LMFDB - Embedded newform 1440.2.cc.a.1391.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(911,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1440.911");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1391.10
Character	$\chi$	$=$	1440.1391
Dual form			1440.2.cc.a.911.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.424591 + 1.67920i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(3.88456 - 2.24275i) q^{7} +(-2.63944 - 1.42595i) q^{9} +O(q^{10})$	\(q+(-0.424591 + 1.67920i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(3.88456 - 2.24275i) q^{7} +(-2.63944 - 1.42595i) q^{9} +(-1.05081 + 0.606687i) q^{11} +(-1.71090 - 0.987790i) q^{13} +(-1.24194 - 1.20731i) q^{15} +5.28743i q^{17} +4.86627 q^{19} +(2.11668 + 7.47521i) q^{21} +(1.40767 - 2.43816i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.51514 - 3.82672i) q^{27} +(4.20865 + 7.28960i) q^{29} +(6.04943 + 3.49264i) q^{31} +(-0.572584 - 2.02212i) q^{33} +4.48550i q^{35} +4.71412i q^{37} +(2.38513 - 2.45355i) q^{39} +(-5.30898 - 3.06514i) q^{41} +(-1.17866 - 2.04150i) q^{43} +(2.55463 - 1.57285i) q^{45} +(5.97373 + 10.3468i) q^{47} +(6.55985 - 11.3620i) q^{49} +(-8.87867 - 2.24500i) q^{51} -0.739256 q^{53} -1.21337i q^{55} +(-2.06618 + 8.17146i) q^{57} +(-1.70932 - 0.986877i) q^{59} +(4.81044 - 2.77731i) q^{61} +(-13.4511 + 0.380430i) q^{63} +(1.71090 - 0.987790i) q^{65} +(-1.58725 + 2.74920i) q^{67} +(3.49648 + 3.39899i) q^{69} +3.40951 q^{71} -6.69774 q^{73} +(1.66653 - 0.471895i) q^{75} +(-2.72129 + 4.71342i) q^{77} +(-11.2535 + 6.49720i) q^{79} +(4.93333 + 7.52743i) q^{81} +(5.00954 - 2.89226i) q^{83} +(-4.57905 - 2.64371i) q^{85} +(-14.0277 + 3.97208i) q^{87} +2.71936i q^{89} -8.86146 q^{91} +(-8.43338 + 8.67527i) q^{93} +(-2.43314 + 4.21431i) q^{95} +(8.61075 + 14.9143i) q^{97} +(3.63867 - 0.102910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5}+O(q^{10}) $ 48 * q - 24 * q^5	$ 48 q - 24 q^{5} - 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} - 16 q^{39} + 12 q^{41} - 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} + 12 q^{61} - 56 q^{63} - 40 q^{69} - 8 q^{81} + 60 q^{83} - 36 q^{87} + 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 - 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 - 16 * q^39 + 12 * q^41 - 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 + 12 * q^61 - 56 * q^63 - 40 * q^69 - 8 * q^81 + 60 * q^83 - 36 * q^87 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	−0.424591	+	1.67920i	−0.245138	+	0.969488i
$3$	−0.424591	+	1.67920i	−0.245138	+	0.969488i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	3.88456	−	2.24275i	1.46822	−	0.847680i	0.468858	−	0.883273i	$-0.344666\pi$
$7$	3.88456	−	2.24275i	1.46822	−	0.847680i	0.999366	+	0.0355937i	$0.0113322\pi$
$8$		0			0
$9$	−2.63944	−	1.42595i	−0.879815	−	0.475317i
$10$		0			0
$11$	−1.05081	+	0.606687i	−0.316832	+	0.182923i	−0.649980	−	0.759952i	$-0.725223\pi$
$11$	−1.05081	+	0.606687i	−0.316832	+	0.182923i	0.333148	+	0.942875i	$0.391889\pi$
$12$		0			0
$13$	−1.71090	−	0.987790i	−0.474519	−	0.273964i	0.243611	−	0.969873i	$-0.421668\pi$
$13$	−1.71090	−	0.987790i	−0.474519	−	0.273964i	−0.718130	+	0.695909i	$0.755001\pi$
$14$		0			0
$15$	−1.24194	−	1.20731i	−0.320667	−	0.311726i
$16$		0			0
$17$			5.28743i			1.28239i	0.767378	+	0.641195i	$0.221561\pi$
$17$			5.28743i			1.28239i	−0.767378	+	0.641195i	$0.778439\pi$
$18$		0			0
$19$	4.86627			1.11640			0.558200	−	0.829707i	$-0.311492\pi$
$19$	4.86627			1.11640			0.558200	+	0.829707i	$0.311492\pi$
$20$		0			0
$21$	2.11668	+	7.47521i	0.461898	+	1.63122i
$22$		0			0
$23$	1.40767	−	2.43816i	0.293520	−	0.508392i	−0.681119	−	0.732172i	$-0.738507\pi$
$23$	1.40767	−	2.43816i	0.293520	−	0.508392i	0.974640	+	0.223781i	$0.0718399\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	3.51514	−	3.82672i	0.676490	−	0.736452i
$28$		0			0
$29$	4.20865	+	7.28960i	0.781527	+	1.35364i	0.931052	+	0.364886i	$0.118892\pi$
$29$	4.20865	+	7.28960i	0.781527	+	1.35364i	−0.149525	+	0.988758i	$0.547775\pi$
$30$		0			0
$31$	6.04943	+	3.49264i	1.08651	+	0.627296i	0.932645	−	0.360796i	$-0.117495\pi$
$31$	6.04943	+	3.49264i	1.08651	+	0.627296i	0.153864	+	0.988092i	$0.450828\pi$
$32$		0			0
$33$	−0.572584	−	2.02212i	−0.0996742	−	0.352006i
$34$		0			0
$35$			4.48550i			0.758188i
$36$		0			0
$37$			4.71412i			0.774997i	0.921870	+	0.387499i	$0.126661\pi$
$37$			4.71412i			0.774997i	−0.921870	+	0.387499i	$0.873339\pi$
$38$		0			0
$39$	2.38513	−	2.45355i	0.381927	−	0.392882i
$40$		0			0
$41$	−5.30898	−	3.06514i	−0.829123	−	0.478695i	0.0244291	−	0.999702i	$-0.492223\pi$
$41$	−5.30898	−	3.06514i	−0.829123	−	0.478695i	−0.853552	+	0.521007i	$0.825557\pi$
$42$		0			0
$43$	−1.17866	−	2.04150i	−0.179744	−	0.311326i	0.762049	−	0.647520i	$-0.224194\pi$
$43$	−1.17866	−	2.04150i	−0.179744	−	0.311326i	−0.941793	+	0.336194i	$0.890860\pi$
$44$		0			0
$45$	2.55463	−	1.57285i	0.380822	−	0.234467i
$46$		0			0
$47$	5.97373	+	10.3468i	0.871358	+	1.50924i	0.860593	+	0.509294i	$0.170093\pi$
$47$	5.97373	+	10.3468i	0.871358	+	1.50924i	0.0107652	+	0.999942i	$0.496573\pi$
$48$		0			0
$49$	6.55985	−	11.3620i	0.937122	−	1.62314i
$50$		0			0
$51$	−8.87867	−	2.24500i	−1.24326	−	0.314362i
$52$		0			0
$53$	−0.739256			−0.101545			−0.0507723	−	0.998710i	$-0.516168\pi$
$53$	−0.739256			−0.101545			−0.0507723	+	0.998710i	$0.516168\pi$
$54$		0			0
$55$		−	1.21337i		−	0.163611i
$56$		0			0
$57$	−2.06618	+	8.17146i	−0.273672	+	1.08234i
$58$		0			0
$59$	−1.70932	−	0.986877i	−0.222535	−	0.128480i	0.384589	−	0.923088i	$-0.374343\pi$
$59$	−1.70932	−	0.986877i	−0.222535	−	0.128480i	−0.607123	+	0.794608i	$0.707677\pi$
$60$		0			0
$61$	4.81044	−	2.77731i	0.615914	−	0.355598i	−0.159362	−	0.987220i	$-0.550944\pi$
$61$	4.81044	−	2.77731i	0.615914	−	0.355598i	0.775277	+	0.631622i	$0.217611\pi$
$62$		0			0
$63$	−13.4511	+	0.380430i	−1.69468	+	0.0479296i
$64$		0			0
$65$	1.71090	−	0.987790i	0.212211	−	0.122520i
$66$		0			0
$67$	−1.58725	+	2.74920i	−0.193913	+	0.335868i	−0.946544	−	0.322576i	$-0.895451\pi$
$67$	−1.58725	+	2.74920i	−0.193913	+	0.335868i	0.752630	+	0.658443i	$0.228785\pi$
$68$		0			0
$69$	3.49648	+	3.39899i	0.420927	+	0.409190i
$70$		0			0
$71$	3.40951			0.404635			0.202317	−	0.979320i	$-0.435153\pi$
$71$	3.40951			0.404635			0.202317	+	0.979320i	$0.435153\pi$
$72$		0			0
$73$	−6.69774			−0.783911			−0.391956	−	0.919984i	$-0.628201\pi$
$73$	−6.69774			−0.783911			−0.391956	+	0.919984i	$0.628201\pi$
$74$		0			0
$75$	1.66653	−	0.471895i	0.192434	−	0.0544897i
$76$		0			0
$77$	−2.72129	+	4.71342i	−0.310120	+	0.537144i
$78$		0			0
