LMFDB - Embedded newform 736.2.x.a.561.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [736,2,Mod(49,736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(736, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("736.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 736 = 2^{5} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	736.x (of order $22$, degree $10$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.87698958877$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			561.3
Character	$\chi$	$=$	736.561
Dual form			736.2.x.a.593.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77342 + 1.53668i) q^{3} +(-3.72983 + 0.536269i) q^{5} +(-1.80644 + 3.95556i) q^{7} +(0.356696 - 2.48088i) q^{9} +O(q^{10})$	\(q+(-1.77342 + 1.53668i) q^{3} +(-3.72983 + 0.536269i) q^{5} +(-1.80644 + 3.95556i) q^{7} +(0.356696 - 2.48088i) q^{9} +(-0.791572 + 2.69585i) q^{11} +(-1.31919 + 0.602452i) q^{13} +(5.79048 - 6.68257i) q^{15} +(0.426368 + 0.274010i) q^{17} +(1.09247 + 1.69992i) q^{19} +(-2.87483 - 9.79078i) q^{21} +(-4.04551 + 2.57562i) q^{23} +(8.82660 - 2.59172i) q^{25} +(-0.626221 - 0.974418i) q^{27} +(0.637426 - 0.991854i) q^{29} +(5.28380 - 6.09783i) q^{31} +(-2.73886 - 5.99726i) q^{33} +(4.61648 - 15.7223i) q^{35} +(1.78283 + 0.256332i) q^{37} +(1.41370 - 3.09556i) q^{39} +(1.06252 + 7.38997i) q^{41} +(-0.318514 + 0.275994i) q^{43} +9.44454i q^{45} -11.5799 q^{47} +(-7.79917 - 9.00072i) q^{49} +(-1.17719 + 0.169255i) q^{51} +(8.99787 + 4.10919i) q^{53} +(1.50673 - 10.4796i) q^{55} +(-4.54963 - 1.33589i) q^{57} +(1.14788 - 0.524220i) q^{59} +(6.78339 + 5.87784i) q^{61} +(9.16890 + 5.89249i) q^{63} +(4.59726 - 2.95448i) q^{65} +(-0.439020 - 1.49516i) q^{67} +(3.21648 - 10.7843i) q^{69} +(3.81036 - 1.11882i) q^{71} +(-3.83656 + 2.46561i) q^{73} +(-11.6706 + 18.1598i) q^{75} +(-9.23365 - 8.00100i) q^{77} +(4.36275 + 9.55308i) q^{79} +(9.82250 + 2.88415i) q^{81} +(-9.43680 - 1.35681i) q^{83} +(-1.73723 - 0.793364i) q^{85} +(0.393735 + 2.73849i) q^{87} +(-7.96093 - 9.18740i) q^{89} -6.30641i q^{91} +18.9335i q^{93} +(-4.98635 - 5.75455i) q^{95} +(0.199115 + 1.38487i) q^{97} +(6.40571 + 2.92539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 22 q^{7}+O(q^{10}) $ 220 * q + 22 * q^7	$ 220 q + 22 q^{7} + 22 q^{15} - 18 q^{17} + 16 q^{23} - 4 q^{25} + 34 q^{31} - 30 q^{33} + 18 q^{39} - 18 q^{41} + 40 q^{47} - 28 q^{49} + 38 q^{55} - 30 q^{57} - 18 q^{63} - 38 q^{65} + 26 q^{71} - 18 q^{73} + 22 q^{79} - 52 q^{81} + 42 q^{87} - 2 q^{89} + 78 q^{95} - 18 q^{97}+O(q^{100}) $ 220 * q + 22 * q^7 + 22 * q^15 - 18 * q^17 + 16 * q^23 - 4 * q^25 + 34 * q^31 - 30 * q^33 + 18 * q^39 - 18 * q^41 + 40 * q^47 - 28 * q^49 + 38 * q^55 - 30 * q^57 - 18 * q^63 - 38 * q^65 + 26 * q^71 - 18 * q^73 + 22 * q^79 - 52 * q^81 + 42 * q^87 - 2 * q^89 + 78 * q^95 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/736\mathbb{Z}\right)^\times$.

$n$	$97$	$415$	$645$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−1.77342	+	1.53668i	−1.02388	+	0.887200i	−0.993669	−	0.112343i	$-0.964164\pi$
$3$	−1.77342	+	1.53668i	−1.02388	+	0.887200i	−0.0302144	+	0.999543i	$0.509619\pi$
$4$		0			0
$5$	−3.72983	+	0.536269i	−1.66803	+	0.239827i	−0.910660	−	0.413157i	$-0.864426\pi$
$5$	−3.72983	+	0.536269i	−1.66803	+	0.239827i	−0.757372	+	0.652984i	$0.773517\pi$
$6$		0			0
$7$	−1.80644	+	3.95556i	−0.682771	+	1.49506i	0.176909	+	0.984227i	$0.443390\pi$
$7$	−1.80644	+	3.95556i	−0.682771	+	1.49506i	−0.859680	+	0.510833i	$0.829337\pi$
$8$		0			0
$9$	0.356696	−	2.48088i	0.118899	−	0.826959i
$10$		0			0
$11$	−0.791572	+	2.69585i	−0.238668	+	0.812828i	0.749835	+	0.661625i	$0.230133\pi$
$11$	−0.791572	+	2.69585i	−0.238668	+	0.812828i	−0.988503	+	0.151203i	$0.951685\pi$
$12$		0			0
$13$	−1.31919	+	0.602452i	−0.365876	+	0.167090i	−0.589865	−	0.807502i	$-0.700819\pi$
$13$	−1.31919	+	0.602452i	−0.365876	+	0.167090i	0.223989	+	0.974592i	$0.428092\pi$
$14$		0			0
$15$	5.79048	−	6.68257i	1.49510	−	1.72543i
$16$		0			0
$17$	0.426368	+	0.274010i	0.103409	+	0.0664572i	0.591323	−	0.806434i	$-0.298606\pi$
$17$	0.426368	+	0.274010i	0.103409	+	0.0664572i	−0.487914	+	0.872892i	$0.662242\pi$
$18$		0			0
$19$	1.09247	+	1.69992i	0.250630	+	0.389988i	0.943658	−	0.330923i	$-0.107360\pi$
$19$	1.09247	+	1.69992i	0.250630	+	0.389988i	−0.693028	+	0.720911i	$0.743724\pi$
$20$		0			0
$21$	−2.87483	−	9.79078i	−0.627340	−	2.13652i
$22$		0			0
$23$	−4.04551	+	2.57562i	−0.843547	+	0.537055i
$23$	−4.04551	+	2.57562i	−0.843547	+	0.537055i
$24$		0			0
$25$	8.82660	−	2.59172i	1.76532	−	0.518345i
$26$		0			0
$27$	−0.626221	−	0.974418i	−0.120516	−	0.187527i
$28$		0			0
$29$	0.637426	−	0.991854i	0.118367	−	0.184183i	−0.777014	−	0.629483i	$-0.783267\pi$
$29$	0.637426	−	0.991854i	0.118367	−	0.184183i	0.895381	+	0.445300i	$0.146903\pi$
$30$		0			0
$31$	5.28380	−	6.09783i	0.948999	−	1.09520i	−0.0463554	−	0.998925i	$-0.514761\pi$
$31$	5.28380	−	6.09783i	0.948999	−	1.09520i	0.995354	−	0.0962782i	$-0.0306939\pi$
$32$		0			0
$33$	−2.73886	−	5.99726i	−0.476773	−	1.04399i
$34$		0			0
$35$	4.61648	−	15.7223i	0.780328	−	2.65755i
$36$		0			0
$37$	1.78283	+	0.256332i	0.293095	+	0.0421407i	0.287294	−	0.957843i	$-0.407244\pi$
$37$	1.78283	+	0.256332i	0.293095	+	0.0421407i	0.00580094	+	0.999983i	$0.498153\pi$
$38$		0			0
$39$	1.41370	−	3.09556i	0.226372	−	0.495686i
$40$		0			0
$41$	1.06252	+	7.38997i	0.165937	+	1.15412i	0.887175	+	0.461433i	$0.152664\pi$
$41$	1.06252	+	7.38997i	0.165937	+	1.15412i	−0.721238	+	0.692687i	$0.756427\pi$
$42$		0			0
$43$	−0.318514	+	0.275994i	−0.0485729	+	0.0420887i	−0.678809	−	0.734315i	$-0.737504\pi$
$43$	−0.318514	+	0.275994i	−0.0485729	+	0.0420887i	0.630236	+	0.776404i	$0.282958\pi$
$44$		0			0
$45$			9.44454i			1.40791i
$46$		0			0
$47$	−11.5799			−1.68910			−0.844549	−	0.535479i	$-0.820131\pi$
$47$	−11.5799			−1.68910			−0.844549	+	0.535479i	$0.820131\pi$
$48$		0			0
$49$	−7.79917	−	9.00072i	−1.11417	−	1.28582i
$50$		0			0
$51$	−1.17719	+	0.169255i	−0.164840	+	0.0237004i
$52$		0			0
$53$	8.99787	+	4.10919i	1.23595	+	0.564440i	0.922806	−	0.385265i	$-0.125890\pi$
$53$	8.99787	+	4.10919i	1.23595	+	0.564440i	0.313146	+	0.949705i	$0.398617\pi$
$54$		0			0
$55$	1.50673	−	10.4796i	0.203168	−	1.41306i
$56$		0			0
$57$	−4.54963	−	1.33589i	−0.602614	−	0.176943i
$58$		0			0
$59$	1.14788	−	0.524220i	0.149441	−	0.0682476i	−0.339290	−	0.940682i	$-0.610187\pi$
$59$	1.14788	−	0.524220i	0.149441	−	0.0682476i	0.488732	+	0.872434i	$0.337460\pi$
$60$		0			0
$61$	6.78339	+	5.87784i	0.868524	+	0.752580i	0.970217	−	0.242236i	$-0.0778807\pi$
$61$	6.78339	+	5.87784i	0.868524	+	0.752580i	−0.101694	+	0.994816i	$0.532426\pi$
$62$		0			0
$63$	9.16890	+	5.89249i	1.15517	+	0.742384i
$64$		0			0
$65$	4.59726	−	2.95448i	0.570220	−	0.366458i
$66$		0			0
$67$	−0.439020	−	1.49516i	−0.0536348	−	0.182663i	0.928319	−	0.371785i	$-0.121254\pi$
$67$	−0.439020	−	1.49516i	−0.0536348	−	0.182663i	−0.981954	+	0.189122i	$0.939436\pi$
