LMFDB - Embedded newform 495.2.bj.a.217.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(28,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 18]))

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

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

chi := DirichletCharacter("495.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			217.3
Character	$\chi$	$=$	495.217
Dual form			495.2.bj.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0763931 - 0.482327i) q^{2} +(1.67531 + 0.544341i) q^{4} +(-1.47656 - 1.67922i) q^{5} +(-1.32402 - 2.59854i) q^{7} +(0.833936 - 1.63669i) q^{8} +(-0.922733 + 0.583903i) q^{10} +(3.15977 - 1.00788i) q^{11} +(-2.89049 - 0.457808i) q^{13} +(-1.35449 + 0.440102i) q^{14} +(2.12449 + 1.54353i) q^{16} +(-5.20325 + 0.824113i) q^{17} +(-1.26677 - 3.89873i) q^{19} +(-1.55962 - 3.61696i) q^{20} +(-0.244743 - 1.60104i) q^{22} +(2.12046 - 2.12046i) q^{23} +(-0.639563 + 4.95893i) q^{25} +(-0.441627 + 1.35919i) q^{26} +(-0.803656 - 5.07408i) q^{28} +(0.817241 - 2.51521i) q^{29} +(5.45328 - 3.96204i) q^{31} +(3.50456 - 3.50456i) q^{32} +2.57262i q^{34} +(-2.40853 + 6.06022i) q^{35} +(1.03649 - 0.528116i) q^{37} +(-1.97724 + 0.313163i) q^{38} +(-3.97972 + 1.01630i) q^{40} +(3.38136 - 1.09867i) q^{41} +(5.07292 + 5.07292i) q^{43} +(5.84223 + 0.0314826i) q^{44} +(-0.860769 - 1.18475i) q^{46} +(-1.67145 + 3.28041i) q^{47} +(-0.884888 + 1.21794i) q^{49} +(2.34297 + 0.687307i) q^{50} +(-4.59325 - 2.34038i) q^{52} +(0.231169 - 1.45955i) q^{53} +(-6.35804 - 3.81777i) q^{55} -5.35716 q^{56} +(-1.15072 - 0.586323i) q^{58} +(-1.52672 - 0.496061i) q^{59} +(-4.07810 + 5.61302i) q^{61} +(-1.49441 - 2.93294i) q^{62} +(1.66445 + 2.29092i) q^{64} +(3.49920 + 5.52974i) q^{65} +(1.31471 + 1.31471i) q^{67} +(-9.16564 - 1.45170i) q^{68} +(2.73902 + 1.62466i) q^{70} +(2.32441 + 1.68878i) q^{71} +(13.1886 - 6.71992i) q^{73} +(-0.175544 - 0.540270i) q^{74} -7.22113i q^{76} +(-6.80264 - 6.87635i) q^{77} +(-12.3342 + 8.96129i) q^{79} +(-0.544999 - 5.84661i) q^{80} +(-0.271606 - 1.71486i) q^{82} +(1.04540 + 6.60041i) q^{83} +(9.06675 + 7.52055i) q^{85} +(2.83434 - 2.05927i) q^{86} +(0.985459 - 6.01208i) q^{88} +11.1726i q^{89} +(2.63744 + 8.11720i) q^{91} +(4.70669 - 2.39818i) q^{92} +(1.45454 + 1.05679i) q^{94} +(-4.67636 + 7.88388i) q^{95} +(-9.94447 - 1.57505i) q^{97} +(0.519848 + 0.519848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0763931	−	0.482327i	0.0540181	−	0.341057i	−0.945847	−	0.324614i	$-0.894766\pi$
$2$	0.0763931	−	0.482327i	0.0540181	−	0.341057i	0.999865	−	0.0164432i	$-0.00523428\pi$
$3$		0			0
$3$		0			0
$4$	1.67531	+	0.544341i	0.837655	+	0.272170i
$5$	−1.47656	−	1.67922i	−0.660336	−	0.750970i
$5$	−1.47656	−	1.67922i	−0.660336	−	0.750970i
$6$		0			0
$7$	−1.32402	−	2.59854i	−0.500434	−	0.982157i	−0.993678	−	0.112266i	$-0.964189\pi$
$7$	−1.32402	−	2.59854i	−0.500434	−	0.982157i	0.493244	−	0.869891i	$-0.335811\pi$
$8$	0.833936	−	1.63669i	0.294841	−	0.578658i
$9$		0			0
$10$	−0.922733	+	0.583903i	−0.291794	+	0.184646i
$11$	3.15977	−	1.00788i	0.952708	−	0.303888i
$11$	3.15977	−	1.00788i	0.952708	−	0.303888i
$12$		0			0
$13$	−2.89049	−	0.457808i	−0.801677	−	0.126973i	−0.257866	−	0.966181i	$-0.583019\pi$
$13$	−2.89049	−	0.457808i	−0.801677	−	0.126973i	−0.543811	+	0.839208i	$0.683019\pi$
$14$	−1.35449	+	0.440102i	−0.362004	+	0.117622i
$15$		0			0
$16$	2.12449	+	1.54353i	0.531123	+	0.385884i
$17$	−5.20325	+	0.824113i	−1.26197	+	0.199877i	−0.751336	−	0.659920i	$-0.770590\pi$
$17$	−5.20325	+	0.824113i	−1.26197	+	0.199877i	−0.510636	+	0.859797i	$0.670590\pi$
$18$		0			0
$19$	−1.26677	−	3.89873i	−0.290618	−	0.894429i	−0.984658	−	0.174494i	$-0.944171\pi$
$19$	−1.26677	−	3.89873i	−0.290618	−	0.894429i	0.694041	−	0.719936i	$-0.255829\pi$
$20$	−1.55962	−	3.61696i	−0.348742	−	0.808778i
$21$		0			0
$22$	−0.244743	−	1.60104i	−0.0521795	−	0.341343i
$23$	2.12046	−	2.12046i	0.442147	−	0.442147i	−0.450586	−	0.892733i	$-0.648785\pi$
$23$	2.12046	−	2.12046i	0.442147	−	0.442147i	0.892733	+	0.450586i	$0.148785\pi$
$24$		0			0
$25$	−0.639563	+	4.95893i	−0.127913	+	0.991785i
$26$	−0.441627	+	1.35919i	−0.0866101	+	0.266558i
$27$		0			0
$28$	−0.803656	−	5.07408i	−0.151877	−	0.958912i
$29$	0.817241	−	2.51521i	0.151758	−	0.467063i	−0.846060	−	0.533088i	$-0.821032\pi$
$29$	0.817241	−	2.51521i	0.151758	−	0.467063i	0.997818	+	0.0660248i	$0.0210316\pi$
$30$		0			0
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.0218548	−	0.999761i	$-0.493043\pi$
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.957583	+	0.288158i	$0.0930429\pi$
$32$	3.50456	−	3.50456i	0.619524	−	0.619524i
$33$		0			0
$34$			2.57262i			0.441201i
$35$	−2.40853	+	6.06022i	−0.407116	+	1.02436i
$36$		0			0
$37$	1.03649	−	0.528116i	0.170397	−	0.0868218i	−0.366712	−	0.930335i	$-0.619516\pi$
$37$	1.03649	−	0.528116i	0.170397	−	0.0868218i	0.537109	+	0.843513i	$0.319516\pi$
$38$	−1.97724	+	0.313163i	−0.320750	+	0.0508018i
$39$		0			0
$40$	−3.97972	+	1.01630i	−0.629249	+	0.160692i
$41$	3.38136	−	1.09867i	0.528080	−	0.171584i	−0.0328289	−	0.999461i	$-0.510452\pi$
$41$	3.38136	−	1.09867i	0.528080	−	0.171584i	0.560909	+	0.827877i	$0.310452\pi$
$42$		0			0
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	0.978736	−	0.205123i	$-0.0657595\pi$
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	−0.205123	+	0.978736i	$0.565759\pi$
$44$	5.84223	+	0.0314826i	0.880749	+	0.00474618i
$45$		0			0
$46$	−0.860769	−	1.18475i	−0.126913	−	0.174681i
$47$	−1.67145	+	3.28041i	−0.243806	+	0.478497i	−0.980188	−	0.198070i	$-0.936533\pi$
$47$	−1.67145	+	3.28041i	−0.243806	+	0.478497i	0.736382	+	0.676566i	$0.236533\pi$
$48$		0			0
$49$	−0.884888	+	1.21794i	−0.126413	+	0.173992i
$50$	2.34297	+	0.687307i	0.331346	+	0.0971998i
$51$		0			0
$52$	−4.59325	−	2.34038i	−0.636970	−	0.324552i
$53$	0.231169	−	1.45955i	0.0317536	−	0.200484i	−0.966712	−	0.255869i	$-0.917639\pi$
$53$	0.231169	−	1.45955i	0.0317536	−	0.200484i	0.998465	+	0.0553847i	$0.0176385\pi$
$54$		0			0
$55$	−6.35804	−	3.81777i	−0.857318	−	0.514787i
$56$	−5.35716			−0.715881
$57$		0			0
$58$	−1.15072	−	0.586323i	−0.151097	−	0.0769879i
$59$	−1.52672	−	0.496061i	−0.198762	−	0.0645817i	0.207944	−	0.978141i	$-0.433323\pi$
$59$	−1.52672	−	0.496061i	−0.198762	−	0.0645817i	−0.406706	+	0.913559i	$0.633323\pi$
$60$		0			0
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	−0.985908	−	0.167286i	$-0.946500\pi$
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	0.463761	+	0.885960i	$0.346500\pi$
$62$	−1.49441	−	2.93294i	−0.189790	−	0.372483i
$63$		0			0
$64$	1.66445	+	2.29092i	0.208056	+	0.286365i
$65$	3.49920	+	5.52974i	0.434023	+	0.685880i
$66$		0			0
$67$	1.31471	+	1.31471i	0.160617	+	0.160617i	0.782840	−	0.622223i	$-0.213770\pi$
$67$	1.31471	+	1.31471i	0.160617	+	0.160617i	−0.622223	+	0.782840i	$0.713770\pi$
$68$	−9.16564	−	1.45170i	−1.11150	−	0.176044i
$69$		0			0
$70$	2.73902	+	1.62466i	0.327375	+	0.194184i
$71$	2.32441	+	1.68878i	0.275857	+	0.200422i	0.717108	−	0.696962i	$-0.245465\pi$
$71$	2.32441	+	1.68878i	0.275857	+	0.200422i	−0.441251	+	0.897384i	$0.645465\pi$
$72$		0			0
$73$	13.1886	−	6.71992i	1.54361	−	0.786507i	0.544957	−	0.838464i	$-0.316546\pi$
$73$	13.1886	−	6.71992i	1.54361	−	0.786507i	0.998649	+	0.0519568i	$0.0165458\pi$
$74$	−0.175544	−	0.540270i	−0.0204066	−	0.0628051i
$75$		0			0
$76$		−	7.22113i		−	0.828321i
$77$	−6.80264	−	6.87635i	−0.775232	−	0.783633i
$78$		0			0
$79$	−12.3342	+	8.96129i	−1.38770	+	1.00822i	−0.391589	+	0.920140i	$0.628074\pi$
$79$	−12.3342	+	8.96129i	−1.38770	+	1.00822i	−0.996113	+	0.0880839i	$0.971926\pi$
$80$	−0.544999	−	5.84661i	−0.0609327	−	0.653671i
$81$		0			0
$82$	−0.271606	−	1.71486i	−0.0299939	−	0.189374i