$79$	−11.2535	+	6.49720i	−1.26612	+	0.730992i	−0.974251	−	0.225467i	$-0.927609\pi$
$79$	−11.2535	+	6.49720i	−1.26612	+	0.730992i	−0.291865	+	0.956459i	$0.594276\pi$
$80$		0			0
$81$	4.93333	+	7.52743i	0.548148	+	0.836381i
$82$		0			0
$83$	5.00954	−	2.89226i	0.549868	−	0.317467i	−0.199201	−	0.979959i	$-0.563835\pi$
$83$	5.00954	−	2.89226i	0.549868	−	0.317467i	0.749069	+	0.662492i	$0.230501\pi$
$84$		0			0
$85$	−4.57905	−	2.64371i	−0.496667	−	0.286751i
$86$		0			0
$87$	−14.0277	+	3.97208i	−1.50392	+	0.425851i
$88$		0			0
$89$			2.71936i			0.288252i	0.989559	+	0.144126i	$0.0460370\pi$
$89$			2.71936i			0.288252i	−0.989559	+	0.144126i	$0.953963\pi$
$90$		0			0
$91$	−8.86146			−0.928934
$92$		0			0
$93$	−8.43338	+	8.67527i	−0.874501	+	0.899584i
$94$		0			0
$95$	−2.43314	+	4.21431i	−0.249634	+	0.432380i
$96$		0			0
$97$	8.61075	+	14.9143i	0.874289	+	1.51431i	0.857518	+	0.514454i	$0.172005\pi$
$97$	8.61075	+	14.9143i	0.874289	+	1.51431i	0.0167712	+	0.999859i	$0.494661\pi$
$98$		0			0
$99$	3.63867	−	0.102910i	0.365700	−	0.0103429i
$100$		0			0
$101$	2.65852	+	4.60469i	0.264532	+	0.458183i	0.967441	−	0.253097i	$-0.0814491\pi$
$101$	2.65852	+	4.60469i	0.264532	+	0.458183i	−0.702909	+	0.711280i	$0.748116\pi$
$102$		0			0
$103$	13.2519	+	7.65097i	1.30575	+	0.753873i	0.981383	−	0.192060i	$-0.0615169\pi$
$103$	13.2519	+	7.65097i	1.30575	+	0.753873i	0.324363	+	0.945933i	$0.394850\pi$
$104$		0			0
$105$	−7.53206	−	1.90450i	−0.735054	−	0.185861i
$106$		0			0
$107$			7.25445i			0.701314i	0.936504	+	0.350657i	$0.114042\pi$
$107$			7.25445i			0.701314i	−0.936504	+	0.350657i	$0.885958\pi$
$108$		0			0
$109$		−	18.6200i		−	1.78347i	−0.452558	−	0.891735i	$-0.649488\pi$
$109$		−	18.6200i		−	1.78347i	0.452558	−	0.891735i	$-0.350512\pi$
$110$		0			0
$111$	−7.91597	−	2.00158i	−0.751351	−	0.189981i
$112$		0			0
$113$	−5.19909	−	3.00170i	−0.489090	−	0.282376i	0.235107	−	0.971969i	$-0.424456\pi$
$113$	−5.19909	−	3.00170i	−0.489090	−	0.282376i	−0.724197	+	0.689593i	$0.757789\pi$
$114$		0			0
$115$	1.40767	+	2.43816i	0.131266	+	0.227360i
$116$		0			0
$117$	3.10729	+	5.04688i	0.287269	+	0.466584i
$118$		0			0
$119$	11.8584	+	20.5393i	1.08706	+	1.88284i
$120$		0			0
$121$	−4.76386	+	8.25125i	−0.433078	+	0.750114i
$122$		0			0
$123$	7.40114	−	7.61342i	0.667338	−	0.686479i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$		−	0.151104i		−	0.0134083i	−0.999978	−	0.00670414i	$-0.997866\pi$
$127$		−	0.151104i		−	0.0134083i	0.999978	−	0.00670414i	$-0.00213401\pi$
$128$		0			0
$129$	3.92854	−	1.11241i	0.345889	−	0.0979420i
$130$		0			0
$131$	−14.8788	−	8.59027i	−1.29997	−	0.750536i	−0.319568	−	0.947563i	$-0.603538\pi$
$131$	−14.8788	−	8.59027i	−1.29997	−	0.750536i	−0.980398	+	0.197028i	$0.936871\pi$
$132$		0			0
$133$	18.9033	−	10.9138i	1.63912	−	0.946349i
$134$		0			0
$135$	1.55646	+	4.95756i	0.133959	+	0.426679i
$136$		0			0
$137$	14.1817	−	8.18778i	1.21162	−	0.699529i	0.248508	−	0.968630i	$-0.420060\pi$
$137$	14.1817	−	8.18778i	1.21162	−	0.699529i	0.963112	+	0.269100i	$0.0867264\pi$
$138$		0			0
$139$	−6.13746	+	10.6304i	−0.520573	+	0.901658i	0.479141	+	0.877738i	$0.340948\pi$
$139$	−6.13746	+	10.6304i	−0.520573	+	0.901658i	−0.999714	+	0.0239203i	$0.992385\pi$
$140$		0			0
$141$	−19.9108	+	5.63794i	−1.67679	+	0.474800i
$142$		0			0
$143$	2.39712			0.200457
$144$		0			0
$145$	−8.41730			−0.699019
$146$		0			0
$147$	16.2938	+	15.8395i	1.34389	+	1.30642i
$148$		0			0
$149$	−10.4468	+	18.0944i	−0.855836	+	1.48235i	0.0200319	+	0.999799i	$0.493623\pi$
$149$	−10.4468	+	18.0944i	−0.855836	+	1.48235i	−0.875868	+	0.482552i	$0.839710\pi$
$150$		0			0
$151$	2.72496	−	1.57326i	0.221754	−	0.128030i	−0.385008	−	0.922913i	$-0.625801\pi$
$151$	2.72496	−	1.57326i	0.221754	−	0.128030i	0.606762	+	0.794883i	$0.292468\pi$
$152$		0			0
$153$	7.53961	−	13.9559i	0.609541	−	1.12827i
$154$		0			0
$155$	−6.04943	+	3.49264i	−0.485902	+	0.280535i
$156$		0			0
$157$	−9.64516	−	5.56863i	−0.769767	−	0.444425i	0.0630243	−	0.998012i	$-0.479925\pi$
$157$	−9.64516	−	5.56863i	−0.769767	−	0.444425i	−0.832792	+	0.553587i	$0.813259\pi$
$158$		0			0
$159$	0.313882	−	1.24136i	0.0248924	−	0.0984463i
$160$		0			0
$161$		−	12.6282i		−	0.995244i
$162$		0			0
$163$	0.567815			0.0444747			0.0222373	−	0.999753i	$-0.492921\pi$
$163$	0.567815			0.0444747			0.0222373	+	0.999753i	$0.492921\pi$
$164$		0			0
$165$	2.03750	+	0.515188i	0.158619	+	0.0401073i
$166$		0			0
$167$	9.59132	−	16.6127i	0.742199	−	1.28553i	−0.209293	−	0.977853i	$-0.567116\pi$
$167$	9.59132	−	16.6127i	0.742199	−	1.28553i	0.951492	−	0.307673i	$-0.0995503\pi$
$168$		0			0
$169$	−4.54854	−	7.87831i	−0.349888	−	0.606023i
$170$		0			0
$171$	−12.8443	−	6.93906i	−0.982224	−	0.530643i
$172$		0			0
$173$	0.727868	+	1.26070i	0.0553388	+	0.0958496i	0.892368	−	0.451309i	$-0.149043\pi$
$173$	0.727868	+	1.26070i	0.0553388	+	0.0958496i	−0.837029	+	0.547159i	$0.815709\pi$
$174$		0			0
$175$	−3.88456	−	2.24275i	−0.293645	−	0.169536i
$176$		0			0
$177$	2.38293	−	2.45128i	0.179112	−	0.184249i
$178$		0			0
$179$		−	21.1074i		−	1.57764i	−0.614623	−	0.788821i	$-0.710692\pi$
$179$		−	21.1074i		−	1.57764i	0.614623	−	0.788821i	$-0.289308\pi$
$180$		0			0
$181$		−	8.53010i		−	0.634037i	−0.948419	−	0.317019i	$-0.897318\pi$
$181$		−	8.53010i		−	0.634037i	0.948419	−	0.317019i	$-0.102682\pi$
$182$		0			0
$183$	2.62120	+	9.25693i	0.193764	+	0.684292i
$184$		0			0
$185$	−4.08255	−	2.35706i	−0.300155	−	0.173295i
$186$		0			0
$187$	−3.20781	−	5.55610i	−0.234579	−	0.406302i
$188$		0			0
$189$	5.07241	−	22.7487i	0.368964	−	1.65472i
$190$		0			0
$191$	0.214023	+	0.370698i	0.0154861	+	0.0268228i	0.873665	−	0.486529i	$-0.161737\pi$
$191$	0.214023	+	0.370698i	0.0154861	+	0.0268228i	−0.858178	+	0.513351i	$0.828404\pi$
$192$		0			0
$193$	−4.74084	+	8.21138i	−0.341253	+	0.591068i	−0.984666	−	0.174452i	$-0.944185\pi$
$193$	−4.74084	+	8.21138i	−0.341253	+	0.591068i	0.643412	+	0.765520i	$0.277518\pi$
$194$		0			0
$195$	0.932265	+	3.29236i	0.0667609	+	0.235771i
$196$		0			0
$197$	4.16402			0.296674			0.148337	−	0.988937i	$-0.452608\pi$
$197$	4.16402			0.296674			0.148337	+	0.988937i	$0.452608\pi$
$198$		0			0
$199$		−	20.4857i		−	1.45219i	−0.687594	−	0.726095i	$-0.741333\pi$
$199$		−	20.4857i		−	1.45219i	0.687594	−	0.726095i	$-0.258667\pi$
$200$		0			0
$201$	−3.94252	−	3.83260i	−0.278084	−	0.270331i
$202$		0			0
$203$	32.6975	+	18.8779i	2.29491	+	1.32497i
$204$		0			0
$205$	5.30898	−	3.06514i	0.370795	−	0.214079i
$206$		0			0
$207$	−7.19217	+	4.42812i	−0.499890	+	0.307776i
$208$		0			0
$209$	−5.11354	+	2.95230i	−0.353711	+	0.204215i
$210$		0			0
$211$	12.8150	−	22.1963i	0.882222	−	1.52805i	0.0333576	−	0.999443i	$-0.489380\pi$
