LMFDB - Embedded newform 288.3.q.b.65.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(65,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("288.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.q (of order $6$, degree $2$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.12
Character	$\chi$	$=$	288.65
Dual form			288.3.q.b.257.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81202 + 1.04524i) q^{3} +(5.41309 - 3.12525i) q^{5} +(3.74855 - 6.49268i) q^{7} +(6.81493 + 5.87850i) q^{9} +O(q^{10})$	\(q+(2.81202 + 1.04524i) q^{3} +(5.41309 - 3.12525i) q^{5} +(3.74855 - 6.49268i) q^{7} +(6.81493 + 5.87850i) q^{9} +(-6.17688 - 3.56622i) q^{11} +(-0.888802 - 1.53945i) q^{13} +(18.4884 - 3.13027i) q^{15} -14.7791i q^{17} -19.9460 q^{19} +(17.3274 - 14.3394i) q^{21} +(-20.8716 + 12.0502i) q^{23} +(7.03438 - 12.1839i) q^{25} +(13.0193 + 23.6537i) q^{27} +(40.1279 + 23.1679i) q^{29} +(14.1547 + 24.5167i) q^{31} +(-13.6419 - 16.4846i) q^{33} -46.8606i q^{35} +63.0770 q^{37} +(-0.890228 - 5.25798i) q^{39} +(-28.0185 + 16.1765i) q^{41} +(-38.8176 + 67.2341i) q^{43} +(55.2616 + 10.5225i) q^{45} +(-38.4719 - 22.2118i) q^{47} +(-3.60324 - 6.24099i) q^{49} +(15.4478 - 41.5593i) q^{51} -42.2846i q^{53} -44.5813 q^{55} +(-56.0887 - 20.8485i) q^{57} +(93.8917 - 54.2084i) q^{59} +(-25.3858 + 43.9695i) q^{61} +(63.7133 - 22.2113i) q^{63} +(-9.62233 - 5.55546i) q^{65} +(56.9484 + 98.6376i) q^{67} +(-71.2869 + 12.0696i) q^{69} -85.2129i q^{71} -94.5357 q^{73} +(32.5160 - 26.9087i) q^{75} +(-46.3086 + 26.7363i) q^{77} +(-35.6059 + 61.6712i) q^{79} +(11.8865 + 80.1231i) q^{81} +(-94.9037 - 54.7927i) q^{83} +(-46.1885 - 80.0009i) q^{85} +(88.6244 + 107.092i) q^{87} +29.6936i q^{89} -13.3269 q^{91} +(14.1774 + 83.7365i) q^{93} +(-107.970 + 62.3363i) q^{95} +(-62.4793 + 108.217i) q^{97} +(-21.1309 - 60.6143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^9	$ 24 q + 12 q^{9} + 24 q^{21} + 60 q^{25} + 72 q^{29} + 108 q^{33} + 252 q^{41} + 72 q^{45} - 36 q^{49} + 12 q^{57} - 96 q^{61} - 288 q^{65} - 432 q^{69} + 24 q^{73} - 720 q^{77} - 372 q^{81} + 96 q^{85} - 132 q^{97}+O(q^{100}) $ 24 * q + 12 * q^9 + 24 * q^21 + 60 * q^25 + 72 * q^29 + 108 * q^33 + 252 * q^41 + 72 * q^45 - 36 * q^49 + 12 * q^57 - 96 * q^61 - 288 * q^65 - 432 * q^69 + 24 * q^73 - 720 * q^77 - 372 * q^81 + 96 * q^85 - 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	2.81202	+	1.04524i	0.937340	+	0.348415i
$3$	2.81202	+	1.04524i	0.937340	+	0.348415i
$4$		0			0
$5$	5.41309	−	3.12525i	1.08262	−	0.625050i	0.151017	−	0.988531i	$-0.451745\pi$
$5$	5.41309	−	3.12525i	1.08262	−	0.625050i	0.931602	+	0.363481i	$0.118412\pi$
$6$		0			0
$7$	3.74855	−	6.49268i	0.535507	−	0.927525i	−0.463632	−	0.886028i	$-0.653454\pi$
$7$	3.74855	−	6.49268i	0.535507	−	0.927525i	0.999139	−	0.0414972i	$-0.0132128\pi$
$8$		0			0
$9$	6.81493	+	5.87850i	0.757214	+	0.653167i
$10$		0			0
$11$	−6.17688	−	3.56622i	−0.561534	−	0.324202i	0.192227	−	0.981351i	$-0.438429\pi$
$11$	−6.17688	−	3.56622i	−0.561534	−	0.324202i	−0.753761	+	0.657149i	$0.771762\pi$
$12$		0			0
$13$	−0.888802	−	1.53945i	−0.0683694	−	0.118419i	0.829814	−	0.558040i	$-0.188446\pi$
$13$	−0.888802	−	1.53945i	−0.0683694	−	0.118419i	−0.898184	+	0.439620i	$0.855113\pi$
$14$		0			0
$15$	18.4884	−	3.13027i	1.23256	−	0.208684i
$16$		0			0
$17$		−	14.7791i		−	0.869362i	−0.900585	−	0.434681i	$-0.856861\pi$
$17$		−	14.7791i		−	0.869362i	0.900585	−	0.434681i	$-0.143139\pi$
$18$		0			0
$19$	−19.9460			−1.04979			−0.524896	−	0.851167i	$-0.675896\pi$
$19$	−19.9460			−1.04979			−0.524896	+	0.851167i	$0.675896\pi$
$20$		0			0
$21$	17.3274	−	14.3394i	0.825116	−	0.682828i
$22$		0			0
$23$	−20.8716	+	12.0502i	−0.907462	+	0.523923i	−0.879614	−	0.475689i	$-0.842199\pi$
$23$	−20.8716	+	12.0502i	−0.907462	+	0.523923i	−0.0278482	+	0.999612i	$0.508866\pi$
$24$		0			0
$25$	7.03438	−	12.1839i	0.281375	−	0.487356i
$26$		0			0
$27$	13.0193	+	23.6537i	0.482195	+	0.876064i
$28$		0			0
$29$	40.1279	+	23.1679i	1.38372	+	0.798891i	0.992598	−	0.121447i	$-0.0387535\pi$
$29$	40.1279	+	23.1679i	1.38372	+	0.798891i	0.391123	+	0.920339i	$0.372087\pi$
$30$		0			0
$31$	14.1547	+	24.5167i	0.456603	+	0.790860i	0.998779	−	0.0494054i	$-0.0157326\pi$
$31$	14.1547	+	24.5167i	0.456603	+	0.790860i	−0.542176	+	0.840265i	$0.682399\pi$
$32$		0			0
$33$	−13.6419	−	16.4846i	−0.413392	−	0.499534i
$34$		0			0
$35$		−	46.8606i		−	1.33887i
$36$		0			0
$37$	63.0770			1.70478			0.852391	−	0.522904i	$-0.175151\pi$
$37$	63.0770			1.70478			0.852391	+	0.522904i	$0.175151\pi$
$38$		0			0
$39$	−0.890228	−	5.25798i	−0.0228264	−	0.134820i
$40$		0			0
$41$	−28.0185	+	16.1765i	−0.683378	+	0.394549i	−0.801127	−	0.598495i	$-0.795766\pi$
$41$	−28.0185	+	16.1765i	−0.683378	+	0.394549i	0.117748	+	0.993043i	$0.462432\pi$
$42$		0			0
$43$	−38.8176	+	67.2341i	−0.902736	+	1.56358i	−0.0788077	+	0.996890i	$0.525111\pi$
$43$	−38.8176	+	67.2341i	−0.902736	+	1.56358i	−0.823928	+	0.566694i	$0.808222\pi$
$44$		0			0
$45$	55.2616	+	10.5225i	1.22804	+	0.233833i
$46$		0			0
$47$	−38.4719	−	22.2118i	−0.818551	−	0.472591i	0.0313654	−	0.999508i	$-0.490014\pi$
$47$	−38.4719	−	22.2118i	−0.818551	−	0.472591i	−0.849917	+	0.526917i	$0.823348\pi$
$48$		0			0
$49$	−3.60324	−	6.24099i	−0.0735354	−	0.127367i
$50$		0			0
$51$	15.4478	−	41.5593i	0.302899	−	0.814888i
$52$		0			0
$53$		−	42.2846i		−	0.797823i	−0.916990	−	0.398911i	$-0.869388\pi$
$53$		−	42.2846i		−	0.797823i	0.916990	−	0.398911i	$-0.130612\pi$
$54$		0			0
$55$	−44.5813			−0.810570
$56$		0			0
$57$	−56.0887	−	20.8485i	−0.984012	−	0.365763i
$58$		0			0
$59$	93.8917	−	54.2084i	1.59138	−	0.918786i	0.598314	−	0.801262i	$-0.295838\pi$
$59$	93.8917	−	54.2084i	1.59138	−	0.918786i	0.993070	−	0.117524i	$-0.0374957\pi$
$60$		0			0
$61$	−25.3858	+	43.9695i	−0.416161	+	0.720812i	−0.995550	−	0.0942396i	$-0.969958\pi$
$61$	−25.3858	+	43.9695i	−0.416161	+	0.720812i	0.579389	+	0.815051i	$0.303291\pi$
$62$		0			0
$63$	63.7133	−	22.2113i	1.01132	−	0.352560i
$64$		0			0
$65$	−9.62233	−	5.55546i	−0.148036	−	0.0854686i
$66$		0			0
$67$	56.9484	+	98.6376i	0.849977	+	1.47220i	0.881228	+	0.472691i	$0.156717\pi$
$67$	56.9484	+	98.6376i	0.849977	+	1.47220i	−0.0312514	+	0.999512i	$0.509949\pi$
$68$		0			0
$69$	−71.2869	+	12.0696i	−1.03314	+	0.174921i
$70$		0			0
$71$		−	85.2129i		−	1.20018i	−0.799932	−	0.600091i	$-0.795131\pi$
$71$		−	85.2129i		−	1.20018i	0.799932	−	0.600091i	$-0.204869\pi$
$72$		0			0
$73$	−94.5357			−1.29501			−0.647505	−	0.762061i	$-0.724188\pi$
$73$	−94.5357			−1.29501			−0.647505	+	0.762061i	$0.724188\pi$
$74$		0			0
$75$	32.5160	−	26.9087i	0.433546	−	0.358783i
$76$		0			0
