LMFDB - Embedded newform 297.2.n.a.280.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([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("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			280.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	297.280
Dual form			297.2.n.a.262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.255585 - 0.283856i) q^{2} +(0.193806 + 1.84395i) q^{4} +(0.827091 + 0.918578i) q^{5} +(-0.913545 - 0.406737i) q^{7} +(1.19098 + 0.865300i) q^{8} +O(q^{10})$	\(q+(0.255585 - 0.283856i) q^{2} +(0.193806 + 1.84395i) q^{4} +(0.827091 + 0.918578i) q^{5} +(-0.913545 - 0.406737i) q^{7} +(1.19098 + 0.865300i) q^{8} +0.472136 q^{10} +(-2.70528 + 1.91872i) q^{11} +(6.33070 + 1.34563i) q^{13} +(-0.348943 + 0.155360i) q^{14} +(-3.07715 + 0.654069i) q^{16} +(-1.50000 + 4.61653i) q^{17} +(-0.809017 - 0.587785i) q^{19} +(-1.53351 + 1.70314i) q^{20} +(-0.146790 + 1.25830i) q^{22} +(2.30902 - 3.99933i) q^{23} +(0.362937 - 3.45312i) q^{25} +(2.00000 - 1.45309i) q^{26} +(0.572949 - 1.76336i) q^{28} +(4.43444 + 1.97434i) q^{29} +(-0.604528 - 0.128496i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 + 1.60570i) q^{34} +(-0.381966 - 1.17557i) q^{35} +(4.11803 - 2.99193i) q^{37} +(-0.373619 + 0.0794152i) q^{38} +(0.190206 + 1.80969i) q^{40} +(2.30932 - 1.02817i) q^{41} +(-0.927051 - 1.60570i) q^{43} +(-4.06231 - 4.61653i) q^{44} +(-0.545085 - 1.67760i) q^{46} +(1.24852 - 11.8788i) q^{47} +(-4.01478 - 4.45887i) q^{49} +(-0.887426 - 0.985587i) q^{50} +(-1.25434 + 11.9343i) q^{52} +(-1.26393 - 3.88998i) q^{53} +(-4.00000 - 0.898056i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.69381 - 0.754131i) q^{58} +(0.169131 + 1.60917i) q^{59} +(-10.6169 + 2.25669i) q^{61} +(-0.190983 + 0.138757i) q^{62} +(-1.45492 - 4.47777i) q^{64} +(4.00000 + 6.92820i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(-8.80333 - 1.87121i) q^{68} +(-0.431318 - 0.192035i) q^{70} +(0.899187 - 2.76741i) q^{71} +(0.118034 - 0.0857567i) q^{73} +(0.203232 - 1.93362i) q^{74} +(0.927051 - 1.60570i) q^{76} +(3.25181 - 0.652498i) q^{77} +(7.06756 - 7.84932i) q^{79} +(-3.14590 - 2.28563i) q^{80} +(0.298374 - 0.918300i) q^{82} +(-9.55057 + 2.03004i) q^{83} +(-5.48127 + 2.44042i) q^{85} +(-0.692728 - 0.147244i) q^{86} +(-4.88220 - 0.0557196i) q^{88} +6.76393 q^{89} +(-5.23607 - 3.80423i) q^{91} +(7.82206 + 3.48260i) q^{92} +(-3.05278 - 3.39045i) q^{94} +(-0.129204 - 1.22930i) q^{95} +(4.01478 - 4.45887i) q^{97} -2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8	$ 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28} + 9 q^{29} - 3 q^{31} - 30 q^{32} - 6 q^{34} - 12 q^{35} + 24 q^{37} + 4 q^{38} + 12 q^{40} - 3 q^{41} + 6 q^{43} + 48 q^{44} + 18 q^{46} - 23 q^{47} - 6 q^{49} + 24 q^{50} + 12 q^{52} - 28 q^{53} - 32 q^{55} + 12 q^{56} + 6 q^{58} - 3 q^{59} - 6 q^{62} - 34 q^{64} + 32 q^{65} - 24 q^{67} + 9 q^{68} - 6 q^{70} - 42 q^{71} - 8 q^{73} - 13 q^{74} - 6 q^{76} + 11 q^{77} - 22 q^{79} - 52 q^{80} - 96 q^{82} + 17 q^{83} - 6 q^{85} - 21 q^{86} + 37 q^{88} + 72 q^{89} - 24 q^{91} + 21 q^{92} + 28 q^{94} + 4 q^{95} + 6 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8 - 32 * q^10 - q^11 + 8 * q^13 + q^14 + 14 * q^16 - 12 * q^17 - 2 * q^19 - 24 * q^20 + 11 * q^22 + 14 * q^23 - 9 * q^25 + 16 * q^26 + 18 * q^28 + 9 * q^29 - 3 * q^31 - 30 * q^32 - 6 * q^34 - 12 * q^35 + 24 * q^37 + 4 * q^38 + 12 * q^40 - 3 * q^41 + 6 * q^43 + 48 * q^44 + 18 * q^46 - 23 * q^47 - 6 * q^49 + 24 * q^50 + 12 * q^52 - 28 * q^53 - 32 * q^55 + 12 * q^56 + 6 * q^58 - 3 * q^59 - 6 * q^62 - 34 * q^64 + 32 * q^65 - 24 * q^67 + 9 * q^68 - 6 * q^70 - 42 * q^71 - 8 * q^73 - 13 * q^74 - 6 * q^76 + 11 * q^77 - 22 * q^79 - 52 * q^80 - 96 * q^82 + 17 * q^83 - 6 * q^85 - 21 * q^86 + 37 * q^88 + 72 * q^89 - 24 * q^91 + 21 * q^92 + 28 * q^94 + 4 * q^95 + 6 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.255585	−	0.283856i	0.180726	−	0.200717i	−0.645974	−	0.763359i	$-0.723549\pi$
$2$	0.255585	−	0.283856i	0.180726	−	0.200717i	0.826700	+	0.562643i	$0.190215\pi$
$3$		0			0
$3$		0			0
$4$	0.193806	+	1.84395i	0.0969032	+	0.921973i
$5$	0.827091	+	0.918578i	0.369886	+	0.410800i	0.899139	−	0.437664i	$-0.144194\pi$
$5$	0.827091	+	0.918578i	0.369886	+	0.410800i	−0.529252	+	0.848465i	$0.677527\pi$
$6$		0			0
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	0.226764	−	0.973950i	$-0.427186\pi$
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	−0.572051	+	0.820218i	$0.693852\pi$
$8$	1.19098	+	0.865300i	0.421076	+	0.305930i
$9$		0			0
$10$	0.472136			0.149302
$11$	−2.70528	+	1.91872i	−0.815672	+	0.578514i
$11$	−2.70528	+	1.91872i	−0.815672	+	0.578514i
$12$		0			0
$13$	6.33070	+	1.34563i	1.75582	+	0.373211i	0.969593	−	0.244724i	$-0.0786974\pi$
$13$	6.33070	+	1.34563i	1.75582	+	0.373211i	0.786229	+	0.617936i	$0.212031\pi$
$14$	−0.348943	+	0.155360i	−0.0932590	+	0.0415216i
$15$		0			0
$16$	−3.07715	+	0.654069i	−0.769288	+	0.163517i
$17$	−1.50000	+	4.61653i	−0.363803	+	1.11967i	0.586924	+	0.809642i	$0.300339\pi$
$17$	−1.50000	+	4.61653i	−0.363803	+	1.11967i	−0.950727	+	0.310029i	$0.899661\pi$
$18$		0			0
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	0.491105	−	0.871100i	$-0.336593\pi$
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	−0.676706	+	0.736253i	$0.736593\pi$
$20$	−1.53351	+	1.70314i	−0.342903	+	0.380833i
$21$		0			0
$22$	−0.146790	+	1.25830i	−0.0312957	+	0.268271i
$23$	2.30902	−	3.99933i	0.481463	−	0.833919i	−0.518310	−	0.855193i	$-0.673439\pi$
$23$	2.30902	−	3.99933i	0.481463	−	0.833919i	0.999774	+	0.0212736i	$0.00677212\pi$
$24$		0			0
$25$	0.362937	−	3.45312i	0.0725874	−	0.690623i
$26$	2.00000	−	1.45309i	0.392232	−	0.284973i
$27$		0			0
$28$	0.572949	−	1.76336i	0.108277	−	0.333243i
$29$	4.43444	+	1.97434i	0.823455	+	0.366626i	0.774813	−	0.632190i	$-0.217844\pi$
$29$	4.43444	+	1.97434i	0.823455	+	0.366626i	0.0486422	+	0.998816i	$0.484511\pi$
$30$		0			0
$31$	−0.604528	−	0.128496i	−0.108577	−	0.0230787i	0.153303	−	0.988179i	$-0.451009\pi$
$31$	−0.604528	−	0.128496i	−0.108577	−	0.0230787i	−0.261879	+	0.965101i	$0.584342\pi$
$32$	−2.07295	+	3.59045i	−0.366449	+	0.634708i
$33$		0			0
$34$	0.927051	+	1.60570i	0.158988	+	0.275375i
$35$	−0.381966	−	1.17557i	−0.0645640	−	0.198708i
$36$		0			0
$37$	4.11803	−	2.99193i	0.677001	−	0.491870i	−0.195361	−	0.980731i	$-0.562588\pi$
$37$	4.11803	−	2.99193i	0.677001	−	0.491870i	0.872361	+	0.488862i	$0.162588\pi$
$38$	−0.373619	+	0.0794152i	−0.0606090	+	0.0128828i
$39$		0			0
$40$	0.190206	+	1.80969i	0.0300743	+	0.286137i
$41$	2.30932	−	1.02817i	0.360655	−	0.160574i	−0.218406	−	0.975858i	$-0.570086\pi$
$41$	2.30932	−	1.02817i	0.360655	−	0.160574i	0.579061	+	0.815284i	$0.303419\pi$
$42$		0			0
$43$	−0.927051	−	1.60570i	−0.141374	−	0.244867i	0.786640	−	0.617412i	$-0.211819\pi$
$43$	−0.927051	−	1.60570i	−0.141374	−	0.244867i	−0.928014	+	0.372545i	$0.878485\pi$
$44$	−4.06231	−	4.61653i	−0.612416	−	0.695967i
$45$		0			0
$46$	−0.545085	−	1.67760i	−0.0803684	−	0.247348i
$47$	1.24852	−	11.8788i	0.182115	−	1.73271i	−0.397313	−	0.917683i	$-0.630057\pi$
$47$	1.24852	−	11.8788i	0.182115	−	1.73271i	0.579428	−	0.815024i	$-0.303276\pi$
$48$		0			0
$49$	−4.01478	−	4.45887i	−0.573541	−	0.636981i
$50$	−0.887426	−	0.985587i	−0.125501	−	0.139383i
$51$		0			0
$52$	−1.25434	+	11.9343i	−0.173946	+	1.65498i
$53$	−1.26393	−	3.88998i	−0.173614	−	0.534330i	0.825953	−	0.563739i	$-0.190638\pi$
$53$	−1.26393	−	3.88998i	−0.173614	−	0.534330i	−0.999567	+	0.0294087i	$0.990638\pi$
$54$		0			0
$55$	−4.00000	−	0.898056i	−0.539360	−	0.121094i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$		0			0
$58$	1.69381	−	0.754131i	0.222408	−	0.0990223i
$59$	0.169131	+	1.60917i	0.0220189	+	0.209496i	1.00000		0.000801000i	$0.000254966\pi$
$59$	0.169131	+	1.60917i	0.0220189	+	0.209496i	−0.977981	+	0.208695i	$0.933078\pi$
$60$		0			0
$61$	−10.6169	+	2.25669i	−1.35936	+	0.288940i	−0.829196	−	0.558957i	$-0.811202\pi$
$61$	−10.6169	+	2.25669i	−1.35936	+	0.288940i	−0.530160	+	0.847898i	$0.677868\pi$
$62$	−0.190983	+	0.138757i	−0.0242549	+	0.0176222i
