LMFDB - Embedded newform 260.2.bf.c.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(37,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 7]))

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			253.2
Root			$-1.14923i$ of defining polynomial
Character	$\chi$	$=$	260.253
Dual form			260.2.bf.c.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44654 + 0.387600i) q^{3} +(1.07994 - 1.95799i) q^{5} +(-1.21558 - 2.10545i) q^{7} +(-0.655821 + 0.378639i) q^{9} +O(q^{10})$	\(q+(-1.44654 + 0.387600i) q^{3} +(1.07994 - 1.95799i) q^{5} +(-1.21558 - 2.10545i) q^{7} +(-0.655821 + 0.378639i) q^{9} +(-2.60249 + 0.697334i) q^{11} +(0.447059 - 3.57773i) q^{13} +(-0.803262 + 3.25091i) q^{15} +(1.62146 - 6.05137i) q^{17} +(1.00046 - 3.73376i) q^{19} +(2.57447 + 2.57447i) q^{21} +(-0.307564 - 1.14784i) q^{23} +(-2.66746 - 4.22902i) q^{25} +(3.97874 - 3.97874i) q^{27} +(5.29270 + 3.05574i) q^{29} +(-6.23000 + 6.23000i) q^{31} +(3.49432 - 2.01745i) q^{33} +(-5.43522 + 0.106341i) q^{35} +(-3.86311 + 6.69111i) q^{37} +(0.740038 + 5.34862i) q^{39} +(0.913943 + 3.41088i) q^{41} +(4.37424 + 1.17207i) q^{43} +(0.0331240 + 1.69300i) q^{45} -6.81282 q^{47} +(0.544711 - 0.943467i) q^{49} +9.38205i q^{51} +(4.88693 + 4.88693i) q^{53} +(-1.44515 + 5.84872i) q^{55} +5.78882i q^{57} +(9.04287 + 2.42303i) q^{59} +(-4.87808 - 8.44908i) q^{61} +(1.59441 + 0.920534i) q^{63} +(-6.52237 - 4.73907i) q^{65} +(-0.878637 - 0.507281i) q^{67} +(0.889809 + 1.54120i) q^{69} +(10.5637 + 2.83054i) q^{71} -9.06732i q^{73} +(5.49777 + 5.08356i) q^{75} +(4.63174 + 4.63174i) q^{77} -11.6191i q^{79} +(-3.07735 + 5.33013i) q^{81} -1.09215 q^{83} +(-10.0975 - 9.70992i) q^{85} +(-8.84053 - 2.36881i) q^{87} +(1.29560 + 4.83523i) q^{89} +(-8.07618 + 3.40777i) q^{91} +(6.59721 - 11.4267i) q^{93} +(-6.23024 - 5.99112i) q^{95} +(2.39272 - 1.38144i) q^{97} +(1.44273 - 1.44273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.44654	+	0.387600i	−0.835162	+	0.223781i	−0.650965	−	0.759108i	$-0.725635\pi$
$3$	−1.44654	+	0.387600i	−0.835162	+	0.223781i	−0.184198	+	0.982889i	$0.558969\pi$
$4$		0			0
$5$	1.07994	−	1.95799i	0.482964	−	0.875640i
$5$	1.07994	−	1.95799i	0.482964	−	0.875640i
$6$		0			0
$7$	−1.21558	−	2.10545i	−0.459448	−	0.795787i	0.539484	−	0.841996i	$-0.318619\pi$
$7$	−1.21558	−	2.10545i	−0.459448	−	0.795787i	−0.998932	+	0.0462092i	$0.985286\pi$
$8$		0			0
$9$	−0.655821	+	0.378639i	−0.218607	+	0.126213i
$10$		0			0
$11$	−2.60249	+	0.697334i	−0.784679	+	0.210254i	−0.628847	−	0.777529i	$-0.716473\pi$
$11$	−2.60249	+	0.697334i	−0.784679	+	0.210254i	−0.155832	+	0.987784i	$0.549806\pi$
$12$		0			0
$13$	0.447059	−	3.57773i	0.123992	−	0.992283i
$13$	0.447059	−	3.57773i	0.123992	−	0.992283i
$14$		0			0
$15$	−0.803262	+	3.25091i	−0.207401	+	0.839380i
$16$		0			0
$17$	1.62146	−	6.05137i	0.393262	−	1.46767i	−0.431459	−	0.902133i	$-0.642001\pi$
$17$	1.62146	−	6.05137i	0.393262	−	1.46767i	0.824721	−	0.565540i	$-0.191332\pi$
$18$		0			0
$19$	1.00046	−	3.73376i	0.229521	−	0.856583i	−0.751022	−	0.660277i	$-0.770439\pi$
$19$	1.00046	−	3.73376i	0.229521	−	0.856583i	0.980543	−	0.196306i	$-0.0628946\pi$
$20$		0			0
$21$	2.57447	+	2.57447i	0.561795	+	0.561795i
$22$		0			0
$23$	−0.307564	−	1.14784i	−0.0641315	−	0.239342i	0.926418	−	0.376496i	$-0.122871\pi$
$23$	−0.307564	−	1.14784i	−0.0641315	−	0.239342i	−0.990550	+	0.137154i	$0.956204\pi$
$24$		0			0
$25$	−2.66746	−	4.22902i	−0.533492	−	0.845805i
$26$		0			0
$27$	3.97874	−	3.97874i	0.765710	−	0.765710i
$28$		0			0
$29$	5.29270	+	3.05574i	0.982830	+	0.567437i	0.903123	−	0.429382i	$-0.141268\pi$
$29$	5.29270	+	3.05574i	0.982830	+	0.567437i	0.0797063	+	0.996818i	$0.474602\pi$
$30$		0			0
$31$	−6.23000	+	6.23000i	−1.11894	+	1.11894i	−0.127043	+	0.991897i	$0.540549\pi$
$31$	−6.23000	+	6.23000i	−1.11894	+	1.11894i	−0.991897	+	0.127043i	$0.959451\pi$
$32$		0			0
$33$	3.49432	−	2.01745i	0.608283	−	0.351193i
$34$		0			0
$35$	−5.43522	+	0.106341i	−0.918719	+	0.0179750i
$36$		0			0
$37$	−3.86311	+	6.69111i	−0.635092	+	1.10001i	0.351404	+	0.936224i	$0.385704\pi$
$37$	−3.86311	+	6.69111i	−0.635092	+	1.10001i	−0.986496	+	0.163787i	$0.947629\pi$
$38$		0			0
$39$	0.740038	+	5.34862i	0.118501	+	0.856465i
$40$		0			0
$41$	0.913943	+	3.41088i	0.142734	+	0.532690i	0.999846	+	0.0175599i	$0.00558976\pi$
$41$	0.913943	+	3.41088i	0.142734	+	0.532690i	−0.857112	+	0.515130i	$0.827744\pi$
$42$		0			0
$43$	4.37424	+	1.17207i	0.667066	+	0.178740i	0.576433	−	0.817145i	$-0.304444\pi$
$43$	4.37424	+	1.17207i	0.667066	+	0.178740i	0.0906330	+	0.995884i	$0.471111\pi$
$44$		0			0
$45$	0.0331240	+	1.69300i	0.00493783	+	0.252377i
$46$		0			0
$47$	−6.81282			−0.993752			−0.496876	−	0.867822i	$-0.665520\pi$
$47$	−6.81282			−0.993752			−0.496876	+	0.867822i	$0.665520\pi$
$48$		0			0
$49$	0.544711	−	0.943467i	0.0778159	−	0.134781i
$50$		0			0
$51$			9.38205i			1.31375i
$52$		0			0
$53$	4.88693	+	4.88693i	0.671272	+	0.671272i	0.958009	−	0.286737i	$-0.0925707\pi$
$53$	4.88693	+	4.88693i	0.671272	+	0.671272i	−0.286737	+	0.958009i	$0.592571\pi$
$54$		0			0
$55$	−1.44515	+	5.84872i	−0.194864	+	0.788642i
$56$		0			0
$57$			5.78882i			0.766748i
$58$		0			0
$59$	9.04287	+	2.42303i	1.17728	+	0.315452i	0.793848	−	0.608116i	$-0.208075\pi$
$59$	9.04287	+	2.42303i	1.17728	+	0.315452i	0.383434	+	0.923568i	$0.374741\pi$
$60$		0			0
$61$	−4.87808	−	8.44908i	−0.624574	−	1.08179i	−0.988623	−	0.150415i	$-0.951939\pi$
$61$	−4.87808	−	8.44908i	−0.624574	−	1.08179i	0.364049	−	0.931380i	$-0.381394\pi$
$62$		0			0
$63$	1.59441	+	0.920534i	0.200877	+	0.115976i
$64$		0			0
$65$	−6.52237	−	4.73907i	−0.809000	−	0.587809i
$66$		0			0
$67$	−0.878637	−	0.507281i	−0.107343	−	0.0619743i	0.445368	−	0.895348i	$-0.353073\pi$
$67$	−0.878637	−	0.507281i	−0.107343	−	0.0619743i	−0.552710	+	0.833374i	$0.686406\pi$
$68$		0			0
$69$	0.889809	+	1.54120i	0.107120	+	0.185538i
$70$		0			0
$71$	10.5637	+	2.83054i	1.25368	+	0.335924i	0.823759	−	0.566941i	$-0.191873\pi$
$71$	10.5637	+	2.83054i	1.25368	+	0.335924i	0.429926	+	0.902864i	$0.358540\pi$
$72$		0			0
$73$		−	9.06732i		−	1.06125i	−0.847607	−	0.530625i	$-0.821957\pi$
$73$		−	9.06732i		−	1.06125i	0.847607	−	0.530625i	$-0.178043\pi$
$74$		0			0
$75$	5.49777	+	5.08356i	0.634828	+	0.586999i
$76$		0			0
$77$	4.63174	+	4.63174i	0.527836	+	0.527836i
$78$		0			0
$79$		−	11.6191i		−	1.30725i	−0.756820	−	0.653623i	$-0.773248\pi$
$79$		−	11.6191i		−	1.30725i	0.756820	−	0.653623i	$-0.226752\pi$
$80$		0			0
$81$	−3.07735	+	5.33013i	−0.341928	+	0.592236i
$82$		0			0
$83$	−1.09215			−0.119879			−0.0599397	−	0.998202i	$-0.519091\pi$
