LMFDB - Embedded newform 2156.2.q.d.901.5

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			901.5
Root			$-0.372250 - 1.20300i$ of defining polynomial
Character	$\chi$	$=$	2156.901
Dual form			2156.2.q.d.2089.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.662827 - 0.382683i) q^{3} +(-0.662827 - 0.382683i) q^{5} +(-1.20711 + 2.09077i) q^{9} +(-2.23861 + 2.44716i) q^{11} +2.42030 q^{13} -0.585786 q^{15} +(-2.92156 - 5.06030i) q^{17} +(1.71141 - 2.96425i) q^{19} +(2.12132 - 3.67423i) q^{23} +(-2.20711 - 3.82282i) q^{25} +4.14386i q^{27} -4.47214i q^{29} +(-1.05110 + 0.606854i) q^{31} +(-0.547324 + 2.47873i) q^{33} +(0.585786 - 1.01461i) q^{37} +(1.60424 - 0.926210i) q^{39} +10.6837 q^{41} -10.7967i q^{43} +(1.60021 - 0.923880i) q^{45} +(5.73800 + 3.31283i) q^{47} +(-3.87298 - 2.23607i) q^{51} +(3.53553 + 6.12372i) q^{53} +(2.42030 - 0.765367i) q^{55} -2.61972i q^{57} +(5.18889 - 2.99581i) q^{59} +(2.92156 - 5.06030i) q^{61} +(-1.60424 - 0.926210i) q^{65} +(-1.53553 - 2.65962i) q^{67} -3.24718i q^{69} +12.2426 q^{71} +(-4.63298 - 8.02455i) q^{73} +(-2.92586 - 1.68925i) q^{75} +(-11.6190 - 6.70820i) q^{79} +(-2.03553 - 3.52565i) q^{81} +11.6863 q^{83} +4.47214i q^{85} +(-1.71141 - 2.96425i) q^{87} +(0.274552 + 0.158513i) q^{89} +(-0.464466 + 0.804479i) q^{93} +(-2.26874 + 1.30986i) q^{95} +12.9343i q^{97} +(-2.41421 - 7.63441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.662827	−	0.382683i	0.382683	−	0.220942i	−0.296302	−	0.955094i	$-0.595753\pi$
$3$	0.662827	−	0.382683i	0.382683	−	0.220942i	0.678985	+	0.734152i	$0.262420\pi$
$4$		0			0
$5$	−0.662827	−	0.382683i	−0.296425	−	0.171141i	0.344411	−	0.938819i	$-0.388079\pi$
$5$	−0.662827	−	0.382683i	−0.296425	−	0.171141i	−0.640836	+	0.767678i	$0.721412\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.20711	+	2.09077i	−0.402369	+	0.696923i
$10$		0			0
$11$	−2.23861	+	2.44716i	−0.674967	+	0.737848i
$11$	−2.23861	+	2.44716i	−0.674967	+	0.737848i
$12$		0			0
$13$	2.42030			0.671271			0.335636	−	0.941992i	$-0.391049\pi$
$13$	2.42030			0.671271			0.335636	+	0.941992i	$0.391049\pi$
$14$		0			0
$15$	−0.585786			−0.151249
$16$		0			0
$17$	−2.92156	−	5.06030i	−0.708583	−	1.22730i	−0.965383	−	0.260837i	$-0.916001\pi$
$17$	−2.92156	−	5.06030i	−0.708583	−	1.22730i	0.256799	−	0.966465i	$-0.417332\pi$
$18$		0			0
$19$	1.71141	−	2.96425i	0.392625	−	0.680046i	−0.600170	−	0.799872i	$-0.704900\pi$
$19$	1.71141	−	2.96425i	0.392625	−	0.680046i	0.992795	+	0.119826i	$0.0382337\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.12132	−	3.67423i	0.442326	−	0.766131i	−0.555536	−	0.831493i	$-0.687487\pi$
$23$	2.12132	−	3.67423i	0.442326	−	0.766131i	0.997862	+	0.0653618i	$0.0208201\pi$
$24$		0			0
$25$	−2.20711	−	3.82282i	−0.441421	−	0.764564i
$26$		0			0
$27$			4.14386i			0.797486i
$28$		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
$31$	−1.05110	+	0.606854i	−0.188784	+	0.108994i	−0.591413	−	0.806369i	$-0.701430\pi$
$31$	−1.05110	+	0.606854i	−0.188784	+	0.108994i	0.402629	+	0.915363i	$0.368096\pi$
$32$		0			0
$33$	−0.547324	+	2.47873i	−0.0952769	+	0.431491i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.585786	−	1.01461i	0.0963027	−	0.166801i	−0.813849	−	0.581077i	$-0.802632\pi$
$37$	0.585786	−	1.01461i	0.0963027	−	0.166801i	0.910152	+	0.414275i	$0.135965\pi$
$38$		0			0
$39$	1.60424	−	0.926210i	0.256884	−	0.148312i
$40$		0			0
$41$	10.6837			1.66852			0.834259	−	0.551372i	$-0.185896\pi$
$41$	10.6837			1.66852			0.834259	+	0.551372i	$0.185896\pi$
$42$		0			0
$43$		−	10.7967i		−	1.64648i	−0.567694	−	0.823240i	$-0.692164\pi$
$43$		−	10.7967i		−	1.64648i	0.567694	−	0.823240i	$-0.307836\pi$
$44$		0			0
$45$	1.60021	−	0.923880i	0.238545	−	0.137724i
$46$		0			0
$47$	5.73800	+	3.31283i	0.836973	+	0.483227i	0.856234	−	0.516588i	$-0.172798\pi$
$47$	5.73800	+	3.31283i	0.836973	+	0.483227i	−0.0192611	+	0.999814i	$0.506131\pi$
$48$		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	0.999864	−	0.0164995i	$-0.00525220\pi$
$53$	3.53553	+	6.12372i	0.485643	+	0.841158i	−0.514221	+	0.857658i	$0.671919\pi$
$54$		0			0
$55$	2.42030	−	0.765367i	0.326354	−	0.103202i
$56$		0			0
$57$		−	2.61972i		−	0.346990i
$58$		0			0
$59$	5.18889	−	2.99581i	0.675536	−	0.390021i	−0.122635	−	0.992452i	$-0.539134\pi$
$59$	5.18889	−	2.99581i	0.675536	−	0.390021i	0.798171	+	0.602431i	$0.205801\pi$
$60$		0			0
$61$	2.92156	−	5.06030i	0.374068	−	0.647905i	−0.616119	−	0.787653i	$-0.711296\pi$
$61$	2.92156	−	5.06030i	0.374068	−	0.647905i	0.990187	+	0.139748i	$0.0446294\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.60424	−	0.926210i	−0.198982	−	0.114882i
$66$		0			0
$67$	−1.53553	−	2.65962i	−0.187595	−	0.324925i	0.756853	−	0.653586i	$-0.226736\pi$
$67$	−1.53553	−	2.65962i	−0.187595	−	0.324925i	−0.944448	+	0.328661i	$0.893403\pi$
$68$		0			0
$69$		−	3.24718i		−	0.390914i
$70$		0			0
$71$	12.2426			1.45293			0.726467	−	0.687201i	$-0.241161\pi$
$71$	12.2426			1.45293			0.726467	+	0.687201i	$0.241161\pi$
$72$		0			0
$73$	−4.63298	−	8.02455i	−0.542249	−	0.939203i	−0.998775	−	0.0494923i	$-0.984240\pi$
$73$	−4.63298	−	8.02455i	−0.542249	−	0.939203i	0.456526	−	0.889710i	$-0.349094\pi$
$74$		0			0
$75$	−2.92586	−	1.68925i	−0.337849	−	0.195057i
$76$		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
$81$	−2.03553	−	3.52565i	−0.226170	−	0.391739i
$82$		0			0
$83$	11.6863			1.28273			0.641367	−	0.767235i	$-0.278368\pi$
$83$	11.6863			1.28273			0.641367	+	0.767235i	$0.278368\pi$
$84$		0			0
$85$			4.47214i			0.485071i
$86$		0			0
$87$	−1.71141	−	2.96425i	−0.183483	−	0.317801i
$88$		0			0
$89$	0.274552	+	0.158513i	0.0291025	+	0.0168023i	0.514481	−	0.857502i	$-0.327985\pi$
$89$	0.274552	+	0.158513i	0.0291025	+	0.0168023i	−0.485378	+	0.874304i	$0.661318\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.464466	+	0.804479i	−0.0481629	+	0.0834206i
$94$		0			0
