LMFDB - Embedded newform 1920.2.bl.a.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.5
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.a.1249.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(1.86022 - 1.24079i) q^{5} +1.58988 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.86022 - 1.24079i) q^{5} +1.58988 q^{7} -1.00000i q^{9} +(-3.92109 + 3.92109i) q^{11} +(-3.10459 + 3.10459i) q^{13} +(-0.438005 + 2.19275i) q^{15} -1.48346i q^{17} +(-4.94087 - 4.94087i) q^{19} +(-1.12422 + 1.12422i) q^{21} -6.61914 q^{23} +(1.92087 - 4.61630i) q^{25} +(0.707107 + 0.707107i) q^{27} +(-4.42607 - 4.42607i) q^{29} -1.50391 q^{31} -5.54525i q^{33} +(2.95754 - 1.97271i) q^{35} +(2.14771 + 2.14771i) q^{37} -4.39055i q^{39} -6.84881i q^{41} +(-0.322458 - 0.322458i) q^{43} +(-1.24079 - 1.86022i) q^{45} +13.3031i q^{47} -4.47227 q^{49} +(1.04897 + 1.04897i) q^{51} +(0.931646 + 0.931646i) q^{53} +(-2.42885 + 12.1594i) q^{55} +6.98744 q^{57} +(-1.14326 + 1.14326i) q^{59} +(-2.67458 - 2.67458i) q^{61} -1.58988i q^{63} +(-1.92308 + 9.62737i) q^{65} +(5.43194 - 5.43194i) q^{67} +(4.68044 - 4.68044i) q^{69} +2.26233i q^{71} -5.27105 q^{73} +(1.90596 + 4.62248i) q^{75} +(-6.23407 + 6.23407i) q^{77} -6.52058 q^{79} -1.00000 q^{81} +(0.973359 - 0.973359i) q^{83} +(-1.84067 - 2.75957i) q^{85} +6.25941 q^{87} +6.83613i q^{89} +(-4.93593 + 4.93593i) q^{91} +(1.06342 - 1.06342i) q^{93} +(-15.3217 - 3.06053i) q^{95} -15.8228i q^{97} +(3.92109 + 3.92109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) $ 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.86022	−	1.24079i	0.831918	−	0.554899i
$5$	1.86022	−	1.24079i	0.831918	−	0.554899i
$6$		0			0
$7$	1.58988			0.600919			0.300460	−	0.953795i	$-0.402860\pi$
$7$	1.58988			0.600919			0.300460	+	0.953795i	$0.402860\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.92109	+	3.92109i	−1.18225	+	1.18225i	−0.203093	+	0.979160i	$0.565099\pi$
$11$	−3.92109	+	3.92109i	−1.18225	+	1.18225i	−0.979160	+	0.203093i	$0.934901\pi$
$12$		0			0
$13$	−3.10459	+	3.10459i	−0.861057	+	0.861057i	−0.991461	−	0.130404i	$-0.958373\pi$
$13$	−3.10459	+	3.10459i	−0.861057	+	0.861057i	0.130404	+	0.991461i	$0.458373\pi$
$14$		0			0
$15$	−0.438005	+	2.19275i	−0.113092	+	0.566166i
$16$		0			0
$17$		−	1.48346i		−	0.359793i	−0.983686	−	0.179896i	$-0.942424\pi$
$17$		−	1.48346i		−	0.359793i	0.983686	−	0.179896i	$-0.0575762\pi$
$18$		0			0
$19$	−4.94087	−	4.94087i	−1.13351	−	1.13351i	−0.989589	−	0.143924i	$-0.954028\pi$
$19$	−4.94087	−	4.94087i	−1.13351	−	1.13351i	−0.143924	−	0.989589i	$-0.545972\pi$
$20$		0			0
$21$	−1.12422	+	1.12422i	−0.245324	+	0.245324i
$22$		0			0
$23$	−6.61914			−1.38019			−0.690094	−	0.723720i	$-0.742431\pi$
$23$	−6.61914			−1.38019			−0.690094	+	0.723720i	$0.742431\pi$
$24$		0			0
$25$	1.92087	−	4.61630i	0.384174	−	0.923261i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−4.42607	−	4.42607i	−0.821901	−	0.821901i	0.164480	−	0.986380i	$-0.447406\pi$
$29$	−4.42607	−	4.42607i	−0.821901	−	0.821901i	−0.986380	+	0.164480i	$0.947406\pi$
$30$		0			0
$31$	−1.50391			−0.270110			−0.135055	−	0.990838i	$-0.543121\pi$
$31$	−1.50391			−0.270110			−0.135055	+	0.990838i	$0.543121\pi$
$32$		0			0
$33$		−	5.54525i		−	0.965305i
$34$		0			0
$35$	2.95754	−	1.97271i	0.499915	−	0.333450i
$36$		0			0
$37$	2.14771	+	2.14771i	0.353082	+	0.353082i	0.861255	−	0.508173i	$-0.169679\pi$
$37$	2.14771	+	2.14771i	0.353082	+	0.353082i	−0.508173	+	0.861255i	$0.669679\pi$
$38$		0			0
$39$		−	4.39055i		−	0.703050i
$40$		0			0
$41$		−	6.84881i		−	1.06960i	−0.844977	−	0.534802i	$-0.820386\pi$
$41$		−	6.84881i		−	1.06960i	0.844977	−	0.534802i	$-0.179614\pi$
$42$		0			0
$43$	−0.322458	−	0.322458i	−0.0491744	−	0.0491744i	0.682092	−	0.731266i	$-0.261070\pi$
$43$	−0.322458	−	0.322458i	−0.0491744	−	0.0491744i	−0.731266	+	0.682092i	$0.761070\pi$
$44$		0			0
$45$	−1.24079	−	1.86022i	−0.184966	−	0.277306i
$46$		0			0
$47$			13.3031i			1.94046i	0.242188	+	0.970229i	$0.422135\pi$
$47$			13.3031i			1.94046i	−0.242188	+	0.970229i	$0.577865\pi$
$48$		0			0
$49$	−4.47227			−0.638896
$50$		0			0
$51$	1.04897	+	1.04897i	0.146885	+	0.146885i
$52$		0			0
$53$	0.931646	+	0.931646i	0.127971	+	0.127971i	0.768192	−	0.640220i	$-0.221157\pi$
$53$	0.931646	+	0.931646i	0.127971	+	0.127971i	−0.640220	+	0.768192i	$0.721157\pi$
$54$		0			0
$55$	−2.42885	+	12.1594i	−0.327506	+	1.63957i
$56$		0			0
$57$	6.98744			0.925509
$58$		0			0
$59$	−1.14326	+	1.14326i	−0.148840	+	0.148840i	−0.777600	−	0.628760i	$-0.783563\pi$
$59$	−1.14326	+	1.14326i	−0.148840	+	0.148840i	0.628760	+	0.777600i	$0.283563\pi$
$60$		0			0
$61$	−2.67458	−	2.67458i	−0.342445	−	0.342445i	0.514841	−	0.857286i	$-0.327851\pi$
$61$	−2.67458	−	2.67458i	−0.342445	−	0.342445i	−0.857286	+	0.514841i	$0.827851\pi$
$62$		0			0
$63$		−	1.58988i		−	0.200306i
$64$		0			0
$65$	−1.92308	+	9.62737i	−0.238529	+	1.19413i
$66$		0			0
$67$	5.43194	−	5.43194i	0.663617	−	0.663617i	−0.292614	−	0.956231i	$-0.594525\pi$
$67$	5.43194	−	5.43194i	0.663617	−	0.663617i	0.956231	+	0.292614i	$0.0945250\pi$
$68$		0			0
$69$	4.68044	−	4.68044i	0.563459	−	0.563459i
$70$		0			0
$71$			2.26233i			0.268489i	0.990948	+	0.134245i	$0.0428608\pi$
$71$			2.26233i			0.268489i	−0.990948	+	0.134245i	$0.957139\pi$
$72$		0			0
$73$	−5.27105			−0.616930			−0.308465	−	0.951236i	$-0.599815\pi$
$73$	−5.27105			−0.616930			−0.308465	+	0.951236i	$0.599815\pi$
$74$		0			0
$75$	1.90596	+	4.62248i	0.220081	+	0.533758i
$76$		0			0
$77$	−6.23407	+	6.23407i	−0.710438	+	0.710438i
$78$		0			0
$79$	−6.52058			−0.733622			−0.366811	−	0.930295i	$-0.619550\pi$
$79$	−6.52058			−0.733622			−0.366811	+	0.930295i	$0.619550\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	0.973359	−	0.973359i	0.106840	−	0.106840i	−0.651666	−	0.758506i	$-0.725930\pi$
$83$	0.973359	−	0.973359i	0.106840	−	0.106840i	0.758506	+	0.651666i	$0.225930\pi$
$84$		0			0
$85$	−1.84067	−	2.75957i	−0.199649	−	0.299318i
$86$		0			0
$87$	6.25941			0.671079
$88$		0			0
$89$			6.83613i			0.724629i	0.932056	+	0.362314i	$0.118013\pi$
$89$			6.83613i			0.724629i	−0.932056	+	0.362314i	$0.881987\pi$
$90$		0			0
$91$	−4.93593	+	4.93593i	−0.517426	+	0.517426i
$92$		0			0
