LMFDB - Embedded newform 675.2.l.h.151.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.5
Character	$\chi$	$=$	675.151
Dual form			675.2.l.h.76.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.990387 - 0.831033i) q^{2} +(-1.55212 - 0.768718i) q^{3} +(-0.0570464 - 0.323526i) q^{4} +(0.898367 + 2.05119i) q^{6} +(-0.134907 + 0.765094i) q^{7} +(-1.50522 + 2.60712i) q^{8} +(1.81814 + 2.38628i) q^{9} +(3.66139 - 1.33264i) q^{11} +(-0.160158 + 0.546003i) q^{12} +(3.91983 - 3.28913i) q^{13} +(0.769429 - 0.645628i) q^{14} +(3.03995 - 1.10645i) q^{16} +(-1.95315 - 3.38295i) q^{17} +(0.182416 - 3.87428i) q^{18} +(1.51356 - 2.62156i) q^{19} +(0.797534 - 1.08381i) q^{21} +(-4.73366 - 1.72291i) q^{22} +(0.560532 + 3.17893i) q^{23} +(4.34042 - 2.88947i) q^{24} -6.61553 q^{26} +(-0.987594 - 5.10144i) q^{27} +0.255224 q^{28} +(0.271790 + 0.228059i) q^{29} +(-0.470061 - 2.66585i) q^{31} +(1.72756 + 0.628781i) q^{32} +(-6.70734 - 0.746168i) q^{33} +(-0.876974 + 4.97357i) q^{34} +(0.668307 - 0.724346i) q^{36} +(-2.13678 - 3.70101i) q^{37} +(-3.67761 + 1.33854i) q^{38} +(-8.61246 + 2.09187i) q^{39} +(-9.24182 + 7.75481i) q^{41} +(-1.69055 + 0.410616i) q^{42} +(-0.331124 + 0.120519i) q^{43} +(-0.640012 - 1.10853i) q^{44} +(2.08666 - 3.61420i) q^{46} +(-0.455464 + 2.58307i) q^{47} +(-5.56890 - 0.619521i) q^{48} +(6.01068 + 2.18771i) q^{49} +(0.430980 + 6.75217i) q^{51} +(-1.28773 - 1.08053i) q^{52} +9.29215 q^{53} +(-3.26136 + 5.87312i) q^{54} +(-1.79163 - 1.50335i) q^{56} +(-4.36446 + 2.90547i) q^{57} +(-0.0796526 - 0.451732i) q^{58} +(-12.4304 - 4.52430i) q^{59} +(1.14463 - 6.49154i) q^{61} +(-1.74987 + 3.03086i) q^{62} +(-2.07101 + 1.06913i) q^{63} +(-4.42346 - 7.66166i) q^{64} +(6.02277 + 6.31302i) q^{66} +(3.04985 - 2.55913i) q^{67} +(-0.983053 + 0.824880i) q^{68} +(1.57369 - 5.36497i) q^{69} +(-6.06946 - 10.5126i) q^{71} +(-8.95804 + 1.14823i) q^{72} +(7.04497 - 12.2022i) q^{73} +(-0.959425 + 5.44117i) q^{74} +(-0.934485 - 0.340125i) q^{76} +(0.525647 + 2.98109i) q^{77} +(10.2681 + 5.08548i) q^{78} +(-8.85574 - 7.43085i) q^{79} +(-2.38871 + 8.67722i) q^{81} +15.5975 q^{82} +(-4.25966 - 3.57428i) q^{83} +(-0.396138 - 0.196195i) q^{84} +(0.428097 + 0.155815i) q^{86} +(-0.246537 - 0.562904i) q^{87} +(-2.03686 + 11.5516i) q^{88} +(2.60530 - 4.51251i) q^{89} +(1.98768 + 3.44277i) q^{91} +(0.996492 - 0.362693i) q^{92} +(-1.31970 + 4.49906i) q^{93} +(2.59770 - 2.17973i) q^{94} +(-2.19803 - 2.30395i) q^{96} +(6.68077 - 2.43160i) q^{97} +(-4.13484 - 7.16175i) q^{98} +(9.83699 + 6.31420i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.990387	−	0.831033i	−0.700309	−	0.587629i	0.221552	−	0.975149i	$-0.428888\pi$
$2$	−0.990387	−	0.831033i	−0.700309	−	0.587629i	−0.921862	+	0.387519i	$0.873332\pi$
$3$	−1.55212	−	0.768718i	−0.896116	−	0.443820i
$3$	−1.55212	−	0.768718i	−0.896116	−	0.443820i
$4$	−0.0570464	−	0.323526i	−0.0285232	−	0.161763i
$5$		0			0
$5$		0			0
$6$	0.898367	+	2.05119i	0.366757	+	0.837395i
$7$	−0.134907	+	0.765094i	−0.0509900	+	0.289179i	−0.999631	−	0.0271771i	$-0.991348\pi$
$7$	−0.134907	+	0.765094i	−0.0509900	+	0.289179i	0.948641	+	0.316356i	$0.102459\pi$
$8$	−1.50522	+	2.60712i	−0.532176	+	0.921756i
$9$	1.81814	+	2.38628i	0.606048	+	0.795428i
$10$		0			0
$11$	3.66139	−	1.33264i	1.10395	−	0.401805i	0.275180	−	0.961393i	$-0.411263\pi$
$11$	3.66139	−	1.33264i	1.10395	−	0.401805i	0.828771	+	0.559587i	$0.189040\pi$
$12$	−0.160158	+	0.546003i	−0.0462335	+	0.157618i
$13$	3.91983	−	3.28913i	1.08717	−	0.912240i	0.0906695	−	0.995881i	$-0.471099\pi$
$13$	3.91983	−	3.28913i	1.08717	−	0.912240i	0.996496	+	0.0836409i	$0.0266549\pi$
$14$	0.769429	−	0.645628i	0.205639	−	0.172551i
$15$		0			0
$16$	3.03995	−	1.10645i	0.759986	−	0.276612i
$17$	−1.95315	−	3.38295i	−0.473708	−	0.820487i	0.525839	−	0.850584i	$-0.323752\pi$
$17$	−1.95315	−	3.38295i	−0.473708	−	0.820487i	−0.999547	+	0.0300976i	$0.990418\pi$
$18$	0.182416	−	3.87428i	0.0429959	−	0.913177i
$19$	1.51356	−	2.62156i	0.347234	−	0.601427i	−0.638523	−	0.769603i	$-0.720454\pi$
$19$	1.51356	−	2.62156i	0.347234	−	0.601427i	0.985757	+	0.168176i	$0.0537877\pi$
$20$		0			0
$21$	0.797534	−	1.08381i	0.174036	−	0.236507i
$22$	−4.73366	−	1.72291i	−1.00922	−	0.367326i
$23$	0.560532	+	3.17893i	0.116879	+	0.662854i	0.985803	+	0.167908i	$0.0537010\pi$
$23$	0.560532	+	3.17893i	0.116879	+	0.662854i	−0.868924	+	0.494946i	$0.835188\pi$
$24$	4.34042	−	2.88947i	0.885985	−	0.589810i
$25$		0			0
$26$	−6.61553			−1.29741
$27$	−0.987594	−	5.10144i	−0.190062	−	0.981772i
$28$	0.255224			0.0482328
$29$	0.271790	+	0.228059i	0.0504701	+	0.0423494i	0.667674	−	0.744454i	$-0.267290\pi$
$29$	0.271790	+	0.228059i	0.0504701	+	0.0423494i	−0.617204	+	0.786803i	$0.711735\pi$
$30$		0			0
$31$	−0.470061	−	2.66585i	−0.0844255	−	0.478801i	−0.997479	−	0.0709611i	$-0.977393\pi$
$31$	−0.470061	−	2.66585i	−0.0844255	−	0.478801i	0.913054	−	0.407840i	$-0.133718\pi$
$32$	1.72756	+	0.628781i	0.305393	+	0.111154i
$33$	−6.70734	−	0.746168i	−1.16760	−	0.129891i
$34$	−0.876974	+	4.97357i	−0.150400	+	0.852959i
$35$		0			0
$36$	0.668307	−	0.724346i	0.111384	−	0.120724i
$37$	−2.13678	−	3.70101i	−0.351285	−	0.608443i	0.635190	−	0.772356i	$-0.280922\pi$
$37$	−2.13678	−	3.70101i	−0.351285	−	0.608443i	−0.986475	+	0.163913i	$0.947588\pi$
$38$	−3.67761	+	1.33854i	−0.596587	+	0.217140i
$39$	−8.61246	+	2.09187i	−1.37910	+	0.334967i
$40$		0			0
$41$	−9.24182	+	7.75481i	−1.44333	+	1.21110i	−0.506059	+	0.862499i	$0.668898\pi$
$41$	−9.24182	+	7.75481i	−1.44333	+	1.21110i	−0.937272	+	0.348599i	$0.886658\pi$
$42$	−1.69055	+	0.410616i	−0.260858	+	0.0633595i
$43$	−0.331124	+	0.120519i	−0.0504960	+	0.0183790i	−0.367145	−	0.930164i	$-0.619665\pi$
$43$	−0.331124	+	0.120519i	−0.0504960	+	0.0183790i	0.316649	+	0.948543i	$0.397442\pi$
$44$	−0.640012	−	1.10853i	−0.0964854	−	0.167118i
$45$		0			0
$46$	2.08666	−	3.61420i	0.307661	−	0.532884i
$47$	−0.455464	+	2.58307i	−0.0664363	+	0.376779i	0.933403	+	0.358831i	$0.116824\pi$
$47$	−0.455464	+	2.58307i	−0.0664363	+	0.376779i	−0.999839	+	0.0179481i	$0.994287\pi$
$48$	−5.56890	−	0.619521i	−0.803802	−	0.0894202i
$49$	6.01068	+	2.18771i	0.858668	+	0.312530i
$50$		0			0
$51$	0.430980	+	6.75217i	0.0603493	+	0.945492i
$52$	−1.28773	−	1.08053i	−0.178576	−	0.149843i
$53$	9.29215			1.27637			0.638187	−	0.769881i	$-0.279685\pi$
$53$	9.29215			1.27637			0.638187	+	0.769881i	$0.279685\pi$
$54$	−3.26136	+	5.87312i	−0.443816	+	0.799230i
$55$		0			0
$56$	−1.79163	−	1.50335i	−0.239416	−	0.200894i
$57$	−4.36446	+	2.90547i	−0.578087	+	0.384839i
$58$	−0.0796526	−	0.451732i	−0.0104589	−	0.0593154i
$59$	−12.4304	−	4.52430i	−1.61830	−	0.589014i	−0.635245	−	0.772311i	$-0.719101\pi$
$59$	−12.4304	−	4.52430i	−1.61830	−	0.589014i	−0.983058	+	0.183296i	$0.941323\pi$
$60$		0			0
$61$	1.14463	−	6.49154i	0.146555	−	0.831156i	−0.819550	−	0.573008i	$-0.805777\pi$
$61$	1.14463	−	6.49154i	0.146555	−	0.831156i	0.966105	−	0.258148i	$-0.0831123\pi$
$62$	−1.74987	+	3.03086i	−0.222233	+	0.384920i
$63$	−2.07101	+	1.06913i	−0.260923	+	0.134697i
$64$	−4.42346	−	7.66166i	−0.552932	−	0.957707i
$65$		0			0
$66$	6.02277	+	6.31302i	0.741352	+	0.777079i
$67$	3.04985	−	2.55913i	0.372599	−	0.312647i	−0.437190	−	0.899369i	$-0.644026\pi$
$67$	3.04985	−	2.55913i	0.372599	−	0.312647i	0.809789	+	0.586722i	$0.199582\pi$
$68$	−0.983053	+	0.824880i	−0.119213	+	0.100031i
$69$	1.57369	−	5.36497i	0.189450	−	0.645867i
$70$		0			0
$71$	−6.06946	−	10.5126i	−0.720312	−	1.24762i	−0.960875	−	0.276983i	$-0.910665\pi$
$71$	−6.06946	−	10.5126i	−0.720312	−	1.24762i	0.240563	−	0.970634i	$-0.422668\pi$
$72$	−8.95804	+	1.14823i	−1.05571	+	0.135320i
$73$	7.04497	−	12.2022i	0.824551	−	1.42816i	−0.0777105	−	0.996976i	$-0.524761\pi$
$73$	7.04497	−	12.2022i	0.824551	−	1.42816i	0.902262	−	0.431189i	$-0.141906\pi$
$74$	−0.959425	+	5.44117i	−0.111531	+	0.632523i
$75$		0			0
$76$	−0.934485	−	0.340125i	−0.107193	−	0.0390150i
$77$	0.525647	+	2.98109i	0.0599030	+	0.339727i
$78$	10.2681	+	5.08548i	1.16263	+	0.575817i
$79$	−8.85574	−	7.43085i	−0.996349	−	0.836036i	−0.00987418	−	0.999951i	$-0.503143\pi$
$79$	−8.85574	−	7.43085i	−0.996349	−	0.836036i	−0.986474	+	0.163916i	$0.947588\pi$
$80$		0			0
$81$	−2.38871	+	8.67722i	−0.265412	+	0.964135i
