LMFDB - Embedded newform 468.2.k.a.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,2,Mod(61,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("468.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.k (of order $3$, 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:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.7
Character	$\chi$	$=$	468.61
Dual form			468.2.k.a.445.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.328747 + 1.70057i) q^{3} +(2.03195 + 3.51944i) q^{5} -1.23400 q^{7} +(-2.78385 - 1.11811i) q^{9} +O(q^{10})$	\(q+(-0.328747 + 1.70057i) q^{3} +(2.03195 + 3.51944i) q^{5} -1.23400 q^{7} +(-2.78385 - 1.11811i) q^{9} +(3.15860 + 5.47085i) q^{11} +(0.199477 - 3.60003i) q^{13} +(-6.65304 + 2.29846i) q^{15} +(-2.45192 - 4.24685i) q^{17} +(0.346591 + 0.600313i) q^{19} +(0.405673 - 2.09850i) q^{21} +1.41399 q^{23} +(-5.75764 + 9.97252i) q^{25} +(2.81661 - 4.36655i) q^{27} +(-3.35150 - 5.80497i) q^{29} +(1.88555 + 3.26586i) q^{31} +(-10.3419 + 3.57288i) q^{33} +(-2.50742 - 4.34298i) q^{35} +(-1.48705 + 2.57565i) q^{37} +(6.05651 + 1.52272i) q^{39} +7.12257 q^{41} -1.13355 q^{43} +(-1.72152 - 12.0695i) q^{45} +(-3.76496 + 6.52111i) q^{47} -5.47725 q^{49} +(8.02812 - 2.77352i) q^{51} +13.1961 q^{53} +(-12.8362 + 22.2330i) q^{55} +(-1.13481 + 0.392049i) q^{57} +(-5.22399 + 9.04821i) q^{59} +5.76307 q^{61} +(3.43527 + 1.37975i) q^{63} +(13.0754 - 6.61303i) q^{65} +7.40886 q^{67} +(-0.464845 + 2.40458i) q^{69} +(-1.36182 - 2.35874i) q^{71} -1.45266 q^{73} +(-15.0661 - 13.0697i) q^{75} +(-3.89770 - 6.75102i) q^{77} +(3.73863 - 6.47550i) q^{79} +(6.49965 + 6.22531i) q^{81} +(4.02165 - 6.96570i) q^{83} +(9.96436 - 17.2588i) q^{85} +(10.9735 - 3.79108i) q^{87} +(6.75612 - 11.7020i) q^{89} +(-0.246154 + 4.44243i) q^{91} +(-6.17368 + 2.13285i) q^{93} +(-1.40851 + 2.43961i) q^{95} +3.06393 q^{97} +(-2.67604 - 18.7617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 28 * q - 4 * q^7 - 2 * q^9	$ 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43} - 38 q^{45} + 11 q^{47} + 24 q^{49} + 5 q^{51} + 52 q^{53} - q^{57} - 8 q^{59} + 14 q^{61} - 21 q^{63} + 38 q^{65} + 14 q^{67} - 21 q^{69} - 12 q^{71} + 14 q^{73} - 14 q^{75} - 28 q^{77} + 5 q^{79} + 10 q^{81} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 11 q^{89} - q^{91} - 9 q^{93} + 28 q^{95} + 50 q^{97} - 29 q^{99}+O(q^{100}) $ 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.328747	+	1.70057i	−0.189802	+	0.981822i
$3$	−0.328747	+	1.70057i	−0.189802	+	0.981822i
$4$		0			0
$5$	2.03195	+	3.51944i	0.908716	+	1.57394i	0.815851	+	0.578263i	$0.196269\pi$
$5$	2.03195	+	3.51944i	0.908716	+	1.57394i	0.0928649	+	0.995679i	$0.470398\pi$
$6$		0			0
$7$	−1.23400			−0.466408			−0.233204	−	0.972428i	$-0.574921\pi$
$7$	−1.23400			−0.466408			−0.233204	+	0.972428i	$0.574921\pi$
$8$		0			0
$9$	−2.78385	−	1.11811i	−0.927950	−	0.372704i
$10$		0			0
$11$	3.15860	+	5.47085i	0.952353	+	1.64952i	0.740314	+	0.672262i	$0.234677\pi$
$11$	3.15860	+	5.47085i	0.952353	+	1.64952i	0.212039	+	0.977261i	$0.431990\pi$
$12$		0			0
$13$	0.199477	−	3.60003i	0.0553249	−	0.998468i
$13$	0.199477	−	3.60003i	0.0553249	−	0.998468i
$14$		0			0
$15$	−6.65304	+	2.29846i	−1.71781	+	0.593460i
$16$		0			0
$17$	−2.45192	−	4.24685i	−0.594678	−	1.03001i	−0.993592	−	0.113025i	$-0.963946\pi$
$17$	−2.45192	−	4.24685i	−0.594678	−	1.03001i	0.398914	−	0.916988i	$-0.369387\pi$
$18$		0			0
$19$	0.346591	+	0.600313i	0.0795134	+	0.137721i	0.903040	−	0.429556i	$-0.141330\pi$
$19$	0.346591	+	0.600313i	0.0795134	+	0.137721i	−0.823527	+	0.567277i	$0.807997\pi$
$20$		0			0
$21$	0.405673	−	2.09850i	0.0885252	−	0.457929i
$22$		0			0
$23$	1.41399			0.294837			0.147419	−	0.989074i	$-0.452904\pi$
$23$	1.41399			0.294837			0.147419	+	0.989074i	$0.452904\pi$
$24$		0			0
$25$	−5.75764	+	9.97252i	−1.15153	+	1.99450i
$26$		0			0
$27$	2.81661	−	4.36655i	0.542056	−	0.840342i
$28$		0			0
$29$	−3.35150	−	5.80497i	−0.622358	−	1.07796i	−0.989045	−	0.147612i	$-0.952841\pi$
$29$	−3.35150	−	5.80497i	−0.622358	−	1.07796i	0.366687	−	0.930344i	$-0.380492\pi$
$30$		0			0
$31$	1.88555	+	3.26586i	0.338654	+	0.586566i	0.984180	−	0.177173i	$-0.0566951\pi$
$31$	1.88555	+	3.26586i	0.338654	+	0.586566i	−0.645526	+	0.763738i	$0.723362\pi$
$32$		0			0
$33$	−10.3419	+	3.57288i	−1.80030	+	0.621958i
$34$		0			0
$35$	−2.50742	−	4.34298i	−0.423832	−	0.734098i
$36$		0			0
$37$	−1.48705	+	2.57565i	−0.244470	+	0.423434i	−0.961982	−	0.273112i	$-0.911947\pi$
$37$	−1.48705	+	2.57565i	−0.244470	+	0.423434i	0.717513	+	0.696545i	$0.245280\pi$
$38$		0			0
$39$	6.05651	+	1.52272i	0.969818	+	0.243831i
$40$		0			0
$41$	7.12257			1.11236			0.556179	−	0.831062i	$-0.312267\pi$
$41$	7.12257			1.11236			0.556179	+	0.831062i	$0.312267\pi$
$42$		0			0
$43$	−1.13355			−0.172864			−0.0864320	−	0.996258i	$-0.527547\pi$
$43$	−1.13355			−0.172864			−0.0864320	+	0.996258i	$0.527547\pi$
$44$		0			0
$45$	−1.72152	−	12.0695i	−0.256629	−	1.79922i
$46$		0			0
$47$	−3.76496	+	6.52111i	−0.549176	+	0.951201i	0.449155	+	0.893454i	$0.351725\pi$
$47$	−3.76496	+	6.52111i	−0.549176	+	0.951201i	−0.998331	+	0.0577473i	$0.981608\pi$
$48$		0			0
$49$	−5.47725			−0.782464
$50$		0			0
$51$	8.02812	−	2.77352i	1.12416	−	0.388370i
$52$		0			0
$53$	13.1961			1.81263			0.906315	−	0.422603i	$-0.138884\pi$
$53$	13.1961			1.81263			0.906315	+	0.422603i	$0.138884\pi$
$54$		0			0
$55$	−12.8362	+	22.2330i	−1.73084	+	2.99789i
$56$		0			0
$57$	−1.13481	+	0.392049i	−0.150310	+	0.0519282i
$58$		0			0
$59$	−5.22399	+	9.04821i	−0.680105	+	1.17798i	0.294844	+	0.955546i	$0.404732\pi$
$59$	−5.22399	+	9.04821i	−0.680105	+	1.17798i	−0.974948	+	0.222431i	$0.928601\pi$
$60$		0			0
$61$	5.76307			0.737886			0.368943	−	0.929452i	$-0.379720\pi$
$61$	5.76307			0.737886			0.368943	+	0.929452i	$0.379720\pi$
$62$		0			0
$63$	3.43527	+	1.37975i	0.432803	+	0.173832i
$64$		0			0
$65$	13.0754	−	6.61303i	1.62181	−	0.820246i
$66$		0			0
$67$	7.40886			0.905136			0.452568	−	0.891730i	$-0.350508\pi$
$67$	7.40886			0.905136			0.452568	+	0.891730i	$0.350508\pi$
$68$		0			0
$69$	−0.464845	+	2.40458i	−0.0559607	+	0.289478i
$70$		0			0
$71$	−1.36182	−	2.35874i	−0.161618	−	0.279930i	0.773831	−	0.633392i	$-0.218338\pi$
$71$	−1.36182	−	2.35874i	−0.161618	−	0.279930i	−0.935449	+	0.353461i	$0.885005\pi$
$72$		0			0
$73$	−1.45266			−0.170021			−0.0850104	−	0.996380i	$-0.527092\pi$
$73$	−1.45266			−0.170021			−0.0850104	+	0.996380i	$0.527092\pi$
$74$		0			0
$75$	−15.0661	−	13.0697i	−1.73969	−	1.50916i
$76$		0			0
