LMFDB - Embedded newform 1920.2.bl.b.289.3

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			289.3
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.b.1249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-1.65754 - 1.50085i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.65754 - 1.50085i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +(4.39624 - 4.39624i) q^{11} +(-0.417468 + 0.417468i) q^{13} +(2.23332 - 0.110799i) q^{15} +4.40417i q^{17} +(-4.53682 - 4.53682i) q^{19} +(1.83125 - 1.83125i) q^{21} -0.281063 q^{23} +(0.494901 + 4.97545i) q^{25} +(0.707107 + 0.707107i) q^{27} +(-3.73710 - 3.73710i) q^{29} +3.05233 q^{31} +6.21722i q^{33} +(4.29266 + 3.88686i) q^{35} +(5.26234 + 5.26234i) q^{37} -0.590389i q^{39} +5.16508i q^{41} +(-2.66933 - 2.66933i) q^{43} +(-1.50085 + 1.65754i) q^{45} -7.45202i q^{47} -0.293066 q^{49} +(-3.11422 - 3.11422i) q^{51} +(2.89462 + 2.89462i) q^{53} +(-13.8850 + 0.688864i) q^{55} +6.41604 q^{57} +(-4.60721 + 4.60721i) q^{59} +(0.211318 + 0.211318i) q^{61} +2.58977i q^{63} +(1.31853 - 0.0654147i) q^{65} +(-7.17140 + 7.17140i) q^{67} +(0.198741 - 0.198741i) q^{69} +15.9477i q^{71} -10.5662 q^{73} +(-3.86812 - 3.16822i) q^{75} +(-11.3853 + 11.3853i) q^{77} -4.53907 q^{79} -1.00000 q^{81} +(-4.56660 + 4.56660i) q^{83} +(6.61000 - 7.30010i) q^{85} +5.28505 q^{87} +10.2745i q^{89} +(1.08115 - 1.08115i) q^{91} +(-2.15832 + 2.15832i) q^{93} +(0.710893 + 14.3291i) q^{95} -6.78053i q^{97} +(-4.39624 - 4.39624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.65754	−	1.50085i	−0.741276	−	0.671200i
$5$	−1.65754	−	1.50085i	−0.741276	−	0.671200i
$6$		0			0
$7$	−2.58977			−0.978843			−0.489421	−	0.872047i	$-0.662792\pi$
$7$	−2.58977			−0.978843			−0.489421	+	0.872047i	$0.662792\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	4.39624	−	4.39624i	1.32552	−	1.32552i	0.416278	−	0.909237i	$-0.363334\pi$
$11$	4.39624	−	4.39624i	1.32552	−	1.32552i	0.909237	−	0.416278i	$-0.136666\pi$
$12$		0			0
$13$	−0.417468	+	0.417468i	−0.115785	+	0.115785i	−0.762625	−	0.646840i	$-0.776090\pi$
$13$	−0.417468	+	0.417468i	−0.115785	+	0.115785i	0.646840	+	0.762625i	$0.276090\pi$
$14$		0			0
$15$	2.23332	−	0.110799i	0.576641	−	0.0286083i
$16$		0			0
$17$			4.40417i			1.06817i	0.845431	+	0.534084i	$0.179343\pi$
$17$			4.40417i			1.06817i	−0.845431	+	0.534084i	$0.820657\pi$
$18$		0			0
$19$	−4.53682	−	4.53682i	−1.04082	−	1.04082i	−0.999131	−	0.0416882i	$-0.986726\pi$
$19$	−4.53682	−	4.53682i	−1.04082	−	1.04082i	−0.0416882	−	0.999131i	$-0.513274\pi$
$20$		0			0
$21$	1.83125	−	1.83125i	0.399611	−	0.399611i
$22$		0			0
$23$	−0.281063			−0.0586056			−0.0293028	−	0.999571i	$-0.509329\pi$
$23$	−0.281063			−0.0586056			−0.0293028	+	0.999571i	$0.509329\pi$
$24$		0			0
$25$	0.494901	+	4.97545i	0.0989802	+	0.995089i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−3.73710	−	3.73710i	−0.693962	−	0.693962i	0.269140	−	0.963101i	$-0.413261\pi$
$29$	−3.73710	−	3.73710i	−0.693962	−	0.693962i	−0.963101	+	0.269140i	$0.913261\pi$
$30$		0			0
$31$	3.05233			0.548214			0.274107	−	0.961699i	$-0.411618\pi$
$31$	3.05233			0.548214			0.274107	+	0.961699i	$0.411618\pi$
$32$		0			0
$33$			6.21722i			1.08228i
$34$		0			0
$35$	4.29266	+	3.88686i	0.725593	+	0.657000i
$36$		0			0
$37$	5.26234	+	5.26234i	0.865124	+	0.865124i	0.991928	−	0.126804i	$-0.0404719\pi$
$37$	5.26234	+	5.26234i	0.865124	+	0.865124i	−0.126804	+	0.991928i	$0.540472\pi$
$38$		0			0
$39$		−	0.590389i		−	0.0945380i
$40$		0			0
$41$			5.16508i			0.806649i	0.915057	+	0.403325i	$0.132145\pi$
$41$			5.16508i			0.806649i	−0.915057	+	0.403325i	$0.867855\pi$
$42$		0			0
$43$	−2.66933	−	2.66933i	−0.407069	−	0.407069i	0.473647	−	0.880715i	$-0.342937\pi$
$43$	−2.66933	−	2.66933i	−0.407069	−	0.407069i	−0.880715	+	0.473647i	$0.842937\pi$
$44$		0			0
$45$	−1.50085	+	1.65754i	−0.223733	+	0.247092i
$46$		0			0
$47$		−	7.45202i		−	1.08699i	−0.839413	−	0.543495i	$-0.817101\pi$
$47$		−	7.45202i		−	1.08699i	0.839413	−	0.543495i	$-0.182899\pi$
$48$		0			0
$49$	−0.293066			−0.0418665
$50$		0			0
$51$	−3.11422	−	3.11422i	−0.436078	−	0.436078i
$52$		0			0
$53$	2.89462	+	2.89462i	0.397606	+	0.397606i	0.877388	−	0.479782i	$-0.159284\pi$
$53$	2.89462	+	2.89462i	0.397606	+	0.397606i	−0.479782	+	0.877388i	$0.659284\pi$
$54$		0			0
$55$	−13.8850	+	0.688864i	−1.87226	+	0.0928863i
$56$		0			0
$57$	6.41604			0.849825
$58$		0			0
$59$	−4.60721	+	4.60721i	−0.599808	+	0.599808i	−0.940261	−	0.340453i	$-0.889420\pi$
$59$	−4.60721	+	4.60721i	−0.599808	+	0.599808i	0.340453	+	0.940261i	$0.389420\pi$
$60$		0			0
$61$	0.211318	+	0.211318i	0.0270564	+	0.0270564i	0.720506	−	0.693449i	$-0.243910\pi$
$61$	0.211318	+	0.211318i	0.0270564	+	0.0270564i	−0.693449	+	0.720506i	$0.743910\pi$
$62$		0			0
$63$			2.58977i			0.326281i
$64$		0			0
$65$	1.31853	−	0.0654147i	0.163543	−	0.00811370i
$66$		0			0
$67$	−7.17140	+	7.17140i	−0.876126	+	0.876126i	−0.993131	−	0.117005i	$-0.962671\pi$
$67$	−7.17140	+	7.17140i	−0.876126	+	0.876126i	0.117005	+	0.993131i	$0.462671\pi$
$68$		0			0
$69$	0.198741	−	0.198741i	0.0239257	−	0.0239257i
$70$		0			0
$71$			15.9477i			1.89265i	0.323222	+	0.946323i	$0.395234\pi$
$71$			15.9477i			1.89265i	−0.323222	+	0.946323i	$0.604766\pi$
$72$		0			0
$73$	−10.5662			−1.23668			−0.618339	−	0.785912i	$-0.712194\pi$
$73$	−10.5662			−1.23668			−0.618339	+	0.785912i	$0.712194\pi$
$74$		0			0
$75$	−3.86812	−	3.16822i	−0.446652	−	0.365835i
$76$		0			0
$77$	−11.3853	+	11.3853i	−1.29747	+	1.29747i
$78$		0			0
$79$	−4.53907			−0.510685			−0.255342	−	0.966851i	$-0.582188\pi$
$79$	−4.53907			−0.510685			−0.255342	+	0.966851i	$0.582188\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	−0.911826	−	0.410577i	$-0.865327\pi$
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	0.410577	+	0.911826i	$0.365327\pi$
$84$		0			0
$85$	6.61000	−	7.30010i	0.716955	−	0.791807i
$86$		0			0
$87$	5.28505			0.566617
$88$		0			0
$89$			10.2745i			1.08910i	0.838730	+	0.544548i	$0.183299\pi$
$89$			10.2745i			1.08910i	−0.838730	+	0.544548i	$0.816701\pi$
$90$		0			0
$91$	1.08115	−	1.08115i	0.113335	−	0.113335i
$92$		0			0
$93$	−2.15832	+	2.15832i	−0.223808	+	0.223808i
$94$		0			0