$82$	15.5975			1.72245
$83$	−4.25966	−	3.57428i	−0.467558	−	0.392328i	0.378345	−	0.925665i	$-0.376493\pi$
$83$	−4.25966	−	3.57428i	−0.467558	−	0.392328i	−0.845903	+	0.533337i	$0.820938\pi$
$84$	−0.396138	−	0.196195i	−0.0432222	−	0.0214067i
$85$		0			0
$86$	0.428097	+	0.155815i	0.0461629	+	0.0168019i
$87$	−0.246537	−	0.562904i	−0.0264315	−	0.0603496i
$88$	−2.03686	+	11.5516i	−0.217130	+	1.23141i
$89$	2.60530	−	4.51251i	0.276161	−	0.478325i	−0.694266	−	0.719718i	$-0.744271\pi$
$89$	2.60530	−	4.51251i	0.276161	−	0.478325i	0.970427	+	0.241393i	$0.0776044\pi$
$90$		0			0
$91$	1.98768	+	3.44277i	0.208366	+	0.360900i
$92$	0.996492	−	0.362693i	0.103891	−	0.0378134i
$93$	−1.31970	+	4.49906i	−0.136846	+	0.466531i
$94$	2.59770	−	2.17973i	0.267932	−	0.224822i
$95$		0			0
$96$	−2.19803	−	2.30395i	−0.224335	−	0.235146i
$97$	6.68077	−	2.43160i	0.678330	−	0.246892i	0.0201995	−	0.999796i	$-0.493570\pi$
$97$	6.68077	−	2.43160i	0.678330	−	0.246892i	0.658130	+	0.752904i	$0.271348\pi$
$98$	−4.13484	−	7.16175i	−0.417682	−	0.723446i
$99$	9.83699	+	6.31420i	0.988655	+	0.634601i
$100$		0			0
$101$	0.306182	−	1.73645i	0.0304663	−	0.172783i	−0.965778	−	0.259370i	$-0.916485\pi$
$101$	0.306182	−	1.73645i	0.0304663	−	0.172783i	0.996244	+	0.0865873i	$0.0275962\pi$
$102$	5.18444	−	7.04542i	0.513336	−	0.697600i
$103$	−18.0087	−	6.55464i	−1.77445	−	0.645848i	−0.999911	−	0.0133237i	$-0.995759\pi$
$103$	−18.0087	−	6.55464i	−1.77445	−	0.645848i	−0.774541	−	0.632524i	$-0.782019\pi$
$104$	2.67494	+	15.1703i	0.262299	+	1.48757i
$105$		0			0
$106$	−9.20282	−	7.72208i	−0.893857	−	0.750035i
$107$	5.51306			0.532968			0.266484	−	0.963839i	$-0.414138\pi$
$107$	5.51306			0.532968			0.266484	+	0.963839i	$0.414138\pi$
$108$	−1.59411	+	0.610531i	−0.153393	+	0.0587483i
$109$	14.2674			1.36657			0.683287	−	0.730150i	$-0.260550\pi$
$109$	14.2674			1.36657			0.683287	+	0.730150i	$0.260550\pi$
$110$		0			0
$111$	0.471500	+	7.38699i	0.0447528	+	0.701142i
$112$	0.436429	+	2.47511i	0.0412387	+	0.233876i
$113$	5.83093	+	2.12228i	0.548527	+	0.199648i	0.601392	−	0.798954i	$-0.294613\pi$
$113$	5.83093	+	2.12228i	0.548527	+	0.199648i	−0.0528647	+	0.998602i	$0.516835\pi$
$114$	6.73705	+	0.749473i	0.630982	+	0.0701946i
$115$		0			0
$116$	0.0582783	−	0.100941i	0.00541100	−	0.00937213i
$117$	14.9756	+	3.37372i	1.38450	+	0.311901i
$118$	8.55108	+	14.8109i	0.787191	+	1.36345i
$119$	2.85177	−	1.03796i	0.261421	−	0.0951496i
$120$		0			0
$121$	3.20338	−	2.68795i	0.291216	−	0.244359i
$122$	−6.52831	+	5.47790i	−0.591046	+	0.495946i
$123$	20.3057	−	4.93203i	1.83090	−	0.444706i
$124$	−0.835656	+	0.304154i	−0.0750442	+	0.0273138i
$125$		0			0
$126$	2.93958	+	0.662233i	0.261879	+	0.0589964i
$127$	−6.04043	+	10.4623i	−0.536002	+	0.928382i	0.463112	+	0.886300i	$0.346733\pi$
$127$	−6.04043	+	10.4623i	−0.536002	+	0.928382i	−0.999114	+	0.0420828i	$0.986601\pi$
$128$	−1.34767	+	7.64304i	−0.119119	+	0.675556i
$129$	0.606590	+	0.0674810i	0.0534072	+	0.00594137i
$130$		0			0
$131$	0.140206	+	0.795145i	0.0122498	+	0.0694722i	0.990320	−	0.138804i	$-0.0443258\pi$
$131$	0.140206	+	0.795145i	0.0122498	+	0.0694722i	−0.978070	+	0.208276i	$0.933215\pi$
$132$	0.141224	+	2.21256i	0.0122920	+	0.192579i
$133$	1.80155	+	1.51168i	0.156214	+	0.131079i
$134$	−5.14726			−0.444655
$135$		0			0
$136$	11.7597			1.00838
$137$	−0.546720	−	0.458752i	−0.0467094	−	0.0391939i	0.619134	−	0.785285i	$-0.287484\pi$
$137$	−0.546720	−	0.458752i	−0.0467094	−	0.0391939i	−0.665844	+	0.746091i	$0.731928\pi$
$138$	−6.01704	+	4.00561i	−0.512204	+	0.340980i
$139$	2.29439	+	13.0121i	0.194607	+	1.10367i	0.912977	+	0.408011i	$0.133778\pi$
$139$	2.29439	+	13.0121i	0.194607	+	1.10367i	−0.718370	+	0.695662i	$0.755111\pi$
$140$		0			0
$141$	2.69258	−	3.65910i	0.226756	−	0.308152i
$142$	−2.72522	+	15.4555i	−0.228695	+	1.29699i
$143$	9.96882	−	17.2665i	0.833635	−	1.44390i
$144$	8.16736	+	5.24249i	0.680614	+	0.436874i
$145$		0			0
$146$	−17.1177	+	6.23034i	−1.41667	+	0.515627i
$147$	−7.64755	−	8.01610i	−0.630760	−	0.661157i
$148$	−1.07548	+	0.902433i	−0.0884038	+	0.0741796i
$149$	4.06706	−	3.41267i	0.333187	−	0.279577i	−0.460810	−	0.887499i	$-0.652441\pi$
$149$	4.06706	−	3.41267i	0.333187	−	0.279577i	0.793997	+	0.607922i	$0.207997\pi$
$150$		0			0
$151$	5.48224	−	1.99537i	0.446138	−	0.162381i	−0.109174	−	0.994023i	$-0.534821\pi$
$151$	5.48224	−	1.99537i	0.446138	−	0.162381i	0.555313	+	0.831641i	$0.312598\pi$
$152$	4.55648	+	7.89205i	0.369579	+	0.640130i
$153$	4.52158	−	10.8115i	0.365548	−	0.874055i
$154$	1.95679	−	3.38927i	0.157683	−	0.273115i
$155$		0			0
$156$	1.16808	+	2.66702i	0.0935216	+	0.213532i
$157$	1.51897	+	0.552860i	0.121227	+	0.0441230i	0.401921	−	0.915674i	$-0.368343\pi$
$157$	1.51897	+	0.552860i	0.121227	+	0.0441230i	−0.280694	+	0.959797i	$0.590565\pi$
$158$	2.59533	+	14.7188i	0.206473	+	1.17097i
$159$	−14.4225	−	7.14304i	−1.14378	−	0.566480i
$160$		0			0
$161$	−2.50780			−0.197643
$162$	9.57680	−	6.60871i	0.752425	−	0.519229i
$163$	3.19497			0.250249			0.125125	−	0.992141i	$-0.460067\pi$
$163$	3.19497			0.250249			0.125125	+	0.992141i	$0.460067\pi$
$164$	3.03610	+	2.54759i	0.237079	+	0.198933i
$165$		0			0
$166$	1.24837	+	7.07983i	0.0968920	+	0.549502i
$167$	5.19103	+	1.88938i	0.401694	+	0.146205i	0.534963	−	0.844875i	$-0.320325\pi$
$167$	5.19103	+	1.88938i	0.401694	+	0.146205i	−0.133270	+	0.991080i	$0.542548\pi$
$168$	1.62516	+	3.71064i	0.125384	+	0.286282i
$169$	2.28928	−	12.9832i	0.176099	−	0.998704i
$170$		0			0
$171$	9.00765	−	1.15459i	0.688832	−	0.0882938i
$172$	0.0578806	+	0.100252i	0.00441335	+	0.00764415i
$173$	−10.0159	+	3.64550i	−0.761497	+	0.277162i	−0.693435	−	0.720519i	$-0.743904\pi$
$173$	−10.0159	+	3.64550i	−0.761497	+	0.277162i	−0.0680619	+	0.997681i	$0.521682\pi$
$174$	−0.223625	+	0.762373i	−0.0169530	+	0.0577953i
$175$		0			0
$176$	9.65594	−	8.10229i	0.727844	−	0.610733i
$177$	15.8156	+	16.5777i	1.18877	+	1.24606i
$178$	−6.33030	+	2.30404i	−0.474476	+	0.172695i
$179$	−7.01872	−	12.1568i	−0.524604	−	0.908640i	−0.999590	−	0.0286466i	$-0.990880\pi$
$179$	−7.01872	−	12.1568i	−0.524604	−	0.908640i	0.474986	−	0.879993i	$-0.342453\pi$
$180$		0			0
$181$	7.75754	−	13.4365i	0.576613	−	0.998723i	−0.419251	−	0.907870i	$-0.637707\pi$
$181$	7.75754	−	13.4365i	0.576613	−	0.998723i	0.995864	−	0.0908531i	$-0.0289594\pi$
$182$	0.892479	−	5.06150i	0.0661550	−	0.375183i
$183$	−6.76677	+	9.19573i	−0.500214	+	0.679768i
$184$	−9.13159	−	3.32363i	−0.673190	−	0.245021i
$185$		0			0
$186$	5.04588	−	3.35910i	0.369982	−	0.246301i
$187$	−11.6595	−	9.78348i	−0.852627	−	0.715439i
$188$	0.861671			0.0628438
$189$	4.03631	−	0.0673839i	0.293599	−	0.00490145i
$190$		0			0
$191$	3.34632	+	2.80790i	0.242131	+	0.203172i	0.755775	−	0.654831i	$-0.227260\pi$
$191$	3.34632	+	2.80790i	0.242131	+	0.203172i	−0.513644	+	0.858004i	$0.671705\pi$
$192$	0.976076	+	15.2922i	0.0704422	+	1.10362i
$193$	−0.571456	−	3.24089i	−0.0411343	−	0.233284i	0.957309	−	0.289068i	$-0.0933453\pi$
$193$	−0.571456	−	3.24089i	−0.0411343	−	0.233284i	−0.998443	+	0.0557838i	$0.982234\pi$
$194$	−8.63729	−	3.14372i	−0.620122	−	0.225706i
$195$		0			0
$196$	0.364893	−	2.06941i	0.0260638	−	0.147815i
$197$	10.7134	−	18.5561i	0.763297	−	1.32207i	−0.177845	−	0.984059i	$-0.556913\pi$
$197$	10.7134	−	18.5561i	0.763297	−	1.32207i	0.941142	−	0.338011i	$-0.109754\pi$
$198$	−4.49512	−	14.4284i	−0.319454	−	1.02538i
$199$	7.03013	+	12.1765i	0.498353	+	0.863172i	0.999998	−	0.00190098i	$-0.000605102\pi$
$199$	7.03013	+	12.1765i	0.498353	+	0.863172i	−0.501645	+	0.865073i	$0.667272\pi$
$200$		0			0
$201$	−6.70098	+	1.62760i	−0.472651	+	0.114802i
$202$	−1.74628	+	1.46531i	−0.122868	+	0.103099i
$203$	−0.211153	+	0.177178i	−0.0148200	+	0.0124355i
$204$	2.15992	−	0.524620i	0.151224	−	0.0367307i
$205$		0			0
$206$	12.3885	+	21.4575i	0.863146	+	1.49501i
$207$	−6.56671	+	7.11735i	−0.456418	+	0.494690i
$208$	8.27682	−	14.3359i	0.573894	−	0.994014i
$209$	2.04814	−	11.6156i	0.141673	−	0.803466i
$210$		0			0
$211$	3.90781	+	1.42233i	0.269025	+	0.0979170i	0.473010	−	0.881057i	$-0.343167\pi$
$211$	3.90781	+	1.42233i	0.269025	+	0.0979170i	−0.203986	+	0.978974i	$0.565390\pi$
$212$	−0.530083	−	3.00625i	−0.0364063	−	0.206470i
