LMFDB - Embedded newform 690.2.w.b.217.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.3
Character	$\chi$	$=$	690.217
Dual form			690.2.w.b.283.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.00142 + 1.99929i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.61943 + 1.43032i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.00142 + 1.99929i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.61943 + 1.43032i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-1.92276 - 1.14149i) q^{10} +(1.89288 + 1.64019i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-0.269413 + 0.493393i) q^{13} +(-1.23980 - 2.71479i) q^{14} +(-0.553550 + 2.16647i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-5.07183 - 3.79672i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-1.00290 + 6.97529i) q^{19} +(1.27575 - 1.83643i) q^{20} +(-2.25553 + 1.95443i) q^{21} +(-1.77104 + 1.77104i) q^{22} +(0.201680 - 4.79159i) q^{23} -1.00000i q^{24} +(-2.99433 - 4.00424i) q^{25} +(-0.472917 - 0.303925i) q^{26} +(0.800541 - 0.599278i) q^{27} +(2.79632 - 1.04297i) q^{28} +(-8.91163 + 1.28130i) q^{29} +(-2.12146 - 0.706694i) q^{30} +(-3.85826 + 2.47955i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(2.19827 + 1.20034i) q^{33} +(4.14887 - 4.78805i) q^{34} +(-0.236483 - 6.66934i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(4.03556 + 1.50519i) q^{37} +(-6.88597 - 1.49795i) q^{38} +(-0.158378 + 0.539386i) q^{39} +(1.74074 + 1.40351i) q^{40} +(-2.06266 + 4.51659i) q^{41} +(-1.78854 - 2.38921i) q^{42} +(-0.109878 - 0.505099i) q^{43} +(-1.64019 - 1.89288i) q^{44} +(-0.0803837 + 2.23462i) q^{45} +(4.76499 + 0.542994i) q^{46} +(-3.07604 - 3.07604i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(1.03111 - 1.60444i) q^{49} +(4.20765 - 2.70105i) q^{50} +(-5.76297 - 2.63186i) q^{51} +(0.336888 - 0.450030i) q^{52} +(6.79606 + 12.4461i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-5.17477 + 2.14190i) q^{55} +(0.840829 + 2.86360i) q^{56} +(0.502729 + 7.02906i) q^{57} +(-0.642286 - 8.98033i) q^{58} +(1.37222 + 4.67337i) q^{59} +(0.856236 - 2.06564i) q^{60} +(1.62580 + 2.52979i) q^{61} +(-2.19799 - 4.02532i) q^{62} +(-1.78854 + 2.38921i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-0.716643 - 1.03273i) q^{65} +(-1.35411 + 2.10703i) q^{66} +(15.5754 + 1.11397i) q^{67} +(4.47987 + 4.47987i) q^{68} +(-0.821454 - 4.72496i) q^{69} +(6.66922 + 0.239905i) q^{70} +(-6.74083 - 7.77933i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(6.31466 + 8.43539i) q^{73} +(-1.78925 + 3.91790i) q^{74} +(-3.77707 - 3.27624i) q^{75} +(1.98537 - 6.76157i) q^{76} +(-7.30424 - 1.58894i) q^{77} +(-0.526713 - 0.196454i) q^{78} +(0.503836 - 0.147940i) q^{79} +(-1.52412 + 1.63618i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.35794 - 2.37961i) q^{82} +(1.02250 - 2.74142i) q^{83} +(2.51072 - 1.61354i) q^{84} +(12.6698 - 6.33796i) q^{85} +(0.511650 - 0.0735642i) q^{86} +(-8.43561 + 3.14632i) q^{87} +(2.00506 - 1.50097i) q^{88} +(8.73923 + 5.61636i) q^{89} +(-2.22319 - 0.239595i) q^{90} -1.67775i q^{91} +(-0.881542 + 4.71412i) q^{92} +(-3.24302 + 3.24302i) q^{93} +(3.28764 - 2.84876i) q^{94} +(-12.9413 - 8.99024i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-1.87424 - 5.02502i) q^{97} +(1.52679 + 1.14294i) q^{98} +(2.40318 + 0.705637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$3$	0.977147	−	0.212565i	0.564156	−	0.122725i
$3$	0.977147	−	0.212565i	0.564156	−	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−1.00142	+	1.99929i	−0.447847	+	0.894110i
$5$	−1.00142	+	1.99929i	−0.447847	+	0.894110i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−2.61943	+	1.43032i	−0.990050	+	0.540608i	−0.890772	−	0.454451i	$-0.849835\pi$
$7$	−2.61943	+	1.43032i	−0.990050	+	0.540608i	−0.0992788	+	0.995060i	$0.531654\pi$
$8$	0.212565	−	0.977147i	0.0751532	−	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	−1.92276	−	1.14149i	−0.608029	−	0.360971i
$11$	1.89288	+	1.64019i	0.570724	+	0.494535i	0.891746	−	0.452537i	$-0.149481\pi$
$11$	1.89288	+	1.64019i	0.570724	+	0.494535i	−0.321022	+	0.947072i	$0.604026\pi$
$12$	−0.997452	+	0.0713392i	−0.287940	+	0.0205938i
$13$	−0.269413	+	0.493393i	−0.0747218	+	0.136843i	−0.912369	−	0.409369i	$-0.865749\pi$
$13$	−0.269413	+	0.493393i	−0.0747218	+	0.136843i	0.837647	+	0.546212i	$0.183931\pi$
$14$	−1.23980	−	2.71479i	−0.331351	−	0.725558i
$15$	−0.553550	+	2.16647i	−0.142926	+	0.559380i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−5.07183	−	3.79672i	−1.23010	−	0.920840i	−0.231452	−	0.972846i	$-0.574347\pi$
$17$	−5.07183	−	3.79672i	−1.23010	−	0.920840i	−0.998647	+	0.0520064i	$0.983438\pi$
$18$	0.349464	+	0.936950i	0.0823695	+	0.220841i
$19$	−1.00290	+	6.97529i	−0.230080	+	1.60024i	0.467672	+	0.883902i	$0.345093\pi$
$19$	−1.00290	+	6.97529i	−0.230080	+	1.60024i	−0.697752	+	0.716339i	$0.745816\pi$
$20$	1.27575	−	1.83643i	0.285267	−	0.410637i
$21$	−2.25553	+	1.95443i	−0.492197	+	0.426491i
$22$	−1.77104	+	1.77104i	−0.377588	+	0.377588i
$23$	0.201680	−	4.79159i	0.0420533	−	0.999115i
$23$	0.201680	−	4.79159i	0.0420533	−	0.999115i
$24$		−	1.00000i		−	0.204124i
$25$	−2.99433	−	4.00424i	−0.598867	−	0.800849i
$26$	−0.472917	−	0.303925i	−0.0927466	−	0.0596046i
$27$	0.800541	−	0.599278i	0.154064	−	0.115331i
$28$	2.79632	−	1.04297i	0.528455	−	0.197103i
$29$	−8.91163	+	1.28130i	−1.65485	+	0.237931i	−0.905531	−	0.424280i	$-0.860527\pi$
$29$	−8.91163	+	1.28130i	−1.65485	+	0.237931i	−0.749317	+	0.662211i	$0.769618\pi$
$30$	−2.12146	−	0.706694i	−0.387323	−	0.129024i
$31$	−3.85826	+	2.47955i	−0.692964	+	0.445341i	−0.839139	−	0.543918i	$-0.816940\pi$
$31$	−3.85826	+	2.47955i	−0.692964	+	0.445341i	0.146174	+	0.989259i	$0.453304\pi$
$32$	−0.349464	+	0.936950i	−0.0617771	+	0.165631i
$33$	2.19827	+	1.20034i	0.382669	+	0.208953i
$34$	4.14887	−	4.78805i	0.711525	−	0.821143i
$35$	−0.236483	−	6.66934i	−0.0399730	−	1.12732i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	4.03556	+	1.50519i	0.663442	+	0.247451i	0.658550	−	0.752537i	$-0.271170\pi$
$37$	4.03556	+	1.50519i	0.663442	+	0.247451i	0.00489211	+	0.999988i	$0.498443\pi$
$38$	−6.88597	−	1.49795i	−1.11705	−	0.243000i
$39$	−0.158378	+	0.539386i	−0.0253608	+	0.0863708i
$40$	1.74074	+	1.40351i	0.275234	+	0.221914i
$41$	−2.06266	+	4.51659i	−0.322133	+	0.705373i	−0.999543	−	0.0302327i	$-0.990375\pi$
$41$	−2.06266	+	4.51659i	−0.322133	+	0.705373i	0.677410	+	0.735606i	$0.263102\pi$
$42$	−1.78854	−	2.38921i	−0.275978	−	0.368663i
$43$	−0.109878	−	0.505099i	−0.0167562	−	0.0770268i	0.968010	−	0.250914i	$-0.0807310\pi$
$43$	−0.109878	−	0.505099i	−0.0167562	−	0.0770268i	−0.984766	+	0.173887i	$0.944367\pi$
$44$	−1.64019	−	1.89288i	−0.247268	−	0.285362i
$45$	−0.0803837	+	2.23462i	−0.0119829	+	0.333118i
$46$	4.76499	+	0.542994i	0.702560	+	0.0800602i
$47$	−3.07604	−	3.07604i	−0.448686	−	0.448686i	0.446232	−	0.894918i	$-0.352766\pi$
$47$	−3.07604	−	3.07604i	−0.448686	−	0.448686i	−0.894918	+	0.446232i	$0.852766\pi$
$48$	0.997452	+	0.0713392i	0.143970	+	0.0102969i
$49$	1.03111	−	1.60444i	0.147302	−	0.229206i
$50$	4.20765	−	2.70105i	0.595052	−	0.381986i
$51$	−5.76297	−	2.63186i	−0.806977	−	0.368534i
$52$	0.336888	−	0.450030i	0.0467180	−	0.0624079i
$53$	6.79606	+	12.4461i	0.933510	+	1.70960i	0.665853	+	0.746083i	$0.268068\pi$
$53$	6.79606	+	12.4461i	0.933510	+	1.70960i	0.267657	+	0.963514i	$0.413751\pi$
$54$	0.540641	+	0.841254i	0.0735719	+	0.114480i
$55$	−5.17477	+	2.14190i	−0.697766	+	0.288814i
$56$	0.840829	+	2.86360i	0.112360	+	0.382665i
$57$	0.502729	+	7.02906i	0.0665880	+	0.931022i
$58$	−0.642286	−	8.98033i	−0.0843363	−	1.17918i
$59$	1.37222	+	4.67337i	0.178648	+	0.608420i	0.999315	+	0.0370128i	$0.0117842\pi$
$59$	1.37222	+	4.67337i	0.178648	+	0.608420i	−0.820666	+	0.571408i	$0.806398\pi$
$60$	0.856236	−	2.06564i	0.110540	−	0.266673i
$61$	1.62580	+	2.52979i	0.208162	+	0.323906i	0.929598	−	0.368575i	$-0.120154\pi$
$61$	1.62580	+	2.52979i	0.208162	+	0.323906i	−0.721436	+	0.692481i	$0.756518\pi$
$62$	−2.19799	−	4.02532i	−0.279145	−	0.511216i
$63$	−1.78854	+	2.38921i	−0.225335	+	0.301012i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−0.716643	−	1.03273i	−0.0888886	−	0.128094i
$66$	−1.35411	+	2.10703i	−0.166679	+	0.259358i
$67$	15.5754	+	1.11397i	1.90284	+	0.136094i	0.972841	−	0.231475i	$-0.0743553\pi$
$67$	15.5754	+	1.11397i	1.90284	+	0.136094i	0.929996	+	0.367569i	$0.119810\pi$
$68$	4.47987	+	4.47987i	0.543264	+	0.543264i
$69$	−0.821454	−	4.72496i	−0.0988915	−	0.568818i
$70$	6.66922	+	0.239905i	0.797124	+	0.0286741i
$71$	−6.74083	−	7.77933i	−0.799989	−	0.923237i	0.198391	−	0.980123i	$-0.436428\pi$
$71$	−6.74083	−	7.77933i	−0.799989	−	0.923237i	−0.998381	+	0.0568859i	$0.981883\pi$
$72$	−0.212565	−	0.977147i	−0.0250511	−	0.115158i
$73$	6.31466	+	8.43539i	0.739075	+	0.987288i	0.999761	+	0.0218646i	$0.00696028\pi$
$73$	6.31466	+	8.43539i	0.739075	+	0.987288i	−0.260686	+	0.965424i	$0.583949\pi$
$74$	−1.78925	+	3.91790i	−0.207996	+	0.455447i
$75$	−3.77707	−	3.27624i	−0.436138	−	0.378308i
$76$	1.98537	−	6.76157i	0.227738	−	0.775605i
$77$	−7.30424	−	1.58894i	−0.832395	−	0.181077i
$78$	−0.526713	−	0.196454i	−0.0596385	−	0.0222440i
$79$	0.503836	−	0.147940i	0.0566860	−	0.0166445i	−0.253267	−	0.967397i	$-0.581505\pi$
$79$	0.503836	−	0.147940i	0.0566860	−	0.0166445i	0.309953	+	0.950752i	$0.399687\pi$
