LMFDB - Embedded newform 2100.2.bi.k.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.29471584693248.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 13x^6 - 36x^5 + 39x^4 - 36x^3 + 54x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.15038 + 1.29484i$ of defining polynomial
Character	$\chi$	$=$	2100.101
Dual form			2100.2.bi.k.1601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.546177 - 1.64368i) q^{3} +(1.08214 - 2.41433i) q^{7} +(-2.40338 + 1.79548i) q^{9} +O(q^{10})$	\(q+(-0.546177 - 1.64368i) q^{3} +(1.08214 - 2.41433i) q^{7} +(-2.40338 + 1.79548i) q^{9} +(-1.17086 - 0.675999i) q^{11} -4.94296i q^{13} +(2.87105 - 4.97280i) q^{17} +(2.84694 - 1.64368i) q^{19} +(-4.55943 - 0.460035i) q^{21} +(-4.33480 + 2.50270i) q^{23} +(4.26388 + 2.96974i) q^{27} +5.68630i q^{29} +(-2.45160 - 1.41543i) q^{31} +(-0.471628 + 2.29374i) q^{33} +(1.92545 + 3.33498i) q^{37} +(-8.12466 + 2.69973i) q^{39} +3.73802 q^{41} -4.06339 q^{43} +(-2.84298 - 4.92419i) q^{47} +(-4.65797 - 5.22526i) q^{49} +(-9.74181 - 2.00306i) q^{51} +(1.26574 + 0.730773i) q^{53} +(-4.25662 - 3.78172i) q^{57} +(4.34239 - 7.52123i) q^{59} +(1.65306 - 0.954394i) q^{61} +(1.73410 + 7.74551i) q^{63} +(2.51939 - 4.36371i) q^{67} +(6.48121 + 5.75812i) q^{69} -3.38259i q^{71} +(-14.1398 - 8.16364i) q^{73} +(-2.89912 + 2.09533i) q^{77} +(-2.41693 - 4.18625i) q^{79} +(2.55248 - 8.63046i) q^{81} -16.6525 q^{83} +(9.34646 - 3.10572i) q^{87} +(8.08150 + 13.9976i) q^{89} +(-11.9339 - 5.34895i) q^{91} +(-0.987510 + 4.80272i) q^{93} +12.0577i q^{97} +(4.02778 - 0.477584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 5 * q^7 - 3 * q^9	$ 10 q + q^{3} + 5 q^{7} - 3 q^{9} - 6 q^{11} - 6 q^{17} + 3 q^{19} + 10 q^{21} - 24 q^{23} - 8 q^{27} + 15 q^{31} + 20 q^{33} + q^{37} + 15 q^{39} - 8 q^{41} + 26 q^{43} - 14 q^{47} - 13 q^{49} - 44 q^{51} + 24 q^{53} - 18 q^{57} + 42 q^{61} + q^{63} - 7 q^{67} - 14 q^{69} + 3 q^{73} + 26 q^{77} + q^{79} + 41 q^{81} + 8 q^{83} + 26 q^{87} + 28 q^{89} - 11 q^{91} + 47 q^{93} + 36 q^{99}+O(q^{100}) $ 10 * q + q^3 + 5 * q^7 - 3 * q^9 - 6 * q^11 - 6 * q^17 + 3 * q^19 + 10 * q^21 - 24 * q^23 - 8 * q^27 + 15 * q^31 + 20 * q^33 + q^37 + 15 * q^39 - 8 * q^41 + 26 * q^43 - 14 * q^47 - 13 * q^49 - 44 * q^51 + 24 * q^53 - 18 * q^57 + 42 * q^61 + q^63 - 7 * q^67 - 14 * q^69 + 3 * q^73 + 26 * q^77 + q^79 + 41 * q^81 + 8 * q^83 + 26 * q^87 + 28 * q^89 - 11 * q^91 + 47 * q^93 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.546177	−	1.64368i	−0.315336	−	0.948980i
$3$	−0.546177	−	1.64368i	−0.315336	−	0.948980i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.08214	−	2.41433i	0.409009	−	0.912531i
$7$	1.08214	−	2.41433i	0.409009	−	0.912531i
$8$		0			0
$9$	−2.40338	+	1.79548i	−0.801127	+	0.598494i
$10$		0			0
$11$	−1.17086	−	0.675999i	−0.353029	−	0.203821i	0.312990	−	0.949757i	$-0.398669\pi$
$11$	−1.17086	−	0.675999i	−0.353029	−	0.203821i	−0.666018	+	0.745935i	$0.732003\pi$
$12$		0			0
$13$		−	4.94296i		−	1.37093i	−0.728105	−	0.685466i	$-0.759599\pi$
$13$		−	4.94296i		−	1.37093i	0.728105	−	0.685466i	$-0.240401\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.87105	−	4.97280i	0.696332	−	1.20608i	−0.273398	−	0.961901i	$-0.588148\pi$
$17$	2.87105	−	4.97280i	0.696332	−	1.20608i	0.969730	−	0.244181i	$-0.0785190\pi$
$18$		0			0
$19$	2.84694	−	1.64368i	0.653133	−	0.377087i	−0.136523	−	0.990637i	$-0.543593\pi$
$19$	2.84694	−	1.64368i	0.653133	−	0.377087i	0.789656	+	0.613550i	$0.210259\pi$
$20$		0			0
$21$	−4.55943	−	0.460035i	−0.994948	−	0.100388i
$22$		0			0
$23$	−4.33480	+	2.50270i	−0.903868	+	0.521849i	−0.878453	−	0.477828i	$-0.841424\pi$
$23$	−4.33480	+	2.50270i	−0.903868	+	0.521849i	−0.0254150	+	0.999677i	$0.508091\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.26388	+	2.96974i	0.820583	+	0.571527i
$28$		0			0
$29$			5.68630i			1.05592i	0.849270	+	0.527959i	$0.177043\pi$
$29$			5.68630i			1.05592i	−0.849270	+	0.527959i	$0.822957\pi$
$30$		0			0
$31$	−2.45160	−	1.41543i	−0.440320	−	0.254219i	0.263414	−	0.964683i	$-0.415152\pi$
$31$	−2.45160	−	1.41543i	−0.440320	−	0.254219i	−0.703733	+	0.710464i	$0.748485\pi$
$32$		0			0
$33$	−0.471628	+	2.29374i	−0.0820998	+	0.399289i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.92545	+	3.33498i	0.316542	+	0.548267i	0.979764	−	0.200156i	$-0.0641448\pi$
$37$	1.92545	+	3.33498i	0.316542	+	0.548267i	−0.663222	+	0.748423i	$0.730811\pi$
$38$		0			0
$39$	−8.12466	+	2.69973i	−1.30099	+	0.432303i
$40$		0			0
$41$	3.73802			0.583781			0.291890	−	0.956452i	$-0.405716\pi$
$41$	3.73802			0.583781			0.291890	+	0.956452i	$0.405716\pi$
$42$		0			0
$43$	−4.06339			−0.619661			−0.309830	−	0.950792i	$-0.600272\pi$
$43$	−4.06339			−0.619661			−0.309830	+	0.950792i	$0.600272\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.84298	−	4.92419i	−0.414691	−	0.718266i	0.580705	−	0.814114i	$-0.302777\pi$
$47$	−2.84298	−	4.92419i	−0.414691	−	0.718266i	−0.995396	+	0.0958478i	$0.969444\pi$
$48$		0			0
$49$	−4.65797	−	5.22526i	−0.665424	−	0.746466i
$50$		0			0
$51$	−9.74181	−	2.00306i	−1.36413	−	0.280484i
$52$		0			0
$53$	1.26574	+	0.730773i	0.173862	+	0.100379i	0.584406	−	0.811462i	$-0.301328\pi$
$53$	1.26574	+	0.730773i	0.173862	+	0.100379i	−0.410544	+	0.911841i	$0.634661\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.25662	−	3.78172i	−0.563804	−	0.500902i
$58$		0			0
$59$	4.34239	−	7.52123i	0.565330	−	0.979181i	−0.431688	−	0.902023i	$-0.642082\pi$
$59$	4.34239	−	7.52123i	0.565330	−	0.979181i	0.997019	−	0.0771582i	$-0.0245846\pi$
$60$		0			0
$61$	1.65306	−	0.954394i	0.211653	−	0.122198i	−0.390427	−	0.920634i	$-0.627672\pi$
$61$	1.65306	−	0.954394i	0.211653	−	0.122198i	0.602079	+	0.798436i	$0.294339\pi$
$62$		0			0
$63$	1.73410	+	7.74551i	0.218477	+	0.975842i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.51939	−	4.36371i	0.307793	−	0.533113i	−0.670086	−	0.742283i	$-0.733743\pi$
$67$	2.51939	−	4.36371i	0.307793	−	0.533113i	0.977879	+	0.209170i	$0.0670763\pi$
$68$		0			0
$69$	6.48121	+	5.75812i	0.780246	+	0.693196i
$70$		0			0
$71$		−	3.38259i		−	0.401440i	−0.979649	−	0.200720i	$-0.935672\pi$
$71$		−	3.38259i		−	0.401440i	0.979649	−	0.200720i	$-0.0643281\pi$
$72$		0			0
$73$	−14.1398	−	8.16364i	−1.65494	−	0.955481i	−0.974997	−	0.222218i	$-0.928670\pi$
$73$	−14.1398	−	8.16364i	−1.65494	−	0.955481i	−0.679945	−	0.733263i	$-0.737996\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.89912	+	2.09533i	−0.330385	+	0.238785i