$95$	0.710893	+	14.3291i	0.0729361	+	1.47013i
$96$		0			0
$97$		−	6.78053i		−	0.688459i	−0.938886	−	0.344229i	$-0.888140\pi$
$97$		−	6.78053i		−	0.688459i	0.938886	−	0.344229i	$-0.111860\pi$
$98$		0			0
$99$	−4.39624	−	4.39624i	−0.441838	−	0.441838i
$100$		0			0
$101$	−10.0764	+	10.0764i	−1.00264	+	1.00264i	−0.00264739	+	0.999996i	$0.500843\pi$
$101$	−10.0764	+	10.0764i	−1.00264	+	1.00264i	−0.999996	+	0.00264739i	$0.999157\pi$
$102$		0			0
$103$	−4.71475			−0.464558			−0.232279	−	0.972649i	$-0.574618\pi$
$103$	−4.71475			−0.464558			−0.232279	+	0.972649i	$0.574618\pi$
$104$		0			0
$105$	−5.78380	+	0.286945i	−0.564441	+	0.0280030i
$106$		0			0
$107$	−12.9687	−	12.9687i	−1.25373	−	1.25373i	−0.954035	−	0.299696i	$-0.903115\pi$
$107$	−12.9687	−	12.9687i	−1.25373	−	1.25373i	−0.299696	−	0.954035i	$-0.596885\pi$
$108$		0			0
$109$	0.382902	+	0.382902i	0.0366754	+	0.0366754i	0.725207	−	0.688531i	$-0.241744\pi$
$109$	0.382902	+	0.382902i	0.0366754	+	0.0366754i	−0.688531	+	0.725207i	$0.741744\pi$
$110$		0			0
$111$	−7.44208			−0.706371
$112$		0			0
$113$			12.1861i			1.14637i	0.819424	+	0.573187i	$0.194293\pi$
$113$			12.1861i			1.14637i	−0.819424	+	0.573187i	$0.805707\pi$
$114$		0			0
$115$	0.465874	+	0.421833i	0.0434430	+	0.0393361i
$116$		0			0
$117$	0.417468	+	0.417468i	0.0385950	+	0.0385950i
$118$		0			0
$119$		−	11.4058i		−	1.04557i
$120$		0			0
$121$		−	27.6538i		−	2.51398i
$122$		0			0
$123$	−3.65226	−	3.65226i	−0.329313	−	0.329313i
$124$		0			0
$125$	6.64708	−	8.98979i	0.594533	−	0.804071i
$126$		0			0
$127$		−	6.75303i		−	0.599234i	−0.954060	−	0.299617i	$-0.903141\pi$
$127$		−	6.75303i		−	0.599234i	0.954060	−	0.299617i	$-0.0968589\pi$
$128$		0			0
$129$	3.77500			0.332370
$130$		0			0
$131$	3.95303	+	3.95303i	0.345378	+	0.345378i	0.858385	−	0.513007i	$-0.171468\pi$
$131$	3.95303	+	3.95303i	0.345378	+	0.345378i	−0.513007	+	0.858385i	$0.671468\pi$
$132$		0			0
$133$	11.7494	+	11.7494i	1.01880	+	1.01880i
$134$		0			0
$135$	−0.110799	−	2.23332i	−0.00953609	−	0.192214i
$136$		0			0
$137$	5.19519			0.443855			0.221927	−	0.975063i	$-0.428765\pi$
$137$	5.19519			0.443855			0.221927	+	0.975063i	$0.428765\pi$
$138$		0			0
$139$	0.977024	−	0.977024i	0.0828701	−	0.0828701i	−0.664457	−	0.747327i	$-0.731337\pi$
$139$	0.977024	−	0.977024i	0.0828701	−	0.0828701i	0.747327	+	0.664457i	$0.231337\pi$
$140$		0			0
$141$	5.26938	+	5.26938i	0.443761	+	0.443761i
$142$		0			0
$143$			3.67058i			0.306949i
$144$		0			0
$145$	0.585580	+	11.8032i	0.0486298	+	0.980204i
$146$		0			0
$147$	0.207229	−	0.207229i	0.0170919	−	0.0170919i
$148$		0			0
$149$	−11.3051	+	11.3051i	−0.926150	+	0.926150i	−0.997455	−	0.0713047i	$-0.977284\pi$
$149$	−11.3051	+	11.3051i	−0.926150	+	0.926150i	0.0713047	+	0.997455i	$0.477284\pi$
$150$		0			0
$151$		−	2.87287i		−	0.233791i	−0.993144	−	0.116895i	$-0.962706\pi$
$151$		−	2.87287i		−	0.233791i	0.993144	−	0.116895i	$-0.0372942\pi$
$152$		0			0
$153$	4.40417			0.356056
$154$		0			0
$155$	−5.05937	−	4.58109i	−0.406378	−	0.367962i
$156$		0			0
$157$	−5.73516	+	5.73516i	−0.457716	+	0.457716i	−0.897905	−	0.440189i	$-0.854911\pi$
$157$	−5.73516	+	5.73516i	−0.457716	+	0.457716i	0.440189	+	0.897905i	$0.354911\pi$
$158$		0			0
$159$	−4.09361			−0.324644
$160$		0			0
$161$	0.727889			0.0573657
$162$		0			0
$163$	11.9561	−	11.9561i	0.936474	−	0.936474i	−0.0616255	−	0.998099i	$-0.519628\pi$
$163$	11.9561	−	11.9561i	0.936474	−	0.936474i	0.998099	+	0.0616255i	$0.0196285\pi$
$164$		0			0
$165$	9.33111	−	10.3053i	0.726426	−	0.802267i
$166$		0			0
$167$	−9.23665			−0.714754			−0.357377	−	0.933960i	$-0.616329\pi$
$167$	−9.23665			−0.714754			−0.357377	+	0.933960i	$0.616329\pi$
$168$		0			0
$169$			12.6514i			0.973188i
$170$		0			0
$171$	−4.53682	+	4.53682i	−0.346940	+	0.346940i
$172$		0			0
$173$	−2.36187	+	2.36187i	−0.179570	+	0.179570i	−0.791168	−	0.611598i	$-0.790527\pi$
$173$	−2.36187	+	2.36187i	−0.179570	+	0.179570i	0.611598	+	0.791168i	$0.290527\pi$
$174$		0			0
$175$	−1.28168	−	12.8853i	−0.0968861	−	0.974036i
$176$		0			0
$177$		−	6.51559i		−	0.489741i
$178$		0			0
$179$	9.27202	+	9.27202i	0.693023	+	0.693023i	0.962896	−	0.269873i	$-0.0869816\pi$
$179$	9.27202	+	9.27202i	0.693023	+	0.693023i	−0.269873	+	0.962896i	$0.586982\pi$
$180$		0			0
$181$	10.5707	−	10.5707i	0.785715	−	0.785715i	−0.195074	−	0.980789i	$-0.562495\pi$
$181$	10.5707	−	10.5707i	0.785715	−	0.785715i	0.980789	+	0.195074i	$0.0624946\pi$
$182$		0			0
$183$	−0.298848			−0.0220915
$184$		0			0
$185$	−0.824577	−	16.6206i	−0.0606241	−	1.22197i
$186$		0			0
$187$	19.3618	+	19.3618i	1.41587	+	1.41587i
$188$		0			0
$189$	−1.83125	−	1.83125i	−0.133204	−	0.133204i
$190$		0			0
$191$	8.32988			0.602729			0.301364	−	0.953509i	$-0.402558\pi$
$191$	8.32988			0.602729			0.301364	+	0.953509i	$0.402558\pi$
$192$		0			0
$193$			5.73404i			0.412745i	0.978473	+	0.206373i	$0.0661659\pi$
$193$			5.73404i			0.412745i	−0.978473	+	0.206373i	$0.933834\pi$
$194$		0			0
$195$	−0.886086	+	0.978596i	−0.0634539	+	0.0700787i
$196$		0			0
$197$	3.23239	+	3.23239i	0.230298	+	0.230298i	0.812817	−	0.582519i	$-0.197933\pi$
$197$	3.23239	+	3.23239i	0.230298	+	0.230298i	−0.582519	+	0.812817i	$0.697933\pi$
$198$		0			0
$199$		−	19.0599i		−	1.35112i	−0.737303	−	0.675562i	$-0.763901\pi$
$199$		−	19.0599i		−	1.35112i	0.737303	−	0.675562i	$-0.236099\pi$
$200$		0			0
$201$		−	10.1419i		−	0.715354i
$202$		0			0
$203$	9.67824	+	9.67824i	0.679279	+	0.679279i
$204$		0			0
$205$	7.75200	−	8.56134i	0.541423	−	0.597950i
$206$		0			0
$207$			0.281063i			0.0195352i
$208$		0			0
$209$	−39.8899			−2.75924
$210$		0			0
$211$	4.43719	+	4.43719i	0.305469	+	0.305469i	0.843149	−	0.537680i	$-0.180699\pi$
$211$	4.43719	+	4.43719i	0.305469	+	0.305469i	−0.537680	+	0.843149i	$0.680699\pi$
$212$		0			0
$213$	−11.2767	−	11.2767i	−0.772670	−	0.772670i
$214$		0			0
$215$	0.418267	+	8.43078i	0.0285256	+	0.574975i
$216$		0			0
$217$	−7.90485			−0.536616
$218$		0			0
$219$	7.47142	−	7.47142i	0.504871	−	0.504871i
$220$		0			0
$221$	−1.83860	−	1.83860i	−0.123678	−	0.123678i
$222$		0			0
$223$			5.10536i			0.341880i	0.985281	+	0.170940i	$0.0546805\pi$
$223$			5.10536i			0.341880i	−0.985281	+	0.170940i	$0.945320\pi$
$224$		0			0
