LMFDB - Embedded newform 855.2.n.e.647.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.3
Character	$\chi$	$=$	855.647
Dual form			855.2.n.e.818.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47221 + 1.47221i) q^{2} -2.33479i q^{4} +(1.56330 - 1.59878i) q^{5} +(1.22506 + 1.22506i) q^{7} +(0.492885 + 0.492885i) q^{8} +O(q^{10})$	\(q+(-1.47221 + 1.47221i) q^{2} -2.33479i q^{4} +(1.56330 - 1.59878i) q^{5} +(1.22506 + 1.22506i) q^{7} +(0.492885 + 0.492885i) q^{8} +(0.0522374 + 4.65524i) q^{10} +0.147276i q^{11} +(3.13257 - 3.13257i) q^{13} -3.60709 q^{14} +3.21833 q^{16} +(-2.67634 + 2.67634i) q^{17} +1.00000i q^{19} +(-3.73282 - 3.64998i) q^{20} +(-0.216820 - 0.216820i) q^{22} +(-5.66932 - 5.66932i) q^{23} +(-0.112198 - 4.99874i) q^{25} +9.22360i q^{26} +(2.86026 - 2.86026i) q^{28} +4.33782 q^{29} +9.06025 q^{31} +(-5.72382 + 5.72382i) q^{32} -7.88026i q^{34} +(3.87374 - 0.0434681i) q^{35} +(-1.36399 - 1.36399i) q^{37} +(-1.47221 - 1.47221i) q^{38} +(1.55854 - 0.0174887i) q^{40} -12.1522i q^{41} +(-0.718458 + 0.718458i) q^{43} +0.343858 q^{44} +16.6928 q^{46} +(3.82900 - 3.82900i) q^{47} -3.99845i q^{49} +(7.52437 + 7.19401i) q^{50} +(-7.31391 - 7.31391i) q^{52} +(6.09276 + 6.09276i) q^{53} +(0.235461 + 0.230236i) q^{55} +1.20763i q^{56} +(-6.38618 + 6.38618i) q^{58} +14.7072 q^{59} -9.05095 q^{61} +(-13.3386 + 13.3386i) q^{62} -10.4166i q^{64} +(-0.111151 - 9.90545i) q^{65} +(3.19212 + 3.19212i) q^{67} +(6.24870 + 6.24870i) q^{68} +(-5.63896 + 5.76694i) q^{70} +6.30955i q^{71} +(-1.43671 + 1.43671i) q^{73} +4.01614 q^{74} +2.33479 q^{76} +(-0.180422 + 0.180422i) q^{77} +1.27210i q^{79} +(5.03121 - 5.14540i) q^{80} +(17.8906 + 17.8906i) q^{82} +(3.60051 + 3.60051i) q^{83} +(0.0949628 + 8.46279i) q^{85} -2.11544i q^{86} +(-0.0725899 + 0.0725899i) q^{88} +2.75160 q^{89} +7.67519 q^{91} +(-13.2367 + 13.2367i) q^{92} +11.2742i q^{94} +(1.59878 + 1.56330i) q^{95} +(1.79223 + 1.79223i) q^{97} +(5.88655 + 5.88655i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7}+O(q^{10}) $ 36 * q + 4 * q^7	$ 36 q + 4 q^{7} + 8 q^{10} + 4 q^{13} - 36 q^{16} - 80 q^{22} + 16 q^{25} - 24 q^{28} - 4 q^{37} + 76 q^{40} - 20 q^{43} + 96 q^{46} - 68 q^{52} + 48 q^{55} - 12 q^{58} + 56 q^{61} - 8 q^{67} - 16 q^{70} - 56 q^{73} + 36 q^{76} - 100 q^{82} + 80 q^{85} - 184 q^{88} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^7 + 8 * q^10 + 4 * q^13 - 36 * q^16 - 80 * q^22 + 16 * q^25 - 24 * q^28 - 4 * q^37 + 76 * q^40 - 20 * q^43 + 96 * q^46 - 68 * q^52 + 48 * q^55 - 12 * q^58 + 56 * q^61 - 8 * q^67 - 16 * q^70 - 56 * q^73 + 36 * q^76 - 100 * q^82 + 80 * q^85 - 184 * q^88 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.47221	+	1.47221i	−1.04101	+	1.04101i	−0.0418859	+	0.999122i	$0.513337\pi$
$2$	−1.47221	+	1.47221i	−1.04101	+	1.04101i	−0.999122	+	0.0418859i	$0.986663\pi$
$3$		0			0
$3$		0			0
$4$		−	2.33479i		−	1.16740i
$5$	1.56330	−	1.59878i	0.699128	−	0.714996i
$5$	1.56330	−	1.59878i	0.699128	−	0.714996i
$6$		0			0
$7$	1.22506	+	1.22506i	0.463030	+	0.463030i	0.899647	−	0.436618i	$-0.143824\pi$
$7$	1.22506	+	1.22506i	0.463030	+	0.463030i	−0.436618	+	0.899647i	$0.643824\pi$
$8$	0.492885	+	0.492885i	0.174261	+	0.174261i
$9$		0			0
$10$	0.0522374	+	4.65524i	0.0165189	+	1.47212i
$11$			0.147276i			0.0444053i	0.999753	+	0.0222026i	$0.00706790\pi$
$11$			0.147276i			0.0444053i	−0.999753	+	0.0222026i	$0.992932\pi$
$12$		0			0
$13$	3.13257	−	3.13257i	0.868820	−	0.868820i	−0.123522	−	0.992342i	$-0.539419\pi$
$13$	3.13257	−	3.13257i	0.868820	−	0.868820i	0.992342	+	0.123522i	$0.0394190\pi$
$14$	−3.60709			−0.964035
$15$		0			0
$16$	3.21833			0.804582
$17$	−2.67634	+	2.67634i	−0.649108	+	0.649108i	−0.952777	−	0.303670i	$-0.901788\pi$
$17$	−2.67634	+	2.67634i	−0.649108	+	0.649108i	0.303670	+	0.952777i	$0.401788\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−3.73282	−	3.64998i	−0.834684	−	0.816160i
$21$		0			0
$22$	−0.216820	−	0.216820i	−0.0462262	−	0.0462262i
$23$	−5.66932	−	5.66932i	−1.18213	−	1.18213i	−0.979190	−	0.202944i	$-0.934949\pi$
$23$	−5.66932	−	5.66932i	−1.18213	−	1.18213i	−0.202944	−	0.979190i	$-0.565051\pi$
$24$		0			0
$25$	−0.112198	−	4.99874i	−0.0224396	−	0.999748i
$26$			9.22360i			1.80890i
$27$		0			0
$28$	2.86026	−	2.86026i	0.540539	−	0.540539i
$29$	4.33782			0.805514			0.402757	−	0.915307i	$-0.368052\pi$
$29$	4.33782			0.805514			0.402757	+	0.915307i	$0.368052\pi$
$30$		0			0
$31$	9.06025			1.62727			0.813635	−	0.581376i	$-0.197486\pi$
$31$	9.06025			1.62727			0.813635	+	0.581376i	$0.197486\pi$
$32$	−5.72382	+	5.72382i	−1.01184	+	1.01184i
$33$		0			0
$34$		−	7.88026i		−	1.35145i
$35$	3.87374	−	0.0434681i	0.654781	−	0.00734744i
$36$		0			0
$37$	−1.36399	−	1.36399i	−0.224238	−	0.224238i	0.586042	−	0.810280i	$-0.300685\pi$
$37$	−1.36399	−	1.36399i	−0.224238	−	0.224238i	−0.810280	+	0.586042i	$0.800685\pi$
$38$	−1.47221	−	1.47221i	−0.238824	−	0.238824i
$39$		0			0
$40$	1.55854	−	0.0174887i	0.246427	−	0.00276521i
$41$		−	12.1522i		−	1.89786i	−0.315485	−	0.948931i	$-0.602167\pi$
$41$		−	12.1522i		−	1.89786i	0.315485	−	0.948931i	$-0.397833\pi$
$42$		0			0
$43$	−0.718458	+	0.718458i	−0.109564	+	0.109564i	−0.759763	−	0.650200i	$-0.774685\pi$
$43$	−0.718458	+	0.718458i	−0.109564	+	0.109564i	0.650200	+	0.759763i	$0.274685\pi$
$44$	0.343858			0.0518385
$45$		0			0
$46$	16.6928			2.46122
$47$	3.82900	−	3.82900i	0.558516	−	0.558516i	−0.370369	−	0.928885i	$-0.620769\pi$
$47$	3.82900	−	3.82900i	0.558516	−	0.558516i	0.928885	+	0.370369i	$0.120769\pi$
$48$		0			0
$49$		−	3.99845i		−	0.571207i
$50$	7.52437	+	7.19401i	1.06411	+	1.01739i
$51$		0			0
$52$	−7.31391	−	7.31391i	−1.01426	−	1.01426i
$53$	6.09276	+	6.09276i	0.836905	+	0.836905i	0.988450	−	0.151545i	$-0.0484249\pi$
$53$	6.09276	+	6.09276i	0.836905	+	0.836905i	−0.151545	+	0.988450i	$0.548425\pi$
$54$		0			0
$55$	0.235461	+	0.230236i	0.0317496	+	0.0310450i
$56$			1.20763i			0.161376i
$57$		0			0
$58$	−6.38618	+	6.38618i	−0.838546	+	0.838546i
$59$	14.7072			1.91471			0.957355	−	0.288913i	$-0.0932937\pi$
$59$	14.7072			1.91471			0.957355	+	0.288913i	$0.0932937\pi$
$60$		0			0
$61$	−9.05095			−1.15886			−0.579428	−	0.815024i	$-0.696724\pi$
$61$	−9.05095			−1.15886			−0.579428	+	0.815024i	$0.696724\pi$
$62$	−13.3386	+	13.3386i	−1.69400	+	1.69400i
$63$		0			0
$64$		−	10.4166i		−	1.30208i
$65$	−0.111151	−	9.90545i	−0.0137866	−	1.22862i
$66$		0			0
$67$	3.19212	+	3.19212i	0.389980	+	0.389980i	0.874680	−	0.484700i	$-0.161071\pi$
$67$	3.19212	+	3.19212i	0.389980	+	0.389980i	−0.484700	+	0.874680i	$0.661071\pi$
$68$	6.24870	+	6.24870i	0.757766	+	0.757766i
$69$		0			0
$70$	−5.63896	+	5.76694i	−0.673984	+	0.689282i
$71$			6.30955i			0.748806i	0.927266	+	0.374403i	$0.122152\pi$
$71$			6.30955i			0.748806i	−0.927266	+	0.374403i	$0.877848\pi$
$72$		0			0
$73$	−1.43671	+	1.43671i	−0.168154	+	0.168154i	−0.786168	−	0.618013i	$-0.787938\pi$
