LMFDB - Embedded newform 288.3.t.b.79.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(79,288)]

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([3, 3, 4]))

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

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

chi := DirichletCharacter("288.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.10
Character	$\chi$	$=$	288.79
Dual form			288.3.t.b.175.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.418145 + 2.97072i) q^{3} +(4.40783 - 2.54486i) q^{5} +(-10.9609 - 6.32830i) q^{7} +(-8.65031 - 2.48438i) q^{9} +O(q^{10})$	\(q+(-0.418145 + 2.97072i) q^{3} +(4.40783 - 2.54486i) q^{5} +(-10.9609 - 6.32830i) q^{7} +(-8.65031 - 2.48438i) q^{9} +(-4.51244 + 7.81578i) q^{11} +(-9.68283 + 5.59038i) q^{13} +(5.71695 + 14.1585i) q^{15} -19.2305 q^{17} -14.2413 q^{19} +(23.3828 - 29.9157i) q^{21} +(4.28195 - 2.47218i) q^{23} +(0.452634 - 0.783986i) q^{25} +(10.9975 - 24.6588i) q^{27} +(-7.55576 - 4.36232i) q^{29} +(33.9931 - 19.6259i) q^{31} +(-21.3316 - 16.6733i) q^{33} -64.4185 q^{35} +19.9238i q^{37} +(-12.5586 - 31.1025i) q^{39} +(-17.3873 - 30.1157i) q^{41} +(3.02841 - 5.24536i) q^{43} +(-44.4515 + 11.0631i) q^{45} +(-52.8256 - 30.4989i) q^{47} +(55.5947 + 96.2928i) q^{49} +(8.04112 - 57.1283i) q^{51} +6.53131i q^{53} +45.9341i q^{55} +(5.95492 - 42.3068i) q^{57} +(25.0669 + 43.4171i) q^{59} +(-0.149359 - 0.0862322i) q^{61} +(79.0936 + 81.9728i) q^{63} +(-28.4535 + 49.2829i) q^{65} +(40.4370 + 70.0389i) q^{67} +(5.55368 + 13.7542i) q^{69} -50.4875i q^{71} +24.0274 q^{73} +(2.13973 + 1.67247i) q^{75} +(98.9211 - 57.1121i) q^{77} +(2.84873 + 1.64471i) q^{79} +(68.6557 + 42.9813i) q^{81} +(-18.4770 + 32.0032i) q^{83} +(-84.7646 + 48.9389i) q^{85} +(16.1186 - 20.6219i) q^{87} +13.0096 q^{89} +141.510 q^{91} +(44.0891 + 109.190i) q^{93} +(-62.7731 + 36.2421i) q^{95} +(44.7519 - 77.5126i) q^{97} +(58.4514 - 56.3983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 18 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 18 * q^9	$ 40 q + 6 q^{3} - 18 q^{9} + 16 q^{11} - 4 q^{17} + 76 q^{19} + 118 q^{25} + 144 q^{27} + 156 q^{33} + 108 q^{35} + 20 q^{41} + 16 q^{43} + 166 q^{49} - 330 q^{51} - 258 q^{57} + 64 q^{59} - 102 q^{65} + 64 q^{67} - 292 q^{73} - 138 q^{75} - 42 q^{81} - 554 q^{83} - 688 q^{89} + 204 q^{91} + 92 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 18 * q^9 + 16 * q^11 - 4 * q^17 + 76 * q^19 + 118 * q^25 + 144 * q^27 + 156 * q^33 + 108 * q^35 + 20 * q^41 + 16 * q^43 + 166 * q^49 - 330 * q^51 - 258 * q^57 + 64 * q^59 - 102 * q^65 + 64 * q^67 - 292 * q^73 - 138 * q^75 - 42 * q^81 - 554 * q^83 - 688 * q^89 + 204 * q^91 + 92 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.418145	+	2.97072i	−0.139382	+	0.990239i
$3$	−0.418145	+	2.97072i	−0.139382	+	0.990239i
$4$		0			0
$5$	4.40783	−	2.54486i	0.881566	−	0.508972i	0.0103914	−	0.999946i	$-0.496692\pi$
$5$	4.40783	−	2.54486i	0.881566	−	0.508972i	0.871174	+	0.490974i	$0.163359\pi$
$6$		0			0
$7$	−10.9609	−	6.32830i	−1.56585	−	0.904042i	−0.996645	−	0.0818449i	$-0.973919\pi$
$7$	−10.9609	−	6.32830i	−1.56585	−	0.904042i	−0.569202	−	0.822198i	$-0.692748\pi$
$8$		0			0
$9$	−8.65031	−	2.48438i	−0.961146	−	0.276042i
$10$		0			0
$11$	−4.51244	+	7.81578i	−0.410222	+	0.710525i	−0.994914	−	0.100730i	$-0.967882\pi$
$11$	−4.51244	+	7.81578i	−0.410222	+	0.710525i	0.584692	+	0.811255i	$0.301215\pi$
$12$		0			0
$13$	−9.68283	+	5.59038i	−0.744833	+	0.430029i	−0.823824	−	0.566846i	$-0.808164\pi$
$13$	−9.68283	+	5.59038i	−0.744833	+	0.430029i	0.0789910	+	0.996875i	$0.474830\pi$
$14$		0			0
$15$	5.71695	+	14.1585i	0.381130	+	0.943902i
$16$		0			0
$17$	−19.2305			−1.13120			−0.565602	−	0.824678i	$-0.691356\pi$
$17$	−19.2305			−1.13120			−0.565602	+	0.824678i	$0.691356\pi$
$18$		0			0
$19$	−14.2413			−0.749541			−0.374770	−	0.927118i	$-0.622278\pi$
$19$	−14.2413			−0.749541			−0.374770	+	0.927118i	$0.622278\pi$
$20$		0			0
$21$	23.3828	−	29.9157i	1.11347	−	1.42456i
$22$		0			0
$23$	4.28195	−	2.47218i	0.186172	−	0.107486i	−0.404017	−	0.914751i	$-0.632386\pi$
$23$	4.28195	−	2.47218i	0.186172	−	0.107486i	0.590189	+	0.807265i	$0.299053\pi$
$24$		0			0
$25$	0.452634	−	0.783986i	0.0181054	−	0.0313594i
$26$		0			0
$27$	10.9975	−	24.6588i	0.407314	−	0.913288i
$28$		0			0
$29$	−7.55576	−	4.36232i	−0.260543	−	0.150425i	0.364039	−	0.931384i	$-0.381397\pi$
$29$	−7.55576	−	4.36232i	−0.260543	−	0.150425i	−0.624582	+	0.780959i	$0.714731\pi$
$30$		0			0
$31$	33.9931	−	19.6259i	1.09655	−	0.633095i	0.161239	−	0.986915i	$-0.448451\pi$
$31$	33.9931	−	19.6259i	1.09655	−	0.633095i	0.935313	+	0.353820i	$0.115118\pi$
$32$		0			0
$33$	−21.3316	−	16.6733i	−0.646412	−	0.505252i
$34$		0			0
$35$	−64.4185			−1.84053
$36$		0			0
$37$			19.9238i			0.538482i	0.963073	+	0.269241i	$0.0867728\pi$
$37$			19.9238i			0.538482i	−0.963073	+	0.269241i	$0.913227\pi$
$38$		0			0
$39$	−12.5586	−	31.1025i	−0.322016	−	0.797501i
$40$		0			0
$41$	−17.3873	−	30.1157i	−0.424081	−	0.734529i	0.572253	−	0.820077i	$-0.306069\pi$
$41$	−17.3873	−	30.1157i	−0.424081	−	0.734529i	−0.996334	+	0.0855475i	$0.972736\pi$
$42$		0			0
$43$	3.02841	−	5.24536i	0.0704281	−	0.121985i	−0.828661	−	0.559751i	$-0.810897\pi$
$43$	3.02841	−	5.24536i	0.0704281	−	0.121985i	0.899089	+	0.437766i	$0.144230\pi$
$44$		0			0
$45$	−44.4515	+	11.0631i	−0.987811	+	0.245847i
$46$		0			0
$47$	−52.8256	−	30.4989i	−1.12395	−	0.648912i	−0.181542	−	0.983383i	$-0.558109\pi$
$47$	−52.8256	−	30.4989i	−1.12395	−	0.648912i	−0.942406	+	0.334471i	$0.891442\pi$
$48$		0			0
$49$	55.5947	+	96.2928i	1.13459	+	1.96516i
$50$		0			0
$51$	8.04112	−	57.1283i	0.157669	−	1.12016i
$52$		0			0
$53$			6.53131i			0.123232i	0.998100	+	0.0616161i	$0.0196254\pi$
$53$			6.53131i			0.123232i	−0.998100	+	0.0616161i	$0.980375\pi$
$54$		0			0
$55$			45.9341i			0.835166i
$56$		0			0
$57$	5.95492	−	42.3068i	0.104472	−	0.742225i
$58$		0			0
$59$	25.0669	+	43.4171i	0.424862	+	0.735882i	0.996408	−	0.0846879i	$-0.0269893\pi$
$59$	25.0669	+	43.4171i	0.424862	+	0.735882i	−0.571546	+	0.820570i	$0.693656\pi$
$60$		0			0
$61$	−0.149359	−	0.0862322i	−0.00244850	−	0.00141364i	0.498775	−	0.866731i	$-0.333783\pi$
$61$	−0.149359	−	0.0862322i	−0.00244850	−	0.00141364i	−0.501224	+	0.865318i	$0.667117\pi$
$62$		0			0
$63$	79.0936	+	81.9728i	1.25545	+	1.30116i
$64$		0			0
$65$	−28.4535	+	49.2829i	−0.437746	+	0.758198i
$66$		0			0
$67$	40.4370	+	70.0389i	0.603537	+	1.04536i	0.992281	+	0.124011i	$0.0395758\pi$
$67$	40.4370	+	70.0389i	0.603537	+	1.04536i	−0.388744	+	0.921346i	$0.627091\pi$
$68$		0			0
$69$	5.55368	+	13.7542i	0.0804882	+	0.199336i
$70$		0			0
$71$		−	50.4875i		−	0.711092i	−0.934659	−	0.355546i	$-0.884295\pi$
$71$		−	50.4875i		−	0.711092i	0.934659	−	0.355546i	$-0.115705\pi$
