LMFDB - Embedded newform 315.2.bb.b.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(89,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("315.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bb (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.3
Character	$\chi$	$=$	315.269
Dual form			315.2.bb.b.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.956572 - 1.65683i) q^{2} +(-0.830062 + 1.43771i) q^{4} +(-2.17319 + 0.526555i) q^{5} +(-1.11878 + 2.39757i) q^{7} -0.650234 q^{8} +(2.95122 + 3.09692i) q^{10} +(2.79501 + 1.61370i) q^{11} +4.86146 q^{13} +(5.04256 - 0.439817i) q^{14} +(2.28212 + 3.95275i) q^{16} +(-0.631456 - 0.364571i) q^{17} +(-6.81691 + 3.93574i) q^{19} +(1.04685 - 3.56148i) q^{20} -6.17449i q^{22} +(2.43410 + 4.21599i) q^{23} +(4.44548 - 2.28861i) q^{25} +(-4.65034 - 8.05463i) q^{26} +(-2.51835 - 3.59861i) q^{28} +7.75958i q^{29} +(-1.23751 - 0.714478i) q^{31} +(3.71579 - 6.43594i) q^{32} +1.39495i q^{34} +(1.16887 - 5.79946i) q^{35} +(-2.74130 + 1.58269i) q^{37} +(13.0417 + 7.52965i) q^{38} +(1.41308 - 0.342384i) q^{40} +1.40264 q^{41} -6.42489i q^{43} +(-4.64007 + 2.67894i) q^{44} +(4.65679 - 8.06579i) q^{46} +(-4.21797 + 2.43524i) q^{47} +(-4.49666 - 5.36470i) q^{49} +(-8.04426 - 5.17620i) q^{50} +(-4.03531 + 6.98937i) q^{52} +(-0.760733 + 1.31763i) q^{53} +(-6.92379 - 2.03515i) q^{55} +(0.727468 - 1.55898i) q^{56} +(12.8563 - 7.42260i) q^{58} +(-3.15081 + 5.45737i) q^{59} +(-2.05442 + 1.18612i) q^{61} +2.73380i q^{62} -5.08921 q^{64} +(-10.5649 + 2.55983i) q^{65} +(9.63531 + 5.56295i) q^{67} +(1.04829 - 0.605233i) q^{68} +(-10.7268 + 3.61099i) q^{70} +10.1351i q^{71} +(-6.91195 + 11.9718i) q^{73} +(5.24450 + 3.02792i) q^{74} -13.0676i q^{76} +(-6.99596 + 4.89586i) q^{77} +(-1.99018 - 3.44710i) q^{79} +(-7.04081 - 7.38839i) q^{80} +(-1.34173 - 2.32395i) q^{82} -4.19208i q^{83} +(1.56424 + 0.459785i) q^{85} +(-10.6450 + 6.14587i) q^{86} +(-1.81741 - 1.04928i) q^{88} +(-5.63672 - 9.76309i) q^{89} +(-5.43891 + 11.6557i) q^{91} -8.08181 q^{92} +(8.06958 + 4.65898i) q^{94} +(12.7420 - 12.1426i) q^{95} -2.21388 q^{97} +(-4.58702 + 12.5819i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 12 q^{10} - 36 q^{19} + 12 q^{25} - 60 q^{31} + 96 q^{40} - 24 q^{46} + 36 q^{49} + 48 q^{61} + 48 q^{64} - 48 q^{70} - 60 q^{79} - 72 q^{85} + 60 q^{91} + 48 q^{94}+O(q^{100}) $ 24 * q - 24 * q^4 - 12 * q^10 - 36 * q^19 + 12 * q^25 - 60 * q^31 + 96 * q^40 - 24 * q^46 + 36 * q^49 + 48 * q^61 + 48 * q^64 - 48 * q^70 - 60 * q^79 - 72 * q^85 + 60 * q^91 + 48 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.956572	−	1.65683i	−0.676399	−	1.17156i	−0.976058	−	0.217511i	$-0.930206\pi$
$2$	−0.956572	−	1.65683i	−0.676399	−	1.17156i	0.299659	−	0.954046i	$-0.403127\pi$
$3$		0			0
$3$		0			0
$4$	−0.830062	+	1.43771i	−0.415031	+	0.718854i
$5$	−2.17319	+	0.526555i	−0.971879	+	0.235483i
$5$	−2.17319	+	0.526555i	−0.971879	+	0.235483i
$6$		0			0
$7$	−1.11878	+	2.39757i	−0.422859	+	0.906196i
$7$	−1.11878	+	2.39757i	−0.422859	+	0.906196i
$8$	−0.650234			−0.229892
$9$		0			0
$10$	2.95122	+	3.09692i	0.933259	+	0.979331i
$11$	2.79501	+	1.61370i	0.842728	+	0.486549i	0.858191	−	0.513331i	$-0.171589\pi$
$11$	2.79501	+	1.61370i	0.842728	+	0.486549i	−0.0154625	+	0.999880i	$0.504922\pi$
$12$		0			0
$13$	4.86146			1.34833			0.674164	−	0.738582i	$-0.264504\pi$
$13$	4.86146			1.34833			0.674164	+	0.738582i	$0.264504\pi$
$14$	5.04256	−	0.439817i	1.34768	−	0.117546i
$15$		0			0
$16$	2.28212	+	3.95275i	0.570530	+	0.988186i
$17$	−0.631456	−	0.364571i	−0.153150	−	0.0884215i	0.421466	−	0.906844i	$-0.361516\pi$
$17$	−0.631456	−	0.364571i	−0.153150	−	0.0884215i	−0.574617	+	0.818423i	$0.694849\pi$
$18$		0			0
$19$	−6.81691	+	3.93574i	−1.56391	+	0.902922i	−0.567051	+	0.823683i	$0.691916\pi$
$19$	−6.81691	+	3.93574i	−1.56391	+	0.902922i	−0.996856	+	0.0792390i	$0.974751\pi$
$20$	1.04685	−	3.56148i	0.234082	−	0.796372i
$21$		0			0
$22$		−	6.17449i		−	1.31641i
$23$	2.43410	+	4.21599i	0.507545	+	0.879094i	0.999962	+	0.00873433i	$0.00278026\pi$
$23$	2.43410	+	4.21599i	0.507545	+	0.879094i	−0.492417	+	0.870360i	$0.663886\pi$
$24$		0			0
$25$	4.44548	−	2.28861i	0.889096	−	0.457721i
$26$	−4.65034	−	8.05463i	−0.912007	−	1.57964i
$27$		0			0
$28$	−2.51835	−	3.59861i	−0.475923	−	0.680073i
$29$			7.75958i			1.44092i	0.693498	+	0.720459i	$0.256069\pi$
$29$			7.75958i			1.44092i	−0.693498	+	0.720459i	$0.743931\pi$
$30$		0			0
$31$	−1.23751	−	0.714478i	−0.222264	−	0.128324i	0.384734	−	0.923027i	$-0.374293\pi$
$31$	−1.23751	−	0.714478i	−0.222264	−	0.128324i	−0.606998	+	0.794703i	$0.707626\pi$
$32$	3.71579	−	6.43594i	0.656865	−	1.13772i
$33$		0			0
$34$			1.39495i			0.239233i
$35$	1.16887	−	5.79946i	0.197574	−	0.980288i
$36$		0			0
$37$	−2.74130	+	1.58269i	−0.450667	+	0.260193i	−0.708112	−	0.706100i	$-0.750453\pi$
$37$	−2.74130	+	1.58269i	−0.450667	+	0.260193i	0.257445	+	0.966293i	$0.417119\pi$
$38$	13.0417	+	7.52965i	2.11565	+	1.22147i
$39$		0			0
$40$	1.41308	−	0.342384i	0.223427	−	0.0541357i
$41$	1.40264			0.219056			0.109528	−	0.993984i	$-0.465066\pi$
$41$	1.40264			0.219056			0.109528	+	0.993984i	$0.465066\pi$
$42$		0			0
$43$		−	6.42489i		−	0.979787i	−0.871782	−	0.489893i	$-0.837036\pi$
$43$		−	6.42489i		−	0.979787i	0.871782	−	0.489893i	$-0.162964\pi$
$44$	−4.64007	+	2.67894i	−0.699516	+	0.403866i
$45$		0			0
$46$	4.65679	−	8.06579i	0.686606	−	1.18924i
$47$	−4.21797	+	2.43524i	−0.615254	+	0.355217i	−0.775019	−	0.631938i	$-0.782260\pi$
$47$	−4.21797	+	2.43524i	−0.615254	+	0.355217i	0.159765	+	0.987155i	$0.448926\pi$
$48$		0			0
$49$	−4.49666	−	5.36470i	−0.642381	−	0.766386i
$50$	−8.04426	−	5.17620i	−1.13763	−	0.732025i
$51$		0			0
$52$	−4.03531	+	6.98937i	−0.559597	+	0.969251i
$53$	−0.760733	+	1.31763i	−0.104495	+	0.180990i	−0.913532	−	0.406768i	$-0.866656\pi$
$53$	−0.760733	+	1.31763i	−0.104495	+	0.180990i	0.809037	+	0.587758i	$0.199989\pi$
$54$		0			0
$55$	−6.92379	−	2.03515i	−0.933603	−	0.274419i
$56$	0.727468	−	1.55898i	0.0972120	−	0.208327i
$57$		0			0
$58$	12.8563	−	7.42260i	1.68812	−	0.974635i
$59$	−3.15081	+	5.45737i	−0.410201	+	0.710489i	−0.994911	−	0.100753i	$-0.967875\pi$
$59$	−3.15081	+	5.45737i	−0.410201	+	0.710489i	0.584711	+	0.811242i	$0.301208\pi$
$60$		0			0
$61$	−2.05442	+	1.18612i	−0.263042	+	0.151867i	−0.625721	−	0.780047i	$-0.715195\pi$
$61$	−2.05442	+	1.18612i	−0.263042	+	0.151867i	0.362680	+	0.931914i	$0.381862\pi$
$62$			2.73380i			0.347193i
$63$		0			0
$64$	−5.08921			−0.636152
$65$	−10.5649	+	2.55983i	−1.31041	+	0.317508i
$66$		0			0
$67$	9.63531	+	5.56295i	1.17714	+	0.679622i	0.955351	−	0.295472i	$-0.0954770\pi$
$67$	9.63531	+	5.56295i	1.17714	+	0.679622i	0.221789	+	0.975095i	$0.428810\pi$
$68$	1.04829	−	0.605233i	0.127124	−	0.0733953i
$69$		0			0
$70$	−10.7268	+	3.61099i	−1.28210	+	0.431596i
$71$			10.1351i			1.20282i	0.798942	+	0.601408i	$0.205393\pi$
$71$			10.1351i			1.20282i	−0.798942	+	0.601408i	$0.794607\pi$
$72$		0			0
$73$	−6.91195	+	11.9718i	−0.808982	+	1.40120i	0.104587	+	0.994516i	$0.466648\pi$
$73$	−6.91195	+	11.9718i	−0.808982	+	1.40120i	−0.913570	+	0.406683i	$0.866686\pi$
$74$	5.24450	+	3.02792i	0.609661	+	0.351988i
$75$		0			0
$76$		−	13.0676i		−	1.49896i
$77$	−6.99596	+	4.89586i	−0.797264	+	0.557935i
$78$		0			0
$79$	−1.99018	−	3.44710i	−0.223913	−	0.387829i	0.732080	−	0.681219i	$-0.238550\pi$
