LMFDB - Embedded newform 783.2.u.a.451.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(181,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([28, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.181"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.u (of order $21$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			451.5
Character	$\chi$	$=$	783.451
Dual form			783.2.u.a.658.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59949 + 1.09051i) q^{2} +(0.638466 - 1.62678i) q^{4} +(-0.303634 - 4.05171i) q^{5} +(-1.40293 - 3.57461i) q^{7} +(-0.108732 - 0.476384i) q^{8} +(4.90411 + 6.14956i) q^{10} +(-0.957158 - 0.888113i) q^{11} +(4.18326 - 1.29036i) q^{13} +(6.14214 + 4.18764i) q^{14} +(3.25556 + 3.02072i) q^{16} -4.03457 q^{17} +(-2.46134 - 3.08642i) q^{19} +(-6.78512 - 2.09293i) q^{20} +(2.49946 + 0.376734i) q^{22} +(5.57787 + 3.80293i) q^{23} +(-11.3800 + 1.71526i) q^{25} +(-5.28392 + 6.62583i) q^{26} -6.71085 q^{28} +(-5.26785 + 1.11791i) q^{29} +(-0.337284 - 4.50074i) q^{31} +(-7.53503 - 1.13572i) q^{32} +(6.45325 - 4.39975i) q^{34} +(-14.0573 + 6.76965i) q^{35} +(-0.0121631 - 0.0532900i) q^{37} +(7.30266 + 2.25257i) q^{38} +(-1.89716 + 0.585196i) q^{40} +(1.95712 + 3.38984i) q^{41} +(-0.356363 + 4.75533i) q^{43} +(-2.05588 + 0.990060i) q^{44} -13.0689 q^{46} +(3.81292 + 3.53787i) q^{47} +(-5.67827 + 5.26866i) q^{49} +(16.3317 - 15.1536i) q^{50} +(0.571723 - 7.62911i) q^{52} +(5.90857 + 2.84542i) q^{53} +(-3.30775 + 4.14779i) q^{55} +(-1.55035 + 1.05701i) q^{56} +(7.20678 - 7.53276i) q^{58} +(-5.54407 - 9.60261i) q^{59} +(2.14867 + 5.47473i) q^{61} +(5.44760 + 6.83107i) q^{62} +(5.28812 - 2.54662i) q^{64} +(-6.49837 - 16.5576i) q^{65} +(1.07318 - 0.995765i) q^{67} +(-2.57593 + 6.56338i) q^{68} +(15.1022 - 26.1577i) q^{70} +(2.24473 - 9.83479i) q^{71} +(3.80506 - 1.83242i) q^{73} +(0.0775682 + 0.0719728i) q^{74} +(-6.59241 + 2.03349i) q^{76} +(-1.83183 + 4.66743i) q^{77} +(-1.69085 - 0.521557i) q^{79} +(11.2506 - 14.1078i) q^{80} +(-6.82706 - 3.28774i) q^{82} +(0.158316 - 0.0238622i) q^{83} +(1.22503 + 16.3469i) q^{85} +(-4.61575 - 7.99472i) q^{86} +(-0.319010 + 0.552541i) q^{88} +(3.79906 + 1.82953i) q^{89} +(-10.4814 - 13.1432i) q^{91} +(9.74782 - 6.64595i) q^{92} +(-9.95683 - 1.50075i) q^{94} +(-11.7579 + 10.9098i) q^{95} +(-13.3447 + 2.01139i) q^{97} +(3.33678 - 14.6194i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 5 q^{2} + 21 q^{4} + 9 q^{5} - 5 q^{7} - 2 q^{8} - 28 q^{10} + q^{11} - 5 q^{13} + 9 q^{14} + 21 q^{16} + 60 q^{17} - 20 q^{19} + 15 q^{20} - 13 q^{22} + 32 q^{23} + 15 q^{25} + 4 q^{26} - 72 q^{28}+ \cdots + 88 q^{98}+O(q^{100}) $ 336 * q + 5 * q^2 + 21 * q^4 + 9 * q^5 - 5 * q^7 - 2 * q^8 - 28 * q^10 + q^11 - 5 * q^13 + 9 * q^14 + 21 * q^16 + 60 * q^17 - 20 * q^19 + 15 * q^20 - 13 * q^22 + 32 * q^23 + 15 * q^25 + 4 * q^26 - 72 * q^28 + q^29 - 5 * q^31 - 7 * q^32 - 15 * q^34 - 16 * q^35 - 20 * q^37 - 63 * q^38 + 5 * q^40 + 20 * q^41 - 5 * q^43 + 8 * q^44 - 80 * q^46 - 5 * q^47 - 19 * q^49 + 3 * q^50 + q^52 + 4 * q^53 - 100 * q^55 + 5 * q^56 - 7 * q^58 - 154 * q^59 + 7 * q^61 + 4 * q^62 + 18 * q^64 + 65 * q^65 - 5 * q^67 + 9 * q^68 - 14 * q^70 - 18 * q^71 - 20 * q^73 + 77 * q^74 - 5 * q^76 - 39 * q^77 - 5 * q^79 + 104 * q^80 + 12 * q^82 + 23 * q^83 - 42 * q^85 - 128 * q^86 - 8 * q^88 - 34 * q^89 + 12 * q^91 + 115 * q^92 - 25 * q^94 - 89 * q^95 + 55 * q^97 + 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.59949	+	1.09051i	−1.13101	+	0.771110i	−0.976208	−	0.216836i	$-0.930426\pi$
$2$	−1.59949	+	1.09051i	−1.13101	+	0.771110i	−0.154802	+	0.987945i	$0.549474\pi$
$3$		0			0
$3$		0			0
$4$	0.638466	−	1.62678i	0.319233	−	0.813392i
