LMFDB - Embedded newform 405.2.k.b.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(46,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("405.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.k (of order $9$, degree $6$, 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			46.2
Character	$\chi$	$=$	405.46
Dual form			405.2.k.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42971 - 1.19967i) q^{2} +(0.257569 + 1.46075i) q^{4} +(0.939693 + 0.342020i) q^{5} +(0.603654 - 3.42349i) q^{7} +(-0.482190 + 0.835177i) q^{8} +O(q^{10})$	\(q+(-1.42971 - 1.19967i) q^{2} +(0.257569 + 1.46075i) q^{4} +(0.939693 + 0.342020i) q^{5} +(0.603654 - 3.42349i) q^{7} +(-0.482190 + 0.835177i) q^{8} +(-0.933178 - 1.61631i) q^{10} +(3.21914 - 1.17167i) q^{11} +(-2.29137 + 1.92269i) q^{13} +(-4.97011 + 4.17042i) q^{14} +(4.47899 - 1.63022i) q^{16} +(0.915007 + 1.58484i) q^{17} +(2.83150 - 4.90430i) q^{19} +(-0.257569 + 1.46075i) q^{20} +(-6.00805 - 2.18675i) q^{22} +(-1.47679 - 8.37528i) q^{23} +(0.766044 + 0.642788i) q^{25} +5.58258 q^{26} +5.15634 q^{28} +(-2.71852 - 2.28111i) q^{29} +(0.629929 + 3.57251i) q^{31} +(-6.54694 - 2.38289i) q^{32} +(0.593087 - 3.36357i) q^{34} +(1.73815 - 3.01057i) q^{35} +(-4.12531 - 7.14525i) q^{37} +(-9.93177 + 3.61487i) q^{38} +(-0.738757 + 0.619891i) q^{40} +(-3.49560 + 2.93316i) q^{41} +(-6.40168 + 2.33002i) q^{43} +(2.54066 + 4.40056i) q^{44} +(-7.93619 + 13.7459i) q^{46} +(0.749097 - 4.24834i) q^{47} +(-4.77806 - 1.73907i) q^{49} +(-0.324089 - 1.83800i) q^{50} +(-3.39874 - 2.85188i) q^{52} +6.55503 q^{53} +3.42573 q^{55} +(2.56815 + 2.15493i) q^{56} +(1.15012 + 6.52266i) q^{58} +(3.06342 + 1.11500i) q^{59} +(0.589476 - 3.34309i) q^{61} +(3.38521 - 5.86336i) q^{62} +(1.73511 + 3.00530i) q^{64} +(-2.81078 + 1.02304i) q^{65} +(-3.19129 + 2.67781i) q^{67} +(-2.07937 + 1.74480i) q^{68} +(-6.09675 + 2.21903i) q^{70} +(-4.35406 - 7.54146i) q^{71} +(3.97200 - 6.87971i) q^{73} +(-2.67394 + 15.1646i) q^{74} +(7.89326 + 2.87291i) q^{76} +(-2.06796 - 11.7280i) q^{77} +(11.2271 + 9.42064i) q^{79} +4.76644 q^{80} +8.51652 q^{82} +(11.0597 + 9.28016i) q^{83} +(0.317778 + 1.80221i) q^{85} +(11.9478 + 4.34865i) q^{86} +(-0.573682 + 3.25351i) q^{88} +(-1.78804 + 3.09697i) q^{89} +(5.19911 + 9.00512i) q^{91} +(11.8538 - 4.31443i) q^{92} +(-6.16760 + 5.17523i) q^{94} +(4.33811 - 3.64011i) q^{95} +(3.43991 - 1.25203i) q^{97} +(4.74493 + 8.21846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 9 q^{8}+O(q^{10}) $ 42 * q + 9 * q^8	$ 42 q + 9 q^{8} - 3 q^{10} + 6 q^{11} - 3 q^{13} + 27 q^{14} - 12 q^{16} + 12 q^{17} - 24 q^{19} + 33 q^{22} - 18 q^{23} + 18 q^{26} + 60 q^{28} - 12 q^{31} - 36 q^{32} + 51 q^{34} + 12 q^{35} - 24 q^{37} + 24 q^{38} - 9 q^{40} - 33 q^{41} - 24 q^{43} - 12 q^{44} - 30 q^{46} - 27 q^{47} + 18 q^{49} - 84 q^{52} - 36 q^{53} + 24 q^{56} - 81 q^{58} + 27 q^{59} - 6 q^{61} + 18 q^{62} - 63 q^{64} - 6 q^{65} + 12 q^{67} + 3 q^{68} + 9 q^{70} - 12 q^{71} - 39 q^{73} + 72 q^{74} + 138 q^{76} + 54 q^{77} - 18 q^{79} - 78 q^{80} + 48 q^{82} - 57 q^{83} + 9 q^{85} - 18 q^{86} + 126 q^{88} - 9 q^{89} - 69 q^{91} - 24 q^{92} - 33 q^{94} - 3 q^{95} + 21 q^{97} + 15 q^{98}+O(q^{100}) $ 42 * q + 9 * q^8 - 3 * q^10 + 6 * q^11 - 3 * q^13 + 27 * q^14 - 12 * q^16 + 12 * q^17 - 24 * q^19 + 33 * q^22 - 18 * q^23 + 18 * q^26 + 60 * q^28 - 12 * q^31 - 36 * q^32 + 51 * q^34 + 12 * q^35 - 24 * q^37 + 24 * q^38 - 9 * q^40 - 33 * q^41 - 24 * q^43 - 12 * q^44 - 30 * q^46 - 27 * q^47 + 18 * q^49 - 84 * q^52 - 36 * q^53 + 24 * q^56 - 81 * q^58 + 27 * q^59 - 6 * q^61 + 18 * q^62 - 63 * q^64 - 6 * q^65 + 12 * q^67 + 3 * q^68 + 9 * q^70 - 12 * q^71 - 39 * q^73 + 72 * q^74 + 138 * q^76 + 54 * q^77 - 18 * q^79 - 78 * q^80 + 48 * q^82 - 57 * q^83 + 9 * q^85 - 18 * q^86 + 126 * q^88 - 9 * q^89 - 69 * q^91 - 24 * q^92 - 33 * q^94 - 3 * q^95 + 21 * q^97 + 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−1.42971	−	1.19967i	−1.01096	−	0.848295i	−0.0224938	−	0.999747i	$-0.507161\pi$
$2$	−1.42971	−	1.19967i	−1.01096	−	0.848295i	−0.988465	+	0.151452i	$0.951605\pi$
$3$		0			0
$3$		0			0
$4$	0.257569	+	1.46075i	0.128785	+	0.730374i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$		0			0
$7$	0.603654	−	3.42349i	0.228160	−	1.29396i	−0.628392	−	0.777897i	$-0.716286\pi$
$7$	0.603654	−	3.42349i	0.228160	−	1.29396i	0.856552	−	0.516062i	$-0.172602\pi$
$8$	−0.482190	+	0.835177i	−0.170480	+	0.295280i
$9$		0			0
$10$	−0.933178	−	1.61631i	−0.295097	−	0.511122i
$11$	3.21914	−	1.17167i	0.970606	−	0.353272i	0.192425	−	0.981312i	$-0.438365\pi$
$11$	3.21914	−	1.17167i	0.970606	−	0.353272i	0.778181	+	0.628040i	$0.216143\pi$
$12$		0			0
$13$	−2.29137	+	1.92269i	−0.635511	+	0.533257i	−0.902636	−	0.430405i	$-0.858371\pi$
$13$	−2.29137	+	1.92269i	−0.635511	+	0.533257i	0.267125	+	0.963662i	$0.413926\pi$
$14$	−4.97011	+	4.17042i	−1.32832	+	1.11459i
$15$		0			0
$16$	4.47899	−	1.63022i	1.11975	−	0.407554i
$17$	0.915007	+	1.58484i	0.221922	+	0.384380i	0.955391	−	0.295342i	$-0.0954337\pi$
$17$	0.915007	+	1.58484i	0.221922	+	0.384380i	−0.733470	+	0.679722i	$0.762100\pi$
$18$		0			0
$19$	2.83150	−	4.90430i	0.649591	−	1.12512i	−0.333630	−	0.942704i	$-0.608274\pi$
$19$	2.83150	−	4.90430i	0.649591	−	1.12512i	0.983221	−	0.182420i	$-0.0583931\pi$
$20$	−0.257569	+	1.46075i	−0.0575942	+	0.326633i
$21$		0			0
$22$	−6.00805	−	2.18675i	−1.28092	−	0.466217i
$23$	−1.47679	−	8.37528i	−0.307931	−	1.74637i	−0.609375	−	0.792882i	$-0.708580\pi$
$23$	−1.47679	−	8.37528i	−0.307931	−	1.74637i	0.301444	−	0.953484i	$-0.402532\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	5.58258			1.09483
$27$		0			0
$28$	5.15634			0.974457
$29$	−2.71852	−	2.28111i	−0.504817	−	0.423592i	0.354484	−	0.935062i	$-0.384657\pi$
$29$	−2.71852	−	2.28111i	−0.504817	−	0.423592i	−0.859301	+	0.511470i	$0.829101\pi$
$30$		0			0
$31$	0.629929	+	3.57251i	0.113139	+	0.641641i	0.987655	+	0.156645i	$0.0500679\pi$
$31$	0.629929	+	3.57251i	0.113139	+	0.641641i	−0.874516	+	0.484996i	$0.838821\pi$
$32$	−6.54694	−	2.38289i	−1.15735	−	0.421240i
$33$		0			0
$34$	0.593087	−	3.36357i	0.101714	−	0.576847i
$35$	1.73815	−	3.01057i	0.293801	−	0.508879i
$36$		0			0
$37$	−4.12531	−	7.14525i	−0.678197	−	1.17467i	−0.975523	−	0.219895i	$-0.929428\pi$
$37$	−4.12531	−	7.14525i	−0.678197	−	1.17467i	0.297327	−	0.954776i	$-0.403905\pi$
$38$	−9.93177	+	3.61487i	−1.61115	+	0.586409i
$39$		0			0
$40$	−0.738757	+	0.619891i	−0.116808	+	0.0980134i
$41$	−3.49560	+	2.93316i	−0.545921	+	0.458082i	−0.873557	−	0.486722i	$-0.838192\pi$
$41$	−3.49560	+	2.93316i	−0.545921	+	0.458082i	0.327636	+	0.944804i	$0.393748\pi$
$42$		0			0
$43$	−6.40168	+	2.33002i	−0.976247	+	0.355325i	−0.780380	−	0.625306i	$-0.784974\pi$
$43$	−6.40168	+	2.33002i	−0.976247	+	0.355325i	−0.195867	+	0.980630i	$0.562752\pi$
$44$	2.54066	+	4.40056i	0.383019	+	0.663409i
$45$		0			0
$46$	−7.93619	+	13.7459i	−1.17013	+	2.02672i
$47$	0.749097	−	4.24834i	0.109267	−	0.619684i	−0.880163	−	0.474672i	$-0.842567\pi$
$47$	0.749097	−	4.24834i	0.109267	−	0.619684i	0.989430	−	0.145012i	$-0.0463222\pi$
$48$		0			0
$49$	−4.77806	−	1.73907i	−0.682579	−	0.248439i
$50$	−0.324089	−	1.83800i	−0.0458331	−	0.259933i
$51$		0			0
$52$	−3.39874	−	2.85188i	−0.471321	−	0.395485i
$53$	6.55503			0.900403			0.450201	−	0.892927i	$-0.351352\pi$
$53$	6.55503			0.900403			0.450201	+	0.892927i	$0.351352\pi$
$54$		0			0
$55$	3.42573			0.461926
$56$	2.56815	+	2.15493i	0.343183	+	0.287965i
$57$		0			0
$58$	1.15012	+	6.52266i	0.151018	+	0.856467i
$59$	3.06342	+	1.11500i	0.398824	+	0.145160i	0.533642	−	0.845710i	$-0.320823\pi$
$59$	3.06342	+	1.11500i	0.398824	+	0.145160i	−0.134818	+	0.990870i	$0.543045\pi$
$60$		0			0
$61$	0.589476	−	3.34309i	0.0754747	−	0.428038i	−0.923534	−	0.383517i	$-0.874713\pi$
$61$	0.589476	−	3.34309i	0.0754747	−	0.428038i	0.999008	−	0.0445212i	$-0.0141762\pi$
