LMFDB - Embedded newform 690.2.w.b.493.10

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			493.10
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.855176 - 2.06608i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.43032 + 2.61943i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.855176 - 2.06608i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.43032 + 2.61943i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(1.00039 - 1.99981i) q^{10} +(1.89288 + 1.64019i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(-0.493393 - 0.269413i) q^{13} +(1.23980 + 2.71479i) q^{14} +(2.20064 + 0.396457i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-3.79672 + 5.07183i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(1.00290 - 6.97529i) q^{19} +(1.14051 - 1.92334i) q^{20} +(-2.25553 + 1.95443i) q^{21} +(1.77104 + 1.77104i) q^{22} +(4.79159 + 0.201680i) q^{23} +1.00000i q^{24} +(-3.53735 - 3.53372i) q^{25} +(-0.472917 - 0.303925i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(1.04297 + 2.79632i) q^{28} +(8.91163 - 1.28130i) q^{29} +(2.16675 + 0.552438i) q^{30} +(-3.85826 + 2.47955i) q^{31} +(0.936950 + 0.349464i) q^{32} +(-1.20034 + 2.19827i) q^{33} +(-4.14887 + 4.78805i) q^{34} +(6.63511 - 0.715070i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.50519 - 4.03556i) q^{37} +(1.49795 - 6.88597i) q^{38} +(0.158378 - 0.539386i) q^{39} +(1.27481 - 1.83708i) q^{40} +(-2.06266 + 4.51659i) q^{41} +(-2.38921 + 1.78854i) q^{42} +(0.505099 - 0.109878i) 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} +(-0.0713392 + 0.997452i) q^{48} +(-1.03111 + 1.60444i) q^{49} +(-3.27624 - 3.77707i) q^{50} +(-5.76297 - 2.63186i) q^{51} +(-0.450030 - 0.336888i) q^{52} +(-12.4461 + 6.79606i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(5.00750 - 2.50818i) q^{55} +(0.840829 + 2.86360i) q^{56} +(7.02906 - 0.502729i) q^{57} +(8.98033 - 0.642286i) q^{58} +(-1.37222 - 4.67337i) q^{59} +(2.12182 + 0.705605i) q^{60} +(1.62580 + 2.52979i) q^{61} +(-4.02532 + 2.19799i) q^{62} +(-2.38921 - 1.78854i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-0.978567 + 0.788993i) q^{65} +(-1.35411 + 2.10703i) q^{66} +(1.11397 - 15.5754i) 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} +(-0.977147 + 0.212565i) q^{72} +(-8.43539 + 6.31466i) q^{73} +(1.78925 - 3.91790i) q^{74} +(2.70105 - 4.20765i) q^{75} +(1.98537 - 6.76157i) q^{76} +(-1.58894 + 7.30424i) q^{77} +(0.196454 - 0.526713i) q^{78} +(-0.503836 + 0.147940i) q^{79} +(1.40262 - 1.74146i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.37961 + 4.35794i) q^{82} +(2.74142 + 1.02250i) q^{83} +(-2.51072 + 1.61354i) q^{84} +(7.23192 + 12.1816i) q^{85} +(0.511650 - 0.0735642i) q^{86} +(3.14632 + 8.43561i) q^{87} +(1.50097 + 2.00506i) q^{88} +(-8.73923 - 5.61636i) q^{89} +(-0.0792373 + 2.23466i) q^{90} -1.67775i q^{91} +(4.71412 + 0.881542i) q^{92} +(-3.24302 - 3.24302i) q^{93} +(-3.28764 + 2.84876i) q^{94} +(-13.5538 - 8.03716i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-5.02502 + 1.87424i) q^{97} +(-1.14294 + 1.52679i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	0.855176	−	2.06608i	0.382446	−	0.923978i
$5$	0.855176	−	2.06608i	0.382446	−	0.923978i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	1.43032	+	2.61943i	0.540608	+	0.990050i	0.995060	+	0.0992788i	$0.0316536\pi$
$7$	1.43032	+	2.61943i	0.540608	+	0.990050i	−0.454451	+	0.890772i	$0.650165\pi$
$8$	0.977147	+	0.212565i	0.345474	+	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	1.00039	−	1.99981i	0.316351	−	0.632394i
$11$	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	$0.604026\pi$
$12$	0.0713392	+	0.997452i	0.0205938	+	0.287940i
$13$	−0.493393	−	0.269413i	−0.136843	−	0.0747218i	0.409369	−	0.912369i	$-0.365749\pi$
$13$	−0.493393	−	0.269413i	−0.136843	−	0.0747218i	−0.546212	+	0.837647i	$0.683931\pi$
$14$	1.23980	+	2.71479i	0.331351	+	0.725558i
$15$	2.20064	+	0.396457i	0.568203	+	0.102365i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−3.79672	+	5.07183i	−0.920840	+	1.23010i	0.0520064	+	0.998647i	$0.483438\pi$
$17$	−3.79672	+	5.07183i	−0.920840	+	1.23010i	−0.972846	+	0.231452i	$0.925653\pi$
$18$	−0.936950	+	0.349464i	−0.220841	+	0.0823695i
$19$	1.00290	−	6.97529i	0.230080	−	1.60024i	−0.467672	−	0.883902i	$-0.654907\pi$
$19$	1.00290	−	6.97529i	0.230080	−	1.60024i	0.697752	−	0.716339i	$-0.254184\pi$
$20$	1.14051	−	1.92334i	0.255025	−	0.430073i
$21$	−2.25553	+	1.95443i	−0.492197	+	0.426491i
$22$	1.77104	+	1.77104i	0.377588	+	0.377588i
$23$	4.79159	+	0.201680i	0.999115	+	0.0420533i
$23$	4.79159	+	0.201680i	0.999115	+	0.0420533i
$24$			1.00000i			0.204124i
$25$	−3.53735	−	3.53372i	−0.707469	−	0.706744i
$26$	−0.472917	−	0.303925i	−0.0927466	−	0.0596046i
$27$	−0.599278	−	0.800541i	−0.115331	−	0.154064i
$28$	1.04297	+	2.79632i	0.197103	+	0.528455i
$29$	8.91163	−	1.28130i	1.65485	−	0.237931i	0.749317	−	0.662211i	$-0.230382\pi$
$29$	8.91163	−	1.28130i	1.65485	−	0.237931i	0.905531	+	0.424280i	$0.139473\pi$
$30$	2.16675	+	0.552438i	0.395593	+	0.100861i
$31$	−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	$0.453304\pi$
$32$	0.936950	+	0.349464i	0.165631	+	0.0617771i
$33$	−1.20034	+	2.19827i	−0.208953	+	0.382669i
$34$	−4.14887	+	4.78805i	−0.711525	+	0.821143i
$35$	6.63511	−	0.715070i	1.12154	−	0.120869i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	1.50519	−	4.03556i	0.247451	−	0.663442i	−0.752537	−	0.658550i	$-0.771170\pi$
$37$	1.50519	−	4.03556i	0.247451	−	0.663442i	0.999988	−	0.00489211i	$-0.00155721\pi$
$38$	1.49795	−	6.88597i	0.243000	−	1.11705i
$39$	0.158378	−	0.539386i	0.0253608	−	0.0863708i
$40$	1.27481	−	1.83708i	0.201565	−	0.290468i
$41$	−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	$0.263102\pi$
$42$	−2.38921	+	1.78854i	−0.368663	+	0.275978i
$43$	0.505099	−	0.109878i	0.0770268	−	0.0167562i	−0.173887	−	0.984766i	$-0.555633\pi$
$43$	0.505099	−	0.109878i	0.0770268	−	0.0167562i	0.250914	+	0.968010i	$0.419269\pi$
$44$	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	−0.894918	−	0.446232i	$-0.852766\pi$
$47$	−3.07604	+	3.07604i	−0.448686	+	0.448686i	0.446232	+	0.894918i	$0.352766\pi$
$48$	−0.0713392	+	0.997452i	−0.0102969	+	0.143970i
$49$	−1.03111	+	1.60444i	−0.147302	+	0.229206i
$50$	−3.27624	−	3.77707i	−0.463331	−	0.534158i
$51$	−5.76297	−	2.63186i	−0.806977	−	0.368534i
$52$	−0.450030	−	0.336888i	−0.0624079	−	0.0467180i
$53$	−12.4461	+	6.79606i	−1.70960	+	0.933510i	−0.746083	+	0.665853i	$0.768068\pi$
$53$	−12.4461	+	6.79606i	−1.70960	+	0.933510i	−0.963514	+	0.267657i	$0.913751\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	5.00750	−	2.50818i	0.675211	−	0.338203i
$56$	0.840829	+	2.86360i	0.112360	+	0.382665i
$57$	7.02906	−	0.502729i	0.931022	−	0.0665880i
$58$	8.98033	−	0.642286i	1.17918	−	0.0843363i
$59$	−1.37222	−	4.67337i	−0.178648	−	0.608420i	−0.999315	−	0.0370128i	$-0.988216\pi$
$59$	−1.37222	−	4.67337i	−0.178648	−	0.608420i	0.820666	−	0.571408i	$-0.193602\pi$
$60$	2.12182	+	0.705605i	0.273926	+	0.0910932i
$61$	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	$0.756518\pi$
$62$	−4.02532	+	2.19799i	−0.511216	+	0.279145i
$63$	−2.38921	−	1.78854i	−0.301012	−	0.225335i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	−0.978567	+	0.788993i	−0.121376	+	0.0978625i
$66$	−1.35411	+	2.10703i	−0.166679	+	0.259358i
$67$	1.11397	−	15.5754i	0.136094	−	1.90284i	−0.231475	−	0.972841i	$-0.574355\pi$
$67$	1.11397	−	15.5754i	0.136094	−	1.90284i	0.367569	−	0.929996i	$-0.380190\pi$
$68$	−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	$0.981883\pi$
$72$	−0.977147	+	0.212565i	−0.115158	+	0.0250511i
$73$	−8.43539	+	6.31466i	−0.987288	+	0.739075i	−0.965424	−	0.260686i	$-0.916051\pi$
$73$	−8.43539	+	6.31466i	−0.987288	+	0.739075i	−0.0218646	+	0.999761i	$0.506960\pi$
$74$	1.78925	−	3.91790i	0.207996	−	0.455447i
$75$	2.70105	−	4.20765i	0.311890	−	0.485858i
$76$	1.98537	−	6.76157i	0.227738	−	0.775605i
$77$	−1.58894	+	7.30424i	−0.181077	+	0.832395i
$78$	0.196454	−	0.526713i	0.0222440	−	0.0596385i
$79$	−0.503836	+	0.147940i	−0.0566860	+	0.0166445i	−0.309953	−	0.950752i	$-0.600313\pi$
$79$	−0.503836	+	0.147940i	−0.0566860	+	0.0166445i	0.253267	+	0.967397i	$0.418495\pi$
$80$	1.40262	−	1.74146i	0.156817	−	0.194701i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−2.37961	+	4.35794i	−0.262784	+	0.481254i
$83$	2.74142	+	1.02250i	0.300910	+	0.112234i	0.495384	−	0.868674i	$-0.335027\pi$
$83$	2.74142	+	1.02250i	0.300910	+	0.112234i	−0.194474	+	0.980908i	$0.562300\pi$