$78$		0			0
$79$	−2.41693	−	4.18625i	−0.271926	−	0.470990i	0.697429	−	0.716654i	$-0.254327\pi$
$79$	−2.41693	−	4.18625i	−0.271926	−	0.470990i	−0.969355	+	0.245664i	$0.920994\pi$
$80$		0			0
$81$	2.55248	−	8.63046i	0.283609	−	0.958940i
$82$		0			0
$83$	−16.6525			−1.82785			−0.913927	−	0.405879i	$-0.866965\pi$
$83$	−16.6525			−1.82785			−0.913927	+	0.405879i	$0.866965\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.34646	−	3.10572i	1.00205	−	0.332969i
$88$		0			0
$89$	8.08150	+	13.9976i	0.856637	+	1.48374i	0.875118	+	0.483909i	$0.160784\pi$
$89$	8.08150	+	13.9976i	0.856637	+	1.48374i	−0.0184813	+	0.999829i	$0.505883\pi$
$90$		0			0
$91$	−11.9339	−	5.34895i	−1.25102	−	0.560723i
$92$		0			0
$93$	−0.987510	+	4.80272i	−0.102400	+	0.498019i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			12.0577i			1.22427i	0.790751	+	0.612137i	$0.209690\pi$
$97$			12.0577i			1.22427i	−0.790751	+	0.612137i	$0.790310\pi$
$98$		0			0
$99$	4.02778	−	0.477584i	0.404807	−	0.0479990i
$100$		0			0
$101$	−9.01683	+	15.6176i	−0.897208	+	1.55401i	−0.0661605	+	0.997809i	$0.521075\pi$
$101$	−9.01683	+	15.6176i	−0.897208	+	1.55401i	−0.831048	+	0.556201i	$0.812258\pi$
$102$		0			0
$103$	−0.533615	+	0.308083i	−0.0525787	+	0.0303563i	−0.526059	−	0.850448i	$-0.676331\pi$
$103$	−0.533615	+	0.308083i	−0.0525787	+	0.0303563i	0.473480	+	0.880804i	$0.342998\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.3374	+	8.85503i	−1.48272	+	0.856048i	−0.999807	−	0.0196209i	$-0.993754\pi$
$107$	−15.3374	+	8.85503i	−1.48272	+	0.856048i	−0.482912	+	0.875669i	$0.660421\pi$
$108$		0			0
$109$	0.855282	−	1.48139i	0.0819211	−	0.141892i	−0.822154	−	0.569265i	$-0.807228\pi$
$109$	0.855282	−	1.48139i	0.0819211	−	0.141892i	0.904075	+	0.427374i	$0.140561\pi$
$110$		0			0
$111$	4.43001	−	4.98632i	0.420478	−	0.473280i
$112$		0			0
$113$			13.1214i			1.23436i	0.786822	+	0.617180i	$0.211725\pi$
$113$			13.1214i			1.23436i	−0.786822	+	0.617180i	$0.788275\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	8.87501	+	11.8798i	0.820495	+	1.09829i
$118$		0			0
$119$	−8.89912	−	12.3129i	−0.815781	−	1.12872i
$120$		0			0
$121$	−4.58605	−	7.94327i	−0.416914	−	0.722116i
$122$		0			0
$123$	−2.04162	−	6.14412i	−0.184087	−	0.553996i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	15.5324			1.37828			0.689139	−	0.724629i	$-0.257989\pi$
$127$	15.5324			1.37828			0.689139	+	0.724629i	$0.257989\pi$
$128$		0			0
$129$	2.21933	+	6.67892i	0.195401	+	0.588046i
$130$		0			0
$131$	4.47822	+	7.75651i	0.391264	+	0.677689i	0.992617	−	0.121295i	$-0.0387046\pi$
$131$	4.47822	+	7.75651i	0.391264	+	0.677689i	−0.601353	+	0.798984i	$0.705371\pi$
$132$		0			0
$133$	−0.887614	−	8.65214i	−0.0769659	−	0.750235i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.4047	+	7.73923i	1.14524	+	0.661207i	0.947724	−	0.319092i	$-0.103378\pi$
$137$	13.4047	+	7.73923i	1.14524	+	0.661207i	0.197520	+	0.980299i	$0.436711\pi$
$138$		0			0
$139$		−	20.1547i		−	1.70950i	−0.519044	−	0.854748i	$-0.673712\pi$
$139$		−	20.1547i		−	1.70950i	0.519044	−	0.854748i	$-0.326288\pi$
$140$		0			0
$141$	−6.54103	+	7.36243i	−0.550854	+	0.620029i
$142$		0			0
$143$	−3.34144	+	5.78754i	−0.279425	+	0.483978i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.04459	+	10.5101i	−0.498549	+	0.866861i
$148$		0			0
$149$	1.24947	−	0.721384i	0.102361	−	0.0590981i	−0.447946	−	0.894061i	$-0.647844\pi$
$149$	1.24947	−	0.721384i	0.102361	−	0.0590981i	0.550307	+	0.834963i	$0.314511\pi$
$150$		0			0
$151$	−8.12108	+	14.0661i	−0.660884	+	1.14468i	0.319500	+	0.947586i	$0.396485\pi$
$151$	−8.12108	+	14.0661i	−0.660884	+	1.14468i	−0.980384	+	0.197098i	$0.936848\pi$
$152$		0			0
$153$	2.02836	+	17.1065i	0.163983	+	1.38298i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−15.7942	−	9.11876i	−1.26051	−	0.727756i	−0.287338	−	0.957829i	$-0.592770\pi$
$157$	−15.7942	−	9.11876i	−1.26051	−	0.727756i	−0.973173	+	0.230073i	$0.926103\pi$
$158$		0			0
$159$	0.509842	−	2.47960i	0.0404331	−	0.196645i
$160$		0			0
$161$	1.35150	+	13.1739i	0.106513	+	1.03825i
$162$		0			0
$163$	−12.1630	−	21.0669i	−0.952679	−	1.65009i	−0.739592	−	0.673055i	$-0.764982\pi$
$163$	−12.1630	−	21.0669i	−0.952679	−	1.65009i	−0.213087	−	0.977033i	$-0.568352\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.5007			0.967336			0.483668	−	0.875252i	$-0.339304\pi$
$167$	12.5007			0.967336			0.483668	+	0.875252i	$0.339304\pi$
$168$		0			0
$169$	−11.4329			−0.879453
$170$		0			0
$171$	−3.89108	+	9.06203i	−0.297558	+	0.692991i
$172$		0			0
$173$	−7.42089	−	12.8534i	−0.564200	−	0.977223i	−0.997124	−	0.0757927i	$-0.975851\pi$
$173$	−7.42089	−	12.8534i	−0.564200	−	0.977223i	0.432923	−	0.901431i	$-0.357482\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−14.7342	−	3.02957i	−1.10749	−	0.227717i
$178$		0			0
$179$	−9.93533	−	5.73617i	−0.742602	−	0.428741i	0.0804127	−	0.996762i	$-0.474376\pi$
$179$	−9.93533	−	5.73617i	−0.742602	−	0.428741i	−0.823015	+	0.568020i	$0.807709\pi$
$180$		0			0
$181$			5.91099i			0.439361i	0.975572	+	0.219680i	$0.0705014\pi$
$181$			5.91099i			0.439361i	−0.975572	+	0.219680i	$0.929499\pi$
$182$		0			0
$183$	−2.47158	−	2.19584i	−0.182705	−	0.162321i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−6.72322	+	3.88165i	−0.491650	+	0.283854i
$188$		0			0
$189$	11.7840	−	7.08073i	0.857162	−	0.515048i
$190$		0			0
$191$	−9.15764	+	5.28716i	−0.662623	+	0.382566i	−0.793276	−	0.608862i	$-0.791626\pi$
$191$	−9.15764	+	5.28716i	−0.662623	+	0.382566i	0.130652	+	0.991428i	$0.458293\pi$
$192$		0			0
$193$	6.03231	−	10.4483i	0.434215	−	0.752082i	−0.563016	−	0.826446i	$-0.690359\pi$
$193$	6.03231	−	10.4483i	0.434215	−	0.752082i	0.997231	+	0.0743635i	$0.0236925\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	17.2423i		−	1.22846i	−0.789126	−	0.614231i	$-0.789466\pi$
$197$		−	17.2423i		−	1.22846i	0.789126	−	0.614231i	$-0.210534\pi$
$198$		0			0
$199$	2.46400	+	1.42259i	0.174668	+	0.100845i	0.584785	−	0.811188i	$-0.301179\pi$
$199$	2.46400	+	1.42259i	0.174668	+	0.100845i	−0.410117	+	0.912033i	$0.634512\pi$
$200$		0			0
$201$	−8.54859	−	1.75772i	−0.602971	−	0.123980i
$202$		0			0
$203$	13.7286	+	6.15334i	0.963558	+	0.431880i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.92462	−	13.7980i	0.411790	−	0.959027i
$208$		0			0
$209$	−4.44451			−0.307433