$62$	3.38521	−	5.86336i	0.429922	−	0.744648i
$63$		0			0
$64$	1.73511	+	3.00530i	0.216889	+	0.375663i
$65$	−2.81078	+	1.02304i	−0.348634	+	0.126892i
$66$		0			0
$67$	−3.19129	+	2.67781i	−0.389878	+	0.327146i	−0.816566	−	0.577253i	$-0.804125\pi$
$67$	−3.19129	+	2.67781i	−0.389878	+	0.327146i	0.426688	+	0.904399i	$0.359680\pi$
$68$	−2.07937	+	1.74480i	−0.252161	+	0.211588i
$69$		0			0
$70$	−6.09675	+	2.21903i	−0.728701	+	0.265225i
$71$	−4.35406	−	7.54146i	−0.516732	−	0.895007i	−0.999811	−	0.0194298i	$-0.993815\pi$
$71$	−4.35406	−	7.54146i	−0.516732	−	0.895007i	0.483079	−	0.875577i	$-0.339518\pi$
$72$		0			0
$73$	3.97200	−	6.87971i	0.464888	−	0.805210i	−0.534309	−	0.845290i	$-0.679428\pi$
$73$	3.97200	−	6.87971i	0.464888	−	0.805210i	0.999196	+	0.0400800i	$0.0127613\pi$
$74$	−2.67394	+	15.1646i	−0.310839	+	1.76285i
$75$		0			0
$76$	7.89326	+	2.87291i	0.905419	+	0.329545i
$77$	−2.06796	−	11.7280i	−0.235666	−	1.33653i
$78$		0			0
$79$	11.2271	+	9.42064i	1.26315	+	1.05990i	0.995340	+	0.0964321i	$0.0307431\pi$
$79$	11.2271	+	9.42064i	1.26315	+	1.05990i	0.267806	+	0.963473i	$0.413701\pi$
$80$	4.76644			0.532904
$81$		0			0
$82$	8.51652			0.940492
$83$	11.0597	+	9.28016i	1.21396	+	1.01863i	0.999118	+	0.0419799i	$0.0133665\pi$
$83$	11.0597	+	9.28016i	1.21396	+	1.01863i	0.214837	+	0.976650i	$0.431078\pi$
$84$		0			0
$85$	0.317778	+	1.80221i	0.0344679	+	0.195477i
$86$	11.9478	+	4.34865i	1.28837	+	0.468927i
$87$		0			0
$88$	−0.573682	+	3.25351i	−0.0611547	+	0.346826i
$89$	−1.78804	+	3.09697i	−0.189531	+	0.328278i	−0.945094	−	0.326798i	$-0.894030\pi$
$89$	−1.78804	+	3.09697i	−0.189531	+	0.328278i	0.755563	+	0.655076i	$0.227364\pi$
$90$		0			0
$91$	5.19911	+	9.00512i	0.545014	+	0.943993i
$92$	11.8538	−	4.31443i	1.23584	−	0.449810i
$93$		0			0
$94$	−6.16760	+	5.17523i	−0.636139	+	0.533784i
$95$	4.33811	−	3.64011i	0.445081	−	0.373467i
$96$		0			0
$97$	3.43991	−	1.25203i	0.349270	−	0.127124i	−0.161427	−	0.986885i	$-0.551610\pi$
$97$	3.43991	−	1.25203i	0.349270	−	0.127124i	0.510697	+	0.859761i	$0.329387\pi$
$98$	4.74493	+	8.21846i	0.479310	+	0.830190i
$99$		0			0
$100$	−0.741641	+	1.28456i	−0.0741641	+	0.128456i
$101$	−0.0680401	+	0.385875i	−0.00677025	+	0.0383960i	−0.988006	−	0.154417i	$-0.950650\pi$
$101$	−0.0680401	+	0.385875i	−0.00677025	+	0.0383960i	0.981235	+	0.192813i	$0.0617611\pi$
$102$		0			0
$103$	15.4578	+	5.62618i	1.52310	+	0.554364i	0.961920	−	0.273330i	$-0.0881249\pi$
$103$	15.4578	+	5.62618i	1.52310	+	0.554364i	0.561181	+	0.827693i	$0.310347\pi$
$104$	−0.500909	−	2.84080i	−0.0491182	−	0.278563i
$105$		0			0
$106$	−9.37180	−	7.86388i	−0.910270	−	0.763807i
$107$	−12.6842			−1.22623			−0.613113	−	0.789995i	$-0.710083\pi$
$107$	−12.6842			−1.22623			−0.613113	+	0.789995i	$0.710083\pi$
$108$		0			0
$109$	14.0464			1.34540			0.672701	−	0.739914i	$-0.265134\pi$
$109$	14.0464			1.34540			0.672701	+	0.739914i	$0.265134\pi$
$110$	−4.89781	−	4.10975i	−0.466988	−	0.391849i
$111$		0			0
$112$	−2.87728	−	16.3179i	−0.271877	−	1.54189i
$113$	7.00413	+	2.54930i	0.658893	+	0.239818i	0.649758	−	0.760141i	$-0.274870\pi$
$113$	7.00413	+	2.54930i	0.658893	+	0.239818i	0.00913486	+	0.999958i	$0.497092\pi$
$114$		0			0
$115$	1.47679	−	8.37528i	0.137711	−	0.780999i
$116$	2.63192	−	4.55862i	0.244368	−	0.423257i
$117$		0			0
$118$	−3.04218	−	5.26922i	−0.280056	−	0.485071i
$119$	5.97803	−	2.17582i	0.548005	−	0.199457i
$120$		0			0
$121$	0.563534	−	0.472862i	0.0512304	−	0.0429874i
$122$	−4.85338	+	4.07247i	−0.439405	+	0.368704i
$123$		0			0
$124$	−5.05628	+	1.84034i	−0.454067	+	0.165267i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	−6.42637	+	11.1308i	−0.570248	+	0.987699i	0.426292	+	0.904586i	$0.359820\pi$
$127$	−6.42637	+	11.1308i	−0.570248	+	0.987699i	−0.996540	+	0.0831130i	$0.973514\pi$
$128$	−1.29499	+	7.34425i	−0.114462	+	0.649146i
$129$		0			0
$130$	5.24591	+	1.90936i	0.460097	+	0.167462i
$131$	3.04490	+	17.2685i	0.266034	+	1.50876i	0.766074	+	0.642753i	$0.222208\pi$
$131$	3.04490	+	17.2685i	0.266034	+	1.50876i	−0.500040	+	0.866003i	$0.666681\pi$
$132$		0			0
$133$	−15.0806	−	12.6541i	−1.30765	−	1.09725i
$134$	7.77510			0.671667
$135$		0			0
$136$	−1.76483			−0.151333
$137$	7.61384	+	6.38877i	0.650495	+	0.545830i	0.907221	−	0.420654i	$-0.138199\pi$
$137$	7.61384	+	6.38877i	0.650495	+	0.545830i	−0.256726	+	0.966484i	$0.582644\pi$
$138$		0			0
$139$	0.556612	+	3.15670i	0.0472112	+	0.267748i	0.999272	−	0.0381621i	$-0.0121503\pi$
$139$	0.556612	+	3.15670i	0.0472112	+	0.267748i	−0.952060	+	0.305910i	$0.901039\pi$
$140$	4.84538	+	1.76357i	0.409509	+	0.149049i
$141$		0			0
$142$	−2.82221	+	16.0055i	−0.236835	+	1.34316i
$143$	−5.12347	+	8.87411i	−0.428446	+	0.742090i
$144$		0			0
$145$	−1.77439	−	3.07333i	−0.147355	−	0.255226i
$146$	−13.9322	+	5.07091i	−1.15304	+	0.419671i
$147$		0			0
$148$	9.37485	−	7.86643i	0.770608	−	0.646617i
$149$	−0.773640	+	0.649161i	−0.0633790	+	0.0531813i	−0.673927	−	0.738798i	$-0.735394\pi$
$149$	−0.773640	+	0.649161i	−0.0633790	+	0.0531813i	0.610548	+	0.791979i	$0.290949\pi$
$150$		0			0
$151$	11.1642	−	4.06345i	0.908533	−	0.330679i	0.154866	−	0.987936i	$-0.450505\pi$
$151$	11.1642	−	4.06345i	0.908533	−	0.330679i	0.753667	+	0.657257i	$0.228283\pi$
$152$	2.73064	+	4.72961i	0.221484	+	0.383622i
$153$		0			0
$154$	−11.1131	+	19.2485i	−0.895520	+	1.55109i
$155$	−0.629929	+	3.57251i	−0.0505971	+	0.286951i
$156$		0			0
$157$	−18.3957	−	6.69550i	−1.46814	−	0.534359i	−0.520545	−	0.853834i	$-0.674271\pi$
$157$	−18.3957	−	6.69550i	−1.46814	−	0.534359i	−0.947595	+	0.319475i	$0.896493\pi$
$158$	−4.74982	−	26.9376i	−0.377876	−	2.14304i
$159$		0			0
$160$	−5.33712	−	4.47837i	−0.421936	−	0.354046i
$161$	−29.5642			−2.32998
$162$		0			0
$163$	9.26458			0.725658			0.362829	−	0.931856i	$-0.381811\pi$
$163$	9.26458			0.725658			0.362829	+	0.931856i	$0.381811\pi$
$164$	−5.18496	−	4.35070i	−0.404877	−	0.339732i
$165$		0			0
$166$	−4.67899	−	26.5359i	−0.363160	−	2.05958i
$167$	9.58151	+	3.48738i	0.741439	+	0.269862i	0.684999	−	0.728544i	$-0.259803\pi$
$167$	9.58151	+	3.48738i	0.741439	+	0.269862i	0.0564405	+	0.998406i	$0.482025\pi$
$168$		0			0
$169$	−0.703782	+	3.99135i	−0.0541371	+	0.307027i
$170$	1.70773	−	2.95787i	0.130977	−	0.226858i
$171$		0			0
$172$	−5.05245	−	8.75110i	−0.385246	−	0.667265i
$173$	−10.6251	+	3.86724i	−0.807815	+	0.294021i	−0.712721	−	0.701448i	$-0.752537\pi$
$173$	−10.6251	+	3.86724i	−0.807815	+	0.294021i	−0.0950941	+	0.995468i	$0.530315\pi$
$174$		0			0
$175$	2.66300	−	2.23453i	0.201304	−	0.168914i
$176$	12.5084	−	10.4958i	0.942855	−	0.791150i
$177$		0			0
$178$	6.27171	−	2.28272i	0.470085	−	0.171097i
$179$	−12.0316	−	20.8394i	−0.899285	−	1.55761i	−0.828410	−	0.560122i	$-0.810754\pi$
$179$	−12.0316	−	20.8394i	−0.899285	−	1.55761i	−0.0708754	−	0.997485i	$-0.522579\pi$
$180$		0			0
$181$	−4.60686	+	7.97931i	−0.342425	+	0.593098i	−0.984882	−	0.173224i	$-0.944582\pi$
$181$	−4.60686	+	7.97931i	−0.342425	+	0.593098i	0.642457	+	0.766321i	$0.277915\pi$
$182$	3.36995	−	19.1119i	0.249797	−	1.41667i
$183$		0			0
$184$	7.70693	+	2.80509i	0.568162	+	0.206794i
$185$	−1.43270	−	8.12527i	−0.105335	−	0.597382i
$186$		0			0
$187$	4.80244	+	4.02972i	0.351189	+	0.294682i
$188$	6.39870			0.466673
$189$		0			0
$190$	−10.5692			−0.766768
$191$	1.50137	+	1.25980i	0.108635	+	0.0911559i	0.695487	−	0.718538i	$-0.255189\pi$
$191$	1.50137	+	1.25980i	0.108635	+	0.0911559i	−0.586852	+	0.809694i	$0.699633\pi$
$192$		0			0
$193$	1.83340	+	10.3977i	0.131971	+	0.748446i	0.976921	+	0.213601i	$0.0685191\pi$
$193$	1.83340	+	10.3977i	0.131971	+	0.748446i	−0.844950	+	0.534846i	$0.820370\pi$
$194$	−6.42010	−	2.33673i	−0.460937	−	0.167767i
$195$		0			0
$196$	1.30966	−	7.42747i	0.0935473	−	0.530533i
$197$	−0.984623	+	1.70542i	−0.0701515	+	0.121506i	−0.898968	−	0.438015i	$-0.855682\pi$