$213$	1.33928	+	20.9825i	0.0917660	+	1.43770i
$214$	−5.46007	−	4.58154i	−0.373242	−	0.313188i
$215$		0			0
$216$	14.7866	+	5.10402i	1.00610	+	0.347284i
$217$	2.10304			0.142764
$218$	−14.1303	−	11.8567i	−0.957024	−	0.803039i
$219$	−20.3147	+	13.5237i	−1.37274	+	0.913849i
$220$		0			0
$221$	−18.7830	−	6.83645i	−1.26348	−	0.459869i
$222$	5.67187	−	7.70781i	0.380671	−	0.517315i
$223$	−2.88459	+	16.3593i	−0.193167	+	1.09550i	0.721839	+	0.692061i	$0.243297\pi$
$223$	−2.88459	+	16.3593i	−0.193167	+	1.09550i	−0.915006	+	0.403441i	$0.867814\pi$
$224$	−0.714137	+	1.23692i	−0.0477153	+	0.0826453i
$225$		0			0
$226$	−4.01118	−	6.94758i	−0.266820	−	0.462146i
$227$	−4.97722	+	1.81156i	−0.330350	+	0.120238i	−0.501870	−	0.864943i	$-0.667354\pi$
$227$	−4.97722	+	1.81156i	−0.330350	+	0.120238i	0.171520	+	0.985181i	$0.445132\pi$
$228$	1.18897	+	1.24627i	0.0787415	+	0.0825362i
$229$	−15.6135	+	13.1012i	−1.03177	+	0.865754i	−0.991060	−	0.133417i	$-0.957405\pi$
$229$	−15.6135	+	13.1012i	−1.03177	+	0.865754i	−0.0407059	+	0.999171i	$0.512961\pi$
$230$		0			0
$231$	1.47575	−	5.03108i	0.0970975	−	0.331021i
$232$	−1.00368	+	0.365309i	−0.0658948	+	0.0239837i
$233$	0.613363	+	1.06238i	0.0401827	+	0.0695985i	0.885417	−	0.464797i	$-0.153873\pi$
$233$	0.613363	+	1.06238i	0.0401827	+	0.0695985i	−0.845235	+	0.534395i	$0.820539\pi$
$234$	−12.0280	−	15.7865i	−0.786293	−	1.03200i
$235$		0			0
$236$	−0.754619	+	4.27966i	−0.0491215	+	0.278582i
$237$	8.03293	+	18.3411i	0.521795	+	1.19138i
$238$	−3.68694	−	1.34194i	−0.238989	−	0.0869848i
$239$	2.66890	+	15.1361i	0.172637	+	0.979073i	0.940836	+	0.338862i	$0.110042\pi$
$239$	2.66890	+	15.1361i	0.172637	+	0.979073i	−0.768199	+	0.640211i	$0.778847\pi$
$240$		0			0
$241$	14.2379	+	11.9470i	0.917146	+	0.769577i	0.973465	−	0.228836i	$-0.0734920\pi$
$241$	14.2379	+	11.9470i	0.917146	+	0.769577i	−0.0563190	+	0.998413i	$0.517936\pi$
$242$	−5.40637			−0.347534
$243$	10.3779	−	11.6318i	0.665742	−	0.746182i
$244$	−2.16548			−0.138630
$245$		0			0
$246$	−24.2092	−	11.9901i	−1.54352	−	0.764460i
$247$	−2.68975	−	15.2543i	−0.171145	−	0.970611i
$248$	7.65774	+	2.78719i	0.486267	+	0.176987i
$249$	3.86388	+	8.82218i	0.244863	+	0.559083i
$250$		0			0
$251$	3.10032	−	5.36991i	0.195691	−	0.338946i	−0.751436	−	0.659806i	$-0.770639\pi$
$251$	3.10032	−	5.36991i	0.195691	−	0.338946i	0.947127	+	0.320860i	$0.103972\pi$
$252$	0.464034	+	0.609037i	0.0292314	+	0.0383657i
$253$	6.28869	+	10.8923i	0.395367	+	0.684795i
$254$	14.6769	−	5.34196i	0.920912	−	0.335185i
$255$		0			0
$256$	−5.86792	+	4.92377i	−0.366745	+	0.307736i
$257$	15.1559	−	12.7173i	0.945401	−	0.793285i	−0.0331163	−	0.999452i	$-0.510543\pi$
$257$	15.1559	−	12.7173i	0.945401	−	0.793285i	0.978517	+	0.206166i	$0.0660987\pi$
$258$	−0.544680	−	0.570929i	−0.0339103	−	0.0355445i
$259$	3.11989	−	1.13555i	0.193861	−	0.0705595i
$260$		0			0
$261$	−0.0500600	+	1.06321i	−0.00309864	+	0.0658111i
$262$	0.521935	−	0.904017i	0.0322452	−	0.0558504i
$263$	2.95564	−	16.7623i	0.182252	−	1.03360i	−0.747183	−	0.664619i	$-0.768594\pi$
$263$	2.95564	−	16.7623i	0.182252	−	1.03360i	0.929435	−	0.368986i	$-0.120295\pi$
$264$	12.0414	−	16.3637i	0.741096	−	1.00712i
$265$		0			0
$266$	−0.527975	−	2.99430i	−0.0323722	−	0.183592i
$267$	−7.51258	+	5.00121i	−0.459762	+	0.306069i
$268$	−1.00193	−	0.840718i	−0.0612025	−	0.0513550i
$269$	−6.07723			−0.370535			−0.185268	−	0.982688i	$-0.559315\pi$
$269$	−6.07723			−0.370535			−0.185268	+	0.982688i	$0.559315\pi$
$270$		0			0
$271$	−30.8933			−1.87664			−0.938318	−	0.345774i	$-0.887617\pi$
$271$	−30.8933			−1.87664			−0.938318	+	0.345774i	$0.887617\pi$
$272$	−9.68054	−	8.12293i	−0.586969	−	0.492525i
$273$	−0.438600	−	6.87155i	−0.0265453	−	0.415885i
$274$	0.160226	+	0.908685i	0.00967958	+	0.0548956i
$275$		0			0
$276$	−1.82548	−	0.203079i	−0.109881	−	0.0122239i
$277$	−4.28682	+	24.3118i	−0.257570	+	1.46075i	0.531818	+	0.846859i	$0.321509\pi$
$277$	−4.28682	+	24.3118i	−0.257570	+	1.46075i	−0.789388	+	0.613895i	$0.789602\pi$
$278$	8.54117	−	14.7937i	0.512265	−	0.887269i
$279$	5.50684	−	5.96860i	0.329686	−	0.357331i
$280$		0			0
$281$	16.7164	−	6.08427i	0.997216	−	0.362957i	0.208706	−	0.977979i	$-0.433075\pi$
$281$	16.7164	−	6.08427i	0.997216	−	0.362957i	0.788510	+	0.615022i	$0.210853\pi$
$282$	−5.70753	+	1.38630i	−0.339879	+	0.0825528i
$283$	−2.22808	+	1.86958i	−0.132446	+	0.111135i	−0.706604	−	0.707609i	$-0.749774\pi$
$283$	−2.22808	+	1.86958i	−0.132446	+	0.111135i	0.574158	+	0.818744i	$0.305329\pi$
$284$	−3.05486	+	2.56333i	−0.181273	+	0.152106i
$285$		0			0
$286$	−24.2220	+	8.81610i	−1.43228	+	0.521307i
$287$	−4.68638	−	8.11705i	−0.276628	−	0.479134i
$288$	1.64051	+	5.26567i	0.0966677	+	0.310283i
$289$	0.870418	−	1.50761i	0.0512011	−	0.0886828i
$290$		0			0
$291$	−12.2386	−	1.36150i	−0.717438	−	0.0798125i
$292$	−4.34963	−	1.58314i	−0.254543	−	0.0926461i
$293$	1.07421	+	6.09217i	0.0627563	+	0.355908i	0.999974	+	0.00716458i	$0.00228058\pi$
$293$	1.07421	+	6.09217i	0.0627563	+	0.355908i	−0.937218	+	0.348744i	$0.886608\pi$
$294$	0.912390	+	14.2944i	0.0532116	+	0.833667i
$295$		0			0
$296$	12.8653			0.747781
$297$	−10.4143	−	17.3623i	−0.604301	−	1.00746i
$298$	−6.86401			−0.397621
$299$	12.6531	+	10.6172i	0.731748	+	0.614010i
$300$		0			0
$301$	−0.0475378	−	0.269600i	−0.00274003	−	0.0155395i
$302$	−7.08776	−	2.57973i	−0.407855	−	0.148447i
$303$	−1.81007	+	2.45980i	−0.103986	+	0.141312i
$304$	1.70051	−	9.64407i	0.0975309	−	0.553125i
$305$		0			0
$306$	−13.4628	+	6.94995i	−0.769617	+	0.397302i
$307$	−13.9233	−	24.1159i	−0.794645	−	1.37637i	−0.923064	−	0.384646i	$-0.874324\pi$
$307$	−13.9233	−	24.1159i	−0.794645	−	1.37637i	0.128419	−	0.991720i	$-0.459010\pi$
$308$	0.934475	−	0.340121i	0.0532466	−	0.0193802i
$309$	22.9130	+	24.0172i	1.30347	+	1.36629i
$310$		0			0
$311$	13.2628	−	11.1288i	0.752062	−	0.631055i	−0.183986	−	0.982929i	$-0.558900\pi$
$311$	13.2628	−	11.1288i	0.752062	−	0.631055i	0.936047	+	0.351874i	$0.114456\pi$
$312$	7.50990	−	25.6024i	0.425164	−	1.44945i
$313$	−9.40628	+	3.42361i	−0.531675	+	0.193514i	−0.593886	−	0.804549i	$-0.702407\pi$
$313$	−9.40628	+	3.42361i	−0.531675	+	0.193514i	0.0622113	+	0.998063i	$0.480185\pi$
$314$	−1.04492	−	1.80986i	−0.0589684	−	0.102136i
$315$		0			0
$316$	−1.89888	+	3.28897i	−0.106821	+	0.185019i
$317$	−1.39206	+	7.89475i	−0.0781857	+	0.443413i	0.920434	+	0.390897i	$0.127835\pi$
$317$	−1.39206	+	7.89475i	−0.0781857	+	0.443413i	−0.998620	+	0.0525162i	$0.983276\pi$
$318$	8.34776	+	19.0600i	0.468119	+	1.06883i
$319$	1.29905	+	0.472815i	0.0727327	+	0.0264725i
$320$		0			0
$321$	−8.55693	−	4.23799i	−0.477601	−	0.236542i
$322$	2.48370	+	2.08407i	0.138411	+	0.116141i
$323$	−11.8248			−0.657950
$324$	2.94357	+	0.277805i	0.163532	+	0.0154336i
$325$		0			0
$326$	−3.16426	−	2.65513i	−0.175252	−	0.147054i
$327$	−22.1448	−	10.9677i	−1.22461	−	0.606513i
$328$	−6.30673	−	35.7673i	−0.348231	−	1.97492i
$329$	−1.91484	−	0.696946i	−0.105569	−	0.0384239i
$330$		0			0
$331$	−4.48752	+	25.4500i	−0.246656	+	1.39886i	0.569958	+	0.821674i	$0.306959\pi$
$331$	−4.48752	+	25.4500i	−0.246656	+	1.39886i	−0.816615	+	0.577183i	$0.804152\pi$
$332$	−0.913374	+	1.58201i	−0.0501279	+	0.0868240i
$333$	4.94669	−	11.8279i	0.271077	−	0.648167i
$334$	−3.57099	−	6.18513i	−0.195396	−	0.338435i
$335$		0			0
$336$	1.22528	−	4.17716i	0.0668443	−	0.227883i
$337$	−15.1328	+	12.6980i	−0.824338	+	0.691702i	−0.953984	−	0.299859i	$-0.903060\pi$
$337$	−15.1328	+	12.6980i	−0.824338	+	0.691702i	0.129646	+	0.991560i	$0.458616\pi$
$338$	−13.0567	+	10.9559i	−0.710191	+	0.595921i
$339$	−7.41885	−	7.77638i	−0.402937	−	0.422355i
$340$		0			0
$341$	−5.27369	−	9.13430i	−0.285586	−	0.494650i
$342$	−9.88056	−	6.34216i	−0.534279	−	0.342945i
$343$	−5.20383	+	9.01329i	−0.280980	+	0.486672i
$344$	0.184207	−	1.04469i	0.00993177	−	0.0563259i
$345$		0			0
$346$	12.9492	+	4.71312i	0.696153	+	0.253379i
$347$	4.37541	+	24.8142i	0.234884	+	1.33210i	0.842857	+	0.538138i	$0.180872\pi$
$347$	4.37541	+	24.8142i	0.234884	+	1.33210i	−0.607973	+	0.793958i	$0.708017\pi$
$348$	−0.168050	+	0.111873i	−0.00900842	+	0.00599701i
$349$	22.8639	+	19.1851i	1.22388	+	1.02695i	0.998613	+	0.0526561i	$0.0167687\pi$
