LMFDB - Embedded newform 828.2.q.c.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(73,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("828.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.q (of order $11$, degree $10$, 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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			577.1
Root			$1.74521 + 2.01408i$ of defining polynomial
Character	$\chi$	$=$	828.577
Dual form			828.2.q.c.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.91931 - 1.15081i) q^{5} +(-0.0825209 + 0.0952342i) q^{7} +O(q^{10})$	$q+(-3.91931 - 1.15081i) q^{5} +(-0.0825209 + 0.0952342i) q^{7} +(1.03818 - 0.667196i) q^{11} +(1.25227 + 1.44519i) q^{13} +(-0.787312 + 1.72397i) q^{17} +(0.0613378 + 0.134311i) q^{19} +(2.15160 + 4.28610i) q^{23} +(9.83034 + 6.31757i) q^{25} +(-3.11768 + 6.82676i) q^{29} +(0.335425 - 2.33293i) q^{31} +(0.433021 - 0.278286i) q^{35} +(-7.41275 + 2.17658i) q^{37} +(10.0522 + 2.95160i) q^{41} +(1.71801 + 11.9490i) q^{43} +5.71564 q^{47} +(0.993944 + 6.91303i) q^{49} +(4.37352 - 5.04731i) q^{53} +(-4.83675 + 1.42020i) q^{55} +(4.98875 + 5.75733i) q^{59} +(-0.180939 + 1.25846i) q^{61} +(-3.24487 - 7.10527i) q^{65} +(-8.94923 - 5.75132i) q^{67} +(-7.77319 - 4.99552i) q^{71} +(-5.25031 - 11.4966i) q^{73} +(-0.0221314 + 0.153928i) q^{77} +(2.44214 + 2.81838i) q^{79} +(-7.82984 + 2.29905i) q^{83} +(5.06969 - 5.85073i) q^{85} +(-1.00479 - 6.98848i) q^{89} -0.240970 q^{91} +(-0.0858348 - 0.596994i) q^{95} +(12.7100 + 3.73198i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^5	$ 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) $ 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.91931	−	1.15081i	−1.75277	−	0.514659i	−0.761690	−	0.647942i	$-0.775630\pi$
$5$	−3.91931	−	1.15081i	−1.75277	−	0.514659i	−0.991078	+	0.133283i	$0.957448\pi$
$6$		0			0
$7$	−0.0825209	+	0.0952342i	−0.0311900	+	0.0359951i	−0.771130	−	0.636677i	$-0.780308\pi$
$7$	−0.0825209	+	0.0952342i	−0.0311900	+	0.0359951i	0.739940	+	0.672673i	$0.234854\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.03818	−	0.667196i	0.313022	−	0.201167i	−0.374691	−	0.927150i	$-0.622251\pi$
$11$	1.03818	−	0.667196i	0.313022	−	0.201167i	0.687713	+	0.725983i	$0.258615\pi$
$12$		0			0
$13$	1.25227	+	1.44519i	0.347316	+	0.400824i	0.902350	−	0.431003i	$-0.141840\pi$
$13$	1.25227	+	1.44519i	0.347316	+	0.400824i	−0.555034	+	0.831827i	$0.687295\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.787312	+	1.72397i	−0.190951	+	0.418125i	−0.980757	−	0.195232i	$-0.937454\pi$
$17$	−0.787312	+	1.72397i	−0.190951	+	0.418125i	0.789806	+	0.613357i	$0.210181\pi$
$18$		0			0
$19$	0.0613378	+	0.134311i	0.0140719	+	0.0308131i	0.916537	−	0.399949i	$-0.130972\pi$
$19$	0.0613378	+	0.134311i	0.0140719	+	0.0308131i	−0.902466	+	0.430762i	$0.858245\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.15160	+	4.28610i	0.448639	+	0.893713i
$23$	2.15160	+	4.28610i	0.448639	+	0.893713i
$24$		0			0
$25$	9.83034	+	6.31757i	1.96607	+	1.26351i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.11768	+	6.82676i	−0.578938	+	1.26770i	0.362962	+	0.931804i	$0.381766\pi$
$29$	−3.11768	+	6.82676i	−0.578938	+	1.26770i	−0.941900	+	0.335894i	$0.890962\pi$
$30$		0			0
$31$	0.335425	−	2.33293i	0.0602441	−	0.419007i	−0.937274	−	0.348594i	$-0.886659\pi$
$31$	0.335425	−	2.33293i	0.0602441	−	0.419007i	0.997518	−	0.0704129i	$-0.0224317\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.433021	−	0.278286i	0.0731940	−	0.0470389i
$36$		0			0
$37$	−7.41275	+	2.17658i	−1.21865	+	0.357828i	−0.826955	−	0.562268i	$-0.809929\pi$
$37$	−7.41275	+	2.17658i	−1.21865	+	0.357828i	−0.391694	+	0.920096i	$0.628111\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	10.0522	+	2.95160i	1.56990	+	0.460963i	0.946971	−	0.321319i	$-0.104126\pi$
$41$	10.0522	+	2.95160i	1.56990	+	0.460963i	0.622925	+	0.782282i	$0.285944\pi$
$42$		0			0
$43$	1.71801	+	11.9490i	0.261994	+	1.82221i	0.517826	+	0.855486i	$0.326741\pi$
$43$	1.71801	+	11.9490i	0.261994	+	1.82221i	−0.255832	+	0.966721i	$0.582350\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.71564			0.833712			0.416856	−	0.908972i	$-0.363132\pi$
$47$	5.71564			0.833712			0.416856	+	0.908972i	$0.363132\pi$
$48$		0			0
$49$	0.993944	+	6.91303i	0.141992	+	0.987576i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.37352	−	5.04731i	0.600749	−	0.693301i	−0.371184	−	0.928559i	$-0.621048\pi$
$53$	4.37352	−	5.04731i	0.600749	−	0.693301i	0.971933	+	0.235258i	$0.0755936\pi$
$54$		0			0
$55$	−4.83675	+	1.42020i	−0.652188	+	0.191500i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.98875	+	5.75733i	0.649480	+	0.749540i	0.981021	−	0.193901i	$-0.0621140\pi$
$59$	4.98875	+	5.75733i	0.649480	+	0.749540i	−0.331541	+	0.943441i	$0.607569\pi$
$60$		0			0
$61$	−0.180939	+	1.25846i	−0.0231668	+	0.161129i	−0.998121	−	0.0612782i	$-0.980482\pi$
$61$	−0.180939	+	1.25846i	−0.0231668	+	0.161129i	0.974954	+	0.222407i	$0.0713914\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.24487	−	7.10527i	−0.402476	−	0.881301i
$66$		0			0
$67$	−8.94923	−	5.75132i	−1.09332	−	0.702636i	−0.135726	−	0.990746i	$-0.543337\pi$
$67$	−8.94923	−	5.75132i	−1.09332	−	0.702636i	−0.957597	+	0.288111i	$0.906973\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.77319	−	4.99552i	−0.922508	−	0.592860i	−0.00912348	−	0.999958i	$-0.502904\pi$
$71$	−7.77319	−	4.99552i	−0.922508	−	0.592860i	−0.913384	+	0.407099i	$0.866540\pi$
$72$		0			0
$73$	−5.25031	−	11.4966i	−0.614502	−	1.34557i	−0.919451	−	0.393204i	$-0.871367\pi$
$73$	−5.25031	−	11.4966i	−0.614502	−	1.34557i	0.304949	−	0.952369i	$-0.401361\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0221314	+	0.153928i	−0.00252211	+	0.0175417i
$78$		0			0
$79$	2.44214	+	2.81838i	0.274762	+	0.317092i	0.876313	−	0.481742i	$-0.159996\pi$
$79$	2.44214	+	2.81838i	0.274762	+	0.317092i	−0.601551	+	0.798834i	$0.705450\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.82984	+	2.29905i	−0.859437	+	0.252353i	−0.681617	−	0.731710i	$-0.738723\pi$
