LMFDB - Embedded newform 1120.2.bq.b.719.14

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			719.14
Character	$\chi$	$=$	1120.719
Dual form			1120.2.bq.b.1039.14

$q$-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 $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.526717	−	0.850041i	$-0.323423\pi$
$3$	−0.818911	−	1.41839i	−0.472798	−	0.818911i	−0.999515	+	0.0311300i	$0.990089\pi$
$4$		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	0.980233	+	0.197846i	$0.0633945\pi$
$11$	2.19380	+	3.79978i	0.661456	+	1.14568i	−0.318777	+	0.947830i	$0.603272\pi$
$12$		0			0
$13$		−	2.75493i		−	0.764081i	−0.924146	−	0.382040i	$-0.875221\pi$
$13$		−	2.75493i		−	0.764081i	0.924146	−	0.382040i	$-0.124779\pi$
$14$		0			0
$15$	−2.09126	−	3.00648i	−0.539962	−	0.776269i
$16$		0			0
$17$	0.648108	+	1.12256i	0.157189	+	0.272260i	0.933854	−	0.357654i	$-0.116423\pi$
$17$	0.648108	+	1.12256i	0.157189	+	0.272260i	−0.776665	+	0.629914i	$0.783090\pi$
$18$		0			0
$19$	3.86514	+	2.23154i	0.886723	+	0.511950i	0.872869	−	0.487954i	$-0.162257\pi$
$19$	3.86514	+	2.23154i	0.886723	+	0.511950i	0.0138541	+	0.999904i	$0.495590\pi$
$20$		0			0
$21$	−1.95256	−	3.86843i	−0.426084	−	0.844160i
$22$		0			0
$23$	0.136303	−	0.236084i	0.0284211	−	0.0492269i	−0.851465	−	0.524411i	$-0.824285\pi$
$23$	0.136303	−	0.236084i	0.0284211	−	0.0492269i	0.879886	+	0.475185i	$0.157619\pi$
$24$		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	$0.366980\pi$
$29$			9.84349i			1.82789i	−0.405838	+	0.913945i	$0.633020\pi$
$30$		0			0
$31$	2.27724	+	3.94429i	0.409004	+	0.708416i	0.994778	−	0.102058i	$-0.0325428\pi$
$31$	2.27724	+	3.94429i	0.409004	+	0.708416i	−0.585774	+	0.810474i	$0.699209\pi$
$32$		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	0.334248	+	0.942485i	$0.391518\pi$
$37$	−3.94827	+	6.83861i	−0.649092	+	1.12426i	−0.983340	+	0.181775i	$0.941816\pi$
$38$		0			0
$39$	−3.90758	+	2.25604i	−0.625714	+	0.361256i
$40$		0			0
$41$		−	3.95081i		−	0.617013i	−0.951222	−	0.308507i	$-0.900171\pi$
$41$		−	3.95081i		−	0.617013i	0.951222	−	0.308507i	$-0.0998292\pi$
$42$		0			0
$43$		−	4.46362i		−	0.680696i	−0.940300	−	0.340348i	$-0.889455\pi$
$43$		−	4.46362i		−	0.680696i	0.940300	−	0.340348i	$-0.110545\pi$
$44$		0			0
$45$	0.302076	−	0.642583i	0.0450309	−	0.0957906i
$46$		0			0
$47$	−7.22329	−	4.17037i	−1.05363	−	0.608311i	−0.129963	−	0.991519i	$-0.541486\pi$
$47$	−7.22329	−	4.17037i	−1.05363	−	0.608311i	−0.923662	+	0.383208i	$0.874819\pi$
$48$		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	−0.951686	−	0.307074i	$-0.900650\pi$
$53$	−5.40022	−	9.35345i	−0.741777	−	1.28479i	0.209909	−	0.977721i	$-0.432683\pi$
$54$		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	−0.700120	−	0.714025i	$-0.746870\pi$
$59$	−3.31684	+	1.91498i	−0.431816	+	0.249309i	0.268304	+	0.963334i	$0.413537\pi$
$60$		0			0
$61$	4.73907	−	8.20831i	0.606776	−	1.05097i	−0.384992	−	0.922920i	$-0.625796\pi$
$61$	4.73907	−	8.20831i	0.606776	−	1.05097i	0.991768	−	0.128047i	$-0.0408708\pi$
$62$		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	0.104079	−	0.994569i	$-0.466810\pi$
$67$	8.32812	−	4.80824i	1.01744	−	0.587420i	0.913362	+	0.407149i	$0.133477\pi$
$68$		0			0
$69$	−0.446480			−0.0537499
$70$		0			0
$71$			1.42046i			0.168578i	0.996441	+	0.0842888i	$0.0268618\pi$
$71$			1.42046i			0.168578i	−0.996441	+	0.0842888i	$0.973138\pi$
$72$		0			0
$73$	−1.84745	−	3.19988i	−0.216228	−	0.374518i	0.737424	−	0.675430i	$-0.236042\pi$