$72$		0			0
$73$	24.0274			0.329142			0.164571	−	0.986365i	$-0.447376\pi$
$73$	24.0274			0.329142			0.164571	+	0.986365i	$0.447376\pi$
$74$		0			0
$75$	2.13973	+	1.67247i	0.0285298	+	0.0222996i
$76$		0			0
$77$	98.9211	−	57.1121i	1.28469	−	0.741716i
$78$		0			0
$79$	2.84873	+	1.64471i	0.0360599	+	0.0208192i	0.517922	−	0.855428i	$-0.326706\pi$
$79$	2.84873	+	1.64471i	0.0360599	+	0.0208192i	−0.481862	+	0.876247i	$0.660039\pi$
$80$		0			0
$81$	68.6557	+	42.9813i	0.847602	+	0.530633i
$82$		0			0
$83$	−18.4770	+	32.0032i	−0.222615	+	0.385580i	−0.955601	−	0.294663i	$-0.904793\pi$
$83$	−18.4770	+	32.0032i	−0.222615	+	0.385580i	0.732986	+	0.680243i	$0.238126\pi$
$84$		0			0
$85$	−84.7646	+	48.9389i	−0.997231	+	0.575752i
$86$		0			0
$87$	16.1186	−	20.6219i	0.185271	−	0.237034i
$88$		0			0
$89$	13.0096			0.146175			0.0730876	−	0.997326i	$-0.476715\pi$
$89$	13.0096			0.146175			0.0730876	+	0.997326i	$0.476715\pi$
$90$		0			0
$91$	141.510			1.55506
$92$		0			0
$93$	44.0891	+	109.190i	0.474076	+	1.17409i
$94$		0			0
$95$	−62.7731	+	36.2421i	−0.660770	+	0.381496i
$96$		0			0
$97$	44.7519	−	77.5126i	0.461360	−	0.799099i	−0.537669	−	0.843156i	$-0.680695\pi$
$97$	44.7519	−	77.5126i	0.461360	−	0.799099i	0.999029	+	0.0440568i	$0.0140283\pi$
$98$		0			0
$99$	58.4514	−	56.3983i	0.590418	−	0.569680i
$100$		0			0
$101$	−98.5033	−	56.8709i	−0.975280	−	0.563078i	−0.0744384	−	0.997226i	$-0.523716\pi$
$101$	−98.5033	−	56.8709i	−0.975280	−	0.563078i	−0.900842	+	0.434147i	$0.857050\pi$
$102$		0			0
$103$	−169.831	+	98.0520i	−1.64885	+	0.951961i	−0.671313	+	0.741174i	$0.734269\pi$
$103$	−169.831	+	98.0520i	−1.64885	+	0.951961i	−0.977532	+	0.210787i	$0.932397\pi$
$104$		0			0
$105$	26.9363	−	191.369i	0.256536	−	1.82256i
$106$		0			0
$107$	−31.7982			−0.297179			−0.148590	−	0.988899i	$-0.547473\pi$
$107$	−31.7982			−0.297179			−0.148590	+	0.988899i	$0.547473\pi$
$108$		0			0
$109$		−	114.940i		−	1.05449i	−0.849712	−	0.527247i	$-0.823224\pi$
$109$		−	114.940i		−	1.05449i	0.849712	−	0.527247i	$-0.176776\pi$
$110$		0			0
$111$	−59.1881	−	8.33105i	−0.533226	−	0.0750545i
$112$		0			0
$113$	−16.4795	−	28.5433i	−0.145836	−	0.252596i	0.783848	−	0.620952i	$-0.213254\pi$
$113$	−16.4795	−	28.5433i	−0.145836	−	0.252596i	−0.929685	+	0.368357i	$0.879921\pi$
$114$		0			0
$115$	12.5827	−	21.7939i	0.109415	−	0.189512i
$116$		0			0
$117$	97.6481	−	24.3027i	0.834599	−	0.207716i
$118$		0			0
$119$	210.784	+	121.696i	1.77129	+	1.02266i
$120$		0			0
$121$	19.7758	+	34.2526i	0.163436	+	0.283079i
$122$		0			0
$123$	96.7356	−	39.0600i	0.786469	−	0.317561i
$124$		0			0
$125$			122.635i			0.981084i
$126$		0			0
$127$		−	74.7526i		−	0.588603i	−0.955713	−	0.294302i	$-0.904913\pi$
$127$		−	74.7526i		−	0.588603i	0.955713	−	0.294302i	$-0.0950870\pi$
$128$		0			0
$129$	14.3162	+	11.1899i	0.110978	+	0.0867431i
$130$		0			0
$131$	−41.0887	−	71.1677i	−0.313654	−	0.543265i	0.665497	−	0.746401i	$-0.268220\pi$
$131$	−41.0887	−	71.1677i	−0.313654	−	0.543265i	−0.979150	+	0.203136i	$0.934887\pi$
$132$		0			0
$133$	156.098	+	90.1230i	1.17367	+	0.677617i
$134$		0			0
$135$	−14.2782	−	136.679i	−0.105765	−	1.01243i
$136$		0			0
$137$	−91.7121	+	158.850i	−0.669432	+	1.15949i	0.308632	+	0.951182i	$0.400129\pi$
$137$	−91.7121	+	158.850i	−0.669432	+	1.15949i	−0.978063	+	0.208308i	$0.933204\pi$
$138$		0			0
$139$	103.570	+	179.388i	0.745105	+	1.29056i	0.950146	+	0.311807i	$0.100934\pi$
$139$	103.570	+	179.388i	0.745105	+	1.29056i	−0.205040	+	0.978754i	$0.565733\pi$
$140$		0			0
$141$	112.692	−	144.177i	0.799235	−	1.02253i
$142$		0			0
$143$		−	100.905i		−	0.705630i
$144$		0			0
$145$	−44.4060			−0.306248
$146$		0			0
$147$	−309.305	+	124.892i	−2.10412	+	0.849603i
$148$		0			0
$149$	−195.664	+	112.967i	−1.31318	+	0.758167i	−0.982622	−	0.185618i	$-0.940571\pi$
$149$	−195.664	+	112.967i	−1.31318	+	0.758167i	−0.330561	+	0.943785i	$0.607238\pi$
$150$		0			0
$151$	123.589	+	71.3540i	0.818469	+	0.472543i	0.849888	−	0.526963i	$-0.176669\pi$
$151$	123.589	+	71.3540i	0.818469	+	0.472543i	−0.0314192	+	0.999506i	$0.510003\pi$
$152$		0			0
$153$	166.350	+	47.7758i	1.08725	+	0.312260i
$154$		0			0
$155$	99.8906	−	173.016i	0.644455	−	1.11623i
$156$		0			0
$157$	8.21204	−	4.74122i	0.0523060	−	0.0301989i	−0.473619	−	0.880730i	$-0.657053\pi$
$157$	8.21204	−	4.74122i	0.0523060	−	0.0301989i	0.525925	+	0.850531i	$0.323719\pi$
$158$		0			0
$159$	−19.4027	−	2.73103i	−0.122029	−	0.0171763i
$160$		0			0
$161$	−62.5789			−0.388689
$162$		0			0
$163$	−305.669			−1.87527			−0.937635	−	0.347622i	$-0.886989\pi$
$163$	−305.669			−1.87527			−0.937635	+	0.347622i	$0.886989\pi$
$164$		0			0
$165$	−136.457	−	19.2071i	−0.827014	−	0.116407i
$166$		0			0
$167$	−13.4105	+	7.74257i	−0.0803026	+	0.0463627i	−0.539614	−	0.841913i	$-0.681430\pi$
$167$	−13.4105	+	7.74257i	−0.0803026	+	0.0463627i	0.459311	+	0.888275i	$0.348096\pi$
$168$		0			0
$169$	−21.9952	+	38.0969i	−0.130149	+	0.225425i
$170$		0			0
$171$	123.191	+	35.3807i	0.720418	+	0.206905i
$172$		0			0
$173$	−79.3643	−	45.8210i	−0.458753	−	0.264861i	0.252767	−	0.967527i	$-0.418659\pi$
$173$	−79.3643	−	45.8210i	−0.458753	−	0.264861i	−0.711520	+	0.702666i	$0.751993\pi$
$174$		0			0
$175$	−9.92259	+	5.72881i	−0.0567005	+	0.0327361i
$176$		0			0
$177$	−139.461	+	56.3119i	−0.787917	+	0.318146i
$178$		0			0
$179$	−125.988			−0.703846			−0.351923	−	0.936029i	$-0.614472\pi$
$179$	−125.988			−0.703846			−0.351923	+	0.936029i	$0.614472\pi$
$180$		0			0
$181$			23.0017i			0.127081i	0.997979	+	0.0635405i	$0.0202392\pi$
$181$			23.0017i			0.127081i	−0.997979	+	0.0635405i	$0.979761\pi$
$182$		0			0
$183$	0.318625	−	0.407644i	0.00174112	−	0.00222757i
$184$		0			0
$185$	50.7034	+	87.8209i	0.274072	+	0.474707i
$186$		0			0
$187$	86.7764	−	150.301i	0.464045	−	0.803749i
$188$		0			0
$189$	−276.591	+	200.688i	−1.46344	+	1.06184i
$190$		0			0
$191$	20.4240	+	11.7918i	0.106932	+	0.0617371i	0.552512	−	0.833505i	$-0.313669\pi$
$191$	20.4240	+	11.7918i	0.106932	+	0.0617371i	−0.445580	+	0.895242i	$0.647003\pi$
$192$		0			0
$193$	−31.0142	−	53.7183i	−0.160696	−	0.278333i	0.774423	−	0.632668i	$-0.218040\pi$
$193$	−31.0142	−	53.7183i	−0.160696	−	0.278333i	−0.935118	+	0.354336i	$0.884707\pi$
$194$		0			0
$195$	−134.508	−	105.135i	−0.689784	−	0.539152i
$196$		0			0
$197$		−	385.821i		−	1.95848i	−0.202698	−	0.979241i	$-0.564971\pi$
$197$		−	385.821i		−	1.95848i	0.202698	−	0.979241i	$-0.435029\pi$
$198$		0			0
$199$		−	214.957i		−	1.08018i	−0.841606	−	0.540092i	$-0.818389\pi$
$199$		−	214.957i		−	1.08018i	0.841606	−	0.540092i	$-0.181611\pi$
$200$		0			0
$201$	−224.974	+	90.8404i	−1.11927	+	0.451942i
$202$		0			0
$203$	55.2121	+	95.6302i	0.271981	+	0.471085i
$204$		0			0
$205$	−153.281	−	88.4966i	−0.747710	−	0.431691i
$206$		0			0
