20189	−	4.68380i	−0.317165	−	0.285576i	−0.812300	+	0.583239i	$0.801785\pi$
$270$	−6.26251	+	1.60382i	−0.381124	+	0.0976057i
$271$	−7.42531	−	16.6775i	−0.451055	−	1.01309i	−0.985777	−	0.168059i	$-0.946250\pi$
$271$	−7.42531	−	16.6775i	−0.451055	−	1.01309i	0.534722	−	0.845028i	$-0.320416\pi$
$272$	30.1040	−	21.8718i	1.82532	−	1.32618i
$273$	−10.6557	−	1.04118i	−0.644910	−	0.0630148i
$274$			14.6663i			0.886026i
$275$	−2.27507	+	14.3959i	−0.137192	+	0.868104i
$276$	−2.21145	−	6.50047i	−0.133114	−	0.391282i
$277$	3.14923	+	14.8160i	0.189219	+	0.890205i	0.965618	+	0.259964i	$0.0837106\pi$
$277$	3.14923	+	14.8160i	0.189219	+	0.890205i	−0.776399	+	0.630241i	$0.782956\pi$
$278$	−0.655815	+	0.0689290i	−0.0393332	+	0.00413408i
$279$	13.2707	+	21.5911i	0.794497	+	1.29263i
$280$	−1.49806	+	4.51149i	−0.0895261	+	0.269613i
$281$	−5.94199	−	18.2876i	−0.354469	−	1.09094i	−0.956317	−	0.292333i	$-0.905568\pi$
$281$	−5.94199	−	18.2876i	−0.354469	−	1.09094i	0.601847	−	0.798611i	$-0.294432\pi$
$282$	11.4792	−	2.60553i	0.683578	−	0.155157i
$283$	−4.85546	+	10.9055i	−0.288627	+	0.648267i	−0.998423	−	0.0561407i	$-0.982120\pi$
$283$	−4.85546	+	10.9055i	−0.288627	+	0.648267i	0.709796	+	0.704407i	$0.248787\pi$
$284$	−0.764415	−	3.59629i	−0.0453597	−	0.213400i
$285$	1.49773	+	1.31171i	0.0887177	+	0.0776987i
$286$	9.62450	−	7.79919i	0.569109	−	0.461176i
$287$	2.56136	+	0.285897i	0.151193	+	0.0168760i
$288$	−5.95345	+	6.98945i	−0.350810	+	0.411857i
$289$	−4.49778	−	42.7935i	−0.264575	−	2.51726i
$290$	2.19697	+	0.230911i	0.129011	+	0.0135596i
$291$	12.0728	+	16.1449i	0.707717	+	0.946431i
$292$	0.732345	−	3.44541i	0.0428572	−	0.201627i
$293$	−4.91146	−	3.56839i	−0.286931	−	0.208467i	0.435004	−	0.900429i	$-0.356747\pi$
$293$	−4.91146	−	3.56839i	−0.286931	−	0.208467i	−0.721935	+	0.691961i	$0.756747\pi$
$294$	4.04663	+	18.9560i	0.236005	+	1.10554i
$295$	−2.84335	+	8.75094i	−0.165546	+	0.509499i
$296$	8.76716	−	15.1852i	0.509581	−	0.882620i
$297$	−0.185231	+	17.2327i	−0.0107482	+	0.999942i
$298$	1.19099	+	2.06285i	0.0689921	+	0.119498i
$299$	11.1501	+	12.3834i	0.644827	+	0.716153i
$300$	−1.77370	−	3.84070i	−0.102404	−	0.221743i
$301$	7.92004	−	8.68300i	0.456503	−	0.500480i
$302$	−25.7483	+	8.36612i	−1.48165	+	0.481416i
$303$	−1.73812	+	4.05304i	−0.0998523	+	0.232841i
$304$	7.05499	+	0.741510i	0.404632	+	0.0425285i
$305$	−4.62147	−	2.05761i	−0.264625	−	0.117819i
$306$	12.4508	+	35.0113i	0.711762	+	2.00146i
$307$		−	22.5829i		−	1.28887i	−0.764658	−	0.644437i	$-0.777092\pi$
$307$		−	22.5829i		−	1.28887i	0.764658	−	0.644437i	$-0.222908\pi$
$308$	−4.07414	−	2.68125i	−0.232146	−	0.152778i
$309$	−3.71132	+	18.7234i	−0.211130	+	1.06513i
$310$	7.81049	−	7.03260i	0.443606	−	0.399425i
$311$	5.27285	−	11.8430i	0.298996	−	0.671555i	−0.700101	−	0.714043i	$-0.746862\pi$
$311$	5.27285	−	11.8430i	0.298996	−	0.671555i	0.999097	+	0.0424883i	$0.0135285\pi$
$312$	2.76461	−	8.92451i	0.156515	−	0.505251i
$313$	−3.00500	−	0.638732i	−0.169853	−	0.0361033i	0.122200	−	0.992505i	$-0.461005\pi$
$313$	−3.00500	−	0.638732i	−0.169853	−	0.0361033i	−0.292053	+	0.956402i	$0.594338\pi$
$314$	4.26618	+	13.1300i	0.240755	+	0.740967i
$315$	−5.07257	−	3.52454i	−0.285807	−	0.198585i
$316$	3.21784	+	4.42898i	0.181018	+	0.249149i
$317$	−12.7559	+	11.4854i	−0.716441	+	0.645087i	−0.944481	−	0.328565i	$-0.893435\pi$
$317$	−12.7559	+	11.4854i	−0.716441	+	0.645087i	0.228040	+	0.973652i	$0.426768\pi$
$318$	5.90109	+	17.3460i	0.330917	+	0.972716i
$319$	2.10858	−	5.49863i	0.118058	−	0.307864i
$320$	−3.17613	−	1.83374i	−0.177551	−	0.102509i
$321$	0.0840901	+	0.0470191i	0.00469345	+	0.00262435i
$322$	15.2519	−	26.0286i	0.849958	−	1.45052i
$323$	6.72662	−	9.25839i	0.374279	−	0.515151i
$324$	−2.73566	−	4.18803i	−0.151981	−	0.232668i
$325$	7.62968	+	6.86979i	0.423218	+	0.381068i
$326$	0.0964279	−	0.917450i	0.00534065	−	0.0508129i
$327$	1.59834	−	17.5229i	0.0883882	−	0.969017i
$328$	−0.694993	+	2.13897i	−0.0383746	+	0.118105i
$329$	9.05642	+	6.66939i	0.499297	+	0.367696i
$330$	7.04245	−	1.21742i	0.387674	−	0.0670167i
$331$	1.56580	−	2.71204i	0.0860641	−	0.149067i	−0.819780	−	0.572678i	$-0.805904\pi$
$331$	1.56580	−	2.71204i	0.0860641	−	0.149067i	0.905844	+	0.423611i	$0.139238\pi$
$332$	4.76791	−	1.01345i	0.261673	−	0.0556204i
$333$	15.7053	+	16.5057i	0.860643	+	0.904508i
$334$	−0.359633	+	0.160119i	−0.0196783	+	0.00876132i
$335$	7.82917	−	2.54385i	0.427753	−	0.138985i
$336$	−22.0081	+	0.161057i	−1.20064	+	0.00878641i
$337$	2.03211	−	2.79695i	0.110696	−	0.152360i	−0.750074	−	0.661353i	$-0.769982\pi$
$337$	2.03211	−	2.79695i	0.110696	−	0.152360i	0.860770	+	0.508994i	$0.169982\pi$
$338$	1.26026	+	11.9906i	0.0685492	+	0.652202i
$339$	6.43498	−	0.0885325i	0.349500	−	0.00480843i
$340$	2.90228	−	1.67563i	0.157398	−	0.0908739i
$341$	−12.7285	−	24.9601i	−0.689286	−	1.35166i
$342$	−2.70222	+	6.54844i	−0.146119	+	0.354099i
$343$	−11.1733	+	14.7701i	−0.603303	+	0.797512i
$344$	6.02820	+	8.29710i	0.325019	+	0.447350i
$345$	2.12797	+	9.37523i	0.114566	+	0.504745i
$346$	4.06385	−	4.51337i	0.218474	−	0.242640i
$347$	−23.4152	+	26.0052i	−1.25699	+	1.39603i	−0.373472	+	0.927641i	$0.621833\pi$
$347$	−23.4152	+	26.0052i	−1.25699	+	1.39603i	−0.883521	+	0.468391i	$0.844834\pi$
$348$	0.378370	+	1.66699i	0.0202828	+	0.0893599i
$349$	1.13850	+	1.56700i	0.0609423	+	0.0838798i	0.838400	−	0.545055i	$-0.183491\pi$
$349$	1.13850	+	1.56700i	0.0609423	+	0.0838798i	−0.777458	+	0.628935i	$0.783491\pi$
$350$	7.66925	−	16.9312i	0.409939	−	0.905009i
$351$	10.1075	+	6.72437i	0.539496	+	0.358920i
$352$	7.17490	−	7.17978i	0.382423	−	0.382684i
$353$	−5.32247	+	3.07293i	−0.283286	+	0.163555i	−0.634910	−	0.772586i	$-0.718963\pi$
$353$	−5.32247	+	3.07293i	−0.283286	+	0.163555i	0.351624	+	0.936141i	$0.385630\pi$
$354$	−32.7368	+	0.450393i	−1.73994	+	0.0239381i
$355$	0.538084	+	5.11953i	0.0285585	+	0.271716i
$356$	−0.308312	+	0.424356i	−0.0163405	+	0.0224908i
$357$	−17.5271	+	30.8774i	−0.927631	+	1.63421i
$358$	0.580505	−	0.188618i	0.0306807	−	0.00996875i
$359$	9.90770	−	4.41119i	0.522908	−	0.232814i	−0.128269	−	0.991739i	$-0.540942\pi$
$359$	9.90770	−	4.41119i	0.522908	−	0.232814i	0.651177	+	0.758926i	$0.274275\pi$
$360$	3.90496	−	3.71558i	0.205809	−	0.195828i
$361$	−16.4508	+	3.49672i	−0.865831	+	0.184038i
$362$	−5.82111	+	10.0825i	−0.305951	+	0.529922i
$363$	1.71778	−	18.9750i	0.0901599	−	0.995927i
$364$	−3.14759	+	1.37718i	−0.164979	+	0.0721840i
$365$	−1.52400	+	4.69038i	−0.0797697	+	0.245506i
$366$	1.63510	−	17.9259i	0.0854678	−	0.937000i
