LMFDB - Embedded newform 99.2.j.a.35.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(8,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$99 = 3^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	99.j (of order $10$ , degree $4$ , 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625$ x^16 + 2x^14 - 16x^12 - 72x^10 + 26x^8 + 360x^6 + 725x^4 + 1000*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.4
Root			$-0.556839 - 1.81878i$ of defining polynomial
Character	$\chi$	$=$	99.35
Dual form			99.2.j.a.17.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.726437 - 2.23574i) q^{2} +(-2.85280 - 2.07268i) q^{4} +(2.13811 - 0.694712i) q^{5} +(-2.38116 + 3.27739i) q^{7} +(-2.90269 + 2.10893i) q^{8} -5.28492i q^{10} +(-3.31656 + 0.0200544i) q^{11} +(4.42495 + 1.43775i) q^{13} +(5.59763 + 7.70448i) q^{14} +(0.427051 + 1.31433i) q^{16} +(-0.0235753 - 0.0725574i) q^{17} +(1.40822 + 1.93825i) q^{19} +(-7.53950 - 2.44973i) q^{20} +(-2.36444 + 7.42955i) q^{22} -3.22717i q^{23} +(0.0437835 - 0.0318106i) q^{25} +(6.42889 - 8.84860i) q^{26} +(13.5860 - 4.41435i) q^{28} +(1.48796 + 1.08107i) q^{29} +(0.517528 - 1.59279i) q^{31} -3.92711 q^{32} -0.179346 q^{34} +(-2.81433 + 8.66162i) q^{35} +(-5.87906 - 4.27138i) q^{37} +(5.35641 - 1.74040i) q^{38} +(-4.74115 + 6.52564i) q^{40} +(-6.82980 + 4.96214i) q^{41} +4.28086i q^{43} +(9.50306 + 6.81697i) q^{44} +(-7.21513 - 2.34434i) q^{46} +(-3.65360 - 5.02874i) q^{47} +(-2.90822 - 8.95058i) q^{49} +(-0.0393143 - 0.120997i) q^{50} +(-9.64348 - 13.2731i) q^{52} +(1.16884 + 0.379779i) q^{53} +(-7.07723 + 2.34694i) q^{55} -14.5349i q^{56} +(3.49789 - 2.54137i) q^{58} +(-0.341086 + 0.469465i) q^{59} +(-3.59710 + 1.16877i) q^{61} +(-3.18511 - 2.31412i) q^{62} +(-3.70690 + 11.4087i) q^{64} +10.4598 q^{65} +12.9984 q^{67} +(-0.0831326 + 0.255856i) q^{68} +(17.3207 + 12.5842i) q^{70} +(1.06563 - 0.346245i) q^{71} +(7.82153 - 10.7654i) q^{73} +(-13.8205 + 10.0412i) q^{74} -8.44824i q^{76} +(7.83155 - 10.9174i) q^{77} +(0.627566 + 0.203908i) q^{79} +(1.82616 + 2.51349i) q^{80} +(6.13265 + 18.8744i) q^{82} +(-3.15542 - 9.71138i) q^{83} +(-0.100813 - 0.138757i) q^{85} +(9.57090 + 3.10977i) q^{86} +(9.58466 - 7.05260i) q^{88} +6.58983i q^{89} +(-15.2486 + 11.0787i) q^{91} +(-6.68890 + 9.20649i) q^{92} +(-13.8971 + 4.51544i) q^{94} +(4.35745 + 3.16587i) q^{95} +(5.08168 - 15.6398i) q^{97} -22.1238 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70}+ \cdots + 60 q^{97}+O(q^{100})$ 16 * q - 4 * q^4 - 20 * q^16 - 48 * q^22 - 32 * q^25 + 40 * q^28 + 16 * q^31 + 40 * q^34 - 12 * q^37 + 60 * q^40 - 40 * q^46 - 24 * q^49 - 40 * q^52 + 16 * q^55 + 12 * q^58 + 36 * q^64 + 96 * q^67 + 76 * q^70 - 20 * q^73 - 12 * q^82 - 100 * q^85 - 12 * q^88 - 72 * q^91 - 80 * q^94 + 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$ .

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.726437	−	2.23574i	0.513668	−	1.58091i	−0.272023	−	0.962291i	$-0.587693\pi$
$2$	0.726437	−	2.23574i	0.513668	−	1.58091i	0.785692	−	0.618618i	$-0.212307\pi$
$3$		0			0
$3$		0			0
$4$	−2.85280	−	2.07268i	−1.42640	−	1.03634i
$5$	2.13811	−	0.694712i	0.956190	−	0.310685i	0.210962	−	0.977494i	$-0.432341\pi$
$5$	2.13811	−	0.694712i	0.956190	−	0.310685i	0.745228	+	0.666809i	$0.232341\pi$
$6$		0			0
$7$	−2.38116	+	3.27739i	−0.899995	+	1.23874i	0.0704753	+	0.997514i	$0.477548\pi$
$7$	−2.38116	+	3.27739i	−0.899995	+	1.23874i	−0.970470	+	0.241223i	$0.922452\pi$
$8$	−2.90269	+	2.10893i	−1.02626	+	0.745618i
$9$		0			0
$10$		−	5.28492i		−	1.67124i
$11$	−3.31656	+	0.0200544i	−0.999982	+	0.00604662i
$11$	−3.31656	+	0.0200544i	−0.999982	+	0.00604662i
$12$		0			0
$13$	4.42495	+	1.43775i	1.22726	+	0.398761i	0.849721	−	0.527233i	$-0.176771\pi$
$13$	4.42495	+	1.43775i	1.22726	+	0.398761i	0.377538	+	0.925994i	$0.376771\pi$
$14$	5.59763	+	7.70448i	1.49603	+	2.05911i
$15$		0			0
$16$	0.427051	+	1.31433i	0.106763	+	0.328582i
$17$	−0.0235753	−	0.0725574i	−0.00571786	−	0.0175978i	0.948157	−	0.317803i	$-0.102945\pi$
$17$	−0.0235753	−	0.0725574i	−0.00571786	−	0.0175978i	−0.953875	+	0.300205i	$0.902945\pi$
$18$		0			0
$19$	1.40822	+	1.93825i	0.323068	+	0.444665i	0.939401	−	0.342821i	$-0.111382\pi$
$19$	1.40822	+	1.93825i	0.323068	+	0.444665i	−0.616333	+	0.787486i	$0.711382\pi$
$20$	−7.53950	−	2.44973i	−1.68588	−	0.547777i
$21$		0			0
$22$	−2.36444	+	7.42955i	−0.504100	+	1.58399i
$23$		−	3.22717i		−	0.672912i	−0.941699	−	0.336456i	$-0.890772\pi$
$23$		−	3.22717i		−	0.672912i	0.941699	−	0.336456i	$-0.109228\pi$
$24$		0			0
$25$	0.0437835	−	0.0318106i	0.00875670	−	0.00636211i
$26$	6.42889	−	8.84860i	1.26081	−	1.73535i
$27$		0			0
$28$	13.5860	−	4.41435i	2.56750	−	0.834233i
$29$	1.48796	+	1.08107i	0.276307	+	0.200749i	0.717305	−	0.696759i	$-0.245375\pi$
$29$	1.48796	+	1.08107i	0.276307	+	0.200749i	−0.440998	+	0.897508i	$0.645375\pi$
$30$		0			0
$31$	0.517528	−	1.59279i	0.0929508	−	0.286073i	−0.893763	−	0.448539i	$-0.851945\pi$
$31$	0.517528	−	1.59279i	0.0929508	−	0.286073i	0.986714	+	0.162466i	$0.0519446\pi$
$32$	−3.92711			−0.694222
$33$		0			0
$34$	−0.179346			−0.0307575
$35$	−2.81433	+	8.66162i	−0.475709	+	1.46408i
$36$		0			0
$37$	−5.87906	−	4.27138i	−0.966511	−	0.702211i	−0.0118571	−	0.999930i	$-0.503774\pi$
$37$	−5.87906	−	4.27138i	−0.966511	−	0.702211i	−0.954654	+	0.297718i	$0.903774\pi$
$38$	5.35641	−	1.74040i	0.868925	−	0.282331i
$39$		0			0
$40$	−4.74115	+	6.52564i	−0.749642	+	1.03179i
$41$	−6.82980	+	4.96214i	−1.06664	+	0.774956i	−0.975305	−	0.220864i	$-0.929112\pi$
$41$	−6.82980	+	4.96214i	−1.06664	+	0.774956i	−0.0913313	+	0.995821i	$0.529112\pi$
$42$		0			0
$43$			4.28086i			0.652825i	0.945227	+	0.326413i	$0.105840\pi$
$43$			4.28086i			0.652825i	−0.945227	+	0.326413i	$0.894160\pi$
$44$	9.50306	+	6.81697i	1.43264	+	1.02770i
$45$		0			0
$46$	−7.21513	−	2.34434i	−1.06381	−	0.345654i
$47$	−3.65360	−	5.02874i	−0.532932	−	0.733518i	0.454642	−	0.890674i	$-0.349767\pi$
$47$	−3.65360	−	5.02874i	−0.532932	−	0.733518i	−0.987574	+	0.157157i	$0.949767\pi$
$48$		0			0
$49$	−2.90822	−	8.95058i	−0.415460	−	1.27865i
$50$	−0.0393143	−	0.120997i	−0.00555988	−	0.0171116i
$51$		0			0
$52$	−9.64348	−	13.2731i	−1.33731	−	1.84065i
$53$	1.16884	+	0.379779i	0.160552	+	0.0521666i	0.388190	−	0.921579i	$-0.373100\pi$
$53$	1.16884	+	0.379779i	0.160552	+	0.0521666i	−0.227638	+	0.973746i	$0.573100\pi$
$54$		0			0
$55$	−7.07723	+	2.34694i	−0.954294	+	0.316461i
$56$		−	14.5349i		−	1.94231i
$57$		0			0
$58$	3.49789	−	2.54137i	0.459296	−	0.333698i
$59$	−0.341086	+	0.469465i	−0.0444056	+	0.0611191i	−0.830642	−	0.556806i	$-0.812027\pi$
$59$	−0.341086	+	0.469465i	−0.0444056	+	0.0611191i	0.786237	+	0.617925i	$0.212027\pi$
$60$		0			0
$61$	−3.59710	+	1.16877i	−0.460561	+	0.149645i	−0.530102	−	0.847934i	$-0.677847\pi$
$61$	−3.59710	+	1.16877i	−0.460561	+	0.149645i	0.0695411	+	0.997579i	$0.477847\pi$
$62$	−3.18511	−	2.31412i	−0.404510	−	0.293893i
$63$		0			0
$64$	−3.70690	+	11.4087i	−0.463363	+	1.42608i
$65$	10.4598			1.29738
$66$		0			0
$67$	12.9984			1.58801			0.794003	−	0.607914i	$-0.207993\pi$
$67$	12.9984			1.58801			0.794003	+	0.607914i	$0.207993\pi$
$68$	−0.0831326	+	0.255856i	−0.0100813	+	0.0310271i
$69$		0			0
$70$	17.3207	+	12.5842i	2.07022	+	1.50410i