$73$	−1.43671	+	1.43671i	−0.168154	+	0.168154i	0.618013	+	0.786168i	$0.287938\pi$
$74$	4.01614			0.466867
$75$		0			0
$76$	2.33479			0.267819
$77$	−0.180422	+	0.180422i	−0.0205609	+	0.0205609i
$78$		0			0
$79$			1.27210i			0.143123i	0.997436	+	0.0715613i	$0.0227982\pi$
$79$			1.27210i			0.143123i	−0.997436	+	0.0715613i	$0.977202\pi$
$80$	5.03121	−	5.14540i	0.562506	−	0.575273i
$81$		0			0
$82$	17.8906	+	17.8906i	1.97569	+	1.97569i
$83$	3.60051	+	3.60051i	0.395207	+	0.395207i	0.876539	−	0.481332i	$-0.159847\pi$
$83$	3.60051	+	3.60051i	0.395207	+	0.395207i	−0.481332	+	0.876539i	$0.659847\pi$
$84$		0			0
$85$	0.0949628	+	8.46279i	0.0103002	+	0.917919i
$86$		−	2.11544i		−	0.228114i
$87$		0			0
$88$	−0.0725899	+	0.0725899i	−0.00773811	+	0.00773811i
$89$	2.75160			0.291669			0.145834	−	0.989309i	$-0.453413\pi$
$89$	2.75160			0.291669			0.145834	+	0.989309i	$0.453413\pi$
$90$		0			0
$91$	7.67519			0.804578
$92$	−13.2367	+	13.2367i	−1.38002	+	1.38002i
$93$		0			0
$94$			11.2742i			1.16284i
$95$	1.59878	+	1.56330i	0.164031	+	0.160391i
$96$		0			0
$97$	1.79223	+	1.79223i	0.181974	+	0.181974i	0.792215	−	0.610242i	$-0.208928\pi$
$97$	1.79223	+	1.79223i	0.181974	+	0.181974i	−0.610242	+	0.792215i	$0.708928\pi$
$98$	5.88655	+	5.88655i	0.594631	+	0.594631i
$99$		0			0
$100$	−11.6710	+	0.261959i	−1.16710	+	0.0261959i
$101$			0.235131i			0.0233964i	0.999932	+	0.0116982i	$0.00372374\pi$
$101$			0.235131i			0.0233964i	−0.999932	+	0.0116982i	$0.996276\pi$
$102$		0			0
$103$	−6.39987	+	6.39987i	−0.630598	+	0.630598i	−0.948218	−	0.317620i	$-0.897116\pi$
$103$	−6.39987	+	6.39987i	−0.630598	+	0.630598i	0.317620	+	0.948218i	$0.397116\pi$
$104$	3.08800			0.302803
$105$		0			0
$106$	−17.9396			−1.74245
$107$	−5.32256	+	5.32256i	−0.514551	+	0.514551i	−0.915917	−	0.401367i	$-0.868535\pi$
$107$	−5.32256	+	5.32256i	−0.514551	+	0.514551i	0.401367	+	0.915917i	$0.368535\pi$
$108$		0			0
$109$			1.57670i			0.151021i	0.997145	+	0.0755104i	$0.0240586\pi$
$109$			1.57670i			0.151021i	−0.997145	+	0.0755104i	$0.975941\pi$
$110$	−0.685603	+	0.00769330i	−0.0653697	+	0.000733527i
$111$		0			0
$112$	3.94265	+	3.94265i	0.372545	+	0.372545i
$113$	4.49106	+	4.49106i	0.422483	+	0.422483i	0.886058	−	0.463575i	$-0.153433\pi$
$113$	4.49106	+	4.49106i	0.422483	+	0.422483i	−0.463575	+	0.886058i	$0.653433\pi$
$114$		0			0
$115$	−17.9268	+	0.201161i	−1.67168	+	0.0187583i
$116$		−	10.1279i		−	0.940354i
$117$		0			0
$118$	−21.6520	+	21.6520i	−1.99323	+	1.99323i
$119$	−6.55736			−0.601112
$120$		0			0
$121$	10.9783			0.998028
$122$	13.3249	−	13.3249i	1.20638	−	1.20638i
$123$		0			0
$124$		−	21.1538i		−	1.89967i
$125$	−8.16729	−	7.63514i	−0.730504	−	0.682908i
$126$		0			0
$127$	−2.43386	−	2.43386i	−0.215970	−	0.215970i	0.590828	−	0.806798i	$-0.298801\pi$
$127$	−2.43386	−	2.43386i	−0.215970	−	0.215970i	−0.806798	+	0.590828i	$0.798801\pi$
$128$	3.88783	+	3.88783i	0.343639	+	0.343639i
$129$		0			0
$130$	14.7465	+	14.4192i	1.29335	+	1.26465i
$131$			14.4509i			1.26258i	0.775547	+	0.631290i	$0.217474\pi$
$131$			14.4509i			1.26258i	−0.775547	+	0.631290i	$0.782526\pi$
$132$		0			0
$133$	−1.22506	+	1.22506i	−0.106226	+	0.106226i
$134$	−9.39894			−0.811945
$135$		0			0
$136$	−2.63825			−0.226228
$137$	9.41417	−	9.41417i	0.804307	−	0.804307i	−0.179459	−	0.983766i	$-0.557435\pi$
$137$	9.41417	−	9.41417i	0.804307	−	0.804307i	0.983766	+	0.179459i	$0.0574346\pi$
$138$		0			0
$139$		−	17.7831i		−	1.50834i	−0.656677	−	0.754172i	$-0.728038\pi$
$139$		−	17.7831i		−	1.50834i	0.656677	−	0.754172i	$-0.271962\pi$
$140$	−0.101489	−	9.04438i	−0.00857738	−	0.764390i
$141$		0			0
$142$	−9.28898	−	9.28898i	−0.779514	−	0.779514i
$143$	0.461352	+	0.461352i	0.0385802	+	0.0385802i
$144$		0			0
$145$	6.78131	−	6.93523i	0.563157	−	0.575939i
$146$		−	4.23027i		−	0.350100i
$147$		0			0
$148$	−3.18463	+	3.18463i	−0.261775	+	0.261775i
$149$	−1.31094			−0.107397			−0.0536984	−	0.998557i	$-0.517101\pi$
$149$	−1.31094			−0.107397			−0.0536984	+	0.998557i	$0.517101\pi$
$150$		0			0
$151$	14.8676			1.20990			0.604952	−	0.796262i	$-0.293192\pi$
$151$	14.8676			1.20990			0.604952	+	0.796262i	$0.293192\pi$
$152$	−0.492885	+	0.492885i	−0.0399782	+	0.0399782i
$153$		0			0
$154$		−	0.531236i		−	0.0428082i
$155$	14.1639	−	14.4854i	1.13767	−	1.16349i
$156$		0			0
$157$	−15.2621	−	15.2621i	−1.21805	−	1.21805i	−0.968314	−	0.249734i	$-0.919657\pi$
$157$	−15.2621	−	15.2621i	−1.21805	−	1.21805i	−0.249734	−	0.968314i	$-0.580343\pi$
$158$	−1.87280	−	1.87280i	−0.148992	−	0.148992i
$159$		0			0
$160$	0.203095	+	18.0992i	0.0160560	+	1.43086i
$161$		−	13.8905i		−	1.09473i
$162$		0			0
$163$	−1.39888	+	1.39888i	−0.109569	+	0.109569i	−0.759766	−	0.650197i	$-0.774686\pi$
$163$	−1.39888	+	1.39888i	−0.109569	+	0.109569i	0.650197	+	0.759766i	$0.274686\pi$
$164$	−28.3730			−2.21556
$165$		0			0
$166$	−10.6014			−0.822827
$167$	4.75260	−	4.75260i	0.367767	−	0.367767i	−0.498895	−	0.866662i	$-0.666261\pi$
$167$	4.75260	−	4.75260i	0.367767	−	0.367767i	0.866662	+	0.498895i	$0.166261\pi$
$168$		0			0
$169$		−	6.62604i		−	0.509696i
$170$	−12.5988	−	12.3192i	−0.966284	−	0.944839i
$171$		0			0
$172$	1.67745	+	1.67745i	0.127904	+	0.127904i
$173$	−11.6113	−	11.6113i	−0.882792	−	0.882792i	0.111026	−	0.993818i	$-0.464586\pi$
$173$	−11.6113	−	11.6113i	−0.882792	−	0.882792i	−0.993818	+	0.111026i	$0.964586\pi$
$174$		0			0
$175$	5.98631	−	6.26121i	0.452523	−	0.473303i
$176$			0.473981i			0.0357277i
$177$		0			0
$178$	−4.05093	+	4.05093i	−0.303630	+	0.303630i
$179$	6.12027			0.457451			0.228725	−	0.973491i	$-0.426544\pi$
$179$	6.12027			0.457451			0.228725	+	0.973491i	$0.426544\pi$
$180$		0			0
$181$	18.1732			1.35080			0.675402	−	0.737450i	$-0.263970\pi$
$181$	18.1732			1.35080			0.675402	+	0.737450i	$0.263970\pi$
$182$	−11.2995	+	11.2995i	−0.837573	+	0.837573i
$183$		0			0
$184$		−	5.58864i		−	0.412000i
$185$	−4.31303	+	0.0483975i	−0.317100	+	0.00355825i
$186$		0			0
$187$	−0.394159	−	0.394159i	−0.0288238	−	0.0288238i
$188$	−8.93991	−	8.93991i	−0.652010	−	0.652010i
$189$		0			0
$190$	−4.65524	+	0.0522374i	−0.337726	+	0.00378970i
$191$			20.1729i			1.45966i	0.683628	+	0.729831i	$0.260401\pi$
$191$			20.1729i			1.45966i	−0.683628	+	0.729831i	$0.739599\pi$
$192$		0			0
$193$	−2.80724	+	2.80724i	−0.202070	+	0.202070i	−0.800886	−	0.598816i	$-0.795638\pi$
$193$	−2.80724	+	2.80724i	−0.202070	+	0.202070i	0.598816	+	0.800886i	$0.295638\pi$
$194$	−5.27708			−0.378872
$195$		0			0
$196$	−9.33555			−0.666825
$197$	−8.95558	+	8.95558i	−0.638059	+	0.638059i	−0.950076	−	0.312018i	$-0.898995\pi$
$197$	−8.95558	+	8.95558i	−0.638059	+	0.638059i	0.312018	+	0.950076i	$0.398995\pi$
$198$		0			0
$199$		−	13.7471i		−	0.974504i	−0.873261	−	0.487252i	$-0.837999\pi$
$199$		−	13.7471i		−	0.974504i	0.873261	−	0.487252i	$-0.162001\pi$
$200$	2.40850	−	2.51910i	0.170307	−	0.178127i
$201$		0			0
$202$	−0.346161	−	0.346161i	−0.0243558	−	0.0243558i
$203$	5.31410	+	5.31410i	0.372977	+	0.372977i
