LMFDB - Embedded newform 1120.2.bq.b.1039.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(719,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("1120.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bq (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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1039.14
Character	$\chi$	$=$	1120.1039
Dual form			1120.2.bq.b.719.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.818911 + 1.41839i) q^{3} +(2.22815 + 0.187962i) q^{5} +(2.64158 - 0.148518i) q^{7} +(0.158771 + 0.274999i) q^{9} +O(q^{10})$	\(q+(-0.818911 + 1.41839i) q^{3} +(2.22815 + 0.187962i) q^{5} +(2.64158 - 0.148518i) q^{7} +(0.158771 + 0.274999i) q^{9} +(2.19380 - 3.79978i) q^{11} +2.75493i q^{13} +(-2.09126 + 3.00648i) q^{15} +(0.648108 - 1.12256i) q^{17} +(3.86514 - 2.23154i) q^{19} +(-1.95256 + 3.86843i) q^{21} +(0.136303 + 0.236084i) q^{23} +(4.92934 + 0.837616i) q^{25} -5.43354 q^{27} -9.84349i q^{29} +(2.27724 - 3.94429i) q^{31} +(3.59306 + 6.22335i) q^{33} +(5.91376 + 0.165595i) q^{35} +(-3.94827 - 6.83861i) q^{37} +(-3.90758 - 2.25604i) q^{39} +3.95081i q^{41} +4.46362i q^{43} +(0.302076 + 0.642583i) q^{45} +(-7.22329 + 4.17037i) q^{47} +(6.95588 - 0.784646i) q^{49} +(1.06148 + 1.83855i) q^{51} +(-5.40022 + 9.35345i) q^{53} +(5.60234 - 8.05413i) q^{55} +7.30972i q^{57} +(-3.31684 - 1.91498i) q^{59} +(4.73907 + 8.20831i) q^{61} +(0.460248 + 0.702851i) q^{63} +(-0.517823 + 6.13841i) q^{65} +(8.32812 + 4.80824i) q^{67} -0.446480 q^{69} -1.42046i q^{71} +(-1.84745 + 3.19988i) q^{73} +(-5.22476 + 6.30582i) q^{75} +(5.23077 - 10.3632i) q^{77} +(-12.3237 + 7.11507i) q^{79} +(3.97327 - 6.88191i) q^{81} +12.8354 q^{83} +(1.65508 - 2.37941i) q^{85} +(13.9620 + 8.06094i) q^{87} +(-3.15758 + 1.82303i) q^{89} +(0.409158 + 7.27737i) q^{91} +(3.72971 + 6.46005i) q^{93} +(9.03157 - 4.24571i) q^{95} +0.0199224 q^{97} +1.39325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 52 q^{9}+O(q^{10}) $ 80 * q - 52 * q^9	$ 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) $ 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	−0.818911	+	1.41839i	−0.472798	+	0.818911i	−0.999515	−	0.0311300i	$-0.990089\pi$
$3$	−0.818911	+	1.41839i	−0.472798	+	0.818911i	0.526717	+	0.850041i	$0.323423\pi$
$4$		0			0
$5$	2.22815	+	0.187962i	0.996461	+	0.0840591i
$5$	2.22815	+	0.187962i	0.996461	+	0.0840591i
$6$		0			0
$7$	2.64158	−	0.148518i	0.998423	−	0.0561347i
$7$	2.64158	−	0.148518i	0.998423	−	0.0561347i
$8$		0			0
$9$	0.158771	+	0.274999i	0.0529235	+	0.0916663i
$10$		0			0
$11$	2.19380	−	3.79978i	0.661456	−	1.14568i	−0.318777	−	0.947830i	$-0.603272\pi$
$11$	2.19380	−	3.79978i	0.661456	−	1.14568i	0.980233	−	0.197846i	$-0.0633945\pi$
$12$		0			0
$13$			2.75493i			0.764081i	0.924146	+	0.382040i	$0.124779\pi$
$13$			2.75493i			0.764081i	−0.924146	+	0.382040i	$0.875221\pi$
$14$		0			0
$15$	−2.09126	+	3.00648i	−0.539962	+	0.776269i
$16$		0			0
$17$	0.648108	−	1.12256i	0.157189	−	0.272260i	−0.776665	−	0.629914i	$-0.783090\pi$
$17$	0.648108	−	1.12256i	0.157189	−	0.272260i	0.933854	+	0.357654i	$0.116423\pi$
$18$		0			0
$19$	3.86514	−	2.23154i	0.886723	−	0.511950i	0.0138541	−	0.999904i	$-0.495590\pi$
$19$	3.86514	−	2.23154i	0.886723	−	0.511950i	0.872869	+	0.487954i	$0.162257\pi$
$20$		0			0
$21$	−1.95256	+	3.86843i	−0.426084	+	0.844160i
$22$		0			0
$23$	0.136303	+	0.236084i	0.0284211	+	0.0492269i	0.879886	−	0.475185i	$-0.157619\pi$
$23$	0.136303	+	0.236084i	0.0284211	+	0.0492269i	−0.851465	+	0.524411i	$0.824285\pi$
$24$		0			0
$25$	4.92934	+	0.837616i	0.985868	+	0.167523i
$26$		0			0
$27$	−5.43354			−1.04569
$28$		0			0
$29$		−	9.84349i		−	1.82789i	−0.405838	−	0.913945i	$-0.633020\pi$
$29$		−	9.84349i		−	1.82789i	0.405838	−	0.913945i	$-0.366980\pi$
$30$		0			0
$31$	2.27724	−	3.94429i	0.409004	−	0.708416i	−0.585774	−	0.810474i	$-0.699209\pi$
$31$	2.27724	−	3.94429i	0.409004	−	0.708416i	0.994778	+	0.102058i	$0.0325428\pi$
$32$		0			0
$33$	3.59306	+	6.22335i	0.625471	+	1.08335i
$34$		0			0
$35$	5.91376	+	0.165595i	0.999608	+	0.0279906i
$36$		0			0
$37$	−3.94827	−	6.83861i	−0.649092	−	1.12426i	−0.983340	−	0.181775i	$-0.941816\pi$
$37$	−3.94827	−	6.83861i	−0.649092	−	1.12426i	0.334248	−	0.942485i	$-0.391518\pi$
$38$		0			0
$39$	−3.90758	−	2.25604i	−0.625714	−	0.361256i
$40$		0			0
$41$			3.95081i			0.617013i	0.951222	+	0.308507i	$0.0998292\pi$
$41$			3.95081i			0.617013i	−0.951222	+	0.308507i	$0.900171\pi$
$42$		0			0
$43$			4.46362i			0.680696i	0.940300	+	0.340348i	$0.110545\pi$
$43$			4.46362i			0.680696i	−0.940300	+	0.340348i	$0.889455\pi$
$44$		0			0
$45$	0.302076	+	0.642583i	0.0450309	+	0.0957906i
$46$		0			0
$47$	−7.22329	+	4.17037i	−1.05363	+	0.608311i	−0.923662	−	0.383208i	$-0.874819\pi$
$47$	−7.22329	+	4.17037i	−1.05363	+	0.608311i	−0.129963	+	0.991519i	$0.541486\pi$
$48$		0			0
$49$	6.95588	−	0.784646i	0.993698	−	0.112092i
$50$		0			0
$51$	1.06148	+	1.83855i	0.148638	+	0.257448i
$52$		0			0
$53$	−5.40022	+	9.35345i	−0.741777	+	1.28479i	0.209909	+	0.977721i	$0.432683\pi$
$53$	−5.40022	+	9.35345i	−0.741777	+	1.28479i	−0.951686	+	0.307074i	$0.900650\pi$
$54$		0			0
$55$	5.60234	−	8.05413i	0.755420	−	1.08602i
$56$		0			0
$57$			7.30972i			0.968196i
$58$		0			0
$59$	−3.31684	−	1.91498i	−0.431816	−	0.249309i	0.268304	−	0.963334i	$-0.413537\pi$
$59$	−3.31684	−	1.91498i	−0.431816	−	0.249309i	−0.700120	+	0.714025i	$0.746870\pi$
$60$		0			0
$61$	4.73907	+	8.20831i	0.606776	+	1.05097i	0.991768	+	0.128047i	$0.0408708\pi$
$61$	4.73907	+	8.20831i	0.606776	+	1.05097i	−0.384992	+	0.922920i	$0.625796\pi$
$62$		0			0
$63$	0.460248	+	0.702851i	0.0579858	+	0.0885509i
$64$		0			0
$65$	−0.517823	+	6.13841i	−0.0642280	+	0.761377i
$66$		0			0
$67$	8.32812	+	4.80824i	1.01744	+	0.587420i	0.913362	−	0.407149i	$-0.133477\pi$
$67$	8.32812	+	4.80824i	1.01744	+	0.587420i	0.104079	+	0.994569i	$0.466810\pi$
$68$		0			0
$69$	−0.446480			−0.0537499
$70$		0			0
$71$		−	1.42046i		−	0.168578i	−0.996441	−	0.0842888i	$-0.973138\pi$
$71$		−	1.42046i		−	0.168578i	0.996441	−	0.0842888i	$-0.0268618\pi$
$72$		0			0
$73$	−1.84745	+	3.19988i	−0.216228	+	0.374518i	−0.953652	−	0.300912i	$-0.902709\pi$
$73$	−1.84745	+	3.19988i	−0.216228	+	0.374518i	0.737424	+	0.675430i	$0.236042\pi$
$74$		0			0
$75$	−5.22476	+	6.30582i	−0.603303	+	0.728133i
$76$		0			0
$77$	5.23077	−	10.3632i	0.596101	−	1.18100i
$78$		0			0
$79$	−12.3237	+	7.11507i	−1.38652	+	0.800508i	−0.992921	−	0.118774i	$-0.962104\pi$
$79$	−12.3237	+	7.11507i	−1.38652	+	0.800508i	−0.393599	+	0.919282i	$0.628770\pi$
$80$		0			0
