LMFDB - Embedded newform 1080.2.m.c.539.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(539,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1080.539");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			539.16
Character	$\chi$	$=$	1080.539
Dual form			1080.2.m.c.539.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.957850 + 1.04044i) q^{2} +(-0.165046 - 1.99318i) q^{4} +(0.214370 - 2.22577i) q^{5} -2.80642 q^{7} +(2.23188 + 1.73744i) q^{8} +O(q^{10})$	\(q+(-0.957850 + 1.04044i) q^{2} +(-0.165046 - 1.99318i) q^{4} +(0.214370 - 2.22577i) q^{5} -2.80642 q^{7} +(2.23188 + 1.73744i) q^{8} +(2.11045 + 2.35499i) q^{10} +2.27115i q^{11} -3.91324 q^{13} +(2.68813 - 2.91992i) q^{14} +(-3.94552 + 0.657933i) q^{16} +1.00493 q^{17} +1.82621 q^{19} +(-4.47173 - 0.0599231i) q^{20} +(-2.36300 - 2.17542i) q^{22} -1.93778i q^{23} +(-4.90809 - 0.954277i) q^{25} +(3.74830 - 4.07151i) q^{26} +(0.463189 + 5.59370i) q^{28} +7.74448 q^{29} +3.94024i q^{31} +(3.09467 - 4.73529i) q^{32} +(-0.962571 + 1.04557i) q^{34} +(-0.601613 + 6.24644i) q^{35} -8.82415 q^{37} +(-1.74923 + 1.90007i) q^{38} +(4.34560 - 4.59519i) q^{40} +2.23967i q^{41} +11.7263i q^{43} +(4.52680 - 0.374844i) q^{44} +(2.01615 + 1.85610i) q^{46} +6.26994i q^{47} +0.875992 q^{49} +(5.69409 - 4.19254i) q^{50} +(0.645866 + 7.79979i) q^{52} +6.73830i q^{53} +(5.05505 + 0.486866i) q^{55} +(-6.26359 - 4.87600i) q^{56} +(-7.41805 + 8.05769i) q^{58} +11.4611i q^{59} -4.08558i q^{61} +(-4.09960 - 3.77416i) q^{62} +(1.96257 + 7.75553i) q^{64} +(-0.838883 + 8.70998i) q^{65} +6.94219i q^{67} +(-0.165860 - 2.00300i) q^{68} +(-5.92282 - 6.60910i) q^{70} -7.36200 q^{71} +5.13736i q^{73} +(8.45222 - 9.18104i) q^{74} +(-0.301409 - 3.63996i) q^{76} -6.37379i q^{77} -4.14620i q^{79} +(0.618605 + 8.92285i) q^{80} +(-2.33025 - 2.14527i) q^{82} +14.8166 q^{83} +(0.215427 - 2.23674i) q^{85} +(-12.2005 - 11.2320i) q^{86} +(-3.94599 + 5.06893i) q^{88} +4.82493i q^{89} +10.9822 q^{91} +(-3.86233 + 0.319823i) q^{92} +(-6.52352 - 6.00566i) q^{94} +(0.391485 - 4.06472i) q^{95} -14.9168i q^{97} +(-0.839069 + 0.911421i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4}+O(q^{10}) $ 48 * q + 4 * q^4	$ 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.957850	+	1.04044i	−0.677302	+	0.735705i
$2$	−0.957850	+	1.04044i	−0.677302	+	0.735705i
$3$		0			0
$3$		0			0
$4$	−0.165046	−	1.99318i	−0.0825231	−	0.996589i
$5$	0.214370	−	2.22577i	0.0958692	−	0.995394i
$5$	0.214370	−	2.22577i	0.0958692	−	0.995394i
$6$		0			0
$7$	−2.80642			−1.06073			−0.530363	−	0.847770i	$-0.677945\pi$
$7$	−2.80642			−1.06073			−0.530363	+	0.847770i	$0.677945\pi$
$8$	2.23188	+	1.73744i	0.789089	+	0.614279i
$9$		0			0
$10$	2.11045	+	2.35499i	0.667384	+	0.744714i
$11$			2.27115i			0.684777i	0.939559	+	0.342388i	$0.111236\pi$
$11$			2.27115i			0.684777i	−0.939559	+	0.342388i	$0.888764\pi$
$12$		0			0
$13$	−3.91324			−1.08534			−0.542669	−	0.839946i	$-0.682586\pi$
$13$	−3.91324			−1.08534			−0.542669	+	0.839946i	$0.682586\pi$
$14$	2.68813	−	2.91992i	0.718433	−	0.780382i
$15$		0			0
$16$	−3.94552	+	0.657933i	−0.986380	+	0.164483i
$17$	1.00493			0.243731			0.121866	−	0.992547i	$-0.461112\pi$
$17$	1.00493			0.243731			0.121866	+	0.992547i	$0.461112\pi$
$18$		0			0
$19$	1.82621			0.418961			0.209481	−	0.977813i	$-0.432823\pi$
$19$	1.82621			0.418961			0.209481	+	0.977813i	$0.432823\pi$
$20$	−4.47173	−	0.0599231i	−0.999910	−	0.0133992i
$21$		0			0
$22$	−2.36300	−	2.17542i	−0.503794	−	0.463801i
$23$		−	1.93778i		−	0.404054i	−0.979380	−	0.202027i	$-0.935247\pi$
$23$		−	1.93778i		−	0.404054i	0.979380	−	0.202027i	$-0.0647529\pi$
$24$		0			0
$25$	−4.90809	−	0.954277i	−0.981618	−	0.190855i
$26$	3.74830	−	4.07151i	0.735102	−	0.798489i
$27$		0			0
$28$	0.463189	+	5.59370i	0.0875345	+	1.05711i
$29$	7.74448			1.43811			0.719057	−	0.694951i	$-0.244574\pi$
$29$	7.74448			1.43811			0.719057	+	0.694951i	$0.244574\pi$
$30$		0			0
$31$			3.94024i			0.707689i	0.935304	+	0.353844i	$0.115126\pi$
$31$			3.94024i			0.707689i	−0.935304	+	0.353844i	$0.884874\pi$
$32$	3.09467	−	4.73529i	0.547066	−	0.837089i
$33$		0			0
$34$	−0.962571	+	1.04557i	−0.165080	+	0.179314i
$35$	−0.601613	+	6.24644i	−0.101691	+	1.05584i
$36$		0			0
$37$	−8.82415			−1.45068			−0.725341	−	0.688390i	$-0.758318\pi$
$37$	−8.82415			−1.45068			−0.725341	+	0.688390i	$0.758318\pi$
$38$	−1.74923	+	1.90007i	−0.283763	+	0.308232i
$39$		0			0
$40$	4.34560	−	4.59519i	0.687099	−	0.726563i
$41$			2.23967i			0.349778i	0.984588	+	0.174889i	$0.0559566\pi$
$41$			2.23967i			0.349778i	−0.984588	+	0.174889i	$0.944043\pi$
$42$		0			0
$43$			11.7263i			1.78824i	0.447829	+	0.894119i	$0.352197\pi$
$43$			11.7263i			1.78824i	−0.447829	+	0.894119i	$0.647803\pi$
$44$	4.52680	−	0.374844i	0.682441	−	0.0565099i
$45$		0			0
$46$	2.01615	+	1.85610i	0.297265	+	0.273667i
$47$			6.26994i			0.914564i	0.889322	+	0.457282i	$0.151177\pi$
$47$			6.26994i			0.914564i	−0.889322	+	0.457282i	$0.848823\pi$
$48$		0			0
$49$	0.875992			0.125142
$50$	5.69409	−	4.19254i	0.805265	−	0.592914i
$51$		0			0
$52$	0.645866	+	7.79979i	0.0895655	+	1.08164i
$53$			6.73830i			0.925576i	0.886469	+	0.462788i	$0.153151\pi$
$53$			6.73830i			0.925576i	−0.886469	+	0.462788i	$0.846849\pi$
$54$		0			0
$55$	5.05505	+	0.486866i	0.681623	+	0.0656490i
$56$	−6.26359	−	4.87600i	−0.837008	−	0.651583i
$57$		0			0
$58$	−7.41805	+	8.05769i	−0.974038	+	1.05803i
$59$			11.4611i			1.49211i	0.665885	+	0.746055i	$0.268054\pi$
$59$			11.4611i			1.49211i	−0.665885	+	0.746055i	$0.731946\pi$
$60$		0			0
$61$		−	4.08558i		−	0.523105i	−0.965189	−	0.261553i	$-0.915765\pi$
$61$		−	4.08558i		−	0.523105i	0.965189	−	0.261553i	$-0.0842345\pi$
$62$	−4.09960	−	3.77416i	−0.520650	−	0.479319i
$63$		0			0
$64$	1.96257	+	7.75553i	0.245321	+	0.969442i
$65$	−0.838883	+	8.70998i	−0.104051	+	1.08034i
$66$		0			0
$67$			6.94219i			0.848123i	0.905633	+	0.424062i	$0.139396\pi$
$67$			6.94219i			0.848123i	−0.905633	+	0.424062i	$0.860604\pi$
$68$	−0.165860	−	2.00300i	−0.0201135	−	0.242900i
$69$		0			0
$70$	−5.92282	−	6.60910i	−0.707912	−	0.789938i
$71$	−7.36200			−0.873709			−0.436854	−	0.899532i	$-0.643908\pi$
$71$	−7.36200			−0.873709			−0.436854	+	0.899532i	$0.643908\pi$
$72$		0			0
$73$			5.13736i			0.601283i	0.953737	+	0.300641i	$0.0972007\pi$
$73$			5.13736i			0.601283i	−0.953737	+	0.300641i	$0.902799\pi$
$74$	8.45222	−	9.18104i	0.982550	−	1.06727i
$75$		0			0
$76$	−0.301409	−	3.63996i	−0.0345740	−	0.417532i
$77$		−	6.37379i		−	0.726361i
$78$		0			0
$79$		−	4.14620i		−	0.466484i	−0.972419	−	0.233242i	$-0.925066\pi$
$79$		−	4.14620i		−	0.466484i	0.972419	−	0.233242i	$-0.0749335\pi$
$80$	0.618605	+	8.92285i	0.0691622	+	0.997605i
$81$		0			0
