LMFDB - Embedded newform 684.3.m.a.353.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.9
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38029 + 1.82598i) q^{3} +5.89395i q^{5} +(-0.351537 + 0.608880i) q^{7} +(2.33159 - 8.69274i) q^{9} +O(q^{10})$	\(q+(-2.38029 + 1.82598i) q^{3} +5.89395i q^{5} +(-0.351537 + 0.608880i) q^{7} +(2.33159 - 8.69274i) q^{9} +(15.3415 + 8.85744i) q^{11} +(7.81809 - 13.5413i) q^{13} +(-10.7622 - 14.0293i) q^{15} +(19.3842 + 11.1915i) q^{17} +(18.0937 - 5.79811i) q^{19} +(-0.275041 - 2.09121i) q^{21} +(2.81046 + 1.62262i) q^{23} -9.73867 q^{25} +(10.3229 + 24.9487i) q^{27} +7.47447i q^{29} +(4.28250 + 7.41751i) q^{31} +(-52.6909 + 6.93003i) q^{33} +(-3.58871 - 2.07194i) q^{35} -37.7752 q^{37} +(6.11685 + 46.5080i) q^{39} -52.3411i q^{41} +(-3.07286 - 5.32236i) q^{43} +(51.2346 + 13.7423i) q^{45} +71.9825i q^{47} +(24.2528 + 42.0072i) q^{49} +(-66.5755 + 8.75617i) q^{51} +(-20.4757 + 11.8217i) q^{53} +(-52.2053 + 90.4223i) q^{55} +(-32.4811 + 46.8399i) q^{57} -54.8968i q^{59} -69.6850 q^{61} +(4.47319 + 4.47548i) q^{63} +(79.8119 + 46.0794i) q^{65} +(51.2608 - 88.7864i) q^{67} +(-9.65260 + 1.26953i) q^{69} +(-7.22572 - 4.17177i) q^{71} +(-39.6816 + 68.7305i) q^{73} +(23.1809 - 17.7826i) q^{75} +(-10.7862 + 6.22743i) q^{77} +(58.3917 + 101.137i) q^{79} +(-70.1273 - 40.5359i) q^{81} +(86.3290 + 49.8421i) q^{83} +(-65.9620 + 114.250i) q^{85} +(-13.6482 - 17.7914i) q^{87} +(4.82896 - 2.78800i) q^{89} +(5.49669 + 9.52055i) q^{91} +(-23.7378 - 9.83609i) q^{93} +(34.1738 + 106.643i) q^{95} +(-52.8639 - 91.5630i) q^{97} +(112.766 - 112.708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.38029	+	1.82598i	−0.793431	+	0.608660i
$3$	−2.38029	+	1.82598i	−0.793431	+	0.608660i
$4$		0			0
$5$			5.89395i			1.17879i	0.807845	+	0.589395i	$0.200634\pi$
$5$			5.89395i			1.17879i	−0.807845	+	0.589395i	$0.799366\pi$
$6$		0			0
$7$	−0.351537	+	0.608880i	−0.0502196	+	0.0869828i	−0.890042	−	0.455878i	$-0.849325\pi$
$7$	−0.351537	+	0.608880i	−0.0502196	+	0.0869828i	0.839823	+	0.542861i	$0.182659\pi$
$8$		0			0
$9$	2.33159	−	8.69274i	0.259066	−	0.965860i
$10$		0			0
$11$	15.3415	+	8.85744i	1.39468	+	0.805222i	0.993829	−	0.110920i	$-0.0353796\pi$
$11$	15.3415	+	8.85744i	1.39468	+	0.805222i	0.400856	+	0.916141i	$0.368713\pi$
$12$		0			0
$13$	7.81809	−	13.5413i	0.601391	−	1.04164i	−0.391219	−	0.920298i	$-0.627947\pi$
$13$	7.81809	−	13.5413i	0.601391	−	1.04164i	0.992611	−	0.121343i	$-0.0387201\pi$
$14$		0			0
$15$	−10.7622	−	14.0293i	−0.717483	−	0.935289i
$16$		0			0
$17$	19.3842	+	11.1915i	1.14025	+	0.658322i	0.946492	−	0.322728i	$-0.104600\pi$
$17$	19.3842	+	11.1915i	1.14025	+	0.658322i	0.193755	+	0.981050i	$0.437933\pi$
$18$		0			0
$19$	18.0937	−	5.79811i	0.952300	−	0.305164i
$19$	18.0937	−	5.79811i	0.952300	−	0.305164i
$20$		0			0
$21$	−0.275041	−	2.09121i	−0.0130972	−	0.0995815i
$22$		0			0
$23$	2.81046	+	1.62262i	0.122194	+	0.0705487i	0.559851	−	0.828593i	$-0.310858\pi$
$23$	2.81046	+	1.62262i	0.122194	+	0.0705487i	−0.437657	+	0.899142i	$0.644192\pi$
$24$		0			0
$25$	−9.73867			−0.389547
$26$		0			0
$27$	10.3229	+	24.9487i	0.382329	+	0.924026i
$28$		0			0
$29$			7.47447i			0.257740i	0.991661	+	0.128870i	$0.0411351\pi$
$29$			7.47447i			0.257740i	−0.991661	+	0.128870i	$0.958865\pi$
$30$		0			0
$31$	4.28250	+	7.41751i	0.138145	+	0.239275i	0.926795	−	0.375569i	$-0.122553\pi$
$31$	4.28250	+	7.41751i	0.138145	+	0.239275i	−0.788649	+	0.614843i	$0.789219\pi$
$32$		0			0
$33$	−52.6909	+	6.93003i	−1.59669	+	0.210001i
$34$		0			0
$35$	−3.58871	−	2.07194i	−0.102535	−	0.0591983i
$36$		0			0
$37$	−37.7752			−1.02095			−0.510476	−	0.859892i	$-0.670531\pi$
$37$	−37.7752			−1.02095			−0.510476	+	0.859892i	$0.670531\pi$
$38$		0			0
$39$	6.11685	+	46.5080i	0.156842	+	1.19251i
$40$		0			0
$41$		−	52.3411i		−	1.27661i	−0.769783	−	0.638306i	$-0.779636\pi$
$41$		−	52.3411i		−	1.27661i	0.769783	−	0.638306i	$-0.220364\pi$
$42$		0			0
$43$	−3.07286	−	5.32236i	−0.0714620	−	0.123776i	0.828080	−	0.560610i	$-0.189433\pi$
$43$	−3.07286	−	5.32236i	−0.0714620	−	0.123776i	−0.899542	+	0.436834i	$0.856100\pi$
$44$		0			0
$45$	51.2346	+	13.7423i	1.13855	+	0.305384i
$46$		0			0
$47$			71.9825i			1.53154i	0.643113	+	0.765771i	$0.277642\pi$
$47$			71.9825i			1.53154i	−0.643113	+	0.765771i	$0.722358\pi$
$48$		0			0
$49$	24.2528	+	42.0072i	0.494956	+	0.857289i
$50$		0			0
$51$	−66.5755	+	8.75617i	−1.30540	+	0.171690i
$52$		0			0
$53$	−20.4757	+	11.8217i	−0.386334	+	0.223050i	−0.680571	−	0.732682i	$-0.738268\pi$
$53$	−20.4757	+	11.8217i	−0.386334	+	0.223050i	0.294236	+	0.955733i	$0.404935\pi$
$54$		0			0
$55$	−52.2053	+	90.4223i	−0.949188	+	1.64404i
$56$		0			0
$57$	−32.4811	+	46.8399i	−0.569843	+	0.821753i
$58$		0			0
$59$		−	54.8968i		−	0.930454i	−0.885192	−	0.465227i	$-0.845973\pi$
$59$		−	54.8968i		−	0.930454i	0.885192	−	0.465227i	$-0.154027\pi$
$60$		0			0
$61$	−69.6850			−1.14238			−0.571189	−	0.820819i	$-0.693518\pi$
$61$	−69.6850			−1.14238			−0.571189	+	0.820819i	$0.693518\pi$
$62$		0			0
$63$	4.47319	+	4.47548i	0.0710030	+	0.0710393i
$64$		0			0
$65$	79.8119	+	46.0794i	1.22788	+	0.708915i
$66$		0			0
$67$	51.2608	−	88.7864i	0.765087	−	1.32517i	−0.175114	−	0.984548i	$-0.556029\pi$
$67$	51.2608	−	88.7864i	0.765087	−	1.32517i	0.940201	−	0.340621i	$-0.110637\pi$
$68$		0			0
$69$	−9.65260	+	1.26953i	−0.139893	+	0.0183990i
$70$		0			0
$71$	−7.22572	−	4.17177i	−0.101771	−	0.0587573i	0.448251	−	0.893908i	$-0.352047\pi$
$71$	−7.22572	−	4.17177i	−0.101771	−	0.0587573i	−0.550021	+	0.835151i	$0.685380\pi$
$72$		0			0
$73$	−39.6816	+	68.7305i	−0.543583	+	0.941513i	0.455112	+	0.890434i	$0.349599\pi$
$73$	−39.6816	+	68.7305i	−0.543583	+	0.941513i	−0.998695	+	0.0510789i	$0.983734\pi$
$74$		0			0
$75$	23.1809	−	17.7826i	0.309079	−	0.237102i
$76$		0			0
$77$	−10.7862	+	6.22743i	−0.140081	+	0.0808758i
$78$		0			0
$79$	58.3917	+	101.137i	0.739136	+	1.28022i	0.952885	+	0.303332i	$0.0980992\pi$
$79$	58.3917	+	101.137i	0.739136	+	1.28022i	−0.213749	+	0.976889i	$0.568567\pi$
$80$		0			0
$81$	−70.1273	−	40.5359i	−0.865770	−	0.500443i
$82$		0			0
$83$	86.3290	+	49.8421i	1.04011	+	0.600507i	0.919864	−	0.392238i	$-0.128299\pi$
$83$	86.3290	+	49.8421i	1.04011	+	0.600507i	0.120244	+	0.992744i	$0.461632\pi$
$84$		0			0
$85$	−65.9620	+	114.250i	−0.776023	+	1.34411i
$86$		0			0
$87$	−13.6482	−	17.7914i	−0.156876	−	0.204499i
$88$		0			0
