LMFDB - Embedded newform 1512.2.c.f.757.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.23
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.f.757.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41290 - 0.0608900i) q^{2} +(1.99258 - 0.172063i) q^{4} -3.11390i q^{5} +1.00000 q^{7} +(2.80485 - 0.364437i) q^{8} +O(q^{10})$	\(q+(1.41290 - 0.0608900i) q^{2} +(1.99258 - 0.172063i) q^{4} -3.11390i q^{5} +1.00000 q^{7} +(2.80485 - 0.364437i) q^{8} +(-0.189605 - 4.39964i) q^{10} -2.37402i q^{11} -1.09044i q^{13} +(1.41290 - 0.0608900i) q^{14} +(3.94079 - 0.685701i) q^{16} -3.69300 q^{17} -1.08263i q^{19} +(-0.535788 - 6.20472i) q^{20} +(-0.144554 - 3.35425i) q^{22} -4.87366 q^{23} -4.69640 q^{25} +(-0.0663968 - 1.54068i) q^{26} +(1.99258 - 0.172063i) q^{28} -1.59607i q^{29} +7.45516 q^{31} +(5.52620 - 1.20878i) q^{32} +(-5.21785 + 0.224867i) q^{34} -3.11390i q^{35} +4.61410i q^{37} +(-0.0659213 - 1.52965i) q^{38} +(-1.13482 - 8.73404i) q^{40} +0.0380616 q^{41} +11.0608i q^{43} +(-0.408481 - 4.73043i) q^{44} +(-6.88600 + 0.296757i) q^{46} -0.337175 q^{47} +1.00000 q^{49} +(-6.63555 + 0.285964i) q^{50} +(-0.187624 - 2.17279i) q^{52} +8.14672i q^{53} -7.39246 q^{55} +(2.80485 - 0.364437i) q^{56} +(-0.0971845 - 2.25509i) q^{58} -15.0761i q^{59} -5.53745i q^{61} +(10.5334 - 0.453944i) q^{62} +(7.73437 - 2.04438i) q^{64} -3.39553 q^{65} -7.70421i q^{67} +(-7.35861 + 0.635429i) q^{68} +(-0.189605 - 4.39964i) q^{70} +13.5472 q^{71} -14.6727 q^{73} +(0.280953 + 6.51928i) q^{74} +(-0.186281 - 2.15723i) q^{76} -2.37402i q^{77} +5.18122 q^{79} +(-2.13521 - 12.2712i) q^{80} +(0.0537773 - 0.00231757i) q^{82} +0.138321i q^{83} +11.4996i q^{85} +(0.673490 + 15.6278i) q^{86} +(-0.865179 - 6.65876i) q^{88} +11.9531 q^{89} -1.09044i q^{91} +(-9.71118 + 0.838577i) q^{92} +(-0.476396 + 0.0205306i) q^{94} -3.37121 q^{95} -5.30202 q^{97} +(1.41290 - 0.0608900i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7}+O(q^{10}) $ 24 * q + 24 * q^7	$ 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.41290	−	0.0608900i	0.999073	−	0.0430557i
$2$	1.41290	−	0.0608900i	0.999073	−	0.0430557i
$3$		0			0
$3$		0			0
$4$	1.99258	−	0.172063i	0.996292	−	0.0860316i
$5$		−	3.11390i		−	1.39258i	−0.717760	−	0.696290i	$-0.754833\pi$
$5$		−	3.11390i		−	1.39258i	0.717760	−	0.696290i	$-0.245167\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.80485	−	0.364437i	0.991664	−	0.128848i
$9$		0			0
$10$	−0.189605	−	4.39964i	−0.0599585	−	1.39129i
$11$		−	2.37402i		−	0.715793i	−0.933761	−	0.357897i	$-0.883494\pi$
$11$		−	2.37402i		−	0.715793i	0.933761	−	0.357897i	$-0.116506\pi$
$12$		0			0
$13$		−	1.09044i		−	0.302434i	−0.988501	−	0.151217i	$-0.951681\pi$
$13$		−	1.09044i		−	0.302434i	0.988501	−	0.151217i	$-0.0483192\pi$
$14$	1.41290	−	0.0608900i	0.377614	−	0.0162735i
$15$		0			0
$16$	3.94079	−	0.685701i	0.985197	−	0.171425i
$17$	−3.69300			−0.895684			−0.447842	−	0.894113i	$-0.647807\pi$
$17$	−3.69300			−0.895684			−0.447842	+	0.894113i	$0.647807\pi$
$18$		0			0
$19$		−	1.08263i		−	0.248372i	−0.992259	−	0.124186i	$-0.960368\pi$
$19$		−	1.08263i		−	0.248372i	0.992259	−	0.124186i	$-0.0396320\pi$
$20$	−0.535788	−	6.20472i	−0.119806	−	1.38742i
$21$		0			0
$22$	−0.144554	−	3.35425i	−0.0308190	−	0.715129i
$23$	−4.87366			−1.01623			−0.508114	−	0.861290i	$-0.669657\pi$
$23$	−4.87366			−1.01623			−0.508114	+	0.861290i	$0.669657\pi$
$24$		0			0
$25$	−4.69640			−0.939280
$26$	−0.0663968	−	1.54068i	−0.0130215	−	0.302153i
$27$		0			0
$28$	1.99258	−	0.172063i	0.376563	−	0.0325169i
$29$		−	1.59607i		−	0.296382i	−0.988959	−	0.148191i	$-0.952655\pi$
$29$		−	1.59607i		−	0.296382i	0.988959	−	0.148191i	$-0.0473451\pi$
$30$		0			0
$31$	7.45516			1.33899			0.669493	−	0.742818i	$-0.266511\pi$
$31$	7.45516			1.33899			0.669493	+	0.742818i	$0.266511\pi$
$32$	5.52620	−	1.20878i	0.976903	−	0.213685i
$33$		0			0
$34$	−5.21785	+	0.224867i	−0.894853	+	0.0385643i
$35$		−	3.11390i		−	0.526346i
$36$		0			0
$37$			4.61410i			0.758554i	0.925283	+	0.379277i	$0.123827\pi$
$37$			4.61410i			0.758554i	−0.925283	+	0.379277i	$0.876173\pi$
$38$	−0.0659213	−	1.52965i	−0.0106938	−	0.248142i
$39$		0			0
$40$	−1.13482	−	8.73404i	−0.179431	−	1.38097i
$41$	0.0380616			0.00594422			0.00297211	−	0.999996i	$-0.499054\pi$
$41$	0.0380616			0.00594422			0.00297211	+	0.999996i	$0.499054\pi$
$42$		0			0
$43$			11.0608i			1.68675i	0.537323	+	0.843377i	$0.319436\pi$
$43$			11.0608i			1.68675i	−0.537323	+	0.843377i	$0.680564\pi$
$44$	−0.408481	−	4.73043i	−0.0615808	−	0.713139i
$45$		0			0
$46$	−6.88600	+	0.296757i	−1.01529	+	0.0437544i
$47$	−0.337175			−0.0491821			−0.0245910	−	0.999698i	$-0.507828\pi$
$47$	−0.337175			−0.0491821			−0.0245910	+	0.999698i	$0.507828\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−6.63555	+	0.285964i	−0.938409	+	0.0404413i
$51$		0			0
$52$	−0.187624	−	2.17279i	−0.0260188	−	0.301312i
$53$			8.14672i			1.11904i	0.828818	+	0.559519i	$0.189014\pi$
$53$			8.14672i			1.11904i	−0.828818	+	0.559519i	$0.810986\pi$
$54$		0			0
$55$	−7.39246			−0.996799
$56$	2.80485	−	0.364437i	0.374814	−	0.0486999i
$57$		0			0
$58$	−0.0971845	−	2.25509i	−0.0127610	−	0.296108i
$59$		−	15.0761i		−	1.96274i	−0.192129	−	0.981370i	$-0.561539\pi$
$59$		−	15.0761i		−	1.96274i	0.192129	−	0.981370i	$-0.438461\pi$
$60$		0			0
$61$		−	5.53745i		−	0.708998i	−0.935056	−	0.354499i	$-0.884651\pi$
$61$		−	5.53745i		−	0.708998i	0.935056	−	0.354499i	$-0.115349\pi$
$62$	10.5334	−	0.453944i	1.33774	−	0.0576510i
$63$		0			0
$64$	7.73437	−	2.04438i	0.966796	−	0.255548i
$65$	−3.39553			−0.421163
$66$		0			0
$67$		−	7.70421i		−	0.941219i	−0.882342	−	0.470609i	$-0.844034\pi$
$67$		−	7.70421i		−	0.941219i	0.882342	−	0.470609i	$-0.155966\pi$
$68$	−7.35861	+	0.635429i	−0.892363	+	0.0770571i
$69$		0			0
$70$	−0.189605	−	4.39964i	−0.0226622	−	0.525858i
$71$	13.5472			1.60776			0.803878	−	0.594794i	$-0.202766\pi$
$71$	13.5472			1.60776			0.803878	+	0.594794i	$0.202766\pi$
$72$		0			0
$73$	−14.6727			−1.71731			−0.858656	−	0.512553i	$-0.828700\pi$
$73$	−14.6727			−1.71731			−0.858656	+	0.512553i	$0.828700\pi$
$74$	0.280953	+	6.51928i	0.0326601	+	0.757851i
$75$		0			0
$76$	−0.186281	−	2.15723i	−0.0213679	−	0.247452i
$77$		−	2.37402i		−	0.270544i
$78$		0			0
$79$	5.18122			0.582932			0.291466	−	0.956581i	$-0.405857\pi$
$79$	5.18122			0.582932			0.291466	+	0.956581i	$0.405857\pi$
$80$	−2.13521	−	12.2712i	−0.238723	−	1.37197i
$81$		0			0
$82$	0.0537773	−	0.00231757i	0.00593870	−	0.000255932i
