LMFDB - Embedded newform 1197.2.db.a.647.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(647,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("1197.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.db (of order $6$, degree $2$, 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:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.20
Character	$\chi$	$=$	1197.647
Dual form			1197.2.db.a.1160.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.509165 + 0.293966i) q^{2} +(-0.827168 + 1.43270i) q^{4} +(-1.37766 - 2.38618i) q^{5} +(-0.00278646 - 2.64575i) q^{7} -2.14850i q^{8} +O(q^{10})$	\(q+(-0.509165 + 0.293966i) q^{2} +(-0.827168 + 1.43270i) q^{4} +(-1.37766 - 2.38618i) q^{5} +(-0.00278646 - 2.64575i) q^{7} -2.14850i q^{8} +(1.40292 + 0.809974i) q^{10} +(3.36563 + 1.94315i) q^{11} +6.54433i q^{13} +(0.779180 + 1.34630i) q^{14} +(-1.02275 - 1.77145i) q^{16} +(2.51026 - 4.34790i) q^{17} +(-0.866025 + 0.500000i) q^{19} +4.55824 q^{20} -2.28488 q^{22} +(-4.97438 + 2.87196i) q^{23} +(-1.29592 + 2.24460i) q^{25} +(-1.92381 - 3.33214i) q^{26} +(3.79286 + 2.18449i) q^{28} -7.04531i q^{29} +(-4.48027 - 2.58668i) q^{31} +(4.76281 + 2.74981i) q^{32} +2.95173i q^{34} +(-6.30941 + 3.65160i) q^{35} +(-3.52719 - 6.10927i) q^{37} +(0.293966 - 0.509165i) q^{38} +(-5.12673 + 2.95992i) q^{40} +4.39034 q^{41} -3.32627 q^{43} +(-5.56788 + 3.21462i) q^{44} +(1.68852 - 2.92460i) q^{46} +(-3.56932 - 6.18224i) q^{47} +(-6.99998 + 0.0147445i) q^{49} -1.52383i q^{50} +(-9.37603 - 5.41326i) q^{52} +(-8.94624 - 5.16511i) q^{53} -10.7080i q^{55} +(-5.68440 + 0.00598671i) q^{56} +(2.07108 + 3.58722i) q^{58} +(1.72947 - 2.99553i) q^{59} +(-10.2209 + 5.90104i) q^{61} +3.04159 q^{62} +0.857584 q^{64} +(15.6160 - 9.01589i) q^{65} +(-1.26162 + 2.18519i) q^{67} +(4.15282 + 7.19289i) q^{68} +(2.13908 - 3.71402i) q^{70} -7.91220i q^{71} +(12.4419 + 7.18334i) q^{73} +(3.59184 + 2.07375i) q^{74} -1.65434i q^{76} +(5.13171 - 8.91004i) q^{77} +(-7.41271 - 12.8392i) q^{79} +(-2.81801 + 4.88093i) q^{80} +(-2.23541 + 1.29061i) q^{82} +2.47367 q^{83} -13.8332 q^{85} +(1.69362 - 0.977813i) q^{86} +(4.17486 - 7.23107i) q^{88} +(0.270665 + 0.468806i) q^{89} +(17.3147 - 0.0182355i) q^{91} -9.50236i q^{92} +(3.63474 + 2.09852i) q^{94} +(2.38618 + 1.37766i) q^{95} -4.30784i q^{97} +(3.55981 - 2.06527i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) $ 96 * q + 48 * q^4 + 8 * q^7	$ 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−0.509165	+	0.293966i	−0.360034	+	0.207866i	−0.669096	−	0.743176i	$-0.733318\pi$
$2$	−0.509165	+	0.293966i	−0.360034	+	0.207866i	0.309062	+	0.951042i	$0.399985\pi$
$3$		0			0
$3$		0			0
$4$	−0.827168	+	1.43270i	−0.413584	+	0.716348i
$5$	−1.37766	−	2.38618i	−0.616110	−	1.06713i	−0.990189	−	0.139737i	$-0.955374\pi$
$5$	−1.37766	−	2.38618i	−0.616110	−	1.06713i	0.374078	−	0.927397i	$-0.377959\pi$
$6$		0			0
$7$	−0.00278646	−	2.64575i	−0.00105318	−	0.999999i
$7$	−0.00278646	−	2.64575i	−0.00105318	−	0.999999i
$8$		−	2.14850i		−	0.759611i
$9$		0			0
$10$	1.40292	+	0.809974i	0.443641	+	0.256136i
$11$	3.36563	+	1.94315i	1.01478	+	0.585881i	0.912587	−	0.408884i	$-0.134082\pi$
$11$	3.36563	+	1.94315i	1.01478	+	0.585881i	0.102190	+	0.994765i	$0.467415\pi$
$12$		0			0
$13$			6.54433i			1.81507i	0.419976	+	0.907535i	$0.362038\pi$
$13$			6.54433i			1.81507i	−0.419976	+	0.907535i	$0.637962\pi$
$14$	0.779180	+	1.34630i	0.208245	+	0.359815i
$15$		0			0
$16$	−1.02275	−	1.77145i	−0.255687	−	0.442863i
$17$	2.51026	−	4.34790i	0.608828	−	1.05452i	−0.382606	−	0.923912i	$-0.624973\pi$
$17$	2.51026	−	4.34790i	0.608828	−	1.05452i	0.991434	−	0.130610i	$-0.0416935\pi$
$18$		0			0
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$20$	4.55824			1.01925
$21$		0			0
$22$	−2.28488			−0.487138
$23$	−4.97438	+	2.87196i	−1.03723	+	0.598845i	−0.919047	−	0.394147i	$-0.871040\pi$
$23$	−4.97438	+	2.87196i	−1.03723	+	0.598845i	−0.118182	+	0.992992i	$0.537707\pi$
$24$		0			0
$25$	−1.29592	+	2.24460i	−0.259184	+	0.448919i
$26$	−1.92381	−	3.33214i	−0.377291	−	0.653487i
$27$		0			0
$28$	3.79286	+	2.18449i	0.716783	+	0.412829i
$29$		−	7.04531i		−	1.30828i	−0.756373	−	0.654141i	$-0.773030\pi$
$29$		−	7.04531i		−	1.30828i	0.756373	−	0.654141i	$-0.226970\pi$
$30$		0			0
$31$	−4.48027	−	2.58668i	−0.804680	−	0.464582i	0.0404253	−	0.999183i	$-0.487129\pi$
$31$	−4.48027	−	2.58668i	−0.804680	−	0.464582i	−0.845105	+	0.534601i	$0.820462\pi$
$32$	4.76281	+	2.74981i	0.841954	+	0.486102i
$33$		0			0
$34$			2.95173i			0.506218i
$35$	−6.30941	+	3.65160i	−1.06648	+	0.617234i
$36$		0			0
$37$	−3.52719	−	6.10927i	−0.579866	−	1.00436i	−0.995494	−	0.0948229i	$-0.969772\pi$
$37$	−3.52719	−	6.10927i	−0.579866	−	1.00436i	0.415628	−	0.909535i	$-0.363562\pi$
$38$	0.293966	−	0.509165i	0.0476876	−	0.0825974i
$39$		0			0
$40$	−5.12673	+	2.95992i	−0.810606	+	0.468004i
$41$	4.39034			0.685656			0.342828	−	0.939398i	$-0.388615\pi$
$41$	4.39034			0.685656			0.342828	+	0.939398i	$0.388615\pi$
$42$		0			0
$43$	−3.32627			−0.507252			−0.253626	−	0.967302i	$-0.581623\pi$
$43$	−3.32627			−0.507252			−0.253626	+	0.967302i	$0.581623\pi$
$44$	−5.56788	+	3.21462i	−0.839390	+	0.484622i
$45$		0			0
$46$	1.68852	−	2.92460i	0.248958	−	0.431209i
$47$	−3.56932	−	6.18224i	−0.520639	−	0.901773i	−0.999712	−	0.0239978i	$-0.992361\pi$
$47$	−3.56932	−	6.18224i	−0.520639	−	0.901773i	0.479073	−	0.877775i	$-0.340973\pi$
$48$		0			0
$49$	−6.99998	+	0.0147445i	−0.999998	+	0.00210636i
$50$		−	1.52383i		−	0.215501i
$51$		0			0
$52$	−9.37603	−	5.41326i	−1.30022	−	0.750684i
$53$	−8.94624	−	5.16511i	−1.22886	−	0.709483i	−0.262069	−	0.965049i	$-0.584405\pi$
$53$	−8.94624	−	5.16511i	−1.22886	−	0.709483i	−0.966791	+	0.255567i	$0.917738\pi$
$54$		0			0
$55$		−	10.7080i		−	1.44387i
$56$	−5.68440	+	0.00598671i	−0.759610	+	0.000800008i
$57$		0			0
$58$	2.07108	+	3.58722i	0.271947	+	0.471025i
$59$	1.72947	−	2.99553i	0.225158	−	0.389985i	−0.731209	−	0.682154i	$-0.761043\pi$
$59$	1.72947	−	2.99553i	0.225158	−	0.389985i	0.956367	+	0.292168i	$0.0943768\pi$
$60$		0			0
$61$	−10.2209	+	5.90104i	−1.30865	+	0.755551i	−0.981871	−	0.189549i	$-0.939298\pi$
$61$	−10.2209	+	5.90104i	−1.30865	+	0.755551i	−0.326782	+	0.945100i	$0.605964\pi$
$62$	3.04159			0.386282
$63$		0			0
$64$	0.857584			0.107198
$65$	15.6160	−	9.01589i	1.93692	−	1.11828i
$66$		0			0
$67$	−1.26162	+	2.18519i	−0.154131	+	0.266963i	−0.932742	−	0.360544i	$-0.882591\pi$
$67$	−1.26162	+	2.18519i	−0.154131	+	0.266963i	0.778611	+	0.627507i	$0.215924\pi$
$68$	4.15282	+	7.19289i	0.503603	+	0.872266i
$69$		0			0
$70$	2.13908	−	3.71402i	0.255669	−	0.443910i
$71$		−	7.91220i		−	0.939005i	−0.882931	−	0.469503i	$-0.844433\pi$
$71$		−	7.91220i		−	0.939005i	0.882931	−	0.469503i	$-0.155567\pi$
$72$		0			0
$73$	12.4419	+	7.18334i	1.45622	+	0.840747i	0.998822	−	0.0485175i	$-0.0154497\pi$
$73$	12.4419	+	7.18334i	1.45622	+	0.840747i	0.457394	+	0.889264i	$0.348783\pi$
$74$	3.59184	+	2.07375i	0.417543	+	0.241068i
$75$		0			0
$76$		−	1.65434i		−	0.189765i
$77$	5.13171	−	8.91004i	0.584812	−	1.01539i
$78$		0			0
