LMFDB - Embedded newform 276.2.i.a.265.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (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:	$2.20387109579$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			265.2
Root			$1.74521 + 2.01408i$ of defining polynomial
Character	$\chi$	$=$	276.265
Dual form			276.2.i.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(3.91931 - 1.15081i) q^{5} +(-0.0825209 - 0.0952342i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(3.91931 - 1.15081i) q^{5} +(-0.0825209 - 0.0952342i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-1.03818 - 0.667196i) q^{11} +(1.25227 - 1.44519i) q^{13} +(0.581323 + 4.04319i) q^{15} +(0.787312 + 1.72397i) q^{17} +(0.0613378 - 0.134311i) q^{19} +(0.106009 - 0.0681277i) q^{21} +(-2.15160 + 4.28610i) q^{23} +(9.83034 - 6.31757i) q^{25} +(0.415415 - 0.909632i) q^{27} +(3.11768 + 6.82676i) q^{29} +(0.335425 + 2.33293i) q^{31} +(0.808153 - 0.932658i) q^{33} +(-0.433021 - 0.278286i) q^{35} +(-7.41275 - 2.17658i) q^{37} +(1.25227 + 1.44519i) q^{39} +(-10.0522 + 2.95160i) q^{41} +(1.71801 - 11.9490i) q^{43} -4.08477 q^{45} -5.71564 q^{47} +(0.993944 - 6.91303i) q^{49} +(-1.81847 + 0.533951i) q^{51} +(-4.37352 - 5.04731i) q^{53} +(-4.83675 - 1.42020i) q^{55} +(0.124215 + 0.0798279i) q^{57} +(-4.98875 + 5.75733i) q^{59} +(-0.180939 - 1.25846i) q^{61} +(0.0523476 + 0.114625i) q^{63} +(3.24487 - 7.10527i) q^{65} +(-8.94923 + 5.75132i) q^{67} +(-3.93627 - 2.73967i) q^{69} +(7.77319 - 4.99552i) q^{71} +(-5.25031 + 11.4966i) q^{73} +(4.85427 + 10.6294i) q^{75} +(0.0221314 + 0.153928i) q^{77} +(2.44214 - 2.81838i) q^{79} +(0.841254 + 0.540641i) q^{81} +(7.82984 + 2.29905i) q^{83} +(5.06969 + 5.85073i) q^{85} +(-7.20097 + 2.11439i) q^{87} +(1.00479 - 6.98848i) q^{89} -0.240970 q^{91} -2.35692 q^{93} +(0.0858348 - 0.596994i) q^{95} +(12.7100 - 3.73198i) q^{97} +(0.808153 + 0.932658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	3.91931	−	1.15081i	1.75277	−	0.514659i	0.761690	−	0.647942i	$-0.224370\pi$
$5$	3.91931	−	1.15081i	1.75277	−	0.514659i	0.991078	+	0.133283i	$0.0425519\pi$
$6$		0			0
$7$	−0.0825209	−	0.0952342i	−0.0311900	−	0.0359951i	0.739940	−	0.672673i	$-0.234854\pi$
$7$	−0.0825209	−	0.0952342i	−0.0311900	−	0.0359951i	−0.771130	+	0.636677i	$0.780308\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	−1.03818	−	0.667196i	−0.313022	−	0.201167i	0.374691	−	0.927150i	$-0.377749\pi$
$11$	−1.03818	−	0.667196i	−0.313022	−	0.201167i	−0.687713	+	0.725983i	$0.741385\pi$
$12$		0			0
$13$	1.25227	−	1.44519i	0.347316	−	0.400824i	−0.555034	−	0.831827i	$-0.687295\pi$
$13$	1.25227	−	1.44519i	0.347316	−	0.400824i	0.902350	+	0.431003i	$0.141840\pi$
$14$		0			0
$15$	0.581323	+	4.04319i	0.150097	+	1.04395i
$16$		0			0
$17$	0.787312	+	1.72397i	0.190951	+	0.418125i	0.980757	−	0.195232i	$-0.0625460\pi$
$17$	0.787312	+	1.72397i	0.190951	+	0.418125i	−0.789806	+	0.613357i	$0.789819\pi$
$18$		0			0
$19$	0.0613378	−	0.134311i	0.0140719	−	0.0308131i	−0.902466	−	0.430762i	$-0.858245\pi$
$19$	0.0613378	−	0.134311i	0.0140719	−	0.0308131i	0.916537	+	0.399949i	$0.130972\pi$
$20$		0			0
$21$	0.106009	−	0.0681277i	0.0231330	−	0.0148667i
$22$		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
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	3.11768	+	6.82676i	0.578938	+	1.26770i	0.941900	+	0.335894i	$0.109038\pi$
$29$	3.11768	+	6.82676i	0.578938	+	1.26770i	−0.362962	+	0.931804i	$0.618234\pi$
$30$		0			0
$31$	0.335425	+	2.33293i	0.0602441	+	0.419007i	0.997518	+	0.0704129i	$0.0224317\pi$
$31$	0.335425	+	2.33293i	0.0602441	+	0.419007i	−0.937274	+	0.348594i	$0.886659\pi$
$32$		0			0
$33$	0.808153	−	0.932658i	0.140681	−	0.162355i
$34$		0			0
$35$	−0.433021	−	0.278286i	−0.0731940	−	0.0470389i
$36$		0			0
$37$	−7.41275	−	2.17658i	−1.21865	−	0.357828i	−0.391694	−	0.920096i	$-0.628111\pi$
$37$	−7.41275	−	2.17658i	−1.21865	−	0.357828i	−0.826955	+	0.562268i	$0.809929\pi$
$38$		0			0
$39$	1.25227	+	1.44519i	0.200523	+	0.231416i
$40$		0			0
$41$	−10.0522	+	2.95160i	−1.56990	+	0.460963i	−0.946971	−	0.321319i	$-0.895874\pi$
$41$	−10.0522	+	2.95160i	−1.56990	+	0.460963i	−0.622925	+	0.782282i	$0.714056\pi$
$42$		0			0
$43$	1.71801	−	11.9490i	0.261994	−	1.82221i	−0.255832	−	0.966721i	$-0.582350\pi$
$43$	1.71801	−	11.9490i	0.261994	−	1.82221i	0.517826	−	0.855486i	$-0.326741\pi$
$44$		0			0
$45$	−4.08477			−0.608921
$46$		0			0
$47$	−5.71564			−0.833712			−0.416856	−	0.908972i	$-0.636868\pi$
$47$	−5.71564			−0.833712			−0.416856	+	0.908972i	$0.636868\pi$
$48$		0			0
$49$	0.993944	−	6.91303i	0.141992	−	0.987576i
$50$		0			0
$51$	−1.81847	+	0.533951i	−0.254637	+	0.0747681i
$52$		0			0
$53$	−4.37352	−	5.04731i	−0.600749	−	0.693301i	0.371184	−	0.928559i	$-0.378952\pi$
$53$	−4.37352	−	5.04731i	−0.600749	−	0.693301i	−0.971933	+	0.235258i	$0.924406\pi$
$54$		0			0
$55$	−4.83675	−	1.42020i	−0.652188	−	0.191500i
$56$		0			0
$57$	0.124215	+	0.0798279i	0.0164526	+	0.0105735i
$58$		0			0
$59$	−4.98875	+	5.75733i	−0.649480	+	0.749540i	−0.981021	−	0.193901i	$-0.937886\pi$
$59$	−4.98875	+	5.75733i	−0.649480	+	0.749540i	0.331541	+	0.943441i	$0.392431\pi$
$60$		0			0
$61$	−0.180939	−	1.25846i	−0.0231668	−	0.161129i	0.974954	−	0.222407i	$-0.0713914\pi$
$61$	−0.180939	−	1.25846i	−0.0231668	−	0.161129i	−0.998121	+	0.0612782i	$0.980482\pi$
$62$		0			0
$63$	0.0523476	+	0.114625i	0.00659518	+	0.0144414i
$64$		0			0
$65$	3.24487	−	7.10527i	0.402476	−	0.881301i
$66$		0			0
$67$	−8.94923	+	5.75132i	−1.09332	+	0.702636i	−0.957597	−	0.288111i	$-0.906973\pi$
$67$	−8.94923	+	5.75132i	−1.09332	+	0.702636i	−0.135726	+	0.990746i	$0.543337\pi$
$68$		0			0
$69$	−3.93627	−	2.73967i	−0.473871	−	0.329818i
$70$		0			0
$71$	7.77319	−	4.99552i	0.922508	−	0.592860i	0.00912348	−	0.999958i	$-0.497096\pi$
$71$	7.77319	−	4.99552i	0.922508	−	0.592860i	0.913384	+	0.407099i	$0.133460\pi$
$72$		0			0
$73$	−5.25031	+	11.4966i	−0.614502	+	1.34557i	0.304949	+	0.952369i	$0.401361\pi$
$73$	−5.25031	+	11.4966i	−0.614502	+	1.34557i	−0.919451	+	0.393204i	$0.871367\pi$
$74$		0			0
$75$	4.85427	+	10.6294i	0.560522	+	1.22737i
$76$		0			0
$77$	0.0221314	+	0.153928i	0.00252211	+	0.0175417i
$78$		0			0
$79$	2.44214	−	2.81838i	0.274762	−	0.317092i	−0.601551	−	0.798834i	$-0.705450\pi$
