LMFDB - Embedded newform 288.3.q.b.257.5

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			257.5
Character	$\chi$	$=$	288.257
Dual form			288.3.q.b.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65353 + 2.50317i) q^{3} +(-0.721152 - 0.416357i) q^{5} +(-1.26051 - 2.18326i) q^{7} +(-3.53169 - 8.27811i) q^{9} +O(q^{10})$	\(q+(-1.65353 + 2.50317i) q^{3} +(-0.721152 - 0.416357i) q^{5} +(-1.26051 - 2.18326i) q^{7} +(-3.53169 - 8.27811i) q^{9} +(-9.47693 + 5.47151i) q^{11} +(4.36453 - 7.55959i) q^{13} +(2.23466 - 1.11671i) q^{15} -20.8637i q^{17} -1.50150 q^{19} +(7.54935 + 0.454827i) q^{21} +(1.00209 + 0.578558i) q^{23} +(-12.1533 - 21.0501i) q^{25} +(26.5612 + 4.84769i) q^{27} +(15.7347 - 9.08444i) q^{29} +(25.6909 - 44.4980i) q^{31} +(1.97428 - 32.7696i) q^{33} +2.09929i q^{35} -7.93951 q^{37} +(11.7060 + 23.4251i) q^{39} +(-21.8881 - 12.6371i) q^{41} +(-19.3418 - 33.5010i) q^{43} +(-0.899770 + 7.44022i) q^{45} +(-59.6559 + 34.4423i) q^{47} +(21.3222 - 36.9312i) q^{49} +(52.2254 + 34.4988i) q^{51} +46.5195i q^{53} +9.11241 q^{55} +(2.48278 - 3.75851i) q^{57} +(-89.1306 - 51.4596i) q^{59} +(44.1651 + 76.4962i) q^{61} +(-13.6216 + 18.1452i) q^{63} +(-6.29498 + 3.63441i) q^{65} +(11.3192 - 19.6054i) q^{67} +(-3.10522 + 1.55174i) q^{69} +104.256i q^{71} -75.2115 q^{73} +(72.7878 + 4.38525i) q^{75} +(23.8915 + 13.7938i) q^{77} +(-51.8676 - 89.8374i) q^{79} +(-56.0544 + 58.4714i) q^{81} +(-53.7499 + 31.0325i) q^{83} +(-8.68677 + 15.0459i) q^{85} +(-3.27792 + 54.4080i) q^{87} -1.95722i q^{89} -22.0061 q^{91} +(68.9052 + 137.887i) q^{93} +(1.08281 + 0.625162i) q^{95} +(59.2171 + 102.567i) q^{97} +(78.7634 + 59.1275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.65353	+	2.50317i	−0.551176	+	0.834389i
$3$	−1.65353	+	2.50317i	−0.551176	+	0.834389i
$4$		0			0
$5$	−0.721152	−	0.416357i	−0.144230	−	0.0832715i	0.426148	−	0.904653i	$-0.359870\pi$
$5$	−0.721152	−	0.416357i	−0.144230	−	0.0832715i	−0.570379	+	0.821382i	$0.693204\pi$
$6$		0			0
$7$	−1.26051	−	2.18326i	−0.180072	−	0.311895i	0.761833	−	0.647774i	$-0.224300\pi$
$7$	−1.26051	−	2.18326i	−0.180072	−	0.311895i	−0.941905	+	0.335879i	$0.890967\pi$
$8$		0			0
$9$	−3.53169	−	8.27811i	−0.392410	−	0.919791i
$10$		0			0
$11$	−9.47693	+	5.47151i	−0.861540	+	0.497410i	−0.864528	−	0.502585i	$-0.832382\pi$
$11$	−9.47693	+	5.47151i	−0.861540	+	0.497410i	0.00298800	+	0.999996i	$0.499049\pi$
$12$		0			0
$13$	4.36453	−	7.55959i	0.335733	−	0.581507i	−0.647892	−	0.761732i	$-0.724349\pi$
$13$	4.36453	−	7.55959i	0.335733	−	0.581507i	0.983625	+	0.180225i	$0.0576826\pi$
$14$		0			0
$15$	2.23466	−	1.11671i	0.148977	−	0.0744470i
$16$		0			0
$17$		−	20.8637i		−	1.22728i	−0.789586	−	0.613639i	$-0.789705\pi$
$17$		−	20.8637i		−	1.22728i	0.789586	−	0.613639i	$-0.210295\pi$
$18$		0			0
$19$	−1.50150			−0.0790265			−0.0395132	−	0.999219i	$-0.512581\pi$
$19$	−1.50150			−0.0790265			−0.0395132	+	0.999219i	$0.512581\pi$
$20$		0			0
$21$	7.54935	+	0.454827i	0.359493	+	0.0216584i
$22$		0			0
$23$	1.00209	+	0.578558i	0.0435692	+	0.0251547i	0.521626	−	0.853174i	$-0.325325\pi$
$23$	1.00209	+	0.578558i	0.0435692	+	0.0251547i	−0.478057	+	0.878329i	$0.658659\pi$
$24$		0			0
$25$	−12.1533	−	21.0501i	−0.486132	−	0.842005i
$26$		0			0
$27$	26.5612	+	4.84769i	0.983750	+	0.179544i
$28$		0			0
$29$	15.7347	−	9.08444i	0.542576	−	0.313257i	−0.203546	−	0.979065i	$-0.565247\pi$
$29$	15.7347	−	9.08444i	0.542576	−	0.313257i	0.746122	+	0.665809i	$0.231913\pi$
$30$		0			0
$31$	25.6909	−	44.4980i	0.828739	−	1.43542i	−0.0702892	−	0.997527i	$-0.522392\pi$
$31$	25.6909	−	44.4980i	0.828739	−	1.43542i	0.899028	−	0.437891i	$-0.144274\pi$
$32$		0			0
$33$	1.97428	−	32.7696i	0.0598266	−	0.993020i
$34$		0			0
$35$			2.09929i			0.0599796i
$36$		0			0
$37$	−7.93951			−0.214581			−0.107291	−	0.994228i	$-0.534218\pi$
$37$	−7.93951			−0.214581			−0.107291	+	0.994228i	$0.534218\pi$
$38$		0			0
$39$	11.7060	+	23.4251i	0.300155	+	0.600645i
$40$		0			0
$41$	−21.8881	−	12.6371i	−0.533857	−	0.308222i	0.208729	−	0.977974i	$-0.433067\pi$
$41$	−21.8881	−	12.6371i	−0.533857	−	0.308222i	−0.742586	+	0.669751i	$0.766401\pi$
$42$		0			0
$43$	−19.3418	−	33.5010i	−0.449810	−	0.779094i	0.548563	−	0.836109i	$-0.315175\pi$
$43$	−19.3418	−	33.5010i	−0.449810	−	0.779094i	−0.998373	+	0.0570153i	$0.981842\pi$
$44$		0			0
$45$	−0.899770	+	7.44022i	−0.0199949	+	0.165338i
$46$		0			0
$47$	−59.6559	+	34.4423i	−1.26927	+	0.732815i	−0.974851	−	0.222860i	$-0.928461\pi$
$47$	−59.6559	+	34.4423i	−1.26927	+	0.732815i	−0.294423	+	0.955675i	$0.595127\pi$
$48$		0			0
$49$	21.3222	−	36.9312i	0.435148	−	0.753698i
$50$		0			0
$51$	52.2254	+	34.4988i	1.02403	+	0.676447i
$52$		0			0
$53$			46.5195i			0.877727i	0.898554	+	0.438864i	$0.144619\pi$
$53$			46.5195i			0.877727i	−0.898554	+	0.438864i	$0.855381\pi$
$54$		0			0
$55$	9.11241			0.165680
$56$		0			0
$57$	2.48278	−	3.75851i	0.0435575	−	0.0659388i
$58$		0			0
$59$	−89.1306	−	51.4596i	−1.51069	−	0.872196i	−0.999922	−	0.0124764i	$-0.996029\pi$
$59$	−89.1306	−	51.4596i	−1.51069	−	0.872196i	−0.510766	−	0.859720i	$-0.670638\pi$
$60$		0			0
$61$	44.1651	+	76.4962i	0.724018	+	1.25404i	0.959377	+	0.282127i	$0.0910401\pi$
$61$	44.1651	+	76.4962i	0.724018	+	1.25404i	−0.235359	+	0.971909i	$0.575627\pi$
$62$		0			0
$63$	−13.6216	+	18.1452i	−0.216216	+	0.288019i
$64$		0			0
$65$	−6.29498	+	3.63441i	−0.0968459	+	0.0559140i
$66$		0			0
$67$	11.3192	−	19.6054i	0.168943	−	0.292618i	−0.769105	−	0.639122i	$-0.779298\pi$
$67$	11.3192	−	19.6054i	0.168943	−	0.292618i	0.938049	+	0.346504i	$0.112631\pi$
$68$		0			0
$69$	−3.10522	+	1.55174i	−0.0450031	+	0.0224890i
$70$		0			0
$71$			104.256i			1.46840i	0.678935	+	0.734198i	$0.262442\pi$
$71$			104.256i			1.46840i	−0.678935	+	0.734198i	$0.737558\pi$
$72$		0			0
$73$	−75.2115			−1.03030			−0.515148	−	0.857101i	$-0.672263\pi$
$73$	−75.2115			−1.03030			−0.515148	+	0.857101i	$0.672263\pi$
$74$		0			0
$75$	72.7878	+	4.38525i	0.970504	+	0.0584701i
$76$		0			0
$77$	23.8915	+	13.7938i	0.310279	+	0.179140i
$78$		0			0
$79$	−51.8676	−	89.8374i	−0.656552	−	1.13718i	−0.981502	−	0.191451i	$-0.938681\pi$
$79$	−51.8676	−	89.8374i	−0.656552	−	1.13718i	0.324950	−	0.945731i	$-0.394653\pi$
$80$		0			0
$81$	−56.0544	+	58.4714i	−0.692029	+	0.721870i
$82$		0			0
$83$	−53.7499	+	31.0325i	−0.647589	+	0.373886i	−0.787532	−	0.616274i	$-0.788641\pi$
$83$	−53.7499	+	31.0325i	−0.647589	+	0.373886i	0.139943	+	0.990160i	$0.455308\pi$
$84$		0			0
$85$	−8.68677	+	15.0459i	−0.102197	+	0.177011i
$86$		0			0
$87$	−3.27792	+	54.4080i	−0.0376773	+	0.625379i