$197$	−0.984623	+	1.70542i	−0.0701515	+	0.121506i	0.828816	+	0.559521i	$0.189015\pi$
$198$		0			0
$199$	−7.27018	−	12.5923i	−0.515369	−	0.892646i	−0.999841	−	0.0178388i	$-0.994321\pi$
$199$	−7.27018	−	12.5923i	−0.515369	−	0.892646i	0.484472	−	0.874807i	$-0.339012\pi$
$200$	−0.906220	+	0.329837i	−0.0640794	+	0.0233230i
$201$		0			0
$202$	0.560200	−	0.470064i	0.0394155	−	0.0330736i
$203$	−9.45041	+	7.92984i	−0.663289	+	0.556565i
$204$		0			0
$205$	−4.28799	+	1.56070i	−0.299486	+	0.109004i
$206$	−15.3506	−	26.5881i	−1.06953	−	1.85248i
$207$		0			0
$208$	−7.12861	+	12.3471i	−0.494280	+	0.856118i
$209$	3.36876	−	19.1052i	0.233022	−	1.32153i
$210$		0			0
$211$	−11.3530	−	4.13217i	−0.781575	−	0.284470i	−0.0797459	−	0.996815i	$-0.525411\pi$
$211$	−11.3530	−	4.13217i	−0.781575	−	0.284470i	−0.701829	+	0.712345i	$0.747633\pi$
$212$	1.68837	+	9.57525i	0.115958	+	0.657631i
$213$		0			0
$214$	18.1347	+	15.2168i	1.23966	+	1.04020i
$215$	−6.81253			−0.464610
$216$		0			0
$217$	12.6107			0.856071
$218$	−20.0823	−	16.8511i	−1.36015	−	1.14130i
$219$		0			0
$220$	0.882363	+	5.00413i	0.0594889	+	0.337378i
$221$	−5.14376	−	1.87218i	−0.346007	−	0.125936i
$222$		0			0
$223$	−3.61394	+	20.4957i	−0.242007	+	1.37249i	0.585334	+	0.810792i	$0.300963\pi$
$223$	−3.61394	+	20.4957i	−0.242007	+	1.37249i	−0.827342	+	0.561699i	$0.810148\pi$
$224$	−12.1099	+	20.9750i	−0.809127	+	1.40145i
$225$		0			0
$226$	−6.95557	−	12.0474i	−0.462678	−	0.801381i
$227$	8.01519	−	2.91729i	0.531987	−	0.193627i	−0.0620383	−	0.998074i	$-0.519760\pi$
$227$	8.01519	−	2.91729i	0.531987	−	0.193627i	0.594025	+	0.804446i	$0.297538\pi$
$228$		0			0
$229$	12.0900	−	10.1447i	0.798931	−	0.670383i	−0.149008	−	0.988836i	$-0.547608\pi$
$229$	12.0900	−	10.1447i	0.798931	−	0.670383i	0.947938	+	0.318453i	$0.103163\pi$
$230$	−12.1589	+	10.2026i	−0.801737	+	0.672738i
$231$		0			0
$232$	3.21597	−	1.17052i	0.211139	−	0.0768483i
$233$	9.08918	+	15.7429i	0.595452	+	1.03135i	0.993483	+	0.113981i	$0.0363603\pi$
$233$	9.08918	+	15.7429i	0.595452	+	1.03135i	−0.398031	+	0.917372i	$0.630306\pi$
$234$		0			0
$235$	2.15694	−	3.73593i	0.140703	−	0.243705i
$236$	−0.839683	+	4.76208i	−0.0546587	+	0.309985i
$237$		0			0
$238$	−11.1571	−	4.06086i	−0.723209	−	0.263227i
$239$	2.15258	+	12.2079i	0.139239	+	0.789663i	0.971814	+	0.235750i	$0.0757547\pi$
$239$	2.15258	+	12.2079i	0.139239	+	0.789663i	−0.832575	+	0.553913i	$0.813134\pi$
$240$		0			0
$241$	−6.87075	−	5.76524i	−0.442584	−	0.371372i	0.394091	−	0.919071i	$-0.371059\pi$
$241$	−6.87075	−	5.76524i	−0.442584	−	0.371372i	−0.836675	+	0.547699i	$0.815504\pi$
$242$	−1.37297			−0.0882578
$243$		0			0
$244$	5.03524			0.322348
$245$	−3.89511	−	3.26838i	−0.248849	−	0.208809i
$246$		0			0
$247$	2.94142	+	16.6816i	0.187158	+	1.06143i
$248$	−3.28742	−	1.19652i	−0.208751	−	0.0759793i
$249$		0			0
$250$	0.324089	−	1.83800i	0.0204972	−	0.116245i
$251$	5.89181	−	10.2049i	0.371888	−	0.644129i	−0.617968	−	0.786203i	$-0.712044\pi$
$251$	5.89181	−	10.2049i	0.371888	−	0.644129i	0.989856	+	0.142074i	$0.0453772\pi$
$252$		0			0
$253$	−14.5670	−	25.2308i	−0.915822	−	1.58625i
$254$	22.5411	−	8.20430i	1.41436	−	0.514784i
$255$		0			0
$256$	15.9788	−	13.4078i	0.998677	−	0.837989i
$257$	7.83057	−	6.57063i	0.488458	−	0.409865i	−0.365015	−	0.931001i	$-0.618936\pi$
$257$	7.83057	−	6.57063i	0.488458	−	0.409865i	0.853473	+	0.521137i	$0.174492\pi$
$258$		0			0
$259$	−26.9520	+	9.80971i	−1.67471	+	0.609546i
$260$	−2.21837	−	3.84233i	−0.137578	−	0.238291i
$261$		0			0
$262$	16.3632	−	28.3418i	1.01092	−	1.75096i
$263$	3.97496	−	22.5431i	0.245107	−	1.39007i	−0.575138	−	0.818056i	$-0.695052\pi$
$263$	3.97496	−	22.5431i	0.245107	−	1.39007i	0.820245	−	0.572013i	$-0.193837\pi$
$264$		0			0
$265$	6.15972	+	2.24195i	0.378388	+	0.137722i
$266$	6.38013	+	36.1835i	0.391191	+	2.21855i
$267$		0			0
$268$	−4.73358	−	3.97194i	−0.289149	−	0.242625i
$269$	−0.457689			−0.0279058			−0.0139529	−	0.999903i	$-0.504441\pi$
$269$	−0.457689			−0.0279058			−0.0139529	+	0.999903i	$0.504441\pi$
$270$		0			0
$271$	−24.7898			−1.50588			−0.752938	−	0.658092i	$-0.771364\pi$
$271$	−24.7898			−1.50588			−0.752938	+	0.658092i	$0.771364\pi$
$272$	6.68193	+	5.60681i	0.405152	+	0.339963i
$273$		0			0
$274$	−3.22118	−	18.2682i	−0.194598	−	1.10362i
$275$	3.21914	+	1.17167i	0.194121	+	0.0706543i
$276$		0			0
$277$	−1.06913	+	6.06336i	−0.0642381	+	0.364312i	0.935696	+	0.352808i	$0.114773\pi$
$277$	−1.06913	+	6.06336i	−0.0642381	+	0.364312i	−0.999934	+	0.0115042i	$0.996338\pi$
$278$	2.99121	−	5.18093i	0.179401	−	0.310731i
$279$		0			0
$280$	1.67624	+	2.90333i	0.100174	+	0.173507i
$281$	−17.0698	+	6.21288i	−1.01830	+	0.370629i	−0.796613	−	0.604489i	$-0.793377\pi$
$281$	−17.0698	+	6.21288i	−1.01830	+	0.370629i	−0.221683	+	0.975119i	$0.571155\pi$
$282$		0			0
$283$	−5.38619	+	4.51955i	−0.320176	+	0.268659i	−0.788683	−	0.614800i	$-0.789237\pi$
$283$	−5.38619	+	4.51955i	−0.320176	+	0.268659i	0.468507	+	0.883460i	$0.344792\pi$
$284$	9.89470	−	8.30264i	0.587142	−	0.492671i
$285$		0			0
$286$	17.9711	−	6.54094i	1.06265	−	0.386774i
$287$	7.93150	+	13.7378i	0.468182	+	0.810915i
$288$		0			0
$289$	6.82553	−	11.8222i	0.401502	−	0.695421i
$290$	−1.15012	+	6.52266i	−0.0675374	+	0.383024i
$291$		0			0
$292$	11.0726	+	4.03009i	0.647974	+	0.235843i
$293$	4.12441	+	23.3907i	0.240951	+	1.36650i	0.829712	+	0.558192i	$0.188505\pi$
$293$	4.12441	+	23.3907i	0.240951	+	1.36650i	−0.588761	+	0.808307i	$0.700384\pi$
$294$		0			0
$295$	2.49733	+	2.09551i	0.145400	+	0.122005i
$296$	7.95672			0.462475
$297$		0			0
$298$	1.88486			0.109187
$299$	19.4869	+	16.3514i	1.12696	+	0.945628i
$300$		0			0
$301$	4.11241	+	23.3226i	0.237035	+	1.34429i
$302$	−20.8364	−	7.58384i	−1.19900	−	0.436401i
$303$		0			0
$304$	4.68717	−	26.5823i	0.268828	−	1.52460i
$305$	1.69733	−	2.93986i	0.0971888	−	0.168336i
$306$		0			0
$307$	9.31264	+	16.1300i	0.531500	+	0.920585i	0.999324	+	0.0367637i	$0.0117049\pi$
$307$	9.31264	+	16.1300i	0.531500	+	0.920585i	−0.467824	+	0.883822i	$0.654962\pi$
$308$	16.5990	−	6.04153i	0.945814	−	0.344248i
$309$		0			0
$310$	5.18645	−	4.35195i	0.294570	−	0.247174i
$311$	−1.48464	+	1.24576i	−0.0841860	+	0.0706404i	−0.683909	−	0.729567i	$-0.739722\pi$
$311$	−1.48464	+	1.24576i	−0.0841860	+	0.0706404i	0.599724	+	0.800207i	$0.295277\pi$
$312$		0			0
$313$	28.4277	−	10.3468i	1.60683	−	0.584838i	0.626021	−	0.779806i	$-0.284683\pi$
$313$	28.4277	−	10.3468i	1.60683	−	0.584838i	0.980810	+	0.194968i	$0.0624603\pi$
$314$	18.2682	+	31.6414i	1.03093	+	1.78563i
$315$		0			0
$316$	−10.8694	+	18.8264i	−0.611453	+	1.05907i
$317$	−0.508892	+	2.88607i	−0.0285822	+	0.162098i	−0.995758	−	0.0920102i	$-0.970671\pi$
$317$	−0.508892	+	2.88607i	−0.0285822	+	0.162098i	0.967176	+	0.254108i	$0.0817819\pi$
$318$		0			0
$319$	−11.4240	−	4.15799i	−0.639621	−	0.232803i
$320$	0.602598	+	3.41750i	0.0336863	+	0.191044i
$321$		0			0
$322$	42.2682	+	35.4673i	2.35552	+	1.97651i
$323$	10.3634			0.576633
$324$		0			0
$325$	−2.99117			−0.165920
$326$	−13.2457	−	11.1144i	−0.733610	−	0.615572i
$327$		0			0
$328$	−0.764162	−	4.33378i	−0.0421938	−	0.239293i
$329$	−14.0920	−	5.12906i	−0.776915	−	0.282774i
$330$		0			0
$331$	−1.87857	+	10.6539i	−0.103255	+	0.585590i	0.888648	+	0.458591i	$0.151646\pi$
$331$	−1.87857	+	10.6539i	−0.103255	+	0.585590i	−0.991903	+	0.126999i	$0.959465\pi$
$332$	−10.7073	+	18.5457i	−0.587642	+	1.01783i
$333$		0			0
$334$	−9.51508	−	16.4806i	−0.520642	−	0.901778i
$335$	−3.91469	+	1.42483i	−0.213883	+	0.0778469i
$336$		0			0
$337$	−10.4808	+	8.79442i	−0.570925	+	0.479063i	−0.881953	−	0.471338i	$-0.843771\pi$
$337$	−10.4808	+	8.79442i	−0.570925	+	0.479063i	0.311028	+	0.950401i	$0.399327\pi$
$338$	5.79450	−	4.86216i	0.315179	−	0.264467i
$339$		0			0
$340$	−2.55073	+	0.928388i	−0.138333	+	0.0503489i
$341$	6.21363	+	10.7623i	0.336487	+	0.582812i