$83$	1.04540	+	6.60041i	0.114748	+	0.724489i	0.976236	+	0.216711i	$0.0695329\pi$
$83$	1.04540	+	6.60041i	0.114748	+	0.724489i	−0.861488	+	0.507778i	$0.830467\pi$
$84$		0			0
$85$	9.06675	+	7.52055i	0.983427	+	0.815718i
$86$	2.83434	−	2.05927i	0.305635	−	0.222057i
$87$		0			0
$88$	0.985459	−	6.01208i	0.105050	−	0.640890i
$89$			11.1726i			1.18429i	0.805830	+	0.592147i	$0.201719\pi$
$89$			11.1726i			1.18429i	−0.805830	+	0.592147i	$0.798281\pi$
$90$		0			0
$91$	2.63744	+	8.11720i	0.276479	+	0.850914i
$92$	4.70669	−	2.39818i	0.490706	−	0.250027i
$93$		0			0
$94$	1.45454	+	1.05679i	0.150025	+	0.108999i
$95$	−4.67636	+	7.88388i	−0.479784	+	0.808869i
$96$		0			0
$97$	−9.94447	−	1.57505i	−1.00971	−	0.159922i	−0.370400	−	0.928873i	$-0.620779\pi$
$97$	−9.94447	−	1.57505i	−1.00971	−	0.159922i	−0.639308	+	0.768951i	$0.720779\pi$
$98$	0.519848	+	0.519848i	0.0525126	+	0.0525126i
$99$		0			0
$100$	−3.77081	+	7.95960i	−0.377081	+	0.795960i
$101$	1.12216	+	1.54452i	0.111659	+	0.153686i	0.861189	−	0.508285i	$-0.169720\pi$
$101$	1.12216	+	1.54452i	0.111659	+	0.153686i	−0.749530	+	0.661971i	$0.769720\pi$
$102$		0			0
$103$	2.80172	+	5.49869i	0.276062	+	0.541802i	0.986857	−	0.161597i	$-0.0516646\pi$
$103$	2.80172	+	5.49869i	0.276062	+	0.541802i	−0.710795	+	0.703399i	$0.751665\pi$
$104$	−3.15977	+	4.34905i	−0.309841	+	0.426459i
$105$		0			0
$106$	−0.686319	−	0.222999i	−0.0666612	−	0.0216595i
$107$	−0.388059	−	0.197726i	−0.0375151	−	0.0191149i	0.435132	−	0.900367i	$-0.356702\pi$
$107$	−0.388059	−	0.197726i	−0.0375151	−	0.0191149i	−0.472647	+	0.881252i	$0.656702\pi$
$108$		0			0
$109$	9.46672			0.906748			0.453374	−	0.891320i	$-0.350220\pi$
$109$	9.46672			0.906748			0.453374	+	0.891320i	$0.350220\pi$
$110$	−2.32712	+	2.77501i	−0.221882	+	0.264586i
$111$		0			0
$112$	1.19806	−	7.56426i	0.113206	−	0.714755i
$113$	18.0576	+	9.20080i	1.69871	+	0.865538i	0.986537	+	0.163539i	$0.0522910\pi$
$113$	18.0576	+	9.20080i	1.69871	+	0.865538i	0.712178	+	0.701999i	$0.247709\pi$
$114$		0			0
$115$	−6.69171	−	0.429742i	−0.624006	−	0.0400737i
$116$	2.73826	−	3.76890i	0.254241	−	0.349933i
$117$		0			0
$118$	−0.355895	+	0.698483i	−0.0327628	+	0.0643005i
$119$	9.03071	+	12.4297i	0.827844	+	1.13943i
$120$		0			0
$121$	8.96835	−	6.36935i	0.815305	−	0.579032i
$122$	2.39578	+	2.39578i	0.216903	+	0.216903i
$123$		0			0
$124$	11.2926	−	3.66920i	1.01411	−	0.329504i
$125$	9.27148	−	6.24817i	0.829267	−	0.558853i
$126$		0			0
$127$	−9.31359	+	1.47513i	−0.826447	+	0.130896i	−0.555309	−	0.831644i	$-0.687400\pi$
$127$	−9.31359	+	1.47513i	−0.826447	+	0.130896i	−0.271138	+	0.962540i	$0.587400\pi$
$128$	10.0641	−	5.12793i	0.889551	−	0.453249i
$129$		0			0
$130$	2.93446	−	1.26533i	0.257369	−	0.110977i
$131$			7.51676i			0.656743i	0.944549	+	0.328371i	$0.106500\pi$
$131$			7.51676i			0.656743i	−0.944549	+	0.328371i	$0.893500\pi$
$132$		0			0
$133$	−8.45377	+	8.45377i	−0.733035	+	0.733035i
$134$	0.734554	−	0.533685i	0.0634558	−	0.0461034i
$135$		0			0
$136$	−2.99035	+	9.20336i	−0.256421	+	0.789182i
$137$	2.40429	+	15.1801i	0.205413	+	1.29692i	0.847706	+	0.530466i	$0.177983\pi$
$137$	2.40429	+	15.1801i	0.205413	+	1.29692i	−0.642294	+	0.766458i	$0.722017\pi$
$138$		0			0
$139$	−1.28625	+	3.95867i	−0.109098	+	0.335770i	−0.990670	−	0.136279i	$-0.956486\pi$
$139$	−1.28625	+	3.95867i	−0.109098	+	0.335770i	0.881572	+	0.472049i	$0.156486\pi$
$140$	−7.33386	+	8.84168i	−0.619824	+	0.747259i
$141$		0			0
$142$	0.992116	−	0.992116i	0.0832565	−	0.0832565i
$143$	−9.59470	+	1.46670i	−0.802349	+	0.122651i
$144$		0			0
$145$	−5.43029	+	2.34152i	−0.450961	+	0.194453i
$146$	−2.23368	−	6.87457i	−0.184861	−	0.568943i
$147$		0			0
$148$	2.02391	−	0.320556i	0.166364	−	0.0263495i
$149$	−14.5440	−	10.5669i	−1.19149	−	0.865672i	−0.198073	−	0.980187i	$-0.563468\pi$
$149$	−14.5440	−	10.5669i	−1.19149	−	0.865672i	−0.993421	+	0.114516i	$0.963468\pi$
$150$		0			0
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.475345	−	0.879800i	$-0.342323\pi$
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.901695	+	0.432372i	$0.142323\pi$
$152$	−7.43742	−	1.17797i	−0.603254	−	0.0955461i
$153$		0			0
$154$	−3.83633	+	2.75579i	−0.309140	+	0.222068i
$155$	−14.7052	−	3.30708i	−1.18115	−	0.265631i
$156$		0			0
$157$	9.74483	−	19.1253i	0.777722	−	1.52636i	−0.0709708	−	0.997478i	$-0.522610\pi$
$157$	9.74483	−	19.1253i	0.777722	−	1.52636i	0.848693	−	0.528887i	$-0.177390\pi$
$158$	3.38003	+	6.63368i	0.268901	+	0.527748i
$159$		0			0
$160$	−11.0596	−	0.710248i	−0.874338	−	0.0561500i
$161$	−8.31766	−	2.70257i	−0.655524	−	0.212993i
$162$		0			0
$163$	−1.63083	+	10.2967i	−0.127737	+	0.806497i	0.837752	+	0.546051i	$0.183870\pi$
$163$	−1.63083	+	10.2967i	−0.127737	+	0.806497i	−0.965488	+	0.260446i	$0.916130\pi$
$164$	6.26288			0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	1.76660	−	11.1538i	0.136703	−	0.863110i	−0.820067	−	0.572267i	$-0.806064\pi$
$167$	1.76660	−	11.1538i	0.136703	−	0.863110i	0.956771	−	0.290843i	$-0.0939359\pi$
$168$		0			0
$169$	−4.21842	−	1.37065i	−0.324493	−	0.105434i
$170$	4.32000	−	3.79862i	0.331329	−	0.291341i
$171$		0			0
$172$	5.73731	+	11.2601i	0.437466	+	0.858575i
$173$	5.99367	−	11.7632i	0.455691	−	0.894343i	−0.542823	−	0.839847i	$-0.682645\pi$
$173$	5.99367	−	11.7632i	0.455691	−	0.894343i	0.998514	−	0.0544963i	$-0.0173553\pi$
$174$		0			0
$175$	13.7328	−	4.90381i	1.03810	−	0.370693i
$176$	8.26862	+	2.73598i	0.623270	+	0.206233i
$177$		0			0
$178$	5.38885	+	0.853510i	0.403912	+	0.0639733i
$179$	2.11776	−	0.688100i	0.158288	−	0.0514310i	−0.228801	−	0.973473i	$-0.573480\pi$
$179$	2.11776	−	0.688100i	0.158288	−	0.0514310i	0.387089	+	0.922042i	$0.373480\pi$
$180$		0			0
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	0.449776	−	0.893141i	$-0.351504\pi$
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	−0.710440	+	0.703758i	$0.751504\pi$
$182$	4.11663	−	0.652010i	0.305145	−	0.0483302i
$183$		0			0
$184$	−1.70221	−	5.23888i	−0.125489	−	0.386215i
$185$	−2.41725	−	0.960696i	−0.177720	−	0.0706318i
$186$		0			0
$187$	−15.6105	+	7.84826i	−1.14155	+	0.573922i
$188$	−4.58586	+	4.58586i	−0.334458	+	0.334458i
$189$		0			0
$190$	3.44537	+	2.85781i	0.249953	+	0.207327i
$191$	1.26010	−	3.87820i	0.0911779	−	0.280617i	−0.895061	−	0.445944i	$-0.852868\pi$
$191$	1.26010	−	3.87820i	0.0911779	−	0.280617i	0.986239	+	0.165327i	$0.0528680\pi$
$192$		0			0
$193$	−3.26960	−	20.6434i	−0.235351	−	1.48595i	−0.768459	−	0.639899i	$-0.778976\pi$
$193$	−3.26960	−	20.6434i	−0.235351	−	1.48595i	0.533108	−	0.846047i	$-0.321024\pi$
$194$	−1.51938	+	4.67617i	−0.109085	+	0.335729i
$195$		0			0
$196$	−2.14544	+	1.55875i	−0.153246	+	0.111339i
$197$	−0.213782	+	0.213782i	−0.0152313	+	0.0152313i	−0.714681	−	0.699450i	$-0.753428\pi$
$197$	−0.213782	+	0.213782i	−0.0152313	+	0.0152313i	0.699450	+	0.714681i	$0.253428\pi$
$198$		0			0
$199$			11.0815i			0.785549i	0.919635	+	0.392775i	$0.128485\pi$
$199$			11.0815i			0.785549i	−0.919635	+	0.392775i	$0.871515\pi$
$200$	7.58288	+	5.18219i	0.536190	+	0.366436i
$201$		0			0
$202$	0.830691	−	0.423258i	0.0584472	−	0.0297803i
$203$	−7.61793	+	1.20656i	−0.534674	+	0.0846840i
$204$		0			0
$205$	−6.83769	−	4.05581i	−0.477565	−	0.283270i
$206$	2.86620	−	0.931285i	0.199698	−	0.0648857i
$207$		0			0
$208$	−5.43417	−	5.43417i	−0.376792	−	0.376792i
$209$	−7.93217	−	11.0423i	−0.548680	−	0.763815i
$210$		0			0
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	0.591349	−	0.806416i	$-0.298596\pi$
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	−0.949684	+	0.313210i	$0.898596\pi$
$212$	1.18177	−	2.31936i	0.0811644	−	0.159294i
$213$		0			0
$214$	−0.125014	+	0.172067i	−0.00854576	+	0.0117622i
$215$	1.02810	−	16.0090i	0.0701158	−	1.09181i
$216$		0			0
$217$	−17.5158	−	8.92474i	−1.18905	−	0.605851i