$211$	12.8150	−	22.1963i	0.882222	−	1.52805i	0.848865	−	0.528610i	$-0.177287\pi$
$212$		0			0
$213$	−1.44765	+	5.72527i	−0.0991914	+	0.392289i
$214$		0			0
$215$	2.35732			0.160768
$216$		0			0
$217$	31.3325			2.12699
$218$		0			0
$219$	2.84380	−	11.2469i	0.192166	−	0.759993i
$220$		0			0
$221$	5.22287	−	9.04628i	0.351328	−	0.608518i
$222$		0			0
$223$	0.577728	−	0.333551i	0.0386875	−	0.0223363i	−0.480531	−	0.876977i	$-0.659556\pi$
$223$	0.577728	−	0.333551i	0.0386875	−	0.0223363i	0.519219	+	0.854641i	$0.326223\pi$
$224$		0			0
$225$	0.0848132	+	2.99880i	0.00565421	+	0.199920i
$226$		0			0
$227$	−3.21685	+	1.85725i	−0.213510	+	0.123270i	−0.602941	−	0.797785i	$-0.706005\pi$
$227$	−3.21685	+	1.85725i	−0.213510	+	0.123270i	0.389432	+	0.921055i	$0.372671\pi$
$228$		0			0
$229$	5.27024	+	3.04277i	0.348267	+	0.201072i	0.663922	−	0.747802i	$-0.268891\pi$
$229$	5.27024	+	3.04277i	0.348267	+	0.201072i	−0.315655	+	0.948874i	$0.602224\pi$
$230$		0			0
$231$	−6.75935	−	6.57088i	−0.444733	−	0.432332i
$232$		0			0
$233$			11.4524i			0.750269i	0.926970	+	0.375134i	$0.122403\pi$
$233$			11.4524i			0.750269i	−0.926970	+	0.375134i	$0.877597\pi$
$234$		0			0
$235$	−11.9475			−0.779366
$236$		0			0
$237$	−6.13199	−	21.6555i	−0.398315	−	1.40668i
$238$		0			0
$239$	5.82006	−	10.0806i	0.376468	−	0.652062i	−0.614077	−	0.789246i	$-0.710472\pi$
$239$	5.82006	−	10.0806i	0.376468	−	0.652062i	0.990546	+	0.137184i	$0.0438050\pi$
$240$		0			0
$241$	3.24695	+	5.62388i	0.209154	+	0.362266i	0.951448	−	0.307808i	$-0.0995955\pi$
$241$	3.24695	+	5.62388i	0.209154	+	0.362266i	−0.742294	+	0.670074i	$0.766262\pi$
$242$		0			0
$243$	−14.7347	+	5.08798i	−0.945234	+	0.326394i
$244$		0			0
$245$	6.55985	+	11.3620i	0.419094	+	0.725892i
$246$		0			0
$247$	−8.32572	−	4.80685i	−0.529753	−	0.305853i
$248$		0			0
$249$	2.72968	+	9.64006i	0.172987	+	0.610914i
$250$		0			0
$251$		−	3.49601i		−	0.220666i	−0.993895	−	0.110333i	$-0.964808\pi$
$251$		−	3.49601i		−	0.220666i	0.993895	−	0.110333i	$-0.0351917\pi$
$252$		0			0
$253$			3.41607i			0.214766i
$254$		0			0
$255$	6.38356	−	6.56665i	0.399754	−	0.411220i
$256$		0			0
$257$	−2.88796	−	1.66737i	−0.180146	−	0.104007i	0.407215	−	0.913332i	$-0.366500\pi$
$257$	−2.88796	−	1.66737i	−0.180146	−	0.104007i	−0.587361	+	0.809325i	$0.699833\pi$
$258$		0			0
$259$	10.5726	+	18.3123i	0.656949	+	1.13787i
$260$		0			0
$261$	−0.713898	−	25.2418i	−0.0441892	−	1.56243i
$262$		0			0
$263$	6.66510	+	11.5443i	0.410988	+	0.711852i	0.994998	−	0.0998946i	$-0.0318505\pi$
$263$	6.66510	+	11.5443i	0.410988	+	0.711852i	−0.584010	+	0.811746i	$0.698517\pi$
$264$		0			0
$265$	0.369628	−	0.640214i	0.0227061	−	0.0393280i
$266$		0			0
$267$	−4.56636	−	1.15462i	−0.279457	−	0.0706615i
$268$		0			0
$269$	1.95866			0.119421			0.0597107	−	0.998216i	$-0.480982\pi$
$269$	1.95866			0.119421			0.0597107	+	0.998216i	$0.480982\pi$
$270$		0			0
$271$		−	22.5736i		−	1.37125i	−0.727955	−	0.685625i	$-0.759529\pi$
$271$		−	22.5736i		−	1.37125i	0.727955	−	0.685625i	$-0.240471\pi$
$272$		0			0
$273$	3.76250	−	14.8802i	0.227717	−	0.900590i
$274$		0			0
$275$	1.05081	+	0.606687i	0.0633664	+	0.0365846i
$276$		0			0
$277$	20.8634	−	12.0455i	1.25356	−	0.723744i	0.281746	−	0.959489i	$-0.409086\pi$
$277$	20.8634	−	12.0455i	1.25356	−	0.723744i	0.971815	+	0.235745i	$0.0757530\pi$
$278$		0			0
$279$	−10.9868	−	17.8448i	−0.657762	−	1.06834i
$280$		0			0
$281$	−26.4445	+	15.2677i	−1.57755	+	0.910796i	−0.582344	+	0.812942i	$0.697864\pi$
$281$	−26.4445	+	15.2677i	−1.57755	+	0.910796i	−0.995201	+	0.0978540i	$0.968802\pi$
$282$		0			0
$283$	−3.84951	+	6.66756i	−0.228830	+	0.396345i	−0.957462	−	0.288561i	$-0.906823\pi$
$283$	−3.84951	+	6.66756i	−0.228830	+	0.396345i	0.728632	+	0.684906i	$0.240157\pi$
$284$		0			0
$285$	−6.04360	−	5.87509i	−0.357992	−	0.348010i
$286$		0			0
$287$	−27.4974			−1.62312
$288$		0			0
$289$	−10.9569			−0.644524
$290$		0			0
$291$	−28.7001	+	8.12673i	−1.68243	+	0.476397i
$292$		0			0
$293$	9.03781	−	15.6539i	0.527994	−	0.914513i	−0.471473	−	0.881880i	$-0.656278\pi$
$293$	9.03781	−	15.6539i	0.527994	−	0.914513i	0.999467	−	0.0326326i	$-0.0103891\pi$
$294$		0			0
$295$	1.70932	−	0.986877i	0.0995206	−	0.0574582i
$296$		0			0
$297$	−1.37214	+	6.15375i	−0.0796196	+	0.357077i
$298$		0			0
$299$	−4.81678	+	2.78097i	−0.278562	+	0.160828i
$300$		0			0
$301$	−9.15715	−	5.28688i	−0.527809	−	0.304731i
$302$		0			0
$303$	−8.86099	+	2.50908i	−0.509050	+	0.144143i
$304$		0			0
$305$			5.55462i			0.318057i
$306$		0			0
$307$	23.7235			1.35397			0.676986	−	0.735996i	$-0.263286\pi$
$307$	23.7235			1.35397			0.676986	+	0.735996i	$0.263286\pi$
$308$		0			0
$309$	−18.4742	+	19.0040i	−1.05096	+	1.08110i
$310$		0			0
$311$	6.24004	−	10.8081i	0.353840	−	0.612869i	−0.633079	−	0.774087i	$-0.718209\pi$
$311$	6.24004	−	10.8081i	0.353840	−	0.612869i	0.986919	+	0.161219i	$0.0515424\pi$
$312$		0			0
$313$	−7.40717	−	12.8296i	−0.418678	−	0.725171i	0.577129	−	0.816653i	$-0.304173\pi$
$313$	−7.40717	−	12.8296i	−0.418678	−	0.725171i	−0.995807	+	0.0914817i	$0.970840\pi$
$314$		0			0
$315$	6.39610	−	11.8392i	0.360379	−	0.667065i
$316$		0			0
$317$	11.5991	+	20.0903i	0.651473	+	1.12838i	0.982766	+	0.184856i	$0.0591820\pi$
$317$	11.5991	+	20.0903i	0.651473	+	1.12838i	−0.331292	+	0.943528i	$0.607485\pi$
$318$		0			0
$319$	−8.84500	−	5.10667i	−0.495225	−	0.285918i
$320$		0			0
$321$	−12.1817	−	3.08018i	−0.679916	−	0.171919i
$322$		0			0
$323$			25.7301i			1.43166i
$324$		0			0
$325$			1.97558i			0.109585i
$326$		0			0
$327$	31.2667	+	7.90588i	1.72905	+	0.437196i
$328$		0			0
$329$	46.4106	+	26.7952i	2.55870	+	1.47726i
$330$		0			0
$331$	−3.40861	−	5.90389i	−0.187354	−	0.324507i	0.757013	−	0.653400i	$-0.226658\pi$
$331$	−3.40861	−	5.90389i	−0.187354	−	0.324507i	−0.944367	+	0.328893i	$0.893325\pi$
$332$		0			0
$333$	6.72210	−	12.4427i	0.368369	−	0.681854i
$334$		0			0
$335$	−1.58725	−	2.74920i	−0.0867207	−	0.150205i
$336$		0			0
$337$	4.18185	−	7.24318i	0.227800	−	0.394561i	−0.729356	−	0.684135i	$-0.760180\pi$
$337$	4.18185	−	7.24318i	0.227800	−	0.394561i	0.957156	+	0.289573i	$0.0935134\pi$
$338$		0			0
$339$	7.24795	−	7.45584i	0.393655	−	0.404945i
$340$		0			0
$341$	−8.47575			−0.458988
$342$		0			0
$343$		−	27.4500i		−	1.48216i
$344$		0			0
$345$	−4.69185	+	1.32855i	−0.252601	+	0.0715265i
$346$		0			0
$347$	12.4465	+	7.18596i	0.668161	+	0.385763i	0.795379	−	0.606112i	$-0.207272\pi$
$347$	12.4465	+	7.18596i	0.668161	+	0.385763i	−0.127219	+	0.991875i	$0.540605\pi$
$348$		0			0
$349$	−5.20288	+	3.00388i	−0.278504	+	0.160794i	−0.632746	−	0.774360i	$-0.718072\pi$
$349$	−5.20288	+	3.00388i	−0.278504	+	0.160794i	0.354242	+	0.935154i	$0.384739\pi$