$367$	−0.947244	+	9.01243i	−0.0494457	+	0.470445i	0.941582	+	0.336785i	$0.109340\pi$
$367$	−0.947244	+	9.01243i	−0.0494457	+	0.470445i	−0.991027	+	0.133660i	$0.957327\pi$
$368$	25.4561	+	22.9208i	1.32699	+	1.19483i
$369$	−2.41059	−	1.65202i	−0.125490	−	0.0860008i
$370$	5.55369	−	7.64399i	0.288722	−	0.397392i
$371$	−8.85078	+	15.1046i	−0.459510	+	0.784189i
$372$	7.09841	+	3.96908i	0.368036	+	0.205787i
$373$	18.0006	+	10.3926i	0.932035	+	0.538111i	0.887455	−	0.460895i	$-0.152472\pi$
$373$	18.0006	+	10.3926i	0.932035	+	0.538111i	0.0445805	+	0.999006i	$0.485805\pi$
$374$	−10.6461	−	39.6777i	−0.550495	−	2.05169i
$375$	4.07828	+	11.9880i	0.210602	+	0.619055i
$376$	−7.29384	+	6.56740i	−0.376151	+	0.338688i
$377$	−2.43838	−	3.35615i	−0.125583	−	0.172850i
$378$	6.05963	−	21.1265i	0.311674	−	1.08663i
$379$	8.05623	+	24.7945i	0.413821	+	1.27361i	0.913301	+	0.407285i	$0.133524\pi$
$379$	8.05623	+	24.7945i	0.413821	+	1.27361i	−0.499480	+	0.866325i	$0.666476\pi$
$380$	0.624926	+	0.132832i	0.0320580	+	0.00681414i
$381$	−2.15610	+	6.96016i	−0.110460	+	0.356580i
$382$	2.19858	−	4.93809i	0.112489	−	0.252655i
$383$	15.1115	−	13.6065i	0.772164	−	0.695260i	−0.185660	−	0.982614i	$-0.559442\pi$
$383$	15.1115	−	13.6065i	0.772164	−	0.695260i	0.957824	+	0.287354i	$0.0927757\pi$
$384$	4.59865	−	23.1998i	0.234674	−	1.18391i
$385$	5.28063	+	4.32976i	0.269126	+	0.220665i
$386$		−	8.22844i		−	0.418817i
$387$	−12.5558	+	4.46510i	−0.638246	+	0.226974i
$388$	5.90993	+	2.63127i	0.300031	+	0.133582i
$389$	9.07312	+	0.953623i	0.460025	+	0.0483506i	0.331707	−	0.943382i	$-0.392375\pi$
$389$	9.07312	+	0.953623i	0.460025	+	0.0483506i	0.128318	+	0.991733i	$0.459042\pi$
$390$	1.98425	−	4.62697i	0.100476	−	0.234296i
$391$	52.5558	−	17.0764i	2.65786	−	0.863592i
$392$	−10.6587	−	12.1487i	−0.538345	−	0.613602i
$393$	−7.65800	−	16.5824i	−0.386295	−	0.836470i
$394$	−16.9613	−	18.8374i	−0.854496	−	0.949014i
$395$	−3.83249	−	6.63807i	−0.192833	−	0.333997i
$396$	2.64696	+	4.85570i	0.133015	+	0.244008i
$397$	−10.5492	+	18.2717i	−0.529449	+	0.917033i	0.469961	+	0.882687i	$0.344268\pi$
$397$	−10.5492	+	18.2717i	−0.529449	+	0.917033i	−0.999410	+	0.0343454i	$0.989065\pi$
$398$	1.91687	−	5.89952i	0.0960840	−	0.295716i
$399$	−6.42195	+	2.13870i	−0.321500	+	0.107069i
$400$	17.0743	+	12.4052i	0.853713	+	0.620259i
$401$	4.85792	−	22.8547i	0.242593	−	1.14131i	−0.673138	−	0.739517i	$-0.735054\pi$
$401$	4.85792	−	22.8547i	0.242593	−	1.14131i	0.915731	−	0.401792i	$-0.131613\pi$
$402$	17.5414	+	23.4581i	0.874883	+	1.16998i
$403$	−19.6287	−	2.06306i	−0.977777	−	0.102769i
$404$	0.147926	+	1.40742i	0.00735959	+	0.0700218i
$405$	3.19634	+	6.23200i	0.158827	+	0.309670i
$406$	−4.45354	+	6.04749i	−0.221025	+	0.300132i
$407$	−15.8581	−	19.5696i	−0.786059	−	0.970027i
$408$	−23.3082	−	20.4132i	−1.15393	−	1.01061i
$409$	−4.43445	−	20.8624i	−0.219269	−	1.03158i	−0.940738	−	0.339134i	$-0.889866\pi$
$409$	−4.43445	−	20.8624i	−0.219269	−	1.03158i	0.721469	−	0.692447i	$-0.243467\pi$
$410$	−0.492930	+	1.10714i	−0.0243441	+	0.0546777i
$411$	15.4956	−	3.51717i	0.764343	−	0.173489i
$412$	1.89280	+	5.82544i	0.0932516	+	0.286999i
$413$	−20.7819	−	23.3817i	−1.02261	−	1.15054i
$414$	−29.1427	+	17.9122i	−1.43229	+	0.880336i
$415$	−6.78740	+	0.713385i	−0.333181	+	0.0350187i
$416$	−1.48660	−	6.99392i	−0.0728867	−	0.342905i
$417$	0.230099	+	0.676367i	0.0112680	+	0.0331218i
$418$	3.55316	−	6.97933i	0.173791	−	0.341370i
$419$			14.1542i			0.691480i	0.938330	+	0.345740i	$0.112372\pi$
$419$			14.1542i			0.691480i	−0.938330	+	0.345740i	$0.887628\pi$
$420$	−1.97276	−	0.192760i	−0.0962607	−	0.00940573i
$421$	−11.5638	+	8.40158i	−0.563584	+	0.409468i	−0.832769	−	0.553621i	$-0.813246\pi$
$421$	−11.5638	+	8.40158i	−0.563584	+	0.409468i	0.269185	+	0.963089i	$0.413246\pi$
$422$	6.72190	+	15.0976i	0.327217	+	0.734941i
$423$	−5.50572	−	11.5035i	−0.267697	−	0.559317i
$424$	−11.3531	−	10.2224i	−0.551357	−	0.496444i
$425$	31.1036	−	13.8482i	1.50874	−	0.671736i
$426$	−16.6290	+	7.67951i	−0.805676	+	0.372074i
$427$	13.9791	−	10.0195i	0.676495	−	0.484878i
$428$	0.0309165			0.00149440
$429$	−10.5483	−	8.29836i	−0.509275	−	0.400649i
$430$	2.76320	+	4.78600i	0.133253	+	0.230802i
$431$	12.0901	−	2.56983i	0.582359	−	0.123784i	0.0926939	−	0.995695i	$-0.470452\pi$
$431$	12.0901	−	2.56983i	0.582359	−	0.123784i	0.489666	+	0.871910i	$0.337119\pi$
$432$	22.1086	+	11.5754i	1.06370	+	0.556924i
$433$	−7.33725	−	5.33083i	−0.352606	−	0.256183i	0.397356	−	0.917665i	$-0.369928\pi$
$433$	−7.33725	−	5.33083i	−0.352606	−	0.256183i	−0.749961	+	0.661482i	$0.769928\pi$
$434$	7.20390	+	34.9983i	0.345798	+	1.67997i
$435$	−0.282894	−	2.37657i	−0.0135637	−	0.113948i
$436$	−2.29661	−	5.15828i	−0.109988	−	0.247037i
$437$	9.62410	+	4.28493i	0.460383	+	0.204976i
$438$	−17.5465	+	0.241405i	−0.838403	+	0.0115348i
$439$	−8.25538	−	4.76624i	−0.394008	−	0.227480i	0.289888	−	0.957061i	$-0.406382\pi$
$439$	−8.25538	−	4.76624i	−0.394008	−	0.227480i	−0.683895	+	0.729580i	$0.739715\pi$
$440$	−4.62981	+	3.75175i	−0.220717	+	0.178858i
$441$	19.0574	−	8.82133i	0.907495	−	0.420063i
$442$	−27.5224	−	8.94258i	−1.30911	−	0.425355i
$443$	−13.2274	+	1.39026i	−0.628453	+	0.0660530i	−0.413400	−	0.910549i	$-0.635659\pi$
$443$	−13.2274	+	1.39026i	−0.628453	+	0.0660530i	−0.215053	+	0.976602i	$0.568992\pi$
$444$	6.98386	+	2.16344i	0.331439	+	0.102672i
$445$	0.491415	−	0.545772i	0.0232953	−	0.0258721i
$446$	44.1906	+	9.39301i	2.09249	+	0.444772i
$447$	1.89388	−	1.75303i	0.0895774	−	0.0829154i
$448$	10.8381	−	6.16468i	0.512053	−	0.291254i
$449$	−1.47343	−	0.478748i	−0.0695356	−	0.0225935i	0.274043	−	0.961718i	$-0.411639\pi$
$449$	−1.47343	−	0.478748i	−0.0695356	−	0.0225935i	−0.343578	+	0.939124i	$0.611639\pi$
$450$	−16.7034	+	12.8525i	−0.787408	+	0.605870i
$451$	2.51148	+	2.03234i	0.118261	+	0.0956992i
$452$	1.78850	−	1.03259i	0.0841241	−	0.0485691i
$453$	15.0139	+	25.1979i	0.705416	+	1.18390i
$454$	−23.2099	+	16.8630i	−1.08929	+	0.791418i
$455$	4.58442	−	1.45700i	0.214921	−	0.0683052i
$456$	−0.698171	−	5.86529i	−0.0326949	−	0.274667i
$457$	−2.39436	+	11.2646i	−0.112003	+	0.526934i	0.885995	+	0.463694i	$0.153476\pi$
$457$	−2.39436	+	11.2646i	−0.112003	+	0.526934i	−0.997998	+	0.0632392i	$0.979857\pi$
$458$	0.223449	−	2.12598i	0.0104411	−	0.0993405i
$459$	34.0051	−	21.5509i	1.58722	−	1.00591i
$460$	2.06429	+	2.29263i	0.0962482	+	0.106894i
$461$	19.0140			0.885570			0.442785	−	0.896628i	$-0.353990\pi$
$461$	19.0140			0.885570			0.442785	+	0.896628i	$0.353990\pi$
