LMFDB - Embedded newform 297.2.f.b.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$297 = 3^{3} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	297.f (of order $5$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 9x^{14} + 51x^{12} - 249x^{10} + 1476x^{8} - 2875x^{6} + 2335x^{4} + 125x^{2} + 25$ x^16 - 9x^14 + 51x^12 - 249x^10 + 1476x^8 - 2875x^6 + 2335x^4 + 125*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$-0.185814 + 0.255752i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.b.136.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85934 + 1.35089i) q^{2} +(1.01420 - 3.12140i) q^{4} +(-1.37287 - 0.997447i) q^{5} +(0.0641710 - 0.197498i) q^{7} +(0.910502 + 2.80224i) q^{8} +3.90006 q^{10} +(1.23459 + 3.07828i) q^{11} +(-1.11803 + 0.812299i) q^{13} +(0.147482 + 0.453903i) q^{14} +(-0.168002 - 0.122061i) q^{16} +(2.97055 + 2.15823i) q^{17} +(2.50390 + 7.70620i) q^{19} +(-4.50580 + 3.27365i) q^{20} +(-6.45393 - 4.05576i) q^{22} +3.99523 q^{23} +(-0.655218 - 2.01655i) q^{25} +(0.981477 - 3.02068i) q^{26} +(-0.551387 - 0.400606i) q^{28} +(0.167656 - 0.515993i) q^{29} +(-7.95145 + 5.77707i) q^{31} -5.41563 q^{32} -8.43878 q^{34} +(-0.285092 + 0.207132i) q^{35} +(-0.381966 + 1.17557i) q^{37} +(-15.0658 - 10.9459i) q^{38} +(1.54508 - 4.75528i) q^{40} +(2.88442 + 8.87735i) q^{41} +7.92847 q^{43} +(10.8606 - 0.731656i) q^{44} +(-7.42847 + 5.39710i) q^{46} +(-2.42759 - 7.47136i) q^{47} +(5.62823 + 4.08915i) q^{49} +(3.94241 + 2.86433i) q^{50} +(1.40159 + 4.31366i) q^{52} +(-5.30674 + 3.85557i) q^{53} +(1.37548 - 5.45751i) q^{55} +0.611864 q^{56} +(0.385319 + 1.18589i) q^{58} +(2.43126 - 7.48266i) q^{59} +(1.12434 + 0.816878i) q^{61} +(6.98026 - 21.4830i) q^{62} +(10.4055 - 7.56003i) q^{64} +2.34514 q^{65} -5.85410 q^{67} +(9.74943 - 7.08338i) q^{68} +(0.250271 - 0.770255i) q^{70} +(10.3214 + 7.49891i) q^{71} +(2.36441 - 7.27691i) q^{73} +(-0.877860 - 2.70177i) q^{74} +26.5936 q^{76} +(0.687179 - 0.0462936i) q^{77} +(4.69888 - 3.41394i) q^{79} +(0.108896 + 0.335146i) q^{80} +(-17.3554 - 12.6094i) q^{82} +(11.2233 + 8.15422i) q^{83} +(-1.92545 - 5.92593i) q^{85} +(-14.7417 + 10.7105i) q^{86} +(-7.50196 + 6.26240i) q^{88} -6.19842 q^{89} +(0.0886822 + 0.272936i) q^{91} +(4.05197 - 12.4707i) q^{92} +(14.6067 + 10.6124i) q^{94} +(4.24901 - 13.0771i) q^{95} +(5.68221 - 4.12836i) q^{97} -15.9888 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 10 q^{4} + 12 q^{10} - 10 q^{16} - 2 q^{19} - 36 q^{22} + 32 q^{25} + 42 q^{28} - 26 q^{31} - 48 q^{34} - 24 q^{37} - 20 q^{40} + 24 q^{43} - 16 q^{46} + 24 q^{49} - 40 q^{52} - 16 q^{55} + 106 q^{58}+ \cdots + 72 q^{97}+O(q^{100})$ 16 * q - 10 * q^4 + 12 * q^10 - 10 * q^16 - 2 * q^19 - 36 * q^22 + 32 * q^25 + 42 * q^28 - 26 * q^31 - 48 * q^34 - 24 * q^37 - 20 * q^40 + 24 * q^43 - 16 * q^46 + 24 * q^49 - 40 * q^52 - 16 * q^55 + 106 * q^58 - 6 * q^61 + 62 * q^64 - 40 * q^67 - 58 * q^70 + 60 * q^76 + 64 * q^79 - 84 * q^82 - 18 * q^85 + 80 * q^88 - 10 * q^91 + 90 * q^94 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$ .

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.85934	+	1.35089i	−1.31475	+	0.955222i	−0.314768	+	0.949169i	$0.601927\pi$
$2$	−1.85934	+	1.35089i	−1.31475	+	0.955222i	−0.999982	+	0.00605296i	$0.998073\pi$
$3$		0			0
$3$		0			0
$4$	1.01420	−	3.12140i	0.507102	−	1.56070i
$5$	−1.37287	−	0.997447i	−0.613965	−	0.446072i	0.236843	−	0.971548i	$-0.423887\pi$
$5$	−1.37287	−	0.997447i	−0.613965	−	0.446072i	−0.850808	+	0.525476i	$0.823887\pi$
$6$		0			0
$7$	0.0641710	−	0.197498i	0.0242544	−	0.0746473i	−0.938197	−	0.346103i	$-0.887505\pi$
$7$	0.0641710	−	0.197498i	0.0242544	−	0.0746473i	0.962451	+	0.271455i	$0.0875049\pi$
$8$	0.910502	+	2.80224i	0.321911	+	0.990741i
$9$		0			0
$10$	3.90006			1.23331
$11$	1.23459	+	3.07828i	0.372244	+	0.928135i
$11$	1.23459	+	3.07828i	0.372244	+	0.928135i
$12$		0			0
$13$	−1.11803	+	0.812299i	−0.310087	+	0.225291i	−0.731934	−	0.681376i	$-0.761382\pi$
$13$	−1.11803	+	0.812299i	−0.310087	+	0.225291i	0.421847	+	0.906667i	$0.361382\pi$
$14$	0.147482	+	0.453903i	0.0394163	+	0.121311i
$15$		0			0
$16$	−0.168002	−	0.122061i	−0.0420005	−	0.0305151i
$17$	2.97055	+	2.15823i	0.720464	+	0.523448i	0.886532	−	0.462666i	$-0.153107\pi$
$17$	2.97055	+	2.15823i	0.720464	+	0.523448i	−0.166068	+	0.986114i	$0.553107\pi$
$18$		0			0
$19$	2.50390	+	7.70620i	0.574433	+	1.76792i	0.638102	+	0.769952i	$0.279720\pi$
$19$	2.50390	+	7.70620i	0.574433	+	1.76792i	−0.0636693	+	0.997971i	$0.520280\pi$
$20$	−4.50580	+	3.27365i	−1.00753	+	0.732011i
$21$		0			0
$22$	−6.45393	−	4.05576i	−1.37598	−	0.864690i
$23$	3.99523			0.833062			0.416531	−	0.909121i	$-0.363246\pi$
$23$	3.99523			0.833062			0.416531	+	0.909121i	$0.363246\pi$
$24$		0			0
$25$	−0.655218	−	2.01655i	−0.131044	−	0.403311i
$26$	0.981477	−	3.02068i	0.192483	−	0.592403i
$27$		0			0
$28$	−0.551387	−	0.400606i	−0.104202	−	0.0757075i
$29$	0.167656	−	0.515993i	0.0311330	−	0.0958175i	−0.934283	−	0.356533i	$-0.883959\pi$
$29$	0.167656	−	0.515993i	0.0311330	−	0.0958175i	0.965416	+	0.260716i	$0.0839586\pi$
$30$		0			0
$31$	−7.95145	+	5.77707i	−1.42812	+	1.03759i	−0.437760	+	0.899092i	$0.644228\pi$
$31$	−7.95145	+	5.77707i	−1.42812	+	1.03759i	−0.990362	+	0.138500i	$0.955772\pi$
$32$	−5.41563			−0.957358
$33$		0			0
$34$	−8.43878			−1.44724
$35$	−0.285092	+	0.207132i	−0.0481894	+	0.0350116i
$36$		0			0
$37$	−0.381966	+	1.17557i	−0.0627948	+	0.193263i	−0.977532	−	0.210787i	$-0.932398\pi$
$37$	−0.381966	+	1.17557i	−0.0627948	+	0.193263i	0.914737	+	0.404049i	$0.132398\pi$
$38$	−15.0658	−	10.9459i	−2.44399	−	1.77567i
$39$		0			0
$40$	1.54508	−	4.75528i	0.244299	−	0.751876i
$41$	2.88442	+	8.87735i	0.450471	+	1.38641i	0.876370	+	0.481638i	$0.159958\pi$
$41$	2.88442	+	8.87735i	0.450471	+	1.38641i	−0.425899	+	0.904771i	$0.640042\pi$
$42$		0			0
$43$	7.92847			1.20908			0.604540	−	0.796575i	$-0.293357\pi$
$43$	7.92847			1.20908			0.604540	+	0.796575i	$0.293357\pi$
$44$	10.8606	−	0.731656i	1.63730	−	0.110301i
$45$		0			0
$46$	−7.42847	+	5.39710i	−1.09527	+	0.795759i
$47$	−2.42759	−	7.47136i	−0.354101	−	1.08981i	−0.956529	−	0.291637i	$-0.905800\pi$
$47$	−2.42759	−	7.47136i	−0.354101	−	1.08981i	0.602429	−	0.798173i	$-0.294200\pi$
$48$		0			0
$49$	5.62823	+	4.08915i	0.804033	+	0.584164i
$50$	3.94241	+	2.86433i	0.557541	+	0.405077i
$51$		0			0
$52$	1.40159	+	4.31366i	0.194366	+	0.598197i
$53$	−5.30674	+	3.85557i	−0.728936	+	0.529603i	−0.889227	−	0.457467i	$-0.848757\pi$
$53$	−5.30674	+	3.85557i	−0.728936	+	0.529603i	0.160290	+	0.987070i	$0.448757\pi$
$54$		0			0
$55$	1.37548	−	5.45751i	0.185470	−	0.735890i
$56$	0.611864			0.0817638
$57$		0			0
$58$	0.385319	+	1.18589i	0.0505949	+	0.155715i
$59$	2.43126	−	7.48266i	0.316524	−	0.974160i	−0.658599	−	0.752494i	$-0.728851\pi$
$59$	2.43126	−	7.48266i	0.316524	−	0.974160i	0.975123	−	0.221666i	$-0.0711494\pi$
$60$		0			0
$61$	1.12434	+	0.816878i	0.143957	+	0.104591i	0.657433	−	0.753513i	$-0.271642\pi$
$61$	1.12434	+	0.816878i	0.143957	+	0.104591i	−0.513476	+	0.858104i	$0.671642\pi$
$62$	6.98026	−	21.4830i	0.886494	−	2.72835i
$63$		0			0
$64$	10.4055	−	7.56003i	1.30069	−	0.945004i
$65$	2.34514			0.290879
$66$		0			0