$79$	−1.99018	−	3.44710i	−0.223913	−	0.387829i	−0.955993	+	0.293390i	$0.905217\pi$
$80$	−7.04081	−	7.38839i	−0.787186	−	0.826047i
$81$		0			0
$82$	−1.34173	−	2.32395i	−0.148169	−	0.256637i
$83$		−	4.19208i		−	0.460141i	−0.973174	−	0.230070i	$-0.926104\pi$
$83$		−	4.19208i		−	0.460141i	0.973174	−	0.230070i	$-0.0738957\pi$
$84$		0			0
$85$	1.56424	+	0.459785i	0.169665	+	0.0498706i
$86$	−10.6450	+	6.14587i	−1.14788	+	0.662727i
$87$		0			0
$88$	−1.81741	−	1.04928i	−0.193737	−	0.111854i
$89$	−5.63672	−	9.76309i	−0.597491	−	1.03489i	−0.993190	−	0.116505i	$-0.962831\pi$
$89$	−5.63672	−	9.76309i	−0.597491	−	1.03489i	0.395699	−	0.918380i	$-0.370502\pi$
$90$		0			0
$91$	−5.43891	+	11.6557i	−0.570152	+	1.22185i
$92$	−8.08181			−0.842587
$93$		0			0
$94$	8.06958	+	4.65898i	0.832314	+	0.480537i
$95$	12.7420	−	12.1426i	1.30730	−	1.24580i
$96$		0			0
$97$	−2.21388			−0.224785			−0.112393	−	0.993664i	$-0.535851\pi$
$97$	−2.21388			−0.224785			−0.112393	+	0.993664i	$0.535851\pi$
$98$	−4.58702	+	12.5819i	−0.463359	+	1.27097i
$99$		0			0
$100$	−0.399674	+	8.29099i	−0.0399674	+	0.829099i
$101$	5.85104	−	10.1343i	0.582201	−	1.00840i	−0.413017	−	0.910723i	$-0.635525\pi$
$101$	5.85104	−	10.1343i	0.582201	−	1.00840i	0.995218	−	0.0976779i	$-0.0311415\pi$
$102$		0			0
$103$	−0.292630	−	0.506851i	−0.0288337	−	0.0499415i	0.851248	−	0.524763i	$-0.175846\pi$
$103$	−0.292630	−	0.506851i	−0.0288337	−	0.0499415i	−0.880082	+	0.474821i	$0.842513\pi$
$104$	−3.16109			−0.309970
$105$		0			0
$106$	2.91079			0.282721
$107$	−0.846073	−	1.46544i	−0.0817929	−	0.141670i	0.822227	−	0.569159i	$-0.192731\pi$
$107$	−0.846073	−	1.46544i	−0.0817929	−	0.141670i	−0.904020	+	0.427490i	$0.859398\pi$
$108$		0			0
$109$	6.70139	−	11.6072i	0.641877	−	1.11176i	−0.343136	−	0.939286i	$-0.611489\pi$
$109$	6.70139	−	11.6072i	0.641877	−	1.11176i	0.985013	−	0.172478i	$-0.0551774\pi$
$110$	3.25121	+	13.4183i	0.309991	+	1.27939i
$111$		0			0
$112$	−12.0302	+	1.04928i	−1.13674	+	0.0991479i
$113$	14.2129			1.33704			0.668520	−	0.743694i	$-0.266928\pi$
$113$	14.2129			1.33704			0.668520	+	0.743694i	$0.266928\pi$
$114$		0			0
$115$	−7.50970	−	7.88044i	−0.700284	−	0.734854i
$116$	−11.1560	−	6.44093i	−1.03581	−	0.598025i
$117$		0			0
$118$	12.0559			1.10984
$119$	1.58054	−	1.10608i	0.144888	−	0.101394i
$120$		0			0
$121$	−0.291934	−	0.505645i	−0.0265395	−	0.0459677i
$122$	3.93041	+	2.26922i	0.355842	+	0.205446i
$123$		0			0
$124$	2.05442	−	1.18612i	0.184493	−	0.106517i
$125$	−8.45578	+	7.31436i	−0.756308	+	0.654216i
$126$		0			0
$127$			2.08954i			0.185417i	0.995693	+	0.0927084i	$0.0295524\pi$
$127$			2.08954i			0.185417i	−0.995693	+	0.0927084i	$0.970448\pi$
$128$	−2.56338	−	4.43990i	−0.226573	−	0.392436i
$129$		0			0
$130$	14.3473	+	15.0555i	1.25834	+	1.32046i
$131$	5.60241	+	9.70365i	0.489484	+	0.847812i	0.999927	−	0.0121001i	$-0.00385167\pi$
$131$	5.60241	+	9.70365i	0.489484	+	0.847812i	−0.510442	+	0.859912i	$0.670518\pi$
$132$		0			0
$133$	−1.80960	−	20.7472i	−0.156912	−	1.79901i
$134$		−	21.2855i		−	1.83878i
$135$		0			0
$136$	0.410594	+	0.237056i	0.0352081	+	0.0203274i
$137$	3.51995	−	6.09673i	0.300730	−	0.520879i	−0.675572	−	0.737294i	$-0.736103\pi$
$137$	3.51995	−	6.09673i	0.300730	−	0.520879i	0.976301	+	0.216415i	$0.0694365\pi$
$138$		0			0
$139$			6.45903i			0.547848i	0.961751	+	0.273924i	$0.0883216\pi$
$139$			6.45903i			0.547848i	−0.961751	+	0.273924i	$0.911678\pi$
$140$	7.36771	+	6.49440i	0.622685	+	0.548877i
$141$		0			0
$142$	16.7922	−	9.69496i	1.40917	−	0.813583i
$143$	13.5879	+	7.84495i	1.13627	+	0.656028i
$144$		0			0
$145$	−4.08584	−	16.8630i	−0.339311	−	1.40040i
$146$	26.4471			2.18878
$147$		0			0
$148$		−	5.25492i		−	0.431952i
$149$	20.3962	−	11.7758i	1.67092	−	0.964709i	0.703802	−	0.710396i	$-0.251484\pi$
$149$	20.3962	−	11.7758i	1.67092	−	0.964709i	0.967122	−	0.254312i	$-0.0818491\pi$
$150$		0			0
$151$	−9.05442	+	15.6827i	−0.736838	+	1.27624i	0.217074	+	0.976155i	$0.430349\pi$
$151$	−9.05442	+	15.6827i	−0.736838	+	1.27624i	−0.953912	+	0.300086i	$0.902985\pi$
$152$	4.43258	−	2.55915i	0.359530	−	0.207575i
$153$		0			0
$154$	14.8038	+	6.90789i	1.19292	+	0.556654i
$155$	3.06556	+	0.901075i	0.246231	+	0.0723761i
$156$		0			0
$157$	1.24227	−	2.15168i	0.0991441	−	0.171723i	−0.812187	−	0.583398i	$-0.801723\pi$
$157$	1.24227	−	2.15168i	0.0991441	−	0.171723i	0.911331	+	0.411675i	$0.135056\pi$
$158$	−3.80751	+	6.59480i	−0.302909	+	0.524654i
$159$		0			0
$160$	−4.68623	+	15.9431i	−0.370479	+	1.26041i
$161$	−12.8313	+	1.11916i	−1.01125	+	0.0882023i
$162$		0			0
$163$	3.41015	−	1.96885i	0.267104	−	0.154212i	−0.360467	−	0.932772i	$-0.617383\pi$
$163$	3.41015	−	1.96885i	0.267104	−	0.154212i	0.627571	+	0.778560i	$0.284049\pi$
$164$	−1.16428	+	2.01659i	−0.0909151	+	0.157470i
$165$		0			0
$166$	−6.94558	+	4.01003i	−0.539081	+	0.311239i
$167$		−	5.31832i		−	0.411544i	−0.978600	−	0.205772i	$-0.934029\pi$
$167$		−	5.31832i		−	0.411544i	0.978600	−	0.205772i	$-0.0659705\pi$
$168$		0			0
$169$	10.6338			0.817986
$170$	−0.734520	−	3.03150i	−0.0563351	−	0.232505i
$171$		0			0
$172$	9.23712	+	5.33306i	0.704324	+	0.406642i
$173$	6.45623	−	3.72751i	0.490858	−	0.283397i	−0.234072	−	0.972219i	$-0.575205\pi$
$173$	6.45623	−	3.72751i	0.490858	−	0.283397i	0.724930	+	0.688822i	$0.241872\pi$
$174$		0			0
$175$	0.513575	+	13.2188i	0.0388226	+	0.999246i
$176$			14.7306i			1.11036i
$177$		0			0
$178$	−10.7839	+	18.6782i	−0.808285	+	1.39999i
$179$	−11.5242	−	6.65349i	−0.861358	−	0.497305i	0.00310866	−	0.999995i	$-0.499010\pi$
$179$	−11.5242	−	6.65349i	−0.861358	−	0.497305i	−0.864467	+	0.502690i	$0.832344\pi$
$180$		0			0
$181$			9.95814i			0.740183i	0.928995	+	0.370091i	$0.120674\pi$
$181$			9.95814i			0.740183i	−0.928995	+	0.370091i	$0.879326\pi$
$182$	24.5142	−	2.13816i	1.81712	−	0.158491i
$183$		0			0
$184$	−1.58273	−	2.74138i	−0.116681	−	0.202097i
$185$	5.12398	−	4.88293i	0.376723	−	0.359000i
$186$		0			0
$187$	−1.17662	−	2.03796i	−0.0860428	−	0.149031i
$188$		−	8.08561i		−	0.589704i
$189$		0			0
$190$	−32.3069	−	9.49614i	−2.34379	−	0.688922i
$191$	21.3140	−	12.3056i	1.54223	−	0.890404i	0.543527	−	0.839392i	$-0.317089\pi$
$191$	21.3140	−	12.3056i	1.54223	−	0.890404i	0.998698	−	0.0510125i	$-0.0162448\pi$
$192$		0			0
$193$	−10.8377	−	6.25714i	−0.780113	−	0.450399i	0.0563571	−	0.998411i	$-0.482051\pi$
$193$	−10.8377	−	6.25714i	−0.780113	−	0.450399i	−0.836470	+	0.548012i	$0.815385\pi$
$194$	2.11773	+	3.66802i	0.152044	+	0.263349i
$195$		0			0
$196$	11.4454	−	2.01186i	0.817528	−	0.143704i
$197$	−15.6968			−1.11835			−0.559177	−	0.829049i	$-0.688883\pi$
$197$	−15.6968			−1.11835			−0.559177	+	0.829049i	$0.688883\pi$
$198$		0			0
$199$	17.1436	+	9.89788i	1.21528	+	0.701642i	0.963905	−	0.266247i	$-0.0857838\pi$
$199$	17.1436	+	9.89788i	1.21528	+	0.701642i	0.251375	+	0.967890i	$0.419117\pi$
$200$	−2.89060	+	1.48813i	−0.204396	+	0.105227i
$201$		0			0
$202$	−22.3878			−1.57520
$203$	−18.6041	−	8.68126i	−1.30575	−	0.609305i
$204$		0			0
$205$	−3.04821	+	0.738570i	−0.212896	+	0.0515839i
$206$	−0.559844	+	0.969678i	−0.0390062	+	0.0675607i
$207$		0			0
$208$	11.0944	+	19.2161i	0.769261	+	1.33240i
$209$	−25.4045			−1.75726
$210$		0			0
$211$	11.5839			0.797466			0.398733	−	0.917067i	$-0.369450\pi$
$211$	11.5839			0.797466			0.398733	+	0.917067i	$0.369450\pi$
$212$	−1.26291	−	2.18743i	−0.0867371	−	0.150233i
$213$		0			0