$83$	−1.09215			−0.119879			−0.0599397	+	0.998202i	$0.519091\pi$
$84$		0			0
$85$	−10.0975	−	9.70992i	−1.09522	−	1.05319i
$86$		0			0
$87$	−8.84053	−	2.36881i	−0.947804	−	0.253963i
$88$		0			0
$89$	1.29560	+	4.83523i	0.137333	+	0.512533i	0.999977	+	0.00672267i	$0.00213991\pi$
$89$	1.29560	+	4.83523i	0.137333	+	0.512533i	−0.862644	+	0.505811i	$0.831193\pi$
$90$		0			0
$91$	−8.07618	+	3.40777i	−0.846613	+	0.357231i
$92$		0			0
$93$	6.59721	−	11.4267i	0.684099	−	1.18489i
$94$		0			0
$95$	−6.23024	−	5.99112i	−0.639209	−	0.614676i
$96$		0			0
$97$	2.39272	−	1.38144i	0.242944	−	0.140264i	−0.373585	−	0.927596i	$-0.621872\pi$
$97$	2.39272	−	1.38144i	0.242944	−	0.140264i	0.616529	+	0.787332i	$0.288538\pi$
$98$		0			0
$99$	1.44273	−	1.44273i	0.145000	−	0.145000i
$100$		0			0
$101$	11.2722	+	6.50799i	1.12162	+	0.647569i	0.941815	−	0.336133i	$-0.109119\pi$
$101$	11.2722	+	6.50799i	1.12162	+	0.647569i	0.179808	+	0.983702i	$0.442452\pi$
$102$		0			0
$103$	3.42536	−	3.42536i	0.337511	−	0.337511i	−0.517919	−	0.855430i	$-0.673293\pi$
$103$	3.42536	−	3.42536i	0.337511	−	0.337511i	0.855430	+	0.517919i	$0.173293\pi$
$104$		0			0
$105$	7.82106	−	2.26052i	0.763257	−	0.220604i
$106$		0			0
$107$	0.613583	+	2.28992i	0.0593173	+	0.221375i	0.989222	−	0.146427i	$-0.0467772\pi$
$107$	0.613583	+	2.28992i	0.0593173	+	0.221375i	−0.929904	+	0.367802i	$0.880111\pi$
$108$		0			0
$109$	2.27846	+	2.27846i	0.218237	+	0.218237i	0.807755	−	0.589518i	$-0.200682\pi$
$109$	2.27846	+	2.27846i	0.218237	+	0.218237i	−0.589518	+	0.807755i	$0.700682\pi$
$110$		0			0
$111$	2.99469	−	11.1763i	0.284243	−	1.06081i
$112$		0			0
$113$	−3.58242	+	13.3698i	−0.337006	+	1.25772i	0.564672	+	0.825315i	$0.309003\pi$
$113$	−3.58242	+	13.3698i	−0.337006	+	1.25772i	−0.901678	+	0.432408i	$0.857664\pi$
$114$		0			0
$115$	−2.57962	−	0.637395i	−0.240551	−	0.0594374i
$116$		0			0
$117$	1.06148	+	2.51562i	0.0981334	+	0.232570i
$118$		0			0
$119$	−14.7119	+	3.94204i	−1.34864	+	0.361366i
$120$		0			0
$121$	−3.23962	+	1.87040i	−0.294511	+	0.170036i
$122$		0			0
$123$	−2.64412	−	4.57974i	−0.238412	−	0.412942i
$124$		0			0
$125$	−11.1611	+	0.655778i	−0.998278	+	0.0586546i
$126$		0			0
$127$	−4.23059	+	1.13358i	−0.375404	+	0.100589i	−0.441587	−	0.897218i	$-0.645584\pi$
$127$	−4.23059	+	1.13358i	−0.375404	+	0.100589i	0.0661832	+	0.997807i	$0.478918\pi$
$128$		0			0
$129$	−6.78183			−0.597107
$130$		0			0
$131$	12.1470			1.06129			0.530643	−	0.847596i	$-0.321951\pi$
$131$	12.1470			1.06129			0.530643	+	0.847596i	$0.321951\pi$
$132$		0			0
$133$	−9.07740	+	2.43228i	−0.787110	+	0.210906i
$134$		0			0
$135$	−3.49355	−	12.0872i	−0.300677	−	1.04030i
$136$		0			0
$137$	−7.15524	−	12.3932i	−0.611313	−	1.05883i	−0.991019	−	0.133719i	$-0.957308\pi$
$137$	−7.15524	−	12.3932i	−0.611313	−	1.05883i	0.379706	−	0.925107i	$-0.376025\pi$
$138$		0			0
$139$	13.2937	−	7.67514i	1.12756	−	0.650997i	0.184239	−	0.982881i	$-0.441018\pi$
$139$	13.2937	−	7.67514i	1.12756	−	0.650997i	0.943320	+	0.331885i	$0.107685\pi$
$140$		0			0
$141$	9.85504	−	2.64065i	0.829944	−	0.222383i
$142$		0			0
$143$	1.33141	+	9.62273i	0.111338	+	0.804694i
$144$		0			0
$145$	11.6989	−	7.06304i	0.971542	−	0.586554i
$146$		0			0
$147$	−0.422260	+	1.57590i	−0.0348274	+	0.129978i
$148$		0			0
$149$	0.861750	−	3.21610i	0.0705973	−	0.263473i	−0.921602	−	0.388137i	$-0.873119\pi$
$149$	0.861750	−	3.21610i	0.0705973	−	0.263473i	0.992199	+	0.124664i	$0.0397854\pi$
$150$		0			0
$151$	−14.6691	−	14.6691i	−1.19375	−	1.19375i	−0.976005	−	0.217749i	$-0.930129\pi$
$151$	−14.6691	−	14.6691i	−1.19375	−	1.19375i	−0.217749	−	0.976005i	$-0.569871\pi$
$152$		0			0
$153$	1.22789	+	4.58257i	0.0992694	+	0.370479i
$154$		0			0
$155$	5.47026	+	18.9263i	0.439382	+	1.52020i
$156$		0			0
$157$	14.7756	−	14.7756i	1.17922	−	1.17922i	0.199281	−	0.979942i	$-0.436139\pi$
$157$	14.7756	−	14.7756i	1.17922	−	1.17922i	0.979942	−	0.199281i	$-0.0638605\pi$
$158$		0			0
$159$	−8.96334	−	5.17499i	−0.710839	−	0.410403i
$160$		0			0
$161$	−2.04286	+	2.04286i	−0.161000	+	0.161000i
$162$		0			0
$163$	7.74127	−	4.46942i	0.606343	−	0.350072i	−0.165190	−	0.986262i	$-0.552824\pi$
$163$	7.74127	−	4.46942i	0.606343	−	0.350072i	0.771533	+	0.636190i	$0.219490\pi$
$164$		0			0
$165$	−0.176490	−	9.02057i	−0.0137397	−	0.702251i
$166$		0			0
$167$	9.10649	−	15.7729i	0.704681	−	1.22054i	−0.262125	−	0.965034i	$-0.584423\pi$
$167$	9.10649	−	15.7729i	0.704681	−	1.22054i	0.966806	−	0.255510i	$-0.0822434\pi$
$168$		0			0
$169$	−12.6003	−	3.19891i	−0.969252	−	0.246070i
$170$		0			0
$171$	0.757624	+	2.82749i	0.0579370	+	0.216224i
$172$		0			0
$173$	−1.75363	−	0.469884i	−0.133326	−	0.0357246i	0.191539	−	0.981485i	$-0.438652\pi$
$173$	−1.75363	−	0.469884i	−0.133326	−	0.0357246i	−0.324865	+	0.945760i	$0.605319\pi$
$174$		0			0
$175$	−5.66149	+	10.7570i	−0.427968	+	0.813149i
$176$		0			0
$177$	−14.0201			−1.05381
$178$		0			0
$179$	9.09987	−	15.7614i	0.680156	−	1.17807i	−0.294776	−	0.955566i	$-0.595245\pi$
$179$	9.09987	−	15.7614i	0.680156	−	1.17807i	0.974933	−	0.222499i	$-0.0714215\pi$
$180$		0			0
$181$			17.4351i			1.29594i	0.761667	+	0.647969i	$0.224381\pi$
$181$			17.4351i			1.29594i	−0.761667	+	0.647969i	$0.775619\pi$
$182$		0			0
$183$	10.3312	+	10.3312i	0.763706	+	0.763706i
$184$		0			0
$185$	8.92921	+	14.7899i	0.656488	+	1.08738i
$186$		0			0
$187$			16.8793i			1.23434i
$188$		0			0
$189$	−13.2136	−	3.54056i	−0.961145	−	0.257538i
$190$		0			0
$191$	−10.5403	−	18.2564i	−0.762672	−	1.32099i	−0.941469	−	0.337101i	$-0.890554\pi$
$191$	−10.5403	−	18.2564i	−0.762672	−	1.32099i	0.178796	−	0.983886i	$-0.442780\pi$
$192$		0			0
$193$	−16.7799	−	9.68786i	−1.20784	−	0.697348i	−0.245554	−	0.969383i	$-0.578970\pi$
$193$	−16.7799	−	9.68786i	−1.20784	−	0.697348i	−0.962287	+	0.272035i	$0.912303\pi$
$194$		0			0
$195$	11.2717	+	4.32720i	0.807187	+	0.309877i
$196$		0			0
$197$	10.7144	+	6.18595i	0.763368	+	0.440731i	0.830504	−	0.557013i	$-0.188053\pi$
$197$	10.7144	+	6.18595i	0.763368	+	0.440731i	−0.0671359	+	0.997744i	$0.521386\pi$
$198$		0			0
$199$	5.08783	+	8.81238i	0.360667	+	0.624693i	0.988071	−	0.154001i	$-0.0492159\pi$
$199$	5.08783	+	8.81238i	0.360667	+	0.624693i	−0.627404	+	0.778694i	$0.715883\pi$
$200$		0			0
$201$	1.46761	+	0.393245i	0.103517	+	0.0277373i
$202$		0			0
$203$		−	14.8580i		−	1.04283i
$204$		0			0
$205$	7.66548	+	1.89405i	0.535380	+	0.132286i
$206$		0			0
$207$	0.636325	+	0.636325i	0.0442277	+	0.0442277i
$208$		0			0
$209$			10.4147i			0.720400i
$210$		0			0
$211$	8.67864	−	15.0319i	0.597463	−	1.03484i	−0.395732	−	0.918366i	$-0.629509\pi$
$211$	8.67864	−	15.0319i	0.597463	−	1.03484i	0.993194	−	0.116469i	$-0.0371577\pi$