$93$	1.06342	−	1.06342i	0.110272	−	0.110272i
$94$		0			0
$95$	−15.3217	−	3.06053i	−1.57197	−	0.314004i
$96$		0			0
$97$		−	15.8228i		−	1.60656i	−0.595599	−	0.803282i	$-0.703085\pi$
$97$		−	15.8228i		−	1.60656i	0.595599	−	0.803282i	$-0.296915\pi$
$98$		0			0
$99$	3.92109	+	3.92109i	0.394084	+	0.394084i
$100$		0			0
$101$	−2.18050	+	2.18050i	−0.216968	+	0.216968i	−0.807220	−	0.590251i	$-0.799029\pi$
$101$	−2.18050	+	2.18050i	−0.216968	+	0.216968i	0.590251	+	0.807220i	$0.299029\pi$
$102$		0			0
$103$	8.09580			0.797703			0.398851	−	0.917016i	$-0.369409\pi$
$103$	8.09580			0.797703			0.398851	+	0.917016i	$0.369409\pi$
$104$		0			0
$105$	−0.696376	+	3.48622i	−0.0679594	+	0.340220i
$106$		0			0
$107$	−9.00752	−	9.00752i	−0.870790	−	0.870790i	0.121768	−	0.992559i	$-0.461144\pi$
$107$	−9.00752	−	9.00752i	−0.870790	−	0.870790i	−0.992559	+	0.121768i	$0.961144\pi$
$108$		0			0
$109$	9.91170	+	9.91170i	0.949369	+	0.949369i	0.998779	−	0.0494097i	$-0.0157340\pi$
$109$	9.91170	+	9.91170i	0.949369	+	0.949369i	−0.0494097	+	0.998779i	$0.515734\pi$
$110$		0			0
$111$	−3.03732			−0.288290
$112$		0			0
$113$			10.4611i			0.984094i	0.870569	+	0.492047i	$0.163751\pi$
$113$			10.4611i			0.984094i	−0.870569	+	0.492047i	$0.836249\pi$
$114$		0			0
$115$	−12.3131	+	8.21298i	−1.14820	+	0.765865i
$116$		0			0
$117$	3.10459	+	3.10459i	0.287019	+	0.287019i
$118$		0			0
$119$		−	2.35853i		−	0.216206i
$120$		0			0
$121$		−	19.7498i		−	1.79544i
$122$		0			0
$123$	4.84284	+	4.84284i	0.436664	+	0.436664i
$124$		0			0
$125$	−2.15462	−	10.9708i	−0.192716	−	0.981255i
$126$		0			0
$127$			1.88264i			0.167057i	0.996505	+	0.0835284i	$0.0266189\pi$
$127$			1.88264i			0.167057i	−0.996505	+	0.0835284i	$0.973381\pi$
$128$		0			0
$129$	0.456025			0.0401507
$130$		0			0
$131$	−0.701725	−	0.701725i	−0.0613100	−	0.0613100i	0.675787	−	0.737097i	$-0.263804\pi$
$131$	−0.701725	−	0.701725i	−0.0613100	−	0.0613100i	−0.737097	+	0.675787i	$0.763804\pi$
$132$		0			0
$133$	−7.85540	−	7.85540i	−0.681150	−	0.681150i
$134$		0			0
$135$	2.19275	+	0.438005i	0.188722	+	0.0376974i
$136$		0			0
$137$	−16.7042			−1.42714			−0.713568	−	0.700586i	$-0.752922\pi$
$137$	−16.7042			−1.42714			−0.713568	+	0.700586i	$0.752922\pi$
$138$		0			0
$139$	5.03646	−	5.03646i	0.427187	−	0.427187i	−0.460482	−	0.887669i	$-0.652323\pi$
$139$	5.03646	−	5.03646i	0.427187	−	0.427187i	0.887669	+	0.460482i	$0.152323\pi$
$140$		0			0
$141$	−9.40672	−	9.40672i	−0.792189	−	0.792189i
$142$		0			0
$143$		−	24.3467i		−	2.03597i
$144$		0			0
$145$	−13.7253	−	2.74165i	−1.13983	−	0.227682i
$146$		0			0
$147$	3.16237	−	3.16237i	0.260828	−	0.260828i
$148$		0			0
$149$	12.2283	−	12.2283i	1.00178	−	1.00178i	0.00178156	−	0.999998i	$-0.499433\pi$
$149$	12.2283	−	12.2283i	1.00178	−	1.00178i	0.999998	−	0.00178156i	$-0.000567087\pi$
$150$		0			0
$151$		−	0.567736i		−	0.0462017i	−0.999733	−	0.0231008i	$-0.992646\pi$
$151$		−	0.567736i		−	0.0462017i	0.999733	−	0.0231008i	$-0.00735388\pi$
$152$		0			0
$153$	−1.48346			−0.119931
$154$		0			0
$155$	−2.79761	+	1.86604i	−0.224709	+	0.149884i
$156$		0			0
$157$	8.06109	−	8.06109i	0.643345	−	0.643345i	−0.308031	−	0.951376i	$-0.599670\pi$
$157$	8.06109	−	8.06109i	0.643345	−	0.643345i	0.951376	+	0.308031i	$0.0996702\pi$
$158$		0			0
$159$	−1.31755			−0.104488
$160$		0			0
$161$	−10.5237			−0.829381
$162$		0			0
$163$	−0.0969036	+	0.0969036i	−0.00759008	+	0.00759008i	−0.710892	−	0.703302i	$-0.751708\pi$
$163$	−0.0969036	+	0.0969036i	−0.00759008	+	0.00759008i	0.703302	+	0.710892i	$0.251708\pi$
$164$		0			0
$165$	−6.88051	−	10.3154i	−0.535647	−	0.803054i
$166$		0			0
$167$	−14.9619			−1.15779			−0.578894	−	0.815403i	$-0.696516\pi$
$167$	−14.9619			−1.15779			−0.578894	+	0.815403i	$0.696516\pi$
$168$		0			0
$169$		−	6.27691i		−	0.482839i
$170$		0			0
$171$	−4.94087	+	4.94087i	−0.377838	+	0.377838i
$172$		0			0
$173$	−13.1447	+	13.1447i	−0.999374	+	0.999374i	−1.00000		0.000626029i	$-0.999801\pi$
$173$	−13.1447	+	13.1447i	−0.999374	+	0.999374i	0.000626029		1.00000i	$0.499801\pi$
$174$		0			0
$175$	3.05396	−	7.33938i	0.230858	−	0.554805i
$176$		0			0
$177$		−	1.61682i		−	0.121527i
$178$		0			0
$179$	−3.56192	−	3.56192i	−0.266230	−	0.266230i	0.561349	−	0.827579i	$-0.310283\pi$
$179$	−3.56192	−	3.56192i	−0.266230	−	0.266230i	−0.827579	+	0.561349i	$0.810283\pi$
$180$		0			0
$181$	−5.89499	+	5.89499i	−0.438171	+	0.438171i	−0.891396	−	0.453225i	$-0.850273\pi$
$181$	−5.89499	+	5.89499i	−0.438171	+	0.438171i	0.453225	+	0.891396i	$0.350273\pi$
$182$		0			0
$183$	3.78243			0.279605
$184$		0			0
$185$	6.66009	+	1.33036i	0.489660	+	0.0978102i
$186$		0			0
$187$	5.81679	+	5.81679i	0.425366	+	0.425366i
$188$		0			0
$189$	1.12422	+	1.12422i	0.0817748	+	0.0817748i
$190$		0			0
$191$	−0.695196			−0.0503026			−0.0251513	−	0.999684i	$-0.508007\pi$
$191$	−0.695196			−0.0503026			−0.0251513	+	0.999684i	$0.508007\pi$
$192$		0			0
$193$			23.8401i			1.71605i	0.513611	+	0.858023i	$0.328307\pi$
$193$			23.8401i			1.71605i	−0.513611	+	0.858023i	$0.671693\pi$
$194$		0			0
$195$	−5.44776	−	8.16740i	−0.390122	−	0.584880i
$196$		0			0
$197$	3.90642	+	3.90642i	0.278321	+	0.278321i	0.832438	−	0.554118i	$-0.186944\pi$
$197$	3.90642	+	3.90642i	0.278321	+	0.278321i	−0.554118	+	0.832438i	$0.686944\pi$
$198$		0			0
$199$		−	3.84627i		−	0.272655i	−0.990664	−	0.136328i	$-0.956470\pi$
$199$		−	3.84627i		−	0.272655i	0.990664	−	0.136328i	$-0.0435300\pi$
$200$		0			0
$201$			7.68192i			0.541841i
$202$		0			0
$203$	−7.03694	−	7.03694i	−0.493896	−	0.493896i
$204$		0			0
$205$	−8.49795	−	12.7403i	−0.593523	−	0.889823i
$206$		0			0
$207$			6.61914i			0.460062i
$208$		0			0
$209$	38.7471			2.68020
$210$		0			0
$211$	−8.77616	−	8.77616i	−0.604176	−	0.604176i	0.337242	−	0.941418i	$-0.390506\pi$
$211$	−8.77616	−	8.77616i	−0.604176	−	0.604176i	−0.941418	+	0.337242i	$0.890506\pi$
$212$		0			0
$213$	−1.59971	−	1.59971i	−0.109610	−	0.109610i
$214$		0			0
$215$	−0.999948	−	0.199741i	−0.0681959	−	0.0136222i
$216$		0			0
$217$	−2.39104			−0.162314
$218$		0			0
$219$	3.72720	−	3.72720i	0.251861	−	0.251861i
$220$		0			0
$221$	4.60554	+	4.60554i	0.309802	+	0.309802i
$222$		0			0
$223$			13.4599i			0.901341i	0.892690	+	0.450671i	$0.148815\pi$