$81$	3.97327	−	6.88191i	0.441475	−	0.764657i
$82$		0			0
$83$	12.8354			1.40887			0.704435	−	0.709769i	$-0.251201\pi$
$83$	12.8354			1.40887			0.704435	+	0.709769i	$0.251201\pi$
$84$		0			0
$85$	1.65508	−	2.37941i	0.179519	−	0.258083i
$86$		0			0
$87$	13.9620	+	8.06094i	1.49688	+	0.864223i
$88$		0			0
$89$	−3.15758	+	1.82303i	−0.334703	+	0.193241i	−0.657927	−	0.753082i	$-0.728567\pi$
$89$	−3.15758	+	1.82303i	−0.334703	+	0.193241i	0.323224	+	0.946322i	$0.395233\pi$
$90$		0			0
$91$	0.409158	+	7.27737i	0.0428914	+	0.762876i
$92$		0			0
$93$	3.72971	+	6.46005i	0.386753	+	0.669876i
$94$		0			0
$95$	9.03157	−	4.24571i	0.926619	−	0.435601i
$96$		0			0
$97$	0.0199224			0.00202282			0.00101141	−	0.999999i	$-0.499678\pi$
$97$	0.0199224			0.00202282			0.00101141	+	0.999999i	$0.499678\pi$
$98$		0			0
$99$	1.39325			0.140026
$100$		0			0
$101$	−3.28413	+	5.68828i	−0.326783	+	0.566005i	−0.981872	−	0.189547i	$-0.939298\pi$
$101$	−3.28413	+	5.68828i	−0.326783	+	0.566005i	0.655088	+	0.755552i	$0.272631\pi$
$102$		0			0
$103$	−9.28337	+	5.35976i	−0.914718	+	0.528112i	−0.881946	−	0.471350i	$-0.843767\pi$
$103$	−9.28337	+	5.35976i	−0.914718	+	0.528112i	−0.0327715	+	0.999463i	$0.510433\pi$
$104$		0			0
$105$	−5.07772	+	8.25244i	−0.495535	+	0.805356i
$106$		0			0
$107$	2.95557	−	1.70640i	0.285725	−	0.164964i	−0.350287	−	0.936642i	$-0.613916\pi$
$107$	2.95557	−	1.70640i	0.285725	−	0.164964i	0.636013	+	0.771679i	$0.280583\pi$
$108$		0			0
$109$	−7.73766	−	4.46734i	−0.741134	−	0.427894i	0.0813476	−	0.996686i	$-0.474078\pi$
$109$	−7.73766	−	4.46734i	−0.741134	−	0.427894i	−0.822481	+	0.568792i	$0.807411\pi$
$110$		0			0
$111$	12.9331			1.22756
$112$		0			0
$113$		−	9.31026i		−	0.875836i	−0.899015	−	0.437918i	$-0.855716\pi$
$113$		−	9.31026i		−	0.875836i	0.899015	−	0.437918i	$-0.144284\pi$
$114$		0			0
$115$	0.259329	+	0.551651i	0.0241826	+	0.0514417i
$116$		0			0
$117$	−0.757603	+	0.437402i	−0.0700405	+	0.0404379i
$118$		0			0
$119$	1.54531	−	3.06158i	0.141658	−	0.280654i
$120$		0			0
$121$	−4.12553	−	7.14563i	−0.375048	−	0.649603i
$122$		0			0
$123$	−5.60381	−	3.23536i	−0.505279	−	0.291723i
$124$		0			0
$125$	10.8259	+	2.79287i	0.968297	+	0.249802i
$126$		0			0
$127$	−2.88968			−0.256418			−0.128209	−	0.991747i	$-0.540923\pi$
$127$	−2.88968			−0.256418			−0.128209	+	0.991747i	$0.540923\pi$
$128$		0			0
$129$	−6.33118	−	3.65531i	−0.557429	−	0.321832i
$130$		0			0
$131$	0.191301	−	0.110448i	0.0167140	−	0.00964984i	−0.491620	−	0.870810i	$-0.663595\pi$
$131$	0.191301	−	0.110448i	0.0167140	−	0.00964984i	0.508334	+	0.861160i	$0.330262\pi$
$132$		0			0
$133$	9.87864	−	6.46883i	0.856587	−	0.560919i
$134$		0			0
$135$	−12.1068	−	1.02130i	−1.04198	−	0.0878994i
$136$		0			0
$137$	−1.81703	−	1.04906i	−0.155239	−	0.0896274i	0.420368	−	0.907354i	$-0.361901\pi$
$137$	−1.81703	−	1.04906i	−0.155239	−	0.0896274i	−0.575607	+	0.817726i	$0.695234\pi$
$138$		0			0
$139$			16.0797i			1.36387i	0.731415	+	0.681933i	$0.238860\pi$
$139$			16.0797i			1.36387i	−0.731415	+	0.681933i	$0.761140\pi$
$140$		0			0
$141$		−	13.6606i		−	1.15043i
$142$		0			0
$143$	10.4681	+	6.04378i	0.875389	+	0.505406i
$144$		0			0
$145$	1.85020	−	21.9328i	0.153651	−	1.82142i
$146$		0			0
$147$	−4.58331	+	10.5087i	−0.378025	+	0.866747i
$148$		0			0
$149$	−10.5922	+	6.11539i	−0.867744	+	0.500992i	−0.866598	−	0.499007i	$-0.833698\pi$
$149$	−10.5922	+	6.11539i	−0.867744	+	0.500992i	−0.00114601	+	0.999999i	$0.500365\pi$
$150$		0			0
$151$	−5.37065	−	3.10075i	−0.437058	−	0.252335i	0.265291	−	0.964168i	$-0.414532\pi$
$151$	−5.37065	−	3.10075i	−0.437058	−	0.252335i	−0.702349	+	0.711833i	$0.747865\pi$
$152$		0			0
$153$	0.411602			0.0332760
$154$		0			0
$155$	5.81542	−	8.36046i	0.467106	−	0.671528i
$156$		0			0
$157$	−8.45018	−	4.87872i	−0.674398	−	0.389364i	0.123343	−	0.992364i	$-0.460638\pi$
$157$	−8.45018	−	4.87872i	−0.674398	−	0.389364i	−0.797741	+	0.603000i	$0.793972\pi$
$158$		0			0
$159$	−8.84459	−	15.3193i	−0.701422	−	1.21490i
$160$		0			0
$161$	0.395118	+	0.603390i	0.0311397	+	0.0475538i
$162$		0			0
$163$	−11.6016	+	6.69821i	−0.908711	+	0.524644i	−0.880016	−	0.474944i	$-0.842468\pi$
$163$	−11.6016	+	6.69821i	−0.908711	+	0.524644i	−0.0286947	+	0.999588i	$0.509135\pi$
$164$		0			0
$165$	6.83613	+	14.5419i	0.532192	+	1.13209i
$166$		0			0
$167$		−	0.950030i		−	0.0735155i	−0.999324	−	0.0367578i	$-0.988297\pi$
$167$		−	0.950030i		−	0.0735155i	0.999324	−	0.0367578i	$-0.0117030\pi$
$168$		0			0
$169$	5.41034			0.416180
$170$		0			0
$171$	1.22734	+	0.708606i	0.0938571	+	0.0541884i
$172$		0			0
$173$	−6.18561	+	3.57127i	−0.470283	+	0.271518i	−0.716358	−	0.697733i	$-0.754192\pi$
$173$	−6.18561	+	3.57127i	−0.470283	+	0.271518i	0.246075	+	0.969251i	$0.420859\pi$
$174$		0			0
$175$	13.1456	+	1.48053i	0.993717	+	0.111918i
$176$		0			0
$177$	5.43239	−	3.13639i	0.408324	−	0.235746i
$178$		0			0
$179$	1.57410	−	2.72641i	0.117653	−	0.203782i	−0.801184	−	0.598418i	$-0.795796\pi$
$179$	1.57410	−	2.72641i	0.117653	−	0.203782i	0.918837	+	0.394636i	$0.129129\pi$
$180$		0			0
$181$	16.4575			1.22328			0.611640	−	0.791136i	$-0.290510\pi$
$181$	16.4575			1.22328			0.611640	+	0.791136i	$0.290510\pi$
$182$		0			0
$183$	−15.5235			−1.14753
$184$		0			0
$185$	−7.51196	−	15.9796i	−0.552290	−	1.17484i
$186$		0			0
$187$	−2.84364	−	4.92533i	−0.207948	−	0.360176i
$188$		0			0
$189$	−14.3531	+	0.806980i	−1.04404	+	0.0586992i
$190$		0			0
$191$	−13.9077	+	8.02964i	−1.00633	+	0.581004i	−0.910115	−	0.414357i	$-0.864007\pi$
$191$	−13.9077	+	8.02964i	−1.00633	+	0.581004i	−0.0962140	+	0.995361i	$0.530673\pi$
$192$		0			0
$193$	−14.2638	−	8.23520i	−1.02673	−	0.592783i	−0.110684	−	0.993856i	$-0.535304\pi$
$193$	−14.2638	−	8.23520i	−1.02673	−	0.592783i	−0.916046	+	0.401073i	$0.868637\pi$
$194$		0			0
$195$	−8.28265	−	5.76129i	−0.593133	−	0.412575i
$196$		0			0
$197$	−4.67126			−0.332814			−0.166407	−	0.986057i	$-0.553216\pi$
$197$	−4.67126			−0.332814			−0.166407	+	0.986057i	$0.553216\pi$
$198$		0			0
$199$	5.83140	−	10.1003i	0.413377	−	0.715990i	−0.581879	−	0.813275i	$-0.697682\pi$
$199$	5.83140	−	10.1003i	0.413377	−	0.715990i	0.995257	+	0.0972849i	$0.0310158\pi$
$200$		0			0
$201$	−13.6400	+	7.87504i	−0.962089	+	0.555462i
$202$		0			0
$203$	−1.46194	−	26.0024i	−0.102608	−	1.82501i
$204$		0			0
$205$	−0.742602	+	8.80302i	−0.0518656	+	0.614829i
$206$		0			0
$207$	−0.0432818	+	0.0749663i	−0.00300829	+	0.00521052i
$208$		0			0
$209$		−	19.5822i		−	1.35453i
$210$		0			0
$211$	−14.7790			−1.01743			−0.508714	−	0.860936i	$-0.669879\pi$
$211$	−14.7790			−1.01743			−0.508714	+	0.860936i	$0.669879\pi$
