LMFDB - Embedded newform 927.2.o.a.881.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(665,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("927.665");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 97x^{12} - 444x^{10} + 1488x^{8} - 2796x^{6} + 3553x^{4} - 60x^{2} + 1 $ x^16 - 12x^14 + 97x^12 - 444x^10 + 1488x^8 - 2796x^6 + 3553x^4 - 60*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.2
Root			$-1.78558 + 1.03090i$ of defining polynomial
Character	$\chi$	$=$	927.881
Dual form			927.2.o.a.665.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78558 + 1.03090i) q^{2} +(1.12553 - 1.94948i) q^{4} +(1.67303 - 2.89778i) q^{5} +(0.774131 - 1.34083i) q^{7} +0.517638i q^{8} +O(q^{10})$	\(q+(-1.78558 + 1.03090i) q^{2} +(1.12553 - 1.94948i) q^{4} +(1.67303 - 2.89778i) q^{5} +(0.774131 - 1.34083i) q^{7} +0.517638i q^{8} +6.89895i q^{10} +(3.20526 - 5.55168i) q^{11} +1.81621 q^{13} +3.19222i q^{14} +(1.71742 + 2.97467i) q^{16} +(-2.81539 - 1.62546i) q^{17} +(-0.0420802 - 0.0728851i) q^{19} +(-3.76610 - 6.52307i) q^{20} +13.2173i q^{22} -0.119021i q^{23} +(-3.09808 - 5.36603i) q^{25} +(-3.24299 + 1.87234i) q^{26} +(-1.74262 - 3.01830i) q^{28} +(-0.858847 + 0.495856i) q^{29} +3.46410i q^{31} +(-7.02977 - 4.05864i) q^{32} +6.70280 q^{34} +(-2.59029 - 4.48652i) q^{35} -7.79790i q^{37} +(0.150275 + 0.0867615i) q^{38} +(1.50000 + 0.866025i) q^{40} +(-3.00085 + 1.73254i) q^{41} +(-7.72502 + 4.46004i) q^{43} +(-7.21524 - 12.4972i) q^{44} +(0.122699 + 0.212521i) q^{46} +(-0.755772 + 1.30904i) q^{47} +(2.30144 + 3.98621i) q^{49} +(11.0637 + 6.38764i) q^{50} +(2.04420 - 3.54066i) q^{52} +(-2.30869 + 3.99876i) q^{53} +(-10.7250 - 18.5763i) q^{55} +(0.694067 + 0.400720i) q^{56} +(1.02236 - 1.77078i) q^{58} +(-5.63407 + 3.25283i) q^{59} -4.54826 q^{61} +(-3.57116 - 6.18543i) q^{62} +9.86659 q^{64} +(3.03858 - 5.26298i) q^{65} +(0.948634 + 0.547694i) q^{67} +(-6.33761 + 3.65902i) q^{68} +(9.25035 + 5.34069i) q^{70} +(-2.89778 + 5.01910i) q^{71} -4.49902i q^{73} +(8.03889 + 13.9238i) q^{74} -0.189450 q^{76} +(-4.96259 - 8.59545i) q^{77} +15.2958 q^{79} +11.4932 q^{80} +(3.57217 - 6.18719i) q^{82} +(14.8770 - 8.58925i) q^{83} +(-9.42047 + 5.43891i) q^{85} +(9.19575 - 15.9275i) q^{86} +(2.87376 + 1.65917i) q^{88} +11.5911 q^{89} +(1.40599 - 2.43524i) q^{91} +(-0.232028 - 0.133962i) q^{92} -3.11652i q^{94} -0.281606 q^{95} +(0.299322 + 0.518441i) q^{97} +(-8.21882 - 4.74514i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^7	$ 16 q + 8 q^{4} + 4 q^{7} + 40 q^{13} + 12 q^{16} - 20 q^{19} - 8 q^{25} + 16 q^{28} + 104 q^{34} + 24 q^{40} + 36 q^{43} - 36 q^{46} - 40 q^{49} + 12 q^{52} - 12 q^{55} - 40 q^{58} - 56 q^{61} + 112 q^{64} + 48 q^{67} + 60 q^{70} - 48 q^{76} + 112 q^{79} - 24 q^{82} - 84 q^{85} - 12 q^{88} + 68 q^{91} - 32 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^7 + 40 * q^13 + 12 * q^16 - 20 * q^19 - 8 * q^25 + 16 * q^28 + 104 * q^34 + 24 * q^40 + 36 * q^43 - 36 * q^46 - 40 * q^49 + 12 * q^52 - 12 * q^55 - 40 * q^58 - 56 * q^61 + 112 * q^64 + 48 * q^67 + 60 * q^70 - 48 * q^76 + 112 * q^79 - 24 * q^82 - 84 * q^85 - 12 * q^88 + 68 * q^91 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.78558	+	1.03090i	−1.26260	+	0.728960i	−0.973576	−	0.228363i	$-0.926663\pi$
$2$	−1.78558	+	1.03090i	−1.26260	+	0.728960i	−0.289020	+	0.957323i	$0.593329\pi$
$3$		0			0
$3$		0			0
$4$	1.12553	−	1.94948i	0.562765	−	0.974738i
$5$	1.67303	−	2.89778i	0.748203	−	1.29593i	−0.200480	−	0.979698i	$-0.564250\pi$
$5$	1.67303	−	2.89778i	0.748203	−	1.29593i	0.948683	−	0.316228i	$-0.102416\pi$
$6$		0			0
$7$	0.774131	−	1.34083i	0.292594	−	0.506788i	−0.681828	−	0.731512i	$-0.738815\pi$
$7$	0.774131	−	1.34083i	0.292594	−	0.506788i	0.974422	+	0.224725i	$0.0721482\pi$
$8$			0.517638i			0.183013i
$9$		0			0
$10$			6.89895i			2.18164i
$11$	3.20526	−	5.55168i	0.966423	−	1.67389i	0.260680	−	0.965425i	$-0.416053\pi$
$11$	3.20526	−	5.55168i	0.966423	−	1.67389i	0.705743	−	0.708468i	$-0.250613\pi$
$12$		0			0
$13$	1.81621			0.503726			0.251863	−	0.967763i	$-0.418957\pi$
$13$	1.81621			0.503726			0.251863	+	0.967763i	$0.418957\pi$
$14$			3.19222i			0.853157i
$15$		0			0
$16$	1.71742	+	2.97467i	0.429356	+	0.743667i
$17$	−2.81539	−	1.62546i	−0.682832	−	0.394233i	0.118089	−	0.993003i	$-0.462323\pi$
$17$	−2.81539	−	1.62546i	−0.682832	−	0.394233i	−0.800921	+	0.598770i	$0.795656\pi$
$18$		0			0
$19$	−0.0420802	−	0.0728851i	−0.00965387	−	0.0167210i	0.861158	−	0.508337i	$-0.169740\pi$
$19$	−0.0420802	−	0.0728851i	−0.00965387	−	0.0167210i	−0.870812	+	0.491616i	$0.836406\pi$
$20$	−3.76610	−	6.52307i	−0.842125	−	1.45860i
$21$		0			0
$22$			13.2173i			2.81793i
$23$		−	0.119021i		−	0.0248176i	−0.999923	−	0.0124088i	$-0.996050\pi$
$23$		−	0.119021i		−	0.0248176i	0.999923	−	0.0124088i	$-0.00394994\pi$
$24$		0			0
$25$	−3.09808	−	5.36603i	−0.619615	−	1.07321i
$26$	−3.24299	+	1.87234i	−0.636003	+	0.367196i
$27$		0			0
$28$	−1.74262	−	3.01830i	−0.329323	−	0.570405i
$29$	−0.858847	+	0.495856i	−0.159484	+	0.0920781i	−0.577618	−	0.816307i	$-0.696018\pi$
$29$	−0.858847	+	0.495856i	−0.159484	+	0.0920781i	0.418134	+	0.908385i	$0.362684\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	−7.02977	−	4.05864i	−1.24270	−	0.717473i
$33$		0			0
$34$	6.70280			1.14952
$35$	−2.59029	−	4.48652i	−0.437839	−	0.758360i
$36$		0			0
$37$		−	7.79790i		−	1.28197i	−0.767555	−	0.640983i	$-0.778527\pi$
$37$		−	7.79790i		−	1.28197i	0.767555	−	0.640983i	$-0.221473\pi$
$38$	0.150275	+	0.0867615i	0.0243779	+	0.0140746i
$39$		0			0
$40$	1.50000	+	0.866025i	0.237171	+	0.136931i
$41$	−3.00085	+	1.73254i	−0.468654	+	0.270578i	−0.715676	−	0.698432i	$-0.753881\pi$
$41$	−3.00085	+	1.73254i	−0.468654	+	0.270578i	0.247022	+	0.969010i	$0.420548\pi$
$42$		0			0
$43$	−7.72502	+	4.46004i	−1.17805	+	0.680150i	−0.955564	−	0.294785i	$-0.904752\pi$
$43$	−7.72502	+	4.46004i	−1.17805	+	0.680150i	−0.222490	+	0.974935i	$0.571419\pi$
$44$	−7.21524	−	12.4972i	−1.08774	−	1.88402i
$45$		0			0
$46$	0.122699	+	0.212521i	0.0180910	+	0.0313346i
$47$	−0.755772	+	1.30904i	−0.110241	+	0.190943i	−0.915867	−	0.401481i	$-0.868496\pi$
$47$	−0.755772	+	1.30904i	−0.110241	+	0.190943i	0.805627	+	0.592424i	$0.201829\pi$
$48$		0			0
$49$	2.30144	+	3.98621i	0.328777	+	0.569459i
$50$	11.0637	+	6.38764i	1.56465	+	0.903349i
$51$		0			0
$52$	2.04420	−	3.54066i	0.283480	−	0.491001i
$53$	−2.30869	+	3.99876i	−0.317122	+	0.549272i	−0.979886	−	0.199556i	$-0.936050\pi$
$53$	−2.30869	+	3.99876i	−0.317122	+	0.549272i	0.662764	+	0.748828i	$0.269383\pi$
$54$		0			0
$55$	−10.7250	−	18.5763i	−1.44616	−	2.50482i
$56$	0.694067	+	0.400720i	0.0927486	+	0.0535484i
$57$		0			0
$58$	1.02236	−	1.77078i	0.134242	−	0.232515i
$59$	−5.63407	+	3.25283i	−0.733493	+	0.423482i	−0.819699	−	0.572795i	$-0.805859\pi$
$59$	−5.63407	+	3.25283i	−0.733493	+	0.423482i	0.0862057	+	0.996277i	$0.472526\pi$
$60$		0			0
$61$	−4.54826			−0.582345			−0.291173	−	0.956671i	$-0.594045\pi$
$61$	−4.54826			−0.582345			−0.291173	+	0.956671i	$0.594045\pi$
$62$	−3.57116	−	6.18543i	−0.453538	−	0.785550i
$63$		0			0
$64$	9.86659			1.23332
$65$	3.03858	−	5.26298i	0.376890	−	0.652792i
$66$		0			0