$218$	0.723193	−	4.56606i	0.0489808	−	0.309253i
$219$		0			0
$220$	−8.57352	−	9.85688i	−0.578026	−	0.664551i
$221$	15.4172			1.03707
$222$		0			0
$223$	5.50839	+	2.80667i	0.368869	+	0.187948i	0.628593	−	0.777735i	$-0.283631\pi$
$223$	5.50839	+	2.80667i	0.368869	+	0.187948i	−0.259723	+	0.965683i	$0.583631\pi$
$224$	−13.7469	−	4.46662i	−0.918500	−	0.298439i
$225$		0			0
$226$	5.81727	−	8.00679i	0.386959	−	0.532604i
$227$	1.50576	+	2.95522i	0.0999406	+	0.196145i	0.935563	−	0.353160i	$-0.114893\pi$
$227$	1.50576	+	2.95522i	0.0999406	+	0.196145i	−0.835622	+	0.549304i	$0.814893\pi$
$228$		0			0
$229$	−3.13876	−	4.32013i	−0.207415	−	0.285482i	0.692618	−	0.721305i	$-0.256457\pi$
$229$	−3.13876	−	4.32013i	−0.207415	−	0.285482i	−0.900032	+	0.435823i	$0.856457\pi$
$230$	−0.718477	+	3.19477i	−0.0473750	+	0.210657i
$231$		0			0
$232$	−3.43509	−	3.43509i	−0.225525	−	0.225525i
$233$	−4.36386	−	0.691167i	−0.285886	−	0.0452799i	0.0118446	−	0.999930i	$-0.496230\pi$
$233$	−4.36386	−	0.691167i	−0.285886	−	0.0452799i	−0.297730	+	0.954650i	$0.596230\pi$
$234$		0			0
$235$	7.97652	−	2.03697i	0.520331	−	0.132877i
$236$	−2.28770	−	1.66211i	−0.148917	−	0.108194i
$237$		0			0
$238$	6.68507	−	3.40621i	0.433329	−	0.220792i
$239$	−3.23012	−	9.94128i	−0.208939	−	0.643048i	−0.999529	−	0.0307017i	$-0.990226\pi$
$239$	−3.23012	−	9.94128i	−0.208939	−	0.643048i	0.790590	−	0.612346i	$-0.209774\pi$
$240$		0			0
$241$			27.8579i			1.79449i	0.441536	+	0.897243i	$0.354434\pi$
$241$			27.8579i			1.79449i	−0.441536	+	0.897243i	$0.645566\pi$
$242$	−2.38699	−	4.81226i	−0.153442	−	0.309344i
$243$		0			0
$244$	−9.88748	+	7.18367i	−0.632981	+	0.459888i
$245$	3.35178	−	0.312441i	0.214138	−	0.0199611i
$246$		0			0
$247$	1.87672	+	11.8492i	0.119413	+	0.753944i
$248$	−1.93695	−	12.2294i	−0.122996	−	0.776569i
$249$		0			0
$250$	−2.30538	−	4.94921i	−0.145805	−	0.313015i
$251$	−8.04670	+	5.84627i	−0.507903	+	0.369013i	−0.812028	−	0.583619i	$-0.801636\pi$
$251$	−8.04670	+	5.84627i	−0.507903	+	0.369013i	0.304124	+	0.952632i	$0.401636\pi$
$252$		0			0
$253$	4.56302	−	8.83737i	0.286874	−	0.555601i
$254$			4.60489i			0.288936i
$255$		0			0
$256$	0.0455968	+	0.140332i	0.00284980	+	0.00877078i
$257$	−3.77828	+	1.92513i	−0.235683	+	0.120086i	−0.567844	−	0.823136i	$-0.692222\pi$
$257$	−3.77828	+	1.92513i	−0.235683	+	0.120086i	0.332161	+	0.943223i	$0.392222\pi$
$258$		0			0
$259$	−2.74467	−	1.99412i	−0.170545	−	0.123908i
$260$	2.85218	+	11.1688i	0.176885	+	0.692659i
$261$		0			0
$262$	3.62554	+	0.574229i	0.223987	+	0.0354760i
$263$	−16.1830	−	16.1830i	−0.997884	−	0.997884i	0.00211364	−	0.999998i	$-0.499327\pi$
$263$	−16.1830	−	16.1830i	−0.997884	−	0.997884i	−0.999998	+	0.00211364i	$0.999327\pi$
$264$		0			0
$265$	−2.79223	+	1.76692i	−0.171526	+	0.108541i
$266$	3.43167	+	4.72330i	0.210409	+	0.289604i
$267$		0			0
$268$	1.48689	+	2.91819i	0.0908265	+	0.178257i
$269$	13.4435	−	18.5034i	0.819666	−	1.12817i	−0.170094	−	0.985428i	$-0.554407\pi$
$269$	13.4435	−	18.5034i	0.819666	−	1.12817i	0.989759	−	0.142745i	$-0.0455930\pi$
$270$		0			0
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	0.268580	−	0.963258i	$-0.413446\pi$
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	−0.348903	+	0.937159i	$0.613446\pi$
$272$	−12.3263	−	6.28057i	−0.747392	−	0.380815i
$273$		0			0
$274$	7.50545			0.453421
$275$	2.97713	+	16.3137i	0.179528	+	0.983753i
$276$		0			0
$277$	−2.23010	+	14.0803i	−0.133994	+	0.846002i	0.825527	+	0.564363i	$0.190878\pi$
$277$	−2.23010	+	14.0803i	−0.133994	+	0.846002i	−0.959520	+	0.281639i	$0.909122\pi$
$278$	1.81111	+	0.922808i	0.108623	+	0.0553464i
$279$		0			0
$280$	7.91015	+	8.99586i	0.472722	+	0.537605i
$281$	−14.9161	+	20.5302i	−0.889818	+	1.22473i	0.0837853	+	0.996484i	$0.473299\pi$
$281$	−14.9161	+	20.5302i	−0.889818	+	1.22473i	−0.973604	+	0.228246i	$0.926701\pi$
$282$		0			0
$283$	3.36440	−	6.60300i	0.199993	−	0.392508i	−0.769128	−	0.639095i	$-0.779309\pi$
$283$	3.36440	−	6.60300i	0.199993	−	0.392508i	0.969121	+	0.246587i	$0.0793092\pi$
$284$	2.97484	+	4.09451i	0.176524	+	0.242964i
$285$		0			0
$286$	−0.0255420	+	4.73983i	−0.00151033	+	0.280272i
$287$	−7.33195	−	7.33195i	−0.432791	−	0.432791i
$288$		0			0
$289$	10.2266	−	3.32284i	0.601567	−	0.195461i
$290$	0.714542	+	2.79806i	0.0419594	+	0.164307i
$291$		0			0
$292$	25.7529	−	4.07886i	1.50707	−	0.238697i
$293$	13.0777	−	6.66340i	0.764005	−	0.389280i	−0.0281472	−	0.999604i	$-0.508961\pi$
$293$	13.0777	−	6.66340i	0.764005	−	0.389280i	0.792152	+	0.610324i	$0.208961\pi$
$294$		0			0
$295$	1.42129	+	3.29616i	0.0827507	+	0.191910i
$296$		−	2.13682i		−	0.124200i
$297$		0			0
$298$	−6.20775	+	6.20775i	−0.359606	+	0.359606i
$299$	−7.09994	+	5.15841i	−0.410600	+	0.298318i
$300$		0			0
$301$	6.46553	−	19.8989i	0.372667	−	1.14695i
$302$	−1.35920	−	8.58165i	−0.0782131	−	0.493818i
$303$		0			0
$304$	3.32657	−	10.2381i	0.190792	−	0.587197i
$305$	15.4471	−	1.43992i	0.884496	−	0.0824494i
$306$		0			0
$307$	−0.874954	+	0.874954i	−0.0499363	+	0.0499363i	−0.731634	−	0.681698i	$-0.761242\pi$
$307$	−0.874954	+	0.874954i	−0.0499363	+	0.0499363i	0.681698	+	0.731634i	$0.261242\pi$
$308$	−7.65344	−	15.2230i	−0.436095	−	0.867409i
$309$		0			0
$310$	−2.71847	+	6.84008i	−0.154399	+	0.388491i
$311$	−4.37162	−	13.4545i	−0.247892	−	0.762933i	−0.995147	−	0.0983958i	$-0.968629\pi$
$311$	−4.37162	−	13.4545i	−0.247892	−	0.762933i	0.747256	−	0.664537i	$-0.231371\pi$
$312$		0			0
$313$	0.730542	−	0.115706i	0.0412927	−	0.00654011i	−0.135754	−	0.990743i	$-0.543346\pi$
$313$	0.730542	−	0.115706i	0.0412927	−	0.00654011i	0.177047	+	0.984202i	$0.443346\pi$
$314$	−8.48022	−	6.16124i	−0.478566	−	0.347699i
$315$		0			0
$316$	−25.5415	+	8.29895i	−1.43682	+	0.466852i
$317$	16.8560	+	2.66972i	0.946726	+	0.149947i	0.610661	−	0.791892i	$-0.290904\pi$
$317$	16.8560	+	2.66972i	0.946726	+	0.149947i	0.336065	+	0.941839i	$0.390904\pi$
$318$		0			0
$319$	0.0472661	−	8.77118i	0.00264640	−	0.491092i
$320$	1.38930	−	6.17765i	0.0776644	−	0.345341i
$321$		0			0
$322$	−1.93894	+	3.80538i	−0.108053	+	0.212065i
$323$	9.80433	+	19.2421i	0.545527	+	1.07066i
$324$		0			0
$325$	4.11888	−	14.0409i	0.228475	−	0.778850i
$326$	4.84178	+	1.57319i	0.268161	+	0.0871309i
$327$		0			0
$328$	1.02165	−	6.45047i	0.0564114	−	0.356168i
$329$	10.7373			0.591967
$330$		0			0
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	−1.84150	+	11.6268i	−0.101065	+	0.638102i
$333$		0			0
$334$	−5.24485	−	1.70415i	−0.286985	−	0.0932472i
$335$	0.266444	−	4.14893i	0.0145574	−	0.226680i
$336$		0			0
$337$	−4.28455	−	8.40891i	−0.233394	−	0.458062i	0.744370	−	0.667767i	$-0.232750\pi$
$337$	−4.28455	−	8.40891i	−0.233394	−	0.458062i	−0.977765	+	0.209705i	$0.932750\pi$
$338$	−0.983358	+	1.92995i	−0.0534876	+	0.104975i
$339$		0			0
$340$	11.0959	+	17.5346i	0.601758	+	0.950950i
$341$	13.2379	−	18.0154i	0.716871	−	0.975589i
$342$		0			0
$343$	−15.8271	−	2.50676i	−0.854581	−	0.135352i
$344$	12.5333	−	4.07231i	0.675750	−	0.219564i
$345$		0			0
$346$	−5.21586	−	3.78954i	−0.280406	−	0.203727i
$347$	19.0026	−	3.00971i	1.02011	−	0.161570i	0.376094	−	0.926581i	$-0.377267\pi$
$347$	19.0026	−	3.00971i	1.02011	−	0.161570i	0.644016	+	0.765012i	$0.277267\pi$
$348$		0			0
$349$	−4.59599	−	14.1450i	−0.246018	−	0.757164i	−0.995467	−	0.0951031i	$-0.969682\pi$
$349$	−4.59599	−	14.1450i	−0.246018	−	0.757164i	0.749450	−	0.662061i	$-0.230318\pi$
$350$	−1.31615	−	6.99831i	−0.0703511	−	0.374075i
$351$		0			0
$352$	7.54143	−	14.6058i	0.401960	−	0.778491i
$353$	−1.78406	+	1.78406i	−0.0949560	+	0.0949560i	−0.752989	−	0.658033i	$-0.771389\pi$
$353$	−1.78406	+	1.78406i	−0.0949560	+	0.0949560i	0.658033	+	0.752989i	$0.271389\pi$
$354$		0			0
$355$	−0.596284	−	6.39679i	−0.0316475	−	0.339506i