$68$		0			0
$69$	3.21648	−	10.7843i	0.387219	−	1.29828i
$70$		0			0
$71$	3.81036	−	1.11882i	0.452206	−	0.132780i	−0.0476954	−	0.998862i	$-0.515188\pi$
$71$	3.81036	−	1.11882i	0.452206	−	0.132780i	0.499902	+	0.866082i	$0.333369\pi$
$72$		0			0
$73$	−3.83656	+	2.46561i	−0.449036	+	0.288578i	−0.745549	−	0.666451i	$-0.767813\pi$
$73$	−3.83656	+	2.46561i	−0.449036	+	0.288578i	0.296513	+	0.955029i	$0.404176\pi$
$74$		0			0
$75$	−11.6706	+	18.1598i	−1.34761	+	2.09692i
$76$		0			0
$77$	−9.23365	−	8.00100i	−1.05227	−	0.911798i
$78$		0			0
$79$	4.36275	+	9.55308i	0.490847	+	1.07481i	0.979337	+	0.202236i	$0.0648208\pi$
$79$	4.36275	+	9.55308i	0.490847	+	1.07481i	−0.488490	+	0.872570i	$0.662452\pi$
$80$		0			0
$81$	9.82250	+	2.88415i	1.09139	+	0.320461i
$82$		0			0
$83$	−9.43680	−	1.35681i	−1.03582	−	0.148929i	−0.396633	−	0.917977i	$-0.629821\pi$
$83$	−9.43680	−	1.35681i	−1.03582	−	0.148929i	−0.639191	+	0.769048i	$0.720731\pi$
$84$		0			0
$85$	−1.73723	−	0.793364i	−0.188429	−	0.0860524i
$86$		0			0
$87$	0.393735	+	2.73849i	0.0422129	+	0.293597i
$88$		0			0
$89$	−7.96093	−	9.18740i	−0.843857	−	0.973862i	0.156047	−	0.987750i	$-0.450125\pi$
$89$	−7.96093	−	9.18740i	−0.843857	−	0.973862i	−0.999904	+	0.0138873i	$0.995579\pi$
$90$		0			0
$91$		−	6.30641i		−	0.661091i
$92$		0			0
$93$			18.9335i			1.96331i
$94$		0			0
$95$	−4.98635	−	5.75455i	−0.511589	−	0.590405i
$96$		0			0
$97$	0.199115	+	1.38487i	0.0202170	+	0.140613i	0.997430	−	0.0716491i	$-0.0228262\pi$
$97$	0.199115	+	1.38487i	0.0202170	+	0.140613i	−0.977213	+	0.212262i	$0.931917\pi$
$98$		0			0
$99$	6.40571	+	2.92539i	0.643799	+	0.294013i
$100$		0			0
$101$	−9.73250	−	1.39932i	−0.968420	−	0.139238i	−0.360086	−	0.932919i	$-0.617253\pi$
$101$	−9.73250	−	1.39932i	−0.968420	−	0.139238i	−0.608334	+	0.793681i	$0.708162\pi$
$102$		0			0
$103$	1.82521	+	0.535931i	0.179844	+	0.0528069i	0.370414	−	0.928867i	$-0.379216\pi$
$103$	1.82521	+	0.535931i	0.179844	+	0.0528069i	−0.190571	+	0.981673i	$0.561034\pi$
$104$		0			0
$105$	15.9731	+	34.9763i	1.55882	+	3.41333i
$106$		0			0
$107$	13.1018	+	11.3528i	1.26660	+	1.09752i	0.990662	+	0.136341i	$0.0435343\pi$
$107$	13.1018	+	11.3528i	1.26660	+	1.09752i	0.275939	+	0.961175i	$0.411011\pi$
$108$		0			0
$109$	5.22510	−	8.13042i	0.500474	−	0.778753i	−0.495480	−	0.868619i	$-0.665008\pi$
$109$	5.22510	−	8.13042i	0.500474	−	0.778753i	0.995954	+	0.0898667i	$0.0286441\pi$
$110$		0			0
$111$	−3.55560	+	2.28504i	−0.337482	+	0.216887i
$112$		0			0
$113$	−14.5526	+	4.27304i	−1.36900	+	0.401974i	−0.881926	−	0.471389i	$-0.843753\pi$
$113$	−14.5526	+	4.27304i	−1.36900	+	0.401974i	−0.487071	+	0.873362i	$0.661935\pi$
$114$		0			0
$115$	13.7078	−	11.7761i	1.27826	−	1.09813i
$116$		0			0
$117$	1.02406	+	3.48763i	0.0946744	+	0.322432i
$118$		0			0
$119$	−1.85407	+	1.19154i	−0.169963	+	0.109228i
$120$		0			0
$121$	2.61278	+	1.67913i	0.237526	+	0.152649i
$122$		0			0
$123$	−13.2403	−	11.4728i	−1.19384	−	1.03447i
$124$		0			0
$125$	−14.3935	+	6.57331i	−1.28740	+	0.587935i
$126$		0			0
$127$	−3.89512	−	1.14371i	−0.345636	−	0.101488i	0.104307	−	0.994545i	$-0.466738\pi$
$127$	−3.89512	−	1.14371i	−0.345636	−	0.101488i	−0.449943	+	0.893057i	$0.648556\pi$
$128$		0			0
$129$	0.140745	−	0.978906i	0.0123919	−	0.0861878i
$130$		0			0
$131$	−12.1401	−	5.54421i	−1.06069	−	0.484400i	−0.192840	−	0.981230i	$-0.561770\pi$
$131$	−12.1401	−	5.54421i	−1.06069	−	0.484400i	−0.867847	+	0.496831i	$0.834497\pi$
$132$		0			0
$133$	−8.69761	+	1.25053i	−0.754178	+	0.108434i
$134$		0			0
$135$	2.85825	+	3.29859i	0.245999	+	0.283898i
$136$		0			0
$137$	−10.9682			−0.937078			−0.468539	−	0.883443i	$-0.655219\pi$
$137$	−10.9682			−0.937078			−0.468539	+	0.883443i	$0.655219\pi$
$138$		0			0
$139$			2.34868i			0.199213i	0.995027	+	0.0996063i	$0.0317583\pi$
$139$			2.34868i			0.199213i	−0.995027	+	0.0996063i	$0.968242\pi$
$140$		0			0
$141$	20.5360	−	17.7945i	1.72944	−	1.49857i
$142$		0			0
$143$	−0.579888	−	4.03321i	−0.0484926	−	0.337274i
$144$		0			0
$145$	−1.84559	+	4.04128i	−0.153268	+	0.335610i
$146$		0			0
$147$	27.6624	+	3.97725i	2.28155	+	0.328038i
$148$		0			0
$149$	3.50526	−	11.9378i	0.287162	−	0.977984i	−0.681958	−	0.731392i	$-0.738871\pi$
$149$	3.50526	−	11.9378i	0.287162	−	0.977984i	0.969119	−	0.246592i	$-0.0793107\pi$
$150$		0			0
$151$	4.28382	+	9.38026i	0.348613	+	0.763355i	0.999989	+	0.00460069i	$0.00146445\pi$
$151$	4.28382	+	9.38026i	0.348613	+	0.763355i	−0.651377	+	0.758754i	$0.725808\pi$
$152$		0			0
$153$	0.831870	−	0.960029i	0.0672527	−	0.0776137i
$154$		0			0
$155$	−16.4376	+	25.5774i	−1.32030	+	2.05443i
$156$		0			0
$157$	7.08344	+	11.0220i	0.565320	+	0.879655i	0.999779	−	0.0210369i	$-0.00669676\pi$
$157$	7.08344	+	11.0220i	0.565320	+	0.879655i	−0.434459	+	0.900692i	$0.643060\pi$
$158$		0			0
$159$	−22.2715	+	6.53950i	−1.76624	+	0.518616i
$160$		0			0
$161$	−2.88005	−	20.6550i	−0.226980	−	1.62784i
$162$		0			0
$163$	−3.25643	−	11.0904i	−0.255063	−	0.868665i	−0.983091	−	0.183118i	$-0.941381\pi$
$163$	−3.25643	−	11.0904i	−0.255063	−	0.868665i	0.728028	−	0.685547i	$-0.240437\pi$
$164$		0			0
$165$	13.4316	+	20.9000i	1.04565	+	1.62706i
$166$		0			0
$167$	−1.02800	−	0.660656i	−0.0795491	−	0.0511231i	0.500262	−	0.865874i	$-0.333237\pi$
$167$	−1.02800	−	0.660656i	−0.0795491	−	0.0511231i	−0.579811	+	0.814751i	$0.696874\pi$
$168$		0			0
$169$	−7.13589	+	8.23525i	−0.548914	+	0.633481i
$170$		0			0
$171$	4.60697	−	2.10393i	0.352304	−	0.160892i
$172$		0			0
$173$	0.868642	−	2.95832i	0.0660417	−	0.224917i	−0.919859	−	0.392249i	$-0.871697\pi$
$173$	0.868642	−	2.95832i	0.0660417	−	0.224917i	0.985901	+	0.167332i	$0.0535152\pi$
$174$		0			0
$175$	−5.69303	+	39.5959i	−0.430353	+	2.99317i
$176$		0			0
$177$	−1.23012	+	2.69358i	−0.0924613	+	0.202462i
$178$		0			0
$179$	0.900585	−	0.129485i	0.0673129	−	0.00967813i	−0.108576	−	0.994088i	$-0.534629\pi$
$179$	0.900585	−	0.129485i	0.0673129	−	0.00967813i	0.175889	+	0.984410i	$0.443720\pi$
$180$		0			0
$181$	−19.0638	+	16.5189i	−1.41700	+	1.22784i	−0.480590	+	0.876945i	$0.659578\pi$
$181$	−19.0638	+	16.5189i	−1.41700	+	1.22784i	−0.936414	+	0.350896i	$0.885877\pi$
$182$		0			0
$183$	−21.0621			−1.55696
$184$		0			0
$185$	−6.78710			−0.498998
$186$		0			0
$187$	−1.07619	+	0.932525i	−0.0786989	+	0.0681930i
$188$		0			0
$189$	4.98560	−	0.716821i	0.362649	−	0.0521410i
$190$		0			0
$191$	5.86082	−	12.8334i	0.424074	−	0.928592i	−0.570177	−	0.821522i	$-0.693126\pi$
$191$	5.86082	−	12.8334i	0.424074	−	0.928592i	0.994251	−	0.107071i	$-0.0341472\pi$
$192$		0			0
$193$	2.43504	−	16.9361i	0.175278	−	1.21909i	−0.692235	−	0.721672i	$-0.743374\pi$
$193$	2.43504	−	16.9361i	0.175278	−	1.21909i	0.867513	−	0.497414i	$-0.165717\pi$
$194$		0			0
$195$	−3.61279	+	12.3040i	−0.258717	+	0.881111i
$196$		0			0
$197$	9.88574	−	4.51467i	0.704330	−	0.321657i	−0.0308544	−	0.999524i	$-0.509823\pi$
$197$	9.88574	−	4.51467i	0.704330	−	0.321657i	0.735184	+	0.677867i	$0.237096\pi$
$198$		0			0