$83$			0.138321i			0.0151827i	0.999971	+	0.00759136i	$0.00241643\pi$
$83$			0.138321i			0.0151827i	−0.999971	+	0.00759136i	$0.997584\pi$
$84$		0			0
$85$			11.4996i			1.24731i
$86$	0.673490	+	15.6278i	0.0726243	+	1.68519i
$87$		0			0
$88$	−0.865179	−	6.65876i	−0.0922284	−	0.709826i
$89$	11.9531			1.26703			0.633514	−	0.773731i	$-0.281612\pi$
$89$	11.9531			1.26703			0.633514	+	0.773731i	$0.281612\pi$
$90$		0			0
$91$		−	1.09044i		−	0.114309i
$92$	−9.71118	+	0.838577i	−1.01246	+	0.0874277i
$93$		0			0
$94$	−0.476396	+	0.0205306i	−0.0491364	+	0.00211757i
$95$	−3.37121			−0.345879
$96$		0			0
$97$	−5.30202			−0.538339			−0.269169	−	0.963093i	$-0.586749\pi$
$97$	−5.30202			−0.538339			−0.269169	+	0.963093i	$0.586749\pi$
$98$	1.41290	−	0.0608900i	0.142725	−	0.00615081i
$99$		0			0
$100$	−9.35797	+	0.808077i	−0.935797	+	0.0808077i
$101$		−	0.0753369i		−	0.00749630i	−0.999993	−	0.00374815i	$-0.998807\pi$
$101$		−	0.0753369i		−	0.00749630i	0.999993	−	0.00374815i	$-0.00119308\pi$
$102$		0			0
$103$	15.3347			1.51097			0.755487	−	0.655163i	$-0.227400\pi$
$103$	15.3347			1.51097			0.755487	+	0.655163i	$0.227400\pi$
$104$	−0.397396	−	3.05852i	−0.0389679	−	0.299913i
$105$		0			0
$106$	0.496053	+	11.5105i	0.0481809	+	1.11800i
$107$			4.03726i			0.390297i	0.980774	+	0.195148i	$0.0625189\pi$
$107$			4.03726i			0.390297i	−0.980774	+	0.195148i	$0.937481\pi$
$108$		0			0
$109$			12.2335i			1.17176i	0.810399	+	0.585879i	$0.199251\pi$
$109$			12.2335i			1.17176i	−0.810399	+	0.585879i	$0.800749\pi$
$110$	−10.4448	+	0.450127i	−0.995875	+	0.0429179i
$111$		0			0
$112$	3.94079	−	0.685701i	0.372370	−	0.0647926i
$113$	11.1934			1.05299			0.526495	−	0.850178i	$-0.323506\pi$
$113$	11.1934			1.05299			0.526495	+	0.850178i	$0.323506\pi$
$114$		0			0
$115$			15.1761i			1.41518i
$116$	−0.274624	−	3.18030i	−0.0254982	−	0.295284i
$117$		0			0
$118$	−0.917982	−	21.3010i	−0.0845071	−	1.96092i
$119$	−3.69300			−0.338537
$120$		0			0
$121$	5.36404			0.487640
$122$	−0.337175	−	7.82388i	−0.0305264	−	0.708340i
$123$		0			0
$124$	14.8550	−	1.28276i	1.33402	−	0.115195i
$125$		−	0.945386i		−	0.0845579i
$126$		0			0
$127$	−2.43139			−0.215751			−0.107876	−	0.994164i	$-0.534405\pi$
$127$	−2.43139			−0.215751			−0.107876	+	0.994164i	$0.534405\pi$
$128$	10.8034	−	3.35946i	0.954897	−	0.296937i
$129$		0			0
$130$	−4.79755	+	0.206753i	−0.420773	+	0.0181335i
$131$		−	8.83723i		−	0.772112i	−0.922475	−	0.386056i	$-0.873837\pi$
$131$		−	8.83723i		−	0.772112i	0.922475	−	0.386056i	$-0.126163\pi$
$132$		0			0
$133$		−	1.08263i		−	0.0938760i
$134$	−0.469109	−	10.8853i	−0.0405248	−	0.940346i
$135$		0			0
$136$	−10.3583	+	1.34586i	−0.888218	+	0.115407i
$137$	−11.1478			−0.952422			−0.476211	−	0.879331i	$-0.657990\pi$
$137$	−11.1478			−0.952422			−0.476211	+	0.879331i	$0.657990\pi$
$138$		0			0
$139$			17.2724i			1.46502i	0.680755	+	0.732511i	$0.261652\pi$
$139$			17.2724i			1.46502i	−0.680755	+	0.732511i	$0.738348\pi$
$140$	−0.535788	−	6.20472i	−0.0452824	−	0.524394i
$141$		0			0
$142$	19.1409	−	0.824888i	1.60627	−	0.0692231i
$143$	−2.58872			−0.216480
$144$		0			0
$145$	−4.97000			−0.412736
$146$	−20.7311	+	0.893421i	−1.71572	+	0.0739400i
$147$		0			0
$148$	0.793917	+	9.19400i	0.0652596	+	0.755742i
$149$			13.7236i			1.12428i	0.827042	+	0.562140i	$0.190022\pi$
$149$			13.7236i			1.12428i	−0.827042	+	0.562140i	$0.809978\pi$
$150$		0			0
$151$	−12.8195			−1.04324			−0.521620	−	0.853178i	$-0.674672\pi$
$151$	−12.8195			−1.04324			−0.521620	+	0.853178i	$0.674672\pi$
$152$	−0.394550	−	3.03662i	−0.0320023	−	0.246302i
$153$		0			0
$154$	−0.144554	−	3.35425i	−0.0116485	−	0.270293i
$155$		−	23.2146i		−	1.86465i
$156$		0			0
$157$			21.1418i			1.68730i	0.536892	+	0.843651i	$0.319598\pi$
$157$			21.1418i			1.68730i	−0.536892	+	0.843651i	$0.680402\pi$
$158$	7.32055	−	0.315484i	0.582392	−	0.0250986i
$159$		0			0
$160$	−3.76403	−	17.2080i	−0.297573	−	1.36042i
$161$	−4.87366			−0.384098
$162$		0			0
$163$		−	0.386568i		−	0.0302784i	−0.999885	−	0.0151392i	$-0.995181\pi$
$163$		−	0.386568i		−	0.0302784i	0.999885	−	0.0151392i	$-0.00481914\pi$
$164$	0.0758409	−	0.00654899i	0.00592218	−	0.000511390i
$165$		0			0
$166$	0.00842236	+	0.195434i	0.000653702	+	0.0151686i
$167$	14.4336			1.11690			0.558451	−	0.829537i	$-0.311396\pi$
$167$	14.4336			1.11690			0.558451	+	0.829537i	$0.311396\pi$
$168$		0			0
$169$	11.8109			0.908534
$170$	0.700213	+	16.2479i	0.0537039	+	1.24615i
$171$		0			0
$172$	1.90315	+	22.0395i	0.145114	+	1.68050i
$173$			13.9493i			1.06055i	0.847826	+	0.530274i	$0.177911\pi$
$173$			13.9493i			1.06055i	−0.847826	+	0.530274i	$0.822089\pi$
$174$		0			0
$175$	−4.69640			−0.355014
$176$	−1.62786	−	9.35550i	−0.122705	−	0.705197i
$177$		0			0
$178$	16.8886	−	0.727825i	1.26585	−	0.0545528i
$179$		−	10.6569i		−	0.796537i	−0.917269	−	0.398269i	$-0.869611\pi$
$179$		−	10.6569i		−	0.796537i	0.917269	−	0.398269i	$-0.130389\pi$
$180$		0			0
$181$			6.63866i			0.493448i	0.969086	+	0.246724i	$0.0793540\pi$
$181$			6.63866i			0.493448i	−0.969086	+	0.246724i	$0.920646\pi$
$182$	−0.0663968	−	1.54068i	−0.00492166	−	0.114203i
$183$		0			0
$184$	−13.6699	+	1.77614i	−1.00776	+	0.130939i
$185$	14.3679			1.05635
$186$		0			0
$187$			8.76724i			0.641124i
$188$	−0.671850	+	0.0580154i	−0.0489997	+	0.00423121i
$189$		0			0
$190$	−4.76319	+	0.205273i	−0.345558	+	0.0148920i
$191$	−9.81148			−0.709934			−0.354967	−	0.934879i	$-0.615508\pi$
$191$	−9.81148			−0.709934			−0.354967	+	0.934879i	$0.615508\pi$
$192$		0			0
$193$	17.4539			1.25636			0.628180	−	0.778068i	$-0.283800\pi$
$193$	17.4539			1.25636			0.628180	+	0.778068i	$0.283800\pi$
$194$	−7.49124	+	0.322840i	−0.537839	+	0.0231785i
$195$		0			0
$196$	1.99258	−	0.172063i	0.142327	−	0.0122902i
$197$			27.6871i			1.97262i	0.164888	+	0.986312i	$0.447274\pi$
$197$			27.6871i			1.97262i	−0.164888	+	0.986312i	$0.552726\pi$
$198$		0			0
$199$	9.29804			0.659121			0.329560	−	0.944134i	$-0.393099\pi$
$199$	9.29804			0.659121			0.329560	+	0.944134i	$0.393099\pi$
$200$	−13.1727	+	1.71154i	−0.931450	+	0.121024i
$201$		0			0
$202$	−0.00458726	−	0.106444i	−0.000322759	−	0.00748935i
$203$		−	1.59607i		−	0.112022i
$204$		0			0
$205$		−	0.118520i		−	0.00827780i
$206$	21.6665	−	0.933730i	1.50957	−	0.0650561i
$207$		0			0
$208$	−0.747715	−	4.29719i	−0.0518447	−	0.297957i
$209$	−2.57018			−0.177783
$210$		0			0
$211$			16.3068i			1.12260i	0.827611	+	0.561302i	$0.189699\pi$
$211$			16.3068i			1.12260i	−0.827611	+	0.561302i	$0.810301\pi$