$77$	−3.89770	−	6.75102i	−0.444185	−	0.769350i
$78$		0			0
$79$	3.73863	−	6.47550i	0.420629	−	0.728550i	−0.575372	−	0.817892i	$-0.695143\pi$
$79$	3.73863	−	6.47550i	0.420629	−	0.728550i	0.996001	+	0.0893413i	$0.0284762\pi$
$80$		0			0
$81$	6.49965	+	6.22531i	0.722184	+	0.691701i
$82$		0			0
$83$	4.02165	−	6.96570i	0.441433	−	0.764585i	−0.556363	−	0.830939i	$-0.687804\pi$
$83$	4.02165	−	6.96570i	0.441433	−	0.764585i	0.997796	+	0.0663546i	$0.0211369\pi$
$84$		0			0
$85$	9.96436	−	17.2588i	1.08079	−	1.87198i
$86$		0			0
$87$	10.9735	−	3.79108i	1.17649	−	0.406447i
$88$		0			0
$89$	6.75612	−	11.7020i	0.716148	−	1.24040i	−0.246367	−	0.969177i	$-0.579237\pi$
$89$	6.75612	−	11.7020i	0.716148	−	1.24040i	0.962515	−	0.271228i	$-0.0874297\pi$
$90$		0			0
$91$	−0.246154	+	4.44243i	−0.0258040	+	0.465693i
$92$		0			0
$93$	−6.17368	+	2.13285i	−0.640181	+	0.221167i
$94$		0			0
$95$	−1.40851	+	2.43961i	−0.144510	+	0.250299i
$96$		0			0
$97$	3.06393			0.311095			0.155547	−	0.987828i	$-0.450286\pi$
$97$	3.06393			0.311095			0.155547	+	0.987828i	$0.450286\pi$
$98$		0			0
$99$	−2.67604	−	18.7617i	−0.268952	−	1.88562i
$100$		0			0
$101$	3.05797	+	5.29656i	0.304279	+	0.527027i	0.977101	−	0.212778i	$-0.0682511\pi$
$101$	3.05797	+	5.29656i	0.304279	+	0.527027i	−0.672821	+	0.739805i	$0.734918\pi$
$102$		0			0
$103$	−2.17185	−	3.76176i	−0.213999	−	0.370657i	0.738964	−	0.673745i	$-0.235316\pi$
$103$	−2.17185	−	3.76176i	−0.213999	−	0.370657i	−0.952962	+	0.303089i	$0.901982\pi$
$104$		0			0
$105$	8.20984	−	2.83630i	0.801198	−	0.276794i
$106$		0			0
$107$	2.96304	−	5.13214i	0.286448	−	0.496143i	−0.686511	−	0.727119i	$-0.740859\pi$
$107$	2.96304	−	5.13214i	0.286448	−	0.496143i	0.972959	+	0.230976i	$0.0741920\pi$
$108$		0			0
$109$	−0.553911			−0.0530550			−0.0265275	−	0.999648i	$-0.508445\pi$
$109$	−0.553911			−0.0530550			−0.0265275	+	0.999648i	$0.508445\pi$
$110$		0			0
$111$	−3.89119	−	3.37556i	−0.369336	−	0.320394i
$112$		0			0
$113$	3.05239	−	5.28690i	0.287145	−	0.497350i	−0.685982	−	0.727618i	$-0.740627\pi$
$113$	3.05239	−	5.28690i	0.287145	−	0.497350i	0.973127	+	0.230269i	$0.0739605\pi$
$114$		0			0
$115$	2.87315	+	4.97645i	0.267923	+	0.464056i
$116$		0			0
$117$	−4.58055	+	9.79891i	−0.423472	+	0.905909i
$118$		0			0
$119$	3.02567	+	5.24061i	0.277363	+	0.480406i
$120$		0			0
$121$	−14.4535	+	25.0341i	−1.31395	+	2.27583i
$122$		0			0
$123$	−2.34152	+	12.1124i	−0.211128	+	1.09214i
$124$		0			0
$125$	−26.4774			−2.36821
$126$		0			0
$127$	4.40433	−	7.62852i	0.390821	−	0.676922i	−0.601737	−	0.798694i	$-0.705525\pi$
$127$	4.40433	−	7.62852i	0.390821	−	0.676922i	0.992558	+	0.121773i	$0.0388579\pi$
$128$		0			0
$129$	0.372649	−	1.92767i	0.0328100	−	0.169722i
$130$		0			0
$131$	5.71507	+	9.89879i	0.499328	+	0.864861i	1.00000		0.000776096i	$-0.000247039\pi$
$131$	5.71507	+	9.89879i	0.499328	+	0.864861i	−0.500672	+	0.865637i	$0.666914\pi$
$132$		0			0
$133$	−0.427692	−	0.740785i	−0.0370856	−	0.0642342i
$134$		0			0
$135$	21.0910	+	1.04027i	1.81522	+	0.0895323i
$136$		0			0
$137$	11.7040			0.999939			0.499969	−	0.866043i	$-0.333345\pi$
$137$	11.7040			0.999939			0.499969	+	0.866043i	$0.333345\pi$
$138$		0			0
$139$	−3.49733	+	6.05755i	−0.296639	+	0.513794i	−0.975365	−	0.220598i	$-0.929199\pi$
$139$	−3.49733	+	6.05755i	−0.296639	+	0.513794i	0.678726	+	0.734392i	$0.262533\pi$
$140$		0			0
$141$	−9.85185	−	8.54636i	−0.829676	−	0.719734i
$142$		0			0
$143$	20.3253	−	10.2797i	1.69969	−	0.859634i
$144$		0			0
$145$	13.6202	−	23.5908i	1.13109	−	1.95911i
$146$		0			0
$147$	1.80063	−	9.31442i	0.148513	−	0.768241i
$148$		0			0
$149$	−4.55253	+	7.88521i	−0.372957	+	0.645981i	−0.990019	−	0.140934i	$-0.954990\pi$
$149$	−4.55253	+	7.88521i	−0.372957	+	0.645981i	0.617062	+	0.786915i	$0.288323\pi$
$150$		0			0
$151$	0.185604	−	0.321476i	0.0151043	−	0.0261614i	−0.858374	−	0.513024i	$-0.828525\pi$
$151$	0.185604	−	0.321476i	0.0151043	−	0.0261614i	0.873479	+	0.486862i	$0.161859\pi$
$152$		0			0
$153$	2.07733	+	14.5641i	0.167942	+	1.17744i
$154$		0			0
$155$	−7.66267	+	13.2721i	−0.615480	+	1.06604i
$156$		0			0
$157$	−0.686457	−	1.18898i	−0.0547852	−	0.0948908i	0.837332	−	0.546694i	$-0.184114\pi$
$157$	−0.686457	−	1.18898i	−0.0547852	−	0.0948908i	−0.892117	+	0.451804i	$0.850781\pi$
$158$		0			0
$159$	−4.33819	+	22.4409i	−0.344041	+	1.77968i
$160$		0			0
$161$	−1.74486			−0.137514
$162$		0			0
$163$	−8.53586	−	14.7845i	−0.668580	−	1.15802i	−0.978301	−	0.207188i	$-0.933569\pi$
$163$	−8.53586	−	14.7845i	−0.668580	−	1.15802i	0.309721	−	0.950828i	$-0.399764\pi$
$164$		0			0
$165$	−33.5888	−	29.1379i	−2.61488	−	2.26838i
$166$		0			0
$167$	3.14950			0.243716			0.121858	−	0.992548i	$-0.461115\pi$
$167$	3.14950			0.243716			0.121858	+	0.992548i	$0.461115\pi$
$168$		0			0
$169$	−12.9204	−	1.43624i	−0.993878	−	0.110480i
$170$		0			0
$171$	−0.293640	−	2.05871i	−0.0224552	−	0.157433i
$172$		0			0
$173$	8.80265			0.669253			0.334626	−	0.942351i	$-0.391390\pi$
$173$	8.80265			0.669253			0.334626	+	0.942351i	$0.391390\pi$
$174$		0			0
$175$	7.10492	−	12.3061i	0.537081	−	0.930252i
$176$		0			0
$177$	−13.6697	−	11.8583i	−1.02748	−	0.891325i
$178$		0			0
$179$	−10.8390	+	18.7736i	−0.810142	+	1.40321i	0.102622	+	0.994720i	$0.467277\pi$
$179$	−10.8390	+	18.7736i	−0.810142	+	1.40321i	−0.912764	+	0.408487i	$0.866056\pi$
$180$		0			0
$181$	17.3637			1.29063			0.645315	−	0.763916i	$-0.276726\pi$
$181$	17.3637			1.29063			0.645315	+	0.763916i	$0.276726\pi$
$182$		0			0
$183$	−1.89459	+	9.80048i	−0.140052	+	0.724473i
$184$		0			0
$185$	−12.0864			−0.888613
$186$		0			0
$187$	15.4893	−	26.8282i	1.13269	−	1.96187i
$188$		0			0
$189$	−3.47569	+	5.38831i	−0.252819	+	0.391942i
$190$		0			0
$191$	2.23950			0.162044			0.0810221	−	0.996712i	$-0.474182\pi$
$191$	2.23950			0.162044			0.0810221	+	0.996712i	$0.474182\pi$
$192$		0			0
$193$	−18.9028			−1.36065			−0.680326	−	0.732909i	$-0.738162\pi$
$193$	−18.9028			−1.36065			−0.680326	+	0.732909i	$0.738162\pi$
$194$		0			0
$195$	6.94739	+	24.4096i	0.497513	+	1.74801i
$196$		0			0
$197$	4.09745	−	7.09699i	0.291931	−	0.505640i	−0.682335	−	0.731039i	$-0.739036\pi$
$197$	4.09745	−	7.09699i	0.291931	−	0.505640i	0.974266	+	0.225400i	$0.0723688\pi$
$198$		0			0
$199$	−0.765637	−	1.32612i	−0.0542745	−	0.0940063i	0.837612	−	0.546266i	$-0.183951\pi$
$199$	−0.765637	−	1.32612i	−0.0542745	−	0.0940063i	−0.891886	+	0.452260i	$0.850618\pi$
$200$		0			0
$201$	−2.43564	+	12.5993i	−0.171797	+	0.888683i
$202$		0			0
$203$	4.13575	+	7.16333i	0.290273	+	0.502767i
$204$		0			0
$205$	14.4727	+	25.0675i	1.01082	+	1.75079i