$79$	−7.41271	−	12.8392i	−0.833995	−	1.44452i	−0.894846	−	0.446375i	$-0.852715\pi$
$79$	−7.41271	−	12.8392i	−0.833995	−	1.44452i	0.0608504	−	0.998147i	$-0.480619\pi$
$80$	−2.81801	+	4.88093i	−0.315063	+	0.545704i
$81$		0			0
$82$	−2.23541	+	1.29061i	−0.246859	+	0.142524i
$83$	2.47367			0.271520			0.135760	−	0.990742i	$-0.456652\pi$
$83$	2.47367			0.271520			0.135760	+	0.990742i	$0.456652\pi$
$84$		0			0
$85$	−13.8332			−1.50042
$86$	1.69362	−	0.977813i	0.182628	−	0.105440i
$87$		0			0
$88$	4.17486	−	7.23107i	0.445042	−	0.770835i
$89$	0.270665	+	0.468806i	0.0286905	+	0.0496934i	0.880014	−	0.474947i	$-0.157533\pi$
$89$	0.270665	+	0.468806i	0.0286905	+	0.0496934i	−0.851324	+	0.524641i	$0.824200\pi$
$90$		0			0
$91$	17.3147	−	0.0182355i	1.81507	−	0.00191160i
$92$		−	9.50236i		−	0.990690i
$93$		0			0
$94$	3.63474	+	2.09852i	0.374895	+	0.216446i
$95$	2.38618	+	1.37766i	0.244817	+	0.141345i
$96$		0			0
$97$		−	4.30784i		−	0.437395i	−0.975793	−	0.218698i	$-0.929819\pi$
$97$		−	4.30784i		−	0.437395i	0.975793	−	0.218698i	$-0.0701808\pi$
$98$	3.55981	−	2.06527i	0.359595	−	0.208624i
$99$		0			0
$100$	−2.14388	−	3.71331i	−0.214388	−	0.371331i
$101$	−3.81725	+	6.61167i	−0.379830	+	0.657885i	−0.991037	−	0.133585i	$-0.957351\pi$
$101$	−3.81725	+	6.61167i	−0.379830	+	0.657885i	0.611207	+	0.791471i	$0.290684\pi$
$102$		0			0
$103$	8.62113	−	4.97741i	0.849465	−	0.490439i	−0.0110054	−	0.999939i	$-0.503503\pi$
$103$	8.62113	−	4.97741i	0.849465	−	0.490439i	0.860470	+	0.509501i	$0.170170\pi$
$104$	14.0605			1.37875
$105$		0			0
$106$	6.07348			0.589908
$107$	−3.57401	+	2.06346i	−0.345513	+	0.199482i	−0.662707	−	0.748879i	$-0.730593\pi$
$107$	−3.57401	+	2.06346i	−0.345513	+	0.199482i	0.317194	+	0.948361i	$0.397259\pi$
$108$		0			0
$109$	−2.54339	+	4.40528i	−0.243612	+	0.421949i	−0.961741	−	0.273962i	$-0.911666\pi$
$109$	−2.54339	+	4.40528i	−0.243612	+	0.421949i	0.718128	+	0.695911i	$0.244999\pi$
$110$	3.14780	+	5.45215i	0.300131	+	0.519842i
$111$		0			0
$112$	−4.68397	+	2.71087i	−0.442593	+	0.256153i
$113$		−	14.7057i		−	1.38340i	−0.722187	−	0.691698i	$-0.756863\pi$
$113$		−	14.7057i		−	1.38340i	0.722187	−	0.691698i	$-0.243137\pi$
$114$		0			0
$115$	13.7060	+	7.91319i	1.27810	+	0.737909i
$116$	10.0938	+	5.82765i	0.937185	+	0.541084i
$117$		0			0
$118$			2.03363i			0.187211i
$119$	−11.5105	−	6.62941i	−1.05516	−	0.607717i
$120$		0			0
$121$	2.05165	+	3.55357i	0.186514	+	0.323052i
$122$	3.46942	−	6.00921i	0.314106	−	0.544048i
$123$		0			0
$124$	7.41186	−	4.27924i	0.665605	−	0.384287i
$125$	−6.63528			−0.593478
$126$		0			0
$127$	3.67297			0.325924			0.162962	−	0.986632i	$-0.447895\pi$
$127$	3.67297			0.325924			0.162962	+	0.986632i	$0.447895\pi$
$128$	−9.96227	+	5.75172i	−0.880549	+	0.508385i
$129$		0			0
$130$	−5.30073	+	9.18114i	−0.464905	+	0.805239i
$131$	−4.52884	−	7.84418i	−0.395687	−	0.685350i	0.597502	−	0.801868i	$-0.296160\pi$
$131$	−4.52884	−	7.84418i	−0.395687	−	0.685350i	−0.993189	+	0.116518i	$0.962827\pi$
$132$		0			0
$133$	1.32529	+	2.28989i	0.114917	+	0.198559i
$134$		−	1.48349i		−	0.128154i
$135$		0			0
$136$	−9.34148	−	5.39331i	−0.801026	−	0.462472i
$137$	−8.81410	−	5.08882i	−0.753039	−	0.434768i	0.0737516	−	0.997277i	$-0.476503\pi$
$137$	−8.81410	−	5.08882i	−0.753039	−	0.434768i	−0.826791	+	0.562509i	$0.809836\pi$
$138$		0			0
$139$			9.07252i			0.769521i	0.923016	+	0.384761i	$0.125716\pi$
$139$			9.07252i			0.769521i	−0.923016	+	0.384761i	$0.874284\pi$
$140$	−0.0127013	−	12.0600i	−0.00107346	−	1.01925i
$141$		0			0
$142$	2.32592	+	4.02861i	0.195187	+	0.338074i
$143$	−12.7166	+	22.0258i	−1.06342	+	1.84189i
$144$		0			0
$145$	−16.8114	+	9.70607i	−1.39611	+	0.806045i
$146$	−8.44665			−0.699049
$147$		0			0
$148$	11.6703			0.959293
$149$	−17.7633	+	10.2556i	−1.45522	+	0.840174i	−0.998771	−	0.0495727i	$-0.984214\pi$
$149$	−17.7633	+	10.2556i	−1.45522	+	0.840174i	−0.456454	+	0.889747i	$0.650881\pi$
$150$		0			0
$151$	−5.00518	+	8.66923i	−0.407316	+	0.705492i	−0.994588	−	0.103898i	$-0.966869\pi$
$151$	−5.00518	+	8.66923i	−0.407316	+	0.705492i	0.587272	+	0.809390i	$0.300202\pi$
$152$	1.07425	+	1.86066i	0.0871333	+	0.150919i
$153$		0			0
$154$	0.00636672	+	6.04522i	0.000513045	+	0.487138i
$155$			14.2543i			1.14493i
$156$		0			0
$157$	16.1510	+	9.32477i	1.28899	+	0.744197i	0.978474	−	0.206371i	$-0.0661655\pi$
$157$	16.1510	+	9.32477i	1.28899	+	0.744197i	0.310514	+	0.950569i	$0.399499\pi$
$158$	7.54858	+	4.35818i	0.600533	+	0.346718i
$159$		0			0
$160$		−	15.1533i		−	1.19797i
$161$	7.61235	+	13.1530i	0.599937	+	1.03660i
$162$		0			0
$163$	−5.21975	−	9.04088i	−0.408843	−	0.708136i	0.585918	−	0.810371i	$-0.300734\pi$
$163$	−5.21975	−	9.04088i	−0.408843	−	0.708136i	−0.994760	+	0.102234i	$0.967401\pi$
$164$	−3.63155	+	6.29003i	−0.283576	+	0.491168i
$165$		0			0
$166$	−1.25950	+	0.727175i	−0.0977565	+	0.0564398i
$167$	1.09990			0.0851130			0.0425565	−	0.999094i	$-0.486450\pi$
$167$	1.09990			0.0851130			0.0425565	+	0.999094i	$0.486450\pi$
$168$		0			0
$169$	−29.8282			−2.29448
$170$	7.04338	−	4.06650i	0.540202	−	0.311886i
$171$		0			0
$172$	2.75139	−	4.76554i	0.209791	−	0.363369i
$173$	−3.83623	−	6.64454i	−0.291663	−	0.505175i	0.682540	−	0.730848i	$-0.260875\pi$
$173$	−3.83623	−	6.64454i	−0.291663	−	0.505175i	−0.974203	+	0.225673i	$0.927542\pi$
$174$		0			0
$175$	5.94225	+	3.42242i	0.449192	+	0.258711i
$176$		−	7.94940i		−	0.599209i
$177$		0			0
$178$	−0.275626	−	0.159133i	−0.0206591	−	0.0119275i
$179$	−14.8388	−	8.56716i	−1.10910	−	0.640339i	−0.170504	−	0.985357i	$-0.554540\pi$
$179$	−14.8388	−	8.56716i	−1.10910	−	0.640339i	−0.938596	+	0.345017i	$0.887873\pi$
$180$		0			0
$181$		−	5.65810i		−	0.420564i	−0.977641	−	0.210282i	$-0.932562\pi$
$181$		−	5.65810i		−	0.420564i	0.977641	−	0.210282i	$-0.0674381\pi$
$182$	−8.81065	+	5.09921i	−0.653089	+	0.377979i
$183$		0			0
$184$	6.17041	+	10.6875i	0.454889	+	0.787891i
$185$	−9.71856	+	16.8330i	−0.714523	+	1.23759i
$186$		0			0
$187$	16.8972	−	9.75563i	1.23565	−	0.713402i
$188$	11.8097			0.861311
$189$		0			0
$190$	−1.61995			−0.117523
$191$	−0.588277	+	0.339642i	−0.0425662	+	0.0245756i	−0.521132	−	0.853476i	$-0.674490\pi$
$191$	−0.588277	+	0.339642i	−0.0425662	+	0.0245756i	0.478566	+	0.878052i	$0.341157\pi$
$192$		0			0
$193$	10.0999	−	17.4936i	0.727009	−	1.25922i	−0.231132	−	0.972922i	$-0.574243\pi$
$193$	10.0999	−	17.4936i	0.727009	−	1.25922i	0.958142	−	0.286295i	$-0.0924236\pi$
$194$	1.26636	+	2.19340i	0.0909194	+	0.157477i
$195$		0			0
$196$	5.76904	−	10.0410i	0.412074	−	0.717218i
$197$		−	2.34023i		−	0.166735i	−0.996519	−	0.0833674i	$-0.973432\pi$
$197$		−	2.34023i		−	0.166735i	0.996519	−	0.0833674i	$-0.0265675\pi$
$198$		0			0
$199$	10.8359	+	6.25613i	0.768139	+	0.443485i	0.832210	−	0.554460i	$-0.187075\pi$
$199$	10.8359	+	6.25613i	0.768139	+	0.443485i	−0.0640711	+	0.997945i	$0.520408\pi$
$200$	4.82252	+	2.78428i	0.341004	+	0.196879i
$201$		0			0
$202$		−	4.48857i		−	0.315815i
$203$	−18.6401	+	0.0196315i	−1.30828	+	0.00137786i
$204$		0			0
$205$	−6.04842	−	10.4762i	−0.422440	−	0.731687i
$206$	−2.92638	+	5.06864i	−0.203891	+	0.353149i