$77$	−46.3086	+	26.7363i	−0.601411	+	0.347225i
$78$		0			0
$79$	−35.6059	+	61.6712i	−0.450707	+	0.780648i	−0.998430	−	0.0560122i	$-0.982161\pi$
$79$	−35.6059	+	61.6712i	−0.450707	+	0.780648i	0.547723	+	0.836660i	$0.315495\pi$
$80$		0			0
$81$	11.8865	+	80.1231i	0.146747	+	0.989174i
$82$		0			0
$83$	−94.9037	−	54.7927i	−1.14342	−	0.660153i	−0.196144	−	0.980575i	$-0.562842\pi$
$83$	−94.9037	−	54.7927i	−1.14342	−	0.660153i	−0.947275	+	0.320422i	$0.896175\pi$
$84$		0			0
$85$	−46.1885	−	80.0009i	−0.543395	−	0.941187i
$86$		0			0
$87$	88.6244	+	107.092i	1.01867	+	1.23094i
$88$		0			0
$89$			29.6936i			0.333635i	0.985988	+	0.166818i	$0.0533491\pi$
$89$			29.6936i			0.333635i	−0.985988	+	0.166818i	$0.946651\pi$
$90$		0			0
$91$	−13.3269			−0.146449
$92$		0			0
$93$	14.1774	+	83.7365i	0.152445	+	0.900392i
$94$		0			0
$95$	−107.970	+	62.3363i	−1.13652	+	0.656172i
$96$		0			0
$97$	−62.4793	+	108.217i	−0.644116	+	1.11564i	0.340389	+	0.940285i	$0.389441\pi$
$97$	−62.4793	+	108.217i	−0.644116	+	1.11564i	−0.984505	+	0.175357i	$0.943892\pi$
$98$		0			0
$99$	−21.1309	−	60.6143i	−0.213444	−	0.612266i
$100$		0			0
$101$	−34.0989	−	19.6870i	−0.337613	−	0.194921i	0.321603	−	0.946875i	$-0.395778\pi$
$101$	−34.0989	−	19.6870i	−0.337613	−	0.194921i	−0.659216	+	0.751954i	$0.729112\pi$
$102$		0			0
$103$	−74.7230	−	129.424i	−0.725466	−	1.25654i	−0.958782	−	0.284143i	$-0.908291\pi$
$103$	−74.7230	−	129.424i	−0.725466	−	1.25654i	0.233316	−	0.972401i	$-0.425042\pi$
$104$		0			0
$105$	48.9808	−	131.773i	0.466484	−	1.25498i
$106$		0			0
$107$		−	0.420211i		−	0.00392721i	−0.999998	−	0.00196360i	$-0.999375\pi$
$107$		−	0.420211i		−	0.00392721i	0.999998	−	0.00196360i	$-0.000625035\pi$
$108$		0			0
$109$	64.4616			0.591391			0.295695	−	0.955282i	$-0.404449\pi$
$109$	64.4616			0.591391			0.295695	+	0.955282i	$0.404449\pi$
$110$		0			0
$111$	177.374	+	65.9309i	1.59796	+	0.593972i
$112$		0			0
$113$	22.4718	−	12.9741i	0.198865	−	0.114815i	−0.397261	−	0.917706i	$-0.630039\pi$
$113$	22.4718	−	12.9741i	0.198865	−	0.114815i	0.596126	+	0.802891i	$0.296706\pi$
$114$		0			0
$115$	−75.3200	+	130.458i	−0.654957	+	1.13442i
$116$		0			0
$117$	2.99254	−	15.7161i	0.0255772	−	0.134325i
$118$		0			0
$119$	−95.9562	−	55.4004i	−0.806355	−	0.465549i
$120$		0			0
$121$	−35.0641	−	60.7329i	−0.289786	−	0.501925i
$122$		0			0
$123$	−95.6971	+	16.2025i	−0.778025	+	0.131727i
$124$		0			0
$125$			68.3258i			0.546606i
$126$		0			0
$127$	−12.0916			−0.0952097			−0.0476049	−	0.998866i	$-0.515159\pi$
$127$	−12.0916			−0.0952097			−0.0476049	+	0.998866i	$0.515159\pi$
$128$		0			0
$129$	−179.432	+	148.490i	−1.39095	+	1.15108i
$130$		0			0
$131$	−45.4518	+	26.2416i	−0.346960	+	0.200318i	−0.663346	−	0.748313i	$-0.730864\pi$
$131$	−45.4518	+	26.2416i	−0.346960	+	0.200318i	0.316385	+	0.948631i	$0.397531\pi$
$132$		0			0
$133$	−74.7687	+	129.503i	−0.562171	+	0.973708i
$134$		0			0
$135$	144.398	+	87.3514i	1.06962	+	0.647047i
$136$		0			0
$137$	−121.224	−	69.9888i	−0.884848	−	0.510867i	−0.0125942	−	0.999921i	$-0.504009\pi$
$137$	−121.224	−	69.9888i	−0.884848	−	0.510867i	−0.872254	+	0.489053i	$0.837342\pi$
$138$		0			0
$139$	19.9656	+	34.5814i	0.143637	+	0.248787i	0.928864	−	0.370422i	$-0.120787\pi$
$139$	19.9656	+	34.5814i	0.143637	+	0.248787i	−0.785226	+	0.619209i	$0.787453\pi$
$140$		0			0
$141$	−84.9671	−	102.673i	−0.602604	−	0.728174i
$142$		0			0
$143$			12.6787i			0.0886619i
$144$		0			0
$145$	289.621			1.99739
$146$		0			0
$147$	−3.60902	−	21.3161i	−0.0245512	−	0.145007i
$148$		0			0
$149$	−3.26226	+	1.88347i	−0.0218944	+	0.0126407i	−0.510907	−	0.859636i	$-0.670690\pi$
$149$	−3.26226	+	1.88347i	−0.0218944	+	0.0126407i	0.489013	+	0.872277i	$0.337357\pi$
$150$		0			0
$151$	74.8795	−	129.695i	0.495891	−	0.858908i	−0.504098	−	0.863646i	$-0.668175\pi$
$151$	74.8795	−	129.695i	0.495891	−	0.858908i	0.999989	+	0.00473848i	$0.00150831\pi$
$152$		0			0
$153$	86.8792	−	100.719i	0.567838	−	0.658293i
$154$		0			0
$155$	153.241	+	88.4739i	0.988654	+	0.570800i
$156$		0			0
$157$	−58.9507	−	102.106i	−0.375482	−	0.650354i	0.614917	−	0.788592i	$-0.289189\pi$
$157$	−58.9507	−	102.106i	−0.375482	−	0.650354i	−0.990399	+	0.138238i	$0.955856\pi$
$158$		0			0
$159$	44.1977	−	118.905i	0.277973	−	0.747831i
$160$		0			0
$161$			180.684i			1.12226i
$162$		0			0
$163$	111.960			0.686874			0.343437	−	0.939176i	$-0.388409\pi$
$163$	111.960			0.686874			0.343437	+	0.939176i	$0.388409\pi$
$164$		0			0
$165$	−125.364	−	46.5984i	−0.759780	−	0.282414i
$166$		0			0
$167$	1.33677	−	0.771783i	0.00800460	−	0.00462146i	−0.495992	−	0.868327i	$-0.665196\pi$
$167$	1.33677	−	0.771783i	0.00800460	−	0.00462146i	0.503997	+	0.863705i	$0.331862\pi$
$168$		0			0
$169$	82.9201	−	143.622i	0.490651	−	0.849833i
$170$		0			0
$171$	−135.931	−	117.253i	−0.794917	−	0.685689i
$172$		0			0
$173$	46.0581	+	26.5917i	0.266232	+	0.153709i	0.627174	−	0.778879i	$-0.284211\pi$
$173$	46.0581	+	26.5917i	0.266232	+	0.153709i	−0.360942	+	0.932588i	$0.617545\pi$
$174$		0			0
$175$	−52.7374	−	91.3439i	−0.301357	−	0.521965i
$176$		0			0
$177$	320.686	−	54.2954i	1.81179	−	0.306753i
$178$		0			0
$179$		−	239.444i		−	1.33768i	−0.743407	−	0.668839i	$-0.766792\pi$
$179$		−	239.444i		−	1.33768i	0.743407	−	0.668839i	$-0.233208\pi$
$180$		0			0
$181$	61.1557			0.337877			0.168938	−	0.985627i	$-0.445966\pi$
$181$	61.1557			0.337877			0.168938	+	0.985627i	$0.445966\pi$
$182$		0			0
$183$	−117.344	+	97.1089i	−0.641226	+	0.530649i
$184$		0			0
$185$	341.441	−	197.131i	1.84563	−	1.06557i
$186$		0			0
$187$	−52.7057	+	91.2890i	−0.281849	+	0.488176i
$188$		0			0
$189$	202.379	+	4.13737i	1.07079	+	0.0218908i
$190$		0			0
$191$	28.9063	+	16.6891i	0.151342	+	0.0873773i	0.573759	−	0.819024i	$-0.305485\pi$
$191$	28.9063	+	16.6891i	0.151342	+	0.0873773i	−0.422417	+	0.906402i	$0.638818\pi$
$192$		0			0
$193$	21.2796	+	36.8573i	0.110257	+	0.190971i	0.915874	−	0.401466i	$-0.131499\pi$
$193$	21.2796	+	36.8573i	0.110257	+	0.190971i	−0.805617	+	0.592437i	$0.798166\pi$
$194$		0			0
$195$	−21.2514	−	25.6798i	−0.108982	−	0.131691i
$196$		0			0
$197$		−	203.372i		−	1.03235i	−0.856484	−	0.516173i	$-0.827356\pi$
$197$		−	203.372i		−	1.03235i	0.856484	−	0.516173i	$-0.172644\pi$
$198$		0			0
$199$	128.160			0.644022			0.322011	−	0.946736i	$-0.395641\pi$
$199$	128.160			0.644022			0.322011	+	0.946736i	$0.395641\pi$
$200$		0			0
$201$	57.0398	+	336.896i	0.283780	+	1.67610i
$202$		0			0
$203$	300.843	−	173.692i	1.48198	−	0.855624i
$204$		0			0
$205$	−101.111	+	175.130i	−0.493225	+	0.854291i
$206$		0			0
$207$	−213.076	−	40.5723i	−1.02935	−	0.196002i
$208$		0			0
$209$	123.204	+	71.1320i	0.589494	+	0.340344i
$210$		0			0