$212$		0			0
$213$	2.01477	+	1.16323i	0.138050	+	0.0797032i
$214$		0			0
$215$	−0.838991	+	9.94563i	−0.0572187	+	0.678287i
$216$		0			0
$217$	5.42971	−	10.7574i	0.368593	−	0.730258i
$218$		0			0
$219$	−3.02580	−	5.24084i	−0.204464	−	0.354143i
$220$		0			0
$221$	3.09257	+	1.78549i	0.208028	+	0.120105i
$222$		0			0
$223$		−	7.00259i		−	0.468928i	−0.972125	−	0.234464i	$-0.924666\pi$
$223$		−	7.00259i		−	0.468928i	0.972125	−	0.234464i	$-0.0753335\pi$
$224$		0			0
$225$	0.552291	+	1.48855i	0.0368194	+	0.0992368i
$226$		0			0
$227$	10.2610	−	17.7725i	0.681043	−	1.17960i	−0.293619	−	0.955922i	$-0.594860\pi$
$227$	10.2610	−	17.7725i	0.681043	−	1.17960i	0.974663	−	0.223679i	$-0.0718068\pi$
$228$		0			0
$229$	−12.4920	−	21.6368i	−0.825496	−	1.42980i	−0.901539	−	0.432697i	$-0.857562\pi$
$229$	−12.4920	−	21.6368i	−0.825496	−	1.42980i	0.0760431	−	0.997105i	$-0.475771\pi$
$230$		0			0
$231$	10.4156	+	15.9058i	0.685298	+	1.04653i
$232$		0			0
$233$	3.61112	−	2.08488i	0.236572	−	0.136585i	−0.377028	−	0.926202i	$-0.623054\pi$
$233$	3.61112	−	2.08488i	0.236572	−	0.136585i	0.613600	+	0.789617i	$0.289721\pi$
$234$		0			0
$235$	−16.8785	+	7.93452i	−1.10103	+	0.517591i
$236$		0			0
$237$		−	23.3064i		−	1.51392i
$238$		0			0
$239$		−	26.5365i		−	1.71651i	−0.513228	−	0.858253i	$-0.671550\pi$
$239$		−	26.5365i		−	1.71651i	0.513228	−	0.858253i	$-0.328450\pi$
$240$		0			0
$241$	26.1925	+	15.1223i	1.68721	+	0.974110i	0.956641	+	0.291268i	$0.0940772\pi$
$241$	26.1925	+	15.1223i	1.68721	+	0.974110i	0.730566	+	0.682842i	$0.239256\pi$
$242$		0			0
$243$	−1.64280	−	2.84541i	−0.105386	−	0.182533i
$244$		0			0
$245$	15.6463	−	0.440870i	0.999603	−	0.0281662i
$246$		0			0
$247$	6.14774	+	10.6482i	0.391171	+	0.677528i
$248$		0			0
$249$	−10.5111	+	18.2057i	−0.666111	+	1.15374i
$250$		0			0
$251$		−	21.4077i		−	1.35124i	−0.737250	−	0.675620i	$-0.763876\pi$
$251$		−	21.4077i		−	1.35124i	0.737250	−	0.675620i	$-0.236124\pi$
$252$		0			0
$253$	1.19609			0.0751973
$254$		0			0
$255$	2.01957	+	4.29608i	0.126471	+	0.269031i
$256$		0			0
$257$	−4.90535	−	8.49632i	−0.305988	−	0.529986i	0.671493	−	0.741011i	$-0.265653\pi$
$257$	−4.90535	−	8.49632i	−0.305988	−	0.529986i	−0.977481	+	0.211025i	$0.932320\pi$
$258$		0			0
$259$	−11.4453	−	17.4783i	−0.711178	−	1.08605i
$260$		0			0
$261$	2.70695	−	1.56286i	0.167556	−	0.0967384i
$262$		0			0
$263$	6.21557	−	10.7657i	0.383268	−	0.663840i	−0.608259	−	0.793739i	$-0.708132\pi$
$263$	6.21557	−	10.7657i	0.383268	−	0.663840i	0.991527	+	0.129898i	$0.0414651\pi$
$264$		0			0
$265$	−13.7906	+	19.8259i	−0.847150	+	1.21789i
$266$		0			0
$267$		−	5.97160i		−	0.365456i
$268$		0			0
$269$	−3.48319	+	6.03307i	−0.212374	+	0.367843i	−0.952457	−	0.304673i	$-0.901453\pi$
$269$	−3.48319	+	6.03307i	−0.212374	+	0.367843i	0.740083	+	0.672516i	$0.234786\pi$
$270$		0			0
$271$	13.3991	+	23.2079i	0.813935	+	1.40978i	0.910090	+	0.414411i	$0.136012\pi$
$271$	13.3991	+	23.2079i	0.813935	+	1.40978i	−0.0961544	+	0.995366i	$0.530654\pi$
$272$		0			0
$273$	−10.6573	−	5.37917i	−0.645006	−	0.325562i
$274$		0			0
$275$	13.9967	−	16.8928i	0.844036	−	1.01868i
$276$		0			0
$277$	−8.59103	+	14.8801i	−0.516185	+	0.894058i	0.483639	+	0.875268i	$0.339315\pi$
$277$	−8.59103	+	14.8801i	−0.516185	+	0.894058i	−0.999823	+	0.0187904i	$0.994018\pi$
$278$		0			0
$279$	1.44624			0.0865838
$280$		0			0
$281$	−24.3194			−1.45078			−0.725388	−	0.688341i	$-0.758339\pi$
$281$	−24.3194			−1.45078			−0.725388	+	0.688341i	$0.758339\pi$
$282$		0			0
$283$	−5.66683	+	9.81524i	−0.336858	+	0.583455i	−0.983840	−	0.179050i	$-0.942698\pi$
$283$	−5.66683	+	9.81524i	−0.336858	+	0.583455i	0.646982	+	0.762505i	$0.276031\pi$
$284$		0			0
$285$	−1.37395	+	16.2872i	−0.0813858	+	0.964770i
$286$		0			0
$287$	0.586768	+	10.4364i	0.0346358	+	0.616040i
$288$		0			0
$289$	7.65991	+	13.2674i	0.450583	+	0.780433i
$290$		0			0
$291$	−0.0163147	+	0.0282579i	−0.000956384	+	0.00165650i
$292$		0			0
$293$		−	13.5647i		−	0.792460i	−0.918151	−	0.396230i	$-0.870318\pi$
$293$		−	13.5647i		−	0.792460i	0.918151	−	0.396230i	$-0.129682\pi$
$294$		0			0
$295$	−7.03049	−	4.89031i	−0.409331	−	0.284725i
$296$		0			0
$297$	−11.9201	+	20.6462i	−0.691675	+	1.19802i
$298$		0			0
$299$	−0.650395	+	0.375506i	−0.0376133	+	0.0217160i
$300$		0			0
$301$	0.662929	+	11.7910i	0.0382106	+	0.679622i
$302$		0			0
$303$	−5.37882	−	9.31639i	−0.309005	−	0.535213i
$304$		0			0
$305$	9.01653	+	19.1801i	0.516285	+	1.09825i
$306$		0			0
$307$	−20.1572			−1.15043			−0.575216	−	0.818002i	$-0.695082\pi$
$307$	−20.1572			−1.15043			−0.575216	+	0.818002i	$0.695082\pi$
$308$		0			0
$309$		−	17.5566i		−	0.998763i
$310$		0			0
$311$	−6.65610	+	11.5287i	−0.377433	+	0.653733i	−0.990688	−	0.136152i	$-0.956526\pi$
$311$	−6.65610	+	11.5287i	−0.377433	+	0.653733i	0.613255	+	0.789885i	$0.289860\pi$
$312$		0			0
$313$	13.3898	+	23.1919i	0.756838	+	1.31088i	0.944456	+	0.328639i	$0.106590\pi$
$313$	13.3898	+	23.1919i	0.756838	+	1.31088i	−0.187618	+	0.982242i	$0.560077\pi$
$314$		0			0
$315$	0.893393	+	1.65257i	0.0503370	+	0.0931117i
$316$		0			0
$317$	15.3924	+	26.6604i	0.864524	+	1.49740i	0.867519	+	0.497403i	$0.165713\pi$
$317$	15.3924	+	26.6604i	0.864524	+	1.49740i	−0.00299582	+	0.999996i	$0.500954\pi$
$318$		0			0
$319$	−37.4031	−	21.5947i	−2.09417	−	1.20907i
$320$		0			0
$321$			5.58955i			0.311978i
$322$		0			0
$323$		−	5.78511i		−	0.321892i
$324$		0			0
$325$	−2.30758	+	13.5800i	−0.128001	+	0.753283i
$326$		0			0
$327$	12.6729	−	7.31671i	0.700814	−	0.404615i
$328$		0			0
$329$	−18.4615	+	12.0892i	−1.01782	+	0.666497i
$330$		0			0
$331$	2.30264	+	3.98829i	0.126564	+	0.219216i	0.922343	−	0.386371i	$-0.126272\pi$
$331$	2.30264	+	3.98829i	0.126564	+	0.219216i	−0.795779	+	0.605587i	$0.792938\pi$
$332$		0			0
$333$	1.25374	−	2.17154i	0.0687045	−	0.119000i
$334$		0			0
$335$	17.6526	+	12.2789i	0.964462	+	0.670866i
$336$		0			0
$337$		−	12.2970i		−	0.669862i	−0.942243	−	0.334931i	$-0.891287\pi$
$337$		−	12.2970i		−	0.669862i	0.942243	−	0.334931i	$-0.108713\pi$
$338$		0			0
$339$	13.2056	+	7.62427i	0.717231	+	0.414094i
$340$		0			0
$341$	−9.99162	−	17.3060i	−0.541077	−	0.937172i
$342$		0			0
$343$	18.2580	−	3.10578i	0.985839	−	0.167696i
$344$		0			0
$345$	−0.994826	−	0.0839212i	−0.0535596	−	0.00451817i
$346$		0			0
$347$	−6.93751	−	4.00537i	−0.372425	−	0.215020i	0.302092	−	0.953279i	$-0.402315\pi$
$347$	−6.93751	−	4.00537i	−0.372425	−	0.215020i	−0.674517	+	0.738259i	$0.735648\pi$
$348$		0			0
$349$	15.3254			0.820347			0.410174	−	0.912007i	$-0.365468\pi$
$349$	15.3254			0.820347			0.410174	+	0.912007i	$0.365468\pi$