$204$		0			0
$205$	−19.4288	−	18.9976i	−1.35696	−	1.32685i
$206$		−	18.8439i		−	1.31292i
$207$		0			0
$208$	10.0817	−	10.0817i	0.699037	−	0.699037i
$209$	−0.147276			−0.0101873
$210$		0			0
$211$	−2.95036			−0.203111			−0.101556	−	0.994830i	$-0.532382\pi$
$211$	−2.95036			−0.203111			−0.101556	+	0.994830i	$0.532382\pi$
$212$	14.2253	−	14.2253i	0.977000	−	0.977000i
$213$		0			0
$214$		−	15.6718i		−	1.07130i
$215$	0.0254926	+	2.27182i	0.00173858	+	0.154937i
$216$		0			0
$217$	11.0994	+	11.0994i	0.753474	+	0.753474i
$218$	−2.32124	−	2.32124i	−0.157214	−	0.157214i
$219$		0			0
$220$	0.537552	−	0.549753i	0.0362418	−	0.0370644i
$221$			16.7677i			1.12791i
$222$		0			0
$223$	−15.7432	+	15.7432i	−1.05424	+	1.05424i	−0.0558020	+	0.998442i	$0.517772\pi$
$223$	−15.7432	+	15.7432i	−1.05424	+	1.05424i	−0.998442	+	0.0558020i	$0.982228\pi$
$224$	−14.0241			−0.937021
$225$		0			0
$226$	−13.2235			−0.879617
$227$	7.81372	−	7.81372i	0.518615	−	0.518615i	−0.398537	−	0.917152i	$-0.630482\pi$
$227$	7.81372	−	7.81372i	0.518615	−	0.518615i	0.917152	+	0.398537i	$0.130482\pi$
$228$		0			0
$229$		−	1.46458i		−	0.0967824i	−0.998828	−	0.0483912i	$-0.984591\pi$
$229$		−	1.46458i		−	0.0967824i	0.998828	−	0.0483912i	$-0.0154094\pi$
$230$	26.0959	−	26.6882i	1.72071	−	1.75977i
$231$		0			0
$232$	2.13805	+	2.13805i	0.140370	+	0.140370i
$233$	6.57592	+	6.57592i	0.430803	+	0.430803i	0.888901	−	0.458099i	$-0.151469\pi$
$233$	6.57592	+	6.57592i	0.430803	+	0.430803i	−0.458099	+	0.888901i	$0.651469\pi$
$234$		0			0
$235$	−0.135862	−	12.1076i	−0.00886265	−	0.789812i
$236$		−	34.3382i		−	2.23523i
$237$		0			0
$238$	9.65379	−	9.65379i	0.625763	−	0.625763i
$239$	−13.0479			−0.843999			−0.421999	−	0.906596i	$-0.638672\pi$
$239$	−13.0479			−0.843999			−0.421999	+	0.906596i	$0.638672\pi$
$240$		0			0
$241$	−24.2904			−1.56468			−0.782340	−	0.622851i	$-0.785974\pi$
$241$	−24.2904			−1.56468			−0.782340	+	0.622851i	$0.785974\pi$
$242$	−16.1624	+	16.1624i	−1.03896	+	1.03896i
$243$		0			0
$244$			21.1321i			1.35284i
$245$	−6.39265	−	6.25077i	−0.408411	−	0.399347i
$246$		0			0
$247$	3.13257	+	3.13257i	0.199321	+	0.199321i
$248$	4.46566	+	4.46566i	0.283570	+	0.283570i
$249$		0			0
$250$	23.2645	−	0.783430i	1.47137	−	0.0495484i
$251$		−	16.5742i		−	1.04616i	−0.852285	−	0.523078i	$-0.824784\pi$
$251$		−	16.5742i		−	1.04616i	0.852285	−	0.523078i	$-0.175216\pi$
$252$		0			0
$253$	0.834952	−	0.834952i	0.0524930	−	0.0524930i
$254$	7.16630			0.449654
$255$		0			0
$256$	9.38590			0.586618
$257$	21.0924	−	21.0924i	1.31571	−	1.31571i	0.398571	−	0.917138i	$-0.369506\pi$
$257$	21.0924	−	21.0924i	1.31571	−	1.31571i	0.917138	−	0.398571i	$-0.130494\pi$
$258$		0			0
$259$		−	3.34193i		−	0.207658i
$260$	−23.1272	+	0.259515i	−1.43429	+	0.0160944i
$261$		0			0
$262$	−21.2747	−	21.2747i	−1.31436	−	1.31436i
$263$	8.08853	+	8.08853i	0.498760	+	0.498760i	0.911052	−	0.412292i	$-0.135272\pi$
$263$	8.08853	+	8.08853i	0.498760	+	0.498760i	−0.412292	+	0.911052i	$0.635272\pi$
$264$		0			0
$265$	19.2658	−	0.216186i	1.18349	−	0.0132802i
$266$		−	3.60709i		−	0.221165i
$267$		0			0
$268$	7.45295	−	7.45295i	0.455261	−	0.455261i
$269$	−32.1518			−1.96033			−0.980164	−	0.198188i	$-0.936494\pi$
$269$	−32.1518			−1.96033			−0.980164	+	0.198188i	$0.936494\pi$
$270$		0			0
$271$	−27.5560			−1.67391			−0.836953	−	0.547274i	$-0.815665\pi$
$271$	−27.5560			−1.67391			−0.836953	+	0.547274i	$0.815665\pi$
$272$	−8.61334	+	8.61334i	−0.522260	+	0.522260i
$273$		0			0
$274$			27.7192i			1.67458i
$275$	0.736192	−	0.0165240i	0.0443941	−	0.000996436i
$276$		0			0
$277$	−14.0295	−	14.0295i	−0.842950	−	0.842950i	0.146291	−	0.989242i	$-0.453266\pi$
$277$	−14.0295	−	14.0295i	−0.842950	−	0.842950i	−0.989242	+	0.146291i	$0.953266\pi$
$278$	26.1804	+	26.1804i	1.57020	+	1.57020i
$279$		0			0
$280$	1.93073	+	1.88788i	0.115383	+	0.112823i
$281$			16.9177i			1.00923i	0.863346	+	0.504613i	$0.168365\pi$
$281$			16.9177i			1.00923i	−0.863346	+	0.504613i	$0.831635\pi$
$282$		0			0
$283$	−10.9147	+	10.9147i	−0.648809	+	0.648809i	−0.952705	−	0.303896i	$-0.901712\pi$
$283$	−10.9147	+	10.9147i	−0.648809	+	0.648809i	0.303896	+	0.952705i	$0.401712\pi$
$284$	14.7315			0.874154
$285$		0			0
$286$	−1.35841			−0.0803245
$287$	14.8872	−	14.8872i	0.878766	−	0.878766i
$288$		0			0
$289$			2.67442i			0.157319i
$290$	0.226597	+	20.1936i	0.0133062	+	1.18581i
$291$		0			0
$292$	3.35442	+	3.35442i	0.196302	+	0.196302i
$293$	−12.3281	−	12.3281i	−0.720217	−	0.720217i	0.248432	−	0.968649i	$-0.420085\pi$
$293$	−12.3281	−	12.3281i	−0.720217	−	0.720217i	−0.968649	+	0.248432i	$0.920085\pi$
$294$		0			0
$295$	22.9917	−	23.5135i	1.33863	−	1.36901i
$296$		−	1.34458i		−	0.0781519i
$297$		0			0
$298$	1.92998	−	1.92998i	0.111801	−	0.111801i
$299$	−35.5191			−2.05412
$300$		0			0
$301$	−1.76031			−0.101463
$302$	−21.8881	+	21.8881i	−1.25952	+	1.25952i
$303$		0			0
$304$			3.21833i			0.184584i
$305$	−14.1493	+	14.4705i	−0.810188	+	0.828577i
$306$		0			0
$307$	11.7629	+	11.7629i	0.671345	+	0.671345i	0.958026	−	0.286681i	$-0.0925521\pi$
$307$	11.7629	+	11.7629i	0.671345	+	0.671345i	−0.286681	+	0.958026i	$0.592552\pi$
$308$	0.421247	+	0.421247i	0.0240028	+	0.0240028i
$309$		0			0
$310$	0.473284	+	42.1776i	0.0268807	+	2.39553i
$311$			8.00587i			0.453971i	0.973898	+	0.226985i	$0.0728870\pi$
$311$			8.00587i			0.453971i	−0.973898	+	0.226985i	$0.927113\pi$
$312$		0			0
$313$	−22.4087	+	22.4087i	−1.26661	+	1.26661i	−0.318788	+	0.947826i	$0.603276\pi$
$313$	−22.4087	+	22.4087i	−1.26661	+	1.26661i	−0.947826	+	0.318788i	$0.896724\pi$
$314$	44.9380			2.53600
$315$		0			0
$316$	2.97009			0.167081
$317$	−1.63822	+	1.63822i	−0.0920114	+	0.0920114i	−0.751614	−	0.659603i	$-0.770724\pi$
$317$	−1.63822	+	1.63822i	−0.0920114	+	0.0920114i	0.659603	+	0.751614i	$0.270724\pi$
$318$		0			0
$319$			0.638856i			0.0357690i
$320$	−16.6539	−	16.2843i	−0.930983	−	0.910321i
$321$		0			0
$322$	20.4497	+	20.4497i	1.13962	+	1.13962i
$323$	−2.67634	−	2.67634i	−0.148915	−	0.148915i
$324$		0			0
$325$	−16.0104	−	15.3075i	−0.888097	−	0.849105i
$326$		−	4.11889i		−	0.228124i
$327$		0			0
$328$	5.98965	−	5.98965i	0.330723	−	0.330723i
$329$	9.38151			0.517219
$330$		0			0
$331$	12.4349			0.683486			0.341743	−	0.939793i	$-0.388983\pi$
$331$	12.4349			0.683486			0.341743	+	0.939793i	$0.388983\pi$
$332$	8.40643	−	8.40643i	0.461363	−	0.461363i
$333$		0			0
$334$			13.9936i			0.765697i
$335$	10.0937	−	0.113264i	0.551480	−	0.00618828i
$336$		0			0
$337$	−5.16764	−	5.16764i	−0.281499	−	0.281499i	0.552207	−	0.833707i	$-0.313786\pi$
$337$	−5.16764	−	5.16764i	−0.281499	−	0.281499i	−0.833707	+	0.552207i	$0.813786\pi$
$338$	9.75491	+	9.75491i	0.530597	+	0.530597i
$339$		0			0
$340$	19.7589	−	0.221719i	1.07158	−	0.0120244i
$341$			1.33435i			0.0722593i
$342$		0			0
$343$	13.4738	−	13.4738i	0.727515	−	0.727515i
$344$	−0.708234			−0.0381854
$345$		0			0
$346$	34.1885			1.83799