$349$	22.8639	+	19.1851i	1.22388	+	1.02695i	0.225263	+	0.974298i	$0.427676\pi$
$350$		0			0
$351$	−20.6505	−	16.7484i	−1.10224	−	0.893966i
$352$	7.16322			0.381801
$353$	−9.94244	−	8.34269i	−0.529182	−	0.444037i	0.338637	−	0.940917i	$-0.390034\pi$
$353$	−9.94244	−	8.34269i	−0.529182	−	0.444037i	−0.867819	+	0.496880i	$0.834479\pi$
$354$	−1.88687	−	29.5617i	−0.100286	−	1.57118i
$355$		0			0
$356$	−1.60854	−	0.585459i	−0.0852523	−	0.0310293i
$357$	−5.22419	−	0.581173i	−0.276493	−	0.0307589i
$358$	−3.15144	+	17.8727i	−0.166559	+	0.944602i
$359$	6.77215	−	11.7297i	0.357421	−	0.619071i	−0.630109	−	0.776507i	$-0.716990\pi$
$359$	6.77215	−	11.7297i	0.357421	−	0.619071i	0.987529	+	0.157436i	$0.0503230\pi$
$360$		0			0
$361$	4.91829	+	8.51873i	0.258857	+	0.448354i
$362$	−18.8491	+	6.86051i	−0.990687	+	0.360581i
$363$	−7.03830	+	1.70953i	−0.369415	+	0.0897269i
$364$	1.00043	−	0.839464i	0.0524370	−	0.0439999i
$365$		0			0
$366$	14.3437	−	3.48392i	0.749756	−	0.182108i
$367$	23.5250	−	8.56238i	1.22799	−	0.446953i	0.355083	−	0.934835i	$-0.384453\pi$
$367$	23.5250	−	8.56238i	1.22799	−	0.446953i	0.872910	+	0.487882i	$0.162230\pi$
$368$	5.22132	+	9.04359i	0.272180	+	0.471430i
$369$	−35.3082	−	7.95426i	−1.83807	−	0.414082i
$370$		0			0
$371$	−1.25357	+	7.10937i	−0.0650823	+	0.369100i
$372$	1.53085	+	0.170301i	0.0793707	+	0.00882972i
$373$	−1.95904	−	0.713033i	−0.101435	−	0.0369195i	0.290804	−	0.956783i	$-0.406077\pi$
$373$	−1.95904	−	0.713033i	−0.101435	−	0.0369195i	−0.392239	+	0.919863i	$0.628299\pi$
$374$	3.41702	+	19.3789i	0.176690	+	1.00206i
$375$		0			0
$376$	−6.04879	−	5.07553i	−0.311942	−	0.261751i
$377$	1.81548			0.0935021
$378$	−4.05351	−	3.28758i	−0.208490	−	0.169095i
$379$	9.13522			0.469245			0.234622	−	0.972087i	$-0.424615\pi$
$379$	9.13522			0.469245			0.234622	+	0.972087i	$0.424615\pi$
$380$		0			0
$381$	17.4181	−	11.5954i	0.892354	−	0.594050i
$382$	−0.980698	−	5.56181i	−0.0501769	−	0.284567i
$383$	9.60103	+	3.49449i	0.490590	+	0.178560i	0.575457	−	0.817832i	$-0.304824\pi$
$383$	9.60103	+	3.49449i	0.490590	+	0.178560i	−0.0848669	+	0.996392i	$0.527047\pi$
$384$	7.96710	−	10.8269i	0.406569	−	0.552509i
$385$		0			0
$386$	−2.12732	+	3.68463i	−0.108278	+	0.187543i
$387$	−0.889625	−	0.571035i	−0.0452222	−	0.0290274i
$388$	−1.16780	−	2.02269i	−0.0592861	−	0.102687i
$389$	−16.4031	+	5.97024i	−0.831670	+	0.302703i	−0.722544	−	0.691325i	$-0.757027\pi$
$389$	−16.4031	+	5.97024i	−0.831670	+	0.302703i	−0.109126	+	0.994028i	$0.534805\pi$
$390$		0			0
$391$	9.65938	−	8.10519i	0.488496	−	0.409897i
$392$	−14.7510	+	12.3776i	−0.745039	+	0.625162i
$393$	0.393627	−	1.34194i	0.0198559	−	0.0676918i
$394$	−26.0312	+	9.47457i	−1.31143	+	0.477322i
$395$		0			0
$396$	1.48164	−	3.54272i	0.0744553	−	0.178029i
$397$	6.61971	−	11.4657i	0.332233	−	0.575445i	−0.650716	−	0.759321i	$-0.725531\pi$
$397$	6.61971	−	11.4657i	0.332233	−	0.575445i	0.982949	+	0.183876i	$0.0588645\pi$
$398$	3.15656	−	17.9018i	0.158224	−	0.897334i
$399$	−1.63416	−	3.73119i	−0.0818105	−	0.186793i
$400$		0			0
$401$	6.80556	+	38.5962i	0.339853	+	1.92740i	0.372717	+	0.927945i	$0.378426\pi$
$401$	6.80556	+	38.5962i	0.339853	+	1.92740i	−0.0328639	+	0.999460i	$0.510463\pi$
$402$	7.98915	+	3.95679i	0.398463	+	0.197347i
$403$	−10.6109	−	8.90359i	−0.528566	−	0.443519i
$404$	−0.579252			−0.0288189
$405$		0			0
$406$	0.356364			0.0176860
$407$	−12.7557	−	10.7033i	−0.632277	−	0.530543i
$408$	−18.2524	−	9.03989i	−0.903630	−	0.447541i
$409$	−3.44309	−	19.5268i	−0.170250	−	0.965536i	−0.943485	−	0.331416i	$-0.892474\pi$
$409$	−3.44309	−	19.5268i	−0.170250	−	0.965536i	0.773235	−	0.634120i	$-0.218637\pi$
$410$		0			0
$411$	0.495922	+	1.13231i	0.0244620	+	0.0558528i
$412$	−1.09326	+	6.20021i	−0.0538612	+	0.305462i
$413$	5.13847	−	8.90009i	0.252847	−	0.437945i
$414$	12.4183	−	1.59177i	0.610328	−	0.0782313i
$415$		0			0
$416$	8.83989	−	3.21746i	0.433411	−	0.157749i
$417$	6.44149	−	21.9601i	0.315441	−	1.07539i
$418$	−11.6814	+	9.80184i	−0.571355	+	0.479424i
$419$	20.8598	−	17.5035i	1.01907	−	0.855101i	0.0295598	−	0.999563i	$-0.490589\pi$
$419$	20.8598	−	17.5035i	1.01907	−	0.855101i	0.989510	+	0.144462i	$0.0461450\pi$
$420$		0			0
$421$	−2.12407	+	0.773098i	−0.103521	+	0.0376785i	−0.393261	−	0.919427i	$-0.628653\pi$
$421$	−2.12407	+	0.773098i	−0.103521	+	0.0376785i	0.289740	+	0.957105i	$0.406431\pi$
$422$	−2.68824	−	4.65617i	−0.130862	−	0.226659i
$423$	−6.99203	+	3.60952i	−0.339964	+	0.175501i
$424$	−13.9867	+	24.2257i	−0.679256	+	1.17651i
$425$		0			0
$426$	16.1108	−	21.8938i	0.780569	−	1.06076i
$427$	4.81222	+	1.75150i	0.232880	+	0.0847612i
$428$	−0.314500	−	1.78362i	−0.0152019	−	0.0862145i
$429$	−28.7459	+	19.1364i	−1.38786	+	0.923916i
$430$		0			0
$431$	9.69510			0.466996			0.233498	−	0.972357i	$-0.424983\pi$
$431$	9.69510			0.466996			0.233498	+	0.972357i	$0.424983\pi$
$432$	−8.64671	−	14.4154i	−0.416015	−	0.693560i
$433$	32.3437			1.55434			0.777169	−	0.629292i	$-0.216655\pi$
$433$	32.3437			1.55434			0.777169	+	0.629292i	$0.216655\pi$
$434$	−2.08282	−	1.74770i	−0.0999788	−	0.0838922i
$435$		0			0
$436$	−0.813906	−	4.61589i	−0.0389790	−	0.221061i
$437$	9.18216	+	3.34203i	0.439242	+	0.159871i
$438$	31.3581	+	3.48848i	1.49835	+	0.166686i
$439$	−1.71544	+	9.72872i	−0.0818733	+	0.464327i	0.916114	+	0.400917i	$0.131308\pi$
$439$	−1.71544	+	9.72872i	−0.0818733	+	0.464327i	−0.997988	+	0.0634094i	$0.979803\pi$
$440$		0			0
$441$	5.70778	+	18.3208i	0.271799	+	0.872417i
$442$	12.9211	+	22.3800i	0.614594	+	1.06451i
$443$	−24.5846	+	8.94805i	−1.16805	+	0.425135i	−0.851966	−	0.523597i	$-0.824590\pi$
$443$	−24.5846	+	8.94805i	−1.16805	+	0.425135i	−0.316082	+	0.948732i	$0.602368\pi$
$444$	2.36299	−	0.573944i	0.112142	−	0.0272382i
$445$		0			0
$446$	16.4520	−	13.8049i	0.779025	−	0.653680i
$447$	−8.93594	+	2.17044i	−0.422656	+	0.102658i
$448$	6.45865	−	2.35075i	0.305142	−	0.111063i
$449$	8.04462	+	13.9337i	0.379649	+	0.657572i	0.991011	−	0.133779i	$-0.0427113\pi$
$449$	8.04462	+	13.9337i	0.379649	+	0.657572i	−0.611362	+	0.791351i	$0.709378\pi$
$450$		0			0
$451$	−23.5036	+	40.7094i	−1.10674	+	1.91693i
$452$	0.353981	−	2.00752i	0.0166499	−	0.0944260i
$453$	−10.0430	−	1.11725i	−0.471860	−	0.0524928i
$454$	6.43484	+	2.34209i	0.302002	+	0.109920i
$455$		0			0
$456$	−1.00543	−	15.7520i	−0.0470835	−	0.737657i
$457$	−23.3162	−	19.5646i	−1.09068	−	0.915193i	−0.0939208	−	0.995580i	$-0.529940\pi$
$457$	−23.3162	−	19.5646i	−1.09068	−	0.915193i	−0.996764	+	0.0803867i	$0.974384\pi$
$458$	26.3509			1.23130
$459$	−15.3290	+	13.3048i	−0.715497	+	0.621017i
$460$		0			0
$461$	12.5270	+	10.5114i	0.583438	+	0.489563i	0.886074	−	0.463543i	$-0.153422\pi$
$461$	12.5270	+	10.5114i	0.583438	+	0.489563i	−0.302636	+	0.953106i	$0.597867\pi$
$462$	−5.64257	+	3.75632i	−0.262516	+	0.174760i
$463$	1.26889	+	7.19625i	0.0589705	+	0.334438i	0.999992	−	0.00390751i	$-0.00124380\pi$
$463$	1.26889	+	7.19625i	0.0589705	+	0.334438i	−0.941022	+	0.338346i	$0.890133\pi$
$464$	1.07856	+	0.392564i	0.0500709	+	0.0182243i
$465$		0			0
$466$	0.275403	−	1.56189i	0.0127578	−	0.0723531i
$467$	−5.03027	+	8.71268i	−0.232773	+	0.403175i	−0.958623	−	0.284678i	$-0.908113\pi$
$467$	−5.03027	+	8.71268i	−0.232773	+	0.403175i	0.725850	+	0.687853i	$0.241447\pi$
$468$	0.237183	−	5.03746i	0.0109638	−	0.232857i
$469$	1.54653	+	2.67867i	0.0714121	+	0.123689i
$470$		0			0
$471$	−1.93263	−	2.02576i	−0.0890508	−	0.0933423i
$472$	30.5059	−	25.5975i	1.40415	−	1.17822i
$473$	−1.05177	+	0.882537i	−0.0483603	+	0.0405791i
$474$	7.28638	−	24.8404i	0.334675	−	1.14096i
$475$		0			0
$476$	−0.498490	−	0.863411i	−0.0228483	−	0.0395744i
$477$	16.8945	+	22.1737i	0.773544	+	1.01526i
$478$	9.93536	−	17.2085i	0.454433	−	0.787100i
$479$	1.39286	−	7.89931i	0.0636415	−	0.360929i	−0.936311	−	0.351172i	$-0.885783\pi$
$479$	1.39286	−	7.89931i	0.0636415	−	0.360929i	0.999952	−	0.00975657i	$-0.00310566\pi$
$480$		0			0
$481$	−20.5489	−	7.47920i	−0.936950	−	0.341022i
$482$	−4.17267	−	23.6644i	−0.190060	−	1.07788i
$483$	3.89241	+	1.92780i	0.177111	+	0.0877177i
$484$	−1.05236	−	0.883038i	−0.0478347	−	0.0401381i
$485$		0			0
$486$	−19.9446	+	2.89563i	−0.904704	+	0.131349i
$487$	1.30014			0.0589151			0.0294575	−	0.999566i	$-0.490622\pi$
$487$	1.30014			0.0589151			0.0294575	+	0.999566i	$0.490622\pi$
