LMFDB - Embedded newform 260.2.bk.c.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bk (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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.4
Root			$-1.14923i$ of defining polynomial
Character	$\chi$	$=$	260.97
Dual form			260.2.bk.c.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.387600 + 1.44654i) q^{3} +(1.95799 - 1.07994i) q^{5} +(2.10545 - 1.21558i) q^{7} +(0.655821 - 0.378639i) q^{9} +O(q^{10})$	\(q+(0.387600 + 1.44654i) q^{3} +(1.95799 - 1.07994i) q^{5} +(2.10545 - 1.21558i) q^{7} +(0.655821 - 0.378639i) q^{9} +(-2.60249 + 0.697334i) q^{11} +(-3.57773 - 0.447059i) q^{13} +(2.32110 + 2.41374i) q^{15} +(6.05137 + 1.62146i) q^{17} +(-1.00046 + 3.73376i) q^{19} +(2.57447 + 2.57447i) q^{21} +(-1.14784 + 0.307564i) q^{23} +(2.66746 - 4.22902i) q^{25} +(3.97874 + 3.97874i) q^{27} +(-5.29270 - 3.05574i) q^{29} +(-6.23000 + 6.23000i) q^{31} +(-2.01745 - 3.49432i) q^{33} +(2.80970 - 4.65387i) q^{35} +(-6.69111 - 3.86311i) q^{37} +(-0.740038 - 5.34862i) q^{39} +(0.913943 + 3.41088i) q^{41} +(1.17207 - 4.37424i) q^{43} +(0.875186 - 1.44962i) q^{45} -6.81282i q^{47} +(-0.544711 + 0.943467i) q^{49} +9.38205i q^{51} +(4.88693 - 4.88693i) q^{53} +(-4.34257 + 4.17590i) q^{55} -5.78882 q^{57} +(-9.04287 - 2.42303i) q^{59} +(-4.87808 - 8.44908i) q^{61} +(0.920534 - 1.59441i) q^{63} +(-7.48796 + 2.98839i) q^{65} +(0.507281 - 0.878637i) q^{67} +(-0.889809 - 1.54120i) q^{69} +(10.5637 + 2.83054i) q^{71} -9.06732 q^{73} +(7.15138 + 2.21943i) q^{75} +(-4.63174 + 4.63174i) q^{77} +11.6191i q^{79} +(-3.07735 + 5.33013i) q^{81} +1.09215i q^{83} +(13.5996 - 3.36031i) q^{85} +(2.36881 - 8.84053i) q^{87} +(-1.29560 - 4.83523i) q^{89} +(-8.07618 + 3.40777i) q^{91} +(-11.4267 - 6.59721i) q^{93} +(2.07335 + 8.39110i) q^{95} +(1.38144 + 2.39272i) q^{97} +(-1.44273 + 1.44273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.387600	+	1.44654i	0.223781	+	0.835162i	0.982889	+	0.184198i	$0.0589687\pi$
$3$	0.387600	+	1.44654i	0.223781	+	0.835162i	−0.759108	+	0.650965i	$0.774365\pi$
$4$		0			0
$5$	1.95799	−	1.07994i	0.875640	−	0.482964i
$5$	1.95799	−	1.07994i	0.875640	−	0.482964i
$6$		0			0
$7$	2.10545	−	1.21558i	0.795787	−	0.459448i	−0.0462092	−	0.998932i	$-0.514714\pi$
$7$	2.10545	−	1.21558i	0.795787	−	0.459448i	0.841996	+	0.539484i	$0.181381\pi$
$8$		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
$13$	−3.57773	−	0.447059i	−0.992283	−	0.123992i
$13$	−3.57773	−	0.447059i	−0.992283	−	0.123992i
$14$		0			0
$15$	2.32110	+	2.41374i	0.599305	+	0.623224i
$16$		0			0
$17$	6.05137	+	1.62146i	1.46767	+	0.393262i	0.902133	−	0.431459i	$-0.142001\pi$
$17$	6.05137	+	1.62146i	1.46767	+	0.393262i	0.565540	+	0.824721i	$0.308668\pi$
$18$		0			0
$19$	−1.00046	+	3.73376i	−0.229521	+	0.856583i	0.751022	+	0.660277i	$0.229561\pi$
$19$	−1.00046	+	3.73376i	−0.229521	+	0.856583i	−0.980543	+	0.196306i	$0.937105\pi$
$20$		0			0
$21$	2.57447	+	2.57447i	0.561795	+	0.561795i
$22$		0			0
$23$	−1.14784	+	0.307564i	−0.239342	+	0.0641315i	−0.376496	−	0.926418i	$-0.622871\pi$
$23$	−1.14784	+	0.307564i	−0.239342	+	0.0641315i	0.137154	+	0.990550i	$0.456204\pi$
$24$		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	−0.0797063	−	0.996818i	$-0.525398\pi$
$29$	−5.29270	−	3.05574i	−0.982830	−	0.567437i	−0.903123	+	0.429382i	$0.858732\pi$
$30$		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
$33$	−2.01745	−	3.49432i	−0.351193	−	0.608283i
$34$		0			0
$35$	2.80970	−	4.65387i	0.474926	−	0.786647i
$36$		0			0
$37$	−6.69111	−	3.86311i	−1.10001	−	0.635092i	−0.163787	−	0.986496i	$-0.552371\pi$
$37$	−6.69111	−	3.86311i	−1.10001	−	0.635092i	−0.936224	+	0.351404i	$0.885704\pi$
$38$		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
$43$	1.17207	−	4.37424i	0.178740	−	0.667066i	−0.817145	−	0.576433i	$-0.804444\pi$
$43$	1.17207	−	4.37424i	0.178740	−	0.667066i	0.995884	−	0.0906330i	$-0.0288890\pi$
$44$		0			0
$45$	0.875186	−	1.44962i	0.130465	−	0.216096i
$46$		0			0
$47$		−	6.81282i		−	0.993752i	−0.867822	−	0.496876i	$-0.834480\pi$
$47$		−	6.81282i		−	0.993752i	0.867822	−	0.496876i	$-0.165520\pi$
$48$		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	−0.286737	−	0.958009i	$-0.592571\pi$
$53$	4.88693	−	4.88693i	0.671272	−	0.671272i	0.958009	+	0.286737i	$0.0925707\pi$
$54$		0			0
$55$	−4.34257	+	4.17590i	−0.585552	+	0.563078i
$56$		0			0
$57$	−5.78882			−0.766748
$58$		0			0
$59$	−9.04287	−	2.42303i	−1.17728	−	0.315452i	−0.383434	−	0.923568i	$-0.625259\pi$
$59$	−9.04287	−	2.42303i	−1.17728	−	0.315452i	−0.793848	+	0.608116i	$0.791925\pi$
$60$		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
$63$	0.920534	−	1.59441i	0.115976	−	0.200877i
$64$		0			0
$65$	−7.48796	+	2.98839i	−0.928767	+	0.370664i
$66$		0			0
$67$	0.507281	−	0.878637i	0.0619743	−	0.107343i	−0.833374	−	0.552710i	$-0.813594\pi$
$67$	0.507281	−	0.878637i	0.0619743	−	0.107343i	0.895348	+	0.445368i	$0.146927\pi$
$68$		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
$73$	−9.06732			−1.06125			−0.530625	−	0.847607i	$-0.678043\pi$
$73$	−9.06732			−1.06125			−0.530625	+	0.847607i	$0.678043\pi$
$74$		0			0
$75$	7.15138	+	2.21943i	0.825770	+	0.256278i
$76$		0			0
$77$	−4.63174	+	4.63174i	−0.527836	+	0.527836i
$78$		0			0
$79$			11.6191i			1.30725i	0.756820	+	0.653623i	$0.226752\pi$