$82$	−2.33025	−	2.14527i	−0.257333	−	0.236905i
$83$	14.8166			1.62633			0.813167	−	0.582031i	$-0.197742\pi$
$83$	14.8166			1.62633			0.813167	+	0.582031i	$0.197742\pi$
$84$		0			0
$85$	0.215427	−	2.23674i	0.0233663	−	0.242608i
$86$	−12.2005	−	11.2320i	−1.31562	−	1.21118i
$87$		0			0
$88$	−3.94599	+	5.06893i	−0.420644	+	0.540350i
$89$			4.82493i			0.511442i	0.966751	+	0.255721i	$0.0823128\pi$
$89$			4.82493i			0.511442i	−0.966751	+	0.255721i	$0.917687\pi$
$90$		0			0
$91$	10.9822			1.15125
$92$	−3.86233	+	0.319823i	−0.402676	+	0.0333438i
$93$		0			0
$94$	−6.52352	−	6.00566i	−0.672849	−	0.619437i
$95$	0.391485	−	4.06472i	0.0401655	−	0.417031i
$96$		0			0
$97$		−	14.9168i		−	1.51457i	−0.653084	−	0.757285i	$-0.726525\pi$
$97$		−	14.9168i		−	1.51457i	0.653084	−	0.757285i	$-0.273475\pi$
$98$	−0.839069	+	0.911421i	−0.0847588	+	0.0920674i
$99$		0			0
$100$	−1.09198	+	9.94020i	−0.109198	+	0.994020i
$101$	−14.9650			−1.48907			−0.744534	−	0.667584i	$-0.767328\pi$
$101$	−14.9650			−1.48907			−0.744534	+	0.667584i	$0.767328\pi$
$102$		0			0
$103$	10.5719			1.04168			0.520839	−	0.853655i	$-0.325619\pi$
$103$	10.5719			1.04168			0.520839	+	0.853655i	$0.325619\pi$
$104$	−8.73389	−	6.79905i	−0.856428	−	0.666701i
$105$		0			0
$106$	−7.01082	−	6.45428i	−0.680951	−	0.626895i
$107$	−15.5918			−1.50731			−0.753657	−	0.657268i	$-0.771712\pi$
$107$	−15.5918			−1.50731			−0.753657	+	0.657268i	$0.771712\pi$
$108$		0			0
$109$			10.9241i			1.04634i	0.852227	+	0.523172i	$0.175251\pi$
$109$			10.9241i			1.04634i	−0.852227	+	0.523172i	$0.824749\pi$
$110$	−5.34854	+	4.79315i	−0.509963	+	0.457009i
$111$		0			0
$112$	11.0728	−	1.84644i	1.04628	−	0.174472i
$113$	−12.8613			−1.20989			−0.604943	−	0.796269i	$-0.706804\pi$
$113$	−12.8613			−1.20989			−0.604943	+	0.796269i	$0.706804\pi$
$114$		0			0
$115$	−4.31304	−	0.415401i	−0.402193	−	0.0387364i
$116$	−1.27820	−	15.4361i	−0.118678	−	1.43321i
$117$		0			0
$118$	−11.9246	−	10.9780i	−1.09775	−	1.01061i
$119$	−2.82025			−0.258532
$120$		0			0
$121$	5.84189			0.531081
$122$	4.25082	+	3.91338i	0.384851	+	0.354301i
$123$		0			0
$124$	7.85361	−	0.650323i	0.705275	−	0.0584007i
$125$	−3.17615	+	10.7197i	−0.284083	+	0.958800i
$126$		0			0
$127$	5.75296			0.510493			0.255246	−	0.966876i	$-0.417843\pi$
$127$	5.75296			0.510493			0.255246	+	0.966876i	$0.417843\pi$
$128$	−9.94905	−	5.38669i	−0.879380	−	0.476121i
$129$		0			0
$130$	−8.25872	−	9.21566i	−0.724337	−	0.808267i
$131$		−	5.24118i		−	0.457924i	−0.973435	−	0.228962i	$-0.926467\pi$
$131$		−	5.24118i		−	0.457924i	0.973435	−	0.228962i	$-0.0735332\pi$
$132$		0			0
$133$	−5.12511			−0.444403
$134$	−7.22296	−	6.64958i	−0.623968	−	0.574436i
$135$		0			0
$136$	2.24288	+	1.74601i	0.192325	+	0.149719i
$137$	20.3736			1.74063			0.870317	−	0.492493i	$-0.163914\pi$
$137$	20.3736			1.74063			0.870317	+	0.492493i	$0.163914\pi$
$138$		0			0
$139$	−19.3603			−1.64212			−0.821058	−	0.570844i	$-0.806616\pi$
$139$	−19.3603			−1.64212			−0.821058	+	0.570844i	$0.806616\pi$
$140$	12.5496	+	0.168170i	1.06063	+	0.0142129i
$141$		0			0
$142$	7.05169	−	7.65975i	0.591765	−	0.642792i
$143$		−	8.88755i		−	0.743215i
$144$		0			0
$145$	1.66019	−	17.2374i	0.137871	−	1.43149i
$146$	−5.34514	−	4.92082i	−0.442367	−	0.407250i
$147$		0			0
$148$	1.45639	+	17.5881i	0.119715	+	1.44573i
$149$	−3.99973			−0.327671			−0.163835	−	0.986488i	$-0.552387\pi$
$149$	−3.99973			−0.327671			−0.163835	+	0.986488i	$0.552387\pi$
$150$		0			0
$151$		−	15.5259i		−	1.26348i	−0.775179	−	0.631741i	$-0.782341\pi$
$151$		−	15.5259i		−	1.26348i	0.775179	−	0.631741i	$-0.217659\pi$
$152$	4.07588	+	3.17294i	0.330597	+	0.257359i
$153$		0			0
$154$	6.63157	+	6.10514i	0.534387	+	0.491966i
$155$	8.77007	+	0.844671i	0.704429	+	0.0678456i
$156$		0			0
$157$	−16.6637			−1.32991			−0.664953	−	0.746885i	$-0.731549\pi$
$157$	−16.6637			−1.32991			−0.664953	+	0.746885i	$0.731549\pi$
$158$	4.31389	+	3.97144i	0.343195	+	0.315951i
$159$		0			0
$160$	−9.87626	−	7.90313i	−0.780787	−	0.624798i
$161$			5.43821i			0.428591i
$162$		0			0
$163$			15.3943i			1.20578i	0.797826	+	0.602888i	$0.205983\pi$
$163$			15.3943i			1.20578i	−0.797826	+	0.602888i	$0.794017\pi$
$164$	4.46406	−	0.369649i	0.348585	−	0.0288648i
$165$		0			0
$166$	−14.1921	+	15.4158i	−1.10152	+	1.19650i
$167$			6.44853i			0.499002i	0.968374	+	0.249501i	$0.0802667\pi$
$167$			6.44853i			0.499002i	−0.968374	+	0.249501i	$0.919733\pi$
$168$		0			0
$169$	2.31348			0.177960
$170$	2.12085	+	2.36660i	0.162662	+	0.181510i
$171$		0			0
$172$	23.3725	−	1.93538i	1.78214	−	0.147571i
$173$		−	7.88649i		−	0.599599i	−0.954002	−	0.299799i	$-0.903080\pi$
$173$		−	7.88649i		−	0.599599i	0.954002	−	0.299799i	$-0.0969198\pi$
$174$		0			0
$175$	13.7742	+	2.67810i	1.04123	+	0.202445i
$176$	−1.49426	−	8.96086i	−0.112634	−	0.675450i
$177$		0			0
$178$	−5.02007	−	4.62156i	−0.376270	−	0.346401i
$179$			14.3041i			1.06914i	0.845124	+	0.534571i	$0.179527\pi$
$179$			14.3041i			1.06914i	−0.845124	+	0.534571i	$0.820473\pi$
$180$		0			0
$181$			22.0087i			1.63589i	0.575293	+	0.817947i	$0.304888\pi$
$181$			22.0087i			1.63589i	−0.575293	+	0.817947i	$0.695112\pi$
$182$	−10.5193	+	11.4264i	−0.779743	+	0.846979i
$183$		0			0
$184$	3.36678	−	4.32488i	0.248202	−	0.318835i
$185$	−1.89164	+	19.6405i	−0.139076	+	1.44400i
$186$		0			0
$187$			2.28234i			0.166901i
$188$	12.4971	−	1.03483i	0.911445	−	0.0754727i
$189$		0			0
$190$	3.85413	+	4.30071i	0.279608	+	0.312006i
$191$	3.10330			0.224547			0.112273	−	0.993677i	$-0.464187\pi$
$191$	3.10330			0.224547			0.112273	+	0.993677i	$0.464187\pi$
$192$		0			0
$193$		−	19.0217i		−	1.36921i	−0.728912	−	0.684607i	$-0.759974\pi$
$193$		−	19.0217i		−	1.36921i	0.728912	−	0.684607i	$-0.240026\pi$
$194$	15.5201	+	14.2880i	1.11428	+	1.02582i
$195$		0			0
$196$	−0.144579	−	1.74601i	−0.0103271	−	0.124715i
$197$		−	11.6269i		−	0.828382i	−0.910190	−	0.414191i	$-0.864065\pi$
$197$		−	11.6269i		−	0.828382i	0.910190	−	0.414191i	$-0.135935\pi$
$198$		0			0
$199$		−	5.80420i		−	0.411449i	−0.978610	−	0.205725i	$-0.934045\pi$
$199$		−	5.80420i		−	0.411449i	0.978610	−	0.205725i	$-0.0659551\pi$
$200$	−9.29626	−	10.6574i	−0.657345	−	0.753590i
$201$		0			0
$202$	14.3342	−	15.5702i	1.00855	−	1.09552i
$203$	−21.7343			−1.52545
$204$		0			0
$205$	4.98499	+	0.480119i	0.348167	+	0.0335329i
$206$	−10.1263	+	10.9994i	−0.705531	+	0.766367i
$207$		0			0
$208$	15.4398	−	2.57465i	1.07056	−	0.178520i
$209$			4.14759i			0.286895i
$210$		0			0
$211$	−8.88390			−0.611593			−0.305797	−	0.952097i	$-0.598923\pi$
$211$	−8.88390			−0.611593			−0.305797	+	0.952097i	$0.598923\pi$
$212$	13.4306	−	1.11213i	0.922419	−	0.0763814i
$213$		0			0
$214$	14.9346	−	16.2224i	1.02091	−	1.10894i