$342$		0			0
$343$	3.32908	−	5.76614i	0.179754	−	0.311342i
$344$	1.14084	−	6.47005i	0.0615102	−	0.348842i
$345$		0			0
$346$	19.8303	+	7.21764i	1.06608	+	0.388023i
$347$	3.12373	+	17.7155i	0.167691	+	0.951020i	0.946247	+	0.323445i	$0.104841\pi$
$347$	3.12373	+	17.7155i	0.167691	+	0.951020i	−0.778556	+	0.627575i	$0.784048\pi$
$348$		0			0
$349$	2.87063	+	2.40875i	0.153661	+	0.128937i	0.716377	−	0.697713i	$-0.245799\pi$
$349$	2.87063	+	2.40875i	0.153661	+	0.128937i	−0.562716	+	0.826650i	$0.690243\pi$
$350$	−6.48802			−0.346799
$351$		0			0
$352$	−23.8675			−1.27214
$353$	0.250470	+	0.210170i	0.0133312	+	0.0111862i	0.649429	−	0.760422i	$-0.275008\pi$
$353$	0.250470	+	0.210170i	0.0133312	+	0.0111862i	−0.636098	+	0.771609i	$0.719452\pi$
$354$		0			0
$355$	−1.51215	−	8.57583i	−0.0802566	−	0.455158i
$356$	−4.98443	−	1.81418i	−0.264174	−	0.0961516i
$357$		0			0
$358$	−7.79863	+	44.2282i	−0.412171	+	2.33754i
$359$	−3.20577	+	5.55255i	−0.169194	+	0.293053i	−0.938137	−	0.346265i	$-0.887450\pi$
$359$	−3.20577	+	5.55255i	−0.169194	+	0.293053i	0.768943	+	0.639318i	$0.220783\pi$
$360$		0			0
$361$	−6.53480	−	11.3186i	−0.343937	−	0.595716i
$362$	16.1590	−	5.88140i	0.849299	−	0.309120i
$363$		0			0
$364$	−11.8151	+	9.91402i	−0.619278	+	0.519636i
$365$	6.08546	−	5.10631i	0.318528	−	0.267277i
$366$		0			0
$367$	7.66491	−	2.78980i	0.400105	−	0.145626i	−0.134127	−	0.990964i	$-0.542823\pi$
$367$	7.66491	−	2.78980i	0.400105	−	0.145626i	0.534232	+	0.845338i	$0.320601\pi$
$368$	−20.2680	−	35.1053i	−1.05654	−	1.82999i
$369$		0			0
$370$	−7.69929	+	13.3356i	−0.400267	+	0.693283i
$371$	3.95697	−	22.4411i	0.205436	−	1.16508i
$372$		0			0
$373$	−0.786850	−	0.286390i	−0.0407415	−	0.0148287i	0.321569	−	0.946886i	$-0.395790\pi$
$373$	−0.786850	−	0.286390i	−0.0407415	−	0.0148287i	−0.362311	+	0.932057i	$0.618012\pi$
$374$	−2.03176	−	11.5227i	−0.105060	−	0.595823i
$375$		0			0
$376$	3.18691	+	2.67413i	0.164352	+	0.137908i
$377$	10.6150			0.546700
$378$		0			0
$379$	−7.38310			−0.379245			−0.189622	−	0.981857i	$-0.560726\pi$
$379$	−7.38310			−0.379245			−0.189622	+	0.981857i	$0.560726\pi$
$380$	6.43464	+	5.39931i	0.330090	+	0.276979i
$381$		0			0
$382$	−0.635182	−	3.60230i	−0.0324988	−	0.184310i
$383$	16.1122	+	5.86435i	0.823293	+	0.299654i	0.719103	−	0.694903i	$-0.244553\pi$
$383$	16.1122	+	5.86435i	0.823293	+	0.299654i	0.104190	+	0.994557i	$0.466775\pi$
$384$		0			0
$385$	2.06796	−	11.7280i	0.105393	−	0.597713i
$386$	9.85263	−	17.0653i	0.501486	−	0.868599i
$387$		0			0
$388$	2.71491	+	4.70236i	0.137829	+	0.238726i
$389$	−6.10545	+	2.22220i	−0.309558	+	0.112670i	−0.492128	−	0.870523i	$-0.663781\pi$
$389$	−6.10545	+	2.22220i	−0.309558	+	0.112670i	0.182569	+	0.983193i	$0.441559\pi$
$390$		0			0
$391$	11.9222	−	10.0039i	0.602931	−	0.505919i
$392$	3.75636	−	3.15196i	0.189725	−	0.159198i
$393$		0			0
$394$	3.45366	−	1.25703i	0.173993	−	0.0633283i
$395$	7.32796	+	12.6924i	0.368710	+	0.638624i
$396$		0			0
$397$	−3.60614	+	6.24602i	−0.180987	+	0.313479i	−0.942217	−	0.335003i	$-0.891263\pi$
$397$	−3.60614	+	6.24602i	−0.180987	+	0.313479i	0.761230	+	0.648482i	$0.224596\pi$
$398$	−4.71237	+	26.7252i	−0.236210	+	1.33961i
$399$		0			0
$400$	4.47899	+	1.63022i	0.223949	+	0.0815109i
$401$	1.84693	+	10.4745i	0.0922313	+	0.523070i	0.995561	+	0.0941220i	$0.0300044\pi$
$401$	1.84693	+	10.4745i	0.0922313	+	0.523070i	−0.903329	+	0.428948i	$0.858885\pi$
$402$		0			0
$403$	−8.31221	−	6.97477i	−0.414060	−	0.347438i
$404$	−0.581191			−0.0289153
$405$		0			0
$406$	23.0245			1.14269
$407$	−21.6518	−	18.1680i	−1.07324	−	0.900555i
$408$		0			0
$409$	1.72049	+	9.75737i	0.0850727	+	0.482471i	0.997341	+	0.0728778i	$0.0232183\pi$
$409$	1.72049	+	9.75737i	0.0850727	+	0.482471i	−0.912268	+	0.409593i	$0.865671\pi$
$410$	8.00291	+	2.91282i	0.395235	+	0.143854i
$411$		0			0
$412$	−4.23697	+	24.0291i	−0.208741	+	1.18383i
$413$	5.66643	−	9.81454i	0.278827	−	0.482942i
$414$		0			0
$415$	7.21868	+	12.5031i	0.354351	+	0.613754i
$416$	19.5830	−	7.12763i	0.960135	−	0.349461i
$417$		0			0
$418$	−27.7363	+	23.2735i	−1.35663	+	1.13834i
$419$	8.15754	−	6.84499i	0.398522	−	0.334400i	−0.421400	−	0.906875i	$-0.638461\pi$
$419$	8.15754	−	6.84499i	0.398522	−	0.334400i	0.819922	+	0.572475i	$0.194017\pi$
$420$		0			0
$421$	−36.2626	+	13.1985i	−1.76733	+	0.643255i	−0.767331	+	0.641251i	$0.778416\pi$
$421$	−36.2626	+	13.1985i	−1.76733	+	0.643255i	−0.999998	+	0.00200391i	$0.999362\pi$
$422$	11.2743	+	19.5277i	0.548826	+	0.950594i
$423$		0			0
$424$	−3.16077	+	5.47461i	−0.153500	+	0.265871i
$425$	−0.317778	+	1.80221i	−0.0154145	+	0.0874201i
$426$		0			0
$427$	−11.0892	−	4.03614i	−0.536644	−	0.195322i
$428$	−3.26706	−	18.5284i	−0.157919	−	0.895604i
$429$		0			0
$430$	9.73994	+	8.17278i	0.469702	+	0.394127i
$431$	24.1205			1.16184			0.580922	−	0.813960i	$-0.302692\pi$
$431$	24.1205			1.16184			0.580922	+	0.813960i	$0.302692\pi$
$432$		0			0
$433$	−9.73516			−0.467842			−0.233921	−	0.972256i	$-0.575156\pi$
$433$	−9.73516			−0.467842			−0.233921	+	0.972256i	$0.575156\pi$
$434$	−18.0297	−	15.1287i	−0.865452	−	0.726201i
$435$		0			0
$436$	3.61793	+	20.5183i	0.173267	+	0.982647i
$437$	−45.2564	−	16.4720i	−2.16491	−	0.787962i
$438$		0			0
$439$	4.96370	−	28.1505i	0.236904	−	1.34355i	−0.601662	−	0.798751i	$-0.705494\pi$
$439$	4.96370	−	28.1505i	0.236904	−	1.34355i	0.838566	−	0.544800i	$-0.183394\pi$
$440$	−1.65185	+	2.86109i	−0.0787490	+	0.136397i
$441$		0			0
$442$	5.10810	+	8.84749i	0.242967	+	0.420832i
$443$	27.5517	−	10.0280i	1.30902	−	0.476444i	0.409096	−	0.912492i	$-0.365844\pi$
$443$	27.5517	−	10.0280i	1.30902	−	0.476444i	0.899924	+	0.436048i	$0.143622\pi$
$444$		0			0
$445$	−2.73943	+	2.29865i	−0.129861	+	0.108967i
$446$	29.7549	−	24.9673i	1.40894	−	1.18224i
$447$		0			0
$448$	11.3360	−	4.12598i	0.535578	−	0.194934i
$449$	−13.6125	−	23.5775i	−0.642413	−	1.11269i	−0.984893	−	0.173167i	$-0.944600\pi$
$449$	−13.6125	−	23.5775i	−0.642413	−	1.11269i	0.342480	−	0.939525i	$-0.388733\pi$
$450$		0			0
$451$	−7.81612	+	13.5379i	−0.368047	+	0.637475i
$452$	−1.91983	+	10.8879i	−0.0903012	+	0.512123i
$453$		0			0
$454$	−14.9592	−	5.44470i	−0.702070	−	0.255533i
$455$	1.80563	+	10.2402i	0.0846493	+	0.480070i
$456$		0			0
$457$	−25.1380	−	21.0933i	−1.17591	−	0.986704i	−0.999997	−	0.00229800i	$-0.999269\pi$
$457$	−25.1380	−	21.0933i	−1.17591	−	0.986704i	−0.175911	−	0.984406i	$-0.556287\pi$
$458$	−29.4556			−1.37637
$459$		0			0
$460$	12.6145			0.588156
$461$	−4.81252	−	4.03819i	−0.224142	−	0.188077i	0.523801	−	0.851841i	$-0.324514\pi$
$461$	−4.81252	−	4.03819i	−0.224142	−	0.188077i	−0.747942	+	0.663764i	$0.768958\pi$
$462$		0			0
$463$	−4.32044	−	24.5024i	−0.200788	−	1.13872i	−0.903932	−	0.427677i	$-0.859332\pi$
$463$	−4.32044	−	24.5024i	−0.200788	−	1.13872i	0.703144	−	0.711047i	$-0.251779\pi$
$464$	−15.8949	−	5.78528i	−0.737904	−	0.268575i
$465$		0			0
$466$	5.89141	−	33.4118i	0.272914	−	1.54777i
$467$	−15.1156	+	26.1809i	−0.699464	+	1.21151i	0.269188	+	0.963088i	$0.413245\pi$
$467$	−15.1156	+	26.1809i	−0.699464	+	1.21151i	−0.968652	+	0.248420i	$0.920089\pi$
$468$		0			0
$469$	7.24102	+	12.5418i	0.334359	+	0.579127i
$470$	−7.56568	+	2.75368i	−0.348979	+	0.127018i
$471$		0			0
$472$	−2.40837	+	2.02086i	−0.110854	+	0.0930177i
$473$	−17.8779	+	15.0013i	−0.822025	+	0.689761i
$474$		0			0
$475$	5.32148	−	1.93686i	0.244166	−	0.0888693i
$476$	4.71809	+	8.17197i	0.216253	+	0.374561i
$477$		0			0
$478$	11.5679	−	20.0361i	0.529102	−	0.916432i
$479$	1.45847	−	8.27140i	0.0666392	−	0.377930i	−0.933189	−	0.359386i	$-0.882986\pi$
$479$	1.45847	−	8.27140i	0.0666392	−	0.377930i	0.999828	−	0.0185434i	$-0.00590289\pi$
$480$		0			0
$481$	23.1907	+	8.44071i	1.05740	+	0.384863i
$482$	2.90680	+	16.4853i	0.132401	+	0.750883i
$483$		0			0
$484$	0.835881	+	0.701387i	0.0379946	+	0.0318812i
$485$	3.66068			0.166223