$206$		0			0
$207$	−3.93634	−	1.58100i	−0.273594	−	0.109887i
$208$		0			0
$209$	−2.18948	+	3.79229i	−0.151449	+	0.262318i
$210$		0			0
$211$	−18.3932			−1.26624			−0.633119	−	0.774055i	$-0.718225\pi$
$211$	−18.3932			−1.26624			−0.633119	+	0.774055i	$0.718225\pi$
$212$		0			0
$213$	4.45888	−	1.54043i	0.305517	−	0.105549i
$214$		0			0
$215$	−2.30331	−	3.98944i	−0.157084	−	0.272078i
$216$		0			0
$217$	−2.32676	−	4.03007i	−0.157951	−	0.273579i
$218$		0			0
$219$	0.477557	−	2.47034i	0.0322703	−	0.166930i
$220$		0			0
$221$	−15.7779	+	7.97984i	−1.06134	+	0.536782i
$222$		0			0
$223$	10.5975	+	18.3553i	0.709658	+	1.22916i	0.964984	+	0.262309i	$0.0844840\pi$
$223$	10.5975	+	18.3553i	0.709658	+	1.22916i	−0.255326	+	0.966855i	$0.582183\pi$
$224$		0			0
$225$	27.1788	−	21.3243i	1.81192	−	1.42162i
$226$		0			0
$227$	19.0279			1.26293			0.631464	−	0.775405i	$-0.282454\pi$
$227$	19.0279			1.26293			0.631464	+	0.775405i	$0.282454\pi$
$228$		0			0
$229$	7.57460	+	13.1196i	0.500544	+	0.866967i	1.00000		0.000627856i	$0.000199853\pi$
$229$	7.57460	+	13.1196i	0.500544	+	0.866967i	−0.499456	+	0.866339i	$0.666467\pi$
$230$		0			0
$231$	12.7619	−	4.40893i	0.839672	−	0.290086i
$232$		0			0
$233$	−20.1509			−1.32013			−0.660064	−	0.751209i	$-0.729471\pi$
$233$	−20.1509			−1.32013			−0.660064	+	0.751209i	$0.729471\pi$
$234$		0			0
$235$	−30.6009			−1.99618
$236$		0			0
$237$	9.78295	+	8.48659i	0.635471	+	0.551263i
$238$		0			0
$239$	−1.15357	−	1.99805i	−0.0746186	−	0.129243i	0.826302	−	0.563228i	$-0.190441\pi$
$239$	−1.15357	−	1.99805i	−0.0746186	−	0.129243i	−0.900920	+	0.433985i	$0.857107\pi$
$240$		0			0
$241$	−11.7563			−0.757288			−0.378644	−	0.925542i	$-0.623610\pi$
$241$	−11.7563			−0.757288			−0.378644	+	0.925542i	$0.623610\pi$
$242$		0			0
$243$	−12.7233	+	9.00654i	−0.816200	+	0.577770i
$244$		0			0
$245$	−11.1295	−	19.2768i	−0.711037	−	1.23155i
$246$		0			0
$247$	2.23028	−	1.12799i	0.141909	−	0.0717722i
$248$		0			0
$249$	10.5235	+	9.12903i	0.666902	+	0.578529i
$250$		0			0
$251$	−9.40736	−	16.2940i	−0.593787	−	1.02847i	−0.993717	−	0.111924i	$-0.964299\pi$
$251$	−9.40736	−	16.2940i	−0.593787	−	1.02847i	0.399929	−	0.916546i	$-0.369035\pi$
$252$		0			0
$253$	4.46622	+	7.73572i	0.280789	+	0.486341i
$254$		0			0
$255$	26.0740	+	22.6188i	1.63281	+	1.41645i
$256$		0			0
$257$	−3.59795			−0.224434			−0.112217	−	0.993684i	$-0.535795\pi$
$257$	−3.59795			−0.224434			−0.112217	+	0.993684i	$0.535795\pi$
$258$		0			0
$259$	1.83502	−	3.17834i	0.114022	−	0.197493i
$260$		0			0
$261$	2.83947	+	19.9075i	0.175759	+	1.23225i
$262$		0			0
$263$	−3.18175	−	5.51095i	−0.196195	−	0.339819i	0.751097	−	0.660192i	$-0.229525\pi$
$263$	−3.18175	−	5.51095i	−0.196195	−	0.339819i	−0.947292	+	0.320373i	$0.896192\pi$
$264$		0			0
$265$	26.8139	+	46.4430i	1.64716	+	2.85297i
$266$		0			0
$267$	17.6789	+	15.3362i	1.08193	+	0.938561i
$268$		0			0
$269$	−4.24582	−	7.35398i	−0.258872	−	0.448380i	0.707068	−	0.707146i	$-0.250018\pi$
$269$	−4.24582	−	7.35398i	−0.258872	−	0.448380i	−0.965940	+	0.258766i	$0.916684\pi$
$270$		0			0
$271$	15.8863	−	27.5159i	0.965023	−	1.67147i	0.255470	−	0.966817i	$-0.417770\pi$
$271$	15.8863	−	27.5159i	0.965023	−	1.67147i	0.709553	−	0.704652i	$-0.248897\pi$
$272$		0			0
$273$	−7.47373	−	1.87904i	−0.452330	−	0.113724i
$274$		0			0
$275$	−72.7442			−4.38664
$276$		0			0
$277$	15.0872			0.906503			0.453252	−	0.891383i	$-0.350264\pi$
$277$	15.0872			0.906503			0.453252	+	0.891383i	$0.350264\pi$
$278$		0			0
$279$	−1.59748	−	11.1999i	−0.0956386	−	0.670522i
$280$		0			0
$281$	−9.06790	+	15.7061i	−0.540945	+	0.936945i	0.457905	+	0.889001i	$0.348600\pi$
$281$	−9.06790	+	15.7061i	−0.540945	+	0.936945i	−0.998850	+	0.0479435i	$0.984733\pi$
$282$		0			0
$283$	−9.52842			−0.566406			−0.283203	−	0.959060i	$-0.591397\pi$
$283$	−9.52842			−0.566406			−0.283203	+	0.959060i	$0.591397\pi$
$284$		0			0
$285$	−3.68568	−	3.19728i	−0.218321	−	0.189390i
$286$		0			0
$287$	−8.78924			−0.518813
$288$		0			0
$289$	−3.52384	+	6.10348i	−0.207285	+	0.359028i
$290$		0			0
$291$	−1.00726	+	5.21042i	−0.0590465	+	0.305440i
$292$		0			0
$293$	0.154098	−	0.266906i	0.00900252	−	0.0155928i	−0.861489	−	0.507776i	$-0.830468\pi$
$293$	0.154098	−	0.266906i	0.00900252	−	0.0155928i	0.870492	+	0.492183i	$0.163801\pi$
$294$		0			0
$295$	−42.4595			−2.47209
$296$		0			0
$297$	32.7852	+	1.61707i	1.90239	+	0.0938317i
$298$		0			0
$299$	0.282058	−	5.09040i	0.0163118	−	0.294386i
$300$		0			0
$301$	1.39879			0.0806251
$302$		0			0
$303$	−10.0124	+	3.45905i	−0.575200	+	0.198717i
$304$		0			0
$305$	11.7103	+	20.2828i	0.670528	+	1.16139i
$306$		0			0
$307$	−30.6770			−1.75083			−0.875415	−	0.483372i	$-0.839412\pi$
$307$	−30.6770			−1.75083			−0.875415	+	0.483372i	$0.839412\pi$
$308$		0			0
$309$	7.11111	−	2.45671i	0.404537	−	0.139757i
$310$		0			0
$311$	11.6222	+	20.1302i	0.659033	+	1.14148i	0.980866	+	0.194682i	$0.0623676\pi$
$311$	11.6222	+	20.1302i	0.659033	+	1.14148i	−0.321833	+	0.946796i	$0.604299\pi$
$312$		0			0
$313$	3.47080	−	6.01160i	0.196181	−	0.339796i	−0.751106	−	0.660182i	$-0.770479\pi$
$313$	3.47080	−	6.01160i	0.196181	−	0.339796i	0.947287	+	0.320386i	$0.103813\pi$
$314$		0			0
$315$	2.12435	+	14.8938i	0.119694	+	0.839171i
$316$		0			0
$317$	6.08590	−	10.5411i	0.341818	−	0.592046i	−0.642952	−	0.765906i	$-0.722291\pi$
$317$	6.08590	−	10.5411i	0.341818	−	0.592046i	0.984770	+	0.173860i	$0.0556241\pi$
$318$		0			0
$319$	21.1721	−	36.6711i	1.18541	−	2.05319i
$320$		0			0
$321$	7.75346	+	6.72603i	0.432756	+	0.375410i
$322$		0			0
$323$	1.69963	−	2.94384i	0.0945698	−	0.163800i
$324$		0			0
$325$	34.7529	+	22.7170i	1.92774	+	1.26011i
$326$		0			0
$327$	0.182096	−	0.941962i	0.0100700	−	0.0520906i
$328$		0			0
$329$	4.64596	−	8.04704i	0.256140	−	0.443648i
$330$		0			0
$331$	−18.6570			−1.02548			−0.512741	−	0.858543i	$-0.671370\pi$
$331$	−18.6570			−1.02548			−0.512741	+	0.858543i	$0.671370\pi$
$332$		0			0
$333$	7.01959	−	5.50753i	0.384671	−	0.301811i
$334$		0			0
$335$	15.0544	+	26.0750i	0.822511	+	1.42463i
$336$		0			0
$337$	−10.0206	−	17.3562i	−0.545858	−	0.945454i	−0.998552	−	0.0537879i	$-0.982871\pi$
$337$	−10.0206	−	17.3562i	−0.545858	−	0.945454i	0.452694	−	0.891666i	$-0.350463\pi$
$338$		0			0
$339$	7.98726	+	6.92885i	0.433808	+	0.376323i
$340$		0			0
$341$	−11.9114	+	20.6311i	−0.645036	+	1.11723i
$342$		0			0
$343$	15.3969			0.831355
$344$		0			0
$345$	−9.40732	+	3.25000i	−0.506473	+	0.174974i
$346$		0			0
$347$	10.1229	−	17.5333i	0.543424	−	0.941239i	−0.455280	−	0.890348i	$-0.650461\pi$