$5$	−0.303634	−	4.05171i	−0.135789	−	1.81198i	−0.484544	−	0.874767i	$-0.661014\pi$
$5$	−0.303634	−	4.05171i	−0.135789	−	1.81198i	0.348754	−	0.937214i	$-0.386605\pi$
$6$		0			0
$7$	−1.40293	−	3.57461i	−0.530258	−	1.35108i	−0.905578	−	0.424181i	$-0.860562\pi$
$7$	−1.40293	−	3.57461i	−0.530258	−	1.35108i	0.375319	−	0.926896i	$-0.377533\pi$
$8$	−0.108732	−	0.476384i	−0.0384424	−	0.168427i
$9$		0			0
$10$	4.90411	+	6.14956i	1.55082	+	1.94466i
$11$	−0.957158	−	0.888113i	−0.288594	−	0.267776i	0.522568	−	0.852598i	$-0.324974\pi$
$11$	−0.957158	−	0.888113i	−0.288594	−	0.267776i	−0.811162	+	0.584821i	$0.801165\pi$
$12$		0			0
$13$	4.18326	−	1.29036i	1.16023	−	0.357883i	0.345890	−	0.938275i	$-0.387577\pi$
$13$	4.18326	−	1.29036i	1.16023	−	0.357883i	0.814337	+	0.580392i	$0.197101\pi$
$14$	6.14214	+	4.18764i	1.64156	+	1.11919i
$15$		0			0
$16$	3.25556	+	3.02072i	0.813891	+	0.755181i
$17$	−4.03457			−0.978527			−0.489263	−	0.872136i	$-0.662734\pi$
$17$	−4.03457			−0.978527			−0.489263	+	0.872136i	$0.662734\pi$
$18$		0			0
$19$	−2.46134	−	3.08642i	−0.564669	−	0.708073i	0.414744	−	0.909938i	$-0.363871\pi$
$19$	−2.46134	−	3.08642i	−0.564669	−	0.708073i	−0.979413	+	0.201865i	$0.935300\pi$
$20$	−6.78512	−	2.09293i	−1.51720	−	0.467994i
$21$		0			0
$22$	2.49946	+	0.376734i	0.532888	+	0.0803199i
$23$	5.57787	+	3.80293i	1.16307	+	0.792965i	0.981697	−	0.190450i	$-0.0609947\pi$
$23$	5.57787	+	3.80293i	1.16307	+	0.792965i	0.181369	+	0.983415i	$0.441947\pi$
$24$		0			0
$25$	−11.3800	+	1.71526i	−2.27601	+	0.343053i
$26$	−5.28392	+	6.62583i	−1.03626	+	1.29943i
$27$		0			0
$28$	−6.71085			−1.26823
$29$	−5.26785	+	1.11791i	−0.978216	+	0.207591i
$29$	−5.26785	+	1.11791i	−0.978216	+	0.207591i
$30$		0			0
$31$	−0.337284	−	4.50074i	−0.0605779	−	0.808356i	−0.941911	−	0.335861i	$-0.890973\pi$
$31$	−0.337284	−	4.50074i	−0.0605779	−	0.808356i	0.881334	−	0.472495i	$-0.156646\pi$
$32$	−7.53503	−	1.13572i	−1.33202	−	0.200769i
$33$		0			0
$34$	6.45325	−	4.39975i	1.10672	−	0.754552i
$35$	−14.0573	+	6.76965i	−2.37612	+	1.14428i
$36$		0			0
$37$	−0.0121631	−	0.0532900i	−0.00199960	−	0.00876082i	0.973918	−	0.226899i	$-0.0728588\pi$
$37$	−0.0121631	−	0.0532900i	−0.00199960	−	0.00876082i	−0.975918	+	0.218138i	$0.930002\pi$
$38$	7.30266	+	2.25257i	1.18465	+	0.365416i
$39$		0			0
$40$	−1.89716	+	0.585196i	−0.299967	+	0.0925276i
$41$	1.95712	+	3.38984i	0.305651	+	0.529403i	0.977406	−	0.211370i	$-0.0677925\pi$
$41$	1.95712	+	3.38984i	0.305651	+	0.529403i	−0.671755	+	0.740773i	$0.734459\pi$
$42$		0			0
$43$	−0.356363	+	4.75533i	−0.0543448	+	0.725181i	0.901775	+	0.432205i	$0.142264\pi$
$43$	−0.356363	+	4.75533i	−0.0543448	+	0.725181i	−0.956120	+	0.292975i	$0.905355\pi$
$44$	−2.05588	+	0.990060i	−0.309936	+	0.149257i
$45$		0			0
$46$	−13.0689			−1.92690
$47$	3.81292	+	3.53787i	0.556172	+	0.516052i	0.907417	−	0.420232i	$-0.138051\pi$
$47$	3.81292	+	3.53787i	0.556172	+	0.516052i	−0.351245	+	0.936284i	$0.614242\pi$
$48$		0			0
$49$	−5.67827	+	5.26866i	−0.811181	+	0.752666i
$50$	16.3317	−	15.1536i	2.30966	−	2.14305i
$51$		0			0
$52$	0.571723	−	7.62911i	0.0792837	−	1.05797i
$53$	5.90857	+	2.84542i	0.811605	+	0.390848i	0.793184	−	0.608982i	$-0.208422\pi$
$53$	5.90857	+	2.84542i	0.811605	+	0.390848i	0.0184209	+	0.999830i	$0.494136\pi$
$54$		0			0
$55$	−3.30775	+	4.14779i	−0.446017	+	0.559288i
$56$	−1.55035	+	1.05701i	−0.207174	+	0.141249i
$57$		0			0
$58$	7.20678	−	7.53276i	0.946296	−	0.989099i
$59$	−5.54407	−	9.60261i	−0.721776	−	1.25015i	−0.960287	−	0.279013i	$-0.909993\pi$
$59$	−5.54407	−	9.60261i	−0.721776	−	1.25015i	0.238511	−	0.971140i	$-0.423341\pi$
$60$		0			0