$350$		0			0
$351$	−9.79406	+	3.07491i	−0.522768	+	0.164127i
$352$		0			0
$353$	−12.6839	+	7.32305i	−0.675096	+	0.389767i	−0.798005	−	0.602651i	$-0.794111\pi$
$353$	−12.6839	+	7.32305i	−0.675096	+	0.389767i	0.122909	+	0.992418i	$0.460778\pi$
$354$		0			0
$355$	−1.70476	+	2.95273i	−0.0904791	+	0.156714i
$356$		0			0
$357$	−39.5246	+	11.1918i	−2.09187	+	0.592333i
$358$		0			0
$359$	−0.983893			−0.0519279			−0.0259639	−	0.999663i	$-0.508266\pi$
$359$	−0.983893			−0.0519279			−0.0259639	+	0.999663i	$0.508266\pi$
$360$		0			0
$361$	4.68059			0.246347
$362$		0			0
$363$	−11.8328	−	11.5029i	−0.621062	−	0.603746i
$364$		0			0
$365$	3.34887	−	5.80041i	0.175288	−	0.303608i
$366$		0			0
$367$	22.8347	−	13.1836i	1.19196	−	0.688180i	0.233211	−	0.972426i	$-0.425077\pi$
$367$	22.8347	−	13.1836i	1.19196	−	0.688180i	0.958751	+	0.284246i	$0.0917433\pi$
$368$		0			0
$369$	9.64202	+	15.6606i	0.501943	+	0.815259i
$370$		0			0
$371$	−2.87168	+	1.65797i	−0.149090	+	0.0860773i
$372$		0			0
$373$	0.428139	+	0.247186i	0.0221682	+	0.0127988i	0.511043	−	0.859555i	$-0.329259\pi$
$373$	0.428139	+	0.247186i	0.0221682	+	0.0127988i	−0.488875	+	0.872354i	$0.662593\pi$
$374$		0			0
$375$	−0.424591	+	1.67920i	−0.0219258	+	0.0867137i
$376$		0			0
$377$		−	16.6291i		−	0.856440i
$378$		0			0
$379$	20.0342			1.02909			0.514544	−	0.857464i	$-0.327961\pi$
$379$	20.0342			1.02909			0.514544	+	0.857464i	$0.327961\pi$
$380$		0			0
$381$	0.253734	+	0.0641573i	0.0129992	+	0.00328688i
$382$		0			0
$383$	−7.16431	+	12.4089i	−0.366079	+	0.634068i	−0.988949	−	0.148258i	$-0.952633\pi$
$383$	−7.16431	+	12.4089i	−0.366079	+	0.634068i	0.622870	+	0.782326i	$0.285967\pi$
$384$		0			0
$385$	−2.72129	−	4.71342i	−0.138690	−	0.240218i
$386$		0			0
$387$	0.199932	+	7.06914i	0.0101631	+	0.359345i
$388$		0			0
$389$	−7.19727	−	12.4660i	−0.364916	−	0.632053i	0.623847	−	0.781547i	$-0.285569\pi$
$389$	−7.19727	−	12.4660i	−0.364916	−	0.632053i	−0.988763	+	0.149494i	$0.952236\pi$
$390$		0			0
$391$	12.8916	+	7.44297i	0.651957	+	0.376407i
$392$		0			0
$393$	20.7422	−	21.3371i	1.04631	−	1.07632i
$394$		0			0
$395$		−	12.9944i		−	0.653820i
$396$		0			0
$397$			12.1034i			0.607454i	0.952759	+	0.303727i	$0.0982311\pi$
$397$			12.1034i			0.607454i	−0.952759	+	0.303727i	$0.901769\pi$
$398$		0			0
$399$	10.3004	+	36.3764i	0.515663	+	1.82110i
$400$		0			0
$401$	−14.6874	−	8.47977i	−0.733454	−	0.423460i	0.0862307	−	0.996275i	$-0.472518\pi$
$401$	−14.6874	−	8.47977i	−0.733454	−	0.423460i	−0.819684	+	0.572816i	$0.805851\pi$
$402$		0			0
$403$	−6.89999	−	11.9511i	−0.343713	−	0.595328i
$404$		0			0
$405$	−8.98561	+	0.508676i	−0.446499	+	0.0252763i
$406$		0			0
$407$	−2.86000	−	4.95366i	−0.141765	−	0.245544i
$408$		0			0
$409$	12.3239	−	21.3456i	0.609376	−	1.05547i	−0.381968	−	0.924176i	$-0.624753\pi$
$409$	12.3239	−	21.3456i	0.609376	−	1.05547i	0.991343	−	0.131294i	$-0.0419132\pi$
$410$		0			0
$411$	7.72754	+	27.2903i	0.381171	+	1.34613i
$412$		0			0
$413$	−8.85328			−0.435641
$414$		0			0
$415$			5.78452i			0.283951i
$416$		0			0
$417$	−15.2447	−	14.8196i	−0.746535	−	0.725720i
$418$		0			0
$419$	−22.0686	−	12.7413i	−1.07812	−	0.622455i	−0.147734	−	0.989027i	$-0.547198\pi$
$419$	−22.0686	−	12.7413i	−1.07812	−	0.622455i	−0.930390	+	0.366572i	$0.880531\pi$
$420$		0			0
$421$	2.84113	−	1.64033i	0.138468	−	0.0799446i	−0.429166	−	0.903226i	$-0.641192\pi$
$421$	2.84113	−	1.64033i	0.138468	−	0.0799446i	0.567634	+	0.823281i	$0.307859\pi$
$422$		0			0
$423$	−1.01330	−	35.8280i	−0.0492684	−	1.74202i
$424$		0			0
$425$	4.57905	−	2.64371i	0.222116	−	0.128239i
$426$		0			0
$427$	12.4576	−	21.5772i	0.602867	−	1.04420i
$428$		0			0
$429$	−1.01780	+	4.02525i	−0.0491396	+	0.194341i
$430$		0			0
$431$	−10.5731			−0.509290			−0.254645	−	0.967035i	$-0.581959\pi$
$431$	−10.5731			−0.509290			−0.254645	+	0.967035i	$0.581959\pi$
$432$		0			0
$433$	−10.9701			−0.527191			−0.263596	−	0.964633i	$-0.584908\pi$
$433$	−10.9701			−0.527191			−0.263596	+	0.964633i	$0.584908\pi$
$434$		0			0
$435$	3.57391	−	14.1344i	0.171356	−	0.677690i
$436$		0			0
$437$	6.85012	−	11.8648i	0.327686	−	0.567568i
$438$		0			0
$439$	8.06638	−	4.65712i	0.384987	−	0.222272i	−0.294999	−	0.955498i	$-0.595319\pi$
$439$	8.06638	−	4.65712i	0.384987	−	0.222272i	0.679986	+	0.733225i	$0.261986\pi$
$440$		0			0
$441$	−33.5160	+	20.6353i	−1.59600	+	0.982636i
$442$		0			0
$443$	1.06647	−	0.615728i	0.0506696	−	0.0292541i	−0.474451	−	0.880282i	$-0.657353\pi$
$443$	1.06647	−	0.615728i	0.0506696	−	0.0292541i	0.525121	+	0.851028i	$0.324020\pi$
$444$		0			0
$445$	−2.35504	−	1.35968i	−0.111639	−	0.0644551i
$446$		0			0
$447$	−25.9485	−	25.2250i	−1.22732	−	1.19310i
$448$		0			0
$449$		−	6.49670i		−	0.306598i	−0.988180	−	0.153299i	$-0.951010\pi$
$449$		−	6.49670i		−	0.306598i	0.988180	−	0.153299i	$-0.0489898\pi$
$450$		0			0
$451$	7.43832			0.350257
$452$		0			0
$453$	1.48482	+	5.24375i	0.0697630	+	0.246373i
$454$		0			0
$455$	4.43073	−	7.67425i	0.207716	−	0.359775i
$456$		0			0
$457$	11.9191	+	20.6444i	0.557550	+	0.965706i	0.997700	+	0.0677813i	$0.0215920\pi$
$457$	11.9191	+	20.6444i	0.557550	+	0.965706i	−0.440150	+	0.897924i	$0.645075\pi$
$458$		0			0
$459$	20.2335	+	18.5861i	0.944418	+	0.867524i
$460$		0			0
$461$	8.00659	+	13.8678i	0.372904	+	0.645889i	0.990011	−	0.140991i	$-0.0450287\pi$
$461$	8.00659	+	13.8678i	0.372904	+	0.645889i	−0.617107	+	0.786879i	$0.711695\pi$
$462$		0			0
$463$	−24.9383	−	14.3982i	−1.15898	−	0.669139i	−0.207923	−	0.978145i	$-0.566670\pi$
$463$	−24.9383	−	14.3982i	−1.15898	−	0.669139i	−0.951060	+	0.309006i	$0.900004\pi$
$464$		0			0
$465$	−3.29631	−	11.6412i	−0.152863	−	0.539846i
$466$		0			0
$467$		−	27.0588i		−	1.25213i	−0.779769	−	0.626067i	$-0.784664\pi$
$467$		−	27.0588i		−	1.25213i	0.779769	−	0.626067i	$-0.215336\pi$
$468$		0			0
$469$			14.2392i			0.657505i
$470$		0			0
$471$	13.4461	−	13.8318i	0.619564	−	0.637335i
$472$		0			0
$473$	2.47710	+	1.43016i	0.113897	+	0.0657587i
$474$		0			0
$475$	−2.43314	−	4.21431i	−0.111640	−	0.193366i
$476$		0			0
$477$	1.95122	+	1.05414i	0.0893404	+	0.0482658i
$478$		0			0
$479$	−5.93681	−	10.2829i	−0.271260	−	0.469836i	0.697925	−	0.716171i	$-0.254107\pi$
$479$	−5.93681	−	10.2829i	−0.271260	−	0.469836i	−0.969185	+	0.246335i	$0.920774\pi$
$480$		0			0
$481$	4.65656	−	8.06541i	0.212321	−	0.367751i
$482$		0			0
$483$	21.2054	+	5.36184i	0.964878	+	0.243972i
$484$		0			0
$485$	−17.2215			−0.781988
$486$		0			0
$487$			11.2361i			0.509158i	0.967052	+	0.254579i	$0.0819369\pi$
$487$			11.2361i			0.509158i	−0.967052	+	0.254579i	$0.918063\pi$
$488$		0			0
$489$	−0.241089	+	0.953476i	−0.0109024	+	0.0431177i