$214$	−1.61866	+	2.80360i	−0.110649	+	0.191650i
$215$	3.38306	+	13.9625i	0.230723	+	0.952234i
$216$		0			0
$217$	3.09751	−	2.16768i	0.210273	−	0.147151i
$218$	−25.6415			−1.73666
$219$		0			0
$220$	8.67312	−	8.26509i	0.584741	−	0.557233i
$221$	−3.06980	−	1.77235i	−0.206497	−	0.119221i
$222$		0			0
$223$	24.1321			1.61600			0.808002	−	0.589180i	$-0.200549\pi$
$223$	24.1321			1.61600			0.808002	+	0.589180i	$0.200549\pi$
$224$	11.2734	+	16.1093i	0.753239	+	1.07634i
$225$		0			0
$226$	−13.5957	−	23.5484i	−0.904372	−	1.56642i
$227$	−8.82377	−	5.09441i	−0.585654	−	0.338128i	0.177723	−	0.984081i	$-0.443127\pi$
$227$	−8.82377	−	5.09441i	−0.585654	−	0.338128i	−0.763377	+	0.645953i	$0.776460\pi$
$228$		0			0
$229$	22.7373	−	13.1274i	1.50252	−	0.867483i	0.502529	−	0.864561i	$-0.332403\pi$
$229$	22.7373	−	13.1274i	1.50252	−	0.867483i	0.999996	−	0.00292226i	$-0.000930186\pi$
$230$	−5.87298	+	19.9805i	−0.387253	+	1.31748i
$231$		0			0
$232$		−	5.04554i		−	0.331256i
$233$	−9.19667	−	15.9291i	−0.602494	−	1.04355i	−0.992442	−	0.122713i	$-0.960840\pi$
$233$	−9.19667	−	15.9291i	−0.602494	−	1.04355i	0.389948	−	0.920837i	$-0.372493\pi$
$234$		0			0
$235$	7.88414	−	7.51323i	0.514305	−	0.490109i
$236$	−5.23074	−	9.05990i	−0.340492	−	0.589749i
$237$		0			0
$238$	−3.34450	−	1.56065i	−0.216792	−	0.101162i
$239$			0.961317i			0.0621824i	0.999517	+	0.0310912i	$0.00989824\pi$
$239$			0.961317i			0.0621824i	−0.999517	+	0.0310912i	$0.990102\pi$
$240$		0			0
$241$	−5.63829	−	3.25527i	−0.363194	−	0.209690i	0.307287	−	0.951617i	$-0.400579\pi$
$241$	−5.63829	−	3.25527i	−0.363194	−	0.209690i	−0.670481	+	0.741927i	$0.733912\pi$
$242$	−0.558512	+	0.967371i	−0.0359025	+	0.0621850i
$243$		0			0
$244$		−	3.93821i		−	0.252118i
$245$	12.5969	+	9.29075i	0.804786	+	0.593564i
$246$		0			0
$247$	−33.1402	+	19.1335i	−2.10866	+	1.21743i
$248$	0.804672	+	0.464578i	0.0510967	+	0.0295007i
$249$		0			0
$250$	20.2072	+	7.01309i	1.27802	+	0.443547i
$251$	−2.02506			−0.127820			−0.0639102	−	0.997956i	$-0.520357\pi$
$251$	−2.02506			−0.127820			−0.0639102	+	0.997956i	$0.520357\pi$
$252$		0			0
$253$			15.7116i			0.987783i
$254$	3.46202	−	1.99880i	0.217226	−	0.125416i
$255$		0			0
$256$	−9.99333	+	17.3090i	−0.624583	+	1.08181i
$257$	−15.7532	+	9.09510i	−0.982656	+	0.567337i	−0.903071	−	0.429491i	$-0.858693\pi$
$257$	−15.7532	+	9.09510i	−0.982656	+	0.567337i	−0.0795849	+	0.996828i	$0.525359\pi$
$258$		0			0
$259$	−0.727697	−	8.34313i	−0.0452169	−	0.518417i
$260$	5.08920	−	17.3140i	0.315619	−	1.07377i
$261$		0			0
$262$	10.7182	−	18.5645i	0.662173	−	1.14692i
$263$	−9.78034	+	16.9400i	−0.603082	+	1.04457i	0.389270	+	0.921124i	$0.372727\pi$
$263$	−9.78034	+	16.9400i	−0.603082	+	1.04457i	−0.992351	+	0.123444i	$0.960606\pi$
$264$		0			0
$265$	0.959411	−	3.26402i	0.0589362	−	0.200507i
$266$	−32.6437	+	22.8444i	−2.00151	+	1.40068i
$267$		0			0
$268$	−15.9958	+	9.23518i	−0.977099	+	0.564128i
$269$	2.30801	−	3.99759i	0.140722	−	0.243738i	−0.787047	−	0.616893i	$-0.788391\pi$
$269$	2.30801	−	3.99759i	0.140722	−	0.243738i	0.927769	+	0.373156i	$0.121724\pi$
$270$		0			0
$271$	−9.33654	+	5.39045i	−0.567154	+	0.327447i	−0.756012	−	0.654558i	$-0.772855\pi$
$271$	−9.33654	+	5.39045i	−0.567154	+	0.327447i	0.188858	+	0.982004i	$0.439522\pi$
$272$		−	3.32798i		−	0.201788i
$273$		0			0
$274$	−13.4684			−0.813653
$275$	16.1183	+	0.776995i	0.971970	+	0.0468546i
$276$		0			0
$277$	17.7594	+	10.2534i	1.06706	+	0.616067i	0.927376	−	0.374130i	$-0.122059\pi$
$277$	17.7594	+	10.2534i	1.06706	+	0.616067i	0.139682	+	0.990196i	$0.455392\pi$
$278$	10.7015	−	6.17853i	0.641835	−	0.370564i
$279$		0			0
$280$	−0.760035	+	3.77101i	−0.0454208	+	0.225361i
$281$		−	0.714666i		−	0.0426334i	−0.999773	−	0.0213167i	$-0.993214\pi$
$281$		−	0.714666i		−	0.0426334i	0.999773	−	0.0213167i	$-0.00678583\pi$
$282$		0			0
$283$	−14.0110	+	24.2677i	−0.832866	+	1.44257i	0.0628908	+	0.998020i	$0.479968\pi$
$283$	−14.0110	+	24.2677i	−0.832866	+	1.44257i	−0.895756	+	0.444545i	$0.853365\pi$
$284$	−14.5713	−	8.41276i	−0.864649	−	0.499206i
$285$		0			0
$286$		−	30.0171i		−	1.77495i
$287$	−1.56925	+	3.36293i	−0.0926299	+	0.198508i
$288$		0			0
$289$	−8.23418	−	14.2620i	−0.484363	−	0.838942i
$290$	−24.0308	+	22.9002i	−1.41113	+	1.34475i
$291$		0			0
$292$	−11.4747	−	19.8747i	−0.671505	−	1.16308i
$293$		−	9.79171i		−	0.572038i	−0.958224	−	0.286019i	$-0.907668\pi$
$293$		−	9.79171i		−	0.572038i	0.958224	−	0.286019i	$-0.0923321\pi$
$294$		0			0
$295$	3.97370	−	13.5190i	0.231358	−	0.787104i
$296$	1.78249	−	1.02912i	0.103605	−	0.0598163i
$297$		0			0
$298$	−39.0209	−	22.5287i	−2.26042	−	1.30506i
$299$	11.8333	+	20.4959i	0.684337	+	1.18531i
$300$		0			0
$301$	15.4041	+	7.18804i	0.887878	+	0.414312i
$302$	34.6448			1.99359
$303$		0			0
$304$	−31.1140	−	17.9637i	−1.78451	−	1.03029i
$305$	3.84008	−	3.65943i	0.219883	−	0.209538i
$306$		0			0
$307$	25.4778			1.45410			0.727048	−	0.686586i	$-0.240892\pi$
$307$	25.4778			1.45410			0.727048	+	0.686586i	$0.240892\pi$
$308$	−1.23174	−	14.1220i	−0.0701847	−	0.804677i
$309$		0			0
$310$	−1.43950	−	5.94106i	−0.0817579	−	0.337429i
$311$	5.05422	−	8.75417i	0.286599	−	0.496404i	−0.686397	−	0.727227i	$-0.740809\pi$
$311$	5.05422	−	8.75417i	0.286599	−	0.496404i	0.972996	+	0.230824i	$0.0741420\pi$
$312$		0			0
$313$	−11.7375	−	20.3300i	−0.663445	−	1.14912i	−0.979705	−	0.200447i	$-0.935760\pi$
$313$	−11.7375	−	20.3300i	−0.663445	−	1.14912i	0.316260	−	0.948673i	$-0.397573\pi$
$314$	−4.75329			−0.268244
$315$		0			0
$316$	6.60790			0.371724
$317$	15.7156	+	27.2202i	0.882677	+	1.52884i	0.848353	+	0.529430i	$0.177594\pi$
$317$	15.7156	+	27.2202i	0.882677	+	1.52884i	0.0343235	+	0.999411i	$0.489072\pi$
$318$		0			0
$319$	−12.5216	+	21.6881i	−0.701077	+	1.21430i
$320$	11.0598	−	2.67975i	0.618262	−	0.149803i
$321$		0			0
$322$	14.1284	+	20.1888i	0.787343	+	1.12508i
$323$	5.73943			0.319351
$324$		0			0
$325$	21.6115	−	11.1260i	1.19879	−	0.617158i
$326$	−6.52412	−	3.76670i	−0.361337	−	0.208618i
$327$		0			0
$328$	−0.912047			−0.0503593
$329$	−1.11969	−	12.8374i	−0.0617304	−	0.707747i
$330$		0			0
$331$	0.589214	+	1.02055i	0.0323861	+	0.0560944i	0.881764	−	0.471691i	$-0.156356\pi$
$331$	0.589214	+	1.02055i	0.0323861	+	0.0560944i	−0.849378	+	0.527785i	$0.823023\pi$
$332$	6.02700	+	3.47969i	0.330774	+	0.190973i
$333$		0			0
$334$	−8.81156	+	5.08736i	−0.482147	+	0.278368i
$335$	−23.8685	−	7.01580i	−1.30408	−	0.383314i
$336$		0			0
$337$			3.92868i			0.214009i	0.994259	+	0.107004i	$0.0341259\pi$
$337$			3.92868i			0.214009i	−0.994259	+	0.107004i	$0.965874\pi$
$338$	−10.1720	−	17.6185i	−0.553285	−	0.958318i
$339$		0			0
$340$	−1.95945	+	1.86727i	−0.106266	+	0.101267i
$341$	−2.30591	−	3.99395i	−0.124872	−	0.216285i
$342$		0			0
$343$	17.8930	−	4.77914i	0.966132	−	0.258049i
$344$			4.17768i			0.225245i
$345$		0			0
$346$	−12.3517	−	7.13126i	−0.664032	−	0.383379i
$347$	−2.41532	+	4.18346i	−0.129661	+	0.224580i	−0.923545	−	0.383489i	$-0.874722\pi$
$347$	−2.41532	+	4.18346i	−0.129661	+	0.224580i	0.793884	+	0.608069i	$0.208056\pi$
$348$		0			0
$349$			16.0461i			0.858927i	0.903084	+	0.429463i	$0.141297\pi$
$349$			16.0461i			0.858927i	−0.903084	+	0.429463i	$0.858703\pi$
$350$	21.4100	−	13.4956i	1.14441	−	0.721372i
$351$		0			0
$352$	20.7714	−	11.9924i	1.10712	−	0.639195i
$353$	−5.09305	−	2.94047i	−0.271075	−	0.156505i	0.358301	−	0.933606i	$-0.383356\pi$