$83$	−7.82984	+	2.29905i	−0.859437	+	0.252353i	−0.177820	+	0.984063i	$0.556905\pi$
$84$		0			0
$85$	5.06969	−	5.85073i	0.549885	−	0.634601i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.00479	−	6.98848i	−0.106508	−	0.740778i	−0.971164	−	0.238413i	$-0.923373\pi$
$89$	−1.00479	−	6.98848i	−0.106508	−	0.740778i	0.864656	−	0.502364i	$-0.167536\pi$
$90$		0			0
$91$	−0.240970			−0.0252605
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0858348	−	0.596994i	−0.00880647	−	0.0612503i
$96$		0			0
$97$	12.7100	+	3.73198i	1.29050	+	0.378925i	0.853762	−	0.520663i	$-0.174315\pi$
$97$	12.7100	+	3.73198i	1.29050	+	0.378925i	0.436739	+	0.899588i	$0.356133\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.47893	−	1.90238i	0.644677	−	0.189294i	0.0569800	−	0.998375i	$-0.481853\pi$
$101$	6.47893	−	1.90238i	0.644677	−	0.189294i	0.587697	+	0.809081i	$0.300035\pi$
$102$		0			0
$103$	−7.13745	+	4.58696i	−0.703274	+	0.451967i	−0.842783	−	0.538254i	$-0.819084\pi$
$103$	−7.13745	+	4.58696i	−0.703274	+	0.451967i	0.139509	+	0.990221i	$0.455448\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.88329	+	13.0986i	−0.182065	+	1.26629i	0.669806	+	0.742536i	$0.266377\pi$
$107$	−1.88329	+	13.0986i	−0.182065	+	1.26629i	−0.851871	+	0.523752i	$0.824532\pi$
$108$		0			0
$109$	3.09393	−	6.77476i	0.296345	−	0.648905i	−0.701628	−	0.712543i	$-0.747543\pi$
$109$	3.09393	−	6.77476i	0.296345	−	0.648905i	0.997973	+	0.0636386i	$0.0202705\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.67658	−	1.72014i	−0.251792	−	0.161817i	0.408657	−	0.912688i	$-0.365997\pi$
$113$	−2.67658	−	1.72014i	−0.251792	−	0.161817i	−0.660448	+	0.750871i	$0.729634\pi$
$114$		0			0
$115$	−3.50027	−	19.2746i	−0.326402	−	1.79737i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.0992114	−	0.217243i	−0.00909470	−	0.0199146i
$120$		0			0
$121$	−3.93690	+	8.62062i	−0.357900	+	0.783692i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−17.8830	−	20.6381i	−1.59950	−	1.84593i
$126$		0			0
$127$	−16.9326	+	10.8819i	−1.50252	+	0.965614i	−0.507972	+	0.861374i	$0.669605\pi$
$127$	−16.9326	+	10.8819i	−1.50252	+	0.965614i	−0.994552	+	0.104240i	$0.966759\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.33360	+	2.69312i	−0.203888	+	0.235299i	−0.848480	−	0.529228i	$-0.822482\pi$
$131$	−2.33360	+	2.69312i	−0.203888	+	0.235299i	0.644592	+	0.764527i	$0.277027\pi$
$132$		0			0
$133$	−0.0178526	−	0.00524201i	−0.00154802	−	0.000454540i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	20.4210			1.74468			0.872342	−	0.488897i	$-0.162601\pi$
$137$	20.4210			1.74468			0.872342	+	0.488897i	$0.162601\pi$
$138$		0			0
$139$	14.3307			1.21551			0.607755	−	0.794125i	$-0.292070\pi$
$139$	14.3307			1.21551			0.607755	+	0.794125i	$0.292070\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.26430	+	0.664858i	0.189350	+	0.0555982i
$144$		0			0
$145$	20.0755	−	23.1683i	1.66718	−	1.92402i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−15.1115	+	9.71156i	−1.23798	+	0.795602i	−0.985114	−	0.171900i	$-0.945009\pi$
$149$	−15.1115	+	9.71156i	−1.23798	+	0.795602i	−0.252866	+	0.967501i	$0.581373\pi$
$150$		0			0
$151$	4.03194	+	4.65311i	0.328115	+	0.378665i	0.895707	−	0.444645i	$-0.146670\pi$
$151$	4.03194	+	4.65311i	0.328115	+	0.378665i	−0.567592	+	0.823310i	$0.692125\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.99940	+	8.75746i	−0.321240	+	0.703416i
$156$		0			0
$157$	−3.21531	−	7.04055i	−0.256610	−	0.561897i	0.736853	−	0.676053i	$-0.236311\pi$
$157$	−3.21531	−	7.04055i	−0.256610	−	0.561897i	−0.993463	+	0.114156i	$0.963584\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.585735	−	0.148787i	−0.0461623	−	0.0117261i
$162$		0			0
$163$	10.7893	+	6.93388i	0.845085	+	0.543103i	0.890038	−	0.455886i	$-0.150678\pi$
$163$	10.7893	+	6.93388i	0.845085	+	0.543103i	−0.0449533	+	0.998989i	$0.514314\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.25256	+	2.74273i	−0.0969262	+	0.212239i	−0.951884	−	0.306459i	$-0.900856\pi$
$167$	−1.25256	+	2.74273i	−0.0969262	+	0.212239i	0.854958	+	0.518698i	$0.173583\pi$
$168$		0			0
$169$	1.32968	−	9.24815i	0.102283	−	0.711396i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.98890	+	1.27819i	−0.151214	+	0.0971791i	−0.614060	−	0.789260i	$-0.710465\pi$
$173$	−1.98890	+	1.27819i	−0.151214	+	0.0971791i	0.462846	+	0.886439i	$0.346828\pi$
$174$		0			0
$175$	−1.41286	+	0.414852i	−0.106802	+	0.0313599i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−20.0574	−	5.88938i	−1.49916	−	0.440193i	−0.573708	−	0.819060i	$-0.694496\pi$
$179$	−20.0574	−	5.88938i	−1.49916	−	0.440193i	−0.925451	+	0.378867i	$0.876314\pi$
$180$		0			0
$181$	−2.18165	−	15.1737i	−0.162161	−	1.12785i	−0.894550	−	0.446967i	$-0.852504\pi$
$181$	−2.18165	−	15.1737i	−0.162161	−	1.12785i	0.732389	−	0.680886i	$-0.238405\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	31.5577			2.32017
$186$		0			0
$187$	0.332858	+	2.31508i	0.0243410	+	0.169295i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.93558	+	6.85002i	−0.429483	+	0.495650i	−0.928703	−	0.370826i	$-0.879075\pi$
$191$	−5.93558	+	6.85002i	−0.429483	+	0.495650i	0.499219	+	0.866476i	$0.333620\pi$
$192$		0			0
$193$	9.14918	−	2.68644i	0.658572	−	0.193374i	0.0646640	−	0.997907i	$-0.479402\pi$
$193$	9.14918	−	2.68644i	0.658572	−	0.193374i	0.593908	+	0.804533i	$0.297584\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.70078	+	1.96280i	0.121175	+	0.139844i	0.813096	−	0.582130i	$-0.197781\pi$
$197$	1.70078	+	1.96280i	0.121175	+	0.139844i	−0.691920	+	0.721974i	$0.743235\pi$
$198$		0			0
$199$	−2.86746	+	19.9437i	−0.203269	+	1.41377i	0.591230	+	0.806503i	$0.298643\pi$
$199$	−2.86746	+	19.9437i	−0.203269	+	1.41377i	−0.794499	+	0.607265i	$0.792267\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.392867	−	0.860260i	−0.0275739	−	0.0603784i
$204$		0			0
$205$	−36.0011	−	23.1365i	−2.51442	−	1.61592i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.153291	+	0.0985143i	0.0106034	+	0.00681438i
$210$		0			0
