LMFDB - Embedded newform 2156.2.q.d.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2156,2,Mod(901,2156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("2156.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2156 = 2^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2156.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.2157466758$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.721389578983833600000000.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 44x^{12} + 128x^{10} + 223x^{8} - 464x^{6} - 724x^{4} + 784x^{2} + 2401 $ x^16 + 8x^14 + 44x^12 + 128x^10 + 223x^8 - 464x^6 - 724x^4 + 784*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$-1.36434 + 1.59774i$ of defining polynomial
Character	$\chi$	$=$	2156.901
Dual form			2156.2.q.d.2089.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60021 + 0.923880i) q^{3} +(1.60021 + 0.923880i) q^{5} +(0.207107 - 0.358719i) q^{9} +(3.23861 - 0.715113i) q^{11} +5.84313 q^{13} -3.41421 q^{15} +(1.21015 + 2.09604i) q^{17} +(-4.13171 + 7.15634i) q^{19} +(-2.12132 + 3.67423i) q^{23} +(-0.792893 - 1.37333i) q^{25} -4.77791i q^{27} -4.47214i q^{29} +(7.06365 - 4.07820i) q^{31} +(-4.52177 + 4.13642i) q^{33} +(3.41421 - 5.91359i) q^{37} +(-9.35021 + 5.39835i) q^{39} +9.26595 q^{41} +1.85242i q^{43} +(0.662827 - 0.382683i) q^{45} +(4.25151 + 2.45461i) q^{47} +(-3.87298 - 2.23607i) q^{51} +(-3.53553 - 6.12372i) q^{53} +(5.84313 + 1.84776i) q^{55} -15.2688i q^{57} +(-3.47496 + 2.00627i) q^{59} +(-1.21015 + 2.09604i) q^{61} +(9.35021 + 5.39835i) q^{65} +(5.53553 + 9.58783i) q^{67} -7.83938i q^{69} +3.75736 q^{71} +(5.34187 + 9.25238i) q^{73} +(2.53759 + 1.46508i) q^{75} +(-11.6190 - 6.70820i) q^{79} +(5.03553 + 8.72180i) q^{81} -4.84061 q^{83} +4.47214i q^{85} +(4.13171 + 7.15634i) q^{87} +(3.86324 + 2.23044i) q^{89} +(-7.53553 + 13.0519i) q^{93} +(-13.2232 + 7.63441i) q^{95} +5.35757i q^{97} +(0.414214 - 1.30986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9} + 8 q^{11} - 32 q^{15} - 24 q^{25} + 32 q^{37} + 32 q^{67} + 128 q^{71} + 24 q^{81} - 64 q^{93} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^9 + 8 * q^11 - 32 * q^15 - 24 * q^25 + 32 * q^37 + 32 * q^67 + 128 * q^71 + 24 * q^81 - 64 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2156\mathbb{Z}\right)^\times$.

$n$	$981$	$1079$	$1277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.884871	−	0.465837i	$-0.845753\pi$
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.0390089	+	0.999239i	$0.512420\pi$
$4$		0			0
$5$	1.60021	+	0.923880i	0.715634	+	0.413171i	0.813144	−	0.582063i	$-0.197754\pi$
$5$	1.60021	+	0.923880i	0.715634	+	0.413171i	−0.0975096	+	0.995235i	$0.531088\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.207107	−	0.358719i	0.0690356	−	0.119573i
$10$		0			0
$11$	3.23861	−	0.715113i	0.976478	−	0.215615i
$11$	3.23861	−	0.715113i	0.976478	−	0.215615i
$12$		0			0
$13$	5.84313			1.62059			0.810296	−	0.586021i	$-0.199306\pi$
$13$	5.84313			1.62059			0.810296	+	0.586021i	$0.199306\pi$
$14$		0			0
$15$	−3.41421			−0.881546
$16$		0			0
$17$	1.21015	+	2.09604i	0.293505	+	0.508365i	0.974636	−	0.223796i	$-0.0718450\pi$
$17$	1.21015	+	2.09604i	0.293505	+	0.508365i	−0.681131	+	0.732161i	$0.738512\pi$
$18$		0			0
$19$	−4.13171	+	7.15634i	−0.947880	+	1.64178i	−0.198002	+	0.980202i	$0.563445\pi$
$19$	−4.13171	+	7.15634i	−0.947880	+	1.64178i	−0.749879	+	0.661575i	$0.769888\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.12132	+	3.67423i	−0.442326	+	0.766131i	−0.997862	−	0.0653618i	$-0.979180\pi$
$23$	−2.12132	+	3.67423i	−0.442326	+	0.766131i	0.555536	+	0.831493i	$0.312513\pi$
$24$		0			0
$25$	−0.792893	−	1.37333i	−0.158579	−	0.274666i
$26$		0			0
$27$		−	4.77791i		−	0.919509i
$28$		0			0
$29$		−	4.47214i		−	0.830455i	−0.909718	−	0.415227i	$-0.863702\pi$
$29$		−	4.47214i		−	0.830455i	0.909718	−	0.415227i	$-0.136298\pi$
$30$		0			0
$31$	7.06365	−	4.07820i	1.26867	−	0.732467i	0.293933	−	0.955826i	$-0.405036\pi$
$31$	7.06365	−	4.07820i	1.26867	−	0.732467i	0.974736	+	0.223359i	$0.0717023\pi$
$32$		0			0
$33$	−4.52177	+	4.13642i	−0.787139	+	0.720058i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.41421	−	5.91359i	0.561293	−	0.972188i	−0.436091	−	0.899903i	$-0.643637\pi$
$37$	3.41421	−	5.91359i	0.561293	−	0.972188i	0.997384	−	0.0722857i	$-0.0230293\pi$
$38$		0			0
$39$	−9.35021	+	5.39835i	−1.49723	+	0.864427i
$40$		0			0
$41$	9.26595			1.44710			0.723549	−	0.690273i	$-0.242509\pi$
$41$	9.26595			1.44710			0.723549	+	0.690273i	$0.242509\pi$
$42$		0			0
$43$			1.85242i			0.282491i	0.989975	+	0.141246i	$0.0451107\pi$
$43$			1.85242i			0.282491i	−0.989975	+	0.141246i	$0.954889\pi$
$44$		0			0
$45$	0.662827	−	0.382683i	0.0988084	−	0.0570471i
$46$		0			0
$47$	4.25151	+	2.45461i	0.620147	+	0.358042i	0.776926	−	0.629592i	$-0.216778\pi$
$47$	4.25151	+	2.45461i	0.620147	+	0.358042i	−0.156779	+	0.987634i	$0.550111\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.87298	−	2.23607i	−0.542326	−	0.313112i
$52$		0			0
$53$	−3.53553	−	6.12372i	−0.485643	−	0.841158i	0.514221	−	0.857658i	$-0.328081\pi$
$53$	−3.53553	−	6.12372i	−0.485643	−	0.841158i	−0.999864	+	0.0164995i	$0.994748\pi$
$54$		0			0
$55$	5.84313	+	1.84776i	0.787887	+	0.249152i
$56$		0			0
$57$		−	15.2688i		−	2.02241i
$58$		0			0
$59$	−3.47496	+	2.00627i	−0.452402	+	0.261194i	−0.708844	−	0.705365i	$-0.750783\pi$
$59$	−3.47496	+	2.00627i	−0.452402	+	0.261194i	0.256442	+	0.966560i	$0.417450\pi$
$60$		0			0
$61$	−1.21015	+	2.09604i	−0.154944	+	0.268371i	−0.933039	−	0.359776i	$-0.882853\pi$
$61$	−1.21015	+	2.09604i	−0.154944	+	0.268371i	0.778095	+	0.628147i	$0.216186\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.35021	+	5.39835i	1.15975	+	0.669582i
$66$		0			0
$67$	5.53553	+	9.58783i	0.676273	+	1.17134i	0.976095	+	0.217344i	$0.0697394\pi$
$67$	5.53553	+	9.58783i	0.676273	+	1.17134i	−0.299822	+	0.953995i	$0.596927\pi$
$68$		0			0
$69$		−	7.83938i		−	0.943750i
$70$		0			0
$71$	3.75736			0.445917			0.222958	−	0.974828i	$-0.428429\pi$
$71$	3.75736			0.445917			0.222958	+	0.974828i	$0.428429\pi$
$72$		0			0
$73$	5.34187	+	9.25238i	0.625218	+	1.08291i	0.988499	+	0.151230i	$0.0483233\pi$