$79$			11.6191i			1.30725i	−0.756820	+	0.653623i	$0.773248\pi$
$80$		0			0
$81$	−3.07735	+	5.33013i	−0.341928	+	0.592236i
$82$		0			0
$83$			1.09215i			0.119879i	0.998202	+	0.0599397i	$0.0190909\pi$
$83$			1.09215i			0.119879i	−0.998202	+	0.0599397i	$0.980909\pi$
$84$		0			0
$85$	13.5996	−	3.36031i	1.47509	−	0.364477i
$86$		0			0
$87$	2.36881	−	8.84053i	0.253963	−	0.947804i
$88$		0			0
$89$	−1.29560	−	4.83523i	−0.137333	−	0.512533i	−0.999977	−	0.00672267i	$-0.997860\pi$
$89$	−1.29560	−	4.83523i	−0.137333	−	0.512533i	0.862644	−	0.505811i	$-0.168807\pi$
$90$		0			0
$91$	−8.07618	+	3.40777i	−0.846613	+	0.357231i
$92$		0			0
$93$	−11.4267	−	6.59721i	−1.18489	−	0.684099i
$94$		0			0
$95$	2.07335	+	8.39110i	0.212721	+	0.860909i
$96$		0			0
$97$	1.38144	+	2.39272i	0.140264	+	0.242944i	0.927596	−	0.373585i	$-0.121872\pi$
$97$	1.38144	+	2.39272i	0.140264	+	0.242944i	−0.787332	+	0.616529i	$0.788538\pi$
$98$		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	$-0.326707\pi$
$103$	−3.42536	−	3.42536i	−0.337511	−	0.337511i	−0.855430	+	0.517919i	$0.826707\pi$
$104$		0			0
$105$	7.82106	+	2.26052i	0.763257	+	0.220604i
$106$		0			0
$107$	−2.28992	+	0.613583i	−0.221375	+	0.0593173i	−0.367802	−	0.929904i	$-0.619889\pi$
$107$	−2.28992	+	0.613583i	−0.221375	+	0.0593173i	0.146427	+	0.989222i	$0.453223\pi$
$108$		0			0
$109$	−2.27846	−	2.27846i	−0.218237	−	0.218237i	0.589518	−	0.807755i	$-0.299318\pi$
$109$	−2.27846	−	2.27846i	−0.218237	−	0.218237i	−0.807755	+	0.589518i	$0.799318\pi$
$110$		0			0
$111$	2.99469	−	11.1763i	0.284243	−	1.06081i
$112$		0			0
$113$	13.3698	+	3.58242i	1.25772	+	0.337006i	0.825315	−	0.564672i	$-0.190997\pi$
$113$	13.3698	+	3.58242i	1.25772	+	0.337006i	0.432408	+	0.901678i	$0.357664\pi$
$114$		0			0
$115$	−1.91532	+	1.84181i	−0.178604	+	0.171750i
$116$		0			0
$117$	−2.51562	+	1.06148i	−0.232570	+	0.0981334i
$118$		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
$123$	−4.57974	+	2.64412i	−0.412942	+	0.238412i
$124$		0			0
$125$	0.655778	−	11.1611i	0.0586546	−	0.998278i
$126$		0			0
$127$	−1.13358	−	4.23059i	−0.100589	−	0.375404i	0.897218	−	0.441587i	$-0.145584\pi$
$127$	−1.13358	−	4.23059i	−0.100589	−	0.375404i	−0.997807	+	0.0661832i	$0.978918\pi$
$128$		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
$133$	2.43228	+	9.07740i	0.210906	+	0.787110i
$134$		0			0
$135$	12.0872	+	3.49355i	1.04030	+	0.300677i
$136$		0			0
$137$	12.3932	−	7.15524i	1.05883	−	0.611313i	0.133719	−	0.991019i	$-0.457308\pi$
$137$	12.3932	−	7.15524i	1.05883	−	0.611313i	0.925107	+	0.379706i	$0.123975\pi$
$138$		0			0
$139$	−13.2937	+	7.67514i	−1.12756	+	0.650997i	−0.943320	−	0.331885i	$-0.892315\pi$
$139$	−13.2937	+	7.67514i	−1.12756	+	0.650997i	−0.184239	+	0.982881i	$0.558982\pi$
$140$		0			0
$141$	9.85504	−	2.64065i	0.829944	−	0.222383i
$142$		0			0
$143$	9.62273	−	1.33141i	0.804694	−	0.111338i
$144$		0			0
$145$	−13.6631	−	0.267322i	−1.13466	−	0.0221998i
$146$		0			0
$147$	−1.57590	−	0.422260i	−0.129978	−	0.0348274i
$148$		0			0
$149$	−0.861750	+	3.21610i	−0.0705973	+	0.263473i	−0.992199	−	0.124664i	$-0.960215\pi$
$149$	−0.861750	+	3.21610i	−0.0705973	+	0.263473i	0.921602	+	0.388137i	$0.126881\pi$
$150$		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
$153$	4.58257	−	1.22789i	0.370479	−	0.0992694i
$154$		0			0
$155$	−5.47026	+	18.9263i	−0.439382	+	1.52020i
$156$		0			0
$157$	14.7756	+	14.7756i	1.17922	+	1.17922i	0.979942	+	0.199281i	$0.0638605\pi$
$157$	14.7756	+	14.7756i	1.17922	+	1.17922i	0.199281	+	0.979942i	$0.436139\pi$
$158$		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
$163$	−4.46942	−	7.74127i	−0.350072	−	0.606343i	0.636190	−	0.771533i	$-0.280510\pi$
$163$	−4.46942	−	7.74127i	−0.350072	−	0.606343i	−0.986262	+	0.165190i	$0.947176\pi$
$164$		0			0
$165$	−7.72380	−	4.66313i	−0.601297	−	0.363024i
$166$		0			0
$167$	15.7729	+	9.10649i	1.22054	+	0.704681i	0.965034	−	0.262125i	$-0.0844232\pi$
$167$	15.7729	+	9.10649i	1.22054	+	0.704681i	0.255510	+	0.966806i	$0.417757\pi$
$168$		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
$173$	−0.469884	+	1.75363i	−0.0357246	+	0.133326i	−0.981485	−	0.191539i	$-0.938652\pi$
$173$	−0.469884	+	1.75363i	−0.0357246	+	0.133326i	0.945760	+	0.324865i	$0.105319\pi$
$174$		0			0
$175$	0.475482	−	12.1465i	0.0359431	−	0.918192i
$176$		0			0
$177$		−	14.0201i		−	1.05381i
$178$		0			0
$179$	−9.09987	+	15.7614i	−0.680156	+	1.17807i	0.294776	+	0.955566i	$0.404755\pi$
$179$	−9.09987	+	15.7614i	−0.680156	+	1.17807i	−0.974933	+	0.222499i	$0.928578\pi$
$180$		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
$185$	−17.2731	−	0.337952i	−1.26994	−	0.0248467i
$186$		0			0
$187$	−16.8793			−1.23434
$188$		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
$193$	−9.68786	+	16.7799i	−0.697348	+	1.20784i	0.272035	+	0.962287i	$0.412303\pi$
$193$	−9.68786	+	16.7799i	−0.697348	+	1.20784i	−0.969383	+	0.245554i	$0.921030\pi$
$194$		0			0
$195$	−7.22517	−	9.67336i	−0.517405	−	0.692723i
$196$		0			0
$197$	−6.18595	+	10.7144i	−0.440731	+	0.763368i	−0.997744	−	0.0671359i	$-0.978614\pi$
$197$	−6.18595	+	10.7144i	−0.440731	+	0.763368i	0.557013	+	0.830504i	$0.311947\pi$
$198$		0			0
$199$	−5.08783	−	8.81238i	−0.360667	−	0.624693i	0.627404	−	0.778694i	$-0.284117\pi$