$225$	4.97545	−	0.494901i	0.331696	−	0.0329934i
$226$		0			0
$227$	−15.0563	+	15.0563i	−0.999320	+	0.999320i	−1.00000		0.000680242i	$-0.999783\pi$
$227$	−15.0563	+	15.0563i	−0.999320	+	0.999320i	0.000680242		1.00000i	$0.499783\pi$
$228$		0			0
$229$	−17.5250	+	17.5250i	−1.15809	+	1.15809i	−0.173200	+	0.984887i	$0.555411\pi$
$229$	−17.5250	+	17.5250i	−1.15809	+	1.15809i	−0.984887	+	0.173200i	$0.944589\pi$
$230$		0			0
$231$		−	16.1012i		−	1.05938i
$232$		0			0
$233$	9.15254			0.599603			0.299802	−	0.954002i	$-0.403080\pi$
$233$	9.15254			0.599603			0.299802	+	0.954002i	$0.403080\pi$
$234$		0			0
$235$	−11.1844	+	12.3521i	−0.729588	+	0.805759i
$236$		0			0
$237$	3.20960	−	3.20960i	0.208486	−	0.208486i
$238$		0			0
$239$	12.9198			0.835713			0.417857	−	0.908513i	$-0.362781\pi$
$239$	12.9198			0.835713			0.417857	+	0.908513i	$0.362781\pi$
$240$		0			0
$241$	10.7071			0.689703			0.344851	−	0.938657i	$-0.387929\pi$
$241$	10.7071			0.689703			0.344851	+	0.938657i	$0.387929\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	0.485769	+	0.439847i	0.0310346	+	0.0281008i
$246$		0			0
$247$	3.78796			0.241022
$248$		0			0
$249$		−	6.45814i		−	0.409268i
$250$		0			0
$251$	−4.48257	+	4.48257i	−0.282937	+	0.282937i	−0.834279	−	0.551342i	$-0.814116\pi$
$251$	−4.48257	+	4.48257i	−0.282937	+	0.282937i	0.551342	+	0.834279i	$0.314116\pi$
$252$		0			0
$253$	−1.23562	+	1.23562i	−0.0776827	+	0.0776827i
$254$		0			0
$255$	0.487979	+	9.83593i	0.0305584	+	0.615950i
$256$		0			0
$257$		−	16.9307i		−	1.05610i	−0.849212	−	0.528052i	$-0.822922\pi$
$257$		−	16.9307i		−	1.05610i	0.849212	−	0.528052i	$-0.177078\pi$
$258$		0			0
$259$	−13.6283	−	13.6283i	−0.846821	−	0.846821i
$260$		0			0
$261$	−3.73710	+	3.73710i	−0.231321	+	0.231321i
$262$		0			0
$263$	2.07893			0.128192			0.0640962	−	0.997944i	$-0.479584\pi$
$263$	2.07893			0.128192			0.0640962	+	0.997944i	$0.479584\pi$
$264$		0			0
$265$	−0.453569	−	9.14234i	−0.0278625	−	0.561609i
$266$		0			0
$267$	−7.26517	−	7.26517i	−0.444621	−	0.444621i
$268$		0			0
$269$	16.0709	+	16.0709i	0.979860	+	0.979860i	0.999801	−	0.0199408i	$-0.00634778\pi$
$269$	16.0709	+	16.0709i	0.979860	+	0.979860i	−0.0199408	+	0.999801i	$0.506348\pi$
$270$		0			0
$271$	−4.18571			−0.254264			−0.127132	−	0.991886i	$-0.540577\pi$
$271$	−4.18571			−0.254264			−0.127132	+	0.991886i	$0.540577\pi$
$272$		0			0
$273$			1.52898i			0.0925378i
$274$		0			0
$275$	24.0489	+	19.6975i	1.45021	+	1.18781i
$276$		0			0
$277$	−15.8235	−	15.8235i	−0.950744	−	0.950744i	0.0480985	−	0.998843i	$-0.484684\pi$
$277$	−15.8235	−	15.8235i	−0.950744	−	0.950744i	−0.998843	+	0.0480985i	$0.984684\pi$
$278$		0			0
$279$		−	3.05233i		−	0.182738i
$280$		0			0
$281$			12.6546i			0.754911i	0.926028	+	0.377455i	$0.123201\pi$
$281$			12.6546i			0.754911i	−0.926028	+	0.377455i	$0.876799\pi$
$282$		0			0
$283$	−1.54865	−	1.54865i	−0.0920579	−	0.0920579i	0.659578	−	0.751636i	$-0.270735\pi$
$283$	−1.54865	−	1.54865i	−0.0920579	−	0.0920579i	−0.751636	+	0.659578i	$0.770735\pi$
$284$		0			0
$285$	−10.6349	−	9.62951i	−0.629955	−	0.570403i
$286$		0			0
$287$		−	13.3764i		−	0.789583i
$288$		0			0
$289$	−2.39672			−0.140983
$290$		0			0
$291$	4.79456	+	4.79456i	0.281062	+	0.281062i
$292$		0			0
$293$	−21.2881	−	21.2881i	−1.24366	−	1.24366i	−0.958470	−	0.285194i	$-0.907942\pi$
$293$	−21.2881	−	21.2881i	−1.24366	−	1.24366i	−0.285194	−	0.958470i	$-0.592058\pi$
$294$		0			0
$295$	14.5514	−	0.721922i	0.847215	−	0.0420319i
$296$		0			0
$297$	6.21722			0.360760
$298$		0			0
$299$	0.117335	−	0.117335i	0.00678565	−	0.00678565i
$300$		0			0
$301$	6.91296	+	6.91296i	0.398456	+	0.398456i
$302$		0			0
$303$		−	14.2502i		−	0.818655i
$304$		0			0
$305$	−0.0331122	−	0.667424i	−0.00189600	−	0.0382166i
$306$		0			0
$307$	−12.2344	+	12.2344i	−0.698255	+	0.698255i	−0.964034	−	0.265779i	$-0.914371\pi$
$307$	−12.2344	+	12.2344i	−0.698255	+	0.698255i	0.265779	+	0.964034i	$0.414371\pi$
$308$		0			0
$309$	3.33383	−	3.33383i	0.189655	−	0.189655i
$310$		0			0
$311$			19.4874i			1.10503i	0.833503	+	0.552515i	$0.186332\pi$
$311$			19.4874i			1.10503i	−0.833503	+	0.552515i	$0.813668\pi$
$312$		0			0
$313$	9.73432			0.550217			0.275108	−	0.961413i	$-0.411286\pi$
$313$	9.73432			0.550217			0.275108	+	0.961413i	$0.411286\pi$
$314$		0			0
$315$	3.88686	−	4.29266i	0.219000	−	0.241864i
$316$		0			0
$317$	8.46658	−	8.46658i	0.475530	−	0.475530i	−0.428168	−	0.903699i	$-0.640841\pi$
$317$	8.46658	−	8.46658i	0.475530	−	0.475530i	0.903699	+	0.428168i	$0.140841\pi$
$318$		0			0
$319$	−32.8583			−1.83971
$320$		0			0
$321$	18.3405			1.02367
$322$		0			0
$323$	19.9809	−	19.9809i	1.11177	−	1.11177i
$324$		0			0
$325$	−2.28370	−	1.87049i	−0.126677	−	0.103756i
$326$		0			0
$327$	−0.541505			−0.0299453
$328$		0			0
$329$			19.2991i			1.06399i
$330$		0			0
$331$	7.11555	−	7.11555i	0.391106	−	0.391106i	−0.483975	−	0.875082i	$-0.660808\pi$
$331$	7.11555	−	7.11555i	0.391106	−	0.391106i	0.875082	+	0.483975i	$0.160808\pi$
$332$		0			0
$333$	5.26234	−	5.26234i	0.288375	−	0.288375i
$334$		0			0
$335$	22.6501	−	1.12371i	1.23751	−	0.0613951i
$336$		0			0
$337$		−	15.8355i		−	0.862613i	−0.902205	−	0.431307i	$-0.858053\pi$
$337$		−	15.8355i		−	0.862613i	0.902205	−	0.431307i	$-0.141947\pi$
$338$		0			0
$339$	−8.61689	−	8.61689i	−0.468005	−	0.468005i
$340$		0			0
$341$	13.4188	−	13.4188i	0.726667	−	0.726667i
$342$		0			0
$343$	18.8874			1.01982
$344$		0			0
$345$	−0.627703	+	0.0311416i	−0.0337944	+	0.00167661i
$346$		0			0
$347$	9.38020	+	9.38020i	0.503555	+	0.503555i	0.912541	−	0.408986i	$-0.134117\pi$
$347$	9.38020	+	9.38020i	0.503555	+	0.503555i	−0.408986	+	0.912541i	$0.634117\pi$
$348$		0			0
$349$	−0.479184	−	0.479184i	−0.0256501	−	0.0256501i	0.694165	−	0.719816i	$-0.255774\pi$
$349$	−0.479184	−	0.479184i	−0.0256501	−	0.0256501i	−0.719816	+	0.694165i	$0.755774\pi$
$350$		0			0
$351$	−0.590389			−0.0315127
$352$		0			0
$353$		−	8.95345i		−	0.476544i	−0.971198	−	0.238272i	$-0.923419\pi$
$353$		−	8.95345i		−	0.476544i	0.971198	−	0.238272i	$-0.0765810\pi$
$354$		0			0
$355$	23.9351	−	26.4340i	1.27034	−	1.40297i
$356$		0			0
$357$	8.06513	+	8.06513i	0.426852	+	0.426852i
$358$		0			0
$359$			3.47704i			0.183511i	0.995782	+	0.0917556i	$0.0292478\pi$