$215$	26.1000	+	2.51376i	1.78000	+	0.171437i
$216$		0			0
$217$		−	11.0580i		−	0.750665i
$218$	−11.3660	−	10.4637i	−0.769800	−	0.708691i
$219$		0			0
$220$	0.136094	−	10.1560i	0.00917548	−	0.684715i
$221$	−3.93253			−0.264531
$222$		0			0
$223$	17.6483			1.18182			0.590909	−	0.806738i	$-0.298769\pi$
$223$	17.6483			1.18182			0.590909	+	0.806738i	$0.298769\pi$
$224$	−8.68495	+	13.2892i	−0.580288	+	0.887923i
$225$		0			0
$226$	12.3192	−	13.3814i	0.819458	−	0.890119i
$227$	13.0114			0.863599			0.431799	−	0.901970i	$-0.357879\pi$
$227$	13.0114			0.863599			0.431799	+	0.901970i	$0.357879\pi$
$228$		0			0
$229$		−	20.6611i		−	1.36532i	−0.730735	−	0.682662i	$-0.760822\pi$
$229$		−	20.6611i		−	1.36532i	0.730735	−	0.682662i	$-0.239178\pi$
$230$	4.56345	−	4.08958i	0.300905	−	0.269659i
$231$		0			0
$232$	17.2847	+	13.4556i	1.13480	+	0.883404i
$233$	8.92752			0.584861			0.292431	−	0.956287i	$-0.405536\pi$
$233$	8.92752			0.584861			0.292431	+	0.956287i	$0.405536\pi$
$234$		0			0
$235$	13.9554	+	1.34409i	0.910352	+	0.0876786i
$236$	22.8440	−	1.89161i	1.48702	−	0.123134i
$237$		0			0
$238$	2.70138	−	2.93431i	0.175104	−	0.190203i
$239$	−3.02879			−0.195916			−0.0979580	−	0.995191i	$-0.531231\pi$
$239$	−3.02879			−0.195916			−0.0979580	+	0.995191i	$0.531231\pi$
$240$		0			0
$241$	−17.1141			−1.10242			−0.551209	−	0.834367i	$-0.685833\pi$
$241$	−17.1141			−1.10242			−0.551209	+	0.834367i	$0.685833\pi$
$242$	−5.59565	+	6.07816i	−0.359702	+	0.390719i
$243$		0			0
$244$	−8.14330	+	0.674310i	−0.521321	+	0.0431683i
$245$	0.187787	−	1.94976i	0.0119972	−	0.124565i
$246$		0			0
$247$	−7.14640			−0.454715
$248$	−6.84596	+	8.79415i	−0.434719	+	0.558429i
$249$		0			0
$250$	−8.11098	−	13.5725i	−0.512983	−	0.858399i
$251$		−	24.5888i		−	1.55203i	−0.630713	−	0.776016i	$-0.717237\pi$
$251$		−	24.5888i		−	1.55203i	0.630713	−	0.776016i	$-0.282763\pi$
$252$		0			0
$253$	4.40098			0.276687
$254$	−5.51047	+	5.98563i	−0.345758	+	0.375572i
$255$		0			0
$256$	15.1342	−	5.19178i	0.945890	−	0.324486i
$257$	−9.91878			−0.618716			−0.309358	−	0.950946i	$-0.600114\pi$
$257$	−9.91878			−0.618716			−0.309358	+	0.950946i	$0.600114\pi$
$258$		0			0
$259$	24.7643			1.53878
$260$	17.4990	+	0.234494i	1.08524	+	0.0145427i
$261$		0			0
$262$	5.45315	+	5.02027i	0.336897	+	0.310153i
$263$			3.87555i			0.238977i	0.992836	+	0.119488i	$0.0381254\pi$
$263$			3.87555i			0.238977i	−0.992836	+	0.119488i	$0.961875\pi$
$264$		0			0
$265$	14.9979	+	1.44449i	0.921313	+	0.0887343i
$266$	4.90909	−	5.33239i	0.300995	−	0.326950i
$267$		0			0
$268$	13.8370	−	1.14578i	0.845230	−	0.0699898i
$269$	22.5216			1.37317			0.686585	−	0.727050i	$-0.259109\pi$
$269$	22.5216			1.37317			0.686585	+	0.727050i	$0.259109\pi$
$270$		0			0
$271$			18.5544i			1.12710i	0.826081	+	0.563551i	$0.190565\pi$
$271$			18.5544i			1.12710i	−0.826081	+	0.563551i	$0.809435\pi$
$272$	−3.96497	+	0.661176i	−0.240411	+	0.0400897i
$273$		0			0
$274$	−19.5148	+	21.1976i	−1.17893	+	1.28059i
$275$	2.16730	−	11.1470i	0.130693	−	0.672189i
$276$		0			0
$277$	−23.9192			−1.43717			−0.718584	−	0.695440i	$-0.755209\pi$
$277$	−23.9192			−1.43717			−0.718584	+	0.695440i	$0.755209\pi$
$278$	18.5442	−	20.1433i	1.11221	−	1.20811i
$279$		0			0
$280$	−12.1956	+	12.8960i	−0.728825	+	0.770685i
$281$		−	23.9246i		−	1.42722i	−0.700541	−	0.713612i	$-0.747058\pi$
$281$		−	23.9246i		−	1.42722i	0.700541	−	0.713612i	$-0.252942\pi$
$282$		0			0
$283$			2.86207i			0.170132i	0.996375	+	0.0850662i	$0.0271102\pi$
$283$			2.86207i			0.170132i	−0.996375	+	0.0850662i	$0.972890\pi$
$284$	1.21507	+	14.6738i	0.0721012	+	0.870729i
$285$		0			0
$286$	9.24700	+	8.51295i	0.546787	+	0.503381i
$287$		−	6.28546i		−	0.371019i
$288$		0			0
$289$	−15.9901			−0.940595
$290$	16.3444	+	18.2382i	0.959774	+	1.07098i
$291$		0			0
$292$	10.2397	−	0.847902i	0.599232	−	0.0496197i
$293$			17.3345i			1.01269i	0.862330	+	0.506347i	$0.169004\pi$
$293$			17.3345i			1.01269i	−0.862330	+	0.506347i	$0.830996\pi$
$294$		0			0
$295$	25.5098	+	2.45692i	1.48524	+	0.143047i
$296$	−19.6944	−	15.3315i	−1.14472	−	0.891124i
$297$		0			0
$298$	3.83114	−	4.16150i	0.221932	−	0.241069i
$299$			7.58299i			0.438536i
$300$		0			0
$301$		−	32.9088i		−	1.89683i
$302$	16.1539	+	14.8715i	0.929550	+	0.855759i
$303$		0			0
$304$	−7.20534	+	1.20152i	−0.413255	+	0.0689121i
$305$	−9.09356	−	0.875827i	−0.520696	−	0.0501497i
$306$		0			0
$307$		−	4.51078i		−	0.257444i	−0.991681	−	0.128722i	$-0.958913\pi$
$307$		−	4.51078i		−	0.257444i	0.991681	−	0.128722i	$-0.0410875\pi$
$308$	−12.7041	+	1.05197i	−0.723884	+	0.0599416i
$309$		0			0
$310$	−9.27925	+	8.31570i	−0.527026	+	0.472300i
$311$	1.96277			0.111299			0.0556493	−	0.998450i	$-0.482277\pi$
$311$	1.96277			0.111299			0.0556493	+	0.998450i	$0.482277\pi$
$312$		0			0
$313$			3.22881i			0.182503i	0.995828	+	0.0912516i	$0.0290867\pi$
$313$			3.22881i			0.182503i	−0.995828	+	0.0912516i	$0.970913\pi$
$314$	15.9613	−	17.3376i	0.900749	−	0.978419i
$315$		0			0
$316$	−8.26412	+	0.684316i	−0.464893	+	0.0384958i
$317$			17.6637i			0.992091i	0.868296	+	0.496046i	$0.165215\pi$
$317$			17.6637i			0.992091i	−0.868296	+	0.496046i	$0.834785\pi$
$318$		0			0
$319$			17.5889i			0.984787i
$320$	17.6827	−	2.70567i	0.988495	−	0.151252i
$321$		0			0
$322$	−5.65815	−	5.20899i	−0.315317	−	0.290286i
$323$	1.83521			0.102114
$324$		0			0
$325$	19.2066	+	3.73432i	1.06539	+	0.207143i
$326$	−16.0169	−	14.7454i	−0.887095	−	0.816674i
$327$		0			0
$328$	−3.89130	+	4.99868i	−0.214861	+	0.276006i
$329$		−	17.5961i		−	0.970103i
$330$		0			0
$331$	−11.3298			−0.622741			−0.311371	−	0.950289i	$-0.600788\pi$
$331$	−11.3298			−0.622741			−0.311371	+	0.950289i	$0.600788\pi$
$332$	−2.44542	−	29.5321i	−0.134210	−	1.62079i
$333$		0			0
$334$	−6.70934	−	6.17673i	−0.367119	−	0.337976i
$335$	15.4517	+	1.48820i	0.844217	+	0.0813089i
$336$		0			0
$337$		−	14.3805i		−	0.783355i	−0.920103	−	0.391677i	$-0.871895\pi$
$337$		−	14.3805i		−	0.783355i	0.920103	−	0.391677i	$-0.128105\pi$
$338$	−2.21597	+	2.40704i	−0.120533	+	0.130926i
$339$		0			0
$340$	−4.49378	−	0.0602185i	−0.243709	−	0.00326581i
$341$	−8.94888			−0.484609
$342$		0			0
$343$	17.1865			0.927986
$344$	−20.3737	+	26.1716i	−1.09848	+	1.41108i
$345$		0			0
$346$	8.20545	+	7.55408i	0.441128	+	0.406110i
$347$	−6.09377			−0.327131			−0.163565	−	0.986533i	$-0.552299\pi$
$347$	−6.09377			−0.327131			−0.163565	+	0.986533i	$0.552299\pi$
$348$		0			0
$349$			18.3257i			0.980954i	0.871454	+	0.490477i	$0.163177\pi$
$349$			18.3257i			0.980954i	−0.871454	+	0.490477i	$0.836823\pi$
$350$	−15.9800	+	11.7660i	−0.854167	+	0.628920i
$351$		0			0
$352$	10.7545	+	7.02846i	0.573219	+	0.374618i
$353$	27.9785			1.48915			0.744573	−	0.667541i	$-0.232653\pi$