$95$	−2.26874	+	1.30986i	−0.232768	+	0.134389i
$96$		0			0
$97$			12.9343i			1.31328i	0.754204	+	0.656640i	$0.228023\pi$
$97$			12.9343i			1.31328i	−0.754204	+	0.656640i	$0.771977\pi$
$98$		0			0
$99$	−2.41421	−	7.63441i	−0.242638	−	0.767287i
$100$		0			0
$101$	−4.63298	−	8.02455i	−0.460998	−	0.798473i	0.538013	−	0.842937i	$-0.319175\pi$
$101$	−4.63298	−	8.02455i	−0.460998	−	0.798473i	−0.999011	+	0.0444642i	$0.985842\pi$
$102$		0			0
$103$	−9.87579	−	5.70179i	−0.973090	−	0.561814i	−0.0729135	−	0.997338i	$-0.523230\pi$
$103$	−9.87579	−	5.70179i	−0.973090	−	0.561814i	−0.900177	+	0.435524i	$0.856563\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.47723	−	3.16228i	−0.529503	−	0.305709i	0.211311	−	0.977419i	$-0.432227\pi$
$107$	−5.47723	−	3.16228i	−0.529503	−	0.305709i	−0.740814	+	0.671710i	$0.765560\pi$
$108$		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
$111$		−	0.896683i		−	0.0851094i
$112$		0			0
$113$	−6.34315			−0.596713			−0.298356	−	0.954455i	$-0.596438\pi$
$113$	−6.34315			−0.596713			−0.298356	+	0.954455i	$0.596438\pi$
$114$		0			0
$115$	−2.81214	+	1.62359i	−0.262233	+	0.151400i
$116$		0			0
$117$	−2.92156	+	5.06030i	−0.270099	+	0.467825i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.977226	−	10.9565i	−0.0888387	−	0.996046i
$122$		0			0
$123$	7.08147	−	4.08849i	0.638514	−	0.368646i
$124$		0			0
$125$			7.20533i			0.644464i
$126$		0			0
$127$		−	6.32456i		−	0.561214i	−0.959823	−	0.280607i	$-0.909464\pi$
$127$		−	6.32456i		−	0.561214i	0.959823	−	0.280607i	$-0.0905357\pi$
$128$		0			0
$129$	−4.13171	−	7.15634i	−0.363777	−	0.630081i
$130$		0			0
$131$	−0.708890	+	1.22783i	−0.0619360	+	0.107276i	−0.895331	−	0.445402i	$-0.853061\pi$
$131$	−0.708890	+	1.22783i	−0.0619360	+	0.107276i	0.833395	+	0.552678i	$0.186394\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.58579	−	2.74666i	0.136483	−	0.236395i
$136$		0			0
$137$	1.58579	+	2.74666i	0.135483	+	0.234663i	0.925782	−	0.378058i	$-0.123408\pi$
$137$	1.58579	+	2.74666i	0.135483	+	0.234663i	−0.790299	+	0.612721i	$0.790075\pi$
$138$		0			0
$139$	8.26343			0.700895			0.350447	−	0.936582i	$-0.386030\pi$
$139$	8.26343			0.700895			0.350447	+	0.936582i	$0.386030\pi$
$140$		0			0
$141$	5.07107			0.427061
$142$		0			0
$143$	−5.41812	+	5.92288i	−0.453086	+	0.495296i
$144$		0			0
$145$	−1.71141	+	2.96425i	−0.142125	+	0.246168i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.47723	−	3.16228i	−0.448712	−	0.259064i	0.258574	−	0.965991i	$-0.416747\pi$
$149$	−5.47723	−	3.16228i	−0.448712	−	0.259064i	−0.707286	+	0.706928i	$0.750081\pi$
$150$		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
$153$	14.1066			1.14045
$154$		0			0
$155$	0.928932			0.0746136
$156$		0			0
$157$	18.5396	−	10.7039i	1.47963	−	0.854262i	0.479891	−	0.877328i	$-0.340676\pi$
$157$	18.5396	−	10.7039i	1.47963	−	0.854262i	0.999734	+	0.0230662i	$0.00734284\pi$
$158$		0			0
$159$	4.68690	+	2.70598i	0.371695	+	0.214598i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.707107	−	1.22474i	0.0553849	−	0.0959294i	−0.837004	−	0.547197i	$-0.815695\pi$
$163$	0.707107	−	1.22474i	0.0553849	−	0.0959294i	0.892389	+	0.451268i	$0.149028\pi$
$164$		0			0
$165$	1.31135	−	1.43352i	0.102088	−	0.111599i
$166$		0			0
$167$	3.42282			0.264866			0.132433	−	0.991192i	$-0.457721\pi$
$167$	3.42282			0.264866			0.132433	+	0.991192i	$0.457721\pi$
$168$		0			0
$169$	−7.14214			−0.549395
$170$		0			0
$171$	4.13171	+	7.15634i	0.315960	+	0.547259i
$172$		0			0
$173$	−1.21015	+	2.09604i	−0.0920061	+	0.159359i	−0.908355	−	0.418200i	$-0.862661\pi$
$173$	−1.21015	+	2.09604i	−0.0920061	+	0.159359i	0.816349	+	0.577559i	$0.195995\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.29289	−	3.97141i	0.172344	−	0.298509i
$178$		0			0
$179$	−2.17157	−	3.76127i	−0.162311	−	0.281131i	0.773386	−	0.633935i	$-0.218561\pi$
$179$	−2.17157	−	3.76127i	−0.162311	−	0.281131i	−0.935697	+	0.352804i	$0.885228\pi$
$180$		0			0
$181$		−	18.1606i		−	1.34986i	−0.737880	−	0.674932i	$-0.764173\pi$
$181$		−	18.1606i		−	1.34986i	0.737880	−	0.674932i	$-0.235827\pi$
$182$		0			0
$183$		−	4.47214i		−	0.330590i
$184$		0			0
$185$	−0.776550	+	0.448342i	−0.0570931	+	0.0329627i
$186$		0			0
$187$	18.9236	+	4.17850i	1.38383	+	0.305562i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.65685	+	9.79796i	−0.409316	+	0.708955i	−0.994813	−	0.101719i	$-0.967566\pi$
$191$	−5.65685	+	9.79796i	−0.409316	+	0.708955i	0.585498	+	0.810674i	$0.300899\pi$
$192$		0			0
$193$	−5.47723	+	3.16228i	−0.394259	+	0.227626i	−0.684004	−	0.729478i	$-0.739763\pi$
$193$	−5.47723	+	3.16228i	−0.394259	+	0.227626i	0.289745	+	0.957104i	$0.406430\pi$
$194$		0			0
$195$	−1.41778			−0.101529
$196$		0			0
$197$			15.2688i			1.08786i	0.839131	+	0.543929i	$0.183064\pi$
$197$			15.2688i			1.08786i	−0.839131	+	0.543929i	$0.816936\pi$
$198$		0			0
$199$	−11.3623	+	6.56001i	−0.805450	+	0.465027i	−0.845373	−	0.534176i	$-0.820622\pi$
$199$	−11.3623	+	6.56001i	−0.805450	+	0.465027i	0.0399232	+	0.999203i	$0.487289\pi$
$200$		0			0
$201$	−2.03559	−	1.17525i	−0.143579	−	0.0828955i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−7.08147	−	4.08849i	−0.494591	−	0.285552i
$206$		0			0
$207$	5.12132	+	8.87039i	0.355956	+	0.616535i
$208$		0			0
$209$	3.42282	+	10.8239i	0.236762	+	0.748706i
$210$		0			0
$211$		−	3.70484i		−	0.255052i	−0.991835	−	0.127526i	$-0.959296\pi$
$211$		−	3.70484i		−	0.255052i	0.991835	−	0.127526i	$-0.0407036\pi$
$212$		0			0
$213$	8.11475	−	4.68506i	0.556014	−	0.321015i
$214$		0			0
$215$	−4.13171	+	7.15634i	−0.281781	+	0.488058i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−6.14172	−	3.54593i	−0.415019	−	0.239611i
$220$		0			0
$221$	−7.07107	−	12.2474i	−0.475651	−	0.823853i
$222$		0			0
$223$			5.80591i			0.388792i	0.980923	+	0.194396i	$0.0622748\pi$
$223$			5.80591i			0.388792i	−0.980923	+	0.194396i	$0.937725\pi$
$224$		0			0
$225$	10.6569			0.710457
$226$		0			0
