LMFDB - Embedded newform 690.2.q.a.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			191.2
Character	$\chi$	$=$	690.191
Dual form			690.2.q.a.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755750 - 0.654861i) q^{2} +(-1.23307 - 1.21636i) q^{3} +(0.142315 + 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.135347 + 1.72675i) q^{6} +(0.0399458 + 0.136043i) q^{7} +(0.540641 - 0.841254i) q^{8} +(0.0409354 + 2.99972i) q^{9} +O(q^{10})$	\(q+(-0.755750 - 0.654861i) q^{2} +(-1.23307 - 1.21636i) q^{3} +(0.142315 + 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.135347 + 1.72675i) q^{6} +(0.0399458 + 0.136043i) q^{7} +(0.540641 - 0.841254i) q^{8} +(0.0409354 + 2.99972i) q^{9} +(0.281733 - 0.959493i) q^{10} +(-2.41826 - 2.79082i) q^{11} +(1.02849 - 1.39363i) q^{12} +(2.41066 + 0.707833i) q^{13} +(0.0589002 - 0.128973i) q^{14} +(0.594203 - 1.62694i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.338271 - 2.35273i) q^{17} +(1.93346 - 2.29384i) q^{18} +(-6.49504 + 0.933846i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(0.116221 - 0.216339i) q^{21} +3.69278i q^{22} +(-2.28044 - 4.21895i) q^{23} +(-1.68992 + 0.379713i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(-1.35832 - 2.11359i) q^{26} +(3.59826 - 3.74867i) q^{27} +(-0.128973 + 0.0589002i) q^{28} +(-3.82536 - 0.550004i) q^{29} +(-1.51449 + 0.840436i) q^{30} +(-4.87810 - 3.13496i) q^{31} +(0.909632 + 0.415415i) q^{32} +(-0.412754 + 6.38276i) q^{33} +(-1.79636 + 1.55655i) q^{34} +(-0.107155 + 0.0928503i) q^{35} +(-2.96336 + 0.467423i) q^{36} +(0.564876 + 0.257970i) q^{37} +(5.52017 + 3.54760i) q^{38} +(-2.11154 - 3.80504i) q^{39} +(0.989821 + 0.142315i) q^{40} +(-5.49265 + 2.50841i) q^{41} +(-0.229506 + 0.0873897i) q^{42} +(0.0168318 + 0.0261909i) q^{43} +(2.41826 - 2.79082i) q^{44} +(-2.71164 + 1.28337i) q^{45} +(-1.03938 + 4.68185i) q^{46} +6.32537i q^{47} +(1.52581 + 0.819692i) q^{48} +(5.87186 - 3.77362i) q^{49} +(0.989821 - 0.142315i) q^{50} +(-3.27888 + 2.48963i) q^{51} +(-0.357556 + 2.48686i) q^{52} +(-8.44483 + 2.47963i) q^{53} +(-5.17424 + 0.476690i) q^{54} +(1.53404 - 3.35907i) q^{55} +(0.136043 + 0.0399458i) q^{56} +(9.14475 + 6.74881i) q^{57} +(2.53084 + 2.92074i) q^{58} +(-3.12347 + 10.6376i) q^{59} +(1.69494 + 0.356618i) q^{60} +(-3.28734 + 5.11521i) q^{61} +(1.63366 + 5.56372i) q^{62} +(-0.406456 + 0.125395i) q^{63} +(-0.415415 - 0.909632i) q^{64} +(0.357556 + 2.48686i) q^{65} +(4.49175 - 4.55347i) q^{66} +(-3.90499 - 3.38369i) q^{67} +2.37692 q^{68} +(-2.31982 + 7.97612i) q^{69} +0.141786 q^{70} +(-11.2888 - 9.78184i) q^{71} +(2.54566 + 1.58733i) q^{72} +(-1.26091 - 8.76982i) q^{73} +(-0.257970 - 0.564876i) q^{74} +(1.72675 - 0.135347i) q^{75} +(-1.84868 - 6.29603i) q^{76} +(0.283072 - 0.440469i) q^{77} +(-0.895978 + 4.25842i) q^{78} +(-4.50080 + 15.3283i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-8.99665 + 0.245589i) q^{81} +(5.79373 + 1.70119i) q^{82} +(0.284540 - 0.623056i) q^{83} +(0.230677 + 0.0842500i) q^{84} +(2.28064 - 0.669656i) q^{85} +(0.00443071 - 0.0308163i) q^{86} +(4.04794 + 5.33121i) q^{87} +(-3.65520 + 0.525538i) q^{88} +(5.96178 - 3.83140i) q^{89} +(2.88974 + 0.805842i) q^{90} +0.356228i q^{91} +(3.85147 - 2.85765i) q^{92} +(2.20180 + 9.79916i) q^{93} +(4.14224 - 4.78040i) q^{94} +(-3.54760 - 5.52017i) q^{95} +(-0.616348 - 1.61868i) q^{96} +(10.3676 - 4.73474i) q^{97} +(-6.90885 - 0.993343i) q^{98} +(8.27269 - 7.36834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.755750	−	0.654861i	−0.534396	−	0.463056i
$2$	−0.755750	−	0.654861i	−0.534396	−	0.463056i
$3$	−1.23307	−	1.21636i	−0.711915	−	0.702266i
$3$	−1.23307	−	1.21636i	−0.711915	−	0.702266i
$4$	0.142315	+	0.989821i	0.0711574	+	0.494911i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$6$	0.135347	+	1.72675i	0.0552553	+	0.704945i
$7$	0.0399458	+	0.136043i	0.0150981	+	0.0514194i	0.966698	−	0.255922i	$-0.0823789\pi$
$7$	0.0399458	+	0.136043i	0.0150981	+	0.0514194i	−0.951599	+	0.307341i	$0.900561\pi$
$8$	0.540641	−	0.841254i	0.191145	−	0.297428i
$9$	0.0409354	+	2.99972i	0.0136451	+	0.999907i
$10$	0.281733	−	0.959493i	0.0890917	−	0.303418i
$11$	−2.41826	−	2.79082i	−0.729132	−	0.841464i	0.263241	−	0.964730i	$-0.415208\pi$
$11$	−2.41826	−	2.79082i	−0.729132	−	0.841464i	−0.992374	+	0.123266i	$0.960663\pi$
$12$	1.02849	−	1.39363i	0.296901	−	0.402306i
$13$	2.41066	+	0.707833i	0.668597	+	0.196318i	0.598378	−	0.801214i	$-0.295812\pi$
$13$	2.41066	+	0.707833i	0.668597	+	0.196318i	0.0702186	+	0.997532i	$0.477630\pi$
$14$	0.0589002	−	0.128973i	0.0157417	−	0.0344696i
$15$	0.594203	−	1.62694i	0.153423	−	0.420073i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.338271	−	2.35273i	0.0820428	−	0.570621i	−0.906789	−	0.421585i	$-0.861474\pi$
$17$	0.338271	−	2.35273i	0.0820428	−	0.570621i	0.988832	−	0.149036i	$-0.0476169\pi$
$18$	1.93346	−	2.29384i	0.455721	−	0.540664i
$19$	−6.49504	+	0.933846i	−1.49007	+	0.214239i	−0.838729	−	0.544550i	$-0.816701\pi$
$19$	−6.49504	+	0.933846i	−1.49007	+	0.214239i	−0.651337	+	0.758789i	$0.725791\pi$
$20$	−0.841254	+	0.540641i	−0.188110	+	0.120891i
$21$	0.116221	−	0.216339i	0.0253616	−	0.0472091i
$22$			3.69278i			0.787304i
$23$	−2.28044	−	4.21895i	−0.475505	−	0.879713i
$23$	−2.28044	−	4.21895i	−0.475505	−	0.879713i
$24$	−1.68992	+	0.379713i	−0.344953	+	0.0775085i
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	−1.35832	−	2.11359i	−0.266389	−	0.414509i
$27$	3.59826	−	3.74867i	0.692486	−	0.721431i
$28$	−0.128973	+	0.0589002i	−0.0243737	+	0.0111311i
$29$	−3.82536	−	0.550004i	−0.710351	−	0.102133i	−0.222339	−	0.974970i	$-0.571369\pi$
$29$	−3.82536	−	0.550004i	−0.710351	−	0.102133i	−0.488013	+	0.872836i	$0.662278\pi$
$30$	−1.51449	+	0.840436i	−0.276506	+	0.153442i
$31$	−4.87810	−	3.13496i	−0.876133	−	0.563056i	0.0234902	−	0.999724i	$-0.492522\pi$
$31$	−4.87810	−	3.13496i	−0.876133	−	0.563056i	−0.899623	+	0.436668i	$0.856159\pi$
$32$	0.909632	+	0.415415i	0.160802	+	0.0734357i
$33$	−0.412754	+	6.38276i	−0.0718512	+	1.11110i
$34$	−1.79636	+	1.55655i	−0.308073	+	0.266947i
$35$	−0.107155	+	0.0928503i	−0.0181125	+	0.0156946i
$36$	−2.96336	+	0.467423i	−0.493894	+	0.0779039i
$37$	0.564876	+	0.257970i	0.0928650	+	0.0424100i	0.461306	−	0.887241i	$-0.347381\pi$
$37$	0.564876	+	0.257970i	0.0928650	+	0.0424100i	−0.368441	+	0.929651i	$0.620108\pi$
$38$	5.52017	+	3.54760i	0.895489	+	0.575496i
$39$	−2.11154	−	3.80504i	−0.338117	−	0.609294i
$40$	0.989821	+	0.142315i	0.156505	+	0.0225020i
$41$	−5.49265	+	2.50841i	−0.857808	+	0.391748i	−0.795241	−	0.606293i	$-0.792656\pi$
$41$	−5.49265	+	2.50841i	−0.857808	+	0.391748i	−0.0625665	+	0.998041i	$0.519929\pi$
$42$	−0.229506	+	0.0873897i	−0.0354136	+	0.0134845i
$43$	0.0168318	+	0.0261909i	0.00256683	+	0.00399407i	0.842535	−	0.538642i	$-0.181063\pi$
$43$	0.0168318	+	0.0261909i	0.00256683	+	0.00399407i	−0.839968	+	0.542636i	$0.817426\pi$
$44$	2.41826	−	2.79082i	0.364566	−	0.420732i
$45$	−2.71164	+	1.28337i	−0.404227	+	0.191313i
$46$	−1.03938	+	4.68185i	−0.153249	+	0.690301i
$47$			6.32537i			0.922650i	0.887231	+	0.461325i	$0.152626\pi$
$47$			6.32537i			0.922650i	−0.887231	+	0.461325i	$0.847374\pi$
$48$	1.52581	+	0.819692i	0.220232	+	0.118312i
$49$	5.87186	−	3.77362i	0.838838	−	0.539088i
$50$	0.989821	−	0.142315i	0.139982	−	0.0201264i
$51$	−3.27888	+	2.48963i	−0.459135	+	0.348617i
$52$	−0.357556	+	2.48686i	−0.0495841	+	0.344865i
$53$	−8.44483	+	2.47963i	−1.15999	+	0.340603i	−0.804427	−	0.594051i	$-0.797528\pi$
$53$	−8.44483	+	2.47963i	−1.15999	+	0.340603i	−0.355559	+	0.934654i	$0.615710\pi$
$54$	−5.17424	+	0.476690i	−0.704125	+	0.0648693i
$55$	1.53404	−	3.35907i	0.206850	−	0.452937i
$56$	0.136043	+	0.0399458i	0.0181795	+	0.00533799i
$57$	9.14475	+	6.74881i	1.21125	+	0.893902i
$58$	2.53084	+	2.92074i	0.332315	+	0.383512i
$59$	−3.12347	+	10.6376i	−0.406641	+	1.38489i	0.460866	+	0.887470i	$0.347539\pi$
$59$	−3.12347	+	10.6376i	−0.406641	+	1.38489i	−0.867508	+	0.497424i	$0.834279\pi$
$60$	1.69494	+	0.356618i	0.218816	+	0.0460392i
$61$	−3.28734	+	5.11521i	−0.420901	+	0.654935i	−0.985352	−	0.170531i	$-0.945452\pi$
$61$	−3.28734	+	5.11521i	−0.420901	+	0.654935i	0.564451	+	0.825467i	$0.309088\pi$
$62$	1.63366	+	5.56372i	0.207475	+	0.706594i
$63$	−0.406456	+	0.125395i	−0.0512086	+	0.0157983i
$64$	−0.415415	−	0.909632i	−0.0519269	−	0.113704i
$65$	0.357556	+	2.48686i	0.0443494	+	0.308457i
$66$	4.49175	−	4.55347i	0.552897	−	0.560493i
$67$	−3.90499	−	3.38369i	−0.477070	−	0.413384i	0.382851	−	0.923810i	$-0.374942\pi$
$67$	−3.90499	−	3.38369i	−0.477070	−	0.413384i	−0.859922	+	0.510426i	$0.829488\pi$
$68$	2.37692			0.288244
$69$	−2.31982	+	7.97612i	−0.279273	+	0.960212i
$70$	0.141786			0.0169467
$71$	−11.2888	−	9.78184i	−1.33974	−	1.16089i	−0.973062	−	0.230542i	$-0.925950\pi$
$71$	−11.2888	−	9.78184i	−1.33974	−	1.16089i	−0.366677	−	0.930348i	$-0.619504\pi$
$72$	2.54566	+	1.58733i	0.300009	+	0.187069i
$73$	−1.26091	−	8.76982i	−0.147578	−	1.02643i	−0.920168	−	0.391524i	$-0.871948\pi$
$73$	−1.26091	−	8.76982i	−0.147578	−	1.02643i	0.772589	−	0.634906i	$-0.218961\pi$
$74$	−0.257970	−	0.564876i	−0.0299884	−	0.0656655i
$75$	1.72675	−	0.135347i	0.199388	−	0.0156286i
$76$	−1.84868	−	6.29603i	−0.212058	−	0.722205i
$77$	0.283072	−	0.440469i	0.0322591	−	0.0501961i
$78$	−0.895978	+	4.25842i	−0.101450	+	0.482171i