$63$		0			0
$64$	−1.45492	−	4.47777i	−0.181864	−	0.559721i
$65$	4.00000	+	6.92820i	0.496139	+	0.859338i
$66$		0			0
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	−8.80333	−	1.87121i	−1.06756	−	0.226917i
$69$		0			0
$70$	−0.431318	−	0.192035i	−0.0515523	−	0.0229526i
$71$	0.899187	−	2.76741i	0.106714	−	0.328431i	−0.883415	−	0.468591i	$-0.844762\pi$
$71$	0.899187	−	2.76741i	0.106714	−	0.328431i	0.990129	+	0.140160i	$0.0447617\pi$
$72$		0			0
$73$	0.118034	−	0.0857567i	0.0138148	−	0.0100371i	−0.580856	−	0.814006i	$-0.697282\pi$
$73$	0.118034	−	0.0857567i	0.0138148	−	0.0100371i	0.594671	+	0.803969i	$0.297282\pi$
$74$	0.203232	−	1.93362i	0.0236252	−	0.224779i
$75$		0			0
$76$	0.927051	−	1.60570i	0.106340	−	0.184186i
$77$	3.25181	−	0.652498i	0.370578	−	0.0743590i
$78$		0			0
$79$	7.06756	−	7.84932i	0.795163	−	0.883118i	−0.200156	−	0.979764i	$-0.564145\pi$
$79$	7.06756	−	7.84932i	0.795163	−	0.883118i	0.995319	+	0.0966462i	$0.0308115\pi$
$80$	−3.14590	−	2.28563i	−0.351722	−	0.255541i
$81$		0			0
$82$	0.298374	−	0.918300i	0.0329499	−	0.101409i
$83$	−9.55057	+	2.03004i	−1.04831	+	0.222825i	−0.699696	−	0.714441i	$-0.746681\pi$
$83$	−9.55057	+	2.03004i	−1.04831	+	0.222825i	−0.348615	+	0.937266i	$0.613348\pi$
$84$		0			0
$85$	−5.48127	+	2.44042i	−0.594528	+	0.264701i
$86$	−0.692728	−	0.147244i	−0.0746988	−	0.0158777i
$87$		0			0
$88$	−4.88220	−	0.0557196i	−0.520445	−	0.00593972i
$89$	6.76393			0.716975			0.358488	−	0.933534i	$-0.383293\pi$
$89$	6.76393			0.716975			0.358488	+	0.933534i	$0.383293\pi$
$90$		0			0
$91$	−5.23607	−	3.80423i	−0.548889	−	0.398791i
$92$	7.82206	+	3.48260i	0.815506	+	0.363087i
$93$		0			0
$94$	−3.05278	−	3.39045i	−0.314870	−	0.349699i
$95$	−0.129204	−	1.22930i	−0.0132561	−	0.126123i
$96$		0			0
$97$	4.01478	−	4.45887i	0.407640	−	0.452730i	−0.504010	−	0.863698i	$-0.668143\pi$
$97$	4.01478	−	4.45887i	0.407640	−	0.452730i	0.911650	+	0.410968i	$0.134809\pi$
$98$	−2.29180			−0.231506
$99$		0			0
$100$	6.43769			0.643769
$101$	5.66897	−	6.29602i	0.564083	−	0.626478i	−0.391862	−	0.920024i	$-0.628169\pi$
$101$	5.66897	−	6.29602i	0.564083	−	0.626478i	0.955945	+	0.293546i	$0.0948355\pi$
$102$		0			0
$103$	1.06996	+	10.1800i	0.105426	+	1.00306i	0.911514	+	0.411269i	$0.134914\pi$
$103$	1.06996	+	10.1800i	0.105426	+	1.00306i	−0.806088	+	0.591796i	$0.798419\pi$
$104$	6.37539	+	7.08058i	0.625158	+	0.694308i
$105$		0			0
$106$	−1.42724	−	0.635447i	−0.138626	−	0.0617201i
$107$	11.3541	+	8.24924i	1.09764	+	0.797484i	0.980673	−	0.195652i	$-0.0626822\pi$
$107$	11.3541	+	8.24924i	1.09764	+	0.797484i	0.116969	+	0.993136i	$0.462682\pi$
$108$		0			0
$109$	7.14590			0.684453			0.342226	−	0.939618i	$-0.388819\pi$
$109$	7.14590			0.684453			0.342226	+	0.939618i	$0.388819\pi$
$110$	−1.27726	+	0.905894i	−0.121782	+	0.0863737i
$111$		0			0
$112$	3.07715	+	0.654069i	0.290764	+	0.0618037i
$113$	−15.7459	+	7.01054i	−1.48125	+	0.659496i	−0.978746	−	0.205077i	$-0.934255\pi$
$113$	−15.7459	+	7.01054i	−1.48125	+	0.659496i	−0.502507	+	0.864573i	$0.667589\pi$
$114$		0			0
$115$	5.58347	−	1.18680i	0.520661	−	0.110670i
$116$	−2.78115	+	8.55951i	−0.258224	+	0.794730i
$117$		0			0
$118$	0.500000	+	0.363271i	0.0460287	+	0.0334418i
$119$	3.24803	−	3.60730i	0.297746	−	0.330681i
$120$		0			0
$121$	3.63706	−	10.3813i	0.330642	−	0.943756i
$122$	−2.07295	+	3.59045i	−0.187676	+	0.325064i
$123$		0			0
$124$	0.119779	−	1.13962i	0.0107565	−	0.102341i
$125$	8.47214	−	6.15537i	0.757771	−	0.550553i
$126$		0			0
$127$	−3.26393	+	10.0453i	−0.289627	+	0.891381i	0.695346	+	0.718675i	$0.255251\pi$
$127$	−3.26393	+	10.0453i	−0.289627	+	0.891381i	−0.984973	+	0.172706i	$0.944749\pi$
$128$	−9.21783	−	4.10404i	−0.814749	−	0.362749i
$129$		0			0
$130$	2.98895	+	0.635322i	0.262149	+	0.0557214i
$131$	10.6180	−	18.3910i	0.927702	−	1.60683i	0.140545	−	0.990074i	$-0.455115\pi$
$131$	10.6180	−	18.3910i	0.927702	−	1.60683i	0.787157	−	0.616753i	$-0.211552\pi$
$132$		0			0
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	0.708204	+	2.17963i	0.0611795	+	0.188291i
$135$		0			0
$136$	−5.78115	+	4.20025i	−0.495730	+	0.360169i
$137$	−8.42971	+	1.79179i	−0.720199	+	0.153083i	−0.553409	−	0.832910i	$-0.686673\pi$
$137$	−8.42971	+	1.79179i	−0.720199	+	0.153083i	−0.166790	+	0.985993i	$0.553340\pi$
$138$		0			0
$139$	−1.01478	−	9.65502i	−0.0860728	−	0.818928i	−0.949355	−	0.314206i	$-0.898262\pi$
$139$	−1.01478	−	9.65502i	−0.0860728	−	0.818928i	0.863282	−	0.504722i	$-0.168405\pi$
$140$	2.09366	−	0.932157i	0.176947	−	0.0787817i
$141$		0			0
$142$	−0.555728	−	0.962549i	−0.0466357	−	0.0807753i
$143$	−19.7082	+	8.50651i	−1.64808	+	0.711350i
$144$		0			0
$145$	1.85410	+	5.70634i	0.153975	+	0.473886i
$146$	0.00582517	−	0.0554228i	0.000482095	−	0.00458682i
$147$		0			0
$148$	6.31505	+	7.01357i	0.519094	+	0.576512i
$149$	10.1576	+	11.2812i	0.832145	+	0.924191i	0.998080	−	0.0619457i	$-0.0197306\pi$
$149$	10.1576	+	11.2812i	0.832145	+	0.924191i	−0.165934	+	0.986137i	$0.553064\pi$
$150$		0			0
$151$	−0.452215	+	4.30254i	−0.0368007	+	0.350136i	0.960591	+	0.277964i	$0.0896596\pi$
$151$	−0.452215	+	4.30254i	−0.0368007	+	0.350136i	−0.997392	+	0.0721716i	$0.977007\pi$
$152$	−0.454915	−	1.40008i	−0.0368985	−	0.113562i
$153$		0			0
$154$	0.645898	−	1.08981i	0.0520479	−	0.0878197i
$155$	−0.381966	−	0.661585i	−0.0306802	−	0.0531397i
$156$		0			0
$157$	6.52810	−	2.90650i	0.520999	−	0.231964i	−0.129350	−	0.991599i	$-0.541289\pi$
$157$	6.52810	−	2.90650i	0.520999	−	0.231964i	0.650349	+	0.759635i	$0.274622\pi$
$158$	−0.421714	−	4.01234i	−0.0335498	−	0.319205i
$159$		0			0
$160$	−5.01263	+	1.06547i	−0.396283	+	0.0842325i
$161$	−3.73607	+	2.71441i	−0.294443	+	0.213926i
$162$		0			0
$163$	6.39919	+	19.6947i	0.501223	+	1.54261i	0.807029	+	0.590512i	$0.201074\pi$
$163$	6.39919	+	19.6947i	0.501223	+	1.54261i	−0.305806	+	0.952094i	$0.598926\pi$
$164$	2.34346	+	4.05899i	0.182993	+	0.316954i
$165$		0			0
$166$	−1.86475	+	3.22983i	−0.144732	+	0.250684i
$167$	−5.63798	−	1.19839i	−0.436280	−	0.0927341i	−0.0154643	−	0.999880i	$-0.504923\pi$
$167$	−5.63798	−	1.19839i	−0.436280	−	0.0927341i	−0.420815	+	0.907146i	$0.638256\pi$
$168$		0			0
$169$	26.3910	+	11.7500i	2.03008	+	0.903848i
$170$	−0.708204	+	2.17963i	−0.0543168	+	0.167170i
$171$		0			0
$172$	2.78115	−	2.02063i	0.212061	−	0.154071i
$173$	−2.41358	+	22.9637i	−0.183501	+	1.74590i	0.384732	+	0.923028i	$0.374294\pi$
$173$	−2.41358	+	22.9637i	−0.183501	+	1.74590i	−0.568233	+	0.822868i	$0.692373\pi$
$174$		0			0
$175$	−1.73607	+	3.00696i	−0.131234	+	0.227305i
$176$	7.06958	−	7.67362i	0.532890	−	0.578421i
$177$		0			0
$178$	1.72876	−	1.91998i	0.129576	−	0.143909i
$179$	−4.09017	−	2.97168i	−0.305714	−	0.222114i	0.424341	−	0.905502i	$-0.360506\pi$
$179$	−4.09017	−	2.97168i	−0.305714	−	0.222114i	−0.730055	+	0.683388i	$0.760506\pi$
$180$		0			0
$181$	−3.06231	+	9.42481i	−0.227619	+	0.700540i	0.770396	+	0.637566i	$0.220059\pi$
$181$	−3.06231	+	9.42481i	−0.227619	+	0.700540i	−0.998015	+	0.0629745i	$0.979941\pi$
$182$	−2.41811	+	0.513986i	−0.179243	+	0.0380992i
$183$		0			0
$184$	6.21062	−	2.76515i	0.457853	−	0.203849i
$185$	6.15431	+	1.30814i	0.452474	+	0.0961762i
$186$		0			0
$187$	−4.79988	−	15.3671i	−0.351002	−	1.12375i
$188$	22.1459			1.61516
$189$		0			0
$190$	−0.381966	−	0.277515i	−0.0277107	−	0.0201330i
$191$	−5.43036	−	2.41775i	−0.392927	−	0.174942i	0.200756	−	0.979641i	$-0.435660\pi$
$191$	−5.43036	−	2.41775i	−0.392927	−	0.174942i	−0.593683	+	0.804699i	$0.702327\pi$
$192$		0			0
$193$	−7.36044	−	8.17459i	−0.529816	−	0.588420i	0.417518	−	0.908669i	$-0.362900\pi$
$193$	−7.36044	−	8.17459i	−0.529816	−	0.588420i	−0.947333	+	0.320249i	$0.896234\pi$
$194$	−0.239558	−	2.27924i	−0.0171993	−	0.163640i
$195$		0			0
$196$	7.44382	−	8.26720i	0.531701	−	0.590514i
$197$	−8.23607			−0.586796			−0.293398	−	0.955990i	$-0.594786\pi$
$197$	−8.23607			−0.586796			−0.293398	+	0.955990i	$0.594786\pi$
$198$		0			0
$199$	−7.14590			−0.506559			−0.253280	−	0.967393i	$-0.581509\pi$
$199$	−7.14590			−0.506559			−0.253280	+	0.967393i	$0.581509\pi$