$212$		0			0
$213$	−16.3780			−1.12220
$214$		0			0
$215$	7.01883	−	7.29896i	0.478680	−	0.497785i
$216$		0			0
$217$	20.6901	+	5.54388i	1.40453	+	0.376343i
$218$		0			0
$219$	3.51450	+	13.1163i	0.237488	+	0.886316i
$220$		0			0
$221$	−20.9253	−	8.50646i	−1.40759	−	0.572207i
$222$		0			0
$223$	−10.9813	+	19.0202i	−0.735362	+	1.27368i	0.219203	+	0.975679i	$0.429654\pi$
$223$	−10.9813	+	19.0202i	−0.735362	+	1.27368i	−0.954564	+	0.298005i	$0.903679\pi$
$224$		0			0
$225$	3.35065	+	1.76348i	0.223377	+	0.117565i
$226$		0			0
$227$	−7.04528	+	4.06760i	−0.467612	+	0.269976i	−0.715239	−	0.698879i	$-0.753682\pi$
$227$	−7.04528	+	4.06760i	−0.467612	+	0.269976i	0.247628	+	0.968855i	$0.420349\pi$
$228$		0			0
$229$	−10.1234	+	10.1234i	−0.668973	+	0.668973i	−0.957478	−	0.288505i	$-0.906842\pi$
$229$	−10.1234	+	10.1234i	−0.668973	+	0.668973i	0.288505	+	0.957478i	$0.406842\pi$
$230$		0			0
$231$	−8.49528	−	4.90475i	−0.558949	−	0.322709i
$232$		0			0
$233$	−1.66935	+	1.66935i	−0.109363	+	0.109363i	−0.759671	−	0.650308i	$-0.774640\pi$
$233$	−1.66935	+	1.66935i	−0.109363	+	0.109363i	0.650308	+	0.759671i	$0.274640\pi$
$234$		0			0
$235$	−7.35743	+	13.3394i	−0.479946	+	0.870169i
$236$		0			0
$237$	4.50355	+	16.8075i	0.292537	+	1.09176i
$238$		0			0
$239$	16.8726	+	16.8726i	1.09140	+	1.09140i	0.995380	+	0.0960168i	$0.0306103\pi$
$239$	16.8726	+	16.8726i	1.09140	+	1.09140i	0.0960168	+	0.995380i	$0.469390\pi$
$240$		0			0
$241$	−1.24155	+	4.63353i	−0.0799753	+	0.298472i	−0.994315	−	0.106475i	$-0.966043\pi$
$241$	−1.24155	+	4.63353i	−0.0799753	+	0.298472i	0.914340	+	0.404947i	$0.132710\pi$
$242$		0			0
$243$	−1.98340	+	7.40216i	−0.127235	+	0.474849i
$244$		0			0
$245$	−1.25905	−	2.08543i	−0.0804375	−	0.133233i
$246$		0			0
$247$	−12.9111	−	5.24858i	−0.821514	−	0.333959i
$248$		0			0
$249$	1.57985	−	0.423319i	0.100119	−	0.0268268i
$250$		0			0
$251$	3.86584	−	2.23194i	0.244009	−	0.140879i	−0.373009	−	0.927828i	$-0.621674\pi$
$251$	3.86584	−	2.23194i	0.244009	−	0.140879i	0.617018	+	0.786949i	$0.288341\pi$
$252$		0			0
$253$	1.60086	+	2.77277i	0.100645	+	0.174323i
$254$		0			0
$255$	18.3700	+	10.1320i	1.15037	+	0.634493i
$256$		0			0
$257$	7.65731	−	2.05177i	0.477650	−	0.127986i	−0.0119581	−	0.999928i	$-0.503806\pi$
$257$	7.65731	−	2.05177i	0.477650	−	0.127986i	0.489608	+	0.871943i	$0.337140\pi$
$258$		0			0
$259$	18.7838			1.16717
$260$		0			0
$261$	−4.62809			−0.286471
$262$		0			0
$263$	−3.88683	+	1.04147i	−0.239672	+	0.0642200i	−0.376656	−	0.926353i	$-0.622926\pi$
$263$	−3.88683	+	1.04147i	−0.239672	+	0.0642200i	0.136983	+	0.990573i	$0.456259\pi$
$264$		0			0
$265$	14.8462	−	4.29098i	0.911993	−	0.263593i
$266$		0			0
$267$	−3.74827	−	6.49220i	−0.229391	−	0.397316i
$268$		0			0
$269$	−16.5636	+	9.56301i	−1.00990	+	0.583067i	−0.911163	−	0.412047i	$-0.864814\pi$
$269$	−16.5636	+	9.56301i	−1.00990	+	0.583067i	−0.0987386	+	0.995113i	$0.531481\pi$
$270$		0			0
$271$	7.39786	−	1.98225i	0.449388	−	0.120413i	−0.0270250	−	0.999635i	$-0.508603\pi$
$271$	7.39786	−	1.98225i	0.449388	−	0.120413i	0.476413	+	0.879222i	$0.341937\pi$
$272$		0			0
$273$	10.3617	−	8.05981i	0.627118	−	0.487802i
$274$		0			0
$275$	9.89107	+	9.14586i	0.596454	+	0.551516i
$276$		0			0
$277$	−3.91430	+	14.6084i	−0.235187	+	0.877731i	0.742877	+	0.669428i	$0.233461\pi$
$277$	−3.91430	+	14.6084i	−0.235187	+	0.877731i	−0.978064	+	0.208303i	$0.933206\pi$
$278$		0			0
$279$	1.72685	−	6.44468i	0.103384	−	0.385833i
$280$		0			0
$281$	13.0253	+	13.0253i	0.777027	+	0.777027i	0.979324	−	0.202297i	$-0.0648407\pi$
$281$	13.0253	+	13.0253i	0.777027	+	0.777027i	−0.202297	+	0.979324i	$0.564841\pi$
$282$		0			0
$283$	2.17335	+	8.11105i	0.129192	+	0.482152i	0.999954	−	0.00955242i	$-0.00304068\pi$
$283$	2.17335	+	8.11105i	0.129192	+	0.482152i	−0.870762	+	0.491705i	$0.836374\pi$
$284$		0			0
$285$	11.3345	+	6.25158i	0.671396	+	0.370312i
$286$		0			0
$287$	6.07048	−	6.07048i	0.358329	−	0.358329i
$288$		0			0
$289$	−19.2675	−	11.1241i	−1.13338	−	0.654360i
$290$		0			0
$291$	−2.92573	+	2.92573i	−0.171510	+	0.171510i
$292$		0			0
$293$	−1.50728	+	0.870229i	−0.0880563	+	0.0508393i	−0.543382	−	0.839486i	$-0.682856\pi$
$293$	−1.50728	+	0.870229i	−0.0880563	+	0.0508393i	0.455325	+	0.890325i	$0.349523\pi$
$294$		0			0
$295$	14.5100	−	15.0891i	0.844807	−	0.878524i
$296$		0			0
$297$	−7.58011	+	13.1291i	−0.439843	+	0.761830i
$298$		0			0
$299$	−4.24417	+	0.587226i	−0.245447	+	0.0339602i
$300$		0			0
$301$	−2.84951	−	10.6345i	−0.164243	−	0.612963i
$302$		0			0
$303$	−18.8282	−	5.04500i	−1.08165	−	0.289827i
$304$		0			0
$305$	−21.8113	+	0.426743i	−1.24891	+	0.0244352i
$306$		0			0
$307$	−9.53050			−0.543934			−0.271967	−	0.962307i	$-0.587674\pi$
$307$	−9.53050			−0.543934			−0.271967	+	0.962307i	$0.587674\pi$
$308$		0			0
$309$	−3.62726	+	6.28260i	−0.206348	+	0.357405i
$310$		0			0
$311$		−	19.5311i		−	1.10751i	−0.832680	−	0.553755i	$-0.813194\pi$
$311$		−	19.5311i		−	1.10751i	0.832680	−	0.553755i	$-0.186806\pi$
$312$		0			0
$313$	17.0195	+	17.0195i	0.962000	+	0.962000i	0.999304	−	0.0373038i	$-0.0118769\pi$
$313$	17.0195	+	17.0195i	0.962000	+	0.962000i	−0.0373038	+	0.999304i	$0.511877\pi$
$314$		0			0
$315$	3.52427	−	2.12772i	0.198570	−	0.119884i
$316$		0			0
$317$			7.07976i			0.397639i	0.980036	+	0.198819i	$0.0637107\pi$
$317$			7.07976i			0.397639i	−0.980036	+	0.198819i	$0.936289\pi$
$318$		0			0
$319$	−15.9050	−	4.26174i	−0.890512	−	0.238612i
$320$		0			0
$321$	−1.77515	−	3.07465i	−0.0990791	−	0.171610i
$322$		0			0
$323$	−20.9722	−	12.1083i	−1.16692	−	0.673723i
$324$		0			0
$325$	−16.3228	+	7.65283i	−0.905427	+	0.424503i
$326$		0			0
$327$	−4.17903	−	2.41276i	−0.231101	−	0.133426i
$328$		0			0
$329$	8.28155	+	14.3441i	0.456577	+	0.790814i
$330$		0			0
$331$	15.2412	+	4.08386i	0.837730	+	0.224469i	0.652083	−	0.758147i	$-0.273895\pi$
$331$	15.2412	+	4.08386i	0.837730	+	0.224469i	0.185647	+	0.982617i	$0.440562\pi$
$332$		0			0
$333$		−	5.85090i		−	0.320627i
$334$		0			0
$335$	−1.94213	+	1.17253i	−0.106110	+	0.0640622i
$336$		0			0
$337$	−4.66232	−	4.66232i	−0.253973	−	0.253973i	0.568625	−	0.822597i	$-0.307476\pi$
$337$	−4.66232	−	4.66232i	−0.253973	−	0.253973i	−0.822597	+	0.568625i	$0.807476\pi$
$338$		0			0
$339$		−	20.7285i		−	1.12582i
$340$		0			0
$341$	11.8691	−	20.5579i	0.642747	−	1.11327i
$342$		0			0
$343$	−19.6667			−1.06190
$344$		0			0
$345$	3.97859	−	0.0778421i	0.214200	−	0.00419088i
$346$		0			0
$347$	24.1728	+	6.47707i	1.29766	+	0.347707i	0.840566	−	0.541710i	$-0.182223\pi$
$347$	24.1728	+	6.47707i	1.29766	+	0.347707i	0.457096	+	0.889417i	$0.348889\pi$
$348$		0			0