$80$	−1.52412	+	1.63618i	−0.170401	+	0.182930i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−4.35794	−	2.37961i	−0.481254	−	0.262784i
$83$	1.02250	−	2.74142i	0.112234	−	0.300910i	−0.868674	−	0.495384i	$-0.835027\pi$
$83$	1.02250	−	2.74142i	0.112234	−	0.300910i	0.980908	+	0.194474i	$0.0623000\pi$
$84$	2.51072	−	1.61354i	0.273942	−	0.176052i
$85$	12.6698	−	6.33796i	1.37423	−	0.687449i
$86$	0.511650	−	0.0735642i	0.0551727	−	0.00793263i
$87$	−8.43561	+	3.14632i	−0.904393	+	0.337321i
$88$	2.00506	−	1.50097i	0.213741	−	0.160004i
$89$	8.73923	+	5.61636i	0.926356	+	0.595333i	0.914495	−	0.404597i	$-0.132588\pi$
$89$	8.73923	+	5.61636i	0.926356	+	0.595333i	0.0118610	+	0.999930i	$0.496224\pi$
$90$	−2.22319	−	0.239595i	−0.234345	−	0.0252555i
$91$		−	1.67775i		−	0.175876i
$92$	−0.881542	+	4.71412i	−0.0919071	+	0.491481i
$93$	−3.24302	+	3.24302i	−0.336286	+	0.336286i
$94$	3.28764	−	2.84876i	0.339094	−	0.293827i
$95$	−12.9413	−	8.99024i	−1.32775	−	0.922380i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−1.87424	−	5.02502i	−0.190300	−	0.510214i	0.806402	−	0.591368i	$-0.201412\pi$
$97$	−1.87424	−	5.02502i	−0.190300	−	0.510214i	−0.996702	+	0.0811545i	$0.974139\pi$
$98$	1.52679	+	1.14294i	0.154229	+	0.115455i
$99$	2.40318	+	0.705637i	0.241529	+	0.0709192i
$100$	2.39399	+	4.38962i	0.239399	+	0.438962i
$101$	−0.112115	−	0.245498i	−0.0111559	−	0.0244279i	0.903972	−	0.427592i	$-0.140638\pi$
$101$	−0.112115	−	0.245498i	−0.0111559	−	0.0244279i	−0.915128	+	0.403164i	$0.867911\pi$
$102$	3.03628	−	5.56053i	0.300636	−	0.550575i
$103$	−1.32655	+	0.0948770i	−0.130709	+	0.00934851i	−0.136540	−	0.990634i	$-0.543598\pi$
$103$	−1.32655	+	0.0948770i	−0.130709	+	0.00934851i	0.00583128	+	0.999983i	$0.498144\pi$
$104$	0.424850	+	0.368135i	0.0416600	+	0.0360986i
$105$	−1.64875	−	6.46666i	−0.160901	−	0.631081i
$106$	−12.8992	+	5.89085i	−1.25288	+	0.572170i
$107$	1.33866	−	6.15374i	0.129414	−	0.594905i	−0.866066	−	0.499930i	$-0.833359\pi$
$107$	1.33866	−	6.15374i	0.129414	−	0.594905i	0.995480	−	0.0949750i	$-0.0302771\pi$
$108$	−0.877679	+	0.479249i	−0.0844547	+	0.0461158i
$109$	2.67003	+	18.5705i	0.255742	+	1.77873i	0.562358	+	0.826894i	$0.309894\pi$
$109$	2.67003	+	18.5705i	0.255742	+	1.77873i	−0.306616	+	0.951833i	$0.599197\pi$
$110$	−1.76728	−	5.31439i	−0.168504	−	0.506707i
$111$	4.26329	+	0.612968i	0.404653	+	0.0581804i
$112$	−2.91629	+	0.634400i	−0.275563	+	0.0599451i
$113$	1.45487	−	20.3418i	0.136863	−	1.91360i	−0.213435	−	0.976957i	$-0.568465\pi$
$113$	1.45487	−	20.3418i	0.136863	−	1.91360i	0.350298	−	0.936638i	$-0.386080\pi$
$114$	−7.04702			−0.660014
$115$	9.37782	+	5.20159i	0.874486	+	0.485051i
$116$	9.00327			0.835933
$117$	−0.0401038	+	0.560725i	−0.00370760	+	0.0518390i
$118$	−4.75935	+	1.03533i	−0.438134	+	0.0953102i
$119$	18.7158	+	2.69092i	1.71567	+	0.246677i
$120$	1.99929	+	1.00142i	0.182510	+	0.0914163i
$121$	−0.672694	−	4.67869i	−0.0611540	−	0.425335i
$122$	−2.63932	+	1.44118i	−0.238953	+	0.130478i
$123$	−1.05545	+	4.85182i	−0.0951667	+	0.437474i
$124$	4.17187	−	1.90523i	0.374645	−	0.171095i
$125$	11.0042	−	1.97664i	0.984248	−	0.176796i
$126$	−2.25553	−	1.95443i	−0.200939	−	0.174114i
$127$	5.19456	−	0.371522i	0.460943	−	0.0329673i	0.161063	−	0.986944i	$-0.448508\pi$
$127$	5.19456	−	0.371522i	0.460943	−	0.0329673i	0.299880	+	0.953977i	$0.403053\pi$
$128$	0.479249	−	0.877679i	0.0423600	−	0.0775766i
$129$	−0.214733	−	0.470200i	−0.0189062	−	0.0413988i
$130$	1.08122	−	0.641143i	0.0948293	−	0.0562320i
$131$	−0.678049	−	0.199093i	−0.0592414	−	0.0173949i	0.251978	−	0.967733i	$-0.418919\pi$
$131$	−0.678049	−	0.199093i	−0.0592414	−	0.0173949i	−0.311219	+	0.950338i	$0.600737\pi$
$132$	−2.00506	−	1.50097i	−0.174518	−	0.130643i
$133$	−7.34986	−	19.7057i	−0.637313	−	1.70870i
$134$	−2.22227	+	15.4562i	−0.191975	+	1.33522i
$135$	0.396457	+	2.20064i	0.0341215	+	0.189401i
$136$	−4.78805	+	4.14887i	−0.410572	+	0.355762i
$137$	1.55815	−	1.55815i	0.133122	−	0.133122i	−0.637406	−	0.770528i	$-0.719993\pi$
$137$	1.55815	−	1.55815i	0.133122	−	0.133122i	0.770528	+	0.637406i	$0.219993\pi$
$138$	4.77152	−	0.482287i	0.406179	−	0.0410550i
$139$		−	6.45255i		−	0.547298i	−0.961830	−	0.273649i	$-0.911769\pi$
$139$		−	6.45255i		−	0.547298i	0.961830	−	0.273649i	$-0.0882306\pi$
$140$	−0.715070	+	6.63511i	−0.0604344	+	0.560769i
$141$	−3.65960	−	2.35188i	−0.308194	−	0.198064i
$142$	8.24040	−	6.16868i	0.691519	−	0.517665i
$143$	−1.31922	+	0.492045i	−0.110319	+	0.0411469i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	6.36255	−	19.1001i	0.528381	−	1.58617i
$146$	−8.86438	+	5.69679i	−0.733622	+	0.471470i
$147$	0.666499	−	1.78695i	0.0549719	−	0.147385i
$148$	−3.78027	−	2.06419i	−0.310737	−	0.169675i
$149$	−8.34352	+	9.62894i	−0.683528	+	0.788833i	−0.986429	−	0.164189i	$-0.947499\pi$
$149$	−8.34352	+	9.62894i	−0.683528	+	0.788833i	0.302901	+	0.953022i	$0.402045\pi$
$150$	3.53735	−	3.53372i	0.288823	−	0.288527i
$151$	−3.25982	+	0.957169i	−0.265280	+	0.0778933i	−0.411668	−	0.911334i	$-0.635054\pi$
$151$	−3.25982	+	0.957169i	−0.265280	+	0.0778933i	0.146388	+	0.989227i	$0.453235\pi$
$152$	6.60270	+	2.46268i	0.535550	+	0.199750i
$153$	−6.19071	−	1.34671i	−0.500489	−	0.108875i
$154$	2.10597	−	7.17227i	0.169704	−	0.577958i
$155$	−1.09363	−	10.1969i	−0.0878425	−	0.819031i
$156$	0.233528	−	0.511356i	0.0186972	−	0.0409413i
$157$	13.9650	+	18.6551i	1.11453	+	1.48884i	0.851723	+	0.523992i	$0.175558\pi$
$157$	13.9650	+	18.6551i	1.11453	+	1.48884i	0.262809	+	0.964848i	$0.415351\pi$
$158$	0.111619	+	0.513107i	0.00887997	+	0.0408206i
$159$	9.28635	+	10.7170i	0.736455	+	0.849915i
$160$	−1.52328	−	1.63696i	−0.120426	−	0.129413i
$161$	6.32520	+	12.8397i	0.498495	+	1.01191i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	1.57516	+	0.112658i	0.123376	+	0.00882403i	0.132891	−	0.991131i	$-0.457574\pi$
$163$	1.57516	+	0.112658i	0.123376	+	0.00882403i	−0.00951456	+	0.999955i	$0.503029\pi$
$164$	2.68444	−	4.17707i	0.209620	−	0.326175i
$165$	−4.60121	+	3.19293i	−0.358204	+	0.248569i
$166$	2.66149	+	1.21546i	0.206572	+	0.0943382i
$167$	−7.28602	+	9.73298i	−0.563809	+	0.753161i	−0.988342	−	0.152252i	$-0.951347\pi$
$167$	−7.28602	+	9.73298i	−0.563809	+	0.753161i	0.424533	+	0.905413i	$0.360438\pi$
$168$	1.43032	+	2.61943i	0.110351	+	0.202093i
$169$	6.85748	+	10.6704i	0.527498	+	0.820803i
$170$	5.41797	+	13.0896i	0.415539	+	1.00393i
$171$	1.98537	+	6.76157i	0.151825	+	0.517070i
$172$	0.0368761	+	0.515595i	0.00281177	+	0.0393137i
$173$	1.08497	+	15.1698i	0.0824884	+	1.15334i	0.855101	+	0.518461i	$0.173495\pi$
$173$	1.08497	+	15.1698i	0.0824884	+	1.15334i	−0.772613	+	0.634878i	$0.781051\pi$
$174$	−2.53651	−	8.63858i	−0.192293	−	0.654889i
$175$	13.5708	+	6.20598i	1.02585	+	0.469128i
$176$	1.35411	+	2.10703i	0.102070	+	0.158824i
$177$	2.33426	+	4.27488i	0.175454	+	0.321319i
$178$	−6.22550	+	8.31629i	−0.466621	+	0.623333i
$179$	6.77381	+	3.09349i	0.506298	+	0.231219i	0.652153	−	0.758087i	$-0.273866\pi$
$179$	6.77381	+	3.09349i	0.506298	+	0.231219i	−0.145855	+	0.989306i	$0.546593\pi$
$180$	0.397585	−	2.20044i	0.0296343	−	0.164011i
$181$	−12.9953	+	20.2211i	−0.965934	+	1.50302i	−0.104895	+	0.994483i	$0.533451\pi$
$181$	−12.9953	+	20.2211i	−0.965934	+	1.50302i	−0.861039	+	0.508539i	$0.830186\pi$
$182$	1.67348	+	0.119690i	0.124047	+	0.00887198i
$183$	2.12639	+	2.12639i	0.157187	+	0.157187i
$184$	−4.63922	−	1.21560i	−0.342008	−	0.0896150i
$185$	−7.05058	+	6.56095i	−0.518369	+	0.482370i
$186$	−3.00340	−	3.46611i	−0.220220	−	0.254148i
$187$	−3.37301	−	15.5055i	−0.246659	−	1.13387i
$188$	2.60696	+	3.48249i	0.190132	+	0.253987i
$189$	−1.23980	+	2.71479i	−0.0901824	+	0.197472i
$190$	9.89056	−	12.2670i	0.717537	−	0.889942i
$191$	−1.38105	+	4.70344i	−0.0999296	+	0.340329i	−0.994248	−	0.107102i	$-0.965843\pi$
$191$	−1.38105	+	4.70344i	−0.0999296	+	0.340329i	0.894318	+	0.447431i	$0.147661\pi$
$192$	−0.977147	−	0.212565i	−0.0705195	−	0.0153406i
$193$	12.2140	+	4.55557i	0.879181	+	0.327917i	0.748205	−	0.663468i	$-0.230916\pi$
$193$	12.2140	+	4.55557i	0.879181	+	0.327917i	0.130976	+	0.991386i	$0.458189\pi$
$194$	5.14593	−	1.51098i	0.369456	−	0.108482i
$195$	−0.919787	−	0.856793i	−0.0658673	−	0.0613562i
$196$	−1.24895	+	1.44137i	−0.0892108	+	0.102955i
$197$	−17.7112	−	9.67105i	−1.26187	−	0.689034i	−0.297788	−	0.954632i	$-0.596249\pi$
$197$	−17.7112	−	9.67105i	−1.26187	−	0.689034i	−0.964084	+	0.265598i	$0.914431\pi$
$198$	−0.875280	+	2.34672i	−0.0622035	+	0.166774i
$199$	4.73484	−	3.04289i	0.335644	−	0.215705i	−0.361952	−	0.932197i	$-0.617890\pi$
$199$	4.73484	−	3.04289i	0.335644	−	0.215705i	0.697596	+	0.716492i	$0.254253\pi$
$200$	−4.54922	+	2.07474i	−0.321679	+	0.146706i
$201$	15.4562	−	2.22227i	1.09020	−	0.156747i
$202$	0.252870	−	0.0943158i	0.0177919	−	0.00663604i
$203$	21.5107	−	16.1027i	1.50976	−	1.13019i
$204$	5.32976	+	3.42523i	0.373158	+	0.239814i
$205$	−6.96441	−	8.64684i	−0.486415	−	0.603922i
$206$		−	1.32994i		−	0.0926615i
$207$	−1.80704	−	4.44236i	−0.125598	−	0.308766i
$208$	−0.397505	+	0.397505i	−0.0275620	+	0.0275620i
$209$	−13.3391	+	11.5584i	−0.922688	+	0.799513i
$210$	6.56780	−	1.18322i	0.453221	−	0.0816501i
$211$	−1.18461	+	8.23912i	−0.0815516	+	0.567204i	0.907547	+	0.419950i	$0.137953\pi$
$211$	−1.18461	+	8.23912i	−0.0815516	+	0.567204i	−0.989099	+	0.147254i	$0.952957\pi$