$71$	1.06563	−	0.346245i	0.126467	−	0.0410917i	−0.245100	−	0.969498i	$-0.578821\pi$
$71$	1.06563	−	0.346245i	0.126467	−	0.0410917i	0.371567	+	0.928406i	$0.378821\pi$
$72$		0			0
$73$	7.82153	−	10.7654i	0.915441	−	1.26000i	−0.0498335	−	0.998758i	$-0.515869\pi$
$73$	7.82153	−	10.7654i	0.915441	−	1.26000i	0.965274	−	0.261239i	$-0.0841309\pi$
$74$	−13.8205	+	10.0412i	−1.60660	+	1.16726i
$75$		0			0
$76$		−	8.44824i		−	0.969079i
$77$	7.83155	−	10.9174i	0.892488	−	1.24416i
$78$		0			0
$79$	0.627566	+	0.203908i	0.0706066	+	0.0229415i	0.344107	−	0.938930i	$-0.388182\pi$
$79$	0.627566	+	0.203908i	0.0706066	+	0.0229415i	−0.273501	+	0.961872i	$0.588182\pi$
$80$	1.82616	+	2.51349i	0.204171	+	0.281017i
$81$		0			0
$82$	6.13265	+	18.8744i	0.677238	+	2.08432i
$83$	−3.15542	−	9.71138i	−0.346352	−	1.06596i	−0.960856	−	0.277048i	$-0.910644\pi$
$83$	−3.15542	−	9.71138i	−0.346352	−	1.06596i	0.614504	−	0.788914i	$-0.289356\pi$
$84$		0			0
$85$	−0.100813	−	0.138757i	−0.0109347	−	0.0150503i
$86$	9.57090	+	3.10977i	1.03206	+	0.335336i
$87$		0			0
$88$	9.58466	−	7.05260i	1.02173	−	0.751810i
$89$			6.58983i			0.698520i	0.937026	+	0.349260i	$0.113567\pi$
$89$			6.58983i			0.698520i	−0.937026	+	0.349260i	$0.886433\pi$
$90$		0			0
$91$	−15.2486	+	11.0787i	−1.59849	+	1.16137i
$92$	−6.68890	+	9.20649i	−0.697366	+	0.959843i
$93$		0			0
$94$	−13.8971	+	4.51544i	−1.43337	+	0.465732i
$95$	4.35745	+	3.16587i	0.447065	+	0.324812i
$96$		0			0
$97$	5.08168	−	15.6398i	0.515966	−	1.58798i	−0.265551	−	0.964097i	$-0.585554\pi$
$97$	5.08168	−	15.6398i	0.515966	−	1.58798i	0.781517	−	0.623883i	$-0.214446\pi$
$98$	−22.1238			−2.23485
$99$		0			0
$100$	−0.190839			−0.0190839
$101$	0.532095	−	1.63762i	0.0529455	−	0.162949i	−0.921087	−	0.389356i	$-0.872698\pi$
$101$	0.532095	−	1.63762i	0.0529455	−	0.162949i	0.974033	+	0.226406i	$0.0726977\pi$
$102$		0			0
$103$	2.61382	+	1.89905i	0.257548	+	0.187119i	0.709065	−	0.705143i	$-0.249117\pi$
$103$	2.61382	+	1.89905i	0.257548	+	0.187119i	−0.451518	+	0.892262i	$0.649117\pi$
$104$	−15.8763	+	5.15854i	−1.55680	+	0.505836i
$105$		0			0
$106$	1.69818	−	2.33734i	0.164941	−	0.227022i
$107$	11.9884	−	8.71006i	1.15896	−	0.842034i	0.169314	−	0.985562i	$-0.445845\pi$
$107$	11.9884	−	8.71006i	1.15896	−	0.842034i	0.989646	+	0.143529i	$0.0458449\pi$
$108$		0			0
$109$			14.9258i			1.42963i	0.699313	+	0.714815i	$0.253489\pi$
$109$			14.9258i			1.42963i	−0.699313	+	0.714815i	$0.746511\pi$
$110$	0.105986	+	17.5278i	0.0101053	+	1.67121i
$111$		0			0
$112$	−5.32444	−	1.73002i	−0.503112	−	0.163471i
$113$	6.61055	+	9.09864i	0.621868	+	0.855928i	0.997487	−	0.0708461i	$-0.0225699\pi$
$113$	6.61055	+	9.09864i	0.621868	+	0.855928i	−0.375619	+	0.926774i	$0.622570\pi$
$114$		0			0
$115$	−2.24196	−	6.90004i	−0.209064	−	0.643432i
$116$	−2.00415	−	6.16813i	−0.186080	−	0.572697i
$117$		0			0
$118$	0.801825	+	1.10362i	0.0738139	+	0.101596i
$119$	0.293935	+	0.0955054i	0.0269450	+	0.00875497i
$120$		0			0
$121$	10.9992	−	0.133023i	0.999927	−	0.0120930i
$122$			8.89122i			0.804973i
$123$		0			0
$124$	−4.77775	+	3.47124i	−0.429054	+	0.311726i
$125$	−6.53559	+	8.99547i	−0.584561	+	0.804580i
$126$		0			0
$127$	−5.76481	+	1.87310i	−0.511544	+	0.166211i	−0.553404	−	0.832913i	$-0.686672\pi$
$127$	−5.76481	+	1.87310i	−0.511544	+	0.166211i	0.0418604	+	0.999123i	$0.486672\pi$
$128$	16.4598	+	11.9588i	1.45486	+	1.05701i
$129$		0			0
$130$	7.59840	−	23.3855i	0.666424	−	2.05104i
$131$	−7.15083			−0.624771			−0.312385	−	0.949955i	$-0.601128\pi$
$131$	−7.15083			−0.624771			−0.312385	+	0.949955i	$0.601128\pi$
$132$		0			0
$133$	−9.70560			−0.841582
$134$	9.44251	−	29.0611i	0.815709	−	2.51049i
$135$		0			0
$136$	0.221450	+	0.160893i	0.0189892	+	0.0137964i
$137$	10.1026	−	3.28252i	0.863120	−	0.280445i	0.156189	−	0.987727i	$-0.450079\pi$
$137$	10.1026	−	3.28252i	0.863120	−	0.280445i	0.706931	+	0.707283i	$0.250079\pi$
$138$		0			0
$139$	−0.0311975	+	0.0429397i	−0.00264614	+	0.00364210i	−0.810338	−	0.585963i	$-0.800716\pi$
$139$	−0.0311975	+	0.0429397i	−0.00264614	+	0.00364210i	0.807692	+	0.589605i	$0.200716\pi$
$140$	25.9815	−	18.8767i	2.19584	−	1.59537i
$141$		0			0
$142$		−	2.63400i		−	0.221041i
$143$	−14.7044	−	4.67966i	−1.22965	−	0.391333i
$144$		0			0
$145$	3.93244	+	1.27773i	0.326572	+	0.106110i
$146$	−18.3868	−	25.3073i	−1.52171	−	2.09445i
$147$		0			0
$148$	7.91856	+	24.3708i	0.650901	+	2.00327i
$149$	−6.30238	−	19.3967i	−0.516311	−	1.58904i	−0.780883	−	0.624677i	$-0.785231\pi$
$149$	−6.30238	−	19.3967i	−0.516311	−	1.58904i	0.264572	−	0.964366i	$-0.414769\pi$
$150$		0			0
$151$	0.698980	+	0.962063i	0.0568822	+	0.0782916i	0.836510	−	0.547951i	$-0.184592\pi$
$151$	0.698980	+	0.962063i	0.0568822	+	0.0782916i	−0.779628	+	0.626243i	$0.784592\pi$
$152$	−8.17525	−	2.65630i	−0.663101	−	0.215454i
$153$		0			0
$154$	−18.7194	−	25.4401i	−1.50845	−	2.05003i
$155$		−	3.76508i		−	0.302419i
$156$		0			0
$157$	1.40210	−	1.01868i	0.111900	−	0.0812998i	−0.530428	−	0.847730i	$-0.677969\pi$
$157$	1.40210	−	1.01868i	0.111900	−	0.0812998i	0.642328	+	0.766430i	$0.277969\pi$
$158$	0.911773	−	1.25495i	0.0725368	−	0.0998383i
$159$		0			0
$160$	−8.39658	+	2.72822i	−0.663808	+	0.215684i
$161$	10.5767	+	7.68443i	0.833561	+	0.605618i
$162$		0			0
$163$	−0.309821	+	0.953532i	−0.0242671	+	0.0746864i	−0.962457	−	0.271435i	$-0.912502\pi$
$163$	−0.309821	+	0.953532i	−0.0242671	+	0.0746864i	0.938190	+	0.346122i	$0.112502\pi$
$164$	29.7690			2.32457
$165$		0			0
$166$	−24.0044			−1.86310
$167$	−4.17734	+	12.8565i	−0.323252	+	0.994868i	0.648971	+	0.760813i	$0.275200\pi$
$167$	−4.17734	+	12.8565i	−0.323252	+	0.994868i	−0.972223	+	0.234055i	$0.924800\pi$
$168$		0			0
$169$	6.99579	+	5.08274i	0.538138	+	0.390980i
$170$	−0.383460	+	0.124594i	−0.0294100	+	0.00955590i
$171$		0			0
$172$	8.87286	−	12.2124i	0.676549	−	0.931190i
$173$	−6.08619	+	4.42188i	−0.462724	+	0.336189i	−0.794599	−	0.607135i	$-0.792319\pi$
$173$	−6.08619	+	4.42188i	−0.462724	+	0.336189i	0.331875	+	0.943324i	$0.392319\pi$
$174$		0			0
$175$			0.219242i			0.0165731i
$176$	−1.44270	−	4.35049i	−0.108748	−	0.327930i
$177$		0			0
$178$	14.7332	+	4.78709i	1.10430	+	0.358808i
$179$	7.34750	+	10.1130i	0.549178	+	0.755879i	0.989900	−	0.141765i	$-0.0452777\pi$
$179$	7.34750	+	10.1130i	0.549178	+	0.755879i	−0.440722	+	0.897643i	$0.645278\pi$
$180$		0			0
$181$	−5.56261	−	17.1200i	−0.413466	−	1.27252i	−0.913616	−	0.406578i	$-0.866722\pi$
$181$	−5.56261	−	17.1200i	−0.413466	−	1.27252i	0.500150	−	0.865939i	$-0.333278\pi$
$182$	13.6921	+	42.1399i	1.01492	+	3.12362i
$183$		0			0
$184$	6.80587	+	9.36748i	0.501736	+	0.690580i
$185$	−15.5374	−	5.04842i	−1.14233	−	0.371167i
$186$		0			0
$187$	0.0796442	+	0.240168i	0.00582416	+	0.0175629i
$188$			21.9187i			1.59859i
$189$		0			0
$190$	10.2435	−	7.44233i	0.743141	−	0.539924i
$191$	−12.7297	+	17.5209i	−0.921085	+	1.26777i	0.0421514	+	0.999111i	$0.486579\pi$
$191$	−12.7297	+	17.5209i	−0.921085	+	1.26777i	−0.963237	+	0.268654i	$0.913421\pi$
$192$		0			0
$193$	−4.93306	+	1.60285i	−0.355090	+	0.115376i	−0.481129	−	0.876650i	$-0.659773\pi$
$193$	−4.93306	+	1.60285i	−0.355090	+	0.115376i	0.126040	+	0.992025i	$0.459773\pi$
$194$	−31.2750	−	22.7226i	−2.24542	−	1.63139i
$195$		0			0
$196$	−10.2551	+	31.5620i	−0.732509	+	2.25443i