$359$			3.47704i			0.183511i	−0.995782	+	0.0917556i	$0.970752\pi$
$360$		0			0
$361$			22.1655i			1.16661i
$362$		0			0
$363$	19.5542	+	19.5542i	1.02633	+	1.02633i
$364$		0			0
$365$	17.5139	+	15.8582i	0.916719	+	0.830058i
$366$		0			0
$367$			15.1190i			0.789206i	0.918852	+	0.394603i	$0.129118\pi$
$367$			15.1190i			0.789206i	−0.918852	+	0.394603i	$0.870882\pi$
$368$		0			0
$369$	5.16508			0.268883
$370$		0			0
$371$	−7.49640	−	7.49640i	−0.389194	−	0.389194i
$372$		0			0
$373$	19.0505	+	19.0505i	0.986398	+	0.986398i	0.999909	−	0.0135107i	$-0.00430073\pi$
$373$	19.0505	+	19.0505i	0.986398	+	0.986398i	−0.0135107	+	0.999909i	$0.504301\pi$
$374$		0			0
$375$	1.65655	+	11.0569i	0.0855438	+	0.570978i
$376$		0			0
$377$	3.12024			0.160701
$378$		0			0
$379$	3.52823	−	3.52823i	0.181233	−	0.181233i	−0.610660	−	0.791893i	$-0.709096\pi$
$379$	3.52823	−	3.52823i	0.181233	−	0.181233i	0.791893	+	0.610660i	$0.209096\pi$
$380$		0			0
$381$	4.77511	+	4.77511i	0.244636	+	0.244636i
$382$		0			0
$383$			3.20268i			0.163649i	0.996647	+	0.0818246i	$0.0260747\pi$
$383$			3.20268i			0.163649i	−0.996647	+	0.0818246i	$0.973925\pi$
$384$		0			0
$385$	35.9591	−	1.78400i	1.83265	−	0.0909211i
$386$		0			0
$387$	−2.66933	+	2.66933i	−0.135690	+	0.135690i
$388$		0			0
$389$	−16.9595	+	16.9595i	−0.859882	+	0.859882i	−0.991324	−	0.131441i	$-0.958039\pi$
$389$	−16.9595	+	16.9595i	−0.859882	+	0.859882i	0.131441	+	0.991324i	$0.458039\pi$
$390$		0			0
$391$		−	1.23785i		−	0.0626007i
$392$		0			0
$393$	−5.59043			−0.282000
$394$		0			0
$395$	7.52370	+	6.81246i	0.378558	+	0.342772i
$396$		0			0
$397$	−15.8392	+	15.8392i	−0.794946	+	0.794946i	−0.982294	−	0.187348i	$-0.940011\pi$
$397$	−15.8392	+	15.8392i	−0.794946	+	0.794946i	0.187348	+	0.982294i	$0.440011\pi$
$398$		0			0
$399$	−16.6161			−0.831845
$400$		0			0
$401$	−10.8608			−0.542364			−0.271182	−	0.962528i	$-0.587414\pi$
$401$	−10.8608			−0.542364			−0.271182	+	0.962528i	$0.587414\pi$
$402$		0			0
$403$	−1.27425	+	1.27425i	−0.0634750	+	0.0634750i
$404$		0			0
$405$	1.65754	+	1.50085i	0.0823640	+	0.0745778i
$406$		0			0
$407$	46.2690			2.29347
$408$		0			0
$409$		−	12.5363i		−	0.619880i	−0.950756	−	0.309940i	$-0.899691\pi$
$409$		−	12.5363i		−	0.619880i	0.950756	−	0.309940i	$-0.100309\pi$
$410$		0			0
$411$	−3.67355	+	3.67355i	−0.181203	+	0.181203i
$412$		0			0
$413$	11.9316	−	11.9316i	0.587118	−	0.587118i
$414$		0			0
$415$	14.4231	−	0.715558i	0.708002	−	0.0351253i
$416$		0			0
$417$			1.38172i			0.0676631i
$418$		0			0
$419$	−21.6745	−	21.6745i	−1.05887	−	1.05887i	−0.998155	−	0.0607123i	$-0.980663\pi$
$419$	−21.6745	−	21.6745i	−1.05887	−	1.05887i	−0.0607123	−	0.998155i	$-0.519337\pi$
$420$		0			0
$421$	9.02933	−	9.02933i	0.440063	−	0.440063i	−0.451970	−	0.892033i	$-0.649279\pi$
$421$	9.02933	−	9.02933i	0.440063	−	0.440063i	0.892033	+	0.451970i	$0.149279\pi$
$422$		0			0
$423$	−7.45202			−0.362330
$424$		0			0
$425$	−21.9127	+	2.17963i	−1.06292	+	0.105727i
$426$		0			0
$427$	−0.547265	−	0.547265i	−0.0264840	−	0.0264840i
$428$		0			0
$429$	−2.59549	−	2.59549i	−0.125312	−	0.125312i
$430$		0			0
$431$	22.1994			1.06931			0.534653	−	0.845072i	$-0.320442\pi$
$431$	22.1994			1.06931			0.534653	+	0.845072i	$0.320442\pi$
$432$		0			0
$433$		−	31.1117i		−	1.49513i	−0.664187	−	0.747566i	$-0.731222\pi$
$433$		−	31.1117i		−	1.49513i	0.664187	−	0.747566i	$-0.268778\pi$
$434$		0			0
$435$	−8.76021	−	7.93207i	−0.420020	−	0.380314i
$436$		0			0
$437$	1.27513	+	1.27513i	0.0609979	+	0.0609979i
$438$		0			0
$439$		−	0.460911i		−	0.0219981i	−0.999940	−	0.0109990i	$-0.996499\pi$
$439$		−	0.460911i		−	0.0219981i	0.999940	−	0.0109990i	$-0.00350117\pi$
$440$		0			0
$441$			0.293066i			0.0139555i
$442$		0			0
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	0.635247	−	0.772309i	$-0.280898\pi$
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	−0.772309	+	0.635247i	$0.780898\pi$
$444$		0			0
$445$	15.4205	−	17.0304i	0.731001	−	0.807321i
$446$		0			0
$447$		−	15.9878i		−	0.756198i
$448$		0			0
$449$	3.02196			0.142615			0.0713075	−	0.997454i	$-0.477283\pi$
$449$	3.02196			0.142615			0.0713075	+	0.997454i	$0.477283\pi$
$450$		0			0
$451$	22.7069	+	22.7069i	1.06923	+	1.06923i
$452$		0			0
$453$	2.03143	+	2.03143i	0.0954447	+	0.0954447i
$454$		0			0
$455$	−3.41469	+	0.169409i	−0.160083	+	0.00794204i
$456$		0			0
$457$	−4.69013			−0.219395			−0.109698	−	0.993965i	$-0.534988\pi$
$457$	−4.69013			−0.219395			−0.109698	+	0.993965i	$0.534988\pi$
$458$		0			0
$459$	−3.11422	+	3.11422i	−0.145359	+	0.145359i
$460$		0			0
$461$	−20.9304	−	20.9304i	−0.974824	−	0.974824i	0.0248664	−	0.999691i	$-0.492084\pi$
$461$	−20.9304	−	20.9304i	−0.974824	−	0.974824i	−0.999691	+	0.0248664i	$0.992084\pi$
$462$		0			0
$463$			25.5190i			1.18597i	0.805215	+	0.592983i	$0.202050\pi$
$463$			25.5190i			1.18597i	−0.805215	+	0.592983i	$0.797950\pi$
$464$		0			0
$465$	6.81683	−	0.338196i	0.316123	−	0.0156835i
$466$		0			0
$467$	20.6018	−	20.6018i	0.953336	−	0.953336i	−0.0456227	−	0.998959i	$-0.514527\pi$
$467$	20.6018	−	20.6018i	0.953336	−	0.953336i	0.998959	+	0.0456227i	$0.0145272\pi$
$468$		0			0
$469$	18.5723	−	18.5723i	0.857590	−	0.857590i
$470$		0			0
$471$		−	8.11074i		−	0.373723i
$472$		0			0
$473$	−23.4700			−1.07915
$474$		0			0
$475$	20.3275	−	24.8180i	0.932687	−	1.13873i
$476$		0			0
$477$	2.89462	−	2.89462i	0.132535	−	0.132535i
$478$		0			0
$479$	−30.6830			−1.40194			−0.700972	−	0.713189i	$-0.747250\pi$
$479$	−30.6830			−1.40194			−0.700972	+	0.713189i	$0.747250\pi$
$480$		0			0
$481$	−4.39372			−0.200337
$482$		0			0
$483$	−0.514696	+	0.514696i	−0.0234195	+	0.0234195i
$484$		0			0
$485$	−10.1766	+	11.2390i	−0.462094	+	0.510338i
$486$		0			0
$487$	4.53105			0.205322			0.102661	−	0.994716i	$-0.467264\pi$
$487$	4.53105			0.205322			0.102661	+	0.994716i	$0.467264\pi$
$488$		0			0
$489$			16.9085i			0.764628i
$490$		0			0
$491$	2.06787	−	2.06787i	0.0933215	−	0.0933215i	−0.658905	−	0.752226i	$-0.728980\pi$
$491$	2.06787	−	2.06787i	0.0933215	−	0.0933215i	0.752226	+	0.658905i	$0.228980\pi$
$492$		0			0
$493$	16.4588	−	16.4588i	0.741268	−	0.741268i
$494$		0			0
$495$	0.688864	+	13.8850i	0.0309621	+	0.624086i