$200$	3.42023	−	3.79855i	0.241847	−	0.268598i
$201$		0			0
$202$	−0.338261	−	3.21834i	−0.0238000	−	0.226442i
$203$	−3.24803	−	3.60730i	−0.227967	−	0.253183i
$204$		0			0
$205$	2.85447	+	1.27089i	0.199365	+	0.0887631i
$206$	3.16312	+	2.29814i	0.220385	+	0.160119i
$207$		0			0
$208$	−20.3607			−1.41176
$209$	3.31641	+	0.0378495i	0.229401	+	0.00261810i
$210$		0			0
$211$	−20.0248	−	4.25640i	−1.37856	−	0.293022i	−0.541762	−	0.840532i	$-0.682243\pi$
$211$	−20.0248	−	4.25640i	−1.37856	−	0.293022i	−0.836800	+	0.547509i	$0.815576\pi$
$212$	6.92796	−	3.08452i	0.475814	−	0.211846i
$213$		0			0
$214$	5.24354	−	1.11455i	0.358441	−	0.0761889i
$215$	0.708204	−	2.17963i	0.0482991	−	0.148649i
$216$		0			0
$217$	0.500000	+	0.363271i	0.0339422	+	0.0246605i
$218$	1.82639	−	2.02841i	0.123698	−	0.137381i
$219$		0			0
$220$	0.880740	−	7.54983i	0.0593795	−	0.509009i
$221$	−15.7082	+	27.2074i	−1.05665	+	1.83017i
$222$		0			0
$223$	1.62088	−	15.4216i	0.108542	−	1.03271i	−0.795701	−	0.605690i	$-0.792897\pi$
$223$	1.62088	−	15.4216i	0.108542	−	1.03271i	0.904243	−	0.427019i	$-0.140436\pi$
$224$	3.35410	−	2.43690i	0.224105	−	0.162822i
$225$		0			0
$226$	−2.03444	+	6.26137i	−0.135329	+	0.416500i
$227$	15.1813	+	6.75916i	1.00762	+	0.448621i	0.843103	−	0.537753i	$-0.180727\pi$
$227$	15.1813	+	6.75916i	1.00762	+	0.448621i	0.164518	+	0.986374i	$0.447393\pi$
$228$		0			0
$229$	−9.95788	−	2.11661i	−0.658035	−	0.139870i	−0.133221	−	0.991086i	$-0.542532\pi$
$229$	−9.95788	−	2.11661i	−0.658035	−	0.139870i	−0.524814	+	0.851217i	$0.675865\pi$
$230$	1.09017	−	1.88823i	0.0718837	−	0.124506i
$231$		0			0
$232$	3.57295	+	6.18853i	0.234576	+	0.406297i
$233$	3.43769	+	10.5801i	0.225211	+	0.693128i	0.998270	+	0.0587939i	$0.0187255\pi$
$233$	3.43769	+	10.5801i	0.225211	+	0.693128i	−0.773059	+	0.634334i	$0.781275\pi$
$234$		0			0
$235$	11.9443	−	8.67802i	0.779158	−	0.566092i
$236$	−2.93444	+	0.623735i	−0.191016	+	0.0406017i
$237$		0			0
$238$	−0.193806	−	1.84395i	−0.0125626	−	0.119525i
$239$	−9.56677	+	4.25940i	−0.618823	+	0.275518i	−0.692109	−	0.721793i	$-0.743318\pi$
$239$	−9.56677	+	4.25940i	−0.618823	+	0.275518i	0.0732857	+	0.997311i	$0.476651\pi$
$240$		0			0
$241$	13.4164	+	23.2379i	0.864227	+	1.49688i	0.867813	+	0.496891i	$0.165525\pi$
$241$	13.4164	+	23.2379i	0.864227	+	1.49688i	−0.00358606	+	0.999994i	$0.501141\pi$
$242$	−2.01722	−	3.68571i	−0.129672	−	0.236927i
$243$		0			0
$244$	−6.21885	−	19.1396i	−0.398121	−	1.22529i
$245$	0.775226	−	7.37578i	0.0495274	−	0.471221i
$246$		0			0
$247$	−4.33070	−	4.80973i	−0.275556	−	0.306036i
$248$	−0.608795	−	0.676135i	−0.0386585	−	0.0429346i
$249$		0			0
$250$	0.418114	−	3.97809i	0.0264438	−	0.251596i
$251$	−6.35410	−	19.5559i	−0.401067	−	1.23436i	−0.924135	−	0.382067i	$-0.875212\pi$
$251$	−6.35410	−	19.5559i	−0.401067	−	1.23436i	0.523067	−	0.852291i	$-0.324788\pi$
$252$		0			0
$253$	1.42705	+	15.2497i	0.0897179	+	0.958738i
$254$	2.01722	+	3.49393i	0.126572	+	0.219229i
$255$		0			0
$256$	5.08142	−	2.26239i	0.317589	−	0.141400i
$257$	−1.55850	−	14.8282i	−0.0972167	−	0.924955i	−0.929056	−	0.369939i	$-0.879379\pi$
$257$	−1.55850	−	14.8282i	−0.0972167	−	0.924955i	0.831840	−	0.555016i	$-0.187288\pi$
$258$		0			0
$259$	−4.97894	+	1.05831i	−0.309376	+	0.0657599i
$260$	−12.0000	+	8.71851i	−0.744208	+	0.540699i
$261$		0			0
$262$	−2.50658	−	7.71445i	−0.154857	−	0.476601i
$263$	−6.35410	−	11.0056i	−0.391811	−	0.678636i	0.600878	−	0.799341i	$-0.294818\pi$
$263$	−6.35410	−	11.0056i	−0.391811	−	0.678636i	−0.992688	+	0.120705i	$0.961485\pi$
$264$		0			0
$265$	2.52786	−	4.37839i	0.155285	−	0.268962i
$266$	0.373619	+	0.0794152i	0.0229081	+	0.00486926i
$267$		0			0
$268$	−10.1628	−	4.52479i	−0.620794	−	0.276395i
$269$	6.57295	−	20.2295i	0.400760	−	1.23341i	−0.523625	−	0.851949i	$-0.675421\pi$
$269$	6.57295	−	20.2295i	0.400760	−	1.23341i	0.924384	−	0.381463i	$-0.124579\pi$
$270$		0			0
$271$	−8.70820	+	6.32688i	−0.528986	+	0.384331i	−0.819978	−	0.572395i	$-0.806015\pi$
$271$	−8.70820	+	6.32688i	−0.528986	+	0.384331i	0.290993	+	0.956725i	$0.406015\pi$
$272$	1.59620	−	15.1869i	0.0967840	−	0.920838i
$273$		0			0
$274$	−1.64590	+	2.85078i	−0.0994323	+	0.172222i
$275$	5.64370	+	10.0380i	0.340328	+	0.605315i
$276$		0			0
$277$	−12.8714	+	14.2952i	−0.773370	+	0.858914i	−0.993176	−	0.116629i	$-0.962791\pi$
$277$	−12.8714	+	14.2952i	−0.773370	+	0.858914i	0.219806	+	0.975544i	$0.429458\pi$
$278$	−3.00000	−	2.17963i	−0.179928	−	0.130725i
$279$		0			0
$280$	0.562306	−	1.73060i	0.0336042	−	0.103423i
$281$	−9.12244	+	1.93903i	−0.544199	+	0.115673i	−0.471805	−	0.881703i	$-0.656397\pi$
$281$	−9.12244	+	1.93903i	−0.544199	+	0.115673i	−0.0723942	+	0.997376i	$0.523064\pi$
$282$		0			0
$283$	−15.5303	+	6.91452i	−0.923179	+	0.411026i	−0.812587	−	0.582840i	$-0.801941\pi$
$283$	−15.5303	+	6.91452i	−0.923179	+	0.411026i	−0.110592	+	0.993866i	$0.535275\pi$
$284$	5.27723	+	1.12171i	0.313146	+	0.0665612i
$285$		0			0
$286$	−2.62250	+	7.76843i	−0.155072	+	0.459357i
$287$	−2.52786			−0.149215
$288$		0			0
$289$	−5.30902	−	3.85723i	−0.312295	−	0.226896i
$290$	2.09366	+	0.932157i	0.122944	+	0.0547382i
$291$		0			0
$292$	0.181006	+	0.201028i	0.0105926	+	0.0117643i
$293$	−3.05018	−	29.0205i	−0.178193	−	1.69539i	−0.609176	−	0.793035i	$-0.708500\pi$
$293$	−3.05018	−	29.0205i	−0.178193	−	1.69539i	0.430983	−	0.902360i	$-0.358167\pi$
$294$		0			0
$295$	−1.33826	+	1.48629i	−0.0779166	+	0.0865351i
$296$	7.49342			0.435546
$297$		0			0
$298$	5.79837			0.335891
$299$	19.9993	−	22.2115i	1.15659	−	1.28453i
$300$		0			0
$301$	0.193806	+	1.84395i	0.0111708	+	0.106283i
$302$	1.10572	+	1.22803i	0.0636272	+	0.0706651i
$303$		0			0
$304$	2.87392	+	1.27955i	0.164831	+	0.0733873i
$305$	−10.8541	−	7.88597i	−0.621504	−	0.451549i
$306$		0			0
$307$	7.85410			0.448257			0.224129	−	0.974560i	$-0.428046\pi$
$307$	7.85410			0.448257			0.224129	+	0.974560i	$0.428046\pi$
$308$	1.83339	+	5.86969i	0.104467	+	0.334457i
$309$		0			0
$310$	−0.285420	−	0.0606678i	−0.0162107	−	0.00344570i
$311$	−13.8679	+	6.17440i	−0.786378	+	0.350118i	−0.760325	−	0.649542i	$-0.774960\pi$
$311$	−13.8679	+	6.17440i	−0.786378	+	0.350118i	−0.0260529	+	0.999661i	$0.508294\pi$
$312$		0			0
$313$	−3.39626	+	0.721898i	−0.191968	+	0.0408041i	−0.302892	−	0.953025i	$-0.597952\pi$
$313$	−3.39626	+	0.721898i	−0.191968	+	0.0408041i	0.110924	+	0.993829i	$0.464619\pi$
$314$	0.843459	−	2.59590i	0.0475991	−	0.146495i
$315$		0			0
$316$	15.8435	+	11.5109i	0.891264	+	0.647541i
$317$	−14.0145	+	15.5646i	−0.787130	+	0.874197i	−0.994572	−	0.104051i	$-0.966820\pi$
$317$	−14.0145	+	15.5646i	−0.787130	+	0.874197i	0.207442	+	0.978247i	$0.433486\pi$
$318$		0			0
$319$	−15.7846	+	3.16729i	−0.883768	+	0.177334i
$320$	2.90983	−	5.03997i	0.162664	−	0.281743i
$321$		0			0
$322$	−0.184381	+	1.75427i	−0.0102752	+	0.0977616i
$323$	3.92705	−	2.85317i	0.218507	−	0.158755i
$324$		0			0
$325$	6.94427	−	21.3723i	0.385199	−	1.18552i
$326$	7.22599	+	3.21722i	0.400211	+	0.178185i
$327$		0			0
$328$	3.64004	+	0.773714i	0.200988	+	0.0427212i
$329$	−5.97214	+	10.3440i	−0.329255	+	0.570286i
$330$		0			0
$331$	−7.20820	−	12.4850i	−0.396199	−	0.686236i	0.597055	−	0.802201i	$-0.296338\pi$
$331$	−7.20820	−	12.4850i	−0.396199	−	0.686236i	−0.993253	+	0.115964i	$0.963004\pi$
$332$	−5.59424	−	17.2173i	−0.307024	−	0.944921i
$333$		0			0
$334$	−1.78115	+	1.29408i	−0.0974604	+	0.0708091i
$335$	−7.25434	+	1.54196i	−0.396347	+	0.0842462i
$336$		0			0
$337$	1.19916	+	11.4093i	0.0653227	+	0.621504i	0.977387	+	0.211457i	$0.0678209\pi$
$337$	1.19916	+	11.4093i	0.0653227	+	0.621504i	−0.912065	+	0.410047i	$0.865512\pi$
$338$	10.0805	−	4.48811i	0.548305	−	0.244121i
$339$		0			0
$340$	−5.56231	−	9.63420i	−0.301658	−	0.522488i
$341$	1.88197	−	0.812299i	0.101914	−	0.0439885i
$342$		0			0
$343$	4.01722	+	12.3637i	0.216910	+	0.667579i
$344$	0.285309	−	2.71454i	0.0153829	−	0.146358i
$345$		0			0
$346$	5.90150	+	6.55428i	0.317267	+	0.352361i
$347$	5.94760	+	6.60548i	0.319284	+	0.354600i	0.881327	−	0.472508i	$-0.156651\pi$
$347$	5.94760	+	6.60548i	0.319284	+	0.354600i	−0.562043	+	0.827108i	$0.689984\pi$