$212$	1.40175	+	16.2330i	0.0962725	+	1.11489i
$213$		0			0
$214$	0.245829	+	5.70426i	0.0168045	+	0.389935i
$215$	34.4422			2.34894
$216$		0			0
$217$	7.45516			0.506089
$218$	0.744898	+	17.2848i	0.0504509	+	1.17067i
$219$		0			0
$220$	−14.7301	+	1.27197i	−0.993103	+	0.0857562i
$221$			4.02699i			0.270885i
$222$		0			0
$223$	−18.8846			−1.26461			−0.632304	−	0.774720i	$-0.717891\pi$
$223$	−18.8846			−1.26461			−0.632304	+	0.774720i	$0.717891\pi$
$224$	5.52620	−	1.20878i	0.369235	−	0.0807652i
$225$		0			0
$226$	15.8152	−	0.681568i	1.05201	−	0.0453372i
$227$		−	12.9709i		−	0.860907i	−0.902613	−	0.430454i	$-0.858354\pi$
$227$		−	12.9709i		−	0.860907i	0.902613	−	0.430454i	$-0.141646\pi$
$228$		0			0
$229$		−	5.92552i		−	0.391569i	−0.980647	−	0.195785i	$-0.937275\pi$
$229$		−	5.92552i		−	0.391569i	0.980647	−	0.195785i	$-0.0627253\pi$
$230$	0.924073	+	21.4424i	0.0609315	+	1.41387i
$231$		0			0
$232$	−0.581666	−	4.47673i	−0.0381882	−	0.293912i
$233$	−12.2093			−0.799861			−0.399930	−	0.916546i	$-0.630966\pi$
$233$	−12.2093			−0.799861			−0.399930	+	0.916546i	$0.630966\pi$
$234$		0			0
$235$			1.04993i			0.0684900i
$236$	−2.59404	−	30.0404i	−0.168858	−	1.95546i
$237$		0			0
$238$	−5.21785	+	0.224867i	−0.338223	+	0.0145759i
$239$	−22.5273			−1.45717			−0.728585	−	0.684956i	$-0.759822\pi$
$239$	−22.5273			−1.45717			−0.728585	+	0.684956i	$0.759822\pi$
$240$		0			0
$241$	−16.1826			−1.04241			−0.521206	−	0.853431i	$-0.674518\pi$
$241$	−16.1826			−1.04241			−0.521206	+	0.853431i	$0.674518\pi$
$242$	7.57887	−	0.326616i	0.487188	−	0.0209957i
$243$		0			0
$244$	−0.952791	−	11.0338i	−0.0609962	−	0.706369i
$245$		−	3.11390i		−	0.198940i
$246$		0			0
$247$	−1.18054			−0.0751162
$248$	20.9106	−	2.71693i	1.32782	−	0.172525i
$249$		0			0
$250$	−0.0575645	−	1.33574i	−0.00364070	−	0.0844794i
$251$		−	6.88454i		−	0.434548i	−0.976111	−	0.217274i	$-0.930283\pi$
$251$		−	6.88454i		−	0.434548i	0.976111	−	0.217274i	$-0.0697166\pi$
$252$		0			0
$253$			11.5702i			0.727409i
$254$	−3.43532	+	0.148047i	−0.215551	+	0.00928932i
$255$		0			0
$256$	15.0596	−	5.40440i	0.941227	−	0.337775i
$257$	2.70139			0.168508			0.0842541	−	0.996444i	$-0.473149\pi$
$257$	2.70139			0.168508			0.0842541	+	0.996444i	$0.473149\pi$
$258$		0			0
$259$			4.61410i			0.286707i
$260$	−6.76587	+	0.584245i	−0.419602	+	0.0362333i
$261$		0			0
$262$	−0.538098	−	12.4861i	−0.0332438	−	0.771396i
$263$	−13.5500			−0.835527			−0.417763	−	0.908556i	$-0.637186\pi$
$263$	−13.5500			−0.835527			−0.417763	+	0.908556i	$0.637186\pi$
$264$		0			0
$265$	25.3681			1.55835
$266$	−0.0659213	−	1.52965i	−0.00404190	−	0.0937889i
$267$		0			0
$268$	−1.32561	−	15.3513i	−0.0809745	−	0.937729i
$269$			6.41522i			0.391143i	0.980689	+	0.195571i	$0.0626562\pi$
$269$			6.41522i			0.391143i	−0.980689	+	0.195571i	$0.937344\pi$
$270$		0			0
$271$	−14.5096			−0.881397			−0.440698	−	0.897655i	$-0.645269\pi$
$271$	−14.5096			−0.881397			−0.440698	+	0.897655i	$0.645269\pi$
$272$	−14.5533	+	2.53229i	−0.882425	+	0.153543i
$273$		0			0
$274$	−15.7508	+	0.678790i	−0.951539	+	0.0410072i
$275$			11.1493i			0.672330i
$276$		0			0
$277$		−	25.3175i		−	1.52118i	−0.649231	−	0.760591i	$-0.724909\pi$
$277$		−	25.3175i		−	1.52118i	0.649231	−	0.760591i	$-0.275091\pi$
$278$	1.05171	+	24.4042i	0.0630776	+	1.46366i
$279$		0			0
$280$	−1.13482	−	8.73404i	−0.0678185	−	0.521958i
$281$	0.719979			0.0429504			0.0214752	−	0.999769i	$-0.493164\pi$
$281$	0.719979			0.0429504			0.0214752	+	0.999769i	$0.493164\pi$
$282$		0			0
$283$			11.3262i			0.673275i	0.941634	+	0.336637i	$0.109290\pi$
$283$			11.3262i			0.673275i	−0.941634	+	0.336637i	$0.890710\pi$
$284$	26.9939	−	2.33097i	1.60180	−	0.138318i
$285$		0			0
$286$	−3.65761	+	0.157627i	−0.216279	+	0.00932069i
$287$	0.0380616			0.00224670
$288$		0			0
$289$	−3.36176			−0.197751
$290$	−7.02213	+	0.302623i	−0.412354	+	0.0177707i
$291$		0			0
$292$	−29.2366	+	2.52463i	−1.71094	+	0.147743i
$293$			15.2567i			0.891304i	0.895206	+	0.445652i	$0.147028\pi$
$293$			15.2567i			0.891304i	−0.895206	+	0.445652i	$0.852972\pi$
$294$		0			0
$295$	−46.9455			−2.73327
$296$	1.68155	+	12.9419i	0.0977381	+	0.752231i
$297$		0			0
$298$	0.835628	+	19.3901i	0.0484066	+	1.12324i
$299$			5.31443i			0.307342i
$300$		0			0
$301$			11.0608i			0.637533i
$302$	−18.1128	+	0.780581i	−1.04227	+	0.0449174i
$303$		0			0
$304$	−0.742360	−	4.26642i	−0.0425773	−	0.244696i
$305$	−17.2431			−0.987337
$306$		0			0
$307$		−	25.5497i		−	1.45820i	−0.684409	−	0.729098i	$-0.739940\pi$
$307$		−	25.5497i		−	1.45820i	0.684409	−	0.729098i	$-0.260060\pi$
$308$	−0.408481	−	4.73043i	−0.0232753	−	0.269541i
$309$		0			0
$310$	−1.41354	−	32.8000i	−0.0802836	−	1.86292i
$311$	−3.00328			−0.170300			−0.0851501	−	0.996368i	$-0.527137\pi$
$311$	−3.00328			−0.170300			−0.0851501	+	0.996368i	$0.527137\pi$
$312$		0			0
$313$	−5.53962			−0.313118			−0.156559	−	0.987669i	$-0.550040\pi$
$313$	−5.53962			−0.313118			−0.156559	+	0.987669i	$0.550040\pi$
$314$	1.28733	+	29.8713i	0.0726480	+	1.68574i
$315$		0			0
$316$	10.3240	−	0.891496i	0.580771	−	0.0501506i
$317$			32.1705i			1.80688i	0.428718	+	0.903439i	$0.358966\pi$
$317$			32.1705i			1.80688i	−0.428718	+	0.903439i	$0.641034\pi$
$318$		0			0
$319$	−3.78909			−0.212148
$320$	−6.36601	−	24.0841i	−0.355871	−	1.34634i
$321$		0			0
$322$	−6.88600	+	0.296757i	−0.383742	+	0.0165376i
$323$			3.99815i			0.222463i
$324$		0			0
$325$			5.12114i			0.284070i
$326$	−0.0235381	−	0.546183i	−0.00130366	−	0.0302503i
$327$		0			0
$328$	0.106757	−	0.0138710i	0.00589467	−	0.000765900i
$329$	−0.337175			−0.0185891
$330$		0			0
$331$		−	24.9617i		−	1.37202i	−0.727592	−	0.686010i	$-0.759361\pi$
$331$		−	24.9617i		−	1.37202i	0.727592	−	0.686010i	$-0.240639\pi$
$332$	0.0238000	+	0.275616i	0.00130619	+	0.0151264i
$333$		0			0
$334$	20.3932	−	0.878859i	1.11587	−	0.0480890i
$335$	−23.9902			−1.31072
$336$		0			0
$337$	17.7899			0.969076			0.484538	−	0.874770i	$-0.338988\pi$
$337$	17.7899			0.969076			0.484538	+	0.874770i	$0.338988\pi$
$338$	16.6877	−	0.719168i	0.907691	−	0.0391176i
$339$		0			0
$340$	1.97866	+	22.9140i	0.107308	+	1.24269i
$341$		−	17.6987i		−	0.958437i
$342$		0			0
$343$	1.00000			0.0539949
$344$	4.03095	+	31.0238i	0.217334	+	1.67269i
$345$		0			0
$346$	0.849375	+	19.7091i	0.0456627	+	1.05957i
$347$		−	2.08108i		−	0.111718i	−0.998439	−	0.0558591i	$-0.982210\pi$
$347$		−	2.08108i		−	0.111718i	0.998439	−	0.0558591i	$-0.0177898\pi$
$348$		0			0
$349$			7.11683i			0.380955i	0.981692	+	0.190477i	$0.0610036\pi$