$223$			13.4599i			0.901341i	−0.892690	+	0.450671i	$0.851185\pi$
$224$		0			0
$225$	−4.61630	−	1.92087i	−0.307754	−	0.128058i
$226$		0			0
$227$	−16.2029	+	16.2029i	−1.07542	+	1.07542i	−0.0785084	+	0.996913i	$0.525016\pi$
$227$	−16.2029	+	16.2029i	−1.07542	+	1.07542i	−0.996913	+	0.0785084i	$0.974984\pi$
$228$		0			0
$229$	−1.34898	+	1.34898i	−0.0891433	+	0.0891433i	−0.750272	−	0.661129i	$-0.770078\pi$
$229$	−1.34898	+	1.34898i	−0.0891433	+	0.0891433i	0.661129	+	0.750272i	$0.270078\pi$
$230$		0			0
$231$		−	8.81631i		−	0.580070i
$232$		0			0
$233$	−13.0887			−0.857470			−0.428735	−	0.903430i	$-0.641041\pi$
$233$	−13.0887			−0.857470			−0.428735	+	0.903430i	$0.641041\pi$
$234$		0			0
$235$	16.5064	+	24.7468i	1.07676	+	1.61430i
$236$		0			0
$237$	4.61074	−	4.61074i	0.299500	−	0.299500i
$238$		0			0
$239$	11.0340			0.713730			0.356865	−	0.934156i	$-0.383846\pi$
$239$	11.0340			0.713730			0.356865	+	0.934156i	$0.383846\pi$
$240$		0			0
$241$	8.31401			0.535553			0.267776	−	0.963481i	$-0.413711\pi$
$241$	8.31401			0.535553			0.267776	+	0.963481i	$0.413711\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−8.31943	+	5.54916i	−0.531509	+	0.354523i
$246$		0			0
$247$	30.6787			1.95204
$248$		0			0
$249$			1.37654i			0.0872345i
$250$		0			0
$251$	−15.0055	+	15.0055i	−0.947138	+	0.947138i	−0.998671	−	0.0515329i	$-0.983589\pi$
$251$	−15.0055	+	15.0055i	−0.947138	+	0.947138i	0.0515329	+	0.998671i	$0.483589\pi$
$252$		0			0
$253$	25.9542	−	25.9542i	1.63173	−	1.63173i
$254$		0			0
$255$	3.25286	+	0.649764i	0.203702	+	0.0406898i
$256$		0			0
$257$			14.3773i			0.896831i	0.893825	+	0.448415i	$0.148011\pi$
$257$			14.3773i			0.896831i	−0.893825	+	0.448415i	$0.851989\pi$
$258$		0			0
$259$	3.41461	+	3.41461i	0.212174	+	0.212174i
$260$		0			0
$261$	−4.42607	+	4.42607i	−0.273967	+	0.273967i
$262$		0			0
$263$	−4.94045			−0.304641			−0.152320	−	0.988331i	$-0.548675\pi$
$263$	−4.94045			−0.304641			−0.152320	+	0.988331i	$0.548675\pi$
$264$		0			0
$265$	2.88905	+	0.577092i	0.177473	+	0.0354505i
$266$		0			0
$267$	−4.83388	−	4.83388i	−0.295828	−	0.295828i
$268$		0			0
$269$	11.5951	+	11.5951i	0.706967	+	0.706967i	0.965896	−	0.258929i	$-0.0833696\pi$
$269$	11.5951	+	11.5951i	0.706967	+	0.706967i	−0.258929	+	0.965896i	$0.583370\pi$
$270$		0			0
$271$	−3.40933			−0.207102			−0.103551	−	0.994624i	$-0.533021\pi$
$271$	−3.40933			−0.207102			−0.103551	+	0.994624i	$0.533021\pi$
$272$		0			0
$273$		−	6.98046i		−	0.422476i
$274$		0			0
$275$	10.5690	+	25.6328i	0.637337	+	1.54572i
$276$		0			0
$277$	11.2957	+	11.2957i	0.678690	+	0.678690i	0.959704	−	0.281014i	$-0.0906707\pi$
$277$	11.2957	+	11.2957i	0.678690	+	0.678690i	−0.281014	+	0.959704i	$0.590671\pi$
$278$		0			0
$279$			1.50391i			0.0900366i
$280$		0			0
$281$			4.72775i			0.282034i	0.990007	+	0.141017i	$0.0450372\pi$
$281$			4.72775i			0.282034i	−0.990007	+	0.141017i	$0.954963\pi$
$282$		0			0
$283$	−6.51882	−	6.51882i	−0.387504	−	0.387504i	0.486292	−	0.873796i	$-0.338349\pi$
$283$	−6.51882	−	6.51882i	−0.387504	−	0.387504i	−0.873796	+	0.486292i	$0.838349\pi$
$284$		0			0
$285$	12.9982	−	8.66996i	0.769948	−	0.513564i
$286$		0			0
$287$		−	10.8888i		−	0.642746i
$288$		0			0
$289$	14.7993			0.870549
$290$		0			0
$291$	11.1884	+	11.1884i	0.655877	+	0.655877i
$292$		0			0
$293$	−2.60652	−	2.60652i	−0.152274	−	0.152274i	0.626859	−	0.779133i	$-0.284340\pi$
$293$	−2.60652	−	2.60652i	−0.152274	−	0.152274i	−0.779133	+	0.626859i	$0.784340\pi$
$294$		0			0
$295$	−0.708173	+	3.54527i	−0.0412314	+	0.206414i
$296$		0			0
$297$	−5.54525			−0.321768
$298$		0			0
$299$	20.5497	−	20.5497i	1.18842	−	1.18842i
$300$		0			0
$301$	−0.512671	−	0.512671i	−0.0295499	−	0.0295499i
$302$		0			0
$303$		−	3.08370i		−	0.177154i
$304$		0			0
$305$	−8.29392	−	1.65672i	−0.474909	−	0.0948636i
$306$		0			0
$307$	9.27735	−	9.27735i	0.529486	−	0.529486i	−0.390933	−	0.920419i	$-0.627848\pi$
$307$	9.27735	−	9.27735i	0.529486	−	0.529486i	0.920419	+	0.390933i	$0.127848\pi$
$308$		0			0
$309$	−5.72459	+	5.72459i	−0.325661	+	0.325661i
$310$		0			0
$311$			8.87398i			0.503197i	0.967832	+	0.251599i	$0.0809563\pi$
$311$			8.87398i			0.503197i	−0.967832	+	0.251599i	$0.919044\pi$
$312$		0			0
$313$	25.6160			1.44790			0.723952	−	0.689850i	$-0.242324\pi$
$313$	25.6160			1.44790			0.723952	+	0.689850i	$0.242324\pi$
$314$		0			0
$315$	−1.97271	−	2.95754i	−0.111150	−	0.166638i
$316$		0			0
$317$	−19.5425	+	19.5425i	−1.09762	+	1.09762i	−0.102929	+	0.994689i	$0.532821\pi$
$317$	−19.5425	+	19.5425i	−1.09762	+	1.09762i	−0.994689	+	0.102929i	$0.967179\pi$
$318$		0			0
$319$	34.7100			1.94339
$320$		0			0
$321$	12.7386			0.710997
$322$		0			0
$323$	−7.32960	+	7.32960i	−0.407830	+	0.407830i
$324$		0			0
$325$	8.36821	+	20.2952i	0.464185	+	1.12578i
$326$		0			0
$327$	−14.0173			−0.775156
$328$		0			0
$329$			21.1504i			1.16606i
$330$		0			0
$331$	17.9546	−	17.9546i	0.986875	−	0.986875i	−0.0130395	−	0.999915i	$-0.504151\pi$
$331$	17.9546	−	17.9546i	0.986875	−	0.986875i	0.999915	+	0.0130395i	$0.00415073\pi$
$332$		0			0
$333$	2.14771	−	2.14771i	0.117694	−	0.117694i
$334$		0			0
$335$	3.36472	−	16.8445i	0.183834	−	0.920315i
$336$		0			0
$337$		−	30.1385i		−	1.64175i	−0.571108	−	0.820875i	$-0.693486\pi$
$337$		−	30.1385i		−	1.64175i	0.571108	−	0.820875i	$-0.306514\pi$
$338$		0			0
$339$	−7.39709	−	7.39709i	−0.401755	−	0.401755i
$340$		0			0
$341$	5.89695	−	5.89695i	0.319338	−	0.319338i
$342$		0			0
$343$	−18.2396			−0.984844
$344$		0			0
$345$	2.89922	−	14.5141i	0.156089	−	0.781414i
$346$		0			0
$347$	−17.1738	−	17.1738i	−0.921936	−	0.921936i	0.0752299	−	0.997166i	$-0.476031\pi$
$347$	−17.1738	−	17.1738i	−0.921936	−	0.921936i	−0.997166	+	0.0752299i	$0.976031\pi$
$348$		0			0
$349$	11.7155	+	11.7155i	0.627115	+	0.627115i	0.947341	−	0.320226i	$-0.103759\pi$
$349$	11.7155	+	11.7155i	0.627115	+	0.627115i	−0.320226	+	0.947341i	$0.603759\pi$
$350$		0			0
$351$	−4.39055			−0.234350
$352$		0			0
$353$			2.34745i			0.124942i	0.998047	+	0.0624712i	$0.0198982\pi$
$353$			2.34745i			0.124942i	−0.998047	+	0.0624712i	$0.980102\pi$
$354$		0			0
$355$	2.80708	+	4.20844i	0.148984	+	0.223361i
$356$		0			0
$357$	1.66773	+	1.66773i	0.0882659	+	0.0882659i