$486$		0			0
$487$	25.5873			1.15947			0.579735	−	0.814805i	$-0.303156\pi$
$487$	25.5873			1.15947			0.579735	+	0.814805i	$0.303156\pi$
$488$	2.50783	+	2.10432i	0.113524	+	0.0952580i
$489$		0			0
$490$	1.64790	+	9.34569i	0.0744444	+	0.422195i
$491$	−2.22987	−	0.811607i	−0.100633	−	0.0366273i	0.291213	−	0.956658i	$-0.405941\pi$
$491$	−2.22987	−	0.811607i	−0.100633	−	0.0366273i	−0.391846	+	0.920031i	$0.628163\pi$
$492$		0			0
$493$	1.12773	−	6.39565i	0.0507902	−	0.288045i
$494$	15.8071	−	27.3787i	0.711194	−	1.23182i
$495$		0			0
$496$	8.64541	+	14.9743i	0.388190	+	0.672366i
$497$	−28.4465	+	10.3537i	−1.27600	+	0.464426i
$498$		0			0
$499$	1.12305	−	0.942347i	0.0502744	−	0.0421853i	−0.617304	−	0.786725i	$-0.711775\pi$
$499$	1.12305	−	0.942347i	0.0502744	−	0.0421853i	0.667579	+	0.744539i	$0.267331\pi$
$500$	−1.13626	+	0.953435i	−0.0508151	+	0.0426389i
$501$		0			0
$502$	−20.6661	+	7.52186i	−0.922374	+	0.335717i
$503$	−13.6055	−	23.5654i	−0.606640	−	1.05073i	−0.991790	−	0.127877i	$-0.959184\pi$
$503$	−13.6055	−	23.5654i	−0.606640	−	1.05073i	0.385150	−	0.922854i	$-0.374150\pi$
$504$		0			0
$505$	−0.195914	+	0.339333i	−0.00871805	+	0.0151001i
$506$	−9.44204	+	53.5485i	−0.419750	+	2.38052i
$507$		0			0
$508$	−17.9145	−	6.52035i	−0.794828	−	0.289294i
$509$	0.472987	+	2.68244i	0.0209648	+	0.118897i	0.993494	−	0.113883i	$-0.0363289\pi$
$509$	0.472987	+	2.68244i	0.0209648	+	0.118897i	−0.972529	+	0.232780i	$0.925218\pi$
$510$		0			0
$511$	−21.1549	−	17.7511i	−0.935839	−	0.785262i
$512$	−24.0150			−1.06132
$513$		0			0
$514$	−19.0781			−0.841497
$515$	12.6013	+	10.5738i	0.555280	+	0.465935i
$516$		0			0
$517$	−2.56621	−	14.5537i	−0.112862	−	0.640070i
$518$	50.3019	+	18.3084i	2.21014	+	0.804425i
$519$		0			0
$520$	0.500909	−	2.84080i	0.0219663	−	0.124577i
$521$	−2.22878	+	3.86036i	−0.0976447	+	0.169126i	−0.910709	−	0.413048i	$-0.864464\pi$
$521$	−2.22878	+	3.86036i	−0.0976447	+	0.169126i	0.813065	+	0.582173i	$0.197798\pi$
$522$		0			0
$523$	18.2523	+	31.6140i	0.798119	+	1.38238i	0.920840	+	0.389941i	$0.127505\pi$
$523$	18.2523	+	31.6140i	0.798119	+	1.38238i	−0.122721	+	0.992441i	$0.539162\pi$
$524$	−24.4406	+	8.89566i	−1.06769	+	0.388609i
$525$		0			0
$526$	−32.7274	+	27.4615i	−1.42698	+	1.19738i
$527$	−5.08545	+	4.26720i	−0.221526	+	0.185882i
$528$		0			0
$529$	−46.3514	+	16.8705i	−2.01528	+	0.733502i
$530$	−6.11701	−	10.5950i	−0.265706	−	0.460216i
$531$		0			0
$532$	14.6002	−	25.2883i	0.632998	−	1.09639i
$533$	2.37016	−	13.4419i	0.102663	−	0.582232i
$534$		0			0
$535$	−11.9192	−	4.33825i	−0.515314	−	0.187559i
$536$	−0.697638	−	3.95650i	−0.0301334	−	0.170895i
$537$		0			0
$538$	0.654364	+	0.549076i	0.0282116	+	0.0236724i
$539$	−17.4188			−0.750282
$540$		0			0
$541$	−5.40959			−0.232577			−0.116288	−	0.993216i	$-0.537100\pi$
$541$	−5.40959			−0.232577			−0.116288	+	0.993216i	$0.537100\pi$
$542$	35.4423	+	29.7396i	1.52238	+	1.27743i
$543$		0			0
$544$	−2.21400	−	12.5562i	−0.0949243	−	0.538343i
$545$	13.1993	+	4.80416i	0.565397	+	0.205788i
$546$		0			0
$547$	3.75894	−	21.3180i	0.160721	−	0.911492i	−0.792647	−	0.609681i	$-0.791298\pi$
$547$	3.75894	−	21.3180i	0.160721	−	0.911492i	0.953368	−	0.301811i	$-0.0975912\pi$
$548$	−7.37129	+	12.7675i	−0.314886	+	0.545399i
$549$		0			0
$550$	−3.19682	−	5.53705i	−0.136313	−	0.236101i
$551$	−18.8848	+	6.87349i	−0.804518	+	0.292820i
$552$		0			0
$553$	39.0288	−	32.7490i	1.65967	−	1.39263i
$554$	8.80259	−	7.38625i	0.373986	−	0.313812i
$555$		0			0
$556$	−4.46778	+	1.62614i	−0.189476	+	0.0689637i
$557$	−2.62910	−	4.55373i	−0.111399	−	0.192948i	0.804936	−	0.593362i	$-0.202200\pi$
$557$	−2.62910	−	4.55373i	−0.111399	−	0.192948i	−0.916334	+	0.400414i	$0.868866\pi$
$558$		0			0
$559$	10.1887	−	17.6473i	0.430936	−	0.746403i
$560$	2.87728	−	16.3179i	0.121587	−	0.689556i
$561$		0			0
$562$	31.8582	+	11.5954i	1.34386	+	0.489124i
$563$	−4.12942	−	23.4191i	−0.174034	−	0.986998i	−0.939253	−	0.343227i	$-0.888480\pi$
$563$	−4.12942	−	23.4191i	−0.174034	−	0.986998i	0.765218	−	0.643771i	$-0.222631\pi$
$564$		0			0
$565$	5.70982	+	4.79111i	0.240214	+	0.201563i
$566$	13.1227			0.551587
$567$		0			0
$568$	8.39794			0.352370
$569$	23.3095	+	19.5590i	0.977185	+	0.819955i	0.983662	−	0.180024i	$-0.0576174\pi$
$569$	23.3095	+	19.5590i	0.977185	+	0.819955i	−0.00647745	+	0.999979i	$0.502062\pi$
$570$		0			0
$571$	3.24490	+	18.4027i	0.135795	+	0.770130i	0.974303	+	0.225241i	$0.0723170\pi$
$571$	3.24490	+	18.4027i	0.135795	+	0.770130i	−0.838508	+	0.544889i	$0.816572\pi$
$572$	−14.2825	−	5.19840i	−0.597181	−	0.217356i
$573$		0			0
$574$	5.14103	−	29.1562i	0.214582	−	1.21696i
$575$	4.25224	−	7.36510i	0.177331	−	0.307146i
$576$		0			0
$577$	−9.24093	−	16.0058i	−0.384705	−	0.666329i	0.607023	−	0.794684i	$-0.292363\pi$
$577$	−9.24093	−	16.0058i	−0.384705	−	0.666329i	−0.991728	+	0.128355i	$0.959030\pi$
$578$	−23.9412	+	8.71389i	−0.995823	+	0.362450i
$579$		0			0
$580$	4.03233	−	3.38353i	0.167434	−	0.140493i
$581$	38.4468	−	32.2607i	1.59504	−	1.33840i
$582$		0			0
$583$	21.1015	−	7.68033i	0.873936	−	0.318087i
$584$	3.83052	+	6.63465i	0.158508	+	0.274544i
$585$		0			0
$586$	22.1644	−	38.3899i	0.915603	−	1.58587i
$587$	−4.62650	+	26.2382i	−0.190956	+	1.08297i	0.727105	+	0.686527i	$0.240865\pi$
$587$	−4.62650	+	26.2382i	−0.190956	+	1.08297i	−0.918061	+	0.396440i	$0.870246\pi$
$588$		0			0
$589$	19.3043	+	7.02619i	0.795420	+	0.289509i
$590$	−1.05654	−	5.99193i	−0.0434971	−	0.246684i
$591$		0			0
$592$	−30.1255	−	25.2783i	−1.23815	−	1.03893i
$593$	4.62357			0.189867			0.0949337	−	0.995484i	$-0.469736\pi$
$593$	4.62357			0.189867			0.0949337	+	0.995484i	$0.469736\pi$
$594$		0			0
$595$	6.36168			0.260804
$596$	−1.14753	−	0.962888i	−0.0470045	−	0.0394414i
$597$		0			0
$598$	−8.24429	−	46.7557i	−0.337134	−	1.91198i
$599$	7.29668	+	2.65577i	0.298134	+	0.108512i	0.486756	−	0.873538i	$-0.338180\pi$
$599$	7.29668	+	2.65577i	0.298134	+	0.108512i	−0.188622	+	0.982050i	$0.560402\pi$
$600$		0			0
$601$	−2.59767	+	14.7321i	−0.105961	+	0.600936i	0.884871	+	0.465837i	$0.154247\pi$
$601$	−2.59767	+	14.7321i	−0.105961	+	0.600936i	−0.990832	+	0.135099i	$0.956865\pi$
$602$	22.0999	−	38.2782i	0.900725	−	1.56010i
$603$		0			0
$604$	8.81124	+	15.2615i	0.358524	+	0.620982i
$605$	0.691277	−	0.251604i	0.0281044	−	0.0102292i
$606$		0			0
$607$	19.7122	−	16.5405i	0.800094	−	0.671359i	−0.148128	−	0.988968i	$-0.547325\pi$
$607$	19.7122	−	16.5405i	0.800094	−	0.671359i	0.948222	+	0.317610i	$0.102880\pi$
$608$	−30.2241	+	25.3610i	−1.22575	+	1.02853i
$609$		0			0
$610$	−5.95355	+	2.16692i	−0.241052	+	0.0877359i
$611$	6.45177	+	11.1748i	0.261011	+	0.452084i
$612$		0			0
$613$	−14.5722	+	25.2399i	−0.588567	+	1.01943i	0.405853	+	0.913938i	$0.366974\pi$
$613$	−14.5722	+	25.2399i	−0.588567	+	1.01943i	−0.994420	+	0.105490i	$0.966359\pi$
$614$	6.03625	−	34.2333i	0.243603	−	1.38154i
$615$		0			0
$616$	10.7921	+	3.92799i	0.434825	+	0.158263i
$617$	−1.48661	−	8.43098i	−0.0598486	−	0.339418i	0.940150	−	0.340760i	$-0.110684\pi$
$617$	−1.48661	−	8.43098i	−0.0598486	−	0.339418i	−0.999999	+	0.00134119i	$0.999573\pi$
$618$		0			0
$619$	16.6721	+	13.9895i	0.670108	+	0.562287i	0.913097	−	0.407741i	$-0.133684\pi$
$619$	16.6721	+	13.9895i	0.670108	+	0.562287i	−0.242989	+	0.970029i	$0.578128\pi$
$620$	−5.38078			−0.216097
$621$		0			0
$622$	3.61710			0.145032
$623$	9.52309	+	7.99082i	0.381535	+	0.320146i
$624$		0			0
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−53.0562	−	19.3109i	−2.12055	−	0.771819i
$627$		0			0
$628$	5.04226	−	28.5961i	0.201208	−	1.14111i
$629$	7.54937	−	13.0759i	0.301013	−	0.521370i
$630$		0			0
$631$	22.3730	+	38.7512i	0.890657	+	1.54266i	0.839090	+	0.543993i	$0.183088\pi$
$631$	22.3730	+	38.7512i	0.890657	+	1.54266i	0.0515673	+	0.998670i	$0.483578\pi$
$632$	−13.2815	+	4.83407i	−0.528309	+	0.192289i
$633$		0			0