$84$	−2.51072	+	1.61354i	−0.273942	+	0.176052i
$85$	7.23192	+	12.1816i	0.784411	+	1.32128i
$86$	0.511650	−	0.0735642i	0.0551727	−	0.00793263i
$87$	3.14632	+	8.43561i	0.337321	+	0.904393i
$88$	1.50097	+	2.00506i	0.160004	+	0.213741i
$89$	−8.73923	−	5.61636i	−0.926356	−	0.595333i	−0.0118610	−	0.999930i	$-0.503776\pi$
$89$	−8.73923	−	5.61636i	−0.926356	−	0.595333i	−0.914495	+	0.404597i	$0.867412\pi$
$90$	−0.0792373	+	2.23466i	−0.00835234	+	0.235554i
$91$		−	1.67775i		−	0.175876i
$92$	4.71412	+	0.881542i	0.491481	+	0.0919071i
$93$	−3.24302	−	3.24302i	−0.336286	−	0.336286i
$94$	−3.28764	+	2.84876i	−0.339094	+	0.293827i
$95$	−13.5538	−	8.03716i	−1.39059	−	0.824595i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−5.02502	+	1.87424i	−0.510214	+	0.190300i	−0.591368	−	0.806402i	$-0.701412\pi$
$97$	−5.02502	+	1.87424i	−0.510214	+	0.190300i	0.0811545	+	0.996702i	$0.474139\pi$
$98$	−1.14294	+	1.52679i	−0.115455	+	0.154229i
$99$	−2.40318	−	0.705637i	−0.241529	−	0.0709192i
$100$	−2.99844	−	4.00117i	−0.299844	−	0.400117i
$101$	−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	$0.867911\pi$
$102$	−5.56053	−	3.03628i	−0.550575	−	0.300636i
$103$	−0.0948770	−	1.32655i	−0.00934851	−	0.130709i	0.990634	−	0.136540i	$-0.0435984\pi$
$103$	−0.0948770	−	1.32655i	−0.00934851	−	0.130709i	−0.999983	+	0.00583128i	$0.998144\pi$
$104$	−0.424850	−	0.368135i	−0.0416600	−	0.0360986i
$105$	2.10912	+	6.33148i	0.205829	+	0.617889i
$106$	−12.8992	+	5.89085i	−1.25288	+	0.572170i
$107$	−6.15374	−	1.33866i	−0.594905	−	0.129414i	−0.0949750	−	0.995480i	$-0.530277\pi$
$107$	−6.15374	−	1.33866i	−0.594905	−	0.129414i	−0.499930	+	0.866066i	$0.666641\pi$
$108$	−0.479249	−	0.877679i	−0.0461158	−	0.0844547i
$109$	−2.67003	−	18.5705i	−0.255742	−	1.77873i	−0.562358	−	0.826894i	$-0.690106\pi$
$109$	−2.67003	−	18.5705i	−0.255742	−	1.77873i	0.306616	−	0.951833i	$-0.400803\pi$
$110$	5.17367	−	2.14456i	0.493290	−	0.204476i
$111$	4.26329	+	0.612968i	0.404653	+	0.0581804i
$112$	0.634400	+	2.91629i	0.0599451	+	0.275563i
$113$	20.3418	+	1.45487i	1.91360	+	0.136863i	0.976957	−	0.213435i	$-0.0684650\pi$
$113$	20.3418	+	1.45487i	1.91360	+	0.136863i	0.936638	+	0.350298i	$0.113920\pi$
$114$	7.04702			0.660014
$115$	4.51434	−	9.72732i	0.420964	−	0.907077i
$116$	9.00327			0.835933
$117$	0.560725	+	0.0401038i	0.0518390	+	0.00370760i
$118$	−1.03533	−	4.75935i	−0.0953102	−	0.438134i
$119$	−18.7158	−	2.69092i	−1.71567	−	0.246677i
$120$	2.06608	+	0.855176i	0.188606	+	0.0780666i
$121$	−0.672694	−	4.67869i	−0.0611540	−	0.425335i
$122$	1.44118	+	2.63932i	0.130478	+	0.238953i
$123$	−4.85182	−	1.05545i	−0.437474	−	0.0951667i
$124$	−4.17187	+	1.90523i	−0.374645	+	0.171095i
$125$	−10.3260	+	4.28648i	−0.923585	+	0.383394i
$126$	−2.25553	−	1.95443i	−0.200939	−	0.174114i
$127$	−0.371522	−	5.19456i	−0.0329673	−	0.460943i	−0.986944	−	0.161063i	$-0.948508\pi$
$127$	−0.371522	−	5.19456i	−0.0329673	−	0.460943i	0.953977	−	0.299880i	$-0.0969467\pi$
$128$	0.877679	+	0.479249i	0.0775766	+	0.0423600i
$129$	0.214733	+	0.470200i	0.0189062	+	0.0413988i
$130$	−1.03236	+	0.717173i	−0.0905439	+	0.0629002i
$131$	−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	$0.600737\pi$
$132$	−1.50097	+	2.00506i	−0.130643	+	0.174518i
$133$	19.7057	−	7.34986i	1.70870	−	0.637313i
$134$	2.22227	−	15.4562i	0.191975	−	1.33522i
$135$	−2.16647	+	0.553550i	−0.186460	+	0.0476420i
$136$	−4.78805	+	4.14887i	−0.410572	+	0.355762i
$137$	−1.55815	−	1.55815i	−0.133122	−	0.133122i	0.637406	−	0.770528i	$-0.280007\pi$
$137$	−1.55815	−	1.55815i	−0.133122	−	0.133122i	−0.770528	+	0.637406i	$0.780007\pi$
$138$	0.482287	+	4.77152i	0.0410550	+	0.406179i
$139$			6.45255i			0.547298i	0.961830	+	0.273649i	$0.0882306\pi$
$139$			6.45255i			0.547298i	−0.961830	+	0.273649i	$0.911769\pi$
$140$	6.66934	+	0.236483i	0.563662	+	0.0199865i
$141$	−3.65960	−	2.35188i	−0.308194	−	0.198064i
$142$	−6.16868	−	8.24040i	−0.517665	−	0.691519i
$143$	−0.492045	−	1.31922i	−0.0411469	−	0.110319i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	4.97375	−	19.5078i	0.413048	−	1.62004i
$146$	−8.86438	+	5.69679i	−0.733622	+	0.471470i
$147$	−1.78695	−	0.666499i	−0.147385	−	0.0549719i
$148$	2.06419	−	3.78027i	0.169675	−	0.310737i
$149$	8.34352	−	9.62894i	0.683528	−	0.788833i	−0.302901	−	0.953022i	$-0.597955\pi$
$149$	8.34352	−	9.62894i	0.683528	−	0.788833i	0.986429	+	0.164189i	$0.0525006\pi$
$150$	2.99433	−	4.00424i	0.244486	−	0.326945i
$151$	−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	$0.453235\pi$
$152$	2.46268	−	6.60270i	0.199750	−	0.535550i
$153$	1.34671	−	6.19071i	0.108875	−	0.500489i
$154$	−2.10597	+	7.17227i	−0.169704	+	0.577958i
$155$	1.82346	+	10.0919i	0.146464	+	0.810603i
$156$	0.233528	−	0.511356i	0.0186972	−	0.0409413i
$157$	18.6551	−	13.9650i	1.48884	−	1.11453i	0.523992	−	0.851723i	$-0.324442\pi$
$157$	18.6551	−	13.9650i	1.48884	−	1.11453i	0.964848	−	0.262809i	$-0.0846489\pi$
$158$	−0.513107	+	0.111619i	−0.0408206	+	0.00887997i
$159$	−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
$163$	−0.112658	+	1.57516i	−0.00882403	+	0.123376i	−0.999955	−	0.00951456i	$-0.996971\pi$
$163$	−0.112658	+	1.57516i	−0.00882403	+	0.123376i	0.991131	+	0.132891i	$0.0424259\pi$
$164$	−2.68444	+	4.17707i	−0.209620	+	0.326175i
$165$	3.51528	+	4.35991i	0.273664	+	0.339418i
$166$	2.66149	+	1.21546i	0.206572	+	0.0943382i
$167$	9.73298	+	7.28602i	0.753161	+	0.563809i	0.905413	−	0.424533i	$-0.139562\pi$
$167$	9.73298	+	7.28602i	0.753161	+	0.563809i	−0.152252	+	0.988342i	$0.548653\pi$
$168$	−2.61943	+	1.43032i	−0.202093	+	0.110351i
$169$	−6.85748	−	10.6704i	−0.527498	−	0.820803i
$170$	6.34446	+	12.6665i	0.486598	+	0.971476i
$171$	1.98537	+	6.76157i	0.151825	+	0.517070i
$172$	0.515595	−	0.0368761i	0.0393137	−	0.00281177i
$173$	−15.1698	+	1.08497i	−1.15334	+	0.0824884i	−0.634878	−	0.772613i	$-0.718949\pi$
$173$	−15.1698	+	1.08497i	−1.15334	+	0.0824884i	−0.518461	+	0.855101i	$0.673495\pi$
$174$	2.53651	+	8.63858i	0.192293	+	0.654889i
$175$	4.19680	−	14.3202i	0.317248	−	1.08250i
$176$	1.35411	+	2.10703i	0.102070	+	0.158824i
$177$	4.27488	−	2.33426i	0.321319	−	0.175454i
$178$	−8.31629	−	6.22550i	−0.623333	−	0.466621i
$179$	−6.77381	−	3.09349i	−0.506298	−	0.231219i	0.145855	−	0.989306i	$-0.453407\pi$
$179$	−6.77381	−	3.09349i	−0.506298	−	0.231219i	−0.652153	+	0.758087i	$0.726134\pi$
$180$	−0.238454	+	2.22332i	−0.0177733	+	0.165716i
$181$	−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	$0.830186\pi$
$182$	0.119690	−	1.67348i	0.00887198	−	0.124047i
$183$	−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
$187$	−15.5055	+	3.37301i	−1.13387	+	0.246659i
$188$	−3.48249	+	2.60696i	−0.253987	+	0.190132i
$189$	1.23980	−	2.71479i	0.0901824	−	0.197472i
$190$	−12.9459	−	8.98360i	−0.939197	−	0.651739i
$191$	−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	$0.147661\pi$
$192$	−0.212565	+	0.977147i	−0.0153406	+	0.0705195i
$193$	−4.55557	+	12.2140i	−0.327917	+	0.879181i	0.663468	+	0.748205i	$0.269084\pi$
$193$	−4.55557	+	12.2140i	−0.327917	+	0.879181i	−0.991386	+	0.130976i	$0.958189\pi$
$194$	−5.14593	+	1.51098i	−0.369456	+	0.108482i
$195$	−0.978971	−	0.788491i	−0.0701056	−	0.0564650i
$196$	−1.24895	+	1.44137i	−0.0892108	+	0.102955i
$197$	−9.67105	+	17.7112i	−0.689034	+	1.26187i	0.265598	+	0.964084i	$0.414431\pi$
$197$	−9.67105	+	17.7112i	−0.689034	+	1.26187i	−0.954632	+	0.297788i	$0.903751\pi$
$198$	−2.34672	−	0.875280i	−0.166774	−	0.0622035i
$199$	−4.73484	+	3.04289i	−0.335644	+	0.215705i	−0.697596	−	0.716492i	$-0.745747\pi$
$199$	−4.73484	+	3.04289i	−0.335644	+	0.215705i	0.361952	+	0.932197i	$0.382110\pi$
$200$	−2.70536	−	4.20488i	−0.191298	−	0.297330i
$201$	15.4562	−	2.22227i	1.09020	−	0.156747i
$202$	−0.0943158	−	0.252870i	−0.00663604	−	0.0177919i
$203$	16.1027	+	21.5107i	1.13019	+	1.50976i
$204$	−5.32976	−	3.42523i	−0.373158	−	0.239814i
$205$	7.56769	+	8.12409i	0.528550	+	0.567411i
$206$		−	1.32994i		−	0.0926615i
$207$	−4.44236	+	1.80704i	−0.308766	+	0.125598i
$208$	−0.397505	−	0.397505i	−0.0275620	−	0.0275620i
$209$	13.3391	−	11.5584i	0.922688	−	0.799513i
$210$	1.65207	+	6.46581i	0.114003	+	0.446183i
$211$	−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	$0.952957\pi$
$212$	−13.2865	+	4.95563i	−0.912524	+	0.340354i
$213$	6.16868	−	8.24040i	0.422671	−	0.564623i
$214$	−6.04256	−	1.77426i	−0.413061	−	0.121286i
$215$	0.204933	−	1.13754i	0.0139763	−	0.0775794i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−12.0135	−	6.55989i	−0.815533	−	0.445315i