$67$	0.948634	+	0.547694i	0.115894	+	0.0669115i	0.556826	−	0.830629i	$-0.312019\pi$
$67$	0.948634	+	0.547694i	0.115894	+	0.0669115i	−0.440932	+	0.897540i	$0.645352\pi$
$68$	−6.33761	+	3.65902i	−0.768548	+	0.443721i
$69$		0			0
$70$	9.25035	+	5.34069i	1.10563	+	0.638335i
$71$	−2.89778	+	5.01910i	−0.343903	+	0.595657i	−0.985154	−	0.171674i	$-0.945082\pi$
$71$	−2.89778	+	5.01910i	−0.343903	+	0.595657i	0.641251	+	0.767331i	$0.278416\pi$
$72$		0			0
$73$		−	4.49902i		−	0.526570i	−0.964718	−	0.263285i	$-0.915194\pi$
$73$		−	4.49902i		−	0.526570i	0.964718	−	0.263285i	$-0.0848060\pi$
$74$	8.03889	+	13.9238i	0.934502	+	1.61861i
$75$		0			0
$76$	−0.189450			−0.0217314
$77$	−4.96259	−	8.59545i	−0.565539	−	0.979542i
$78$		0			0
$79$	15.2958			1.72091			0.860455	−	0.509527i	$-0.170179\pi$
$79$	15.2958			1.72091			0.860455	+	0.509527i	$0.170179\pi$
$80$	11.4932			1.28498
$81$		0			0
$82$	3.57217	−	6.18719i	0.394481	−	0.683261i
$83$	14.8770	−	8.58925i	1.63297	−	0.942793i	0.649793	−	0.760111i	$-0.274856\pi$
$83$	14.8770	−	8.58925i	1.63297	−	0.942793i	0.983172	−	0.182682i	$-0.0584778\pi$
$84$		0			0
$85$	−9.42047	+	5.43891i	−1.02179	+	0.589933i
$86$	9.19575	−	15.9275i	0.991604	−	1.71751i
$87$		0			0
$88$	2.87376	+	1.65917i	0.306344	+	0.176868i
$89$	11.5911			1.22866			0.614328	−	0.789051i	$-0.289427\pi$
$89$	11.5911			1.22866			0.614328	+	0.789051i	$0.289427\pi$
$90$		0			0
$91$	1.40599	−	2.43524i	0.147387	−	0.255282i
$92$	−0.232028	−	0.133962i	−0.0241906	−	0.0139665i
$93$		0			0
$94$		−	3.11652i		−	0.321444i
$95$	−0.281606			−0.0288922
$96$		0			0
$97$	0.299322	+	0.518441i	0.0303916	+	0.0526397i	0.880821	−	0.473449i	$-0.156991\pi$
$97$	0.299322	+	0.518441i	0.0303916	+	0.0526397i	−0.850430	+	0.526089i	$0.823658\pi$
$98$	−8.21882	−	4.74514i	−0.830226	−	0.479331i
$99$		0			0
$100$	−13.9479			−1.39479
$101$	6.53064	+	11.3114i	0.649823	+	1.12553i	0.983165	+	0.182721i	$0.0584904\pi$
$101$	6.53064	+	11.3114i	0.649823	+	1.12553i	−0.333342	+	0.942806i	$0.608176\pi$
$102$		0			0
$103$	10.0000	−	1.73205i	0.985329	−	0.170664i
$103$	10.0000	−	1.73205i	0.985329	−	0.170664i
$104$			0.940140i			0.0921883i
$105$		0			0
$106$		−	9.52015i		−	0.924678i
$107$	−15.4372	−	8.91268i	−1.49237	−	0.861622i	−0.492410	−	0.870363i	$-0.663884\pi$
$107$	−15.4372	−	8.91268i	−1.49237	−	0.861622i	−0.999962	+	0.00874155i	$0.997217\pi$
$108$		0			0
$109$	5.87376	−	3.39122i	0.562604	−	0.324820i	−0.191586	−	0.981476i	$-0.561363\pi$
$109$	5.87376	−	3.39122i	0.562604	−	0.324820i	0.754190	+	0.656656i	$0.228030\pi$
$110$	38.3007	+	22.1129i	3.65183	+	2.10839i
$111$		0			0
$112$	5.31805			0.502508
$113$	10.8217			1.01802			0.509012	−	0.860759i	$-0.330011\pi$
$113$	10.8217			1.01802			0.509012	+	0.860759i	$0.330011\pi$
$114$		0			0
$115$	−0.344896	−	0.199126i	−0.0321617	−	0.0185686i
$116$			2.23240i			0.207273i
$117$		0			0
$118$	6.70672	−	11.6164i	0.617403	−	1.06937i
$119$	−4.35896	+	2.51665i	−0.399585	+	0.230700i
$120$		0			0
$121$	−15.0474	−	26.0629i	−1.36795	−	2.36935i
$122$	8.12128	−	4.68883i	0.735267	−	0.424506i
$123$		0			0
$124$	6.75318	+	3.89895i	0.606453	+	0.350136i
$125$	−4.00240			−0.357986
$126$		0			0
$127$			4.73205i			0.419902i	0.977712	+	0.209951i	$0.0673304\pi$
$127$			4.73205i			0.419902i	−0.977712	+	0.209951i	$0.932670\pi$
$128$	−3.55805	+	2.05424i	−0.314490	+	0.181571i
$129$		0			0
$130$			12.5300i			1.09895i
$131$	−9.36481	+	5.40678i	−0.818208	+	0.472392i	−0.849798	−	0.527109i	$-0.823276\pi$
$131$	−9.36481	+	5.40678i	−0.818208	+	0.472392i	0.0315904	+	0.999501i	$0.489943\pi$
$132$		0			0
$133$	−0.130302			−0.0112987
$134$	−2.25848			−0.195103
$135$		0			0
$136$	0.841402	−	1.45735i	0.0721497	−	0.124967i
$137$			13.9216i			1.18940i	0.803947	+	0.594700i	$0.202729\pi$
$137$			13.9216i			1.18940i	−0.803947	+	0.594700i	$0.797271\pi$
$138$		0			0
$139$	7.82309	−	13.5500i	0.663546	−	1.14930i	−0.316131	−	0.948715i	$-0.602384\pi$
$139$	7.82309	−	13.5500i	0.663546	−	1.14930i	0.979677	−	0.200580i	$-0.0642826\pi$
$140$	−11.6618			−0.985603
$141$		0			0
$142$		−	11.9493i		−	1.00277i
$143$	5.82143	−	10.0830i	0.486813	−	0.843184i
$144$		0			0
$145$			3.31833i			0.275572i
$146$	4.63806	+	8.03335i	0.383848	+	0.664845i
$147$		0			0
$148$	−15.2018	−	8.77677i	−1.24958	−	0.721446i
$149$	−15.2672	+	8.81455i	−1.25074	+	0.722116i	−0.971257	−	0.238034i	$-0.923497\pi$
$149$	−15.2672	+	8.81455i	−1.25074	+	0.722116i	−0.279485	+	0.960150i	$0.590164\pi$
$150$		0			0
$151$	17.2949	−	9.98523i	1.40744	−	0.812587i	0.412300	−	0.911048i	$-0.364725\pi$
$151$	17.2949	−	9.98523i	1.40744	−	0.812587i	0.995141	+	0.0984614i	$0.0313921\pi$
$152$	0.0377281	−	0.0217823i	0.00306015	−	0.00176678i
$153$		0			0
$154$	17.7222	+	10.2319i	1.42809	+	0.824511i
$155$	10.0382	+	5.79555i	0.806287	+	0.465510i
$156$		0			0
$157$	−13.2661	+	7.65917i	−1.05875	+	0.611268i	−0.925085	−	0.379759i	$-0.876007\pi$
$157$	−13.2661	+	7.65917i	−1.05875	+	0.611268i	−0.133662	+	0.991027i	$0.542674\pi$
$158$	−27.3118	+	15.7685i	−2.17281	+	1.25447i
$159$		0			0
$160$	−23.5221	+	13.5805i	−1.85958	+	1.07363i
$161$	−0.159587	−	0.0921378i	−0.0125772	−	0.00726147i
$162$		0			0
$163$	5.97028	+	10.3408i	0.467629	+	0.809957i	0.999316	−	0.0369842i	$-0.0117751\pi$
$163$	5.97028	+	10.3408i	0.467629	+	0.809957i	−0.531687	+	0.846941i	$0.678442\pi$
$164$			7.80012i			0.609087i
$165$		0			0
$166$	−17.7094	+	30.6736i	−1.37452	+	2.38073i
$167$			1.69962i			0.131521i	0.997835	+	0.0657603i	$0.0209473\pi$
$167$			1.69962i			0.131521i	−0.997835	+	0.0657603i	$0.979053\pi$
$168$		0			0
$169$	−9.70138			−0.746260
$170$	11.2140	−	19.4232i	0.860075	−	1.48969i
$171$		0			0
$172$			20.0796i			1.53106i
$173$	8.95945	−	15.5182i	0.681174	−	1.17983i	−0.293449	−	0.955975i	$-0.594803\pi$
$173$	8.95945	−	15.5182i	0.681174	−	1.17983i	0.974623	−	0.223853i	$-0.0718637\pi$
$174$		0			0
$175$	−9.59327			−0.725183
$176$	22.0192			1.65976
$177$		0			0
$178$	−20.6969	+	11.9493i	−1.55129	+	0.895640i
$179$		−	7.27882i		−	0.544045i	−0.962291	−	0.272022i	$-0.912307\pi$
$179$		−	7.27882i		−	0.544045i	0.962291	−	0.272022i	$-0.0876925\pi$
$180$		0			0
$181$	−18.1173	+	10.4600i	−1.34665	+	0.777489i	−0.987773	−	0.155896i	$-0.950173\pi$
$181$	−18.1173	+	10.4600i	−1.34665	+	0.777489i	−0.358876	+	0.933385i	$0.616840\pi$
$182$			5.79775i			0.429758i
$183$		0			0
$184$	0.0616097			0.00454193
$185$	−22.5966	−	13.0461i	−1.66133	−	0.959171i
$186$		0			0
$187$	−18.0481	+	10.4201i	−1.31981	+	0.761992i
$188$	1.70129	+	2.94672i	0.124079	+	0.214912i
$189$		0			0
$190$	0.502831	−	0.290309i	0.0364792	−	0.0210613i
$191$	10.1018	−	17.4968i	0.730941	−	1.26603i	−0.225541	−	0.974234i	$-0.572415\pi$
$191$	10.1018	−	17.4968i	0.730941	−	1.26603i	0.956482	−	0.291793i	$-0.0942518\pi$
$192$		0			0
$193$		−	14.0309i		−	1.00997i	−0.863128	−	0.504984i	$-0.831498\pi$
$193$		−	14.0309i		−	1.00997i	0.863128	−	0.504984i	$-0.168502\pi$
$194$	−1.06893	−	0.617145i	−0.0767445	−	0.0443085i
$195$		0			0
$196$	10.3614			0.740098
$197$	−24.9416			−1.77702			−0.888508	−	0.458861i	$-0.848257\pi$
$197$	−24.9416			−1.77702			−0.888508	+	0.458861i	$0.848257\pi$
$198$		0			0
$199$	2.05137	+	1.18436i	0.145417	+	0.0839568i	0.570943	−	0.820989i	$-0.306578\pi$