$73$	5.34187	+	9.25238i	0.625218	+	1.08291i	−0.363280	+	0.931680i	$0.618343\pi$
$74$		0			0
$75$	2.53759	+	1.46508i	0.293015	+	0.169172i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−11.6190	−	6.70820i	−1.30723	−	0.754732i	−0.325600	−	0.945507i	$-0.605566\pi$
$79$	−11.6190	−	6.70820i	−1.30723	−	0.754732i	−0.981634	+	0.190776i	$0.938900\pi$
$80$		0			0
$81$	5.03553	+	8.72180i	0.559504	+	0.969089i
$82$		0			0
$83$	−4.84061			−0.531325			−0.265663	−	0.964066i	$-0.585591\pi$
$83$	−4.84061			−0.531325			−0.265663	+	0.964066i	$0.585591\pi$
$84$		0			0
$85$			4.47214i			0.485071i
$86$		0			0
$87$	4.13171	+	7.15634i	0.442966	+	0.767240i
$88$		0			0
$89$	3.86324	+	2.23044i	0.409503	+	0.236426i	0.690576	−	0.723260i	$-0.257357\pi$
$89$	3.86324	+	2.23044i	0.409503	+	0.236426i	−0.281073	+	0.959686i	$0.590690\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−7.53553	+	13.0519i	−0.781398	+	1.35342i
$94$		0			0
$95$	−13.2232	+	7.63441i	−1.35667	+	0.783274i
$96$		0			0
$97$			5.35757i			0.543979i	0.962300	+	0.271989i	$0.0876815\pi$
$97$			5.35757i			0.543979i	−0.962300	+	0.271989i	$0.912318\pi$
$98$		0			0
$99$	0.414214	−	1.30986i	0.0416300	−	0.131646i
$100$		0			0
$101$	5.34187	+	9.25238i	0.531536	+	0.920647i	0.999322	+	0.0368053i	$0.0117181\pi$
$101$	5.34187	+	9.25238i	0.531536	+	0.920647i	−0.467787	+	0.883841i	$0.654949\pi$
$102$		0			0
$103$	−7.84020	−	4.52654i	−0.772518	−	0.446014i	0.0612540	−	0.998122i	$-0.480490\pi$
$103$	−7.84020	−	4.52654i	−0.772518	−	0.446014i	−0.833772	+	0.552109i	$0.813823\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.47723	+	3.16228i	0.529503	+	0.305709i	0.740814	−	0.671710i	$-0.234440\pi$
$107$	5.47723	+	3.16228i	0.529503	+	0.305709i	−0.211311	+	0.977419i	$0.567773\pi$
$108$		0			0
$109$	−11.6190	+	6.70820i	−1.11289	+	0.642529i	−0.939577	−	0.342337i	$-0.888782\pi$
$109$	−11.6190	+	6.70820i	−1.11289	+	0.642529i	−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$			12.6173i			1.19758i
$112$		0			0
$113$	−17.6569			−1.66102			−0.830509	−	0.557006i	$-0.811950\pi$
$113$	−17.6569			−1.66102			−0.830509	+	0.557006i	$0.811950\pi$
$114$		0			0
$115$	−6.78910	+	3.91969i	−0.633087	+	0.365513i
$116$		0			0
$117$	1.21015	−	2.09604i	0.111879	−	0.193779i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	9.97723	−	4.63195i	0.907021	−	0.421086i
$122$		0			0
$123$	−14.8274	+	8.56062i	−1.33694	+	0.771885i
$124$		0			0
$125$		−	12.1689i		−	1.08842i
$126$		0			0
$127$			6.32456i			0.561214i	0.959823	+	0.280607i	$0.0905357\pi$
$127$			6.32456i			0.561214i	−0.959823	+	0.280607i	$0.909464\pi$
$128$		0			0
$129$	−1.71141	−	2.96425i	−0.150681	−	0.260988i
$130$		0			0
$131$	−9.97484	+	17.2769i	−0.871506	+	1.50949i	−0.0110673	+	0.999939i	$0.503523\pi$
$131$	−9.97484	+	17.2769i	−0.871506	+	1.50949i	−0.860439	+	0.509554i	$0.829810\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	4.41421	−	7.64564i	0.379915	−	0.658032i
$136$		0			0
$137$	4.41421	+	7.64564i	0.377132	+	0.653211i	0.990644	−	0.136474i	$-0.0435771\pi$
$137$	4.41421	+	7.64564i	0.377132	+	0.653211i	−0.613512	+	0.789685i	$0.710244\pi$
$138$		0			0
$139$	3.42282			0.290320			0.145160	−	0.989408i	$-0.453630\pi$
$139$	3.42282			0.290320			0.145160	+	0.989408i	$0.453630\pi$
$140$		0			0
$141$	−9.07107			−0.763922
$142$		0			0
$143$	18.9236	−	4.17850i	1.58247	−	0.349424i
$144$		0			0
$145$	4.13171	−	7.15634i	0.343120	−	0.594302i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.47723	+	3.16228i	0.448712	+	0.259064i	0.707286	−	0.706928i	$-0.249919\pi$
$149$	5.47723	+	3.16228i	0.448712	+	0.259064i	−0.258574	+	0.965991i	$0.583253\pi$
$150$		0			0
$151$	−3.87298	+	2.23607i	−0.315179	+	0.181969i	−0.649242	−	0.760582i	$-0.724914\pi$
$151$	−3.87298	+	2.23607i	−0.315179	+	0.181969i	0.334063	+	0.942551i	$0.391580\pi$
$152$		0			0
$153$	1.00252			0.0810491
$154$		0			0
$155$	15.0711			1.21054
$156$		0			0
$157$	9.55413	−	5.51608i	0.762503	−	0.440231i	−0.0676909	−	0.997706i	$-0.521563\pi$
$157$	9.55413	−	5.51608i	0.762503	−	0.440231i	0.830194	+	0.557475i	$0.188230\pi$
$158$		0			0
$159$	11.3152	+	6.53281i	0.897351	+	0.518086i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.707107	+	1.22474i	−0.0553849	+	0.0959294i	−0.892389	−	0.451268i	$-0.850972\pi$
$163$	−0.707107	+	1.22474i	−0.0553849	+	0.0959294i	0.837004	+	0.547197i	$0.184305\pi$
$164$		0			0
$165$	−11.0573	+	2.44155i	−0.860811	+	0.190074i
$166$		0			0
$167$	−8.26343			−0.639443			−0.319722	−	0.947511i	$-0.603589\pi$
$167$	−8.26343			−0.639443			−0.319722	+	0.947511i	$0.603589\pi$
$168$		0			0
$169$	21.1421			1.62632
$170$		0			0
$171$	1.71141	+	2.96425i	0.130875	+	0.226682i
$172$		0			0
$173$	−2.92156	+	5.06030i	−0.222122	+	0.384727i	−0.955452	−	0.295146i	$-0.904632\pi$
$173$	−2.92156	+	5.06030i	−0.222122	+	0.384727i	0.733330	+	0.679873i	$0.237965\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.70711	−	6.42090i	0.278643	−	0.482624i
$178$		0			0
$179$	−7.82843	−	13.5592i	−0.585124	−	1.01346i	−0.994860	−	0.101260i	$-0.967712\pi$
$179$	−7.82843	−	13.5592i	−0.585124	−	1.01346i	0.409736	−	0.912204i	$-0.365621\pi$
$180$		0			0
$181$		−	3.19278i		−	0.237318i	−0.992935	−	0.118659i	$-0.962141\pi$
$181$		−	3.19278i		−	0.237318i	0.992935	−	0.118659i	$-0.0378595\pi$
$182$		0			0
$183$		−	4.47214i		−	0.330590i
$184$		0			0
$185$	10.9269	−	6.30864i	0.803361	−	0.463821i
$186$		0			0
$187$	5.41812	+	5.92288i	0.396212	+	0.433124i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.65685	−	9.79796i	0.409316	−	0.708955i	−0.585498	−	0.810674i	$-0.699101\pi$
$191$	5.65685	−	9.79796i	0.409316	−	0.708955i	0.994813	+	0.101719i	$0.0324342\pi$
$192$		0			0
$193$	5.47723	−	3.16228i	0.394259	−	0.227626i	−0.289745	−	0.957104i	$-0.593570\pi$
$193$	5.47723	−	3.16228i	0.394259	−	0.227626i	0.684004	+	0.729478i	$0.260237\pi$
$194$		0			0
$195$	−19.9497			−1.42863
$196$		0			0
$197$			2.61972i			0.186647i	0.995636	+	0.0933235i	$0.0297491\pi$
$197$			2.61972i			0.186647i	−0.995636	+	0.0933235i	$0.970251\pi$
$198$		0			0
$199$	−17.8297	+	10.2940i	−1.26392	+	0.729722i	−0.973830	−	0.227279i	$-0.927017\pi$
$199$	−17.8297	+	10.2940i	−1.26392	+	0.729722i	−0.290085	+	0.957001i	$0.593684\pi$
$200$		0			0