$79$	−4.50080	+	15.3283i	−0.506380	+	1.72457i	0.167630	+	0.985850i	$0.446389\pi$
$79$	−4.50080	+	15.3283i	−0.506380	+	1.72457i	−0.674010	+	0.738722i	$0.735430\pi$
$80$	−0.654861	−	0.755750i	−0.0732157	−	0.0844954i
$81$	−8.99665	+	0.245589i	−0.999628	+	0.0272877i
$82$	5.79373	+	1.70119i	0.639810	+	0.187865i
$83$	0.284540	−	0.623056i	0.0312323	−	0.0683892i	−0.893373	−	0.449316i	$-0.851668\pi$
$83$	0.284540	−	0.623056i	0.0312323	−	0.0683892i	0.924605	+	0.380927i	$0.124395\pi$
$84$	0.230677	+	0.0842500i	0.0251690	+	0.00919242i
$85$	2.28064	−	0.669656i	0.247370	−	0.0726344i
$86$	0.00443071	−	0.0308163i	0.000477776	−	0.00332300i
$87$	4.04794	+	5.33121i	0.433985	+	0.571566i
$88$	−3.65520	+	0.525538i	−0.389645	+	0.0560225i
$89$	5.96178	−	3.83140i	0.631947	−	0.406128i	−0.185083	−	0.982723i	$-0.559255\pi$
$89$	5.96178	−	3.83140i	0.631947	−	0.406128i	0.817030	+	0.576595i	$0.195619\pi$
$90$	2.88974	+	0.805842i	0.304606	+	0.0849432i
$91$			0.356228i			0.0373429i
$92$	3.85147	−	2.85765i	0.401544	−	0.297931i
$93$	2.20180	+	9.79916i	0.228316	+	1.01613i
$94$	4.14224	−	4.78040i	0.427239	−	0.493060i
$95$	−3.54760	−	5.52017i	−0.363976	−	0.566357i
$96$	−0.616348	−	1.61868i	−0.0629057	−	0.165206i
$97$	10.3676	−	4.73474i	1.05267	−	0.480740i	0.187528	−	0.982259i	$-0.439952\pi$
$97$	10.3676	−	4.73474i	1.05267	−	0.480740i	0.865147	+	0.501519i	$0.167225\pi$
$98$	−6.90885	−	0.993343i	−0.697899	−	0.100343i
$99$	8.27269	−	7.36834i	0.831436	−	0.740546i
$100$	−0.841254	−	0.540641i	−0.0841254	−	0.0540641i
$101$	−10.7083	−	4.89031i	−1.06551	−	0.486604i	−0.196047	−	0.980594i	$-0.562811\pi$
$101$	−10.7083	−	4.89031i	−1.06551	−	0.486604i	−0.869467	+	0.493990i	$0.835538\pi$
$102$	4.10837	+	0.265676i	0.406789	+	0.0263058i
$103$	6.94726	−	6.01983i	0.684533	−	0.593152i	−0.241587	−	0.970379i	$-0.577668\pi$
$103$	6.94726	−	6.01983i	0.684533	−	0.593152i	0.926121	+	0.377228i	$0.123123\pi$
$104$	1.89877	−	1.64529i	0.186190	−	0.161334i
$105$	0.245069	+	0.0158479i	0.0239163	+	0.00154660i
$106$	8.00599	+	3.65621i	0.777610	+	0.355123i
$107$	0.171173	+	0.110006i	0.0165479	+	0.0106347i	0.548889	−	0.835895i	$-0.315051\pi$
$107$	0.171173	+	0.110006i	0.0165479	+	0.0106347i	−0.532341	+	0.846530i	$0.678687\pi$
$108$	4.22260	+	3.02815i	0.406319	+	0.291384i
$109$	6.06894	+	0.872582i	0.581299	+	0.0835782i	0.426691	−	0.904398i	$-0.359679\pi$
$109$	6.06894	+	0.872582i	0.581299	+	0.0835782i	0.154609	+	0.987976i	$0.450588\pi$
$110$	−3.35907	+	1.53404i	−0.320275	+	0.146265i
$111$	−0.382748	−	1.00519i	−0.0363289	−	0.0954083i
$112$	−0.0766555	−	0.119278i	−0.00724327	−	0.0112707i
$113$	−0.964427	+	1.11301i	−0.0907256	+	0.104703i	−0.799297	−	0.600936i	$-0.794795\pi$
$113$	−0.964427	+	1.11301i	−0.0907256	+	0.104703i	0.708571	+	0.705639i	$0.249340\pi$
$114$	−2.49161	−	11.0890i	−0.233361	−	1.03858i
$115$	2.89037	−	3.82698i	0.269528	−	0.356868i
$116$		−	3.86470i		−	0.358828i
$117$	−2.02462	+	7.26028i	−0.187176	+	0.671213i
$118$	9.32669	−	5.99390i	0.858591	−	0.551783i
$119$	0.333585	−	0.0479623i	0.0305797	−	0.00439669i
$120$	−1.04742	−	1.37946i	−0.0956155	−	0.125927i
$121$	−0.375234	+	2.60981i	−0.0341122	+	0.237255i
$122$	5.83416	−	1.71306i	0.528200	−	0.155093i
$123$	9.82396	+	3.58799i	0.885797	+	0.323518i
$124$	2.40883	−	5.27460i	0.216319	−	0.473673i
$125$	−0.959493	−	0.281733i	−0.0858197	−	0.0251989i
$126$	0.389295	+	0.171405i	0.0346812	+	0.0152699i
$127$	−14.4873	−	16.7193i	−1.28554	−	1.48359i	−0.787321	−	0.616543i	$-0.788533\pi$
$127$	−14.4873	−	16.7193i	−1.28554	−	1.48359i	−0.498220	−	0.867051i	$-0.666013\pi$
$128$	−0.281733	+	0.959493i	−0.0249019	+	0.0848080i
$129$	0.0111026	−	0.0527688i	0.000977533	−	0.00464604i
$130$	1.35832	−	2.11359i	0.119133	−	0.185374i
$131$	−5.28112	−	17.9859i	−0.461414	−	1.57143i	−0.781413	−	0.624014i	$-0.785501\pi$
$131$	−5.28112	−	17.9859i	−0.461414	−	1.57143i	0.319999	−	0.947418i	$-0.396317\pi$
$132$	−6.37653	+	0.499809i	−0.555006	+	0.0435028i
$133$	−0.386493	−	0.846302i	−0.0335132	−	0.0733837i
$134$	0.735347	+	5.11445i	0.0635243	+	0.441821i
$135$	4.90468	+	1.71584i	0.422128	+	0.147676i
$136$	−1.79636	−	1.55655i	−0.154036	−	0.133473i
$137$	−4.00237			−0.341946			−0.170973	−	0.985276i	$-0.554691\pi$
$137$	−4.00237			−0.341946			−0.170973	+	0.985276i	$0.554691\pi$
$138$	6.97645	−	4.50879i	0.593875	−	0.383814i
$139$	7.87451			0.667908			0.333954	−	0.942589i	$-0.391617\pi$
$139$	7.87451			0.667908			0.333954	+	0.942589i	$0.391617\pi$
$140$	−0.107155	−	0.0928503i	−0.00905625	−	0.00784729i
$141$	7.69393	−	7.79964i	0.647946	−	0.656848i
$142$	2.12580	+	14.7852i	0.178393	+	1.24075i
$143$	−3.85416	−	8.43944i	−0.322301	−	0.705741i
$144$	−0.884396	−	2.86668i	−0.0736997	−	0.238890i
$145$	−1.08881	−	3.70815i	−0.0904208	−	0.307945i
$146$	−4.79008	+	7.45351i	−0.396430	+	0.616857i
$147$	−11.8305	−	2.48916i	−0.975764	−	0.205302i
$148$	−0.174954	+	0.595839i	−0.0143811	+	0.0489777i
$149$	7.39422	+	8.53338i	0.605758	+	0.699082i	0.972938	−	0.231068i	$-0.0742220\pi$
$149$	7.39422	+	8.53338i	0.605758	+	0.699082i	−0.367180	+	0.930150i	$0.619677\pi$
$150$	−1.39363	−	1.02849i	−0.113789	−	0.0839763i
$151$	16.7304	+	4.91248i	1.36150	+	0.399772i	0.879291	−	0.476284i	$-0.158017\pi$
$151$	16.7304	+	4.91248i	1.36150	+	0.399772i	0.482208	+	0.876057i	$0.339835\pi$
$152$	−2.72588	+	5.96885i	−0.221098	+	0.484138i
$153$	7.07138	+	0.918410i	0.571687	+	0.0742490i
$154$	−0.502378	+	0.147511i	−0.0404827	+	0.0118868i
$155$	0.825228	−	5.73959i	0.0662839	−	0.461015i
$156$	3.46581	−	2.63156i	0.277487	−	0.210693i
$157$	−18.1398	+	2.60810i	−1.44771	+	0.208149i	−0.820922	−	0.571040i	$-0.806540\pi$
$157$	−18.1398	+	2.60810i	−1.44771	+	0.208149i	−0.626789	+	0.779189i	$0.715631\pi$
$158$	13.4394	−	8.63698i	1.06918	−	0.687121i
$159$	13.4292	+	7.21440i	1.06501	+	0.572139i
$160$			1.00000i			0.0790569i
$161$	0.482865	−	0.478768i	0.0380551	−	0.0377322i
$162$	6.96004	+	5.70595i	0.546832	+	0.448302i
$163$	3.42509	−	3.95277i	0.268274	−	0.309605i	−0.605588	−	0.795778i	$-0.707062\pi$
$163$	3.42509	−	3.95277i	0.268274	−	0.309605i	0.873862	+	0.486173i	$0.161608\pi$
$164$	−3.26456	−	5.07976i	−0.254920	−	0.396663i
$165$	−5.97742	+	2.27604i	−0.465342	+	0.177189i
$166$	−0.623056	+	0.284540i	−0.0483585	+	0.0220846i
$167$	17.4627	+	2.51076i	1.35131	+	0.194289i	0.779656	−	0.626208i	$-0.215394\pi$
$167$	17.4627	+	2.51076i	1.35131	+	0.194289i	0.571651	+	0.820497i	$0.306303\pi$
$168$	−0.119162	−	0.214733i	−0.00919358	−	0.0165670i
$169$	−5.62605	−	3.61564i	−0.432773	−	0.278126i
$170$	−2.16212	−	0.987409i	−0.165827	−	0.0757308i
$171$	−3.06716	−	19.4451i	−0.234551	−	1.48700i
$172$	−0.0235289	+	0.0203879i	−0.00179406	+	0.00155456i
$173$	−6.66705	+	5.77703i	−0.506886	+	0.439219i	−0.870382	−	0.492376i	$-0.836128\pi$
$173$	−6.66705	+	5.77703i	−0.506886	+	0.439219i	0.363496	+	0.931596i	$0.381583\pi$
$174$	0.431969	−	6.67990i	0.0327475	−	0.506402i
$175$	−0.128973	−	0.0589002i	−0.00974948	−	0.00445244i
$176$	3.10657	+	1.99647i	0.234166	+	0.150490i
$177$	16.7906	−	9.31762i	1.26206	−	0.700356i
$178$	−7.01465	−	1.00855i	−0.525770	−	0.0755943i
$179$	10.1456	−	4.63335i	0.758320	−	0.346313i	0.00155360	−	0.999999i	$-0.499505\pi$
$179$	10.1456	−	4.63335i	0.758320	−	0.346313i	0.756766	+	0.653686i	$0.226778\pi$
$180$	−1.65621	−	2.50139i	−0.123446	−	0.186443i
$181$	−3.61357	−	5.62282i	−0.268594	−	0.417941i	0.680589	−	0.732666i	$-0.261724\pi$
$181$	−3.61357	−	5.62282i	−0.268594	−	0.417941i	−0.949183	+	0.314725i	$0.898088\pi$
$182$	0.233280	−	0.269220i	0.0172919	−	0.0199559i
$183$	10.2755	−	2.30883i	0.759585	−	0.170673i
$184$	−4.78211	−	0.362508i	−0.352542	−	0.0267244i
$185$			0.620994i			0.0456564i
$186$	4.75308	−	8.84759i	0.348512	−	0.648737i
$187$	−7.38407	+	4.74545i	−0.539977	+	0.347022i
$188$	−6.26099	+	0.900194i	−0.456630	+	0.0656534i
$189$	0.653716	+	0.339775i	0.0475508	+	0.0247150i
$190$	−0.933846	+	6.49504i	−0.0677483	+	0.471200i
$191$	3.90367	−	1.14622i	0.282459	−	0.0829375i	−0.137434	−	0.990511i	$-0.543886\pi$
$191$	3.90367	−	1.14622i	0.282459	−	0.0829375i	0.419894	+	0.907573i	$0.362067\pi$
$192$	−0.594203	+	1.62694i	−0.0428829	+	0.117414i
$193$	6.50795	−	14.2504i	0.468453	−	1.02577i	−0.517026	−	0.855970i	$-0.672961\pi$
$193$	6.50795	−	14.2504i	0.468453	−	1.02577i	0.985479	−	0.169799i	$-0.0543118\pi$
$194$	−10.9359	−	3.21108i	−0.785155	−	0.230542i
$195$	2.58402	−	3.50139i	0.185046	−	0.250740i
$196$	4.57086	+	5.27505i	0.326490	+	0.376790i
$197$	−4.86308	+	16.5621i	−0.346480	+	1.18000i	0.583414	+	0.812175i	$0.301716\pi$
$197$	−4.86308	+	16.5621i	−0.346480	+	1.18000i	−0.929894	+	0.367827i	$0.880102\pi$
$198$	−11.0773	+	0.151165i	−0.787231	+	0.0107429i
$199$	2.59104	−	4.03174i	0.183674	−	0.285803i	−0.737190	−	0.675685i	$-0.763848\pi$
$199$	2.59104	−	4.03174i	0.183674	−	0.285803i	0.920865	+	0.389882i	$0.127484\pi$
$200$	0.281733	+	0.959493i	0.0199215	+	0.0678464i
$201$	0.699346	+	8.92221i	0.0493280	+	0.629324i
$202$	4.89031	+	10.7083i	0.344081	+	0.753433i
$203$	−0.0779830	−	0.542384i	−0.00547334	−	0.0380679i
$204$	−2.93092	−	2.89119i	−0.205205	−	0.202424i
$205$	−4.56346	−	3.95426i	−0.318726	−	0.276177i
$206$	−9.19254			−0.640474
$207$	12.5623	−	7.01340i	0.873143	−	0.487465i
$208$	−2.51243			−0.174206
$209$	18.3129	+	15.8682i	1.26673	+	1.09763i
$210$	−0.174833	−	0.172463i	−0.0120646	−	0.0119011i
$211$	0.449943	+	3.12942i	0.0309753	+	0.215438i	0.999430	−	0.0337504i	$-0.0107451\pi$