$353$	27.9785			1.48915			0.744573	+	0.667541i	$0.232653\pi$
$354$		0			0
$355$	−1.57819	+	16.3861i	−0.0837618	+	0.869684i
$356$	9.61695	−	0.796337i	0.509697	−	0.0422058i
$357$		0			0
$358$	−14.8826	−	13.7012i	−0.786572	−	0.724132i
$359$	−25.5787			−1.34999			−0.674996	−	0.737822i	$-0.735855\pi$
$359$	−25.5787			−1.34999			−0.674996	+	0.737822i	$0.735855\pi$
$360$		0			0
$361$	−15.6650			−0.824472
$362$	−22.8988	−	21.0810i	−1.20354	−	1.10799i
$363$		0			0
$364$	−1.81257	−	21.8895i	−0.0950046	−	1.14732i
$365$	11.4346	+	1.10130i	0.598513	+	0.0576445i
$366$		0			0
$367$	−14.7018			−0.767426			−0.383713	−	0.923452i	$-0.625355\pi$
$367$	−14.7018			−0.767426			−0.383713	+	0.923452i	$0.625355\pi$
$368$	1.27493	+	7.64553i	0.0664602	+	0.398551i
$369$		0			0
$370$	−18.6230	−	20.7808i	−0.968162	−	1.08034i
$371$		−	18.9105i		−	0.981783i
$372$		0			0
$373$	10.1670			0.526428			0.263214	−	0.964737i	$-0.415217\pi$
$373$	10.1670			0.526428			0.263214	+	0.964737i	$0.415217\pi$
$374$	−2.37465	−	2.18614i	−0.122790	−	0.113043i
$375$		0			0
$376$	−10.8937	+	13.9937i	−0.561798	+	0.721672i
$377$	−30.3060			−1.56084
$378$		0			0
$379$	21.2106			1.08951			0.544757	−	0.838594i	$-0.316622\pi$
$379$	21.2106			1.08951			0.544757	+	0.838594i	$0.316622\pi$
$380$	−8.16632	−	0.109432i	−0.418923	−	0.00561375i
$381$		0			0
$382$	−2.97250	+	3.22881i	−0.152086	+	0.165200i
$383$			25.4830i			1.30212i	0.759026	+	0.651060i	$0.225676\pi$
$383$			25.4830i			1.30212i	−0.759026	+	0.651060i	$0.774324\pi$
$384$		0			0
$385$	−14.1866	−	1.36635i	−0.723016	−	0.0696357i
$386$	19.7910	+	18.2200i	1.00734	+	0.927372i
$387$		0			0
$388$	−29.7318	+	2.46196i	−1.50940	+	0.124987i
$389$	9.85609			0.499723			0.249862	−	0.968282i	$-0.419615\pi$
$389$	9.85609			0.499723			0.249862	+	0.968282i	$0.419615\pi$
$390$		0			0
$391$		−	1.94733i		−	0.0984806i
$392$	1.95511	+	1.52199i	0.0987479	+	0.0768720i
$393$		0			0
$394$	12.0971	+	11.1368i	0.609444	+	0.561065i
$395$	−9.22849	−	0.888822i	−0.464336	−	0.0447215i
$396$		0			0
$397$	−30.5167			−1.53159			−0.765795	−	0.643085i	$-0.777654\pi$
$397$	−30.5167			−1.53159			−0.765795	+	0.643085i	$0.777654\pi$
$398$	6.03895	+	5.55956i	0.302705	+	0.278675i
$399$		0			0
$400$	19.9928	+	0.535921i	0.999641	+	0.0267960i
$401$		−	23.8072i		−	1.18888i	−0.804142	−	0.594438i	$-0.797375\pi$
$401$		−	23.8072i		−	1.18888i	0.804142	−	0.594438i	$-0.202625\pi$
$402$		0			0
$403$		−	15.4191i		−	0.768082i
$404$	2.46991	+	29.8278i	0.122883	+	1.48399i
$405$		0			0
$406$	20.8182	−	22.6133i	1.03319	−	1.12228i
$407$		−	20.0410i		−	0.993393i
$408$		0			0
$409$	10.7023			0.529197			0.264598	−	0.964359i	$-0.414761\pi$
$409$	10.7023			0.529197			0.264598	+	0.964359i	$0.414761\pi$
$410$	−5.27441	+	4.72672i	−0.260484	+	0.233436i
$411$		0			0
$412$	−1.74485	−	21.0716i	−0.0859625	−	1.03812i
$413$		−	32.1647i		−	1.58272i
$414$		0			0
$415$	3.17624	−	32.9783i	0.155915	−	1.61884i
$416$	−12.1102	+	18.5304i	−0.593752	+	0.908525i
$417$		0			0
$418$	−4.31533	−	3.97277i	−0.211070	−	0.194315i
$419$			10.4707i			0.511525i	0.966740	+	0.255762i	$0.0823265\pi$
$419$			10.4707i			0.511525i	−0.966740	+	0.255762i	$0.917674\pi$
$420$		0			0
$421$		−	0.935700i		−	0.0456033i	−0.999740	−	0.0228016i	$-0.992741\pi$
$421$		−	0.935700i		−	0.0456033i	0.999740	−	0.0228016i	$-0.00725861\pi$
$422$	8.50945	−	9.24320i	0.414233	−	0.449952i
$423$		0			0
$424$	−11.7074	+	15.0391i	−0.568562	+	0.730361i
$425$	−4.93228	−	0.958980i	−0.239251	−	0.0465174i
$426$		0			0
$427$			11.4659i			0.554872i
$428$	2.57336	+	31.0772i	0.124388	+	1.50217i
$429$		0			0
$430$	−27.6153	+	24.7477i	−1.33173	+	1.19344i
$431$	−12.1803			−0.586703			−0.293351	−	0.956005i	$-0.594771\pi$
$431$	−12.1803			−0.586703			−0.293351	+	0.956005i	$0.594771\pi$
$432$		0			0
$433$		−	20.5905i		−	0.989514i	−0.869031	−	0.494757i	$-0.835257\pi$
$433$		−	20.5905i		−	0.989514i	0.869031	−	0.494757i	$-0.164743\pi$
$434$	11.5052	+	10.5919i	0.552268	+	0.508427i
$435$		0			0
$436$	21.7738	−	1.80299i	1.04277	−	0.0863475i
$437$		−	3.53878i		−	0.169283i
$438$		0			0
$439$			12.3535i			0.589598i	0.955559	+	0.294799i	$0.0952527\pi$
$439$			12.3535i			0.589598i	−0.955559	+	0.294799i	$0.904747\pi$
$440$	10.4364	+	9.86949i	0.497534	+	0.470510i
$441$		0			0
$442$	3.76678	−	4.09158i	0.179167	−	0.194617i
$443$	20.4381			0.971043			0.485521	−	0.874225i	$-0.338630\pi$
$443$	20.4381			0.971043			0.485521	+	0.874225i	$0.338630\pi$
$444$		0			0
$445$	10.7392	+	1.03432i	0.509086	+	0.0490315i
$446$	−16.9044	+	18.3621i	−0.800448	+	0.869469i
$447$		0			0
$448$	−5.50780	−	21.7653i	−0.260219	−	1.02831i
$449$		−	40.9555i		−	1.93281i	−0.257029	−	0.966404i	$-0.582744\pi$
$449$		−	40.9555i		−	1.93281i	0.257029	−	0.966404i	$-0.417256\pi$
$450$		0			0
$451$	−5.08662			−0.239520
$452$	2.12270	+	25.6348i	0.0998435	+	1.20576i
$453$		0			0
$454$	−12.4630	+	13.5377i	−0.584917	+	0.635354i
$455$	2.35426	−	24.4438i	0.110369	−	1.14595i
$456$		0			0
$457$			17.1652i			0.802953i	0.915869	+	0.401476i	$0.131503\pi$
$457$			17.1652i			0.802953i	−0.915869	+	0.401476i	$0.868497\pi$
$458$	21.4967	+	19.7902i	1.00447	+	0.924736i
$459$		0			0
$460$	−0.116118	+	8.66522i	−0.00541401	+	0.404018i
$461$	4.53444			0.211190			0.105595	−	0.994409i	$-0.466325\pi$
$461$	4.53444			0.211190			0.105595	+	0.994409i	$0.466325\pi$
$462$		0			0
$463$	2.82358			0.131223			0.0656114	−	0.997845i	$-0.479100\pi$
$463$	2.82358			0.131223			0.0656114	+	0.997845i	$0.479100\pi$
$464$	−30.5560	+	5.09535i	−1.41853	+	0.236546i
$465$		0			0
$466$	−8.55122	+	9.28858i	−0.396128	+	0.430285i
$467$	18.3153			0.847532			0.423766	−	0.905772i	$-0.360708\pi$
$467$	18.3153			0.847532			0.423766	+	0.905772i	$0.360708\pi$
$468$		0			0
$469$		−	19.4827i		−	0.899627i
$470$	−14.7657	+	13.2324i	−0.681089	+	0.610365i
$471$		0			0
$472$	−19.9130	+	25.5798i	−0.916572	+	1.17741i
$473$	−26.6321			−1.22454
$474$		0			0
$475$	−8.96320	−	1.74271i	−0.411260	−	0.0799609i
$476$	0.465472	+	5.62127i	0.0213349	+	0.257650i
$477$		0			0
$478$	2.90113	−	3.15128i	0.132694	−	0.144136i
$479$	−34.5811			−1.58005			−0.790026	−	0.613073i	$-0.789933\pi$
$479$	−34.5811			−1.58005			−0.790026	+	0.613073i	$0.789933\pi$
$480$		0			0
$481$	34.5311			1.57448
$482$	16.3928	−	17.8063i	0.746670	−	0.811054i
$483$		0			0
$484$	−0.964182	−	11.6439i	−0.0438264	−	0.529269i
$485$	−33.2013	−	3.19771i	−1.50759	−	0.145201i
$486$		0			0
$487$	−36.1948			−1.64014			−0.820072	−	0.572260i	$-0.806067\pi$
$487$	−36.1948			−1.64014			−0.820072	+	0.572260i	$0.806067\pi$
$488$	7.09848	−	9.11853i	0.321333	−	0.412776i
$489$		0			0
$490$	1.84874	+	2.06296i	0.0835176	+	0.0931948i
$491$		−	11.9287i		−	0.538335i	−0.963093	−	0.269168i	$-0.913251\pi$