$462$	−8.53366	+	22.7502i	−0.397022	+	1.05843i
$463$	−35.6503			−1.65681			−0.828406	−	0.560128i	$-0.810752\pi$
$463$	−35.6503			−1.65681			−0.828406	+	0.560128i	$0.810752\pi$
$464$	−5.70618	−	6.33736i	−0.264903	−	0.294205i
$465$	−9.30330	−	6.56562i	−0.431430	−	0.304473i
$466$	0.758076	−	7.21261i	0.0351172	−	0.334118i
$467$	5.18285	−	24.3834i	0.239834	−	1.12833i	−0.679139	−	0.734009i	$-0.737647\pi$
$467$	5.18285	−	24.3834i	0.239834	−	1.12833i	0.918973	−	0.394320i	$-0.129020\pi$
$468$	3.88410	+	0.300471i	0.179543	+	0.0138893i
$469$	−5.99506	+	27.3377i	−0.276826	+	1.26234i
$470$	−4.27872	+	3.10867i	−0.197363	+	0.143392i
$471$	12.8493	−	7.65614i	0.592064	−	0.352776i
$472$	23.6412	−	13.6493i	1.08818	−	0.628258i
$473$	14.2292	−	3.81790i	0.654262	−	0.175547i
$474$	17.9690	−	20.5173i	0.825341	−	0.942389i
$475$	6.17308	+	2.00575i	0.283240	+	0.0920303i
$476$	−0.0733650	+	11.3934i	−0.00336268	+	0.522214i
$477$	16.9117	−	10.3945i	0.774332	−	0.475933i
$478$	42.2354	+	8.97740i	1.93180	+	0.410617i
$479$	−18.9427	+	21.0380i	−0.865513	+	0.961250i	−0.999558	−	0.0297256i	$-0.990537\pi$
$479$	−18.9427	+	21.0380i	−0.865513	+	0.961250i	0.134045	+	0.990975i	$0.457203\pi$
$480$	1.22065	−	3.94041i	0.0557147	−	0.179854i
$481$	−17.6462	+	1.85469i	−0.804596	+	0.0845664i
$482$	−28.9687	−	9.41249i	−1.31949	−	0.428727i
$483$	−31.1580	−	9.87235i	−1.41774	−	0.449207i
$484$	−2.49058	−	5.58370i	−0.113208	−	0.253805i
$485$	−7.84419	−	4.52884i	−0.356186	−	0.205644i
$486$	−17.3301	+	17.9090i	−0.786109	+	0.812367i
$487$	25.0177	+	11.1386i	1.13366	+	0.504738i	0.885805	−	0.464059i	$-0.153607\pi$
$487$	25.0177	+	11.1386i	1.13366	+	0.504738i	0.247856	+	0.968797i	$0.420274\pi$
$488$	6.10456	+	13.7111i	0.276341	+	0.620671i
$489$	−0.992451	+	0.118136i	−0.0448802	+	0.00534228i
$490$	−5.02776	−	7.11092i	−0.227131	−	0.321238i
$491$	−12.9391	−	9.40084i	−0.583935	−	0.424254i	0.256205	−	0.966622i	$-0.417528\pi$
$491$	−12.9391	−	9.40084i	−0.583935	−	0.424254i	−0.840141	+	0.542368i	$0.817528\pi$
$492$	−0.933906	−	0.0851856i	−0.0421038	−	0.00384047i
$493$	−13.4566	+	2.86029i	−0.606054	+	0.128821i
$494$	−2.75845	−	4.77778i	−0.124109	−	0.214963i
$495$	−2.97512	−	7.14870i	−0.133722	−	0.321310i
$496$	−40.5723			−1.82175
$497$	−15.9420	−	7.22119i	−0.715096	−	0.323914i
$498$	−10.1814	−	22.0465i	−0.456240	−	0.987926i
$499$	−31.8385	+	14.1754i	−1.42529	+	0.634580i	−0.967128	−	0.254290i	$-0.918158\pi$
$499$	−31.8385	+	14.1754i	−1.42529	+	0.634580i	−0.458161	+	0.888869i	$0.651492\pi$
$500$	3.01974	+	2.71898i	0.135047	+	0.121597i
$501$	0.255417	+	0.341570i	0.0114112	+	0.0152602i
$502$	1.27013	+	2.85277i	0.0566888	+	0.127325i
$503$	0.0605913	−	0.0440221i	0.00270163	−	0.00196285i	−0.586434	−	0.809997i	$-0.699469\pi$
$503$	0.0605913	−	0.0440221i	0.00270163	−	0.00196285i	0.589135	+	0.808034i	$0.299469\pi$
$504$	4.18700	+	17.8408i	0.186504	+	0.794694i
$505$		−	1.98141i		−	0.0881717i
$506$	33.6899	−	17.1803i	1.49770	−	0.763758i
$507$	12.3663	−	4.20701i	0.549209	−	0.186840i
$508$	0.486145	+	2.28713i	0.0215692	+	0.101475i
$509$	−34.5318	+	3.62944i	−1.53059	+	0.160872i	−0.832053	−	0.554697i	$-0.812834\pi$
$509$	−34.5318	+	3.62944i	−1.53059	+	0.160872i	−0.698542	+	0.715569i	$0.746168\pi$
$510$	−11.3412	−	12.2524i	−0.502196	−	0.542546i
$511$	−11.1388	−	12.5323i	−0.492753	−	0.554395i
$512$	2.31104	+	7.11265i	0.102135	+	0.314338i
$513$	7.56673	+	1.28462i	0.334079	+	0.0567172i
$514$	3.85793	−	8.66506i	0.170166	−	0.382200i
$515$	−1.78306	−	8.38865i	−0.0785712	−	0.369648i
$516$	−2.81745	+	3.21701i	−0.124031	+	0.141621i
$517$	5.05715	+	13.1609i	0.222413	+	0.578817i
$518$	12.8764	+	29.4293i	0.565754	+	1.29305i
$519$	−5.74313	−	3.21128i	−0.252095	−	0.140959i
$520$	0.438786	+	4.17477i	0.0192420	+	0.183076i
$521$	32.3486	+	3.39997i	1.41722	+	0.148956i	0.781952	−	0.623339i	$-0.214224\pi$
$521$	32.3486	+	3.39997i	1.41722	+	0.148956i	0.635265	+	0.772294i	$0.280891\pi$
$522$	7.68151	−	3.67648i	0.336211	−	0.160915i
$523$	−0.570491	+	2.68395i	−0.0249458	+	0.117361i	−0.988859	−	0.148857i	$-0.952441\pi$
$523$	−0.570491	+	2.68395i	−0.0249458	+	0.117361i	0.963913	+	0.266218i	$0.0857740\pi$
$524$	−4.74192	−	3.44521i	−0.207152	−	0.150504i
$525$	−19.7277	−	4.04259i	−0.860987	−	0.176433i
$526$	−3.81359	+	11.7370i	−0.166280	+	0.511758i
$527$	−32.7262	+	56.6834i	−1.42557	+	2.46917i
$528$	−23.3480	−	14.6986i	−1.01609	−	0.639675i
$529$	13.9353	+	24.1367i	0.605883	+	1.04942i
$530$	−5.50842	−	6.11771i	−0.239270	−	0.265737i
$531$	8.32655	+	34.4798i	0.361342	+	1.49630i
$532$	−1.46377	+	1.60478i	−0.0634626	+	0.0695761i
$533$	2.16447	−	0.703279i	0.0937536	−	0.0304624i
$534$	2.40164	+	1.02993i	0.103929	+	0.0445694i
$535$	−0.0430496	−	0.00452470i	−0.00186120	−	0.000195620i
$536$	−22.3116	−	9.93376i	−0.963714	−	0.429073i
$537$	−0.338495	−	0.568096i	−0.0146071	−	0.0245152i
$538$			11.1906i			0.482460i
$539$	−21.7770	+	8.04760i	−0.938000	+	0.346635i
$540$	1.87126	+	1.24493i	0.0805264	+	0.0535732i
$541$	30.5219	−	27.4820i	1.31224	−	1.18154i	0.341916	−	0.939731i	$-0.388924\pi$
$541$	30.5219	−	27.4820i	1.31224	−	1.18154i	0.970323	−	0.241814i	$-0.0777424\pi$
$542$	−11.8708	+	26.6622i	−0.509894	+	1.14524i
$543$	12.0485	+	3.73235i	0.517051	+	0.160171i
$544$	−23.1936	−	4.92995i	−0.994417	−	0.211370i
$545$	2.44299	+	7.51876i	0.104646	+	0.322068i
$546$	10.1617	+	13.7733i	0.434882	+	0.589445i
$547$	22.8109	+	31.3964i	0.975322	+	1.34242i	0.939312	+	0.343064i	$0.111465\pi$
$547$	22.8109	+	31.3964i	0.975322	+	1.34242i	0.0360094	+	0.999351i	$0.488535\pi$
$548$	3.78932	−	3.41192i	0.161872	−	0.145750i
$549$	−19.3316	+	2.57130i	−0.825051	+	0.109740i
$550$	19.5369	−	12.6968i	0.833055	−	0.541395i
$551$	−2.27131	−	1.31134i	−0.0967611	−	0.0558651i
$552$	13.9199	−	24.8947i	0.592470	−	1.05959i
$553$	26.0588	+	0.167800i	1.10813	+	0.00713557i
$554$	14.2334	−	19.5906i	0.604720	−	0.832325i
$555$	−9.40805	−	4.03459i	−0.399350	−	0.171259i
$556$	0.170375	+	0.153407i	0.00722552	+	0.00650589i
$557$	1.91203	−	18.1918i	0.0810153	−	0.770809i	−0.876300	−	0.481765i	$-0.839996\pi$
$557$	1.91203	−	18.1918i	0.0810153	−	0.770809i	0.957316	−	0.289044i	$-0.0933375\pi$
$558$	11.4554	−	38.8632i	0.484946	−	1.64521i
$559$	3.20699	−	9.87011i	0.135641	−	0.417461i
$560$	9.05931	−	3.96377i	0.382826	−	0.167500i
$561$	−39.3682	+	20.7632i	−1.66212	+	0.876625i
$562$	−15.3704	+	26.6223i	−0.648360	+	1.12299i
$563$	−33.9181	+	7.20952i	−1.42948	+	0.303845i	−0.856679	−	0.515850i	$-0.827476\pi$
$563$	−33.9181	+	7.20952i	−1.42948	+	0.303845i	−0.572800	+	0.819695i	$0.694143\pi$