$227$	7.55454	+	13.0848i	0.501412	+	0.868472i	0.999999	+	0.00163167i	$0.000519376\pi$
$227$	7.55454	+	13.0848i	0.501412	+	0.868472i	−0.498586	+	0.866840i	$0.666147\pi$
$228$		0			0
$229$	9.87579	+	5.70179i	0.652611	+	0.376785i	0.789456	−	0.613808i	$-0.210363\pi$
$229$	9.87579	+	5.70179i	0.652611	+	0.376785i	−0.136845	+	0.990592i	$0.543696\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.8877	+	8.01806i	0.909813	+	0.525281i	0.880371	−	0.474286i	$-0.157294\pi$
$233$	13.8877	+	8.01806i	0.909813	+	0.525281i	0.0294419	+	0.999566i	$0.490627\pi$
$234$		0			0
$235$	−2.53553	−	4.39167i	−0.165400	−	0.286481i
$236$		0			0
$237$	−10.2685			−0.667009
$238$		0			0
$239$		−	21.5934i		−	1.39676i	−0.715727	−	0.698380i	$-0.753905\pi$
$239$		−	21.5934i		−	1.39676i	0.715727	−	0.698380i	$-0.246095\pi$
$240$		0			0
$241$	−1.21015	−	2.09604i	−0.0779527	−	0.135018i	0.824414	−	0.565988i	$-0.191505\pi$
$241$	−1.21015	−	2.09604i	−0.0779527	−	0.135018i	−0.902366	+	0.430970i	$0.858172\pi$
$242$		0			0
$243$	−13.4645	−	7.77372i	−0.863747	−	0.498684i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.14214	−	7.17439i	0.263558	−	0.456495i
$248$		0			0
$249$	7.74597	−	4.47214i	0.490881	−	0.283410i
$250$		0			0
$251$			0.317025i			0.0200105i	0.999950	+	0.0100052i	$0.00318482\pi$
$251$			0.317025i			0.0200105i	−0.999950	+	0.0100052i	$0.996815\pi$
$252$		0			0
$253$	4.24264	+	13.4164i	0.266733	+	0.843482i
$254$		0			0
$255$	1.71141	+	2.96425i	0.107173	+	0.185629i
$256$		0			0
$257$	−23.0657	−	13.3170i	−1.43880	−	0.830691i	−0.441033	−	0.897491i	$-0.645388\pi$
$257$	−23.0657	−	13.3170i	−1.43880	−	0.830691i	−0.997766	+	0.0667993i	$0.978721\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	9.35021	+	5.39835i	0.578763	+	0.334149i
$262$		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
$265$		−	5.41196i		−	0.332454i
$266$		0			0
$267$	0.242641			0.0148494
$268$		0			0
$269$	−25.4896	+	14.7164i	−1.55413	+	0.897276i	−0.556328	+	0.830963i	$0.687790\pi$
$269$	−25.4896	+	14.7164i	−1.55413	+	0.897276i	−0.997799	+	0.0663129i	$0.978876\pi$
$270$		0			0
$271$	11.6863	−	20.2412i	0.709889	−	1.22956i	−0.255008	−	0.966939i	$-0.582078\pi$
$271$	11.6863	−	20.2412i	0.709889	−	1.22956i	0.964898	−	0.262626i	$-0.0845884\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	14.2959	+	3.15666i	0.862077	+	0.190354i
$276$		0			0
$277$	−24.1776	+	13.9590i	−1.45269	+	0.838713i	−0.998634	−	0.0522579i	$-0.983358\pi$
$277$	−24.1776	+	13.9590i	−1.45269	+	0.838713i	−0.454060	+	0.890971i	$0.650025\pi$
$278$		0			0
$279$		−	2.93015i		−	0.175424i
$280$		0			0
$281$			5.55726i			0.331518i	0.986166	+	0.165759i	$0.0530074\pi$
$281$			5.55726i			0.331518i	−0.986166	+	0.165759i	$0.946993\pi$
$282$		0			0
$283$	8.97232	+	15.5405i	0.533349	+	0.923788i	0.999241	+	0.0389462i	$0.0124001\pi$
$283$	8.97232	+	15.5405i	0.533349	+	0.923788i	−0.465892	+	0.884841i	$0.654267\pi$
$284$		0			0
$285$	−1.00252	+	1.73642i	−0.0593843	+	0.102857i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.57107	+	14.8455i	−0.504180	+	0.873266i
$290$		0			0
$291$	4.94975	+	8.57321i	0.290159	+	0.502571i
$292$		0			0
$293$	−5.84313			−0.341359			−0.170680	−	0.985327i	$-0.554596\pi$
$293$	−5.84313			−0.341359			−0.170680	+	0.985327i	$0.554596\pi$
$294$		0			0
$295$	−4.58579			−0.266995
$296$		0			0
$297$	−10.1407	−	9.27650i	−0.588423	−	0.538277i
$298$		0			0
$299$	5.13424	−	8.89276i	0.296921	−	0.514282i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.14172	−	3.54593i	−0.352833	−	0.203708i
$304$		0			0
$305$	−3.87298	+	2.23607i	−0.221766	+	0.128037i
$306$		0			0
$307$	−15.1091			−0.862321			−0.431160	−	0.902275i	$-0.641896\pi$
$307$	−15.1091			−0.862321			−0.431160	+	0.902275i	$0.641896\pi$
$308$		0			0
$309$	−8.72792			−0.496514
$310$		0			0
$311$	11.9780	−	6.91550i	0.679210	−	0.392142i	−0.120347	−	0.992732i	$-0.538401\pi$
$311$	11.9780	−	6.91550i	0.679210	−	0.392142i	0.799557	+	0.600590i	$0.205068\pi$
$312$		0			0
$313$	12.2997	+	7.10121i	0.695217	+	0.401384i	0.805564	−	0.592509i	$-0.201863\pi$
$313$	12.2997	+	7.10121i	0.695217	+	0.401384i	−0.110346	+	0.993893i	$0.535196\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.48528	+	2.57258i	−0.0834217	+	0.144491i	−0.904718	−	0.426012i	$-0.859918\pi$
$317$	−1.48528	+	2.57258i	−0.0834217	+	0.144491i	0.821296	+	0.570502i	$0.193252\pi$
$318$		0			0
$319$	10.9441	+	10.0114i	0.612749	+	0.560530i
$320$		0			0
$321$	−4.84061			−0.270176
$322$		0			0
$323$	−20.0000			−1.11283
$324$		0			0
$325$	−5.34187	−	9.25238i	−0.296313	−	0.513230i
$326$		0			0
$327$	−5.13424	+	8.89276i	−0.283924	+	0.491771i
$328$		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
$335$			2.35049i			0.128421i
$336$		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
$339$	−4.20441	+	2.42742i	−0.228352	+	0.131839i
$340$		0			0
$341$	0.867939	−	3.93073i	0.0470015	−	0.212861i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.24264	+	2.15232i	−0.0669015	+	0.115877i
$346$		0			0
$347$	0.664499	−	0.383649i	0.0356722	−	0.0205953i	−0.482058	−	0.876139i	$-0.660111\pi$
$347$	0.664499	−	0.383649i	0.0356722	−	0.0205953i	0.517730	+	0.855544i	$0.326777\pi$
$348$		0			0
$349$	−32.6385			−1.74710			−0.873548	−	0.486737i	$-0.838187\pi$
$349$	−32.6385			−1.74710			−0.873548	+	0.486737i	$0.838187\pi$
$350$		0			0
$351$			10.0294i			0.535329i
$352$		0			0
$353$	14.2410	−	8.22206i	0.757973	−	0.437616i	−0.0705942	−	0.997505i	$-0.522490\pi$
$353$	14.2410	−	8.22206i	0.757973	−	0.437616i	0.828568	+	0.559889i	$0.189156\pi$
$354$		0			0
$355$	−8.11475	−	4.68506i	−0.430686	−	0.248657i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	23.5131	+	13.5753i	1.24098	+	0.716478i	0.969293	−	0.245909i	$-0.0790863\pi$
$359$	23.5131	+	13.5753i	1.24098	+	0.716478i	0.271683	+	0.962387i	$0.412420\pi$
$360$		0			0
$361$	3.64214	+	6.30836i	0.191691	+	0.332019i
$362$		0			0