$79$	2.44214	−	2.81838i	0.274762	−	0.317092i	0.876313	+	0.481742i	$0.159996\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	7.82984	+	2.29905i	0.859437	+	0.252353i	0.681617	−	0.731710i	$-0.261277\pi$
$83$	7.82984	+	2.29905i	0.859437	+	0.252353i	0.177820	+	0.984063i	$0.443095\pi$
$84$		0			0
$85$	5.06969	+	5.85073i	0.549885	+	0.634601i
$86$		0			0
$87$	−7.20097	+	2.11439i	−0.772025	+	0.226687i
$88$		0			0
$89$	1.00479	−	6.98848i	0.106508	−	0.740778i	−0.864656	−	0.502364i	$-0.832464\pi$
$89$	1.00479	−	6.98848i	0.106508	−	0.740778i	0.971164	−	0.238413i	$-0.0766273\pi$
$90$		0			0
$91$	−0.240970			−0.0252605
$92$		0			0
$93$	−2.35692			−0.244401
$94$		0			0
$95$	0.0858348	−	0.596994i	0.00880647	−	0.0612503i
$96$		0			0
$97$	12.7100	−	3.73198i	1.29050	−	0.378925i	0.436739	−	0.899588i	$-0.356133\pi$
$97$	12.7100	−	3.73198i	1.29050	−	0.378925i	0.853762	+	0.520663i	$0.174315\pi$
$98$		0			0
$99$	0.808153	+	0.932658i	0.0812224	+	0.0937357i
$100$		0			0
$101$	−6.47893	−	1.90238i	−0.644677	−	0.189294i	−0.0569800	−	0.998375i	$-0.518147\pi$
$101$	−6.47893	−	1.90238i	−0.644677	−	0.189294i	−0.587697	+	0.809081i	$0.699965\pi$
$102$		0			0
$103$	−7.13745	−	4.58696i	−0.703274	−	0.451967i	0.139509	−	0.990221i	$-0.455448\pi$
$103$	−7.13745	−	4.58696i	−0.703274	−	0.451967i	−0.842783	+	0.538254i	$0.819084\pi$
$104$		0			0
$105$	0.337079	−	0.389010i	0.0328955	−	0.0379635i
$106$		0			0
$107$	1.88329	+	13.0986i	0.182065	+	1.26629i	0.851871	+	0.523752i	$0.175468\pi$
$107$	1.88329	+	13.0986i	0.182065	+	1.26629i	−0.669806	+	0.742536i	$0.733623\pi$
$108$		0			0
$109$	3.09393	+	6.77476i	0.296345	+	0.648905i	0.997973	−	0.0636386i	$-0.0202705\pi$
$109$	3.09393	+	6.77476i	0.296345	+	0.648905i	−0.701628	+	0.712543i	$0.747543\pi$
$110$		0			0
$111$	3.20937	−	7.02754i	0.304620	−	0.667025i
$112$		0			0
$113$	2.67658	−	1.72014i	0.251792	−	0.161817i	−0.408657	−	0.912688i	$-0.634003\pi$
$113$	2.67658	−	1.72014i	0.251792	−	0.161817i	0.660448	+	0.750871i	$0.270366\pi$
$114$		0			0
$115$	−3.50027	+	19.2746i	−0.326402	+	1.79737i
$116$		0			0
$117$	−1.60870	+	1.03385i	−0.148724	+	0.0955792i
$118$		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
$123$	−1.49098	−	10.3700i	−0.134437	−	0.935029i
$124$		0			0
$125$	17.8830	−	20.6381i	1.59950	−	1.84593i
$126$		0			0
$127$	−16.9326	−	10.8819i	−1.50252	−	0.965614i	−0.994552	−	0.104240i	$-0.966759\pi$
$127$	−16.9326	−	10.8819i	−1.50252	−	0.965614i	−0.507972	−	0.861374i	$-0.669605\pi$
$128$		0			0
$129$	11.5829	+	3.40104i	1.01982	+	0.299445i
$130$		0			0
$131$	2.33360	+	2.69312i	0.203888	+	0.235299i	0.848480	−	0.529228i	$-0.177518\pi$
$131$	2.33360	+	2.69312i	0.203888	+	0.235299i	−0.644592	+	0.764527i	$0.722973\pi$
$132$		0			0
$133$	−0.0178526	+	0.00524201i	−0.00154802	+	0.000454540i
$134$		0			0
$135$	0.581323	−	4.04319i	0.0500323	−	0.347983i
$136$		0			0
$137$	−20.4210			−1.74468			−0.872342	−	0.488897i	$-0.837399\pi$
$137$	−20.4210			−1.74468			−0.872342	+	0.488897i	$0.837399\pi$
$138$		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
$141$	0.813421	−	5.65747i	0.0685024	−	0.476445i
$142$		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
$147$	6.70121	+	1.96765i	0.552707	+	0.162289i
$148$		0			0
$149$	15.1115	+	9.71156i	1.23798	+	0.795602i	0.985114	−	0.171900i	$-0.0549905\pi$
$149$	15.1115	+	9.71156i	1.23798	+	0.795602i	0.252866	+	0.967501i	$0.418627\pi$
$150$		0			0
$151$	4.03194	−	4.65311i	0.328115	−	0.378665i	−0.567592	−	0.823310i	$-0.692125\pi$
$151$	4.03194	−	4.65311i	0.328115	−	0.378665i	0.895707	+	0.444645i	$0.146670\pi$
$152$		0			0
$153$	−0.269721	−	1.87595i	−0.0218056	−	0.151662i
$154$		0			0
$155$	3.99940	+	8.75746i	0.321240	+	0.703416i
$156$		0			0
$157$	−3.21531	+	7.04055i	−0.256610	+	0.561897i	−0.993463	−	0.114156i	$-0.963584\pi$
$157$	−3.21531	+	7.04055i	−0.256610	+	0.561897i	0.736853	+	0.676053i	$0.236311\pi$
$158$		0			0
$159$	5.61835	−	3.61069i	0.445564	−	0.286347i
$160$		0			0
$161$	0.585735	−	0.148787i	0.0461623	−	0.0117261i
$162$		0			0
$163$	10.7893	−	6.93388i	0.845085	−	0.543103i	−0.0449533	−	0.998989i	$-0.514314\pi$
$163$	10.7893	−	6.93388i	0.845085	−	0.543103i	0.890038	+	0.455886i	$0.150678\pi$
$164$		0			0
$165$	2.09409	−	4.58541i	0.163024	−	0.356973i
$166$		0			0
$167$	1.25256	+	2.74273i	0.0969262	+	0.212239i	0.951884	−	0.306459i	$-0.0991442\pi$
$167$	1.25256	+	2.74273i	0.0969262	+	0.212239i	−0.854958	+	0.518698i	$0.826417\pi$
$168$		0			0
$169$	1.32968	+	9.24815i	0.102283	+	0.711396i
$170$		0			0
$171$	−0.0966929	+	0.111590i	−0.00739429	+	0.00853347i
$172$		0			0
$173$	1.98890	+	1.27819i	0.151214	+	0.0971791i	0.614060	−	0.789260i	$-0.289535\pi$
$173$	1.98890	+	1.27819i	0.151214	+	0.0971791i	−0.462846	+	0.886439i	$0.653172\pi$
$174$		0			0
$175$	−1.41286	−	0.414852i	−0.106802	−	0.0313599i
$176$		0			0
$177$	−4.98875	−	5.75733i	−0.374978	−	0.432747i
$178$		0			0
$179$	20.0574	−	5.88938i	1.49916	−	0.440193i	0.573708	−	0.819060i	$-0.305504\pi$
$179$	20.0574	−	5.88938i	1.49916	−	0.440193i	0.925451	+	0.378867i	$0.123686\pi$
$180$		0			0
$181$	−2.18165	+	15.1737i	−0.162161	+	1.12785i	0.732389	+	0.680886i	$0.238405\pi$
$181$	−2.18165	+	15.1737i	−0.162161	+	1.12785i	−0.894550	+	0.446967i	$0.852504\pi$
$182$		0			0
$183$	1.27140			0.0939845
$184$		0			0
$185$	−31.5577			−2.32017
$186$		0			0
$187$	0.332858	−	2.31508i	0.0243410	−	0.169295i
$188$		0			0
$189$	−0.120908	+	0.0355019i	−0.00879480	+	0.00258239i
$190$		0			0
$191$	5.93558	+	6.85002i	0.429483	+	0.495650i	0.928703	−	0.370826i	$-0.120925\pi$
$191$	5.93558	+	6.85002i	0.429483	+	0.495650i	−0.499219	+	0.866476i	$0.666380\pi$
$192$		0			0
$193$	9.14918	+	2.68644i	0.658572	+	0.193374i	0.593908	−	0.804533i	$-0.297584\pi$
$193$	9.14918	+	2.68644i	0.658572	+	0.193374i	0.0646640	+	0.997907i	$0.479402\pi$
$194$		0			0
$195$	6.57116	+	4.22303i	0.470570	+	0.302417i
$196$		0			0
$197$	−1.70078	+	1.96280i	−0.121175	+	0.139844i	−0.813096	−	0.582130i	$-0.802219\pi$
$197$	−1.70078	+	1.96280i	−0.121175	+	0.139844i	0.691920	+	0.721974i	$0.256765\pi$
$198$		0			0
$199$	−2.86746	−	19.9437i	−0.203269	−	1.41377i	−0.794499	−	0.607265i	$-0.792267\pi$
$199$	−2.86746	−	19.9437i	−0.203269	−	1.41377i	0.591230	−	0.806503i	$-0.298643\pi$