$356$	−6.08171	+	18.7176i	−0.322330	+	0.992029i
$357$		0			0
$358$	−0.170108	−	1.07402i	−0.00899047	−	0.0567636i
$359$	−2.62416	+	8.07635i	−0.138498	+	0.426253i	−0.996118	−	0.0880312i	$-0.971942\pi$
$359$	−2.62416	+	8.07635i	−0.138498	+	0.426253i	0.857620	+	0.514285i	$0.171942\pi$
$360$		0			0
$361$	1.77596	−	1.29031i	0.0934717	−	0.0679111i
$362$	−1.49682	+	1.49682i	−0.0786711	+	0.0786711i
$363$		0			0
$364$			15.0345i			0.788021i
$365$	−30.7579	−	12.2242i	−1.60994	−	0.639844i
$366$		0			0
$367$	18.9156	−	9.63799i	0.987387	−	0.503099i	0.115765	−	0.993277i	$-0.463068\pi$
$367$	18.9156	−	9.63799i	0.987387	−	0.503099i	0.871622	+	0.490178i	$0.163068\pi$
$368$	7.77792	−	1.23190i	0.405452	−	0.0642173i
$369$		0			0
$370$	−0.648032	+	1.09252i	−0.0336896	+	0.0567973i
$371$	−4.09877	+	1.33177i	−0.212797	+	0.0691420i
$372$		0			0
$373$	2.57445	+	2.57445i	0.133300	+	0.133300i	0.770609	−	0.637309i	$-0.219952\pi$
$373$	2.57445	+	2.57445i	0.133300	+	0.133300i	−0.637309	+	0.770609i	$0.719952\pi$
$374$	2.59290	+	8.12891i	0.134076	+	0.420336i
$375$		0			0
$376$	3.97513	+	5.47130i	0.205002	+	0.282161i
$377$	−3.51371	+	6.89604i	−0.180965	+	0.355164i
$378$		0			0
$379$	9.74713	−	13.4158i	0.500677	−	0.689122i	−0.481636	−	0.876371i	$-0.659957\pi$
$379$	9.74713	−	13.4158i	0.500677	−	0.689122i	0.982312	+	0.187249i	$0.0599572\pi$
$380$	−12.1259	+	10.6624i	−0.622044	+	0.546970i
$381$		0			0
$382$	−1.77430	−	0.904051i	−0.0907810	−	0.0462553i
$383$	−1.77402	+	11.2007i	−0.0906481	+	0.572330i	0.900000	+	0.435890i	$0.143566\pi$
$383$	−1.77402	+	11.2007i	−0.0906481	+	0.572330i	−0.990648	+	0.136440i	$0.956434\pi$
$384$		0			0
$385$	−1.50243	+	21.5764i	−0.0765710	+	1.09964i
$386$	−10.2067			−0.519505
$387$		0			0
$388$	−15.8027	−	8.05188i	−0.802260	−	0.408772i
$389$	0.777554	+	0.252643i	0.0394236	+	0.0128095i	0.328662	−	0.944447i	$-0.393402\pi$
$389$	0.777554	+	0.252643i	0.0394236	+	0.0128095i	−0.289239	+	0.957257i	$0.593402\pi$
$390$		0			0
$391$	−9.28580	+	12.7808i	−0.469603	+	0.646353i
$392$	1.25546	+	2.46398i	0.0634102	+	0.124450i
$393$		0			0
$394$	0.0867814	+	0.119444i	0.00437198	+	0.00601752i
$395$	33.2601	+	7.47992i	1.67350	+	0.376356i
$396$		0			0
$397$	11.8504	+	11.8504i	0.594752	+	0.594752i	0.938911	−	0.344159i	$-0.111836\pi$
$397$	11.8504	+	11.8504i	0.594752	+	0.594752i	−0.344159	+	0.938911i	$0.611836\pi$
$398$	5.34493	+	0.846553i	0.267917	+	0.0424339i
$399$		0			0
$400$	−9.01302	+	9.54802i	−0.450651	+	0.477401i
$401$	−23.0228	−	16.7270i	−1.14970	−	0.835308i	−0.161262	−	0.986912i	$-0.551556\pi$
$401$	−23.0228	−	16.7270i	−1.14970	−	0.835308i	−0.988441	+	0.151603i	$0.951556\pi$
$402$		0			0
$403$	−17.5765	+	8.95566i	−0.875547	+	0.446113i
$404$	1.03922	+	3.19839i	0.0517032	+	0.159126i
$405$		0			0
$406$			3.76651i			0.186929i
$407$	2.74279	−	2.71338i	0.135955	−	0.134497i
$408$		0			0
$409$	−1.95998	+	1.42401i	−0.0969146	+	0.0704126i	−0.635187	−	0.772358i	$-0.719077\pi$
$409$	−1.95998	+	1.42401i	−0.0969146	+	0.0704126i	0.538273	+	0.842771i	$0.319077\pi$
$410$	−2.47858	+	2.98817i	−0.122408	+	0.147575i
$411$		0			0
$412$	1.70059	+	10.7371i	0.0837820	+	0.528979i
$413$	0.732376	+	4.62404i	0.0360379	+	0.227534i
$414$		0			0
$415$	9.53994	−	11.5013i	0.468297	−	0.564578i
$416$	−11.7343	+	8.52546i	−0.575321	+	0.417995i
$417$		0			0
$418$	−5.93199	+	2.98234i	−0.290143	+	0.145871i
$419$			16.4371i			0.803006i	0.915858	+	0.401503i	$0.131512\pi$
$419$			16.4371i			0.803006i	−0.915858	+	0.401503i	$0.868488\pi$
$420$		0			0
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	0.812204	−	0.583373i	$-0.198267\pi$
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	−0.999985	+	0.00544310i	$0.998267\pi$
$422$	−3.85314	+	1.96327i	−0.187568	+	0.0955707i
$423$		0			0
$424$	−2.19605	−	1.59552i	−0.106649	−	0.0774853i
$425$	−0.758915	−	26.3296i	−0.0368128	−	1.27717i
$426$		0			0
$427$	19.9852	+	3.16534i	0.967151	+	0.153182i
$428$	−0.542488	−	0.542488i	−0.0262222	−	0.0262222i
$429$		0			0
$430$	−7.64304	−	1.71886i	−0.368580	−	0.0828907i
$431$	11.6588	+	16.0470i	0.561586	+	0.772957i	0.991527	−	0.129900i	$-0.0414655\pi$
$431$	11.6588	+	16.0470i	0.561586	+	0.772957i	−0.429941	+	0.902857i	$0.641466\pi$
$432$		0			0
$433$	12.9956	+	25.5054i	0.624531	+	1.22571i	0.959027	+	0.283314i	$0.0914339\pi$
$433$	12.9956	+	25.5054i	0.624531	+	1.22571i	−0.334496	+	0.942397i	$0.608566\pi$
$434$	−5.64273	+	7.76656i	−0.270860	+	0.372807i
$435$		0			0
$436$	15.8597	+	5.15313i	0.759541	+	0.246790i
$437$	−10.9533	−	5.58097i	−0.523966	−	0.266974i
$438$		0			0
$439$	−3.12279			−0.149043			−0.0745214	−	0.997219i	$-0.523743\pi$
$439$	−3.12279			−0.149043			−0.0745214	+	0.997219i	$0.523743\pi$
$440$	−11.5507	+	7.22238i	−0.550658	+	0.344313i
$441$		0			0
$442$	1.17777	−	7.43613i	0.0560207	−	0.353701i
$443$	−28.2787	−	14.4087i	−1.34356	−	0.684579i	−0.373545	−	0.927612i	$-0.621858\pi$
$443$	−28.2787	−	14.4087i	−1.34356	−	0.684579i	−0.970018	+	0.243033i	$0.921858\pi$
$444$		0			0
$445$	18.7613	−	16.4970i	0.889369	−	0.782032i
$446$	1.77454	−	2.44244i	0.0840267	−	0.115653i
$447$		0			0
$448$	3.74928	−	7.35837i	0.177137	−	0.347650i
$449$	−20.5693	−	28.3112i	−0.970726	−	1.33609i	−0.941679	−	0.336511i	$-0.890753\pi$
$449$	−20.5693	−	28.3112i	−0.970726	−	1.33609i	−0.0290462	−	0.999578i	$-0.509247\pi$
$450$		0			0
$451$	9.57702	−	6.87957i	0.450964	−	0.323946i
$452$	25.2437	+	25.2437i	1.18736	+	1.18736i
$453$		0			0
$454$	1.54041	−	0.500510i	0.0722951	−	0.0234901i
$455$	9.73624	−	16.4143i	0.456442	−	0.769516i
$456$		0			0
$457$	−5.03728	+	0.797826i	−0.235634	+	0.0373207i	−0.273134	−	0.961976i	$-0.588060\pi$
$457$	−5.03728	+	0.797826i	−0.235634	+	0.0373207i	0.0375006	+	0.999297i	$0.488060\pi$
$458$	−2.32350	+	1.18388i	−0.108570	+	0.0553191i
$459$		0			0
$460$	−10.9768	−	4.36253i	−0.511794	−	0.203404i
$461$		−	12.4703i		−	0.580801i	−0.956905	−	0.290400i	$-0.906211\pi$
$461$		−	12.4703i		−	0.580801i	0.956905	−	0.290400i	$-0.0937885\pi$
$462$		0			0
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	−0.995051	−	0.0993669i	$-0.968318\pi$
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	0.0993669	+	0.995051i	$0.468318\pi$
$464$	5.61854	−	4.08211i	0.260834	−	0.189507i
$465$		0			0
$466$	−0.666738	+	2.05201i	−0.0308860	+	0.0950574i
$467$	6.20937	+	39.2044i	0.287335	+	1.81416i	0.534476	+	0.845184i	$0.320509\pi$
$467$	6.20937	+	39.2044i	0.287335	+	1.81416i	−0.247141	+	0.968980i	$0.579491\pi$
$468$		0			0
$469$	1.67562	−	5.15703i	0.0773730	−	0.238130i
$470$	−0.373136	−	4.00290i	−0.0172115	−	0.184640i
$471$		0			0
$472$	−2.08508	+	2.08508i	−0.0959738	+	0.0959738i
$473$	21.1422	+	10.9164i	0.972119	+	0.501936i
$474$		0			0
$475$	20.1437	−	3.78836i	0.924256	−	0.173822i
$476$	8.36324	+	25.7394i	0.383328	+	1.17976i
$477$		0			0
$478$	−5.04171	+	0.798528i	−0.230602	+	0.0365238i
$479$	30.9491	+	22.4858i	1.41410	+	1.02740i	0.992711	+	0.120523i	$0.0384570\pi$
$479$	30.9491	+	22.4858i	1.41410	+	1.02740i	0.421388	+	0.906880i	$0.361543\pi$
$480$		0			0
$481$	−3.23773	+	1.05200i	−0.147628	+	0.0479671i
$482$	13.4366	+	2.12815i	0.612022	+	0.0969348i
$483$		0			0
$484$	18.4919	−	5.78879i	0.840539	−	0.263127i
$485$	12.0387	+	19.0246i	0.546650	+	0.863863i
$486$		0			0
$487$	−12.3391	+	24.2169i	−0.559139	+	1.09737i	0.422454	+	0.906384i	$0.361169\pi$
$487$	−12.3391	+	24.2169i	−0.559139	+	1.09737i	−0.981593	+	0.190987i	$0.938831\pi$
$488$	5.78591	+	11.3555i	0.261916	+	0.514039i
$489$		0			0
$490$	0.105355	−	1.64053i	0.00475944	−	0.0741114i
$491$	−3.77748	−	1.22738i	−0.170475	−	0.0553907i	0.222536	−	0.974925i	$-0.428567\pi$
$491$	−3.77748	−	1.22738i	−0.170475	−	0.0553907i	−0.393011	+	0.919534i	$0.628567\pi$
$492$		0			0
$493$	−2.17949	+	13.7608i	−0.0981593	+	0.619753i
$494$	5.85854			0.263588
$495$		0			0
$496$	17.7010			0.794798