$88$		0			0
$89$		−	1.95722i		−	0.0219912i	−0.999940	−	0.0109956i	$-0.996500\pi$
$89$		−	1.95722i		−	0.0219912i	0.999940	−	0.0109956i	$-0.00350008\pi$
$90$		0			0
$91$	−22.0061			−0.241825
$92$		0			0
$93$	68.9052	+	137.887i	0.740916	+	1.48266i
$94$		0			0
$95$	1.08281	+	0.625162i	0.0113980	+	0.00658065i
$96$		0			0
$97$	59.2171	+	102.567i	0.610486	+	1.05739i	0.991159	+	0.132682i	$0.0423590\pi$
$97$	59.2171	+	102.567i	0.610486	+	1.05739i	−0.380673	+	0.924710i	$0.624308\pi$
$98$		0			0
$99$	78.7634	+	59.1275i	0.795590	+	0.597247i
$100$		0			0
$101$	−48.2410	+	27.8519i	−0.477633	+	0.275762i	−0.719430	−	0.694565i	$-0.755597\pi$
$101$	−48.2410	+	27.8519i	−0.477633	+	0.275762i	0.241796	+	0.970327i	$0.422263\pi$
$102$		0			0
$103$	100.974	−	174.892i	0.980328	−	1.69798i	0.319230	−	0.947677i	$-0.396576\pi$
$103$	100.974	−	174.892i	0.980328	−	1.69798i	0.661098	−	0.750300i	$-0.270091\pi$
$104$		0			0
$105$	−5.25486	−	3.47123i	−0.0500463	−	0.0330593i
$106$		0			0
$107$		−	55.1900i		−	0.515794i	−0.966172	−	0.257897i	$-0.916970\pi$
$107$		−	55.1900i		−	0.515794i	0.966172	−	0.257897i	$-0.0830295\pi$
$108$		0			0
$109$	−44.6887			−0.409988			−0.204994	−	0.978763i	$-0.565717\pi$
$109$	−44.6887			−0.409988			−0.204994	+	0.978763i	$0.565717\pi$
$110$		0			0
$111$	13.1282	−	19.8739i	0.118272	−	0.179044i
$112$		0			0
$113$	93.6725	+	54.0818i	0.828960	+	0.478600i	0.853497	−	0.521099i	$-0.174478\pi$
$113$	93.6725	+	54.0818i	0.828960	+	0.478600i	−0.0245363	+	0.999699i	$0.507811\pi$
$114$		0			0
$115$	−0.481774	−	0.834457i	−0.00418934	−	0.00725615i
$116$		0			0
$117$	−77.9933	−	9.43198i	−0.666610	−	0.0806152i
$118$		0			0
$119$	−45.5510	+	26.2989i	−0.382782	+	0.220999i
$120$		0			0
$121$	−0.625137	+	1.08277i	−0.00516642	+	0.00894850i
$122$		0			0
$123$	67.8254	−	33.8938i	0.551426	−	0.275559i
$124$		0			0
$125$			41.0583i			0.328467i
$126$		0			0
$127$	172.177			1.35573			0.677863	−	0.735188i	$-0.262906\pi$
$127$	172.177			1.35573			0.677863	+	0.735188i	$0.262906\pi$
$128$		0			0
$129$	115.841	+	6.97908i	0.897992	+	0.0541014i
$130$		0			0
$131$	−76.8188	−	44.3514i	−0.586403	−	0.338560i	0.177271	−	0.984162i	$-0.443273\pi$
$131$	−76.8188	−	44.3514i	−0.586403	−	0.338560i	−0.763674	+	0.645602i	$0.776606\pi$
$132$		0			0
$133$	1.89265	+	3.27817i	0.0142305	+	0.0246479i
$134$		0			0
$135$	−17.1363	−	14.5549i	−0.126936	−	0.107814i
$136$		0			0
$137$	−77.6156	+	44.8114i	−0.566537	+	0.327090i	−0.755765	−	0.654843i	$-0.772735\pi$
$137$	−77.6156	+	44.8114i	−0.566537	+	0.327090i	0.189228	+	0.981933i	$0.439401\pi$
$138$		0			0
$139$	−74.7919	+	129.543i	−0.538071	+	0.931966i	0.460937	+	0.887433i	$0.347513\pi$
$139$	−74.7919	+	129.543i	−0.538071	+	0.931966i	−0.999008	+	0.0445333i	$0.985820\pi$
$140$		0			0
$141$	12.4278	−	206.280i	0.0881402	−	1.46298i
$142$		0			0
$143$			95.5223i			0.667988i
$144$		0			0
$145$	−15.1295			−0.104341
$146$		0			0
$147$	57.1880	+	114.440i	0.389034	+	0.778503i
$148$		0			0
$149$	−121.312	−	70.0397i	−0.814177	−	0.470065i	0.0342275	−	0.999414i	$-0.489103\pi$
$149$	−121.312	−	70.0397i	−0.814177	−	0.470065i	−0.848404	+	0.529349i	$0.822436\pi$
$150$		0			0
$151$	−72.5660	−	125.688i	−0.480570	−	0.832371i	0.519182	−	0.854664i	$-0.326237\pi$
$151$	−72.5660	−	125.688i	−0.480570	−	0.832371i	−0.999751	+	0.0222926i	$0.992903\pi$
$152$		0			0
$153$	−172.712	+	73.6842i	−1.12884	+	0.481596i
$154$		0			0
$155$	−37.0541	+	21.3932i	−0.239059	+	0.138021i
$156$		0			0
$157$	123.540	−	213.977i	0.786876	−	1.36291i	−0.140996	−	0.990010i	$-0.545030\pi$
$157$	123.540	−	213.977i	0.786876	−	1.36291i	0.927872	−	0.372899i	$-0.121636\pi$
$158$		0			0
$159$	−116.446	−	76.9214i	−0.732366	−	0.483782i
$160$		0			0
$161$		−	2.91711i		−	0.0181187i
$162$		0			0
$163$	−189.342			−1.16161			−0.580805	−	0.814043i	$-0.697262\pi$
$163$	−189.342			−1.16161			−0.580805	+	0.814043i	$0.697262\pi$
$164$		0			0
$165$	−15.0676	+	22.8099i	−0.0913190	+	0.138242i
$166$		0			0
$167$	200.563	+	115.795i	1.20098	+	0.693384i	0.960772	−	0.277339i	$-0.0894524\pi$
$167$	200.563	+	115.795i	1.20098	+	0.693384i	0.240204	+	0.970722i	$0.422786\pi$
$168$		0			0
$169$	46.4017	+	80.3701i	0.274566	+	0.475563i
$170$		0			0
$171$	5.30284	+	12.4296i	0.0310108	+	0.0726878i
$172$		0			0
$173$	224.906	−	129.849i	1.30003	−	0.750574i	0.319623	−	0.947545i	$-0.396444\pi$
$173$	224.906	−	129.849i	1.30003	−	0.750574i	0.980409	+	0.196971i	$0.0631103\pi$
$174$		0			0
$175$	−30.6386	+	53.0677i	−0.175078	+	0.303244i
$176$		0			0
$177$	276.192	−	138.019i	1.56041	−	0.779768i
$178$		0			0
$179$		−	220.358i		−	1.23105i	−0.788118	−	0.615524i	$-0.788944\pi$
$179$		−	220.358i		−	1.23105i	0.788118	−	0.615524i	$-0.211056\pi$
$180$		0			0
$181$	−286.189			−1.58116			−0.790578	−	0.612362i	$-0.790220\pi$
$181$	−286.189			−1.58116			−0.790578	+	0.612362i	$0.790220\pi$
$182$		0			0
$183$	−264.511	−	15.9360i	−1.44542	−	0.0870821i
$184$		0			0
$185$	5.72560	+	3.30567i	0.0309492	+	0.0178685i
$186$		0			0
$187$	114.156	+	197.724i	0.610461	+	1.05735i
$188$		0			0
$189$	−22.8969	−	64.1007i	−0.121147	−	0.339157i
$190$		0			0
$191$	1.36792	−	0.789768i	0.00716188	−	0.00413491i	−0.496415	−	0.868085i	$-0.665350\pi$
$191$	1.36792	−	0.789768i	0.00716188	−	0.00413491i	0.503577	+	0.863951i	$0.332017\pi$
$192$		0			0
$193$	116.067	−	201.033i	0.601381	−	1.04162i	−0.391231	−	0.920293i	$-0.627951\pi$
$193$	116.067	−	201.033i	0.601381	−	1.04162i	0.992612	−	0.121330i	$-0.0387161\pi$
$194$		0			0
$195$	1.31140	−	21.7670i	0.00672512	−	0.111626i
$196$		0			0
$197$		−	214.012i		−	1.08636i	−0.839618	−	0.543178i	$-0.817221\pi$
$197$		−	214.012i		−	1.08636i	0.839618	−	0.543178i	$-0.182779\pi$
$198$		0			0
$199$	−25.8912			−0.130106			−0.0650532	−	0.997882i	$-0.520722\pi$
$199$	−25.8912			−0.130106			−0.0650532	+	0.997882i	$0.520722\pi$
$200$		0			0
$201$	30.3590	+	60.7519i	0.151040	+	0.302248i
$202$		0			0
$203$	−39.6674	−	22.9020i	−0.195406	−	0.112818i
$204$		0			0
$205$	10.5231	+	18.2266i	0.0513322	+	0.0889100i
$206$		0			0
$207$	1.25029	−	10.3387i	0.00604007	−	0.0499455i
$208$		0			0
$209$	14.2296	−	8.21549i	0.0680844	−	0.0393086i
$210$		0			0
$211$	−46.9752	+	81.3635i	−0.222631	+	0.385609i	−0.955606	−	0.294647i	$-0.904798\pi$
$211$	−46.9752	+	81.3635i	−0.222631	+	0.385609i	0.732975	+	0.680256i	$0.238131\pi$
$212$		0			0
$213$	−260.971	−	172.391i	−1.22521	−	0.809345i
$214$		0			0
$215$			32.2124i			0.149825i
$216$		0			0
$217$	−129.534			−0.596932
$218$		0			0
$219$	124.364	−	188.267i	0.567874	−	0.859667i
$220$		0			0