$363$	−4.84061	−	6.88830i	−0.254066	−	0.361542i
$364$		0			0
$365$			7.09185i			0.371205i
$366$		0			0
$367$	19.7045	−	11.3764i	1.02857	−	0.593842i	0.111992	−	0.993709i	$-0.464277\pi$
$367$	19.7045	−	11.3764i	1.02857	−	0.593842i	0.916573	+	0.399867i	$0.130944\pi$
$368$		0			0
$369$	−12.8964	+	22.3372i	−0.671360	+	1.16283i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.9545	+	6.32456i	0.567200	+	0.327473i	0.756030	−	0.654537i	$-0.227136\pi$
$373$	10.9545	+	6.32456i	0.567200	+	0.327473i	−0.188830	+	0.982010i	$0.560470\pi$
$374$		0			0
$375$	2.75736	+	4.77589i	0.142389	+	0.246626i
$376$		0			0
$377$		−	10.8239i		−	0.557460i
$378$		0			0
$379$	36.7279			1.88659			0.943293	−	0.331960i	$-0.107710\pi$
$379$	36.7279			1.88659			0.943293	+	0.331960i	$0.107710\pi$
$380$		0			0
$381$	−2.42030	−	4.19209i	−0.123996	−	0.214767i
$382$		0			0
$383$	26.3327	+	15.2032i	1.34554	+	0.776848i	0.987614	−	0.156902i	$-0.0501506\pi$
$383$	26.3327	+	15.2032i	1.34554	+	0.776848i	0.357926	+	0.933750i	$0.383484\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	22.5734	+	13.0328i	1.14747	+	0.662492i
$388$		0			0
$389$	−15.7782	−	27.3286i	−0.799985	−	1.38562i	−0.919625	−	0.392798i	$-0.871507\pi$
$389$	−15.7782	−	27.3286i	−0.799985	−	1.38562i	0.119640	−	0.992817i	$-0.461826\pi$
$390$		0			0
$391$	−24.7903			−1.25370
$392$		0			0
$393$			1.08512i			0.0547372i
$394$		0			0
$395$	5.13424	+	8.89276i	0.258331	+	0.447443i
$396$		0			0
$397$	−3.79662	−	2.19198i	−0.190547	−	0.110012i	0.401692	−	0.915775i	$-0.368422\pi$
$397$	−3.79662	−	2.19198i	−0.190547	−	0.110012i	−0.592239	+	0.805763i	$0.701756\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.22183	+	3.84831i	−0.110953	+	0.192176i	−0.916155	−	0.400825i	$-0.868724\pi$
$401$	−2.22183	+	3.84831i	−0.110953	+	0.192176i	0.805202	+	0.593001i	$0.202057\pi$
$402$		0			0
$403$	−2.54399	+	1.46877i	−0.126725	+	0.0731647i
$404$		0			0
$405$			3.11586i			0.154828i
$406$		0			0
$407$	1.17157	+	3.70484i	0.0580727	+	0.183642i
$408$		0			0
$409$	10.4761	+	18.1451i	0.518010	+	0.897220i	0.999781	+	0.0209225i	$0.00666032\pi$
$409$	10.4761	+	18.1451i	0.518010	+	0.897220i	−0.481771	+	0.876297i	$0.660006\pi$
$410$		0			0
$411$	2.10220	+	1.21371i	0.103694	+	0.0598678i
$412$		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
$419$		−	10.9552i		−	0.535198i	−0.963530	−	0.267599i	$-0.913770\pi$
$419$		−	10.9552i		−	0.535198i	0.963530	−	0.267599i	$-0.0862303\pi$
$420$		0			0
$421$	−35.5563			−1.73291			−0.866455	−	0.499255i	$-0.833607\pi$
$421$	−35.5563			−1.73291			−0.866455	+	0.499255i	$0.833607\pi$
$422$		0			0
$423$	−13.8528	+	7.99789i	−0.673544	+	0.388871i
$424$		0			0
$425$	−12.8964	+	22.3372i	−0.625568	+	1.08351i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.32469	+	5.99927i	−0.0639566	+	0.289647i
$430$		0			0
$431$	21.6337	−	12.4902i	1.04206	−	0.601632i	0.121641	−	0.992574i	$-0.461184\pi$
$431$	21.6337	−	12.4902i	1.04206	−	0.601632i	0.920415	+	0.390942i	$0.127851\pi$
$432$		0			0
$433$		−	21.4077i		−	1.02879i	−0.857553	−	0.514395i	$-0.828016\pi$
$433$		−	21.4077i		−	1.02879i	0.857553	−	0.514395i	$-0.171984\pi$
$434$		0			0
$435$			2.61972i			0.125606i
$436$		0			0
$437$	−7.26091	−	12.5763i	−0.347336	−	0.601604i
$438$		0			0
$439$	14.8154	−	25.6611i	0.707103	−	1.22474i	−0.258825	−	0.965924i	$-0.583335\pi$
$439$	14.8154	−	25.6611i	0.707103	−	1.22474i	0.965927	−	0.258813i	$-0.0833315\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.3137	+	17.8639i	−0.490019	+	0.848738i	−0.999934	−	0.0114869i	$-0.996344\pi$
$443$	−10.3137	+	17.8639i	−0.490019	+	0.848738i	0.509915	+	0.860225i	$0.329677\pi$
$444$		0			0
$445$	−0.121320	−	0.210133i	−0.00575114	−	0.00996126i
$446$		0			0
$447$	−4.84061			−0.228953
$448$		0			0
$449$	−14.5858			−0.688346			−0.344173	−	0.938906i	$-0.611841\pi$
$449$	−14.5858			−0.688346			−0.344173	+	0.938906i	$0.611841\pi$
$450$		0			0
$451$	−23.9167	+	26.1448i	−1.12620	+	1.23111i
$452$		0			0
$453$	−1.71141	+	2.96425i	−0.0804092	+	0.139273i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	26.4464	+	15.2688i	1.23711	+	0.714246i	0.968502	−	0.249004i	$-0.0801033\pi$
$457$	26.4464	+	15.2688i	1.23711	+	0.714246i	0.268607	+	0.963250i	$0.413437\pi$
$458$		0			0
$459$	20.9692	−	12.1065i	0.978757	−	0.565085i
$460$		0			0
$461$	−10.6837			−0.497591			−0.248796	−	0.968556i	$-0.580035\pi$
$461$	−10.6837			−0.497591			−0.248796	+	0.968556i	$0.580035\pi$
$462$		0			0
$463$	15.0711			0.700412			0.350206	−	0.936673i	$-0.386112\pi$
$463$	15.0711			0.700412			0.350206	+	0.936673i	$0.386112\pi$
$464$		0			0
$465$	0.615721	−	0.355487i	0.0285534	−	0.0164853i
$466$		0			0
$467$	2.69841	+	1.55793i	0.124868	+	0.0720924i	0.561133	−	0.827726i	$-0.310366\pi$
$467$	2.69841	+	1.55793i	0.124868	+	0.0720924i	−0.436265	+	0.899818i	$0.643699\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	8.19239	−	14.1896i	0.377485	−	0.653824i
$472$		0			0
$473$	26.4213	+	24.1696i	1.21485	+	1.11132i
$474$		0			0
$475$	−15.1091			−0.693252
$476$		0			0
$477$	−17.0711			−0.781631
$478$		0			0
$479$	18.2383	+	31.5896i	0.833328	+	1.44337i	0.895385	+	0.445294i	$0.146901\pi$
$479$	18.2383	+	31.5896i	0.833328	+	1.44337i	−0.0620567	+	0.998073i	$0.519766\pi$
$480$		0			0
$481$	1.41778	−	2.45567i	0.0646452	−	0.111969i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.94975	−	8.57321i	0.224756	−	0.389290i
$486$		0			0
$487$	−16.3640	−	28.3432i	−0.741522	−	1.28435i	−0.951802	−	0.306712i	$-0.900771\pi$
$487$	−16.3640	−	28.3432i	−0.741522	−	1.28435i	0.210280	−	0.977641i	$-0.432562\pi$
$488$		0			0
$489$		−	1.08239i		−	0.0489475i
$490$		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
$493$	−22.6303	+	13.0656i	−1.01922	+	0.588446i
$494$		0			0
$495$	−1.32136	+	5.98418i	−0.0593906	+	0.268969i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	5.05025	−	8.74729i	0.226080	−	0.391583i	−0.730563	−	0.682846i	$-0.760742\pi$