$199$	0.336842	−	0.388736i	0.0238781	−	0.0275568i	−0.743685	−	0.668530i	$-0.766924\pi$
$199$	0.336842	−	0.388736i	0.0238781	−	0.0275568i	0.767563	+	0.640974i	$0.221469\pi$
$200$		0			0
$201$	3.07615	+	1.97692i	0.216975	+	0.139441i
$202$		0			0
$203$	2.77186	+	4.31310i	0.194546	+	0.302720i
$204$		0			0
$205$	−7.92603	−	26.9936i	−0.553578	−	1.88531i
$206$		0			0
$207$	4.94679	+	10.9551i	0.343826	+	0.761434i
$208$		0			0
$209$	−5.44749	+	1.59953i	−0.376811	+	0.110642i
$210$		0			0
$211$	5.51272	+	8.57796i	0.379511	+	0.590531i	0.977490	−	0.210981i	$-0.0676657\pi$
$211$	5.51272	+	8.57796i	0.379511	+	0.590531i	−0.597979	+	0.801512i	$0.704029\pi$
$212$		0			0
$213$	−5.03809	+	7.83943i	−0.345204	+	0.537149i
$214$		0			0
$215$	1.04000	−	1.20022i	0.0709272	−	0.0818543i
$216$		0			0
$217$	14.5754	+	31.9158i	0.989445	+	2.16658i
$218$		0			0
$219$	3.01499	−	10.2681i	0.203734	−	0.693855i
$220$		0			0
$221$	−0.727537	−	0.104604i	−0.0489394	−	0.00703643i
$222$		0			0
$223$	2.09834	−	4.59472i	0.140515	−	0.307685i	−0.826271	−	0.563273i	$-0.809542\pi$
$223$	2.09834	−	4.59472i	0.140515	−	0.307685i	0.966786	+	0.255588i	$0.0822691\pi$
$224$		0			0
$225$	−3.28133	−	22.8222i	−0.218755	−	1.52148i
$226$		0			0
$227$	2.43310	−	2.10829i	0.161490	−	0.139932i	−0.570367	−	0.821390i	$-0.693199\pi$
$227$	2.43310	−	2.10829i	0.161490	−	0.139932i	0.731857	+	0.681458i	$0.238654\pi$
$228$		0			0
$229$		−	10.8110i		−	0.714408i	−0.934026	−	0.357204i	$-0.883730\pi$
$229$		−	10.8110i		−	0.714408i	0.934026	−	0.357204i	$-0.116270\pi$
$230$		0			0
$231$	28.6701			1.88635
$232$		0			0
$233$	16.9126	+	19.5182i	1.10798	+	1.27868i	0.956982	+	0.290148i	$0.0937046\pi$
$233$	16.9126	+	19.5182i	1.10798	+	1.27868i	0.151002	+	0.988533i	$0.451750\pi$
$234$		0			0
$235$	43.1910	−	6.20992i	2.81747	−	0.405091i
$236$		0			0
$237$	−22.4170	−	10.2375i	−1.45614	−	0.664996i
$238$		0			0
$239$	3.19587	−	22.2278i	0.206724	−	1.43780i	−0.577030	−	0.816723i	$-0.695788\pi$
$239$	3.19587	−	22.2278i	0.206724	−	1.43780i	0.783754	−	0.621072i	$-0.213303\pi$
$240$		0			0
$241$	12.6543	+	3.71563i	0.815134	+	0.239345i	0.662619	−	0.748956i	$-0.269445\pi$
$241$	12.6543	+	3.71563i	0.815134	+	0.239345i	0.152514	+	0.988301i	$0.451263\pi$
$242$		0			0
$243$	−18.6906	+	8.53569i	−1.19900	+	0.547565i
$244$		0			0
$245$	33.9164	+	29.3887i	2.16684	+	1.87758i
$246$		0			0
$247$	−2.46529	−	1.58435i	−0.156863	−	0.100810i
$248$		0			0
$249$	18.8204	−	12.0951i	1.19269	−	0.766497i
$250$		0			0
$251$	−5.77516	−	19.6684i	−0.364525	−	1.24146i	−0.913920	−	0.405894i	$-0.866960\pi$
$251$	−5.77516	−	19.6684i	−0.364525	−	1.24146i	0.549395	−	0.835563i	$-0.314858\pi$
$252$		0			0
$253$	−3.74118	−	12.9449i	−0.235206	−	0.813837i
$254$		0			0
$255$	4.29997	−	1.26259i	0.269275	−	0.0790662i
$256$		0			0
$257$	7.33589	−	4.71449i	0.457600	−	0.294082i	−0.291461	−	0.956583i	$-0.594141\pi$
$257$	7.33589	−	4.71449i	0.457600	−	0.294082i	0.749061	+	0.662501i	$0.230505\pi$
$258$		0			0
$259$	−4.23451	+	6.58902i	−0.263119	+	0.409422i
$260$		0			0
$261$	−2.23330	−	1.93517i	−0.138238	−	0.119784i
$262$		0			0
$263$	2.15069	+	4.70935i	0.132617	+	0.290391i	0.964278	−	0.264893i	$-0.0853367\pi$
$263$	2.15069	+	4.70935i	0.132617	+	0.290391i	−0.831661	+	0.555284i	$0.812609\pi$
$264$		0			0
$265$	−35.7642	−	10.5013i	−2.19697	−	0.645090i
$266$		0			0
$267$	28.2361	+	4.05974i	1.72802	+	0.248452i
$268$		0			0
$269$	−3.85840	−	1.76207i	−0.235251	−	0.107435i	0.294302	−	0.955712i	$-0.404913\pi$
$269$	−3.85840	−	1.76207i	−0.235251	−	0.107435i	−0.529553	+	0.848277i	$0.677640\pi$
$270$		0			0
$271$	0.393604	+	2.73758i	0.0239097	+	0.166296i	0.998278	−	0.0586639i	$-0.0186840\pi$
$271$	0.393604	+	2.73758i	0.0239097	+	0.166296i	−0.974368	+	0.224960i	$0.927775\pi$
$272$		0			0
$273$	9.69091	+	11.1839i	0.586520	+	0.676881i
$274$		0			0
$275$			25.8467i			1.55861i
$276$		0			0
$277$		−	6.75364i		−	0.405787i	−0.979201	−	0.202894i	$-0.934965\pi$
$277$		−	6.75364i		−	0.405787i	0.979201	−	0.202894i	$-0.0650345\pi$
$278$		0			0
$279$	−13.2433	−	15.2835i	−0.792854	−	0.915002i
$280$		0			0
$281$	2.17338	+	15.1162i	0.129653	+	0.901755i	0.945994	+	0.324185i	$0.105090\pi$
$281$	2.17338	+	15.1162i	0.129653	+	0.901755i	−0.816341	+	0.577570i	$0.804001\pi$
$282$		0			0
$283$	−6.08878	−	2.78065i	−0.361940	−	0.165293i	0.226141	−	0.974095i	$-0.427389\pi$
$283$	−6.08878	−	2.78065i	−0.361940	−	0.165293i	−0.588081	+	0.808802i	$0.700116\pi$
$284$		0			0
$285$	17.6858	+	2.54283i	1.04761	+	0.150624i
$286$		0			0
$287$	−31.1508	−	9.14671i	−1.83878	−	0.539913i
$288$		0			0
$289$	−6.95535	−	15.2301i	−0.409138	−	0.895887i
$290$		0			0
$291$	−2.48122	−	2.14999i	−0.145451	−	0.126034i
$292$		0			0
$293$	4.65883	−	7.24928i	0.272172	−	0.423507i	−0.678081	−	0.734987i	$-0.737188\pi$
$293$	4.65883	−	7.24928i	0.272172	−	0.423507i	0.950253	+	0.311480i	$0.100825\pi$
$294$		0			0
$295$	−4.00028	+	2.57082i	−0.232905	+	0.149679i
$296$		0			0
$297$	3.12258	−	0.916872i	0.181191	−	0.0532023i
$298$		0			0
$299$	3.78509	−	5.83495i	0.218897	−	0.337444i
$300$		0			0
$301$	−0.516332	−	1.75847i	−0.0297609	−	0.101356i
$302$		0			0
$303$	19.4101	−	12.4741i	1.11508	−	0.716619i
$304$		0			0
$305$	−28.4530	−	18.2856i	−1.62921	−	1.04703i
$306$		0			0
$307$	−15.9592	−	13.8288i	−0.910842	−	0.789250i	0.0671817	−	0.997741i	$-0.478599\pi$
$307$	−15.9592	−	13.8288i	−0.910842	−	0.789250i	−0.978024	+	0.208491i	$0.933145\pi$
$308$		0			0
$309$	−4.06042	+	1.85433i	−0.230989	+	0.105489i
$310$		0			0
$311$	−14.2023	−	4.17017i	−0.805339	−	0.236469i	−0.146947	−	0.989144i	$-0.546945\pi$
$311$	−14.2023	−	4.17017i	−0.805339	−	0.236469i	−0.658392	+	0.752675i	$0.728763\pi$
$312$		0			0
$313$	0.312501	−	2.17349i	0.0176636	−	0.122853i	−0.979082	−	0.203467i	$-0.934779\pi$
$313$	0.312501	−	2.17349i	0.0176636	−	0.122853i	0.996745	+	0.0806140i	$0.0256881\pi$
$314$		0			0
$315$	−37.3584	−	17.0610i	−2.10491	−	0.961279i
$316$		0			0
$317$	−26.5488	+	3.81714i	−1.49113	+	0.214392i	−0.839173	−	0.543865i	$-0.816960\pi$
$317$	−26.5488	+	3.81714i	−1.49113	+	0.214392i	−0.651956	+	0.758257i	$0.726051\pi$
$318$		0			0
$319$	2.16932	+	2.50353i	0.121458	+	0.140171i
$320$		0			0
$321$	−40.6806			−2.27057
$322$		0			0
$323$			1.02414i			0.0569847i
$324$		0			0
$325$	−10.0825	+	8.73656i	−0.559278	+	0.484617i
$326$		0			0
$327$	3.22752	+	22.4479i	0.178483	+	1.24137i
$328$		0			0
$329$	20.9184	−	45.8048i	1.15327	−	2.52530i
$330$		0			0
$331$	−10.8132	−	1.55470i	−0.594348	−	0.0854543i	−0.161424	−	0.986885i	$-0.551609\pi$
$331$	−10.8132	−	1.55470i	−0.594348	−	0.0854543i	−0.432923	+	0.901431i	$0.642518\pi$
$332$		0			0
$333$	1.27185	−	4.33154i	0.0696972	−	0.237367i
$334$		0			0
$335$	2.43928	+	5.34128i	0.133272	+	0.291825i
$336$		0			0
$337$	−11.6349	+	13.4274i	−0.633794	+	0.731437i	−0.978265	−	0.207360i	$-0.933513\pi$
$337$	−11.6349	+	13.4274i	−0.633794	+	0.731437i	0.344471	+	0.938797i	$0.388058\pi$
$338$		0			0
$339$	19.2416	−	29.9406i	1.04506	−	1.62615i