$349$	−7.28299	−	27.1805i	−0.389850	−	1.45494i	−0.830378	−	0.557200i	$-0.811876\pi$
$349$	−7.28299	−	27.1805i	−0.389850	−	1.45494i	0.440528	−	0.897739i	$-0.354791\pi$
$350$		0			0
$351$	−12.4561	−	16.0136i	−0.664859	−	0.854743i
$352$		0			0
$353$	4.85187	−	8.40368i	0.258239	−	0.447283i	−0.707531	−	0.706682i	$-0.750191\pi$
$353$	4.85187	−	8.40368i	0.258239	−	0.447283i	0.965770	+	0.259399i	$0.0835245\pi$
$354$		0			0
$355$	16.9504	−	17.6269i	0.899632	−	0.935538i
$356$		0			0
$357$	19.7535	−	11.4047i	1.04546	−	0.603599i
$358$		0			0
$359$	2.09591	−	2.09591i	0.110618	−	0.110618i	−0.649631	−	0.760249i	$-0.725077\pi$
$359$	2.09591	−	2.09591i	0.110618	−	0.110618i	0.760249	+	0.649631i	$0.225077\pi$
$360$		0			0
$361$	3.51444	+	2.02906i	0.184970	+	0.106793i
$362$		0			0
$363$	3.96129	−	3.96129i	0.207914	−	0.207914i
$364$		0			0
$365$	−17.7537	−	9.79216i	−0.929273	−	0.512545i
$366$		0			0
$367$	2.71499	+	10.1325i	0.141721	+	0.528912i	0.999879	+	0.0155260i	$0.00494229\pi$
$367$	2.71499	+	10.1325i	0.141721	+	0.528912i	−0.858158	+	0.513386i	$0.828391\pi$
$368$		0			0
$369$	−1.89087	−	1.89087i	−0.0984350	−	0.0984350i
$370$		0			0
$371$	4.34873	−	16.2297i	0.225775	−	0.842603i
$372$		0			0
$373$	−4.04666	+	15.1023i	−0.209528	+	0.781969i	0.778493	+	0.627653i	$0.215984\pi$
$373$	−4.04666	+	15.1023i	−0.209528	+	0.781969i	−0.988021	+	0.154317i	$0.950682\pi$
$374$		0			0
$375$	15.8908	−	5.27465i	0.820599	−	0.272382i
$376$		0			0
$377$	13.2988	−	17.5697i	0.684921	−	0.904888i
$378$		0			0
$379$	−12.4625	+	3.33930i	−0.640153	+	0.171529i	−0.564273	−	0.825588i	$-0.690843\pi$
$379$	−12.4625	+	3.33930i	−0.640153	+	0.171529i	−0.0758805	+	0.997117i	$0.524177\pi$
$380$		0			0
$381$	5.68036	−	3.27956i	0.291014	−	0.168017i
$382$		0			0
$383$	14.3371	+	24.8327i	0.732594	+	1.26889i	0.955771	+	0.294112i	$0.0950239\pi$
$383$	14.3371	+	24.8327i	0.732594	+	1.26889i	−0.223177	+	0.974778i	$0.571643\pi$
$384$		0			0
$385$	14.0709	−	4.06691i	0.717120	−	0.207269i
$386$		0			0
$387$	−3.31251	+	0.887585i	−0.168385	+	0.0451185i
$388$		0			0
$389$	−35.3120			−1.79039			−0.895194	−	0.445677i	$-0.852963\pi$
$389$	−35.3120			−1.79039			−0.895194	+	0.445677i	$0.852963\pi$
$390$		0			0
$391$	−7.44474			−0.376496
$392$		0			0
$393$	−17.5711	+	4.70817i	−0.886346	+	0.237496i
$394$		0			0
$395$	−22.7500	−	12.5479i	−1.14468	−	0.631352i
$396$		0			0
$397$	−4.48566	−	7.76940i	−0.225129	−	0.389935i	0.731229	−	0.682132i	$-0.238947\pi$
$397$	−4.48566	−	7.76940i	−0.225129	−	0.389935i	−0.956358	+	0.292197i	$0.905614\pi$
$398$		0			0
$399$	12.1881	−	7.03680i	0.610168	−	0.352281i
$400$		0			0
$401$	−1.05240	+	0.281990i	−0.0525543	+	0.0140819i	−0.285000	−	0.958527i	$-0.591994\pi$
$401$	−1.05240	+	0.281990i	−0.0525543	+	0.0140819i	0.232446	+	0.972609i	$0.425327\pi$
$402$		0			0
$403$	19.5041	+	25.0744i	0.971566	+	1.24905i
$404$		0			0
$405$	7.11299	+	11.7816i	0.353447	+	0.585434i
$406$		0			0
$407$	5.38776	−	20.1074i	0.267061	−	0.996686i
$408$		0			0
$409$	7.28956	−	27.2050i	0.360446	−	1.34520i	−0.513046	−	0.858361i	$-0.671483\pi$
$409$	7.28956	−	27.2050i	0.360446	−	1.34520i	0.873491	−	0.486840i	$-0.161850\pi$
$410$		0			0
$411$	15.1540	+	15.1540i	0.747491	+	0.747491i
$412$		0			0
$413$	−5.89080	−	21.9847i	−0.289867	−	1.08180i
$414$		0			0
$415$	−1.17946	+	2.13843i	−0.0578974	+	0.104971i
$416$		0			0
$417$	−16.2551	+	16.2551i	−0.796014	+	0.796014i
$418$		0			0
$419$	3.96691	+	2.29029i	0.193796	+	0.111888i	0.593758	−	0.804643i	$-0.297643\pi$
$419$	3.96691	+	2.29029i	0.193796	+	0.111888i	−0.399962	+	0.916532i	$0.630977\pi$
$420$		0			0
$421$	16.0987	−	16.0987i	0.784602	−	0.784602i	−0.196002	−	0.980604i	$-0.562796\pi$
$421$	16.0987	−	16.0987i	0.784602	−	0.784602i	0.980604	+	0.196002i	$0.0627959\pi$
$422$		0			0
$423$	4.46799	−	2.57960i	0.217241	−	0.125424i
$424$		0			0
$425$	−29.9166	+	9.28461i	−1.45117	+	0.450370i
$426$		0			0
$427$	−11.8594	+	20.5411i	−0.573918	+	0.994056i
$428$		0			0
$429$	−5.65571	−	13.4037i	−0.273060	−	0.647134i
$430$		0			0
$431$	−0.0745698	−	0.278298i	−0.00359190	−	0.0134051i	0.964107	−	0.265515i	$-0.0855421\pi$
$431$	−0.0745698	−	0.278298i	−0.00359190	−	0.0134051i	−0.967699	+	0.252110i	$0.918875\pi$
$432$		0			0
$433$	37.6152	+	10.0790i	1.80767	+	0.484364i	0.995133	−	0.0985457i	$-0.0314191\pi$
$433$	37.6152	+	10.0790i	1.80767	+	0.484364i	0.812537	+	0.582909i	$0.198086\pi$
$434$		0			0
$435$	−14.1853	+	14.7515i	−0.680135	+	0.707280i
$436$		0			0
$437$	−4.59348			−0.219736
$438$		0			0
$439$	−14.3895	+	24.9233i	−0.686771	+	1.18952i	0.286105	+	0.958198i	$0.407639\pi$
$439$	−14.3895	+	24.9233i	−0.686771	+	1.18952i	−0.972877	+	0.231324i	$0.925694\pi$
$440$		0			0
$441$			0.824995i			0.0392855i
$442$		0			0
$443$	−25.9217	−	25.9217i	−1.23158	−	1.23158i	−0.963357	−	0.268222i	$-0.913564\pi$
$443$	−25.9217	−	25.9217i	−1.23158	−	1.23158i	−0.268222	−	0.963357i	$-0.586436\pi$
$444$		0			0
$445$	10.8665	+	2.68499i	0.515122	+	0.127281i
$446$		0			0
$447$			4.98624i			0.235841i
$448$		0			0
$449$	38.4485	+	10.3023i	1.81450	+	0.486193i	0.996082	−	0.0884331i	$-0.0281860\pi$
$449$	38.4485	+	10.3023i	1.81450	+	0.486193i	0.818416	+	0.574626i	$0.194853\pi$
$450$		0			0
$451$	−4.75705	−	8.23944i	−0.224001	−	0.387980i
$452$		0			0
$453$	26.9052	+	15.5337i	1.26412	+	0.729839i
$454$		0			0
$455$	−2.04940	+	19.4933i	−0.0960774	+	0.913859i
$456$		0			0
$457$	−6.80646	−	3.92971i	−0.318393	−	0.183824i	0.332283	−	0.943180i	$-0.392181\pi$
$457$	−6.80646	−	3.92971i	−0.318393	−	0.183824i	−0.650676	+	0.759355i	$0.725514\pi$
$458$		0			0
$459$	−17.6255	−	30.5282i	−0.822687	−	1.42494i
$460$		0			0
$461$	−19.4014	−	5.19859i	−0.903614	−	0.242123i	−0.223046	−	0.974808i	$-0.571600\pi$
$461$	−19.4014	−	5.19859i	−0.903614	−	0.242123i	−0.680568	+	0.732685i	$0.738267\pi$
$462$		0			0
$463$		−	1.60260i		−	0.0744790i	−0.999306	−	0.0372395i	$-0.988144\pi$
$463$		−	1.60260i		−	0.0744790i	0.999306	−	0.0372395i	$-0.0118564\pi$
$464$		0			0
$465$	−15.2488	−	25.2574i	−0.707147	−	1.17129i
$466$		0			0
$467$	−17.6094	−	17.6094i	−0.814864	−	0.814864i	0.170495	−	0.985359i	$-0.445463\pi$
$467$	−17.6094	−	17.6094i	−0.814864	−	0.814864i	−0.985359	+	0.170495i	$0.945463\pi$
$468$		0			0
$469$			2.46657i			0.113896i
$470$		0			0
$471$	−15.6465	+	27.1006i	−0.720955	+	1.24873i
$472$		0			0
$473$	−12.2012			−0.561013
$474$		0			0
$475$	−18.4588	+	5.72870i	−0.846950	+	0.262851i
$476$		0			0
$477$	−5.05534	−	1.35457i	−0.231468	−	0.0620216i
$478$		0			0
$479$	5.67830	+	21.1917i	0.259448	+	0.968273i	0.965562	+	0.260175i	$0.0837802\pi$
$479$	5.67830	+	21.1917i	0.259448	+	0.968273i	−0.706113	+	0.708099i	$0.749553\pi$
$480$		0			0