$210$		0			0
$211$	22.4677			1.54674			0.773372	−	0.633953i	$-0.218569\pi$
$211$	22.4677			1.54674			0.773372	+	0.633953i	$0.218569\pi$
$212$		0			0
$213$	−5.55991	+	1.84749i	−0.380958	+	0.126588i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.07027	+	4.38727i	−0.412077	+	0.297828i
$218$		0			0
$219$	−5.69557	+	27.7002i	−0.384871	+	1.87180i
$220$		0			0
$221$	−24.5804	−	14.1915i	−1.65346	−	0.954623i
$222$		0			0
$223$		−	5.27620i		−	0.353321i	−0.984272	−	0.176660i	$-0.943471\pi$
$223$		−	5.27620i		−	0.353321i	0.984272	−	0.176660i	$-0.0565294\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.24055	−	10.8090i	0.414200	−	0.717416i	−0.581144	−	0.813801i	$-0.697395\pi$
$227$	6.24055	−	10.8090i	0.414200	−	0.717416i	0.995344	+	0.0963851i	$0.0307280\pi$
$228$		0			0
$229$	−14.0882	+	8.13380i	−0.930971	+	0.537496i	−0.887119	−	0.461542i	$-0.847297\pi$
$229$	−14.0882	+	8.13380i	−0.930971	+	0.537496i	−0.0438526	+	0.999038i	$0.513963\pi$
$230$		0			0
$231$	5.02749	+	3.62080i	0.330784	+	0.238231i
$232$		0			0
$233$	7.64788	−	4.41551i	0.501029	−	0.289269i	−0.228109	−	0.973636i	$-0.573254\pi$
$233$	7.64788	−	4.41551i	0.501029	−	0.289269i	0.729139	+	0.684366i	$0.239921\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.56079	+	6.25911i	−0.361212	+	0.406573i
$238$		0			0
$239$		−	12.3333i		−	0.797773i	−0.917000	−	0.398886i	$-0.869397\pi$
$239$		−	12.3333i		−	0.797773i	0.917000	−	0.398886i	$-0.130603\pi$
$240$		0			0
$241$	6.88815	+	3.97688i	0.443705	+	0.256173i	0.705168	−	0.709040i	$-0.250872\pi$
$241$	6.88815	+	3.97688i	0.443705	+	0.256173i	−0.261463	+	0.965214i	$0.584205\pi$
$242$		0			0
$243$	−15.5798	+	0.518295i	−0.999447	+	0.0332486i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.12466	−	14.0723i	−0.516960	−	0.895401i
$248$		0			0
$249$	9.09524	+	27.3715i	0.576387	+	1.73460i
$250$		0			0
$251$	7.64756			0.482710			0.241355	−	0.970437i	$-0.422408\pi$
$251$	7.64756			0.482710			0.241355	+	0.970437i	$0.422408\pi$
$252$		0			0
$253$	6.76728			0.425455
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.7478	+	23.8118i	0.857563	+	1.48534i	0.874247	+	0.485482i	$0.161356\pi$
$257$	13.7478	+	23.8118i	0.857563	+	1.48534i	−0.0166841	+	0.999861i	$0.505311\pi$
$258$		0			0
$259$	10.1353	−	1.03977i	0.629779	−	0.0646084i
$260$		0			0
$261$	−10.2096	−	13.6663i	−0.631961	−	0.845925i
$262$		0			0
$263$	16.4738	+	9.51115i	1.01582	+	0.586483i	0.912890	−	0.408206i	$-0.133845\pi$
$263$	16.4738	+	9.51115i	1.01582	+	0.586483i	0.102928	+	0.994689i	$0.467179\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.5936	−	20.9286i	1.13791	−	1.28081i
$268$		0			0
$269$	−4.46010	+	7.72512i	−0.271937	+	0.471009i	−0.969358	−	0.245653i	$-0.920998\pi$
$269$	−4.46010	+	7.72512i	−0.271937	+	0.471009i	0.697421	+	0.716662i	$0.254331\pi$
$270$		0			0
$271$	6.53123	−	3.77081i	0.396744	−	0.229060i	−0.288334	−	0.957530i	$-0.593101\pi$
$271$	6.53123	−	3.77081i	0.396744	−	0.229060i	0.685078	+	0.728470i	$0.259768\pi$
$272$		0			0
$273$	−2.27393	+	22.5371i	−0.137625	+	1.36401i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.888562	+	1.53903i	−0.0533885	+	0.0924716i	−0.891485	−	0.453051i	$-0.850336\pi$
$277$	−0.888562	+	1.53903i	−0.0533885	+	0.0924716i	0.838096	+	0.545523i	$0.183669\pi$
$278$		0			0
$279$	8.43350	−	0.999983i	0.504900	−	0.0598674i
$280$		0			0
$281$		−	25.3819i		−	1.51416i	−0.653324	−	0.757079i	$-0.726626\pi$
$281$		−	25.3819i		−	1.51416i	0.653324	−	0.757079i	$-0.273374\pi$
$282$		0			0
$283$	13.9774	+	8.06987i	0.830872	+	0.479704i	0.854151	−	0.520025i	$-0.174077\pi$
$283$	13.9774	+	8.06987i	0.830872	+	0.479704i	−0.0232795	+	0.999729i	$0.507411\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.04504	−	9.02481i	0.238771	−	0.532718i
$288$		0			0
$289$	−7.98584	−	13.8319i	−0.469755	−	0.813640i
$290$		0			0
$291$	19.8190	−	6.58564i	1.16181	−	0.386057i
$292$		0			0
$293$	19.5542			1.14237			0.571186	−	0.820821i	$-0.306484\pi$
$293$	19.5542			1.14237			0.571186	+	0.820821i	$0.306484\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.98488	−	6.35954i	−0.173200	−	0.369018i
$298$		0			0
$299$	12.3707	+	21.4268i	0.715419	+	1.23914i
$300$		0			0
$301$	−4.39713	+	9.81035i	−0.253447	+	0.565459i
$302$		0			0
$303$	30.5952	+	6.29082i	1.75765	+	0.361398i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			11.8231i			0.674777i	0.941365	+	0.337389i	$0.109544\pi$
$307$			11.8231i			0.674777i	−0.941365	+	0.337389i	$0.890456\pi$
$308$		0			0
$309$	0.797839	+	0.708826i	0.0453875	+	0.0403237i
$310$		0			0
$311$	11.1689	−	19.3451i	0.633331	−	1.09696i	−0.353535	−	0.935421i	$-0.615020\pi$
$311$	11.1689	−	19.3451i	0.633331	−	1.09696i	0.986866	−	0.161540i	$-0.0516462\pi$
$312$		0			0
$313$	11.5250	−	6.65398i	0.651433	−	0.376105i	−0.137572	−	0.990492i	$-0.543930\pi$
$313$	11.5250	−	6.65398i	0.651433	−	0.376105i	0.789005	+	0.614387i	$0.210596\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−29.3395	+	16.9392i	−1.64787	+	0.951400i	−0.669958	+	0.742399i	$0.733688\pi$
$317$	−29.3395	+	16.9392i	−1.64787	+	0.951400i	−0.977915	+	0.209001i	$0.932979\pi$
$318$		0			0
$319$	3.84393	−	6.65788i	0.215219	−	0.372770i
$320$		0			0
$321$	22.9318	+	20.3733i	1.27993	+	1.13713i
$322$		0			0
$323$		−	18.8764i		−	1.05031i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.90207	−	0.596709i	−0.160485	−	0.0329981i
$328$		0			0
$329$	−14.9651	+	1.53525i	−0.825052	+	0.0846413i
$330$		0			0
$331$	0.989824	+	1.71443i	0.0544057	+	0.0942334i	0.891946	−	0.452143i	$-0.149340\pi$
$331$	0.989824	+	1.71443i	0.0544057	+	0.0942334i	−0.837540	+	0.546376i	$0.816007\pi$
$332$		0			0
$333$	−10.6155	−	4.55811i	−0.581725	−	0.249783i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	12.0217			0.654862			0.327431	−	0.944875i	$-0.393817\pi$
$337$	12.0217			0.654862			0.327431	+	0.944875i	$0.393817\pi$
$338$		0			0
$339$	21.5674	−	7.16662i	1.17138	−	0.389237i
$340$		0			0
$341$	1.91366	+	3.31455i	0.103630	+	0.179493i
$342$		0			0
$343$	−17.6560	+	5.59143i	−0.953337	+	0.301909i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.6992	−	7.33186i	−0.681726	−	0.393595i	0.118779	−	0.992921i	$-0.462102\pi$
$347$	−12.6992	−	7.33186i	−0.681726	−	0.393595i	−0.800505	+	0.599326i	$0.795435\pi$
$348$		0			0
$349$		−	25.0573i		−	1.34129i	−0.741780	−	0.670644i	$-0.766018\pi$
$349$		−	25.0573i		−	1.34129i	0.741780	−	0.670644i	$-0.233982\pi$
$350$		0			0