$353$	−5.09305	−	2.94047i	−0.271075	−	0.156505i	−0.629376	+	0.777101i	$0.716690\pi$
$354$		0			0
$355$	−5.33669	−	22.0255i	−0.283242	−	1.16899i
$356$	18.7153			0.991909
$357$		0			0
$358$			25.4582i			1.34551i
$359$	−7.00295	+	4.04315i	−0.369601	+	0.213389i	−0.673284	−	0.739384i	$-0.735117\pi$
$359$	−7.00295	+	4.04315i	−0.369601	+	0.213389i	0.303683	+	0.952773i	$0.401784\pi$
$360$		0			0
$361$	21.4802	−	37.2048i	1.13054	−	1.95815i
$362$	16.4990	−	9.52569i	0.867167	−	0.500659i
$363$		0			0
$364$	−12.2429	−	17.4945i	−0.641700	−	0.916961i
$365$	8.71711	−	29.6566i	0.456275	−	1.55230i
$366$		0			0
$367$	9.28484	−	16.0818i	0.484665	−	0.839464i	−0.515180	−	0.857082i	$-0.672275\pi$
$367$	9.28484	−	16.0818i	0.484665	−	0.839464i	0.999845	+	0.0176181i	$0.00560829\pi$
$368$	−11.1098	+	19.2428i	−0.579139	+	1.00310i
$369$		0			0
$370$	−12.9916	−	3.81870i	−0.675404	−	0.198525i
$371$	−2.30801	−	3.29805i	−0.119826	−	0.171226i
$372$		0			0
$373$	−2.28930	+	1.32173i	−0.118536	+	0.0684365i	−0.558095	−	0.829777i	$-0.688468\pi$
$373$	−2.28930	+	1.32173i	−0.118536	+	0.0684365i	0.439560	+	0.898213i	$0.355134\pi$
$374$	−2.25104	+	3.89892i	−0.116399	+	0.201608i
$375$		0			0
$376$	2.74266	−	1.58348i	0.141442	−	0.0816617i
$377$			37.7229i			1.94283i
$378$		0			0
$379$	−23.8582			−1.22551			−0.612756	−	0.790272i	$-0.709939\pi$
$379$	−23.8582			−1.22551			−0.612756	+	0.790272i	$0.709939\pi$
$380$	6.88083	+	28.3984i	0.352979	+	1.45681i
$381$		0			0
$382$	−40.7767	−	23.5425i	−2.08632	−	1.20454i
$383$	−9.62590	+	5.55752i	−0.491861	+	0.283976i	−0.725346	−	0.688384i	$-0.758320\pi$
$383$	−9.62590	+	5.55752i	−0.491861	+	0.283976i	0.233485	+	0.972360i	$0.424987\pi$
$384$		0			0
$385$	12.6256	−	14.3234i	0.643460	−	0.729987i
$386$			23.9416i			1.21860i
$387$		0			0
$388$	1.83765	−	3.18291i	0.0932928	−	0.161588i
$389$	10.8957	+	6.29064i	0.552434	+	0.318948i	0.750103	−	0.661321i	$-0.230004\pi$
$389$	10.8957	+	6.29064i	0.552434	+	0.318948i	−0.197669	+	0.980269i	$0.563337\pi$
$390$		0			0
$391$		−	3.54961i		−	0.179512i
$392$	2.92388	+	3.48831i	0.147678	+	0.176186i
$393$		0			0
$394$	15.0152	+	26.0070i	0.756453	+	1.31021i
$395$	6.14013	+	6.44325i	0.308944	+	0.324195i
$396$		0			0
$397$	14.3154	+	24.7951i	0.718471	+	1.24443i	0.961605	+	0.274436i	$0.0884912\pi$
$397$	14.3154	+	24.7951i	0.718471	+	1.24443i	−0.243134	+	0.969993i	$0.578175\pi$
$398$		−	37.8722i		−	1.89836i
$399$		0			0
$400$	19.1914	+	12.3490i	0.959569	+	0.617449i
$401$	−10.2994	+	5.94639i	−0.514330	+	0.296948i	−0.734612	−	0.678488i	$-0.762636\pi$
$401$	−10.2994	+	5.94639i	−0.514330	+	0.296948i	0.220282	+	0.975436i	$0.429302\pi$
$402$		0			0
$403$	−6.01612	−	3.47341i	−0.299684	−	0.173023i
$404$	9.71345	+	16.8242i	0.483262	+	0.837035i
$405$		0			0
$406$	3.41280	+	39.1281i	0.169374	+	1.94190i
$407$	−10.2160			−0.506386
$408$		0			0
$409$	−12.4855	−	7.20852i	−0.617369	−	0.356438i	0.158475	−	0.987363i	$-0.449342\pi$
$409$	−12.4855	−	7.20852i	−0.617369	−	0.356438i	−0.775844	+	0.630925i	$0.782676\pi$
$410$	4.13952	+	4.34387i	0.204436	+	0.214529i
$411$		0			0
$412$	0.971605			0.0478675
$413$	−9.55934	−	13.6599i	−0.470384	−	0.672159i
$414$		0			0
$415$	2.20736	+	9.11018i	0.108355	+	0.447201i
$416$	18.0642	−	31.2881i	0.885669	−	1.53402i
$417$		0			0
$418$	24.3012	+	42.0909i	1.18861	+	2.05874i
$419$	34.9400			1.70693			0.853466	−	0.521149i	$-0.174496\pi$
$419$	34.9400			1.70693			0.853466	+	0.521149i	$0.174496\pi$
$420$		0			0
$421$	23.8515			1.16245			0.581226	−	0.813742i	$-0.302573\pi$
$421$	23.8515			1.16245			0.581226	+	0.813742i	$0.302573\pi$
$422$	−11.0808	−	19.1925i	−0.539405	−	0.934277i
$423$		0			0
$424$	0.494655	−	0.856767i	0.0240225	−	0.0416083i
$425$	−3.64148	−	0.175540i	−0.176638	−	0.00851496i
$426$		0			0
$427$	−0.545360	−	6.25262i	−0.0263918	−	0.302586i
$428$	2.80917			0.135786
$429$		0			0
$430$	19.8974	−	18.9613i	0.959536	−	0.914395i
$431$	7.06551	+	4.07928i	0.340334	+	0.196492i	0.660420	−	0.750897i	$-0.270378\pi$
$431$	7.06551	+	4.07928i	0.340334	+	0.196492i	−0.320086	+	0.947389i	$0.603712\pi$
$432$		0			0
$433$	−25.2667			−1.21424			−0.607121	−	0.794610i	$-0.707676\pi$
$433$	−25.2667			−1.21424			−0.607121	+	0.794610i	$0.707676\pi$
$434$	−6.55447	−	3.05852i	−0.314625	−	0.146814i
$435$		0			0
$436$	11.1251	+	19.2693i	0.532798	+	0.922832i
$437$	−33.1861	−	19.1600i	−1.58751	−	0.916547i
$438$		0			0
$439$	−0.688243	+	0.397357i	−0.0328480	+	0.0189648i	−0.516334	−	0.856387i	$-0.672704\pi$
$439$	−0.688243	+	0.397357i	−0.0328480	+	0.0189648i	0.483486	+	0.875352i	$0.339370\pi$
$440$	4.50208	+	1.32332i	0.214628	+	0.0630868i
$441$		0			0
$442$			6.78152i			0.322564i
$443$	11.3244	+	19.6145i	0.538040	+	0.931913i	0.999010	+	0.0444966i	$0.0141684\pi$
$443$	11.3244	+	19.6145i	0.538040	+	0.931913i	−0.460970	+	0.887416i	$0.652498\pi$
$444$		0			0
$445$	17.3905	+	18.2490i	0.824387	+	0.865084i
$446$	−23.0841	−	39.9828i	−1.09306	−	1.89324i
$447$		0			0
$448$	5.69371	−	12.2017i	0.269002	−	0.576478i
$449$		−	2.15664i		−	0.101778i	−0.998704	−	0.0508891i	$-0.983794\pi$
$449$		−	2.15664i		−	0.101778i	0.998704	−	0.0508891i	$-0.0162055\pi$
$450$		0			0
$451$	3.92041	+	2.26345i	0.184605	+	0.106582i
$452$	−11.7976	+	20.4340i	−0.554913	+	0.961137i
$453$		0			0
$454$			19.4927i			0.914836i
$455$	5.68239	−	28.1939i	0.266395	−	1.32175i
$456$		0			0
$457$	−4.74004	+	2.73666i	−0.221730	+	0.128016i	−0.606751	−	0.794892i	$-0.707527\pi$
$457$	−4.74004	+	2.73666i	−0.221730	+	0.128016i	0.385021	+	0.922908i	$0.374194\pi$
$458$	−43.4998	−	25.1146i	−2.03261	−	1.17353i
$459$		0			0
$460$	17.5633	−	4.25552i	0.818893	−	0.198415i
$461$	10.1084			0.470797			0.235399	−	0.971899i	$-0.424360\pi$
$461$	10.1084			0.470797			0.235399	+	0.971899i	$0.424360\pi$
$462$		0			0
$463$			12.0455i			0.559800i	0.960029	+	0.279900i	$0.0903014\pi$
$463$			12.0455i			0.559800i	−0.960029	+	0.279900i	$0.909699\pi$
$464$	−30.6716	+	17.7083i	−1.42389	+	0.822086i
$465$		0			0
$466$	−17.5946	+	30.4747i	−0.815052	+	1.41171i
$467$	17.2622	−	9.96636i	0.798801	−	0.461188i	−0.0442505	−	0.999020i	$-0.514090\pi$
$467$	17.2622	−	9.96636i	0.798801	−	0.461188i	0.843052	+	0.537832i	$0.180757\pi$
$468$		0			0
$469$	−24.1173	+	16.8776i	−1.11363	+	0.779335i
$470$	−19.9899	−	5.87574i	−0.922066	−	0.271028i
$471$		0			0
$472$	2.04876	−	3.54856i	0.0943020	−	0.163336i
$473$	10.3679	−	17.9577i	0.476715	−	0.825694i
$474$		0			0
$475$	−21.2971	+	33.0975i	−0.977176	+	1.51862i
$476$	0.278277	+	3.19048i	0.0127548	+	0.146235i
$477$		0			0
$478$	1.59274	−	0.919569i	0.0728503	−	0.0420601i
$479$	−9.69290	+	16.7886i	−0.442880	+	0.767091i	−0.997902	−	0.0647451i	$-0.979377\pi$
$479$	−9.69290	+	16.7886i	−0.442880	+	0.767091i	0.555022	+	0.831836i	$0.312710\pi$
$480$		0			0
$481$	−13.3267	+	7.69419i	−0.607646	+	0.350825i
$482$			12.4556i			0.567337i
$483$		0			0
$484$	0.969293			0.0440588
$485$	4.81117	−	1.16573i	0.218464	−	0.0529330i
$486$		0			0
$487$	1.60056	+	0.924082i	0.0725282	+	0.0418742i	0.535826	−	0.844329i	$-0.320000\pi$
$487$	1.60056	+	0.924082i	0.0725282	+	0.0418742i	−0.463297	+	0.886203i	$0.653334\pi$
$488$	1.33585	−	0.771256i	0.0604713	−	0.0349131i
$489$		0			0
$490$	3.34337	−	29.7582i	0.151038	−	1.34434i
$491$			25.4836i			1.15006i	0.818133	+	0.575030i	$0.195009\pi$
$491$			25.4836i			1.15006i	−0.818133	+	0.575030i	$0.804991\pi$
$492$		0			0
$493$	2.82892	−	4.89983i	0.127408	−	0.220677i