$197$	−5.14679			−0.366693			−0.183347	−	0.983048i	$-0.558693\pi$
$197$	−5.14679			−0.366693			−0.183347	+	0.983048i	$0.558693\pi$
$198$		0			0
$199$	24.2595			1.71971			0.859855	−	0.510539i	$-0.170554\pi$
$199$	24.2595			1.71971			0.859855	+	0.510539i	$0.170554\pi$
$200$	−0.0600037	+	0.184672i	−0.00424290	+	0.0130583i
$201$		0			0
$202$	−3.27477	−	2.37926i	−0.230412	−	0.167404i
$203$	−7.08615	+	2.30243i	−0.497350	+	0.161599i
$204$		0			0
$205$	−11.1556	+	15.3543i	−0.779139	+	1.07239i
$206$	6.14457	−	4.46429i	0.428113	−	0.311042i
$207$		0			0
$208$			6.42982i			0.445828i
$209$	−4.70933	−	6.40009i	−0.325751	−	0.442704i
$210$		0			0
$211$	−17.8262	−	5.79210i	−1.22721	−	0.398744i	−0.377506	−	0.926007i	$-0.623218\pi$
$211$	−17.8262	−	5.79210i	−1.22721	−	0.398744i	−0.849702	+	0.527263i	$0.823218\pi$
$212$	−2.54730	−	3.50606i	−0.174950	−	0.240797i
$213$		0			0
$214$	−10.7647	−	33.1302i	−0.735857	−	2.26474i
$215$	2.97397	+	9.15293i	0.202823	+	0.624225i
$216$		0			0
$217$	3.98787	+	5.48883i	0.270714	+	0.372606i
$218$	33.3702	+	10.8426i	2.26012	+	0.734356i
$219$		0			0
$220$	25.0544	+	7.97350i	1.68917	+	0.537573i
$221$		−	0.354958i		−	0.0238771i
$222$		0			0
$223$	4.44037	−	3.22612i	0.297349	−	0.216037i	−0.429100	−	0.903257i	$-0.641169\pi$
$223$	4.44037	−	3.22612i	0.297349	−	0.216037i	0.726449	+	0.687220i	$0.241169\pi$
$224$	9.35109	−	12.8707i	0.624796	−	0.859958i
$225$		0			0
$226$	25.1444	−	8.16990i	1.67258	−	0.543454i
$227$	−11.1352	−	8.09016i	−0.739066	−	0.536963i	0.153352	−	0.988172i	$-0.450993\pi$
$227$	−11.1352	−	8.09016i	−0.739066	−	0.536963i	−0.892419	+	0.451209i	$0.850993\pi$
$228$		0			0
$229$	−6.53035	+	20.0983i	−0.431538	+	1.32814i	0.465056	+	0.885281i	$0.346034\pi$
$229$	−6.53035	+	20.0983i	−0.431538	+	1.32814i	−0.896593	+	0.442855i	$0.853966\pi$
$230$	−17.0554			−1.12460
$231$		0			0
$232$	−6.59897			−0.433244
$233$	−4.62458	+	14.2330i	−0.302967	+	0.932435i	0.677462	+	0.735558i	$0.263080\pi$
$233$	−4.62458	+	14.2330i	−0.302967	+	0.932435i	−0.980428	+	0.196877i	$0.936920\pi$
$234$		0			0
$235$	−11.3053	−	8.21378i	−0.737477	−	0.535808i
$236$	1.94610	−	0.632327i	0.126680	−	0.0411610i
$237$		0			0
$238$	0.427051	−	0.587785i	0.0276816	−	0.0381005i
$239$	4.37274	−	3.17698i	0.282849	−	0.205502i	−0.437310	−	0.899311i	$-0.644069\pi$
$239$	4.37274	−	3.17698i	0.282849	−	0.205502i	0.720159	+	0.693809i	$0.244069\pi$
$240$		0			0
$241$			11.7091i			0.754252i	0.926162	+	0.377126i	$0.123088\pi$
$241$			11.7091i			0.754252i	−0.926162	+	0.377126i	$0.876912\pi$
$242$	7.69281	−	24.6880i	0.494513	−	1.58700i
$243$		0			0
$244$	12.6843	+	4.12137i	0.812028	+	0.263844i
$245$	−12.4362	−	17.1169i	−0.794518	−	1.09356i
$246$		0			0
$247$	3.44458	+	10.6013i	0.219173	+	0.674546i
$248$	1.85685	+	5.71479i	0.117910	+	0.362890i
$249$		0			0
$250$	15.3639	+	21.1465i	0.971696	+	1.33743i
$251$	21.4920	+	6.98319i	1.35657	+	0.440775i	0.894895	−	0.446276i	$-0.147250\pi$
$251$	21.4920	+	6.98319i	1.35657	+	0.440775i	0.461671	+	0.887051i	$0.347250\pi$
$252$		0			0
$253$	0.0647190	+	10.7031i	0.00406885	+	0.672900i
$254$			14.2493i			0.894081i
$255$		0			0
$256$	19.2841	−	14.0107i	1.20526	−	0.875671i
$257$	16.1737	−	22.2612i	1.00889	−	1.38862i	0.0891801	−	0.996016i	$-0.471575\pi$
$257$	16.1737	−	22.2612i	1.00889	−	1.38862i	0.919709	−	0.392601i	$-0.128425\pi$
$258$		0			0
$259$	27.9980	−	9.09709i	1.73971	−	0.565266i
$260$	−29.8398	−	21.6799i	−1.85059	−	1.34453i
$261$		0			0
$262$	−5.19462	+	15.9874i	−0.320925	+	0.987705i
$263$	32.0386			1.97559			0.987793	−	0.155773i	$-0.0497868\pi$
$263$	32.0386			1.97559			0.987793	+	0.155773i	$0.0497868\pi$
$264$		0			0
$265$	2.76294			0.169726
$266$	−7.05051	+	21.6992i	−0.432294	+	1.33046i
$267$		0			0
$268$	−37.0818	−	26.9415i	−2.26513	−	1.64572i
$269$	−25.7177	+	8.35619i	−1.56804	+	0.509486i	−0.958940	−	0.283610i	$-0.908468\pi$
$269$	−25.7177	+	8.35619i	−1.56804	+	0.509486i	−0.609097	+	0.793096i	$0.708468\pi$
$270$		0			0
$271$	8.74690	−	12.0391i	0.531336	−	0.731322i	−0.455997	−	0.889981i	$-0.650717\pi$
$271$	8.74690	−	12.0391i	0.531336	−	0.731322i	0.987333	+	0.158660i	$0.0507172\pi$
$272$	0.0852963	−	0.0619714i	0.00517185	−	0.00375757i
$273$		0			0
$274$		−	24.9713i		−	1.50857i
$275$	−0.144573	+	0.106380i	−0.00871807	+	0.00641495i
$276$		0			0
$277$	−7.49418	−	2.43501i	−0.450282	−	0.146305i	0.0750927	−	0.997177i	$-0.476075\pi$
$277$	−7.49418	−	2.43501i	−0.450282	−	0.146305i	−0.525374	+	0.850871i	$0.676075\pi$
$278$	0.0733391	+	0.100943i	0.00439859	+	0.00605414i
$279$		0			0
$280$	−10.0976	−	31.0772i	−0.603447	−	1.85722i
$281$	6.56034	+	20.1906i	0.391357	+	1.20447i	0.931763	+	0.363068i	$0.118271\pi$
$281$	6.56034	+	20.1906i	0.391357	+	1.20447i	−0.540406	+	0.841405i	$0.681729\pi$
$282$		0			0
$283$	−2.52460	−	3.47482i	−0.150072	−	0.206556i	0.727362	−	0.686254i	$-0.240746\pi$
$283$	−2.52460	−	3.47482i	−0.150072	−	0.206556i	−0.877434	+	0.479698i	$0.840746\pi$
$284$	−3.75769	−	1.22095i	−0.222978	−	0.0724499i
$285$		0			0
$286$	−21.1444	+	29.4759i	−1.25029	+	1.74295i
$287$		−	34.1996i		−	2.01874i
$288$		0			0
$289$	13.7486	−	9.98893i	0.808740	−	0.587584i
$290$	5.71335	−	7.86374i	0.335499	−	0.461775i
$291$		0			0
$292$	−44.6265	+	14.5000i	−2.61157	+	0.848550i
$293$	15.4486	+	11.2241i	0.902518	+	0.655717i	0.939111	−	0.343613i	$-0.111651\pi$
$293$	15.4486	+	11.2241i	0.902518	+	0.655717i	−0.0365938	+	0.999330i	$0.511651\pi$
$294$		0			0
$295$	−0.403135	+	1.24072i	−0.0234714	+	0.0722376i
$296$	26.0731			1.51547
$297$		0			0
$298$	−47.9444			−2.77735
$299$	4.63988	−	14.2801i	0.268331	−	0.825838i
$300$		0			0
$301$	−14.0300	−	10.1934i	−0.808678	−	0.587539i
$302$	2.65869	−	0.863861i	0.152990	−	0.0497096i
$303$		0			0
$304$	−1.94611	+	2.67860i	−0.111617	+	0.153628i
$305$	−6.87902	+	4.99790i	−0.393891	+	0.286179i
$306$		0			0
$307$			1.86240i			0.106293i	0.998587	+	0.0531463i	$0.0169250\pi$
$307$			1.86240i			0.106293i	−0.998587	+	0.0531463i	$0.983075\pi$
$308$	−44.9702	+	14.9129i	−2.56241	+	0.849742i
$309$		0			0
$310$	−8.41775	−	2.73509i	−0.478096	−	0.155343i
$311$	5.26339	+	7.24443i	0.298459	+	0.410794i	0.931739	−	0.363129i	$-0.118292\pi$
$311$	5.26339	+	7.24443i	0.298459	+	0.410794i	−0.633279	+	0.773923i	$0.718292\pi$
$312$		0			0
$313$	5.29558	+	16.2981i	0.299324	+	0.921224i	0.981735	+	0.190255i	$0.0609316\pi$
$313$	5.29558	+	16.2981i	0.299324	+	0.921224i	−0.682411	+	0.730969i	$0.739068\pi$
$314$	−1.25898	−	3.87474i	−0.0710483	−	0.218664i
$315$		0			0
$316$	−1.36768	−	1.88245i	−0.0769381	−	0.105896i
$317$	−25.9678	−	8.43746i	−1.45850	−	0.473895i	−0.530888	−	0.847442i	$-0.678141\pi$
$317$	−25.9678	−	8.43746i	−1.45850	−	0.473895i	−0.927611	+	0.373547i	$0.878141\pi$
$318$		0			0
$319$	−4.95659	−	3.55558i	−0.277516	−	0.199075i
$320$			26.9682i			1.50757i
$321$		0			0
$322$	24.8637	−	18.0645i	1.38560	−	1.00670i
$323$	0.107435	−	0.147872i	0.00597785	−	0.00822781i
$324$		0			0
$325$	0.239475	−	0.0778102i	0.0132837	−	0.00431614i
$326$	1.90679	+	1.38536i	0.105607	+	0.0767281i
$327$		0			0
$328$	9.35999	−	28.8071i	0.516819	−	1.59061i
$329$	25.1809			1.38827
$330$		0			0
$331$	−5.87217			−0.322764			−0.161382	−	0.986892i	$-0.551595\pi$
$331$	−5.87217			−0.322764			−0.161382	+	0.986892i	$0.551595\pi$
$332$	−11.1268	+	34.2448i	−0.610663	+	1.87943i