$358$		0			0
$359$		−	28.6304i		−	1.51106i	−0.655116	−	0.755529i	$-0.727380\pi$
$359$		−	28.6304i		−	1.51106i	0.655116	−	0.755529i	$-0.272620\pi$
$360$		0			0
$361$			29.8243i			1.56970i
$362$		0			0
$363$	13.9652	+	13.9652i	0.732986	+	0.732986i
$364$		0			0
$365$	−9.80534	+	6.54028i	−0.513235	+	0.342334i
$366$		0			0
$367$			12.5964i			0.657527i	0.944412	+	0.328764i	$0.106632\pi$
$367$			12.5964i			0.657527i	−0.944412	+	0.328764i	$0.893368\pi$
$368$		0			0
$369$	−6.84881			−0.356535
$370$		0			0
$371$	1.48121	+	1.48121i	0.0769005	+	0.0769005i
$372$		0			0
$373$	−10.5946	−	10.5946i	−0.548568	−	0.548568i	0.377458	−	0.926027i	$-0.376798\pi$
$373$	−10.5946	−	10.5946i	−0.548568	−	0.548568i	−0.926027	+	0.377458i	$0.876798\pi$
$374$		0			0
$375$	9.28105	+	6.23395i	0.479271	+	0.321920i
$376$		0			0
$377$	27.4822			1.41541
$378$		0			0
$379$	25.8712	−	25.8712i	1.32891	−	1.32891i	0.422593	−	0.906320i	$-0.361120\pi$
$379$	25.8712	−	25.8712i	1.32891	−	1.32891i	0.906320	−	0.422593i	$-0.138880\pi$
$380$		0			0
$381$	−1.33122	−	1.33122i	−0.0682007	−	0.0682007i
$382$		0			0
$383$			4.25894i			0.217622i	0.994062	+	0.108811i	$0.0347043\pi$
$383$			4.25894i			0.217622i	−0.994062	+	0.108811i	$0.965296\pi$
$384$		0			0
$385$	−3.86158	+	19.3320i	−0.196805	+	0.985247i
$386$		0			0
$387$	−0.322458	+	0.322458i	−0.0163915	+	0.0163915i
$388$		0			0
$389$	−22.1209	+	22.1209i	−1.12158	+	1.12158i	−0.130071	+	0.991505i	$0.541520\pi$
$389$	−22.1209	+	22.1209i	−1.12158	+	1.12158i	−0.991505	+	0.130071i	$0.958480\pi$
$390$		0			0
$391$			9.81926i			0.496581i
$392$		0			0
$393$	0.992388			0.0500594
$394$		0			0
$395$	−12.1297	+	8.09068i	−0.610313	+	0.407086i
$396$		0			0
$397$	−12.9968	+	12.9968i	−0.652290	+	0.652290i	−0.953544	−	0.301254i	$-0.902595\pi$
$397$	−12.9968	+	12.9968i	−0.652290	+	0.652290i	0.301254	+	0.953544i	$0.402595\pi$
$398$		0			0
$399$	11.1092			0.556156
$400$		0			0
$401$	−35.3598			−1.76578			−0.882892	−	0.469577i	$-0.844406\pi$
$401$	−35.3598			−1.76578			−0.882892	+	0.469577i	$0.844406\pi$
$402$		0			0
$403$	4.66901	−	4.66901i	0.232580	−	0.232580i
$404$		0			0
$405$	−1.86022	+	1.24079i	−0.0924353	+	0.0616555i
$406$		0			0
$407$	−16.8427			−0.834863
$408$		0			0
$409$			27.3933i			1.35451i	0.735747	+	0.677256i	$0.236831\pi$
$409$			27.3933i			1.35451i	−0.735747	+	0.677256i	$0.763169\pi$
$410$		0			0
$411$	11.8117	−	11.8117i	0.582626	−	0.582626i
$412$		0			0
$413$	−1.81765	+	1.81765i	−0.0894408	+	0.0894408i
$414$		0			0
$415$	0.602930	−	3.01840i	0.0295967	−	0.148168i
$416$		0			0
$417$			7.12264i			0.348797i
$418$		0			0
$419$	−3.71334	−	3.71334i	−0.181409	−	0.181409i	0.610561	−	0.791969i	$-0.290944\pi$
$419$	−3.71334	−	3.71334i	−0.181409	−	0.181409i	−0.791969	+	0.610561i	$0.790944\pi$
$420$		0			0
$421$	10.7755	−	10.7755i	0.525167	−	0.525167i	−0.393960	−	0.919127i	$-0.628895\pi$
$421$	10.7755	−	10.7755i	0.525167	−	0.525167i	0.919127	+	0.393960i	$0.128895\pi$
$422$		0			0
$423$	13.3031			0.646820
$424$		0			0
$425$	−6.84812	−	2.84954i	−0.332182	−	0.138223i
$426$		0			0
$427$	−4.25227	−	4.25227i	−0.205782	−	0.205782i
$428$		0			0
$429$	17.2157	+	17.2157i	0.831183	+	0.831183i
$430$		0			0
$431$	30.0581			1.44785			0.723924	−	0.689880i	$-0.242337\pi$
$431$	30.0581			1.44785			0.723924	+	0.689880i	$0.242337\pi$
$432$		0			0
$433$		−	20.1636i		−	0.968999i	−0.874791	−	0.484500i	$-0.839002\pi$
$433$		−	20.1636i		−	0.968999i	0.874791	−	0.484500i	$-0.160998\pi$
$434$		0			0
$435$	11.6439	−	7.76663i	0.558283	−	0.372381i
$436$		0			0
$437$	32.7043	+	32.7043i	1.56446	+	1.56446i
$438$		0			0
$439$		−	28.0789i		−	1.34013i	−0.742302	−	0.670065i	$-0.766266\pi$
$439$		−	28.0789i		−	1.34013i	0.742302	−	0.670065i	$-0.233734\pi$
$440$		0			0
$441$			4.47227i			0.212965i
$442$		0			0
$443$	3.23844	+	3.23844i	0.153863	+	0.153863i	0.779841	−	0.625978i	$-0.215300\pi$
$443$	3.23844	+	3.23844i	0.153863	+	0.153863i	−0.625978	+	0.779841i	$0.715300\pi$
$444$		0			0
$445$	8.48222	+	12.7167i	0.402096	+	0.602831i
$446$		0			0
$447$			17.2934i			0.817950i
$448$		0			0
$449$	1.06033			0.0500401			0.0250201	−	0.999687i	$-0.492035\pi$
$449$	1.06033			0.0500401			0.0250201	+	0.999687i	$0.492035\pi$
$450$		0			0
$451$	26.8548	+	26.8548i	1.26454	+	1.26454i
$452$		0			0
$453$	0.401450	+	0.401450i	0.0188618	+	0.0188618i
$454$		0			0
$455$	−3.05747	+	15.3064i	−0.143337	+	0.717575i
$456$		0			0
$457$	−3.95861			−0.185176			−0.0925880	−	0.995705i	$-0.529514\pi$
$457$	−3.95861			−0.185176			−0.0925880	+	0.995705i	$0.529514\pi$
$458$		0			0
$459$	1.04897	−	1.04897i	0.0489616	−	0.0489616i
$460$		0			0
$461$	17.2310	+	17.2310i	0.802526	+	0.802526i	0.983490	−	0.180963i	$-0.0579216\pi$
$461$	17.2310	+	17.2310i	0.802526	+	0.802526i	−0.180963	+	0.983490i	$0.557922\pi$
$462$		0			0
$463$			14.4839i			0.673122i	0.941662	+	0.336561i	$0.109264\pi$
$463$			14.4839i			0.673122i	−0.941662	+	0.336561i	$0.890736\pi$
$464$		0			0
$465$	0.658719	−	3.29769i	0.0305473	−	0.152927i
$466$		0			0
$467$	26.0437	−	26.0437i	1.20516	−	1.20516i	0.232585	−	0.972576i	$-0.425282\pi$
$467$	26.0437	−	26.0437i	1.20516	−	1.20516i	0.972576	−	0.232585i	$-0.0747183\pi$
$468$		0			0
$469$	8.63615	−	8.63615i	0.398780	−	0.398780i
$470$		0			0
$471$			11.4001i			0.525289i
$472$		0			0
$473$	2.52877			0.116273
$474$		0			0
$475$	−32.2993	+	13.3178i	−1.48199	+	0.611062i
$476$		0			0
$477$	0.931646	−	0.931646i	0.0426572	−	0.0426572i
$478$		0			0
$479$	−18.5284			−0.846586			−0.423293	−	0.905993i	$-0.639126\pi$
$479$	−18.5284			−0.846586			−0.423293	+	0.905993i	$0.639126\pi$
$480$		0			0
$481$	−13.3355			−0.608047
$482$		0			0
$483$	7.44135	−	7.44135i	0.338593	−	0.338593i
$484$		0			0
$485$	−19.6328	−	29.4340i	−0.891481	−	1.33653i
$486$		0			0
$487$	4.16579			0.188770			0.0943851	−	0.995536i	$-0.469912\pi$
$487$	4.16579			0.188770			0.0943851	+	0.995536i	$0.469912\pi$
$488$		0			0
$489$		−	0.137042i		−	0.00619727i
$490$		0			0
$491$	20.2554	−	20.2554i	0.914115	−	0.914115i	−0.0824778	−	0.996593i	$-0.526283\pi$
$491$	20.2554	−	20.2554i	0.914115	−	0.914115i	0.996593	+	0.0824778i	$0.0262833\pi$
$492$		0			0
$493$	−6.56591	+	6.56591i	−0.295714	+	0.295714i
$494$		0			0