$212$	−4.95563	−	13.2865i	−0.340354	−	0.912524i
$213$	−8.24040	−	6.16868i	−0.564623	−	0.422671i
$214$	6.04256	+	1.77426i	0.413061	+	0.121286i
$215$	1.11987	+	0.286136i	0.0763747	+	0.0195143i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	6.55989	−	12.0135i	0.445315	−	0.815533i
$218$	−18.7136	+	1.33842i	−1.26745	+	0.0906495i
$219$	7.96342	+	6.90034i	0.538118	+	0.466282i
$220$	5.42692	−	1.38366i	0.365883	−	0.0932861i
$221$	3.23969	−	1.47952i	0.217925	−	0.0995232i
$222$	−0.915546	+	4.20870i	−0.0614474	+	0.282469i
$223$	−9.23581	+	5.04313i	−0.618475	+	0.337713i	−0.757754	−	0.652540i	$-0.773703\pi$
$223$	−9.23581	+	5.04313i	−0.618475	+	0.337713i	0.139279	+	0.990253i	$0.455522\pi$
$224$	−0.424738	−	2.95412i	−0.0283790	−	0.197380i
$225$	−4.38717	−	2.39850i	−0.292478	−	0.159900i
$226$	20.1862	+	2.90234i	1.34276	+	0.193060i
$227$	−18.0518	+	3.92693i	−1.19814	+	0.260639i	−0.767001	−	0.641646i	$-0.778252\pi$
$227$	−18.0518	+	3.92693i	−1.19814	+	0.260639i	−0.431139	+	0.902286i	$0.641888\pi$
$228$	0.502729	−	7.02906i	0.0332940	−	0.465511i
$229$	−2.94851			−0.194843			−0.0974215	−	0.995243i	$-0.531060\pi$
$229$	−2.94851			−0.194843			−0.0974215	+	0.995243i	$0.531060\pi$
$230$	−5.85734	+	8.98285i	−0.386222	+	0.592311i
$231$	−7.47507			−0.491823
$232$	−0.642286	+	8.98033i	−0.0421681	+	0.589588i
$233$	20.6819	−	4.49908i	1.35492	−	0.294745i	0.524275	−	0.851549i	$-0.324336\pi$
$233$	20.6819	−	4.49908i	1.35492	−	0.294745i	0.830644	+	0.556804i	$0.187973\pi$
$234$	−0.556435	−	0.0800033i	−0.0363753	−	0.00522998i
$235$	9.23028	−	3.06950i	0.602117	−	0.200232i
$236$	−0.693167	−	4.82109i	−0.0451214	−	0.313826i
$237$	0.460875	−	0.251657i	0.0299371	−	0.0163469i
$238$	−4.01924	+	18.4761i	−0.260528	+	1.19763i
$239$	25.8952	−	11.8259i	1.67502	−	0.764957i	0.675400	−	0.737451i	$-0.263971\pi$
$239$	25.8952	−	11.8259i	1.67502	−	0.764957i	0.999622	−	0.0275058i	$-0.00875647\pi$
$240$	−1.14149	+	1.92276i	−0.0736830	+	0.124113i
$241$	3.08360	+	2.67195i	0.198632	+	0.172116i	0.748498	−	0.663138i	$-0.230776\pi$
$241$	3.08360	+	2.67195i	0.198632	+	0.172116i	−0.549865	+	0.835253i	$0.685321\pi$
$242$	4.71476	−	0.337206i	0.303076	−	0.0216764i
$243$	0.479249	−	0.877679i	0.0307438	−	0.0563031i
$244$	−1.24922	−	2.73541i	−0.0799732	−	0.175117i
$245$	2.17517	+	3.66820i	0.138967	+	0.234353i
$246$	−4.76417	−	1.39889i	−0.303752	−	0.0891897i
$247$	−3.17137	−	2.37406i	−0.201789	−	0.151058i
$248$	1.60276	+	4.29716i	0.101775	+	0.272870i
$249$	0.416399	−	2.89612i	0.0263882	−	0.183534i
$250$	1.18657	+	11.1172i	0.0750452	+	0.703113i
$251$	10.5939	−	9.17967i	0.668681	−	0.579416i	−0.252951	−	0.967479i	$-0.581401\pi$
$251$	10.5939	−	9.17967i	0.668681	−	0.579416i	0.921633	+	0.388063i	$0.126856\pi$
$252$	2.11036	−	2.11036i	0.132940	−	0.132940i
$253$	8.24086	−	8.73910i	0.518098	−	0.549422i
$254$			5.20783i			0.326768i
$255$	11.0330	−	8.88627i	0.690912	−	0.556480i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−15.1941	+	11.3741i	−0.947781	+	0.709500i	−0.956888	−	0.290459i	$-0.906192\pi$
$257$	−15.1941	+	11.3741i	−0.947781	+	0.709500i	0.00910663	+	0.999959i	$0.497101\pi$
$258$	0.484320	−	0.180642i	0.0301525	−	0.0112463i
$259$	−12.7238	+	1.82940i	−0.790615	+	0.113673i
$260$	0.562376	+	1.12420i	0.0348771	+	0.0697202i
$261$	−7.57403	+	4.86754i	−0.468821	+	0.301293i
$262$	0.246957	−	0.662118i	0.0152571	−	0.0409058i
$263$	−26.9433	−	14.7122i	−1.66140	−	0.907191i	−0.985394	−	0.170291i	$-0.945529\pi$
$263$	−26.9433	−	14.7122i	−1.66140	−	0.907191i	−0.676002	−	0.736900i	$-0.736289\pi$
$264$	1.64019	−	1.89288i	0.100947	−	0.116499i
$265$	−31.6890	+	1.12364i	−1.94664	+	0.0690244i
$266$	20.1798	−	5.92534i	1.23731	−	0.363306i
$267$	9.73335	+	3.63035i	0.595671	+	0.222174i
$268$	−15.2583	−	3.31924i	−0.932050	−	0.202755i
$269$	5.96439	−	20.3129i	0.363656	−	1.23850i	−0.551083	−	0.834451i	$-0.685785\pi$
$269$	5.96439	−	20.3129i	0.363656	−	1.23850i	0.914738	−	0.404047i	$-0.132397\pi$
$270$	−2.22332	+	0.238454i	−0.135307	+	0.0145119i
$271$	−4.15588	+	9.10010i	−0.252452	+	0.552792i	−0.992849	−	0.119378i	$-0.961910\pi$
$271$	−4.15588	+	9.10010i	−0.252452	+	0.552792i	0.740397	+	0.672169i	$0.234637\pi$
$272$	−3.79672	−	5.07183i	−0.230210	−	0.307525i
$273$	−0.356632	−	1.63941i	−0.0215844	−	0.0992217i
$274$	1.44303	+	1.66534i	0.0871764	+	0.100607i
$275$	0.899801	−	12.4908i	0.0542601	−	0.753224i
$276$	0.140662	+	4.79377i	0.00846683	+	0.288551i
$277$	−1.31549	−	1.31549i	−0.0790400	−	0.0790400i	0.666482	−	0.745522i	$-0.267800\pi$
$277$	−1.31549	−	1.31549i	−0.0790400	−	0.0790400i	−0.745522	+	0.666482i	$0.767800\pi$
$278$	6.43611	+	0.460319i	0.386012	+	0.0276081i
$279$	−2.47955	+	3.85826i	−0.148447	+	0.230988i
$280$	−6.56719	−	1.18659i	−0.392465	−	0.0709124i
$281$	7.78865	+	3.55696i	0.464632	+	0.212190i	0.633955	−	0.773370i	$-0.281431\pi$
$281$	7.78865	+	3.55696i	0.464632	+	0.212190i	−0.169322	+	0.985561i	$0.554158\pi$
$282$	2.60696	−	3.48249i	0.155242	−	0.207379i
$283$	−10.8020	−	19.7823i	−0.642109	−	1.17594i	−0.972679	−	0.232154i	$-0.925423\pi$
$283$	−10.8020	−	19.7823i	−0.642109	−	1.17594i	0.330570	−	0.943782i	$-0.392759\pi$
$284$	5.56510	+	8.65947i	0.330228	+	0.513845i
$285$	−14.5566	−	6.03391i	−0.862258	−	0.357418i
$286$	−0.396679	−	1.35096i	−0.0234561	−	0.0798842i
$287$	−1.05717	−	14.7811i	−0.0624026	−	0.872503i
$288$	0.0713392	+	0.997452i	0.00420370	+	0.0587754i
$289$	6.51887	+	22.2012i	0.383463	+	1.30595i
$290$	18.5975	+	7.70892i	1.09208	+	0.452684i
$291$	−2.89955	−	4.51179i	−0.169975	−	0.264486i
$292$	−5.04990	−	9.24820i	−0.295523	−	0.541210i
$293$	−13.0438	+	17.4245i	−0.762028	+	1.01795i	0.236895	+	0.971535i	$0.423870\pi$
$293$	−13.0438	+	17.4245i	−0.762028	+	1.01795i	−0.998922	+	0.0464144i	$0.985221\pi$
$294$	1.73485	+	0.792280i	0.101179	+	0.0462067i
$295$	−10.7176	−	1.93650i	−0.624002	−	0.112748i
$296$	2.32861	−	3.62339i	0.135348	−	0.210605i
$297$	2.49825	+	0.178679i	0.144963	+	0.0103680i
$298$	−9.00918	−	9.00918i	−0.521888	−	0.521888i
$299$	2.30980	+	1.39043i	0.133579	+	0.0804104i
$300$	3.27236	+	3.78043i	0.188930	+	0.218263i
$301$	1.01027	+	1.16591i	0.0582308	+	0.0672019i
$302$	−0.722177	−	3.31980i	−0.0415566	−	0.191033i
$303$	−0.161737	−	0.216056i	−0.00929156	−	0.0124121i
$304$	−2.92744	+	6.41019i	−0.167900	+	0.367650i
$305$	−6.68588	+	0.717072i	−0.382832	+	0.0410594i
$306$	1.78492	−	6.07886i	0.102037	−	0.347505i
$307$	9.26483	+	2.01544i	0.528772	+	0.115027i	0.469023	−	0.883186i	$-0.344606\pi$
$307$	9.26483	+	2.01544i	0.528772	+	0.115027i	0.0597492	+	0.998213i	$0.480970\pi$
$308$	7.00376	+	2.61227i	0.399076	+	0.148848i
$309$	−1.27607	+	0.374688i	−0.0725931	+	0.0213153i
$310$	10.2489	−	0.363408i	0.582098	−	0.0206402i
$311$	16.2666	−	18.7726i	0.922393	−	1.06450i	−0.0753369	−	0.997158i	$-0.524003\pi$
$311$	16.2666	−	18.7726i	0.922393	−	1.06450i	0.997730	−	0.0673403i	$-0.0214513\pi$
$312$	0.493393	+	0.269413i	0.0279329	+	0.0152525i
$313$	8.18288	−	21.9391i	0.462524	−	1.24007i	−0.471183	−	0.882035i	$-0.656173\pi$
$313$	8.18288	−	21.9391i	0.462524	−	1.24007i	0.933707	−	0.358038i	$-0.116554\pi$
$314$	−19.6038	+	12.5986i	−1.10631	+	0.710981i
$315$	−2.98566	−	5.96841i	−0.168223	−	0.336282i
$316$	−0.519762	+	0.0747305i	−0.0292389	+	0.00420392i
$317$	−22.1265	+	8.25277i	−1.24275	+	0.463522i	−0.882932	−	0.469501i	$-0.844434\pi$
$317$	−22.1265	+	8.25277i	−1.24275	+	0.463522i	−0.359818	+	0.933023i	$0.617161\pi$
$318$	−11.3522	+	8.49814i	−0.636599	+	0.476552i
$319$	−18.9702	−	12.1914i	−1.06213	−	0.682587i
$320$	1.74146	−	1.40262i	0.0973503	−	0.0784087i
$321$		−	6.29766i		−	0.351501i
$322$	−13.2582	+	5.39311i	−0.738851	+	0.300546i
$323$	31.5697	−	31.5697i	1.75659	−	1.75659i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	2.78238	−	0.398589i	0.154339	−	0.0221097i
$326$	−0.224741	+	1.56311i	−0.0124473	+	0.0865727i
$327$	6.55644	+	17.5785i	0.362572	+	0.972094i
$328$	3.97492	+	2.97559i	0.219478	+	0.164300i
$329$	12.4572	+	3.65775i	0.686785	+	0.201658i
$330$	−2.85655	−	4.81727i	−0.157248	−	0.265182i
$331$	−9.71322	−	21.2690i	−0.533887	−	1.16905i	−0.963909	−	0.266231i	$-0.914222\pi$
$331$	−9.71322	−	21.2690i	−0.533887	−	1.16905i	0.430023	−	0.902818i	$-0.358506\pi$
$332$	−1.40223	+	2.56800i	−0.0769576	+	0.140937i
$333$	4.29615	−	0.307267i	0.235428	−	0.0168381i
$334$	−9.18840	−	7.96180i	−0.502767	−	0.435650i
$335$	−17.8246	+	30.0242i	−0.973862	+	1.64040i
$336$	−2.71479	+	1.23980i	−0.148104	+	0.0676368i
$337$	−4.84473	+	22.2709i	−0.263909	+	1.21317i	0.634120	+	0.773235i	$0.281363\pi$
$337$	−4.84473	+	22.2709i	−0.263909	+	1.21317i	−0.898029	+	0.439937i	$0.855001\pi$
$338$	−11.1325	+	6.07878i	−0.605526	+	0.330642i
$339$	−2.90234	−	20.1862i	−0.157633	−	1.09636i
$340$	−13.4428	+	4.47036i	−0.729037	+	0.242439i
$341$	−11.3702	−	1.63478i	−0.615728	−	0.0885284i
$342$	−6.88597	+	1.49795i	−0.372351	+	0.0810000i
$343$	1.08431	−	15.1607i	0.0585475	−	0.818601i
$344$	−0.516912			−0.0278700
$345$	10.2692	+	3.08932i	0.552874	+	0.166323i
$346$	−15.2086			−0.817617
$347$	−0.915459	+	12.7998i	−0.0491444	+	0.687129i	0.911843	+	0.410538i	$0.134659\pi$
$347$	−0.915459	+	12.7998i	−0.0491444	+	0.687129i	−0.960988	+	0.276591i	$0.910795\pi$
$348$	8.79752	−	1.91378i	0.471596	−	0.102590i
$349$	−7.61352	−	1.09466i	−0.407542	−	0.0585958i	−0.0645047	−	0.997917i	$-0.520547\pi$
$349$	−7.61352	−	1.09466i	−0.407542	−	0.0585958i	−0.343038	+	0.939322i	$0.611456\pi$