$211$	0.449943	+	3.12942i	0.0309753	+	0.215438i	−0.968455	+	0.249189i	$0.919836\pi$
$212$	−3.65621	−	8.00599i	−0.251110	−	0.549853i
$213$	2.02172	+	25.7930i	0.138526	+	1.76731i
$214$	−0.0573253	−	0.195232i	−0.00391867	−	0.0133458i
$215$	−0.0168318	+	0.0261909i	−0.00114792	+	0.00178620i
$216$	−1.20821	−	5.05373i	−0.0822082	−	0.343863i
$217$	0.231630	−	0.788860i	0.0157241	−	0.0535513i
$218$	−4.01518	−	4.63377i	−0.271942	−	0.313838i
$219$	−9.11247	+	12.3475i	−0.615764	+	0.834370i
$220$	3.54320	+	1.04038i	0.238882	+	0.0701422i
$221$	2.48080	−	5.43219i	0.166876	−	0.365408i
$222$	−0.368997	+	1.01032i	−0.0247654	+	0.0678081i
$223$	2.41441	−	0.708936i	0.161681	−	0.0474738i	−0.199890	−	0.979818i	$-0.564059\pi$
$223$	2.41441	−	0.708936i	0.161681	−	0.0474738i	0.361571	+	0.932344i	$0.382240\pi$
$224$	−0.0201783	+	0.140343i	−0.00134822	+	0.00937708i
$225$	−2.29384	−	1.93346i	−0.152923	−	0.128897i
$226$	1.45773	−	0.209590i	0.0969668	−	0.0139417i
$227$	10.4223	−	6.69800i	0.691752	−	0.444562i	−0.146957	−	0.989143i	$-0.546948\pi$
$227$	10.4223	−	6.69800i	0.691752	−	0.444562i	0.838708	+	0.544581i	$0.183311\pi$
$228$	−5.37869	+	10.0121i	−0.356212	+	0.663069i
$229$			7.76551i			0.513159i	0.966523	+	0.256580i	$0.0825956\pi$
$229$			7.76551i			0.513159i	−0.966523	+	0.256580i	$0.917404\pi$
$230$	−4.69053	+	0.999453i	−0.309285	+	0.0659020i
$231$	−0.884817	+	0.198812i	−0.0582167	+	0.0130809i
$232$	−2.53084	+	2.92074i	−0.166158	+	0.191756i
$233$	5.54285	+	8.62484i	0.363124	+	0.565032i	0.973959	−	0.226726i	$-0.0728022\pi$
$233$	5.54285	+	8.62484i	0.363124	+	0.565032i	−0.610834	+	0.791758i	$0.709166\pi$
$234$	6.28458	−	4.16111i	0.410836	−	0.272020i
$235$	−5.75376	+	2.62765i	−0.375334	+	0.171409i
$236$	−10.9738	−	1.57780i	−0.714334	−	0.102706i
$237$	24.1946	−	13.4263i	1.57161	−	0.872135i
$238$	−0.283515	−	0.182204i	−0.0183776	−	0.0118105i
$239$	8.41908	+	3.84487i	0.544585	+	0.248704i	0.668659	−	0.743569i	$-0.266869\pi$
$239$	8.41908	+	3.84487i	0.544585	+	0.248704i	−0.124074	+	0.992273i	$0.539596\pi$
$240$	−0.111773	+	1.72844i	−0.00721492	+	0.111570i
$241$	−3.65993	+	3.17135i	−0.235757	+	0.204285i	−0.764724	−	0.644358i	$-0.777125\pi$
$241$	−3.65993	+	3.17135i	−0.235757	+	0.204285i	0.528967	+	0.848642i	$0.322579\pi$
$242$	1.99265	−	1.72664i	0.128092	−	0.110992i
$243$	11.3922	+	10.6403i	0.730813	+	0.682578i
$244$	−5.53098	−	2.52591i	−0.354085	−	0.161705i
$245$	5.87186	+	3.77362i	0.375140	+	0.241088i
$246$	−5.07482	−	9.14495i	−0.323559	−	0.583061i
$247$	−16.3183	−	2.34622i	−1.03831	−	0.149287i
$248$	−5.27460	+	2.40883i	−0.334937	+	0.152961i
$249$	−1.10872	+	0.422170i	−0.0702622	+	0.0267539i
$250$	0.540641	+	0.841254i	0.0341931	+	0.0532055i
$251$	−19.1887	+	22.1449i	−1.21118	+	1.39778i	−0.317991	+	0.948094i	$0.603008\pi$
$251$	−19.1887	+	22.1449i	−1.21118	+	1.39778i	−0.893189	+	0.449682i	$0.851537\pi$
$252$	−0.181964	−	0.384473i	−0.0114626	−	0.0242195i
$253$	−6.25964	+	16.5668i	−0.393540	+	1.04155i
$254$			22.1227i			1.38810i
$255$	−3.62674	−	1.94835i	−0.227115	−	0.122010i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−0.243446	+	0.0350022i	−0.0151857	+	0.00218338i	−0.149904	−	0.988701i	$-0.547896\pi$
$257$	−0.243446	+	0.0350022i	−0.0151857	+	0.00218338i	0.134718	+	0.990884i	$0.456987\pi$
$258$	−0.0429471	+	0.0326093i	−0.00267377	+	0.00203017i
$259$	−0.0125306	+	0.0871523i	−0.000778614	+	0.00541538i
$260$	−2.41066	+	0.707833i	−0.149503	+	0.0438980i
$261$	1.49326	−	11.4975i	0.0924308	−	0.711679i
$262$	−7.78702	+	17.0512i	−0.481084	+	1.05343i
$263$	−17.8213	−	5.23280i	−1.09891	−	0.322668i	−0.318489	−	0.947927i	$-0.603175\pi$
$263$	−17.8213	−	5.23280i	−1.09891	−	0.322668i	−0.780418	+	0.625259i	$0.784993\pi$
$264$	5.14636	+	3.79801i	0.316737	+	0.233751i
$265$	−5.76366	−	6.65161i	−0.354059	−	0.408605i
$266$	−0.262118	+	0.892692i	−0.0160715	+	0.0547345i
$267$	−12.0117	−	2.52727i	−0.735102	−	0.154667i
$268$	2.79351	−	4.34679i	0.170641	−	0.265523i
$269$	−0.643168	−	2.19043i	−0.0392146	−	0.133553i	0.937559	−	0.347826i	$-0.113080\pi$
$269$	−0.643168	−	2.19043i	−0.0392146	−	0.133553i	−0.976774	+	0.214273i	$0.931262\pi$
$270$	−2.58307	−	4.50863i	−0.157201	−	0.274387i
$271$	0.447630	+	0.980173i	0.0271916	+	0.0595413i	0.922740	−	0.385422i	$-0.125944\pi$
$271$	0.447630	+	0.980173i	0.0271916	+	0.0595413i	−0.895549	+	0.444963i	$0.853217\pi$
$272$	0.338271	+	2.35273i	0.0205107	+	0.142655i
$273$	0.433302	−	0.439256i	0.0262246	−	0.0265850i
$274$	3.02479	+	2.62100i	0.182734	+	0.158340i
$275$	3.69278			0.222683
$276$	−8.22508	−	1.16108i	−0.495091	−	0.0698890i
$277$	16.7974			1.00926			0.504630	−	0.863335i	$-0.331629\pi$
$277$	16.7974			1.00926			0.504630	+	0.863335i	$0.331629\pi$
$278$	−5.95116	−	5.15671i	−0.356927	−	0.309279i
$279$	9.20433	−	14.7613i	0.551049	−	0.883734i
$280$	0.0201783	+	0.140343i	0.00120588	+	0.00838711i
$281$	5.50246	+	12.0487i	0.328249	+	0.718765i	0.999753	−	0.0222361i	$-0.00707854\pi$
$281$	5.50246	+	12.0487i	0.328249	+	0.718765i	−0.671504	+	0.741001i	$0.734351\pi$
$282$	−10.9224	+	0.856123i	−0.650417	+	0.0509814i
$283$	−4.64699	−	15.8262i	−0.276235	−	0.940769i	−0.974398	−	0.224830i	$-0.927817\pi$
$283$	−4.64699	−	15.8262i	−0.276235	−	0.940769i	0.698163	−	0.715939i	$-0.254001\pi$
$284$	8.07570	−	12.5660i	0.479205	−	0.745657i
$285$	−2.34007	+	11.1219i	−0.138614	+	0.658806i
$286$	−2.61388	+	8.90204i	−0.154562	+	0.526389i
$287$	−0.560660	−	0.647036i	−0.0330947	−	0.0381933i
$288$	−1.20889	+	2.74565i	−0.0712347	+	0.161789i
$289$	10.8905	+	3.19773i	0.640616	+	0.188102i
$290$	−1.60545	+	3.51545i	−0.0942754	+	0.206434i
$291$	−18.5432	−	6.77251i	−1.08702	−	0.397011i
$292$	8.50111	−	2.49615i	0.497490	−	0.146076i
$293$	1.93799	−	13.4790i	0.113219	−	0.787454i	−0.851535	−	0.524298i	$-0.824328\pi$
$293$	1.93799	−	13.4790i	0.113219	−	0.787454i	0.964753	−	0.263156i	$-0.0847633\pi$
$294$	7.31085	+	9.62852i	0.426378	+	0.561546i
$295$	−10.9738	+	1.57780i	−0.638920	+	0.0918628i
$296$	0.522413	−	0.335735i	0.0303647	−	0.0195142i
$297$	−19.1634	−	0.976865i	−1.11197	−	0.0566834i
$298$		−	11.2913i		−	0.654086i
$299$	−2.51106	−	11.7846i	−0.145218	−	0.681523i
$300$	0.379713	+	1.68992i	0.0219227	+	0.0975674i
$301$	−0.00289072	+	0.00333607i	−0.000166619	+	0.000192288i
$302$	−9.42699	−	14.6687i	−0.542462	−	0.844088i
$303$	7.25572	+	19.0552i	0.416830	+	1.09470i
$304$	5.96885	−	2.72588i	0.342337	−	0.156340i
$305$	−6.01857	−	0.865340i	−0.344622	−	0.0495492i
$306$	−4.74276	−	5.32485i	−0.271125	−	0.304402i
$307$	11.3528	+	7.29603i	0.647941	+	0.416406i	0.822913	−	0.568167i	$-0.192347\pi$
$307$	11.3528	+	7.29603i	0.647941	+	0.416406i	−0.174972	+	0.984573i	$0.555984\pi$
$308$	0.476271	+	0.217506i	0.0271381	+	0.0123935i
$309$	−15.8888	−	1.02748i	−0.903880	−	0.0584512i
$310$	−4.38230	+	3.79728i	−0.248898	+	0.215671i
$311$	23.5507	−	20.4068i	1.33544	−	1.15716i	0.360986	−	0.932571i	$-0.382440\pi$
$311$	23.5507	−	20.4068i	1.33544	−	1.15716i	0.974453	−	0.224593i	$-0.0721052\pi$
$312$	−4.34259	−	0.280822i	−0.245851	−	0.0158984i
$313$	−22.7704	−	10.3989i	−1.28706	−	0.587781i	−0.349935	−	0.936774i	$-0.613796\pi$
$313$	−22.7704	−	10.3989i	−1.28706	−	0.587781i	−0.937125	+	0.348994i	$0.886524\pi$
$314$	15.4171	+	9.90795i	0.870035	+	0.559138i
$315$	−0.282912	−	0.317634i	−0.0159403	−	0.0178967i
$316$	−15.8128	−	2.27354i	−0.889542	−	0.127897i
$317$	19.7230	−	9.00719i	1.10775	−	0.505894i	0.224351	−	0.974508i	$-0.427974\pi$
$317$	19.7230	−	9.00719i	1.10775	−	0.505894i	0.883403	+	0.468614i	$0.155247\pi$
$318$	−5.42469	−	14.2465i	−0.304202	−	0.798906i
$319$	7.71575	+	12.0059i	0.431999	+	0.672204i
$320$	0.654861	−	0.755750i	0.0366078	−	0.0422477i
$321$	−0.0772617	−	0.343854i	−0.00431233	−	0.0191921i
$322$	−0.678452	+	0.0456194i	−0.0378086	+	0.00254227i
$323$			15.5970i			0.867839i
$324$	−1.52345	−	8.87012i	−0.0846359	−	0.492785i
$325$	−2.11359	+	1.35832i	−0.117241	+	0.0753462i
$326$	−5.17702	+	0.744344i	−0.286729	+	0.0412254i
$327$	−6.42207	−	8.45798i	−0.355141	−	0.467727i
$328$	−0.859343	+	5.97686i	−0.0474493	+	0.330017i
$329$	−0.860523	+	0.252672i	−0.0474422	+	0.0139303i
$330$	6.00792	+	2.19426i	0.330725	+	0.120790i
$331$	−11.8404	+	25.9268i	−0.650806	+	1.42507i	0.240041	+	0.970763i	$0.422839\pi$
$331$	−11.8404	+	25.9268i	−0.650806	+	1.42507i	−0.890847	+	0.454304i	$0.849888\pi$
$332$	0.657208	+	0.192974i	0.0360690	+	0.0105908i
$333$	−0.750715	+	1.70503i	−0.0411389	+	0.0934351i
$334$	−11.5533	−	13.3332i	−0.632166	−	0.729559i
$335$	1.45572	−	4.95774i	0.0795347	−	0.270870i
$336$	−0.0505636	+	0.240320i	−0.00275847	+	0.0131105i
$337$	−8.42888	+	13.1156i	−0.459151	+	0.714452i	−0.991216	−	0.132251i	$-0.957780\pi$
$337$	−8.42888	+	13.1156i	−0.459151	+	0.714452i	0.532066	+	0.846703i	$0.321416\pi$
$338$	1.88414	+	6.41679i	0.102484	+	0.349028i
$339$	2.54303	−	0.199329i	0.138118	−	0.0108261i
$340$	0.987409	+	2.16212i	0.0535498	+	0.117258i
$341$	3.04739	+	21.1950i	0.165025	+	1.14778i
$342$	−10.4158	+	16.7042i	−0.563223	+	0.903259i
$343$	1.49802	+	1.29804i	0.0808853	+	0.0700875i
$344$	0.0311331			0.00167859
$345$	−8.21902	+	1.20322i	−0.442497	+	0.0647792i
$346$	8.82177			0.474261
$347$	5.63893	+	4.88616i	0.302714	+	0.262303i	0.792950	−	0.609287i	$-0.208544\pi$
$347$	5.63893	+	4.88616i	0.302714	+	0.262303i	−0.490236	+	0.871590i	$0.663090\pi$
$348$	−4.70086	+	4.76545i	−0.251993	+	0.255455i