$89$	4.82896	−	2.78800i	0.0542580	−	0.0313259i	−0.472626	−	0.881263i	$-0.656694\pi$
$89$	4.82896	−	2.78800i	0.0542580	−	0.0313259i	0.526884	+	0.849937i	$0.323360\pi$
$90$		0			0
$91$	5.49669	+	9.52055i	0.0604032	+	0.104621i
$92$		0			0
$93$	−23.7378	−	9.83609i	−0.255246	−	0.105764i
$94$		0			0
$95$	34.1738	+	106.643i	0.359724	+	1.12256i
$96$		0			0
$97$	−52.8639	−	91.5630i	−0.544989	−	0.943948i	−0.998608	−	0.0527524i	$-0.983201\pi$
$97$	−52.8639	−	91.5630i	−0.544989	−	0.943948i	0.453619	−	0.891196i	$-0.350133\pi$
$98$		0			0
$99$	112.766	−	112.708i	1.13905	−	1.13846i
$100$		0			0
$101$		−	116.203i		−	1.15053i	−0.817969	−	0.575263i	$-0.804900\pi$
$101$		−	116.203i		−	1.15053i	0.817969	−	0.575263i	$-0.195100\pi$
$102$		0			0
$103$	42.8692	+	74.2516i	0.416205	+	0.720889i	0.995554	−	0.0941908i	$-0.0300264\pi$
$103$	42.8692	+	74.2516i	0.416205	+	0.720889i	−0.579349	+	0.815080i	$0.696693\pi$
$104$		0			0
$105$	12.3255	−	1.62108i	0.117386	−	0.0154389i
$106$		0			0
$107$			197.729i			1.84794i	0.382467	+	0.923969i	$0.375075\pi$
$107$			197.729i			1.84794i	−0.382467	+	0.923969i	$0.624925\pi$
$108$		0			0
$109$	−30.6364	+	53.0638i	−0.281068	+	0.486824i	−0.971648	−	0.236432i	$-0.924022\pi$
$109$	−30.6364	+	53.0638i	−0.281068	+	0.486824i	0.690580	+	0.723256i	$0.257355\pi$
$110$		0			0
$111$	89.9161	−	68.9768i	0.810055	−	0.621412i
$112$		0			0
$113$	14.7705	−	8.52775i	0.130712	−	0.0754668i	−0.433218	−	0.901289i	$-0.642622\pi$
$113$	14.7705	−	8.52775i	0.130712	−	0.0754668i	0.563930	+	0.825822i	$0.309289\pi$
$114$		0			0
$115$	−9.56365	+	16.5647i	−0.0831622	+	0.144041i
$116$		0			0
$117$	−99.4826	−	99.5335i	−0.850279	−	0.850713i
$118$		0			0
$119$	−13.6285	+	7.86843i	−0.114525	+	0.0661213i
$120$		0			0
$121$	96.4084	+	166.984i	0.796764	+	1.38004i
$122$		0			0
$123$	95.5737	+	124.587i	0.777022	+	1.01290i
$124$		0			0
$125$			89.9495i			0.719596i
$126$		0			0
$127$	−13.0431	−	22.5913i	−0.102702	−	0.177885i	0.810095	−	0.586298i	$-0.199415\pi$
$127$	−13.0431	−	22.5913i	−0.102702	−	0.177885i	−0.912797	+	0.408414i	$0.866082\pi$
$128$		0			0
$129$	17.0328	+	7.05778i	0.132038	+	0.0547115i
$130$		0			0
$131$		−	47.2412i		−	0.360619i	−0.983610	−	0.180310i	$-0.942290\pi$
$131$		−	47.2412i		−	0.360619i	0.983610	−	0.180310i	$-0.0577100\pi$
$132$		0			0
$133$	−2.83025	+	13.0551i	−0.0212801	+	0.0981589i
$134$		0			0
$135$	−147.046	+	60.8426i	−1.08923	+	0.450686i
$136$		0			0
$137$		−	199.989i		−	1.45977i	−0.683568	−	0.729887i	$-0.739573\pi$
$137$		−	199.989i		−	1.45977i	0.683568	−	0.729887i	$-0.260427\pi$
$138$		0			0
$139$	26.1789	−	45.3431i	0.188337	−	0.326210i	−0.756359	−	0.654157i	$-0.773024\pi$
$139$	26.1789	−	45.3431i	0.188337	−	0.326210i	0.944696	+	0.327947i	$0.106357\pi$
$140$		0			0
$141$	−131.439	−	171.339i	−0.932188	−	1.21517i
$142$		0			0
$143$	239.883	−	138.496i	1.67750	−	0.968507i
$144$		0			0
$145$	−44.0542			−0.303822
$146$		0			0
$147$	−134.433	−	55.7042i	−0.914511	−	0.378940i
$148$		0			0
$149$		−	95.0740i		−	0.638081i	−0.947741	−	0.319040i	$-0.896639\pi$
$149$		−	95.0740i		−	0.638081i	0.947741	−	0.319040i	$-0.103361\pi$
$150$		0			0
$151$	−17.7076	+	30.6705i	−0.117269	+	0.203116i	−0.918684	−	0.394992i	$-0.870747\pi$
$151$	−17.7076	+	30.6705i	−0.117269	+	0.203116i	0.801416	+	0.598108i	$0.204081\pi$
$152$		0			0
$153$	142.481	−	142.408i	0.931245	−	0.930770i
$154$		0			0
$155$	−43.7185	+	25.2409i	−0.282055	+	0.162844i
$156$		0			0
$157$	52.3742			0.333593			0.166797	−	0.985991i	$-0.446658\pi$
$157$	52.3742			0.333593			0.166797	+	0.985991i	$0.446658\pi$
$158$		0			0
$159$	27.1521	−	65.5273i	0.170768	−	0.412121i
$160$		0			0
$161$	−1.97596	+	1.14082i	−0.0122731	+	0.00708585i
$162$		0			0
$163$	−263.493			−1.61652			−0.808261	−	0.588824i	$-0.799591\pi$
$163$	−263.493			−1.61652			−0.808261	+	0.588824i	$0.799591\pi$
$164$		0			0
$165$	−40.8453	−	310.557i	−0.247547	−	1.88217i
$166$		0			0
$167$	−225.097	−	129.960i	−1.34789	−	0.778202i	−0.359936	−	0.932977i	$-0.617201\pi$
$167$	−225.097	−	129.960i	−1.34789	−	0.778202i	−0.987950	+	0.154775i	$0.950535\pi$
$168$		0			0
$169$	−37.7450	−	65.3763i	−0.223343	−	0.386842i
$170$		0			0
$171$	−8.21430	−	170.803i	−0.0480369	−	0.998846i
$172$		0			0
$173$	45.1264	−	26.0537i	0.260846	−	0.150600i	−0.363874	−	0.931448i	$-0.618546\pi$
$173$	45.1264	−	26.0537i	0.260846	−	0.150600i	0.624721	+	0.780848i	$0.285213\pi$
$174$		0			0
$175$	3.42350	−	5.92968i	0.0195629	−	0.0338839i
$176$		0			0
$177$	100.240	+	130.670i	0.566330	+	0.738251i
$178$		0			0
$179$			173.576i			0.969697i	0.874598	+	0.484849i	$0.161125\pi$
$179$			173.576i			0.969697i	−0.874598	+	0.484849i	$0.838875\pi$
$180$		0			0
$181$	−116.587	−	201.934i	−0.644125	−	1.11566i	−0.984503	−	0.175369i	$-0.943888\pi$
$181$	−116.587	−	201.934i	−0.644125	−	1.11566i	0.340378	−	0.940289i	$-0.389445\pi$
$182$		0			0
$183$	165.871	−	127.243i	0.906398	−	0.695320i
$184$		0			0
$185$		−	222.645i		−	1.20349i
$186$		0			0
$187$	198.256	+	343.389i	1.06019	+	1.83630i
$188$		0			0
$189$	−18.8196	−	2.48499i	−0.0995748	−	0.0131481i
$190$		0			0
$191$	120.700	+	69.6861i	0.631936	+	0.364849i	0.781502	−	0.623903i	$-0.214454\pi$
$191$	120.700	+	69.6861i	0.631936	+	0.364849i	−0.149565	+	0.988752i	$0.547787\pi$
$192$		0			0
$193$	−95.5330			−0.494990			−0.247495	−	0.968889i	$-0.579607\pi$
$193$	−95.5330			−0.494990			−0.247495	+	0.968889i	$0.579607\pi$
$194$		0			0
$195$	−274.116	+	36.0524i	−1.40572	+	0.184884i
$196$		0			0
$197$		−	310.234i		−	1.57479i	−0.616446	−	0.787397i	$-0.711428\pi$
$197$		−	310.234i		−	1.57479i	0.616446	−	0.787397i	$-0.288572\pi$
$198$		0			0
$199$	119.255	+	206.556i	0.599271	+	1.03797i	0.992929	+	0.118711i	$0.0378761\pi$
$199$	119.255	+	206.556i	0.599271	+	1.03797i	−0.393658	+	0.919257i	$0.628791\pi$
$200$		0			0
$201$	40.1063	+	304.939i	0.199534	+	1.51711i
$202$		0			0
$203$	−4.55106	−	2.62755i	−0.0224190	−	0.0129436i
$204$		0			0
$205$	308.496			1.50486
$206$		0			0
$207$	20.6579	−	20.6473i	0.0997965	−	0.0997455i
$208$		0			0
$209$	328.941	+	71.3119i	1.57388	+	0.341205i
$210$		0			0
$211$	−8.65754			−0.0410310			−0.0205155	−	0.999790i	$-0.506531\pi$
$211$	−8.65754			−0.0410310			−0.0205155	+	0.999790i	$0.506531\pi$
$212$		0			0
$213$	24.8169	−	3.26398i	0.116511	−	0.0153238i
$214$		0			0
$215$	31.3697	−	18.1113i	0.145906	−	0.0842387i
$216$		0			0
$217$	−6.02183			−0.0277504
$218$		0			0
$219$	−31.0467	−	236.056i	−0.141766	−	1.07788i
