LMFDB - Embedded newform 693.2.by.b.361.5

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			361.5
Character	$\chi$	$=$	693.361
Dual form			693.2.by.b.478.5

$q$-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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

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

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	0.833861	−	0.551975i	$-0.186125\pi$
$2$	2.57407	−	0.547134i	1.82014	−	0.386883i	0.986278	+	0.165092i	$0.0527921\pi$
$3$		0			0
$3$		0			0
$4$	4.49937	−	2.00325i	2.24968	−	1.00162i
$5$	0.787136	−	0.874203i	0.352018	−	0.390956i	−0.540966	−	0.841045i	$-0.681941\pi$
$5$	0.787136	−	0.874203i	0.352018	−	0.390956i	0.892984	+	0.450089i	$0.148608\pi$
$6$		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	−0.949483	−	0.313820i	$-0.898391\pi$
$13$	0.0112624	−	0.0346622i	0.00312364	−	0.00961357i	0.952606	+	0.304206i	$0.0983912\pi$
$14$	−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	−0.582003	−	0.813187i	$-0.697731\pi$
$17$	−5.95559	−	1.26590i	−1.44444	−	0.307026i	−0.862439	+	0.506161i	$0.831064\pi$
$18$		0			0
$19$	1.75961	+	0.783430i	0.403683	+	0.179731i	0.598526	−	0.801103i	$-0.295753\pi$
$19$	1.75961	+	0.783430i	0.403683	+	0.179731i	−0.194843	+	0.980834i	$0.562420\pi$
$20$	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	0.952655	−	0.304055i	$-0.0983406\pi$
$23$	1.02155	+	1.76938i	0.213008	+	0.368941i	−0.739647	+	0.672996i	$0.765007\pi$
$24$		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	0.147261	−	0.989098i	$-0.452954\pi$
$29$	−4.02767	−	2.92628i	−0.747920	−	0.543396i	−0.895182	+	0.445702i	$0.852954\pi$
$30$		0			0
$31$	1.89509	+	2.10472i	0.340369	+	0.378018i	0.888892	−	0.458118i	$-0.151476\pi$
$31$	1.89509	+	2.10472i	0.340369	+	0.378018i	−0.548523	+	0.836136i	$0.684810\pi$
$32$	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	−0.947538	−	0.319643i	$-0.896437\pi$
$37$	0.278295	−	2.64780i	0.0457515	−	0.435296i	0.993290	−	0.115653i	$-0.0368962\pi$
$38$	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	−0.968925	−	0.247357i	$-0.920438\pi$
$41$	−6.61499	+	4.80607i	−1.03309	+	0.750583i	−0.0641641	+	0.997939i	$0.520438\pi$
$42$		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	0.182741	−	0.983161i	$-0.441503\pi$
$47$	−2.91785	−	1.29911i	−0.425612	−	0.189495i	−0.608353	+	0.793666i	$0.708170\pi$
$48$		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	0.999873	+	0.0159294i	$0.00507070\pi$
$53$	6.63364	+	7.36740i	0.911200	+	1.01199i	−0.0886731	+	0.996061i	$0.528263\pi$
$54$		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	−0.633696	−	0.773582i	$-0.718463\pi$
$59$	−3.70874	+	1.65124i	−0.482837	+	0.214973i	0.150858	+	0.988555i	$0.451796\pi$
$60$		0			0
$61$	−5.80710	+	6.44943i	−0.743522	+	0.825765i	−0.989655	−	0.143471i	$-0.954174\pi$
$61$	−5.80710	+	6.44943i	−0.743522	+	0.825765i	0.246132	+	0.969236i	$0.420840\pi$
$62$	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	−0.926605	−	0.376035i	$-0.877287\pi$
$67$	−1.12669	+	1.95148i	−0.137647	+	0.238411i	0.788959	+	0.614446i	$0.210621\pi$
$68$	−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	0.842329	−	0.538963i	$-0.181184\pi$
$71$	−1.31384	−	4.04359i	−0.155924	−	0.479885i	−0.998253	+	0.0590780i	$0.981184\pi$
$72$		0			0
$73$	3.92144	−	1.74594i	0.458970	−	0.204347i	−0.164209	−	0.986426i	$-0.552507\pi$
$73$	3.92144	−	1.74594i	0.458970	−	0.204347i	0.623180	+	0.782079i	$0.285841\pi$
$74$	−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	−0.0339076	−	0.999425i	$-0.510795\pi$
$79$	3.03638	−	0.645402i	0.341619	−	0.0726133i	0.375527	+	0.926812i	$0.377462\pi$
$80$	−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	−0.999675	−	0.0254778i	$-0.991889\pi$
$83$	−1.87581	−	5.77314i	−0.205896	−	0.633684i	0.793779	−	0.608206i	$-0.208111\pi$
$84$		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	0.957551	−	0.288265i	$-0.0930784\pi$