$349$	−0.771285	−	5.36440i	−0.0412859	−	0.287150i	−0.999996	−	0.00276523i	$-0.999120\pi$
$349$	−0.771285	−	5.36440i	−0.0412859	−	0.287150i	0.958710	−	0.284385i	$-0.0917893\pi$
$350$	0.0589002	+	0.128973i	0.00314835	+	0.00689392i
$351$	11.3276	−	6.48978i	0.604624	−	0.346399i
$352$	−1.04038	−	3.54320i	−0.0554523	−	0.188853i
$353$	12.5256	−	19.4903i	0.666673	−	1.03736i	−0.328990	−	0.944333i	$-0.606708\pi$
$353$	12.5256	−	19.4903i	0.666673	−	1.03736i	0.995663	−	0.0930300i	$-0.0296552\pi$
$354$	−18.7912	−	3.95370i	−0.998742	−	0.210137i
$355$	4.20832	−	14.3322i	0.223354	−	0.760675i
$356$	4.64085	+	5.35583i	0.245965	+	0.283858i
$357$	−0.469674	−	0.346618i	−0.0248578	−	0.0183450i
$358$	−10.7018	−	3.14232i	−0.565605	−	0.166077i
$359$	−4.58179	+	10.0327i	−0.241818	+	0.529507i	−0.991159	−	0.132677i	$-0.957643\pi$
$359$	−4.58179	+	10.0327i	−0.241818	+	0.529507i	0.749342	+	0.662183i	$0.230370\pi$
$360$	−0.386386	+	2.97501i	−0.0203643	+	0.156797i
$361$	23.0832	−	6.77783i	1.21490	−	0.356728i
$362$	−0.951212	+	6.61582i	−0.0499946	+	0.347720i
$363$	3.63716	−	2.76167i	0.190901	−	0.144950i
$364$	−0.352603	+	0.0506966i	−0.0184814	+	0.00265722i
$365$	7.45351	−	4.79008i	0.390135	−	0.250724i
$366$	−9.27764	−	4.98411i	−0.484950	−	0.260523i
$367$			22.1944i			1.15854i	0.815136	+	0.579269i	$0.196662\pi$
$367$			22.1944i			1.15854i	−0.815136	+	0.579269i	$0.803338\pi$
$368$	3.37669	+	3.40558i	0.176022	+	0.177528i
$369$	−7.74937	−	16.3737i	−0.403416	−	0.852383i
$370$	0.406665	−	0.469316i	0.0211415	−	0.0243986i
$371$	−0.674672	−	1.04981i	−0.0350272	−	0.0545034i
$372$	−9.38607	+	3.57396i	−0.486645	+	0.185301i
$373$	−15.8632	+	7.24448i	−0.821366	+	0.375105i	−0.781349	−	0.624094i	$-0.785468\pi$
$373$	−15.8632	+	7.24448i	−0.821366	+	0.375105i	−0.0400163	+	0.999199i	$0.512741\pi$
$374$	8.68812	+	1.24916i	0.449252	+	0.0645927i
$375$	0.840436	+	1.51449i	0.0433999	+	0.0782077i
$376$	5.32124	+	3.41975i	0.274422	+	0.176360i
$377$	−8.83233	−	4.03359i	−0.454888	−	0.207740i
$378$	−0.271540	−	0.684878i	−0.0139665	−	0.0352263i
$379$	−2.22214	+	1.92549i	−0.114144	+	0.0989060i	−0.710063	−	0.704139i	$-0.751333\pi$
$379$	−2.22214	+	1.92549i	−0.114144	+	0.0989060i	0.595919	+	0.803045i	$0.296788\pi$
$380$	4.95910	−	4.29709i	0.254397	−	0.220436i
$381$	−2.47273	+	38.2378i	−0.126682	+	1.95898i
$382$	−3.70081	−	1.69010i	−0.189350	−	0.0864732i
$383$	23.8442	+	15.3237i	1.21838	+	0.783007i	0.982042	−	0.188663i	$-0.0604155\pi$
$383$	23.8442	+	15.3237i	1.21838	+	0.783007i	0.236341	+	0.971670i	$0.424052\pi$
$384$	1.51449	−	0.840436i	0.0772858	−	0.0428883i
$385$	0.518257	+	0.0745141i	0.0264128	+	0.00379759i
$386$	−14.2504	+	6.50795i	−0.725328	+	0.331246i
$387$	−0.0778763	+	0.0515630i	−0.00395867	+	0.00262109i
$388$	6.16202	+	9.58829i	0.312829	+	0.486772i
$389$	−9.07318	+	10.4710i	−0.460028	+	0.530901i	−0.937611	−	0.347686i	$-0.886968\pi$
$389$	−9.07318	+	10.4710i	−0.460028	+	0.530901i	0.477583	+	0.878587i	$0.341513\pi$
$390$	−4.24580	+	0.954001i	−0.214994	+	0.0483077i
$391$	−10.6975	+	3.93811i	−0.540994	+	0.199159i
$392$		−	6.97990i		−	0.352538i
$393$	−15.3653	+	28.6016i	−0.775076	+	1.44276i
$394$	14.5211	−	9.33217i	0.731565	−	0.470148i
$395$	−15.8128	+	2.27354i	−0.795630	+	0.114394i
$396$	8.47067	+	7.13986i	0.425667	+	0.358791i
$397$	1.40357	−	9.76204i	0.0704431	−	0.489943i	−0.923807	−	0.382859i	$-0.874940\pi$
$397$	1.40357	−	9.76204i	0.0704431	−	0.489943i	0.994250	−	0.107084i	$-0.0341513\pi$
$398$	−4.59841	+	1.35022i	−0.230498	+	0.0676802i
$399$	−0.552834	+	1.51367i	−0.0276763	+	0.0757781i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	−9.96439	−	2.92581i	−0.497598	−	0.146108i	0.0232974	−	0.999729i	$-0.492584\pi$
$401$	−9.96439	−	2.92581i	−0.497598	−	0.146108i	−0.520895	+	0.853621i	$0.674402\pi$
$402$	5.31428	−	7.20093i	0.265052	−	0.359150i
$403$	−9.54040	−	11.0102i	−0.475241	−	0.548458i
$404$	3.31659	−	11.2953i	0.165006	−	0.561960i
$405$	−3.96074	−	8.08162i	−0.196811	−	0.401579i
$406$	−0.296250	+	0.460974i	−0.0147027	+	0.0228778i
$407$	−0.646068	−	2.20031i	−0.0320244	−	0.109065i
$408$	0.321710	+	4.10436i	0.0159270	+	0.203196i
$409$	−1.15586	−	2.53098i	−0.0571536	−	0.125149i	0.878900	−	0.477005i	$-0.158278\pi$
$409$	−1.15586	−	2.53098i	−0.0571536	−	0.125149i	−0.936054	+	0.351856i	$0.885551\pi$
$410$	0.859343	+	5.97686i	0.0424399	+	0.295176i
$411$	4.93521	+	4.86833i	0.243436	+	0.240137i
$412$	6.94726	+	6.01983i	0.342267	+	0.296576i
$413$	−1.57194			−0.0773500
$414$	−14.0868	−	2.92621i	−0.692327	−	0.143815i
$415$	0.684954			0.0336230
$416$	1.89877	+	1.64529i	0.0930948	+	0.0806671i
$417$	−9.70985	−	9.57825i	−0.475493	−	0.469049i
$418$	−3.44849	−	23.9848i	−0.168671	−	1.17313i
$419$	−4.05291	−	8.87463i	−0.197997	−	0.433554i	0.784425	−	0.620223i	$-0.212958\pi$
$419$	−4.05291	−	8.87463i	−0.197997	−	0.433554i	−0.982423	+	0.186669i	$0.940231\pi$
$420$	0.0191904	+	0.244830i	0.000936397	+	0.0119465i
$421$	−4.05609	−	13.8138i	−0.197682	−	0.673242i	−0.997347	−	0.0727960i	$-0.976808\pi$
$421$	−4.05609	−	13.8138i	−0.197682	−	0.673242i	0.799665	−	0.600446i	$-0.205010\pi$
$422$	1.70929	−	2.65971i	0.0832070	−	0.129473i
$423$	−18.9743	+	0.258932i	−0.922564	+	0.0125897i
$424$	−2.47963	+	8.44483i	−0.120421	+	0.410117i
$425$	1.55655	+	1.79636i	0.0755039	+	0.0871362i
$426$	15.3629	−	20.8170i	0.744336	−	1.00859i
$427$	−0.827204	−	0.242889i	−0.0400312	−	0.0117542i
$428$	−0.0845262	+	0.185087i	−0.00408573	+	0.00894650i
$429$	−5.51294	+	15.0945i	−0.266167	+	0.728769i
$430$	0.0298720	−	0.00877122i	0.00144056	−	0.000422986i
$431$	5.40524	−	37.5943i	0.260361	−	1.81085i	−0.269755	−	0.962929i	$-0.586943\pi$
$431$	5.40524	−	37.5943i	0.260361	−	1.81085i	0.530117	−	0.847925i	$-0.322148\pi$
$432$	−2.39639	+	4.61057i	−0.115296	+	0.221826i
$433$	−19.9101	+	2.86264i	−0.956820	+	0.137570i	−0.602998	−	0.797743i	$-0.706027\pi$
$433$	−19.9101	+	2.86264i	−0.956820	+	0.137570i	−0.353822	+	0.935313i	$0.615118\pi$
$434$	−0.691648	+	0.444495i	−0.0332002	+	0.0213365i
$435$	−3.16786	+	5.89680i	−0.151887	+	0.282730i
$436$			6.13135i			0.293639i
$437$	18.7514	+	25.2727i	0.897003	+	1.20896i
$438$	14.9727	−	3.36426i	0.715422	−	0.160750i
$439$	−15.5822	+	17.9828i	−0.743697	+	0.858273i	−0.993942	−	0.109910i	$-0.964944\pi$
$439$	−15.5822	+	17.9828i	−0.743697	+	0.858273i	0.250244	+	0.968183i	$0.419489\pi$
$440$	−1.99647	−	3.10657i	−0.0951779	−	0.148100i
$441$	11.5602	+	17.4595i	0.550484	+	0.831404i
$442$	−5.43219	+	2.48080i	−0.258383	+	0.117999i
$443$	−0.369448	−	0.0531186i	−0.0175530	−	0.00252374i	0.133533	−	0.991044i	$-0.457368\pi$
$443$	−0.369448	−	0.0531186i	−0.0175530	−	0.00252374i	−0.151086	+	0.988521i	$0.548277\pi$
$444$	0.940486	−	0.521906i	0.0446335	−	0.0247685i
$445$	5.96178	+	3.83140i	0.282615	+	0.181626i
$446$	−2.28895	−	1.04533i	−0.108385	−	0.0494976i
$447$	1.26206	−	19.5163i	0.0596934	−	0.923090i
$448$	0.107155	−	0.0928503i	0.00506260	−	0.00438677i
$449$	5.49546	−	4.76184i	0.259347	−	0.224725i	−0.515476	−	0.856904i	$-0.672385\pi$
$449$	5.49546	−	4.76184i	0.259347	−	0.224725i	0.774822	+	0.632179i	$0.217839\pi$
$450$	0.467423	+	2.96336i	0.0220346	+	0.139694i
$451$	20.2832	+	9.26301i	0.955097	+	0.436178i
$452$	−1.23893	−	0.796213i	−0.0582744	−	0.0374507i
$453$	−14.6544	−	26.4076i	−0.688525	−	1.24074i
$454$	−12.2629	−	1.76314i	−0.575526	−	0.0827482i
$455$	−0.324037	+	0.147983i	−0.0151911	+	0.00693753i
$456$	10.6215	−	4.04437i	0.497397	−	0.189395i
$457$	−7.99061	−	12.4336i	−0.373785	−	0.581621i	0.602498	−	0.798121i	$-0.294172\pi$
$457$	−7.99061	−	12.4336i	−0.373785	−	0.581621i	−0.976283	+	0.216500i	$0.930536\pi$
$458$	5.08533	−	5.86878i	0.237622	−	0.274230i
$459$	−7.60240	−	9.73381i	−0.354850	−	0.454335i
$460$	4.19937	+	2.31631i	0.195797	+	0.107998i
$461$			11.2713i			0.524956i	0.964938	+	0.262478i	$0.0845398\pi$
$461$			11.2713i			0.524956i	−0.964938	+	0.262478i	$0.915460\pi$
$462$	0.798895	+	0.429180i	0.0371680	+	0.0199673i
$463$	−10.5899	+	6.80572i	−0.492155	+	0.316289i	−0.763071	−	0.646314i	$-0.776310\pi$
$463$	−10.5899	+	6.80572i	−0.492155	+	0.316289i	0.270917	+	0.962603i	$0.412673\pi$
$464$	3.82536	−	0.550004i	0.177588	−	0.0255333i
$465$	−7.99897	+	6.07355i	−0.370943	+	0.281654i
$466$	1.45906	−	10.1480i	0.0675899	−	0.470098i
$467$	−24.8543	+	7.29789i	−1.15012	+	0.337706i	−0.800587	−	0.599217i	$-0.795479\pi$
$467$	−24.8543	+	7.29789i	−1.15012	+	0.337706i	−0.349535	+	0.936923i	$0.613661\pi$
$468$	−7.47451	−	0.970768i	−0.345510	−	0.0448738i
$469$	0.304340	−	0.666411i	0.0140531	−	0.0307720i
$470$	6.06915	+	1.78206i	0.279949	+	0.0822004i
$471$	25.5400	+	18.8485i	1.17682	+	0.868493i
$472$	7.26021	+	8.37873i	0.334178	+	0.385663i
$473$	0.0323902	−	0.110311i	0.00148930	−	0.00507210i
$474$	−27.0774	−	5.69713i	−1.24371	−	0.261678i
$475$	3.54760	−	5.52017i	0.162775	−	0.253283i
$476$	0.0949482	+	0.323364i	0.00435194	+	0.0148214i
$477$	−7.78388	−	25.2306i	−0.356399	−	1.15523i
$478$	−3.84487	−	8.41908i	−0.175860	−	0.385080i
$479$	3.25186	+	22.6172i	0.148581	+	1.03341i	0.918545	+	0.395317i	$0.129365\pi$
$479$	3.25186	+	22.6172i	0.148581	+	1.03341i	−0.769963	+	0.638088i	$0.779725\pi$
$480$	1.21636	−	1.23307i	0.0555190	−	0.0562818i
$481$	1.17912	+	1.02172i	0.0537634	+	0.0465863i
$482$	4.84279			0.220583
$483$	−1.17776	+	0.00301786i	−0.0535900	+	0.000137318i
$484$	−2.63665			−0.119848
$485$	8.61375	+	7.46386i	0.391130	+	0.338916i
$486$	−1.64175	−	15.5018i	−0.0744711	−	0.703174i