$488$	15.2013	+	12.7554i	0.688130	+	0.577409i
$489$	−4.95897	−	2.45603i	−0.224253	−	0.111066i
$490$		0			0
$491$	10.4561	+	3.80573i	0.471879	+	0.171750i	0.567003	−	0.823715i	$-0.308103\pi$
$491$	10.4561	+	3.80573i	0.471879	+	0.171750i	−0.0951242	+	0.995465i	$0.530325\pi$
$492$	−2.75400	−	6.28806i	−0.124160	−	0.283488i
$493$	0.240666	−	1.36488i	0.0108390	−	0.0614713i
$494$	−10.0130	+	17.3430i	−0.450505	+	0.780298i
$495$		0			0
$496$	−4.37859	−	7.58394i	−0.196604	−	0.340529i
$497$	8.86195	−	3.22548i	0.397513	−	0.144683i
$498$	3.50479	−	11.9484i	0.157053	−	0.535420i
$499$	13.6131	−	11.4227i	0.609404	−	0.511351i	−0.285049	−	0.958513i	$-0.592010\pi$
$499$	13.6131	−	11.4227i	0.609404	−	0.511351i	0.894453	+	0.447162i	$0.147565\pi$
$500$		0			0
$501$	−6.60469	−	6.92298i	−0.295076	−	0.309296i
$502$	−7.53309	+	2.74182i	−0.336218	+	0.122374i
$503$	−6.51241	−	11.2798i	−0.290374	−	0.502942i	0.683524	−	0.729928i	$-0.260446\pi$
$503$	−6.51241	−	11.2798i	−0.290374	−	0.502942i	−0.973898	+	0.226985i	$0.927113\pi$
$504$	0.329994	−	7.00865i	0.0146991	−	0.312190i
$505$		0			0
$506$	2.82366	−	16.0137i	0.125527	−	0.711898i
$507$	−13.5336	+	18.3916i	−0.601050	+	0.816799i
$508$	3.72942	+	1.35740i	0.165466	+	0.0602248i
$509$	−3.60691	−	20.4558i	−0.159873	−	0.906687i	−0.954194	−	0.299188i	$-0.903284\pi$
$509$	−3.60691	−	20.4558i	−0.159873	−	0.906687i	0.794321	−	0.607499i	$-0.207827\pi$
$510$		0			0
$511$	8.38545	+	7.03623i	0.370951	+	0.311265i
$512$	25.4252			1.12365
$513$	−14.8685	−	5.13228i	−0.656460	−	0.226596i
$514$	−25.5788			−1.12823
$515$		0			0
$516$	−0.0127719	−	0.200097i	−0.000562250	−	0.00880878i
$517$	1.77466	+	10.0646i	0.0780493	+	0.442640i
$518$	−4.03358	−	1.46810i	−0.177225	−	0.0645047i
$519$	18.3483	+	2.04118i	0.805400	+	0.0895980i
$520$		0			0
$521$	12.5826	−	21.7937i	0.551255	−	0.954801i	−0.446930	−	0.894569i	$-0.647483\pi$
$521$	12.5826	−	21.7937i	0.551255	−	0.954801i	0.998184	−	0.0602320i	$-0.0191841\pi$
$522$	0.933142	−	1.01139i	0.0408425	−	0.0442673i
$523$	−12.3608	−	21.4096i	−0.540502	−	0.936177i	−0.998875	−	0.0474173i	$-0.984901\pi$
$523$	−12.3608	−	21.4096i	−0.540502	−	0.936177i	0.458373	−	0.888760i	$-0.348432\pi$
$524$	0.249252	−	0.0907203i	0.0108886	−	0.00396313i
$525$		0			0
$526$	−16.8572	+	14.1449i	−0.735010	+	0.616746i
$527$	−8.10034	+	6.79700i	−0.352857	+	0.296082i
$528$	−21.2155	+	5.15302i	−0.923288	+	0.224256i
$529$	11.8215	−	4.30268i	0.513978	−	0.187073i
$530$		0			0
$531$	−11.8040	−	37.8884i	−0.512251	−	1.64421i
$532$	0.386296	−	0.669084i	0.0167481	−	0.0290085i
$533$	−10.7198	+	60.7951i	−0.464327	+	2.63333i
$534$	11.5965	+	1.29007i	0.501831	+	0.0558270i
$535$		0			0
$536$	2.08126	+	11.8034i	0.0898966	+	0.509829i
$537$	1.54874	+	24.2642i	0.0668332	+	1.04708i
$538$	6.01881	+	5.05038i	0.259489	+	0.217737i
$539$	24.9229			1.07350
$540$		0			0
$541$	16.9208			0.727482			0.363741	−	0.931500i	$-0.381499\pi$
$541$	16.9208			0.727482			0.363741	+	0.931500i	$0.381499\pi$
$542$	30.5964	+	25.6734i	1.31423	+	1.10277i
$543$	−22.3695	+	14.8916i	−0.959966	+	0.639060i
$544$	−1.24705	−	7.07237i	−0.0534668	−	0.303225i
$545$		0			0
$546$	−5.27610	+	7.16999i	−0.225796	+	0.306847i
$547$	0.247344	−	1.40276i	0.0105757	−	0.0599776i	−0.979063	−	0.203556i	$-0.934750\pi$
$547$	0.247344	−	1.40276i	0.0105757	−	0.0599776i	0.989639	+	0.143579i	$0.0458611\pi$
$548$	−0.117230	+	0.203048i	−0.00500781	+	0.00867379i
$549$	17.5718	−	9.07112i	0.749944	−	0.387146i
$550$		0			0
$551$	1.00924	−	0.367332i	0.0429950	−	0.0156489i
$552$	11.6184	+	12.1783i	0.494511	+	0.518342i
$553$	6.88000	−	5.77301i	0.292567	−	0.245493i
$554$	24.4495	−	20.5156i	1.03876	−	0.871624i
$555$		0			0
$556$	4.07887	−	1.48459i	0.172983	−	0.0629605i
$557$	4.83922	+	8.38178i	0.205044	+	0.355147i	0.950147	−	0.311803i	$-0.100933\pi$
$557$	4.83922	+	8.38178i	0.205044	+	0.355147i	−0.745102	+	0.666950i	$0.767599\pi$
$558$	−10.4140	+	1.33486i	−0.440860	+	0.0565090i
$559$	−0.901548	+	1.56153i	−0.0381314	+	0.0660455i
$560$		0			0
$561$	10.5762	+	24.1480i	0.446527	+	1.01953i
$562$	−21.6119	−	7.86609i	−0.911644	−	0.331811i
$563$	6.62845	+	37.5918i	0.279356	+	1.58431i	0.724776	+	0.688985i	$0.241943\pi$
$563$	6.62845	+	37.5918i	0.279356	+	1.58431i	−0.445420	+	0.895322i	$0.646945\pi$
$564$	−1.33742	−	0.662383i	−0.0563154	−	0.0278913i
$565$		0			0
$566$	3.76035			0.158059
$567$	−6.31664	−	2.99820i	−0.265274	−	0.125913i
$568$	36.5435			1.53333
$569$	−25.8444	−	21.6860i	−1.08345	−	0.909126i	−0.0872516	−	0.996186i	$-0.527808\pi$
$569$	−25.8444	−	21.6860i	−1.08345	−	0.909126i	−0.996203	+	0.0870599i	$0.972253\pi$
$570$		0			0
$571$	0.954517	+	5.41334i	0.0399453	+	0.226541i	0.998245	−	0.0592252i	$-0.0188630\pi$
$571$	0.954517	+	5.41334i	0.0399453	+	0.226541i	−0.958299	+	0.285766i	$0.907752\pi$
$572$	−6.15485	−	2.24018i	−0.257347	−	0.0936667i
$573$	−3.03541	−	6.93057i	−0.126806	−	0.289529i
$574$	−2.10421	+	11.9336i	−0.0878279	+	0.498097i
$575$		0			0
$576$	10.2404	−	24.4856i	0.426684	−	1.02023i
$577$	13.6599	+	23.6596i	0.568668	+	0.984962i	0.996698	+	0.0811975i	$0.0258745\pi$
$577$	13.6599	+	23.6596i	0.568668	+	0.984962i	−0.428030	+	0.903765i	$0.640792\pi$
$578$	−2.11492	+	0.769769i	−0.0879692	+	0.0320182i
$579$	−1.60436	+	5.46953i	−0.0666750	+	0.227306i
$580$		0			0
$581$	3.30932	−	2.77685i	0.137294	−	0.115203i
$582$	10.9895	+	11.5191i	0.455528	+	0.477481i
$583$	34.0222	−	12.3831i	1.40906	−	0.512854i
$584$	21.2085	+	36.7342i	0.877613	+	1.52007i
$585$		0			0
$586$	3.99891	−	6.92632i	0.165193	−	0.286123i
$587$	2.06533	−	11.7130i	0.0852451	−	0.483449i	−0.912058	−	0.410061i	$-0.865508\pi$
$587$	2.06533	−	11.7130i	0.0852451	−	0.483449i	0.997303	−	0.0733885i	$-0.0233813\pi$
$588$	−2.15715	+	2.93147i	−0.0889595	+	0.120892i
$589$	−7.70014	−	2.80262i	−0.317279	−	0.115480i
$590$		0			0
$591$	−30.8929	+	20.5657i	−1.27076	+	0.845961i
$592$	−10.5907	−	8.88664i	−0.435274	−	0.365239i
$593$	9.14301			0.375459			0.187729	−	0.982221i	$-0.439887\pi$
$593$	9.14301			0.375459			0.187729	+	0.982221i	$0.439887\pi$
$594$	−4.11439	+	25.8500i	−0.168816	+	1.06064i
$595$		0			0
$596$	−1.33610	−	1.12112i	−0.0547287	−	0.0459229i
$597$	−1.55126	−	24.3036i	−0.0634889	−	0.994681i
$598$	−3.70821	−	21.0303i	−0.151640	−	0.859994i
$599$	−24.8634	−	9.04955i	−1.01589	−	0.369755i	−0.220200	−	0.975455i	$-0.570671\pi$
$599$	−24.8634	−	9.04955i	−1.01589	−	0.369755i	−0.795693	+	0.605700i	$0.792893\pi$
$600$		0			0
$601$	3.19159	−	18.1004i	0.130188	−	0.738330i	−0.847903	−	0.530151i	$-0.822135\pi$
$601$	3.19159	−	18.1004i	0.130188	−	0.738330i	0.978091	−	0.208179i	$-0.0667537\pi$
$602$	−0.176966	+	0.306514i	−0.00721260	+	0.0124926i
$603$	11.6519	+	2.62495i	0.474501	+	0.106896i
$604$	−0.958297	−	1.65982i	−0.0389925	−	0.0675371i
$605$		0			0
$606$	3.83685	−	0.931928i	0.155861	−	0.0378570i
$607$	−23.4111	+	19.6443i	−0.950228	+	0.797336i	−0.979336	−	0.202240i	$-0.935178\pi$
$607$	−23.4111	+	19.6443i	−0.950228	+	0.797336i	0.0291076	+	0.999576i	$0.490733\pi$
$608$	4.26315	−	3.57721i	0.172894	−	0.145075i
$609$	0.463934	−	0.112684i	0.0187995	−	0.00456620i
$610$		0			0
$611$	6.71069	+	11.6233i	0.271486	+	0.470227i
$612$	−3.75573	−	0.846095i	−0.151816	−	0.0342014i
$613$	−10.0248	+	17.3635i	−0.404898	+	0.701304i	−0.994310	−	0.106529i	$-0.966026\pi$
$613$	−10.0248	+	17.3635i	−0.404898	+	0.701304i	0.589411	+	0.807833i	$0.299360\pi$
$614$	−6.25164	+	35.4548i	−0.252295	+	1.43084i
$615$		0			0
$616$	−8.56328	−	3.11678i	−0.345024	−	0.125579i
$617$	4.38720	+	24.8810i	0.176622	+	1.00167i	0.936255	+	0.351321i	$0.114267\pi$
$617$	4.38720	+	24.8810i	0.176622	+	1.00167i	−0.759633	+	0.650352i	$0.774621\pi$
$618$	−2.73363	−	42.8278i	−0.109963	−	1.72279i
$619$	13.4670	+	11.3002i	0.541285	+	0.454192i	0.871977	−	0.489547i	$-0.162838\pi$
$619$	13.4670	+	11.3002i	0.541285	+	0.454192i	−0.330692	+	0.943739i	$0.607282\pi$
$620$		0			0
$621$	15.6636	−	5.99901i	0.628557	−	0.240732i
$622$	−22.3836			−0.897502
$623$	3.10102	+	2.60207i	0.124240	+	0.104250i
$624$	−23.8669	+	15.8884i	−0.955439	+	0.636046i
$625$		0			0
$626$	12.1610	+	4.42624i	0.486051	+	0.176908i
$627$	−12.1081	+	16.4543i	−0.483549	+	0.657122i
$628$	0.0922128	−	0.522965i	0.00367969	−	0.0208686i