$348$		0			0
$349$	0.433364	−	4.12319i	0.0231975	−	0.220709i	−0.976782	−	0.214238i	$-0.931273\pi$
$349$	0.433364	−	4.12319i	0.0231975	−	0.220709i	0.999979	−	0.00647159i	$-0.00205999\pi$
$350$	0.409830	+	1.26133i	0.0219063	+	0.0674208i
$351$		0			0
$352$	−1.28115	−	13.6906i	−0.0682857	−	0.729710i
$353$	−8.20820	−	14.2170i	−0.436879	−	0.756696i	0.560568	−	0.828108i	$-0.310583\pi$
$353$	−8.20820	−	14.2170i	−0.436879	−	0.756696i	−0.997447	+	0.0714123i	$0.977249\pi$
$354$		0			0
$355$	3.28579	−	1.46293i	0.174392	−	0.0776442i
$356$	1.31089	+	12.4723i	0.0694772	+	0.661032i
$357$		0			0
$358$	−1.88892	+	0.401502i	−0.0998324	+	0.0212200i
$359$	−18.4894	+	13.4333i	−0.975831	+	0.708983i	−0.956773	−	0.290836i	$-0.906067\pi$
$359$	−18.4894	+	13.4333i	−0.975831	+	0.708983i	−0.0190579	+	0.999818i	$0.506067\pi$
$360$		0			0
$361$	−5.56231	−	17.1190i	−0.292753	−	0.901001i
$362$	1.89261	+	3.27810i	0.0994733	+	0.172293i
$363$		0			0
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$	0.176399	+	0.0374948i	0.00923315	+	0.00196257i
$366$		0			0
$367$	−11.6095	−	5.16889i	−0.606012	−	0.269814i	0.0807058	−	0.996738i	$-0.474283\pi$
$367$	−11.6095	−	5.16889i	−0.606012	−	0.269814i	−0.686718	+	0.726924i	$0.740949\pi$
$368$	−4.48936	+	13.8168i	−0.234024	+	0.720252i
$369$		0			0
$370$	1.94427	−	1.41260i	0.101078	−	0.0734374i
$371$	−0.427539	+	4.06776i	−0.0221967	+	0.211188i
$372$		0			0
$373$	2.82624	−	4.89519i	0.146337	−	0.253463i	−0.783534	−	0.621349i	$-0.786585\pi$
$373$	2.82624	−	4.89519i	0.146337	−	0.253463i	0.929871	+	0.367886i	$0.119918\pi$
$374$	−5.58881	−	2.56512i	−0.288991	−	0.132639i
$375$		0			0
$376$	11.7657	−	13.0672i	0.606771	−	0.673887i
$377$	25.4164	+	18.4661i	1.30901	+	0.951053i
$378$		0			0
$379$	4.88197	−	15.0251i	0.250770	−	0.771790i	−0.743864	−	0.668331i	$-0.767009\pi$
$379$	4.88197	−	15.0251i	0.250770	−	0.771790i	0.994634	−	0.103459i	$-0.0329910\pi$
$380$	2.24171	−	0.476491i	0.114998	−	0.0244435i
$381$		0			0
$382$	−2.07421	+	0.923500i	−0.106126	+	0.0472503i
$383$	19.4202	+	4.12790i	0.992328	+	0.210926i	0.675342	−	0.737504i	$-0.263996\pi$
$383$	19.4202	+	4.12790i	0.992328	+	0.210926i	0.316986	+	0.948430i	$0.397329\pi$
$384$		0			0
$385$	3.28891	+	2.44736i	0.167618	+	0.124729i
$386$	−4.20163			−0.213857
$387$		0			0
$388$	9.00000	+	6.53888i	0.456906	+	0.331961i
$389$	20.6941	+	9.21359i	1.04923	+	0.467148i	0.857599	−	0.514319i	$-0.171955\pi$
$389$	20.6941	+	9.21359i	1.04923	+	0.467148i	0.191632	+	0.981467i	$0.438622\pi$
$390$		0			0
$391$	14.9995	+	16.6586i	0.758558	+	0.842464i
$392$	−0.923281	−	8.78443i	−0.0466327	−	0.443681i
$393$		0			0
$394$	−2.10502	+	2.33786i	−0.106049	+	0.117780i
$395$	13.0557			0.656905
$396$		0			0
$397$	−2.12461			−0.106631			−0.0533156	−	0.998578i	$-0.516979\pi$
$397$	−2.12461			−0.106631			−0.0533156	+	0.998578i	$0.516979\pi$
$398$	−1.82639	+	2.02841i	−0.0915484	+	0.101675i
$399$		0			0
$400$	1.14176	+	10.8631i	0.0570881	+	0.543157i
$401$	−9.74408	−	10.8219i	−0.486596	−	0.540420i	0.448981	−	0.893541i	$-0.351787\pi$
$401$	−9.74408	−	10.8219i	−0.486596	−	0.540420i	−0.935578	+	0.353121i	$0.885120\pi$
$402$		0			0
$403$	−3.65418	−	1.62695i	−0.182028	−	0.0810440i
$404$	12.7082	+	9.23305i	0.632257	+	0.459361i
$405$		0			0
$406$	−1.85410			−0.0920175
$407$	−5.39977	+	15.9953i	−0.267657	+	0.792859i
$408$		0			0
$409$	33.0053	+	7.01549i	1.63201	+	0.346894i	0.930648	−	0.365915i	$-0.119244\pi$
$409$	33.0053	+	7.01549i	1.63201	+	0.346894i	0.701358	+	0.712809i	$0.252577\pi$
$410$	1.09031	−	0.485438i	0.0538467	−	0.0239741i
$411$		0			0
$412$	−18.5640	+	3.94590i	−0.914582	+	0.194400i
$413$	0.500000	−	1.53884i	0.0246034	−	0.0757215i
$414$		0			0
$415$	−9.76393	−	7.09391i	−0.479293	−	0.348226i
$416$	−17.9547	+	19.9407i	−0.880300	+	0.977672i
$417$		0			0
$418$	0.858369	−	0.931709i	0.0419842	−	0.0455714i
$419$	4.04508	−	7.00629i	0.197615	−	0.342280i	−0.750139	−	0.661280i	$-0.770014\pi$
$419$	4.04508	−	7.00629i	0.197615	−	0.342280i	0.947755	+	0.319000i	$0.103347\pi$
$420$		0			0
$421$	−1.06996	+	10.1800i	−0.0521467	+	0.496143i	0.937013	+	0.349296i	$0.113579\pi$
$421$	−1.06996	+	10.1800i	−0.0521467	+	0.496143i	−0.989159	+	0.146847i	$0.953088\pi$
$422$	−6.32624	+	4.59628i	−0.307956	+	0.223743i
$423$		0			0
$424$	1.86068	−	5.72658i	0.0903626	−	0.278107i
$425$	15.3970	+	6.85518i	0.746864	+	0.332525i
$426$		0			0
$427$	10.6169	+	2.25669i	0.513788	+	0.109209i
$428$	−13.0106	+	22.5351i	−0.628893	+	1.08927i
$429$		0			0
$430$	−0.437694	−	0.758108i	−0.0211075	−	0.0365592i
$431$	10.5279	+	32.4014i	0.507109	+	1.56072i	0.797195	+	0.603722i	$0.206316\pi$
$431$	10.5279	+	32.4014i	0.507109	+	1.56072i	−0.290086	+	0.957001i	$0.593684\pi$
$432$		0			0
$433$	−11.9271	+	8.66551i	−0.573177	+	0.416438i	−0.836258	−	0.548336i	$-0.815261\pi$
$433$	−11.9271	+	8.66551i	−0.573177	+	0.416438i	0.263081	+	0.964774i	$0.415261\pi$
$434$	0.230909	−	0.0490813i	0.0110840	−	0.00235598i
$435$		0			0
$436$	1.38492	+	13.1766i	0.0663257	+	0.631047i
$437$	−4.21878	+	1.87832i	−0.201812	+	0.0898524i
$438$		0			0
$439$	0.354102	+	0.613323i	0.0169004	+	0.0292723i	0.874352	−	0.485292i	$-0.161287\pi$
$439$	0.354102	+	0.613323i	0.0169004	+	0.0292723i	−0.857452	+	0.514565i	$0.827954\pi$
$440$	−3.98684	−	4.53077i	−0.190065	−	0.215996i
$441$		0			0
$442$	3.70820	+	11.4127i	0.176381	+	0.542846i
$443$	−0.129204	+	1.22930i	−0.00613868	+	0.0584056i	−0.997162	−	0.0752806i	$-0.976015\pi$
$443$	−0.129204	+	1.22930i	−0.00613868	+	0.0584056i	0.991024	+	0.133686i	$0.0426814\pi$
$444$		0			0
$445$	5.59439	+	6.21320i	0.265199	+	0.294534i
$446$	−3.96325	−	4.40164i	−0.187665	−	0.208424i
$447$		0			0
$448$	−0.492141	+	4.68241i	−0.0232515	+	0.221223i
$449$	−2.30902	−	7.10642i	−0.108969	−	0.335373i	0.881672	−	0.471862i	$-0.156418\pi$
$449$	−2.30902	−	7.10642i	−0.108969	−	0.335373i	−0.990642	+	0.136489i	$0.956418\pi$
$450$		0			0
$451$	−4.27458	+	7.21242i	−0.201282	+	0.339620i
$452$	−15.9787	−	27.6759i	−0.751575	−	1.30177i
$453$		0			0
$454$	5.79875	−	2.58177i	0.272149	−	0.121169i
$455$	−0.836228	−	7.95618i	−0.0392030	−	0.372991i
$456$		0			0
$457$	0.978148	−	0.207912i	0.0457558	−	0.00972570i	−0.184977	−	0.982743i	$-0.559221\pi$
$457$	0.978148	−	0.207912i	0.0457558	−	0.00972570i	0.230733	+	0.973017i	$0.425888\pi$
$458$	−3.14590	+	2.28563i	−0.146998	+	0.106800i
$459$		0			0
$460$	3.27051	+	10.0656i	0.152488	+	0.469311i
$461$	−8.07295	−	13.9828i	−0.375995	−	0.651242i	0.614481	−	0.788932i	$-0.289366\pi$
$461$	−8.07295	−	13.9828i	−0.375995	−	0.651242i	−0.990475	+	0.137690i	$0.956032\pi$
$462$		0			0
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	−0.993105	−	0.117230i	$-0.962599\pi$
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	0.598076	+	0.801439i	$0.295932\pi$
$464$	−14.9368	−	3.17492i	−0.693424	−	0.147392i
$465$		0			0
$466$	3.88186	+	1.72831i	0.179824	+	0.0800626i
$467$	0.236068	−	0.726543i	0.0109239	−	0.0336204i	−0.945446	−	0.325779i	$-0.894373\pi$
$467$	0.236068	−	0.726543i	0.0109239	−	0.0336204i	0.956370	+	0.292159i	$0.0943735\pi$
$468$		0			0
$469$	4.85410	−	3.52671i	0.224142	−	0.162848i
$470$	0.589469	−	5.60843i	0.0271902	−	0.258697i
$471$		0			0
$472$	−1.19098	+	2.06284i	−0.0548194	+	0.0949500i
$473$	5.58881	+	2.56512i	0.256974	+	0.117944i
$474$		0			0
$475$	−2.32331	+	2.58030i	−0.106601	+	0.118392i
$476$	7.28115	+	5.29007i	0.333731	+	0.242470i
$477$		0			0
$478$	−1.23607	+	3.80423i	−0.0565364	+	0.174001i
$479$	−11.5069	+	2.44586i	−0.525762	+	0.111754i	−0.463143	−	0.886283i	$-0.653278\pi$
$479$	−11.5069	+	2.44586i	−0.525762	+	0.111754i	−0.0626186	+	0.998038i	$0.519945\pi$
$480$		0			0
$481$	30.0961	−	13.3996i	1.37226	−	0.610971i
$482$	10.0253	+	2.13093i	0.456638	+	0.0970614i
$483$		0			0
$484$	19.8475	+	4.69458i	0.902158	+	0.213390i
$485$	7.41641			0.336762
$486$		0			0
$487$	10.5000	+	7.62870i	0.475800	+	0.345689i	0.799698	−	0.600403i	$-0.204993\pi$
$487$	10.5000	+	7.62870i	0.475800	+	0.345689i	−0.323897	+	0.946092i	$0.604993\pi$
$488$	−14.5973	−	6.49913i	−0.660788	−	0.294202i
$489$		0			0
$490$	−1.89552	−	2.10519i	−0.0856310	−	0.0951029i