$481$	22.2119	+	16.8125i	1.01278	+	0.766583i
$482$		0			0
$483$	2.16328	−	3.74690i	0.0984325	−	0.170490i
$484$		0			0
$485$	−0.120851	−	6.17681i	−0.00548755	−	0.280474i
$486$		0			0
$487$	−11.8691	+	6.85260i	−0.537838	+	0.310521i	−0.744202	−	0.667954i	$-0.767170\pi$
$487$	−11.8691	+	6.85260i	−0.537838	+	0.310521i	0.206364	+	0.978475i	$0.433837\pi$
$488$		0			0
$489$	−9.46573	+	9.46573i	−0.428055	+	0.428055i
$490$		0			0
$491$	20.0133	+	11.5547i	0.903187	+	0.521455i	0.878233	−	0.478234i	$-0.158723\pi$
$491$	20.0133	+	11.5547i	0.903187	+	0.521455i	0.0249539	+	0.999689i	$0.492056\pi$
$492$		0			0
$493$	27.0733	−	27.0733i	1.21932	−	1.21932i
$494$		0			0
$495$	−1.26679	−	4.38291i	−0.0569380	−	0.196997i
$496$		0			0
$497$	−6.88153	−	25.6822i	−0.308679	−	1.15200i
$498$		0			0
$499$	15.3195	+	15.3195i	0.685795	+	0.685795i	0.961300	−	0.275505i	$-0.0888450\pi$
$499$	15.3195	+	15.3195i	0.685795	+	0.685795i	−0.275505	+	0.961300i	$0.588845\pi$
$500$		0			0
$501$	−7.05936	+	26.3459i	−0.315389	+	1.17705i
$502$		0			0
$503$	−8.98181	+	33.5206i	−0.400479	+	1.49461i	0.411765	+	0.911290i	$0.364913\pi$
$503$	−8.98181	+	33.5206i	−0.400479	+	1.49461i	−0.812244	+	0.583318i	$0.801754\pi$
$504$		0			0
$505$	24.9158	−	15.0426i	1.10874	−	0.669386i
$506$		0			0
$507$	19.4667	−	0.256508i	0.864549	−	0.0113919i
$508$		0			0
$509$	17.1190	−	4.58701i	0.758785	−	0.203316i	0.141374	−	0.989956i	$-0.454848\pi$
$509$	17.1190	−	4.58701i	0.758785	−	0.203316i	0.617411	+	0.786641i	$0.288181\pi$
$510$		0			0
$511$	−19.0908	+	11.0221i	−0.844528	+	0.487589i
$512$		0			0
$513$	−10.8751	−	18.8362i	−0.480148	−	0.831640i
$514$		0			0
$515$	−3.00765	−	10.4060i	−0.132533	−	0.458544i
$516$		0			0
$517$	17.7303	−	4.75081i	0.779776	−	0.208940i
$518$		0			0
$519$	2.71883			0.119343
$520$		0			0
$521$	−13.1460			−0.575938			−0.287969	−	0.957640i	$-0.592980\pi$
$521$	−13.1460			−0.575938			−0.287969	+	0.957640i	$0.592980\pi$
$522$		0			0
$523$	21.9352	−	5.87752i	0.959160	−	0.257006i	0.254915	−	0.966963i	$-0.417952\pi$
$523$	21.9352	−	5.87752i	0.959160	−	0.257006i	0.704245	+	0.709957i	$0.251286\pi$
$524$		0			0
$525$	4.02019	−	17.7548i	0.175456	−	0.774883i
$526$		0			0
$527$	27.5983	+	47.8017i	1.20220	+	2.08228i
$528$		0			0
$529$	18.6956	−	10.7939i	0.812854	−	0.469301i
$530$		0			0
$531$	−6.84796	+	1.83491i	−0.297176	+	0.0796282i
$532$		0			0
$533$	12.6118	−	1.74497i	0.546277	−	0.0755832i
$534$		0			0
$535$	5.14628	+	1.27159i	0.222493	+	0.0549755i
$536$		0			0
$537$	−7.05423	+	26.3267i	−0.304412	+	1.13608i
$538$		0			0
$539$	−0.759691	+	2.83521i	−0.0327222	+	0.122121i
$540$		0			0
$541$	12.3506	+	12.3506i	0.530993	+	0.530993i	0.920868	−	0.389875i	$-0.127482\pi$
$541$	12.3506	+	12.3506i	0.530993	+	0.530993i	−0.389875	+	0.920868i	$0.627482\pi$
$542$		0			0
$543$	−6.75783	−	25.2206i	−0.290006	−	1.08232i
$544$		0			0
$545$	6.92181	−	2.00061i	0.296498	−	0.0856967i
$546$		0			0
$547$	−7.96444	+	7.96444i	−0.340535	+	0.340535i	−0.856568	−	0.516034i	$-0.827408\pi$
$547$	−7.96444	+	7.96444i	−0.340535	+	0.340535i	0.516034	+	0.856568i	$0.327408\pi$
$548$		0			0
$549$	6.39830	+	3.69406i	0.273073	+	0.157659i
$550$		0			0
$551$	16.7045	−	16.7045i	0.711637	−	0.711637i
$552$		0			0
$553$	−24.4634	+	14.1239i	−1.04029	+	0.600611i
$554$		0			0
$555$	−18.6491	−	17.9333i	−0.791609	−	0.761227i
$556$		0			0
$557$	−13.1520	+	22.7800i	−0.557269	+	0.965219i	0.440454	+	0.897775i	$0.354818\pi$
$557$	−13.1520	+	22.7800i	−0.557269	+	0.965219i	−0.997723	+	0.0674437i	$0.978516\pi$
$558$		0			0
$559$	6.14891	−	15.1259i	0.260071	−	0.639756i
$560$		0			0
$561$	−6.54242	−	24.4167i	−0.276221	−	1.03087i
$562$		0			0
$563$	−44.5258	−	11.9307i	−1.87654	−	0.502817i	−0.999760	−	0.0219234i	$-0.993021\pi$
$563$	−44.5258	−	11.9307i	−1.87654	−	0.502817i	−0.876779	−	0.480894i	$-0.840312\pi$
$564$		0			0
$565$	22.3091	+	21.4529i	0.938552	+	0.902530i
$566$		0			0
$567$	14.9631			0.628391
$568$		0			0
$569$	−15.3819	+	26.6422i	−0.644841	+	1.11690i	0.339497	+	0.940607i	$0.389743\pi$
$569$	−15.3819	+	26.6422i	−0.644841	+	1.11690i	−0.984338	+	0.176290i	$0.943590\pi$
$570$		0			0
$571$			20.6467i			0.864038i	0.901865	+	0.432019i	$0.142199\pi$
$571$			20.6467i			0.864038i	−0.901865	+	0.432019i	$0.857801\pi$
$572$		0			0
$573$	22.3232	+	22.3232i	0.932567	+	0.932567i
$574$		0			0
$575$	−4.03385	+	4.36253i	−0.168223	+	0.181930i
$576$		0			0
$577$		−	20.3744i		−	0.848198i	−0.905616	−	0.424099i	$-0.860591\pi$
$577$		−	20.3744i		−	0.848198i	0.905616	−	0.424099i	$-0.139409\pi$
$578$		0			0
$579$	28.0278	+	7.51004i	1.16480	+	0.312106i
$580$		0			0
$581$	1.32761	+	2.29948i	0.0550783	+	0.0953985i
$582$		0			0
$583$	−16.1260	−	9.31035i	−0.667870	−	0.385595i
$584$		0			0
$585$	6.07190	+	0.638362i	0.251042	+	0.0263930i
$586$		0			0
$587$	−37.3781	−	21.5802i	−1.54276	−	0.890712i	−0.998663	−	0.0516879i	$-0.983540\pi$
$587$	−37.3781	−	21.5802i	−1.54276	−	0.890712i	−0.544095	−	0.839024i	$-0.683127\pi$
$588$		0			0
$589$	17.0285	+	29.4942i	0.701645	+	1.21529i
$590$		0			0
$591$	−17.8965	−	4.79535i	−0.736163	−	0.197254i
$592$		0			0
$593$		−	34.3448i		−	1.41037i	−0.709022	−	0.705186i	$-0.750863\pi$
$593$		−	34.3448i		−	1.41037i	0.709022	−	0.705186i	$-0.249137\pi$
$594$		0			0
$595$	−8.16948	+	33.0629i	−0.334916	+	1.35545i
$596$		0			0
$597$	−10.7754	−	10.7754i	−0.441010	−	0.441010i
$598$		0			0
$599$		−	8.69200i		−	0.355146i	−0.984108	−	0.177573i	$-0.943175\pi$
$599$		−	8.69200i		−	0.355146i	0.984108	−	0.177573i	$-0.0568245\pi$
$600$		0			0
$601$	−1.73390	+	3.00320i	−0.0707271	+	0.122503i	−0.899220	−	0.437496i	$-0.855865\pi$
$601$	−1.73390	+	3.00320i	−0.0707271	+	0.122503i	0.828493	+	0.559999i	$0.189199\pi$
$602$		0			0
$603$	0.768305			0.0312878
$604$		0			0
$605$	0.163626	+	8.36307i	0.00665233	+	0.340007i
$606$		0			0
$607$	18.0287	+	4.83078i	0.731764	+	0.196075i	0.605414	−	0.795910i	$-0.293007\pi$
$607$	18.0287	+	4.83078i	0.731764	+	0.196075i	0.126349	+	0.991986i	$0.459674\pi$
$608$		0			0
$609$	5.75898	+	21.4928i	0.233366	+	0.870932i
$610$		0			0
$611$	−3.04573	+	24.3744i	−0.123217	+	0.986083i
$612$		0			0
$613$	12.1155	−	20.9846i	0.489339	−	0.847560i	−0.510586	−	0.859827i	$-0.670571\pi$
$613$	12.1155	−	20.9846i	0.489339	−	0.847560i	0.999925	+	0.0122667i	$0.00390470\pi$
$614$		0			0
$615$	−11.8226	+	0.231312i	−0.476733	+	0.00932740i
$616$		0			0
$617$	13.7644	−	7.94688i	0.554134	−	0.319930i	−0.196654	−	0.980473i	$-0.563007\pi$
$617$	13.7644	−	7.94688i	0.554134	−	0.319930i	0.750788	+	0.660544i	$0.229674\pi$
$618$		0			0
$619$	−10.3555	+	10.3555i	−0.416225	+	0.416225i	−0.883900	−	0.467676i	$-0.845092\pi$
$619$	−10.3555	+	10.3555i	−0.416225	+	0.416225i	0.467676	+	0.883900i	$0.345092\pi$