$629$	−8.34690	+	14.4573i	−0.332813	+	0.576449i
$630$		0			0
$631$	15.3587	+	26.6020i	0.611420	+	1.05901i	0.991001	+	0.133852i	$0.0427347\pi$
$631$	15.3587	+	26.6020i	0.611420	+	1.05901i	−0.379581	+	0.925158i	$0.623932\pi$
$632$	32.7030	−	11.9029i	1.30085	−	0.473472i
$633$	−4.97202	−	5.21163i	−0.197620	−	0.207143i
$634$	7.93948	−	6.66201i	0.315317	−	0.264582i
$635$		0			0
$636$	−1.48821	+	5.07354i	−0.0590113	+	0.201179i
$637$	30.7565	−	11.1944i	1.21862	−	0.443540i
$638$	−0.893635	−	1.54782i	−0.0353794	−	0.0612788i
$639$	14.0509	−	33.5969i	0.555846	−	1.32907i
$640$		0			0
$641$	1.59110	−	9.02357i	0.0628446	−	0.356409i	−0.937128	−	0.348986i	$-0.886526\pi$
$641$	1.59110	−	9.02357i	0.0628446	−	0.356409i	0.999972	−	0.00742320i	$-0.00236290\pi$
$642$	4.95276	+	11.3083i	0.195470	+	0.446305i
$643$	13.6800	+	4.97910i	0.539486	+	0.196357i	0.597369	−	0.801967i	$-0.296213\pi$
$643$	13.6800	+	4.97910i	0.539486	+	0.196357i	−0.0578831	+	0.998323i	$0.518435\pi$
$644$	0.143061	+	0.811340i	0.00563740	+	0.0319713i
$645$		0			0
$646$	11.7111	+	9.82681i	0.460769	+	0.386631i
$647$	−16.6946			−0.656331			−0.328165	−	0.944620i	$-0.606430\pi$
$647$	−16.6946			−0.656331			−0.328165	+	0.944620i	$0.606430\pi$
$648$	−19.0270	−	19.2888i	−0.747452	−	0.757735i
$649$	−51.5419			−2.02320
$650$		0			0
$651$	−3.26417	−	1.61665i	−0.127933	−	0.0633614i
$652$	−0.182262	−	1.03366i	−0.00713791	−	0.0404811i
$653$	17.3438	+	6.31264i	0.678716	+	0.247033i	0.658296	−	0.752759i	$-0.271277\pi$
$653$	17.3438	+	6.31264i	0.678716	+	0.247033i	0.0204201	+	0.999791i	$0.493500\pi$
$654$	12.8174	+	29.2653i	0.501200	+	1.14436i
$655$		0			0
$656$	−19.5143	+	33.7998i	−0.761907	+	1.31966i
$657$	41.9268	−	5.37413i	1.63572	−	0.209665i
$658$	1.31725	+	2.28155i	0.0513518	+	0.0889439i
$659$	−8.26055	+	3.00660i	−0.321785	+	0.117120i	−0.497862	−	0.867256i	$-0.665882\pi$
$659$	−8.26055	+	3.00660i	−0.321785	+	0.117120i	0.176077	+	0.984376i	$0.443659\pi$
$660$		0			0
$661$	−13.7931	+	11.5737i	−0.536487	+	0.450166i	−0.870335	−	0.492461i	$-0.836097\pi$
$661$	−13.7931	+	11.5737i	−0.536487	+	0.450166i	0.333847	+	0.942627i	$0.391653\pi$
$662$	25.5942	−	21.4760i	0.994745	−	0.834690i
$663$	23.8981	+	25.0498i	0.928126	+	0.972854i
$664$	15.7303	−	5.72536i	0.610454	−	0.222187i
$665$		0			0
$666$	−14.7286	+	7.60337i	−0.570720	+	0.294625i
$667$	−0.572636	+	0.991835i	−0.0221726	+	0.0384040i
$668$	0.315134	−	1.78721i	0.0121929	−	0.0691494i
$669$	17.0529	−	23.1742i	0.659305	−	0.895966i
$670$		0			0
$671$	−4.45992	−	25.2934i	−0.172173	−	0.976442i
$672$	2.05927	−	1.37088i	0.0794380	−	0.0528828i
$673$	6.26057	+	5.25324i	0.241327	+	0.202498i	0.755427	−	0.655233i	$-0.227429\pi$
$673$	6.26057	+	5.25324i	0.241327	+	0.202498i	−0.514100	+	0.857730i	$0.671874\pi$
$674$	25.5398			0.983756
$675$		0			0
$676$	−4.33098			−0.166576
$677$	0.630907	+	0.529394i	0.0242477	+	0.0203462i	0.654831	−	0.755775i	$-0.272740\pi$
$677$	0.630907	+	0.529394i	0.0242477	+	0.0203462i	−0.630583	+	0.776122i	$0.717184\pi$
$678$	0.885104	+	13.8669i	0.0339922	+	0.532556i
$679$	0.959124	+	5.43946i	0.0368078	+	0.208747i
$680$		0			0
$681$	9.11782	+	1.01433i	0.349396	+	0.0388690i
$682$	−2.36791	+	13.4291i	−0.0906721	+	0.514227i
$683$	−19.4328	+	33.6587i	−0.743577	+	1.28791i	0.207280	+	0.978282i	$0.433539\pi$
$683$	−19.4328	+	33.6587i	−0.743577	+	1.28791i	−0.950857	+	0.309631i	$0.899794\pi$
$684$	−0.887394	−	2.84834i	−0.0339303	−	0.108909i
$685$		0			0
$686$	12.6441	−	4.60209i	0.482756	−	0.175709i
$687$	34.3051	−	8.33233i	1.30882	−	0.317898i
$688$	−0.873251	+	0.732745i	−0.0332924	+	0.0279356i
$689$	36.4236	−	30.5631i	1.38763	−	1.16436i
$690$		0			0
$691$	33.1809	−	12.0769i	1.26226	−	0.459426i	0.377734	−	0.925914i	$-0.376703\pi$
$691$	33.1809	−	12.0769i	1.26226	−	0.459426i	0.884527	+	0.466488i	$0.154481\pi$
$692$	1.75079	+	3.03245i	0.0665549	+	0.115277i
$693$	−6.15803	+	6.67440i	−0.233924	+	0.253539i
$694$	16.2881	−	28.2118i	0.618287	−	1.07090i
$695$		0			0
$696$	1.83865	+	0.204543i	0.0696938	+	0.00775320i
$697$	44.2848	+	16.1184i	1.67741	+	0.610526i
$698$	−6.70066	−	38.0013i	−0.253624	−	1.43837i
$699$	−0.135344	−	2.12044i	−0.00511918	−	0.0802023i
$700$		0			0
$701$	−26.7698			−1.01108			−0.505541	−	0.862803i	$-0.668707\pi$
$701$	−26.7698			−1.01108			−0.505541	+	0.862803i	$0.668707\pi$
$702$	6.53345	+	33.7487i	0.246589	+	1.27376i
$703$	−12.9366			−0.487912
$704$	−26.4062	−	22.1575i	−0.995222	−	0.835091i
$705$		0			0
$706$	2.91380	+	16.5250i	0.109662	+	0.621926i
$707$	1.28724	+	0.468517i	0.0484116	+	0.0176204i
$708$	4.46111	−	6.06245i	0.167659	−	0.227841i
$709$	−5.90817	+	33.5069i	−0.221886	+	1.25838i	0.646664	+	0.762775i	$0.276164\pi$
$709$	−5.90817	+	33.5069i	−0.221886	+	1.25838i	−0.868550	+	0.495602i	$0.834947\pi$
$710$		0			0
$711$	1.63111	−	34.6427i	0.0611714	−	1.29920i
$712$	7.84310	+	13.5846i	0.293933	+	0.509106i
$713$	8.21108	−	2.98859i	0.307507	−	0.111923i
$714$	4.69099	+	4.91706i	0.175556	+	0.184016i
$715$		0			0
$716$	−3.53264	+	2.96424i	−0.132021	+	0.110779i
$717$	7.49295	−	25.5447i	0.279829	−	0.953983i
$718$	−16.4548	+	5.98907i	−0.614089	+	0.223510i
$719$	−3.78251	−	6.55150i	−0.141064	−	0.244330i	0.786834	−	0.617165i	$-0.211719\pi$
$719$	−3.78251	−	6.55150i	−0.141064	−	0.244330i	−0.927898	+	0.372835i	$0.878386\pi$
$720$		0			0
$721$	7.44442	−	12.8941i	0.277245	−	0.480202i
$722$	2.20834	−	12.5241i	0.0821858	−	0.466099i
$723$	−12.9150	−	29.4882i	−0.480316	−	1.09668i
$724$	−4.78958	−	1.74326i	−0.178003	−	0.0647879i
$725$		0			0
$726$	8.39132	+	4.15597i	0.311431	+	0.154243i
$727$	22.3698	+	18.7705i	0.829649	+	0.696158i	0.955210	−	0.295927i	$-0.0956286\pi$
$727$	22.3698	+	18.7705i	0.829649	+	0.696158i	−0.125561	+	0.992086i	$0.540073\pi$
$728$	−11.9676			−0.443549
$729$	−25.0493	+	10.0763i	−0.927753	+	0.373196i
$730$		0			0
$731$	1.05445	+	0.884786i	0.0390001	+	0.0327250i
$732$	3.36108	+	1.66464i	0.124229	+	0.0615270i
$733$	3.71565	+	21.0725i	0.137241	+	0.778330i	0.973273	+	0.229650i	$0.0737583\pi$
$733$	3.71565	+	21.0725i	0.137241	+	0.778330i	−0.836033	+	0.548680i	$0.815131\pi$
$734$	−30.4144	−	11.0699i	−1.12262	−	0.408599i
$735$		0			0
$736$	−1.03050	+	5.84426i	−0.0379847	+	0.215422i
$737$	7.75631	−	13.4343i	0.285707	−	0.494860i
$738$	28.3585	+	37.2201i	1.04389	+	1.37009i
$739$	1.12801	+	1.95377i	0.0414944	+	0.0718704i	0.886027	−	0.463634i	$-0.153455\pi$
$739$	1.12801	+	1.95377i	0.0414944	+	0.0718704i	−0.844532	+	0.535505i	$0.820121\pi$
$740$		0			0
$741$	−7.55148	+	25.7442i	−0.277411	+	0.945737i
$742$	7.14965	−	5.99927i	0.262472	−	0.220240i
$743$	2.52675	−	2.12019i	0.0926974	−	0.0777823i	−0.595261	−	0.803532i	$-0.702951\pi$
$743$	2.52675	−	2.12019i	0.0926974	−	0.0777823i	0.687959	+	0.725750i	$0.258507\pi$
$744$	−9.74315	−	10.2127i	−0.357201	−	0.374415i
$745$		0			0
$746$	1.34766	+	2.33421i	0.0493412	+	0.0854615i
$747$	0.784572	−	16.6633i	0.0287060	−	0.609678i
$748$	−2.50008	+	4.33026i	−0.0914119	+	0.158330i
$749$	−0.743750	+	4.21801i	−0.0271760	+	0.154123i
$750$		0			0
$751$	−29.9156	−	10.8884i	−1.09164	−	0.397323i	−0.267410	−	0.963583i	$-0.586168\pi$
$751$	−29.9156	−	10.8884i	−1.09164	−	0.397323i	−0.824227	+	0.566260i	$0.808390\pi$
$752$	1.47345	+	8.35633i	0.0537310	+	0.304724i
$753$	−8.94002	+	5.95147i	−0.325792	+	0.216884i
$754$	−1.79803	−	1.50873i	−0.0654804	−	0.0549446i
$755$		0			0
$756$	−0.252057	−	1.30201i	−0.00916724	−	0.0473536i
$757$	−18.5287			−0.673436			−0.336718	−	0.941605i	$-0.609317\pi$
$757$	−18.5287			−0.673436			−0.336718	+	0.941605i	$0.609317\pi$
$758$	−9.04740	−	7.59167i	−0.328616	−	0.275742i
$759$	−1.38766	−	21.7404i	−0.0503688	−	0.789128i
$760$		0			0
$761$	−38.6363	−	14.0625i	−1.40057	−	0.509764i	−0.472219	−	0.881481i	$-0.656547\pi$
$761$	−38.6363	−	14.0625i	−1.40057	−	0.509764i	−0.928346	+	0.371717i	$0.878769\pi$
$762$	−26.8868	−	2.99106i	−0.974005	−	0.108355i
$763$	−1.92478	+	10.9159i	−0.0696816	+	0.395184i
$764$	0.717533	−	1.24280i	0.0259594	−	0.0449630i
$765$		0			0
$766$	−6.60470	−	11.4397i	−0.238638	−	0.413332i
$767$	−63.6062	+	23.1507i	−2.29669	+	0.835925i
$768$	12.8927	−	3.13150i	0.465226	−	0.112998i
$769$	26.1339	−	21.9289i	0.942412	−	0.790777i	−0.0355917	−	0.999366i	$-0.511332\pi$
$769$	26.1339	−	21.9289i	0.942412	−	0.790777i	0.978003	+	0.208589i	$0.0668871\pi$