$73$	−1.84745	−	3.19988i	−0.216228	−	0.374518i	−0.953652	+	0.300912i	$0.902709\pi$
$74$		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	−0.393599	−	0.919282i	$-0.628770\pi$
$79$	−12.3237	−	7.11507i	−1.38652	−	0.800508i	−0.992921	+	0.118774i	$0.962104\pi$
$80$		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	0.323224	−	0.946322i	$-0.395233\pi$
$89$	−3.15758	−	1.82303i	−0.334703	−	0.193241i	−0.657927	+	0.753082i	$0.728567\pi$
$90$		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	0.655088	−	0.755552i	$-0.272631\pi$
$101$	−3.28413	−	5.68828i	−0.326783	−	0.566005i	−0.981872	+	0.189547i	$0.939298\pi$
$102$		0			0
$103$	−9.28337	−	5.35976i	−0.914718	−	0.528112i	−0.0327715	−	0.999463i	$-0.510433\pi$
$103$	−9.28337	−	5.35976i	−0.914718	−	0.528112i	−0.881946	+	0.471350i	$0.843767\pi$
$104$		0			0
$105$	−5.07772	−	8.25244i	−0.495535	−	0.805356i
$106$		0			0
$107$	2.95557	+	1.70640i	0.285725	+	0.164964i	0.636013	−	0.771679i	$-0.280583\pi$
$107$	2.95557	+	1.70640i	0.285725	+	0.164964i	−0.350287	+	0.936642i	$0.613916\pi$
$108$		0			0
$109$	−7.73766	+	4.46734i	−0.741134	+	0.427894i	−0.822481	−	0.568792i	$-0.807411\pi$
$109$	−7.73766	+	4.46734i	−0.741134	+	0.427894i	0.0813476	+	0.996686i	$0.474078\pi$
$110$		0			0
$111$	12.9331			1.22756
$112$		0			0
$113$			9.31026i			0.875836i	0.899015	+	0.437918i	$0.144284\pi$
$113$			9.31026i			0.875836i	−0.899015	+	0.437918i	$0.855716\pi$
$114$		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	0.508334	−	0.861160i	$-0.330262\pi$
$131$	0.191301	+	0.110448i	0.0167140	+	0.00964984i	−0.491620	+	0.870810i	$0.663595\pi$
$132$		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	−0.575607	−	0.817726i	$-0.695234\pi$
$137$	−1.81703	+	1.04906i	−0.155239	+	0.0896274i	0.420368	+	0.907354i	$0.361901\pi$
$138$		0			0
$139$		−	16.0797i		−	1.36387i	−0.731415	−	0.681933i	$-0.761140\pi$
$139$		−	16.0797i		−	1.36387i	0.731415	−	0.681933i	$-0.238860\pi$
$140$		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	−0.00114601	−	0.999999i	$-0.500365\pi$
$149$	−10.5922	−	6.11539i	−0.867744	−	0.500992i	−0.866598	+	0.499007i	$0.833698\pi$
$150$		0			0
$151$	−5.37065	+	3.10075i	−0.437058	+	0.252335i	−0.702349	−	0.711833i	$-0.747865\pi$
$151$	−5.37065	+	3.10075i	−0.437058	+	0.252335i	0.265291	+	0.964168i	$0.414532\pi$
$152$		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	−0.797741	−	0.603000i	$-0.793972\pi$
$157$	−8.45018	+	4.87872i	−0.674398	+	0.389364i	0.123343	+	0.992364i	$0.460638\pi$
$158$		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	−0.0286947	−	0.999588i	$-0.509135\pi$
$163$	−11.6016	−	6.69821i	−0.908711	−	0.524644i	−0.880016	+	0.474944i	$0.842468\pi$
$164$		0			0
$165$	6.83613	−	14.5419i	0.532192	−	1.13209i
$166$		0			0
$167$			0.950030i			0.0735155i	0.999324	+	0.0367578i	$0.0117030\pi$
$167$			0.950030i			0.0735155i	−0.999324	+	0.0367578i	$0.988297\pi$
$168$		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	0.246075	−	0.969251i	$-0.420859\pi$
$173$	−6.18561	−	3.57127i	−0.470283	−	0.271518i	−0.716358	+	0.697733i	$0.754192\pi$
$174$		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	0.918837	−	0.394636i	$-0.129129\pi$
$179$	1.57410	+	2.72641i	0.117653	+	0.203782i	−0.801184	+	0.598418i	$0.795796\pi$
$180$		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	−0.0962140	−	0.995361i	$-0.530673\pi$
$191$	−13.9077	−	8.02964i	−1.00633	−	0.581004i	−0.910115	+	0.414357i	$0.864007\pi$