$497$	1.31080	−	8.27608i	0.0587975	−	0.371233i
$498$		0			0
$499$	6.11060	+	1.98546i	0.273548	+	0.0888812i	0.442579	−	0.896730i	$-0.354064\pi$
$499$	6.11060	+	1.98546i	0.273548	+	0.0888812i	−0.169031	+	0.985611i	$0.554064\pi$
$500$	18.9337	−	5.42077i	0.846742	−	0.242424i
$501$		0			0
$502$	2.20510	+	4.32776i	0.0984186	+	0.193157i
$503$	−18.4896	+	36.2878i	−0.824409	+	1.61799i	−0.0388190	+	0.999246i	$0.512360\pi$
$503$	−18.4896	+	36.2878i	−0.824409	+	1.61799i	−0.785590	+	0.618747i	$0.787640\pi$
$504$		0			0
$505$	0.936660	−	4.16493i	0.0416808	−	0.185337i
$506$	−3.91392	−	2.87598i	−0.173995	−	0.127853i
$507$		0			0
$508$	−16.4061	−	2.59847i	−0.727904	−	0.115289i
$509$	8.83124	−	2.86944i	0.391438	−	0.127186i	−0.106684	−	0.994293i	$-0.534023\pi$
$509$	8.83124	−	2.86944i	0.391438	−	0.127186i	0.498122	+	0.867107i	$0.334023\pi$
$510$		0			0
$511$	−34.9240	−	25.3738i	−1.54495	−	1.12247i
$512$	22.3835	−	3.54520i	0.989220	−	0.156677i
$513$		0			0
$514$	0.639909	+	1.96944i	0.0282252	+	0.0868681i
$515$	5.09661	−	12.8238i	0.224584	−	0.565086i
$516$		0			0
$517$	−1.97515	+	12.0500i	−0.0868669	+	0.529957i
$518$	−1.17149	+	1.17149i	−0.0514723	+	0.0514723i
$519$		0			0
$520$	11.9686	−	1.11567i	0.524857	−	0.0489252i
$521$	4.57564	−	14.0824i	0.200462	−	0.616960i	−0.799407	−	0.600790i	$-0.794853\pi$
$521$	4.57564	−	14.0824i	0.200462	−	0.616960i	0.999869	−	0.0161698i	$-0.00514724\pi$
$522$		0			0
$523$	6.07643	+	38.3651i	0.265704	+	1.67759i	0.654344	+	0.756197i	$0.272945\pi$
$523$	6.07643	+	38.3651i	0.265704	+	1.67759i	−0.388640	+	0.921390i	$0.627055\pi$
$524$	−4.09168	+	12.5929i	−0.178746	+	0.550124i
$525$		0			0
$526$	−9.04175	+	6.56922i	−0.394239	+	0.286431i
$527$	−25.1096	+	25.1096i	−1.09379	+	1.09379i
$528$		0			0
$529$			14.0073i			0.609011i
$530$	0.638925	+	1.48175i	0.0277531	+	0.0643632i
$531$		0			0
$532$	−18.7644	+	9.56095i	−0.813541	+	0.414520i
$533$	−10.2768	+	1.62768i	−0.445136	+	0.0705027i
$534$		0			0
$535$	0.240966	+	0.943590i	0.0104178	+	0.0407950i
$536$	3.24815	−	1.05539i	0.140299	−	0.0455859i
$537$		0			0
$538$	−7.89771	−	7.89771i	−0.340495	−	0.340495i
$539$	−1.56850	+	4.74029i	−0.0675603	+	0.204179i
$540$		0			0
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	0.970260	−	0.242064i	$-0.0778243\pi$
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	−0.530043	+	0.847971i	$0.677824\pi$
$542$	−0.308241	+	0.604957i	−0.0132401	+	0.0259851i
$543$		0			0
$544$	−15.3469	+	21.1232i	−0.657994	+	0.905650i
$545$	−13.9781	−	15.8967i	−0.598758	−	0.680940i
$546$		0			0
$547$	34.9333	+	17.7994i	1.49364	+	0.761048i	0.994427	−	0.105430i	$-0.0336219\pi$
$547$	34.9333	+	17.7994i	1.49364	+	0.761048i	0.499215	+	0.866478i	$0.333622\pi$
$548$	−4.23522	+	26.7401i	−0.180920	+	1.14228i
$549$		0			0
$550$	8.09597	−	0.189699i	0.345213	−	0.00808877i
$551$	−10.8414			−0.461858
$552$		0			0
$553$	39.6170	+	20.1859i	1.68469	+	0.858391i
$554$	6.62094	+	2.15127i	0.281297	+	0.0913989i
$555$		0			0
$556$	−4.30973	+	5.93184i	−0.182773	+	0.251566i
$557$	−16.6620	−	32.7010i	−0.705991	−	1.38558i	−0.913291	−	0.407307i	$-0.866468\pi$
$557$	−16.6620	−	32.7010i	−0.705991	−	1.38558i	0.207301	−	0.978277i	$-0.433532\pi$
$558$		0			0
$559$	−12.3408	−	16.9856i	−0.521959	−	0.718416i
$560$	−14.4711	+	9.15725i	−0.611514	+	0.386964i
$561$		0			0
$562$	8.76280	+	8.76280i	0.369636	+	0.369636i
$563$	−16.6732	−	2.64077i	−0.702690	−	0.111295i	−0.205143	−	0.978732i	$-0.565766\pi$
$563$	−16.6732	−	2.64077i	−0.702690	−	0.111295i	−0.497547	+	0.867437i	$0.665766\pi$
$564$		0			0
$565$	−11.2129	−	43.9082i	−0.471729	−	1.84723i
$566$	−2.92779	−	2.12716i	−0.123064	−	0.0894114i
$567$		0			0
$568$	4.70243	−	2.39601i	0.197310	−	0.100534i
$569$	0.818531	+	2.51918i	0.0343146	+	0.105609i	0.966747	−	0.255736i	$-0.0823176\pi$
$569$	0.818531	+	2.51918i	0.0343146	+	0.105609i	−0.932432	+	0.361345i	$0.882318\pi$
$570$		0			0
$571$		−	29.8675i		−	1.24992i	−0.780658	−	0.624959i	$-0.785116\pi$
$571$		−	29.8675i		−	1.24992i	0.780658	−	0.624959i	$-0.214884\pi$
$572$	−16.8725	−	2.76562i	−0.705473	−	0.115636i
$573$		0			0
$574$	−4.09651	+	2.97629i	−0.170985	+	0.124228i
$575$	9.15906	+	11.8714i	0.381959	+	0.495072i
$576$		0			0
$577$	−0.0561437	−	0.354477i	−0.00233729	−	0.0147571i	0.986492	−	0.163809i	$-0.0523780\pi$
$577$	−0.0561437	−	0.354477i	−0.00233729	−	0.0147571i	−0.988829	+	0.149052i	$0.952378\pi$
$578$	−0.821450	−	5.18643i	−0.0341678	−	0.215727i
$579$		0			0
$580$	−10.3720	+	0.966840i	−0.430674	+	0.0401458i
$581$	15.7673	−	11.4556i	0.654138	−	0.475259i
$582$		0			0
$583$	−0.740605	−	4.84483i	−0.0306727	−	0.200652i
$584$		−	27.1896i		−	1.12511i
$585$		0			0
$586$	−2.21490	−	6.81675i	−0.0914965	−	0.281597i
$587$	23.0298	−	11.7343i	0.950543	−	0.484326i	0.0912603	−	0.995827i	$-0.470910\pi$
$587$	23.0298	−	11.7343i	0.950543	−	0.484326i	0.859282	+	0.511501i	$0.170910\pi$
$588$		0			0
$589$	−22.3550	−	16.2418i	−0.921121	−	0.669233i
$590$	1.69840	−	0.433723i	0.0699222	−	0.0178561i
$591$		0			0
$592$	3.01717	+	0.477873i	0.124005	+	0.0196405i
$593$	9.56872	+	9.56872i	0.392940	+	0.392940i	0.875734	−	0.482794i	$-0.160378\pi$
$593$	9.56872	+	9.56872i	0.392940	+	0.392940i	−0.482794	+	0.875734i	$0.660378\pi$
$594$		0			0
$595$	7.53787	−	33.5177i	0.309022	−	1.37409i
$596$	−18.6138	−	25.6197i	−0.762451	−	1.04942i
$597$		0			0
$598$	1.94565	+	3.81856i	0.0795637	+	0.156153i
$599$	6.65542	−	9.16040i	0.271933	−	0.374284i	−0.651108	−	0.758985i	$-0.725696\pi$
$599$	6.65542	−	9.16040i	0.271933	−	0.374284i	0.923041	+	0.384701i	$0.125696\pi$
$600$		0			0
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.0288267	−	0.999584i	$-0.509177\pi$
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.610862	+	0.791737i	$0.709177\pi$
$602$	−9.10384	−	4.63864i	−0.371045	−	0.189057i
$603$		0			0
$604$	31.3413			1.27526
$605$	−23.9378	−	5.65513i	−0.973211	−	0.229914i
$606$		0			0
$607$	−0.779724	+	4.92298i	−0.0316480	+	0.199818i	−0.998446	−	0.0557232i	$-0.982254\pi$
$607$	−0.779724	+	4.92298i	−0.0316480	+	0.199818i	0.966798	+	0.255541i	$0.0822535\pi$
$608$	−18.1028	−	9.22383i	−0.734165	−	0.374076i
$609$		0			0
$610$	0.485538	−	7.56053i	0.0196589	−	0.306117i
$611$	6.33310	−	8.71677i	0.256210	−	0.352643i
$612$		0			0
$613$	8.29879	−	16.2873i	0.335185	−	0.657837i	−0.660481	−	0.750843i	$-0.729648\pi$
$613$	8.29879	−	16.2873i	0.335185	−	0.657837i	0.995666	+	0.0930058i	$0.0296475\pi$
$614$	0.355174	+	0.488855i	0.0143337	+	0.0197286i
$615$		0			0
$616$	−16.9274	+	5.39938i	−0.682025	+	0.217547i
$617$	−15.4942	−	15.4942i	−0.623773	−	0.623773i	0.322721	−	0.946494i	$-0.395402\pi$
$617$	−15.4942	−	15.4942i	−0.623773	−	0.623773i	−0.946494	+	0.322721i	$0.895402\pi$
$618$		0			0
$619$	−46.8070	+	15.2085i	−1.88133	+	0.611282i	−0.895114	+	0.445837i	$0.852906\pi$
$619$	−46.8070	+	15.2085i	−1.88133	+	0.611282i	−0.986219	+	0.165445i	$0.947094\pi$
$620$	−22.8356	−	13.5450i	−0.917099	−	0.543982i
$621$		0			0
$622$	−6.82342	+	1.08072i	−0.273594	+	0.0433330i
$623$	29.0325	−	14.7928i	1.16316	−	0.592661i
$624$		0			0
$625$	−24.1819	−	6.34309i	−0.967277	−	0.253724i
$626$		−	0.361199i		−	0.0144364i
$627$		0			0
$628$	26.7363	−	26.7363i	1.06689	−	1.06689i
$629$	−4.95787	+	3.60210i	−0.197683	+	0.143625i
$630$		0			0
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	−0.991170	−	0.132595i	$-0.957669\pi$
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	0.879811	+	0.475324i	$0.157669\pi$
$632$	4.38097	+	27.6604i	0.174266	+	1.10027i
$633$		0			0
$634$	2.57536	−	7.92615i	0.102281	−	0.314788i
$635$	16.2291	+	13.4615i	0.644032	+	0.534202i
$636$		0			0
$637$	3.11534	−	3.11534i	0.123434	−	0.123434i
$638$	−4.22697	−	0.692856i	−0.167347	−	0.0274304i
$639$		0			0
$640$	−23.4712	−	9.32821i	−0.927779	−	0.368730i