$207$	−43.1820	+	10.7472i	−0.208609	+	0.0519187i
$208$		0			0
$209$	64.2629	−	111.307i	0.307478	−	0.532568i
$210$		0			0
$211$	−50.4896	−	87.4505i	−0.239287	−	0.414457i	0.721223	−	0.692703i	$-0.243580\pi$
$211$	−50.4896	−	87.4505i	−0.239287	−	0.414457i	−0.960510	+	0.278246i	$0.910247\pi$
$212$		0			0
$213$	149.984	+	21.1111i	0.704151	+	0.0991131i
$214$		0			0
$215$		−	30.8275i		−	0.143384i
$216$		0			0
$217$	−496.795			−2.28938
$218$		0			0
$219$	−10.0469	+	71.3785i	−0.0458764	+	0.325929i
$220$		0			0
$221$	186.205	−	107.506i	0.842558	−	0.486451i
$222$		0			0
$223$	−66.2290	−	38.2373i	−0.296991	−	0.171468i	0.344099	−	0.938933i	$-0.388184\pi$
$223$	−66.2290	−	38.2373i	−0.296991	−	0.171468i	−0.641090	+	0.767465i	$0.721518\pi$
$224$		0			0
$225$	−5.86315	+	5.65720i	−0.0260584	+	0.0251431i
$226$		0			0
$227$	−37.4197	+	64.8128i	−0.164844	+	0.285519i	−0.936600	−	0.350400i	$-0.886046\pi$
$227$	−37.4197	+	64.8128i	−0.164844	+	0.285519i	0.771756	+	0.635919i	$0.219379\pi$
$228$		0			0
$229$	255.666	−	147.609i	1.11645	−	0.644581i	0.175956	−	0.984398i	$-0.443698\pi$
$229$	255.666	−	147.609i	1.11645	−	0.644581i	0.940492	+	0.339817i	$0.110365\pi$
$230$		0			0
$231$	128.301	+	317.748i	0.555414	+	1.37553i
$232$		0			0
$233$	354.235			1.52032			0.760162	−	0.649734i	$-0.225120\pi$
$233$	354.235			1.52032			0.760162	+	0.649734i	$0.225120\pi$
$234$		0			0
$235$	−310.461			−1.32111
$236$		0			0
$237$	−6.07716	+	7.77504i	−0.0256420	+	0.0328061i
$238$		0			0
$239$	107.843	−	62.2632i	0.451226	−	0.260516i	−0.257122	−	0.966379i	$-0.582774\pi$
$239$	107.843	−	62.2632i	0.451226	−	0.260516i	0.708348	+	0.705863i	$0.249441\pi$
$240$		0			0
$241$	189.676	−	328.528i	0.787036	−	1.36319i	−0.140740	−	0.990047i	$-0.544948\pi$
$241$	189.676	−	328.528i	0.787036	−	1.36319i	0.927775	−	0.373139i	$-0.121719\pi$
$242$		0			0
$243$	−156.393	+	185.984i	−0.643594	+	0.765367i
$244$		0			0
$245$	490.104	+	282.961i	2.00042	+	1.15494i
$246$		0			0
$247$	137.896	−	79.6142i	0.558283	−	0.322325i
$248$		0			0
$249$	−87.3462	−	68.2720i	−0.350788	−	0.274185i
$250$		0			0
$251$	385.891			1.53741			0.768707	−	0.639601i	$-0.220901\pi$
$251$	385.891			1.53741			0.768707	+	0.639601i	$0.220901\pi$
$252$		0			0
$253$			44.6223i			0.176373i
$254$		0			0
$255$	−109.940	−	272.275i	−0.431136	−	1.06775i
$256$		0			0
$257$	−228.629	−	395.997i	−0.889607	−	1.54084i	−0.840341	−	0.542058i	$-0.817645\pi$
$257$	−228.629	−	395.997i	−0.889607	−	1.54084i	−0.0492659	−	0.998786i	$-0.515688\pi$
$258$		0			0
$259$	126.084	−	218.384i	0.486811	−	0.843181i
$260$		0			0
$261$	54.5220	+	56.5068i	0.208897	+	0.216501i
$262$		0			0
$263$	−404.801	−	233.712i	−1.53917	−	0.888638i	−0.998888	−	0.0471517i	$-0.984986\pi$
$263$	−404.801	−	233.712i	−1.53917	−	0.888638i	−0.540278	−	0.841486i	$-0.681681\pi$
$264$		0			0
$265$	16.6213	+	28.7889i	0.0627218	+	0.108637i
$266$		0			0
$267$	−5.43989	+	38.6478i	−0.0203741	+	0.144748i
$268$		0			0
$269$			463.103i			1.72157i	0.508966	+	0.860787i	$0.330028\pi$
$269$			463.103i			1.72157i	−0.508966	+	0.860787i	$0.669972\pi$
$270$		0			0
$271$			324.633i			1.19791i	0.800784	+	0.598954i	$0.204417\pi$
$271$			324.633i			1.19791i	−0.800784	+	0.598954i	$0.795583\pi$
$272$		0			0
$273$	−59.1718	+	420.387i	−0.216747	+	1.53988i
$274$		0			0
$275$	4.08497	+	7.07538i	0.0148544	+	0.0257287i
$276$		0			0
$277$	−249.678	−	144.151i	−0.901363	−	0.520402i	−0.0237212	−	0.999719i	$-0.507551\pi$
$277$	−249.678	−	144.151i	−0.901363	−	0.520402i	−0.877642	+	0.479316i	$0.840885\pi$
$278$		0			0
$279$	−342.809	+	85.3187i	−1.22871	+	0.305802i
$280$		0			0
$281$	172.969	−	299.590i	0.615546	−	1.06616i	−0.374742	−	0.927129i	$-0.622269\pi$
$281$	172.969	−	299.590i	0.615546	−	1.06616i	0.990288	−	0.139028i	$-0.0443980\pi$
$282$		0			0
$283$	7.83064	+	13.5631i	0.0276701	+	0.0479260i	0.879529	−	0.475846i	$-0.157858\pi$
$283$	7.83064	+	13.5631i	0.0276701	+	0.0479260i	−0.851859	+	0.523772i	$0.824525\pi$
$284$		0			0
$285$	−81.4167	−	201.636i	−0.285673	−	0.707493i
$286$		0			0
$287$			440.128i			1.53355i
$288$		0			0
$289$	80.8112			0.279623
$290$		0			0
$291$	211.555	+	165.357i	0.726994	+	0.568236i
$292$		0			0
$293$	−91.8784	+	53.0460i	−0.313578	+	0.181045i	−0.648527	−	0.761192i	$-0.724614\pi$
$293$	−91.8784	+	53.0460i	−0.313578	+	0.181045i	0.334948	+	0.942237i	$0.391281\pi$
$294$		0			0
$295$	220.981	+	127.583i	0.749087	+	0.432486i
$296$		0			0
$297$	143.102	+	197.225i	0.481825	+	0.664057i
$298$		0			0
$299$	−27.6409	+	47.8755i	−0.0924445	+	0.160119i
$300$		0			0
$301$	−66.3884	+	38.3294i	−0.220559	+	0.127340i
$302$		0			0
$303$	210.136	−	268.845i	0.693518	−	0.887278i
$304$		0			0
$305$	−0.877796			−0.00287802
$306$		0			0
$307$	−329.540			−1.07342			−0.536710	−	0.843767i	$-0.680333\pi$
$307$	−329.540			−1.07342			−0.536710	+	0.843767i	$0.680333\pi$
$308$		0			0
$309$	−220.271	−	545.520i	−0.712850	−	1.76544i
$310$		0			0
$311$	−342.791	+	197.911i	−1.10222	+	0.636369i	−0.936804	−	0.349855i	$-0.886231\pi$
$311$	−342.791	+	197.911i	−1.10222	+	0.636369i	−0.165419	+	0.986223i	$0.552898\pi$
$312$		0			0
$313$	−51.1983	+	88.6781i	−0.163573	+	0.283317i	−0.936148	−	0.351607i	$-0.885635\pi$
$313$	−51.1983	+	88.6781i	−0.163573	+	0.283317i	0.772575	+	0.634924i	$0.218969\pi$
$314$		0			0
$315$	557.240	+	160.040i	1.76902	+	0.508064i
$316$		0			0
$317$	−237.016	−	136.841i	−0.747685	−	0.431676i	0.0771716	−	0.997018i	$-0.475411\pi$
$317$	−237.016	−	136.841i	−0.747685	−	0.431676i	−0.824857	+	0.565341i	$0.808744\pi$
$318$		0			0
$319$	68.1898	−	39.3694i	0.213761	−	0.123415i
$320$		0			0
$321$	13.2963	−	94.4634i	0.0414213	−	0.294279i
$322$		0			0
$323$	273.867			0.847884
$324$		0			0
$325$			10.1216i			0.0311434i
$326$		0			0
$327$	341.454	+	48.0615i	1.04420	+	0.146977i
$328$		0			0
$329$	386.012	+	668.592i	1.17329	+	2.03219i
$330$		0			0
$331$	145.019	−	251.179i	0.438122	−	0.758850i	−0.559422	−	0.828883i	$-0.688977\pi$
$331$	145.019	−	251.179i	0.438122	−	0.758850i	0.997545	+	0.0700325i	$0.0223103\pi$
$332$		0			0
$333$	49.4984	−	172.347i	0.148644	−	0.517560i
$334$		0			0
$335$	356.479	+	205.813i	1.06412	+	0.614367i
$336$		0			0
$337$	190.788	+	330.455i	0.566137	+	0.980578i	0.996943	+	0.0781332i	$0.0248960\pi$
$337$	190.788	+	330.455i	0.566137	+	0.980578i	−0.430806	+	0.902445i	$0.641771\pi$
$338$		0			0
$339$	91.6848	−	37.0206i	0.270457	−	0.109205i
$340$		0			0
$341$			354.244i			1.03884i
$342$		0			0
$343$		−	787.105i		−	2.29477i
$344$		0			0
$345$	59.4822	+	46.4927i	0.172412	+	0.134762i
$346$		0			0
$347$	71.1923	+	123.309i	0.205165	+	0.355356i	0.950185	−	0.311686i	$-0.100894\pi$
$347$	71.1923	+	123.309i	0.205165	+	0.355356i	−0.745020	+	0.667042i	$0.767560\pi$
$348$		0			0
$349$	533.855	+	308.222i	1.52967	+	0.883156i	0.999375	+	0.0353439i	$0.0112527\pi$