$487$	0.00640831	+	0.0445707i	0.000290388	+	0.00201969i	0.989966	−	0.141305i	$-0.0451298\pi$
$487$	0.00640831	+	0.0445707i	0.000290388	+	0.00201969i	−0.989676	+	0.143325i	$0.954221\pi$
$488$	2.52591	+	5.53098i	0.114343	+	0.250376i
$489$	−9.03137	+	0.707902i	−0.408413	+	0.0320124i
$490$	−1.96646	−	6.69716i	−0.0888358	−	0.302547i
$491$	19.1205	−	29.7520i	0.862895	−	1.34269i	−0.0755071	−	0.997145i	$-0.524058\pi$
$491$	19.1205	−	29.7520i	0.862895	−	1.34269i	0.938402	−	0.345545i	$-0.112306\pi$
$492$	−2.15337	+	10.2346i	−0.0970816	+	0.461411i
$493$	−2.58802	+	8.81398i	−0.116559	+	0.396962i
$494$	10.7961	+	12.4594i	0.485741	+	0.560575i
$495$	10.1391	+	4.46418i	0.455718	+	0.200650i
$496$	5.56372	+	1.63366i	0.249819	+	0.0733534i
$497$	0.879809	−	1.92651i	0.0394648	−	0.0864159i
$498$	1.11438	+	0.407002i	0.0499364	+	0.0182382i
$499$	−2.48688	+	0.730213i	−0.111328	+	0.0326888i	−0.336922	−	0.941533i	$-0.609386\pi$
$499$	−2.48688	+	0.730213i	−0.111328	+	0.0326888i	0.225594	+	0.974221i	$0.427568\pi$
$500$	0.142315	−	0.989821i	0.00636451	−	0.0442662i
$501$	−18.4788	−	24.3369i	−0.825573	−	1.08729i
$502$	29.0037	−	4.17010i	1.29450	−	0.186121i
$503$	26.0180	−	16.7207i	1.16008	−	0.745541i	0.188462	−	0.982080i	$-0.439650\pi$
$503$	26.0180	−	16.7207i	1.16008	−	0.745541i	0.971622	+	0.236540i	$0.0760133\pi$
$504$	−0.114257	+	0.409726i	−0.00508943	+	0.0182507i
$505$		−	11.7721i		−	0.523852i
$506$	15.5797	−	8.42118i	0.692601	−	0.374367i
$507$	2.53940	+	11.3016i	0.112779	+	0.501924i
$508$	14.4873	−	16.7193i	0.642771	−	0.741797i
$509$	−12.2439	−	19.0519i	−0.542702	−	0.844461i	0.456268	−	0.889843i	$-0.349186\pi$
$509$	−12.2439	−	19.0519i	−0.542702	−	0.844461i	−0.998970	+	0.0453817i	$0.985550\pi$
$510$	1.46501	+	3.84747i	0.0648718	+	0.170369i
$511$	1.14271	−	0.521856i	0.0505503	−	0.0230856i
$512$	−0.989821	−	0.142315i	−0.0437443	−	0.00628949i
$513$	−19.8702	+	27.7080i	−0.877291	+	1.22334i
$514$	0.206905	+	0.132970i	0.00912621	+	0.00586506i
$515$	8.36183	+	3.81872i	0.368466	+	0.168273i
$516$	0.0538118	+	0.00347985i	0.00236893	+	0.000153192i
$517$	17.6530	−	15.2964i	0.776377	−	0.672734i
$518$	0.0665426	−	0.0576595i	0.00292371	−	0.00253341i
$519$	15.2479	+	0.986036i	0.669309	+	0.0432822i
$520$	2.28539	+	1.04370i	0.100221	+	0.0457693i
$521$	31.2427	+	20.0784i	1.36877	+	0.879653i	0.998780	−	0.0493843i	$-0.0157259\pi$
$521$	31.2427	+	20.0784i	1.36877	+	0.879653i	0.369987	+	0.929037i	$0.379362\pi$
$522$	−8.65781	+	7.71137i	−0.378942	+	0.337517i
$523$	35.7237	+	5.13630i	1.56209	+	0.224595i	0.868468	−	0.495744i	$-0.165105\pi$
$523$	35.7237	+	5.13630i	1.56209	+	0.224595i	0.693622	+	0.720339i	$0.256014\pi$
$524$	17.0512	−	7.78702i	0.744885	−	0.340178i
$525$	0.0873897	+	0.229506i	0.00381400	+	0.0100165i
$526$	10.0417	+	15.6251i	0.437837	+	0.681288i
$527$	−9.02584	+	10.4164i	−0.393172	+	0.453744i
$528$	−1.40220	−	6.24050i	−0.0610228	−	0.271583i
$529$	−12.5992	+	19.2422i	−0.547789	+	0.836616i
$530$			8.80135i			0.382306i
$531$	−32.0376	−	8.93409i	−1.39031	−	0.387706i
$532$	0.782684	−	0.503001i	0.0339337	−	0.0218078i
$533$	−15.0164	+	2.15904i	−0.650434	+	0.0935184i
$534$	7.42280	+	9.77596i	0.321216	+	0.423047i
$535$	−0.0289574	+	0.201403i	−0.00125194	+	0.00870741i
$536$	−4.95774	+	1.45572i	−0.214142	+	0.0628777i
$537$	−18.1461	−	6.62748i	−0.783063	−	0.285997i
$538$	−0.948352	+	2.07660i	−0.0408864	+	0.0895286i
$539$	−24.7312	−	7.26173i	−1.06525	−	0.312785i
$540$	−1.00037	+	5.09895i	−0.0430491	+	0.219424i
$541$	4.36030	+	5.03205i	0.187464	+	0.216345i	0.841700	−	0.539945i	$-0.181555\pi$
$541$	4.36030	+	5.03205i	0.187464	+	0.216345i	−0.654236	+	0.756290i	$0.727010\pi$
$542$	0.303581	−	1.03390i	0.0130399	−	0.0444099i
$543$	−2.38358	+	11.3287i	−0.102289	+	0.486163i
$544$	1.28506	−	1.99959i	0.0550965	−	0.0857319i
$545$	1.72740	+	5.88299i	0.0739938	+	0.252000i
$546$	−0.615119	+	0.0482146i	−0.0263247	+	0.00206339i
$547$	9.21812	+	20.1849i	0.394138	+	0.863042i	0.997831	+	0.0658254i	$0.0209680\pi$
$547$	9.21812	+	20.1849i	0.394138	+	0.863042i	−0.603693	+	0.797217i	$0.706305\pi$
$548$	−0.569597	−	3.96163i	−0.0243320	−	0.169233i
$549$	−15.4788	−	9.65172i	−0.660618	−	0.411926i
$550$	−2.79082	−	2.41826i	−0.119001	−	0.103115i
$551$	25.3595			1.08035
$552$	5.45575	+	6.26377i	0.232212	+	0.266604i
$553$	−2.26510			−0.0963219
$554$	−12.6947	−	11.0000i	−0.539345	−	0.467345i
$555$	0.755352	−	0.765730i	0.0320629	−	0.0325034i
$556$	1.12066	+	7.79436i	0.0475266	+	0.330555i
$557$	−6.15217	−	13.4714i	−0.260676	−	0.570800i	0.733362	−	0.679839i	$-0.237950\pi$
$557$	−6.15217	−	13.4714i	−0.260676	−	0.570800i	−0.994038	+	0.109038i	$0.965223\pi$
$558$	−16.6227	+	5.12827i	−0.703697	+	0.217097i
$559$	0.0220371	+	0.0750514i	0.000932069	+	0.00317434i
$560$	0.0766555	−	0.119278i	0.00323929	−	0.00504043i
$561$	14.8773	+	3.13020i	0.628119	+	0.132157i
$562$	3.73174	−	12.7091i	0.157414	−	0.536103i
$563$	−3.99975	−	4.61596i	−0.168570	−	0.194540i	0.665179	−	0.746684i	$-0.268355\pi$
$563$	−3.99975	−	4.61596i	−0.168570	−	0.194540i	−0.833749	+	0.552144i	$0.813810\pi$
$564$	8.81521	+	6.50561i	0.371187	+	0.273936i
$565$	−1.41306	−	0.414913i	−0.0594481	−	0.0174555i
$566$	−6.85199	+	15.0038i	−0.288010	+	0.630655i
$567$	−0.392789	−	1.21412i	−0.0164956	−	0.0509883i
$568$	−14.3322	+	4.20832i	−0.601366	+	0.176577i
$569$	−4.82382	+	33.5504i	−0.202225	+	1.40651i	0.595437	+	0.803402i	$0.296979\pi$
$569$	−4.82382	+	33.5504i	−0.202225	+	1.40651i	−0.797662	+	0.603105i	$0.793930\pi$
$570$	9.05181	−	6.87297i	0.379139	−	0.287877i
$571$	−11.1666	+	1.60552i	−0.467308	+	0.0671888i	−0.371947	−	0.928254i	$-0.621310\pi$
$571$	−11.1666	+	1.60552i	−0.467308	+	0.0671888i	−0.0953611	+	0.995443i	$0.530401\pi$
$572$	7.80503	−	5.01599i	0.326345	−	0.209729i
$573$	−6.20772	−	3.33489i	−0.259331	−	0.139317i
$574$			0.856152i			0.0357351i
$575$	4.68185	+	1.03938i	0.195246	+	0.0433453i
$576$	2.71164	−	1.28337i	0.112985	−	0.0534735i
$577$	30.2558	−	34.9171i	1.25957	−	1.45362i	0.422643	−	0.906296i	$-0.361102\pi$
$577$	30.2558	−	34.9171i	1.25957	−	1.45362i	0.836923	−	0.547321i	$-0.184352\pi$
$578$	−6.13640	−	9.54843i	−0.255241	−	0.397162i
$579$	−25.3584	+	9.65580i	−1.05386	+	0.401281i
$580$	3.51545	−	1.60545i	0.145971	−	0.0666628i
$581$	0.0961286	+	0.0138212i	0.00398809	+	0.000573400i
$582$	9.57897	+	17.2615i	0.397061	+	0.715514i
$583$	27.3420	+	17.5716i	1.13239	+	0.727742i
$584$	−8.05934	−	3.68058i	−0.333498	−	0.152303i
$585$	−7.44524	+	1.17437i	−0.307823	+	0.0485542i
$586$	−10.2915	+	8.91766i	−0.425139	+	0.368385i
$587$	−18.7108	+	16.2130i	−0.772278	+	0.669183i	−0.949070	−	0.315065i	$-0.897974\pi$
$587$	−18.7108	+	16.2130i	−0.772278	+	0.669183i	0.176792	+	0.984248i	$0.443428\pi$
$588$	0.780164	−	12.0643i	0.0321734	−	0.497525i
$589$	34.6110	+	15.8063i	1.42612	+	0.651289i
$590$	9.32669	+	5.99390i	0.383974	+	0.246765i
$591$	26.1420	−	14.5070i	1.07534	−	0.596740i
$592$	−0.614673	−	0.0883766i	−0.0252629	−	0.00363226i
$593$	37.3958	−	17.0781i	1.53566	−	0.701313i	0.545099	−	0.838372i	$-0.316492\pi$
$593$	37.3958	−	17.0781i	1.53566	−	0.701313i	0.990563	+	0.137059i	$0.0437649\pi$
$594$	13.8430	+	13.2876i	0.567985	+	0.545197i
$595$	0.182204	+	0.283515i	0.00746964	+	0.0116230i
$596$	−7.39422	+	8.53338i	−0.302879	+	0.349541i
$597$	−8.09900	+	1.81979i	−0.331470	+	0.0744790i
$598$	−5.81957	+	10.5506i	−0.237980	+	0.431447i
$599$			11.4063i			0.466050i	0.972471	+	0.233025i	$0.0748624\pi$
$599$			11.4063i			0.466050i	−0.972471	+	0.233025i	$0.925138\pi$
$600$	0.819692	−	1.52581i	0.0334638	−	0.0622910i
$601$	22.3913	−	14.3900i	0.913358	−	0.586980i	0.00263503	−	0.999997i	$-0.499161\pi$
$601$	22.3913	−	14.3900i	0.913358	−	0.586980i	0.910723	+	0.413017i	$0.135525\pi$
$602$	0.00436933		0.000628214i	0.000178080		2.56041e-5i
$603$	9.99028	−	11.8524i	0.406836	−	0.482667i
$604$	−2.48150	+	17.2592i	−0.100971	+	0.702267i
$605$	−2.52984	+	0.742829i	−0.102853	+	0.0302003i
$606$	6.99503	−	19.1525i	0.284154	−	0.778016i
$607$	15.9539	−	34.9342i	0.647550	−	1.41794i	−0.246132	−	0.969236i	$-0.579160\pi$
$607$	15.9539	−	34.9342i	0.647550	−	1.41794i	0.893682	−	0.448701i	$-0.148113\pi$
$608$	−6.29603	−	1.84868i	−0.255338	−	0.0749740i
$609$	−0.563576	+	0.763654i	−0.0228372	+	0.0309448i
$610$	3.98185	+	4.59531i	0.161221	+	0.186058i
$611$	−4.47731	+	15.2483i	−0.181133	+	0.616881i
$612$	0.0973002	+	7.13010i	0.00393313	+	0.288217i
$613$	20.8995	−	32.5202i	0.844122	−	1.31348i	−0.103677	−	0.994611i	$-0.533061\pi$
$613$	20.8995	−	32.5202i	0.844122	−	1.31348i	0.947799	−	0.318868i	$-0.103303\pi$
$614$	−3.80202	−	12.9485i	−0.153437	−	0.522559i
$615$	0.817271	+	10.4267i	0.0329556	+	0.420445i
$616$	−0.217506	−	0.476271i	−0.00876355	−	0.0191895i
$617$	−3.46110	−	24.0725i	−0.139339	−	0.969123i	−0.932772	−	0.360466i	$-0.882618\pi$
$617$	−3.46110	−	24.0725i	−0.139339	−	0.969123i	0.793434	−	0.608657i	$-0.208291\pi$
$618$	11.3351	+	11.1814i	0.455963	+	0.449783i
$619$	−34.5751	−	29.9595i	−1.38969	−	1.20417i	−0.952399	−	0.304854i	$-0.901392\pi$
$619$	−34.5751	−	29.9595i	−1.38969	−	1.20417i	−0.437292	−	0.899320i	$-0.644062\pi$
$620$	5.79861			0.232878
$621$	−24.0211	−	6.63230i	−0.963933	−	0.266145i
$622$	−31.1621			−1.24948
$623$	0.759384	+	0.658010i	0.0304241	+	0.0263626i
$624$	3.09801	+	3.05602i	0.124020	+	0.122339i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	10.3989	+	22.7704i	0.415624	+	0.910089i