$199$	−5.08783	−	8.81238i	−0.360667	−	0.624693i	−0.988071	+	0.154001i	$0.950784\pi$
$200$		0			0
$201$	1.46761	+	0.393245i	0.103517	+	0.0277373i
$202$		0			0
$203$	−14.8580			−1.04283
$204$		0			0
$205$	5.47304	+	5.69147i	0.382253	+	0.397510i
$206$		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
$213$			16.3780i			1.12220i
$214$		0			0
$215$	−2.42900	−	9.83050i	−0.165657	−	0.670434i
$216$		0			0
$217$	−5.54388	+	20.6901i	−0.376343	+	1.40453i
$218$		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
$223$	19.0202	+	10.9813i	1.27368	+	0.735362i	0.975679	−	0.219203i	$-0.0703455\pi$
$223$	19.0202	+	10.9813i	1.27368	+	0.735362i	0.298005	+	0.954564i	$0.403679\pi$
$224$		0			0
$225$	0.148107	−	3.78349i	0.00987377	−	0.252233i
$226$		0			0
$227$	−4.06760	−	7.04528i	−0.269976	−	0.467612i	0.698879	−	0.715239i	$-0.253682\pi$
$227$	−4.06760	−	7.04528i	−0.269976	−	0.467612i	−0.968855	+	0.247628i	$0.920349\pi$
$228$		0			0
$229$	10.1234	−	10.1234i	0.668973	−	0.668973i	−0.288505	−	0.957478i	$-0.593158\pi$
$229$	10.1234	−	10.1234i	0.668973	−	0.668973i	0.957478	+	0.288505i	$0.0931582\pi$
$230$		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	$-0.225360\pi$
$233$	1.66935	+	1.66935i	0.109363	+	0.109363i	−0.650308	+	0.759671i	$0.725360\pi$
$234$		0			0
$235$	−7.35743	−	13.3394i	−0.479946	−	0.870169i
$236$		0			0
$237$	−16.8075	+	4.50355i	−1.09176	+	0.292537i
$238$		0			0
$239$	−16.8726	−	16.8726i	−1.09140	−	1.09140i	−0.995380	−	0.0960168i	$-0.969390\pi$
$239$	−16.8726	−	16.8726i	−1.09140	−	1.09140i	−0.0960168	−	0.995380i	$-0.530610\pi$
$240$		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
$243$	7.40216	+	1.98340i	0.474849	+	0.127235i
$244$		0			0
$245$	−0.0476523	+	2.43556i	−0.00304439	+	0.155602i
$246$		0			0
$247$	5.24858	−	12.9111i	0.333959	−	0.821514i
$248$		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
$253$	2.77277	−	1.60086i	0.174323	−	0.100645i
$254$		0			0
$255$	10.1320	+	18.3700i	0.634493	+	1.15037i
$256$		0			0
$257$	2.05177	+	7.65731i	0.127986	+	0.477650i	0.999928	−	0.0119581i	$-0.00380647\pi$
$257$	2.05177	+	7.65731i	0.127986	+	0.477650i	−0.871943	+	0.489608i	$0.837140\pi$
$258$		0			0
$259$	−18.7838			−1.16717
$260$		0			0
$261$	−4.62809			−0.286471
$262$		0			0
$263$	1.04147	+	3.88683i	0.0642200	+	0.239672i	0.990573	−	0.136983i	$-0.0437407\pi$
$263$	1.04147	+	3.88683i	0.0642200	+	0.239672i	−0.926353	+	0.376656i	$0.877074\pi$
$264$		0			0
$265$	4.29098	−	14.8462i	0.263593	−	0.911993i
$266$		0			0
$267$	6.49220	−	3.74827i	0.397316	−	0.229391i
$268$		0			0
$269$	16.5636	−	9.56301i	1.00990	−	0.583067i	0.0987386	−	0.995113i	$-0.468519\pi$
$269$	16.5636	−	9.56301i	1.00990	−	0.583067i	0.911163	+	0.412047i	$0.135186\pi$
$270$		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
$273$	−8.05981	−	10.3617i	−0.487802	−	0.627118i
$274$		0			0
$275$	−3.99299	+	12.8661i	−0.240786	+	0.775854i
$276$		0			0
$277$	−14.6084	−	3.91430i	−0.877731	−	0.235187i	−0.208303	−	0.978064i	$-0.566794\pi$
$277$	−14.6084	−	3.91430i	−0.877731	−	0.235187i	−0.669428	+	0.742877i	$0.733461\pi$
$278$		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
$283$	8.11105	−	2.17335i	0.482152	−	0.129192i	−0.00955242	−	0.999954i	$-0.503041\pi$
$283$	8.11105	−	2.17335i	0.482152	−	0.129192i	0.491705	+	0.870762i	$0.336374\pi$
$284$		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
$293$	0.870229	+	1.50728i	0.0508393	+	0.0880563i	0.890325	−	0.455325i	$-0.150477\pi$
$293$	0.870229	+	1.50728i	0.0508393	+	0.0880563i	−0.839486	+	0.543382i	$0.817144\pi$
$294$		0			0
$295$	−20.3226	+	5.02148i	−1.18323	+	0.292362i
$296$		0			0
$297$	−13.1291	−	7.58011i	−0.761830	−	0.439843i
$298$		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
$303$	−5.04500	+	18.8282i	−0.289827	+	1.08165i
$304$		0			0
$305$	−18.6757	−	11.2752i	−1.06937	−	0.645616i
$306$		0			0
$307$		−	9.53050i		−	0.543934i	−0.962307	−	0.271967i	$-0.912326\pi$
$307$		−	9.53050i		−	0.543934i	0.962307	−	0.271967i	$-0.0876742\pi$
$308$		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	−0.0373038	−	0.999304i	$-0.511877\pi$
$313$	17.0195	−	17.0195i	0.962000	−	0.962000i	0.999304	+	0.0373038i	$0.0118769\pi$
$314$		0			0
$315$	0.0805299	−	4.11597i	0.00453735	−	0.231908i
$316$		0			0
$317$	−7.07976			−0.397639			−0.198819	−	0.980036i	$-0.563711\pi$
$317$	−7.07976			−0.397639			−0.198819	+	0.980036i	$0.563711\pi$
$318$		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
$323$	−12.1083	+	20.9722i	−0.673723	+	1.16692i
$324$		0			0
$325$	−11.4341	+	13.9378i	−0.634248	+	0.773129i
$326$		0			0
$327$	2.41276	−	4.17903i	0.133426	−	0.231101i
$328$		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
$333$	−5.85090			−0.320627
$334$		0			0
$335$	0.0443778	−	2.26820i	0.00242462	−	0.123925i
$336$		0			0
$337$	4.66232	−	4.66232i	0.253973	−	0.253973i	−0.568625	−	0.822597i	$-0.692524\pi$
$337$	4.66232	−	4.66232i	0.253973	−	0.253973i	0.822597	+	0.568625i	$0.192524\pi$
$338$		0			0
$339$			20.7285i			1.12582i
$340$		0			0
$341$	11.8691	−	20.5579i	0.642747	−	1.11327i
$342$		0			0
$343$			19.6667i			1.06190i
$344$		0			0
$345$	−3.40664	−	2.05671i	−0.183407	−	0.110729i
$346$		0			0
$347$	−6.47707	+	24.1728i	−0.347707	+	1.29766i	0.541710	+	0.840566i	$0.317777\pi$
$347$	−6.47707	+	24.1728i	−0.347707	+	1.29766i	−0.889417	+	0.457096i	$0.848889\pi$
$348$		0			0