$61$	2.14867	+	5.47473i	0.275109	+	0.700967i	0.999928	+	0.0120272i	$0.00382847\pi$
$61$	2.14867	+	5.47473i	0.275109	+	0.700967i	−0.724818	+	0.688940i	$0.758076\pi$
$62$	5.44760	+	6.83107i	0.691845	+	0.867547i
$63$		0			0
$64$	5.28812	−	2.54662i	0.661015	−	0.318328i
$65$	−6.49837	−	16.5576i	−0.806023	−	2.05371i
$66$		0			0
$67$	1.07318	−	0.995765i	0.131110	−	0.121652i	−0.611893	−	0.790941i	$-0.709592\pi$
$67$	1.07318	−	0.995765i	0.131110	−	0.121652i	0.743002	+	0.669289i	$0.233401\pi$
$68$	−2.57593	+	6.56338i	−0.312378	+	0.795926i
$69$		0			0
$70$	15.1022	−	26.1577i	1.80505	−	3.12644i
$71$	2.24473	−	9.83479i	0.266400	−	1.16717i	−0.647768	−	0.761838i	$-0.724297\pi$
$71$	2.24473	−	9.83479i	0.266400	−	1.16717i	0.914168	−	0.405337i	$-0.132846\pi$
$72$		0			0
$73$	3.80506	−	1.83242i	0.445349	−	0.214469i	−0.197749	−	0.980253i	$-0.563363\pi$
$73$	3.80506	−	1.83242i	0.445349	−	0.214469i	0.643098	+	0.765784i	$0.277649\pi$
$74$	0.0775682	+	0.0719728i	0.00901712	+	0.00836666i
$75$		0			0
$76$	−6.59241	+	2.03349i	−0.756202	+	0.233257i
$77$	−1.83183	+	4.66743i	−0.208757	+	0.531903i
$78$		0			0
$79$	−1.69085	−	0.521557i	−0.190235	−	0.0586797i	0.198174	−	0.980167i	$-0.436499\pi$
$79$	−1.69085	−	0.521557i	−0.190235	−	0.0586797i	−0.388409	+	0.921487i	$0.626975\pi$
$80$	11.2506	−	14.1078i	1.25786	−	1.57730i
$81$		0			0
$82$	−6.82706	−	3.28774i	−0.753923	−	0.363070i
$83$	0.158316	−	0.0238622i	0.0173774	−	0.00261922i	−0.140348	−	0.990102i	$-0.544822\pi$
$83$	0.158316	−	0.0238622i	0.0173774	−	0.00261922i	0.157725	+	0.987483i	$0.449584\pi$
$84$		0			0
$85$	1.22503	+	16.3469i	0.132873	+	1.77307i
$86$	−4.61575	−	7.99472i	−0.497730	−	0.862093i
$87$		0			0
$88$	−0.319010	+	0.552541i	−0.0340066	+	0.0589011i
$89$	3.79906	+	1.82953i	0.402700	+	0.193930i	0.624260	−	0.781217i	$-0.285401\pi$
$89$	3.79906	+	1.82953i	0.402700	+	0.193930i	−0.221560	+	0.975147i	$0.571115\pi$
$90$		0			0
$91$	−10.4814	−	13.1432i	−1.09875	−	1.37779i
$92$	9.74782	−	6.64595i	1.01628	−	0.692888i
$93$		0			0
$94$	−9.95683	−	1.50075i	−1.02697	−	0.154791i
$95$	−11.7579	+	10.9098i	−1.20634	+	1.11932i
$96$		0			0
$97$	−13.3447	+	2.01139i	−1.35495	+	0.204226i	−0.786040	−	0.618175i	$-0.787872\pi$
$97$	−13.3447	+	2.01139i	−1.35495	+	0.204226i	−0.568908	+	0.822401i	$0.692634\pi$
$98$	3.33678	−	14.6194i	0.337066	−	1.47678i
$99$		0			0
$100$	−4.47540	+	19.6080i	−0.447540	+	1.96080i
$101$	−0.0342914	+	0.457586i	−0.00341212	+	0.0455315i	−0.998650	−	0.0519448i	$-0.983458\pi$
$101$	−0.0342914	+	0.457586i	−0.00341212	+	0.0455315i	0.995238	+	0.0974764i	$0.0310770\pi$
$102$		0			0
$103$	7.13224	−	2.20000i	0.702761	−	0.216773i	0.0772763	−	0.997010i	$-0.475378\pi$
$103$	7.13224	−	2.20000i	0.702761	−	0.216773i	0.625484	+	0.780237i	$0.284901\pi$
$104$	−1.06956	−	1.85254i	−0.104879	−	0.181656i
$105$		0			0
$106$	−12.5537	+	1.89216i	−1.21932	+	0.183783i
$107$	−0.458441	−	2.00856i	−0.0443192	−	0.194175i	0.947922	−	0.318502i	$-0.103180\pi$
$107$	−0.458441	−	2.00856i	−0.0443192	−	0.194175i	−0.992241	+	0.124327i	$0.960323\pi$
$108$		0			0
$109$	−5.40439	+	6.77689i	−0.517647	+	0.649108i	−0.970107	−	0.242676i	$-0.921975\pi$
$109$	−5.40439	+	6.77689i	−0.517647	+	0.649108i	0.452461	+	0.891784i	$0.350546\pi$
$110$	0.767494	−	10.2415i	0.0731777	−	0.976489i
$111$		0			0
$112$	6.23058	−	15.8752i	0.588734	−	1.50007i
$113$	−3.25899	−	0.491213i	−0.306580	−	0.0462095i	−0.00604940	−	0.999982i	$-0.501926\pi$
$113$	−3.25899	−	0.491213i	−0.306580	−	0.0462095i	−0.300530	+	0.953772i	$0.597164\pi$
$114$		0			0
$115$	13.7147	−	23.7546i	1.27891	−	2.21513i
$116$	−1.54474	+	9.28341i	−0.143426	+	0.861943i
$117$		0			0
$118$	19.3395	+	9.31339i	1.78034	+	0.857367i
$119$	5.66023	+	14.4220i	0.518872	+	1.32206i