$349$			7.11683i			0.380955i	−0.981692	+	0.190477i	$0.938996\pi$
$350$	−6.63555	+	0.285964i	−0.354685	+	0.0152854i
$351$		0			0
$352$	−2.86967	−	13.1193i	−0.152954	−	0.699260i
$353$	−28.9449			−1.54058			−0.770290	−	0.637694i	$-0.779889\pi$
$353$	−28.9449			−1.54058			−0.770290	+	0.637694i	$0.779889\pi$
$354$		0			0
$355$		−	42.1847i		−	2.23893i
$356$	23.8176	−	2.05669i	1.26233	−	0.109004i
$357$		0			0
$358$	−0.648901	−	15.0572i	−0.0342955	−	0.795799i
$359$	10.0190			0.528780			0.264390	−	0.964416i	$-0.414829\pi$
$359$	10.0190			0.528780			0.264390	+	0.964416i	$0.414829\pi$
$360$		0			0
$361$	17.8279			0.938311
$362$	0.404228	+	9.37977i	0.0212457	+	0.492990i
$363$		0			0
$364$	−0.187624	−	2.17279i	−0.00983420	−	0.113885i
$365$			45.6894i			2.39149i
$366$		0			0
$367$	31.4662			1.64252			0.821261	−	0.570552i	$-0.193271\pi$
$367$	31.4662			1.64252			0.821261	+	0.570552i	$0.193271\pi$
$368$	−19.2061	+	3.34187i	−1.00119	+	0.174207i
$369$		0			0
$370$	20.3004	−	0.874860i	1.05537	−	0.0454818i
$371$			8.14672i			0.422956i
$372$		0			0
$373$		−	31.8121i		−	1.64717i	−0.567193	−	0.823585i	$-0.691970\pi$
$373$		−	31.8121i		−	1.64717i	0.567193	−	0.823585i	$-0.308030\pi$
$374$	0.533837	+	12.3873i	0.0276041	+	0.640530i
$375$		0			0
$376$	−0.945726	+	0.122879i	−0.0487721	+	0.00633700i
$377$	−1.74042			−0.0896360
$378$		0			0
$379$			15.2806i			0.784911i	0.919771	+	0.392456i	$0.128374\pi$
$379$			15.2806i			0.784911i	−0.919771	+	0.392456i	$0.871626\pi$
$380$	−6.71742	+	0.580060i	−0.344596	+	0.0297565i
$381$		0			0
$382$	−13.8627	+	0.597420i	−0.709275	+	0.0305667i
$383$	−19.0555			−0.973691			−0.486845	−	0.873488i	$-0.661853\pi$
$383$	−19.0555			−0.973691			−0.486845	+	0.873488i	$0.661853\pi$
$384$		0			0
$385$	−7.39246			−0.376755
$386$	24.6607	−	1.06277i	1.25520	−	0.0540935i
$387$		0			0
$388$	−10.5647	+	0.912282i	−0.536343	+	0.0463141i
$389$		−	3.69055i		−	0.187118i	−0.995614	−	0.0935591i	$-0.970176\pi$
$389$		−	3.69055i		−	0.187118i	0.995614	−	0.0935591i	$-0.0298244\pi$
$390$		0			0
$391$	17.9984			0.910219
$392$	2.80485	−	0.364437i	0.141666	−	0.0184068i
$393$		0			0
$394$	1.68587	+	39.1192i	0.0849327	+	1.97080i
$395$		−	16.1338i		−	0.811780i
$396$		0			0
$397$		−	14.8184i		−	0.743715i	−0.928290	−	0.371857i	$-0.878721\pi$
$397$		−	14.8184i		−	0.743715i	0.928290	−	0.371857i	$-0.121279\pi$
$398$	13.1372	−	0.566157i	0.658510	−	0.0283789i
$399$		0			0
$400$	−18.5075	+	3.22032i	−0.925376	+	0.161016i
$401$	1.80006			0.0898908			0.0449454	−	0.998989i	$-0.485689\pi$
$401$	1.80006			0.0898908			0.0449454	+	0.998989i	$0.485689\pi$
$402$		0			0
$403$		−	8.12940i		−	0.404954i
$404$	−0.0129627	−	0.150115i	−0.000644919	−	0.00746851i
$405$		0			0
$406$	−0.0971845	−	2.25509i	−0.00482319	−	0.111918i
$407$	10.9540			0.542968
$408$		0			0
$409$	−25.6731			−1.26945			−0.634727	−	0.772736i	$-0.718888\pi$
$409$	−25.6731			−1.26945			−0.634727	+	0.772736i	$0.718888\pi$
$410$	−0.00721668	−	0.167457i	−0.000356406	−	0.00827012i
$411$		0			0
$412$	30.5557	−	2.63854i	1.50537	−	0.129992i
$413$		−	15.0761i		−	0.741846i
$414$		0			0
$415$	0.430719			0.0211431
$416$	−1.31810	−	6.02599i	−0.0646254	−	0.295448i
$417$		0			0
$418$	−3.63142	+	0.156498i	−0.177618	+	0.00765458i
$419$			17.3661i			0.848392i	0.905571	+	0.424196i	$0.139443\pi$
$419$			17.3661i			0.848392i	−0.905571	+	0.424196i	$0.860557\pi$
$420$		0			0
$421$			30.4837i			1.48568i	0.669468	+	0.742841i	$0.266522\pi$
$421$			30.4837i			1.48568i	−0.669468	+	0.742841i	$0.733478\pi$
$422$	0.992918	+	23.0398i	0.0483345	+	1.12156i
$423$		0			0
$424$	2.96896	+	22.8503i	0.144186	+	1.10971i
$425$	17.3438			0.841298
$426$		0			0
$427$		−	5.53745i		−	0.267976i
$428$	0.694664	+	8.04459i	0.0335778	+	0.388850i
$429$		0			0
$430$	48.6635	−	2.09718i	2.34676	−	0.101135i
$431$	9.49698			0.457453			0.228727	−	0.973491i	$-0.426544\pi$
$431$	9.49698			0.457453			0.228727	+	0.973491i	$0.426544\pi$
$432$		0			0
$433$	25.6935			1.23475			0.617376	−	0.786668i	$-0.288196\pi$
$433$	25.6935			1.23475			0.617376	+	0.786668i	$0.288196\pi$
$434$	10.5334	−	0.453944i	0.505620	−	0.0217900i
$435$		0			0
$436$	2.10494	+	24.3763i	0.100808	+	1.16741i
$437$			5.27637i			0.252403i
$438$		0			0
$439$	11.0047			0.525227			0.262614	−	0.964901i	$-0.415416\pi$
$439$	11.0047			0.525227			0.262614	+	0.964901i	$0.415416\pi$
$440$	−20.7347	+	2.69408i	−0.988490	+	0.128435i
$441$		0			0
$442$	0.245203	+	5.68975i	0.0116631	+	0.270634i
$443$			32.0650i			1.52346i	0.647897	+	0.761728i	$0.275649\pi$
$443$			32.0650i			1.52346i	−0.647897	+	0.761728i	$0.724351\pi$
$444$		0			0
$445$		−	37.2208i		−	1.76444i
$446$	−26.6821	+	1.14988i	−1.26344	+	0.0544486i
$447$		0			0
$448$	7.73437	−	2.04438i	0.365415	−	0.0965879i
$449$	−16.5474			−0.780922			−0.390461	−	0.920619i	$-0.627684\pi$
$449$	−16.5474			−0.780922			−0.390461	+	0.920619i	$0.627684\pi$
$450$		0			0
$451$		−	0.0903588i		−	0.00425483i
$452$	22.3039	−	1.92598i	1.04909	−	0.0905904i
$453$		0			0
$454$	−0.789796	−	18.3266i	−0.0370670	−	0.860109i
$455$	−3.39553			−0.159185
$456$		0			0
$457$	−26.9067			−1.25864			−0.629321	−	0.777145i	$-0.716667\pi$
$457$	−26.9067			−1.25864			−0.629321	+	0.777145i	$0.716667\pi$
$458$	−0.360804	−	8.37217i	−0.0168593	−	0.391206i
$459$		0			0
$460$	2.61125	+	30.2397i	0.121750	+	1.40993i
$461$			28.9351i			1.34764i	0.738895	+	0.673821i	$0.235348\pi$
$461$			28.9351i			1.34764i	−0.738895	+	0.673821i	$0.764652\pi$
$462$		0			0
$463$	10.3287			0.480017			0.240009	−	0.970771i	$-0.422850\pi$
$463$	10.3287			0.480017			0.240009	+	0.970771i	$0.422850\pi$
$464$	−1.09442	−	6.28977i	−0.0508074	−	0.291995i
$465$		0			0
$466$	−17.2506	+	0.743426i	−0.799119	+	0.0344386i
$467$		−	22.1113i		−	1.02319i	−0.859227	−	0.511595i	$-0.829055\pi$
$467$		−	22.1113i		−	1.02319i	0.859227	−	0.511595i	$-0.170945\pi$
$468$		0			0
$469$		−	7.70421i		−	0.355747i
$470$	0.0639303	+	1.48345i	0.00294888	+	0.0684264i
$471$		0			0
$472$	−5.49428	−	42.2862i	−0.252895	−	1.94638i
$473$	26.2585			1.20737
$474$		0			0
$475$			5.08446i			0.233291i
$476$	−7.35861	+	0.635429i	−0.337281	+	0.0291248i
$477$		0			0
$478$	−31.8289	+	1.37169i	−1.45582	+	0.0627395i
$479$	5.77499			0.263866			0.131933	−	0.991259i	$-0.457882\pi$
$479$	5.77499			0.263866			0.131933	+	0.991259i	$0.457882\pi$
$480$		0			0
$481$	5.03140			0.229412
$482$	−22.8644	+	0.985357i	−1.04145	+	0.0448818i
$483$		0			0
$484$	10.6883	−	0.922954i	0.485832	−	0.0419525i
$485$			16.5100i			0.749680i
$486$		0			0