$211$	97.2675	+	168.472i	0.460983	+	0.798446i	0.999010	−	0.0444812i	$-0.0141635\pi$
$211$	97.2675	+	168.472i	0.460983	+	0.798446i	−0.538027	+	0.842928i	$0.680830\pi$
$212$		0			0
$213$	89.0683	−	239.620i	0.418161	−	1.12498i
$214$		0			0
$215$			485.259i			2.25702i
$216$		0			0
$217$	212.238			0.978057
$218$		0			0
$219$	−265.837	−	98.8130i	−1.21387	−	0.451201i
$220$		0			0
$221$	−22.7518	+	13.1357i	−0.102949	+	0.0594377i
$222$		0			0
$223$	95.1454	−	164.797i	0.426661	−	0.738998i	−0.569913	−	0.821705i	$-0.693023\pi$
$223$	95.1454	−	164.797i	0.426661	−	0.738998i	0.996574	+	0.0827067i	$0.0263565\pi$
$224$		0			0
$225$	119.562	−	41.6808i	0.531386	−	0.185248i
$226$		0			0
$227$	320.930	+	185.289i	1.41379	+	0.816252i	0.995743	−	0.0921738i	$-0.0293815\pi$
$227$	320.930	+	185.289i	1.41379	+	0.816252i	0.418047	+	0.908426i	$0.362715\pi$
$228$		0			0
$229$	−203.685	−	352.793i	−0.889455	−	1.54058i	−0.840521	−	0.541779i	$-0.817751\pi$
$229$	−203.685	−	352.793i	−0.889455	−	1.54058i	−0.0489338	−	0.998802i	$-0.515582\pi$
$230$		0			0
$231$	−158.167	+	26.7792i	−0.684705	+	0.115927i
$232$		0			0
$233$		−	21.5267i		−	0.0923895i	−0.998932	−	0.0461947i	$-0.985291\pi$
$233$		−	21.5267i		−	0.0923895i	0.998932	−	0.0461947i	$-0.0147095\pi$
$234$		0			0
$235$	−277.669			−1.18157
$236$		0			0
$237$	−164.586	+	136.204i	−0.694455	+	0.574699i
$238$		0			0
$239$	−172.020	+	99.3155i	−0.719747	+	0.415546i	−0.814660	−	0.579939i	$-0.803076\pi$
$239$	−172.020	+	99.3155i	−0.719747	+	0.415546i	0.0949125	+	0.995486i	$0.469743\pi$
$240$		0			0
$241$	−138.940	+	240.652i	−0.576516	+	0.998556i	0.419359	+	0.907821i	$0.362255\pi$
$241$	−138.940	+	240.652i	−0.576516	+	0.998556i	−0.995875	+	0.0907351i	$0.971078\pi$
$242$		0			0
$243$	−50.3232	+	237.732i	−0.207091	+	0.978322i
$244$		0			0
$245$	−39.0093	−	22.5220i	−0.159222	−	0.0919267i
$246$		0			0
$247$	17.7281	+	30.7059i	0.0717736	+	0.124315i
$248$		0			0
$249$	−209.600	−	253.276i	−0.841765	−	1.01717i
$250$		0			0
$251$			128.325i			0.511253i	0.966776	+	0.255627i	$0.0822817\pi$
$251$			128.325i			0.511253i	−0.966776	+	0.255627i	$0.917718\pi$
$252$		0			0
$253$	171.895			0.679428
$254$		0			0
$255$	−46.2627	−	273.243i	−0.181422	−	1.07154i
$256$		0			0
$257$	62.3584	−	36.0026i	0.242640	−	0.140088i	−0.373750	−	0.927530i	$-0.621928\pi$
$257$	62.3584	−	36.0026i	0.242640	−	0.140088i	0.616389	+	0.787442i	$0.288595\pi$
$258$		0			0
$259$	236.447	−	409.538i	0.912923	−	1.58123i
$260$		0			0
$261$	137.277	+	393.779i	0.525964	+	1.50873i
$262$		0			0
$263$	−113.783	−	65.6926i	−0.432634	−	0.249782i	0.267834	−	0.963465i	$-0.413692\pi$
$263$	−113.783	−	65.6926i	−0.432634	−	0.249782i	−0.700468	+	0.713683i	$0.747025\pi$
$264$		0			0
$265$	−132.150	−	228.890i	−0.498679	−	0.863737i
$266$		0			0
$267$	−31.0370	+	83.4989i	−0.116244	+	0.312730i
$268$		0			0
$269$		−	38.8284i		−	0.144344i	−0.997392	−	0.0721718i	$-0.977007\pi$
$269$		−	38.8284i		−	0.144344i	0.997392	−	0.0721718i	$-0.0229930\pi$
$270$		0			0
$271$	−0.802525			−0.00296135			−0.00148067	−	0.999999i	$-0.500471\pi$
$271$	−0.802525			−0.00296135			−0.00148067	+	0.999999i	$0.500471\pi$
$272$		0			0
$273$	−37.4754	−	13.9298i	−0.137273	−	0.0510250i
$274$		0			0
$275$	−86.9009	+	50.1723i	−0.316003	+	0.182445i
$276$		0			0
$277$	61.1932	−	105.990i	0.220914	−	0.382635i	−0.734172	−	0.678964i	$-0.762429\pi$
$277$	61.1932	−	105.990i	0.220914	−	0.382635i	0.955086	+	0.296329i	$0.0957626\pi$
$278$		0			0
$279$	−47.6579	+	250.288i	−0.170817	+	0.897088i
$280$		0			0
$281$	−254.139	−	146.727i	−0.904408	−	0.522160i	−0.0257801	−	0.999668i	$-0.508207\pi$
$281$	−254.139	−	146.727i	−0.904408	−	0.522160i	−0.878628	+	0.477508i	$0.841540\pi$
$282$		0			0
$283$	−90.6191	−	156.957i	−0.320209	−	0.554618i	0.660322	−	0.750983i	$-0.270420\pi$
$283$	−90.6191	−	156.957i	−0.320209	−	0.554618i	−0.980531	+	0.196364i	$0.937086\pi$
$284$		0			0
$285$	−368.770	+	62.4364i	−1.29393	+	0.219075i
$286$		0			0
$287$			242.554i			0.845134i
$288$		0			0
$289$	70.5768			0.244210
$290$		0			0
$291$	−288.806	+	239.003i	−0.992462	+	0.821316i
$292$		0			0
$293$	−290.545	+	167.746i	−0.991622	+	0.572513i	−0.905759	−	0.423794i	$-0.860698\pi$
$293$	−290.545	+	167.746i	−0.991622	+	0.572513i	−0.0858631	+	0.996307i	$0.527365\pi$
$294$		0			0
$295$	338.829	−	586.870i	1.14857	−	1.98939i
$296$		0			0
$297$	3.93612	−	192.536i	0.0132529	−	0.648268i
$298$		0			0
$299$	37.1015	+	21.4205i	0.124085	+	0.0716406i
$300$		0			0
$301$	291.020	+	504.061i	0.966843	+	1.67462i
$302$		0			0
$303$	−75.3090	−	91.0019i	−0.248545	−	0.300336i
$304$		0			0
$305$			317.348i			1.04049i
$306$		0			0
$307$	289.210			0.942053			0.471027	−	0.882119i	$-0.343884\pi$
$307$	289.210			0.942053			0.471027	+	0.882119i	$0.343884\pi$
$308$		0			0
$309$	−74.8429	−	442.047i	−0.242210	−	1.43057i
$310$		0			0
$311$	−23.6987	+	13.6824i	−0.0762016	+	0.0439950i	−0.537617	−	0.843189i	$-0.680675\pi$
$311$	−23.6987	+	13.6824i	−0.0762016	+	0.0439950i	0.461415	+	0.887184i	$0.347342\pi$
$312$		0			0
$313$	−293.572	+	508.481i	−0.937928	+	1.62454i	−0.168601	+	0.985684i	$0.553925\pi$
$313$	−293.572	+	508.481i	−0.937928	+	1.62454i	−0.769327	+	0.638855i	$0.779408\pi$
$314$		0			0
$315$	275.470	−	319.352i	0.874508	−	1.01381i
$316$		0			0
$317$	326.081	+	188.263i	1.02865	+	0.593889i	0.916596	−	0.399814i	$-0.130925\pi$
$317$	326.081	+	188.263i	1.02865	+	0.593889i	0.112049	+	0.993703i	$0.464259\pi$
$318$		0			0
$319$	−165.243	−	286.210i	−0.518004	−	0.897210i
$320$		0			0
$321$	0.439223	−	1.18164i	0.00136830	−	0.00368113i
$322$		0			0
$323$			294.785i			0.912648i
$324$		0			0
$325$	−25.0087			−0.0769497
$326$		0			0
$327$	181.267	+	67.3781i	0.554335	+	0.206049i
$328$		0			0
$329$	−288.428	+	166.524i	−0.876680	+	0.506151i
$330$		0			0
$331$	1.48388	−	2.57015i	0.00448301	−	0.00776480i	−0.863775	−	0.503877i	$-0.831906\pi$
$331$	1.48388	−	2.57015i	0.00448301	−	0.00776480i	0.868258	+	0.496113i	$0.165240\pi$
$332$		0			0
$333$	429.865	+	370.798i	1.29089	+	1.11351i
$334$		0			0
$335$	616.534	+	355.956i	1.84040	+	1.06256i
$336$		0			0
$337$	−329.235	−	570.251i	−0.976958	−	1.69214i	−0.673317	−	0.739354i	$-0.735131\pi$
$337$	−329.235	−	570.251i	−0.976958	−	1.69214i	−0.303641	−	0.952786i	$-0.598202\pi$
$338$		0			0
$339$	76.7522	−	12.9949i	0.226408	−	0.0383330i
$340$		0			0
$341$		−	201.915i		−	0.592126i
$342$		0			0
$343$	313.330			0.913499
$344$		0			0
$345$	−348.162	+	288.123i	−1.00917	+	0.835139i
$346$		0			0
$347$	−255.949	+	147.772i	−0.737606	+	0.425857i	−0.821198	−	0.570643i	$-0.806694\pi$
$347$	−255.949	+	147.772i	−0.737606	+	0.425857i	0.0835920	+	0.996500i	$0.473361\pi$
$348$		0			0
$349$	106.379	−	184.254i	0.304811	−	0.527949i	−0.672408	−	0.740181i	$-0.734740\pi$