$211$	−9.89338	−	21.6635i	−0.681089	−	1.49138i	−0.861486	−	0.507782i	$-0.830466\pi$
$211$	−9.89338	−	21.6635i	−0.681089	−	1.49138i	0.180397	−	0.983594i	$-0.442262\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.01767	−	48.8090i	0.478601	−	3.32874i
$216$		0			0
$217$	0.194495	+	0.224459i	0.0132032	+	0.0152373i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.47739	+	1.02105i	−0.233915	+	0.0686836i
$222$		0			0
$223$	−13.1936	+	15.2262i	−0.883507	+	1.01962i	0.116145	+	0.993232i	$0.462946\pi$
$223$	−13.1936	+	15.2262i	−0.883507	+	1.01962i	−0.999652	+	0.0263890i	$0.991599\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.33377	+	9.27656i	0.0885253	+	0.615707i	0.984993	+	0.172597i	$0.0552158\pi$
$227$	1.33377	+	9.27656i	0.0885253	+	0.615707i	−0.896467	+	0.443110i	$0.853875\pi$
$228$		0			0
$229$	2.99434			0.197872			0.0989359	−	0.995094i	$-0.468456\pi$
$229$	2.99434			0.197872			0.0989359	+	0.995094i	$0.468456\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.47396	+	10.2516i	0.0965624	+	0.671607i	0.979400	+	0.201929i	$0.0647209\pi$
$233$	1.47396	+	10.2516i	0.0965624	+	0.671607i	−0.882838	+	0.469678i	$0.844370\pi$
$234$		0			0
$235$	−22.4014	−	6.57764i	−1.46130	−	0.429078i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.25694	−	0.956324i	0.210674	−	0.0618595i	−0.174693	−	0.984623i	$-0.555893\pi$
$239$	3.25694	−	0.956324i	0.210674	−	0.0618595i	0.385367	+	0.922764i	$0.374075\pi$
$240$		0			0
$241$	14.4551	−	9.28973i	0.931135	−	0.598404i	0.0152666	−	0.999883i	$-0.495140\pi$
$241$	14.4551	−	9.28973i	0.931135	−	0.598404i	0.915868	+	0.401480i	$0.131504\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.06003	−	28.2381i	0.259386	−	1.80407i
$246$		0			0
$247$	−0.117294	+	0.256838i	−0.00746323	+	0.0163422i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−13.5073	−	8.68061i	−0.852572	−	0.547915i	0.0398037	−	0.999208i	$-0.487327\pi$
$251$	−13.5073	−	8.68061i	−0.852572	−	0.547915i	−0.892376	+	0.451293i	$0.850963\pi$
$252$		0			0
$253$	5.09341	+	3.01419i	0.320220	+	0.189501i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.14370	+	20.0219i	0.570368	+	1.24893i	0.946601	+	0.322407i	$0.104492\pi$
$257$	9.14370	+	20.0219i	0.570368	+	1.24893i	−0.376233	+	0.926525i	$0.622781\pi$
$258$		0			0
$259$	0.404422	−	0.885560i	0.0251296	−	0.0550260i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.9296	−	17.2297i	−0.920601	−	1.06243i	−0.997858	−	0.0654188i	$-0.979162\pi$
$263$	−14.9296	−	17.2297i	−0.920601	−	1.06243i	0.0772571	−	0.997011i	$-0.475384\pi$
$264$		0			0
$265$	−22.9497	+	14.7489i	−1.40979	+	0.906015i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.55143	−	4.09857i	0.216534	−	0.249894i	−0.637082	−	0.770796i	$-0.719859\pi$
$269$	3.55143	−	4.09857i	0.216534	−	0.249894i	0.853617	+	0.520902i	$0.174404\pi$
$270$		0			0
$271$	24.3625	+	7.15346i	1.47991	+	0.434542i	0.919307	−	0.393541i	$-0.128750\pi$
$271$	24.3625	+	7.15346i	1.47991	+	0.434542i	0.560606	+	0.828082i	$0.310568\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	14.4207			0.869600
$276$		0			0
$277$	−28.3536			−1.70360			−0.851800	−	0.523867i	$-0.824489\pi$
$277$	−28.3536			−1.70360			−0.851800	+	0.523867i	$0.824489\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.14061	−	2.09667i	−0.425973	−	0.125077i	0.0617174	−	0.998094i	$-0.480342\pi$
$281$	−7.14061	−	2.09667i	−0.425973	−	0.125077i	−0.487690	+	0.873017i	$0.662160\pi$
$282$		0			0
$283$	15.9165	−	18.3687i	0.946141	−	1.09190i	−0.0495133	−	0.998773i	$-0.515767\pi$
$283$	15.9165	−	18.3687i	0.946141	−	1.09190i	0.995654	−	0.0931309i	$-0.0296875\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.11061	+	0.713748i	−0.0655574	+	0.0421312i
$288$		0			0
$289$	8.78041	+	10.1331i	0.516495	+	0.596067i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.78323	+	14.8532i	−0.396281	+	0.867733i	0.601353	+	0.798983i	$0.294628\pi$
$293$	−6.78323	+	14.8532i	−0.396281	+	0.867733i	−0.997634	+	0.0687502i	$0.978099\pi$
$294$		0			0
$295$	−12.9269	−	28.3059i	−0.752630	−	1.64803i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.49986	+	8.47680i	−0.202402	+	0.490226i
$300$		0			0
$301$	−1.27973	−	0.822430i	−0.0737622	−	0.0474041i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.15740	−	4.72406i	0.123533	−	0.270499i
$306$		0			0
$307$	−3.54574	+	24.6612i	−0.202366	+	1.40749i	0.594871	+	0.803821i	$0.297203\pi$
$307$	−3.54574	+	24.6612i	−0.202366	+	1.40749i	−0.797237	+	0.603667i	$0.793706\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	23.7744	−	15.2789i	1.34813	−	0.866388i	0.350588	−	0.936530i	$-0.385982\pi$
$311$	23.7744	−	15.2789i	1.34813	−	0.866388i	0.997537	+	0.0701421i	$0.0223453\pi$
$312$		0			0
$313$	5.29010	−	1.55331i	0.299014	−	0.0877985i	−0.128784	−	0.991673i	$-0.541107\pi$
$313$	5.29010	−	1.55331i	0.299014	−	0.0877985i	0.427798	+	0.903874i	$0.359289\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.12306	−	0.917014i	−0.175409	−	0.0515047i	0.192849	−	0.981228i	$-0.438227\pi$
$317$	−3.12306	−	0.917014i	−0.175409	−	0.0515047i	−0.368258	+	0.929724i	$0.620046\pi$
$318$		0			0
$319$	1.31809	+	9.16749i	0.0737987	+	0.513281i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.279840			−0.0155707
$324$		0			0
$325$	3.18009	+	22.1180i	0.176400	+	1.22689i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.471660	+	0.544325i	−0.0260035	+	0.0300096i
$330$		0			0
$331$	−6.54037	+	1.92043i	−0.359491	+	0.105556i	−0.456490	−	0.889728i	$-0.650894\pi$
$331$	−6.54037	+	1.92043i	−0.359491	+	0.105556i	0.0969992	+	0.995284i	$0.469076\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	28.4561	+	32.8401i	1.55472	+	1.79425i
$336$		0			0
$337$	−0.655700	+	4.56049i	−0.0357183	+	0.248426i	−0.999856	−	0.0169769i	$-0.994596\pi$
$337$	−0.655700	+	4.56049i	−0.0357183	+	0.248426i	0.964138	+	0.265403i	$0.0855049\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.20829	−	2.64579i	−0.0654327	−	0.143278i
$342$		0			0
$343$	−1.48244	−	0.952706i	−0.0800442	−	0.0514413i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	18.8312	+	12.1021i	1.01091	+	0.649674i	0.937629	−	0.347637i	$-0.113016\pi$