$347$	−3.26984	+	3.26984i	−0.175534	+	0.175534i	−0.789406	−	0.613872i	$-0.789611\pi$
$347$	−3.26984	+	3.26984i	−0.175534	+	0.175534i	0.613872	+	0.789406i	$0.289611\pi$
$348$		0			0
$349$			25.7089i			1.37616i	0.725633	+	0.688082i	$0.241547\pi$
$349$			25.7089i			1.37616i	−0.725633	+	0.688082i	$0.758453\pi$
$350$	0.404708	+	18.0309i	0.0216326	+	0.963792i
$351$		0			0
$352$	−0.842979	−	0.842979i	−0.0449309	−	0.0449309i
$353$	−8.22601	−	8.22601i	−0.437827	−	0.437827i	0.453453	−	0.891280i	$-0.350192\pi$
$353$	−8.22601	−	8.22601i	−0.437827	−	0.437827i	−0.891280	+	0.453453i	$0.850192\pi$
$354$		0			0
$355$	10.0876	+	9.86371i	0.535394	+	0.523512i
$356$		−	6.42441i		−	0.340493i
$357$		0			0
$358$	−9.01031	+	9.01031i	−0.476210	+	0.476210i
$359$	−11.5563			−0.609918			−0.304959	−	0.952365i	$-0.598643\pi$
$359$	−11.5563			−0.609918			−0.304959	+	0.952365i	$0.598643\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−26.7547	+	26.7547i	−1.40620	+	1.40620i
$363$		0			0
$364$		−	17.9200i		−	0.939262i
$365$	0.0509778	+	4.54299i	0.00266830	+	0.237791i
$366$		0			0
$367$	5.85680	+	5.85680i	0.305723	+	0.305723i	0.843248	−	0.537525i	$-0.180641\pi$
$367$	5.85680	+	5.85680i	0.305723	+	0.305723i	−0.537525	+	0.843248i	$0.680641\pi$
$368$	−18.2457	−	18.2457i	−0.951124	−	0.951124i
$369$		0			0
$370$	6.27843	−	6.42093i	0.326400	−	0.333808i
$371$			14.9280i			0.775024i
$372$		0			0
$373$	−20.4324	+	20.4324i	−1.05795	+	1.05795i	−0.0597374	+	0.998214i	$0.519026\pi$
$373$	−20.4324	+	20.4324i	−1.05795	+	1.05795i	−0.998214	+	0.0597374i	$0.980974\pi$
$374$	1.16057			0.0600116
$375$		0			0
$376$	3.77451			0.194655
$377$	13.5886	−	13.5886i	0.699846	−	0.699846i
$378$		0			0
$379$			7.33698i			0.376876i	0.982085	+	0.188438i	$0.0603424\pi$
$379$			7.33698i			0.376876i	−0.982085	+	0.188438i	$0.939658\pi$
$380$	3.64998	−	3.73282i	0.187240	−	0.191490i
$381$		0			0
$382$	−29.6988	−	29.6988i	−1.51952	−	1.51952i
$383$	27.6038	+	27.6038i	1.41049	+	1.41049i	0.756519	+	0.653972i	$0.226899\pi$
$383$	27.6038	+	27.6038i	1.41049	+	1.41049i	0.653972	+	0.756519i	$0.273101\pi$
$384$		0			0
$385$	0.00640178	+	0.570507i	0.000326265	+	0.0290757i
$386$		−	8.26569i		−	0.420713i
$387$		0			0
$388$	4.18449	−	4.18449i	0.212436	−	0.212436i
$389$	35.4647			1.79813			0.899066	−	0.437813i	$-0.144247\pi$
$389$	35.4647			1.79813			0.899066	+	0.437813i	$0.144247\pi$
$390$		0			0
$391$	30.3460			1.53466
$392$	1.97077	−	1.97077i	0.0995392	−	0.0995392i
$393$		0			0
$394$		−	26.3690i		−	1.32845i
$395$	2.03381	+	1.98867i	0.102332	+	0.100061i
$396$		0			0
$397$	−12.6406	−	12.6406i	−0.634415	−	0.634415i	0.314757	−	0.949172i	$-0.398077\pi$
$397$	−12.6406	−	12.6406i	−0.634415	−	0.634415i	−0.949172	+	0.314757i	$0.898077\pi$
$398$	20.2385	+	20.2385i	1.01447	+	1.01447i
$399$		0			0
$400$	−0.361090	−	16.0876i	−0.0180545	−	0.804379i
$401$			9.49335i			0.474075i	0.971500	+	0.237038i	$0.0761765\pi$
$401$			9.49335i			0.474075i	−0.971500	+	0.237038i	$0.923824\pi$
$402$		0			0
$403$	28.3819	−	28.3819i	1.41380	−	1.41380i
$404$	0.548982			0.0273129
$405$		0			0
$406$	−15.6469			−0.776544
$407$	0.200882	−	0.200882i	0.00995735	−	0.00995735i
$408$		0			0
$409$			14.0542i			0.694934i	0.937692	+	0.347467i	$0.112958\pi$
$409$			14.0542i			0.694934i	−0.937692	+	0.347467i	$0.887042\pi$
$410$	56.5716	−	0.634802i	2.79387	−	0.0313506i
$411$		0			0
$412$	14.9424	+	14.9424i	0.736158	+	0.736158i
$413$	18.0172	+	18.0172i	0.886568	+	0.886568i
$414$		0			0
$415$	11.3851	−	0.127754i	0.558872	−	0.00627122i
$416$			35.8606i			1.75821i
$417$		0			0
$418$	0.216820	−	0.216820i	0.0106050	−	0.0106050i
$419$	−12.4864			−0.610001			−0.305001	−	0.952352i	$-0.598657\pi$
$419$	−12.4864			−0.610001			−0.305001	+	0.952352i	$0.598657\pi$
$420$		0			0
$421$	−22.2564			−1.08471			−0.542355	−	0.840150i	$-0.682467\pi$
$421$	−22.2564			−1.08471			−0.542355	+	0.840150i	$0.682467\pi$
$422$	4.34355	−	4.34355i	0.211441	−	0.211441i
$423$		0			0
$424$			6.00606i			0.291680i
$425$	13.6786	+	13.0780i	0.663510	+	0.634378i
$426$		0			0
$427$	−11.0880	−	11.0880i	−0.536584	−	0.536584i
$428$	12.4271	+	12.4271i	0.600685	+	0.600685i
$429$		0			0
$430$	−3.38212	−	3.30706i	−0.163100	−	0.159481i
$431$		−	2.77775i		−	0.133799i	−0.997760	−	0.0668997i	$-0.978689\pi$
$431$		−	2.77775i		−	0.133799i	0.997760	−	0.0668997i	$-0.0213107\pi$
$432$		0			0
$433$	−0.0228978	+	0.0228978i	−0.00110040	+	0.00110040i	−0.707657	−	0.706556i	$-0.750248\pi$
$433$	−0.0228978	+	0.0228978i	−0.00110040	+	0.00110040i	0.706556	+	0.707657i	$0.250248\pi$
$434$	−32.6811			−1.56874
$435$		0			0
$436$	3.68128			0.176301
$437$	5.66932	−	5.66932i	0.271200	−	0.271200i
$438$		0			0
$439$			21.5829i			1.03010i	0.857161	+	0.515048i	$0.172226\pi$
$439$			21.5829i			1.03010i	−0.857161	+	0.515048i	$0.827774\pi$
$440$	0.00257566	+	0.229535i	0.000122790	+	0.0109426i
$441$		0			0
$442$	−24.6855	−	24.6855i	−1.17417	−	1.17417i
$443$	3.68932	+	3.68932i	0.175285	+	0.175285i	0.789297	−	0.614012i	$-0.210445\pi$
$443$	3.68932	+	3.68932i	0.175285	+	0.175285i	−0.614012	+	0.789297i	$0.710445\pi$
$444$		0			0
$445$	4.30157	−	4.39920i	0.203914	−	0.208542i
$446$		−	46.3546i		−	2.19495i
$447$		0			0
$448$	12.7610	−	12.7610i	0.602902	−	0.602902i
$449$	−28.0088			−1.32182			−0.660909	−	0.750466i	$-0.729829\pi$
$449$	−28.0088			−1.32182			−0.660909	+	0.750466i	$0.729829\pi$
$450$		0			0
$451$	1.78973			0.0842750
$452$	10.4857	−	10.4857i	0.493206	−	0.493206i
$453$		0			0
$454$			23.0068i			1.07976i
$455$	11.9986	−	12.2709i	0.562503	−	0.575271i
$456$		0			0
$457$	−0.185080	−	0.185080i	−0.00865770	−	0.00865770i	0.702765	−	0.711422i	$-0.251949\pi$
$457$	−0.185080	−	0.185080i	−0.00865770	−	0.00865770i	−0.711422	+	0.702765i	$0.751949\pi$
$458$	2.15617	+	2.15617i	0.100751	+	0.100751i
$459$		0			0
$460$	0.469669	+	41.8554i	0.0218984	+	1.95152i
$461$			12.5045i			0.582391i	0.956664	+	0.291196i	$0.0940531\pi$
$461$			12.5045i			0.582391i	−0.956664	+	0.291196i	$0.905947\pi$
$462$		0			0
$463$	15.8872	−	15.8872i	0.738340	−	0.738340i	−0.233917	−	0.972257i	$-0.575154\pi$
$463$	15.8872	−	15.8872i	0.738340	−	0.738340i	0.972257	+	0.233917i	$0.0751543\pi$
$464$	13.9605			0.648102
$465$		0			0
$466$	−19.3622			−0.896939
$467$	−22.1956	+	22.1956i	−1.02709	+	1.02709i	−0.0274656	+	0.999623i	$0.508744\pi$
$467$	−22.1956	+	22.1956i	−1.02709	+	1.02709i	−0.999623	+	0.0274656i	$0.991256\pi$
$468$		0			0
$469$			7.82109i			0.361145i
$470$	18.0249	+	17.6249i	0.831427	+	0.812974i
$471$		0			0
$472$	7.24894	+	7.24894i	0.333660	+	0.333660i
$473$	−0.105811	−	0.105811i	−0.00486521	−	0.00486521i
$474$		0			0
$475$	4.99874	−	0.112198i	0.229358	−	0.00514800i
$476$			15.3101i			0.701736i
$477$		0			0
$478$	19.2092	−	19.2092i	0.878610	−	0.878610i
$479$	−11.1518			−0.509541			−0.254770	−	0.967002i	$-0.582000\pi$
$479$	−11.1518			−0.509541			−0.254770	+	0.967002i	$0.582000\pi$
$480$		0			0
$481$	−8.54558			−0.389645