$67$	−5.85410			−0.715192			−0.357596	−	0.933876i	$-0.616404\pi$
$67$	−5.85410			−0.715192			−0.357596	+	0.933876i	$0.616404\pi$
$68$	9.74943	−	7.08338i	1.18229	−	0.858986i
$69$		0			0
$70$	0.250271	−	0.770255i	0.0299131	−	0.0920631i
$71$	10.3214	+	7.49891i	1.22492	+	0.889957i	0.996499	−	0.0836058i	$-0.0266437\pi$
$71$	10.3214	+	7.49891i	1.22492	+	0.889957i	0.228421	+	0.973562i	$0.426644\pi$
$72$		0			0
$73$	2.36441	−	7.27691i	0.276733	−	0.851697i	−0.712022	−	0.702157i	$-0.752221\pi$
$73$	2.36441	−	7.27691i	0.276733	−	0.851697i	0.988756	−	0.149541i	$-0.0477795\pi$
$74$	−0.877860	−	2.70177i	−0.102049	−	0.314075i
$75$		0			0
$76$	26.5936			3.05049
$77$	0.687179	−	0.0462936i	0.0783113	−	0.00527564i
$78$		0			0
$79$	4.69888	−	3.41394i	0.528666	−	0.384098i	−0.291193	−	0.956664i	$-0.594052\pi$
$79$	4.69888	−	3.41394i	0.528666	−	0.384098i	0.819858	+	0.572566i	$0.194052\pi$
$80$	0.108896	+	0.335146i	0.0121749	+	0.0374705i
$81$		0			0
$82$	−17.3554	−	12.6094i	−1.91658	−	1.39248i
$83$	11.2233	+	8.15422i	1.23192	+	0.895042i	0.997033	−	0.0769806i	$-0.0245280\pi$
$83$	11.2233	+	8.15422i	1.23192	+	0.895042i	0.234887	+	0.972023i	$0.424528\pi$
$84$		0			0
$85$	−1.92545	−	5.92593i	−0.208845	−	0.642758i
$86$	−14.7417	+	10.7105i	−1.58964	+	1.15494i
$87$		0			0
$88$	−7.50196	+	6.26240i	−0.799712	+	0.667574i
$89$	−6.19842			−0.657031			−0.328515	−	0.944499i	$-0.606548\pi$
$89$	−6.19842			−0.657031			−0.328515	+	0.944499i	$0.606548\pi$
$90$		0			0
$91$	0.0886822	+	0.272936i	0.00929642	+	0.0286114i
$92$	4.05197	−	12.4707i	0.422447	−	1.30016i
$93$		0			0
$94$	14.6067	+	10.6124i	1.50656	+	1.09458i
$95$	4.24901	−	13.0771i	0.435939	−	1.34168i
$96$		0			0
$97$	5.68221	−	4.12836i	0.576941	−	0.419172i	−0.260679	−	0.965425i	$-0.583947\pi$
$97$	5.68221	−	4.12836i	0.576941	−	0.419172i	0.837620	+	0.546254i	$0.183947\pi$
$98$	−15.9888			−1.61511
$99$		0			0
$100$	−6.95899			−0.695899
$101$	−9.23533	+	6.70986i	−0.918949	+	0.667656i	−0.943262	−	0.332049i	$-0.892260\pi$
$101$	−9.23533	+	6.70986i	−0.918949	+	0.667656i	0.0243129	+	0.999704i	$0.492260\pi$
$102$		0			0
$103$	−0.389798	+	1.19968i	−0.0384080	+	0.118208i	−0.968422	−	0.249316i	$-0.919794\pi$
$103$	−0.389798	+	1.19968i	−0.0384080	+	0.118208i	0.930014	+	0.367523i	$0.119794\pi$
$104$	−3.29423	−	2.39340i	−0.323026	−	0.234692i
$105$		0			0
$106$	4.65857	−	14.3376i	0.452480	−	1.39259i
$107$	2.38967	+	7.35465i	0.231018	+	0.711001i	0.997625	+	0.0688836i	$0.0219437\pi$
$107$	2.38967	+	7.35465i	0.231018	+	0.711001i	−0.766607	+	0.642117i	$0.778056\pi$
$108$		0			0
$109$	−10.2673			−0.983430			−0.491715	−	0.870756i	$-0.663630\pi$
$109$	−10.2673			−0.983430			−0.491715	+	0.870756i	$0.663630\pi$
$110$	4.81499	+	12.0055i	0.459091	+	1.14468i
$111$		0			0
$112$	−0.0348876	+	0.0253473i	−0.00329657	+	0.00239510i
$113$	−3.66218	−	11.2710i	−0.344509	−	1.06029i	−0.961846	−	0.273591i	$-0.911788\pi$
$113$	−3.66218	−	11.2710i	−0.344509	−	1.06029i	0.617337	−	0.786699i	$-0.288212\pi$
$114$		0			0
$115$	−5.48492	−	3.98503i	−0.511471	−	0.371606i
$116$	−1.44058	−	1.04664i	−0.133755	−	0.0971784i
$117$		0			0
$118$	5.58769	+	17.1972i	0.514389	+	1.58313i
$119$	0.616870	−	0.448182i	0.0565483	−	0.0410848i
$120$		0			0
$121$	−7.95156	+	7.60083i	−0.722869	+	0.690985i
$122$	−3.19403			−0.289174
$123$		0			0
$124$	9.96813	+	30.6788i	0.895165	+	2.75503i
$125$	−3.73382	+	11.4915i	−0.333963	+	1.02783i
$126$		0			0
$127$	−13.8799	−	10.0844i	−1.23164	−	0.894842i	−0.234632	−	0.972084i	$-0.575388\pi$
$127$	−13.8799	−	10.0844i	−1.23164	−	0.894842i	−0.997012	+	0.0772427i	$0.975388\pi$
$128$	−5.78752	+	17.8121i	−0.511549	+	1.57439i
$129$		0			0
$130$	−4.36040	+	3.16802i	−0.382433	+	0.277854i
$131$	−8.00969			−0.699810			−0.349905	−	0.936785i	$-0.613786\pi$
$131$	−8.00969			−0.699810			−0.349905	+	0.936785i	$0.613786\pi$
$132$		0			0
$133$	1.68264			0.145903
$134$	10.8847	−	7.90823i	0.940299	−	0.683167i
$135$		0			0
$136$	−3.34318	+	10.2893i	−0.286676	+	0.882297i
$137$	−7.30502	−	5.30740i	−0.624110	−	0.453442i	0.230245	−	0.973133i	$-0.426047\pi$
$137$	−7.30502	−	5.30740i	−0.624110	−	0.453442i	−0.854355	+	0.519691i	$0.826047\pi$
$138$		0			0
$139$	0.961286	−	2.95853i	0.0815352	−	0.250940i	−0.901976	−	0.431786i	$-0.857884\pi$
$139$	0.961286	−	2.95853i	0.0815352	−	0.250940i	0.983511	+	0.180846i	$0.0578836\pi$
$140$	0.357399	+	1.09996i	0.0302057	+	0.0929636i
$141$		0			0
$142$	−29.3211			−2.46057
$143$	−3.88080	−	2.43876i	−0.324529	−	0.203939i
$144$		0			0
$145$	−0.744846	+	0.541162i	−0.0618561	+	0.0449411i
$146$	5.43404	+	16.7243i	0.449725	+	1.38411i
$147$		0			0
$148$	3.28203	+	2.38453i	0.269781	+	0.196008i
$149$	12.1956	+	8.86062i	0.999102	+	0.725890i	0.961895	−	0.273418i	$-0.0881541\pi$
$149$	12.1956	+	8.86062i	0.999102	+	0.725890i	0.0372065	+	0.999308i	$0.488154\pi$
$150$		0			0
$151$	−3.97542	−	12.2351i	−0.323515	−	0.995677i	−0.972106	−	0.234540i	$-0.924642\pi$
$151$	−3.97542	−	12.2351i	−0.323515	−	0.995677i	0.648591	−	0.761137i	$-0.275358\pi$
$152$	−19.3148	+	14.0330i	−1.56664	+	1.13823i
$153$		0			0
$154$	−1.21516	+	1.01438i	−0.0979203	+	0.0817408i
$155$	16.6786			1.33966
$156$		0			0
$157$	0.325627	+	1.00218i	0.0259879	+	0.0799825i	0.963209	−	0.268752i	$-0.0866113\pi$
$157$	0.325627	+	1.00218i	0.0259879	+	0.0799825i	−0.937221	+	0.348735i	$0.886611\pi$
$158$	−4.12496	+	12.6953i	−0.328164	+	1.00999i
$159$		0			0
$160$	7.43495	+	5.40181i	0.587785	+	0.427050i
$161$	0.256378	−	0.789049i	0.0202054	−	0.0621858i
$162$		0			0
$163$	11.3245	−	8.22775i	0.887006	−	0.644447i	−0.0480900	−	0.998843i	$-0.515313\pi$
$163$	11.3245	−	8.22775i	0.887006	−	0.644447i	0.935096	+	0.354396i	$0.115313\pi$
$164$	30.6351			2.39220
$165$		0			0
$166$	−31.8834			−2.47463
$167$	−4.20514	+	3.05521i	−0.325404	+	0.236420i	−0.738478	−	0.674278i	$-0.764455\pi$
$167$	−4.20514	+	3.05521i	−0.325404	+	0.236420i	0.413074	+	0.910697i	$0.364455\pi$
$168$		0			0
$169$	−3.42705	+	10.5474i	−0.263619	+	0.811337i
$170$	11.5853	+	8.41724i	0.888555	+	0.645573i
$171$		0			0
$172$	8.04108	−	24.7479i	0.613127	−	1.88701i
$173$	−3.27054	−	10.0657i	−0.248654	−	0.765279i	−0.995014	−	0.0997365i	$-0.968200\pi$
$173$	−3.27054	−	10.0657i	−0.248654	−	0.765279i	0.746360	−	0.665543i	$-0.231800\pi$
$174$		0			0
$175$	−0.440312			−0.0332844
$176$	0.168322	−	0.667851i	0.0126878	−	0.0503412i
$177$		0			0
$178$	11.5249	−	8.37336i	0.863831	−	0.627610i
$179$	−2.16300	−	6.65703i	−0.161670	−	0.497569i	0.837105	−	0.547042i	$-0.184246\pi$
$179$	−2.16300	−	6.65703i	−0.161670	−	0.497569i	−0.998776	+	0.0494722i	$0.984246\pi$
$180$		0			0
$181$	−0.933353	−	0.678121i	−0.0693756	−	0.0504043i	0.552557	−	0.833475i	$-0.313652\pi$
$181$	−0.933353	−	0.678121i	−0.0693756	−	0.0504043i	−0.621933	+	0.783071i	$0.713652\pi$
$182$	−0.533595	−	0.387680i	−0.0395527	−	0.0287367i
$183$		0			0
$184$	3.63766	+	11.1956i	0.268172	+	0.825349i
$185$	1.69696	−	1.23291i	0.124763	−	0.0906456i
$186$		0			0
$187$	−2.97621	+	11.8087i	−0.217642	+	0.863538i
$188$	−25.7831			−1.88043
$189$		0			0
$190$	9.76535	+	30.0547i	0.708453	+	2.18039i
$191$	7.27171	−	22.3800i	0.526162	−	1.61936i	−0.235844	−	0.971791i	$-0.575785\pi$
$191$	7.27171	−	22.3800i	0.526162	−	1.61936i	0.762006	−	0.647570i	$-0.224215\pi$
$192$		0			0