$333$		0			0
$334$	25.7093	+	18.6789i	1.40675	+	1.02206i
$335$	27.7919	−	9.03014i	1.51844	−	0.493370i
$336$		0			0
$337$	−9.74004	+	13.4060i	−0.530574	+	0.730272i	−0.987218	−	0.159377i	$-0.949051\pi$
$337$	−9.74004	+	13.4060i	−0.530574	+	0.730272i	0.456644	+	0.889650i	$0.349051\pi$
$338$	16.4457	−	11.9485i	0.894528	−	0.649912i
$339$		0			0
$340$			0.604800i			0.0327999i
$341$	−1.68447	+	5.29296i	−0.0912193	+	0.286630i
$342$		0			0
$343$	9.28988	+	3.01847i	0.501606	+	0.162982i
$344$	−9.02802	−	12.4260i	−0.486758	−	0.669965i
$345$		0			0
$346$	5.46494	+	16.8194i	0.293797	+	0.904215i
$347$	0.778158	+	2.39492i	0.0417737	+	0.128566i	0.969768	−	0.244027i	$-0.0784686\pi$
$347$	0.778158	+	2.39492i	0.0417737	+	0.128566i	−0.927995	+	0.372593i	$0.878469\pi$
$348$		0			0
$349$	5.13104	+	7.06228i	0.274658	+	0.378035i	0.923955	−	0.382500i	$-0.124937\pi$
$349$	5.13104	+	7.06228i	0.274658	+	0.378035i	−0.649297	+	0.760535i	$0.724937\pi$
$350$	0.490168	+	0.159265i	0.0262006	+	0.00851308i
$351$		0			0
$352$	13.0245	−	0.0787558i	0.694210	−	0.00419770i
$353$		−	0.536500i		−	0.0285550i	−0.999898	−	0.0142775i	$-0.995455\pi$
$353$		−	0.536500i		−	0.0285550i	0.999898	−	0.0142775i	$-0.00454483\pi$
$354$		0			0
$355$	2.03789	−	1.48062i	0.108160	−	0.0785829i
$356$	13.6586	−	18.7995i	0.723905	−	0.996370i
$357$		0			0
$358$	27.9475	−	9.08069i	1.47707	−	0.479929i
$359$	−12.7871	−	9.29040i	−0.674880	−	0.490329i	0.196775	−	0.980449i	$-0.436953\pi$
$359$	−12.7871	−	9.29040i	−0.674880	−	0.490329i	−0.871655	+	0.490120i	$0.836953\pi$
$360$		0			0
$361$	4.09760	−	12.6111i	0.215663	−	0.663742i
$362$	−42.3167			−2.22412
$363$		0			0
$364$	66.4639			3.48365
$365$	9.24439	−	28.4513i	0.483873	−	1.48921i
$366$		0			0
$367$	−23.4075	−	17.0065i	−1.22186	−	0.887734i	−0.225608	−	0.974218i	$-0.572437\pi$
$367$	−23.4075	−	17.0065i	−1.22186	−	0.887734i	−0.996253	+	0.0864843i	$0.972437\pi$
$368$	4.24157	−	1.37817i	0.221107	−	0.0718420i
$369$		0			0
$370$	−22.5739	+	31.0703i	−1.17356	+	1.61527i
$371$	−4.02788	+	2.92642i	−0.209117	+	0.151932i
$372$		0			0
$373$		−	6.60935i		−	0.342219i	−0.985252	−	0.171109i	$-0.945265\pi$
$373$		−	6.60935i		−	0.342219i	0.985252	−	0.171109i	$-0.0547352\pi$
$374$	0.594811	−	0.00359666i	0.0307570	−	0.000185979i
$375$		0			0
$376$	21.2105	+	6.89171i	1.09385	+	0.355413i
$377$	5.02984	+	6.92297i	0.259050	+	0.356551i
$378$		0			0
$379$	0.478524	+	1.47275i	0.0245801	+	0.0756498i	0.962594	−	0.270948i	$-0.0873370\pi$
$379$	0.478524	+	1.47275i	0.0245801	+	0.0756498i	−0.938014	+	0.346597i	$0.887337\pi$
$380$	−5.86909	−	18.0632i	−0.301078	−	0.926623i
$381$		0			0
$382$	29.9249	+	41.1880i	1.53109	+	2.10736i
$383$	−12.8467	−	4.17415i	−0.656436	−	0.213289i	−0.0381861	−	0.999271i	$-0.512158\pi$
$383$	−12.8467	−	4.17415i	−0.656436	−	0.213289i	−0.618250	+	0.785982i	$0.712158\pi$
$384$		0			0
$385$	9.16021	−	28.7833i	0.466847	−	1.46693i
$386$			12.1934i			0.620629i
$387$		0			0
$388$	−46.9133	+	34.0845i	−2.38166	+	1.73038i
$389$	−8.80471	+	12.1186i	−0.446416	+	0.614440i	−0.971623	−	0.236535i	$-0.923988\pi$
$389$	−8.80471	+	12.1186i	−0.446416	+	0.614440i	0.525206	+	0.850975i	$0.323988\pi$
$390$		0			0
$391$	−0.234155	+	0.0760817i	−0.0118417	+	0.00384762i
$392$	27.3178	+	19.8475i	1.37976	+	1.00245i
$393$		0			0
$394$	−3.73882	+	11.5069i	−0.188359	+	0.579709i
$395$	1.48346			0.0746409
$396$		0			0
$397$	−20.7132			−1.03956			−0.519782	−	0.854299i	$-0.673987\pi$
$397$	−20.7132			−1.03956			−0.519782	+	0.854299i	$0.673987\pi$
$398$	17.6230	−	54.2380i	0.883360	−	2.71870i
$399$		0			0
$400$	0.0605073	+	0.0439611i	0.00302537	+	0.00219806i
$401$	−25.7211	+	8.35730i	−1.28445	+	0.417343i	−0.870146	−	0.492795i	$-0.835975\pi$
$401$	−25.7211	+	8.35730i	−1.28445	+	0.417343i	−0.414305	+	0.910138i	$0.635975\pi$
$402$		0			0
$403$	4.58007	−	6.30392i	0.228149	−	0.314021i
$404$	−4.91223	+	3.56894i	−0.244392	+	0.177561i
$405$		0			0
$406$			17.5154i			0.869273i
$407$	19.5839	+	14.0484i	0.970739	+	0.696354i
$408$		0			0
$409$	−5.80668	−	1.88670i	−0.287122	−	0.0932915i	0.161915	−	0.986805i	$-0.448233\pi$
$409$	−5.80668	−	1.88670i	−0.287122	−	0.0932915i	−0.449037	+	0.893513i	$0.648233\pi$
$410$	26.2245	+	36.0949i	1.29514	+	1.78260i
$411$		0			0
$412$	−3.52058	−	10.8352i	−0.173447	−	0.533814i
$413$	−0.726437	−	2.23574i	−0.0357456	−	0.110014i
$414$		0			0
$415$	−13.4932	−	18.5718i	−0.662357	−	0.911656i
$416$	−17.3773	−	5.64622i	−0.851991	−	0.276829i
$417$		0			0
$418$	−17.7300	+	5.87958i	−0.867202	+	0.287580i
$419$			35.6619i			1.74220i	0.491110	+	0.871098i	$0.336591\pi$
$419$			35.6619i			1.74220i	−0.491110	+	0.871098i	$0.663409\pi$
$420$		0			0
$421$	−11.5751	+	8.40982i	−0.564137	+	0.409870i	−0.832971	−	0.553317i	$-0.813362\pi$
$421$	−11.5751	+	8.40982i	−0.564137	+	0.409870i	0.268834	+	0.963187i	$0.413362\pi$
$422$	−25.8993	+	35.6473i	−1.26076	+	1.73528i
$423$		0			0
$424$	−4.19370	+	1.36262i	−0.203664	+	0.0661745i
$425$	−0.00334030	−	0.00242687i	−0.000162028	−	0.000117721i
$426$		0			0
$427$	4.73477	−	14.5721i	0.229131	−	0.705194i
$428$	−52.2536			−2.52577
$429$		0			0
$430$	22.6240			1.09103
$431$	−2.68944	+	8.27725i	−0.129546	+	0.398701i	−0.994702	−	0.102802i	$-0.967219\pi$
$431$	−2.68944	+	8.27725i	−0.129546	+	0.398701i	0.865156	+	0.501503i	$0.167219\pi$
$432$		0			0
$433$	30.3812	+	22.0733i	1.46003	+	1.06077i	0.983355	+	0.181693i	$0.0581576\pi$
$433$	30.3812	+	22.0733i	1.46003	+	1.06077i	0.476673	+	0.879080i	$0.341842\pi$
$434$	15.1685	−	4.92856i	0.728113	−	0.236578i
$435$		0			0
$436$	30.9364	−	42.5803i	1.48158	−	2.03923i
$437$	6.25507	−	4.54458i	0.299221	−	0.217397i
$438$		0			0
$439$		−	32.4669i		−	1.54956i	−0.632232	−	0.774779i	$-0.717861\pi$
$439$		−	32.4669i		−	1.54956i	0.632232	−	0.774779i	$-0.282139\pi$
$440$	15.5935	−	21.7378i	0.743390	−	1.03631i
$441$		0			0
$442$	−0.793595	−	0.257855i	−0.0377474	−	0.0122649i
$443$	11.0630	+	15.2269i	0.525618	+	0.723451i	0.986455	−	0.164034i	$-0.0524506\pi$
$443$	11.0630	+	15.2269i	0.525618	+	0.723451i	−0.460837	+	0.887485i	$0.652451\pi$
$444$		0			0
$445$	4.57804	+	14.0897i	0.217020	+	0.667918i
$446$	−3.98712	−	12.2711i	−0.188796	−	0.581053i
$447$		0			0
$448$	−28.5639	−	39.3149i	−1.34952	−	1.85745i
$449$	6.86840	+	2.23168i	0.324140	+	0.105319i	0.466567	−	0.884486i	$-0.345491\pi$
$449$	6.86840	+	2.23168i	0.324140	+	0.105319i	−0.142427	+	0.989805i	$0.545491\pi$
$450$		0			0
$451$	22.5520	−	16.5942i	1.06193	−	0.781392i
$452$		−	39.6582i		−	1.86536i
$453$		0			0
$454$	−26.1765	+	19.0183i	−1.22852	+	0.892575i
$455$	−24.9065	+	34.2809i	−1.16764	+	1.60711i
$456$		0			0
$457$	4.01554	−	1.30473i	0.187839	−	0.0610326i	−0.213587	−	0.976924i	$-0.568515\pi$
$457$	4.01554	−	1.30473i	0.187839	−	0.0610326i	0.401426	+	0.915891i	$0.368515\pi$
$458$	40.1908	+	29.2004i	1.87799	+	1.36444i
$459$		0			0
$460$	−7.90572	+	24.3313i	−0.368606	+	1.13445i
$461$	−14.1922			−0.660997			−0.330499	−	0.943806i	$-0.607217\pi$
$461$	−14.1922			−0.660997			−0.330499	+	0.943806i	$0.607217\pi$
$462$		0			0
$463$	−40.3784			−1.87654			−0.938271	−	0.345902i	$-0.887573\pi$
$463$	−40.3784			−1.87654			−0.938271	+	0.345902i	$0.887573\pi$
$464$	−0.785440	+	2.41734i	−0.0364632	+	0.112222i
$465$		0			0
$466$	28.4619	+	20.6788i	1.31847	+	0.957925i
