LMFDB - Embedded newform 693.2.by.b.478.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(37,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 6]))

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

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

chi := DirichletCharacter("693.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.by (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			478.5
Character	$\chi$	$=$	693.478
Dual form			693.2.by.b.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.57407 + 0.547134i) q^{2} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(-2.31119 - 1.28778i) q^{7} +(6.22764 + 4.52465i) q^{8} +O(q^{10})$	\(q+(2.57407 + 0.547134i) q^{2} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(-2.31119 - 1.28778i) q^{7} +(6.22764 + 4.52465i) q^{8} +(1.54783 + 2.68093i) q^{10} +(3.26165 + 0.601380i) q^{11} +(0.0112624 + 0.0346622i) q^{13} +(-5.24457 - 4.57937i) q^{14} +(6.96361 + 7.73387i) q^{16} +(-5.95559 + 1.26590i) q^{17} +(1.75961 - 0.783430i) q^{19} +(1.79037 + 5.51019i) q^{20} +(8.06666 + 3.33255i) q^{22} +(1.02155 - 1.76938i) q^{23} +(0.377994 - 3.59637i) q^{25} +(0.0100254 + 0.0953849i) q^{26} +(-7.81916 - 10.4241i) q^{28} +(-4.02767 + 2.92628i) q^{29} +(1.89509 - 2.10472i) q^{31} +(5.99553 + 10.3846i) q^{32} -16.0227 q^{34} +(-0.693441 - 3.03411i) q^{35} +(0.278295 + 2.64780i) q^{37} +(4.95800 - 1.05386i) q^{38} +(0.946542 + 9.00574i) q^{40} +(-6.61499 - 4.80607i) q^{41} -2.96835 q^{43} +(13.4706 + 9.23971i) q^{44} +(3.59762 - 3.99557i) q^{46} +(-2.91785 + 1.29911i) q^{47} +(3.68323 + 5.95263i) q^{49} +(2.94068 - 9.05049i) q^{50} +(-0.0187631 + 0.178519i) q^{52} +(6.63364 - 7.36740i) q^{53} +(2.04163 + 3.32471i) q^{55} +(-8.56653 - 18.4772i) q^{56} +(-11.9686 + 5.32875i) q^{58} +(-3.70874 - 1.65124i) q^{59} +(-5.80710 - 6.44943i) q^{61} +(6.02966 - 4.38080i) q^{62} +(3.31928 + 10.2157i) q^{64} +(-0.0214368 + 0.0371295i) q^{65} +(-1.12669 - 1.95148i) q^{67} +(-29.3323 - 6.23477i) q^{68} +(-0.124894 - 8.18941i) q^{70} +(-1.31384 + 4.04359i) q^{71} +(3.92144 + 1.74594i) q^{73} +(-0.732354 + 6.96788i) q^{74} +9.48655 q^{76} +(-6.76385 - 5.59020i) q^{77} +(3.03638 + 0.645402i) q^{79} +(-1.27967 + 12.1752i) q^{80} +(-14.3979 - 15.9904i) q^{82} +(-1.87581 + 5.77314i) q^{83} +(-5.79451 - 4.20996i) q^{85} +(-7.64073 - 1.62409i) q^{86} +(17.5913 + 18.5030i) q^{88} +(2.16161 - 3.74402i) q^{89} +(0.0186077 - 0.0946147i) q^{91} +(8.14083 - 5.91466i) q^{92} +(-8.22152 + 1.74754i) q^{94} +(2.06993 + 0.921593i) q^{95} +(1.43258 + 4.40904i) q^{97} +(6.22400 + 17.3377i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8}+O(q^{10}) $ 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8	$ 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8} + 14 q^{10} + 9 q^{11} + 6 q^{13} + 3 q^{14} - 5 q^{16} + 7 q^{17} - 4 q^{19} + 30 q^{20} + 44 q^{22} + 14 q^{23} + 21 q^{25} + 16 q^{28} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 24 q^{37} - 12 q^{38} + 10 q^{40} - 60 q^{41} - 72 q^{43} - 18 q^{44} + 8 q^{46} - 13 q^{47} - 10 q^{49} - 6 q^{50} + 2 q^{52} - 33 q^{53} - 6 q^{55} - 24 q^{56} - 17 q^{58} - 21 q^{59} + 52 q^{62} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 3 q^{70} - 20 q^{71} + 11 q^{73} + 41 q^{74} - 96 q^{76} - 36 q^{77} + 21 q^{79} - 12 q^{80} + 6 q^{82} + 46 q^{83} - 78 q^{85} - 7 q^{86} + 32 q^{88} + 10 q^{89} - 14 q^{91} + 110 q^{92} + 37 q^{94} - 7 q^{95} - 54 q^{97} - 116 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8 + 14 * q^10 + 9 * q^11 + 6 * q^13 + 3 * q^14 - 5 * q^16 + 7 * q^17 - 4 * q^19 + 30 * q^20 + 44 * q^22 + 14 * q^23 + 21 * q^25 + 16 * q^28 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 24 * q^37 - 12 * q^38 + 10 * q^40 - 60 * q^41 - 72 * q^43 - 18 * q^44 + 8 * q^46 - 13 * q^47 - 10 * q^49 - 6 * q^50 + 2 * q^52 - 33 * q^53 - 6 * q^55 - 24 * q^56 - 17 * q^58 - 21 * q^59 + 52 * q^62 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 3 * q^70 - 20 * q^71 + 11 * q^73 + 41 * q^74 - 96 * q^76 - 36 * q^77 + 21 * q^79 - 12 * q^80 + 6 * q^82 + 46 * q^83 - 78 * q^85 - 7 * q^86 + 32 * q^88 + 10 * q^89 - 14 * q^91 + 110 * q^92 + 37 * q^94 - 7 * q^95 - 54 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	2.57407	+	0.547134i	1.82014	+	0.386883i	0.986278	−	0.165092i	$-0.0527921\pi$
$2$	2.57407	+	0.547134i	1.82014	+	0.386883i	0.833861	+	0.551975i	$0.186125\pi$
$3$		0			0
$3$		0			0
$4$	4.49937	+	2.00325i	2.24968	+	1.00162i
$5$	0.787136	+	0.874203i	0.352018	+	0.390956i	0.892984	−	0.450089i	$-0.148608\pi$
$5$	0.787136	+	0.874203i	0.352018	+	0.390956i	−0.540966	+	0.841045i	$0.681941\pi$
$6$		0			0
$7$	−2.31119	−	1.28778i	−0.873549	−	0.486736i
$7$	−2.31119	−	1.28778i	−0.873549	−	0.486736i
$8$	6.22764	+	4.52465i	2.20180	+	1.59970i
$9$		0			0
$10$	1.54783	+	2.68093i	0.489468	+	0.847783i
$11$	3.26165	+	0.601380i	0.983424	+	0.181323i
$11$	3.26165	+	0.601380i	0.983424	+	0.181323i
$12$		0			0
$13$	0.0112624	+	0.0346622i	0.00312364	+	0.00961357i	0.952606	−	0.304206i	$-0.0983912\pi$
$13$	0.0112624	+	0.0346622i	0.00312364	+	0.00961357i	−0.949483	+	0.313820i	$0.898391\pi$
$14$	−5.24457	−	4.57937i	−1.40167	−	1.22389i
$15$		0			0
$16$	6.96361	+	7.73387i	1.74090	+	1.93347i
$17$	−5.95559	+	1.26590i	−1.44444	+	0.307026i	−0.862439	−	0.506161i	$-0.831064\pi$
$17$	−5.95559	+	1.26590i	−1.44444	+	0.307026i	−0.582003	+	0.813187i	$0.697731\pi$
$18$		0			0
$19$	1.75961	−	0.783430i	0.403683	−	0.179731i	−0.194843	−	0.980834i	$-0.562420\pi$
$19$	1.75961	−	0.783430i	0.403683	−	0.179731i	0.598526	+	0.801103i	$0.295753\pi$
$20$	1.79037	+	5.51019i	0.400339	+	1.23212i
$21$		0			0
$22$	8.06666	+	3.33255i	1.71982	+	0.710502i
$23$	1.02155	−	1.76938i	0.213008	−	0.368941i	−0.739647	−	0.672996i	$-0.765007\pi$
$23$	1.02155	−	1.76938i	0.213008	−	0.368941i	0.952655	+	0.304055i	$0.0983406\pi$
$24$		0			0
$25$	0.377994	−	3.59637i	0.0755988	−	0.719275i
$26$	0.0100254	+	0.0953849i	0.00196613	+	0.0187065i
$27$		0			0
$28$	−7.81916	−	10.4241i	−1.47768	−	1.96997i
$29$	−4.02767	+	2.92628i	−0.747920	+	0.543396i	−0.895182	−	0.445702i	$-0.852954\pi$
$29$	−4.02767	+	2.92628i	−0.747920	+	0.543396i	0.147261	+	0.989098i	$0.452954\pi$
$30$		0			0
$31$	1.89509	−	2.10472i	0.340369	−	0.378018i	−0.548523	−	0.836136i	$-0.684810\pi$
$31$	1.89509	−	2.10472i	0.340369	−	0.378018i	0.888892	+	0.458118i	$0.151476\pi$
$32$	5.99553	+	10.3846i	1.05987	+	1.83575i
$33$		0			0
$34$	−16.0227			−2.74787
$35$	−0.693441	−	3.03411i	−0.117213	−	0.512859i
$36$		0			0
$37$	0.278295	+	2.64780i	0.0457515	+	0.435296i	0.993290	+	0.115653i	$0.0368962\pi$
$37$	0.278295	+	2.64780i	0.0457515	+	0.435296i	−0.947538	+	0.319643i	$0.896437\pi$
$38$	4.95800	−	1.05386i	0.804294	−	0.170958i
$39$		0			0
$40$	0.946542	+	9.00574i	0.149661	+	1.42393i
$41$	−6.61499	−	4.80607i	−1.03309	−	0.750583i	−0.0641641	−	0.997939i	$-0.520438\pi$
$41$	−6.61499	−	4.80607i	−1.03309	−	0.750583i	−0.968925	+	0.247357i	$0.920438\pi$
$42$		0			0
$43$	−2.96835			−0.452669			−0.226335	−	0.974050i	$-0.572674\pi$
$43$	−2.96835			−0.452669			−0.226335	+	0.974050i	$0.572674\pi$
$44$	13.4706	+	9.23971i	2.03077	+	1.39294i
$45$		0			0
$46$	3.59762	−	3.99557i	0.530441	−	0.589114i
$47$	−2.91785	+	1.29911i	−0.425612	+	0.189495i	−0.608353	−	0.793666i	$-0.708170\pi$
$47$	−2.91785	+	1.29911i	−0.425612	+	0.189495i	0.182741	+	0.983161i	$0.441503\pi$
$48$		0			0
$49$	3.68323	+	5.95263i	0.526176	+	0.850375i
$50$	2.94068	−	9.05049i	0.415875	−	1.27993i
$51$		0			0
$52$	−0.0187631	+	0.178519i	−0.00260198	+	0.0247562i
$53$	6.63364	−	7.36740i	0.911200	−	1.01199i	−0.0886731	−	0.996061i	$-0.528263\pi$
$53$	6.63364	−	7.36740i	0.911200	−	1.01199i	0.999873	−	0.0159294i	$-0.00507070\pi$
$54$		0			0
$55$	2.04163	+	3.32471i	0.275294	+	0.448304i
$56$	−8.56653	−	18.4772i	−1.14475	−	2.46912i
$57$		0			0
$58$	−11.9686	+	5.32875i	−1.57155	+	0.699699i
$59$	−3.70874	−	1.65124i	−0.482837	−	0.214973i	0.150858	−	0.988555i	$-0.451796\pi$
$59$	−3.70874	−	1.65124i	−0.482837	−	0.214973i	−0.633696	+	0.773582i	$0.718463\pi$
$60$		0			0
$61$	−5.80710	−	6.44943i	−0.743522	−	0.825765i	0.246132	−	0.969236i	$-0.420840\pi$
$61$	−5.80710	−	6.44943i	−0.743522	−	0.825765i	−0.989655	+	0.143471i	$0.954174\pi$
$62$	6.02966	−	4.38080i	0.765767	−	0.556363i
$63$		0			0