$207$		0			0
$208$	11.5930	−	6.69319i	0.803827	−	0.464090i
$209$	−3.88630			−0.268821
$210$		0			0
$211$	−7.86465			−0.541425			−0.270712	−	0.962660i	$-0.587259\pi$
$211$	−7.86465			−0.541425			−0.270712	+	0.962660i	$0.587259\pi$
$212$	14.8001	−	8.54483i	1.01647	−	0.586861i
$213$		0			0
$214$	1.21317	−	2.10128i	0.0829308	−	0.143640i
$215$	4.58249	+	7.93710i	0.312523	+	0.541306i
$216$		0			0
$217$	−6.83123	+	11.8609i	−0.463734	+	0.805168i
$218$		−	2.99068i		−	0.202555i
$219$		0			0
$220$	15.3413	+	8.85733i	1.03431	+	0.597161i
$221$	28.4541	+	16.4280i	1.91403	+	1.10507i
$222$		0			0
$223$			0.662229i			0.0443461i	0.999754	+	0.0221731i	$0.00705849\pi$
$223$			0.662229i			0.0443461i	−0.999754	+	0.0221731i	$0.992942\pi$
$224$	7.26204	−	12.6089i	0.485215	−	0.842465i
$225$		0			0
$226$	4.32298	+	7.48762i	0.287560	+	0.498069i
$227$	8.08076	−	13.9963i	0.536339	−	0.928966i	−0.462758	−	0.886484i	$-0.653140\pi$
$227$	8.08076	−	13.9963i	0.536339	−	0.928966i	0.999097	−	0.0424818i	$-0.0135264\pi$
$228$		0			0
$229$	13.8982	−	8.02414i	0.918421	−	0.530250i	0.0352897	−	0.999377i	$-0.488765\pi$
$229$	13.8982	−	8.02414i	0.918421	−	0.530250i	0.883131	+	0.469127i	$0.155431\pi$
$230$	−9.30485			−0.613543
$231$		0			0
$232$	−15.1369			−0.993784
$233$	7.25822	−	4.19054i	0.475502	−	0.274531i	−0.243038	−	0.970017i	$-0.578144\pi$
$233$	7.25822	−	4.19054i	0.475502	−	0.274531i	0.718540	+	0.695486i	$0.244811\pi$
$234$		0			0
$235$	−9.83465	+	17.0341i	−0.641542	+	1.11118i
$236$	2.86113	+	4.95562i	0.186244	+	0.322583i
$237$		0			0
$238$	7.80954	−	0.00822487i	0.506217	−	0.000533139i
$239$			24.1276i			1.56069i	0.625352	+	0.780343i	$0.284956\pi$
$239$			24.1276i			1.56069i	−0.625352	+	0.780343i	$0.715044\pi$
$240$		0			0
$241$	15.0929	+	8.71389i	0.972219	+	0.561311i	0.899912	−	0.436071i	$-0.143630\pi$
$241$	15.0929	+	8.71389i	0.972219	+	0.561311i	0.0723072	+	0.997382i	$0.476964\pi$
$242$	−2.08926	−	1.20623i	−0.134303	−	0.0775397i
$243$		0			0
$244$		−	19.5246i		−	1.24993i
$245$	9.67881	+	16.6829i	0.618357	+	1.06583i
$246$		0			0
$247$	−3.27216	−	5.66755i	−0.208203	−	0.360618i
$248$	−5.55750	+	9.62587i	−0.352901	+	0.611243i
$249$		0			0
$250$	3.37845	−	1.95055i	0.213672	−	0.123364i
$251$	9.90074			0.624929			0.312465	−	0.949929i	$-0.398845\pi$
$251$	9.90074			0.624929			0.312465	+	0.949929i	$0.398845\pi$
$252$		0			0
$253$	−22.3226			−1.40341
$254$	−1.87015	+	1.07973i	−0.117344	+	0.0677483i
$255$		0			0
$256$	2.52404	−	4.37177i	0.157753	−	0.273235i
$257$	3.67523	+	6.36569i	0.229255	+	0.397081i	0.957587	−	0.288143i	$-0.0930378\pi$
$257$	3.67523	+	6.36569i	0.229255	+	0.397081i	−0.728333	+	0.685224i	$0.759704\pi$
$258$		0			0
$259$	−16.1538	+	9.34908i	−1.00375	+	0.580924i
$260$			29.8306i			1.85002i
$261$		0			0
$262$	4.61185	+	2.66265i	0.284921	+	0.164499i
$263$	10.9850	+	6.34221i	0.677366	+	0.391077i	0.798862	−	0.601515i	$-0.205436\pi$
$263$	10.9850	+	6.34221i	0.677366	+	0.391077i	−0.121496	+	0.992592i	$0.538769\pi$
$264$		0			0
$265$			28.4632i			1.74848i
$266$	−1.34794	−	0.776343i	−0.0826476	−	0.0476006i
$267$		0			0
$268$	−2.08714	−	3.61503i	−0.127492	−	0.220823i
$269$	−7.77415	+	13.4652i	−0.473998	+	0.820989i	−0.999557	−	0.0297681i	$-0.990523\pi$
$269$	−7.77415	+	13.4652i	−0.473998	+	0.820989i	0.525558	+	0.850758i	$0.323856\pi$
$270$		0			0
$271$	−3.48613	+	2.01272i	−0.211767	+	0.122264i	−0.602132	−	0.798396i	$-0.705682\pi$
$271$	−3.48613	+	2.01272i	−0.211767	+	0.122264i	0.390365	+	0.920660i	$0.372349\pi$
$272$	−10.2695			−0.622678
$273$		0			0
$274$	5.98377			0.361493
$275$	−8.72317	+	5.03632i	−0.526027	+	0.303702i
$276$		0			0
$277$	14.4166	−	24.9704i	0.866212	−	1.50032i	0.000373477	−	1.00000i	$-0.499881\pi$
$277$	14.4166	−	24.9704i	0.866212	−	1.50032i	0.865839	−	0.500323i	$-0.166786\pi$
$278$	−2.66702	−	4.61941i	−0.159957	−	0.277054i
$279$		0			0
$280$	7.84548	+	13.5558i	0.468857	+	0.810113i
$281$			1.04688i			0.0624516i	0.999512	+	0.0312258i	$0.00994110\pi$
$281$			1.04688i			0.0624516i	−0.999512	+	0.0312258i	$0.990059\pi$
$282$		0			0
$283$	−15.7980	−	9.12100i	−0.939096	−	0.542187i	−0.0494188	−	0.998778i	$-0.515737\pi$
$283$	−15.7980	−	9.12100i	−0.939096	−	0.542187i	−0.889677	+	0.456591i	$0.849070\pi$
$284$	11.3358	+	6.54472i	0.672655	+	0.388357i
$285$		0			0
$286$		−	14.9530i		−	0.884190i
$287$	−0.0122335	−	11.6157i	−0.000722121	−	0.685656i
$288$		0			0
$289$	−4.10284	−	7.10633i	−0.241344	−	0.418019i
$290$	5.70652	−	9.88398i	0.335098	−	0.580407i
$291$		0			0
$292$	−20.5831	+	11.8837i	−1.20453	+	0.695438i
$293$	−8.99601			−0.525552			−0.262776	−	0.964857i	$-0.584638\pi$
$293$	−8.99601			−0.525552			−0.262776	+	0.964857i	$0.584638\pi$
$294$		0			0
$295$	−9.53053			−0.554889
$296$	−13.1258	+	7.57817i	−0.762921	+	0.440472i
$297$		0			0
$298$	6.02962	−	10.4436i	0.349287	−	0.604982i
$299$	−18.7950	−	32.5540i	−1.08695	−	1.88264i
$300$		0			0
$301$	0.00926852	+	8.80049i	0.000534229	+	0.507252i
$302$		−	5.88542i		−	0.338668i
$303$		0			0
$304$	1.77145	+	1.02275i	0.101600	+	0.0586586i
$305$	28.1620	+	16.2593i	1.61255	+	0.931006i
$306$		0			0
$307$			31.1615i			1.77848i	0.457439	+	0.889241i	$0.348767\pi$
$307$			31.1615i			1.77848i	−0.457439	+	0.889241i	$0.651233\pi$
$308$	8.52059	+	14.7223i	0.485506	+	0.838879i
$309$		0			0
$310$	−4.19029	−	7.25780i	−0.237993	−	0.412215i
$311$	−3.69420	+	6.39854i	−0.209479	+	0.362828i	−0.951550	−	0.307493i	$-0.900510\pi$
$311$	−3.69420	+	6.39854i	−0.209479	+	0.362828i	0.742072	+	0.670321i	$0.233843\pi$
$312$		0			0
$313$	27.3203	−	15.7734i	1.54423	−	0.891563i	0.545668	−	0.838002i	$-0.316276\pi$
$313$	27.3203	−	15.7734i	1.54423	−	0.891563i	0.998565	−	0.0535612i	$-0.0170572\pi$
$314$	−10.9647			−0.618772
$315$		0			0
$316$	24.5262			1.37971
$317$	12.4435	−	7.18424i	0.698895	−	0.403507i	−0.108041	−	0.994146i	$-0.534458\pi$
$317$	12.4435	−	7.18424i	0.698895	−	0.403507i	0.806936	+	0.590639i	$0.201124\pi$
$318$		0			0
$319$	13.6901	−	23.7119i	0.766498	−	1.32761i
$320$	−1.18146	−	2.04635i	−0.0660458	−	0.114395i
$321$		0			0
$322$	−7.74246	−	4.45925i	−0.431471	−	0.248504i
$323$			5.02053i			0.279350i
$324$		0			0
$325$	−14.6894	−	8.48091i	−0.814820	−	0.470436i
$326$	5.31543	+	3.06886i	0.294394	+	0.169969i
$327$		0			0
$328$		−	9.43266i		−	0.520832i
$329$	−16.3467	+	9.46075i	−0.901224	+	0.521588i
$330$		0			0
$331$	12.3438	+	21.3801i	0.678477	+	1.17516i	0.975440	+	0.220267i	$0.0706928\pi$
$331$	12.3438	+	21.3801i	0.678477	+	1.17516i	−0.296963	+	0.954889i	$0.595974\pi$
$332$	−2.04614	+	3.54402i	−0.112296	+	0.194503i
$333$		0			0
$334$	−0.560031	+	0.323334i	−0.0306435	+	0.0176921i
$335$	6.95234			0.379847
$336$		0			0
$337$	8.62844			0.470021			0.235011	−	0.971993i	$-0.424488\pi$
$337$	8.62844			0.470021			0.235011	+	0.971993i	$0.424488\pi$
$338$	15.1875	−	8.76850i	0.826090	−	0.476943i
$339$		0			0
$340$	11.4424	−	19.8188i	0.620550	−	1.07482i
$341$	−10.0526	−	17.4116i	−0.544380	−	0.942894i
$342$		0			0
$343$	0.0585155	+	18.5202i	0.00315954	+	0.999995i
$344$			7.14651i			0.385314i
$345$		0			0
$346$	3.90654	+	2.25544i	0.210017	+	0.121253i
