LMFDB - Embedded newform 891.2.n.f.433.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			433.2
Character	$\chi$	$=$	891.433
Dual form			891.2.n.f.784.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0378659 + 0.360270i) q^{2} +(1.82793 + 0.388540i) q^{4} +(0.280735 + 2.67101i) q^{5} +(-1.66890 + 1.85350i) q^{7} +(-0.433081 + 1.33288i) q^{8} -0.972914 q^{10} +(3.26867 - 0.561950i) q^{11} +(3.48756 - 1.55276i) q^{13} +(-0.604567 - 0.671439i) q^{14} +(2.95062 + 1.31370i) q^{16} +(-0.909782 + 0.660995i) q^{17} +(2.09612 - 6.45120i) q^{19} +(-0.524629 + 4.99151i) q^{20} +(0.0786824 + 1.19888i) q^{22} +(-3.37470 + 5.84515i) q^{23} +(-2.16475 + 0.460133i) q^{25} +(0.427353 + 1.31526i) q^{26} +(-3.77080 + 2.73965i) q^{28} +(-4.96799 + 5.51751i) q^{29} +(-6.12482 + 2.72695i) q^{31} +(-1.98649 + 3.44070i) q^{32} +(-0.203687 - 0.352796i) q^{34} +(-5.41925 - 3.93732i) q^{35} +(-0.0589927 - 0.181561i) q^{37} +(2.24480 + 0.999449i) q^{38} +(-3.68173 - 0.782576i) q^{40} +(0.425779 + 0.472875i) q^{41} +(-2.36375 - 4.09413i) q^{43} +(6.19326 + 0.242800i) q^{44} +(-1.97805 - 1.43713i) q^{46} +(11.0461 - 2.34792i) q^{47} +(0.0814578 + 0.775019i) q^{49} +(-0.0838015 - 0.797318i) q^{50} +(6.97834 - 1.48329i) q^{52} +(-4.45732 - 3.23843i) q^{53} +(2.41860 + 8.57290i) q^{55} +(-1.74774 - 3.02717i) q^{56} +(-1.79967 - 1.99874i) q^{58} +(-8.24507 - 1.75254i) q^{59} +(1.57297 + 0.700331i) q^{61} +(-0.750514 - 2.30984i) q^{62} +(4.06165 + 2.95096i) q^{64} +(5.12652 + 8.87939i) q^{65} +(-2.25335 + 3.90292i) q^{67} +(-1.91984 + 0.854770i) q^{68} +(1.62370 - 1.80330i) q^{70} +(9.95124 - 7.23000i) q^{71} +(-0.658284 - 2.02599i) q^{73} +(0.0676446 - 0.0143783i) q^{74} +(6.33812 - 10.9779i) q^{76} +(-4.41352 + 6.99633i) q^{77} +(1.21066 - 11.5186i) q^{79} +(-2.68057 + 8.24994i) q^{80} +(-0.186485 + 0.135489i) q^{82} +(-0.747666 - 0.332882i) q^{83} +(-2.02093 - 2.24447i) q^{85} +(1.56449 - 0.696558i) q^{86} +(-0.666583 + 4.60013i) q^{88} -1.42041 q^{89} +(-2.94234 + 9.05560i) q^{91} +(-8.43981 + 9.37336i) q^{92} +(0.427615 + 4.06848i) q^{94} +(17.8197 + 3.78769i) q^{95} +(-1.05273 + 10.0160i) q^{97} -0.282300 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 4 q^{4} - q^{5} + 2 q^{7} + 12 q^{10} - 13 q^{11} + 2 q^{13} + 22 q^{14} + 24 q^{16} - 4 q^{17} - 4 q^{19} - 15 q^{22} - 14 q^{23} + 19 q^{25} + 42 q^{26} + 30 q^{28} - q^{29} - 14 q^{31}+ \cdots + 52 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 + 4 * q^4 - q^5 + 2 * q^7 + 12 * q^10 - 13 * q^11 + 2 * q^13 + 22 * q^14 + 24 * q^16 - 4 * q^17 - 4 * q^19 - 15 * q^22 - 14 * q^23 + 19 * q^25 + 42 * q^26 + 30 * q^28 - q^29 - 14 * q^31 + 48 * q^32 - 10 * q^34 - 36 * q^35 + 18 * q^37 - 11 * q^38 - 33 * q^40 - 25 * q^41 - 14 * q^43 + 28 * q^44 + 8 * q^46 + 28 * q^47 + 4 * q^49 + 63 * q^50 - 10 * q^52 + 2 * q^53 - 80 * q^55 - 96 * q^56 + 20 * q^58 - 41 * q^59 - 10 * q^62 - 184 * q^64 + 60 * q^65 + 48 * q^67 - 25 * q^68 + 31 * q^70 + 6 * q^71 - 26 * q^73 - 29 * q^74 + 58 * q^76 + 2 * q^77 - 166 * q^80 + 82 * q^82 + 14 * q^83 + 10 * q^85 + 56 * q^86 - 86 * q^88 + 164 * q^89 + 28 * q^91 - 74 * q^92 + 2 * q^94 + 56 * q^95 - 12 * q^97 + 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0378659	+	0.360270i	−0.0267752	+	0.254749i	0.972944	+	0.231042i	$0.0742135\pi$
$2$	−0.0378659	+	0.360270i	−0.0267752	+	0.254749i	−0.999719	+	0.0237069i	$0.992453\pi$
$3$		0			0
$3$		0			0
$4$	1.82793	+	0.388540i	0.913967	+	0.194270i
$5$	0.280735	+	2.67101i	0.125548	+	1.19451i	0.857984	+	0.513676i	$0.171717\pi$
$5$	0.280735	+	2.67101i	0.125548	+	1.19451i	−0.732436	+	0.680836i	$0.761616\pi$
$6$		0			0
$7$	−1.66890	+	1.85350i	−0.630786	+	0.700559i	−0.970808	−	0.239859i	$-0.922899\pi$
$7$	−1.66890	+	1.85350i	−0.630786	+	0.700559i	0.340022	+	0.940417i	$0.389565\pi$
$8$	−0.433081	+	1.33288i	−0.153117	+	0.471246i
$9$		0			0
$10$	−0.972914			−0.307663
$11$	3.26867	−	0.561950i	0.985541	−	0.169434i
$11$	3.26867	−	0.561950i	0.985541	−	0.169434i
$12$		0			0
$13$	3.48756	−	1.55276i	0.967274	−	0.430658i	0.138575	−	0.990352i	$-0.455748\pi$
$13$	3.48756	−	1.55276i	0.967274	−	0.430658i	0.828700	+	0.559694i	$0.189081\pi$
$14$	−0.604567	−	0.671439i	−0.161577	−	0.179450i
$15$		0			0
$16$	2.95062	+	1.31370i	0.737654	+	0.328425i
$17$	−0.909782	+	0.660995i	−0.220654	+	0.160315i	−0.692621	−	0.721301i	$-0.743544\pi$
$17$	−0.909782	+	0.660995i	−0.220654	+	0.160315i	0.471967	+	0.881616i	$0.343544\pi$
$18$		0			0
$19$	2.09612	−	6.45120i	0.480883	−	1.48001i	−0.356973	−	0.934115i	$-0.616191\pi$
$19$	2.09612	−	6.45120i	0.480883	−	1.48001i	0.837856	−	0.545891i	$-0.183809\pi$
$20$	−0.524629	+	4.99151i	−0.117311	+	1.11614i
$21$		0			0
$22$	0.0786824	+	1.19888i	0.0167751	+	0.255602i
$23$	−3.37470	+	5.84515i	−0.703674	+	1.21880i	0.263494	+	0.964661i	$0.415125\pi$
$23$	−3.37470	+	5.84515i	−0.703674	+	1.21880i	−0.967168	+	0.254138i	$0.918208\pi$
$24$		0			0
$25$	−2.16475	+	0.460133i	−0.432951	+	0.0920266i
$26$	0.427353	+	1.31526i	0.0838108	+	0.257943i
$27$		0			0
$28$	−3.77080	+	2.73965i	−0.712615	+	0.517745i
$29$	−4.96799	+	5.51751i	−0.922532	+	1.02458i	0.0770882	+	0.997024i	$0.475438\pi$
$29$	−4.96799	+	5.51751i	−0.922532	+	1.02458i	−0.999620	+	0.0275515i	$0.991229\pi$
$30$		0			0
$31$	−6.12482	+	2.72695i	−1.10005	+	0.489774i	−0.874779	−	0.484522i	$-0.838994\pi$
$31$	−6.12482	+	2.72695i	−1.10005	+	0.489774i	−0.225271	+	0.974296i	$0.572327\pi$
$32$	−1.98649	+	3.44070i	−0.351165	+	0.608236i
$33$		0			0
$34$	−0.203687	−	0.352796i	−0.0349320	−	0.0605040i
$35$	−5.41925	−	3.93732i	−0.916020	−	0.665528i
$36$		0			0
$37$	−0.0589927	−	0.181561i	−0.00969834	−	0.0298484i	0.946090	−	0.323903i	$-0.104995\pi$
$37$	−0.0589927	−	0.181561i	−0.00969834	−	0.0298484i	−0.955789	+	0.294055i	$0.904995\pi$
$38$	2.24480	+	0.999449i	0.364154	+	0.162132i
$39$		0			0
$40$	−3.68173	−	0.782576i	−0.582133	−	0.123736i
$41$	0.425779	+	0.472875i	0.0664954	+	0.0738507i	0.775475	−	0.631379i	$-0.217511\pi$
$41$	0.425779	+	0.472875i	0.0664954	+	0.0738507i	−0.708979	+	0.705229i	$0.750844\pi$
$42$		0			0
$43$	−2.36375	−	4.09413i	−0.360468	−	0.624349i	0.627570	−	0.778560i	$-0.284050\pi$
$43$	−2.36375	−	4.09413i	−0.360468	−	0.624349i	−0.988038	+	0.154212i	$0.950716\pi$
$44$	6.19326	+	0.242800i	0.933669	+	0.0366035i
$45$		0			0
$46$	−1.97805	−	1.43713i	−0.291647	−	0.211894i
$47$	11.0461	−	2.34792i	1.61124	−	0.342480i	0.687704	−	0.725991i	$-0.258619\pi$
$47$	11.0461	−	2.34792i	1.61124	−	0.342480i	0.923536	+	0.383512i	$0.125285\pi$
$48$		0			0
$49$	0.0814578	+	0.775019i	0.0116368	+	0.110717i
$50$	−0.0838015	−	0.797318i	−0.0118513	−	0.112758i
$51$		0			0
$52$	6.97834	−	1.48329i	0.967721	−	0.205695i
$53$	−4.45732	−	3.23843i	−0.612259	−	0.444833i	0.237950	−	0.971277i	$-0.423525\pi$
$53$	−4.45732	−	3.23843i	−0.612259	−	0.444833i	−0.850209	+	0.526445i	$0.823525\pi$
$54$		0			0
$55$	2.41860	+	8.57290i	0.326125	+	1.15597i
$56$	−1.74774	−	3.02717i	−0.233551	−	0.404523i
$57$		0			0
$58$	−1.79967	−	1.99874i	−0.236309	−	0.262447i
$59$	−8.24507	−	1.75254i	−1.07342	−	0.228162i	−0.362890	−	0.931832i	$-0.618210\pi$
$59$	−8.24507	−	1.75254i	−1.07342	−	0.228162i	−0.710527	+	0.703670i	$0.751543\pi$
$60$		0			0
$61$	1.57297	+	0.700331i	0.201398	+	0.0896682i	0.504957	−	0.863144i	$-0.331508\pi$
$61$	1.57297	+	0.700331i	0.201398	+	0.0896682i	−0.303559	+	0.952813i	$0.598175\pi$
$62$	−0.750514	−	2.30984i	−0.0953154	−	0.293351i
$63$		0			0
$64$	4.06165	+	2.95096i	0.507706	+	0.368870i
$65$	5.12652	+	8.87939i	0.635866	+	1.10135i
$66$		0			0
$67$	−2.25335	+	3.90292i	−0.275291	+	0.476817i	−0.970208	−	0.242272i	$-0.922107\pi$
$67$	−2.25335	+	3.90292i	−0.275291	+	0.476817i	0.694918	+	0.719089i	$0.255441\pi$
$68$	−1.91984	+	0.854770i	−0.232815	+	0.103656i
$69$		0			0
$70$	1.62370	−	1.80330i	0.194069	−	0.215536i
$71$	9.95124	−	7.23000i	1.18099	−	0.858043i	0.188711	−	0.982033i	$-0.439569\pi$