$620$		0			0
$621$	−5.79070	−	3.34326i	−0.232373	−	0.134160i
$622$		0			0
$623$	8.60545	−	8.60545i	0.344770	−	0.344770i
$624$		0			0
$625$	−10.7693	+	22.5615i	−0.430772	+	0.902461i
$626$		0			0
$627$	−4.03674	−	15.0653i	−0.161212	−	0.601651i
$628$		0			0
$629$	34.2265	+	34.2265i	1.36470	+	1.36470i
$630$		0			0
$631$	−10.7149	+	39.9887i	−0.426555	+	1.59193i	0.333948	+	0.942591i	$0.391619\pi$
$631$	−10.7149	+	39.9887i	−0.426555	+	1.59193i	−0.760503	+	0.649334i	$0.775048\pi$
$632$		0			0
$633$	−6.72769	+	25.1081i	−0.267402	+	0.997956i
$634$		0			0
$635$	−2.34923	+	9.50766i	−0.0932265	+	0.377300i
$636$		0			0
$637$	−3.13195	−	2.37061i	−0.124092	−	0.0939271i
$638$		0			0
$639$	−7.99967	+	2.14351i	−0.316462	+	0.0847958i
$640$		0			0
$641$	−3.26442	+	1.88471i	−0.128937	+	0.0744417i	−0.563081	−	0.826402i	$-0.690384\pi$
$641$	−3.26442	+	1.88471i	−0.128937	+	0.0744417i	0.434144	+	0.900843i	$0.357051\pi$
$642$		0			0
$643$	11.4509	+	19.8336i	0.451580	+	0.782159i	0.998484	−	0.0550358i	$-0.0175273\pi$
$643$	11.4509	+	19.8336i	0.451580	+	0.782159i	−0.546905	+	0.837195i	$0.684194\pi$
$644$		0			0
$645$	−7.32396	+	13.2788i	−0.288381	+	0.522851i
$646$		0			0
$647$	−23.6258	+	6.33051i	−0.928825	+	0.248878i	−0.691353	−	0.722517i	$-0.742985\pi$
$647$	−23.6258	+	6.33051i	−0.928825	+	0.248878i	−0.237471	+	0.971395i	$0.576319\pi$
$648$		0			0
$649$	−25.2236			−0.990113
$650$		0			0
$651$	−32.0779			−1.25723
$652$		0			0
$653$	28.2335	−	7.56514i	1.10486	−	0.296047i	0.340119	−	0.940383i	$-0.389533\pi$
$653$	28.2335	−	7.56514i	1.10486	−	0.296047i	0.764743	+	0.644336i	$0.222866\pi$
$654$		0			0
$655$	13.1180	−	23.7837i	0.512562	−	0.929304i
$656$		0			0
$657$	3.43324	+	5.94654i	0.133943	+	0.231997i
$658$		0			0
$659$	11.0616	−	6.38643i	0.430900	−	0.248780i	−0.268830	−	0.963188i	$-0.586637\pi$
$659$	11.0616	−	6.38643i	0.430900	−	0.248780i	0.699730	+	0.714407i	$0.253304\pi$
$660$		0			0
$661$	−16.9009	+	4.52859i	−0.657370	+	0.176142i	−0.572059	−	0.820213i	$-0.693855\pi$
$661$	−16.9009	+	4.52859i	−0.657370	+	0.176142i	−0.0853110	+	0.996354i	$0.527188\pi$
$662$		0			0
$663$	33.5664	+	4.19433i	1.30361	+	0.162894i
$664$		0			0
$665$	−5.04065	+	20.4002i	−0.195468	+	0.791085i
$666$		0			0
$667$	1.87967	−	7.01503i	0.0727812	−	0.271623i
$668$		0			0
$669$	8.51270	−	31.7698i	0.329120	−	1.22829i
$670$		0			0
$671$	18.5870	+	18.5870i	0.717542	+	0.717542i
$672$		0			0
$673$	−6.17489	−	23.0450i	−0.238025	−	0.888320i	−0.976762	−	0.214326i	$-0.931244\pi$
$673$	−6.17489	−	23.0450i	−0.238025	−	0.888320i	0.738738	−	0.673993i	$-0.235422\pi$
$674$		0			0
$675$	−27.4394	−	6.21306i	−1.05614	−	0.239141i
$676$		0			0
$677$	18.9432	−	18.9432i	0.728048	−	0.728048i	−0.242183	−	0.970231i	$-0.577863\pi$
$677$	18.9432	−	18.9432i	0.728048	−	0.728048i	0.970231	+	0.242183i	$0.0778634\pi$
$678$		0			0
$679$	−5.81711	−	3.35851i	−0.223240	−	0.128888i
$680$		0			0
$681$	8.61471	−	8.61471i	0.330116	−	0.330116i
$682$		0			0
$683$	−2.93042	+	1.69188i	−0.112129	+	0.0647380i	−0.555016	−	0.831840i	$-0.687288\pi$
$683$	−2.93042	+	1.69188i	−0.112129	+	0.0647380i	0.442886	+	0.896578i	$0.353954\pi$
$684$		0			0
$685$	−31.9931	+	0.625953i	−1.22239	+	0.0239164i
$686$		0			0
$687$	10.7201	−	18.5678i	0.408998	−	0.708405i
$688$		0			0
$689$	19.6689	−	15.2994i	0.749324	−	0.582860i
$690$		0			0
$691$	12.8180	+	47.8376i	0.487621	+	1.81983i	0.567954	+	0.823060i	$0.307735\pi$
$691$	12.8180	+	47.8376i	0.487621	+	1.81983i	−0.0803328	+	0.996768i	$0.525598\pi$
$692$		0			0
$693$	−4.79135	−	1.28384i	−0.182008	−	0.0487690i
$694$		0			0
$695$	−0.671434	−	34.3177i	−0.0254690	−	1.30174i
$696$		0			0
$697$	22.1224			0.837947
$698$		0			0
$699$	1.76775	−	3.06183i	0.0668625	−	0.115809i
$700$		0			0
$701$			5.71523i			0.215861i	0.994158	+	0.107931i	$0.0344224\pi$
$701$			5.71523i			0.215861i	−0.994158	+	0.107931i	$0.965578\pi$
$702$		0			0
$703$	21.1181	+	21.1181i	0.796485	+	0.796485i
$704$		0			0
$705$	5.47247	−	22.1478i	0.206105	−	0.834135i
$706$		0			0
$707$		−	31.6440i		−	1.19010i
$708$		0			0
$709$	−9.56101	−	2.56186i	−0.359071	−	0.0962128i	0.0747734	−	0.997201i	$-0.476177\pi$
$709$	−9.56101	−	2.56186i	−0.359071	−	0.0962128i	−0.433845	+	0.900988i	$0.642843\pi$
$710$		0			0
$711$	4.39942	+	7.62003i	0.164991	+	0.285773i
$712$		0			0
$713$	9.06719	+	5.23494i	0.339569	+	0.196050i
$714$		0			0
$715$	20.2791	+	7.78509i	0.758394	+	0.291146i
$716$		0			0
$717$	−30.9467	−	17.8671i	−1.15573	−	0.667259i
$718$		0			0
$719$	−5.37245	−	9.30535i	−0.200358	−	0.347031i	0.748286	−	0.663377i	$-0.230877\pi$
$719$	−5.37245	−	9.30535i	−0.200358	−	0.347031i	−0.948644	+	0.316346i	$0.897544\pi$
$720$		0			0
$721$	−11.3758	−	3.04812i	−0.423655	−	0.113518i
$722$		0			0
$723$		−	7.18383i		−	0.267169i
$724$		0			0
$725$	−1.19527	−	30.5340i	−0.0443912	−	1.13401i
$726$		0			0
$727$	−14.2084	−	14.2084i	−0.526961	−	0.526961i	0.392704	−	0.919665i	$-0.371540\pi$
$727$	−14.2084	−	14.2084i	−0.526961	−	0.526961i	−0.919665	+	0.392704i	$0.871540\pi$
$728$		0			0
$729$		−	29.9404i		−	1.10890i
$730$		0			0
$731$	14.1853	−	24.5697i	0.524663	−	0.908743i
$732$		0			0
$733$	−37.5445			−1.38674			−0.693369	−	0.720582i	$-0.743875\pi$
$733$	−37.5445			−1.38674			−0.693369	+	0.720582i	$0.743875\pi$
$734$		0			0
$735$	2.62958	+	2.52866i	0.0969934	+	0.0932709i
$736$		0			0
$737$	2.64038	+	0.707489i	0.0972598	+	0.0260607i
$738$		0			0
$739$	−7.64320	−	28.5248i	−0.281160	−	1.04930i	−0.951600	−	0.307339i	$-0.900561\pi$
$739$	−7.64320	−	28.5248i	−0.281160	−	1.04930i	0.670440	−	0.741964i	$-0.266105\pi$
$740$		0			0
$741$	20.7108	+	2.58794i	0.760832	+	0.0950705i
$742$		0			0
$743$	19.4772	−	33.7356i	0.714551	−	1.23764i	−0.248582	−	0.968611i	$-0.579964\pi$
$743$	19.4772	−	33.7356i	0.714551	−	1.23764i	0.963133	−	0.269027i	$-0.0867022\pi$
$744$		0			0
$745$	−5.36645	−	5.16049i	−0.196612	−	0.189066i
$746$		0			0
$747$	0.716258	−	0.413532i	0.0262065	−	0.0151303i
$748$		0			0
$749$	4.07546	−	4.07546i	0.148914	−	0.148914i
$750$		0			0
$751$	−22.7530	−	13.1365i	−0.830270	−	0.479357i	0.0236752	−	0.999720i	$-0.492463\pi$
$751$	−22.7530	−	13.1365i	−0.830270	−	0.479357i	−0.853945	+	0.520363i	$0.825797\pi$
$752$		0			0
$753$	−4.72700	+	4.72700i	−0.172261	+	0.172261i
$754$		0			0
$755$	−44.5637	+	12.8802i	−1.62184	+	0.468759i
$756$		0			0
$757$	−7.16401	−	26.7365i	−0.260380	−	0.971753i	−0.965018	−	0.262185i	$-0.915557\pi$
$757$	−7.16401	−	26.7365i	−0.260380	−	0.971753i	0.704637	−	0.709568i	$-0.251110\pi$
$758$		0			0
$759$	−3.39044	−	3.39044i	−0.123065	−	0.123065i
$760$		0			0
$761$	−10.2417	+	38.2227i	−0.371263	+	1.38557i	0.487466	+	0.873142i	$0.337921\pi$