$200$		0			0
$201$	−4.41917	−	9.67664i	−0.311705	−	0.682538i
$202$		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
$207$	3.27197	−	3.50631i	0.227418	−	0.243705i
$208$		0			0
$209$	−0.153291	+	0.0985143i	−0.0106034	+	0.00681438i
$210$		0			0
$211$	−9.89338	+	21.6635i	−0.681089	+	1.49138i	0.180397	+	0.983594i	$0.442262\pi$
$211$	−9.89338	+	21.6635i	−0.681089	+	1.49138i	−0.861486	+	0.507782i	$0.830466\pi$
$212$		0			0
$213$	3.83844	+	8.40501i	0.263005	+	0.575901i
$214$		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
$219$	−10.6324	−	6.83300i	−0.718468	−	0.461732i
$220$		0			0
$221$	3.47739	+	1.02105i	0.233915	+	0.0686836i
$222$		0			0
$223$	−13.1936	−	15.2262i	−0.883507	−	1.01962i	−0.999652	−	0.0263890i	$-0.991599\pi$
$223$	−13.1936	−	15.2262i	−0.883507	−	1.01962i	0.116145	−	0.993232i	$-0.462946\pi$
$224$		0			0
$225$	−11.2120	+	3.29214i	−0.747467	+	0.219476i
$226$		0			0
$227$	−1.33377	+	9.27656i	−0.0885253	+	0.615707i	0.896467	+	0.443110i	$0.146125\pi$
$227$	−1.33377	+	9.27656i	−0.0885253	+	0.615707i	−0.984993	+	0.172597i	$0.944784\pi$
$228$		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
$231$	−0.155510			−0.0102318
$232$		0			0
$233$	−1.47396	+	10.2516i	−0.0965624	+	0.671607i	0.882838	+	0.469678i	$0.155630\pi$
$233$	−1.47396	+	10.2516i	−0.0965624	+	0.671607i	−0.979400	+	0.201929i	$0.935279\pi$
$234$		0			0
$235$	−22.4014	+	6.57764i	−1.46130	+	0.429078i
$236$		0			0
$237$	2.44214	+	2.81838i	0.158634	+	0.183073i
$238$		0			0
$239$	−3.25694	−	0.956324i	−0.210674	−	0.0618595i	0.174693	−	0.984623i	$-0.444107\pi$
$239$	−3.25694	−	0.956324i	−0.210674	−	0.0618595i	−0.385367	+	0.922764i	$0.625925\pi$
$240$		0			0
$241$	14.4551	+	9.28973i	0.931135	+	0.598404i	0.915868	−	0.401480i	$-0.131504\pi$
$241$	14.4551	+	9.28973i	0.931135	+	0.598404i	0.0152666	+	0.999883i	$0.495140\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		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
$249$	−3.38995	+	7.42296i	−0.214829	+	0.470411i
$250$		0			0
$251$	13.5073	−	8.68061i	0.852572	−	0.547915i	−0.0398037	−	0.999208i	$-0.512673\pi$
$251$	13.5073	−	8.68061i	0.852572	−	0.547915i	0.892376	+	0.451293i	$0.149037\pi$
$252$		0			0
$253$	5.09341	−	3.01419i	0.320220	−	0.189501i
$254$		0			0
$255$	−6.51267	+	4.18544i	−0.407839	+	0.262102i
$256$		0			0
$257$	−9.14370	+	20.0219i	−0.570368	+	1.24893i	0.376233	+	0.926525i	$0.377219\pi$
$257$	−9.14370	+	20.0219i	−0.570368	+	1.24893i	−0.946601	+	0.322407i	$0.895508\pi$
$258$		0			0
$259$	0.404422	+	0.885560i	0.0251296	+	0.0550260i
$260$		0			0
$261$	−1.06807	−	7.42858i	−0.0661118	−	0.459818i
$262$		0			0
$263$	14.9296	−	17.2297i	0.920601	−	1.06243i	−0.0772571	−	0.997011i	$-0.524616\pi$
$263$	14.9296	−	17.2297i	0.920601	−	1.06243i	0.997858	−	0.0654188i	$-0.0208383\pi$
$264$		0			0
$265$	−22.9497	−	14.7489i	−1.40979	−	0.906015i
$266$		0			0
$267$	6.77435	+	1.98913i	0.414584	+	0.121733i
$268$		0			0
$269$	−3.55143	−	4.09857i	−0.216534	−	0.249894i	0.637082	−	0.770796i	$-0.280141\pi$
$269$	−3.55143	−	4.09857i	−0.216534	−	0.249894i	−0.853617	+	0.520902i	$0.825596\pi$
$270$		0			0
$271$	24.3625	−	7.15346i	1.47991	−	0.434542i	0.560606	−	0.828082i	$-0.310568\pi$
$271$	24.3625	−	7.15346i	1.47991	−	0.434542i	0.919307	+	0.393541i	$0.128750\pi$
$272$		0			0
$273$	0.0342936	−	0.238517i	0.00207554	−	0.0144357i
$274$		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
$279$	0.335425	−	2.33293i	0.0200814	−	0.139669i
$280$		0			0
$281$	7.14061	−	2.09667i	0.425973	−	0.125077i	−0.0617174	−	0.998094i	$-0.519658\pi$
$281$	7.14061	−	2.09667i	0.425973	−	0.125077i	0.487690	+	0.873017i	$0.337840\pi$
$282$		0			0
$283$	15.9165	+	18.3687i	0.946141	+	1.09190i	0.995654	+	0.0931309i	$0.0296875\pi$
$283$	15.9165	+	18.3687i	0.946141	+	1.09190i	−0.0495133	+	0.998773i	$0.515767\pi$
$284$		0			0
$285$	0.578702	+	0.169922i	0.0342794	+	0.0100653i
$286$		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
$291$	1.88518	+	13.1117i	0.110511	+	0.768622i
$292$		0			0
$293$	6.78323	+	14.8532i	0.396281	+	0.867733i	0.997634	+	0.0687502i	$0.0219012\pi$
$293$	6.78323	+	14.8532i	0.396281	+	0.867733i	−0.601353	+	0.798983i	$0.705372\pi$
$294$		0			0
$295$	−12.9269	+	28.3059i	−0.752630	+	1.64803i
$296$		0			0
$297$	−1.03818	+	0.667196i	−0.0602412	+	0.0387146i
$298$		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
$303$	2.80507	−	6.14224i	0.161147	−	0.352863i
$304$		0			0
$305$	−2.15740	−	4.72406i	−0.123533	−	0.270499i
$306$		0			0
$307$	−3.54574	−	24.6612i	−0.202366	−	1.40749i	−0.797237	−	0.603667i	$-0.793706\pi$
$307$	−3.54574	−	24.6612i	−0.202366	−	1.40749i	0.594871	−	0.803821i	$-0.297203\pi$
$308$		0			0
$309$	5.55604	−	6.41201i	0.316072	−	0.364766i
$310$		0			0
$311$	−23.7744	−	15.2789i	−1.34813	−	0.866388i	−0.350588	−	0.936530i	$-0.614018\pi$
$311$	−23.7744	−	15.2789i	−1.34813	−	0.866388i	−0.997537	+	0.0701421i	$0.977655\pi$
$312$		0			0
$313$	5.29010	+	1.55331i	0.299014	+	0.0877985i	0.427798	−	0.903874i	$-0.359289\pi$
$313$	5.29010	+	1.55331i	0.299014	+	0.0877985i	−0.128784	+	0.991673i	$0.541107\pi$
$314$		0			0
$315$	0.337079	+	0.389010i	0.0189922	+	0.0219182i
$316$		0			0
$317$	3.12306	−	0.917014i	0.175409	−	0.0515047i	−0.192849	−	0.981228i	$-0.561773\pi$
$317$	3.12306	−	0.917014i	0.175409	−	0.0515047i	0.368258	+	0.929724i	$0.379954\pi$
$318$		0			0
$319$	1.31809	−	9.16749i	0.0737987	−	0.513281i
$320$		0			0
$321$	−13.2333			−0.738610
$322$		0			0
$323$	0.279840			0.0155707
$324$		0			0
$325$	3.18009	−	22.1180i	0.176400	−	1.22689i
$326$		0			0
$327$	−7.14612	+	2.09829i	−0.395181	+	0.116036i
$328$		0			0
$329$	0.471660	+	0.544325i	0.0260035	+	0.0300096i
$330$		0			0
$331$	−6.54037	−	1.92043i	−0.359491	−	0.105556i	0.0969992	−	0.995284i	$-0.469076\pi$
$331$	−6.54037	−	1.92043i	−0.359491	−	0.105556i	−0.456490	+	0.889728i	$0.650894\pi$
$332$		0			0
$333$	6.49927	+	4.17683i	0.356158	+	0.228889i
$334$		0			0
$335$	−28.4561	+	32.8401i	−1.55472	+	1.79425i
$336$		0			0
$337$	−0.655700	−	4.56049i	−0.0357183	−	0.248426i	0.964138	−	0.265403i	$-0.0855049\pi$
$337$	−0.655700	−	4.56049i	−0.0357183	−	0.248426i	−0.999856	+	0.0169769i	$0.994596\pi$
$338$		0			0
$339$	1.32171	+	2.89414i	0.0717854	+	0.157188i