$220$		0			0
$221$	303.095	−	174.992i	1.37147	−	0.791818i
$222$		0			0
$223$	151.382	+	262.201i	0.678842	+	1.17579i	0.975330	+	0.220753i	$0.0708513\pi$
$223$	151.382	+	262.201i	0.678842	+	1.17579i	−0.296488	+	0.955037i	$0.595815\pi$
$224$		0			0
$225$	−22.7066	+	84.6557i	−0.100918	+	0.376248i
$226$		0			0
$227$	16.6155	+	9.59297i	0.0731961	+	0.0422598i	0.536151	−	0.844122i	$-0.319878\pi$
$227$	16.6155	+	9.59297i	0.0731961	+	0.0422598i	−0.462955	+	0.886382i	$0.653211\pi$
$228$		0			0
$229$	−193.340	−	334.875i	−0.844281	−	1.46234i	−0.886245	−	0.463218i	$-0.846695\pi$
$229$	−193.340	−	334.875i	−0.844281	−	1.46234i	0.0419640	−	0.999119i	$-0.486639\pi$
$230$		0			0
$231$	14.3032	−	34.5186i	0.0619187	−	0.149431i
$232$		0			0
$233$	284.002	+	163.969i	1.21889	+	0.703728i	0.964681	−	0.263421i	$-0.0848508\pi$
$233$	284.002	+	163.969i	1.21889	+	0.703728i	0.254211	+	0.967149i	$0.418184\pi$
$234$		0			0
$235$	−424.261			−1.80537
$236$		0			0
$237$	−323.664	−	134.115i	−1.36567	−	0.565885i
$238$		0			0
$239$	244.966	−	141.431i	1.02496	−	0.591762i	0.109425	−	0.993995i	$-0.465099\pi$
$239$	244.966	−	141.431i	1.02496	−	0.591762i	0.915538	+	0.402233i	$0.131766\pi$
$240$		0			0
$241$	−237.088			−0.983767			−0.491884	−	0.870661i	$-0.663691\pi$
$241$	−237.088			−0.983767			−0.491884	+	0.870661i	$0.663691\pi$
$242$		0			0
$243$	240.941	−	31.5639i	0.991528	−	0.129893i
$244$		0			0
$245$	−247.588	+	142.945i	−1.01056	+	0.583449i
$246$		0			0
$247$	62.9440	−	290.343i	0.254834	−	1.17548i
$248$		0			0
$249$	−296.499	+	38.9963i	−1.19076	+	0.156612i
$250$		0			0
$251$	85.5177	−	49.3737i	0.340708	−	0.196708i	−0.319877	−	0.947459i	$-0.603642\pi$
$251$	85.5177	−	49.3737i	0.340708	−	0.196708i	0.660585	+	0.750751i	$0.270308\pi$
$252$		0			0
$253$	28.7445	+	49.7870i	0.113615	+	0.196787i
$254$		0			0
$255$	−51.6085	−	392.393i	−0.202386	−	1.53879i
$256$		0			0
$257$	129.972	+	75.0395i	0.505728	+	0.291982i	0.731076	−	0.682296i	$-0.239018\pi$
$257$	129.972	+	75.0395i	0.505728	+	0.291982i	−0.225348	+	0.974278i	$0.572352\pi$
$258$		0			0
$259$	13.2794	−	23.0006i	0.0512717	−	0.0888053i
$260$		0			0
$261$	64.9736	+	17.4274i	0.248941	+	0.0667718i
$262$		0			0
$263$	−303.157	+	175.028i	−1.15269	+	0.665505i	−0.949541	−	0.313643i	$-0.898451\pi$
$263$	−303.157	+	175.028i	−1.15269	+	0.665505i	−0.203148	+	0.979148i	$0.565117\pi$
$264$		0			0
$265$	−69.6763	−	120.683i	−0.262930	−	0.455407i
$266$		0			0
$267$	−6.40351	+	15.4539i	−0.0239832	+	0.0578796i
$268$		0			0
$269$	86.7627	+	50.0925i	0.322538	+	0.186217i	0.652523	−	0.757769i	$-0.273710\pi$
$269$	86.7627	+	50.0925i	0.322538	+	0.186217i	−0.329985	+	0.943986i	$0.607044\pi$
$270$		0			0
$271$	102.668	−	177.826i	0.378849	−	0.656186i	−0.612046	−	0.790822i	$-0.709653\pi$
$271$	102.668	−	177.826i	0.378849	−	0.656186i	0.990895	+	0.134636i	$0.0429865\pi$
$272$		0			0
$273$	−30.4681	−	12.6249i	−0.111605	−	0.0462449i
$274$		0			0
$275$	−149.406	−	86.2597i	−0.543295	−	0.313672i
$276$		0			0
$277$	−111.754	+	193.564i	−0.403444	+	0.698786i	−0.994139	−	0.108109i	$-0.965520\pi$
$277$	−111.754	+	193.564i	−0.403444	+	0.698786i	0.590695	+	0.806895i	$0.298854\pi$
$278$		0			0
$279$	74.4635	−	19.9320i	0.266894	−	0.0714410i
$280$		0			0
$281$		−	174.168i		−	0.619817i	−0.950766	−	0.309908i	$-0.899702\pi$
$281$		−	174.168i		−	0.619817i	0.950766	−	0.309908i	$-0.100298\pi$
$282$		0			0
$283$	−421.632			−1.48987			−0.744933	−	0.667139i	$-0.767519\pi$
$283$	−421.632			−1.48987			−0.744933	+	0.667139i	$0.767519\pi$
$284$		0			0
$285$	−276.072	−	191.442i	−0.968675	−	0.671726i
$286$		0			0
$287$	31.8694	+	18.3998i	0.111043	+	0.0641108i
$288$		0			0
$289$	105.998	+	183.594i	0.366775	+	0.635273i
$290$		0			0
$291$	293.024	+	121.418i	1.00695	+	0.417245i
$292$		0			0
$293$	−411.502	+	237.581i	−1.40444	+	0.810855i	−0.994845	−	0.101411i	$-0.967664\pi$
$293$	−411.502	+	237.581i	−1.40444	+	0.810855i	−0.409598	+	0.912266i	$0.634331\pi$
$294$		0			0
$295$	323.559			1.09681
$296$		0			0
$297$	−62.6127	+	474.186i	−0.210817	+	1.59659i
$298$		0			0
$299$	43.9449	−	25.3716i	0.146973	−	0.0848548i
$300$		0			0
$301$	4.32090			0.0143552
$302$		0			0
$303$	212.184	+	276.597i	0.700279	+	0.912863i
$304$		0			0
$305$		−	410.720i		−	1.34662i
$306$		0			0
$307$	112.818	−	195.406i	0.367485	−	0.636503i	−0.621687	−	0.783266i	$-0.713552\pi$
$307$	112.818	−	195.406i	0.367485	−	0.636503i	0.989172	+	0.146763i	$0.0468856\pi$
$308$		0			0
$309$	−237.623	−	98.4623i	−0.769007	−	0.318648i
$310$		0			0
$311$	239.811	−	138.455i	0.771095	−	0.445192i	−0.0621700	−	0.998066i	$-0.519802\pi$
$311$	239.811	−	138.455i	0.771095	−	0.445192i	0.833265	+	0.552874i	$0.186469\pi$
$312$		0			0
$313$	−506.860			−1.61936			−0.809681	−	0.586870i	$-0.800360\pi$
$313$	−506.860			−1.61936			−0.809681	+	0.586870i	$0.800360\pi$
$314$		0			0
$315$	−26.3783	+	26.3648i	−0.0837405	+	0.0836977i
$316$		0			0
$317$			518.454i			1.63550i	0.575573	+	0.817750i	$0.304779\pi$
$317$			518.454i			1.63550i	−0.575573	+	0.817750i	$0.695221\pi$
$318$		0			0
$319$	−66.2047	+	114.670i	−0.207538	+	0.359467i
$320$		0			0
$321$	−361.050	−	470.654i	−1.12477	−	1.46621i
$322$		0			0
$323$	415.621	+	90.1034i	1.28675	+	0.278958i
$324$		0			0
$325$	−76.1378	+	131.875i	−0.234270	+	0.405768i
$326$		0			0
$327$	−23.9698	−	182.249i	−0.0733022	−	0.557336i
$328$		0			0
$329$	−43.8287	−	25.3045i	−0.133218	−	0.0769134i
$330$		0			0
$331$	155.993	−	270.188i	0.471278	−	0.816278i	−0.528182	−	0.849131i	$-0.677126\pi$
$331$	155.993	−	270.188i	0.471278	−	0.816278i	0.999460	+	0.0328536i	$0.0104595\pi$
$332$		0			0
$333$	−88.0764	+	328.370i	−0.264494	+	0.986096i
$334$		0			0
$335$	523.303	+	302.129i	1.56210	+	0.901877i
$336$		0			0
$337$	523.845			1.55444			0.777218	−	0.629232i	$-0.216630\pi$
$337$	523.845			1.55444			0.777218	+	0.629232i	$0.216630\pi$
$338$		0			0
$339$	−19.5866	+	47.2692i	−0.0577776	+	0.139437i
$340$		0			0
$341$			151.728i			0.444950i
$342$		0			0
$343$	−68.5537			−0.199865
$344$		0			0
$345$	−7.48257	−	56.8920i	−0.0216886	−	0.164904i
$346$		0			0
$347$			297.721i			0.857986i	0.903308	+	0.428993i	$0.141132\pi$
$347$			297.721i			0.857986i	−0.903308	+	0.428993i	$0.858868\pi$
$348$		0			0
$349$	−45.0994	+	78.1145i	−0.129225	+	0.223824i	−0.923376	−	0.383896i	$-0.874582\pi$
$349$	−45.0994	+	78.1145i	−0.129225	+	0.223824i	0.794152	+	0.607720i	$0.207916\pi$
$350$		0			0
$351$	418.544	+	55.2656i	1.19243	+	0.157452i