$192$		0			0
$193$	−14.2638	+	8.23520i	−1.02673	+	0.592783i	−0.916046	−	0.401073i	$-0.868637\pi$
$193$	−14.2638	+	8.23520i	−1.02673	+	0.592783i	−0.110684	+	0.993856i	$0.535304\pi$
$194$		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	0.995257	−	0.0972849i	$-0.0310158\pi$
$199$	5.83140	+	10.1003i	0.413377	+	0.715990i	−0.581879	+	0.813275i	$0.697682\pi$
$200$		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	$0.0753335\pi$
$223$			7.00259i			0.468928i	−0.972125	+	0.234464i	$0.924666\pi$
$224$		0			0
$225$	0.552291	−	1.48855i	0.0368194	−	0.0992368i
$226$		0			0
$227$	10.2610	+	17.7725i	0.681043	+	1.17960i	0.974663	+	0.223679i	$0.0718068\pi$
$227$	10.2610	+	17.7725i	0.681043	+	1.17960i	−0.293619	+	0.955922i	$0.594860\pi$
$228$		0			0
$229$	−12.4920	+	21.6368i	−0.825496	+	1.42980i	0.0760431	+	0.997105i	$0.475771\pi$
$229$	−12.4920	+	21.6368i	−0.825496	+	1.42980i	−0.901539	+	0.432697i	$0.857562\pi$
$230$		0			0
$231$	10.4156	−	15.9058i	0.685298	−	1.04653i
$232$		0			0
$233$	3.61112	+	2.08488i	0.236572	+	0.136585i	0.613600	−	0.789617i	$-0.289721\pi$
$233$	3.61112	+	2.08488i	0.236572	+	0.136585i	−0.377028	+	0.926202i	$0.623054\pi$
$234$		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	$0.328450\pi$
$239$			26.5365i			1.71651i	−0.513228	+	0.858253i	$0.671550\pi$
$240$		0			0
$241$	26.1925	−	15.1223i	1.68721	−	0.974110i	0.730566	−	0.682842i	$-0.239256\pi$
$241$	26.1925	−	15.1223i	1.68721	−	0.974110i	0.956641	−	0.291268i	$-0.0940772\pi$
$242$		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	$0.236124\pi$
$251$			21.4077i			1.35124i	−0.737250	+	0.675620i	$0.763876\pi$
$252$		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	−0.977481	−	0.211025i	$-0.932320\pi$
$257$	−4.90535	+	8.49632i	−0.305988	+	0.529986i	0.671493	+	0.741011i	$0.265653\pi$
$258$		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	0.991527	−	0.129898i	$-0.0414651\pi$
$263$	6.21557	+	10.7657i	0.383268	+	0.663840i	−0.608259	+	0.793739i	$0.708132\pi$
$264$		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	0.740083	−	0.672516i	$-0.234786\pi$
$269$	−3.48319	−	6.03307i	−0.212374	−	0.367843i	−0.952457	+	0.304673i	$0.901453\pi$
$270$		0			0
$271$	13.3991	−	23.2079i	0.813935	−	1.40978i	−0.0961544	−	0.995366i	$-0.530654\pi$
$271$	13.3991	−	23.2079i	0.813935	−	1.40978i	0.910090	−	0.414411i	$-0.136012\pi$
$272$		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	−0.999823	−	0.0187904i	$-0.994018\pi$
$277$	−8.59103	−	14.8801i	−0.516185	−	0.894058i	0.483639	−	0.875268i	$-0.339315\pi$
$278$		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	0.646982	−	0.762505i	$-0.276031\pi$
$283$	−5.66683	−	9.81524i	−0.336858	−	0.583455i	−0.983840	+	0.179050i	$0.942698\pi$
$284$		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	$0.129682\pi$
$293$			13.5647i			0.792460i	−0.918151	+	0.396230i	$0.870318\pi$
$294$		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	0.613255	−	0.789885i	$-0.289860\pi$
$311$	−6.65610	−	11.5287i	−0.377433	−	0.653733i	−0.990688	+	0.136152i	$0.956526\pi$
$312$		0			0
$313$	13.3898	−	23.1919i	0.756838	−	1.31088i	−0.187618	−	0.982242i	$-0.560077\pi$
$313$	13.3898	−	23.1919i	0.756838	−	1.31088i	0.944456	−	0.328639i	$-0.106590\pi$
$314$		0			0
$315$	0.893393	−	1.65257i	0.0503370	−	0.0931117i
$316$		0			0
$317$	15.3924	−	26.6604i	0.864524	−	1.49740i	−0.00299582	−	0.999996i	$-0.500954\pi$
$317$	15.3924	−	26.6604i	0.864524	−	1.49740i	0.867519	−	0.497403i	$-0.165713\pi$