$761$	−10.2417	+	38.2227i	−0.371263	+	1.38557i	−0.858729	+	0.512430i	$0.828745\pi$
$762$		0			0
$763$	2.02753	−	7.56686i	0.0734017	−	0.273939i
$764$		0			0
$765$	10.2987	+	2.54469i	0.372349	+	0.0920033i
$766$		0			0
$767$	12.7116	−	31.2697i	0.458991	−	1.12908i
$768$		0			0
$769$	−0.642529	+	0.172165i	−0.0231702	+	0.00620843i	−0.270386	−	0.962752i	$-0.587151\pi$
$769$	−0.642529	+	0.172165i	−0.0231702	+	0.00620843i	0.247215	+	0.968961i	$0.420484\pi$
$770$		0			0
$771$	−10.2814	+	5.93595i	−0.370275	+	0.213778i
$772$		0			0
$773$	−8.07445	−	13.9854i	−0.290418	−	0.503018i	0.683491	−	0.729959i	$-0.260461\pi$
$773$	−8.07445	−	13.9854i	−0.290418	−	0.503018i	−0.973909	+	0.226941i	$0.927128\pi$
$774$		0			0
$775$	42.9651	+	9.72853i	1.54335	+	0.349459i
$776$		0			0
$777$	−27.1715	+	7.28059i	−0.974773	+	0.261190i
$778$		0			0
$779$	13.6498			0.489054
$780$		0			0
$781$	−29.4658			−1.05437
$782$		0			0
$783$	33.2163	−	8.90028i	1.18705	−	0.318070i
$784$		0			0
$785$	−12.9738	−	44.8873i	−0.463054	−	1.60210i
$786$		0			0
$787$	16.0612	+	27.8188i	0.572520	+	0.991633i	0.996306	+	0.0858710i	$0.0273673\pi$
$787$	16.0612	+	27.8188i	0.572520	+	0.991633i	−0.423787	+	0.905762i	$0.639299\pi$
$788$		0			0
$789$	5.21880	−	3.01307i	0.185794	−	0.107268i
$790$		0			0
$791$	32.5042	−	8.70947i	1.15572	−	0.309673i
$792$		0			0
$793$	−32.4093	+	13.6752i	−1.15089	+	0.485621i
$794$		0			0
$795$	−19.8124	+	11.9615i	−0.702675	+	0.424230i
$796$		0			0
$797$	0.423892	−	1.58199i	0.0150150	−	0.0560369i	−0.958012	−	0.286729i	$-0.907432\pi$
$797$	0.423892	−	1.58199i	0.0150150	−	0.0560369i	0.973027	+	0.230692i	$0.0740989\pi$
$798$		0			0
$799$	−11.0467	+	41.2269i	−0.390805	+	1.45850i
$800$		0			0
$801$	−2.68048	−	2.68048i	−0.0947103	−	0.0947103i
$802$		0			0
$803$	6.32295	+	23.5976i	0.223132	+	0.832740i
$804$		0			0
$805$	1.79374	+	6.20608i	0.0632210	+	0.218735i
$806$		0			0
$807$	20.2534	−	20.2534i	0.712952	−	0.712952i
$808$		0			0
$809$	9.27418	+	5.35445i	0.326063	+	0.188253i	0.654092	−	0.756415i	$-0.273051\pi$
$809$	9.27418	+	5.35445i	0.326063	+	0.188253i	−0.328029	+	0.944668i	$0.606384\pi$
$810$		0			0
$811$	37.8784	−	37.8784i	1.33009	−	1.33009i	0.424809	−	0.905283i	$-0.360341\pi$
$811$	37.8784	−	37.8784i	1.33009	−	1.33009i	0.905283	−	0.424809i	$-0.139659\pi$
$812$		0			0
$813$	−9.93301	+	5.73482i	−0.348366	+	0.201129i
$814$		0			0
$815$	−0.390993	−	19.9840i	−0.0136959	−	0.700011i
$816$		0			0
$817$	8.75249	−	15.1598i	0.306211	−	0.530373i
$818$		0			0
$819$	4.00622	−	5.29284i	0.139989	−	0.184947i
$820$		0			0
$821$	5.96951	+	22.2785i	0.208337	+	0.777526i	0.988406	+	0.151832i	$0.0485173\pi$
$821$	5.96951	+	22.2785i	0.208337	+	0.777526i	−0.780069	+	0.625694i	$0.784816\pi$
$822$		0			0
$823$	7.29458	+	1.95458i	0.254273	+	0.0681323i	0.383704	−	0.923456i	$-0.374648\pi$
$823$	7.29458	+	1.95458i	0.254273	+	0.0681323i	−0.129431	+	0.991588i	$0.541315\pi$
$824$		0			0
$825$	−17.8528	−	9.39611i	−0.621555	−	0.327130i
$826$		0			0
$827$	−38.2354			−1.32957			−0.664787	−	0.747033i	$-0.731478\pi$
$827$	−38.2354			−1.32957			−0.664787	+	0.747033i	$0.731478\pi$
$828$		0			0
$829$	24.4408	−	42.3328i	0.848865	−	1.47028i	−0.0333566	−	0.999444i	$-0.510620\pi$
$829$	24.4408	−	42.3328i	0.848865	−	1.47028i	0.882222	−	0.470834i	$-0.156047\pi$
$830$		0			0
$831$		−	22.6488i		−	0.785679i
$832$		0			0
$833$	−4.82604	−	4.82604i	−0.167213	−	0.167213i
$834$		0			0
$835$	−21.0488	−	34.8642i	−0.728422	−	1.20653i
$836$		0			0
$837$			49.5751i			1.71357i
$838$		0			0
$839$	−24.6702	−	6.61035i	−0.851709	−	0.228215i	−0.193547	−	0.981091i	$-0.561999\pi$
$839$	−24.6702	−	6.61035i	−0.851709	−	0.228215i	−0.658162	+	0.752876i	$0.728666\pi$
$840$		0			0
$841$	4.17511	+	7.23150i	0.143969	+	0.249362i
$842$		0			0
$843$	−23.8904	−	13.7931i	−0.822828	−	0.475060i
$844$		0			0
$845$	−19.8710	+	21.2166i	−0.683582	+	0.729874i
$846$		0			0
$847$	7.87607	+	4.54725i	0.270625	+	0.156245i
$848$		0			0
$849$	−6.28769	−	10.8906i	−0.215793	−	0.373765i
$850$		0			0
$851$	8.86851	+	2.37631i	0.304008	+	0.0814588i
$852$		0			0
$853$			7.17091i			0.245527i	0.992436	+	0.122764i	$0.0391757\pi$
$853$			7.17091i			0.245527i	−0.992436	+	0.122764i	$0.960824\pi$
$854$		0			0
$855$	6.35439	+	1.57010i	0.217316	+	0.0536962i
$856$		0			0
$857$	−10.7248	−	10.7248i	−0.366350	−	0.366350i	0.499794	−	0.866144i	$-0.333409\pi$
$857$	−10.7248	−	10.7248i	−0.366350	−	0.366350i	−0.866144	+	0.499794i	$0.833409\pi$
$858$		0			0
$859$			27.2503i			0.929770i	0.885371	+	0.464885i	$0.153904\pi$
$859$			27.2503i			0.929770i	−0.885371	+	0.464885i	$0.846096\pi$
$860$		0			0
$861$	−6.42829	+	11.1341i	−0.219076	+	0.379450i
$862$		0			0
$863$	−8.34796			−0.284168			−0.142084	−	0.989855i	$-0.545380\pi$
$863$	−8.34796			−0.284168			−0.142084	+	0.989855i	$0.545380\pi$
$864$		0			0
$865$	−2.81384	+	2.92615i	−0.0956736	+	0.0994921i
$866$		0			0
$867$	32.1830	+	8.62342i	1.09299	+	0.292867i
$868$		0			0
$869$	8.10236	+	30.2384i	0.274854	+	1.02577i
$870$		0			0
$871$	−2.20772	+	2.91674i	−0.0748056	+	0.0988299i
$872$		0			0
$873$	−1.04613	+	1.81196i	−0.0354062	+	0.0613254i
$874$		0			0
$875$	14.9480	+	22.7020i	0.505333	+	0.767468i
$876$		0			0
$877$	−26.5085	+	15.3047i	−0.895130	+	0.516803i	−0.875617	−	0.483006i	$-0.839545\pi$
$877$	−26.5085	+	15.3047i	−0.895130	+	0.516803i	−0.0195127	+	0.999810i	$0.506211\pi$
$878$		0			0
$879$	1.84305	−	1.84305i	0.0621644	−	0.0621644i
$880$		0			0
$881$	−6.20042	−	3.57981i	−0.208897	−	0.120607i	0.391901	−	0.920007i	$-0.371817\pi$
$881$	−6.20042	−	3.57981i	−0.208897	−	0.120607i	−0.600799	+	0.799400i	$0.705151\pi$
$882$		0			0
$883$	31.1878	−	31.1878i	1.04955	−	1.04955i	0.0508451	−	0.998707i	$-0.483809\pi$
$883$	31.1878	−	31.1878i	1.04955	−	1.04955i	0.998707	−	0.0508451i	$-0.0161915\pi$
$884$		0			0
$885$	−15.1408	+	27.4512i	−0.508954	+	0.922762i
$886$		0			0
$887$	11.3507	+	42.3613i	0.381118	+	1.42235i	0.844196	+	0.536035i	$0.180079\pi$
$887$	11.3507	+	42.3613i	0.381118	+	1.42235i	−0.463077	+	0.886318i	$0.653255\pi$
$888$		0			0
$889$	7.52935	+	7.52935i	0.252526	+	0.252526i
$890$		0			0
$891$	4.29188	−	16.0175i	0.143783	−	0.536607i
$892$		0			0
$893$	−6.81594	+	25.4374i	−0.228087	+	0.851231i
$894$		0			0
$895$	−21.0335	−	34.8389i	−0.703071	−	1.16454i
$896$		0			0
$897$	5.91177	−	2.49449i	0.197388	−	0.0832887i
$898$		0			0
$899$	−52.0108	+	13.9362i	−1.73466	+	0.464800i
$900$		0			0
$901$	37.4966	−	21.6487i	1.24919	−	0.721222i
$902$		0			0
$903$	8.24388	+	14.2788i	0.274339	+	0.475169i
$904$		0			0
$905$	34.1377	+	18.8288i	1.13478	+	0.625891i
$906$		0			0