$221$	−157.721	−	91.0604i	−0.713671	−	0.412038i
$222$		0			0
$223$	149.686	+	259.264i	0.671237	+	1.16262i	0.977554	+	0.210687i	$0.0675702\pi$
$223$	149.686	+	259.264i	0.671237	+	1.16262i	−0.306316	+	0.951930i	$0.599096\pi$
$224$		0			0
$225$	−131.334	+	174.949i	−0.583705	+	0.777550i
$226$		0			0
$227$	315.904	−	182.387i	1.39165	−	0.803467i	0.398149	−	0.917321i	$-0.369653\pi$
$227$	315.904	−	182.387i	1.39165	−	0.803467i	0.993498	+	0.113853i	$0.0363194\pi$
$228$		0			0
$229$	140.979	−	244.183i	0.615629	−	1.06630i	−0.374645	−	0.927168i	$-0.622236\pi$
$229$	140.979	−	244.183i	0.615629	−	1.06630i	0.990274	−	0.139132i	$-0.0444311\pi$
$230$		0			0
$231$	−74.0333	+	36.9960i	−0.320491	+	0.160156i
$232$		0			0
$233$		−	208.568i		−	0.895140i	−0.894249	−	0.447570i	$-0.852290\pi$
$233$		−	208.568i		−	0.895140i	0.894249	−	0.447570i	$-0.147710\pi$
$234$		0			0
$235$	57.3613			0.244090
$236$		0			0
$237$	310.643	+	18.7153i	1.31073	+	0.0789676i
$238$		0			0
$239$	25.1232	+	14.5049i	0.105118	+	0.0606899i	0.551637	−	0.834084i	$-0.314003\pi$
$239$	25.1232	+	14.5049i	0.105118	+	0.0606899i	−0.446519	+	0.894774i	$0.647337\pi$
$240$		0			0
$241$	116.456	+	201.707i	0.483218	+	0.836959i	0.999814	−	0.0192706i	$-0.00613439\pi$
$241$	116.456	+	201.707i	0.483218	+	0.836959i	−0.516596	+	0.856229i	$0.672801\pi$
$242$		0			0
$243$	−53.6763	−	236.998i	−0.220890	−	0.975299i
$244$		0			0
$245$	−30.7532	+	17.7553i	−0.125523	+	0.0724708i
$246$		0			0
$247$	−6.55336	+	11.3507i	−0.0265318	+	0.0459544i
$248$		0			0
$249$	11.1974	−	185.858i	0.0449695	−	0.746418i
$250$		0			0
$251$		−	112.869i		−	0.449676i	−0.974396	−	0.224838i	$-0.927815\pi$
$251$		−	112.869i		−	0.449676i	0.974396	−	0.224838i	$-0.0721853\pi$
$252$		0			0
$253$	−12.6624			−0.0500488
$254$		0			0
$255$	−23.2986	−	46.6233i	−0.0913672	−	0.182836i
$256$		0			0
$257$	292.209	+	168.707i	1.13700	+	0.656448i	0.945686	−	0.325081i	$-0.105392\pi$
$257$	292.209	+	168.707i	1.13700	+	0.656448i	0.191315	+	0.981529i	$0.438725\pi$
$258$		0			0
$259$	10.0078	+	17.3340i	0.0386402	+	0.0669268i
$260$		0			0
$261$	−130.772	−	98.1703i	−0.501043	−	0.376132i
$262$		0			0
$263$	437.975	−	252.865i	1.66530	−	0.961464i	0.695187	−	0.718829i	$-0.255321\pi$
$263$	437.975	−	252.865i	1.66530	−	0.961464i	0.970118	−	0.242635i	$-0.0780119\pi$
$264$		0			0
$265$	19.3688	−	33.5477i	0.0730896	−	0.126595i
$266$		0			0
$267$	4.89925	+	3.23632i	0.0183492	+	0.0121210i
$268$		0			0
$269$			337.414i			1.25433i	0.778887	+	0.627164i	$0.215784\pi$
$269$			337.414i			1.25433i	−0.778887	+	0.627164i	$0.784216\pi$
$270$		0			0
$271$	12.0273			0.0443813			0.0221907	−	0.999754i	$-0.492936\pi$
$271$	12.0273			0.0443813			0.0221907	+	0.999754i	$0.492936\pi$
$272$		0			0
$273$	36.3877	−	55.0849i	0.133288	−	0.201776i
$274$		0			0
$275$	230.352	+	132.994i	0.837643	+	0.483614i
$276$		0			0
$277$	99.9431	+	173.107i	0.360805	+	0.624933i	0.988094	−	0.153854i	$-0.0491685\pi$
$277$	99.9431	+	173.107i	0.360805	+	0.624933i	−0.627288	+	0.778787i	$0.715835\pi$
$278$		0			0
$279$	−459.091	−	55.5194i	−1.64549	−	0.198994i
$280$		0			0
$281$	−290.037	+	167.453i	−1.03216	+	0.595918i	−0.917603	−	0.397499i	$-0.869878\pi$
$281$	−290.037	+	167.453i	−1.03216	+	0.595918i	−0.114557	+	0.993417i	$0.536545\pi$
$282$		0			0
$283$	−235.076	+	407.164i	−0.830659	+	1.43874i	0.0668583	+	0.997762i	$0.478702\pi$
$283$	−235.076	+	407.164i	−0.830659	+	1.43874i	−0.897517	+	0.440980i	$0.854631\pi$
$284$		0			0
$285$	−3.35534	+	1.67674i	−0.0117731	+	0.00588328i
$286$		0			0
$287$			63.7167i			0.222009i
$288$		0			0
$289$	−146.296			−0.506213
$290$		0			0
$291$	−354.660	−	21.3672i	−1.21876	−	0.0734269i
$292$		0			0
$293$	−131.252	−	75.7785i	−0.447960	−	0.258630i	0.259008	−	0.965875i	$-0.416604\pi$
$293$	−131.252	−	75.7785i	−0.447960	−	0.258630i	−0.706968	+	0.707245i	$0.749938\pi$
$294$		0			0
$295$	42.8511	+	74.2204i	0.145258	+	0.251594i
$296$		0			0
$297$	−278.243	+	99.3889i	−0.936847	+	0.334643i
$298$		0			0
$299$	8.74733	−	5.05027i	0.0292553	−	0.0168905i
$300$		0			0
$301$	−48.7610	+	84.4566i	−0.161997	+	0.280587i
$302$		0			0
$303$	10.0498	−	166.809i	0.0331676	−	0.550525i
$304$		0			0
$305$		−	73.5538i		−	0.241160i
$306$		0			0
$307$	−123.852			−0.403426			−0.201713	−	0.979445i	$-0.564651\pi$
$307$	−123.852			−0.403426			−0.201713	+	0.979445i	$0.564651\pi$
$308$		0			0
$309$	270.820	+	541.942i	0.876440	+	1.75386i
$310$		0			0
$311$	83.9131	+	48.4472i	0.269817	+	0.155779i	0.628804	−	0.777563i	$-0.283545\pi$
$311$	83.9131	+	48.4472i	0.269817	+	0.155779i	−0.358987	+	0.933342i	$0.616878\pi$
$312$		0			0
$313$	48.2500	+	83.5714i	0.154153	+	0.267001i	0.932750	−	0.360523i	$-0.117402\pi$
$313$	48.2500	+	83.5714i	0.154153	+	0.267001i	−0.778597	+	0.627524i	$0.784068\pi$
$314$		0			0
$315$	17.3781	−	7.41402i	0.0551686	−	0.0235366i
$316$		0			0
$317$	119.837	−	69.1878i	0.378034	−	0.218258i	−0.298928	−	0.954276i	$-0.596629\pi$
$317$	119.837	−	69.1878i	0.378034	−	0.218258i	0.676963	+	0.736017i	$0.263296\pi$
$318$		0			0
$319$	−99.4112	+	172.185i	−0.311634	+	0.539766i
$320$		0			0
$321$	138.150	+	91.2582i	0.430373	+	0.284293i
$322$		0			0
$323$			31.3270i			0.0969875i
$324$		0			0
$325$	−212.174			−0.652842
$326$		0			0
$327$	73.8940	−	111.863i	0.225976	−	0.342089i
$328$		0			0
$329$	150.393	+	86.8296i	0.457122	+	0.263920i
$330$		0			0
$331$	149.493	+	258.929i	0.451641	+	0.782264i	0.998488	−	0.0549678i	$-0.0175056\pi$
$331$	149.493	+	258.929i	0.451641	+	0.782264i	−0.546848	+	0.837232i	$0.684172\pi$
$332$		0			0
$333$	28.0399	+	65.7242i	0.0842039	+	0.197370i
$334$		0			0
$335$	−16.3257	+	9.42565i	−0.0487334	+	0.0281363i
$336$		0			0
$337$	23.8541	−	41.3165i	0.0707837	−	0.122601i	−0.828461	−	0.560046i	$-0.810783\pi$
$337$	23.8541	−	41.3165i	0.0707837	−	0.122601i	0.899245	+	0.437445i	$0.144117\pi$
$338$		0			0
$339$	−290.266	+	145.052i	−0.856242	+	0.427882i
$340$		0			0
$341$			562.272i			1.64889i
$342$		0			0
$343$	−231.037			−0.673577
$344$		0			0
$345$	2.88541	+	0.173838i	0.00836351	+	0.000503878i
$346$		0			0
$347$	−104.774	−	60.4914i	−0.301943	−	0.174327i	0.341372	−	0.939928i	$-0.389108\pi$
$347$	−104.774	−	60.4914i	−0.301943	−	0.174327i	−0.643315	+	0.765601i	$0.722442\pi$
$348$		0			0
$349$	193.756	+	335.595i	0.555175	+	0.961592i	0.997890	+	0.0649291i	$0.0206821\pi$
$349$	193.756	+	335.595i	0.555175	+	0.961592i	−0.442715	+	0.896663i	$0.645985\pi$
$350$		0			0
$351$	152.574	−	179.634i	0.434684	−	0.511778i
$352$		0			0
$353$	−6.85970	+	3.96045i	−0.0194326	+	0.0112194i	−0.509685	−	0.860361i	$-0.670238\pi$