$120$		0			0
$121$	−0.694624	−	9.26911i	−0.0631476	−	0.842647i
$122$	−9.40705	−	6.41362i	−0.851674	−	0.580662i
$123$		0			0
$124$	−7.53707	−	2.32488i	−0.676849	−	0.208780i
$125$	5.88453	+	25.7818i	0.526328	+	2.30599i
$126$		0			0
$127$	1.85976	−	8.14812i	0.165027	−	0.723029i	−0.822910	−	0.568171i	$-0.807651\pi$
$127$	1.85976	−	8.14812i	0.165027	−	0.723029i	0.987937	−	0.154857i	$-0.0494918\pi$
$128$	1.93898	−	3.35840i	0.171383	−	0.296844i
$129$		0			0
$130$	28.4503	+	19.3971i	2.49526	+	1.70124i
$131$	10.6529	+	7.26304i	0.930750	+	0.634575i	0.930841	−	0.365425i	$-0.119076\pi$
$131$	10.6529	+	7.26304i	0.930750	+	0.634575i	−9.06149e−5		1.00000i	$0.500029\pi$
$132$		0			0
$133$	−7.57966	+	13.1284i	−0.657240	+	1.13837i
$134$	−0.630644	+	2.76303i	−0.0544793	+	0.238690i
$135$		0			0
$136$	0.438685	+	1.92201i	0.0376170	+	0.164811i
$137$	−5.37309	−	1.65738i	−0.459054	−	0.141599i	0.0565990	−	0.998397i	$-0.481974\pi$
$137$	−5.37309	−	1.65738i	−0.459054	−	0.141599i	−0.515653	+	0.856798i	$0.672451\pi$
$138$		0			0
$139$	−10.8875	−	7.42295i	−0.923463	−	0.629607i	0.00541755	−	0.999985i	$-0.498276\pi$
$139$	−10.8875	−	7.42295i	−0.923463	−	0.629607i	−0.928881	+	0.370379i	$0.879228\pi$
$140$	2.03764	+	27.1904i	0.172212	+	2.29801i
$141$		0			0
$142$	7.13456	+	18.1786i	0.598719	+	1.52551i
$143$	−5.15003	−	2.48012i	−0.430667	−	0.207398i
$144$		0			0
$145$	6.12896	+	21.0044i	0.508982	+	1.74432i
$146$	−4.08788	+	7.08041i	−0.338315	+	0.585979i
$147$		0			0
$148$	−0.0944570	−	0.0142371i	−0.00776432	−	0.00117028i
$149$	4.49445	−	11.4517i	0.368200	−	0.938158i	−0.619946	−	0.784644i	$-0.712846\pi$
$149$	4.49445	−	11.4517i	0.368200	−	0.938158i	0.988146	−	0.153514i	$-0.0490591\pi$
$150$		0			0
$151$	1.06527	−	14.2151i	0.0866906	−	1.15681i	−0.768976	−	0.639278i	$-0.779233\pi$
$151$	1.06527	−	14.2151i	0.0866906	−	1.15681i	0.855666	−	0.517528i	$-0.173148\pi$
$152$	−1.20270	+	1.50813i	−0.0975515	+	0.122326i
$153$		0			0
$154$	−2.15990	−	9.46314i	−0.174050	−	0.762562i
$155$	−18.1333	+	2.73315i	−1.45650	+	0.219532i
$156$		0			0
$157$	4.01648	+	6.95674i	0.320550	+	0.555209i	0.980602	−	0.196012i	$-0.0627990\pi$
$157$	4.01648	+	6.95674i	0.320550	+	0.555209i	−0.660052	+	0.751220i	$0.729466\pi$
$158$	3.27326	−	1.00967i	0.260406	−	0.0803247i
$159$		0			0
$160$	−2.31373	+	30.8746i	−0.182917	+	2.44085i
$161$	5.76862	−	25.2740i	0.454631	−	1.99187i
$162$		0			0
$163$	−1.21278	+	5.31353i	−0.0949921	+	0.416187i	−0.999957	−	0.00929923i	$-0.997040\pi$
$163$	−1.21278	+	5.31353i	−0.0949921	+	0.416187i	0.904965	+	0.425487i	$0.139897\pi$
$164$	6.76409	−	1.01952i	0.528186	−	0.0796113i
$165$		0			0
$166$	−0.227202	+	0.210813i	−0.0176343	+	0.0163622i
$167$	−5.52797	−	0.833208i	−0.427767	−	0.0644756i	−0.0683697	−	0.997660i	$-0.521780\pi$
$167$	−5.52797	−	0.833208i	−0.427767	−	0.0644756i	−0.359398	+	0.933184i	$0.617018\pi$
$168$		0			0
$169$	5.09352	−	3.47270i	0.391809	−	0.267131i
$170$	−19.7860	−	24.8108i	−1.51751	−	1.90290i
$171$		0			0
$172$	7.50837	+	3.61584i	0.572508	+	0.275705i
$173$	−8.22022	+	14.2378i	−0.624971	+	1.08248i	0.363575	+	0.931565i	$0.381556\pi$
$173$	−8.22022	+	14.2378i	−0.624971	+	1.08248i	−0.988546	+	0.150917i	$0.951777\pi$
$174$		0			0
$175$	22.0968	+	38.2728i	1.67036	+	2.89315i
$176$	−0.433347	−	5.78262i	−0.0326648	−	0.435881i
$177$		0			0
$178$	−8.07169	+	1.21661i	−0.604999	+	0.0911889i
$179$	9.74766	+	4.69422i	0.728574	+	0.350863i	0.761123	−	0.648607i	$-0.224648\pi$
$179$	9.74766	+	4.69422i	0.728574	+	0.350863i	−0.0325491	+	0.999470i	$0.510363\pi$
$180$		0			0
$181$	−2.01346	+	2.52480i	−0.149659	+	0.187667i	−0.851010	−	0.525150i	$-0.824009\pi$
$181$	−2.01346	+	2.52480i	−0.149659	+	0.187667i	0.701351	+	0.712816i	$0.252581\pi$