$89$	2.16161	+	3.74402i	0.229130	+	0.396866i	−0.728420	+	0.685131i	$0.759745\pi$
$90$		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	−0.851613	−	0.524172i	$-0.824375\pi$
$97$	1.43258	−	4.40904i	0.145457	−	0.447670i	0.997069	+	0.0765015i	$0.0243750\pi$
$98$	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	0.962137	+	0.272566i	$0.0878722\pi$
$101$	11.3829	+	12.6420i	1.13264	+	1.25792i	0.170502	+	0.985357i	$0.445461\pi$
$102$		0			0
$103$	1.76150	−	16.7595i	0.173566	−	1.65137i	−0.467583	−	0.883949i	$-0.654875\pi$
$103$	1.76150	−	16.7595i	0.173566	−	1.65137i	0.641149	−	0.767417i	$-0.278458\pi$
$104$	−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	0.447506	−	0.894281i	$-0.352312\pi$
$107$	0.852002	+	0.379336i	0.0823661	+	0.0366718i	−0.365140	+	0.930953i	$0.618979\pi$
$108$		0			0
$109$	−0.811795	+	1.40607i	−0.0777558	+	0.134677i	−0.902281	−	0.431148i	$-0.858109\pi$
$109$	−0.811795	+	1.40607i	−0.0777558	+	0.134677i	0.824526	+	0.565825i	$0.191442\pi$
$110$	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	−0.444915	−	0.895573i	$-0.646766\pi$
$113$	2.86311	−	2.08017i	0.269338	−	0.195686i	0.714254	+	0.699887i	$0.246766\pi$
$114$		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	−0.731419	−	0.681928i	$-0.761142\pi$
$127$	−6.09131	−	18.7471i	−0.540516	−	1.66354i	0.190903	−	0.981609i	$-0.438858\pi$
$128$	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	−0.965969	−	0.258659i	$-0.916719\pi$
$131$	−8.09187	−	14.0155i	−0.706990	−	1.22454i	0.258979	−	0.965883i	$-0.416614\pi$
$132$		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	−0.566191	−	0.824274i	$-0.691583\pi$
$137$	−16.6054	−	3.52958i	−1.41869	−	0.301553i	−0.852504	+	0.522721i	$0.824917\pi$
$138$		0			0
$139$	5.94380	+	4.31842i	0.504146	+	0.366284i	0.810598	−	0.585602i	$-0.199142\pi$
$139$	5.94380	+	4.31842i	0.504146	+	0.366284i	−0.306452	+	0.951886i	$0.599142\pi$
$140$	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	−0.589641	−	0.807665i	$-0.700731\pi$
$149$	3.35966	−	3.73128i	0.275234	−	0.305679i	0.864875	+	0.501987i	$0.167397\pi$
$150$		0			0
$151$	−0.877823	−	8.35192i	−0.0714362	−	0.679670i	−0.970376	−	0.241598i	$-0.922328\pi$
$151$	−0.877823	−	8.35192i	−0.0714362	−	0.679670i	0.898940	−	0.438072i	$-0.144338\pi$
$152$	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	0.860606	+	0.509271i	$0.170085\pi$
$157$	1.56236	+	14.8648i	0.124690	+	1.18634i	−0.735917	+	0.677072i	$0.763248\pi$
$158$	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	−0.302254	−	0.953227i	$-0.597739\pi$
$163$	−2.43424	+	0.517414i	−0.190665	+	0.0405270i	0.111590	+	0.993754i	$0.464406\pi$
$164$	−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	−0.689216	−	0.724556i	$-0.742045\pi$
$167$	3.80261	−	11.7032i	0.294255	−	0.905624i	0.983471	−	0.181068i	$-0.0579553\pi$
$168$		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	−0.0635449	−	0.997979i	$-0.520241\pi$
$173$	−11.1499	−	4.96423i	−0.847708	−	0.377424i	−0.784163	+	0.620555i	$0.786907\pi$
$174$		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	0.999267	+	0.0382910i	$0.0121914\pi$
$179$	0.398664	+	3.79303i	0.0297975	+	0.283504i	−0.969469	+	0.245213i	$0.921142\pi$
$180$		0			0
$181$	2.17667	+	6.69911i	0.161791	+	0.497941i	0.998785	−	0.0492703i	$-0.0156896\pi$
$181$	2.17667	+	6.69911i	0.161791	+	0.497941i	−0.836995	+	0.547211i	$0.815690\pi$
$182$	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	0.752616	+	0.658460i	$0.228792\pi$
$191$	−1.66472	+	15.8388i	−0.120455	+	1.14605i	−0.873071	+	0.487593i	$0.837875\pi$
$192$		0			0
$193$	−14.4744	−	3.07662i	−1.04189	−	0.221460i	−0.344972	−	0.938613i	$-0.612112\pi$
$193$	−14.4744	−	3.07662i	−1.04189	−	0.221460i	−0.696916	+	0.717153i	$0.745445\pi$
$194$	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	0.335509	+	0.942037i	$0.391092\pi$