$627$	−3.27966	−	41.8417i	−0.130977	−	1.67100i
$628$	−5.16312	−	17.5840i	−0.206031	−	0.701676i
$629$	0.798015	−	1.24174i	0.0318189	−	0.0495112i
$630$	0.00580408	+	0.425320i	0.000231240	+	0.0169451i
$631$	−12.5786	+	42.8388i	−0.500747	+	1.70539i	0.189559	+	0.981869i	$0.439294\pi$
$631$	−12.5786	+	42.8388i	−0.500747	+	1.70539i	−0.690306	+	0.723517i	$0.742524\pi$
$632$	10.4617	+	12.0734i	0.416144	+	0.480256i
$633$	3.25169	−	4.40610i	0.129243	−	0.175127i
$634$	−20.8041	−	6.10863i	−0.826236	−	0.242605i
$635$	9.19012	−	20.1236i	0.364699	−	0.798579i
$636$	−5.22979	+	14.3192i	−0.207375	+	0.567794i
$637$	16.8262	−	4.94060i	0.666676	−	0.195754i
$638$	2.03104	−	14.1262i	0.0804098	−	0.559263i
$639$	28.8807	−	34.2638i	1.14250	−	1.35545i
$640$	−0.989821	+	0.142315i	−0.0391261	+	0.00562549i
$641$	30.7222	−	19.7439i	1.21345	−	0.779839i	0.232219	−	0.972663i	$-0.425401\pi$
$641$	30.7222	−	19.7439i	1.21345	−	0.779839i	0.981233	+	0.192825i	$0.0617649\pi$
$642$	−0.166786	+	0.310463i	−0.00658253	+	0.0122530i
$643$		−	46.9420i		−	1.85121i	−0.378491	−	0.925605i	$-0.623557\pi$
$643$		−	46.9420i		−	1.85121i	0.378491	−	0.925605i	$-0.376443\pi$
$644$	0.542614	+	0.409815i	0.0213820	+	0.0161490i
$645$	0.0526124	−	0.0118216i	0.00207161	−	0.000465477i
$646$	10.2138	−	11.7874i	0.401858	−	0.463769i
$647$	5.33289	+	8.29813i	0.209657	+	0.326233i	0.930117	−	0.367264i	$-0.119705\pi$
$647$	5.33289	+	8.29813i	0.209657	+	0.326233i	−0.720459	+	0.693497i	$0.756069\pi$
$648$	−4.65735	+	7.70124i	−0.182958	+	0.302533i
$649$	37.2409	−	17.0073i	1.46183	−	0.667597i
$650$	2.48686	+	0.357556i	0.0975426	+	0.0140245i
$651$	−1.24516	+	0.690976i	−0.0488015	+	0.0270815i
$652$	4.39997	+	2.82769i	0.172316	+	0.110741i
$653$	−19.6638	−	8.98018i	−0.769506	−	0.351422i	−0.00832853	−	0.999965i	$-0.502651\pi$
$653$	−19.6638	−	8.98018i	−0.769506	−	0.351422i	−0.761177	+	0.648544i	$0.775378\pi$
$654$	−0.685320	+	10.5977i	−0.0267981	+	0.414402i
$655$	14.1667	−	12.2755i	0.553537	−	0.479643i
$656$	4.56346	−	3.95426i	0.178173	−	0.154388i
$657$	26.2554	−	4.14137i	1.02432	−	0.161570i
$658$	0.815805	+	0.372566i	0.0318034	+	0.0145241i
$659$	−32.6578	−	20.9879i	−1.27217	−	0.817573i	−0.282268	−	0.959336i	$-0.591087\pi$
$659$	−32.6578	−	20.9879i	−1.27217	−	0.817573i	−0.989901	+	0.141763i	$0.954723\pi$
$660$	−3.10355	−	5.59267i	−0.120805	−	0.217694i
$661$	23.8572	+	3.43015i	0.927937	+	0.133417i	0.589680	−	0.807637i	$-0.299254\pi$
$661$	23.8572	+	3.43015i	0.927937	+	0.133417i	0.338257	+	0.941054i	$0.390163\pi$
$662$	25.9268	−	11.8404i	1.00767	−	0.460189i
$663$	−9.66650	+	3.68074i	−0.375416	+	0.142948i
$664$	−0.370314	−	0.576220i	−0.0143710	−	0.0223617i
$665$	0.609269	−	0.703133i	0.0236264	−	0.0272663i
$666$	1.68391	−	0.796962i	0.0652502	−	0.0308816i
$667$	6.40308	+	17.3933i	0.247928	+	0.673470i
$668$			17.6423i			0.682602i
$669$	−3.83947	−	2.06263i	−0.148442	−	0.0797458i
$670$	−4.34679	+	2.79351i	−0.167931	+	0.107923i
$671$	22.2253	−	3.19551i	0.857997	−	0.123361i
$672$	0.195589	−	0.148509i	0.00754502	−	0.00572887i
$673$	0.507012	−	3.52635i	0.0195439	−	0.135931i	−0.977713	−	0.209944i	$-0.932672\pi$
$673$	0.507012	−	3.52635i	0.0195439	−	0.135931i	0.997257	+	0.0740136i	$0.0235808\pi$
$674$	14.9590	−	4.39236i	0.576200	−	0.169188i
$675$	0.476690	+	5.17424i	0.0183478	+	0.199157i
$676$	2.77817	−	6.08334i	0.106853	−	0.233975i
$677$	−43.1162	−	12.6601i	−1.65709	−	0.486566i	−0.686465	−	0.727163i	$-0.740839\pi$
$677$	−43.1162	−	12.6601i	−1.65709	−	0.486566i	−0.970625	+	0.240597i	$0.922657\pi$
$678$	−2.05242	−	1.51469i	−0.0788229	−	0.0581711i
$679$	1.05827	+	1.22131i	0.0406128	+	0.0468697i
$680$	0.669656	−	2.28064i	0.0256802	−	0.0874586i
$681$	−20.9986	−	4.41814i	−0.804669	−	0.169304i
$682$	11.5767	−	18.0138i	0.443296	−	0.689783i
$683$	9.29001	+	31.6389i	0.355472	+	1.21063i	0.922197	+	0.386721i	$0.126392\pi$
$683$	9.29001	+	31.6389i	0.355472	+	1.21063i	−0.566725	+	0.823907i	$0.691790\pi$
$684$	18.8107	−	5.80326i	0.719244	−	0.221893i
$685$	−1.66265	−	3.64069i	−0.0635264	−	0.139103i
$686$	−0.282091	−	1.96198i	−0.0107703	−	0.0749089i
$687$	9.44566	−	9.57544i	0.360374	−	0.365326i
$688$	−0.0235289	−	0.0203879i	−0.000897029	−	0.000777280i
$689$	−22.1128			−0.842429
$690$	6.99946	+	4.47298i	0.266465	+	0.170283i
$691$	−20.6090			−0.784002			−0.392001	−	0.919965i	$-0.628217\pi$
$691$	−20.6090			−0.784002			−0.392001	+	0.919965i	$0.628217\pi$
$692$	−6.66705	−	5.77703i	−0.253443	−	0.219610i
$693$	1.33287	+	0.831107i	0.0506316	+	0.0315711i
$694$	−1.06186	−	7.38543i	−0.0403078	−	0.280347i
$695$	3.27119	+	7.16291i	0.124083	+	0.271705i
$696$	6.67338	−	0.523077i	0.252954	−	0.0198272i
$697$	4.04360	+	13.7712i	0.153162	+	0.521623i
$698$	−2.93004	+	4.55923i	−0.110904	+	0.172569i
$699$	3.65618	−	17.3772i	0.138289	−	0.657265i
$700$	0.0399458	−	0.136043i	0.00150981	−	0.00514194i
$701$	−7.76356	−	8.95962i	−0.293226	−	0.338400i	0.589953	−	0.807438i	$-0.299146\pi$
$701$	−7.76356	−	8.95962i	−0.293226	−	0.338400i	−0.883178	+	0.469038i	$0.844601\pi$
$702$	−12.8107	−	2.51336i	−0.483511	−	0.0948608i
$703$	−3.90980	−	1.14802i	−0.147461	−	0.0432984i
$704$	−1.53404	+	3.35907i	−0.0578162	+	0.126600i
$705$	10.2910	+	3.75856i	0.387581	+	0.141555i
$706$	−22.2297	+	6.52722i	−0.836625	+	0.245655i
$707$	0.237541	−	1.65214i	0.00893366	−	0.0621350i
$708$	11.6123	+	15.2936i	0.436418	+	0.574770i
$709$	−22.7044	+	3.26441i	−0.852683	+	0.122597i	−0.554778	−	0.831998i	$-0.687197\pi$
$709$	−22.7044	+	3.26441i	−0.852683	+	0.122597i	−0.297905	+	0.954596i	$0.596288\pi$
$710$	−12.5660	+	8.07570i	−0.471595	+	0.303076i
$711$	−46.1650	−	12.8737i	−1.73132	−	0.482801i
$712$		−	7.08678i		−	0.265588i
$713$	−2.10204	+	27.7296i	−0.0787220	+	1.03848i
$714$	0.127969	+	0.569528i	0.00478912	+	0.0213140i
$715$	6.07571	−	7.01174i	0.227219	−	0.262224i
$716$	6.03006	+	9.38296i	0.225354	+	0.350658i
$717$	−5.70460	−	14.9816i	−0.213042	−	0.559500i
$718$	10.0327	−	4.58179i	0.374418	−	0.170991i
$719$	−28.1033	−	4.04065i	−1.04808	−	0.150691i	−0.403305	−	0.915066i	$-0.632139\pi$
$719$	−28.1033	−	4.04065i	−1.04808	−	0.150691i	−0.644772	+	0.764375i	$0.723048\pi$
$720$	2.24023	−	1.99534i	0.0834885	−	0.0743618i
$721$	1.09647	+	0.704659i	0.0408347	+	0.0262429i
$722$	−21.8836	−	9.99392i	−0.814424	−	0.371935i
$723$	8.37047	+	0.541293i	0.311301	+	0.0201309i
$724$	5.05132	−	4.37699i	0.187731	−	0.162670i
$725$	2.92074	−	2.53084i	0.108474	−	0.0939930i
$726$	−4.55729	−	0.294706i	−0.169137	−	0.0109376i
$727$	−12.8775	−	5.88095i	−0.477599	−	0.218112i	0.162045	−	0.986783i	$-0.448191\pi$
$727$	−12.8775	−	5.88095i	−0.477599	−	0.218112i	−0.639644	+	0.768671i	$0.720918\pi$
$728$	0.299678	+	0.192592i	0.0111068	+	0.00713792i
$729$	−1.10498	−	26.9774i	−0.0409252	−	0.999162i
$730$	−8.76982	−	1.26091i	−0.324586	−	0.0466684i
$731$	0.0673137	−	0.0307412i	0.00248969	−	0.00113700i
$732$	3.74768	+	9.84230i	0.138518	+	0.363782i
$733$	3.96790	+	6.17417i	0.146558	+	0.228048i	0.906769	−	0.421628i	$-0.138541\pi$
$733$	3.96790	+	6.17417i	0.146558	+	0.228048i	−0.760211	+	0.649676i	$0.774905\pi$
$734$	14.5342	−	16.7734i	0.536469	−	0.619118i
$735$	−2.65035	−	11.7954i	−0.0977598	−	0.435081i
$736$	−0.321748	−	4.78503i	−0.0118598	−	0.176378i
$737$			19.0808i			0.702849i
$738$	−4.86593	+	17.4492i	−0.179117	+	0.642314i
$739$	−38.7352	+	24.8936i	−1.42490	+	0.915725i	−0.424951	+	0.905216i	$0.639709\pi$
$739$	−38.7352	+	24.8936i	−1.42490	+	0.915725i	−0.999945	+	0.0105090i	$0.996655\pi$
$740$	−0.614673	+	0.0883766i	−0.0225958	+	0.00324879i
$741$	17.2679	+	22.7421i	0.634350	+	0.835450i
$742$	−0.177596	+	1.23521i	−0.00651976	+	0.0453460i
$743$	13.1307	−	3.85553i	0.481720	−	0.141446i	−0.0318515	−	0.999493i	$-0.510140\pi$
$743$	13.1307	−	3.85553i	0.481720	−	0.141446i	0.513571	+	0.858047i	$0.328322\pi$
$744$	9.43397	+	3.44555i	0.345866	+	0.126320i
$745$	−4.69057	+	10.2709i	−0.171849	+	0.376297i
$746$	16.7327	+	4.91318i	0.612629	+	0.179884i
$747$	1.88064	+	0.828035i	0.0688090	+	0.0302962i
$748$	−5.74801	−	6.63356i	−0.210168	−	0.242547i
$749$	−0.00812794	+	0.0276812i	−0.000296989	+	0.00101145i
$750$	0.356618	−	1.69494i	0.0130219	−	0.0618905i
$751$	−25.3427	+	39.4339i	−0.924767	+	1.43897i	−0.0264334	+	0.999651i	$0.508415\pi$
$751$	−25.3427	+	39.4339i	−0.924767	+	1.43897i	−0.898333	+	0.439315i	$0.855221\pi$
$752$	−1.78206	−	6.06915i	−0.0649852	−	0.221319i
$753$	50.5973	−	3.96594i	1.84387	−	0.144527i
$754$	4.03359	+	8.83233i	0.146895	+	0.321654i
$755$	2.48150	+	17.2592i	0.0903110	+	0.628127i
$756$	−0.243283	+	0.695417i	−0.00884813	+	0.0252921i
$757$	7.16437	+	6.20796i	0.260393	+	0.225632i	0.775267	−	0.631634i	$-0.217616\pi$
$757$	7.16437	+	6.20796i	0.260393	+	0.225632i	−0.514873	+	0.857266i	$0.672161\pi$
$758$	2.94031			0.106797
$759$	27.8698	−	12.8141i	1.01161	−	0.465123i
$760$	−6.56183			−0.238023
$761$	25.8116	+	22.3659i	0.935669	+	0.810762i	0.982139	−	0.188158i	$-0.0602516\pi$
$761$	25.8116	+	22.3659i	0.935669	+	0.810762i	−0.0464696	+	0.998920i	$0.514797\pi$
$762$	26.9092	−	27.2789i	0.974818	−	0.988212i
$763$	0.123720	+	0.860494i	0.00447898	+	0.0311520i
$764$	1.69010	+	3.70081i	0.0611458	+	0.133891i
$765$	2.10214	+	6.81387i	0.0760031	+	0.246356i
$766$	−7.98534	−	27.1956i	−0.288522	−	0.982615i
$767$	−15.0593	+	23.4327i	−0.543758	+	0.846104i
$768$	−1.69494	−	0.356618i	−0.0611609	−	0.0128683i
$769$	12.0414	−	41.0094i	0.434226	−	1.47884i	−0.394351	−	0.918960i	$-0.629030\pi$