$182$	31.0977	+	9.59238i	2.30512	+	0.711035i
$183$		0			0
$184$	1.20516	−	3.07071i	0.0888459	−	0.226376i
$185$	−0.212223	+	0.0654620i	−0.0156029	+	0.00481286i
$186$		0			0
$187$	3.86172	+	3.58315i	0.282397	+	0.262026i
$188$	8.18978	−	3.94399i	0.597301	−	0.287645i
$189$		0			0
$190$	6.90944	−	30.2723i	0.501264	−	2.19618i
$191$	7.35761	−	12.7438i	0.532378	−	0.922106i	−0.466907	−	0.884306i	$-0.654632\pi$
$191$	7.35761	−	12.7438i	0.532378	−	0.922106i	0.999285	−	0.0377999i	$-0.0120349\pi$
$192$		0			0
$193$	−6.70185	+	17.0760i	−0.482410	+	1.22916i	0.457950	+	0.888978i	$0.348584\pi$
$193$	−6.70185	+	17.0760i	−0.482410	+	1.22916i	−0.940360	+	0.340182i	$0.889511\pi$
$194$	19.1513	−	17.7698i	1.37498	−	1.27580i
$195$		0			0
$196$	4.94560	+	12.6012i	0.353257	+	0.900084i
$197$	−6.23462	+	3.00243i	−0.444198	+	0.213915i	−0.642593	−	0.766208i	$-0.722141\pi$
$197$	−6.23462	+	3.00243i	−0.444198	+	0.213915i	0.198395	+	0.980122i	$0.436427\pi$
$198$		0			0
$199$	−2.28709	−	2.86792i	−0.162127	−	0.203301i	0.694132	−	0.719848i	$-0.255789\pi$
$199$	−2.28709	−	2.86792i	−0.162127	−	0.203301i	−0.856259	+	0.516547i	$0.827217\pi$
$200$	2.05449	+	5.23477i	0.145275	+	0.370154i
$201$		0			0
$202$	−0.444156	−	0.769300i	−0.0312507	−	0.0541278i
$203$	11.3865	+	17.2622i	0.799178	+	1.21157i
$204$		0			0
$205$	13.1404	−	8.95897i	0.917765	−	0.625721i
$206$	−9.00881	+	11.2967i	−0.627674	+	0.787078i
$207$		0			0
$208$	17.5167	+	8.43560i	1.21457	+	0.584904i
$209$	−0.385200	+	5.14013i	−0.0266448	+	0.355550i
$210$		0			0
$211$	−10.8741	+	10.0897i	−0.748604	+	0.694603i	−0.959124	−	0.282986i	$-0.908675\pi$
$211$	−10.8741	+	10.0897i	−0.748604	+	0.694603i	0.210520	+	0.977590i	$0.432484\pi$
$212$	8.40131	−	7.79527i	0.577004	−	0.535382i
$213$		0			0
$214$	2.92364	+	2.71274i	0.199856	+	0.185439i
$215$	19.3754			1.32139
$216$		0			0
$217$	−15.6152	+	7.51988i	−1.06003	+	0.510483i
$218$	1.25397	−	16.7331i	0.0849299	−	1.13331i
$219$		0			0
$220$	4.63567	+	8.02922i	0.312537	+	0.541330i
$221$	−16.8777	+	5.20607i	−1.13531	+	0.350198i
$222$		0			0
$223$	2.56327	+	0.790664i	0.171649	+	0.0529468i	0.379389	−	0.925237i	$-0.376134\pi$
$223$	2.56327	+	0.790664i	0.171649	+	0.0529468i	−0.207739	+	0.978184i	$0.566611\pi$
$224$	6.51136	+	28.5281i	0.435059	+	1.90612i
$225$		0			0
$226$	5.74839	−	2.76828i	0.382377	−	0.184143i
$227$	3.44471	−	2.34857i	0.228634	−	0.155880i	−0.443585	−	0.896232i	$-0.646294\pi$
$227$	3.44471	−	2.34857i	0.228634	−	0.155880i	0.672219	+	0.740352i	$0.265341\pi$
$228$		0			0
$229$	−1.42309	−	0.214496i	−0.0940402	−	0.0141743i	0.101854	−	0.994799i	$-0.467523\pi$
$229$	−1.42309	−	0.214496i	−0.0940402	−	0.0141743i	−0.195894	+	0.980625i	$0.562761\pi$
$230$	3.96816	+	52.9514i	0.261653	+	3.49151i
$231$		0			0
$232$	1.10534	+	2.38797i	0.0725690	+	0.156778i
$233$	13.2578			0.868545			0.434272	−	0.900782i	$-0.357006\pi$
$233$	13.2578			0.868545			0.434272	+	0.900782i	$0.357006\pi$
$234$		0			0
$235$	13.1767	−	16.5231i	0.859554	−	1.07785i
$236$	−19.1611	+	2.88807i	−1.24728	+	0.187997i
$237$		0			0
$238$	−24.7809	−	16.8953i	−1.60631	−	1.09516i
$239$	−24.8642	−	3.74767i	−1.60833	−	0.242417i	−0.717434	−	0.696626i	$-0.754684\pi$
$239$	−24.8642	−	3.74767i	−1.60833	−	0.242417i	−0.890895	+	0.454210i	$0.849922\pi$
$240$		0			0
$241$	−2.52723	−	0.779546i	−0.162793	−	0.0502150i	0.212287	−	0.977207i	$-0.431909\pi$
$241$	−2.52723	−	0.779546i	−0.162793	−	0.0502150i	−0.375080	+	0.926992i	$0.622385\pi$
$242$	11.2191	+	14.0684i	0.721194	+	0.904348i
$243$		0			0
$244$	10.2781			0.657985
$245$	23.0712	+	21.4070i	1.47397	+	1.36764i
$246$		0			0
$247$	−14.2790	−	9.73526i	−0.908552	−	0.619440i