$491$	0.765800	+	7.28610i	0.0345601	+	0.328817i	0.998118	+	0.0613184i	$0.0195305\pi$
$491$	0.765800	+	7.28610i	0.0345601	+	0.328817i	−0.963558	+	0.267499i	$0.913803\pi$
$492$		0			0
$493$	−15.7663	+	17.5102i	−0.710077	+	0.788620i
$494$	−2.47214			−0.111227
$495$		0			0
$496$	1.94427			0.0873004
$497$	−1.94706	+	2.16243i	−0.0873374	+	0.0969980i
$498$		0			0
$499$	−4.01561	−	38.2060i	−0.179763	−	1.71033i	−0.597586	−	0.801805i	$-0.703873\pi$
$499$	−4.01561	−	38.2060i	−0.179763	−	1.71033i	0.417823	−	0.908529i	$-0.362793\pi$
$500$	12.9921	+	14.4292i	0.581025	+	0.645294i
$501$		0			0
$502$	−7.17508	−	3.19455i	−0.320239	−	0.142580i
$503$	−7.70820	−	5.60034i	−0.343692	−	0.249707i	0.402526	−	0.915409i	$-0.368132\pi$
$503$	−7.70820	−	5.60034i	−0.343692	−	0.249707i	−0.746218	+	0.665702i	$0.768132\pi$
$504$		0			0
$505$	10.4721			0.466004
$506$	4.69344	+	3.49251i	0.208649	+	0.155261i
$507$		0			0
$508$	−19.1556	−	4.07166i	−0.849894	−	0.180651i
$509$	24.8305	−	11.0552i	1.10059	−	0.490015i	0.225633	−	0.974212i	$-0.427555\pi$
$509$	24.8305	−	11.0552i	1.10059	−	0.490015i	0.874959	+	0.484198i	$0.160888\pi$
$510$		0			0
$511$	−0.142710	+	0.0303339i	−0.00631311	+	0.00134189i
$512$	6.89261	−	21.2133i	0.304613	−	0.937503i
$513$		0			0
$514$	−4.60739	−	3.34747i	−0.203223	−	0.147650i
$515$	−8.46616	+	9.40262i	−0.373064	+	0.414329i
$516$		0			0
$517$	19.4145	+	34.5311i	0.853850	+	1.51868i
$518$	−0.972136	+	1.68379i	−0.0427132	+	0.0739814i
$519$		0			0
$520$	−1.23104	+	11.7126i	−0.0539847	+	0.513630i
$521$	−32.6525	+	23.7234i	−1.43053	+	1.03934i	−0.440613	+	0.897697i	$0.645239\pi$
$521$	−32.6525	+	23.7234i	−1.43053	+	1.03934i	−0.989918	+	0.141645i	$0.954761\pi$
$522$		0			0
$523$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$523$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$524$	35.9698	+	16.0148i	1.57135	+	0.699609i
$525$		0			0
$526$	−4.74803	−	1.00922i	−0.207024	−	0.0440043i
$527$	1.50000	−	2.59808i	0.0653410	−	0.113174i
$528$		0			0
$529$	0.836881	+	1.44952i	0.0363861	+	0.0630226i
$530$	−0.596748	−	1.83660i	−0.0259211	−	0.0797768i
$531$		0			0
$532$	−1.50000	+	1.08981i	−0.0650332	+	0.0472494i
$533$	16.0032	−	3.40158i	0.693174	−	0.147339i
$534$		0			0
$535$	1.81331	+	17.2525i	0.0783962	+	0.745890i
$536$	−8.06918	+	3.59263i	−0.348535	+	0.155178i
$537$		0			0
$538$	−4.06231	−	7.03612i	−0.175138	−	0.303349i
$539$	19.4164	+	4.35926i	0.836324	+	0.187766i
$540$		0			0
$541$	−3.68034	−	11.3269i	−0.158230	−	0.486982i	0.840244	−	0.542209i	$-0.182412\pi$
$541$	−3.68034	−	11.3269i	−0.158230	−	0.486982i	−0.998474	+	0.0552266i	$0.982412\pi$
$542$	−0.429764	+	4.08893i	−0.0184600	+	0.175635i
$543$		0			0
$544$	−13.4660	−	14.9555i	−0.577350	−	0.641212i
$545$	5.91031	+	6.56406i	0.253170	+	0.281173i
$546$		0			0
$547$	3.37901	−	32.1492i	0.144476	−	1.37460i	−0.646576	−	0.762850i	$-0.723800\pi$
$547$	3.37901	−	32.1492i	0.144476	−	1.37460i	0.791052	−	0.611749i	$-0.209534\pi$
$548$	−4.93769	−	15.1967i	−0.210928	−	0.649169i
$549$		0			0
$550$	4.29180	+	0.963568i	0.183003	+	0.0410867i
$551$	−2.42705	−	4.20378i	−0.103396	−	0.179087i
$552$		0			0
$553$	−9.64915	+	4.29608i	−0.410323	+	0.182688i
$554$	0.768025	+	7.30727i	0.0326303	+	0.310456i
$555$		0			0
$556$	17.6067	−	3.74241i	0.746689	−	0.158714i
$557$	−0.527864	+	0.383516i	−0.0223663	+	0.0162501i	−0.598912	−	0.800815i	$-0.704400\pi$
$557$	−0.527864	+	0.383516i	−0.0223663	+	0.0162501i	0.576546	+	0.817065i	$0.304400\pi$
$558$		0			0
$559$	−3.70820	−	11.4127i	−0.156840	−	0.482705i
$560$	1.94427	+	3.36758i	0.0821605	+	0.142306i
$561$		0			0
$562$	−1.78115	+	3.08505i	−0.0751334	+	0.130135i
$563$	−19.8612	−	4.22164i	−0.837051	−	0.177921i	−0.230607	−	0.973047i	$-0.574071\pi$
$563$	−19.8612	−	4.22164i	−0.837051	−	0.177921i	−0.606444	+	0.795126i	$0.707405\pi$
$564$		0			0
$565$	−19.4630	−	8.66550i	−0.818816	−	0.364561i
$566$	−2.00658	+	6.17561i	−0.0843428	+	0.259580i
$567$		0			0
$568$	3.46556	−	2.51788i	0.145412	−	0.105648i
$569$	4.05553	−	38.5858i	0.170017	−	1.61760i	−0.493710	−	0.869627i	$-0.664359\pi$
$569$	4.05553	−	38.5858i	0.170017	−	1.61760i	0.663726	−	0.747975i	$-0.268974\pi$
$570$		0			0
$571$	9.26393	−	16.0456i	0.387683	−	0.671488i	−0.604454	−	0.796640i	$-0.706609\pi$
$571$	9.26393	−	16.0456i	0.387683	−	0.671488i	0.992138	+	0.125153i	$0.0399420\pi$
$572$	−19.5051	−	34.6922i	−0.815550	−	1.45055i
$573$		0			0
$574$	−0.646085	+	0.717550i	−0.0269670	+	0.0299499i
$575$	−12.9721	−	9.42481i	−0.540975	−	0.393042i
$576$		0			0
$577$	10.9443	−	33.6830i	0.455616	−	1.40224i	−0.414794	−	0.909915i	$-0.636147\pi$
$577$	10.9443	−	33.6830i	0.455616	−	1.40224i	0.870410	−	0.492327i	$-0.163853\pi$
$578$	−2.45180	+	0.521147i	−0.101982	+	0.0216769i
$579$		0			0
$580$	−10.1628	+	4.52479i	−0.421989	+	0.187882i
$581$	9.55057	+	2.03004i	0.396224	+	0.0842201i
$582$		0			0
$583$	10.8831	+	8.09836i	0.450730	+	0.335400i
$584$	0.214782			0.00888773
$585$		0			0
$586$	−9.01722	−	6.55139i	−0.372498	−	0.270636i
$587$	−12.2565	−	5.45694i	−0.505880	−	0.225232i	0.137895	−	0.990447i	$-0.455966\pi$
$587$	−12.2565	−	5.45694i	−0.505880	−	0.225232i	−0.643775	+	0.765215i	$0.722633\pi$
$588$		0			0
$589$	0.413545	+	0.459289i	0.0170398	+	0.0189247i
$590$	0.0798526	+	0.759747i	0.00328748	+	0.0312783i
$591$		0			0
$592$	−10.7149	+	11.9001i	−0.440379	+	0.489091i
$593$	10.9443			0.449427			0.224714	−	0.974425i	$-0.427855\pi$
$593$	10.9443			0.449427			0.224714	+	0.974425i	$0.427855\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$	−18.8333	+	20.9165i	−0.771441	+	0.856772i
$597$		0			0
$598$	−1.19334	−	11.3539i	−0.0487993	−	0.464294i
$599$	8.94004	+	9.92892i	0.365280	+	0.405685i	0.897566	−	0.440880i	$-0.145334\pi$
$599$	8.94004	+	9.92892i	0.365280	+	0.405685i	−0.532286	+	0.846565i	$0.678667\pi$
$600$		0			0
$601$	−15.9616	−	7.10656i	−0.651087	−	0.289883i	0.0544917	−	0.998514i	$-0.482646\pi$
$601$	−15.9616	−	7.10656i	−0.651087	−	0.289883i	−0.705579	+	0.708632i	$0.749313\pi$
$602$	0.572949	+	0.416272i	0.0233517	+	0.0169660i
$603$		0			0
$604$	−8.02129			−0.326382
$605$	12.5442	−	5.24537i	0.509995	−	0.213255i
$606$		0			0
$607$	3.50528	+	0.745071i	0.142275	+	0.0302415i	0.278499	−	0.960437i	$-0.410163\pi$
$607$	3.50528	+	0.745071i	0.142275	+	0.0302415i	−0.136224	+	0.990678i	$0.543497\pi$
$608$	3.78747	−	1.68629i	0.153602	−	0.0683880i
$609$		0			0
$610$	−5.01263	+	1.06547i	−0.202955	+	0.0431395i
$611$	23.8885	−	73.5214i	0.966427	−	2.97436i
$612$		0			0
$613$	−16.0623	−	11.6699i	−0.648750	−	0.471345i	0.214095	−	0.976813i	$-0.431320\pi$
$613$	−16.0623	−	11.6699i	−0.648750	−	0.471345i	−0.862845	+	0.505468i	$0.831320\pi$
$614$	2.00739	−	2.22943i	0.0810117	−	0.0899727i
$615$		0			0
$616$	4.43745	+	2.03667i	0.178790	+	0.0820599i
$617$	−13.5795	+	23.5204i	−0.546691	+	0.946897i	0.451807	+	0.892116i	$0.350779\pi$
$617$	−13.5795	+	23.5204i	−0.546691	+	0.946897i	−0.998498	+	0.0547813i	$0.982554\pi$
$618$		0			0
$619$	−2.88105	+	27.4113i	−0.115799	+	1.10175i	0.770115	+	0.637905i	$0.220199\pi$
$619$	−2.88105	+	27.4113i	−0.115799	+	1.10175i	−0.885914	+	0.463849i	$0.846468\pi$
$620$	1.14590	−	0.832544i	0.0460204	−	0.0334358i
$621$		0			0
$622$	−1.79180	+	5.51458i	−0.0718445	+	0.221115i
$623$	−6.17916	−	2.75114i	−0.247563	−	0.110222i
$624$		0			0
$625$	−4.31990	−	0.918223i	−0.172796	−	0.0367289i
$626$	−0.663119	+	1.14856i	−0.0265036	+	0.0459055i
$627$		0			0
$628$	6.62461	+	11.4742i	0.264351	+	0.457869i
$629$	7.63525	+	23.4989i	0.304438	+	0.936962i
$630$		0			0
$631$	8.80902	−	6.40013i	0.350681	−	0.254785i	−0.398473	−	0.917180i	$-0.630460\pi$
$631$	8.80902	−	6.40013i	0.350681	−	0.254785i	0.749155	+	0.662395i	$0.230460\pi$
$632$	15.2094	−	3.23285i	0.604996	−	0.128596i
$633$		0			0
$634$	0.836228	+	7.95618i	0.0332108	+	0.315980i
$635$	−11.9270	+	5.31024i	−0.473309	+	0.210731i
$636$		0			0
$637$	−19.4164	−	33.6302i	−0.769306	−	1.33248i
$638$	−3.13525	+	5.29007i	−0.124126	+	0.209436i
$639$		0			0
$640$	−3.85410	−	11.8617i	−0.152347	−	0.468875i
$641$	−2.13770	+	20.3388i	−0.0844339	+	0.803335i	0.867584	+	0.497291i	$0.165672\pi$