$201$	−17.7160	−	10.2283i	−1.24959	−	0.721451i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	14.8274	+	8.56062i	1.03559	+	0.597900i
$206$		0			0
$207$	0.878680	+	1.52192i	0.0610725	+	0.105781i
$208$		0			0
$209$	−8.26343	+	26.1313i	−0.571593	+	1.80754i
$210$		0			0
$211$			21.5934i			1.48655i	0.668986	+	0.743275i	$0.266729\pi$
$211$			21.5934i			1.48655i	−0.668986	+	0.743275i	$0.733271\pi$
$212$		0			0
$213$	−6.01255	+	3.47135i	−0.411973	+	0.237853i
$214$		0			0
$215$	−1.71141	+	2.96425i	−0.116717	+	0.202160i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−17.0962	−	9.87048i	−1.15525	−	0.666985i
$220$		0			0
$221$	7.07107	+	12.2474i	0.475651	+	0.823853i
$222$		0			0
$223$		−	19.2430i		−	1.28860i	−0.764771	−	0.644302i	$-0.777148\pi$
$223$		−	19.2430i		−	1.28860i	0.764771	−	0.644302i	$-0.222852\pi$
$224$		0			0
$225$	−0.656854			−0.0437903
$226$		0			0
$227$	−6.55202	−	11.3484i	−0.434873	−	0.753222i	0.562413	−	0.826857i	$-0.309873\pi$
$227$	−6.55202	−	11.3484i	−0.434873	−	0.753222i	−0.997285	+	0.0736352i	$0.976540\pi$
$228$		0			0
$229$	7.84020	+	4.52654i	0.518095	+	0.299122i	0.736155	−	0.676813i	$-0.236639\pi$
$229$	7.84020	+	4.52654i	0.518095	+	0.299122i	−0.218060	+	0.975935i	$0.569973\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	24.8421	+	14.3426i	1.62746	+	0.939616i	0.984847	+	0.173428i	$0.0554844\pi$
$233$	24.8421	+	14.3426i	1.62746	+	0.939616i	0.642616	+	0.766188i	$0.277849\pi$
$234$		0			0
$235$	4.53553	+	7.85578i	0.295866	+	0.512454i
$236$		0			0
$237$	24.7903			1.61030
$238$		0			0
$239$			3.70484i			0.239646i	0.992795	+	0.119823i	$0.0382327\pi$
$239$			3.70484i			0.239646i	−0.992795	+	0.119823i	$0.961767\pi$
$240$		0			0
$241$	−2.92156	−	5.06030i	−0.188194	−	0.325962i	0.756454	−	0.654047i	$-0.226930\pi$
$241$	−2.92156	−	5.06030i	−0.188194	−	0.325962i	−0.944648	+	0.328085i	$0.893597\pi$
$242$		0			0
$243$	−3.70241	−	2.13759i	−0.237510	−	0.137126i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−24.1421	+	41.8154i	−1.53613	+	2.66065i
$248$		0			0
$249$	7.74597	−	4.47214i	0.490881	−	0.283410i
$250$		0			0
$251$			4.46088i			0.281569i	0.990040	+	0.140784i	$0.0449624\pi$
$251$			4.46088i			0.281569i	−0.990040	+	0.140784i	$0.955038\pi$
$252$		0			0
$253$	−4.24264	+	13.4164i	−0.266733	+	0.843482i
$254$		0			0
$255$	−4.13171	−	7.15634i	−0.258738	−	0.448147i
$256$		0			0
$257$	−7.67937	−	4.43369i	−0.479026	−	0.276566i	0.240984	−	0.970529i	$-0.422530\pi$
$257$	−7.67937	−	4.43369i	−0.479026	−	0.276566i	−0.720011	+	0.693963i	$0.755863\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.60424	−	0.926210i	−0.0993001	−	0.0573309i
$262$		0			0
$263$	23.2379	−	13.4164i	1.43291	−	0.827291i	0.435568	−	0.900156i	$-0.356547\pi$
$263$	23.2379	−	13.4164i	1.43291	−	0.827291i	0.997342	+	0.0728645i	$0.0232141\pi$
$264$		0			0
$265$		−	13.0656i		−	0.802615i
$266$		0			0
$267$	−8.24264			−0.504441
$268$		0			0
$269$	−19.9319	+	11.5077i	−1.21527	+	0.701637i	−0.963903	−	0.266255i	$-0.914214\pi$
$269$	−19.9319	+	11.5077i	−1.21527	+	0.701637i	−0.251368	+	0.967892i	$0.580880\pi$
$270$		0			0
$271$	−4.84061	+	8.38417i	−0.294046	+	0.509302i	−0.974762	−	0.223245i	$-0.928335\pi$
$271$	−4.84061	+	8.38417i	−0.294046	+	0.509302i	0.680717	+	0.732547i	$0.261668\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.54996	−	3.88068i	−0.214071	−	0.234014i
$276$		0			0
$277$	8.68571	−	5.01470i	0.521874	−	0.301304i	−0.215827	−	0.976432i	$-0.569245\pi$
$277$	8.68571	−	5.01470i	0.521874	−	0.301304i	0.737701	+	0.675128i	$0.235911\pi$
$278$		0			0
$279$		−	3.37849i		−	0.202265i
$280$		0			0
$281$		−	32.3901i		−	1.93223i	−0.258112	−	0.966115i	$-0.583100\pi$
$281$		−	32.3901i		−	1.93223i	0.258112	−	0.966115i	$-0.416900\pi$
$282$		0			0
$283$	13.3977	+	23.2054i	0.796409	+	1.37942i	0.921941	+	0.387331i	$0.126603\pi$
$283$	13.3977	+	23.2054i	0.796409	+	1.37942i	−0.125532	+	0.992090i	$0.540064\pi$
$284$		0			0
$285$	14.1066	−	24.4333i	0.835600	−	1.44730i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.57107	−	9.64937i	0.327710	−	0.567610i
$290$		0			0
$291$	−4.94975	−	8.57321i	−0.290159	−	0.502571i
$292$		0			0
$293$	2.42030			0.141396			0.0706978	−	0.997498i	$-0.477477\pi$
$293$	2.42030			0.141396			0.0706978	+	0.997498i	$0.477477\pi$
$294$		0			0
$295$	−7.41421			−0.431672
$296$		0			0
$297$	−3.41675	−	15.4738i	−0.198260	−	0.897881i
$298$		0			0
$299$	−12.3951	+	21.4690i	−0.716830	+	1.24159i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−17.0962	−	9.87048i	−0.982150	−	0.567044i
$304$		0			0
$305$	−3.87298	+	2.23607i	−0.221766	+	0.128037i
$306$		0			0
$307$	13.1040			0.747887			0.373943	−	0.927452i	$-0.378005\pi$
$307$	13.1040			0.747887			0.373943	+	0.927452i	$0.378005\pi$
$308$		0			0
$309$	16.7279			0.951618
$310$		0			0
$311$	−6.28710	+	3.62986i	−0.356509	+	0.205830i	−0.667548	−	0.744567i	$-0.732656\pi$
$311$	−6.28710	+	3.62986i	−0.356509	+	0.205830i	0.311039	+	0.950397i	$0.399323\pi$
$312$		0			0
$313$	20.0927	+	11.6006i	1.13571	+	0.655702i	0.945365	−	0.326015i	$-0.105706\pi$
$313$	20.0927	+	11.6006i	1.13571	+	0.655702i	0.190345	+	0.981717i	$0.439039\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.4853	−	26.8213i	0.869740	−	1.50643i	0.00747772	−	0.999972i	$-0.497620\pi$
$317$	15.4853	−	26.8213i	0.869740	−	1.50643i	0.862262	−	0.506462i	$-0.169047\pi$
$318$		0			0
$319$	−3.19808	−	14.4835i	−0.179058	−	0.810921i
$320$		0			0
$321$	−11.6863			−0.652263
$322$		0			0
$323$	−20.0000			−1.11283
$324$		0			0
$325$	−4.63298	−	8.02455i	−0.256991	−	0.445122i
$326$		0			0
$327$	12.3951	−	21.4690i	0.685453	−	1.18724i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.00000	+	5.19615i	−0.164895	+	0.285606i	−0.936618	−	0.350352i	$-0.886062\pi$
$331$	−3.00000	+	5.19615i	−0.164895	+	0.285606i	0.771723	+	0.635959i	$0.219395\pi$
$332$		0			0
$333$	−1.41421	−	2.44949i	−0.0774984	−	0.134231i
$334$		0			0
$335$			20.4567i			1.11767i
$336$		0			0
$337$			22.3607i			1.21806i	0.793146	+	0.609032i	$0.208442\pi$
$337$			22.3607i			1.21806i	−0.793146	+	0.609032i	$0.791558\pi$
$338$		0			0
$339$	28.2546	−	16.3128i	1.53458	−	0.885990i
$340$		0			0
$341$	19.9601	−	18.2590i	1.08090	−	0.988782i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	7.24264	−	12.5446i	0.389931	−	0.675380i