$71$	9.95124	−	7.23000i	1.18099	−	0.858043i	0.992284	+	0.123990i	$0.0395689\pi$
$72$		0			0
$73$	−0.658284	−	2.02599i	−0.0770463	−	0.237124i	0.905114	−	0.425168i	$-0.139785\pi$
$73$	−0.658284	−	2.02599i	−0.0770463	−	0.237124i	−0.982161	+	0.188044i	$0.939785\pi$
$74$	0.0676446	−	0.0143783i	0.00786353	−	0.00167144i
$75$		0			0
$76$	6.33812	−	10.9779i	0.727032	−	1.25926i
$77$	−4.41352	+	6.99633i	−0.502967	+	0.797306i
$78$		0			0
$79$	1.21066	−	11.5186i	0.136210	−	1.29595i	−0.686351	−	0.727270i	$-0.740789\pi$
$79$	1.21066	−	11.5186i	0.136210	−	1.29595i	0.822561	−	0.568677i	$-0.192545\pi$
$80$	−2.68057	+	8.24994i	−0.299696	+	0.922371i
$81$		0			0
$82$	−0.186485	+	0.135489i	−0.0205938	+	0.0149623i
$83$	−0.747666	−	0.332882i	−0.0820670	−	0.0365386i	0.365293	−	0.930893i	$-0.380969\pi$
$83$	−0.747666	−	0.332882i	−0.0820670	−	0.0365386i	−0.447360	+	0.894354i	$0.647636\pi$
$84$		0			0
$85$	−2.02093	−	2.24447i	−0.219201	−	0.243447i
$86$	1.56449	−	0.696558i	0.168704	−	0.0751118i
$87$		0			0
$88$	−0.666583	+	4.60013i	−0.0710580	+	0.490376i
$89$	−1.42041			−0.150564			−0.0752818	−	0.997162i	$-0.523986\pi$
$89$	−1.42041			−0.150564			−0.0752818	+	0.997162i	$0.523986\pi$
$90$		0			0
$91$	−2.94234	+	9.05560i	−0.308441	+	0.949285i
$92$	−8.43981	+	9.37336i	−0.879911	+	0.977240i
$93$		0			0
$94$	0.427615	+	4.06848i	0.0441051	+	0.419632i
$95$	17.8197	+	3.78769i	1.82826	+	0.388609i
$96$		0			0
$97$	−1.05273	+	10.0160i	−0.106888	+	1.01697i	0.801257	+	0.598320i	$0.204165\pi$
$97$	−1.05273	+	10.0160i	−0.106888	+	1.01697i	−0.908146	+	0.418654i	$0.862502\pi$
$98$	−0.282300			−0.0285166
$99$		0			0
$100$	−4.13581			−0.413581
$101$	2.00110	−	19.0392i	0.199117	−	1.89447i	−0.203464	−	0.979082i	$-0.565220\pi$
$101$	2.00110	−	19.0392i	0.199117	−	1.89447i	0.402580	−	0.915385i	$-0.368113\pi$
$102$		0			0
$103$	3.03862	+	0.645879i	0.299404	+	0.0636404i	0.355164	−	0.934804i	$-0.384425\pi$
$103$	3.03862	+	0.645879i	0.299404	+	0.0636404i	−0.0557601	+	0.998444i	$0.517758\pi$
$104$	0.559258	+	5.32098i	0.0548397	+	0.521765i
$105$		0			0
$106$	1.33549	−	1.48321i	0.129714	−	0.144062i
$107$	−3.05389	+	9.39890i	−0.295231	+	0.908626i	0.687913	+	0.725793i	$0.258527\pi$
$107$	−3.05389	+	9.39890i	−0.295231	+	0.908626i	−0.983144	+	0.182833i	$0.941473\pi$
$108$		0			0
$109$	18.0851			1.73224			0.866121	−	0.499834i	$-0.166606\pi$
$109$	18.0851			1.73224			0.866121	+	0.499834i	$0.166606\pi$
$110$	−3.18014	+	0.546729i	−0.303214	+	0.0521286i
$111$		0			0
$112$	−7.35924	+	3.27654i	−0.695383	+	0.309604i
$113$	−3.39913	−	3.77511i	−0.319763	−	0.355133i	0.561738	−	0.827315i	$-0.310133\pi$
$113$	−3.39913	−	3.77511i	−0.319763	−	0.355133i	−0.881501	+	0.472183i	$0.843466\pi$
$114$		0			0
$115$	−16.5599	−	7.37293i	−1.54422	−	0.687529i
$116$	−11.2249	+	8.15539i	−1.04221	+	0.757209i
$117$		0			0
$118$	0.943595	−	2.90409i	0.0868650	−	0.267343i
$119$	0.293180	−	2.78942i	0.0268758	−	0.255706i
$120$		0			0
$121$	10.3684	−	3.67366i	0.942584	−	0.333969i
$122$	−0.311870	+	0.540174i	−0.0282354	+	0.0489051i
$123$		0			0
$124$	−12.2553	+	2.60494i	−1.10056	+	0.233931i
$125$	2.31293	+	7.11847i	0.206875	+	0.636695i
$126$		0			0
$127$	−0.674959	+	0.490387i	−0.0598930	+	0.0435148i	−0.617329	−	0.786705i	$-0.711785\pi$
$127$	−0.674959	+	0.490387i	−0.0598930	+	0.0435148i	0.557436	+	0.830220i	$0.311785\pi$
$128$	−6.53383	+	7.25655i	−0.577514	+	0.641395i
$129$		0			0
$130$	−3.39309	+	1.51070i	−0.297594	+	0.132497i
$131$	9.87633	−	17.1063i	0.862899	−	1.49459i	−0.00621860	−	0.999981i	$-0.501979\pi$
$131$	9.87633	−	17.1063i	0.862899	−	1.49459i	0.869118	−	0.494605i	$-0.164687\pi$
$132$		0			0
$133$	8.45910	+	14.6516i	0.733497	+	1.27045i
$134$	−1.32078	−	0.959601i	−0.114098	−	0.0828969i
$135$		0			0
$136$	−0.487022	−	1.49890i	−0.0417618	−	0.128529i
$137$	−3.62037	−	1.61189i	−0.309309	−	0.137713i	0.246211	−	0.969216i	$-0.420814\pi$
$137$	−3.62037	−	1.61189i	−0.309309	−	0.137713i	−0.555520	+	0.831503i	$0.687481\pi$
$138$		0			0
$139$	3.33035	+	0.707887i	0.282476	+	0.0600422i	0.346971	−	0.937876i	$-0.387210\pi$
$139$	3.33035	+	0.707887i	0.282476	+	0.0600422i	−0.0644947	+	0.997918i	$0.520544\pi$
$140$	−8.37623	−	9.30275i	−0.707921	−	0.786226i
$141$		0			0
$142$	2.22794	+	3.85890i	0.186964	+	0.323832i
$143$	10.5271	−	7.03530i	0.880321	−	0.588321i
$144$		0			0
$145$	−16.1320	−	11.7206i	−1.33969	−	0.973343i
$146$	0.754828	−	0.160444i	0.0624700	−	0.0132784i
$147$		0			0
$148$	−0.0372912	−	0.354802i	−0.00306532	−	0.0291646i
$149$	−0.538739	−	5.12576i	−0.0441352	−	0.419918i	−0.994174	−	0.107787i	$-0.965624\pi$
$149$	−0.538739	−	5.12576i	−0.0441352	−	0.419918i	0.950039	−	0.312132i	$-0.101043\pi$
$150$		0			0
$151$	13.4449	−	2.85780i	1.09413	−	0.232564i	0.374710	−	0.927142i	$-0.377742\pi$
$151$	13.4449	−	2.85780i	1.09413	−	0.232564i	0.719418	+	0.694578i	$0.244409\pi$
$152$	7.69091	+	5.58778i	0.623816	+	0.453229i
$153$		0			0
$154$	−2.35344	−	1.85498i	−0.189646	−	0.149478i
$155$	−9.00316	−	15.5939i	−0.723151	−	1.25253i
$156$		0			0
$157$	11.1305	+	12.3617i	0.888311	+	0.986569i	0.999974	−	0.00717663i	$-0.00228441\pi$
$157$	11.1305	+	12.3617i	0.888311	+	0.986569i	−0.111663	+	0.993746i	$0.535618\pi$
$158$	4.10397	+	0.872326i	0.326494	+	0.0693985i
$159$		0			0
$160$	−9.74784	−	4.34002i	−0.770634	−	0.343109i
$161$	−5.20197	−	16.0100i	−0.409973	−	1.26177i
$162$		0			0
$163$	−18.4445	−	13.4007i	−1.44469	−	1.04963i	−0.987037	−	0.160492i	$-0.948692\pi$
$163$	−18.4445	−	13.4007i	−1.44469	−	1.04963i	−0.457648	−	0.889134i	$-0.651308\pi$
$164$	0.594565	+	1.02982i	0.0464277	+	0.0804152i
$165$		0			0
$166$	0.148238	−	0.256756i	0.0115055	−	0.0199282i
$167$	11.5103	−	5.12470i	0.890691	−	0.396561i	0.0902121	−	0.995923i	$-0.471245\pi$
$167$	11.5103	−	5.12470i	0.890691	−	0.396561i	0.800478	+	0.599362i	$0.204579\pi$
$168$		0			0
$169$	1.05329	−	1.16980i	0.0810222	−	0.0899843i
$170$	0.885140	−	0.643092i	0.0678871	−	0.0493229i
$171$		0			0
$172$	−2.73004	−	8.40221i	−0.208164	−	0.640662i
$173$	7.02306	−	1.49280i	0.533954	−	0.113495i	0.0669594	−	0.997756i	$-0.478670\pi$
$173$	7.02306	−	1.49280i	0.533954	−	0.113495i	0.466994	+	0.884260i	$0.345337\pi$
$174$		0			0
$175$	2.75991	−	4.78030i	0.208629	−	0.361357i
$176$	10.3828	+	2.63595i	0.782635	+	0.198692i
$177$		0			0
$178$	0.0537852	−	0.511732i	0.00403137	−	0.0383559i
$179$	2.78001	−	8.55598i	0.207788	−	0.639504i	−0.791800	−	0.610781i	$-0.790856\pi$
$179$	2.78001	−	8.55598i	0.207788	−	0.639504i	0.999587	−	0.0287236i	$-0.00914427\pi$
$180$		0			0
$181$	−1.51882	+	1.10349i	−0.112893	+	0.0820215i	−0.642799	−	0.766035i	$-0.722227\pi$
$181$	−1.51882	+	1.10349i	−0.112893	+	0.0820215i	0.529906	+	0.848056i	$0.322227\pi$
$182$	−3.15104	−	1.40294i	−0.233571	−	0.103992i
$183$		0			0
$184$	−6.32940	−	7.02951i	−0.466610	−	0.518222i
$185$	0.468390	−	0.208541i	0.0344367	−	0.0153322i
$186$		0			0
$187$	−2.60233	+	2.67183i	−0.190301	+	0.195383i
$188$	21.1038			1.53915
$189$		0			0
$190$	−2.03935	+	6.27646i	−0.147950	+	0.455343i
$191$	4.28583	−	4.75989i	0.310111	−	0.344414i	−0.567861	−	0.823124i	$-0.692229\pi$
$191$	4.28583	−	4.75989i	0.310111	−	0.344414i	0.877973	+	0.478711i	$0.158896\pi$
$192$		0			0
$193$	−0.294602	−	2.80295i	−0.0212059	−	0.201761i	0.978789	−	0.204870i	$-0.0656771\pi$
$193$	−0.294602	−	2.80295i	−0.0212059	−	0.201761i	−0.999995	+	0.00310888i	$0.999010\pi$
$194$	−3.56861	−	0.758531i	−0.256211	−	0.0544594i
$195$		0			0
$196$	−0.152226	+	1.44833i	−0.0108733	+	0.103452i
$197$	−25.7193			−1.83243			−0.916213	−	0.400692i	$-0.868770\pi$
$197$	−25.7193			−1.83243			−0.916213	+	0.400692i	$0.868770\pi$
$198$		0			0
$199$	13.3474			0.946174			0.473087	−	0.881016i	$-0.343140\pi$
$199$	13.3474			0.946174			0.473087	+	0.881016i	$0.343140\pi$
$200$	0.324209	−	3.08464i	0.0229250	−	0.218117i
$201$		0			0
$202$	6.78346	+	1.44187i	0.477282	+	0.101449i
$203$	−1.93564	−	18.4164i	−0.135855	−	1.29258i
$204$		0			0
$205$	−1.14352	+	1.27001i	−0.0798672	+	0.0887015i