$467$	10.7476	−	3.49210i	0.497338	−	0.161595i	−0.0495980	−	0.998769i	$-0.515794\pi$
$467$	10.7476	−	3.49210i	0.497338	−	0.161595i	0.546936	+	0.837174i	$0.315794\pi$
$468$		0			0
$469$	−30.9513	+	42.6008i	−1.42920	+	1.96712i
$470$	−26.5765	+	19.3090i	−1.22588	+	0.890656i
$471$		0			0
$472$		−	2.08203i		−	0.0958334i
$473$	−0.0858500	−	14.1977i	−0.00394739	−	0.652813i
$474$		0			0
$475$	0.123314	+	0.0400671i	0.00565802	+	0.00183840i
$476$	−0.640587	−	0.881692i	−0.0293612	−	0.0404123i
$477$		0			0
$478$	−3.92639	−	12.0842i	−0.179589	−	0.552718i
$479$	−7.07597	−	21.7776i	−0.323309	−	0.995044i	−0.972198	−	0.234161i	$-0.924766\pi$
$479$	−7.07597	−	21.7776i	−0.323309	−	0.995044i	0.648889	−	0.760883i	$-0.275234\pi$
$480$		0			0
$481$	−19.8733	−	27.3533i	−0.906145	−	1.24720i
$482$	26.1786	+	8.50595i	1.19240	+	0.387436i
$483$		0			0
$484$	−31.6542	−	22.4183i	−1.43883	−	1.01902i
$485$		−	36.9698i		−	1.67871i
$486$		0			0
$487$	6.10169	−	4.43314i	0.276494	−	0.200885i	−0.440893	−	0.897560i	$-0.645338\pi$
$487$	6.10169	−	4.43314i	0.276494	−	0.200885i	0.717387	+	0.696675i	$0.245338\pi$
$488$	7.97641	−	10.9786i	0.361075	−	0.496977i
$489$		0			0
$490$	−47.3031	+	15.3697i	−2.13694	+	0.694333i
$491$	−30.8965	−	22.4476i	−1.39434	−	1.01305i	−0.995373	−	0.0960820i	$-0.969369\pi$
$491$	−30.8965	−	22.4476i	−1.39434	−	1.01305i	−0.398967	−	0.916965i	$-0.630631\pi$
$492$		0			0
$493$	0.0433602	−	0.133449i	0.00195285	−	0.00601024i
$494$	26.2041			1.17898
$495$		0			0
$496$	2.31446			0.103922
$497$	−1.40266	+	4.31695i	−0.0629181	+	0.193642i
$498$		0			0
$499$	6.51994	+	4.73701i	0.291873	+	0.212058i	0.724079	−	0.689717i	$-0.242265\pi$
$499$	6.51994	+	4.73701i	0.291873	+	0.212058i	−0.432207	+	0.901775i	$0.642265\pi$
$500$	37.2895	−	12.1161i	1.66764	−	0.541848i
$501$		0			0
$502$	31.2252	−	42.9778i	1.39365	−	1.91820i
$503$	21.0846	−	15.3188i	0.940115	−	0.683033i	−0.00833362	−	0.999965i	$-0.502653\pi$
$503$	21.0846	−	15.3188i	0.940115	−	0.683033i	0.948448	+	0.316932i	$0.102653\pi$
$504$		0			0
$505$		−	3.87106i		−	0.172260i
$506$	23.9765	+	7.63045i	1.06588	+	0.339215i
$507$		0			0
$508$	20.3282	+	6.60503i	0.901917	+	0.293051i
$509$	−16.4364	−	22.6228i	−0.728531	−	1.00274i	−0.999197	−	0.0400639i	$-0.987244\pi$
$509$	−16.4364	−	22.6228i	−0.728531	−	1.00274i	0.270666	−	0.962673i	$-0.412756\pi$
$510$		0			0
$511$	16.6581	+	51.2684i	0.736911	+	2.26798i
$512$	−4.74153	−	14.5929i	−0.209548	−	0.644922i
$513$		0			0
$514$	−38.0212	−	52.3316i	−1.67704	−	2.30825i
$515$	6.90792	+	2.24452i	0.304399	+	0.0989054i
$516$		0			0
$517$	12.2182	+	16.6049i	0.537357	+	0.730282i
$518$		−	69.2047i		−	3.04068i
$519$		0			0
$520$	−30.3616	+	22.0590i	−1.33144	+	0.967351i
$521$	18.9804	−	26.1242i	0.831545	−	1.14452i	−0.156088	−	0.987743i	$-0.549888\pi$
$521$	18.9804	−	26.1242i	0.831545	−	1.14452i	0.987633	−	0.156781i	$-0.0501117\pi$
$522$		0			0
$523$	16.5104	−	5.36454i	0.721948	−	0.234575i	0.0750804	−	0.997177i	$-0.476079\pi$
$523$	16.5104	−	5.36454i	0.721948	−	0.234575i	0.646868	+	0.762602i	$0.276079\pi$
$524$	20.3999	+	14.8214i	0.891173	+	0.647475i
$525$		0			0
$526$	23.2740	−	71.6301i	1.01480	−	3.12322i
$527$	−0.127769			−0.00556572
$528$		0			0
$529$	12.5853			0.547189
$530$	2.00710	−	6.17722i	0.0871828	−	0.268321i
$531$		0			0
$532$	27.6881	+	20.1166i	1.20043	+	0.872166i
$533$	−37.3558	+	12.1376i	−1.61806	+	0.525740i
$534$		0			0
$535$	19.5814	−	26.9515i	0.846578	−	1.16522i
$536$	−37.7303	+	27.4126i	−1.62970	+	1.18405i
$537$		0			0
$538$			63.5684i			2.74063i
$539$	9.82480	+	29.6269i	0.423184	+	1.27612i
$540$		0			0
$541$	−9.58312	−	3.11375i	−0.412011	−	0.133870i	0.0956753	−	0.995413i	$-0.469499\pi$
$541$	−9.58312	−	3.11375i	−0.412011	−	0.133870i	−0.507686	+	0.861542i	$0.669499\pi$
$542$	−20.5622	−	28.3014i	−0.883222	−	1.21565i
$543$		0			0
$544$	0.0925830	+	0.284941i	0.00396946	+	0.0122168i
$545$	10.3691	+	31.9129i	0.444165	+	1.36700i
$546$		0			0
$547$	14.0244	+	19.3029i	0.599639	+	0.825333i	0.995675	−	0.0929023i	$-0.0296144\pi$
$547$	14.0244	+	19.3029i	0.599639	+	0.825333i	−0.396036	+	0.918235i	$0.629614\pi$
$548$	−35.6242	−	11.5750i	−1.52179	−	0.494460i
$549$		0			0
$550$	0.132815	+	0.400506i	0.00566325	+	0.0170776i
$551$			4.40642i			0.187720i
$552$		0			0
$553$	−2.16262	+	1.57124i	−0.0919640	+	0.0668158i
$554$	−10.8881	+	14.9862i	−0.462591	+	0.636702i
$555$		0			0
$556$	0.178001	−	0.0578359i	0.00754891	−	0.00245279i
$557$	31.6776	+	23.0151i	1.34222	+	0.975181i	0.999359	+	0.0357950i	$0.0113963\pi$
$557$	31.6776	+	23.0151i	1.34222	+	0.975181i	0.342862	+	0.939386i	$0.388604\pi$
$558$		0			0
$559$	−6.15482	+	18.9426i	−0.260321	+	0.801185i
$560$	−12.5861			−0.531859
$561$		0			0
$562$	49.9068			2.10519
$563$	−1.55147	+	4.77494i	−0.0653868	+	0.201240i	−0.978412	−	0.206663i	$-0.933740\pi$
$563$	−1.55147	+	4.77494i	−0.0653868	+	0.201240i	0.913025	+	0.407903i	$0.133740\pi$
$564$		0			0
$565$	20.4550	+	14.8614i	0.860548	+	0.625225i
$566$	−9.60276	+	3.12012i	−0.403634	+	0.131149i
$567$		0			0
$568$	−2.36299	+	3.25238i	−0.0991489	+	0.136467i
$569$	−7.69308	+	5.58935i	−0.322511	+	0.234318i	−0.737246	−	0.675624i	$-0.763874\pi$
$569$	−7.69308	+	5.58935i	−0.322511	+	0.234318i	0.414735	+	0.909942i	$0.363874\pi$
$570$		0			0
$571$			39.8291i			1.66680i	0.552673	+	0.833398i	$0.313608\pi$
$571$			39.8291i			1.66680i	−0.552673	+	0.833398i	$0.686392\pi$
$572$	32.2494	+	43.8278i	1.34842	+	1.83253i
$573$		0			0
$574$	−76.4614	−	24.8438i	−3.19144	−	1.03696i
$575$	−0.102658	−	0.141297i	−0.00428115	−	0.00589249i
$576$		0			0
$577$	−4.03506	−	12.4186i	−0.167982	−	0.516994i	0.831262	−	0.555881i	$-0.187619\pi$
$577$	−4.03506	−	12.4186i	−0.167982	−	0.516994i	−0.999244	+	0.0388866i	$0.987619\pi$
$578$	−12.3452	−	37.9946i	−0.513493	−	1.58037i
$579$		0			0
$580$	−8.57016	−	11.7958i	−0.355856	−	0.489794i
$581$	39.3415	+	12.7828i	1.63216	+	0.530321i
$582$		0			0
$583$	−3.88415	−	1.23612i	−0.160865	−	0.0511949i
$584$			47.7437i			1.97565i
$585$		0			0
$586$	36.3166	−	26.3855i	1.50022	−	1.08998i
$587$	13.9608	−	19.2153i	0.576222	−	0.793102i	−0.417053	−	0.908882i	$-0.636937\pi$
$587$	13.9608	−	19.2153i	0.576222	−	0.793102i	0.993275	+	0.115780i	$0.0369369\pi$
$588$		0			0
$589$	3.81602	−	1.23990i	0.157236	−	0.0510891i
$590$	2.48108	+	1.80261i	0.102145	+	0.0742123i
$591$		0			0
$592$	3.10334	−	9.55111i	0.127547	−	0.392548i
$593$	−37.1489			−1.52552			−0.762761	−	0.646680i	$-0.776157\pi$
$593$	−37.1489			−1.52552			−0.762761	+	0.646680i	$0.776157\pi$
$594$		0			0
$595$	0.694814			0.0284846
$596$	−22.2238	+	68.3979i	−0.910323	+	2.80169i
$597$		0			0
$598$	−28.5560	−	20.7471i	−1.16774	−	0.848414i
$599$	−2.26902	+	0.737248i	−0.0927095	+	0.0301231i	−0.355004	−	0.934865i	$-0.615521\pi$
$599$	−2.26902	+	0.737248i	−0.0927095	+	0.0301231i	0.262295	+	0.964988i	$0.415521\pi$
$600$		0			0
$601$	3.99333	−	5.49635i	0.162891	−	0.224201i	−0.719767	−	0.694216i	$-0.755751\pi$
$601$	3.99333	−	5.49635i	0.162891	−	0.224201i	0.882658	+	0.470015i	$0.155751\pi$
$602$	−32.9818	+	23.9627i	−1.34424	+	0.976646i
$603$		0			0
$604$		−	4.19334i		−	0.170624i
$605$	23.4250	−	7.92570i	0.952363	−	0.322225i
$606$		0			0
$607$	−38.5143	−	12.5141i	−1.56325	−	0.507930i	−0.605575	−	0.795788i	$-0.707057\pi$