$199$	2.05137	+	1.18436i	0.145417	+	0.0839568i	−0.425526	+	0.904946i	$0.639911\pi$
$200$	2.77766	−	1.60368i	0.196410	−	0.113397i
$201$		0			0
$202$	−23.3220	−	13.4649i	−1.64093	−	0.947390i
$203$			1.53543i			0.107766i
$204$		0			0
$205$			11.5944i			0.809788i
$206$	−16.0702	+	13.4018i	−1.11967	+	0.933745i
$207$		0			0
$208$	3.11921	+	5.40262i	0.216278	+	0.374604i
$209$	−0.539513			−0.0373189
$210$		0			0
$211$	20.2903	+	11.7146i	1.39684	+	0.806466i	0.994060	−	0.108831i	$-0.0347108\pi$
$211$	20.2903	+	11.7146i	1.39684	+	0.806466i	0.402780	+	0.915297i	$0.368044\pi$
$212$	5.19699	+	9.00145i	0.356931	+	0.618222i
$213$		0			0
$214$	36.7525			2.51235
$215$			29.8472i			2.03556i
$216$		0			0
$217$	4.64479	+	2.68167i	0.315309	+	0.182044i
$218$	−6.99204	+	12.1106i	−0.473561	+	0.820232i
$219$		0			0
$220$	−48.2853			−3.25539
$221$	−5.11334	−	2.95219i	−0.343960	−	0.198586i
$222$		0			0
$223$	0.316211	−	0.547694i	0.0211751	−	0.0366763i	−0.855244	−	0.518226i	$-0.826593\pi$
$223$	0.316211	−	0.547694i	0.0211751	−	0.0366763i	0.876419	+	0.481550i	$0.159926\pi$
$224$	−10.8839	+	6.28384i	−0.727213	+	0.419857i
$225$		0			0
$226$	−19.3231	+	11.1562i	−1.28535	+	0.742099i
$227$	6.42237	−	11.1239i	0.426268	−	0.738318i	−0.570270	−	0.821457i	$-0.693161\pi$
$227$	6.42237	−	11.1239i	0.426268	−	0.738318i	0.996538	+	0.0831396i	$0.0264947\pi$
$228$		0			0
$229$	4.49617			0.297115			0.148558	−	0.988904i	$-0.452537\pi$
$229$	4.49617			0.297115			0.148558	+	0.988904i	$0.452537\pi$
$230$	0.821119			0.0541430
$231$		0			0
$232$	−0.256674	−	0.444572i	−0.0168515	−	0.0291876i
$233$	−29.8545			−1.95583			−0.977915	−	0.209003i	$-0.932978\pi$
$233$	−29.8545			−1.95583			−0.977915	+	0.209003i	$0.932978\pi$
$234$		0			0
$235$	2.52886	+	4.38012i	0.164965	+	0.285727i
$236$			14.6446i			0.953284i
$237$		0			0
$238$	5.18884	−	8.98734i	0.336343	−	0.582563i
$239$	1.28455	+	0.741635i	0.0830906	+	0.0479724i	0.540970	−	0.841042i	$-0.318057\pi$
$239$	1.28455	+	0.741635i	0.0830906	+	0.0479724i	−0.457879	+	0.889015i	$0.651391\pi$
$240$		0			0
$241$	19.6005	−	11.3163i	1.26258	−	0.728950i	0.289005	−	0.957328i	$-0.406675\pi$
$241$	19.6005	−	11.3163i	1.26258	−	0.728950i	0.973573	+	0.228378i	$0.0733422\pi$
$242$	53.7367	+	31.0249i	3.45433	+	1.99436i
$243$		0			0
$244$	−5.11921	+	8.86672i	−0.327724	+	0.567634i
$245$	15.4016			0.983969
$246$		0			0
$247$	−0.0764266	−	0.132375i	−0.00486291	−	0.00842280i
$248$	−1.79315			−0.113865
$249$		0			0
$250$	7.14661	−	4.12610i	0.451991	−	0.260957i
$251$	−11.5875	+	20.0701i	−0.731395	+	1.26681i	0.224893	+	0.974384i	$0.427797\pi$
$251$	−11.5875	+	20.0701i	−0.731395	+	1.26681i	−0.956287	+	0.292429i	$0.905537\pi$
$252$		0			0
$253$	−0.660766	−	0.381493i	−0.0415420	−	0.0239843i
$254$	−4.87829	−	8.44945i	−0.306091	−	0.530166i
$255$		0			0
$256$	−5.63114	+	9.75343i	−0.351946	+	0.609589i
$257$	9.06252	−	15.6967i	0.565305	−	0.979136i	−0.431717	−	0.902009i	$-0.642092\pi$
$257$	9.06252	−	15.6967i	0.565305	−	0.979136i	0.997021	−	0.0771270i	$-0.0245747\pi$
$258$		0			0
$259$	−10.4557	−	6.03660i	−0.649685	−	0.375096i
$260$	−6.84003	−	11.8473i	−0.424201	−	0.734737i
$261$		0			0
$262$	11.1477	−	19.3085i	0.688710	−	1.19288i
$263$	6.18214	+	10.7078i	0.381207	+	0.660270i	0.991235	−	0.132110i	$-0.0421752\pi$
$263$	6.18214	+	10.7078i	0.381207	+	0.660270i	−0.610028	+	0.792380i	$0.708842\pi$
$264$		0			0
$265$	7.72502	+	13.3801i	0.474544	+	0.821934i
$266$	0.232665	−	0.134329i	0.0142656	−	0.00823627i
$267$		0			0
$268$	2.13543	−	1.23289i	0.130442	−	0.0753109i
$269$	2.32557	+	1.34267i	0.141792	+	0.0818639i	0.569218	−	0.822187i	$-0.307246\pi$
$269$	2.32557	+	1.34267i	0.141792	+	0.0818639i	−0.427426	+	0.904051i	$0.640579\pi$
$270$		0			0
$271$	18.2820	+	10.5551i	1.11056	+	0.641179i	0.938973	−	0.343991i	$-0.111779\pi$
$271$	18.2820	+	10.5551i	1.11056	+	0.641179i	0.171582	+	0.985170i	$0.445112\pi$
$272$		−	11.1665i		−	0.677065i
$273$		0			0
$274$	−14.3518	−	24.8581i	−0.867025	−	1.50173i
$275$	−39.7206			−2.39524
$276$		0			0
$277$	−14.7539	−	8.51816i	−0.886475	−	0.511806i	−0.0136869	−	0.999906i	$-0.504357\pi$
$277$	−14.7539	−	8.51816i	−0.886475	−	0.511806i	−0.872788	+	0.488100i	$0.837690\pi$
$278$			32.2595i			1.93479i
$279$		0			0
$280$	2.32239	−	1.34083i	0.138790	−	0.0801302i
$281$	2.02189	+	3.50201i	0.120616	+	0.208912i	0.920011	−	0.391893i	$-0.128180\pi$
$281$	2.02189	+	3.50201i	0.120616	+	0.208912i	−0.799395	+	0.600806i	$0.794846\pi$
$282$		0			0
$283$	11.9476	−	6.89797i	0.710213	−	0.410042i	−0.100927	−	0.994894i	$-0.532181\pi$
$283$	11.9476	−	6.89797i	0.710213	−	0.410042i	0.811140	+	0.584852i	$0.198848\pi$
$284$	6.52307	+	11.2983i	0.387073	+	0.670430i
$285$		0			0
$286$			24.0054i			1.41947i
$287$			5.36486i			0.316678i
$288$		0			0
$289$	−3.21573	−	5.56981i	−0.189161	−	0.327636i
$290$	−3.42088	−	5.92515i	−0.200881	−	0.347937i
$291$		0			0
$292$	−8.77072	−	5.06378i	−0.513268	−	0.296335i
$293$	−12.3111	−	21.3234i	−0.719220	−	1.24572i	−0.961309	−	0.275471i	$-0.911166\pi$
$293$	−12.3111	−	21.3234i	−0.719220	−	1.24572i	0.242090	−	0.970254i	$-0.422167\pi$
$294$		0			0
$295$			21.7684i			1.26740i
$296$	4.03649			0.234616
$297$		0			0
$298$	18.1739	−	31.4782i	1.05279	−	1.82348i
$299$		−	0.216167i		−	0.0125013i
$300$		0			0
$301$			13.8106i			0.796031i
$302$	−20.5876	+	35.6589i	−1.18469	+	2.05194i
$303$		0			0
$304$	0.144539	−	0.250349i	0.00828990	−	0.0143585i
$305$	−7.60939	+	13.1799i	−0.435712	+	0.754676i
$306$		0			0
$307$	−15.9950	+	9.23474i	−0.912885	+	0.527054i	−0.881358	−	0.472449i	$-0.843370\pi$
$307$	−15.9950	+	9.23474i	−0.912885	+	0.527054i	−0.0315267	+	0.999503i	$0.510037\pi$
$308$	−22.3422			−1.27306
$309$		0			0
$310$	−23.8987			−1.35735
$311$	−1.64161	+	0.947785i	−0.0930873	+	0.0537440i	−0.545821	−	0.837902i	$-0.683782\pi$
$311$	−1.64161	+	0.947785i	−0.0930873	+	0.0537440i	0.452734	+	0.891646i	$0.350449\pi$
$312$		0			0
$313$	−1.15355	+	1.99801i	−0.0652026	+	0.112934i	−0.896784	−	0.442469i	$-0.854103\pi$
$313$	−1.15355	+	1.99801i	−0.0652026	+	0.112934i	0.831581	+	0.555403i	$0.187436\pi$
$314$	15.7917	−	27.3521i	0.891180	−	1.54357i
$315$		0			0
$316$	17.2159	−	29.8187i	0.968468	−	1.67744i
$317$		−	9.48079i		−	0.532494i	−0.963905	−	0.266247i	$-0.914216\pi$
$317$		−	9.48079i		−	0.532494i	0.963905	−	0.266247i	$-0.0857838\pi$
$318$		0			0
$319$			6.35739i			0.355946i
$320$	16.5071	−	28.5912i	0.922777	−	1.59830i
$321$		0			0
$322$	0.379941			0.0211733
$323$			0.273600i			0.0152235i
$324$		0			0
$325$	−5.62676	−	9.74584i	−0.312117	−	0.540602i
$326$	−21.3208	−	12.3096i	−1.18085	−	0.681765i
$327$		0			0
$328$	−0.896830	−	1.55336i	−0.0495192	−	0.0857697i
$329$	1.17013	+	2.02673i	0.0645115	+	0.111737i
$330$		0			0
$331$		−	2.85423i		−	0.156883i	−0.996919	−	0.0784413i	$-0.975006\pi$
$331$		−	2.85423i		−	0.156883i	0.996919	−	0.0784413i	$-0.0249943\pi$
$332$		−	38.6698i		−	2.12228i
$333$		0			0
$334$	−1.75215	−	3.03481i	−0.0958733	−	0.166057i
$335$	3.17419	−	1.83262i	0.173425	−	0.100127i
$336$		0			0
$337$	−8.40811	−	14.5633i	−0.458019	−	0.793312i	0.540837	−	0.841127i	$-0.318107\pi$
$337$	−8.40811	−	14.5633i	−0.458019	−	0.793312i	−0.998856	+	0.0478154i	$0.984774\pi$
$338$	17.3226	−	10.0012i	0.942224	−	0.543993i
$339$		0			0