$634$	4.18990	−	3.51574i	0.166402	−	0.139628i
$635$	−9.84577	+	8.26158i	−0.390717	+	0.327851i
$636$		0			0
$637$	14.2920	−	5.20185i	0.566268	−	0.206105i
$638$	11.3448	+	19.6498i	0.449145	+	0.777941i
$639$		0			0
$640$	−3.72877	+	6.45842i	−0.147393	+	0.255292i
$641$	−4.57420	+	25.9416i	−0.180670	+	1.02463i	0.750723	+	0.660617i	$0.229705\pi$
$641$	−4.57420	+	25.9416i	−0.180670	+	1.02463i	−0.931393	+	0.364014i	$0.881406\pi$
$642$		0			0
$643$	−34.1452	−	12.4278i	−1.34656	−	0.490106i	−0.434684	−	0.900583i	$-0.643140\pi$
$643$	−34.1452	−	12.4278i	−1.34656	−	0.490106i	−0.911871	+	0.410477i	$0.865362\pi$
$644$	−7.61482	−	43.1858i	−0.300066	−	1.70176i
$645$		0			0
$646$	−14.8166	−	12.4326i	−0.582952	−	0.489155i
$647$	39.1069			1.53745			0.768725	−	0.639580i	$-0.220892\pi$
$647$	39.1069			1.53745			0.768725	+	0.639580i	$0.220892\pi$
$648$		0			0
$649$	11.1680			0.438382
$650$	4.27651	+	3.58841i	0.167738	+	0.140749i
$651$		0			0
$652$	2.38627	+	13.5332i	0.0934536	+	0.530002i
$653$	−13.7430	−	5.00203i	−0.537804	−	0.195744i	0.0588158	−	0.998269i	$-0.481268\pi$
$653$	−13.7430	−	5.00203i	−0.537804	−	0.195744i	−0.596619	+	0.802524i	$0.703490\pi$
$654$		0			0
$655$	−3.04490	+	17.2685i	−0.118974	+	0.674736i
$656$	−10.8751	+	18.8362i	−0.424600	+	0.735428i
$657$		0			0
$658$	13.9943	+	24.2388i	0.545553	+	0.944926i
$659$	−19.5964	+	7.13252i	−0.763369	+	0.277844i	−0.694220	−	0.719763i	$-0.744251\pi$
$659$	−19.5964	+	7.13252i	−0.763369	+	0.277844i	−0.0691489	+	0.997606i	$0.522028\pi$
$660$		0			0
$661$	13.5383	−	11.3600i	0.526580	−	0.441853i	−0.340339	−	0.940303i	$-0.610542\pi$
$661$	13.5383	−	11.3600i	0.526580	−	0.441853i	0.866918	+	0.498450i	$0.166097\pi$
$662$	15.4669	−	12.9783i	0.601140	−	0.504416i
$663$		0			0
$664$	−13.0834	+	4.76198i	−0.507735	+	0.184801i
$665$	−9.84316	−	17.0489i	−0.381701	−	0.661126i
$666$		0			0
$667$	−15.0903	+	26.1371i	−0.584297	+	1.01203i
$668$	−2.62629	+	14.8944i	−0.101614	+	0.576282i
$669$		0			0
$670$	7.30621	+	2.65924i	0.282263	+	0.102735i
$671$	−2.01939	−	11.4525i	−0.0779576	−	0.442120i
$672$		0			0
$673$	−18.0270	−	15.1265i	−0.694890	−	0.583082i	0.225425	−	0.974261i	$-0.427623\pi$
$673$	−18.0270	−	15.1265i	−0.694890	−	0.583082i	−0.920315	+	0.391179i	$0.872067\pi$
$674$	25.5349			0.983567
$675$		0			0
$676$	−6.01162			−0.231216
$677$	−29.2846	−	24.5727i	−1.12550	−	0.944407i	−0.126631	−	0.991950i	$-0.540416\pi$
$677$	−29.2846	−	24.5727i	−1.12550	−	0.944407i	−0.998869	+	0.0475429i	$0.984861\pi$
$678$		0			0
$679$	−2.20978	−	12.5323i	−0.0848038	−	0.480946i
$680$	−1.65839	−	0.603606i	−0.0635965	−	0.0231472i
$681$		0			0
$682$	4.02754	−	22.8413i	0.154222	−	0.874639i
$683$	2.77501	−	4.80646i	0.106183	−	0.183914i	−0.808038	−	0.589130i	$-0.799470\pi$
$683$	2.77501	−	4.80646i	0.106183	−	0.183914i	0.914221	+	0.405216i	$0.132804\pi$
$684$		0			0
$685$	4.96958	+	8.60757i	0.189878	+	0.328878i
$686$	−11.6771	+	4.25011i	−0.445833	+	0.162270i
$687$		0			0
$688$	−24.8746	+	20.8723i	−0.948335	+	0.795748i
$689$	−15.0200	+	12.6033i	−0.572216	+	0.480146i
$690$		0			0
$691$	28.6323	−	10.4213i	1.08922	−	0.396445i	0.265890	−	0.964003i	$-0.414334\pi$
$691$	28.6323	−	10.4213i	1.08922	−	0.396445i	0.823333	+	0.567559i	$0.192112\pi$
$692$	−8.38577	−	14.5246i	−0.318779	−	0.552142i
$693$		0			0
$694$	16.7868	−	29.0756i	0.637217	−	1.10369i
$695$	−0.556612	+	3.15670i	−0.0211135	+	0.119741i
$696$		0			0
$697$	−7.84707	−	2.85610i	−0.297229	−	0.108183i
$698$	−1.21447	−	6.88762i	−0.0459685	−	0.260700i
$699$		0			0
$700$	3.94999	+	3.31443i	0.149295	+	0.125274i
$701$	9.84780			0.371946			0.185973	−	0.982555i	$-0.440456\pi$
$701$	9.84780			0.371946			0.185973	+	0.982555i	$0.440456\pi$
$702$		0			0
$703$	−46.7233			−1.76220
$704$	9.10678	+	7.64150i	0.343225	+	0.288000i
$705$		0			0
$706$	−0.105966	−	0.600964i	−0.00398809	−	0.0226176i
$707$	1.27997	+	0.465870i	0.0481381	+	0.0175208i
$708$		0			0
$709$	−7.42637	+	42.1171i	−0.278903	+	1.58174i	0.447380	+	0.894344i	$0.352357\pi$
$709$	−7.42637	+	42.1171i	−0.278903	+	1.58174i	−0.726284	+	0.687395i	$0.758754\pi$
$710$	−8.12623	+	14.0750i	−0.304972	+	0.528227i
$711$		0			0
$712$	−1.72434	−	2.98665i	−0.0646225	−	0.111929i
$713$	28.9905	−	10.5517i	1.08570	−	0.395163i
$714$		0			0
$715$	−7.84961	+	6.58661i	−0.293559	+	0.246325i
$716$	27.3421	−	22.9427i	1.02182	−	0.857410i
$717$		0			0
$718$	11.2446	−	4.09268i	0.419643	−	0.152738i
$719$	−5.28698	−	9.15732i	−0.197171	−	0.341510i	0.750439	−	0.660940i	$-0.229842\pi$
$719$	−5.28698	−	9.15732i	−0.197171	−	0.341510i	−0.947610	+	0.319429i	$0.896509\pi$
$720$		0			0
$721$	28.5923	−	49.5234i	1.06483	−	1.84435i
$722$	−4.23571	+	24.0219i	−0.157637	+	0.894004i
$723$		0			0
$724$	−12.8423	−	4.67423i	−0.477282	−	0.173716i
$725$	−0.616239	−	3.49486i	−0.0228865	−	0.129796i
$726$		0			0
$727$	30.8438	+	25.8811i	1.14393	+	0.959875i	0.999560	−	0.0296480i	$-0.00943865\pi$
$727$	30.8438	+	25.8811i	1.14393	+	0.959875i	0.144374	+	0.989523i	$0.453883\pi$
$728$	−10.0278			−0.371656
$729$		0			0
$730$	−14.8263			−0.548748
$731$	−9.55028	−	8.01364i	−0.353230	−	0.296395i
$732$		0			0
$733$	7.76303	+	44.0263i	0.286734	+	1.62615i	0.699025	+	0.715098i	$0.253618\pi$
$733$	7.76303	+	44.0263i	0.286734	+	1.62615i	−0.412290	+	0.911052i	$0.635271\pi$
$734$	−14.3054	−	5.20676i	−0.528024	−	0.192185i
$735$		0			0
$736$	−10.2889	+	58.3515i	−0.379255	+	2.15086i
$737$	−7.13568	+	12.3594i	−0.262846	+	0.455263i
$738$		0			0
$739$	−7.15194	−	12.3875i	−0.263088	−	0.455682i	0.703973	−	0.710227i	$-0.251408\pi$
$739$	−7.15194	−	12.3875i	−0.263088	−	0.455682i	−0.967061	+	0.254545i	$0.918074\pi$
$740$	11.5000	−	4.18564i	0.422747	−	0.153867i
$741$		0			0
$742$	−32.5792	+	27.3372i	−1.19602	+	1.00358i
$743$	−16.7804	+	14.0804i	−0.615612	+	0.516560i	−0.896421	−	0.443204i	$-0.853842\pi$
$743$	−16.7804	+	14.0804i	−0.615612	+	0.516560i	0.280809	+	0.959764i	$0.409397\pi$
$744$		0			0
$745$	−0.949009	+	0.345411i	−0.0347690	+	0.0126549i
$746$	0.781395	+	1.35342i	0.0286089	+	0.0495521i
$747$		0			0
$748$	−4.64945	+	8.05308i	−0.170001	+	0.294450i
$749$	−7.65686	+	43.4242i	−0.279776	+	1.58669i
$750$		0			0
$751$	−2.77841	−	1.01126i	−0.101386	−	0.0369014i	0.290829	−	0.956775i	$-0.406069\pi$
$751$	−2.77841	−	1.01126i	−0.101386	−	0.0369014i	−0.392215	+	0.919874i	$0.628291\pi$
$752$	−3.57053	−	20.2495i	−0.130204	−	0.738422i
$753$		0			0
$754$	−15.1764	−	12.7345i	−0.552691	−	0.463763i
$755$	11.8807			0.432384
$756$		0			0
$757$	31.6130			1.14899			0.574497	−	0.818507i	$-0.305198\pi$
$757$	31.6130			1.14899			0.574497	+	0.818507i	$0.305198\pi$
$758$	10.5557	+	8.85729i	0.383401	+	0.321711i
$759$		0			0
$760$	0.948342	+	5.37831i	0.0344000	+	0.195092i
$761$	−15.9097	−	5.79066i	−0.576727	−	0.209911i	0.0371547	−	0.999310i	$-0.488171\pi$
$761$	−15.9097	−	5.79066i	−0.576727	−	0.209911i	−0.613882	+	0.789398i	$0.710393\pi$
$762$		0			0
$763$	8.47918	−	48.0878i	0.306967	−	1.74090i
$764$	−1.45354	+	2.51761i	−0.0525873	+	0.0910839i
$765$		0			0
$766$	−16.0005	−	27.7136i	−0.578120	−	1.00133i
$767$	−9.16321	+	3.33514i	−0.330864	+	0.120425i
$768$		0			0
$769$	−15.8071	+	13.2638i	−0.570020	+	0.478303i	−0.881653	−	0.471899i	$-0.843569\pi$
$769$	−15.8071	+	13.2638i	−0.570020	+	0.478303i	0.311633	+	0.950203i	$0.399124\pi$
$770$	−17.0263	+	14.2867i	−0.613584	+	0.514858i
$771$		0			0
$772$	−14.7163	+	5.35628i	−0.529650	+	0.192777i
$773$	7.16157	+	12.4042i	0.257584	+	0.446148i	0.965594	−	0.260054i	$-0.0837403\pi$
$773$	7.16157	+	12.4042i	0.257584	+	0.446148i	−0.708010	+	0.706202i	$0.750407\pi$
$774$		0			0
$775$	−1.81381	+	3.14161i	−0.0651540	+	0.112850i
$776$	−0.613027	+	3.47665i	−0.0220064	+	0.124804i
$777$		0			0
$778$	11.3949	+	4.14742i	0.408528	+	0.148692i
$779$	4.48729	+	25.4487i	0.160774	+	0.911795i
$780$		0			0
$781$	−22.8524	−	19.1755i	−0.817724	−	0.686152i
$782$	−29.0467			−1.03871
$783$		0			0