$64$	3.31928	+	10.2157i	0.414910	+	1.27696i
$65$	−0.0214368	+	0.0371295i	−0.00265890	+	0.00460535i
$66$		0			0
$67$	−1.12669	−	1.95148i	−0.137647	−	0.238411i	0.788959	−	0.614446i	$-0.210621\pi$
$67$	−1.12669	−	1.95148i	−0.137647	−	0.238411i	−0.926605	+	0.376035i	$0.877287\pi$
$68$	−29.3323	−	6.23477i	−3.55706	−	0.756076i
$69$		0			0
$70$	−0.124894	−	8.18941i	−0.0149277	−	0.978822i
$71$	−1.31384	+	4.04359i	−0.155924	+	0.479885i	−0.998253	−	0.0590780i	$-0.981184\pi$
$71$	−1.31384	+	4.04359i	−0.155924	+	0.479885i	0.842329	+	0.538963i	$0.181184\pi$
$72$		0			0
$73$	3.92144	+	1.74594i	0.458970	+	0.204347i	0.623180	−	0.782079i	$-0.285841\pi$
$73$	3.92144	+	1.74594i	0.458970	+	0.204347i	−0.164209	+	0.986426i	$0.552507\pi$
$74$	−0.732354	+	6.96788i	−0.0851344	+	0.810000i
$75$		0			0
$76$	9.48655			1.08818
$77$	−6.76385	−	5.59020i	−0.770813	−	0.637062i
$78$		0			0
$79$	3.03638	+	0.645402i	0.341619	+	0.0726133i	0.375527	−	0.926812i	$-0.377462\pi$
$79$	3.03638	+	0.645402i	0.341619	+	0.0726133i	−0.0339076	+	0.999425i	$0.510795\pi$
$80$	−1.27967	+	12.1752i	−0.143071	+	1.36123i
$81$		0			0
$82$	−14.3979	−	15.9904i	−1.58998	−	1.76585i
$83$	−1.87581	+	5.77314i	−0.205896	+	0.633684i	0.793779	+	0.608206i	$0.208111\pi$
$83$	−1.87581	+	5.77314i	−0.205896	+	0.633684i	−0.999675	+	0.0254778i	$0.991889\pi$
$84$		0			0
$85$	−5.79451	−	4.20996i	−0.628503	−	0.456634i
$86$	−7.64073	−	1.62409i	−0.823921	−	0.175130i
$87$		0			0
$88$	17.5913	+	18.5030i	1.87524	+	1.97242i
$89$	2.16161	−	3.74402i	0.229130	−	0.396866i	−0.728420	−	0.685131i	$-0.759745\pi$
$89$	2.16161	−	3.74402i	0.229130	−	0.396866i	0.957551	+	0.288265i	$0.0930784\pi$
$90$		0			0
$91$	0.0186077	−	0.0946147i	0.00195062	−	0.00991831i
$92$	8.14083	−	5.91466i	0.848740	−	0.616646i
$93$		0			0
$94$	−8.22152	+	1.74754i	−0.847985	+	0.180245i
$95$	2.06993	+	0.921593i	0.212371	+	0.0945535i
$96$		0			0
$97$	1.43258	+	4.40904i	0.145457	+	0.447670i	0.997069	−	0.0765015i	$-0.0243750\pi$
$97$	1.43258	+	4.40904i	0.145457	+	0.447670i	−0.851613	+	0.524172i	$0.824375\pi$
$98$	6.22400	+	17.3377i	0.628719	+	1.75137i
$99$		0			0
$100$	8.90516	−	15.4242i	0.890516	−	1.54242i
$101$	11.3829	−	12.6420i	1.13264	−	1.25792i	0.170502	−	0.985357i	$-0.445461\pi$
$101$	11.3829	−	12.6420i	1.13264	−	1.25792i	0.962137	−	0.272566i	$-0.0878722\pi$
$102$		0			0
$103$	1.76150	+	16.7595i	0.173566	+	1.65137i	0.641149	+	0.767417i	$0.278458\pi$
$103$	1.76150	+	16.7595i	0.173566	+	1.65137i	−0.467583	+	0.883949i	$0.654875\pi$
$104$	−0.0866959	+	0.266822i	−0.00850123	+	0.0261641i
$105$		0			0
$106$	21.1064	−	15.3347i	2.05003	−	1.48944i
$107$	0.852002	−	0.379336i	0.0823661	−	0.0366718i	−0.365140	−	0.930953i	$-0.618979\pi$
$107$	0.852002	−	0.379336i	0.0823661	−	0.0366718i	0.447506	+	0.894281i	$0.352312\pi$
$108$		0			0
$109$	−0.811795	−	1.40607i	−0.0777558	−	0.134677i	0.824526	−	0.565825i	$-0.191442\pi$
$109$	−0.811795	−	1.40607i	−0.0777558	−	0.134677i	−0.902281	+	0.431148i	$0.858109\pi$
$110$	3.43623	+	9.67507i	0.327632	+	0.922482i
$111$		0			0
$112$	−6.13471	−	26.8421i	−0.579676	−	2.53634i
$113$	2.86311	+	2.08017i	0.269338	+	0.195686i	0.714254	−	0.699887i	$-0.246766\pi$
$113$	2.86311	+	2.08017i	0.269338	+	0.195686i	−0.444915	+	0.895573i	$0.646766\pi$
$114$		0			0
$115$	2.35090	−	0.499698i	0.219222	−	0.0465971i
$116$	−23.9840	+	5.09796i	−2.22686	+	0.473334i
$117$		0			0
$118$	−8.64310	−	6.27958i	−0.795662	−	0.578082i
$119$	15.3947	+	4.74376i	1.41123	+	0.434860i
$120$		0			0
$121$	10.2767	+	3.92298i	0.934244	+	0.356634i
$122$	−11.4191	−	19.7785i	−1.03384	−	1.79066i
$123$		0			0
$124$	12.7430	−	5.67354i	1.14435	−	0.509499i
$125$	8.19996	−	5.95762i	0.733427	−	0.532866i
$126$		0			0
$127$	−6.09131	+	18.7471i	−0.540516	+	1.66354i	0.190903	+	0.981609i	$0.438858\pi$
$127$	−6.09131	+	18.7471i	−0.540516	+	1.66354i	−0.731419	+	0.681928i	$0.761142\pi$
$128$	0.447872	+	4.26121i	0.0395866	+	0.376642i
$129$		0			0
$130$	−0.0754945	+	0.0838451i	−0.00662130	+	0.00735370i
$131$	−8.09187	+	14.0155i	−0.706990	+	1.22454i	0.258979	+	0.965883i	$0.416614\pi$
$131$	−8.09187	+	14.0155i	−0.706990	+	1.22454i	−0.965969	+	0.258659i	$0.916719\pi$
$132$		0			0
$133$	−5.07569	−	0.455339i	−0.440119	−	0.0394829i
$134$	−1.83244	−	5.63968i	−0.158299	−	0.487194i
$135$		0			0
$136$	−42.8170	−	19.0634i	−3.67153	−	1.63467i
$137$	−16.6054	+	3.52958i	−1.41869	+	0.301553i	−0.852504	−	0.522721i	$-0.824917\pi$
$137$	−16.6054	+	3.52958i	−1.41869	+	0.301553i	−0.566191	+	0.824274i	$0.691583\pi$
$138$		0			0
$139$	5.94380	−	4.31842i	0.504146	−	0.366284i	−0.306452	−	0.951886i	$-0.599142\pi$
$139$	5.94380	−	4.31842i	0.504146	−	0.366284i	0.810598	+	0.585602i	$0.199142\pi$
$140$	2.95803	−	15.0407i	0.249999	−	1.27117i
$141$		0			0
$142$	−5.59430	+	9.68961i	−0.469463	+	0.813134i
$143$	0.0158889	+	0.119829i	0.00132870	+	0.0100206i
$144$		0			0
$145$	−5.72849	−	1.21763i	−0.475725	−	0.101119i
$146$	9.13879	+	6.63972i	0.756332	+	0.549507i
$147$		0			0
$148$	−4.05205	+	12.4709i	−0.333076	+	1.02510i
$149$	3.35966	+	3.73128i	0.275234	+	0.305679i	0.864875	−	0.501987i	$-0.167397\pi$
$149$	3.35966	+	3.73128i	0.275234	+	0.305679i	−0.589641	+	0.807665i	$0.700731\pi$
$150$		0			0
$151$	−0.877823	+	8.35192i	−0.0714362	+	0.679670i	0.898940	+	0.438072i	$0.144338\pi$
$151$	−0.877823	+	8.35192i	−0.0714362	+	0.679670i	−0.970376	+	0.241598i	$0.922328\pi$
$152$	14.5030	+	3.08271i	1.17635	+	0.250040i
$153$		0			0
$154$	−14.3520	−	18.0903i	−1.15652	−	1.45776i
$155$	3.33165			0.267604
$156$		0			0
$157$	1.56236	−	14.8648i	0.124690	−	1.18634i	−0.735917	−	0.677072i	$-0.763248\pi$
$157$	1.56236	−	14.8648i	0.124690	−	1.18634i	0.860606	−	0.509271i	$-0.170085\pi$
$158$	7.46271	+	3.32261i	0.593701	+	0.264333i
$159$		0			0
$160$	−4.35892	+	13.4154i	−0.344603	+	1.06058i
$161$	−4.63957	+	2.77384i	−0.365650	+	0.218609i
$162$		0			0
$163$	−2.43424	−	0.517414i	−0.190665	−	0.0405270i	0.111590	−	0.993754i	$-0.464406\pi$
$163$	−2.43424	−	0.517414i	−0.190665	−	0.0405270i	−0.302254	+	0.953227i	$0.597739\pi$
$164$	−20.1355	−	34.8758i	−1.57232	−	2.72334i
$165$		0			0
$166$	−7.98713	+	13.8341i	−0.619921	+	1.07374i
$167$	3.80261	+	11.7032i	0.294255	+	0.905624i	0.983471	+	0.181068i	$0.0579553\pi$
$167$	3.80261	+	11.7032i	0.294255	+	0.905624i	−0.689216	+	0.724556i	$0.742045\pi$
$168$		0			0
$169$	10.5161	−	7.64043i	0.808934	−	0.587725i
$170$	−12.6120	−	14.0071i	−0.967299	−	1.07429i
$171$		0			0
$172$	−13.3557	−	5.94634i	−1.01836	−	0.453404i
$173$	−11.1499	+	4.96423i	−0.847708	+	0.377424i	−0.784163	−	0.620555i	$-0.786907\pi$
$173$	−11.1499	+	4.96423i	−0.847708	+	0.377424i	−0.0635449	+	0.997979i	$0.520241\pi$
$174$		0			0
$175$	−5.50497	+	7.82515i	−0.416136	+	0.591525i
$176$	18.0618	+	29.4129i	1.36146	+	2.21708i
$177$		0			0
$178$	7.61261	−	8.45466i	0.570590	−	0.633704i
$179$	0.398664	−	3.79303i	0.0297975	−	0.283504i	−0.969469	−	0.245213i	$-0.921142\pi$
$179$	0.398664	−	3.79303i	0.0297975	−	0.283504i	0.999267	−	0.0382910i	$-0.0121914\pi$
$180$		0			0
$181$	2.17667	−	6.69911i	0.161791	−	0.497941i	−0.836995	−	0.547211i	$-0.815690\pi$
$181$	2.17667	−	6.69911i	0.161791	−	0.497941i	0.998785	+	0.0492703i	$0.0156896\pi$
$182$	0.0996644	−	0.233363i	0.00738762	−	0.0172980i
$183$		0			0
$184$	14.3677	−	6.39689i	1.05920	−	0.471585i
$185$	−2.09566	+	2.32747i	−0.154076	+	0.171119i
$186$		0			0
$187$	−20.1863	+	0.547348i	−1.47617	+	0.0400261i
$188$	−15.7309			−1.14729
$189$		0			0
$190$	4.82391	+	3.50477i	0.349963	+	0.254263i
$191$	−1.66472	−	15.8388i	−0.120455	−	1.14605i	−0.873071	−	0.487593i	$-0.837875\pi$
$191$	−1.66472	−	15.8388i	−0.120455	−	1.14605i	0.752616	−	0.658460i	$-0.228792\pi$
$192$		0			0
$193$	−14.4744	+	3.07662i	−1.04189	+	0.221460i	−0.696916	−	0.717153i	$-0.745445\pi$
$193$	−14.4744	+	3.07662i	−1.04189	+	0.221460i	−0.344972	+	0.938613i	$0.612112\pi$
$194$	1.27523	+	12.1330i	0.0915560	+	0.871097i
$195$		0			0
$196$	4.64764	+	34.1615i	0.331974	+	2.44011i
$197$	−8.28808			−0.590501			−0.295251	−	0.955420i	$-0.595403\pi$
$197$	−8.28808			−0.590501			−0.295251	+	0.955420i	$0.595403\pi$
$198$		0			0
$199$	−9.14220	−	15.8348i	−0.648073	−	1.12250i	−0.983582	−	0.180459i	$-0.942242\pi$
$199$	−9.14220	−	15.8348i	−0.648073	−	1.12250i	0.335509	−	0.942037i	$-0.391092\pi$
$200$	18.6263	−	20.6866i	1.31708	−	1.46277i