$564$	−3.34367	−	2.35973i	−0.140794	−	0.0993625i
$565$	−2.64152	+	1.17608i	−0.111130	+	0.0494781i
$566$	18.1505	−	5.89744i	0.762921	−	0.247888i
$567$	−23.7743	−	1.33586i	−0.998425	−	0.0561009i
$568$	8.97687	−	12.3556i	0.376661	−	0.518430i
$569$	−3.68841	−	35.0928i	−0.154626	−	1.47117i	−0.746633	−	0.665236i	$-0.768331\pi$
$569$	−3.68841	−	35.0928i	−0.154626	−	1.47117i	0.592007	−	0.805933i	$-0.298336\pi$
$570$	−0.0437857	−	3.18256i	−0.00183398	−	0.133303i
$571$	−12.0766	+	6.97243i	−0.505390	+	0.291787i	−0.730937	−	0.682445i	$-0.760917\pi$
$571$	−12.0766	+	6.97243i	−0.505390	+	0.291787i	0.225547	+	0.974232i	$0.427583\pi$
$572$	−4.25407	−	0.672296i	−0.177872	−	0.0281101i
$573$	−5.74455	−	1.13868i	−0.239982	−	0.0475690i
$574$	−2.40031	−	3.34889i	−0.100187	−	0.139780i
$575$	18.4226	+	25.3565i	0.768275	+	1.05744i
$576$	−14.1328	+	0.388952i	−0.588867	+	0.0162063i
$577$	17.9028	−	19.8831i	0.745304	−	0.827744i	−0.244579	−	0.969629i	$-0.578650\pi$
$577$	17.9028	−	19.8831i	0.745304	−	0.827744i	0.989883	+	0.141885i	$0.0453163\pi$
$578$	−46.0298	+	51.1213i	−1.91459	+	2.12636i
$579$	−8.69370	+	1.97328i	−0.361298	+	0.0820068i
$580$	−0.451435	−	0.621347i	−0.0187448	−	0.0258000i
$581$	9.57376	−	21.1357i	0.397186	−	0.876856i
$582$	6.26647	−	31.6139i	0.259754	−	1.31044i
$583$	−19.5504	+	9.96983i	−0.809697	+	0.412908i
$584$	12.6714	−	7.31582i	0.524345	−	0.302731i
$585$	−5.36444	−	0.986839i	−0.221793	−	0.0408008i
$586$	1.01450	+	9.65234i	0.0419087	+	0.398734i
$587$	1.65507	−	2.27801i	0.0683122	−	0.0940237i	−0.773494	−	0.633804i	$-0.781493\pi$
$587$	1.65507	−	2.27801i	0.0683122	−	0.0940237i	0.841806	+	0.539780i	$0.181493\pi$
$588$	3.95624	−	5.45537i	0.163153	−	0.224976i
$589$	−11.8672	+	3.85588i	−0.488978	+	0.158879i
$590$	13.4383	−	5.98310i	0.553245	−	0.246320i
$591$	−15.8350	+	22.4377i	−0.651365	+	0.922965i
$592$	−35.6773	+	7.58344i	−1.46633	+	0.311677i
$593$	−4.97990	+	8.62544i	−0.204500	+	0.354204i	−0.949973	−	0.312331i	$-0.898890\pi$
$593$	−4.97990	+	8.62544i	−0.204500	+	0.354204i	0.745473	+	0.666535i	$0.232223\pi$
$594$	20.6716	−	18.2143i	0.848167	−	0.747343i
$595$	1.76960	−	15.8540i	0.0725467	−	0.649949i
$596$	0.255909	−	0.787608i	0.0104824	−	0.0322617i
$597$	−6.69279	−	0.610478i	−0.273918	−	0.0249852i
$598$	2.78463	−	26.4940i	0.113872	−	1.08342i
$599$	21.1787	+	19.0694i	0.865339	+	0.779155i	0.976696	−	0.214625i	$-0.0688531\pi$
$599$	21.1787	+	19.0694i	0.865339	+	0.779155i	−0.111357	+	0.993780i	$0.535520\pi$
$600$	6.92607	−	16.1506i	0.282756	−	0.659344i
$601$	−3.23224	+	4.44880i	−0.131846	+	0.181470i	−0.869836	−	0.493342i	$-0.835775\pi$
$601$	−3.23224	+	4.44880i	−0.131846	+	0.181470i	0.737990	+	0.674812i	$0.235775\pi$
$602$	−18.7882	−	0.120983i	−0.765752	−	0.00493088i
$603$	20.5778	−	24.1587i	0.837994	−	0.983820i
$604$	8.15152	+	4.70628i	0.331681	+	0.191496i
$605$	2.65081	+	8.13953i	0.107771	+	0.330919i
$606$	6.67457	−	2.27068i	0.271136	−	0.0922401i
$607$	22.9946	−	20.7044i	0.933322	−	0.840367i	−0.0540901	−	0.998536i	$-0.517226\pi$
$607$	22.9946	−	20.7044i	0.933322	−	0.840367i	0.987412	+	0.158169i	$0.0505592\pi$
$608$	−2.65704	−	3.65710i	−0.107757	−	0.148315i
$609$	7.45745	+	3.25509i	0.302191	+	0.131903i
$610$	2.49918	+	7.69168i	0.101189	+	0.311427i
$611$	9.71481	+	2.06495i	0.393019	+	0.0835388i
$612$	6.14932	−	11.3618i	0.248572	−	0.459272i
$613$	−12.6936	+	28.5102i	−0.512688	+	1.15152i	0.452928	+	0.891547i	$0.350379\pi$
$613$	−12.6936	+	28.5102i	−0.512688	+	1.15152i	−0.965617	+	0.259970i	$0.916287\pi$
$614$	−26.8298	+	24.1577i	−1.08276	+	0.974924i
$615$	1.28795	+	0.255296i	0.0519352	+	0.0102945i
$616$	−3.04721	−	20.0292i	−0.122776	−	0.807000i
$617$		−	14.7608i		−	0.594245i	−0.954839	−	0.297123i	$-0.903973\pi$
$617$		−	14.7608i		−	0.594245i	0.954839	−	0.297123i	$-0.0960270\pi$
$618$	26.2146	−	15.6197i	1.05451	−	0.628318i
$619$	22.9434	+	10.2151i	0.922173	+	0.410578i	0.812215	−	0.583358i	$-0.198262\pi$
$619$	22.9434	+	10.2151i	0.922173	+	0.410578i	0.109958	+	0.993936i	$0.464928\pi$
$620$	−3.63401	−	0.381949i	−0.145945	−	0.0153395i
$621$	25.9138	+	26.4949i	1.03988	+	1.06321i
$622$	−19.7107	+	6.40441i	−0.790329	+	0.256793i
$623$	0.756259	+	2.37955i	0.0302989	+	0.0953348i
$624$	−17.6442	+	8.14835i	−0.706332	+	0.326195i
$625$	10.8952	+	12.1003i	0.435808	+	0.484014i
$626$	2.45570	+	4.25339i	0.0981494	+	0.170000i
$627$	−8.22606	−	2.08034i	−0.328517	−	0.0830806i
$628$	2.39990	−	4.15675i	0.0957665	−	0.165872i
$629$	−18.1830	+	55.9615i	−0.725003	+	2.23133i
$630$	1.23893	+	9.79684i	0.0493603	+	0.390315i
$631$	−17.0094	−	12.3581i	−0.677135	−	0.491967i	0.195271	−	0.980749i	$-0.437441\pi$
$631$	−17.0094	−	12.3581i	−0.677135	−	0.491967i	−0.872406	+	0.488782i	$0.837441\pi$
$632$	−4.72804	+	22.2437i	−0.188071	+	0.884806i
$633$	14.3393	−	10.7226i	0.569936	−	0.426184i
$634$	27.2908	+	2.86838i	1.08386	+	0.113918i
$635$	−0.342206	−	3.25587i	−0.0135800	−	0.129205i
$636$	3.10886	−	5.55996i	0.123274	−	0.220467i
$637$	−3.60598	+	15.9518i	−0.142874	+	0.632034i
$638$	−8.78831	+	3.37695i	−0.347933	+	0.133695i
$639$	12.1016	+	15.7276i	0.478731	+	0.622173i
$640$	2.20937	+	10.3943i	0.0873330	+	0.410869i
$641$	11.4819	−	25.7887i	0.453506	−	1.01859i	−0.531655	−	0.846961i	$-0.678430\pi$
$641$	11.4819	−	25.7887i	0.453506	−	1.01859i	0.985161	−	0.171630i	$-0.0549035\pi$
$642$	−0.0340926	−	0.150202i	−0.00134553	−	0.00592800i
$643$	0.121692	+	0.374530i	0.00479907	+	0.0147700i	0.953427	−	0.301623i	$-0.0975283\pi$
$643$	0.121692	+	0.374530i	0.00479907	+	0.0147700i	−0.948628	+	0.316393i	$0.897528\pi$
$644$	−10.2731	+	2.11458i	−0.404818	+	0.0833260i
$645$	4.39397	−	4.06718i	0.173012	−	0.160145i
$646$	−18.1952	+	1.91239i	−0.715881	+	0.0752421i
$647$	8.58461	+	40.3874i	0.337496	+	1.58779i	0.740151	+	0.672441i	$0.234754\pi$
$647$	8.58461	+	40.3874i	0.337496	+	1.58779i	−0.402655	+	0.915352i	$0.631912\pi$
$648$	5.32448	−	20.0855i	0.209165	−	0.789033i
$649$	−6.14769	−	38.7298i	−0.241318	−	1.52028i
$650$		−	16.4134i		−	0.643785i
$651$	35.2497	−	16.0043i	1.38154	−	0.627256i
$652$	−0.259473	+	0.188518i	−0.0101617	+	0.00738294i
$653$	−11.7241	−	26.3328i	−0.458801	−	1.03048i	−0.983782	−	0.179370i	$-0.942594\pi$
$653$	−11.7241	−	26.3328i	−0.458801	−	1.03048i	0.524981	−	0.851114i	$-0.324073\pi$
$654$	−22.5280	+	16.8459i	−0.880915	+	0.658726i
$655$	6.09867	+	5.49127i	0.238295	+	0.214562i
$656$	4.27392	−	1.90287i	0.166869	−	0.0742947i
$657$	4.46292	+	18.4807i	0.174115	+	0.721002i
$658$	−1.76432	−	17.8940i	−0.0687804	−	0.697582i
$659$	−8.81987			−0.343573			−0.171787	−	0.985134i	$-0.554954\pi$