$353$	−6.85970	+	3.96045i	−0.0194326	+	0.0112194i	0.490252	+	0.871581i	$0.336905\pi$
$354$		0			0
$355$	43.4078	−	75.1845i	0.122276	−	0.211787i
$356$		0			0
$357$	9.48939	−	157.508i	0.0265809	−	0.441198i
$358$		0			0
$359$		−	210.527i		−	0.586425i	−0.956047	−	0.293212i	$-0.905276\pi$
$359$		−	210.527i		−	0.586425i	0.956047	−	0.293212i	$-0.0947243\pi$
$360$		0			0
$361$	−358.745			−0.993755
$362$		0			0
$363$	−1.67667	−	3.35521i	−0.00461892	−	0.00924300i
$364$		0			0
$365$	54.2390	+	31.3149i	0.148600	+	0.0857942i
$366$		0			0
$367$	171.940	+	297.809i	0.468502	+	0.811469i	0.999352	−	0.0359967i	$-0.0114606\pi$
$367$	171.940	+	297.809i	0.468502	+	0.811469i	−0.530850	+	0.847466i	$0.678127\pi$
$368$		0			0
$369$	−27.3095	+	225.823i	−0.0740094	+	0.611986i
$370$		0			0
$371$	101.564	−	58.6382i	0.273758	−	0.158054i
$372$		0			0
$373$	−177.354	+	307.186i	−0.475480	+	0.823556i	−0.999606	−	0.0280853i	$-0.991059\pi$
$373$	−177.354	+	307.186i	−0.475480	+	0.823556i	0.524125	+	0.851641i	$0.324392\pi$
$374$		0			0
$375$	−102.776	−	67.8911i	−0.274069	−	0.181043i
$376$		0			0
$377$		−	158.597i		−	0.420682i
$378$		0			0
$379$	269.497			0.711073			0.355536	−	0.934662i	$-0.384298\pi$
$379$	269.497			0.711073			0.355536	+	0.934662i	$0.384298\pi$
$380$		0			0
$381$	−284.700	+	430.988i	−0.747244	+	1.13120i
$382$		0			0
$383$	−72.6913	−	41.9684i	−0.189795	−	0.109578i	0.402092	−	0.915599i	$-0.368283\pi$
$383$	−72.6913	−	41.9684i	−0.189795	−	0.109578i	−0.591886	+	0.806021i	$0.701617\pi$
$384$		0			0
$385$	−11.4863	−	19.8948i	−0.0298344	−	0.0516748i
$386$		0			0
$387$	−209.016	+	278.429i	−0.540093	+	0.719455i
$388$		0			0
$389$	269.017	−	155.317i	0.691559	−	0.399272i	−0.112637	−	0.993636i	$-0.535930\pi$
$389$	269.017	−	155.317i	0.691559	−	0.399272i	0.804196	+	0.594364i	$0.202596\pi$
$390$		0			0
$391$	12.0709	−	20.9074i	0.0308718	−	0.0534716i
$392$		0			0
$393$	238.041	−	118.954i	0.605702	−	0.302682i
$394$		0			0
$395$			86.3819i			0.218688i
$396$		0			0
$397$	436.104			1.09850			0.549249	−	0.835658i	$-0.314914\pi$
$397$	436.104			1.09850			0.549249	+	0.835658i	$0.314914\pi$
$398$		0			0
$399$	−11.3354	−	0.682924i	−0.0284095	−	0.00171159i
$400$		0			0
$401$	−354.774	−	204.829i	−0.884723	−	0.510795i	−0.0125102	−	0.999922i	$-0.503982\pi$
$401$	−354.774	−	204.829i	−0.884723	−	0.510795i	−0.872213	+	0.489127i	$0.837316\pi$
$402$		0			0
$403$	−224.258	−	388.425i	−0.556470	−	0.963835i
$404$		0			0
$405$	64.7687	−	18.8281i	0.159923	−	0.0464892i
$406$		0			0
$407$	75.2423	−	43.4411i	0.184870	−	0.106735i
$408$		0			0
$409$	211.082	−	365.604i	0.516092	−	0.893897i	−0.483734	−	0.875215i	$-0.660720\pi$
$409$	211.082	−	365.604i	0.516092	−	0.893897i	0.999825	−	0.0186821i	$-0.00594703\pi$
$410$		0			0
$411$	16.1692	−	268.382i	0.0393412	−	0.652997i
$412$		0			0
$413$			259.461i			0.628234i
$414$		0			0
$415$	51.6825			0.124536
$416$		0			0
$417$	−200.598	−	401.420i	−0.481050	−	0.962638i
$418$		0			0
$419$	549.980	+	317.531i	1.31260	+	0.757830i	0.982526	−	0.186124i	$-0.0595927\pi$
$419$	549.980	+	317.531i	1.31260	+	0.757830i	0.330075	+	0.943955i	$0.392926\pi$
$420$		0			0
$421$	23.7781	+	41.1849i	0.0564800	+	0.0978263i	0.892883	−	0.450289i	$-0.148679\pi$
$421$	23.7781	+	41.1849i	0.0564800	+	0.0978263i	−0.836403	+	0.548115i	$0.815346\pi$
$422$		0			0
$423$	495.803	+	372.198i	1.17211	+	0.879902i
$424$		0			0
$425$	−439.184	+	253.563i	−1.03337	+	0.596619i
$426$		0			0
$427$	111.341	−	192.848i	0.260751	−	0.451635i
$428$		0			0
$429$	−239.108	−	157.949i	−0.557362	−	0.368179i
$430$		0			0
$431$		−	614.503i		−	1.42576i	−0.701286	−	0.712880i	$-0.747390\pi$
$431$		−	614.503i		−	1.42576i	0.701286	−	0.712880i	$-0.252610\pi$
$432$		0			0
$433$	118.672			0.274070			0.137035	−	0.990566i	$-0.456243\pi$
$433$	118.672			0.274070			0.137035	+	0.990566i	$0.456243\pi$
$434$		0			0
$435$	25.0170	−	37.8716i	0.0575104	−	0.0870612i
$436$		0			0
$437$	−1.50464	−	0.868707i	−0.00344312	−	0.00198789i
$438$		0			0
$439$	−245.073	−	424.479i	−0.558254	−	0.966924i	−0.997642	−	0.0686266i	$-0.978138\pi$
$439$	−245.073	−	424.479i	−0.558254	−	0.966924i	0.439389	−	0.898297i	$-0.355195\pi$
$440$		0			0
$441$	−381.024	−	46.0785i	−0.864001	−	0.104486i
$442$		0			0
$443$	−167.219	+	96.5440i	−0.377470	+	0.217932i	−0.676717	−	0.736243i	$-0.736598\pi$
$443$	−167.219	+	96.5440i	−0.377470	+	0.217932i	0.299247	+	0.954176i	$0.403264\pi$
$444$		0			0
$445$	−0.814903	+	1.41145i	−0.00183124	+	0.00317180i
$446$		0			0
$447$	375.914	−	187.852i	0.840972	−	0.420251i
$448$		0			0
$449$		−	449.191i		−	1.00043i	−0.865902	−	0.500213i	$-0.833255\pi$
$449$		−	449.191i		−	1.00043i	0.865902	−	0.500213i	$-0.166745\pi$
$450$		0			0
$451$	276.576			0.613252
$452$		0			0
$453$	434.608	+	26.1839i	0.959400	+	0.0578011i
$454$		0			0
$455$	15.8697	+	9.16240i	0.0348785	+	0.0201371i
$456$		0			0
$457$	−47.0282	−	81.4553i	−0.102906	−	0.178239i	0.809975	−	0.586465i	$-0.199481\pi$
$457$	−47.0282	−	81.4553i	−0.102906	−	0.178239i	−0.912881	+	0.408226i	$0.866148\pi$
$458$		0			0
$459$	101.141	−	554.167i	0.220351	−	1.20734i
$460$		0			0
$461$	295.285	−	170.483i	0.640532	−	0.369811i	−0.144288	−	0.989536i	$-0.546089\pi$
$461$	295.285	−	170.483i	0.640532	−	0.369811i	0.784819	+	0.619725i	$0.212756\pi$
$462$		0			0
$463$	−285.649	+	494.759i	−0.616953	+	1.06859i	0.373085	+	0.927797i	$0.378300\pi$
$463$	−285.649	+	494.759i	−0.616953	+	1.06859i	−0.990038	+	0.140798i	$0.955033\pi$
$464$		0			0
$465$	7.71927	−	128.127i	0.0166006	−	0.275542i
$466$		0			0
$467$			421.650i			0.902891i	0.892299	+	0.451446i	$0.149091\pi$
$467$			421.650i			0.902891i	−0.892299	+	0.451446i	$0.850909\pi$
$468$		0			0
$469$	−57.0716			−0.121688
$470$		0			0
$471$	331.343	+	663.057i	0.703489	+	1.40776i
$472$		0			0
$473$	366.602	+	211.658i	0.775058	+	0.447480i
$474$		0			0
$475$	18.2482	+	31.6068i	0.0384173	+	0.0665407i
$476$		0			0
$477$	385.094	−	164.292i	0.807325	−	0.344429i
$478$		0			0
$479$	−700.337	+	404.340i	−1.46208	+	0.844133i	−0.999108	−	0.0422395i	$-0.986551\pi$
$479$	−700.337	+	404.340i	−1.46208	+	0.844133i	−0.462973	+	0.886372i	$0.653217\pi$
$480$		0			0
$481$	−34.6523	+	60.0195i	−0.0720421	+	0.124781i
$482$		0			0
$483$	7.30201	+	4.82352i	0.0151180	+	0.00998658i
$484$		0			0
$485$		−	98.6219i		−	0.203344i
$486$		0			0
$487$	−155.199			−0.318684			−0.159342	−	0.987223i	$-0.550937\pi$
$487$	−155.199			−0.318684			−0.159342	+	0.987223i	$0.550937\pi$
$488$		0			0
$489$	313.083	−	473.956i	0.640252	−	0.969234i
$490$		0			0
$491$	−546.817	−	315.705i	−1.11368	−	0.642984i	−0.173901	−	0.984763i	$-0.555637\pi$