$496$		0			0
$497$		−	41.3010i		−	1.85260i
$498$		0			0
$499$	−27.0618	−	27.0618i	−1.21145	−	1.21145i	−0.970549	−	0.240906i	$-0.922556\pi$
$499$	−27.0618	−	27.0618i	−1.21145	−	1.21145i	−0.240906	−	0.970549i	$-0.577444\pi$
$500$		0			0
$501$	6.53130	−	6.53130i	0.291797	−	0.291797i
$502$		0			0
$503$	−8.42170			−0.375505			−0.187753	−	0.982216i	$-0.560120\pi$
$503$	−8.42170			−0.375505			−0.187753	+	0.982216i	$0.560120\pi$
$504$		0			0
$505$	31.8254	−	1.57892i	1.41621	−	0.0702609i
$506$		0			0
$507$	−8.94592	−	8.94592i	−0.397302	−	0.397302i
$508$		0			0
$509$	−22.5863	−	22.5863i	−1.00112	−	1.00112i	−0.999999	−	0.00112047i	$-0.999643\pi$
$509$	−22.5863	−	22.5863i	−1.00112	−	1.00112i	−0.00112047	−	0.999999i	$-0.500357\pi$
$510$		0			0
$511$	27.3640			1.21051
$512$		0			0
$513$		−	6.41604i		−	0.283275i
$514$		0			0
$515$	7.81490	+	7.07612i	0.344365	+	0.311811i
$516$		0			0
$517$	−32.7609	−	32.7609i	−1.44082	−	1.44082i
$518$		0			0
$519$		−	3.34020i		−	0.146618i
$520$		0			0
$521$			30.9260i			1.35489i	0.735572	+	0.677447i	$0.236914\pi$
$521$			30.9260i			1.35489i	−0.735572	+	0.677447i	$0.763086\pi$
$522$		0			0
$523$	−26.4425	−	26.4425i	−1.15625	−	1.15625i	−0.985276	−	0.170974i	$-0.945309\pi$
$523$	−26.4425	−	26.4425i	−1.15625	−	1.15625i	−0.170974	−	0.985276i	$-0.554691\pi$
$524$		0			0
$525$	10.0176	+	8.20499i	0.437202	+	0.358095i
$526$		0			0
$527$			13.4430i			0.585585i
$528$		0			0
$529$	−22.9210			−0.996565
$530$		0			0
$531$	4.60721	+	4.60721i	0.199936	+	0.199936i
$532$		0			0
$533$	−2.15626	−	2.15626i	−0.0933978	−	0.0933978i
$534$		0			0
$535$	2.03211	+	40.9602i	0.0878560	+	1.77086i
$536$		0			0
$537$	−13.1126			−0.565851
$538$		0			0
$539$	−1.28839	+	1.28839i	−0.0554947	+	0.0554947i
$540$		0			0
$541$	−21.6730	−	21.6730i	−0.931794	−	0.931794i	0.0660242	−	0.997818i	$-0.478969\pi$
$541$	−21.6730	−	21.6730i	−0.931794	−	0.931794i	−0.997818	+	0.0660242i	$0.978969\pi$
$542$		0			0
$543$			14.9492i			0.641533i
$544$		0			0
$545$	−0.0599984	−	1.20935i	−0.00257005	−	0.0518031i
$546$		0			0
$547$	2.92159	−	2.92159i	0.124918	−	0.124918i	−0.641884	−	0.766802i	$-0.721847\pi$
$547$	2.92159	−	2.92159i	0.124918	−	0.124918i	0.766802	+	0.641884i	$0.221847\pi$
$548$		0			0
$549$	0.211318	−	0.211318i	0.00901881	−	0.00901881i
$550$		0			0
$551$			33.9091i			1.44458i
$552$		0			0
$553$	11.7552			0.499880
$554$		0			0
$555$	12.3356	+	11.1694i	0.523616	+	0.474116i
$556$		0			0
$557$	25.5453	−	25.5453i	1.08239	−	1.08239i	0.0861022	−	0.996286i	$-0.472559\pi$
$557$	25.5453	−	25.5453i	1.08239	−	1.08239i	0.996286	−	0.0861022i	$-0.0274412\pi$
$558$		0			0
$559$	2.22872			0.0942648
$560$		0			0
$561$	−27.3817			−1.15606
$562$		0			0
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	−0.908223	−	0.418487i	$-0.862561\pi$
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	0.418487	+	0.908223i	$0.362561\pi$
$564$		0			0
$565$	18.2895	−	20.1990i	0.769447	−	0.849780i
$566$		0			0
$567$	2.58977			0.108760
$568$		0			0
$569$		−	13.3498i		−	0.559654i	−0.960050	−	0.279827i	$-0.909723\pi$
$569$		−	13.3498i		−	0.559654i	0.960050	−	0.279827i	$-0.0902771\pi$
$570$		0			0
$571$	−23.5430	+	23.5430i	−0.985244	+	0.985244i	−0.999893	−	0.0146492i	$-0.995337\pi$
$571$	−23.5430	+	23.5430i	−0.985244	+	0.985244i	0.0146492	+	0.999893i	$0.495337\pi$
$572$		0			0
$573$	−5.89011	+	5.89011i	−0.246063	+	0.246063i
$574$		0			0
$575$	−0.139098	−	1.39841i	−0.00580080	−	0.0583179i
$576$		0			0
$577$			34.7117i			1.44507i	0.691335	+	0.722534i	$0.257023\pi$
$577$			34.7117i			1.44507i	−0.691335	+	0.722534i	$0.742977\pi$
$578$		0			0
$579$	−4.05458	−	4.05458i	−0.168503	−	0.168503i
$580$		0			0
$581$	11.8265	−	11.8265i	0.490644	−	0.490644i
$582$		0			0
$583$	25.4508			1.05407
$584$		0			0
$585$	−0.0654147	−	1.31853i	−0.00270457	−	0.0545145i
$586$		0			0
$587$	26.8949	+	26.8949i	1.11007	+	1.11007i	0.993140	+	0.116931i	$0.0373057\pi$
$587$	26.8949	+	26.8949i	1.11007	+	1.11007i	0.116931	+	0.993140i	$0.462694\pi$
$588$		0			0
$589$	−13.8479	−	13.8479i	−0.570592	−	0.570592i
$590$		0			0
$591$	−4.57128			−0.188037
$592$		0			0
$593$			8.25028i			0.338798i	0.985548	+	0.169399i	$0.0541827\pi$
$593$			8.25028i			0.338798i	−0.985548	+	0.169399i	$0.945817\pi$
$594$		0			0
$595$	−17.1184	+	18.9056i	−0.701786	+	0.775055i
$596$		0			0
$597$	13.4774	+	13.4774i	0.551594	+	0.551594i
$598$		0			0
$599$		−	19.6734i		−	0.803832i	−0.915677	−	0.401916i	$-0.868344\pi$
$599$		−	19.6734i		−	0.803832i	0.915677	−	0.401916i	$-0.131656\pi$
$600$		0			0
$601$		−	30.0313i		−	1.22500i	−0.790470	−	0.612501i	$-0.790164\pi$
$601$		−	30.0313i		−	1.22500i	0.790470	−	0.612501i	$-0.209836\pi$
$602$		0			0
$603$	7.17140	+	7.17140i	0.292042	+	0.292042i
$604$		0			0
$605$	−41.5042	+	45.8374i	−1.68739	+	1.86355i
$606$		0			0
$607$			5.52944i			0.224433i	0.993684	+	0.112217i	$0.0357950\pi$
$607$			5.52944i			0.224433i	−0.993684	+	0.112217i	$0.964205\pi$
$608$		0			0
$609$	−13.6871			−0.554629
$610$		0			0
$611$	3.11098	+	3.11098i	0.125857	+	0.125857i
$612$		0			0
$613$	−28.9851	−	28.9851i	−1.17070	−	1.17070i	−0.982044	−	0.188653i	$-0.939588\pi$
$613$	−28.9851	−	28.9851i	−1.17070	−	1.17070i	−0.188653	−	0.982044i	$-0.560412\pi$
$614$		0			0
$615$	0.572287	+	11.5353i	0.0230768	+	0.465147i
$616$		0			0
$617$	26.5578			1.06918			0.534588	−	0.845113i	$-0.320467\pi$
$617$	26.5578			1.06918			0.534588	+	0.845113i	$0.320467\pi$
$618$		0			0
$619$	5.91235	−	5.91235i	0.237638	−	0.237638i	−0.578234	−	0.815871i	$-0.696258\pi$
$619$	5.91235	−	5.91235i	0.237638	−	0.237638i	0.815871	+	0.578234i	$0.196258\pi$
$620$		0			0
$621$	−0.198741	−	0.198741i	−0.00797522	−	0.00797522i
$622$		0			0
$623$		−	26.6087i		−	1.06605i
$624$		0			0
$625$	−24.5101	+	4.92471i	−0.980406	+	0.196988i
$626$		0			0
$627$	28.2064	−	28.2064i	1.12646	−	1.12646i
$628$		0			0
$629$	−23.1763	+	23.1763i	−0.924098	+	0.924098i
$630$		0			0
$631$		−	37.6881i		−	1.50034i	−0.661246	−	0.750169i	$-0.729972\pi$
$631$		−	37.6881i		−	1.50034i	0.661246	−	0.750169i	$-0.270028\pi$
$632$		0			0
$633$	−6.27514			−0.249414
$634$		0			0
$635$	−10.1353	+	11.1934i	−0.402206	+	0.444198i
$636$		0			0
$637$	0.122346	−	0.122346i	0.00484751	−	0.00484751i
$638$		0			0