$349$	533.855	+	308.222i	1.52967	+	0.883156i	0.530296	+	0.847812i	$0.322081\pi$
$350$		0			0
$351$	31.3655	+	300.247i	0.0893604	+	0.855404i
$352$		0			0
$353$	205.510	−	355.953i	0.582181	−	1.00837i	−0.413040	−	0.910713i	$-0.635533\pi$
$353$	205.510	−	355.953i	0.582181	−	1.00837i	0.995220	−	0.0976536i	$-0.0311337\pi$
$354$		0			0
$355$	−128.484	−	222.540i	−0.361926	−	0.626874i
$356$		0			0
$357$	−449.663	+	575.293i	−1.25956	+	1.61146i
$358$		0			0
$359$			131.102i			0.365186i	0.983189	+	0.182593i	$0.0584491\pi$
$359$			131.102i			0.365186i	−0.983189	+	0.182593i	$0.941551\pi$
$360$		0			0
$361$	−158.186			−0.438188
$362$		0			0
$363$	−110.024	+	44.4256i	−0.303096	+	0.122385i
$364$		0			0
$365$	105.909	−	61.1463i	0.290160	−	0.167524i
$366$		0			0
$367$	−93.3059	−	53.8702i	−0.254239	−	0.146785i	0.367465	−	0.930038i	$-0.380226\pi$
$367$	−93.3059	−	53.8702i	−0.254239	−	0.146785i	−0.621704	+	0.783252i	$0.713559\pi$
$368$		0			0
$369$	75.5868	+	303.707i	0.204842	+	0.823054i
$370$		0			0
$371$	41.3320	−	71.5892i	0.111407	−	0.192963i
$372$		0			0
$373$	−560.553	+	323.636i	−1.50282	+	0.867656i	−0.502829	+	0.864386i	$0.667707\pi$
$373$	−560.553	+	323.636i	−1.50282	+	0.867656i	−0.999995	+	0.00326975i	$0.998959\pi$
$374$		0			0
$375$	−364.315	−	51.2794i	−0.971507	−	0.136745i
$376$		0			0
$377$	97.5482			0.258748
$378$		0			0
$379$	225.686			0.595477			0.297739	−	0.954647i	$-0.403768\pi$
$379$	225.686			0.595477			0.297739	+	0.954647i	$0.403768\pi$
$380$		0			0
$381$	222.069	+	31.2574i	0.582858	+	0.0820405i
$382$		0			0
$383$	413.047	−	238.473i	1.07845	−	0.622644i	0.147973	−	0.988991i	$-0.452725\pi$
$383$	413.047	−	238.473i	1.07845	−	0.622644i	0.930478	+	0.366348i	$0.119392\pi$
$384$		0			0
$385$	290.685	−	503.481i	0.755026	−	1.30774i
$386$		0			0
$387$	−39.2281	+	37.8503i	−0.101365	+	0.0978043i
$388$		0			0
$389$	10.3892	+	5.99823i	0.0267076	+	0.0154196i	0.513294	−	0.858213i	$-0.328425\pi$
$389$	10.3892	+	5.99823i	0.0267076	+	0.0154196i	−0.486587	+	0.873632i	$0.661758\pi$
$390$		0			0
$391$	−82.3439	+	47.5413i	−0.210598	+	0.121589i
$392$		0			0
$393$	228.600	−	92.3044i	0.581679	−	0.234871i
$394$		0			0
$395$	16.7423			0.0423855
$396$		0			0
$397$			3.42581i			0.00862924i	0.999991	+	0.00431462i	$0.00137339\pi$
$397$			3.42581i			0.00862924i	−0.999991	+	0.00431462i	$0.998627\pi$
$398$		0			0
$399$	−333.001	+	426.037i	−0.834590	+	1.06776i
$400$		0			0
$401$	23.8998	+	41.3956i	0.0596004	+	0.103231i	0.894286	−	0.447496i	$-0.147684\pi$
$401$	23.8998	+	41.3956i	0.0596004	+	0.103231i	−0.834686	+	0.550727i	$0.814351\pi$
$402$		0			0
$403$	−219.433	+	380.069i	−0.544499	+	0.943100i
$404$		0			0
$405$	412.004	+	14.7349i	1.01729	+	0.0363825i
$406$		0			0
$407$	−155.720	−	89.9052i	−0.382605	−	0.220897i
$408$		0			0
$409$	−113.468	−	196.532i	−0.277428	−	0.480519i	0.693317	−	0.720633i	$-0.256149\pi$
$409$	−113.468	−	196.532i	−0.277428	−	0.480519i	−0.970745	+	0.240114i	$0.922815\pi$
$410$		0			0
$411$	−433.550	−	338.873i	−1.05487	−	0.824509i
$412$		0			0
$413$		−	634.522i		−	1.53637i
$414$		0			0
$415$			188.086i			0.453219i
$416$		0			0
$417$	−576.218	+	232.666i	−1.38182	+	0.557952i
$418$		0			0
$419$	−174.977	−	303.068i	−0.417605	−	0.723314i	0.578093	−	0.815971i	$-0.303797\pi$
$419$	−174.977	−	303.068i	−0.417605	−	0.723314i	−0.995698	+	0.0926575i	$0.970464\pi$
$420$		0			0
$421$	173.344	+	100.080i	0.411743	+	0.237720i	0.691538	−	0.722340i	$-0.256933\pi$
$421$	173.344	+	100.080i	0.411743	+	0.237720i	−0.279796	+	0.960060i	$0.590267\pi$
$422$		0			0
$423$	381.187	+	395.063i	0.901151	+	0.933956i
$424$		0			0
$425$	−8.70438	+	15.0764i	−0.0204809	+	0.0354739i
$426$		0			0
$427$	1.09141	+	1.89037i	0.00255599	+	0.00442710i
$428$		0			0
$429$	299.760	+	42.1929i	0.698742	+	0.0983518i
$430$		0			0
$431$		−	332.817i		−	0.772198i	−0.922457	−	0.386099i	$-0.873822\pi$
$431$		−	332.817i		−	0.772198i	0.922457	−	0.386099i	$-0.126178\pi$
$432$		0			0
$433$	276.314			0.638139			0.319069	−	0.947731i	$-0.396630\pi$
$433$	276.314			0.638139			0.319069	+	0.947731i	$0.396630\pi$
$434$		0			0
$435$	18.5681	−	131.918i	0.0426854	−	0.303259i
$436$		0			0
$437$	−60.9804	+	35.2071i	−0.139543	+	0.0805654i
$438$		0			0
$439$	41.6495	+	24.0464i	0.0948736	+	0.0547753i	0.546686	−	0.837338i	$-0.315889\pi$
$439$	41.6495	+	24.0464i	0.0948736	+	0.0547753i	−0.451813	+	0.892113i	$0.649222\pi$
$440$		0			0
$441$	−241.683	−	971.081i	−0.548035	−	2.20200i
$442$		0			0
$443$	190.236	−	329.498i	0.429426	−	0.743787i	−0.567397	−	0.823445i	$-0.692049\pi$
$443$	190.236	−	329.498i	0.429426	−	0.743787i	0.996822	+	0.0796575i	$0.0253827\pi$
$444$		0			0
$445$	57.3440	−	33.1076i	0.128863	−	0.0743991i
$446$		0			0
$447$	−253.776	−	628.500i	−0.567732	−	1.40604i
$448$		0			0
$449$	−638.660			−1.42240			−0.711202	−	0.702987i	$-0.751849\pi$
$449$	−638.660			−1.42240			−0.711202	+	0.702987i	$0.751849\pi$
$450$		0			0
$451$	313.837			0.695869
$452$		0			0
$453$	−263.651	+	337.311i	−0.582010	+	0.744616i
$454$		0			0
$455$	623.754	−	360.124i	1.37089	−	0.791482i
$456$		0			0
$457$	−278.126	+	481.729i	−0.608591	+	1.05411i	0.382882	+	0.923797i	$0.374932\pi$
$457$	−278.126	+	481.729i	−0.608591	+	1.05411i	−0.991473	+	0.130313i	$0.958402\pi$
$458$		0			0
$459$	−211.487	+	474.200i	−0.460755	+	1.03312i
$460$		0			0
$461$	−181.920	−	105.032i	−0.394620	−	0.227834i	0.289540	−	0.957166i	$-0.406498\pi$
$461$	−181.920	−	105.032i	−0.394620	−	0.227834i	−0.684160	+	0.729332i	$0.739831\pi$
$462$		0			0
$463$	−156.561	+	90.3903i	−0.338144	+	0.195227i	−0.659451	−	0.751748i	$-0.729211\pi$
$463$	−156.561	+	90.3903i	−0.338144	+	0.195227i	0.321307	+	0.946975i	$0.395878\pi$
$464$		0			0
$465$	472.211	+	369.092i	1.01551	+	0.793747i
$466$		0			0
$467$	−10.4709			−0.0224215			−0.0112108	−	0.999937i	$-0.503569\pi$
$467$	−10.4709			−0.0224215			−0.0112108	+	0.999937i	$0.503569\pi$
$468$		0			0
$469$		−	1023.59i		−	2.18249i
$470$		0			0
$471$	10.6510	+	26.3782i	0.0226136	+	0.0560046i
$472$		0			0
$473$	27.3310	+	47.3388i	0.0577823	+	0.100082i
$474$		0			0
$475$	−6.44609	+	11.1650i	−0.0135707	+	0.0235052i
$476$		0			0
$477$	16.2262	−	56.4978i	0.0340173	−	0.118444i
$478$		0			0
$479$	−364.147	−	210.240i	−0.760223	−	0.438915i	0.0691526	−	0.997606i	$-0.477970\pi$
$479$	−364.147	−	210.240i	−0.760223	−	0.438915i	−0.829376	+	0.558691i	$0.811304\pi$
$480$		0			0
$481$	−111.382	−	192.919i	−0.231563	−	0.401079i
$482$		0			0
$483$	26.1670	−	185.904i	0.0541760	−	0.384895i
$484$		0			0
$485$		−	455.550i		−	0.939278i
$486$		0			0
$487$			865.055i			1.77629i	0.459560	+	0.888147i	$0.348007\pi$
$487$			865.055i			1.77629i	−0.459560	+	0.888147i	$0.651993\pi$
$488$		0			0
$489$	127.814	−	908.056i	0.261378	−	1.85696i
$490$		0			0
$491$	31.8734	+	55.2063i	0.0649152	+	0.112436i	0.896656	−	0.442727i	$-0.145989\pi$