$347$	18.8312	+	12.1021i	1.01091	+	0.649674i	0.0732832	+	0.997311i	$0.476652\pi$
$348$		0			0
$349$	8.84062	+	19.3583i	0.473228	+	1.03622i	0.984270	+	0.176669i	$0.0565321\pi$
$349$	8.84062	+	19.3583i	0.473228	+	1.03622i	−0.511043	+	0.859555i	$0.670741\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.895635	+	6.22928i	−0.0476698	+	0.331551i	0.952006	+	0.306080i	$0.0990176\pi$
$353$	−0.895635	+	6.22928i	−0.0476698	+	0.331551i	−0.999676	+	0.0254708i	$0.991892\pi$
$354$		0			0
$355$	24.7166	+	28.5245i	1.31182	+	1.51392i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.4027	+	4.22900i	−0.760143	+	0.223198i	−0.638758	−	0.769407i	$-0.720552\pi$
$359$	−14.4027	+	4.22900i	−0.760143	+	0.223198i	−0.121385	+	0.992606i	$0.538733\pi$
$360$		0			0
$361$	12.4281	−	14.3428i	0.654109	−	0.754882i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.34718	+	51.1007i	0.384569	+	2.67474i
$366$		0			0
$367$	8.18117			0.427053			0.213527	−	0.976937i	$-0.431505\pi$
$367$	8.18117			0.427053			0.213527	+	0.976937i	$0.431505\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.119770	+	0.833016i	0.00621813	+	0.0432481i
$372$		0			0
$373$	8.42461	+	2.47369i	0.436210	+	0.128083i	0.492462	−	0.870334i	$-0.336097\pi$
$373$	8.42461	+	2.47369i	0.436210	+	0.128083i	−0.0562525	+	0.998417i	$0.517915\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−13.7701	+	4.04328i	−0.709198	+	0.208239i
$378$		0			0
$379$	5.68742	−	3.65509i	0.292143	−	0.187749i	−0.386357	−	0.922349i	$-0.626267\pi$
$379$	5.68742	−	3.65509i	0.292143	−	0.187749i	0.678500	+	0.734600i	$0.262630\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.0756551	−	0.526193i	0.00386580	−	0.0268872i	−0.987797	−	0.155745i	$-0.950222\pi$
$383$	0.0756551	−	0.526193i	0.00386580	−	0.0268872i	0.991663	+	0.128858i	$0.0411312\pi$
$384$		0			0
$385$	0.263882	−	0.577820i	0.0134487	−	0.0294485i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.93689	+	2.53008i	0.199608	+	0.128280i	0.636627	−	0.771172i	$-0.280329\pi$
$389$	3.93689	+	2.53008i	0.199608	+	0.128280i	−0.437019	+	0.899452i	$0.643966\pi$
$390$		0			0
$391$	−9.08309	+	0.334795i	−0.459352	+	0.0169313i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6.32807	−	13.8565i	−0.318400	−	0.697198i
$396$		0			0
$397$	1.42758	−	3.12596i	0.0716480	−	0.156887i	−0.870419	−	0.492311i	$-0.836152\pi$
$397$	1.42758	−	3.12596i	0.0716480	−	0.156887i	0.942067	+	0.335424i	$0.108880\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.58668	−	9.90955i	−0.428798	−	0.494859i	0.499699	−	0.866199i	$-0.333444\pi$
$401$	−8.58668	−	9.90955i	−0.428798	−	0.494859i	−0.928497	+	0.371340i	$0.878899\pi$
$402$		0			0
$403$	3.79157	−	2.43670i	0.188872	−	0.121380i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.24354	+	7.20543i	−0.309481	+	0.357160i
$408$		0			0
$409$	3.93864	+	1.15649i	0.194753	+	0.0571848i	0.377655	−	0.925947i	$-0.376731\pi$
$409$	3.93864	+	1.15649i	0.194753	+	0.0571848i	−0.182901	+	0.983131i	$0.558549\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.959971			−0.0472371
$414$		0			0
$415$	33.3333			1.63627
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−35.7570	−	10.4992i	−1.74684	−	0.512919i	−0.756795	−	0.653652i	$-0.773236\pi$
$419$	−35.7570	−	10.4992i	−1.74684	−	0.512919i	−0.990048	+	0.140733i	$0.955054\pi$
$420$		0			0
$421$	6.30973	−	7.28181i	0.307517	−	0.354894i	−0.580864	−	0.814001i	$-0.697285\pi$
$421$	6.30973	−	7.28181i	0.307517	−	0.354894i	0.888381	+	0.459107i	$0.151831\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−18.6309	+	11.9733i	−0.903729	+	0.580792i
$426$		0			0
$427$	−0.104917	−	0.121081i	−0.00507729	−	0.00585950i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.3144	+	29.1546i	−0.641334	+	1.40433i	0.257604	+	0.966251i	$0.417067\pi$
$431$	−13.3144	+	29.1546i	−0.641334	+	1.40433i	−0.898938	+	0.438076i	$0.855660\pi$
$432$		0			0
$433$	10.2767	+	22.5027i	0.493865	+	1.08141i	0.978415	+	0.206649i	$0.0662559\pi$
$433$	10.2767	+	22.5027i	0.493865	+	1.08141i	−0.484551	+	0.874763i	$0.661017\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.443696	+	0.551883i	−0.0212249	+	0.0264001i
$438$		0			0
$439$	−7.03424	−	4.52063i	−0.335726	−	0.215758i	0.361905	−	0.932215i	$-0.382126\pi$
$439$	−7.03424	−	4.52063i	−0.335726	−	0.215758i	−0.697632	+	0.716457i	$0.745763\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.68541	−	8.06992i	0.175099	−	0.383413i	−0.801652	−	0.597791i	$-0.796045\pi$
$443$	3.68541	−	8.06992i	0.175099	−	0.383413i	0.976751	+	0.214378i	$0.0687724\pi$
$444$		0			0
$445$	−4.10435	+	28.5463i	−0.194565	+	1.35323i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.42408	−	5.41383i	0.397557	−	0.255494i	−0.326553	−	0.945179i	$-0.605887\pi$
$449$	8.42408	−	5.41383i	0.397557	−	0.255494i	0.724110	+	0.689685i	$0.242251\pi$
$450$		0			0
$451$	12.4053	−	3.64253i	0.584143	−	0.171520i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.944434	+	0.277311i	0.0442758	+	0.0130005i
$456$		0			0
$457$	4.20875	+	29.2725i	0.196877	+	1.36931i	0.813277	+	0.581877i	$0.197681\pi$
$457$	4.20875	+	29.2725i	0.196877	+	1.36931i	−0.616400	+	0.787433i	$0.711410\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	17.8301			0.830430			0.415215	−	0.909723i	$-0.363706\pi$
$461$	17.8301			0.830430			0.415215	+	0.909723i	$0.363706\pi$
$462$		0			0
$463$	1.40293	+	9.75762i	0.0651999	+	0.453475i	0.996102	+	0.0882069i	$0.0281137\pi$
$463$	1.40293	+	9.75762i	0.0651999	+	0.453475i	−0.930902	+	0.365268i	$0.880977\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.2767	−	29.1708i	1.16966	−	1.34986i	0.244797	−	0.969574i	$-0.421279\pi$
$467$	25.2767	−	29.1708i	1.16966	−	1.34986i	0.924867	−	0.380290i	$-0.124176\pi$
$468$		0			0
$469$	1.28622	−	0.377669i	0.0593922	−	0.0174391i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	9.75593	+	11.2589i	0.448578	+	0.517687i
$474$		0			0
$475$	−0.245549	+	1.70783i	−0.0112665	+	0.0783605i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.81750	−	6.16945i	−0.128735	−	0.281890i	0.834279	−	0.551343i	$-0.185884\pi$