$340$			24.4866i			1.32797i
$341$	19.2316	+	11.1034i	1.04145	+	0.601280i
$342$		0			0
$343$	17.9643			0.969981
$344$	−2.30869	−	3.99876i	−0.124476	−	0.215599i
$345$		0			0
$346$			36.9454i			1.98619i
$347$	−3.46999	−	2.00340i	−0.186279	−	0.107548i	0.403961	−	0.914776i	$-0.367633\pi$
$347$	−3.46999	−	2.00340i	−0.186279	−	0.107548i	−0.590239	+	0.807228i	$0.700967\pi$
$348$		0			0
$349$	14.7999	+	8.54472i	0.792220	+	0.457388i	0.840743	−	0.541434i	$-0.182118\pi$
$349$	14.7999	+	8.54472i	0.792220	+	0.457388i	−0.0485235	+	0.998822i	$0.515452\pi$
$350$	17.1295	−	9.88975i	0.915613	−	0.528629i
$351$		0			0
$352$	−45.0645	+	26.0180i	−2.40195	+	1.38676i
$353$	12.8436	+	22.2458i	0.683598	+	1.18403i	0.973875	+	0.227083i	$0.0729190\pi$
$353$	12.8436	+	22.2458i	0.683598	+	1.18403i	−0.290278	+	0.956942i	$0.593748\pi$
$354$		0			0
$355$	9.69615	+	16.7942i	0.514618	+	0.891345i
$356$	13.0461	−	22.5966i	0.691444	−	1.19762i
$357$		0			0
$358$	7.50378	+	12.9969i	0.396587	+	0.686909i
$359$	31.1572	+	17.9886i	1.64441	+	0.949402i	0.979238	+	0.202713i	$0.0649759\pi$
$359$	31.1572	+	17.9886i	1.64441	+	0.949402i	0.665174	+	0.746689i	$0.268357\pi$
$360$		0			0
$361$	9.49646	−	16.4483i	0.499814	−	0.865703i
$362$	21.5666	−	37.3545i	1.13352	−	1.96331i
$363$		0			0
$364$	−3.16496	−	5.48187i	−0.165889	−	0.287328i
$365$	−13.0371	−	7.52700i	−0.682395	−	0.393981i
$366$		0			0
$367$	7.25781	−	12.5709i	0.378855	−	0.656195i	−0.612041	−	0.790826i	$-0.709651\pi$
$367$	7.25781	−	12.5709i	0.378855	−	0.656195i	0.990896	+	0.134630i	$0.0429847\pi$
$368$	0.354047	−	0.204409i	0.0184560	−	0.0106556i
$369$		0			0
$370$	53.7973			2.79679
$371$	3.57445	+	6.19113i	0.185576	+	0.321428i
$372$		0			0
$373$	2.85139			0.147639			0.0738196	−	0.997272i	$-0.476481\pi$
$373$	2.85139			0.147639			0.0738196	+	0.997272i	$0.476481\pi$
$374$	21.4842	−	37.2118i	1.11092	−	1.92417i
$375$		0			0
$376$	−0.677607	−	0.391216i	−0.0349449	−	0.0201755i
$377$	−1.55985	+	0.900579i	−0.0803363	+	0.0463822i
$378$		0			0
$379$	26.1623	+	15.1048i	1.34387	+	0.775883i	0.987373	−	0.158414i	$-0.0506381\pi$
$379$	26.1623	+	15.1048i	1.34387	+	0.775883i	0.356496	+	0.934297i	$0.383971\pi$
$380$	−0.316957	+	0.548985i	−0.0162595	+	0.0281623i
$381$		0			0
$382$			41.6560i			2.13131i
$383$	13.2487	+	22.9473i	0.676974	+	1.17255i	0.975888	+	0.218274i	$0.0700426\pi$
$383$	13.2487	+	22.9473i	0.676974	+	1.17255i	−0.298913	+	0.954280i	$0.596624\pi$
$384$		0			0
$385$	−33.2103			−1.69255
$386$	14.4646	+	25.0534i	0.736227	+	1.27518i
$387$		0			0
$388$	1.34758			0.0684132
$389$	−35.4703			−1.79842			−0.899209	−	0.437520i	$-0.855857\pi$
$389$	−35.4703			−1.79842			−0.899209	+	0.437520i	$0.855857\pi$
$390$		0			0
$391$	−0.193464	+	0.335090i	−0.00978391	+	0.0169462i
$392$	−2.06342	+	1.19131i	−0.104218	+	0.0601705i
$393$		0			0
$394$	44.5352	−	25.7124i	2.24365	−	1.29537i
$395$	25.5903	−	44.3238i	1.28759	−	2.23017i
$396$		0			0
$397$	−8.43335	−	4.86900i	−0.423258	−	0.244368i	0.273212	−	0.961954i	$-0.411914\pi$
$397$	−8.43335	−	4.86900i	−0.423258	−	0.244368i	−0.696470	+	0.717586i	$0.745247\pi$
$398$	−4.88384			−0.244805
$399$		0			0
$400$	10.6414	−	18.4315i	0.532071	−	0.921574i
$401$	23.4464	+	13.5368i	1.17086	+	0.675996i	0.953882	−	0.300181i	$-0.0970471\pi$
$401$	23.4464	+	13.5368i	1.17086	+	0.675996i	0.216977	+	0.976177i	$0.430380\pi$
$402$		0			0
$403$			6.29154i			0.313404i
$404$	29.4017			1.46279
$405$		0			0
$406$	−1.58288	−	2.74163i	−0.0785571	−	0.136065i
$407$	−43.2914	−	24.9943i	−2.14588	−	1.23892i
$408$		0			0
$409$	−8.75036			−0.432678			−0.216339	−	0.976318i	$-0.569412\pi$
$409$	−8.75036			−0.432678			−0.216339	+	0.976318i	$0.569412\pi$
$410$	−11.9527	−	20.7027i	−0.590303	−	1.02244i
$411$		0			0
$412$	7.87871	−	21.4442i	0.388156	−	1.05648i
$413$			10.0725i			0.495634i
$414$		0			0
$415$		−	57.4804i		−	2.82160i
$416$	−12.7676	−	7.37135i	−0.625981	−	0.361410i
$417$		0			0
$418$	0.963343	−	0.556186i	0.0471187	−	0.0272040i
$419$	12.0545	+	6.95969i	0.588903	+	0.340003i	0.764664	−	0.644430i	$-0.222905\pi$
$419$	12.0545	+	6.95969i	0.588903	+	0.340003i	−0.175761	+	0.984433i	$0.556239\pi$
$420$		0			0
$421$	−18.4614			−0.899751			−0.449876	−	0.893091i	$-0.648532\pi$
$421$	−18.4614			−0.899751			−0.449876	+	0.893091i	$0.648532\pi$
$422$	−48.3065			−2.35153
$423$		0			0
$424$	−2.06991	−	1.19506i	−0.100524	−	0.0580374i
$425$			20.1433i			0.977091i
$426$		0			0
$427$	−3.52095	+	6.09847i	−0.170391	+	0.295125i
$428$	−34.7501	+	20.0630i	−1.67971	+	0.969781i
$429$		0			0
$430$	−30.7696	−	53.2945i	−1.48384	−	2.57009i
$431$	11.5741	−	6.68229i	0.557503	−	0.321875i	−0.194640	−	0.980875i	$-0.562354\pi$
$431$	11.5741	−	6.68229i	0.557503	−	0.321875i	0.752143	+	0.659000i	$0.229020\pi$
$432$		0			0
$433$	−5.02816	−	2.90301i	−0.241638	−	0.139510i	0.374291	−	0.927311i	$-0.377886\pi$
$433$	−5.02816	−	2.90301i	−0.241638	−	0.139510i	−0.615929	+	0.787801i	$0.711219\pi$
$434$	−11.0582			−0.530810
$435$		0			0
$436$		−	15.2677i		−	0.731188i
$437$	−0.00867485	+	0.00500843i	−0.000414974	+	0.000239586i
$438$		0			0
$439$		−	20.0149i		−	0.955259i	−0.878561	−	0.477629i	$-0.841496\pi$
$439$		−	20.0149i		−	0.955259i	0.878561	−	0.477629i	$-0.158504\pi$
$440$	9.61579	−	5.55168i	0.458415	−	0.264666i
$441$		0			0
$442$	12.1737			0.579044
$443$	18.5714			0.882355			0.441178	−	0.897420i	$-0.354561\pi$
$443$	18.5714			0.882355			0.441178	+	0.897420i	$0.354561\pi$
$444$		0			0
$445$	19.3923	−	33.5885i	0.919283	−	1.59225i
$446$			1.30394i			0.0617431i
$447$		0			0
$448$	7.63804	−	13.2295i	0.360863	−	0.625034i
$449$	−18.6100			−0.878261			−0.439131	−	0.898423i	$-0.644713\pi$
$449$	−18.6100			−0.878261			−0.439131	+	0.898423i	$0.644713\pi$
$450$		0			0
$451$			22.2130i			1.04597i
$452$	12.1802	−	21.0967i	0.572908	−	0.992307i
$453$		0			0
$454$			26.4834i			1.24293i
$455$	−4.70452	−	8.14847i	−0.220551	−	0.382006i
$456$		0			0
$457$	9.28204	+	5.35899i	0.434196	+	0.250683i	0.701132	−	0.713031i	$-0.252678\pi$
$457$	9.28204	+	5.35899i	0.434196	+	0.250683i	−0.266937	+	0.963714i	$0.586011\pi$
$458$	−8.02828	+	4.63513i	−0.375137	+	0.216585i
$459$		0			0
$460$	−0.776382	+	0.448244i	−0.0361990	+	0.0208995i
$461$	1.70921	−	0.986812i	0.0796058	−	0.0459604i	−0.459669	−	0.888090i	$-0.652032\pi$
$461$	1.70921	−	0.986812i	0.0796058	−	0.0459604i	0.539275	+	0.842130i	$0.318699\pi$
$462$		0			0
$463$	6.55307	+	3.78342i	0.304547	+	0.175830i	0.644484	−	0.764618i	$-0.277072\pi$
$463$	6.55307	+	3.78342i	0.304547	+	0.175830i	−0.339937	+	0.940448i	$0.610406\pi$
$464$	−2.95001	−	1.70319i	−0.136951	−	0.0790686i
$465$		0			0
$466$	53.3075	−	30.7771i	2.46942	−	1.42572i
$467$	−4.24454	+	2.45059i	−0.196414	+	0.113400i	−0.594982	−	0.803739i	$-0.702841\pi$
$467$	−4.24454	+	2.45059i	−0.196414	+	0.113400i	0.398568	+	0.917139i	$0.369507\pi$
$468$		0			0
$469$	1.46873	−	0.847974i	0.0678198	−	0.0391558i
$470$	−9.03097	−	5.21404i	−0.416568	−	0.240506i
$471$		0			0
$472$	−1.68379	−	2.91641i	−0.0775027	−	0.134239i
$473$			57.1824i			2.62925i
$474$		0			0
$475$	−0.260736	+	0.451607i	−0.0119634	+	0.0207212i
$476$			11.3302i			0.519321i
$477$		0			0
$478$	−3.05822			−0.139880
$479$	16.2721	−	28.1841i	0.743491	−	1.28776i	−0.207406	−	0.978255i	$-0.566502\pi$