$193$	−6.61563	−	4.80653i	−0.476203	−	0.345982i	0.323651	−	0.946177i	$-0.395090\pi$
$193$	−6.61563	−	4.80653i	−0.476203	−	0.345982i	−0.799854	+	0.600195i	$0.795090\pi$
$194$	−4.98818	+	15.3520i	−0.358130	+	1.10221i
$195$		0			0
$196$	18.4720	−	13.4207i	1.31943	−	0.958622i
$197$	−13.5502			−0.965411			−0.482705	−	0.875783i	$-0.660346\pi$
$197$	−13.5502			−0.965411			−0.482705	+	0.875783i	$0.660346\pi$
$198$		0			0
$199$	21.1166			1.49692			0.748458	−	0.663182i	$-0.230795\pi$
$199$	21.1166			1.49692			0.748458	+	0.663182i	$0.230795\pi$
$200$	5.05429	−	3.67215i	0.357392	−	0.259661i
$201$		0			0
$202$	8.10732	−	24.9518i	0.570429	−	1.75560i
$203$	−0.0911490	−	0.0662236i	−0.00639740	−	0.00464799i
$204$		0			0
$205$	4.89475	−	15.0645i	0.341864	−	1.05215i
$206$	−0.895861	−	2.75718i	−0.0624176	−	0.192102i
$207$		0			0
$208$	0.286982			0.0198986
$209$	−20.6305	+	17.2217i	−1.42704	+	1.19125i
$210$		0			0
$211$	12.6961	−	9.22427i	0.874037	−	0.635025i	−0.0576303	−	0.998338i	$-0.518354\pi$
$211$	12.6961	−	9.22427i	0.874037	−	0.635025i	0.931667	+	0.363313i	$0.118354\pi$
$212$	6.65265	+	20.4748i	0.456906	+	1.40621i
$213$		0			0
$214$	−14.3785	−	10.4466i	−0.982894	−	0.714114i
$215$	−10.8847	−	7.90823i	−0.742334	−	0.539337i
$216$		0			0
$217$	0.630707	+	1.94112i	0.0428152	+	0.131772i
$218$	19.0904	−	13.8700i	1.29296	−	0.939394i
$219$		0			0
$220$	−15.6400	−	9.82846i	−1.05445	−	0.662634i
$221$	−5.07430			−0.341335
$222$		0			0
$223$	3.06417	+	9.43055i	0.205192	+	0.631516i	0.999705	+	0.0242696i	$0.00772601\pi$
$223$	3.06417	+	9.43055i	0.205192	+	0.631516i	−0.794513	+	0.607247i	$0.792274\pi$
$224$	−0.347527	+	1.06958i	−0.0232201	+	0.0714641i
$225$		0			0
$226$	22.0351	+	16.0095i	1.46576	+	1.06493i
$227$	−3.43225	+	10.5634i	−0.227806	+	0.701116i	0.770188	+	0.637817i	$0.220162\pi$
$227$	−3.43225	+	10.5634i	−0.227806	+	0.701116i	−0.997995	+	0.0632994i	$0.979838\pi$
$228$		0			0
$229$	1.69470	−	1.23127i	0.111989	−	0.0813647i	−0.530381	−	0.847759i	$-0.677951\pi$
$229$	1.69470	−	1.23127i	0.111989	−	0.0813647i	0.642370	+	0.766395i	$0.277951\pi$
$230$	15.5816			1.02742
$231$		0			0
$232$	1.59859			0.104952
$233$	−17.5799	+	12.7726i	−1.15170	+	0.836758i	−0.988706	−	0.149869i	$-0.952115\pi$
$233$	−17.5799	+	12.7726i	−1.15170	+	0.836758i	−0.162993	+	0.986627i	$0.552115\pi$
$234$		0			0
$235$	−4.11952	+	12.6786i	−0.268728	+	0.827060i
$236$	−20.8906	−	15.1779i	−1.35986	−	0.987996i
$237$		0			0
$238$	−0.541525	+	1.66664i	−0.0351019	+	0.108032i
$239$	−4.17617	−	12.8529i	−0.270134	−	0.831388i	−0.990466	−	0.137758i	$-0.956010\pi$
$239$	−4.17617	−	12.8529i	−0.270134	−	0.831388i	0.720332	−	0.693630i	$-0.243990\pi$
$240$		0			0
$241$	9.51009			0.612599			0.306299	−	0.951935i	$-0.400909\pi$
$241$	9.51009			0.612599			0.306299	+	0.951935i	$0.400909\pi$
$242$	4.51676	−	24.8742i	0.290349	−	1.59897i
$243$		0			0
$244$	3.69011	−	2.68102i	0.236235	−	0.171635i
$245$	−3.64811	−	11.2277i	−0.233069	−	0.717313i
$246$		0			0
$247$	−9.05918	−	6.58188i	−0.576422	−	0.418795i
$248$	−23.4285	−	17.0218i	−1.48771	−	1.08089i
$249$		0			0
$250$	−8.58132	−	26.4106i	−0.542731	−	1.67035i
$251$	23.4285	−	17.0218i	1.47880	−	1.07441i	0.500854	−	0.865532i	$-0.333019\pi$
$251$	23.4285	−	17.0218i	1.47880	−	1.07441i	0.977942	−	0.208876i	$-0.0669806\pi$
$252$		0			0
$253$	4.93248	+	12.2984i	0.310102	+	0.773194i
$254$	39.4303			2.47408
$255$		0			0
$256$	−5.35217	−	16.4723i	−0.334511	−	1.02952i
$257$	−2.93523	+	9.03369i	−0.183094	+	0.563506i	−0.999910	−	0.0133919i	$-0.995737\pi$
$257$	−2.93523	+	9.03369i	−0.183094	+	0.563506i	0.816816	+	0.576898i	$0.195737\pi$
$258$		0			0
$259$	0.207662	+	0.150875i	0.0129035	+	0.00937492i
$260$	2.37845	−	7.32011i	0.147505	−	0.453974i
$261$		0			0
$262$	14.8927	−	10.8202i	0.920074	−	0.668473i
$263$	10.0485			0.619616			0.309808	−	0.950799i	$-0.399735\pi$
$263$	10.0485			0.619616			0.309808	+	0.950799i	$0.399735\pi$
$264$		0			0
$265$	11.1312			0.683783
$266$	−3.12859	+	2.27305i	−0.191826	+	0.139370i
$267$		0			0
$268$	−5.93725	+	18.2730i	−0.362675	+	1.11620i
$269$	18.4856	+	13.4305i	1.12708	+	0.818874i	0.985268	−	0.171019i	$-0.0547058\pi$
$269$	18.4856	+	13.4305i	1.12708	+	0.818874i	0.141816	+	0.989893i	$0.454706\pi$
$270$		0			0
$271$	−4.83254	+	14.8730i	−0.293556	+	0.903472i	0.690147	+	0.723669i	$0.257546\pi$
$271$	−4.83254	+	14.8730i	−0.293556	+	0.903472i	−0.983703	+	0.179803i	$0.942454\pi$
$272$	−0.235623	−	0.725174i	−0.0142868	−	0.0439701i
$273$		0			0
$274$	20.7522			1.25369
$275$	5.39858	−	4.50657i	0.325547	−	0.271756i
$276$		0			0
$277$	−16.7326	+	12.1569i	−1.00536	+	0.730440i	−0.963232	−	0.268672i	$-0.913415\pi$
$277$	−16.7326	+	12.1569i	−1.00536	+	0.730440i	−0.0421330	+	0.999112i	$0.513415\pi$
$278$	2.20929	+	6.79950i	0.132504	+	0.407807i
$279$		0			0
$280$	−0.840010	−	0.610303i	−0.0502002	−	0.0364726i
$281$	−7.50832	−	5.45512i	−0.447909	−	0.325425i	0.340861	−	0.940114i	$-0.389282\pi$
$281$	−7.50832	−	5.45512i	−0.447909	−	0.325425i	−0.788770	+	0.614689i	$0.789282\pi$
$282$		0			0
$283$	5.42068	+	16.6831i	0.322226	+	0.991710i	0.972677	+	0.232162i	$0.0745798\pi$
$283$	5.42068	+	16.6831i	0.322226	+	0.991710i	−0.650451	+	0.759548i	$0.725420\pi$
$284$	33.8750	−	24.6116i	2.01011	−	1.46043i
$285$		0			0
$286$	10.5102	−	0.708047i	0.621481	−	0.0418677i
$287$	1.93836			0.114417
$288$		0			0
$289$	−1.08708	−	3.34570i	−0.0639461	−	0.196806i
$290$	0.653870	−	2.01241i	0.0383966	−	0.118173i
$291$		0			0
$292$	−20.3161	−	14.7605i	−1.18891	−	0.863794i
$293$	3.68537	−	11.3424i	0.215301	−	0.662629i	−0.783831	−	0.620975i	$-0.786737\pi$
$293$	3.68537	−	11.3424i	0.215301	−	0.662629i	0.999132	−	0.0416549i	$-0.0132630\pi$
$294$		0			0
$295$	−10.8014	+	7.84765i	−0.628880	+	0.456908i
$296$	−3.64201			−0.211687
$297$		0			0
$298$	−34.6454			−2.00695
$299$	−4.46680	+	3.24532i	−0.258322	+	0.187682i
$300$		0			0
$301$	0.508778	−	1.56586i	0.0293255	−	0.0902545i
$302$	23.9199	+	17.3788i	1.37643	+	1.00004i
$303$		0			0
$304$	0.519963	−	1.60028i	0.0298219	−	0.0917825i
$305$	−0.728773	−	2.24293i	−0.0417294	−	0.128430i
$306$		0			0
$307$	8.18209			0.466977			0.233488	−	0.972360i	$-0.424986\pi$
$307$	8.18209			0.466977			0.233488	+	0.972360i	$0.424986\pi$
$308$	0.552438	−	2.19191i	0.0314781	−	0.124896i
$309$		0			0
$310$	−31.0112	+	22.5309i	−1.76132	+	1.27967i
$311$	−10.8027	−	33.2473i	−0.612565	−	1.88528i	−0.432521	−	0.901624i	$-0.642376\pi$
$311$	−10.8027	−	33.2473i	−0.612565	−	1.88528i	−0.180044	−	0.983659i	$-0.557624\pi$
$312$		0			0
$313$	0.553974	+	0.402485i	0.0313124	+	0.0227498i	0.603331	−	0.797491i	$-0.293840\pi$
$313$	0.553974	+	0.402485i	0.0313124	+	0.0227498i	−0.572019	+	0.820240i	$0.693840\pi$
$314$	−1.95928	−	1.42350i	−0.110569	−	0.0803328i
$315$		0			0
$316$	−5.89063	−	18.1295i	−0.331374	−	1.01986i
$317$	11.4843	−	8.34384i	0.645023	−	0.468637i	−0.216549	−	0.976272i	$-0.569480\pi$
$317$	11.4843	−	8.34384i	0.645023	−	0.468637i	0.861572	+	0.507635i	$0.169480\pi$
$318$		0			0
$319$	1.79536	−	0.120949i	0.100521	−	0.00677184i
$320$	−21.8261			−1.22012
$321$		0			0
$322$	0.589224	+	1.81345i	0.0328362	+	0.101059i
$323$	−9.19380	+	28.2956i	−0.511557	+	1.57441i
$324$		0			0
$325$	2.37060	+	1.72234i	0.131497	+	0.0955384i
$326$	−9.94135	+	30.5963i	−0.550600	+	1.69457i