$352$		0			0
$353$	360.529	+	208.152i	1.02133	+	0.589665i	0.914489	−	0.404611i	$-0.132593\pi$
$353$	360.529	+	208.152i	1.02133	+	0.589665i	0.106841	+	0.994276i	$0.465927\pi$
$354$		0			0
$355$	24.5882	−	42.5880i	0.0692626	−	0.119966i
$356$		0			0
$357$	18.0723	−	43.6146i	0.0506226	−	0.122170i
$358$		0			0
$359$	53.4979	+	30.8870i	0.149019	+	0.0860362i	0.572656	−	0.819796i	$-0.305913\pi$
$359$	53.4979	+	30.8870i	0.149019	+	0.0860362i	−0.423636	+	0.905832i	$0.639247\pi$
$360$		0			0
$361$	293.764	−	209.819i	0.813750	−	0.581215i
$362$		0			0
$363$	−534.390	−	221.432i	−1.47215	−	0.610005i
$364$		0			0
$365$	−405.094	−	233.881i	−1.10985	−	0.640770i
$366$		0			0
$367$	−314.752			−0.857635			−0.428818	−	0.903391i	$-0.641070\pi$
$367$	−314.752			−0.857635			−0.428818	+	0.903391i	$0.641070\pi$
$368$		0			0
$369$	−454.987	−	122.038i	−1.23303	−	0.330726i
$370$		0			0
$371$		−	16.6230i		−	0.0448060i
$372$		0			0
$373$	83.5260	+	144.671i	0.223930	+	0.387859i	0.955998	−	0.293373i	$-0.0947778\pi$
$373$	83.5260	+	144.671i	0.223930	+	0.387859i	−0.732068	+	0.681232i	$0.761445\pi$
$374$		0			0
$375$	−164.246	−	214.106i	−0.437989	−	0.570950i
$376$		0			0
$377$	101.214	+	58.4361i	0.268473	+	0.155003i
$378$		0			0
$379$	61.9252			0.163391			0.0816955	−	0.996657i	$-0.473967\pi$
$379$	61.9252			0.163391			0.0816955	+	0.996657i	$0.473967\pi$
$380$		0			0
$381$	72.2978	+	29.9575i	0.189758	+	0.0786287i
$382$		0			0
$383$		−	612.419i		−	1.59900i	−0.600663	−	0.799502i	$-0.705097\pi$
$383$		−	612.419i		−	1.59900i	0.600663	−	0.799502i	$-0.294903\pi$
$384$		0			0
$385$	−36.7042	−	63.5735i	−0.0953356	−	0.165126i
$386$		0			0
$387$	−53.4305	+	14.3020i	−0.138063	+	0.0369561i
$388$		0			0
$389$		−	90.5540i		−	0.232787i	−0.993203	−	0.116393i	$-0.962867\pi$
$389$		−	90.5540i		−	0.232787i	0.993203	−	0.116393i	$-0.0371333\pi$
$390$		0			0
$391$	36.3190	+	62.9064i	0.0928876	+	0.160886i
$392$		0			0
$393$	86.2614	+	112.448i	0.219495	+	0.286127i
$394$		0			0
$395$	−596.099	+	344.158i	−1.50911	+	0.871286i
$396$		0			0
$397$	−23.3966	+	40.5241i	−0.0589335	+	0.102076i	−0.893987	−	0.448093i	$-0.852103\pi$
$397$	−23.3966	+	40.5241i	−0.0589335	+	0.102076i	0.835053	+	0.550169i	$0.185437\pi$
$398$		0			0
$399$	−17.1016	−	36.2430i	−0.0428611	−	0.0908347i
$400$		0			0
$401$		−	157.389i		−	0.392491i	−0.980555	−	0.196245i	$-0.937125\pi$
$401$		−	157.389i		−	0.392491i	0.980555	−	0.196245i	$-0.0628749\pi$
$402$		0			0
$403$	133.924			0.332318
$404$		0			0
$405$	238.916	−	413.327i	0.589917	−	1.02056i
$406$		0			0
$407$	−579.530	−	334.592i	−1.42391	−	0.822092i
$408$		0			0
$409$	185.625	−	321.512i	0.453851	−	0.786094i	−0.544770	−	0.838586i	$-0.683383\pi$
$409$	185.625	−	321.512i	0.453851	−	0.786094i	0.998621	+	0.0524919i	$0.0167164\pi$
$410$		0			0
$411$	365.176	+	476.032i	0.888506	+	1.15823i
$412$		0			0
$413$	33.4255	+	19.2982i	0.0809335	+	0.0467270i
$414$		0			0
$415$	−293.767	+	508.819i	−0.707872	+	1.22607i
$416$		0			0
$417$	20.4823	+	155.732i	0.0491181	+	0.373458i
$418$		0			0
$419$	−587.569	+	339.233i	−1.40231	+	0.809625i	−0.994630	−	0.103499i	$-0.966996\pi$
$419$	−587.569	+	339.233i	−1.40231	+	0.809625i	−0.407682	+	0.913124i	$0.633663\pi$
$420$		0			0
$421$	254.605	+	440.988i	0.604761	+	1.04748i	0.992089	+	0.125535i	$0.0400648\pi$
$421$	254.605	+	440.988i	0.604761	+	1.04748i	−0.387328	+	0.921942i	$0.626602\pi$
$422$		0			0
$423$	625.725	+	167.834i	1.47925	+	0.396770i
$424$		0			0
$425$	−188.776	−	108.990i	−0.444180	−	0.256447i
$426$		0			0
$427$	24.4969	−	42.4298i	0.0573697	−	0.0993673i
$428$		0			0
$429$	−318.100	+	767.684i	−0.741492	+	1.78947i
$430$		0			0
$431$	399.240	−	230.501i	0.926311	−	0.534806i	0.0406683	−	0.999173i	$-0.487051\pi$
$431$	399.240	−	230.501i	0.926311	−	0.534806i	0.885643	+	0.464367i	$0.153718\pi$
$432$		0			0
$433$	369.211	+	639.492i	0.852681	+	1.47689i	0.878780	+	0.477227i	$0.158358\pi$
$433$	369.211	+	639.492i	0.852681	+	1.47689i	−0.0260989	+	0.999659i	$0.508308\pi$
$434$		0			0
$435$	104.862	−	80.4421i	0.241062	−	0.184924i
$436$		0			0
$437$	60.2598	+	13.0638i	0.137894	+	0.0298944i
$438$		0			0
$439$	−259.366	−	449.236i	−0.590812	−	1.02332i	−0.994123	−	0.108253i	$-0.965474\pi$
$439$	−259.366	−	449.236i	−0.590812	−	1.02332i	0.403312	−	0.915063i	$-0.367859\pi$
$440$		0			0
$441$	421.705	−	112.880i	0.956247	−	0.255964i
$442$		0			0
$443$		−	147.886i		−	0.333828i	−0.985971	−	0.166914i	$-0.946620\pi$
$443$		−	147.886i		−	0.333828i	0.985971	−	0.166914i	$-0.0533802\pi$
$444$		0			0
$445$	16.4324	+	28.4617i	0.0369266	+	0.0639588i
$446$		0			0
$447$	173.603	+	226.304i	0.388374	+	0.506273i
$448$		0			0
$449$			134.495i			0.299543i	0.988721	+	0.149771i	$0.0478538\pi$
$449$			134.495i			0.299543i	−0.988721	+	0.149771i	$0.952146\pi$
$450$		0			0
$451$	463.608	−	802.992i	1.02795	−	1.78047i
$452$		0			0
$453$	−13.8544	−	105.339i	−0.0305836	−	0.232535i
$454$		0			0
$455$	−56.1137	+	32.3973i	−0.123327	+	0.0712028i
$456$		0			0
$457$	−144.575	+	250.411i	−0.316356	+	0.547944i	−0.979725	−	0.200348i	$-0.935793\pi$
$457$	−144.575	+	250.411i	−0.316356	+	0.547944i	0.663369	+	0.748292i	$0.269126\pi$
$458$		0			0
$459$	−79.1118	+	599.139i	−0.172357	+	1.30531i
$460$		0			0
$461$	−397.301	+	229.382i	−0.861824	+	0.497574i	−0.864623	−	0.502422i	$-0.832443\pi$
$461$	−397.301	+	229.382i	−0.861824	+	0.497574i	0.00279853	+	0.999996i	$0.499109\pi$
$462$		0			0
$463$	21.5817	+	37.3807i	0.0466128	+	0.0807358i	0.888390	−	0.459089i	$-0.151824\pi$
$463$	21.5817	+	37.3807i	0.0466128	+	0.0807358i	−0.841778	+	0.539824i	$0.818491\pi$
$464$		0			0
$465$	57.9735	−	139.910i	0.124674	−	0.300881i
$466$		0			0
$467$			41.0873i			0.0879814i	0.999032	+	0.0439907i	$0.0140072\pi$
$467$			41.0873i			0.0879814i	−0.999032	+	0.0439907i	$0.985993\pi$
$468$		0			0
$469$	36.0402	+	62.4234i	0.0768447	+	0.133099i
$470$		0			0
$471$	−124.666	+	95.6342i	−0.264683	+	0.203045i
$472$		0			0
$473$		−	108.871i		−	0.230171i
$474$		0			0
$475$	−176.209	+	56.4659i	−0.370966	+	0.118876i
$476$		0			0
$477$	55.0216	+	205.553i	0.115349	+	0.430930i
$478$		0			0
$479$			901.802i			1.88268i	0.337465	+	0.941338i	$0.390430\pi$
$479$			901.802i			1.88268i	−0.337465	+	0.941338i	$0.609570\pi$
$480$		0			0
$481$	−295.330	+	511.526i	−0.613992	+	1.06346i
$482$		0			0
$483$	2.62025	−	6.32356i	0.00542495	−	0.0130923i
$484$		0			0
$485$	539.668	−	311.577i	1.11272	−	0.642428i
$486$		0			0