$347$	−1.54054	−	0.889429i	−0.0827003	−	0.0477471i	0.458080	−	0.888911i	$-0.348537\pi$
$347$	−1.54054	−	0.889429i	−0.0827003	−	0.0477471i	−0.540780	+	0.841164i	$0.681871\pi$
$348$		0			0
$349$			18.1932i			0.973857i	0.873442	+	0.486929i	$0.161883\pi$
$349$			18.1932i			0.973857i	−0.873442	+	0.486929i	$0.838117\pi$
$350$	−4.03166	+	0.00424607i	−0.215501	+	0.000226962i
$351$		0			0
$352$	10.6866	+	18.5097i	0.569597	+	0.986570i
$353$	8.54323	−	14.7973i	0.454710	−	0.787581i	−0.543961	−	0.839110i	$-0.683076\pi$
$353$	8.54323	−	14.7973i	0.454710	−	0.787581i	0.998671	+	0.0515292i	$0.0164095\pi$
$354$		0			0
$355$	−18.8800	+	10.9004i	−1.00204	+	0.578531i
$356$	−0.895542			−0.0474637
$357$		0			0
$358$	10.0738			0.532418
$359$	8.72302	−	5.03624i	0.460383	−	0.265803i	−0.251822	−	0.967774i	$-0.581030\pi$
$359$	8.72302	−	5.03624i	0.460383	−	0.265803i	0.712205	+	0.701971i	$0.247696\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	1.66329	+	2.88091i	0.0874207	+	0.151417i
$363$		0			0
$364$	−14.2960	+	24.8217i	−0.749314	+	1.30101i
$365$		−	39.5849i		−	2.07197i
$366$		0			0
$367$	−23.8893	−	13.7925i	−1.24701	−	0.719962i	−0.276498	−	0.961014i	$-0.589174\pi$
$367$	−23.8893	−	13.7925i	−1.24701	−	0.719962i	−0.970512	+	0.241053i	$0.922507\pi$
$368$	10.1751	+	5.87458i	0.530412	+	0.306234i
$369$		0			0
$370$		−	11.4277i		−	0.594099i
$371$	−13.6407	+	23.6839i	−0.708188	+	1.22961i
$372$		0			0
$373$	8.07070	+	13.9789i	0.417885	+	0.723798i	0.995727	−	0.0923508i	$-0.0294381\pi$
$373$	8.07070	+	13.9789i	0.417885	+	0.723798i	−0.577841	+	0.816149i	$0.696105\pi$
$374$	−5.73565	+	9.93444i	−0.296584	+	0.513698i
$375$		0			0
$376$	−13.2826	+	7.66869i	−0.684996	+	0.395483i
$377$	46.1068			2.37462
$378$		0			0
$379$	6.57301			0.337633			0.168816	−	0.985647i	$-0.446005\pi$
$379$	6.57301			0.337633			0.168816	+	0.985647i	$0.446005\pi$
$380$	−3.94755	+	2.27912i	−0.202505	+	0.116916i
$381$		0			0
$382$	0.199686	−	0.345867i	0.0102168	−	0.0176961i
$383$	−2.81139	−	4.86948i	−0.143656	−	0.248819i	0.785215	−	0.619223i	$-0.212552\pi$
$383$	−2.81139	−	4.86948i	−0.143656	−	0.248819i	−0.928871	+	0.370405i	$0.879219\pi$
$384$		0			0
$385$	−28.3308	+	0.0298375i	−1.44387	+	0.00152066i
$386$			11.8762i			0.604481i
$387$		0			0
$388$	6.17183	+	3.56331i	0.313327	+	0.180899i
$389$	1.70483	+	0.984282i	0.0864381	+	0.0499051i	0.542596	−	0.839994i	$-0.317441\pi$
$389$	1.70483	+	0.984282i	0.0864381	+	0.0499051i	−0.456158	+	0.889899i	$0.650775\pi$
$390$		0			0
$391$			28.8375i			1.45837i
$392$	0.0316787	+	15.0395i	0.00160002	+	0.759609i
$393$		0			0
$394$	0.687950	+	1.19156i	0.0346584	+	0.0600302i
$395$	−20.4245	+	35.3762i	−1.02767	+	1.77997i
$396$		0			0
$397$	22.1049	−	12.7623i	1.10941	−	0.640519i	0.170735	−	0.985317i	$-0.445386\pi$
$397$	22.1049	−	12.7623i	1.10941	−	0.640519i	0.938677	+	0.344798i	$0.112053\pi$
$398$	−7.35637			−0.368742
$399$		0			0
$400$	5.30159			0.265079
$401$	25.0524	−	14.4640i	1.25106	−	0.722298i	0.279738	−	0.960077i	$-0.409753\pi$
$401$	25.0524	−	14.4640i	1.25106	−	0.722298i	0.971319	+	0.237778i	$0.0764192\pi$
$402$		0			0
$403$	16.9281	−	29.3203i	0.843249	−	1.46055i
$404$	−6.31501	−	10.9379i	−0.314183	−	0.544181i
$405$		0			0
$406$	9.48512	−	5.48957i	0.470739	−	0.272443i
$407$		−	27.4154i		−	1.35893i
$408$		0			0
$409$	2.46460	+	1.42294i	0.121867	+	0.0703597i	0.559694	−	0.828699i	$-0.310919\pi$
$409$	2.46460	+	1.42294i	0.121867	+	0.0703597i	−0.437828	+	0.899059i	$0.644252\pi$
$410$	6.15928	+	3.55606i	0.304185	+	0.175621i
$411$		0			0
$412$			16.4686i			0.811350i
$413$	−7.93025	−	4.56740i	−0.390222	−	0.224747i
$414$		0			0
$415$	−3.40789	−	5.90263i	−0.167287	−	0.289749i
$416$	−17.9957	+	31.1694i	−0.882310	+	1.52821i
$417$		0			0
$418$	1.97877	−	1.14244i	0.0967846	−	0.0558786i
$419$	−36.8020			−1.79790			−0.898949	−	0.438054i	$-0.855668\pi$
$419$	−36.8020			−1.79790			−0.898949	+	0.438054i	$0.855668\pi$
$420$		0			0
$421$	25.4064			1.23823			0.619116	−	0.785299i	$-0.287491\pi$
$421$	25.4064			1.23823			0.619116	+	0.785299i	$0.287491\pi$
$422$	4.00440	−	2.31194i	0.194931	−	0.112544i
$423$		0			0
$424$	−11.0973	+	19.2210i	−0.538931	+	0.933455i
$425$	6.50619	+	11.2691i	0.315597	+	0.546629i
$426$		0			0
$427$	15.6412	+	27.0255i	0.756929	+	1.30786i
$428$		−	6.82729i		−	0.330010i
$429$		0			0
$430$	−4.66648	−	2.69419i	−0.225038	−	0.129926i
$431$	−17.1940	−	9.92695i	−0.828205	−	0.478164i	0.0250330	−	0.999687i	$-0.492031\pi$
$431$	−17.1940	−	9.92695i	−0.828205	−	0.478164i	−0.853238	+	0.521523i	$0.825364\pi$
$432$		0			0
$433$		−	21.3054i		−	1.02387i	−0.859023	−	0.511936i	$-0.828928\pi$
$433$		−	21.3054i		−	1.02387i	0.859023	−	0.511936i	$-0.171072\pi$
$434$	−0.00847526	−	8.04729i	−0.000406826	−	0.386282i
$435$		0			0
$436$	−4.20762	−	7.28780i	−0.201508	−	0.349023i
$437$	2.87196	−	4.97438i	0.137384	−	0.237957i
$438$		0			0
$439$	0.217037	−	0.125307i	0.0103586	−	0.00598055i	−0.494812	−	0.869000i	$-0.664763\pi$
$439$	0.217037	−	0.125307i	0.0103586	−	0.00598055i	0.505170	+	0.863020i	$0.331430\pi$
$440$	−23.0062			−1.09678
$441$		0			0
$442$	−19.3171			−0.918821
$443$	19.7653	−	11.4115i	0.939077	−	0.542176i	0.0494061	−	0.998779i	$-0.484267\pi$
$443$	19.7653	−	11.4115i	0.939077	−	0.542176i	0.889671	+	0.456602i	$0.150934\pi$
$444$		0			0
$445$	0.745772	−	1.29172i	0.0353530	−	0.0612332i
$446$	−0.194673	−	0.337184i	−0.00921804	−	0.0159661i
$447$		0			0
$448$	−0.00238962	−	2.26895i	−0.000112899	−	0.107198i
$449$		−	39.7883i		−	1.87772i	−0.344294	−	0.938862i	$-0.611882\pi$
$449$		−	39.7883i		−	1.87772i	0.344294	−	0.938862i	$-0.388118\pi$
$450$		0			0
$451$	14.7763	+	8.53109i	0.695788	+	0.401713i
$452$	21.0688	+	12.1641i	0.990993	+	0.572150i
$453$		0			0
$454$			9.50189i			0.445946i
$455$	−23.8973	−	41.2908i	−1.12032	−	1.93574i
$456$		0			0
$457$	4.75782	+	8.24078i	0.222561	+	0.385488i	0.955585	−	0.294716i	$-0.0952249\pi$
$457$	4.75782	+	8.24078i	0.222561	+	0.385488i	−0.733024	+	0.680203i	$0.761892\pi$
$458$	−4.71766	+	8.17122i	−0.220442	+	0.381816i
$459$		0			0
$460$	−22.6744	+	13.0911i	−1.05720	+	0.610374i
$461$	−21.4157			−0.997427			−0.498713	−	0.866767i	$-0.666194\pi$
$461$	−21.4157			−0.997427			−0.498713	+	0.866767i	$0.666194\pi$
$462$		0			0
$463$	−19.4555			−0.904173			−0.452086	−	0.891974i	$-0.649320\pi$
$463$	−19.4555			−0.904173			−0.452086	+	0.891974i	$0.649320\pi$
$464$	−12.4804	+	7.20557i	−0.579389	+	0.334510i
$465$		0			0
$466$	−2.46375	+	4.26735i	−0.114131	+	0.197681i
$467$	16.3907	+	28.3896i	0.758472	+	1.31371i	0.943629	+	0.331004i	$0.107387\pi$
$467$	16.3907	+	28.3896i	0.758472	+	1.31371i	−0.185157	+	0.982709i	$0.559279\pi$
$468$		0			0
$469$	5.78497	+	3.33184i	0.267125	+	0.153850i
$470$		−	11.5642i		−	0.533418i
$471$		0			0
$472$	−6.43591	−	3.71578i	−0.296237	−	0.171032i
$473$	−11.1950	−	6.46344i	−0.514747	−	0.297189i
$474$		0			0
$475$		−	2.59184i		−	0.118922i
$476$	19.0190	−	11.0074i	0.871735	−	0.504521i
$477$		0			0
$478$	−7.09271	−	12.2849i	−0.324413	−	0.561900i
$479$	7.41990	−	12.8516i	0.339024	−	0.587206i	−0.645226	−	0.763992i	$-0.723237\pi$