$218$	−1.33842	−	18.7136i	−0.0906495	−	1.26745i
$219$	−7.96342	−	6.90034i	−0.538118	−	0.466282i
$220$	5.31348	−	1.77001i	0.358235	−	0.119334i
$221$	3.23969	−	1.47952i	0.217925	−	0.0995232i
$222$	4.20870	+	0.915546i	0.282469	+	0.0614474i
$223$	−5.04313	−	9.23581i	−0.337713	−	0.618475i	0.652540	−	0.757754i	$-0.273703\pi$
$223$	−5.04313	−	9.23581i	−0.337713	−	0.618475i	−0.990253	+	0.139279i	$0.955522\pi$
$224$	0.424738	+	2.95412i	0.0283790	+	0.197380i
$225$	4.68564	+	1.74492i	0.312376	+	0.116328i
$226$	20.1862	+	2.90234i	1.34276	+	0.193060i
$227$	3.92693	+	18.0518i	0.260639	+	1.19814i	0.902286	+	0.431139i	$0.141888\pi$
$227$	3.92693	+	18.0518i	0.260639	+	1.19814i	−0.641646	+	0.767001i	$0.721748\pi$
$228$	7.02906	+	0.502729i	0.465511	+	0.0332940i
$229$	2.94851			0.194843			0.0974215	−	0.995243i	$-0.468940\pi$
$229$	2.94851			0.194843			0.0974215	+	0.995243i	$0.468940\pi$
$230$	5.19678	−	9.38049i	0.342665	−	0.618531i
$231$	−7.47507			−0.491823
$232$	8.98033	+	0.642286i	0.589588	+	0.0421681i
$233$	4.49908	+	20.6819i	0.294745	+	1.35492i	0.851549	+	0.524275i	$0.175664\pi$
$233$	4.49908	+	20.6819i	0.294745	+	1.35492i	−0.556804	+	0.830644i	$0.687973\pi$
$234$	0.556435	+	0.0800033i	0.0363753	+	0.00522998i
$235$	3.72477	+	8.98588i	0.242977	+	0.586174i
$236$	−0.693167	−	4.82109i	−0.0451214	−	0.313826i
$237$	−0.251657	−	0.460875i	−0.0163469	−	0.0299371i
$238$	−18.4761	−	4.01924i	−1.19763	−	0.260528i
$239$	−25.8952	+	11.8259i	−1.67502	+	0.764957i	−0.675400	+	0.737451i	$0.736029\pi$
$239$	−25.8952	+	11.8259i	−1.67502	+	0.764957i	−0.999622	+	0.0275058i	$0.991244\pi$
$240$	1.99981	+	1.00039i	0.129087	+	0.0645749i
$241$	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	$0.685321\pi$
$242$	−0.337206	−	4.71476i	−0.0216764	−	0.303076i
$243$	0.877679	+	0.479249i	0.0563031	+	0.0307438i
$244$	1.24922	+	2.73541i	0.0799732	+	0.175117i
$245$	2.43311	+	3.50243i	0.155446	+	0.223762i
$246$	−4.76417	−	1.39889i	−0.303752	−	0.0891897i
$247$	−2.37406	+	3.17137i	−0.151058	+	0.201789i
$248$	−4.29716	+	1.60276i	−0.272870	+	0.101775i
$249$	−0.416399	+	2.89612i	−0.0263882	+	0.183534i
$250$	−10.6055	+	3.53891i	−0.670749	+	0.223820i
$251$	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
$253$	8.73910	+	8.24086i	0.549422	+	0.518098i
$254$		−	5.20783i		−	0.326768i
$255$	−10.3660	+	9.65603i	−0.649143	+	0.604684i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	11.3741	+	15.1941i	0.709500	+	0.947781i	0.999959	−	0.00910663i	$-0.00289877\pi$
$257$	11.3741	+	15.1941i	0.709500	+	0.947781i	−0.290459	+	0.956888i	$0.593808\pi$
$258$	0.180642	+	0.484320i	0.0112463	+	0.0301525i
$259$	12.7238	−	1.82940i	0.790615	−	0.113673i
$260$	−1.08089	+	0.641698i	−0.0670341	+	0.0397964i
$261$	−7.57403	+	4.86754i	−0.468821	+	0.301293i
$262$	−0.662118	−	0.246957i	−0.0409058	−	0.0152571i
$263$	14.7122	−	26.9433i	0.907191	−	1.66140i	0.170291	−	0.985394i	$-0.445529\pi$
$263$	14.7122	−	26.9433i	0.907191	−	1.66140i	0.736900	−	0.676002i	$-0.236289\pi$
$264$	−1.64019	+	1.89288i	−0.100947	+	0.116499i
$265$	3.39761	+	31.5263i	0.208714	+	1.93665i
$266$	20.1798	−	5.92534i	1.23731	−	0.363306i
$267$	3.63035	−	9.73335i	0.222174	−	0.595671i
$268$	3.31924	−	15.2583i	0.202755	−	0.932050i
$269$	−5.96439	+	20.3129i	−0.363656	+	1.23850i	0.551083	+	0.834451i	$0.314215\pi$
$269$	−5.96439	+	20.3129i	−0.363656	+	1.23850i	−0.914738	+	0.404047i	$0.867603\pi$
$270$	−2.20044	+	0.397585i	−0.133914	+	0.0241963i
$271$	−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	$0.234637\pi$
$272$	−5.07183	+	3.79672i	−0.307525	+	0.230210i
$273$	1.63941	−	0.356632i	0.0992217	−	0.0215844i
$274$	−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	−0.745522	−	0.666482i	$-0.767800\pi$
$277$	−1.31549	+	1.31549i	−0.0790400	+	0.0790400i	0.666482	+	0.745522i	$0.267800\pi$
$278$	−0.460319	+	6.43611i	−0.0276081	+	0.386012i
$279$	2.47955	−	3.85826i	0.148447	−	0.230988i
$280$	6.63548	+	0.711666i	0.396546	+	0.0425302i
$281$	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	$0.554158\pi$
$282$	−3.48249	−	2.60696i	−0.207379	−	0.155242i
$283$	19.7823	−	10.8020i	1.17594	−	0.642109i	0.232154	−	0.972679i	$-0.425423\pi$
$283$	19.7823	−	10.8020i	1.17594	−	0.642109i	0.943782	+	0.330570i	$0.107241\pi$
$284$	−5.56510	−	8.65947i	−0.330228	−	0.513845i
$285$	4.97241	−	14.9525i	0.294540	−	0.885710i
$286$	−0.396679	−	1.35096i	−0.0234561	−	0.0798842i
$287$	−14.7811	+	1.05717i	−0.872503	+	0.0624026i
$288$	−0.997452	+	0.0713392i	−0.0587754	+	0.00420370i
$289$	−6.51887	−	22.2012i	−0.383463	−	1.30595i
$290$	6.35275	−	19.1033i	0.373047	−	1.12179i
$291$	−2.89955	−	4.51179i	−0.169975	−	0.264486i
$292$	−9.24820	+	5.04990i	−0.541210	+	0.295523i
$293$	−17.4245	−	13.0438i	−1.01795	−	0.762028i	−0.0464144	−	0.998922i	$-0.514779\pi$
$293$	−17.4245	−	13.0438i	−1.01795	−	0.762028i	−0.971535	+	0.236895i	$0.923870\pi$
$294$	−1.73485	−	0.792280i	−0.101179	−	0.0462067i
$295$	−10.8290	−	1.16143i	−0.630490	−	0.0676211i
$296$	2.32861	−	3.62339i	0.135348	−	0.210605i
$297$	0.178679	−	2.49825i	0.0103680	−	0.144963i
$298$	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
$302$	−3.31980	+	0.722177i	−0.191033	+	0.0415566i
$303$	0.216056	−	0.161737i	0.0124121	−	0.00929156i
$304$	2.92744	−	6.41019i	0.167900	−	0.367650i
$305$	6.61708	−	1.19560i	0.378893	−	0.0684601i
$306$	1.78492	−	6.07886i	0.102037	−	0.347505i
$307$	2.01544	−	9.26483i	0.115027	−	0.528772i	−0.883186	−	0.469023i	$-0.844606\pi$
$307$	2.01544	−	9.26483i	0.115027	−	0.528772i	0.998213	−	0.0597492i	$-0.0190301\pi$
$308$	−2.61227	+	7.00376i	−0.148848	+	0.399076i
$309$	1.27607	−	0.374688i	0.0725931	−	0.0213153i
$310$	1.09886	+	10.1963i	0.0624111	+	0.579111i
$311$	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	$-0.0214513\pi$
$312$	0.269413	−	0.493393i	0.0152525	−	0.0279329i
$313$	21.9391	+	8.18288i	1.24007	+	0.462524i	0.882035	−	0.471183i	$-0.156173\pi$
$313$	21.9391	+	8.18288i	1.24007	+	0.462524i	0.358038	+	0.933707i	$0.383446\pi$
$314$	19.6038	−	12.5986i	1.10631	−	0.710981i
$315$	−5.73846	+	3.40677i	−0.323325	+	0.191950i
$316$	−0.519762	+	0.0747305i	−0.0292389	+	0.00420392i
$317$	8.25277	+	22.1265i	0.463522	+	1.24275i	0.933023	+	0.359818i	$0.117161\pi$
$317$	8.25277	+	22.1265i	0.463522	+	1.24275i	−0.469501	+	0.882932i	$0.655566\pi$
$318$	−8.49814	−	11.3522i	−0.476552	−	0.636599i
$319$	18.9702	+	12.1914i	1.06213	+	0.682587i
$320$	1.63618	−	1.52412i	0.0914650	−	0.0852007i
$321$		−	6.29766i		−	0.351501i
$322$	5.39311	+	13.2582i	0.300546	+	0.738851i
$323$	31.5697	+	31.5697i	1.75659	+	1.75659i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	0.793273	+	2.69652i	0.0440029	+	0.149576i
$326$	−0.224741	+	1.56311i	−0.0124473	+	0.0865727i
$327$	17.5785	−	6.55644i	0.972094	−	0.362572i
$328$	−2.97559	+	3.97492i	−0.164300	+	0.219478i
$329$	−12.4572	−	3.65775i	−0.686785	−	0.201658i
$330$	3.19529	+	4.59958i	0.175895	+	0.253198i
$331$	−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	$-0.358506\pi$
$332$	2.56800	+	1.40223i	0.140937	+	0.0769576i
$333$	0.307267	+	4.29615i	0.0168381	+	0.235428i
$334$	9.18840	+	7.96180i	0.502767	+	0.435650i
$335$	−31.2273	−	15.6213i	−1.70613	−	0.853481i
$336$	−2.71479	+	1.23980i	−0.148104	+	0.0676368i
$337$	22.2709	+	4.84473i	1.21317	+	0.263909i	0.773235	−	0.634120i	$-0.218637\pi$
$337$	22.2709	+	4.84473i	1.21317	+	0.263909i	0.439937	+	0.898029i	$0.355001\pi$
$338$	−6.07878	−	11.1325i	−0.330642	−	0.605526i
$339$	2.90234	+	20.1862i	0.157633	+	1.09636i
$340$	5.42468	+	13.0868i	0.294195	+	0.709734i
$341$	−11.3702	−	1.63478i	−0.615728	−	0.0885284i
$342$	1.49795	+	6.88597i	0.0810000	+	0.372351i
$343$	15.1607	+	1.08431i	0.818601	+	0.0585475i
$344$	0.516912			0.0278700
$345$	10.4646	+	2.34348i	0.563396	+	0.126169i
$346$	−15.2086			−0.817617
$347$	12.7998	+	0.915459i	0.687129	+	0.0491444i	0.410538	−	0.911843i	$-0.365341\pi$
$347$	12.7998	+	0.915459i	0.687129	+	0.0491444i	0.276591	+	0.960988i	$0.410795\pi$
$348$	1.91378	+	8.79752i	0.102590	+	0.471596i
$349$	7.61352	+	1.09466i	0.407542	+	0.0585958i	0.343038	−	0.939322i	$-0.388544\pi$
$349$	7.61352	+	1.09466i	0.407542	+	0.0585958i	0.0645047	+	0.997917i	$0.479453\pi$
$350$	5.20769	−	13.9843i	0.278363	−	0.747491i
$351$	0.0800033	+	0.556435i	0.00427026	+	0.0297003i
$352$	1.20034	+	2.19827i	0.0639785	+	0.117168i
$353$	7.82457	+	1.70213i	0.416460	+	0.0905953i	0.415913	−	0.909405i	$-0.363462\pi$
$353$	7.82457	+	1.70213i	0.416460	+	0.0905953i	0.000547293		1.00000i	$0.499826\pi$
$354$	4.43051	−	2.02335i	0.235479	−	0.107540i