$206$	−0.347751	+	1.07027i	−0.0242289	+	0.0745690i
$207$		0			0
$208$	12.3303			0.854953
$209$	3.22628	−	22.2648i	0.223167	−	1.54009i
$210$		0			0
$211$	−14.3717	+	6.39869i	−0.989388	+	0.440504i	−0.836635	−	0.547761i	$-0.815480\pi$
$211$	−14.3717	+	6.39869i	−0.989388	+	0.440504i	−0.152753	+	0.988264i	$0.548814\pi$
$212$	−6.88943	−	7.65148i	−0.473168	−	0.525506i
$213$		0			0
$214$	−3.27050	−	1.45612i	−0.223567	−	0.0995384i
$215$	10.2719	−	7.46296i	0.700536	−	0.508969i
$216$		0			0
$217$	5.16732	−	15.9034i	0.350781	−	1.07959i
$218$	−0.684809	+	6.51553i	−0.0463811	+	0.441287i
$219$		0			0
$220$	1.09014	+	16.6104i	0.0734972	+	1.11987i
$221$	−2.14655	+	3.71793i	−0.144392	+	0.250095i
$222$		0			0
$223$	18.4700	−	3.92592i	1.23684	−	0.262899i	0.457337	−	0.889293i	$-0.348803\pi$
$223$	18.4700	−	3.92592i	1.23684	−	0.262899i	0.779506	+	0.626394i	$0.215470\pi$
$224$	−3.06210	−	9.42417i	−0.204595	−	0.629679i
$225$		0			0
$226$	1.48877	−	1.08165i	0.0990314	−	0.0719505i
$227$	0.722287	−	0.802181i	0.0479399	−	0.0532426i	−0.718698	−	0.695322i	$-0.755262\pi$
$227$	0.722287	−	0.802181i	0.0479399	−	0.0532426i	0.766638	+	0.642080i	$0.221928\pi$
$228$		0			0
$229$	−11.2023	+	4.98760i	−0.740272	+	0.329590i	−0.741992	−	0.670408i	$-0.766119\pi$
$229$	−11.2023	+	4.98760i	−0.740272	+	0.329590i	0.00172076	+	0.999999i	$0.499452\pi$
$230$	3.28330	−	5.68684i	0.216494	−	0.374979i
$231$		0			0
$232$	−5.20267	−	9.01128i	−0.341572	−	0.591620i
$233$	12.1863	+	8.85388i	0.798353	+	0.580037i	0.910430	−	0.413662i	$-0.135751\pi$
$233$	12.1863	+	8.85388i	0.798353	+	0.580037i	−0.112078	+	0.993699i	$0.535751\pi$
$234$		0			0
$235$	9.37235	+	28.8451i	0.611385	+	1.88165i
$236$	−14.3905	−	6.40707i	−0.936743	−	0.417065i
$237$		0			0
$238$	0.993842	+	0.211248i	0.0644212	+	0.0136931i
$239$	−9.63117	−	10.6965i	−0.622988	−	0.691899i	0.346216	−	0.938155i	$-0.387466\pi$
$239$	−9.63117	−	10.6965i	−0.622988	−	0.691899i	−0.969205	+	0.246256i	$0.920800\pi$
$240$		0			0
$241$	6.01413	+	10.4168i	0.387404	+	0.671004i	0.992100	−	0.125453i	$-0.0400384\pi$
$241$	6.01413	+	10.4168i	0.387404	+	0.671004i	−0.604695	+	0.796457i	$0.706705\pi$
$242$	0.930898	+	3.87453i	0.0598404	+	0.249064i
$243$		0			0
$244$	2.60318	+	1.89132i	0.166651	+	0.121079i
$245$	−2.04722	+	0.435150i	−0.130792	+	0.0278007i
$246$		0			0
$247$	−2.70682	−	25.7537i	−0.172231	−	1.63867i
$248$	−0.982164	−	9.34467i	−0.0623675	−	0.593387i
$249$		0			0
$250$	−2.65215	+	0.563732i	−0.167737	+	0.0356535i
$251$	−11.5075	−	8.36069i	−0.726347	−	0.527722i	0.162058	−	0.986781i	$-0.448187\pi$
$251$	−11.5075	−	8.36069i	−0.726347	−	0.527722i	−0.888406	+	0.459059i	$0.848187\pi$
$252$		0			0
$253$	−7.74611	+	21.0023i	−0.486994	+	1.32040i
$254$	−0.151113	−	0.261736i	−0.00948170	−	0.0164228i
$255$		0			0
$256$	4.35180	+	4.83317i	0.271988	+	0.302073i
$257$	10.6299	+	2.25945i	0.663073	+	0.140941i	0.527141	−	0.849778i	$-0.323264\pi$
$257$	10.6299	+	2.25945i	0.663073	+	0.140941i	0.135932	+	0.990718i	$0.456597\pi$
$258$		0			0
$259$	0.434977	+	0.193664i	0.0270281	+	0.0120337i
$260$	5.92095	+	18.2228i	0.367202	+	1.13013i
$261$		0			0
$262$	5.78891	+	4.20589i	0.357640	+	0.259841i
$263$	1.29031	+	2.23489i	0.0795640	+	0.137809i	0.903062	−	0.429510i	$-0.141314\pi$
$263$	1.29031	+	2.23489i	0.0795640	+	0.137809i	−0.823498	+	0.567319i	$0.807981\pi$
$264$		0			0
$265$	7.39856	−	12.8147i	0.454490	−	0.787200i
$266$	−5.59883	+	2.49276i	−0.343286	+	0.152841i
$267$		0			0
$268$	−5.63542	+	6.25876i	−0.344238	+	0.382315i
$269$	4.58187	−	3.32892i	0.279361	−	0.202968i	−0.439277	−	0.898351i	$-0.644765\pi$
$269$	4.58187	−	3.32892i	0.279361	−	0.202968i	0.718639	+	0.695383i	$0.244765\pi$
$270$		0			0
$271$	0.742616	+	2.28554i	0.0451107	+	0.138836i	0.971075	−	0.238775i	$-0.0767457\pi$
$271$	0.742616	+	2.28554i	0.0451107	+	0.138836i	−0.925964	+	0.377611i	$0.876746\pi$
$272$	−3.55277	+	0.755164i	−0.215418	+	0.0457885i
$273$		0			0
$274$	0.717804	−	1.24327i	0.0433641	−	0.0751088i
$275$	−6.81730	+	2.72051i	−0.411099	+	0.164053i
$276$		0			0
$277$	−0.272826	+	2.59577i	−0.0163925	+	0.155965i	−0.999656	−	0.0262243i	$-0.991652\pi$
$277$	−0.272826	+	2.59577i	−0.0163925	+	0.155965i	0.983264	+	0.182189i	$0.0583183\pi$
$278$	−0.381136	+	1.17302i	−0.0228590	+	0.0703529i
$279$		0			0
$280$	7.59496	−	5.51806i	0.453886	−	0.329767i
$281$	−8.09216	−	3.60286i	−0.482738	−	0.214929i	0.150914	−	0.988547i	$-0.451778\pi$
$281$	−8.09216	−	3.60286i	−0.482738	−	0.214929i	−0.633652	+	0.773618i	$0.718445\pi$
$282$		0			0
$283$	−9.04049	−	10.0405i	−0.537401	−	0.596845i	0.411893	−	0.911232i	$-0.364868\pi$
$283$	−9.04049	−	10.0405i	−0.537401	−	0.596845i	−0.949295	+	0.314387i	$0.898201\pi$
$284$	20.9994	−	9.34952i	1.24608	−	0.554792i
$285$		0			0
$286$	2.13598	+	4.05899i	0.126303	+	0.240013i
$287$	−1.58706			−0.0936811
$288$		0			0
$289$	−4.86250	+	14.9652i	−0.286029	+	0.880308i
$290$	4.83343	−	5.36806i	0.283829	−	0.315224i
$291$		0			0
$292$	−0.416123	−	3.95914i	−0.0243517	−	0.231691i
$293$	17.3312	+	3.68386i	1.01250	+	0.215213i	0.684149	−	0.729342i	$-0.260174\pi$
$293$	17.3312	+	3.68386i	1.01250	+	0.215213i	0.328351	+	0.944556i	$0.393507\pi$
$294$		0			0
$295$	2.36639	−	22.5147i	0.137776	−	1.31086i
$296$	0.267548			0.0155509
$297$		0			0
$298$	1.86705			0.108156
$299$	−2.69334	+	25.6254i	−0.155760	+	1.48196i
$300$		0			0
$301$	11.5333	+	2.45149i	0.664771	+	0.141301i
$302$	0.520475	+	4.95199i	0.0299500	+	0.284955i
$303$		0			0
$304$	14.6598	−	16.2813i	0.840797	−	0.933799i
$305$	−1.42901	+	4.39803i	−0.0818246	+	0.251830i
$306$		0			0
$307$	11.3039			0.645145			0.322573	−	0.946545i	$-0.395452\pi$
$307$	11.3039			0.645145			0.322573	+	0.946545i	$0.395452\pi$
$308$	−10.7860	+	11.0740i	−0.614588	+	0.631001i
$309$		0			0
$310$	5.95893	−	2.65309i	0.338444	−	0.150685i
$311$	4.41971	+	4.90859i	0.250619	+	0.278340i	0.855307	−	0.518122i	$-0.173369\pi$
$311$	4.41971	+	4.90859i	0.250619	+	0.278340i	−0.604688	+	0.796463i	$0.706702\pi$
$312$		0			0
$313$	28.5934	+	12.7306i	1.61619	+	0.719576i	0.997800	−	0.0662913i	$-0.0211167\pi$
$313$	28.5934	+	12.7306i	1.61619	+	0.719576i	0.618395	+	0.785868i	$0.287783\pi$
$314$	−4.87500	+	3.54190i	−0.275112	+	0.199881i
$315$		0			0
$316$	6.68845	−	20.5849i	0.376254	−	1.15799i
$317$	1.34281	−	12.7759i	0.0754195	−	0.717569i	−0.889839	−	0.456274i	$-0.849184\pi$
$317$	1.34281	−	12.7759i	0.0754195	−	0.717569i	0.965259	−	0.261295i	$-0.0841495\pi$
$318$		0			0
$319$	−13.1382	+	20.8267i	−0.735595	+	1.16607i
$320$	−6.74181	+	11.6772i	−0.376879	+	0.652773i
$321$		0			0
$322$	5.96490	−	1.26788i	0.332411	−	0.0706561i
$323$	2.35720	+	7.25471i	0.131158	+	0.403663i
$324$		0			0
$325$	−6.83523	+	4.96608i	−0.379150	+	0.275469i
$326$	5.52629	−	6.13756i	0.306073	−	0.339928i
$327$		0			0
$328$	−0.814684	+	0.362721i	−0.0449834	+	0.0200279i
$329$	−14.0830	+	24.3924i	−0.776420	+	1.34480i
$330$		0			0
$331$	−9.58347	−	16.5991i	−0.526755	−	0.912367i	−0.999514	−	0.0311751i	$-0.990075\pi$
$331$	−9.58347	−	16.5991i	−0.526755	−	0.912367i	0.472759	−	0.881192i	$-0.343258\pi$
$332$	−1.23735	−	0.898985i	−0.0679082	−	0.0493382i
$333$		0			0
$334$	1.41043	+	4.34085i	0.0771751	+	0.237521i
$335$	−11.0573	−	4.92304i	−0.604127	−	0.268975i
$336$		0			0
$337$	−31.9855	−	6.79873i	−1.74236	−	0.370350i	−0.776643	−	0.629941i	$-0.783079\pi$
$337$	−31.9855	−	6.79873i	−1.74236	−	0.370350i	−0.965719	+	0.259591i	$0.916412\pi$
$338$	0.381558	+	0.423763i	0.0207540	+	0.0230497i
$339$		0			0
$340$	−2.82207	−	4.88796i	−0.153048	−	0.265087i
$341$	−18.4876	+	12.3553i	−1.00116	+	0.669079i
$342$		0			0
$343$	−15.6970	−	11.4046i	−0.847560	−	0.615788i
$344$	6.48069	−	1.37751i	0.349416	−	0.0742706i
$345$		0			0
$346$	0.271875	+	2.58672i	0.0146161	+	0.139063i
$347$	1.14779	+	10.9205i	0.0616165	+	0.586242i	0.981152	+	0.193236i	$0.0618982\pi$
$347$	1.14779	+	10.9205i	0.0616165	+	0.586242i	−0.919536	+	0.393006i	$0.871435\pi$
$348$		0			0