$351$	14.6793	−	21.0762i	0.783525	−	1.12496i
$352$		0			0
$353$	3.88365	−	6.72669i	0.206706	−	0.358025i	−0.743969	−	0.668214i	$-0.767059\pi$
$353$	3.88365	−	6.72669i	0.206706	−	0.358025i	0.950675	+	0.310189i	$0.100392\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−15.3780	+	21.3523i	−0.813890	+	1.13009i
$358$		0			0
$359$	3.86952	−	2.23407i	0.204225	−	0.117910i	−0.394399	−	0.918939i	$-0.629047\pi$
$359$	3.86952	−	2.23407i	0.204225	−	0.117910i	0.598625	+	0.801030i	$0.295714\pi$
$360$		0			0
$361$	−4.09662	+	7.09555i	−0.215612	+	0.373450i
$362$		0			0
$363$	−10.5514	+	11.8764i	−0.553806	+	0.623352i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.45880	−	0.842240i	−0.0761489	−	0.0439646i	0.461442	−	0.887170i	$-0.347332\pi$
$367$	−1.45880	−	0.842240i	−0.0761489	−	0.0439646i	−0.537591	+	0.843206i	$0.680666\pi$
$368$		0			0
$369$	−8.98389	+	6.71155i	−0.467682	+	0.349389i
$370$		0			0
$371$	3.13402	−	2.26511i	0.162710	−	0.117599i
$372$		0			0
$373$	6.92322	+	11.9914i	0.358471	+	0.620890i	0.987706	−	0.156325i	$-0.0499649\pi$
$373$	6.92322	+	11.9914i	0.358471	+	0.620890i	−0.629235	+	0.777215i	$0.716632\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	28.1072			1.44759
$378$		0			0
$379$	−2.15603			−0.110748			−0.0553739	−	0.998466i	$-0.517635\pi$
$379$	−2.15603			−0.110748			−0.0553739	+	0.998466i	$0.517635\pi$
$380$		0			0
$381$	−8.48345	−	25.5303i	−0.434620	−	1.30796i
$382$		0			0
$383$	−1.86598	−	3.23197i	−0.0953471	−	0.165146i	0.814406	−	0.580295i	$-0.197063\pi$
$383$	−1.86598	−	3.23197i	−0.0953471	−	0.165146i	−0.909753	+	0.415149i	$0.863729\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	9.76587	−	7.29574i	0.496427	−	0.370863i
$388$		0			0
$389$	11.9512	+	6.90001i	0.605948	+	0.349844i	0.771378	−	0.636377i	$-0.219568\pi$
$389$	11.9512	+	6.90001i	0.605948	+	0.349844i	−0.165430	+	0.986222i	$0.552901\pi$
$390$		0			0
$391$			28.7415i			1.45352i
$392$		0			0
$393$	10.3033	−	11.5972i	0.519734	−	0.585001i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.1606	−	8.17565i	0.710702	−	0.410324i	−0.100619	−	0.994925i	$-0.532082\pi$
$397$	14.1606	−	8.17565i	0.710702	−	0.410324i	0.811321	+	0.584601i	$0.198749\pi$
$398$		0			0
$399$	−13.7366	+	6.18456i	−0.687688	+	0.309615i
$400$		0			0
$401$	11.9669	−	6.90910i	0.597599	−	0.345024i	−0.170497	−	0.985358i	$-0.554537\pi$
$401$	11.9669	−	6.90910i	0.597599	−	0.345024i	0.768096	+	0.640334i	$0.221204\pi$
$402$		0			0
$403$	−6.99642	+	12.1182i	−0.348516	+	0.603648i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	5.20641i		−	0.258072i
$408$		0			0
$409$	−8.26987	−	4.77461i	−0.408919	−	0.236089i	0.281406	−	0.959589i	$-0.409199\pi$
$409$	−8.26987	−	4.77461i	−0.408919	−	0.236089i	−0.690325	+	0.723499i	$0.742533\pi$
$410$		0			0
$411$	5.39947	−	26.2601i	0.266336	−	1.29532i
$412$		0			0
$413$	−13.4597	−	18.6229i	−0.662307	−	0.916375i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−33.1278	+	11.0080i	−1.62228	+	0.539065i
$418$		0			0
$419$	−9.71886			−0.474797			−0.237399	−	0.971412i	$-0.576295\pi$
$419$	−9.71886			−0.474797			−0.237399	+	0.971412i	$0.576295\pi$
$420$		0			0
$421$	34.8713			1.69953			0.849763	−	0.527165i	$-0.176745\pi$
$421$	34.8713			1.69953			0.849763	+	0.527165i	$0.176745\pi$
$422$		0			0
$423$	15.6741	+	6.73017i	0.762099	+	0.327232i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.515388	−	5.02381i	−0.0249414	−	0.243119i
$428$		0			0
$429$	11.3379	+	2.33124i	0.547399	+	0.112553i
$430$		0			0
$431$	1.57279	+	0.908052i	0.0757587	+	0.0437393i	0.537401	−	0.843327i	$-0.319406\pi$
$431$	1.57279	+	0.908052i	0.0757587	+	0.0437393i	−0.461642	+	0.887066i	$0.652740\pi$
$432$		0			0
$433$		−	10.6773i		−	0.513117i	−0.966529	−	0.256558i	$-0.917411\pi$
$433$		−	10.6773i		−	0.513117i	0.966529	−	0.256558i	$-0.0825886\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.22728	+	14.2501i	−0.393564	+	0.681673i
$438$		0			0
$439$	26.6759	−	15.4013i	1.27317	−	0.735066i	0.297588	−	0.954694i	$-0.403818\pi$
$439$	26.6759	−	15.4013i	1.27317	−	0.735066i	0.975584	+	0.219628i	$0.0704845\pi$
$440$		0			0
$441$	20.5767	+	4.19499i	0.979845	+	0.199761i
$442$		0			0
$443$	−14.3178	+	8.26640i	−0.680260	+	0.392749i	−0.799953	−	0.600062i	$-0.795142\pi$
$443$	−14.3178	+	8.26640i	−0.680260	+	0.392749i	0.119693	+	0.992811i	$0.461809\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.86816	−	1.65974i	−0.0883610	−	0.0785028i
$448$		0			0
$449$			2.59098i			0.122276i	0.998129	+	0.0611380i	$0.0194730\pi$
$449$			2.59098i			0.122276i	−0.998129	+	0.0611380i	$0.980527\pi$
$450$		0			0
$451$	−4.37671	−	2.52690i	−0.206091	−	0.118987i
$452$		0			0
$453$	27.5558	+	5.66588i	1.29468	+	0.266206i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.0874	−	19.2040i	−0.518647	−	0.898323i	−0.999765	−	0.0216672i	$-0.993103\pi$
$457$	−11.0874	−	19.2040i	−0.518647	−	0.898323i	0.481118	−	0.876656i	$-0.340231\pi$
$458$		0			0
$459$	27.0097	−	12.6771i	1.26071	−	0.591718i
$460$		0			0
$461$	30.5304			1.42194			0.710971	−	0.703221i	$-0.248256\pi$
$461$	30.5304			1.42194			0.710971	+	0.703221i	$0.248256\pi$
$462$		0			0
$463$	−3.54824			−0.164901			−0.0824504	−	0.996595i	$-0.526275\pi$
$463$	−3.54824			−0.164901			−0.0824504	+	0.996595i	$0.526275\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.1564	−	29.7157i	−0.793901	−	1.37508i	−0.923534	−	0.383515i	$-0.874713\pi$
$467$	−17.1564	−	29.7157i	−0.793901	−	1.37508i	0.129633	−	0.991562i	$-0.458620\pi$
$468$		0			0
$469$	−7.80912	−	10.8048i	−0.360592	−	0.498918i
$470$		0			0
$471$	−6.36193	+	30.9410i	−0.293142	+	1.42569i
$472$		0			0
$473$	4.75767	+	2.74684i	0.218758	+	0.126300i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.35414	+	0.516282i	−0.199362	+	0.0236389i
$478$		0			0
$479$	9.78624	−	16.9503i	0.447145	−	0.774477i	−0.551054	−	0.834469i	$-0.685774\pi$
$479$	9.78624	−	16.9503i	0.447145	−	0.774477i	0.998199	+	0.0599923i	$0.0191076\pi$
$480$		0			0
$481$	16.4847	−	9.51743i	0.751637	−	0.433958i
$482$		0			0
$483$	20.9155	−	9.41671i	0.951689	−	0.428475i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	12.6133	−	21.8468i	0.571561	−	0.989973i	−0.424844	−	0.905266i	$-0.639671\pi$
$487$	12.6133	−	21.8468i	0.571561	−	0.989973i	0.996406	−	0.0847071i	$-0.0269955\pi$
$488$		0			0
$489$	−27.9842	+	31.4984i	−1.26549	+	1.42441i
$490$		0			0
$491$		−	38.6556i		−	1.74450i	−0.489057	−	0.872252i	$-0.662659\pi$