$487$	7.53975			0.0154820			0.00774102	−	0.999970i	$-0.497536\pi$
$487$	7.53975			0.0154820			0.00774102	+	0.999970i	$0.497536\pi$
$488$		0			0
$489$	627.191	−	481.133i	1.28260	−	0.983913i
$490$		0			0
$491$		−	672.915i		−	1.37050i	−0.728309	−	0.685249i	$-0.759693\pi$
$491$		−	672.915i		−	1.37050i	0.728309	−	0.685249i	$-0.240307\pi$
$492$		0			0
$493$	−83.6504	+	144.887i	−0.169676	+	0.293888i
$494$		0			0
$495$	664.295	+	664.635i	1.34201	+	1.34270i
$496$		0			0
$497$	5.08021	−	2.93306i	0.0102218	−	0.00590153i
$498$		0			0
$499$	835.632			1.67461			0.837307	−	0.546733i	$-0.184129\pi$
$499$	835.632			1.67461			0.837307	+	0.546733i	$0.184129\pi$
$500$		0			0
$501$	773.101	−	101.680i	1.54311	−	0.202954i
$502$		0			0
$503$	−229.542	+	132.526i	−0.456347	+	0.263472i	−0.710507	−	0.703690i	$-0.751534\pi$
$503$	−229.542	+	132.526i	−0.456347	+	0.263472i	0.254160	+	0.967162i	$0.418201\pi$
$504$		0			0
$505$	684.895			1.35623
$506$		0			0
$507$	209.220	+	86.6931i	0.412663	+	0.170992i
$508$		0			0
$509$	−44.0537	−	25.4344i	−0.0865496	−	0.0499694i	0.456101	−	0.889928i	$-0.349246\pi$
$509$	−44.0537	−	25.4344i	−0.0865496	−	0.0499694i	−0.542650	+	0.839959i	$0.682579\pi$
$510$		0			0
$511$	−27.8991	−	48.3226i	−0.0545970	−	0.0945648i
$512$		0			0
$513$	331.435	+	391.561i	0.646071	+	0.763277i
$514$		0			0
$515$	−437.635	+	252.669i	−0.849777	+	0.490619i
$516$		0			0
$517$	−637.580	+	1104.32i	−1.23323	+	2.13602i
$518$		0			0
$519$	−59.8405	+	144.415i	−0.115300	+	0.278257i
$520$		0			0
$521$		−	775.621i		−	1.48872i	−0.667781	−	0.744358i	$-0.732756\pi$
$521$		−	775.621i		−	1.48872i	0.667781	−	0.744358i	$-0.267244\pi$
$522$		0			0
$523$	−422.410	−	731.635i	−0.807667	−	1.39892i	−0.914476	−	0.404641i	$-0.867396\pi$
$523$	−422.410	−	731.635i	−0.807667	−	1.39892i	0.106808	−	0.994280i	$-0.465937\pi$
$524$		0			0
$525$	2.67854	+	20.3656i	0.00510198	+	0.0387917i
$526$		0			0
$527$			191.710i			0.363776i
$528$		0			0
$529$	−259.234	−	449.007i	−0.490046	−	0.848784i
$530$		0			0
$531$	−477.203	−	127.997i	−0.898688	−	0.241049i
$532$		0			0
$533$	−708.767	−	409.207i	−1.32977	−	0.767743i
$534$		0			0
$535$	−1165.41			−2.17833
$536$		0			0
$537$	−316.946	−	413.161i	−0.590216	−	0.769388i
$538$		0			0
$539$			859.272i			1.59420i
$540$		0			0
$541$	451.156	+	781.425i	0.833929	+	1.44441i	0.894899	+	0.446268i	$0.147247\pi$
$541$	451.156	+	781.425i	0.833929	+	1.44441i	−0.0609701	+	0.998140i	$0.519419\pi$
$542$		0			0
$543$	646.238	+	267.777i	1.19012	+	0.493144i
$544$		0			0
$545$	−312.755	−	180.569i	−0.573863	−	0.331320i
$546$		0			0
$547$	−184.656			−0.337580			−0.168790	−	0.985652i	$-0.553986\pi$
$547$	−184.656			−0.337580			−0.168790	+	0.985652i	$0.553986\pi$
$548$		0			0
$549$	−162.477	+	605.754i	−0.295951	+	1.10338i
$550$		0			0
$551$	43.3378	+	135.241i	0.0786530	+	0.245446i
$552$		0			0
$553$	−82.1074			−0.148476
$554$		0			0
$555$	406.546	+	529.961i	0.732515	+	0.954885i
$556$		0			0
$557$	218.277	−	126.022i	0.391880	−	0.226252i	−0.291095	−	0.956694i	$-0.594019\pi$
$557$	218.277	−	126.022i	0.391880	−	0.226252i	0.682974	+	0.730442i	$0.260686\pi$
$558$		0			0
$559$	−96.0957			−0.171906
$560$		0			0
$561$	−1098.93	−	455.355i	−1.95887	−	0.811685i
$562$		0			0
$563$	−561.132	+	323.970i	−0.996683	+	0.575435i	−0.907265	−	0.420559i	$-0.861834\pi$
$563$	−561.132	+	323.970i	−0.996683	+	0.575435i	−0.0894175	+	0.995994i	$0.528501\pi$
$564$		0			0
$565$	50.2622	+	87.0566i	0.0889596	+	0.154083i
$566$		0			0
$567$	49.3338	−	28.4493i	0.0870085	−	0.0501751i
$568$		0			0
$569$	−154.886	−	89.4234i	−0.272207	−	0.157159i	0.357683	−	0.933843i	$-0.383567\pi$
$569$	−154.886	−	89.4234i	−0.272207	−	0.157159i	−0.629890	+	0.776684i	$0.716900\pi$
$570$		0			0
$571$	291.759	+	505.342i	0.510962	+	0.885012i	0.999919	+	0.0127040i	$0.00404393\pi$
$571$	291.759	+	505.342i	0.510962	+	0.885012i	−0.488958	+	0.872308i	$0.662623\pi$
$572$		0			0
$573$	−414.546	+	54.5222i	−0.723467	+	0.0951521i
$574$		0			0
$575$	−27.3702	−	15.8022i	−0.0476003	−	0.0274821i
$576$		0			0
$577$	536.087			0.929094			0.464547	−	0.885549i	$-0.346217\pi$
$577$	536.087			0.929094			0.464547	+	0.885549i	$0.346217\pi$
$578$		0			0
$579$	227.397	−	174.441i	0.392740	−	0.301280i
$580$		0			0
$581$	−60.6957	+	35.0427i	−0.104468	+	0.0603144i
$582$		0			0
$583$	−418.839			−0.718420
$584$		0			0
$585$	586.645	−	586.346i	1.00281	−	1.00230i
$586$		0			0
$587$	−382.920	+	221.079i	−0.652334	+	0.376625i	−0.789350	−	0.613944i	$-0.789582\pi$
$587$	−382.920	+	221.079i	−0.652334	+	0.376625i	0.137016	+	0.990569i	$0.456249\pi$
$588$		0			0
$589$	120.494	+	109.380i	0.204574	+	0.185704i
$590$		0			0
$591$	566.482	+	738.449i	0.958514	+	1.24949i
$592$		0			0
$593$	−410.110	+	236.777i	−0.691585	+	0.399287i	−0.804205	−	0.594351i	$-0.797409\pi$
$593$	−410.110	+	236.777i	−0.691585	+	0.399287i	0.112621	+	0.993638i	$0.464076\pi$
$594$		0			0
$595$	−46.3762	−	80.3259i	−0.0779431	−	0.135001i
$596$		0			0
$597$	−661.028	−	273.906i	−1.10725	−	0.458804i
$598$		0			0
$599$	774.211	+	446.991i	1.29251	+	0.746228i	0.979098	−	0.203391i	$-0.0651961\pi$
$599$	774.211	+	446.991i	1.29251	+	0.746228i	0.313407	+	0.949619i	$0.398529\pi$
$600$		0			0
$601$	42.3132	−	73.2886i	0.0704047	−	0.121944i	−0.828674	−	0.559731i	$-0.810904\pi$
$601$	42.3132	−	73.2886i	0.0704047	−	0.121944i	0.899079	+	0.437787i	$0.144238\pi$
$602$		0			0
$603$	−652.277	−	652.611i	−1.08172	−	1.08227i
$604$		0			0
$605$	−984.198	+	568.227i	−1.62677	+	0.939218i
$606$		0			0
$607$	−444.617	−	770.099i	−0.732483	−	1.26870i	−0.955819	−	0.293956i	$-0.905028\pi$
$607$	−444.617	−	770.099i	−0.732483	−	1.26870i	0.223336	−	0.974741i	$-0.428305\pi$
$608$		0			0
$609$	15.6307	−	2.05579i	0.0256662	−	0.00337568i
$610$		0			0
$611$	974.738	+	562.765i	1.59532	+	0.921056i
$612$		0			0
$613$	329.622	−	570.923i	0.537720	−	0.931359i	−0.461306	−	0.887241i	$-0.652619\pi$
$613$	329.622	−	570.923i	0.537720	−	0.931359i	0.999026	−	0.0441175i	$-0.0140476\pi$
$614$		0			0
$615$	−734.310	+	563.307i	−1.19400	+	0.915946i
$616$		0			0
$617$	−179.946	−	103.892i	−0.291646	−	0.168382i	0.347038	−	0.937851i	$-0.387188\pi$
$617$	−179.946	−	103.892i	−0.291646	−	0.168382i	−0.638684	+	0.769469i	$0.720521\pi$
$618$		0			0
$619$	403.579	−	699.019i	0.651985	−	1.12927i	−0.330656	−	0.943751i	$-0.607270\pi$
$619$	403.579	−	699.019i	0.651985	−	1.12927i	0.982641	−	0.185520i	$-0.0593968\pi$
$620$		0			0
$621$	−11.4702	+	86.8675i	−0.0184706	+	0.139883i