$349$	106.379	−	184.254i	0.304811	−	0.527949i	0.977219	+	0.212232i	$0.0680733\pi$
$350$		0			0
$351$	24.8422	−	41.0660i	0.0707755	−	0.116997i
$352$		0			0
$353$	−124.287	−	71.7570i	−0.352087	−	0.203278i	0.313517	−	0.949583i	$-0.398493\pi$
$353$	−124.287	−	71.7570i	−0.352087	−	0.203278i	−0.665604	+	0.746305i	$0.731826\pi$
$354$		0			0
$355$	−266.312	−	461.265i	−0.750173	−	1.29934i
$356$		0			0
$357$	−211.924	−	256.085i	−0.593625	−	0.717324i
$358$		0			0
$359$		−	270.973i		−	0.754799i	−0.926051	−	0.377400i	$-0.876818\pi$
$359$		−	270.973i		−	0.754799i	0.926051	−	0.377400i	$-0.123182\pi$
$360$		0			0
$361$	36.8443			0.102062
$362$		0			0
$363$	−35.1204	−	207.433i	−0.0967504	−	0.571440i
$364$		0			0
$365$	−511.731	+	295.448i	−1.40200	+	0.809446i
$366$		0			0
$367$	−200.855	+	347.892i	−0.547290	+	0.947934i	0.451169	+	0.892438i	$0.351007\pi$
$367$	−200.855	+	347.892i	−0.547290	+	0.947934i	−0.998459	+	0.0554953i	$0.982326\pi$
$368$		0			0
$369$	−286.038	−	54.4652i	−0.775170	−	0.147602i
$370$		0			0
$371$	−274.540	−	158.506i	−0.740001	−	0.427240i
$372$		0			0
$373$	−146.890	−	254.422i	−0.393808	−	0.682095i	0.599140	−	0.800644i	$-0.295509\pi$
$373$	−146.890	−	254.422i	−0.393808	−	0.682095i	−0.992948	+	0.118549i	$0.962176\pi$
$374$		0			0
$375$	−71.4171	+	192.134i	−0.190446	+	0.512356i
$376$		0			0
$377$		−	82.3665i		−	0.218479i
$378$		0			0
$379$	280.802			0.740903			0.370452	−	0.928852i	$-0.379203\pi$
$379$	280.802			0.740903			0.370452	+	0.928852i	$0.379203\pi$
$380$		0			0
$381$	−34.0019	−	12.6387i	−0.0892439	−	0.0331725i
$382$		0			0
$383$	546.665	−	315.617i	1.42732	−	0.824066i	0.430416	−	0.902631i	$-0.358367\pi$
$383$	546.665	−	315.617i	1.42732	−	0.824066i	0.996909	+	0.0785646i	$0.0250337\pi$
$384$		0			0
$385$	−167.115	+	289.452i	−0.434066	+	0.751824i
$386$		0			0
$387$	−659.775	+	230.006i	−1.70485	+	0.594331i
$388$		0			0
$389$	378.049	+	218.267i	0.971849	+	0.561097i	0.899799	−	0.436304i	$-0.143713\pi$
$389$	378.049	+	218.267i	0.971849	+	0.561097i	0.0720497	+	0.997401i	$0.477046\pi$
$390$		0			0
$391$	178.092	+	308.465i	0.455479	+	0.788913i
$392$		0			0
$393$	−155.240	+	26.2837i	−0.395014	+	0.0668797i
$394$		0			0
$395$			445.109i			1.12686i
$396$		0			0
$397$	−405.382			−1.02111			−0.510557	−	0.859844i	$-0.670561\pi$
$397$	−405.382			−1.02111			−0.510557	+	0.859844i	$0.670561\pi$
$398$		0			0
$399$	−345.614	+	286.014i	−0.866199	+	0.716827i
$400$		0			0
$401$	−66.9595	+	38.6591i	−0.166981	+	0.0964068i	−0.581162	−	0.813788i	$-0.697402\pi$
$401$	−66.9595	+	38.6591i	−0.166981	+	0.0964068i	0.414180	+	0.910195i	$0.364068\pi$
$402$		0			0
$403$	25.1614	−	43.5809i	0.0624353	−	0.108141i
$404$		0			0
$405$	314.747	+	396.565i	0.777154	+	0.979174i
$406$		0			0
$407$	−389.619	−	224.946i	−0.957294	−	0.552694i
$408$		0			0
$409$	85.3306	+	147.797i	0.208632	+	0.361362i	0.951284	−	0.308316i	$-0.0997655\pi$
$409$	85.3306	+	147.797i	0.208632	+	0.361362i	−0.742652	+	0.669678i	$0.766432\pi$
$410$		0			0
$411$	−267.730	−	323.519i	−0.651410	−	0.787151i
$412$		0			0
$413$		−	812.811i		−	1.96807i
$414$		0			0
$415$	−684.964			−1.65051
$416$		0			0
$417$	19.9976	+	118.113i	0.0479559	+	0.283244i
$418$		0			0
$419$	−123.529	+	71.3195i	−0.294819	+	0.170214i	−0.640113	−	0.768281i	$-0.721112\pi$
$419$	−123.529	+	71.3195i	−0.294819	+	0.170214i	0.345294	+	0.938494i	$0.387779\pi$
$420$		0			0
$421$	−307.819	+	533.158i	−0.731162	+	1.26641i	0.225226	+	0.974307i	$0.427688\pi$
$421$	−307.819	+	533.158i	−0.731162	+	1.26641i	−0.956387	+	0.292102i	$0.905645\pi$
$422$		0			0
$423$	−131.611	−	377.529i	−0.311138	−	0.892503i
$424$		0			0
$425$	−180.068	−	103.962i	−0.423689	−	0.244617i
$426$		0			0
$427$	190.320	+	329.644i	0.445714	+	0.772000i
$428$		0			0
$429$	−13.2523	+	35.6526i	−0.0308911	+	0.0831064i
$430$		0			0
$431$		−	405.961i		−	0.941905i	−0.882159	−	0.470953i	$-0.843910\pi$
$431$		−	405.961i		−	0.941905i	0.882159	−	0.470953i	$-0.156090\pi$
$432$		0			0
$433$	50.1302			0.115774			0.0578870	−	0.998323i	$-0.481564\pi$
$433$	50.1302			0.115774			0.0578870	+	0.998323i	$0.481564\pi$
$434$		0			0
$435$	814.421	+	302.725i	1.87223	+	0.695920i
$436$		0			0
$437$	416.306	−	240.354i	0.952646	−	0.550010i
$438$		0			0
$439$	−363.552	+	629.690i	−0.828136	+	1.43437i	0.0713624	+	0.997450i	$0.477265\pi$
$439$	−363.552	+	629.690i	−0.828136	+	1.43437i	−0.899499	+	0.436924i	$0.856068\pi$
$440$		0			0
$441$	12.1319	−	63.7135i	0.0275099	−	0.144475i
$442$		0			0
$443$	324.072	+	187.103i	0.731540	+	0.422355i	0.818985	−	0.573815i	$-0.194537\pi$
$443$	324.072	+	187.103i	0.731540	+	0.422355i	−0.0874454	+	0.996169i	$0.527870\pi$
$444$		0			0
$445$	92.7998	+	160.734i	0.208539	+	0.361200i
$446$		0			0
$447$	−11.1422	+	1.88649i	−0.0249267	+	0.00422033i
$448$		0			0
$449$		−	225.368i		−	0.501934i	−0.967996	−	0.250967i	$-0.919251\pi$
$449$		−	225.368i		−	0.501934i	0.967996	−	0.250967i	$-0.0807486\pi$
$450$		0			0
$451$	230.756			0.511654
$452$		0			0
$453$	346.126	−	286.438i	0.764075	−	0.632313i
$454$		0			0
$455$	−72.1396	+	41.6498i	−0.158549	+	0.0915380i
$456$		0			0
$457$	390.263	−	675.955i	0.853966	−	1.47911i	−0.0236344	−	0.999721i	$-0.507524\pi$
$457$	390.263	−	675.955i	0.853966	−	1.47911i	0.877601	−	0.479392i	$-0.159143\pi$
$458$		0			0
$459$	349.582	−	192.413i	0.761617	−	0.419201i
$460$		0			0
$461$	474.085	+	273.713i	1.02838	+	0.593738i	0.916521	−	0.399986i	$-0.130985\pi$
$461$	474.085	+	273.713i	1.02838	+	0.593738i	0.111863	+	0.993724i	$0.464318\pi$
$462$		0			0
$463$	174.664	+	302.526i	0.377243	+	0.653404i	0.990660	−	0.136355i	$-0.0435388\pi$
$463$	174.664	+	302.526i	0.377243	+	0.653404i	−0.613417	+	0.789759i	$0.710205\pi$
$464$		0			0
$465$	338.441	+	408.965i	0.727830	+	0.879495i
$466$		0			0
$467$		−	499.358i		−	1.06929i	−0.845077	−	0.534645i	$-0.820445\pi$
$467$		−	499.358i		−	1.06929i	0.845077	−	0.534645i	$-0.179555\pi$
$468$		0			0
$469$	853.896			1.82067
$470$		0			0
$471$	−59.0453	−	348.741i	−0.125361	−	0.740426i
$472$		0			0
$473$	479.543	−	276.865i	1.01383	−	0.585337i
$474$		0			0
$475$	−140.308	+	243.020i	−0.295385	+	0.511622i
$476$		0			0
$477$	248.570	−	288.166i	0.521111	−	0.604123i
$478$		0			0
$479$	571.640	+	330.036i	1.19340	+	0.689011i	0.959076	−	0.283147i	$-0.0913785\pi$
$479$	571.640	+	330.036i	1.19340	+	0.689011i	0.234326	+	0.972158i	$0.424712\pi$
$480$		0			0
$481$	−56.0629	−	97.1038i	−0.116555	−	0.201879i
$482$		0			0
$483$	−188.859	+	508.086i	−0.391011	+	1.05194i
$484$		0			0
$485$			781.053i			1.61042i
$486$		0			0
$487$	217.861			0.447352			0.223676	−	0.974664i	$-0.428194\pi$
$487$	217.861			0.447352			0.223676	+	0.974664i	$0.428194\pi$