$769$	12.0414	−	41.0094i	0.434226	−	1.47884i	0.828576	−	0.559876i	$-0.189151\pi$
$770$	−0.342876	−	0.395700i	−0.0123564	−	0.0142600i
$771$	0.342761	+	0.252957i	0.0123442	+	0.00911003i
$772$	15.0316	+	4.41366i	0.540998	+	0.158851i
$773$	−17.7549	+	38.8779i	−0.638601	+	1.39834i	0.262585	+	0.964909i	$0.415425\pi$
$773$	−17.7549	+	38.8779i	−0.638601	+	1.39834i	−0.901186	+	0.433432i	$0.857302\pi$
$774$	0.0926215	+	0.0120294i	0.00332921	+	0.000432388i
$775$	5.56372	−	1.63366i	0.199855	−	0.0586827i
$776$	1.62205	−	11.2816i	0.0582282	−	0.404986i
$777$	0.121460	−	0.0922233i	0.00435734	−	0.00330849i
$778$	13.7141	−	1.97179i	0.491674	−	0.0706921i
$779$	33.3325	−	21.4215i	1.19426	−	0.767506i
$780$	3.83350	+	2.05942i	0.137261	+	0.0737391i
$781$			55.1601i			1.97378i
$782$	10.6635	+	4.02912i	0.381327	+	0.144081i
$783$	−15.8264	+	12.3609i	−0.565591	+	0.441744i
$784$	−4.57086	+	5.27505i	−0.163245	+	0.188395i
$785$	−9.90795	−	15.4171i	−0.353630	−	0.550259i
$786$	30.3424	−	11.5535i	1.08228	−	0.412101i
$787$	12.0020	−	5.48115i	0.427827	−	0.195382i	−0.189852	−	0.981813i	$-0.560801\pi$
$787$	12.0020	−	5.48115i	0.427827	−	0.195382i	0.617678	+	0.786431i	$0.288073\pi$
$788$	−17.0856	−	2.45654i	−0.608650	−	0.0875107i
$789$	15.6099	+	28.1295i	0.555729	+	1.00144i
$790$	13.4394	+	8.63698i	0.478152	+	0.307290i
$791$	−0.189942	−	0.0867435i	−0.00675355	−	0.00308424i
$792$	−1.72609	−	10.9431i	−0.0613341	−	0.388844i
$793$	−11.5454	+	10.0041i	−0.409989	+	0.355257i
$794$	−7.45352	+	6.45851i	−0.264516	+	0.229204i
$795$	−0.983753	+	15.2126i	−0.0348901	+	0.539535i
$796$	4.35945	+	1.99089i	0.154517	+	0.0705654i
$797$	−21.3452	−	13.7177i	−0.756084	−	0.485906i	0.104934	−	0.994479i	$-0.466537\pi$
$797$	−21.3452	−	13.7177i	−0.756084	−	0.485906i	−0.861019	+	0.508573i	$0.830173\pi$
$798$	1.40905	−	0.781924i	0.0498797	−	0.0276798i
$799$	14.8819	+	2.13969i	0.526483	+	0.0756969i
$800$	−0.909632	+	0.415415i	−0.0321603	+	0.0146871i
$801$	11.7372	+	17.7268i	0.414713	+	0.626347i
$802$	5.61458	+	8.73646i	0.198258	+	0.308495i
$803$	−21.4258	+	24.7267i	−0.756100	+	0.872585i
$804$	−8.73187	+	1.96199i	−0.307949	+	0.0691941i
$805$	0.636092	+	0.240342i	0.0224193	+	0.00847095i
$806$			14.5686i			0.513157i
$807$	−1.87128	+	3.48328i	−0.0658721	+	0.122617i
$808$	−9.90333	+	6.36448i	−0.348398	+	0.223902i
$809$	−30.4396	+	4.37656i	−1.07020	+	0.153872i	−0.654827	−	0.755779i	$-0.727258\pi$
$809$	−30.4396	+	4.37656i	−1.07020	+	0.153872i	−0.415374	+	0.909651i	$0.636349\pi$
$810$	−2.29901	+	8.70141i	−0.0807789	+	0.305736i
$811$	4.72253	−	32.8459i	0.165831	−	1.15338i	−0.721558	−	0.692354i	$-0.756574\pi$
$811$	4.72253	−	32.8459i	0.165831	−	1.15338i	0.887388	−	0.461023i	$-0.152517\pi$
$812$	0.525765	−	0.154379i	0.0184507	−	0.00541763i
$813$	0.640284	−	1.75310i	0.0224557	−	0.0614841i
$814$	−0.952628	+	2.08596i	−0.0333896	+	0.0731130i
$815$	5.01840	+	1.47353i	0.175787	+	0.0516157i
$816$	2.44465	−	3.31254i	0.0855800	−	0.115962i
$817$	−0.133782	−	0.154392i	−0.00468043	−	0.00540151i
$818$	−0.783899	+	2.66971i	−0.0274084	+	0.0933444i
$819$	−1.06859	+	0.0145823i	−0.0373394	+	0.000509549i
$820$	3.26456	−	5.07976i	0.114003	−	0.177393i
$821$	6.52479	+	22.2214i	0.227717	+	0.775532i	0.991505	+	0.130066i	$0.0415188\pi$
$821$	6.52479	+	22.2214i	0.227717	+	0.775532i	−0.763789	+	0.645466i	$0.776663\pi$
$822$	−0.541711	−	6.91111i	−0.0188943	−	0.241053i
$823$	−11.2165	−	24.5606i	−0.390981	−	0.856129i	−0.998106	−	0.0615226i	$-0.980404\pi$
$823$	−11.2165	−	24.5606i	−0.390981	−	0.856129i	0.607125	−	0.794607i	$-0.292323\pi$
$824$	−1.30823	−	9.09897i	−0.0455745	−	0.316978i
$825$	−4.55347	−	4.49175i	−0.158531	−	0.156383i
$826$	1.18799	+	1.02940i	0.0413355	+	0.0358174i
$827$	−35.4538			−1.23285			−0.616424	−	0.787414i	$-0.711419\pi$
$827$	−35.4538			−1.23285			−0.616424	+	0.787414i	$0.711419\pi$
$828$	8.72982	+	11.4364i	0.303382	+	0.397441i
$829$	35.1296			1.22010			0.610051	−	0.792362i	$-0.291149\pi$
$829$	35.1296			1.22010			0.610051	+	0.792362i	$0.291149\pi$
$830$	−0.517653	−	0.448549i	−0.0179680	−	0.0155694i
$831$	−20.7125	−	20.4317i	−0.718508	−	0.708770i
$832$	−0.357556	−	2.48686i	−0.0123960	−	0.0862163i
$833$	−6.89201	−	15.0914i	−0.238794	−	0.522886i
$834$	1.06580	+	13.5974i	0.0369055	+	0.470838i
$835$	4.97041	+	16.9277i	0.172008	+	0.585806i
$836$	−13.1005	+	20.3848i	−0.453090	+	0.705022i
$837$	−29.3046	+	7.00593i	−1.01292	+	0.242160i
$838$	−2.74866	+	9.36109i	−0.0949510	+	0.323373i
$839$	−9.32180	−	10.7579i	−0.321824	−	0.371405i	0.571667	−	0.820486i	$-0.306297\pi$
$839$	−9.32180	−	10.7579i	−0.321824	−	0.371405i	−0.893491	+	0.449081i	$0.851751\pi$
$840$	0.145827	−	0.197597i	0.00503150	−	0.00681776i
$841$	−13.4944	−	3.96232i	−0.465325	−	0.136632i
$842$	−5.98071	+	13.0959i	−0.206109	+	0.451316i
$843$	7.87063	−	21.5499i	0.271079	−	0.742218i
$844$	−3.03354	+	0.890726i	−0.104419	+	0.0306601i
$845$	0.951758	−	6.61962i	0.0327415	−	0.227722i
$846$	14.5094	+	12.2299i	0.498844	+	0.420472i
$847$	−0.370036	+	0.0532031i	−0.0127146	+	0.00182808i
$848$	7.40416	−	4.75837i	0.254260	−	0.163403i
$849$	−13.5203	+	25.1672i	−0.464014	+	0.863737i
$850$		−	2.37692i		−	0.0815278i
$851$	−0.199803	−	2.97147i	−0.00684917	−	0.101861i
$852$	−25.2428	+	5.67187i	−0.864803	+	0.194315i
$853$	4.46792	−	5.15626i	0.152979	−	0.176547i	−0.674087	−	0.738652i	$-0.735463\pi$
$853$	4.46792	−	5.15626i	0.152979	−	0.176547i	0.827066	+	0.562105i	$0.190008\pi$
$854$	0.466101	+	0.725267i	0.0159496	+	0.0248181i
$855$	16.4137	−	10.8678i	0.561338	−	0.371670i
$856$	0.185087	−	0.0845262i	0.00632613	−	0.00288905i
$857$	6.61118	+	0.950545i	0.225834	+	0.0324700i	0.254303	−	0.967125i	$-0.418154\pi$
$857$	6.61118	+	0.950545i	0.225834	+	0.0324700i	−0.0284689	+	0.999595i	$0.509063\pi$
$858$	14.0512	−	7.79745i	0.479700	−	0.266201i
$859$	−3.36188	−	2.16055i	−0.114706	−	0.0737170i	0.482030	−	0.876155i	$-0.339900\pi$
$859$	−3.36188	−	2.16055i	−0.114706	−	0.0737170i	−0.596736	+	0.802438i	$0.703536\pi$
$860$	−0.0283197	−	0.0129332i	−0.000965694	−	0.000441018i
$861$	−0.0956947	+	1.47981i	−0.00326127	+	0.0504317i
$862$	−28.7040	+	24.8722i	−0.977663	+	0.847150i
$863$	−39.6503	+	34.3571i	−1.34971	+	1.16953i	−0.380080	+	0.924953i	$0.624104\pi$
$863$	−39.6503	+	34.3571i	−1.34971	+	1.16953i	−0.969630	+	0.244577i	$0.921351\pi$
$864$	4.83035	−	1.91513i	0.164332	−	0.0651541i
$865$	−8.02456	−	3.66470i	−0.272843	−	0.124603i
$866$	16.9217	+	10.8749i	0.575023	+	0.369545i
$867$	−9.53915	−	17.1898i	−0.323967	−	0.583795i
$868$	0.813795	+	0.117006i	0.0276220	+	0.00397145i
$869$	53.6627	−	24.5069i	1.82038	−	0.831341i
$870$	6.25570	−	2.38200i	0.212088	−	0.0807573i
$871$	−7.01851	−	10.9210i	−0.237813	−	0.370044i
$872$	4.01518	−	4.63377i	0.135971	−	0.156919i
$873$	14.6273	+	30.9062i	0.495060	+	1.04602i
$874$	2.37872	−	31.3794i	0.0804612	−	1.06142i
$875$		−	0.141786i		−	0.00479326i
$876$	−13.5187	−	7.26248i	−0.456755	−	0.245376i
$877$	−27.4457	+	17.6383i	−0.926775	+	0.595602i	−0.914616	−	0.404324i	$-0.867507\pi$
$877$	−27.4457	+	17.6383i	−0.926775	+	0.595602i	−0.0121592	+	0.999926i	$0.503870\pi$
$878$	23.5525	−	3.38633i	0.794857	−	0.114283i
$879$	−18.7851	+	14.2633i	−0.633604	+	0.481090i
$880$	−0.525538	+	3.65520i	−0.0177159	+	0.123217i
$881$	−42.2901	+	12.4175i	−1.42479	+	0.418356i	−0.901122	−	0.433566i	$-0.857255\pi$
$881$	−42.2901	+	12.4175i	−1.42479	+	0.418356i	−0.523668	+	0.851922i	$0.675437\pi$
$882$	2.69693	−	20.7653i	0.0908105	−	0.699204i
$883$	14.2842	−	31.2780i	0.480701	−	1.05259i	−0.501569	−	0.865118i	$-0.667244\pi$
$883$	14.2842	−	31.2780i	0.480701	−	1.05259i	0.982270	−	0.187471i	$-0.0600291\pi$
$884$	5.72995	+	1.68247i	0.192719	+	0.0565874i
$885$	15.4507	+	11.4026i	0.519369	+	0.383293i
$886$	0.244425	+	0.282081i	0.00821161	+	0.00947671i
$887$	7.58079	−	25.8178i	0.254538	−	0.866877i	−0.728744	−	0.684786i	$-0.759895\pi$
$887$	7.58079	−	25.8178i	0.254538	−	0.866877i	0.983282	−	0.182090i	$-0.0582863\pi$
$888$	−1.05255	−	0.221458i	−0.0353212	−	0.00743163i
$889$	1.69583	−	2.63876i	0.0568763	−	0.0885013i
$890$	−1.99658	−	6.79971i	−0.0669254	−	0.227927i
$891$	22.4416	+	24.5141i	0.751823	+	0.821254i
$892$	1.04533	+	2.28895i	0.0350001	+	0.0766396i
$893$	−5.90693	−	41.0836i	−0.197668	−	1.37481i
$894$	−13.7343	+	13.9230i	−0.459343	+	0.465654i
$895$	8.42929	+	7.30402i	0.281760	+	0.244147i
$896$	−0.141786			−0.00473675
$897$	−11.2380	+	17.5857i	−0.375228	+	0.587168i
$898$	−7.27154			−0.242654
$899$	16.9362	+	14.6753i	0.564855	+	0.489450i
$900$	1.58733	−	2.54566i	0.0529111	−	0.0848552i
$901$	2.97724	+	20.7072i	0.0991863	+	0.689856i
$902$	−9.26301	−	20.2832i	−0.308425	−	0.675356i
$903$	0.00762234		0.000597458i	0.000253655		1.98822e-5i
$904$	0.414913	+	1.41306i	0.0137998	+	0.0469978i
$905$	3.61357	−	5.62282i	0.120119	−	0.186909i
$906$	−6.21824	+	29.5542i	−0.206587	+	0.981871i
$907$	−14.9655	+	50.9678i	−0.496921	+	1.69236i	0.203877	+	0.978997i	$0.434646\pi$
$907$	−14.9655	+	50.9678i	−0.496921	+	1.69236i	−0.700798	+	0.713360i	$0.747172\pi$
$908$	8.11307	+	9.36298i	0.269242	+	0.310721i
$909$	14.2312	−	32.3221i	0.472020	−	1.07206i
$910$	0.341799	+	0.100361i	0.0113305	+	0.00332694i
$911$	−0.752150	+	1.64698i	−0.0249198	+	0.0545668i	−0.921683	−	0.387945i	$-0.873185\pi$
$911$	−0.752150	+	1.64698i	−0.0249198	+	0.0545668i	0.896763	+	0.442512i	$0.145912\pi$
$912$	−10.6757	−	3.89906i	−0.353507	−	0.129111i