$479$	−2.81750	−	6.16945i	−0.128735	−	0.281890i	−0.963013	+	0.269453i	$0.913157\pi$
$480$		0			0
$481$	−12.4283	−	7.98719i	−0.566682	−	0.364184i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−45.5195	−	29.2536i	−2.06693	−	1.32834i
$486$		0			0
$487$	−2.77299	−	6.07200i	−0.125656	−	0.275149i	0.836340	−	0.548211i	$-0.184691\pi$
$487$	−2.77299	−	6.07200i	−0.125656	−	0.275149i	−0.961996	+	0.273062i	$0.911964\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.53163	+	17.6079i	−0.114251	+	0.794632i	0.849454	+	0.527662i	$0.176931\pi$
$491$	−2.53163	+	17.6079i	−0.114251	+	0.794632i	−0.963705	+	0.266969i	$0.913978\pi$
$492$		0			0
$493$	−9.31456	−	10.7496i	−0.419507	−	0.484137i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.11719	−	0.328038i	0.0501130	−	0.0147145i
$498$		0			0
$499$	0.992242	−	1.14511i	0.0444189	−	0.0512621i	−0.733105	−	0.680115i	$-0.761930\pi$
$499$	0.992242	−	1.14511i	0.0444189	−	0.0512621i	0.777524	+	0.628853i	$0.216475\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.54825	−	17.7235i	−0.113621	−	0.790250i	−0.964347	−	0.264641i	$-0.914747\pi$
$503$	−2.54825	−	17.7235i	−0.113621	−	0.790250i	0.850726	−	0.525609i	$-0.176163\pi$
$504$		0			0
$505$	−27.5822			−1.22739
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.69998	−	18.7788i	−0.119675	−	0.832355i	−0.957915	−	0.287053i	$-0.907324\pi$
$509$	−2.69998	−	18.7788i	−0.119675	−	0.832355i	0.838240	−	0.545301i	$-0.183585\pi$
$510$		0			0
$511$	1.52813	+	0.448699i	0.0676004	+	0.0198493i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	33.2526	−	9.76384i	1.46528	−	0.430246i
$516$		0			0
$517$	5.93385	−	3.81346i	0.260971	−	0.167716i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.48410	−	31.1876i	0.196452	−	1.36635i	−0.618026	−	0.786158i	$-0.712067\pi$
$521$	4.48410	−	31.1876i	0.196452	−	1.36635i	0.814478	−	0.580195i	$-0.197024\pi$
$522$		0			0
$523$	−7.15195	+	15.6606i	−0.312733	+	0.684790i	−0.999098	−	0.0424676i	$-0.986478\pi$
$523$	−7.15195	+	15.6606i	−0.312733	+	0.684790i	0.686365	+	0.727257i	$0.259205\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.75783	+	2.41501i	0.163693	+	0.105199i
$528$		0			0
$529$	−13.7413	+	18.4439i	−0.597447	+	0.801909i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	8.32244	+	18.2236i	0.360485	+	0.789352i
$534$		0			0
$535$	22.4552	−	49.1701i	0.970824	−	2.12581i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.64424	+	6.51380i	0.243115	+	0.280569i
$540$		0			0
$541$	0.229819	−	0.147696i	0.00988070	−	0.00634994i	−0.535691	−	0.844414i	$-0.679949\pi$
$541$	0.229819	−	0.147696i	0.00988070	−	0.00634994i	0.545572	+	0.838064i	$0.316312\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−19.9225	+	22.9918i	−0.853388	+	0.984863i
$546$		0			0
$547$	−25.3716	−	7.44978i	−1.08481	−	0.318530i	−0.310010	−	0.950733i	$-0.600332\pi$
$547$	−25.3716	−	7.44978i	−1.08481	−	0.318530i	−0.774802	+	0.632203i	$0.782151\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.10814			−0.0472084
$552$		0			0
$553$	−0.469934			−0.0199836
$554$		0			0
$555$		0			0
$556$		0			0
$557$	23.7086	+	6.96147i	1.00457	+	0.294967i	0.742328	−	0.670036i	$-0.233722\pi$
$557$	23.7086	+	6.96147i	1.00457	+	0.294967i	0.262237	+	0.965003i	$0.415540\pi$
$558$		0			0
$559$	−15.1172	+	17.4462i	−0.639390	+	0.737895i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.2024	+	9.12730i	−0.598558	+	0.384670i	−0.804551	−	0.593884i	$-0.797594\pi$
$563$	−14.2024	+	9.12730i	−0.598558	+	0.384670i	0.205993	+	0.978553i	$0.433958\pi$
$564$		0			0
$565$	8.51080	+	9.82198i	0.358052	+	0.413214i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.05486	+	8.87892i	−0.169989	+	0.372223i	−0.975384	−	0.220515i	$-0.929226\pi$
$569$	−4.05486	+	8.87892i	−0.169989	+	0.372223i	0.805395	+	0.592739i	$0.201953\pi$
$570$		0			0
$571$	−6.08106	−	13.3157i	−0.254484	−	0.557243i	0.738668	−	0.674070i	$-0.235455\pi$
$571$	−6.08106	−	13.3157i	−0.254484	−	0.557243i	−0.993152	+	0.116826i	$0.962728\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.92684	+	55.7266i	−0.247166	+	2.32396i
$576$		0			0
$577$	10.3558	+	6.65529i	0.431119	+	0.277063i	0.738151	−	0.674636i	$-0.235699\pi$
$577$	10.3558	+	6.65529i	0.431119	+	0.277063i	−0.307032	+	0.951699i	$0.599336\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.427177	−	0.935388i	0.0177223	−	0.0388064i
$582$		0			0
$583$	1.17294	−	8.15799i	0.0485783	−	0.337870i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.1633	+	6.53159i	−0.419486	+	0.269587i	−0.733311	−	0.679893i	$-0.762026\pi$
$587$	−10.1633	+	6.53159i	−0.419486	+	0.269587i	0.313825	+	0.949481i	$0.398390\pi$
$588$		0			0
$589$	0.333913	−	0.0980456i	0.0137586	−	0.00403990i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−41.6427	−	12.2274i	−1.71006	−	0.502119i	−0.727193	−	0.686433i	$-0.759176\pi$
$593$	−41.6427	−	12.2274i	−1.71006	−	0.502119i	−0.982867	+	0.184314i	$0.940994\pi$
$594$		0			0
$595$	0.138834	+	0.965615i	0.00569166	+	0.0395863i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	36.5272			1.49246			0.746230	−	0.665688i	$-0.231862\pi$
$599$	36.5272			1.49246			0.746230	+	0.665688i	$0.231862\pi$
$600$		0			0
$601$	0.0953083	+	0.662884i	0.00388771	+	0.0270396i	0.991673	−	0.128782i	$-0.0411067\pi$
$601$	0.0953083	+	0.662884i	0.00388771	+	0.0270396i	−0.987785	+	0.155821i	$0.950198\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	25.3506	−	29.2562i	1.03065	−	1.18943i
$606$		0			0
$607$	−34.6753	+	10.1816i	−1.40743	+	0.413258i	−0.895228	−	0.445608i	$-0.852988\pi$
$607$	−34.6753	+	10.1816i	−1.40743	+	0.413258i	−0.512200	+	0.858866i	$0.671169\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.15750	+	8.26020i	0.289562	+	0.334172i
$612$		0			0
$613$	5.62930	−	39.1526i	0.227365	−	1.58136i	−0.481776	−	0.876294i	$-0.660008\pi$
$613$	5.62930	−	39.1526i	0.227365	−	1.58136i	0.709142	−	0.705066i	$-0.249083\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.38060	+	5.21278i	0.0958393	+	0.209859i	0.951479	−	0.307712i	$-0.0995635\pi$