$482$	35.7605	−	35.7605i	1.62885	−	1.62885i
$483$		0			0
$484$		−	25.6321i		−	1.16509i
$485$	5.66718	−	0.0635927i	0.257334	−	0.00288759i
$486$		0			0
$487$	−21.2114	−	21.2114i	−0.961182	−	0.961182i	0.0380923	−	0.999274i	$-0.487872\pi$
$487$	−21.2114	−	21.2114i	−0.961182	−	0.961182i	−0.999274	+	0.0380923i	$0.987872\pi$
$488$	−4.46107	−	4.46107i	−0.201943	−	0.201943i
$489$		0			0
$490$	18.6137	−	0.208869i	0.840883	−	0.00943573i
$491$			28.4638i			1.28455i	0.766474	+	0.642276i	$0.222010\pi$
$491$			28.4638i			1.28455i	−0.766474	+	0.642276i	$0.777990\pi$
$492$		0			0
$493$	−11.6095	+	11.6095i	−0.522865	+	0.522865i
$494$	−9.22360			−0.414989
$495$		0			0
$496$	29.1589			1.30927
$497$	−7.72959	+	7.72959i	−0.346719	+	0.346719i
$498$		0			0
$499$		−	24.9887i		−	1.11865i	−0.828949	−	0.559324i	$-0.811061\pi$
$499$		−	24.9887i		−	1.11865i	0.828949	−	0.559324i	$-0.188939\pi$
$500$	−17.8265	+	19.0689i	−0.797224	+	0.852788i
$501$		0			0
$502$	24.4007	+	24.4007i	1.08906	+	1.08906i
$503$	21.8207	+	21.8207i	0.972938	+	0.972938i	0.999643	−	0.0267057i	$-0.00850169\pi$
$503$	21.8207	+	21.8207i	0.972938	+	0.972938i	−0.0267057	+	0.999643i	$0.508502\pi$
$504$		0			0
$505$	0.375923	+	0.367580i	0.0167283	+	0.0163571i
$506$			2.45845i			0.109291i
$507$		0			0
$508$	−5.68256	+	5.68256i	−0.252123	+	0.252123i
$509$	19.7962			0.877450			0.438725	−	0.898621i	$-0.355430\pi$
$509$	19.7962			0.877450			0.438725	+	0.898621i	$0.355430\pi$
$510$		0			0
$511$	−3.52011			−0.155721
$512$	−21.5937	+	21.5937i	−0.954314	+	0.954314i
$513$		0			0
$514$			62.1048i			2.73933i
$515$	0.227083	+	20.2369i	0.0100065	+	0.891745i
$516$		0			0
$517$	0.563918	+	0.563918i	0.0248011	+	0.0248011i
$518$	4.92002	+	4.92002i	0.216173	+	0.216173i
$519$		0			0
$520$	4.82746	−	4.93703i	0.211698	−	0.216503i
$521$		−	45.0406i		−	1.97326i	−0.162967	−	0.986632i	$-0.552106\pi$
$521$		−	45.0406i		−	1.97326i	0.162967	−	0.986632i	$-0.447894\pi$
$522$		0			0
$523$	14.9124	−	14.9124i	0.652075	−	0.652075i	−0.301417	−	0.953492i	$-0.597460\pi$
$523$	14.9124	−	14.9124i	0.652075	−	0.652075i	0.953492	+	0.301417i	$0.0974597\pi$
$524$	33.7398			1.47393
$525$		0			0
$526$	−23.8160			−1.03843
$527$	−24.2483	+	24.2483i	−1.05627	+	1.05627i
$528$		0			0
$529$			41.2823i			1.79488i
$530$	−28.0450	+	28.6815i	−1.21820	+	1.24585i
$531$		0			0
$532$	2.86026	+	2.86026i	0.124008	+	0.124008i
$533$	−38.0678	−	38.0678i	−1.64890	−	1.64890i
$534$		0			0
$535$	0.188857	+	16.8303i	0.00816499	+	0.727639i
$536$			3.14670i			0.135917i
$537$		0			0
$538$	47.3341	−	47.3341i	2.04072	−	2.04072i
$539$	0.588874			0.0253646
$540$		0			0
$541$	−17.3903			−0.747668			−0.373834	−	0.927496i	$-0.621957\pi$
$541$	−17.3903			−0.747668			−0.373834	+	0.927496i	$0.621957\pi$
$542$	40.5681	−	40.5681i	1.74255	−	1.74255i
$543$		0			0
$544$		−	30.6378i		−	1.31358i
$545$	2.52080	+	2.46486i	0.107979	+	0.105583i
$546$		0			0
$547$	19.7612	+	19.7612i	0.844929	+	0.844929i	0.989495	−	0.144566i	$-0.0461786\pi$
$547$	19.7612	+	19.7612i	0.844929	+	0.844929i	−0.144566	+	0.989495i	$0.546179\pi$
$548$	−21.9801	−	21.9801i	−0.938945	−	0.938945i
$549$		0			0
$550$	−1.05950	+	1.10816i	−0.0451773	+	0.0472519i
$551$			4.33782i			0.184798i
$552$		0			0
$553$	−1.55840	+	1.55840i	−0.0662700	+	0.0662700i
$554$	41.3087			1.75504
$555$		0			0
$556$	−41.5199			−1.76084
$557$	19.5420	−	19.5420i	0.828021	−	0.828021i	−0.159222	−	0.987243i	$-0.550899\pi$
$557$	19.5420	−	19.5420i	0.828021	−	0.828021i	0.987243	+	0.159222i	$0.0508985\pi$
$558$		0			0
$559$			4.50125i			0.190382i
$560$	12.4670	−	0.139894i	0.526825	−	0.00591162i
$561$		0			0
$562$	−24.9064	−	24.9064i	−1.05061	−	1.05061i
$563$	−13.5744	−	13.5744i	−0.572093	−	0.572093i	0.360620	−	0.932713i	$-0.382565\pi$
$563$	−13.5744	−	13.5744i	−0.572093	−	0.572093i	−0.932713	+	0.360620i	$0.882565\pi$
$564$		0			0
$565$	14.2011	−	0.159353i	0.597444	−	0.00670405i
$566$		−	32.1373i		−	1.35083i
$567$		0			0
$568$	−3.10988	+	3.10988i	−0.130488	+	0.130488i
$569$	−37.9666			−1.59164			−0.795821	−	0.605532i	$-0.792960\pi$
$569$	−37.9666			−1.59164			−0.795821	+	0.605532i	$0.792960\pi$
$570$		0			0
$571$	10.6623			0.446205			0.223102	−	0.974795i	$-0.428382\pi$
$571$	10.6623			0.446205			0.223102	+	0.974795i	$0.428382\pi$
$572$	1.07716	−	1.07716i	0.0450383	−	0.0450383i
$573$		0			0
$574$			43.8342i			1.82961i
$575$	−27.7034	+	28.9755i	−1.15531	+	1.20836i
$576$		0			0
$577$	14.5773	+	14.5773i	0.606860	+	0.606860i	0.942124	−	0.335264i	$-0.108825\pi$
$577$	14.5773	+	14.5773i	0.606860	+	0.606860i	−0.335264	+	0.942124i	$0.608825\pi$
$578$	−3.93730	−	3.93730i	−0.163770	−	0.163770i
$579$		0			0
$580$	−16.1923	−	15.8330i	−0.672350	−	0.657428i
$581$			8.82168i			0.365985i
$582$		0			0
$583$	−0.897315	+	0.897315i	−0.0371630	+	0.0371630i
$584$	−1.41626			−0.0586054
$585$		0			0
$586$	36.2992			1.49950
$587$	10.6183	−	10.6183i	0.438266	−	0.438266i	−0.453162	−	0.891428i	$-0.649704\pi$
$587$	10.6183	−	10.6183i	0.438266	−	0.438266i	0.891428	+	0.453162i	$0.149704\pi$
$588$		0			0
$589$			9.06025i			0.373321i
$590$	0.768265	+	68.4654i	0.0316290	+	2.81868i
$591$		0			0
$592$	−4.38976	−	4.38976i	−0.180418	−	0.180418i
$593$	−12.5320	−	12.5320i	−0.514626	−	0.514626i	0.401315	−	0.915940i	$-0.368553\pi$
$593$	−12.5320	−	12.5320i	−0.514626	−	0.514626i	−0.915940	+	0.401315i	$0.868553\pi$
$594$		0			0
$595$	−10.2511	+	10.4838i	−0.420254	+	0.429793i
$596$			3.06078i			0.125375i
$597$		0			0
$598$	52.2915	−	52.2915i	2.13836	−	2.13836i
$599$	−34.3822			−1.40482			−0.702410	−	0.711773i	$-0.747893\pi$
$599$	−34.3822			−1.40482			−0.702410	+	0.711773i	$0.747893\pi$
$600$		0			0
$601$	−0.758299			−0.0309317			−0.0154658	−	0.999880i	$-0.504923\pi$
$601$	−0.758299			−0.0309317			−0.0154658	+	0.999880i	$0.504923\pi$
$602$	2.59154	−	2.59154i	0.105623	−	0.105623i
$603$		0			0
$604$		−	34.7127i		−	1.41244i
$605$	17.1624	−	17.5519i	0.697750	−	0.713587i
$606$		0			0
$607$	−6.61680	−	6.61680i	−0.268568	−	0.268568i	0.559955	−	0.828523i	$-0.310818\pi$
$607$	−6.61680	−	6.61680i	−0.268568	−	0.268568i	−0.828523	+	0.559955i	$0.810818\pi$
$608$	−5.72382	−	5.72382i	−0.232131	−	0.232131i
$609$		0			0
$610$	−0.472798	−	42.1343i	−0.0191430	−	1.70597i
$611$		−	23.9892i		−	0.970500i
$612$		0			0
$613$	28.4049	−	28.4049i	1.14726	−	1.14726i	0.160176	−	0.987089i	$-0.448794\pi$
$613$	28.4049	−	28.4049i	1.14726	−	1.14726i	0.987089	−	0.160176i	$-0.0512061\pi$
$614$	−34.6349			−1.39775
$615$		0			0
$616$	−0.177854			−0.00716594
$617$	−26.4325	+	26.4325i	−1.06413	+	1.06413i	−0.0663338	+	0.997797i	$0.521130\pi$
$617$	−26.4325	+	26.4325i	−1.06413	+	1.06413i	−0.997797	+	0.0663338i	$0.978870\pi$
$618$		0			0
$619$		−	32.0696i		−	1.28899i	−0.764610	−	0.644494i	$-0.777068\pi$
$619$		−	32.0696i		−	1.28899i	0.764610	−	0.644494i	$-0.222932\pi$
$620$	−33.8203	−	33.0697i	−1.35826	−	1.32811i
$621$		0			0
$622$	−11.7863	−	11.7863i	−0.472588	−	0.472588i
$623$	3.37088	+	3.37088i	0.135051	+	0.135051i