$327$		0			0
$328$	−22.2502	+	16.1657i	−1.22856	+	0.892601i
$329$	−1.63136			−0.0899398
$330$		0			0
$331$	−15.3465			−0.843520			−0.421760	−	0.906708i	$-0.638587\pi$
$331$	−15.3465			−0.843520			−0.421760	+	0.906708i	$0.638587\pi$
$332$	36.8353	−	26.7624i	2.02160	−	1.46878i
$333$		0			0
$334$	3.69153	−	11.3613i	0.201991	−	0.621665i
$335$	8.03691	+	5.83916i	0.439103	+	0.319027i
$336$		0			0
$337$	0.348342	−	1.07209i	0.0189754	−	0.0584002i	−0.941120	−	0.338071i	$-0.890225\pi$
$337$	0.348342	−	1.07209i	0.0189754	−	0.0584002i	0.960096	+	0.279671i	$0.0902255\pi$
$338$	−7.87628	−	24.2407i	−0.428413	−	1.31852i
$339$		0			0
$340$	−20.4500			−1.10906
$341$	−27.6002	−	17.3444i	−1.49464	−	0.939254i
$342$		0			0
$343$	2.34478	−	1.70358i	0.126606	−	0.0919849i
$344$	7.21889	+	22.2175i	0.389216	+	1.19789i
$345$		0			0
$346$	19.6786	+	14.2974i	1.05793	+	0.768631i
$347$	−2.88335	−	2.09487i	−0.154786	−	0.112459i	0.507696	−	0.861536i	$-0.330497\pi$
$347$	−2.88335	−	2.09487i	−0.154786	−	0.112459i	−0.662483	+	0.749077i	$0.730497\pi$
$348$		0			0
$349$	5.58911	+	17.2015i	0.299178	+	0.920776i	0.981786	+	0.189991i	$0.0608459\pi$
$349$	5.58911	+	17.2015i	0.299178	+	0.920776i	−0.682607	+	0.730785i	$0.739154\pi$
$350$	0.818688	−	0.594811i	0.0437607	−	0.0317940i
$351$		0			0
$352$	−6.68610	−	16.6708i	−0.356370	−	0.888557i
$353$	−14.3798			−0.765362			−0.382681	−	0.923881i	$-0.624999\pi$
$353$	−14.3798			−0.765362			−0.382681	+	0.923881i	$0.624999\pi$
$354$		0			0
$355$	−6.69011	−	20.5900i	−0.355074	−	1.09281i
$356$	−6.28645	+	19.3477i	−0.333181	+	1.02543i
$357$		0			0
$358$	13.0146	+	9.45569i	0.687845	+	0.499749i
$359$	−3.27240	+	10.0714i	−0.172710	+	0.531548i	−0.999522	−	0.0309316i	$-0.990153\pi$
$359$	−3.27240	+	10.0714i	−0.172710	+	0.531548i	0.826811	+	0.562480i	$0.190153\pi$
$360$		0			0
$361$	−37.7447	+	27.4231i	−1.98656	+	1.44332i
$362$	2.65148			0.139359
$363$		0			0
$364$	0.941882			0.0493680
$365$	−10.5044	+	7.63186i	−0.549823	+	0.399470i
$366$		0			0
$367$	−4.46675	+	13.7473i	−0.233163	+	0.717601i	0.764197	+	0.644983i	$0.223135\pi$
$367$	−4.46675	+	13.7473i	−0.233163	+	0.717601i	−0.997360	+	0.0726181i	$0.976865\pi$
$368$	−0.671206	−	0.487659i	−0.0349890	−	0.0254210i
$369$		0			0
$370$	−1.48969	+	4.58480i	−0.0774454	+	0.238352i
$371$	0.420929	+	1.29549i	0.0218535	+	0.0672583i
$372$		0			0
$373$	34.5181			1.78728			0.893640	−	0.448785i	$-0.148143\pi$
$373$	34.5181			1.78728			0.893640	+	0.448785i	$0.148143\pi$
$374$	−10.4185	−	25.9769i	−0.538725	−	1.34323i
$375$		0			0
$376$	18.7262	−	13.6054i	0.965730	−	0.701644i
$377$	0.231695	+	0.713085i	0.0119329	+	0.0367257i
$378$		0			0
$379$	4.72788	+	3.43500i	0.242855	+	0.176444i	0.702554	−	0.711630i	$-0.252043\pi$
$379$	4.72788	+	3.43500i	0.242855	+	0.176444i	−0.459699	+	0.888075i	$0.652043\pi$
$380$	−36.5094	−	26.5257i	−1.87290	−	1.36074i
$381$		0			0
$382$	16.7123	+	51.4352i	0.855077	+	2.63166i
$383$	3.61724	−	2.62808i	0.184832	−	0.134289i	−0.491521	−	0.870865i	$-0.663559\pi$
$383$	3.61724	−	2.62808i	0.184832	−	0.134289i	0.676354	+	0.736577i	$0.263559\pi$
$384$		0			0
$385$	−0.989581	−	0.621869i	−0.0504337	−	0.0316934i
$386$	18.7938			0.956577
$387$		0			0
$388$	−7.12335	−	21.9234i	−0.361633	−	1.11299i
$389$	−0.757488	+	2.33131i	−0.0384061	+	0.118202i	−0.968421	−	0.249319i	$-0.919793\pi$
$389$	−0.757488	+	2.33131i	−0.0384061	+	0.118202i	0.930015	+	0.367521i	$0.119793\pi$
$390$		0			0
$391$	11.8680	+	8.62262i	0.600191	+	0.436065i
$392$	−6.33425	+	19.4948i	−0.319928	+	0.984637i
$393$		0			0
$394$	25.1944	−	18.3048i	1.26927	−	0.922181i
$395$	−9.85617			−0.495918
$396$		0			0
$397$	4.85892			0.243862			0.121931	−	0.992539i	$-0.461091\pi$
$397$	4.85892			0.243862			0.121931	+	0.992539i	$0.461091\pi$
$398$	−39.2629	+	28.5261i	−1.96807	+	1.42989i
$399$		0			0
$400$	−0.136064	+	0.418761i	−0.00680319	+	0.0209381i
$401$	2.29934	+	1.67057i	0.114824	+	0.0834243i	0.643715	−	0.765265i	$-0.277392\pi$
$401$	2.29934	+	1.67057i	0.114824	+	0.0834243i	−0.528891	+	0.848689i	$0.677392\pi$
$402$		0			0
$403$	4.19729	−	12.9179i	0.209082	−	0.643487i
$404$	11.5776	+	35.6323i	0.576009	+	1.77277i
$405$		0			0
$406$	0.258937			0.0128508
$407$	−4.09030	+	0.275554i	−0.202749	+	0.0136587i
$408$		0			0
$409$	−8.89642	+	6.46363i	−0.439900	+	0.319606i	−0.785595	−	0.618741i	$-0.787643\pi$
$409$	−8.89642	+	6.46363i	−0.439900	+	0.319606i	0.345695	+	0.938347i	$0.387643\pi$
$410$	11.2494	+	34.6222i	0.555570	+	1.70987i
$411$		0			0
$412$	3.34933	+	2.43343i	0.165010	+	0.119887i
$413$	−1.32179	−	0.960340i	−0.0650413	−	0.0472552i
$414$		0			0
$415$	−7.27474	−	22.3893i	−0.357103	−	1.09905i
$416$	6.05486	−	4.39911i	0.296864	−	0.215684i
$417$		0			0
$418$	15.0945	−	59.8904i	0.738296	−	2.92934i
$419$	14.3966			0.703320			0.351660	−	0.936128i	$-0.385617\pi$
$419$	14.3966			0.703320			0.351660	+	0.936128i	$0.385617\pi$
$420$		0			0
$421$	−0.787498	−	2.42367i	−0.0383803	−	0.118122i	0.930031	−	0.367482i	$-0.119780\pi$
$421$	−0.787498	−	2.42367i	−0.0383803	−	0.118122i	−0.968411	+	0.249359i	$0.919780\pi$
$422$	−11.1454	+	34.3021i	−0.542550	+	1.66980i
$423$		0			0
$424$	−15.6360	−	11.3602i	−0.759352	−	0.551702i
$425$	2.40583	−	7.40439i	0.116700	−	0.359165i
$426$		0			0
$427$	0.233482	−	0.169634i	0.0112990	−	0.00820918i
$428$	25.3804			1.22681
$429$		0			0
$430$	30.9215			1.49117
$431$	19.6549	−	14.2801i	0.946743	−	0.687849i	−0.00329155	−	0.999995i	$-0.501048\pi$
$431$	19.6549	−	14.2801i	0.946743	−	0.687849i	0.950034	+	0.312146i	$0.101048\pi$
$432$		0			0
$433$	11.6717	−	35.9219i	0.560907	−	1.72629i	−0.118903	−	0.992906i	$-0.537938\pi$
$433$	11.6717	−	35.9219i	0.560907	−	1.72629i	0.679810	−	0.733388i	$-0.262062\pi$
$434$	−3.79493	−	2.75718i	−0.182162	−	0.132349i
$435$		0			0
$436$	−10.4131	+	32.0484i	−0.498699	+	1.53484i
$437$	10.0036	+	30.7880i	0.478538	+	1.47279i
$438$		0			0
$439$	−3.61817			−0.172686			−0.0863429	−	0.996265i	$-0.527518\pi$
$439$	−3.61817			−0.172686			−0.0863429	+	0.996265i	$0.527518\pi$
$440$	16.5456	−	1.11464i	0.788782	−	0.0531383i
$441$		0			0
$442$	9.43484	−	6.85481i	0.448770	−	0.326050i
$443$	2.00397	+	6.16758i	0.0952114	+	0.293031i	0.987309	−	0.158813i	$-0.0507666\pi$
$443$	2.00397	+	6.16758i	0.0952114	+	0.293031i	−0.892097	+	0.451843i	$0.850767\pi$
$444$		0			0
$445$	8.50961	+	6.18259i	0.403394	+	0.293083i
$446$	−18.4369	−	13.3952i	−0.873014	−	0.634282i
$447$		0			0
$448$	−0.825361	−	2.54020i	−0.0389946	−	0.120013i
$449$	28.0402	−	20.3724i	1.32330	−	0.961433i	0.323415	−	0.946257i	$-0.395169\pi$
$449$	28.0402	−	20.3724i	1.32330	−	0.961433i	0.999885	−	0.0151762i	$-0.00483092\pi$
$450$		0			0
$451$	−23.7658	+	19.8390i	−1.11909	+	0.934180i
$452$	−38.8956			−1.82949
$453$		0			0
$454$	−7.88823	−	24.2775i	−0.370213	−	1.13940i
$455$	0.150490	−	0.463161i	0.00705508	−	0.0217133i
$456$		0			0
$457$	−29.5150	−	21.4439i	−1.38065	−	1.00310i	−0.996819	−	0.0797015i	$-0.974603\pi$
$457$	−29.5150	−	21.4439i	−1.38065	−	1.00310i	−0.383835	−	0.923402i	$-0.625397\pi$
$458$	−1.48771	+	4.57869i	−0.0695160	+	0.213948i
$459$		0			0
$460$	−18.0017	+	13.0790i	−0.839332	+	0.609811i
$461$	−17.2602			−0.803887			−0.401943	−	0.915665i	$-0.631665\pi$
$461$	−17.2602			−0.803887			−0.401943	+	0.915665i	$0.631665\pi$