$340$		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
$345$	−18.5803	−	6.20770i	−1.00033	−	0.334212i
$346$		0			0
$347$	−18.8312	+	12.1021i	−1.01091	+	0.649674i	−0.937629	−	0.347637i	$-0.886984\pi$
$347$	−18.8312	+	12.1021i	−1.01091	+	0.649674i	−0.0732832	+	0.997311i	$0.523348\pi$
$348$		0			0
$349$	8.84062	−	19.3583i	0.473228	−	1.03622i	−0.511043	−	0.859555i	$-0.670741\pi$
$349$	8.84062	−	19.3583i	0.473228	−	1.03622i	0.984270	−	0.176669i	$-0.0565321\pi$
$350$		0			0
$351$	−0.794382	−	1.73945i	−0.0424010	−	0.0928452i
$352$		0			0
$353$	0.895635	+	6.22928i	0.0476698	+	0.331551i	0.999676	+	0.0254708i	$0.00810848\pi$
$353$	0.895635	+	6.22928i	0.0476698	+	0.331551i	−0.952006	+	0.306080i	$0.900982\pi$
$354$		0			0
$355$	24.7166	−	28.5245i	1.31182	−	1.51392i
$356$		0			0
$357$	0.200912	+	0.129118i	0.0106334	+	0.00683367i
$358$		0			0
$359$	14.4027	+	4.22900i	0.760143	+	0.223198i	0.638758	−	0.769407i	$-0.279448\pi$
$359$	14.4027	+	4.22900i	0.760143	+	0.223198i	0.121385	+	0.992606i	$0.461267\pi$
$360$		0			0
$361$	12.4281	+	14.3428i	0.654109	+	0.754882i
$362$		0			0
$363$	9.09315	−	2.66999i	0.477267	−	0.140138i
$364$		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
$369$	10.4766			0.545391
$370$		0			0
$371$	−0.119770	+	0.833016i	−0.00621813	+	0.0432481i
$372$		0			0
$373$	8.42461	−	2.47369i	0.436210	−	0.128083i	−0.0562525	−	0.998417i	$-0.517915\pi$
$373$	8.42461	−	2.47369i	0.436210	−	0.128083i	0.492462	+	0.870334i	$0.336097\pi$
$374$		0			0
$375$	17.8830	+	20.6381i	0.923474	+	1.06575i
$376$		0			0
$377$	13.7701	+	4.04328i	0.709198	+	0.208239i
$378$		0			0
$379$	5.68742	+	3.65509i	0.292143	+	0.187749i	0.678500	−	0.734600i	$-0.262630\pi$
$379$	5.68742	+	3.65509i	0.292143	+	0.187749i	−0.386357	+	0.922349i	$0.626267\pi$
$380$		0			0
$381$	13.1809	−	15.2116i	0.675278	−	0.779313i
$382$		0			0
$383$	−0.0756551	−	0.526193i	−0.00386580	−	0.0268872i	0.987797	−	0.155745i	$-0.0497779\pi$
$383$	−0.0756551	−	0.526193i	−0.00386580	−	0.0268872i	−0.991663	+	0.128858i	$0.958869\pi$
$384$		0			0
$385$	0.263882	+	0.577820i	0.0134487	+	0.0294485i
$386$		0			0
$387$	−5.01484	+	10.9810i	−0.254919	+	0.558194i
$388$		0			0
$389$	−3.93689	+	2.53008i	−0.199608	+	0.128280i	−0.636627	−	0.771172i	$-0.719671\pi$
$389$	−3.93689	+	2.53008i	−0.199608	+	0.128280i	0.437019	+	0.899452i	$0.356034\pi$
$390$		0			0
$391$	−9.08309	−	0.334795i	−0.459352	−	0.0169313i
$392$		0			0
$393$	−2.99782	+	1.92658i	−0.151220	+	0.0971831i
$394$		0			0
$395$	6.32807	−	13.8565i	0.318400	−	0.697198i
$396$		0			0
$397$	1.42758	+	3.12596i	0.0716480	+	0.156887i	0.942067	−	0.335424i	$-0.108880\pi$
$397$	1.42758	+	3.12596i	0.0716480	+	0.156887i	−0.870419	+	0.492311i	$0.836152\pi$
$398$		0			0
$399$	−0.00264796	−	0.0184169i	−0.000132564	−	0.000922001i
$400$		0			0
$401$	8.58668	−	9.90955i	0.428798	−	0.494859i	−0.499699	−	0.866199i	$-0.666556\pi$
$401$	8.58668	−	9.90955i	0.428798	−	0.494859i	0.928497	+	0.371340i	$0.121101\pi$
$402$		0			0
$403$	3.79157	+	2.43670i	0.188872	+	0.121380i
$404$		0			0
$405$	3.91931	+	1.15081i	0.194752	+	0.0571843i
$406$		0			0
$407$	6.24354	+	7.20543i	0.309481	+	0.357160i
$408$		0			0
$409$	3.93864	−	1.15649i	0.194753	−	0.0571848i	−0.182901	−	0.983131i	$-0.558549\pi$
$409$	3.93864	−	1.15649i	0.194753	−	0.0571848i	0.377655	+	0.925947i	$0.376731\pi$
$410$		0			0
$411$	2.90621	−	20.2131i	0.143353	−	0.997040i
$412$		0			0
$413$	0.959971			0.0472371
$414$		0			0
$415$	33.3333			1.63627
$416$		0			0
$417$	−2.03946	+	14.1848i	−0.0998730	+	0.694632i
$418$		0			0
$419$	35.7570	−	10.4992i	1.74684	−	0.512919i	0.756795	−	0.653652i	$-0.226764\pi$
$419$	35.7570	−	10.4992i	1.74684	−	0.512919i	0.990048	+	0.140733i	$0.0449460\pi$
$420$		0			0
$421$	6.30973	+	7.28181i	0.307517	+	0.354894i	0.888381	−	0.459107i	$-0.151831\pi$
$421$	6.30973	+	7.28181i	0.307517	+	0.354894i	−0.580864	+	0.814001i	$0.697285\pi$
$422$		0			0
$423$	5.48412	+	1.61028i	0.266647	+	0.0782946i
$424$		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
$429$	−0.335848	−	2.33587i	−0.0162149	−	0.112777i
$430$		0			0
$431$	13.3144	+	29.1546i	0.641334	+	1.40433i	0.898938	+	0.438076i	$0.144340\pi$
$431$	13.3144	+	29.1546i	0.641334	+	1.40433i	−0.257604	+	0.966251i	$0.582933\pi$
$432$		0			0
$433$	10.2767	−	22.5027i	0.493865	−	1.08141i	−0.484551	−	0.874763i	$-0.661017\pi$
$433$	10.2767	−	22.5027i	0.493865	−	1.08141i	0.978415	−	0.206649i	$-0.0662559\pi$
$434$		0			0
$435$	−25.7895	+	16.5739i	−1.23651	+	0.794659i
$436$		0			0
$437$	0.443696	+	0.551883i	0.0212249	+	0.0264001i
$438$		0			0
$439$	−7.03424	+	4.52063i	−0.335726	+	0.215758i	−0.697632	−	0.716457i	$-0.745763\pi$
$439$	−7.03424	+	4.52063i	−0.335726	+	0.215758i	0.361905	+	0.932215i	$0.382126\pi$
$440$		0			0
$441$	−2.90131	+	6.35298i	−0.138158	+	0.302523i
$442$		0			0
$443$	−3.68541	−	8.06992i	−0.175099	−	0.383413i	0.801652	−	0.597791i	$-0.203955\pi$
$443$	−3.68541	−	8.06992i	−0.175099	−	0.383413i	−0.976751	+	0.214378i	$0.931228\pi$
$444$		0			0
$445$	−4.10435	−	28.5463i	−0.194565	−	1.35323i
$446$		0			0
$447$	−11.7633	+	13.5756i	−0.556385	+	0.642102i
$448$		0			0
$449$	−8.42408	−	5.41383i	−0.397557	−	0.255494i	0.326553	−	0.945179i	$-0.394113\pi$
$449$	−8.42408	−	5.41383i	−0.397557	−	0.255494i	−0.724110	+	0.689685i	$0.757749\pi$
$450$		0			0
$451$	12.4053	+	3.64253i	0.584143	+	0.171520i
$452$		0			0
$453$	4.03194	+	4.65311i	0.189437	+	0.218622i
$454$		0			0
$455$	−0.944434	+	0.277311i	−0.0442758	+	0.0130005i
$456$		0			0
$457$	4.20875	−	29.2725i	0.196877	−	1.36931i	−0.616400	−	0.787433i	$-0.711410\pi$
$457$	4.20875	−	29.2725i	0.196877	−	1.36931i	0.813277	−	0.581877i	$-0.197681\pi$
$458$		0			0
$459$	1.89524			0.0884623
$460$		0			0
$461$	−17.8301			−0.830430			−0.415215	−	0.909723i	$-0.636294\pi$
$461$	−17.8301			−0.830430			−0.415215	+	0.909723i	$0.636294\pi$
$462$		0			0
$463$	1.40293	−	9.75762i	0.0651999	−	0.453475i	−0.930902	−	0.365268i	$-0.880977\pi$
$463$	1.40293	−	9.75762i	0.0651999	−	0.453475i	0.996102	−	0.0882069i	$-0.0281137\pi$
$464$		0			0
$465$	−9.23750	+	2.71237i	−0.428379	+	0.125783i
$466$		0			0
$467$	−25.2767	−	29.1708i	−1.16966	−	1.34986i	−0.924867	−	0.380290i	$-0.875824\pi$
$467$	−25.2767	−	29.1708i	−1.16966	−	1.34986i	−0.244797	−	0.969574i	$-0.578721\pi$