$494$	63.4019	+	36.6051i	2.85259	+	1.64694i
$495$		0			0
$496$		−	6.52209i		−	0.292851i
$497$	−24.2996	−	11.3390i	−1.08999	−	0.508621i
$498$		0			0
$499$	13.1142	+	22.7144i	0.587072	+	1.01684i	0.994614	+	0.103652i	$0.0330527\pi$
$499$	13.1142	+	22.7144i	0.587072	+	1.01684i	−0.407542	+	0.913187i	$0.633614\pi$
$500$	−3.49710	−	18.2283i	−0.156395	−	0.815195i
$501$		0			0
$502$	1.93711	+	3.35518i	0.0864576	+	0.149749i
$503$		−	4.25713i		−	0.189816i	−0.995486	−	0.0949081i	$-0.969744\pi$
$503$		−	4.25713i		−	0.189816i	0.995486	−	0.0949081i	$-0.0302557\pi$
$504$		0			0
$505$	−7.37914	+	25.1046i	−0.328367	+	1.11714i
$506$	26.0316	−	15.0293i	1.15724	−	0.668135i
$507$		0			0
$508$	−3.00415	−	1.73445i	−0.133288	−	0.0769537i
$509$	9.55960	+	16.5577i	0.423722	+	0.733907i	0.996300	−	0.0859425i	$-0.0273901\pi$
$509$	9.55960	+	16.5577i	0.423722	+	0.733907i	−0.572578	+	0.819850i	$0.694057\pi$
$510$		0			0
$511$	−20.9704	−	29.9657i	−0.927674	−	1.32561i
$512$	27.9839			1.23672
$513$		0			0
$514$	30.1381	+	17.4002i	1.32933	+	0.767492i
$515$	0.902825	+	0.947395i	0.0397832	+	0.0417472i
$516$		0			0
$517$	−15.7190			−0.691322
$518$	−13.1271	+	9.18648i	−0.576771	+	0.403631i
$519$		0			0
$520$	6.86963	−	1.66449i	0.301253	−	0.0729926i
$521$	−11.4068	+	19.7571i	−0.499739	+	0.865573i	−1.00000		0.000301478i	$-0.999904\pi$
$521$	−11.4068	+	19.7571i	−0.499739	+	0.865573i	0.500261	+	0.865875i	$0.333237\pi$
$522$		0			0
$523$	−1.56468	−	2.71011i	−0.0684188	−	0.118505i	0.829787	−	0.558081i	$-0.188462\pi$
$523$	−1.56468	−	2.71011i	−0.0684188	−	0.118505i	−0.898205	+	0.439576i	$0.855129\pi$
$524$	−18.6014			−0.812604
$525$		0			0
$526$	37.4224			1.63169
$527$	0.520956	+	0.902322i	0.0226932	+	0.0393058i
$528$		0			0
$529$	−0.349692	+	0.605685i	−0.0152040	+	0.0263341i
$530$	−6.32568	+	1.53269i	−0.274770	+	0.0665758i
$531$		0			0
$532$	31.3306	+	14.6198i	1.35835	+	0.633849i
$533$	6.81890			0.295359
$534$		0			0
$535$	2.61031	+	2.73917i	0.112854	+	0.118425i
$536$	−6.26520	−	3.61722i	−0.270616	−	0.156240i
$537$		0			0
$538$	−8.83112			−0.380737
$539$	−3.91121	−	22.2507i	−0.168468	−	0.958405i
$540$		0			0
$541$	11.2308	+	19.4524i	0.482852	+	0.836323i	0.999806	−	0.0196894i	$-0.00626775\pi$
$541$	11.2308	+	19.4524i	0.482852	+	0.836323i	−0.516955	+	0.856013i	$0.672934\pi$
$542$	17.8622	+	10.3127i	0.767245	+	0.442969i
$543$		0			0
$544$	−4.69271	+	2.70934i	−0.201198	+	0.116162i
$545$	−8.45157	+	28.7532i	−0.362026	+	1.23165i
$546$		0			0
$547$			10.4567i			0.447097i	0.974693	+	0.223549i	$0.0717642\pi$
$547$			10.4567i			0.447097i	−0.974693	+	0.223549i	$0.928236\pi$
$548$	5.84355	+	10.1213i	0.249624	+	0.432362i
$549$		0			0
$550$	−14.1310	−	27.4486i	−0.602547	−	1.17041i
$551$	−30.5397	−	52.8963i	−1.30104	−	2.25346i
$552$		0			0
$553$	10.4912	−	0.915056i	0.446133	−	0.0389122i
$554$		−	39.2324i		−	1.66683i
$555$		0			0
$556$	−9.28620	−	5.36139i	−0.393823	−	0.227374i
$557$	15.6239	−	27.0614i	0.662006	−	1.14663i	−0.318082	−	0.948063i	$-0.603039\pi$
$557$	15.6239	−	27.0614i	0.662006	−	1.14663i	0.980088	−	0.198564i	$-0.0636278\pi$
$558$		0			0
$559$		−	31.2344i		−	1.32107i
$560$	25.5913	−	8.61483i	1.08143	−	0.364043i
$561$		0			0
$562$	−1.18408	+	0.683630i	−0.0499475	+	0.0288372i
$563$	25.8689	+	14.9354i	1.09024	+	0.629452i	0.933641	−	0.358210i	$-0.116613\pi$
$563$	25.8689	+	14.9354i	1.09024	+	0.629452i	0.156601	+	0.987662i	$0.449946\pi$
$564$		0			0
$565$	−30.8873	+	7.48389i	−1.29944	+	0.314850i
$566$	53.6100			2.25340
$567$		0			0
$568$		−	6.59019i		−	0.276518i
$569$	−25.0218	+	14.4464i	−1.04897	+	0.605623i	−0.922361	−	0.386330i	$-0.873743\pi$
$569$	−25.0218	+	14.4464i	−1.04897	+	0.605623i	−0.126608	+	0.991953i	$0.540409\pi$
$570$		0			0
$571$	3.68844	−	6.38856i	0.154356	−	0.267353i	−0.778468	−	0.627684i	$-0.784003\pi$
$571$	3.68844	−	6.38856i	0.154356	−	0.267353i	0.932824	+	0.360331i	$0.117336\pi$
$572$	−22.5575	+	13.0236i	−0.943177	+	0.544543i
$573$		0			0
$574$	7.07292	−	0.616907i	0.295218	−	0.0257492i
$575$	20.4695	+	13.1714i	0.853636	+	0.549285i
$576$		0			0
$577$	9.03785	−	15.6540i	0.376251	−	0.651686i	−0.614263	−	0.789102i	$-0.710546\pi$
$577$	9.03785	−	15.6540i	0.376251	−	0.651686i	0.990513	+	0.137416i	$0.0438798\pi$
$578$	−15.7532	+	27.2853i	−0.655246	+	1.13492i
$579$		0			0
$580$	27.6356	+	8.12308i	1.14751	+	0.337292i
$581$	10.0508	+	4.69002i	0.416978	+	0.194575i
$582$		0			0
$583$	−4.25252	+	2.45519i	−0.176121	+	0.101684i
$584$	4.49438	−	7.78450i	0.185979	−	0.322125i
$585$		0			0
$586$	−16.2232	+	9.36648i	−0.670175	+	0.386926i
$587$		−	35.0876i		−	1.44822i	−0.689684	−	0.724111i	$-0.742250\pi$
$587$		−	35.0876i		−	1.44822i	0.689684	−	0.724111i	$-0.257750\pi$
$588$		0			0
$589$	11.2480			0.463466
$590$	−26.1998	+	6.34811i	−1.07863	+	0.261347i
$591$		0			0
$592$	−12.5119	−	7.22377i	−0.514238	−	0.296895i
$593$	−6.11233	+	3.52896i	−0.251003	+	0.144917i	−0.620224	−	0.784425i	$-0.712958\pi$
$593$	−6.11233	+	3.52896i	−0.251003	+	0.144917i	0.369220	+	0.929342i	$0.379625\pi$
$594$		0			0
$595$	−2.85240	+	3.23597i	−0.116937	+	0.132662i
$596$			39.0984i			1.60153i
$597$		0			0
$598$	22.6388	−	39.2115i	0.925769	−	1.60348i
$599$	−4.23198	−	2.44333i	−0.172914	−	0.0998318i	0.411045	−	0.911615i	$-0.365164\pi$
$599$	−4.23198	−	2.44333i	−0.172914	−	0.0998318i	−0.583959	+	0.811783i	$0.698497\pi$
$600$		0			0
$601$		−	36.1905i		−	1.47624i	−0.674669	−	0.738121i	$-0.735714\pi$
$601$		−	36.1905i		−	1.47624i	0.674669	−	0.738121i	$-0.264286\pi$
$602$	−2.82578	−	32.3979i	−0.115170	−	1.32044i
$603$		0			0
$604$	−15.0315	−	26.0352i	−0.611621	−	1.05936i
$605$	0.900677	+	0.945141i	0.0366177	+	0.0384254i
$606$		0			0
$607$	−8.46272	−	14.6579i	−0.343491	−	0.594944i	0.641587	−	0.767050i	$-0.278276\pi$
$607$	−8.46272	−	14.6579i	−0.343491	−	0.594944i	−0.985078	+	0.172106i	$0.944943\pi$
$608$			58.4976i			2.37239i
$609$		0			0
$610$	−9.73638	−	2.86187i	−0.394214	−	0.115874i
$611$	−20.5055	+	11.8389i	−0.829563	+	0.478949i
$612$		0			0
$613$	−16.1128	−	9.30275i	−0.650792	−	0.375735i	0.137968	−	0.990437i	$-0.455943\pi$
$613$	−16.1128	−	9.30275i	−0.650792	−	0.375735i	−0.788759	+	0.614702i	$0.789276\pi$
$614$	−24.3714	−	42.2125i	−0.983549	−	1.70356i
$615$		0			0
$616$	4.54901	−	3.18345i	0.183285	−	0.128265i
$617$	44.6022			1.79562			0.897809	−	0.440384i	$-0.145158\pi$
$617$	44.6022			1.79562			0.897809	+	0.440384i	$0.145158\pi$
$618$		0			0
$619$	−9.80175	−	5.65904i	−0.393966	−	0.227456i	0.289911	−	0.957053i	$-0.406374\pi$
$619$	−9.80175	−	5.65904i	−0.393966	−	0.227456i	−0.683877	+	0.729597i	$0.739707\pi$
$620$	−3.84008	+	3.65943i	−0.154221	+	0.146966i
$621$		0			0
$622$	−19.3389			−0.775420
$623$	29.7139	−	2.59168i	1.19046	−	0.103833i
$624$		0			0
$625$	14.5246	−	20.3479i	0.580983	−	0.813916i
$626$	−22.4556	+	38.8942i	−0.897506	+	1.55453i
$627$		0			0
$628$	2.06233	+	3.57205i	0.0822957	+	0.142540i
$629$	2.30801			0.0920265
$630$		0			0
$631$	−6.29394			−0.250558			−0.125279	−	0.992122i	$-0.539983\pi$
$631$	−6.29394			−0.250558			−0.125279	+	0.992122i	$0.539983\pi$
$632$	1.29409	+	2.24142i	0.0514759	+	0.0891589i
$633$		0			0
$634$	30.0662	−	52.0763i	1.19408	−	2.06821i
$635$	−1.10026	−	4.54096i	−0.0436624	−	0.180203i
$636$		0			0
$637$	−21.8604	−	26.0803i	−0.866139	−	1.03334i
$638$	47.9114			1.89683
$639$		0			0
$640$	7.90855	+	8.29897i	0.312613	+	0.328046i
$641$	−0.511044	−	0.295051i	−0.0201850	−	0.0116538i	0.489874	−	0.871794i	$-0.337043\pi$