$462$		0			0
$463$	37.5981			1.74733			0.873667	−	0.486524i	$-0.161736\pi$
$463$	37.5981			1.74733			0.873667	+	0.486524i	$0.161736\pi$
$464$	−0.0911490	+	0.0662236i	−0.00423148	+	0.00307435i
$465$		0			0
$466$	15.4327	−	47.4970i	0.714906	−	2.20025i
$467$	28.6222	+	20.7952i	1.32448	+	0.962288i	0.999865	+	0.0164409i	$0.00523352\pi$
$467$	28.6222	+	20.7952i	1.32448	+	0.962288i	0.324611	+	0.945847i	$0.394766\pi$
$468$		0			0
$469$	−0.375664	+	1.15617i	−0.0173465	+	0.0533872i
$470$	−9.46776	−	29.1388i	−0.436715	−	1.34407i
$471$		0			0
$472$	23.1819			1.06703
$473$	9.78843	+	24.4060i	0.450073	+	1.12219i
$474$		0			0
$475$	13.8994	−	10.0985i	0.637747	−	0.463350i
$476$	−0.773322	−	2.38004i	−0.0354452	−	0.109089i
$477$		0			0
$478$	25.1278	+	18.2564i	1.14932	+	0.835029i
$479$	19.2138	+	13.9596i	0.877900	+	0.637831i	0.932695	−	0.360666i	$-0.117451\pi$
$479$	19.2138	+	13.9596i	0.877900	+	0.637831i	−0.0547953	+	0.998498i	$0.517451\pi$
$480$		0			0
$481$	−0.527864	−	1.62460i	−0.0240685	−	0.0740753i
$482$	−17.6825	+	12.8471i	−0.805414	+	0.585167i
$483$		0			0
$484$	15.6607	+	32.5288i	0.711851	+	1.47858i
$485$	−11.9187			−0.541202
$486$		0			0
$487$	−7.50153	−	23.0873i	−0.339927	−	1.04619i	−0.964244	−	0.265016i	$-0.914623\pi$
$487$	−7.50153	−	23.0873i	−0.339927	−	1.04619i	0.624317	−	0.781171i	$-0.285377\pi$
$488$	−1.26538	+	3.89443i	−0.0572809	+	0.176292i
$489$		0			0
$490$	21.9505	+	15.9479i	0.991621	+	0.720455i
$491$	−0.117847	+	0.362697i	−0.00531838	+	0.0163683i	−0.953680	−	0.300821i	$-0.902739\pi$
$491$	−0.117847	+	0.362697i	−0.00531838	+	0.0163683i	0.948362	+	0.317190i	$0.102739\pi$
$492$		0			0
$493$	1.61166	−	1.17094i	0.0725857	−	0.0527366i
$494$	25.7354			1.15789
$495$		0			0
$496$	2.04101			0.0916441
$497$	2.14335	−	1.55724i	0.0961425	−	0.0698516i
$498$		0			0
$499$	−0.981860	+	3.02185i	−0.0439541	+	0.135277i	−0.970625	−	0.240596i	$-0.922657\pi$
$499$	−0.981860	+	3.02185i	−0.0439541	+	0.135277i	0.926671	+	0.375873i	$0.122657\pi$
$500$	32.0828	+	23.3095i	1.43478	+	1.04243i
$501$		0			0
$502$	−20.5670	+	63.2986i	−0.917949	+	2.82516i
$503$	−13.3297	−	41.0245i	−0.594341	−	1.82919i	−0.557980	−	0.829854i	$-0.688424\pi$
$503$	−13.3297	−	41.0245i	−0.594341	−	1.82919i	−0.0363603	−	0.999339i	$-0.511576\pi$
$504$		0			0
$505$	19.3716			0.862026
$506$	−25.7849	−	16.2037i	−1.14628	−	0.720341i
$507$		0			0
$508$	−45.5543	+	33.0972i	−2.02115	+	1.46845i
$509$	8.63067	+	26.5625i	0.382548	+	1.17736i	0.938244	+	0.345975i	$0.112452\pi$
$509$	8.63067	+	26.5625i	0.382548	+	1.17736i	−0.555696	+	0.831386i	$0.687548\pi$
$510$		0			0
$511$	−1.28545	−	0.933933i	−0.0568649	−	0.0413148i
$512$	1.89985	+	1.38032i	0.0839625	+	0.0610023i
$513$		0			0
$514$	−6.74593	−	20.7618i	−0.297550	−	0.915765i
$515$	1.73176	−	1.25819i	0.0763103	−	0.0554427i
$516$		0			0
$517$	20.0018	−	16.6969i	0.879679	−	0.734328i
$518$	−0.589928			−0.0259200
$519$		0			0
$520$	2.13525	+	6.57164i	0.0936371	+	0.288185i
$521$	2.17716	−	6.70060i	0.0953830	−	0.293559i	−0.891970	−	0.452094i	$-0.850677\pi$
$521$	2.17716	−	6.70060i	0.0953830	−	0.293559i	0.987353	+	0.158535i	$0.0506772\pi$
$522$		0			0
$523$	−10.8399	−	7.87565i	−0.473996	−	0.344378i	0.325001	−	0.945714i	$-0.394635\pi$
$523$	−10.8399	−	7.87565i	−0.473996	−	0.344378i	−0.798996	+	0.601336i	$0.794635\pi$
$524$	−8.12345	+	25.0014i	−0.354875	+	1.09219i
$525$		0			0
$526$	−18.6835	+	13.5744i	−0.814640	+	0.591871i
$527$	−36.0884			−1.57204
$528$		0			0
$529$	−7.03817			−0.306007
$530$	−20.6966	+	15.0370i	−0.899004	+	0.653164i
$531$		0			0
$532$	1.70654	−	5.25218i	0.0739877	−	0.227711i
$533$	−10.4359	−	7.58216i	−0.452031	−	0.328420i
$534$		0			0
$535$	4.05517	−	12.4805i	0.175320	−	0.539581i
$536$	−5.33017	−	16.4046i	−0.230228	−	0.708570i
$537$		0			0
$538$	−52.5140			−2.26404
$539$	−5.63896	+	22.3737i	−0.242887	+	0.963703i
$540$		0			0
$541$	10.9773	−	7.97545i	0.471950	−	0.342892i	−0.326251	−	0.945283i	$-0.605785\pi$
$541$	10.9773	−	7.97545i	0.471950	−	0.342892i	0.798201	+	0.602392i	$0.205785\pi$
$542$	−11.1065	−	34.1822i	−0.477064	−	1.46825i
$543$		0			0
$544$	−16.0874	−	11.6882i	−0.689742	−	0.501127i
$545$	14.0957	+	10.2411i	0.603792	+	0.438681i
$546$		0			0
$547$	9.97497	+	30.6998i	0.426499	+	1.31263i	0.901552	+	0.432672i	$0.142429\pi$
$547$	9.97497	+	30.6998i	0.426499	+	1.31263i	−0.475052	+	0.879958i	$0.657571\pi$
$548$	−23.9753	+	17.4191i	−1.02417	+	0.744105i
$549$		0			0
$550$	−3.94992	+	15.6721i	−0.168425	+	0.668261i
$551$	4.39614			0.187282
$552$		0			0
$553$	−0.372714	−	1.14710i	−0.0158494	−	0.0487795i
$554$	14.6889	−	45.2077i	0.624071	−	1.92069i
$555$		0			0
$556$	−8.25982	−	6.00111i	−0.350294	−	0.254504i
$557$	−1.31597	+	4.05013i	−0.0557593	+	0.171609i	−0.975058	−	0.221952i	$-0.928757\pi$
$557$	−1.31597	+	4.05013i	−0.0557593	+	0.171609i	0.919298	+	0.393562i	$0.128757\pi$
$558$		0			0
$559$	−8.86430	+	6.44029i	−0.374920	+	0.272395i
$560$	0.0731787			0.00309236
$561$		0			0
$562$	21.3297			0.899741
$563$	−10.8181	+	7.85982i	−0.455929	+	0.331252i	−0.791932	−	0.610609i	$-0.790925\pi$
$563$	−10.8181	+	7.85982i	−0.455929	+	0.331252i	0.336003	+	0.941861i	$0.390925\pi$
$564$		0			0
$565$	−6.21457	+	19.1265i	−0.261449	+	0.804658i
$566$	−32.6159	−	23.6968i	−1.37095	−	0.996053i
$567$		0			0
$568$	−11.6161	+	35.7507i	−0.487401	+	1.50007i
$569$	−3.47017	−	10.6801i	−0.145477	−	0.447733i	0.851595	−	0.524200i	$-0.175636\pi$
$569$	−3.47017	−	10.6801i	−0.145477	−	0.447733i	−0.997072	+	0.0764679i	$0.975636\pi$
$570$		0			0
$571$	−7.08202			−0.296373			−0.148187	−	0.988959i	$-0.547344\pi$
$571$	−7.08202			−0.296373			−0.148187	+	0.988959i	$0.547344\pi$
$572$	−11.5482	+	9.64011i	−0.482856	+	0.403073i
$573$		0			0
$574$	−3.60406	+	2.61850i	−0.150430	+	0.109294i
$575$	−2.61774	−	8.05659i	−0.109167	−	0.335983i
$576$		0			0
$577$	12.5556	+	9.12216i	0.522695	+	0.379760i	0.817618	−	0.575761i	$-0.195294\pi$
$577$	12.5556	+	9.12216i	0.522695	+	0.379760i	−0.294923	+	0.955521i	$0.595294\pi$
$578$	6.54092	+	4.75226i	0.272066	+	0.197668i
$579$		0			0
$580$	0.933757	+	2.87381i	0.0387721	+	0.119328i
$581$	2.33066	−	1.69332i	0.0966919	−	0.0702508i
$582$		0			0
$583$	−18.4202	−	11.5755i	−0.762885	−	0.479410i
$584$	22.5444			0.932895
$585$		0			0
$586$	8.46995	+	26.0678i	0.349891	+	1.07685i
$587$	−8.31220	+	25.5823i	−0.343081	+	1.05590i	0.619522	+	0.784979i	$0.287327\pi$
$587$	−8.31220	+	25.5823i	−0.343081	+	1.05590i	−0.962603	+	0.270916i	$0.912673\pi$
$588$		0			0
$589$	−64.4288	−	46.8103i	−2.65474	−	1.92878i
$590$	9.48209	−	29.1829i	0.390371	−	1.20144i
$591$		0			0
$592$	0.207662	−	0.150875i	0.00853485	−	0.00620093i
$593$	40.9970			1.68355			0.841773	−	0.539832i	$-0.181512\pi$
$593$	40.9970			1.68355			0.841773	+	0.539832i	$0.181512\pi$
$594$		0			0
$595$	−1.29392			−0.0530455
$596$	40.0263	−	29.0808i	1.63954	−	1.19120i
$597$		0			0
$598$	3.92122	−	12.0683i	0.160351	−	0.493509i
$599$	−34.5769	−	25.1216i	−1.41278	−	1.02644i	−0.992912	−	0.118854i	$-0.962078\pi$
$599$	−34.5769	−	25.1216i	−1.41278	−	1.02644i	−0.419863	−	0.907587i	$-0.637922\pi$
$600$		0			0
$601$	5.24244	−	16.1346i	0.213844	−	0.658143i	−0.785390	−	0.619001i	$-0.787538\pi$
$601$	5.24244	−	16.1346i	0.213844	−	0.658143i	0.999234	−	0.0391417i	$-0.0124624\pi$