$770$		0			0
$771$	−33.2998	+	8.08817i	−1.19926	+	0.291288i
$772$	−1.01591	+	0.369762i	−0.0365635	+	0.0133080i
$773$	−2.64111	−	4.57453i	−0.0949940	−	0.164534i	0.814612	−	0.580006i	$-0.196950\pi$
$773$	−2.64111	−	4.57453i	−0.0949940	−	0.164534i	−0.909606	+	0.415472i	$0.863617\pi$
$774$	0.406524	+	1.30485i	0.0146122	+	0.0469020i
$775$		0			0
$776$	−3.71656	+	21.0777i	−0.133417	+	0.756645i
$777$	−5.71536	−	0.635814i	−0.205037	−	0.0228097i
$778$	21.2069	+	7.71867i	0.760303	+	0.276728i
$779$	6.34166	+	35.9653i	0.227213	+	1.28859i
$780$		0			0
$781$	−36.2321	−	30.4024i	−1.29649	−	1.08788i
$782$	−16.3022			−0.582966
$783$	0.895009	−	1.61175i	0.0319850	−	0.0575991i
$784$	20.6927			0.739026
$785$		0			0
$786$	−1.50504	+	1.00192i	−0.0536830	+	0.0357373i
$787$	2.03562	+	11.5446i	0.0725620	+	0.411520i	0.999354	+	0.0359440i	$0.0114438\pi$
$787$	2.03562	+	11.5446i	0.0725620	+	0.411520i	−0.926792	+	0.375575i	$0.877445\pi$
$788$	−6.61455	−	2.40750i	−0.235634	−	0.0857636i
$789$	−17.4730	+	23.7450i	−0.622054	+	0.845343i
$790$		0			0
$791$	−2.41038	+	4.17490i	−0.0857032	+	0.148442i
$792$	−31.2687	+	16.1419i	−1.11109	+	0.573579i
$793$	−16.8647	−	29.2106i	−0.598884	−	1.03730i
$794$	−16.0844	+	5.85425i	−0.570815	+	0.207760i
$795$		0			0
$796$	3.53839	−	2.96906i	0.125415	−	0.105235i
$797$	−18.6441	+	15.6442i	−0.660406	+	0.554147i	−0.910209	−	0.414150i	$-0.864079\pi$
$797$	−18.6441	+	15.6442i	−0.660406	+	0.554147i	0.249802	+	0.968297i	$0.419634\pi$
$798$	−1.48229	+	5.05337i	−0.0524725	+	0.178887i
$799$	9.62798	−	3.50430i	0.340613	−	0.123973i
$800$		0			0
$801$	15.5049	−	1.98741i	0.547840	−	0.0702216i
$802$	25.3346	−	43.8809i	0.894597	−	1.54949i
$803$	9.53322	−	54.0656i	0.336420	−	1.90793i
$804$	0.908836	+	2.07509i	0.0320522	+	0.0731829i
$805$		0			0
$806$	3.10970	+	17.6360i	0.109535	+	0.621201i
$807$	9.43258	+	4.67168i	0.332042	+	0.164451i
$808$	4.06625	+	3.41199i	0.143050	+	0.120033i
$809$	−2.84260			−0.0999405			−0.0499703	−	0.998751i	$-0.515913\pi$
$809$	−2.84260			−0.0999405			−0.0499703	+	0.998751i	$0.515913\pi$
$810$		0			0
$811$	25.2940			0.888194			0.444097	−	0.895979i	$-0.353525\pi$
$811$	25.2940			0.888194			0.444097	+	0.895979i	$0.353525\pi$
$812$	0.0693672	+	0.0582060i	0.00243431	+	0.00204263i
$813$	47.9501	+	23.7483i	1.68168	+	0.832888i
$814$	3.73828	+	21.2008i	0.131027	+	0.743089i
$815$		0			0
$816$	8.78109	+	20.0494i	0.307400	+	0.701868i
$817$	−0.185227	+	1.05047i	−0.00648027	+	0.0367514i
$818$	−12.8174	+	22.2004i	−0.448149	+	0.776218i
$819$	−4.60153	+	11.0026i	−0.160790	+	0.384463i
$820$		0			0
$821$	−39.7487	+	14.4673i	−1.38724	+	0.504914i	−0.924365	−	0.381510i	$-0.875404\pi$
$821$	−39.7487	+	14.4673i	−1.38724	+	0.504914i	−0.462874	+	0.886424i	$0.653182\pi$
$822$	0.449834	−	1.53355i	0.0156897	−	0.0534889i
$823$	1.70055	−	1.42693i	0.0592774	−	0.0497397i	−0.612668	−	0.790341i	$-0.709904\pi$
$823$	1.70055	−	1.42693i	0.0592774	−	0.0497397i	0.671945	+	0.740601i	$0.265459\pi$
$824$	44.1958	−	37.0847i	1.53964	−	1.29191i
$825$		0			0
$826$	−12.4853	+	4.54429i	−0.434421	+	0.158116i
$827$	−9.11184	−	15.7822i	−0.316850	−	0.548800i	0.662979	−	0.748638i	$-0.269292\pi$
$827$	−9.11184	−	15.7822i	−0.316850	−	0.548800i	−0.979829	+	0.199838i	$0.935958\pi$
$828$	2.67725	+	1.71848i	0.0930410	+	0.0597214i
$829$	−15.8943	+	27.5298i	−0.552033	+	0.956149i	0.446095	+	0.894986i	$0.352814\pi$
$829$	−15.8943	+	27.5298i	−0.552033	+	0.956149i	−0.998128	+	0.0611633i	$0.980519\pi$
$830$		0			0
$831$	25.3426	−	34.4394i	0.879124	−	1.19469i
$832$	−42.5394	−	15.4831i	−1.47479	−	0.536779i
$833$	−4.33884	−	24.6068i	−0.150332	−	0.852574i
$834$	−24.6291	+	16.3959i	−0.852837	+	0.567743i
$835$		0			0
$836$	−3.87478			−0.134012
$837$	−13.1354	+	5.03076i	−0.454027	+	0.173889i
$838$	−35.2053			−1.21615
$839$	14.1865	+	11.9039i	0.489772	+	0.410968i	0.853945	−	0.520364i	$-0.174204\pi$
$839$	14.1865	+	11.9039i	0.489772	+	0.410968i	−0.364173	+	0.931331i	$0.618648\pi$
$840$		0			0
$841$	−5.01394	−	28.4355i	−0.172894	−	0.980533i
$842$	2.74612	+	0.999506i	0.0946376	+	0.0344453i
$843$	−30.6229	−	3.40669i	−1.05471	−	0.117333i
$844$	0.237233	−	1.34542i	0.00816591	−	0.0463112i
$845$		0			0
$846$	9.92444	+	2.23579i	0.341209	+	0.0768680i
$847$	1.62438	+	2.81351i	0.0558144	+	0.0966734i
$848$	28.2476	−	10.2813i	0.970027	−	0.353061i
$849$	4.89543	−	1.18905i	0.168011	−	0.0408080i
$850$		0			0
$851$	10.5675	−	8.86722i	0.362251	−	0.303964i
$852$	6.71199	−	1.63027i	0.229949	−	0.0558521i
$853$	−21.7616	+	7.92056i	−0.745102	+	0.271195i	−0.686543	−	0.727089i	$-0.740873\pi$
$853$	−21.7616	+	7.92056i	−0.745102	+	0.271195i	−0.0585587	+	0.998284i	$0.518650\pi$
$854$	−3.31040	−	5.73378i	−0.113280	−	0.196206i
$855$		0			0
$856$	−8.29838	+	14.3732i	−0.283633	+	0.491266i
$857$	−4.14002	+	23.4792i	−0.141420	+	0.802035i	0.828751	+	0.559617i	$0.189052\pi$
$857$	−4.14002	+	23.4792i	−0.141420	+	0.802035i	−0.970172	+	0.242418i	$0.922059\pi$
$858$	44.3726	+	4.93629i	1.51485	+	0.168522i
$859$	7.58350	+	2.76017i	0.258746	+	0.0941757i	0.468136	−	0.883656i	$-0.344926\pi$
$859$	7.58350	+	2.76017i	0.258746	+	0.0941757i	−0.209390	+	0.977832i	$0.567148\pi$
$860$		0			0
$861$	1.03409	+	16.2011i	0.0352417	+	0.552133i
$862$	−9.60190	−	8.05695i	−0.327042	−	0.274421i
$863$	18.5552			0.631628			0.315814	−	0.948821i	$-0.397723\pi$
$863$	18.5552			0.631628			0.315814	+	0.948821i	$0.397723\pi$
$864$	1.50156	−	9.43403i	0.0510841	−	0.320952i
$865$		0			0
$866$	−32.0328	−	26.8787i	−1.08852	−	0.913375i
$867$	−2.50992	+	1.67088i	−0.0852413	+	0.0567461i
$868$	−0.119971	−	0.680388i	−0.00407208	−	0.0230939i
$869$	−42.3270	−	15.4058i	−1.43584	−	0.522604i
$870$		0			0
$871$	3.53760	−	20.0627i	0.119867	−	0.679799i
$872$	−21.4757	+	37.1970i	−0.727258	+	1.25965i
$873$	17.9491	+	11.5212i	0.607485	+	0.389934i
$874$	−6.31655	−	10.9406i	−0.213660	−	0.370071i
$875$		0			0
$876$	5.53416	+	5.80086i	0.186982	+	0.195993i
$877$	−8.10128	+	6.79778i	−0.273561	+	0.229545i	−0.769238	−	0.638962i	$-0.779364\pi$
$877$	−8.10128	+	6.79778i	−0.273561	+	0.229545i	0.495678	+	0.868507i	$0.334920\pi$
$878$	9.78384	−	8.20962i	0.330189	−	0.277061i
$879$	3.01586	−	10.2815i	0.101722	−	0.346788i
$880$		0			0
$881$	−5.52419	−	9.56817i	−0.186115	−	0.322360i	0.757837	−	0.652444i	$-0.226256\pi$
$881$	−5.52419	−	9.56817i	−0.186115	−	0.322360i	−0.943952	+	0.330084i	$0.892923\pi$
$882$	9.57225	−	22.8880i	0.322314	−	0.770679i
$883$	−26.3618	+	45.6600i	−0.887146	+	1.53658i	−0.0439118	+	0.999035i	$0.513982\pi$
$883$	−26.3618	+	45.6600i	−0.887146	+	1.53658i	−0.843234	+	0.537546i	$0.819351\pi$
$884$	−1.14027	+	6.46678i	−0.0383513	+	0.217501i
$885$		0			0
$886$	31.7844	+	11.5686i	1.06782	+	0.388654i
$887$	−7.30927	−	41.4529i	−0.245421	−	1.39185i	−0.819512	−	0.573062i	$-0.805755\pi$
$887$	−7.30927	−	41.4529i	−0.245421	−	1.39185i	0.574091	−	0.818792i	$-0.305356\pi$
$888$	−19.9685	−	9.88980i	−0.670099	−	0.331880i
$889$	−7.18978	−	6.03294i	−0.241138	−	0.202338i
$890$		0			0
$891$	2.81759	+	34.9540i	0.0943929	+	1.17100i
$892$	5.45722			0.182721
$893$	6.08228	+	5.10364i	0.203536	+	0.170787i
$894$	10.6538	+	5.27649i	0.356315	+	0.176472i
$895$		0			0
$896$	−5.66584	−	2.06220i	−0.189282	−	0.0688932i
$897$	−11.4775	−	26.2059i	−0.383222	−	0.874989i
$898$	3.61208	−	20.4851i	0.120537	−	0.683597i
$899$	0.480212	−	0.831752i	0.0160160	−	0.0277405i
$900$		0			0
$901$	−18.1489	−	31.4349i	−0.604629	−	1.04725i
$902$	57.1085	−	20.7858i	1.90151	−	0.692092i
$903$	−0.133462	+	0.454995i	−0.00444135	+	0.0151413i
$904$	−14.3099	+	12.0074i	−0.475940	+	0.399361i
$905$		0			0
$906$	9.01796	+	9.45255i	0.299602	+	0.314040i
$907$	0.590592	−	0.214958i	0.0196103	−	0.00713756i	−0.332196	−	0.943210i	$-0.607790\pi$
$907$	0.590592	−	0.214958i	0.0196103	−	0.00713756i	0.351807	+	0.936073i	$0.385567\pi$
$908$	0.870019	+	1.50692i	0.0288726	+	0.0500088i
$909$	4.70034	−	2.42647i	0.155900	−	0.0804810i
$910$		0			0
$911$	4.64690	−	26.3539i	0.153959	−	0.873144i	−0.805773	−	0.592225i	$-0.798250\pi$
$911$	4.64690	−	26.3539i	0.153959	−	0.873144i	0.959731	−	0.280919i	$-0.0906392\pi$
$912$	−10.0530	+	13.6615i	−0.332887	+	0.452378i
$913$	−20.3595	−	7.41025i	−0.673801	−	0.245243i
$914$	6.83321	+	38.7530i	0.226022	+	1.28184i
$915$		0			0