$349$	7.28299	+	27.1805i	0.389850	+	1.45494i	0.830378	+	0.557200i	$0.188124\pi$
$349$	7.28299	+	27.1805i	0.389850	+	1.45494i	−0.440528	+	0.897739i	$0.645209\pi$
$350$		0			0
$351$	−12.4561	−	16.0136i	−0.664859	−	0.854743i
$352$		0			0
$353$	−8.40368	−	4.85187i	−0.447283	−	0.258239i	0.259399	−	0.965770i	$-0.416475\pi$
$353$	−8.40368	−	4.85187i	−0.447283	−	0.258239i	−0.706682	+	0.707531i	$0.749809\pi$
$354$		0			0
$355$	23.7405	−	5.86601i	1.26002	−	0.311335i
$356$		0			0
$357$	11.4047	+	19.7535i	0.603599	+	1.04546i
$358$		0			0
$359$	−2.09591	+	2.09591i	−0.110618	+	0.110618i	−0.760249	−	0.649631i	$-0.774923\pi$
$359$	−2.09591	+	2.09591i	−0.110618	+	0.110618i	0.649631	+	0.760249i	$0.274923\pi$
$360$		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
$367$	−10.1325	+	2.71499i	−0.528912	+	0.141721i	−0.513386	−	0.858158i	$-0.671609\pi$
$367$	−10.1325	+	2.71499i	−0.528912	+	0.141721i	−0.0155260	+	0.999879i	$0.504942\pi$
$368$		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
$373$	15.1023	+	4.04666i	0.781969	+	0.209528i	0.627653	−	0.778493i	$-0.284016\pi$
$373$	15.1023	+	4.04666i	0.781969	+	0.209528i	0.154317	+	0.988021i	$0.450682\pi$
$374$		0			0
$375$	16.3992	−	3.37743i	0.846850	−	0.174410i
$376$		0			0
$377$	17.5697	+	13.2988i	0.904888	+	0.684921i
$378$		0			0
$379$	12.4625	−	3.33930i	0.640153	−	0.171529i	0.0758805	−	0.997117i	$-0.475823\pi$
$379$	12.4625	−	3.33930i	0.640153	−	0.171529i	0.564273	+	0.825588i	$0.309157\pi$
$380$		0			0
$381$	5.68036	−	3.27956i	0.291014	−	0.168017i
$382$		0			0
$383$	24.8327	−	14.3371i	1.26889	−	0.732594i	0.294112	−	0.955771i	$-0.404976\pi$
$383$	24.8327	−	14.3371i	1.26889	−	0.732594i	0.974778	+	0.223177i	$0.0716428\pi$
$384$		0			0
$385$	−4.06691	+	14.0709i	−0.207269	+	0.717120i
$386$		0			0
$387$	−0.887585	−	3.31251i	−0.0451185	−	0.168385i
$388$		0			0
$389$	35.3120			1.79039			0.895194	−	0.445677i	$-0.147037\pi$
$389$	35.3120			1.79039			0.895194	+	0.445677i	$0.147037\pi$
$390$		0			0
$391$	−7.44474			−0.376496
$392$		0			0
$393$	4.70817	+	17.5711i	0.237496	+	0.886346i
$394$		0			0
$395$	12.5479	+	22.7500i	0.631352	+	1.14468i
$396$		0			0
$397$	7.76940	−	4.48566i	0.389935	−	0.225129i	−0.292197	−	0.956358i	$-0.594386\pi$
$397$	7.76940	−	4.48566i	0.389935	−	0.225129i	0.682132	+	0.731229i	$0.261053\pi$
$398$		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
$403$	25.0744	−	19.5041i	1.24905	−	0.971566i
$404$		0			0
$405$	−0.269212	+	13.7597i	−0.0133772	+	0.683725i
$406$		0			0
$407$	20.1074	+	5.38776i	0.996686	+	0.267061i
$408$		0			0
$409$	−7.28956	+	27.2050i	−0.360446	+	1.34520i	0.513046	+	0.858361i	$0.328517\pi$
$409$	−7.28956	+	27.2050i	−0.360446	+	1.34520i	−0.873491	+	0.486840i	$0.838150\pi$
$410$		0			0
$411$	15.1540	+	15.1540i	0.747491	+	0.747491i
$412$		0			0
$413$	−21.9847	+	5.89080i	−1.08180	+	0.289867i
$414$		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	0.399962	−	0.916532i	$-0.369023\pi$
$419$	−3.96691	−	2.29029i	−0.193796	−	0.111888i	−0.593758	+	0.804643i	$0.702357\pi$
$420$		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
$423$	−2.57960	−	4.46799i	−0.125424	−	0.217241i
$424$		0			0
$425$	22.9990	−	21.2662i	1.11562	−	1.03156i
$426$		0			0
$427$	−20.5411	−	11.8594i	−0.994056	−	0.573918i
$428$		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
$433$	10.0790	−	37.6152i	0.484364	−	1.80767i	−0.0985457	−	0.995133i	$-0.531419\pi$
$433$	10.0790	−	37.6152i	0.484364	−	1.80767i	0.582909	−	0.812537i	$-0.301914\pi$
$434$		0			0
$435$	−4.90912	−	19.8678i	−0.235374	−	0.952590i
$436$		0			0
$437$		−	4.59348i		−	0.219736i
$438$		0			0
$439$	14.3895	−	24.9233i	0.686771	−	1.18952i	−0.286105	−	0.958198i	$-0.592361\pi$
$439$	14.3895	−	24.9233i	0.686771	−	1.18952i	0.972877	−	0.231324i	$-0.0743059\pi$
$440$		0			0
$441$			0.824995i			0.0392855i
$442$		0			0
$443$	−25.9217	+	25.9217i	−1.23158	+	1.23158i	−0.268222	+	0.963357i	$0.586436\pi$
$443$	−25.9217	+	25.9217i	−1.23158	+	1.23158i	−0.963357	+	0.268222i	$0.913564\pi$
$444$		0			0
$445$	−7.75852	−	8.06817i	−0.367789	−	0.382468i
$446$		0			0
$447$	−4.98624			−0.235841
$448$		0			0
$449$	−38.4485	−	10.3023i	−1.81450	−	0.486193i	−0.818416	−	0.574626i	$-0.805147\pi$
$449$	−38.4485	−	10.3023i	−1.81450	−	0.486193i	−0.996082	+	0.0884331i	$0.971814\pi$
$450$		0			0
$451$	−4.75705	−	8.23944i	−0.224001	−	0.387980i
$452$		0			0
$453$	15.5337	−	26.9052i	0.729839	−	1.26412i
$454$		0			0
$455$	−12.1329	+	15.3942i	−0.568799	+	0.721689i
$456$		0			0
$457$	3.92971	−	6.80646i	0.183824	−	0.318393i	−0.759355	−	0.650676i	$-0.774486\pi$
$457$	3.92971	−	6.80646i	0.183824	−	0.318393i	0.943180	+	0.332283i	$0.107819\pi$
$458$		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
$463$	−1.60260			−0.0744790			−0.0372395	−	0.999306i	$-0.511856\pi$
$463$	−1.60260			−0.0744790			−0.0372395	+	0.999306i	$0.511856\pi$
$464$		0			0
$465$	−29.4980	−	0.577136i	−1.36794	−	0.0267640i
$466$		0			0
$467$	17.6094	−	17.6094i	0.814864	−	0.814864i	−0.170495	−	0.985359i	$-0.554537\pi$
$467$	17.6094	−	17.6094i	0.814864	−	0.814864i	0.985359	+	0.170495i	$0.0545366\pi$
$468$		0			0
$469$		−	2.46657i		−	0.113896i
$470$		0			0
$471$	−15.6465	+	27.1006i	−0.720955	+	1.24873i
$472$		0			0
$473$			12.2012i			0.561013i
$474$		0			0
$475$	13.1215	+	14.1906i	0.602055	+	0.651110i
$476$		0			0