$602$	1.16931	+	3.59876i	0.0476574	+	0.146674i
$603$		0			0
$604$	−42.2224			−1.71801
$605$	18.4979	−	2.50368i	0.752046	−	0.101789i
$606$		0			0
$607$	−15.7067	+	11.4116i	−0.637514	+	0.463181i	−0.858995	−	0.511983i	$-0.828911\pi$
$607$	−15.7067	+	11.4116i	−0.637514	+	0.463181i	0.221481	+	0.975165i	$0.428911\pi$
$608$	−13.5602	−	41.7339i	−0.549938	−	1.69253i
$609$		0			0
$610$	4.38498	+	3.18588i	0.177543	+	0.128992i
$611$	8.78311	+	6.38130i	0.355326	+	0.258160i
$612$		0			0
$613$	−8.52386	−	26.2337i	−0.344275	−	1.05957i	−0.961971	−	0.273153i	$-0.911933\pi$
$613$	−8.52386	−	26.2337i	−0.344275	−	1.05957i	0.617695	−	0.786418i	$-0.288067\pi$
$614$	−15.2133	+	11.0531i	−0.613958	+	0.446066i
$615$		0			0
$616$	0.755403	+	1.88349i	0.0304361	+	0.0758879i
$617$	31.9850			1.28767			0.643835	−	0.765165i	$-0.277343\pi$
$617$	31.9850			1.28767			0.643835	+	0.765165i	$0.277343\pi$
$618$		0			0
$619$	−3.71721	−	11.4404i	−0.149407	−	0.459828i	0.848144	−	0.529765i	$-0.177720\pi$
$619$	−3.71721	−	11.4404i	−0.149407	−	0.459828i	−0.997551	+	0.0699375i	$0.977720\pi$
$620$	16.9155	−	52.0606i	0.679343	−	2.09080i
$621$		0			0
$622$	64.9993	+	47.2247i	2.60623	+	1.89354i
$623$	−0.397759	+	1.22418i	−0.0159359	+	0.0490455i
$624$		0			0
$625$	8.01133	−	5.82057i	0.320453	−	0.232823i
$626$	−1.57374			−0.0628991
$627$		0			0
$628$	3.45845			0.138007
$629$	−3.67180	+	2.66772i	−0.146404	+	0.106369i
$630$		0			0
$631$	−13.4511	+	41.3983i	−0.535480	+	1.64804i	0.207128	+	0.978314i	$0.433588\pi$
$631$	−13.4511	+	41.3983i	−0.535480	+	1.64804i	−0.742609	+	0.669726i	$0.766412\pi$
$632$	13.8450	+	10.0590i	0.550725	+	0.400125i
$633$		0			0
$634$	−10.0816	+	31.0280i	−0.400392	+	1.23228i
$635$	8.99670	+	27.6890i	0.357023	+	1.09880i
$636$		0			0
$637$	−9.61417			−0.380927
$638$	−3.17478	+	2.65021i	−0.125691	+	0.104923i
$639$		0			0
$640$	25.7122	−	18.6810i	1.01636	−	0.738431i
$641$	3.08773	+	9.50306i	0.121958	+	0.375348i	0.993335	−	0.115267i	$-0.0367722\pi$
$641$	3.08773	+	9.50306i	0.121958	+	0.375348i	−0.871377	+	0.490615i	$0.836772\pi$
$642$		0			0
$643$	−10.2644	−	7.45750i	−0.404787	−	0.294095i	0.366701	−	0.930339i	$-0.380487\pi$
$643$	−10.2644	−	7.45750i	−0.404787	−	0.294095i	−0.771488	+	0.636244i	$0.780487\pi$
$644$	−2.20292	−	1.60051i	−0.0868071	−	0.0630690i
$645$		0			0
$646$	−21.1298	−	65.0309i	−0.831341	−	2.55861i
$647$	17.3064	−	12.5738i	0.680384	−	0.494328i	−0.193101	−	0.981179i	$-0.561855\pi$
$647$	17.3064	−	12.5738i	0.680384	−	0.494328i	0.873485	+	0.486851i	$0.161855\pi$
$648$		0			0
$649$	26.0353	−	1.75394i	1.02198	−	0.0688481i
$650$	−6.73444			−0.264146
$651$		0			0
$652$	−14.1967	−	43.6930i	−0.555986	−	1.71115i
$653$	8.77002	−	26.9914i	0.343198	−	1.05625i	−0.619344	−	0.785120i	$-0.712601\pi$
$653$	8.77002	−	26.9914i	0.343198	−	1.05625i	0.962542	−	0.271134i	$-0.0873986\pi$
$654$		0			0
$655$	10.9962	+	7.98924i	0.429659	+	0.312165i
$656$	0.598985	−	1.84349i	0.0233864	−	0.0719760i
$657$		0			0
$658$	3.03325	−	2.20378i	0.118248	−	0.0859124i
$659$	21.3927			0.833340			0.416670	−	0.909058i	$-0.363197\pi$
$659$	21.3927			0.833340			0.416670	+	0.909058i	$0.363197\pi$
$660$		0			0
$661$	−7.45589			−0.290001			−0.145000	−	0.989432i	$-0.546318\pi$
$661$	−7.45589			−0.290001			−0.145000	+	0.989432i	$0.546318\pi$
$662$	28.5343	−	20.7314i	1.10902	−	0.805748i
$663$		0			0
$664$	−12.6312	+	38.8749i	−0.490186	+	1.50864i
$665$	−2.31004	−	1.67834i	−0.0895795	−	0.0650833i
$666$		0			0
$667$	0.669825	−	2.06151i	0.0259357	−	0.0798219i
$668$	5.27167	+	16.2245i	0.203967	+	0.627746i
$669$		0			0
$670$	−22.8314			−0.882053
$671$	−1.12648	+	4.46953i	−0.0434872	+	0.172544i
$672$		0			0
$673$	23.8617	−	17.3365i	0.919801	−	0.668275i	−0.0236731	−	0.999720i	$-0.507536\pi$
$673$	23.8617	−	17.3365i	0.919801	−	0.668275i	0.943475	+	0.331445i	$0.107536\pi$
$674$	0.800582	+	2.46394i	0.0308373	+	0.0949074i
$675$		0			0
$676$	29.4468	+	21.3944i	1.13257	+	0.822860i
$677$	6.28907	+	4.56928i	0.241709	+	0.175612i	0.702044	−	0.712133i	$-0.252271\pi$
$677$	6.28907	+	4.56928i	0.241709	+	0.175612i	−0.460336	+	0.887745i	$0.652271\pi$
$678$		0			0
$679$	−0.450711	−	1.38715i	−0.0172967	−	0.0532338i
$680$	14.8527	−	10.7912i	0.569577	−	0.413822i
$681$		0			0
$682$	74.7485	−	5.03563i	2.86227	−	0.192824i
$683$	7.88885			0.301858			0.150929	−	0.988545i	$-0.451773\pi$
$683$	7.88885			0.301858			0.150929	+	0.988545i	$0.451773\pi$
$684$		0			0
$685$	4.73497	+	14.5727i	0.180914	+	0.556796i
$686$	−2.05839	+	6.33507i	−0.0785897	+	0.241874i
$687$		0			0
$688$	−1.33200	−	0.967753i	−0.0507820	−	0.0368952i
$689$	2.80124	−	8.62132i	0.106719	−	0.328446i
$690$		0			0
$691$	6.65092	−	4.83218i	0.253013	−	0.183825i	−0.454048	−	0.890977i	$-0.650021\pi$
$691$	6.65092	−	4.83218i	0.253013	−	0.183825i	0.707061	+	0.707152i	$0.250021\pi$
$692$	−34.7360			−1.32046
$693$		0			0
$694$	8.19105			0.310928
$695$	−4.27070	+	3.10285i	−0.161997	+	0.117698i
$696$		0			0
$697$	−10.5910	+	32.5958i	−0.401164	+	1.23466i
$698$	−33.6294	−	24.4332i	−1.27289	−	0.924809i
$699$		0			0
$700$	−0.446565	+	1.37439i	−0.0168786	+	0.0519469i
$701$	−2.64646	−	8.14496i	−0.0999554	−	0.307631i	0.888558	−	0.458764i	$-0.151708\pi$
$701$	−2.64646	−	8.14496i	−0.0999554	−	0.307631i	−0.988513	+	0.151133i	$0.951708\pi$
$702$		0			0
$703$	−10.0156			−0.377745
$704$	36.1184	+	22.6974i	1.36126	+	0.855441i
$705$		0			0
$706$	26.7370	−	19.4255i	1.00626	−	0.731090i
$707$	0.732544	+	2.25454i	0.0275501	+	0.0847906i
$708$		0			0
$709$	−0.947014	−	0.688046i	−0.0355659	−	0.0258401i	0.569860	−	0.821742i	$-0.306997\pi$
$709$	−0.947014	−	0.688046i	−0.0355659	−	0.0258401i	−0.605426	+	0.795901i	$0.706997\pi$
$710$	40.2540	+	29.2462i	1.51070	+	1.09759i
$711$		0			0
$712$	−5.64367	−	17.3694i	−0.211506	−	0.650947i
$713$	−31.7678	+	23.0807i	−1.18972	+	0.864379i
$714$		0			0
$715$	2.89529	+	7.21899i	0.108278	+	0.269975i
$716$	−22.9729			−0.858539
$717$		0			0
$718$	−7.52084	−	23.1468i	−0.280675	−	0.863830i
$719$	3.54766	−	10.9186i	0.132305	−	0.407194i	−0.862856	−	0.505450i	$-0.831326\pi$
$719$	3.54766	−	10.9186i	0.132305	−	0.407194i	0.995161	+	0.0982562i	$0.0313265\pi$
$720$		0			0
$721$	0.211920	+	0.153969i	0.00789231	+	0.00573410i
$722$	33.1345	−	101.978i	1.23314	−	3.79521i
$723$		0			0
$724$	−3.06329	+	2.22561i	−0.113846	+	0.0827143i
$725$	−1.15038			−0.0427240
$726$		0			0
$727$	30.5458			1.13288			0.566441	−	0.824102i	$-0.308320\pi$
$727$	30.5458			1.13288			0.566441	+	0.824102i	$0.308320\pi$
$728$	−0.684085	+	0.497017i	−0.0253539	+	0.0184207i
$729$		0			0
$730$	9.22135	−	28.3804i	0.341298	−	1.05041i
$731$	23.5519	+	17.1115i	0.871099	+	0.632890i
$732$		0			0
$733$	1.56318	−	4.81098i	0.0577375	−	0.177698i	−0.918028	−	0.396514i	$-0.870220\pi$
$733$	1.56318	−	4.81098i	0.0577375	−	0.177698i	0.975766	+	0.218817i	$0.0702197\pi$
$734$	−10.2658	−	31.5949i	−0.378917	−	1.16619i
$735$		0			0
$736$	−21.6367			−0.797538
$737$	−7.22743	−	18.0205i	−0.266226	−	0.663795i
$738$		0			0
$739$	22.9584	−	16.6802i	0.844537	−	0.613592i	−0.0790973	−	0.996867i	$-0.525204\pi$
$739$	22.9584	−	16.6802i	0.844537	−	0.613592i	0.923634	+	0.383275i	$0.125204\pi$
$740$	−2.12735	−	6.54730i	−0.0782029	−	0.240684i
$741$		0			0