$617$	2.38060	+	5.21278i	0.0958393	+	0.209859i	−0.855640	+	0.517571i	$0.826836\pi$
$618$		0			0
$619$	22.1415	+	14.2295i	0.889942	+	0.571931i	0.903792	−	0.427973i	$-0.140772\pi$
$619$	22.1415	+	14.2295i	0.889942	+	0.571931i	−0.0138494	+	0.999904i	$0.504409\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.748459	+	0.481005i	0.0299864	+	0.0192711i
$624$		0			0
$625$	22.0671	+	48.3201i	0.882682	+	1.93280i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.08378	−	14.4930i	0.0830858	−	0.577875i
$630$		0			0
$631$	−18.8138	−	21.7123i	−0.748967	−	0.864354i	0.245501	−	0.969396i	$-0.421048\pi$
$631$	−18.8138	−	21.7123i	−0.748967	−	0.864354i	−0.994468	+	0.105042i	$0.966502\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	78.8871	−	23.1633i	3.13054	−	0.919209i
$636$		0			0
$637$	−8.74597	+	10.0934i	−0.346528	+	0.399915i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.14585	−	21.8799i	−0.124254	−	0.864202i	−0.952652	−	0.304063i	$-0.901657\pi$
$641$	−3.14585	−	21.8799i	−0.124254	−	0.864202i	0.828398	−	0.560139i	$-0.189252\pi$
$642$		0			0
$643$	−11.1875			−0.441193			−0.220596	−	0.975365i	$-0.570800\pi$
$643$	−11.1875			−0.441193			−0.220596	+	0.975365i	$0.570800\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.70136	+	25.7436i	0.145516	+	1.01208i	0.923445	+	0.383731i	$0.125361\pi$
$647$	3.70136	+	25.7436i	0.145516	+	1.01208i	−0.777929	+	0.628352i	$0.783730\pi$
$648$		0			0
$649$	9.02048	+	2.64865i	0.354085	+	0.103969i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	43.7741	−	12.8532i	1.71301	−	0.502986i	0.729525	−	0.683954i	$-0.239741\pi$
$653$	43.7741	−	12.8532i	1.71301	−	0.502986i	0.983489	+	0.180967i	$0.0579228\pi$
$654$		0			0
$655$	12.2454	−	7.86963i	0.478467	−	0.307492i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.36052	+	30.3281i	−0.169862	+	1.18141i	0.709306	+	0.704901i	$0.249008\pi$
$659$	−4.36052	+	30.3281i	−0.169862	+	1.18141i	−0.879168	+	0.476513i	$0.841901\pi$
$660$		0			0
$661$	6.54464	−	14.3308i	0.254557	−	0.557402i	−0.738606	−	0.674137i	$-0.764516\pi$
$661$	6.54464	−	14.3308i	0.254557	−	0.557402i	0.993163	+	0.116735i	$0.0372429\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.0639374	+	0.0410901i	0.00247939	+	0.00159341i
$666$		0			0
$667$	−35.9681	+	1.32575i	−1.39269	+	0.0513334i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.651791	+	1.42722i	0.0251621	+	0.0550974i
$672$		0			0
$673$	4.20807	−	9.21438i	0.162209	−	0.355188i	−0.811023	−	0.585015i	$-0.801089\pi$
$673$	4.20807	−	9.21438i	0.162209	−	0.355188i	0.973232	+	0.229827i	$0.0738159\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.73175	−	8.92291i	−0.297155	−	0.342935i	0.587463	−	0.809251i	$-0.300127\pi$
$677$	−7.73175	−	8.92291i	−0.297155	−	0.342935i	−0.884619	+	0.466315i	$0.845581\pi$
$678$		0			0
$679$	−1.40425	+	0.902457i	−0.0538902	+	0.0346331i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.85265	+	9.06244i	−0.300473	+	0.346765i	−0.885829	−	0.464012i	$-0.846409\pi$
$683$	−7.85265	+	9.06244i	−0.300473	+	0.346765i	0.585356	+	0.810777i	$0.300955\pi$
$684$		0			0
$685$	−80.0361	−	23.5007i	−3.05802	−	0.897917i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.7711			0.486541
$690$		0			0
$691$	20.6233			0.784548			0.392274	−	0.919848i	$-0.371689\pi$
$691$	20.6233			0.784548			0.392274	+	0.919848i	$0.371689\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−56.1662	−	16.4919i	−2.13051	−	0.625573i
$696$		0			0
$697$	−13.0027	+	15.0059i	−0.492513	+	0.568391i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	37.7052	−	24.2316i	1.42410	−	0.915216i	0.424150	−	0.905592i	$-0.360573\pi$
$701$	37.7052	−	24.2316i	1.42410	−	0.915216i	0.999954	−	0.00962419i	$-0.00306352\pi$
$702$		0			0
$703$	−0.747020	−	0.862107i	−0.0281744	−	0.0325150i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.353475	+	0.774002i	−0.0132938	+	0.0291093i
$708$		0			0
$709$	15.7599	+	34.5095i	0.591877	+	1.29603i	0.934301	+	0.356485i	$0.116025\pi$
$709$	15.7599	+	34.5095i	0.591877	+	1.29603i	−0.342424	+	0.939546i	$0.611248\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.7209	−	3.58186i	0.401500	−	0.134142i
$714$		0			0
$715$	−8.10936	−	5.21157i	−0.303273	−	0.194902i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.3632	−	33.6408i	0.572952	−	1.25459i	−0.372258	−	0.928129i	$-0.621416\pi$
$719$	15.3632	−	33.6408i	0.572952	−	1.25459i	0.945210	−	0.326462i	$-0.105856\pi$
$720$		0			0
$721$	0.152153	−	1.05825i	0.00566648	−	0.0394113i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−73.7764	+	47.4132i	−2.73999	+	1.76088i
$726$		0			0
$727$	44.6395	−	13.1073i	1.65559	−	0.486124i	0.685336	−	0.728227i	$-0.259655\pi$
$727$	44.6395	−	13.1073i	1.65559	−	0.486124i	0.970250	+	0.242103i	$0.0778373\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.9524	−	6.44580i	−0.811938	−	0.238406i
$732$		0			0
$733$	0.437796	+	3.04494i	0.0161704	+	0.112467i	0.996308	−	0.0858513i	$-0.0273610\pi$
$733$	0.437796	+	3.04494i	0.0161704	+	0.112467i	−0.980138	+	0.198319i	$0.936452\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.1282			−0.483582
$738$		0			0
$739$	−3.33533	−	23.1977i	−0.122692	−	0.853341i	−0.954486	−	0.298257i	$-0.903595\pi$
$739$	−3.33533	−	23.1977i	−0.122692	−	0.853341i	0.831794	−	0.555085i	$-0.187314\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.07237	−	1.23758i	0.0393413	−	0.0454023i	−0.735738	−	0.677266i	$-0.763164\pi$
$743$	1.07237	−	1.23758i	0.0393413	−	0.0454023i	0.775079	+	0.631864i	$0.217710\pi$
$744$		0			0
$745$	70.4027	−	20.6721i	2.57936	−	0.757367i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.09202	−	1.26026i	−0.0399016	−	0.0460489i
$750$		0			0
$751$	6.05226	−	42.0944i	0.220850	−	1.53605i	−0.513984	−	0.857800i	$-0.671831\pi$
$751$	6.05226	−	42.0944i	0.220850	−	1.53605i	0.734834	−	0.678247i	$-0.237260\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10.4476	−	22.8770i	−0.380226	−	0.832579i
$756$		0			0
$757$	−7.49246	−	4.81511i	−0.272318	−	0.175008i	0.397353	−	0.917666i	$-0.369929\pi$