$499$	5.05025	−	8.74729i	0.226080	−	0.391583i	0.956643	+	0.291263i	$0.0940755\pi$
$500$		0			0
$501$	2.26874	−	1.30986i	0.101360	−	0.0585202i
$502$		0			0
$503$	−14.5218			−0.647496			−0.323748	−	0.946143i	$-0.604943\pi$
$503$	−14.5218			−0.647496			−0.323748	+	0.946143i	$0.604943\pi$
$504$		0			0
$505$			7.09185i			0.315583i
$506$		0			0
$507$	−4.73400	+	2.73318i	−0.210244	+	0.121385i
$508$		0			0
$509$	−24.1639	−	13.9510i	−1.07105	−	0.618369i	−0.142580	−	0.989783i	$-0.545540\pi$
$509$	−24.1639	−	13.9510i	−1.07105	−	0.618369i	−0.928467	+	0.371414i	$0.878873\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	12.2834	+	7.09185i	0.542328	+	0.313113i
$514$		0			0
$515$	4.36396	+	7.55860i	0.192299	+	0.333072i
$516$		0			0
$517$	−20.9522	+	6.62567i	−0.921477	+	0.291397i
$518$		0			0
$519$			1.85242i			0.0813122i
$520$		0			0
$521$	36.1614	−	20.8778i	1.58426	−	0.914674i	0.590034	−	0.807379i	$-0.299114\pi$
$521$	36.1614	−	20.8778i	1.58426	−	0.914674i	0.994227	−	0.107295i	$-0.0342189\pi$
$522$		0			0
$523$	22.3700	−	38.7460i	0.978171	−	1.69424i	0.309125	−	0.951021i	$-0.399964\pi$
$523$	22.3700	−	38.7460i	0.978171	−	1.69424i	0.669046	−	0.743221i	$-0.266703\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.14172	+	3.54593i	0.267538	+	0.154463i
$528$		0			0
$529$	2.50000	+	4.33013i	0.108696	+	0.188266i
$530$		0			0
$531$			14.4650i			0.627730i
$532$		0			0
$533$	25.8579			1.12003
$534$		0			0
$535$	2.42030	+	4.19209i	0.104639	+	0.181240i
$536$		0			0
$537$	−2.87875	−	1.66205i	−0.124227	−	0.0717227i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−20.9692	−	12.1065i	−0.901535	−	0.520501i	−0.0238368	−	0.999716i	$-0.507588\pi$
$541$	−20.9692	−	12.1065i	−0.901535	−	0.520501i	−0.877698	+	0.479215i	$0.840922\pi$
$542$		0			0
$543$	−6.94975	−	12.0373i	−0.298242	−	0.516571i
$544$		0			0
$545$	10.2685			0.439853
$546$		0			0
$547$			39.4819i			1.68813i	0.536245	+	0.844063i	$0.319842\pi$
$547$			39.4819i			1.68813i	−0.536245	+	0.844063i	$0.680158\pi$
$548$		0			0
$549$	7.05328	+	12.2166i	0.301027	+	0.521393i
$550$		0			0
$551$	−13.2565	−	7.65367i	−0.564748	−	0.326057i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.343146	+	0.594346i	−0.0145657	+	0.0252286i
$556$		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
$559$		−	26.1313i		−	1.10523i
$560$		0			0
$561$	14.1421	−	4.47214i	0.597081	−	0.188814i
$562$		0			0
$563$	7.55454	+	13.0848i	0.318386	+	0.551461i	0.980151	−	0.198250i	$-0.0635259\pi$
$563$	7.55454	+	13.0848i	0.318386	+	0.551461i	−0.661766	+	0.749711i	$0.730193\pi$
$564$		0			0
$565$	4.20441	+	2.42742i	0.176881	+	0.102122i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.0359	+	10.4130i	0.756105	+	0.436537i	0.827896	−	0.560882i	$-0.189538\pi$
$569$	18.0359	+	10.4130i	0.756105	+	0.436537i	−0.0717905	+	0.997420i	$0.522871\pi$
$570$		0			0
$571$	−13.2232	+	7.63441i	−0.553373	+	0.319490i	−0.750481	−	0.660891i	$-0.770178\pi$
$571$	−13.2232	+	7.63441i	−0.553373	+	0.319490i	0.197108	+	0.980382i	$0.436845\pi$
$572$		0			0
$573$			8.65914i			0.361741i
$574$		0			0
$575$	−18.7279			−0.781008
$576$		0			0
$577$	−22.7441	+	13.1313i	−0.946848	+	0.546663i	−0.892100	−	0.451838i	$-0.850769\pi$
$577$	−22.7441	+	13.1313i	−0.946848	+	0.546663i	−0.0547473	+	0.998500i	$0.517435\pi$
$578$		0			0
$579$	−2.42030	+	4.19209i	−0.100584	+	0.174217i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−22.9005	−	5.05662i	−0.948440	−	0.209424i
$584$		0			0
$585$	3.87298	−	2.23607i	0.160128	−	0.0924500i
$586$		0			0
$587$		−	13.5684i		−	0.560026i	−0.959996	−	0.280013i	$-0.909661\pi$
$587$		−	13.5684i		−	0.560026i	0.959996	−	0.280013i	$-0.0903388\pi$
$588$		0			0
$589$			4.15431i			0.171175i
$590$		0			0
$591$	5.84313	+	10.1206i	0.240354	+	0.416306i
$592$		0			0
$593$	−17.7370	+	30.7214i	−0.728372	+	1.26158i	0.229199	+	0.973380i	$0.426389\pi$
$593$	−17.7370	+	30.7214i	−0.728372	+	1.26158i	−0.957571	+	0.288197i	$0.906944\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.02082	+	8.69631i	−0.205488	+	0.355916i
$598$		0			0
$599$	19.1924	+	33.2422i	0.784180	+	1.35824i	0.929488	+	0.368853i	$0.120249\pi$
$599$	19.1924	+	33.2422i	0.784180	+	1.35824i	−0.145308	+	0.989386i	$0.546417\pi$
$600$		0			0
$601$	−22.3700			−0.912491			−0.456245	−	0.889854i	$-0.650806\pi$
$601$	−22.3700			−0.912491			−0.456245	+	0.889854i	$0.650806\pi$
$602$		0			0
$603$	7.41421			0.301930
$604$		0			0
$605$	−3.54514	+	7.63624i	−0.144131	+	0.310457i
$606$		0			0
$607$	0.708890	−	1.22783i	0.0287730	−	0.0498362i	−0.851280	−	0.524711i	$-0.824173\pi$
$607$	0.708890	−	1.22783i	0.0287730	−	0.0498362i	0.880053	+	0.474875i	$0.157507\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	13.8877	+	8.01806i	0.561836	+	0.324376i
$612$		0			0
$613$	−4.81273	+	2.77863i	−0.194384	+	0.112228i	−0.594033	−	0.804440i	$-0.702465\pi$
$613$	−4.81273	+	2.77863i	−0.194384	+	0.112228i	0.399649	+	0.916668i	$0.369132\pi$
$614$		0			0
$615$	−6.25839			−0.252362
$616$		0			0
$617$	6.14214			0.247273			0.123637	−	0.992328i	$-0.460544\pi$
$617$	6.14214			0.247273			0.123637	+	0.992328i	$0.460544\pi$
$618$		0			0
$619$	27.5918	−	15.9301i	1.10901	−	0.640286i	0.170435	−	0.985369i	$-0.445483\pi$
$619$	27.5918	−	15.9301i	1.10901	−	0.640286i	0.938572	+	0.345083i	$0.112149\pi$
$620$		0			0
$621$	15.2255	+	8.79045i	0.610979	+	0.352749i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.27817	+	14.3382i	−0.331127	+	0.573529i
$626$		0			0
$627$	6.41088	+	5.86453i	0.256026	+	0.234207i
$628$		0			0
$629$	−6.84565			−0.272954
$630$		0			0
$631$	−46.9706			−1.86987			−0.934934	−	0.354821i	$-0.884542\pi$
$631$	−46.9706			−1.86987			−0.934934	+	0.354821i	$0.884542\pi$
$632$		0			0
$633$	−1.41778	−	2.45567i	−0.0563517	−	0.0976040i
$634$		0			0
$635$	−2.42030	+	4.19209i	−0.0960468	+	0.166358i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−14.7782	+	25.5965i	−0.584616	+	1.01258i