$201$		0			0
$202$	36.2171	−	26.3133i	2.54823	−	1.85140i
$203$	13.0771	−	1.57643i	0.917836	−	0.110643i
$204$		0			0
$205$	−1.00542	−	9.56589i	−0.0702212	−	0.668111i
$206$	−4.63551	+	44.1039i	−0.322971	+	3.07286i
$207$		0			0
$208$	−0.189646	+	0.328476i	−0.0131496	+	0.0227757i
$209$	6.21038	−	1.49708i	0.429581	−	0.103555i
$210$		0			0
$211$	7.29409	+	22.4489i	0.502146	+	1.54545i	0.805516	+	0.592573i	$0.201888\pi$
$211$	7.29409	+	22.4489i	0.502146	+	1.54545i	−0.303370	+	0.952873i	$0.598112\pi$
$212$	44.6059	−	19.8598i	3.06354	−	1.36398i
$213$		0			0
$214$	2.40066	−	0.510275i	0.164105	−	0.0348817i
$215$	−2.33650	−	2.59494i	−0.159348	−	0.176974i
$216$		0			0
$217$	−7.09035	+	2.42394i	−0.481324	+	0.164548i
$218$	−1.32030	−	4.06348i	−0.0894222	−	0.275213i
$219$		0			0
$220$	2.52584	+	19.0490i	0.170292	+	1.28428i
$221$	−0.110953	−	0.192177i	−0.00746352	−	0.0129272i
$222$		0			0
$223$	9.76962	+	7.09804i	0.654222	+	0.475320i	0.864707	−	0.502277i	$-0.167504\pi$
$223$	9.76962	+	7.09804i	0.654222	+	0.475320i	−0.210485	+	0.977597i	$0.567504\pi$
$224$	−0.483778	−	31.7217i	−0.0323238	−	2.11949i
$225$		0			0
$226$	6.23169	+	6.92100i	0.414526	+	0.460378i
$227$	9.43447	+	4.20050i	0.626188	+	0.278797i	0.695197	−	0.718819i	$-0.255317\pi$
$227$	9.43447	+	4.20050i	0.626188	+	0.278797i	−0.0690091	+	0.997616i	$0.521984\pi$
$228$		0			0
$229$	26.9582	+	5.73015i	1.78145	+	0.378659i	0.976641	−	0.214875i	$-0.0689345\pi$
$229$	26.9582	+	5.73015i	1.78145	+	0.378659i	0.804809	+	0.593534i	$0.202268\pi$
$230$	6.32476			0.417042
$231$		0			0
$232$	−38.3233			−2.51605
$233$	3.91278	+	0.831687i	0.256335	+	0.0544856i	0.334286	−	0.942472i	$-0.391505\pi$
$233$	3.91278	+	0.831687i	0.256335	+	0.0544856i	−0.0779518	+	0.996957i	$0.524838\pi$
$234$		0			0
$235$	−3.43243	−	1.52822i	−0.223907	−	0.0996899i
$236$	−13.3792	−	14.8591i	−0.870909	−	0.967242i
$237$		0			0
$238$	37.0315	+	20.6337i	2.40040	+	1.33749i
$239$	17.1705	+	12.4751i	1.11067	+	0.806946i	0.982768	−	0.184842i	$-0.0591772\pi$
$239$	17.1705	+	12.4751i	1.11067	+	0.806946i	0.127897	+	0.991787i	$0.459177\pi$
$240$		0			0
$241$	6.80326	+	11.7836i	0.438237	+	0.759048i	0.997554	−	0.0699056i	$-0.0222698\pi$
$241$	6.80326	+	11.7836i	0.438237	+	0.759048i	−0.559317	+	0.828954i	$0.688936\pi$
$242$	24.3065	+	15.7207i	1.56248	+	1.01057i
$243$		0			0
$244$	−13.2084	−	40.6514i	−0.845584	−	2.60244i
$245$	−2.30460	+	7.90543i	−0.147236	+	0.505059i
$246$		0			0
$247$	0.0469730	+	0.0521687i	0.00298882	+	0.00331942i
$248$	21.3251	−	4.53278i	1.35414	−	0.287832i
$249$		0			0
$250$	24.3669	−	10.8488i	1.54109	−	0.686140i
$251$	5.10309	+	15.7057i	0.322104	+	0.991334i	0.972731	+	0.231937i	$0.0745062\pi$
$251$	5.10309	+	15.7057i	0.322104	+	0.991334i	−0.650627	+	0.759398i	$0.725494\pi$
$252$		0			0
$253$	4.39600	−	5.15674i	0.276374	−	0.324202i
$254$	−25.9366	+	44.9235i	−1.62741	+	2.81875i
$255$		0			0
$256$	1.06696	−	10.1514i	0.0666850	−	0.634465i
$257$	3.05781	+	29.0931i	0.190741	+	1.81478i	0.502454	+	0.864604i	$0.332430\pi$
$257$	3.05781	+	29.0931i	0.190741	+	1.81478i	−0.311713	+	0.950176i	$0.600903\pi$
$258$		0			0
$259$	2.76660	−	6.47797i	0.171908	−	0.402521i
$260$	−0.170831	+	0.124116i	−0.0105945	+	0.00769737i
$261$		0			0
$262$	−28.4974	+	31.6495i	−1.76057	+	1.95531i
$263$	−9.96601	−	17.2616i	−0.614530	−	1.06440i	−0.990467	−	0.137752i	$-0.956012\pi$
$263$	−9.96601	−	17.2616i	−0.614530	−	1.06440i	0.375936	−	0.926646i	$-0.377321\pi$
$264$		0			0
$265$	11.6622			0.716402
$266$	−12.8160	−	3.94916i	−0.785802	−	0.242139i
$267$		0			0
$268$	−1.16008	−	11.0374i	−0.0708633	−	0.674219i
$269$	0.605177	−	0.128634i	0.0368983	−	0.00784298i	−0.189426	−	0.981895i	$-0.560663\pi$
$269$	0.605177	−	0.128634i	0.0368983	−	0.00784298i	0.226324	+	0.974052i	$0.427329\pi$
$270$		0			0
$271$	0.0121050	+	0.115172i	0.000735328	+	0.00699618i	0.994883	−	0.101030i	$-0.0322137\pi$
$271$	0.0121050	+	0.115172i	0.000735328	+	0.00699618i	−0.994148	+	0.108026i	$0.965547\pi$
$272$	−51.2627	−	37.2445i	−3.10826	−	2.25828i
$273$		0			0
$274$	−44.6745			−2.69889
$275$	3.39567	−	11.5028i	0.204767	−	0.693644i
$276$		0			0
$277$	6.46626	−	7.18151i	0.388520	−	0.431495i	−0.516878	−	0.856059i	$-0.672906\pi$
$277$	6.46626	−	7.18151i	0.388520	−	0.431495i	0.905398	+	0.424564i	$0.139573\pi$
$278$	17.6625	−	7.86384i	1.05932	−	0.471642i
$279$		0			0
$280$	9.40979	−	22.0330i	0.562343	−	1.31672i
$281$	1.07026	−	3.29393i	0.0638466	−	0.196500i	−0.914045	−	0.405613i	$-0.867058\pi$
$281$	1.07026	−	3.29393i	0.0638466	−	0.196500i	0.977891	+	0.209114i	$0.0670579\pi$
$282$		0			0
$283$	−2.75322	+	26.1952i	−0.163662	+	1.55714i	0.536959	+	0.843608i	$0.319573\pi$
$283$	−2.75322	+	26.1952i	−0.163662	+	1.55714i	−0.700621	+	0.713533i	$0.747094\pi$
$284$	−14.0118	+	15.5616i	−0.831445	+	0.923413i
$285$		0			0
$286$	−0.0246633	+	0.317141i	−0.00145837	+	0.0187529i
$287$	9.09936	+	19.6264i	0.537118	+	1.15851i
$288$		0			0
$289$	18.3362	−	8.16382i	1.07860	−	0.480225i
$290$	−14.0793	−	6.26851i	−0.826765	−	0.368100i
$291$		0			0
$292$	14.1465	+	15.7112i	0.827859	+	0.919431i
$293$	12.3700	−	8.98734i	0.722664	−	0.525046i	−0.164570	−	0.986365i	$-0.552624\pi$
$293$	12.3700	−	8.98734i	0.722664	−	0.525046i	0.887234	+	0.461319i	$0.152624\pi$
$294$		0			0
$295$	−1.47577	−	4.54195i	−0.0859226	−	0.264442i
$296$	−10.2473	+	17.7488i	−0.595609	+	1.03163i
$297$		0			0
$298$	6.60648	+	11.4428i	0.382703	+	0.662861i
$299$	0.0728357	+	0.0154817i	0.00421220	+	0.000895330i
$300$		0			0
$301$	6.86044	+	3.82259i	0.395429	+	0.220330i
$302$	−6.82920	+	21.0181i	−0.392976	+	1.20946i
$303$		0			0
$304$	18.3122	+	8.15312i	1.05028	+	0.467613i
$305$	1.06714	−	10.1532i	0.0611043	−	0.581369i
$306$		0			0
$307$	32.1611			1.83553			0.917766	−	0.397123i	$-0.129991\pi$
$307$	32.1611			1.83553			0.917766	+	0.397123i	$0.129991\pi$
$308$	−19.2345	−	38.7020i	−1.09599	−	2.20525i
$309$		0			0
$310$	8.57588	+	1.82286i	0.487077	+	0.103531i
$311$	0.221418	−	2.10666i	0.0125555	−	0.119458i	−0.986449	−	0.164069i	$-0.947538\pi$
$311$	0.221418	−	2.10666i	0.0125555	−	0.119458i	0.999004	+	0.0446110i	$0.0142048\pi$
$312$		0			0
$313$	−4.10743	−	4.56176i	−0.232166	−	0.257846i	0.615794	−	0.787907i	$-0.288835\pi$
$313$	−4.10743	−	4.56176i	−0.232166	−	0.257846i	−0.847959	+	0.530062i	$0.822169\pi$
$314$	12.1547	−	37.4082i	0.685928	−	2.11107i
$315$		0			0
$316$	12.3689	+	8.98651i	0.695803	+	0.505530i
$317$	−17.3855	−	3.69540i	−0.976468	−	0.207555i	−0.308074	−	0.951362i	$-0.599684\pi$
$317$	−17.3855	−	3.69540i	−0.976468	−	0.207555i	−0.668394	+	0.743808i	$0.733018\pi$
$318$		0			0
$319$	−14.8967	+	7.12232i	−0.834053	+	0.398773i
$320$	−6.31787	+	10.9429i	−0.353179	+	0.611725i
$321$		0			0
$322$	−13.4602	+	4.60157i	−0.750109	+	0.256436i
$323$	−9.48778	+	6.89328i	−0.527914	+	0.383552i
$324$		0			0
$325$	0.128915	−	0.0274018i	0.00715094	−	0.00151998i
$326$	−5.98280	−	2.66372i	−0.331357	−	0.147530i
$327$		0			0
$328$	−19.4500	−	59.8610i	−1.07395	−	3.30527i
$329$	8.41668	+	0.755058i	0.464027	+	0.0416277i
$330$		0			0
$331$	−9.78286	+	16.9444i	−0.537714	+	0.931349i	0.461312	+	0.887238i	$0.347379\pi$
$331$	−9.78286	+	16.9444i	−0.537714	+	0.931349i	−0.999027	+	0.0441108i	$0.985955\pi$
$332$	−20.0050	+	22.2178i	−1.09791	+	1.21936i
$333$		0			0
$334$	3.38493	+	32.2054i	0.185215	+	1.76220i
$335$	0.819133	−	2.52103i	0.0447540	−	0.137739i
$336$		0			0
$337$	−18.6594	+	13.5569i	−1.01644	+	0.738489i	−0.965551	−	0.260215i	$-0.916207\pi$
$337$	−18.6594	+	13.5569i	−1.01644	+	0.738489i	−0.0508925	+	0.998704i	$0.516207\pi$
$338$	31.2496	−	13.9132i	1.69975	−	0.756779i
$339$		0			0
$340$	−17.6380	−	30.5500i	−0.956557	−	1.65681i
$341$	7.44686	−	5.72517i	0.403270	−	0.310035i
$342$		0			0
$343$	−0.846981	−	18.5009i	−0.0457327	−	0.998954i
$344$	−18.4858	−	13.4307i	−0.996690	−	0.724137i
$345$		0			0
$346$	−31.4166	+	6.67780i	−1.68896	+	0.359001i
$347$	−24.4941	+	5.20638i	−1.31491	+	0.279493i	−0.811398	−	0.584494i	$-0.801293\pi$
$347$	−24.4941	+	5.20638i	−1.31491	+	0.279493i	−0.503514	+	0.863987i	$0.667960\pi$
$348$		0			0
$349$	−15.8320	−	11.5026i	−0.847467	−	0.615721i	0.0769797	−	0.997033i	$-0.475472\pi$
$349$	−15.8320	−	11.5026i	−0.847467	−	0.615721i	−0.924446	+	0.381312i	$0.875472\pi$
$350$	−18.4515	+	17.1305i	−0.986277	+	0.915663i
$351$		0			0