$491$		−	38.6556i		−	1.74450i	0.489057	−	0.872252i	$-0.337341\pi$
$492$		0			0
$493$	28.2768	+	16.3256i	1.27352	+	0.735269i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.16669	−	3.66042i	−0.366326	−	0.164192i
$498$		0			0
$499$	−2.80910	−	4.86551i	−0.125753	−	0.217810i	0.796274	−	0.604936i	$-0.206801\pi$
$499$	−2.80910	−	4.86551i	−0.125753	−	0.217810i	−0.922027	+	0.387126i	$0.873468\pi$
$500$		0			0
$501$	−6.82761	−	20.5472i	−0.305035	−	0.917982i
$502$		0			0
$503$	25.8655			1.15329			0.576644	−	0.816996i	$-0.304362\pi$
$503$	25.8655			1.15329			0.576644	+	0.816996i	$0.304362\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.24438	+	18.7920i	0.277323	+	0.834584i
$508$		0			0
$509$	−15.2306	−	26.3801i	−0.675082	−	1.16928i	−0.976445	−	0.215767i	$-0.930775\pi$
$509$	−15.2306	−	26.3801i	−0.675082	−	1.16928i	0.301362	−	0.953510i	$-0.402559\pi$
$510$		0			0
$511$	−35.0109	+	25.3040i	−1.54879	+	1.11939i
$512$		0			0
$513$	17.0203	+	1.44622i	0.751465	+	0.0638524i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			7.68740i			0.338092i
$518$		0			0
$519$	−17.0737	+	19.2178i	−0.749453	+	0.843568i
$520$		0			0
$521$	10.6182	−	18.3913i	0.465192	−	0.805737i	−0.534018	−	0.845473i	$-0.679319\pi$
$521$	10.6182	−	18.3913i	0.465192	−	0.805737i	0.999210	+	0.0397366i	$0.0126519\pi$
$522$		0			0
$523$	10.7227	−	6.19077i	0.468872	−	0.270704i	−0.246895	−	0.969042i	$-0.579410\pi$
$523$	10.7227	−	6.19077i	0.468872	−	0.270704i	0.715768	+	0.698339i	$0.246077\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.0773	+	8.12754i	−0.613217	+	0.354041i
$528$		0			0
$529$	1.02699	−	1.77880i	0.0446518	−	0.0773392i
$530$		0			0
$531$	3.06784	+	25.8731i	0.133133	+	1.12280i
$532$		0			0
$533$		−	18.4769i		−	0.800323i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.00198	+	19.4635i	−0.172698	+	0.839912i
$538$		0			0
$539$	1.92158	+	9.26685i	0.0827682	+	0.399151i
$540$		0			0
$541$	−6.93001	−	12.0031i	−0.297944	−	0.516055i	0.677721	−	0.735319i	$-0.262968\pi$
$541$	−6.93001	−	12.0031i	−0.297944	−	0.516055i	−0.975665	+	0.219264i	$0.929634\pi$
$542$		0			0
$543$	9.71579	−	3.22845i	0.416945	−	0.138546i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−17.7100			−0.757226			−0.378613	−	0.925555i	$-0.623599\pi$
$547$	−17.7100			−0.757226			−0.378613	+	0.925555i	$0.623599\pi$
$548$		0			0
$549$	−2.25933	+	5.26181i	−0.0964260	+	0.224569i
$550$		0			0
$551$	9.34646	+	16.1885i	0.398173	+	0.689655i
$552$		0			0
$553$	−12.7224	+	1.30518i	−0.541013	+	0.0555020i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.01129	+	1.73857i	0.127593	+	0.0736656i	0.562438	−	0.826840i	$-0.309864\pi$
$557$	3.01129	+	1.73857i	0.127593	+	0.0736656i	−0.434845	+	0.900505i	$0.643197\pi$
$558$		0			0
$559$			20.0852i			0.849512i
$560$		0			0
$561$	10.0523	+	8.93076i	0.424407	+	0.377057i
$562$		0			0
$563$	−6.02897	+	10.4425i	−0.254091	+	0.440098i	−0.964648	−	0.263541i	$-0.915110\pi$
$563$	−6.02897	+	10.4425i	−0.254091	+	0.440098i	0.710557	+	0.703639i	$0.248443\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−18.0746	−	15.5019i	−0.759064	−	0.651017i
$568$		0			0
$569$	11.8065	−	6.81650i	0.494955	−	0.285762i	−0.231673	−	0.972794i	$-0.574420\pi$
$569$	11.8065	−	6.81650i	0.494955	−	0.285762i	0.726628	+	0.687031i	$0.241087\pi$
$570$		0			0
$571$	22.0474	−	38.1873i	0.922657	−	1.59809i	0.127369	−	0.991855i	$-0.459347\pi$
$571$	22.0474	−	38.1873i	0.922657	−	1.59809i	0.795287	−	0.606233i	$-0.207320\pi$
$572$		0			0
$573$	13.6921	+	12.1645i	0.571996	+	0.508180i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	6.06103	+	3.49934i	0.252324	+	0.145679i	0.620828	−	0.783947i	$-0.286797\pi$
$577$	6.06103	+	3.49934i	0.252324	+	0.145679i	−0.368504	+	0.929626i	$0.620130\pi$
$578$		0			0
$579$	−20.4683	−	4.20859i	−0.850635	−	0.174903i
$580$		0			0
$581$	−18.0203	+	40.2047i	−0.747608	+	1.66797i
$582$		0			0
$583$	−0.988003	−	1.71127i	−0.0409189	−	0.0708736i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	29.9161			1.23477			0.617385	−	0.786661i	$-0.288192\pi$
$587$	29.9161			1.23477			0.617385	+	0.786661i	$0.288192\pi$
$588$		0			0
$589$	−9.30607			−0.383450
$590$		0			0
$591$	−28.3408	+	9.41734i	−1.16579	+	0.387378i
$592$		0			0
$593$	−12.0426	−	20.8583i	−0.494529	−	0.856549i	0.505451	−	0.862855i	$-0.331326\pi$
$593$	−12.0426	−	20.8583i	−0.494529	−	0.856549i	−0.999980	+	0.00630583i	$0.997993\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.992506	−	4.82702i	0.0406206	−	0.197557i
$598$		0			0
$599$	5.14773	+	2.97205i	0.210331	+	0.121434i	0.601465	−	0.798899i	$-0.294584\pi$
$599$	5.14773	+	2.97205i	0.210331	+	0.121434i	−0.391134	+	0.920334i	$0.627917\pi$
$600$		0			0
$601$			46.9992i			1.91714i	0.284863	+	0.958568i	$0.408052\pi$
$601$			46.9992i			1.91714i	−0.284863	+	0.958568i	$0.591948\pi$
$602$		0			0
$603$	1.77992	+	15.0112i	0.0724839	+	0.611303i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	8.61387	−	4.97322i	0.349626	−	0.201857i	−0.314894	−	0.949127i	$-0.601969\pi$
$607$	8.61387	−	4.97322i	0.349626	−	0.201857i	0.664521	+	0.747270i	$0.268636\pi$
$608$		0			0
$609$	2.61589	−	25.9262i	0.106001	−	1.05058i
$610$		0			0
$611$	−24.3401	+	14.0528i	−0.984694	+	0.568513i
$612$		0			0
$613$	−16.2739	+	28.1873i	−0.657298	+	1.13847i	0.324014	+	0.946052i	$0.394967\pi$
$613$	−16.2739	+	28.1873i	−0.657298	+	1.13847i	−0.981312	+	0.192421i	$0.938366\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			7.69843i			0.309927i	0.987920	+	0.154964i	$0.0495260\pi$
$617$			7.69843i			0.309927i	−0.987920	+	0.154964i	$0.950474\pi$
$618$		0			0
$619$	2.76170	+	1.59447i	0.111002	+	0.0640872i	0.554473	−	0.832202i	$-0.312920\pi$
$619$	2.76170	+	1.59447i	0.111002	+	0.0640872i	−0.443471	+	0.896289i	$0.646253\pi$
$620$		0			0
$621$	−25.9154	−	2.20205i	−1.03995	−	0.0883650i
$622$		0			0
$623$	42.5400	−	4.36414i	1.70433	−	0.174845i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	2.42749	+	7.30536i	0.0969446	+	0.291748i
$628$		0			0
$629$	22.1122			0.881673
$630$		0			0
$631$	7.97461			0.317464			0.158732	−	0.987322i	$-0.449259\pi$
$631$	7.97461			0.317464			0.158732	+	0.987322i	$0.449259\pi$
$632$		0			0
$633$	−12.2714	−	36.9298i	−0.487743	−	1.46783i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−25.8283	+	23.0242i	−1.02335	+	0.912251i
$638$		0			0
$639$	6.07339	+	8.12966i	0.240259	+	0.321604i
$640$		0			0