$491$	−546.817	−	315.705i	−1.11368	−	0.642984i	−0.939780	+	0.341779i	$0.888970\pi$
$492$		0			0
$493$	−189.535	−	328.285i	−0.384453	−	0.665892i
$494$		0			0
$495$	−32.1822	−	75.4336i	−0.0650145	−	0.152391i
$496$		0			0
$497$	227.619	−	131.416i	0.457985	−	0.264418i
$498$		0			0
$499$	445.820	−	772.183i	0.893427	−	1.54746i	0.0576878	−	0.998335i	$-0.481627\pi$
$499$	445.820	−	772.183i	0.893427	−	1.54746i	0.835739	−	0.549126i	$-0.185039\pi$
$500$		0			0
$501$	−621.491	+	310.572i	−1.24050	+	0.619905i
$502$		0			0
$503$			281.433i			0.559509i	0.960072	+	0.279754i	$0.0902531\pi$
$503$			281.433i			0.559509i	−0.960072	+	0.279754i	$0.909747\pi$
$504$		0			0
$505$	46.3854			0.0918523
$506$		0			0
$507$	−277.906	−	16.7431i	−0.548139	−	0.0330238i
$508$		0			0
$509$	−426.209	−	246.072i	−0.837346	−	0.483442i	0.0190149	−	0.999819i	$-0.493947\pi$
$509$	−426.209	−	246.072i	−0.837346	−	0.483442i	−0.856361	+	0.516377i	$0.827280\pi$
$510$		0			0
$511$	94.8047	+	164.207i	0.185528	+	0.321344i
$512$		0			0
$513$	−39.8818	−	7.27883i	−0.0777423	−	0.0141887i
$514$		0			0
$515$	−145.635	+	84.0823i	−0.282786	+	0.163267i
$516$		0			0
$517$	376.903	−	652.815i	0.729020	−	1.26270i
$518$		0			0
$519$	−46.8533	+	777.686i	−0.0902762	+	1.49843i
$520$		0			0
$521$		−	633.968i		−	1.21683i	−0.793619	−	0.608415i	$-0.791806\pi$
$521$		−	633.968i		−	1.21683i	0.793619	−	0.608415i	$-0.208194\pi$
$522$		0			0
$523$	42.6893			0.0816240			0.0408120	−	0.999167i	$-0.487006\pi$
$523$	42.6893			0.0816240			0.0408120	+	0.999167i	$0.487006\pi$
$524$		0			0
$525$	−82.1753	−	164.442i	−0.156524	−	0.313224i
$526$		0			0
$527$	−928.394	−	536.008i	−1.76166	−	1.01709i
$528$		0			0
$529$	−263.831	−	456.968i	−0.498734	−	0.863833i
$530$		0			0
$531$	−111.207	+	919.572i	−0.209429	+	1.73177i
$532$		0			0
$533$	−191.063	+	110.310i	−0.358467	+	0.206961i
$534$		0			0
$535$	−22.9787	+	39.8004i	−0.0429509	+	0.0743932i
$536$		0			0
$537$	551.592	+	364.368i	1.02717	+	0.678525i
$538$		0			0
$539$			466.660i			0.865788i
$540$		0			0
$541$	−585.520			−1.08229			−0.541146	−	0.840929i	$-0.682009\pi$
$541$	−585.520			−1.08229			−0.541146	+	0.840929i	$0.682009\pi$
$542$		0			0
$543$	473.222	−	716.379i	0.871495	−	1.31930i
$544$		0			0
$545$	32.2273	+	18.6065i	0.0591327	+	0.0341403i
$546$		0			0
$547$	−429.811	−	744.455i	−0.785761	−	1.36098i	−0.928544	−	0.371223i	$-0.878938\pi$
$547$	−429.811	−	744.455i	−0.785761	−	1.36098i	0.142783	−	0.989754i	$-0.454395\pi$
$548$		0			0
$549$	477.267	−	635.764i	0.869339	−	1.15804i
$550$		0			0
$551$	−23.6257	+	13.6403i	−0.0428779	+	0.0247556i
$552$		0			0
$553$	−130.759	+	226.481i	−0.236454	+	0.409550i
$554$		0			0
$555$	−17.7421	+	8.86610i	−0.0319677	+	0.0159749i
$556$		0			0
$557$		−	394.616i		−	0.708467i	−0.935157	−	0.354234i	$-0.884742\pi$
$557$		−	394.616i		−	0.708467i	0.935157	−	0.354234i	$-0.115258\pi$
$558$		0			0
$559$	−337.672			−0.604065
$560$		0			0
$561$	−683.697	−	41.1908i	−1.21871	−	0.0734239i
$562$		0			0
$563$	375.650	+	216.882i	0.667229	+	0.385225i	0.795026	−	0.606576i	$-0.207457\pi$
$563$	375.650	+	216.882i	0.667229	+	0.385225i	−0.127797	+	0.991800i	$0.540791\pi$
$564$		0			0
$565$	−45.0347	−	78.0025i	−0.0797075	−	0.138057i
$566$		0			0
$567$	198.315	+	48.6777i	0.349763	+	0.0858514i
$568$		0			0
$569$	187.251	−	108.110i	0.329088	−	0.189999i	−0.326348	−	0.945250i	$-0.605818\pi$
$569$	187.251	−	108.110i	0.329088	−	0.189999i	0.655436	+	0.755250i	$0.272485\pi$
$570$		0			0
$571$	525.111	−	909.518i	0.919633	−	1.59285i	0.119661	−	0.992815i	$-0.461819\pi$
$571$	525.111	−	909.518i	0.919633	−	1.59285i	0.799972	−	0.600037i	$-0.204848\pi$
$572$		0			0
$573$	−0.284971	+	4.73003i	−0.000497331	+	0.00825486i
$574$		0			0
$575$		−	28.1256i		−	0.0489140i
$576$		0			0
$577$	235.000			0.407279			0.203640	−	0.979046i	$-0.434723\pi$
$577$	235.000			0.407279			0.203640	+	0.979046i	$0.434723\pi$
$578$		0			0
$579$	311.300	+	622.948i	0.537652	+	1.07590i
$580$		0			0
$581$	135.504	+	78.2334i	0.233226	+	0.134653i
$582$		0			0
$583$	−254.532	−	440.863i	−0.436590	−	0.756197i
$584$		0			0
$585$	52.3180	+	39.2750i	0.0894324	+	0.0671367i
$586$		0			0
$587$	−669.449	+	386.506i	−1.14046	+	0.658443i	−0.946544	−	0.322575i	$-0.895452\pi$
$587$	−669.449	+	386.506i	−1.14046	+	0.658443i	−0.193914	+	0.981019i	$0.562118\pi$
$588$		0			0
$589$	−38.5750	+	66.8138i	−0.0654923	+	0.113436i
$590$		0			0
$591$	535.708	+	353.875i	0.906443	+	0.598773i
$592$		0			0
$593$			504.381i			0.850557i	0.905062	+	0.425279i	$0.139824\pi$
$593$			504.381i			0.850557i	−0.905062	+	0.425279i	$0.860176\pi$
$594$		0			0
$595$	43.7989			0.0736117
$596$		0			0
$597$	42.8118	−	64.8099i	0.0717115	−	0.108559i
$598$		0			0
$599$	−37.9297	−	21.8987i	−0.0633217	−	0.0365588i	0.468005	−	0.883726i	$-0.344973\pi$
$599$	−37.9297	−	21.8987i	−0.0633217	−	0.0365588i	−0.531327	+	0.847167i	$0.678306\pi$
$600$		0			0
$601$	4.89587	+	8.47990i	0.00814621	+	0.0141096i	0.870070	−	0.492929i	$-0.164074\pi$
$601$	4.89587	+	8.47990i	0.00814621	+	0.0141096i	−0.861924	+	0.507038i	$0.830740\pi$
$602$		0			0
$603$	−202.272	−	24.4613i	−0.335442	−	0.0405661i
$604$		0			0
$605$	0.901637	−	0.520561i	0.00149031	−	0.000860431i
$606$		0			0
$607$	175.724	−	304.363i	0.289496	−	0.501421i	−0.684194	−	0.729300i	$-0.739846\pi$
$607$	175.724	−	304.363i	0.289496	−	0.501421i	0.973689	+	0.227879i	$0.0731791\pi$
$608$		0			0
$609$	122.919	−	61.4251i	0.201837	−	0.100862i
$610$		0			0
$611$			601.298i			0.984122i
$612$		0			0
$613$	733.118			1.19595			0.597976	−	0.801514i	$-0.295972\pi$
$613$	733.118			1.19595			0.597976	+	0.801514i	$0.295972\pi$
$614$		0			0
$615$	−63.0244	−	3.79704i	−0.102479	−	0.00617404i
$616$		0			0
$617$	557.311	+	321.764i	0.903260	+	0.521497i	0.878256	−	0.478190i	$-0.158707\pi$
$617$	557.311	+	321.764i	0.903260	+	0.521497i	0.0250035	+	0.999687i	$0.492040\pi$
$618$		0			0
$619$	124.319	+	215.327i	0.200839	+	0.347863i	0.948799	−	0.315880i	$-0.102300\pi$
$619$	124.319	+	215.327i	0.200839	+	0.347863i	−0.747960	+	0.663744i	$0.768967\pi$
$620$		0			0
$621$	23.8121	+	20.2251i	0.0383448	+	0.0325685i
$622$		0			0
$623$	−4.27312	+	2.46709i	−0.00685895	+	0.00396001i
$624$		0			0
$625$	−286.737	+	496.644i	−0.458780	+	0.794630i
$626$		0			0
$627$	−2.96438	+	49.2037i	−0.00472788	+	0.0784748i
$628$		0			0
$629$			165.648i			0.263351i
$630$		0			0
$631$	479.055			0.759200			0.379600	−	0.925151i	$-0.376062\pi$
$631$	479.055			0.759200			0.379600	+	0.925151i	$0.376062\pi$
$632$		0			0
$633$	−125.991	−	252.124i	−0.199039	−	0.398300i
$634$		0			0