$487$	12.5566			0.568993			0.284497	−	0.958677i	$-0.408174\pi$
$487$	12.5566			0.568993			0.284497	+	0.958677i	$0.408174\pi$
$488$	−2.01805	−	15.5317i	−0.0913529	−	0.703088i
$489$		0			0
$490$	−0.189605	−	4.39964i	−0.00856550	−	0.198756i
$491$		−	20.9548i		−	0.945677i	−0.881149	−	0.472839i	$-0.843229\pi$
$491$		−	20.9548i		−	0.945677i	0.881149	−	0.472839i	$-0.156771\pi$
$492$		0			0
$493$			5.89428i			0.265465i
$494$	−1.66799	+	0.0718832i	−0.0750465	+	0.00323418i
$495$		0			0
$496$	29.3792	−	5.11201i	1.31916	−	0.229536i
$497$	13.5472			0.607675
$498$		0			0
$499$			13.0152i			0.582641i	0.956626	+	0.291320i	$0.0940946\pi$
$499$			13.0152i			0.582641i	−0.956626	+	0.291320i	$0.905905\pi$
$500$	−0.162666	−	1.88376i	−0.00727464	−	0.0842443i
$501$		0			0
$502$	−0.419200	−	9.72718i	−0.0187098	−	0.434146i
$503$	22.9100			1.02150			0.510752	−	0.859728i	$-0.329367\pi$
$503$	22.9100			1.02150			0.510752	+	0.859728i	$0.329367\pi$
$504$		0			0
$505$	−0.234592			−0.0104392
$506$	0.704506	+	16.3475i	0.0313191	+	0.726735i
$507$		0			0
$508$	−4.84475	+	0.418353i	−0.214951	+	0.0185614i
$509$		−	24.5703i		−	1.08906i	−0.838741	−	0.544530i	$-0.816708\pi$
$509$		−	24.5703i		−	1.08906i	0.838741	−	0.544530i	$-0.183292\pi$
$510$		0			0
$511$	−14.6727			−0.649083
$512$	20.9487	−	8.55287i	0.925811	−	0.377987i
$513$		0			0
$514$	3.81680	−	0.164488i	0.168352	−	0.00725524i
$515$		−	47.7508i		−	2.10415i
$516$		0			0
$517$			0.800460i			0.0352042i
$518$	0.280953	+	6.51928i	0.0123444	+	0.286441i
$519$		0			0
$520$	−9.52394	+	1.23745i	−0.417652	+	0.0542660i
$521$	−1.51316			−0.0662929			−0.0331465	−	0.999451i	$-0.510553\pi$
$521$	−1.51316			−0.0662929			−0.0331465	+	0.999451i	$0.510553\pi$
$522$		0			0
$523$		−	0.202190i		−	0.00884117i	−0.999990	−	0.00442059i	$-0.998593\pi$
$523$		−	0.202190i		−	0.00884117i	0.999990	−	0.00442059i	$-0.00140712\pi$
$524$	−1.52056	−	17.6089i	−0.0664260	−	0.769249i
$525$		0			0
$526$	−19.1448	+	0.825057i	−0.834752	+	0.0359742i
$527$	−27.5319			−1.19931
$528$		0			0
$529$	0.752559			0.0327199
$530$	35.8426	−	1.54466i	1.55690	−	0.0670958i
$531$		0			0
$532$	−0.186281	−	2.15723i	−0.00807629	−	0.0935279i
$533$		−	0.0415038i		−	0.00179773i
$534$		0			0
$535$	12.5716			0.543520
$536$	−2.80770	−	21.6092i	−0.121274	−	0.933373i
$537$		0			0
$538$	0.390623	+	9.06408i	0.0168409	+	0.390780i
$539$		−	2.37402i		−	0.102256i
$540$		0			0
$541$		−	28.5045i		−	1.22550i	−0.790275	−	0.612752i	$-0.790062\pi$
$541$		−	28.5045i		−	1.22550i	0.790275	−	0.612752i	$-0.209938\pi$
$542$	−20.5007	+	0.883490i	−0.880580	+	0.0379492i
$543$		0			0
$544$	−20.4082	+	4.46403i	−0.874996	+	0.191394i
$545$	38.0940			1.63177
$546$		0			0
$547$		−	37.9150i		−	1.62113i	−0.585648	−	0.810565i	$-0.699160\pi$
$547$		−	37.9150i		−	1.62113i	0.585648	−	0.810565i	$-0.300840\pi$
$548$	−22.2130	+	1.91813i	−0.948891	+	0.0819383i
$549$		0			0
$550$	0.678882	+	15.7529i	0.0289476	+	0.671706i
$551$	−1.72795			−0.0736132
$552$		0			0
$553$	5.18122			0.220328
$554$	−1.54158	−	35.7712i	−0.0654956	−	1.51977i
$555$		0			0
$556$	2.97194	+	34.4166i	0.126038	+	1.45959i
$557$		−	16.6109i		−	0.703828i	−0.936032	−	0.351914i	$-0.885531\pi$
$557$		−	16.6109i		−	0.703828i	0.936032	−	0.351914i	$-0.114469\pi$
$558$		0			0
$559$	12.0611			0.510131
$560$	−2.13521	−	12.2712i	−0.0902289	−	0.518554i
$561$		0			0
$562$	1.01726	−	0.0438395i	0.0429105	−	0.00184926i
$563$		−	6.84219i		−	0.288364i	−0.989551	−	0.144182i	$-0.953945\pi$
$563$		−	6.84219i		−	0.288364i	0.989551	−	0.144182i	$-0.0460551\pi$
$564$		0			0
$565$		−	34.8553i		−	1.46637i
$566$	0.689654	+	16.0029i	0.0289883	+	0.672651i
$567$		0			0
$568$	37.9979	−	4.93710i	1.59435	−	0.207156i
$569$	15.3184			0.642180			0.321090	−	0.947049i	$-0.395951\pi$
$569$	15.3184			0.642180			0.321090	+	0.947049i	$0.395951\pi$
$570$		0			0
$571$		−	36.6853i		−	1.53523i	−0.640911	−	0.767616i	$-0.721443\pi$
$571$		−	36.6853i		−	1.53523i	0.640911	−	0.767616i	$-0.278557\pi$
$572$	−5.15825	+	0.445424i	−0.215677	+	0.0186241i
$573$		0			0
$574$	0.0537773	−	0.00231757i	0.00224462	−	9.67334e-5i
$575$	22.8886			0.954523
$576$		0			0
$577$	−23.9150			−0.995596			−0.497798	−	0.867293i	$-0.665858\pi$
$577$	−23.9150			−0.995596			−0.497798	+	0.867293i	$0.665858\pi$
$578$	−4.74984	+	0.204697i	−0.197567	+	0.00851429i
$579$		0			0
$580$	−9.90315	+	0.855154i	−0.411206	+	0.0355083i
$581$			0.138321i			0.00573852i
$582$		0			0
$583$	19.3404			0.800999
$584$	−41.1548	+	5.34728i	−1.70300	+	0.221272i
$585$		0			0
$586$	0.928978	+	21.5562i	0.0383757	+	0.890477i
$587$			45.0433i			1.85914i	0.368651	+	0.929568i	$0.379820\pi$
$587$			45.0433i			1.85914i	−0.368651	+	0.929568i	$0.620180\pi$
$588$		0			0
$589$		−	8.07118i		−	0.332567i
$590$	−66.3294	+	2.85851i	−2.73074	+	0.117683i
$591$		0			0
$592$	3.16389	+	18.1832i	0.130035	+	0.747325i
$593$	−13.4524			−0.552425			−0.276212	−	0.961097i	$-0.589079\pi$
$593$	−13.4524			−0.552425			−0.276212	+	0.961097i	$0.589079\pi$
$594$		0			0
$595$			11.4996i			0.471439i
$596$	2.36132	+	27.3454i	0.0967235	+	1.12011i
$597$		0			0
$598$	0.323596	+	7.50877i	0.0132328	+	0.307057i
$599$	21.8377			0.892263			0.446132	−	0.894967i	$-0.352801\pi$
$599$	21.8377			0.892263			0.446132	+	0.894967i	$0.352801\pi$
$600$		0			0
$601$	−16.3704			−0.667764			−0.333882	−	0.942615i	$-0.608359\pi$
$601$	−16.3704			−0.667764			−0.333882	+	0.942615i	$0.608359\pi$
$602$	0.673490	+	15.6278i	0.0274494	+	0.636942i
$603$		0			0
$604$	−25.5440	+	2.20577i	−1.03937	+	0.0897515i
$605$		−	16.7031i		−	0.679078i
$606$		0			0
$607$	28.8256			1.17000			0.584998	−	0.811034i	$-0.301095\pi$
$607$	28.8256			1.17000			0.584998	+	0.811034i	$0.301095\pi$
$608$	−1.30866	−	5.98283i	−0.0530734	−	0.242636i
$609$		0			0
$610$	−24.3628	+	1.04993i	−0.986421	+	0.0425105i
$611$			0.367669i			0.0148743i
$612$		0			0
$613$		−	34.6397i		−	1.39908i	−0.714592	−	0.699541i	$-0.753388\pi$
$613$		−	34.6397i		−	1.39908i	0.714592	−	0.699541i	$-0.246612\pi$
$614$	−1.55572	−	36.0992i	−0.0627837	−	1.45684i
$615$		0			0
$616$	−0.865179	−	6.65876i	−0.0348591	−	0.268289i
$617$	−38.6359			−1.55542			−0.777711	−	0.628622i	$-0.783619\pi$
$617$	−38.6359			−1.55542			−0.777711	+	0.628622i	$0.783619\pi$
$618$		0			0
$619$			25.9642i			1.04359i	0.853071	+	0.521794i	$0.174737\pi$
$619$			25.9642i			1.04359i	−0.853071	+	0.521794i	$0.825263\pi$
$620$	−3.99438	−	46.2571i	−0.160418	−	1.85773i
$621$		0			0
$622$	−4.24333	+	0.182869i	−0.170142	+	0.00733239i
$623$	11.9531			0.478891
$624$		0			0
$625$	−26.4258			−1.05703