$355$	−21.8373	+	7.27437i	−1.15900	+	0.386084i
$356$	−7.85098	−	6.80292i	−0.416101	−	0.360554i
$357$	−1.34890	−	18.8601i	−0.0713913	−	0.998181i
$358$	−6.53586	−	3.56885i	−0.345431	−	0.188620i
$359$	2.46715	+	5.40232i	0.130211	+	0.285123i	0.963497	−	0.267720i	$-0.0862701\pi$
$359$	2.46715	+	5.40232i	0.130211	+	0.285123i	−0.833285	+	0.552843i	$0.813543\pi$
$360$	−0.396457	+	2.20064i	−0.0208951	+	0.115984i
$361$	−29.4185	−	8.63806i	−1.54834	−	0.454635i
$362$	−14.4048	+	19.2425i	−0.757097	+	1.01136i
$363$	4.42878	−	1.65185i	0.232450	−	0.0866995i
$364$	0.238769	−	1.66068i	0.0125149	−	0.0870431i
$365$	5.83282	+	22.8283i	0.305304	+	1.19489i
$366$	−2.27266	+	1.96927i	−0.118794	+	0.102936i
$367$	15.4537	+	15.4537i	0.806677	+	0.806677i	0.984129	−	0.177452i	$-0.0567855\pi$
$367$	15.4537	+	15.4537i	0.806677	+	0.806677i	−0.177452	+	0.984129i	$0.556785\pi$
$368$	4.54068	+	1.54346i	0.236699	+	0.0804583i
$369$		−	4.96530i		−	0.258483i
$370$	−6.56456	−	7.04721i	−0.341275	−	0.366367i
$371$	−35.6036	−	22.8810i	−1.84844	−	1.18792i
$372$	−2.74848	−	3.67154i	−0.142502	−	0.190361i
$373$	−5.86802	−	15.7328i	−0.303834	−	0.814612i	−0.995704	−	0.0925895i	$-0.970486\pi$
$373$	−5.86802	−	15.7328i	−0.303834	−	0.814612i	0.691870	−	0.722022i	$-0.256787\pi$
$374$	−15.7066	+	2.25827i	−0.812168	+	0.116772i
$375$	−6.38347	−	9.17885i	−0.329641	−	0.473994i
$376$	−3.65960	+	2.35188i	−0.188729	+	0.121289i
$377$	−4.74214	−	1.76873i	−0.244233	−	0.0910940i
$378$	1.43032	−	2.61943i	0.0735675	−	0.134729i
$379$	0.0661737	−	0.0763685i	0.00339911	−	0.00392279i	−0.754047	−	0.656820i	$-0.771901\pi$
$379$	0.0661737	−	0.0763685i	0.00339911	−	0.00392279i	0.757447	+	0.652897i	$0.226447\pi$
$380$	−12.2721	−	9.88427i	−0.629544	−	0.507052i
$381$	4.99688	−	1.46722i	0.255998	−	0.0751677i
$382$	−1.71308	+	4.59293i	−0.0876485	+	0.234995i
$383$	−1.97827	+	9.09396i	−0.101085	+	0.464680i	0.898580	+	0.438809i	$0.144599\pi$
$383$	−1.97827	+	9.09396i	−0.101085	+	0.464680i	−0.999665	+	0.0258708i	$0.991764\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	13.7323	+	9.52928i	0.699863	+	0.485657i
$386$	−5.41530	+	11.8579i	−0.275632	+	0.603549i
$387$	−0.413809	+	0.309774i	−0.0210351	+	0.0157467i
$388$	−5.24061	+	1.14002i	−0.266051	+	0.0578760i
$389$	2.70268	+	3.11905i	0.137031	+	0.158142i	0.820117	−	0.572195i	$-0.193908\pi$
$389$	2.70268	+	3.11905i	0.137031	+	0.158142i	−0.683086	+	0.730338i	$0.739363\pi$
$390$	−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
$393$	0.0504136	−	0.704874i	0.00254303	−	0.0355562i
$394$	−10.9099	+	16.9762i	−0.549634	+	0.855247i
$395$	−0.125214	+	1.16748i	−0.00630020	+	0.0587422i
$396$	−2.27830	−	1.04046i	−0.114489	−	0.0522852i
$397$	−2.03297	−	1.52186i	−0.102032	−	0.0763800i	0.547044	−	0.837104i	$-0.315753\pi$
$397$	−2.03297	−	1.52186i	−0.102032	−	0.0763800i	−0.649075	+	0.760724i	$0.724844\pi$
$398$	−4.93985	+	2.69736i	−0.247612	+	0.135207i
$399$	11.3706	+	17.6931i	0.569244	+	0.885761i
$400$	−2.39850	−	4.38717i	−0.119925	−	0.219358i
$401$	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	$0.847387\pi$
$402$	15.5754	−	1.11397i	0.776830	−	0.0555600i
$403$	2.57167	−	0.183929i	0.128104	−	0.00916217i
$404$	−0.0760359	−	0.258955i	−0.00378293	−	0.0128835i
$405$	−1.00142	−	1.99929i	−0.0497607	−	0.0993456i
$406$	14.5271	+	22.6047i	0.720969	+	1.12185i
$407$	9.46821	−	5.17003i	0.469322	−	0.256269i
$408$	−5.07183	−	3.79672i	−0.251093	−	0.187966i
$409$	10.0553	+	4.59209i	0.497201	+	0.227064i	0.648201	−	0.761470i	$-0.275522\pi$
$409$	10.0553	+	4.59209i	0.497201	+	0.227064i	−0.150999	+	0.988534i	$0.548249\pi$
$410$	6.96884	+	8.64327i	0.344167	+	0.426861i
$411$	1.19133	−	1.85375i	0.0587642	−	0.0914389i
$412$	0.0948770	−	1.32655i	0.00467425	−	0.0653546i
$413$	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
$417$	−6.30508	+	1.37159i	−0.308761	+	0.0671669i
$418$	14.1297	−	10.5774i	0.691107	−	0.517357i
$419$	−1.79476	+	3.92998i	−0.0876799	+	0.191992i	−0.948392	−	0.317099i	$-0.897291\pi$
$419$	−1.79476	+	3.92998i	−0.0876799	+	0.191992i	0.860712	+	0.509091i	$0.170018\pi$
$420$	1.18659	+	6.56719i	0.0578997	+	0.320446i
$421$	−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	$0.145552\pi$
$422$	−1.76936	+	8.13362i	−0.0861311	+	0.395938i
$423$	1.52023	−	4.07589i	0.0739161	−	0.198177i
$424$	−13.6062	+	3.99515i	−0.660777	+	0.194022i
$425$	31.3527	−	4.52426i	1.52083	−	0.219459i
$426$	6.74083	−	7.77933i	0.326594	−	0.376910i
$427$	−4.30119	+	7.87705i	−0.208149	+	0.381197i
$428$	−5.90059	−	2.20081i	−0.285216	−	0.106380i
$429$	1.18448	−	0.761221i	0.0571874	−	0.0367521i
$430$	0.285562	−	1.12002i	0.0137710	−	0.0540121i
$431$	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	$0.211466\pi$
$432$	−0.349464	−	0.936950i	−0.0168136	−	0.0450790i
$433$	−11.6987	−	15.6276i	−0.562203	−	0.751016i	0.425906	−	0.904767i	$-0.359955\pi$
$433$	−11.6987	−	15.6276i	−0.562203	−	0.751016i	−0.988110	+	0.153752i	$0.950864\pi$
$434$	−11.5150	−	7.40022i	−0.552736	−	0.355222i
$435$	20.1193	+	0.713395i	0.964646	+	0.0342047i
$436$		−	18.7614i		−	0.898509i
$437$	6.21224	−	33.2205i	0.297172	−	1.58915i
$438$	−7.45086	−	7.45086i	−0.356016	−	0.356016i
$439$	−19.6822	+	17.0548i	−0.939382	+	0.813979i	−0.982723	−	0.185082i	$-0.940745\pi$
$439$	−19.6822	+	17.0548i	−0.939382	+	0.813979i	0.0433416	+	0.999060i	$0.486200\pi$
$440$	5.42621	−	1.38644i	0.258684	−	0.0660960i
$441$	0.271423	−	1.88779i	0.0129249	−	0.0898947i
$442$	3.33699	−	1.24463i	0.158724	−	0.0592011i
$443$	−0.197115	+	0.263314i	−0.00936519	+	0.0125104i	−0.805199	−	0.593004i	$-0.797942\pi$
$443$	−0.197115	+	0.263314i	−0.00936519	+	0.0125104i	0.795834	+	0.605515i	$0.207033\pi$
$444$	4.13266	+	1.21346i	0.196127	+	0.0575882i
$445$	−19.0774	+	13.2529i	−0.904356	+	0.628249i
$446$	−4.37141	−	9.57205i	−0.206992	−	0.453250i
$447$	11.1824	+	6.10607i	0.528911	+	0.288807i
$448$	0.212911	+	2.97689i	0.0100591	+	0.140645i
$449$	8.86767	+	7.68388i	0.418491	+	0.362625i	0.838506	−	0.544893i	$-0.183430\pi$
$449$	8.86767	+	7.68388i	0.418491	+	0.362625i	−0.420015	+	0.907517i	$0.637975\pi$
$450$	4.54922	+	2.07474i	0.214453	+	0.0978043i
$451$	−11.3124	+	5.16621i	−0.532681	+	0.243267i
$452$	19.9277	+	4.33501i	0.937320	+	0.203902i
$453$	−1.62822	−	2.98186i	−0.0765004	−	0.140100i
$454$	2.62912	+	18.2859i	0.123391	+	0.858202i
$455$	−3.46637	−	1.43478i	−0.162506	−	0.0672633i
$456$	6.97529	+	1.00290i	0.326648	+	0.0469649i
$457$	4.15030	+	19.0786i	0.194143	+	0.892461i	0.966378	+	0.257124i	$0.0827750\pi$
$457$	4.15030	+	19.0786i	0.194143	+	0.892461i	−0.772235	+	0.635337i	$0.780861\pi$
$458$	2.94100	+	0.210344i	0.137424	+	0.00982875i
$459$	6.33550			0.295716
$460$	5.85273	−	8.98585i	0.272885	−	0.418967i
$461$	18.2925			0.851966			0.425983	−	0.904731i	$-0.359928\pi$
$461$	18.2925			0.851966			0.425983	+	0.904731i	$0.359928\pi$
$462$	−7.45602	−	0.533265i	−0.346886	−	0.0248097i
$463$	−0.734162	−	3.37489i	−0.0341194	−	0.156844i	0.956935	−	0.290302i	$-0.0937557\pi$
$463$	−0.734162	−	3.37489i	−0.0341194	−	0.156844i	−0.991055	+	0.133457i	$0.957392\pi$
$464$	8.91163	+	1.28130i	0.413712	+	0.0594828i
$465$	−9.47369	+	3.92698i	−0.439332	+	0.182109i
$466$	3.01219	+	20.9502i	0.139537	+	0.970500i
$467$	−4.78928	−	8.77091i	−0.221621	−	0.405869i	0.743085	−	0.669197i	$-0.233362\pi$
$467$	−4.78928	−	8.77091i	−0.221621	−	0.405869i	−0.964706	+	0.263328i	$0.915180\pi$
$468$	0.549310	+	0.119495i	0.0253919	+	0.00552366i
$469$	42.3919	−	19.3598i	1.95748	−	0.893950i
$470$	3.07424	+	9.22871i	0.141804	+	0.425688i
$471$	17.6113	+	15.2603i	0.811487	+	0.703158i
$472$	−0.347469	−	4.85825i	−0.0159936	−	0.223619i
$473$	1.13631	+	0.620472i	0.0522476	+	0.0285293i
$474$	−0.218137	−	0.477654i	−0.0100194	−	0.0219394i
$475$	−28.1963	+	21.1301i	−1.29374	+	0.969514i
$476$	−18.1423	−	5.32707i	−0.831552	−	0.244166i
$477$	8.49814	−	11.3522i	0.389103	−	0.519781i
$478$	−26.6729	+	9.94847i	−1.21999	+	0.455033i
$479$	4.04200	−	28.1127i	0.184684	−	1.28450i	−0.660825	−	0.750540i	$-0.729793\pi$
$479$	4.04200	−	28.1127i	0.184684	−	1.28450i	0.845508	−	0.533962i	$-0.179298\pi$
$480$	1.92334	+	1.14051i	0.0877882	+	0.0520567i
$481$	−1.82988	+	1.58560i	−0.0834355	+	0.0722972i
$482$	2.88513	+	2.88513i	0.131414	+	0.131414i
$483$	−11.2017	+	8.90992i	−0.509697	+	0.405415i
$484$		−	4.72680i		−	0.214855i
$485$	−0.424963	+	11.9849i	−0.0192966	+	0.544206i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	3.36129	+	4.49016i	0.152315	+	0.203468i	0.870208	−	0.492685i	$-0.163984\pi$
$487$	3.36129	+	4.49016i	0.152315	+	0.203468i	−0.717893	+	0.696153i	$0.754893\pi$