$318$		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	−0.795779	−	0.605587i	$-0.792938\pi$
$331$	2.30264	−	3.98829i	0.126564	−	0.219216i	0.922343	+	0.386371i	$0.126272\pi$
$332$		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	$0.108713\pi$
$337$			12.2970i			0.669862i	−0.942243	+	0.334931i	$0.891287\pi$
$338$		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	−0.674517	−	0.738259i	$-0.735648\pi$
$347$	−6.93751	+	4.00537i	−0.372425	+	0.215020i	0.302092	+	0.953279i	$0.402315\pi$
$348$		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	0.930198	+	0.367059i	$0.119635\pi$
$353$	14.7109	+	25.4800i	0.782981	+	1.35616i	−0.147216	+	0.989104i	$0.547031\pi$
$354$		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	0.416289	−	0.909233i	$-0.363331\pi$
$359$	−3.08814	−	1.78294i	−0.162986	−	0.0940998i	−0.579274	+	0.815133i	$0.696664\pi$
$360$		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	−0.697453	−	0.716631i	$-0.745683\pi$
$367$	−8.15253	+	4.70686i	−0.425558	+	0.245696i	0.271894	+	0.962327i	$0.412350\pi$
$368$		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	−0.932397	−	0.361435i	$-0.882287\pi$
$373$	−2.95853	+	5.12432i	−0.153187	+	0.265327i	0.779211	+	0.626762i	$0.215620\pi$
$374$		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	0.889637	−	0.456669i	$-0.150958\pi$
$383$	18.3760	+	10.6094i	0.938968	+	0.542113i	0.0493313	+	0.998782i	$0.484291\pi$
$384$		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	−0.866349	−	0.499440i	$-0.833539\pi$
$389$	−17.0998	+	9.87258i	−0.866995	+	0.500560i	−0.000646573		1.00000i	$0.500206\pi$
$390$		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	0.677740	−	0.735301i	$-0.262959\pi$
$397$	7.56788	+	4.36932i	0.379821	+	0.219290i	−0.297919	+	0.954591i	$0.596293\pi$
$398$		0			0
$399$	1.08563	−	19.3092i	0.0543494	−	0.966670i
$400$		0			0
$401$	−12.7155	+	22.0240i	−0.634984	+	1.09982i	0.351535	+	0.936175i	$0.385660\pi$
$401$	−12.7155	+	22.0240i	−0.634984	+	1.09982i	−0.986519	+	0.163649i	$0.947673\pi$
$402$		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	−0.736093	−	0.676880i	$-0.763331\pi$
$409$	−10.4748	+	6.04761i	−0.517944	+	0.299035i	0.218149	+	0.975915i	$0.429998\pi$
$410$		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	$-0.900728\pi$
$419$		−	12.5618i		−	0.613682i	0.951761	−	0.306841i	$-0.0992719\pi$
$420$		0			0
$421$			3.98711i			0.194320i	0.995269	+	0.0971600i	$0.0309759\pi$
$421$			3.98711i			0.194320i	−0.995269	+	0.0971600i	$0.969024\pi$
$422$		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	−0.407016	−	0.913421i	$-0.633431\pi$
$431$	3.74772	−	2.16375i	0.180521	−	0.104224i	0.587538	+	0.809197i	$0.300097\pi$
$432$		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	−0.752245	−	0.658884i	$-0.771029\pi$
$439$	4.07497	−	7.05805i	0.194488	−	0.336862i	0.946732	+	0.322021i	$0.104362\pi$
$440$		0			0
$441$	1.32017	−	1.78828i	0.0628651	−	0.0851563i
$442$		0			0
$443$	−13.7175	−	7.91978i	−0.651737	−	0.376280i	0.137385	−	0.990518i	$-0.456130\pi$
$443$	−13.7175	−	7.91978i	−0.651737	−	0.376280i	−0.789121	+	0.614237i	$0.789464\pi$
$444$		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	0.275893	−	0.961188i	$-0.411027\pi$
$457$	−8.94810	−	5.16619i	−0.418574	−	0.241664i	−0.694467	+	0.719524i	$0.744360\pi$
$458$		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	−0.980399	−	0.197021i	$-0.936873\pi$