$659$	−8.81987			−0.343573			−0.171787	+	0.985134i	$0.554954\pi$
$660$	−1.95287	−	1.53633i	−0.0760154	−	0.0598017i
$661$	−15.1042	−	26.1613i	−0.587486	−	1.01756i	−0.994560	−	0.104161i	$-0.966784\pi$
$661$	−15.1042	−	26.1613i	−0.587486	−	1.01756i	0.407074	−	0.913395i	$-0.366549\pi$
$662$	−4.89706	+	1.04090i	−0.190329	+	0.0404558i
$663$	−2.84800	+	31.2232i	−0.110607	+	1.21261i
$664$	16.3809	+	11.9014i	0.635703	+	0.461865i
$665$	2.27309	−	2.02035i	0.0881468	−	0.0783458i
$666$	2.80934	−	36.3155i	0.108860	−	1.40720i
$667$	−5.15105	−	11.5695i	−0.199450	−	0.447971i
$668$	0.125033	+	0.0556685i	0.00483769	+	0.00215388i
$669$	−0.673342	−	48.9419i	−0.0260329	−	1.89220i
$670$	−11.3974	−	6.58028i	−0.440319	−	0.254218i
$671$	21.5301	−	1.13569i	0.831162	−	0.0438428i
$672$	9.46034	+	10.3534i	0.364940	+	0.399391i
$673$	44.7217	+	14.5310i	1.72389	+	0.560127i	0.992545	−	0.121876i	$-0.0388909\pi$
$673$	44.7217	+	14.5310i	1.72389	+	0.560127i	0.731349	+	0.682003i	$0.238891\pi$
$674$	−5.49676	+	0.577733i	−0.211727	+	0.0222534i
$675$	17.5849	+	14.5657i	0.676842	+	0.560635i
$676$	2.80481	−	3.11506i	0.107877	−	0.119810i
$677$	16.8544	+	3.58252i	0.647768	+	0.137687i	0.520067	−	0.854125i	$-0.325907\pi$
$677$	16.8544	+	3.58252i	0.647768	+	0.137687i	0.127701	+	0.991813i	$0.459240\pi$
$678$	−6.98890	−	7.55044i	−0.268407	−	0.289973i
$679$	26.7672	−	15.2251i	1.02723	−	0.584286i
$680$	13.2395	+	4.30177i	0.507711	+	0.164965i
$681$	23.3825	+	20.4783i	0.896018	+	0.784729i
$682$	−16.0380	+	41.8228i	−0.614126	+	1.60148i
$683$	30.7616	−	17.7602i	1.17706	−	0.679577i	0.221729	−	0.975108i	$-0.428830\pi$
$683$	30.7616	−	17.7602i	1.17706	−	0.679577i	0.955333	+	0.295531i	$0.0954967\pi$
$684$	2.32054	−	0.825234i	0.0887282	−	0.0315536i
$685$	−5.77578	+	4.19635i	−0.220681	+	0.160334i
$686$	29.5003	−	2.52553i	1.12633	−	0.0964253i
$687$	−2.29978	+	0.273752i	−0.0877419	+	0.0104443i
$688$	4.43553	−	20.8675i	0.169103	−	0.795568i
$689$	−1.61593	+	15.3746i	−0.0615622	+	0.585725i
$690$	8.86196	−	12.5572i	0.337369	−	0.478043i
$691$	−11.4715	−	12.7404i	−0.436398	−	0.484669i	0.484324	−	0.874889i	$-0.339066\pi$
$691$	−11.4715	−	12.7404i	−0.436398	−	0.484669i	−0.920722	+	0.390220i	$0.872399\pi$
$692$	−2.11151			−0.0802676
$693$	26.0830	+	3.56041i	0.990812	+	0.135249i
$694$	55.9438			2.12360
$695$	−0.214788	−	0.238546i	−0.00814736	−	0.00904856i
$696$	−4.09423	+	5.80141i	−0.155191	+	0.219902i
$697$	0.788909	−	7.50597i	0.0298821	−	0.284309i
$698$	0.643808	−	3.02888i	0.0243685	−	0.114645i
$699$	−7.80223	+	0.928733i	−0.295107	+	0.0351279i
$700$	−6.15862	+	1.95731i	−0.232774	+	0.0739792i
$701$	20.6077	−	14.9724i	0.778343	−	0.565499i	−0.126138	−	0.992013i	$-0.540258\pi$
$701$	20.6077	−	14.9724i	0.778343	−	0.565499i	0.904481	+	0.426513i	$0.140258\pi$
$702$	−2.82334	−	19.2015i	−0.106560	−	0.724716i
$703$	−9.71469	+	5.60878i	−0.366397	+	0.211539i
$704$	15.6092	+	0.812720i	0.588293	+	0.0306305i
$705$	4.31054	+	3.77516i	0.162344	+	0.142181i
$706$	9.34444	+	3.03619i	0.351683	+	0.114269i
$707$	5.81208	+	3.40569i	0.218586	+	0.128084i
$708$	7.73213	+	8.35338i	0.290591	+	0.313939i
$709$	17.8079	+	3.78518i	0.668788	+	0.142155i	0.529779	−	0.848136i	$-0.322275\pi$
$709$	17.8079	+	3.78518i	0.668788	+	0.142155i	0.139009	+	0.990291i	$0.455608\pi$
$710$	5.50669	−	6.11580i	0.206663	−	0.229522i
$711$	−25.9865	−	14.0647i	−0.974572	−	0.527467i
$712$	−2.16692	+	0.227753i	−0.0812088	+	0.00853539i
$713$	−57.3038	−	18.6191i	−2.14605	−	0.697293i
$714$	55.4335	−	12.2074i	2.07455	−	0.456851i
$715$	5.82519	+	1.55873i	0.217850	+	0.0582933i
$716$	−0.183779	−	0.106105i	−0.00686816	−	0.00396533i
$717$	−0.643549	−	46.7764i	−0.0240338	−	1.74690i
$718$	−15.8394	−	7.05213i	−0.591119	−	0.263183i
$719$	20.1278	+	45.2078i	0.750640	+	1.68597i	0.727379	+	0.686236i	$0.240738\pi$
$719$	20.1278	+	45.2078i	0.750640	+	1.68597i	0.0232608	+	0.999729i	$0.492595\pi$
$720$	−11.1791	−	0.864808i	−0.416621	−	0.0322295i
$721$	27.6712	+	9.18833i	1.03053	+	0.342191i
$722$	21.7523	+	15.8040i	0.809536	+	0.588162i
$723$	−2.99766	+	32.8639i	−0.111484	+	1.22222i
$724$	3.95919	−	0.841551i	0.147142	−	0.0312760i
$725$	−3.90138	−	6.75739i	−0.144894	−	0.250963i
$726$	−24.3810	+	18.2573i	−0.904862	+	0.677593i
$727$	28.5734			1.05973			0.529864	−	0.848083i	$-0.322243\pi$
$727$	28.5734			1.05973			0.529864	+	0.848083i	$0.322243\pi$
$728$	−13.0000	−	5.88859i	−0.481814	−	0.218245i
$729$	23.0776	+	14.0152i	0.854725	+	0.519081i
$730$	7.20273	−	3.20686i	0.266585	−	0.118691i
$731$	−25.5762	−	23.0289i	−0.945970	−	0.851755i
$732$	−5.01186	+	3.74775i	−0.185244	+	0.138521i
$733$	11.9446	+	26.8281i	0.441185	+	0.990917i	0.988112	+	0.153737i	$0.0491308\pi$
$733$	11.9446	+	26.8281i	0.441185	+	0.990917i	−0.546927	+	0.837180i	$0.684203\pi$
$734$	11.7206	−	8.51551i	0.432615	−	0.314313i
$735$	−6.30727	+	7.01733i	−0.232647	+	0.258838i
$736$		−	21.8281i		−	0.804594i
$737$	−24.7997	+	24.8166i	−0.913509	+	0.914131i
$738$	0.615990	+	4.63115i	0.0226749	+	0.170475i
$739$	−7.02463	−	33.0483i	−0.258405	−	1.21570i	−0.895552	−	0.444958i	$-0.853219\pi$
$739$	−7.02463	−	33.0483i	−0.258405	−	1.21570i	0.637146	−	0.770743i	$-0.280115\pi$
$740$	−3.26696	+	0.343371i	−0.120096	+	0.0126226i
$741$	−4.38642	+	4.06020i	−0.161139	+	0.149155i
$742$	27.4131	−	5.64259i	1.00637	−	0.207146i
$743$	2.12830	+	6.55024i	0.0780799	+	0.240305i	0.982476	−	0.186388i	$-0.0596783\pi$
$743$	2.12830	+	6.55024i	0.0780799	+	0.240305i	−0.904396	+	0.426694i	$0.859678\pi$
$744$	7.47770	+	32.9445i	0.274146	+	1.20781i
$745$	−0.471609	+	1.05925i	−0.0172784	+	0.0388080i
$746$	−6.90875	−	32.5031i	−0.252947	−	1.19002i
$747$	−20.8514	+	16.0441i	−0.762914	+	0.587023i
$748$	−7.77481	+	11.9811i	−0.284275	+	0.438072i
$749$	0.0872669	−	0.118500i	0.00318866	−	0.00432991i
$750$	9.87972	−	17.6692i	0.360757	−	0.645186i
$751$	0.938845	+	8.93251i	0.0342589	+	0.325952i	0.998207	+	0.0598606i	$0.0190656\pi$
$751$	0.938845	+	8.93251i	0.0342589	+	0.325952i	−0.963948	+	0.266091i	$0.914268\pi$
$752$	20.3046	+	2.13410i	0.740434	+	0.0778228i
$753$	2.70948	−	2.02608i	0.0987388	−	0.0738344i
$754$	−1.37888	+	6.48713i	−0.0502159	+	0.236247i
$755$	−10.6618	−	7.74626i	−0.388023	−	0.281915i
$756$	−6.86812	+	3.34917i	−0.249791	+	0.121808i
$757$	12.3838	−	38.1135i	0.450098	−	1.38526i	−0.426697	−	0.904395i	$-0.640323\pi$
$757$	12.3838	−	38.1135i	0.450098	−	1.38526i	0.876795	−	0.480865i	$-0.159677\pi$
$758$	20.8394	−	36.0948i	0.756920	−	1.31102i
$759$	−26.2310	−	31.4748i	−0.952125	−	1.14246i
$760$	1.32694	+	2.29832i	0.0481331	+	0.0833689i