$626$	−7.82694	+	0.337307i	−0.312828	+	0.0134815i
$627$		0			0
$628$	3.63773	+	42.1269i	0.145161	+	1.68105i
$629$		−	17.0399i		−	0.679425i
$630$		0			0
$631$	5.94731			0.236759			0.118379	−	0.992968i	$-0.462230\pi$
$631$	5.94731			0.236759			0.118379	+	0.992968i	$0.462230\pi$
$632$	14.5325	−	1.88823i	0.578073	−	0.0751096i
$633$		0			0
$634$	1.95886	+	45.4538i	0.0777964	+	1.80520i
$635$			7.57112i			0.300451i
$636$		0			0
$637$		−	1.09044i		−	0.0432048i
$638$	−5.35362	+	0.230718i	−0.211952	+	0.00913420i
$639$		0			0
$640$	−10.4610	−	33.6408i	−0.413508	−	1.32977i
$641$	41.7290			1.64820			0.824098	−	0.566447i	$-0.191682\pi$
$641$	41.7290			1.64820			0.824098	+	0.566447i	$0.191682\pi$
$642$		0			0
$643$			36.9825i			1.45845i	0.684275	+	0.729224i	$0.260119\pi$
$643$			36.9825i			1.45845i	−0.684275	+	0.729224i	$0.739881\pi$
$644$	−9.71118	+	0.838577i	−0.382674	+	0.0330446i
$645$		0			0
$646$	0.243447	+	5.64900i	0.00957831	+	0.222257i
$647$	2.39044			0.0939778			0.0469889	−	0.998895i	$-0.485037\pi$
$647$	2.39044			0.0939778			0.0469889	+	0.998895i	$0.485037\pi$
$648$		0			0
$649$	−35.7909			−1.40492
$650$	0.311826	+	7.23567i	0.0122308	+	0.283806i
$651$		0			0
$652$	−0.0665141	−	0.770270i	−0.00260489	−	0.0301661i
$653$		−	27.1588i		−	1.06280i	−0.847120	−	0.531402i	$-0.821665\pi$
$653$		−	27.1588i		−	1.06280i	0.847120	−	0.531402i	$-0.178335\pi$
$654$		0			0
$655$	−27.5183			−1.07523
$656$	0.149993	−	0.0260988i	0.00585623	−	0.00101899i
$657$		0			0
$658$	−0.476396	+	0.0205306i	−0.0185718	+	0.000800365i
$659$		−	41.3343i		−	1.61016i	−0.593169	−	0.805078i	$-0.702123\pi$
$659$		−	41.3343i		−	1.61016i	0.593169	−	0.805078i	$-0.297877\pi$
$660$		0			0
$661$			6.44768i			0.250786i	0.992107	+	0.125393i	$0.0400192\pi$
$661$			6.44768i			0.250786i	−0.992107	+	0.125393i	$0.959981\pi$
$662$	−1.51992	−	35.2684i	−0.0590733	−	1.37075i
$663$		0			0
$664$	0.0504093	+	0.387970i	0.00195626	+	0.0150562i
$665$	−3.37121			−0.130730
$666$		0			0
$667$			7.77869i			0.301192i
$668$	28.7601	−	2.48348i	1.11276	−	0.0960889i
$669$		0			0
$670$	−33.8958	+	1.46076i	−1.30951	+	0.0564341i
$671$	−13.1460			−0.507496
$672$		0			0
$673$	−36.1564			−1.39373			−0.696863	−	0.717204i	$-0.745421\pi$
$673$	−36.1564			−1.39373			−0.696863	+	0.717204i	$0.745421\pi$
$674$	25.1354	−	1.08322i	0.968178	−	0.0417243i
$675$		0			0
$676$	23.5343	−	2.03223i	0.905165	−	0.0781626i
$677$		−	47.4088i		−	1.82207i	−0.412330	−	0.911035i	$-0.635285\pi$
$677$		−	47.4088i		−	1.82207i	0.412330	−	0.911035i	$-0.364715\pi$
$678$		0			0
$679$	−5.30202			−0.203473
$680$	4.19089	+	32.2548i	0.160713	+	1.23691i
$681$		0			0
$682$	−1.07767	−	25.0065i	−0.0412662	−	0.957548i
$683$		−	3.55646i		−	0.136084i	−0.997682	−	0.0680420i	$-0.978325\pi$
$683$		−	3.55646i		−	0.136084i	0.997682	−	0.0680420i	$-0.0216752\pi$
$684$		0			0
$685$			34.7132i			1.32632i
$686$	1.41290	−	0.0608900i	0.0539449	−	0.00232479i
$687$		0			0
$688$	7.58438	+	43.5882i	0.289152	+	1.66178i
$689$	8.88350			0.338435
$690$		0			0
$691$		−	41.6181i		−	1.58323i	−0.611023	−	0.791613i	$-0.709242\pi$
$691$		−	41.6181i		−	1.58323i	0.611023	−	0.791613i	$-0.290758\pi$
$692$	2.40017	+	27.7952i	0.0912407	+	1.05662i
$693$		0			0
$694$	−0.126717	−	2.94036i	−0.00481010	−	0.111615i
$695$	53.7845			2.04016
$696$		0			0
$697$	−0.140561			−0.00532414
$698$	0.433343	+	10.0554i	0.0164023	+	0.380602i
$699$		0			0
$700$	−9.35797	+	0.808077i	−0.353698	+	0.0305424i
$701$			34.8945i			1.31795i	0.752166	+	0.658973i	$0.229009\pi$
$701$			34.8945i			1.31795i	−0.752166	+	0.658973i	$0.770991\pi$
$702$		0			0
$703$	4.99537			0.188404
$704$	−4.85340	−	18.3615i	−0.182919	−	0.692026i
$705$		0			0
$706$	−40.8963	+	1.76245i	−1.53915	+	0.0663308i
$707$		−	0.0753369i		−	0.00283334i
$708$		0			0
$709$			49.2296i			1.84886i	0.381357	+	0.924428i	$0.375457\pi$
$709$			49.2296i			1.84886i	−0.381357	+	0.924428i	$0.624543\pi$
$710$	−2.56862	−	59.6028i	−0.0963987	−	2.23685i
$711$		0			0
$712$	33.5267	−	4.35615i	1.25647	−	0.163254i
$713$	−36.3339			−1.36072
$714$		0			0
$715$			8.06103i			0.301466i
$716$	−1.83367	−	21.2349i	−0.0685274	−	0.793584i
$717$		0			0
$718$	14.1558	−	0.610054i	0.528290	−	0.0227670i
$719$	−10.9969			−0.410117			−0.205058	−	0.978750i	$-0.565738\pi$
$719$	−10.9969			−0.410117			−0.205058	+	0.978750i	$0.565738\pi$
$720$		0			0
$721$	15.3347			0.571095
$722$	25.1891	−	1.08554i	0.937441	−	0.0403996i
$723$		0			0
$724$	1.14227	+	13.2281i	0.0424521	+	0.491618i
$725$			7.49577i			0.278386i
$726$		0			0
$727$	9.03008			0.334907			0.167454	−	0.985880i	$-0.446446\pi$
$727$	9.03008			0.334907			0.167454	+	0.985880i	$0.446446\pi$
$728$	−0.397396	−	3.05852i	−0.0147285	−	0.113356i
$729$		0			0
$730$	2.78203	+	64.5547i	0.102967	+	2.38928i
$731$		−	40.8474i		−	1.51080i
$732$		0			0
$733$			41.6840i			1.53963i	0.638265	+	0.769817i	$0.279653\pi$
$733$			41.6840i			1.53963i	−0.638265	+	0.769817i	$0.720347\pi$
$734$	44.4587	−	1.91598i	1.64100	−	0.0707200i
$735$		0			0
$736$	−26.9328	+	5.89119i	−0.992756	+	0.217152i
$737$	−18.2899			−0.673718
$738$		0			0
$739$		−	34.7320i		−	1.27764i	−0.769358	−	0.638818i	$-0.779424\pi$
$739$		−	34.7320i		−	1.27764i	0.769358	−	0.638818i	$-0.220576\pi$
$740$	28.6292	−	2.47218i	1.05243	−	0.0908792i
$741$		0			0
$742$	0.496053	+	11.5105i	0.0182107	+	0.422564i
$743$	−15.9173			−0.583951			−0.291975	−	0.956426i	$-0.594313\pi$
$743$	−15.9173			−0.583951			−0.291975	+	0.956426i	$0.594313\pi$
$744$		0			0
$745$	42.7339			1.56565
$746$	−1.93704	−	44.9474i	−0.0709201	−	1.64564i
$747$		0			0
$748$	1.50852	+	17.4695i	0.0551569	+	0.638747i
$749$			4.03726i			0.147518i
$750$		0			0
$751$	13.7001			0.499925			0.249963	−	0.968255i	$-0.419582\pi$
$751$	13.7001			0.499925			0.249963	+	0.968255i	$0.419582\pi$
$752$	−1.32874	+	0.231201i	−0.0484540	+	0.00843104i
$753$		0			0
$754$	−2.45904	+	0.105974i	−0.0895529	+	0.00385934i
$755$			39.9188i			1.45279i
$756$		0			0
$757$		−	27.3072i		−	0.992496i	−0.868181	−	0.496248i	$-0.834711\pi$
$757$		−	27.3072i		−	0.992496i	0.868181	−	0.496248i	$-0.165289\pi$
$758$	0.930435	+	21.5900i	0.0337949	+	0.784183i
$759$		0			0
$760$	−9.45573	+	1.22859i	−0.342995	+	0.0445657i
$761$	−18.3078			−0.663657			−0.331829	−	0.943340i	$-0.607666\pi$
$761$	−18.3078			−0.663657			−0.331829	+	0.943340i	$0.607666\pi$
$762$		0			0
$763$			12.2335i			0.442883i
$764$	−19.5502	+	1.68819i	−0.707301	+	0.0610767i
$765$		0			0
$766$	−26.9236	+	1.16029i	−0.972788	+	0.0419229i
$767$	−16.4396			−0.593598
$768$		0			0