$641$	8.63030	+	26.5613i	0.340876	+	1.04911i	0.963755	+	0.266791i	$0.0859632\pi$
$641$	8.63030	+	26.5613i	0.340876	+	1.04911i	−0.622878	+	0.782319i	$0.714037\pi$
$642$		0			0
$643$	−9.51085	+	1.50637i	−0.375071	+	0.0594055i	−0.341124	−	0.940018i	$-0.610808\pi$
$643$	−9.51085	+	1.50637i	−0.375071	+	0.0594055i	−0.0339470	+	0.999424i	$0.510808\pi$
$644$	−12.4635	−	9.05529i	−0.491132	−	0.356828i
$645$		0			0
$646$	10.0300	−	3.25893i	0.394624	−	0.128221i
$647$	−30.5702	−	4.84185i	−1.20184	−	0.190353i	−0.476770	−	0.879028i	$-0.658193\pi$
$647$	−30.5702	−	4.84185i	−1.20184	−	0.190353i	−0.725070	+	0.688675i	$0.758193\pi$
$648$		0			0
$649$	−5.32406	−	0.0286903i	−0.208988	−	0.00112619i
$650$	−6.45766	−	3.05928i	−0.253290	−	0.119995i
$651$		0			0
$652$	−8.33705	+	16.3624i	−0.326504	+	0.640800i
$653$	−2.77406	−	5.44440i	−0.108557	−	0.213056i	0.830337	−	0.557262i	$-0.188148\pi$
$653$	−2.77406	−	5.44440i	−0.108557	−	0.213056i	−0.938894	+	0.344206i	$0.888148\pi$
$654$		0			0
$655$	12.6223	−	11.0989i	0.493194	−	0.433671i
$656$	8.87952	+	2.88513i	0.346687	+	0.112645i
$657$		0			0
$658$	0.820257	−	5.17890i	0.0319770	−	0.201895i
$659$	−12.0647			−0.469975			−0.234988	−	0.971998i	$-0.575505\pi$
$659$	−12.0647			−0.469975			−0.234988	+	0.971998i	$0.575505\pi$
$660$		0			0
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	−1.13970	+	7.19579i	−0.0442957	+	0.279672i
$663$		0			0
$664$	11.6746	+	3.79331i	0.453063	+	0.147209i
$665$	26.6782	+	1.71328i	1.03454	+	0.0664380i
$666$		0			0
$667$	−3.60048	−	7.06635i	−0.139411	−	0.273610i
$668$	9.03109	−	17.7245i	0.349423	−	0.685782i
$669$		0			0
$670$	−1.98079	−	0.445463i	−0.0765244	−	0.0172097i
$671$	−7.22862	+	21.8461i	−0.279058	+	0.843361i
$672$		0			0
$673$	−4.97380	−	0.787773i	−0.191726	−	0.0303664i	0.0598329	−	0.998208i	$-0.480943\pi$
$673$	−4.97380	−	0.787773i	−0.191726	−	0.0303664i	−0.251559	+	0.967842i	$0.580943\pi$
$674$	−4.38316	+	1.42417i	−0.168833	+	0.0548571i
$675$		0			0
$676$	−6.32105	−	4.59251i	−0.243117	−	0.176635i
$677$	35.9579	−	5.69516i	1.38197	−	0.218883i	0.579208	−	0.815180i	$-0.303362\pi$
$677$	35.9579	−	5.69516i	1.38197	−	0.218883i	0.802764	+	0.596297i	$0.203362\pi$
$678$		0			0
$679$	9.07388	+	27.9265i	0.348223	+	1.07172i
$680$	19.8699	−	8.56782i	0.761976	−	0.328561i
$681$		0			0
$682$	−7.67804	−	7.76124i	−0.294007	−	0.297193i
$683$	8.07353	−	8.07353i	0.308925	−	0.308925i	−0.535567	−	0.844492i	$-0.679902\pi$
$683$	8.07353	−	8.07353i	0.308925	−	0.308925i	0.844492	+	0.535567i	$0.179902\pi$
$684$		0			0
$685$	21.9407	−	26.4516i	0.838310	−	1.01066i
$686$	−2.41816	+	7.44232i	−0.0923257	+	0.284149i
$687$		0			0
$688$	2.94716	+	18.6076i	0.112359	+	0.709408i
$689$	−1.33638	+	4.11297i	−0.0509122	+	0.156692i
$690$		0			0
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	−0.389778	−	0.920909i	$-0.627448\pi$
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	0.755388	+	0.655277i	$0.227448\pi$
$692$	16.4445	−	16.4445i	0.625125	−	0.625125i
$693$		0			0
$694$		−	9.39538i		−	0.356644i
$695$	8.54670	−	3.68530i	0.324195	−	0.139791i
$696$		0			0
$697$	−16.6886	+	8.50329i	−0.632127	+	0.322085i
$698$	−7.17362	+	1.13619i	−0.271526	+	0.0430054i
$699$		0			0
$700$	25.6760	−	0.740076i	0.970461	−	0.0279722i
$701$	25.2475	−	8.20342i	0.953586	−	0.309839i	0.209414	−	0.977827i	$-0.432844\pi$
$701$	25.2475	−	8.20342i	0.953586	−	0.309839i	0.744172	+	0.667988i	$0.232844\pi$
$702$		0			0
$703$	−3.37197	−	3.37197i	−0.127176	−	0.127176i
$704$	7.56826	+	5.56122i	0.285239	+	0.209596i
$705$		0			0
$706$	0.724212	+	0.996792i	0.0272561	+	0.0375148i
$707$	2.52774	−	4.96097i	0.0950654	−	0.186576i
$708$		0			0
$709$	10.4984	−	14.4498i	0.394275	−	0.542673i	−0.565021	−	0.825077i	$-0.691132\pi$
$709$	10.4984	−	14.4498i	0.394275	−	0.542673i	0.959296	+	0.282404i	$0.0911318\pi$
$710$	−3.13090	−	0.201066i	−0.117500	−	0.00754589i
$711$		0			0
$712$	18.2861	+	9.31723i	0.685301	+	0.349178i
$713$	3.16212	−	19.9648i	0.118422	−	0.747689i
$714$		0			0
$715$	16.6300	+	13.9460i	0.621927	+	0.521549i
$716$	3.92246			0.146589
$717$		0			0
$718$	3.69497	+	1.88268i	0.137895	+	0.0702611i
$719$	−31.1609	−	10.1248i	−1.16211	−	0.377592i	−0.336416	−	0.941714i	$-0.609215\pi$
$719$	−31.1609	−	10.1248i	−1.16211	−	0.377592i	−0.825691	+	0.564122i	$0.809215\pi$
$720$		0			0
$721$	10.5790	−	14.5608i	0.393984	−	0.542272i
$722$	−0.486681	−	0.955166i	−0.0181124	−	0.0355476i
$723$		0			0
$724$	−4.48818	−	6.17744i	−0.166802	−	0.229583i
$725$	11.9501	+	5.66127i	0.443814	+	0.210254i
$726$		0			0
$727$	0.964903	+	0.964903i	0.0357863	+	0.0357863i	0.724773	−	0.688987i	$-0.241944\pi$
$727$	0.964903	+	0.964903i	0.0357863	+	0.0357863i	−0.688987	+	0.724773i	$0.741944\pi$
$728$	15.4848	+	2.45255i	0.573905	+	0.0908976i
$729$		0			0
$730$	−8.24576	+	13.9015i	−0.305189	+	0.514519i
$731$	−30.5763	−	22.2150i	−1.13091	−	0.821651i
$732$		0			0
$733$	−10.5079	+	5.35405i	−0.388119	+	0.197756i	−0.637151	−	0.770739i	$-0.719887\pi$
$733$	−10.5079	+	5.35405i	−0.388119	+	0.197756i	0.249033	+	0.968495i	$0.419887\pi$
$734$	−3.20364	−	9.85979i	−0.118249	−	0.363932i
$735$		0			0
$736$		−	14.8626i		−	0.547842i
$737$	5.47925	+	2.82911i	0.201831	+	0.104212i
$738$		0			0
$739$	34.8645	−	25.3305i	1.28251	−	0.931798i	0.282884	−	0.959154i	$-0.408709\pi$
$739$	34.8645	−	25.3305i	1.28251	−	0.931798i	0.999626	+	0.0273561i	$0.00870880\pi$
$740$	−3.52670	−	2.92527i	−0.129644	−	0.107535i
$741$		0			0
$742$	0.329231	+	2.07868i	0.0120865	+	0.0763109i
$743$	5.93105	+	37.4472i	0.217589	+	1.37380i	0.818509	+	0.574494i	$0.194801\pi$
$743$	5.93105	+	37.4472i	0.217589	+	1.37380i	−0.600920	+	0.799309i	$0.705199\pi$
$744$		0			0
$745$	3.73100	+	40.0252i	0.136693	+	1.46641i
$746$	1.43840	−	1.04506i	0.0526636	−	0.0382623i
$747$		0			0
$748$	−30.4245	+	4.65085i	−1.11243	+	0.170052i
$749$			1.27018i			0.0464114i
$750$		0			0
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	0.929996	+	0.367569i	$0.119810\pi$
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	−0.536331	+	0.844008i	$0.680190\pi$
$752$	−8.61441	+	4.38926i	−0.314135	+	0.160060i
$753$		0			0
$754$	3.05772	+	2.22157i	0.111356	+	0.0809047i
$755$	−34.2178	−	20.2965i	−1.24531	−	0.738664i
$756$		0			0
$757$	34.0513	+	5.39320i	1.23762	+	0.196019i	0.740734	−	0.671798i	$-0.234478\pi$
$757$	34.0513	+	5.39320i	1.23762	+	0.196019i	0.496883	+	0.867818i	$0.334478\pi$
$758$	−5.72618	−	5.72618i	−0.207984	−	0.207984i
$759$		0			0
$760$	9.00370	+	14.2284i	0.326598	+	0.516119i
$761$	8.17878	+	11.2571i	0.296481	+	0.408071i	0.931106	−	0.364750i	$-0.118845\pi$
$761$	8.17878	+	11.2571i	0.296481	+	0.408071i	−0.634625	+	0.772820i	$0.718845\pi$
$762$		0			0
$763$	−12.5342	−	24.5997i	−0.453767	−	0.890568i
$764$	4.22213	−	5.81126i	0.152751	−	0.210244i
$765$		0			0
$766$	5.26689	+	1.71132i	0.190300	+	0.0618323i
$767$	4.18586	+	2.13280i	0.151143	+	0.0770110i
$768$		0			0
$769$	−13.3273			−0.480596			−0.240298	−	0.970699i	$-0.577245\pi$
$769$	−13.3273			−0.480596			−0.240298	+	0.970699i	$0.577245\pi$
$770$	10.2921	+	2.37296i	0.370903	+	0.0855154i
$771$		0			0
$772$	5.75948	−	36.3639i	0.207288	−	1.30877i
$773$	−11.1372	−	5.67471i	−0.400579	−	0.204105i	0.242082	−	0.970256i	$-0.422170\pi$
$773$	−11.1372	−	5.67471i	−0.400579	−	0.204105i	−0.642661	+	0.766151i	$0.722170\pi$
$774$		0			0
$775$	16.1597	+	29.5764i	0.580475	+	1.06241i
$776$	−10.8709	+	14.9625i	−0.390243	+	0.537124i
$777$		0			0
$778$	0.181256	−	0.355735i	0.00649835	−	0.0127537i
$779$	−8.56685	−	11.7913i	−0.306939	−	0.422465i
$780$		0			0
$781$	9.04671	+	2.99345i	0.323717	+	0.107114i
$782$	5.45516	+	5.45516i	0.195076	+	0.195076i
$783$		0			0
$784$	−3.75988	+	1.22166i	−0.134281	+	0.0436306i
$785$	−46.5044	+	11.8759i	−1.65981	+	0.423868i
$786$		0			0