$495$	12.1594	+	2.42885i	0.546522	+	0.109169i
$496$		0			0
$497$			3.59684i			0.161340i
$498$		0			0
$499$	−5.41192	−	5.41192i	−0.242271	−	0.242271i	0.575518	−	0.817789i	$-0.304800\pi$
$499$	−5.41192	−	5.41192i	−0.242271	−	0.242271i	−0.817789	+	0.575518i	$0.804800\pi$
$500$		0			0
$501$	10.5797	−	10.5797i	0.472665	−	0.472665i
$502$		0			0
$503$	2.09459			0.0933934			0.0466967	−	0.998909i	$-0.485131\pi$
$503$	2.09459			0.0933934			0.0466967	+	0.998909i	$0.485131\pi$
$504$		0			0
$505$	−1.35067	+	6.76178i	−0.0601042	+	0.300895i
$506$		0			0
$507$	4.43845	+	4.43845i	0.197118	+	0.197118i
$508$		0			0
$509$	26.2653	+	26.2653i	1.16419	+	1.16419i	0.983550	+	0.180638i	$0.0578161\pi$
$509$	26.2653	+	26.2653i	1.16419	+	1.16419i	0.180638	+	0.983550i	$0.442184\pi$
$510$		0			0
$511$	−8.38036			−0.370725
$512$		0			0
$513$		−	6.98744i		−	0.308503i
$514$		0			0
$515$	15.0600	−	10.0452i	0.663623	−	0.442644i
$516$		0			0
$517$	−52.1627	−	52.1627i	−2.29411	−	2.29411i
$518$		0			0
$519$		−	18.5894i		−	0.815985i
$520$		0			0
$521$		−	10.2533i		−	0.449205i	−0.974450	−	0.224602i	$-0.927892\pi$
$521$		−	10.2533i		−	0.449205i	0.974450	−	0.224602i	$-0.0721083\pi$
$522$		0			0
$523$	−7.87557	−	7.87557i	−0.344375	−	0.344375i	0.513634	−	0.858009i	$-0.328299\pi$
$523$	−7.87557	−	7.87557i	−0.344375	−	0.344375i	−0.858009	+	0.513634i	$0.828299\pi$
$524$		0			0
$525$	3.03025	+	7.34920i	0.132251	+	0.320745i
$526$		0			0
$527$			2.23099i			0.0971835i
$528$		0			0
$529$	20.8131			0.904916
$530$		0			0
$531$	1.14326	+	1.14326i	0.0496133	+	0.0496133i
$532$		0			0
$533$	21.2627	+	21.2627i	0.920991	+	0.920991i
$534$		0			0
$535$	−27.9325	−	5.57955i	−1.20763	−	0.241225i
$536$		0			0
$537$	5.03731			0.217376
$538$		0			0
$539$	17.5362	−	17.5362i	0.755336	−	0.755336i
$540$		0			0
$541$	−23.6782	−	23.6782i	−1.01800	−	1.01800i	−0.999835	−	0.0181698i	$-0.994216\pi$
$541$	−23.6782	−	23.6782i	−1.01800	−	1.01800i	−0.0181698	−	0.999835i	$-0.505784\pi$
$542$		0			0
$543$		−	8.33678i		−	0.357765i
$544$		0			0
$545$	30.7364	+	6.13963i	1.31660	+	0.262993i
$546$		0			0
$547$	6.60366	−	6.60366i	0.282352	−	0.282352i	−0.551694	−	0.834046i	$-0.686018\pi$
$547$	6.60366	−	6.60366i	0.282352	−	0.282352i	0.834046	+	0.551694i	$0.186018\pi$
$548$		0			0
$549$	−2.67458	+	2.67458i	−0.114148	+	0.114148i
$550$		0			0
$551$			43.7373i			1.86327i
$552$		0			0
$553$	−10.3670			−0.440848
$554$		0			0
$555$	−5.65010	+	3.76869i	−0.239834	+	0.159972i
$556$		0			0
$557$	11.5466	−	11.5466i	0.489245	−	0.489245i	−0.418823	−	0.908068i	$-0.637557\pi$
$557$	11.5466	−	11.5466i	0.489245	−	0.489245i	0.908068	+	0.418823i	$0.137557\pi$
$558$		0			0
$559$	2.00220			0.0846840
$560$		0			0
$561$	−8.22618			−0.347310
$562$		0			0
$563$	−13.3335	+	13.3335i	−0.561940	+	0.561940i	−0.929858	−	0.367918i	$-0.880071\pi$
$563$	−13.3335	+	13.3335i	−0.561940	+	0.561940i	0.367918	+	0.929858i	$0.380071\pi$
$564$		0			0
$565$	12.9800	+	19.4599i	0.546073	+	0.818685i
$566$		0			0
$567$	−1.58988			−0.0667688
$568$		0			0
$569$		−	13.8256i		−	0.579600i	−0.957087	−	0.289800i	$-0.906411\pi$
$569$		−	13.8256i		−	0.579600i	0.957087	−	0.289800i	$-0.0935887\pi$
$570$		0			0
$571$	−17.8448	+	17.8448i	−0.746781	+	0.746781i	−0.973873	−	0.227092i	$-0.927078\pi$
$571$	−17.8448	+	17.8448i	−0.746781	+	0.746781i	0.227092	+	0.973873i	$0.427078\pi$
$572$		0			0
$573$	0.491578	−	0.491578i	0.0205360	−	0.0205360i
$574$		0			0
$575$	−12.7145	+	30.5560i	−0.530232	+	1.27427i
$576$		0			0
$577$		−	22.6737i		−	0.943918i	−0.881620	−	0.471959i	$-0.843547\pi$
$577$		−	22.6737i		−	0.943918i	0.881620	−	0.471959i	$-0.156453\pi$
$578$		0			0
$579$	−16.8575	−	16.8575i	−0.700573	−	0.700573i
$580$		0			0
$581$	1.54753	−	1.54753i	0.0642022	−	0.0642022i
$582$		0			0
$583$	−7.30613			−0.302589
$584$		0			0
$585$	9.62737	+	1.92308i	0.398043	+	0.0795096i
$586$		0			0
$587$	−9.96994	−	9.96994i	−0.411504	−	0.411504i	0.470758	−	0.882262i	$-0.343980\pi$
$587$	−9.96994	−	9.96994i	−0.411504	−	0.411504i	−0.882262	+	0.470758i	$0.843980\pi$
$588$		0			0
$589$	7.43061	+	7.43061i	0.306173	+	0.306173i
$590$		0			0
$591$	−5.52451			−0.227248
$592$		0			0
$593$		−	36.5396i		−	1.50050i	−0.661153	−	0.750251i	$-0.729933\pi$
$593$		−	36.5396i		−	1.50050i	0.661153	−	0.750251i	$-0.270067\pi$
$594$		0			0
$595$	−2.92645	−	4.38740i	−0.119973	−	0.179866i
$596$		0			0
$597$	2.71973	+	2.71973i	0.111311	+	0.111311i
$598$		0			0
$599$		−	7.77638i		−	0.317734i	−0.987300	−	0.158867i	$-0.949216\pi$
$599$		−	7.77638i		−	0.317734i	0.987300	−	0.158867i	$-0.0507841\pi$
$600$		0			0
$601$			31.7530i			1.29523i	0.761966	+	0.647617i	$0.224234\pi$
$601$			31.7530i			1.29523i	−0.761966	+	0.647617i	$0.775766\pi$
$602$		0			0
$603$	−5.43194	−	5.43194i	−0.221206	−	0.221206i
$604$		0			0
$605$	−24.5055	−	36.7391i	−0.996288	−	1.49366i
$606$		0			0
$607$		−	30.7877i		−	1.24963i	−0.780771	−	0.624817i	$-0.785174\pi$
$607$		−	30.7877i		−	1.24963i	0.780771	−	0.624817i	$-0.214826\pi$
$608$		0			0
$609$	9.95173			0.403264
$610$		0			0
$611$	−41.3007	−	41.3007i	−1.67085	−	1.67085i
$612$		0			0
$613$	18.1437	+	18.1437i	0.732818	+	0.732818i	0.971177	−	0.238359i	$-0.0766094\pi$
$613$	18.1437	+	18.1437i	0.732818	+	0.732818i	−0.238359	+	0.971177i	$0.576609\pi$
$614$		0			0
$615$	15.0177	+	2.99981i	0.605573	+	0.120964i
$616$		0			0
$617$	−14.8136			−0.596372			−0.298186	−	0.954508i	$-0.596381\pi$
$617$	−14.8136			−0.596372			−0.298186	+	0.954508i	$0.596381\pi$
$618$		0			0
$619$	−6.05155	+	6.05155i	−0.243232	+	0.243232i	−0.818186	−	0.574954i	$-0.805020\pi$
$619$	−6.05155	+	6.05155i	−0.243232	+	0.243232i	0.574954	+	0.818186i	$0.305020\pi$
$620$		0			0
$621$	−4.68044	−	4.68044i	−0.187820	−	0.187820i
$622$		0			0
$623$			10.8687i			0.435443i
$624$		0			0
$625$	−17.6205	−	17.7346i	−0.704821	−	0.709385i
$626$		0			0
$627$	−27.3984	+	27.3984i	−1.09419	+	1.09419i
$628$		0			0
$629$	3.18605	−	3.18605i	0.127036	−	0.127036i
$630$		0			0
$631$		−	35.8534i		−	1.42730i	−0.700502	−	0.713650i	$-0.747041\pi$
$631$		−	35.8534i		−	1.42730i	0.700502	−	0.713650i	$-0.252959\pi$
$632$		0			0
$633$	12.4114			0.493307
$634$		0			0
$635$	2.33596	+	3.50212i	0.0926997	+	0.138978i
$636$		0			0
$637$	13.8846	−	13.8846i	0.550126	−	0.550126i