$352$	13.3102	+	37.4763i	0.709438	+	1.99750i
$353$	10.1136	+	17.5172i	0.538292	+	0.932349i	0.998996	+	0.0447952i	$0.0142635\pi$
$353$	10.1136	+	17.5172i	0.538292	+	0.932349i	−0.460704	+	0.887554i	$0.652403\pi$
$354$		0			0
$355$	−4.56909	+	2.03429i	−0.242502	+	0.107969i
$356$	17.2261	−	12.5155i	0.912981	−	0.663319i
$357$		0			0
$358$	3.10148	−	9.54539i	0.163919	−	0.504489i
$359$	−2.60519	−	24.7867i	−0.137497	−	1.30819i	−0.817902	−	0.575357i	$-0.804863\pi$
$359$	−2.60519	−	24.7867i	−0.137497	−	1.30819i	0.680405	−	0.732836i	$-0.261804\pi$
$360$		0			0
$361$	−10.2310	+	11.3627i	−0.538474	+	0.598036i
$362$	9.26821	−	16.0530i	0.487126	−	0.843727i
$363$		0			0
$364$	0.273259	−	0.388430i	0.0143227	−	0.0203593i
$365$	1.56040	+	4.80243i	0.0816753	+	0.251371i
$366$		0			0
$367$	6.84200	+	3.04625i	0.357149	+	0.159013i	0.577465	−	0.816416i	$-0.304042\pi$
$367$	6.84200	+	3.04625i	0.357149	+	0.159013i	−0.220316	+	0.975429i	$0.570709\pi$
$368$	20.7978	−	4.42071i	1.08416	−	0.230446i
$369$		0			0
$370$	−6.66781	+	4.84445i	−0.346643	+	0.251851i
$371$	−24.8192	+	8.48481i	−1.28855	+	0.440509i
$372$		0			0
$373$	0.802488	−	1.38995i	0.0415513	−	0.0719689i	−0.844502	−	0.535553i	$-0.820103\pi$
$373$	0.802488	−	1.38995i	0.0415513	−	0.0719689i	0.886053	+	0.463584i	$0.153437\pi$
$374$	−52.2603	−	9.63572i	−2.70232	−	0.498251i
$375$		0			0
$376$	−24.0493	−	5.11184i	−1.24025	−	0.263623i
$377$	−0.146793	−	0.106651i	−0.00756021	−	0.00549281i
$378$		0			0
$379$	5.26757	−	16.2119i	0.270577	−	0.832751i	−0.719779	−	0.694204i	$-0.755757\pi$
$379$	5.26757	−	16.2119i	0.270577	−	0.832751i	0.990356	−	0.138547i	$-0.0442433\pi$
$380$	7.46721	+	8.29317i	0.383060	+	0.425431i
$381$		0			0
$382$	4.38084	−	41.6809i	0.224143	−	2.13258i
$383$	−17.0414	−	3.62225i	−0.870773	−	0.185089i	−0.249207	−	0.968450i	$-0.580170\pi$
$383$	−17.0414	−	3.62225i	−0.870773	−	0.185089i	−0.621566	+	0.783362i	$0.713503\pi$
$384$		0			0
$385$	−0.437106	−	10.3132i	−0.0222770	−	0.525611i
$386$	−38.9413			−1.98206
$387$		0			0
$388$	−2.38668	+	22.7077i	−0.121165	+	1.15281i
$389$	10.2642	+	4.56993i	0.520417	+	0.231705i	0.650097	−	0.759851i	$-0.274728\pi$
$389$	10.2642	+	4.56993i	0.520417	+	0.231705i	−0.129680	+	0.991556i	$0.541395\pi$
$390$		0			0
$391$	−3.84408	+	11.8309i	−0.194403	+	0.598312i
$392$	−3.99568	+	53.7362i	−0.201812	+	2.71409i
$393$		0			0
$394$	−21.3341	−	4.53470i	−1.07479	−	0.228455i
$395$	1.82583	+	3.16243i	0.0918674	+	0.159119i
$396$		0			0
$397$	−9.85421	+	17.0680i	−0.494568	+	0.856618i	−0.999980	−	0.00626047i	$-0.998007\pi$
$397$	−9.85421	+	17.0680i	−0.494568	+	0.856618i	0.505412	+	0.862878i	$0.331341\pi$
$398$	−14.8689	−	45.7617i	−0.745310	−	2.29383i
$399$		0			0
$400$	30.4461	−	22.1204i	1.52231	−	1.10602i
$401$	8.38973	+	9.31774i	0.418963	+	0.465306i	0.915270	−	0.402842i	$-0.131977\pi$
$401$	8.38973	+	9.31774i	0.418963	+	0.465306i	−0.496306	+	0.868147i	$0.665311\pi$
$402$		0			0
$403$	0.0942975	+	0.0419839i	0.00469729	+	0.00209137i
$404$	76.5407	−	34.0781i	3.80804	−	1.69545i
$405$		0			0
$406$	34.5239	+	3.09713i	1.71339	+	0.153708i
$407$	−0.684633	+	8.80356i	−0.0339360	+	0.436376i
$408$		0			0
$409$	10.4423	−	11.5973i	0.516337	−	0.573450i	−0.427436	−	0.904046i	$-0.640583\pi$
$409$	10.4423	−	11.5973i	0.516337	−	0.573450i	0.943773	+	0.330596i	$0.107250\pi$
$410$	2.64582	−	25.1733i	0.130668	−	1.24322i
$411$		0			0
$412$	−25.6479	+	78.9360i	−1.26358	+	3.88890i
$413$	6.44519	+	8.59239i	0.317147	+	0.422804i
$414$		0			0
$415$	−6.52341	+	2.90441i	−0.320222	+	0.142572i
$416$	−0.292427	+	0.324774i	−0.0143374	+	0.0159233i
$417$		0			0
$418$	16.8050	−	0.455665i	0.821960	−	0.0222873i
$419$	31.8183			1.55443			0.777213	−	0.629238i	$-0.216633\pi$
$419$	31.8183			1.55443			0.777213	+	0.629238i	$0.216633\pi$
$420$		0			0
$421$	−19.3204	−	14.0371i	−0.941617	−	0.684125i	0.00719220	−	0.999974i	$-0.497711\pi$
$421$	−19.3204	−	14.0371i	−0.941617	−	0.684125i	−0.948809	+	0.315849i	$0.897711\pi$
$422$	6.49290	+	61.7758i	0.316069	+	3.00720i
$423$		0			0
$424$	74.6468	−	15.8667i	3.62517	−	0.770554i
$425$	2.30147	+	21.8970i	0.111638	+	1.06216i
$426$		0			0
$427$	5.11586	+	22.3842i	0.247574	+	1.08325i
$428$	4.59337			0.222029
$429$		0			0
$430$	−4.59452	−	7.95793i	−0.221567	−	0.383766i
$431$	5.58314	−	6.20070i	0.268930	−	0.298677i	−0.593520	−	0.804819i	$-0.702262\pi$
$431$	5.58314	−	6.20070i	0.268930	−	0.298677i	0.862450	+	0.506142i	$0.168929\pi$
$432$		0			0
$433$	−10.3850	+	7.54511i	−0.499069	+	0.362595i	−0.808661	−	0.588275i	$-0.799807\pi$
$433$	−10.3850	+	7.54511i	−0.499069	+	0.362595i	0.309592	+	0.950869i	$0.399807\pi$
$434$	−19.5772	+	2.36000i	−0.939737	+	0.113284i
$435$		0			0
$436$	−0.835857	−	7.95265i	−0.0400303	−	0.380863i
$437$	0.411350	−	3.91373i	0.0196775	−	0.187219i
$438$		0			0
$439$	12.2991	−	21.3026i	0.587002	−	1.01672i	−0.407620	−	0.913151i	$-0.633641\pi$
$439$	12.2991	−	21.3026i	0.587002	−	1.01672i	0.994623	−	0.103566i	$-0.0330253\pi$
$440$	−2.32858	+	29.9428i	−0.111011	+	1.42747i
$441$		0			0
$442$	−0.180454	−	0.555382i	−0.00858334	−	0.0264168i
$443$	14.7328	−	6.55945i	0.699975	−	0.311649i	−0.0257164	−	0.999669i	$-0.508187\pi$
$443$	14.7328	−	6.55945i	0.699975	−	0.311649i	0.725691	+	0.688020i	$0.241520\pi$
$444$		0			0
$445$	4.97452	−	1.05737i	0.235815	−	0.0501240i
$446$	21.2641	+	23.6161i	1.00688	+	1.11826i
$447$		0			0
$448$	5.48408	−	27.8849i	0.259099	−	1.31744i
$449$	−10.6496	−	32.7763i	−0.502588	−	1.54681i	−0.804788	−	0.593562i	$-0.797721\pi$
$449$	−10.6496	−	32.7763i	−0.502588	−	1.54681i	0.302200	−	0.953245i	$-0.402279\pi$
$450$		0			0
$451$	−18.6855	−	19.6538i	−0.879866	−	0.925463i
$452$	8.71507	+	15.0950i	0.409923	+	0.710007i
$453$		0			0
$454$	21.9867	+	15.9743i	1.03189	+	0.749710i
$455$	0.0973593	−	0.0582077i	0.00456427	−	0.00272882i
$456$		0			0
$457$	−21.7120	−	24.1137i	−1.01565	−	1.12799i	−0.991739	−	0.128275i	$-0.959056\pi$
$457$	−21.7120	−	24.1137i	−1.01565	−	1.12799i	−0.0239074	−	0.999714i	$-0.507611\pi$
$458$	66.2571	+	29.4996i	3.09599	+	1.37842i
$459$		0			0
$460$	11.5786	+	2.46110i	0.539853	+	0.114749i
$461$	29.4973			1.37383			0.686914	−	0.726739i	$-0.258965\pi$
$461$	29.4973			1.37383			0.686914	+	0.726739i	$0.258965\pi$
$462$		0			0
$463$	22.2588			1.03445			0.517227	−	0.855848i	$-0.326964\pi$
$463$	22.2588			1.03445			0.517227	+	0.855848i	$0.326964\pi$
$464$	−50.6786	−	10.7721i	−2.35269	−	0.500081i
$465$		0			0
$466$	9.61670	+	4.28163i	0.445485	+	0.198343i
$467$	−15.8303	−	17.5813i	−0.732539	−	0.813567i	0.255656	−	0.966768i	$-0.417708\pi$
$467$	−15.8303	−	17.5813i	−0.732539	−	0.813567i	−0.988195	+	0.153201i	$0.951042\pi$
$468$		0			0
$469$	0.0909121	+	5.96117i	0.00419793	+	0.275261i
$470$	−7.99916	−	5.81173i	−0.368974	−	0.268075i
$471$		0			0
$472$	−15.6255	−	27.0641i	−0.719220	−	1.24573i
$473$	−9.68172	−	1.78511i	−0.445166	−	0.0820793i
$474$		0			0
$475$	−2.15239	−	6.62436i	−0.0987582	−	0.303946i
$476$	59.7635	+	52.1833i	2.73926	+	2.39182i
$477$		0			0
$478$	37.3724	+	41.5062i	1.70937	+	1.89845i
$479$	−11.3019	+	2.40230i	−0.516399	+	0.109764i	−0.458737	−	0.888572i	$-0.651698\pi$
$479$	−11.3019	+	2.40230i	−0.516399	+	0.109764i	−0.0576623	+	0.998336i	$0.518365\pi$
$480$		0			0
$481$	−0.0886444	+	0.0394670i	−0.00404184	+	0.00179954i
$482$	11.0648	+	34.0541i	0.503989	+	1.55112i
$483$		0			0
$484$	38.3799	+	38.2376i	1.74454	+	1.73807i
$485$	−2.72676	+	4.72289i	−0.123816	+	0.214455i
$486$		0			0
$487$	−0.0137727	+	0.131038i	−0.000624101	+	0.00593792i	−0.994830	−	0.101559i	$-0.967617\pi$
$487$	−0.0137727	+	0.131038i	−0.000624101	+	0.00593792i	0.994205	+	0.107497i	$0.0342836\pi$
$488$	−6.98311	−	66.4398i	−0.316110	−	3.00759i
$489$		0			0
$490$	−10.2575	+	19.0882i	−0.463388	+	0.862315i
$491$	−0.0180456	+	0.0131109i	−0.000814388	+	0.000591687i	−0.588192	−	0.808721i	$-0.700160\pi$
$491$	−0.0180456	+	0.0131109i	−0.000814388	+	0.000591687i	0.587378	+	0.809313i	$0.300160\pi$
$492$		0			0
$493$	20.2828	−	22.5263i	0.913491	−	1.01453i
$494$	0.0923681	+	0.159986i	0.00415584	+	0.00719812i
$495$		0			0
$496$	29.4743			1.32343
$497$	8.24380	−	7.65357i	0.369785	−	0.343310i
$498$		0			0
$499$	0.724289	+	6.89115i	0.0324236	+	0.308490i	0.998700	+	0.0509816i	$0.0162350\pi$
$499$	0.724289	+	6.89115i	0.0324236	+	0.308490i	−0.966276	+	0.257509i	$0.917098\pi$