$635$	−124.166	−	71.6873i	−0.195537	−	0.112893i
$636$		0			0
$637$	−186.123	−	322.375i	−0.292187	−	0.506083i
$638$		0			0
$639$	863.044	−	368.200i	1.35062	−	0.576213i
$640$		0			0
$641$	−1019.97	+	588.880i	−1.59122	+	0.918689i	−0.598118	+	0.801408i	$0.704084\pi$
$641$	−1019.97	+	588.880i	−1.59122	+	0.918689i	−0.993099	+	0.117281i	$0.962582\pi$
$642$		0			0
$643$	88.0856	−	152.569i	0.136992	−	0.237276i	−0.789365	−	0.613924i	$-0.789590\pi$
$643$	88.0856	−	152.569i	0.136992	−	0.237276i	0.926356	+	0.376648i	$0.122923\pi$
$644$		0			0
$645$	−80.6331	−	53.2642i	−0.125013	−	0.0825801i
$646$		0			0
$647$		−	317.529i		−	0.490771i	−0.969426	−	0.245386i	$-0.921085\pi$
$647$		−	317.529i		−	0.490771i	0.969426	−	0.245386i	$-0.0789146\pi$
$648$		0			0
$649$	1126.25			1.73536
$650$		0			0
$651$	214.189	−	324.246i	0.329015	−	0.498074i
$652$		0			0
$653$	−883.885	−	510.311i	−1.35358	−	0.781488i	−0.364828	−	0.931075i	$-0.618872\pi$
$653$	−883.885	−	510.311i	−1.35358	−	0.781488i	−0.988749	+	0.149587i	$0.952206\pi$
$654$		0			0
$655$	36.9320	+	63.9681i	0.0563848	+	0.0976613i
$656$		0			0
$657$	265.624	+	622.610i	0.404298	+	0.947656i
$658$		0			0
$659$	127.595	−	73.6669i	0.193619	−	0.111786i	−0.400057	−	0.916490i	$-0.631010\pi$
$659$	127.595	−	73.6669i	0.193619	−	0.111786i	0.593676	+	0.804704i	$0.297676\pi$
$660$		0			0
$661$	−386.978	+	670.266i	−0.585444	+	1.01402i	0.409376	+	0.912366i	$0.365746\pi$
$661$	−386.978	+	670.266i	−0.585444	+	1.01402i	−0.994820	+	0.101653i	$0.967587\pi$
$662$		0			0
$663$	488.736	−	244.232i	0.737159	−	0.368374i
$664$		0			0
$665$		−	3.15208i		−	0.00473997i
$666$		0			0
$667$	21.0235			0.0315195
$668$		0			0
$669$	−896.490	−	54.0109i	−1.34004	−	0.0807338i
$670$		0			0
$671$	−837.100	−	483.300i	−1.24754	−	0.720268i
$672$		0			0
$673$	62.7363	+	108.663i	0.0932189	+	0.161460i	0.908864	−	0.417093i	$-0.136951\pi$
$673$	62.7363	+	108.663i	0.0932189	+	0.161460i	−0.815645	+	0.578553i	$0.803618\pi$
$674$		0			0
$675$	−220.762	−	618.033i	−0.327055	−	0.915604i
$676$		0			0
$677$	953.760	−	550.654i	1.40880	−	0.813374i	0.413531	−	0.910490i	$-0.364295\pi$
$677$	953.760	−	550.654i	1.40880	−	0.813374i	0.995273	+	0.0971164i	$0.0309619\pi$
$678$		0			0
$679$	149.287	−	258.573i	0.219863	−	0.380814i
$680$		0			0
$681$	−65.8105	+	1092.34i	−0.0966380	+	1.60403i
$682$		0			0
$683$			469.992i			0.688128i	0.938946	+	0.344064i	$0.111804\pi$
$683$			469.992i			0.688128i	−0.938946	+	0.344064i	$0.888196\pi$
$684$		0			0
$685$	74.6302			0.108949
$686$		0			0
$687$	378.117	+	756.657i	0.550389	+	1.10139i
$688$		0			0
$689$	351.669	+	203.036i	0.510404	+	0.294682i
$690$		0			0
$691$	−263.870	−	457.036i	−0.381866	−	0.661412i	0.609463	−	0.792815i	$-0.291385\pi$
$691$	−263.870	−	457.036i	−0.381866	−	0.661412i	−0.991329	+	0.131403i	$0.958052\pi$
$692$		0			0
$693$	29.8090	−	246.492i	0.0430145	−	0.355688i
$694$		0			0
$695$	107.873	−	62.2803i	0.155212	−	0.0896119i
$696$		0			0
$697$	−263.657	+	456.668i	−0.378275	+	0.655191i
$698$		0			0
$699$	522.080	+	344.873i	0.746895	+	0.493380i
$700$		0			0
$701$			1162.38i			1.65818i	0.559116	+	0.829089i	$0.311141\pi$
$701$			1162.38i			1.65818i	−0.559116	+	0.829089i	$0.688859\pi$
$702$		0			0
$703$	11.9212			0.0169576
$704$		0			0
$705$	−94.8485	+	143.585i	−0.134537	+	0.203666i
$706$		0			0
$707$	121.616	+	70.2151i	0.172017	+	0.0993142i
$708$		0			0
$709$	−100.029	−	173.255i	−0.141085	−	0.244366i	0.786821	−	0.617182i	$-0.211726\pi$
$709$	−100.029	−	173.255i	−0.141085	−	0.244366i	−0.927905	+	0.372816i	$0.878392\pi$
$710$		0			0
$711$	−560.504	+	746.644i	−0.788332	+	1.05013i
$712$		0			0
$713$	51.4893	−	29.7274i	0.0722150	−	0.0416934i
$714$		0			0
$715$	39.7714	−	68.8861i	0.0556244	−	0.0963442i
$716$		0			0
$717$	−77.8501	+	38.9033i	−0.108577	+	0.0542585i
$718$		0			0
$719$		−	447.907i		−	0.622958i	−0.950253	−	0.311479i	$-0.899176\pi$
$719$		−	447.907i		−	0.622958i	0.950253	−	0.311479i	$-0.100824\pi$
$720$		0			0
$721$	−509.112			−0.706120
$722$		0			0
$723$	−697.469	−	42.0205i	−0.964688	−	0.0581196i
$724$		0			0
$725$	−382.457	−	220.812i	−0.527527	−	0.304568i
$726$		0			0
$727$	−253.737	−	439.486i	−0.349020	−	0.604520i	0.637056	−	0.770818i	$-0.280152\pi$
$727$	−253.737	−	439.486i	−0.349020	−	0.604520i	−0.986076	+	0.166298i	$0.946819\pi$
$728$		0			0
$729$	682.000	+	257.522i	0.935528	+	0.353253i
$730$		0			0
$731$	−698.957	+	403.543i	−0.956165	+	0.552042i
$732$		0			0
$733$	−545.542	+	944.907i	−0.744260	+	1.28910i	0.206280	+	0.978493i	$0.433864\pi$
$733$	−545.542	+	944.907i	−0.744260	+	1.28910i	−0.950540	+	0.310603i	$0.899469\pi$
$734$		0			0
$735$	6.40663	−	106.339i	0.00871651	−	0.144679i
$736$		0			0
$737$			247.732i			0.336136i
$738$		0			0
$739$	114.753			0.155281			0.0776406	−	0.996981i	$-0.475261\pi$
$739$	114.753			0.155281			0.0776406	+	0.996981i	$0.475261\pi$
$740$		0			0
$741$	−17.5766	−	35.1729i	−0.0237202	−	0.0474668i
$742$		0			0
$743$	531.028	+	306.589i	0.714708	+	0.412637i	0.812802	−	0.582540i	$-0.197941\pi$
$743$	531.028	+	306.589i	0.714708	+	0.412637i	−0.0980939	+	0.995177i	$0.531275\pi$
$744$		0			0
$745$	58.3231	+	101.019i	0.0782860	+	0.135595i
$746$		0			0
$747$	446.719	+	335.351i	0.598017	+	0.448930i
$748$		0			0
$749$	−120.494	+	69.5673i	−0.160873	+	0.0928803i
$750$		0			0
$751$	−193.945	+	335.922i	−0.258248	+	0.447299i	−0.965773	−	0.259390i	$-0.916479\pi$
$751$	−193.945	+	335.922i	−0.258248	+	0.447299i	0.707524	+	0.706689i	$0.249812\pi$
$752$		0			0
$753$	282.529	+	186.631i	0.375205	+	0.247851i
$754$		0			0
$755$			120.854i			0.160071i
$756$		0			0
$757$	732.340			0.967424			0.483712	−	0.875227i	$-0.339288\pi$
$757$	732.340			0.967424			0.483712	+	0.875227i	$0.339288\pi$
$758$		0			0
$759$	20.9376	−	31.6960i	0.0275857	−	0.0417602i
$760$		0			0
$761$	771.356	+	445.342i	1.01361	+	0.585207i	0.912246	−	0.409643i	$-0.134347\pi$
$761$	771.356	+	445.342i	1.01361	+	0.585207i	0.101362	+	0.994850i	$0.467680\pi$
$762$		0			0
$763$	56.3304	+	97.5671i	0.0738275	+	0.127873i
$764$		0			0
$765$	155.231	+	18.7726i	0.202916	+	0.0245393i
$766$		0			0
$767$	−778.027	+	449.194i	−1.01438	+	0.585650i
$768$		0			0
$769$	−244.356	+	423.237i	−0.317758	+	0.550373i	−0.980020	−	0.198899i	$-0.936263\pi$
$769$	−244.356	+	423.237i	−0.317758	+	0.550373i	0.662262	+	0.749272i	$0.269597\pi$
$770$		0			0
$771$	−905.478	+	452.487i	−1.17442	+	0.586883i
$772$		0			0
$773$		−	579.450i		−	0.749612i	−0.927103	−	0.374806i	$-0.877709\pi$
$773$		−	579.450i		−	0.749612i	0.927103	−	0.374806i	$-0.122291\pi$
$774$		0			0
$775$	−1248.92			−1.61150