$467$	−6.90606	+	11.9616i	−0.319574	+	0.553519i	0.660825	+	0.750540i	$0.270207\pi$
$468$		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	−0.992181	−	0.124807i	$-0.960169\pi$
$479$	−13.2230	−	22.9030i	−0.604176	−	1.04646i	0.388005	−	0.921657i	$-0.373164\pi$
$480$		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	0.742447	−	0.669905i	$-0.233665\pi$
$487$	−4.61070	−	7.98597i	−0.208931	−	0.361879i	−0.951378	+	0.308026i	$0.900332\pi$
$488$		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	−0.708212	−	0.706000i	$-0.750498\pi$
$499$	5.74782	−	9.95552i	0.257308	−	0.445670i	0.965520	+	0.260330i	$0.0838313\pi$
$500$		0			0
$501$	1.34752	−	0.777990i	0.0602027	−	0.0347580i
$502$		0			0
$503$			34.0508i			1.51825i	0.650944	+	0.759125i	$0.274373\pi$
$503$			34.0508i			1.51825i	−0.650944	+	0.759125i	$0.725627\pi$
$504$		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	−0.932900	−	0.360136i	$-0.882730\pi$
$509$	−3.48710	+	6.03983i	−0.154563	+	0.267711i	0.778337	+	0.627847i	$0.216064\pi$
$510$		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	−0.220454	−	0.975397i	$-0.570754\pi$
$521$	11.7331	−	6.77412i	0.514037	−	0.296780i	0.734492	+	0.678618i	$0.237421\pi$
$522$		0			0
$523$	19.7080	−	34.1352i	0.861769	−	1.49263i	−0.00845156	−	0.999964i	$-0.502690\pi$
$523$	19.7080	−	34.1352i	0.861769	−	1.49263i	0.870220	−	0.492663i	$-0.163976\pi$
$524$		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	−0.369181	−	0.929358i	$-0.620362\pi$
$541$	−31.6007	−	18.2447i	−1.35862	−	0.784399i	−0.989438	+	0.144959i	$0.953695\pi$
$542$		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	$0.0138437\pi$
$547$			2.03370i			0.0869549i	−0.999054	+	0.0434775i	$0.986156\pi$
$548$		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	0.999784	+	0.0207606i	$0.00660877\pi$
$557$	12.2222	+	21.1695i	0.517871	+	0.896980i	−0.481913	+	0.876219i	$0.660058\pi$
$558$		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	0.990860	+	0.134892i	$0.0430689\pi$
$563$	14.5272	+	25.1619i	0.612250	+	1.06045i	−0.378610	+	0.925556i	$0.623598\pi$
$564$		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	−0.999369	−	0.0355198i	$-0.988691\pi$
$569$	−11.1856	+	19.3740i	−0.468923	+	0.812199i	0.530446	+	0.847719i	$0.322025\pi$
$570$		0			0
$571$	21.2867	+	36.8696i	0.890820	+	1.54295i	0.838895	+	0.544294i	$0.183202\pi$
$571$	21.2867	+	36.8696i	0.890820	+	1.54295i	0.0519252	+	0.998651i	$0.483464\pi$
$572$		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	−0.975593	−	0.219588i	$-0.929529\pi$
$577$	−16.2853	−	28.2069i	−0.677965	−	1.17427i	0.297628	−	0.954682i	$-0.403805\pi$
$578$		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	−0.776403	−	0.630236i	$-0.782958\pi$
$593$	3.83778	−	6.64723i	0.157599	−	0.272969i	0.934002	+	0.357267i	$0.116291\pi$
$594$		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	0.152909	−	0.988240i	$-0.451136\pi$
$599$	26.5598	−	15.3343i	1.08520	−	0.626543i	0.932296	+	0.361697i	$0.117803\pi$
$600$		0			0
$601$			4.23258i			0.172650i	0.996267	+	0.0863252i	$0.0275124\pi$
$601$			4.23258i			0.172650i	−0.996267	+	0.0863252i	$0.972488\pi$
$602$		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	0.485723	−	0.874113i	$-0.338556\pi$
$607$	−0.700185	−	0.404252i	−0.0284196	−	0.0164081i	−0.514142	+	0.857705i	$0.671890\pi$
$608$		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	0.984746	+	0.173995i	$0.0556678\pi$
$613$	15.9214	+	27.5766i	0.643058	+	1.11381i	−0.341689	+	0.939813i	$0.610999\pi$