$641$	−0.511044	−	0.295051i	−0.0201850	−	0.0116538i	−0.510059	+	0.860140i	$0.670376\pi$
$642$		0			0
$643$	28.7107			1.13224			0.566119	−	0.824323i	$-0.308444\pi$
$643$	28.7107			1.13224			0.566119	+	0.824323i	$0.308444\pi$
$644$	9.04177	−	19.3767i	0.356296	−	0.763549i
$645$		0			0
$646$	−5.49018	−	9.50928i	−0.216008	−	0.374138i
$647$	−10.3303	−	5.96420i	−0.406126	−	0.234477i	0.282998	−	0.959121i	$-0.408671\pi$
$647$	−10.3303	−	5.96420i	−0.406126	−	0.234477i	−0.689124	+	0.724644i	$0.742004\pi$
$648$		0			0
$649$	−17.6131	+	10.1689i	−0.691375	+	0.399166i
$650$	−39.1069	−	25.1639i	−1.53390	−	0.987009i
$651$		0			0
$652$			6.53708i			0.256012i
$653$	−7.99647	−	13.8503i	−0.312926	−	0.542004i	0.666068	−	0.745891i	$-0.267976\pi$
$653$	−7.99647	−	13.8503i	−0.312926	−	0.542004i	−0.978994	+	0.203887i	$0.934643\pi$
$654$		0			0
$655$	−17.2846	−	18.1379i	−0.675364	−	0.708705i
$656$	3.20100	+	5.54430i	0.124978	+	0.216468i
$657$		0			0
$658$	−20.1983	+	14.1350i	−0.787412	+	0.551040i
$659$		−	27.6958i		−	1.07887i	−0.842026	−	0.539437i	$-0.818637\pi$
$659$		−	27.6958i		−	1.07887i	0.842026	−	0.539437i	$-0.181363\pi$
$660$		0			0
$661$	−36.1490	−	20.8706i	−1.40603	−	0.811773i	−0.411030	−	0.911622i	$-0.634831\pi$
$661$	−36.1490	−	20.8706i	−1.40603	−	0.811773i	−0.995003	+	0.0998487i	$0.968164\pi$
$662$	1.12725	−	1.95246i	0.0438119	−	0.0758844i
$663$		0			0
$664$			2.72583i			0.105783i
$665$	14.8572	+	44.1348i	0.576136	+	1.71147i
$666$		0			0
$667$	−32.7143	+	18.8876i	−1.26670	+	0.731330i
$668$	7.64620	+	4.41453i	0.295840	+	0.170803i
$669$		0			0
$670$	11.2080	+	46.2573i	0.433001	+	1.78707i
$671$	−7.65618			−0.295564
$672$		0			0
$673$			7.91950i			0.305274i	0.988282	+	0.152637i	$0.0487766\pi$
$673$			7.91950i			0.305274i	−0.988282	+	0.152637i	$0.951223\pi$
$674$	6.50916	−	3.75807i	0.250724	−	0.144755i
$675$		0			0
$676$	−8.82673	+	15.2883i	−0.339489	+	0.588013i
$677$	−9.23807	+	5.33360i	−0.355048	+	0.204987i	−0.666906	−	0.745142i	$-0.732382\pi$
$677$	−9.23807	+	5.33360i	−0.355048	+	0.204987i	0.311858	+	0.950129i	$0.399049\pi$
$678$		0			0
$679$	2.47684	−	5.30792i	0.0950524	−	0.203699i
$680$	−1.01712	−	0.298967i	−0.0390048	−	0.0114649i
$681$		0			0
$682$	−4.41154	+	7.64100i	−0.168926	+	0.292589i
$683$	1.10463	−	1.91327i	0.0422674	−	0.0732093i	−0.844118	−	0.536158i	$-0.819875\pi$
$683$	1.10463	−	1.91327i	0.0422674	−	0.0732093i	0.886385	+	0.462948i	$0.153209\pi$
$684$		0			0
$685$	−4.43924	+	15.1028i	−0.169615	+	0.577048i
$686$	−25.0342	−	25.0741i	−0.955810	−	0.957334i
$687$		0			0
$688$	25.3960	−	14.6624i	0.968212	−	0.558997i
$689$	−3.69828	+	6.40560i	−0.140893	+	0.244034i
$690$		0			0
$691$	−8.02498	+	4.63322i	−0.305284	+	0.176256i	−0.644814	−	0.764339i	$-0.723065\pi$
$691$	−8.02498	+	4.63322i	−0.305284	+	0.176256i	0.339530	+	0.940595i	$0.389732\pi$
$692$			12.3762i			0.470474i
$693$		0			0
$694$	9.24172			0.350811
$695$	−3.40104	−	14.0367i	−0.129009	−	0.532441i
$696$		0			0
$697$	−0.885707	−	0.511363i	−0.0335486	−	0.0193693i
$698$	26.5857	−	15.3492i	1.00628	−	0.580977i
$699$		0			0
$700$	−19.4311	−	10.2340i	−0.734425	−	0.386810i
$701$			6.99882i			0.264342i	0.991227	+	0.132171i	$0.0421948\pi$
$701$			6.99882i			0.264342i	−0.991227	+	0.132171i	$0.957805\pi$
$702$		0			0
$703$	12.4581	−	21.5781i	0.469867	−	0.813834i
$704$	−14.2244	−	8.21247i	−0.536103	−	0.309519i
$705$		0			0
$706$			11.2511i			0.423441i
$707$	17.7517	+	25.3663i	0.667620	+	0.953999i
$708$		0			0
$709$	15.5805	+	26.9863i	0.585139	+	1.01349i	0.994858	+	0.101279i	$0.0322935\pi$
$709$	15.5805	+	26.9863i	0.585139	+	1.01349i	−0.409719	+	0.912212i	$0.634373\pi$
$710$	−31.3876	+	29.9110i	−1.17795	+	1.12254i
$711$		0			0
$712$	3.66519	+	6.34829i	0.137359	+	0.237912i
$713$		−	6.95644i		−	0.260521i
$714$		0			0
$715$	−33.6597	−	9.89379i	−1.25880	−	0.370007i
$716$	19.1316	−	11.0456i	0.714980	−	0.412794i
$717$		0			0
$718$	13.3976	+	7.73514i	0.499996	+	0.288673i
$719$	4.53080	+	7.84758i	0.168970	+	0.292665i	0.938058	−	0.346478i	$-0.112622\pi$
$719$	4.53080	+	7.84758i	0.168970	+	0.292665i	−0.769088	+	0.639143i	$0.779289\pi$
$720$		0			0
$721$	1.54260	−	0.134547i	0.0574493	−	0.00501079i
$722$	−82.1894			−3.05877
$723$		0			0
$724$	−14.3169	−	8.26587i	−0.532084	−	0.307199i
$725$	17.7586	+	34.4950i	0.659538	+	1.28111i
$726$		0			0
$727$	17.0567			0.632599			0.316300	−	0.948659i	$-0.397559\pi$
$727$	17.0567			0.632599			0.316300	+	0.948659i	$0.397559\pi$
$728$	3.53656	−	7.57892i	0.131074	−	0.280893i
$729$		0			0
$730$	−57.4745	+	13.9259i	−2.12723	+	0.515419i
$731$	−2.34233	+	4.05703i	−0.0866342	+	0.150055i
$732$		0			0
$733$	−7.98301	−	13.8270i	−0.294859	−	0.510711i	0.680093	−	0.733126i	$-0.261939\pi$
$733$	−7.98301	−	13.8270i	−0.294859	−	0.510711i	−0.974952	+	0.222415i	$0.928606\pi$
$734$	−35.5265			−1.31131
$735$		0			0
$736$	36.1784			1.33355
$737$	17.9539	+	31.0970i	0.661340	+	1.14547i
$738$		0			0
$739$	6.92575	−	11.9958i	0.254768	−	0.441271i	−0.710064	−	0.704137i	$-0.751334\pi$
$739$	6.92575	−	11.9958i	0.254768	−	0.441271i	0.964832	+	0.262866i	$0.0846676\pi$
$740$	2.76701	+	11.4199i	0.101717	+	0.419805i
$741$		0			0
$742$	−3.25653	+	6.97881i	−0.119551	+	0.256200i
$743$	−27.6801			−1.01548			−0.507741	−	0.861510i	$-0.669519\pi$
$743$	−27.6801			−1.01548			−0.507741	+	0.861510i	$0.669519\pi$
$744$		0			0
$745$	−38.1242	+	36.3307i	−1.39676	+	1.33105i
$746$	4.37976	+	2.52866i	0.160355	+	0.0925807i
$747$		0			0
$748$	3.90666			0.142842
$749$	4.46006	−	0.389011i	0.162967	−	0.0142142i
$750$		0			0
$751$	−16.6666	−	28.8674i	−0.608173	−	1.05339i	−0.991541	−	0.129791i	$-0.958569\pi$
$751$	−16.6666	−	28.8674i	−0.608173	−	1.05339i	0.383368	−	0.923596i	$-0.374764\pi$
$752$	−19.2518	−	11.1150i	−0.702041	−	0.405324i
$753$		0			0
$754$	62.5005	−	36.0847i	2.27613	−	1.31413i
$755$	11.4191	−	38.8491i	0.415585	−	1.41386i
$756$		0			0
$757$			10.1442i			0.368697i	0.982861	+	0.184348i	$0.0590175\pi$
$757$			10.1442i			0.368697i	−0.982861	+	0.184348i	$0.940983\pi$
$758$	22.8221	+	39.5290i	0.828935	+	1.43576i
$759$		0			0
$760$	−8.28530	+	7.89552i	−0.300539	+	0.286401i
$761$	−7.35057	−	12.7316i	−0.266458	−	0.461519i	0.701487	−	0.712683i	$-0.252520\pi$
$761$	−7.35057	−	12.7316i	−0.266458	−	0.461519i	−0.967945	+	0.251164i	$0.919187\pi$
$762$		0			0
$763$	20.3316	+	29.0529i	0.736052	+	1.05179i
$764$			40.8577i			1.47818i
$765$		0			0
$766$	18.4157	+	10.6323i	0.665388	+	0.384162i
$767$	−15.3176	+	26.5308i	−0.553085	+	0.957971i
$768$		0			0
$769$		−	22.4992i		−	0.811340i	−0.914020	−	0.405670i	$-0.867038\pi$
$769$		−	22.4992i		−	0.811340i	0.914020	−	0.405670i	$-0.132962\pi$
$770$	−35.8087	−	7.21715i	−1.29046	−	0.260088i
$771$		0			0
$772$	17.9919	−	10.3876i	0.647542	−	0.373859i
$773$	18.4057	+	10.6266i	0.662008	+	0.382211i	0.793042	−	0.609167i	$-0.208496\pi$
$773$	18.4057	+	10.6266i	0.662008	+	0.382211i	−0.131034	+	0.991378i	$0.541830\pi$
$774$		0			0
$775$	−7.13649	−	0.344020i	−0.256350	−	0.0123576i
$776$	1.43954			0.0516764
$777$		0			0
$778$		−	24.0698i		−	0.862945i
$779$	−9.56170	+	5.52045i	−0.342583	+	0.197791i
$780$		0			0
$781$	−16.3550	+	28.3278i	−0.585229	+	1.01365i
$782$	−5.88111	+	3.39546i	−0.210308	+	0.121421i
$783$		0			0
$784$	10.9434	−	30.0171i	0.390835	−	1.07204i
$785$	−1.56671	+	5.33012i	−0.0559183	+	0.190240i
$786$		0			0
$787$	−7.85952	+	13.6131i	−0.280162	+	0.485254i	−0.971424	−	0.237349i	$-0.923721\pi$