$761$	−13.7841	−	15.3088i	−0.499674	−	0.554944i	0.439564	−	0.898211i	$-0.355133\pi$
$761$	−13.7841	−	15.3088i	−0.499674	−	0.554944i	−0.939238	+	0.343267i	$0.888466\pi$
$762$	10.5755	−	4.88395i	0.383111	−	0.176927i
$763$	−26.2539	−	5.75737i	−0.950454	−	0.208431i
$764$	−1.78732	+	0.580734i	−0.0646628	+	0.0210102i
$765$	−10.2254	+	14.9207i	−0.369702	+	0.539460i
$766$	−32.3307	−	3.39809i	−1.16815	−	0.122778i
$767$	−25.2358	−	11.2357i	−0.911210	−	0.405697i
$768$	−18.4576	+	10.9978i	−0.666031	+	0.396849i
$769$		−	29.6176i		−	1.06804i	−0.845473	−	0.534019i	$-0.820681\pi$
$769$		−	29.6176i		−	1.06804i	0.845473	−	0.534019i	$-0.179319\pi$
$770$	−0.504852	−	10.9054i	−0.0181936	−	0.393003i
$771$	−10.0802	−	1.99808i	−0.363029	−	0.0719593i
$772$	−2.12597	+	1.91423i	−0.0765154	+	0.0688947i
$773$	−8.56195	+	19.2305i	−0.307952	+	0.691671i	−0.999531	−	0.0306296i	$-0.990249\pi$
$773$	−8.56195	+	19.2305i	−0.307952	+	0.691671i	0.691579	+	0.722301i	$0.256915\pi$
$774$	18.7361	+	10.1405i	0.673457	+	0.364494i
$775$	−36.3117	−	7.71830i	−1.30436	−	0.277249i
$776$	8.30407	+	25.5573i	0.298099	+	0.917453i
$777$	28.0054	−	20.6619i	1.00469	−	0.741243i
$778$	−8.57286	−	11.7995i	−0.307352	−	0.423034i
$779$	1.06925	−	0.962761i	0.0383100	−	0.0344945i
$780$	−1.65707	+	0.563734i	−0.0593327	+	0.0201849i
$781$	−11.9551	−	18.3955i	−0.427785	−	0.658242i
$782$	−76.5086	−	44.1723i	−2.73594	−	1.57960i
$783$	−5.72649	−	7.23418i	−0.204648	−	0.258529i
$784$	−3.94441	+	33.3867i	−0.140872	+	1.19238i
$785$	−3.95009	+	5.43684i	−0.140985	+	0.194049i
$786$	−11.5088	+	26.8369i	−0.410506	+	0.957240i
$787$	−37.8121	−	34.0462i	−1.34786	−	1.21361i	−0.955922	−	0.293621i	$-0.905140\pi$
$787$	−37.8121	−	34.0462i	−1.34786	−	1.21361i	−0.391934	−	0.919993i	$-0.628194\pi$
$788$	−0.921187	+	8.76451i	−0.0328159	+	0.312223i
$789$	13.3152	+	1.21454i	0.474034	+	0.0432387i
$790$	−3.78668	+	11.6542i	−0.134724	+	0.414637i
$791$	1.09050	−	9.76986i	0.0387738	−	0.347376i
$792$	−7.63205	+	21.6675i	−0.271193	+	0.769920i
$793$	7.59378	−	13.1528i	0.269663	−	0.467070i
$794$	32.9928	−	7.01283i	1.17087	−	0.248876i
$795$	−5.14264	+	7.28698i	−0.182391	+	0.258443i
$796$	−1.97018	+	0.877182i	−0.0698313	+	0.0310909i
$797$	27.1683	−	8.82750i	0.962349	−	0.312686i	0.214625	−	0.976696i	$-0.431147\pi$
$797$	27.1683	−	8.82750i	0.962349	−	0.312686i	0.747723	+	0.664010i	$0.231147\pi$
$798$	9.41068	+	5.34182i	0.333135	+	0.189098i
$799$	19.3596	−	26.6461i	0.684892	−	0.942673i
$800$	−1.40577	−	13.3750i	−0.0497016	−	0.472879i
$801$	0.512221	−	2.78443i	0.0180984	−	0.0983829i
$802$	−32.3494	+	18.6769i	−1.14230	+	0.659506i
$803$	−3.29508	−	20.7586i	−0.116281	−	0.732556i
$804$	1.98007	−	9.98933i	0.0698318	−	0.352296i
$805$	14.6143	−	1.44094i	0.515086	−	0.0507866i
$806$	18.5465	+	25.5270i	0.653272	+	0.899152i
$807$	11.8233	−	2.68364i	0.416201	−	0.0944686i
$808$	−3.93348	+	4.36857i	−0.138379	+	0.153686i
$809$	−26.4368	+	29.3610i	−0.929467	+	1.03228i	0.0699303	+	0.997552i	$0.477722\pi$
$809$	−26.4368	+	29.3610i	−0.929467	+	1.03228i	−0.999397	+	0.0347254i	$0.988944\pi$
$810$	3.98475	−	10.4640i	0.140010	−	0.367668i
$811$	4.64335	+	6.39102i	0.163050	+	0.224419i	0.882723	−	0.469895i	$-0.155708\pi$
$811$	4.64335	+	6.39102i	0.163050	+	0.224419i	−0.719673	+	0.694314i	$0.755708\pi$
$812$	2.59853	−	0.256211i	0.0911907	−	0.00899124i
$813$	31.0165	+	6.14806i	1.08780	+	0.215622i
$814$	−6.28582	+	39.7746i	−0.220318	+	1.39410i
$815$	0.388893	−	0.224528i	0.0136223	−	0.00786486i
$816$	0.886629	+	64.4446i	0.0310382	+	2.25601i
$817$	−0.685824	−	6.52518i	−0.0239939	−	0.228287i
$818$	−20.0421	+	27.5856i	−0.700757	+	0.964509i
$819$	12.1152	−	14.0393i	0.423340	−	0.490574i
$820$	0.400723	−	0.130203i	0.0139939	−	0.00454688i
$821$	21.2069	−	9.44192i	0.740126	−	0.329525i	−0.00180784	−	0.999998i	$-0.500575\pi$
$821$	21.2069	−	9.44192i	0.740126	−	0.329525i	0.741934	+	0.670473i	$0.233909\pi$
$822$	−20.7548	−	14.6473i	−0.723907	−	0.510883i
$823$	−11.3154	+	2.40516i	−0.394430	+	0.0838386i	−0.400857	−	0.916141i	$-0.631288\pi$
$823$	−11.3154	+	2.40516i	−0.394430	+	0.0838386i	0.00642705	+	0.999979i	$0.497954\pi$
$824$	−12.7218	+	22.0348i	−0.443185	+	0.767620i
$825$	−18.1000	−	17.5967i	−0.630160	−	0.612638i
$826$	−5.54773	+	49.7024i	−0.193030	+	1.72937i
$827$	−1.75810	+	5.41089i	−0.0611353	+	0.188155i	−0.976960	−	0.213424i	$-0.931538\pi$
$827$	−1.75810	+	5.41089i	−0.0611353	+	0.188155i	0.915824	+	0.401579i	$0.131538\pi$
$828$	11.4076	+	3.36253i	0.396441	+	0.116856i
$829$	−3.57358	+	34.0003i	−0.124115	+	1.18088i	0.738227	+	0.674553i	$0.235664\pi$
$829$	−3.57358	+	34.0003i	−0.124115	+	1.18088i	−0.862342	+	0.506326i	$0.831003\pi$
$830$	8.10826	+	7.30071i	0.281442	+	0.253411i
$831$	−24.1117	−	10.3401i	−0.836425	−	0.358695i
$832$	6.47179	−	8.90766i	0.224369	−	0.308817i
$833$	43.4628	+	32.4409i	1.50590	+	1.12401i
$834$	0.557420	−	0.996904i	0.0193019	−	0.0345200i
$835$	−0.165956	−	0.0958145i	−0.00574313	−	0.00331580i
$836$	−2.62983	+	0.705620i	−0.0909547	+	0.0244044i
$837$	−43.8078	−	2.78327i	−1.51422	−	0.0962038i
$838$	16.8161	−	15.1413i	0.580902	−	0.523046i
$839$	−30.9404	−	42.5858i	−1.06818	−	1.47023i	−0.871903	−	0.489678i	$-0.837114\pi$
$839$	−30.9404	−	42.5858i	−1.06818	−	1.47023i	−0.196278	−	0.980548i	$-0.562886\pi$
$840$	−4.88824	−	6.62558i	−0.168660	−	0.228604i
$841$	−7.98722	−	24.5821i	−0.275421	−	0.847660i
$842$	22.3517	+	4.75101i	0.770292	+	0.163731i
$843$	31.8136	+	9.85511i	1.09572	+	0.339428i
$844$	2.33700	−	5.24898i	0.0804428	−	0.180677i
$845$	−4.36145	+	3.92707i	−0.150038	+	0.135095i
$846$	−7.77713	+	18.8468i	−0.267383	+	0.647965i
$847$	−28.4320	−	6.21475i	−0.976934	−	0.213541i
$848$			31.7790i			1.09130i
$849$	−10.5836	−	17.7625i	−0.363229	−	0.609606i
$850$	−49.7250	−	22.1390i	−1.70555	−	0.759361i
$851$	−53.8703	−	5.66200i	−1.84665	−	0.194091i
$852$	5.85264	+	2.50987i	0.200508	+	0.0859867i
$853$	−23.0791	+	7.49886i	−0.790214	+	0.256756i	−0.676195	−	0.736723i	$-0.736372\pi$
$853$	−23.0791	+	7.49886i	−0.790214	+	0.256756i	−0.114019	+	0.993479i	$0.536372\pi$
$854$	−26.8577	−	5.88978i	−0.919051	−	0.201544i
$855$	−3.35202	+	0.809480i	−0.114637	+	0.0276836i
$856$	0.0859324	+	0.0954376i	0.00293711	+	0.00326199i
$857$	13.2900	+	23.0189i	0.453976	+	0.786310i	0.998629	−	0.0523517i	$-0.0166717\pi$
$857$	13.2900	+	23.0189i	0.453976	+	0.786310i	−0.544652	+	0.838662i	$0.683338\pi$
$858$	1.42488	+	21.4090i	0.0486445	+	0.730891i
$859$	−15.8694	+	27.4865i	−0.541455	+	0.937828i	0.457365	+	0.889279i	$0.348793\pi$