$350$	−7.15830	+	13.0935i	−0.382627	+	0.699875i
$351$	0.0800033	+	0.556435i	0.00427026	+	0.0297003i
$352$	−2.19827	+	1.20034i	−0.117168	+	0.0639785i
$353$	1.70213	−	7.82457i	0.0905953	−	0.416460i	−0.909405	−	0.415913i	$-0.863462\pi$
$353$	1.70213	−	7.82457i	0.0905953	−	0.416460i	1.00000		0.000547293i	$-0.000174209\pi$
$354$	−4.43051	+	2.02335i	−0.235479	+	0.107540i
$355$	22.3035	−	5.68654i	1.18375	−	0.301810i
$356$	−7.85098	−	6.80292i	−0.416101	−	0.360554i
$357$	18.8601	−	1.34890i	0.998181	−	0.0713913i
$358$	−3.56885	+	6.53586i	−0.188620	+	0.345431i
$359$	−2.46715	−	5.40232i	−0.130211	−	0.285123i	0.833285	−	0.552843i	$-0.186457\pi$
$359$	−2.46715	−	5.40232i	−0.130211	−	0.285123i	−0.963497	+	0.267720i	$0.913730\pi$
$360$	2.16647	+	0.553550i	0.114183	+	0.0291746i
$361$	−29.4185	−	8.63806i	−1.54834	−	0.454635i
$362$	−19.2425	−	14.4048i	−1.01136	−	0.757097i
$363$	−1.65185	−	4.42878i	−0.0866995	−	0.232450i
$364$	−0.238769	+	1.66068i	−0.0125149	+	0.0870431i
$365$	−23.1884	+	4.17751i	−1.21374	+	0.218661i
$366$	−2.27266	+	1.96927i	−0.118794	+	0.102936i
$367$	−15.4537	+	15.4537i	−0.806677	+	0.806677i	−0.984129	−	0.177452i	$-0.943215\pi$
$367$	−15.4537	+	15.4537i	−0.806677	+	0.806677i	0.177452	+	0.984129i	$0.443215\pi$
$368$	1.54346	−	4.54068i	0.0804583	−	0.236699i
$369$			4.96530i			0.258483i
$370$	−6.04125	−	7.50067i	−0.314070	−	0.389941i
$371$	−35.6036	−	22.8810i	−1.84844	−	1.18792i
$372$	3.67154	−	2.74848i	0.190361	−	0.142502i
$373$	−15.7328	+	5.86802i	−0.814612	+	0.303834i	−0.722022	−	0.691870i	$-0.756787\pi$
$373$	−15.7328	+	5.86802i	−0.814612	+	0.303834i	−0.0925895	+	0.995704i	$0.529514\pi$
$374$	15.7066	−	2.25827i	0.812168	−	0.116772i
$375$	10.3326	−	4.27058i	0.533572	−	0.220532i
$376$	−3.65960	+	2.35188i	−0.188729	+	0.121289i
$377$	1.76873	−	4.74214i	0.0910940	−	0.244233i
$378$	−2.61943	−	1.43032i	−0.134729	−	0.0735675i
$379$	−0.0661737	+	0.0763685i	−0.00339911	+	0.00392279i	−0.757447	−	0.652897i	$-0.773553\pi$
$379$	−0.0661737	+	0.0763685i	−0.00339911	+	0.00392279i	0.754047	+	0.656820i	$0.228099\pi$
$380$	11.5302	+	10.7405i	0.591485	+	0.550975i
$381$	4.99688	−	1.46722i	0.255998	−	0.0751677i
$382$	−4.59293	−	1.71308i	−0.234995	−	0.0876485i
$383$	9.09396	+	1.97827i	0.464680	+	0.101085i	0.438809	−	0.898580i	$-0.355401\pi$
$383$	9.09396	+	1.97827i	0.464680	+	0.101085i	0.0258708	+	0.999665i	$0.491764\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	10.4913	−	13.0121i	0.534688	−	0.663159i
$386$	−5.41530	+	11.8579i	−0.275632	+	0.603549i
$387$	−0.309774	−	0.413809i	−0.0157467	−	0.0210351i
$388$	1.14002	+	5.24061i	0.0578760	+	0.266051i
$389$	−2.70268	−	3.11905i	−0.137031	−	0.158142i	0.683086	−	0.730338i	$-0.260637\pi$
$389$	−2.70268	−	3.11905i	−0.137031	−	0.158142i	−0.820117	+	0.572195i	$0.806092\pi$
$390$	0.920227	−	0.856321i	0.0465975	−	0.0433615i
$391$	−19.2152	+	23.5364i	−0.971755	+	1.19029i
$392$	−1.34860	−	1.34860i	−0.0681143	−	0.0681143i
$393$	−0.704874	−	0.0504136i	−0.0355562	−	0.00254303i
$394$	10.9099	−	16.9762i	0.549634	−	0.855247i
$395$	−0.208775	+	1.15546i	−0.0105046	+	0.0581377i
$396$	−2.27830	−	1.04046i	−0.114489	−	0.0522852i
$397$	1.52186	−	2.03297i	0.0763800	−	0.102032i	−0.760724	−	0.649075i	$-0.775156\pi$
$397$	1.52186	−	2.03297i	0.0763800	−	0.102032i	0.837104	+	0.547044i	$0.184247\pi$
$398$	2.69736	+	4.93985i	0.135207	+	0.247612i
$399$	−11.3706	−	17.6931i	−0.569244	−	0.885761i
$400$	−1.74492	−	4.68564i	−0.0872459	−	0.234282i
$401$	2.17359	+	7.40258i	0.108544	+	0.369667i	0.995794	−	0.0916223i	$-0.0292052\pi$
$401$	2.17359	+	7.40258i	0.108544	+	0.369667i	−0.887250	+	0.461289i	$0.847387\pi$
$402$	1.11397	+	15.5754i	0.0555600	+	0.776830i
$403$	−0.183929	−	2.57167i	−0.00916217	−	0.128104i
$404$	0.0760359	+	0.258955i	0.00378293	+	0.0128835i
$405$	0.855176	+	2.06608i	0.0424940	+	0.102664i
$406$	14.5271	+	22.6047i	0.720969	+	1.12185i
$407$	5.17003	+	9.46821i	0.256269	+	0.469322i
$408$	−3.79672	+	5.07183i	−0.187966	+	0.251093i
$409$	−10.0553	−	4.59209i	−0.497201	−	0.227064i	0.150999	−	0.988534i	$-0.451751\pi$
$409$	−10.0553	−	4.59209i	−0.497201	−	0.227064i	−0.648201	+	0.761470i	$0.724478\pi$
$410$	9.12164	−	6.32980i	0.450486	−	0.312607i
$411$	1.19133	−	1.85375i	0.0587642	−	0.0914389i
$412$	1.32655	+	0.0948770i	0.0653546	+	0.00467425i
$413$	−10.2788	−	10.2788i	−0.505788	−	0.505788i
$414$	4.55996	−	1.48552i	0.224110	−	0.0730095i
$415$	4.45695	+	4.78957i	0.218783	+	0.235111i
$416$	−0.368135	−	0.424850i	−0.0180493	−	0.0208300i
$417$	−1.37159	−	6.30508i	−0.0671669	−	0.308761i
$418$	−10.5774	−	14.1297i	−0.517357	−	0.691107i
$419$	1.79476	−	3.92998i	0.0876799	−	0.191992i	−0.860712	−	0.509091i	$-0.829982\pi$
$419$	1.79476	−	3.92998i	0.0876799	−	0.191992i	0.948392	+	0.317099i	$0.102709\pi$
$420$	0.711666	+	6.63548i	0.0347257	+	0.323778i
$421$	−1.97497	+	6.72611i	−0.0962539	+	0.327811i	−0.993517	−	0.113686i	$-0.963734\pi$
$421$	−1.97497	+	6.72611i	−0.0962539	+	0.327811i	0.897263	+	0.441497i	$0.145552\pi$
$422$	−8.13362	−	1.76936i	−0.395938	−	0.0861311i
$423$	−4.07589	−	1.52023i	−0.198177	−	0.0739161i
$424$	13.6062	−	3.99515i	0.660777	−	0.194022i
$425$	−0.0162508	+	31.6775i	−0.000788279	+	1.53658i
$426$	6.74083	−	7.77933i	0.326594	−	0.376910i
$427$	−7.87705	−	4.30119i	−0.381197	−	0.208149i
$428$	−2.20081	+	5.90059i	−0.106380	+	0.285216i
$429$	−1.18448	+	0.761221i	−0.0571874	+	0.0367521i
$430$	−0.365298	+	1.09661i	−0.0176162	+	0.0528831i
$431$	28.4223	−	4.08651i	1.36905	−	0.196840i	0.581732	−	0.813381i	$-0.302375\pi$
$431$	28.4223	−	4.08651i	1.36905	−	0.196840i	0.787323	+	0.616540i	$0.211466\pi$
$432$	0.936950	−	0.349464i	0.0450790	−	0.0168136i
$433$	−15.6276	+	11.6987i	−0.751016	+	0.562203i	−0.904767	−	0.425906i	$-0.859955\pi$
$433$	−15.6276	+	11.6987i	−0.751016	+	0.562203i	0.153752	+	0.988110i	$0.450864\pi$
$434$	11.5150	+	7.40022i	0.552736	+	0.355222i
$435$	2.15714	−	20.0160i	0.103427	−	0.959695i
$436$		−	18.7614i		−	0.898509i
$437$	33.2205	+	6.21224i	1.58915	+	0.297172i
$438$	−7.45086	+	7.45086i	−0.356016	+	0.356016i
$439$	19.6822	−	17.0548i	0.939382	−	0.813979i	−0.0433416	−	0.999060i	$-0.513800\pi$
$439$	19.6822	−	17.0548i	0.939382	−	0.813979i	0.982723	+	0.185082i	$0.0592549\pi$
$440$	0.992979	+	5.51180i	0.0473384	+	0.262765i
$441$	0.271423	−	1.88779i	0.0129249	−	0.0898947i
$442$	1.24463	+	3.33699i	0.0592011	+	0.158724i
$443$	0.263314	+	0.197115i	0.0125104	+	0.00936519i	0.605515	−	0.795834i	$-0.292967\pi$
$443$	0.263314	+	0.197115i	0.0125104	+	0.00936519i	−0.593004	+	0.805199i	$0.702058\pi$
$444$	−4.13266	−	1.21346i	−0.196127	−	0.0575882i
$445$	−19.9803	+	11.8480i	−0.947159	+	0.561647i
$446$	−4.37141	−	9.57205i	−0.206992	−	0.453250i
$447$	−6.10607	+	11.1824i	−0.288807	+	0.528911i
$448$	2.97689	−	0.212911i	0.140645	−	0.0100591i
$449$	−8.86767	−	7.68388i	−0.418491	−	0.362625i	0.420015	−	0.907517i	$-0.362025\pi$
$449$	−8.86767	−	7.68388i	−0.418491	−	0.362625i	−0.838506	+	0.544893i	$0.816570\pi$
$450$	2.70536	−	4.20488i	0.127532	−	0.198220i
$451$	−11.3124	+	5.16621i	−0.532681	+	0.243267i
$452$	−4.33501	+	19.9277i	−0.203902	+	0.937320i
$453$	−2.98186	+	1.62822i	−0.140100	+	0.0765004i
$454$	−2.62912	−	18.2859i	−0.123391	−	0.858202i
$455$	3.35432	+	1.68013i	0.157253	+	0.0787657i
$456$	6.97529	+	1.00290i	0.326648	+	0.0469649i
$457$	−19.0786	+	4.15030i	−0.892461	+	0.194143i	−0.635337	−	0.772235i	$-0.719139\pi$
$457$	−19.0786	+	4.15030i	−0.892461	+	0.194143i	−0.257124	+	0.966378i	$0.582775\pi$
$458$	0.210344	−	2.94100i	0.00982875	−	0.137424i
$459$	−6.33550			−0.295716
$460$	−8.54210	−	6.48325i	−0.398278	−	0.302283i
$461$	18.2925			0.851966			0.425983	−	0.904731i	$-0.359928\pi$
$461$	18.2925			0.851966			0.425983	+	0.904731i	$0.359928\pi$
$462$	0.533265	−	7.45602i	0.0248097	−	0.346886i
$463$	−3.37489	+	0.734162i	−0.156844	+	0.0341194i	−0.290302	−	0.956935i	$-0.593756\pi$
$463$	−3.37489	+	0.734162i	−0.156844	+	0.0341194i	0.133457	+	0.991055i	$0.457392\pi$
$464$	−8.91163	−	1.28130i	−0.413712	−	0.0594828i
$465$	−3.23613	−	9.73136i	−0.150072	−	0.451281i
$466$	3.01219	+	20.9502i	0.139537	+	0.970500i
$467$	8.77091	−	4.78928i	0.405869	−	0.221621i	−0.263328	−	0.964706i	$-0.584820\pi$
$467$	8.77091	−	4.78928i	0.405869	−	0.221621i	0.669197	+	0.743085i	$0.266638\pi$
$468$	0.119495	−	0.549310i	0.00552366	−	0.0253919i
$469$	−42.3919	+	19.3598i	−1.95748	+	0.893950i
$470$	2.40320	+	9.42574i	0.110851	+	0.434777i
$471$	17.6113	+	15.2603i	0.811487	+	0.703158i
$472$	4.85825	−	0.347469i	0.223619	−	0.0159936i
$473$	0.620472	−	1.13631i	0.0285293	−	0.0522476i
$474$	0.218137	+	0.477654i	0.0100194	+	0.0219394i
$475$	30.9338	−	16.8705i	1.41934	−	0.774072i
$476$	−18.1423	−	5.32707i	−0.831552	−	0.244166i
$477$	11.3522	+	8.49814i	0.519781	+	0.389103i
$478$	9.94847	+	26.6729i	0.455033	+	1.21999i
$479$	−4.04200	+	28.1127i	−0.184684	+	1.28450i	0.660825	+	0.750540i	$0.270207\pi$
$479$	−4.04200	+	28.1127i	−0.184684	+	1.28450i	−0.845508	+	0.533962i	$0.820702\pi$
$480$	−1.83643	−	1.27575i	−0.0838210	−	0.0582298i
$481$	−1.82988	+	1.58560i	−0.0834355	+	0.0722972i
$482$	−2.88513	+	2.88513i	−0.131414	+	0.131414i
$483$	8.90992	+	11.2017i	0.405415	+	0.509697i
$484$			4.72680i			0.214855i
$485$	11.9234	+	1.28499i	0.541413	+	0.0583484i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	−4.49016	+	3.36129i	−0.203468	+	0.152315i	−0.696153	−	0.717893i	$-0.745107\pi$