$640$		0			0
$641$	6.41421	+	11.1097i	0.253346	+	0.438808i	0.964445	−	0.264284i	$-0.0851355\pi$
$641$	6.41421	+	11.1097i	0.253346	+	0.438808i	−0.711099	+	0.703092i	$0.751802\pi$
$642$		0			0
$643$			17.0012i			0.670464i	0.942136	+	0.335232i	$0.108815\pi$
$643$			17.0012i			0.670464i	−0.942136	+	0.335232i	$0.891185\pi$
$644$		0			0
$645$			6.32456i			0.249029i
$646$		0			0
$647$	−16.1158	+	9.30445i	−0.633577	+	0.365796i	−0.782136	−	0.623108i	$-0.785870\pi$
$647$	−16.1158	+	9.30445i	−0.633577	+	0.365796i	0.148559	+	0.988904i	$0.452536\pi$
$648$		0			0
$649$	−4.28469	+	19.4045i	−0.168189	+	0.761695i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.60660	+	7.97887i	−0.180270	+	0.312237i	−0.941973	−	0.335690i	$-0.891031\pi$
$653$	−4.60660	+	7.97887i	−0.180270	+	0.312237i	0.761702	+	0.647927i	$0.224364\pi$
$654$		0			0
$655$	0.939743	−	0.542561i	0.0367188	−	0.0211996i
$656$		0			0
$657$	22.3700			0.872736
$658$		0			0
$659$		−	27.1506i		−	1.05764i	−0.848734	−	0.528819i	$-0.822635\pi$
$659$		−	27.1506i		−	1.05764i	0.848734	−	0.528819i	$-0.177365\pi$
$660$		0			0
$661$	10.4249	−	6.01882i	0.405481	−	0.234105i	−0.283365	−	0.959012i	$-0.591451\pi$
$661$	10.4249	−	6.01882i	0.405481	−	0.234105i	0.688846	+	0.724907i	$0.258117\pi$
$662$		0			0
$663$	−9.37379	−	5.41196i	−0.364048	−	0.210183i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−16.4317	−	9.48683i	−0.636237	−	0.367332i
$668$		0			0
$669$	2.22183	+	3.84831i	0.0859007	+	0.148784i
$670$		0			0
$671$	5.84313	+	18.4776i	0.225571	+	0.713319i
$672$		0			0
$673$			32.3901i			1.24855i	0.781206	+	0.624273i	$0.214605\pi$
$673$			32.3901i			1.24855i	−0.781206	+	0.624273i	$0.785395\pi$
$674$		0			0
$675$	15.8412	−	9.14594i	0.609729	−	0.352027i
$676$		0			0
$677$	1.91904	−	3.32388i	0.0737548	−	0.127747i	−0.826789	−	0.562512i	$-0.809835\pi$
$677$	1.91904	−	3.32388i	0.0737548	−	0.127747i	0.900544	+	0.434765i	$0.143168\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	10.0147	+	5.78199i	0.383764	+	0.221567i
$682$		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
$685$		−	2.42742i		−	0.0927468i
$686$		0			0
$687$	8.72792			0.332991
$688$		0			0
$689$	8.55706	+	14.8213i	0.325998	+	0.564645i
$690$		0			0
$691$	36.2556	+	20.9322i	1.37923	+	0.796299i	0.992067	−	0.125713i	$-0.0401218\pi$
$691$	36.2556	+	20.9322i	1.37923	+	0.796299i	0.387163	+	0.922011i	$0.373455\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.47723	−	3.16228i	−0.207763	−	0.119952i
$696$		0			0
$697$	−31.2132	−	54.0629i	−1.18228	−	2.04778i
$698$		0			0
$699$	12.2735			0.464227
$700$		0			0
$701$			16.0361i			0.605676i	0.953042	+	0.302838i	$0.0979341\pi$
$701$			16.0361i			0.605676i	−0.953042	+	0.302838i	$0.902066\pi$
$702$		0			0
$703$	−2.00504	−	3.47284i	−0.0756217	−	0.130981i
$704$		0			0
$705$	−3.36124	−	1.94061i	−0.126592	−	0.0730877i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	19.9203	−	34.5030i	0.748123	−	1.29579i	−0.200598	−	0.979674i	$-0.564289\pi$
$709$	19.9203	−	34.5030i	0.748123	−	1.29579i	0.948721	−	0.316113i	$-0.102378\pi$
$710$		0			0
$711$	28.0506	−	16.1950i	1.05198	−	0.607361i
$712$		0			0
$713$			5.14933i			0.192844i
$714$		0			0
$715$	5.85786	−	1.85242i	0.219072	−	0.0692766i
$716$		0			0
$717$	−8.26343	−	14.3127i	−0.308603	−	0.534517i
$718$		0			0
$719$	−33.2161	−	19.1773i	−1.23875	−	0.715193i	−0.269911	−	0.962885i	$-0.586994\pi$
$719$	−33.2161	−	19.1773i	−1.23875	−	0.715193i	−0.968839	+	0.247693i	$0.920328\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.60424	−	0.926210i	−0.0596624	−	0.0344461i
$724$		0			0
$725$	−17.0962	+	9.87048i	−0.634936	+	0.366580i
$726$		0			0
$727$		−	7.89377i		−	0.292764i	−0.989228	−	0.146382i	$-0.953237\pi$
$727$		−	7.89377i		−	0.292764i	0.989228	−	0.146382i	$-0.0467628\pi$
$728$		0			0
$729$	0.313708			0.0116188
$730$		0			0
$731$	−54.6345	+	31.5432i	−2.02073	+	1.16667i
$732$		0			0
$733$	14.3142	−	24.7929i	0.528707	−	0.915747i	−0.470733	−	0.882276i	$-0.656011\pi$
$733$	14.3142	−	24.7929i	0.528707	−	0.915747i	0.999440	−	0.0334709i	$-0.0106561\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.94600	+	2.19616i	0.366366	+	0.0808967i
$738$		0			0
$739$	−18.7004	+	10.7967i	−0.687906	+	0.397163i	−0.802827	−	0.596212i	$-0.796672\pi$
$739$	−18.7004	+	10.7967i	−0.687906	+	0.397163i	0.114921	+	0.993375i	$0.463338\pi$
$740$		0			0
$741$		−	6.34051i		−	0.232924i
$742$		0			0
$743$			25.2982i			0.928102i	0.885809	+	0.464051i	$0.153605\pi$
$743$			25.2982i			0.928102i	−0.885809	+	0.464051i	$0.846395\pi$
$744$		0			0
$745$	2.42030	+	4.19209i	0.0886730	+	0.153586i
$746$		0			0
$747$	−14.1066	+	24.4333i	−0.516132	+	0.893967i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	11.0503	−	19.1396i	0.403229	−	0.698414i	−0.590884	−	0.806756i	$-0.701221\pi$
$751$	11.0503	−	19.1396i	0.403229	−	0.698414i	0.994114	+	0.108343i	$0.0345543\pi$
$752$		0			0
$753$	0.121320	+	0.210133i	0.00442116	+	0.00765767i
$754$		0			0
$755$	3.42282			0.124569
$756$		0			0
$757$	10.1005			0.367109			0.183555	−	0.983010i	$-0.441240\pi$
$757$	10.1005			0.367109			0.183555	+	0.983010i	$0.441240\pi$
$758$		0			0
$759$	7.94637	+	7.26917i	0.288435	+	0.263854i
$760$		0			0
$761$	−13.6053	+	23.5651i	−0.493192	+	0.854233i	−0.999969	−	0.00784391i	$-0.997503\pi$
$761$	−13.6053	+	23.5651i	−0.493192	+	0.854233i	0.506778	+	0.862077i	$0.330837\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−9.35021	−	5.39835i	−0.338058	−	0.195178i
$766$		0			0
$767$	12.5587	−	7.25077i	0.453468	−	0.261810i
$768$		0			0
$769$	−23.7878			−0.857809			−0.428904	−	0.903350i	$-0.641100\pi$
$769$	−23.7878			−0.857809			−0.428904	+	0.903350i	$0.641100\pi$
$770$		0			0
$771$	−20.3848			−0.734140
$772$		0			0
$773$	17.2140	−	9.93850i	0.619144	−	0.357463i	−0.157391	−	0.987536i	$-0.550308\pi$
$773$	17.2140	−	9.93850i	0.619144	−	0.357463i	0.776536	+	0.630073i	$0.216975\pi$
$774$		0			0