$488$	1.05090	+	2.81756i	0.0475718	+	0.127545i
$489$	−1.56311	+	0.224741i	−0.0706863	+	0.0101632i
$490$	2.17705	+	3.66709i	0.0983493	+	0.165662i
$491$	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	$0.180452\pi$
$492$	−4.65223	−	1.73519i	−0.209739	−	0.0782285i
$493$	−27.3364	+	50.0630i	−1.23117	+	2.25472i
$494$	−2.59425	+	2.99393i	−0.116721	+	0.134703i
$495$	−3.51304	+	4.36171i	−0.157900	+	0.196044i
$496$	−4.40055	+	1.29212i	−0.197590	+	0.0580178i
$497$	10.7359	−	28.7840i	0.481570	−	1.29114i
$498$	−0.621945	+	2.85903i	−0.0278700	+	0.128116i
$499$	−0.922745	+	3.14258i	−0.0413077	+	0.140681i	−0.977565	−	0.210634i	$-0.932447\pi$
$499$	−0.922745	+	3.14258i	−0.0413077	+	0.140681i	0.936257	+	0.351315i	$0.114265\pi$
$500$	−10.8309	+	2.77331i	−0.484373	+	0.124026i
$501$	−5.05062	+	11.0593i	−0.225645	+	0.494093i
$502$	11.2218	−	8.40052i	0.500853	−	0.374934i
$503$	23.7696	−	5.17075i	1.05983	−	0.230552i	0.351323	−	0.936254i	$-0.385732\pi$
$503$	23.7696	−	5.17075i	1.05983	−	0.230552i	0.708509	+	0.705702i	$0.249368\pi$
$504$	−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
$508$	0.371522	−	5.19456i	0.0164836	−	0.230471i
$509$	−13.4724	+	20.9635i	−0.597153	+	0.929189i	0.402750	+	0.915310i	$0.368054\pi$
$509$	−13.4724	+	20.9635i	−0.597153	+	0.929189i	−0.999904	+	0.0138789i	$0.995582\pi$
$510$	−11.0284	+	8.89193i	−0.488347	+	0.393741i
$511$	−28.6061	−	13.0639i	−1.26546	−	0.577915i
$512$	0.800541	+	0.599278i	0.0353793	+	0.0264846i
$513$	−6.18502	+	3.37728i	−0.273075	+	0.149110i
$514$	10.2612	+	15.9668i	0.452604	+	0.704265i
$515$	−2.82190	−	0.938414i	−0.124348	−	0.0413515i
$516$	0.145631	+	0.495973i	0.00641104	+	0.0218340i
$517$	−10.8678	+	0.777283i	−0.477967	+	0.0341849i
$518$	12.8218	−	0.917036i	0.563359	−	0.0402923i
$519$	−4.28474	−	14.5925i	−0.188079	−	0.640540i
$520$	−1.12392	+	0.562953i	−0.0492870	+	0.0246871i
$521$	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	$0.614664\pi$
$522$	−7.90198	+	4.31481i	−0.345860	+	0.188854i
$523$	9.75017	+	7.29888i	0.426345	+	0.319158i	0.790813	−	0.612058i	$-0.209658\pi$
$523$	9.75017	+	7.29888i	0.426345	+	0.319158i	−0.364468	+	0.931216i	$0.618749\pi$
$524$	−0.642814	−	0.293563i	−0.0280814	−	0.0128244i
$525$	14.8850	+	1.05692i	0.649634	+	0.0461278i
$526$	16.5968	−	25.8251i	0.723654	−	1.12603i
$527$	2.07288	−	28.9826i	0.0902960	−	1.26250i
$528$	−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
$532$	20.5511	−	4.47063i	0.891005	−	0.193826i
$533$	2.23453	−	1.67275i	0.0967883	−	0.0724548i
$534$	4.31547	−	9.44957i	0.186749	−	0.408923i
$535$	−8.02832	+	11.5693i	−0.347094	+	0.500185i
$536$	4.39930	−	14.9827i	0.190021	−	0.647152i
$537$	1.58292	−	7.27657i	0.0683081	−	0.314007i
$538$	−7.39830	+	19.8356i	−0.318963	+	0.855174i
$539$	−4.58335	+	1.34579i	−0.197419	+	0.0579674i
$540$	−2.22319	+	0.239595i	−0.0956711	+	0.0103105i
$541$	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	$0.0266848\pi$
$542$	−4.79448	+	8.78044i	−0.205941	+	0.377152i
$543$	−22.5213	−	8.40002i	−0.966483	−	0.360480i
$544$	−5.32976	+	3.42523i	−0.228511	+	0.146855i
$545$	−40.6513	−	10.3645i	−1.74131	−	0.443968i
$546$	1.66068	−	0.238769i	0.0710704	−	0.0102184i
$547$	8.30725	+	22.2726i	0.355192	+	0.952307i	0.984536	+	0.175181i	$0.0560509\pi$
$547$	8.30725	+	22.2726i	0.355192	+	0.952307i	−0.629344	+	0.777127i	$0.716676\pi$
$548$	−1.32054	−	1.76404i	−0.0564109	−	0.0753561i
$549$	−2.52979	−	1.62580i	−0.107969	−	0.0693873i
$550$	−0.00642448	−	12.5232i	−0.000273941	−	0.533990i
$551$		−	63.4462i		−	2.70290i
$552$	−0.201680	+	4.79159i	−0.00858408	+	0.203944i
$553$	−1.10816	−	1.10816i	−0.0471238	−	0.0471238i
$554$	−1.40598	+	1.21829i	−0.0597345	+	0.0517602i
$555$	4.91230	−	8.28408i	0.208516	−	0.351640i
$556$	−0.918293	+	6.38687i	−0.0389443	+	0.270864i
$557$	−11.8788	+	4.43056i	−0.503320	+	0.187729i	−0.588283	−	0.808655i	$-0.700196\pi$
$557$	−11.8788	+	4.43056i	−0.503320	+	0.187729i	0.0849623	+	0.996384i	$0.472923\pi$
$558$	2.74848	−	3.67154i	0.116353	−	0.155429i
$559$	−0.278815	−	0.0818674i	−0.0117926	−	0.00346262i
$560$	6.56780	+	1.18322i	0.277540	+	0.0500003i
$561$	−6.59185	−	14.4341i	−0.278308	−	0.609410i
$562$	7.51506	+	4.10353i	0.317004	+	0.173097i
$563$	−0.0690051	−	0.964818i	−0.00290822	−	0.0406622i	0.995791	−	0.0916555i	$-0.0292158\pi$
$563$	−0.0690051	−	0.964818i	−0.00290822	−	0.0406622i	−0.998699	+	0.0509933i	$0.983761\pi$
$564$	−3.28764	−	2.84876i	−0.138435	−	0.119954i
$565$	20.4017	−	40.7836i	0.858306	−	1.71578i
$566$	20.5025	−	9.36318i	0.861784	−	0.393564i
$567$	2.91629	+	0.634400i	0.122473	+	0.0266423i
$568$	−4.93317	−	9.03442i	−0.206991	−	0.379076i
$569$	−2.15974	−	15.0213i	−0.0905410	−	0.629726i	−0.983677	−	0.179941i	$-0.942409\pi$
$569$	−2.15974	−	15.0213i	−0.0905410	−	0.629726i	0.893136	−	0.449786i	$-0.148500\pi$
$570$	6.02644	−	14.5597i	0.252420	−	0.609838i
$571$	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	$0.373589\pi$
$572$	−0.299292	−	1.37582i	−0.0125140	−	0.0575260i
$573$	−4.88951	−	0.349705i	−0.204262	−	0.0146091i
$574$	−14.8189			−0.618529
$575$	−16.2368	−	17.6455i	−0.677123	−	0.735870i
$576$	−1.00000			−0.0416667
$577$	−19.3832	−	1.38631i	−0.806934	−	0.0577130i	−0.338224	−	0.941065i	$-0.609826\pi$
$577$	−19.3832	−	1.38631i	−0.806934	−	0.0577130i	−0.468709	+	0.883352i	$0.655281\pi$
$578$	−4.91844	−	22.6097i	−0.204580	−	0.940440i
$579$	−12.9032	−	1.85520i	−0.536239	−	0.0770995i
$580$	7.69938	−	18.6014i	0.319699	−	0.772383i
$581$	1.24274	+	8.64344i	0.0515575	+	0.358591i
$582$	−2.57029	−	4.70714i	−0.106542	−	0.195117i
$583$	−34.7057	−	7.54975i	−1.43736	−	0.312679i
$584$	−9.58490	+	4.37728i	−0.396626	+	0.181133i
$585$	0.562376	−	1.12420i	0.0232514	−	0.0464801i
$586$	−16.4496	−	14.2536i	−0.679525	−	0.588812i
$587$	1.63130	+	22.8085i	0.0673308	+	0.941408i	0.913068	+	0.407808i	$0.133707\pi$
$587$	1.63130	+	22.8085i	0.0673308	+	0.941408i	−0.845737	+	0.533600i	$0.820839\pi$
$588$	−1.67391	−	0.914024i	−0.0690309	−	0.0376937i
$589$	13.4262	+	29.3992i	0.553216	+	1.21137i
$590$	−10.7186	−	1.93101i	−0.441277	−	0.0794982i
$591$	−19.3622	−	5.68525i	−0.796454	−	0.233860i
$592$	2.58117	−	3.44803i	0.106085	−	0.141713i
$593$	−17.4713	+	6.51645i	−0.717459	+	0.267598i	−0.681565	−	0.731757i	$-0.738700\pi$
$593$	−17.4713	+	6.51645i	−0.717459	+	0.267598i	−0.0358936	+	0.999356i	$0.511428\pi$
$594$	0.356447	−	2.47914i	0.0146252	−	0.101720i
$595$	−21.5650	+	36.3670i	−0.884077	+	1.49090i
$596$	9.62894	−	8.34352i	0.394417	−	0.341764i
$597$	−3.97982	−	3.97982i	−0.162883	−	0.162883i
$598$	−2.20473	−	1.55166i	−0.0901580	−	0.0634522i
$599$		−	32.1140i		−	1.31214i	−0.754699	−	0.656072i	$-0.772217\pi$
$599$		−	32.1140i		−	1.31214i	0.754699	−	0.656072i	$-0.227783\pi$
$600$	3.53372	−	3.53735i	0.144264	−	0.144412i
$601$	−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	$0.790150\pi$
$602$	0.924518	+	1.23501i	0.0376805	+	0.0503353i
$603$	5.45695	+	14.6306i	0.222224	+	0.595806i
$604$	−3.36286	+	0.483506i	−0.136833	+	0.0196736i
$605$	−10.2418	−	2.61127i	−0.416389	−	0.106163i
$606$	0.227043	−	0.145912i	0.00922300	−	0.00592726i
$607$	−16.0318	−	5.97957i	−0.650713	−	0.242703i	0.00236158	−	0.999997i	$-0.499248\pi$
$607$	−16.0318	−	5.97957i	−0.650713	−	0.242703i	−0.653074	+	0.757294i	$0.726521\pi$
$608$	3.37728	−	6.18502i	0.136967	−	0.250836i
$609$	−17.5962	+	20.3071i	−0.713036	+	0.822887i
$610$	6.68551	−	0.720502i	0.270688	−	0.0291723i
$611$	2.34642	−	0.688971i	0.0949260	−	0.0278728i
$612$	2.21403	−	5.93604i	0.0894968	−	0.239950i
$613$	−7.57271	+	34.8112i	−0.305859	+	1.40601i	0.525745	+	0.850642i	$0.323786\pi$
$613$	−7.57271	+	34.8112i	−0.305859	+	1.40601i	−0.831604	+	0.555369i	$0.812577\pi$
$614$	2.67125	−	9.09745i	0.107803	−	0.367143i
$615$	−6.32980	+	9.12164i	−0.255242	+	0.367820i
$616$	−3.10526	+	6.79956i	−0.125114	+	0.273962i
$617$	−31.7943	+	23.8009i	−1.27999	+	0.958188i	−0.999998	−	0.00181517i	$-0.999422\pi$
$617$	−31.7943	+	23.8009i	−1.27999	+	0.958188i	−0.279990	+	0.960003i	$0.590331\pi$
$618$	1.29955	−	0.282700i	0.0522755	−	0.0113718i
$619$	−17.1180	−	19.7553i	−0.688032	−	0.794031i	0.299052	−	0.954237i	$-0.403330\pi$
$619$	−17.1180	−	19.7553i	−0.688032	−	0.794031i	−0.987084	+	0.160206i	$0.948784\pi$
$620$	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
$623$	2.21180	−	30.9249i	0.0886137	−	1.23898i
$624$	0.303925	−	0.472917i	0.0121667	−	0.0189318i
$625$	0.0256504	+	25.0000i	0.00102601	+	0.999999i
$626$	21.2995	+	9.72715i	0.851299	+	0.388775i
$627$	14.1297	+	10.5774i	0.564287	+	0.422420i