$491$	31.8734	+	55.2063i	0.0649152	+	0.112436i	−0.831741	+	0.555164i	$0.812656\pi$
$492$		0			0
$493$	145.301	+	83.8895i	0.294728	+	0.170161i
$494$		0			0
$495$	114.118	−	397.345i	0.230541	−	0.802716i
$496$		0			0
$497$	−319.500	+	553.390i	−0.642857	+	1.11346i
$498$		0			0
$499$	363.674	+	629.902i	0.728806	+	1.26233i	0.957388	+	0.288805i	$0.0932578\pi$
$499$	363.674	+	629.902i	0.728806	+	1.26233i	−0.228582	+	0.973525i	$0.573409\pi$
$500$		0			0
$501$	−17.3934	−	43.0764i	−0.0347175	−	0.0859808i
$502$		0			0
$503$			348.449i			0.692742i	0.938098	+	0.346371i	$0.112586\pi$
$503$			348.449i			0.692742i	−0.938098	+	0.346371i	$0.887414\pi$
$504$		0			0
$505$	−578.914			−1.14636
$506$		0			0
$507$	−103.978	−	81.2716i	−0.205084	−	0.160299i
$508$		0			0
$509$	−706.201	+	407.725i	−1.38743	+	0.801032i	−0.993025	−	0.117906i	$-0.962382\pi$
$509$	−706.201	+	407.725i	−1.38743	+	0.801032i	−0.394403	+	0.918938i	$0.629048\pi$
$510$		0			0
$511$	−263.362	−	152.052i	−0.515386	−	0.297559i
$512$		0			0
$513$	−156.618	+	351.173i	−0.305298	+	0.684547i
$514$		0			0
$515$	−499.057	+	864.393i	−0.969043	+	1.67843i
$516$		0			0
$517$	476.745	−	275.249i	0.922136	−	0.532396i
$518$		0			0
$519$	169.307	−	216.609i	0.326218	−	0.417358i
$520$		0			0
$521$	−335.561			−0.644072			−0.322036	−	0.946727i	$-0.604367\pi$
$521$	−335.561			−0.644072			−0.322036	+	0.946727i	$0.604367\pi$
$522$		0			0
$523$	−215.728			−0.412481			−0.206241	−	0.978501i	$-0.566123\pi$
$523$	−215.728			−0.412481			−0.206241	+	0.978501i	$0.566123\pi$
$524$		0			0
$525$	−12.8696	−	31.8727i	−0.0245135	−	0.0607098i
$526$		0			0
$527$	−653.704	+	377.416i	−1.24043	+	0.716160i
$528$		0			0
$529$	−252.277	+	436.956i	−0.476893	+	0.826004i
$530$		0			0
$531$	−108.972	−	437.847i	−0.205220	−	0.824570i
$532$		0			0
$533$	336.717	+	194.403i	0.631739	+	0.364734i
$534$		0			0
$535$	−140.161	+	80.9220i	−0.261983	+	0.151256i
$536$		0			0
$537$	52.6814	−	374.276i	0.0981031	−	0.696975i
$538$		0			0
$539$	−1003.47			−1.86173
$540$		0			0
$541$			130.450i			0.241128i	0.992706	+	0.120564i	$0.0384703\pi$
$541$			130.450i			0.241128i	−0.992706	+	0.120564i	$0.961530\pi$
$542$		0			0
$543$	−68.3314	−	9.61802i	−0.125841	−	0.0177127i
$544$		0			0
$545$	−292.506	−	506.635i	−0.536708	−	0.929605i
$546$		0			0
$547$	−130.466	+	225.973i	−0.238511	+	0.413114i	−0.960287	−	0.279013i	$-0.909993\pi$
$547$	−130.466	+	225.973i	−0.238511	+	0.413114i	0.721776	+	0.692127i	$0.243326\pi$
$548$		0			0
$549$	1.07776	+	1.11700i	0.00196314	+	0.00203461i
$550$		0			0
$551$	107.604	+	62.1250i	0.195288	+	0.112750i
$552$		0			0
$553$	−20.8165	−	36.0552i	−0.0376428	−	0.0651993i
$554$		0			0
$555$	−282.092	+	113.904i	−0.508274	+	0.205232i
$556$		0			0
$557$			133.587i			0.239833i	0.992784	+	0.119917i	$0.0382627\pi$
$557$			133.587i			0.239833i	−0.992784	+	0.119917i	$0.961737\pi$
$558$		0			0
$559$			67.7199i			0.121145i
$560$		0			0
$561$	410.217	+	320.636i	0.731224	+	0.571543i
$562$		0			0
$563$	−438.575	−	759.634i	−0.778997	−	1.34926i	−0.932521	−	0.361117i	$-0.882396\pi$
$563$	−438.575	−	759.634i	−0.778997	−	1.34926i	0.153524	−	0.988145i	$-0.450938\pi$
$564$		0			0
$565$	−145.277	−	83.8760i	−0.257128	−	0.148453i
$566$		0			0
$567$	−480.532	−	905.589i	−0.847500	−	1.59716i
$568$		0			0
$569$	−346.763	+	600.612i	−0.609426	+	1.05556i	0.381909	+	0.924200i	$0.375267\pi$
$569$	−346.763	+	600.612i	−0.609426	+	1.05556i	−0.991335	+	0.131357i	$0.958067\pi$
$570$		0			0
$571$	159.760	+	276.712i	0.279789	+	0.484609i	0.971332	−	0.237726i	$-0.0764021\pi$
$571$	159.760	+	276.712i	0.279789	+	0.484609i	−0.691543	+	0.722335i	$0.743069\pi$
$572$		0			0
$573$	−43.5702	+	55.7432i	−0.0760388	+	0.0972830i
$574$		0			0
$575$		−	4.47598i		−	0.00778432i
$576$		0			0
$577$	878.170			1.52196			0.760979	−	0.648776i	$-0.224719\pi$
$577$	878.170			1.52196			0.760979	+	0.648776i	$0.224719\pi$
$578$		0			0
$579$	172.550	−	69.6725i	0.298014	−	0.120333i
$580$		0			0
$581$	405.051	−	233.856i	0.697162	−	0.402507i
$582$		0			0
$583$	−51.0472	−	29.4721i	−0.0875596	−	0.0505525i
$584$		0			0
$585$	368.569	−	355.623i	0.630032	−	0.607903i
$586$		0			0
$587$	−277.395	+	480.462i	−0.472564	+	0.818505i	−0.999507	−	0.0313957i	$-0.990005\pi$
$587$	−277.395	+	480.462i	−0.472564	+	0.818505i	0.526943	+	0.849901i	$0.323338\pi$
$588$		0			0
$589$	−484.106	+	279.499i	−0.821911	+	0.474531i
$590$		0			0
$591$	1146.17	+	161.329i	1.93937	+	0.272976i
$592$		0			0
$593$	−673.984			−1.13657			−0.568283	−	0.822833i	$-0.692392\pi$
$593$	−673.984			−1.13657			−0.568283	+	0.822833i	$0.692392\pi$
$594$		0			0
$595$	1238.80			2.08202
$596$		0			0
$597$	638.575	+	89.8830i	1.06964	+	0.150558i
$598$		0			0
$599$	222.534	−	128.480i	0.371509	−	0.214491i	−0.302608	−	0.953115i	$-0.597857\pi$
$599$	222.534	−	128.480i	0.371509	−	0.214491i	0.674118	+	0.738624i	$0.264524\pi$
$600$		0			0
$601$	196.757	−	340.793i	0.327383	−	0.567044i	−0.654609	−	0.755968i	$-0.727167\pi$
$601$	196.757	−	340.793i	0.327383	−	0.567044i	0.981992	+	0.188924i	$0.0605000\pi$
$602$		0			0
$603$	−175.789	−	706.319i	−0.291524	−	1.17134i
$604$		0			0
$605$	174.336	+	100.653i	0.288159	+	0.166369i
$606$		0			0
$607$	501.576	−	289.585i	0.826319	−	0.477076i	−0.0262715	−	0.999655i	$-0.508363\pi$
$607$	501.576	−	289.585i	0.826319	−	0.477076i	0.852591	+	0.522579i	$0.175030\pi$
$608$		0			0
$609$	−307.177	+	124.032i	−0.504395	+	0.203665i
$610$		0			0
$611$	682.001			1.11621
$612$		0			0
$613$			825.194i			1.34616i	0.739571	+	0.673079i	$0.235028\pi$
$613$			825.194i			1.34616i	−0.739571	+	0.673079i	$0.764972\pi$
$614$		0			0
$615$	326.992	−	418.349i	0.531694	−	0.680242i
$616$		0			0
$617$	146.033	+	252.936i	0.236682	+	0.409945i	0.959760	−	0.280821i	$-0.0906068\pi$
$617$	146.033	+	252.936i	0.236682	+	0.409945i	−0.723078	+	0.690766i	$0.757273\pi$
$618$		0			0
$619$	−230.497	+	399.233i	−0.372370	+	0.644964i	−0.989930	−	0.141560i	$-0.954788\pi$
$619$	−230.497	+	399.233i	−0.372370	+	0.644964i	0.617559	+	0.786524i	$0.288122\pi$
$620$		0			0
$621$	−13.8705	−	132.775i	−0.0223357	−	0.213809i
$622$		0			0
$623$	−142.597	−	82.3285i	−0.228888	−	0.132148i
$624$		0			0
$625$	323.406	+	560.156i	0.517450	+	0.896249i
$626$		0			0
$627$	303.789	+	237.449i	0.484512	+	0.378707i
$628$		0			0
$629$		−	383.145i		−	0.609133i
$630$		0			0
$631$			110.500i			0.175119i	0.996159	+	0.0875597i	$0.0279069\pi$
$631$			110.500i			0.175119i	−0.996159	+	0.0875597i	$0.972093\pi$
$632$		0			0
$633$	280.902	−	113.423i	0.443764	−	0.179184i
$634$		0			0
$635$	−190.235	−	329.497i	−0.299583	−	0.518892i
$636$		0			0
$637$	−1076.63	−	621.591i	−1.69015	−	0.975810i
$638$		0			0
$639$	−125.430	+	436.733i	−0.196291	+	0.683463i
$640$		0			0
$641$	134.761	−	233.413i	0.210236	−	0.364139i	−0.741553	−	0.670895i	$-0.765910\pi$