$468$		0			0
$469$	1.28622	+	0.377669i	0.0593922	+	0.0174391i
$470$		0			0
$471$	−6.51130	−	4.18456i	−0.300025	−	0.192814i
$472$		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
$477$	2.77437	+	6.07502i	0.127030	+	0.278156i
$478$		0			0
$479$	2.81750	−	6.16945i	0.128735	−	0.281890i	−0.834279	−	0.551343i	$-0.814116\pi$
$479$	2.81750	−	6.16945i	0.128735	−	0.281890i	0.963013	+	0.269453i	$0.0868430\pi$
$480$		0			0
$481$	−12.4283	+	7.98719i	−0.566682	+	0.364184i
$482$		0			0
$483$	0.0639141	+	0.600947i	0.00290819	+	0.0273440i
$484$		0			0
$485$	45.5195	−	29.2536i	2.06693	−	1.32834i
$486$		0			0
$487$	−2.77299	+	6.07200i	−0.125656	+	0.275149i	−0.961996	−	0.273062i	$-0.911964\pi$
$487$	−2.77299	+	6.07200i	−0.125656	+	0.275149i	0.836340	+	0.548211i	$0.184691\pi$
$488$		0			0
$489$	5.32782	+	11.6663i	0.240932	+	0.527568i
$490$		0			0
$491$	2.53163	+	17.6079i	0.114251	+	0.794632i	0.963705	+	0.266969i	$0.0860222\pi$
$491$	2.53163	+	17.6079i	0.114251	+	0.794632i	−0.849454	+	0.527662i	$0.823069\pi$
$492$		0			0
$493$	−9.31456	+	10.7496i	−0.419507	+	0.484137i
$494$		0			0
$495$	4.24072	+	2.72534i	0.190606	+	0.122495i
$496$		0			0
$497$	−1.11719	−	0.328038i	−0.0501130	−	0.0147145i
$498$		0			0
$499$	0.992242	+	1.14511i	0.0444189	+	0.0512621i	0.777524	−	0.628853i	$-0.216475\pi$
$499$	0.992242	+	1.14511i	0.0444189	+	0.0512621i	−0.733105	+	0.680115i	$0.761930\pi$
$500$		0			0
$501$	−2.89307	+	0.849482i	−0.129253	+	0.0379521i
$502$		0			0
$503$	2.54825	−	17.7235i	0.113621	−	0.790250i	−0.850726	−	0.525609i	$-0.823837\pi$
$503$	2.54825	−	17.7235i	0.113621	−	0.790250i	0.964347	−	0.264641i	$-0.0852535\pi$
$504$		0			0
$505$	−27.5822			−1.22739
$506$		0			0
$507$	−9.34325			−0.414948
$508$		0			0
$509$	2.69998	−	18.7788i	0.119675	−	0.832355i	−0.838240	−	0.545301i	$-0.816415\pi$
$509$	2.69998	−	18.7788i	0.119675	−	0.832355i	0.957915	−	0.287053i	$-0.0926757\pi$
$510$		0			0
$511$	1.52813	−	0.448699i	0.0676004	−	0.0198493i
$512$		0			0
$513$	−0.0966929	−	0.111590i	−0.00426910	−	0.00492680i
$514$		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
$519$	−1.54823	+	1.78675i	−0.0679598	+	0.0784298i
$520$		0			0
$521$	−4.48410	−	31.1876i	−0.196452	−	1.36635i	−0.814478	−	0.580195i	$-0.802976\pi$
$521$	−4.48410	−	31.1876i	−0.196452	−	1.36635i	0.618026	−	0.786158i	$-0.287933\pi$
$522$		0			0
$523$	−7.15195	−	15.6606i	−0.312733	−	0.684790i	0.686365	−	0.727257i	$-0.259205\pi$
$523$	−7.15195	−	15.6606i	−0.312733	−	0.684790i	−0.999098	+	0.0424676i	$0.986478\pi$
$524$		0			0
$525$	0.611700	−	1.33944i	0.0266968	−	0.0584578i
$526$		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
$531$	6.40870	−	4.11862i	0.278114	−	0.178733i
$532$		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
$537$	2.97497	+	20.6914i	0.128379	+	0.892899i
$538$		0			0
$539$	−5.64424	+	6.51380i	−0.243115	+	0.280569i
$540$		0			0
$541$	0.229819	+	0.147696i	0.00988070	+	0.00634994i	0.545572	−	0.838064i	$-0.316312\pi$
$541$	0.229819	+	0.147696i	0.00988070	+	0.00634994i	−0.535691	+	0.844414i	$0.679949\pi$
$542$		0			0
$543$	−14.7088	−	4.31889i	−0.631214	−	0.185341i
$544$		0			0
$545$	19.9225	+	22.9918i	0.853388	+	0.984863i
$546$		0			0
$547$	−25.3716	+	7.44978i	−1.08481	+	0.318530i	−0.774802	−	0.632203i	$-0.782151\pi$
$547$	−25.3716	+	7.44978i	−1.08481	+	0.318530i	−0.310010	+	0.950733i	$0.600332\pi$
$548$		0			0
$549$	−0.180939	+	1.25846i	−0.00772228	+	0.0537097i
$550$		0			0
$551$	1.10814			0.0472084
$552$		0			0
$553$	−0.469934			−0.0199836
$554$		0			0
$555$	4.49113	−	31.2365i	0.190638	−	1.32591i
$556$		0			0
$557$	−23.7086	+	6.96147i	−1.00457	+	0.294967i	−0.742328	−	0.670036i	$-0.766278\pi$
$557$	−23.7086	+	6.96147i	−1.00457	+	0.294967i	−0.262237	+	0.965003i	$0.584460\pi$
$558$		0			0
$559$	−15.1172	−	17.4462i	−0.639390	−	0.737895i
$560$		0			0
$561$	2.24415	+	0.658941i	0.0947479	+	0.0278205i
$562$		0			0
$563$	14.2024	+	9.12730i	0.598558	+	0.384670i	0.804551	−	0.593884i	$-0.202406\pi$
$563$	14.2024	+	9.12730i	0.598558	+	0.384670i	−0.205993	+	0.978553i	$0.566042\pi$
$564$		0			0
$565$	8.51080	−	9.82198i	0.358052	−	0.413214i
$566$		0			0
$567$	−0.0179335	−	0.124730i	−0.000753136	−	0.00523818i
$568$		0			0
$569$	4.05486	+	8.87892i	0.169989	+	0.372223i	0.975384	−	0.220515i	$-0.0707739\pi$
$569$	4.05486	+	8.87892i	0.169989	+	0.372223i	−0.805395	+	0.592739i	$0.798047\pi$
$570$		0			0
$571$	−6.08106	+	13.3157i	−0.254484	+	0.557243i	−0.993152	−	0.116826i	$-0.962728\pi$
$571$	−6.08106	+	13.3157i	−0.254484	+	0.557243i	0.738668	+	0.674070i	$0.235455\pi$
$572$		0			0
$573$	−7.62502	+	4.90030i	−0.318540	+	0.204713i
$574$		0			0
$575$	5.92684	+	55.7266i	0.247166	+	2.32396i
$576$		0			0
$577$	10.3558	−	6.65529i	0.431119	−	0.277063i	−0.307032	−	0.951699i	$-0.599336\pi$
$577$	10.3558	−	6.65529i	0.431119	−	0.277063i	0.738151	+	0.674636i	$0.235699\pi$
$578$		0			0
$579$	−3.96116	+	8.67373i	−0.164620	+	0.360468i
$580$		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
$585$	−5.11522	+	5.90327i	−0.211488	+	0.244070i
$586$		0			0
$587$	10.1633	+	6.53159i	0.419486	+	0.269587i	0.733311	−	0.679893i	$-0.237974\pi$
$587$	10.1633	+	6.53159i	0.419486	+	0.269587i	−0.313825	+	0.949481i	$0.601610\pi$
$588$		0			0
$589$	0.333913	+	0.0980456i	0.0137586	+	0.00403990i
$590$		0			0
$591$	−1.70078	−	1.96280i	−0.0699606	−	0.0807388i
$592$		0			0
$593$	41.6427	−	12.2274i	1.71006	−	0.502119i	0.727193	−	0.686433i	$-0.240824\pi$
$593$	41.6427	−	12.2274i	1.71006	−	0.502119i	0.982867	+	0.184314i	$0.0590063\pi$
$594$		0			0
$595$	0.138834	−	0.965615i	0.00569166	−	0.0395863i
$596$		0			0
$597$	20.1487			0.824633
$598$		0			0
$599$	−36.5272			−1.49246			−0.746230	−	0.665688i	$-0.768138\pi$
$599$	−36.5272			−1.49246			−0.746230	+	0.665688i	$0.768138\pi$
$600$		0			0
$601$	0.0953083	−	0.662884i	0.00388771	−	0.0270396i	−0.987785	−	0.155821i	$-0.950198\pi$
$601$	0.0953083	−	0.662884i	0.00388771	−	0.0270396i	0.991673	+	0.128782i	$0.0411067\pi$
$602$		0			0
$603$	10.2071	−	2.99706i	0.415664	−	0.122050i
$604$		0			0
$605$	−25.3506	−	29.2562i	−1.03065	−	1.18943i
$606$		0			0
$607$	−34.6753	−	10.1816i	−1.40743	−	0.413258i	−0.512200	−	0.858866i	$-0.671169\pi$
$607$	−34.6753	−	10.1816i	−1.40743	−	0.413258i	−0.895228	+	0.445608i	$0.852988\pi$