$628$	20.4527	−	11.1680i	0.816150	−	0.445652i
$629$	14.7529	+	22.9559i	0.588236	+	0.915313i
$630$	−5.96687	+	2.98872i	−0.237726	+	0.119073i
$631$	−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	$-0.186839\pi$
$632$	−0.523769	+	0.0374607i	−0.0208344	+	0.00149011i
$633$	−8.30263	+	0.593816i	−0.330000	+	0.0236021i
$634$	6.65325	+	22.6589i	0.264234	+	0.899900i
$635$	−11.0501	−	3.67467i	−0.438509	−	0.145825i
$636$	−7.66663	−	11.9295i	−0.304002	−	0.473036i
$637$	0.941001	−	0.513825i	0.0372838	−	0.0203585i
$638$	18.0521	+	13.5137i	0.714691	+	0.535011i
$639$	9.36333	+	4.27609i	0.370408	+	0.169159i
$640$	1.74074	−	1.40351i	0.0688086	−	0.0554786i
$641$	−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	$0.256093\pi$
$642$	0.449270	−	6.28162i	0.0177313	−	0.247916i
$643$	−23.7953	+	23.7953i	−0.938394	+	0.938394i	−0.998209	−	0.0598151i	$-0.980949\pi$
$643$	−23.7953	+	23.7953i	−0.938394	+	0.938394i	0.0598151	+	0.998209i	$0.480949\pi$
$644$	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
$647$	−34.3387	+	7.46993i	−1.34999	+	0.293673i	−0.828695	−	0.559700i	$-0.810916\pi$
$647$	−34.3387	+	7.46993i	−1.34999	+	0.293673i	−0.521300	+	0.853374i	$0.674553\pi$
$648$	0.800541	−	0.599278i	0.0314482	−	0.0235419i
$649$	5.06774	−	11.0968i	0.198926	−	0.435588i
$650$	0.598884	+	2.74624i	0.0234902	+	0.107717i
$651$	3.85632	−	13.1334i	0.151141	−	0.514739i
$652$	−0.335680	+	1.54310i	−0.0131462	+	0.0604323i
$653$	−13.5064	+	36.2120i	−0.528545	+	1.41708i	0.348788	+	0.937202i	$0.386593\pi$
$653$	−13.5064	+	36.2120i	−0.528545	+	1.41708i	−0.877333	+	0.479882i	$0.840679\pi$
$654$	18.0015	−	5.28570i	0.703912	−	0.206687i
$655$	−0.991193	+	1.23064i	−0.0387291	+	0.0480851i
$656$	−3.25158	+	3.75252i	−0.126953	+	0.146511i
$657$	5.04990	−	9.24820i	0.197015	−	0.360807i
$658$	−12.1645	−	4.53711i	−0.474221	−	0.176875i
$659$	40.9327	−	26.3058i	1.59451	−	1.02473i	0.624701	−	0.780864i	$-0.285221\pi$
$659$	40.9327	−	26.3058i	1.59451	−	1.02473i	0.969809	−	0.243866i	$-0.0784155\pi$
$660$	2.85902	+	4.81581i	0.111287	+	0.187455i
$661$	−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	$0.672364\pi$
$662$	−8.17116	−	21.9077i	−0.317581	−	0.851468i
$663$	2.13435	+	2.85116i	0.0828914	+	0.110730i
$664$	2.46142	+	1.58186i	0.0955217	+	0.0613881i
$665$	1.66650	−	46.9990i	0.0646242	−	1.82254i
$666$			4.30713i			0.166898i
$667$	42.9593	−	4.34216i	1.66339	−	0.168129i
$668$	8.59700	+	8.59700i	0.332628	+	0.332628i
$669$	7.95275	−	6.89109i	0.307471	−	0.266425i
$670$	−30.0333	−	17.8092i	−1.16029	−	0.688029i
$671$	−1.07189	+	7.45519i	−0.0413800	+	0.287804i
$672$	−2.79632	+	1.04297i	−0.107870	+	0.0402336i
$673$	14.6978	−	19.6339i	0.566557	−	0.756831i	−0.422177	−	0.906513i	$-0.638734\pi$
$673$	14.6978	−	19.6339i	0.566557	−	0.756831i	0.988734	+	0.149682i	$0.0478250\pi$
$674$	21.8685	+	6.42117i	0.842343	+	0.247334i
$675$	−0.709035	+	4.94947i	−0.0272908	+	0.190505i
$676$	−5.26912	−	11.5378i	−0.202658	−	0.443760i
$677$	−41.7690	−	22.8076i	−1.60531	−	0.876566i	−0.996531	−	0.0832281i	$-0.973477\pi$
$677$	−41.7690	−	22.8076i	−1.60531	−	0.876566i	−0.608781	−	0.793338i	$-0.708341\pi$
$678$	1.45487	+	20.3418i	0.0558741	+	0.781222i
$679$	−12.0968	−	10.4819i	−0.464232	−	0.402260i
$680$	4.47725	+	13.4405i	0.171695	+	0.515419i
$681$	−16.8045	+	7.67437i	−0.643951	+	0.294082i
$682$	−11.2246	−	2.44175i	−0.429811	−	0.0934996i
$683$	−14.9361	−	27.3534i	−0.571514	−	1.04665i	−0.990350	−	0.138588i	$-0.955744\pi$
$683$	−14.9361	−	27.3534i	−0.571514	−	1.04665i	0.418836	−	0.908062i	$-0.362438\pi$
$684$	1.00290	+	6.97529i	0.0383467	+	0.266707i
$685$	−4.55176	+	1.88677i	−0.173914	+	0.0720897i
$686$	15.0447	+	2.16310i	0.574410	+	0.0825877i
$687$	0.626751	+	2.88113i	0.0239120	+	0.109922i
$688$	0.515595	+	0.0368761i	0.0196569	+	0.00140589i
$689$	7.97175			0.303699
$690$	10.2708	+	3.08405i	0.391001	+	0.117408i
$691$	30.6797			1.16711			0.583556	−	0.812073i	$-0.301661\pi$
$691$	30.6797			1.16711			0.583556	+	0.812073i	$0.301661\pi$
$692$	−15.1698	−	1.08497i	−0.576669	−	0.0412442i
$693$	−1.58894	−	7.30424i	−0.0603588	−	0.277465i
$694$	12.7019	+	1.82625i	0.482157	+	0.0693237i
$695$	13.3315	+	5.51806i	0.505691	+	0.209312i
$696$	1.28130	+	8.91163i	0.0485675	+	0.337794i
$697$	−15.0760	−	27.6097i	−0.571045	−	1.04579i
$698$	7.51603	+	1.63501i	0.284486	+	0.0618861i
$699$	−19.2529	+	8.79253i	−0.728213	+	0.332564i
$700$	6.19205	−	13.5771i	0.234038	−	0.513167i
$701$	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	$0.723068\pi$
$702$	0.0401038	+	0.560725i	0.00151362	+	0.0211632i
$703$	−26.6397	−	14.5464i	−1.00473	−	0.548626i
$704$	1.04046	+	2.27830i	0.0392139	+	0.0858665i
$705$	−7.98877	+	5.54974i	−0.300874	+	0.209015i
$706$	7.68321	+	2.25599i	0.289161	+	0.0849055i
$707$	0.482704	−	0.644817i	0.0181539	−	0.0242508i
$708$	4.56356	−	1.70212i	0.171509	−	0.0639696i
$709$	−4.44269	+	30.8996i	−0.166849	+	1.16046i	0.718499	+	0.695528i	$0.244830\pi$
$709$	−4.44269	+	30.8996i	−0.166849	+	1.16046i	−0.885347	+	0.464930i	$0.846079\pi$
$710$	−22.3006	+	5.69798i	−0.836927	+	0.213842i
$711$	0.396849	−	0.343872i	0.0148830	−	0.0128962i
$712$	−7.34567	−	7.34567i	−0.275290	−	0.275290i
$713$	−18.9873	+	11.1029i	−0.711079	+	0.415806i
$714$		−	18.9082i		−	0.707623i
$715$	−3.14640	−	0.111566i	−0.117669	−	0.00417233i
$716$	−6.26461	−	4.02602i	−0.234119	−	0.150459i
$717$	−17.0601	−	22.7896i	−0.637122	−	0.851095i
$718$	2.07547	+	5.56456i	0.0774559	+	0.207667i
$719$	19.9233	−	2.86454i	0.743015	−	0.106829i	0.239597	−	0.970872i	$-0.422985\pi$
$719$	19.9233	−	2.86454i	0.743015	−	0.106829i	0.503418	+	0.864043i	$0.332076\pi$
$720$	−0.552438	+	2.16675i	−0.0205882	+	0.0807501i
$721$	3.33911	−	2.14591i	0.124355	−	0.0799180i
$722$	−28.7273	−	10.7147i	−1.06912	−	0.398761i
$723$	−1.95542	+	3.58109i	−0.0727230	+	0.133182i
$724$	−15.7408	+	18.1659i	−0.585002	+	0.675129i
$725$	−36.0513	−	26.9588i	−1.33891	−	1.00122i
$726$	4.53533	−	1.33169i	0.168322	−	0.0494238i
$727$	10.8634	−	29.1260i	0.402902	−	1.08022i	−0.564156	−	0.825668i	$-0.690798\pi$
$727$	10.8634	−	29.1260i	0.402902	−	1.08022i	0.967058	−	0.254555i	$-0.0819289\pi$
$728$	0.356632	−	1.63941i	0.0132177	−	0.0607607i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	4.18940	+	23.1863i	0.155057	+	0.858162i
$731$	−1.36044	+	2.97895i	−0.0503177	+	0.110180i
$732$	−2.40736	+	1.80213i	−0.0889785	+	0.0666085i
$733$	−30.0254	+	6.53163i	−1.10901	+	0.241251i	−0.729532	−	0.683947i	$-0.760262\pi$
$733$	−30.0254	+	6.53163i	−1.10901	+	0.241251i	−0.379483	+	0.925199i	$0.623898\pi$
$734$	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
$738$	0.354220	−	4.95265i	0.0130390	−	0.182309i
$739$	−8.74185	+	13.6026i	−0.321574	+	0.500379i	−0.963976	−	0.265989i	$-0.914302\pi$
$739$	−8.74185	+	13.6026i	−0.321574	+	0.500379i	0.642402	+	0.766368i	$0.277938\pi$
$740$	−6.04510	−	7.49757i	−0.222222	−	0.275616i
$741$	−3.60354	−	1.64568i	−0.132379	−	0.0604556i
$742$	−33.8805	−	25.3627i	−1.24379	−	0.931092i
$743$	16.5263	−	9.02406i	0.606293	−	0.331061i	−0.146608	−	0.989195i	$-0.546836\pi$
$743$	16.5263	−	9.02406i	0.606293	−	0.331061i	0.752901	+	0.658134i	$0.228654\pi$
$744$	−2.47955	−	3.85826i	−0.0909049	−	0.141451i
$745$	−12.7589	−	25.4728i	−0.467451	−	0.933251i
$746$	−4.73070	−	16.1113i	−0.173203	−	0.589877i
$747$	−2.91844	+	0.208731i	−0.106780	+	0.00763708i
$748$	−15.8277	+	1.13202i	−0.578717	+	0.0413907i
$749$	−5.29526	−	18.0340i	−0.193484	−	0.658948i
$750$	−5.71239	−	9.61086i	−0.208587	−	0.350939i
$751$	−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	$0.830083\pi$
$752$	−3.81805	+	2.08482i	−0.139230	+	0.0760254i
$753$	11.2218	+	8.40052i	0.408944	+	0.306132i
$754$	−4.60388	−	2.10252i	−0.167663	−	0.0765693i
$755$	−0.810134	+	7.55358i	−0.0294838	+	0.274903i
$756$	1.61354	−	2.51072i	0.0586838	−	0.0913138i
$757$	3.56413	−	49.8330i	0.129540	−	1.81121i	−0.353309	−	0.935507i	$-0.614943\pi$
$757$	3.56413	−	49.8330i	0.129540	−	1.81121i	0.482849	−	0.875704i	$-0.339602\pi$
$758$	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	$0.491798\pi$
$762$	5.08882	−	1.10700i	0.184348	−	0.0401025i
$763$	44.8250	−	33.5556i	1.62277	−	1.21479i
$764$	−2.03637	+	4.45902i	−0.0736731	+	0.161322i
$765$	−11.6388	−	8.07655i	−0.420802	−	0.292008i
$766$	−2.62198	+	8.92966i	−0.0947362	+	0.322642i
$767$	−0.582020	+	2.67550i	−0.0210155	+	0.0966068i
$768$	−0.349464	+	0.936950i	−0.0126102	+	0.0338093i
$769$	6.11550	−	1.79567i	0.220531	−	0.0647537i	−0.169601	−	0.985513i	$-0.554248\pi$
$769$	6.11550	−	1.79567i	0.220531	−	0.0647537i	0.390131	+	0.920759i	$0.372430\pi$