$641$	134.761	−	233.413i	0.210236	−	0.364139i	0.951788	+	0.306756i	$0.0992435\pi$
$642$		0			0
$643$	−284.721	−	493.151i	−0.442800	−	0.766953i	0.555096	−	0.831787i	$-0.312682\pi$
$643$	−284.721	−	493.151i	−0.442800	−	0.766953i	−0.997896	+	0.0648336i	$0.979348\pi$
$644$		0			0
$645$	91.5798	+	12.8904i	0.141984	+	0.0199851i
$646$		0			0
$647$		−	420.048i		−	0.649223i	−0.945847	−	0.324612i	$-0.894766\pi$
$647$		−	420.048i		−	0.649223i	0.945847	−	0.324612i	$-0.105234\pi$
$648$		0			0
$649$	−452.451			−0.697151
$650$		0			0
$651$	207.732	−	1475.84i	0.319097	−	2.26703i
$652$		0			0
$653$	−211.083	+	121.869i	−0.323251	+	0.186629i	−0.652841	−	0.757495i	$-0.726423\pi$
$653$	−211.083	+	121.869i	−0.323251	+	0.186629i	0.329590	+	0.944124i	$0.393090\pi$
$654$		0			0
$655$	−362.224	−	209.130i	−0.553013	−	0.319282i
$656$		0			0
$657$	−207.844	−	59.6931i	−0.316354	−	0.0908571i
$658$		0			0
$659$	268.514	−	465.080i	0.407457	−	0.705736i	−0.587147	−	0.809480i	$-0.699749\pi$
$659$	268.514	−	465.080i	0.407457	−	0.705736i	0.994604	+	0.103744i	$0.0330823\pi$
$660$		0			0
$661$	190.176	−	109.798i	0.287710	−	0.166109i	−0.349199	−	0.937049i	$-0.613546\pi$
$661$	190.176	−	109.798i	0.287710	−	0.166109i	0.636909	+	0.770939i	$0.280213\pi$
$662$		0			0
$663$	241.508	+	598.116i	0.364266	+	0.902136i
$664$		0			0
$665$	917.402			1.37955
$666$		0			0
$667$	−43.1378			−0.0646744
$668$		0			0
$669$	141.286	−	180.759i	0.211189	−	0.270193i
$670$		0			0
$671$	1.34794	−	0.778236i	0.00200886	−	0.00115981i
$672$		0			0
$673$	52.2858	−	90.5617i	0.0776907	−	0.134564i	−0.824563	−	0.565771i	$-0.808579\pi$
$673$	52.2858	−	90.5617i	0.0776907	−	0.134564i	0.902253	+	0.431207i	$0.141912\pi$
$674$		0			0
$675$	−14.3543	−	19.7833i	−0.0212656	−	0.0293086i
$676$		0			0
$677$	−460.805	−	266.046i	−0.680657	−	0.392977i	0.119446	−	0.992841i	$-0.461888\pi$
$677$	−460.805	−	266.046i	−0.680657	−	0.392977i	−0.800102	+	0.599863i	$0.795222\pi$
$678$		0			0
$679$	−981.046	+	566.407i	−1.44484	+	0.834178i
$680$		0			0
$681$	−176.894	−	138.264i	−0.259756	−	0.203031i
$682$		0			0
$683$	−782.844			−1.14618			−0.573092	−	0.819491i	$-0.694256\pi$
$683$	−782.844			−1.14618			−0.573092	+	0.819491i	$0.694256\pi$
$684$		0			0
$685$			933.579i			1.36289i
$686$		0			0
$687$	331.599	+	821.235i	0.482677	+	1.19539i
$688$		0			0
$689$	−36.5125	−	63.2415i	−0.0529935	−	0.0917874i
$690$		0			0
$691$	445.414	−	771.480i	0.644593	−	1.11647i	−0.339802	−	0.940497i	$-0.610360\pi$
$691$	445.414	−	771.480i	0.644593	−	1.11647i	0.984395	−	0.175971i	$-0.0563066\pi$
$692$		0			0
$693$	−997.586	+	248.280i	−1.43952	+	0.358269i
$694$		0			0
$695$	913.034	+	527.141i	1.31372	+	0.758476i
$696$		0			0
$697$	334.366	+	579.139i	0.479722	+	0.830903i
$698$		0			0
$699$	−148.122	+	1052.33i	−0.211905	+	1.50548i
$700$		0			0
$701$		−	292.848i		−	0.417757i	−0.977942	−	0.208878i	$-0.933019\pi$
$701$		−	292.848i		−	0.417757i	0.977942	−	0.208878i	$-0.0669813\pi$
$702$		0			0
$703$		−	283.741i		−	0.403614i
$704$		0			0
$705$	129.818	−	922.293i	0.184139	−	1.30822i
$706$		0			0
$707$	719.792	+	1246.72i	1.01809	+	1.76339i
$708$		0			0
$709$	−251.105	−	144.976i	−0.354168	−	0.204479i	0.312351	−	0.949967i	$-0.398883\pi$
$709$	−251.105	−	144.976i	−0.354168	−	0.204479i	−0.666520	+	0.745487i	$0.732217\pi$
$710$		0			0
$711$	−20.5563	−	21.3046i	−0.0289118	−	0.0299643i
$712$		0			0
$713$	97.0379	−	168.075i	0.136098	−	0.235729i
$714$		0			0
$715$	−256.789	−	444.772i	−0.359146	−	0.622059i
$716$		0			0
$717$	139.872	+	346.406i	0.195080	+	0.483133i
$718$		0			0
$719$		−	1132.71i		−	1.57540i	−0.616058	−	0.787701i	$-0.711271\pi$
$719$		−	1132.71i		−	1.57540i	0.616058	−	0.787701i	$-0.288729\pi$
$720$		0			0
$721$	2482.01			3.44245
$722$		0			0
$723$	896.651	+	700.845i	1.24018	+	0.969356i
$724$		0			0
$725$	−6.83999	+	3.94907i	−0.00943447	+	0.00544700i
$726$		0			0
$727$	42.5708	+	24.5783i	0.0585569	+	0.0338078i	0.528993	−	0.848626i	$-0.322570\pi$
$727$	42.5708	+	24.5783i	0.0585569	+	0.0338078i	−0.470436	+	0.882434i	$0.655903\pi$
$728$		0			0
$729$	−487.111	−	542.368i	−0.668191	−	0.743989i
$730$		0			0
$731$	−58.2378	+	100.871i	−0.0796686	+	0.137990i
$732$		0			0
$733$	827.604	−	477.817i	1.12906	−	0.651865i	0.185364	−	0.982670i	$-0.440653\pi$
$733$	827.604	−	477.817i	1.12906	−	0.651865i	0.943699	+	0.330805i	$0.107320\pi$
$734$		0			0
$735$	−1045.53	+	1337.64i	−1.42249	+	1.81992i
$736$		0			0
$737$	−729.878			−0.990337
$738$		0			0
$739$	279.034			0.377583			0.188791	−	0.982017i	$-0.439543\pi$
$739$	279.034			0.377583			0.188791	+	0.982017i	$0.439543\pi$
$740$		0			0
$741$	178.851	+	442.940i	0.241364	+	0.597759i
$742$		0			0
$743$	−19.7539	+	11.4049i	−0.0265866	+	0.0153498i	−0.513234	−	0.858248i	$-0.671553\pi$
$743$	−19.7539	+	11.4049i	−0.0265866	+	0.0153498i	0.486648	+	0.873598i	$0.338220\pi$
$744$		0			0
$745$	−574.970	+	995.877i	−0.771771	+	1.33675i
$746$		0			0
$747$	239.340	−	230.933i	0.320402	−	0.309148i
$748$		0			0
$749$	348.538	+	201.228i	0.465338	+	0.268663i
$750$		0			0
$751$	983.960	−	568.090i	1.31020	−	0.756444i	0.328071	−	0.944653i	$-0.393602\pi$
$751$	983.960	−	568.090i	1.31020	−	0.756444i	0.982129	+	0.188209i	$0.0602682\pi$
$752$		0			0
$753$	−161.358	+	1146.37i	−0.214287	+	1.52241i
$754$		0			0
$755$	726.344			0.962046
$756$		0			0
$757$			1067.71i			1.41045i	0.708984	+	0.705224i	$0.249154\pi$
$757$			1067.71i			1.41045i	−0.708984	+	0.705224i	$0.750846\pi$
$758$		0			0
$759$	−132.560	−	18.6586i	−0.174651	−	0.0245831i
$760$		0			0
$761$	291.003	+	504.031i	0.382395	+	0.662327i	0.991404	−	0.130836i	$-0.0417661\pi$
$761$	291.003	+	504.031i	0.382395	+	0.662327i	−0.609009	+	0.793163i	$0.708433\pi$
$762$		0			0
$763$	−727.373	+	1259.85i	−0.953307	+	1.65118i
$764$		0			0
$765$	854.823	−	212.749i	1.11742	−	0.278103i
$766$		0			0
$767$	−485.436	−	280.267i	−0.632902	−	0.365406i
$768$		0			0
$769$	−517.987	−	897.181i	−0.673586	−	1.16668i	−0.976880	−	0.213788i	$-0.931420\pi$
$769$	−517.987	−	897.181i	−0.673586	−	1.16668i	0.303294	−	0.952897i	$-0.401913\pi$
$770$		0			0
$771$	1271.99	−	513.608i	1.64980	−	0.666158i
$772$		0			0
$773$			1067.29i			1.38071i	0.723471	+	0.690355i	$0.242546\pi$
$773$			1067.29i			1.38071i	−0.723471	+	0.690355i	$0.757454\pi$
$774$		0			0
$775$		−	35.5335i		−	0.0458497i
$776$		0			0
$777$	596.035	+	465.876i	0.767098	+	0.599583i
$778$		0			0
$779$	247.618	+	428.886i	0.317866	+	0.550560i
$780$		0			0
$781$	394.599	+	227.822i	0.505249	+	0.291705i
$782$		0			0
$783$	−190.664	+	138.341i	−0.243504	+	0.176681i
$784$		0			0
$785$	24.1315	−	41.7970i	0.0307408	−	0.0532446i
$786$		0			0
$787$	549.400	+	951.588i	0.698094	+	1.20913i	0.969127	+	0.246564i	$0.0793014\pi$
$787$	549.400	+	951.588i	0.698094	+	1.20913i	−0.271033	+	0.962570i	$0.587365\pi$
$788$		0			0
$789$	863.557	−	1104.82i	1.09450	−	1.40028i