$490$		0			0
$491$	−26.2016	−	15.1275i	−1.18246	−	0.682694i	−0.225877	−	0.974156i	$-0.572525\pi$
$491$	−26.2016	−	15.1275i	−1.18246	−	0.682694i	−0.956582	+	0.291462i	$0.905858\pi$
$492$		0			0
$493$	−38.5432	+	22.2529i	−1.73590	+	1.00222i
$494$		0			0
$495$	−1.73021	+	3.20263i	−0.0777672	+	0.143948i
$496$		0			0
$497$	13.2445	−	7.64669i	0.594095	−	0.343001i
$498$		0			0
$499$	−4.81293	+	8.33624i	−0.215456	+	0.373182i	−0.953414	−	0.301666i	$-0.902457\pi$
$499$	−4.81293	+	8.33624i	−0.215456	+	0.373182i	0.737957	+	0.674847i	$0.235791\pi$
$500$		0			0
$501$	23.8236	+	23.1594i	1.06436	+	1.03468i
$502$		0			0
$503$	−28.3463			−1.26390			−0.631950	−	0.775009i	$-0.717745\pi$
$503$	−28.3463			−1.26390			−0.631950	+	0.775009i	$0.717745\pi$
$504$		0			0
$505$	−5.31703			−0.236605
$506$		0			0
$507$	15.1605	−	4.29286i	0.673303	−	0.190653i
$508$		0			0
$509$	19.7957	−	34.2872i	0.877431	−	1.51976i	0.0232807	−	0.999729i	$-0.492589\pi$
$509$	19.7957	−	34.2872i	0.877431	−	1.51976i	0.854150	−	0.520026i	$-0.174078\pi$
$510$		0			0
$511$	−26.0178	+	15.0214i	−1.15096	+	0.664506i
$512$		0			0
$513$	17.1056	−	18.6218i	0.755233	−	0.822174i
$514$		0			0
$515$	−13.2519	+	7.65097i	−0.583947	+	0.337142i
$516$		0			0
$517$	−12.5545	−	7.24837i	−0.552148	−	0.318783i
$518$		0			0
$519$	−2.42603	+	0.686954i	−0.106491	+	0.0301539i
$520$		0			0
$521$		−	35.6218i		−	1.56062i	−0.625393	−	0.780310i	$-0.715061\pi$
$521$		−	35.6218i		−	1.56062i	0.625393	−	0.780310i	$-0.284939\pi$
$522$		0			0
$523$	−13.0675			−0.571404			−0.285702	−	0.958319i	$-0.592227\pi$
$523$	−13.0675			−0.571404			−0.285702	+	0.958319i	$0.592227\pi$
$524$		0			0
$525$	5.41538	−	5.57071i	0.236347	−	0.243126i
$526$		0			0
$527$	−18.4671	+	31.9859i	−0.804438	+	1.39333i
$528$		0			0
$529$	7.53691	+	13.0543i	0.327692	+	0.567579i
$530$		0			0
$531$	3.10442	+	5.04222i	0.134720	+	0.218814i
$532$		0			0
$533$	6.05543	+	10.4883i	0.262290	+	0.454299i
$534$		0			0
$535$	−6.28254	−	3.62723i	−0.271618	−	0.156819i
$536$		0			0
$537$	35.4436	+	8.96203i	1.52951	+	0.386740i
$538$		0			0
$539$			15.9191i			0.685685i
$540$		0			0
$541$			41.8805i			1.80059i	0.435285	+	0.900293i	$0.356647\pi$
$541$			41.8805i			1.80059i	−0.435285	+	0.900293i	$0.643353\pi$
$542$		0			0
$543$	14.3238	+	3.62181i	0.614692	+	0.155427i
$544$		0			0
$545$	16.1254	+	9.30999i	0.690735	+	0.398796i
$546$		0			0
$547$	−8.32180	−	14.4138i	−0.355814	−	0.616288i	0.631443	−	0.775423i	$-0.282463\pi$
$547$	−8.32180	−	14.4138i	−0.355814	−	0.616288i	−0.987257	+	0.159134i	$0.949130\pi$
$548$		0			0
$549$	−16.6572	+	0.471105i	−0.710912	+	0.0201063i
$550$		0			0
$551$	20.4804	+	35.4732i	0.872496	+	1.51121i
$552$		0			0
$553$	−29.1432	+	50.4775i	−1.23930	+	2.14652i
$554$		0			0
$555$	5.69140	−	5.85464i	0.241587	−	0.248516i
$556$		0			0
$557$	10.8296			0.458863			0.229431	−	0.973325i	$-0.426313\pi$
$557$	10.8296			0.458863			0.229431	+	0.973325i	$0.426313\pi$
$558$		0			0
$559$			4.65708i			0.196973i
$560$		0			0
$561$	10.6918	−	3.02750i	0.451409	−	0.127821i
$562$		0			0
$563$	16.4450	+	9.49453i	0.693074	+	0.400147i	0.804763	−	0.593597i	$-0.202293\pi$
$563$	16.4450	+	9.49453i	0.693074	+	0.400147i	−0.111688	+	0.993743i	$0.535626\pi$
$564$		0			0
$565$	5.19909	−	3.00170i	0.218727	−	0.126282i
$566$		0			0
$567$	36.0460	+	18.1765i	1.51379	+	0.763341i
$568$		0			0
$569$	−7.51839	+	4.34075i	−0.315187	+	0.181974i	−0.649245	−	0.760579i	$-0.724915\pi$
$569$	−7.51839	+	4.34075i	−0.315187	+	0.181974i	0.334058	+	0.942553i	$0.391582\pi$
$570$		0			0
$571$	−18.8435	+	32.6378i	−0.788574	+	1.36585i	0.138266	+	0.990395i	$0.455847\pi$
$571$	−18.8435	+	32.6378i	−0.788574	+	1.36585i	−0.926840	+	0.375456i	$0.877486\pi$
$572$		0			0
$573$	−0.713349	+	0.201992i	−0.0298006	+	0.00843834i
$574$		0			0
$575$	−2.81535			−0.117408
$576$		0			0
$577$	−45.5995			−1.89833			−0.949166	−	0.314776i	$-0.898071\pi$
$577$	−45.5995			−1.89833			−0.949166	+	0.314776i	$0.898071\pi$
$578$		0			0
$579$	−11.7757	−	11.4473i	−0.489379	−	0.475734i
$580$		0			0
$581$	12.9732	−	22.4703i	0.538220	−	0.932225i
$582$		0			0
$583$	0.776819	−	0.448497i	0.0321726	−	0.0185748i
$584$		0			0
$585$	−5.92437	+	0.167555i	−0.244943	+	0.00692756i
$586$		0			0
$587$	−8.14708	+	4.70372i	−0.336266	+	0.194143i	−0.658620	−	0.752476i	$-0.728859\pi$
$587$	−8.14708	+	4.70372i	−0.336266	+	0.194143i	0.322354	+	0.946619i	$0.395526\pi$
$588$		0			0
$589$	29.4381	+	16.9961i	1.21298	+	0.700313i
$590$		0			0
$591$	−1.76801	+	6.99224i	−0.0727261	+	0.287622i
$592$		0			0
$593$			14.4808i			0.594657i	0.954775	+	0.297328i	$0.0960956\pi$
$593$			14.4808i			0.594657i	−0.954775	+	0.297328i	$0.903904\pi$
$594$		0			0
$595$	−23.7168			−0.972292
$596$		0			0
$597$	34.3996	+	8.69804i	1.40788	+	0.355987i
$598$		0			0
$599$	2.00132	−	3.46639i	0.0817718	−	0.141633i	−0.822239	−	0.569142i	$-0.807275\pi$
$599$	2.00132	−	3.46639i	0.0817718	−	0.141633i	0.904011	+	0.427509i	$0.140609\pi$
$600$		0			0
$601$	−21.9214	−	37.9690i	−0.894193	−	1.54879i	−0.834800	−	0.550553i	$-0.814417\pi$
$601$	−21.9214	−	37.9690i	−0.894193	−	1.54879i	−0.0593924	−	0.998235i	$-0.518916\pi$
$602$		0			0
$603$	8.10967	−	4.99301i	0.330251	−	0.203331i
$604$		0			0
$605$	−4.76386	−	8.25125i	−0.193679	−	0.335461i
$606$		0			0
$607$	5.60723	+	3.23734i	0.227591	+	0.131399i	0.609460	−	0.792817i	$-0.291386\pi$
$607$	5.60723	+	3.23734i	0.227591	+	0.131399i	−0.381869	+	0.924216i	$0.624720\pi$
$608$		0			0
$609$	−45.5829	+	46.8903i	−1.84711	+	1.90009i
$610$		0			0
$611$		−	23.6032i		−	0.954882i
$612$		0			0
$613$		−	40.2895i		−	1.62728i	−0.581370	−	0.813639i	$-0.697483\pi$
$613$		−	40.2895i		−	1.62728i	0.581370	−	0.813639i	$-0.302517\pi$
$614$		0			0
$615$	2.89285	+	10.2163i	0.116651	+	0.411960i
$616$		0			0
$617$	−13.7460	−	7.93629i	−0.553395	−	0.319503i	0.197095	−	0.980384i	$-0.436849\pi$
$617$	−13.7460	−	7.93629i	−0.553395	−	0.319503i	−0.750490	+	0.660882i	$0.770183\pi$
$618$		0			0
$619$	20.1549	+	34.9094i	0.810095	+	1.40313i	0.912797	+	0.408413i	$0.133918\pi$
$619$	20.1549	+	34.9094i	0.810095	+	1.40313i	−0.102702	+	0.994712i	$0.532749\pi$
$620$		0			0
$621$	−4.38198	−	13.9573i	−0.175843	−	0.560085i
$622$		0			0
$623$	6.09885	+	10.5635i	0.244345	+	0.423218i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−2.78635	−	9.84019i	−0.111276	−	0.392979i
$628$		0			0
$629$	−24.9256			−0.993849
$630$		0			0
$631$		−	9.05567i		−	0.360500i	−0.983621	−	0.180250i	$-0.942309\pi$
$631$		−	9.05567i		−	0.360500i	0.983621	−	0.180250i	$-0.0576908\pi$
$632$		0			0
$633$	31.8309	+	30.9434i	1.26516	+	1.22989i
$634$		0			0
$635$	0.130860	+	0.0755518i	0.00519300	+	0.00299818i
$636$		0			0