$624$		0			0
$625$	−24.9748	+	1.12170i	−0.998993	+	0.0448679i
$626$		−	65.9805i		−	2.63711i
$627$		0			0
$628$	−35.6339	+	35.6339i	−1.42195	+	1.42195i
$629$	7.30098			0.291109
$630$		0			0
$631$	40.7328			1.62155			0.810774	−	0.585359i	$-0.199046\pi$
$631$	40.7328			1.62155			0.810774	+	0.585359i	$0.199046\pi$
$632$	−0.626999	+	0.626999i	−0.0249407	+	0.0249407i
$633$		0			0
$634$		−	4.82359i		−	0.191569i
$635$	−7.69606	+	0.0863592i	−0.305409	+	0.00342706i
$636$		0			0
$637$	−12.5254	−	12.5254i	−0.496276	−	0.496276i
$638$	−0.940528	−	0.940528i	−0.0372359	−	0.0372359i
$639$		0			0
$640$	12.2936	−	0.137949i	0.485948	−	0.00545293i
$641$			17.0501i			0.673437i	0.941605	+	0.336719i	$0.109317\pi$
$641$			17.0501i			0.673437i	−0.941605	+	0.336719i	$0.890683\pi$
$642$		0			0
$643$	−30.3493	+	30.3493i	−1.19686	+	1.19686i	−0.221759	+	0.975101i	$0.571180\pi$
$643$	−30.3493	+	30.3493i	−1.19686	+	1.19686i	−0.975101	+	0.221759i	$0.928820\pi$
$644$	−32.4315			−1.27798
$645$		0			0
$646$	7.88026			0.310044
$647$	−6.08468	+	6.08468i	−0.239214	+	0.239214i	−0.816524	−	0.577311i	$-0.804102\pi$
$647$	−6.08468	+	6.08468i	−0.239214	+	0.239214i	0.577311	+	0.816524i	$0.304102\pi$
$648$		0			0
$649$			2.16601i			0.0850232i
$650$	46.1064	−	1.03487i	1.80844	−	0.0405909i
$651$		0			0
$652$	3.26610	+	3.26610i	0.127910	+	0.127910i
$653$	−1.86065	−	1.86065i	−0.0728129	−	0.0728129i	0.669762	−	0.742575i	$-0.266396\pi$
$653$	−1.86065	−	1.86065i	−0.0728129	−	0.0728129i	−0.742575	+	0.669762i	$0.766396\pi$
$654$		0			0
$655$	23.1038	+	22.5910i	0.902739	+	0.882705i
$656$		−	39.1099i		−	1.52699i
$657$		0			0
$658$	−13.8115	+	13.8115i	−0.538429	+	0.538429i
$659$	−16.6353			−0.648020			−0.324010	−	0.946054i	$-0.605031\pi$
$659$	−16.6353			−0.648020			−0.324010	+	0.946054i	$0.605031\pi$
$660$		0			0
$661$	−16.9027			−0.657437			−0.328718	−	0.944428i	$-0.606617\pi$
$661$	−16.9027			−0.657437			−0.328718	+	0.944428i	$0.606617\pi$
$662$	−18.3068	+	18.3068i	−0.711515	+	0.711515i
$663$		0			0
$664$			3.54927i			0.137738i
$665$	0.0434681	+	3.87374i	0.00168562	+	0.150217i
$666$		0			0
$667$	−24.5925	−	24.5925i	−0.952225	−	0.952225i
$668$	−11.0963	−	11.0963i	−0.429330	−	0.429330i
$669$		0			0
$670$	−14.6933	+	15.0268i	−0.567654	+	0.580538i
$671$		−	1.33298i		−	0.0514593i
$672$		0			0
$673$	−6.71892	+	6.71892i	−0.258995	+	0.258995i	−0.824645	−	0.565650i	$-0.808625\pi$
$673$	−6.71892	+	6.71892i	−0.258995	+	0.258995i	0.565650	+	0.824645i	$0.308625\pi$
$674$	15.2157			0.586086
$675$		0			0
$676$	−15.4704			−0.595017
$677$	6.24806	−	6.24806i	0.240132	−	0.240132i	−0.576773	−	0.816905i	$-0.695688\pi$
$677$	6.24806	−	6.24806i	0.240132	−	0.240132i	0.816905	+	0.576773i	$0.195688\pi$
$678$		0			0
$679$			4.39119i			0.168518i
$680$	−4.12438	+	4.21799i	−0.158163	+	0.161752i
$681$		0			0
$682$	−1.96445	−	1.96445i	−0.0752225	−	0.0752225i
$683$	−17.0660	−	17.0660i	−0.653013	−	0.653013i	0.300704	−	0.953717i	$-0.402778\pi$
$683$	−17.0660	−	17.0660i	−0.653013	−	0.653013i	−0.953717	+	0.300704i	$0.902778\pi$
$684$		0			0
$685$	−0.334037	−	29.7684i	−0.0127629	−	1.13739i
$686$			39.6724i			1.51470i
$687$		0			0
$688$	−2.31223	+	2.31223i	−0.0881531	+	0.0881531i
$689$	38.1721			1.45424
$690$		0			0
$691$	16.4778			0.626846			0.313423	−	0.949614i	$-0.398524\pi$
$691$	16.4778			0.626846			0.313423	+	0.949614i	$0.398524\pi$
$692$	−27.1100	+	27.1100i	−1.03057	+	1.03057i
$693$		0			0
$694$		−	9.62776i		−	0.365465i
$695$	−28.4313	−	27.8003i	−1.07846	−	1.05453i
$696$		0			0
$697$	32.5235	+	32.5235i	1.23192	+	1.23192i
$698$	−37.8488	−	37.8488i	−1.43260	−	1.43260i
$699$		0			0
$700$	−14.6186	−	13.9768i	−0.552532	−	0.528273i
$701$			41.2916i			1.55956i	0.626051	+	0.779782i	$0.284670\pi$
$701$			41.2916i			1.55956i	−0.626051	+	0.779782i	$0.715330\pi$
$702$		0			0
$703$	1.36399	−	1.36399i	0.0514437	−	0.0514437i
$704$	1.53412			0.0578192
$705$		0			0
$706$	24.2208			0.911562
$707$	−0.288050	+	0.288050i	−0.0108332	+	0.0108332i
$708$		0			0
$709$			25.1571i			0.944793i	0.881386	+	0.472397i	$0.156611\pi$
$709$			25.1571i			0.944793i	−0.881386	+	0.472397i	$0.843389\pi$
$710$	−29.3725	+	0.329595i	−1.10233	+	0.0123695i
$711$		0			0
$712$	1.35622	+	1.35622i	0.0508265	+	0.0508265i
$713$	−51.3654	−	51.3654i	−1.92365	−	1.92365i
$714$		0			0
$715$	1.45883	−	0.0163698i	0.0545572	−	0.000612198i
$716$		−	14.2896i		−	0.534026i
$717$		0			0
$718$	17.0133	−	17.0133i	0.634930	−	0.634930i
$719$	10.8956			0.406337			0.203168	−	0.979144i	$-0.434876\pi$
$719$	10.8956			0.406337			0.203168	+	0.979144i	$0.434876\pi$
$720$		0			0
$721$	−15.6805			−0.583971
$722$	1.47221	−	1.47221i	0.0547899	−	0.0547899i
$723$		0			0
$724$		−	42.4307i		−	1.57692i
$725$	−0.486695	−	21.6837i	−0.0180754	−	0.805311i
$726$		0			0
$727$	28.5725	+	28.5725i	1.05969	+	1.05969i	0.998101	+	0.0615924i	$0.0196179\pi$
$727$	28.5725	+	28.5725i	1.05969	+	1.05969i	0.0615924	+	0.998101i	$0.480382\pi$
$728$	3.78298	+	3.78298i	0.140207	+	0.140207i
$729$		0			0
$730$	−6.76327	−	6.61317i	−0.250320	−	0.244765i
$731$		−	3.84567i		−	0.142237i
$732$		0			0
$733$	−10.6309	+	10.6309i	−0.392660	+	0.392660i	−0.875634	−	0.482974i	$-0.839556\pi$
$733$	−10.6309	+	10.6309i	−0.392660	+	0.392660i	0.482974	+	0.875634i	$0.339556\pi$
$734$	−17.2449			−0.636520
$735$		0			0
$736$	64.9003			2.39226
$737$	−0.470122	+	0.470122i	−0.0173172	+	0.0173172i
$738$		0			0
$739$			29.0105i			1.06717i	0.845747	+	0.533584i	$0.179155\pi$
$739$			29.0105i			1.06717i	−0.845747	+	0.533584i	$0.820845\pi$
$740$	0.112998	+	10.0700i	0.00415389	+	0.370182i
$741$		0			0
$742$	−21.9771	−	21.9771i	−0.806806	−	0.806806i
$743$	4.42767	+	4.42767i	0.162435	+	0.162435i	0.783645	−	0.621209i	$-0.213358\pi$
$743$	4.42767	+	4.42767i	0.162435	+	0.162435i	−0.621209	+	0.783645i	$0.713358\pi$
$744$		0			0
$745$	−2.04940	+	2.09591i	−0.0750841	+	0.0767883i
$746$		−	60.1616i		−	2.20267i
$747$		0			0
$748$	−0.920280	+	0.920280i	−0.0336488	+	0.0336488i
$749$	−13.0409			−0.476504
$750$		0			0
$751$	−46.1045			−1.68238			−0.841188	−	0.540743i	$-0.818143\pi$
$751$	−46.1045			−1.68238			−0.841188	+	0.540743i	$0.818143\pi$
$752$	12.3230	−	12.3230i	0.449372	−	0.449372i
$753$		0			0
$754$			40.0104i			1.45709i
$755$	23.2424	−	23.7700i	0.845878	−	0.865077i
$756$		0			0
$757$	13.3543	+	13.3543i	0.485371	+	0.485371i	0.906842	−	0.421471i	$-0.138486\pi$
$757$	13.3543	+	13.3543i	0.485371	+	0.485371i	−0.421471	+	0.906842i	$0.638486\pi$
$758$	−10.8016	−	10.8016i	−0.392331	−	0.392331i
$759$		0			0
$760$	0.0174887	+	1.55854i	0.000634382	+	0.0565342i
$761$			0.0241997i			0.000877240i	1.00000		0.000438620i	$0.000139617\pi$
$761$			0.0241997i			0.000877240i	−1.00000		0.000438620i	$0.999860\pi$
$762$		0			0
$763$	−1.93156	+	1.93156i	−0.0699271	+	0.0699271i
$764$	47.0996			1.70400
$765$		0			0
$766$	−81.2772			−2.93667
$767$	46.0713	−	46.0713i	1.66354	−	1.66354i
$768$		0			0
$769$		−	14.4346i		−	0.520525i	−0.965538	−	0.260262i	$-0.916191\pi$