$622$		0			0
$623$			3.92034i			0.00629269i
$624$		0			0
$625$	−773.625			−1.23780
$626$		0			0
$627$	−913.191	+	430.897i	−1.45645	+	0.687237i
$628$		0			0
$629$	−732.242	−	422.760i	−1.16414	−	0.672115i
$630$		0			0
$631$	−496.871	−	860.606i	−0.787435	−	1.36388i	−0.927534	−	0.373740i	$-0.878075\pi$
$631$	−496.871	−	860.606i	−0.787435	−	1.36388i	0.140099	−	0.990138i	$-0.455258\pi$
$632$		0			0
$633$	20.6075	−	15.8085i	0.0325553	−	0.0249739i
$634$		0			0
$635$	133.152	−	76.8755i	0.209689	−	0.121064i
$636$		0			0
$637$	758.444			1.19065
$638$		0			0
$639$	−53.1115	+	53.0844i	−0.0831166	+	0.0830741i
$640$		0			0
$641$	−751.727	+	434.010i	−1.17274	+	0.677083i	−0.954324	−	0.298773i	$-0.903423\pi$
$641$	−751.727	+	434.010i	−1.17274	+	0.677083i	−0.218417	+	0.975855i	$0.570089\pi$
$642$		0			0
$643$	209.372			0.325617			0.162808	−	0.986658i	$-0.447945\pi$
$643$	209.372			0.325617			0.162808	+	0.986658i	$0.447945\pi$
$644$		0			0
$645$	−41.5982	+	100.391i	−0.0644934	+	0.155645i
$646$		0			0
$647$			570.098i			0.881140i	0.897718	+	0.440570i	$0.145224\pi$
$647$			570.098i			0.881140i	−0.897718	+	0.440570i	$0.854776\pi$
$648$		0			0
$649$	486.245	−	842.201i	0.749221	−	1.29769i
$650$		0			0
$651$	14.3337	−	10.9957i	0.0220180	−	0.0168905i
$652$		0			0
$653$	343.712	−	198.442i	0.526358	−	0.303893i	−0.213174	−	0.977014i	$-0.568380\pi$
$653$	343.712	−	198.442i	0.526358	−	0.303893i	0.739532	+	0.673121i	$0.235047\pi$
$654$		0			0
$655$	278.437			0.425095
$656$		0			0
$657$	504.935	+	505.193i	0.768546	+	0.768939i
$658$		0			0
$659$		−	395.517i		−	0.600178i	−0.953911	−	0.300089i	$-0.902984\pi$
$659$		−	395.517i		−	0.600178i	0.953911	−	0.300089i	$-0.0970164\pi$
$660$		0			0
$661$	209.238	−	362.411i	0.316548	−	0.548278i	−0.663217	−	0.748427i	$-0.730809\pi$
$661$	209.238	−	362.411i	0.316548	−	0.548278i	0.979765	+	0.200149i	$0.0641428\pi$
$662$		0			0
$663$	−401.923	+	969.977i	−0.606218	+	1.46301i
$664$		0			0
$665$	−76.9464	−	16.6814i	−0.115709	−	0.0250848i
$666$		0			0
$667$	−12.1282	+	21.0067i	−0.0181833	+	0.0314943i
$668$		0			0
$669$	−839.107	−	347.695i	−1.25427	−	0.519724i
$670$		0			0
$671$	−1069.08	−	617.231i	−1.59326	−	0.919867i
$672$		0			0
$673$	197.751	−	342.514i	0.293835	−	0.508936i	−0.680879	−	0.732396i	$-0.738402\pi$
$673$	197.751	−	342.514i	0.293835	−	0.508936i	0.974713	+	0.223460i	$0.0717352\pi$
$674$		0			0
$675$	−100.531	−	242.967i	−0.148935	−	0.359952i
$676$		0			0
$677$	592.263	+	341.943i	0.874835	+	0.505086i	0.868952	−	0.494896i	$-0.164794\pi$
$677$	592.263	+	341.943i	0.874835	+	0.505086i	0.00588308	+	0.999983i	$0.498127\pi$
$678$		0			0
$679$	74.3345			0.109476
$680$		0			0
$681$	−57.0664	+	7.50551i	−0.0837979	+	0.0110213i
$682$		0			0
$683$		−	692.506i		−	1.01392i	−0.861970	−	0.506959i	$-0.830770\pi$
$683$		−	692.506i		−	1.01392i	0.861970	−	0.506959i	$-0.169230\pi$
$684$		0			0
$685$	1178.73			1.72077
$686$		0			0
$687$	1071.68	+	444.066i	1.55994	+	0.646384i
$688$		0			0
$689$			369.691i			0.536562i
$690$		0			0
$691$	672.752	−	1165.24i	0.973591	−	1.68631i	0.289084	−	0.957304i	$-0.406649\pi$
$691$	672.752	−	1165.24i	0.973591	−	1.68631i	0.684507	−	0.729006i	$-0.260017\pi$
$692$		0			0
$693$	28.9843	+	108.282i	0.0418244	+	0.156251i
$694$		0			0
$695$	267.250	+	154.297i	0.384533	+	0.222010i
$696$		0			0
$697$	585.773	−	1014.59i	0.840421	−	1.45565i
$698$		0			0
$699$	−975.411	+	128.289i	−1.39544	+	0.183531i
$700$		0			0
$701$	−208.828	−	120.567i	−0.297900	−	0.171993i	0.343599	−	0.939116i	$-0.388354\pi$
$701$	−208.828	−	120.567i	−0.297900	−	0.171993i	−0.641499	+	0.767124i	$0.721687\pi$
$702$		0			0
$703$	−683.493	+	219.025i	−0.972252	+	0.311557i
$704$		0			0
$705$	1009.87	−	774.693i	1.43243	−	1.09885i
$706$		0			0
$707$	70.7537	+	40.8497i	0.100076	+	0.0577789i
$708$		0			0
$709$	238.357			0.336187			0.168093	−	0.985771i	$-0.446239\pi$
$709$	238.357			0.336187			0.168093	+	0.985771i	$0.446239\pi$
$710$		0			0
$711$	1015.31	−	271.773i	1.42800	−	0.382240i
$712$		0			0
$713$			27.7955i			0.0389839i
$714$		0			0
$715$	816.292	+	1413.86i	1.14167	+	1.97742i
$716$		0			0
$717$	−324.841	+	783.951i	−0.453055	+	1.09338i
$718$		0			0
$719$	101.612	+	58.6655i	0.141324	+	0.0815933i	0.568995	−	0.822341i	$-0.307332\pi$
$719$	101.612	+	58.6655i	0.141324	+	0.0815933i	−0.427671	+	0.903934i	$0.640666\pi$
$720$		0			0
$721$	−60.2804			−0.0836066
$722$		0			0
$723$	564.339	−	432.918i	0.780551	−	0.598780i
$724$		0			0
$725$		−	72.7915i		−	0.100402i
$726$		0			0
$727$	−123.015	−	213.068i	−0.169209	−	0.293078i	0.768933	−	0.639329i	$-0.220788\pi$
$727$	−123.015	−	213.068i	−0.169209	−	0.293078i	−0.938142	+	0.346251i	$0.887455\pi$
$728$		0			0
$729$	−515.876	+	515.085i	−0.707649	+	0.706564i
$730$		0			0
$731$		−	137.559i		−	0.188180i
$732$		0			0
$733$	−573.658	−	993.605i	−0.782617	−	1.35553i	−0.930412	−	0.366514i	$-0.880551\pi$
$733$	−573.658	−	993.605i	−0.782617	−	1.35553i	0.147796	−	0.989018i	$-0.452782\pi$
$734$		0			0
$735$	328.318	−	792.342i	0.446691	−	1.07802i
$736$		0			0
$737$	1572.84	−	908.079i	2.13411	−	1.23213i
$738$		0			0
$739$	−331.543	+	574.249i	−0.448637	+	0.777062i	−0.998298	−	0.0583262i	$-0.981424\pi$
$739$	−331.543	+	574.249i	−0.448637	+	0.777062i	0.549661	+	0.835388i	$0.314757\pi$
$740$		0			0
$741$	380.335	+	806.036i	0.513273	+	1.08777i
$742$		0			0
$743$			895.276i			1.20495i	0.798139	+	0.602474i	$0.205818\pi$
$743$			895.276i			1.20495i	−0.798139	+	0.602474i	$0.794182\pi$
$744$		0			0
$745$	560.362			0.752163
$746$		0			0
$747$	634.548	−	634.224i	0.849462	−	0.849028i
$748$		0			0
$749$	−120.393	−	69.5092i	−0.160739	−	0.0928027i
$750$		0			0
$751$	659.782	−	1142.78i	0.878538	−	1.52167i	0.0255919	−	0.999672i	$-0.491853\pi$
$751$	659.782	−	1142.78i	0.878538	−	1.52167i	0.852946	−	0.522000i	$-0.174814\pi$
$752$		0			0
$753$	−113.402	+	273.677i	−0.150600	+	0.363449i
$754$		0			0
$755$	−180.770	−	104.368i	−0.239431	−	0.138236i
$756$		0			0
$757$	571.887	−	990.537i	0.755465	−	1.30850i	−0.189678	−	0.981846i	$-0.560744\pi$
$757$	571.887	−	990.537i	0.755465	−	1.30850i	0.945143	−	0.326657i	$-0.105922\pi$
$758$		0			0
$759$	−159.330	−	66.0207i	−0.209922	−	0.0869838i
$760$		0			0
$761$	228.476	−	131.910i	0.300231	−	0.173338i	−0.342316	−	0.939585i	$-0.611211\pi$
$761$	228.476	−	131.910i	0.300231	−	0.173338i	0.642547	+	0.766247i	$0.277878\pi$
$762$		0			0
$763$	−21.5396	−	37.3078i	−0.0282302	−	0.0488961i
$764$		0			0