$913$	−2.42693	+	0.712610i	−0.0803196	+	0.0235840i
$914$	−2.10340	+	14.6295i	−0.0695742	+	0.483899i
$915$	6.36877	+	8.38778i	0.210545	+	0.277291i
$916$	−7.68647	+	1.10515i	−0.253968	+	0.0365151i
$917$	2.23589	−	1.43692i	0.0738357	−	0.0474513i
$918$	−0.628775	+	12.3348i	−0.0207527	+	0.407110i
$919$			24.2892i			0.801226i	0.916247	+	0.400613i	$0.131203\pi$
$919$			24.2892i			0.801226i	−0.916247	+	0.400613i	$0.868797\pi$
$920$	−1.65681	−	4.50055i	−0.0546235	−	0.148379i
$921$	−5.12428	−	22.8057i	−0.168851	−	0.751472i
$922$	7.38113	−	8.51827i	0.243084	−	0.280534i
$923$	−20.2896	−	31.5713i	−0.667842	−	1.03918i
$924$	−0.322711	−	0.847517i	−0.0106164	−	0.0278813i
$925$	−0.564876	+	0.257970i	−0.0185730	+	0.00848201i
$926$	12.4601	+	1.79149i	0.409465	+	0.0588721i
$927$	18.3422	+	20.5934i	0.602437	+	0.676376i
$928$	−3.25119	−	2.08941i	−0.106726	−	0.0685883i
$929$	−37.2877	−	17.0287i	−1.22337	−	0.558694i	−0.304219	−	0.952602i	$-0.598396\pi$
$929$	−37.2877	−	17.0287i	−1.22337	−	0.558694i	−0.919150	+	0.393908i	$0.871123\pi$
$930$	10.0225	+	0.648128i	0.328652	+	0.0212530i
$931$	−34.6140	+	29.9932i	−1.13443	+	0.982988i
$932$	−7.74823	+	6.71388i	−0.253802	+	0.219920i
$933$	−53.8618	−	3.48308i	−1.76336	−	0.114031i
$934$	23.5628	+	10.7608i	0.770997	+	0.352103i
$935$	−7.38407	−	4.74545i	−0.241485	−	0.155193i
$936$	5.01314	+	5.62842i	0.163860	+	0.183971i
$937$	−38.1994	−	5.49224i	−1.24792	−	0.179424i	−0.513482	−	0.858100i	$-0.671645\pi$
$937$	−38.1994	−	5.49224i	−1.24792	−	0.179424i	−0.734437	+	0.678677i	$0.762554\pi$
$938$	−0.666411	+	0.304340i	−0.0217591	+	0.00993704i
$939$	15.4288	+	40.5196i	0.503499	+	1.32231i
$940$	−3.41975	−	5.32124i	−0.111540	−	0.173560i
$941$	8.18365	−	9.44444i	0.266779	−	0.307880i	−0.606516	−	0.795072i	$-0.707433\pi$
$941$	8.18365	−	9.44444i	0.266779	−	0.307880i	0.873295	+	0.487192i	$0.161979\pi$
$942$	−6.95873	−	30.9699i	−0.226728	−	1.00905i
$943$	23.1085	+	17.4530i	0.752518	+	0.568346i
$944$		−	11.0867i		−	0.360840i
$945$	−0.0375072	+	0.735788i	−0.00122011	+	0.0239352i
$946$	−0.0967172	+	0.0621564i	−0.00314455	+	0.00202088i
$947$	−17.8932	+	2.57265i	−0.581451	+	0.0836000i	−0.426763	−	0.904363i	$-0.640346\pi$
$947$	−17.8932	+	2.57265i	−0.581451	+	0.0836000i	−0.154688	+	0.987963i	$0.549437\pi$
$948$	16.7329	+	22.0376i	0.543460	+	0.715747i
$949$	3.16795	−	22.0336i	0.102836	−	0.715240i
$950$	−6.29603	+	1.84868i	−0.204270	+	0.0599792i
$951$	−35.2759	−	12.8837i	−1.14390	−	0.417784i
$952$	0.140001	−	0.306560i	0.00453746	−	0.00993566i
$953$	−15.3747	−	4.51442i	−0.498036	−	0.146237i	0.0230610	−	0.999734i	$-0.492659\pi$
$953$	−15.3747	−	4.51442i	−0.498036	−	0.146237i	−0.521097	+	0.853498i	$0.674477\pi$
$954$	−10.6399	+	24.1654i	−0.344479	+	0.782383i
$955$	2.66428	+	3.07474i	0.0862141	+	0.0994963i
$956$	−2.60757	+	8.88057i	−0.0843349	+	0.287218i
$957$	5.08947	−	24.1893i	0.164519	−	0.781930i
$958$	12.3535	−	19.2224i	0.399124	−	0.621049i
$959$	−0.159878	−	0.544495i	−0.00516273	−	0.0175827i
$960$	−1.72675	+	0.135347i	−0.0557308	+	0.00436832i
$961$	1.08999	+	2.38674i	0.0351610	+	0.0769918i
$962$	−0.222040	−	1.54432i	−0.00715886	−	0.0497910i
$963$	−0.322981	+	0.517975i	−0.0104079	+	0.0166915i
$964$	−3.65993	−	3.17135i	−0.117879	−	0.102142i
$965$	15.6661			0.504311
$966$	0.892070	+	0.768990i	0.0287019	+	0.0247418i
$967$	−54.2637			−1.74500			−0.872502	−	0.488610i	$-0.837504\pi$
$967$	−54.2637			−1.74500			−0.872502	+	0.488610i	$0.837504\pi$
$968$	1.99265	+	1.72664i	0.0640460	+	0.0554962i
$969$	18.9715	−	19.2322i	0.609453	−	0.617827i
$970$	−1.62205	−	11.2816i	−0.0520809	−	0.362231i
$971$	15.5814	+	34.1186i	0.500032	+	1.09492i	0.976459	+	0.215703i	$0.0692043\pi$
$971$	15.5814	+	34.1186i	0.500032	+	1.09492i	−0.476427	+	0.879214i	$0.658068\pi$
$972$	−8.91075	+	12.7906i	−0.285812	+	0.410258i
$973$	0.314554	+	1.07127i	0.0100841	+	0.0343434i
$974$	0.0243446	−	0.0378809i	0.000780050	−	0.00121378i
$975$	4.25842	+	0.895978i	0.136379	+	0.0286943i
$976$	1.71306	−	5.83416i	0.0548338	−	0.186747i
$977$	−12.4135	−	14.3259i	−0.397142	−	0.458326i	0.521597	−	0.853192i	$-0.325337\pi$
$977$	−12.4135	−	14.3259i	−0.397142	−	0.458326i	−0.918739	+	0.394866i	$0.870791\pi$
$978$	7.28903	+	5.37930i	0.233078	+	0.172011i
$979$	−25.1099	−	7.37292i	−0.802515	−	0.235640i
$980$	−2.89955	+	6.34914i	−0.0926228	+	0.202816i
$981$	−2.36907	+	18.2409i	−0.0756386	+	0.582386i
$982$	−33.9337	+	9.96384i	−1.08287	+	0.317959i
$983$	1.03487	−	7.19766i	0.0330071	−	0.229570i	−0.966640	−	0.256140i	$-0.917549\pi$
$983$	1.03487	−	7.19766i	0.0330071	−	0.229570i	0.999647	+	0.0265698i	$0.00845843\pi$
$984$	8.32965	−	6.32463i	0.265539	−	0.201622i
$985$	−17.0856	+	2.45654i	−0.544393	+	0.0782719i
$986$	7.72783	−	4.96637i	0.246104	−	0.158161i
$987$	1.36843	+	0.735143i	0.0435575	+	0.0233998i
$988$		−	16.4862i		−	0.524494i
$989$	0.0721140	−	0.130740i	0.00229309	−	0.00415728i
$990$	−4.73919	−	10.0135i	−0.150621	−	0.318249i
$991$	15.1021	−	17.4287i	0.479734	−	0.553642i	−0.463360	−	0.886170i	$-0.653356\pi$
$991$	15.1021	−	17.4287i	0.479734	−	0.553642i	0.943093	+	0.332528i	$0.107902\pi$
$992$	−3.13496	−	4.87810i	−0.0995352	−	0.154880i
$993$	46.1364	−	17.5675i	1.46409	−	0.557487i
$994$	−1.92651	+	0.879809i	−0.0611053	+	0.0279058i
$995$	4.74376	+	0.682050i	0.150387	+	0.0216224i
$996$	−0.575660	−	1.03735i	−0.0182405	−	0.0328698i
$997$	19.1057	+	12.2785i	0.605085	+	0.388864i	0.807011	−	0.590536i	$-0.201084\pi$
$997$	19.1057	+	12.2785i	0.605085	+	0.388864i	−0.201926	+	0.979401i	$0.564720\pi$
$998$	2.35764	+	1.07670i	0.0746299	+	0.0340823i
$999$	2.99962	−	1.18929i	0.0949037	−	0.0376273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.191.2	✓	160
3.2	odd	2		690.2.q.b.191.14	yes	160
23.10	odd	22		690.2.q.b.401.14	yes	160
69.56	even	22	inner	690.2.q.a.401.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.191.2	✓	160	1.1	even	1	trivial
690.2.q.a.401.2	yes	160	69.56	even	22	inner
690.2.q.b.191.14	yes	160	3.2	odd	2
690.2.q.b.401.14	yes	160	23.10	odd	22

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.755750 - 0.654861i) q^{2} +(-1.23307 - 1.21636i) q^{3} +(0.142315 + 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.135347 + 1.72675i) q^{6} +(0.0399458 + 0.136043i) q^{7} +(0.540641 - 0.841254i) q^{8} +(0.0409354 + 2.99972i) q^{9} +O(q^{10})\)	\(q+(-0.755750 - 0.654861i) q^{2} +(-1.23307 - 1.21636i) q^{3} +(0.142315 + 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.135347 + 1.72675i) q^{6} +(0.0399458 + 0.136043i) q^{7} +(0.540641 - 0.841254i) q^{8} +(0.0409354 + 2.99972i) q^{9} +(0.281733 - 0.959493i) q^{10} +(-2.41826 - 2.79082i) q^{11} +(1.02849 - 1.39363i) q^{12} +(2.41066 + 0.707833i) q^{13} +(0.0589002 - 0.128973i) q^{14} +(0.594203 - 1.62694i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.338271 - 2.35273i) q^{17} +(1.93346 - 2.29384i) q^{18} +(-6.49504 + 0.933846i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(0.116221 - 0.216339i) q^{21} +3.69278i q^{22} +(-2.28044 - 4.21895i) q^{23} +(-1.68992 + 0.379713i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(-1.35832 - 2.11359i) q^{26} +(3.59826 - 3.74867i) q^{27} +(-0.128973 + 0.0589002i) q^{28} +(-3.82536 - 0.550004i) q^{29} +(-1.51449 + 0.840436i) q^{30} +(-4.87810 - 3.13496i) q^{31} +(0.909632 + 0.415415i) q^{32} +(-0.412754 + 6.38276i) q^{33} +(-1.79636 + 1.55655i) q^{34} +(-0.107155 + 0.0928503i) q^{35} +(-2.96336 + 0.467423i) q^{36} +(0.564876 + 0.257970i) q^{37} +(5.52017 + 3.54760i) q^{38} +(-2.11154 - 3.80504i) q^{39} +(0.989821 + 0.142315i) q^{40} +(-5.49265 + 2.50841i) q^{41} +(-0.229506 + 0.0873897i) q^{42} +(0.0168318 + 0.0261909i) q^{43} +(2.41826 - 2.79082i) q^{44} +(-2.71164 + 1.28337i) q^{45} +(-1.03938 + 4.68185i) q^{46} +6.32537i q^{47} +(1.52581 + 0.819692i) q^{48} +(5.87186 - 3.77362i) q^{49} +(0.989821 - 0.142315i) q^{50} +(-3.27888 + 2.48963i) q^{51} +(-0.357556 + 2.48686i) q^{52} +(-8.44483 + 2.47963i) q^{53} +(-5.17424 + 0.476690i) q^{54} +(1.53404 - 3.35907i) q^{55} +(0.136043 + 0.0399458i) q^{56} +(9.14475 + 6.74881i) q^{57} +(2.53084 + 2.92074i) q^{58} +(-3.12347 + 10.6376i) q^{59} +(1.69494 + 0.356618i) q^{60} +(-3.28734 + 5.11521i) q^{61} +(1.63366 + 5.56372i) q^{62} +(-0.406456 + 0.125395i) q^{63} +(-0.415415 - 0.909632i) q^{64} +(0.357556 + 2.48686i) q^{65} +(4.49175 - 4.55347i) q^{66} +(-3.90499 - 3.38369i) q^{67} +2.37692 q^{68} +(-2.31982 + 7.97612i) q^{69} +0.141786 q^{70} +(-11.2888 - 9.78184i) q^{71} +(2.54566 + 1.58733i) q^{72} +(-1.26091 - 8.76982i) q^{73} +(-0.257970 - 0.564876i) q^{74} +(1.72675 - 0.135347i) q^{75} +(-1.84868 - 6.29603i) q^{76} +(0.283072 - 0.440469i) q^{77} +(-0.895978 + 4.25842i) q^{78} +(-4.50080 + 15.3283i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-8.99665 + 0.245589i) q^{81} +(5.79373 + 1.70119i) q^{82} +(0.284540 - 0.623056i) q^{83} +(0.230677 + 0.0842500i) q^{84} +(2.28064 - 0.669656i) q^{85} +(0.00443071 - 0.0308163i) q^{86} +(4.04794 + 5.33121i) q^{87} +(-3.65520 + 0.525538i) q^{88} +(5.96178 - 3.83140i) q^{89} +(2.88974 + 0.805842i) q^{90} +0.356228i q^{91} +(3.85147 - 2.85765i) q^{92} +(2.20180 + 9.79916i) q^{93} +(4.14224 - 4.78040i) q^{94} +(-3.54760 - 5.52017i) q^{95} +(-0.616348 - 1.61868i) q^{96} +(10.3676 - 4.73474i) q^{97} +(-6.90885 - 0.993343i) q^{98} +(8.27269 - 7.36834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more