$349$	−23.1824	+	4.92757i	−1.24093	+	0.263767i	−0.781192	−	0.624290i	$-0.785388\pi$
$349$	−23.1824	+	4.92757i	−1.24093	+	0.263767i	−0.459733	+	0.888057i	$0.652055\pi$
$350$	1.61769	+	1.17532i	0.0864691	+	0.0628235i
$351$		0			0
$352$	−4.55968	+	12.3628i	−0.243032	+	0.658942i
$353$	14.7938	+	25.6236i	0.787394	+	1.36381i	0.927559	+	0.373678i	$0.121903\pi$
$353$	14.7938	+	25.6236i	0.787394	+	1.36381i	−0.140165	+	0.990128i	$0.544763\pi$
$354$		0			0
$355$	22.1051	+	24.5502i	1.17322	+	1.30299i
$356$	−2.59642	−	0.551887i	−0.137610	−	0.0292499i
$357$		0			0
$358$	2.97719	+	1.32553i	0.157350	+	0.0700565i
$359$	−8.83869	−	27.2027i	−0.466488	−	1.43570i	−0.857102	−	0.515148i	$-0.827737\pi$
$359$	−8.83869	−	27.2027i	−0.466488	−	1.43570i	0.390614	−	0.920555i	$-0.372263\pi$
$360$		0			0
$361$	−21.8529	−	15.8771i	−1.15015	−	0.835635i
$362$	−0.340041	−	0.588968i	−0.0178722	−	0.0309555i
$363$		0			0
$364$	−8.89687	+	15.4098i	−0.466323	+	0.807695i
$365$	5.22664	−	2.32705i	0.273575	−	0.121803i
$366$		0			0
$367$	−2.39541	+	2.66037i	−0.125039	+	0.138870i	−0.802414	−	0.596768i	$-0.796451\pi$
$367$	−2.39541	+	2.66037i	−0.125039	+	0.138870i	0.677374	+	0.735639i	$0.263118\pi$
$368$	−17.6362	+	12.8135i	−0.919352	+	0.667948i
$369$		0			0
$370$	0.0573948	+	0.176643i	0.00298382	+	0.00918324i
$371$	13.4413	−	2.85703i	0.697836	−	0.148330i
$372$		0			0
$373$	18.4968	−	32.0373i	0.957726	−	1.65883i	0.229722	−	0.973256i	$-0.426218\pi$
$373$	18.4968	−	32.0373i	0.957726	−	1.65883i	0.728004	−	0.685573i	$-0.240448\pi$
$374$	−0.864039	−	1.03871i	−0.0446784	−	0.0537105i
$375$		0			0
$376$	−1.65434	+	15.7400i	−0.0853162	+	0.811730i
$377$	−8.75877	+	26.9567i	−0.451100	+	1.38834i
$378$		0			0
$379$	19.4747	−	14.1492i	1.00035	−	0.726796i	0.0381863	−	0.999271i	$-0.487842\pi$
$379$	19.4747	−	14.1492i	1.00035	−	0.726796i	0.962163	+	0.272474i	$0.0878420\pi$
$380$	31.1015	+	13.8473i	1.59548	+	0.710352i
$381$		0			0
$382$	1.55256	+	1.72429i	0.0794357	+	0.0882223i
$383$	−31.9916	+	14.2436i	−1.63469	+	0.727812i	−0.999025	−	0.0441515i	$-0.985942\pi$
$383$	−31.9916	+	14.2436i	−1.63469	+	0.727812i	−0.635667	+	0.771963i	$0.719275\pi$
$384$		0			0
$385$	−19.9263	−	9.82444i	−1.01554	−	0.500700i
$386$	1.02097			0.0519662
$387$		0			0
$388$	−5.81594	+	17.8996i	−0.295260	+	0.908716i
$389$	2.74982	−	3.05399i	0.139422	−	0.154843i	−0.669390	−	0.742911i	$-0.733444\pi$
$389$	2.74982	−	3.05399i	0.139422	−	0.154843i	0.808812	+	0.588068i	$0.200111\pi$
$390$		0			0
$391$	−0.793377	−	7.54848i	−0.0401228	−	0.381743i
$392$	−1.06829	−	0.227072i	−0.0539568	−	0.0114689i
$393$		0			0
$394$	0.973884	−	9.26589i	0.0490636	−	0.466809i
$395$	31.1063			1.56513
$396$		0			0
$397$	−23.0629			−1.15749			−0.578747	−	0.815507i	$-0.696458\pi$
$397$	−23.0629			−1.15749			−0.578747	+	0.815507i	$0.696458\pi$
$398$	−0.505412	+	4.80867i	−0.0253340	+	0.241037i
$399$		0			0
$400$	−6.99184	−	1.48616i	−0.349592	−	0.0743081i
$401$	0.392024	+	3.72986i	0.0195768	+	0.186260i	0.999940	−	0.0109389i	$-0.00348203\pi$
$401$	0.392024	+	3.72986i	0.0195768	+	0.186260i	−0.980363	+	0.197199i	$0.936815\pi$
$402$		0			0
$403$	−17.1264	+	19.0208i	−0.853125	+	0.947492i
$404$	11.0553	−	34.0248i	0.550024	−	1.69280i
$405$		0			0
$406$	6.70815			0.332920
$407$	−0.294856	−	0.560312i	−0.0146155	−	0.0277736i
$408$		0			0
$409$	−25.0719	+	11.1627i	−1.23972	+	0.551960i	−0.918642	−	0.395091i	$-0.870713\pi$
$409$	−25.0719	+	11.1627i	−1.23972	+	0.551960i	−0.321081	+	0.947052i	$0.604046\pi$
$410$	−0.414246	−	0.460067i	−0.0204582	−	0.0227211i
$411$		0			0
$412$	5.30345	+	2.36125i	0.261282	+	0.116330i
$413$	17.0086	−	12.3574i	0.836937	−	0.608070i
$414$		0			0
$415$	0.679237	−	2.09048i	0.0333424	−	0.102617i
$416$	−1.58541	+	15.0842i	−0.0777313	+	0.739564i
$417$		0			0
$418$	7.89915	+	2.00540i	0.386360	+	0.0980876i
$419$	10.7023	−	18.5369i	0.522840	−	0.905586i	−0.476806	−	0.879008i	$-0.658206\pi$
$419$	10.7023	−	18.5369i	0.522840	−	0.905586i	0.999647	−	0.0265777i	$-0.00846093\pi$
$420$		0			0
$421$	−10.6840	+	2.27096i	−0.520708	+	0.110680i	−0.460765	−	0.887522i	$-0.652425\pi$
$421$	−10.6840	+	2.27096i	−0.520708	+	0.110680i	−0.0599425	+	0.998202i	$0.519092\pi$
$422$	−1.76106	−	5.41997i	−0.0857269	−	0.263840i
$423$		0			0
$424$	6.24683	−	4.53859i	0.303373	−	0.220413i
$425$	1.66531	−	1.84951i	0.0807793	−	0.0897145i
$426$		0			0
$427$	−3.92320	+	1.74672i	−0.189857	+	0.0845297i
$428$	−9.23416	+	15.9940i	−0.446350	+	0.773101i
$429$		0			0
$430$	2.29972	+	3.98324i	0.110902	+	0.192089i
$431$	9.56381	+	6.94852i	0.460673	+	0.334698i	0.793795	−	0.608185i	$-0.208102\pi$
$431$	9.56381	+	6.94852i	0.460673	+	0.334698i	−0.333122	+	0.942884i	$0.608102\pi$
$432$		0			0
$433$	−7.50566	−	23.1000i	−0.360699	−	1.11012i	−0.952631	−	0.304129i	$-0.901635\pi$
$433$	−7.50566	−	23.1000i	−0.360699	−	1.11012i	0.591932	−	0.805988i	$-0.298365\pi$
$434$	5.53384	+	2.46382i	0.265633	+	0.118267i
$435$		0			0
$436$	33.0585	+	7.02679i	1.58321	+	0.336522i
$437$	30.6345	+	34.0230i	1.46545	+	1.62754i
$438$		0			0
$439$	9.28957	+	16.0900i	0.443367	+	0.767934i	0.997937	−	0.0642030i	$-0.0204505\pi$
$439$	9.28957	+	16.0900i	0.443367	+	0.767934i	−0.554570	+	0.832137i	$0.687117\pi$
$440$	−12.4741	−	0.489035i	−0.594681	−	0.0233139i
$441$		0			0
$442$	−1.25818	−	0.914119i	−0.0598453	−	0.0434802i
$443$	−19.3148	+	4.10548i	−0.917672	+	0.195057i	−0.642454	−	0.766325i	$-0.722083\pi$
$443$	−19.3148	+	4.10548i	−0.917672	+	0.195057i	−0.275218	+	0.961382i	$0.588750\pi$
$444$		0			0
$445$	−0.398759	−	3.79394i	−0.0189030	−	0.179850i
$446$	0.715007	+	6.80284i	0.0338566	+	0.322124i
$447$		0			0
$448$	−12.2481	+	2.60342i	−0.578669	+	0.123000i
$449$	−1.68475	−	1.22404i	−0.0795083	−	0.0577662i	0.547321	−	0.836923i	$-0.315648\pi$
$449$	−1.68475	−	1.22404i	−0.0795083	−	0.0577662i	−0.626829	+	0.779157i	$0.715648\pi$
$450$		0			0
$451$	1.65746	+	1.30641i	0.0780468	+	0.0615163i
$452$	−4.74660	−	8.22135i	−0.223261	−	0.386700i
$453$		0			0
$454$	0.261651	+	0.290593i	0.0122799	+	0.0136382i
$455$	−25.0136	−	5.31681i	−1.17266	−	0.249256i
$456$		0			0
$457$	−7.57135	−	3.37098i	−0.354173	−	0.157688i	0.221935	−	0.975061i	$-0.428763\pi$
$457$	−7.57135	−	3.37098i	−0.354173	−	0.157688i	−0.576108	+	0.817373i	$0.695429\pi$
$458$	−1.37270	−	4.22472i	−0.0641418	−	0.197408i
$459$		0			0
$460$	−27.4057	−	19.9114i	−1.27780	−	0.928374i
$461$	3.27711	+	5.67613i	0.152630	+	0.264364i	0.932194	−	0.361960i	$-0.117892\pi$
$461$	3.27711	+	5.67613i	0.152630	+	0.264364i	−0.779563	+	0.626324i	$0.784559\pi$
$462$		0			0
$463$	−0.136703	+	0.236776i	−0.00635310	+	0.0110039i	−0.869184	−	0.494488i	$-0.835356\pi$
$463$	−0.136703	+	0.236776i	−0.00635310	+	0.0110039i	0.862831	+	0.505492i	$0.168689\pi$
$464$	−21.9070	+	9.75362i	−1.01701	+	0.452800i
$465$		0			0
$466$	−3.65123	+	4.05510i	−0.169140	+	0.187849i
$467$	−6.19971	+	4.50435i	−0.286888	+	0.208437i	−0.721916	−	0.691980i	$-0.756738\pi$
$467$	−6.19971	+	4.50435i	−0.286888	+	0.208437i	0.435028	+	0.900417i	$0.356738\pi$
$468$		0			0
$469$	−3.47345	−	10.6902i	−0.160389	−	0.493627i
$470$	−10.7469	+	2.28433i	−0.495718	+	0.105368i
$471$		0			0
$472$	5.90672	−	10.2307i	0.271879	−	0.470908i
$473$	−10.0270	−	12.0541i	−0.461042	−	0.554246i
$474$		0			0
$475$	−1.56918	+	14.9298i	−0.0719989	+	0.685024i
$476$	1.61971	−	4.98497i	0.0742395	−	0.228486i
$477$		0			0
$478$	4.21831	−	3.06478i	0.192941	−	0.140180i
$479$	21.2009	+	9.43926i	0.968695	+	0.431291i	0.829212	−	0.558934i	$-0.188789\pi$
$479$	21.2009	+	9.43926i	0.968695	+	0.431291i	0.139482	+	0.990225i	$0.455456\pi$
$480$		0			0
$481$	−0.487661	−	0.541602i	−0.0222354	−	0.0246949i
$482$	−3.98058	+	1.77227i	−0.181310	+	0.0807246i
$483$		0			0
$484$	20.3802	−	2.68667i	0.926371	−	0.122121i
$485$	−27.0485			−1.22821
$486$		0			0
$487$	−7.44592	+	22.9162i	−0.337407	+	1.03843i	0.628117	+	0.778119i	$0.283826\pi$
$487$	−7.44592	+	22.9162i	−0.337407	+	1.03843i	−0.965524	+	0.260313i	$0.916174\pi$