$641$	−2.13770	+	20.3388i	−0.0844339	+	0.803335i	−0.952017	+	0.306044i	$0.900995\pi$
$642$		0			0
$643$	−4.58629	−	5.09359i	−0.180866	−	0.200872i	0.645894	−	0.763427i	$-0.276485\pi$
$643$	−4.58629	−	5.09359i	−0.180866	−	0.200872i	−0.826759	+	0.562556i	$0.809818\pi$
$644$	−5.72930	−	6.36303i	−0.225766	−	0.250739i
$645$		0			0
$646$	0.193806	−	1.84395i	0.00762521	−	0.0725490i
$647$	1.29180	+	3.97574i	0.0507857	+	0.156302i	0.973233	−	0.229821i	$-0.0738140\pi$
$647$	1.29180	+	3.97574i	0.0507857	+	0.156302i	−0.922447	+	0.386123i	$0.873814\pi$
$648$		0			0
$649$	−3.54508	−	4.02874i	−0.139157	−	0.158142i
$650$	−4.29180	−	7.43361i	−0.168338	−	0.291570i
$651$		0			0
$652$	−35.0757	+	15.6167i	−1.37367	+	0.611597i
$653$	−0.142230	−	1.35323i	−0.00556588	−	0.0529558i	0.991386	−	0.130969i	$-0.0418089\pi$
$653$	−0.142230	−	1.35323i	−0.00556588	−	0.0529558i	−0.996952	+	0.0780135i	$0.975142\pi$
$654$		0			0
$655$	25.6756	−	5.45752i	1.00323	−	0.213243i
$656$	−6.43363	+	4.67430i	−0.251191	+	0.182501i
$657$		0			0
$658$	1.40983	+	4.33901i	0.0549609	+	0.169152i
$659$	4.98936	+	8.64182i	0.194358	+	0.336637i	0.946690	−	0.322147i	$-0.104404\pi$
$659$	4.98936	+	8.64182i	0.194358	+	0.336637i	−0.752332	+	0.658784i	$0.771071\pi$
$660$		0			0
$661$	2.14590	−	3.71680i	0.0834658	−	0.144567i	−0.821271	−	0.570539i	$-0.806734\pi$
$661$	2.14590	−	3.71680i	0.0834658	−	0.144567i	0.904736	+	0.425972i	$0.140068\pi$
$662$	−5.38625	−	1.14488i	−0.209342	−	0.0444971i
$663$		0			0
$664$	−13.1312	−	5.84637i	−0.509588	−	0.226883i
$665$	−0.381966	+	1.17557i	−0.0148120	+	0.0455867i
$666$		0			0
$667$	18.1353	−	13.1760i	0.702200	−	0.510178i
$668$	1.11709	−	10.6284i	0.0432214	−	0.411224i
$669$		0			0
$670$	−1.41641	+	2.45329i	−0.0547206	+	0.0947789i
$671$	24.3918	−	26.4758i	0.941633	−	1.02209i
$672$		0			0
$673$	−19.7810	+	21.9691i	−0.762503	+	0.846846i	−0.991970	−	0.126471i	$-0.959635\pi$
$673$	−19.7810	+	21.9691i	−0.762503	+	0.846846i	0.229467	+	0.973316i	$0.426302\pi$
$674$	3.54508	+	2.57565i	0.136552	+	0.0992105i
$675$		0			0
$676$	−16.5517	+	50.9408i	−0.636602	+	1.95926i
$677$	5.92340	−	1.25906i	0.227655	−	0.0483895i	−0.0926718	−	0.995697i	$-0.529541\pi$
$677$	5.92340	−	1.25906i	0.227655	−	0.0483895i	0.320326	+	0.947307i	$0.396207\pi$
$678$		0			0
$679$	−5.48127	+	2.44042i	−0.210352	+	0.0936547i
$680$	−8.63980	−	1.83645i	−0.331321	−	0.0704245i
$681$		0			0
$682$	0.250426	−	0.741819i	0.00958933	−	0.0284057i
$683$	5.52786			0.211518			0.105759	−	0.994392i	$-0.466273\pi$
$683$	5.52786			0.211518			0.105759	+	0.994392i	$0.466273\pi$
$684$		0			0
$685$	−8.61803	−	6.26137i	−0.329278	−	0.239235i
$686$	4.53626	+	2.01967i	0.173195	+	0.0771115i
$687$		0			0
$688$	3.90292	+	4.33463i	0.148797	+	0.165256i
$689$	−2.76709	−	26.3271i	−0.105418	−	1.00298i
$690$		0			0
$691$	9.76713	−	10.8475i	0.371559	−	0.412658i	−0.528148	−	0.849152i	$-0.677113\pi$
$691$	9.76713	−	10.8475i	0.371559	−	0.412658i	0.899707	+	0.436494i	$0.143780\pi$
$692$	−42.8115			−1.62745
$693$		0			0
$694$	3.39512			0.128877
$695$	8.02957	−	8.91774i	0.304579	−	0.338269i
$696$		0			0
$697$	1.28262	+	12.2033i	0.0485826	+	0.462233i
$698$	−1.05963	−	1.17684i	−0.0401076	−	0.0445440i
$699$		0			0
$700$	−5.88113	−	2.61845i	−0.222286	−	0.0989680i
$701$	−38.6074	−	28.0499i	−1.45818	−	1.05943i	−0.983832	−	0.179094i	$-0.942683\pi$
$701$	−38.6074	−	28.0499i	−1.45818	−	1.05943i	−0.474349	−	0.880337i	$-0.657317\pi$
$702$		0			0
$703$	−5.09017			−0.191979
$704$	12.5275	+	9.32204i	0.472148	+	0.351338i
$705$		0			0
$706$	−6.13348	−	1.30371i	−0.230837	−	0.0490659i
$707$	−7.73968	+	3.44593i	−0.291081	+	0.129597i
$708$		0			0
$709$	25.2009	−	5.35662i	0.946441	−	0.201172i	0.291260	−	0.956644i	$-0.405926\pi$
$709$	25.2009	−	5.35662i	0.946441	−	0.201172i	0.655181	+	0.755472i	$0.272592\pi$
$710$	0.424538	−	1.30660i	0.0159326	−	0.0490356i
$711$		0			0
$712$	8.05573	+	5.85283i	0.301901	+	0.219344i
$713$	−1.90977	+	2.12101i	−0.0715213	+	0.0794325i
$714$		0			0
$715$	−24.1144	−	11.0679i	−0.901826	−	0.413914i
$716$	4.68692	−	8.11798i	0.175158	−	0.303383i
$717$		0			0
$718$	−0.912480	+	8.68167i	−0.0340535	+	0.323997i
$719$	−15.8541	+	11.5187i	−0.591258	+	0.429574i	−0.842765	−	0.538281i	$-0.819074\pi$
$719$	−15.8541	+	11.5187i	−0.591258	+	0.429574i	0.251507	+	0.967855i	$0.419074\pi$
$720$		0			0
$721$	3.16312	−	9.73508i	0.117801	−	0.362553i
$722$	−6.28098	−	2.79647i	−0.233754	−	0.104074i
$723$		0			0
$724$	−17.9723	−	3.82014i	−0.667936	−	0.141974i
$725$	8.42705	−	14.5961i	0.312973	−	0.542085i
$726$		0			0
$727$	−9.41641	−	16.3097i	−0.349235	−	0.604893i	0.636879	−	0.770964i	$-0.280225\pi$
$727$	−9.41641	−	16.3097i	−0.349235	−	0.604893i	−0.986114	+	0.166071i	$0.946892\pi$
$728$	−2.94427	−	9.06154i	−0.109122	−	0.335843i
$729$		0			0
$730$	0.0557281	−	0.0404888i	0.00206259	−	0.00149856i
$731$	8.80333	−	1.87121i	0.325603	−	0.0692090i
$732$		0			0
$733$	−5.06672	−	48.2066i	−0.187143	−	1.78055i	−0.536836	−	0.843687i	$-0.680381\pi$
$733$	−5.06672	−	48.2066i	−0.187143	−	1.78055i	0.349692	−	0.936865i	$-0.386286\pi$
$734$	−4.43444	+	1.97434i	−0.163678	+	0.0728743i
$735$		0			0
$736$	9.57295	+	16.5808i	0.352864	+	0.611178i
$737$	−1.85410	−	19.8132i	−0.0682967	−	0.729828i
$738$		0			0
$739$	13.1459	+	40.4589i	0.483580	+	1.48831i	0.834027	+	0.551723i	$0.186029\pi$
$739$	13.1459	+	40.4589i	0.483580	+	1.48831i	−0.350448	+	0.936582i	$0.613971\pi$
$740$	−1.21939	+	11.6017i	−0.0448257	+	0.426488i
$741$		0			0
$742$	1.04539	+	1.16102i	0.0383774	+	0.0426224i
$743$	28.3448	+	31.4801i	1.03987	+	1.15489i	0.987717	+	0.156255i	$0.0499420\pi$
$743$	28.3448	+	31.4801i	1.03987	+	1.15489i	0.0521540	+	0.998639i	$0.483391\pi$
$744$		0			0
$745$	−1.96136	+	18.6611i	−0.0718589	+	0.683691i
$746$	−0.667184	−	2.05338i	−0.0244274	−	0.0751797i
$747$		0			0
$748$	27.4058	−	11.8290i	1.00205	−	0.432509i
$749$	−7.01722	−	12.1542i	−0.256404	−	0.444104i
$750$		0			0
$751$	−28.5476	+	12.7102i	−1.04172	+	0.463802i	−0.855009	−	0.518614i	$-0.826448\pi$
$751$	−28.5476	+	12.7102i	−1.04172	+	0.463802i	−0.186707	+	0.982416i	$0.559782\pi$
$752$	3.92771	+	37.3696i	0.143229	+	1.36273i
$753$		0			0
$754$	11.7378	−	2.49494i	0.427464	−	0.0908604i
$755$	−4.32624	+	3.14320i	−0.157448	+	0.114393i
$756$		0			0
$757$	3.39919	+	10.4616i	0.123546	+	0.380234i	0.993633	−	0.112663i	$-0.0359380\pi$
$757$	3.39919	+	10.4616i	0.123546	+	0.380234i	−0.870088	+	0.492897i	$0.835938\pi$
$758$	−3.01722	−	5.22598i	−0.109590	−	0.189816i
$759$		0			0
$760$	0.909830	−	1.57587i	0.0330030	−	0.0571629i
$761$	6.82621	+	1.45096i	0.247450	+	0.0525971i	0.329967	−	0.943993i	$-0.392962\pi$
$761$	6.82621	+	1.45096i	0.247450	+	0.0525971i	−0.0825167	+	0.996590i	$0.526296\pi$
$762$		0			0
$763$	−6.52810	−	2.90650i	−0.236333	−	0.105222i
$764$	3.40576	−	10.4819i	0.123216	−	0.379221i
$765$		0			0
$766$	6.13525	−	4.45752i	0.221676	−	0.161057i
$767$	−1.09464	+	10.4148i	−0.0395250	+	0.376055i
$768$		0			0
$769$	7.89919	−	13.6818i	0.284852	−	0.493378i	−0.687721	−	0.725975i	$-0.741389\pi$
$769$	7.89919	−	13.6818i	0.284852	−	0.493378i	0.972573	+	0.232597i	$0.0747222\pi$
$770$	1.53529	−	0.308068i	0.0553282	−	0.0111020i
$771$		0			0
$772$	13.6470	−	15.1565i	0.491166	−	0.545495i
$773$	19.1353	+	13.9026i	0.688247	+	0.500041i	0.876083	−	0.482159i	$-0.160147\pi$
$773$	19.1353	+	13.9026i	0.688247	+	0.500041i	−0.187836	+	0.982200i	$0.560147\pi$
$774$		0			0
$775$	−0.663119	+	2.04087i	−0.0238199	+	0.0733102i
$776$	8.63980	−	1.83645i	0.310151	−	0.0659246i
$777$		0			0
$778$	7.90443	−	3.51928i	0.283388	−	0.126172i
$779$	−2.47262	−	0.525572i	−0.0885910	−	0.0188306i
$780$		0			0
$781$	2.87733	+	9.21191i	0.102959	+	0.329628i
$782$	8.56231			0.306187
$783$		0			0
$784$	15.2705	+	11.0947i	0.545375	+	0.396238i
$785$	8.06918	+	3.59263i	0.288001	+	0.128226i
$786$		0			0
$787$	24.0887	+	26.7532i	0.858669	+	0.953649i	0.999337	−	0.0364078i	$-0.0115915\pi$
$787$	24.0887	+	26.7532i	0.858669	+	0.953649i	−0.140668	+	0.990057i	$0.544925\pi$
$788$	−1.59620	−	15.1869i	−0.0568624	−	0.541009i
$789$		0			0
$790$	3.33685	−	3.70595i	0.118720	−	0.131852i