$350$		0			0
$351$		−	14.9690i		−	0.798988i
$352$		0			0
$353$	14.7109	−	25.4800i	0.782981	−	1.35616i	−0.147216	−	0.989104i	$-0.547031\pi$
$353$	14.7109	−	25.4800i	0.782981	−	1.35616i	0.930198	−	0.367059i	$-0.119635\pi$
$354$		0			0
$355$	0.266992	−	3.16500i	0.0141705	−	0.167981i
$356$		0			0
$357$	3.07705	+	4.69901i	0.162855	+	0.248698i
$358$		0			0
$359$	−3.08814	+	1.78294i	−0.162986	+	0.0940998i	−0.579274	−	0.815133i	$-0.696664\pi$
$359$	−3.08814	+	1.78294i	−0.162986	+	0.0940998i	0.416289	+	0.909233i	$0.363331\pi$
$360$		0			0
$361$	0.459526	−	0.795923i	0.0241856	−	0.0418907i
$362$		0			0
$363$	13.5138			0.709289
$364$		0			0
$365$	−4.71787	+	6.78258i	−0.246944	+	0.355016i
$366$		0			0
$367$	−8.15253	−	4.70686i	−0.425558	−	0.245696i	0.271894	−	0.962327i	$-0.412350\pi$
$367$	−8.15253	−	4.70686i	−0.425558	−	0.245696i	−0.697453	+	0.716631i	$0.745683\pi$
$368$		0			0
$369$	−1.08647	+	0.627273i	−0.0565593	+	0.0326545i
$370$		0			0
$371$	−12.8759	+	25.5099i	−0.668486	+	1.32441i
$372$		0			0
$373$	−2.95853	−	5.12432i	−0.153187	−	0.265327i	0.779211	−	0.626762i	$-0.215620\pi$
$373$	−2.95853	−	5.12432i	−0.153187	−	0.265327i	−0.932397	+	0.361435i	$0.882287\pi$
$374$		0			0
$375$	−12.8268	+	13.0683i	−0.662374	+	0.674843i
$376$		0			0
$377$	27.1182			1.39666
$378$		0			0
$379$	−10.0919			−0.518388			−0.259194	−	0.965825i	$-0.583457\pi$
$379$	−10.0919			−0.518388			−0.259194	+	0.965825i	$0.583457\pi$
$380$		0			0
$381$	2.36639	−	4.09871i	0.121234	−	0.209983i
$382$		0			0
$383$	18.3760	−	10.6094i	0.938968	−	0.542113i	0.0493313	−	0.998782i	$-0.484291\pi$
$383$	18.3760	−	10.6094i	0.938968	−	0.542113i	0.889637	+	0.456669i	$0.150958\pi$
$384$		0			0
$385$	13.6028	−	22.1077i	0.693265	−	1.12671i
$386$		0			0
$387$	−1.22749	+	0.708692i	−0.0623968	+	0.0360248i
$388$		0			0
$389$	−17.0998	−	9.87258i	−0.866995	−	0.500560i	−0.000646573	−	1.00000i	$-0.500206\pi$
$389$	−17.0998	−	9.87258i	−0.866995	−	0.500560i	−0.866349	+	0.499440i	$0.833539\pi$
$390$		0			0
$391$	0.353356			0.0178700
$392$		0			0
$393$			0.361787i			0.0182497i
$394$		0			0
$395$	−28.7964	+	13.5371i	−1.44890	+	0.681125i
$396$		0			0
$397$	7.56788	−	4.36932i	0.379821	−	0.219290i	−0.297919	−	0.954591i	$-0.596293\pi$
$397$	7.56788	−	4.36932i	0.379821	−	0.219290i	0.677740	+	0.735301i	$0.262959\pi$
$398$		0			0
$399$	1.08563	+	19.3092i	0.0543494	+	0.966670i
$400$		0			0
$401$	−12.7155	−	22.0240i	−0.634984	−	1.09982i	−0.986519	−	0.163649i	$-0.947673\pi$
$401$	−12.7155	−	22.0240i	−0.634984	−	1.09982i	0.351535	−	0.936175i	$-0.385660\pi$
$402$		0			0
$403$	10.8663	+	6.27364i	0.541287	+	0.312512i
$404$		0			0
$405$	10.1466	−	14.5871i	0.504189	−	0.724840i
$406$		0			0
$407$	−34.6469			−1.71738
$408$		0			0
$409$	−10.4748	−	6.04761i	−0.517944	−	0.299035i	0.218149	−	0.975915i	$-0.429998\pi$
$409$	−10.4748	−	6.04761i	−0.517944	−	0.299035i	−0.736093	+	0.676880i	$0.763331\pi$
$410$		0			0
$411$	2.97597	−	1.71818i	0.146794	−	0.0847514i
$412$		0			0
$413$	−9.04611	−	4.56596i	−0.445130	−	0.224676i
$414$		0			0
$415$	28.5993	+	2.41257i	1.40388	+	0.118428i
$416$		0			0
$417$	−22.8074	−	13.1679i	−1.11688	−	0.644833i
$418$		0			0
$419$			12.5618i			0.613682i	0.951761	+	0.306841i	$0.0992719\pi$
$419$			12.5618i			0.613682i	−0.951761	+	0.306841i	$0.900728\pi$
$420$		0			0
$421$		−	3.98711i		−	0.194320i	−0.995269	−	0.0971600i	$-0.969024\pi$
$421$		−	3.98711i		−	0.194320i	0.995269	−	0.0971600i	$-0.0309759\pi$
$422$		0			0
$423$	−2.29369	−	1.32426i	−0.111523	−	0.0643879i
$424$		0			0
$425$	4.13501	−	4.99059i	0.200578	−	0.242079i
$426$		0			0
$427$	13.7377	+	20.9791i	0.664815	+	1.01525i
$428$		0			0
$429$	−17.1449	+	9.89863i	−0.827765	+	0.477910i
$430$		0			0
$431$	3.74772	+	2.16375i	0.180521	+	0.104224i	0.587538	−	0.809197i	$-0.300097\pi$
$431$	3.74772	+	2.16375i	0.180521	+	0.104224i	−0.407016	+	0.913421i	$0.633431\pi$
$432$		0			0
$433$	4.33970			0.208552			0.104276	−	0.994548i	$-0.466747\pi$
$433$	4.33970			0.208552			0.104276	+	0.994548i	$0.466747\pi$
$434$		0			0
$435$	29.5942	+	20.5853i	1.41894	+	0.986991i
$436$		0			0
$437$	1.05366	+	0.608331i	0.0504034	+	0.0291004i
$438$		0			0
$439$	4.07497	+	7.05805i	0.194488	+	0.336862i	0.946732	−	0.322021i	$-0.104362\pi$
$439$	4.07497	+	7.05805i	0.194488	+	0.336862i	−0.752245	+	0.658884i	$0.771029\pi$
$440$		0			0
$441$	1.32017	+	1.78828i	0.0628651	+	0.0851563i
$442$		0			0
$443$	−13.7175	+	7.91978i	−0.651737	+	0.376280i	−0.789121	−	0.614237i	$-0.789464\pi$
$443$	−13.7175	+	7.91978i	−0.651737	+	0.376280i	0.137385	+	0.990518i	$0.456130\pi$
$444$		0			0
$445$	−7.37824	+	3.46849i	−0.349762	+	0.164422i
$446$		0			0
$447$		−	20.0318i		−	0.947473i
$448$		0			0
$449$	35.2873			1.66531			0.832656	−	0.553790i	$-0.186819\pi$
$449$	35.2873			1.66531			0.832656	+	0.553790i	$0.186819\pi$
$450$		0			0
$451$	15.0122	+	8.66730i	0.706897	+	0.408127i
$452$		0			0
$453$	8.79617	−	5.07847i	0.413280	−	0.238607i
$454$		0			0
$455$	−0.456202	+	16.2920i	−0.0213871	+	0.763782i
$456$		0			0
$457$	−8.94810	+	5.16619i	−0.418574	+	0.241664i	−0.694467	−	0.719524i	$-0.744360\pi$
$457$	−8.94810	+	5.16619i	−0.418574	+	0.241664i	0.275893	+	0.961188i	$0.411027\pi$
$458$		0			0
$459$	−3.52152	+	6.09945i	−0.164370	+	0.284698i
$460$		0			0
$461$	17.9765			0.837247			0.418624	−	0.908160i	$-0.362513\pi$
$461$	17.9765			0.837247			0.418624	+	0.908160i	$0.362513\pi$
$462$		0			0
$463$	−10.7604			−0.500076			−0.250038	−	0.968236i	$-0.580443\pi$
$463$	−10.7604			−0.500076			−0.250038	+	0.968236i	$0.580443\pi$
$464$		0			0
$465$	7.09613	+	15.0950i	0.329075	+	0.700015i
$466$		0			0
$467$	−6.90606	−	11.9616i	−0.319574	−	0.553519i	0.660825	−	0.750540i	$-0.270207\pi$
$467$	−6.90606	−	11.9616i	−0.319574	−	0.553519i	−0.980399	+	0.197021i	$0.936873\pi$
$468$		0			0
$469$	22.7135	+	11.4645i	1.04881	+	0.529380i
$470$		0			0
$471$	13.8399	−	7.99046i	0.637708	−	0.368181i
$472$		0			0
$473$	16.9608	+	9.79230i	0.779856	+	0.450250i
$474$		0			0
$475$	20.9218	−	7.76251i	0.959956	−	0.356168i
$476$		0			0
$477$	−3.42958			−0.157030
$478$		0			0
$479$	−13.2230	+	22.9030i	−0.604176	+	1.04646i	0.388005	+	0.921657i	$0.373164\pi$
$479$	−13.2230	+	22.9030i	−0.604176	+	1.04646i	−0.992181	+	0.124807i	$0.960169\pi$
$480$		0			0
$481$	18.8399	−	10.8772i	0.859025	−	0.495959i
$482$		0			0
$483$	−1.17941	+	0.0663104i	−0.0536651	+	0.00301723i
$484$		0			0
$485$	0.0443902	+	0.00374466i	0.00201566	+	0.000170036i
$486$		0			0
$487$	−4.61070	+	7.98597i	−0.208931	+	0.361879i	−0.951378	−	0.308026i	$-0.900332\pi$