$347$	10.1229	−	17.5333i	0.543424	−	0.941239i	0.998704	−	0.0508902i	$-0.0162059\pi$
$348$		0			0
$349$	−17.9009	−	31.0052i	−0.958212	−	1.65967i	−0.726840	−	0.686807i	$-0.759012\pi$
$349$	−17.9009	−	31.0052i	−0.958212	−	1.65967i	−0.231372	−	0.972865i	$-0.574322\pi$
$350$		0			0
$351$	−15.1578	−	11.0109i	−0.809066	−	0.587718i
$352$		0			0
$353$	−13.2650	−	22.9756i	−0.706022	−	1.22287i	−0.966321	−	0.257339i	$-0.917154\pi$
$353$	−13.2650	−	22.9756i	−0.706022	−	1.22287i	0.260299	−	0.965528i	$-0.416179\pi$
$354$		0			0
$355$	5.53429	−	9.58566i	0.293729	−	0.508754i
$356$		0			0
$357$	−9.90669	+	3.42251i	−0.524317	+	0.181139i
$358$		0			0
$359$	−5.94247			−0.313632			−0.156816	−	0.987628i	$-0.550123\pi$
$359$	−5.94247			−0.313632			−0.156816	+	0.987628i	$0.550123\pi$
$360$		0			0
$361$	9.25975	−	16.0384i	0.487355	−	0.844124i
$362$		0			0
$363$	−37.8207	−	32.8090i	−1.98507	−	1.72202i
$364$		0			0
$365$	−2.95173	−	5.11255i	−0.154501	−	0.267603i
$366$		0			0
$367$	−10.0026	−	17.3250i	−0.522130	−	0.904356i	−0.999669	−	0.0257451i	$-0.991804\pi$
$367$	−10.0026	−	17.3250i	−0.522130	−	0.904356i	0.477538	−	0.878611i	$-0.341529\pi$
$368$		0			0
$369$	−19.8282	−	7.96383i	−1.03221	−	0.414580i
$370$		0			0
$371$	−16.2840			−0.845424
$372$		0			0
$373$	9.86899	−	17.0936i	0.510997	−	0.885073i	−0.488922	−	0.872328i	$-0.662610\pi$
$373$	9.86899	−	17.0936i	0.510997	−	0.885073i	0.999919	−	0.0127450i	$-0.00405696\pi$
$374$		0			0
$375$	8.70437	−	45.0266i	0.449492	−	2.32517i
$376$		0			0
$377$	−21.5666	+	10.9075i	−1.11074	+	0.561767i
$378$		0			0
$379$	−1.58794	+	2.75040i	−0.0815672	+	0.141278i	−0.903923	−	0.427695i	$-0.859326\pi$
$379$	−1.58794	+	2.75040i	−0.0815672	+	0.141278i	0.822356	+	0.568973i	$0.192659\pi$
$380$		0			0
$381$	11.5249	+	9.99770i	0.590438	+	0.512198i
$382$		0			0
$383$	−1.75166	+	3.03397i	−0.0895058	+	0.155029i	−0.907302	−	0.420479i	$-0.861862\pi$
$383$	−1.75166	+	3.03397i	−0.0895058	+	0.155029i	0.817797	+	0.575507i	$0.195195\pi$
$384$		0			0
$385$	15.8399	−	27.4355i	0.807275	−	1.39824i
$386$		0			0
$387$	3.15562	+	1.26743i	0.160409	+	0.0644271i
$388$		0			0
$389$	7.61988	−	13.1980i	0.386343	−	0.669166i	−0.605612	−	0.795760i	$-0.707071\pi$
$389$	7.61988	−	13.1980i	0.386343	−	0.669166i	0.991955	+	0.126595i	$0.0404048\pi$
$390$		0			0
$391$	−3.46699	−	6.00501i	−0.175333	−	0.303686i
$392$		0			0
$393$	−18.7124	+	6.46465i	−0.943913	+	0.326099i
$394$		0			0
$395$	30.3868			1.52893
$396$		0			0
$397$	−6.12766	−	10.6134i	−0.307538	−	0.532672i	0.670285	−	0.742104i	$-0.266172\pi$
$397$	−6.12766	−	10.6134i	−0.307538	−	0.532672i	−0.977823	+	0.209432i	$0.932839\pi$
$398$		0			0
$399$	1.40036	−	0.483789i	0.0701055	−	0.0242197i
$400$		0			0
$401$	14.1903			0.708632			0.354316	−	0.935126i	$-0.384714\pi$
$401$	14.1903			0.708632			0.354316	+	0.935126i	$0.384714\pi$
$402$		0			0
$403$	12.1333	−	6.13655i	0.604403	−	0.305684i
$404$		0			0
$405$	−8.70265	+	35.5247i	−0.432438	+	1.76523i
$406$		0			0
$407$	−18.7880			−0.931285
$408$		0			0
$409$	−7.54929	+	13.0758i	−0.373289	+	0.646555i	−0.990069	−	0.140580i	$-0.955103\pi$
$409$	−7.54929	+	13.0758i	−0.373289	+	0.646555i	0.616781	+	0.787135i	$0.288437\pi$
$410$		0			0
$411$	−3.84765	+	19.9034i	−0.189790	+	0.981762i
$412$		0			0
$413$	6.44639	−	11.1655i	0.317206	−	0.549417i
$414$		0			0
$415$	32.6872			1.60455
$416$		0			0
$417$	−9.15152	−	7.93884i	−0.448152	−	0.388766i
$418$		0			0
$419$	14.9144			0.728617			0.364309	−	0.931278i	$-0.381305\pi$
$419$	14.9144			0.728617			0.364309	+	0.931278i	$0.381305\pi$
$420$		0			0
$421$	5.12630	−	8.87902i	0.249841	−	0.432737i	−0.713641	−	0.700512i	$-0.752955\pi$
$421$	5.12630	−	8.87902i	0.249841	−	0.432737i	0.963481	+	0.267775i	$0.0862884\pi$
$422$		0			0
$423$	17.7724	−	13.9441i	0.864125	−	0.677987i
$424$		0			0
$425$	56.4691			2.73915
$426$		0			0
$427$	−7.11162			−0.344156
$428$		0			0
$429$	10.7995	+	37.9439i	0.521404	+	1.83195i
$430$		0			0
$431$	4.95272	−	8.57837i	0.238564	−	0.413206i	−0.721738	−	0.692166i	$-0.756657\pi$
$431$	4.95272	−	8.57837i	0.238564	−	0.413206i	0.960303	+	0.278961i	$0.0899899\pi$
$432$		0			0
$433$	4.64659	+	8.04813i	0.223301	+	0.386768i	0.955808	−	0.293991i	$-0.0949834\pi$
$433$	4.64659	+	8.04813i	0.223301	+	0.386768i	−0.732507	+	0.680759i	$0.761650\pi$
$434$		0			0
$435$	35.6402	+	30.9174i	1.70881	+	1.48238i
$436$		0			0
$437$	0.490076	+	0.848836i	0.0234435	+	0.0406053i
$438$		0			0
$439$	−4.44439	−	7.69790i	−0.212119	−	0.367401i	0.740259	−	0.672322i	$-0.234703\pi$
$439$	−4.44439	−	7.69790i	−0.212119	−	0.367401i	−0.952377	+	0.304922i	$0.901370\pi$
$440$		0			0
$441$	15.2478	+	6.12418i	0.726088	+	0.291627i
$442$		0			0
$443$	−16.7207	+	28.9612i	−0.794426	+	1.37599i	0.128777	+	0.991674i	$0.458895\pi$
$443$	−16.7207	+	28.9612i	−0.794426	+	1.37599i	−0.923203	+	0.384313i	$0.874438\pi$
$444$		0			0
$445$	54.9124			2.60310
$446$		0			0
$447$	−11.9127	−	10.3341i	−0.563451	−	0.488787i
$448$		0			0
$449$	6.81689	+	11.8072i	0.321709	+	0.557216i	0.980841	−	0.194811i	$-0.0624095\pi$
$449$	6.81689	+	11.8072i	0.321709	+	0.557216i	−0.659132	+	0.752027i	$0.729076\pi$
$450$		0			0
$451$	22.4973	+	38.9665i	1.05936	+	1.83486i
$452$		0			0
$453$	0.485675	+	0.421317i	0.0228190	+	0.0197952i
$454$		0			0
$455$	−16.1350	+	8.16047i	−0.756422	+	0.382569i
$456$		0			0
$457$	−2.40357	−	4.16311i	−0.112434	−	0.194742i	0.804317	−	0.594201i	$-0.202531\pi$
$457$	−2.40357	−	4.16311i	−0.112434	−	0.194742i	−0.916751	+	0.399459i	$0.869198\pi$
$458$		0			0
$459$	−25.4502	−	1.25528i	−1.18791	−	0.0585914i
$460$		0			0
$461$	27.9065			1.29973			0.649867	−	0.760048i	$-0.274825\pi$
$461$	27.9065			1.29973			0.649867	+	0.760048i	$0.274825\pi$
$462$		0			0
$463$	5.16665	+	8.94891i	0.240115	+	0.415891i	0.960747	−	0.277427i	$-0.0894816\pi$
$463$	5.16665	+	8.94891i	0.240115	+	0.415891i	−0.720632	+	0.693318i	$0.756148\pi$
$464$		0			0
$465$	−20.0511	−	17.3940i	−0.929845	−	0.806629i
$466$		0			0
$467$	−10.3158			−0.477359			−0.238679	−	0.971098i	$-0.576714\pi$
$467$	−10.3158			−0.477359			−0.238679	+	0.971098i	$0.576714\pi$
$468$		0			0
$469$	−9.14252			−0.422162
$470$		0			0
$471$	2.24761	−	0.776492i	0.103564	−	0.0357789i
$472$		0			0
$473$	−3.58041	−	6.20145i	−0.164627	−	0.285143i
$474$		0			0
$475$	−7.98218			−0.366247
$476$		0			0
$477$	−36.7361	−	14.7548i	−1.68203	−	0.675574i
$478$		0			0
$479$	12.2295	+	21.1821i	0.558780	+	0.967836i	0.997599	+	0.0692603i	$0.0220639\pi$
$479$	12.2295	+	21.1821i	0.558780	+	0.967836i	−0.438818	+	0.898576i	$0.644603\pi$
$480$		0			0