$770$	13.0175	+	10.4847i	0.469118	+	0.377841i
$771$	−12.4291	+	14.3439i	−0.447623	+	0.516585i
$772$	−6.24743	+	11.4413i	−0.224850	+	0.411782i
$773$	8.81084	+	3.28627i	0.316904	+	0.118199i	0.502883	−	0.864355i	$-0.332273\pi$
$773$	8.81084	+	3.28627i	0.316904	+	0.118199i	−0.185979	+	0.982554i	$0.559546\pi$
$774$	−0.434854	+	0.279464i	−0.0156305	+	0.0100451i
$775$	22.4101	+	4.86297i	0.804993	+	0.174683i
$776$	−5.30858	+	0.763259i	−0.190567	+	0.0273994i
$777$	4.49222	+	12.0441i	0.161157	+	0.432080i
$778$	2.47328	+	3.30391i	0.0886714	+	0.118451i
$779$	29.4359	+	18.9173i	1.05465	+	0.677783i
$780$	−0.856793	−	0.919787i	−0.0306781	−	0.0329337i
$781$		−	25.7815i		−	0.922536i
$782$	−20.8453	+	22.1056i	−0.745427	+	0.790495i
$783$	−6.36627	−	6.36627i	−0.227512	−	0.227512i
$784$	−1.44137	+	1.24895i	−0.0514774	+	0.0446054i
$785$	−12.8994	−	50.4855i	−0.460401	−	1.80190i
$786$	0.100570	−	0.699481i	0.00358722	−	0.0249497i
$787$	−50.0505	+	18.6679i	−1.78411	+	0.665437i	−0.785172	+	0.619277i	$0.787426\pi$
$787$	−50.0505	+	18.6679i	−1.78411	+	0.665437i	−0.998934	+	0.0461601i	$0.985302\pi$
$788$	−12.0932	+	16.1546i	−0.430802	+	0.575484i
$789$	29.4549	+	8.64873i	1.04862	+	0.307903i
$790$	−0.208182	+	1.15557i	−0.00740679	+	0.0411134i
$791$	25.2843	+	55.3648i	0.899005	+	1.96855i
$792$	−2.19827	−	1.20034i	−0.0781120	−	0.0426524i
$793$	−0.120599	−	1.68619i	−0.00428259	−	0.0598784i
$794$	−1.91922	−	1.66301i	−0.0681105	−	0.0590181i
$795$	−30.0836	+	10.0214i	−1.06696	+	0.355421i
$796$	−5.11969	+	2.33808i	−0.181463	+	0.0828712i
$797$	9.03096	+	1.96456i	0.319893	+	0.0695885i	0.369645	−	0.929173i	$-0.379479\pi$
$797$	9.03096	+	1.96456i	0.319893	+	0.0695885i	−0.0497518	+	0.998762i	$0.515843\pi$
$798$	10.0795	+	18.4592i	0.356809	+	0.653447i
$799$	−3.92227	−	27.2800i	−0.138760	−	0.965096i
$800$	−2.07941	−	4.54709i	−0.0735182	−	0.160764i
$801$	10.2826	+	1.47841i	0.363318	+	0.0522372i
$802$	1.63996	+	7.53878i	0.0579090	+	0.266203i
$803$	−26.3244	−	1.88276i	−0.928967	−	0.0664411i
$804$	15.6152			0.550705
$805$	31.9369	−	2.08815i	1.12563	−	0.0735976i
$806$	2.57824			0.0908145
$807$	−21.1165	−	1.51028i	−0.743335	−	0.0531644i
$808$	−0.0573686	−	0.263719i	−0.00201822	−	0.00927761i
$809$	−25.5354	−	3.67144i	−0.897778	−	0.129081i	−0.322050	−	0.946723i	$-0.604372\pi$
$809$	−25.5354	−	3.67144i	−0.897778	−	0.129081i	−0.575728	+	0.817642i	$0.695281\pi$
$810$	−0.856236	−	2.06564i	−0.0300851	−	0.0725791i
$811$	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	$0.911108\pi$
$812$	12.8775	+	23.5834i	0.451912	+	0.827616i
$813$	−9.77553	−	2.12654i	−0.342843	−	0.0745809i
$814$	9.81291	−	4.48141i	0.343942	−	0.157073i
$815$	3.15806	+	1.57980i	0.110622	+	0.0553380i
$816$	−4.78805	−	4.14887i	−0.167615	−	0.145239i
$817$	−0.259866	−	3.63341i	−0.00909157	−	0.127117i
$818$	9.70206	+	5.29773i	0.339225	+	0.185231i
$819$	0.696964	+	1.52614i	0.0243539	+	0.0533276i
$820$	6.33448	+	9.11840i	0.221210	+	0.318428i
$821$	−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	$0.660992\pi$
$822$	1.32054	−	1.76404i	0.0460593	−	0.0615280i
$823$	−13.3148	+	4.96616i	−0.464124	+	0.173109i	−0.570638	−	0.821202i	$-0.693304\pi$
$823$	−13.3148	+	4.96616i	−0.464124	+	0.173109i	0.106514	+	0.994311i	$0.466031\pi$
$824$	0.189271	−	1.31641i	0.00659355	−	0.0458592i
$825$	12.0141	−	3.53435i	0.418277	−	0.123050i
$826$	10.9859	−	9.51936i	0.382249	−	0.331221i
$827$	14.0883	+	14.0883i	0.489899	+	0.489899i	0.908274	−	0.418375i	$-0.137400\pi$
$827$	14.0883	+	14.0883i	0.489899	+	0.489899i	−0.418375	+	0.908274i	$0.637400\pi$
$828$	−4.65432	+	1.15644i	−0.161749	+	0.0401889i
$829$			4.72510i			0.164110i	0.996628	+	0.0820548i	$0.0261483\pi$
$829$			4.72510i			0.164110i	−0.996628	+	0.0820548i	$0.973852\pi$
$830$	4.78728	−	4.45941i	0.166169	−	0.154788i
$831$	−1.56505	−	1.00580i	−0.0542911	−	0.0348907i
$832$	−0.336888	−	0.450030i	−0.0116795	−	0.0156020i
$833$	−4.22260	−	11.3212i	−0.146304	−	0.392257i
$834$	−6.38687	+	0.918293i	−0.221159	+	0.0317979i
$835$	23.3769	−	13.8783i	0.808991	−	0.480277i
$836$	14.8483	−	9.54243i	0.513539	−	0.330032i
$837$	4.29716	+	1.60276i	0.148531	+	0.0553994i
$838$	−2.07055	+	3.79193i	−0.0715260	+	0.130990i
$839$	−17.3592	+	20.0336i	−0.599307	+	0.691638i	−0.971641	−	0.236461i	$-0.924012\pi$
$839$	−17.3592	+	20.0336i	−0.599307	+	0.691638i	0.372334	+	0.928099i	$0.378558\pi$
$840$	0.715070	+	6.63511i	0.0246723	+	0.228933i
$841$	49.9501	−	14.6667i	1.72242	−	0.505748i
$842$	−2.44977	+	6.56808i	−0.0844246	+	0.226351i
$843$	−1.82007	+	8.36675i	−0.0626867	+	0.288166i
$844$	−2.34510	+	7.98667i	−0.0807216	+	0.274912i
$845$	−27.9103	+	5.04297i	−0.960144	+	0.173483i
$846$	1.80713	−	3.95705i	0.0621303	−	0.136046i
$847$	11.2933	−	8.45408i	0.388043	−	0.290485i
$848$	−13.8566	+	3.01431i	−0.475837	+	0.103512i
$849$	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
$853$	1.88641	−	26.3754i	0.0645894	−	0.903077i	−0.857100	−	0.515149i	$-0.827736\pi$
$853$	1.88641	−	26.3754i	0.0645894	−	0.903077i	0.921690	−	0.387928i	$-0.126809\pi$
$854$	−4.85218	+	7.55013i	−0.166038	+	0.258360i
$855$	15.6678	+	1.68039i	0.535826	+	0.0574682i
$856$	−5.72855	−	2.61614i	−0.195798	−	0.0894179i
$857$	−26.8309	−	20.0853i	−0.916525	−	0.686102i	0.0331131	−	0.999452i	$-0.489458\pi$
$857$	−26.8309	−	20.0853i	−0.916525	−	0.686102i	−0.949638	+	0.313350i	$0.898549\pi$
$858$	1.23577	−	0.674782i	0.0421885	−	0.0230367i
$859$	11.0001	+	17.1165i	0.375320	+	0.584009i	0.976609	−	0.215022i	$-0.0689824\pi$
$859$	11.0001	+	17.1165i	0.375320	+	0.584009i	−0.601289	+	0.799031i	$0.705346\pi$
$860$	0.364736	−	1.09679i	0.0124374	−	0.0374004i
$861$	−4.17496	−	14.2186i	−0.142282	−	0.484569i
$862$	28.6414	−	2.04848i	0.975531	−	0.0697714i
$863$	−26.2350	+	1.87636i	−0.893049	+	0.0638722i	−0.510316	−	0.859987i	$-0.670472\pi$
$863$	−26.2350	+	1.87636i	−0.893049	+	0.0638722i	−0.382733	+	0.923859i	$0.625017\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−10.7312	+	32.2698i	−0.364873	+	1.09721i
$866$	−10.5540	−	16.4224i	−0.358640	−	0.558055i
$867$	20.3082	−	11.0891i	0.689702	−	0.376606i
$868$	−10.9577	−	8.20283i	−0.371928	−	0.278422i
$869$	−1.19635	−	0.546354i	−0.0405834	−	0.0185338i
$870$	20.0171	+	2.14687i	0.678644	+	0.0727857i
$871$	−4.74584	+	7.38468i	−0.160807	+	0.250220i
$872$	1.33842	−	18.7136i	0.0453248	−	0.633723i
$873$	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
$877$	−26.3211	+	5.72581i	−0.888801	+	0.193347i	−0.633710	−	0.773570i	$-0.718469\pi$
$877$	−26.3211	+	5.72581i	−0.888801	+	0.193347i	−0.255090	+	0.966917i	$0.582105\pi$
$878$	−20.8488	+	15.6072i	−0.703611	+	0.526717i
$879$	9.04188	−	19.7990i	0.304975	−	0.667802i
$880$	5.51129	−	0.995807i	0.185786	−	0.0335686i
$881$	−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	$0.738995\pi$
$882$	0.405405	−	1.86362i	0.0136507	−	0.0627512i
$883$	1.66874	−	4.47406i	0.0561575	−	0.150564i	−0.905842	−	0.423616i	$-0.860760\pi$
$883$	1.66874	−	4.47406i	0.0561575	−	0.150564i	0.961999	+	0.273052i	$0.0880332\pi$
$884$	3.41728	−	1.00340i	0.114935	−	0.0337481i
$885$	−1.16699	−	10.8284i	−0.0392278	−	0.363994i
$886$	−0.215397	+	0.248581i	−0.00723640	+	0.00835125i
$887$	26.3051	−	48.1742i	0.883239	−	1.61753i	0.100711	−	0.994916i	$-0.467888\pi$
$887$	26.3051	−	48.1742i	0.883239	−	1.61753i	0.782528	−	0.622616i	$-0.213930\pi$
$888$	4.03556	+	1.50519i	0.135425	+	0.0505108i
$889$	13.0754	−	8.40304i	0.438534	−	0.281829i
$890$	−19.9743	+	11.8582i	−0.669539	+	0.397488i
$891$	2.47914	−	0.356447i	0.0830544	−	0.0119414i
$892$	−3.67741	−	9.85951i	−0.123129	−	0.330121i
$893$	18.3713	+	24.5412i	0.614772	+	0.821239i
$894$	10.7183	+	6.88825i	0.358475	+	0.230378i
$895$	−12.1842	+	11.3497i	−0.407273	+	0.379379i
$896$			2.98449i			0.0997049i
$897$	0.867666	−	2.55257i	0.0289705	−	0.0852279i
$898$	8.29691	+	8.29691i	0.276872	+	0.276872i
$899$	−31.2064	+	27.0405i	−1.04079	+	0.901850i
$900$	4.38962	+	2.39399i	0.146321	+	0.0797998i
$901$	12.7858	−	88.9269i	0.425956	−	2.96259i
$902$	−11.6521	+	4.34603i	−0.387974	+	0.144707i
$903$	−0.924518	+	1.23501i	−0.0307660	+	0.0410986i
$904$	19.5677	+	5.74559i	0.650811	+	0.191095i
$905$	30.6651	+	44.1419i	1.01934	+	1.46733i
$906$	−1.41135	−	3.09042i	−0.0468888	−	0.102672i
$907$	6.79154	+	3.70846i	0.225510	+	0.123138i	0.588032	−	0.808837i	$-0.299903\pi$
$907$	6.79154	+	3.70846i	0.225510	+	0.123138i	−0.362523	+	0.931975i	$0.618085\pi$
$908$	1.31792	+	18.4269i	0.0437367	+	0.611518i
$909$	0.203967	+	0.176738i	0.00676516	+	0.00586204i
$910$	−3.35518	−	1.67841i	−0.111223	−	0.0556387i