$769$		−	14.4346i		−	0.520525i	0.965538	−	0.260262i	$-0.0838091\pi$
$770$	−0.849330	−	0.830480i	−0.0306077	−	0.0299284i
$771$		0			0
$772$	6.55433	+	6.55433i	0.235896	+	0.235896i
$773$	27.9027	+	27.9027i	1.00359	+	1.00359i	0.999994	+	0.00359848i	$0.00114543\pi$
$773$	27.9027	+	27.9027i	1.00359	+	1.00359i	0.00359848	+	0.999994i	$0.498855\pi$
$774$		0			0
$775$	−1.01654	−	45.2899i	−0.0365153	−	1.62686i
$776$			1.76673i			0.0634219i
$777$		0			0
$778$	−52.2114	+	52.2114i	−1.87187	+	1.87187i
$779$	12.1522			0.435399
$780$		0			0
$781$	−0.929243			−0.0332509
$782$	−44.6757	+	44.6757i	−1.59760	+	1.59760i
$783$		0			0
$784$		−	12.8683i		−	0.459583i
$785$	−48.2600	+	0.541536i	−1.72247	+	0.0193282i
$786$		0			0
$787$	17.6383	+	17.6383i	0.628736	+	0.628736i	0.947750	−	0.319014i	$-0.103352\pi$
$787$	17.6383	+	17.6383i	0.628736	+	0.628736i	−0.319014	+	0.947750i	$0.603352\pi$
$788$	20.9094	+	20.9094i	0.744867	+	0.744867i
$789$		0			0
$790$	−5.92193	+	0.0664513i	−0.210693	+	0.00236423i
$791$			11.0036i			0.391245i
$792$		0			0
$793$	−28.3528	+	28.3528i	−1.00684	+	1.00684i
$794$	37.2193			1.32086
$795$		0			0
$796$	−32.0966			−1.13763
$797$	22.7807	−	22.7807i	0.806934	−	0.806934i	−0.177235	−	0.984169i	$-0.556715\pi$
$797$	22.7807	−	22.7807i	0.806934	−	0.806934i	0.984169	+	0.177235i	$0.0567152\pi$
$798$		0			0
$799$			20.4954i			0.725074i
$800$	29.2541	+	27.9697i	1.03429	+	0.988878i
$801$		0			0
$802$	−13.9762	−	13.9762i	−0.493516	−	0.493516i
$803$	−0.211592	−	0.211592i	−0.00746693	−	0.00746693i
$804$		0			0
$805$	−22.2079	−	21.7150i	−0.782725	−	0.765354i
$806$			83.5682i			2.94356i
$807$		0			0
$808$	−0.115892	+	0.115892i	−0.00407708	+	0.00407708i
$809$	14.8789			0.523115			0.261557	−	0.965188i	$-0.415764\pi$
$809$	14.8789			0.523115			0.261557	+	0.965188i	$0.415764\pi$
$810$		0			0
$811$	35.5985			1.25003			0.625016	−	0.780612i	$-0.285092\pi$
$811$	35.5985			1.25003			0.625016	+	0.780612i	$0.285092\pi$
$812$	12.4073	−	12.4073i	0.435412	−	0.435412i
$813$		0			0
$814$			0.591480i			0.0207314i
$815$	0.0496356	+	4.42338i	0.00173866	+	0.154944i
$816$		0			0
$817$	−0.718458	−	0.718458i	−0.0251357	−	0.0251357i
$818$	−20.6907	−	20.6907i	−0.723432	−	0.723432i
$819$		0			0
$820$	−44.3554	+	45.3621i	−1.54896	+	1.58411i
$821$		−	10.7562i		−	0.375395i	−0.982227	−	0.187698i	$-0.939898\pi$
$821$		−	10.7562i		−	0.375395i	0.982227	−	0.187698i	$-0.0601025\pi$
$822$		0			0
$823$	−1.78230	+	1.78230i	−0.0621270	+	0.0621270i	−0.737488	−	0.675361i	$-0.763988\pi$
$823$	−1.78230	+	1.78230i	−0.0621270	+	0.0621270i	0.675361	+	0.737488i	$0.263988\pi$
$824$	−6.30880			−0.219777
$825$		0			0
$826$	−53.0501			−1.84585
$827$	34.8112	−	34.8112i	1.21051	−	1.21051i	0.239644	−	0.970861i	$-0.422969\pi$
$827$	34.8112	−	34.8112i	1.21051	−	1.21051i	0.970861	−	0.239644i	$-0.0770309\pi$
$828$		0			0
$829$		−	10.6569i		−	0.370128i	−0.982726	−	0.185064i	$-0.940751\pi$
$829$		−	10.6569i		−	0.370128i	0.982726	−	0.185064i	$-0.0592493\pi$
$830$	−16.5731	+	16.9493i	−0.575262	+	0.588318i
$831$		0			0
$832$	−32.6309	−	32.6309i	−1.13127	−	1.13127i
$833$	10.7012	+	10.7012i	0.370775	+	0.370775i
$834$		0			0
$835$	−0.168633	−	15.0281i	−0.00583580	−	0.520069i
$836$			0.343858i			0.0118926i
$837$		0			0
$838$	18.3826	−	18.3826i	0.635016	−	0.635016i
$839$	−25.7041			−0.887405			−0.443702	−	0.896174i	$-0.646335\pi$
$839$	−25.7041			−0.887405			−0.443702	+	0.896174i	$0.646335\pi$
$840$		0			0
$841$	−10.1833			−0.351148
$842$	32.7660	−	32.7660i	1.12919	−	1.12919i
$843$		0			0
$844$			6.88849i			0.237111i
$845$	−10.5936	−	10.3585i	−0.364430	−	0.356343i
$846$		0			0
$847$	13.4491	+	13.4491i	0.462117	+	0.462117i
$848$	19.6085	+	19.6085i	0.673359	+	0.673359i
$849$		0			0
$850$	−39.3914	+	0.884149i	−1.35111	+	0.0303261i
$851$			15.4657i			0.530159i
$852$		0			0
$853$	14.8438	−	14.8438i	0.508243	−	0.508243i	−0.405744	−	0.913987i	$-0.632987\pi$
$853$	14.8438	−	14.8438i	0.508243	−	0.508243i	0.913987	+	0.405744i	$0.132987\pi$
$854$	32.6476			1.11718
$855$		0			0
$856$	−5.24681			−0.179332
$857$	33.1451	−	33.1451i	1.13222	−	1.13222i	0.142407	−	0.989808i	$-0.454516\pi$
$857$	33.1451	−	33.1451i	1.13222	−	1.13222i	0.989808	−	0.142407i	$-0.0454842\pi$
$858$		0			0
$859$			7.10139i			0.242296i	0.992634	+	0.121148i	$0.0386576\pi$
$859$			7.10139i			0.242296i	−0.992634	+	0.121148i	$0.961342\pi$
$860$	5.30423	−	0.0595199i	0.180873	−	0.00202961i
$861$		0			0
$862$	4.08942	+	4.08942i	0.139286	+	0.139286i
$863$	15.6999	+	15.6999i	0.534430	+	0.534430i	0.921887	−	0.387458i	$-0.126647\pi$
$863$	15.6999	+	15.6999i	0.534430	+	0.534430i	−0.387458	+	0.921887i	$0.626647\pi$
$864$		0			0
$865$	−36.7159	+	0.411997i	−1.24838	+	0.0140083i
$866$		−	0.0674207i		−	0.00229105i
$867$		0			0
$868$	25.9147	−	25.9147i	0.879603	−	0.879603i
$869$	−0.187349			−0.00635540
$870$		0			0
$871$	19.9991			0.677645
$872$	−0.777133	+	0.777133i	−0.0263170	+	0.0263170i
$873$		0			0
$874$			16.6928i			0.564643i
$875$	−0.651911	−	19.3589i	−0.0220386	−	0.654452i
$876$		0			0
$877$	−28.4935	−	28.4935i	−0.962156	−	0.962156i	0.0371536	−	0.999310i	$-0.488171\pi$
$877$	−28.4935	−	28.4935i	−0.962156	−	0.962156i	−0.999310	+	0.0371536i	$0.988171\pi$
$878$	−31.7745	−	31.7745i	−1.07234	−	1.07234i
$879$		0			0
$880$	0.757792	+	0.740974i	0.0255452	+	0.0249782i
$881$			18.6727i			0.629101i	0.949241	+	0.314550i	$0.101854\pi$
$881$			18.6727i			0.629101i	−0.949241	+	0.314550i	$0.898146\pi$
$882$		0			0
$883$	31.3804	−	31.3804i	1.05603	−	1.05603i	0.0576995	−	0.998334i	$-0.481623\pi$
$883$	31.3804	−	31.3804i	1.05603	−	1.05603i	0.998334	−	0.0576995i	$-0.0183765\pi$
$884$	39.1490			1.31672
$885$		0			0
$886$	−10.8629			−0.364946
$887$	−9.40448	+	9.40448i	−0.315772	+	0.315772i	−0.847141	−	0.531369i	$-0.821678\pi$
$887$	−9.40448	+	9.40448i	−0.315772	+	0.315772i	0.531369	+	0.847141i	$0.321678\pi$
$888$		0			0
$889$		−	5.96326i		−	0.200001i
$890$	0.143736	+	12.8093i	0.00481806	+	0.429370i
$891$		0			0
$892$	36.7572	+	36.7572i	1.23072	+	1.23072i
$893$	3.82900	+	3.82900i	0.128132	+	0.128132i
$894$		0			0
$895$	9.56781	−	9.78497i	0.319817	−	0.327076i
$896$			9.52566i			0.318230i
$897$		0			0
$898$	41.2348	−	41.2348i	1.37602	−	1.37602i
$899$	39.3018			1.31079
$900$		0			0
$901$	−32.6126			−1.08648
$902$	−2.63485	+	2.63485i	−0.0877310	+	0.0877310i
$903$		0			0
$904$			4.42715i			0.147245i
$905$	28.4101	−	29.0550i	0.944385	−	0.965820i
$906$		0			0
$907$	1.34108	+	1.34108i	0.0445298	+	0.0445298i	0.729021	−	0.684491i	$-0.239976\pi$
$907$	1.34108	+	1.34108i	0.0445298	+	0.0445298i	−0.684491	+	0.729021i	$0.739976\pi$
$908$	−18.2434	−	18.2434i	−0.605429	−	0.605429i
$909$		0			0
$910$	0.400932	+	35.7298i	0.0132908	+	1.18443i
$911$		−	24.5926i		−	0.814789i	−0.913252	−	0.407394i	$-0.866437\pi$
$911$		−	24.5926i		−	0.814789i	0.913252	−	0.407394i	$-0.133563\pi$
$912$		0			0
$913$	−0.530267	+	0.530267i	−0.0175493	+	0.0175493i