$742$	−2.53270	−	1.84012i	−0.0929785	−	0.0675528i
$743$	16.9950	+	12.3476i	0.623487	+	0.452990i	0.854138	−	0.520047i	$-0.174086\pi$
$743$	16.9950	+	12.3476i	0.623487	+	0.452990i	−0.230651	+	0.973037i	$0.574086\pi$
$744$		0			0
$745$	−7.90495	−	24.3289i	−0.289615	−	0.891343i
$746$	−64.1808	+	46.6301i	−2.34983	+	1.70725i
$747$		0			0
$748$	33.8412	+	21.2664i	1.23736	+	0.777575i
$749$	1.60588			0.0586774
$750$		0			0
$751$	−1.94283	−	5.97940i	−0.0708947	−	0.218192i	0.909331	−	0.416073i	$-0.136594\pi$
$751$	−1.94283	−	5.97940i	−0.0708947	−	0.218192i	−0.980226	+	0.197881i	$0.936594\pi$
$752$	−0.504118	+	1.55152i	−0.0183833	+	0.0565779i
$753$		0			0
$754$	−1.39410	−	1.01287i	−0.0507700	−	0.0368866i
$755$	−6.74612	+	20.7624i	−0.245517	+	0.755622i
$756$		0			0
$757$	22.7711	−	16.5442i	0.827630	−	0.601308i	−0.0912581	−	0.995827i	$-0.529089\pi$
$757$	22.7711	−	16.5442i	0.827630	−	0.601308i	0.918888	+	0.394519i	$0.129089\pi$
$758$	−13.4310			−0.487837
$759$		0			0
$760$	40.5139			1.46959
$761$	17.6923	−	12.8542i	0.641347	−	0.465966i	−0.218966	−	0.975733i	$-0.570268\pi$
$761$	17.6923	−	12.8542i	0.641347	−	0.465966i	0.860313	+	0.509767i	$0.170268\pi$
$762$		0			0
$763$	−0.658864	+	2.02777i	−0.0238525	+	0.0734104i
$764$	−62.4819	−	45.3958i	−2.26052	−	1.64236i
$765$		0			0
$766$	−3.17543	+	9.77297i	−0.114733	+	0.353112i
$767$	3.35992	+	10.3408i	0.121320	+	0.373384i
$768$		0			0
$769$	−41.3397			−1.49075			−0.745374	−	0.666647i	$-0.767729\pi$
$769$	−41.3397			−1.49075			−0.745374	+	0.666647i	$0.767729\pi$
$770$	2.68004	−	0.180548i	0.0965820	−	0.00650650i
$771$		0			0
$772$	−21.7127	+	15.7752i	−0.781457	+	0.567762i
$773$	1.05855	+	3.25789i	0.0380735	+	0.117178i	0.968287	−	0.249841i	$-0.0803783\pi$
$773$	1.05855	+	3.25789i	0.0380735	+	0.117178i	−0.930213	+	0.367019i	$0.880378\pi$
$774$		0			0
$775$	16.8597	+	12.2493i	0.605619	+	0.440008i
$776$	16.7423	+	12.1640i	0.601014	+	0.436662i
$777$		0			0
$778$	−1.74091	−	5.35797i	−0.0624146	−	0.192092i
$779$	−61.1883	+	44.4559i	−2.19230	+	1.59280i
$780$		0			0
$781$	−10.3410	+	41.0301i	−0.370031	+	1.46817i
$782$	−33.7148			−1.20564
$783$		0			0
$784$	−0.446430	−	1.37397i	−0.0159439	−	0.0490703i
$785$	0.552576	−	1.70065i	0.0197223	−	0.0606990i
$786$		0			0
$787$	8.14921	+	5.92074i	0.290488	+	0.211052i	0.723479	−	0.690346i	$-0.242542\pi$
$787$	8.14921	+	5.92074i	0.290488	+	0.211052i	−0.432991	+	0.901398i	$0.642542\pi$
$788$	−13.7426	+	42.2955i	−0.489561	+	1.50671i
$789$		0			0
$790$	18.3259	−	13.3146i	0.652008	−	0.473712i
$791$	−2.46102			−0.0875036
$792$		0			0
$793$	−1.92060			−0.0682024
$794$	−9.03436	+	6.56385i	−0.320618	+	0.232942i
$795$		0			0
$796$	21.4165	−	65.9133i	0.759088	−	2.33623i
$797$	15.1927	+	11.0381i	0.538151	+	0.390990i	0.823398	−	0.567464i	$-0.192076\pi$
$797$	15.1927	+	11.0381i	0.538151	+	0.390990i	−0.285247	+	0.958454i	$0.592076\pi$
$798$		0			0
$799$	8.91363	−	27.4333i	0.315342	−	0.970522i
$800$	3.54842	+	10.9209i	0.125456	+	0.386113i
$801$		0			0
$802$	−6.53201			−0.230653
$803$	25.3194	−	1.70571i	0.893502	−	0.0601931i
$804$		0			0
$805$	−1.13901	+	0.827538i	−0.0401448	+	0.0291669i
$806$	9.64648	+	29.6888i	0.339783	+	1.04574i
$807$		0			0
$808$	−27.2114	−	19.7702i	−0.957294	−	0.695515i
$809$	−32.4991	−	23.6120i	−1.14261	−	0.830152i	−0.155126	−	0.987895i	$-0.549578\pi$
$809$	−32.4991	−	23.6120i	−1.14261	−	0.830152i	−0.987480	+	0.157742i	$0.949578\pi$
$810$		0			0
$811$	−6.95555	−	21.4070i	−0.244243	−	0.751701i	−0.995760	−	0.0919881i	$-0.970678\pi$
$811$	−6.95555	−	21.4070i	−0.244243	−	0.751701i	0.751518	−	0.659713i	$-0.229322\pi$
$812$	−0.299154	+	0.217348i	−0.0104982	+	0.00762741i
$813$		0			0
$814$	7.23301	−	6.03789i	0.253517	−	0.211628i
$815$	−23.7538			−0.832061
$816$		0			0
$817$	19.8521	+	61.0984i	0.694536	+	2.13756i
$818$	7.80981	−	24.0361i	0.273064	−	0.840403i
$819$		0			0
$820$	−42.0580	−	30.5569i	−1.46873	−	1.06709i
$821$	13.8301	−	42.5647i	0.482674	−	1.48552i	−0.352648	−	0.935756i	$-0.614719\pi$
$821$	13.8301	−	42.5647i	0.482674	−	1.48552i	0.835322	−	0.549761i	$-0.185281\pi$
$822$		0			0
$823$	−2.56435	+	1.86311i	−0.0893876	+	0.0649439i	−0.631581	−	0.775310i	$-0.717594\pi$
$823$	−2.56435	+	1.86311i	−0.0893876	+	0.0649439i	0.542194	+	0.840253i	$0.317594\pi$
$824$	−3.71669			−0.129477
$825$		0			0
$826$	3.75497			0.130652
$827$	−19.0904	+	13.8700i	−0.663838	+	0.482307i	−0.867957	−	0.496640i	$-0.834567\pi$
$827$	−19.0904	+	13.8700i	−0.663838	+	0.482307i	0.204119	+	0.978946i	$0.434567\pi$
$828$		0			0
$829$	−7.87416	+	24.2342i	−0.273481	+	0.841688i	0.716136	+	0.697960i	$0.245909\pi$
$829$	−7.87416	+	24.2342i	−0.273481	+	0.841688i	−0.989617	+	0.143727i	$0.954091\pi$
$830$	43.7717	+	31.8020i	1.51934	+	1.10386i
$831$		0			0
$832$	−5.49268	+	16.9047i	−0.190425	+	0.586066i
$833$	7.89361	+	24.2940i	0.273497	+	0.841739i
$834$		0			0
$835$	8.82052			0.305247
$836$	32.8322	+	81.8623i	1.13553	+	2.83127i
$837$		0			0
$838$	−26.7681	+	19.4482i	−0.924690	+	0.671827i
$839$	−4.23546	−	13.0354i	−0.146224	−	0.450032i	0.850942	−	0.525260i	$-0.176032\pi$
$839$	−4.23546	−	13.0354i	−0.146224	−	0.450032i	−0.997166	+	0.0752273i	$0.976032\pi$
$840$		0			0
$841$	23.2234	+	16.8728i	0.800805	+	0.581819i
$842$	4.73833	+	3.44260i	0.163293	+	0.118640i
$843$		0			0
$844$	−15.9162	−	48.9849i	−0.547857	−	1.68613i
$845$	15.2253	−	11.0619i	0.523768	−	0.380540i
$846$		0			0
$847$	0.990890	+	2.05817i	0.0340474	+	0.0707196i
$848$	1.36215			0.0467766
$849$		0			0
$850$	5.52924	+	17.0173i	0.189651	+	0.583687i
$851$	−1.52604	+	4.69667i	−0.0523120	+	0.161000i
$852$		0			0
$853$	13.7910	+	10.0197i	0.472195	+	0.343069i	0.798296	−	0.602265i	$-0.205735\pi$
$853$	13.7910	+	10.0197i	0.472195	+	0.343069i	−0.326101	+	0.945335i	$0.605735\pi$
$854$	−0.204964	+	0.630815i	−0.00701373	+	0.0215860i
$855$		0			0
$856$	−18.4337	+	13.3928i	−0.630050	+	0.457758i
$857$	−48.3488			−1.65156			−0.825781	−	0.563990i	$-0.809265\pi$
$857$	−48.3488			−1.65156			−0.825781	+	0.563990i	$0.809265\pi$
$858$		0			0
$859$	−3.58643			−0.122367			−0.0611837	−	0.998127i	$-0.519488\pi$
$859$	−3.58643			−0.122367			−0.0611837	+	0.998127i	$0.519488\pi$
$860$	−35.7241	+	25.9551i	−1.21818	+	0.885060i
$861$		0			0
$862$	−17.2542	+	53.1031i	−0.587682	+	1.80870i
$863$	−31.4913	−	22.8798i	−1.07198	−	0.778836i	−0.0957096	−	0.995409i	$-0.530512\pi$
$863$	−31.4913	−	22.8798i	−1.07198	−	0.778836i	−0.976266	+	0.216573i	$0.930512\pi$
$864$		0			0
$865$	−5.54997	+	17.0810i	−0.188705	+	0.580773i
$866$	26.8247	+	82.5580i	0.911541	+	2.80544i
$867$		0			0
$868$	6.69866			0.227367
$869$	16.3103	+	10.2496i	0.553287	+	0.347695i
$870$		0			0
$871$	6.54508	−	4.75528i	0.221772	−	0.161127i
$872$	−9.34841	−	28.7715i	−0.316577	−	0.974324i
$873$		0			0
$874$	−60.1912	−	43.7315i	−2.03600	−	1.47924i
$875$	2.02995	+	1.47485i	0.0686249	+	0.0498589i
$876$		0			0
$877$	7.00935	+	21.5725i	0.236689	+	0.728453i	0.996893	+	0.0787689i	$0.0250989\pi$
$877$	7.00935	+	21.5725i	0.236689	+	0.728453i	−0.760204	+	0.649684i	$0.774901\pi$
$878$	6.72740	−	4.88774i	0.227039	−	0.164953i
$879$		0			0
$880$	−0.897230	+	0.748980i	−0.0302456	+	0.0252481i
$881$	48.0217			1.61789			0.808946	−	0.587882i	$-0.200038\pi$
$881$	48.0217			1.61789			0.808946	+	0.587882i	$0.200038\pi$