$639$	15.9477			0.630882
$640$		0			0
$641$	36.5113			1.44211			0.721055	−	0.692878i	$-0.243657\pi$
$641$	36.5113			1.44211			0.721055	+	0.692878i	$0.243657\pi$
$642$		0			0
$643$	−12.1973	+	12.1973i	−0.481014	+	0.481014i	−0.905455	−	0.424441i	$-0.860471\pi$
$643$	−12.1973	+	12.1973i	−0.481014	+	0.481014i	0.424441	+	0.905455i	$0.360471\pi$
$644$		0			0
$645$	−6.25722	−	5.66570i	−0.246378	−	0.223087i
$646$		0			0
$647$	−16.5371			−0.650142			−0.325071	−	0.945690i	$-0.605388\pi$
$647$	−16.5371			−0.650142			−0.325071	+	0.945690i	$0.605388\pi$
$648$		0			0
$649$			40.5088i			1.59011i
$650$		0			0
$651$	5.58957	−	5.58957i	0.219073	−	0.219073i
$652$		0			0
$653$	2.73228	−	2.73228i	0.106923	−	0.106923i	−0.651622	−	0.758544i	$-0.725911\pi$
$653$	2.73228	−	2.73228i	0.106923	−	0.106923i	0.758544	+	0.651622i	$0.225911\pi$
$654$		0			0
$655$	−0.619416	−	12.4852i	−0.0242026	−	0.487838i
$656$		0			0
$657$			10.5662i			0.412226i
$658$		0			0
$659$	14.1442	+	14.1442i	0.550982	+	0.550982i	0.926724	−	0.375743i	$-0.122612\pi$
$659$	14.1442	+	14.1442i	0.550982	+	0.550982i	−0.375743	+	0.926724i	$0.622612\pi$
$660$		0			0
$661$	−14.2173	+	14.2173i	−0.552991	+	0.552991i	−0.927303	−	0.374312i	$-0.877879\pi$
$661$	−14.2173	+	14.2173i	−0.552991	+	0.552991i	0.374312	+	0.927303i	$0.377879\pi$
$662$		0			0
$663$	2.60018			0.100982
$664$		0			0
$665$	−1.84105	−	37.1091i	−0.0713929	−	1.43903i
$666$		0			0
$667$	1.05036	+	1.05036i	0.0406701	+	0.0406701i
$668$		0			0
$669$	−3.61003	−	3.61003i	−0.139572	−	0.139572i
$670$		0			0
$671$	1.85800			0.0717274
$672$		0			0
$673$		−	17.6236i		−	0.679341i	−0.940545	−	0.339670i	$-0.889684\pi$
$673$		−	17.6236i		−	0.679341i	0.940545	−	0.339670i	$-0.110316\pi$
$674$		0			0
$675$	−3.16822	+	3.86812i	−0.121945	+	0.148884i
$676$		0			0
$677$	33.4900	+	33.4900i	1.28713	+	1.28713i	0.936525	+	0.350601i	$0.114023\pi$
$677$	33.4900	+	33.4900i	1.28713	+	1.28713i	0.350601	+	0.936525i	$0.385977\pi$
$678$		0			0
$679$			17.5601i			0.673893i
$680$		0			0
$681$		−	21.2928i		−	0.815941i
$682$		0			0
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	0.695476	−	0.718549i	$-0.255193\pi$
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	−0.718549	+	0.695476i	$0.755193\pi$
$684$		0			0
$685$	−8.61125	−	7.79720i	−0.329019	−	0.297916i
$686$		0			0
$687$		−	24.7841i		−	0.945574i
$688$		0			0
$689$	−2.41682			−0.0920736
$690$		0			0
$691$	−14.0957	−	14.0957i	−0.536226	−	0.536226i	0.386192	−	0.922418i	$-0.373790\pi$
$691$	−14.0957	−	14.0957i	−0.536226	−	0.536226i	−0.922418	+	0.386192i	$0.873790\pi$
$692$		0			0
$693$	11.3853	+	11.3853i	0.432490	+	0.432490i
$694$		0			0
$695$	−3.08582	+	0.153094i	−0.117052	+	0.00580717i
$696$		0			0
$697$	−22.7479			−0.861637
$698$		0			0
$699$	−6.47183	+	6.47183i	−0.244787	+	0.244787i
$700$		0			0
$701$	−23.9043	−	23.9043i	−0.902854	−	0.902854i	0.0928282	−	0.995682i	$-0.470409\pi$
$701$	−23.9043	−	23.9043i	−0.902854	−	0.902854i	−0.995682	+	0.0928282i	$0.970409\pi$
$702$		0			0
$703$		−	47.7487i		−	1.80087i
$704$		0			0
$705$	−0.825679	−	16.6428i	−0.0310969	−	0.626803i
$706$		0			0
$707$	26.0957	−	26.0957i	0.981431	−	0.981431i
$708$		0			0
$709$	−30.0855	+	30.0855i	−1.12989	+	1.12989i	−0.139691	+	0.990195i	$0.544611\pi$
$709$	−30.0855	+	30.0855i	−1.12989	+	1.12989i	−0.990195	+	0.139691i	$0.955389\pi$
$710$		0			0
$711$			4.53907i			0.170228i
$712$		0			0
$713$	−0.857896			−0.0321285
$714$		0			0
$715$	5.50899	−	6.08415i	0.206024	−	0.227534i
$716$		0			0
$717$	−9.13569	+	9.13569i	−0.341178	+	0.341178i
$718$		0			0
$719$	−20.9727			−0.782148			−0.391074	−	0.920359i	$-0.627896\pi$
$719$	−20.9727			−0.782148			−0.391074	+	0.920359i	$0.627896\pi$
$720$		0			0
$721$	12.2101			0.454729
$722$		0			0
$723$	−7.57104	+	7.57104i	−0.281570	+	0.281570i
$724$		0			0
$725$	16.7442	−	20.4432i	0.621865	−	0.759242i
$726$		0			0
$727$	−19.5823			−0.726269			−0.363134	−	0.931737i	$-0.618293\pi$
$727$	−19.5823			−0.726269			−0.363134	+	0.931737i	$0.618293\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	11.7562	−	11.7562i	0.434818	−	0.434818i
$732$		0			0
$733$	3.95752	−	3.95752i	0.146174	−	0.146174i	−0.630232	−	0.776407i	$-0.717040\pi$
$733$	3.95752	−	3.95752i	0.146174	−	0.146174i	0.776407	+	0.630232i	$0.217040\pi$
$734$		0			0
$735$	−0.654510	+	0.0324715i	−0.0241420	+	0.00119773i
$736$		0			0
$737$			63.0544i			2.32264i
$738$		0			0
$739$	−1.94684	−	1.94684i	−0.0716155	−	0.0716155i	0.670392	−	0.742007i	$-0.266126\pi$
$739$	−1.94684	−	1.94684i	−0.0716155	−	0.0716155i	−0.742007	+	0.670392i	$0.766126\pi$
$740$		0			0
$741$	−2.67849	+	2.67849i	−0.0983969	+	0.0983969i
$742$		0			0
$743$	−10.5553			−0.387238			−0.193619	−	0.981077i	$-0.562023\pi$
$743$	−10.5553			−0.387238			−0.193619	+	0.981077i	$0.562023\pi$
$744$		0			0
$745$	35.7060	−	1.77144i	1.30816	−	0.0649006i
$746$		0			0
$747$	4.56660	+	4.56660i	0.167083	+	0.167083i
$748$		0			0
$749$	33.5860	+	33.5860i	1.22721	+	1.22721i
$750$		0			0
$751$	−49.4390			−1.80405			−0.902027	−	0.431680i	$-0.857921\pi$
$751$	−49.4390			−1.80405			−0.902027	+	0.431680i	$0.857921\pi$
$752$		0			0
$753$		−	6.33931i		−	0.231017i
$754$		0			0
$755$	−4.31174	+	4.76191i	−0.156920	+	0.173304i
$756$		0			0
$757$	−4.11693	−	4.11693i	−0.149632	−	0.149632i	0.628321	−	0.777954i	$-0.283742\pi$
$757$	−4.11693	−	4.11693i	−0.149632	−	0.149632i	−0.777954	+	0.628321i	$0.783742\pi$
$758$		0			0
$759$		−	1.74743i		−	0.0634276i
$760$		0			0
$761$			14.6496i			0.531049i	0.964104	+	0.265525i	$0.0855452\pi$
$761$			14.6496i			0.531049i	−0.964104	+	0.265525i	$0.914455\pi$
$762$		0			0
$763$	−0.991630	−	0.991630i	−0.0358994	−	0.0358994i
$764$		0			0
$765$	−7.30010	−	6.61000i	−0.263936	−	0.238985i
$766$		0			0
$767$		−	3.84673i		−	0.138897i
$768$		0			0
$769$	2.44453			0.0881520			0.0440760	−	0.999028i	$-0.485966\pi$
$769$	2.44453			0.0881520			0.0440760	+	0.999028i	$0.485966\pi$
$770$		0			0
$771$	11.9718	+	11.9718i	0.431153	+	0.431153i
$772$		0			0
$773$	12.2398	+	12.2398i	0.440234	+	0.440234i	0.892091	−	0.451857i	$-0.149238\pi$
$773$	12.2398	+	12.2398i	0.440234	+	0.440234i	−0.451857	+	0.892091i	$0.649238\pi$
$774$		0			0
$775$	1.51060	+	15.1867i	0.0542624	+	0.545522i
$776$		0			0