$637$	−22.4465	+	12.9595i	−0.889365	+	0.513475i
$638$		0			0
$639$	−8.99922	−	4.86180i	−0.356004	−	0.192330i
$640$		0			0
$641$	−7.53980	+	4.35311i	−0.297804	+	0.171937i	−0.641456	−	0.767160i	$-0.721669\pi$
$641$	−7.53980	+	4.35311i	−0.297804	+	0.171937i	0.343652	+	0.939097i	$0.388336\pi$
$642$		0			0
$643$	−10.5478	+	18.2693i	−0.415963	+	0.720469i	−0.995529	−	0.0944562i	$-0.969889\pi$
$643$	−10.5478	+	18.2693i	−0.415963	+	0.720469i	0.579566	+	0.814925i	$0.303222\pi$
$644$		0			0
$645$	−1.00090	+	3.95842i	−0.0394103	+	0.155863i
$646$		0			0
$647$	36.6479			1.44078			0.720388	−	0.693571i	$-0.243964\pi$
$647$	36.6479			1.44078			0.720388	+	0.693571i	$0.243964\pi$
$648$		0			0
$649$	2.39490			0.0940081
$650$		0			0
$651$	−13.3035	+	52.6135i	−0.521405	+	2.06209i
$652$		0			0
$653$	−0.680992	+	1.17951i	−0.0266493	+	0.0461579i	−0.879042	−	0.476743i	$-0.841817\pi$
$653$	−0.680992	+	1.17951i	−0.0266493	+	0.0461579i	0.852393	+	0.522901i	$0.175150\pi$
$654$		0			0
$655$	14.8788	−	8.59027i	0.581362	−	0.335650i
$656$		0			0
$657$	17.6783	+	9.55065i	0.689697	+	0.372606i
$658$		0			0
$659$	17.5744	−	10.1466i	0.684600	−	0.395254i	−0.116986	−	0.993134i	$-0.537323\pi$
$659$	17.5744	−	10.1466i	0.684600	−	0.395254i	0.801586	+	0.597879i	$0.203990\pi$
$660$		0			0
$661$	6.63502	+	3.83073i	0.258073	+	0.148998i	0.623455	−	0.781859i	$-0.285728\pi$
$661$	6.63502	+	3.83073i	0.258073	+	0.148998i	−0.365382	+	0.930857i	$0.619062\pi$
$662$		0			0
$663$	12.9729	+	12.6112i	0.503828	+	0.489780i
$664$		0			0
$665$			21.8277i			0.846440i
$666$		0			0
$667$	23.6976			0.917575
$668$		0			0
$669$	0.314802	+	1.11175i	0.0121710	+	0.0429826i
$670$		0			0
$671$	−3.36992	+	5.83686i	−0.130094	+	0.225330i
$672$		0			0
$673$	9.53849	+	16.5212i	0.367682	+	0.636844i	0.989203	−	0.146554i	$-0.0468182\pi$
$673$	9.53849	+	16.5212i	0.367682	+	0.636844i	−0.621521	+	0.783398i	$0.713485\pi$
$674$		0			0
$675$	−5.07161	−	1.13085i	−0.195206	−	0.0435263i
$676$		0			0
$677$	−9.09868	−	15.7594i	−0.349690	−	0.605682i	0.636504	−	0.771273i	$-0.280380\pi$
$677$	−9.09868	−	15.7594i	−0.349690	−	0.605682i	−0.986194	+	0.165592i	$0.947047\pi$
$678$		0			0
$679$	66.8979	+	38.6235i	2.56731	+	1.48223i
$680$		0			0
$681$	−1.75285	−	6.19031i	−0.0671694	−	0.237213i
$682$		0			0
$683$		−	4.17953i		−	0.159925i	−0.996798	−	0.0799626i	$-0.974520\pi$
$683$		−	4.17953i		−	0.159925i	0.996798	−	0.0799626i	$-0.0254801\pi$
$684$		0			0
$685$			16.3756i			0.625678i
$686$		0			0
$687$	−7.34713	+	7.55786i	−0.280311	+	0.288351i
$688$		0			0
$689$	1.26479	+	0.730229i	0.0481848	+	0.0278195i
$690$		0			0
$691$	2.99450	+	5.18663i	0.113916	+	0.197309i	0.917346	−	0.398091i	$-0.130327\pi$
$691$	2.99450	+	5.18663i	0.113916	+	0.197309i	−0.803430	+	0.595400i	$0.796994\pi$
$692$		0			0
$693$	13.9038	−	8.56038i	0.528162	−	0.325182i
$694$		0			0
$695$	−6.13746	−	10.6304i	−0.232807	−	0.403234i
$696$		0			0
$697$	16.2067	−	28.0709i	0.613873	−	1.06326i
$698$		0			0
$699$	−19.2308	−	4.86257i	−0.727377	−	0.183919i
$700$		0			0
$701$	18.5227			0.699592			0.349796	−	0.936826i	$-0.386251\pi$
$701$	18.5227			0.699592			0.349796	+	0.936826i	$0.386251\pi$
$702$		0			0
$703$			22.9402i			0.865206i
$704$		0			0
$705$	5.07279	−	20.0622i	0.191052	−	0.755586i
$706$		0			0
$707$	20.6543	+	11.9248i	0.776786	+	0.448477i
$708$		0			0
$709$	17.4280	−	10.0621i	0.654522	−	0.377888i	−0.135665	−	0.990755i	$-0.543317\pi$
$709$	17.4280	−	10.0621i	0.654522	−	0.377888i	0.790187	+	0.612866i	$0.209984\pi$
$710$		0			0
$711$	38.9676	−	1.10210i	1.46140	−	0.0413319i
$712$		0			0
$713$	17.0312	−	9.83299i	0.637825	−	0.368248i
$714$		0			0
$715$	−1.19856	+	2.07596i	−0.0448235	+	0.0776367i
$716$		0			0
$717$	14.4563	+	14.0532i	0.539880	+	0.524827i
$718$		0			0
$719$	−26.2181			−0.977768			−0.488884	−	0.872349i	$-0.662596\pi$
$719$	−26.2181			−0.977768			−0.488884	+	0.872349i	$0.662596\pi$
$720$		0			0
$721$	68.6369			2.55617
$722$		0			0
$723$	−10.8223	+	3.06444i	−0.402484	+	0.113968i
$724$		0			0
$725$	4.20865	−	7.28960i	0.156305	−	0.270729i
$726$		0			0
$727$	−20.5836	+	11.8839i	−0.763402	+	0.440750i	−0.830516	−	0.556995i	$-0.811954\pi$
$727$	−20.5836	+	11.8839i	−0.763402	+	0.440750i	0.0671138	+	0.997745i	$0.478621\pi$
$728$		0			0
$729$	−2.28752	−	26.9029i	−0.0847228	−	0.996405i
$730$		0			0
$731$	10.7943	−	6.23209i	0.399241	−	0.230502i
$732$		0			0
$733$	−17.5140	−	10.1117i	−0.646894	−	0.373485i	0.140371	−	0.990099i	$-0.455170\pi$
$733$	−17.5140	−	10.1117i	−0.646894	−	0.373485i	−0.787265	+	0.616614i	$0.788504\pi$
$734$		0			0
$735$	−21.8644	+	6.19112i	−0.806479	+	0.228363i
$736$		0			0
$737$		−	3.85185i		−	0.141885i
$738$		0			0
$739$	−25.0224			−0.920463			−0.460232	−	0.887799i	$-0.652234\pi$
$739$	−25.0224			−0.920463			−0.460232	+	0.887799i	$0.652234\pi$
$740$		0			0
$741$	11.6067	−	11.9396i	0.426383	−	0.438613i
$742$		0			0
$743$	−0.871379	+	1.50927i	−0.0319678	+	0.0553699i	−0.881567	−	0.472060i	$-0.843511\pi$
$743$	−0.871379	+	1.50927i	−0.0319678	+	0.0553699i	0.849599	+	0.527429i	$0.176844\pi$
$744$		0			0
$745$	−10.4468	−	18.0944i	−0.382741	−	0.662927i
$746$		0			0
$747$	−17.3466	+	0.490603i	−0.634680	+	0.0179502i
$748$		0			0
$749$	16.2699	+	28.1803i	0.594490	+	1.02969i
$750$		0			0
$751$	−14.6053	−	8.43240i	−0.532957	−	0.307703i	0.209263	−	0.977859i	$-0.432894\pi$
$751$	−14.6053	−	8.43240i	−0.532957	−	0.307703i	−0.742220	+	0.670157i	$0.766227\pi$
$752$		0			0
$753$	5.87050	+	1.48437i	0.213933	+	0.0540936i
$754$		0			0
$755$			3.14651i			0.114513i
$756$		0			0
$757$			25.4545i			0.925160i	0.886577	+	0.462580i	$0.153076\pi$
$757$			25.4545i			0.925160i	−0.886577	+	0.462580i	$0.846924\pi$
$758$		0			0
$759$	−5.73627	−	1.45043i	−0.208213	−	0.0526474i
$760$		0			0
$761$	−39.3748	−	22.7331i	−1.42734	−	0.824073i	−0.430427	−	0.902625i	$-0.641637\pi$
$761$	−39.3748	−	22.7331i	−1.42734	−	0.824073i	−0.996910	+	0.0785520i	$0.974970\pi$
$762$		0			0
$763$	−41.7600	−	72.3304i	−1.51181	−	2.61853i
$764$		0			0
$765$	8.31634	+	13.5074i	0.300678	+	0.488362i
$766$		0			0
$767$	1.94966	+	3.37690i	0.0703980	+	0.121933i
$768$		0			0
$769$	6.11507	−	10.5916i	0.220515	−	0.381943i	−0.734449	−	0.678663i	$-0.762559\pi$
$769$	6.11507	−	10.5916i	0.220515	−	0.381943i	0.954965	+	0.296720i	$0.0958928\pi$
$770$		0			0
$771$	4.02605	−	4.14153i	0.144995	−	0.149153i
$772$		0			0
$773$	−23.0762			−0.829992			−0.414996	−	0.909823i	$-0.636217\pi$
$773$	−23.0762			−0.829992			−0.414996	+	0.909823i	$0.636217\pi$
$774$		0			0
$775$		−	6.98528i		−	0.250919i
$776$		0			0
$777$	−35.2391	+	9.97830i	−1.26419	+	0.357970i
$778$		0			0
$779$	−25.8349	−	14.9158i	−0.925633	−	0.534414i
$780$		0			0