$911$	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	$0.172956\pi$
$912$	6.88597	+	1.49795i	0.228017	+	0.0496021i
$913$	3.51209	+	6.43190i	0.116233	+	0.212865i
$914$	2.77867	+	19.3261i	0.0919104	+	0.639251i
$915$	2.57484	+	6.21171i	0.0851217	+	0.205353i
$916$	2.91850	+	0.419617i	0.0964299	+	0.0138645i
$917$	−0.448314	−	2.06087i	−0.0148046	−	0.0680558i
$918$	6.31935	+	0.451969i	0.208570	+	0.0149172i
$919$	−53.5065			−1.76502			−0.882509	−	0.470296i	$-0.844147\pi$
$919$	−53.5065			−1.76502			−0.882509	+	0.470296i	$0.844147\pi$
$920$	6.47886	−	8.54543i	0.213602	−	0.281734i
$921$	9.48151			0.312427
$922$	18.2459	+	1.30497i	0.600896	+	0.0429769i
$923$	1.23003	+	5.65434i	0.0404868	+	0.186115i
$924$	−7.39898	−	1.06381i	−0.243409	−	0.0349969i
$925$	−19.5849	+	8.95627i	−0.643948	+	0.294480i
$926$	−0.491530	−	3.41867i	−0.0161527	−	0.112344i
$927$	0.637373	+	1.16726i	0.0209341	+	0.0383379i
$928$	8.79752	+	1.91378i	0.288793	+	0.0628230i
$929$	29.1322	−	13.3042i	0.955795	−	0.436497i	0.124433	−	0.992228i	$-0.460289\pi$
$929$	29.1322	−	13.3042i	0.955795	−	0.436497i	0.831362	+	0.555731i	$0.187562\pi$
$930$	−9.72970	+	3.24113i	−0.319049	+	0.106281i
$931$	10.1573	+	8.80139i	0.332893	+	0.288454i
$932$	1.50994	+	21.1117i	0.0494597	+	0.691537i
$933$	21.8013	+	11.9044i	0.713744	+	0.389733i
$934$	−4.15137	−	9.09023i	−0.135837	−	0.297441i
$935$	−6.29101	+	34.9200i	−0.205738	+	1.14201i
$936$	0.539386	+	0.158378i	0.0176304	+	0.00517675i
$937$	13.5742	−	18.1330i	0.443451	−	0.592381i	−0.522007	−	0.852941i	$-0.674816\pi$
$937$	13.5742	−	18.1330i	0.443451	−	0.592381i	0.965457	+	0.260561i	$0.0839074\pi$
$938$	43.6650	−	16.2862i	1.42571	−	0.531764i
$939$	−3.33237	+	23.1772i	−0.108748	+	0.756358i
$940$	2.40804	+	9.42451i	0.0785415	+	0.307393i
$941$	−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
$943$	−10.7943	+	21.2257i	−0.351511	+	0.691202i
$944$		−	4.87066i		−	0.158527i
$945$	−4.54872	−	4.88315i	−0.147970	−	0.158849i
$946$	1.08915	+	0.699954i	0.0354113	+	0.0227575i
$947$	27.1558	+	36.2759i	0.882446	+	1.17881i	0.982950	+	0.183873i	$0.0588635\pi$
$947$	27.1558	+	36.2759i	0.882446	+	1.17881i	−0.100504	+	0.994937i	$0.532046\pi$
$948$	−0.183506	−	0.491999i	−0.00596000	−	0.0159794i
$949$	5.86322	−	0.843004i	0.190328	−	0.0273651i
$950$	−29.6319	+	19.0647i	−0.961385	+	0.618542i
$951$	−19.8666	+	12.7675i	−0.644219	+	0.414015i
$952$	−17.7161	−	6.60775i	−0.574181	−	0.214159i
$953$	6.55275	−	12.0005i	0.212264	−	0.388733i	−0.749755	−	0.661716i	$-0.769828\pi$
$953$	6.55275	−	12.0005i	0.212264	−	0.388733i	0.962019	+	0.272983i	$0.0880103\pi$
$954$	9.28635	−	10.7170i	0.300657	−	0.346976i
$955$	8.53662	+	6.87563i	0.276239	+	0.222490i
$956$	−27.3146	+	8.02030i	−0.883419	+	0.259395i
$957$	−7.88039	+	21.1281i	−0.254737	+	0.682975i
$958$	6.03724	−	27.7527i	0.195054	−	0.896650i
$959$	1.85282	−	6.31012i	0.0598306	−	0.203764i
$960$	1.83708	+	1.27481i	0.0592915	+	0.0411443i
$961$	−4.13987	+	9.06504i	−0.133544	+	0.292421i
$962$	−1.93834	+	1.45102i	−0.0624945	+	0.0467828i
$963$	6.15374	−	1.33866i	0.198302	−	0.0431379i
$964$	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	−0.881767	−	0.471684i	$-0.843646\pi$
$967$	−12.7522	+	12.7522i	−0.410083	+	0.410083i	0.471684	+	0.881767i	$0.343646\pi$
$968$	0.337206	−	4.71476i	0.0108382	−	0.151538i
$969$	−24.1376	+	37.5589i	−0.775413	+	1.20657i
$970$	−1.27887	+	11.9240i	−0.0410621	+	0.382858i
$971$	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	$0.243885\pi$
$972$	0.800541	+	0.599278i	0.0256774	+	0.0192218i
$973$	−16.9020	+	9.22918i	−0.541852	+	0.295874i
$974$	3.03240	+	4.71851i	0.0971644	+	0.151191i
$975$	−2.46628	+	1.34833i	−0.0789840	+	0.0431812i
$976$	0.847216	+	2.88535i	0.0271187	+	0.0923579i
$977$	19.1932	−	1.37273i	0.614045	−	0.0439174i	0.239147	−	0.970983i	$-0.423132\pi$
$977$	19.1932	−	1.37273i	0.614045	−	0.0439174i	0.374898	+	0.927066i	$0.377678\pi$
$978$	−1.57516	+	0.112658i	−0.0503681	+	0.00360240i
$979$	−7.33040	−	24.9650i	−0.234281	−	0.797886i
$980$	1.90990	+	3.81305i	0.0610095	+	0.121803i
$981$	10.1432	+	15.7831i	0.323847	+	0.503916i
$982$	16.3098	−	8.90580i	0.520465	−	0.284196i
$983$	−49.5977	−	37.1283i	−1.58192	−	1.18421i	−0.883401	−	0.468618i	$-0.844752\pi$
$983$	−49.5977	−	37.1283i	−1.58192	−	1.18421i	−0.698518	−	0.715592i	$-0.746157\pi$
$984$	−4.51659	−	2.06266i	−0.143984	−	0.0657552i
$985$	28.3223	+	35.1274i	0.902423	+	1.11925i
$986$	−30.8382	+	47.9853i	−0.982090	+	1.52816i
$987$	0.926201	−	12.9500i	0.0294813	−	0.412202i
$988$	−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	$0.831621\pi$
$992$	−4.48151	+	0.974894i	−0.142288	+	0.0309529i
$993$	18.7182	−	14.0123i	0.594005	−	0.444666i
$994$	12.7620	−	27.9448i	0.404785	−	0.886355i
$995$	2.23773	+	12.3847i	0.0709410	+	0.392623i
$996$	−0.824321	+	2.80738i	−0.0261196	+	0.0889552i
$997$	1.25012	−	5.74670i	0.0395916	−	0.182000i	−0.953105	−	0.302641i	$-0.902132\pi$
$997$	1.25012	−	5.74670i	0.0395916	−	0.182000i	0.992696	+	0.120642i	$0.0384952\pi$
$998$	−1.14458	+	3.06875i	−0.0362312	+	0.0971395i
$999$	−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.493.10	yes	240
5.2	odd	4	inner	690.2.w.b.217.3	yes	240
23.7	odd	22	inner	690.2.w.b.283.3	yes	240
115.7	even	44	inner	690.2.w.b.7.10	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.10	✓	240	115.7	even	44	inner
690.2.w.b.217.3	yes	240	5.2	odd	4	inner
690.2.w.b.283.3	yes	240	23.7	odd	22	inner
690.2.w.b.493.10	yes	240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.855176 - 2.06608i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.43032 + 2.61943i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.855176 - 2.06608i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.43032 + 2.61943i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(1.00039 - 1.99981i) q^{10} +(1.89288 + 1.64019i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(-0.493393 - 0.269413i) q^{13} +(1.23980 + 2.71479i) q^{14} +(2.20064 + 0.396457i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-3.79672 + 5.07183i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(1.00290 - 6.97529i) q^{19} +(1.14051 - 1.92334i) q^{20} +(-2.25553 + 1.95443i) q^{21} +(1.77104 + 1.77104i) q^{22} +(4.79159 + 0.201680i) q^{23} +1.00000i q^{24} +(-3.53735 - 3.53372i) q^{25} +(-0.472917 - 0.303925i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(1.04297 + 2.79632i) q^{28} +(8.91163 - 1.28130i) q^{29} +(2.16675 + 0.552438i) q^{30} +(-3.85826 + 2.47955i) q^{31} +(0.936950 + 0.349464i) q^{32} +(-1.20034 + 2.19827i) q^{33} +(-4.14887 + 4.78805i) q^{34} +(6.63511 - 0.715070i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.50519 - 4.03556i) q^{37} +(1.49795 - 6.88597i) q^{38} +(0.158378 - 0.539386i) q^{39} +(1.27481 - 1.83708i) q^{40} +(-2.06266 + 4.51659i) q^{41} +(-2.38921 + 1.78854i) q^{42} +(0.505099 - 0.109878i) 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} +(-0.0713392 + 0.997452i) q^{48} +(-1.03111 + 1.60444i) q^{49} +(-3.27624 - 3.77707i) q^{50} +(-5.76297 - 2.63186i) q^{51} +(-0.450030 - 0.336888i) q^{52} +(-12.4461 + 6.79606i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(5.00750 - 2.50818i) q^{55} +(0.840829 + 2.86360i) q^{56} +(7.02906 - 0.502729i) q^{57} +(8.98033 - 0.642286i) q^{58} +(-1.37222 - 4.67337i) q^{59} +(2.12182 + 0.705605i) q^{60} +(1.62580 + 2.52979i) q^{61} +(-4.02532 + 2.19799i) q^{62} +(-2.38921 - 1.78854i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-0.978567 + 0.788993i) q^{65} +(-1.35411 + 2.10703i) q^{66} +(1.11397 - 15.5754i) 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} +(-0.977147 + 0.212565i) q^{72} +(-8.43539 + 6.31466i) q^{73} +(1.78925 - 3.91790i) q^{74} +(2.70105 - 4.20765i) q^{75} +(1.98537 - 6.76157i) q^{76} +(-1.58894 + 7.30424i) q^{77} +(0.196454 - 0.526713i) q^{78} +(-0.503836 + 0.147940i) q^{79} +(1.40262 - 1.74146i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.37961 + 4.35794i) q^{82} +(2.74142 + 1.02250i) q^{83} +(-2.51072 + 1.61354i) q^{84} +(7.23192 + 12.1816i) q^{85} +(0.511650 - 0.0735642i) q^{86} +(3.14632 + 8.43561i) q^{87} +(1.50097 + 2.00506i) q^{88} +(-8.73923 - 5.61636i) q^{89} +(-0.0792373 + 2.23466i) q^{90} -1.67775i q^{91} +(4.71412 + 0.881542i) q^{92} +(-3.24302 - 3.24302i) q^{93} +(-3.28764 + 2.84876i) q^{94} +(-13.5538 - 8.03716i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-5.02502 + 1.87424i) q^{97} +(-1.14294 + 1.52679i) 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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