$608$		0			0
$609$	0.795593	+	0.511296i	0.0322390	+	0.0207188i
$610$		0			0
$611$	−7.15750	+	8.26020i	−0.289562	+	0.334172i
$612$		0			0
$613$	5.62930	+	39.1526i	0.227365	+	1.58136i	0.709142	+	0.705066i	$0.249083\pi$
$613$	5.62930	+	39.1526i	0.227365	+	1.58136i	−0.481776	+	0.876294i	$0.660008\pi$
$614$		0			0
$615$	−17.7775	−	38.9273i	−0.716858	−	1.56970i
$616$		0			0
$617$	−2.38060	+	5.21278i	−0.0958393	+	0.209859i	−0.951479	−	0.307712i	$-0.900437\pi$
$617$	−2.38060	+	5.21278i	−0.0958393	+	0.209859i	0.855640	+	0.517571i	$0.173164\pi$
$618$		0			0
$619$	22.1415	−	14.2295i	0.889942	−	0.571931i	−0.0138494	−	0.999904i	$-0.504409\pi$
$619$	22.1415	−	14.2295i	0.889942	−	0.571931i	0.903792	+	0.427973i	$0.140772\pi$
$620$		0			0
$621$	3.00497	+	3.73767i	0.120585	+	0.149988i
$622$		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
$627$	−0.0756960	−	0.165751i	−0.00302301	−	0.00661946i
$628$		0			0
$629$	−2.08378	−	14.4930i	−0.0830858	−	0.577875i
$630$		0			0
$631$	−18.8138	+	21.7123i	−0.748967	+	0.864354i	−0.994468	−	0.105042i	$-0.966502\pi$
$631$	−18.8138	+	21.7123i	−0.748967	+	0.864354i	0.245501	+	0.969396i	$0.421048\pi$
$632$		0			0
$633$	−20.0350	−	12.8757i	−0.796320	−	0.511764i
$634$		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
$639$	−8.86572	+	2.60321i	−0.350722	+	0.102981i
$640$		0			0
$641$	3.14585	−	21.8799i	0.124254	−	0.864202i	−0.828398	−	0.560139i	$-0.810748\pi$
$641$	3.14585	−	21.8799i	0.124254	−	0.864202i	0.952652	−	0.304063i	$-0.0983433\pi$
$642$		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
$645$	49.3109			1.94161
$646$		0			0
$647$	−3.70136	+	25.7436i	−0.145516	+	1.01208i	0.777929	+	0.628352i	$0.216270\pi$
$647$	−3.70136	+	25.7436i	−0.145516	+	1.01208i	−0.923445	+	0.383731i	$0.874639\pi$
$648$		0			0
$649$	9.02048	−	2.64865i	0.354085	−	0.103969i
$650$		0			0
$651$	0.194495	+	0.224459i	0.00762287	+	0.00879726i
$652$		0			0
$653$	−43.7741	−	12.8532i	−1.71301	−	0.502986i	−0.729525	−	0.683954i	$-0.760259\pi$
$653$	−43.7741	−	12.8532i	−1.71301	−	0.502986i	−0.983489	+	0.180967i	$0.942077\pi$
$654$		0			0
$655$	12.2454	+	7.86963i	0.478467	+	0.307492i
$656$		0			0
$657$	8.27660	−	9.55170i	0.322901	−	0.372647i
$658$		0			0
$659$	4.36052	+	30.3281i	0.169862	+	1.18141i	0.879168	+	0.476513i	$0.158099\pi$
$659$	4.36052	+	30.3281i	0.169862	+	1.18141i	−0.709306	+	0.704901i	$0.750992\pi$
$660$		0			0
$661$	6.54464	+	14.3308i	0.254557	+	0.557402i	0.993163	−	0.116735i	$-0.0372429\pi$
$661$	6.54464	+	14.3308i	0.254557	+	0.557402i	−0.738606	+	0.674137i	$0.764516\pi$
$662$		0			0
$663$	−1.50555	+	3.29669i	−0.0584706	+	0.128033i
$664$		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
$669$	16.9489	−	10.8924i	0.655280	−	0.421123i
$670$		0			0
$671$	−0.651791	+	1.42722i	−0.0251621	+	0.0550974i
$672$		0			0
$673$	4.20807	+	9.21438i	0.162209	+	0.355188i	0.973232	−	0.229827i	$-0.0738159\pi$
$673$	4.20807	+	9.21438i	0.162209	+	0.355188i	−0.811023	+	0.585015i	$0.801089\pi$
$674$		0			0
$675$	−1.66300	−	11.5664i	−0.0640088	−	0.445191i
$676$		0			0
$677$	7.73175	−	8.92291i	0.297155	−	0.342935i	−0.587463	−	0.809251i	$-0.699873\pi$
$677$	7.73175	−	8.92291i	0.297155	−	0.342935i	0.884619	+	0.466315i	$0.154419\pi$
$678$		0			0
$679$	−1.40425	−	0.902457i	−0.0538902	−	0.0346331i
$680$		0			0
$681$	−8.99232	−	2.64038i	−0.344586	−	0.101180i
$682$		0			0
$683$	7.85265	+	9.06244i	0.300473	+	0.346765i	0.885829	−	0.464012i	$-0.153591\pi$
$683$	7.85265	+	9.06244i	0.300473	+	0.346765i	−0.585356	+	0.810777i	$0.699045\pi$
$684$		0			0
$685$	−80.0361	+	23.5007i	−3.05802	+	0.897917i
$686$		0			0
$687$	−0.426139	+	2.96386i	−0.0162582	+	0.113078i
$688$		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
$693$	0.0221314	−	0.153928i	0.000840704	−	0.00584722i
$694$		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
$699$	−9.93752	−	2.91792i	−0.375871	−	0.110366i
$700$		0			0
$701$	−37.7052	−	24.2316i	−1.42410	−	0.915216i	−0.999954	−	0.00962419i	$-0.996936\pi$
$701$	−37.7052	−	24.2316i	−1.42410	−	0.915216i	−0.424150	−	0.905592i	$-0.639427\pi$
$702$		0			0
$703$	−0.747020	+	0.862107i	−0.0281744	+	0.0325150i
$704$		0			0
$705$	−3.32264	−	23.1095i	−0.125138	−	0.870352i
$706$		0			0
$707$	0.353475	+	0.774002i	0.0132938	+	0.0291093i
$708$		0			0
$709$	15.7599	−	34.5095i	0.591877	−	1.29603i	−0.342424	−	0.939546i	$-0.611248\pi$
$709$	15.7599	−	34.5095i	0.591877	−	1.29603i	0.934301	−	0.356485i	$-0.116025\pi$
$710$		0			0
$711$	−3.13725	+	2.01619i	−0.117656	+	0.0756128i
$712$		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
$717$	1.41010	−	3.08769i	0.0526612	−	0.115312i
$718$		0			0
$719$	−15.3632	−	33.6408i	−0.572952	−	1.25459i	−0.945210	−	0.326462i	$-0.894144\pi$
$719$	−15.3632	−	33.6408i	−0.572952	−	1.25459i	0.372258	−	0.928129i	$-0.378584\pi$
$720$		0			0
$721$	0.152153	+	1.05825i	0.00566648	+	0.0394113i
$722$		0			0
$723$	−11.2523	+	12.9859i	−0.418479	+	0.482951i
$724$		0			0
$725$	73.7764	+	47.4132i	2.73999	+	1.76088i
$726$		0			0
$727$	44.6395	+	13.1073i	1.65559	+	0.486124i	0.970250	−	0.242103i	$-0.0778373\pi$
$727$	44.6395	+	13.1073i	1.65559	+	0.486124i	0.685336	+	0.728227i	$0.259655\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	21.9524	−	6.44580i	0.811938	−	0.238406i
$732$		0			0
$733$	0.437796	−	3.04494i	0.0161704	−	0.112467i	−0.980138	−	0.198319i	$-0.936452\pi$
$733$	0.437796	−	3.04494i	0.0161704	−	0.112467i	0.996308	+	0.0858513i	$0.0273610\pi$
$734$		0			0
$735$	28.5285			1.05229
$736$		0			0
$737$	13.1282			0.483582
$738$		0			0
$739$	−3.33533	+	23.1977i	−0.122692	+	0.853341i	0.831794	+	0.555085i	$0.187314\pi$
$739$	−3.33533	+	23.1977i	−0.122692	+	0.853341i	−0.954486	+	0.298257i	$0.903595\pi$
$740$		0			0
$741$	0.270916	−	0.0795482i	0.00995236	−	0.00292228i
$742$		0			0
$743$	−1.07237	−	1.23758i	−0.0393413	−	0.0454023i	0.735738	−	0.677266i	$-0.236836\pi$
$743$	−1.07237	−	1.23758i	−0.0393413	−	0.0454023i	−0.775079	+	0.631864i	$0.782290\pi$
$744$		0			0
$745$	70.4027	+	20.6721i	2.57936	+	0.757367i
$746$		0			0
$747$	−6.86496	−	4.41184i	−0.251176	−	0.161421i
$748$		0			0
$749$	1.09202	−	1.26026i	0.0399016	−	0.0460489i
$750$		0			0
$751$	6.05226	+	42.0944i	0.220850	+	1.53605i	0.734834	+	0.678247i	$0.237260\pi$