$487$	−4.49016	+	3.36129i	−0.203468	+	0.152315i	0.492685	+	0.870208i	$0.336016\pi$
$488$	2.81756	−	1.05090i	0.127545	−	0.0475718i
$489$	1.56311	−	0.224741i	0.0706863	−	0.0101632i
$490$	−3.81403	+	1.90794i	−0.172300	+	0.0861921i
$491$	15.6329	−	10.0466i	0.705501	−	0.453398i	−0.138065	−	0.990423i	$-0.544088\pi$
$491$	15.6329	−	10.0466i	0.705501	−	0.453398i	0.843566	+	0.537025i	$0.180452\pi$
$492$	1.73519	−	4.65223i	0.0782285	−	0.209739i
$493$	50.0630	+	27.3364i	2.25472	+	1.23117i
$494$	2.59425	−	2.99393i	0.116721	−	0.134703i
$495$	−3.81736	+	4.09802i	−0.171577	+	0.184192i
$496$	−4.40055	+	1.29212i	−0.197590	+	0.0580178i
$497$	28.7840	+	10.7359i	1.29114	+	0.481570i
$498$	2.85903	+	0.621945i	0.128116	+	0.0278700i
$499$	0.922745	−	3.14258i	0.0413077	−	0.140681i	−0.936257	−	0.351315i	$-0.885735\pi$
$499$	0.922745	−	3.14258i	0.0413077	−	0.140681i	0.977565	+	0.210634i	$0.0675528\pi$
$500$	−11.1735	+	0.390454i	−0.499695	+	0.0174617i
$501$	−5.05062	+	11.0593i	−0.225645	+	0.494093i
$502$	8.40052	+	11.2218i	0.374934	+	0.500853i
$503$	−5.17075	−	23.7696i	−0.230552	−	1.05983i	−0.936254	−	0.351323i	$-0.885732\pi$
$503$	−5.17075	−	23.7696i	−0.230552	−	1.05983i	0.705702	−	0.708509i	$-0.250632\pi$
$504$	1.95443	+	2.25553i	0.0870571	+	0.100469i
$505$	0.603095	+	0.0216945i	0.0268374	+	0.000965393i
$506$	8.12893	+	8.84330i	0.361375	+	0.393133i
$507$	8.96893	+	8.96893i	0.398324	+	0.398324i
$508$	−5.19456	−	0.371522i	−0.230471	−	0.0164836i
$509$	13.4724	−	20.9635i	0.597153	−	0.929189i	−0.402750	−	0.915310i	$-0.631946\pi$
$509$	13.4724	−	20.9635i	0.597153	−	0.929189i	0.999904	−	0.0138789i	$-0.00441792\pi$
$510$	8.07655	+	11.6388i	0.357635	+	0.515375i
$511$	−28.6061	−	13.0639i	−1.26546	−	0.577915i
$512$	−0.599278	+	0.800541i	−0.0264846	+	0.0353793i
$513$	3.37728	+	6.18502i	0.149110	+	0.273075i
$514$	−10.2612	−	15.9668i	−0.452604	−	0.704265i
$515$	1.13874	−	2.74718i	0.0501791	−	0.121055i
$516$	0.145631	+	0.495973i	0.00641104	+	0.0218340i
$517$	−0.777283	−	10.8678i	−0.0341849	−	0.477967i
$518$	−0.917036	−	12.8218i	−0.0402923	−	0.563359i
$519$	4.28474	+	14.5925i	0.188079	+	0.640540i
$520$	−1.16146	+	0.480743i	−0.0509334	+	0.0210820i
$521$	14.7268	+	22.9153i	0.645191	+	1.00394i	0.997677	+	0.0681199i	$0.0217000\pi$
$521$	14.7268	+	22.9153i	0.645191	+	1.00394i	−0.352486	+	0.935817i	$0.614664\pi$
$522$	−4.31481	−	7.90198i	−0.188854	−	0.345860i
$523$	7.29888	−	9.75017i	0.319158	−	0.426345i	−0.612058	−	0.790813i	$-0.709658\pi$
$523$	7.29888	−	9.75017i	0.319158	−	0.426345i	0.931216	+	0.364468i	$0.118749\pi$
$524$	0.642814	+	0.293563i	0.0280814	+	0.0128244i
$525$	14.5798	+	3.17948i	0.636315	+	0.138764i
$526$	16.5968	−	25.8251i	0.723654	−	1.12603i
$527$	28.9826	+	2.07288i	1.26250	+	0.0902960i
$528$	1.77104	+	1.77104i	0.0770748	+	0.0770748i
$529$	−22.9187	−	1.93274i	−0.996463	−	0.0840321i
$530$	1.13989	−	31.6884i	0.0495138	−	1.37646i
$531$	3.18960	+	3.68100i	0.138417	+	0.159742i
$532$	4.47063	+	20.5511i	0.193826	+	0.891005i
$533$	−1.67275	−	2.23453i	−0.0724548	−	0.0967883i
$534$	−4.31547	+	9.44957i	−0.186749	+	0.408923i
$535$	10.9626	+	8.83883i	0.473953	+	0.382136i
$536$	4.39930	−	14.9827i	0.190021	−	0.647152i
$537$	7.27657	+	1.58292i	0.314007	+	0.0683081i
$538$	19.8356	+	7.39830i	0.855174	+	0.318963i
$539$	4.58335	−	1.34579i	0.197419	−	0.0579674i
$540$	−0.0792373	−	2.23466i	−0.00340983	−	0.0961646i
$541$	17.9514	−	20.7170i	0.771791	−	0.890694i	−0.224697	−	0.974429i	$-0.572139\pi$
$541$	17.9514	−	20.7170i	0.771791	−	0.890694i	0.996488	+	0.0837346i	$0.0266848\pi$
$542$	−8.78044	−	4.79448i	−0.377152	−	0.205941i
$543$	−8.40002	+	22.5213i	−0.360480	+	0.966483i
$544$	5.32976	−	3.42523i	0.228511	−	0.146855i
$545$	−39.8016	−	13.2586i	−1.70491	−	0.567935i
$546$	1.66068	−	0.238769i	0.0710704	−	0.0102184i
$547$	−22.2726	+	8.30725i	−0.952307	+	0.355192i	−0.777127	−	0.629344i	$-0.783324\pi$
$547$	−22.2726	+	8.30725i	−0.952307	+	0.355192i	−0.175181	+	0.984536i	$0.556051\pi$
$548$	−1.76404	+	1.32054i	−0.0753561	+	0.0564109i
$549$	2.52979	+	1.62580i	0.107969	+	0.0693873i
$550$	12.3948	+	1.78859i	0.528516	+	0.0762658i
$551$		−	63.4462i		−	2.70290i
$552$	−4.79159	−	0.201680i	−0.203944	−	0.00858408i
$553$	−1.10816	+	1.10816i	−0.0471238	+	0.0471238i
$554$	1.40598	−	1.21829i	0.0597345	−	0.0517602i
$555$	−5.49482	+	7.90972i	−0.233242	+	0.335749i
$556$	−0.918293	+	6.38687i	−0.0389443	+	0.270864i
$557$	−4.43056	−	11.8788i	−0.187729	−	0.503320i	0.808655	−	0.588283i	$-0.200196\pi$
$557$	−4.43056	−	11.8788i	−0.187729	−	0.503320i	−0.996384	+	0.0849623i	$0.972923\pi$
$558$	−3.67154	−	2.74848i	−0.155429	−	0.116353i
$559$	0.278815	+	0.0818674i	0.0117926	+	0.00346262i
$560$	1.65207	−	6.46581i	0.0698125	−	0.273230i
$561$	−6.59185	−	14.4341i	−0.278308	−	0.609410i
$562$	−4.10353	+	7.51506i	−0.173097	+	0.317004i
$563$	−0.964818	+	0.0690051i	−0.0406622	+	0.00290822i	−0.0916555	−	0.995791i	$-0.529216\pi$
$563$	−0.964818	+	0.0690051i	−0.0406622	+	0.00290822i	0.0509933	+	0.998699i	$0.483761\pi$
$564$	3.28764	+	2.84876i	0.138435	+	0.119954i
$565$	39.2123	+	23.2793i	1.64967	+	0.979368i
$566$	20.5025	−	9.36318i	0.861784	−	0.393564i
$567$	−0.634400	+	2.91629i	−0.0266423	+	0.122473i
$568$	−9.03442	+	4.93317i	−0.379076	+	0.206991i
$569$	2.15974	+	15.0213i	0.0905410	+	0.629726i	0.983677	+	0.179941i	$0.0575906\pi$
$569$	2.15974	+	15.0213i	0.0905410	+	0.629726i	−0.893136	+	0.449786i	$0.851500\pi$
$570$	7.05699	−	14.0890i	0.295585	−	0.590125i
$571$	24.3183	+	3.49644i	1.01769	+	0.146322i	0.630914	−	0.775853i	$-0.282680\pi$
$571$	24.3183	+	3.49644i	1.01769	+	0.146322i	0.386775	+	0.922174i	$0.373589\pi$
$572$	1.37582	−	0.299292i	0.0575260	−	0.0125140i
$573$	−0.349705	+	4.88951i	−0.0146091	+	0.204262i
$574$	14.8189			0.618529
$575$	−19.7906	+	13.5400i	−0.825324	+	0.564659i
$576$	−1.00000			−0.0416667
$577$	1.38631	−	19.3832i	0.0577130	−	0.806934i	−0.883352	−	0.468709i	$-0.844719\pi$
$577$	1.38631	−	19.3832i	0.0577130	−	0.806934i	0.941065	−	0.338224i	$-0.109826\pi$
$578$	−22.6097	+	4.91844i	−0.940440	+	0.204580i
$579$	12.9032	+	1.85520i	0.536239	+	0.0770995i
$580$	−9.01601	+	18.0002i	−0.374370	+	0.747416i
$581$	1.24274	+	8.64344i	0.0515575	+	0.358591i
$582$	4.70714	−	2.57029i	0.195117	−	0.106542i
$583$	−7.54975	+	34.7057i	−0.312679	+	1.43736i
$584$	9.58490	−	4.37728i	0.396626	−	0.181133i
$585$	−1.08089	−	0.641698i	−0.0446894	−	0.0265309i
$586$	−16.4496	−	14.2536i	−0.679525	−	0.588812i
$587$	−22.8085	+	1.63130i	−0.941408	+	0.0673308i	−0.533600	−	0.845737i	$-0.679161\pi$
$587$	−22.8085	+	1.63130i	−0.941408	+	0.0673308i	−0.407808	+	0.913068i	$0.633707\pi$
$588$	−0.914024	+	1.67391i	−0.0376937	+	0.0690309i
$589$	−13.4262	−	29.3992i	−0.553216	−	1.21137i
$590$	2.69615	−	10.5521i	0.110999	−	0.434424i
$591$	−19.3622	−	5.68525i	−0.796454	−	0.233860i
$592$	3.44803	+	2.58117i	0.141713	+	0.106085i
$593$	6.51645	+	17.4713i	0.267598	+	0.717459i	0.999356	+	0.0358936i	$0.0114277\pi$
$593$	6.51645	+	17.4713i	0.267598	+	0.717459i	−0.731757	+	0.681565i	$0.761300\pi$
$594$	−0.356447	+	2.47914i	−0.0146252	+	0.101720i
$595$	−24.1222	+	34.7236i	−0.988915	+	1.42353i
$596$	9.62894	−	8.34352i	0.394417	−	0.341764i
$597$	3.97982	−	3.97982i	0.162883	−	0.162883i
$598$	−1.55166	+	2.20473i	−0.0634522	+	0.0901580i
$599$			32.1140i			1.31214i	0.754699	+	0.656072i	$0.227783\pi$
$599$			32.1140i			1.31214i	−0.754699	+	0.656072i	$0.772217\pi$
$600$	−4.00424	+	2.99433i	−0.163473	+	0.122243i
$601$	−13.7684	−	8.84844i	−0.561627	−	0.360935i	0.228818	−	0.973469i	$-0.426514\pi$
$601$	−13.7684	−	8.84844i	−0.561627	−	0.360935i	−0.790444	+	0.612534i	$0.790150\pi$
$602$	−1.23501	+	0.924518i	−0.0503353	+	0.0376805i
$603$	14.6306	−	5.45695i	0.595806	−	0.222224i
$604$	3.36286	−	0.483506i	0.136833	−	0.0196736i
$605$	10.0277	+	3.34040i	0.407684	+	0.135807i
$606$	0.227043	−	0.145912i	0.00922300	−	0.00592726i
$607$	5.97957	−	16.0318i	0.242703	−	0.650713i	−0.757294	−	0.653074i	$-0.773479\pi$
$607$	5.97957	−	16.0318i	0.242703	−	0.650713i	0.999997	+	0.00236158i	$0.000751714\pi$
$608$	−6.18502	−	3.37728i	−0.250836	−	0.136967i
$609$	17.5962	−	20.3071i	0.713036	−	0.822887i
$610$	−0.238280	−	6.72000i	−0.00964766	−	0.272085i
$611$	2.34642	−	0.688971i	0.0949260	−	0.0278728i
$612$	5.93604	+	2.21403i	0.239950	+	0.0894968i
$613$	34.8112	+	7.57271i	1.40601	+	0.305859i	0.850642	−	0.525745i	$-0.176214\pi$
$613$	34.8112	+	7.57271i	1.40601	+	0.305859i	0.555369	+	0.831604i	$0.312577\pi$
$614$	−2.67125	+	9.09745i	−0.107803	+	0.367143i
$615$	−8.64327	−	6.96884i	−0.348530	−	0.281011i
$616$	−3.10526	+	6.79956i	−0.125114	+	0.273962i
$617$	−23.8009	−	31.7943i	−0.958188	−	1.27999i	−0.960003	−	0.279990i	$-0.909669\pi$
$617$	−23.8009	−	31.7943i	−0.958188	−	1.27999i	0.00181517	−	0.999998i	$-0.499422\pi$
$618$	−0.282700	−	1.29955i	−0.0113718	−	0.0522755i
$619$	17.1180	+	19.7553i	0.688032	+	0.794031i	0.987084	−	0.160206i	$-0.0512157\pi$
$619$	17.1180	+	19.7553i	0.688032	+	0.794031i	−0.299052	+	0.954237i	$0.596670\pi$
$620$	−0.368666	+	10.2487i	−0.0148060	+	0.411598i
$621$	−2.71004	−	3.95673i	−0.108750	−	0.158778i
$622$	17.5644	+	17.5644i	0.704267	+	0.704267i
$623$	−30.9249	−	2.21180i	−1.23898	−	0.0886137i
$624$	−0.303925	+	0.472917i	−0.0121667	+	0.0189318i
$625$	−7.06792	+	23.9801i	−0.282717	+	0.959203i
$626$	21.2995	+	9.72715i	0.851299	+	0.388775i
$627$	−10.5774	+	14.1297i	−0.422420	+	0.564287i