$500$	48.8292	−	10.3790i	2.18371	−	0.464161i
$501$		0			0
$502$	4.54256	+	43.2195i	0.202744	+	1.92898i
$503$	−6.79200	−	4.93468i	−0.302840	−	0.220026i	0.425978	−	0.904734i	$-0.359930\pi$
$503$	−6.79200	−	4.93468i	−0.302840	−	0.220026i	−0.728818	+	0.684707i	$0.759930\pi$
$504$		0			0
$505$	20.0115			0.890502
$506$	14.1370	−	10.8686i	0.628468	−	0.483168i
$507$		0			0
$508$	−64.9621	+	72.1477i	−2.88223	+	3.20104i
$509$	1.13266	−	0.504291i	0.0502041	−	0.0223523i	−0.381481	−	0.924377i	$-0.624586\pi$
$509$	1.13266	−	0.504291i	0.0502041	−	0.0223523i	0.431685	+	0.902024i	$0.357919\pi$
$510$		0			0
$511$	−6.81483	−	9.08517i	−0.301470	−	0.401904i
$512$	10.9487	−	33.6967i	0.483869	−	1.48920i
$513$		0			0
$514$	−8.04685	+	76.5607i	−0.354931	+	3.37695i
$515$	−13.2647	+	14.7319i	−0.584513	+	0.649167i
$516$		0			0
$517$	−10.2983	+	2.48250i	−0.452917	+	0.109180i
$518$	10.6657	−	15.1610i	0.468625	−	0.666137i
$519$		0			0
$520$	−0.301499	+	0.134236i	−0.0132216	+	0.00588663i
$521$	−39.9641	−	17.7932i	−1.75086	−	0.779532i	−0.991692	−	0.128635i	$-0.958940\pi$
$521$	−39.9641	−	17.7932i	−1.75086	−	0.779532i	−0.759166	−	0.650897i	$-0.774393\pi$
$522$		0			0
$523$	−20.4158	−	22.6740i	−0.892721	−	0.991467i	0.107275	−	0.994229i	$-0.465787\pi$
$523$	−20.4158	−	22.6740i	−0.892721	−	0.991467i	−0.999996	+	0.00276239i	$0.999121\pi$
$524$	−64.4848	+	46.8510i	−2.81703	+	2.04669i
$525$		0			0
$526$	−16.2087	−	49.8853i	−0.706734	−	2.17510i
$527$	−8.62204	+	14.9338i	−0.375582	+	0.650527i
$528$		0			0
$529$	9.41287	+	16.3036i	0.409255	+	0.708851i
$530$	30.0192	+	6.38078i	1.30395	+	0.277163i
$531$		0			0
$532$	−21.9252	−	12.2166i	−0.950580	−	0.529657i
$533$	0.0920882	−	0.283418i	0.00398878	−	0.0122762i
$534$		0			0
$535$	1.00226	+	0.446234i	0.0433314	+	0.0192924i
$536$	1.81315	−	17.2510i	0.0783161	−	0.745128i
$537$		0			0
$538$	1.62815			0.0701944
$539$	8.43362	+	21.6304i	0.363262	+	0.931687i
$540$		0			0
$541$	−0.277681	−	0.0590230i	−0.0119384	−	0.00253760i	0.201939	−	0.979398i	$-0.435276\pi$
$541$	−0.277681	−	0.0590230i	−0.0119384	−	0.00253760i	−0.213877	+	0.976861i	$0.568609\pi$
$542$	−0.0318553	+	0.303083i	−0.00136830	+	0.0130185i
$543$		0			0
$544$	−48.8527	−	54.2564i	−2.09454	−	2.32622i
$545$	0.590198	−	1.81644i	0.0252813	−	0.0778078i
$546$		0			0
$547$	−8.71258	−	6.33006i	−0.372523	−	0.270654i	0.385733	−	0.922610i	$-0.373948\pi$
$547$	−8.71258	−	6.33006i	−0.372523	−	0.270654i	−0.758256	+	0.651957i	$0.773948\pi$
$548$	−81.7844	−	17.3838i	−3.49365	−	0.742599i
$549$		0			0
$550$	15.0342	−	27.7510i	0.641063	−	1.18331i
$551$	−4.79461	+	8.30452i	−0.204257	+	0.353784i
$552$		0			0
$553$	−6.18652	−	5.40184i	−0.263077	−	0.229710i
$554$	20.5738	−	14.9478i	0.874098	−	0.635070i
$555$		0			0
$556$	35.3942	−	7.52326i	1.50105	−	0.319057i
$557$	−36.4980	−	16.2499i	−1.54647	−	0.688532i	−0.556634	−	0.830758i	$-0.687908\pi$
$557$	−36.4980	−	16.2499i	−1.54647	−	0.688532i	−0.989834	+	0.142225i	$0.954574\pi$
$558$		0			0
$559$	−0.0334309	−	0.102890i	−0.00141398	−	0.00435177i
$560$	18.6366	−	26.4914i	0.787540	−	1.11946i
$561$		0			0
$562$	4.55716	−	7.89323i	0.192232	−	0.332956i
$563$	7.99139	−	8.87534i	0.336797	−	0.374051i	−0.550827	−	0.834619i	$-0.685688\pi$
$563$	7.99139	−	8.87534i	0.336797	−	0.374051i	0.887624	+	0.460568i	$0.152354\pi$
$564$		0			0
$565$	0.435165	+	4.14031i	0.0183075	+	0.174184i
$566$	−21.4193	+	65.9217i	−0.900319	+	2.77090i
$567$		0			0
$568$	−26.4779	+	19.2374i	−1.11099	+	0.807181i
$569$	10.0266	−	4.46414i	0.420337	−	0.187146i	−0.185658	−	0.982614i	$-0.559442\pi$
$569$	10.0266	−	4.46414i	0.420337	−	0.187146i	0.605995	+	0.795468i	$0.292775\pi$
$570$		0			0
$571$	−3.74628	−	6.48874i	−0.156777	−	0.271545i	0.776928	−	0.629590i	$-0.216777\pi$
$571$	−3.74628	−	6.48874i	−0.156777	−	0.271545i	−0.933705	+	0.358044i	$0.883444\pi$
$572$	−0.168557	+	0.570984i	−0.00704771	+	0.0238740i
$573$		0			0
$574$	12.6840	+	55.4983i	0.529422	+	2.31646i
$575$	−5.97720	−	4.34269i	−0.249267	−	0.181103i
$576$		0			0
$577$	35.0599	−	7.45221i	1.45956	−	0.310240i	0.591343	−	0.806420i	$-0.298598\pi$
$577$	35.0599	−	7.45221i	1.45956	−	0.310240i	0.868220	+	0.496180i	$0.165264\pi$
$578$	51.6654	−	10.9818i	2.14900	−	0.456783i
$579$		0			0
$580$	−23.3354	−	16.9541i	−0.968948	−	0.703982i
$581$	11.7699	−	10.9272i	0.488297	−	0.453337i
$582$		0			0
$583$	26.0672	−	20.0405i	1.07959	−	0.829994i
$584$	16.5216	+	28.6162i	0.683668	+	1.18415i
$585$		0			0
$586$	36.7585	−	16.3659i	1.51848	−	0.676071i
$587$	8.11634	−	5.89686i	0.334997	−	0.243390i	−0.407551	−	0.913182i	$-0.633617\pi$
$587$	8.11634	−	5.89686i	0.334997	−	0.243390i	0.742548	+	0.669793i	$0.233617\pi$
$588$		0			0
$589$	1.68574	−	5.18816i	0.0694595	−	0.213774i
$590$	−1.31367	−	12.4987i	−0.0540828	−	0.514564i
$591$		0			0
$592$	−18.5398	+	20.5906i	−0.761982	+	0.846267i
$593$	14.1715	−	24.5458i	0.581954	−	1.00797i	−0.413293	−	0.910598i	$-0.635622\pi$
$593$	14.1715	−	24.5458i	0.581954	−	1.00797i	0.995248	−	0.0973765i	$-0.0310451\pi$
$594$		0			0
$595$	7.97073	+	17.1921i	0.326768	+	0.704807i
$596$	7.64167	+	23.5186i	0.313015	+	0.963361i
$597$		0			0
$598$	0.179013	+	0.0797018i	0.00732039	+	0.00325925i
$599$	32.6564	−	6.94133i	1.33430	−	0.283615i	0.515106	−	0.857127i	$-0.327753\pi$
$599$	32.6564	−	6.94133i	1.33430	−	0.283615i	0.819197	+	0.573512i	$0.194419\pi$
$600$		0			0
$601$	1.42697	−	1.03676i	0.0582074	−	0.0422901i	−0.558301	−	0.829638i	$-0.688547\pi$
$601$	1.42697	−	1.03676i	0.0582074	−	0.0422901i	0.616508	+	0.787348i	$0.288547\pi$
$602$	15.5677	+	13.5932i	0.634494	+	0.554017i
$603$		0			0
$604$	−20.6806	+	35.8199i	−0.841482	+	1.45749i
$605$	4.65967	+	12.0718i	0.189443	+	0.490790i
$606$		0			0
$607$	13.9937	+	2.97445i	0.567985	+	0.120729i	0.482948	−	0.875649i	$-0.339566\pi$
$607$	13.9937	+	2.97445i	0.567985	+	0.120729i	0.0850370	+	0.996378i	$0.472899\pi$
$608$	18.6854	+	13.5757i	0.757792	+	0.550568i
$609$		0			0
$610$	8.30204	−	25.5510i	0.336140	−	1.03453i
$611$	−0.0778921	−	0.0865080i	−0.00315118	−	0.00349974i
$612$		0			0
$613$	0.595783	−	5.66850i	0.0240634	−	0.228948i	−0.975880	−	0.218308i	$-0.929946\pi$
$613$	0.595783	−	5.66850i	0.0240634	−	0.228948i	0.999943	−	0.0106405i	$-0.00338703\pi$
$614$	82.7848	+	17.5964i	3.34092	+	0.710135i
$615$		0			0
$616$	−16.8292	−	65.4178i	−0.678068	−	2.63576i
$617$	−17.9653			−0.723257			−0.361628	−	0.932322i	$-0.617779\pi$
$617$	−17.9653			−0.723257			−0.361628	+	0.932322i	$0.617779\pi$
$618$		0			0
$619$	−0.636885	+	6.05956i	−0.0255986	+	0.243554i	0.974239	+	0.225519i	$0.0724078\pi$
$619$	−0.636885	+	6.05956i	−0.0255986	+	0.243554i	−0.999837	+	0.0180353i	$0.994259\pi$
$620$	14.9903	+	6.67411i	0.602025	+	0.268039i
$621$		0			0
$622$	1.72257	−	5.30152i	0.0690688	−	0.212572i
$623$	−9.81739	+	5.86948i	−0.393325	+	0.235156i
$624$		0			0
$625$	−6.02315	−	1.28026i	−0.240926	−	0.0512104i
$626$	−8.07689	−	13.9896i	−0.322817	−	0.559136i
$627$		0			0
$628$	36.8076	−	63.7526i	1.46878	−	2.54400i
$629$	−5.00926	−	15.4169i	−0.199732	−	0.614713i
$630$		0			0
$631$	−35.8264	+	26.0294i	−1.42623	+	1.03621i	−0.435522	+	0.900178i	$0.643436\pi$
$631$	−35.8264	+	26.0294i	−1.42623	+	1.03621i	−0.990704	+	0.136036i	$0.956564\pi$
$632$	15.9893	+	17.7579i	0.636018	+	0.706370i
$633$		0			0
$634$	−42.7296	−	19.0244i	−1.69701	−	0.755556i
$635$	−21.1835	+	9.43149i	−0.840641	+	0.374277i
$636$		0			0
$637$	−0.164849	+	0.194710i	−0.00653156	+	0.00771470i
$638$	−42.2418	+	10.1828i	−1.67237	+	0.403143i
$639$		0			0
$640$	−3.37263	+	3.74569i	−0.133315	+	0.148061i
$641$	4.00363	−	38.0920i	0.158134	−	1.50454i	−0.571441	−	0.820643i	$-0.693615\pi$
$641$	4.00363	−	38.0920i	0.158134	−	1.50454i	0.729575	−	0.683901i	$-0.239718\pi$
$642$		0			0
$643$	−8.87538	+	27.3156i	−0.350011	+	1.07722i	0.608835	+	0.793297i	$0.291637\pi$
$643$	−8.87538	+	27.3156i	−0.350011	+	1.07722i	−0.958846	+	0.283926i	$0.908363\pi$
$644$	−26.4318	+	3.18631i	−1.04156	+	0.125558i
$645$		0			0
$646$	−28.1937	+	12.5527i	−1.10927	+	0.493878i
$647$	13.6948	−	15.2096i	0.538399	−	0.597953i	−0.411152	−	0.911567i	$-0.634873\pi$
$647$	13.6948	−	15.2096i	0.538399	−	0.597953i	0.949550	+	0.313614i	$0.101540\pi$
$648$		0			0
$649$	−11.1036	−	7.61612i	−0.435854	−	0.298959i
$650$	0.346829			0.0136038
$651$		0			0
$652$	−9.91604	−	7.20442i	−0.388342	−	0.282147i