$199$	−9.14220	+	15.8348i	−0.648073	+	1.12250i	−0.983582	+	0.180459i	$0.942242\pi$
$200$	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	−0.303370	−	0.952873i	$-0.598112\pi$
$211$	7.29409	−	22.4489i	0.502146	−	1.54545i	0.805516	−	0.592573i	$-0.201888\pi$
$212$	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	−0.210485	−	0.977597i	$-0.567504\pi$
$223$	9.76962	−	7.09804i	0.654222	−	0.475320i	0.864707	+	0.502277i	$0.167504\pi$
$224$	−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	−0.0690091	−	0.997616i	$-0.521984\pi$
$227$	9.43447	−	4.20050i	0.626188	−	0.278797i	0.695197	+	0.718819i	$0.255317\pi$
$228$		0			0
$229$	26.9582	−	5.73015i	1.78145	−	0.378659i	0.804809	−	0.593534i	$-0.202268\pi$
$229$	26.9582	−	5.73015i	1.78145	−	0.378659i	0.976641	+	0.214875i	$0.0689345\pi$
$230$	6.32476			0.417042
$231$		0			0
$232$	−38.3233			−2.51605
$233$	3.91278	−	0.831687i	0.256335	−	0.0544856i	−0.0779518	−	0.996957i	$-0.524838\pi$
$233$	3.91278	−	0.831687i	0.256335	−	0.0544856i	0.334286	+	0.942472i	$0.391505\pi$
$234$		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	0.127897	−	0.991787i	$-0.459177\pi$
$239$	17.1705	−	12.4751i	1.11067	−	0.806946i	0.982768	+	0.184842i	$0.0591772\pi$
$240$		0			0
$241$	6.80326	−	11.7836i	0.438237	−	0.759048i	−0.559317	−	0.828954i	$-0.688936\pi$
$241$	6.80326	−	11.7836i	0.438237	−	0.759048i	0.997554	+	0.0699056i	$0.0222698\pi$
$242$	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	−0.650627	−	0.759398i	$-0.725494\pi$
$251$	5.10309	−	15.7057i	0.322104	−	0.991334i	0.972731	−	0.231937i	$-0.0745062\pi$
$252$		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	−0.311713	−	0.950176i	$-0.600903\pi$
$257$	3.05781	−	29.0931i	0.190741	−	1.81478i	0.502454	−	0.864604i	$-0.332430\pi$
$258$		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	0.375936	+	0.926646i	$0.377321\pi$
$263$	−9.96601	+	17.2616i	−0.614530	+	1.06440i	−0.990467	+	0.137752i	$0.956012\pi$
$264$		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	0.226324	−	0.974052i	$-0.427329\pi$
$269$	0.605177	+	0.128634i	0.0368983	+	0.00784298i	−0.189426	+	0.981895i	$0.560663\pi$
$270$		0			0
$271$	0.0121050	−	0.115172i	0.000735328	−	0.00699618i	−0.994148	−	0.108026i	$-0.965547\pi$
$271$	0.0121050	−	0.115172i	0.000735328	−	0.00699618i	0.994883	+	0.101030i	$0.0322137\pi$
$272$	−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	0.905398	−	0.424564i	$-0.139573\pi$
$277$	6.46626	+	7.18151i	0.388520	+	0.431495i	−0.516878	+	0.856059i	$0.672906\pi$
$278$	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	0.977891	−	0.209114i	$-0.0670579\pi$
$281$	1.07026	+	3.29393i	0.0638466	+	0.196500i	−0.914045	+	0.405613i	$0.867058\pi$
$282$		0			0
$283$	−2.75322	−	26.1952i	−0.163662	−	1.55714i	−0.700621	−	0.713533i	$-0.747094\pi$
$283$	−2.75322	−	26.1952i	−0.163662	−	1.55714i	0.536959	−	0.843608i	$-0.319573\pi$
$284$	−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	0.887234	−	0.461319i	$-0.152624\pi$
$293$	12.3700	+	8.98734i	0.722664	+	0.525046i	−0.164570	+	0.986365i	$0.552624\pi$
$294$		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	0.999004	−	0.0446110i	$-0.0142048\pi$
$311$	0.221418	+	2.10666i	0.0125555	+	0.119458i	−0.986449	+	0.164069i	$0.947538\pi$
$312$		0			0
$313$	−4.10743	+	4.56176i	−0.232166	+	0.257846i	−0.847959	−	0.530062i	$-0.822169\pi$
$313$	−4.10743	+	4.56176i	−0.232166	+	0.257846i	0.615794	+	0.787907i	$0.288835\pi$
$314$	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	−0.668394	−	0.743808i	$-0.733018\pi$
$317$	−17.3855	+	3.69540i	−0.976468	+	0.207555i	−0.308074	+	0.951362i	$0.599684\pi$
$318$		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	−0.999027	−	0.0441108i	$-0.985955\pi$
$331$	−9.78286	−	16.9444i	−0.537714	−	0.931349i	0.461312	−	0.887238i	$-0.347379\pi$
$332$	−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	−0.0508925	−	0.998704i	$-0.516207\pi$