$859$	−15.8694	+	27.4865i	−0.541455	+	0.937828i	−0.998821	+	0.0485493i	$0.984540\pi$
$860$	0.593733	−	1.82732i	0.0202461	−	0.0623112i
$861$	−2.96262	+	3.33914i	−0.100966	+	0.113798i
$862$	−15.9863	−	11.6147i	−0.544495	−	0.395599i
$863$	1.34926	−	6.34779i	0.0459295	−	0.216081i	−0.949198	−	0.314680i	$-0.898103\pi$
$863$	1.34926	−	6.34779i	0.0459295	−	0.216081i	0.995127	+	0.0985990i	$0.0314361\pi$
$864$	−3.94528	−	15.4053i	−0.134221	−	0.524098i
$865$	2.94017	+	0.309025i	0.0999689	+	0.0105072i
$866$	1.51557	+	14.4197i	0.0515011	+	0.490000i
$867$	65.0503	+	36.3729i	2.20922	+	1.23529i
$868$	7.36658	−	10.0031i	0.250038	−	0.339528i
$869$	27.4030	+	17.7825i	0.929583	+	0.603229i
$870$	−2.52089	+	2.87839i	−0.0854661	+	0.0975867i
$871$	5.13838	+	24.1742i	0.174107	+	0.819111i
$872$	9.53992	−	21.4270i	0.323062	−	0.725610i
$873$	−34.9042	+	0.960607i	−1.18133	+	0.0325116i
$874$	−5.20448	−	16.0177i	−0.176044	−	0.541808i
$875$	18.9454	−	3.89963i	0.640471	−	0.131832i
$876$	4.14432	+	4.47730i	0.140023	+	0.151274i
$877$	27.9141	−	2.93389i	0.942593	−	0.0990705i	0.379250	−	0.925294i	$-0.376182\pi$
$877$	27.9141	−	2.93389i	0.942593	−	0.0990705i	0.563342	+	0.826224i	$0.309515\pi$
$878$	3.16847	+	14.9065i	0.106931	+	0.503070i
$879$	9.95482	−	3.38662i	0.335768	−	0.114228i
$880$	12.2439	+	1.93498i	0.412743	+	0.0652282i
$881$			26.2026i			0.882788i	0.897313	+	0.441394i	$0.145516\pi$
$881$			26.2026i			0.882788i	−0.897313	+	0.441394i	$0.854484\pi$
$882$	−30.8666	−	13.2048i	−1.03933	−	0.444630i
$883$	21.7773	−	15.8222i	0.732866	−	0.532458i	−0.157603	−	0.987503i	$-0.550377\pi$
$883$	21.7773	−	15.8222i	0.732866	−	0.532458i	0.890469	+	0.455044i	$0.150377\pi$
$884$	4.09223	+	9.19129i	0.137636	+	0.309137i
$885$	−9.54407	−	12.7633i	−0.320820	−	0.429033i
$886$	15.8015	+	14.2277i	0.530862	+	0.477990i
$887$	−25.7638	+	11.4708i	−0.865063	+	0.385151i	−0.790790	−	0.612087i	$-0.790330\pi$
$887$	−25.7638	+	11.4708i	−0.865063	+	0.385151i	−0.0742727	+	0.997238i	$0.523664\pi$
$888$	12.7332	+	27.5721i	0.427299	+	0.925260i
$889$	10.1386	+	4.59246i	0.340039	+	0.154026i
$890$	−1.17409			−0.0393557
$891$	−24.2015	−	17.4724i	−0.810782	−	0.585348i
$892$	−7.85348	−	13.6026i	−0.262954	−	0.455449i
$893$	6.14181	−	1.30548i	0.205528	−	0.0436863i
$894$	−4.10865	−	0.374767i	−0.137414	−	0.0125341i
$895$	0.240375	+	0.174642i	0.00803484	+	0.00583765i
$896$	−34.2870	−	11.3851i	−1.14545	−	0.380351i
$897$	−28.6598	+	3.41150i	−0.956923	+	0.113907i
$898$	1.00740	+	2.26266i	0.0336174	+	0.0755059i
$899$	13.7032	+	6.10108i	0.457029	+	0.203482i
$900$	7.20649	+	1.32570i	0.240216	+	0.0441900i
$901$	44.3983	+	25.6334i	1.47912	+	0.853972i
$902$	−0.272070	−	5.15785i	−0.00905895	−	0.171738i
$903$	4.37783	+	19.8796i	0.145685	+	0.661552i
$904$	8.15871	+	2.65093i	0.271355	+	0.0881685i
$905$	−5.63613	+	0.592382i	−0.187351	+	0.0196914i
$906$	13.8757	−	44.7925i	0.460988	−	1.48813i
$907$	−7.43502	+	8.25742i	−0.246876	+	0.274183i	−0.853828	−	0.520555i	$-0.825725\pi$
$907$	−7.43502	+	8.25742i	−0.246876	+	0.274183i	0.606953	+	0.794738i	$0.292392\pi$
$908$	9.75631	+	2.07377i	0.323775	+	0.0688204i
$909$	−3.99972	−	6.50744i	−0.132662	−	0.215838i
$910$	−6.63511	−	3.88796i	−0.219952	−	0.128885i
$911$	21.9258	+	7.12411i	0.726433	+	0.236032i	0.648810	−	0.760950i	$-0.275267\pi$
$911$	21.9258	+	7.12411i	0.726433	+	0.236032i	0.0776229	+	0.996983i	$0.475267\pi$
$912$	−8.09516	+	9.24319i	−0.268058	+	0.306073i
$913$	24.3885	−	15.8499i	0.807141	−	0.524554i
$914$	15.9443	−	9.20544i	0.527390	−	0.304489i
$915$	7.52726	−	4.48505i	0.248844	−	0.148271i
$916$	−0.601269	+	0.436847i	−0.0198665	+	0.0144338i
$917$	−26.5901	+	8.45074i	−0.878081	+	0.279068i
$918$	−61.9802	−	17.3464i	−2.04565	−	0.572515i
$919$	−5.72196	+	26.9197i	−0.188750	+	0.887999i	0.777197	+	0.629258i	$0.216641\pi$
$919$	−5.72196	+	26.9197i	−0.188750	+	0.887999i	−0.965947	+	0.258741i	$0.916692\pi$
$920$	−1.33953	+	12.7448i	−0.0441629	+	0.420182i
$921$	31.9577	+	22.5535i	1.05304	+	0.743164i
$922$	−20.3399	−	22.5898i	−0.669860	−	0.743954i
$923$	−15.4544			−0.508689
$924$	7.86317	−	3.08768i	0.258679	−	0.101577i
$925$	−33.3734			−1.09731
$926$	38.1364	+	42.3547i	1.25324	+	1.39186i
$927$	−22.7895	−	23.9510i	−0.748506	−	0.786655i
$928$	−0.568023	+	5.40438i	−0.0186463	+	0.177407i
$929$	8.19119	−	38.5365i	0.268744	−	1.26434i	−0.612041	−	0.790826i	$-0.709651\pi$
$929$	8.19119	−	38.5365i	0.268744	−	1.26434i	0.880785	−	0.473516i	$-0.157016\pi$
$930$	2.15171	+	18.0763i	0.0705572	+	0.592746i
$931$	2.01926	+	10.1403i	0.0661786	+	0.332335i
$932$	−2.03987	+	1.48205i	−0.0668181	+	0.0485462i
$933$	11.4934	+	19.2894i	0.376277	+	0.631506i
$934$	−34.5132	+	19.9262i	−1.12931	+	0.652005i
$935$	12.5795	−	15.5452i	0.411393	−	0.508382i
$936$	9.86834	+	12.8252i	0.322557	+	0.419205i
$937$	−45.9219	−	14.9209i	−1.50020	−	0.487445i	−0.560125	−	0.828408i	$-0.689247\pi$
$937$	−45.9219	−	14.9209i	−1.50020	−	0.487445i	−0.940077	+	0.340963i	$0.889247\pi$
$938$	38.8920	−	22.1216i	1.26987	−	0.722297i
$939$	3.90498	−	3.61456i	0.127434	−	0.117957i
$940$	1.79857	+	0.382298i	0.0586629	+	0.0124692i
$941$	−1.72960	+	1.92091i	−0.0563833	+	0.0626200i	−0.770677	−	0.637226i	$-0.780082\pi$
$941$	−1.72960	+	1.92091i	−0.0563833	+	0.0626200i	0.714293	+	0.699846i	$0.246748\pi$
$942$	−22.8413	−	7.07570i	−0.744209	−	0.230539i
$943$	6.90969	−	0.726238i	0.225011	−	0.0236496i
$944$	−54.0062	−	17.5477i	−1.75775	−	0.571129i
$945$	10.0537	−	3.65839i	0.327046	−	0.119007i
$946$	−19.7574	−	12.8211i	−0.642369	−	0.416849i
$947$	−12.0732	−	6.97046i	−0.392326	−	0.226509i	0.290842	−	0.956771i	$-0.406065\pi$
$947$	−12.0732	−	6.97046i	−0.392326	−	0.226509i	−0.683167	+	0.730262i	$0.739398\pi$
$948$	−9.48124	+	0.130443i	−0.307936	+	0.00423659i
$949$	−13.5260	−	6.02217i	−0.439073	−	0.195488i
$950$	−4.22059	−	9.47961i	−0.136934	−	0.307559i
$951$	−3.51410	−	29.5218i	−0.113953	−	0.957308i
$952$	−35.3747	+	31.4414i	−1.14650	+	1.01902i
$953$	−37.8204	−	27.4781i	−1.22512	−	0.890104i	−0.228608	−	0.973519i	$-0.573417\pi$
$953$	−37.8204	−	27.4781i	−1.22512	−	0.890104i	−0.996515	+	0.0834146i	$0.973417\pi$
$954$	−30.4403	−	8.97267i	−0.985541	−	0.290501i
$955$	2.57374	−	0.547065i	0.0832843	−	0.0177026i
$956$	−7.50599	−	13.0008i	−0.242761	−	0.420474i
$957$	5.67544	+	8.47540i	0.183461	+	0.273971i
$958$	45.2580			1.46222
$959$	−2.38163	−	24.1549i	−0.0769068	−	0.780002i
$960$	5.76699	−	2.66329i	0.186129	−	0.0859572i
$961$	36.8757	−	16.4181i	1.18954	−	0.529616i
$962$	21.0802	+	18.9807i	0.679652	+	0.611961i
$963$	−0.150519	+	0.0720406i	−0.00485041	+	0.00232148i