$757$	−7.49246	−	4.81511i	−0.272318	−	0.175008i	−0.669671	+	0.742657i	$0.733565\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−32.4340	−	20.8441i	−1.17573	−	0.755597i	−0.201134	−	0.979564i	$-0.564463\pi$
$761$	−32.4340	−	20.8441i	−1.17573	−	0.755597i	−0.974597	+	0.223967i	$0.928099\pi$
$762$		0			0
$763$	0.389875	+	0.853707i	0.0141144	+	0.0309063i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.07320	+	14.4194i	−0.0748588	+	0.520654i
$768$		0			0
$769$	−33.6719	−	38.8594i	−1.21424	−	1.40131i	−0.890390	−	0.455199i	$-0.849568\pi$
$769$	−33.6719	−	38.8594i	−1.21424	−	1.40131i	−0.323850	−	0.946108i	$-0.604977\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−24.4813	+	7.18835i	−0.880530	+	0.258547i	−0.690588	−	0.723249i	$-0.742648\pi$
$773$	−24.4813	+	7.18835i	−0.880530	+	0.258547i	−0.189942	+	0.981795i	$0.560830\pi$
$774$		0			0
$775$	18.0358	−	20.8144i	0.647865	−	0.747676i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.220149	+	1.53117i	0.00788766	+	0.0548599i
$780$		0			0
$781$	−11.4029			−0.408029
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.49944	+	31.2943i	0.160592	+	1.11694i
$786$		0			0
$787$	9.82123	+	2.88377i	0.350089	+	0.102795i	0.452049	−	0.891993i	$-0.350693\pi$
$787$	9.82123	+	2.88377i	0.350089	+	0.102795i	−0.101960	+	0.994789i	$0.532511\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.384690	−	0.112955i	0.0136780	−	0.00401622i
$792$		0			0
$793$	−2.04530	+	1.31443i	−0.0726306	+	0.0466768i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.236974	−	1.64819i	0.00839403	−	0.0583818i	−0.985194	−	0.171444i	$-0.945157\pi$
$797$	0.236974	−	1.64819i	0.00839403	−	0.0583818i	0.993588	+	0.113062i	$0.0360659\pi$
$798$		0			0
$799$	−4.49999	+	9.85361i	−0.159198	+	0.348596i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−13.1212	−	8.43250i	−0.463038	−	0.297576i
$804$		0			0
$805$	2.12445	+	1.25721i	0.0748769	+	0.0443110i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.33499	−	7.30261i	−0.117252	−	0.256746i	0.841902	−	0.539630i	$-0.181436\pi$
$809$	−3.33499	−	7.30261i	−0.117252	−	0.256746i	−0.959154	+	0.282884i	$0.908709\pi$
$810$		0			0
$811$	22.8369	−	50.0059i	0.801912	−	1.75594i	0.163057	−	0.986617i	$-0.447865\pi$
$811$	22.8369	−	50.0059i	0.801912	−	1.75594i	0.638856	−	0.769326i	$-0.279408\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−34.3071	−	39.5925i	−1.20172	−	1.38686i
$816$		0			0
$817$	−1.49950	+	0.963673i	−0.0524610	+	0.0337147i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.5323	−	14.4630i	0.437379	−	0.504763i	−0.493673	−	0.869647i	$-0.664346\pi$
$821$	12.5323	−	14.4630i	0.437379	−	0.504763i	0.931053	+	0.364885i	$0.118892\pi$
$822$		0			0
$823$	−20.3321	−	5.97006i	−0.708734	−	0.208103i	−0.0925530	−	0.995708i	$-0.529503\pi$
$823$	−20.3321	−	5.97006i	−0.708734	−	0.208103i	−0.616181	+	0.787605i	$0.711321\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−29.2748			−1.01798			−0.508992	−	0.860771i	$-0.669982\pi$
$827$	−29.2748			−1.01798			−0.508992	+	0.860771i	$0.669982\pi$
$828$		0			0
$829$	−31.5164			−1.09461			−0.547304	−	0.836934i	$-0.684346\pi$
$829$	−31.5164			−1.09461			−0.547304	+	0.836934i	$0.684346\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.7004	−	3.72918i	−0.440043	−	0.129208i
$834$		0			0
$835$	8.06555	−	9.30814i	0.279120	−	0.322121i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.78578	−	5.64628i	0.303319	−	0.194931i	−0.380123	−	0.924936i	$-0.624118\pi$
$839$	8.78578	−	5.64628i	0.303319	−	0.194931i	0.683442	+	0.730005i	$0.260482\pi$
$840$		0			0
$841$	−17.8938	−	20.6505i	−0.617027	−	0.712087i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−15.8543	+	34.7161i	−0.545405	+	1.19427i
$846$		0			0
$847$	−0.496101	−	1.08631i	−0.0170462	−	0.0373260i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−25.2783	−	27.0887i	−0.866528	−	0.928587i
$852$		0			0
$853$	−15.3790	−	9.88346i	−0.526566	−	0.338403i	0.250199	−	0.968195i	$-0.419504\pi$
$853$	−15.3790	−	9.88346i	−0.526566	−	0.338403i	−0.776764	+	0.629791i	$0.783140\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.9983	−	28.4623i	0.444014	−	0.972255i	−0.546830	−	0.837244i	$-0.684166\pi$
$857$	12.9983	−	28.4623i	0.444014	−	0.972255i	0.990844	−	0.135012i	$-0.0431072\pi$
$858$		0			0
$859$	1.37199	−	9.54240i	0.0468117	−	0.325582i	−0.952937	−	0.303168i	$-0.901956\pi$
$859$	1.37199	−	9.54240i	0.0468117	−	0.325582i	0.999749	−	0.0224143i	$-0.00713529\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.91655	−	5.73032i	0.303523	−	0.195062i	−0.380009	−	0.924983i	$-0.624079\pi$
$863$	8.91655	−	5.73032i	0.303523	−	0.195062i	0.683532	+	0.729920i	$0.260443\pi$
$864$		0			0
$865$	9.26609	−	2.72077i	0.315056	−	0.0925089i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.41579	+	1.29659i	0.149795	+	0.0439839i
$870$		0			0
$871$	−2.89505	−	20.1355i	−0.0980951	−	0.682267i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.44117			0.116333
$876$		0			0
$877$	−0.805286	−	5.60089i	−0.0271926	−	0.189129i	0.971698	−	0.236228i	$-0.0759113\pi$
$877$	−0.805286	−	5.60089i	−0.0271926	−	0.189129i	−0.998890	+	0.0470996i	$0.985002\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	32.9426	−	38.0177i	1.10986	−	1.28085i	0.153667	−	0.988123i	$-0.450892\pi$
$881$	32.9426	−	38.0177i	1.10986	−	1.28085i	0.956196	−	0.292728i	$-0.0945629\pi$
$882$		0			0
$883$	−16.8285	+	4.94130i	−0.566325	+	0.166288i	−0.552347	−	0.833614i	$-0.686268\pi$
$883$	−16.8285	+	4.94130i	−0.566325	+	0.166288i	−0.0139782	+	0.999902i	$0.504450\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.7918	−	20.5329i	−0.597392	−	0.689427i	0.373859	−	0.927486i	$-0.378034\pi$
$887$	−17.7918	−	20.5329i	−0.597392	−	0.689427i	−0.971251	+	0.238059i	$0.923489\pi$
$888$		0			0
$889$	0.360962	−	2.51055i	0.0121063	−	0.0842010i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.350585	+	0.767674i	0.0117319	+	0.0256892i
$894$		0			0
$895$	71.8335	+	46.1646i	2.40113	+	1.54311i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	14.8806	+	9.56319i	0.496296	+	0.318950i