$914$	0.544954			0.0180255
$915$		0			0
$916$	−3.41950			−0.112983
$917$	−17.7032	+	17.7032i	−0.584611	+	0.584611i
$918$		0			0
$919$			13.5314i			0.446361i	0.974777	+	0.223180i	$0.0716439\pi$
$919$			13.5314i			0.446361i	−0.974777	+	0.223180i	$0.928356\pi$
$920$	−8.93500	−	8.73671i	−0.294578	−	0.288041i
$921$		0			0
$922$	−18.4092	−	18.4092i	−0.606274	−	0.606274i
$923$	19.7651	+	19.7651i	0.650578	+	0.650578i
$924$		0			0
$925$	−6.66518	+	6.97125i	−0.219150	+	0.229213i
$926$			46.7785i			1.53724i
$927$		0			0
$928$	−24.8289	+	24.8289i	−0.815049	+	0.815049i
$929$	−4.42619			−0.145219			−0.0726093	−	0.997360i	$-0.523133\pi$
$929$	−4.42619			−0.145219			−0.0726093	+	0.997360i	$0.523133\pi$
$930$		0			0
$931$	3.99845			0.131044
$932$	15.3534	−	15.3534i	0.502918	−	0.502918i
$933$		0			0
$934$		−	65.3530i		−	2.13841i
$935$	−1.24636	+	0.0139857i	−0.0407604	+	0.000457381i
$936$		0			0
$937$	28.4331	+	28.4331i	0.928869	+	0.928869i	0.997633	−	0.0687638i	$-0.0219055\pi$
$937$	28.4331	+	28.4331i	0.928869	+	0.928869i	−0.0687638	+	0.997633i	$0.521905\pi$
$938$	−11.5143	−	11.5143i	−0.375954	−	0.375954i
$939$		0			0
$940$	−28.2687	+	0.317209i	−0.922023	+	0.0103462i
$941$			29.8854i			0.974237i	0.873336	+	0.487118i	$0.161952\pi$
$941$			29.8854i			0.974237i	−0.873336	+	0.487118i	$0.838048\pi$
$942$		0			0
$943$	−68.8949	+	68.8949i	−2.24353	+	2.24353i
$944$	47.3325			1.54054
$945$		0			0
$946$	0.311552			0.0101294
$947$	−25.9937	+	25.9937i	−0.844682	+	0.844682i	−0.989464	−	0.144782i	$-0.953752\pi$
$947$	−25.9937	+	25.9937i	−0.844682	+	0.844682i	0.144782	+	0.989464i	$0.453752\pi$
$948$		0			0
$949$			9.00120i			0.292191i
$950$	−7.19401	+	7.52437i	−0.233404	+	0.244123i
$951$		0			0
$952$	−3.23202	−	3.23202i	−0.104750	−	0.104750i
$953$	2.26174	+	2.26174i	0.0732649	+	0.0732649i	0.742790	−	0.669525i	$-0.233502\pi$
$953$	2.26174	+	2.26174i	0.0732649	+	0.0732649i	−0.669525	+	0.742790i	$0.733502\pi$
$954$		0			0
$955$	32.2521	+	31.5363i	1.04365	+	1.02049i
$956$			30.4642i			0.985281i
$957$		0			0
$958$	16.4178	−	16.4178i	0.530436	−	0.530436i
$959$	23.0659			0.744836
$960$		0			0
$961$	51.0882			1.64801
$962$	12.5809	−	12.5809i	0.405623	−	0.405623i
$963$		0			0
$964$			56.7130i			1.82660i
$965$	0.0996077	+	8.87673i	0.00320648	+	0.285752i
$966$		0			0
$967$	34.5302	+	34.5302i	1.11042	+	1.11042i	0.993094	+	0.117322i	$0.0374308\pi$
$967$	34.5302	+	34.5302i	1.11042	+	1.11042i	0.117322	+	0.993094i	$0.462569\pi$
$968$	5.41104	+	5.41104i	0.173917	+	0.173917i
$969$		0			0
$970$	−8.24965	+	8.43689i	−0.264880	+	0.270892i
$971$			42.9247i			1.37752i	0.724990	+	0.688759i	$0.241844\pi$
$971$			42.9247i			1.37752i	−0.724990	+	0.688759i	$0.758156\pi$
$972$		0			0
$973$	21.7854	−	21.7854i	0.698408	−	0.698408i
$974$	62.4553			2.00120
$975$		0			0
$976$	−29.1289			−0.932394
$977$	16.3401	−	16.3401i	0.522766	−	0.522766i	−0.395640	−	0.918406i	$-0.629477\pi$
$977$	16.3401	−	16.3401i	0.522766	−	0.522766i	0.918406	+	0.395640i	$0.129477\pi$
$978$		0			0
$979$			0.405243i			0.0129516i
$980$	−14.5943	+	14.9255i	−0.466196	+	0.476778i
$981$		0			0
$982$	−41.9046	−	41.9046i	−1.33723	−	1.33723i
$983$	18.4843	+	18.4843i	0.589559	+	0.589559i	0.937512	−	0.347953i	$-0.113123\pi$
$983$	18.4843	+	18.4843i	0.589559	+	0.589559i	−0.347953	+	0.937512i	$0.613123\pi$
$984$		0			0
$985$	0.317765	+	28.3183i	0.0101248	+	0.902294i
$986$		−	34.1832i		−	1.08861i
$987$		0			0
$988$	7.31391	−	7.31391i	0.232687	−	0.232687i
$989$	8.14633			0.259038
$990$		0			0
$991$	−14.5248			−0.461396			−0.230698	−	0.973025i	$-0.574101\pi$
$991$	−14.5248			−0.461396			−0.230698	+	0.973025i	$0.574101\pi$
$992$	−51.8592	+	51.8592i	−1.64653	+	1.64653i
$993$		0			0
$994$		−	22.7591i		−	0.721876i
$995$	−21.9785	−	21.4908i	−0.696767	−	0.681303i
$996$		0			0
$997$	37.0493	+	37.0493i	1.17336	+	1.17336i	0.981403	+	0.191959i	$0.0614839\pi$
$997$	37.0493	+	37.0493i	1.17336	+	1.17336i	0.191959	+	0.981403i	$0.438516\pi$
$998$	36.7886	+	36.7886i	1.16452	+	1.16452i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.e.647.3	✓	36
3.2	odd	2	inner	855.2.n.e.647.16	yes	36
5.3	odd	4	inner	855.2.n.e.818.16	yes	36
15.8	even	4	inner	855.2.n.e.818.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.e.647.3	✓	36	1.1	even	1	trivial
855.2.n.e.647.16	yes	36	3.2	odd	2	inner
855.2.n.e.818.3	yes	36	15.8	even	4	inner
855.2.n.e.818.16	yes	36	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47221 + 1.47221i) q^{2} -2.33479i q^{4} +(1.56330 - 1.59878i) q^{5} +(1.22506 + 1.22506i) q^{7} +(0.492885 + 0.492885i) q^{8} +O(q^{10})\)	\(q+(-1.47221 + 1.47221i) q^{2} -2.33479i q^{4} +(1.56330 - 1.59878i) q^{5} +(1.22506 + 1.22506i) q^{7} +(0.492885 + 0.492885i) q^{8} +(0.0522374 + 4.65524i) q^{10} +0.147276i q^{11} +(3.13257 - 3.13257i) q^{13} -3.60709 q^{14} +3.21833 q^{16} +(-2.67634 + 2.67634i) q^{17} +1.00000i q^{19} +(-3.73282 - 3.64998i) q^{20} +(-0.216820 - 0.216820i) q^{22} +(-5.66932 - 5.66932i) q^{23} +(-0.112198 - 4.99874i) q^{25} +9.22360i q^{26} +(2.86026 - 2.86026i) q^{28} +4.33782 q^{29} +9.06025 q^{31} +(-5.72382 + 5.72382i) q^{32} -7.88026i q^{34} +(3.87374 - 0.0434681i) q^{35} +(-1.36399 - 1.36399i) q^{37} +(-1.47221 - 1.47221i) q^{38} +(1.55854 - 0.0174887i) q^{40} -12.1522i q^{41} +(-0.718458 + 0.718458i) q^{43} +0.343858 q^{44} +16.6928 q^{46} +(3.82900 - 3.82900i) q^{47} -3.99845i q^{49} +(7.52437 + 7.19401i) q^{50} +(-7.31391 - 7.31391i) q^{52} +(6.09276 + 6.09276i) q^{53} +(0.235461 + 0.230236i) q^{55} +1.20763i q^{56} +(-6.38618 + 6.38618i) q^{58} +14.7072 q^{59} -9.05095 q^{61} +(-13.3386 + 13.3386i) q^{62} -10.4166i q^{64} +(-0.111151 - 9.90545i) q^{65} +(3.19212 + 3.19212i) q^{67} +(6.24870 + 6.24870i) q^{68} +(-5.63896 + 5.76694i) q^{70} +6.30955i q^{71} +(-1.43671 + 1.43671i) q^{73} +4.01614 q^{74} +2.33479 q^{76} +(-0.180422 + 0.180422i) q^{77} +1.27210i q^{79} +(5.03121 - 5.14540i) q^{80} +(17.8906 + 17.8906i) q^{82} +(3.60051 + 3.60051i) q^{83} +(0.0949628 + 8.46279i) q^{85} -2.11544i q^{86} +(-0.0725899 + 0.0725899i) q^{88} +2.75160 q^{89} +7.67519 q^{91} +(-13.2367 + 13.2367i) q^{92} +11.2742i q^{94} +(1.59878 + 1.56330i) q^{95} +(1.79223 + 1.79223i) q^{97} +(5.88655 + 5.88655i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7}+O(q^{10}) \) 36 * q + 4 * q^7	\( 36 q + 4 q^{7} + 8 q^{10} + 4 q^{13} - 36 q^{16} - 80 q^{22} + 16 q^{25} - 24 q^{28} - 4 q^{37} + 76 q^{40} - 20 q^{43} + 96 q^{46} - 68 q^{52} + 48 q^{55} - 12 q^{58} + 56 q^{61} - 8 q^{67} - 16 q^{70} - 56 q^{73} + 36 q^{76} - 100 q^{82} + 80 q^{85} - 184 q^{88} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^7 + 8 * q^10 + 4 * q^13 - 36 * q^16 - 80 * q^22 + 16 * q^25 - 24 * q^28 - 4 * q^37 + 76 * q^40 - 20 * q^43 + 96 * q^46 - 68 * q^52 + 48 * q^55 - 12 * q^58 + 56 * q^61 - 8 * q^67 - 16 * q^70 - 56 * q^73 + 36 * q^76 - 100 * q^82 + 80 * q^85 - 184 * q^88 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more