$479$	7.41990	−	12.8516i	0.339024	−	0.587206i	0.984249	+	0.176786i	$0.0565699\pi$
$480$		0			0
$481$	39.9811	−	23.0831i	1.82298	−	1.05250i
$482$	−10.2464			−0.466709
$483$		0			0
$484$	−6.78824			−0.308557
$485$	−10.2793	+	5.93476i	−0.466759	+	0.269484i
$486$		0			0
$487$	−20.3091	+	35.1765i	−0.920295	+	1.59400i	−0.121337	+	0.992611i	$0.538718\pi$
$487$	−20.3091	+	35.1765i	−0.920295	+	1.59400i	−0.798958	+	0.601387i	$0.794615\pi$
$488$	12.6784	+	21.9597i	0.573925	+	0.994067i
$489$		0			0
$490$	−9.83233	−	5.64912i	−0.444180	−	0.255201i
$491$			37.3742i			1.68667i	0.537384	+	0.843337i	$0.319412\pi$
$491$			37.3742i			1.68667i	−0.537384	+	0.843337i	$0.680588\pi$
$492$		0			0
$493$	−30.6323	−	17.6856i	−1.37961	−	0.796518i
$494$	3.33214	+	1.92381i	0.149920	+	0.0865564i
$495$		0			0
$496$			10.5821i			0.475150i
$497$	−20.9337	+	0.0220470i	−0.939005	+	0.000988944i
$498$		0			0
$499$	−10.6576	−	18.4595i	−0.477100	−	0.826361i	0.522556	−	0.852605i	$-0.324979\pi$
$499$	−10.6576	−	18.4595i	−0.477100	−	0.826361i	−0.999656	+	0.0262440i	$0.991645\pi$
$500$	5.48849	−	9.50635i	0.245453	−	0.425137i
$501$		0			0
$502$	−5.04111	+	2.91048i	−0.224996	+	0.129901i
$503$	38.4548			1.71462			0.857308	−	0.514803i	$-0.172135\pi$
$503$	38.4548			1.71462			0.857308	+	0.514803i	$0.172135\pi$
$504$		0			0
$505$	21.0355			0.936069
$506$	11.3659	−	6.56208i	0.505274	−	0.291720i
$507$		0			0
$508$	−3.03816	+	5.26226i	−0.134797	+	0.233475i
$509$	−12.5919	−	21.8098i	−0.558125	−	0.966700i	−0.997653	−	0.0684715i	$-0.978188\pi$
$509$	−12.5919	−	21.8098i	−0.558125	−	0.966700i	0.439528	−	0.898229i	$-0.355146\pi$
$510$		0			0
$511$	18.9707	−	32.9382i	0.839213	−	1.45710i
$512$		−	20.0389i		−	0.885605i
$513$		0			0
$514$	−3.74260	−	2.16079i	−0.165079	−	0.0953083i
$515$	−23.7540	−	13.7144i	−1.04673	−	0.604329i
$516$		0			0
$517$		−	27.7429i		−	1.22013i
$518$	5.47661	−	9.50888i	0.240629	−	0.417796i
$519$		0			0
$520$	−19.3707	−	33.5510i	−0.849460	−	1.47131i
$521$	−18.3334	+	31.7544i	−0.803201	+	1.39119i	0.114297	+	0.993447i	$0.463538\pi$
$521$	−18.3334	+	31.7544i	−0.803201	+	1.39119i	−0.917499	+	0.397739i	$0.869795\pi$
$522$		0			0
$523$	−1.97217	+	1.13864i	−0.0862372	+	0.0497891i	−0.542498	−	0.840057i	$-0.682522\pi$
$523$	−1.97217	+	1.13864i	−0.0862372	+	0.0497891i	0.456261	+	0.889846i	$0.349188\pi$
$524$	14.9844			0.654598
$525$		0			0
$526$	−7.45758			−0.325166
$527$	−22.4933	+	12.9865i	−0.979823	+	0.565701i
$528$		0			0
$529$	4.99629	−	8.65384i	0.217230	−	0.376254i
$530$	−8.36721	−	14.4924i	−0.363448	−	0.629511i
$531$		0			0
$532$	−4.37696	+	0.00460973i	−0.189765	+	0.000199857i
$533$			28.7318i			1.24451i
$534$		0			0
$535$	9.84757	+	5.68550i	0.425748	+	0.245806i
$536$	4.69488	+	2.71059i	0.202788	+	0.117080i
$537$		0			0
$538$		−	9.14136i		−	0.394112i
$539$	−23.5880	−	13.5524i	−1.01601	−	0.583743i
$540$		0			0
$541$	−3.66970	−	6.35610i	−0.157773	−	0.273270i	0.776293	−	0.630373i	$-0.217098\pi$
$541$	−3.66970	−	6.35610i	−0.157773	−	0.273270i	−0.934065	+	0.357103i	$0.883765\pi$
$542$	1.18334	−	2.04961i	0.0508289	−	0.0880383i
$543$		0			0
$544$	23.9118	−	13.8055i	1.02521	−	0.591906i
$545$	14.0157			0.600368
$546$		0			0
$547$	20.0419			0.856930			0.428465	−	0.903558i	$-0.359054\pi$
$547$	20.0419			0.856930			0.428465	+	0.903558i	$0.359054\pi$
$548$	14.5815	−	8.41862i	0.622890	−	0.359626i
$549$		0			0
$550$	2.96102	−	5.12864i	0.126258	−	0.218686i
$551$	3.52265	+	6.10142i	0.150070	+	0.259929i
$552$		0			0
$553$	−33.9486	+	19.6480i	−1.44364	+	0.835516i
$554$			16.9520i			0.720223i
$555$		0			0
$556$	−12.9982	−	7.50449i	−0.551245	−	0.318261i
$557$	24.0561	+	13.8888i	1.01929	+	0.588487i	0.913898	−	0.405944i	$-0.133057\pi$
$557$	24.0561	+	13.8888i	1.01929	+	0.588487i	0.105391	+	0.994431i	$0.466391\pi$
$558$		0			0
$559$		−	21.7682i		−	0.920698i
$560$	12.9216	+	7.44214i	0.546036	+	0.314488i
$561$		0			0
$562$	−0.307748	−	0.533034i	−0.0129815	−	0.0224847i
$563$	3.61642	−	6.26382i	0.152414	−	0.263988i	−0.779701	−	0.626153i	$-0.784629\pi$
$563$	3.61642	−	6.26382i	0.152414	−	0.263988i	0.932114	+	0.362164i	$0.117962\pi$
$564$		0			0
$565$	−35.0905	+	20.2595i	−1.47627	+	0.852324i
$566$	10.7251			0.450808
$567$		0			0
$568$	−16.9994			−0.713278
$569$	18.1588	−	10.4840i	0.761258	−	0.439512i	−0.0684895	−	0.997652i	$-0.521818\pi$
$569$	18.1588	−	10.4840i	0.761258	−	0.439512i	0.829747	+	0.558140i	$0.188485\pi$
$570$		0			0
$571$	3.62755	−	6.28311i	0.151808	−	0.262940i	−0.780084	−	0.625675i	$-0.784824\pi$
$571$	3.62755	−	6.28311i	0.151808	−	0.262940i	0.931892	+	0.362735i	$0.118157\pi$
$572$	−21.0375	−	36.4381i	−0.879623	−	1.52355i
$573$		0			0
$574$	3.42087	+	5.91073i	0.142784	+	0.246709i
$575$		−	14.8873i		−	0.620843i
$576$		0			0
$577$	−19.0783	−	11.0149i	−0.794241	−	0.458555i	0.0472128	−	0.998885i	$-0.484966\pi$
$577$	−19.0783	−	11.0149i	−0.794241	−	0.458555i	−0.841453	+	0.540330i	$0.818299\pi$
$578$	4.17804	+	2.41219i	0.173784	+	0.100334i
$579$		0			0
$580$		−	32.1142i		−	1.33347i
$581$	−0.00689277	−	6.54471i	−0.000285960	−	0.271520i
$582$		0			0
$583$	−20.0732	−	34.7677i	−0.831345	−	1.43993i
$584$	15.4334	−	26.7315i	0.638640	−	1.10616i
$585$		0			0
$586$	4.58045	−	2.64452i	0.189217	−	0.109244i
$587$	13.3446			0.550790			0.275395	−	0.961331i	$-0.411191\pi$
$587$	13.3446			0.550790			0.275395	+	0.961331i	$0.411191\pi$
$588$		0			0
$589$	5.17337			0.213165
$590$	4.85261	−	2.80166i	0.199779	−	0.115342i
$591$		0			0
$592$	−7.21484	+	12.4965i	−0.296528	+	0.513602i
$593$	0.996680	+	1.72630i	0.0409287	+	0.0708906i	0.885764	−	0.464136i	$-0.153635\pi$
$593$	0.996680	+	1.72630i	0.0409287	+	0.0708906i	−0.844835	+	0.535026i	$0.820302\pi$
$594$		0			0
$595$	0.0385456	+	36.5992i	0.00158022	+	1.50042i
$596$		−	33.9325i		−	1.38993i
$597$		0			0
$598$	19.1395	+	11.0502i	0.782674	+	0.451877i
$599$	25.6026	+	14.7817i	1.04609	+	0.603962i	0.921553	−	0.388252i	$-0.126921\pi$
$599$	25.6026	+	14.7817i	1.04609	+	0.603962i	0.124540	+	0.992215i	$0.460254\pi$
$600$		0			0
$601$		−	45.6163i		−	1.86073i	−0.366639	−	0.930363i	$-0.619491\pi$
$601$		−	45.6163i		−	1.86073i	0.366639	−	0.930363i	$-0.380509\pi$
$602$	−2.59177	−	4.47817i	−0.105633	−	0.182517i
$603$		0			0
$604$	−8.28025	−	14.3418i	−0.336918	−	0.583560i
$605$	5.65298	−	9.79125i	0.229826	−	0.398071i
$606$		0			0
$607$	−10.7258	+	6.19255i	−0.435347	+	0.251348i	−0.701622	−	0.712549i	$-0.747540\pi$
$607$	−10.7258	+	6.19255i	−0.435347	+	0.251348i	0.266275	+	0.963897i	$0.414207\pi$
$608$	−5.49962			−0.223039
$609$		0			0
$610$	−19.1188			−0.774096
$611$	40.4586	−	23.3588i	1.63678	−	0.944996i
$612$		0			0
$613$	−14.8306	+	25.6873i	−0.599001	+	1.03750i	0.393967	+	0.919124i	$0.371102\pi$
$613$	−14.8306	+	25.6873i	−0.599001	+	1.03750i	−0.992969	+	0.118376i	$0.962231\pi$
$614$	−9.16044	−	15.8663i	−0.369685	−	0.640314i
$615$		0			0
$616$	−19.1432	−	11.0255i	−0.771303	−	0.444230i
$617$			4.31153i			0.173576i	0.996227	+	0.0867878i	$0.0276602\pi$
$617$			4.31153i			0.173576i	−0.996227	+	0.0867878i	$0.972340\pi$
$618$		0			0
$619$	13.0436	+	7.53075i	0.524268	+	0.302686i	0.738679	−	0.674057i	$-0.235450\pi$