$900$		0			0
$901$	5.25810	+	11.5136i	0.175173	+	0.383574i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.91154	+	61.9811i	−0.296230	+	2.06032i
$906$		0			0
$907$	21.7863	+	25.1427i	0.723402	+	0.834850i	0.991712	−	0.128483i	$-0.0410107\pi$
$907$	21.7863	+	25.1427i	0.723402	+	0.834850i	−0.268310	+	0.963333i	$0.586465\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	36.5227	−	10.7240i	1.21005	−	0.355303i	0.386363	−	0.922347i	$-0.373731\pi$
$911$	36.5227	−	10.7240i	1.21005	−	0.355303i	0.823687	+	0.567044i	$0.191913\pi$
$912$		0			0
$913$	−6.59485	+	7.61086i	−0.218258	+	0.251883i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.0639062	−	0.444477i	−0.00211037	−	0.0146779i
$918$		0			0
$919$	24.8732			0.820491			0.410246	−	0.911975i	$-0.365443\pi$
$919$	24.8732			0.820491			0.410246	+	0.911975i	$0.365443\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.51461	−	17.4895i	−0.0827693	−	0.575673i
$924$		0			0
$925$	−86.6205	−	25.4341i	−2.84807	−	0.836267i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.8053	+	4.64085i	−0.518554	+	0.152261i	−0.530529	−	0.847667i	$-0.678007\pi$
$929$	−15.8053	+	4.64085i	−0.518554	+	0.152261i	0.0119743	+	0.999928i	$0.496188\pi$
$930$		0			0
$931$	−0.867530	+	0.557528i	−0.0284321	+	0.0182722i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.35965	−	9.45657i	0.0444653	−	0.309263i
$936$		0			0
$937$	−3.43363	+	7.51861i	−0.112172	+	0.245622i	−0.957389	−	0.288800i	$-0.906744\pi$
$937$	−3.43363	+	7.51861i	−0.112172	+	0.245622i	0.845217	+	0.534423i	$0.179471\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.74409	−	3.04884i	−0.154653	−	0.0993894i	0.461026	−	0.887387i	$-0.347482\pi$
$941$	−4.74409	−	3.04884i	−0.154653	−	0.0993894i	−0.615679	+	0.787997i	$0.711118\pi$
$942$		0			0
$943$	8.97748	+	49.4355i	0.292347	+	1.60984i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.3235	+	22.6053i	0.335468	+	0.734572i	0.999919	−	0.0127598i	$-0.00406168\pi$
$947$	10.3235	+	22.6053i	0.335468	+	0.734572i	−0.664451	+	0.747332i	$0.731334\pi$
$948$		0			0
$949$	10.0400	−	21.9845i	0.325911	−	0.713646i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	33.0490	+	38.1406i	1.07056	+	1.23549i	0.970650	+	0.240497i	$0.0773106\pi$
$953$	33.0490	+	38.1406i	1.07056	+	1.23549i	0.0999117	+	0.994996i	$0.468144\pi$
$954$		0			0
$955$	31.1464	−	20.0166i	1.00788	−	0.647722i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.68516	+	1.94478i	−0.0544166	+	0.0628001i
$960$		0			0
$961$	24.4142	+	7.16866i	0.787556	+	0.231247i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−38.9500			−1.25385
$966$		0			0
$967$	1.31499			0.0422872			0.0211436	−	0.999776i	$-0.493269\pi$
$967$	1.31499			0.0422872			0.0211436	+	0.999776i	$0.493269\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.0575	+	6.18304i	0.675768	+	0.198423i	0.601570	−	0.798820i	$-0.294542\pi$
$971$	21.0575	+	6.18304i	0.675768	+	0.198423i	0.0741980	+	0.997244i	$0.476360\pi$
$972$		0			0
$973$	−1.18258	+	1.36477i	−0.0379117	+	0.0437525i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.0341	+	12.2324i	−0.608953	+	0.391351i	−0.808465	−	0.588545i	$-0.799701\pi$
$977$	−19.0341	+	12.2324i	−0.608953	+	0.391351i	0.199511	+	0.979896i	$0.436065\pi$
$978$		0			0
$979$	−5.70584	−	6.58489i	−0.182359	−	0.210454i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.32096	−	18.2204i	0.265398	−	0.581140i	−0.729275	−	0.684220i	$-0.760143\pi$
$983$	8.32096	−	18.2204i	0.265398	−	0.581140i	0.994673	+	0.103081i	$0.0328700\pi$
$984$		0			0
$985$	−4.40705	−	9.65010i	−0.140420	−	0.307478i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−47.5182	+	33.0730i	−1.51099	+	1.05166i
$990$		0			0
$991$	−46.2705	−	29.7363i	−1.46983	−	0.944604i	−0.998020	−	0.0629045i	$-0.979964\pi$
$991$	−46.2705	−	29.7363i	−1.46983	−	0.944604i	−0.471812	−	0.881699i	$-0.656400\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	34.1899	−	74.8654i	1.08389	−	2.37339i
$996$		0			0
$997$	−4.83245	+	33.6105i	−0.153045	+	1.06445i	0.758032	+	0.652218i	$0.226161\pi$
$997$	−4.83245	+	33.6105i	−0.153045	+	1.06445i	−0.911077	+	0.412236i	$0.864748\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.q.c.577.1		20
3.2	odd	2		276.2.i.a.25.2	✓	20
23.12	even	11	inner	828.2.q.c.541.1		20
69.14	even	22		6348.2.a.t.1.10		10
69.32	odd	22		6348.2.a.s.1.1		10
69.35	odd	22		276.2.i.a.265.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.25.2	✓	20	3.2	odd	2
276.2.i.a.265.2	yes	20	69.35	odd	22
828.2.q.c.541.1		20	23.12	even	11	inner
828.2.q.c.577.1		20	1.1	even	1	trivial
6348.2.a.s.1.1		10	69.32	odd	22
6348.2.a.t.1.10		10	69.14	even	22

Overview	Random
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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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.91931 - 1.15081i) q^{5} +(-0.0825209 + 0.0952342i) q^{7} +O(q^{10})\)	\(q+(-3.91931 - 1.15081i) q^{5} +(-0.0825209 + 0.0952342i) q^{7} +(1.03818 - 0.667196i) q^{11} +(1.25227 + 1.44519i) q^{13} +(-0.787312 + 1.72397i) q^{17} +(0.0613378 + 0.134311i) q^{19} +(2.15160 + 4.28610i) q^{23} +(9.83034 + 6.31757i) q^{25} +(-3.11768 + 6.82676i) q^{29} +(0.335425 - 2.33293i) q^{31} +(0.433021 - 0.278286i) q^{35} +(-7.41275 + 2.17658i) q^{37} +(10.0522 + 2.95160i) q^{41} +(1.71801 + 11.9490i) q^{43} +5.71564 q^{47} +(0.993944 + 6.91303i) q^{49} +(4.37352 - 5.04731i) q^{53} +(-4.83675 + 1.42020i) q^{55} +(4.98875 + 5.75733i) q^{59} +(-0.180939 + 1.25846i) q^{61} +(-3.24487 - 7.10527i) q^{65} +(-8.94923 - 5.75132i) q^{67} +(-7.77319 - 4.99552i) q^{71} +(-5.25031 - 11.4966i) q^{73} +(-0.0221314 + 0.153928i) q^{77} +(2.44214 + 2.81838i) q^{79} +(-7.82984 + 2.29905i) q^{83} +(5.06969 - 5.85073i) q^{85} +(-1.00479 - 6.98848i) q^{89} -0.240970 q^{91} +(-0.0858348 - 0.596994i) q^{95} +(12.7100 + 3.73198i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^5	\( 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) \) 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

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