$488$	−1.61468	+	1.79329i	−0.0730932	+	0.0811783i
$489$		0			0
$490$	−0.0792515	−	0.754028i	−0.00358022	−	0.0340635i
$491$	−34.3994	−	7.31181i	−1.55242	−	0.329977i	−0.649696	−	0.760194i	$-0.725104\pi$
$491$	−34.3994	−	7.31181i	−1.55242	−	0.329977i	−0.902725	+	0.430217i	$0.858437\pi$
$492$		0			0
$493$	0.872738	−	8.30354i	0.0393061	−	0.373973i
$494$	9.38077			0.422061
$495$		0			0
$496$	−21.6544			−0.972311
$497$	−3.20682	+	30.5108i	−0.143845	+	1.36860i
$498$		0			0
$499$	22.2539	+	4.73022i	0.996222	+	0.211754i	0.677045	−	0.735941i	$-0.263260\pi$
$499$	22.2539	+	4.73022i	0.996222	+	0.211754i	0.319177	+	0.947695i	$0.396593\pi$
$500$	1.46208	+	13.9108i	0.0653862	+	0.622108i
$501$		0			0
$502$	3.44784	−	3.82922i	0.153885	−	0.170906i
$503$	1.55585	−	4.78840i	0.0693718	−	0.213504i	−0.910360	−	0.413816i	$-0.864196\pi$
$503$	1.55585	−	4.78840i	0.0693718	−	0.213504i	0.979732	+	0.200312i	$0.0641956\pi$
$504$		0			0
$505$	51.4156			2.28796
$506$	−7.27318	−	3.58596i	−0.323332	−	0.159415i
$507$		0			0
$508$	−1.42432	+	0.634146i	−0.0631938	+	0.0281357i
$509$	−6.22700	−	6.91578i	−0.276007	−	0.306537i	0.589164	−	0.808013i	$-0.299457\pi$
$509$	−6.22700	−	6.91578i	−0.276007	−	0.306537i	−0.865171	+	0.501476i	$0.832790\pi$
$510$		0			0
$511$	4.85379	+	2.16105i	0.214719	+	0.0955990i
$512$	−17.7056	+	12.8639i	−0.782483	+	0.568507i
$513$		0			0
$514$	−1.21652	+	3.74406i	−0.0536584	+	0.165144i
$515$	−0.872104	+	8.29752i	−0.0384295	+	0.365632i
$516$		0			0
$517$	34.7867	−	13.8819i	1.52992	−	0.610527i
$518$	−0.0862420	+	0.149376i	−0.00378926	+	0.00656319i
$519$		0			0
$520$	−14.0554	+	2.98757i	−0.616370	+	0.131014i
$521$	−3.41257	−	10.5028i	−0.149507	−	0.460136i	0.848056	−	0.529907i	$-0.177773\pi$
$521$	−3.41257	−	10.5028i	−0.149507	−	0.460136i	−0.997563	+	0.0697708i	$0.977773\pi$
$522$		0			0
$523$	15.7075	−	11.4122i	0.686841	−	0.499019i	−0.188779	−	0.982020i	$-0.560453\pi$
$523$	15.7075	−	11.4122i	0.686841	−	0.499019i	0.875620	+	0.483001i	$0.160453\pi$
$524$	24.6998	−	27.4319i	1.07901	−	1.19837i
$525$		0			0
$526$	−0.854020	+	0.380234i	−0.0372370	+	0.0165790i
$527$	3.76975	−	6.52940i	0.164213	−	0.284425i
$528$		0			0
$529$	−11.2772	−	19.5327i	−0.490314	−	0.849249i
$530$	4.33659	+	3.15071i	0.188369	+	0.136858i
$531$		0			0
$532$	9.76996	+	30.0688i	0.423581	+	1.30365i
$533$	2.21919	+	0.988046i	0.0961237	+	0.0427970i
$534$		0			0
$535$	−25.9619	−	5.51838i	−1.12243	−	0.238580i
$536$	−4.22626	−	4.69374i	−0.182547	−	0.202738i
$537$		0			0
$538$	1.02581	+	1.77676i	0.0442259	+	0.0766016i
$539$	0.701781	+	2.48751i	0.0302278	+	0.107145i
$540$		0			0
$541$	17.0772	+	12.4073i	0.734205	+	0.533431i	0.890891	−	0.454217i	$-0.150081\pi$
$541$	17.0772	+	12.4073i	0.734205	+	0.533431i	−0.156686	+	0.987649i	$0.550081\pi$
$542$	−0.851529	+	0.180998i	−0.0365763	+	0.00777453i
$543$		0			0
$544$	−0.467015	−	4.44335i	−0.0200231	−	0.190507i
$545$	5.07713	+	48.3056i	0.217480	+	2.06919i
$546$		0			0
$547$	13.7372	−	2.91993i	0.587360	−	0.124847i	0.0953606	−	0.995443i	$-0.469600\pi$
$547$	13.7372	−	2.91993i	0.587360	−	0.124847i	0.491999	+	0.870596i	$0.336266\pi$
$548$	−5.99151	−	4.35309i	−0.255945	−	0.185955i
$549$		0			0
$550$	−0.721973	−	2.55908i	−0.0307850	−	0.109120i
$551$	25.1810	+	43.6148i	1.07275	+	1.85805i
$552$		0			0
$553$	19.3294	+	21.4674i	0.821968	+	0.912888i
$554$	−0.924846	−	0.196582i	−0.0392929	−	0.00835197i
$555$		0			0
$556$	5.81261	+	2.58794i	0.246510	+	0.109753i
$557$	12.8094	+	39.4233i	0.542752	+	1.67042i	0.726276	+	0.687403i	$0.241249\pi$
$557$	12.8094	+	39.4233i	0.542752	+	1.67042i	−0.183524	+	0.983015i	$0.558751\pi$
$558$		0			0
$559$	−14.6009	−	10.6082i	−0.617552	−	0.448678i
$560$	−10.8177	−	18.7368i	−0.457131	−	0.791773i
$561$		0			0
$562$	1.60442	−	2.77893i	0.0676783	−	0.117222i
$563$	6.80544	−	3.02998i	0.286815	−	0.127698i	−0.258286	−	0.966068i	$-0.583158\pi$
$563$	6.80544	−	3.02998i	0.286815	−	0.127698i	0.545101	+	0.838370i	$0.316491\pi$
$564$		0			0
$565$	9.12911	−	10.1389i	0.384065	−	0.426547i
$566$	3.95961	−	2.87682i	0.166435	−	0.120922i
$567$		0			0
$568$	5.32707	+	16.3950i	0.223519	+	0.687920i
$569$	−23.8888	+	5.07772i	−1.00147	+	0.212869i	−0.679338	−	0.733825i	$-0.737733\pi$
$569$	−23.8888	+	5.07772i	−1.00147	+	0.212869i	−0.322133	+	0.946694i	$0.604400\pi$
$570$		0			0
$571$	6.40805	−	11.0991i	0.268169	−	0.464482i	−0.700220	−	0.713927i	$-0.746915\pi$
$571$	6.40805	−	11.0991i	0.268169	−	0.464482i	0.968389	+	0.249445i	$0.0802482\pi$
$572$	21.9763	−	8.76987i	0.918877	−	0.366687i
$573$		0			0
$574$	0.0600953	−	0.571769i	0.00250833	−	0.0238652i
$575$	4.61585	−	14.2061i	0.192494	−	0.592437i
$576$		0			0
$577$	11.7428	−	8.53166i	0.488860	−	0.355178i	−0.315886	−	0.948797i	$-0.602302\pi$
$577$	11.7428	−	8.53166i	0.488860	−	0.355178i	0.804746	+	0.593620i	$0.202302\pi$
$578$	−5.20740	−	2.31848i	−0.216599	−	0.0964362i
$579$		0			0
$580$	−24.9344	−	27.6924i	−1.03534	−	1.14987i
$581$	1.86478	−	0.830253i	0.0773641	−	0.0344447i
$582$		0			0
$583$	−16.3893	−	8.08057i	−0.678777	−	0.334663i
$584$	2.98550			0.123541
$585$		0			0
$586$	−1.98344	+	6.10441i	−0.0819353	+	0.252171i
$587$	14.9988	−	16.6579i	0.619069	−	0.687545i	−0.349317	−	0.937005i	$-0.613586\pi$
$587$	14.9988	−	16.6579i	0.619069	−	0.687545i	0.968385	+	0.249459i	$0.0802529\pi$
$588$		0			0
$589$	4.75370	+	45.2284i	0.195873	+	1.86361i
$590$	8.02175	+	1.70508i	0.330250	+	0.0701969i
$591$		0			0
$592$	0.0644515	−	0.613215i	0.00264894	−	0.0252030i
$593$	−18.2533			−0.749572			−0.374786	−	0.927111i	$-0.622284\pi$
$593$	−18.2533			−0.749572			−0.374786	+	0.927111i	$0.622284\pi$
$594$		0			0
$595$	7.53288			0.308818
$596$	1.00678	−	9.57887i	0.0412393	−	0.392366i
$597$		0			0
$598$	−9.13007	−	1.94066i	−0.373356	−	0.0793593i
$599$	−2.76195	−	26.2782i	−0.112850	−	1.07370i	−0.893603	−	0.448859i	$-0.851831\pi$
$599$	−2.76195	−	26.2782i	−0.112850	−	1.07370i	0.780753	−	0.624840i	$-0.214836\pi$
$600$		0			0
$601$	9.25098	−	10.2743i	0.377355	−	0.419096i	−0.524312	−	0.851526i	$-0.675677\pi$
$601$	9.25098	−	10.2743i	0.377355	−	0.419096i	0.901667	+	0.432431i	$0.142344\pi$
$602$	−1.31992	+	4.06228i	−0.0537958	+	0.165566i
$603$		0			0
$604$	25.6867			1.04518
$605$	12.7232	+	26.6629i	0.517270	+	1.08400i
$606$		0			0
$607$	−13.3213	+	5.93104i	−0.540696	+	0.240733i	−0.658866	−	0.752260i	$-0.728964\pi$
$607$	−13.3213	+	5.93104i	−0.540696	+	0.240733i	0.118170	+	0.992993i	$0.462297\pi$
$608$	18.0327	+	20.0274i	0.731324	+	0.812218i
$609$		0			0
$610$	−1.53036	−	0.681362i	−0.0619626	−	0.0275875i
$611$	34.8782	−	25.3405i	1.41102	−	1.02517i
$612$		0			0
$613$	−9.31252	+	28.6610i	−0.376129	+	1.15761i	0.566585	+	0.824004i	$0.308264\pi$
$613$	−9.31252	+	28.6610i	−0.376129	+	1.15761i	−0.942714	+	0.333603i	$0.891736\pi$
$614$	−0.428030	+	4.07244i	−0.0172739	+	0.164350i
$615$		0			0
$616$	−7.41390	−	8.91269i	−0.298715	−	0.359102i
$617$	−9.84784	+	17.0570i	−0.396459	+	0.686687i	−0.993286	−	0.115683i	$-0.963094\pi$
$617$	−9.84784	+	17.0570i	−0.396459	+	0.686687i	0.596827	+	0.802370i	$0.296428\pi$
$618$		0			0
$619$	−1.26485	+	0.268852i	−0.0508387	+	0.0108061i	−0.233261	−	0.972414i	$-0.574940\pi$
$619$	−1.26485	+	0.268852i	−0.0508387	+	0.0108061i	0.182422	+	0.983220i	$0.441606\pi$
$620$	−10.3983	−	32.0028i	−0.417607	−	1.28526i
$621$		0			0
$622$	−1.93577	+	1.40642i	−0.0776173	+	0.0563923i
$623$	2.37053	−	2.63274i	0.0949733	−	0.105479i
$624$		0			0
$625$	−28.4731	+	12.6770i	−1.13892	+	0.507082i
$626$	−5.66916	+	9.81928i	−0.226585	+	0.392457i
$627$		0			0
$628$	15.5428	+	26.9210i	0.620227	+	1.07426i
$629$	0.173681	+	0.126187i	0.00692513	+	0.00503140i
$630$		0			0
$631$	13.6277	+	41.9417i	0.542509	+	1.66967i	0.726839	+	0.686808i	$0.240988\pi$
$631$	13.6277	+	41.9417i	0.542509	+	1.66967i	−0.184330	+	0.982864i	$0.559012\pi$
$632$	14.8287	+	6.60216i	0.589854	+	0.262620i
$633$		0			0
$634$	4.55194	+	0.967544i	0.180781	+	0.0384261i