$781$	−3.58276	+	2.06851i	−0.128201	+	0.0740170i
$782$		0			0
$783$	42.6892	+	9.51867i	1.52559	+	0.340170i
$784$		0			0
$785$	9.64516	−	5.56863i	0.344250	−	0.198753i
$786$		0			0
$787$	−8.21382	+	14.2268i	−0.292791	+	0.507129i	−0.974469	−	0.224524i	$-0.927917\pi$
$787$	−8.21382	+	14.2268i	−0.292791	+	0.507129i	0.681678	+	0.731653i	$0.261251\pi$
$788$		0			0
$789$	−22.2152	+	6.29045i	−0.790881	+	0.223946i
$790$		0			0
$791$	−26.9282			−0.957458
$792$		0			0
$793$	−10.9736			−0.389684
$794$		0			0
$795$	0.918109	+	0.892510i	0.0325620	+	0.0316541i
$796$		0			0
$797$	18.7569	−	32.4878i	0.664402	−	1.15078i	−0.315045	−	0.949077i	$-0.602020\pi$
$797$	18.7569	−	32.4878i	0.664402	−	1.15078i	0.979447	−	0.201701i	$-0.0646470\pi$
$798$		0			0
$799$	−54.7080	+	31.5857i	−1.93543	+	1.11742i
$800$		0			0
$801$	3.87768	−	7.17761i	0.137011	−	0.253608i
$802$		0			0
$803$	7.03807	−	4.06343i	0.248368	−	0.143395i
$804$		0			0
$805$	10.9364	+	6.31412i	0.385457	+	0.222543i
$806$		0			0
$807$	−0.831628	+	3.28898i	−0.0292747	+	0.115778i
$808$		0			0
$809$			13.7094i			0.481998i	0.970525	+	0.240999i	$0.0774751\pi$
$809$			13.7094i			0.481998i	−0.970525	+	0.240999i	$0.922525\pi$
$810$		0			0
$811$	47.6781			1.67420			0.837102	−	0.547047i	$-0.184248\pi$
$811$	47.6781			1.67420			0.837102	+	0.547047i	$0.184248\pi$
$812$		0			0
$813$	37.9057	+	9.58457i	1.32941	+	0.336146i
$814$		0			0
$815$	−0.283907	+	0.491742i	−0.00994484	+	0.0172250i
$816$		0			0
$817$	−5.73568	−	9.93450i	−0.200666	−	0.347564i
$818$		0			0
$819$	23.3893	+	12.6360i	0.817290	+	0.441538i
$820$		0			0
$821$	−14.6238	−	25.3292i	−0.510376	−	0.883997i	−0.999928	−	0.0120227i	$-0.996173\pi$
$821$	−14.6238	−	25.3292i	−0.510376	−	0.883997i	0.489552	−	0.871974i	$-0.337160\pi$
$822$		0			0
$823$	29.6471	+	17.1168i	1.03343	+	0.596653i	0.917966	−	0.396659i	$-0.129830\pi$
$823$	29.6471	+	17.1168i	1.03343	+	0.596653i	0.115466	+	0.993311i	$0.463164\pi$
$824$		0			0
$825$	−1.46492	+	1.50693i	−0.0510018	+	0.0524647i
$826$		0			0
$827$		−	18.2917i		−	0.636065i	−0.948080	−	0.318032i	$-0.896978\pi$
$827$		−	18.2917i		−	0.636065i	0.948080	−	0.318032i	$-0.103022\pi$
$828$		0			0
$829$			11.0727i			0.384572i	0.981339	+	0.192286i	$0.0615902\pi$
$829$			11.0727i			0.384572i	−0.981339	+	0.192286i	$0.938410\pi$
$830$		0			0
$831$	11.3684	+	40.1483i	0.394366	+	1.39273i
$832$		0			0
$833$	60.0758	+	34.6848i	2.08150	+	1.20176i
$834$		0			0
$835$	9.59132	+	16.6127i	0.331921	+	0.574905i
$836$		0			0
$837$	34.6299	−	10.8723i	1.19699	−	0.375802i
$838$		0			0
$839$	−21.6805	−	37.5517i	−0.748494	−	1.29643i	−0.948545	−	0.316643i	$-0.897444\pi$
$839$	−21.6805	−	37.5517i	−0.748494	−	1.29643i	0.200051	−	0.979785i	$-0.435889\pi$
$840$		0			0
$841$	−20.9255	+	36.2440i	−0.721568	+	1.24979i
$842$		0			0
$843$	−14.4095	−	50.8882i	−0.496290	−	1.75268i
$844$		0			0
$845$	9.09708			0.312949
$846$		0			0
$847$			42.7366i			1.46845i
$848$		0			0
$849$	−9.56171	−	9.29510i	−0.328157	−	0.319007i
$850$		0			0
$851$	11.4938	+	6.63595i	0.394002	+	0.227477i
$852$		0			0
$853$	−18.7351	+	10.8167i	−0.641479	+	0.370358i	−0.785184	−	0.619263i	$-0.787432\pi$
$853$	−18.7351	+	10.8167i	−0.641479	+	0.370358i	0.143705	+	0.989621i	$0.454098\pi$
$854$		0			0
$855$	12.4315	−	7.65392i	0.425149	−	0.261758i
$856$		0			0
$857$	−10.5218	+	6.07474i	−0.359417	+	0.207509i	−0.668825	−	0.743420i	$-0.733202\pi$
$857$	−10.5218	+	6.07474i	−0.359417	+	0.207509i	0.309408	+	0.950929i	$0.399869\pi$
$858$		0			0
$859$	16.1108	−	27.9048i	0.549694	−	0.952098i	−0.448601	−	0.893732i	$-0.648078\pi$
$859$	16.1108	−	27.9048i	0.549694	−	0.952098i	0.998295	−	0.0583659i	$-0.0185890\pi$
$860$		0			0
$861$	11.6751	−	46.1737i	0.397888	−	1.57359i
$862$		0			0
$863$	−7.86707			−0.267798			−0.133899	−	0.990995i	$-0.542750\pi$
$863$	−7.86707			−0.267798			−0.133899	+	0.990995i	$0.542750\pi$
$864$		0			0
$865$	−1.45574			−0.0494965
$866$		0			0
$867$	4.65221	−	18.3989i	0.157997	−	0.624858i
$868$		0			0
$869$	7.88354	−	13.6547i	0.267431	−	0.463203i
$870$		0			0
$871$	5.43126	−	3.13574i	0.184031	−	0.106250i
$872$		0			0
$873$	−1.46061	−	51.6438i	−0.0494342	−	1.74788i
$874$		0			0
$875$	3.88456	−	2.24275i	0.131322	−	0.0758188i
$876$		0			0
$877$	9.62451	+	5.55672i	0.324997	+	0.187637i	0.653618	−	0.756825i	$-0.273250\pi$
$877$	9.62451	+	5.55672i	0.324997	+	0.187637i	−0.328621	+	0.944462i	$0.606584\pi$
$878$		0			0
$879$	22.4488	+	21.8228i	0.757178	+	0.736066i
$880$		0			0
$881$			1.03742i			0.0349514i	0.999847	+	0.0174757i	$0.00556298\pi$
$881$			1.03742i			0.0349514i	−0.999847	+	0.0174757i	$0.994437\pi$
$882$		0			0
$883$	−47.3991			−1.59511			−0.797554	−	0.603248i	$-0.793873\pi$
$883$	−47.3991			−1.59511			−0.797554	+	0.603248i	$0.793873\pi$
$884$		0			0
$885$	0.931404	+	3.28932i	0.0313088	+	0.110569i
$886$		0			0
$887$	7.80889	−	13.5254i	0.262197	−	0.454139i	−0.704628	−	0.709576i	$-0.748886\pi$
$887$	7.80889	−	13.5254i	0.262197	−	0.454139i	0.966825	+	0.255438i	$0.0822196\pi$
$888$		0			0
$889$	−0.338887	−	0.586970i	−0.0113659	−	0.0196864i
$890$		0			0
$891$	−9.75080	−	4.91693i	−0.326664	−	0.164723i
$892$		0			0
$893$	29.0698	+	50.3503i	0.972783	+	1.68491i
$894$		0			0
$895$	18.2796	+	10.5537i	0.611018	+	0.352772i
$896$		0			0
$897$	−2.62465	−	9.26913i	−0.0876345	−	0.309487i
$898$		0			0
$899$			58.7972i			1.96100i
$900$		0			0
$901$		−	3.90876i		−	0.130220i
$902$		0			0
$903$	12.7658	−	13.1319i	0.424819	−	0.437004i
$904$		0			0
$905$	7.38728	+	4.26505i	0.245562	+	0.141775i
$906$		0			0
$907$	25.0385	+	43.3680i	0.831390	+	1.44001i	0.896936	+	0.442160i	$0.145788\pi$
$907$	25.0385	+	43.3680i	0.831390	+	1.44001i	−0.0655459	+	0.997850i	$0.520879\pi$
$908$		0			0
$909$	−0.450955	−	15.9447i	−0.0149572	−	0.528853i
$910$		0			0
$911$	−10.7564	−	18.6307i	−0.356376	−	0.617262i	0.630976	−	0.775802i	$-0.282655\pi$
$911$	−10.7564	−	18.6307i	−0.356376	−	0.617262i	−0.987353	+	0.158540i	$0.949321\pi$
$912$		0			0
$913$	−3.50939	+	6.07844i	−0.116144	+	0.201167i
$914$		0			0
$915$	−9.32733	−	2.35844i	−0.308352	−	0.0779678i
$916$		0			0
$917$	−77.0633			−2.54486
$918$		0			0
$919$			28.7522i			0.948448i	0.880404	+	0.474224i	$0.157271\pi$
$919$			28.7522i			0.948448i	−0.880404	+	0.474224i	$0.842729\pi$
$920$		0			0
$921$	−10.0728	+	39.8366i	−0.331910	+	1.31266i
$922$		0			0
$923$	−5.83335	−	3.36788i	−0.192007	−	0.110855i
$924$		0			0
$925$	4.08255	−	2.35706i	0.134233	−	0.0774997i
$926$		0			0
$927$	−24.0677	−	39.0908i	−0.790486	−	1.28391i
$928$		0			0
$929$	29.7995	−	17.2047i	0.977689	−	0.564469i	0.0761173	−	0.997099i	$-0.475748\pi$
$929$	29.7995	−	17.2047i	0.977689	−	0.564469i	0.901572	+	0.432630i	$0.142414\pi$