$491$		−	11.9287i		−	0.538335i	0.963093	−	0.269168i	$-0.0867486\pi$
$492$		0			0
$493$	7.78265			0.350513
$494$	6.84518	−	7.43543i	0.307979	−	0.334536i
$495$		0			0
$496$	−2.59242	−	15.5463i	−0.116403	−	0.698050i
$497$	20.6609			0.926767
$498$		0			0
$499$	−20.7402			−0.928459			−0.464230	−	0.885715i	$-0.653669\pi$
$499$	−20.7402			−0.928459			−0.464230	+	0.885715i	$0.653669\pi$
$500$	21.8905	+	4.56138i	0.978973	+	0.203991i
$501$		0			0
$502$	25.5833	+	23.5524i	1.14184	+	1.05120i
$503$			3.89107i			0.173494i	0.996230	+	0.0867471i	$0.0276472\pi$
$503$			3.89107i			0.173494i	−0.996230	+	0.0867471i	$0.972353\pi$
$504$		0			0
$505$	−3.20804	+	33.3085i	−0.142756	+	1.48221i
$506$	−4.21547	+	4.57897i	−0.187401	+	0.203560i
$507$		0			0
$508$	−0.949504	−	11.4667i	−0.0421274	−	0.508751i
$509$	44.3736			1.96683			0.983413	−	0.181382i	$-0.0580571\pi$
$509$	44.3736			1.96683			0.983413	+	0.181382i	$0.0580571\pi$
$510$		0			0
$511$		−	14.4176i		−	0.637797i
$512$	−9.09459	+	20.7193i	−0.401928	+	0.915671i
$513$		0			0
$514$	9.50070	−	10.3199i	0.419058	−	0.455193i
$515$	2.26629	−	23.5305i	0.0998648	−	1.03688i
$516$		0			0
$517$	−14.2400			−0.626273
$518$	−23.7205	+	25.7658i	−1.04222	+	1.13209i
$519$		0			0
$520$	−17.0054	+	17.9821i	−0.745735	+	0.788567i
$521$			3.66605i			0.160613i	0.996770	+	0.0803064i	$0.0255899\pi$
$521$			3.66605i			0.160613i	−0.996770	+	0.0803064i	$0.974410\pi$
$522$		0			0
$523$			0.548243i			0.0239730i	0.999928	+	0.0119865i	$0.00381552\pi$
$523$			0.548243i			0.0239730i	−0.999928	+	0.0119865i	$0.996184\pi$
$524$	−10.4466	+	0.865037i	−0.456362	+	0.0377893i
$525$		0			0
$526$	−4.03229	−	3.71220i	−0.175816	−	0.161860i
$527$			3.95967i			0.172486i
$528$		0			0
$529$	19.2450			0.836740
$530$	−15.8686	+	14.2209i	−0.689289	+	0.617714i
$531$		0			0
$532$	0.845880	+	10.2153i	0.0366735	+	0.442887i
$533$		−	8.76438i		−	0.379627i
$534$		0			0
$535$	−3.34241	+	34.7037i	−0.144505	+	1.50037i
$536$	−12.0617	+	15.4941i	−0.520985	+	0.669244i
$537$		0			0
$538$	−21.5724	+	23.4325i	−0.930051	+	1.01025i
$539$			1.98951i			0.0856942i
$540$		0			0
$541$			42.7910i			1.83973i	0.392238	+	0.919864i	$0.371701\pi$
$541$			42.7910i			1.83973i	−0.392238	+	0.919864i	$0.628299\pi$
$542$	−19.3048	−	17.7724i	−0.829214	−	0.763388i
$543$		0			0
$544$	3.10993	−	4.75863i	0.133337	−	0.204025i
$545$	24.3146	+	2.34181i	1.04152	+	0.100312i
$546$		0			0
$547$			15.6821i			0.670520i	0.942126	+	0.335260i	$0.108824\pi$
$547$			15.6821i			0.670520i	−0.942126	+	0.335260i	$0.891176\pi$
$548$	−3.36258	−	40.6082i	−0.143642	−	1.73470i
$549$		0			0
$550$	9.52187	+	12.9321i	0.406014	+	0.551427i
$551$	14.1430			0.602514
$552$		0			0
$553$			11.6360i			0.494813i
$554$	22.9110	−	24.8866i	0.973397	−	1.05733i
$555$		0			0
$556$	3.19534	+	38.5885i	0.135513	+	1.63652i
$557$			12.6435i			0.535721i	0.963458	+	0.267861i	$0.0863166\pi$
$557$			12.6435i			0.535721i	−0.963458	+	0.267861i	$0.913683\pi$
$558$		0			0
$559$		−	45.8877i		−	1.94084i
$560$	−1.73607	−	25.0413i	−0.0733622	−	1.05819i
$561$		0			0
$562$	24.8922	+	22.9162i	1.05002	+	0.966663i
$563$	−46.3326			−1.95268			−0.976342	−	0.216231i	$-0.930624\pi$
$563$	−46.3326			−1.95268			−0.976342	+	0.216231i	$0.930624\pi$
$564$		0			0
$565$	−2.75707	+	28.6262i	−0.115991	+	1.20431i
$566$	−2.97782	−	2.74144i	−0.125167	−	0.115231i
$567$		0			0
$568$	−16.4311	−	12.7911i	−0.689434	−	0.536701i
$569$		−	37.9125i		−	1.58938i	−0.607018	−	0.794688i	$-0.707634\pi$
$569$		−	37.9125i		−	1.58938i	0.607018	−	0.794688i	$-0.292366\pi$
$570$		0			0
$571$	−22.8483			−0.956172			−0.478086	−	0.878313i	$-0.658669\pi$
$571$	−22.8483			−0.956172			−0.478086	+	0.878313i	$0.658669\pi$
$572$	−17.7145	+	1.46686i	−0.740680	+	0.0613324i
$573$		0			0
$574$	6.53966	+	6.02053i	0.272960	+	0.251292i
$575$	−1.84917	+	9.51078i	−0.0771159	+	0.396627i
$576$		0			0
$577$			34.7210i			1.44545i	0.691134	+	0.722727i	$0.257111\pi$
$577$			34.7210i			1.44545i	−0.691134	+	0.722727i	$0.742889\pi$
$578$	15.3161	−	16.6368i	0.637067	−	0.692000i
$579$		0			0
$580$	−34.6313	−	0.464074i	−1.43798	−	0.0192696i
$581$	−41.5816			−1.72510
$582$		0			0
$583$	−15.3037			−0.633813
$584$	−8.92588	+	11.4660i	−0.369356	+	0.474465i
$585$		0			0
$586$	−18.0356	−	16.6039i	−0.745043	−	0.685899i
$587$	−22.3865			−0.923988			−0.461994	−	0.886883i	$-0.652866\pi$
$587$	−22.3865			−0.923988			−0.461994	+	0.886883i	$0.652866\pi$
$588$		0			0
$589$			7.19571i			0.296494i
$590$	−26.9908	+	24.1881i	−1.11119	+	0.995809i
$591$		0			0
$592$	34.8159	−	5.80570i	1.43092	−	0.238613i
$593$	1.73287			0.0711603			0.0355802	−	0.999367i	$-0.488672\pi$
$593$	1.73287			0.0711603			0.0355802	+	0.999367i	$0.488672\pi$
$594$		0			0
$595$	−0.604578	+	6.27723i	−0.0247853	+	0.257341i
$596$	0.660141	+	7.97218i	0.0270404	+	0.326553i
$597$		0			0
$598$	−7.88967	−	7.26337i	−0.322633	−	0.297021i
$599$	−11.2417			−0.459325			−0.229662	−	0.973270i	$-0.573762\pi$
$599$	−11.2417			−0.459325			−0.229662	+	0.973270i	$0.573762\pi$
$600$		0			0
$601$	4.09680			0.167112			0.0835559	−	0.996503i	$-0.473372\pi$
$601$	4.09680			0.167112			0.0835559	+	0.996503i	$0.473372\pi$
$602$	34.2398	+	31.5217i	1.39551	+	1.28473i
$603$		0			0
$604$	−30.9459	+	2.56250i	−1.25917	+	0.104266i
$605$	1.25233	−	13.0027i	0.0509143	−	0.528635i
$606$		0			0
$607$	−38.4524			−1.56073			−0.780366	−	0.625323i	$-0.784967\pi$
$607$	−38.4524			−1.56073			−0.780366	+	0.625323i	$0.784967\pi$
$608$	5.65152	−	8.64763i	0.229199	−	0.350708i
$609$		0			0
$610$	9.62152	−	8.62243i	0.389564	−	0.349112i
$611$		−	24.5358i		−	0.992612i
$612$		0			0
$613$	−3.08629			−0.124654			−0.0623271	−	0.998056i	$-0.519852\pi$
$613$	−3.08629			−0.124654			−0.0623271	+	0.998056i	$0.519852\pi$
$614$	4.69321	+	4.32065i	0.189403	+	0.174367i
$615$		0			0
$616$	11.0741	−	14.2255i	0.446189	−	0.573163i
$617$	−7.92538			−0.319064			−0.159532	−	0.987193i	$-0.550998\pi$
$617$	−7.92538			−0.319064			−0.159532	+	0.987193i	$0.550998\pi$
$618$		0			0
$619$	16.1896			0.650716			0.325358	−	0.945591i	$-0.394515\pi$
$619$	16.1896			0.650716			0.325358	+	0.945591i	$0.394515\pi$
$620$	0.236112	−	17.6197i	0.00948248	−	0.707625i
$621$		0			0
$622$	−1.88004	+	2.04215i	−0.0753828	+	0.0818829i
$623$		−	13.5408i		−	0.542500i
$624$		0			0
$625$	23.1787	+	9.36735i	0.927148	+	0.374694i
$626$	−3.35939	−	3.09272i	−0.134268	−	0.123610i
$627$		0			0
$628$	2.75028	+	33.2137i	0.109748	+	1.32537i
$629$	−8.86765			−0.353576
$630$		0			0
$631$		−	17.3661i		−	0.691333i	−0.938357	−	0.345666i	$-0.887653\pi$
$631$		−	17.3661i		−	0.691333i	0.938357	−	0.345666i	$-0.112347\pi$
$632$	7.20380	−	9.25383i	0.286552	−	0.368098i
$633$		0			0
$634$	−18.3781	−	16.9192i	−0.729886	−	0.671946i