$614$		0			0
$615$	−11.8780	+	8.26219i	−0.478968	+	0.333164i
$616$		0			0
$617$		−	23.7720i		−	0.957025i	−0.878081	−	0.478513i	$-0.841176\pi$
$617$		−	23.7720i		−	0.957025i	0.878081	−	0.478513i	$-0.158824\pi$
$618$		0			0
$619$	12.8725	−	7.43195i	0.517390	−	0.298715i	−0.218476	−	0.975842i	$-0.570109\pi$
$619$	12.8725	−	7.43195i	0.517390	−	0.298715i	0.735866	+	0.677127i	$0.236775\pi$
$620$		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	$-0.913619\pi$
$631$		−	13.4670i		−	0.536112i	0.963403	−	0.268056i	$-0.0863812\pi$
$632$		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	0.966823	+	0.255445i	$0.0822221\pi$
$641$	17.8399	+	30.8996i	0.704634	+	1.22046i	−0.262189	+	0.965016i	$0.584445\pi$
$642$		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	−0.842290	−	0.539025i	$-0.818793\pi$
$647$	−20.2631	+	11.6989i	−0.796625	+	0.459932i	0.0456648	+	0.998957i	$0.485459\pi$
$648$		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	−0.420466	−	0.907308i	$-0.638133\pi$
$653$	14.7067	−	25.4728i	0.575519	−	0.996829i	0.995985	−	0.0895203i	$-0.0285334\pi$
$654$		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	−0.888058	−	0.459731i	$-0.847946\pi$
$661$	−21.6521	−	37.5025i	−0.842168	−	1.45868i	0.0458899	−	0.998947i	$-0.485388\pi$
$662$		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	$-0.950011\pi$
$673$		−	8.11472i		−	0.312799i	0.987694	−	0.156400i	$-0.0499888\pi$
$674$		0			0
$675$	−26.7838	+	4.55122i	−1.03091	+	0.175177i
$676$		0			0
$677$	−37.9364	−	21.9026i	−1.45802	−	0.841786i	−0.459102	−	0.888383i	$-0.651829\pi$
$677$	−37.9364	−	21.9026i	−1.45802	−	0.841786i	−0.998914	+	0.0465975i	$0.985162\pi$
$678$		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	−0.0641905	−	0.997938i	$-0.520447\pi$
$683$	20.0699	−	11.5874i	0.767954	−	0.443378i	0.832144	+	0.554559i	$0.187113\pi$
$684$		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	−0.0713493	−	0.997451i	$-0.522731\pi$
$691$	−25.5204	−	14.7342i	−0.970842	−	0.560516i	−0.899493	+	0.436935i	$0.856064\pi$
$692$		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	$-0.918609\pi$
$701$		−	13.3928i		−	0.505839i	0.967487	−	0.252919i	$-0.0813907\pi$
$702$		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	0.885392	−	0.464846i	$-0.153890\pi$
$709$	24.6438	+	14.2281i	0.925519	+	0.534349i	0.0401274	+	0.999195i	$0.487224\pi$
$710$		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	−0.984042	−	0.177935i	$-0.943058\pi$
$719$	−9.06118	+	15.6944i	−0.337925	+	0.585303i	0.646117	+	0.763238i	$0.276392\pi$
$720$		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	$0.186943\pi$
$727$			29.8811i			1.10823i	−0.832441	+	0.554114i	$0.813057\pi$
$728$		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	0.750864	−	0.660456i	$-0.229637\pi$
$733$	15.0078	+	8.66474i	0.554325	+	0.320040i	−0.196540	+	0.980496i	$0.562970\pi$
$734$		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	0.824350	−	0.566081i	$-0.191541\pi$
$739$	−2.12219	−	3.67574i	−0.0780659	−	0.135214i	−0.902415	+	0.430867i	$0.858208\pi$
$740$		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	0.213155	−	0.977018i	$-0.431626\pi$
$751$	−14.4254	−	8.32852i	−0.526391	−	0.303912i	−0.739546	+	0.673107i	$0.764960\pi$
$752$		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	0.336345	−	0.941739i	$-0.390809\pi$
$761$	−8.58074	−	4.95409i	−0.311052	−	0.179586i	−0.647397	+	0.762153i	$0.724142\pi$