$248$	−2.10741	+	0.650049i	−0.133820	+	0.0412782i
$249$		0			0
$250$	−37.5276	−	34.8206i	−2.37346	−	2.20225i
$251$	2.53977	+	3.18478i	0.160309	+	0.201021i	0.855498	−	0.517805i	$-0.173251\pi$
$251$	2.53977	+	3.18478i	0.160309	+	0.201021i	−0.695189	+	0.718827i	$0.744679\pi$
$252$		0			0
$253$	−1.96147	−	8.59378i	−0.123317	−	0.540286i
$254$	5.91098	+	15.0609i	0.370888	+	0.945007i
$255$		0			0
$256$	1.43825	+	19.1921i	0.0898907	+	1.19951i
$257$	2.49978	−	6.36933i	0.155932	−	0.397308i	−0.831464	−	0.555579i	$-0.812497\pi$
$257$	2.49978	−	6.36933i	0.155932	−	0.397308i	0.987396	+	0.158271i	$0.0505919\pi$
$258$		0			0
$259$	−0.173427	+	0.118240i	−0.0107762	+	0.00734711i
$260$	−31.0846			−1.92778
$261$		0			0
$262$	−24.9597			−1.54201
$263$	−9.97453	+	6.80052i	−0.615056	+	0.419338i	−0.830374	−	0.557206i	$-0.811873\pi$
$263$	−9.97453	+	6.80052i	−0.615056	+	0.419338i	0.215318	+	0.976544i	$0.430921\pi$
$264$		0			0
$265$	9.73478	−	24.8038i	0.598003	−	1.52369i
$266$	−2.19306	−	29.2644i	−0.134465	−	1.79431i
$267$		0			0
$268$	−0.934706	−	2.38159i	−0.0570963	−	0.145479i
$269$	−5.36370	−	23.4999i	−0.327031	−	1.43281i	−0.824760	−	0.565482i	$-0.808690\pi$
$269$	−5.36370	−	23.4999i	−0.327031	−	1.43281i	0.497730	−	0.867332i	$-0.334167\pi$
$270$		0			0
$271$	−15.1249	−	18.9661i	−0.918775	−	1.15211i	−0.987992	−	0.154506i	$-0.950621\pi$
$271$	−15.1249	−	18.9661i	−0.918775	−	1.15211i	0.0692168	−	0.997602i	$-0.477950\pi$
$272$	−13.1348	−	12.1873i	−0.796415	−	0.738965i
$273$		0			0
$274$	10.4016	−	3.20847i	0.628383	−	0.193830i
$275$	12.4158	+	8.46498i	0.748703	+	0.510457i
$276$		0			0
$277$	−6.57570	−	6.10136i	−0.395096	−	0.366595i	0.457461	−	0.889230i	$-0.348759\pi$
$277$	−6.57570	−	6.10136i	−0.395096	−	0.366595i	−0.852557	+	0.522634i	$0.824949\pi$
$278$	25.5092			1.52994
$279$		0			0
$280$	4.75343	+	5.96061i	0.284072	+	0.356215i
$281$	0.722142	+	0.222751i	0.0430794	+	0.0132882i	0.316220	−	0.948686i	$-0.397586\pi$
$281$	0.722142	+	0.222751i	0.0430794	+	0.0132882i	−0.273141	+	0.961974i	$0.588062\pi$
$282$		0			0
$283$	22.9052	+	3.45240i	1.36157	+	0.205224i	0.788880	−	0.614547i	$-0.210661\pi$
$283$	22.9052	+	3.45240i	1.36157	+	0.205224i	0.572691	+	0.819771i	$0.305899\pi$
$284$	−14.5659	−	9.93086i	−0.864327	−	0.589288i
$285$		0			0
$286$	10.9420	−	1.64925i	0.647016	−	0.0975219i
$287$	9.37164	−	11.7517i	0.553190	−	0.693679i
$288$		0			0
$289$	−0.722244			−0.0424850
$290$	−32.7088	−	26.9126i	−1.92073	−	1.58036i
$291$		0			0
$292$	−0.551552	−	7.35995i	−0.0322771	−	0.430709i
$293$	−15.8817	−	2.39378i	−0.927817	−	0.139846i	−0.332287	−	0.943178i	$-0.607820\pi$
$293$	−15.8817	−	2.39378i	−0.927817	−	0.139846i	−0.595531	+	0.803332i	$0.703058\pi$
$294$		0			0
$295$	−37.2237	+	25.3787i	−2.16724	+	1.47760i
$296$	−0.0240640	+	0.0115886i	−0.00139869	+	0.000673574i
$297$		0			0
$298$	5.29938	+	23.2181i	0.306985	+	1.34499i
$299$	28.2408	+	8.71115i	1.63321	+	0.503779i
$300$		0			0
$301$	17.4984	−	5.39754i	1.00859	−	0.311109i
$302$	13.7978	+	23.8986i	0.793977	+	1.37521i
$303$		0			0
$304$	1.31017	−	17.4830i	0.0751436	−	1.00272i
$305$	21.5296	−	10.3681i	1.23278	−	0.593677i
$306$		0			0
$307$	25.5077			1.45580			0.727900	−	0.685683i	$-0.240496\pi$
$307$	25.5077			1.45580			0.727900	+	0.685683i	$0.240496\pi$
$308$	6.42334	+	5.95999i	0.366004	+	0.339602i
$309$		0			0
$310$	26.0235	−	24.1462i	1.47803	−	1.37141i
$311$	2.01101	−	1.86594i	0.114034	−	0.105808i	−0.621095	−	0.783735i	$-0.713312\pi$
$311$	2.01101	−	1.86594i	0.114034	−	0.105808i	0.735129	+	0.677927i	$0.237122\pi$
$312$		0			0
$313$	1.75008	−	23.3532i	0.0989202	−	1.32000i	−0.698080	−	0.716020i	$-0.745962\pi$
$313$	1.75008	−	23.3532i	0.0989202	−	1.32000i	0.797000	−	0.603979i	$-0.206419\pi$