$340$		0			0
$341$	12.2563	+	19.0712i	0.663717	+	1.03276i
$342$		0			0
$343$	20.4849	−	6.01492i	1.10608	−	0.324775i
$344$		0			0
$345$	−6.21366	+	41.9485i	−0.334532	+	2.25843i
$346$		0			0
$347$	4.43254	+	15.0959i	0.237951	+	0.810388i	0.988714	+	0.149816i	$0.0478681\pi$
$347$	4.43254	+	15.0959i	0.237951	+	0.810388i	−0.750763	+	0.660572i	$0.770314\pi$
$348$		0			0
$349$	−1.64712	−	2.56297i	−0.0881685	−	0.137193i	0.794368	−	0.607437i	$-0.207802\pi$
$349$	−1.64712	−	2.56297i	−0.0881685	−	0.137193i	−0.882536	+	0.470244i	$0.844166\pi$
$350$		0			0
$351$	1.41314	+	0.908171i	0.0754279	+	0.0484746i
$352$		0			0
$353$	10.1083	−	11.6656i	0.538010	−	0.620896i	−0.420037	−	0.907507i	$-0.637983\pi$
$353$	10.1083	−	11.6656i	0.538010	−	0.620896i	0.958047	+	0.286610i	$0.0925285\pi$
$354$		0			0
$355$	−13.6120	+	6.21639i	−0.722450	+	0.329932i
$356$		0			0
$357$	1.45704	−	4.96221i	0.0771145	−	0.262628i
$358$		0			0
$359$	4.15934	−	28.9289i	0.219522	−	1.52681i	−0.520288	−	0.853991i	$-0.674175\pi$
$359$	4.15934	−	28.9289i	0.219522	−	1.52681i	0.739810	−	0.672816i	$-0.234915\pi$
$360$		0			0
$361$	6.19666	−	13.5688i	0.326140	−	0.714146i
$362$		0			0
$363$	−7.21385	+	1.03719i	−0.378629	+	0.0544386i
$364$		0			0
$365$	12.9875	−	11.2537i	0.679797	−	0.589048i
$366$		0			0
$367$	20.1083			1.04965			0.524823	−	0.851212i	$-0.324132\pi$
$367$	20.1083			1.04965			0.524823	+	0.851212i	$0.324132\pi$
$368$		0			0
$369$	18.7126			0.974140
$370$		0			0
$371$	−32.5082	+	28.1686i	−1.68774	+	1.46244i
$372$		0			0
$373$	−6.08669	+	0.875134i	−0.315157	+	0.0453127i	−0.298078	−	0.954541i	$-0.596346\pi$
$373$	−6.08669	+	0.875134i	−0.315157	+	0.0453127i	−0.0170786	+	0.999854i	$0.505437\pi$
$374$		0			0
$375$	15.4247	−	33.7755i	0.796530	−	1.74416i
$376$		0			0
$377$	−0.243339	+	1.69246i	−0.0125326	+	0.0871660i
$378$		0			0
$379$	6.96944	−	23.7357i	0.357996	−	1.21922i	−0.561948	−	0.827172i	$-0.689948\pi$
$379$	6.96944	−	23.7357i	0.357996	−	1.21922i	0.919944	−	0.392050i	$-0.128234\pi$
$380$		0			0
$381$	8.66519	−	3.95726i	0.443931	−	0.202737i
$382$		0			0
$383$	−7.18892	+	8.29646i	−0.367337	+	0.423929i	−0.909084	−	0.416612i	$-0.863217\pi$
$383$	−7.18892	+	8.29646i	−0.367337	+	0.423929i	0.541748	+	0.840541i	$0.317763\pi$
$384$		0			0
$385$	38.7306	+	24.8907i	1.97390	+	1.26855i
$386$		0			0
$387$	0.571094	+	0.888640i	0.0290304	+	0.0451721i
$388$		0			0
$389$	2.44620	+	8.33101i	0.124028	+	0.422399i	0.997974	−	0.0636233i	$-0.0202656\pi$
$389$	2.44620	+	8.33101i	0.124028	+	0.422399i	−0.873946	+	0.486022i	$0.838447\pi$
$390$		0			0
$391$	−2.43062	−	0.0103468i	−0.122922	−	0.000523258i
$392$		0			0
$393$	30.0492	−	8.82323i	1.51578	−	0.445073i
$394$		0			0
$395$	−21.3953	−	33.2918i	−1.07652	−	1.67509i
$396$		0			0
$397$	−11.0312	+	17.1648i	−0.553638	+	0.861477i	−0.999433	−	0.0336576i	$-0.989284\pi$
$397$	−11.0312	+	17.1648i	−0.553638	+	0.861477i	0.445796	+	0.895135i	$0.352921\pi$
$398$		0			0
$399$	13.5029	−	15.5831i	0.675988	−	0.780132i
$400$		0			0
$401$	−1.71260	−	3.75006i	−0.0855230	−	0.187269i	0.862038	−	0.506843i	$-0.169188\pi$
$401$	−1.71260	−	3.75006i	−0.0855230	−	0.187269i	−0.947561	+	0.319574i	$0.896460\pi$
$402$		0			0
$403$	−3.29667	+	11.2274i	−0.164219	+	0.559277i
$404$		0			0
$405$	−38.1830	−	5.48988i	−1.89733	−	0.272794i
$406$		0			0
$407$	−2.10227	+	4.60332i	−0.104205	+	0.228178i
$408$		0			0
$409$	1.46362	+	10.1797i	0.0723714	+	0.503354i	0.993476	+	0.114040i	$0.0363791\pi$
$409$	1.46362	+	10.1797i	0.0723714	+	0.503354i	−0.921105	+	0.389315i	$0.872712\pi$
$410$		0			0
$411$	19.4512	−	16.8546i	0.959459	−	0.831376i
$412$		0			0
$413$			5.48748i			0.270021i
$414$		0			0
$415$	35.9253			1.76350
$416$		0			0
$417$	−3.60916	−	4.16520i	−0.176741	−	0.203971i
$418$		0			0
$419$	−9.09133	+	1.30714i	−0.444141	+	0.0638578i	−0.360757	−	0.932660i	$-0.617482\pi$
$419$	−9.09133	+	1.30714i	−0.444141	+	0.0638578i	−0.0833834	+	0.996518i	$0.526573\pi$
$420$		0			0
$421$	−7.70117	−	3.51700i	−0.375332	−	0.171408i	0.218812	−	0.975767i	$-0.429782\pi$
$421$	−7.70117	−	3.51700i	−0.375332	−	0.171408i	−0.594144	+	0.804359i	$0.702509\pi$
$422$		0			0
$423$	−4.13050	+	28.7282i	−0.200832	+	1.39681i
$424$		0			0
$425$	4.47354	+	1.31355i	0.216999	+	0.0637165i
$426$		0			0
$427$	−35.5039	+	16.2141i	−1.71816	+	0.784655i
$428$		0			0
$429$	7.22612	+	6.26147i	0.348880	+	0.302306i
$430$		0			0
$431$	−9.02696	−	5.80128i	−0.434814	−	0.279438i	0.304868	−	0.952395i	$-0.401388\pi$
$431$	−9.02696	−	5.80128i	−0.434814	−	0.279438i	−0.739682	+	0.672957i	$0.765024\pi$
$432$		0			0
$433$	9.21955	−	5.92504i	0.443063	−	0.284739i	−0.300027	−	0.953931i	$-0.596996\pi$
$433$	9.21955	−	5.92504i	0.443063	−	0.284739i	0.743090	+	0.669191i	$0.233359\pi$
$434$		0			0
$435$	−2.93713	−	10.0030i	−0.140825	−	0.479605i
$436$		0			0
$437$	−8.79796	−	4.06324i	−0.420863	−	0.194371i
$438$		0			0
$439$	11.4045	−	3.34867i	0.544308	−	0.159823i	0.00199234	−	0.999998i	$-0.499366\pi$
$439$	11.4045	−	3.34867i	0.544308	−	0.159823i	0.542316	+	0.840175i	$0.317548\pi$
$440$		0			0
$441$	−25.1116	+	16.1383i	−1.19579	+	0.768488i
$442$		0			0
$443$	1.20636	−	1.87713i	0.0573159	−	0.0891852i	−0.811413	−	0.584473i	$-0.801301\pi$
$443$	1.20636	−	1.87713i	0.0573159	−	0.0891852i	0.868729	+	0.495288i	$0.164938\pi$
$444$		0			0
$445$	34.6198	+	29.9983i	1.64114	+	1.42205i
$446$		0			0
$447$	12.1283	+	26.5572i	0.573647	+	1.25611i
$448$		0			0
$449$	−18.6315	−	5.47072i	−0.879277	−	0.258179i	−0.189221	−	0.981935i	$-0.560596\pi$
$449$	−18.6315	−	5.47072i	−0.879277	−	0.258179i	−0.690056	+	0.723756i	$0.742414\pi$
$450$		0			0
$451$	−20.7633	−	2.98531i	−0.977705	−	0.140573i
$452$		0			0
$453$	−22.0114	−	10.0523i	−1.03419	−	0.472298i
$454$		0			0
$455$	3.38193	+	23.5218i	0.158547	+	1.10272i
$456$		0			0
$457$	−6.17617	−	7.12768i	−0.288909	−	0.333419i	0.592679	−	0.805439i	$-0.298070\pi$
$457$	−6.17617	−	7.12768i	−0.288909	−	0.333419i	−0.881588	+	0.472020i	$0.843525\pi$
$458$		0			0
$459$		−	0.587052i		−	0.0274012i
$460$		0			0
$461$			28.8547i			1.34390i	0.740598	+	0.671949i	$0.234543\pi$
$461$			28.8547i			1.34390i	−0.740598	+	0.671949i	$0.765457\pi$
$462$		0			0
$463$	−20.7264	−	23.9195i	−0.963236	−	1.11163i	−0.993697	−	0.112098i	$-0.964243\pi$
$463$	−20.7264	−	23.9195i	−0.963236	−	1.11163i	0.0304610	−	0.999536i	$-0.490302\pi$
$464$		0			0
$465$	−10.1535	−	70.6188i	−0.470855	−	3.27487i
$466$		0			0
$467$	13.6582	+	6.23749i	0.632026	+	0.288637i	0.705554	−	0.708657i	$-0.250698\pi$
$467$	13.6582	+	6.23749i	0.632026	+	0.288637i	−0.0735275	+	0.997293i	$0.523426\pi$
$468$		0			0
$469$	6.70727	+	0.964360i	0.309713	+	0.0445300i
$470$		0			0
$471$	−29.4992	−	8.66175i	−1.35925	−	0.399112i
$472$		0			0
$473$	−0.491911	−	1.07713i	−0.0226181	−	0.0495267i
$474$		0			0
$475$	14.0485	+	12.1731i	0.644590	+	0.558541i
$476$		0			0
$477$	13.4039	−	20.8569i	0.613722	−	0.954971i
$478$		0			0
$479$	14.8705	−	9.55667i	0.679449	−	0.436655i	−0.154872	−	0.987935i	$-0.549497\pi$