$346$		0			0
$347$	22.5734	−	13.0328i	1.21180	−	0.699635i	0.248652	−	0.968593i	$-0.420013\pi$
$347$	22.5734	−	13.0328i	1.21180	−	0.699635i	0.963152	+	0.268958i	$0.0866792\pi$
$348$		0			0
$349$	20.3649			1.09011			0.545055	−	0.838400i	$-0.316509\pi$
$349$	20.3649			1.09011			0.545055	+	0.838400i	$0.316509\pi$
$350$		0			0
$351$		−	27.9179i		−	1.49015i
$352$		0			0
$353$	−7.22448	+	4.17106i	−0.384520	+	0.222003i	−0.679783	−	0.733413i	$-0.737926\pi$
$353$	−7.22448	+	4.17106i	−0.384520	+	0.222003i	0.295263	+	0.955416i	$0.404593\pi$
$354$		0			0
$355$	6.01255	+	3.47135i	0.319113	+	0.184240i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−31.2591	−	18.0475i	−1.64979	−	0.952508i	−0.977153	−	0.212539i	$-0.931827\pi$
$359$	−31.2591	−	18.0475i	−1.64979	−	0.952508i	−0.672640	−	0.739970i	$-0.734840\pi$
$360$		0			0
$361$	−24.6421	−	42.6814i	−1.29695	−	2.24639i
$362$		0			0
$363$	−11.6863	+	16.6298i	−0.613369	+	0.872840i
$364$		0			0
$365$			19.7410i			1.03329i
$366$		0			0
$367$	−6.83621	+	3.94689i	−0.356847	+	0.206026i	−0.667697	−	0.744433i	$-0.732720\pi$
$367$	−6.83621	+	3.94689i	−0.356847	+	0.206026i	0.310850	+	0.950459i	$0.399386\pi$
$368$		0			0
$369$	1.91904	−	3.32388i	0.0999013	−	0.173034i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−10.9545	−	6.32456i	−0.567200	−	0.327473i	0.188830	−	0.982010i	$-0.439530\pi$
$373$	−10.9545	−	6.32456i	−0.567200	−	0.327473i	−0.756030	+	0.654537i	$0.772864\pi$
$374$		0			0
$375$	11.2426	+	19.4728i	0.580567	+	1.00557i
$376$		0			0
$377$		−	26.1313i		−	1.34583i
$378$		0			0
$379$	11.2721			0.579008			0.289504	−	0.957177i	$-0.406510\pi$
$379$	11.2721			0.579008			0.289504	+	0.957177i	$0.406510\pi$
$380$		0			0
$381$	−5.84313	−	10.1206i	−0.299352	−	0.518494i
$382$		0			0
$383$	−22.8383	−	13.1857i	−1.16698	−	0.673757i	−0.214014	−	0.976831i	$-0.568654\pi$
$383$	−22.8383	−	13.1857i	−1.16698	−	0.673757i	−0.952967	+	0.303074i	$0.901987\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.664499	+	0.383649i	0.0337784	+	0.0195020i
$388$		0			0
$389$	−0.221825	−	0.384213i	−0.0112470	−	0.0194804i	0.860347	−	0.509709i	$-0.170247\pi$
$389$	−0.221825	−	0.384213i	−0.0112470	−	0.0194804i	−0.871594	+	0.490228i	$0.836913\pi$
$390$		0			0
$391$	−10.2685			−0.519299
$392$		0			0
$393$		−	36.8622i		−	1.85945i
$394$		0			0
$395$	−12.3951	−	21.4690i	−0.623667	−	1.08022i
$396$		0			0
$397$	−31.5687	−	18.2262i	−1.58439	−	0.914748i	−0.994207	−	0.107478i	$-0.965722\pi$
$397$	−31.5687	−	18.2262i	−1.58439	−	0.914748i	−0.590182	−	0.807270i	$-0.700944\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.7782	+	30.7927i	−0.887800	+	1.53771i	−0.0453289	+	0.998972i	$0.514434\pi$
$401$	−17.7782	+	30.7927i	−0.887800	+	1.53771i	−0.842471	+	0.538742i	$0.818900\pi$
$402$		0			0
$403$	41.2738	−	23.8295i	2.05600	−	1.18703i
$404$		0			0
$405$			18.6089i			0.924684i
$406$		0			0
$407$	6.82843	−	21.5934i	0.338473	−	1.07034i
$408$		0			0
$409$	−7.76217	−	13.4445i	−0.383815	−	0.664786i	0.607789	−	0.794098i	$-0.292056\pi$
$409$	−7.76217	−	13.4445i	−0.383815	−	0.664786i	−0.991604	+	0.129312i	$0.958723\pi$
$410$		0			0
$411$	−14.1273	−	8.15640i	−0.696849	−	0.402326i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−7.74597	−	4.47214i	−0.380235	−	0.219529i
$416$		0			0
$417$	−5.47723	+	3.16228i	−0.268221	+	0.154857i
$418$		0			0
$419$		−	15.3617i		−	0.750470i	−0.926930	−	0.375235i	$-0.877562\pi$
$419$		−	15.3617i		−	0.750470i	0.926930	−	0.375235i	$-0.122438\pi$
$420$		0			0
$421$	−4.44365			−0.216570			−0.108285	−	0.994120i	$-0.534536\pi$
$421$	−4.44365			−0.216570			−0.108285	+	0.994120i	$0.534536\pi$
$422$		0			0
$423$	1.76104	−	1.01673i	0.0856245	−	0.0494353i
$424$		0			0
$425$	1.91904	−	3.32388i	0.0930872	−	0.161232i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−26.4213	+	24.1696i	−1.27563	+	1.16692i
$430$		0			0
$431$	32.5881	−	18.8148i	1.56971	−	0.906275i	0.573512	−	0.819197i	$-0.305580\pi$
$431$	32.5881	−	18.8148i	1.56971	−	0.906275i	0.996202	−	0.0870780i	$-0.0277529\pi$
$432$		0			0
$433$		−	11.0322i		−	0.530172i	−0.964225	−	0.265086i	$-0.914600\pi$
$433$		−	11.0322i		−	0.530172i	0.964225	−	0.265086i	$-0.0854003\pi$
$434$		0			0
$435$			15.2688i			0.732084i
$436$		0			0
$437$	−17.5294	−	30.3618i	−0.838544	−	1.45240i
$438$		0			0
$439$	10.9774	−	19.0134i	0.523921	−	0.907458i	−0.475691	−	0.879612i	$-0.657802\pi$
$439$	10.9774	−	19.0134i	0.523921	−	0.907458i	0.999612	−	0.0278455i	$-0.00886464\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.3137	−	21.3280i	0.585042	−	1.01332i	−0.409828	−	0.912163i	$-0.634411\pi$
$443$	12.3137	−	21.3280i	0.585042	−	1.01332i	0.994870	−	0.101160i	$-0.0322553\pi$
$444$		0			0
$445$	4.12132	+	7.13834i	0.195369	+	0.338390i
$446$		0			0
$447$	−11.6863			−0.552741
$448$		0			0
$449$	−17.4142			−0.821828			−0.410914	−	0.911674i	$-0.634790\pi$
$449$	−17.4142			−0.821828			−0.410914	+	0.911674i	$0.634790\pi$
$450$		0			0
$451$	30.0088	−	6.62621i	1.41306	−	0.312016i
$452$		0			0
$453$	4.13171	−	7.15634i	0.194125	−	0.336234i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.53748	+	2.61972i	0.212254	+	0.122545i	0.602359	−	0.798226i	$-0.294228\pi$
$457$	4.53748	+	2.61972i	0.212254	+	0.122545i	−0.390104	+	0.920771i	$0.627561\pi$
$458$		0			0
$459$	10.0147	−	5.78199i	0.467447	−	0.269880i
$460$		0			0
$461$	−9.26595			−0.431558			−0.215779	−	0.976442i	$-0.569229\pi$
$461$	−9.26595			−0.431558			−0.215779	+	0.976442i	$0.569229\pi$
$462$		0			0
$463$	0.928932			0.0431711			0.0215856	−	0.999767i	$-0.493129\pi$
$463$	0.928932			0.0431711			0.0215856	+	0.999767i	$0.493129\pi$
$464$		0			0
$465$	−24.1168	+	13.9239i	−1.11839	+	0.645703i
$466$		0			0
$467$	16.1158	+	9.30445i	0.745750	+	0.430559i	0.824156	−	0.566363i	$-0.191650\pi$
$467$	16.1158	+	9.30445i	0.745750	+	0.430559i	−0.0784065	+	0.996921i	$0.524983\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−10.1924	+	17.6537i	−0.469640	+	0.813441i
$472$		0			0
$473$	1.32469	+	5.99927i	0.0609093	+	0.275847i
$474$		0			0
$475$	13.1040			0.601254
$476$		0			0
$477$	−2.92893			−0.134107
$478$		0			0
$479$	2.71393	+	4.70067i	0.124003	+	0.214779i	0.921343	−	0.388751i	$-0.127093\pi$