$607$	−38.5143	−	12.5141i	−1.56325	−	0.507930i	−0.957673	+	0.287859i	$0.907057\pi$
$608$	−5.53025	−	7.61173i	−0.224281	−	0.308696i
$609$		0			0
$610$	6.17684	+	19.0104i	0.250093	+	0.769707i
$611$	−8.93688	−	27.5049i	−0.361547	−	1.11273i
$612$		0			0
$613$	0.119072	+	0.163888i	0.00480926	+	0.00661938i	0.811415	−	0.584471i	$-0.198698\pi$
$613$	0.119072	+	0.163888i	0.00480926	+	0.00661938i	−0.806606	+	0.591090i	$0.798698\pi$
$614$	4.16384	+	1.35291i	0.168039	+	0.0545991i
$615$		0			0
$616$	0.291489	+	48.2060i	0.0117444	+	1.94228i
$617$			8.08426i			0.325460i	0.986671	+	0.162730i	$0.0520299\pi$
$617$			8.08426i			0.325460i	−0.986671	+	0.162730i	$0.947970\pi$
$618$		0			0
$619$	−16.9785	+	12.3356i	−0.682424	+	0.495810i	−0.874161	−	0.485636i	$-0.838588\pi$
$619$	−16.9785	+	12.3356i	−0.682424	+	0.495810i	0.191737	+	0.981446i	$0.438588\pi$
$620$	−7.80381	+	10.7410i	−0.313409	+	0.431370i
$621$		0			0
$622$	20.0202	−	6.50496i	0.802737	−	0.260825i
$623$	−21.5974	−	15.6914i	−0.865282	−	0.628664i
$624$		0			0
$625$	−7.80814	+	24.0310i	−0.312326	+	0.961239i
$626$	40.2853			1.61012
$627$		0			0
$628$	−6.11131			−0.243868
$629$	−0.171320	+	0.527268i	−0.00683097	+	0.0210236i
$630$		0			0
$631$	19.6268	+	14.2597i	0.781332	+	0.567671i	0.905378	−	0.424606i	$-0.139587\pi$
$631$	19.6268	+	14.2597i	0.781332	+	0.567671i	−0.124047	+	0.992276i	$0.539587\pi$
$632$	−2.25165	+	0.731607i	−0.0895660	+	0.0291018i
$633$		0			0
$634$	−37.7280	+	51.9281i	−1.49837	+	2.06233i
$635$	−11.0245	+	8.00977i	−0.437494	+	0.317858i
$636$		0			0
$637$		−	43.7871i		−	1.73491i
$638$	−11.5500	+	8.49876i	−0.457270	+	0.336469i
$639$		0			0
$640$	43.5007	+	14.1342i	1.71952	+	0.558705i
$641$	9.48633	+	13.0568i	0.374688	+	0.515713i	0.954167	−	0.299273i	$-0.0967442\pi$
$641$	9.48633	+	13.0568i	0.374688	+	0.515713i	−0.579480	+	0.814987i	$0.696744\pi$
$642$		0			0
$643$	3.88866	+	11.9681i	0.153354	+	0.471975i	0.997990	−	0.0633656i	$-0.0201834\pi$
$643$	3.88866	+	11.9681i	0.153354	+	0.471975i	−0.844637	+	0.535340i	$0.820183\pi$
$644$	−14.2459	−	43.8443i	−0.561366	−	1.72771i
$645$		0			0
$646$	−0.252558	−	0.347617i	−0.00993678	−	0.0136768i
$647$	−28.7701	−	9.34797i	−1.13107	−	0.367507i	−0.317087	−	0.948396i	$-0.602705\pi$
$647$	−28.7701	−	9.34797i	−1.13107	−	0.367507i	−0.813982	+	0.580890i	$0.802705\pi$
$648$		0			0
$649$	1.12182	−	1.56385i	0.0440352	−	0.0613865i
$650$		−	0.591929i		−	0.0232174i
$651$		0			0
$652$	2.86023	−	2.07808i	0.112015	−	0.0813837i
$653$	11.5162	−	15.8507i	0.450664	−	0.620286i	−0.521876	−	0.853021i	$-0.674768\pi$
$653$	11.5162	−	15.8507i	0.450664	−	0.620286i	0.972540	+	0.232735i	$0.0747676\pi$
$654$		0			0
$655$	−15.2892	+	4.96777i	−0.597399	+	0.194107i
$656$	−9.43855	−	6.85751i	−0.368514	−	0.267741i
$657$		0			0
$658$	18.2924	−	56.2981i	0.713111	−	2.19473i
$659$	−1.34943			−0.0525664			−0.0262832	−	0.999655i	$-0.508367\pi$
$659$	−1.34943			−0.0525664			−0.0262832	+	0.999655i	$0.508367\pi$
$660$		0			0
$661$	28.7859			1.11964			0.559821	−	0.828614i	$-0.310870\pi$
$661$	28.7859			1.11964			0.559821	+	0.828614i	$0.310870\pi$
$662$	−4.26576	+	13.1287i	−0.165794	+	0.510260i
$663$		0			0
$664$	29.6398	+	21.5346i	1.15025	+	0.835703i
$665$	−20.7516	+	6.74260i	−0.804712	+	0.261467i
$666$		0			0
$667$	3.48879	−	4.80191i	0.135086	−	0.185931i
$668$	38.5646	−	28.0188i	1.49211	−	1.08408i
$669$		0			0
$670$		−	68.6954i		−	2.65394i
$671$	11.9066	−	3.94843i	0.459648	−	0.152428i
$672$		0			0
$673$	20.6864	+	6.72140i	0.797400	+	0.259091i	0.679252	−	0.733905i	$-0.262304\pi$
$673$	20.6864	+	6.72140i	0.797400	+	0.259091i	0.118148	+	0.992996i	$0.462304\pi$
$674$	22.8969	+	31.5149i	0.881955	+	1.21391i
$675$		0			0
$676$	−9.42270	−	29.0001i	−0.362411	−	1.11539i
$677$	5.84208	+	17.9801i	0.224529	+	0.691030i	0.998339	+	0.0576121i	$0.0183487\pi$
$677$	5.84208	+	17.9801i	0.224529	+	0.691030i	−0.773810	+	0.633418i	$0.781651\pi$
$678$		0			0
$679$	39.1574	+	53.8955i	1.50272	+	2.06832i
$680$	0.585258	+	0.190162i	0.0224436	+	0.00729237i
$681$		0			0
$682$	10.6100	+	7.61105i	0.406279	+	0.291442i
$683$		−	33.7466i		−	1.29128i	−0.763642	−	0.645640i	$-0.776591\pi$
$683$		−	33.7466i		−	1.29128i	0.763642	−	0.645640i	$-0.223409\pi$
$684$		0			0
$685$	19.3199	−	14.0367i	0.738176	−	0.536316i
$686$	13.4970	−	18.5771i	0.515319	−	0.709275i
$687$		0			0
$688$	−5.62645	+	1.82815i	−0.214507	+	0.0696974i
$689$	4.62602	+	3.36100i	0.176237	+	0.128044i
$690$		0			0
$691$	−8.50814	+	26.1854i	−0.323665	+	0.996138i	0.648375	+	0.761321i	$0.275449\pi$
$691$	−8.50814	+	26.1854i	−0.323665	+	0.996138i	−0.972040	+	0.234817i	$0.924551\pi$
$692$	26.5278			1.00844
$693$		0			0
$694$	5.91971			0.224709
$695$	−0.0368728	+	0.113483i	−0.00139867	+	0.00430465i
$696$		0			0
$697$	0.521055	+	0.378569i	0.0197364	+	0.0143393i
$698$	19.5168	−	6.34140i	0.738722	−	0.240025i
$699$		0			0
$700$	0.454418	−	0.625453i	0.0171754	−	0.0236399i
$701$	8.43699	−	6.12983i	0.318661	−	0.231521i	−0.416943	−	0.908933i	$-0.636899\pi$
$701$	8.43699	−	6.12983i	0.318661	−	0.231521i	0.735604	+	0.677412i	$0.236899\pi$
$702$		0			0
$703$		−	17.4101i		−	0.656636i
$704$	12.0654	−	37.9119i	0.454731	−	1.42886i
$705$		0			0
$706$	−1.19948	−	0.389734i	−0.0451429	−	0.0146678i
$707$	4.10011	+	5.64332i	0.154201	+	0.212239i
$708$		0			0
$709$	−6.19477	−	19.0655i	−0.232649	−	0.716021i	−0.997425	−	0.0717239i	$-0.977150\pi$
$709$	−6.19477	−	19.0655i	−0.232649	−	0.716021i	0.764775	−	0.644297i	$-0.222850\pi$
$710$	−1.82988	−	5.63178i	−0.0686740	−	0.211357i
$711$		0			0
$712$	−13.8975	−	19.1282i	−0.520829	−	0.716860i
$713$	−5.14021	−	1.67015i	−0.192502	−	0.0625478i
$714$		0			0
$715$	−34.6907	+	0.209765i	−1.29736	+	0.00784477i
$716$		−	44.0793i		−	1.64732i
$717$		0			0
$718$	−30.0600	+	21.8399i	−1.12183	+	0.815057i
$719$	6.01752	−	8.28241i	0.224416	−	0.308882i	−0.681931	−	0.731417i	$-0.738860\pi$
$719$	6.01752	−	8.28241i	0.224416	−	0.308882i	0.906347	+	0.422535i	$0.138860\pi$
$720$		0			0
$721$	−12.4479	+	4.04456i	−0.463583	+	0.150627i
$722$	−25.2185	−	18.3223i	−0.938537	−	0.681887i
$723$		0			0
$724$	−19.6152	+	60.3694i	−0.728993	+	2.24361i
$725$	0.0995374			0.00369673
$726$		0			0
$727$	−14.4456			−0.535759			−0.267880	−	0.963452i	$-0.586323\pi$
$727$	−14.4456			−0.535759			−0.267880	+	0.963452i	$0.586323\pi$
$728$	20.8976	−	64.3163i	0.774517	−	2.38372i
$729$		0			0
$730$	−56.8943	−	41.3361i	−2.10575	−	1.52992i
$731$	0.310608	−	0.100923i	0.0114883	−	0.00373276i
$732$		0			0
$733$	4.29622	−	5.91324i	0.158685	−	0.218411i	−0.722270	−	0.691611i	$-0.756901\pi$
$733$	4.29622	−	5.91324i	0.158685	−	0.218411i	0.880955	+	0.473200i	$0.156901\pi$
$734$	−55.0263	+	39.9789i	−2.03106	+	1.47565i
$735$		0			0
$736$			12.6735i			0.467151i
$737$	−43.1100	+	0.260675i	−1.58798	+	0.00960207i
$738$		0			0
$739$	−12.4909	−	4.05854i	−0.459485	−	0.149296i	0.0701229	−	0.997538i	$-0.477661\pi$
$739$	−12.4909	−	4.05854i	−0.459485	−	0.149296i	−0.529608	+	0.848243i	$0.677661\pi$
$740$	33.8614	+	46.6062i	1.24477	+	1.71328i
$741$		0			0
$742$	3.61673	+	11.1312i	0.132774	+	0.408638i
$743$	10.9307	+	33.6412i	0.401008	+	1.23418i	0.924183	+	0.381950i	$0.124747\pi$
$743$	10.9307	+	33.6412i	0.401008	+	1.23418i	−0.523175	+	0.852225i	$0.675253\pi$
$744$		0			0
$745$	−26.9503	−	37.0939i	−0.987383	−	1.35902i