$479$	14.8705	−	9.55667i	0.679449	−	0.436655i	0.834321	+	0.551279i	$0.185860\pi$
$480$		0			0
$481$	−2.50631	+	0.735918i	−0.114278	+	0.0335550i
$482$		0			0
$483$	36.8475	+	32.2042i	1.67662	+	1.46534i
$484$		0			0
$485$	−1.48533	−	5.05857i	−0.0674453	−	0.229698i
$486$		0			0
$487$	−1.20320	+	0.773252i	−0.0545223	+	0.0350394i	−0.567618	−	0.823292i	$-0.692135\pi$
$487$	−1.20320	+	0.773252i	−0.0545223	+	0.0350394i	0.513096	+	0.858331i	$0.328499\pi$
$488$		0			0
$489$	22.8173	+	14.6638i	1.03184	+	0.663120i
$490$		0			0
$491$	25.7550	+	22.3168i	1.16231	+	1.00714i	0.999791	+	0.0204371i	$0.00650577\pi$
$491$	25.7550	+	22.3168i	1.16231	+	1.00714i	0.162514	+	0.986706i	$0.448040\pi$
$492$		0			0
$493$	0.543556	−	0.248234i	0.0244805	−	0.0111799i
$494$		0			0
$495$	−25.4610	−	7.47603i	−1.14439	−	0.336023i
$496$		0			0
$497$	−2.45763	+	17.0932i	−0.110240	+	0.766734i
$498$		0			0
$499$	15.2152	+	6.94853i	0.681124	+	0.311059i	0.725763	−	0.687944i	$-0.241487\pi$
$499$	15.2152	+	6.94853i	0.681124	+	0.311059i	−0.0446396	+	0.999003i	$0.514214\pi$
$500$		0			0
$501$	2.83829	−	0.408085i	0.126805	−	0.0182319i
$502$		0			0
$503$	12.3171	+	14.2147i	0.549192	+	0.633801i	0.960695	−	0.277608i	$-0.0895415\pi$
$503$	12.3171	+	14.2147i	0.549192	+	0.633801i	−0.411503	+	0.911408i	$0.634996\pi$
$504$		0			0
$505$	37.0510			1.64875
$506$		0			0
$507$		−	25.5701i		−	1.13561i
$508$		0			0
$509$	−29.0005	+	25.1290i	−1.28542	+	1.11383i	−0.298196	+	0.954505i	$0.596385\pi$
$509$	−29.0005	+	25.1290i	−1.28542	+	1.11383i	−0.987227	+	0.159321i	$0.949070\pi$
$510$		0			0
$511$	−2.82233	−	19.6297i	−0.124852	−	0.868368i
$512$		0			0
$513$	0.972304	−	2.12905i	0.0429283	−	0.0939998i
$514$		0			0
$515$	−7.09515	−	1.02013i	−0.312649	−	0.0449522i
$516$		0			0
$517$	9.16630	−	31.2176i	0.403134	−	1.37295i
$518$		0			0
$519$	3.00552	+	6.58117i	0.131928	+	0.288881i
$520$		0			0
$521$	−18.0677	+	20.8512i	−0.791558	+	0.913507i	−0.997887	−	0.0649758i	$-0.979303\pi$
$521$	−18.0677	+	20.8512i	−0.791558	+	0.913507i	0.206329	+	0.978483i	$0.433848\pi$
$522$		0			0
$523$	9.70638	−	15.1034i	0.424430	−	0.660426i	−0.561520	−	0.827463i	$-0.689783\pi$
$523$	9.70638	−	15.1034i	0.424430	−	0.660426i	0.985951	+	0.167036i	$0.0534198\pi$
$524$		0			0
$525$	−50.7499	−	78.9685i	−2.21491	−	3.44647i
$526$		0			0
$527$	3.92371	−	1.15211i	0.170920	−	0.0501865i
$528$		0			0
$529$	9.73231	−	20.8394i	0.423144	−	0.906062i
$530$		0			0
$531$	−0.891080	−	3.03474i	−0.0386696	−	0.131696i
$532$		0			0
$533$	−5.85376	−	9.10863i	−0.253555	−	0.394539i
$534$		0			0
$535$	−54.9558	−	35.3179i	−2.37594	−	1.52693i
$536$		0			0
$537$	−1.39814	+	1.61354i	−0.0603341	+	0.0696293i
$538$		0			0
$539$	30.4382	−	13.9006i	1.31106	−	0.598743i
$540$		0			0
$541$	−5.80666	+	19.7757i	−0.249648	+	0.850222i	0.735355	+	0.677682i	$0.237015\pi$
$541$	−5.80666	+	19.7757i	−0.249648	+	0.850222i	−0.985003	+	0.172540i	$0.944803\pi$
$542$		0			0
$543$	8.42396	−	58.5899i	0.361507	−	2.51433i
$544$		0			0
$545$	−15.1287	+	33.1272i	−0.648041	+	1.41901i
$546$		0			0
$547$	0.000226772	0	3.26049e-5i	9.69607e−6	0	1.39408e-6i	−0.142310	−	0.989822i	$-0.545453\pi$
$547$	0.000226772	0	3.26049e-5i	9.69607e−6	0	1.39408e-6i	0.142320	+	0.989821i	$0.454544\pi$
$548$		0			0
$549$	17.0018	−	14.7322i	0.725620	−	0.628753i
$550$		0			0
$551$	2.38244			0.101495
$552$		0			0
$553$	−45.6688			−1.94203
$554$		0			0
$555$	12.0364	−	10.4296i	0.510916	−	0.442711i
$556$		0			0
$557$	17.2082	−	2.47416i	0.729134	−	0.104834i	0.232257	−	0.972654i	$-0.425389\pi$
$557$	17.2082	−	2.47416i	0.729134	−	0.104834i	0.496877	+	0.867821i	$0.334480\pi$
$558$		0			0
$559$	0.253906	−	0.555976i	0.0107391	−	0.0235153i
$560$		0			0
$561$	0.475549	−	3.30751i	0.0200777	−	0.139643i
$562$		0			0
$563$	−4.06993	+	13.8609i	−0.171527	+	0.584167i	0.828192	+	0.560445i	$0.189370\pi$
$563$	−4.06993	+	13.8609i	−0.171527	+	0.584167i	−0.999719	+	0.0237221i	$0.992448\pi$
$564$		0			0
$565$	51.9874	−	23.7418i	2.18713	−	0.998827i
$566$		0			0
$567$	−29.1522	+	33.6434i	−1.22428	+	1.41289i
$568$		0			0
$569$	−12.3544	−	7.93970i	−0.517924	−	0.332849i	0.255426	−	0.966828i	$-0.417784\pi$
$569$	−12.3544	−	7.93970i	−0.517924	−	0.332849i	−0.773350	+	0.633979i	$0.781421\pi$
$570$		0			0
$571$	20.9913	+	32.6632i	0.878460	+	1.36691i	0.929736	+	0.368226i	$0.120035\pi$
$571$	20.9913	+	32.6632i	0.878460	+	1.36691i	−0.0512764	+	0.998685i	$0.516329\pi$
$572$		0			0
$573$	9.32710	+	31.7652i	0.389645	+	1.32701i
$574$		0			0
$575$	−29.0328	+	33.2188i	−1.21075	+	1.38532i
$576$		0			0
$577$	40.0050	−	11.7465i	1.66543	−	0.489014i	0.692752	−	0.721175i	$-0.256398\pi$
$577$	40.0050	−	11.7465i	1.66543	−	0.489014i	0.972677	+	0.232161i	$0.0745797\pi$
$578$		0			0
$579$	21.7069	+	33.7766i	0.902109	+	1.40371i
$580$		0			0
$581$	22.4140	−	34.8768i	0.929888	−	1.44693i
$582$		0			0
$583$	−18.2002	+	21.0042i	−0.753775	+	0.869903i
$584$		0			0
$585$	−5.68988	−	12.4591i	−0.235248	−	0.515120i
$586$		0			0
$587$	−5.86972	+	19.9904i	−0.242269	+	0.825094i	0.745140	+	0.666908i	$0.232383\pi$
$587$	−5.86972	+	19.9904i	−0.242269	+	0.825094i	−0.987409	+	0.158186i	$0.949435\pi$
$588$		0			0
$589$	16.1382	+	2.32033i	0.664964	+	0.0956074i
$590$		0			0
$591$	−10.5940	+	23.1976i	−0.435778	+	0.954221i
$592$		0			0
$593$	−1.49188	−	10.3762i	−0.0612641	−	0.426101i	−0.997253	−	0.0740714i	$-0.976401\pi$
$593$	−1.49188	−	10.3762i	−0.0612641	−	0.426101i	0.935989	−	0.352030i	$-0.114508\pi$
$594$		0			0
$595$	6.27639	−	5.43853i	0.257307	−	0.222958i
$596$		0			0
$597$			1.20701i			0.0493995i
$598$		0			0
$599$	−22.5473			−0.921257			−0.460629	−	0.887593i	$-0.652376\pi$
$599$	−22.5473			−0.921257			−0.460629	+	0.887593i	$0.652376\pi$
$600$		0			0
$601$	−4.49088	−	5.18275i	−0.183187	−	0.211409i	0.656727	−	0.754128i	$-0.271940\pi$
$601$	−4.49088	−	5.18275i	−0.183187	−	0.211409i	−0.839914	+	0.542719i	$0.817395\pi$
$602$		0			0
$603$	−3.86592	+	0.555835i	−0.157432	+	0.0226354i
$604$		0			0
$605$	−10.6457	−	4.86174i	−0.432810	−	0.197658i
$606$		0			0
$607$	−6.75226	+	46.9630i	−0.274066	+	1.90617i	0.130130	+	0.991497i	$0.458460\pi$
$607$	−6.75226	+	46.9630i	−0.274066	+	1.90617i	−0.404196	+	0.914672i	$0.632449\pi$
$608$		0			0
$609$	−11.5435	−	3.38948i	−0.467767	−	0.137349i
$610$		0			0
$611$	15.2760	−	6.97631i	0.618001	−	0.282231i
$612$		0			0
$613$	−4.41121	−	3.82233i	−0.178167	−	0.154383i	0.561212	−	0.827672i	$-0.310335\pi$
$613$	−4.41121	−	3.82233i	−0.178167	−	0.154383i	−0.739379	+	0.673290i	$0.764881\pi$
$614$		0			0
$615$	55.5365	+	35.6912i	2.23945	+	1.43921i
$616$		0			0
$617$	10.9555	−	7.04068i	0.441052	−	0.283447i	−0.301208	−	0.953558i	$-0.597390\pi$
$617$	10.9555	−	7.04068i	0.441052	−	0.283447i	0.742261	+	0.670111i	$0.233754\pi$
$618$		0			0
$619$	1.12593	+	3.83457i	0.0452550	+	0.154125i	0.979021	−	0.203760i	$-0.0653163\pi$
$619$	1.12593	+	3.83457i	0.0452550	+	0.154125i	−0.933766	+	0.357885i	$0.883498\pi$
$620$		0			0
$621$	5.04312	+	2.32911i	0.202373	+	0.0934640i
$622$		0			0