$751$	6.05226	+	42.0944i	0.220850	+	1.53605i	−0.513984	+	0.857800i	$0.671831\pi$
$752$		0			0
$753$	6.66996	+	14.6052i	0.243067	+	0.532242i
$754$		0			0
$755$	10.4476	−	22.8770i	0.380226	−	0.832579i
$756$		0			0
$757$	−7.49246	+	4.81511i	−0.272318	+	0.175008i	−0.669671	−	0.742657i	$-0.733565\pi$
$757$	−7.49246	+	4.81511i	−0.272318	+	0.175008i	0.397353	+	0.917666i	$0.369929\pi$
$758$		0			0
$759$	2.25865	+	5.47053i	0.0819837	+	0.198568i
$760$		0			0
$761$	32.4340	−	20.8441i	1.17573	−	0.755597i	0.201134	−	0.979564i	$-0.435537\pi$
$761$	32.4340	−	20.8441i	1.17573	−	0.755597i	0.974597	+	0.223967i	$0.0719008\pi$
$762$		0			0
$763$	0.389875	−	0.853707i	0.0141144	−	0.0309063i
$764$		0			0
$765$	−3.21599	−	7.04203i	−0.116274	−	0.254605i
$766$		0			0
$767$	2.07320	+	14.4194i	0.0748588	+	0.520654i
$768$		0			0
$769$	−33.6719	+	38.8594i	−1.21424	+	1.40131i	−0.323850	+	0.946108i	$0.604977\pi$
$769$	−33.6719	+	38.8594i	−1.21424	+	1.40131i	−0.890390	+	0.455199i	$0.849568\pi$
$770$		0			0
$771$	−18.5168	−	11.9000i	−0.666867	−	0.428569i
$772$		0			0
$773$	24.4813	+	7.18835i	0.880530	+	0.258547i	0.690588	−	0.723249i	$-0.257352\pi$
$773$	24.4813	+	7.18835i	0.880530	+	0.258547i	0.189942	+	0.981795i	$0.439170\pi$
$774$		0			0
$775$	18.0358	+	20.8144i	0.647865	+	0.747676i
$776$		0			0
$777$	−0.934102	+	0.274277i	−0.0335107	+	0.00983964i
$778$		0			0
$779$	−0.220149	+	1.53117i	−0.00788766	+	0.0548599i
$780$		0			0
$781$	−11.4029			−0.408029
$782$		0			0
$783$	7.50497			0.268206
$784$		0			0
$785$	−4.49944	+	31.2943i	−0.160592	+	1.11694i
$786$		0			0
$787$	9.82123	−	2.88377i	0.350089	−	0.102795i	−0.101960	−	0.994789i	$-0.532511\pi$
$787$	9.82123	−	2.88377i	0.350089	−	0.102795i	0.452049	+	0.891993i	$0.350693\pi$
$788$		0			0
$789$	14.9296	+	17.2297i	0.531509	+	0.613394i
$790$		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
$795$	17.8648	−	20.6171i	0.633599	−	0.731213i
$796$		0			0
$797$	−0.236974	−	1.64819i	−0.00839403	−	0.0583818i	0.985194	−	0.171444i	$-0.0548432\pi$
$797$	−0.236974	−	1.64819i	−0.00839403	−	0.0583818i	−0.993588	+	0.113062i	$0.963934\pi$
$798$		0			0
$799$	−4.49999	−	9.85361i	−0.159198	−	0.348596i
$800$		0			0
$801$	−2.93297	+	6.42232i	−0.103632	+	0.226921i
$802$		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
$807$	4.56227	−	2.93199i	0.160600	−	0.103211i
$808$		0			0
$809$	3.33499	−	7.30261i	0.117252	−	0.256746i	−0.841902	−	0.539630i	$-0.818564\pi$
$809$	3.33499	−	7.30261i	0.117252	−	0.256746i	0.959154	+	0.282884i	$0.0912912\pi$
$810$		0			0
$811$	22.8369	+	50.0059i	0.801912	+	1.75594i	0.638856	+	0.769326i	$0.279408\pi$
$811$	22.8369	+	50.0059i	0.801912	+	1.75594i	0.163057	+	0.986617i	$0.447865\pi$
$812$		0			0
$813$	3.61351	+	25.1325i	0.126731	+	0.881436i
$814$		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
$819$	0.231209	+	0.0678890i	0.00807909	+	0.00237223i
$820$		0			0
$821$	−12.5323	−	14.4630i	−0.437379	−	0.504763i	0.493673	−	0.869647i	$-0.335654\pi$
$821$	−12.5323	−	14.4630i	−0.437379	−	0.504763i	−0.931053	+	0.364885i	$0.881108\pi$
$822$		0			0
$823$	−20.3321	+	5.97006i	−0.708734	+	0.208103i	−0.616181	−	0.787605i	$-0.711321\pi$
$823$	−20.3321	+	5.97006i	−0.708734	+	0.208103i	−0.0925530	+	0.995708i	$0.529503\pi$
$824$		0			0
$825$	2.05228	−	14.2739i	0.0714512	−	0.496954i
$826$		0			0
$827$	29.2748			1.01798			0.508992	−	0.860771i	$-0.330018\pi$
$827$	29.2748			1.01798			0.508992	+	0.860771i	$0.330018\pi$
$828$		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
$831$	4.03513	−	28.0650i	0.139977	−	0.973562i
$832$		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
$837$	2.26145	+	0.664021i	0.0781671	+	0.0229519i
$838$		0			0
$839$	−8.78578	−	5.64628i	−0.303319	−	0.194931i	0.380123	−	0.924936i	$-0.375882\pi$
$839$	−8.78578	−	5.64628i	−0.303319	−	0.194931i	−0.683442	+	0.730005i	$0.739518\pi$
$840$		0			0
$841$	−17.8938	+	20.6505i	−0.617027	+	0.712087i
$842$		0			0
$843$	1.05912	+	7.36631i	0.0364779	+	0.253709i
$844$		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
$849$	−20.4469	+	13.1404i	−0.701735	+	0.450978i
$850$		0			0
$851$	25.2783	−	27.0887i	0.866528	−	0.928587i
$852$		0			0
$853$	−15.3790	+	9.88346i	−0.526566	+	0.338403i	−0.776764	−	0.629791i	$-0.783140\pi$
$853$	−15.3790	+	9.88346i	−0.526566	+	0.338403i	0.250199	+	0.968195i	$0.419504\pi$
$854$		0			0
$855$	−0.250551	+	0.548629i	−0.00856865	+	0.0187627i
$856$		0			0
$857$	−12.9983	−	28.4623i	−0.444014	−	0.972255i	−0.990844	−	0.135012i	$-0.956893\pi$
$857$	−12.9983	−	28.4623i	−0.444014	−	0.972255i	0.546830	−	0.837244i	$-0.315834\pi$
$858$		0			0
$859$	1.37199	+	9.54240i	0.0468117	+	0.325582i	0.999749	+	0.0224143i	$0.00713529\pi$
$859$	1.37199	+	9.54240i	0.0468117	+	0.325582i	−0.952937	+	0.303168i	$0.901956\pi$
$860$		0			0
$861$	−0.864539	+	0.997732i	−0.0294634	+	0.0340026i
$862$		0			0
$863$	−8.91655	−	5.73032i	−0.303523	−	0.195062i	0.380009	−	0.924983i	$-0.375921\pi$
$863$	−8.91655	−	5.73032i	−0.303523	−	0.195062i	−0.683532	+	0.729920i	$0.739557\pi$
$864$		0			0
$865$	9.26609	+	2.72077i	0.315056	+	0.0925089i
$866$		0			0
$867$	8.78041	+	10.1331i	0.298198	+	0.344139i
$868$		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
$873$	−13.2465			−0.448328
$874$		0			0
$875$	−3.44117			−0.116333
$876$		0			0
$877$	−0.805286	+	5.60089i	−0.0271926	+	0.189129i	−0.998890	−	0.0470996i	$-0.985002\pi$
$877$	−0.805286	+	5.60089i	−0.0271926	+	0.189129i	0.971698	+	0.236228i	$0.0759113\pi$
$878$		0			0
$879$	−15.6674	+	4.60036i	−0.528447	+	0.155166i
$880$		0			0
$881$	−32.9426	−	38.0177i	−1.10986	−	1.28085i	−0.956196	−	0.292728i	$-0.905437\pi$
$881$	−32.9426	−	38.0177i	−1.10986	−	1.28085i	−0.153667	−	0.988123i	$-0.549108\pi$
$882$		0			0
$883$	−16.8285	−	4.94130i	−0.566325	−	0.166288i	−0.0139782	−	0.999902i	$-0.504450\pi$
$883$	−16.8285	−	4.94130i	−0.566325	−	0.166288i	−0.552347	+	0.833614i	$0.686268\pi$
$884$		0			0
$885$	−26.1781	−	16.8236i	−0.879966	−	0.565520i
$886$		0			0
$887$	17.7918	−	20.5329i	0.597392	−	0.689427i	−0.373859	−	0.927486i	$-0.621966\pi$
$887$	17.7918	−	20.5329i	0.597392	−	0.689427i	0.971251	+	0.238059i	$0.0765111\pi$
$888$		0			0
$889$	0.360962	+	2.51055i	0.0121063	+	0.0842010i
$890$		0			0
$891$	−0.512657	−	1.12256i	−0.0171747	−	0.0376072i