$477$	1.35457	−	5.05534i	0.0620216	−	0.231468i
$478$		0			0
$479$	−5.67830	−	21.1917i	−0.259448	−	0.968273i	−0.965562	−	0.260175i	$-0.916220\pi$
$479$	−5.67830	−	21.1917i	−0.259448	−	0.968273i	0.706113	−	0.708099i	$-0.250447\pi$
$480$		0			0
$481$	22.2119	+	16.8125i	1.01278	+	0.766583i
$482$		0			0
$483$	−3.74690	−	2.16328i	−0.170490	−	0.0984325i
$484$		0			0
$485$	5.28885	+	3.19306i	0.240154	+	0.144990i
$486$		0			0
$487$	−6.85260	−	11.8691i	−0.310521	−	0.537838i	0.667954	−	0.744202i	$-0.267170\pi$
$487$	−6.85260	−	11.8691i	−0.310521	−	0.537838i	−0.978475	+	0.206364i	$0.933837\pi$
$488$		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
$497$	25.6822	−	6.88153i	1.15200	−	0.308679i
$498$		0			0
$499$	−15.3195	−	15.3195i	−0.685795	−	0.685795i	0.275505	−	0.961300i	$-0.411155\pi$
$499$	−15.3195	−	15.3195i	−0.685795	−	0.685795i	−0.961300	+	0.275505i	$0.911155\pi$
$500$		0			0
$501$	−7.05936	+	26.3459i	−0.315389	+	1.17705i
$502$		0			0
$503$	33.5206	+	8.98181i	1.49461	+	0.400479i	0.911290	−	0.411765i	$-0.135087\pi$
$503$	33.5206	+	8.98181i	1.49461	+	0.400479i	0.583318	+	0.812244i	$0.301754\pi$
$504$		0			0
$505$	29.0990	+	0.569330i	1.29489	+	0.0253349i
$506$		0			0
$507$	0.256508	+	19.4667i	0.0113919	+	0.864549i
$508$		0			0
$509$	−17.1190	+	4.58701i	−0.758785	+	0.203316i	−0.617411	−	0.786641i	$-0.711819\pi$
$509$	−17.1190	+	4.58701i	−0.758785	+	0.203316i	−0.141374	+	0.989956i	$0.545152\pi$
$510$		0			0
$511$	−19.0908	+	11.0221i	−0.844528	+	0.487589i
$512$		0			0
$513$	−18.8362	+	10.8751i	−0.831640	+	0.480148i
$514$		0			0
$515$	−10.4060	−	3.00765i	−0.458544	−	0.132533i
$516$		0			0
$517$	4.75081	+	17.7303i	0.208940	+	0.779776i
$518$		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
$523$	−5.87752	−	21.9352i	−0.257006	−	0.959160i	−0.966963	−	0.254915i	$-0.917952\pi$
$523$	−5.87752	−	21.9352i	−0.257006	−	0.959160i	0.709957	−	0.704245i	$-0.248714\pi$
$524$		0			0
$525$	17.7548	−	4.02019i	0.774883	−	0.175456i
$526$		0			0
$527$	−47.8017	+	27.5983i	−2.08228	+	1.20220i
$528$		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
$533$	−1.74497	−	12.6118i	−0.0755832	−	0.546277i
$534$		0			0
$535$	−3.82101	+	3.67437i	−0.165197	+	0.158857i
$536$		0			0
$537$	−26.3267	−	7.05423i	−1.13608	−	0.304412i
$538$		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
$543$	−25.2206	+	6.75783i	−1.08232	+	0.290006i
$544$		0			0
$545$	−6.92181	−	2.00061i	−0.296498	−	0.0856967i
$546$		0			0
$547$	−7.96444	−	7.96444i	−0.340535	−	0.340535i	0.516034	−	0.856568i	$-0.327408\pi$
$547$	−7.96444	−	7.96444i	−0.340535	−	0.340535i	−0.856568	+	0.516034i	$0.827408\pi$
$548$		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
$553$	14.1239	+	24.4634i	0.600611	+	1.04029i
$554$		0			0
$555$	−6.20618	−	25.1172i	−0.263438	−	1.06617i
$556$		0			0
$557$	−22.7800	−	13.1520i	−0.965219	−	0.557269i	−0.0674437	−	0.997723i	$-0.521484\pi$
$557$	−22.7800	−	13.1520i	−0.965219	−	0.557269i	−0.897775	+	0.440454i	$0.854818\pi$
$558$		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
$563$	−11.9307	+	44.5258i	−0.502817	+	1.87654i	−0.0219234	+	0.999760i	$0.506979\pi$
$563$	−11.9307	+	44.5258i	−0.502817	+	1.87654i	−0.480894	+	0.876779i	$0.659688\pi$
$564$		0			0
$565$	30.0467	−	7.42420i	1.26407	−	0.312338i
$566$		0			0
$567$			14.9631i			0.628391i
$568$		0			0
$569$	15.3819	−	26.6422i	0.644841	−	1.11690i	−0.339497	−	0.940607i	$-0.610257\pi$
$569$	15.3819	−	26.6422i	0.644841	−	1.11690i	0.984338	−	0.176290i	$-0.0564097\pi$
$570$		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
$575$	−1.76114	+	5.67468i	−0.0734444	+	0.236650i
$576$		0			0
$577$	20.3744			0.848198			0.424099	−	0.905616i	$-0.360591\pi$
$577$	20.3744			0.848198			0.424099	+	0.905616i	$0.360591\pi$
$578$		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
$583$	−9.31035	+	16.1260i	−0.385595	+	0.667870i
$584$		0			0
$585$	−3.77924	+	4.79508i	−0.156252	+	0.198252i
$586$		0			0
$587$	21.5802	−	37.3781i	0.890712	−	1.54276i	0.0516879	−	0.998663i	$-0.483540\pi$
$587$	21.5802	−	37.3781i	0.890712	−	1.54276i	0.839024	−	0.544095i	$-0.183127\pi$
$588$		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
$593$	−34.3448			−1.41037			−0.705186	−	0.709022i	$-0.749137\pi$
$593$	−34.3448			−1.41037			−0.705186	+	0.709022i	$0.749137\pi$
$594$		0			0
$595$	24.5486	−	23.6064i	1.00639	−	0.967770i
$596$		0			0
$597$	10.7754	−	10.7754i	0.441010	−	0.441010i
$598$		0			0
$599$			8.69200i			0.355146i	0.984108	+	0.177573i	$0.0568245\pi$
$599$			8.69200i			0.355146i	−0.984108	+	0.177573i	$0.943175\pi$
$600$		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
$603$		−	0.768305i		−	0.0312878i
$604$		0			0
$605$	−4.32324	+	7.16082i	−0.175765	+	0.291129i
$606$		0			0
$607$	−4.83078	+	18.0287i	−0.196075	+	0.731764i	0.795910	+	0.605414i	$0.206993\pi$
$607$	−4.83078	+	18.0287i	−0.196075	+	0.731764i	−0.991986	+	0.126349i	$0.959674\pi$
$608$		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
$613$	−20.9846	−	12.1155i	−0.847560	−	0.489339i	0.0122667	−	0.999925i	$-0.496095\pi$
$613$	−20.9846	−	12.1155i	−0.847560	−	0.489339i	−0.859827	+	0.510586i	$0.829429\pi$
$614$		0			0
$615$	−6.11161	+	10.1230i	−0.246444	+	0.408199i
$616$		0			0
$617$	7.94688	+	13.7644i	0.319930	+	0.554134i	0.980473	−	0.196654i	$-0.0630074\pi$