$762$		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	$-0.800743\pi$
$769$		−	32.4947i		−	1.17179i	0.810387	−	0.585895i	$-0.199257\pi$
$770$		0			0
$771$	16.0682			0.578681
$772$		0			0
$773$	15.9884	−	9.23089i	0.575062	−	0.332012i	−0.184107	−	0.982906i	$-0.558939\pi$
$773$	15.9884	−	9.23089i	0.575062	−	0.332012i	0.759168	+	0.650894i	$0.225606\pi$
$774$		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	0.839007	−	0.544120i	$-0.183136\pi$
$787$	−1.45087	−	2.51298i	−0.0517179	−	0.0895780i	−0.890725	+	0.454542i	$0.849803\pi$
$788$		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	$0.121269\pi$
$797$			20.9944i			0.743659i	−0.928301	+	0.371829i	$0.878731\pi$
$798$		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	−0.964351	−	0.264627i	$-0.914751\pi$
$809$	−20.2328	−	35.0443i	−0.711349	−	1.23209i	0.253002	−	0.967466i	$-0.418582\pi$
$810$		0			0
$811$		−	25.9549i		−	0.911401i	−0.890133	−	0.455701i	$-0.849389\pi$
$811$		−	25.9549i		−	0.911401i	0.890133	−	0.455701i	$-0.150611\pi$
$812$		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	0.635374	−	0.772205i	$-0.280846\pi$
$821$	8.14642	+	4.70334i	0.284312	+	0.164148i	−0.351062	+	0.936352i	$0.614179\pi$
$822$		0			0
$823$	−11.7204	−	20.3003i	−0.408547	−	0.707624i	0.586180	−	0.810181i	$-0.300631\pi$
$823$	−11.7204	−	20.3003i	−0.408547	−	0.707624i	−0.994727	+	0.102557i	$0.967298\pi$
$824$		0			0
$825$	12.4986	−	33.6866i	0.435146	−	1.17282i
$826$		0			0
$827$		−	21.4901i		−	0.747285i	−0.927573	−	0.373642i	$-0.878109\pi$
$827$		−	21.4901i		−	0.747285i	0.927573	−	0.373642i	$-0.121891\pi$
$828$		0			0
$829$	11.6683	+	20.2101i	0.405256	+	0.701925i	0.994351	−	0.106139i	$-0.0338489\pi$
$829$	11.6683	+	20.2101i	0.405256	+	0.701925i	−0.589095	+	0.808064i	$0.700516\pi$
$830$		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	$-0.930675\pi$
$853$		−	12.6214i		−	0.432149i	0.976377	−	0.216075i	$-0.0693255\pi$
$854$		0			0
$855$	2.60151	−	1.80958i	0.0889699	−	0.0618862i
$856$		0			0
$857$	−0.489774	−	0.848313i	−0.0167303	−	0.0289778i	0.857539	−	0.514419i	$-0.171992\pi$
$857$	−0.489774	−	0.848313i	−0.0167303	−	0.0289778i	−0.874269	+	0.485441i	$0.838659\pi$
$858$		0			0
$859$	35.4285	+	20.4546i	1.20880	+	0.697904i	0.962498	−	0.271288i	$-0.0874497\pi$
$859$	35.4285	+	20.4546i	1.20880	+	0.697904i	0.246306	+	0.969192i	$0.420783\pi$
$860$		0			0
$861$	−15.2834	+	7.71420i	−0.520858	+	0.262899i
$862$		0			0
$863$	−6.10169	+	10.5684i	−0.207704	+	0.359754i	−0.950991	−	0.309219i	$-0.899932\pi$
$863$	−6.10169	+	10.5684i	−0.207704	+	0.359754i	0.743287	+	0.668973i	$0.233266\pi$
$864$		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	0.276467	+	0.961024i	$0.410836\pi$
$877$	−20.5534	+	35.5995i	−0.694037	+	1.20211i	−0.970504	+	0.241085i	$0.922497\pi$
$878$		0			0
$879$	19.2401	−	11.1083i	0.648954	−	0.374674i
$880$		0			0
$881$		−	13.8734i		−	0.467407i	−0.972308	−	0.233704i	$-0.924915\pi$
$881$		−	13.8734i		−	0.467407i	0.972308	−	0.233704i	$-0.0750846\pi$
$882$		0			0
$883$			40.4927i			1.36269i	0.731963	+	0.681344i	$0.238604\pi$
$883$			40.4927i			1.36269i	−0.731963	+	0.681344i	$0.761396\pi$
$884$		0			0
$885$	12.6937	+	5.96728i	0.426695	+	0.200588i
$886$		0			0
$887$	−10.5341	−	6.08189i	−0.353702	−	0.204210i	0.312613	−	0.949881i	$-0.398796\pi$
$887$	−10.5341	−	6.08189i	−0.353702	−	0.204210i	−0.666314	+	0.745671i	$0.732129\pi$
$888$		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	−0.634302	−	0.773085i	$-0.718712\pi$