$337$	−18.6594	−	13.5569i	−1.01644	−	0.738489i	−0.965551	+	0.260215i	$0.916207\pi$
$338$	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	−0.503514	−	0.863987i	$-0.667960\pi$
$347$	−24.4941	−	5.20638i	−1.31491	−	0.279493i	−0.811398	+	0.584494i	$0.801293\pi$
$348$		0			0
$349$	−15.8320	+	11.5026i	−0.847467	+	0.615721i	−0.924446	−	0.381312i	$-0.875472\pi$
$349$	−15.8320	+	11.5026i	−0.847467	+	0.615721i	0.0769797	+	0.997033i	$0.475472\pi$
$350$	−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	−0.460704	−	0.887554i	$-0.652403\pi$
$353$	10.1136	−	17.5172i	0.538292	−	0.932349i	0.998996	−	0.0447952i	$-0.0142635\pi$
$354$		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	0.680405	+	0.732836i	$0.261804\pi$
$359$	−2.60519	+	24.7867i	−0.137497	+	1.30819i	−0.817902	+	0.575357i	$0.804863\pi$
$360$		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	−0.220316	−	0.975429i	$-0.570709\pi$
$367$	6.84200	−	3.04625i	0.357149	−	0.159013i	0.577465	+	0.816416i	$0.304042\pi$
$368$	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	0.886053	−	0.463584i	$-0.153437\pi$
$373$	0.802488	+	1.38995i	0.0415513	+	0.0719689i	−0.844502	+	0.535553i	$0.820103\pi$
$374$	−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	0.990356	+	0.138547i	$0.0442433\pi$
$379$	5.26757	+	16.2119i	0.270577	+	0.832751i	−0.719779	+	0.694204i	$0.755757\pi$
$380$	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	−0.621566	−	0.783362i	$-0.713503\pi$
$383$	−17.0414	+	3.62225i	−0.870773	+	0.185089i	−0.249207	+	0.968450i	$0.580170\pi$
$384$		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	−0.129680	−	0.991556i	$-0.541395\pi$
$389$	10.2642	−	4.56993i	0.520417	−	0.231705i	0.650097	+	0.759851i	$0.274728\pi$
$390$		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	0.505412	−	0.862878i	$-0.331341\pi$
$397$	−9.85421	−	17.0680i	−0.494568	−	0.856618i	−0.999980	+	0.00626047i	$0.998007\pi$
$398$	−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	−0.496306	−	0.868147i	$-0.665311\pi$
$401$	8.38973	−	9.31774i	0.418963	−	0.465306i	0.915270	+	0.402842i	$0.131977\pi$
$402$		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	0.943773	−	0.330596i	$-0.107250\pi$
$409$	10.4423	+	11.5973i	0.516337	+	0.573450i	−0.427436	+	0.904046i	$0.640583\pi$
$410$	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	−0.948809	−	0.315849i	$-0.897711\pi$
$421$	−19.3204	+	14.0371i	−0.941617	+	0.684125i	0.00719220	+	0.999974i	$0.497711\pi$
$422$	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	0.862450	−	0.506142i	$-0.168929\pi$
$431$	5.58314	+	6.20070i	0.268930	+	0.298677i	−0.593520	+	0.804819i	$0.702262\pi$
$432$		0			0
$433$	−10.3850	−	7.54511i	−0.499069	−	0.362595i	0.309592	−	0.950869i	$-0.399807\pi$
$433$	−10.3850	−	7.54511i	−0.499069	−	0.362595i	−0.808661	+	0.588275i	$0.799807\pi$
$434$	−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	0.994623	+	0.103566i	$0.0330253\pi$
$439$	12.2991	+	21.3026i	0.587002	+	1.01672i	−0.407620	+	0.913151i	$0.633641\pi$
$440$	−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	0.725691	−	0.688020i	$-0.241520\pi$
$443$	14.7328	+	6.55945i	0.699975	+	0.311649i	−0.0257164	+	0.999669i	$0.508187\pi$
$444$		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	0.302200	+	0.953245i	$0.402279\pi$
$449$	−10.6496	+	32.7763i	−0.502588	+	1.54681i	−0.804788	+	0.593562i	$0.797721\pi$
$450$		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	−0.0239074	+	0.999714i	$0.507611\pi$
$457$	−21.7120	+	24.1137i	−1.01565	+	1.12799i	−0.991739	+	0.128275i	$0.959056\pi$
$458$	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	−0.988195	−	0.153201i	$-0.951042\pi$
$467$	−15.8303	+	17.5813i	−0.732539	+	0.813567i	0.255656	+	0.966768i	$0.417708\pi$
$468$		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	−0.0576623	−	0.998336i	$-0.518365\pi$
$479$	−11.3019	−	2.40230i	−0.516399	−	0.109764i	−0.458737	+	0.888572i	$0.651698\pi$