$892$		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
$897$	−8.88860	+	2.25787i	−0.296782	+	0.0753880i
$898$		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
$903$	−0.631935	−	1.38374i	−0.0210295	−	0.0460481i
$904$		0			0
$905$	8.91154	+	61.9811i	0.296230	+	2.06032i
$906$		0			0
$907$	21.7863	−	25.1427i	0.723402	−	0.834850i	−0.268310	−	0.963333i	$-0.586465\pi$
$907$	21.7863	−	25.1427i	0.723402	−	0.834850i	0.991712	+	0.128483i	$0.0410107\pi$
$908$		0			0
$909$	5.68052	+	3.65065i	0.188411	+	0.121084i
$910$		0			0
$911$	−36.5227	−	10.7240i	−1.21005	−	0.355303i	−0.386363	−	0.922347i	$-0.626269\pi$
$911$	−36.5227	−	10.7240i	−1.21005	−	0.355303i	−0.823687	+	0.567044i	$0.808087\pi$
$912$		0			0
$913$	−6.59485	−	7.61086i	−0.218258	−	0.251883i
$914$		0			0
$915$	4.98300	−	1.46314i	0.164733	−	0.0483700i
$916$		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
$921$	24.9148			0.820970
$922$		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
$927$	5.55604	+	6.41201i	0.182484	+	0.210598i
$928$		0			0
$929$	15.8053	+	4.64085i	0.518554	+	0.152261i	0.530529	−	0.847667i	$-0.321993\pi$
$929$	15.8053	+	4.64085i	0.518554	+	0.152261i	−0.0119743	+	0.999928i	$0.503812\pi$
$930$		0			0
$931$	−0.867530	−	0.557528i	−0.0284321	−	0.0182722i
$932$		0			0
$933$	18.5069	−	21.3580i	0.605887	−	0.699231i
$934$		0			0
$935$	−1.35965	−	9.45657i	−0.0444653	−	0.309263i
$936$		0			0
$937$	−3.43363	−	7.51861i	−0.112172	−	0.245622i	0.845217	−	0.534423i	$-0.179471\pi$
$937$	−3.43363	−	7.51861i	−0.112172	−	0.245622i	−0.957389	+	0.288800i	$0.906744\pi$
$938$		0			0
$939$	−2.29036	+	5.01520i	−0.0747432	+	0.163665i
$940$		0			0
$941$	4.74409	−	3.04884i	0.154653	−	0.0993894i	−0.461026	−	0.887387i	$-0.652518\pi$
$941$	4.74409	−	3.04884i	0.154653	−	0.0993894i	0.615679	+	0.787997i	$0.288882\pi$
$942$		0			0
$943$	8.97748	−	49.4355i	0.292347	−	1.60984i
$944$		0			0
$945$	−0.433021	+	0.278286i	−0.0140862	+	0.00905264i
$946$		0			0
$947$	−10.3235	+	22.6053i	−0.335468	+	0.734572i	−0.999919	−	0.0127598i	$-0.995938\pi$
$947$	−10.3235	+	22.6053i	−0.335468	+	0.734572i	0.664451	+	0.747332i	$0.268666\pi$
$948$		0			0
$949$	10.0400	+	21.9845i	0.325911	+	0.713646i
$950$		0			0
$951$	0.463222	+	3.22178i	0.0150210	+	0.104473i
$952$		0			0
$953$	−33.0490	+	38.1406i	−1.07056	+	1.23549i	−0.0999117	+	0.994996i	$0.531856\pi$
$953$	−33.0490	+	38.1406i	−1.07056	+	1.23549i	−0.970650	+	0.240497i	$0.922689\pi$
$954$		0			0
$955$	31.1464	+	20.0166i	1.00788	+	0.647722i
$956$		0			0
$957$	8.88660	+	2.60934i	0.287263	+	0.0843480i
$958$		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
$963$	1.88329	−	13.0986i	0.0606883	−	0.422096i
$964$		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
$969$	−0.0398254	+	0.276992i	−0.00127938	+	0.00889827i
$970$		0			0
$971$	−21.0575	+	6.18304i	−0.675768	+	0.198423i	−0.601570	−	0.798820i	$-0.705458\pi$
$971$	−21.0575	+	6.18304i	−0.675768	+	0.198423i	−0.0741980	+	0.997244i	$0.523640\pi$
$972$		0			0
$973$	−1.18258	−	1.36477i	−0.0379117	−	0.0437525i
$974$		0			0
$975$	21.4403	+	6.29544i	0.686639	+	0.201615i
$976$		0			0
$977$	19.0341	+	12.2324i	0.608953	+	0.391351i	0.808465	−	0.588545i	$-0.200299\pi$
$977$	19.0341	+	12.2324i	0.608953	+	0.391351i	−0.199511	+	0.979896i	$0.563935\pi$
$978$		0			0
$979$	−5.70584	+	6.58489i	−0.182359	+	0.210454i
$980$		0			0
$981$	−1.05993	−	7.37200i	−0.0338411	−	0.235370i
$982$		0			0
$983$	−8.32096	−	18.2204i	−0.265398	−	0.581140i	0.729275	−	0.684220i	$-0.239857\pi$
$983$	−8.32096	−	18.2204i	−0.265398	−	0.581140i	−0.994673	+	0.103081i	$0.967130\pi$
$984$		0			0
$985$	−4.40705	+	9.65010i	−0.140420	+	0.307478i
$986$		0			0
$987$	−0.605908	+	0.389394i	−0.0192863	+	0.0123945i
$988$		0			0
$989$	47.5182	+	33.0730i	1.51099	+	1.05166i
$990$		0			0
$991$	−46.2705	+	29.7363i	−1.46983	+	0.944604i	−0.471812	+	0.881699i	$0.656400\pi$
$991$	−46.2705	+	29.7363i	−1.46983	+	0.944604i	−0.998020	+	0.0629045i	$0.979964\pi$
$992$		0			0
$993$	2.83167	−	6.20049i	0.0898603	−	0.196767i
$994$		0			0
$995$	−34.1899	−	74.8654i	−1.08389	−	2.37339i
$996$		0			0
$997$	−4.83245	−	33.6105i	−0.153045	−	1.06445i	−0.911077	−	0.412236i	$-0.864748\pi$
$997$	−4.83245	−	33.6105i	−0.153045	−	1.06445i	0.758032	−	0.652218i	$-0.226161\pi$
$998$		0			0
$999$	−5.05925	+	5.83869i	−0.160068	+	0.184728i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.25.2	✓	20	23.2	even	11	inner
276.2.i.a.265.2	yes	20	1.1	even	1	trivial
828.2.q.c.541.1		20	3.2	odd	2
828.2.q.c.577.1		20	69.2	odd	22
6348.2.a.s.1.1		10	23.18	even	11
6348.2.a.t.1.10		10	23.5	odd	22

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(3.91931 - 1.15081i) q^{5} +(-0.0825209 - 0.0952342i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(3.91931 - 1.15081i) q^{5} +(-0.0825209 - 0.0952342i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-1.03818 - 0.667196i) q^{11} +(1.25227 - 1.44519i) q^{13} +(0.581323 + 4.04319i) q^{15} +(0.787312 + 1.72397i) q^{17} +(0.0613378 - 0.134311i) q^{19} +(0.106009 - 0.0681277i) q^{21} +(-2.15160 + 4.28610i) q^{23} +(9.83034 - 6.31757i) q^{25} +(0.415415 - 0.909632i) q^{27} +(3.11768 + 6.82676i) q^{29} +(0.335425 + 2.33293i) q^{31} +(0.808153 - 0.932658i) q^{33} +(-0.433021 - 0.278286i) q^{35} +(-7.41275 - 2.17658i) q^{37} +(1.25227 + 1.44519i) q^{39} +(-10.0522 + 2.95160i) q^{41} +(1.71801 - 11.9490i) q^{43} -4.08477 q^{45} -5.71564 q^{47} +(0.993944 - 6.91303i) q^{49} +(-1.81847 + 0.533951i) q^{51} +(-4.37352 - 5.04731i) q^{53} +(-4.83675 - 1.42020i) q^{55} +(0.124215 + 0.0798279i) q^{57} +(-4.98875 + 5.75733i) q^{59} +(-0.180939 - 1.25846i) q^{61} +(0.0523476 + 0.114625i) q^{63} +(3.24487 - 7.10527i) q^{65} +(-8.94923 + 5.75132i) q^{67} +(-3.93627 - 2.73967i) q^{69} +(7.77319 - 4.99552i) q^{71} +(-5.25031 + 11.4966i) q^{73} +(4.85427 + 10.6294i) q^{75} +(0.0221314 + 0.153928i) q^{77} +(2.44214 - 2.81838i) q^{79} +(0.841254 + 0.540641i) q^{81} +(7.82984 + 2.29905i) q^{83} +(5.06969 + 5.85073i) q^{85} +(-7.20097 + 2.11439i) q^{87} +(1.00479 - 6.98848i) q^{89} -0.240970 q^{91} -2.35692 q^{93} +(0.0858348 - 0.596994i) q^{95} +(12.7100 - 3.73198i) q^{97} +(0.808153 + 0.932658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more