$635$	1.23326	−	12.8048i	0.0489405	−	0.508141i
$636$		0			0
$637$	−3.42797			−0.135821
$638$	−18.3002	−	16.8475i	−0.724512	−	0.666998i
$639$		0			0
$640$	−14.1223	+	20.9895i	−0.558233	+	0.829684i
$641$			14.3388i			0.566350i	0.959068	+	0.283175i	$0.0913878\pi$
$641$			14.3388i			0.566350i	−0.959068	+	0.283175i	$0.908612\pi$
$642$		0			0
$643$		−	15.2489i		−	0.601357i	−0.953726	−	0.300678i	$-0.902787\pi$
$643$		−	15.2489i		−	0.601357i	0.953726	−	0.300678i	$-0.0972131\pi$
$644$	10.8393	−	0.897557i	0.427129	−	0.0353687i
$645$		0			0
$646$	−1.75786	+	1.90943i	−0.0691619	+	0.0751256i
$647$			38.3484i			1.50763i	0.657087	+	0.753815i	$0.271788\pi$
$647$			38.3484i			1.50763i	−0.657087	+	0.753815i	$0.728212\pi$
$648$		0			0
$649$	−26.0299			−1.02176
$650$	−22.2824	+	16.4064i	−0.873986	+	0.643513i
$651$		0			0
$652$	30.6836	−	2.54077i	1.20166	−	0.0995043i
$653$			21.7545i			0.851319i	0.904883	+	0.425659i	$0.139958\pi$
$653$			21.7545i			0.851319i	−0.904883	+	0.425659i	$0.860042\pi$
$654$		0			0
$655$	−11.6657	−	1.12355i	−0.455815	−	0.0439008i
$656$	−1.47355	−	8.83667i	−0.0575326	−	0.345014i
$657$		0			0
$658$	18.3077	+	16.8544i	0.713710	+	0.657053i
$659$			8.22885i			0.320551i	0.987072	+	0.160275i	$0.0512382\pi$
$659$			8.22885i			0.320551i	−0.987072	+	0.160275i	$0.948762\pi$
$660$		0			0
$661$		−	10.7212i		−	0.417007i	−0.978022	−	0.208503i	$-0.933141\pi$
$661$		−	10.7212i		−	0.417007i	0.978022	−	0.208503i	$-0.0668592\pi$
$662$	10.8522	−	11.7880i	0.421784	−	0.458154i
$663$		0			0
$664$	33.0689	+	25.7430i	1.28332	+	0.999023i
$665$	−1.09867	+	11.4073i	−0.0426046	+	0.442356i
$666$		0			0
$667$		−	15.0071i		−	0.581076i
$668$	12.8531	−	1.06431i	0.497300	−	0.0411792i
$669$		0			0
$670$	−16.3488	+	14.6512i	−0.631609	+	0.566024i
$671$	9.27896			0.358210
$672$		0			0
$673$		−	3.76512i		−	0.145135i	−0.997364	−	0.0725673i	$-0.976881\pi$
$673$		−	3.76512i		−	0.145135i	0.997364	−	0.0725673i	$-0.0231192\pi$
$674$	14.9621	+	13.7743i	0.576318	+	0.530568i
$675$		0			0
$676$	−0.381831	−	4.61118i	−0.0146858	−	0.177353i
$677$			36.2409i			1.39285i	0.717630	+	0.696425i	$0.245227\pi$
$677$			36.2409i			1.39285i	−0.717630	+	0.696425i	$0.754773\pi$
$678$		0			0
$679$			41.8628i			1.60655i
$680$	4.36702	−	4.61784i	0.167467	−	0.177086i
$681$		0			0
$682$	8.57168	−	9.31080i	0.328227	−	0.356529i
$683$	20.4976			0.784320			0.392160	−	0.919897i	$-0.371728\pi$
$683$	20.4976			0.784320			0.392160	+	0.919897i	$0.371728\pi$
$684$		0			0
$685$	4.36749	−	45.3469i	0.166873	−	1.73262i
$686$	−16.4621	+	17.8816i	−0.628527	+	0.682724i
$687$		0			0
$688$	−7.71510	−	46.2662i	−0.294135	−	1.76388i
$689$		−	26.3686i		−	1.00456i
$690$		0			0
$691$	46.8335			1.78163			0.890815	−	0.454366i	$-0.150134\pi$
$691$	46.8335			1.78163			0.890815	+	0.454366i	$0.150134\pi$
$692$	−15.7192	+	1.30164i	−0.597554	+	0.0494808i
$693$		0			0
$694$	5.83692	−	6.34022i	0.221566	−	0.240672i
$695$	−4.15026	+	43.0915i	−0.157428	+	1.63455i
$696$		0			0
$697$			2.25071i			0.0852517i
$698$	−19.0669	−	17.5533i	−0.721692	−	0.664402i
$699$		0			0
$700$	3.06456	−	27.8964i	0.115829	−	1.05438i
$701$	37.7416			1.42548			0.712740	−	0.701428i	$-0.247454\pi$
$701$	37.7416			1.42548			0.712740	+	0.701428i	$0.247454\pi$
$702$		0			0
$703$	−16.1147			−0.607779
$704$	−17.6140	+	4.45729i	−0.663851	+	0.167990i
$705$		0			0
$706$	−26.7992	+	29.1101i	−1.00860	+	1.09557i
$707$	41.9980			1.57950
$708$		0			0
$709$			7.35664i			0.276285i	0.990412	+	0.138142i	$0.0441131\pi$
$709$			7.35664i			0.276285i	−0.990412	+	0.138142i	$0.955887\pi$
$710$	−15.5372	−	17.3375i	−0.583099	−	0.650663i
$711$		0			0
$712$	−8.38305	+	10.7687i	−0.314168	+	0.403573i
$713$	7.63531			0.285945
$714$		0			0
$715$	−19.7816	−	1.90523i	−0.739791	−	0.0712514i
$716$	28.5107	−	2.36084i	1.06549	−	0.0882289i
$717$		0			0
$718$	24.5005	−	26.6132i	0.914352	−	0.993195i
$719$	29.9929			1.11855			0.559274	−	0.828983i	$-0.311080\pi$
$719$	29.9929			1.11855			0.559274	+	0.828983i	$0.311080\pi$
$720$		0			0
$721$	−29.6691			−1.10494
$722$	15.0047	−	16.2985i	0.558417	−	0.606568i
$723$		0			0
$724$	43.8673	−	3.63245i	1.63031	−	0.134999i
$725$	−38.0106	−	7.39038i	−1.41168	−	0.274472i
$726$		0			0
$727$	−27.7756			−1.03014			−0.515069	−	0.857148i	$-0.672234\pi$
$727$	−27.7756			−1.03014			−0.515069	+	0.857148i	$0.672234\pi$
$728$	24.5110	+	19.0810i	0.908437	+	0.707188i
$729$		0			0
$730$	−12.0985	+	10.8422i	−0.447784	+	0.401286i
$731$			11.7841i			0.435849i
$732$		0			0
$733$	4.84099			0.178806			0.0894031	−	0.995996i	$-0.471504\pi$
$733$	4.84099			0.178806			0.0894031	+	0.995996i	$0.471504\pi$
$734$	14.0821	−	15.2964i	0.519780	−	0.564599i
$735$		0			0
$736$	−9.17594	−	5.99678i	−0.338229	−	0.221044i
$737$	−15.7667			−0.580775
$738$		0			0
$739$	−38.2911			−1.40856			−0.704280	−	0.709923i	$-0.748730\pi$
$739$	−38.2911			−1.40856			−0.704280	+	0.709923i	$0.748730\pi$
$740$	39.4593	+	0.528771i	1.45055	+	0.0194380i
$741$		0			0
$742$	19.6753	+	18.1134i	0.722303	+	0.664964i
$743$		−	20.4534i		−	0.750361i	−0.926952	−	0.375181i	$-0.877581\pi$
$743$		−	20.4534i		−	0.750361i	0.926952	−	0.375181i	$-0.122419\pi$
$744$		0			0
$745$	−0.857423	+	8.90248i	−0.0314136	+	0.326162i
$746$	−9.73848	+	10.5782i	−0.356551	+	0.387296i
$747$		0			0
$748$	4.54912	−	0.376692i	0.166332	−	0.0137732i
$749$	43.7571			1.59885
$750$		0			0
$751$			43.5967i			1.59087i	0.606041	+	0.795433i	$0.292757\pi$
$751$			43.5967i			1.59087i	−0.606041	+	0.795433i	$0.707243\pi$
$752$	−4.12520	−	24.7382i	−0.150431	−	0.902108i
$753$		0			0
$754$	29.0286	−	31.5317i	1.05716	−	1.14832i
$755$	−34.5571	−	3.32830i	−1.25766	−	0.121129i
$756$		0			0
$757$	15.0079			0.545472			0.272736	−	0.962089i	$-0.412071\pi$
$757$	15.0079			0.545472			0.272736	+	0.962089i	$0.412071\pi$
$758$	−20.3165	+	22.0684i	−0.737930	+	0.801560i
$759$		0			0
$760$	7.93597	−	8.39178i	0.287868	−	0.304402i
$761$			36.9239i			1.33849i	0.743041	+	0.669246i	$0.233383\pi$
$761$			36.9239i			1.33849i	−0.743041	+	0.669246i	$0.766617\pi$
$762$		0			0
$763$		−	30.6577i		−	1.10988i
$764$	−0.512188	−	6.18543i	−0.0185303	−	0.223781i
$765$		0			0
$766$	−26.5136	−	24.4089i	−0.957977	−	0.881929i
$767$		−	44.8501i		−	1.61944i
$768$		0			0
$769$	1.84339			0.0664745			0.0332372	−	0.999447i	$-0.489418\pi$
$769$	1.84339			0.0664745			0.0332372	+	0.999447i	$0.489418\pi$
$770$	15.0102	−	13.4516i	0.540931	−	0.484762i
$771$		0			0
$772$	−37.9137	+	3.13947i	−1.36454	+	0.112992i
$773$		−	1.25203i		−	0.0450322i	−0.999746	−	0.0225161i	$-0.992832\pi$
$773$		−	1.25203i		−	0.0450322i	0.999746	−	0.0225161i	$-0.00716771\pi$
$774$		0			0
$775$	3.76008	−	19.3391i	0.135066	−	0.694680i
$776$	25.9171	−	33.2925i	0.930370	−	1.19513i
$777$		0			0