$480$		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	0.994205	−	0.107497i	$-0.0342836\pi$
$487$	−0.0137727	−	0.131038i	−0.000624101	−	0.00593792i	−0.994830	+	0.101559i	$0.967617\pi$
$488$	−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	0.587378	−	0.809313i	$-0.300160\pi$
$491$	−0.0180456	−	0.0131109i	−0.000814388	−	0.000591687i	−0.588192	+	0.808721i	$0.700160\pi$
$492$		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	−0.966276	−	0.257509i	$-0.917098\pi$
$499$	0.724289	−	6.89115i	0.0324236	−	0.308490i	0.998700	−	0.0509816i	$-0.0162350\pi$
$500$	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	−0.728818	−	0.684707i	$-0.759930\pi$
$503$	−6.79200	+	4.93468i	−0.302840	+	0.220026i	0.425978	+	0.904734i	$0.359930\pi$
$504$		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	0.431685	−	0.902024i	$-0.357919\pi$
$509$	1.13266	+	0.504291i	0.0502041	+	0.0223523i	−0.381481	+	0.924377i	$0.624586\pi$
$510$		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	−0.759166	+	0.650897i	$0.774393\pi$
$521$	−39.9641	+	17.7932i	−1.75086	+	0.779532i	−0.991692	+	0.128635i	$0.958940\pi$
$522$		0			0
$523$	−20.4158	+	22.6740i	−0.892721	+	0.991467i	−0.999996	−	0.00276239i	$-0.999121\pi$
$523$	−20.4158	+	22.6740i	−0.892721	+	0.991467i	0.107275	+	0.994229i	$0.465787\pi$
$524$	−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	−0.213877	−	0.976861i	$-0.568609\pi$
$541$	−0.277681	+	0.0590230i	−0.0119384	+	0.00253760i	0.201939	+	0.979398i	$0.435276\pi$
$542$	−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	−0.758256	−	0.651957i	$-0.773948\pi$
$547$	−8.71258	+	6.33006i	−0.372523	+	0.270654i	0.385733	+	0.922610i	$0.373948\pi$
$548$	−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	−0.989834	−	0.142225i	$-0.954574\pi$
$557$	−36.4980	+	16.2499i	−1.54647	+	0.688532i	−0.556634	+	0.830758i	$0.687908\pi$
$558$		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	0.887624	−	0.460568i	$-0.152354\pi$
$563$	7.99139	+	8.87534i	0.336797	+	0.374051i	−0.550827	+	0.834619i	$0.685688\pi$
$564$		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	0.605995	−	0.795468i	$-0.292775\pi$
$569$	10.0266	+	4.46414i	0.420337	+	0.187146i	−0.185658	+	0.982614i	$0.559442\pi$
$570$		0			0
$571$	−3.74628	+	6.48874i	−0.156777	+	0.271545i	−0.933705	−	0.358044i	$-0.883444\pi$
$571$	−3.74628	+	6.48874i	−0.156777	+	0.271545i	0.776928	+	0.629590i	$0.216777\pi$
$572$	−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	0.868220	−	0.496180i	$-0.165264\pi$
$577$	35.0599	+	7.45221i	1.45956	+	0.310240i	0.591343	+	0.806420i	$0.298598\pi$
$578$	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	0.742548	−	0.669793i	$-0.233617\pi$
$587$	8.11634	+	5.89686i	0.334997	+	0.243390i	−0.407551	+	0.913182i	$0.633617\pi$
$588$		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	0.995248	+	0.0973765i	$0.0310451\pi$
$593$	14.1715	+	24.5458i	0.581954	+	1.00797i	−0.413293	+	0.910598i	$0.635622\pi$
$594$		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	0.819197	−	0.573512i	$-0.194419\pi$
$599$	32.6564	+	6.94133i	1.33430	+	0.283615i	0.515106	+	0.857127i	$0.327753\pi$
$600$		0			0
$601$	1.42697	+	1.03676i	0.0582074	+	0.0422901i	0.616508	−	0.787348i	$-0.288547\pi$
$601$	1.42697	+	1.03676i	0.0582074	+	0.0422901i	−0.558301	+	0.829638i	$0.688547\pi$
$602$	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	0.0850370	−	0.996378i	$-0.472899\pi$
$607$	13.9937	−	2.97445i	0.567985	−	0.120729i	0.482948	+	0.875649i	$0.339566\pi$
$608$	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	0.999943	+	0.0106405i	$0.00338703\pi$
$613$	0.595783	+	5.66850i	0.0240634	+	0.228948i	−0.975880	+	0.218308i	$0.929946\pi$
$614$	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	−0.999837	−	0.0180353i	$-0.994259\pi$
$619$	−0.636885	−	6.05956i	−0.0255986	−	0.243554i	0.974239	−	0.225519i	$-0.0724078\pi$