$487$	−4.61070	+	7.98597i	−0.208931	+	0.361879i	0.742447	+	0.669905i	$0.233665\pi$
$488$		0			0
$489$		−	21.9409i		−	0.992204i
$490$		0			0
$491$	5.89733			0.266143			0.133071	−	0.991106i	$-0.457516\pi$
$491$	5.89733			0.266143			0.133071	+	0.991106i	$0.457516\pi$
$492$		0			0
$493$	−11.0499	−	6.37964i	−0.497661	−	0.287325i
$494$		0			0
$495$	3.10436	+	0.261877i	0.139531	+	0.0117705i
$496$		0			0
$497$	−0.210964	−	3.75226i	−0.00946304	−	0.168312i
$498$		0			0
$499$	5.74782	+	9.95552i	0.257308	+	0.445670i	0.965520	−	0.260330i	$-0.0838313\pi$
$499$	5.74782	+	9.95552i	0.257308	+	0.445670i	−0.708212	+	0.706000i	$0.750498\pi$
$500$		0			0
$501$	1.34752	+	0.777990i	0.0602027	+	0.0347580i
$502$		0			0
$503$		−	34.0508i		−	1.51825i	−0.650944	−	0.759125i	$-0.725627\pi$
$503$		−	34.0508i		−	1.51825i	0.650944	−	0.759125i	$-0.274373\pi$
$504$		0			0
$505$	−8.38673	+	12.0571i	−0.373205	+	0.536533i
$506$		0			0
$507$	−4.43059	+	7.67400i	−0.196769	+	0.340815i
$508$		0			0
$509$	−3.48710	−	6.03983i	−0.154563	−	0.267711i	0.778337	−	0.627847i	$-0.216064\pi$
$509$	−3.48710	−	6.03983i	−0.154563	−	0.267711i	−0.932900	+	0.360136i	$0.882730\pi$
$510$		0			0
$511$	−4.40495	+	8.72713i	−0.194864	+	0.386065i
$512$		0			0
$513$	−21.0014	+	12.1252i	−0.927234	+	0.535339i
$514$		0			0
$515$	−21.6922	+	10.1974i	−0.955873	+	0.449353i
$516$		0			0
$517$			36.5958i			1.60948i
$518$		0			0
$519$		−	11.6982i		−	0.513494i
$520$		0			0
$521$	11.7331	+	6.77412i	0.514037	+	0.296780i	0.734492	−	0.678618i	$-0.237421\pi$
$521$	11.7331	+	6.77412i	0.514037	+	0.296780i	−0.220454	+	0.975397i	$0.570754\pi$
$522$		0			0
$523$	19.7080	+	34.1352i	0.861769	+	1.49263i	0.870220	+	0.492663i	$0.163976\pi$
$523$	19.7080	+	34.1352i	0.861769	+	1.49263i	−0.00845156	+	0.999964i	$0.502690\pi$
$524$		0			0
$525$	−12.8651	+	17.4333i	−0.561479	+	0.760851i
$526$		0			0
$527$	−2.95179	−	5.11266i	−0.128582	−	0.222711i
$528$		0			0
$529$	11.4628	−	19.8542i	0.498384	−	0.863227i
$530$		0			0
$531$		−	1.21617i		−	0.0527773i
$532$		0			0
$533$	−10.8842			−0.471448
$534$		0			0
$535$	6.90619	−	3.24658i	0.298581	−	0.140362i
$536$		0			0
$537$	2.57809	+	4.46538i	0.111253	+	0.192695i
$538$		0			0
$539$	12.2784	−	28.1522i	0.528866	−	1.21260i
$540$		0			0
$541$	−31.6007	+	18.2447i	−1.35862	+	0.784399i	−0.989438	−	0.144959i	$-0.953695\pi$
$541$	−31.6007	+	18.2447i	−1.35862	+	0.784399i	−0.369181	+	0.929358i	$0.620362\pi$
$542$		0			0
$543$	−13.4773	+	23.3433i	−0.578365	+	1.00176i
$544$		0			0
$545$	−16.4010	−	11.4083i	−0.702542	−	0.488678i
$546$		0			0
$547$		−	2.03370i		−	0.0869549i	−0.999054	−	0.0434775i	$-0.986156\pi$
$547$		−	2.03370i		−	0.0869549i	0.999054	−	0.0434775i	$-0.0138437\pi$
$548$		0			0
$549$	−1.50485	+	2.60648i	−0.0642255	+	0.111242i
$550$		0			0
$551$	−21.9661	−	38.0464i	−0.935788	−	1.62083i
$552$		0			0
$553$	−31.4972	+	20.6253i	−1.33940	+	0.877078i
$554$		0			0
$555$	28.8170	+	2.43094i	1.22321	+	0.103187i
$556$		0			0
$557$	12.2222	−	21.1695i	0.517871	−	0.896980i	−0.481913	−	0.876219i	$-0.660058\pi$
$557$	12.2222	−	21.1695i	0.517871	−	0.896980i	0.999784	−	0.0207606i	$-0.00660877\pi$
$558$		0			0
$559$	−12.2970			−0.520107
$560$		0			0
$561$	9.31475			0.393269
$562$		0			0
$563$	14.5272	−	25.1619i	0.612250	−	1.06045i	−0.378610	−	0.925556i	$-0.623598\pi$
$563$	14.5272	−	25.1619i	0.612250	−	1.06045i	0.990860	−	0.134892i	$-0.0430689\pi$
$564$		0			0
$565$	1.74998	−	20.7447i	0.0736220	−	0.872736i
$566$		0			0
$567$	9.47362	−	18.7692i	0.397855	−	0.788233i
$568$		0			0
$569$	−11.1856	−	19.3740i	−0.468923	−	0.812199i	0.530446	−	0.847719i	$-0.322025\pi$
$569$	−11.1856	−	19.3740i	−0.468923	−	0.812199i	−0.999369	+	0.0355198i	$0.988691\pi$
$570$		0			0
$571$	21.2867	−	36.8696i	0.890820	−	1.54295i	0.0519252	−	0.998651i	$-0.483464\pi$
$571$	21.2867	−	36.8696i	0.890820	−	1.54295i	0.838895	−	0.544294i	$-0.183202\pi$
$572$		0			0
$573$		−	26.3022i		−	1.09879i
$574$		0			0
$575$	0.474136	+	1.27791i	0.0197728	+	0.0532924i
$576$		0			0
$577$	−16.2853	+	28.2069i	−0.677965	+	1.17427i	0.297628	+	0.954682i	$0.403805\pi$
$577$	−16.2853	+	28.2069i	−0.677965	+	1.17427i	−0.975593	+	0.219588i	$0.929529\pi$
$578$		0			0
$579$	23.3615	−	13.4878i	0.970873	−	0.560534i
$580$		0			0
$581$	33.9058	−	1.90629i	1.40665	−	0.0790864i
$582$		0			0
$583$	23.6940	+	41.0392i	0.981305	+	1.69967i
$584$		0			0
$585$	−1.77027	+	0.832199i	−0.0731917	+	0.0344072i
$586$		0			0
$587$	21.4007			0.883301			0.441650	−	0.897187i	$-0.354393\pi$
$587$	21.4007			0.883301			0.441650	+	0.897187i	$0.354393\pi$
$588$		0			0
$589$		−	20.3270i		−	0.837559i
$590$		0			0
$591$	3.82535	−	6.62569i	0.157354	−	0.272545i
$592$		0			0
$593$	3.83778	+	6.64723i	0.157599	+	0.272969i	0.934002	−	0.357267i	$-0.116291\pi$
$593$	3.83778	+	6.64723i	0.157599	+	0.272969i	−0.776403	+	0.630236i	$0.782958\pi$
$594$		0			0
$595$	4.01864	−	6.53120i	0.164748	−	0.267753i
$596$		0			0
$597$	9.55079	+	16.5425i	0.390888	+	0.677038i
$598$		0			0
$599$	26.5598	+	15.3343i	1.08520	+	0.626543i	0.932296	−	0.361697i	$-0.117803\pi$
$599$	26.5598	+	15.3343i	1.08520	+	0.626543i	0.152909	+	0.988240i	$0.451136\pi$
$600$		0			0
$601$		−	4.23258i		−	0.172650i	−0.996267	−	0.0863252i	$-0.972488\pi$
$601$		−	4.23258i		−	0.172650i	0.996267	−	0.0863252i	$-0.0275124\pi$
$602$		0			0
$603$			3.05363i			0.124353i
$604$		0			0
$605$	−7.84921	−	16.6970i	−0.319116	−	0.678830i
$606$		0			0
$607$	−0.700185	+	0.404252i	−0.0284196	+	0.0164081i	−0.514142	−	0.857705i	$-0.671890\pi$
$607$	−0.700185	+	0.404252i	−0.0284196	+	0.0164081i	0.485723	+	0.874113i	$0.338556\pi$
$608$		0			0
$609$	38.0788	+	19.2200i	1.54303	+	0.778834i
$610$		0			0
$611$	−11.4891	−	19.8997i	−0.464799	−	0.805055i
$612$		0			0
$613$	15.9214	−	27.5766i	0.643058	−	1.11381i	−0.341689	−	0.939813i	$-0.610999\pi$
$613$	15.9214	−	27.5766i	0.643058	−	1.11381i	0.984746	−	0.173995i	$-0.0556678\pi$
$614$		0			0
$615$	−11.8780	−	8.26219i	−0.478968	−	0.333164i
$616$		0			0
$617$			23.7720i			0.957025i	0.878081	+	0.478513i	$0.158824\pi$
$617$			23.7720i			0.957025i	−0.878081	+	0.478513i	$0.841176\pi$
$618$		0			0
$619$	12.8725	+	7.43195i	0.517390	+	0.298715i	0.735866	−	0.677127i	$-0.236775\pi$
$619$	12.8725	+	7.43195i	0.517390	+	0.298715i	−0.218476	+	0.975842i	$0.570109\pi$
$620$		0			0
$621$	−0.740608	−	1.28277i	−0.0297196	−	0.0514758i
$622$		0			0
$623$	−8.07025	+	5.28464i	−0.323328	+	0.211725i
$624$		0			0
$625$	23.5968	+	8.25779i	0.943872	+	0.330312i
$626$		0			0
$627$	27.7753	+	16.0361i	1.10924	+	0.640419i
$628$		0			0
$629$	−10.2356			−0.408121
$630$		0			0
$631$			13.4670i			0.536112i	0.963403	+	0.268056i	$0.0863812\pi$