$776$		0			0
$777$	−59.9382	−	3.61110i	−0.0771405	−	0.00464750i
$778$		0			0
$779$	32.8651	+	18.9747i	0.0421888	+	0.0243577i
$780$		0			0
$781$	−570.439	−	988.029i	−0.730395	−	1.26508i
$782$		0			0
$783$	461.972	−	165.017i	0.590003	−	0.210750i
$784$		0			0
$785$	−178.182	+	102.873i	−0.226983	+	0.131049i
$786$		0			0
$787$	87.9405	−	152.317i	0.111741	−	0.193542i	−0.804731	−	0.593640i	$-0.797690\pi$
$787$	87.9405	−	152.317i	0.111741	−	0.193542i	0.916472	+	0.400098i	$0.131024\pi$
$788$		0			0
$789$	−91.2409	+	1514.44i	−0.115641	+	1.91945i
$790$		0			0
$791$		−	272.682i		−	0.344731i
$792$		0			0
$793$	771.040			0.972308
$794$		0			0
$795$	51.9486	+	103.955i	0.0653442	+	0.130761i
$796$		0			0
$797$	397.577	+	229.541i	0.498841	+	0.288006i	0.728235	−	0.685328i	$-0.240341\pi$
$797$	397.577	+	229.541i	0.498841	+	0.288006i	−0.229394	+	0.973334i	$0.573674\pi$
$798$		0			0
$799$	718.596	+	1244.64i	0.899369	+	1.55775i
$800$		0			0
$801$	−16.2021	+	6.91229i	−0.0202273	+	0.00862957i
$802$		0			0
$803$	712.775	−	411.521i	0.887640	−	0.512479i
$804$		0			0
$805$	−1.21456	+	2.10368i	−0.00150877	+	0.00261326i
$806$		0			0
$807$	−844.604	−	557.924i	−1.04660	−	0.691355i
$808$		0			0
$809$		−	89.1339i		−	0.110178i	−0.998481	−	0.0550890i	$-0.982456\pi$
$809$		−	89.1339i		−	0.110178i	0.998481	−	0.0550890i	$-0.0175442\pi$
$810$		0			0
$811$	625.256			0.770969			0.385484	−	0.922714i	$-0.374034\pi$
$811$	625.256			0.770969			0.385484	+	0.922714i	$0.374034\pi$
$812$		0			0
$813$	−19.8875	+	30.1064i	−0.0244619	+	0.0370313i
$814$		0			0
$815$	136.545	+	78.8341i	0.167539	+	0.0967290i
$816$		0			0
$817$	29.0418	+	50.3019i	0.0355469	+	0.0615690i
$818$		0			0
$819$	77.7186	+	182.169i	0.0948946	+	0.222429i
$820$		0			0
$821$	−625.391	+	361.070i	−0.761743	+	0.439793i	−0.829921	−	0.557880i	$-0.811615\pi$
$821$	−625.391	+	361.070i	−0.761743	+	0.439793i	0.0681779	+	0.997673i	$0.478281\pi$
$822$		0			0
$823$	−149.534	+	259.000i	−0.181693	+	0.314702i	−0.942457	−	0.334327i	$-0.891491\pi$
$823$	−149.534	+	259.000i	−0.181693	+	0.314702i	0.760764	+	0.649029i	$0.224824\pi$
$824$		0			0
$825$	−713.799	+	356.700i	−0.865211	+	0.432364i
$826$		0			0
$827$		−	1178.17i		−	1.42463i	−0.701858	−	0.712317i	$-0.747646\pi$
$827$		−	1178.17i		−	1.42463i	0.701858	−	0.712317i	$-0.252354\pi$
$828$		0			0
$829$	−451.760			−0.544946			−0.272473	−	0.962163i	$-0.587841\pi$
$829$	−451.760			−0.544946			−0.272473	+	0.962163i	$0.587841\pi$
$830$		0			0
$831$	−598.573	−	36.0623i	−0.720305	−	0.0433963i
$832$		0			0
$833$	−770.523	−	444.862i	−0.924998	−	0.534048i
$834$		0			0
$835$	−96.4243	−	167.012i	−0.115478	−	0.200014i
$836$		0			0
$837$	898.095	−	1057.38i	1.07299	−	1.26330i
$838$		0			0
$839$	274.743	−	158.623i	0.327465	−	0.189062i	−0.327250	−	0.944938i	$-0.606122\pi$
$839$	274.743	−	158.623i	0.327465	−	0.189062i	0.654715	+	0.755876i	$0.272789\pi$
$840$		0			0
$841$	−255.446	+	442.445i	−0.303741	+	0.526094i
$842$		0			0
$843$	60.4218	−	1002.90i	0.0716747	−	1.18968i
$844$		0			0
$845$		−	77.2788i		−	0.0914542i
$846$		0			0
$847$	3.15196			0.00372132
$848$		0			0
$849$	−630.494	−	1261.69i	−0.742632	−	1.48609i
$850$		0			0
$851$	−7.95613	−	4.59347i	−0.00934915	−	0.00539773i
$852$		0			0
$853$	55.9234	+	96.8622i	0.0655609	+	0.113555i	0.896943	−	0.442147i	$-0.145783\pi$
$853$	55.9234	+	96.8622i	0.0655609	+	0.113555i	−0.831382	+	0.555702i	$0.812450\pi$
$854$		0			0
$855$	1.35101	−	11.1715i	0.00158013	−	0.0130661i
$856$		0			0
$857$	−522.040	+	301.400i	−0.609148	+	0.351692i	−0.772632	−	0.634854i	$-0.781060\pi$
$857$	−522.040	+	301.400i	−0.609148	+	0.351692i	0.163484	+	0.986546i	$0.447727\pi$
$858$		0			0
$859$	−649.175	+	1124.40i	−0.755733	+	1.30897i	0.189276	+	0.981924i	$0.439386\pi$
$859$	−649.175	+	1124.40i	−0.755733	+	1.30897i	−0.945009	+	0.327044i	$0.893947\pi$
$860$		0			0
$861$	−159.493	−	105.357i	−0.185242	−	0.122366i
$862$		0			0
$863$			1332.38i			1.54390i	0.635685	+	0.771949i	$0.280718\pi$
$863$			1332.38i			1.54390i	−0.635685	+	0.771949i	$0.719282\pi$
$864$		0			0
$865$	−216.255			−0.250006
$866$		0			0
$867$	241.904	−	366.202i	0.279012	−	0.422378i
$868$		0			0
$869$	983.092	+	567.589i	1.13129	+	0.653151i
$870$		0			0
$871$	−98.8059	−	171.137i	−0.113440	−	0.196483i
$872$		0			0
$873$	639.925	−	852.441i	0.733019	−	0.976450i
$874$		0			0
$875$	89.6411	−	51.7543i	0.102447	−	0.0591478i
$876$		0			0
$877$	407.412	−	705.658i	0.464551	−	0.804627i	−0.534630	−	0.845086i	$-0.679549\pi$
$877$	407.412	−	705.658i	0.464551	−	0.804627i	0.999181	+	0.0404597i	$0.0128822\pi$
$878$		0			0
$879$	406.716	−	203.244i	0.462703	−	0.231222i
$880$		0			0
$881$			86.4877i			0.0981700i	0.998795	+	0.0490850i	$0.0156305\pi$
$881$			86.4877i			0.0981700i	−0.998795	+	0.0490850i	$0.984369\pi$
$882$		0			0
$883$	−367.217			−0.415875			−0.207937	−	0.978142i	$-0.566675\pi$
$883$	−367.217			−0.415875			−0.207937	+	0.978142i	$0.566675\pi$
$884$		0			0
$885$	−256.641	−	15.4619i	−0.289990	−	0.0174711i
$886$		0			0
$887$	587.456	+	339.168i	0.662295	+	0.382376i	0.793151	−	0.609025i	$-0.208439\pi$
$887$	587.456	+	339.168i	0.662295	+	0.382376i	−0.130856	+	0.991401i	$0.541773\pi$
$888$		0			0
$889$	−217.031	−	375.908i	−0.244129	−	0.422844i
$890$		0			0
$891$	211.297	−	860.832i	0.237145	−	0.966141i
$892$		0			0
$893$	89.5734	−	51.7152i	0.100306	−	0.0579118i
$894$		0			0
$895$	−91.7475	+	158.911i	−0.102511	+	0.177555i
$896$		0			0
$897$	−1.82228	+	30.2468i	−0.00203153	+	0.0337199i
$898$		0			0
$899$		−	933.550i		−	1.03843i
$900$		0			0
$901$	970.571			1.07722
$902$		0			0
$903$	−130.781	−	261.708i	−0.144830	−	0.289821i
$904$		0			0
$905$	206.386	+	119.157i	0.228051	+	0.131665i
$906$		0			0
$907$	431.371	+	747.156i	0.475602	+	0.823767i	0.999609	−	0.0279469i	$-0.00889694\pi$
$907$	431.371	+	747.156i	0.475602	+	0.823767i	−0.524007	+	0.851714i	$0.675564\pi$
$908$		0			0
$909$	400.934	+	300.980i	0.441071	+	0.331111i
$910$		0			0
$911$	1007.57	−	581.718i	1.10600	−	0.638549i	0.168209	−	0.985751i	$-0.446202\pi$
$911$	1007.57	−	581.718i	1.10600	−	0.638549i	0.937790	+	0.347202i	$0.112868\pi$
$912$		0			0
$913$	339.590	−	588.186i	0.371949	−	0.644235i
$914$		0			0
$915$	184.118	+	121.623i	0.201221	+	0.132922i
$916$		0			0
$917$			223.621i			0.243861i
$918$		0			0
$919$	832.360			0.905724			0.452862	−	0.891581i	$-0.350403\pi$
$919$	832.360			0.905724			0.452862	+	0.891581i	$0.350403\pi$
$920$		0			0
$921$	204.792	−	310.021i	0.222359	−	0.336614i
$922$		0			0
$923$	788.134	+	455.029i	0.853883	+	0.492990i
$924$		0			0