$488$		0			0
$489$	314.835	+	117.026i	0.643835	+	0.239317i
$490$		0			0
$491$	−132.712	+	76.6214i	−0.270289	+	0.156052i	−0.629019	−	0.777390i	$-0.716543\pi$
$491$	−132.712	+	76.6214i	−0.270289	+	0.156052i	0.358730	+	0.933441i	$0.383210\pi$
$492$		0			0
$493$	342.401	−	593.056i	0.694526	−	1.20295i
$494$		0			0
$495$	−303.819	−	262.071i	−0.613775	−	0.529437i
$496$		0			0
$497$	−553.260	−	319.425i	−1.11320	−	0.642706i
$498$		0			0
$499$	−153.693	−	266.204i	−0.308002	−	0.533476i	0.669923	−	0.742431i	$-0.266327\pi$
$499$	−153.693	−	266.204i	−0.308002	−	0.533476i	−0.977925	+	0.208955i	$0.932994\pi$
$500$		0			0
$501$	4.56572	−	0.773022i	0.00911322	−	0.00154296i
$502$		0			0
$503$		−	797.972i		−	1.58643i	−0.608945	−	0.793213i	$-0.708407\pi$
$503$		−	797.972i		−	1.58643i	0.608945	−	0.793213i	$-0.291593\pi$
$504$		0			0
$505$	−246.107			−0.487341
$506$		0			0
$507$	383.293	−	317.196i	0.756002	−	0.625633i
$508$		0			0
$509$	260.405	−	150.345i	0.511602	−	0.295373i	−0.221890	−	0.975072i	$-0.571223\pi$
$509$	260.405	−	150.345i	0.511602	−	0.295373i	0.733492	+	0.679698i	$0.237889\pi$
$510$		0			0
$511$	−354.372	+	613.790i	−0.693487	+	1.20115i
$512$		0			0
$513$	−259.682	−	471.798i	−0.506204	−	0.919685i
$514$		0			0
$515$	−808.965	−	467.056i	−1.57081	−	0.906905i
$516$		0			0
$517$	158.424	+	274.399i	0.306430	+	0.530752i
$518$		0			0
$519$	101.722	+	122.918i	0.195995	+	0.236837i
$520$		0			0
$521$			928.990i			1.78309i	0.452932	+	0.891545i	$0.350378\pi$
$521$			928.990i			1.78309i	−0.452932	+	0.891545i	$0.649622\pi$
$522$		0			0
$523$	−519.086			−0.992516			−0.496258	−	0.868175i	$-0.665293\pi$
$523$	−519.086			−0.992516			−0.496258	+	0.868175i	$0.665293\pi$
$524$		0			0
$525$	−52.8220	−	311.984i	−0.100613	−	0.594256i
$526$		0			0
$527$	362.335	−	209.194i	0.687543	−	0.396953i
$528$		0			0
$529$	25.9164	−	44.8885i	0.0489913	−	0.0848554i
$530$		0			0
$531$	958.529	+	182.516i	1.80514	+	0.343721i
$532$		0			0
$533$	49.8058	+	28.7554i	0.0934443	+	0.0539501i
$534$		0			0
$535$	−1.31326	−	2.27464i	−0.00245470	−	0.00425167i
$536$		0			0
$537$	250.278	−	673.322i	0.466067	−	1.25386i
$538$		0			0
$539$			51.3997i			0.0953613i
$540$		0			0
$541$	−109.959			−0.203251			−0.101625	−	0.994823i	$-0.532404\pi$
$541$	−109.959			−0.203251			−0.101625	+	0.994823i	$0.532404\pi$
$542$		0			0
$543$	171.971	+	63.9227i	0.316706	+	0.117721i
$544$		0			0
$545$	348.937	−	201.459i	0.640251	−	0.369649i
$546$		0			0
$547$	489.119	−	847.180i	0.894185	−	1.54877i	0.0593757	−	0.998236i	$-0.481089\pi$
$547$	489.119	−	847.180i	0.894185	−	1.54877i	0.834810	−	0.550539i	$-0.185578\pi$
$548$		0			0
$549$	−431.477	+	150.419i	−0.785933	+	0.273987i
$550$		0			0
$551$	−800.392	−	462.107i	−1.45262	−	0.838669i
$552$		0			0
$553$	266.941	+	462.355i	0.482714	+	0.836084i
$554$		0			0
$555$	1166.19	−	197.448i	2.10125	−	0.355762i
$556$		0			0
$557$		−	322.002i		−	0.578100i	−0.957314	−	0.289050i	$-0.906661\pi$
$557$		−	322.002i		−	0.578100i	0.957314	−	0.289050i	$-0.0933394\pi$
$558$		0			0
$559$	138.005			0.246878
$560$		0			0
$561$	−243.629	+	201.616i	−0.434276	+	0.359387i
$562$		0			0
$563$	−174.603	+	100.807i	−0.310129	+	0.179053i	−0.646984	−	0.762503i	$-0.723970\pi$
$563$	−174.603	+	100.807i	−0.310129	+	0.179053i	0.336855	+	0.941556i	$0.390637\pi$
$564$		0			0
$565$	81.0945	−	140.460i	0.143530	−	0.248601i
$566$		0			0
$567$	564.770	+	223.170i	0.996068	+	0.393598i
$568$		0			0
$569$	−123.786	−	71.4677i	−0.217549	−	0.125602i	0.387266	−	0.921968i	$-0.373420\pi$
$569$	−123.786	−	71.4677i	−0.217549	−	0.125602i	−0.604815	+	0.796366i	$0.706753\pi$
$570$		0			0
$571$	−45.7205	−	79.1902i	−0.0800709	−	0.138687i	0.823209	−	0.567738i	$-0.192181\pi$
$571$	−45.7205	−	79.1902i	−0.0800709	−	0.138687i	−0.903280	+	0.429051i	$0.858848\pi$
$572$		0			0
$573$	63.8410	+	77.1441i	0.111415	+	0.134632i
$574$		0			0
$575$			339.064i			0.589676i
$576$		0			0
$577$	404.739			0.701455			0.350727	−	0.936478i	$-0.385934\pi$
$577$	404.739			0.701455			0.350727	+	0.936478i	$0.385934\pi$
$578$		0			0
$579$	21.3137	+	125.886i	0.0368113	+	0.217420i
$580$		0			0
$581$	−711.503	+	410.786i	−1.22462	+	0.707033i
$582$		0			0
$583$	−150.796	+	261.187i	−0.258656	+	0.448005i
$584$		0			0
$585$	−32.9178	−	94.4249i	−0.0562697	−	0.161410i
$586$		0			0
$587$	−702.845	−	405.788i	−1.19735	−	0.691291i	−0.237387	−	0.971415i	$-0.576291\pi$
$587$	−702.845	−	405.788i	−1.19735	−	0.691291i	−0.959964	+	0.280125i	$0.909624\pi$
$588$		0			0
$589$	−282.330	−	489.010i	−0.479338	−	0.830238i
$590$		0			0
$591$	212.574	−	571.887i	0.359684	−	0.967659i
$592$		0			0
$593$			95.3026i			0.160713i	0.996766	+	0.0803563i	$0.0256058\pi$
$593$			95.3026i			0.160713i	−0.996766	+	0.0803563i	$0.974394\pi$
$594$		0			0
$595$	−692.560			−1.16397
$596$		0			0
$597$	360.390	+	133.959i	0.603668	+	0.224387i
$598$		0			0
$599$	−381.733	+	220.393i	−0.637283	+	0.367936i	−0.783567	−	0.621307i	$-0.786602\pi$
$599$	−381.733	+	220.393i	−0.637283	+	0.367936i	0.146284	+	0.989243i	$0.453269\pi$
$600$		0			0
$601$	90.4814	−	156.718i	0.150551	−	0.260763i	−0.780879	−	0.624682i	$-0.785228\pi$
$601$	90.4814	−	156.718i	0.150551	−	0.260763i	0.931430	+	0.363920i	$0.118562\pi$
$602$		0			0
$603$	−191.742	+	1006.98i	−0.317979	+	1.66995i
$604$		0			0
$605$	−379.611	−	219.168i	−0.627456	−	0.362262i
$606$		0			0
$607$	277.996	+	481.504i	0.457984	+	0.793252i	0.998854	−	0.0478542i	$-0.0152383\pi$
$607$	277.996	+	481.504i	0.457984	+	0.793252i	−0.540870	+	0.841106i	$0.681905\pi$
$608$		0			0
$609$	1027.53	−	173.970i	1.68724	−	0.285666i
$610$		0			0
$611$			78.9674i			0.129243i
$612$		0			0
$613$	−335.352			−0.547067			−0.273534	−	0.961862i	$-0.588192\pi$
$613$	−335.352			−0.547067			−0.273534	+	0.961862i	$0.588192\pi$
$614$		0			0
$615$	−467.380	+	386.783i	−0.759968	+	0.628915i
$616$		0			0
$617$	1020.64	−	589.268i	1.65420	−	0.955053i	0.678884	−	0.734246i	$-0.262464\pi$
$617$	1020.64	−	589.268i	1.65420	−	0.955053i	0.975317	−	0.220808i	$-0.0708694\pi$
$618$		0			0
$619$	−449.292	+	778.197i	−0.725835	+	1.25718i	0.232794	+	0.972526i	$0.425213\pi$
$619$	−449.292	+	778.197i	−0.725835	+	1.25718i	−0.958629	+	0.284658i	$0.908120\pi$
$620$		0			0
$621$	−556.766	−	336.807i	−0.896564	−	0.542362i
$622$		0			0
$623$	192.791	+	111.308i	0.309455	+	0.178664i
$624$		0			0
$625$	389.395	+	674.451i	0.623031	+	1.07912i
$626$		0			0
$627$	272.102	+	328.803i	0.433975	+	0.524407i
$628$		0			0
$629$		−	932.224i		−	1.48207i
$630$		0			0
$631$	431.017			0.683070			0.341535	−	0.939869i	$-0.389053\pi$
$631$	431.017			0.683070			0.341535	+	0.939869i	$0.389053\pi$
$632$		0			0
$633$	97.4236	+	575.416i	0.153908	+	0.909030i
$634$		0			0