$631$			13.4670i			0.536112i	−0.963403	+	0.268056i	$0.913619\pi$
$632$		0			0
$633$	12.1027	−	20.9624i	0.481038	−	0.833182i
$634$		0			0
$635$	−6.43866	−	0.543151i	−0.255510	−	0.0215543i
$636$		0			0
$637$	2.16165	+	19.1630i	0.0856476	+	0.759266i
$638$		0			0
$639$	0.390625	−	0.225527i	0.0154529	−	0.00892172i
$640$		0			0
$641$	17.8399	−	30.8996i	0.704634	−	1.22046i	−0.262189	−	0.965016i	$-0.584445\pi$
$641$	17.8399	−	30.8996i	0.704634	−	1.22046i	0.966823	−	0.255445i	$-0.0822221\pi$
$642$		0			0
$643$	−18.9130			−0.745857			−0.372929	−	0.927860i	$-0.621646\pi$
$643$	−18.9130			−0.745857			−0.372929	+	0.927860i	$0.621646\pi$
$644$		0			0
$645$	−13.4198	−	9.33461i	−0.528403	−	0.367550i
$646$		0			0
$647$	−20.2631	−	11.6989i	−0.796625	−	0.459932i	0.0456648	−	0.998957i	$-0.485459\pi$
$647$	−20.2631	−	11.6989i	−0.796625	−	0.459932i	−0.842290	+	0.539025i	$0.818793\pi$
$648$		0			0
$649$	−14.5530	+	8.40217i	−0.571254	+	0.329814i
$650$		0			0
$651$	10.8118	+	16.5108i	0.423746	+	0.647109i
$652$		0			0
$653$	14.7067	+	25.4728i	0.575519	+	0.996829i	0.995985	+	0.0895203i	$0.0285334\pi$
$653$	14.7067	+	25.4728i	0.575519	+	0.996829i	−0.420466	+	0.907308i	$0.638133\pi$
$654$		0			0
$655$	0.447007	−	0.210137i	0.0174660	−	0.00821072i
$656$		0			0
$657$	−1.17329			−0.0457742
$658$		0			0
$659$	−33.7483			−1.31465			−0.657323	−	0.753609i	$-0.728311\pi$
$659$	−33.7483			−1.31465			−0.657323	+	0.753609i	$0.728311\pi$
$660$		0			0
$661$	−21.6521	+	37.5025i	−0.842168	+	1.45868i	0.0458899	+	0.998947i	$0.485388\pi$
$661$	−21.6521	+	37.5025i	−0.842168	+	1.45868i	−0.888058	+	0.459731i	$0.847946\pi$
$662$		0			0
$663$	−5.06507	+	2.92432i	−0.196711	+	0.113571i
$664$		0			0
$665$	23.2270	−	12.5567i	0.900706	−	0.486929i
$666$		0			0
$667$	2.32389	−	1.34170i	0.0899813	−	0.0519507i
$668$		0			0
$669$	9.93244	+	5.73450i	0.384010	+	0.221708i
$670$		0			0
$671$	41.5863			1.60542
$672$		0			0
$673$			8.11472i			0.312799i	0.987694	+	0.156400i	$0.0499888\pi$
$673$			8.11472i			0.312799i	−0.987694	+	0.156400i	$0.950011\pi$
$674$		0			0
$675$	−26.7838	−	4.55122i	−1.03091	−	0.175177i
$676$		0			0
$677$	−37.9364	+	21.9026i	−1.45802	+	0.841786i	−0.998914	−	0.0465975i	$-0.985162\pi$
$677$	−37.9364	+	21.9026i	−1.45802	+	0.841786i	−0.459102	+	0.888383i	$0.651829\pi$
$678$		0			0
$679$	0.0526267	−	0.00295884i	0.00201963	−	0.000113550i
$680$		0			0
$681$	16.8056	+	29.1082i	0.643992	+	1.11543i
$682$		0			0
$683$	20.0699	+	11.5874i	0.767954	+	0.443378i	0.832144	−	0.554559i	$-0.187113\pi$
$683$	20.0699	+	11.5874i	0.767954	+	0.443378i	−0.0641905	+	0.997938i	$0.520447\pi$
$684$		0			0
$685$	−3.85144	−	2.67900i	−0.147156	−	0.102359i
$686$		0			0
$687$	40.9194			1.56117
$688$		0			0
$689$	−25.7681	−	14.8772i	−0.981687	−	0.566777i
$690$		0			0
$691$	−25.5204	+	14.7342i	−0.970842	+	0.560516i	−0.899493	−	0.436935i	$-0.856064\pi$
$691$	−25.5204	+	14.7342i	−0.970842	+	0.560516i	−0.0713493	+	0.997451i	$0.522731\pi$
$692$		0			0
$693$	3.68037	−	0.206922i	0.139806	−	0.00786033i
$694$		0			0
$695$	−3.02238	+	35.8281i	−0.114645	+	1.35904i
$696$		0			0
$697$	4.43501	+	2.56055i	0.167988	+	0.0969878i
$698$		0			0
$699$			6.82932i			0.258308i
$700$		0			0
$701$			13.3928i			0.505839i	0.967487	+	0.252919i	$0.0813907\pi$
$701$			13.3928i			0.505839i	−0.967487	+	0.252919i	$0.918609\pi$
$702$		0			0
$703$	−30.5212	−	17.6214i	−1.15113	−	0.664605i
$704$		0			0
$705$	2.56768	−	30.4380i	0.0967044	−	1.14636i
$706$		0			0
$707$	−7.83048	+	15.5138i	−0.294496	+	0.583457i
$708$		0			0
$709$	24.6438	−	14.2281i	0.925519	−	0.534349i	0.0401274	−	0.999195i	$-0.487224\pi$
$709$	24.6438	−	14.2281i	0.925519	−	0.534349i	0.885392	+	0.464846i	$0.153890\pi$
$710$		0			0
$711$	−3.91327	−	2.25933i	−0.146759	−	0.0847315i
$712$		0			0
$713$	1.24158			0.0464975
$714$		0			0
$715$	22.1886	+	15.4341i	0.829807	+	0.577202i
$716$		0			0
$717$	37.6393	+	21.7310i	1.40566	+	0.811561i
$718$		0			0
$719$	−9.06118	−	15.6944i	−0.337925	−	0.585303i	0.646117	−	0.763238i	$-0.276392\pi$
$719$	−9.06118	−	15.6944i	−0.337925	−	0.585303i	−0.984042	+	0.177935i	$0.943058\pi$
$720$		0			0
$721$	−23.7267	+	15.5370i	−0.883630	+	0.578627i
$722$		0			0
$723$	−42.8987	+	24.7675i	−1.59542	+	0.921115i
$724$		0			0
$725$	8.24507	−	48.5219i	0.306214	−	1.80206i
$726$		0			0
$727$		−	29.8811i		−	1.10823i	−0.832441	−	0.554114i	$-0.813057\pi$
$727$		−	29.8811i		−	1.10823i	0.832441	−	0.554114i	$-0.186943\pi$
$728$		0			0
$729$	29.2209			1.08225
$730$		0			0
$731$	5.01066	+	2.89291i	0.185326	+	0.106998i
$732$		0			0
$733$	15.0078	−	8.66474i	0.554325	−	0.320040i	−0.196540	−	0.980496i	$-0.562970\pi$
$733$	15.0078	−	8.66474i	0.554325	−	0.320040i	0.750864	+	0.660456i	$0.229637\pi$
$734$		0			0
$735$	−12.1876	+	22.5536i	−0.449545	+	0.831903i
$736$		0			0
$737$	36.5405	−	21.0966i	1.34599	−	0.777105i
$738$		0			0
$739$	−2.12219	+	3.67574i	−0.0780659	+	0.135214i	−0.902415	−	0.430867i	$-0.858208\pi$
$739$	−2.12219	+	3.67574i	−0.0780659	+	0.135214i	0.824350	+	0.566081i	$0.191541\pi$
$740$		0			0
$741$	−20.1378			−0.739780
$742$		0			0
$743$	30.6848			1.12571			0.562857	−	0.826554i	$-0.309702\pi$
$743$	30.6848			1.12571			0.562857	+	0.826554i	$0.309702\pi$
$744$		0			0
$745$	−24.7504	+	11.6351i	−0.906786	+	0.426277i
$746$		0			0
$747$	2.03789	+	3.52972i	0.0745624	+	0.129146i
$748$		0			0
$749$	7.55393	−	4.94654i	0.276015	−	0.180743i
$750$		0			0
$751$	−14.4254	+	8.32852i	−0.526391	+	0.303912i	−0.739546	−	0.673107i	$-0.764960\pi$
$751$	−14.4254	+	8.32852i	−0.526391	+	0.303912i	0.213155	+	0.977018i	$0.431626\pi$
$752$		0			0
$753$	30.3645	+	17.5310i	1.10655	+	0.638864i
$754$		0			0
$755$	−11.3838	−	7.91842i	−0.414300	−	0.288181i
$756$		0			0
$757$	−19.7599			−0.718184			−0.359092	−	0.933302i	$-0.616914\pi$
$757$	−19.7599			−0.718184			−0.359092	+	0.933302i	$0.616914\pi$
$758$		0			0
$759$	−0.979488	+	1.69652i	−0.0355532	+	0.0615799i
$760$		0			0
$761$	−8.58074	+	4.95409i	−0.311052	+	0.179586i	−0.647397	−	0.762153i	$-0.724142\pi$
$761$	−8.58074	+	4.95409i	−0.311052	+	0.179586i	0.336345	+	0.941739i	$0.390809\pi$
$762$		0			0
$763$	−21.1031	−	10.6517i	−0.763985	−	0.385616i
$764$		0			0
$765$	0.917113	+	0.0773655i	0.0331583	+	0.00279716i
$766$		0			0
$767$	5.27564	−	9.13767i	0.190492	−	0.329942i
$768$		0			0
$769$			32.4947i			1.17179i	0.810387	+	0.585895i	$0.199257\pi$
$769$			32.4947i			1.17179i	−0.810387	+	0.585895i	$0.800743\pi$
$770$		0			0
$771$	16.0682			0.578681
$772$		0			0
$773$	15.9884	+	9.23089i	0.575062	+	0.332012i	0.759168	−	0.650894i	$-0.225606\pi$