$791$	17.2361			0.612844
$792$		0			0
$793$	−70.2492			−2.49462
$794$	−0.543019	+	0.603084i	−0.0192710	+	0.0214026i
$795$		0			0
$796$	−1.38492	−	13.1766i	−0.0490872	−	0.467034i
$797$	−16.2401	−	18.0365i	−0.575255	−	0.638886i	0.383357	−	0.923600i	$-0.374768\pi$
$797$	−16.2401	−	18.0365i	−0.575255	−	0.638886i	−0.958612	+	0.284714i	$0.908101\pi$
$798$		0			0
$799$	52.9662	+	23.5821i	1.87381	+	0.834274i
$800$	11.6459	+	8.46124i	0.411745	+	0.299150i
$801$		0			0
$802$	−5.56231			−0.196412
$803$	−0.154772	+	0.458469i	−0.00546179	+	0.0161790i
$804$		0			0
$805$	−5.58347	−	1.18680i	−0.196791	−	0.0418293i
$806$	−1.39577	+	0.621438i	−0.0491640	+	0.0218892i
$807$		0			0
$808$	12.1996	−	2.59310i	0.429180	−	0.0912250i
$809$	5.59017	−	17.2048i	0.196540	−	0.604888i	−0.803415	−	0.595419i	$-0.796986\pi$
$809$	5.59017	−	17.2048i	0.196540	−	0.604888i	0.999955	−	0.00946853i	$-0.00301397\pi$
$810$		0			0
$811$	−7.02786	−	5.10604i	−0.246782	−	0.179297i	0.457518	−	0.889201i	$-0.348739\pi$
$811$	−7.02786	−	5.10604i	−0.246782	−	0.179297i	−0.704299	+	0.709903i	$0.748739\pi$
$812$	6.02218	−	6.68830i	0.211337	−	0.234713i
$813$		0			0
$814$	3.16027	+	5.62093i	0.110767	+	0.197013i
$815$	−12.7984	+	22.1674i	−0.448307	+	0.776491i
$816$		0			0
$817$	−0.193806	+	1.84395i	−0.00678043	+	0.0645115i
$818$	10.4271	−	7.57570i	0.364573	−	0.264878i
$819$		0			0
$820$	−1.79024	+	5.50980i	−0.0625180	+	0.192411i
$821$	−34.9109	−	15.5434i	−1.21840	−	0.542467i	−0.306104	−	0.951998i	$-0.599026\pi$
$821$	−34.9109	−	15.5434i	−1.21840	−	0.542467i	−0.912296	+	0.409531i	$0.865692\pi$
$822$		0			0
$823$	41.3676	+	8.79296i	1.44198	+	0.306503i	0.861496	−	0.507765i	$-0.169528\pi$
$823$	41.3676	+	8.79296i	1.44198	+	0.306503i	0.580489	+	0.814268i	$0.302861\pi$
$824$	−7.53444	+	13.0500i	−0.262475	+	0.454620i
$825$		0			0
$826$	−0.309017	−	0.535233i	−0.0107521	−	0.0186231i
$827$	17.6246	+	54.2430i	0.612868	+	1.88621i	0.429147	+	0.903235i	$0.358814\pi$
$827$	17.6246	+	54.2430i	0.612868	+	1.88621i	0.183721	+	0.982978i	$0.441186\pi$
$828$		0			0
$829$	−35.2254	+	25.5928i	−1.22343	+	0.888874i	−0.996380	−	0.0850096i	$-0.972908\pi$
$829$	−35.2254	+	25.5928i	−1.22343	+	0.888874i	−0.227049	+	0.973883i	$0.572908\pi$
$830$	−4.50917	+	0.958453i	−0.156515	+	0.0332684i
$831$		0			0
$832$	−3.18521	−	30.3052i	−0.110427	−	1.05064i
$833$	26.6067	−	11.8460i	0.921866	−	0.410441i
$834$		0			0
$835$	−3.56231	−	6.17009i	−0.123279	−	0.213525i
$836$	0.572949	+	6.12261i	0.0198159	+	0.211755i
$837$		0			0
$838$	−0.954915	−	2.93893i	−0.0329870	−	0.101524i
$839$	−1.80748	+	17.1971i	−0.0624013	+	0.593709i	0.917984	+	0.396618i	$0.129816\pi$
$839$	−1.80748	+	17.1971i	−0.0624013	+	0.593709i	−0.980385	+	0.197091i	$0.936851\pi$
$840$		0			0
$841$	−3.63853	−	4.04099i	−0.125466	−	0.139345i
$842$	2.61619	+	2.90557i	0.0901598	+	0.100133i
$843$		0			0
$844$	3.96763	−	37.7495i	0.136572	−	1.29939i
$845$	11.0344	+	33.9605i	0.379596	+	1.16828i
$846$		0			0
$847$	−7.54508	+	8.00448i	−0.259252	+	0.275037i
$848$	6.43363	+	11.1434i	0.220932	+	0.382665i
$849$		0			0
$850$	5.88113	−	2.61845i	0.201721	−	0.0898120i
$851$	−2.45711	−	23.3778i	−0.0842285	−	0.801381i
$852$		0			0
$853$	34.6633	−	7.36791i	1.18685	−	0.252272i	0.428146	−	0.903710i	$-0.359167\pi$
$853$	34.6633	−	7.36791i	1.18685	−	0.252272i	0.758703	+	0.651437i	$0.225834\pi$
$854$	3.35410	−	2.43690i	0.114775	−	0.0833889i
$855$		0			0
$856$	6.38448	+	19.6494i	0.218217	+	0.671603i
$857$	12.6803	+	21.9630i	0.433152	+	0.750242i	0.997143	−	0.0755396i	$-0.0240679\pi$
$857$	12.6803	+	21.9630i	0.433152	+	0.750242i	−0.563991	+	0.825781i	$0.690735\pi$
$858$		0			0
$859$	16.2812	−	28.1998i	0.555506	−	0.962164i	−0.442358	−	0.896838i	$-0.645858\pi$
$859$	16.2812	−	28.1998i	0.555506	−	0.962164i	0.997864	−	0.0653258i	$-0.0208087\pi$
$860$	4.15637	+	0.883463i	0.141731	+	0.0301258i
$861$		0			0
$862$	11.8881	+	5.29293i	0.404911	+	0.180278i
$863$	−4.46556	+	13.7436i	−0.152009	+	0.467837i	−0.997846	−	0.0656059i	$-0.979102\pi$
$863$	−4.46556	+	13.7436i	−0.152009	+	0.467837i	0.845836	+	0.533443i	$0.179102\pi$
$864$		0			0
$865$	−23.0902	+	16.7760i	−0.785089	+	0.570401i
$866$	−0.588620	+	5.60034i	−0.0200021	+	0.190307i
$867$		0			0
$868$	−0.572949	+	0.992377i	−0.0194472	+	0.0336835i
$869$	−4.05911	+	34.7952i	−0.137696	+	1.18035i
$870$		0			0
$871$	−25.9842	+	28.8584i	−0.880442	+	0.977830i
$872$	8.51064	+	6.18334i	0.288207	+	0.209394i
$873$		0			0
$874$	−0.545085	+	1.67760i	−0.0184378	+	0.0567456i
$875$	−10.2433	+	2.17728i	−0.346287	+	0.0736055i
$876$		0			0
$877$	10.5942	−	4.71682i	0.357739	−	0.159276i	−0.219994	−	0.975501i	$-0.570604\pi$
$877$	10.5942	−	4.71682i	0.357739	−	0.159276i	0.577734	+	0.816225i	$0.303937\pi$
$878$	0.264599	+	0.0562422i	0.00892977	+	0.00189808i
$879$		0			0
$880$	12.8960	+	0.147179i	0.434724	+	0.00496141i
$881$	−1.81966			−0.0613059			−0.0306530	−	0.999530i	$-0.509759\pi$
$881$	−1.81966			−0.0613059			−0.0306530	+	0.999530i	$0.509759\pi$
$882$		0			0
$883$	28.8435	+	20.9560i	0.970660	+	0.705226i	0.955602	−	0.294661i	$-0.0952068\pi$
$883$	28.8435	+	20.9560i	0.970660	+	0.705226i	0.0150579	+	0.999887i	$0.495207\pi$
$884$	−53.2133	−	23.6921i	−1.78976	−	0.796851i
$885$		0			0
$886$	0.315921	+	0.350865i	0.0106136	+	0.0117876i
$887$	−0.421714	−	4.01234i	−0.0141598	−	0.134721i	0.985158	−	0.171649i	$-0.0549095\pi$
$887$	−0.421714	−	4.01234i	−0.0141598	−	0.134721i	−0.999318	+	0.0369278i	$0.988243\pi$
$888$		0			0
$889$	7.06756	−	7.84932i	0.237038	−	0.263258i
$890$	3.19350			0.107046
$891$		0			0
$892$	28.7508			0.962647
$893$	−7.99228	+	8.87632i	−0.267451	+	0.297035i
$894$		0			0
$895$	−0.653222	−	6.21499i	−0.0218348	−	0.207744i
$896$	6.75164	+	7.49846i	0.225557	+	0.250506i
$897$		0			0
$898$	−2.60735	−	1.16087i	−0.0870085	−	0.0387387i
$899$	−2.42705	−	1.76336i	−0.0809467	−	0.0588112i
$900$		0			0
$901$	19.8541			0.661436
$902$	0.954773	+	3.05675i	0.0317904	+	0.101779i
$903$		0			0
$904$	−24.8194	−	5.27552i	−0.825480	−	0.175461i
$905$	−11.1902	+	4.98221i	−0.371976	+	0.165614i
$906$		0			0
$907$	14.2649	−	3.03210i	0.473658	−	0.100679i	0.0351037	−	0.999384i	$-0.488824\pi$
$907$	14.2649	−	3.03210i	0.473658	−	0.100679i	0.438555	+	0.898704i	$0.355491\pi$
$908$	−9.52129	+	29.3035i	−0.315975	+	0.972471i
$909$		0			0
$910$	−2.47214	−	1.79611i	−0.0819505	−	0.0595405i
$911$	12.8342	−	14.2538i	0.425214	−	0.472248i	−0.492027	−	0.870580i	$-0.663744\pi$
$911$	12.8342	−	14.2538i	0.425214	−	0.472248i	0.917242	+	0.398331i	$0.130411\pi$
$912$		0			0
$913$	21.9419	−	23.8166i	0.726170	−	0.788215i
$914$	0.190983	−	0.330792i	0.00631716	−	0.0109416i
$915$		0			0
$916$	1.97302	−	18.7720i	0.0651903	−	0.620244i
$917$	−17.1803	+	12.4822i	−0.567345	+	0.412200i
$918$		0			0
$919$	−8.30244	+	25.5523i	−0.273872	+	0.842892i	0.715643	+	0.698466i	$0.246134\pi$
$919$	−8.30244	+	25.5523i	−0.273872	+	0.842892i	−0.989516	+	0.144426i	$0.953866\pi$
$920$	7.67675	+	3.41791i	0.253095	+	0.112685i
$921$		0			0
$922$	−6.03242	−	1.28223i	−0.198667	−	0.0422280i
$923$	9.41641	−	16.3097i	0.309945	−	0.536840i
$924$		0			0
$925$	−8.83688	−	15.3059i	−0.290555	−	0.503256i
$926$	2.00658	+	6.17561i	0.0659402	+	0.202943i
$927$		0			0
$928$	−16.2812	+	11.8290i	−0.534455	+	0.388304i
$929$	−47.2157	+	10.0360i	−1.54910	+	0.329271i	−0.901523	−	0.432732i	$-0.857550\pi$
$929$	−47.2157	+	10.0360i	−1.54910	+	0.329271i	−0.647574	+	0.762003i	$0.724216\pi$
$930$		0			0
$931$	0.627171	+	5.96713i	0.0205547	+	0.195565i
$932$	−18.8429	+	8.38942i	−0.617221	+	0.274804i
$933$		0			0
$934$	−0.145898	−	0.252703i	−0.00477393	−	0.00826869i
$935$	10.1459	−	17.1190i	0.331806	−	0.559852i
$936$		0			0
$937$	−7.11803	−	21.9071i	−0.232536	−	0.715672i	−0.997439	−	0.0715265i	$-0.977213\pi$
$937$	−7.11803	−	21.9071i	−0.232536	−	0.715672i	0.764903	−	0.644146i	$-0.222787\pi$
$938$	0.239558	−	2.27924i	0.00782184	−	0.0744199i
$939$		0			0
$940$	18.3167	+	20.3427i	0.597424	+	0.663507i
$941$	−18.1730	−	20.1831i	−0.592421	−	0.657951i	0.370152	−	0.928971i	$-0.379306\pi$
$941$	−18.1730	−	20.1831i	−0.592421	−	0.657951i	−0.962574	+	0.271021i	$0.912639\pi$