$778$	−9.44065	+	10.2547i	−0.338464	+	0.367649i
$779$			4.09011i			0.146543i
$780$		0			0
$781$		−	16.7202i		−	0.598296i
$782$	2.02608	+	1.86525i	0.0724526	+	0.0667011i
$783$		0			0
$784$	−3.45624	+	0.576344i	−0.123437	+	0.0205837i
$785$	−3.57220	+	37.0895i	−0.127497	+	1.32378i
$786$		0			0
$787$		−	35.1540i		−	1.25310i	−0.779380	−	0.626552i	$-0.784466\pi$
$787$		−	35.1540i		−	1.25310i	0.779380	−	0.626552i	$-0.215534\pi$
$788$	−23.1745	+	1.91897i	−0.825556	+	0.0683606i
$789$		0			0
$790$	9.76428	−	8.75037i	0.347398	−	0.311324i
$791$	36.0941			1.28336
$792$		0			0
$793$			15.9879i			0.567747i
$794$	29.2304	−	31.7509i	1.03735	−	1.12680i
$795$		0			0
$796$	−11.5688	+	0.957962i	−0.410046	+	0.0339541i
$797$		−	36.2717i		−	1.28481i	−0.766366	−	0.642404i	$-0.777937\pi$
$797$		−	36.2717i		−	1.28481i	0.766366	−	0.642404i	$-0.222063\pi$
$798$		0			0
$799$			6.30084i			0.222908i
$800$	−19.7077	+	20.2881i	−0.696773	+	0.717292i
$801$		0			0
$802$	24.7701	+	22.8037i	0.874661	+	0.805228i
$803$	−11.6677			−0.411745
$804$		0			0
$805$	12.1042	+	1.16579i	0.426617	+	0.0410887i
$806$	16.0427	+	14.7692i	0.565082	+	0.520224i
$807$		0			0
$808$	−33.4000	−	26.0008i	−1.17501	−	0.914704i
$809$		−	3.68656i		−	0.129612i	−0.997898	−	0.0648062i	$-0.979357\pi$
$809$		−	3.68656i		−	0.129612i	0.997898	−	0.0648062i	$-0.0206429\pi$
$810$		0			0
$811$	38.1790			1.34065			0.670323	−	0.742070i	$-0.266156\pi$
$811$	38.1790			1.34065			0.670323	+	0.742070i	$0.266156\pi$
$812$	3.58716	+	43.3203i	0.125885	+	1.52024i
$813$		0			0
$814$	20.8515	+	19.1962i	0.730844	+	0.672828i
$815$	34.2642	+	3.30008i	1.20022	+	0.115597i
$816$		0			0
$817$			21.4146i			0.749202i
$818$	−10.2512	+	11.1352i	−0.358426	+	0.389333i
$819$		0			0
$820$	0.134208	−	10.0152i	0.00468675	−	0.349746i
$821$	−41.1529			−1.43624			−0.718122	−	0.695917i	$-0.754998\pi$
$821$	−41.1529			−1.43624			−0.718122	+	0.695917i	$0.754998\pi$
$822$		0			0
$823$	−3.17378			−0.110631			−0.0553155	−	0.998469i	$-0.517616\pi$
$823$	−3.17378			−0.110631			−0.0553155	+	0.998469i	$0.517616\pi$
$824$	23.5951	+	18.3680i	0.821976	+	0.639881i
$825$		0			0
$826$	33.4655	+	30.8090i	1.16442	+	1.07198i
$827$	25.7874			0.896715			0.448358	−	0.893854i	$-0.352009\pi$
$827$	25.7874			0.896715			0.448358	+	0.893854i	$0.352009\pi$
$828$		0			0
$829$		−	9.86692i		−	0.342692i	−0.985211	−	0.171346i	$-0.945188\pi$
$829$		−	9.86692i		−	0.342692i	0.985211	−	0.171346i	$-0.0548117\pi$
$830$	31.2697	+	34.8930i	1.08539	+	1.21115i
$831$		0			0
$832$	−7.68002	−	30.3493i	−0.266257	−	1.05217i
$833$	0.880310			0.0305009
$834$		0			0
$835$	14.3529	+	1.38237i	0.496704	+	0.0478390i
$836$	8.26689	−	0.684544i	0.285916	−	0.0236755i
$837$		0			0
$838$	−10.8941	−	10.0293i	−0.376331	−	0.346457i
$839$	−9.25026			−0.319355			−0.159677	−	0.987169i	$-0.551045\pi$
$839$	−9.25026			−0.319355			−0.159677	+	0.987169i	$0.551045\pi$
$840$		0			0
$841$	30.9770			1.06817
$842$	0.973544	+	0.896261i	0.0335505	+	0.0308872i
$843$		0			0
$844$	1.46626	+	17.7072i	0.0504706	+	0.609507i
$845$	0.495941	−	5.14927i	0.0170609	−	0.177140i
$846$		0			0
$847$	−16.3948			−0.563332
$848$	−4.43335	−	26.5861i	−0.152242	−	0.912970i
$849$		0			0
$850$	5.72215	−	4.21320i	0.196268	−	0.144512i
$851$			17.0992i			0.586154i
$852$		0			0
$853$	47.7095			1.63354			0.816771	−	0.576962i	$-0.195762\pi$
$853$	47.7095			1.63354			0.816771	+	0.576962i	$0.195762\pi$
$854$	−11.9296	−	10.9826i	−0.408222	−	0.375816i
$855$		0			0
$856$	−34.7990	−	27.0899i	−1.18940	−	0.925912i
$857$	−24.3588			−0.832079			−0.416040	−	0.909346i	$-0.636582\pi$
$857$	−24.3588			−0.832079			−0.416040	+	0.909346i	$0.636582\pi$
$858$		0			0
$859$	−19.8902			−0.678644			−0.339322	−	0.940670i	$-0.610198\pi$
$859$	−19.8902			−0.678644			−0.339322	+	0.940670i	$0.610198\pi$
$860$	0.702675	−	52.4367i	0.0239610	−	1.78808i
$861$		0			0
$862$	11.6669	−	12.6729i	0.397375	−	0.431640i
$863$		−	23.9506i		−	0.815287i	−0.913141	−	0.407643i	$-0.866351\pi$
$863$		−	23.9506i		−	0.815287i	0.913141	−	0.407643i	$-0.133649\pi$
$864$		0			0
$865$	−17.5535	−	1.69063i	−0.596837	−	0.0574831i
$866$	21.4232	+	19.7226i	0.727990	+	0.670200i
$867$		0			0
$868$	−22.0405	+	1.82508i	−0.748104	+	0.0619472i
$869$	9.41664			0.319438
$870$		0			0
$871$		−	27.1665i		−	0.920501i
$872$	−18.9801	+	24.3814i	−0.642747	+	0.825657i
$873$		0			0
$874$	3.68190	+	3.38962i	0.124542	+	0.114656i
$875$	8.91360	−	30.0840i	0.301335	−	1.01702i
$876$		0			0
$877$	9.60517			0.324343			0.162172	−	0.986763i	$-0.448150\pi$
$877$	9.60517			0.324343			0.162172	+	0.986763i	$0.448150\pi$
$878$	−12.8531	−	11.8328i	−0.433770	−	0.399336i
$879$		0			0
$880$	−20.2651	+	1.40494i	−0.683137	+	0.0473607i
$881$			54.0320i			1.82038i	0.414186	+	0.910192i	$0.364066\pi$
$881$			54.0320i			1.82038i	−0.414186	+	0.910192i	$0.635934\pi$
$882$		0			0
$883$		−	57.1178i		−	1.92217i	−0.276260	−	0.961083i	$-0.589095\pi$
$883$		−	57.1178i		−	1.92217i	0.276260	−	0.961083i	$-0.410905\pi$
$884$	0.649050	+	7.83824i	0.0218299	+	0.263628i
$885$		0			0
$886$	−19.5766	+	21.2647i	−0.657690	+	0.714401i
$887$		−	45.5832i		−	1.53053i	−0.643712	−	0.765267i	$-0.722607\pi$
$887$		−	45.5832i		−	1.53053i	0.643712	−	0.765267i	$-0.277393\pi$
$888$		0			0
$889$	−16.1452			−0.541493
$890$	−11.3627	+	10.1828i	−0.380878	+	0.341328i
$891$		0			0
$892$	−2.91279	−	35.1762i	−0.0975273	−	1.17779i
$893$			11.4502i			0.383167i
$894$		0			0
$895$	31.8377	+	3.06638i	1.06422	+	0.102498i
$896$	27.9212	+	15.1173i	0.932782	+	0.505034i
$897$		0			0
$898$	42.6118	+	39.2292i	1.42198	+	1.30909i
$899$			30.5151i			1.01774i
$900$		0			0
$901$			6.77151i			0.225592i
$902$	4.87222	−	5.29235i	0.162227	−	0.176216i
$903$		0			0
$904$	−28.7048	−	22.3457i	−0.954707	−	0.743208i
$905$	48.9863	+	4.71801i	1.62836	+	0.156832i
$906$		0			0
$907$		−	25.0428i		−	0.831534i	−0.909471	−	0.415767i	$-0.863513\pi$
$907$		−	25.0428i		−	0.831534i	0.909471	−	0.415767i	$-0.136487\pi$
$908$	−2.14749	−	25.9341i	−0.0712669	−	0.860653i
$909$		0			0
$910$	23.1774	+	25.8630i	0.768324	+	0.857351i
$911$	34.0216			1.12719			0.563593	−	0.826053i	$-0.309419\pi$
$911$	34.0216			1.12719			0.563593	+	0.826053i	$0.309419\pi$
$912$		0			0
$913$			33.6507i			1.11368i
$914$	−17.8594	−	16.4417i	−0.590736	−	0.543842i
$915$		0			0
$916$	−41.1812	+	3.41003i	−1.36067	+	0.112671i
$917$			14.7090i			0.485732i
$918$		0			0
$919$		−	14.8359i		−	0.489391i	−0.969600	−	0.244695i	$-0.921312\pi$
$919$		−	14.8359i		−	0.489391i	0.969600	−	0.244695i	$-0.0786879\pi$
$920$	−8.90445	−	8.42080i	−0.293571	−	0.277625i
$921$		0			0
$922$	−4.34331	+	4.71783i	−0.143039	+	0.155373i
$923$	28.8093			0.948270
$924$		0			0
$925$	43.3098	+	8.42068i	1.42402	+	0.276870i
$926$	−2.70456	+	2.93777i	−0.0888775	+	0.0965413i