$773$	15.9884	+	9.23089i	0.575062	+	0.332012i	−0.184107	+	0.982906i	$0.558939\pi$
$774$		0			0
$775$	14.5291	−	17.5353i	0.521900	−	0.629887i
$776$		0			0
$777$	34.1639	−	1.92081i	1.22562	−	0.0689085i
$778$		0			0
$779$	8.81639	+	15.2704i	0.315880	+	0.547120i
$780$		0			0
$781$	−5.39743	−	3.11621i	−0.193135	−	0.111507i
$782$		0			0
$783$			53.4850i			1.91140i
$784$		0			0
$785$	−17.9113	−	12.4588i	−0.639282	−	0.444675i
$786$		0			0
$787$	−1.45087	+	2.51298i	−0.0517179	+	0.0895780i	−0.890725	−	0.454542i	$-0.849803\pi$
$787$	−1.45087	+	2.51298i	−0.0517179	+	0.0895780i	0.839007	+	0.544120i	$0.183136\pi$
$788$		0			0
$789$	10.1800	+	17.6323i	0.362417	+	0.627725i
$790$		0			0
$791$	−1.38274	−	24.5938i	−0.0491647	−	0.874455i
$792$		0			0
$793$	−22.6134	+	13.0558i	−0.803024	+	0.463626i
$794$		0			0
$795$	−16.8277	−	35.7962i	−0.596816	−	1.26956i
$796$		0			0
$797$		−	20.9944i		−	0.743659i	−0.928301	−	0.371829i	$-0.878731\pi$
$797$		−	20.9944i		−	0.743659i	0.928301	−	0.371829i	$-0.121269\pi$
$798$		0			0
$799$			10.8114i			0.382480i
$800$		0			0
$801$	−1.00266	−	0.578887i	−0.0354273	−	0.0204540i
$802$		0			0
$803$	8.10589	+	14.0398i	0.286051	+	0.495454i
$804$		0			0
$805$	0.766969	+	1.41871i	0.0270321	+	0.0500031i
$806$		0			0
$807$	−5.70485	−	9.88109i	−0.200820	−	0.347831i
$808$		0			0
$809$	−20.2328	+	35.0443i	−0.711349	+	1.23209i	0.253002	+	0.967466i	$0.418582\pi$
$809$	−20.2328	+	35.0443i	−0.711349	+	1.23209i	−0.964351	+	0.264627i	$0.914751\pi$
$810$		0			0
$811$			25.9549i			0.911401i	0.890133	+	0.455701i	$0.150611\pi$
$811$			25.9549i			0.911401i	−0.890133	+	0.455701i	$0.849389\pi$
$812$		0			0
$813$	−43.8906			−1.53931
$814$		0			0
$815$	−27.1093	+	12.7440i	−0.949596	+	0.446402i
$816$		0			0
$817$	9.96074	+	17.2525i	0.348482	+	0.603589i
$818$		0			0
$819$	−1.93631	+	1.26795i	−0.0676600	+	0.0443058i
$820$		0			0
$821$	8.14642	−	4.70334i	0.284312	−	0.164148i	−0.351062	−	0.936352i	$-0.614179\pi$
$821$	8.14642	−	4.70334i	0.284312	−	0.164148i	0.635374	+	0.772205i	$0.280846\pi$
$822$		0			0
$823$	−11.7204	+	20.3003i	−0.408547	+	0.707624i	−0.994727	−	0.102557i	$-0.967298\pi$
$823$	−11.7204	+	20.3003i	−0.408547	+	0.707624i	0.586180	+	0.810181i	$0.300631\pi$
$824$		0			0
$825$	12.4986	+	33.6866i	0.435146	+	1.17282i
$826$		0			0
$827$			21.4901i			0.747285i	0.927573	+	0.373642i	$0.121891\pi$
$827$			21.4901i			0.747285i	−0.927573	+	0.373642i	$0.878109\pi$
$828$		0			0
$829$	11.6683	−	20.2101i	0.405256	−	0.701925i	−0.589095	−	0.808064i	$-0.700516\pi$
$829$	11.6683	−	20.2101i	0.405256	−	0.701925i	0.994351	+	0.106139i	$0.0338489\pi$
$830$		0			0
$831$	−14.0706	−	24.3709i	−0.488102	−	0.845418i
$832$		0			0
$833$	3.62735	−	8.31690i	0.125680	−	0.288164i
$834$		0			0
$835$	0.178570	−	2.11681i	0.00617965	−	0.0732553i
$836$		0			0
$837$	−12.3735	+	21.4315i	−0.427690	+	0.740780i
$838$		0			0
$839$	47.9666			1.65599			0.827995	−	0.560735i	$-0.189481\pi$
$839$	47.9666			1.65599			0.827995	+	0.560735i	$0.189481\pi$
$840$		0			0
$841$	−67.8943			−2.34118
$842$		0			0
$843$	19.9154	−	34.4945i	0.685924	−	1.18806i
$844$		0			0
$845$	12.0551	+	1.01694i	0.414707	+	0.0349838i
$846$		0			0
$847$	−11.9592	−	18.2630i	−0.410922	−	0.627525i
$848$		0			0
$849$	−9.28126	−	16.0756i	−0.318532	−	0.551713i
$850$		0			0
$851$	1.07632	−	1.86424i	0.0368958	−	0.0639055i
$852$		0			0
$853$			12.6214i			0.432149i	0.976377	+	0.216075i	$0.0693255\pi$
$853$			12.6214i			0.432149i	−0.976377	+	0.216075i	$0.930675\pi$
$854$		0			0
$855$	2.60151	+	1.80958i	0.0889699	+	0.0618862i
$856$		0			0
$857$	−0.489774	+	0.848313i	−0.0167303	+	0.0289778i	−0.874269	−	0.485441i	$-0.838659\pi$
$857$	−0.489774	+	0.848313i	−0.0167303	+	0.0289778i	0.857539	+	0.514419i	$0.171992\pi$
$858$		0			0
$859$	35.4285	−	20.4546i	1.20880	−	0.697904i	0.246306	−	0.969192i	$-0.420783\pi$
$859$	35.4285	−	20.4546i	1.20880	−	0.697904i	0.962498	+	0.271288i	$0.0874497\pi$
$860$		0			0
$861$	−15.2834	−	7.71420i	−0.520858	−	0.262899i
$862$		0			0
$863$	−6.10169	−	10.5684i	−0.207704	−	0.359754i	0.743287	−	0.668973i	$-0.233266\pi$
$863$	−6.10169	−	10.5684i	−0.207704	−	0.359754i	−0.950991	+	0.309219i	$0.899932\pi$
$864$		0			0
$865$	−14.4538	+	6.79467i	−0.491443	+	0.231026i
$866$		0			0
$867$	−25.0911			−0.852140
$868$		0			0
$869$			62.4362i			2.11800i
$870$		0			0
$871$	−13.2464	+	22.9434i	−0.448836	+	0.777407i
$872$		0			0
$873$	0.00316310	+	0.00547864i	0.000107055	+	0.000185424i
$874$		0			0
$875$	29.0122	+	5.76974i	0.980793	+	0.195053i
$876$		0			0
$877$	−20.5534	−	35.5995i	−0.694037	−	1.20211i	−0.970504	−	0.241085i	$-0.922497\pi$
$877$	−20.5534	−	35.5995i	−0.694037	−	1.20211i	0.276467	−	0.961024i	$-0.410836\pi$
$878$		0			0
$879$	19.2401	+	11.1083i	0.648954	+	0.374674i
$880$		0			0
$881$			13.8734i			0.467407i	0.972308	+	0.233704i	$0.0750846\pi$
$881$			13.8734i			0.467407i	−0.972308	+	0.233704i	$0.924915\pi$
$882$		0			0
$883$		−	40.4927i		−	1.36269i	−0.731963	−	0.681344i	$-0.761396\pi$
$883$		−	40.4927i		−	1.36269i	0.731963	−	0.681344i	$-0.238604\pi$
$884$		0			0
$885$	12.6937	−	5.96728i	0.426695	−	0.200588i
$886$		0			0
$887$	−10.5341	+	6.08189i	−0.353702	+	0.204210i	−0.666314	−	0.745671i	$-0.732129\pi$
$887$	−10.5341	+	6.08189i	−0.353702	+	0.204210i	0.312613	+	0.949881i	$0.398796\pi$
$888$		0			0
$889$	−7.63333	+	0.429171i	−0.256014	+	0.0143939i
$890$		0			0
$891$	−17.4331	−	30.1951i	−0.584032	−	1.01157i
$892$		0			0
$893$	−18.6127	+	32.2381i	−0.622849	+	1.07881i
$894$		0			0
$895$	4.01979	−	5.77900i	0.134367	−	0.193171i
$896$		0			0
$897$		−	1.23002i		−	0.0410692i
$898$		0			0
$899$	−38.8256	−	22.4160i	−1.29491	−	0.747615i
$900$		0			0
$901$	6.99984	+	12.1241i	0.233199	+	0.403912i
$902$		0			0
$903$	−17.2672	−	8.71549i	−0.574616	−	0.290033i
$904$		0			0
$905$	36.6700	+	3.09339i	1.21895	+	0.102828i
$906$		0			0
$907$	−8.49106	−	4.90232i	−0.281941	−	0.162779i	0.352361	−	0.935864i	$-0.385379\pi$
$907$	−8.49106	−	4.90232i	−0.281941	−	0.162779i	−0.634302	+	0.773085i	$0.718712\pi$
$908$		0			0
$909$	−2.08569			−0.0691781
$910$		0			0
$911$		−	37.9772i		−	1.25824i	−0.777307	−	0.629121i	$-0.783415\pi$
$911$		−	37.9772i		−	1.25824i	0.777307	−	0.629121i	$-0.216585\pi$
$912$		0			0
$913$	28.1583	−	48.7717i	0.931905	−	1.61411i
$914$		0			0
$915$	−34.5888	−	2.91783i	−1.14347	−	0.0964604i
$916$		0			0
$917$	0.488933	−	0.320168i	0.0161460	−	0.0105729i
$918$		0			0
$919$	31.8722	−	18.4014i	1.05137	−	0.607008i	0.128336	−	0.991731i	$-0.459036\pi$
$919$	31.8722	−	18.4014i	1.05137	−	0.607008i	0.923032	+	0.384723i	$0.125703\pi$
$920$		0			0
$921$	16.5069	−	28.5909i	0.543922	−	0.942101i