$479$	16.2721	−	28.1841i	0.743491	−	1.28776i	0.950897	−	0.309509i	$-0.100165\pi$
$480$		0			0
$481$		−	14.1626i		−	0.645761i
$482$	−23.3321	+	40.4125i	−1.06275	+	1.84074i
$483$		0			0
$484$	−67.7452			−3.07933
$485$	2.00310			0.0909562
$486$		0			0
$487$	21.4622	−	12.3912i	0.972546	−	0.561500i	0.0725344	−	0.997366i	$-0.476891\pi$
$487$	21.4622	−	12.3912i	0.972546	−	0.561500i	0.900011	+	0.435866i	$0.143558\pi$
$488$		−	2.35435i		−	0.106577i
$489$		0			0
$490$	−27.5007	+	15.8775i	−1.24235	+	0.717274i
$491$		−	33.5220i		−	1.51283i	−0.654093	−	0.756414i	$-0.726950\pi$
$491$		−	33.5220i		−	1.51283i	0.654093	−	0.756414i	$-0.273050\pi$
$492$		0			0
$493$	3.22398			0.145201
$494$	0.272932	+	0.157577i	0.0122798	+	0.00708973i
$495$		0			0
$496$	−10.3045	+	5.94933i	−0.462688	+	0.267133i
$497$	4.48652	+	7.77088i	0.201248	+	0.348572i
$498$		0			0
$499$	2.03282	−	1.17365i	0.0910015	−	0.0525398i	−0.453809	−	0.891099i	$-0.649935\pi$
$499$	2.03282	−	1.17365i	0.0910015	−	0.0525398i	0.544810	+	0.838559i	$0.316602\pi$
$500$	−4.50483	+	7.80259i	−0.201462	+	0.348942i
$501$		0			0
$502$		−	47.7823i		−	2.13263i
$503$	−33.4371	−	19.3049i	−1.49089	−	0.860764i	−0.490942	−	0.871193i	$-0.663347\pi$
$503$	−33.4371	−	19.3049i	−1.49089	−	0.860764i	−0.999946	+	0.0104284i	$0.996680\pi$
$504$		0			0
$505$	43.7039			1.94480
$506$	1.57313			0.0699343
$507$		0			0
$508$	9.22502	+	5.32607i	0.409294	+	0.236306i
$509$	13.2490	−	7.64931i	0.587252	−	0.339050i	−0.176758	−	0.984254i	$-0.556561\pi$
$509$	13.2490	−	7.64931i	0.587252	−	0.339050i	0.764010	+	0.645204i	$0.223228\pi$
$510$		0			0
$511$	−6.03244	−	3.48283i	−0.266859	−	0.154071i
$512$		−	31.4377i		−	1.38936i
$513$		0			0
$514$			37.3704i			1.64834i
$515$	11.7112	−	31.8756i	0.516058	−	1.40460i
$516$		0			0
$517$	4.84490	+	8.39161i	0.213078	+	0.369062i
$518$	24.8926			1.09372
$519$		0			0
$520$	2.72432	+	1.57289i	0.119469	+	0.0689756i
$521$	6.20802	+	10.7526i	0.271978	+	0.471080i	0.969368	−	0.245612i	$-0.0789888\pi$
$521$	6.20802	+	10.7526i	0.271978	+	0.471080i	−0.697390	+	0.716692i	$0.745656\pi$
$522$		0			0
$523$	−7.00424			−0.306274			−0.153137	−	0.988205i	$-0.548938\pi$
$523$	−7.00424			−0.306274			−0.153137	+	0.988205i	$0.548938\pi$
$524$			24.3420i			1.06338i
$525$		0			0
$526$	−22.0774	−	12.7464i	−0.962620	−	0.555769i
$527$	5.63077	−	9.75279i	0.245280	−	0.424838i
$528$		0			0
$529$	22.9858			0.999384
$530$	−27.5873	−	15.9275i	−1.19831	−	0.691847i
$531$		0			0
$532$	−0.146659	+	0.254021i	−0.00635849	+	0.0110132i
$533$	−5.45018	+	3.14666i	−0.236074	+	0.136297i
$534$		0			0
$535$	−51.6539	+	29.8224i	−2.23319	+	1.28934i
$536$	−0.283507	+	0.491049i	−0.0122456	+	0.0212101i
$537$		0			0
$538$	−5.53665			−0.238702
$539$	29.5069			1.27095
$540$		0			0
$541$	11.9258	+	20.6561i	0.512730	+	0.888075i	0.999891	+	0.0147624i	$0.00469918\pi$
$541$	11.9258	+	20.6561i	0.512730	+	0.888075i	−0.487161	+	0.873312i	$0.661967\pi$
$542$	−43.5254			−1.86958
$543$		0			0
$544$	13.1944	+	22.8533i	0.565703	+	0.979827i
$545$		−	22.6945i		−	0.972124i
$546$		0			0
$547$	−10.4827	+	18.1566i	−0.448209	+	0.776320i	−0.998270	−	0.0588042i	$-0.981271\pi$
$547$	−10.4827	+	18.1566i	−0.448209	+	0.776320i	0.550061	+	0.835125i	$0.314605\pi$
$548$	27.1398	+	15.6692i	1.15935	+	0.669353i
$549$		0			0
$550$	70.9243	−	40.9481i	3.02422	−	1.74603i
$551$	0.0722810	+	0.0417315i	0.00307927	+	0.00177782i
$552$		0			0
$553$	11.8409	−	20.5091i	0.503528	−	0.872136i
$554$	35.1256			1.49235
$555$		0			0
$556$	−17.6102	−	30.5018i	−0.746841	−	1.29357i
$557$	−12.6348			−0.535353			−0.267677	−	0.963509i	$-0.586256\pi$
$557$	−12.6348			−0.535353			−0.267677	+	0.963509i	$0.586256\pi$
$558$		0			0
$559$	−14.0303	+	8.10037i	−0.593417	+	0.342609i
$560$	8.89726	−	15.4105i	0.375978	−	0.651213i
$561$		0			0
$562$	−7.22048	−	4.16875i	−0.304578	−	0.175848i
$563$	22.1035	+	38.2843i	0.931550	+	1.61349i	0.780673	+	0.624940i	$0.214877\pi$
$563$	22.1035	+	38.2843i	0.931550	+	1.61349i	0.150877	+	0.988552i	$0.451790\pi$
$564$		0			0
$565$	18.1051	−	31.3590i	0.761689	−	1.31928i
$566$	−14.2223	+	24.6337i	−0.597808	+	1.03543i
$567$		0			0
$568$	−2.59808	−	1.50000i	−0.109013	−	0.0629386i
$569$	19.5867	+	33.9252i	0.821119	+	1.42222i	0.904850	+	0.425731i	$0.139983\pi$
$569$	19.5867	+	33.9252i	0.821119	+	1.42222i	−0.0837313	+	0.996488i	$0.526684\pi$
$570$		0			0
$571$	2.14520	−	3.71560i	0.0897739	−	0.155493i	−0.817642	−	0.575728i	$-0.804719\pi$
$571$	2.14520	−	3.71560i	0.0897739	−	0.155493i	0.907415	+	0.420235i	$0.138052\pi$
$572$	−13.1044	−	22.6975i	−0.547922	−	0.949029i
$573$		0			0
$574$	−5.53066	−	9.57939i	−0.230845	−	0.399836i
$575$	−0.638669	+	0.368736i	−0.0266343	+	0.0153773i
$576$		0			0
$577$	−28.7482	+	16.5978i	−1.19680	+	0.690975i	−0.959841	−	0.280544i	$-0.909485\pi$
$577$	−28.7482	+	16.5978i	−1.19680	+	0.690975i	−0.236963	+	0.971519i	$0.576152\pi$
$578$	11.4839	+	6.63022i	0.477667	+	0.275781i
$579$		0			0
$580$	6.46900	+	3.73488i	0.268611	+	0.155083i
$581$		−	26.5968i		−	1.10342i
$582$		0			0
$583$	14.7999	+	25.6342i	0.612949	+	1.06166i
$584$	2.32886			0.0963690
$585$		0			0
$586$	43.9647	+	25.3831i	1.81617	+	1.04856i
$587$		−	11.9322i		−	0.492493i	−0.969207	−	0.246246i	$-0.920803\pi$
$587$		−	11.9322i		−	0.492493i	0.969207	−	0.246246i	$-0.0791973\pi$
$588$		0			0
$589$	0.252481	−	0.145770i	0.0104033	−	0.00600636i
$590$	−22.4411	−	38.8691i	−0.923886	−	1.60022i
$591$		0			0
$592$	23.1962	−	13.3923i	0.953356	−	0.550420i
$593$	8.57511	+	14.8525i	0.352138	+	0.609920i	0.986624	−	0.163014i	$-0.0521215\pi$
$593$	8.57511	+	14.8525i	0.352138	+	0.609920i	−0.634486	+	0.772934i	$0.718788\pi$
$594$		0			0
$595$			16.8417i			0.690443i
$596$			39.6842i			1.62553i
$597$		0			0
$598$	0.222848	+	0.385984i	0.00911292	+	0.0157840i
$599$	13.2793	+	23.0004i	0.542577	+	0.939771i	0.998755	+	0.0498823i	$0.0158846\pi$
$599$	13.2793	+	23.0004i	0.542577	+	0.939771i	−0.456178	+	0.889888i	$0.650782\pi$
$600$		0			0
$601$	−1.29819	−	0.749508i	−0.0529541	−	0.0305731i	0.473289	−	0.880907i	$-0.343067\pi$
$601$	−1.29819	−	0.749508i	−0.0529541	−	0.0305731i	−0.526243	+	0.850334i	$0.676400\pi$
$602$	−14.2374	−	24.6600i	−0.580275	−	1.00507i
$603$		0			0
$604$		−	44.9547i		−	1.82918i
$605$	−100.699			−4.09401
$606$		0			0
$607$	−10.5678	+	18.3040i	−0.428933	+	0.742934i	−0.996779	−	0.0802008i	$-0.974444\pi$
$607$	−10.5678	+	18.3040i	−0.428933	+	0.742934i	0.567845	+	0.823135i	$0.307777\pi$
$608$			0.683154i			0.0277056i
$609$		0			0
$610$		−	31.3782i		−	1.27047i
$611$	−1.37264	+	2.37749i	−0.0555312	+	0.0961828i
$612$		0			0
$613$	−1.16220	+	2.01298i	−0.0469406	+	0.0813036i	−0.888541	−	0.458797i	$-0.848280\pi$
$613$	−1.16220	+	2.01298i	−0.0469406	+	0.0813036i	0.841600	+	0.540101i	$0.181614\pi$
$614$	19.0403	−	32.9787i	0.768403	−	1.33091i
$615$		0			0
$616$	4.44933	−	2.56882i	0.179269	−	0.103501i
$617$	−9.14922			−0.368334			−0.184167	−	0.982895i	$-0.558959\pi$
$617$	−9.14922			−0.368334			−0.184167	+	0.982895i	$0.558959\pi$
$618$		0			0
$619$	22.2510			0.894345			0.447172	−	0.894448i	$-0.352431\pi$
$619$	22.2510			0.894345			0.447172	+	0.894448i	$0.352431\pi$
$620$	22.5966	−	13.0461i	0.907501	−	0.523946i
$621$		0			0