$635$	−65.4531	+	37.7894i	−0.103076	+	0.0595108i
$636$		0			0
$637$	−6.40513	+	11.0940i	−0.0100551	+	0.0174160i
$638$		0			0
$639$	500.924	−	580.720i	0.783919	−	0.908795i
$640$		0			0
$641$	775.987	+	448.016i	1.21059	+	0.698933i	0.962887	−	0.269903i	$-0.0869917\pi$
$641$	775.987	+	448.016i	1.21059	+	0.698933i	0.247701	+	0.968837i	$0.420325\pi$
$642$		0			0
$643$	−110.854	−	192.004i	−0.172401	−	0.298607i	0.766858	−	0.641817i	$-0.221819\pi$
$643$	−110.854	−	192.004i	−0.172401	−	0.298607i	−0.939259	+	0.343210i	$0.888486\pi$
$644$		0			0
$645$	−507.215	+	1364.56i	−0.786379	+	2.11560i
$646$		0			0
$647$		−	536.838i		−	0.829734i	−0.909882	−	0.414867i	$-0.863828\pi$
$647$		−	536.838i		−	0.829734i	0.909882	−	0.414867i	$-0.136172\pi$
$648$		0			0
$649$	−773.276			−1.19149
$650$		0			0
$651$	596.819	+	221.841i	0.916772	+	0.340769i
$652$		0			0
$653$	−483.774	+	279.307i	−0.740848	+	0.427729i	−0.822378	−	0.568942i	$-0.807353\pi$
$653$	−483.774	+	279.307i	−0.740848	+	0.427729i	0.0815296	+	0.996671i	$0.474019\pi$
$654$		0			0
$655$	−164.023	+	284.096i	−0.250417	+	0.433735i
$656$		0			0
$657$	−644.254	−	555.728i	−0.980600	−	0.845857i
$658$		0			0
$659$	−933.150	−	538.755i	−1.41601	−	0.817534i	−0.420064	−	0.907494i	$-0.637993\pi$
$659$	−933.150	−	538.755i	−1.41601	−	0.817534i	−0.995945	+	0.0899606i	$0.971326\pi$
$660$		0			0
$661$	147.880	+	256.135i	0.223721	+	0.387496i	0.955935	−	0.293579i	$-0.0948463\pi$
$661$	147.880	+	256.135i	0.223721	+	0.387496i	−0.732214	+	0.681075i	$0.761513\pi$
$662$		0			0
$663$	−77.7085	+	13.1568i	−0.117207	+	0.0198444i
$664$		0			0
$665$			934.683i			1.40554i
$666$		0			0
$667$	−1116.71			−1.67423
$668$		0			0
$669$	439.804	−	363.961i	0.657404	−	0.544038i
$670$		0			0
$671$	313.610	−	181.063i	0.467377	−	0.269840i
$672$		0			0
$673$	283.724	−	491.424i	0.421580	−	0.730199i	−0.574514	−	0.818495i	$-0.694809\pi$
$673$	283.724	−	491.424i	0.421580	−	0.730199i	0.996094	+	0.0882963i	$0.0281422\pi$
$674$		0			0
$675$	379.777	+	7.76401i	0.562633	+	0.0115022i
$676$		0			0
$677$	−813.905	−	469.908i	−1.20222	−	0.694104i	−0.241174	−	0.970482i	$-0.577533\pi$
$677$	−813.905	−	469.908i	−1.20222	−	0.694104i	−0.961049	+	0.276378i	$0.910866\pi$
$678$		0			0
$679$	468.413	+	811.315i	0.689857	+	1.19487i
$680$		0			0
$681$	708.790	+	856.488i	1.04081	+	1.25769i
$682$		0			0
$683$		−	14.2541i		−	0.0208699i	−0.999946	−	0.0104349i	$-0.996678\pi$
$683$		−	14.2541i		−	0.0208699i	0.999946	−	0.0104349i	$-0.00332161\pi$
$684$		0			0
$685$	−874.930			−1.27727
$686$		0			0
$687$	−204.012	−	1204.96i	−0.296961	−	1.75395i
$688$		0			0
$689$	−65.0950	+	37.5826i	−0.0944775	+	0.0545466i
$690$		0			0
$691$	−83.1353	+	143.995i	−0.120312	+	0.208386i	−0.919891	−	0.392175i	$-0.871723\pi$
$691$	−83.1353	+	143.995i	−0.120312	+	0.208386i	0.799579	+	0.600561i	$0.205056\pi$
$692$		0			0
$693$	−472.759	−	90.0193i	−0.682192	−	0.129898i
$694$		0			0
$695$	216.151	+	124.795i	0.311009	+	0.179561i
$696$		0			0
$697$	239.075	+	414.090i	0.343006	+	0.594103i
$698$		0			0
$699$	22.5007	−	60.5337i	0.0321899	−	0.0866004i
$700$		0			0
$701$			506.174i			0.722074i	0.932551	+	0.361037i	$0.117577\pi$
$701$			506.174i			0.722074i	−0.932551	+	0.361037i	$0.882423\pi$
$702$		0			0
$703$	−1258.14			−1.78967
$704$		0			0
$705$	−780.812	−	290.232i	−1.10753	−	0.411677i
$706$		0			0
$707$	−255.643	+	147.595i	−0.361588	+	0.208763i
$708$		0			0
$709$	−259.993	+	450.321i	−0.366704	+	0.635150i	−0.989048	−	0.147594i	$-0.952847\pi$
$709$	−259.993	+	450.321i	−0.366704	+	0.635150i	0.622344	+	0.782744i	$0.286181\pi$
$710$		0			0
$711$	−605.185	+	210.975i	−0.851175	+	0.296731i
$712$		0			0
$713$	−590.863	−	341.135i	−0.828700	−	0.478450i
$714$		0			0
$715$	39.6240	+	68.6307i	0.0554181	+	0.0959870i
$716$		0			0
$717$	−587.532	+	99.4749i	−0.819431	+	0.138738i
$718$		0			0
$719$		−	467.630i		−	0.650390i	−0.945647	−	0.325195i	$-0.894570\pi$
$719$		−	467.630i		−	0.650390i	0.945647	−	0.325195i	$-0.105430\pi$
$720$		0			0
$721$	−1120.41			−1.55397
$722$		0			0
$723$	−642.244	+	531.492i	−0.888304	+	0.735120i
$724$		0			0
$725$	564.549	−	325.943i	0.778689	−	0.449576i
$726$		0			0
$727$	262.371	−	454.439i	0.360895	−	0.625088i	−0.627214	−	0.778847i	$-0.715805\pi$
$727$	262.371	−	454.439i	0.360895	−	0.625088i	0.988108	+	0.153759i	$0.0491380\pi$
$728$		0			0
$729$	−389.998	+	615.908i	−0.534977	+	0.844867i
$730$		0			0
$731$	993.663	+	573.692i	1.35932	+	0.784804i
$732$		0			0
$733$	−329.348	−	570.447i	−0.449315	−	0.778236i	0.549027	−	0.835805i	$-0.314998\pi$
$733$	−329.348	−	570.447i	−0.449315	−	0.778236i	−0.998342	+	0.0575688i	$0.981665\pi$
$734$		0			0
$735$	−86.1540	−	104.107i	−0.117216	−	0.141642i
$736$		0			0
$737$		−	812.363i		−	1.10226i
$738$		0			0
$739$	1209.27			1.63637			0.818183	−	0.574957i	$-0.194981\pi$
$739$	1209.27			1.63637			0.818183	+	0.574957i	$0.194981\pi$
$740$		0			0
$741$	17.7565	+	104.876i	0.0239629	+	0.141533i
$742$		0			0
$743$	339.650	−	196.097i	0.457134	−	0.263926i	−0.253704	−	0.967282i	$-0.581649\pi$
$743$	339.650	−	196.097i	0.457134	−	0.263926i	0.710838	+	0.703355i	$0.248316\pi$
$744$		0			0
$745$	−11.7726	+	20.3908i	−0.0158022	+	0.0273701i
$746$		0			0
$747$	−324.663	−	931.300i	−0.434623	−	1.24672i
$748$		0			0
$749$	−2.72829	−	1.57518i	−0.00364258	−	0.00210305i
$750$		0			0
$751$	558.493	+	967.339i	0.743666	+	1.28807i	0.950815	+	0.309758i	$0.100248\pi$
$751$	558.493	+	967.339i	0.743666	+	1.28807i	−0.207149	+	0.978309i	$0.566419\pi$
$752$		0			0
$753$	−134.131	+	360.851i	−0.178128	+	0.479218i
$754$		0			0
$755$		−	936.069i		−	1.23983i
$756$		0			0
$757$	−623.892			−0.824164			−0.412082	−	0.911147i	$-0.635198\pi$
$757$	−623.892			−0.824164			−0.412082	+	0.911147i	$0.635198\pi$
$758$		0			0
$759$	483.373	+	179.673i	0.636855	+	0.236723i
$760$		0			0
$761$	−832.456	+	480.619i	−1.09390	+	0.631562i	−0.934611	−	0.355671i	$-0.884252\pi$
$761$	−832.456	+	480.619i	−1.09390	+	0.631562i	−0.159286	+	0.987233i	$0.550919\pi$
$762$		0			0
$763$	241.638	−	418.528i	0.316694	−	0.548530i
$764$		0			0
$765$	155.514	−	816.720i	0.203286	−	1.06761i
$766$		0			0
$767$	−166.902	−	96.3610i	−0.217604	−	0.125634i
$768$		0			0
$769$	−109.653	−	189.924i	−0.142592	−	0.246976i	0.785880	−	0.618379i	$-0.212210\pi$
$769$	−109.653	−	189.924i	−0.142592	−	0.246976i	−0.928472	+	0.371403i	$0.878877\pi$
$770$		0			0
$771$	212.985	−	36.0604i	0.276245	−	0.0467709i
$772$		0			0
$773$			761.394i			0.984986i	0.870316	+	0.492493i	$0.163914\pi$
$773$			761.394i			0.984986i	−0.870316	+	0.492493i	$0.836086\pi$
$774$		0			0
$775$	398.278			0.513907
$776$		0			0
$777$	1092.96	−	904.486i	1.40664	−	1.16407i
$778$		0			0
$779$	558.858	−	322.657i	0.717405	−	0.414194i