$481$	8.97577	+	5.86721i	0.409260	+	0.267522i
$482$		0			0
$483$	0.573618	−	2.96725i	0.0261005	−	0.135015i
$484$		0			0
$485$	6.22575	+	10.7833i	0.282697	+	0.489645i
$486$		0			0
$487$	−2.64195	−	4.57600i	−0.119718	−	0.207358i	0.799938	−	0.600083i	$-0.204866\pi$
$487$	−2.64195	−	4.57600i	−0.119718	−	0.207358i	−0.919656	+	0.392725i	$0.871532\pi$
$488$		0			0
$489$	27.9482	−	9.65542i	1.26386	−	0.436633i
$490$		0			0
$491$	−20.0941			−0.906834			−0.453417	−	0.891299i	$-0.649795\pi$
$491$	−20.0941			−0.906834			−0.453417	+	0.891299i	$0.649795\pi$
$492$		0			0
$493$	−16.4352	+	28.4667i	−0.740206	+	1.28207i
$494$		0			0
$495$	60.5931	−	47.5410i	2.72346	−	2.13681i
$496$		0			0
$497$	1.68048	+	2.91068i	0.0753798	+	0.130562i
$498$		0			0
$499$	−13.0843	−	22.6626i	−0.585733	−	1.01452i	−0.994784	−	0.102007i	$-0.967473\pi$
$499$	−13.0843	−	22.6626i	−0.585733	−	1.01452i	0.409051	−	0.912512i	$-0.365860\pi$
$500$		0			0
$501$	−1.03539	+	5.35593i	−0.0462577	+	0.239285i
$502$		0			0
$503$	−10.6471	−	18.4414i	−0.474732	−	0.822260i	0.524849	−	0.851195i	$-0.324122\pi$
$503$	−10.6471	−	18.4414i	−0.474732	−	0.822260i	−0.999581	+	0.0289349i	$0.990788\pi$
$504$		0			0
$505$	−12.4273	+	21.5247i	−0.553006	+	0.957835i
$506$		0			0
$507$	6.68998	−	21.4999i	0.297112	−	0.954843i
$508$		0			0
$509$	22.6648			1.00460			0.502299	−	0.864694i	$-0.332487\pi$
$509$	22.6648			1.00460			0.502299	+	0.864694i	$0.332487\pi$
$510$		0			0
$511$	1.79258			0.0792990
$512$		0			0
$513$	3.59750	+	0.177440i	0.158834	+	0.00783415i
$514$		0			0
$515$	8.82618	−	15.2874i	0.388928	−	0.673643i
$516$		0			0
$517$	−47.5680			−2.09204
$518$		0			0
$519$	−2.89384	+	14.9695i	−0.127026	+	0.657087i
$520$		0			0
$521$	12.1834			0.533765			0.266883	−	0.963729i	$-0.414006\pi$
$521$	12.1834			0.533765			0.266883	+	0.963729i	$0.414006\pi$
$522$		0			0
$523$	17.2158	−	29.8186i	0.752794	−	1.30388i	−0.193670	−	0.981067i	$-0.562039\pi$
$523$	17.2158	−	29.8186i	0.752794	−	1.30388i	0.946464	−	0.322810i	$-0.104628\pi$
$524$		0			0
$525$	18.5916	+	16.1280i	0.811403	+	0.703882i
$526$		0			0
$527$	9.24642	−	16.0153i	0.402780	−	0.697636i
$528$		0			0
$529$	−21.0006			−0.913071
$530$		0			0
$531$	24.6597	−	19.3479i	1.07014	−	0.839626i
$532$		0			0
$533$	1.42079	−	25.6415i	0.0615412	−	1.11066i
$534$		0			0
$535$	24.0830			1.04120
$536$		0			0
$537$	−28.3625	−	24.6042i	−1.22393	−	1.06175i
$538$		0			0
$539$	−17.3004	−	29.9652i	−0.745181	−	1.29069i
$540$		0			0
$541$	−44.8888			−1.92992			−0.964960	−	0.262398i	$-0.915487\pi$
$541$	−44.8888			−1.92992			−0.964960	+	0.262398i	$0.915487\pi$
$542$		0			0
$543$	−5.70825	+	29.5281i	−0.244964	+	1.26717i
$544$		0			0
$545$	−1.12552	−	1.94946i	−0.0482119	−	0.0835055i
$546$		0			0
$547$	0.758838	−	1.31435i	0.0324456	−	0.0561974i	−0.849347	−	0.527835i	$-0.823004\pi$
$547$	0.758838	−	1.31435i	0.0324456	−	0.0561974i	0.881792	+	0.471638i	$0.156337\pi$
$548$		0			0
$549$	−16.0435	−	6.44376i	−0.684721	−	0.275013i
$550$		0			0
$551$	2.32320	−	4.02390i	0.0989716	−	0.171424i
$552$		0			0
$553$	−4.61346	+	7.99075i	−0.196184	+	0.339801i
$554$		0			0
$555$	3.97338	−	20.5538i	0.168661	−	0.872460i
$556$		0			0
$557$	−11.0013	+	19.0548i	−0.466139	+	0.807376i	−0.999252	−	0.0386680i	$-0.987689\pi$
$557$	−11.0013	+	19.0548i	−0.466139	+	0.807376i	0.533114	+	0.846044i	$0.321022\pi$
$558$		0			0
$559$	−0.226116	+	4.08080i	−0.00956369	+	0.172599i
$560$		0			0
$561$	40.5311	+	35.1602i	1.71122	+	1.48446i
$562$		0			0
$563$	3.71374	−	6.43238i	0.156515	−	0.271093i	−0.777094	−	0.629384i	$-0.783307\pi$
$563$	3.71374	−	6.43238i	0.156515	−	0.271093i	0.933610	+	0.358291i	$0.116641\pi$
$564$		0			0
$565$	24.8092			1.04373
$566$		0			0
$567$	−8.02056	−	7.68203i	−0.336832	−	0.322615i
$568$		0			0
$569$	−12.7578	−	22.0972i	−0.534836	−	0.926362i	−0.999171	−	0.0407030i	$-0.987040\pi$
$569$	−12.7578	−	22.0972i	−0.534836	−	0.926362i	0.464336	−	0.885659i	$-0.346293\pi$
$570$		0			0
$571$	−13.2087	−	22.8782i	−0.552769	−	0.957423i	−0.998073	−	0.0620443i	$-0.980238\pi$
$571$	−13.2087	−	22.8782i	−0.552769	−	0.957423i	0.445305	−	0.895379i	$-0.353095\pi$
$572$		0			0
$573$	−0.736228	+	3.80841i	−0.0307564	+	0.159099i
$574$		0			0
$575$	−8.14124	+	14.1010i	−0.339513	+	0.588054i
$576$		0			0
$577$	8.20970			0.341774			0.170887	−	0.985291i	$-0.445337\pi$
$577$	8.20970			0.341774			0.170887	+	0.985291i	$0.445337\pi$
$578$		0			0
$579$	6.21424	−	32.1455i	0.258255	−	1.33592i
$580$		0			0
$581$	−4.96271	+	8.59566i	−0.205888	+	0.356608i
$582$		0			0
$583$	41.6813	+	72.1941i	1.72626	+	2.98997i
$584$		0			0
$585$	−43.7941	+	3.78992i	−1.81066	+	0.156694i
$586$		0			0
$587$	−8.07874	−	13.9928i	−0.333445	−	0.577544i	0.649740	−	0.760157i	$-0.274878\pi$
$587$	−8.07874	−	13.9928i	−0.333445	−	0.577544i	−0.983185	+	0.182612i	$0.941545\pi$
$588$		0			0
$589$	−1.30702	+	2.26383i	−0.0538550	+	0.0932796i
$590$		0			0
$591$	10.7219	+	9.30110i	0.441039	+	0.382596i
$592$		0			0
$593$	38.1696			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$593$	38.1696			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$594$		0			0
$595$	−12.2960	+	21.2973i	−0.504087	+	0.873105i
$596$		0			0
$597$	2.50686	−	0.866057i	0.102599	−	0.0354454i
$598$		0			0
$599$	−10.0046	−	17.3285i	−0.408778	−	0.708024i	0.585975	−	0.810329i	$-0.300712\pi$
$599$	−10.0046	−	17.3285i	−0.408778	−	0.708024i	−0.994753	+	0.102305i	$0.967378\pi$
$600$		0			0
$601$	4.50392	+	7.80102i	0.183719	+	0.318210i	0.943144	−	0.332384i	$-0.107853\pi$
$601$	4.50392	+	7.80102i	0.183719	+	0.318210i	−0.759425	+	0.650595i	$0.774520\pi$
$602$		0			0
$603$	−20.6252	−	8.28393i	−0.839921	−	0.337348i
$604$		0			0
$605$	−117.475			−4.77603
$606$		0			0
$607$	−14.3741	+	24.8967i	−0.583427	+	1.01053i	0.411642	+	0.911345i	$0.364955\pi$
$607$	−14.3741	+	24.8967i	−0.583427	+	1.01053i	−0.995070	+	0.0991800i	$0.968378\pi$
$608$		0			0
$609$	−13.5413	+	4.67819i	−0.548722	+	0.189570i
$610$		0			0
$611$	22.7252	+	14.8548i	0.919361	+	0.600960i
$612$		0			0
$613$	4.46519	−	7.73394i	0.180347	−	0.312371i	−0.761651	−	0.647987i	$-0.775611\pi$
$613$	4.46519	−	7.73394i	0.180347	−	0.312371i	0.941999	+	0.335616i	$0.108944\pi$
$614$		0			0
$615$	−47.3867	+	16.3709i	−1.91082	+	0.660140i
$616$		0			0
$617$	−9.34148	+	16.1799i	−0.376074	+	0.651379i	−0.990487	−	0.137605i	$-0.956059\pi$
$617$	−9.34148	+	16.1799i	−0.376074	+	0.651379i	0.614413	+	0.788984i	$0.289393\pi$
$618$		0			0
$619$	9.16531	−	15.8748i	0.368385	−	0.638061i	−0.620928	−	0.783867i	$-0.713244\pi$
$619$	9.16531	−	15.8748i	0.368385	−	0.638061i	0.989313	+	0.145806i	$0.0465776\pi$