$769$	−13.3631			−0.481884			−0.240942	−	0.970540i	$-0.577456\pi$
$769$	−13.3631			−0.481884			−0.240942	+	0.970540i	$0.577456\pi$
$770$	−10.4448	+	0.450127i	−0.376405	+	0.0162214i
$771$		0			0
$772$	34.7784	−	3.00317i	1.25170	−	0.108087i
$773$			39.3918i			1.41682i	0.705799	+	0.708412i	$0.250588\pi$
$773$			39.3918i			1.41682i	−0.705799	+	0.708412i	$0.749412\pi$
$774$		0			0
$775$	−35.0124			−1.25768
$776$	−14.8714	+	1.93225i	−0.533851	+	0.0693638i
$777$		0			0
$778$	−0.224717	−	5.21438i	−0.00805651	−	0.186945i
$779$		−	0.0412066i		−	0.00147638i
$780$		0			0
$781$		−	32.1613i		−	1.15082i
$782$	25.4300	−	1.09592i	0.909375	−	0.0391901i
$783$		0			0
$784$	3.94079	−	0.685701i	0.140742	−	0.0244893i
$785$	65.8336			2.34970
$786$		0			0
$787$		−	36.3862i		−	1.29703i	−0.761203	−	0.648514i	$-0.775391\pi$
$787$		−	36.3862i		−	1.29703i	0.761203	−	0.648514i	$-0.224609\pi$
$788$	4.76393	+	55.1689i	0.169708	+	1.96531i
$789$		0			0
$790$	−0.982387	−	22.7955i	−0.0349518	−	0.811027i
$791$	11.1934			0.397993
$792$		0			0
$793$	−6.03826			−0.214425
$794$	−0.902292	−	20.9370i	−0.0320212	−	0.743025i
$795$		0			0
$796$	18.5271	−	1.59985i	0.656677	−	0.0567052i
$797$		−	33.1598i		−	1.17458i	−0.809377	−	0.587290i	$-0.800195\pi$
$797$		−	33.1598i		−	1.17458i	0.809377	−	0.587290i	$-0.199805\pi$
$798$		0			0
$799$	1.24519			0.0440516
$800$	−25.9532	+	5.67692i	−0.917585	+	0.200710i
$801$		0			0
$802$	2.54331	−	0.109606i	0.0898074	−	0.00387031i
$803$			34.8333i			1.22924i
$804$		0			0
$805$			15.1761i			0.534888i
$806$	−0.494999	−	11.4860i	−0.0174356	−	0.404579i
$807$		0			0
$808$	−0.0274555	−	0.211309i	−0.000965883	−	0.00743382i
$809$	−44.9173			−1.57921			−0.789604	−	0.613616i	$-0.789714\pi$
$809$	−44.9173			−1.57921			−0.789604	+	0.613616i	$0.789714\pi$
$810$		0			0
$811$			37.5222i			1.31758i	0.752325	+	0.658792i	$0.228932\pi$
$811$			37.5222i			1.31758i	−0.752325	+	0.658792i	$0.771068\pi$
$812$	−0.274624	−	3.18030i	−0.00963743	−	0.111607i
$813$		0			0
$814$	15.4769	−	0.666986i	0.542464	−	0.0233779i
$815$	−1.20374			−0.0421650
$816$		0			0
$817$	11.9747			0.418943
$818$	−36.2736	+	1.56324i	−1.26828	+	0.0546573i
$819$		0			0
$820$	−0.0203929	−	0.236161i	−0.000712152	−	0.00824711i
$821$		−	0.214362i		−	0.00748129i	−0.999993	−	0.00374065i	$-0.998809\pi$
$821$		−	0.214362i		−	0.00748129i	0.999993	−	0.00374065i	$-0.00119069\pi$
$822$		0			0
$823$	−4.84153			−0.168765			−0.0843825	−	0.996433i	$-0.526892\pi$
$823$	−4.84153			−0.168765			−0.0843825	+	0.996433i	$0.526892\pi$
$824$	43.0116	−	5.58854i	1.49838	−	0.194686i
$825$		0			0
$826$	−0.917982	−	21.3010i	−0.0319407	−	0.741158i
$827$			9.13088i			0.317512i	0.987318	+	0.158756i	$0.0507483\pi$
$827$			9.13088i			0.317512i	−0.987318	+	0.158756i	$0.949252\pi$
$828$		0			0
$829$		−	22.8115i		−	0.792275i	−0.918191	−	0.396138i	$-0.870350\pi$
$829$		−	22.8115i		−	0.792275i	0.918191	−	0.396138i	$-0.129650\pi$
$830$	0.608563	−	0.0262264i	0.0211235	−	0.000910333i
$831$		0			0
$832$	−2.22927	−	8.43387i	−0.0772862	−	0.292392i
$833$	−3.69300			−0.127955
$834$		0			0
$835$		−	44.9447i		−	1.55538i
$836$	−5.12131	+	0.442234i	−0.177124	+	0.0152950i
$837$		0			0
$838$	1.05742	+	24.5367i	0.0365281	+	0.847605i
$839$	−37.9537			−1.31031			−0.655154	−	0.755496i	$-0.727396\pi$
$839$	−37.9537			−1.31031			−0.655154	+	0.755496i	$0.727396\pi$
$840$		0			0
$841$	26.4526			0.912157
$842$	1.85615	+	43.0704i	0.0639671	+	1.48430i
$843$		0			0
$844$	2.80579	+	32.4926i	0.0965793	+	1.11844i
$845$		−	36.7781i		−	1.26521i
$846$		0			0
$847$	5.36404			0.184311
$848$	5.58621	+	32.1045i	0.191831	+	1.10247i
$849$		0			0
$850$	24.5051	−	1.05606i	0.840517	−	0.0362227i
$851$		−	22.4876i		−	0.770864i
$852$		0			0
$853$			35.9465i			1.23078i	0.788221	+	0.615392i	$0.211002\pi$
$853$			35.9465i			1.23078i	−0.788221	+	0.615392i	$0.788998\pi$
$854$	−0.337175	−	7.82388i	−0.0115379	−	0.267728i
$855$		0			0
$856$	1.47133	+	11.3239i	0.0502889	+	0.387043i
$857$	36.9904			1.26357			0.631783	−	0.775145i	$-0.282323\pi$
$857$	36.9904			1.26357			0.631783	+	0.775145i	$0.282323\pi$
$858$		0			0
$859$			0.924367i			0.0315390i	0.999876	+	0.0157695i	$0.00501979\pi$
$859$			0.924367i			0.0315390i	−0.999876	+	0.0157695i	$0.994980\pi$
$860$	68.6290	−	5.92623i	2.34023	−	0.202083i
$861$		0			0
$862$	13.4183	−	0.578271i	0.457029	−	0.0196960i
$863$	−11.2057			−0.381445			−0.190723	−	0.981644i	$-0.561083\pi$
$863$	−11.2057			−0.381445			−0.190723	+	0.981644i	$0.561083\pi$
$864$		0			0
$865$	43.4369			1.47690
$866$	36.3024	−	1.56448i	1.23361	−	0.0531631i
$867$		0			0
$868$	14.8550	−	1.28276i	0.504213	−	0.0435396i
$869$		−	12.3003i		−	0.417259i
$870$		0			0
$871$	−8.40098			−0.284656
$872$	4.45834	+	34.3132i	0.150978	+	1.16199i
$873$		0			0
$874$	0.321278	+	7.45500i	0.0108674	+	0.252169i
$875$		−	0.945386i		−	0.0319599i
$876$		0			0
$877$		−	38.6354i		−	1.30463i	−0.757950	−	0.652313i	$-0.773799\pi$
$877$		−	38.6354i		−	1.30463i	0.757950	−	0.652313i	$-0.226201\pi$
$878$	15.5486	−	0.670078i	0.524740	−	0.0226140i
$879$		0			0
$880$	−29.1321	+	5.06902i	−0.982044	+	0.170876i
$881$	−47.0860			−1.58637			−0.793184	−	0.608982i	$-0.791578\pi$
$881$	−47.0860			−1.58637			−0.793184	+	0.608982i	$0.791578\pi$
$882$		0			0
$883$			2.23864i			0.0753362i	0.999290	+	0.0376681i	$0.0119930\pi$
$883$			2.23864i			0.0753362i	−0.999290	+	0.0376681i	$0.988007\pi$
$884$	0.692897	+	8.02413i	0.0233046	+	0.269881i
$885$		0			0
$886$	1.95244	+	45.3048i	0.0655935	+	1.52204i
$887$	−56.5911			−1.90014			−0.950071	−	0.312032i	$-0.898990\pi$
$887$	−56.5911			−1.90014			−0.950071	+	0.312032i	$0.898990\pi$
$888$		0			0
$889$	−2.43139			−0.0815463
$890$	−2.26638	−	52.5894i	−0.0759691	−	1.76280i
$891$		0			0
$892$	−37.6292	+	3.24935i	−1.25992	+	0.108796i
$893$			0.365036i			0.0122155i
$894$		0			0
$895$	−33.1847			−1.10924
$896$	10.8034	−	3.35946i	0.360917	−	0.112232i
$897$		0			0
$898$	−23.3799	+	1.00757i	−0.780198	+	0.0336231i
$899$		−	11.8989i		−	0.396852i
$900$		0			0
$901$		−	30.0858i		−	1.00230i
$902$	−0.00550194	−	0.127668i	−0.000183195	−	0.00425088i
$903$		0			0
$904$	31.3959	−	4.07930i	1.04421	−	0.135676i
$905$	20.6721			0.687165
$906$		0			0
$907$		−	37.0996i		−	1.23187i	−0.787797	−	0.615935i	$-0.788778\pi$
$907$		−	37.0996i		−	1.23187i	0.787797	−	0.615935i	$-0.211222\pi$
$908$	−2.23181	−	25.8456i	−0.0740652	−	0.857715i
$909$		0			0
$910$	−4.79755	+	0.206753i	−0.159037	+	0.00685381i
$911$	−45.3701			−1.50318			−0.751589	−	0.659632i	$-0.770712\pi$