$653$	2.95381	+	28.1036i	0.115591	+	1.09978i	0.886467	+	0.462793i	$0.153153\pi$
$653$	2.95381	+	28.1036i	0.115591	+	1.09978i	−0.770875	+	0.636986i	$0.780181\pi$
$654$		0			0
$655$	−18.6218	+	3.95819i	−0.727615	+	0.154659i
$656$	−8.89467	−	84.6271i	−0.347279	−	3.30413i
$657$		0			0
$658$	21.2520	+	6.54863i	0.828488	+	0.255292i
$659$	−25.1666			−0.980350			−0.490175	−	0.871624i	$-0.663067\pi$
$659$	−25.1666			−0.980350			−0.490175	+	0.871624i	$0.663067\pi$
$660$		0			0
$661$	−10.3561	−	17.9373i	−0.402805	−	0.697679i	0.591258	−	0.806483i	$-0.298632\pi$
$661$	−10.3561	−	17.9373i	−0.402805	−	0.697679i	−0.994063	+	0.108803i	$0.965298\pi$
$662$	−34.4526	+	38.2635i	−1.33904	+	1.48715i
$663$		0			0
$664$	−37.8033	+	27.4657i	−1.46705	+	1.06588i
$665$	−3.59720	−	4.79560i	−0.139494	−	0.185966i
$666$		0			0
$667$	1.06321	+	10.1158i	0.0411678	+	0.391686i
$668$	−6.33513	+	60.2747i	−0.245114	+	2.33210i
$669$		0			0
$670$	3.48785	−	6.04113i	0.134747	−	0.233389i
$671$	−15.0621	−	24.5280i	−0.581467	−	0.946895i
$672$		0			0
$673$	−6.06417	−	18.6636i	−0.233757	−	0.719429i	−0.997284	−	0.0736535i	$-0.976534\pi$
$673$	−6.06417	−	18.6636i	−0.233757	−	0.719429i	0.763527	−	0.645776i	$-0.223466\pi$
$674$	−55.4480	+	24.6870i	−2.13578	+	0.950909i
$675$		0			0
$676$	62.6216	−	13.3106i	2.40852	−	0.511948i
$677$	−15.2531	−	16.9403i	−0.586226	−	0.651070i	0.374938	−	0.927050i	$-0.377664\pi$
$677$	−15.2531	−	16.9403i	−0.586226	−	0.651070i	−0.961163	+	0.275981i	$0.910997\pi$
$678$		0			0
$679$	2.36690	−	12.0350i	0.0908334	−	0.461861i
$680$	−17.0376	−	52.4363i	−0.653361	−	2.01084i
$681$		0			0
$682$	22.3011	−	10.6625i	0.853955	−	0.408289i
$683$	−11.9753	−	20.7418i	−0.458222	−	0.793664i	0.540645	−	0.841251i	$-0.318180\pi$
$683$	−11.9753	−	20.7418i	−0.458222	−	0.793664i	−0.998867	+	0.0475871i	$0.984847\pi$
$684$		0			0
$685$	−16.1563	−	11.7382i	−0.617300	−	0.448495i
$686$	7.94229	−	48.0859i	0.303238	−	1.83593i
$687$		0			0
$688$	−20.6704	−	22.9569i	−0.788053	−	0.875222i
$689$	0.330081	+	0.146962i	0.0125751	+	0.00559879i
$690$		0			0
$691$	−40.0438	−	8.51156i	−1.52334	−	0.323795i	−0.631221	−	0.775603i	$-0.717446\pi$
$691$	−40.0438	−	8.51156i	−1.52334	−	0.323795i	−0.892115	+	0.451808i	$0.850779\pi$
$692$	−60.1119			−2.28511
$693$		0			0
$694$	−65.8980			−2.50145
$695$	8.45376	+	1.79690i	0.320669	+	0.0681603i
$696$		0			0
$697$	45.4802	+	20.2491i	1.72268	+	0.766989i
$698$	−34.4591	−	38.2707i	−1.30430	−	1.44857i
$699$		0			0
$700$	−40.4445	+	24.1804i	−1.52866	+	0.913933i
$701$	8.05784	+	5.85436i	0.304340	+	0.221116i	0.729464	−	0.684019i	$-0.239769\pi$
$701$	8.05784	+	5.85436i	0.304340	+	0.221116i	−0.425124	+	0.905135i	$0.639769\pi$
$702$		0			0
$703$	2.56406	+	4.44108i	0.0967054	+	0.167499i
$704$	4.68281	+	35.3161i	0.176490	+	1.33103i
$705$		0			0
$706$	16.4487	+	50.6240i	0.619057	+	1.90526i
$707$	−42.5882	+	14.5594i	−1.60169	+	0.547562i
$708$		0			0
$709$	−31.7961	−	35.3132i	−1.19413	−	1.32621i	−0.932554	−	0.361031i	$-0.882425\pi$
$709$	−31.7961	−	35.3132i	−1.19413	−	1.32621i	−0.261574	−	0.965183i	$-0.584242\pi$
$710$	−12.8742	+	2.73649i	−0.483159	+	0.102699i
$711$		0			0
$712$	30.4021	−	13.5359i	1.13937	−	0.507279i
$713$	−1.78810	−	5.50321i	−0.0669649	−	0.206097i
$714$		0			0
$715$	−0.0922481	+	0.108212i	−0.00344988	+	0.00404689i
$716$	9.39211	−	16.2676i	0.351000	−	0.607949i
$717$		0			0
$718$	6.85574	−	65.2280i	0.255854	−	2.43429i
$719$	2.06385	+	19.6362i	0.0769686	+	0.732307i	0.963149	+	0.268968i	$0.0866824\pi$
$719$	2.06385	+	19.6362i	0.0769686	+	0.732307i	−0.886181	+	0.463340i	$0.846651\pi$
$720$		0			0
$721$	17.5115	−	41.0030i	0.652161	−	1.52703i
$722$	−32.5522	+	23.6506i	−1.21147	+	0.880182i
$723$		0			0
$724$	23.2136	−	25.7813i	0.862727	−	0.958155i
$725$	9.00155	+	15.5911i	0.334309	+	0.579040i
$726$		0			0
$727$	38.0241			1.41024			0.705118	−	0.709090i	$-0.250894\pi$
$727$	38.0241			1.41024			0.705118	+	0.709090i	$0.250894\pi$
$728$	0.543980	−	0.505033i	0.0201612	−	0.0187178i
$729$		0			0
$730$	1.38901	+	13.2155i	0.0514095	+	0.489129i
$731$	17.6783	−	3.75763i	0.653855	−	0.138981i
$732$		0			0
$733$	−2.99094	−	28.4569i	−0.110473	−	1.05108i	−0.899559	−	0.436798i	$-0.856112\pi$
$733$	−2.99094	−	28.4569i	−0.110473	−	1.05108i	0.789086	−	0.614282i	$-0.210554\pi$
$734$	15.9450	+	11.5847i	0.588542	+	0.427601i
$735$		0			0
$736$	24.4989			0.903042
$737$	−2.50127	−	7.04260i	−0.0921356	−	0.259417i
$738$		0			0
$739$	6.06096	−	6.73137i	0.222956	−	0.247618i	−0.621281	−	0.783588i	$-0.713387\pi$
$739$	6.06096	−	6.73137i	0.222956	−	0.247618i	0.844237	+	0.535970i	$0.180054\pi$
$740$	−14.0916	+	6.27400i	−0.518019	+	0.230637i
$741$		0			0
$742$	−68.5286	+	8.26100i	−2.51577	+	0.303271i
$743$	−2.57977	+	7.93973i	−0.0946427	+	0.291280i	−0.987160	−	0.159732i	$-0.948937\pi$
$743$	−2.57977	+	7.93973i	−0.0946427	+	0.291280i	0.892518	+	0.451012i	$0.148937\pi$
$744$		0			0
$745$	−0.617388	+	5.87406i	−0.0226194	+	0.215209i
$746$	2.82615	−	3.13875i	0.103473	−	0.114918i
$747$		0			0
$748$	−91.9221	−	37.9754i	−3.36100	−	1.38852i
$749$	−2.45764	−	0.220474i	−0.0898003	−	0.00805596i
$750$		0			0
$751$	44.9611	−	20.0180i	1.64065	−	0.730466i	0.641330	−	0.767265i	$-0.278383\pi$
$751$	44.9611	−	20.0180i	1.64065	−	0.730466i	0.999323	+	0.0367995i	$0.0117163\pi$
$752$	−30.3659	−	13.5198i	−1.10733	−	0.493015i
$753$		0			0
$754$	−0.319501	−	0.354842i	−0.0116356	−	0.0129226i
$755$	−7.99225	+	5.80671i	−0.290868	+	0.211328i
$756$		0			0
$757$	6.92221	+	21.3044i	0.251592	+	0.774320i	0.994482	+	0.104907i	$0.0334545\pi$
$757$	6.92221	+	21.3044i	0.251592	+	0.774320i	−0.742890	+	0.669413i	$0.766546\pi$
$758$	22.4292	−	38.8485i	0.814665	−	1.41104i
$759$		0			0
$760$	8.72092	+	15.1051i	0.316341	+	0.547919i
$761$	−24.8315	−	5.27809i	−0.900140	−	0.191331i	−0.265474	−	0.964118i	$-0.585529\pi$
$761$	−24.8315	−	5.27809i	−0.900140	−	0.191331i	−0.634665	+	0.772787i	$0.718862\pi$
$762$		0			0
$763$	0.0655036	+	4.29511i	0.00237139	+	0.155494i
$764$	24.2388	−	74.5993i	0.876928	−	2.69891i
$765$		0			0
$766$	−41.8837	−	18.6478i	−1.51332	−	0.673774i
$767$	0.0154661	−	0.147150i	0.000558449	−	0.00531329i
$768$		0			0
$769$	−44.5582			−1.60681			−0.803406	−	0.595432i	$-0.796981\pi$
$769$	−44.5582			−1.60681			−0.803406	+	0.595432i	$0.796981\pi$
$770$	4.51758	−	26.7861i	0.162802	−	0.965304i
$771$		0			0
$772$	−71.2887	−	15.1529i	−2.56574	−	0.545364i
$773$	3.45360	−	32.8588i	0.124217	−	1.18185i	−0.737818	−	0.675000i	$-0.764144\pi$
$773$	3.45360	−	32.8588i	0.124217	−	1.18185i	0.862035	−	0.506848i	$-0.169190\pi$
$774$		0			0
$775$	−6.85301	−	7.61104i	−0.246167	−	0.273397i
$776$	−11.0277	+	33.9399i	−0.395873	+	1.21837i
$777$		0			0
$778$	23.9204	+	17.3792i	0.857589	+	0.623075i
$779$	−15.4051	−	3.27445i	−0.551943	−	0.117319i
$780$		0			0
$781$	−6.71702	+	12.3986i	−0.240354	+	0.443658i
$782$	−16.3680	+	28.3502i	−0.585318	+	1.01380i
$783$		0			0
$784$	−20.3883	+	69.9374i	−0.728152	+	2.49777i
$785$	14.2247	−	10.3348i	0.507701	−	0.368866i
$786$		0			0
$787$	−42.2344	+	8.97720i	−1.50549	+	0.320003i	−0.885513	−	0.464615i	$-0.846193\pi$
$787$	−42.2344	+	8.97720i	−1.50549	+	0.320003i	−0.619981	+	0.784617i	$0.712860\pi$
$788$	−37.2911	−	16.6031i	−1.32844	−	0.591460i
$789$		0			0
$790$	2.96953	+	9.13927i	0.105651	+	0.325161i
$791$	−3.93839	−	8.49473i	−0.140033	−	0.302038i
$792$		0			0
$793$	0.158150	−	0.273923i	0.00561606	−	0.00972729i
$794$	−34.7039	+	38.5425i	−1.23159	+	1.36782i
$795$		0			0
$796$	−9.41318	−	89.5604i	−0.333641	−	3.17439i
$797$	3.31341	−	10.1976i	0.117367	−	0.361218i	−0.875066	−	0.484003i	$-0.839182\pi$
$797$	3.31341	−	10.1976i	0.117367	−	0.361218i	0.992433	+	0.122785i	$0.0391825\pi$
$798$		0			0
$799$	15.7330	−	11.4307i	0.556592	−	0.404388i
$800$	39.6130	−	17.6369i	1.40053	−	0.623557i
$801$		0			0
$802$	16.4977	+	28.5748i	0.582553	+	1.00901i
$803$	11.7404	+	8.05291i	0.414309	+	0.284181i
$804$		0			0
$805$	−6.07688	−	1.87254i	−0.214182	−	0.0659984i
$806$	0.219757	+	0.159663i	0.00774061	+	0.00562388i
$807$		0			0
$808$	128.089	−	27.2262i	4.50616	−	0.957813i
$809$	−1.12546	+	0.239224i	−0.0395690	+	0.00841066i	−0.227654	−	0.973742i	$-0.573105\pi$
$809$	−1.12546	+	0.239224i	−0.0395690	+	0.00841066i	0.188085	+	0.982153i	$0.439772\pi$
$810$		0			0