$479$	2.71393	+	4.70067i	0.124003	+	0.214779i	−0.797340	+	0.603531i	$0.793760\pi$
$480$		0			0
$481$	19.9497	−	34.5539i	0.909627	−	1.57552i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.94975	+	8.57321i	−0.224756	+	0.389290i
$486$		0			0
$487$	−3.63604	−	6.29780i	−0.164765	−	0.285381i	0.771807	−	0.635857i	$-0.219353\pi$
$487$	−3.63604	−	6.29780i	−0.164765	−	0.285381i	−0.936572	+	0.350476i	$0.886020\pi$
$488$		0			0
$489$		−	2.61313i		−	0.118170i
$490$		0			0
$491$			4.47214i			0.201825i	0.994895	+	0.100912i	$0.0321762\pi$
$491$			4.47214i			0.201825i	−0.994895	+	0.100912i	$0.967824\pi$
$492$		0			0
$493$	9.37379	−	5.41196i	0.422174	−	0.243742i
$494$		0			0
$495$	1.87298	−	1.71336i	0.0841841	−	0.0770098i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.9497	−	25.8937i	0.669243	−	1.15916i	−0.308874	−	0.951103i	$-0.599952\pi$
$499$	14.9497	−	25.8937i	0.669243	−	1.15916i	0.978116	−	0.208059i	$-0.0667146\pi$
$500$		0			0
$501$	13.2232	−	7.63441i	0.590769	−	0.341080i
$502$		0			0
$503$	−35.0588			−1.56319			−0.781596	−	0.623784i	$-0.785594\pi$
$503$	−35.0588			−1.56319			−0.781596	+	0.623784i	$0.785594\pi$
$504$		0			0
$505$			19.7410i			0.878461i
$506$		0			0
$507$	−33.8318	+	19.5328i	−1.50252	+	0.867481i
$508$		0			0
$509$	−23.1323	−	13.3555i	−1.02532	−	0.591970i	−0.109681	−	0.993967i	$-0.534983\pi$
$509$	−23.1323	−	13.3555i	−1.02532	−	0.591970i	−0.915641	+	0.401997i	$0.868316\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	34.1924	+	19.7410i	1.50963	+	0.871585i
$514$		0			0
$515$	−8.36396	−	14.4868i	−0.368560	−	0.638365i
$516$		0			0
$517$	15.5243	+	4.90923i	0.682760	+	0.215908i
$518$		0			0
$519$		−	10.7967i		−	0.473922i
$520$		0			0
$521$	−37.5147	+	21.6591i	−1.64355	+	0.948903i	−0.663990	+	0.747742i	$0.731138\pi$
$521$	−37.5147	+	21.6591i	−1.64355	+	0.948903i	−0.979558	+	0.201161i	$0.935529\pi$
$522$		0			0
$523$	4.42535	−	7.66493i	0.193507	−	0.335164i	−0.752903	−	0.658131i	$-0.771347\pi$
$523$	4.42535	−	7.66493i	0.193507	−	0.335164i	0.946410	+	0.322968i	$0.104680\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.0962	+	9.87048i	0.744721	+	0.429965i
$528$		0			0
$529$	2.50000	+	4.33013i	0.108696	+	0.188266i
$530$		0			0
$531$			1.66205i			0.0721268i
$532$		0			0
$533$	54.1421			2.34516
$534$		0			0
$535$	5.84313	+	10.1206i	0.252620	+	0.437551i
$536$		0			0
$537$	25.0542	+	14.4650i	1.08117	+	0.624213i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.0147	−	5.78199i	−0.430566	−	0.248587i	0.269022	−	0.963134i	$-0.413300\pi$
$541$	−10.0147	−	5.78199i	−0.430566	−	0.248587i	−0.699588	+	0.714547i	$0.746633\pi$
$542$		0			0
$543$	2.94975	+	5.10911i	0.126586	+	0.219253i
$544$		0			0
$545$	−24.7903			−1.06190
$546$		0			0
$547$			14.1837i			0.606451i	0.952919	+	0.303226i	$0.0980636\pi$
$547$			14.1837i			0.606451i	−0.952919	+	0.303226i	$0.901936\pi$
$548$		0			0
$549$	0.501261	+	0.868210i	0.0213933	+	0.0370543i
$550$		0			0
$551$	32.0041	+	18.4776i	1.36342	+	0.787172i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−11.6569	+	20.1903i	−0.494806	+	0.857029i
$556$		0			0
$557$	−23.2379	+	13.4164i	−0.984621	+	0.568471i	−0.903662	−	0.428246i	$-0.859132\pi$
$557$	−23.2379	+	13.4164i	−0.984621	+	0.568471i	−0.0809592	+	0.996717i	$0.525798\pi$
$558$		0			0
$559$			10.8239i			0.457803i
$560$		0			0
$561$	−14.1421	−	4.47214i	−0.597081	−	0.188814i
$562$		0			0
$563$	−6.55202	−	11.3484i	−0.276135	−	0.478279i	0.694286	−	0.719699i	$-0.255720\pi$
$563$	−6.55202	−	11.3484i	−0.276135	−	0.478279i	−0.970421	+	0.241420i	$0.922387\pi$
$564$		0			0
$565$	−28.2546	−	16.3128i	−1.18868	−	0.686285i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−25.7819	−	14.8852i	−1.08083	−	0.624019i	−0.149712	−	0.988730i	$-0.547835\pi$
$569$	−25.7819	−	14.8852i	−1.08083	−	0.624019i	−0.931121	+	0.364711i	$0.881168\pi$
$570$		0			0
$571$	−2.26874	+	1.30986i	−0.0949439	+	0.0548159i	−0.546720	−	0.837315i	$-0.684124\pi$
$571$	−2.26874	+	1.30986i	−0.0949439	+	0.0548159i	0.451776	+	0.892131i	$0.350791\pi$
$572$		0			0
$573$			20.9050i			0.873319i
$574$		0			0
$575$	6.72792			0.280574
$576$		0			0
$577$	18.7005	−	10.7967i	0.778511	−	0.449474i	−0.0573913	−	0.998352i	$-0.518278\pi$
$577$	18.7005	−	10.7967i	0.778511	−	0.449474i	0.835902	+	0.548878i	$0.184945\pi$
$578$		0			0
$579$	−5.84313	+	10.1206i	−0.242832	+	0.420598i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−15.8294	−	17.3041i	−0.655586	−	0.716661i
$584$		0			0
$585$	3.87298	−	2.23607i	0.160128	−	0.0924500i
$586$		0			0
$587$		−	14.2793i		−	0.589371i	−0.955594	−	0.294686i	$-0.904785\pi$
$587$		−	14.2793i		−	0.589371i	0.955594	−	0.294686i	$-0.0952149\pi$
$588$		0			0
$589$			67.3999i			2.77716i
$590$		0			0
$591$	−2.42030	−	4.19209i	−0.0995579	−	0.172439i
$592$		0			0
$593$	−9.76721	+	16.9173i	−0.401091	+	0.694711i	−0.993858	−	0.110664i	$-0.964702\pi$
$593$	−9.76721	+	16.9173i	−0.401091	+	0.694711i	0.592767	+	0.805374i	$0.298036\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	19.0208	−	32.9450i	0.778470	−	1.34835i
$598$		0			0
$599$	0.807612	+	1.39882i	0.0329981	+	0.0571544i	0.882053	−	0.471150i	$-0.156161\pi$
$599$	0.807612	+	1.39882i	0.0329981	+	0.0571544i	−0.849055	+	0.528305i	$0.822828\pi$
$600$		0			0
$601$	−4.42535			−0.180514			−0.0902568	−	0.995919i	$-0.528769\pi$
$601$	−4.42535			−0.180514			−0.0902568	+	0.995919i	$0.528769\pi$
$602$		0			0
$603$	4.58579			0.186748
$604$		0			0
$605$	20.2450	+	1.80568i	0.823076	+	0.0734112i
$606$		0			0
$607$	9.97484	−	17.2769i	0.404866	−	0.701249i	−0.589440	−	0.807812i	$-0.700651\pi$
$607$	9.97484	−	17.2769i	0.404866	−	0.701249i	0.994306	+	0.106563i	$0.0339847\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	24.8421	+	14.3426i	1.00501	+	0.580240i
$612$		0			0
$613$	28.0506	−	16.1950i	1.13295	−	0.654111i	0.188278	−	0.982116i	$-0.439709\pi$
$613$	28.0506	−	16.1950i	1.13295	−	0.654111i	0.944676	+	0.328004i	$0.106376\pi$
$614$		0			0
$615$	−31.6359			−1.27568
$616$		0			0
$617$	−22.1421			−0.891409			−0.445704	−	0.895180i	$-0.647047\pi$
$617$	−22.1421			−0.891409			−0.445704	+	0.895180i	$0.647047\pi$
$618$		0			0
$619$	5.80462	−	3.35130i	0.233307	−	0.134700i	−0.378790	−	0.925483i	$-0.623660\pi$
$619$	5.80462	−	3.35130i	0.233307	−	0.134700i	0.612097	+	0.790783i	$0.290326\pi$