$911$	−45.3701			−1.50318			−0.751589	+	0.659632i	$0.770712\pi$
$912$		0			0
$913$	0.328377			0.0108677
$914$	−38.0165	+	1.63835i	−1.25748	+	0.0541917i
$915$		0			0
$916$	−1.01956	−	11.8071i	−0.0336873	−	0.390117i
$917$		−	8.83723i		−	0.291831i
$918$		0			0
$919$	28.8038			0.950148			0.475074	−	0.879946i	$-0.342421\pi$
$919$	28.8038			0.950148			0.475074	+	0.879946i	$0.342421\pi$
$920$	5.53073	+	42.5667i	0.182343	+	1.40338i
$921$		0			0
$922$	1.76186	+	40.8825i	0.0580237	+	1.34639i
$923$		−	14.7724i		−	0.486240i
$924$		0			0
$925$		−	21.6697i		−	0.712495i
$926$	14.5935	−	0.628917i	0.479572	−	0.0206675i
$927$		0			0
$928$	−1.92930	−	8.82019i	−0.0633323	−	0.289537i
$929$	−45.5518			−1.49451			−0.747254	−	0.664539i	$-0.768628\pi$
$929$	−45.5518			−1.49451			−0.747254	+	0.664539i	$0.768628\pi$
$930$		0			0
$931$		−	1.08263i		−	0.0354818i
$932$	−24.3282	+	2.10078i	−0.796895	+	0.0688133i
$933$		0			0
$934$	−1.34636	−	31.2411i	−0.0440541	−	1.02224i
$935$	27.3003			0.892817
$936$		0			0
$937$	−43.3973			−1.41773			−0.708864	−	0.705346i	$-0.750792\pi$
$937$	−43.3973			−1.41773			−0.708864	+	0.705346i	$0.750792\pi$
$938$	−0.469109	−	10.8853i	−0.0153169	−	0.355417i
$939$		0			0
$940$	0.180654	+	2.09208i	0.00589230	+	0.0682360i
$941$			17.5629i			0.572534i	0.958150	+	0.286267i	$0.0924145\pi$
$941$			17.5629i			0.572534i	−0.958150	+	0.286267i	$0.907586\pi$
$942$		0			0
$943$	−0.185499			−0.00604068
$944$	−10.3377	−	59.4117i	−0.336463	−	1.93369i
$945$		0			0
$946$	37.1007	−	1.59888i	1.20625	−	0.0519840i
$947$			33.8968i			1.10150i	0.834671	+	0.550749i	$0.185658\pi$
$947$			33.8968i			1.10150i	−0.834671	+	0.550749i	$0.814342\pi$
$948$		0			0
$949$			15.9997i			0.519373i
$950$	0.309593	+	7.18385i	0.0100445	+	0.233075i
$951$		0			0
$952$	−10.3583	+	1.34586i	−0.335715	+	0.0436197i
$953$	−42.7021			−1.38326			−0.691628	−	0.722254i	$-0.743106\pi$
$953$	−42.7021			−1.38326			−0.691628	+	0.722254i	$0.743106\pi$
$954$		0			0
$955$			30.5520i			0.988639i
$956$	−44.8875	+	3.87612i	−1.45177	+	0.125363i
$957$		0			0
$958$	8.15950	−	0.351639i	0.263621	−	0.0113609i
$959$	−11.1478			−0.359982
$960$		0			0
$961$	24.5794			0.792883
$962$	7.10888	−	0.306362i	0.229200	−	0.00987751i
$963$		0			0
$964$	−32.2452	+	2.78443i	−1.03855	+	0.0896804i
$965$		−	54.3498i		−	1.74958i
$966$		0			0
$967$	23.9796			0.771132			0.385566	−	0.922680i	$-0.374006\pi$
$967$	23.9796			0.771132			0.385566	+	0.922680i	$0.374006\pi$
$968$	15.0453	−	1.95485i	0.483576	−	0.0628314i
$969$		0			0
$970$	1.00529	+	23.3270i	0.0322780	+	0.748985i
$971$			13.2383i			0.424837i	0.977179	+	0.212418i	$0.0681340\pi$
$971$			13.2383i			0.424837i	−0.977179	+	0.212418i	$0.931866\pi$
$972$		0			0
$973$			17.2724i			0.553726i
$974$	17.7412	−	0.764570i	0.568466	−	0.0244984i
$975$		0			0
$976$	−3.79703	−	21.8219i	−0.121540	−	0.698503i
$977$	49.7224			1.59076			0.795380	−	0.606110i	$-0.207271\pi$
$977$	49.7224			1.59076			0.795380	+	0.606110i	$0.207271\pi$
$978$		0			0
$979$		−	28.3769i		−	0.906929i
$980$	−0.535788	−	6.20472i	−0.0171151	−	0.198202i
$981$		0			0
$982$	−1.27594	−	29.6071i	−0.0407168	−	0.944800i
$983$	33.8135			1.07848			0.539241	−	0.842151i	$-0.318711\pi$
$983$	33.8135			1.07848			0.539241	+	0.842151i	$0.318711\pi$
$984$		0			0
$985$	86.2150			2.74704
$986$	0.358902	+	8.32804i	0.0114298	+	0.265219i
$987$		0			0
$988$	−2.35233	+	0.203128i	−0.0748377	+	0.00646236i
$989$		−	53.9065i		−	1.71413i
$990$		0			0
$991$	36.2781			1.15241			0.576206	−	0.817304i	$-0.304532\pi$
$991$	36.2781			1.15241			0.576206	+	0.817304i	$0.304532\pi$
$992$	41.1987	−	9.01166i	1.30806	−	0.286121i
$993$		0			0
$994$	19.1409	−	0.824888i	0.607111	−	0.0261639i
$995$		−	28.9532i		−	0.917879i
$996$		0			0
$997$		−	22.7054i		−	0.719088i	−0.933128	−	0.359544i	$-0.882932\pi$
$997$		−	22.7054i		−	0.719088i	0.933128	−	0.359544i	$-0.117068\pi$
$998$	0.792496	+	18.3892i	0.0250860	+	0.582101i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.f.757.23	yes	24
3.2	odd	2	inner	1512.2.c.f.757.2	yes	24
4.3	odd	2		6048.2.c.g.3025.3		24
8.3	odd	2		6048.2.c.g.3025.22		24
8.5	even	2	inner	1512.2.c.f.757.24	yes	24
12.11	even	2		6048.2.c.g.3025.21		24
24.5	odd	2	inner	1512.2.c.f.757.1	✓	24
24.11	even	2		6048.2.c.g.3025.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.f.757.1	✓	24	24.5	odd	2	inner
1512.2.c.f.757.2	yes	24	3.2	odd	2	inner
1512.2.c.f.757.23	yes	24	1.1	even	1	trivial
1512.2.c.f.757.24	yes	24	8.5	even	2	inner
6048.2.c.g.3025.3		24	4.3	odd	2
6048.2.c.g.3025.4		24	24.11	even	2
6048.2.c.g.3025.21		24	12.11	even	2
6048.2.c.g.3025.22		24	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41290 - 0.0608900i) q^{2} +(1.99258 - 0.172063i) q^{4} -3.11390i q^{5} +1.00000 q^{7} +(2.80485 - 0.364437i) q^{8} +O(q^{10})\)	\(q+(1.41290 - 0.0608900i) q^{2} +(1.99258 - 0.172063i) q^{4} -3.11390i q^{5} +1.00000 q^{7} +(2.80485 - 0.364437i) q^{8} +(-0.189605 - 4.39964i) q^{10} -2.37402i q^{11} -1.09044i q^{13} +(1.41290 - 0.0608900i) q^{14} +(3.94079 - 0.685701i) q^{16} -3.69300 q^{17} -1.08263i q^{19} +(-0.535788 - 6.20472i) q^{20} +(-0.144554 - 3.35425i) q^{22} -4.87366 q^{23} -4.69640 q^{25} +(-0.0663968 - 1.54068i) q^{26} +(1.99258 - 0.172063i) q^{28} -1.59607i q^{29} +7.45516 q^{31} +(5.52620 - 1.20878i) q^{32} +(-5.21785 + 0.224867i) q^{34} -3.11390i q^{35} +4.61410i q^{37} +(-0.0659213 - 1.52965i) q^{38} +(-1.13482 - 8.73404i) q^{40} +0.0380616 q^{41} +11.0608i q^{43} +(-0.408481 - 4.73043i) q^{44} +(-6.88600 + 0.296757i) q^{46} -0.337175 q^{47} +1.00000 q^{49} +(-6.63555 + 0.285964i) q^{50} +(-0.187624 - 2.17279i) q^{52} +8.14672i q^{53} -7.39246 q^{55} +(2.80485 - 0.364437i) q^{56} +(-0.0971845 - 2.25509i) q^{58} -15.0761i q^{59} -5.53745i q^{61} +(10.5334 - 0.453944i) q^{62} +(7.73437 - 2.04438i) q^{64} -3.39553 q^{65} -7.70421i q^{67} +(-7.35861 + 0.635429i) q^{68} +(-0.189605 - 4.39964i) q^{70} +13.5472 q^{71} -14.6727 q^{73} +(0.280953 + 6.51928i) q^{74} +(-0.186281 - 2.15723i) q^{76} -2.37402i q^{77} +5.18122 q^{79} +(-2.13521 - 12.2712i) q^{80} +(0.0537773 - 0.00231757i) q^{82} +0.138321i q^{83} +11.4996i q^{85} +(0.673490 + 15.6278i) q^{86} +(-0.865179 - 6.65876i) q^{88} +11.9531 q^{89} -1.09044i q^{91} +(-9.71118 + 0.838577i) q^{92} +(-0.476396 + 0.0205306i) q^{94} -3.37121 q^{95} -5.30202 q^{97} +(1.41290 - 0.0608900i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7}+O(q^{10}) \) 24 * q + 24 * q^7	\( 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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