$784$	−24.2359			−0.865568
$785$	−14.9963	−	12.5834i	−0.535242	−	0.449122i
$786$		0			0
$787$	5.33548	+	30.2590i	0.190189	+	1.07862i	0.919105	+	0.394013i	$0.128914\pi$
$787$	5.33548	+	30.2590i	0.190189	+	1.07862i	−0.728916	+	0.684603i	$0.759975\pi$
$788$	−2.74479	−	0.999023i	−0.0977792	−	0.0355887i
$789$		0			0
$790$	4.74982	−	26.9376i	0.168991	−	0.958397i
$791$	12.9556	−	22.4397i	0.460647	−	0.797864i
$792$		0			0
$793$	5.07700	+	8.79362i	0.180289	+	0.312270i
$794$	12.6489	−	4.60382i	0.448893	−	0.163384i
$795$		0			0
$796$	16.5216	−	13.8633i	0.585594	−	0.491371i
$797$	23.7219	−	19.9050i	0.840271	−	0.705071i	−0.117354	−	0.993090i	$-0.537441\pi$
$797$	23.7219	−	19.9050i	0.840271	−	0.705071i	0.957625	+	0.288019i	$0.0929966\pi$
$798$		0			0
$799$	7.41836	−	2.70006i	0.262443	−	0.0955213i
$800$	−3.48355	−	6.03369i	−0.123162	−	0.213323i
$801$		0			0
$802$	9.92532	−	17.1912i	0.350475	−	0.607041i
$803$	4.72567	−	26.8006i	0.166765	−	0.945773i
$804$		0			0
$805$	−27.7812	−	10.1115i	−0.979160	−	0.356385i
$806$	3.51663	+	19.9438i	0.123868	+	0.702491i
$807$		0			0
$808$	−0.289465	−	0.242890i	−0.0101834	−	0.00854485i
$809$	2.58326			0.0908226			0.0454113	−	0.998968i	$-0.485540\pi$
$809$	2.58326			0.0908226			0.0454113	+	0.998968i	$0.485540\pi$
$810$		0			0
$811$	−24.6638			−0.866064			−0.433032	−	0.901379i	$-0.642556\pi$
$811$	−24.6638			−0.866064			−0.433032	+	0.901379i	$0.642556\pi$
$812$	−14.0176	−	11.7622i	−0.491922	−	0.412772i
$813$		0			0
$814$	9.16019	+	51.9500i	0.321065	+	1.82085i
$815$	8.70586	+	3.16867i	0.304953	+	0.110994i
$816$		0			0
$817$	−6.69923	+	37.9932i	−0.234376	+	1.32922i
$818$	9.24583	−	16.0142i	0.323273	−	0.559925i
$819$		0			0
$820$	−3.38424	−	5.86168i	−0.118183	−	0.204699i
$821$	21.3469	−	7.76964i	0.745013	−	0.271162i	0.0585070	−	0.998287i	$-0.481366\pi$
$821$	21.3469	−	7.76964i	0.745013	−	0.271162i	0.686505	+	0.727125i	$0.259144\pi$
$822$		0			0
$823$	20.4763	−	17.1816i	0.713758	−	0.598914i	−0.211893	−	0.977293i	$-0.567963\pi$
$823$	20.4763	−	17.1816i	0.713758	−	0.598914i	0.925651	+	0.378379i	$0.123518\pi$
$824$	−12.1524	+	10.1971i	−0.423350	+	0.355233i
$825$		0			0
$826$	−19.8756	+	7.23411i	−0.691559	+	0.251707i
$827$	7.72449	+	13.3792i	0.268607	+	0.465241i	0.968502	−	0.249005i	$-0.0801034\pi$
$827$	7.72449	+	13.3792i	0.268607	+	0.465241i	−0.699895	+	0.714245i	$0.746770\pi$
$828$		0			0
$829$	6.87832	−	11.9136i	0.238894	−	0.413776i	−0.721503	−	0.692411i	$-0.756549\pi$
$829$	6.87832	−	11.9136i	0.238894	−	0.413776i	0.960397	+	0.278635i	$0.0898819\pi$
$830$	4.67899	−	26.5359i	0.162410	−	0.921074i
$831$		0			0
$832$	−9.75403	−	3.55018i	−0.338160	−	0.123080i
$833$	−1.61581	−	9.16370i	−0.0559844	−	0.317504i
$834$		0			0
$835$	7.81092	+	6.55414i	0.270308	+	0.226815i
$836$	28.7756			0.995224
$837$		0			0
$838$	−19.8747			−0.686559
$839$	−7.36180	−	6.17729i	−0.254158	−	0.213264i	0.506803	−	0.862062i	$-0.330827\pi$
$839$	−7.36180	−	6.17729i	−0.254158	−	0.213264i	−0.760960	+	0.648799i	$0.775272\pi$
$840$		0			0
$841$	−2.84890	−	16.1569i	−0.0982380	−	0.557135i
$842$	67.6788	+	24.6331i	2.33237	+	0.848912i
$843$		0			0
$844$	3.11186	−	17.6482i	0.107115	−	0.607477i
$845$	−2.02646	+	3.50993i	−0.0697123	+	0.120745i
$846$		0			0
$847$	−1.27866	−	2.21470i	−0.0439352	−	0.0760980i
$848$	29.3599	−	10.6861i	1.00822	−	0.366963i
$849$		0			0
$850$	2.61639	−	2.19541i	0.0897414	−	0.0753020i
$851$	−53.7512	+	45.1026i	−1.84257	+	1.54610i
$852$		0			0
$853$	19.3174	−	7.03097i	0.661416	−	0.240736i	0.0105685	−	0.999944i	$-0.496636\pi$
$853$	19.3174	−	7.03097i	0.661416	−	0.240736i	0.650848	+	0.759208i	$0.274414\pi$
$854$	11.0123	+	19.0739i	0.376834	+	0.652695i
$855$		0			0
$856$	6.11618	−	10.5935i	0.209047	−	0.362080i
$857$	7.03369	−	39.8901i	0.240266	−	1.36262i	−0.590967	−	0.806695i	$-0.701254\pi$
$857$	7.03369	−	39.8901i	0.240266	−	1.36262i	0.831234	−	0.555923i	$-0.187635\pi$
$858$		0			0
$859$	−23.7524	−	8.64516i	−0.810421	−	0.294969i	−0.0966234	−	0.995321i	$-0.530804\pi$
$859$	−23.7524	−	8.64516i	−0.810421	−	0.294969i	−0.713798	+	0.700352i	$0.753026\pi$
$860$	−1.75470	−	9.95138i	−0.0598347	−	0.339339i
$861$		0			0
$862$	−34.4853	−	28.9366i	−1.17458	−	0.985585i
$863$	−47.4531			−1.61532			−0.807661	−	0.589648i	$-0.799267\pi$
$863$	−47.4531			−1.61532			−0.807661	+	0.589648i	$0.799267\pi$
$864$		0			0
$865$	−11.3070			−0.384451
$866$	13.9185	+	11.6790i	0.472969	+	0.396868i
$867$		0			0
$868$	3.24813	+	18.4211i	0.110249	+	0.625252i
$869$	47.1794	+	17.1719i	1.60045	+	0.582516i
$870$		0			0
$871$	2.16383	−	12.2717i	0.0733185	−	0.415810i
$872$	−6.77304	+	11.7312i	−0.229364	+	0.397270i
$873$		0			0
$874$	44.9427	+	77.8430i	1.52021	+	2.63308i
$875$	3.26666	−	1.18897i	0.110433	−	0.0401944i
$876$		0			0
$877$	−2.59201	+	2.17496i	−0.0875260	+	0.0734430i	−0.685501	−	0.728072i	$-0.740417\pi$
$877$	−2.59201	+	2.17496i	−0.0875260	+	0.0734430i	0.597975	+	0.801515i	$0.295972\pi$
$878$	−40.8680	+	34.2923i	−1.37923	+	1.15731i
$879$		0			0
$880$	15.3438	−	5.58469i	0.517240	−	0.188260i
$881$	11.9030	+	20.6166i	0.401022	+	0.694591i	0.993850	−	0.110738i	$-0.0353216\pi$
$881$	11.9030	+	20.6166i	0.401022	+	0.694591i	−0.592827	+	0.805330i	$0.701988\pi$
$882$		0			0
$883$	−11.6829	+	20.2353i	−0.393159	+	0.680972i	−0.992864	−	0.119249i	$-0.961951\pi$
$883$	−11.6829	+	20.2353i	−0.393159	+	0.680972i	0.599705	+	0.800221i	$0.295285\pi$
$884$	1.40990	−	7.99595i	0.0474201	−	0.268933i
$885$		0			0
$886$	−51.4212	−	18.7158i	−1.72753	−	0.628769i
$887$	−5.36066	−	30.4018i	−0.179993	−	1.02079i	−0.932221	−	0.361890i	$-0.882132\pi$
$887$	−5.36066	−	30.4018i	−0.179993	−	1.02079i	0.752228	−	0.658903i	$-0.228979\pi$
$888$		0			0
$889$	34.2269	+	28.7198i	1.14793	+	0.963231i
$890$	6.67422			0.223720
$891$		0			0
$892$	−30.8698			−1.03360
$893$	−18.7141	−	15.7030i	−0.626243	−	0.525480i
$894$		0			0
$895$	−4.17854	−	23.6977i	−0.139673	−	0.792125i
$896$	24.3613	+	8.86677i	0.813853	+	0.296218i
$897$		0			0
$898$	−8.82332	+	50.0395i	−0.294438	+	1.66984i
$899$	6.43681	−	11.1489i	0.214680	−	0.371836i
$900$		0			0
$901$	5.99790	+	10.3887i	0.199819	+	0.346097i
$902$	27.4158	−	9.97854i	0.912847	−	0.332249i
$903$		0			0
$904$	−5.50643	+	4.62045i	−0.183141	+	0.153674i
$905$	−7.05812	+	5.92246i	−0.234620	+	0.196869i
$906$		0			0
$907$	10.5268	−	3.83144i	0.349537	−	0.127221i	−0.161284	−	0.986908i	$-0.551564\pi$
$907$	10.5268	−	3.83144i	0.349537	−	0.127221i	0.510821	+	0.859687i	$0.329341\pi$
$908$	6.32589	+	10.9568i	0.209932	+	0.363613i
$909$		0			0
$910$	9.70338	−	16.8067i	0.321664	−	0.557138i
$911$	4.51397	−	25.6000i	0.149555	−	0.848166i	−0.814042	−	0.580806i	$-0.802738\pi$
$911$	4.51397	−	25.6000i	0.149555	−	0.848166i	0.963597	−	0.267360i	$-0.0861514\pi$
$912$		0			0
$913$	46.4758	+	16.9158i	1.53813	+	0.559832i
$914$	10.6351	+	60.3147i	0.351778	+	1.99503i
$915$		0			0
$916$	17.9329	+	15.0475i	0.592520	+	0.497183i
$917$	60.9566			2.01296
$918$		0			0
$919$	−9.14191			−0.301564			−0.150782	−	0.988567i	$-0.548179\pi$
$919$	−9.14191			−0.301564			−0.150782	+	0.988567i	$0.548179\pi$
$920$	6.28275	+	5.27185i	0.207136	+	0.173808i
$921$		0			0
$922$	2.03603	+	11.5469i	0.0670530	+	0.380276i
$923$	24.4766	+	8.90876i	0.805657	+	0.293235i
$924$		0			0
$925$	1.43270	−	8.12527i	0.0471070	−	0.267157i
$926$	−23.2178	+	40.2145i	−0.762986	+	1.32153i
$927$		0			0
$928$	12.3624	+	21.4122i	0.405814	+	0.702891i
$929$	−51.0829	+	18.5927i	−1.67598	+	0.610005i	−0.992749	−	0.120202i	$-0.961646\pi$
$929$	−51.0829	+	18.5927i	−1.67598	+	0.610005i	−0.683226	+	0.730207i	$0.739424\pi$
$930$		0			0
$931$	−22.0580	+	18.5089i	−0.722922	+	0.606603i
$932$	−20.6553	+	17.3319i	−0.676588	+	0.567725i
$933$		0			0
$934$	53.0193	−	19.2975i	1.73485	−	0.631432i
$935$	3.13457	+	5.42923i	0.102511	+	0.177555i
$936$		0			0
$937$	0.513624	−	0.889623i	0.0167794	−	0.0290627i	−0.857514	−	0.514461i	$-0.827992\pi$