$628$	−11.1680	−	20.4527i	−0.445652	−	0.816150i
$629$	−14.7529	−	22.9559i	−0.588236	−	0.915313i
$630$	6.16619	−	2.55227i	0.245667	−	0.101685i
$631$	−4.20137	−	14.3086i	−0.167254	−	0.569615i	−0.999876	−	0.0157725i	$-0.994979\pi$
$631$	−4.20137	−	14.3086i	−0.167254	−	0.569615i	0.832622	−	0.553842i	$-0.186839\pi$
$632$	−0.0374607	−	0.523769i	−0.00149011	−	0.0208344i
$633$	0.593816	+	8.30263i	0.0236021	+	0.330000i
$634$	−6.65325	−	22.6589i	−0.264234	−	0.899900i
$635$	−4.45913	+	10.7575i	−0.176955	+	0.426898i
$636$	−7.66663	−	11.9295i	−0.304002	−	0.473036i
$637$	0.513825	+	0.941001i	0.0203585	+	0.0372838i
$638$	13.5137	−	18.0521i	0.535011	−	0.714691i
$639$	−9.36333	−	4.27609i	−0.370408	−	0.169159i
$640$	1.27481	+	1.83708i	0.0503913	+	0.0726170i
$641$	−6.33013	+	9.84987i	−0.250025	+	0.389046i	−0.943467	−	0.331466i	$-0.892457\pi$
$641$	−6.33013	+	9.84987i	−0.250025	+	0.389046i	0.693442	+	0.720512i	$0.256093\pi$
$642$	6.28162	+	0.449270i	0.247916	+	0.0177313i
$643$	23.7953	+	23.7953i	0.938394	+	0.938394i	0.998209	−	0.0598151i	$-0.0190511\pi$
$643$	23.7953	+	23.7953i	0.938394	+	0.938394i	−0.0598151	+	0.998209i	$0.519051\pi$
$644$	−4.43354	−	13.6092i	−0.174706	−	0.536276i
$645$	1.15510	+	0.0415513i	0.0454821	+	0.00163608i
$646$	29.2371	+	33.7415i	1.15032	+	1.32754i
$647$	−7.46993	−	34.3387i	−0.293673	−	1.34999i	−0.853374	−	0.521300i	$-0.825447\pi$
$647$	−7.46993	−	34.3387i	−0.293673	−	1.34999i	0.559700	−	0.828695i	$-0.310916\pi$
$648$	−0.599278	−	0.800541i	−0.0235419	−	0.0314482i
$649$	−5.06774	+	11.0968i	−0.198926	+	0.435588i
$650$	0.199081	+	2.80373i	0.00780859	+	0.109971i
$651$	3.85632	−	13.1334i	0.151141	−	0.514739i
$652$	−1.54310	−	0.335680i	−0.0604323	−	0.0131462i
$653$	36.2120	+	13.5064i	1.41708	+	0.528545i	0.937202	−	0.348788i	$-0.113407\pi$
$653$	36.2120	+	13.5064i	1.41708	+	0.528545i	0.479882	+	0.877333i	$0.340679\pi$
$654$	−18.0015	+	5.28570i	−0.703912	+	0.206687i
$655$	1.07705	−	1.15624i	0.0420840	−	0.0451781i
$656$	−3.25158	+	3.75252i	−0.126953	+	0.146511i
$657$	9.24820	+	5.04990i	0.360807	+	0.197015i
$658$	−4.53711	+	12.1645i	−0.176875	+	0.474221i
$659$	−40.9327	+	26.3058i	−1.59451	+	1.02473i	−0.624701	+	0.780864i	$0.714779\pi$
$659$	−40.9327	+	26.3058i	−1.59451	+	1.02473i	−0.969809	+	0.243866i	$0.921584\pi$
$660$	5.00878	−	2.50561i	0.194967	−	0.0975308i
$661$	−32.1731	+	4.62580i	−1.25139	+	0.179923i	−0.735969	−	0.677015i	$-0.763273\pi$
$661$	−32.1731	+	4.62580i	−1.25139	+	0.179923i	−0.515420	+	0.856938i	$0.672364\pi$
$662$	21.9077	−	8.17116i	0.851468	−	0.317581i
$663$	2.85116	−	2.13435i	0.110730	−	0.0828914i
$664$	−2.46142	−	1.58186i	−0.0955217	−	0.0613881i
$665$	46.7577	+	5.03911i	1.81319	+	0.195408i
$666$			4.30713i			0.166898i
$667$	4.34216	+	42.9593i	0.168129	+	1.66339i
$668$	8.59700	−	8.59700i	0.332628	−	0.332628i
$669$	−7.95275	+	6.89109i	−0.307471	+	0.266425i
$670$	−28.6761	−	19.9211i	−1.10785	−	0.769619i
$671$	−1.07189	+	7.45519i	−0.0413800	+	0.287804i
$672$	−1.04297	−	2.79632i	−0.0402336	−	0.107870i
$673$	−19.6339	−	14.6978i	−0.756831	−	0.566557i	0.149682	−	0.988734i	$-0.452175\pi$
$673$	−19.6339	−	14.6978i	−0.756831	−	0.566557i	−0.906513	+	0.422177i	$0.861266\pi$
$674$	−21.8685	−	6.42117i	−0.842343	−	0.247334i
$675$	−4.79674	−	1.41112i	−0.184627	−	0.0543142i
$676$	−5.26912	−	11.5378i	−0.202658	−	0.443760i
$677$	22.8076	−	41.7690i	0.876566	−	1.60531i	0.0832281	−	0.996531i	$-0.473477\pi$
$677$	22.8076	−	41.7690i	0.876566	−	1.60531i	0.793338	−	0.608781i	$-0.208341\pi$
$678$	20.3418	−	1.45487i	0.781222	−	0.0558741i
$679$	12.0968	+	10.4819i	0.464232	+	0.402260i
$680$	−3.49997	−	13.7274i	−0.134218	−	0.526423i
$681$	−16.8045	+	7.67437i	−0.643951	+	0.294082i
$682$	2.44175	−	11.2246i	0.0934996	−	0.429811i
$683$	−27.3534	+	14.9361i	−1.04665	+	0.571514i	−0.908062	−	0.418836i	$-0.862438\pi$
$683$	−27.3534	+	14.9361i	−1.04665	+	0.571514i	−0.138588	+	0.990350i	$0.544256\pi$
$684$	−1.00290	−	6.97529i	−0.0383467	−	0.266707i
$685$	1.55484	+	4.67556i	0.0594075	+	0.178644i
$686$	15.0447	+	2.16310i	0.574410	+	0.0825877i
$687$	−2.88113	+	0.626751i	−0.109922	+	0.0239120i
$688$	0.0368761	−	0.515595i	0.00140589	−	0.0196569i
$689$	−7.97175			−0.303699
$690$	−3.81404	+	10.0226i	−0.145198	+	0.381555i
$691$	30.6797			1.16711			0.583556	−	0.812073i	$-0.301661\pi$
$691$	30.6797			1.16711			0.583556	+	0.812073i	$0.301661\pi$
$692$	1.08497	−	15.1698i	0.0412442	−	0.576669i
$693$	−7.30424	+	1.58894i	−0.277465	+	0.0603588i
$694$	−12.7019	−	1.82625i	−0.482157	−	0.0693237i
$695$	12.9005	+	6.46168i	0.489345	+	0.245105i
$696$	1.28130	+	8.91163i	0.0485675	+	0.337794i
$697$	27.6097	−	15.0760i	1.04579	−	0.571045i
$698$	1.63501	−	7.51603i	0.0618861	−	0.284486i
$699$	19.2529	−	8.79253i	0.728213	−	0.332564i
$700$	−12.5494	−	8.07413i	−0.474324	−	0.305174i
$701$	0.528675	+	0.458100i	0.0199678	+	0.0173022i	0.664787	−	0.747033i	$-0.268522\pi$
$701$	0.528675	+	0.458100i	0.0199678	+	0.0173022i	−0.644820	+	0.764335i	$0.723068\pi$
$702$	−0.560725	+	0.0401038i	−0.0211632	+	0.00151362i
$703$	−14.5464	+	26.6397i	−0.548626	+	1.00473i
$704$	−1.04046	−	2.27830i	−0.0392139	−	0.0858665i
$705$	8.36687	−	4.96139i	0.315115	−	0.186857i
$706$	7.68321	+	2.25599i	0.289161	+	0.0849055i
$707$	0.644817	+	0.482704i	0.0242508	+	0.0181539i
$708$	−1.70212	−	4.56356i	−0.0639696	−	0.171509i
$709$	4.44269	−	30.8996i	0.166849	−	1.16046i	−0.718499	−	0.695528i	$-0.755170\pi$
$709$	4.44269	−	30.8996i	0.166849	−	1.16046i	0.885347	−	0.464930i	$-0.153921\pi$
$710$	4.08094	+	22.6524i	0.153155	+	0.850128i
$711$	0.396849	−	0.343872i	0.0148830	−	0.0128962i
$712$	7.34567	−	7.34567i	0.275290	−	0.275290i
$713$	11.1029	+	18.9873i	0.415806	+	0.711079i
$714$			18.9082i			0.707623i
$715$	0.337349	−	3.13025i	0.0126162	−	0.117065i
$716$	−6.26461	−	4.02602i	−0.234119	−	0.150459i
$717$	22.7896	−	17.0601i	0.851095	−	0.637122i
$718$	5.56456	−	2.07547i	0.207667	−	0.0774559i
$719$	−19.9233	+	2.86454i	−0.743015	+	0.106829i	−0.503418	−	0.864043i	$-0.667924\pi$
$719$	−19.9233	+	2.86454i	−0.743015	+	0.106829i	−0.239597	+	0.970872i	$0.577015\pi$
$720$	−0.706694	+	2.12146i	−0.0263369	+	0.0790621i
$721$	3.33911	−	2.14591i	0.124355	−	0.0799180i
$722$	10.7147	−	28.7273i	0.398761	−	1.06912i
$723$	3.58109	+	1.95542i	0.133182	+	0.0727230i
$724$	15.7408	−	18.1659i	0.585002	−	0.675129i
$725$	31.8150	+	31.8477i	1.18158	+	1.18279i
$726$	4.53533	−	1.33169i	0.168322	−	0.0494238i
$727$	29.1260	+	10.8634i	1.08022	+	0.402902i	0.825668	−	0.564156i	$-0.190798\pi$
$727$	29.1260	+	10.8634i	1.08022	+	0.402902i	0.254555	+	0.967058i	$0.418071\pi$
$728$	−1.63941	−	0.356632i	−0.0607607	−	0.0132177i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	−2.51262	−	23.4273i	−0.0929963	−	0.867085i
$731$	−1.36044	+	2.97895i	−0.0503177	+	0.110180i
$732$	−1.80213	−	2.40736i	−0.0666085	−	0.0889785i
$733$	6.53163	+	30.0254i	0.241251	+	1.10901i	0.925199	+	0.379483i	$0.123898\pi$
$733$	6.53163	+	30.0254i	0.241251	+	1.10901i	−0.683947	+	0.729532i	$0.739738\pi$
$734$	−14.3119	−	16.5168i	−0.528261	−	0.609646i
$735$	2.90520	+	3.12201i	0.107160	+	0.115157i
$736$	4.41900	+	1.86345i	0.162886	+	0.0686878i
$737$	27.6552	+	27.6552i	1.01869	+	1.01869i
$738$	−4.95265	−	0.354220i	−0.182309	−	0.0130390i
$739$	8.74185	−	13.6026i	0.321574	−	0.500379i	−0.642402	−	0.766368i	$-0.722062\pi$
$739$	8.74185	−	13.6026i	0.321574	−	0.500379i	0.963976	+	0.265989i	$0.0856984\pi$
$740$	7.91254	−	5.49076i	0.290871	−	0.201845i
$741$	−3.60354	−	1.64568i	−0.132379	−	0.0604556i
$742$	25.3627	−	33.8805i	0.931092	−	1.24379i
$743$	−9.02406	−	16.5263i	−0.331061	−	0.606293i	0.658134	−	0.752901i	$-0.271346\pi$
$743$	−9.02406	−	16.5263i	−0.331061	−	0.606293i	−0.989195	+	0.146608i	$0.953164\pi$
$744$	2.47955	+	3.85826i	0.0909049	+	0.141451i
$745$	−10.8957	−	26.3237i	−0.399188	−	0.964426i
$746$	−4.73070	−	16.1113i	−0.173203	−	0.589877i
$747$	−0.208731	−	2.91844i	−0.00763708	−	0.106780i
$748$	1.13202	+	15.8277i	0.0413907	+	0.578717i
$749$	5.29526	+	18.0340i	0.193484	+	0.658948i
$750$	3.52258	+	10.6109i	0.128627	+	0.387456i
$751$	−1.10765	−	1.72354i	−0.0404188	−	0.0628930i	0.820456	−	0.571709i	$-0.193720\pi$
$751$	−1.10765	−	1.72354i	−0.0404188	−	0.0628930i	−0.860875	+	0.508816i	$0.830083\pi$
$752$	−2.08482	−	3.81805i	−0.0760254	−	0.139230i
$753$	8.40052	−	11.2218i	0.306132	−	0.408944i
$754$	4.60388	+	2.10252i	0.167663	+	0.0765693i
$755$	1.35077	−	7.47585i	0.0491596	−	0.272074i
$756$	1.61354	−	2.51072i	0.0586838	−	0.0913138i
$757$	49.8330	+	3.56413i	1.81121	+	0.129540i	0.935507	−	0.353309i	$-0.114943\pi$
$757$	49.8330	+	3.56413i	1.81121	+	0.129540i	0.875704	+	0.482849i	$0.160398\pi$
$758$	−0.0714531	−	0.0714531i	−0.00259529	−	0.00259529i
$759$	6.19490	−	10.2911i	0.224861	−	0.373543i
$760$	−11.5357	+	10.7346i	−0.418443	+	0.389384i
$761$	27.9059	+	32.2052i	1.01159	+	1.16744i	0.985826	+	0.167769i	$0.0536561\pi$
$761$	27.9059	+	32.2052i	1.01159	+	1.16744i	0.0257632	+	0.999668i	$0.491798\pi$
$762$	1.10700	+	5.08882i	0.0401025	+	0.184348i
$763$	−33.5556	−	44.8250i	−1.21479	−	1.62277i
$764$	2.03637	−	4.45902i	0.0736731	−	0.161322i
$765$	8.89193	−	11.0284i	0.321488	−	0.398733i
$766$	−2.62198	+	8.92966i	−0.0947362	+	0.322642i
$767$	−2.67550	−	0.582020i	−0.0966068	−	0.0210155i
$768$	0.936950	+	0.349464i	0.0338093	+	0.0126102i
$769$	−6.11550	+	1.79567i	−0.220531	+	0.0647537i	−0.390131	−	0.920759i	$-0.627570\pi$