$620$	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	−0.990704	−	0.136036i	$-0.956564\pi$
$631$	−35.8264	−	26.0294i	−1.42623	−	1.03621i	−0.435522	−	0.900178i	$-0.643436\pi$
$632$	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	0.729575	+	0.683901i	$0.239718\pi$
$641$	4.00363	+	38.0920i	0.158134	+	1.50454i	−0.571441	+	0.820643i	$0.693615\pi$
$642$		0			0
$643$	−8.87538	−	27.3156i	−0.350011	−	1.07722i	−0.958846	−	0.283926i	$-0.908363\pi$
$643$	−8.87538	−	27.3156i	−0.350011	−	1.07722i	0.608835	−	0.793297i	$-0.291637\pi$
$644$	−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	0.949550	−	0.313614i	$-0.101540\pi$
$647$	13.6948	+	15.2096i	0.538399	+	0.597953i	−0.411152	+	0.911567i	$0.634873\pi$
$648$		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	−0.770875	−	0.636986i	$-0.780181\pi$
$653$	2.95381	−	28.1036i	0.115591	−	1.09978i	0.886467	−	0.462793i	$-0.153153\pi$
$654$		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	−0.994063	−	0.108803i	$-0.965298\pi$
$661$	−10.3561	+	17.9373i	−0.402805	+	0.697679i	0.591258	+	0.806483i	$0.298632\pi$
$662$	−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	0.763527	+	0.645776i	$0.223466\pi$
$673$	−6.06417	+	18.6636i	−0.233757	+	0.719429i	−0.997284	+	0.0736535i	$0.976534\pi$
$674$	−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	−0.961163	−	0.275981i	$-0.910997\pi$
$677$	−15.2531	+	16.9403i	−0.586226	+	0.651070i	0.374938	+	0.927050i	$0.377664\pi$
$678$		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	−0.998867	−	0.0475871i	$-0.984847\pi$
$683$	−11.9753	+	20.7418i	−0.458222	+	0.793664i	0.540645	+	0.841251i	$0.318180\pi$
$684$		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	−0.892115	−	0.451808i	$-0.850779\pi$
$691$	−40.0438	+	8.51156i	−1.52334	+	0.323795i	−0.631221	+	0.775603i	$0.717446\pi$
$692$	−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	−0.425124	−	0.905135i	$-0.639769\pi$
$701$	8.05784	−	5.85436i	0.304340	−	0.221116i	0.729464	+	0.684019i	$0.239769\pi$
$702$		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	−0.261574	+	0.965183i	$0.584242\pi$
$709$	−31.7961	+	35.3132i	−1.19413	+	1.32621i	−0.932554	+	0.361031i	$0.882425\pi$
$710$	−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	−0.886181	−	0.463340i	$-0.846651\pi$
$719$	2.06385	−	19.6362i	0.0769686	−	0.732307i	0.963149	−	0.268968i	$-0.0866824\pi$
$720$		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	0.789086	+	0.614282i	$0.210554\pi$
$733$	−2.99094	+	28.4569i	−0.110473	+	1.05108i	−0.899559	+	0.436798i	$0.856112\pi$
$734$	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	0.844237	−	0.535970i	$-0.180054\pi$
$739$	6.06096	+	6.73137i	0.222956	+	0.247618i	−0.621281	+	0.783588i	$0.713387\pi$
$740$	−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	0.892518	−	0.451012i	$-0.148937\pi$
$743$	−2.57977	−	7.93973i	−0.0946427	−	0.291280i	−0.987160	+	0.159732i	$0.948937\pi$
$744$		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	0.999323	−	0.0367995i	$-0.0117163\pi$
$751$	44.9611	+	20.0180i	1.64065	+	0.730466i	0.641330	+	0.767265i	$0.278383\pi$
$752$	−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	−0.742890	−	0.669413i	$-0.766546\pi$
$757$	6.92221	−	21.3044i	0.251592	−	0.774320i	0.994482	−	0.104907i	$-0.0334545\pi$
$758$	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	−0.634665	−	0.772787i	$-0.718862\pi$
$761$	−24.8315	+	5.27809i	−0.900140	+	0.191331i	−0.265474	+	0.964118i	$0.585529\pi$
$762$		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	0.862035	+	0.506848i	$0.169190\pi$
$773$	3.45360	+	32.8588i	0.124217	+	1.18185i	−0.737818	+	0.675000i	$0.764144\pi$
$774$		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	−0.619981	−	0.784617i	$-0.712860\pi$
$787$	−42.2344	−	8.97720i	−1.50549	−	0.320003i	−0.885513	+	0.464615i	$0.846193\pi$
$788$	−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	0.992433	−	0.122785i	$-0.0391825\pi$