$925$	96.4912	+	167.128i	0.104315	+	0.180679i
$926$		0			0
$927$	−1804.38	−	218.210i	−1.94647	−	0.235393i
$928$		0			0
$929$	1540.10	−	889.178i	1.65781	−	0.957135i	0.684082	−	0.729405i	$-0.260203\pi$
$929$	1540.10	−	889.178i	1.65781	−	0.957135i	0.973724	−	0.227730i	$-0.0731302\pi$
$930$		0			0
$931$	−32.0154	+	55.4523i	−0.0343882	+	0.0595621i
$932$		0			0
$933$	−260.024	+	129.940i	−0.278697	+	0.139271i
$934$		0			0
$935$		−	190.119i		−	0.203336i
$936$		0			0
$937$	432.361			0.461431			0.230715	−	0.973021i	$-0.425893\pi$
$937$	432.361			0.461431			0.230715	+	0.973021i	$0.425893\pi$
$938$		0			0
$939$	−288.976	−	17.4100i	−0.307748	−	0.0185410i
$940$		0			0
$941$	−1521.40	−	878.378i	−1.61679	−	0.933452i	−0.987744	−	0.156080i	$-0.950114\pi$
$941$	−1521.40	−	878.378i	−1.61679	−	0.933452i	−0.629041	−	0.777372i	$-0.716552\pi$
$942$		0			0
$943$	−14.6226	−	25.3271i	−0.0155065	−	0.0268580i
$944$		0			0
$945$	−10.1767	+	55.7596i	−0.0107690	+	0.0590049i
$946$		0			0
$947$	980.755	−	566.239i	1.03564	−	0.597929i	0.117048	−	0.993126i	$-0.462657\pi$
$947$	980.755	−	566.239i	1.03564	−	0.597929i	0.918596	+	0.395197i	$0.129324\pi$
$948$		0			0
$949$	−328.263	+	568.568i	−0.345904	+	0.599124i
$950$		0			0
$951$	−24.9649	+	414.376i	−0.0262512	+	0.435726i
$952$		0			0
$953$		−	1509.90i		−	1.58436i	−0.610286	−	0.792181i	$-0.708945\pi$
$953$		−	1509.90i		−	1.58436i	0.610286	−	0.792181i	$-0.291055\pi$
$954$		0			0
$955$	−1.31530			−0.00137728
$956$		0			0
$957$	−266.629	−	533.556i	−0.278609	−	0.557530i
$958$		0			0
$959$	195.670	+	112.970i	0.204035	+	0.117800i
$960$		0			0
$961$	−839.545	−	1454.13i	−0.873616	−	1.51315i
$962$		0			0
$963$	−456.869	+	194.914i	−0.474423	+	0.202403i
$964$		0			0
$965$	−167.403	+	96.6503i	−0.173475	+	0.100156i
$966$		0			0
$967$	244.990	−	424.335i	0.253350	−	0.438816i	−0.711096	−	0.703095i	$-0.751801\pi$
$967$	244.990	−	424.335i	0.253350	−	0.438816i	0.964446	+	0.264279i	$0.0851341\pi$
$968$		0			0
$969$	−78.4166	−	51.8000i	−0.0809253	−	0.0534572i
$970$		0			0
$971$		−	253.051i		−	0.260608i	−0.991474	−	0.130304i	$-0.958405\pi$
$971$		−	253.051i		−	0.260608i	0.991474	−	0.130304i	$-0.0415954\pi$
$972$		0			0
$973$	377.103			0.387567
$974$		0			0
$975$	350.835	−	531.106i	0.359831	−	0.544724i
$976$		0			0
$977$	−1407.52	−	812.635i	−1.44066	−	0.831765i	−0.442766	−	0.896637i	$-0.646003\pi$
$977$	−1407.52	−	812.635i	−1.44066	−	0.831765i	−0.997894	+	0.0648717i	$0.979336\pi$
$978$		0			0
$979$	10.7089	+	18.5484i	0.0109387	+	0.0189463i
$980$		0			0
$981$	157.826	+	369.938i	0.160883	+	0.377103i
$982$		0			0
$983$	1007.16	−	581.483i	1.02458	−	0.591540i	0.109150	−	0.994025i	$-0.465187\pi$
$983$	1007.16	−	581.483i	1.02458	−	0.591540i	0.915426	+	0.402486i	$0.131854\pi$
$984$		0			0
$985$	−89.1055	+	154.335i	−0.0904624	+	0.156686i
$986$		0			0
$987$	−466.028	+	232.884i	−0.472167	+	0.235952i
$988$		0			0
$989$		−	44.7615i		−	0.0452594i
$990$		0			0
$991$	1411.24			1.42405			0.712027	−	0.702152i	$-0.247777\pi$
$991$	1411.24			1.42405			0.712027	+	0.702152i	$0.247777\pi$
$992$		0			0
$993$	−895.335	−	53.9413i	−0.901646	−	0.0543216i
$994$		0			0
$995$	18.6715	+	10.7800i	0.0187653	+	0.0108341i
$996$		0			0
$997$	−561.614	−	972.744i	−0.563304	−	0.975671i	−0.997205	−	0.0747104i	$-0.976197\pi$
$997$	−561.614	−	972.744i	−0.563304	−	0.975671i	0.433902	−	0.900960i	$-0.357137\pi$
$998$		0			0
$999$	−210.883	−	38.4883i	−0.211095	−	0.0385269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.q.b.257.5	yes	24
3.2	odd	2		864.3.q.a.449.6		24
4.3	odd	2	inner	288.3.q.b.257.8	yes	24
8.3	odd	2		576.3.q.l.257.5		24
8.5	even	2		576.3.q.l.257.8		24
9.2	odd	6	inner	288.3.q.b.65.5	✓	24
9.4	even	3		2592.3.e.i.161.14		24
9.5	odd	6		2592.3.e.i.161.13		24
9.7	even	3		864.3.q.a.737.6		24
12.11	even	2		864.3.q.a.449.5		24
24.5	odd	2		1728.3.q.k.449.8		24
24.11	even	2		1728.3.q.k.449.7		24
36.7	odd	6		864.3.q.a.737.5		24
36.11	even	6	inner	288.3.q.b.65.8	yes	24
36.23	even	6		2592.3.e.i.161.11		24
36.31	odd	6		2592.3.e.i.161.12		24
72.11	even	6		576.3.q.l.65.5		24
72.29	odd	6		576.3.q.l.65.8		24
72.43	odd	6		1728.3.q.k.1601.7		24
72.61	even	6		1728.3.q.k.1601.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.3.q.b.65.5	✓	24	9.2	odd	6	inner
288.3.q.b.65.8	yes	24	36.11	even	6	inner
288.3.q.b.257.5	yes	24	1.1	even	1	trivial
288.3.q.b.257.8	yes	24	4.3	odd	2	inner
576.3.q.l.65.5		24	72.11	even	6
576.3.q.l.65.8		24	72.29	odd	6
576.3.q.l.257.5		24	8.3	odd	2
576.3.q.l.257.8		24	8.5	even	2
864.3.q.a.449.5		24	12.11	even	2
864.3.q.a.449.6		24	3.2	odd	2
864.3.q.a.737.5		24	36.7	odd	6
864.3.q.a.737.6		24	9.7	even	3
1728.3.q.k.449.7		24	24.11	even	2
1728.3.q.k.449.8		24	24.5	odd	2
1728.3.q.k.1601.7		24	72.43	odd	6
1728.3.q.k.1601.8		24	72.61	even	6
2592.3.e.i.161.11		24	36.23	even	6
2592.3.e.i.161.12		24	36.31	odd	6
2592.3.e.i.161.13		24	9.5	odd	6
2592.3.e.i.161.14		24	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.65353 + 2.50317i) q^{3} +(-0.721152 - 0.416357i) q^{5} +(-1.26051 - 2.18326i) q^{7} +(-3.53169 - 8.27811i) q^{9} +O(q^{10})\)	\(q+(-1.65353 + 2.50317i) q^{3} +(-0.721152 - 0.416357i) q^{5} +(-1.26051 - 2.18326i) q^{7} +(-3.53169 - 8.27811i) q^{9} +(-9.47693 + 5.47151i) q^{11} +(4.36453 - 7.55959i) q^{13} +(2.23466 - 1.11671i) q^{15} -20.8637i q^{17} -1.50150 q^{19} +(7.54935 + 0.454827i) q^{21} +(1.00209 + 0.578558i) q^{23} +(-12.1533 - 21.0501i) q^{25} +(26.5612 + 4.84769i) q^{27} +(15.7347 - 9.08444i) q^{29} +(25.6909 - 44.4980i) q^{31} +(1.97428 - 32.7696i) q^{33} +2.09929i q^{35} -7.93951 q^{37} +(11.7060 + 23.4251i) q^{39} +(-21.8881 - 12.6371i) q^{41} +(-19.3418 - 33.5010i) q^{43} +(-0.899770 + 7.44022i) q^{45} +(-59.6559 + 34.4423i) q^{47} +(21.3222 - 36.9312i) q^{49} +(52.2254 + 34.4988i) q^{51} +46.5195i q^{53} +9.11241 q^{55} +(2.48278 - 3.75851i) q^{57} +(-89.1306 - 51.4596i) q^{59} +(44.1651 + 76.4962i) q^{61} +(-13.6216 + 18.1452i) q^{63} +(-6.29498 + 3.63441i) q^{65} +(11.3192 - 19.6054i) q^{67} +(-3.10522 + 1.55174i) q^{69} +104.256i q^{71} -75.2115 q^{73} +(72.7878 + 4.38525i) q^{75} +(23.8915 + 13.7938i) q^{77} +(-51.8676 - 89.8374i) q^{79} +(-56.0544 + 58.4714i) q^{81} +(-53.7499 + 31.0325i) q^{83} +(-8.68677 + 15.0459i) q^{85} +(-3.27792 + 54.4080i) q^{87} -1.95722i q^{89} -22.0061 q^{91} +(68.9052 + 137.887i) q^{93} +(1.08281 + 0.625162i) q^{95} +(59.2171 + 102.567i) q^{97} +(78.7634 + 59.1275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

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Database

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