$314$	−14.0107	−	6.74722i	−0.790672	−	0.380767i
$315$		0			0
$316$	−1.92801	+	2.41765i	−0.108459	+	0.136003i
$317$	21.4695	−	14.6376i	1.20585	−	0.822132i	0.217755	−	0.976003i	$-0.430127\pi$
$317$	21.4695	−	14.6376i	1.20585	−	0.822132i	0.988091	+	0.153872i	$0.0491742\pi$
$318$		0			0
$319$	6.03500	+	3.60843i	0.337895	+	0.202033i
$320$	−11.9238	−	20.6527i	−0.666563	−	1.15452i
$321$		0			0
$322$	18.3348	+	46.7162i	1.02176	+	2.60339i
$323$	9.93043	+	12.4524i	0.552544	+	0.692868i
$324$		0			0
$325$	−45.3923	+	21.8598i	−2.51791	+	1.21256i
$326$	−3.85465	−	9.82148i	−0.213489	−	0.543962i
$327$		0			0
$328$	1.40206	−	1.30092i	0.0774160	−	0.0718316i
$329$	7.29726	−	18.5931i	0.402311	−	1.02507i
$330$		0			0
$331$	−3.65144	+	6.32449i	−0.200702	+	0.347625i	−0.948755	−	0.316014i	$-0.897655\pi$
$331$	−3.65144	+	6.32449i	−0.200702	+	0.347625i	0.748053	+	0.663639i	$0.230989\pi$
$332$	0.0622604	−	0.272781i	0.00341698	−	0.0149708i
$333$		0			0
$334$	9.75056	−	4.69562i	0.533527	−	0.256933i
$335$	−4.36041	−	4.04587i	−0.238234	−	0.221049i
$336$		0			0
$337$	−18.6233	+	5.74452i	−1.01447	+	0.312924i	−0.757037	−	0.653371i	$-0.773354\pi$
$337$	−18.6233	+	5.74452i	−1.01447	+	0.312924i	−0.257436	+	0.966295i	$0.582878\pi$
$338$	−4.36000	+	11.1091i	−0.237153	+	0.604255i
$339$		0			0
$340$	27.3751	+	8.44409i	1.48462	+	0.457945i
$341$	−3.67433	+	4.60746i	−0.198976	+	0.249508i
$342$		0			0
$343$	2.58121	+	1.24304i	0.139372	+	0.0671181i
$344$	2.30411	−	0.347289i	0.124229	−	0.0187246i
$345$		0			0
$346$	−2.37840	−	31.7375i	−0.127864	−	1.70622i
$347$	−15.3781	−	26.6357i	−0.825542	−	1.42988i	−0.901505	−	0.432770i	$-0.857536\pi$
$347$	−15.3781	−	26.6357i	−0.825542	−	1.42988i	0.0759627	−	0.997111i	$-0.475797\pi$
$348$		0			0
$349$	16.4569	−	28.5041i	0.880916	−	1.52579i	0.0305922	−	0.999532i	$-0.490261\pi$
$349$	16.4569	−	28.5041i	0.880916	−	1.52579i	0.850324	−	0.526260i	$-0.176406\pi$
$350$	−77.0806	−	37.1201i	−4.12013	−	1.98415i
$351$		0			0
$352$	6.20356	+	7.77902i	0.330651	+	0.414623i
$353$	−25.4906	+	17.3792i	−1.35673	+	0.925002i	−0.999958	−	0.00918938i	$-0.997075\pi$
$353$	−25.4906	+	17.3792i	−1.35673	+	0.925002i	−0.356771	+	0.934192i	$0.616123\pi$
$354$		0			0
$355$	−40.5293	−	6.10881i	−2.15107	−	0.324222i
$356$	5.40182	−	5.01216i	0.286296	−	0.265644i
$357$		0			0
$358$	−20.7104	+	3.12159i	−1.09458	+	0.164981i
$359$	1.00719	−	4.41280i	0.0531576	−	0.232899i	−0.941370	−	0.337377i	$-0.890460\pi$
$359$	1.00719	−	4.41280i	0.0531576	−	0.232899i	0.994527	+	0.104479i	$0.0333174\pi$
$360$		0			0
$361$	0.760099	−	3.33021i	0.0400052	−	0.175274i
$362$	0.467180	−	6.23409i	0.0245544	−	0.327656i
$363$		0			0
$364$	−28.0732	+	8.65944i	−1.47144	+	0.453878i
$365$	−8.57979	−	14.8606i	−0.449087	−	0.777841i
$366$		0			0
$367$	20.7328	−	3.12497i	1.08225	−	0.163122i	0.416378	−	0.909192i	$-0.363299\pi$
$367$	20.7328	−	3.12497i	1.08225	−	0.163122i	0.665868	+	0.746070i	$0.268061\pi$
$368$	6.67153	+	29.2299i	0.347777	+	1.52371i
$369$		0			0
$370$	0.268061	−	0.336137i	0.0139358	−	0.0174750i
$371$	1.88194	−	25.1128i	0.0977056	−	1.30379i
$372$		0			0
$373$	0.236722	−	0.603158i	0.0122570	−	0.0312303i	−0.924614	−	0.380905i	$-0.875613\pi$
$373$	0.236722	−	0.603158i	0.0122570	−	0.0312303i	0.936871	+	0.349674i	$0.113708\pi$
$374$	−10.0843	−	1.51996i	−0.521445	−	0.0785952i
$375$		0			0
$376$	1.27080	−	2.20109i	0.0655366	−	0.113513i
$377$	−20.5943	+	11.4740i	−1.06066	+	0.590939i
$378$		0			0
$379$	−26.2054	−	12.6199i	−1.34608	−	0.648238i	−0.384593	−	0.923086i	$-0.625658\pi$
$379$	−26.2054	−	12.6199i	−1.34608	−	0.648238i	−0.961488	+	0.274848i	$0.911373\pi$
$380$	10.2408	+	26.0931i	0.525342	+	1.33855i
$381$		0			0