$797$	3.31341	+	10.1976i	0.117367	+	0.361218i	−0.875066	+	0.484003i	$0.839182\pi$
$798$		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	0.188085	−	0.982153i	$-0.439772\pi$
$809$	−1.12546	−	0.239224i	−0.0395690	−	0.00841066i	−0.227654	+	0.973742i	$0.573105\pi$
$810$		0			0
$811$	28.6938	−	20.8473i	1.00758	−	0.732047i	0.0438772	−	0.999037i	$-0.486029\pi$
$811$	28.6938	−	20.8473i	1.00758	−	0.732047i	0.963699	+	0.266990i	$0.0860290\pi$
$812$	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	−0.897796	−	0.440411i	$-0.854833\pi$
$821$	2.06152	−	19.6140i	0.0719475	−	0.684535i	0.969744	−	0.244124i	$-0.0785005\pi$
$822$		0			0
$823$	27.3181	+	30.3398i	0.952248	+	1.05758i	0.998279	+	0.0586382i	$0.0186758\pi$
$823$	27.3181	+	30.3398i	0.952248	+	1.05758i	−0.0460316	+	0.998940i	$0.514658\pi$
$824$	−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	−0.945894	−	0.324476i	$-0.894812\pi$
$827$	0.289657	−	0.891474i	0.0100724	−	0.0309996i	0.955966	+	0.293476i	$0.0948121\pi$
$828$		0			0
$829$	−13.9732	+	6.22128i	−0.485310	+	0.216074i	−0.634781	−	0.772692i	$-0.718910\pi$
$829$	−13.9732	+	6.22128i	−0.485310	+	0.216074i	0.149471	+	0.988766i	$0.452243\pi$
$830$	−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	−0.374166	−	0.927362i	$-0.622071\pi$
$839$	11.3598	−	8.25338i	0.392184	−	0.284938i	0.766350	+	0.642423i	$0.222071\pi$
$840$		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	0.968567	−	0.248751i	$-0.0800201\pi$
$853$	1.13225	+	3.48472i	0.0387677	+	0.119315i	−0.929800	+	0.368066i	$0.880020\pi$
$854$	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	−0.819752	−	0.572718i	$-0.805889\pi$
$857$	2.52090	−	4.36633i	0.0861124	−	0.149151i	0.905865	+	0.423567i	$0.139222\pi$
$858$		0			0
$859$	−26.8888	−	46.5728i	−0.917434	−	1.58904i	−0.803298	−	0.595578i	$-0.796923\pi$
$859$	−26.8888	−	46.5728i	−0.917434	−	1.58904i	−0.114137	−	0.993465i	$-0.536410\pi$
$860$	−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	−0.233529	−	0.972350i	$-0.575027\pi$
$863$	22.2649	−	24.7276i	0.757904	−	0.841738i	0.991434	+	0.130612i	$0.0416941\pi$
$864$		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	0.193475	−	0.981105i	$-0.438024\pi$
$877$	−12.0283	−	5.35537i	−0.406168	−	0.180838i	−0.599643	+	0.800267i	$0.704691\pi$
$878$	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	−0.0764906	−	0.997070i	$-0.524372\pi$
$883$	25.2028	−	18.3109i	0.848143	−	0.616212i	0.924633	+	0.380859i	$0.124372\pi$
$884$	−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	0.768320	+	0.640066i	$0.221093\pi$
$887$	−3.46334	+	32.9515i	−0.116288	+	1.10640i	−0.884608	+	0.466336i	$0.845574\pi$
$888$		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	0.0200127	−	0.999800i	$-0.493629\pi$
$907$	−11.0937	−	2.35804i	−0.368360	−	0.0782973i	−0.388373	+	0.921502i	$0.626963\pi$
$908$	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	−0.682966	−	0.730450i	$-0.739310\pi$
$911$	9.02202	−	27.7669i	0.298913	−	0.919959i	0.981879	−	0.189509i	$-0.0606897\pi$
$912$		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	−0.560780	−	0.827965i	$-0.689499\pi$
$919$	9.73920	−	10.8165i	0.321266	−	0.356803i	0.882047	+	0.471162i	$0.156165\pi$
$920$	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	−0.666604	−	0.745412i	$-0.732253\pi$
$929$	4.40136	−	4.88821i	0.144404	−	0.160377i	0.811008	+	0.585035i	$0.198919\pi$
$930$		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	0.672833	+	0.739794i	$0.265077\pi$
$937$	−9.37722	+	28.8601i	−0.306340	+	0.942818i	−0.979174	+	0.203024i	$0.934923\pi$
$938$	−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	−0.0416850	−	0.999131i	$-0.513273\pi$
$941$	−14.9130	−	3.16985i	−0.486149	−	0.103334i	−0.444464	+	0.895797i	$0.646606\pi$
$942$		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	0.999966	+	0.00818941i	$0.00260680\pi$