$635$	−1.49931	−	1.66516i	−0.0594984	−	0.0660797i
$636$		0			0
$637$	1.48751	+	2.57644i	0.0589372	+	0.102082i
$638$	−7.00573	−	5.52190i	−0.277360	−	0.218614i
$639$		0			0
$640$	−21.2166	−	15.4148i	−0.838660	−	0.609322i
$641$	−26.4042	+	5.61239i	−1.04290	+	0.221676i	−0.697356	−	0.716725i	$-0.745640\pi$
$641$	−26.4042	+	5.61239i	−1.04290	+	0.221676i	−0.345548	+	0.938401i	$0.612307\pi$
$642$		0			0
$643$	1.06164	+	10.1009i	0.0418671	+	0.398339i	0.995308	+	0.0967587i	$0.0308475\pi$
$643$	1.06164	+	10.1009i	0.0418671	+	0.398339i	−0.953441	+	0.301580i	$0.902486\pi$
$644$	−3.28834	−	31.2864i	−0.129579	−	1.23286i
$645$		0			0
$646$	−2.70291	+	0.574521i	−0.106344	+	0.0226042i
$647$	27.2093	+	19.7687i	1.06971	+	0.777189i	0.975860	−	0.218397i	$-0.0700828\pi$
$647$	27.2093	+	19.7687i	1.06971	+	0.777189i	0.0938493	+	0.995586i	$0.470083\pi$
$648$		0			0
$649$	−27.9353	−	1.09517i	−1.09656	−	0.0429893i
$650$	−1.53031	−	2.65057i	−0.0600236	−	0.103964i
$651$		0			0
$652$	−28.5086	−	31.6621i	−1.11648	−	1.23998i
$653$	11.0802	+	2.35516i	0.433600	+	0.0921645i	0.419540	−	0.907737i	$-0.362191\pi$
$653$	11.0802	+	2.35516i	0.433600	+	0.0921645i	0.0140596	+	0.999901i	$0.495525\pi$
$654$		0			0
$655$	48.4638	+	21.5775i	1.89364	+	0.843102i
$656$	0.635094	+	1.95462i	0.0247963	+	0.0763150i
$657$		0			0
$658$	−8.25459	−	5.99731i	−0.321797	−	0.233800i
$659$	−16.1903	−	28.0424i	−0.630684	−	1.09238i	−0.987412	−	0.158168i	$-0.949441\pi$
$659$	−16.1903	−	28.0424i	−0.630684	−	1.09238i	0.356729	−	0.934208i	$-0.383892\pi$
$660$		0			0
$661$	−1.57119	+	2.72139i	−0.0611123	+	0.105850i	−0.894963	−	0.446141i	$-0.852798\pi$
$661$	−1.57119	+	2.72139i	−0.0611123	+	0.105850i	0.833851	+	0.551990i	$0.186131\pi$
$662$	6.34302	−	2.82410i	0.246529	−	0.109762i
$663$		0			0
$664$	0.767493	−	0.852388i	0.0297845	−	0.0330791i
$665$	−36.7598	+	26.7076i	−1.42548	+	1.03567i
$666$		0			0
$667$	−15.4852	−	47.6586i	−0.599590	−	1.84535i
$668$	23.0312	−	4.89542i	0.891102	−	0.189410i
$669$		0			0
$670$	2.19232	−	3.79721i	0.0846966	−	0.146699i
$671$	5.53507	+	1.40522i	0.213679	+	0.0542480i
$672$		0			0
$673$	4.04197	−	38.4567i	0.155806	−	1.48240i	−0.585194	−	0.810894i	$-0.698982\pi$
$673$	4.04197	−	38.4567i	0.155806	−	1.48240i	0.741000	−	0.671505i	$-0.234352\pi$
$674$	3.66053	−	11.2660i	0.140998	−	0.433949i
$675$		0			0
$676$	2.37986	−	1.72907i	0.0915329	−	0.0665025i
$677$	−41.7683	−	18.5964i	−1.60528	−	0.714719i	−0.608403	−	0.793628i	$-0.708190\pi$
$677$	−41.7683	−	18.5964i	−1.60528	−	0.714719i	−0.996882	+	0.0789093i	$0.974856\pi$
$678$		0			0
$679$	−16.8079	−	18.6670i	−0.645027	−	0.716375i
$680$	3.86685	−	1.72163i	0.148287	−	0.0660216i
$681$		0			0
$682$	−3.75120	−	7.12837i	−0.143641	−	0.272959i
$683$	−11.3550			−0.434485			−0.217243	−	0.976118i	$-0.569706\pi$
$683$	−11.3550			−0.434485			−0.217243	+	0.976118i	$0.569706\pi$
$684$		0			0
$685$	3.28902	−	10.1226i	0.125667	−	0.386763i
$686$	4.70310	−	5.22332i	0.179565	−	0.199427i
$687$		0			0
$688$	−1.59606	−	15.1855i	−0.0608491	−	0.578940i
$689$	−20.5736	−	4.37306i	−0.783793	−	0.166600i
$690$		0			0
$691$	−0.911473	+	8.67209i	−0.0346741	+	0.329902i	0.963410	+	0.268032i	$0.0863731\pi$
$691$	−0.911473	+	8.67209i	−0.0346741	+	0.329902i	−0.998084	+	0.0618702i	$0.980294\pi$
$692$	13.4177			0.510065
$693$		0			0
$694$	−3.97778			−0.150994
$695$	−0.955831	+	9.09412i	−0.0362567	+	0.344960i
$696$		0			0
$697$	−0.699934	−	0.148775i	−0.0265119	−	0.00563527i
$698$	−0.897432	−	8.53850i	−0.0339683	−	0.323187i
$699$		0			0
$700$	6.90226	−	7.66574i	0.260881	−	0.289738i
$701$	−12.5650	+	38.6712i	−0.474575	+	1.46059i	0.371954	+	0.928251i	$0.378688\pi$
$701$	−12.5650	+	38.6712i	−0.474575	+	1.46059i	−0.846530	+	0.532342i	$0.821312\pi$
$702$		0			0
$703$	−1.29494			−0.0488396
$704$	14.9345	+	7.36328i	0.562865	+	0.277514i
$705$		0			0
$706$	−9.79158	+	4.35949i	−0.368511	+	0.164072i
$707$	31.9495	+	35.4835i	1.20159	+	1.33450i
$708$		0			0
$709$	−15.2948	−	6.80970i	−0.574410	−	0.255744i	0.0989083	−	0.995097i	$-0.468465\pi$
$709$	−15.2948	−	6.80970i	−0.574410	−	0.255744i	−0.673318	+	0.739353i	$0.735132\pi$
$710$	−9.68171	+	7.03417i	−0.363348	+	0.263988i
$711$		0			0
$712$	0.615154	−	1.89325i	0.0230539	−	0.0709525i
$713$	4.73002	−	45.0032i	0.177141	−	1.68538i
$714$		0			0
$715$	21.7467	+	26.1430i	0.813280	+	0.977691i
$716$	8.40601	−	14.5596i	0.314147	−	0.544119i
$717$		0			0
$718$	10.1350	−	2.15426i	0.378234	−	0.0803961i
$719$	5.99373	+	18.4468i	0.223528	+	0.687949i	0.998438	+	0.0558770i	$0.0177955\pi$
$719$	5.99373	+	18.4468i	0.223528	+	0.687949i	−0.774909	+	0.632072i	$0.782205\pi$
$720$		0			0
$721$	−6.26830	+	4.55419i	−0.233444	+	0.169607i
$722$	6.54750	−	7.27174i	0.243673	−	0.270626i
$723$		0			0
$724$	−3.20505	+	1.42698i	−0.119115	+	0.0530333i
$725$	8.21569	−	14.2300i	0.305123	−	0.528488i
$726$		0			0
$727$	−2.89216	−	5.00937i	−0.107264	−	0.185787i	0.807397	−	0.590009i	$-0.200876\pi$
$727$	−2.89216	−	5.00937i	−0.107264	−	0.185787i	−0.914661	+	0.404222i	$0.867542\pi$
$728$	−10.7958	−	7.84361i	−0.400119	−	0.290704i
$729$		0			0
$730$	0.640454	+	1.97111i	0.0237043	+	0.0729542i
$731$	4.85669	+	2.16234i	0.179631	+	0.0799770i
$732$		0			0
$733$	−22.2159	−	4.72214i	−0.820563	−	0.174416i	−0.221544	−	0.975150i	$-0.571109\pi$
$733$	−22.2159	−	4.72214i	−0.820563	−	0.174416i	−0.599020	+	0.800734i	$0.704443\pi$
$734$	−0.867748	−	0.963731i	−0.0320291	−	0.0355720i
$735$		0			0
$736$	−13.4076	−	23.2227i	−0.494212	−	0.856000i
$737$	−5.17222	+	14.0236i	−0.190521	+	0.516567i
$738$		0			0
$739$	9.31755	+	6.76960i	0.342752	+	0.249024i	0.745822	−	0.666145i	$-0.232057\pi$
$739$	9.31755	+	6.76960i	0.342752	+	0.249024i	−0.403070	+	0.915169i	$0.632057\pi$
$740$	0.937212	−	0.199211i	0.0344526	−	0.00732313i
$741$		0			0
$742$	0.520336	+	4.95066i	0.0191021	+	0.181745i
$743$	−4.49533	−	42.7703i	−0.164918	−	1.56909i	−0.693658	−	0.720305i	$-0.744002\pi$
$743$	−4.49533	−	42.7703i	−0.164918	−	1.56909i	0.528740	−	0.848784i	$-0.322665\pi$
$744$		0			0
$745$	13.5397	−	2.87796i	0.496057	−	0.105440i
$746$	10.8417	+	7.87694i	0.396942	+	0.288395i
$747$		0			0
$748$	−5.79500	+	3.87282i	−0.211886	+	0.141604i
$749$	−12.3243	−	21.3462i	−0.450319	−	0.779975i
$750$		0			0
$751$	2.40813	+	2.67449i	0.0878738	+	0.0975937i	0.785478	−	0.618890i	$-0.212417\pi$
$751$	2.40813	+	2.67449i	0.0878738	+	0.0975937i	−0.697604	+	0.716483i	$0.745751\pi$
$752$	35.6773	+	7.58344i	1.30102	+	0.276540i
$753$		0			0
$754$	−9.38003	−	4.17626i	−0.341600	−	0.152090i
$755$	11.4076	+	35.1091i	0.415167	+	1.27775i
$756$		0			0
$757$	12.2911	+	8.93000i	0.446727	+	0.324566i	0.788302	−	0.615288i	$-0.210960\pi$
$757$	12.2911	+	8.93000i	0.446727	+	0.324566i	−0.341575	+	0.939855i	$0.610960\pi$
$758$	4.36010	+	7.55192i	0.158366	+	0.274298i
$759$		0			0
$760$	−12.7659	+	22.1112i	−0.463068	+	0.802058i
$761$	−14.9046	+	6.63596i	−0.540292	+	0.240553i	−0.658692	−	0.752413i	$-0.728890\pi$
$761$	−14.9046	+	6.63596i	−0.540292	+	0.240553i	0.118400	+	0.992966i	$0.462223\pi$
$762$		0			0
$763$	−30.1823	+	33.5209i	−1.09267	+	1.21354i
$764$	9.68362	−	7.03556i	0.350341	−	0.254538i
$765$		0			0
$766$	−3.92013	−	12.0649i	−0.141640	−	0.435923i
$767$	−31.4764	+	6.69052i	−1.13655	+	0.241581i
$768$		0			0
$769$	−3.33336	+	5.77355i	−0.120204	+	0.208200i	−0.919848	−	0.392275i	$-0.871688\pi$
$769$	−3.33336	+	5.77355i	−0.120204	+	0.208200i	0.799644	+	0.600474i	$0.205022\pi$
$770$	4.29397	−	6.80683i	0.154744	−	0.245301i
$771$		0			0
$772$	0.550544	−	5.23808i	0.0198145	−	0.188523i
$773$	15.7232	−	48.3910i	0.565524	−	1.74050i	−0.100865	−	0.994900i	$-0.532161\pi$
$773$	15.7232	−	48.3910i	0.565524	−	1.74050i	0.666389	−	0.745604i	$-0.267839\pi$
$774$		0			0
$775$	12.0040	−	8.72140i	0.431196	−	0.313282i
$776$	−12.8943	−	5.74092i	−0.462879	−	0.206087i
$777$		0			0
$778$	0.996135	+	1.10632i	0.0357132	+	0.0396635i
$779$	3.94309	−	1.75558i	0.141276	−	0.0629001i
$780$		0			0