$622$	1.95415	−	3.38469i	0.0783544	−	0.135714i
$623$	8.97304	−	15.5418i	0.359497	−	0.622667i
$624$		0			0
$625$	8.79423	−	15.2321i	0.351769	−	0.609282i
$626$		−	4.75681i		−	0.190120i
$627$		0			0
$628$			34.4825i			1.37600i
$629$	−12.6752	+	21.9541i	−0.505394	+	0.875368i
$630$		0			0
$631$	−31.5198			−1.25478			−0.627391	−	0.778704i	$-0.715877\pi$
$631$	−31.5198			−1.25478			−0.627391	+	0.778704i	$0.715877\pi$
$632$			7.91768i			0.314948i
$633$		0			0
$634$	9.77380	+	16.9287i	0.388167	+	0.672325i
$635$	13.7124	+	7.91688i	0.544161	+	0.314172i
$636$		0			0
$637$	4.17991	+	7.23981i	0.165614	+	0.286852i
$638$	−6.55387	−	11.3516i	−0.259470	−	0.449415i
$639$		0			0
$640$			13.7472i			0.543407i
$641$			20.0290i			0.791099i	0.918445	+	0.395549i	$0.129446\pi$
$641$			20.0290i			0.791099i	−0.918445	+	0.395549i	$0.870554\pi$
$642$		0			0
$643$	−5.13708	−	8.89768i	−0.202587	−	0.350890i	0.746775	−	0.665077i	$-0.231601\pi$
$643$	−5.13708	−	8.89768i	−0.202587	−	0.350890i	−0.949361	+	0.314187i	$0.898268\pi$
$644$	−0.359241	+	0.207408i	−0.0141561	+	0.00817301i
$645$		0			0
$646$	−0.282055	−	0.488534i	−0.0110973	−	0.0192211i
$647$	26.3758	−	15.2281i	1.03694	−	0.598677i	0.117974	−	0.993017i	$-0.462360\pi$
$647$	26.3758	−	15.2281i	1.03694	−	0.598677i	0.918965	+	0.394339i	$0.129027\pi$
$648$		0			0
$649$			41.7047i			1.63705i
$650$	20.0941	+	11.6013i	0.788154	+	0.455041i
$651$		0			0
$652$	26.8789			1.05266
$653$	−9.55028	−	16.5416i	−0.373731	−	0.647322i	0.616405	−	0.787429i	$-0.288588\pi$
$653$	−9.55028	−	16.5416i	−0.373731	−	0.647322i	−0.990136	+	0.140108i	$0.955255\pi$
$654$		0			0
$655$			36.1829i			1.41378i
$656$	−10.3075	−	5.95102i	−0.402439	−	0.232348i
$657$		0			0
$658$	−4.17873	−	2.41259i	−0.162904	−	0.0940527i
$659$	23.0728	−	13.3211i	0.898790	−	0.518917i	0.0219827	−	0.999758i	$-0.493002\pi$
$659$	23.0728	−	13.3211i	0.898790	−	0.518917i	0.876807	+	0.480842i	$0.159669\pi$
$660$		0			0
$661$	−34.6848	+	20.0253i	−1.34908	+	0.778894i	−0.988120	−	0.153686i	$-0.950886\pi$
$661$	−34.6848	+	20.0253i	−1.34908	+	0.778894i	−0.360964	+	0.932580i	$0.617552\pi$
$662$	2.94244	+	5.09645i	0.114361	+	0.198079i
$663$		0			0
$664$	4.44612	+	7.70091i	0.172543	+	0.298853i
$665$	−0.218000	+	0.377588i	−0.00845369	+	0.0146422i
$666$		0			0
$667$	0.0590172	+	0.102221i	0.00228515	+	0.00395800i
$668$	3.31337	+	1.91298i	0.128198	+	0.0740152i
$669$		0			0
$670$	−3.77851	+	6.54458i	−0.145977	+	0.252839i
$671$	−14.5784	+	25.2505i	−0.562792	+	0.974784i
$672$		0			0
$673$	18.6790	+	32.3529i	0.720022	+	1.24711i	0.960991	+	0.276581i	$0.0892015\pi$
$673$	18.6790	+	32.3529i	0.720022	+	1.24711i	−0.240969	+	0.970533i	$0.577465\pi$
$674$	30.0267	+	17.3359i	1.15658	+	0.667755i
$675$		0			0
$676$	−10.9192	+	18.9126i	−0.419969	+	0.727407i
$677$	34.5847	−	19.9675i	1.32920	−	0.767412i	0.344021	−	0.938962i	$-0.388211\pi$
$677$	34.5847	−	19.9675i	1.32920	−	0.767412i	0.985175	+	0.171550i	$0.0548775\pi$
$678$		0			0
$679$	0.926858			0.0355696
$680$	−2.81539	−	4.87639i	−0.107965	−	0.187001i
$681$		0			0
$682$	−45.7860			−1.75324
$683$	−8.57337	+	14.8495i	−0.328051	+	0.568201i	−0.982125	−	0.188229i	$-0.939725\pi$
$683$	−8.57337	+	14.8495i	−0.328051	+	0.568201i	0.654074	+	0.756431i	$0.273058\pi$
$684$		0			0
$685$	40.3416	+	23.2913i	1.54137	+	0.889913i
$686$	−32.0767	+	18.5195i	−1.22469	+	0.707077i
$687$		0			0
$688$	−26.5343	−	15.3196i	−1.01161	−	0.584053i
$689$	−4.19306	+	7.26260i	−0.159743	+	0.276683i
$690$		0			0
$691$			33.4266i			1.27161i	0.771850	+	0.635805i	$0.219332\pi$
$691$			33.4266i			1.27161i	−0.771850	+	0.635805i	$0.780668\pi$
$692$	−20.1683	−	34.9324i	−0.766682	−	1.32793i
$693$		0			0
$694$	8.26125			0.313593
$695$	−26.1766	−	45.3392i	−0.992934	−	1.71981i
$696$		0			0
$697$	11.2647			0.426683
$698$	−35.2352			−1.33367
$699$		0			0
$700$	−10.7975	+	18.7018i	−0.408108	+	0.706863i
$701$	−33.8015	+	19.5153i	−1.27666	+	0.737082i	−0.976233	−	0.216722i	$-0.930464\pi$
$701$	−33.8015	+	19.5153i	−1.27666	+	0.737082i	−0.300430	+	0.953804i	$0.597130\pi$
$702$		0			0
$703$	−0.568351	+	0.328138i	−0.0214358	+	0.0123759i
$704$	31.6250	−	54.7761i	1.19191	−	2.06445i
$705$		0			0
$706$	−45.8667	−	26.4811i	−1.72621	−	0.996631i
$707$	20.2223			0.760538
$708$		0			0
$709$	−0.819137	+	1.41879i	−0.0307633	+	0.0532837i	−0.880997	−	0.473122i	$-0.843127\pi$
$709$	−0.819137	+	1.41879i	−0.0307633	+	0.0532837i	0.850234	+	0.526405i	$0.176460\pi$
$710$	−34.6265	−	19.9916i	−1.29951	−	0.750272i
$711$		0			0
$712$			6.00000i			0.224860i
$713$	0.412300			0.0154408
$714$		0			0
$715$	−19.4789	−	33.7384i	−0.728469	−	1.26175i
$716$	−14.1899	−	8.19254i	−0.530301	−	0.306169i
$717$		0			0
$718$	−74.1781			−2.76830
$719$	−8.24140	−	14.2745i	−0.307352	−	0.532350i	0.670430	−	0.741973i	$-0.266110\pi$
$719$	−8.24140	−	14.2745i	−0.307352	−	0.532350i	−0.977782	+	0.209623i	$0.932776\pi$
$720$		0			0
$721$	5.41892	−	14.7492i	0.201811	−	0.549288i
$722$			39.1598i			1.45738i
$723$		0			0
$724$			47.0924i			1.75017i
$725$	5.32155	+	3.07240i	0.197637	+	0.114106i
$726$		0			0
$727$	−17.1840	+	9.92117i	−0.637318	+	0.367956i	−0.783581	−	0.621290i	$-0.786609\pi$
$727$	−17.1840	+	9.92117i	−0.637318	+	0.367956i	0.146263	+	0.989246i	$0.453276\pi$
$728$	1.26057	+	0.727792i	0.0467199	+	0.0269738i
$729$		0			0
$730$	31.0385			1.14879
$731$	28.9985			1.07255
$732$		0			0
$733$	−33.0079	−	19.0571i	−1.21918	−	0.703891i	−0.254434	−	0.967090i	$-0.581889\pi$
$733$	−33.0079	−	19.0571i	−1.21918	−	0.703891i	−0.964742	+	0.263199i	$0.915222\pi$
$734$			29.9284i			1.10468i
$735$		0			0
$736$	−0.483063	+	0.836690i	−0.0178059	+	0.0308408i
$737$	6.08124	−	3.51101i	0.224005	−	0.129330i
$738$		0			0
$739$	−2.09596	−	3.63030i	−0.0771010	−	0.133543i	0.824897	−	0.565283i	$-0.191233\pi$
$739$	−2.09596	−	3.63030i	−0.0771010	−	0.133543i	−0.901998	+	0.431740i	$0.857900\pi$
$740$	−50.8663	+	29.3676i	−1.86988	+	1.07958i
$741$		0			0
$742$	−12.7649	−	7.36984i	−0.468616	−	0.270555i
$743$	−17.3932			−0.638096			−0.319048	−	0.947738i	$-0.603363\pi$
$743$	−17.3932			−0.638096			−0.319048	+	0.947738i	$0.603363\pi$
$744$		0			0
$745$			58.9881i			2.16116i
$746$	−5.09138	+	2.93951i	−0.186409	+	0.107623i
$747$		0			0
$748$			46.9125i			1.71529i
$749$	−23.9009	+	13.7992i	−0.873318	+	0.504211i
$750$		0			0
$751$	24.9344			0.909870			0.454935	−	0.890525i	$-0.349663\pi$
$751$	24.9344			0.909870			0.454935	+	0.890525i	$0.349663\pi$
$752$	−5.19193			−0.189330
$753$		0			0
$754$	1.85682	−	3.21611i	0.0676215	−	0.117124i
$755$		−	66.8225i		−	2.43192i
$756$		0			0
$757$	−10.7281	+	18.5816i	−0.389920	+	0.675361i	−0.992438	−	0.122744i	$-0.960831\pi$
$757$	−10.7281	+	18.5816i	−0.389920	+	0.675361i	0.602518	+	0.798105i	$0.294164\pi$
$758$	−62.2866			−2.26235
$759$		0			0
$760$		−	0.145770i		−	0.00528764i
$761$	12.6168	−	21.8529i	0.457359	−	0.792168i	−0.541462	−	0.840725i	$-0.682129\pi$
$761$	12.6168	−	21.8529i	0.457359	−	0.792168i	0.998820	+	0.0485570i	$0.0154623\pi$
$762$		0			0
$763$		−	10.5010i		−	0.380161i
$764$	−22.7398	−	39.3864i	−0.822696	−	1.42495i
$765$		0			0
$766$	−47.3130	−	27.3162i	−1.70949	−	0.986974i
$767$	−10.2327	+	5.90783i	−0.369480	+	0.213319i
$768$		0			0