$641$	23.7774	+	13.7279i	0.939152	+	0.542219i	0.889694	−	0.456557i	$-0.150917\pi$
$641$	23.7774	+	13.7279i	0.939152	+	0.542219i	0.0494573	+	0.998776i	$0.484251\pi$
$642$		0			0
$643$		−	29.0919i		−	1.14727i	−0.819110	−	0.573637i	$-0.805532\pi$
$643$		−	29.0919i		−	1.14727i	0.819110	−	0.573637i	$-0.194468\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.5999	+	37.4122i	−0.849181	+	1.47082i	0.0327597	+	0.999463i	$0.489570\pi$
$647$	−21.5999	+	37.4122i	−0.849181	+	1.47082i	−0.881940	+	0.471361i	$0.843763\pi$
$648$		0			0
$649$	−10.1687	+	5.87089i	−0.399156	+	0.230453i
$650$		0			0
$651$	10.5267	+	7.58137i	0.412575	+	0.297137i
$652$		0			0
$653$	−6.27142	+	3.62080i	−0.245420	+	0.141693i	−0.617665	−	0.786441i	$-0.711921\pi$
$653$	−6.27142	+	3.62080i	−0.245420	+	0.141693i	0.372246	+	0.928134i	$0.378588\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	48.6411	−	5.76750i	1.89767	−	0.225012i
$658$		0			0
$659$		−	5.29324i		−	0.206196i	−0.994671	−	0.103098i	$-0.967125\pi$
$659$		−	5.29324i		−	0.206196i	0.994671	−	0.103098i	$-0.0328755\pi$
$660$		0			0
$661$	43.2638	+	24.9783i	1.68276	+	0.971545i	0.959810	+	0.280649i	$0.0905497\pi$
$661$	43.2638	+	24.9783i	1.68276	+	0.971545i	0.722954	+	0.690896i	$0.242784\pi$
$662$		0			0
$663$	−9.90105	+	48.1534i	−0.384525	+	1.87012i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−14.2311	−	24.6490i	−0.551030	−	0.954411i
$668$		0			0
$669$	−8.67240	+	2.88174i	−0.335294	+	0.111415i
$670$		0			0
$671$	−2.58068			−0.0996259
$672$		0			0
$673$	21.8855			0.843625			0.421812	−	0.906683i	$-0.361394\pi$
$673$	21.8855			0.843625			0.421812	+	0.906683i	$0.361394\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.87236	−	11.9033i	−0.264126	−	0.457480i	0.703208	−	0.710984i	$-0.251750\pi$
$677$	−6.87236	−	11.9033i	−0.264126	−	0.457480i	−0.967334	+	0.253504i	$0.918417\pi$
$678$		0			0
$679$	29.1113	+	13.0481i	1.11719	+	0.500739i
$680$		0			0
$681$	−21.1749	−	4.35388i	−0.811425	−	0.166841i
$682$		0			0
$683$	−37.1547	−	21.4513i	−1.42169	−	0.820811i	−0.425243	−	0.905079i	$-0.639811\pi$
$683$	−37.1547	−	21.4513i	−1.42169	−	0.820811i	−0.996443	+	0.0842682i	$0.973145\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	21.0640	+	18.7139i	0.803642	+	0.713982i
$688$		0			0
$689$	3.61218	−	6.25649i	0.137613	−	0.238353i
$690$		0			0
$691$	−20.5494	+	11.8642i	−0.781735	+	0.451335i	−0.837045	−	0.547134i	$-0.815719\pi$
$691$	−20.5494	+	11.8642i	−0.781735	+	0.451335i	0.0553098	+	0.998469i	$0.482385\pi$
$692$		0			0
$693$	3.20555	−	10.2412i	0.121769	−	0.389031i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.7320	−	18.5884i	0.406505	−	0.704087i
$698$		0			0
$699$	−11.4348	−	10.1590i	−0.432503	−	0.384250i
$700$		0			0
$701$			21.2721i			0.803436i	0.915763	+	0.401718i	$0.131587\pi$
$701$			21.2721i			0.803436i	−0.915763	+	0.401718i	$0.868413\pi$
$702$		0			0
$703$	10.9633	+	6.32966i	0.413488	+	0.238728i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	27.9486	+	38.6700i	1.05112	+	1.45433i
$708$		0			0
$709$	22.8069	+	39.5026i	0.856529	+	1.48355i	0.875219	+	0.483727i	$0.160717\pi$
$709$	22.8069	+	39.5026i	0.856529	+	1.48355i	−0.0186897	+	0.999825i	$0.505949\pi$
$710$		0			0
$711$	13.3252	+	5.72160i	0.499733	+	0.214577i
$712$		0			0
$713$	14.1696			0.530655
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20.2720	+	6.73615i	−0.757071	+	0.251566i
$718$		0			0
$719$	9.50850	+	16.4692i	0.354607	+	0.614198i	0.987051	−	0.160409i	$-0.0512812\pi$
$719$	9.50850	+	16.4692i	0.354607	+	0.614198i	−0.632443	+	0.774607i	$0.717948\pi$
$720$		0			0
$721$	0.166370	+	1.62171i	0.00619593	+	0.0603956i
$722$		0			0
$723$	2.77457	−	13.4940i	0.103187	−	0.501848i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			34.0540i			1.26299i	0.775379	+	0.631496i	$0.217559\pi$
$727$			34.0540i			1.26299i	−0.775379	+	0.631496i	$0.782441\pi$
$728$		0			0
$729$	9.36126	+	25.3252i	0.346714	+	0.937971i
$730$		0			0
$731$	−11.6662	+	20.2064i	−0.431489	+	0.747361i
$732$		0			0
$733$	6.71837	−	3.87885i	0.248148	−	0.143269i	−0.370768	−	0.928726i	$-0.620905\pi$
$733$	6.71837	−	3.87885i	0.248148	−	0.143269i	0.618916	+	0.785457i	$0.287572\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.89973	+	3.40621i	−0.217319	+	0.125469i
$738$		0			0
$739$	4.19659	−	7.26871i	0.154374	−	0.267384i	−0.778457	−	0.627698i	$-0.783997\pi$
$739$	4.19659	−	7.26871i	0.154374	−	0.267384i	0.932831	+	0.360314i	$0.117331\pi$
$740$		0			0
$741$	−18.6929	+	21.0403i	−0.686702	+	0.772936i
$742$		0			0
$743$			14.7540i			0.541273i	0.962682	+	0.270636i	$0.0872341\pi$
$743$			14.7540i			0.541273i	−0.962682	+	0.270636i	$0.912766\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	40.0224	−	29.8994i	1.46434	−	1.09396i
$748$		0			0
$749$	4.78186	+	46.6118i	0.174725	+	1.70316i
$750$		0			0
$751$	−20.6067	−	35.6918i	−0.751948	−	1.30241i	−0.946877	−	0.321595i	$-0.895781\pi$
$751$	−20.6067	−	35.6918i	−0.751948	−	1.30241i	0.194929	−	0.980817i	$-0.437552\pi$
$752$		0			0
$753$	−4.17692	−	12.5702i	−0.152216	−	0.458082i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	11.8681			0.431354			0.215677	−	0.976465i	$-0.430804\pi$
$757$	11.8681			0.431354			0.215677	+	0.976465i	$0.430804\pi$
$758$		0			0
$759$	−3.69613	−	11.1233i	−0.134161	−	0.403749i
$760$		0			0
$761$	−17.7705	−	30.7795i	−0.644181	−	1.11575i	−0.984490	−	0.175441i	$-0.943865\pi$
$761$	−17.7705	−	30.7795i	−0.644181	−	1.11575i	0.340309	−	0.940314i	$-0.389468\pi$
$762$		0			0
$763$	−2.65104	−	3.66800i	−0.0959739	−	0.132790i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.1772	−	21.4643i	−1.34239	−	0.775029i
$768$		0			0
$769$			6.25608i			0.225600i	0.993618	+	0.112800i	$0.0359820\pi$
$769$			6.25608i			0.225600i	−0.993618	+	0.112800i	$0.964018\pi$
$770$		0			0
$771$	31.6304	−	35.6025i	1.13914	−	1.28219i
$772$		0			0
$773$	−10.0161	+	17.3483i	−0.360253	+	0.623977i	−0.988002	−	0.154439i	$-0.950643\pi$
$773$	−10.0161	+	17.3483i	−0.360253	+	0.623977i	0.627749	+	0.778416i	$0.283976\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.24474	−	16.0914i	−0.259904	−	0.577274i
$778$		0			0
$779$	10.6419	−	6.14412i	0.381286	−	0.220136i
$780$		0			0
$781$	−2.28663	+	3.96056i	−0.0818220	+	0.141720i
$782$		0			0
$783$	−16.8868	+	24.2457i	−0.603486	+	0.866469i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.27835	+	0.738053i	0.0455681	+	0.0263088i	0.522611	−	0.852571i	$-0.324958\pi$