$775$	4.63979	+	2.67878i	0.166666	+	0.0962248i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.2843	−	31.6693i	0.655102	−	1.13467i
$780$		0			0
$781$	−27.4065	+	29.9598i	−0.980683	+	1.07204i
$782$		0			0
$783$	18.5319			0.662276
$784$		0			0
$785$	−16.3848			−0.584798
$786$		0			0
$787$	−23.3725	−	40.4824i	−0.833140	−	1.44304i	−0.895536	−	0.444989i	$-0.853207\pi$
$787$	−23.3725	−	40.4824i	−0.833140	−	1.44304i	0.0623959	−	0.998051i	$-0.480126\pi$
$788$		0			0
$789$	10.2685	−	17.7855i	0.365567	−	0.633181i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	7.07107	−	12.2474i	0.251101	−	0.434920i
$794$		0			0
$795$	−2.07107	−	3.58719i	−0.0734532	−	0.127225i
$796$		0			0
$797$		−	28.2417i		−	1.00037i	−0.865918	−	0.500185i	$-0.833265\pi$
$797$		−	28.2417i		−	1.00037i	0.865918	−	0.500185i	$-0.166735\pi$
$798$		0			0
$799$		−	38.7146i		−	1.36963i
$800$		0			0
$801$	−0.662827	+	0.382683i	−0.0234198	+	0.0135215i
$802$		0			0
$803$	30.0088	+	6.62621i	1.05899	+	0.233834i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11.2635	+	19.5089i	−0.396492	+	0.686745i
$808$		0			0
$809$	19.6402	−	11.3393i	0.690511	−	0.398667i	−0.113292	−	0.993562i	$-0.536140\pi$
$809$	19.6402	−	11.3393i	0.690511	−	0.398667i	0.803804	+	0.594895i	$0.202806\pi$
$810$		0			0
$811$	42.7349			1.50063			0.750313	−	0.661083i	$-0.229903\pi$
$811$	42.7349			1.50063			0.750313	+	0.661083i	$0.229903\pi$
$812$		0			0
$813$		−	17.8885i		−	0.627379i
$814$		0			0
$815$	−0.937379	+	0.541196i	−0.0328350	+	0.0189573i
$816$		0			0
$817$	−32.0041	−	18.4776i	−1.11968	−	0.646449i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.5522	−	8.40171i	−0.507875	−	0.293222i	0.224085	−	0.974570i	$-0.428061\pi$
$821$	−14.5522	−	8.40171i	−0.507875	−	0.293222i	−0.731960	+	0.681348i	$0.761394\pi$
$822$		0			0
$823$	1.82843	+	3.16693i	0.0637350	+	0.110392i	0.896132	−	0.443787i	$-0.146365\pi$
$823$	1.82843	+	3.16693i	0.0637350	+	0.110392i	−0.832397	+	0.554180i	$0.813032\pi$
$824$		0			0
$825$	10.6837	−	3.37849i	0.371960	−	0.117624i
$826$		0			0
$827$		−	9.71157i		−	0.337704i	−0.985641	−	0.168852i	$-0.945994\pi$
$827$		−	9.71157i		−	0.337704i	0.985641	−	0.168852i	$-0.0540060\pi$
$828$		0			0
$829$	35.6123	−	20.5608i	1.23687	−	0.714106i	0.268415	−	0.963303i	$-0.413500\pi$
$829$	35.6123	−	20.5608i	1.23687	−	0.714106i	0.968453	+	0.249198i	$0.0801670\pi$
$830$		0			0
$831$	−10.6837	+	18.5048i	−0.370615	+	0.641923i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.26874	−	1.30986i	−0.0785130	−	0.0453295i
$836$		0			0
$837$	−2.51472	−	4.35562i	−0.0869214	−	0.150552i
$838$		0			0
$839$			3.19278i			0.110227i	0.998480	+	0.0551136i	$0.0175521\pi$
$839$			3.19278i			0.110227i	−0.998480	+	0.0551136i	$0.982448\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$		0			0
$843$	2.12667	+	3.68350i	0.0732464	+	0.126867i
$844$		0			0
$845$	4.73400	+	2.73318i	0.162855	+	0.0940241i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	11.8942	+	6.86712i	0.408208	+	0.235679i
$850$		0			0
$851$	−2.48528	−	4.30463i	−0.0851943	−	0.147561i
$852$		0			0
$853$	−14.6938			−0.503107			−0.251553	−	0.967843i	$-0.580941\pi$
$853$	−14.6938			−0.503107			−0.251553	+	0.967843i	$0.580941\pi$
$854$		0			0
$855$		−	6.32456i		−	0.216295i
$856$		0			0
$857$	−16.0256	−	27.7572i	−0.547424	−	0.948166i	−0.998450	−	0.0556554i	$-0.982275\pi$
$857$	−16.0256	−	27.7572i	−0.547424	−	0.948166i	0.451026	−	0.892511i	$-0.351058\pi$
$858$		0			0
$859$	1.92186	+	1.10959i	0.0655732	+	0.0378587i	0.532428	−	0.846475i	$-0.321280\pi$
$859$	1.92186	+	1.10959i	0.0655732	+	0.0378587i	−0.466855	+	0.884334i	$0.654613\pi$
$860$		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
$865$	1.60424	−	0.926210i	0.0545459	−	0.0314921i
$866$		0			0
$867$			13.1200i			0.445579i
$868$		0			0
$869$	42.4264	−	13.4164i	1.43922	−	0.455120i
$870$		0			0
$871$	−3.71646	−	6.43709i	−0.125927	−	0.218113i
$872$		0			0
$873$	−27.0427	−	15.6131i	−0.915256	−	0.528423i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−34.4676	−	19.8999i	−1.16389	−	0.671971i	−0.211655	−	0.977344i	$-0.567885\pi$
$877$	−34.4676	−	19.8999i	−1.16389	−	0.671971i	−0.952233	+	0.305373i	$0.901219\pi$
$878$		0			0
$879$	−3.87298	+	2.23607i	−0.130632	+	0.0754207i
$880$		0			0
$881$			20.4023i			0.687370i	0.939085	+	0.343685i	$0.111675\pi$
$881$			20.4023i			0.687370i	−0.939085	+	0.343685i	$0.888325\pi$
$882$		0			0
$883$	−22.2843			−0.749925			−0.374963	−	0.927040i	$-0.622344\pi$
$883$	−22.2843			−0.749925			−0.374963	+	0.927040i	$0.622344\pi$
$884$		0			0
$885$	−3.03958	+	1.75490i	−0.102174	+	0.0589905i
$886$		0			0
$887$	−10.9774	+	19.0134i	−0.368584	+	0.638406i	−0.989344	−	0.145594i	$-0.953491\pi$
$887$	−10.9774	+	19.0134i	−0.368584	+	0.638406i	0.620761	+	0.784000i	$0.286824\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	13.1846	+	2.91128i	0.441701	+	0.0975314i
$892$		0			0
$893$	19.6402	−	11.3393i	0.657233	−	0.379454i
$894$		0			0
$895$			3.32410i			0.111112i
$896$		0			0
$897$		−	7.85915i		−	0.262409i
$898$		0			0
$899$	2.71393	+	4.70067i	0.0905148	+	0.156776i
$900$		0			0
$901$	20.6586	−	35.7817i	0.688237	−	1.19206i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.94975	+	12.0373i	−0.231017	+	0.400134i
$906$		0			0
$907$	23.5355	+	40.7647i	0.781485	+	1.35357i	0.931077	+	0.364823i	$0.118871\pi$
$907$	23.5355	+	40.7647i	0.781485	+	1.35357i	−0.149592	+	0.988748i	$0.547796\pi$
$908$		0			0
$909$	22.3700			0.741966
$910$		0			0
$911$	49.6985			1.64658			0.823292	−	0.567618i	$-0.192135\pi$
$911$	49.6985			1.64658			0.823292	+	0.567618i	$0.192135\pi$
$912$		0			0
$913$	−26.1610	+	28.5982i	−0.865803	+	0.946462i
$914$		0			0
$915$	−1.71141	+	2.96425i	−0.0565775	+	0.0979952i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−36.4611	−	21.0508i	−1.20274	−	0.694403i	−0.241577	−	0.970382i	$-0.577665\pi$
$919$	−36.4611	−	21.0508i	−1.20274	−	0.694403i	−0.961164	+	0.275979i	$0.910998\pi$