$781$	28.4644	−	29.2246i	1.01854	−	1.04574i
$782$	2.74953			0.0983229
$783$		0			0
$784$	−0.777792	+	2.39380i	−0.0277783	+	0.0854928i
$785$	−29.8935	+	33.2001i	−1.06694	+	1.18496i
$786$		0			0
$787$	3.17288	+	30.1879i	0.113101	+	1.07608i	0.892963	+	0.450131i	$0.148623\pi$
$787$	3.17288	+	30.1879i	0.113101	+	1.07608i	−0.779862	+	0.625952i	$0.784711\pi$
$788$	−47.0132	−	9.99297i	−1.67478	−	0.355985i
$789$		0			0
$790$	−1.17787	+	11.2066i	−0.0419066	+	0.398714i
$791$	12.6700			0.450493
$792$		0			0
$793$	6.57326			0.233423
$794$	0.873297	−	8.30886i	0.0309921	−	0.294870i
$795$		0			0
$796$	24.3982	+	5.18600i	0.864772	+	0.183813i
$797$	−0.415201	−	3.95037i	−0.0147072	−	0.139929i	0.984704	−	0.174234i	$-0.0557450\pi$
$797$	−0.415201	−	3.95037i	−0.0147072	−	0.139929i	−0.999411	+	0.0343048i	$0.989078\pi$
$798$		0			0
$799$	−8.49758	+	9.43752i	−0.300623	+	0.333875i
$800$	2.71709	−	8.36233i	0.0960635	−	0.295653i
$801$		0			0
$802$	−1.35860			−0.0479738
$803$	−3.29022	−	6.25237i	−0.116109	−	0.220641i
$804$		0			0
$805$	41.3026	−	18.3891i	1.45572	−	0.648130i
$806$	−6.20410	−	6.89035i	−0.218530	−	0.242702i
$807$		0			0
$808$	24.5104	+	10.9127i	0.862272	+	0.383908i
$809$	4.26011	−	3.09515i	0.149778	−	0.108820i	−0.510373	−	0.859953i	$-0.670493\pi$
$809$	4.26011	−	3.09515i	0.149778	−	0.108820i	0.660150	+	0.751133i	$0.270493\pi$
$810$		0			0
$811$	11.6366	−	35.8137i	0.408615	−	1.25759i	−0.509223	−	0.860635i	$-0.670067\pi$
$811$	11.6366	−	35.8137i	0.408615	−	1.25759i	0.917838	−	0.396954i	$-0.129933\pi$
$812$	3.61727	−	34.4160i	0.126941	−	1.20776i
$813$		0			0
$814$	0.213028	−	0.0850109i	0.00746663	−	0.00297963i
$815$	30.6155	−	53.0275i	1.07241	−	1.85747i
$816$		0			0
$817$	−31.3667	+	6.66720i	−1.09738	+	0.233256i
$818$	−3.07222	−	9.45531i	−0.107418	−	0.330597i
$819$		0			0
$820$	−2.58374	+	1.87719i	−0.0902280	+	0.0655545i
$821$	−1.40616	+	1.56170i	−0.0490753	+	0.0545037i	−0.767183	−	0.641429i	$-0.778342\pi$
$821$	−1.40616	+	1.56170i	−0.0490753	+	0.0545037i	0.718107	+	0.695932i	$0.245009\pi$
$822$		0			0
$823$	−6.07498	+	2.70475i	−0.211760	+	0.0942818i	−0.509876	−	0.860248i	$-0.670309\pi$
$823$	−6.07498	+	2.70475i	−0.211760	+	0.0942818i	0.298115	+	0.954530i	$0.403642\pi$
$824$	−2.17685	+	3.77042i	−0.0758342	+	0.131349i
$825$		0			0
$826$	3.80797	+	6.59559i	0.132496	+	0.229490i
$827$	−17.8702	−	12.9834i	−0.621407	−	0.451479i	0.232006	−	0.972714i	$-0.425471\pi$
$827$	−17.8702	−	12.9834i	−0.621407	−	0.451479i	−0.853413	+	0.521236i	$0.825471\pi$
$828$		0			0
$829$	1.19544	+	3.67920i	0.0415195	+	0.127784i	0.969668	−	0.244427i	$-0.0785998\pi$
$829$	1.19544	+	3.67920i	0.0415195	+	0.127784i	−0.928148	+	0.372211i	$0.878600\pi$
$830$	0.727415	+	0.323866i	0.0252489	+	0.0112416i
$831$		0			0
$832$	18.7474	+	3.98488i	0.649948	+	0.138151i
$833$	−0.586393	−	0.651255i	−0.0203173	−	0.0225647i
$834$		0			0
$835$	16.9195	+	29.3054i	0.585522	+	1.01415i
$836$	14.5482	−	39.4450i	0.503159	−	1.36423i
$837$		0			0
$838$	6.27302	+	4.55762i	0.216698	+	0.157440i
$839$	−22.9258	+	4.87302i	−0.791486	+	0.168235i	−0.585878	−	0.810399i	$-0.699250\pi$
$839$	−22.9258	+	4.87302i	−0.791486	+	0.168235i	−0.205607	+	0.978635i	$0.565917\pi$
$840$		0			0
$841$	−2.73068	−	25.9807i	−0.0941614	−	0.895886i
$842$	−0.413598	−	3.93512i	−0.0142535	−	0.135613i
$843$		0			0
$844$	−28.7567	+	6.11242i	−0.989845	+	0.210398i
$845$	3.42023	+	2.48494i	0.117660	+	0.0854847i
$846$		0			0
$847$	−10.4947	+	25.3489i	−0.360604	+	0.870998i
$848$	−8.89751	−	15.4109i	−0.305542	−	0.529214i
$849$		0			0
$850$	0.603265	+	0.669993i	0.0206918	+	0.0229806i
$851$	1.26033	+	0.267892i	0.0432037	+	0.00918323i
$852$		0			0
$853$	−19.1776	−	8.53842i	−0.656629	−	0.292350i	0.0512479	−	0.998686i	$-0.483680\pi$
$853$	−19.1776	−	8.53842i	−0.656629	−	0.292350i	−0.707877	+	0.706336i	$0.750347\pi$
$854$	−0.480735	−	1.47955i	−0.0164504	−	0.0506291i
$855$		0			0
$856$	−11.2051	−	8.14097i	−0.382982	−	0.278252i
$857$	14.1590	+	24.5241i	0.483662	+	0.837728i	0.999824	−	0.0187634i	$-0.00597292\pi$
$857$	14.1590	+	24.5241i	0.483662	+	0.837728i	−0.516162	+	0.856491i	$0.672640\pi$
$858$		0			0
$859$	27.8536	−	48.2438i	0.950351	−	1.64606i	0.205687	−	0.978618i	$-0.434057\pi$
$859$	27.8536	−	48.2438i	0.950351	−	1.64606i	0.744665	−	0.667439i	$-0.232609\pi$
$860$	21.6760	−	9.65077i	0.739145	−	0.329088i
$861$		0			0
$862$	−2.86548	+	3.18244i	−0.0975986	+	0.108394i
$863$	24.8932	−	18.0860i	0.847375	−	0.615654i	−0.0770462	−	0.997028i	$-0.524549\pi$
$863$	24.8932	−	18.0860i	0.847375	−	0.615654i	0.924421	+	0.381374i	$0.124549\pi$
$864$		0			0
$865$	5.95890	+	18.3396i	0.202609	+	0.623565i
$866$	8.60645	−	1.82936i	0.292459	−	0.0621641i
$867$		0			0
$868$	15.6246	−	27.0626i	0.530334	−	0.918566i
$869$	−2.51565	−	38.3309i	−0.0853377	−	1.30029i
$870$		0			0
$871$	−1.79839	+	17.1106i	−0.0609362	+	0.579769i
$872$	−7.83232	+	24.1054i	−0.265236	+	0.816312i
$873$		0			0
$874$	−13.4175	+	9.74835i	−0.453852	+	0.329743i
$875$	−17.0542	−	7.59300i	−0.576536	−	0.256690i
$876$		0			0
$877$	20.7384	+	23.0323i	0.700286	+	0.777747i	0.983422	−	0.181333i	$-0.0580413\pi$
$877$	20.7384	+	23.0323i	0.700286	+	0.777747i	−0.283136	+	0.959080i	$0.591375\pi$
$878$	−6.14850	+	2.73749i	−0.207502	+	0.0923857i
$879$		0			0
$880$	−4.12584	+	28.4727i	−0.139082	+	0.959814i
$881$	−29.9198			−1.00802			−0.504012	−	0.863697i	$-0.668143\pi$
$881$	−29.9198			−1.00802			−0.504012	+	0.863697i	$0.668143\pi$
$882$		0			0
$883$	4.39514	−	13.5269i	0.147908	−	0.455215i	−0.849465	−	0.527645i	$-0.823075\pi$
$883$	4.39514	−	13.5269i	0.147908	−	0.455215i	0.997374	+	0.0724296i	$0.0230753\pi$
$884$	−5.36831	+	5.96212i	−0.180556	+	0.200528i
$885$		0			0
$886$	−0.747709	−	7.11398i	−0.0251198	−	0.238999i
$887$	−2.57329	−	0.546971i	−0.0864028	−	0.0183655i	0.164507	−	0.986376i	$-0.447397\pi$
$887$	−2.57329	−	0.546971i	−0.0864028	−	0.0183655i	−0.250910	+	0.968010i	$0.580730\pi$
$888$		0			0
$889$	0.217508	−	2.06945i	0.00729497	−	0.0694070i
$890$	1.38194			0.0463228
$891$		0			0
$892$	35.2874			1.18151
$893$	8.00706	−	76.1821i	0.267946	−	2.54934i
$894$		0			0
$895$	23.6336	+	5.02347i	0.789983	+	0.167916i
$896$	−2.54572	−	24.2210i	−0.0850467	−	0.809165i
$897$		0			0
$898$	0.504780	−	0.560615i	0.0168447	−	0.0187080i
$899$	15.3821	−	47.3412i	0.513021	−	1.57892i
$900$		0			0
$901$	6.19577			0.206411
$902$	−0.533420	+	0.547665i	−0.0177609	+	0.0182352i
$903$		0			0
$904$	6.50388	−	2.89572i	0.216316	−	0.0963101i
$905$	−3.37381	−	3.74700i	−0.112149	−	0.124554i
$906$		0			0
$907$	−9.28389	−	4.13345i	−0.308266	−	0.137249i	0.246772	−	0.969073i	$-0.420630\pi$
$907$	−9.28389	−	4.13345i	−0.308266	−	0.137249i	−0.555039	+	0.831824i	$0.687297\pi$
$908$	1.63197	−	1.18570i	0.0541589	−	0.0393488i
$909$		0			0
$910$	2.86265	−	8.81033i	0.0948959	−	0.292060i
$911$	−0.615910	+	5.85999i	−0.0204060	+	0.194150i	−0.999976	−	0.00695428i	$-0.997786\pi$
$911$	−0.615910	+	5.85999i	−0.0204060	+	0.194150i	0.979570	+	0.201104i	$0.0644530\pi$
$912$		0			0
$913$	−2.63094	−	0.667932i	−0.0870713	−	0.0221053i
$914$	1.50116	−	2.60008i	0.0496539	−	0.0860031i
$915$		0			0
$916$	−22.4150	+	4.76446i	−0.740613	+	0.157422i
$917$	15.2240	+	46.8546i	0.502740	+	1.54727i
$918$		0			0
$919$	−26.1285	+	18.9835i	−0.861899	+	0.626206i	−0.928401	−	0.371580i	$-0.878816\pi$
$919$	−26.1285	+	18.9835i	−0.861899	+	0.626206i	0.0665018	+	0.997786i	$0.478816\pi$
$920$	16.9990	−	18.8793i	0.560441	−	0.622433i
$921$		0			0
$922$	−2.16903	+	0.965713i	−0.0714331	+	0.0318041i
$923$	23.4791	−	40.6669i	0.772823	−	1.33857i
$924$		0			0
$925$	0.211247	+	0.365890i	0.00694575	+	0.0120304i
$926$	−0.0801267	−	0.0582155i	−0.00263313	−	0.00191308i
$927$		0			0
$928$	−9.11525	−	28.0539i	−0.299223	−	0.920913i
$929$	44.6570	+	19.8826i	1.46515	+	0.652327i	0.975581	−	0.219639i	$-0.0704878\pi$
$929$	44.6570	+	19.8826i	1.46515	+	0.652327i	0.489568	+	0.871965i	$0.337154\pi$
$930$		0			0