$790$		0			0
$791$			417.148i			0.527368i
$792$		0			0
$793$	1.92828			0.00243163
$794$		0			0
$795$	−92.4737	+	37.3391i	−0.116319	+	0.0469675i
$796$		0			0
$797$	973.877	−	562.268i	1.22193	−	0.705481i	0.256600	−	0.966518i	$-0.417398\pi$
$797$	973.877	−	562.268i	1.22193	−	0.705481i	0.965329	+	0.261037i	$0.0840645\pi$
$798$		0			0
$799$	1015.86	+	586.508i	1.27142	+	0.734052i
$800$		0			0
$801$	−112.537	−	32.3207i	−0.140496	−	0.0403505i
$802$		0			0
$803$	−108.422	+	187.793i	−0.135021	+	0.233864i
$804$		0			0
$805$	−275.837	+	159.255i	−0.342655	+	0.197832i
$806$		0			0
$807$	−1375.75	−	193.644i	−1.70477	−	0.239956i
$808$		0			0
$809$	1468.01			1.81460			0.907300	−	0.420484i	$-0.138140\pi$
$809$	1468.01			1.81460			0.907300	+	0.420484i	$0.138140\pi$
$810$		0			0
$811$	90.2707			0.111308			0.0556540	−	0.998450i	$-0.482276\pi$
$811$	90.2707			0.111308			0.0556540	+	0.998450i	$0.482276\pi$
$812$		0			0
$813$	−964.392	−	135.744i	−1.18621	−	0.166966i
$814$		0			0
$815$	−1347.34	+	777.885i	−1.65317	+	0.954460i
$816$		0			0
$817$	−43.1284	+	74.7006i	−0.0527888	+	0.0914328i
$818$		0			0
$819$	−1224.11	−	351.565i	−1.49464	−	0.429262i
$820$		0			0
$821$	−1001.79	−	578.386i	−1.22021	−	0.704489i	−0.255248	−	0.966875i	$-0.582157\pi$
$821$	−1001.79	−	578.386i	−1.22021	−	0.704489i	−0.964963	+	0.262386i	$0.915491\pi$
$822$		0			0
$823$	516.742	−	298.341i	0.627876	−	0.362504i	−0.152053	−	0.988372i	$-0.548588\pi$
$823$	516.742	−	298.341i	0.627876	−	0.362504i	0.779929	+	0.625868i	$0.215255\pi$
$824$		0			0
$825$	−22.7271	+	9.17676i	−0.0275479	+	0.0111233i
$826$		0			0
$827$	−601.527			−0.727360			−0.363680	−	0.931524i	$-0.618480\pi$
$827$	−601.527			−0.727360			−0.363680	+	0.931524i	$0.618480\pi$
$828$		0			0
$829$		−	375.459i		−	0.452906i	−0.974022	−	0.226453i	$-0.927287\pi$
$829$		−	375.459i		−	0.452906i	0.974022	−	0.226453i	$-0.0727130\pi$
$830$		0			0
$831$	532.635	−	681.445i	0.640956	−	0.820031i
$832$		0			0
$833$	−1069.11	−	1851.76i	−1.28345	−	2.22300i
$834$		0			0
$835$	−39.4075	+	68.2559i	−0.0471947	+	0.0817435i
$836$		0			0
$837$	−110.114	−	1054.07i	−0.131557	−	1.25934i
$838$		0			0
$839$	−856.558	−	494.534i	−1.02093	−	0.589433i	−0.106555	−	0.994307i	$-0.533982\pi$
$839$	−856.558	−	494.534i	−1.02093	−	0.589433i	−0.914372	+	0.404874i	$0.867315\pi$
$840$		0			0
$841$	−382.440	−	662.406i	−0.454745	−	0.787641i
$842$		0			0
$843$	817.672	+	639.113i	0.969955	+	0.758141i
$844$		0			0
$845$			223.899i			0.264969i
$846$		0			0
$847$		−	500.587i		−	0.591012i
$848$		0			0
$849$	−43.5664	+	17.5913i	−0.0513149	+	0.0207200i
$850$		0			0
$851$	49.2554	+	85.3129i	0.0578795	+	0.100250i
$852$		0			0
$853$	329.989	+	190.519i	0.386857	+	0.223352i	0.680798	−	0.732472i	$-0.261633\pi$
$853$	329.989	+	190.519i	0.386857	+	0.223352i	−0.293940	+	0.955824i	$0.594967\pi$
$854$		0			0
$855$	633.046	−	157.553i	0.740405	−	0.184272i
$856$		0			0
$857$	−82.2028	+	142.379i	−0.0959193	+	0.166137i	−0.909992	−	0.414626i	$-0.863912\pi$
$857$	−82.2028	+	142.379i	−0.0959193	+	0.166137i	0.814073	+	0.580763i	$0.197246\pi$
$858$		0			0
$859$	−813.298	−	1408.67i	−0.946796	−	1.63990i	−0.752114	−	0.659033i	$-0.770966\pi$
$859$	−813.298	−	1408.67i	−0.946796	−	1.63990i	−0.194682	−	0.980866i	$-0.562368\pi$
$860$		0			0
$861$	−1307.50	−	184.037i	−1.51858	−	0.213748i
$862$		0			0
$863$			1256.44i			1.45590i	0.685628	+	0.727952i	$0.259527\pi$
$863$			1256.44i			1.45590i	−0.685628	+	0.727952i	$0.740473\pi$
$864$		0			0
$865$	−466.432			−0.539228
$866$		0			0
$867$	−33.7908	+	240.067i	−0.0389744	+	0.276894i
$868$		0			0
$869$	−25.7094	+	14.8434i	−0.0295851	+	0.0170810i
$870$		0			0
$871$	−783.089	−	452.117i	−0.899069	−	0.519077i
$872$		0			0
$873$	−579.689	+	559.327i	−0.664019	+	0.640696i
$874$		0			0
$875$	776.074	−	1344.20i	0.886941	−	1.53623i
$876$		0			0
$877$	6.97163	−	4.02507i	0.00794940	−	0.00458959i	−0.496020	−	0.868311i	$-0.665206\pi$
$877$	6.97163	−	4.02507i	0.00794940	−	0.00458959i	0.503969	+	0.863721i	$0.331872\pi$
$878$		0			0
$879$	−119.166	−	295.126i	−0.135570	−	0.335752i
$880$		0			0
$881$	842.573			0.956382			0.478191	−	0.878256i	$-0.341293\pi$
$881$	842.573			0.956382			0.478191	+	0.878256i	$0.341293\pi$
$882$		0			0
$883$	−621.919			−0.704325			−0.352163	−	0.935939i	$-0.614554\pi$
$883$	−621.919			−0.704325			−0.352163	+	0.935939i	$0.614554\pi$
$884$		0			0
$885$	−471.416	+	603.123i	−0.532673	+	0.681495i
$886$		0			0
$887$	−413.440	+	238.700i	−0.466110	+	0.269109i	−0.714610	−	0.699523i	$-0.753396\pi$
$887$	−413.440	+	238.700i	−0.466110	+	0.269109i	0.248500	+	0.968632i	$0.420063\pi$
$888$		0			0
$889$	−473.057	+	819.358i	−0.532122	+	0.921663i
$890$		0			0
$891$	−645.737	+	342.647i	−0.724733	+	0.384565i
$892$		0			0
$893$	752.304	+	434.343i	0.842445	+	0.486386i
$894$		0			0
$895$	−555.335	+	320.623i	−0.620486	+	0.358238i
$896$		0			0
$897$	−130.667	−	102.132i	−0.145671	−	0.113860i
$898$		0			0
$899$	−342.459			−0.380933
$900$		0			0
$901$		−	125.600i		−	0.139401i
$902$		0			0
$903$	−86.1057	−	213.248i	−0.0953551	−	0.236155i
$904$		0			0
$905$	58.5360	+	101.387i	0.0646807	+	0.112030i
$906$		0			0
$907$	310.221	−	537.319i	0.342030	−	0.592414i	−0.642779	−	0.766051i	$-0.722219\pi$
$907$	310.221	−	537.319i	0.342030	−	0.592414i	0.984810	+	0.173638i	$0.0555521\pi$
$908$		0			0
$909$	710.795	+	736.671i	0.781953	+	0.810419i
$910$		0			0
$911$	1065.40	+	615.107i	1.16948	+	0.675200i	0.953558	−	0.301210i	$-0.0973907\pi$
$911$	1065.40	+	615.107i	1.16948	+	0.675200i	0.215923	+	0.976410i	$0.430724\pi$
$912$		0			0
$913$	−166.753	−	288.825i	−0.182643	−	0.316347i
$914$		0			0
$915$	0.367046	−	2.60768i	0.000401143	−	0.00284993i
$916$		0			0
$917$			1040.09i			1.13423i
$918$		0			0
$919$			211.088i			0.229693i	0.993383	+	0.114847i	$0.0366377\pi$
$919$			211.088i			0.229693i	−0.993383	+	0.114847i	$0.963362\pi$
$920$		0			0
$921$	137.795	−	978.969i	0.149615	−	1.06294i
$922$		0			0
$923$	282.245	+	488.862i	0.305790	+	0.529645i
$924$		0			0
$925$	15.6200	+	9.01822i	0.0168865	+	0.00974942i
$926$		0			0
$927$	1712.69	−	426.256i	1.84756	−	0.459823i
$928$		0			0
$929$	524.859	−	909.082i	0.564972	−	0.978560i	−0.432081	−	0.901835i	$-0.642220\pi$
$929$	524.859	−	909.082i	0.564972	−	0.978560i	0.997052	−	0.0767247i	$-0.0244462\pi$
$930$		0			0
$931$	−791.739	−	1371.33i	−0.850418	−	1.47297i
$932$		0			0
$933$	−444.600	−	1101.09i	−0.476527	−	1.18016i
$934$		0			0
$935$		−	883.335i		−	0.944744i
$936$		0			0
$937$	−14.8972			−0.0158988			−0.00794939	−	0.999968i	$-0.502530\pi$
$937$	−14.8972			−0.0158988			−0.00794939	+	0.999968i	$0.502530\pi$
$938$		0			0
$939$	−242.029	−	189.176i	−0.257752	−	0.201465i
$940$		0			0
$941$	494.297	−	285.383i	0.525289	−	0.303276i	−0.213807	−	0.976876i	$-0.568586\pi$