$769$	−3.13090	+	1.80762i	−0.112903	+	0.0651846i	−0.555388	−	0.831591i	$-0.687430\pi$
$769$	−3.13090	+	1.80762i	−0.112903	+	0.0651846i	0.442485	+	0.896776i	$0.354097\pi$
$770$	59.2996	−	34.2366i	2.13701	−	1.23380i
$771$		0			0
$772$	−27.3530	−	15.7922i	−0.984455	−	0.568375i
$773$	30.0031	+	17.3223i	1.07914	+	0.623040i	0.930663	−	0.365876i	$-0.119231\pi$
$773$	30.0031	+	17.3223i	1.07914	+	0.623040i	0.148474	+	0.988916i	$0.452564\pi$
$774$		0			0
$775$	18.5885	−	10.7321i	0.667717	−	0.385507i
$776$	−0.268365	+	0.154941i	−0.00963374	+	0.00556204i
$777$		0			0
$778$	63.3351	−	36.5665i	2.27067	−	1.31097i
$779$	0.252553	+	0.145812i	0.00904866	+	0.00522424i
$780$		0			0
$781$	18.5763	+	32.1750i	0.664711	+	1.15131i
$782$		−	0.797773i		−	0.0285283i
$783$		0			0
$784$	−7.90511	+	13.6920i	−0.282325	+	0.489002i
$785$			51.2561i			1.82941i
$786$		0			0
$787$	−43.6675			−1.55658			−0.778289	−	0.627906i	$-0.783912\pi$
$787$	−43.6675			−1.55658			−0.778289	+	0.627906i	$0.783912\pi$
$788$	−28.0725	+	48.6230i	−1.00004	+	1.73212i
$789$		0			0
$790$			105.525i			3.75441i
$791$	8.37745	−	14.5102i	0.297868	−	0.515922i
$792$		0			0
$793$	−8.26060			−0.293343
$794$	20.0779			0.712538
$795$		0			0
$796$	4.61775	−	2.66606i	0.163672	−	0.0944959i
$797$			30.6976i			1.08736i	0.839291	+	0.543682i	$0.182970\pi$
$797$			30.6976i			1.08736i	−0.839291	+	0.543682i	$0.817030\pi$
$798$		0			0
$799$	4.25558	−	2.45696i	0.150552	−	0.0869211i
$800$			50.2959i			1.77823i
$801$		0			0
$802$	−55.8206			−1.97110
$803$	−24.9771	−	14.4205i	−0.881422	−	0.508889i
$804$		0			0
$805$	−0.533990	+	0.308299i	−0.0188207	+	0.0108661i
$806$	−6.48598	−	11.2340i	−0.228459	−	0.395702i
$807$		0			0
$808$	−5.85521	+	3.38051i	−0.205986	+	0.118926i
$809$	−18.5375	+	32.1079i	−0.651744	+	1.12885i	0.330956	+	0.943646i	$0.392629\pi$
$809$	−18.5375	+	32.1079i	−0.651744	+	1.12885i	−0.982699	+	0.185207i	$0.940704\pi$
$810$		0			0
$811$		−	27.3092i		−	0.958955i	−0.877554	−	0.479478i	$-0.840826\pi$
$811$		−	27.3092i		−	0.958955i	0.877554	−	0.479478i	$-0.159174\pi$
$812$	2.99328	+	1.72817i	0.105044	+	0.0606469i
$813$		0			0
$814$	103.067			3.61250
$815$	39.9539			1.39952
$816$		0			0
$817$	0.650141	+	0.375359i	0.0227456	+	0.0131322i
$818$	15.6245	−	9.02079i	0.546297	−	0.315405i
$819$		0			0
$820$	22.6030	+	13.0498i	0.789331	+	0.455721i
$821$			22.7819i			0.795094i	0.917582	+	0.397547i	$0.130138\pi$
$821$			22.7819i			0.795094i	−0.917582	+	0.397547i	$0.869862\pi$
$822$		0			0
$823$			9.09264i			0.316950i	0.987363	+	0.158475i	$0.0506577\pi$
$823$			9.09264i			0.316950i	−0.987363	+	0.158475i	$0.949342\pi$
$824$	0.896575	+	5.17638i	0.0312337	+	0.180328i
$825$		0			0
$826$	−10.3838	−	17.9852i	−0.361297	−	0.625785i
$827$	4.07786			0.141801			0.0709005	−	0.997483i	$-0.477413\pi$
$827$	4.07786			0.141801			0.0709005	+	0.997483i	$0.477413\pi$
$828$		0			0
$829$	21.5670	+	12.4517i	0.749051	+	0.432465i	0.825351	−	0.564620i	$-0.190977\pi$
$829$	21.5670	+	12.4517i	0.749051	+	0.432465i	−0.0762996	+	0.997085i	$0.524311\pi$
$830$	59.2568	+	102.636i	2.05683	+	3.56254i
$831$		0			0
$832$	17.9198			0.621258
$833$		−	14.9637i		−	0.518460i
$834$		0			0
$835$	4.92513	+	2.84352i	0.170441	+	0.0984042i
$836$	−0.607238	+	1.05177i	−0.0210018	+	0.0363761i
$837$		0			0
$838$	−28.6991			−0.991395
$839$	6.37140	+	3.67853i	0.219965	+	0.126997i	0.605934	−	0.795515i	$-0.292799\pi$
$839$	6.37140	+	3.67853i	0.219965	+	0.126997i	−0.385969	+	0.922512i	$0.626133\pi$
$840$		0			0
$841$	−14.0083	+	24.2630i	−0.483043	+	0.836655i
$842$	32.9642	−	19.0319i	1.13602	−	0.655883i
$843$		0			0
$844$	45.6746	−	26.3703i	1.57219	−	0.907702i
$845$	−16.2307	+	28.1124i	−0.558354	+	0.967097i
$846$		0			0
$847$	−46.5947			−1.60101
$848$	−15.8600			−0.544634
$849$		0			0
$850$	−20.7658	−	35.9674i	−0.712260	−	1.23367i
$851$	−0.928113			−0.0318153
$852$		0			0
$853$	−26.4219	−	45.7640i	−0.904667	−	1.56693i	−0.821363	−	0.570406i	$-0.806786\pi$
$853$	−26.4219	−	45.7640i	−0.904667	−	1.56693i	−0.0833045	−	0.996524i	$-0.526547\pi$
$854$		−	14.5191i		−	0.496832i
$855$		0			0
$856$	4.61354	−	7.99089i	0.157688	−	0.273123i
$857$	36.8225	+	21.2595i	1.25783	+	0.726210i	0.972653	−	0.232264i	$-0.0746135\pi$
$857$	36.8225	+	21.2595i	1.25783	+	0.726210i	0.285179	+	0.958474i	$0.407947\pi$
$858$		0			0
$859$	−12.4053	+	7.16222i	−0.423264	+	0.244372i	−0.696473	−	0.717583i	$-0.745248\pi$
$859$	−12.4053	+	7.16222i	−0.423264	+	0.244372i	0.273209	+	0.961955i	$0.411915\pi$
$860$	58.1863	+	33.5939i	1.98414	+	1.14554i
$861$		0			0
$862$	−13.7776	+	23.8635i	−0.469267	+	0.812795i
$863$	38.2577			1.30231			0.651153	−	0.758946i	$-0.274285\pi$
$863$	38.2577			1.30231			0.651153	+	0.758946i	$0.274285\pi$
$864$		0			0
$865$	−29.9789	−	51.9250i	−1.01931	−	1.76550i
$866$	11.9709			0.406788
$867$		0			0
$868$	10.4557	−	6.03660i	0.354889	−	0.204895i
$869$	49.0270	−	84.9172i	1.66313	−	2.88062i
$870$		0			0
$871$	1.72292	+	0.994728i	0.0583789	+	0.0337051i
$872$	1.75542	+	3.04048i	0.0594461	+	0.102964i
$873$		0			0
$874$	0.0103264	−	0.0178859i	0.000349297	−	0.000604999i
$875$	−3.09839	+	5.36656i	−0.104745	+	0.181423i
$876$		0			0
$877$	4.15201	+	2.39716i	0.140203	+	0.0809465i	0.568461	−	0.822710i	$-0.307539\pi$
$877$	4.15201	+	2.39716i	0.140203	+	0.0809465i	−0.428258	+	0.903657i	$0.640872\pi$
$878$	20.6335	+	35.7382i	0.696345	+	1.20611i
$879$		0			0
$880$	36.8388	−	63.8067i	1.24184	−	2.15092i
$881$	−7.48234	−	12.9598i	−0.252086	−	0.436626i	0.712014	−	0.702166i	$-0.247783\pi$
$881$	−7.48234	−	12.9598i	−0.252086	−	0.436626i	−0.964100	+	0.265539i	$0.914450\pi$
$882$		0			0
$883$	−12.0287	−	20.8343i	−0.404797	−	0.701130i	0.589500	−	0.807768i	$-0.299325\pi$
$883$	−12.0287	−	20.8343i	−0.404797	−	0.701130i	−0.994298	+	0.106638i	$0.965991\pi$
$884$	−11.5104	+	6.64555i	−0.387138	+	0.223514i
$885$		0			0
$886$	−33.1608	+	19.1454i	−1.11406	+	0.643202i
$887$	−15.9160	−	9.18910i	−0.534406	−	0.308540i	0.208403	−	0.978043i	$-0.433174\pi$
$887$	−15.9160	−	9.18910i	−0.534406	−	0.308540i	−0.742809	+	0.669503i	$0.766507\pi$
$888$		0			0
$889$	6.34490	+	3.66323i	0.212801	+	0.122861i
$890$			79.9665i			2.68048i
$891$		0			0
$892$	−0.711811	−	1.23289i	−0.0238332	−	0.0412803i
$893$	0.127212			0.00425700
$894$		0			0
$895$	−21.0924	−	12.1777i	−0.705042	−	0.407056i
$896$			6.36100i			0.212506i
$897$		0			0
$898$	33.2297	−	19.1852i	1.10889	−	0.640217i
$899$	−1.71769	−	2.97513i	−0.0572883	−	0.0992263i
$900$		0			0
$901$	12.9997	−	7.50538i	0.433083	−	0.250040i
$902$	−22.8995	−	39.6631i	−0.762470	−	1.32064i
$903$		0			0
$904$			5.60175i			0.186311i
$905$			70.0000i			2.32688i
$906$		0			0
$907$	19.6020	+	33.9517i	0.650875	+	1.12735i	0.982911	+	0.184082i	$0.0589310\pi$
$907$	19.6020	+	33.9517i	0.650875	+	1.12735i	−0.332036	+	0.943267i	$0.607736\pi$
$908$	−14.4571	−	25.0405i	−0.479777	−	0.830999i
$909$		0			0
$910$	16.8006	+	9.69982i	0.556934	+	0.321546i
$911$	−5.94709	−	10.3007i	−0.197036	−	0.341276i	0.750530	−	0.660836i	$-0.229798\pi$
$911$	−5.94709	−	10.3007i	−0.197036	−	0.341276i	−0.947566	+	0.319560i	$0.896465\pi$
$912$		0			0
$913$		−	110.123i		−	3.64455i
$914$	−22.0984			−0.730951
$915$		0			0
$916$	5.06058	−	8.76518i	0.167206	−	0.289610i
$917$			16.7422i			0.552877i