$920$		0			0
$921$	−10.0147	+	5.78199i	−0.329996	+	0.190523i
$922$		0			0
$923$	29.6309			0.975313
$924$		0			0
$925$	−5.17157			−0.170040
$926$		0			0
$927$	23.8423	−	13.7653i	0.783083	−	0.452113i
$928$		0			0
$929$	41.3308	+	23.8624i	1.35602	+	0.782898i	0.989085	−	0.147348i	$-0.0470737\pi$
$929$	41.3308	+	23.8624i	1.35602	+	0.782898i	0.366935	+	0.930246i	$0.380407\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	5.29289	−	9.16756i	0.173282	−	0.300132i
$934$		0			0
$935$	−10.9441	−	10.0114i	−0.357909	−	0.327407i
$936$		0			0
$937$	15.5243			0.507158			0.253579	−	0.967315i	$-0.418392\pi$
$937$	15.5243			0.507158			0.253579	+	0.967315i	$0.418392\pi$
$938$		0			0
$939$	10.8701			0.354731
$940$		0			0
$941$	−4.92661	−	8.53314i	−0.160603	−	0.278172i	0.774482	−	0.632596i	$-0.218010\pi$
$941$	−4.92661	−	8.53314i	−0.160603	−	0.278172i	−0.935085	+	0.354423i	$0.884677\pi$
$942$		0			0
$943$	22.6636	−	39.2545i	0.738029	−	1.27830i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.4853	+	35.4815i	−0.665682	+	1.15300i	0.313418	+	0.949615i	$0.398526\pi$
$947$	−20.4853	+	35.4815i	−0.665682	+	1.15300i	−0.979100	+	0.203380i	$0.934807\pi$
$948$		0			0
$949$	−11.2132	−	19.4218i	−0.363996	−	0.630460i
$950$		0			0
$951$			2.27357i			0.0737256i
$952$		0			0
$953$		−	38.3968i		−	1.24379i	−0.783099	−	0.621897i	$-0.786362\pi$
$953$		−	38.3968i		−	1.24379i	0.783099	−	0.621897i	$-0.213638\pi$
$954$		0			0
$955$	7.49903	−	4.32957i	0.242663	−	0.140102i
$956$		0			0
$957$	11.0852	+	2.44771i	0.358334	+	0.0791232i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14.7635	+	25.5711i	−0.476241	+	0.824873i
$962$		0			0
$963$	13.2232	−	7.63441i	0.426111	−	0.246016i
$964$		0			0
$965$	4.84061			0.155825
$966$		0			0
$967$			17.1212i			0.550582i	0.961361	+	0.275291i	$0.0887742\pi$
$967$			17.1212i			0.550582i	−0.961361	+	0.275291i	$0.911226\pi$
$968$		0			0
$969$	−13.2565	+	7.65367i	−0.425862	+	0.245871i
$970$		0			0
$971$	−26.1995	−	15.1263i	−0.840782	−	0.485426i	0.0167478	−	0.999860i	$-0.494669\pi$
$971$	−26.1995	−	15.1263i	−0.840782	−	0.485426i	−0.857530	+	0.514434i	$0.828002\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.08147	−	4.08849i	−0.226788	−	0.130936i
$976$		0			0
$977$	8.60660	+	14.9071i	0.275350	+	0.476919i	0.970223	−	0.242212i	$-0.0778731\pi$
$977$	8.60660	+	14.9071i	0.275350	+	0.476919i	−0.694874	+	0.719132i	$0.744540\pi$
$978$		0			0
$979$	−1.00252	+	0.317025i	−0.0320407	+	0.0101322i
$980$		0			0
$981$		−	32.3901i		−	1.03414i
$982$		0			0
$983$	45.8569	−	26.4755i	1.46261	−	0.844437i	0.463476	−	0.886109i	$-0.346602\pi$
$983$	45.8569	−	26.4755i	1.46261	−	0.844437i	0.999131	+	0.0416728i	$0.0132687\pi$
$984$		0			0
$985$	5.84313	−	10.1206i	0.186178	−	0.322469i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−39.6696	−	22.9032i	−1.26142	−	0.728281i
$990$		0			0
$991$	7.77817	+	13.4722i	0.247082	+	0.427958i	0.962715	−	0.270518i	$-0.0871950\pi$
$991$	7.77817	+	13.4722i	0.247082	+	0.427958i	−0.715633	+	0.698476i	$0.753862\pi$
$992$		0			0
$993$			4.59220i			0.145729i
$994$		0			0
$995$	10.0416			0.318341
$996$		0			0
$997$	−13.8989	−	24.0736i	−0.440183	−	0.762420i	0.557519	−	0.830164i	$-0.311753\pi$
$997$	−13.8989	−	24.0736i	−0.440183	−	0.762420i	−0.997703	+	0.0677439i	$0.978420\pi$
$998$		0			0
$999$	4.20441	+	2.42742i	0.133022	+	0.0768001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2156.2.q.d.901.5		16
7.2	even	3		2156.2.c.a.1077.5	yes	8
7.3	odd	6	inner	2156.2.q.d.2089.6		16
7.4	even	3	inner	2156.2.q.d.2089.4		16
7.5	odd	6		2156.2.c.a.1077.3	✓	8
7.6	odd	2	inner	2156.2.q.d.901.3		16
11.10	odd	2	inner	2156.2.q.d.901.6		16
77.10	even	6	inner	2156.2.q.d.2089.5		16
77.32	odd	6	inner	2156.2.q.d.2089.3		16
77.54	even	6		2156.2.c.a.1077.4	yes	8
77.65	odd	6		2156.2.c.a.1077.6	yes	8
77.76	even	2	inner	2156.2.q.d.901.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2156.2.c.a.1077.3	✓	8	7.5	odd	6
2156.2.c.a.1077.4	yes	8	77.54	even	6
2156.2.c.a.1077.5	yes	8	7.2	even	3
2156.2.c.a.1077.6	yes	8	77.65	odd	6
2156.2.q.d.901.3		16	7.6	odd	2	inner
2156.2.q.d.901.4		16	77.76	even	2	inner
2156.2.q.d.901.5		16	1.1	even	1	trivial
2156.2.q.d.901.6		16	11.10	odd	2	inner
2156.2.q.d.2089.3		16	77.32	odd	6	inner
2156.2.q.d.2089.4		16	7.4	even	3	inner
2156.2.q.d.2089.5		16	77.10	even	6	inner
2156.2.q.d.2089.6		16	7.3	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)

\(f(q)\)	\(=\)	\(q+(0.662827 - 0.382683i) q^{3} +(-0.662827 - 0.382683i) q^{5} +(-1.20711 + 2.09077i) q^{9} +(-2.23861 + 2.44716i) q^{11} +2.42030 q^{13} -0.585786 q^{15} +(-2.92156 - 5.06030i) q^{17} +(1.71141 - 2.96425i) q^{19} +(2.12132 - 3.67423i) q^{23} +(-2.20711 - 3.82282i) q^{25} +4.14386i q^{27} -4.47214i q^{29} +(-1.05110 + 0.606854i) q^{31} +(-0.547324 + 2.47873i) q^{33} +(0.585786 - 1.01461i) q^{37} +(1.60424 - 0.926210i) q^{39} +10.6837 q^{41} -10.7967i q^{43} +(1.60021 - 0.923880i) q^{45} +(5.73800 + 3.31283i) q^{47} +(-3.87298 - 2.23607i) q^{51} +(3.53553 + 6.12372i) q^{53} +(2.42030 - 0.765367i) q^{55} -2.61972i q^{57} +(5.18889 - 2.99581i) q^{59} +(2.92156 - 5.06030i) q^{61} +(-1.60424 - 0.926210i) q^{65} +(-1.53553 - 2.65962i) q^{67} -3.24718i q^{69} +12.2426 q^{71} +(-4.63298 - 8.02455i) q^{73} +(-2.92586 - 1.68925i) q^{75} +(-11.6190 - 6.70820i) q^{79} +(-2.03553 - 3.52565i) q^{81} +11.6863 q^{83} +4.47214i q^{85} +(-1.71141 - 2.96425i) q^{87} +(0.274552 + 0.158513i) q^{89} +(-0.464466 + 0.804479i) q^{93} +(-2.26874 + 1.30986i) q^{95} +12.9343i q^{97} +(-2.41421 - 7.63441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} + 8 q^{11} - 32 q^{15} - 24 q^{25} + 32 q^{37} + 32 q^{67} + 128 q^{71} + 24 q^{81} - 64 q^{93} - 16 q^{99}+O(q^{100}) \) 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

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Database

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