$787$	−6.21530	+	0.984406i	−0.221551	+	0.0350903i	−0.266223	−	0.963911i	$-0.585776\pi$
$787$	−6.21530	+	0.984406i	−0.221551	+	0.0350903i	0.0446718	+	0.999002i	$0.485776\pi$
$788$	−0.474521	+	0.241781i	−0.0169041	+	0.00861308i
$789$		0			0
$790$	6.14861	−	15.4708i	0.218758	−	0.550427i
$791$		−	59.1055i		−	2.10155i
$792$		0			0
$793$	14.3574	−	14.3574i	0.509846	−	0.509846i
$794$	6.62104	−	4.81046i	0.234972	−	0.170717i
$795$		0			0
$796$	−6.03213	+	18.5650i	−0.213803	+	0.658019i
$797$	0.276667	+	1.74680i	0.00980003	+	0.0618750i	0.992104	−	0.125420i	$-0.0400279\pi$
$797$	0.276667	+	1.74680i	0.00980003	+	0.0618750i	−0.982304	+	0.187295i	$0.940028\pi$
$798$		0			0
$799$	5.99354	−	18.4462i	0.212036	−	0.652581i
$800$	15.1375	+	19.6202i	0.535190	+	0.693680i
$801$		0			0
$802$	−9.82669	+	9.82669i	−0.346992	+	0.346992i
$803$	34.9001	−	34.5259i	1.23160	−	1.21839i
$804$		0			0
$805$	7.74328	+	17.9577i	0.272915	+	0.632925i
$806$	2.97684	+	9.16176i	0.104855	+	0.322709i
$807$		0			0
$808$	3.46372	−	0.548599i	0.121853	−	0.0192996i
$809$	−14.9294	−	10.8468i	−0.524889	−	0.381354i	0.293553	−	0.955943i	$-0.405162\pi$
$809$	−14.9294	−	10.8468i	−0.524889	−	0.381354i	−0.818443	+	0.574588i	$0.805162\pi$
$810$		0			0
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	−0.518616	−	0.855007i	$-0.673552\pi$
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	0.0829918	+	0.996550i	$0.473552\pi$
$812$	−13.4192	−	2.12539i	−0.470920	−	0.0745865i
$813$		0			0
$814$	−1.09921	−	1.53020i	−0.0385273	−	0.0536336i
$815$	19.6984	−	12.4651i	0.690004	−	0.436633i
$816$		0			0
$817$	13.3517	−	26.2042i	0.467117	−	0.916768i
$818$	0.537108	+	1.05413i	0.0187796	+	0.0368569i
$819$		0			0
$820$	−9.24750	−	10.5168i	−0.322937	−	0.367261i
$821$	24.7703	+	8.04835i	0.864489	+	0.280889i	0.707502	−	0.706711i	$-0.249822\pi$
$821$	24.7703	+	8.04835i	0.864489	+	0.280889i	0.156987	+	0.987601i	$0.449822\pi$
$822$		0			0
$823$	0.785962	−	4.96237i	0.0273969	−	0.172977i	−0.970196	−	0.242322i	$-0.922091\pi$
$823$	0.785962	−	4.96237i	0.0273969	−	0.172977i	0.997593	+	0.0693449i	$0.0220909\pi$
$824$	11.3361			0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−1.90393	+	12.0210i	−0.0662062	+	0.418010i	0.932218	+	0.361897i	$0.117871\pi$
$827$	−1.90393	+	12.0210i	−0.0662062	+	0.418010i	−0.998424	+	0.0561130i	$0.982129\pi$
$828$		0			0
$829$	−10.4727	−	3.40277i	−0.363730	−	0.118183i	0.121449	−	0.992598i	$-0.461246\pi$
$829$	−10.4727	−	3.40277i	−0.363730	−	0.118183i	−0.485180	+	0.874415i	$0.661246\pi$
$830$	−4.81862	−	5.48000i	−0.167257	−	0.190213i
$831$		0			0
$832$	−3.76227	−	7.38386i	−0.130433	−	0.255989i
$833$	3.60057	−	7.06651i	0.124752	−	0.244840i
$834$		0			0
$835$	−21.3382	+	13.5028i	−0.738440	+	0.467283i
$836$	−7.27804	−	22.8171i	−0.251716	−	0.789148i
$837$		0			0
$838$	7.92807	+	1.25568i	0.273871	+	0.0433769i
$839$	−8.83685	+	2.87127i	−0.305082	+	0.0991272i	−0.457557	−	0.889180i	$-0.651276\pi$
$839$	−8.83685	+	2.87127i	−0.305082	+	0.0991272i	0.152475	+	0.988307i	$0.451276\pi$
$840$		0			0
$841$	17.8031	+	12.9347i	0.613900	+	0.446024i
$842$	−6.01384	+	0.952498i	−0.207251	+	0.0328253i
$843$		0			0
$844$	−4.82040	−	14.8357i	−0.165925	−	0.510665i
$845$	3.92711	+	9.10749i	0.135097	+	0.313307i
$846$		0			0
$847$	−28.4253	−	14.8715i	−0.976706	−	0.510990i
$848$	2.74398	−	2.74398i	0.0942286	−	0.0942286i
$849$		0			0
$850$	−12.7575	−	1.64535i	−0.437577	−	0.0564352i
$851$	1.07798	−	3.31768i	0.0369527	−	0.113729i
$852$		0			0
$853$	4.23097	+	26.7133i	0.144866	+	0.914645i	0.947867	+	0.318667i	$0.103235\pi$
$853$	4.23097	+	26.7133i	0.144866	+	0.914645i	−0.803001	+	0.595978i	$0.796765\pi$
$854$	3.05346	−	9.39759i	0.104487	−	0.321579i
$855$		0			0
$856$	−0.647232	+	0.470242i	−0.0221220	+	0.0160725i
$857$	−33.1497	+	33.1497i	−1.13237	+	1.13237i	−0.142591	+	0.989782i	$0.545543\pi$
$857$	−33.1497	+	33.1497i	−1.13237	+	1.13237i	−0.989782	+	0.142591i	$0.954457\pi$
$858$		0			0
$859$		−	47.2517i		−	1.61221i	−0.591775	−	0.806103i	$-0.701573\pi$
$859$		−	47.2517i		−	1.61221i	0.591775	−	0.806103i	$-0.298427\pi$
$860$	10.4367	−	26.2604i	0.355890	−	0.895472i
$861$		0			0
$862$	8.63057	−	4.39749i	0.293958	−	0.149779i
$863$	−15.3690	+	2.43422i	−0.523168	+	0.0828617i	−0.412432	−	0.910988i	$-0.635321\pi$
$863$	−15.3690	+	2.43422i	−0.523168	+	0.0828617i	−0.110736	+	0.993850i	$0.535321\pi$
$864$		0			0
$865$	−28.6031	+	7.30440i	−0.972534	+	0.248357i
$866$	13.2947	−	4.31972i	0.451773	−	0.146790i
$867$		0			0
$868$	−24.4863	−	24.4863i	−0.831118	−	0.831118i
$869$	−29.9413	+	40.7470i	−1.01569	+	1.38225i
$870$		0			0
$871$	−3.19826	−	4.40203i	−0.108369	−	0.149157i
$872$	7.89464	−	15.4941i	0.267346	−	0.524696i
$873$		0			0
$874$	−3.52861	+	4.85671i	−0.119357	+	0.164281i
$875$	−28.5118	−	15.8196i	−0.963875	−	0.534801i
$876$		0			0
$877$	−25.9562	−	13.2254i	−0.876480	−	0.446589i	−0.0429592	−	0.999077i	$-0.513679\pi$
$877$	−25.9562	−	13.2254i	−0.876480	−	0.446589i	−0.833521	+	0.552488i	$0.813679\pi$
$878$	−0.238560	+	1.50621i	−0.00805101	+	0.0508321i
$879$		0			0
$880$	−7.61476	−	17.9247i	−0.256693	−	0.604240i
$881$	−4.18815			−0.141102			−0.0705512	−	0.997508i	$-0.522476\pi$
$881$	−4.18815			−0.141102			−0.0705512	+	0.997508i	$0.522476\pi$
$882$		0			0
$883$	−40.7349	−	20.7555i	−1.37084	−	0.698477i	−0.395351	−	0.918530i	$-0.629377\pi$
$883$	−40.7349	−	20.7555i	−1.37084	−	0.698477i	−0.975488	+	0.220053i	$0.929377\pi$
$884$	25.8286	+	8.39221i	0.868709	+	0.282261i
$885$		0			0
$886$	−9.11003	+	12.5389i	−0.306057	+	0.421252i
$887$	15.6438	+	30.7027i	0.525267	+	1.03090i	0.989412	+	0.145136i	$0.0463619\pi$
$887$	15.6438	+	30.7027i	0.525267	+	1.03090i	−0.464144	+	0.885760i	$0.653638\pi$
$888$		0			0
$889$	16.1646	+	22.2487i	0.542143	+	0.746196i
$890$	−6.52371	−	10.3093i	−0.218675	−	0.345569i
$891$		0			0
$892$	7.70048	+	7.70048i	0.257831	+	0.257831i
$893$	14.9068	+	2.36100i	0.498836	+	0.0790078i
$894$		0			0
$895$	−4.28246	−	2.54016i	−0.143147	−	0.0849081i
$896$	−26.6503	−	19.3626i	−0.890323	−	0.646857i
$897$		0			0
$898$	−15.2266	+	7.75836i	−0.508119	+	0.258900i
$899$	−5.50871	−	16.9541i	−0.183726	−	0.565450i
$900$		0			0
$901$			7.78489i			0.259352i
$902$	−2.58659	−	5.14481i	−0.0861239	−	0.171303i
$903$		0			0
$904$	30.1177	−	21.8818i	1.00170	−	0.727778i
$905$	0.899623	+	9.65092i	0.0299045	+	0.320807i
$906$		0			0
$907$	6.02474	+	38.0387i	0.200048	+	1.26306i	0.859433	+	0.511249i	$0.170817\pi$
$907$	6.02474	+	38.0387i	0.200048	+	1.26306i	−0.659384	+	0.751806i	$0.729183\pi$
$908$	0.913965	+	5.77055i	0.0303310	+	0.191502i
$909$		0			0
$910$	−7.17330	−	5.95000i	−0.237793	−	0.197241i
$911$	−29.8280	+	21.6713i	−0.988244	+	0.718002i	−0.959536	−	0.281586i	$-0.909139\pi$
$911$	−29.8280	+	21.6713i	−0.988244	+	0.718002i	−0.0287085	+	0.999588i	$0.509139\pi$
$912$		0			0
$913$	9.95566	+	19.8022i	0.329484	+	0.655356i
$914$			2.49056i			0.0823805i
$915$		0			0
$916$	−2.90677	−	8.94611i	−0.0960423	−	0.295588i
$917$	19.5326	−	9.95237i	0.645024	−	0.328656i
$918$		0			0
$919$	24.5973	+	17.8710i	0.811392	+	0.589510i	0.914234	−	0.405187i	$-0.132794\pi$
$919$	24.5973	+	17.8710i	0.811392	+	0.589510i	−0.102842	+	0.994698i	$0.532794\pi$
$920$	−6.28381	+	10.5939i	−0.207171	+	0.349270i
$921$		0			0
$922$	−6.01478	−	0.952647i	−0.198086	−	0.0313738i
$923$	−5.94554	−	5.94554i	−0.195700	−	0.195700i
$924$		0			0
$925$	1.95599	+	5.47762i	0.0643126	+	0.180103i
$926$	7.82350	+	10.7681i	0.257096	+	0.353862i
$927$		0			0
$928$	−5.95063	−	11.6788i	−0.195339	−	0.383374i
$929$	13.6936	−	18.8477i	0.449273	−	0.618372i	−0.522968	−	0.852352i	$-0.675175\pi$
$929$	13.6936	−	18.8477i	0.449273	−	0.618372i	0.972241	+	0.233981i	$0.0751752\pi$
$930$		0			0
$931$	5.86938	+	1.90708i	0.192361	+	0.0625020i
$932$	−6.93458	−	3.53335i	−0.227150	−	0.115739i
$933$		0			0