$916$	5.12928	+	4.30398i	0.169476	+	0.142207i
$917$	−0.627276			−0.0207145
$918$	26.2384	−	0.438035i	0.865997	−	0.0144573i
$919$	8.32555			0.274634			0.137317	−	0.990527i	$-0.456152\pi$
$919$	8.32555			0.274634			0.137317	+	0.990527i	$0.456152\pi$
$920$		0			0
$921$	3.07230	+	48.1338i	0.101236	+	1.58606i
$922$	−3.67124	−	20.8206i	−0.120906	−	0.685691i
$923$	−58.3685	−	21.2444i	−1.92122	−	0.699268i
$924$	−1.71187	−	0.190440i	−0.0563165	−	0.00626501i
$925$		0			0
$926$	4.72363	−	8.18157i	0.155228	−	0.268863i
$927$	−17.1012	−	54.8912i	−0.561677	−	1.80286i
$928$	0.326134	+	0.564881i	0.0107059	+	0.0185431i
$929$	−20.0134	+	7.28427i	−0.656618	+	0.238989i	−0.648775	−	0.760980i	$-0.724719\pi$
$929$	−20.0134	+	7.28427i	−0.656618	+	0.238989i	−0.00784221	+	0.999969i	$0.502496\pi$
$930$		0			0
$931$	14.8327	−	12.4461i	0.486122	−	0.407905i
$932$	0.308716	−	0.259044i	0.0101123	−	0.00848525i
$933$	−29.1403	+	7.07785i	−0.954009	+	0.231718i
$934$	12.2224	−	4.44860i	0.399930	−	0.145563i
$935$		0			0
$936$	−31.3373	+	33.9650i	−1.02429	+	1.11018i
$937$	−1.54921	+	2.68331i	−0.0506104	+	0.0876598i	−0.890221	−	0.455529i	$-0.849450\pi$
$937$	−1.54921	+	2.68331i	−0.0506104	+	0.0876598i	0.839610	+	0.543189i	$0.182783\pi$
$938$	0.694400	−	3.93814i	0.0226730	−	0.128585i
$939$	17.2315	+	1.91694i	0.562327	+	0.0625570i
$940$		0			0
$941$	−2.52290	−	14.3081i	−0.0822442	−	0.466430i	−0.997917	−	0.0645063i	$-0.979453\pi$
$941$	−2.52290	−	14.3081i	−0.0822442	−	0.466430i	0.915673	−	0.401924i	$-0.131658\pi$
$942$	0.230572	+	3.61237i	0.00751243	+	0.117697i
$943$	−29.8324	−	25.0323i	−0.971476	−	0.815165i
$944$	−42.7937			−1.39282
$945$		0			0
$946$	1.77507			0.0577127
$947$	−3.14077	−	2.63542i	−0.102061	−	0.0856396i	0.590329	−	0.807163i	$-0.298998\pi$
$947$	−3.14077	−	2.63542i	−0.102061	−	0.0856396i	−0.692390	+	0.721523i	$0.743442\pi$
$948$	5.47558	−	3.64516i	0.177839	−	0.118389i
$949$	−12.5197	−	71.0025i	−0.406406	−	2.30484i
$950$		0			0
$951$	8.22948	−	11.1835i	0.266859	−	0.362649i
$952$	−1.58646	+	8.99727i	−0.0514175	+	0.291603i
$953$	14.3224	−	24.8072i	0.463950	−	0.803584i	−0.535204	−	0.844723i	$-0.679765\pi$
$953$	14.3224	−	24.8072i	0.463950	−	0.803584i	0.999153	+	0.0411387i	$0.0130986\pi$
$954$	1.69504	−	36.0004i	0.0548788	−	1.16556i
$955$		0			0
$956$	4.74467	−	1.72692i	0.153454	−	0.0558525i
$957$	−1.65281	−	1.73247i	−0.0534279	−	0.0560027i
$958$	−7.94406	+	6.66586i	−0.256661	+	0.215364i
$959$	0.424745	−	0.356403i	0.0137157	−	0.0115089i
$960$		0			0
$961$	22.2447	−	8.09640i	0.717570	−	0.261174i
$962$	14.1359	+	24.4841i	0.455761	+	0.789401i
$963$	10.0235	+	13.1557i	0.323004	+	0.423938i
$964$	3.05296	−	5.28788i	0.0983291	−	0.170311i
$965$		0			0
$966$	−2.25293	−	5.14399i	−0.0724868	−	0.165505i
$967$	20.2015	+	7.35273i	0.649635	+	0.236448i	0.645755	−	0.763545i	$-0.276543\pi$
$967$	20.2015	+	7.35273i	0.649635	+	0.236448i	0.00388011	+	0.999992i	$0.498765\pi$
$968$	2.18602	+	12.3976i	0.0702615	+	0.398473i
$969$	18.3535	+	9.08995i	0.589600	+	0.292011i
$970$		0			0
$971$	39.3784			1.26371			0.631857	−	0.775085i	$-0.282293\pi$
$971$	39.3784			1.26371			0.631857	+	0.775085i	$0.282293\pi$
$972$	−4.35522	−	2.69396i	−0.139694	−	0.0864090i
$973$	−10.2650			−0.329081
$974$	−1.28764	−	1.08046i	−0.0412588	−	0.0346202i
$975$		0			0
$976$	−3.70294	−	21.0004i	−0.118528	−	0.672206i
$977$	19.3119	+	7.02896i	0.617843	+	0.224876i	0.631931	−	0.775024i	$-0.282262\pi$
$977$	19.3119	+	7.02896i	0.617843	+	0.224876i	−0.0140884	+	0.999901i	$0.504485\pi$
$978$	2.87026	+	6.55350i	0.0917807	+	0.209558i
$979$	3.52548	−	19.9940i	0.112675	−	0.639010i
$980$		0			0
$981$	25.9403	+	34.0462i	0.828209	+	1.08701i
$982$	−7.19295	−	12.4585i	−0.229536	−	0.397568i
$983$	21.3818	−	7.78235i	0.681975	−	0.248218i	0.0222795	−	0.999752i	$-0.492908\pi$
$983$	21.3818	−	7.78235i	0.681975	−	0.248218i	0.659695	+	0.751533i	$0.270685\pi$
$984$	−17.7062	+	60.3631i	−0.564452	+	1.92431i
$985$		0			0
$986$	−1.37262	+	1.15176i	−0.0437130	+	0.0366796i
$987$	2.43631	+	2.55372i	0.0775486	+	0.0812858i
$988$	−4.78174	+	1.74041i	−0.152127	+	0.0553698i
$989$	−0.568729	−	0.985067i	−0.0180845	−	0.0313233i
$990$		0			0
$991$	−8.61401	+	14.9199i	−0.273633	+	0.473946i	−0.969789	−	0.243944i	$-0.921559\pi$
$991$	−8.61401	+	14.9199i	−0.273633	+	0.473946i	0.696156	+	0.717890i	$0.254892\pi$
$992$	0.864176	−	4.90099i	0.0274376	−	0.155606i
$993$	26.5290	−	36.0517i	0.841873	−	1.14407i
$994$	−11.4572	−	4.17010i	−0.363402	−	0.132267i
$995$		0			0
$996$	2.63378	−	1.75334i	0.0834546	−	0.0555567i
$997$	−10.3528	−	8.68705i	−0.327877	−	0.275122i	0.463957	−	0.885858i	$-0.346429\pi$
$997$	−10.3528	−	8.68705i	−0.327877	−	0.275122i	−0.791834	+	0.610736i	$0.790874\pi$
$998$	−22.9749			−0.727256
$999$	−16.7702	+	14.5557i	−0.530586	+	0.460524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.h.151.5		96
5.2	odd	4		135.2.p.a.124.12	yes	96
5.3	odd	4		135.2.p.a.124.5	yes	96
5.4	even	2	inner	675.2.l.h.151.12		96
15.2	even	4		405.2.p.a.289.5		96
15.8	even	4		405.2.p.a.289.12		96
27.22	even	9	inner	675.2.l.h.76.5		96
135.22	odd	36		135.2.p.a.49.5	✓	96
135.32	even	36		405.2.p.a.199.12		96
135.49	even	18	inner	675.2.l.h.76.12		96
135.103	odd	36		135.2.p.a.49.12	yes	96
135.113	even	36		405.2.p.a.199.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.5	✓	96	135.22	odd	36
135.2.p.a.49.12	yes	96	135.103	odd	36
135.2.p.a.124.5	yes	96	5.3	odd	4
135.2.p.a.124.12	yes	96	5.2	odd	4
405.2.p.a.199.5		96	135.113	even	36
405.2.p.a.199.12		96	135.32	even	36
405.2.p.a.289.5		96	15.2	even	4
405.2.p.a.289.12		96	15.8	even	4
675.2.l.h.76.5		96	27.22	even	9	inner
675.2.l.h.76.12		96	135.49	even	18	inner
675.2.l.h.151.5		96	1.1	even	1	trivial
675.2.l.h.151.12		96	5.4	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.990387 - 0.831033i) q^{2} +(-1.55212 - 0.768718i) q^{3} +(-0.0570464 - 0.323526i) q^{4} +(0.898367 + 2.05119i) q^{6} +(-0.134907 + 0.765094i) q^{7} +(-1.50522 + 2.60712i) q^{8} +(1.81814 + 2.38628i) q^{9} +(3.66139 - 1.33264i) q^{11} +(-0.160158 + 0.546003i) q^{12} +(3.91983 - 3.28913i) q^{13} +(0.769429 - 0.645628i) q^{14} +(3.03995 - 1.10645i) q^{16} +(-1.95315 - 3.38295i) q^{17} +(0.182416 - 3.87428i) q^{18} +(1.51356 - 2.62156i) q^{19} +(0.797534 - 1.08381i) q^{21} +(-4.73366 - 1.72291i) q^{22} +(0.560532 + 3.17893i) q^{23} +(4.34042 - 2.88947i) q^{24} -6.61553 q^{26} +(-0.987594 - 5.10144i) q^{27} +0.255224 q^{28} +(0.271790 + 0.228059i) q^{29} +(-0.470061 - 2.66585i) q^{31} +(1.72756 + 0.628781i) q^{32} +(-6.70734 - 0.746168i) q^{33} +(-0.876974 + 4.97357i) q^{34} +(0.668307 - 0.724346i) q^{36} +(-2.13678 - 3.70101i) q^{37} +(-3.67761 + 1.33854i) q^{38} +(-8.61246 + 2.09187i) q^{39} +(-9.24182 + 7.75481i) q^{41} +(-1.69055 + 0.410616i) q^{42} +(-0.331124 + 0.120519i) q^{43} +(-0.640012 - 1.10853i) q^{44} +(2.08666 - 3.61420i) q^{46} +(-0.455464 + 2.58307i) q^{47} +(-5.56890 - 0.619521i) q^{48} +(6.01068 + 2.18771i) q^{49} +(0.430980 + 6.75217i) q^{51} +(-1.28773 - 1.08053i) q^{52} +9.29215 q^{53} +(-3.26136 + 5.87312i) q^{54} +(-1.79163 - 1.50335i) q^{56} +(-4.36446 + 2.90547i) q^{57} +(-0.0796526 - 0.451732i) q^{58} +(-12.4304 - 4.52430i) q^{59} +(1.14463 - 6.49154i) q^{61} +(-1.74987 + 3.03086i) q^{62} +(-2.07101 + 1.06913i) q^{63} +(-4.42346 - 7.66166i) q^{64} +(6.02277 + 6.31302i) q^{66} +(3.04985 - 2.55913i) q^{67} +(-0.983053 + 0.824880i) q^{68} +(1.57369 - 5.36497i) q^{69} +(-6.06946 - 10.5126i) q^{71} +(-8.95804 + 1.14823i) q^{72} +(7.04497 - 12.2022i) q^{73} +(-0.959425 + 5.44117i) q^{74} +(-0.934485 - 0.340125i) q^{76} +(0.525647 + 2.98109i) q^{77} +(10.2681 + 5.08548i) q^{78} +(-8.85574 - 7.43085i) q^{79} +(-2.38871 + 8.67722i) q^{81} +15.5975 q^{82} +(-4.25966 - 3.57428i) q^{83} +(-0.396138 - 0.196195i) q^{84} +(0.428097 + 0.155815i) q^{86} +(-0.246537 - 0.562904i) q^{87} +(-2.03686 + 11.5516i) q^{88} +(2.60530 - 4.51251i) q^{89} +(1.98768 + 3.44277i) q^{91} +(0.996492 - 0.362693i) q^{92} +(-1.31970 + 4.49906i) q^{93} +(2.59770 - 2.17973i) q^{94} +(-2.19803 - 2.30395i) q^{96} +(6.68077 - 2.43160i) q^{97} +(-4.13484 - 7.16175i) q^{98} +(9.83699 + 6.31420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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