$765$	839.344	+	839.774i	1.09718	+	1.09774i
$766$		0			0
$767$	−743.375	−	429.188i	−0.969198	−	0.559567i
$768$		0			0
$769$	197.800	−	342.599i	0.257217	−	0.445512i	−0.708279	−	0.705933i	$-0.750528\pi$
$769$	197.800	−	342.599i	0.257217	−	0.445512i	0.965495	+	0.260421i	$0.0838613\pi$
$770$		0			0
$771$	−446.393	+	58.7107i	−0.578979	+	0.0761487i
$772$		0			0
$773$	1281.12	−	739.656i	1.65734	−	0.956864i	0.683400	−	0.730044i	$-0.260500\pi$
$773$	1281.12	−	739.656i	1.65734	−	0.956864i	0.973937	−	0.226820i	$-0.0728330\pi$
$774$		0			0
$775$	−41.7059	−	72.2367i	−0.0538141	−	0.0932087i
$776$		0			0
$777$	10.3897	+	78.9960i	0.0133716	+	0.101668i
$778$		0			0
$779$	−303.479	−	947.043i	−0.389575	−	1.21572i
$780$		0			0
$781$	−73.9024	−	128.003i	−0.0946253	−	0.163896i
$782$		0			0
$783$	−186.478	+	77.1582i	−0.238159	+	0.0985417i
$784$		0			0
$785$			308.691i			0.393237i
$786$		0			0
$787$	−454.543	−	787.291i	−0.577564	−	1.00037i	−0.995758	−	0.0920122i	$-0.970670\pi$
$787$	−454.543	−	787.291i	−0.577564	−	1.00037i	0.418194	−	0.908358i	$-0.362663\pi$
$788$		0			0
$789$	402.006	−	970.177i	0.509513	−	1.22963i
$790$		0			0
$791$			11.9913i			0.0151596i
$792$		0			0
$793$	−544.804	+	943.628i	−0.687016	+	1.18995i
$794$		0			0
$795$	386.215	+	160.033i	0.485805	+	0.201300i
$796$		0			0
$797$	196.814	−	113.631i	0.246944	−	0.142573i	−0.371420	−	0.928465i	$-0.621129\pi$
$797$	196.814	−	113.631i	0.246944	−	0.142573i	0.618364	+	0.785892i	$0.287796\pi$
$798$		0			0
$799$	−805.590	+	1395.32i	−1.00825	+	1.74634i
$800$		0			0
$801$	−12.9762	−	48.4774i	−0.0162000	−	0.0605211i
$802$		0			0
$803$	−1217.55	+	702.954i	−1.51625	+	0.875410i
$804$		0			0
$805$	−6.72395	−	11.6462i	−0.00835274	−	0.0144674i
$806$		0			0
$807$	−297.988	+	39.1922i	−0.369255	+	0.0485653i
$808$		0			0
$809$		−	1244.41i		−	1.53820i	−0.639127	−	0.769101i	$-0.720704\pi$
$809$		−	1244.41i		−	1.53820i	0.639127	−	0.769101i	$-0.279296\pi$
$810$		0			0
$811$	−668.064	−	1157.12i	−0.823753	−	1.42678i	−0.902868	−	0.429917i	$-0.858543\pi$
$811$	−668.064	−	1157.12i	−0.823753	−	1.42678i	0.0791151	−	0.996865i	$-0.474791\pi$
$812$		0			0
$813$	80.3272	+	610.749i	0.0988035	+	0.751229i
$814$		0			0
$815$		−	1553.02i		−	1.90554i
$816$		0			0
$817$	−86.4591	−	78.4843i	−0.105825	−	0.0960640i
$818$		0			0
$819$	95.5757	−	25.5833i	0.116698	−	0.0312372i
$820$		0			0
$821$		−	1101.94i		−	1.34219i	−0.741373	−	0.671094i	$-0.765825\pi$
$821$		−	1101.94i		−	1.34219i	0.741373	−	0.671094i	$-0.234175\pi$
$822$		0			0
$823$	125.920	−	218.099i	0.153001	−	0.265005i	−0.779328	−	0.626616i	$-0.784440\pi$
$823$	125.920	−	218.099i	0.153001	−	0.265005i	0.932329	+	0.361610i	$0.117773\pi$
$824$		0			0
$825$	513.139	−	67.4893i	0.621987	−	0.0818052i
$826$		0			0
$827$	−152.841	+	88.2427i	−0.184814	+	0.106702i	−0.589552	−	0.807730i	$-0.700696\pi$
$827$	−152.841	+	88.2427i	−0.184814	+	0.106702i	0.404739	+	0.914432i	$0.367362\pi$
$828$		0			0
$829$	−1408.64			−1.69920			−0.849602	−	0.527424i	$-0.823158\pi$
$829$	−1408.64			−1.69920			−0.849602	+	0.527424i	$0.823158\pi$
$830$		0			0
$831$	−87.4360	−	664.799i	−0.105218	−	0.799999i
$832$		0			0
$833$			1085.70i			1.30336i
$834$		0			0
$835$	765.977	−	1326.71i	0.917337	−	1.58887i
$836$		0			0
$837$	−140.850	+	183.413i	−0.168279	+	0.219132i
$838$		0			0
$839$	−151.349	+	87.3816i	−0.180393	+	0.104150i	−0.587477	−	0.809241i	$-0.699879\pi$
$839$	−151.349	+	87.3816i	−0.180393	+	0.104150i	0.407084	+	0.913391i	$0.366545\pi$
$840$		0			0
$841$	785.132			0.933570
$842$		0			0
$843$	318.028	+	414.572i	0.377258	+	0.491782i
$844$		0			0
$845$	385.325	−	222.467i	0.456006	−	0.263275i
$846$		0			0
$847$	−135.565			−0.160053
$848$		0			0
$849$	1003.61	−	769.892i	1.18211	−	0.906822i
$850$		0			0
$851$	−106.166	−	61.2949i	−0.124754	−	0.0720269i
$852$		0			0
$853$	−336.670	−	583.130i	−0.394690	−	0.683622i	0.598372	−	0.801218i	$-0.295815\pi$
$853$	−336.670	−	583.130i	−0.394690	−	0.683622i	−0.993062	+	0.117596i	$0.962481\pi$
$854$		0			0
$855$	1006.70	−	48.4147i	1.17743	−	0.0566254i
$856$		0			0
$857$	227.664	−	131.442i	0.265652	−	0.153374i	−0.361258	−	0.932466i	$-0.617653\pi$
$857$	227.664	−	131.442i	0.265652	−	0.153374i	0.626910	+	0.779092i	$0.284319\pi$
$858$		0			0
$859$	−277.678	+	480.952i	−0.323257	+	0.559897i	−0.981158	−	0.193207i	$-0.938111\pi$
$859$	−277.678	+	480.952i	−0.323257	+	0.559897i	0.657901	+	0.753104i	$0.271444\pi$
$860$		0			0
$861$	−109.456	+	14.3960i	−0.127127	+	0.0167200i
$862$		0			0
$863$		−	923.240i		−	1.06980i	−0.844914	−	0.534902i	$-0.820349\pi$
$863$		−	923.240i		−	1.06980i	0.844914	−	0.534902i	$-0.179651\pi$
$864$		0			0
$865$	153.559	+	265.973i	0.177525	+	0.307483i
$866$		0			0
$867$	−587.545	−	243.457i	−0.677676	−	0.280804i
$868$		0			0
$869$			2068.80i			2.38067i
$870$		0			0
$871$	−801.523	−	1388.28i	−0.920234	−	1.59389i
$872$		0			0
$873$	−919.190	+	246.044i	−1.05291	+	0.281838i
$874$		0			0
$875$	−54.7685	−	31.6206i	−0.0625925	−	0.0361378i
$876$		0			0
$877$	−1178.10			−1.34333			−0.671666	−	0.740854i	$-0.734421\pi$
$877$	−1178.10			−1.34333			−0.671666	+	0.740854i	$0.734421\pi$
$878$		0			0
$879$	545.677	−	1316.91i	0.620793	−	1.49819i
$880$		0			0
$881$		−	140.552i		−	0.159537i	−0.996813	−	0.0797684i	$-0.974582\pi$
$881$		−	140.552i		−	0.159537i	0.996813	−	0.0797684i	$-0.0254181\pi$
$882$		0			0
$883$	384.661	+	666.252i	0.435629	+	0.754532i	0.997347	−	0.0727970i	$-0.0231925\pi$
$883$	384.661	+	666.252i	0.435629	+	0.754532i	−0.561717	+	0.827329i	$0.689859\pi$
$884$		0			0
$885$	−770.165	+	590.812i	−0.870243	+	0.667584i
$886$		0			0
$887$	−773.195	−	446.405i	−0.871697	−	0.503275i	−0.00378525	−	0.999993i	$-0.501205\pi$
$887$	−773.195	−	446.405i	−0.871697	−	0.503275i	−0.867912	+	0.496718i	$0.834538\pi$
$888$		0			0
$889$	18.3405			0.0206305
$890$		0			0
$891$	−716.817	−	1243.03i	−0.804509	−	1.39510i
$892$		0			0
$893$	417.362	+	1302.43i	0.467371	+	1.45849i
$894$		0			0
$895$	−1023.05			−1.14307
$896$		0			0
$897$	−58.2737	+	140.634i	−0.0649651	+	0.156783i
$898$		0			0
$899$	−55.4420	+	32.0095i	−0.0616708	+	0.0356056i
$900$		0			0
$901$	−529.207			−0.587355
$902$		0			0
$903$	−10.2850	+	7.88988i	−0.0113898	+	0.00873741i
$904$		0			0
$905$	1190.19	−	687.156i	1.31513	−	0.759288i
$906$		0			0
$907$	20.4713	+	35.4573i	0.0225703	+	0.0390929i	0.877090	−	0.480326i	$-0.159482\pi$
$907$	20.4713	+	35.4573i	0.0225703	+	0.0390929i	−0.854520	+	0.519419i	$0.826148\pi$