$780$		0			0
$781$	−303.888	+	526.349i	−0.389101	+	0.673943i
$782$		0			0
$783$	−25.5709	+	1250.80i	−0.0326576	+	1.59745i
$784$		0			0
$785$	−638.211	−	368.471i	−0.813007	−	0.469390i
$786$		0			0
$787$	263.023	+	455.569i	0.334210	+	0.578868i	0.983333	−	0.181815i	$-0.0581972\pi$
$787$	263.023	+	455.569i	0.334210	+	0.578868i	−0.649123	+	0.760684i	$0.724864\pi$
$788$		0			0
$789$	−251.295	−	303.660i	−0.318498	−	0.384867i
$790$		0			0
$791$		−	194.536i		−	0.245937i
$792$		0			0
$793$	90.2518			0.113811
$794$		0			0
$795$	−132.362	−	781.774i	−0.166493	−	0.983363i
$796$		0			0
$797$	−1230.12	+	710.212i	−1.54344	+	0.891107i	−0.544824	+	0.838551i	$0.683403\pi$
$797$	−1230.12	+	710.212i	−1.54344	+	0.891107i	−0.998618	+	0.0525560i	$0.983263\pi$
$798$		0			0
$799$	−328.271	+	568.582i	−0.410852	+	0.711617i
$800$		0			0
$801$	−174.554	+	202.359i	−0.217920	+	0.252633i
$802$		0			0
$803$	583.935	+	337.135i	0.727192	+	0.419845i
$804$		0			0
$805$	564.681	+	978.057i	0.701468	+	1.21498i
$806$		0			0
$807$	40.5852	−	109.186i	0.0502914	−	0.135299i
$808$		0			0
$809$			749.612i			0.926590i	0.886204	+	0.463295i	$0.153333\pi$
$809$			749.612i			0.926590i	−0.886204	+	0.463295i	$0.846667\pi$
$810$		0			0
$811$	238.446			0.294015			0.147008	−	0.989135i	$-0.453036\pi$
$811$	238.446			0.294015			0.147008	+	0.989135i	$0.453036\pi$
$812$		0			0
$813$	−2.25672	−	0.838834i	−0.00277579	−	0.00103178i
$814$		0			0
$815$	606.052	−	349.905i	0.743623	−	0.429331i
$816$		0			0
$817$	774.258	−	1341.05i	0.947684	−	1.64144i
$818$		0			0
$819$	−90.8217	−	78.3420i	−0.110893	−	0.0956557i
$820$		0			0
$821$	937.937	+	541.518i	1.14243	+	0.659583i	0.947032	−	0.321140i	$-0.104066\pi$
$821$	937.937	+	541.518i	1.14243	+	0.659583i	0.195400	+	0.980724i	$0.437399\pi$
$822$		0			0
$823$	−787.881	−	1364.65i	−0.957328	−	1.65814i	−0.728949	−	0.684568i	$-0.759991\pi$
$823$	−787.881	−	1364.65i	−0.957328	−	1.65814i	−0.228379	−	0.973572i	$-0.573343\pi$
$824$		0			0
$825$	−296.810	+	50.2528i	−0.359769	+	0.0609125i
$826$		0			0
$827$			124.799i			0.150906i	0.997149	+	0.0754529i	$0.0240403\pi$
$827$			124.799i			0.150906i	−0.997149	+	0.0754529i	$0.975960\pi$
$828$		0			0
$829$	426.486			0.514458			0.257229	−	0.966350i	$-0.417190\pi$
$829$	426.486			0.514458			0.257229	+	0.966350i	$0.417190\pi$
$830$		0			0
$831$	282.862	−	234.084i	0.340387	−	0.281689i
$832$		0			0
$833$	−92.2365	+	53.2528i	−0.110728	+	0.0639289i
$834$		0			0
$835$	4.82403	−	8.35547i	0.00577728	−	0.0100065i
$836$		0			0
$837$	−395.627	+	654.000i	−0.472672	+	0.781362i
$838$		0			0
$839$	430.710	+	248.671i	0.513362	+	0.296389i	0.734214	−	0.678918i	$-0.237551\pi$
$839$	430.710	+	248.671i	0.513362	+	0.296389i	−0.220853	+	0.975307i	$0.570884\pi$
$840$		0			0
$841$	652.999	+	1131.03i	0.776455	+	1.34486i
$842$		0			0
$843$	−561.278	−	678.236i	−0.665810	−	0.804551i
$844$		0			0
$845$		−	1036.58i		−	1.22673i
$846$		0			0
$847$	−525.759			−0.620730
$848$		0			0
$849$	−90.7645	−	536.085i	−0.106908	−	0.631431i
$850$		0			0
$851$	−1316.52	+	760.092i	−1.54703	+	0.893176i
$852$		0			0
$853$	767.481	−	1329.32i	0.899743	−	1.55840i	0.0719203	−	0.997410i	$-0.477087\pi$
$853$	767.481	−	1329.32i	0.899743	−	1.55840i	0.827823	−	0.560990i	$-0.189579\pi$
$854$		0			0
$855$	−1102.25	−	209.882i	−1.28918	−	0.245476i
$856$		0			0
$857$	1055.08	+	609.149i	1.23113	+	0.710792i	0.967265	−	0.253768i	$-0.0816699\pi$
$857$	1055.08	+	609.149i	1.23113	+	0.710792i	0.263863	+	0.964560i	$0.415003\pi$
$858$		0			0
$859$	−289.720	−	501.811i	−0.337276	−	0.584180i	0.646643	−	0.762793i	$-0.276172\pi$
$859$	−289.720	−	501.811i	−0.337276	−	0.584180i	−0.983919	+	0.178613i	$0.942839\pi$
$860$		0			0
$861$	−253.528	+	682.066i	−0.294457	+	0.792179i
$862$		0			0
$863$			1361.09i			1.57716i	0.614934	+	0.788579i	$0.289183\pi$
$863$			1361.09i			1.57716i	−0.614934	+	0.788579i	$0.710817\pi$
$864$		0			0
$865$	332.422			0.384303
$866$		0			0
$867$	198.463	+	73.7700i	0.228908	+	0.0850865i
$868$		0			0
$869$	439.866	−	253.957i	0.506175	−	0.292240i
$870$		0			0
$871$	101.232	−	175.339i	0.116225	−	0.201307i
$872$		0			0
$873$	−1061.95	+	370.208i	−1.21643	+	0.424065i
$874$		0			0
$875$	443.617	+	256.122i	0.506991	+	0.292711i
$876$		0			0
$877$	150.947	+	261.448i	0.172118	+	0.298117i	0.939160	−	0.343480i	$-0.111606\pi$
$877$	150.947	+	261.448i	0.172118	+	0.298117i	−0.767042	+	0.641597i	$0.778272\pi$
$878$		0			0
$879$	−992.355	+	168.016i	−1.12896	+	0.191144i
$880$		0			0
$881$		−	1170.94i		−	1.32911i	−0.747240	−	0.664554i	$-0.768622\pi$
$881$		−	1170.94i		−	1.32911i	0.747240	−	0.664554i	$-0.231378\pi$
$882$		0			0
$883$	1339.68			1.51719			0.758597	−	0.651560i	$-0.225885\pi$
$883$	1339.68			1.51719			0.758597	+	0.651560i	$0.225885\pi$
$884$		0			0
$885$	1566.22	−	1296.13i	1.76974	−	1.46455i
$886$		0			0
$887$	14.4375	−	8.33547i	0.0162767	−	0.00939738i	−0.491840	−	0.870686i	$-0.663675\pi$
$887$	14.4375	−	8.33547i	0.0162767	−	0.00939738i	0.508116	+	0.861288i	$0.330342\pi$
$888$		0			0
$889$	−45.3261	+	78.5071i	−0.0509855	+	0.0883094i
$890$		0			0
$891$	212.315	−	537.300i	0.238289	−	0.603031i
$892$		0			0
$893$	767.362	+	443.037i	0.859308	+	0.496122i
$894$		0			0
$895$	−748.323	−	1296.13i	−0.836115	−	1.44819i
$896$		0			0
$897$	81.9404	+	99.0151i	0.0913494	+	0.110385i
$898$		0			0
$899$			1311.74i			1.45911i
$900$		0			0
$901$	−624.930			−0.693596
$902$		0			0
$903$	291.487	+	1721.62i	0.322798	+	1.90655i
$904$		0			0
$905$	331.042	−	191.127i	0.365792	−	0.211190i
$906$		0			0
$907$	225.668	−	390.868i	0.248807	−	0.430946i	−0.714388	−	0.699750i	$-0.753295\pi$
$907$	225.668	−	390.868i	0.248807	−	0.430946i	0.963195	+	0.268803i	$0.0866282\pi$
$908$		0			0
$909$	−116.651	−	334.616i	−0.128329	−	0.368114i
$910$		0			0
$911$	−1243.11	−	717.711i	−1.36456	−	0.787827i	−0.374331	−	0.927295i	$-0.622127\pi$
$911$	−1243.11	−	717.711i	−1.36456	−	0.787827i	−0.990227	+	0.139468i	$0.955461\pi$
$912$		0			0
$913$	390.806	+	676.895i	0.428046	+	0.741397i
$914$		0			0
$915$	−331.706	+	892.390i	−0.362521	+	0.975289i
$916$		0			0
$917$			393.472i			0.429086i
$918$		0			0
$919$	380.633			0.414181			0.207091	−	0.978322i	$-0.433600\pi$
$919$	380.633			0.414181			0.207091	+	0.978322i	$0.433600\pi$
$920$		0			0
$921$	813.266	+	302.295i	0.883024	+	0.328225i
$922$		0			0
$923$	−131.181	+	75.7374i	−0.142125	+	0.0820557i
$924$		0			0
$925$	443.707	−	768.523i	0.479683	−	0.830836i
$926$		0			0
$927$	251.587	−	1321.27i	0.271399	−	1.42532i
$928$		0			0
$929$	−856.635	−	494.578i	−0.922104	−	0.532377i	−0.0377985	−	0.999285i	$-0.512035\pi$
$929$	−856.635	−	494.578i	−0.922104	−	0.532377i	−0.884306	+	0.466908i	$0.845368\pi$
$930$		0			0