$787$	1.27835	+	0.738053i	0.0455681	+	0.0263088i	−0.477043	+	0.878880i	$0.658291\pi$
$788$		0			0
$789$	6.63570	−	32.2725i	0.236237	−	1.14893i
$790$		0			0
$791$	31.6794	+	14.1991i	1.12639	+	0.504863i
$792$		0			0
$793$	−4.71754	−	8.17101i	−0.167525	−	0.290161i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.9470			−0.812823			−0.406411	−	0.913690i	$-0.633220\pi$
$797$	−22.9470			−0.812823			−0.406411	+	0.913690i	$0.633220\pi$
$798$		0			0
$799$	−32.6493			−1.15505
$800$		0			0
$801$	−44.5553	−	19.1313i	−1.57428	−	0.675971i
$802$		0			0
$803$	11.0372	+	19.1170i	0.389495	+	0.674625i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.1336	+	3.11170i	0.532729	+	0.109537i
$808$		0			0
$809$	−19.5613	−	11.2937i	−0.687739	−	0.397066i	0.115026	−	0.993363i	$-0.463305\pi$
$809$	−19.5613	−	11.2937i	−0.687739	−	0.397066i	−0.802764	+	0.596296i	$0.796638\pi$
$810$		0			0
$811$		−	41.9366i		−	1.47259i	−0.676659	−	0.736296i	$-0.736573\pi$
$811$		−	41.9366i		−	1.47259i	0.676659	−	0.736296i	$-0.263427\pi$
$812$		0			0
$813$	−9.76522	−	8.67573i	−0.342481	−	0.304271i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−11.5682	+	6.67892i	−0.404721	+	0.233666i
$818$		0			0
$819$	38.2858	−	8.57161i	1.33781	−	0.299516i
$820$		0			0
$821$	−0.447025	+	0.258090i	−0.0156013	+	0.00900741i	−0.507780	−	0.861487i	$-0.669534\pi$
$821$	−0.447025	+	0.258090i	−0.0156013	+	0.00900741i	0.492179	+	0.870494i	$0.336201\pi$
$822$		0			0
$823$	−10.2841	+	17.8125i	−0.358480	+	0.620906i	−0.987707	−	0.156316i	$-0.950038\pi$
$823$	−10.2841	+	17.8125i	−0.358480	+	0.620906i	0.629227	+	0.777222i	$0.283372\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	24.0587i		−	0.836603i	−0.908308	−	0.418301i	$-0.862626\pi$
$827$		−	24.0587i		−	0.836603i	0.908308	−	0.418301i	$-0.137374\pi$
$828$		0			0
$829$	−39.3074	−	22.6941i	−1.36520	−	0.788200i	−0.374891	−	0.927069i	$-0.622320\pi$
$829$	−39.3074	−	22.6941i	−1.36520	−	0.788200i	−0.990311	+	0.138869i	$0.955653\pi$
$830$		0			0
$831$	3.01500	+	0.619928i	0.104589	+	0.0215051i
$832$		0			0
$833$	−39.3574	+	8.16117i	−1.36365	+	0.282768i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−6.24984	−	13.3158i	−0.216026	−	0.460262i
$838$		0			0
$839$	−39.8758			−1.37666			−0.688332	−	0.725395i	$-0.741657\pi$
$839$	−39.8758			−1.37666			−0.688332	+	0.725395i	$0.741657\pi$
$840$		0			0
$841$	−3.33396			−0.114964
$842$		0			0
$843$	−41.7198	+	13.8630i	−1.43691	+	0.477468i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−24.1404	+	2.47654i	−0.829474	+	0.0850949i
$848$		0			0
$849$	5.63015	−	27.3820i	0.193226	−	0.939748i
$850$		0			0
$851$	−16.6929	−	9.63764i	−0.572225	−	0.330374i
$852$		0			0
$853$		−	16.9504i		−	0.580372i	−0.956970	−	0.290186i	$-0.906283\pi$
$853$		−	16.9504i		−	0.580372i	0.956970	−	0.290186i	$-0.0937172\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.315644	+	0.546711i	−0.0107822	+	0.0186753i	−0.871366	−	0.490633i	$-0.836765\pi$
$857$	−0.315644	+	0.546711i	−0.0107822	+	0.0186753i	0.860584	+	0.509309i	$0.170099\pi$
$858$		0			0
$859$	−5.59642	+	3.23109i	−0.190947	+	0.110243i	−0.592426	−	0.805625i	$-0.701830\pi$
$859$	−5.59642	+	3.23109i	−0.190947	+	0.110243i	0.401479	+	0.915868i	$0.368496\pi$
$860$		0			0
$861$	−17.0432	−	1.71962i	−0.580832	−	0.0586045i
$862$		0			0
$863$	−6.31821	+	3.64782i	−0.215074	+	0.124173i	−0.603667	−	0.797236i	$-0.706295\pi$
$863$	−6.31821	+	3.64782i	−0.215074	+	0.124173i	0.388593	+	0.921409i	$0.372961\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.3735	+	20.6808i	−0.623998	+	0.702358i
$868$		0			0
$869$			6.53538i			0.221698i
$870$		0			0
$871$	−21.5697	−	12.4533i	−0.730861	−	0.421963i
$872$		0			0
$873$	−21.6494	−	28.9793i	−0.732722	−	0.980800i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	14.8442	+	25.7109i	0.501253	+	0.868196i	0.999999	+	0.00144772i	$0.000460824\pi$
$877$	14.8442	+	25.7109i	0.501253	+	0.868196i	−0.498746	+	0.866748i	$0.666206\pi$
$878$		0			0
$879$	−10.6801	−	32.1410i	−0.360230	−	1.08409i
$880$		0			0
$881$	21.6272			0.728638			0.364319	−	0.931274i	$-0.381302\pi$
$881$	21.6272			0.728638			0.364319	+	0.931274i	$0.381302\pi$
$882$		0			0
$883$	29.9462			1.00777			0.503884	−	0.863771i	$-0.331904\pi$
$883$	29.9462			1.00777			0.503884	+	0.863771i	$0.331904\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.89821	−	10.2160i	−0.198043	−	0.343020i	0.749851	−	0.661607i	$-0.230125\pi$
$887$	−5.89821	−	10.2160i	−0.198043	−	0.343020i	−0.947894	+	0.318587i	$0.896792\pi$
$888$		0			0
$889$	16.8082	−	37.5003i	0.563728	−	1.25772i
$890$		0			0
$891$	−8.82279	+	8.37962i	−0.295574	+	0.280728i
$892$		0			0
$893$	−16.1876	−	9.34591i	−0.541697	−	0.312749i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	28.4622	−	32.0364i	0.950324	−	1.06966i
$898$		0			0
$899$	8.04855	−	13.9405i	0.268434	−	0.464942i
$900$		0			0
$901$	7.26798	−	4.19617i	0.242131	−	0.139795i
$902$		0			0
$903$	18.5267	+	1.86930i	0.616530	+	0.0622064i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.2455	+	24.6739i	−0.473014	+	0.819284i	−0.999523	−	0.0308855i	$-0.990167\pi$
$907$	−14.2455	+	24.6739i	−0.473014	+	0.819284i	0.526509	+	0.850169i	$0.323501\pi$
$908$		0			0
$909$	−6.37028	−	53.7246i	−0.211289	−	1.78193i
$910$		0			0
$911$		−	14.4884i		−	0.480023i	−0.970770	−	0.240011i	$-0.922849\pi$
$911$		−	14.4884i		−	0.480023i	0.970770	−	0.240011i	$-0.0771511\pi$
$912$		0			0
$913$	19.4979	+	11.2571i	0.645285	+	0.372555i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	23.5728	−	2.41831i	0.778442	−	0.0798597i
$918$		0			0
$919$	2.83403	+	4.90869i	0.0934861	+	0.161923i	0.908976	−	0.416849i	$-0.136866\pi$
$919$	2.83403	+	4.90869i	0.0934861	+	0.161923i	−0.815490	+	0.578772i	$0.803532\pi$
$920$		0			0
$921$	19.4333	−	6.45748i	0.640350	−	0.212781i
$922$		0			0
$923$	−16.7200			−0.550346
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.729323	−	1.69854i	0.0239541	−	0.0557873i
$928$		0			0
$929$	−8.51159	−	14.7425i	−0.279256	−	0.483686i	0.691944	−	0.721951i	$-0.256755\pi$
$929$	−8.51159	−	14.7425i	−0.279256	−	0.483686i	−0.971200	+	0.238265i	$0.923421\pi$
$930$		0			0
$931$	−21.8496	−	7.21979i	−0.716092	−	0.236619i
$932$		0			0
$933$	−37.8974	−	7.79228i	−1.24071	−	0.255108i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			11.1936i			0.365678i	0.983143	+	0.182839i	$0.0585287\pi$
$937$			11.1936i			0.365678i	−0.983143	+	0.182839i	$0.941471\pi$