$619$	13.0436	+	7.53075i	0.524268	+	0.302686i	−0.214411	+	0.976743i	$0.568783\pi$
$620$	−20.4221	−	11.7907i	−0.820172	−	0.473526i
$621$		0			0
$622$		−	4.34388i		−	0.174174i
$623$	1.23959	−	0.717419i	0.0496631	−	0.0287428i
$624$		0			0
$625$	15.6208	+	27.0560i	0.624831	+	1.08224i
$626$	−9.27367	+	16.0625i	−0.370651	+	0.641986i
$627$		0			0
$628$	−26.7191	+	15.4263i	−1.06621	+	0.615576i
$629$	−35.4167			−1.41216
$630$		0			0
$631$	−31.9531			−1.27203			−0.636017	−	0.771675i	$-0.719419\pi$
$631$	−31.9531			−1.27203			−0.636017	+	0.771675i	$0.719419\pi$
$632$	−27.5851	+	15.9262i	−1.09727	+	0.633512i
$633$		0			0
$634$	−4.22385	+	7.31592i	−0.167751	+	0.290552i
$635$	−5.06012	−	8.76439i	−0.200805	−	0.347804i
$636$		0			0
$637$	−0.0964931	−	45.8102i	−0.00382320	−	1.81507i
$638$			16.0977i			0.637314i
$639$		0			0
$640$	27.4493	+	15.8479i	1.08503	+	0.626442i
$641$	−21.7045	−	12.5311i	−0.857275	−	0.494948i	0.00582370	−	0.999983i	$-0.498146\pi$
$641$	−21.7045	−	12.5311i	−0.857275	−	0.494948i	−0.863099	+	0.505035i	$0.831480\pi$
$642$		0			0
$643$			46.1942i			1.82172i	0.412714	+	0.910861i	$0.364581\pi$
$643$			46.1942i			1.82172i	−0.412714	+	0.910861i	$0.635419\pi$
$644$	−25.1409	+	0.0264779i	−0.990689	+	0.00104338i
$645$		0			0
$646$	−1.47587	−	2.55627i	−0.0580672	−	0.100575i
$647$	−10.7420	+	18.6057i	−0.422312	+	0.731466i	−0.996165	−	0.0874925i	$-0.972115\pi$
$647$	−10.7420	+	18.6057i	−0.422312	+	0.731466i	0.573853	+	0.818958i	$0.305448\pi$
$648$		0			0
$649$	11.6415	−	6.72124i	0.456970	−	0.263832i
$650$	9.97241			0.391150
$651$		0			0
$652$	17.2704			0.676363
$653$	32.7781	−	18.9245i	1.28271	−	0.740571i	0.305365	−	0.952235i	$-0.401222\pi$
$653$	32.7781	−	18.9245i	1.28271	−	0.740571i	0.977342	+	0.211664i	$0.0678883\pi$
$654$		0			0
$655$	−12.4784	+	21.6133i	−0.487573	+	0.844502i
$656$	−4.49021	−	7.77727i	−0.175313	−	0.303651i
$657$		0			0
$658$	5.54203	−	9.62247i	0.216051	−	0.375123i
$659$		−	43.7289i		−	1.70344i	−0.524001	−	0.851718i	$-0.675561\pi$
$659$		−	43.7289i		−	1.70344i	0.524001	−	0.851718i	$-0.324439\pi$
$660$		0			0
$661$	17.3793	+	10.0340i	0.675978	+	0.390276i	0.798338	−	0.602210i	$-0.205713\pi$
$661$	17.3793	+	10.0340i	0.675978	+	0.390276i	−0.122360	+	0.992486i	$0.539046\pi$
$662$	−12.5701	−	7.25732i	−0.488549	−	0.282064i
$663$		0			0
$664$		−	5.31468i		−	0.206250i
$665$	3.63831	−	6.31709i	0.141087	−	0.244966i
$666$		0			0
$667$	20.2338	+	35.0460i	0.783457	+	1.35699i
$668$	−0.909803	+	1.57583i	−0.0352013	+	0.0609705i
$669$		0			0
$670$	−3.53989	+	2.04375i	−0.136758	+	0.0789571i
$671$	−45.8664			−1.77065
$672$		0			0
$673$	−41.2321			−1.58938			−0.794690	−	0.607016i	$-0.792366\pi$
$673$	−41.2321			−1.58938			−0.794690	+	0.607016i	$0.792366\pi$
$674$	−4.39330	+	2.53647i	−0.169224	+	0.0977012i
$675$		0			0
$676$	24.6729	−	42.7348i	0.948959	−	1.64365i
$677$	15.0406	+	26.0511i	0.578057	+	1.00122i	0.995702	+	0.0926138i	$0.0295222\pi$
$677$	15.0406	+	26.0511i	0.578057	+	1.00122i	−0.417645	+	0.908610i	$0.637144\pi$
$678$		0			0
$679$	−11.3975	+	0.0120036i	−0.437395	+	0.000460657i
$680$			29.7207i			1.13974i
$681$		0			0
$682$	10.2369	+	5.91026i	0.391990	+	0.226316i
$683$	−24.3289	−	14.0463i	−0.930919	−	0.537466i	−0.0438170	−	0.999040i	$-0.513952\pi$
$683$	−24.3289	−	14.0463i	−0.930919	−	0.537466i	−0.887102	+	0.461573i	$0.847285\pi$
$684$		0			0
$685$			28.0428i			1.07146i
$686$	−5.47410	−	9.41261i	−0.209002	−	0.359375i
$687$		0			0
$688$	3.40194	+	5.89233i	0.129698	+	0.224643i
$689$	33.8022	−	58.5471i	1.28776	−	2.23047i
$690$		0			0
$691$	−15.6047	+	9.00938i	−0.593631	+	0.342733i	−0.766532	−	0.642206i	$-0.778019\pi$
$691$	−15.6047	+	9.00938i	−0.593631	+	0.342733i	0.172901	+	0.984939i	$0.444686\pi$
$692$	12.6928			0.482508
$693$		0			0
$694$	1.04585			0.0396999
$695$	21.6487	−	12.4989i	0.821182	−	0.474110i
$696$		0			0
$697$	11.0209	−	19.0888i	0.417447	−	0.723039i
$698$	−5.34818	−	9.26331i	−0.202431	−	0.350622i
$699$		0			0
$700$	−9.81853	+	5.68252i	−0.371105	+	0.214779i
$701$		−	15.1204i		−	0.571090i	−0.958365	−	0.285545i	$-0.907825\pi$
$701$		−	15.1204i		−	0.571090i	0.958365	−	0.285545i	$-0.0921746\pi$
$702$		0			0
$703$	6.10927	+	3.52719i	0.230415	+	0.133030i
$704$	2.88631	+	1.66641i	0.108782	+	0.0628053i
$705$		0			0
$706$			10.0457i			0.378074i
$707$	17.5035	+	10.0811i	0.658285	+	0.379137i
$708$		0			0
$709$	4.18663	+	7.25145i	0.157232	+	0.272334i	0.933870	−	0.357614i	$-0.116410\pi$
$709$	4.18663	+	7.25145i	0.157232	+	0.272334i	−0.776637	+	0.629948i	$0.783076\pi$
$710$	6.40868	−	11.1002i	0.240513	−	0.416581i
$711$		0			0
$712$	1.00723	−	0.581525i	0.0377476	−	0.0217936i
$713$	29.7154			1.11285
$714$		0			0
$715$	70.0768			2.62073
$716$	24.5483	−	14.1730i	0.917412	−	0.529668i
$717$		0			0
$718$	−2.96097	+	5.12855i	−0.110502	+	0.191396i
$719$	0.218121	+	0.377797i	0.00813454	+	0.0140894i	0.870064	−	0.492939i	$-0.164077\pi$
$719$	0.218121	+	0.377797i	0.00813454	+	0.0140894i	−0.861929	+	0.507028i	$0.830744\pi$
$720$		0			0
$721$	−13.1930	−	22.7955i	−0.491333	−	0.848948i
$722$			0.587933i			0.0218806i
$723$		0			0
$724$	8.10634	+	4.68020i	0.301270	+	0.173938i
$725$	15.8139	+	9.13014i	0.587313	+	0.339085i
$726$		0			0
$727$		−	0.354061i		−	0.0131314i	−0.999978	−	0.00656569i	$-0.997910\pi$
$727$		−	0.354061i		−	0.0131314i	0.999978	−	0.00656569i	$-0.00208994\pi$
$728$	−0.0391790	−	37.2006i	−0.00145207	−	1.37875i
$729$		0			0
$730$	11.6366	+	20.1553i	0.430691	+	0.745979i
$731$	−8.34982	+	14.4623i	−0.308829	+	0.534908i
$732$		0			0
$733$	11.1020	−	6.40976i	0.410063	−	0.236750i	−0.280754	−	0.959780i	$-0.590584\pi$
$733$	11.1020	−	6.40976i	0.410063	−	0.236750i	0.690817	+	0.723030i	$0.257251\pi$
$734$	16.2181			0.598621
$735$		0			0
$736$	−31.5894			−1.16440
$737$	−8.49228	+	4.90302i	−0.312817	+	0.180605i
$738$		0			0
$739$	−3.95449	+	6.84937i	−0.145468	+	0.251958i	−0.929548	−	0.368702i	$-0.879802\pi$
$739$	−3.95449	+	6.84937i	−0.145468	+	0.251958i	0.784079	+	0.620661i	$0.213136\pi$
$740$	−16.0778	−	27.8475i	−0.591030	−	1.02369i
$741$		0			0
$742$	−0.0169235	−	16.0689i	−0.000621281	−	0.589908i
$743$			6.06167i			0.222381i	0.993799	+	0.111191i	$0.0354664\pi$
$743$			6.06167i			0.222381i	−0.993799	+	0.111191i	$0.964534\pi$
$744$		0			0
$745$	48.9437	+	28.2576i	1.79316	+	1.03528i
$746$	−8.21863	−	4.74503i	−0.300906	−	0.173728i
$747$		0			0
$748$			32.2782i			1.18021i
$749$	5.46935	+	9.45019i	0.199846	+	0.345302i
$750$		0			0
$751$	2.56874	+	4.44919i	0.0937348	+	0.162353i	0.909080	−	0.416622i	$-0.136786\pi$
$751$	2.56874	+	4.44919i	0.0937348	+	0.162353i	−0.815345	+	0.578975i	$0.803453\pi$
$752$	−7.30102	+	12.6457i	−0.266241	+	0.461143i
$753$		0			0
$754$	−23.4760	+	13.5539i	−0.854944	+	0.493602i
$755$	27.5818			1.00381
$756$		0			0
$757$	−22.6388			−0.822820			−0.411410	−	0.911450i	$-0.634964\pi$
$757$	−22.6388			−0.822820			−0.411410	+	0.911450i	$0.634964\pi$
$758$	−3.34675	+	1.93224i	−0.121559	+	0.0701823i
$759$		0			0
$760$	2.95992	−	5.12673i	0.107367	−	0.185966i
$761$	19.0148	+	32.9346i	0.689285	+	1.19388i	0.972069	+	0.234693i	$0.0754086\pi$