$617$	7.94688	+	13.7644i	0.319930	+	0.554134i	−0.660544	+	0.750788i	$0.729674\pi$
$618$		0			0
$619$	10.3555	−	10.3555i	0.416225	−	0.416225i	−0.467676	−	0.883900i	$-0.654908\pi$
$619$	10.3555	−	10.3555i	0.416225	−	0.416225i	0.883900	+	0.467676i	$0.154908\pi$
$620$		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
$627$	15.0653	−	4.03674i	0.601651	−	0.161212i
$628$		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
$633$	25.1081	+	6.72769i	0.997956	+	0.267402i
$634$		0			0
$635$	−6.78833	−	7.05926i	−0.269387	−	0.280138i
$636$		0			0
$637$	2.37061	−	3.13195i	0.0939271	−	0.124092i
$638$		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
$643$	19.8336	−	11.4509i	0.782159	−	0.451580i	−0.0550358	−	0.998484i	$-0.517527\pi$
$643$	19.8336	−	11.4509i	0.782159	−	0.451580i	0.837195	+	0.546905i	$0.184194\pi$
$644$		0			0
$645$	13.2788	−	7.32396i	0.522851	−	0.288381i
$646$		0			0
$647$	−6.33051	−	23.6258i	−0.248878	−	0.928825i	−0.971395	−	0.237471i	$-0.923681\pi$
$647$	−6.33051	−	23.6258i	−0.248878	−	0.928825i	0.722517	−	0.691353i	$-0.242985\pi$
$648$		0			0
$649$	25.2236			0.990113
$650$		0			0
$651$	−32.0779			−1.25723
$652$		0			0
$653$	−7.56514	−	28.2335i	−0.296047	−	1.10486i	−0.940383	−	0.340119i	$-0.889533\pi$
$653$	−7.56514	−	28.2335i	−0.296047	−	1.10486i	0.644336	−	0.764743i	$-0.277134\pi$
$654$		0			0
$655$	23.7837	−	13.1180i	0.929304	−	0.512562i
$656$		0			0
$657$	−5.94654	+	3.43324i	−0.231997	+	0.133943i
$658$		0			0
$659$	−11.0616	+	6.38643i	−0.430900	+	0.248780i	−0.699730	−	0.714407i	$-0.746696\pi$
$659$	−11.0616	+	6.38643i	−0.430900	+	0.248780i	0.268830	+	0.963188i	$0.413363\pi$
$660$		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
$663$	4.19433	−	33.5664i	0.162894	−	1.30361i
$664$		0			0
$665$	14.5654	+	15.1468i	0.564823	+	0.587366i
$666$		0			0
$667$	7.01503	+	1.87967i	0.271623	+	0.0727812i
$668$		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
$673$	−23.0450	+	6.17489i	−0.888320	+	0.238025i	−0.673993	−	0.738738i	$-0.735422\pi$
$673$	−23.0450	+	6.17489i	−0.888320	+	0.238025i	−0.214326	+	0.976762i	$0.568756\pi$
$674$		0			0
$675$	27.4394	−	6.21306i	1.05614	−	0.239141i
$676$		0			0
$677$	18.9432	+	18.9432i	0.728048	+	0.728048i	0.970231	−	0.242183i	$-0.0778634\pi$
$677$	18.9432	+	18.9432i	0.728048	+	0.728048i	−0.242183	+	0.970231i	$0.577863\pi$
$678$		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
$683$	1.69188	+	2.93042i	0.0647380	+	0.112129i	0.896578	−	0.442886i	$-0.146046\pi$
$683$	1.69188	+	2.93042i	0.0647380	+	0.112129i	−0.831840	+	0.555016i	$0.812712\pi$
$684$		0			0
$685$	16.5386	−	27.3938i	0.631909	−	1.04666i
$686$		0			0
$687$	18.5678	+	10.7201i	0.708405	+	0.408998i
$688$		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
$693$	−1.28384	+	4.79135i	−0.0487690	+	0.182008i
$694$		0			0
$695$	−17.7403	+	29.3843i	−0.672929	+	1.11461i
$696$		0			0
$697$			22.1224i			0.837947i
$698$		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
$705$	16.4443	−	15.8132i	0.619330	−	0.595560i
$706$		0			0
$707$	31.6440			1.19010
$708$		0			0
$709$	9.56101	+	2.56186i	0.359071	+	0.0962128i	0.433845	−	0.900988i	$-0.357157\pi$
$709$	9.56101	+	2.56186i	0.359071	+	0.0962128i	−0.0747734	+	0.997201i	$0.523823\pi$
$710$		0			0
$711$	4.39942	+	7.62003i	0.164991	+	0.285773i
$712$		0			0
$713$	5.23494	−	9.06719i	0.196050	−	0.339569i
$714$		0			0
$715$	17.4034	−	12.9989i	0.650850	−	0.486130i
$716$		0			0
$717$	17.8671	−	30.9467i	0.667259	−	1.15573i
$718$		0			0
$719$	5.37245	+	9.30535i	0.200358	+	0.347031i	0.948644	−	0.316346i	$-0.102456\pi$
$719$	5.37245	+	9.30535i	0.200358	+	0.347031i	−0.748286	+	0.663377i	$0.769123\pi$
$720$		0			0
$721$	−11.3758	−	3.04812i	−0.423655	−	0.113518i
$722$		0			0
$723$	−7.18383			−0.267169
$724$		0			0
$725$	−27.0409	+	14.2319i	−1.00427	+	0.528559i
$726$		0			0
$727$	14.2084	−	14.2084i	0.526961	−	0.526961i	−0.392704	−	0.919665i	$-0.628460\pi$
$727$	14.2084	−	14.2084i	0.526961	−	0.526961i	0.919665	+	0.392704i	$0.128460\pi$
$728$		0			0
$729$			29.9404i			1.10890i
$730$		0			0
$731$	14.1853	−	24.5697i	0.524663	−	0.908743i
$732$		0			0
$733$			37.5445i			1.38674i	0.720582	+	0.693369i	$0.243875\pi$
$733$			37.5445i			1.38674i	−0.720582	+	0.693369i	$0.756125\pi$
$734$		0			0
$735$	−3.54161	+	0.875091i	−0.130634	+	0.0322782i
$736$		0			0
$737$	−0.707489	+	2.64038i	−0.0260607	+	0.0972598i
$738$		0			0
$739$	7.64320	+	28.5248i	0.281160	+	1.04930i	0.951600	+	0.307339i	$0.0994386\pi$
$739$	7.64320	+	28.5248i	0.281160	+	1.04930i	−0.670440	+	0.741964i	$0.733895\pi$
$740$		0			0
$741$	20.7108	+	2.58794i	0.760832	+	0.0950705i
$742$		0			0
$743$	−33.7356	−	19.4772i	−1.23764	−	0.714551i	−0.269027	−	0.963133i	$-0.586702\pi$
$743$	−33.7356	−	19.4772i	−1.23764	−	0.714551i	−0.968611	+	0.248582i	$0.920036\pi$
$744$		0			0
$745$	1.78589	+	7.22773i	0.0654299	+	0.264803i
$746$		0			0
$747$	0.413532	+	0.716258i	0.0151303	+	0.0262065i
$748$		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
$757$	26.7365	−	7.16401i	0.971753	−	0.260380i	0.262185	−	0.965018i	$-0.415557\pi$
$757$	26.7365	−	7.16401i	0.971753	−	0.260380i	0.709568	+	0.704637i	$0.248890\pi$
$758$		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
$763$	−7.56686	−	2.02753i	−0.273939	−	0.0734017i
$764$		0			0
$765$	7.64657	−	7.35310i	0.276462	−	0.265852i
$766$		0			0