$938$		0			0
$939$	−17.2317	−	15.3092i	−0.562336	−	0.499598i
$940$		0			0
$941$	−11.0101	+	19.0700i	−0.358919	+	0.621665i	−0.987780	−	0.155852i	$-0.950188\pi$
$941$	−11.0101	+	19.0700i	−0.358919	+	0.621665i	0.628862	+	0.777517i	$0.283521\pi$
$942$		0			0
$943$	−16.2036	+	9.35513i	−0.527661	+	0.304645i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	24.7743	−	14.3035i	0.805057	−	0.464800i	−0.0401795	−	0.999192i	$-0.512793\pi$
$947$	24.7743	−	14.3035i	0.805057	−	0.464800i	0.845236	+	0.534393i	$0.179460\pi$
$948$		0			0
$949$	−40.3526	+	69.8927i	−1.30990	+	2.26881i
$950$		0			0
$951$	43.8672	+	38.9731i	1.42249	+	1.26379i
$952$		0			0
$953$			45.2210i			1.46485i	0.680846	+	0.732426i	$0.261612\pi$
$953$			45.2210i			1.46485i	−0.680846	+	0.732426i	$0.738388\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−13.0429	−	2.68181i	−0.421617	−	0.0866907i
$958$		0			0
$959$	33.1908	−	23.9886i	1.07179	−	0.774631i
$960$		0			0
$961$	−11.4931	−	19.9067i	−0.370746	−	0.642150i
$962$		0			0
$963$	20.9625	−	48.8200i	0.675506	−	1.57320i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	54.5961			1.75569			0.877846	−	0.478943i	$-0.158980\pi$
$967$	54.5961			1.75569			0.877846	+	0.478943i	$0.158980\pi$
$968$		0			0
$969$	−31.0267	+	10.3098i	−0.996722	+	0.331200i
$970$		0			0
$971$	−12.1591	−	21.0603i	−0.390206	−	0.675856i	0.602271	−	0.798292i	$-0.294263\pi$
$971$	−12.1591	−	21.0603i	−0.390206	−	0.675856i	−0.992476	+	0.122436i	$0.960929\pi$
$972$		0			0
$973$	−48.6600	−	21.8101i	−1.55997	−	0.699198i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.94835	+	4.58898i	0.254290	+	0.146815i	0.621727	−	0.783234i	$-0.286431\pi$
$977$	7.94835	+	4.58898i	0.254290	+	0.146815i	−0.367437	+	0.930048i	$0.619765\pi$
$978$		0			0
$979$		−	21.8523i		−	0.698403i
$980$		0			0
$981$	0.604246	+	5.09599i	0.0192921	+	0.162703i
$982$		0			0
$983$	8.29768	−	14.3720i	0.264655	−	0.458396i	−0.702818	−	0.711369i	$-0.748075\pi$
$983$	8.29768	−	14.3720i	0.264655	−	0.458396i	0.967473	+	0.252974i	$0.0814086\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	10.6971	+	23.7593i	0.340491	+	0.756268i
$988$		0			0
$989$	17.6140	−	10.1694i	0.560092	−	0.323369i
$990$		0			0
$991$	−9.44914	+	16.3664i	−0.300162	+	0.519895i	−0.976172	−	0.216996i	$-0.930374\pi$
$991$	−9.44914	+	16.3664i	−0.300162	+	0.519895i	0.676011	+	0.736892i	$0.263707\pi$
$992$		0			0
$993$	2.27735	−	2.56334i	0.0722696	−	0.0813450i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−12.7670	−	7.37103i	−0.404335	−	0.233443i	0.284018	−	0.958819i	$-0.408333\pi$
$997$	−12.7670	−	7.37103i	−0.404335	−	0.233443i	−0.688353	+	0.725376i	$0.741666\pi$
$998$		0			0
$999$	−1.69414	+	19.9380i	−0.0536003	+	0.630811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.k.101.2		10
3.2	odd	2		2100.2.bi.j.101.1		10
5.2	odd	4		2100.2.bo.h.1949.2		20
5.3	odd	4		2100.2.bo.h.1949.9		20
5.4	even	2		420.2.bh.a.101.4	✓	10
7.5	odd	6		2100.2.bi.j.1601.1		10
15.2	even	4		2100.2.bo.g.1949.6		20
15.8	even	4		2100.2.bo.g.1949.5		20
15.14	odd	2		420.2.bh.b.101.5	yes	10
21.5	even	6	inner	2100.2.bi.k.1601.2		10
35.4	even	6		2940.2.d.b.881.7		10
35.12	even	12		2100.2.bo.g.1349.5		20
35.19	odd	6		420.2.bh.b.341.5	yes	10
35.24	odd	6		2940.2.d.a.881.4		10
35.33	even	12		2100.2.bo.g.1349.6		20
105.47	odd	12		2100.2.bo.h.1349.9		20
105.59	even	6		2940.2.d.b.881.8		10
105.68	odd	12		2100.2.bo.h.1349.2		20
105.74	odd	6		2940.2.d.a.881.3		10
105.89	even	6		420.2.bh.a.341.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.4	✓	10	5.4	even	2
420.2.bh.a.341.4	yes	10	105.89	even	6
420.2.bh.b.101.5	yes	10	15.14	odd	2
420.2.bh.b.341.5	yes	10	35.19	odd	6
2100.2.bi.j.101.1		10	3.2	odd	2
2100.2.bi.j.1601.1		10	7.5	odd	6
2100.2.bi.k.101.2		10	1.1	even	1	trivial
2100.2.bi.k.1601.2		10	21.5	even	6	inner
2100.2.bo.g.1349.5		20	35.12	even	12
2100.2.bo.g.1349.6		20	35.33	even	12
2100.2.bo.g.1949.5		20	15.8	even	4
2100.2.bo.g.1949.6		20	15.2	even	4
2100.2.bo.h.1349.2		20	105.68	odd	12
2100.2.bo.h.1349.9		20	105.47	odd	12
2100.2.bo.h.1949.2		20	5.2	odd	4
2100.2.bo.h.1949.9		20	5.3	odd	4
2940.2.d.a.881.3		10	105.74	odd	6
2940.2.d.a.881.4		10	35.24	odd	6
2940.2.d.b.881.7		10	35.4	even	6
2940.2.d.b.881.8		10	105.59	even	6

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.546177 - 1.64368i) q^{3} +(1.08214 - 2.41433i) q^{7} +(-2.40338 + 1.79548i) q^{9} +O(q^{10})\)	\(q+(-0.546177 - 1.64368i) q^{3} +(1.08214 - 2.41433i) q^{7} +(-2.40338 + 1.79548i) q^{9} +(-1.17086 - 0.675999i) q^{11} -4.94296i q^{13} +(2.87105 - 4.97280i) q^{17} +(2.84694 - 1.64368i) q^{19} +(-4.55943 - 0.460035i) q^{21} +(-4.33480 + 2.50270i) q^{23} +(4.26388 + 2.96974i) q^{27} +5.68630i q^{29} +(-2.45160 - 1.41543i) q^{31} +(-0.471628 + 2.29374i) q^{33} +(1.92545 + 3.33498i) q^{37} +(-8.12466 + 2.69973i) q^{39} +3.73802 q^{41} -4.06339 q^{43} +(-2.84298 - 4.92419i) q^{47} +(-4.65797 - 5.22526i) q^{49} +(-9.74181 - 2.00306i) q^{51} +(1.26574 + 0.730773i) q^{53} +(-4.25662 - 3.78172i) q^{57} +(4.34239 - 7.52123i) q^{59} +(1.65306 - 0.954394i) q^{61} +(1.73410 + 7.74551i) q^{63} +(2.51939 - 4.36371i) q^{67} +(6.48121 + 5.75812i) q^{69} -3.38259i q^{71} +(-14.1398 - 8.16364i) q^{73} +(-2.89912 + 2.09533i) q^{77} +(-2.41693 - 4.18625i) q^{79} +(2.55248 - 8.63046i) q^{81} -16.6525 q^{83} +(9.34646 - 3.10572i) q^{87} +(8.08150 + 13.9976i) q^{89} +(-11.9339 - 5.34895i) q^{91} +(-0.987510 + 4.80272i) q^{93} +12.0577i q^{97} +(4.02778 - 0.477584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 5 * q^7 - 3 * q^9	\( 10 q + q^{3} + 5 q^{7} - 3 q^{9} - 6 q^{11} - 6 q^{17} + 3 q^{19} + 10 q^{21} - 24 q^{23} - 8 q^{27} + 15 q^{31} + 20 q^{33} + q^{37} + 15 q^{39} - 8 q^{41} + 26 q^{43} - 14 q^{47} - 13 q^{49} - 44 q^{51} + 24 q^{53} - 18 q^{57} + 42 q^{61} + q^{63} - 7 q^{67} - 14 q^{69} + 3 q^{73} + 26 q^{77} + q^{79} + 41 q^{81} + 8 q^{83} + 26 q^{87} + 28 q^{89} - 11 q^{91} + 47 q^{93} + 36 q^{99}+O(q^{100}) \) 10 * q + q^3 + 5 * q^7 - 3 * q^9 - 6 * q^11 - 6 * q^17 + 3 * q^19 + 10 * q^21 - 24 * q^23 - 8 * q^27 + 15 * q^31 + 20 * q^33 + q^37 + 15 * q^39 - 8 * q^41 + 26 * q^43 - 14 * q^47 - 13 * q^49 - 44 * q^51 + 24 * q^53 - 18 * q^57 + 42 * q^61 + q^63 - 7 * q^67 - 14 * q^69 + 3 * q^73 + 26 * q^77 + q^79 + 41 * q^81 + 8 * q^83 + 26 * q^87 + 28 * q^89 - 11 * q^91 + 47 * q^93 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more