$941$	494.297	−	285.383i	0.525289	−	0.303276i	0.739096	+	0.673600i	$0.235253\pi$
$942$		0			0
$943$	−148.903	−	85.9693i	−0.157904	−	0.0911657i
$944$		0			0
$945$	−708.441	+	1588.48i	−0.749673	+	1.68093i
$946$		0			0
$947$	15.4417	−	26.7459i	0.0163059	−	0.0282427i	−0.857757	−	0.514055i	$-0.828143\pi$
$947$	15.4417	−	26.7459i	0.0163059	−	0.0282427i	0.874063	+	0.485812i	$0.161476\pi$
$948$		0			0
$949$	−232.653	+	134.322i	−0.245156	+	0.141541i
$950$		0			0
$951$	505.624	−	646.889i	0.531676	−	0.680219i
$952$		0			0
$953$	−1048.23			−1.09993			−0.549965	−	0.835188i	$-0.685359\pi$
$953$	−1048.23			−1.09993			−0.549965	+	0.835188i	$0.685359\pi$
$954$		0			0
$955$	120.034			0.125690
$956$		0			0
$957$	88.4422	+	219.035i	0.0924161	+	0.228876i
$958$		0			0
$959$	2010.50	−	1160.76i	2.09646	−	1.21039i
$960$		0			0
$961$	289.855	−	502.044i	0.301618	−	0.522418i
$962$		0			0
$963$	275.064	+	78.9988i	0.285633	+	0.0820340i
$964$		0			0
$965$	−273.411	−	157.854i	−0.283327	−	0.163579i
$966$		0			0
$967$	833.473	−	481.206i	0.861916	−	0.497628i	−0.00273711	−	0.999996i	$-0.500871\pi$
$967$	833.473	−	481.206i	0.861916	−	0.497628i	0.864654	+	0.502369i	$0.167538\pi$
$968$		0			0
$969$	−114.516	+	813.580i	−0.118179	+	0.839608i
$970$		0			0
$971$	−848.612			−0.873957			−0.436978	−	0.899472i	$-0.643951\pi$
$971$	−848.612			−0.873957			−0.436978	+	0.899472i	$0.643951\pi$
$972$		0			0
$973$		−	2621.68i		−	2.69443i
$974$		0			0
$975$	−30.0684	−	4.23229i	−0.0308394	−	0.00434081i
$976$		0			0
$977$	559.484	+	969.055i	0.572655	+	0.991868i	0.996292	+	0.0860361i	$0.0274201\pi$
$977$	559.484	+	969.055i	0.572655	+	0.991868i	−0.423637	+	0.905832i	$0.639247\pi$
$978$		0			0
$979$	−58.7050	+	101.680i	−0.0599642	+	0.103861i
$980$		0			0
$981$	−285.554	+	994.265i	−0.291085	+	1.01352i
$982$		0			0
$983$	598.966	+	345.813i	0.609324	+	0.351793i	0.772701	−	0.634770i	$-0.218905\pi$
$983$	598.966	+	345.813i	0.609324	+	0.351793i	−0.163377	+	0.986564i	$0.552239\pi$
$984$		0			0
$985$	−981.861	−	1700.63i	−0.996813	−	1.72653i
$986$		0			0
$987$	−2147.61	+	867.163i	−2.17589	+	0.878585i
$988$		0			0
$989$		−	29.9472i		−	0.0302802i
$990$		0			0
$991$			361.650i			0.364935i	0.983212	+	0.182467i	$0.0584084\pi$
$991$			361.650i			0.364935i	−0.983212	+	0.182467i	$0.941592\pi$
$992$		0			0
$993$	685.544	+	535.838i	0.690377	+	0.539616i
$994$		0			0
$995$	−547.035	−	947.492i	−0.549784	−	0.952254i
$996$		0			0
$997$	−1162.72	−	671.298i	−1.16622	−	0.673318i	−0.213434	−	0.976958i	$-0.568465\pi$
$997$	−1162.72	−	671.298i	−1.16622	−	0.673318i	−0.952787	+	0.303640i	$0.901798\pi$
$998$		0			0
$999$	491.298	+	219.112i	0.491790	+	0.219331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.t.b.79.10		40
3.2	odd	2		864.3.t.b.559.6		40
4.3	odd	2		72.3.p.b.43.11	yes	40
8.3	odd	2	inner	288.3.t.b.79.9		40
8.5	even	2		72.3.p.b.43.5	✓	40
9.2	odd	6		2592.3.b.f.1135.6		20
9.4	even	3	inner	288.3.t.b.175.9		40
9.5	odd	6		864.3.t.b.847.15		40
9.7	even	3		2592.3.b.e.1135.15		20
12.11	even	2		216.3.p.b.19.10		40
24.5	odd	2		216.3.p.b.19.16		40
24.11	even	2		864.3.t.b.559.15		40
36.7	odd	6		648.3.b.f.163.17		20
36.11	even	6		648.3.b.e.163.4		20
36.23	even	6		216.3.p.b.91.16		40
36.31	odd	6		72.3.p.b.67.5	yes	40
72.5	odd	6		216.3.p.b.91.10		40
72.11	even	6		2592.3.b.f.1135.15		20
72.13	even	6		72.3.p.b.67.11	yes	40
72.29	odd	6		648.3.b.e.163.3		20
72.43	odd	6		2592.3.b.e.1135.6		20
72.59	even	6		864.3.t.b.847.6		40
72.61	even	6		648.3.b.f.163.18		20
72.67	odd	6	inner	288.3.t.b.175.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.5	✓	40	8.5	even	2
72.3.p.b.43.11	yes	40	4.3	odd	2
72.3.p.b.67.5	yes	40	36.31	odd	6
72.3.p.b.67.11	yes	40	72.13	even	6
216.3.p.b.19.10		40	12.11	even	2
216.3.p.b.19.16		40	24.5	odd	2
216.3.p.b.91.10		40	72.5	odd	6
216.3.p.b.91.16		40	36.23	even	6
288.3.t.b.79.9		40	8.3	odd	2	inner
288.3.t.b.79.10		40	1.1	even	1	trivial
288.3.t.b.175.9		40	9.4	even	3	inner
288.3.t.b.175.10		40	72.67	odd	6	inner
648.3.b.e.163.3		20	72.29	odd	6
648.3.b.e.163.4		20	36.11	even	6
648.3.b.f.163.17		20	36.7	odd	6
648.3.b.f.163.18		20	72.61	even	6
864.3.t.b.559.6		40	3.2	odd	2
864.3.t.b.559.15		40	24.11	even	2
864.3.t.b.847.6		40	72.59	even	6
864.3.t.b.847.15		40	9.5	odd	6
2592.3.b.e.1135.6		20	72.43	odd	6
2592.3.b.e.1135.15		20	9.7	even	3
2592.3.b.f.1135.6		20	9.2	odd	6
2592.3.b.f.1135.15		20	72.11	even	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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.418145 + 2.97072i) q^{3} +(4.40783 - 2.54486i) q^{5} +(-10.9609 - 6.32830i) q^{7} +(-8.65031 - 2.48438i) q^{9} +O(q^{10})\)	\(q+(-0.418145 + 2.97072i) q^{3} +(4.40783 - 2.54486i) q^{5} +(-10.9609 - 6.32830i) q^{7} +(-8.65031 - 2.48438i) q^{9} +(-4.51244 + 7.81578i) q^{11} +(-9.68283 + 5.59038i) q^{13} +(5.71695 + 14.1585i) q^{15} -19.2305 q^{17} -14.2413 q^{19} +(23.3828 - 29.9157i) q^{21} +(4.28195 - 2.47218i) q^{23} +(0.452634 - 0.783986i) q^{25} +(10.9975 - 24.6588i) q^{27} +(-7.55576 - 4.36232i) q^{29} +(33.9931 - 19.6259i) q^{31} +(-21.3316 - 16.6733i) q^{33} -64.4185 q^{35} +19.9238i q^{37} +(-12.5586 - 31.1025i) q^{39} +(-17.3873 - 30.1157i) q^{41} +(3.02841 - 5.24536i) q^{43} +(-44.4515 + 11.0631i) q^{45} +(-52.8256 - 30.4989i) q^{47} +(55.5947 + 96.2928i) q^{49} +(8.04112 - 57.1283i) q^{51} +6.53131i q^{53} +45.9341i q^{55} +(5.95492 - 42.3068i) q^{57} +(25.0669 + 43.4171i) q^{59} +(-0.149359 - 0.0862322i) q^{61} +(79.0936 + 81.9728i) q^{63} +(-28.4535 + 49.2829i) q^{65} +(40.4370 + 70.0389i) q^{67} +(5.55368 + 13.7542i) q^{69} -50.4875i q^{71} +24.0274 q^{73} +(2.13973 + 1.67247i) q^{75} +(98.9211 - 57.1121i) q^{77} +(2.84873 + 1.64471i) q^{79} +(68.6557 + 42.9813i) q^{81} +(-18.4770 + 32.0032i) q^{83} +(-84.7646 + 48.9389i) q^{85} +(16.1186 - 20.6219i) q^{87} +13.0096 q^{89} +141.510 q^{91} +(44.0891 + 109.190i) q^{93} +(-62.7731 + 36.2421i) q^{95} +(44.7519 - 77.5126i) q^{97} +(58.4514 - 56.3983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 18 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 18 * q^9	\( 40 q + 6 q^{3} - 18 q^{9} + 16 q^{11} - 4 q^{17} + 76 q^{19} + 118 q^{25} + 144 q^{27} + 156 q^{33} + 108 q^{35} + 20 q^{41} + 16 q^{43} + 166 q^{49} - 330 q^{51} - 258 q^{57} + 64 q^{59} - 102 q^{65} + 64 q^{67} - 292 q^{73} - 138 q^{75} - 42 q^{81} - 554 q^{83} - 688 q^{89} + 204 q^{91} + 92 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 18 * q^9 + 16 * q^11 - 4 * q^17 + 76 * q^19 + 118 * q^25 + 144 * q^27 + 156 * q^33 + 108 * q^35 + 20 * q^41 + 16 * q^43 + 166 * q^49 - 330 * q^51 - 258 * q^57 + 64 * q^59 - 102 * q^65 + 64 * q^67 - 292 * q^73 - 138 * q^75 - 42 * q^81 - 554 * q^83 - 688 * q^89 + 204 * q^91 + 92 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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