$767$	31.2697	+	12.7116i	1.12908	+	0.458991i
$768$		0			0
$769$	0.642529	−	0.172165i	0.0231702	−	0.00620843i	−0.247215	−	0.968961i	$-0.579516\pi$
$769$	0.642529	−	0.172165i	0.0231702	−	0.00620843i	0.270386	+	0.962752i	$0.412849\pi$
$770$		0			0
$771$	−10.2814	+	5.93595i	−0.370275	+	0.213778i
$772$		0			0
$773$	−13.9854	+	8.07445i	−0.503018	+	0.290418i	−0.729959	−	0.683491i	$-0.760461\pi$
$773$	−13.9854	+	8.07445i	−0.503018	+	0.290418i	0.226941	+	0.973909i	$0.427128\pi$
$774$		0			0
$775$	9.72853	+	42.9651i	0.349459	+	1.54335i
$776$		0			0
$777$	−7.28059	−	27.1715i	−0.261190	−	0.974773i
$778$		0			0
$779$	−13.6498			−0.489054
$780$		0			0
$781$	−29.4658			−1.05437
$782$		0			0
$783$	−8.90028	−	33.2163i	−0.318070	−	1.18705i
$784$		0			0
$785$	44.8873	+	12.9738i	1.60210	+	0.463054i
$786$		0			0
$787$	−27.8188	+	16.0612i	−0.991633	+	0.572520i	−0.905762	−	0.423787i	$-0.860701\pi$
$787$	−27.8188	+	16.0612i	−0.991633	+	0.572520i	−0.0858710	+	0.996306i	$0.527367\pi$
$788$		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
$793$	13.6752	+	32.4093i	0.485621	+	1.15089i
$794$		0			0
$795$	23.1388	+	0.452717i	0.820649	+	0.0160562i
$796$		0			0
$797$	1.58199	+	0.423892i	0.0560369	+	0.0150150i	0.286729	−	0.958012i	$-0.407432\pi$
$797$	1.58199	+	0.423892i	0.0560369	+	0.0150150i	−0.230692	+	0.973027i	$0.574099\pi$
$798$		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
$803$	23.5976	−	6.32295i	0.832740	−	0.223132i
$804$		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	0.328029	−	0.944668i	$-0.393616\pi$
$809$	−9.27418	−	5.35445i	−0.326063	−	0.188253i	−0.654092	+	0.756415i	$0.726949\pi$
$810$		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
$813$	5.73482	+	9.93301i	0.201129	+	0.348366i
$814$		0			0
$815$	−17.1112	−	10.3306i	−0.599379	−	0.361866i
$816$		0			0
$817$	15.1598	+	8.75249i	0.530373	+	0.306211i
$818$		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
$823$	1.95458	−	7.29458i	0.0681323	−	0.254273i	−0.923456	−	0.383704i	$-0.874648\pi$
$823$	1.95458	−	7.29458i	0.0681323	−	0.254273i	0.991588	+	0.129431i	$0.0413150\pi$
$824$		0			0
$825$	−20.1590	−	0.789136i	−0.701848	−	0.0274742i
$826$		0			0
$827$		−	38.2354i		−	1.32957i	−0.747033	−	0.664787i	$-0.768522\pi$
$827$		−	38.2354i		−	1.32957i	0.747033	−	0.664787i	$-0.231478\pi$
$828$		0			0
$829$	−24.4408	+	42.3328i	−0.848865	+	1.47028i	0.0333566	+	0.999444i	$0.489380\pi$
$829$	−24.4408	+	42.3328i	−0.848865	+	1.47028i	−0.882222	+	0.470834i	$0.843953\pi$
$830$		0			0
$831$		−	22.6488i		−	0.785679i
$832$		0			0
$833$	−4.82604	+	4.82604i	−0.167213	+	0.167213i
$834$		0			0
$835$	40.7177	+	0.796652i	1.40909	+	0.0275693i
$836$		0			0
$837$	−49.5751			−1.71357
$838$		0			0
$839$	24.6702	+	6.61035i	0.851709	+	0.228215i	0.658162	−	0.752876i	$-0.271334\pi$
$839$	24.6702	+	6.61035i	0.851709	+	0.228215i	0.193547	+	0.981091i	$0.438001\pi$
$840$		0			0
$841$	4.17511	+	7.23150i	0.143969	+	0.249362i
$842$		0			0
$843$	−13.7931	+	23.8904i	−0.475060	+	0.822828i
$844$		0			0
$845$	28.1259	−	7.34410i	0.967559	−	0.252645i
$846$		0			0
$847$	−4.54725	+	7.87607i	−0.156245	+	0.270625i
$848$		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
$853$	7.17091			0.245527			0.122764	−	0.992436i	$-0.460824\pi$
$853$	7.17091			0.245527			0.122764	+	0.992436i	$0.460824\pi$
$854$		0			0
$855$	4.53694	+	4.71802i	0.155160	+	0.161353i
$856$		0			0
$857$	10.7248	−	10.7248i	0.366350	−	0.366350i	−0.499794	−	0.866144i	$-0.666591\pi$
$857$	10.7248	−	10.7248i	0.366350	−	0.366350i	0.866144	+	0.499794i	$0.166591\pi$
$858$		0			0
$859$		−	27.2503i		−	0.929770i	−0.885371	−	0.464885i	$-0.846096\pi$
$859$		−	27.2503i		−	0.929770i	0.885371	−	0.464885i	$-0.153904\pi$
$860$		0			0
$861$	−6.42829	+	11.1341i	−0.219076	+	0.379450i
$862$		0			0
$863$			8.34796i			0.284168i	0.989855	+	0.142084i	$0.0453803\pi$
$863$			8.34796i			0.284168i	−0.989855	+	0.142084i	$0.954620\pi$
$864$		0			0
$865$	0.973787	+	3.94104i	0.0331097	+	0.133999i
$866$		0			0
$867$	−8.62342	+	32.1830i	−0.292867	+	1.09299i
$868$		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
$873$	1.81196	+	1.04613i	0.0613254	+	0.0354062i
$874$		0			0
$875$	−12.1865	−	24.2963i	−0.411980	−	0.821365i
$876$		0			0
$877$	−15.3047	−	26.5085i	−0.516803	−	0.895130i	−0.999810	−	0.0195127i	$-0.993789\pi$
$877$	−15.3047	−	26.5085i	−0.516803	−	0.895130i	0.483006	−	0.875617i	$-0.339545\pi$
$878$		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	−0.998707	−	0.0508451i	$-0.983809\pi$
$883$	−31.1878	−	31.1878i	−1.04955	−	1.04955i	−0.0508451	−	0.998707i	$-0.516191\pi$
$884$		0			0
$885$	−15.1408	−	27.4512i	−0.508954	−	0.922762i
$886$		0			0
$887$	−42.3613	+	11.3507i	−1.42235	+	0.381118i	−0.886318	−	0.463077i	$-0.846745\pi$
$887$	−42.3613	+	11.3507i	−1.42235	+	0.381118i	−0.536035	+	0.844196i	$0.680079\pi$
$888$		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
$893$	25.4374	+	6.81594i	0.851231	+	0.228087i
$894$		0			0
$895$	−0.796073	+	40.6881i	−0.0266098	+	1.36005i
$896$		0			0
$897$	2.49449	+	5.91177i	0.0832887	+	0.197388i
$898$		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
$903$	14.2788	−	8.24388i	0.475169	−	0.274339i
$904$		0			0
$905$	18.8288	+	34.1377i	0.625891	+	1.13478i
$906$		0			0
$907$	0.524912	+	1.95900i	0.0174294	+	0.0650475i	0.974093	−	0.226149i	$-0.0726135\pi$