$930$		0			0
$931$	31.9220	−	55.2906i	1.04620	−	1.81208i
$932$		0			0
$933$	15.4995	+	15.0673i	0.507430	+	0.493281i
$934$		0			0
$935$	6.41563			0.209813
$936$		0			0
$937$	9.52071			0.311028			0.155514	−	0.987834i	$-0.450297\pi$
$937$	9.52071			0.311028			0.155514	+	0.987834i	$0.450297\pi$
$938$		0			0
$939$	24.6885	−	6.99080i	0.805679	−	0.228136i
$940$		0			0
$941$	−22.3517	+	38.7143i	−0.728646	+	1.26205i	0.228810	+	0.973471i	$0.426517\pi$
$941$	−22.3517	+	38.7143i	−0.728646	+	1.26205i	−0.957456	+	0.288580i	$0.906817\pi$
$942$		0			0
$943$	−14.9466	+	8.62943i	−0.486729	+	0.281013i
$944$		0			0
$945$	17.1647	+	15.7672i	0.558369	+	0.512906i
$946$		0			0
$947$	−7.64574	+	4.41427i	−0.248453	+	0.143444i	−0.619056	−	0.785347i	$-0.712485\pi$
$947$	−7.64574	+	4.41427i	−0.248453	+	0.143444i	0.370603	+	0.928792i	$0.379151\pi$
$948$		0			0
$949$	11.4592	+	6.61596i	0.371981	+	0.214763i
$950$		0			0
$951$	−38.6606	+	10.9471i	−1.25366	+	0.354986i
$952$		0			0
$953$			25.0780i			0.812356i	0.913794	+	0.406178i	$0.133139\pi$
$953$			25.0780i			0.812356i	−0.913794	+	0.406178i	$0.866861\pi$
$954$		0			0
$955$	−0.428045			−0.0138512
$956$		0			0
$957$	12.3306	−	12.6843i	0.398593	−	0.410026i
$958$		0			0
$959$	36.7263	−	63.6118i	1.18595	−	2.05413i
$960$		0			0
$961$	8.89704	+	15.4101i	0.287001	+	0.497101i
$962$		0			0
$963$	10.3445	−	19.1477i	0.333346	−	0.617027i
$964$		0			0
$965$	−4.74084	−	8.21138i	−0.152613	−	0.264334i
$966$		0			0
$967$	−46.2843	−	26.7222i	−1.48840	−	0.859329i	−0.488489	−	0.872570i	$-0.662452\pi$
$967$	−46.2843	−	26.7222i	−1.48840	−	0.859329i	−0.999912	+	0.0132411i	$0.995785\pi$
$968$		0			0
$969$	−43.2060	−	10.9248i	−1.38798	−	0.350954i
$970$		0			0
$971$			1.47479i			0.0473284i	0.999720	+	0.0236642i	$0.00753325\pi$
$971$			1.47479i			0.0473284i	−0.999720	+	0.0236642i	$0.992467\pi$
$972$		0			0
$973$			55.0592i			1.76512i
$974$		0			0
$975$	−3.31740	−	0.838814i	−0.106242	−	0.0268636i
$976$		0			0
$977$	−37.3937	−	21.5892i	−1.19633	−	0.690701i	−0.236594	−	0.971609i	$-0.576031\pi$
$977$	−37.3937	−	21.5892i	−1.19633	−	0.690701i	−0.959735	+	0.280908i	$0.909365\pi$
$978$		0			0
$979$	−1.64980	−	2.85754i	−0.0527279	−	0.0913274i
$980$		0			0
$981$	−26.5512	+	49.1464i	−0.847713	+	1.56912i
$982$		0			0
$983$	3.00102	+	5.19791i	0.0957175	+	0.165788i	0.909908	−	0.414810i	$-0.136152\pi$
$983$	3.00102	+	5.19791i	0.0957175	+	0.165788i	−0.814190	+	0.580598i	$0.802819\pi$
$984$		0			0
$985$	−2.08201	+	3.60615i	−0.0663384	+	0.114901i
$986$		0			0
$987$	−64.7000	+	66.5558i	−2.05942	+	2.11849i
$988$		0			0
$989$	−6.63668			−0.211034
$990$		0			0
$991$			60.8130i			1.93179i	0.258939	+	0.965894i	$0.416627\pi$
$991$			60.8130i			1.93179i	−0.258939	+	0.965894i	$0.583373\pi$
$992$		0			0
$993$	11.3611	−	3.21701i	0.360533	−	0.102089i
$994$		0			0
$995$	17.7411	+	10.2428i	0.562431	+	0.324720i
$996$		0			0
$997$	1.61374	−	0.931694i	0.0511077	−	0.0295070i	−0.474228	−	0.880402i	$-0.657273\pi$
$997$	1.61374	−	0.931694i	0.0511077	−	0.0295070i	0.525336	+	0.850895i	$0.323940\pi$
$998$		0			0
$999$	18.0396	+	16.5708i	0.570748	+	0.524278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.cc.a.1391.10		48
3.2	odd	2		4320.2.cc.b.3311.22		48
4.3	odd	2		360.2.bm.a.131.6	yes	48
8.3	odd	2		1440.2.cc.b.1391.10		48
8.5	even	2		360.2.bm.b.131.3	yes	48
9.2	odd	6		1440.2.cc.b.911.10		48
9.7	even	3		4320.2.cc.a.1871.3		48
12.11	even	2		1080.2.bm.b.611.19		48
24.5	odd	2		1080.2.bm.a.611.22		48
24.11	even	2		4320.2.cc.a.3311.3		48
36.7	odd	6		1080.2.bm.a.251.22		48
36.11	even	6		360.2.bm.b.11.3	yes	48
72.11	even	6	inner	1440.2.cc.a.911.10		48
72.29	odd	6		360.2.bm.a.11.6	✓	48
72.43	odd	6		4320.2.cc.b.1871.22		48
72.61	even	6		1080.2.bm.b.251.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.6	✓	48	72.29	odd	6
360.2.bm.a.131.6	yes	48	4.3	odd	2
360.2.bm.b.11.3	yes	48	36.11	even	6
360.2.bm.b.131.3	yes	48	8.5	even	2
1080.2.bm.a.251.22		48	36.7	odd	6
1080.2.bm.a.611.22		48	24.5	odd	2
1080.2.bm.b.251.19		48	72.61	even	6
1080.2.bm.b.611.19		48	12.11	even	2
1440.2.cc.a.911.10		48	72.11	even	6	inner
1440.2.cc.a.1391.10		48	1.1	even	1	trivial
1440.2.cc.b.911.10		48	9.2	odd	6
1440.2.cc.b.1391.10		48	8.3	odd	2
4320.2.cc.a.1871.3		48	9.7	even	3
4320.2.cc.a.3311.3		48	24.11	even	2
4320.2.cc.b.1871.22		48	72.43	odd	6
4320.2.cc.b.3311.22		48	3.2	odd	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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.424591 + 1.67920i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(3.88456 - 2.24275i) q^{7} +(-2.63944 - 1.42595i) q^{9} +O(q^{10})\)	\(q+(-0.424591 + 1.67920i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(3.88456 - 2.24275i) q^{7} +(-2.63944 - 1.42595i) q^{9} +(-1.05081 + 0.606687i) q^{11} +(-1.71090 - 0.987790i) q^{13} +(-1.24194 - 1.20731i) q^{15} +5.28743i q^{17} +4.86627 q^{19} +(2.11668 + 7.47521i) q^{21} +(1.40767 - 2.43816i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.51514 - 3.82672i) q^{27} +(4.20865 + 7.28960i) q^{29} +(6.04943 + 3.49264i) q^{31} +(-0.572584 - 2.02212i) q^{33} +4.48550i q^{35} +4.71412i q^{37} +(2.38513 - 2.45355i) q^{39} +(-5.30898 - 3.06514i) q^{41} +(-1.17866 - 2.04150i) q^{43} +(2.55463 - 1.57285i) q^{45} +(5.97373 + 10.3468i) q^{47} +(6.55985 - 11.3620i) q^{49} +(-8.87867 - 2.24500i) q^{51} -0.739256 q^{53} -1.21337i q^{55} +(-2.06618 + 8.17146i) q^{57} +(-1.70932 - 0.986877i) q^{59} +(4.81044 - 2.77731i) q^{61} +(-13.4511 + 0.380430i) q^{63} +(1.71090 - 0.987790i) q^{65} +(-1.58725 + 2.74920i) q^{67} +(3.49648 + 3.39899i) q^{69} +3.40951 q^{71} -6.69774 q^{73} +(1.66653 - 0.471895i) q^{75} +(-2.72129 + 4.71342i) q^{77} +(-11.2535 + 6.49720i) q^{79} +(4.93333 + 7.52743i) q^{81} +(5.00954 - 2.89226i) q^{83} +(-4.57905 - 2.64371i) q^{85} +(-14.0277 + 3.97208i) q^{87} +2.71936i q^{89} -8.86146 q^{91} +(-8.43338 + 8.67527i) q^{93} +(-2.43314 + 4.21431i) q^{95} +(8.61075 + 14.9143i) q^{97} +(3.63867 - 0.102910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5}+O(q^{10}) \) 48 * q - 24 * q^5	\( 48 q - 24 q^{5} - 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} - 16 q^{39} + 12 q^{41} - 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} + 12 q^{61} - 56 q^{63} - 40 q^{69} - 8 q^{81} + 60 q^{83} - 36 q^{87} + 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 - 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 - 16 * q^39 + 12 * q^41 - 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 + 12 * q^61 - 56 * q^63 - 40 * q^69 - 8 * q^81 + 60 * q^83 - 36 * q^87 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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