$907$	1.95900	−	0.524912i	0.0650475	−	0.0174294i	−0.226149	−	0.974093i	$-0.572613\pi$
$907$	1.95900	−	0.524912i	0.0650475	−	0.0174294i	0.291196	+	0.956663i	$0.405947\pi$
$908$		0			0
$909$	−9.85671			−0.326926
$910$		0			0
$911$	−11.7972			−0.390859			−0.195429	−	0.980718i	$-0.562610\pi$
$911$	−11.7972			−0.390859			−0.195429	+	0.980718i	$0.562610\pi$
$912$		0			0
$913$	2.84232	−	0.761596i	0.0940669	−	0.0252052i
$914$		0			0
$915$	31.3855	−	9.07135i	1.03757	−	0.299890i
$916$		0			0
$917$	−14.7657	−	25.5749i	−0.487605	−	0.844557i
$918$		0			0
$919$	32.9872	−	19.0452i	1.08815	−	0.628242i	0.155065	−	0.987904i	$-0.450441\pi$
$919$	32.9872	−	19.0452i	1.08815	−	0.628242i	0.933083	+	0.359662i	$0.117108\pi$
$920$		0			0
$921$	13.7863	−	3.69402i	0.454274	−	0.121722i
$922$		0			0
$923$	14.8495	−	36.5287i	0.488778	−	1.20236i
$924$		0			0
$925$	38.6016	−	1.51108i	1.26921	−	0.0496839i
$926$		0			0
$927$	−0.949451	+	3.54340i	−0.0311841	+	0.116380i
$928$		0			0
$929$	−2.43693	+	9.09474i	−0.0799530	+	0.298389i	−0.994311	−	0.106519i	$-0.966030\pi$
$929$	−2.43693	+	9.09474i	−0.0799530	+	0.298389i	0.914358	+	0.404907i	$0.132696\pi$
$930$		0			0
$931$	−2.97772	−	2.97772i	−0.0975908	−	0.0975908i
$932$		0			0
$933$	7.57028	+	28.2527i	0.247840	+	0.924951i
$934$		0			0
$935$	33.0495	+	18.2286i	1.08084	+	0.596140i
$936$		0			0
$937$	−39.2985	+	39.2985i	−1.28382	+	1.28382i	−0.345351	+	0.938474i	$0.612240\pi$
$937$	−39.2985	+	39.2985i	−1.28382	+	1.28382i	−0.938474	+	0.345351i	$0.887760\pi$
$938$		0			0
$939$	−31.2162	−	18.0227i	−1.01870	−	0.588149i
$940$		0			0
$941$	−19.4526	+	19.4526i	−0.634137	+	0.634137i	−0.949103	−	0.314966i	$-0.898007\pi$
$941$	−19.4526	+	19.4526i	−0.634137	+	0.634137i	0.314966	+	0.949103i	$0.398007\pi$
$942$		0			0
$943$	3.63406	−	2.09813i	0.118341	−	0.0683244i
$944$		0			0
$945$	−21.2022	+	22.0484i	−0.689709	+	0.717236i
$946$		0			0
$947$	−8.19763	+	14.1987i	−0.266387	+	0.461396i	−0.967926	−	0.251235i	$-0.919163\pi$
$947$	−8.19763	+	14.1987i	−0.266387	+	0.461396i	0.701539	+	0.712631i	$0.252497\pi$
$948$		0			0
$949$	−32.4404	−	4.05363i	−1.05306	−	0.131586i
$950$		0			0
$951$	−2.74411	−	10.2412i	−0.0889840	−	0.332093i
$952$		0			0
$953$	28.2762	+	7.57657i	0.915955	+	0.245429i	0.685855	−	0.727738i	$-0.259428\pi$
$953$	28.2762	+	7.57657i	0.915955	+	0.245429i	0.230099	+	0.973167i	$0.426095\pi$
$954$		0			0
$955$	−47.1288	+	0.922087i	−1.52505	+	0.0298380i
$956$		0			0
$957$	24.6592			0.797119
$958$		0			0
$959$	−17.3956	+	30.1300i	−0.561733	+	0.972950i
$960$		0			0
$961$		−	46.6257i		−	1.50406i
$962$		0			0
$963$	−1.26945	−	1.26945i	−0.0409076	−	0.0409076i
$964$		0			0
$965$	−37.0900	+	22.3925i	−1.19397	+	0.720842i
$966$		0			0
$967$			50.2534i			1.61604i	0.589154	+	0.808021i	$0.299461\pi$
$967$			50.2534i			1.61604i	−0.589154	+	0.808021i	$0.700539\pi$
$968$		0			0
$969$	35.0303	+	9.38635i	1.12534	+	0.301533i
$970$		0			0
$971$	23.9370	+	41.4601i	0.768175	+	1.33052i	0.938551	+	0.345139i	$0.112168\pi$
$971$	23.9370	+	41.4601i	0.768175	+	1.33052i	−0.170376	+	0.985379i	$0.554498\pi$
$972$		0			0
$973$	−32.3193	−	18.6595i	−1.03611	−	0.598198i
$974$		0			0
$975$	20.6454	−	17.3969i	0.661183	−	0.557146i
$976$		0			0
$977$	28.4527	+	16.4272i	0.910283	+	0.525552i	0.880522	−	0.474005i	$-0.157192\pi$
$977$	28.4527	+	16.4272i	0.910283	+	0.525552i	0.0297606	+	0.999557i	$0.490526\pi$
$978$		0			0
$979$	−6.74354	−	11.6802i	−0.215524	−	0.373299i
$980$		0			0
$981$	−2.35698	−	0.631551i	−0.0752526	−	0.0201639i
$982$		0			0
$983$			23.3463i			0.744631i	0.928106	+	0.372315i	$0.121436\pi$
$983$			23.3463i			0.744631i	−0.928106	+	0.372315i	$0.878564\pi$
$984$		0			0
$985$	23.6829	−	14.2982i	0.754600	−	0.455579i
$986$		0			0
$987$	−17.5394	−	17.5394i	−0.558285	−	0.558285i
$988$		0			0
$989$		−	5.38144i		−	0.171120i
$990$		0			0
$991$	−20.4952	+	35.4988i	−0.651053	+	1.12766i	0.331815	+	0.943345i	$0.392339\pi$
$991$	−20.4952	+	35.4988i	−0.651053	+	1.12766i	−0.982868	+	0.184312i	$0.940994\pi$
$992$		0			0
$993$	−23.6299			−0.749873
$994$		0			0
$995$	22.7491	−	0.445092i	0.721195	−	0.0141104i
$996$		0			0
$997$	39.8616	+	10.6809i	1.26243	+	0.338267i	0.827125	−	0.562018i	$-0.189975\pi$
$997$	39.8616	+	10.6809i	1.26243	+	0.338267i	0.435303	+	0.900284i	$0.356641\pi$
$998$		0			0
$999$	11.2519	+	41.9926i	0.355993	+	1.32859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.c.253.2	yes	20
5.2	odd	4		260.2.bk.c.97.4	yes	20
5.3	odd	4		1300.2.bs.d.357.2		20
5.4	even	2		1300.2.bn.d.1293.4		20
13.11	odd	12		260.2.bk.c.193.4	yes	20
65.24	odd	12		1300.2.bs.d.193.2		20
65.37	even	12	inner	260.2.bf.c.37.2	✓	20
65.63	even	12		1300.2.bn.d.557.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.2	✓	20	65.37	even	12	inner
260.2.bf.c.253.2	yes	20	1.1	even	1	trivial
260.2.bk.c.97.4	yes	20	5.2	odd	4
260.2.bk.c.193.4	yes	20	13.11	odd	12
1300.2.bn.d.557.4		20	65.63	even	12
1300.2.bn.d.1293.4		20	5.4	even	2
1300.2.bs.d.193.2		20	65.24	odd	12
1300.2.bs.d.357.2		20	5.3	odd	4

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44654 + 0.387600i) q^{3} +(1.07994 - 1.95799i) q^{5} +(-1.21558 - 2.10545i) q^{7} +(-0.655821 + 0.378639i) q^{9} +O(q^{10})\)	\(q+(-1.44654 + 0.387600i) q^{3} +(1.07994 - 1.95799i) q^{5} +(-1.21558 - 2.10545i) q^{7} +(-0.655821 + 0.378639i) q^{9} +(-2.60249 + 0.697334i) q^{11} +(0.447059 - 3.57773i) q^{13} +(-0.803262 + 3.25091i) q^{15} +(1.62146 - 6.05137i) q^{17} +(1.00046 - 3.73376i) q^{19} +(2.57447 + 2.57447i) q^{21} +(-0.307564 - 1.14784i) q^{23} +(-2.66746 - 4.22902i) q^{25} +(3.97874 - 3.97874i) q^{27} +(5.29270 + 3.05574i) q^{29} +(-6.23000 + 6.23000i) q^{31} +(3.49432 - 2.01745i) q^{33} +(-5.43522 + 0.106341i) q^{35} +(-3.86311 + 6.69111i) q^{37} +(0.740038 + 5.34862i) q^{39} +(0.913943 + 3.41088i) q^{41} +(4.37424 + 1.17207i) q^{43} +(0.0331240 + 1.69300i) q^{45} -6.81282 q^{47} +(0.544711 - 0.943467i) q^{49} +9.38205i q^{51} +(4.88693 + 4.88693i) q^{53} +(-1.44515 + 5.84872i) q^{55} +5.78882i q^{57} +(9.04287 + 2.42303i) q^{59} +(-4.87808 - 8.44908i) q^{61} +(1.59441 + 0.920534i) q^{63} +(-6.52237 - 4.73907i) q^{65} +(-0.878637 - 0.507281i) q^{67} +(0.889809 + 1.54120i) q^{69} +(10.5637 + 2.83054i) q^{71} -9.06732i q^{73} +(5.49777 + 5.08356i) q^{75} +(4.63174 + 4.63174i) q^{77} -11.6191i q^{79} +(-3.07735 + 5.33013i) q^{81} -1.09215 q^{83} +(-10.0975 - 9.70992i) q^{85} +(-8.84053 - 2.36881i) q^{87} +(1.29560 + 4.83523i) q^{89} +(-8.07618 + 3.40777i) q^{91} +(6.59721 - 11.4267i) q^{93} +(-6.23024 - 5.99112i) q^{95} +(2.39272 - 1.38144i) q^{97} +(1.44273 - 1.44273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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