$638$		0			0
$639$	2.26233			0.0894964
$640$		0			0
$641$	15.4688			0.610979			0.305490	−	0.952195i	$-0.401180\pi$
$641$	15.4688			0.610979			0.305490	+	0.952195i	$0.401180\pi$
$642$		0			0
$643$	11.6098	−	11.6098i	0.457847	−	0.457847i	−0.440101	−	0.897948i	$-0.645057\pi$
$643$	11.6098	−	11.6098i	0.457847	−	0.457847i	0.897948	+	0.440101i	$0.145057\pi$
$644$		0			0
$645$	0.848308	−	0.565832i	0.0334021	−	0.0222796i
$646$		0			0
$647$	18.0688			0.710357			0.355178	−	0.934799i	$-0.384420\pi$
$647$	18.0688			0.710357			0.355178	+	0.934799i	$0.384420\pi$
$648$		0			0
$649$		−	8.96566i		−	0.351933i
$650$		0			0
$651$	1.69072	−	1.69072i	0.0662645	−	0.0662645i
$652$		0			0
$653$	−3.64829	+	3.64829i	−0.142769	+	0.142769i	−0.774879	−	0.632110i	$-0.782189\pi$
$653$	−3.64829	+	3.64829i	−0.142769	+	0.142769i	0.632110	+	0.774879i	$0.282189\pi$
$654$		0			0
$655$	−2.17606	−	0.434671i	−0.0850257	−	0.0169840i
$656$		0			0
$657$			5.27105i			0.205643i
$658$		0			0
$659$	20.7113	+	20.7113i	0.806796	+	0.806796i	0.984148	−	0.177351i	$-0.0567529\pi$
$659$	20.7113	+	20.7113i	0.806796	+	0.806796i	−0.177351	+	0.984148i	$0.556753\pi$
$660$		0			0
$661$	−11.7363	+	11.7363i	−0.456488	+	0.456488i	−0.897501	−	0.441013i	$-0.854619\pi$
$661$	−11.7363	+	11.7363i	−0.456488	+	0.456488i	0.441013	+	0.897501i	$0.354619\pi$
$662$		0			0
$663$	−6.51322			−0.252952
$664$		0			0
$665$	−24.3597	−	4.86589i	−0.944630	−	0.188691i
$666$		0			0
$667$	29.2968	+	29.2968i	1.13438	+	1.13438i
$668$		0			0
$669$	−9.51759	−	9.51759i	−0.367971	−	0.367971i
$670$		0			0
$671$	20.9745			0.809713
$672$		0			0
$673$			42.5085i			1.63858i	0.573379	+	0.819290i	$0.305632\pi$
$673$			42.5085i			1.63858i	−0.573379	+	0.819290i	$0.694368\pi$
$674$		0			0
$675$	4.62248	−	1.90596i	0.177919	−	0.0733604i
$676$		0			0
$677$	−16.5124	−	16.5124i	−0.634623	−	0.634623i	0.314601	−	0.949224i	$-0.398129\pi$
$677$	−16.5124	−	16.5124i	−0.634623	−	0.634623i	−0.949224	+	0.314601i	$0.898129\pi$
$678$		0			0
$679$		−	25.1564i		−	0.965416i
$680$		0			0
$681$		−	22.9143i		−	0.878078i
$682$		0			0
$683$	18.1836	+	18.1836i	0.695777	+	0.695777i	0.963497	−	0.267720i	$-0.0862702\pi$
$683$	18.1836	+	18.1836i	0.695777	+	0.695777i	−0.267720	+	0.963497i	$0.586270\pi$
$684$		0			0
$685$	−31.0736	+	20.7264i	−1.18726	+	0.791917i
$686$		0			0
$687$		−	1.90775i		−	0.0727852i
$688$		0			0
$689$	−5.78475			−0.220382
$690$		0			0
$691$	13.9630	+	13.9630i	0.531178	+	0.531178i	0.920923	−	0.389745i	$-0.127437\pi$
$691$	13.9630	+	13.9630i	0.531178	+	0.531178i	−0.389745	+	0.920923i	$0.627437\pi$
$692$		0			0
$693$	6.23407	+	6.23407i	0.236813	+	0.236813i
$694$		0			0
$695$	3.11975	−	15.6182i	0.118339	−	0.592430i
$696$		0			0
$697$	−10.1600			−0.384836
$698$		0			0
$699$	9.25511	−	9.25511i	0.350061	−	0.350061i
$700$		0			0
$701$	15.7918	+	15.7918i	0.596448	+	0.596448i	0.939365	−	0.342918i	$-0.111415\pi$
$701$	15.7918	+	15.7918i	0.596448	+	0.596448i	−0.342918	+	0.939365i	$0.611415\pi$
$702$		0			0
$703$		−	21.2231i		−	0.800445i
$704$		0			0
$705$	−29.1704	−	5.82683i	−1.09862	−	0.219451i
$706$		0			0
$707$	−3.46675	+	3.46675i	−0.130380	+	0.130380i
$708$		0			0
$709$	12.4875	−	12.4875i	0.468977	−	0.468977i	−0.432606	−	0.901583i	$-0.642406\pi$
$709$	12.4875	−	12.4875i	0.468977	−	0.468977i	0.901583	+	0.432606i	$0.142406\pi$
$710$		0			0
$711$			6.52058i			0.244541i
$712$		0			0
$713$	9.95458			0.372802
$714$		0			0
$715$	−30.2092	−	45.2903i	−1.12976	−	1.69376i
$716$		0			0
$717$	−7.80221	+	7.80221i	−0.291379	+	0.291379i
$718$		0			0
$719$	26.6025			0.992107			0.496053	−	0.868292i	$-0.334782\pi$
$719$	26.6025			0.992107			0.496053	+	0.868292i	$0.334782\pi$
$720$		0			0
$721$	12.8714			0.479355
$722$		0			0
$723$	−5.87890	+	5.87890i	−0.218638	+	0.218638i
$724$		0			0
$725$	−28.9340	+	11.9302i	−1.07458	+	0.443076i
$726$		0			0
$727$	5.84475			0.216770			0.108385	−	0.994109i	$-0.465432\pi$
$727$	5.84475			0.216770			0.108385	+	0.994109i	$0.465432\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−0.478355	+	0.478355i	−0.0176926	+	0.0176926i
$732$		0			0
$733$	−34.4267	+	34.4267i	−1.27158	+	1.27158i	−0.326318	+	0.945260i	$0.605808\pi$
$733$	−34.4267	+	34.4267i	−1.27158	+	1.27158i	−0.945260	+	0.326318i	$0.894192\pi$
$734$		0			0
$735$	1.95888	−	9.80657i	0.0722542	−	0.361721i
$736$		0			0
$737$			42.5982i			1.56913i
$738$		0			0
$739$	8.03861	+	8.03861i	0.295705	+	0.295705i	0.839329	−	0.543624i	$-0.182948\pi$
$739$	8.03861	+	8.03861i	0.295705	+	0.295705i	−0.543624	+	0.839329i	$0.682948\pi$
$740$		0			0
$741$	−21.6931	+	21.6931i	−0.796917	+	0.796917i
$742$		0			0
$743$	4.14206			0.151957			0.0759787	−	0.997109i	$-0.475792\pi$
$743$	4.14206			0.151957			0.0759787	+	0.997109i	$0.475792\pi$
$744$		0			0
$745$	7.57459	−	37.9201i	0.277512	−	1.38929i
$746$		0			0
$747$	−0.973359	−	0.973359i	−0.0356133	−	0.0356133i
$748$		0			0
$749$	−14.3209	−	14.3209i	−0.523275	−	0.523275i
$750$		0			0
$751$	−53.0366			−1.93533			−0.967667	−	0.252232i	$-0.918835\pi$
$751$	−53.0366			−1.93533			−0.967667	+	0.252232i	$0.918835\pi$
$752$		0			0
$753$		−	21.2210i		−	0.773335i
$754$		0			0
$755$	−0.704442	−	1.05612i	−0.0256373	−	0.0384360i
$756$		0			0
$757$	4.39557	+	4.39557i	0.159760	+	0.159760i	0.782460	−	0.622701i	$-0.213965\pi$
$757$	4.39557	+	4.39557i	0.159760	+	0.159760i	−0.622701	+	0.782460i	$0.713965\pi$
$758$		0			0
$759$			36.7048i			1.33230i
$760$		0			0
$761$		−	17.0961i		−	0.619732i	−0.950780	−	0.309866i	$-0.899716\pi$
$761$		−	17.0961i		−	0.619732i	0.950780	−	0.309866i	$-0.100284\pi$
$762$		0			0
$763$	15.7584	+	15.7584i	0.570494	+	0.570494i
$764$		0			0
$765$	−2.75957	+	1.84067i	−0.0997726	+	0.0665495i
$766$		0			0
$767$		−	7.09871i		−	0.256320i
$768$		0			0
$769$	33.3744			1.20351			0.601756	−	0.798680i	$-0.294468\pi$
$769$	33.3744			1.20351			0.601756	+	0.798680i	$0.294468\pi$
$770$		0			0
$771$	−10.1663	−	10.1663i	−0.366130	−	0.366130i
$772$		0			0
$773$	−23.0507	−	23.0507i	−0.829078	−	0.829078i	0.158312	−	0.987389i	$-0.449395\pi$
$773$	−23.0507	−	23.0507i	−0.829078	−	0.829078i	−0.987389	+	0.158312i	$0.949395\pi$
$774$		0			0
$775$	−2.88881	+	6.94249i	−0.103769	+	0.249382i
$776$		0			0
$777$	−4.82899			−0.173239