$927$		0			0
$928$	23.9666	−	36.6724i	0.786743	−	1.20383i
$929$			3.53367i			0.115936i	0.998318	+	0.0579679i	$0.0184621\pi$
$929$			3.53367i			0.115936i	−0.998318	+	0.0579679i	$0.981538\pi$
$930$		0			0
$931$	1.59974			0.0524295
$932$	−1.47345	−	17.7941i	−0.0482646	−	0.582866i
$933$		0			0
$934$	−17.5433	+	19.0561i	−0.574035	+	0.623533i
$935$	5.07997	+	0.489266i	0.166133	+	0.0160007i
$936$		0			0
$937$		−	29.4410i		−	0.961794i	−0.876777	−	0.480897i	$-0.840311\pi$
$937$		−	29.4410i		−	0.961794i	0.876777	−	0.480897i	$-0.159689\pi$
$938$	20.2706	+	18.6615i	0.661860	+	0.609320i
$939$		0			0
$940$	0.375714	−	28.0375i	0.0122545	−	0.914482i
$941$	33.6670			1.09751			0.548757	−	0.835982i	$-0.315101\pi$
$941$	33.6670			1.09751			0.548757	+	0.835982i	$0.315101\pi$
$942$		0			0
$943$	4.33998			0.141329
$944$	−7.54065	−	45.2200i	−0.245427	−	1.47179i
$945$		0			0
$946$	25.5095	−	27.7092i	0.829387	−	0.900903i
$947$	−54.4568			−1.76961			−0.884804	−	0.465963i	$-0.845708\pi$
$947$	−54.4568			−1.76961			−0.884804	+	0.465963i	$0.845708\pi$
$948$		0			0
$949$		−	20.1038i		−	0.652595i
$950$	10.3986	−	7.65645i	0.337375	−	0.248408i
$951$		0			0
$952$	−6.29446	−	4.90003i	−0.204005	−	0.158811i
$953$	11.0742			0.358728			0.179364	−	0.983783i	$-0.442596\pi$
$953$	11.0742			0.358728			0.179364	+	0.983783i	$0.442596\pi$
$954$		0			0
$955$	0.665255	−	6.90723i	0.0215271	−	0.223513i
$956$	0.499890	+	6.03692i	0.0161676	+	0.195248i
$957$		0			0
$958$	33.1235	−	35.9797i	1.07017	−	1.16245i
$959$	−57.1768			−1.84634
$960$		0			0
$961$	15.4745			0.499176
$962$	−33.0756	+	35.9276i	−1.06640	+	1.15835i
$963$		0			0
$964$	2.82462	+	34.1115i	0.0909750	+	1.09866i
$965$	−42.3380	−	4.07769i	−1.36291	−	0.131266i
$966$		0			0
$967$	27.6897			0.890442			0.445221	−	0.895421i	$-0.353125\pi$
$967$	27.6897			0.890442			0.445221	+	0.895421i	$0.353125\pi$
$968$	13.0384	+	10.1500i	0.419070	+	0.326232i
$969$		0			0
$970$	35.1289	−	31.4812i	1.12792	−	1.01080i
$971$			23.7464i			0.762058i	0.924563	+	0.381029i	$0.124430\pi$
$971$			23.7464i			0.762058i	−0.924563	+	0.381029i	$0.875570\pi$
$972$		0			0
$973$	54.3330			1.74184
$974$	34.6692	−	37.6587i	1.11087	−	1.20666i
$975$		0			0
$976$	2.68804	+	16.1198i	0.0860421	+	0.515981i
$977$	0.687528			0.0219960			0.0109980	−	0.999940i	$-0.496499\pi$
$977$	0.687528			0.0219960			0.0109980	+	0.999940i	$0.496499\pi$
$978$		0			0
$979$	−10.9581			−0.350223
$980$	−3.91720	−	0.0524922i	−0.125131	−	0.00167680i
$981$		0			0
$982$	12.4112	+	11.4259i	0.396056	+	0.364616i
$983$			27.8527i			0.888363i	0.895937	+	0.444181i	$0.146505\pi$
$983$			27.8527i			0.888363i	−0.895937	+	0.444181i	$0.853495\pi$
$984$		0			0
$985$	−25.8788	−	2.49246i	−0.824566	−	0.0794163i
$986$	−7.45461	+	8.09741i	−0.237403	+	0.257874i
$987$		0			0
$988$	1.17949	+	14.2441i	0.0375245	+	0.453164i
$989$	22.7229			0.722545
$990$		0			0
$991$			42.7921i			1.35934i	0.733519	+	0.679668i	$0.237876\pi$
$991$			42.7921i			1.35934i	−0.733519	+	0.679668i	$0.762124\pi$
$992$	18.6582	+	12.1938i	0.592399	+	0.387153i
$993$		0			0
$994$	−19.7900	+	21.4965i	−0.627701	+	0.681827i
$995$	−12.9188	−	1.24425i	−0.409554	−	0.0394453i
$996$		0			0
$997$	13.2645			0.420091			0.210045	−	0.977692i	$-0.432639\pi$
$997$	13.2645			0.420091			0.210045	+	0.977692i	$0.432639\pi$
$998$	19.8660	−	21.5790i	0.628848	−	0.683072i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.m.c.539.16	yes	48
3.2	odd	2	inner	1080.2.m.c.539.33	yes	48
4.3	odd	2		4320.2.m.c.2159.26		48
5.4	even	2	inner	1080.2.m.c.539.34	yes	48
8.3	odd	2	inner	1080.2.m.c.539.13	✓	48
8.5	even	2		4320.2.m.c.2159.23		48
12.11	even	2		4320.2.m.c.2159.24		48
15.14	odd	2	inner	1080.2.m.c.539.15	yes	48
20.19	odd	2		4320.2.m.c.2159.27		48
24.5	odd	2		4320.2.m.c.2159.25		48
24.11	even	2	inner	1080.2.m.c.539.36	yes	48
40.19	odd	2	inner	1080.2.m.c.539.35	yes	48
40.29	even	2		4320.2.m.c.2159.22		48
60.59	even	2		4320.2.m.c.2159.21		48
120.29	odd	2		4320.2.m.c.2159.28		48
120.59	even	2	inner	1080.2.m.c.539.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.m.c.539.13	✓	48	8.3	odd	2	inner
1080.2.m.c.539.14	yes	48	120.59	even	2	inner
1080.2.m.c.539.15	yes	48	15.14	odd	2	inner
1080.2.m.c.539.16	yes	48	1.1	even	1	trivial
1080.2.m.c.539.33	yes	48	3.2	odd	2	inner
1080.2.m.c.539.34	yes	48	5.4	even	2	inner
1080.2.m.c.539.35	yes	48	40.19	odd	2	inner
1080.2.m.c.539.36	yes	48	24.11	even	2	inner
4320.2.m.c.2159.21		48	60.59	even	2
4320.2.m.c.2159.22		48	40.29	even	2
4320.2.m.c.2159.23		48	8.5	even	2
4320.2.m.c.2159.24		48	12.11	even	2
4320.2.m.c.2159.25		48	24.5	odd	2
4320.2.m.c.2159.26		48	4.3	odd	2
4320.2.m.c.2159.27		48	20.19	odd	2
4320.2.m.c.2159.28		48	120.29	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.957850 + 1.04044i) q^{2} +(-0.165046 - 1.99318i) q^{4} +(0.214370 - 2.22577i) q^{5} -2.80642 q^{7} +(2.23188 + 1.73744i) q^{8} +O(q^{10})\)	\(q+(-0.957850 + 1.04044i) q^{2} +(-0.165046 - 1.99318i) q^{4} +(0.214370 - 2.22577i) q^{5} -2.80642 q^{7} +(2.23188 + 1.73744i) q^{8} +(2.11045 + 2.35499i) q^{10} +2.27115i q^{11} -3.91324 q^{13} +(2.68813 - 2.91992i) q^{14} +(-3.94552 + 0.657933i) q^{16} +1.00493 q^{17} +1.82621 q^{19} +(-4.47173 - 0.0599231i) q^{20} +(-2.36300 - 2.17542i) q^{22} -1.93778i q^{23} +(-4.90809 - 0.954277i) q^{25} +(3.74830 - 4.07151i) q^{26} +(0.463189 + 5.59370i) q^{28} +7.74448 q^{29} +3.94024i q^{31} +(3.09467 - 4.73529i) q^{32} +(-0.962571 + 1.04557i) q^{34} +(-0.601613 + 6.24644i) q^{35} -8.82415 q^{37} +(-1.74923 + 1.90007i) q^{38} +(4.34560 - 4.59519i) q^{40} +2.23967i q^{41} +11.7263i q^{43} +(4.52680 - 0.374844i) q^{44} +(2.01615 + 1.85610i) q^{46} +6.26994i q^{47} +0.875992 q^{49} +(5.69409 - 4.19254i) q^{50} +(0.645866 + 7.79979i) q^{52} +6.73830i q^{53} +(5.05505 + 0.486866i) q^{55} +(-6.26359 - 4.87600i) q^{56} +(-7.41805 + 8.05769i) q^{58} +11.4611i q^{59} -4.08558i q^{61} +(-4.09960 - 3.77416i) q^{62} +(1.96257 + 7.75553i) q^{64} +(-0.838883 + 8.70998i) q^{65} +6.94219i q^{67} +(-0.165860 - 2.00300i) q^{68} +(-5.92282 - 6.60910i) q^{70} -7.36200 q^{71} +5.13736i q^{73} +(8.45222 - 9.18104i) q^{74} +(-0.301409 - 3.63996i) q^{76} -6.37379i q^{77} -4.14620i q^{79} +(0.618605 + 8.92285i) q^{80} +(-2.33025 - 2.14527i) q^{82} +14.8166 q^{83} +(0.215427 - 2.23674i) q^{85} +(-12.2005 - 11.2320i) q^{86} +(-3.94599 + 5.06893i) q^{88} +4.82493i q^{89} +10.9822 q^{91} +(-3.86233 + 0.319823i) q^{92} +(-6.52352 - 6.00566i) q^{94} +(0.391485 - 4.06472i) q^{95} -14.9168i q^{97} +(-0.839069 + 0.911421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4}+O(q^{10}) \) 48 * q + 4 * q^4	\( 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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