$907$	0.524912	+	1.95900i	0.0174294	+	0.0650475i	−0.956663	+	0.291196i	$0.905947\pi$
$908$		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
$913$	−0.761596	−	2.84232i	−0.0252052	−	0.0940669i
$914$		0			0
$915$	9.07135	−	31.3855i	0.299890	−	1.03757i
$916$		0			0
$917$	25.5749	−	14.7657i	0.844557	−	0.487605i
$918$		0			0
$919$	−32.9872	+	19.0452i	−1.08815	+	0.628242i	−0.933083	−	0.359662i	$-0.882892\pi$
$919$	−32.9872	+	19.0452i	−1.08815	+	0.628242i	−0.155065	+	0.987904i	$0.549559\pi$
$920$		0			0
$921$	13.7863	−	3.69402i	0.454274	−	0.121722i
$922$		0			0
$923$	−36.5287	−	14.8495i	−1.20236	−	0.488778i
$924$		0			0
$925$	−34.1855	+	17.9922i	−1.12401	+	0.591578i
$926$		0			0
$927$	−3.54340	−	0.949451i	−0.116380	−	0.0311841i
$928$		0			0
$929$	2.43693	−	9.09474i	0.0799530	−	0.298389i	−0.914358	−	0.404907i	$-0.867304\pi$
$929$	2.43693	−	9.09474i	0.0799530	−	0.298389i	0.994311	+	0.106519i	$0.0339704\pi$
$930$		0			0
$931$	−2.97772	−	2.97772i	−0.0975908	−	0.0975908i
$932$		0			0
$933$	28.2527	−	7.57028i	0.924951	−	0.247840i
$934$		0			0
$935$	−33.0495	+	18.2286i	−1.08084	+	0.596140i
$936$		0			0
$937$	−39.2985	−	39.2985i	−1.28382	−	1.28382i	−0.938474	−	0.345351i	$-0.887760\pi$
$937$	−39.2985	−	39.2985i	−1.28382	−	1.28382i	−0.345351	−	0.938474i	$-0.612240\pi$
$938$		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
$943$	−2.09813	−	3.63406i	−0.0683244	−	0.118341i
$944$		0			0
$945$	29.6956	−	7.33745i	0.965999	−	0.238687i
$946$		0			0
$947$	−14.1987	−	8.19763i	−0.461396	−	0.266387i	0.251235	−	0.967926i	$-0.419163\pi$
$947$	−14.1987	−	8.19763i	−0.461396	−	0.266387i	−0.712631	+	0.701539i	$0.752497\pi$
$948$		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
$953$	7.57657	−	28.2762i	0.245429	−	0.915955i	−0.727738	−	0.685855i	$-0.759428\pi$
$953$	7.57657	−	28.2762i	0.245429	−	0.915955i	0.973167	−	0.230099i	$-0.0739051\pi$
$954$		0			0
$955$	−40.3537	−	24.3630i	−1.30582	−	0.788367i
$956$		0			0
$957$			24.6592i			0.797119i
$958$		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
$965$	−0.847511	+	43.3172i	−0.0272824	+	1.39443i
$966$		0			0
$967$	−50.2534			−1.61604			−0.808021	−	0.589154i	$-0.799461\pi$
$967$	−50.2534			−1.61604			−0.808021	+	0.589154i	$0.799461\pi$
$968$		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
$973$	−18.6595	+	32.3193i	−0.598198	+	1.03611i
$974$		0			0
$975$	−24.5935	−	11.1376i	−0.787621	−	0.356689i
$976$		0			0
$977$	−16.4272	+	28.4527i	−0.525552	+	0.910283i	0.474005	+	0.880522i	$0.342808\pi$
$977$	−16.4272	+	28.4527i	−0.525552	+	0.910283i	−0.999557	+	0.0297606i	$0.990526\pi$
$978$		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
$983$	23.3463			0.744631			0.372315	−	0.928106i	$-0.378564\pi$
$983$	23.3463			0.744631			0.372315	+	0.928106i	$0.378564\pi$
$984$		0			0
$985$	−0.541158	+	27.6591i	−0.0172427	+	0.881292i
$986$		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
$993$			23.6299i			0.749873i
$994$		0			0
$995$	−19.4788	−	11.7600i	−0.617518	−	0.372817i
$996$		0			0
$997$	−10.6809	+	39.8616i	−0.338267	+	1.26243i	0.562018	+	0.827125i	$0.310025\pi$
$997$	−10.6809	+	39.8616i	−0.338267	+	1.26243i	−0.900284	+	0.435303i	$0.856641\pi$
$998$		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.bk.c.97.4	yes	20
5.2	odd	4		1300.2.bn.d.1293.4		20
5.3	odd	4		260.2.bf.c.253.2	yes	20
5.4	even	2		1300.2.bs.d.357.2		20
13.11	odd	12		260.2.bf.c.37.2	✓	20
65.24	odd	12		1300.2.bn.d.557.4		20
65.37	even	12		1300.2.bs.d.193.2		20
65.63	even	12	inner	260.2.bk.c.193.4	yes	20

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

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.bk (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.387600 + 1.44654i) q^{3} +(1.95799 - 1.07994i) q^{5} +(2.10545 - 1.21558i) q^{7} +(0.655821 - 0.378639i) q^{9} +O(q^{10})\)	\(q+(0.387600 + 1.44654i) q^{3} +(1.95799 - 1.07994i) q^{5} +(2.10545 - 1.21558i) q^{7} +(0.655821 - 0.378639i) q^{9} +(-2.60249 + 0.697334i) q^{11} +(-3.57773 - 0.447059i) q^{13} +(2.32110 + 2.41374i) q^{15} +(6.05137 + 1.62146i) q^{17} +(-1.00046 + 3.73376i) q^{19} +(2.57447 + 2.57447i) q^{21} +(-1.14784 + 0.307564i) q^{23} +(2.66746 - 4.22902i) q^{25} +(3.97874 + 3.97874i) q^{27} +(-5.29270 - 3.05574i) q^{29} +(-6.23000 + 6.23000i) q^{31} +(-2.01745 - 3.49432i) q^{33} +(2.80970 - 4.65387i) q^{35} +(-6.69111 - 3.86311i) q^{37} +(-0.740038 - 5.34862i) q^{39} +(0.913943 + 3.41088i) q^{41} +(1.17207 - 4.37424i) q^{43} +(0.875186 - 1.44962i) q^{45} -6.81282i q^{47} +(-0.544711 + 0.943467i) q^{49} +9.38205i q^{51} +(4.88693 - 4.88693i) q^{53} +(-4.34257 + 4.17590i) q^{55} -5.78882 q^{57} +(-9.04287 - 2.42303i) q^{59} +(-4.87808 - 8.44908i) q^{61} +(0.920534 - 1.59441i) q^{63} +(-7.48796 + 2.98839i) q^{65} +(0.507281 - 0.878637i) q^{67} +(-0.889809 - 1.54120i) q^{69} +(10.5637 + 2.83054i) q^{71} -9.06732 q^{73} +(7.15138 + 2.21943i) q^{75} +(-4.63174 + 4.63174i) q^{77} +11.6191i q^{79} +(-3.07735 + 5.33013i) q^{81} +1.09215i q^{83} +(13.5996 - 3.36031i) q^{85} +(2.36881 - 8.84053i) q^{87} +(-1.29560 - 4.83523i) q^{89} +(-8.07618 + 3.40777i) q^{91} +(-11.4267 - 6.59721i) q^{93} +(2.07335 + 8.39110i) q^{95} +(1.38144 + 2.39272i) q^{97} +(-1.44273 + 1.44273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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