$623$	50.7222	−	14.8934i	2.03214	−	0.596691i
$624$		0			0
$625$	11.4660	−	7.36877i	0.458641	−	0.294751i
$626$		0			0
$627$	7.20273	−	11.2077i	0.287649	−	0.447591i
$628$		0			0
$629$	0.689903	+	0.597804i	0.0275082	+	0.0238360i
$630$		0			0
$631$	−8.05333	−	17.6343i	−0.320598	−	0.702011i	0.678882	−	0.734247i	$-0.262465\pi$
$631$	−8.05333	−	17.6343i	−0.320598	−	0.702011i	−0.999480	+	0.0322357i	$0.989737\pi$
$632$		0			0
$633$	−22.9579	−	6.74105i	−0.912495	−	0.267933i
$634$		0			0
$635$	15.1415	+	2.17701i	0.600871	+	0.0863922i
$636$		0			0
$637$	15.7110	+	7.17500i	0.622494	+	0.284284i
$638$		0			0
$639$	−1.41652	−	9.85211i	−0.0560367	−	0.389743i
$640$		0			0
$641$	19.1166	+	22.0618i	0.755061	+	0.871387i	0.995049	−	0.0993890i	$-0.0316888\pi$
$641$	19.1166	+	22.0618i	0.755061	+	0.871387i	−0.239988	+	0.970776i	$0.577143\pi$
$642$		0			0
$643$		−	35.9063i		−	1.41601i	−0.706210	−	0.708003i	$-0.749596\pi$
$643$		−	35.9063i		−	1.41601i	0.706210	−	0.708003i	$-0.250404\pi$
$644$		0			0
$645$			3.72663i			0.146736i
$646$		0			0
$647$	14.9350	+	17.2359i	0.587154	+	0.677612i	0.969127	−	0.246561i	$-0.0793006\pi$
$647$	14.9350	+	17.2359i	0.587154	+	0.677612i	−0.381973	+	0.924174i	$0.624755\pi$
$648$		0			0
$649$	0.504585	+	3.50947i	0.0198067	+	0.137759i
$650$		0			0
$651$	−74.8926	−	34.2023i	−2.93527	−	1.34049i
$652$		0			0
$653$	−12.7167	−	1.82839i	−0.497644	−	0.0715503i	−0.111077	−	0.993812i	$-0.535430\pi$
$653$	−12.7167	−	1.82839i	−0.497644	−	0.0715503i	−0.386567	+	0.922261i	$0.626339\pi$
$654$		0			0
$655$	48.2538	+	14.1686i	1.88543	+	0.553613i
$656$		0			0
$657$	4.74839	+	10.3975i	0.185252	+	0.405646i
$658$		0			0
$659$	−14.5604	−	12.6166i	−0.567192	−	0.491474i	0.323410	−	0.946259i	$-0.395171\pi$
$659$	−14.5604	−	12.6166i	−0.567192	−	0.491474i	−0.890601	+	0.454785i	$0.849716\pi$
$660$		0			0
$661$	−23.3876	+	36.3917i	−0.909670	+	1.41547i	−6.58022e−5		1.00000i	$0.500021\pi$
$661$	−23.3876	+	36.3917i	−0.909670	+	1.41547i	−0.909605	+	0.415475i	$0.863615\pi$
$662$		0			0
$663$	1.45097	−	0.932482i	0.0563510	−	0.0362146i
$664$		0			0
$665$	31.7700	−	9.32852i	1.23199	−	0.361744i
$666$		0			0
$667$	−0.0240695	+	5.65432i	−0.000931976	+	0.218936i
$668$		0			0
$669$	3.33936	+	11.3728i	0.129107	+	0.439699i
$670$		0			0
$671$	−21.2153	+	13.6342i	−0.819007	+	0.526344i
$672$		0			0
$673$	10.0249	+	6.44259i	0.386430	+	0.248343i	0.719403	−	0.694593i	$-0.244415\pi$
$673$	10.0249	+	6.44259i	0.386430	+	0.248343i	−0.332973	+	0.942936i	$0.608052\pi$
$674$		0			0
$675$	−8.05282	−	6.97781i	−0.309953	−	0.268576i
$676$		0			0
$677$	−15.3516	+	7.01085i	−0.590010	+	0.269449i	−0.687967	−	0.725742i	$-0.741497\pi$
$677$	−15.3516	+	7.01085i	−0.590010	+	0.269449i	0.0979566	+	0.995191i	$0.468769\pi$
$678$		0			0
$679$	−5.83763	−	1.71408i	−0.224028	−	0.0657805i
$680$		0			0
$681$	−1.07514	+	7.47776i	−0.0411994	+	0.286548i
$682$		0			0
$683$	21.6742	+	9.89828i	0.829340	+	0.378747i	0.784410	−	0.620243i	$-0.212966\pi$
$683$	21.6742	+	9.89828i	0.829340	+	0.378747i	0.0449307	+	0.998990i	$0.485693\pi$
$684$		0			0
$685$	40.9096	−	5.88191i	1.56307	−	0.224736i
$686$		0			0
$687$	16.6129	+	19.1724i	0.633823	+	0.731471i
$688$		0			0
$689$	−14.3454			−0.546518
$690$		0			0
$691$			35.4576i			1.34887i	0.738334	+	0.674435i	$0.235613\pi$
$691$			35.4576i			1.34887i	−0.738334	+	0.674435i	$0.764387\pi$
$692$		0			0
$693$	−23.1431	+	20.0536i	−0.879134	+	0.761774i
$694$		0			0
$695$	−1.25952	−	8.76019i	−0.0477765	−	0.332293i
$696$		0			0
$697$	−1.57190	+	3.44199i	−0.0595401	+	0.130375i
$698$		0			0
$699$	−59.9864	−	8.62474i	−2.26889	−	0.326218i
$700$		0			0
$701$	−6.13170	+	20.8826i	−0.231591	+	0.788727i	0.758907	+	0.651199i	$0.225734\pi$
$701$	−6.13170	+	20.8826i	−0.231591	+	0.788727i	−0.990498	+	0.137528i	$0.956084\pi$
$702$		0			0
$703$	1.51194	+	3.31069i	0.0570240	+	0.124865i
$704$		0			0
$705$	−67.0530	+	77.3833i	−2.52536	+	2.91443i
$706$		0			0
$707$	23.1163	−	35.9697i	0.869378	−	1.35278i
$708$		0			0
$709$	−24.1178	−	37.5281i	−0.905764	−	1.40940i	−0.912347	−	0.409419i	$-0.865732\pi$
$709$	−24.1178	−	37.5281i	−0.905764	−	1.40940i	0.00658224	−	0.999978i	$-0.497905\pi$
$710$		0			0
$711$	25.2562	−	7.41589i	0.947181	−	0.278118i
$712$		0			0
$713$	−5.66995	+	38.2779i	−0.212341	+	1.43352i
$714$		0			0
$715$	4.32577	+	14.7322i	0.161774	+	0.550953i
$716$		0			0
$717$	28.4893	+	44.3302i	1.06395	+	1.65554i
$718$		0			0
$719$	−33.4839	−	21.5188i	−1.24874	−	0.802516i	−0.262038	−	0.965058i	$-0.584395\pi$
$719$	−33.4839	−	21.5188i	−1.24874	−	0.802516i	−0.986702	+	0.162541i	$0.948031\pi$
$720$		0			0
$721$	−5.41705	+	6.25161i	−0.201741	+	0.232822i
$722$		0			0
$723$	−28.1511	+	12.8562i	−1.04695	+	0.478126i
$724$		0			0
$725$	3.05569	−	10.4067i	0.113485	−	0.386496i
$726$		0			0
$727$	−1.66744	+	11.5973i	−0.0618421	+	0.430121i	0.935255	+	0.353976i	$0.115170\pi$
$727$	−1.66744	+	11.5973i	−0.0618421	+	0.430121i	−0.997097	+	0.0761455i	$0.975739\pi$
$728$		0			0
$729$	7.27155	−	15.9225i	0.269317	−	0.589722i
$730$		0			0
$731$	−0.211429	+	0.0303990i	−0.00782000	+	0.00112435i
$732$		0			0
$733$	−25.6740	+	22.2466i	−0.948290	+	0.821698i	−0.984092	−	0.177661i	$-0.943147\pi$
$733$	−25.6740	+	22.2466i	−0.948290	+	0.821698i	0.0358014	+	0.999359i	$0.488602\pi$
$734$		0			0
$735$	−105.309			−3.88438
$736$		0			0
$737$	4.37825			0.161275
$738$		0			0
$739$	−35.8290	+	31.0460i	−1.31799	+	1.14204i	−0.338408	+	0.941000i	$0.609888\pi$
$739$	−35.8290	+	31.0460i	−1.31799	+	1.14204i	−0.979582	+	0.201045i	$0.935566\pi$
$740$		0			0
$741$	6.80662	−	0.978645i	0.250048	−	0.0359514i
$742$		0			0
$743$	−7.71882	+	16.9019i	−0.283176	+	0.620069i	−0.996754	−	0.0805067i	$-0.974346\pi$
$743$	−7.71882	+	16.9019i	−0.283176	+	0.620069i	0.713578	+	0.700576i	$0.247073\pi$
$744$		0			0
$745$	−6.67215	+	46.4058i	−0.244448	+	1.70018i
$746$		0			0
$747$	−6.73215	+	22.9276i	−0.246316	+	0.838876i
$748$		0			0
$749$	−68.5743	+	31.3168i	−2.50565	+	1.14429i
$750$		0			0
$751$	−17.8831	+	20.6382i	−0.652562	+	0.753097i	−0.981543	−	0.191240i	$-0.938749\pi$
$751$	−17.8831	+	20.6382i	−0.652562	+	0.753097i	0.328981	+	0.944336i	$0.393295\pi$
$752$		0			0
$753$	40.4657	+	26.0057i	1.47465	+	0.947701i
$754$		0			0
$755$	−21.0083	−	32.6895i	−0.764570	−	1.18969i
$756$		0			0
$757$	10.9495	+	37.2905i	0.397966	+	1.35535i	0.878236	+	0.478227i	$0.158720\pi$
$757$	10.9495	+	37.2905i	0.397966	+	1.35535i	−0.480270	+	0.877120i	$0.659461\pi$
$758$		0			0
$759$	26.5267	+	17.2077i	0.962860	+	0.624600i
$760$		0			0
$761$	−20.5414	+	6.03149i	−0.744624	+	0.218641i	−0.631970	−	0.774993i	$-0.717753\pi$
$761$	−20.5414	+	6.03149i	−0.744624	+	0.218641i	−0.112654	+	0.993634i	$0.535935\pi$
$762$		0			0
$763$	22.7215	+	35.3553i	0.822573	+	1.27995i
$764$		0			0
$765$	−2.58790	+	4.02685i	−0.0935657	+	0.145591i
$766$		0			0
$767$	−1.19845	+	1.38309i	−0.0432735	+	0.0499403i
$768$		0			0
$769$	20.0017	+	43.7976i	0.721280	+	1.57938i	0.812102	+	0.583515i	$0.198323\pi$