$787$	−7.85952	+	13.6131i	−0.280162	+	0.485254i	0.691263	+	0.722603i	$0.257055\pi$
$788$	13.0293	−	22.5675i	0.464151	−	0.803933i
$789$		0			0
$790$	4.80190	−	16.3366i	0.170844	−	0.581230i
$791$	−15.9011	+	34.0765i	−0.565379	+	1.21162i
$792$		0			0
$793$	−9.98750	+	5.76628i	−0.354666	+	0.204767i
$794$	27.3875	−	47.4366i	0.971946	−	1.68346i
$795$		0			0
$796$	−28.4605	+	16.4317i	−1.00876	+	0.582406i
$797$		−	39.5812i		−	1.40204i	−0.713143	−	0.701019i	$-0.752729\pi$
$797$		−	39.5812i		−	1.40204i	0.713143	−	0.701019i	$-0.247271\pi$
$798$		0			0
$799$	3.55128			0.125635
$800$	1.78915	−	37.1148i	0.0632559	−	1.31221i
$801$		0			0
$802$	19.7043	+	11.3763i	0.695784	+	0.401711i
$803$	−38.6380	+	22.3076i	−1.36350	+	0.787220i
$804$		0			0
$805$	27.2956	−	9.18855i	0.962043	−	0.323854i
$806$			13.2903i			0.468130i
$807$		0			0
$808$	−3.80455	+	6.58967i	−0.133843	+	0.231824i
$809$	−38.1053	−	22.0001i	−1.33971	−	0.773483i	−0.352947	−	0.935643i	$-0.614820\pi$
$809$	−38.1053	−	22.0001i	−1.33971	−	0.773483i	−0.986764	+	0.162160i	$0.948154\pi$
$810$		0			0
$811$		−	44.9306i		−	1.57773i	−0.614567	−	0.788864i	$-0.710669\pi$
$811$		−	44.9306i		−	1.57773i	0.614567	−	0.788864i	$-0.289331\pi$
$812$	27.9237	−	19.5413i	0.979929	−	0.685766i
$813$		0			0
$814$	9.77230	+	16.9261i	0.342519	+	0.593260i
$815$	−6.37419	+	6.07432i	−0.223278	+	0.212774i
$816$		0			0
$817$	25.2867	+	43.7979i	0.884671	+	1.53229i
$818$			27.5819i			0.964378i
$819$		0			0
$820$	1.46835	−	4.99549i	0.0512771	−	0.174450i
$821$	−13.1026	+	7.56481i	−0.457285	+	0.264014i	−0.710902	−	0.703291i	$-0.751713\pi$
$821$	−13.1026	+	7.56481i	−0.457285	+	0.264014i	0.253617	+	0.967305i	$0.418380\pi$
$822$		0			0
$823$	27.3487	+	15.7898i	0.953316	+	0.550397i	0.894109	−	0.447848i	$-0.147810\pi$
$823$	27.3487	+	15.7898i	0.953316	+	0.550397i	0.0592066	+	0.998246i	$0.481143\pi$
$824$	0.190278	+	0.329571i	0.00662865	+	0.0114812i
$825$		0			0
$826$	−13.4879	+	28.9049i	−0.469305	+	1.00573i
$827$	−48.6368			−1.69127			−0.845633	−	0.533765i	$-0.820777\pi$
$827$	−48.6368			−1.69127			−0.845633	+	0.533765i	$0.820777\pi$
$828$		0			0
$829$	40.4900	+	23.3769i	1.40628	+	0.811914i	0.995027	−	0.0996095i	$-0.0317594\pi$
$829$	40.4900	+	23.3769i	1.40628	+	0.811914i	0.411249	+	0.911523i	$0.365093\pi$
$830$	12.9825	−	12.3718i	0.450630	−	0.429431i
$831$		0			0
$832$	−24.7410			−0.857741
$833$	0.883629	+	5.02692i	0.0306159	+	0.174173i
$834$		0			0
$835$	2.80039	+	11.5577i	0.0969115	+	0.399971i
$836$	21.0873	−	36.5242i	0.729319	−	1.26322i
$837$		0			0
$838$	−33.4227	−	57.8898i	−1.15457	−	1.99977i
$839$	29.1067			1.00488			0.502438	−	0.864613i	$-0.332437\pi$
$839$	29.1067			1.00488			0.502438	+	0.864613i	$0.332437\pi$
$840$		0			0
$841$	−31.2110			−1.07624
$842$	−22.8157	−	39.5179i	−0.786281	−	1.36188i
$843$		0			0
$844$	−9.61532	+	16.6542i	−0.330973	+	0.573262i
$845$	−23.1093	+	5.59929i	−0.794983	+	0.192622i
$846$		0			0
$847$	1.53893	−	0.134227i	0.0528782	−	0.00461209i
$848$	−6.94434			−0.238469
$849$		0			0
$850$	3.19250	+	6.20124i	0.109502	+	0.212701i
$851$	−13.3452	−	7.70485i	−0.457467	−	0.264119i
$852$		0			0
$853$	−28.4915			−0.975531			−0.487766	−	0.872975i	$-0.662188\pi$
$853$	−28.4915			−0.975531			−0.487766	+	0.872975i	$0.662188\pi$
$854$	−9.83787	+	6.88466i	−0.336645	+	0.235588i
$855$		0			0
$856$	0.550145	+	0.952879i	0.0188036	+	0.0325687i
$857$	35.1219	+	20.2776i	1.19974	+	0.692670i	0.960497	−	0.278290i	$-0.0897675\pi$
$857$	35.1219	+	20.2776i	1.19974	+	0.692670i	0.239243	+	0.970960i	$0.423101\pi$
$858$		0			0
$859$	32.6686	−	18.8612i	1.11464	−	0.643537i	0.174612	−	0.984637i	$-0.444133\pi$
$859$	32.6686	−	18.8612i	1.11464	−	0.643537i	0.940027	+	0.341100i	$0.110800\pi$
$860$	−22.8821	−	6.72587i	−0.780274	−	0.229350i
$861$		0			0
$862$		−	15.6085i		−	0.531627i
$863$	12.8395	+	22.2387i	0.437062	+	0.757014i	0.997461	−	0.0712087i	$-0.0226856\pi$
$863$	12.8395	+	22.2387i	0.437062	+	0.757014i	−0.560399	+	0.828223i	$0.689352\pi$
$864$		0			0
$865$	−12.0679	+	11.5001i	−0.410319	+	0.391016i
$866$	24.1695	+	41.8627i	0.821311	+	1.42255i
$867$		0			0
$868$	0.545360	+	6.25262i	0.0185107	+	0.212228i
$869$		−	12.8463i		−	0.435779i
$870$		0			0
$871$	46.8417	+	27.0441i	1.58717	+	0.916353i
$872$	−4.35747	+	7.54736i	−0.147563	+	0.255586i
$873$		0			0
$874$			73.3117i			2.47981i
$875$	−8.07651	−	28.4565i	−0.273036	−	0.962004i
$876$		0			0
$877$	16.4938	−	9.52270i	0.556956	−	0.321559i	−0.194967	−	0.980810i	$-0.562460\pi$
$877$	16.4938	−	9.52270i	0.556956	−	0.321559i	0.751923	+	0.659251i	$0.229127\pi$
$878$	1.31671	+	0.760202i	0.0444367	+	0.0256556i
$879$		0			0
$880$	−7.75649	−	32.0124i	−0.261471	−	1.07914i
$881$	30.7115			1.03470			0.517349	−	0.855774i	$-0.326919\pi$
$881$	30.7115			1.03470			0.517349	+	0.855774i	$0.326919\pi$
$882$		0			0
$883$		−	36.8466i		−	1.23999i	−0.784607	−	0.619993i	$-0.787135\pi$
$883$		−	36.8466i		−	1.23999i	0.784607	−	0.619993i	$-0.212865\pi$
$884$	5.09624	−	2.94232i	0.171405	−	0.0989608i
$885$		0			0
$886$	21.6653	−	37.5254i	0.727859	−	1.26069i
$887$	29.3385	−	16.9386i	0.985090	−	0.568742i	0.0812870	−	0.996691i	$-0.474097\pi$
$887$	29.3385	−	16.9386i	0.985090	−	0.568742i	0.903803	+	0.427949i	$0.140764\pi$
$888$		0			0
$889$	−5.00982	−	2.33774i	−0.168024	−	0.0784051i
$890$	13.6002	−	46.2695i	0.455881	−	1.55096i
$891$		0			0
$892$	−20.0311	+	34.6949i	−0.670691	+	1.16167i
$893$	19.1690	−	33.2017i	0.641466	−	1.11105i
$894$		0			0
$895$	28.5476	+	8.39116i	0.954242	+	0.280486i
$896$	13.5128	−	1.17860i	0.451432	−	0.0393743i
$897$		0			0
$898$	−3.57319	+	2.06298i	−0.119239	+	0.0688427i
$899$	5.54404	−	9.60257i	0.184904	−	0.320264i
$900$		0			0
$901$	0.960739	−	0.554683i	0.0320068	−	0.0184792i
$902$		−	8.66061i		−	0.288367i
$903$		0			0
$904$	−9.24172			−0.307375
$905$	−5.24351	−	21.6409i	−0.174300	−	0.719368i
$906$		0			0
$907$	0.923888	+	0.533407i	0.0306772	+	0.0177115i	0.515260	−	0.857034i	$-0.327695\pi$
$907$	0.923888	+	0.533407i	0.0306772	+	0.0177115i	−0.484583	+	0.874745i	$0.661029\pi$
$908$	14.6485	−	8.45734i	0.486129	−	0.280667i
$909$		0			0
$910$	−52.1481	+	17.5547i	−1.72869	+	0.581933i
$911$		−	9.61157i		−	0.318445i	−0.987243	−	0.159223i	$-0.949101\pi$
$911$		−	9.61157i		−	0.318445i	0.987243	−	0.159223i	$-0.0508988\pi$
$912$		0			0
$913$	6.76477	−	11.7169i	0.223881	−	0.387774i
$914$	9.06839	+	5.23564i	0.299956	+	0.173179i
$915$		0			0
$916$			43.5862i			1.44013i
$917$	−29.5330	+	2.57590i	−0.975266	+	0.0850637i
$918$		0			0
$919$	3.41594	+	5.91658i	0.112681	+	0.195170i	0.916851	−	0.399231i	$-0.130723\pi$
$919$	3.41594	+	5.91658i	0.112681	+	0.195170i	−0.804169	+	0.594401i	$0.797389\pi$
$920$	4.88306	+	5.12412i	0.160990	+	0.168937i
$921$		0			0
$922$	−9.66946	−	16.7480i	−0.318447	−	0.551566i
$923$			49.2714i			1.62179i
$924$		0			0
$925$	−8.56424	+	13.3096i	−0.281590	+	0.437616i
$926$	19.9573	−	11.5224i	0.655838	−	0.378648i
$927$		0			0
$928$	49.9401	+	28.8330i	1.63937	+	0.946488i
$929$	26.9383	+	46.6585i	0.883818	+	1.53082i	0.847063	+	0.531493i	$0.178369\pi$
$929$	26.9383	+	46.6585i	0.883818	+	1.53082i	0.0367547	+	0.999324i	$0.488298\pi$
$930$		0			0
$931$	51.7674	+	18.8730i	1.69661	+	0.618536i
$932$	30.5352			1.00021
$933$		0			0
$934$	−33.0252	−	19.0671i	−1.08062	−	0.623894i
$935$	3.63011	+	3.80932i	0.118717	+	0.124578i
$936$		0			0
$937$	21.6036			0.705759			0.352880	−	0.935669i	$-0.385203\pi$