$620$		0			0
$621$	3.98265	−	6.17425i	0.159818	−	0.247764i
$622$		0			0
$623$	−8.33705	+	14.4402i	−0.334017	+	0.578534i
$624$		0			0
$625$	−25.0126	−	43.3231i	−1.00050	−	1.73292i
$626$		0			0
$627$	−5.72926	−	4.97006i	−0.228804	−	0.198485i
$628$		0			0
$629$	14.5845			0.581523
$630$		0			0
$631$	−4.52993	−	7.84607i	−0.180334	−	0.312347i	0.761660	−	0.647976i	$-0.224384\pi$
$631$	−4.52993	−	7.84607i	−0.180334	−	0.312347i	−0.941994	+	0.335629i	$0.891051\pi$
$632$		0			0
$633$	6.04669	−	31.2788i	0.240334	−	1.24322i
$634$		0			0
$635$	35.7975			1.42058
$636$		0			0
$637$	−1.09258	+	19.7182i	−0.0432898	+	0.781265i
$638$		0			0
$639$	1.15376	+	8.08903i	0.0456422	+	0.319997i
$640$		0			0
$641$	17.6912			0.698760			0.349380	−	0.936981i	$-0.386392\pi$
$641$	17.6912			0.698760			0.349380	+	0.936981i	$0.386392\pi$
$642$		0			0
$643$	−22.9864	+	39.8137i	−0.906497	+	1.57010i	−0.0876021	+	0.996156i	$0.527920\pi$
$643$	−22.9864	+	39.8137i	−0.906497	+	1.57010i	−0.818895	+	0.573943i	$0.805413\pi$
$644$		0			0
$645$	7.54152	−	2.60541i	0.296947	−	0.102588i
$646$		0			0
$647$	18.5411	−	32.1142i	0.728927	−	1.26254i	−0.228411	−	0.973565i	$-0.573353\pi$
$647$	18.5411	−	32.1142i	0.728927	−	1.26254i	0.957337	−	0.288973i	$-0.0933138\pi$
$648$		0			0
$649$	−66.0018			−2.59080
$650$		0			0
$651$	7.61831	−	2.63194i	0.298585	−	0.103154i
$652$		0			0
$653$	25.8466			1.01146			0.505728	−	0.862693i	$-0.331224\pi$
$653$	25.8466			1.01146			0.505728	+	0.862693i	$0.331224\pi$
$654$		0			0
$655$	−23.2255	+	40.2277i	−0.907494	+	1.57183i
$656$		0			0
$657$	4.04399	+	1.62424i	0.157771	+	0.0633675i
$658$		0			0
$659$	−0.943057			−0.0367363			−0.0183681	−	0.999831i	$-0.505847\pi$
$659$	−0.943057			−0.0367363			−0.0183681	+	0.999831i	$0.505847\pi$
$660$		0			0
$661$	9.86572			0.383732			0.191866	−	0.981421i	$-0.438546\pi$
$661$	9.86572			0.383732			0.191866	+	0.981421i	$0.438546\pi$
$662$		0			0
$663$	−8.38331	−	29.4547i	−0.325581	−	1.14393i
$664$		0			0
$665$	1.73810	−	3.01048i	0.0674006	−	0.116741i
$666$		0			0
$667$	−4.73899	−	8.20817i	−0.183494	−	0.317821i
$668$		0			0
$669$	−34.6983	+	11.9874i	−1.34152	+	0.463460i
$670$		0			0
$671$	18.2032	+	31.5289i	0.702727	+	1.21716i
$672$		0			0
$673$	12.6742	+	21.9524i	0.488555	+	0.846202i	0.999913	−	0.0131657i	$-0.00419088\pi$
$673$	12.6742	+	21.9524i	0.488555	+	0.846202i	−0.511358	+	0.859368i	$0.670858\pi$
$674$		0			0
$675$	27.3285	+	53.2297i	1.05187	+	2.04881i
$676$		0			0
$677$	−20.2261	+	35.0326i	−0.777352	+	1.34641i	0.156111	+	0.987740i	$0.450104\pi$
$677$	−20.2261	+	35.0326i	−0.777352	+	1.34641i	−0.933463	+	0.358674i	$0.883229\pi$
$678$		0			0
$679$	−3.78089			−0.145097
$680$		0			0
$681$	−6.25538	+	32.3583i	−0.239707	+	1.23997i
$682$		0			0
$683$	−11.6007	−	20.0931i	−0.443890	−	0.768840i	0.554084	−	0.832461i	$-0.313069\pi$
$683$	−11.6007	−	20.0931i	−0.443890	−	0.768840i	−0.997974	+	0.0636208i	$0.979735\pi$
$684$		0			0
$685$	23.7819	+	41.1915i	0.908660	+	1.57384i
$686$		0			0
$687$	−24.8009	+	8.56808i	−0.946212	+	0.326893i
$688$		0			0
$689$	2.63233	−	47.5065i	0.100284	−	1.80985i
$690$		0			0
$691$	1.21656	+	2.10714i	0.0462801	+	0.0801595i	0.888238	−	0.459384i	$-0.151930\pi$
$691$	1.21656	+	2.10714i	0.0462801	+	0.0801595i	−0.841957	+	0.539544i	$0.818597\pi$
$692$		0			0
$693$	3.30223	+	23.1519i	0.125441	+	0.879468i
$694$		0			0
$695$	−28.4256			−1.07824
$696$		0			0
$697$	−17.4640	−	30.2485i	−0.661496	−	1.14574i
$698$		0			0
$699$	6.62454	−	34.2679i	0.250563	−	1.29613i
$700$		0			0
$701$	0.254890			0.00962706			0.00481353	−	0.999988i	$-0.498468\pi$
$701$	0.254890			0.00962706			0.00481353	+	0.999988i	$0.498468\pi$
$702$		0			0
$703$	−2.06159			−0.0777544
$704$		0			0
$705$	10.0599	−	52.0388i	0.378879	−	1.95989i
$706$		0			0
$707$	−3.77353	−	6.53594i	−0.141918	−	0.245809i
$708$		0			0
$709$	12.1334			0.455681			0.227840	−	0.973698i	$-0.426834\pi$
$709$	12.1334			0.455681			0.227840	+	0.973698i	$0.426834\pi$
$710$		0			0
$711$	−17.6481	+	13.8466i	−0.661856	+	0.519288i
$712$		0			0
$713$	2.66614	+	4.61789i	0.0998478	+	0.172941i
$714$		0			0
$715$	77.4788	+	50.6457i	2.89754	+	1.89404i
$716$		0			0
$717$	3.77705	−	1.30488i	0.141057	−	0.0487315i
$718$		0			0
$719$	26.3387	+	45.6200i	0.982268	+	1.70134i	0.653497	+	0.756929i	$0.273301\pi$
$719$	26.3387	+	45.6200i	0.982268	+	1.70134i	0.328771	+	0.944410i	$0.393365\pi$
$720$		0			0
$721$	2.68006	+	4.64200i	0.0998107	+	0.172877i
$722$		0			0
$723$	3.86484	−	19.9923i	0.143735	−	0.743522i
$724$		0			0
$725$	77.1869			2.86665
$726$		0			0
$727$	−1.58322	+	2.74222i	−0.0587184	+	0.101703i	−0.893890	−	0.448286i	$-0.852035\pi$
$727$	−1.58322	+	2.74222i	−0.0587184	+	0.101703i	0.835172	+	0.549989i	$0.185368\pi$
$728$		0			0
$729$	−11.1335	−	24.5977i	−0.412351	−	0.911025i
$730$		0			0
$731$	2.77936	+	4.81400i	0.102799	+	0.178052i
$732$		0			0
$733$	11.4180	+	19.7766i	0.421734	+	0.730466i	0.996109	−	0.0881269i	$-0.0280881\pi$
$733$	11.4180	+	19.7766i	0.421734	+	0.730466i	−0.574375	+	0.818592i	$0.694755\pi$
$734$		0			0
$735$	36.4403	−	12.5892i	1.34412	−	0.464361i
$736$		0			0
$737$	23.4016	+	40.5327i	0.862009	+	1.49304i
$738$		0			0
$739$	10.9208	−	18.9154i	0.401728	−	0.695813i	−0.592207	−	0.805786i	$-0.701743\pi$
$739$	10.9208	−	18.9154i	0.401728	−	0.695813i	0.993935	+	0.109973i	$0.0350765\pi$
$740$		0			0
$741$	1.18502	+	4.16356i	0.0435328	+	0.152952i
$742$		0			0
$743$	−10.9092			−0.400218			−0.200109	−	0.979774i	$-0.564130\pi$
$743$	−10.9092			−0.400218			−0.200109	+	0.979774i	$0.564130\pi$
$744$		0			0
$745$	−37.0020			−1.35565
$746$		0			0
$747$	−18.9841	+	14.8948i	−0.694592	+	0.544973i
$748$		0			0
$749$	−3.65639	+	6.33306i	−0.133602	+	0.231405i
$750$		0			0
$751$	−29.2500			−1.06735			−0.533674	−	0.845690i	$-0.679189\pi$
$751$	−29.2500			−1.06735			−0.533674	+	0.845690i	$0.679189\pi$
$752$		0			0
$753$	30.8017	−	10.6412i	1.12248	−	0.387788i
$754$		0			0
$755$	1.50856			0.0549020
$756$		0			0
$757$	−15.6746	+	27.1492i	−0.569703	+	0.986755i	0.426892	+	0.904303i	$0.359609\pi$
$757$	−15.6746	+	27.1492i	−0.569703	+	0.986755i	−0.996595	+	0.0824524i	$0.973725\pi$
$758$		0			0
$759$	−14.6234	+	5.05201i	−0.530794	+	0.183376i
$760$		0			0
$761$	−11.6645	+	20.2035i	−0.422838	+	0.732377i	−0.996216	−	0.0869143i	$-0.972299\pi$
$761$	−11.6645	+	20.2035i	−0.422838	+	0.732377i	0.573378	+	0.819291i	$0.305633\pi$
$762$		0			0
$763$	0.683525			0.0247453
$764$		0			0
$765$	−47.0366	+	36.9046i	−1.70061	+	1.33429i
$766$		0			0
$767$	31.5317	+	20.6114i	1.13855	+	0.744235i