$811$	28.6938	+	20.8473i	1.00758	+	0.732047i	0.963699	−	0.266990i	$-0.0860290\pi$
$811$	28.6938	+	20.8473i	1.00758	+	0.732047i	0.0438772	+	0.999037i	$0.486029\pi$
$812$	61.9968	+	19.1038i	2.17566	+	0.670413i
$813$		0			0
$814$	−6.57902	+	22.2864i	−0.230595	+	0.781136i
$815$	−1.46375	−	2.53530i	−0.0512731	−	0.0888076i
$816$		0			0
$817$	−5.22315	+	2.32550i	−0.182735	+	0.0813588i
$818$	33.2244	−	24.1389i	1.16166	−	0.843997i
$819$		0			0
$820$	14.6391	−	45.0545i	0.511220	−	1.57337i
$821$	2.06152	+	19.6140i	0.0719475	+	0.684535i	0.969744	+	0.244124i	$0.0785005\pi$
$821$	2.06152	+	19.6140i	0.0719475	+	0.684535i	−0.897796	+	0.440411i	$0.854833\pi$
$822$		0			0
$823$	27.3181	−	30.3398i	0.952248	−	1.05758i	−0.0460316	−	0.998940i	$-0.514658\pi$
$823$	27.3181	−	30.3398i	0.952248	−	1.05758i	0.998279	−	0.0586382i	$-0.0186758\pi$
$824$	−64.8610	+	112.343i	−2.25954	+	3.91364i
$825$		0			0
$826$	11.8892	+	25.6438i	0.413676	+	0.892260i
$827$	0.289657	+	0.891474i	0.0100724	+	0.0309996i	0.955966	−	0.293476i	$-0.0948121\pi$
$827$	0.289657	+	0.891474i	0.0100724	+	0.0309996i	−0.945894	+	0.324476i	$0.894812\pi$
$828$		0			0
$829$	−13.9732	−	6.22128i	−0.485310	−	0.216074i	0.149471	−	0.988766i	$-0.452243\pi$
$829$	−13.9732	−	6.22128i	−0.485310	−	0.216074i	−0.634781	+	0.772692i	$0.718910\pi$
$830$	−18.3808	+	3.90696i	−0.638007	+	0.135612i
$831$		0			0
$832$	−0.316715	+	0.230107i	−0.0109801	+	0.00797753i
$833$	−29.4712	−	30.7888i	−1.02112	−	1.06677i
$834$		0			0
$835$	−7.23784	+	12.5363i	−0.250476	+	0.433837i
$836$	30.9418	+	5.70501i	1.07014	+	0.197312i
$837$		0			0
$838$	81.9024	+	17.4089i	2.82927	+	0.601380i
$839$	11.3598	+	8.25338i	0.392184	+	0.284938i	0.766350	−	0.642423i	$-0.222071\pi$
$839$	11.3598	+	8.25338i	0.392184	+	0.284938i	−0.374166	+	0.927362i	$0.622071\pi$
$840$		0			0
$841$	−1.30243	+	4.00846i	−0.0449113	+	0.138223i
$842$	−42.0517	−	46.7032i	−1.44920	−	1.60950i
$843$		0			0
$844$	−12.1519	+	115.618i	−0.418286	+	3.97972i
$845$	14.9569	+	3.17919i	0.514534	+	0.109368i
$846$		0			0
$847$	−18.6995	−	22.3009i	−0.642522	−	0.766268i
$848$	103.173			3.54296
$849$		0			0
$850$	−6.05648	+	57.6236i	−0.207736	+	1.97647i
$851$	4.96925	+	2.21245i	0.170344	+	0.0758420i
$852$		0			0
$853$	1.13225	−	3.48472i	0.0387677	−	0.119315i	−0.929800	−	0.368066i	$-0.880020\pi$
$853$	1.13225	−	3.48472i	0.0387677	−	0.119315i	0.968567	+	0.248751i	$0.0800201\pi$
$854$	0.921408	+	60.4174i	0.0315299	+	2.06744i
$855$		0			0
$856$	7.02232	+	1.49264i	0.240018	+	0.0510174i
$857$	2.52090	+	4.36633i	0.0861124	+	0.149151i	0.905865	−	0.423567i	$-0.139222\pi$
$857$	2.52090	+	4.36633i	0.0861124	+	0.149151i	−0.819752	+	0.572718i	$0.805889\pi$
$858$		0			0
$859$	−26.8888	+	46.5728i	−0.917434	+	1.58904i	−0.114137	+	0.993465i	$0.536410\pi$
$859$	−26.8888	+	46.5728i	−0.917434	+	1.58904i	−0.803298	+	0.595578i	$0.796923\pi$
$860$	−5.31445	−	16.3562i	−0.181221	−	0.557741i
$861$		0			0
$862$	17.7640	−	12.9063i	0.605043	−	0.439590i
$863$	22.2649	+	24.7276i	0.757904	+	0.841738i	0.991434	−	0.130612i	$-0.0416941\pi$
$863$	22.2649	+	24.7276i	0.757904	+	0.841738i	−0.233529	+	0.972350i	$0.575027\pi$
$864$		0			0
$865$	−13.1162	−	5.83971i	−0.445964	−	0.198556i
$866$	−30.8597	+	13.7396i	−1.04866	+	0.466892i
$867$		0			0
$868$	−36.7578	−	3.29753i	−1.24764	−	0.111926i
$869$	9.51545	+	3.93109i	0.322790	+	0.133353i
$870$		0			0
$871$	0.0549533	−	0.0610318i	0.00186202	−	0.00206798i
$872$	1.30640	−	12.4296i	0.0442404	−	0.420919i
$873$		0			0
$874$	3.20018	−	9.84914i	0.108248	−	0.333152i
$875$	−26.6238	+	3.20945i	−0.900049	+	0.108499i
$876$		0			0
$877$	−12.0283	+	5.35537i	−0.406168	+	0.180838i	−0.599643	−	0.800267i	$-0.704691\pi$
$877$	−12.0283	+	5.35537i	−0.406168	+	0.180838i	0.193475	+	0.981105i	$0.438024\pi$
$878$	43.3140	−	48.1050i	1.46178	−	1.62347i
$879$		0			0
$880$	−11.4958	+	38.9417i	−0.387522	+	1.31272i
$881$	33.1960			1.11840			0.559201	−	0.829032i	$-0.311108\pi$
$881$	33.1960			1.11840			0.559201	+	0.829032i	$0.311108\pi$
$882$		0			0
$883$	25.2028	+	18.3109i	0.848143	+	0.616212i	0.924633	−	0.380859i	$-0.124372\pi$
$883$	25.2028	+	18.3109i	0.848143	+	0.616212i	−0.0764906	+	0.997070i	$0.524372\pi$
$884$	−0.114242	−	1.08694i	−0.00384237	−	0.0365577i
$885$		0			0
$886$	41.5120	−	8.82365i	1.39462	−	0.296436i
$887$	−3.46334	−	32.9515i	−0.116288	−	1.10640i	−0.884608	−	0.466336i	$-0.845574\pi$
$887$	−3.46334	−	32.9515i	−0.116288	−	1.10640i	0.768320	−	0.640066i	$-0.221093\pi$
$888$		0			0
$889$	38.2204	−	35.4839i	1.28187	−	1.19009i
$890$	13.3833			0.448608
$891$		0			0
$892$	29.7380	+	51.5076i	0.995700	+	1.72460i
$893$	−4.11652	+	4.57186i	−0.137754	+	0.152992i
$894$		0			0
$895$	3.62968	−	2.63712i	0.121327	−	0.0881492i
$896$	4.45240	−	10.4253i	0.148744	−	0.348283i
$897$		0			0
$898$	−9.47988	−	90.1950i	−0.316348	−	3.00985i
$899$	−1.47384	+	14.0227i	−0.0491554	+	0.467683i
$900$		0			0
$901$	−30.1808	+	52.2747i	−1.00547	+	1.74152i
$902$	−37.3444	−	60.8138i	−1.24343	−	2.02488i
$903$		0			0
$904$	8.41838	+	25.9091i	0.279991	+	0.861724i
$905$	7.56972	−	3.37026i	0.251626	−	0.112031i
$906$		0			0
$907$	−11.0937	+	2.35804i	−0.368360	+	0.0782973i	−0.388373	−	0.921502i	$-0.626963\pi$
$907$	−11.0937	+	2.35804i	−0.368360	+	0.0782973i	0.0200127	+	0.999800i	$0.493629\pi$
$908$	34.0345	+	37.7992i	1.12947	+	1.25441i
$909$		0			0
$910$	0.282457	−	0.0965619i	0.00936334	−	0.00320099i
$911$	9.02202	+	27.7669i	0.298913	+	0.919959i	0.981879	+	0.189509i	$0.0606897\pi$
$911$	9.02202	+	27.7669i	0.298913	+	0.919959i	−0.682966	+	0.730450i	$0.739310\pi$
$912$		0			0
$913$	−9.59006	+	17.7019i	−0.317385	+	0.585846i
$914$	−42.6948	−	73.9495i	−1.41222	−	2.44603i
$915$		0			0
$916$	109.816	+	79.7860i	3.62842	+	2.63620i
$917$	36.7508	−	21.9720i	1.21362	−	0.725580i
$918$		0			0
$919$	9.73920	+	10.8165i	0.321266	+	0.356803i	0.882047	−	0.471162i	$-0.156165\pi$
$919$	9.73920	+	10.8165i	0.321266	+	0.356803i	−0.560780	+	0.827965i	$0.689499\pi$
$920$	16.9015	+	7.52503i	0.557226	+	0.248093i
$921$		0			0
$922$	75.9280	+	16.1390i	2.50056	+	0.531510i
$923$	−0.154957			−0.00510046
$924$		0			0
$925$	9.62768			0.316556
$926$	57.2956	+	12.1786i	1.88285	+	0.400212i
$927$		0			0
$928$	−54.5361	−	24.2810i	−1.79024	−	0.797064i
$929$	4.40136	+	4.88821i	0.144404	+	0.160377i	0.811008	−	0.585035i	$-0.198919\pi$
$929$	4.40136	+	4.88821i	0.144404	+	0.160377i	−0.666604	+	0.745412i	$0.732253\pi$
$930$		0			0
$931$	11.1445	+	7.58877i	0.365247	+	0.248712i
$932$	15.9389	+	11.5803i	0.522098	+	0.379326i
$933$		0			0
$934$	−31.1289	−	53.9168i	−1.01857	−	1.76421i
$935$	−16.3679	−	17.2161i	−0.535287	−	0.563027i
$936$		0			0
$937$	−9.37722	−	28.8601i	−0.306340	−	0.942818i	−0.979174	−	0.203024i	$-0.934923\pi$
$937$	−9.37722	−	28.8601i	−0.306340	−	0.942818i	0.672833	−	0.739794i	$-0.265077\pi$
$938$	−3.02755	+	15.3942i	−0.0988530	+	0.502638i
$939$		0			0
$940$	−12.3824	−	13.7520i	−0.403868	−	0.448541i
$941$	−14.9130	+	3.16985i	−0.486149	+	0.103334i	−0.444464	−	0.895797i	$-0.646606\pi$
$941$	−14.9130	+	3.16985i	−0.486149	+	0.103334i	−0.0416850	+	0.999131i	$0.513273\pi$
$942$		0			0
$943$	−15.2613	+	6.79477i	−0.496977	+	0.221268i
$944$	−13.0558	−	40.1815i	−0.424929	−	1.30780i
$945$		0			0
$946$	−23.9447	−	9.89218i	−0.778509	−	0.321623i
$947$	15.6044	−	27.0276i	0.507075	−	0.878280i	−0.492891	−	0.870091i	$-0.664060\pi$
$947$	15.6044	−	27.0276i	0.507075	−	0.878280i	0.999966	−	0.00818941i	$-0.00260680\pi$
$948$		0			0
$949$	−0.0163531	+	0.155589i	−0.000530844	+	0.00505065i
$950$	−1.91596	−	18.2292i	−0.0621621	−	0.591433i
$951$		0			0
$952$	74.4090	+	99.1981i	2.41161	+	3.21503i
$953$	17.4834	−	12.7024i	0.566342	−	0.411471i	−0.267433	−	0.963577i	$-0.586175\pi$
$953$	17.4834	−	12.7024i	0.566342	−	0.411471i	0.833774	+	0.552105i	$0.186175\pi$
$954$		0			0
$955$	12.5359	−	13.9226i	0.405654	−	0.450524i
$956$	52.2656	+	90.5266i	1.69039	+	2.92784i
$957$		0			0
$958$	−30.4063			−0.982384
$959$	42.9236	+	13.2266i	1.38608	+	0.427108i
$960$		0			0
$961$	2.40194	+	22.8529i	0.0774819	+	0.737191i
$962$	−0.249770	+	0.0530903i	−0.00805292	+	0.00171170i
$963$		0			0
$964$	7.00492	+	66.6473i	0.225613	+	2.14657i
$965$	−14.0829	−	10.2318i	−0.453345	−	0.329374i
$966$		0			0
$967$	5.74025			0.184594			0.0922970	−	0.995732i	$-0.470579\pi$
$967$	5.74025			0.184594			0.0922970	+	0.995732i	$0.470579\pi$