$937$	21.6036			0.705759			0.352880	+	0.935669i	$0.385203\pi$
$938$	51.0333	+	23.8137i	1.66630	+	0.777546i
$939$		0			0
$940$	4.25752	+	17.5715i	0.138865	+	0.573121i
$941$	29.1006	−	50.4038i	0.948654	−	1.64312i	0.200389	−	0.979716i	$-0.435779\pi$
$941$	29.1006	−	50.4038i	0.948654	−	1.64312i	0.748265	−	0.663400i	$-0.230887\pi$
$942$		0			0
$943$	3.41418	+	5.91353i	0.111181	+	0.192571i
$944$	−28.7621			−0.936127
$945$		0			0
$946$	−39.6704			−1.28980
$947$	10.2347	+	17.7271i	0.332584	+	0.576053i	0.983018	−	0.183510i	$-0.0587461\pi$
$947$	10.2347	+	17.7271i	0.332584	+	0.576053i	−0.650434	+	0.759563i	$0.725413\pi$
$948$		0			0
$949$	−33.6022	+	58.2007i	−1.09077	+	1.88927i
$950$	75.2092	+	3.62552i	2.44011	+	0.117627i
$951$		0			0
$952$	−1.02772	+	0.719212i	−0.0333087	+	0.0233098i
$953$	10.4745			0.339303			0.169651	−	0.985504i	$-0.445736\pi$
$953$	10.4745			0.339303			0.169651	+	0.985504i	$0.445736\pi$
$954$		0			0
$955$	−39.8397	+	37.9654i	−1.28918	+	1.22853i
$956$	−1.38209	−	0.797952i	−0.0447001	−	0.0258076i
$957$		0			0
$958$	37.0879			1.19825
$959$	10.6793	+	15.2602i	0.344852	+	0.492778i
$960$		0			0
$961$	−14.4790	−	25.0784i	−0.467066	−	0.808982i
$962$	25.4960	+	14.7201i	0.822023	+	0.474595i
$963$		0			0
$964$	9.36026	−	5.40415i	0.301474	−	0.174056i
$965$	26.8470	+	7.89129i	0.864236	+	0.254030i
$966$		0			0
$967$		−	43.1242i		−	1.38678i	−0.720562	−	0.693391i	$-0.756116\pi$
$967$		−	43.1242i		−	1.38678i	0.720562	−	0.693391i	$-0.243884\pi$
$968$	0.189825	+	0.328787i	0.00610122	+	0.0105676i
$969$		0			0
$970$	−6.53365	−	6.85619i	−0.209783	−	0.220139i
$971$	4.17572	+	7.23256i	0.134005	+	0.232104i	0.925217	−	0.379438i	$-0.123883\pi$
$971$	4.17572	+	7.23256i	0.134005	+	0.232104i	−0.791212	+	0.611542i	$0.790549\pi$
$972$		0			0
$973$	−15.4860	−	7.22623i	−0.496457	−	0.231662i
$974$		−	3.53581i		−	0.113295i
$975$		0			0
$976$	−9.37687	−	5.41374i	−0.300146	−	0.173290i
$977$	−13.4044	+	23.2171i	−0.428845	+	0.742781i	−0.996771	−	0.0802983i	$-0.974413\pi$
$977$	−13.4044	+	23.2171i	−0.428845	+	0.742781i	0.567926	+	0.823080i	$0.307746\pi$
$978$		0			0
$979$		−	36.3840i		−	1.16284i
$980$	−23.8136	+	10.3988i	−0.760698	+	0.332177i
$981$		0			0
$982$	42.2221	−	24.3769i	1.34736	−	0.777899i
$983$	−25.5109	−	14.7287i	−0.813671	−	0.469773i	0.0345581	−	0.999403i	$-0.488998\pi$
$983$	−25.5109	−	14.7287i	−0.813671	−	0.469773i	−0.848229	+	0.529630i	$0.822331\pi$
$984$		0			0
$985$	34.1122	−	8.26525i	1.08690	−	0.263353i
$986$	−10.8243			−0.344714
$987$		0			0
$988$		−	63.5279i		−	2.02109i
$989$	27.0873	−	15.6388i	0.861325	−	0.497286i
$990$		0			0
$991$	2.50334	−	4.33591i	0.0795211	−	0.137735i	−0.823522	−	0.567284i	$-0.807994\pi$
$991$	2.50334	−	4.33591i	0.0795211	−	0.137735i	0.903043	+	0.429549i	$0.141328\pi$
$992$	−9.19667	+	5.30970i	−0.291995	+	0.168583i
$993$		0			0
$994$	4.45760	+	51.1069i	0.141386	+	1.62101i
$995$	−42.4681	−	12.4829i	−1.34633	−	0.395734i
$996$		0			0
$997$	4.43960	−	7.68960i	0.140603	−	0.243532i	−0.787121	−	0.616799i	$-0.788429\pi$
$997$	4.43960	−	7.68960i	0.140603	−	0.243532i	0.927724	+	0.373267i	$0.121762\pi$
$998$	25.0893	−	43.4560i	0.794189	−	1.37558i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bb.b.269.3	yes	24
3.2	odd	2	inner	315.2.bb.b.269.10	yes	24
5.2	odd	4		1575.2.bk.i.1151.9		24
5.3	odd	4		1575.2.bk.i.1151.3		24
5.4	even	2	inner	315.2.bb.b.269.9	yes	24
7.3	odd	6		2205.2.g.b.2204.17		24
7.4	even	3		2205.2.g.b.2204.18		24
7.5	odd	6	inner	315.2.bb.b.89.4	yes	24
15.2	even	4		1575.2.bk.i.1151.4		24
15.8	even	4		1575.2.bk.i.1151.10		24
15.14	odd	2	inner	315.2.bb.b.269.4	yes	24
21.5	even	6	inner	315.2.bb.b.89.9	yes	24
21.11	odd	6		2205.2.g.b.2204.8		24
21.17	even	6		2205.2.g.b.2204.7		24
35.4	even	6		2205.2.g.b.2204.6		24
35.12	even	12		1575.2.bk.i.26.4		24
35.19	odd	6	inner	315.2.bb.b.89.10	yes	24
35.24	odd	6		2205.2.g.b.2204.5		24
35.33	even	12		1575.2.bk.i.26.10		24
105.47	odd	12		1575.2.bk.i.26.9		24
105.59	even	6		2205.2.g.b.2204.19		24
105.68	odd	12		1575.2.bk.i.26.3		24
105.74	odd	6		2205.2.g.b.2204.20		24
105.89	even	6	inner	315.2.bb.b.89.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bb.b.89.3	✓	24	105.89	even	6	inner
315.2.bb.b.89.4	yes	24	7.5	odd	6	inner
315.2.bb.b.89.9	yes	24	21.5	even	6	inner
315.2.bb.b.89.10	yes	24	35.19	odd	6	inner
315.2.bb.b.269.3	yes	24	1.1	even	1	trivial
315.2.bb.b.269.4	yes	24	15.14	odd	2	inner
315.2.bb.b.269.9	yes	24	5.4	even	2	inner
315.2.bb.b.269.10	yes	24	3.2	odd	2	inner
1575.2.bk.i.26.3		24	105.68	odd	12
1575.2.bk.i.26.4		24	35.12	even	12
1575.2.bk.i.26.9		24	105.47	odd	12
1575.2.bk.i.26.10		24	35.33	even	12
1575.2.bk.i.1151.3		24	5.3	odd	4
1575.2.bk.i.1151.4		24	15.2	even	4
1575.2.bk.i.1151.9		24	5.2	odd	4
1575.2.bk.i.1151.10		24	15.8	even	4
2205.2.g.b.2204.5		24	35.24	odd	6
2205.2.g.b.2204.6		24	35.4	even	6
2205.2.g.b.2204.7		24	21.17	even	6
2205.2.g.b.2204.8		24	21.11	odd	6
2205.2.g.b.2204.17		24	7.3	odd	6
2205.2.g.b.2204.18		24	7.4	even	3
2205.2.g.b.2204.19		24	105.59	even	6
2205.2.g.b.2204.20		24	105.74	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.956572 - 1.65683i) q^{2} +(-0.830062 + 1.43771i) q^{4} +(-2.17319 + 0.526555i) q^{5} +(-1.11878 + 2.39757i) q^{7} -0.650234 q^{8} +(2.95122 + 3.09692i) q^{10} +(2.79501 + 1.61370i) q^{11} +4.86146 q^{13} +(5.04256 - 0.439817i) q^{14} +(2.28212 + 3.95275i) q^{16} +(-0.631456 - 0.364571i) q^{17} +(-6.81691 + 3.93574i) q^{19} +(1.04685 - 3.56148i) q^{20} -6.17449i q^{22} +(2.43410 + 4.21599i) q^{23} +(4.44548 - 2.28861i) q^{25} +(-4.65034 - 8.05463i) q^{26} +(-2.51835 - 3.59861i) q^{28} +7.75958i q^{29} +(-1.23751 - 0.714478i) q^{31} +(3.71579 - 6.43594i) q^{32} +1.39495i q^{34} +(1.16887 - 5.79946i) q^{35} +(-2.74130 + 1.58269i) q^{37} +(13.0417 + 7.52965i) q^{38} +(1.41308 - 0.342384i) q^{40} +1.40264 q^{41} -6.42489i q^{43} +(-4.64007 + 2.67894i) q^{44} +(4.65679 - 8.06579i) q^{46} +(-4.21797 + 2.43524i) q^{47} +(-4.49666 - 5.36470i) q^{49} +(-8.04426 - 5.17620i) q^{50} +(-4.03531 + 6.98937i) q^{52} +(-0.760733 + 1.31763i) q^{53} +(-6.92379 - 2.03515i) q^{55} +(0.727468 - 1.55898i) q^{56} +(12.8563 - 7.42260i) q^{58} +(-3.15081 + 5.45737i) q^{59} +(-2.05442 + 1.18612i) q^{61} +2.73380i q^{62} -5.08921 q^{64} +(-10.5649 + 2.55983i) q^{65} +(9.63531 + 5.56295i) q^{67} +(1.04829 - 0.605233i) q^{68} +(-10.7268 + 3.61099i) q^{70} +10.1351i q^{71} +(-6.91195 + 11.9718i) q^{73} +(5.24450 + 3.02792i) q^{74} -13.0676i q^{76} +(-6.99596 + 4.89586i) q^{77} +(-1.99018 - 3.44710i) q^{79} +(-7.04081 - 7.38839i) q^{80} +(-1.34173 - 2.32395i) q^{82} -4.19208i q^{83} +(1.56424 + 0.459785i) q^{85} +(-10.6450 + 6.14587i) q^{86} +(-1.81741 - 1.04928i) q^{88} +(-5.63672 - 9.76309i) q^{89} +(-5.43891 + 11.6557i) q^{91} -8.08181 q^{92} +(8.06958 + 4.65898i) q^{94} +(12.7420 - 12.1426i) q^{95} -2.21388 q^{97} +(-4.58702 + 12.5819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 12 q^{10} - 36 q^{19} + 12 q^{25} - 60 q^{31} + 96 q^{40} - 24 q^{46} + 36 q^{49} + 48 q^{61} + 48 q^{64} - 48 q^{70} - 60 q^{79} - 72 q^{85} + 60 q^{91} + 48 q^{94}+O(q^{100}) \) 24 * q - 24 * q^4 - 12 * q^10 - 36 * q^19 + 12 * q^25 - 60 * q^31 + 96 * q^40 - 24 * q^46 + 36 * q^49 + 48 * q^61 + 48 * q^64 - 48 * q^70 - 60 * q^79 - 72 * q^85 + 60 * q^91 + 48 * q^94

Introduction

L-functions

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