$769$	20.0017	+	43.7976i	0.721280	+	1.57938i	−0.0908222	+	0.995867i	$0.528950\pi$
$770$		0			0
$771$	−5.76496	+	19.6337i	−0.207620	+	0.707089i
$772$		0			0
$773$	19.2235	+	2.76392i	0.691421	+	0.0994113i	0.479063	−	0.877781i	$-0.340977\pi$
$773$	19.2235	+	2.76392i	0.691421	+	0.0994113i	0.212358	+	0.977192i	$0.431886\pi$
$774$		0			0
$775$	30.8341	−	67.5173i	1.10759	−	2.42529i
$776$		0			0
$777$	−2.61564	−	18.1922i	−0.0938355	−	0.652640i
$778$		0			0
$779$	−11.4016	+	9.87953i	−0.408504	+	0.353971i
$780$		0			0
$781$			11.1578i			0.399256i
$782$		0			0
$783$	−1.36565			−0.0488043
$784$		0			0
$785$	−32.3308	−	37.3117i	−1.15394	−	1.33171i
$786$		0			0
$787$	20.2238	−	2.90775i	0.720902	−	0.103650i	0.227908	−	0.973683i	$-0.426812\pi$
$787$	20.2238	−	2.90775i	0.720902	−	0.103650i	0.492994	+	0.870033i	$0.335902\pi$
$788$		0			0
$789$	−11.0508	−	5.04674i	−0.393420	−	0.179669i
$790$		0			0
$791$	9.38624	−	65.2828i	0.333736	−	2.32119i
$792$		0			0
$793$	−12.4897	−	3.66730i	−0.443521	−	0.130230i
$794$		0			0
$795$	79.5619	−	36.3347i	2.82177	−	1.28866i
$796$		0			0
$797$	12.8296	+	11.1169i	0.454447	+	0.393781i	0.851785	−	0.523892i	$-0.175520\pi$
$797$	12.8296	+	11.1169i	0.454447	+	0.393781i	−0.397338	+	0.917672i	$0.630066\pi$
$798$		0			0
$799$	−4.93729	−	3.17300i	−0.174669	−	0.112253i
$800$		0			0
$801$	−25.6324	+	16.4730i	−0.905678	+	0.582044i
$802$		0			0
$803$	−3.60999	−	12.2945i	−0.127394	−	0.433863i
$804$		0			0
$805$	21.8187	+	75.4951i	0.769008	+	2.66085i
$806$		0			0
$807$	9.55029	−	2.80422i	0.336186	−	0.0987131i
$808$		0			0
$809$	−9.55545	+	6.14091i	−0.335952	+	0.215903i	−0.697730	−	0.716361i	$-0.745806\pi$
$809$	−9.55545	+	6.14091i	−0.335952	+	0.215903i	0.361778	+	0.932264i	$0.382170\pi$
$810$		0			0
$811$	12.1494	−	18.9048i	0.426622	−	0.663837i	−0.559695	−	0.828699i	$-0.689082\pi$
$811$	12.1494	−	18.9048i	0.426622	−	0.663837i	0.986317	+	0.164862i	$0.0527179\pi$
$812$		0			0
$813$	−4.90479	−	4.25003i	−0.172019	−	0.149055i
$814$		0			0
$815$	18.0933	+	39.6189i	0.633782	+	1.38779i
$816$		0			0
$817$	−0.817135	−	0.239932i	−0.0285879	−	0.00839417i
$818$		0			0
$819$	−15.6454	−	2.24947i	−0.546695	−	0.0786029i
$820$		0			0
$821$	1.79090	+	0.817876i	0.0625028	+	0.0285441i	0.446421	−	0.894823i	$-0.352698\pi$
$821$	1.79090	+	0.817876i	0.0625028	+	0.0285441i	−0.383918	+	0.923367i	$0.625426\pi$
$822$		0			0
$823$	−0.839493	−	5.83880i	−0.0292629	−	0.203528i	0.969945	−	0.243325i	$-0.0782380\pi$
$823$	−0.839493	−	5.83880i	−0.0292629	−	0.203528i	−0.999208	+	0.0397968i	$0.987329\pi$
$824$		0			0
$825$	−39.7180	−	45.8370i	−1.38280	−	1.59584i
$826$		0			0
$827$			44.5253i			1.54830i	0.633003	+	0.774149i	$0.281822\pi$
$827$			44.5253i			1.54830i	−0.633003	+	0.774149i	$0.718178\pi$
$828$		0			0
$829$		−	49.1041i		−	1.70546i	−0.522354	−	0.852729i	$-0.674946\pi$
$829$		−	49.1041i		−	1.70546i	0.522354	−	0.852729i	$-0.325054\pi$
$830$		0			0
$831$	10.3782	+	11.9770i	0.360014	+	0.415479i
$832$		0			0
$833$	−0.859028	−	5.97467i	−0.0297636	−	0.207010i
$834$		0			0
$835$	4.18856	+	1.91285i	0.144951	+	0.0661969i
$836$		0			0
$837$	−9.25067	−	1.33004i	−0.319750	−	0.0459731i
$838$		0			0
$839$	25.6433	+	7.52955i	0.885304	+	0.259949i	0.692612	−	0.721310i	$-0.256460\pi$
$839$	25.6433	+	7.52955i	0.885304	+	0.259949i	0.192692	+	0.981259i	$0.438278\pi$
$840$		0			0
$841$	11.4696	+	25.1149i	0.395503	+	0.866030i
$842$		0			0
$843$	−27.0830	−	23.4675i	−0.932786	−	0.808264i
$844$		0			0
$845$	22.1994	−	34.5429i	0.763681	−	1.18831i
$846$		0			0
$847$	−11.3618	+	7.30176i	−0.390395	+	0.250891i
$848$		0			0
$849$	15.0709	−	4.42522i	0.517233	−	0.151873i
$850$		0			0
$851$	−7.87265	+	3.55490i	−0.269871	+	0.121860i
$852$		0			0
$853$	−15.9516	−	54.3261i	−0.546172	−	1.86009i	−0.508971	−	0.860784i	$-0.669974\pi$
$853$	−15.9516	−	54.3261i	−0.546172	−	1.86009i	−0.0372009	−	0.999308i	$-0.511844\pi$
$854$		0			0
$855$	−16.0550	+	10.3179i	−0.549068	+	0.352864i
$856$		0			0
$857$	−16.5433	−	10.6317i	−0.565108	−	0.363173i	0.226680	−	0.973969i	$-0.427213\pi$
$857$	−16.5433	−	10.6317i	−0.565108	−	0.363173i	−0.791788	+	0.610797i	$0.790849\pi$
$858$		0			0
$859$	−11.1325	−	9.64636i	−0.379836	−	0.329129i	0.443928	−	0.896062i	$-0.353584\pi$
$859$	−11.1325	−	9.64636i	−0.379836	−	0.329129i	−0.823764	+	0.566933i	$0.808130\pi$
$860$		0			0
$861$	69.2990	−	31.6478i	2.36170	−	1.07855i
$862$		0			0
$863$	19.7261	+	5.79210i	0.671483	+	0.197165i	0.599663	−	0.800252i	$-0.295301\pi$
$863$	19.7261	+	5.79210i	0.671483	+	0.197165i	0.0718198	+	0.997418i	$0.477119\pi$
$864$		0			0
$865$	−1.65343	+	11.4999i	−0.0562184	+	0.391008i
$866$		0			0
$867$	35.7385	+	16.3212i	1.21374	+	0.554297i
$868$		0			0
$869$	−29.2071	+	4.19934i	−0.990782	+	0.142453i
$870$		0			0
$871$	1.47991	+	1.70791i	0.0501450	+	0.0578704i
$872$		0			0
$873$	3.50672			0.118685
$874$		0			0
$875$		−	68.8088i		−	2.32616i
$876$		0			0
$877$	41.8601	−	36.2720i	1.41352	−	1.22482i	0.474816	−	0.880085i	$-0.342515\pi$
$877$	41.8601	−	36.2720i	1.41352	−	1.22482i	0.938700	−	0.344734i	$-0.112031\pi$
$878$		0			0
$879$	2.87774	+	20.0151i	0.0970637	+	0.675093i
$880$		0			0
$881$	10.0822	−	22.0770i	0.339679	−	0.743792i	−0.660295	−	0.751006i	$-0.729569\pi$
$881$	10.0822	−	22.0770i	0.339679	−	0.743792i	0.999974	+	0.00721360i	$0.00229618\pi$
$882$		0			0
$883$	−40.5406	−	5.82886i	−1.36430	−	0.196157i	−0.579028	−	0.815308i	$-0.696568\pi$
$883$	−40.5406	−	5.82886i	−1.36430	−	0.196157i	−0.785272	+	0.619151i	$0.787477\pi$
$884$		0			0
$885$	3.14365	−	10.7063i	0.105673	−	0.359888i
$886$		0			0
$887$	−1.02700	−	2.24881i	−0.0344832	−	0.0755076i	0.891607	−	0.452811i	$-0.149579\pi$
$887$	−1.02700	−	2.24881i	−0.0344832	−	0.0755076i	−0.926090	+	0.377303i	$0.876851\pi$
$888$		0			0
$889$	11.5603	−	13.3413i	0.387720	−	0.447453i
$890$		0			0
$891$	−15.5504	+	24.1970i	−0.520959	+	0.810629i
$892$		0			0
$893$	−12.6507	−	19.6848i	−0.423339	−	0.658728i
$894$		0			0
$895$	−3.28959	+	0.965912i	−0.109959	+	0.0322869i
$896$		0			0
$897$	2.25388	+	16.1643i	0.0752550	+	0.539709i
$898$		0			0
$899$	−2.68013	−	9.12768i	−0.0893873	−	0.304425i
$900$		0			0
$901$	2.71045	+	4.21753i	0.0902980	+	0.140506i
$902$		0			0
$903$	3.61787	+	2.32506i	0.120395	+	0.0773732i
$904$		0			0
$905$	62.2464	−	71.8361i	2.06914	−	2.38791i
$906$		0			0
$907$	−1.83239	+	0.836822i	−0.0608433	+	0.0277862i	−0.445604	−	0.895230i	$-0.647011\pi$
$907$	−1.83239	+	0.836822i	−0.0608433	+	0.0277862i	0.384761	+	0.923016i	$0.374284\pi$
$908$		0			0
$909$	−6.94309	+	23.6460i	−0.230288	+	0.784289i
$910$		0			0
$911$	−6.52745	+	45.3994i	−0.216264	+	1.50415i	0.535398	+	0.844600i	$0.320162\pi$
$911$	−6.52745	+	45.3994i	−0.216264	+	1.50415i	−0.751662	+	0.659549i	$0.770747\pi$
$912$		0			0
$913$	11.1277	−	24.3662i	0.368272	−	0.806402i
$914$		0			0
$915$	78.5582	−	11.2950i	2.59705	−	0.373400i
$916$		0			0
$917$	43.8608	−	38.0056i	1.44841	−	1.25506i
$918$		0			0
$919$	−20.3140			−0.670096			−0.335048	−	0.942201i	$-0.608753\pi$