$968$	46.2494	+	70.9293i	1.48651	+	2.27975i
$969$		0			0
$970$	−9.60291	+	10.6651i	−0.308331	+	0.342436i
$971$	6.26859	−	2.79096i	0.201169	−	0.0895660i	−0.303679	−	0.952774i	$-0.598215\pi$
$971$	6.26859	−	2.79096i	0.201169	−	0.0895660i	0.504848	+	0.863208i	$0.331549\pi$
$972$		0			0
$973$	−19.2984	+	2.32639i	−0.618680	+	0.0745807i
$974$	−0.107148	+	0.329766i	−0.00343323	+	0.0105664i
$975$		0			0
$976$	9.44074	−	89.8227i	0.302191	−	2.87515i
$977$	6.96892	−	7.73977i	0.222955	−	0.247617i	−0.621281	−	0.783588i	$-0.713388\pi$
$977$	6.96892	−	7.73977i	0.222955	−	0.247617i	0.844237	+	0.535971i	$0.180054\pi$
$978$		0			0
$979$	9.30199	−	10.9117i	0.297293	−	0.348740i
$980$	−26.2058	+	30.9527i	−0.837112	+	0.988748i
$981$		0			0
$982$	−0.0536241	+	0.0238750i	−0.00171121	+	0.000761881i
$983$	−14.3900	−	6.40682i	−0.458969	−	0.204346i	0.164210	−	0.986425i	$-0.447492\pi$
$983$	−14.3900	−	6.40682i	−0.458969	−	0.204346i	−0.623179	+	0.782079i	$0.714159\pi$
$984$		0			0
$985$	−6.52385	−	7.24547i	−0.207867	−	0.230860i
$986$	64.5342	−	46.8868i	2.05519	−	1.49318i
$987$		0			0
$988$	0.106842	+	0.328825i	0.00339908	+	0.0104613i
$989$	−3.03232	+	5.25213i	−0.0964222	+	0.167008i
$990$		0			0
$991$	−4.05884	−	7.03011i	−0.128933	−	0.223319i	0.794330	−	0.607486i	$-0.207822\pi$
$991$	−4.05884	−	7.03011i	−0.128933	−	0.223319i	−0.923264	+	0.384167i	$0.874489\pi$
$992$	33.2186	+	7.06084i	1.05469	+	0.224182i
$993$		0			0
$994$	25.4076	−	15.1903i	0.805881	−	0.481808i
$995$	6.64664	−	20.4563i	0.210713	−	0.648507i
$996$		0			0
$997$	−37.6879	−	16.7797i	−1.19359	−	0.531420i	−0.288845	−	0.957376i	$-0.593271\pi$
$997$	−37.6879	−	16.7797i	−1.19359	−	0.531420i	−0.904744	+	0.425956i	$0.859938\pi$
$998$	−1.90602	+	18.1346i	−0.0603340	+	0.574040i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.by.b.478.5		40
3.2	odd	2		77.2.m.b.16.1	yes	40
7.4	even	3	inner	693.2.by.b.676.1		40
11.9	even	5	inner	693.2.by.b.163.1		40
21.2	odd	6		539.2.f.h.148.5		20
21.5	even	6		539.2.f.g.148.5		20
21.11	odd	6		77.2.m.b.60.5	yes	40
21.17	even	6		539.2.q.h.214.5		40
21.20	even	2		539.2.q.h.324.1		40
33.2	even	10		847.2.n.j.9.1		40
33.5	odd	10		847.2.n.i.807.5		40
33.8	even	10		847.2.e.h.485.10		20
33.14	odd	10		847.2.e.i.485.1		20
33.17	even	10		847.2.n.h.807.1		40
33.20	odd	10		77.2.m.b.9.5	✓	40
33.26	odd	10		847.2.n.i.366.1		40
33.29	even	10		847.2.n.h.366.5		40
33.32	even	2		847.2.n.j.632.5		40
77.53	even	15	inner	693.2.by.b.361.5		40
231.20	even	10		539.2.q.h.471.5		40
231.32	even	6		847.2.n.j.753.1		40
231.47	even	30		5929.2.a.bx.1.10		10
231.53	odd	30		77.2.m.b.53.1	yes	40
231.74	even	30		847.2.e.h.606.10		20
231.86	odd	30		539.2.f.h.295.5		20
231.95	even	30		847.2.n.h.487.1		40
231.107	even	30		5929.2.a.by.1.1		10
231.116	even	30		847.2.n.h.81.5		40
231.137	odd	30		847.2.n.i.81.1		40
231.152	even	30		539.2.f.g.295.5		20
231.158	odd	30		847.2.n.i.487.5		40
231.173	odd	30		5929.2.a.bz.1.1		10
231.179	odd	30		847.2.e.i.606.1		20
231.185	even	30		539.2.q.h.361.1		40
231.200	even	30		847.2.n.j.130.5		40
231.212	odd	30		5929.2.a.bw.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.5	✓	40	33.20	odd	10
77.2.m.b.16.1	yes	40	3.2	odd	2
77.2.m.b.53.1	yes	40	231.53	odd	30
77.2.m.b.60.5	yes	40	21.11	odd	6
539.2.f.g.148.5		20	21.5	even	6
539.2.f.g.295.5		20	231.152	even	30
539.2.f.h.148.5		20	21.2	odd	6
539.2.f.h.295.5		20	231.86	odd	30
539.2.q.h.214.5		40	21.17	even	6
539.2.q.h.324.1		40	21.20	even	2
539.2.q.h.361.1		40	231.185	even	30
539.2.q.h.471.5		40	231.20	even	10
693.2.by.b.163.1		40	11.9	even	5	inner
693.2.by.b.361.5		40	77.53	even	15	inner
693.2.by.b.478.5		40	1.1	even	1	trivial
693.2.by.b.676.1		40	7.4	even	3	inner
847.2.e.h.485.10		20	33.8	even	10
847.2.e.h.606.10		20	231.74	even	30
847.2.e.i.485.1		20	33.14	odd	10
847.2.e.i.606.1		20	231.179	odd	30
847.2.n.h.81.5		40	231.116	even	30
847.2.n.h.366.5		40	33.29	even	10
847.2.n.h.487.1		40	231.95	even	30
847.2.n.h.807.1		40	33.17	even	10
847.2.n.i.81.1		40	231.137	odd	30
847.2.n.i.366.1		40	33.26	odd	10
847.2.n.i.487.5		40	231.158	odd	30
847.2.n.i.807.5		40	33.5	odd	10
847.2.n.j.9.1		40	33.2	even	10
847.2.n.j.130.5		40	231.200	even	30
847.2.n.j.632.5		40	33.32	even	2
847.2.n.j.753.1		40	231.32	even	6
5929.2.a.bw.1.10		10	231.212	odd	30
5929.2.a.bx.1.10		10	231.47	even	30
5929.2.a.by.1.1		10	231.107	even	30
5929.2.a.bz.1.1		10	231.173	odd	30

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.by (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.57407 + 0.547134i) q^{2} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(-2.31119 - 1.28778i) q^{7} +(6.22764 + 4.52465i) q^{8} +O(q^{10})\)	\(q+(2.57407 + 0.547134i) q^{2} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(-2.31119 - 1.28778i) q^{7} +(6.22764 + 4.52465i) q^{8} +(1.54783 + 2.68093i) q^{10} +(3.26165 + 0.601380i) q^{11} +(0.0112624 + 0.0346622i) q^{13} +(-5.24457 - 4.57937i) q^{14} +(6.96361 + 7.73387i) q^{16} +(-5.95559 + 1.26590i) q^{17} +(1.75961 - 0.783430i) q^{19} +(1.79037 + 5.51019i) q^{20} +(8.06666 + 3.33255i) q^{22} +(1.02155 - 1.76938i) q^{23} +(0.377994 - 3.59637i) q^{25} +(0.0100254 + 0.0953849i) q^{26} +(-7.81916 - 10.4241i) q^{28} +(-4.02767 + 2.92628i) q^{29} +(1.89509 - 2.10472i) q^{31} +(5.99553 + 10.3846i) q^{32} -16.0227 q^{34} +(-0.693441 - 3.03411i) q^{35} +(0.278295 + 2.64780i) q^{37} +(4.95800 - 1.05386i) q^{38} +(0.946542 + 9.00574i) q^{40} +(-6.61499 - 4.80607i) q^{41} -2.96835 q^{43} +(13.4706 + 9.23971i) q^{44} +(3.59762 - 3.99557i) q^{46} +(-2.91785 + 1.29911i) q^{47} +(3.68323 + 5.95263i) q^{49} +(2.94068 - 9.05049i) q^{50} +(-0.0187631 + 0.178519i) q^{52} +(6.63364 - 7.36740i) q^{53} +(2.04163 + 3.32471i) q^{55} +(-8.56653 - 18.4772i) q^{56} +(-11.9686 + 5.32875i) q^{58} +(-3.70874 - 1.65124i) q^{59} +(-5.80710 - 6.44943i) q^{61} +(6.02966 - 4.38080i) q^{62} +(3.31928 + 10.2157i) q^{64} +(-0.0214368 + 0.0371295i) q^{65} +(-1.12669 - 1.95148i) q^{67} +(-29.3323 - 6.23477i) q^{68} +(-0.124894 - 8.18941i) q^{70} +(-1.31384 + 4.04359i) q^{71} +(3.92144 + 1.74594i) q^{73} +(-0.732354 + 6.96788i) q^{74} +9.48655 q^{76} +(-6.76385 - 5.59020i) q^{77} +(3.03638 + 0.645402i) q^{79} +(-1.27967 + 12.1752i) q^{80} +(-14.3979 - 15.9904i) q^{82} +(-1.87581 + 5.77314i) q^{83} +(-5.79451 - 4.20996i) q^{85} +(-7.64073 - 1.62409i) q^{86} +(17.5913 + 18.5030i) q^{88} +(2.16161 - 3.74402i) q^{89} +(0.0186077 - 0.0946147i) q^{91} +(8.14083 - 5.91466i) q^{92} +(-8.22152 + 1.74754i) q^{94} +(2.06993 + 0.921593i) q^{95} +(1.43258 + 4.40904i) q^{97} +(6.22400 + 17.3377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8}+O(q^{10}) \) 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8	\( 40 q + 3 q^{2} - 3 q^{4} - 4 q^{5} - 2 q^{7} + 38 q^{8} + 14 q^{10} + 9 q^{11} + 6 q^{13} + 3 q^{14} - 5 q^{16} + 7 q^{17} - 4 q^{19} + 30 q^{20} + 44 q^{22} + 14 q^{23} + 21 q^{25} + 16 q^{28} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 24 q^{37} - 12 q^{38} + 10 q^{40} - 60 q^{41} - 72 q^{43} - 18 q^{44} + 8 q^{46} - 13 q^{47} - 10 q^{49} - 6 q^{50} + 2 q^{52} - 33 q^{53} - 6 q^{55} - 24 q^{56} - 17 q^{58} - 21 q^{59} + 52 q^{62} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 3 q^{70} - 20 q^{71} + 11 q^{73} + 41 q^{74} - 96 q^{76} - 36 q^{77} + 21 q^{79} - 12 q^{80} + 6 q^{82} + 46 q^{83} - 78 q^{85} - 7 q^{86} + 32 q^{88} + 10 q^{89} - 14 q^{91} + 110 q^{92} + 37 q^{94} - 7 q^{95} - 54 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 - 3 * q^4 - 4 * q^5 - 2 * q^7 + 38 * q^8 + 14 * q^10 + 9 * q^11 + 6 * q^13 + 3 * q^14 - 5 * q^16 + 7 * q^17 - 4 * q^19 + 30 * q^20 + 44 * q^22 + 14 * q^23 + 21 * q^25 + 16 * q^28 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 24 * q^37 - 12 * q^38 + 10 * q^40 - 60 * q^41 - 72 * q^43 - 18 * q^44 + 8 * q^46 - 13 * q^47 - 10 * q^49 - 6 * q^50 + 2 * q^52 - 33 * q^53 - 6 * q^55 - 24 * q^56 - 17 * q^58 - 21 * q^59 + 52 * q^62 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 3 * q^70 - 20 * q^71 + 11 * q^73 + 41 * q^74 - 96 * q^76 - 36 * q^77 + 21 * q^79 - 12 * q^80 + 6 * q^82 + 46 * q^83 - 78 * q^85 - 7 * q^86 + 32 * q^88 + 10 * q^89 - 14 * q^91 + 110 * q^92 + 37 * q^94 - 7 * q^95 - 54 * q^97 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more