$761$	19.0148	+	32.9346i	0.689285	+	1.19388i	−0.282784	+	0.959184i	$0.591258\pi$
$762$		0			0
$763$	11.6623	+	6.71689i	0.422205	+	0.243168i
$764$		−	1.12376i		−	0.0406563i
$765$		0			0
$766$	2.86293	+	1.65291i	0.103442	+	0.0597221i
$767$	19.6038	+	11.3182i	0.707851	+	0.408678i
$768$		0			0
$769$		−	11.5559i		−	0.416716i	−0.978053	−	0.208358i	$-0.933188\pi$
$769$		−	11.5559i		−	0.416716i	0.978053	−	0.208358i	$-0.0668120\pi$
$770$	14.4162	−	8.34348i	0.519526	−	0.300678i
$771$		0			0
$772$	16.7087	+	28.9403i	0.601358	+	1.04158i
$773$	10.0562	−	17.4178i	0.361696	−	0.626476i	−0.626544	−	0.779386i	$-0.715531\pi$
$773$	10.0562	−	17.4178i	0.361696	−	0.626476i	0.988240	+	0.152910i	$0.0488645\pi$
$774$		0			0
$775$	11.6121	−	6.70426i	0.417119	−	0.240824i
$776$	−9.25541			−0.332250
$777$		0			0
$778$	−1.15738			−0.0414942
$779$	−3.80215	+	2.19517i	−0.136226	+	0.0786501i
$780$		0			0
$781$	15.3746	−	26.6296i	0.550146	−	0.952880i
$782$	−8.47725	−	14.6830i	−0.303146	−	0.525064i
$783$		0			0
$784$	7.18534	+	12.3850i	0.256619	+	0.442323i
$785$		−	51.3856i		−	1.83403i
$786$		0			0
$787$	−28.0201	−	16.1774i	−0.998810	−	0.576663i	−0.0909139	−	0.995859i	$-0.528979\pi$
$787$	−28.0201	−	16.1774i	−0.998810	−	0.576663i	−0.907896	+	0.419196i	$0.862312\pi$
$788$	3.35285	+	1.93577i	0.119440	+	0.0689588i
$789$		0			0
$790$		−	24.0164i		−	0.854466i
$791$	−38.9076	+	0.0409768i	−1.38339	+	0.00145697i
$792$		0			0
$793$	−38.6184	−	66.8890i	−1.37138	−	2.37530i
$794$	−7.50334	+	12.9962i	−0.266284	+	0.461217i
$795$		0			0
$796$	−17.9263	+	10.3497i	−0.635380	+	0.366837i
$797$	−23.8653			−0.845353			−0.422677	−	0.906281i	$-0.638909\pi$
$797$	−23.8653			−0.845353			−0.422677	+	0.906281i	$0.638909\pi$
$798$		0			0
$799$	−35.8397			−1.26792
$800$	−12.3444	+	7.12706i	−0.436441	+	0.251979i
$801$		0			0
$802$	−8.50386	+	14.7291i	−0.300282	+	0.520103i
$803$	27.9166	+	48.3530i	0.985156	+	1.70634i
$804$		0			0
$805$	20.8981	−	36.2848i	0.736562	−	1.27887i
$806$			19.9052i			0.701130i
$807$		0			0
$808$	14.2052	+	8.20137i	0.499737	+	0.288523i
$809$	13.3563	+	7.71126i	0.469582	+	0.271113i	0.716065	−	0.698034i	$-0.245942\pi$
$809$	13.3563	+	7.71126i	0.469582	+	0.271113i	−0.246483	+	0.969147i	$0.579275\pi$
$810$		0			0
$811$		−	8.44878i		−	0.296677i	−0.988937	−	0.148338i	$-0.952608\pi$
$811$		−	8.44878i		−	0.296677i	0.988937	−	0.148338i	$-0.0473925\pi$
$812$	15.3904	−	26.7219i	0.540097	−	0.937754i
$813$		0			0
$814$	8.05921	+	13.9590i	0.282475	+	0.489261i
$815$	−14.3821	+	24.9106i	−0.503784	+	0.872580i
$816$		0			0
$817$	2.88064	−	1.66314i	0.100781	−	0.0581858i
$818$	−1.67318			−0.0585014
$819$		0			0
$820$	20.0122			0.698857
$821$	−4.99392	+	2.88324i	−0.174289	+	0.100626i	−0.584607	−	0.811317i	$-0.698751\pi$
$821$	−4.99392	+	2.88324i	−0.174289	+	0.100626i	0.410318	+	0.911943i	$0.365418\pi$
$822$		0			0
$823$	22.2720	−	38.5762i	0.776352	−	1.34468i	−0.157680	−	0.987490i	$-0.550401\pi$
$823$	22.2720	−	38.5762i	0.776352	−	1.34468i	0.934032	−	0.357190i	$-0.116265\pi$
$824$	−10.6940	−	18.5225i	−0.372542	−	0.645263i
$825$		0			0
$826$	5.38047	−	0.00566661i	0.187210	−	0.000197167i
$827$		−	33.6953i		−	1.17170i	−0.810419	−	0.585851i	$-0.800761\pi$
$827$		−	33.6953i		−	1.17170i	0.810419	−	0.585851i	$-0.199239\pi$
$828$		0			0
$829$	−30.1445	−	17.4040i	−1.04696	−	0.604465i	−0.125166	−	0.992136i	$-0.539946\pi$
$829$	−30.1445	−	17.4040i	−1.04696	−	0.604465i	−0.921798	+	0.387671i	$0.873280\pi$
$830$	3.47035	+	2.00361i	0.120458	+	0.0695462i
$831$		0			0
$832$			5.61231i			0.194572i
$833$	−17.5077	+	30.4723i	−0.606606	+	1.05580i
$834$		0			0
$835$	−1.51530	−	2.62457i	−0.0524390	−	0.0908269i
$836$	3.21462	−	5.56788i	0.111180	−	0.192569i
$837$		0			0
$838$	18.7383	−	10.8186i	0.647304	−	0.373721i
$839$	−20.5131			−0.708190			−0.354095	−	0.935209i	$-0.615211\pi$
$839$	−20.5131			−0.708190			−0.354095	+	0.935209i	$0.615211\pi$
$840$		0			0
$841$	−20.6364			−0.711600
$842$	−12.9360	+	7.46863i	−0.445806	+	0.257386i
$843$		0			0
$844$	6.50538	−	11.2677i	0.223925	−	0.387849i
$845$	41.0933	+	71.1757i	1.41365	+	2.44852i
$846$		0			0
$847$	9.39613	−	5.43806i	0.322855	−	0.186854i
$848$			21.1304i			0.725622i
$849$		0			0
$850$	−6.62544	−	3.82520i	−0.227251	−	0.131203i
$851$	35.0911	+	20.2599i	1.20291	+	0.694500i
$852$		0			0
$853$		−	23.0628i		−	0.789654i	−0.918755	−	0.394827i	$-0.870805\pi$
$853$		−	23.0628i		−	0.789654i	0.918755	−	0.394827i	$-0.129195\pi$
$854$	−15.9085	−	9.16246i	−0.544378	−	0.313533i
$855$		0			0
$856$	4.43334	+	7.67877i	0.151528	+	0.262455i
$857$	17.2558	−	29.8879i	0.589446	−	1.02095i	−0.404859	−	0.914379i	$-0.632679\pi$
$857$	17.2558	−	29.8879i	0.589446	−	1.02095i	0.994305	−	0.106572i	$-0.0339874\pi$
$858$		0			0
$859$	−39.4515	+	22.7773i	−1.34607	+	0.777153i	−0.987690	−	0.156423i	$-0.950004\pi$
$859$	−39.4515	+	22.7773i	−1.34607	+	0.777153i	−0.358378	+	0.933576i	$0.616670\pi$
$860$	−15.1619			−0.517018
$861$		0			0
$862$	11.6728			0.397575
$863$	−16.4111	+	9.47492i	−0.558639	+	0.322530i	−0.752599	−	0.658479i	$-0.771200\pi$
$863$	−16.4111	+	9.47492i	−0.558639	+	0.322530i	0.193960	+	0.981009i	$0.437867\pi$
$864$		0			0
$865$	−10.5701	+	18.3079i	−0.359393	+	0.622487i
$866$	6.26307	+	10.8480i	0.212828	+	0.368629i
$867$		0			0
$868$	−11.3425	−	19.5980i	−0.384988	−	0.665200i
$869$		−	57.6160i		−	1.95449i
$870$		0			0
$871$	−14.3006	−	8.25644i	−0.484556	−	0.279759i
$872$	9.46475	+	5.46448i	0.320517	+	0.185051i
$873$		0			0
$874$			3.37704i			0.114230i
$875$	0.0184889	+	17.5553i	0.000625040	+	0.593477i
$876$		0			0
$877$	−2.97999	−	5.16150i	−0.100627	−	0.174291i	0.811316	−	0.584608i	$-0.198752\pi$
$877$	−2.97999	−	5.16150i	−0.100627	−	0.174291i	−0.911943	+	0.410316i	$0.865418\pi$
$878$	−0.0736718	+	0.127603i	−0.00248630	+	0.00430640i
$879$		0			0
$880$	−18.9687	+	10.9516i	−0.639436	+	0.369179i
$881$	34.2160			1.15277			0.576384	−	0.817179i	$-0.304463\pi$
$881$	34.2160			1.15277			0.576384	+	0.817179i	$0.304463\pi$
$882$		0			0
$883$	−8.36371			−0.281461			−0.140731	−	0.990048i	$-0.544945\pi$
$883$	−8.36371			−0.281461			−0.140731	+	0.990048i	$0.544945\pi$
$884$	−47.0726	+	27.1774i	−1.58322	+	0.914075i
$885$		0			0
$886$	−6.70919	+	11.6207i	−0.225400	+	0.390404i
$887$	4.96071	+	8.59221i	0.166564	+	0.288498i	0.937210	−	0.348766i	$-0.113399\pi$
$887$	4.96071	+	8.59221i	0.166564	+	0.288498i	−0.770645	+	0.637264i	$0.780066\pi$
$888$		0			0
$889$	−0.0102346	−	9.71777i	−0.000343257	−	0.325924i
$890$			0.876928i			0.0293947i
$891$		0			0
$892$	−0.948773	−	0.547775i	−0.0317673	−	0.0183408i
$893$	6.18224	+	3.56932i	0.206881	+	0.119443i
$894$		0			0
$895$			47.2107i			1.57808i
$896$	15.2454	+	26.3417i	0.509312	+	0.880013i
$897$		0			0
$898$	11.6964	+	20.2588i	0.390314	+	0.676044i
$899$	−18.2240	+	31.5649i	−0.607804	+	1.05275i
$900$		0			0
$901$	−44.9148	+	25.9316i	−1.49633	+	0.863906i
$902$	−10.0314			−0.334009
$903$		0			0
$904$	−31.5952			−1.05084
$905$	−13.5013	+	7.79497i	−0.448798	+	0.259113i
$906$		0			0
$907$	9.60140	−	16.6301i	0.318809	−	0.552194i	−0.661431	−	0.750006i	$-0.730050\pi$