$931$	5.17055	+	1.09903i	0.169458	+	0.0360194i
$932$	18.8357	+	20.9192i	0.616985	+	0.685231i
$933$		0			0
$934$	−1.38802	−	2.40413i	−0.0454175	−	0.0786655i
$935$	−7.86705	−	6.20078i	−0.257280	−	0.202787i
$936$		0			0
$937$	−36.4628	−	26.4917i	−1.19119	−	0.865447i	−0.197797	−	0.980243i	$-0.563379\pi$
$937$	−36.4628	−	26.4917i	−1.19119	−	0.865447i	−0.993389	+	0.114796i	$0.963379\pi$
$938$	3.98287	−	0.846586i	0.130045	−	0.0276420i
$939$		0			0
$940$	5.92457	+	56.3686i	0.193238	+	1.83854i
$941$	1.71991	+	16.3639i	0.0560675	+	0.533447i	0.986122	+	0.166024i	$0.0530930\pi$
$941$	1.71991	+	16.3639i	0.0560675	+	0.533447i	−0.930054	+	0.367423i	$0.880240\pi$
$942$		0			0
$943$	−4.20090	+	0.892929i	−0.136800	+	0.0290778i
$944$	−22.0257	−	16.0026i	−0.716877	−	0.520841i
$945$		0			0
$946$	4.72239	−	3.15599i	0.153538	−	0.102610i
$947$	3.50636	+	6.07320i	0.113942	+	0.197352i	0.917356	−	0.398067i	$-0.130319\pi$
$947$	3.50636	+	6.07320i	0.113942	+	0.197352i	−0.803415	+	0.595420i	$0.796986\pi$
$948$		0			0
$949$	−5.44168	−	6.04359i	−0.176644	−	0.196183i
$950$	−5.31932	−	1.13066i	−0.172581	−	0.0366833i
$951$		0			0
$952$	3.59101	+	1.59882i	0.116385	+	0.0518180i
$953$	3.34588	+	10.2976i	0.108384	+	0.333571i	0.990510	−	0.137443i	$-0.0438883\pi$
$953$	3.34588	+	10.2976i	0.108384	+	0.333571i	−0.882126	+	0.471014i	$0.843888\pi$
$954$		0			0
$955$	13.9169	+	10.1112i	0.450341	+	0.327192i
$956$	−13.4491	−	23.2946i	−0.434976	−	0.753401i
$957$		0			0
$958$	−4.20347	+	7.28062i	−0.135808	+	0.235226i
$959$	9.02969	−	4.02028i	0.291584	−	0.129821i
$960$		0			0
$961$	9.33416	−	10.3666i	0.301102	−	0.334407i
$962$	0.213588	−	0.155181i	0.00688637	−	0.00500324i
$963$		0			0
$964$	6.94611	+	21.3779i	0.223719	+	0.688537i
$965$	7.40401	−	1.57377i	0.238344	−	0.0506615i
$966$		0			0
$967$	−2.94103	+	5.09401i	−0.0945771	+	0.163812i	−0.909432	−	0.415853i	$-0.863483\pi$
$967$	−2.94103	+	5.09401i	−0.0945771	+	0.163812i	0.814855	+	0.579665i	$0.196817\pi$
$968$	0.406202	+	15.4109i	0.0130558	+	0.495325i
$969$		0			0
$970$	1.02421	−	9.74475i	0.0328855	−	0.312885i
$971$	5.64280	−	17.3667i	0.181086	−	0.557325i	−0.818773	−	0.574117i	$-0.805345\pi$
$971$	5.64280	−	17.3667i	0.181086	−	0.557325i	0.999859	+	0.0167920i	$0.00534530\pi$
$972$		0			0
$973$	−6.87009	+	4.99141i	−0.220245	+	0.160017i
$974$	−7.97406	−	3.55028i	−0.255505	−	0.113758i
$975$		0			0
$976$	3.72120	+	4.13282i	0.119113	+	0.132288i
$977$	−1.53328	+	0.682658i	−0.0490538	+	0.0218402i	−0.431117	−	0.902296i	$-0.641880\pi$
$977$	−1.53328	+	0.682658i	−0.0490538	+	0.0218402i	0.382063	+	0.924136i	$0.375214\pi$
$978$		0			0
$979$	−4.64287	+	0.798201i	−0.148387	+	0.0255106i
$980$	−3.91125			−0.124940
$981$		0			0
$982$	3.93678	−	12.1162i	0.125628	−	0.386643i
$983$	7.50703	−	8.33740i	0.239437	−	0.265922i	−0.611435	−	0.791295i	$-0.709407\pi$
$983$	7.50703	−	8.33740i	0.239437	−	0.265922i	0.850872	+	0.525373i	$0.176074\pi$
$984$		0			0
$985$	−7.22030	−	68.6966i	−0.230058	−	2.18886i
$986$	2.95847	+	0.628842i	0.0942168	+	0.0200264i
$987$		0			0
$988$	5.05843	−	48.1278i	0.160930	−	1.53115i
$989$	31.9077			1.01461
$990$		0			0
$991$	−7.78978			−0.247451			−0.123725	−	0.992317i	$-0.539484\pi$
$991$	−7.78978			−0.247451			−0.123725	+	0.992317i	$0.539484\pi$
$992$	2.78429	−	26.4908i	0.0884013	−	0.841082i
$993$		0			0
$994$	−10.8707	−	2.31064i	−0.344797	−	0.0732890i
$995$	3.74709	+	35.6511i	0.118791	+	1.13022i
$996$		0			0
$997$	−28.9889	+	32.1954i	−0.918088	+	1.01964i	0.0816479	+	0.996661i	$0.473982\pi$
$997$	−28.9889	+	32.1954i	−0.918088	+	1.01964i	−0.999736	+	0.0229789i	$0.992685\pi$
$998$	−2.54682	+	7.83830i	−0.0806181	+	0.248117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.f.433.2		32
3.2	odd	2		891.2.n.i.433.3		32
9.2	odd	6		891.2.n.i.136.2		32
9.4	even	3		297.2.f.d.136.2	yes	16
9.5	odd	6		297.2.f.a.136.3	✓	16
9.7	even	3	inner	891.2.n.f.136.3		32
11.3	even	5	inner	891.2.n.f.190.3		32
33.14	odd	10		891.2.n.i.190.2		32
99.5	odd	30		3267.2.a.bm.1.3		8
99.14	odd	30		297.2.f.a.190.3	yes	16
99.25	even	15	inner	891.2.n.f.784.2		32
99.47	odd	30		891.2.n.i.784.3		32
99.49	even	15		3267.2.a.be.1.6		8
99.50	even	30		3267.2.a.bf.1.6		8
99.58	even	15		297.2.f.d.190.2	yes	16
99.94	odd	30		3267.2.a.bl.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.136.3	✓	16	9.5	odd	6
297.2.f.a.190.3	yes	16	99.14	odd	30
297.2.f.d.136.2	yes	16	9.4	even	3
297.2.f.d.190.2	yes	16	99.58	even	15
891.2.n.f.136.3		32	9.7	even	3	inner
891.2.n.f.190.3		32	11.3	even	5	inner
891.2.n.f.433.2		32	1.1	even	1	trivial
891.2.n.f.784.2		32	99.25	even	15	inner
891.2.n.i.136.2		32	9.2	odd	6
891.2.n.i.190.2		32	33.14	odd	10
891.2.n.i.433.3		32	3.2	odd	2
891.2.n.i.784.3		32	99.47	odd	30
3267.2.a.be.1.6		8	99.49	even	15
3267.2.a.bf.1.6		8	99.50	even	30
3267.2.a.bl.1.3		8	99.94	odd	30
3267.2.a.bm.1.3		8	99.5	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0378659 + 0.360270i) q^{2} +(1.82793 + 0.388540i) q^{4} +(0.280735 + 2.67101i) q^{5} +(-1.66890 + 1.85350i) q^{7} +(-0.433081 + 1.33288i) q^{8} -0.972914 q^{10} +(3.26867 - 0.561950i) q^{11} +(3.48756 - 1.55276i) q^{13} +(-0.604567 - 0.671439i) q^{14} +(2.95062 + 1.31370i) q^{16} +(-0.909782 + 0.660995i) q^{17} +(2.09612 - 6.45120i) q^{19} +(-0.524629 + 4.99151i) q^{20} +(0.0786824 + 1.19888i) q^{22} +(-3.37470 + 5.84515i) q^{23} +(-2.16475 + 0.460133i) q^{25} +(0.427353 + 1.31526i) q^{26} +(-3.77080 + 2.73965i) q^{28} +(-4.96799 + 5.51751i) q^{29} +(-6.12482 + 2.72695i) q^{31} +(-1.98649 + 3.44070i) q^{32} +(-0.203687 - 0.352796i) q^{34} +(-5.41925 - 3.93732i) q^{35} +(-0.0589927 - 0.181561i) q^{37} +(2.24480 + 0.999449i) q^{38} +(-3.68173 - 0.782576i) q^{40} +(0.425779 + 0.472875i) q^{41} +(-2.36375 - 4.09413i) q^{43} +(6.19326 + 0.242800i) q^{44} +(-1.97805 - 1.43713i) q^{46} +(11.0461 - 2.34792i) q^{47} +(0.0814578 + 0.775019i) q^{49} +(-0.0838015 - 0.797318i) q^{50} +(6.97834 - 1.48329i) q^{52} +(-4.45732 - 3.23843i) q^{53} +(2.41860 + 8.57290i) q^{55} +(-1.74774 - 3.02717i) q^{56} +(-1.79967 - 1.99874i) q^{58} +(-8.24507 - 1.75254i) q^{59} +(1.57297 + 0.700331i) q^{61} +(-0.750514 - 2.30984i) q^{62} +(4.06165 + 2.95096i) q^{64} +(5.12652 + 8.87939i) q^{65} +(-2.25335 + 3.90292i) q^{67} +(-1.91984 + 0.854770i) q^{68} +(1.62370 - 1.80330i) q^{70} +(9.95124 - 7.23000i) q^{71} +(-0.658284 - 2.02599i) q^{73} +(0.0676446 - 0.0143783i) q^{74} +(6.33812 - 10.9779i) q^{76} +(-4.41352 + 6.99633i) q^{77} +(1.21066 - 11.5186i) q^{79} +(-2.68057 + 8.24994i) q^{80} +(-0.186485 + 0.135489i) q^{82} +(-0.747666 - 0.332882i) q^{83} +(-2.02093 - 2.24447i) q^{85} +(1.56449 - 0.696558i) q^{86} +(-0.666583 + 4.60013i) q^{88} -1.42041 q^{89} +(-2.94234 + 9.05560i) q^{91} +(-8.43981 + 9.37336i) q^{92} +(0.427615 + 4.06848i) q^{94} +(17.8197 + 3.78769i) q^{95} +(-1.05273 + 10.0160i) q^{97} -0.282300 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 4 q^{4} - q^{5} + 2 q^{7} + 12 q^{10} - 13 q^{11} + 2 q^{13} + 22 q^{14} + 24 q^{16} - 4 q^{17} - 4 q^{19} - 15 q^{22} - 14 q^{23} + 19 q^{25} + 42 q^{26} + 30 q^{28} - q^{29} - 14 q^{31}+ \cdots + 52 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 + 4 * q^4 - q^5 + 2 * q^7 + 12 * q^10 - 13 * q^11 + 2 * q^13 + 22 * q^14 + 24 * q^16 - 4 * q^17 - 4 * q^19 - 15 * q^22 - 14 * q^23 + 19 * q^25 + 42 * q^26 + 30 * q^28 - q^29 - 14 * q^31 + 48 * q^32 - 10 * q^34 - 36 * q^35 + 18 * q^37 - 11 * q^38 - 33 * q^40 - 25 * q^41 - 14 * q^43 + 28 * q^44 + 8 * q^46 + 28 * q^47 + 4 * q^49 + 63 * q^50 - 10 * q^52 + 2 * q^53 - 80 * q^55 - 96 * q^56 + 20 * q^58 - 41 * q^59 - 10 * q^62 - 184 * q^64 + 60 * q^65 + 48 * q^67 - 25 * q^68 + 31 * q^70 + 6 * q^71 - 26 * q^73 - 29 * q^74 + 58 * q^76 + 2 * q^77 - 166 * q^80 + 82 * q^82 + 14 * q^83 + 10 * q^85 + 56 * q^86 - 86 * q^88 + 164 * q^89 + 28 * q^91 - 74 * q^92 + 2 * q^94 + 56 * q^95 - 12 * q^97 + 52 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more