$769$	−6.11550	+	1.79567i	−0.220531	+	0.0647537i	0.169601	+	0.985513i	$0.445752\pi$
$770$	12.2305	+	11.3929i	0.440757	+	0.410571i
$771$	−12.4291	+	14.3439i	−0.447623	+	0.516585i
$772$	−11.4413	−	6.24743i	−0.411782	−	0.224850i
$773$	3.28627	−	8.81084i	0.118199	−	0.316904i	−0.864355	−	0.502883i	$-0.832273\pi$
$773$	3.28627	−	8.81084i	0.118199	−	0.316904i	0.982554	+	0.185979i	$0.0595456\pi$
$774$	0.434854	−	0.279464i	0.0156305	−	0.0100451i
$775$	21.4817	+	8.02480i	0.771644	+	0.288259i
$776$	−5.30858	+	0.763259i	−0.190567	+	0.0273994i
$777$	−12.0441	+	4.49222i	−0.432080	+	0.161157i
$778$	3.30391	−	2.47328i	0.118451	−	0.0886714i
$779$	−29.4359	−	18.9173i	−1.05465	−	0.677783i
$780$	0.788491	+	0.978971i	0.0282325	+	0.0350528i
$781$		−	25.7815i		−	0.922536i
$782$	−22.1056	−	20.8453i	−0.790495	−	0.745427i
$783$	−6.36627	+	6.36627i	−0.227512	+	0.227512i
$784$	1.44137	−	1.24895i	0.0514774	−	0.0446054i
$785$	−51.2818	+	9.23868i	−1.83033	+	0.329743i
$786$	0.100570	−	0.699481i	0.00358722	−	0.0249497i
$787$	−18.6679	−	50.0505i	−0.665437	−	1.78411i	−0.619277	−	0.785172i	$-0.712574\pi$
$787$	−18.6679	−	50.0505i	−0.665437	−	1.78411i	−0.0461601	−	0.998934i	$-0.514698\pi$
$788$	16.1546	+	12.0932i	0.575484	+	0.430802i
$789$	−29.4549	−	8.64873i	−1.04862	−	0.307903i
$790$	−1.13763	−	0.290673i	−0.0404750	−	0.0103417i
$791$	25.2843	+	55.3648i	0.899005	+	1.96855i
$792$	1.20034	−	2.19827i	0.0426524	−	0.0781120i
$793$	−1.68619	+	0.120599i	−0.0598784	+	0.00428259i
$794$	1.91922	+	1.66301i	0.0681105	+	0.0590181i
$795$	−30.7259	+	7.83393i	−1.08974	+	0.277841i
$796$	−5.11969	+	2.33808i	−0.181463	+	0.0828712i
$797$	−1.96456	+	9.03096i	−0.0695885	+	0.319893i	−0.998762	−	0.0497518i	$-0.984157\pi$
$797$	−1.96456	+	9.03096i	−0.0695885	+	0.319893i	0.929173	+	0.369645i	$0.120521\pi$
$798$	18.4592	−	10.0795i	0.653447	−	0.356809i
$799$	3.92227	+	27.2800i	0.138760	+	0.965096i
$800$	4.79819	−	1.40620i	0.169642	−	0.0497167i
$801$	10.2826	+	1.47841i	0.363318	+	0.0522372i
$802$	−7.53878	+	1.63996i	−0.266203	+	0.0579090i
$803$	−1.88276	+	26.3244i	−0.0664411	+	0.928967i
$804$	−15.6152			−0.550705
$805$	−32.0044	−	0.211944i	−1.12801	−	0.00747005i
$806$	2.57824			0.0908145
$807$	1.51028	−	21.1165i	0.0531644	−	0.743335i
$808$	−0.263719	+	0.0573686i	−0.00927761	+	0.00201822i
$809$	25.5354	+	3.67144i	0.897778	+	0.129081i	0.575728	−	0.817642i	$-0.304719\pi$
$809$	25.5354	+	3.67144i	0.897778	+	0.129081i	0.322050	+	0.946723i	$0.395628\pi$
$810$	−2.12182	+	0.705605i	−0.0745532	+	0.0247924i
$811$	1.10270	+	7.66943i	0.0387209	+	0.269310i	0.999980	−	0.00633682i	$-0.00201709\pi$
$811$	1.10270	+	7.66943i	0.0387209	+	0.269310i	−0.961259	+	0.275647i	$0.911108\pi$
$812$	−23.5834	+	12.8775i	−0.827616	+	0.451912i
$813$	−2.12654	+	9.77553i	−0.0745809	+	0.342843i
$814$	−9.81291	+	4.48141i	−0.343942	+	0.157073i
$815$	−1.80263	+	3.03639i	−0.0631432	+	0.106360i
$816$	−4.78805	−	4.14887i	−0.167615	−	0.145239i
$817$	3.63341	−	0.259866i	0.127117	−	0.00909157i
$818$	5.29773	−	9.70206i	0.185231	−	0.339225i
$819$	−0.696964	−	1.52614i	−0.0243539	−	0.0533276i
$820$	5.66295	+	9.54997i	0.197759	+	0.333499i
$821$	−12.0086	−	3.52603i	−0.419102	−	0.123059i	0.0653805	−	0.997860i	$-0.479174\pi$
$821$	−12.0086	−	3.52603i	−0.419102	−	0.123059i	−0.484483	+	0.874801i	$0.660992\pi$
$822$	1.76404	+	1.32054i	0.0615280	+	0.0460593i
$823$	4.96616	+	13.3148i	0.173109	+	0.464124i	0.994311	−	0.106514i	$-0.0339688\pi$
$823$	4.96616	+	13.3148i	0.173109	+	0.464124i	−0.821202	+	0.570638i	$0.806696\pi$
$824$	−0.189271	+	1.31641i	−0.00659355	+	0.0458592i
$825$	−1.77587	−	12.3966i	−0.0618280	−	0.431595i
$826$	10.9859	−	9.51936i	0.382249	−	0.331221i
$827$	−14.0883	+	14.0883i	−0.489899	+	0.489899i	−0.908274	−	0.418375i	$-0.862600\pi$
$827$	−14.0883	+	14.0883i	−0.489899	+	0.489899i	0.418375	+	0.908274i	$0.362600\pi$
$828$	1.15644	+	4.65432i	0.0401889	+	0.161749i
$829$		−	4.72510i		−	0.164110i	−0.996628	−	0.0820548i	$-0.973852\pi$
$829$		−	4.72510i		−	0.164110i	0.996628	−	0.0820548i	$-0.0261483\pi$
$830$	−5.09532	+	4.10392i	−0.176861	+	0.142449i
$831$	−1.56505	−	1.00580i	−0.0542911	−	0.0348907i
$832$	0.450030	−	0.336888i	0.0156020	−	0.0116795i
$833$	−11.3212	+	4.22260i	−0.392257	+	0.146304i
$834$	6.38687	−	0.918293i	0.221159	−	0.0317979i
$835$	−12.1627	−	24.3136i	−0.420909	−	0.841408i
$836$	14.8483	−	9.54243i	0.513539	−	0.330032i
$837$	−1.60276	+	4.29716i	−0.0553994	+	0.148531i
$838$	3.79193	+	2.07055i	0.130990	+	0.0715260i
$839$	17.3592	−	20.0336i	0.599307	−	0.691638i	−0.372334	−	0.928099i	$-0.621442\pi$
$839$	17.3592	−	20.0336i	0.599307	−	0.691638i	0.971641	+	0.236461i	$0.0759877\pi$
$840$	−6.66934	+	0.236483i	−0.230114	+	0.00815944i
$841$	49.9501	−	14.6667i	1.72242	−	0.505748i
$842$	−6.56808	−	2.44977i	−0.226351	−	0.0844246i
$843$	8.36675	+	1.82007i	0.288166	+	0.0626867i
$844$	2.34510	−	7.98667i	0.0807216	−	0.274912i
$845$	−28.2005	+	3.02455i	−0.970127	+	0.104048i
$846$	1.80713	−	3.95705i	0.0621303	−	0.136046i
$847$	8.45408	+	11.2933i	0.290485	+	0.388043i
$848$	3.01431	+	13.8566i	0.103512	+	0.475837i
$849$	−14.7601	−	17.0341i	−0.506566	−	0.584609i
$850$	−31.5956	−	2.27605i	−1.08372	−	0.0780680i
$851$	8.02613	−	19.0332i	0.275132	−	0.652449i
$852$	7.27863	+	7.27863i	0.249362	+	0.249362i
$853$	−26.3754	−	1.88641i	−0.903077	−	0.0645894i	−0.387928	−	0.921690i	$-0.626809\pi$
$853$	−26.3754	−	1.88641i	−0.903077	−	0.0645894i	−0.515149	+	0.857100i	$0.672264\pi$
$854$	4.85218	−	7.55013i	0.166038	−	0.258360i
$855$	−15.5065	−	2.80179i	−0.530312	−	0.0958193i
$856$	−5.72855	−	2.61614i	−0.195798	−	0.0894179i
$857$	20.0853	−	26.8309i	0.686102	−	0.916525i	−0.313350	−	0.949638i	$-0.601451\pi$
$857$	20.0853	−	26.8309i	0.686102	−	0.916525i	0.999452	+	0.0331131i	$0.0105422\pi$
$858$	−0.674782	−	1.23577i	−0.0230367	−	0.0421885i
$859$	−11.0001	−	17.1165i	−0.375320	−	0.584009i	0.601289	−	0.799031i	$-0.294654\pi$
$859$	−11.0001	−	17.1165i	−0.375320	−	0.584009i	−0.976609	+	0.215022i	$0.931018\pi$
$860$	−1.06775	−	0.442599i	−0.0364101	−	0.0150925i
$861$	−4.17496	−	14.2186i	−0.142282	−	0.484569i
$862$	2.04848	+	28.6414i	0.0697714	+	0.975531i
$863$	1.87636	+	26.2350i	0.0638722	+	0.893049i	0.923859	+	0.382733i	$0.125017\pi$
$863$	1.87636	+	26.2350i	0.0638722	+	0.893049i	−0.859987	+	0.510316i	$0.829528\pi$
$864$	0.281733	+	0.959493i	0.00958474	+	0.0326426i
$865$	−31.4154	−	13.0221i	−1.06815	−	0.442765i
$866$	−10.5540	−	16.4224i	−0.358640	−	0.558055i
$867$	11.0891	+	20.3082i	0.376606	+	0.689702i
$868$	−8.20283	+	10.9577i	−0.278422	+	0.371928i
$869$	1.19635	+	0.546354i	0.0405834	+	0.0185338i
$870$	19.8111	+	3.57957i	0.671660	+	0.121359i
$871$	−4.74584	+	7.38468i	−0.160807	+	0.250220i
$872$	18.7136	+	1.33842i	0.633723	+	0.0453248i
$873$	−3.79234	−	3.79234i	−0.128351	−	0.128351i
$874$	−8.56633	+	32.6926i	−0.289761	+	1.10585i
$875$	−25.9975	+	20.9172i	−0.878877	+	0.707129i
$876$	−6.90034	−	7.96342i	−0.233141	−	0.269059i
$877$	−5.72581	−	26.3211i	−0.193347	−	0.888801i	−0.966917	−	0.255090i	$-0.917895\pi$
$877$	−5.72581	−	26.3211i	−0.193347	−	0.888801i	0.773570	−	0.633710i	$-0.218469\pi$
$878$	15.6072	+	20.8488i	0.526717	+	0.703611i
$879$	−9.04188	+	19.7990i	−0.304975	+	0.667802i
$880$	−5.56860	+	0.597241i	−0.187717	+	0.0201330i
$881$	−14.9471	+	50.9052i	−0.503581	+	1.71504i	0.178660	+	0.983911i	$0.442824\pi$
$881$	−14.9471	+	50.9052i	−0.503581	+	1.71504i	−0.682241	+	0.731127i	$0.738995\pi$
$882$	1.86362	+	0.405405i	0.0627512	+	0.0136507i
$883$	−4.47406	−	1.66874i	−0.150564	−	0.0561575i	0.273052	−	0.961999i	$-0.411967\pi$
$883$	−4.47406	−	1.66874i	−0.150564	−	0.0561575i	−0.423616	+	0.905842i	$0.639240\pi$
$884$	−3.41728	+	1.00340i	−0.114935	+	0.0337481i
$885$	−10.8843	+	0.385938i	−0.365871	+	0.0129732i
$886$	−0.215397	+	0.248581i	−0.00723640	+	0.00835125i
$887$	48.1742	+	26.3051i	1.61753	+	0.883239i	0.994916	+	0.100711i	$0.0321119\pi$
$887$	48.1742	+	26.3051i	1.61753	+	0.883239i	0.622616	+	0.782528i	$0.286070\pi$
$888$	1.50519	−	4.03556i	0.0505108	−	0.135425i
$889$	−13.0754	+	8.40304i	−0.438534	+	0.281829i
$890$	−10.3924	−	20.7747i	−0.348354	−	0.696368i
$891$	2.47914	−	0.356447i	0.0830544	−	0.0119414i
$892$	9.85951	−	3.67741i	0.330121	−	0.123129i
$893$	24.5412	−	18.3713i	0.821239	−	0.614772i
$894$	−10.7183	−	6.88825i	−0.358475	−	0.230378i
$895$	−12.9682	+	10.4449i	−0.433479	+	0.349136i
$896$			2.98449i			0.0997049i
$897$	2.55257	+	0.867666i	0.0852279	+	0.0289705i
$898$	8.29691	−	8.29691i	0.276872	−	0.276872i
$899$	31.2064	−	27.0405i	1.04079	−	0.901850i
$900$	4.00117	+	2.99844i	0.133372	+	0.0999480i
$901$	12.7858	−	88.9269i	0.425956	−	2.96259i
$902$	−4.34603	−	11.6521i	−0.144707	−	0.387974i
$903$	1.23501	+	0.924518i	0.0410986	+	0.0307660i
$904$	−19.5677	−	5.74559i	−0.650811	−	0.191095i
$905$	−27.4142	−	46.2311i	−0.911278	−	1.53678i
$906$	−1.41135	−	3.09042i	−0.0468888	−	0.102672i
$907$	−3.70846	+	6.79154i	−0.123138	+	0.225510i	−0.931975	−	0.362523i	$-0.881915\pi$
$907$	−3.70846	+	6.79154i	−0.123138	+	0.225510i	0.808837	+	0.588032i	$0.200097\pi$
$908$	18.4269	−	1.31792i	0.611518	−	0.0437367i
$909$	−0.203967	−	0.176738i	−0.00676516	−	0.00586204i
$910$	−1.91514	+	3.22591i	−0.0634864	+	0.106938i
$911$	30.9612	−	14.1395i	1.02579	−	0.468463i	0.169814	−	0.985476i	$-0.445683\pi$
$911$	30.9612	−	14.1395i	1.02579	−	0.468463i	0.855978	+	0.517013i	$0.172956\pi$