$620$		0			0
$621$	17.5552	+	10.1355i	0.704464	+	0.406723i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	7.27817	−	12.6062i	0.291127	−	0.504247i
$626$		0			0
$627$	−10.9189	−	49.4498i	−0.436061	−	1.97484i
$628$		0			0
$629$	16.5269			0.658969
$630$		0			0
$631$	−13.0294			−0.518694			−0.259347	−	0.965784i	$-0.583507\pi$
$631$	−13.0294			−0.518694			−0.259347	+	0.965784i	$0.583507\pi$
$632$		0			0
$633$	−19.9497	−	34.5539i	−0.792929	−	1.37339i
$634$		0			0
$635$	−5.84313	+	10.1206i	−0.231877	+	0.401623i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.778175	−	1.34784i	0.0307841	−	0.0533196i
$640$		0			0
$641$	3.58579	+	6.21076i	0.141630	+	0.245310i	0.928111	−	0.372305i	$-0.121432\pi$
$641$	3.58579	+	6.21076i	0.141630	+	0.245310i	−0.786481	+	0.617615i	$0.788099\pi$
$642$		0			0
$643$			37.3491i			1.47291i	0.676489	+	0.736453i	$0.263501\pi$
$643$			37.3491i			1.47291i	−0.676489	+	0.736453i	$0.736499\pi$
$644$		0			0
$645$		−	6.32456i		−	0.249029i
$646$		0			0
$647$	2.69841	−	1.55793i	0.106086	−	0.0612486i	−0.446018	−	0.895024i	$-0.647158\pi$
$647$	2.69841	−	1.55793i	0.106086	−	0.0612486i	0.552104	+	0.833775i	$0.313825\pi$
$648$		0			0
$649$	−9.81935	+	8.98253i	−0.385443	+	0.352595i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.6066	−	28.7635i	0.649867	−	1.12560i	−0.333288	−	0.942825i	$-0.608158\pi$
$653$	16.6066	−	28.7635i	0.649867	−	1.12560i	0.983154	−	0.182777i	$-0.0585086\pi$
$654$		0			0
$655$	−31.9236	+	18.4311i	−1.24736	+	0.720163i
$656$		0			0
$657$	4.42535			0.172649
$658$		0			0
$659$			36.0949i			1.40606i	0.711161	+	0.703029i	$0.248170\pi$
$659$			36.0949i			1.40606i	−0.711161	+	0.703029i	$0.751830\pi$
$660$		0			0
$661$	15.5667	−	8.98743i	0.605474	−	0.349570i	−0.165718	−	0.986173i	$-0.552994\pi$
$661$	15.5667	−	8.98743i	0.605474	−	0.349570i	0.771192	+	0.636603i	$0.219661\pi$
$662$		0			0
$663$	−22.6303	−	13.0656i	−0.878889	−	0.507427i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.4317	+	9.48683i	0.636237	+	0.367332i
$668$		0			0
$669$	17.7782	+	30.7927i	0.687344	+	1.19051i
$670$		0			0
$671$	−2.42030	+	7.65367i	−0.0934347	+	0.295467i
$672$		0			0
$673$		−	5.55726i		−	0.214217i	−0.994247	−	0.107108i	$-0.965841\pi$
$673$		−	5.55726i		−	0.214217i	0.994247	−	0.107108i	$-0.0341592\pi$
$674$		0			0
$675$	−6.56165	+	3.78837i	−0.252558	+	0.145815i
$676$		0			0
$677$	12.8964	−	22.3372i	0.495649	−	0.858489i	−0.504338	−	0.863506i	$-0.668264\pi$
$677$	12.8964	−	22.3372i	0.495649	−	0.858489i	0.999987	+	0.00501668i	$0.00159687\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	20.9692	+	12.1065i	0.803540	+	0.463924i
$682$		0			0
$683$	−8.00000	−	13.8564i	−0.306111	−	0.530201i	0.671397	−	0.741098i	$-0.265695\pi$
$683$	−8.00000	−	13.8564i	−0.306111	−	0.530201i	−0.977508	+	0.210898i	$0.932361\pi$
$684$		0			0
$685$			16.3128i			0.623280i
$686$		0			0
$687$	−16.7279			−0.638210
$688$		0			0
$689$	−20.6586	−	35.7817i	−0.787029	−	1.36317i
$690$		0			0
$691$	7.51854	+	4.34083i	0.286019	+	0.165133i	0.636145	−	0.771569i	$-0.280528\pi$
$691$	7.51854	+	4.34083i	0.286019	+	0.165133i	−0.350126	+	0.936703i	$0.613861\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.47723	+	3.16228i	0.207763	+	0.119952i
$696$		0			0
$697$	11.2132	+	19.4218i	0.424730	+	0.735655i
$698$		0			0
$699$	−53.0034			−2.00477
$700$		0			0
$701$			28.6852i			1.08343i	0.840563	+	0.541713i	$0.182224\pi$
$701$			28.6852i			1.08343i	−0.840563	+	0.541713i	$0.817776\pi$
$702$		0			0
$703$	28.2131	+	48.8665i	1.06408	+	1.84304i
$704$		0			0
$705$	−14.5156	−	8.38057i	−0.546688	−	0.315631i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−23.9203	+	41.4312i	−0.898346	+	1.55598i	−0.0687382	+	0.997635i	$0.521897\pi$
$709$	−23.9203	+	41.4312i	−0.898346	+	1.55598i	−0.829608	+	0.558346i	$0.811436\pi$
$710$		0			0
$711$	−4.81273	+	2.77863i	−0.180491	+	0.104207i
$712$		0			0
$713$			34.6047i			1.29596i
$714$		0			0
$715$	34.1421	+	10.7967i	1.27684	+	0.403773i
$716$		0			0
$717$	−3.42282	−	5.92851i	−0.127828	−	0.221404i
$718$		0			0
$719$	−19.3828	−	11.1907i	−0.722857	−	0.417342i	0.0929463	−	0.995671i	$-0.470372\pi$
$719$	−19.3828	−	11.1907i	−0.722857	−	0.417342i	−0.815803	+	0.578329i	$0.803705\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	9.35021	+	5.39835i	0.347738	+	0.200767i
$724$		0			0
$725$	−6.14172	+	3.54593i	−0.228098	+	0.131692i
$726$		0			0
$727$		−	22.7528i		−	0.843853i	−0.906630	−	0.421927i	$-0.861354\pi$
$727$		−	22.7528i		−	0.843853i	0.906630	−	0.421927i	$-0.138646\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$		0			0
$731$	−3.88275	+	2.24171i	−0.143609	+	0.0829126i
$732$		0			0
$733$	18.0306	−	31.2300i	0.665977	−	1.15351i	−0.313042	−	0.949739i	$-0.601348\pi$
$733$	18.0306	−	31.2300i	0.665977	−	1.15351i	0.979019	−	0.203767i	$-0.0653184\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.7838	+	27.0927i	0.912924	+	0.997973i
$738$		0			0
$739$	3.20848	−	1.85242i	0.118026	−	0.0681423i	−0.439825	−	0.898084i	$-0.644959\pi$
$739$	3.20848	−	1.85242i	0.118026	−	0.0681423i	0.557851	+	0.829941i	$0.311626\pi$
$740$		0			0
$741$		−	89.2177i		−	3.27749i
$742$		0			0
$743$		−	25.2982i		−	0.928102i	−0.885809	−	0.464051i	$-0.846395\pi$
$743$		−	25.2982i		−	0.928102i	0.885809	−	0.464051i	$-0.153605\pi$
$744$		0			0
$745$	5.84313	+	10.1206i	0.214076	+	0.370790i
$746$		0			0
$747$	−1.00252	+	1.73642i	−0.0366804	+	0.0635323i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	20.9497	−	36.2860i	0.764467	−	1.32410i	−0.176061	−	0.984379i	$-0.556336\pi$
$751$	20.9497	−	36.2860i	0.764467	−	1.32410i	0.940528	−	0.339717i	$-0.110331\pi$
$752$		0			0
$753$	−4.12132	−	7.13834i	−0.150189	−	0.260135i
$754$		0			0
$755$	−8.26343			−0.300737
$756$		0			0
$757$	29.8995			1.08672			0.543358	−	0.839501i	$-0.317153\pi$
$757$	29.8995			1.08672			0.543358	+	0.839501i	$0.317153\pi$
$758$		0			0
$759$	−5.60604	−	25.3887i	−0.203487	−	0.921552i
$760$		0			0
$761$	−8.05580	+	13.9531i	−0.292023	+	0.505798i	−0.974288	−	0.225307i	$-0.927662\pi$
$761$	−8.05580	+	13.9531i	−0.292023	+	0.505798i	0.682265	+	0.731105i	$0.260995\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.60424	+	0.926210i	0.0580015	+	0.0334872i