$746$	−14.7768	−	4.80127i	−0.541017	−	0.175787i
$747$		0			0
$748$	0.270584	−	0.850230i	0.00989352	−	0.0310875i
$749$			60.0306i			2.19347i
$750$		0			0
$751$	18.6629	−	13.5594i	0.681018	−	0.494789i	−0.192677	−	0.981262i	$-0.561717\pi$
$751$	18.6629	−	13.5594i	0.681018	−	0.494789i	0.873695	+	0.486473i	$0.161717\pi$
$752$	5.04914	−	6.94955i	0.184123	−	0.253424i
$753$		0			0
$754$	19.1318	−	6.21631i	0.696741	−	0.226385i
$755$	2.16285	+	1.57140i	0.0787141	+	0.0571892i
$756$		0			0
$757$	3.02640	−	9.31430i	0.109996	−	0.338534i	−0.880874	−	0.473350i	$-0.843044\pi$
$757$	3.02640	−	9.31430i	0.109996	−	0.338534i	0.990871	+	0.134816i	$0.0430445\pi$
$758$	3.64030			0.132222
$759$		0			0
$760$	−19.3249			−0.700988
$761$	14.9642	−	46.0550i	0.542452	−	1.66949i	−0.184522	−	0.982828i	$-0.559074\pi$
$761$	14.9642	−	46.0550i	0.542452	−	1.66949i	0.726973	−	0.686666i	$-0.240926\pi$
$762$		0			0
$763$	−48.9176	−	35.5407i	−1.77094	−	1.28666i
$764$	72.6303	−	23.5990i	2.62767	−	0.853783i
$765$		0			0
$766$	−18.6646	+	25.6897i	−0.674381	+	0.928205i
$767$	−2.18426	+	1.58696i	−0.0788691	+	0.0573017i
$768$		0			0
$769$		−	33.4223i		−	1.20524i	−0.798029	−	0.602619i	$-0.794124\pi$
$769$		−	33.4223i		−	1.20524i	0.798029	−	0.602619i	$-0.205876\pi$
$770$	−57.6977	−	41.3891i	−2.07928	−	1.49156i
$771$		0			0
$772$	17.3952	+	5.65205i	0.626068	+	0.203422i
$773$	−3.82924	−	5.27050i	−0.137728	−	0.189567i	0.734581	−	0.678521i	$-0.237379\pi$
$773$	−3.82924	−	5.27050i	−0.137728	−	0.189567i	−0.872310	+	0.488954i	$0.837379\pi$
$774$		0			0
$775$	−0.0280083	−	0.0862007i	−0.00100609	−	0.00309642i
$776$	18.2326	+	56.1143i	0.654514	+	2.01439i
$777$		0			0
$778$	20.6981	+	28.4885i	0.742063	+	1.02136i
$779$	−19.2357	−	6.25007i	−0.689192	−	0.223932i
$780$		0			0
$781$	−3.52729	+	1.16971i	−0.126216	+	0.0418556i
$782$			0.578780i			0.0206971i
$783$		0			0
$784$	10.5220	−	7.64471i	0.375787	−	0.273025i
$785$	2.29014	−	3.15211i	0.0817386	−	0.112503i
$786$		0			0
$787$	27.5749	−	8.95962i	0.982939	−	0.319376i	0.226911	−	0.973916i	$-0.427137\pi$
$787$	27.5749	−	8.95962i	0.982939	−	0.319376i	0.756028	+	0.654539i	$0.227137\pi$
$788$	14.6828	+	10.6676i	0.523052	+	0.380019i
$789$		0			0
$790$	1.07764	−	3.31663i	0.0383407	−	0.118000i
$791$	−45.5606			−1.61995
$792$		0			0
$793$	−17.5974			−0.624901
$794$	−15.0468	+	46.3093i	−0.533991	+	1.64346i
$795$		0			0
$796$	−69.2075	−	50.2822i	−2.45299	−	1.78220i
$797$	25.7264	−	8.35900i	0.911274	−	0.296091i	0.184392	−	0.982853i	$-0.440968\pi$
$797$	25.7264	−	8.35900i	0.911274	−	0.296091i	0.726882	+	0.686762i	$0.240968\pi$
$798$		0			0
$799$	−0.278738	+	0.383650i	−0.00986103	+	0.0135725i
$800$	−0.171943	+	0.124924i	−0.00607910	+	0.00441672i
$801$		0			0
$802$			63.5768i			2.24498i
$803$	−25.7247	+	35.8610i	−0.907805	+	1.26551i
$804$		0			0
$805$	27.9526	+	9.08234i	0.985199	+	0.320110i
$806$	−10.7668	−	14.8193i	−0.379245	−	0.521986i
$807$		0			0
$808$	1.90911	+	5.87565i	0.0671624	+	0.206705i
$809$	12.9385	+	39.8205i	0.454892	+	1.40001i	0.871262	+	0.490818i	$0.163302\pi$
$809$	12.9385	+	39.8205i	0.454892	+	1.40001i	−0.416370	+	0.909195i	$0.636698\pi$
$810$		0			0
$811$	−7.51871	−	10.3486i	−0.264018	−	0.363389i	0.656341	−	0.754464i	$-0.272103\pi$
$811$	−7.51871	−	10.3486i	−0.264018	−	0.363389i	−0.920359	+	0.391075i	$0.872103\pi$
$812$	24.9876	+	8.11895i	0.876891	+	0.284919i
$813$		0			0
$814$	45.6351	−	33.5793i	1.59951	−	1.17695i
$815$			2.25399i			0.0789538i
$816$		0			0
$817$	−8.29738	+	6.02840i	−0.290289	+	0.210907i
$818$	−8.43637	+	11.6117i	−0.294971	+	0.405992i
$819$		0			0
$820$	63.6493	−	20.6809i	2.22273	−	0.722208i
$821$	9.59682	+	6.97250i	0.334931	+	0.243342i	0.742520	−	0.669824i	$-0.233630\pi$
$821$	9.59682	+	6.97250i	0.334931	+	0.243342i	−0.407589	+	0.913166i	$0.633630\pi$
$822$		0			0
$823$	8.11976	−	24.9900i	0.283037	−	0.871098i	−0.703943	−	0.710256i	$-0.748579\pi$
$823$	8.11976	−	24.9900i	0.283037	−	0.871098i	0.986980	−	0.160842i	$-0.0514210\pi$
$824$	−11.5921			−0.403829
$825$		0			0
$826$	−5.52626			−0.192283
$827$	7.99992	−	24.6212i	0.278184	−	0.856163i	−0.710175	−	0.704025i	$-0.751384\pi$
$827$	7.99992	−	24.6212i	0.278184	−	0.856163i	0.988359	−	0.152138i	$-0.0486159\pi$
$828$		0			0
$829$	−14.0195	−	10.1858i	−0.486918	−	0.353766i	0.317080	−	0.948399i	$-0.397298\pi$
$829$	−14.0195	−	10.1858i	−0.486918	−	0.353766i	−0.803998	+	0.594632i	$0.797298\pi$
$830$	−51.3238	+	16.6761i	−1.78148	+	0.578837i
$831$		0			0
$832$	−32.8057	+	45.1531i	−1.13733	+	1.56540i
$833$	−0.580869	+	0.422026i	−0.0201259	+	0.0146223i
$834$		0			0
$835$			30.3907i			1.05171i
$836$	0.169424	+	28.0191i	0.00585965	+	0.969061i
$837$		0			0
$838$	79.7307	+	25.9061i	2.75425	+	0.894911i
$839$	18.2513	+	25.1207i	0.630104	+	0.867264i	0.998039	−	0.0625873i	$-0.0199352\pi$
$839$	18.2513	+	25.1207i	0.630104	+	0.867264i	−0.367935	+	0.929851i	$0.619935\pi$
$840$		0			0
$841$	−7.91617	−	24.3635i	−0.272971	−	0.840120i
$842$	10.3936	+	31.9882i	0.358187	+	1.10239i
$843$		0			0
$844$	38.8495	+	53.4718i	1.33726	+	1.84058i
$845$	18.4888	+	6.00737i	0.636033	+	0.206660i
$846$		0			0
$847$	−25.7549	+	36.3654i	−0.884949	+	1.24953i
$848$			1.69842i			0.0583241i
$849$		0			0
$850$	−0.00785238	+	0.00570509i	−0.000269334	+	0.000195683i
$851$	−13.7845	+	18.9727i	−0.472527	+	0.650377i
$852$		0			0
$853$	0.303737	−	0.0986902i	0.0103998	−	0.00337909i	−0.303812	−	0.952732i	$-0.598260\pi$
$853$	0.303737	−	0.0986902i	0.0103998	−	0.00337909i	0.314212	+	0.949353i	$0.398260\pi$
$854$	−29.1400	−	21.1714i	−0.997150	−	0.724472i
$855$		0			0
$856$	−16.4296	+	50.5652i	−0.561553	+	1.72828i
$857$	13.2476			0.452528			0.226264	−	0.974066i	$-0.427349\pi$
$857$	13.2476			0.452528			0.226264	+	0.974066i	$0.427349\pi$
$858$		0			0
$859$	−8.58152			−0.292798			−0.146399	−	0.989226i	$-0.546768\pi$
$859$	−8.58152			−0.292798			−0.146399	+	0.989226i	$0.546768\pi$
$860$	10.4870	−	32.2756i	0.357603	−	1.10059i
$861$		0			0
$862$	16.5521	+	12.0258i	0.563766	+	0.409600i
$863$	51.0889	−	16.5998i	1.73909	−	0.565063i	0.744374	−	0.667763i	$-0.232748\pi$
$863$	51.0889	−	16.5998i	1.73909	−	0.565063i	0.994712	+	0.102700i	$0.0327482\pi$
$864$		0			0
$865$	−9.94098	+	13.6826i	−0.338004	+	0.465222i
$866$	71.4202	−	51.8898i	2.42696	−	1.76329i
$867$		0			0
$868$		−	23.9241i		−	0.812037i
$869$	−2.08545	−	0.663690i	−0.0707441	−	0.0225141i
$870$		0			0
$871$	57.5172	+	18.6885i	1.94889	+	0.633234i
$872$	−31.4774	−	43.3249i	−1.06596	−	1.46717i
$873$		0			0
$874$	−5.61659	−	17.2861i	−0.189984	−	0.584710i
$875$	−13.9193	−	42.8394i	−0.470560	−	1.44823i
$876$		0			0
$877$	−25.8716	−	35.6092i	−0.873623	−	1.20244i	−0.978147	−	0.207916i	$-0.933332\pi$
$877$	−25.8716	−	35.6092i	−0.873623	−	1.20244i	0.104524	−	0.994522i	$-0.466668\pi$
$878$	−72.5876	−	23.5851i	−2.44971	−	0.795959i
$879$		0			0
$880$	−6.10698	−	8.29954i	−0.205866	−	0.279777i
$881$		−	7.44194i		−	0.250725i	−0.992111	−	0.125363i	$-0.959991\pi$
$881$		−	7.44194i		−	0.250725i	0.992111	−	0.125363i	$-0.0400095\pi$
$882$		0			0
$883$	7.59369	−	5.51714i	0.255548	−	0.185667i	−0.452634	−	0.891696i	$-0.649516\pi$
$883$	7.59369	−	5.51714i	0.255548	−	0.185667i	0.708182	+	0.706030i	$0.249516\pi$
$884$	−0.735715	+	1.01262i	−0.0247448	+	0.0340582i
$885$		0			0
$886$	42.0799	−	13.6726i	1.41370	−	0.459340i