$937$	0.513624	−	0.889623i	0.0167794	−	0.0290627i	0.874293	+	0.485398i	$0.161325\pi$
$938$	4.69347	−	26.6180i	0.153247	−	0.869109i
$939$		0			0
$940$	6.01281	+	2.18848i	0.196116	+	0.0713805i
$941$	−8.92999	−	50.6445i	−0.291109	−	1.65096i	−0.682608	−	0.730785i	$-0.739154\pi$
$941$	−8.92999	−	50.6445i	−0.291109	−	1.65096i	0.391499	−	0.920179i	$-0.371957\pi$
$942$		0			0
$943$	29.7283	+	24.9450i	0.968085	+	0.812320i
$944$	15.5387			0.505742
$945$		0			0
$946$	43.5568			1.41615
$947$	20.8637	+	17.5068i	0.677980	+	0.568893i	0.915415	−	0.402510i	$-0.131862\pi$
$947$	20.8637	+	17.5068i	0.677980	+	0.568893i	−0.237435	+	0.971403i	$0.576307\pi$
$948$		0			0
$949$	4.12620	+	23.4009i	0.133942	+	0.759624i
$950$	−9.93177	−	3.61487i	−0.322229	−	0.117282i
$951$		0			0
$952$	−1.06534	+	6.04187i	−0.0345280	+	0.195818i
$953$	−6.60432	+	11.4390i	−0.213935	+	0.370546i	−0.952943	−	0.303151i	$-0.901961\pi$
$953$	−6.60432	+	11.4390i	−0.213935	+	0.370546i	0.739008	+	0.673697i	$0.235295\pi$
$954$		0			0
$955$	0.979950	+	1.69732i	0.0317104	+	0.0549241i
$956$	−17.2782	+	6.28875i	−0.558817	+	0.203393i
$957$		0			0
$958$	−12.0081	+	10.0760i	−0.387965	+	0.325542i
$959$	26.4680	−	22.2093i	0.854698	−	0.717177i
$960$		0			0
$961$	16.7645	−	6.10177i	0.540790	−	0.196831i
$962$	−23.0299	−	39.8889i	−0.742513	−	1.28607i
$963$		0			0
$964$	6.65187	−	11.5214i	0.214242	−	0.371079i
$965$	−1.83340	+	10.3977i	−0.0590194	+	0.334715i
$966$		0			0
$967$	8.14181	+	2.96338i	0.261823	+	0.0952958i	0.469596	−	0.882881i	$-0.344399\pi$
$967$	8.14181	+	2.96338i	0.261823	+	0.0952958i	−0.207773	+	0.978177i	$0.566622\pi$
$968$	0.123193	+	0.698660i	0.00395956	+	0.0224558i
$969$		0			0
$970$	−5.23372	−	4.39161i	−0.168044	−	0.141006i
$971$	−27.5409			−0.883831			−0.441915	−	0.897057i	$-0.645701\pi$
$971$	−27.5409			−0.883831			−0.441915	+	0.897057i	$0.645701\pi$
$972$		0			0
$973$	11.1430			0.357227
$974$	−36.5824	−	30.6963i	−1.17218	−	0.983572i
$975$		0			0
$976$	−2.80970	−	15.9346i	−0.0899364	−	0.510055i
$977$	6.21685	+	2.26275i	0.198895	+	0.0723917i	0.439547	−	0.898220i	$-0.355139\pi$
$977$	6.21685	+	2.26275i	0.198895	+	0.0723917i	−0.240652	+	0.970611i	$0.577361\pi$
$978$		0			0
$979$	−2.12730	+	12.0645i	−0.0679889	+	0.385584i
$980$	3.77102	−	6.53160i	0.120461	−	0.208644i
$981$		0			0
$982$	2.21441	+	3.83548i	0.0706648	+	0.122395i
$983$	35.0558	−	12.7593i	1.11811	−	0.406958i	0.284147	−	0.958781i	$-0.408290\pi$
$983$	35.0558	−	12.7593i	1.11811	−	0.406958i	0.833961	+	0.551823i	$0.186068\pi$
$984$		0			0
$985$	−1.50853	+	1.26581i	−0.0480658	+	0.0403320i
$986$	−9.28499	+	7.79103i	−0.295694	+	0.248117i
$987$		0			0
$988$	−23.6101	+	8.59336i	−0.751136	+	0.273391i
$989$	28.9685	+	50.1749i	0.921144	+	1.59547i
$990$		0			0
$991$	20.4866	−	35.4838i	0.650777	−	1.12718i	−0.332158	−	0.943224i	$-0.607777\pi$
$991$	20.4866	−	35.4838i	0.650777	−	1.12718i	0.982935	−	0.183955i	$-0.0588900\pi$
$992$	4.38879	−	24.8900i	0.139344	−	0.790260i
$993$		0			0
$994$	53.0912	+	19.3236i	1.68395	+	0.612908i
$995$	−2.52491	−	14.3195i	−0.0800449	−	0.453957i
$996$		0			0
$997$	−17.7398	−	14.8855i	−0.561826	−	0.471428i	0.317096	−	0.948393i	$-0.397292\pi$
$997$	−17.7398	−	14.8855i	−0.561826	−	0.471428i	−0.878922	+	0.476965i	$0.841737\pi$
$998$	−2.73614			−0.0866109
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.k.b.46.2		42
3.2	odd	2		135.2.k.b.16.6	✓	42
15.2	even	4		675.2.u.d.124.3		84
15.8	even	4		675.2.u.d.124.12		84
15.14	odd	2		675.2.l.e.151.2		42
27.5	odd	18		135.2.k.b.76.6	yes	42
27.7	even	9		3645.2.a.k.1.5		21
27.20	odd	18		3645.2.a.l.1.17		21
27.22	even	9	inner	405.2.k.b.361.2		42
135.32	even	36		675.2.u.d.49.12		84
135.59	odd	18		675.2.l.e.76.2		42
135.113	even	36		675.2.u.d.49.3		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.b.16.6	✓	42	3.2	odd	2
135.2.k.b.76.6	yes	42	27.5	odd	18
405.2.k.b.46.2		42	1.1	even	1	trivial
405.2.k.b.361.2		42	27.22	even	9	inner
675.2.l.e.76.2		42	135.59	odd	18
675.2.l.e.151.2		42	15.14	odd	2
675.2.u.d.49.3		84	135.113	even	36
675.2.u.d.49.12		84	135.32	even	36
675.2.u.d.124.3		84	15.2	even	4
675.2.u.d.124.12		84	15.8	even	4
3645.2.a.k.1.5		21	27.7	even	9
3645.2.a.l.1.17		21	27.20	odd	18

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.k (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42971 - 1.19967i) q^{2} +(0.257569 + 1.46075i) q^{4} +(0.939693 + 0.342020i) q^{5} +(0.603654 - 3.42349i) q^{7} +(-0.482190 + 0.835177i) q^{8} +O(q^{10})\)	\(q+(-1.42971 - 1.19967i) q^{2} +(0.257569 + 1.46075i) q^{4} +(0.939693 + 0.342020i) q^{5} +(0.603654 - 3.42349i) q^{7} +(-0.482190 + 0.835177i) q^{8} +(-0.933178 - 1.61631i) q^{10} +(3.21914 - 1.17167i) q^{11} +(-2.29137 + 1.92269i) q^{13} +(-4.97011 + 4.17042i) q^{14} +(4.47899 - 1.63022i) q^{16} +(0.915007 + 1.58484i) q^{17} +(2.83150 - 4.90430i) q^{19} +(-0.257569 + 1.46075i) q^{20} +(-6.00805 - 2.18675i) q^{22} +(-1.47679 - 8.37528i) q^{23} +(0.766044 + 0.642788i) q^{25} +5.58258 q^{26} +5.15634 q^{28} +(-2.71852 - 2.28111i) q^{29} +(0.629929 + 3.57251i) q^{31} +(-6.54694 - 2.38289i) q^{32} +(0.593087 - 3.36357i) q^{34} +(1.73815 - 3.01057i) q^{35} +(-4.12531 - 7.14525i) q^{37} +(-9.93177 + 3.61487i) q^{38} +(-0.738757 + 0.619891i) q^{40} +(-3.49560 + 2.93316i) q^{41} +(-6.40168 + 2.33002i) q^{43} +(2.54066 + 4.40056i) q^{44} +(-7.93619 + 13.7459i) q^{46} +(0.749097 - 4.24834i) q^{47} +(-4.77806 - 1.73907i) q^{49} +(-0.324089 - 1.83800i) q^{50} +(-3.39874 - 2.85188i) q^{52} +6.55503 q^{53} +3.42573 q^{55} +(2.56815 + 2.15493i) q^{56} +(1.15012 + 6.52266i) q^{58} +(3.06342 + 1.11500i) q^{59} +(0.589476 - 3.34309i) q^{61} +(3.38521 - 5.86336i) q^{62} +(1.73511 + 3.00530i) q^{64} +(-2.81078 + 1.02304i) q^{65} +(-3.19129 + 2.67781i) q^{67} +(-2.07937 + 1.74480i) q^{68} +(-6.09675 + 2.21903i) q^{70} +(-4.35406 - 7.54146i) q^{71} +(3.97200 - 6.87971i) q^{73} +(-2.67394 + 15.1646i) q^{74} +(7.89326 + 2.87291i) q^{76} +(-2.06796 - 11.7280i) q^{77} +(11.2271 + 9.42064i) q^{79} +4.76644 q^{80} +8.51652 q^{82} +(11.0597 + 9.28016i) q^{83} +(0.317778 + 1.80221i) q^{85} +(11.9478 + 4.34865i) q^{86} +(-0.573682 + 3.25351i) q^{88} +(-1.78804 + 3.09697i) q^{89} +(5.19911 + 9.00512i) q^{91} +(11.8538 - 4.31443i) q^{92} +(-6.16760 + 5.17523i) q^{94} +(4.33811 - 3.64011i) q^{95} +(3.43991 - 1.25203i) q^{97} +(4.74493 + 8.21846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 9 q^{8}+O(q^{10}) \) 42 * q + 9 * q^8	\( 42 q + 9 q^{8} - 3 q^{10} + 6 q^{11} - 3 q^{13} + 27 q^{14} - 12 q^{16} + 12 q^{17} - 24 q^{19} + 33 q^{22} - 18 q^{23} + 18 q^{26} + 60 q^{28} - 12 q^{31} - 36 q^{32} + 51 q^{34} + 12 q^{35} - 24 q^{37} + 24 q^{38} - 9 q^{40} - 33 q^{41} - 24 q^{43} - 12 q^{44} - 30 q^{46} - 27 q^{47} + 18 q^{49} - 84 q^{52} - 36 q^{53} + 24 q^{56} - 81 q^{58} + 27 q^{59} - 6 q^{61} + 18 q^{62} - 63 q^{64} - 6 q^{65} + 12 q^{67} + 3 q^{68} + 9 q^{70} - 12 q^{71} - 39 q^{73} + 72 q^{74} + 138 q^{76} + 54 q^{77} - 18 q^{79} - 78 q^{80} + 48 q^{82} - 57 q^{83} + 9 q^{85} - 18 q^{86} + 126 q^{88} - 9 q^{89} - 69 q^{91} - 24 q^{92} - 33 q^{94} - 3 q^{95} + 21 q^{97} + 15 q^{98}+O(q^{100}) \) 42 * q + 9 * q^8 - 3 * q^10 + 6 * q^11 - 3 * q^13 + 27 * q^14 - 12 * q^16 + 12 * q^17 - 24 * q^19 + 33 * q^22 - 18 * q^23 + 18 * q^26 + 60 * q^28 - 12 * q^31 - 36 * q^32 + 51 * q^34 + 12 * q^35 - 24 * q^37 + 24 * q^38 - 9 * q^40 - 33 * q^41 - 24 * q^43 - 12 * q^44 - 30 * q^46 - 27 * q^47 + 18 * q^49 - 84 * q^52 - 36 * q^53 + 24 * q^56 - 81 * q^58 + 27 * q^59 - 6 * q^61 + 18 * q^62 - 63 * q^64 - 6 * q^65 + 12 * q^67 + 3 * q^68 + 9 * q^70 - 12 * q^71 - 39 * q^73 + 72 * q^74 + 138 * q^76 + 54 * q^77 - 18 * q^79 - 78 * q^80 + 48 * q^82 - 57 * q^83 + 9 * q^85 - 18 * q^86 + 126 * q^88 - 9 * q^89 - 69 * q^91 - 24 * q^92 - 33 * q^94 - 3 * q^95 + 21 * q^97 + 15 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more