$907$	−8.49106	+	4.90232i	−0.281941	+	0.162779i	0.352361	+	0.935864i	$0.385379\pi$
$908$		0			0
$909$	−2.08569			−0.0691781
$910$		0			0
$911$			37.9772i			1.25824i	0.777307	+	0.629121i	$0.216585\pi$
$911$			37.9772i			1.25824i	−0.777307	+	0.629121i	$0.783415\pi$
$912$		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	0.923032	−	0.384723i	$-0.125703\pi$
$919$	31.8722	+	18.4014i	1.05137	+	0.607008i	0.128336	+	0.991731i	$0.459036\pi$
$920$		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	−0.144120	−	0.989560i	$-0.546035\pi$
$929$	−32.7095	−	18.8849i	−1.07316	−	0.619592i	−0.929044	+	0.369968i	$0.879369\pi$
$930$		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	0.801961	+	0.597376i	$0.203790\pi$
$941$	28.1702	+	48.7923i	0.918323	+	1.59058i	0.116362	+	0.993207i	$0.462877\pi$
$942$		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	0.831888	−	0.554943i	$-0.187260\pi$
$947$	23.6105	+	13.6315i	0.767238	+	0.442965i	−0.0646505	+	0.997908i	$0.520593\pi$
$948$		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	$0.306213\pi$
$953$			50.6486i			1.64067i	−0.571884	+	0.820334i	$0.693787\pi$
$954$		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	−0.177166	−	0.984181i	$-0.556693\pi$
$971$	−34.8402	−	20.1150i	−1.11807	−	0.645521i	−0.940909	+	0.338660i	$0.890026\pi$
$972$		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	−0.837708	−	0.546118i	$-0.816105\pi$
$977$	−24.4933	+	14.1412i	−0.783610	+	0.452417i	0.0540981	+	0.998536i	$0.482772\pi$
$978$		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	−0.229060	−	0.973412i	$-0.573565\pi$
$983$	15.6579	−	9.04010i	0.499410	−	0.288335i	0.728470	+	0.685078i	$0.240232\pi$
$984$		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	−0.179814	−	0.983701i	$-0.557550\pi$
$991$	18.3274	−	10.5813i	0.582188	−	0.336126i	0.762002	+	0.647574i	$0.224216\pi$
$992$		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	−0.451510	−	0.892266i	$-0.649114\pi$
$997$	3.01420	−	1.74025i	0.0954607	−	0.0551143i	0.546970	+	0.837152i	$0.315781\pi$
$998$		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.719.14		80
4.3	odd	2		280.2.ba.b.19.32	yes	80
5.4	even	2	inner	1120.2.bq.b.719.27		80
7.3	odd	6	inner	1120.2.bq.b.1039.28		80
8.3	odd	2	inner	1120.2.bq.b.719.13		80
8.5	even	2		280.2.ba.b.19.34	yes	80
20.19	odd	2		280.2.ba.b.19.9	yes	80
28.3	even	6		280.2.ba.b.59.7	yes	80
35.24	odd	6	inner	1120.2.bq.b.1039.13		80
40.19	odd	2	inner	1120.2.bq.b.719.28		80
40.29	even	2		280.2.ba.b.19.7	✓	80
56.3	even	6	inner	1120.2.bq.b.1039.27		80
56.45	odd	6		280.2.ba.b.59.9	yes	80
140.59	even	6		280.2.ba.b.59.34	yes	80
280.59	even	6	inner	1120.2.bq.b.1039.14		80
280.269	odd	6		280.2.ba.b.59.32	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.7	✓	80	40.29	even	2
280.2.ba.b.19.9	yes	80	20.19	odd	2
280.2.ba.b.19.32	yes	80	4.3	odd	2
280.2.ba.b.19.34	yes	80	8.5	even	2
280.2.ba.b.59.7	yes	80	28.3	even	6
280.2.ba.b.59.9	yes	80	56.45	odd	6
280.2.ba.b.59.32	yes	80	280.269	odd	6
280.2.ba.b.59.34	yes	80	140.59	even	6
1120.2.bq.b.719.13		80	8.3	odd	2	inner
1120.2.bq.b.719.14		80	1.1	even	1	trivial
1120.2.bq.b.719.27		80	5.4	even	2	inner
1120.2.bq.b.719.28		80	40.19	odd	2	inner
1120.2.bq.b.1039.13		80	35.24	odd	6	inner
1120.2.bq.b.1039.14		80	280.59	even	6	inner
1120.2.bq.b.1039.27		80	56.3	even	6	inner
1120.2.bq.b.1039.28		80	7.3	odd	6	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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