$918$		0			0
$919$			24.5353i			0.809346i	0.914462	+	0.404673i	$0.132615\pi$
$919$			24.5353i			0.809346i	−0.914462	+	0.404673i	$0.867385\pi$
$920$	0.103075	−	0.178531i	0.00339829	−	0.00588600i
$921$		0			0
$922$	−2.03462	+	3.52406i	−0.0670066	+	0.116059i
$923$	−5.26298	+	9.11574i	−0.173233	+	0.300048i
$924$		0			0
$925$	−41.8437	+	24.1585i	−1.37581	+	0.794326i
$926$	−15.6014			−0.512693
$927$		0			0
$928$	8.05000			0.264254
$929$	3.41962	−	1.97432i	0.112194	−	0.0647753i	−0.442853	−	0.896594i	$-0.646034\pi$
$929$	3.41962	−	1.97432i	0.112194	−	0.0647753i	0.555047	+	0.831819i	$0.312700\pi$
$930$		0			0
$931$	0.193690	−	0.335482i	0.00634795	−	0.0109950i
$932$	−33.6021	+	58.2005i	−1.10067	+	1.90642i
$933$		0			0
$934$	5.05264	−	8.75144i	0.165328	−	0.286356i
$935$			69.7325i			2.28050i
$936$		0			0
$937$		−	17.8830i		−	0.584212i	−0.956386	−	0.292106i	$-0.905644\pi$
$937$		−	17.8830i		−	0.584212i	0.956386	−	0.292106i	$-0.0943560\pi$
$938$	−1.74836	+	3.02825i	−0.0570860	+	0.0988759i
$939$		0			0
$940$	11.3852			0.371346
$941$		−	36.2692i		−	1.18234i	−0.806546	−	0.591171i	$-0.798666\pi$
$941$		−	36.2692i		−	1.18234i	0.806546	−	0.591171i	$-0.201334\pi$
$942$		0			0
$943$	0.206209	+	0.357164i	0.00671508	+	0.0116309i
$944$	−19.3522	−	11.1730i	−0.629859	−	0.363649i
$945$		0			0
$946$	−58.9496	−	102.104i	−1.91662	−	3.31968i
$947$	4.21565	+	7.30172i	0.136990	+	0.237274i	0.926356	−	0.376649i	$-0.122924\pi$
$947$	4.21565	+	7.30172i	0.136990	+	0.237274i	−0.789366	+	0.613923i	$0.789590\pi$
$948$		0			0
$949$		−	8.17116i		−	0.265247i
$950$		−	1.07517i		−	0.0348833i
$951$		0			0
$952$	−1.30271	−	2.25636i	−0.0422211	−	0.0731291i
$953$	28.7590	−	16.6040i	0.931595	−	0.537857i	0.0442793	−	0.999019i	$-0.485901\pi$
$953$	28.7590	−	16.6040i	0.931595	−	0.537857i	0.887316	+	0.461163i	$0.152568\pi$
$954$		0			0
$955$	−33.8013	−	58.5455i	−1.09378	−	1.89449i
$956$	2.89160	−	1.66946i	0.0935210	−	0.0539943i
$957$		0			0
$958$			67.0999i			2.16790i
$959$	18.6665	+	10.7771i	0.602774	+	0.348012i
$960$		0			0
$961$	19.0000			0.612903
$962$	14.6003	+	25.2885i	0.470734	+	0.815334i
$963$		0			0
$964$		−	50.9475i		−	1.64091i
$965$	−40.6585	−	23.4742i	−1.30884	−	0.755662i
$966$		0			0
$967$	−27.6180	−	15.9453i	−0.888136	−	0.512765i	−0.0148034	−	0.999890i	$-0.504712\pi$
$967$	−27.6180	−	15.9453i	−0.888136	−	0.512765i	−0.873332	+	0.487125i	$0.838046\pi$
$968$	13.4911	−	7.78911i	0.433622	−	0.250352i
$969$		0			0
$970$	−3.57670	+	2.06501i	−0.114841	+	0.0663034i
$971$	1.10149	+	1.90784i	0.0353486	+	0.0612256i	0.883158	−	0.469075i	$-0.155413\pi$
$971$	1.10149	+	1.90784i	0.0353486	+	0.0612256i	−0.847810	+	0.530300i	$0.822079\pi$
$972$		0			0
$973$	−12.1122	−	20.9789i	−0.388299	−	0.672554i
$974$	−25.5483	+	44.2510i	−0.818621	+	1.41789i
$975$		0			0
$976$	−7.81130	−	13.5296i	−0.250033	−	0.433071i
$977$	21.8001	+	12.5863i	0.697448	+	0.402672i	0.806396	−	0.591376i	$-0.201415\pi$
$977$	21.8001	+	12.5863i	0.697448	+	0.402672i	−0.108948	+	0.994047i	$0.534748\pi$
$978$		0			0
$979$	37.1525	−	64.3501i	1.18740	−	2.05664i
$980$	17.3349	−	30.0249i	0.553743	−	0.959112i
$981$		0			0
$982$	34.5580	+	59.8562i	1.10279	+	1.91009i
$983$	−5.95403	−	3.43756i	−0.189904	−	0.109641i	0.402034	−	0.915625i	$-0.368303\pi$
$983$	−5.95403	−	3.43756i	−0.189904	−	0.109641i	−0.591938	+	0.805984i	$0.701637\pi$
$984$		0			0
$985$	−41.7281	+	72.2752i	−1.32957	+	2.30288i
$986$	−5.75668	+	3.32362i	−0.183330	+	0.105846i
$987$		0			0
$988$	−0.344082			−0.0109467
$989$	0.530838	+	0.919438i	0.0168797	+	0.0292364i
$990$		0			0
$991$	5.98868			0.190237			0.0951183	−	0.995466i	$-0.469677\pi$
$991$	5.98868			0.190237			0.0951183	+	0.995466i	$0.469677\pi$
$992$	14.0595	−	24.3518i	0.446391	−	0.773172i
$993$		0			0
$994$	−16.0221	−	9.25035i	−0.508189	−	0.293403i
$995$	6.86400	−	3.96294i	0.217604	−	0.125633i
$996$		0			0
$997$	9.25458	+	5.34313i	0.293095	+	0.169219i	0.639337	−	0.768927i	$-0.279209\pi$
$997$	9.25458	+	5.34313i	0.293095	+	0.169219i	−0.346242	+	0.938145i	$0.612542\pi$
$998$	−2.41984	+	4.19129i	−0.0765988	+	0.132673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.o.a.881.2	yes	16
3.2	odd	2	inner	927.2.o.a.881.7	yes	16
103.47	odd	6	inner	927.2.o.a.665.7	yes	16
309.47	even	6	inner	927.2.o.a.665.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.o.a.665.2	✓	16	309.47	even	6	inner
927.2.o.a.665.7	yes	16	103.47	odd	6	inner
927.2.o.a.881.2	yes	16	1.1	even	1	trivial
927.2.o.a.881.7	yes	16	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78558 + 1.03090i) q^{2} +(1.12553 - 1.94948i) q^{4} +(1.67303 - 2.89778i) q^{5} +(0.774131 - 1.34083i) q^{7} +0.517638i q^{8} +O(q^{10})\)	\(q+(-1.78558 + 1.03090i) q^{2} +(1.12553 - 1.94948i) q^{4} +(1.67303 - 2.89778i) q^{5} +(0.774131 - 1.34083i) q^{7} +0.517638i q^{8} +6.89895i q^{10} +(3.20526 - 5.55168i) q^{11} +1.81621 q^{13} +3.19222i q^{14} +(1.71742 + 2.97467i) q^{16} +(-2.81539 - 1.62546i) q^{17} +(-0.0420802 - 0.0728851i) q^{19} +(-3.76610 - 6.52307i) q^{20} +13.2173i q^{22} -0.119021i q^{23} +(-3.09808 - 5.36603i) q^{25} +(-3.24299 + 1.87234i) q^{26} +(-1.74262 - 3.01830i) q^{28} +(-0.858847 + 0.495856i) q^{29} +3.46410i q^{31} +(-7.02977 - 4.05864i) q^{32} +6.70280 q^{34} +(-2.59029 - 4.48652i) q^{35} -7.79790i q^{37} +(0.150275 + 0.0867615i) q^{38} +(1.50000 + 0.866025i) q^{40} +(-3.00085 + 1.73254i) q^{41} +(-7.72502 + 4.46004i) q^{43} +(-7.21524 - 12.4972i) q^{44} +(0.122699 + 0.212521i) q^{46} +(-0.755772 + 1.30904i) q^{47} +(2.30144 + 3.98621i) q^{49} +(11.0637 + 6.38764i) q^{50} +(2.04420 - 3.54066i) q^{52} +(-2.30869 + 3.99876i) q^{53} +(-10.7250 - 18.5763i) q^{55} +(0.694067 + 0.400720i) q^{56} +(1.02236 - 1.77078i) q^{58} +(-5.63407 + 3.25283i) q^{59} -4.54826 q^{61} +(-3.57116 - 6.18543i) q^{62} +9.86659 q^{64} +(3.03858 - 5.26298i) q^{65} +(0.948634 + 0.547694i) q^{67} +(-6.33761 + 3.65902i) q^{68} +(9.25035 + 5.34069i) q^{70} +(-2.89778 + 5.01910i) q^{71} -4.49902i q^{73} +(8.03889 + 13.9238i) q^{74} -0.189450 q^{76} +(-4.96259 - 8.59545i) q^{77} +15.2958 q^{79} +11.4932 q^{80} +(3.57217 - 6.18719i) q^{82} +(14.8770 - 8.58925i) q^{83} +(-9.42047 + 5.43891i) q^{85} +(9.19575 - 15.9275i) q^{86} +(2.87376 + 1.65917i) q^{88} +11.5911 q^{89} +(1.40599 - 2.43524i) q^{91} +(-0.232028 - 0.133962i) q^{92} -3.11652i q^{94} -0.281606 q^{95} +(0.299322 + 0.518441i) q^{97} +(-8.21882 - 4.74514i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^7	\( 16 q + 8 q^{4} + 4 q^{7} + 40 q^{13} + 12 q^{16} - 20 q^{19} - 8 q^{25} + 16 q^{28} + 104 q^{34} + 24 q^{40} + 36 q^{43} - 36 q^{46} - 40 q^{49} + 12 q^{52} - 12 q^{55} - 40 q^{58} - 56 q^{61} + 112 q^{64} + 48 q^{67} + 60 q^{70} - 48 q^{76} + 112 q^{79} - 24 q^{82} - 84 q^{85} - 12 q^{88} + 68 q^{91} - 32 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^7 + 40 * q^13 + 12 * q^16 - 20 * q^19 - 8 * q^25 + 16 * q^28 + 104 * q^34 + 24 * q^40 + 36 * q^43 - 36 * q^46 - 40 * q^49 + 12 * q^52 - 12 * q^55 - 40 * q^58 - 56 * q^61 + 112 * q^64 + 48 * q^67 + 60 * q^70 - 48 * q^76 + 112 * q^79 - 24 * q^82 - 84 * q^85 - 12 * q^88 + 68 * q^91 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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