$882$		0			0
$883$	−12.6278	−	38.8642i	−0.424958	−	1.30789i	−0.903035	−	0.429568i	$-0.858666\pi$
$883$	−12.6278	−	38.8642i	−0.424958	−	1.30789i	0.478077	−	0.878318i	$-0.341334\pi$
$884$	−5.14638	+	15.8389i	−0.173091	+	0.532720i
$885$		0			0
$886$	−12.0578	−	8.76047i	−0.405088	−	0.294314i
$887$	9.56688	−	29.4438i	0.321224	−	0.988627i	−0.651892	−	0.758312i	$-0.726024\pi$
$887$	9.56688	−	29.4438i	0.321224	−	0.988627i	0.973116	−	0.230315i	$-0.0739757\pi$
$888$		0			0
$889$	−2.88233	+	2.09413i	−0.0966702	+	0.0702350i
$890$	−24.1742			−0.810322
$891$		0			0
$892$	32.5442			1.08966
$893$	51.4973	−	37.4150i	1.72329	−	1.25204i
$894$		0			0
$895$	−3.67052	+	11.2967i	−0.122692	+	0.377607i
$896$	3.14647	+	2.28605i	0.105116	+	0.0763715i
$897$		0			0
$898$	−24.6154	+	75.7583i	−0.821426	+	2.52809i
$899$	1.64782	+	5.07146i	0.0549577	+	0.169143i
$900$		0			0
$901$	−24.0851			−0.802392
$902$	17.3885	−	68.9923i	0.578973	−	2.29719i
$903$		0			0
$904$	28.2497	−	20.5246i	0.939572	−	0.682639i
$905$	0.604982	+	1.86194i	0.0201103	+	0.0618930i
$906$		0			0
$907$	−20.1030	−	14.6057i	−0.667510	−	0.484974i	0.201681	−	0.979451i	$-0.435360\pi$
$907$	−20.1030	−	14.6057i	−0.667510	−	0.484974i	−0.869191	+	0.494477i	$0.835360\pi$
$908$	29.4915	+	21.4268i	0.978710	+	0.711074i
$909$		0			0
$910$	0.345866	+	1.06447i	0.0114654	+	0.0352867i
$911$	−24.1302	+	17.5316i	−0.799469	+	0.580848i	−0.910758	−	0.412940i	$-0.864502\pi$
$911$	−24.1302	+	17.5316i	−0.799469	+	0.580848i	0.111289	+	0.993788i	$0.464502\pi$
$912$		0			0
$913$	−11.2447	+	44.6156i	−0.372146	+	1.47656i
$914$	83.8466			2.77340
$915$		0			0
$916$	−2.12452	−	6.53859i	−0.0701960	−	0.216041i
$917$	−0.513990	+	1.58190i	−0.0169734	+	0.0522389i
$918$		0			0
$919$	10.0050	+	7.26908i	0.330035	+	0.239785i	0.740446	−	0.672116i	$-0.234615\pi$
$919$	10.0050	+	7.26908i	0.330035	+	0.239785i	−0.410410	+	0.911901i	$0.634615\pi$
$920$	6.17296	−	18.9984i	0.203517	−	0.626360i
$921$		0			0
$922$	32.0925	−	23.3166i	1.05691	−	0.767890i
$923$	−17.6310			−0.580331
$924$		0			0
$925$	2.62087			0.0861738
$926$	−69.9076	+	50.7909i	−2.29731	+	1.66909i
$927$		0			0
$928$	−0.907965	+	2.79443i	−0.0298054	+	0.0917316i
$929$	−16.7613	−	12.1778i	−0.549919	−	0.399540i	0.277837	−	0.960628i	$-0.410383\pi$
$929$	−16.7613	−	12.1778i	−0.549919	−	0.399540i	−0.827756	+	0.561089i	$0.810383\pi$
$930$		0			0
$931$	−17.4193	+	53.6111i	−0.570894	+	1.75703i
$932$	22.0386	+	67.8278i	0.721898	+	2.22177i
$933$		0			0
$934$	−81.3103			−2.66055
$935$	15.8645	−	13.2432i	0.518825	−	0.433099i
$936$		0			0
$937$	−26.7917	+	19.4653i	−0.875247	+	0.635904i	−0.931990	−	0.362485i	$-0.881929\pi$
$937$	−26.7917	+	19.4653i	−0.875247	+	0.635904i	0.0567426	+	0.998389i	$0.481929\pi$
$938$	−0.863375	−	2.65720i	−0.0281902	−	0.0867605i
$939$		0			0
$940$	35.3969	+	25.7173i	1.15452	+	0.838806i
$941$	30.4872	+	22.1503i	0.993855	+	0.722078i	0.960762	−	0.277374i	$-0.0894641\pi$
$941$	30.4872	+	22.1503i	0.993855	+	0.722078i	0.0330933	+	0.999452i	$0.489464\pi$
$942$		0			0
$943$	11.5239	+	35.4670i	0.375271	+	1.15496i
$944$	−1.32179	+	0.960340i	−0.0430208	+	0.0312564i
$945$		0			0
$946$	−51.1698	−	32.1559i	−1.66367	−	1.04548i
$947$	−34.0284			−1.10577			−0.552887	−	0.833256i	$-0.686474\pi$
$947$	−34.0284			−1.10577			−0.552887	+	0.833256i	$0.686474\pi$
$948$		0			0
$949$	3.26753	+	10.0564i	0.106069	+	0.326446i
$950$	−12.2017	+	37.5530i	−0.395875	+	1.21838i
$951$		0			0
$952$	1.81757	+	1.32054i	0.0589079	+	0.0427991i
$953$	1.29564	−	3.98756i	0.0419697	−	0.129170i	−0.927876	−	0.372888i	$-0.878367\pi$
$953$	1.29564	−	3.98756i	0.0419697	−	0.129170i	0.969846	+	0.243719i	$0.0783674\pi$
$954$		0			0
$955$	−32.3060	+	23.4717i	−1.04540	+	0.759525i
$956$	−44.3546			−1.43453
$957$		0			0
$958$	−54.5828			−1.76349
$959$	−1.51697	+	1.10215i	−0.0489856	+	0.0355901i
$960$		0			0
$961$	20.2715	−	62.3894i	0.653921	−	2.01256i
$962$	3.17613	+	2.30759i	0.102402	+	0.0743997i
$963$		0			0
$964$	9.64516	−	29.6847i	0.310650	−	0.956081i
$965$	4.28812	+	13.1975i	0.138039	+	0.424842i
$966$		0			0
$967$	16.7939			0.540054			0.270027	−	0.962853i	$-0.412967\pi$
$967$	16.7939			0.540054			0.270027	+	0.962853i	$0.412967\pi$
$968$	−28.5393	−	15.3616i	−0.917287	−	0.493740i
$969$		0			0
$970$	22.1610	−	16.1009i	0.711546	−	0.516968i
$971$	9.32489	+	28.6991i	0.299250	+	0.920997i	0.981761	+	0.190121i	$0.0608881\pi$
$971$	9.32489	+	28.6991i	0.299250	+	0.920997i	−0.682511	+	0.730876i	$0.739112\pi$
$972$		0			0
$973$	−0.522618	−	0.379704i	−0.0167544	−	0.0121728i
$974$	45.1363	+	32.7934i	1.44626	+	1.05077i
$975$		0			0
$976$	−0.0891821	−	0.274474i	−0.00285465	−	0.00878570i
$977$	−32.8429	+	23.8618i	−1.05074	+	0.763406i	−0.972353	−	0.233517i	$-0.924977\pi$
$977$	−32.8429	+	23.8618i	−1.05074	+	0.763406i	−0.0783856	+	0.996923i	$0.524977\pi$
$978$		0			0
$979$	−7.65252	−	19.0804i	−0.244576	−	0.609813i
$980$	−38.7461			−1.23770
$981$		0			0
$982$	−0.270845	−	0.833575i	−0.00864301	−	0.0266004i
$983$	−1.75230	+	5.39303i	−0.0558897	+	0.172011i	−0.975105	−	0.221745i	$-0.928825\pi$
$983$	−1.75230	+	5.39303i	−0.0558897	+	0.172011i	0.919215	+	0.393756i	$0.128825\pi$
$984$		0			0
$985$	18.6026	+	13.5156i	0.592729	+	0.430643i
$986$	−1.41481	+	4.35435i	−0.0450569	+	0.138671i
$987$		0			0
$988$	−29.7325	+	21.6019i	−0.945917	+	0.687249i
$989$	31.6760			1.00724
$990$		0			0
$991$	41.6198			1.32210			0.661049	−	0.750343i	$-0.270112\pi$
$991$	41.6198			1.32210			0.661049	+	0.750343i	$0.270112\pi$
$992$	43.0621	−	31.2865i	1.36722	−	0.993347i
$993$		0			0
$994$	−1.88156	+	5.79085i	−0.0596795	+	0.183675i
$995$	−28.9903	−	21.0627i	−0.919055	−	0.667732i
$996$		0			0
$997$	14.0461	−	43.2295i	0.444844	−	1.36909i	−0.437810	−	0.899068i	$-0.644246\pi$
$997$	14.0461	−	43.2295i	0.444844	−	1.36909i	0.882654	−	0.470023i	$-0.155754\pi$
$998$	−2.25658	−	6.94502i	−0.0714306	−	0.219841i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.b.190.1	yes	16
3.2	odd	2	inner	297.2.f.b.190.4	yes	16
9.2	odd	6		891.2.n.h.190.1		32
9.4	even	3		891.2.n.h.784.1		32
9.5	odd	6		891.2.n.h.784.4		32
9.7	even	3		891.2.n.h.190.4		32
11.2	odd	10		3267.2.a.bi.1.2		8
11.4	even	5	inner	297.2.f.b.136.1	✓	16
11.9	even	5		3267.2.a.bj.1.7		8
33.2	even	10		3267.2.a.bi.1.7		8
33.20	odd	10		3267.2.a.bj.1.2		8
33.26	odd	10	inner	297.2.f.b.136.4	yes	16
99.4	even	15		891.2.n.h.136.4		32
99.59	odd	30		891.2.n.h.136.1		32
99.70	even	15		891.2.n.h.433.1		32
99.92	odd	30		891.2.n.h.433.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.136.1	✓	16	11.4	even	5	inner
297.2.f.b.136.4	yes	16	33.26	odd	10	inner
297.2.f.b.190.1	yes	16	1.1	even	1	trivial
297.2.f.b.190.4	yes	16	3.2	odd	2	inner
891.2.n.h.136.1		32	99.59	odd	30
891.2.n.h.136.4		32	99.4	even	15
891.2.n.h.190.1		32	9.2	odd	6
891.2.n.h.190.4		32	9.7	even	3
891.2.n.h.433.1		32	99.70	even	15
891.2.n.h.433.4		32	99.92	odd	30
891.2.n.h.784.1		32	9.4	even	3
891.2.n.h.784.4		32	9.5	odd	6
3267.2.a.bi.1.2		8	11.2	odd	10
3267.2.a.bi.1.7		8	33.2	even	10
3267.2.a.bj.1.2		8	33.20	odd	10
3267.2.a.bj.1.7		8	11.9	even	5

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	297.2.f.b.190.1

Level	$297$
Weight	$2$
Character	297.190
Analytic conductor	$2.372$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$