$777$	19.2733			0.691426
$778$		0			0
$779$	23.4330	−	23.4330i	0.839576	−	0.839576i
$780$		0			0
$781$	70.1100	+	70.1100i	2.50873	+	2.50873i
$782$		0			0
$783$		−	5.28505i		−	0.188872i
$784$		0			0
$785$	18.1139	−	0.898665i	0.646512	−	0.0320747i
$786$		0			0
$787$	−18.2070	+	18.2070i	−0.649009	+	0.649009i	−0.952753	−	0.303745i	$-0.901763\pi$
$787$	−18.2070	+	18.2070i	−0.649009	+	0.649009i	0.303745	+	0.952753i	$0.401763\pi$
$788$		0			0
$789$	−1.47003	+	1.47003i	−0.0523343	+	0.0523343i
$790$		0			0
$791$		−	31.5593i		−	1.12212i
$792$		0			0
$793$	−0.176437			−0.00626545
$794$		0			0
$795$	6.78533	+	6.14389i	0.240651	+	0.217901i
$796$		0			0
$797$	5.02164	−	5.02164i	0.177876	−	0.177876i	−0.612553	−	0.790429i	$-0.709858\pi$
$797$	5.02164	−	5.02164i	0.177876	−	0.177876i	0.790429	+	0.612553i	$0.209858\pi$
$798$		0			0
$799$	32.8200			1.16109
$800$		0			0
$801$	10.2745			0.363032
$802$		0			0
$803$	−46.4514	+	46.4514i	−1.63923	+	1.63923i
$804$		0			0
$805$	−1.20651	−	1.09245i	−0.0425238	−	0.0385039i
$806$		0			0
$807$	−22.7277			−0.800053
$808$		0			0
$809$		−	23.6476i		−	0.831404i	−0.909501	−	0.415702i	$-0.863536\pi$
$809$		−	23.6476i		−	0.831404i	0.909501	−	0.415702i	$-0.136464\pi$
$810$		0			0
$811$	−24.2614	+	24.2614i	−0.851934	+	0.851934i	−0.990371	−	0.138438i	$-0.955792\pi$
$811$	−24.2614	+	24.2614i	−0.851934	+	0.851934i	0.138438	+	0.990371i	$0.455792\pi$
$812$		0			0
$813$	2.95975	−	2.95975i	0.103803	−	0.103803i
$814$		0			0
$815$	−37.7621	+	1.87345i	−1.32275	+	0.0656240i
$816$		0			0
$817$			24.2205i			0.847369i
$818$		0			0
$819$	−1.08115	−	1.08115i	−0.0377784	−	0.0377784i
$820$		0			0
$821$	38.9257	−	38.9257i	1.35852	−	1.35852i	0.482771	−	0.875746i	$-0.339630\pi$
$821$	38.9257	−	38.9257i	1.35852	−	1.35852i	0.875746	−	0.482771i	$-0.160370\pi$
$822$		0			0
$823$	−38.6799			−1.34830			−0.674148	−	0.738596i	$-0.735489\pi$
$823$	−38.6799			−1.34830			−0.674148	+	0.738596i	$0.735489\pi$
$824$		0			0
$825$	−30.9334	+	3.07691i	−1.07696	+	0.107124i
$826$		0			0
$827$	−25.6217	−	25.6217i	−0.890955	−	0.890955i	0.103658	−	0.994613i	$-0.466945\pi$
$827$	−25.6217	−	25.6217i	−0.890955	−	0.890955i	−0.994613	+	0.103658i	$0.966945\pi$
$828$		0			0
$829$	14.8962	+	14.8962i	0.517367	+	0.517367i	0.916774	−	0.399407i	$-0.130784\pi$
$829$	14.8962	+	14.8962i	0.517367	+	0.517367i	−0.399407	+	0.916774i	$0.630784\pi$
$830$		0			0
$831$	22.3779			0.776279
$832$		0			0
$833$		−	1.29071i		−	0.0447205i
$834$		0			0
$835$	15.3102	+	13.8628i	0.529830	+	0.479743i
$836$		0			0
$837$	2.15832	+	2.15832i	0.0746025	+	0.0746025i
$838$		0			0
$839$		−	14.5709i		−	0.503045i	−0.967851	−	0.251522i	$-0.919069\pi$
$839$		−	14.5709i		−	0.503045i	0.967851	−	0.251522i	$-0.0809312\pi$
$840$		0			0
$841$		−	1.06820i		−	0.0368344i
$842$		0			0
$843$	−8.94816	−	8.94816i	−0.308191	−	0.308191i
$844$		0			0
$845$	18.9879	−	20.9703i	0.653204	−	0.721401i
$846$		0			0
$847$			71.6171i			2.46079i
$848$		0			0
$849$	2.19013			0.0751650
$850$		0			0
$851$	−1.47905	−	1.47905i	−0.0507011	−	0.0507011i
$852$		0			0
$853$	−11.9474	−	11.9474i	−0.409070	−	0.409070i	0.472344	−	0.881414i	$-0.343408\pi$
$853$	−11.9474	−	11.9474i	−0.409070	−	0.409070i	−0.881414	+	0.472344i	$0.843408\pi$
$854$		0			0
$855$	14.3291	−	0.710893i	0.490044	−	0.0243120i
$856$		0			0
$857$	18.3405			0.626498			0.313249	−	0.949671i	$-0.398583\pi$
$857$	18.3405			0.626498			0.313249	+	0.949671i	$0.398583\pi$
$858$		0			0
$859$	−17.4227	+	17.4227i	−0.594455	+	0.594455i	−0.938832	−	0.344377i	$-0.888090\pi$
$859$	−17.4227	+	17.4227i	−0.594455	+	0.594455i	0.344377	+	0.938832i	$0.388090\pi$
$860$		0			0
$861$	9.45853	+	9.45853i	0.322346	+	0.322346i
$862$		0			0
$863$			40.5444i			1.38015i	0.723740	+	0.690073i	$0.242422\pi$
$863$			40.5444i			1.38015i	−0.723740	+	0.690073i	$0.757578\pi$
$864$		0			0
$865$	7.45973	−	0.370091i	0.253638	−	0.0125835i
$866$		0			0
$867$	1.69474	−	1.69474i	0.0575562	−	0.0575562i
$868$		0			0
$869$	−19.9548	+	19.9548i	−0.676921	+	0.676921i
$870$		0			0
$871$		−	5.98767i		−	0.202884i
$872$		0			0
$873$	−6.78053			−0.229486
$874$		0			0
$875$	−17.2144	+	23.2815i	−0.581954	+	0.787060i
$876$		0			0
$877$	−31.0594	+	31.0594i	−1.04880	+	1.04880i	−0.0500546	+	0.998746i	$0.515940\pi$
$877$	−31.0594	+	31.0594i	−1.04880	+	1.04880i	−0.998746	+	0.0500546i	$0.984060\pi$
$878$		0			0
$879$	30.1059			1.01545
$880$		0			0
$881$	−18.0615			−0.608506			−0.304253	−	0.952591i	$-0.598407\pi$
$881$	−18.0615			−0.608506			−0.304253	+	0.952591i	$0.598407\pi$
$882$		0			0
$883$	18.0110	−	18.0110i	0.606117	−	0.606117i	−0.335812	−	0.941929i	$-0.609011\pi$
$883$	18.0110	−	18.0110i	0.606117	−	0.606117i	0.941929	+	0.335812i	$0.109011\pi$
$884$		0			0
$885$	−9.77891	+	10.7999i	−0.328715	+	0.363034i
$886$		0			0
$887$	−37.8699			−1.27155			−0.635774	−	0.771876i	$-0.719319\pi$
$887$	−37.8699			−1.27155			−0.635774	+	0.771876i	$0.719319\pi$
$888$		0			0
$889$			17.4888i			0.586556i
$890$		0			0
$891$	−4.39624	+	4.39624i	−0.147279	+	0.147279i
$892$		0			0
$893$	−33.8085	+	33.8085i	−1.13136	+	1.13136i
$894$		0			0
$895$	−1.45287	−	29.2847i	−0.0485641	−	0.978879i
$896$		0			0
$897$			0.165936i			0.00554046i
$898$		0			0
$899$	−11.4069	−	11.4069i	−0.380440	−	0.380440i
$900$		0			0
$901$	−12.7484	+	12.7484i	−0.424710	+	0.424710i
$902$		0			0
$903$	−9.77640			−0.325338
$904$		0			0
$905$	−33.3865	+	1.65637i	−1.10980	+	0.0550595i
$906$		0			0
$907$	−13.1614	−	13.1614i	−0.437018	−	0.437018i	0.453989	−	0.891007i	$-0.350001\pi$
$907$	−13.1614	−	13.1614i	−0.437018	−	0.437018i	−0.891007	+	0.453989i	$0.850001\pi$
$908$		0			0
$909$	10.0764	+	10.0764i	0.334215	+	0.334215i
$910$		0			0
$911$	−4.85931			−0.160996			−0.0804981	−	0.996755i	$-0.525651\pi$
$911$	−4.85931			−0.160996			−0.0804981	+	0.996755i	$0.525651\pi$
$912$		0			0
$913$			40.1517i			1.32883i
$914$		0			0
$915$	0.495354	+	0.448526i	0.0163759	+	0.0148278i
$916$		0			0
$917$	−10.2375	−	10.2375i	−0.338071	−	0.338071i
$918$		0			0
$919$		−	37.6319i		−	1.24136i	−0.784063	−	0.620681i	$-0.786856\pi$
$919$		−	37.6319i		−	1.24136i	0.784063	−	0.620681i	$-0.213144\pi$
$920$		0			0
$921$		−	17.3021i		−	0.570123i
$922$		0			0
$923$	−6.65767	−	6.65767i	−0.219140	−	0.219140i
$924$		0			0