$766$		0			0
$767$	−20.3047	+	11.7229i	−0.733159	+	0.423289i
$768$		0			0
$769$	−24.3750			−0.878986			−0.439493	−	0.898246i	$-0.644842\pi$
$769$	−24.3750			−0.878986			−0.439493	+	0.898246i	$0.644842\pi$
$770$		0			0
$771$	16.3848			0.590083
$772$		0			0
$773$	12.7545	−	7.36384i	0.458749	−	0.264859i	−0.252769	−	0.967527i	$-0.581341\pi$
$773$	12.7545	−	7.36384i	0.458749	−	0.264859i	0.711518	+	0.702668i	$0.248008\pi$
$774$		0			0
$775$	−11.2014	−	6.46716i	−0.402368	−	0.232307i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−38.2843	+	66.3103i	−1.37168	+	2.37581i
$780$		0			0
$781$	12.1686	−	2.68694i	0.435428	−	0.0961462i
$782$		0			0
$783$	−21.3675			−0.763611
$784$		0			0
$785$	20.3848			0.727564
$786$		0			0
$787$	9.68121	+	16.7683i	0.345098	+	0.597727i	0.985372	−	0.170420i	$-0.0545124\pi$
$787$	9.68121	+	16.7683i	0.345098	+	0.597727i	−0.640274	+	0.768147i	$0.721179\pi$
$788$		0			0
$789$	−24.7903	+	42.9380i	−0.882558	+	1.52863i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−7.07107	+	12.2474i	−0.251101	+	0.434920i
$794$		0			0
$795$	12.0711	+	20.9077i	0.428117	+	0.741520i
$796$		0			0
$797$			31.5976i			1.11924i	0.828748	+	0.559622i	$0.189054\pi$
$797$			31.5976i			1.11924i	−0.828748	+	0.559622i	$0.810946\pi$
$798$		0			0
$799$			11.8818i			0.420348i
$800$		0			0
$801$	1.60021	−	0.923880i	0.0565405	−	0.0326437i
$802$		0			0
$803$	23.9167	+	26.1448i	0.844003	+	0.922632i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	21.2635	−	36.8294i	0.748509	−	1.29646i
$808$		0			0
$809$	−35.1321	+	20.2835i	−1.23518	+	0.713131i	−0.968105	−	0.250545i	$-0.919390\pi$
$809$	−35.1321	+	20.2835i	−1.23518	+	0.713131i	−0.267074	+	0.963676i	$0.586057\pi$
$810$		0			0
$811$	37.0638			1.30149			0.650743	−	0.759298i	$-0.274457\pi$
$811$	37.0638			1.30149			0.650743	+	0.759298i	$0.274457\pi$
$812$		0			0
$813$		−	17.8885i		−	0.627379i
$814$		0			0
$815$	−2.26303	+	1.30656i	−0.0792706	+	0.0457669i
$816$		0			0
$817$	−13.2565	−	7.65367i	−0.463788	−	0.267768i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−47.4155	−	27.3754i	−1.65481	−	0.955407i	−0.975053	−	0.221974i	$-0.928750\pi$
$821$	−47.4155	−	27.3754i	−1.65481	−	0.955407i	−0.679761	−	0.733433i	$-0.737917\pi$
$822$		0			0
$823$	−3.82843	−	6.63103i	−0.133451	−	0.231143i	0.791554	−	0.611099i	$-0.209272\pi$
$823$	−3.82843	−	6.63103i	−0.133451	−	0.231143i	−0.925005	+	0.379956i	$0.875939\pi$
$824$		0			0
$825$	9.26595	+	2.93015i	0.322599	+	0.102015i
$826$		0			0
$827$		−	35.0098i		−	1.21741i	−0.793397	−	0.608705i	$-0.791689\pi$
$827$		−	35.0098i		−	1.21741i	0.793397	−	0.608705i	$-0.208311\pi$
$828$		0			0
$829$	−45.2412	+	26.1200i	−1.57129	+	0.907185i	−0.575279	+	0.817957i	$0.695107\pi$
$829$	−45.2412	+	26.1200i	−1.57129	+	0.907185i	−0.996011	+	0.0892277i	$0.971560\pi$
$830$		0			0
$831$	−9.26595	+	16.0491i	−0.321432	+	0.556737i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−13.2232	−	7.63441i	−0.457607	−	0.264200i
$836$		0			0
$837$	−19.4853	−	33.7495i	−0.673510	−	1.16655i
$838$		0			0
$839$		−	18.1606i		−	0.626972i	−0.949593	−	0.313486i	$-0.898503\pi$
$839$		−	18.1606i		−	0.626972i	0.949593	−	0.313486i	$-0.101497\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$		0			0
$843$	29.9245	+	51.8308i	1.03066	+	1.78515i
$844$		0			0
$845$	33.8318	+	19.5328i	1.16385	+	0.671948i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−42.8781	−	24.7557i	−1.47157	−	0.849612i
$850$		0			0
$851$	14.4853	+	25.0892i	0.496549	+	0.860048i
$852$		0			0
$853$	47.1603			1.61474			0.807369	−	0.590047i	$-0.200891\pi$
$853$	47.1603			1.61474			0.807369	+	0.590047i	$0.200891\pi$
$854$		0			0
$855$			6.32456i			0.216295i
$856$		0			0
$857$	−13.8989	−	24.0736i	−0.474778	−	0.822340i	0.524804	−	0.851223i	$-0.324138\pi$
$857$	−13.8989	−	24.0736i	−0.474778	−	0.822340i	−0.999583	+	0.0288826i	$0.990805\pi$
$858$		0			0
$859$	27.0427	+	15.6131i	0.922684	+	0.532712i	0.884490	−	0.466558i	$-0.154506\pi$
$859$	27.0427	+	15.6131i	0.922684	+	0.532712i	0.0381938	+	0.999270i	$0.487840\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	−0.829976	−	0.557800i	$-0.811646\pi$
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	0.898056	+	0.439880i	$0.144979\pi$
$864$		0			0
$865$	−9.35021	+	5.39835i	−0.317917	+	0.183549i
$866$		0			0
$867$			20.5880i			0.699205i
$868$		0			0
$869$	−42.4264	−	13.4164i	−1.43922	−	0.455120i
$870$		0			0
$871$	32.3448	+	56.0229i	1.09596	+	1.89826i
$872$		0			0
$873$	1.92186	+	1.10959i	0.0650452	+	0.0375539i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	42.2136	+	24.3720i	1.42545	+	0.822984i	0.996757	−	0.0804657i	$-0.0256408\pi$
$877$	42.2136	+	24.3720i	1.42545	+	0.822984i	0.428693	+	0.903450i	$0.358974\pi$
$878$		0			0
$879$	−3.87298	+	2.23607i	−0.130632	+	0.0754207i
$880$		0			0
$881$		−	28.3504i		−	0.955150i	−0.878591	−	0.477575i	$-0.841516\pi$
$881$		−	28.3504i		−	0.955150i	0.878591	−	0.477575i	$-0.158484\pi$
$882$		0			0
$883$	34.2843			1.15376			0.576879	−	0.816830i	$-0.304270\pi$
$883$	34.2843			1.15376			0.576879	+	0.816830i	$0.304270\pi$
$884$		0			0
$885$	11.8643	−	6.84984i	0.398813	−	0.230255i
$886$		0			0
$887$	14.8154	−	25.6611i	0.497454	−	0.861616i	−0.502542	−	0.864553i	$-0.667602\pi$
$887$	14.8154	−	25.6611i	0.497454	−	0.861616i	0.999996	+	0.00293734i	$0.000934986\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	22.5452	+	24.6456i	0.755293	+	0.825657i
$892$		0			0
$893$	−35.1321	+	20.2835i	−1.17565	+	0.678762i
$894$		0			0
$895$		−	28.9301i		−	0.967026i
$896$		0			0
$897$		−	45.8065i		−	1.52943i
$898$		0			0
$899$	−18.2383	−	31.5896i	−0.608280	−	1.05357i
$900$		0			0
$901$	8.55706	−	14.8213i	0.285077	−	0.493768i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.94975	−	5.10911i	0.0980529	−	0.169833i
$906$		0			0
$907$	16.4645	+	28.5173i	0.546694	+	0.946901i	0.998498	+	0.0547842i	$0.0174471\pi$
$907$	16.4645	+	28.5173i	0.546694	+	0.946901i	−0.451805	+	0.892117i	$0.649220\pi$
$908$		0			0
$909$	4.42535			0.146779
$910$		0			0
$911$	−9.69848			−0.321325			−0.160663	−	0.987009i	$-0.551363\pi$
$911$	−9.69848			−0.321325			−0.160663	+	0.987009i	$0.551363\pi$
$912$		0			0
$913$	−15.6768	+	3.46158i	−0.518828	+	0.114562i
$914$		0			0