$778$		0			0
$779$	−33.8391	+	33.8391i	−1.21241	+	1.21241i
$780$		0			0
$781$	−8.87079	−	8.87079i	−0.317422	−	0.317422i
$782$		0			0
$783$		−	6.25941i		−	0.223693i
$784$		0			0
$785$	4.99330	−	24.9976i	0.178218	−	0.892201i
$786$		0			0
$787$	10.1563	−	10.1563i	0.362034	−	0.362034i	−0.502527	−	0.864561i	$-0.667596\pi$
$787$	10.1563	−	10.1563i	0.362034	−	0.362034i	0.864561	+	0.502527i	$0.167596\pi$
$788$		0			0
$789$	3.49342	−	3.49342i	0.124369	−	0.124369i
$790$		0			0
$791$			16.6319i			0.591361i
$792$		0			0
$793$	16.6069			0.589730
$794$		0			0
$795$	−2.45093	+	1.63480i	−0.0869256	+	0.0579804i
$796$		0			0
$797$	24.6189	−	24.6189i	0.872046	−	0.872046i	−0.120649	−	0.992695i	$-0.538498\pi$
$797$	24.6189	−	24.6189i	0.872046	−	0.872046i	0.992695	+	0.120649i	$0.0384975\pi$
$798$		0			0
$799$	19.7347			0.698163
$800$		0			0
$801$	6.83613			0.241543
$802$		0			0
$803$	20.6683	−	20.6683i	0.729367	−	0.729367i
$804$		0			0
$805$	−19.5764	+	13.0577i	−0.689977	+	0.460223i
$806$		0			0
$807$	−16.3980			−0.577236
$808$		0			0
$809$			24.5505i			0.863150i	0.902077	+	0.431575i	$0.142042\pi$
$809$			24.5505i			0.863150i	−0.902077	+	0.431575i	$0.857958\pi$
$810$		0			0
$811$	−13.4539	+	13.4539i	−0.472430	+	0.472430i	−0.902700	−	0.430270i	$-0.858418\pi$
$811$	−13.4539	+	13.4539i	−0.472430	+	0.472430i	0.430270	+	0.902700i	$0.358418\pi$
$812$		0			0
$813$	2.41076	−	2.41076i	0.0845491	−	0.0845491i
$814$		0			0
$815$	−0.0600252	+	0.300500i	−0.00210259	+	0.0105260i
$816$		0			0
$817$			3.18645i			0.111480i
$818$		0			0
$819$	4.93593	+	4.93593i	0.172475	+	0.172475i
$820$		0			0
$821$	7.23091	−	7.23091i	0.252360	−	0.252360i	−0.569577	−	0.821938i	$-0.692893\pi$
$821$	7.23091	−	7.23091i	0.252360	−	0.252360i	0.821938	+	0.569577i	$0.192893\pi$
$822$		0			0
$823$	42.5825			1.48433			0.742167	−	0.670215i	$-0.233798\pi$
$823$	42.5825			1.48433			0.742167	+	0.670215i	$0.233798\pi$
$824$		0			0
$825$	−25.5986	−	10.6517i	−0.891228	−	0.370845i
$826$		0			0
$827$	18.4053	+	18.4053i	0.640014	+	0.640014i	0.950559	−	0.310545i	$-0.100512\pi$
$827$	18.4053	+	18.4053i	0.640014	+	0.640014i	−0.310545	+	0.950559i	$0.600512\pi$
$828$		0			0
$829$	−10.8176	−	10.8176i	−0.375710	−	0.375710i	0.493842	−	0.869552i	$-0.335592\pi$
$829$	−10.8176	−	10.8176i	−0.375710	−	0.375710i	−0.869552	+	0.493842i	$0.835592\pi$
$830$		0			0
$831$	−15.9745			−0.554148
$832$		0			0
$833$			6.63445i			0.229870i
$834$		0			0
$835$	−27.8325	+	18.5646i	−0.963185	+	0.642456i
$836$		0			0
$837$	−1.06342	−	1.06342i	−0.0367573	−	0.0367573i
$838$		0			0
$839$		−	10.8332i		−	0.374004i	−0.982360	−	0.187002i	$-0.940123\pi$
$839$		−	10.8332i		−	0.374004i	0.982360	−	0.187002i	$-0.0598771\pi$
$840$		0			0
$841$			10.1802i			0.351042i
$842$		0			0
$843$	−3.34302	−	3.34302i	−0.115140	−	0.115140i
$844$		0			0
$845$	−7.78834	−	11.6765i	−0.267927	−	0.401683i
$846$		0			0
$847$		−	31.3999i		−	1.07891i
$848$		0			0
$849$	9.21901			0.316396
$850$		0			0
$851$	−14.2160	−	14.2160i	−0.487319	−	0.487319i
$852$		0			0
$853$	31.7242	+	31.7242i	1.08622	+	1.08622i	0.995915	+	0.0903009i	$0.0287829\pi$
$853$	31.7242	+	31.7242i	1.08622	+	1.08622i	0.0903009	+	0.995915i	$0.471217\pi$
$854$		0			0
$855$	−3.06053	+	15.3217i	−0.104668	+	0.523992i
$856$		0			0
$857$	39.9570			1.36490			0.682452	−	0.730930i	$-0.260914\pi$
$857$	39.9570			1.36490			0.682452	+	0.730930i	$0.260914\pi$
$858$		0			0
$859$	−23.9624	+	23.9624i	−0.817587	+	0.817587i	−0.985758	−	0.168171i	$-0.946214\pi$
$859$	−23.9624	+	23.9624i	−0.817587	+	0.817587i	0.168171	+	0.985758i	$0.446214\pi$
$860$		0			0
$861$	7.69955	+	7.69955i	0.262400	+	0.262400i
$862$		0			0
$863$			12.5202i			0.426192i	0.977031	+	0.213096i	$0.0683547\pi$
$863$			12.5202i			0.426192i	−0.977031	+	0.213096i	$0.931645\pi$
$864$		0			0
$865$	−8.14226	+	40.7620i	−0.276845	+	1.38595i
$866$		0			0
$867$	−10.4647	+	10.4647i	−0.355400	+	0.355400i
$868$		0			0
$869$	25.5678	−	25.5678i	0.867327	−	0.867327i
$870$		0			0
$871$			33.7279i			1.14282i
$872$		0			0
$873$	−15.8228			−0.535522
$874$		0			0
$875$	−3.42560	−	17.4422i	−0.115806	−	0.589655i
$876$		0			0
$877$	22.4582	−	22.4582i	0.758358	−	0.758358i	−0.217666	−	0.976023i	$-0.569844\pi$
$877$	22.4582	−	22.4582i	0.758358	−	0.758358i	0.976023	+	0.217666i	$0.0698442\pi$
$878$		0			0
$879$	3.68618			0.124332
$880$		0			0
$881$	−44.4416			−1.49728			−0.748638	−	0.662979i	$-0.769292\pi$
$881$	−44.4416			−1.49728			−0.748638	+	0.662979i	$0.769292\pi$
$882$		0			0
$883$	−38.6128	+	38.6128i	−1.29942	+	1.29942i	−0.370653	+	0.928771i	$0.620866\pi$
$883$	−38.6128	+	38.6128i	−1.29942	+	1.29942i	−0.928771	+	0.370653i	$0.879134\pi$
$884$		0			0
$885$	−2.00613	−	3.00764i	−0.0674354	−	0.101101i
$886$		0			0
$887$	−27.1077			−0.910186			−0.455093	−	0.890444i	$-0.650394\pi$
$887$	−27.1077			−0.910186			−0.455093	+	0.890444i	$0.650394\pi$
$888$		0			0
$889$			2.99317i			0.100388i
$890$		0			0
$891$	3.92109	−	3.92109i	0.131361	−	0.131361i
$892$		0			0
$893$	65.7289	−	65.7289i	2.19953	−	2.19953i
$894$		0			0
$895$	−11.0456	−	2.20637i	−0.369212	−	0.0737507i
$896$		0			0
$897$			29.0617i			0.970341i
$898$		0			0
$899$	6.65640	+	6.65640i	0.222003	+	0.222003i
$900$		0			0
$901$	1.38206	−	1.38206i	0.0460432	−	0.0460432i
$902$		0			0
$903$	0.725026			0.0241274
$904$		0			0
$905$	−3.65155	+	18.2805i	−0.121382	+	0.607663i
$906$		0			0
$907$	7.29362	+	7.29362i	0.242181	+	0.242181i	0.817752	−	0.575571i	$-0.195220\pi$
$907$	7.29362	+	7.29362i	0.242181	+	0.242181i	−0.575571	+	0.817752i	$0.695220\pi$
$908$		0			0
$909$	2.18050	+	2.18050i	0.0723228	+	0.0723228i
$910$		0			0
$911$	−32.2468			−1.06838			−0.534192	−	0.845363i	$-0.679384\pi$
$911$	−32.2468			−1.06838			−0.534192	+	0.845363i	$0.679384\pi$
$912$		0			0
$913$			7.63325i			0.252624i
$914$		0			0
$915$	7.03617	−	4.69321i	0.232609	−	0.155153i
$916$		0			0
$917$	−1.11566	−	1.11566i	−0.0368423	−	0.0368423i
$918$		0			0
$919$			27.5668i			0.909346i	0.890659	+	0.454673i	$0.150244\pi$
$919$			27.5668i			0.909346i	−0.890659	+	0.454673i	$0.849756\pi$
$920$		0			0
$921$			13.1202i			0.432324i
$922$		0			0
$923$	−7.02360	−	7.02360i	−0.231185	−	0.231185i
$924$		0			0
$925$	14.0400	−	5.78902i	0.461631	−	0.190342i