$922$		0			0
$923$	3.91327			0.128807
$924$		0			0
$925$	−13.7342	−	37.0170i	−0.451579	−	1.21711i
$926$		0			0
$927$	−2.94785	−	1.70194i	−0.0968202	−	0.0558992i
$928$		0			0
$929$	−32.7095	+	18.8849i	−1.07316	+	0.619592i	−0.929044	−	0.369968i	$-0.879369\pi$
$929$	−32.7095	+	18.8849i	−1.07316	+	0.619592i	−0.144120	+	0.989560i	$0.546035\pi$
$930$		0			0
$931$	25.1345	−	18.5551i	0.823749	−	0.608118i
$932$		0			0
$933$	−10.9015	−	18.8820i	−0.356899	−	0.618168i
$934$		0			0
$935$	−5.41029	−	11.5089i	−0.176935	−	0.376381i
$936$		0			0
$937$	−35.4048			−1.15663			−0.578313	−	0.815815i	$-0.696289\pi$
$937$	−35.4048			−1.15663			−0.578313	+	0.815815i	$0.696289\pi$
$938$		0			0
$939$	−43.8603			−1.43133
$940$		0			0
$941$	28.1702	−	48.7923i	0.918323	−	1.59058i	0.116362	−	0.993207i	$-0.462877\pi$
$941$	28.1702	−	48.7923i	0.918323	−	1.59058i	0.801961	−	0.597376i	$-0.203790\pi$
$942$		0			0
$943$	−0.932722	+	0.538507i	−0.0303736	+	0.0175362i
$944$		0			0
$945$	−32.1327	−	0.899766i	−1.04528	−	0.0292694i
$946$		0			0
$947$	23.6105	−	13.6315i	0.767238	−	0.442965i	−0.0646505	−	0.997908i	$-0.520593\pi$
$947$	23.6105	−	13.6315i	0.767238	−	0.442965i	0.831888	+	0.554943i	$0.187260\pi$
$948$		0			0
$949$	−8.81546	−	5.08961i	−0.286162	−	0.165216i
$950$		0			0
$951$	−50.4200			−1.63498
$952$		0			0
$953$		−	50.6486i		−	1.64067i	−0.571884	−	0.820334i	$-0.693787\pi$
$953$		−	50.6486i		−	1.64067i	0.571884	−	0.820334i	$-0.306213\pi$
$954$		0			0
$955$	−32.4979	+	15.2771i	−1.05161	+	0.494357i
$956$		0			0
$957$	61.2595	−	35.3682i	1.98024	−	1.14329i
$958$		0			0
$959$	−4.95563	−	2.50132i	−0.160026	−	0.0807718i
$960$		0			0
$961$	5.12836	+	8.88258i	0.165431	+	0.286535i
$962$		0			0
$963$	0.938514	+	0.541851i	0.0302432	+	0.0174609i
$964$		0			0
$965$	−30.2340	−	21.0304i	−0.973268	−	0.676991i
$966$		0			0
$967$	−13.9730			−0.449342			−0.224671	−	0.974435i	$-0.572131\pi$
$967$	−13.9730			−0.449342			−0.224671	+	0.974435i	$0.572131\pi$
$968$		0			0
$969$	8.20557	+	4.73749i	0.263601	+	0.152190i
$970$		0			0
$971$	−34.8402	+	20.1150i	−1.11807	+	0.645521i	−0.940909	−	0.338660i	$-0.890026\pi$
$971$	−34.8402	+	20.1150i	−1.11807	+	0.645521i	−0.177166	+	0.984181i	$0.556693\pi$
$972$		0			0
$973$	2.38814	+	42.4759i	0.0765601	+	1.36171i
$974$		0			0
$975$	−17.3721	−	14.3939i	−0.556353	−	0.460973i
$976$		0			0
$977$	−24.4933	−	14.1412i	−0.783610	−	0.452417i	0.0540981	−	0.998536i	$-0.482772\pi$
$977$	−24.4933	−	14.1412i	−0.783610	−	0.452417i	−0.837708	+	0.546118i	$0.816105\pi$
$978$		0			0
$979$			15.9975i			0.511281i
$980$		0			0
$981$		−	2.83713i		−	0.0905826i
$982$		0			0
$983$	15.6579	+	9.04010i	0.499410	+	0.288335i	0.728470	−	0.685078i	$-0.240232\pi$
$983$	15.6579	+	9.04010i	0.499410	+	0.288335i	−0.229060	+	0.973412i	$0.573565\pi$
$984$		0			0
$985$	−10.4083	−	0.878019i	−0.331636	−	0.0279760i
$986$		0			0
$987$	−2.02886	−	36.0857i	−0.0645792	−	1.14862i
$988$		0			0
$989$	−1.05379	+	0.608405i	−0.0335085	+	0.0193461i
$990$		0			0
$991$	18.3274	+	10.5813i	0.582188	+	0.336126i	0.762002	−	0.647574i	$-0.224216\pi$
$991$	18.3274	+	10.5813i	0.582188	+	0.336126i	−0.179814	+	0.983701i	$0.557550\pi$
$992$		0			0
$993$	−7.54262			−0.239358
$994$		0			0
$995$	14.8917	−	21.4089i	0.472100	−	0.678708i
$996$		0			0
$997$	3.01420	+	1.74025i	0.0954607	+	0.0551143i	0.546970	−	0.837152i	$-0.315781\pi$
$997$	3.01420	+	1.74025i	0.0954607	+	0.0551143i	−0.451510	+	0.892266i	$0.649114\pi$
$998$		0			0
$999$	21.4531	+	37.1578i	0.678746	+	1.17562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bq.b.1039.14		80
4.3	odd	2		280.2.ba.b.59.32	yes	80
5.4	even	2	inner	1120.2.bq.b.1039.27		80
7.5	odd	6	inner	1120.2.bq.b.719.28		80
8.3	odd	2	inner	1120.2.bq.b.1039.13		80
8.5	even	2		280.2.ba.b.59.34	yes	80
20.19	odd	2		280.2.ba.b.59.9	yes	80
28.19	even	6		280.2.ba.b.19.7	✓	80
35.19	odd	6	inner	1120.2.bq.b.719.13		80
40.19	odd	2	inner	1120.2.bq.b.1039.28		80
40.29	even	2		280.2.ba.b.59.7	yes	80
56.5	odd	6		280.2.ba.b.19.9	yes	80
56.19	even	6	inner	1120.2.bq.b.719.27		80
140.19	even	6		280.2.ba.b.19.34	yes	80
280.19	even	6	inner	1120.2.bq.b.719.14		80
280.229	odd	6		280.2.ba.b.19.32	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.7	✓	80	28.19	even	6
280.2.ba.b.19.9	yes	80	56.5	odd	6
280.2.ba.b.19.32	yes	80	280.229	odd	6
280.2.ba.b.19.34	yes	80	140.19	even	6
280.2.ba.b.59.7	yes	80	40.29	even	2
280.2.ba.b.59.9	yes	80	20.19	odd	2
280.2.ba.b.59.32	yes	80	4.3	odd	2
280.2.ba.b.59.34	yes	80	8.5	even	2
1120.2.bq.b.719.13		80	35.19	odd	6	inner
1120.2.bq.b.719.14		80	280.19	even	6	inner
1120.2.bq.b.719.27		80	56.19	even	6	inner
1120.2.bq.b.719.28		80	7.5	odd	6	inner
1120.2.bq.b.1039.13		80	8.3	odd	2	inner
1120.2.bq.b.1039.14		80	1.1	even	1	trivial
1120.2.bq.b.1039.27		80	5.4	even	2	inner
1120.2.bq.b.1039.28		80	40.19	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.818911 + 1.41839i) q^{3} +(2.22815 + 0.187962i) q^{5} +(2.64158 - 0.148518i) q^{7} +(0.158771 + 0.274999i) q^{9} +O(q^{10})\)	\(q+(-0.818911 + 1.41839i) q^{3} +(2.22815 + 0.187962i) q^{5} +(2.64158 - 0.148518i) q^{7} +(0.158771 + 0.274999i) q^{9} +(2.19380 - 3.79978i) q^{11} +2.75493i q^{13} +(-2.09126 + 3.00648i) q^{15} +(0.648108 - 1.12256i) q^{17} +(3.86514 - 2.23154i) q^{19} +(-1.95256 + 3.86843i) q^{21} +(0.136303 + 0.236084i) q^{23} +(4.92934 + 0.837616i) q^{25} -5.43354 q^{27} -9.84349i q^{29} +(2.27724 - 3.94429i) q^{31} +(3.59306 + 6.22335i) q^{33} +(5.91376 + 0.165595i) q^{35} +(-3.94827 - 6.83861i) q^{37} +(-3.90758 - 2.25604i) q^{39} +3.95081i q^{41} +4.46362i q^{43} +(0.302076 + 0.642583i) q^{45} +(-7.22329 + 4.17037i) q^{47} +(6.95588 - 0.784646i) q^{49} +(1.06148 + 1.83855i) q^{51} +(-5.40022 + 9.35345i) q^{53} +(5.60234 - 8.05413i) q^{55} +7.30972i q^{57} +(-3.31684 - 1.91498i) q^{59} +(4.73907 + 8.20831i) q^{61} +(0.460248 + 0.702851i) q^{63} +(-0.517823 + 6.13841i) q^{65} +(8.32812 + 4.80824i) q^{67} -0.446480 q^{69} -1.42046i q^{71} +(-1.84745 + 3.19988i) q^{73} +(-5.22476 + 6.30582i) q^{75} +(5.23077 - 10.3632i) q^{77} +(-12.3237 + 7.11507i) q^{79} +(3.97327 - 6.88191i) q^{81} +12.8354 q^{83} +(1.65508 - 2.37941i) q^{85} +(13.9620 + 8.06094i) q^{87} +(-3.15758 + 1.82303i) q^{89} +(0.409158 + 7.27737i) q^{91} +(3.72971 + 6.46005i) q^{93} +(9.03157 - 4.24571i) q^{95} +0.0199224 q^{97} +1.39325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 52 q^{9}+O(q^{10}) \) 80 * q - 52 * q^9	\( 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) \) 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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