$934$	19.3837			0.634254
$935$	36.2287	+	14.6250i	1.18481	+	0.478290i
$936$		0			0
$937$	1.25828	−	7.94449i	0.0411063	−	0.259535i	−0.958573	−	0.284846i	$-0.908058\pi$
$937$	1.25828	−	7.94449i	0.0411063	−	0.259535i	0.999680	+	0.0253108i	$0.00805753\pi$
$938$	−2.35937	−	1.20216i	−0.0770362	−	0.0392519i
$939$		0			0
$940$	14.4719	+	0.929389i	0.472023	+	0.0303133i
$941$	−28.1490	+	38.7438i	−0.917631	+	1.26301i	0.0468615	+	0.998901i	$0.485078\pi$
$941$	−28.1490	+	38.7438i	−0.917631	+	1.26301i	−0.964493	+	0.264110i	$0.914922\pi$
$942$		0			0
$943$	4.84037	−	9.49976i	0.157624	−	0.309355i
$944$	−2.47782	−	3.41042i	−0.0806460	−	0.111000i
$945$		0			0
$946$	6.88039	−	9.36352i	0.223701	−	0.304434i
$947$	−9.38618	−	9.38618i	−0.305010	−	0.305010i	0.537960	−	0.842970i	$-0.319195\pi$
$947$	−9.38618	−	9.38618i	−0.305010	−	0.305010i	−0.842970	+	0.537960i	$0.819195\pi$
$948$		0			0
$949$	−41.1978	+	13.3860i	−1.33734	+	0.434528i
$950$	−0.288388	−	10.0053i	−0.00935654	−	0.324613i
$951$		0			0
$952$	27.8746	−	4.41491i	0.903422	−	0.143088i
$953$	−47.4428	+	24.1733i	−1.53682	+	0.783051i	−0.998228	−	0.0595128i	$-0.981045\pi$
$953$	−47.4428	+	24.1733i	−1.53682	+	0.783051i	−0.538597	+	0.842564i	$0.681045\pi$
$954$		0			0
$955$	−8.37297	+	3.61039i	−0.270943	+	0.116829i
$956$		−	18.4130i		−	0.595519i
$957$		0			0
$958$	13.2098	−	13.2098i	0.426790	−	0.426790i
$959$	36.2628	−	26.3465i	1.17099	−	0.850772i
$960$		0			0
$961$	4.46097	−	13.7294i	0.143902	−	0.442885i
$962$	0.260069	+	1.64201i	0.00838495	+	0.0529405i
$963$		0			0
$964$	−15.1642	+	46.6706i	−0.488406	+	1.50316i
$965$	−29.8371	+	35.9716i	−0.960491	+	1.15797i
$966$		0			0
$967$	−38.6475	+	38.6475i	−1.24282	+	1.24282i	−0.283994	+	0.958826i	$0.591660\pi$
$967$	−38.6475	+	38.6475i	−1.24282	+	1.24282i	−0.958826	+	0.283994i	$0.908340\pi$
$968$	−2.94563	−	19.9901i	−0.0946763	−	0.642505i
$969$		0			0
$970$	10.0958	−	4.35325i	0.324155	−	0.139774i
$971$	−2.55556	−	7.86521i	−0.0820119	−	0.252407i	0.901640	−	0.432487i	$-0.142364\pi$
$971$	−2.55556	−	7.86521i	−0.0820119	−	0.252407i	−0.983652	+	0.180081i	$0.942364\pi$
$972$		0			0
$973$	11.9898	−	1.89900i	0.384375	−	0.0608790i
$974$	10.7378	+	7.80149i	0.344062	+	0.249976i
$975$		0			0
$976$	−17.3278	+	5.63014i	−0.554649	+	0.180216i
$977$	54.0805	+	8.56551i	1.73019	+	0.274035i	0.940579	−	0.339575i	$-0.110283\pi$
$977$	54.0805	+	8.56551i	1.73019	+	0.274035i	0.789610	+	0.613610i	$0.210283\pi$
$978$		0			0
$979$	11.2607	+	35.3029i	0.359892	+	1.12829i
$980$	5.78535	+	1.30108i	0.184806	+	0.0415614i
$981$		0			0
$982$	−0.880571	+	1.72822i	−0.0281001	+	0.0551496i
$983$	6.19202	+	12.1525i	0.197495	+	0.387606i	0.968422	−	0.249318i	$-0.0802065\pi$
$983$	6.19202	+	12.1525i	0.197495	+	0.387606i	−0.770927	+	0.636924i	$0.780207\pi$
$984$		0			0
$985$	0.674648	+	0.0433259i	0.0214961	+	0.00138048i
$986$	6.47069	+	2.10245i	0.206069	+	0.0669558i
$987$		0			0
$988$	−3.30589	+	20.8726i	−0.105174	+	0.664045i
$989$	21.5139			0.684102
$990$		0			0
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	5.22613	−	32.9965i	0.165930	−	1.04764i
$993$		0			0
$994$	−3.89164	−	1.26447i	−0.123435	−	0.0401066i
$995$	18.6083	−	16.3625i	0.589924	−	0.518726i
$996$		0			0
$997$	−9.65934	−	18.9575i	−0.305914	−	0.600391i	0.685956	−	0.727643i	$-0.259384\pi$
$997$	−9.65934	−	18.9575i	−0.305914	−	0.600391i	−0.991870	+	0.127252i	$0.959384\pi$
$998$	1.42445	−	2.79564i	0.0450901	−	0.0884943i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.217.3		32
3.2	odd	2		55.2.l.a.52.2	yes	32
5.3	odd	4	inner	495.2.bj.a.118.2		32
11.7	odd	10	inner	495.2.bj.a.172.2		32
12.11	even	2		880.2.cm.a.657.3		32
15.2	even	4		275.2.bm.b.118.2		32
15.8	even	4		55.2.l.a.8.3	yes	32
15.14	odd	2		275.2.bm.b.107.3		32
33.2	even	10		605.2.e.b.362.8		32
33.5	odd	10		605.2.m.d.112.2		32
33.8	even	10		605.2.m.d.457.2		32
33.14	odd	10		605.2.m.c.457.3		32
33.17	even	10		605.2.m.c.112.3		32
33.20	odd	10		605.2.e.b.362.9		32
33.26	odd	10		605.2.m.e.282.2		32
33.29	even	10		55.2.l.a.7.3	✓	32
33.32	even	2		605.2.m.e.602.3		32
55.18	even	20	inner	495.2.bj.a.73.3		32
60.23	odd	4		880.2.cm.a.833.2		32
132.95	odd	10		880.2.cm.a.337.2		32
165.8	odd	20		605.2.m.d.578.2		32
165.29	even	10		275.2.bm.b.7.2		32
165.38	even	20		605.2.m.d.233.2		32
165.53	even	20		605.2.e.b.483.8		32
165.62	odd	20		275.2.bm.b.18.3		32
165.68	odd	20		605.2.e.b.483.9		32
165.83	odd	20		605.2.m.c.233.3		32
165.98	odd	4		605.2.m.e.118.2		32
165.113	even	20		605.2.m.c.578.3		32
165.128	odd	20		55.2.l.a.18.2	yes	32
165.158	even	20		605.2.m.e.403.3		32
660.623	even	20		880.2.cm.a.513.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	33.29	even	10
55.2.l.a.8.3	yes	32	15.8	even	4
55.2.l.a.18.2	yes	32	165.128	odd	20
55.2.l.a.52.2	yes	32	3.2	odd	2
275.2.bm.b.7.2		32	165.29	even	10
275.2.bm.b.18.3		32	165.62	odd	20
275.2.bm.b.107.3		32	15.14	odd	2
275.2.bm.b.118.2		32	15.2	even	4
495.2.bj.a.73.3		32	55.18	even	20	inner
495.2.bj.a.118.2		32	5.3	odd	4	inner
495.2.bj.a.172.2		32	11.7	odd	10	inner
495.2.bj.a.217.3		32	1.1	even	1	trivial
605.2.e.b.362.8		32	33.2	even	10
605.2.e.b.362.9		32	33.20	odd	10
605.2.e.b.483.8		32	165.53	even	20
605.2.e.b.483.9		32	165.68	odd	20
605.2.m.c.112.3		32	33.17	even	10
605.2.m.c.233.3		32	165.83	odd	20
605.2.m.c.457.3		32	33.14	odd	10
605.2.m.c.578.3		32	165.113	even	20
605.2.m.d.112.2		32	33.5	odd	10
605.2.m.d.233.2		32	165.38	even	20
605.2.m.d.457.2		32	33.8	even	10
605.2.m.d.578.2		32	165.8	odd	20
605.2.m.e.118.2		32	165.98	odd	4
605.2.m.e.282.2		32	33.26	odd	10
605.2.m.e.403.3		32	165.158	even	20
605.2.m.e.602.3		32	33.32	even	2
880.2.cm.a.337.2		32	132.95	odd	10
880.2.cm.a.513.3		32	660.623	even	20
880.2.cm.a.657.3		32	12.11	even	2
880.2.cm.a.833.2		32	60.23	odd	4

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0763931 - 0.482327i) q^{2} +(1.67531 + 0.544341i) q^{4} +(-1.47656 - 1.67922i) q^{5} +(-1.32402 - 2.59854i) q^{7} +(0.833936 - 1.63669i) q^{8} +(-0.922733 + 0.583903i) q^{10} +(3.15977 - 1.00788i) q^{11} +(-2.89049 - 0.457808i) q^{13} +(-1.35449 + 0.440102i) q^{14} +(2.12449 + 1.54353i) q^{16} +(-5.20325 + 0.824113i) q^{17} +(-1.26677 - 3.89873i) q^{19} +(-1.55962 - 3.61696i) q^{20} +(-0.244743 - 1.60104i) q^{22} +(2.12046 - 2.12046i) q^{23} +(-0.639563 + 4.95893i) q^{25} +(-0.441627 + 1.35919i) q^{26} +(-0.803656 - 5.07408i) q^{28} +(0.817241 - 2.51521i) q^{29} +(5.45328 - 3.96204i) q^{31} +(3.50456 - 3.50456i) q^{32} +2.57262i q^{34} +(-2.40853 + 6.06022i) q^{35} +(1.03649 - 0.528116i) q^{37} +(-1.97724 + 0.313163i) q^{38} +(-3.97972 + 1.01630i) q^{40} +(3.38136 - 1.09867i) q^{41} +(5.07292 + 5.07292i) q^{43} +(5.84223 + 0.0314826i) q^{44} +(-0.860769 - 1.18475i) q^{46} +(-1.67145 + 3.28041i) q^{47} +(-0.884888 + 1.21794i) q^{49} +(2.34297 + 0.687307i) q^{50} +(-4.59325 - 2.34038i) q^{52} +(0.231169 - 1.45955i) q^{53} +(-6.35804 - 3.81777i) q^{55} -5.35716 q^{56} +(-1.15072 - 0.586323i) q^{58} +(-1.52672 - 0.496061i) q^{59} +(-4.07810 + 5.61302i) q^{61} +(-1.49441 - 2.93294i) q^{62} +(1.66445 + 2.29092i) q^{64} +(3.49920 + 5.52974i) q^{65} +(1.31471 + 1.31471i) q^{67} +(-9.16564 - 1.45170i) q^{68} +(2.73902 + 1.62466i) q^{70} +(2.32441 + 1.68878i) q^{71} +(13.1886 - 6.71992i) q^{73} +(-0.175544 - 0.540270i) q^{74} -7.22113i q^{76} +(-6.80264 - 6.87635i) q^{77} +(-12.3342 + 8.96129i) q^{79} +(-0.544999 - 5.84661i) q^{80} +(-0.271606 - 1.71486i) q^{82} +(1.04540 + 6.60041i) q^{83} +(9.06675 + 7.52055i) q^{85} +(2.83434 - 2.05927i) q^{86} +(0.985459 - 6.01208i) q^{88} +11.1726i q^{89} +(2.63744 + 8.11720i) q^{91} +(4.70669 - 2.39818i) q^{92} +(1.45454 + 1.05679i) q^{94} +(-4.67636 + 7.88388i) q^{95} +(-9.94447 - 1.57505i) q^{97} +(0.519848 + 0.519848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more