$887$	−19.5658	−	14.2154i	−0.656957	−	0.477307i	0.208677	−	0.977985i	$-0.433084\pi$
$887$	−19.5658	−	14.2154i	−0.656957	−	0.477307i	−0.865634	+	0.500678i	$0.833084\pi$
$888$		0			0
$889$	7.58806	−	23.3537i	0.254496	−	0.783257i
$890$	34.8267			1.16739
$891$		0			0
$892$	−19.3542			−0.648026
$893$	4.60189	−	14.1632i	0.153996	−	0.473952i
$894$		0			0
$895$	22.7353	+	16.5182i	0.759958	+	0.552142i
$896$	−78.3870	+	25.4695i	−2.61873	+	0.850875i
$897$		0			0
$898$	9.97892	−	13.7348i	0.333001	−	0.458336i
$899$	2.49197	−	1.81052i	0.0831119	−	0.0603843i
$900$		0			0
$901$		−	0.0937613i		−	0.00312364i
$902$	−20.7178	−	62.4750i	−0.689829	−	2.08019i
$903$		0			0
$904$	−38.3767	−	12.4693i	−1.27639	−	0.414724i
$905$	−23.7869	−	32.7399i	−0.790703	−	1.08831i
$906$		0			0
$907$	−11.0734	−	34.0803i	−0.367685	−	1.13162i	−0.948282	−	0.317428i	$-0.897181\pi$
$907$	−11.0734	−	34.0803i	−0.367685	−	1.13162i	0.580597	−	0.814191i	$-0.302819\pi$
$908$	14.9980	+	46.1592i	0.497728	+	1.53185i
$909$		0			0
$910$	58.5502	+	80.5875i	1.94092	+	2.67145i
$911$	8.33061	+	2.70678i	0.276005	+	0.0896796i	0.443749	−	0.896151i	$-0.353648\pi$
$911$	8.33061	+	2.70678i	0.276005	+	0.0896796i	−0.167744	+	0.985831i	$0.553648\pi$
$912$		0			0
$913$	10.6599	+	32.1451i	0.352791	+	1.06385i
$914$		−	9.92552i		−	0.328307i
$915$		0			0
$916$	60.2872	−	43.8012i	1.99195	−	1.44723i
$917$	17.0273	−	23.4360i	0.562290	−	0.773926i
$918$		0			0
$919$	−39.4876	+	12.8303i	−1.30258	+	0.423233i	−0.876477	−	0.481443i	$-0.840113\pi$
$919$	−39.4876	+	12.8303i	−1.30258	+	0.423233i	−0.426100	+	0.904676i	$0.640113\pi$
$920$	21.0594	+	15.3005i	0.694307	+	0.504444i
$921$		0			0
$922$	−10.3097	+	31.7301i	−0.339533	+	1.04498i
$923$	5.21318			0.171594
$924$		0			0
$925$	−0.393281			−0.0129310
$926$	−29.3323	+	90.2756i	−0.963920	+	2.96664i
$927$		0			0
$928$	−5.84339	−	4.24547i	−0.191819	−	0.139364i
$929$	51.5363	−	16.7451i	1.69085	−	0.549390i	0.703883	−	0.710316i	$-0.251448\pi$
$929$	51.5363	−	16.7451i	1.69085	−	0.549390i	0.986967	+	0.160925i	$0.0514478\pi$
$930$		0			0
$931$	13.2531	−	18.2413i	0.434351	−	0.597833i
$932$	42.6935	−	31.0186i	1.39847	−	1.01605i
$933$		0			0
$934$		−	26.5656i		−	0.869253i
$935$	0.337136	+	0.458176i	0.0110255	+	0.0149839i
$936$		0			0
$937$	−16.5444	−	5.37559i	−0.540480	−	0.175613i	0.0260393	−	0.999661i	$-0.491710\pi$
$937$	−16.5444	−	5.37559i	−0.540480	−	0.175613i	−0.566520	+	0.824048i	$0.691710\pi$
$938$	72.7602	+	100.146i	2.37571	+	3.26988i
$939$		0			0
$940$	15.2272	+	46.8646i	0.496657	+	1.52855i
$941$	−6.64708	−	20.4576i	−0.216689	−	0.666899i	−0.999029	−	0.0440486i	$-0.985974\pi$
$941$	−6.64708	−	20.4576i	−0.216689	−	0.666899i	0.782341	−	0.622851i	$-0.214026\pi$
$942$		0			0
$943$	16.0137	+	22.0410i	0.521478	+	0.717753i
$944$	−0.762692	−	0.247814i	−0.0248235	−	0.00806564i
$945$		0			0
$946$	−31.8049	−	10.1218i	−1.03407	−	0.329089i
$947$			44.7887i			1.45544i	0.685875	+	0.727719i	$0.259420\pi$
$947$			44.7887i			1.45544i	−0.685875	+	0.727719i	$0.740580\pi$
$948$		0			0
$949$	50.0878	−	36.3909i	1.62592	−	1.18130i
$950$	0.179159	−	0.246592i	0.00581269	−	0.00800049i
$951$		0			0
$952$	−1.05462	+	0.342666i	−0.0341803	+	0.0111059i
$953$	8.11741	+	5.89765i	0.262949	+	0.191043i	0.711446	−	0.702741i	$-0.248041\pi$
$953$	8.11741	+	5.89765i	0.262949	+	0.191043i	−0.448497	+	0.893784i	$0.648041\pi$
$954$		0			0
$955$	−15.0454	+	46.3049i	−0.486857	+	1.49839i
$956$	−19.0594			−0.616425
$957$		0			0
$958$	−53.8294			−1.73915
$959$	−13.2977	+	40.9262i	−0.429406	+	1.32158i
$960$		0			0
$961$	22.8104	+	16.5727i	0.735819	+	0.534604i
$962$	−75.5916	+	24.5612i	−2.43717	+	0.791884i
$963$		0			0
$964$	24.2693	−	33.4039i	0.781662	−	1.07587i
$965$	−9.43388	+	6.85412i	−0.303688	+	0.220642i
$966$		0			0
$967$		−	4.32167i		−	0.138976i	−0.997583	−	0.0694878i	$-0.977863\pi$
$967$		−	4.32167i		−	0.138976i	0.997583	−	0.0694878i	$-0.0221365\pi$
$968$	−31.6467	+	23.5826i	−1.01716	+	0.757974i
$969$		0			0
$970$	−82.6550	−	26.8562i	−2.65389	−	0.862302i
$971$	−33.7344	−	46.4314i	−1.08259	−	1.49005i	−0.856640	−	0.515914i	$-0.827452\pi$
$971$	−33.7344	−	46.4314i	−1.08259	−	1.49005i	−0.225947	−	0.974140i	$-0.572548\pi$
$972$		0			0
$973$	−0.0664437	−	0.204493i	−0.00213009	−	0.00655574i
$974$	−5.47886	−	16.8622i	−0.175554	−	0.540300i
$975$		0			0
$976$	−3.07229	−	4.22864i	−0.0983416	−	0.135356i
$977$	−3.28130	−	1.06616i	−0.104978	−	0.0341095i	0.256057	−	0.966662i	$-0.417577\pi$
$977$	−3.28130	−	1.06616i	−0.104978	−	0.0341095i	−0.361035	+	0.932552i	$0.617577\pi$
$978$		0			0
$979$	−0.132155	−	21.8556i	−0.00422369	−	0.698508i
$980$			74.6073i			2.38324i
$981$		0			0
$982$	−72.6315	+	52.7699i	−2.31776	+	1.68395i
$983$	−0.608167	+	0.837070i	−0.0193975	+	0.0266984i	−0.818606	−	0.574356i	$-0.805253\pi$
$983$	−0.608167	+	0.837070i	−0.0193975	+	0.0266984i	0.799208	+	0.601054i	$0.205253\pi$
$984$		0			0
$985$	−11.0044	+	3.57554i	−0.350628	+	0.113926i
$986$	−0.266859	−	0.193884i	−0.00849853	−	0.00617454i
$987$		0			0
$988$	12.1465	−	37.3830i	0.386431	−	1.18931i
$989$	13.8151			0.439294
$990$		0			0
$991$	9.78910			0.310961			0.155481	−	0.987839i	$-0.450307\pi$
$991$	9.78910			0.310961			0.155481	+	0.987839i	$0.450307\pi$
$992$	−2.03239	+	6.25506i	−0.0645285	+	0.198598i
$993$		0			0
$994$	8.63265	+	6.27199i	0.273811	+	0.198935i
$995$	51.8693	−	16.8534i	1.64437	−	0.534288i
$996$		0			0
$997$	−6.82690	+	9.39642i	−0.216210	+	0.297588i	−0.903321	−	0.428965i	$-0.858878\pi$
$997$	−6.82690	+	9.39642i	−0.216210	+	0.297588i	0.687111	+	0.726552i	$0.258878\pi$
$998$	15.3271	−	11.1358i	0.485170	−	0.352496i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.j.a.35.4	yes	16
3.2	odd	2	inner	99.2.j.a.35.1	yes	16
4.3	odd	2		1584.2.cd.c.1025.4		16
9.2	odd	6		891.2.u.c.134.4		32
9.4	even	3		891.2.u.c.431.4		32
9.5	odd	6		891.2.u.c.431.1		32
9.7	even	3		891.2.u.c.134.1		32
11.4	even	5		1089.2.d.g.1088.13		16
11.6	odd	10	inner	99.2.j.a.17.1	✓	16
11.7	odd	10		1089.2.d.g.1088.3		16
12.11	even	2		1584.2.cd.c.1025.1		16
33.17	even	10	inner	99.2.j.a.17.4	yes	16
33.26	odd	10		1089.2.d.g.1088.4		16
33.29	even	10		1089.2.d.g.1088.14		16
44.39	even	10		1584.2.cd.c.17.1		16
99.50	even	30		891.2.u.c.512.1		32
99.61	odd	30		891.2.u.c.215.1		32
99.83	even	30		891.2.u.c.215.4		32
99.94	odd	30		891.2.u.c.512.4		32
132.83	odd	10		1584.2.cd.c.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.1	✓	16	11.6	odd	10	inner
99.2.j.a.17.4	yes	16	33.17	even	10	inner
99.2.j.a.35.1	yes	16	3.2	odd	2	inner
99.2.j.a.35.4	yes	16	1.1	even	1	trivial
891.2.u.c.134.1		32	9.7	even	3
891.2.u.c.134.4		32	9.2	odd	6
891.2.u.c.215.1		32	99.61	odd	30
891.2.u.c.215.4		32	99.83	even	30
891.2.u.c.431.1		32	9.5	odd	6
891.2.u.c.431.4		32	9.4	even	3
891.2.u.c.512.1		32	99.50	even	30
891.2.u.c.512.4		32	99.94	odd	30
1089.2.d.g.1088.3		16	11.7	odd	10
1089.2.d.g.1088.4		16	33.26	odd	10
1089.2.d.g.1088.13		16	11.4	even	5
1089.2.d.g.1088.14		16	33.29	even	10
1584.2.cd.c.17.1		16	44.39	even	10
1584.2.cd.c.17.4		16	132.83	odd	10
1584.2.cd.c.1025.1		16	12.11	even	2
1584.2.cd.c.1025.4		16	4.3	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	99.2.j.a.35.4

Level	$99$
Weight	$2$
Character	99.35
Analytic conductor	$0.791$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$