$907$	9.60140	−	16.6301i	0.318809	−	0.552194i	0.980240	+	0.197813i	$0.0633837\pi$
$908$	13.3683	+	23.1546i	0.443642	+	0.768411i
$909$		0			0
$910$	24.3058	+	13.9988i	0.805729	+	0.464057i
$911$			47.4609i			1.57245i	0.617941	+	0.786225i	$0.287967\pi$
$911$			47.4609i			1.57245i	−0.617941	+	0.786225i	$0.712033\pi$
$912$		0			0
$913$	8.32546	+	4.80671i	0.275532	+	0.159079i
$914$	−4.84503	−	2.79728i	−0.160259	−	0.0925257i
$915$		0			0
$916$			26.5492i			0.877212i
$917$	−20.7411	+	12.0040i	−0.684932	+	0.396408i
$918$		0			0
$919$	13.7717	+	23.8533i	0.454288	+	0.786849i	0.998647	−	0.0520028i	$-0.0165605\pi$
$919$	13.7717	+	23.8533i	0.454288	+	0.786849i	−0.544359	+	0.838852i	$0.683227\pi$
$920$	17.0015	−	29.4475i	0.560523	−	0.970855i
$921$		0			0
$922$	10.9041	−	6.29548i	0.359107	−	0.207331i
$923$	51.7800			1.70436
$924$		0			0
$925$	18.2838			0.601167
$926$	9.90604	−	5.71926i	0.325533	−	0.187946i
$927$		0			0
$928$	19.3733	−	33.5555i	0.635958	−	1.10151i
$929$	−6.58487	−	11.4053i	−0.216043	−	0.374197i	0.737552	−	0.675290i	$-0.235982\pi$
$929$	−6.58487	−	11.4053i	−0.216043	−	0.374197i	−0.953595	+	0.301094i	$0.902648\pi$
$930$		0			0
$931$	6.05479	−	3.51276i	0.198438	−	0.115126i
$932$			13.8651i			0.454166i
$933$		0			0
$934$	−16.6912	−	9.63664i	−0.546151	−	0.315321i
$935$	−46.5575	−	26.8800i	−1.52259	−	0.879069i
$936$		0			0
$937$			17.2450i			0.563369i	0.959507	+	0.281685i	$0.0908932\pi$
$937$			17.2450i			0.563369i	−0.959507	+	0.281685i	$0.909107\pi$
$938$	−3.92495	+	0.00413369i	−0.128154	+	0.000134970i
$939$		0			0
$940$	−16.2698	−	28.1801i	−0.530662	−	0.919134i
$941$	10.4888	−	18.1671i	0.341924	−	0.592230i	−0.642866	−	0.765979i	$-0.722255\pi$
$941$	10.4888	−	18.1671i	0.341924	−	0.592230i	0.984790	+	0.173749i	$0.0555881\pi$
$942$		0			0
$943$	−21.8392	+	12.6089i	−0.711183	+	0.410602i
$944$	−7.07525			−0.230280
$945$		0			0
$946$	7.60014			0.247102
$947$	−47.4387	+	27.3888i	−1.54155	+	0.890015i	−0.542810	+	0.839856i	$0.682640\pi$
$947$	−47.4387	+	27.3888i	−1.54155	+	0.890015i	−0.998741	+	0.0501593i	$0.984027\pi$
$948$		0			0
$949$	−47.0102	+	81.4240i	−1.52601	+	2.64313i
$950$	0.761913	+	1.31967i	0.0247197	+	0.0428158i
$951$		0			0
$952$	−14.2433	+	24.7303i	−0.461628	+	0.801512i
$953$			41.9134i			1.35771i	0.734273	+	0.678854i	$0.237523\pi$
$953$			41.9134i			1.35771i	−0.734273	+	0.678854i	$0.762477\pi$
$954$		0			0
$955$	1.62090	+	0.935824i	0.0524509	+	0.0302826i
$956$	−34.5676	−	19.9576i	−1.11799	−	0.645475i
$957$		0			0
$958$			8.72480i			0.281886i
$959$	−13.4392	+	23.3341i	−0.433974	+	0.753497i
$960$		0			0
$961$	−2.11814	−	3.66873i	−0.0683272	−	0.118346i
$962$	−13.5713	+	23.5062i	−0.437556	+	0.757869i
$963$		0			0
$964$	−24.9687	+	14.4157i	−0.804188	+	0.464298i
$965$	−55.6573			−1.79167
$966$		0			0
$967$	45.9754			1.47847			0.739235	−	0.673447i	$-0.235187\pi$
$967$	45.9754			1.47847			0.739235	+	0.673447i	$0.235187\pi$
$968$	7.63485	−	4.40798i	0.245393	−	0.141678i
$969$		0			0
$970$	3.48924	−	6.04354i	0.112033	−	0.194046i
$971$	−13.7328	−	23.7860i	−0.440708	−	0.763328i	0.557034	−	0.830489i	$-0.311939\pi$
$971$	−13.7328	−	23.7860i	−0.440708	−	0.763328i	−0.997742	+	0.0671611i	$0.978606\pi$
$972$		0			0
$973$	24.0036	−	0.0252802i	0.769521	−	0.000810446i
$974$		−	23.8808i		−	0.765191i
$975$		0			0
$976$	20.9068	+	12.0706i	0.669211	+	0.386369i
$977$	−20.4411	−	11.8017i	−0.653969	−	0.377569i	0.136006	−	0.990708i	$-0.456573\pi$
$977$	−20.4411	−	11.8017i	−0.653969	−	0.377569i	−0.789975	+	0.613139i	$0.789907\pi$
$978$		0			0
$979$			2.10377i			0.0672369i
$980$	−31.9076	+	0.0672091i	−1.01925	+	0.00214692i
$981$		0			0
$982$	−10.9868	−	19.0296i	−0.350602	−	0.607260i
$983$	19.3021	−	33.4323i	0.615643	−	1.06632i	−0.374628	−	0.927175i	$-0.622230\pi$
$983$	19.3021	−	33.4323i	0.615643	−	1.06632i	0.990271	−	0.139150i	$-0.0444370\pi$
$984$		0			0
$985$	−5.58423	+	3.22406i	−0.177928	+	0.102727i
$986$	20.7959			0.662275
$987$		0			0
$988$	10.8265			0.344437
$989$	16.5461	−	9.55292i	0.526137	−	0.303765i
$990$		0			0
$991$	4.76357	−	8.25075i	0.151320	−	0.262094i	−0.780393	−	0.625289i	$-0.784981\pi$
$991$	4.76357	−	8.25075i	0.151320	−	0.262094i	0.931713	+	0.363196i	$0.118314\pi$
$992$	−14.2258	−	24.6398i	−0.451669	−	0.782313i
$993$		0			0
$994$	10.6522	−	6.16503i	0.337868	−	0.195543i
$995$		−	34.4754i		−	1.09294i
$996$		0			0
$997$	16.3541	+	9.44204i	0.517939	+	0.299032i	0.736091	−	0.676883i	$-0.236670\pi$
$997$	16.3541	+	9.44204i	0.517939	+	0.299032i	−0.218152	+	0.975915i	$0.570003\pi$
$998$	10.8529	+	6.26595i	0.343544	+	0.198345i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.db.a.647.20	✓	96
3.2	odd	2	inner	1197.2.db.a.647.29	yes	96
7.5	odd	6	inner	1197.2.db.a.1160.29	yes	96
21.5	even	6	inner	1197.2.db.a.1160.20	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1197.2.db.a.647.20	✓	96	1.1	even	1	trivial
1197.2.db.a.647.29	yes	96	3.2	odd	2	inner
1197.2.db.a.1160.20	yes	96	21.5	even	6	inner
1197.2.db.a.1160.29	yes	96	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.509165 + 0.293966i) q^{2} +(-0.827168 + 1.43270i) q^{4} +(-1.37766 - 2.38618i) q^{5} +(-0.00278646 - 2.64575i) q^{7} -2.14850i q^{8} +O(q^{10})\)	\(q+(-0.509165 + 0.293966i) q^{2} +(-0.827168 + 1.43270i) q^{4} +(-1.37766 - 2.38618i) q^{5} +(-0.00278646 - 2.64575i) q^{7} -2.14850i q^{8} +(1.40292 + 0.809974i) q^{10} +(3.36563 + 1.94315i) q^{11} +6.54433i q^{13} +(0.779180 + 1.34630i) q^{14} +(-1.02275 - 1.77145i) q^{16} +(2.51026 - 4.34790i) q^{17} +(-0.866025 + 0.500000i) q^{19} +4.55824 q^{20} -2.28488 q^{22} +(-4.97438 + 2.87196i) q^{23} +(-1.29592 + 2.24460i) q^{25} +(-1.92381 - 3.33214i) q^{26} +(3.79286 + 2.18449i) q^{28} -7.04531i q^{29} +(-4.48027 - 2.58668i) q^{31} +(4.76281 + 2.74981i) q^{32} +2.95173i q^{34} +(-6.30941 + 3.65160i) q^{35} +(-3.52719 - 6.10927i) q^{37} +(0.293966 - 0.509165i) q^{38} +(-5.12673 + 2.95992i) q^{40} +4.39034 q^{41} -3.32627 q^{43} +(-5.56788 + 3.21462i) q^{44} +(1.68852 - 2.92460i) q^{46} +(-3.56932 - 6.18224i) q^{47} +(-6.99998 + 0.0147445i) q^{49} -1.52383i q^{50} +(-9.37603 - 5.41326i) q^{52} +(-8.94624 - 5.16511i) q^{53} -10.7080i q^{55} +(-5.68440 + 0.00598671i) q^{56} +(2.07108 + 3.58722i) q^{58} +(1.72947 - 2.99553i) q^{59} +(-10.2209 + 5.90104i) q^{61} +3.04159 q^{62} +0.857584 q^{64} +(15.6160 - 9.01589i) q^{65} +(-1.26162 + 2.18519i) q^{67} +(4.15282 + 7.19289i) q^{68} +(2.13908 - 3.71402i) q^{70} -7.91220i q^{71} +(12.4419 + 7.18334i) q^{73} +(3.59184 + 2.07375i) q^{74} -1.65434i q^{76} +(5.13171 - 8.91004i) q^{77} +(-7.41271 - 12.8392i) q^{79} +(-2.81801 + 4.88093i) q^{80} +(-2.23541 + 1.29061i) q^{82} +2.47367 q^{83} -13.8332 q^{85} +(1.69362 - 0.977813i) q^{86} +(4.17486 - 7.23107i) q^{88} +(0.270665 + 0.468806i) q^{89} +(17.3147 - 0.0182355i) q^{91} -9.50236i q^{92} +(3.63474 + 2.09852i) q^{94} +(2.38618 + 1.37766i) q^{95} -4.30784i q^{97} +(3.55981 - 2.06527i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) \) 96 * q + 48 * q^4 + 8 * q^7	\( 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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