$931$	71.8703	+	124.483i	0.0771969	+	0.133709i
$932$		0			0
$933$	−80.9427	+	13.7044i	−0.0867553	+	0.0146885i
$934$		0			0
$935$			658.874i			0.704678i
$936$		0			0
$937$	−549.202			−0.586128			−0.293064	−	0.956093i	$-0.594675\pi$
$937$	−549.202			−0.586128			−0.293064	+	0.956093i	$0.594675\pi$
$938$		0			0
$939$	−1357.02	+	1123.00i	−1.44517	+	1.19596i
$940$		0			0
$941$	405.479	−	234.103i	0.430902	−	0.248781i	−0.268829	−	0.963188i	$-0.586637\pi$
$941$	405.479	−	234.103i	0.430902	−	0.248781i	0.699731	+	0.714407i	$0.253303\pi$
$942$		0			0
$943$	389.861	−	675.259i	0.413427	−	0.716076i
$944$		0			0
$945$	1108.43	−	610.090i	1.17294	−	0.645598i
$946$		0			0
$947$	260.869	+	150.613i	0.275469	+	0.159042i	0.631370	−	0.775482i	$-0.282493\pi$
$947$	260.869	+	150.613i	0.275469	+	0.159042i	−0.355902	+	0.934523i	$0.615826\pi$
$948$		0			0
$949$	84.0235	+	145.533i	0.0885390	+	0.153354i
$950$		0			0
$951$	720.165	+	870.233i	0.757271	+	0.915071i
$952$		0			0
$953$		−	319.384i		−	0.335135i	−0.985861	−	0.167567i	$-0.946409\pi$
$953$		−	319.384i		−	0.335135i	0.985861	−	0.167567i	$-0.0535912\pi$
$954$		0			0
$955$	208.630			0.218461
$956$		0			0
$957$	−165.509	−	977.548i	−0.172945	−	1.02147i
$958$		0			0
$959$	−908.829	+	524.713i	−0.947685	+	0.547146i
$960$		0			0
$961$	79.7892	−	138.199i	0.0830272	−	0.143807i
$962$		0			0
$963$	2.47021	−	2.86371i	0.00256512	−	0.00297374i
$964$		0			0
$965$	230.377	+	133.008i	0.238732	+	0.137832i
$966$		0			0
$967$	−302.086	−	523.229i	−0.312395	−	0.541085i	0.666485	−	0.745518i	$-0.267798\pi$
$967$	−302.086	−	523.229i	−0.312395	−	0.541085i	−0.978880	+	0.204434i	$0.934465\pi$
$968$		0			0
$969$	−308.123	+	828.943i	−0.317980	+	0.855462i
$970$		0			0
$971$			465.068i			0.478958i	0.970902	+	0.239479i	$0.0769766\pi$
$971$			465.068i			0.478958i	−0.970902	+	0.239479i	$0.923023\pi$
$972$		0			0
$973$	299.368			0.307675
$974$		0			0
$975$	−70.3249	−	26.1402i	−0.0721281	−	0.0268104i
$976$		0			0
$977$	−332.512	+	191.976i	−0.340340	+	0.196495i	−0.660422	−	0.750894i	$-0.729623\pi$
$977$	−332.512	+	191.976i	−0.340340	+	0.196495i	0.320083	+	0.947390i	$0.396289\pi$
$978$		0			0
$979$	105.894	−	183.413i	0.108165	−	0.187348i
$980$		0			0
$981$	439.301	+	378.938i	0.447810	+	0.386277i
$982$		0			0
$983$	586.197	+	338.441i	0.596335	+	0.344294i	0.767598	−	0.640931i	$-0.221452\pi$
$983$	586.197	+	338.441i	0.596335	+	0.344294i	−0.171264	+	0.985225i	$0.554785\pi$
$984$		0			0
$985$	−635.589	−	1100.87i	−0.645268	−	1.11764i
$986$		0			0
$987$	−985.123	+	166.791i	−0.998098	+	0.168988i
$988$		0			0
$989$		−	1871.05i		−	1.89186i
$990$		0			0
$991$	1097.79			1.10776			0.553878	−	0.832598i	$-0.313147\pi$
$991$	1097.79			1.10776			0.553878	+	0.832598i	$0.313147\pi$
$992$		0			0
$993$	6.85912	−	5.67630i	0.00690748	−	0.00571631i
$994$		0			0
$995$	693.744	−	400.533i	0.697230	−	0.402546i
$996$		0			0
$997$	−90.7127	+	157.119i	−0.0909857	+	0.157592i	−0.907926	−	0.419130i	$-0.862335\pi$
$997$	−90.7127	+	157.119i	−0.0909857	+	0.157592i	0.816940	+	0.576722i	$0.195668\pi$
$998$		0			0
$999$	821.215	+	1492.01i	0.822037	+	1.49350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.q.b.65.12	yes	24
3.2	odd	2		864.3.q.a.737.4		24
4.3	odd	2	inner	288.3.q.b.65.1	✓	24
8.3	odd	2		576.3.q.l.65.12		24
8.5	even	2		576.3.q.l.65.1		24
9.2	odd	6		2592.3.e.i.161.5		24
9.4	even	3		864.3.q.a.449.4		24
9.5	odd	6	inner	288.3.q.b.257.12	yes	24
9.7	even	3		2592.3.e.i.161.6		24
12.11	even	2		864.3.q.a.737.3		24
24.5	odd	2		1728.3.q.k.1601.10		24
24.11	even	2		1728.3.q.k.1601.9		24
36.7	odd	6		2592.3.e.i.161.20		24
36.11	even	6		2592.3.e.i.161.19		24
36.23	even	6	inner	288.3.q.b.257.1	yes	24
36.31	odd	6		864.3.q.a.449.3		24
72.5	odd	6		576.3.q.l.257.1		24
72.13	even	6		1728.3.q.k.449.10		24
72.59	even	6		576.3.q.l.257.12		24
72.67	odd	6		1728.3.q.k.449.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.3.q.b.65.1	✓	24	4.3	odd	2	inner
288.3.q.b.65.12	yes	24	1.1	even	1	trivial
288.3.q.b.257.1	yes	24	36.23	even	6	inner
288.3.q.b.257.12	yes	24	9.5	odd	6	inner
576.3.q.l.65.1		24	8.5	even	2
576.3.q.l.65.12		24	8.3	odd	2
576.3.q.l.257.1		24	72.5	odd	6
576.3.q.l.257.12		24	72.59	even	6
864.3.q.a.449.3		24	36.31	odd	6
864.3.q.a.449.4		24	9.4	even	3
864.3.q.a.737.3		24	12.11	even	2
864.3.q.a.737.4		24	3.2	odd	2
1728.3.q.k.449.9		24	72.67	odd	6
1728.3.q.k.449.10		24	72.13	even	6
1728.3.q.k.1601.9		24	24.11	even	2
1728.3.q.k.1601.10		24	24.5	odd	2
2592.3.e.i.161.5		24	9.2	odd	6
2592.3.e.i.161.6		24	9.7	even	3
2592.3.e.i.161.19		24	36.11	even	6
2592.3.e.i.161.20		24	36.7	odd	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81202 + 1.04524i) q^{3} +(5.41309 - 3.12525i) q^{5} +(3.74855 - 6.49268i) q^{7} +(6.81493 + 5.87850i) q^{9} +O(q^{10})\)	\(q+(2.81202 + 1.04524i) q^{3} +(5.41309 - 3.12525i) q^{5} +(3.74855 - 6.49268i) q^{7} +(6.81493 + 5.87850i) q^{9} +(-6.17688 - 3.56622i) q^{11} +(-0.888802 - 1.53945i) q^{13} +(18.4884 - 3.13027i) q^{15} -14.7791i q^{17} -19.9460 q^{19} +(17.3274 - 14.3394i) q^{21} +(-20.8716 + 12.0502i) q^{23} +(7.03438 - 12.1839i) q^{25} +(13.0193 + 23.6537i) q^{27} +(40.1279 + 23.1679i) q^{29} +(14.1547 + 24.5167i) q^{31} +(-13.6419 - 16.4846i) q^{33} -46.8606i q^{35} +63.0770 q^{37} +(-0.890228 - 5.25798i) q^{39} +(-28.0185 + 16.1765i) q^{41} +(-38.8176 + 67.2341i) q^{43} +(55.2616 + 10.5225i) q^{45} +(-38.4719 - 22.2118i) q^{47} +(-3.60324 - 6.24099i) q^{49} +(15.4478 - 41.5593i) q^{51} -42.2846i q^{53} -44.5813 q^{55} +(-56.0887 - 20.8485i) q^{57} +(93.8917 - 54.2084i) q^{59} +(-25.3858 + 43.9695i) q^{61} +(63.7133 - 22.2113i) q^{63} +(-9.62233 - 5.55546i) q^{65} +(56.9484 + 98.6376i) q^{67} +(-71.2869 + 12.0696i) q^{69} -85.2129i q^{71} -94.5357 q^{73} +(32.5160 - 26.9087i) q^{75} +(-46.3086 + 26.7363i) q^{77} +(-35.6059 + 61.6712i) q^{79} +(11.8865 + 80.1231i) q^{81} +(-94.9037 - 54.7927i) q^{83} +(-46.1885 - 80.0009i) q^{85} +(88.6244 + 107.092i) q^{87} +29.6936i q^{89} -13.3269 q^{91} +(14.1774 + 83.7365i) q^{93} +(-107.970 + 62.3363i) q^{95} +(-62.4793 + 108.217i) q^{97} +(-21.1309 - 60.6143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^9	\( 24 q + 12 q^{9} + 24 q^{21} + 60 q^{25} + 72 q^{29} + 108 q^{33} + 252 q^{41} + 72 q^{45} - 36 q^{49} + 12 q^{57} - 96 q^{61} - 288 q^{65} - 432 q^{69} + 24 q^{73} - 720 q^{77} - 372 q^{81} + 96 q^{85} - 132 q^{97}+O(q^{100}) \) 24 * q + 12 * q^9 + 24 * q^21 + 60 * q^25 + 72 * q^29 + 108 * q^33 + 252 * q^41 + 72 * q^45 - 36 * q^49 + 12 * q^57 - 96 * q^61 - 288 * q^65 - 432 * q^69 + 24 * q^73 - 720 * q^77 - 372 * q^81 + 96 * q^85 - 132 * q^97

Introduction

L-functions

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