$768$		0			0
$769$	8.21952			0.296404			0.148202	−	0.988957i	$-0.452651\pi$
$769$	8.21952			0.296404			0.148202	+	0.988957i	$0.452651\pi$
$770$		0			0
$771$	1.18281	−	6.11855i	0.0425980	−	0.220354i
$772$		0			0
$773$	−19.9461	−	34.5476i	−0.717411	−	1.24259i	−0.962022	−	0.272971i	$-0.911994\pi$
$773$	−19.9461	−	34.5476i	−0.717411	−	1.24259i	0.244611	−	0.969621i	$-0.421340\pi$
$774$		0			0
$775$	−43.4252			−1.55988
$776$		0			0
$777$	4.80173	+	4.16544i	0.172261	+	0.149434i
$778$		0			0
$779$	2.46862	+	4.27577i	0.0884474	+	0.153195i
$780$		0			0
$781$	8.60286	−	14.9006i	0.307834	−	0.533185i
$782$		0			0
$783$	−34.7875	−	1.71583i	−1.24321	−	0.0613186i
$784$		0			0
$785$	2.78969	−	4.83189i	0.0995683	−	0.172457i
$786$		0			0
$787$	−21.0076	+	36.3863i	−0.748841	+	1.29703i	0.199538	+	0.979890i	$0.436056\pi$
$787$	−21.0076	+	36.3863i	−0.748841	+	1.29703i	−0.948379	+	0.317140i	$0.897277\pi$
$788$		0			0
$789$	10.4177	−	3.59906i	0.370881	−	0.128130i
$790$		0			0
$791$	−3.76665	+	6.52403i	−0.133927	+	0.231968i
$792$		0			0
$793$	1.14960	−	20.7472i	0.0408235	−	0.736755i
$794$		0			0
$795$	−87.7944	+	30.3308i	−3.11375	+	1.07572i
$796$		0			0
$797$	14.2345	−	24.6549i	0.504212	−	0.873321i	−0.495776	−	0.868451i	$-0.665116\pi$
$797$	14.2345	−	24.6549i	0.504212	−	0.873321i	0.999988	−	0.00487082i	$-0.00155044\pi$
$798$		0			0
$799$	36.9256			1.30633
$800$		0			0
$801$	−31.8921	+	25.0224i	−1.12685	+	0.884122i
$802$		0			0
$803$	−4.58836	−	7.94728i	−0.161920	−	0.280453i
$804$		0			0
$805$	−3.54547	−	6.14093i	−0.124961	−	0.216439i
$806$		0			0
$807$	13.9017	−	4.80271i	0.489364	−	0.169063i
$808$		0			0
$809$	−25.8229	+	44.7266i	−0.907885	+	1.57250i	−0.0908889	+	0.995861i	$0.528971\pi$
$809$	−25.8229	+	44.7266i	−0.907885	+	1.57250i	−0.816997	+	0.576643i	$0.804363\pi$
$810$		0			0
$811$	−14.1240			−0.495959			−0.247980	−	0.968765i	$-0.579767\pi$
$811$	−14.1240			−0.495959			−0.247980	+	0.968765i	$0.579767\pi$
$812$		0			0
$813$	41.5700	+	36.0614i	1.45792	+	1.26473i
$814$		0			0
$815$	34.6889	−	60.0829i	1.21510	−	2.10461i
$816$		0			0
$817$	−0.392876	−	0.680482i	−0.0137450	−	0.0238070i
$818$		0			0
$819$	5.65239	−	12.0918i	0.197511	−	0.422523i
$820$		0			0
$821$	11.3074	+	19.5850i	0.394632	+	0.683522i	0.993054	−	0.117659i	$-0.0375389\pi$
$821$	11.3074	+	19.5850i	0.394632	+	0.683522i	−0.598422	+	0.801181i	$0.704206\pi$
$822$		0			0
$823$	2.12463	−	3.67997i	0.0740600	−	0.128276i	−0.826617	−	0.562765i	$-0.809738\pi$
$823$	2.12463	−	3.67997i	0.0740600	−	0.128276i	0.900677	+	0.434489i	$0.143071\pi$
$824$		0			0
$825$	23.9144	−	123.706i	0.832594	−	4.30690i
$826$		0			0
$827$	−4.50665			−0.156711			−0.0783557	−	0.996925i	$-0.524967\pi$
$827$	−4.50665			−0.156711			−0.0783557	+	0.996925i	$0.524967\pi$
$828$		0			0
$829$	4.99777	−	8.65638i	0.173580	−	0.300649i	−0.766089	−	0.642734i	$-0.777800\pi$
$829$	4.99777	−	8.65638i	0.173580	−	0.300649i	0.939669	+	0.342086i	$0.111133\pi$
$830$		0			0
$831$	−4.95988	+	25.6568i	−0.172056	+	0.890025i
$832$		0			0
$833$	13.4298	+	23.2611i	0.465314	+	0.805948i
$834$		0			0
$835$	6.39962	+	11.0845i	0.221468	+	0.383594i
$836$		0			0
$837$	19.5714	+	0.965319i	0.676485	+	0.0333663i
$838$		0			0
$839$	9.27534			0.320220			0.160110	−	0.987099i	$-0.448815\pi$
$839$	9.27534			0.320220			0.160110	+	0.987099i	$0.448815\pi$
$840$		0			0
$841$	−7.96513	+	13.7960i	−0.274660	+	0.475724i
$842$		0			0
$843$	−23.7281	−	20.5839i	−0.817241	−	0.708946i
$844$		0			0
$845$	−21.1989	−	48.3910i	−0.729263	−	1.66470i
$846$		0			0
$847$	17.8355	−	30.8921i	0.612837	−	1.06146i
$848$		0			0
$849$	3.13244	−	16.2037i	0.107505	−	0.556110i
$850$		0			0
$851$	−2.10267	+	3.64194i	−0.0720787	+	0.124844i
$852$		0			0
$853$	8.60320	−	14.9012i	0.294568	−	0.510207i	−0.680316	−	0.732919i	$-0.738158\pi$
$853$	8.60320	−	14.9012i	0.294568	−	0.510207i	0.974884	+	0.222712i	$0.0714909\pi$
$854$		0			0
$855$	6.64884	−	5.21664i	0.227385	−	0.178405i
$856$		0			0
$857$	10.2451	−	17.7450i	0.349964	−	0.606156i	−0.636278	−	0.771460i	$-0.719527\pi$
$857$	10.2451	−	17.7450i	0.349964	−	0.606156i	0.986243	+	0.165303i	$0.0528603\pi$
$858$		0			0
$859$	8.09018	+	14.0126i	0.276034	+	0.478104i	0.970395	−	0.241522i	$-0.0776466\pi$
$859$	8.09018	+	14.0126i	0.276034	+	0.478104i	−0.694362	+	0.719626i	$0.744313\pi$
$860$		0			0
$861$	2.88944	−	14.9467i	0.0984717	−	0.509382i
$862$		0			0
$863$	−26.3268			−0.896176			−0.448088	−	0.893989i	$-0.647895\pi$
$863$	−26.3268			−0.896176			−0.448088	+	0.893989i	$0.647895\pi$
$864$		0			0
$865$	17.8865	+	30.9804i	0.608160	+	1.05336i
$866$		0			0
$867$	−9.22091	−	7.99903i	−0.313159	−	0.271661i
$868$		0			0
$869$	47.2353			1.60235
$870$		0			0
$871$	1.47790	−	26.6721i	0.0500766	−	0.903750i
$872$		0			0
$873$	−8.52952	−	3.42582i	−0.288681	−	0.115946i
$874$		0			0
$875$	32.6731			1.10455
$876$		0			0
$877$	16.7190	−	28.9581i	0.564559	−	0.977845i	−0.432532	−	0.901619i	$-0.642380\pi$
$877$	16.7190	−	28.9581i	0.564559	−	0.977845i	0.997091	−	0.0762261i	$-0.0242871\pi$
$878$		0			0
$879$	0.403232	+	0.349799i	0.0136007	+	0.0117984i
$880$		0			0
$881$	−1.74235	+	3.01783i	−0.0587011	+	0.101673i	−0.893883	−	0.448301i	$-0.852029\pi$
$881$	−1.74235	+	3.01783i	−0.0587011	+	0.101673i	0.835181	+	0.549974i	$0.185363\pi$
$882$		0			0
$883$	−21.7609			−0.732313			−0.366156	−	0.930553i	$-0.619326\pi$
$883$	−21.7609			−0.732313			−0.366156	+	0.930553i	$0.619326\pi$
$884$		0			0
$885$	13.9584	−	72.2052i	0.469208	−	2.42715i
$886$		0			0
$887$	−34.8933			−1.17160			−0.585802	−	0.810454i	$-0.699220\pi$
$887$	−34.8933			−1.17160			−0.585802	+	0.810454i	$0.699220\pi$
$888$		0			0
$889$	−5.43493	+	9.41358i	−0.182282	+	0.315721i
$890$		0			0
$891$	−13.5280	+	55.2219i	−0.453204	+	1.85000i
$892$		0			0
$893$	−5.21960			−0.174667
$894$		0			0
$895$	−88.0969			−2.94476
$896$		0			0
$897$	8.56384	+	2.15311i	0.285938	+	0.0718903i
$898$		0			0
$899$	12.6388	−	21.8911i	0.421528	−	0.730108i
$900$		0			0
$901$	−32.3559	−	56.0421i	−1.07793	−	1.86703i
$902$		0			0
$903$	−0.459849	+	2.37874i	−0.0153028	+	0.0791595i
$904$		0			0
$905$	35.2821	+	61.1104i	1.17282	+	2.03138i
$906$		0			0
$907$	−9.01748	−	15.6187i	−0.299420	−	0.518611i	0.676583	−	0.736366i	$-0.263460\pi$
$907$	−9.01748	−	15.6187i	−0.299420	−	0.518611i	−0.976003	+	0.217755i	$0.930127\pi$
$908$		0			0
$909$	−2.59079	−	18.1640i	−0.0859309	−	0.602461i
$910$		0			0
$911$	−25.8853	+	44.8346i	−0.857617	+	1.48544i	0.0165778	+	0.999863i	$0.494723\pi$
$911$	−25.8853	+	44.8346i	−0.857617	+	1.48544i	−0.874195	+	0.485574i	$0.838610\pi$