$908$		0			0
$909$	−1010.12	−	270.938i	−1.11125	−	0.298062i
$910$		0			0
$911$	196.890	+	113.674i	0.216125	+	0.124780i	0.604155	−	0.796867i	$-0.293511\pi$
$911$	196.890	+	113.674i	0.216125	+	0.124780i	−0.388030	+	0.921647i	$0.626844\pi$
$912$		0			0
$913$	882.946	+	1529.31i	0.967082	+	1.67504i
$914$		0			0
$915$	749.967	+	977.635i	0.819636	+	1.06845i
$916$		0			0
$917$	28.7642	+	16.6070i	0.0313677	+	0.0181102i
$918$		0			0
$919$	−211.772			−0.230438			−0.115219	−	0.993340i	$-0.536757\pi$
$919$	−211.772			−0.230438			−0.115219	+	0.993340i	$0.536757\pi$
$920$		0			0
$921$	88.2684	+	671.128i	0.0958397	+	0.728694i
$922$		0			0
$923$	−112.983	+	65.2305i	−0.122408	+	0.0706723i
$924$		0			0
$925$	367.880			0.397709
$926$		0			0
$927$	745.403	−	199.526i	0.804102	−	0.215238i
$928$		0			0
$929$	−139.817	+	80.7233i	−0.150502	+	0.0868926i	−0.573360	−	0.819304i	$-0.694360\pi$
$929$	−139.817	+	80.7233i	−0.150502	+	0.0868926i	0.422858	+	0.906196i	$0.361027\pi$
$930$		0			0
$931$	682.386	+	619.444i	0.732960	+	0.665354i
$932$		0			0
$933$	−318.004	+	767.452i	−0.340840	+	0.822564i
$934$		0			0
$935$	−2023.92	+	1168.51i	−2.16462	+	1.24974i
$936$		0			0
$937$	381.188	+	660.237i	0.406817	+	0.704628i	0.994531	−	0.104441i	$-0.0333052\pi$
$937$	381.188	+	660.237i	0.406817	+	0.704628i	−0.587714	+	0.809069i	$0.699972\pi$
$938$		0			0
$939$	1206.48	−	925.517i	1.28485	−	0.985641i
$940$		0			0
$941$	−1251.65	−	722.643i	−1.33013	−	0.767952i	−0.344813	−	0.938671i	$-0.612058\pi$
$941$	−1251.65	−	722.643i	−1.33013	−	0.767952i	−0.985320	+	0.170719i	$0.945391\pi$
$942$		0			0
$943$	84.9297	−	147.103i	0.0900633	−	0.155994i
$944$		0			0
$945$	14.6464	−	110.922i	0.0154989	−	0.117378i
$946$		0			0
$947$	576.543	−	332.867i	0.608810	−	0.351496i	−0.163690	−	0.986512i	$-0.552340\pi$
$947$	576.543	−	332.867i	0.608810	−	0.351496i	0.772499	+	0.635015i	$0.219006\pi$
$948$		0			0
$949$	620.468	+	1074.68i	0.653812	+	1.13244i
$950$		0			0
$951$	−946.686	−	1234.07i	−0.995464	−	1.29766i
$952$		0			0
$953$	346.885	+	200.274i	0.363992	+	0.210151i	0.670831	−	0.741611i	$-0.265938\pi$
$953$	346.885	+	200.274i	0.363992	+	0.210151i	−0.306838	+	0.951762i	$0.599271\pi$
$954$		0			0
$955$	−410.726	+	711.399i	−0.430080	+	0.744920i
$956$		0			0
$957$	−51.7983	−	393.836i	−0.0541258	−	0.411532i
$958$		0			0
$959$	121.769	+	70.3035i	0.126975	+	0.0733092i
$960$		0			0
$961$	443.820	−	768.719i	0.461832	−	0.799916i
$962$		0			0
$963$	1718.81	+	461.025i	1.78485	+	0.478738i
$964$		0			0
$965$		−	563.067i		−	0.583489i
$966$		0			0
$967$	−10.4178			−0.0107733			−0.00538664	−	0.999985i	$-0.501715\pi$
$967$	−10.4178			−0.0107733			−0.00538664	+	0.999985i	$0.501715\pi$
$968$		0			0
$969$	−1153.83	+	544.443i	−1.19074	+	0.561861i
$970$		0			0
$971$	−112.459	−	64.9283i	−0.115818	−	0.0668675i	0.440972	−	0.897521i	$-0.354634\pi$
$971$	−112.459	−	64.9283i	−0.115818	−	0.0668675i	−0.556790	+	0.830653i	$0.687967\pi$
$972$		0			0
$973$	18.4057	+	31.8796i	0.0189164	+	0.0327642i
$974$		0			0
$975$	−59.5700	−	452.926i	−0.0610974	−	0.464540i
$976$		0			0
$977$	−509.607	+	294.222i	−0.521604	+	0.301148i	−0.737591	−	0.675248i	$-0.764037\pi$
$977$	−509.607	+	294.222i	−0.521604	+	0.301148i	0.215987	+	0.976396i	$0.430703\pi$
$978$		0			0
$979$	98.7783			0.100897
$980$		0			0
$981$	389.838	+	390.037i	0.397388	+	0.397591i
$982$		0			0
$983$	−706.945	+	408.155i	−0.719171	+	0.415213i	−0.814447	−	0.580237i	$-0.802960\pi$
$983$	−706.945	+	408.155i	−0.719171	+	0.415213i	0.0952766	+	0.995451i	$0.469626\pi$
$984$		0			0
$985$	1828.51			1.85635
$986$		0			0
$987$	150.531	−	19.7982i	0.152513	−	0.0200589i
$988$		0			0
$989$		−	19.9444i		−	0.0201662i
$990$		0			0
$991$	−23.6772	+	41.0101i	−0.0238922	+	0.0413826i	−0.877724	−	0.479166i	$-0.840939\pi$
$991$	−23.6772	+	41.0101i	−0.0238922	+	0.0413826i	0.853832	+	0.520549i	$0.174273\pi$
$992$		0			0
$993$	122.048	+	927.967i	0.122909	+	0.934508i
$994$		0			0
$995$	−1217.43	+	702.883i	−1.22355	+	0.706415i
$996$		0			0
$997$	−1782.01			−1.78737			−0.893686	−	0.448693i	$-0.851890\pi$
$997$	−1782.01			−1.78737			−0.893686	+	0.448693i	$0.851890\pi$
$998$		0			0
$999$	−389.949	−	942.443i	−0.390340	−	0.943386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.9	✓	80
3.2	odd	2		2052.3.m.a.1493.6		80
9.4	even	3		2052.3.be.a.125.35		80
9.5	odd	6		684.3.be.a.581.19	yes	80
19.7	even	3		684.3.be.a.425.19	yes	80
57.26	odd	6		2052.3.be.a.197.35		80
171.121	even	3		2052.3.m.a.881.35		80
171.140	odd	6	inner	684.3.m.a.653.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.9	✓	80	1.1	even	1	trivial
684.3.m.a.653.9	yes	80	171.140	odd	6	inner
684.3.be.a.425.19	yes	80	19.7	even	3
684.3.be.a.581.19	yes	80	9.5	odd	6
2052.3.m.a.881.35		80	171.121	even	3
2052.3.m.a.1493.6		80	3.2	odd	2
2052.3.be.a.125.35		80	9.4	even	3
2052.3.be.a.197.35		80	57.26	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38029 + 1.82598i) q^{3} +5.89395i q^{5} +(-0.351537 + 0.608880i) q^{7} +(2.33159 - 8.69274i) q^{9} +O(q^{10})\)	\(q+(-2.38029 + 1.82598i) q^{3} +5.89395i q^{5} +(-0.351537 + 0.608880i) q^{7} +(2.33159 - 8.69274i) q^{9} +(15.3415 + 8.85744i) q^{11} +(7.81809 - 13.5413i) q^{13} +(-10.7622 - 14.0293i) q^{15} +(19.3842 + 11.1915i) q^{17} +(18.0937 - 5.79811i) q^{19} +(-0.275041 - 2.09121i) q^{21} +(2.81046 + 1.62262i) q^{23} -9.73867 q^{25} +(10.3229 + 24.9487i) q^{27} +7.47447i q^{29} +(4.28250 + 7.41751i) q^{31} +(-52.6909 + 6.93003i) q^{33} +(-3.58871 - 2.07194i) q^{35} -37.7752 q^{37} +(6.11685 + 46.5080i) q^{39} -52.3411i q^{41} +(-3.07286 - 5.32236i) q^{43} +(51.2346 + 13.7423i) q^{45} +71.9825i q^{47} +(24.2528 + 42.0072i) q^{49} +(-66.5755 + 8.75617i) q^{51} +(-20.4757 + 11.8217i) q^{53} +(-52.2053 + 90.4223i) q^{55} +(-32.4811 + 46.8399i) q^{57} -54.8968i q^{59} -69.6850 q^{61} +(4.47319 + 4.47548i) q^{63} +(79.8119 + 46.0794i) q^{65} +(51.2608 - 88.7864i) q^{67} +(-9.65260 + 1.26953i) q^{69} +(-7.22572 - 4.17177i) q^{71} +(-39.6816 + 68.7305i) q^{73} +(23.1809 - 17.7826i) q^{75} +(-10.7862 + 6.22743i) q^{77} +(58.3917 + 101.137i) q^{79} +(-70.1273 - 40.5359i) q^{81} +(86.3290 + 49.8421i) q^{83} +(-65.9620 + 114.250i) q^{85} +(-13.6482 - 17.7914i) q^{87} +(4.82896 - 2.78800i) q^{89} +(5.49669 + 9.52055i) q^{91} +(-23.7378 - 9.83609i) q^{93} +(34.1738 + 106.643i) q^{95} +(-52.8639 - 91.5630i) q^{97} +(112.766 - 112.708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more