$947$	15.6044	+	27.0276i	0.507075	+	0.878280i	−0.492891	+	0.870091i	$0.664060\pi$
$948$		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	0.833774	−	0.552105i	$-0.186175\pi$
$953$	17.4834	+	12.7024i	0.566342	+	0.411471i	−0.267433	+	0.963577i	$0.586175\pi$
$954$		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	0.504848	−	0.863208i	$-0.331549\pi$
$971$	6.26859	+	2.79096i	0.201169	+	0.0895660i	−0.303679	+	0.952774i	$0.598215\pi$
$972$		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	0.844237	−	0.535971i	$-0.180054\pi$
$977$	6.96892	+	7.73977i	0.222955	+	0.247617i	−0.621281	+	0.783588i	$0.713388\pi$
$978$		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	−0.623179	−	0.782079i	$-0.714159\pi$
$983$	−14.3900	+	6.40682i	−0.458969	+	0.204346i	0.164210	+	0.986425i	$0.447492\pi$
$984$		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	−0.923264	−	0.384167i	$-0.874489\pi$
$991$	−4.05884	+	7.03011i	−0.128933	+	0.223319i	0.794330	+	0.607486i	$0.207822\pi$
$992$	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	−0.904744	−	0.425956i	$-0.859938\pi$
$997$	−37.6879	+	16.7797i	−1.19359	+	0.531420i	−0.288845	+	0.957376i	$0.593271\pi$
$998$	−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.361.5		40
3.2	odd	2		77.2.m.b.53.1	yes	40
7.2	even	3	inner	693.2.by.b.163.1		40
11.5	even	5	inner	693.2.by.b.676.1		40
21.2	odd	6		77.2.m.b.9.5	✓	40
21.5	even	6		539.2.q.h.471.5		40
21.11	odd	6		539.2.f.h.295.5		20
21.17	even	6		539.2.f.g.295.5		20
21.20	even	2		539.2.q.h.361.1		40
33.2	even	10		847.2.n.h.487.1		40
33.5	odd	10		77.2.m.b.60.5	yes	40
33.8	even	10		847.2.n.h.81.5		40
33.14	odd	10		847.2.n.i.81.1		40
33.17	even	10		847.2.n.j.753.1		40
33.20	odd	10		847.2.n.i.487.5		40
33.26	odd	10		847.2.e.i.606.1		20
33.29	even	10		847.2.e.h.606.10		20
33.32	even	2		847.2.n.j.130.5		40
77.16	even	15	inner	693.2.by.b.478.5		40
231.2	even	30		847.2.n.h.366.5		40
231.5	even	30		539.2.q.h.324.1		40
231.38	even	30		539.2.f.g.148.5		20
231.59	even	30		5929.2.a.bx.1.10		10
231.65	even	6		847.2.n.j.9.1		40
231.86	odd	30		847.2.n.i.366.1		40
231.95	even	30		5929.2.a.by.1.1		10
231.104	even	10		539.2.q.h.214.5		40
231.107	even	30		847.2.n.h.807.1		40
231.128	even	30		847.2.e.h.485.10		20
231.137	odd	30		539.2.f.h.148.5		20
231.149	even	30		847.2.n.j.632.5		40
231.158	odd	30		5929.2.a.bw.1.10		10
231.170	odd	30		77.2.m.b.16.1	yes	40
231.191	odd	30		847.2.e.i.485.1		20
231.212	odd	30		847.2.n.i.807.5		40
231.227	odd	30		5929.2.a.bz.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.5	✓	40	21.2	odd	6
77.2.m.b.16.1	yes	40	231.170	odd	30
77.2.m.b.53.1	yes	40	3.2	odd	2
77.2.m.b.60.5	yes	40	33.5	odd	10
539.2.f.g.148.5		20	231.38	even	30
539.2.f.g.295.5		20	21.17	even	6
539.2.f.h.148.5		20	231.137	odd	30
539.2.f.h.295.5		20	21.11	odd	6
539.2.q.h.214.5		40	231.104	even	10
539.2.q.h.324.1		40	231.5	even	30
539.2.q.h.361.1		40	21.20	even	2
539.2.q.h.471.5		40	21.5	even	6
693.2.by.b.163.1		40	7.2	even	3	inner
693.2.by.b.361.5		40	1.1	even	1	trivial
693.2.by.b.478.5		40	77.16	even	15	inner
693.2.by.b.676.1		40	11.5	even	5	inner
847.2.e.h.485.10		20	231.128	even	30
847.2.e.h.606.10		20	33.29	even	10
847.2.e.i.485.1		20	231.191	odd	30
847.2.e.i.606.1		20	33.26	odd	10
847.2.n.h.81.5		40	33.8	even	10
847.2.n.h.366.5		40	231.2	even	30
847.2.n.h.487.1		40	33.2	even	10
847.2.n.h.807.1		40	231.107	even	30
847.2.n.i.81.1		40	33.14	odd	10
847.2.n.i.366.1		40	231.86	odd	30
847.2.n.i.487.5		40	33.20	odd	10
847.2.n.i.807.5		40	231.212	odd	30
847.2.n.j.9.1		40	231.65	even	6
847.2.n.j.130.5		40	33.32	even	2
847.2.n.j.632.5		40	231.149	even	30
847.2.n.j.753.1		40	33.17	even	10
5929.2.a.bw.1.10		10	231.158	odd	30
5929.2.a.bx.1.10		10	231.59	even	30
5929.2.a.by.1.1		10	231.95	even	30
5929.2.a.bz.1.1		10	231.227	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

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