$912$		0			0
$913$	50.8111			1.68160
$914$		0			0
$915$	−38.3419	+	13.2462i	−1.26755	+	0.437905i
$916$		0			0
$917$	−7.05239	−	12.2151i	−0.232890	−	0.403378i
$918$		0			0
$919$	25.9608	+	44.9655i	0.856369	+	1.48327i	0.875369	+	0.483455i	$0.160618\pi$
$919$	25.9608	+	44.9655i	0.856369	+	1.48327i	−0.0190005	+	0.999819i	$0.506048\pi$
$920$		0			0
$921$	10.0850	−	52.1683i	0.332311	−	1.71900i
$922$		0			0
$923$	−8.76317	+	4.43207i	−0.288443	+	0.145883i
$924$		0			0
$925$	−17.1238	−	29.6593i	−0.563027	−	0.975191i
$926$		0			0
$927$	1.84005	+	12.9005i	0.0604350	+	0.423709i
$928$		0			0
$929$	−41.6437			−1.36629			−0.683144	−	0.730284i	$-0.739388\pi$
$929$	−41.6437			−1.36629			−0.683144	+	0.730284i	$0.739388\pi$
$930$		0			0
$931$	−1.89836	−	3.28806i	−0.0622163	−	0.107762i
$932$		0			0
$933$	−38.0535	+	13.1465i	−1.24581	+	0.430398i
$934$		0			0
$935$	125.894			4.11716
$936$		0			0
$937$	24.2358			0.791749			0.395875	−	0.918305i	$-0.370441\pi$
$937$	24.2358			0.791749			0.395875	+	0.918305i	$0.370441\pi$
$938$		0			0
$939$	9.08211	+	7.87862i	0.296383	+	0.257109i
$940$		0			0
$941$	0.333504	+	0.577647i	0.0108719	+	0.0188307i	0.871410	−	0.490555i	$-0.163206\pi$
$941$	0.333504	+	0.577647i	0.0108719	+	0.0188307i	−0.860538	+	0.509386i	$0.829873\pi$
$942$		0			0
$943$	10.0712			0.327965
$944$		0			0
$945$	−26.0263	−	1.28369i	−0.846635	−	0.0417586i
$946$		0			0
$947$	6.27850	+	10.8747i	0.204024	+	0.353380i	0.949821	−	0.312793i	$-0.101265\pi$
$947$	6.27850	+	10.8747i	0.204024	+	0.353380i	−0.745797	+	0.666173i	$0.767931\pi$
$948$		0			0
$949$	−0.289772	+	5.22961i	−0.00940639	+	0.169760i
$950$		0			0
$951$	15.9251	+	13.8148i	0.516406	+	0.447976i
$952$		0			0
$953$	3.43257	+	5.94539i	0.111192	+	0.192590i	0.916251	−	0.400604i	$-0.131200\pi$
$953$	3.43257	+	5.94539i	0.111192	+	0.192590i	−0.805059	+	0.593194i	$0.797867\pi$
$954$		0			0
$955$	4.55054	+	7.88177i	0.147252	+	0.255048i
$956$		0			0
$957$	55.4014	+	48.0600i	1.79087	+	1.55356i
$958$		0			0
$959$	−14.4427			−0.466379
$960$		0			0
$961$	8.38944	−	14.5309i	0.270627	−	0.468740i
$962$		0			0
$963$	−13.9870	+	10.9741i	−0.450724	+	0.353636i
$964$		0			0
$965$	−38.4095	−	66.5272i	−1.23645	−	2.14159i
$966$		0			0
$967$	−22.6585	−	39.2457i	−0.728648	−	1.26206i	−0.957455	−	0.288583i	$-0.906816\pi$
$967$	−22.6585	−	39.2457i	−0.728648	−	1.26206i	0.228807	−	0.973472i	$-0.426518\pi$
$968$		0			0
$969$	4.44745	+	3.85811i	0.142873	+	0.123940i
$970$		0			0
$971$	22.8736	+	39.6183i	0.734049	+	1.27141i	0.955139	+	0.296157i	$0.0957052\pi$
$971$	22.8736	+	39.6183i	0.734049	+	1.27141i	−0.221090	+	0.975253i	$0.570961\pi$
$972$		0			0
$973$	4.31570	−	7.47501i	0.138355	−	0.239638i
$974$		0			0
$975$	−50.0566	+	51.6314i	−1.60309	+	1.65353i
$976$		0			0
$977$	−19.6241			−0.627830			−0.313915	−	0.949451i	$-0.601641\pi$
$977$	−19.6241			−0.627830			−0.313915	+	0.949451i	$0.601641\pi$
$978$		0			0
$979$	85.3595			2.72810
$980$		0			0
$981$	1.54200	+	0.619334i	0.0492324	+	0.0197738i
$982$		0			0
$983$	21.4131	−	37.0886i	0.682972	−	1.18294i	−0.291098	−	0.956693i	$-0.594020\pi$
$983$	21.4131	−	37.0886i	0.682972	−	1.18294i	0.974070	−	0.226249i	$-0.0726462\pi$
$984$		0			0
$985$	33.3032			1.06113
$986$		0			0
$987$	12.1572	+	10.5462i	0.386967	+	0.335689i
$988$		0			0
$989$	−1.60282			−0.0509667
$990$		0			0
$991$	24.4276	−	42.3099i	0.775969	−	1.34402i	−0.158279	−	0.987394i	$-0.550595\pi$
$991$	24.4276	−	42.3099i	0.775969	−	1.34402i	0.934248	−	0.356623i	$-0.116072\pi$
$992$		0			0
$993$	6.13343	−	31.7275i	0.194639	−	1.00684i
$994$		0			0
$995$	3.11147	−	5.38922i	0.0986402	−	0.170850i
$996$		0			0
$997$	17.0256			0.539208			0.269604	−	0.962971i	$-0.413107\pi$
$997$	17.0256			0.539208			0.269604	+	0.962971i	$0.413107\pi$
$998$		0			0
$999$	7.05825	+	13.7479i	0.223313	+	0.434963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.k.a.61.7	yes	28
3.2	odd	2		1404.2.k.a.1153.1		28
9.4	even	3		468.2.j.a.373.3	yes	28
9.5	odd	6		1404.2.j.a.685.1		28
13.3	even	3		468.2.j.a.133.3	✓	28
39.29	odd	6		1404.2.j.a.289.1		28
117.68	odd	6		1404.2.k.a.1225.1		28
117.94	even	3	inner	468.2.k.a.445.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.3	✓	28	13.3	even	3
468.2.j.a.373.3	yes	28	9.4	even	3
468.2.k.a.61.7	yes	28	1.1	even	1	trivial
468.2.k.a.445.7	yes	28	117.94	even	3	inner
1404.2.j.a.289.1		28	39.29	odd	6
1404.2.j.a.685.1		28	9.5	odd	6
1404.2.k.a.1153.1		28	3.2	odd	2
1404.2.k.a.1225.1		28	117.68	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.328747 + 1.70057i) q^{3} +(2.03195 + 3.51944i) q^{5} -1.23400 q^{7} +(-2.78385 - 1.11811i) q^{9} +O(q^{10})\)	\(q+(-0.328747 + 1.70057i) q^{3} +(2.03195 + 3.51944i) q^{5} -1.23400 q^{7} +(-2.78385 - 1.11811i) q^{9} +(3.15860 + 5.47085i) q^{11} +(0.199477 - 3.60003i) q^{13} +(-6.65304 + 2.29846i) q^{15} +(-2.45192 - 4.24685i) q^{17} +(0.346591 + 0.600313i) q^{19} +(0.405673 - 2.09850i) q^{21} +1.41399 q^{23} +(-5.75764 + 9.97252i) q^{25} +(2.81661 - 4.36655i) q^{27} +(-3.35150 - 5.80497i) q^{29} +(1.88555 + 3.26586i) q^{31} +(-10.3419 + 3.57288i) q^{33} +(-2.50742 - 4.34298i) q^{35} +(-1.48705 + 2.57565i) q^{37} +(6.05651 + 1.52272i) q^{39} +7.12257 q^{41} -1.13355 q^{43} +(-1.72152 - 12.0695i) q^{45} +(-3.76496 + 6.52111i) q^{47} -5.47725 q^{49} +(8.02812 - 2.77352i) q^{51} +13.1961 q^{53} +(-12.8362 + 22.2330i) q^{55} +(-1.13481 + 0.392049i) q^{57} +(-5.22399 + 9.04821i) q^{59} +5.76307 q^{61} +(3.43527 + 1.37975i) q^{63} +(13.0754 - 6.61303i) q^{65} +7.40886 q^{67} +(-0.464845 + 2.40458i) q^{69} +(-1.36182 - 2.35874i) q^{71} -1.45266 q^{73} +(-15.0661 - 13.0697i) q^{75} +(-3.89770 - 6.75102i) q^{77} +(3.73863 - 6.47550i) q^{79} +(6.49965 + 6.22531i) q^{81} +(4.02165 - 6.96570i) q^{83} +(9.96436 - 17.2588i) q^{85} +(10.9735 - 3.79108i) q^{87} +(6.75612 - 11.7020i) q^{89} +(-0.246154 + 4.44243i) q^{91} +(-6.17368 + 2.13285i) q^{93} +(-1.40851 + 2.43961i) q^{95} +3.06393 q^{97} +(-2.67604 - 18.7617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 28 * q - 4 * q^7 - 2 * q^9	\( 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43} - 38 q^{45} + 11 q^{47} + 24 q^{49} + 5 q^{51} + 52 q^{53} - q^{57} - 8 q^{59} + 14 q^{61} - 21 q^{63} + 38 q^{65} + 14 q^{67} - 21 q^{69} - 12 q^{71} + 14 q^{73} - 14 q^{75} - 28 q^{77} + 5 q^{79} + 10 q^{81} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 11 q^{89} - q^{91} - 9 q^{93} + 28 q^{95} + 50 q^{97} - 29 q^{99}+O(q^{100}) \) 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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