$925$	−23.5782	+	28.7869i	−0.775246	+	0.946506i
$926$		0			0
$927$			4.71475i			0.154853i
$928$		0			0
$929$	37.6717			1.23597			0.617984	−	0.786191i	$-0.287950\pi$
$929$	37.6717			1.23597			0.617984	+	0.786191i	$0.287950\pi$
$930$		0			0
$931$	1.32959	+	1.32959i	0.0435755	+	0.0435755i
$932$		0			0
$933$	−13.7797	−	13.7797i	−0.451126	−	0.451126i
$934$		0			0
$935$	−3.03387	−	61.1521i	−0.0992182	−	1.99989i
$936$		0			0
$937$	−22.1390			−0.723251			−0.361625	−	0.932323i	$-0.617778\pi$
$937$	−22.1390			−0.723251			−0.361625	+	0.932323i	$0.617778\pi$
$938$		0			0
$939$	−6.88321	+	6.88321i	−0.224625	+	0.224625i
$940$		0			0
$941$	6.24976	+	6.24976i	0.203736	+	0.203736i	0.801599	−	0.597862i	$-0.203983\pi$
$941$	6.24976	+	6.24976i	0.203736	+	0.203736i	−0.597862	+	0.801599i	$0.703983\pi$
$942$		0			0
$943$		−	1.45171i		−	0.0472742i
$944$		0			0
$945$	0.286945	+	5.78380i	0.00933433	+	0.188147i
$946$		0			0
$947$	−4.23108	+	4.23108i	−0.137492	+	0.137492i	−0.772503	−	0.635011i	$-0.780995\pi$
$947$	−4.23108	+	4.23108i	−0.137492	+	0.137492i	0.635011	+	0.772503i	$0.280995\pi$
$948$		0			0
$949$	4.41104	−	4.41104i	0.143189	−	0.143189i
$950$		0			0
$951$			11.9736i			0.388269i
$952$		0			0
$953$	−0.585699			−0.0189726			−0.00948632	−	0.999955i	$-0.503020\pi$
$953$	−0.585699			−0.0189726			−0.00948632	+	0.999955i	$0.503020\pi$
$954$		0			0
$955$	−13.8071	−	12.5019i	−0.446789	−	0.404552i
$956$		0			0
$957$	23.2344	−	23.2344i	0.751060	−	0.751060i
$958$		0			0
$959$	−13.4544			−0.434464
$960$		0			0
$961$	−21.6833			−0.699461
$962$		0			0
$963$	−12.9687	+	12.9687i	−0.417910	+	0.417910i
$964$		0			0
$965$	8.60594	−	9.50443i	0.277035	−	0.305958i
$966$		0			0
$967$	41.5832			1.33722			0.668612	−	0.743611i	$-0.266889\pi$
$967$	41.5832			1.33722			0.668612	+	0.743611i	$0.266889\pi$
$968$		0			0
$969$			28.2573i			0.907756i
$970$		0			0
$971$	18.8728	−	18.8728i	0.605656	−	0.605656i	−0.336152	−	0.941808i	$-0.609126\pi$
$971$	18.8728	−	18.8728i	0.605656	−	0.605656i	0.941808	+	0.336152i	$0.109126\pi$
$972$		0			0
$973$	−2.53027	+	2.53027i	−0.0811168	+	0.0811168i
$974$		0			0
$975$	2.93745	−	0.292184i	0.0940737	−	0.00935739i
$976$		0			0
$977$			17.3929i			0.556448i	0.960516	+	0.278224i	$0.0897457\pi$
$977$			17.3929i			0.556448i	−0.960516	+	0.278224i	$0.910254\pi$
$978$		0			0
$979$	45.1692	+	45.1692i	1.44361	+	1.44361i
$980$		0			0
$981$	0.382902	−	0.382902i	0.0122251	−	0.0122251i
$982$		0			0
$983$	−28.6927			−0.915154			−0.457577	−	0.889170i	$-0.651283\pi$
$983$	−28.6927			−0.915154			−0.457577	+	0.889170i	$0.651283\pi$
$984$		0			0
$985$	−0.506495	−	10.2091i	−0.0161383	−	0.325290i
$986$		0			0
$987$	−13.6465	−	13.6465i	−0.434373	−	0.434373i
$988$		0			0
$989$	0.750248	+	0.750248i	0.0238565	+	0.0238565i
$990$		0			0
$991$	−5.67944			−0.180413			−0.0902066	−	0.995923i	$-0.528753\pi$
$991$	−5.67944			−0.180413			−0.0902066	+	0.995923i	$0.528753\pi$
$992$		0			0
$993$			10.0629i			0.319337i
$994$		0			0
$995$	−28.6061	+	31.5927i	−0.906875	+	1.00156i
$996$		0			0
$997$	25.4723	+	25.4723i	0.806717	+	0.806717i	0.984135	−	0.177419i	$-0.0567747\pi$
$997$	25.4723	+	25.4723i	0.806717	+	0.806717i	−0.177419	+	0.984135i	$0.556775\pi$
$998$		0			0
$999$			7.44208i			0.235457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.b.289.3		48
4.3	odd	2		1920.2.bl.a.289.22		48
5.4	even	2	inner	1920.2.bl.b.289.22		48
8.3	odd	2		240.2.bl.a.109.15	yes	48
8.5	even	2		960.2.bl.a.529.22		48
16.3	odd	4		240.2.bl.a.229.10	yes	48
16.5	even	4	inner	1920.2.bl.b.1249.22		48
16.11	odd	4		1920.2.bl.a.1249.3		48
16.13	even	4		960.2.bl.a.49.4		48
20.19	odd	2		1920.2.bl.a.289.3		48
24.11	even	2		720.2.bm.h.109.10		48
40.19	odd	2		240.2.bl.a.109.10	✓	48
40.29	even	2		960.2.bl.a.529.4		48
48.35	even	4		720.2.bm.h.469.15		48
80.19	odd	4		240.2.bl.a.229.15	yes	48
80.29	even	4		960.2.bl.a.49.22		48
80.59	odd	4		1920.2.bl.a.1249.22		48
80.69	even	4	inner	1920.2.bl.b.1249.3		48
120.59	even	2		720.2.bm.h.109.15		48
240.179	even	4		720.2.bm.h.469.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.10	✓	48	40.19	odd	2
240.2.bl.a.109.15	yes	48	8.3	odd	2
240.2.bl.a.229.10	yes	48	16.3	odd	4
240.2.bl.a.229.15	yes	48	80.19	odd	4
720.2.bm.h.109.10		48	24.11	even	2
720.2.bm.h.109.15		48	120.59	even	2
720.2.bm.h.469.10		48	240.179	even	4
720.2.bm.h.469.15		48	48.35	even	4
960.2.bl.a.49.4		48	16.13	even	4
960.2.bl.a.49.22		48	80.29	even	4
960.2.bl.a.529.4		48	40.29	even	2
960.2.bl.a.529.22		48	8.5	even	2
1920.2.bl.a.289.3		48	20.19	odd	2
1920.2.bl.a.289.22		48	4.3	odd	2
1920.2.bl.a.1249.3		48	16.11	odd	4
1920.2.bl.a.1249.22		48	80.59	odd	4
1920.2.bl.b.289.3		48	1.1	even	1	trivial
1920.2.bl.b.289.22		48	5.4	even	2	inner
1920.2.bl.b.1249.3		48	80.69	even	4	inner
1920.2.bl.b.1249.22		48	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.65754 - 1.50085i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.65754 - 1.50085i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +(4.39624 - 4.39624i) q^{11} +(-0.417468 + 0.417468i) q^{13} +(2.23332 - 0.110799i) q^{15} +4.40417i q^{17} +(-4.53682 - 4.53682i) q^{19} +(1.83125 - 1.83125i) q^{21} -0.281063 q^{23} +(0.494901 + 4.97545i) q^{25} +(0.707107 + 0.707107i) q^{27} +(-3.73710 - 3.73710i) q^{29} +3.05233 q^{31} +6.21722i q^{33} +(4.29266 + 3.88686i) q^{35} +(5.26234 + 5.26234i) q^{37} -0.590389i q^{39} +5.16508i q^{41} +(-2.66933 - 2.66933i) q^{43} +(-1.50085 + 1.65754i) q^{45} -7.45202i q^{47} -0.293066 q^{49} +(-3.11422 - 3.11422i) q^{51} +(2.89462 + 2.89462i) q^{53} +(-13.8850 + 0.688864i) q^{55} +6.41604 q^{57} +(-4.60721 + 4.60721i) q^{59} +(0.211318 + 0.211318i) q^{61} +2.58977i q^{63} +(1.31853 - 0.0654147i) q^{65} +(-7.17140 + 7.17140i) q^{67} +(0.198741 - 0.198741i) q^{69} +15.9477i q^{71} -10.5662 q^{73} +(-3.86812 - 3.16822i) q^{75} +(-11.3853 + 11.3853i) q^{77} -4.53907 q^{79} -1.00000 q^{81} +(-4.56660 + 4.56660i) q^{83} +(6.61000 - 7.30010i) q^{85} +5.28505 q^{87} +10.2745i q^{89} +(1.08115 - 1.08115i) q^{91} +(-2.15832 + 2.15832i) q^{93} +(0.710893 + 14.3291i) q^{95} -6.78053i q^{97} +(-4.39624 - 4.39624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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