$915$	4.13171	−	7.15634i	0.136590	−	0.236581i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−25.5066	−	14.7263i	−0.841386	−	0.485775i	0.0163488	−	0.999866i	$-0.494796\pi$
$919$	−25.5066	−	14.7263i	−0.841386	−	0.485775i	−0.857735	+	0.514092i	$0.828129\pi$
$920$		0			0
$921$	−20.9692	+	12.1065i	−0.690957	+	0.398924i
$922$		0			0
$923$	21.9547			0.722649
$924$		0			0
$925$	−10.8284			−0.356036
$926$		0			0
$927$	−3.24752	+	1.87496i	−0.106662	+	0.0615816i
$928$		0			0
$929$	13.3703	+	7.71933i	0.438664	+	0.253263i	0.703031	−	0.711159i	$-0.251830\pi$
$929$	13.3703	+	7.71933i	0.438664	+	0.253263i	−0.264367	+	0.964422i	$0.585163\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6.70711	−	11.6170i	0.219581	−	0.380325i
$934$		0			0
$935$	3.19808	+	14.4835i	0.104589	+	0.473662i
$936$		0			0
$937$	20.9522			0.684479			0.342239	−	0.939613i	$-0.388815\pi$
$937$	20.9522			0.684479			0.342239	+	0.939613i	$0.388815\pi$
$938$		0			0
$939$	−42.8701			−1.39901
$940$		0			0
$941$	29.4233	+	50.9626i	0.959171	+	1.66133i	0.724521	+	0.689253i	$0.242061\pi$
$941$	29.4233	+	50.9626i	0.959171	+	1.66133i	0.234650	+	0.972080i	$0.424605\pi$
$942$		0			0
$943$	−19.6561	+	34.0453i	−0.640089	+	1.10867i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.51472	+	6.08767i	−0.114213	+	0.197823i	−0.917465	−	0.397817i	$-0.869768\pi$
$947$	−3.51472	+	6.08767i	−0.114213	+	0.197823i	0.803252	+	0.595640i	$0.203101\pi$
$948$		0			0
$949$	31.2132	+	54.0629i	1.01322	+	1.75495i
$950$		0			0
$951$			57.2261i			1.85568i
$952$		0			0
$953$		−	51.0459i		−	1.65354i	−0.562541	−	0.826770i	$-0.690176\pi$
$953$		−	51.0459i		−	1.65354i	0.562541	−	0.826770i	$-0.309824\pi$
$954$		0			0
$955$	18.1043	−	10.4525i	0.585840	−	0.338235i
$956$		0			0
$957$	18.4986	+	20.2220i	0.597975	+	0.653683i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	17.7635	−	30.7672i	0.573015	−	0.992491i
$962$		0			0
$963$	2.26874	−	1.30986i	0.0731092	−	0.0422096i
$964$		0			0
$965$	11.6863			0.376194
$966$		0			0
$967$		−	8.17697i		−	0.262954i	−0.991319	−	0.131477i	$-0.958028\pi$
$967$		−	8.17697i		−	0.262954i	0.991319	−	0.131477i	$-0.0419719\pi$
$968$		0			0
$969$	32.0041	−	18.4776i	1.02812	−	0.593586i
$970$		0			0
$971$	−40.8483	−	23.5838i	−1.31089	−	0.756840i	−0.328642	−	0.944454i	$-0.606591\pi$
$971$	−40.8483	−	23.5838i	−1.31089	−	0.756840i	−0.982243	+	0.187615i	$0.939924\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	14.8274	+	8.56062i	0.474858	+	0.274159i
$976$		0			0
$977$	−12.6066	−	21.8353i	−0.403321	−	0.698572i	0.590804	−	0.806815i	$-0.298811\pi$
$977$	−12.6066	−	21.8353i	−0.403321	−	0.698572i	−0.994124	+	0.108243i	$0.965478\pi$
$978$		0			0
$979$	14.1066	+	4.46088i	0.450848	+	0.142571i
$980$		0			0
$981$			5.55726i			0.177430i
$982$		0			0
$983$	11.4955	−	6.63693i	0.366650	−	0.211685i	−0.305344	−	0.952242i	$-0.598771\pi$
$983$	11.4955	−	6.63693i	0.366650	−	0.211685i	0.671994	+	0.740557i	$0.265438\pi$
$984$		0			0
$985$	−2.42030	+	4.19209i	−0.0771173	+	0.133571i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.80622	−	3.92957i	−0.216425	−	0.124953i
$990$		0			0
$991$	−7.77817	−	13.4722i	−0.247082	−	0.427958i	0.715633	−	0.698476i	$-0.246138\pi$
$991$	−7.77817	−	13.4722i	−0.247082	−	0.427958i	−0.962715	+	0.270518i	$0.912805\pi$
$992$		0			0
$993$		−	11.0866i		−	0.351821i
$994$		0			0
$995$	−38.0416			−1.20600
$996$		0			0
$997$	16.0256	+	27.7572i	0.507536	+	0.879078i	0.999962	+	0.00872355i	$0.00277683\pi$
$997$	16.0256	+	27.7572i	0.507536	+	0.879078i	−0.492426	+	0.870354i	$0.663890\pi$
$998$		0			0
$999$	−28.2546	−	16.3128i	−0.893936	−	0.516114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2156.2.q.d.901.2		16
7.2	even	3		2156.2.c.a.1077.2	yes	8
7.3	odd	6	inner	2156.2.q.d.2089.1		16
7.4	even	3	inner	2156.2.q.d.2089.7		16
7.5	odd	6		2156.2.c.a.1077.8	yes	8
7.6	odd	2	inner	2156.2.q.d.901.8		16
11.10	odd	2	inner	2156.2.q.d.901.1		16
77.10	even	6	inner	2156.2.q.d.2089.2		16
77.32	odd	6	inner	2156.2.q.d.2089.8		16
77.54	even	6		2156.2.c.a.1077.7	yes	8
77.65	odd	6		2156.2.c.a.1077.1	✓	8
77.76	even	2	inner	2156.2.q.d.901.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2156.2.c.a.1077.1	✓	8	77.65	odd	6
2156.2.c.a.1077.2	yes	8	7.2	even	3
2156.2.c.a.1077.7	yes	8	77.54	even	6
2156.2.c.a.1077.8	yes	8	7.5	odd	6
2156.2.q.d.901.1		16	11.10	odd	2	inner
2156.2.q.d.901.2		16	1.1	even	1	trivial
2156.2.q.d.901.7		16	77.76	even	2	inner
2156.2.q.d.901.8		16	7.6	odd	2	inner
2156.2.q.d.2089.1		16	7.3	odd	6	inner
2156.2.q.d.2089.2		16	77.10	even	6	inner
2156.2.q.d.2089.7		16	7.4	even	3	inner
2156.2.q.d.2089.8		16	77.32	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2156.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.60021 + 0.923880i) q^{3} +(1.60021 + 0.923880i) q^{5} +(0.207107 - 0.358719i) q^{9} +(3.23861 - 0.715113i) q^{11} +5.84313 q^{13} -3.41421 q^{15} +(1.21015 + 2.09604i) q^{17} +(-4.13171 + 7.15634i) q^{19} +(-2.12132 + 3.67423i) q^{23} +(-0.792893 - 1.37333i) q^{25} -4.77791i q^{27} -4.47214i q^{29} +(7.06365 - 4.07820i) q^{31} +(-4.52177 + 4.13642i) q^{33} +(3.41421 - 5.91359i) q^{37} +(-9.35021 + 5.39835i) q^{39} +9.26595 q^{41} +1.85242i q^{43} +(0.662827 - 0.382683i) q^{45} +(4.25151 + 2.45461i) q^{47} +(-3.87298 - 2.23607i) q^{51} +(-3.53553 - 6.12372i) q^{53} +(5.84313 + 1.84776i) q^{55} -15.2688i q^{57} +(-3.47496 + 2.00627i) q^{59} +(-1.21015 + 2.09604i) q^{61} +(9.35021 + 5.39835i) q^{65} +(5.53553 + 9.58783i) q^{67} -7.83938i q^{69} +3.75736 q^{71} +(5.34187 + 9.25238i) q^{73} +(2.53759 + 1.46508i) q^{75} +(-11.6190 - 6.70820i) q^{79} +(5.03553 + 8.72180i) q^{81} -4.84061 q^{83} +4.47214i q^{85} +(4.13171 + 7.15634i) q^{87} +(3.86324 + 2.23044i) q^{89} +(-7.53553 + 13.0519i) q^{93} +(-13.2232 + 7.63441i) q^{95} +5.35757i q^{97} +(0.414214 - 1.30986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} + 8 q^{11} - 32 q^{15} - 24 q^{25} + 32 q^{37} + 32 q^{67} + 128 q^{71} + 24 q^{81} - 64 q^{93} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^9 + 8 * q^11 - 32 * q^15 - 24 * q^25 + 32 * q^37 + 32 * q^67 + 128 * q^71 + 24 * q^81 - 64 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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