$919$	−20.3140			−0.670096			−0.335048	+	0.942201i	$0.608753\pi$
$920$		0			0
$921$	49.5528			1.63282
$922$		0			0
$923$	−4.35253	+	3.77149i	−0.143265	+	0.124140i
$924$		0			0
$925$	16.4006	−	2.35805i	0.539249	−	0.0775323i
$926$		0			0
$927$	1.98063	−	4.33697i	0.0650523	−	0.142445i
$928$		0			0
$929$	−0.277648	+	1.93108i	−0.00910934	+	0.0633568i	−0.993869	−	0.110564i	$-0.964734\pi$
$929$	−0.277648	+	1.93108i	−0.00910934	+	0.0633568i	0.984760	+	0.173920i	$0.0556435\pi$
$930$		0			0
$931$	6.78012	−	23.0910i	0.222210	−	0.756776i
$932$		0			0
$933$	31.5949	−	14.4289i	1.03437	−	0.472381i
$934$		0			0
$935$	3.51393	−	4.05529i	0.114918	−	0.132622i
$936$		0			0
$937$	−41.5535	−	26.7048i	−1.35749	−	0.872408i	−0.359343	−	0.933206i	$-0.616999\pi$
$937$	−41.5535	−	26.7048i	−1.35749	−	0.872408i	−0.998150	+	0.0607977i	$0.980636\pi$
$938$		0			0
$939$	2.78576	+	4.33472i	0.0909098	+	0.141458i
$940$		0			0
$941$	0.942988	+	3.21152i	0.0307405	+	0.104693i	0.973434	−	0.228967i	$-0.0735347\pi$
$941$	0.942988	+	3.21152i	0.0307405	+	0.104693i	−0.942694	+	0.333659i	$0.891716\pi$
$942$		0			0
$943$	−23.3322	−	27.1596i	−0.759802	−	0.884437i
$944$		0			0
$945$	−18.2110	+	5.34724i	−0.592405	+	0.173946i
$946$		0			0
$947$	−32.2646	−	50.2048i	−1.04846	−	1.63144i	−0.729928	−	0.683524i	$-0.760447\pi$
$947$	−32.2646	−	50.2048i	−1.04846	−	1.63144i	−0.318532	−	0.947912i	$-0.603190\pi$
$948$		0			0
$949$	3.57573	−	5.56394i	0.116073	−	0.180613i
$950$		0			0
$951$	41.2164	−	47.5663i	1.33653	−	1.54244i
$952$		0			0
$953$	−9.93661	−	21.7581i	−0.321878	−	0.704815i	0.677654	−	0.735380i	$-0.262997\pi$
$953$	−9.93661	−	21.7581i	−0.321878	−	0.704815i	−0.999533	+	0.0305653i	$0.990269\pi$
$954$		0			0
$955$	−14.9777	+	51.0094i	−0.484667	+	1.65063i
$956$		0			0
$957$	−7.69422	−	1.10626i	−0.248719	−	0.0357604i
$958$		0			0
$959$	19.8134	−	43.3854i	0.639809	−	1.40099i
$960$		0			0
$961$	−4.85324	−	33.7550i	−0.156556	−	1.08887i
$962$		0			0
$963$	32.8383	−	28.4545i	1.05820	−	0.916934i
$964$		0			0
$965$			64.4746i			2.07551i
$966$		0			0
$967$	−11.7429			−0.377627			−0.188813	−	0.982013i	$-0.560464\pi$
$967$	−11.7429			−0.377627			−0.188813	+	0.982013i	$0.560464\pi$
$968$		0			0
$969$	−1.57377	−	1.81623i	−0.0505568	−	0.0583457i
$970$		0			0
$971$	5.97258	−	0.858727i	0.191669	−	0.0275579i	−0.0458117	−	0.998950i	$-0.514587\pi$
$971$	5.97258	−	0.858727i	0.191669	−	0.0275579i	0.237481	+	0.971392i	$0.423678\pi$
$972$		0			0
$973$	−9.29034	−	4.24276i	−0.297835	−	0.136017i
$974$		0			0
$975$	4.45528	−	30.9872i	0.142683	−	0.992384i
$976$		0			0
$977$	20.1171	+	5.90692i	0.643604	+	0.188979i	0.587217	−	0.809430i	$-0.300224\pi$
$977$	20.1171	+	5.90692i	0.643604	+	0.188979i	0.0563872	+	0.998409i	$0.482042\pi$
$978$		0			0
$979$	31.0695	−	14.1890i	0.992985	−	0.453481i
$980$		0			0
$981$	−18.3068	−	15.8629i	−0.584491	−	0.506464i
$982$		0			0
$983$	−24.0028	−	15.4257i	−0.765572	−	0.492003i	0.0986451	−	0.995123i	$-0.468549\pi$
$983$	−24.0028	−	15.4257i	−0.765572	−	0.492003i	−0.864217	+	0.503120i	$0.832186\pi$
$984$		0			0
$985$	−34.4511	+	22.1404i	−1.09770	+	0.705451i
$986$		0			0
$987$	33.2902	+	113.376i	1.05964	+	3.60879i
$988$		0			0
$989$	0.577695	−	1.93691i	0.0183696	−	0.0615901i
$990$		0			0
$991$	25.4809	−	7.48187i	0.809427	−	0.237669i	0.149270	−	0.988797i	$-0.452308\pi$
$991$	25.4809	−	7.48187i	0.809427	−	0.237669i	0.660157	+	0.751127i	$0.270490\pi$
$992$		0			0
$993$	21.5654	−	13.8593i	0.684358	−	0.439810i
$994$		0			0
$995$	−1.04790	+	1.63056i	−0.0332205	+	0.0516921i
$996$		0			0
$997$	−31.6297	−	27.4073i	−1.00172	−	0.867999i	−0.0104670	−	0.999945i	$-0.503332\pi$
$997$	−31.6297	−	27.4073i	−1.00172	−	0.867999i	−0.991257	+	0.131947i	$0.957877\pi$
$998$		0			0
$999$	−0.866668	−	1.89774i	−0.0274202	−	0.0600418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	736.2.x.a.561.3		220
4.3	odd	2		184.2.p.a.101.3	✓	220
8.3	odd	2		184.2.p.a.101.7	yes	220
8.5	even	2	inner	736.2.x.a.561.20		220
23.18	even	11	inner	736.2.x.a.593.20		220
92.87	odd	22		184.2.p.a.133.7	yes	220
184.133	even	22	inner	736.2.x.a.593.3		220
184.179	odd	22		184.2.p.a.133.3	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.p.a.101.3	✓	220	4.3	odd	2
184.2.p.a.101.7	yes	220	8.3	odd	2
184.2.p.a.133.3	yes	220	184.179	odd	22
184.2.p.a.133.7	yes	220	92.87	odd	22
736.2.x.a.561.3		220	1.1	even	1	trivial
736.2.x.a.561.20		220	8.5	even	2	inner
736.2.x.a.593.3		220	184.133	even	22	inner
736.2.x.a.593.20		220	23.18	even	11	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:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	736.x (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.77342 + 1.53668i) q^{3} +(-3.72983 + 0.536269i) q^{5} +(-1.80644 + 3.95556i) q^{7} +(0.356696 - 2.48088i) q^{9} +O(q^{10})\)	\(q+(-1.77342 + 1.53668i) q^{3} +(-3.72983 + 0.536269i) q^{5} +(-1.80644 + 3.95556i) q^{7} +(0.356696 - 2.48088i) q^{9} +(-0.791572 + 2.69585i) q^{11} +(-1.31919 + 0.602452i) q^{13} +(5.79048 - 6.68257i) q^{15} +(0.426368 + 0.274010i) q^{17} +(1.09247 + 1.69992i) q^{19} +(-2.87483 - 9.79078i) q^{21} +(-4.04551 + 2.57562i) q^{23} +(8.82660 - 2.59172i) q^{25} +(-0.626221 - 0.974418i) q^{27} +(0.637426 - 0.991854i) q^{29} +(5.28380 - 6.09783i) q^{31} +(-2.73886 - 5.99726i) q^{33} +(4.61648 - 15.7223i) q^{35} +(1.78283 + 0.256332i) q^{37} +(1.41370 - 3.09556i) q^{39} +(1.06252 + 7.38997i) q^{41} +(-0.318514 + 0.275994i) q^{43} +9.44454i q^{45} -11.5799 q^{47} +(-7.79917 - 9.00072i) q^{49} +(-1.17719 + 0.169255i) q^{51} +(8.99787 + 4.10919i) q^{53} +(1.50673 - 10.4796i) q^{55} +(-4.54963 - 1.33589i) q^{57} +(1.14788 - 0.524220i) q^{59} +(6.78339 + 5.87784i) q^{61} +(9.16890 + 5.89249i) q^{63} +(4.59726 - 2.95448i) q^{65} +(-0.439020 - 1.49516i) q^{67} +(3.21648 - 10.7843i) q^{69} +(3.81036 - 1.11882i) q^{71} +(-3.83656 + 2.46561i) q^{73} +(-11.6706 + 18.1598i) q^{75} +(-9.23365 - 8.00100i) q^{77} +(4.36275 + 9.55308i) q^{79} +(9.82250 + 2.88415i) q^{81} +(-9.43680 - 1.35681i) q^{83} +(-1.73723 - 0.793364i) q^{85} +(0.393735 + 2.73849i) q^{87} +(-7.96093 - 9.18740i) q^{89} -6.30641i q^{91} +18.9335i q^{93} +(-4.98635 - 5.75455i) q^{95} +(0.199115 + 1.38487i) q^{97} +(6.40571 + 2.92539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 22 q^{7}+O(q^{10}) \) 220 * q + 22 * q^7	\( 220 q + 22 q^{7} + 22 q^{15} - 18 q^{17} + 16 q^{23} - 4 q^{25} + 34 q^{31} - 30 q^{33} + 18 q^{39} - 18 q^{41} + 40 q^{47} - 28 q^{49} + 38 q^{55} - 30 q^{57} - 18 q^{63} - 38 q^{65} + 26 q^{71} - 18 q^{73} + 22 q^{79} - 52 q^{81} + 42 q^{87} - 2 q^{89} + 78 q^{95} - 18 q^{97}+O(q^{100}) \) 220 * q + 22 * q^7 + 22 * q^15 - 18 * q^17 + 16 * q^23 - 4 * q^25 + 34 * q^31 - 30 * q^33 + 18 * q^39 - 18 * q^41 + 40 * q^47 - 28 * q^49 + 38 * q^55 - 30 * q^57 - 18 * q^63 - 38 * q^65 + 26 * q^71 - 18 * q^73 + 22 * q^79 - 52 * q^81 + 42 * q^87 - 2 * q^89 + 78 * q^95 - 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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