$912$	−1.49795	+	6.88597i	−0.0496021	+	0.228017i
$913$	6.43190	−	3.51209i	0.212865	−	0.116233i
$914$	−2.77867	−	19.3261i	−0.0919104	−	0.639251i
$915$	−6.38066	+	2.12187i	−0.210938	+	0.0701469i
$916$	2.91850	+	0.419617i	0.0964299	+	0.0138645i
$917$	2.06087	−	0.448314i	0.0680558	−	0.0148046i
$918$	0.451969	−	6.31935i	0.0149172	−	0.208570i
$919$	53.5065			1.76502			0.882509	−	0.470296i	$-0.155853\pi$
$919$	53.5065			1.76502			0.882509	+	0.470296i	$0.155853\pi$
$920$	7.07611	−	8.05783i	0.233293	−	0.265659i
$921$	9.48151			0.312427
$922$	−1.30497	+	18.2459i	−0.0429769	+	0.600896i
$923$	5.65434	−	1.23003i	0.186115	−	0.0404868i
$924$	7.39898	+	1.06381i	0.243409	+	0.0349969i
$925$	−6.05669	−	20.6664i	−0.199143	−	0.679507i
$926$	−0.491530	−	3.41867i	−0.0161527	−	0.112344i
$927$	−1.16726	+	0.637373i	−0.0383379	+	0.0209341i
$928$	1.91378	−	8.79752i	0.0628230	−	0.288793i
$929$	−29.1322	+	13.3042i	−0.955795	+	0.436497i	−0.831362	−	0.555731i	$-0.812438\pi$
$929$	−29.1322	+	13.3042i	−0.955795	+	0.436497i	−0.124433	+	0.992228i	$0.539711\pi$
$930$	9.93743	−	2.53366i	0.325861	−	0.0830821i
$931$	10.1573	+	8.80139i	0.332893	+	0.288454i
$932$	−21.1117	+	1.50994i	−0.691537	+	0.0494597i
$933$	11.9044	−	21.8013i	0.389733	−	0.713744i
$934$	4.15137	+	9.09023i	0.135837	+	0.297441i
$935$	34.3777	+	8.78379i	1.12427	+	0.287261i
$936$	0.539386	+	0.158378i	0.0176304	+	0.00517675i
$937$	18.1330	+	13.5742i	0.592381	+	0.443451i	0.852941	−	0.522007i	$-0.174816\pi$
$937$	18.1330	+	13.5742i	0.592381	+	0.443451i	−0.260561	+	0.965457i	$0.583907\pi$
$938$	−16.2862	−	43.6650i	−0.531764	−	1.42571i
$939$	3.33237	−	23.1772i	0.108748	−	0.756358i
$940$	−9.57317	+	1.72465i	−0.312242	+	0.0562520i
$941$	−34.1565	+	29.5968i	−1.11347	+	0.964827i	−0.999589	−	0.0286676i	$-0.990874\pi$
$941$	−34.1565	+	29.5968i	−1.11347	+	0.964827i	−0.113881	+	0.993494i	$0.536328\pi$
$942$	−16.4778	+	16.4778i	−0.536876	+	0.536876i
$943$	21.2257	+	10.7943i	0.691202	+	0.351511i
$944$			4.87066i			0.158527i
$945$	−4.18610	−	5.19736i	−0.136174	−	0.169070i
$946$	1.08915	+	0.699954i	0.0354113	+	0.0227575i
$947$	−36.2759	+	27.1558i	−1.17881	+	0.882446i	−0.994937	−	0.100504i	$-0.967954\pi$
$947$	−36.2759	+	27.1558i	−1.17881	+	0.882446i	−0.183873	+	0.982950i	$0.558863\pi$
$948$	−0.491999	+	0.183506i	−0.0159794	+	0.00596000i
$949$	−5.86322	+	0.843004i	−0.190328	+	0.0273651i
$950$	14.6207	+	32.0585i	0.474360	+	1.04011i
$951$	−19.8666	+	12.7675i	−0.644219	+	0.414015i
$952$	6.60775	−	17.7161i	0.214159	−	0.574181i
$953$	−12.0005	−	6.55275i	−0.388733	−	0.212264i	0.272983	−	0.962019i	$-0.411990\pi$
$953$	−12.0005	−	6.55275i	−0.388733	−	0.212264i	−0.661716	+	0.749755i	$0.730172\pi$
$954$	−9.28635	+	10.7170i	−0.300657	+	0.346976i
$955$	−8.02054	−	7.47123i	−0.259539	−	0.241763i
$956$	−27.3146	+	8.02030i	−0.883419	+	0.259395i
$957$	−21.1281	−	7.88039i	−0.682975	−	0.254737i
$958$	−27.7527	−	6.03724i	−0.896650	−	0.195054i
$959$	−1.85282	+	6.31012i	−0.0598306	+	0.203764i
$960$	1.40351	−	1.74074i	0.0452981	−	0.0561820i
$961$	−4.13987	+	9.06504i	−0.133544	+	0.292421i
$962$	−1.45102	−	1.93834i	−0.0467828	−	0.0624945i
$963$	−1.33866	−	6.15374i	−0.0431379	−	0.198302i
$964$	−2.67195	−	3.08360i	−0.0860578	−	0.0993160i
$965$	−21.3392	+	19.8573i	−0.686932	+	0.639228i
$966$	−11.8088	+	8.08809i	−0.379943	+	0.260230i
$967$	−12.7522	−	12.7522i	−0.410083	−	0.410083i	0.471684	−	0.881767i	$-0.343646\pi$
$967$	−12.7522	−	12.7522i	−0.410083	−	0.410083i	−0.881767	+	0.471684i	$0.843646\pi$
$968$	−4.71476	−	0.337206i	−0.151538	−	0.0108382i
$969$	24.1376	−	37.5589i	0.775413	−	1.20657i
$970$	−2.13232	+	11.8013i	−0.0684646	+	0.378918i
$971$	53.4863	+	24.4264i	1.71646	+	0.783880i	0.995898	+	0.0904861i	$0.0288421\pi$
$971$	53.4863	+	24.4264i	1.71646	+	0.783880i	0.720559	+	0.693393i	$0.243885\pi$
$972$	−0.599278	+	0.800541i	−0.0192218	+	0.0256774i
$973$	9.22918	+	16.9020i	0.295874	+	0.541852i
$974$	−3.03240	−	4.71851i	−0.0971644	−	0.151191i
$975$	2.63407	−	0.980918i	0.0843577	−	0.0314145i
$976$	0.847216	+	2.88535i	0.0271187	+	0.0923579i
$977$	1.37273	+	19.1932i	0.0439174	+	0.614045i	0.970983	+	0.239147i	$0.0768678\pi$
$977$	1.37273	+	19.1932i	0.0439174	+	0.614045i	−0.927066	+	0.374898i	$0.877678\pi$
$978$	0.112658	+	1.57516i	0.00360240	+	0.0503681i
$979$	7.33040	+	24.9650i	0.234281	+	0.797886i
$980$	−1.63099	−	3.94042i	−0.0521002	−	0.125872i
$981$	10.1432	+	15.7831i	0.323847	+	0.503916i
$982$	8.90580	+	16.3098i	0.284196	+	0.520465i
$983$	−37.1283	+	49.5977i	−1.18421	+	1.58192i	−0.468618	+	0.883401i	$0.655248\pi$
$983$	−37.1283	+	49.5977i	−1.18421	+	1.58192i	−0.715592	+	0.698518i	$0.753843\pi$
$984$	4.51659	+	2.06266i	0.143984	+	0.0657552i
$985$	37.0715	−	25.7251i	1.18120	−	0.819671i
$986$	−30.8382	+	47.9853i	−0.982090	+	1.52816i
$987$	12.9500	+	0.926201i	0.412202	+	0.0294813i
$988$	2.80123	+	2.80123i	0.0891189	+	0.0891189i
$989$	−2.44239	+	0.424619i	−0.0776634	+	0.0135021i
$990$	−3.81525	−	4.09998i	−0.121257	−	0.130306i
$991$	−7.58501	−	8.75357i	−0.240946	−	0.278066i	0.622378	−	0.782717i	$-0.286167\pi$
$991$	−7.58501	−	8.75357i	−0.240946	−	0.278066i	−0.863324	+	0.504651i	$0.831621\pi$
$992$	−0.974894	−	4.48151i	−0.0309529	−	0.142288i
$993$	−14.0123	−	18.7182i	−0.444666	−	0.594005i
$994$	−12.7620	+	27.9448i	−0.404785	+	0.886355i
$995$	1.34210	+	12.5135i	0.0425473	+	0.396705i
$996$	−0.824321	+	2.80738i	−0.0261196	+	0.0889552i
$997$	5.74670	+	1.25012i	0.182000	+	0.0395916i	0.302641	−	0.953105i	$-0.402132\pi$
$997$	5.74670	+	1.25012i	0.182000	+	0.0395916i	−0.120642	+	0.992696i	$0.538495\pi$
$998$	3.06875	+	1.14458i	0.0971395	+	0.0362312i
$999$	4.13266	−	1.21346i	0.130752	−	0.0383921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.217.3	yes	240
5.3	odd	4	inner	690.2.w.b.493.10	yes	240
23.7	odd	22	inner	690.2.w.b.7.10	✓	240
115.53	even	44	inner	690.2.w.b.283.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.10	✓	240	23.7	odd	22	inner
690.2.w.b.217.3	yes	240	1.1	even	1	trivial
690.2.w.b.283.3	yes	240	115.53	even	44	inner
690.2.w.b.493.10	yes	240	5.3	odd	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.00142 + 1.99929i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.61943 + 1.43032i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.00142 + 1.99929i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.61943 + 1.43032i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-1.92276 - 1.14149i) q^{10} +(1.89288 + 1.64019i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-0.269413 + 0.493393i) q^{13} +(-1.23980 - 2.71479i) q^{14} +(-0.553550 + 2.16647i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-5.07183 - 3.79672i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-1.00290 + 6.97529i) q^{19} +(1.27575 - 1.83643i) q^{20} +(-2.25553 + 1.95443i) q^{21} +(-1.77104 + 1.77104i) q^{22} +(0.201680 - 4.79159i) q^{23} -1.00000i q^{24} +(-2.99433 - 4.00424i) q^{25} +(-0.472917 - 0.303925i) q^{26} +(0.800541 - 0.599278i) q^{27} +(2.79632 - 1.04297i) q^{28} +(-8.91163 + 1.28130i) q^{29} +(-2.12146 - 0.706694i) q^{30} +(-3.85826 + 2.47955i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(2.19827 + 1.20034i) q^{33} +(4.14887 - 4.78805i) q^{34} +(-0.236483 - 6.66934i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(4.03556 + 1.50519i) q^{37} +(-6.88597 - 1.49795i) q^{38} +(-0.158378 + 0.539386i) q^{39} +(1.74074 + 1.40351i) q^{40} +(-2.06266 + 4.51659i) q^{41} +(-1.78854 - 2.38921i) q^{42} +(-0.109878 - 0.505099i) q^{43} +(-1.64019 - 1.89288i) q^{44} +(-0.0803837 + 2.23462i) q^{45} +(4.76499 + 0.542994i) q^{46} +(-3.07604 - 3.07604i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(1.03111 - 1.60444i) q^{49} +(4.20765 - 2.70105i) q^{50} +(-5.76297 - 2.63186i) q^{51} +(0.336888 - 0.450030i) q^{52} +(6.79606 + 12.4461i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-5.17477 + 2.14190i) q^{55} +(0.840829 + 2.86360i) q^{56} +(0.502729 + 7.02906i) q^{57} +(-0.642286 - 8.98033i) q^{58} +(1.37222 + 4.67337i) q^{59} +(0.856236 - 2.06564i) q^{60} +(1.62580 + 2.52979i) q^{61} +(-2.19799 - 4.02532i) q^{62} +(-1.78854 + 2.38921i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-0.716643 - 1.03273i) q^{65} +(-1.35411 + 2.10703i) q^{66} +(15.5754 + 1.11397i) q^{67} +(4.47987 + 4.47987i) q^{68} +(-0.821454 - 4.72496i) q^{69} +(6.66922 + 0.239905i) q^{70} +(-6.74083 - 7.77933i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(6.31466 + 8.43539i) q^{73} +(-1.78925 + 3.91790i) q^{74} +(-3.77707 - 3.27624i) q^{75} +(1.98537 - 6.76157i) q^{76} +(-7.30424 - 1.58894i) q^{77} +(-0.526713 - 0.196454i) q^{78} +(0.503836 - 0.147940i) q^{79} +(-1.52412 + 1.63618i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.35794 - 2.37961i) q^{82} +(1.02250 - 2.74142i) q^{83} +(2.51072 - 1.61354i) q^{84} +(12.6698 - 6.33796i) q^{85} +(0.511650 - 0.0735642i) q^{86} +(-8.43561 + 3.14632i) q^{87} +(2.00506 - 1.50097i) q^{88} +(8.73923 + 5.61636i) q^{89} +(-2.22319 - 0.239595i) q^{90} -1.67775i q^{91} +(-0.881542 + 4.71412i) q^{92} +(-3.24302 + 3.24302i) q^{93} +(3.28764 - 2.84876i) q^{94} +(-12.9413 - 8.99024i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-1.87424 - 5.02502i) q^{97} +(1.52679 + 1.14294i) q^{98} +(2.40318 + 0.705637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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