$926$		0			0
$927$		−	8.09580i		−	0.265901i
$928$		0			0
$929$	10.3630			0.339999			0.169999	−	0.985444i	$-0.445623\pi$
$929$	10.3630			0.339999			0.169999	+	0.985444i	$0.445623\pi$
$930$		0			0
$931$	22.0969	+	22.0969i	0.724197	+	0.724197i
$932$		0			0
$933$	−6.27485	−	6.27485i	−0.205430	−	0.205430i
$934$		0			0
$935$	18.0380	+	3.60311i	0.589904	+	0.117834i
$936$		0			0
$937$	−49.6196			−1.62100			−0.810501	−	0.585738i	$-0.800805\pi$
$937$	−49.6196			−1.62100			−0.810501	+	0.585738i	$0.800805\pi$
$938$		0			0
$939$	−18.1133	+	18.1133i	−0.591104	+	0.591104i
$940$		0			0
$941$	−24.3629	−	24.3629i	−0.794208	−	0.794208i	0.187967	−	0.982175i	$-0.439810\pi$
$941$	−24.3629	−	24.3629i	−0.794208	−	0.794208i	−0.982175	+	0.187967i	$0.939810\pi$
$942$		0			0
$943$			45.3333i			1.47625i
$944$		0			0
$945$	3.48622	+	0.696376i	0.113407	+	0.0226531i
$946$		0			0
$947$	−34.0132	+	34.0132i	−1.10528	+	1.10528i	−0.111518	+	0.993762i	$0.535571\pi$
$947$	−34.0132	+	34.0132i	−1.10528	+	1.10528i	−0.993762	+	0.111518i	$0.964429\pi$
$948$		0			0
$949$	16.3644	−	16.3644i	0.531212	−	0.531212i
$950$		0			0
$951$		−	27.6373i		−	0.896201i
$952$		0			0
$953$	−21.9707			−0.711700			−0.355850	−	0.934543i	$-0.615809\pi$
$953$	−21.9707			−0.711700			−0.355850	+	0.934543i	$0.615809\pi$
$954$		0			0
$955$	−1.29322	+	0.862594i	−0.0418476	+	0.0279129i
$956$		0			0
$957$	−24.5437	+	24.5437i	−0.793385	+	0.793385i
$958$		0			0
$959$	−26.5577			−0.857594
$960$		0			0
$961$	−28.7383			−0.927041
$962$		0			0
$963$	−9.00752	+	9.00752i	−0.290263	+	0.290263i
$964$		0			0
$965$	29.5806	+	44.3479i	0.952233	+	1.42761i
$966$		0			0
$967$	20.8251			0.669690			0.334845	−	0.942273i	$-0.391316\pi$
$967$	20.8251			0.669690			0.334845	+	0.942273i	$0.391316\pi$
$968$		0			0
$969$		−	10.3656i		−	0.332991i
$970$		0			0
$971$	−27.3561	+	27.3561i	−0.877898	+	0.877898i	−0.993317	−	0.115418i	$-0.963179\pi$
$971$	−27.3561	+	27.3561i	−0.877898	+	0.877898i	0.115418	+	0.993317i	$0.463179\pi$
$972$		0			0
$973$	8.00739	−	8.00739i	0.256705	−	0.256705i
$974$		0			0
$975$	−20.2681	−	8.43367i	−0.649099	−	0.270094i
$976$		0			0
$977$			25.5428i			0.817188i	0.912716	+	0.408594i	$0.133981\pi$
$977$			25.5428i			0.817188i	−0.912716	+	0.408594i	$0.866019\pi$
$978$		0			0
$979$	−26.8051	−	26.8051i	−0.856694	−	0.856694i
$980$		0			0
$981$	9.91170	−	9.91170i	0.316456	−	0.316456i
$982$		0			0
$983$	26.0467			0.830760			0.415380	−	0.909648i	$-0.363649\pi$
$983$	26.0467			0.830760			0.415380	+	0.909648i	$0.363649\pi$
$984$		0			0
$985$	12.1139	+	2.41976i	0.385980	+	0.0771000i
$986$		0			0
$987$	−14.9556	−	14.9556i	−0.476042	−	0.476042i
$988$		0			0
$989$	2.13440	+	2.13440i	0.0678699	+	0.0678699i
$990$		0			0
$991$	30.2000			0.959334			0.479667	−	0.877451i	$-0.340758\pi$
$991$	30.2000			0.959334			0.479667	+	0.877451i	$0.340758\pi$
$992$		0			0
$993$			25.3917i			0.805780i
$994$		0			0
$995$	−4.77243	−	7.15493i	−0.151296	−	0.226827i
$996$		0			0
$997$	−32.7172	−	32.7172i	−1.03617	−	1.03617i	−0.999321	−	0.0368444i	$-0.988269\pi$
$997$	−32.7172	−	32.7172i	−1.03617	−	1.03617i	−0.0368444	−	0.999321i	$-0.511731\pi$
$998$		0			0
$999$			3.03732i			0.0960967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.a.289.5		48
4.3	odd	2		1920.2.bl.b.289.20		48
5.4	even	2	inner	1920.2.bl.a.289.20		48
8.3	odd	2		960.2.bl.a.529.3		48
8.5	even	2		240.2.bl.a.109.6	✓	48
16.3	odd	4		960.2.bl.a.49.16		48
16.5	even	4	inner	1920.2.bl.a.1249.20		48
16.11	odd	4		1920.2.bl.b.1249.5		48
16.13	even	4		240.2.bl.a.229.19	yes	48
20.19	odd	2		1920.2.bl.b.289.5		48
24.5	odd	2		720.2.bm.h.109.19		48
40.19	odd	2		960.2.bl.a.529.16		48
40.29	even	2		240.2.bl.a.109.19	yes	48
48.29	odd	4		720.2.bm.h.469.6		48
80.19	odd	4		960.2.bl.a.49.3		48
80.29	even	4		240.2.bl.a.229.6	yes	48
80.59	odd	4		1920.2.bl.b.1249.20		48
80.69	even	4	inner	1920.2.bl.a.1249.5		48
120.29	odd	2		720.2.bm.h.109.6		48
240.29	odd	4		720.2.bm.h.469.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.6	✓	48	8.5	even	2
240.2.bl.a.109.19	yes	48	40.29	even	2
240.2.bl.a.229.6	yes	48	80.29	even	4
240.2.bl.a.229.19	yes	48	16.13	even	4
720.2.bm.h.109.6		48	120.29	odd	2
720.2.bm.h.109.19		48	24.5	odd	2
720.2.bm.h.469.6		48	48.29	odd	4
720.2.bm.h.469.19		48	240.29	odd	4
960.2.bl.a.49.3		48	80.19	odd	4
960.2.bl.a.49.16		48	16.3	odd	4
960.2.bl.a.529.3		48	8.3	odd	2
960.2.bl.a.529.16		48	40.19	odd	2
1920.2.bl.a.289.5		48	1.1	even	1	trivial
1920.2.bl.a.289.20		48	5.4	even	2	inner
1920.2.bl.a.1249.5		48	80.69	even	4	inner
1920.2.bl.a.1249.20		48	16.5	even	4	inner
1920.2.bl.b.289.5		48	20.19	odd	2
1920.2.bl.b.289.20		48	4.3	odd	2
1920.2.bl.b.1249.5		48	16.11	odd	4
1920.2.bl.b.1249.20		48	80.59	odd	4

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.86022 - 1.24079i) q^{5} +1.58988 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.86022 - 1.24079i) q^{5} +1.58988 q^{7} -1.00000i q^{9} +(-3.92109 + 3.92109i) q^{11} +(-3.10459 + 3.10459i) q^{13} +(-0.438005 + 2.19275i) q^{15} -1.48346i q^{17} +(-4.94087 - 4.94087i) q^{19} +(-1.12422 + 1.12422i) q^{21} -6.61914 q^{23} +(1.92087 - 4.61630i) q^{25} +(0.707107 + 0.707107i) q^{27} +(-4.42607 - 4.42607i) q^{29} -1.50391 q^{31} -5.54525i q^{33} +(2.95754 - 1.97271i) q^{35} +(2.14771 + 2.14771i) q^{37} -4.39055i q^{39} -6.84881i q^{41} +(-0.322458 - 0.322458i) q^{43} +(-1.24079 - 1.86022i) q^{45} +13.3031i q^{47} -4.47227 q^{49} +(1.04897 + 1.04897i) q^{51} +(0.931646 + 0.931646i) q^{53} +(-2.42885 + 12.1594i) q^{55} +6.98744 q^{57} +(-1.14326 + 1.14326i) q^{59} +(-2.67458 - 2.67458i) q^{61} -1.58988i q^{63} +(-1.92308 + 9.62737i) q^{65} +(5.43194 - 5.43194i) q^{67} +(4.68044 - 4.68044i) q^{69} +2.26233i q^{71} -5.27105 q^{73} +(1.90596 + 4.62248i) q^{75} +(-6.23407 + 6.23407i) q^{77} -6.52058 q^{79} -1.00000 q^{81} +(0.973359 - 0.973359i) q^{83} +(-1.84067 - 2.75957i) q^{85} +6.25941 q^{87} +6.83613i q^{89} +(-4.93593 + 4.93593i) q^{91} +(1.06342 - 1.06342i) q^{93} +(-15.3217 - 3.06053i) q^{95} -15.8228i q^{97} +(3.92109 + 3.92109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) \) 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

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