$964$	4.30727	+	9.67428i	0.138728	+	0.311588i
$965$	3.24046	−	2.35433i	0.104314	−	0.0757886i
$966$	21.6018	+	47.5783i	0.695026	+	1.53081i
$967$		−	4.93191i		−	0.158600i	−0.996851	−	0.0792998i	$-0.974732\pi$
$967$		−	4.93191i		−	0.158600i	0.996851	−	0.0792998i	$-0.0252684\pi$
$968$	10.3141	−	23.2082i	0.331506	−	0.745940i
$969$	6.38396	+	18.7654i	0.205082	+	0.602832i
$970$	3.01066	+	14.1640i	0.0966663	+	0.454779i
$971$	32.0610	−	3.36975i	1.02889	−	0.108140i	0.424986	−	0.905200i	$-0.360279\pi$
$971$	32.0610	−	3.36975i	1.02889	−	0.108140i	0.603901	+	0.797060i	$0.293612\pi$
$972$	8.65872	+	0.311277i	0.277729	+	0.00998422i
$973$	1.06891	−	0.220020i	0.0342677	−	0.00705350i
$974$	−13.5290	−	41.6379i	−0.433496	−	1.33416i
$975$	−17.3414	+	3.93613i	−0.555370	+	0.126057i
$976$	12.6985	−	28.5213i	0.406469	−	0.912945i
$977$	−5.73703	−	26.9906i	−0.183544	−	0.863505i	−0.969475	−	0.245191i	$-0.921149\pi$
$977$	−5.73703	−	26.9906i	−0.183544	−	0.863505i	0.785931	−	0.618314i	$-0.212184\pi$
$978$	1.20201	+	1.05272i	0.0384360	+	0.0336622i
$979$	−0.809063	+	3.02358i	−0.0258578	+	0.0966339i
$980$	−0.667600	+	2.95327i	−0.0213257	+	0.0943387i
$981$	23.2009	+	19.7620i	0.740748	+	0.630951i
$982$	2.67268	+	25.4289i	0.0852887	+	0.811468i
$983$	−4.27224	−	0.449031i	−0.136263	−	0.0143219i	0.0361512	−	0.999346i	$-0.488490\pi$
$983$	−4.27224	−	0.449031i	−0.136263	−	0.0143219i	−0.172415	+	0.985024i	$0.555157\pi$
$984$	−2.33283	−	3.11970i	−0.0743680	−	0.0994523i
$985$	2.56541	−	12.0693i	0.0817409	−	0.384561i
$986$	17.7932	+	12.9275i	0.566650	+	0.411695i
$987$	−18.4827	+	6.15530i	−0.588312	+	0.195925i
$988$	−0.592713	+	1.82418i	−0.0188567	+	0.0580350i
$989$	15.8411	−	27.4376i	0.503717	−	0.872464i
$990$	−5.31050	+	11.1818i	−0.168779	+	0.355382i
$991$	−26.7075	−	46.2588i	−0.848393	−	1.46946i	−0.882642	−	0.470046i	$-0.844237\pi$
$991$	−26.7075	−	46.2588i	−0.848393	−	1.46946i	0.0342489	−	0.999413i	$-0.489096\pi$
$992$	17.2996	+	19.2132i	0.549264	+	0.610020i
$993$	2.27413	+	4.92433i	0.0721674	+	0.156269i
$994$	8.47448	+	26.6648i	0.268794	+	0.845755i
$995$	2.87176	−	0.933091i	0.0910409	−	0.0295810i
$996$	−3.32755	+	7.75936i	−0.105438	+	0.245865i
$997$	−16.9620	−	1.78278i	−0.537193	−	0.0564613i	−0.167952	−	0.985795i	$-0.553715\pi$
$997$	−16.9620	−	1.78278i	−0.537193	−	0.0564613i	−0.369241	+	0.929334i	$0.620382\pi$
$998$	50.9000	+	22.6622i	1.61121	+	0.717358i
$999$	−39.0426	+	5.74072i	−1.23525	+	0.181628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.2.6	✓	224
3.2	odd	2	inner	231.2.be.a.2.23	yes	224
7.4	even	3	inner	231.2.be.a.200.23	yes	224
11.6	odd	10	inner	231.2.be.a.149.6	yes	224
21.11	odd	6	inner	231.2.be.a.200.6	yes	224
33.17	even	10	inner	231.2.be.a.149.23	yes	224
77.39	odd	30	inner	231.2.be.a.116.23	yes	224
231.116	even	30	inner	231.2.be.a.116.6	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.6	✓	224	1.1	even	1	trivial
231.2.be.a.2.23	yes	224	3.2	odd	2	inner
231.2.be.a.116.6	yes	224	231.116	even	30	inner
231.2.be.a.116.23	yes	224	77.39	odd	30	inner
231.2.be.a.149.6	yes	224	11.6	odd	10	inner
231.2.be.a.149.23	yes	224	33.17	even	10	inner
231.2.be.a.200.6	yes	224	21.11	odd	6	inner
231.2.be.a.200.23	yes	224	7.4	even	3	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06973 - 1.18806i) q^{2} +(-0.998701 + 1.41513i) q^{3} +(-0.0580986 + 0.552771i) q^{4} +(0.161799 - 0.761203i) q^{5} +(2.74960 - 0.327297i) q^{6} +(1.95474 + 1.78298i) q^{7} +(-1.86786 + 1.35708i) q^{8} +(-1.00519 - 2.82659i) q^{9} +O(q^{10})\)	\(q+(-1.06973 - 1.18806i) q^{2} +(-0.998701 + 1.41513i) q^{3} +(-0.0580986 + 0.552771i) q^{4} +(0.161799 - 0.761203i) q^{5} +(2.74960 - 0.327297i) q^{6} +(1.95474 + 1.78298i) q^{7} +(-1.86786 + 1.35708i) q^{8} +(-1.00519 - 2.82659i) q^{9} +(-1.07744 + 0.622058i) q^{10} +(0.859495 + 3.20332i) q^{11} +(-0.724221 - 0.634270i) q^{12} +(2.22198 + 0.721966i) q^{13} +(0.0272359 - 4.22965i) q^{14} +(0.915614 + 0.989181i) q^{15} +(4.69775 + 0.998538i) q^{16} +(5.18432 - 5.75778i) q^{17} +(-2.28286 + 4.21792i) q^{18} +(1.46896 - 0.154394i) q^{19} +(0.411371 + 0.133662i) q^{20} +(-4.47534 + 0.985548i) q^{21} +(2.88631 - 4.44783i) q^{22} +(6.17681 + 3.56618i) q^{23} +(-0.0550126 - 3.99859i) q^{24} +(4.01448 + 1.78736i) q^{25} +(-1.51919 - 3.41216i) q^{26} +(5.00388 + 1.40043i) q^{27} +(-1.09915 + 0.976933i) q^{28} +(-1.43650 - 1.04368i) q^{29} +(0.195743 - 2.14596i) q^{30} +(-8.26320 + 1.75640i) q^{31} +(-1.53021 - 2.65041i) q^{32} +(-5.39150 - 1.98286i) q^{33} -12.3864 q^{34} +(1.67348 - 1.19947i) q^{35} +(1.62086 - 0.391421i) q^{36} +(-6.93796 + 3.08898i) q^{37} +(-1.75483 - 1.58006i) q^{38} +(-3.24077 + 2.42337i) q^{39} +(0.730797 + 1.64140i) q^{40} +(0.788077 - 0.572571i) q^{41} +(5.95831 + 4.26270i) q^{42} -4.44203i q^{43} +(-1.82064 + 0.288996i) q^{44} +(-2.31425 + 0.307818i) q^{45} +(-2.37070 - 11.1533i) q^{46} +(4.22776 - 0.444355i) q^{47} +(-6.10471 + 5.65069i) q^{48} +(0.641986 + 6.97050i) q^{49} +(-2.17093 - 6.68144i) q^{50} +(2.97042 + 13.0868i) q^{51} +(-0.528176 + 1.18630i) q^{52} +(1.37573 + 6.47231i) q^{53} +(-3.68902 - 7.44300i) q^{54} +(2.57744 - 0.135957i) q^{55} +(-6.07082 - 0.677620i) q^{56} +(-1.24857 + 2.23297i) q^{57} +(0.296721 + 2.82311i) q^{58} +(-11.7589 - 1.23591i) q^{59} +(-0.599986 + 0.448655i) q^{60} +(1.35155 - 6.35855i) q^{61} +(10.9261 + 7.93830i) q^{62} +(3.07485 - 7.31747i) q^{63} +(1.45631 - 4.48206i) q^{64} +(0.909076 - 1.57457i) q^{65} +(3.41171 + 8.52656i) q^{66} +(5.28912 + 9.16102i) q^{67} +(2.88153 + 3.20026i) q^{68} +(-11.2154 + 5.17945i) q^{69} +(-3.21522 - 0.705085i) q^{70} +(-6.29108 + 2.04410i) q^{71} +(5.71347 + 3.91555i) q^{72} +(-6.30260 - 0.662430i) q^{73} +(11.0917 + 4.93833i) q^{74} +(-6.53861 + 3.89597i) q^{75} +0.820971i q^{76} +(-4.03136 + 7.79411i) q^{77} +(6.34587 + 1.25787i) q^{78} +(7.31961 - 6.59061i) q^{79} +(1.52018 - 3.41438i) q^{80} +(-6.97917 + 5.68253i) q^{81} +(-1.52328 - 0.323783i) q^{82} +(-2.71004 - 8.34064i) q^{83} +(-0.284771 - 2.53110i) q^{84} +(-3.54402 - 4.87793i) q^{85} +(-5.27740 + 4.75179i) q^{86} +(2.91159 - 0.990517i) q^{87} +(-5.95259 - 4.81696i) q^{88} +(0.817282 + 0.471858i) q^{89} +(2.84133 + 2.42018i) q^{90} +(3.05614 + 5.37299i) q^{91} +(-2.33015 + 3.20717i) q^{92} +(5.76693 - 13.4476i) q^{93} +(-5.05049 - 4.54748i) q^{94} +(0.120151 - 1.14316i) q^{95} +(5.27890 + 0.481511i) q^{96} +(3.59669 - 11.0695i) q^{97} +(7.59461 - 8.21930i) q^{98} +(8.19050 - 5.64939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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