$942$		0			0
$943$	1.22024	−	11.6098i	0.0397365	−	0.378067i
$944$	−1.57295	−	4.84104i	−0.0511951	−	0.157562i
$945$		0			0
$946$	2.15654	−	0.930812i	0.0701152	−	0.0302633i
$947$	18.3541	+	31.7902i	0.596428	+	1.03304i	0.993344	+	0.115189i	$0.0367473\pi$
$947$	18.3541	+	31.7902i	0.596428	+	1.03304i	−0.396915	+	0.917855i	$0.629919\pi$
$948$		0			0
$949$	0.862635	−	0.384070i	0.0280023	−	0.0124674i
$950$	0.138630	+	1.31897i	0.00449774	+	0.0427931i
$951$		0			0
$952$	6.98974	−	1.48572i	0.226539	−	0.0481523i
$953$	−7.68034	+	5.58009i	−0.248791	+	0.180757i	−0.705191	−	0.709018i	$-0.749139\pi$
$953$	−7.68034	+	5.58009i	−0.248791	+	0.180757i	0.456400	+	0.889775i	$0.349139\pi$
$954$		0			0
$955$	−2.27051	−	6.98791i	−0.0734720	−	0.226123i
$956$	−9.70820	−	16.8151i	−0.313986	−	0.543839i
$957$		0			0
$958$	−2.24671	+	3.89142i	−0.0725879	+	0.125726i
$959$	8.42971	+	1.79179i	0.272210	+	0.0578599i
$960$		0			0
$961$	−27.9710	−	12.4535i	−0.902289	−	0.401725i
$962$	3.88854	−	11.9677i	0.125372	−	0.385854i
$963$		0			0
$964$	−40.2492	+	29.2428i	−1.29634	+	0.941846i
$965$	1.42125	−	13.5223i	0.0457516	−	0.435297i
$966$		0			0
$967$	−26.2426	+	45.4536i	−0.843907	+	1.46169i	0.0426608	+	0.999090i	$0.486417\pi$
$967$	−26.2426	+	45.4536i	−0.843907	+	1.46169i	−0.886567	+	0.462599i	$0.846917\pi$
$968$	13.3146	−	9.21682i	0.427949	−	0.296240i
$969$		0			0
$970$	1.89552	−	2.10519i	0.0608616	−	0.0675937i
$971$	7.50000	+	5.44907i	0.240686	+	0.174869i	0.701589	−	0.712582i	$-0.252474\pi$
$971$	7.50000	+	5.44907i	0.240686	+	0.174869i	−0.460903	+	0.887451i	$0.652474\pi$
$972$		0			0
$973$	−3.00000	+	9.23305i	−0.0961756	+	0.295998i
$974$	4.84910	−	1.03071i	0.155375	−	0.0330260i
$975$		0			0
$976$	31.1938	−	13.8884i	0.998490	−	0.444556i
$977$	15.4195	+	3.27751i	0.493312	+	0.104857i	0.447849	−	0.894109i	$-0.352190\pi$
$977$	15.4195	+	3.27751i	0.493312	+	0.104857i	0.0454632	+	0.998966i	$0.485524\pi$
$978$		0			0
$979$	−18.2983	+	12.9781i	−0.584817	+	0.414781i
$980$	13.7508			0.439252
$981$		0			0
$982$	2.26393	+	1.64484i	0.0722450	+	0.0524890i
$983$	−8.45701	−	3.76531i	−0.269737	−	0.120095i	0.267411	−	0.963582i	$-0.413832\pi$
$983$	−8.45701	−	3.76531i	−0.269737	−	0.120095i	−0.537148	+	0.843488i	$0.680498\pi$
$984$		0			0
$985$	−6.81198	−	7.56547i	−0.217048	−	0.241056i
$986$	0.940756	+	8.95070i	0.0299598	+	0.285048i
$987$		0			0
$988$	8.02957	−	8.91774i	0.255455	−	0.283711i
$989$	−8.56231			−0.272265
$990$		0			0
$991$	20.5967			0.654277			0.327139	−	0.944976i	$-0.393916\pi$
$991$	20.5967			0.654277			0.327139	+	0.944976i	$0.393916\pi$
$992$	1.71452	−	1.90416i	0.0544360	−	0.0604573i
$993$		0			0
$994$	0.116179	+	1.10537i	0.00368497	+	0.0350601i
$995$	−5.91031	−	6.56406i	−0.187369	−	0.208095i
$996$		0			0
$997$	6.74376	+	3.00252i	0.213577	+	0.0950906i	0.510737	−	0.859737i	$-0.329373\pi$
$997$	6.74376	+	3.00252i	0.213577	+	0.0950906i	−0.297160	+	0.954828i	$0.596039\pi$
$998$	−11.8713	−	8.62502i	−0.375780	−	0.273020i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.a.280.1		8
3.2	odd	2		99.2.m.a.49.1	yes	8
9.2	odd	6		99.2.m.a.16.1	✓	8
9.4	even	3		891.2.f.a.82.1		4
9.5	odd	6		891.2.f.b.82.1		4
9.7	even	3	inner	297.2.n.a.181.1		8
11.9	even	5	inner	297.2.n.a.64.1		8
33.8	even	10		1089.2.e.d.364.2		4
33.14	odd	10		1089.2.e.g.364.1		4
33.20	odd	10		99.2.m.a.31.1	yes	8
99.14	odd	30		9801.2.a.n.1.2		2
99.20	odd	30		99.2.m.a.97.1	yes	8
99.31	even	15		891.2.f.a.163.1		4
99.41	even	30		9801.2.a.bc.1.1		2
99.47	odd	30		1089.2.e.g.727.1		4
99.58	even	15		9801.2.a.bb.1.1		2
99.74	even	30		1089.2.e.d.727.2		4
99.85	odd	30		9801.2.a.m.1.2		2
99.86	odd	30		891.2.f.b.163.1		4
99.97	even	15	inner	297.2.n.a.262.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.16.1	✓	8	9.2	odd	6
99.2.m.a.31.1	yes	8	33.20	odd	10
99.2.m.a.49.1	yes	8	3.2	odd	2
99.2.m.a.97.1	yes	8	99.20	odd	30
297.2.n.a.64.1		8	11.9	even	5	inner
297.2.n.a.181.1		8	9.7	even	3	inner
297.2.n.a.262.1		8	99.97	even	15	inner
297.2.n.a.280.1		8	1.1	even	1	trivial
891.2.f.a.82.1		4	9.4	even	3
891.2.f.a.163.1		4	99.31	even	15
891.2.f.b.82.1		4	9.5	odd	6
891.2.f.b.163.1		4	99.86	odd	30
1089.2.e.d.364.2		4	33.8	even	10
1089.2.e.d.727.2		4	99.74	even	30
1089.2.e.g.364.1		4	33.14	odd	10
1089.2.e.g.727.1		4	99.47	odd	30
9801.2.a.m.1.2		2	99.85	odd	30
9801.2.a.n.1.2		2	99.14	odd	30
9801.2.a.bb.1.1		2	99.58	even	15
9801.2.a.bc.1.1		2	99.41	even	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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.255585 - 0.283856i) q^{2} +(0.193806 + 1.84395i) q^{4} +(0.827091 + 0.918578i) q^{5} +(-0.913545 - 0.406737i) q^{7} +(1.19098 + 0.865300i) q^{8} +O(q^{10})\)	\(q+(0.255585 - 0.283856i) q^{2} +(0.193806 + 1.84395i) q^{4} +(0.827091 + 0.918578i) q^{5} +(-0.913545 - 0.406737i) q^{7} +(1.19098 + 0.865300i) q^{8} +0.472136 q^{10} +(-2.70528 + 1.91872i) q^{11} +(6.33070 + 1.34563i) q^{13} +(-0.348943 + 0.155360i) q^{14} +(-3.07715 + 0.654069i) q^{16} +(-1.50000 + 4.61653i) q^{17} +(-0.809017 - 0.587785i) q^{19} +(-1.53351 + 1.70314i) q^{20} +(-0.146790 + 1.25830i) q^{22} +(2.30902 - 3.99933i) q^{23} +(0.362937 - 3.45312i) q^{25} +(2.00000 - 1.45309i) q^{26} +(0.572949 - 1.76336i) q^{28} +(4.43444 + 1.97434i) q^{29} +(-0.604528 - 0.128496i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 + 1.60570i) q^{34} +(-0.381966 - 1.17557i) q^{35} +(4.11803 - 2.99193i) q^{37} +(-0.373619 + 0.0794152i) q^{38} +(0.190206 + 1.80969i) q^{40} +(2.30932 - 1.02817i) q^{41} +(-0.927051 - 1.60570i) q^{43} +(-4.06231 - 4.61653i) q^{44} +(-0.545085 - 1.67760i) q^{46} +(1.24852 - 11.8788i) q^{47} +(-4.01478 - 4.45887i) q^{49} +(-0.887426 - 0.985587i) q^{50} +(-1.25434 + 11.9343i) q^{52} +(-1.26393 - 3.88998i) q^{53} +(-4.00000 - 0.898056i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.69381 - 0.754131i) q^{58} +(0.169131 + 1.60917i) q^{59} +(-10.6169 + 2.25669i) q^{61} +(-0.190983 + 0.138757i) q^{62} +(-1.45492 - 4.47777i) q^{64} +(4.00000 + 6.92820i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(-8.80333 - 1.87121i) q^{68} +(-0.431318 - 0.192035i) q^{70} +(0.899187 - 2.76741i) q^{71} +(0.118034 - 0.0857567i) q^{73} +(0.203232 - 1.93362i) q^{74} +(0.927051 - 1.60570i) q^{76} +(3.25181 - 0.652498i) q^{77} +(7.06756 - 7.84932i) q^{79} +(-3.14590 - 2.28563i) q^{80} +(0.298374 - 0.918300i) q^{82} +(-9.55057 + 2.03004i) q^{83} +(-5.48127 + 2.44042i) q^{85} +(-0.692728 - 0.147244i) q^{86} +(-4.88220 - 0.0557196i) q^{88} +6.76393 q^{89} +(-5.23607 - 3.80423i) q^{91} +(7.82206 + 3.48260i) q^{92} +(-3.05278 - 3.39045i) q^{94} +(-0.129204 - 1.22930i) q^{95} +(4.01478 - 4.45887i) q^{97} -2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8	\( 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28} + 9 q^{29} - 3 q^{31} - 30 q^{32} - 6 q^{34} - 12 q^{35} + 24 q^{37} + 4 q^{38} + 12 q^{40} - 3 q^{41} + 6 q^{43} + 48 q^{44} + 18 q^{46} - 23 q^{47} - 6 q^{49} + 24 q^{50} + 12 q^{52} - 28 q^{53} - 32 q^{55} + 12 q^{56} + 6 q^{58} - 3 q^{59} - 6 q^{62} - 34 q^{64} + 32 q^{65} - 24 q^{67} + 9 q^{68} - 6 q^{70} - 42 q^{71} - 8 q^{73} - 13 q^{74} - 6 q^{76} + 11 q^{77} - 22 q^{79} - 52 q^{80} - 96 q^{82} + 17 q^{83} - 6 q^{85} - 21 q^{86} + 37 q^{88} + 72 q^{89} - 24 q^{91} + 21 q^{92} + 28 q^{94} + 4 q^{95} + 6 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8 - 32 * q^10 - q^11 + 8 * q^13 + q^14 + 14 * q^16 - 12 * q^17 - 2 * q^19 - 24 * q^20 + 11 * q^22 + 14 * q^23 - 9 * q^25 + 16 * q^26 + 18 * q^28 + 9 * q^29 - 3 * q^31 - 30 * q^32 - 6 * q^34 - 12 * q^35 + 24 * q^37 + 4 * q^38 + 12 * q^40 - 3 * q^41 + 6 * q^43 + 48 * q^44 + 18 * q^46 - 23 * q^47 - 6 * q^49 + 24 * q^50 + 12 * q^52 - 28 * q^53 - 32 * q^55 + 12 * q^56 + 6 * q^58 - 3 * q^59 - 6 * q^62 - 34 * q^64 + 32 * q^65 - 24 * q^67 + 9 * q^68 - 6 * q^70 - 42 * q^71 - 8 * q^73 - 13 * q^74 - 6 * q^76 + 11 * q^77 - 22 * q^79 - 52 * q^80 - 96 * q^82 + 17 * q^83 - 6 * q^85 - 21 * q^86 + 37 * q^88 + 72 * q^89 - 24 * q^91 + 21 * q^92 + 28 * q^94 + 4 * q^95 + 6 * q^97 - 72 * q^98

Introduction

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