$382$	2.12882	+	28.4071i	0.108920	+	1.45343i
$383$	12.6788	+	8.64428i	0.647858	+	0.441702i	0.842151	−	0.539242i	$-0.181289\pi$
$383$	12.6788	+	8.64428i	0.647858	+	0.441702i	−0.194293	+	0.980943i	$0.562241\pi$
$384$		0			0
$385$	19.4673	+	6.00486i	0.992145	+	0.306036i
$386$	−7.90211	−	34.6214i	−0.402207	−	1.76218i
$387$		0			0
$388$	−5.24804	+	22.9931i	−0.266429	+	1.16730i
$389$	−15.8577	+	27.4664i	−0.804018	+	1.39260i	0.112934	+	0.993602i	$0.463975\pi$
$389$	−15.8577	+	27.4664i	−0.804018	+	1.39260i	−0.916952	+	0.398998i	$0.869358\pi$
$390$		0			0
$391$	−22.5043	−	15.3432i	−1.13809	−	0.775938i
$392$	3.12731	+	2.13217i	0.157953	+	0.107691i
$393$		0			0
$394$	6.69801	−	11.6013i	0.337441	−	0.584465i
$395$	−1.59980	+	7.00919i	−0.0804947	+	0.352670i
$396$		0			0
$397$	7.02476	+	30.7775i	0.352563	+	1.54468i	0.771241	+	0.636543i	$0.219636\pi$
$397$	7.02476	+	30.7775i	0.352563	+	1.54468i	−0.418678	+	0.908135i	$0.637507\pi$
$398$	6.78567	+	2.09310i	0.340135	+	0.104918i
$399$		0			0
$400$	−42.2298	−	28.7918i	−2.11149	−	1.43959i
$401$	0.469905	+	6.27044i	0.0234659	+	0.313131i	0.996569	+	0.0827621i	$0.0263742\pi$
$401$	0.469905	+	6.27044i	0.0234659	+	0.313131i	−0.973103	+	0.230369i	$0.926007\pi$
$402$		0			0
$403$	−7.21854	−	18.3925i	−0.359581	−	0.916197i
$404$	0.722500	+	0.347938i	0.0359457	+	0.0173106i
$405$		0			0
$406$	−37.0373	−	15.1935i	−1.83813	−	0.754040i
$407$	−0.0356855	+	0.0618091i	−0.00176887	+	0.00306376i
$408$		0			0
$409$	12.4615	+	1.87828i	0.616184	+	0.0928748i	0.449715	−	0.893172i	$-0.351525\pi$
$409$	12.4615	+	1.87828i	0.616184	+	0.0928748i	0.166469	+	0.986047i	$0.446764\pi$
$410$	−11.2480	+	28.6596i	−0.555502	+	1.41539i
$411$		0			0
$412$	0.974758	−	13.0072i	0.0480229	−	0.640821i
$413$	−26.5476	+	33.2897i	−1.30632	+	1.63808i
$414$		0			0
$415$	−0.144753	−	0.634204i	−0.00710564	−	0.0311318i
$416$	−32.9865	+	4.97191i	−1.61729	+	0.243768i
$417$		0			0
$418$	−4.98926	−	8.64166i	−0.244033	−	0.422677i
$419$	14.1569	−	4.36682i	0.691609	−	0.213333i	0.0710268	−	0.997474i	$-0.477372\pi$
$419$	14.1569	−	4.36682i	0.691609	−	0.213333i	0.620582	+	0.784141i	$0.286896\pi$
$420$		0			0
$421$	−1.13215	+	15.1076i	−0.0551778	+	0.736297i	0.899170	+	0.437600i	$0.144171\pi$
$421$	−1.13215	+	15.1076i	−0.0551778	+	0.736297i	−0.954348	+	0.298698i	$0.903448\pi$
$422$	6.39007	−	27.9967i	0.311064	−	1.36286i
$423$		0			0
$424$	0.713064	−	3.12414i	0.0346295	−	0.151722i
$425$	45.9135	−	6.92035i	2.22713	−	0.335686i
$426$		0			0
$427$	16.5556	−	15.3613i	0.801181	−	0.743387i
$428$	−3.56020	−	0.536613i	−0.172089	−	0.0259382i
$429$		0			0
$430$	−30.9908	+	21.1292i	−1.49451	+	1.01894i
$431$	−24.2562	−	30.4164i	−1.16838	−	1.46511i	−0.857371	−	0.514699i	$-0.827904\pi$
$431$	−24.2562	−	30.4164i	−1.16838	−	1.46511i	−0.311011	−	0.950406i	$-0.600668\pi$
$432$		0			0
$433$	23.3421	+	11.2410i	1.12175	+	0.540206i	0.900432	−	0.434996i	$-0.143250\pi$
$433$	23.3421	+	11.2410i	1.12175	+	0.540206i	0.221317	+	0.975202i	$0.428965\pi$
$434$	16.7758	−	29.0566i	0.805265	−	1.39476i
$435$		0			0
$436$	7.57402	+	13.1186i	0.362730	+	0.628266i
$437$	−1.99159	−	26.5759i	−0.0952707	−	1.27130i
$438$		0			0
$439$	35.2700	−	5.31609i	1.68334	−	0.253723i	0.763443	−	0.645875i	$-0.223507\pi$
$439$	35.2700	−	5.31609i	1.68334	−	0.253723i	0.919901	+	0.392152i	$0.128269\pi$
$440$	2.33560	+	1.12477i	0.111345	+	0.0536211i
$441$		0			0
$442$	21.3184	−	26.7324i	1.01401	−	1.27153i
$443$	−27.2025	−	8.39087i	−1.29243	−	0.398662i	−0.429080	−	0.903267i	$-0.641162\pi$
$443$	−27.2025	−	8.39087i	−1.29243	−	0.398662i	−0.863351	+	0.504604i	$0.831638\pi$
$444$		0			0
$445$	6.25921	−	15.9482i	0.296715	−	0.756018i
$446$	−4.96215	+	1.53062i	−0.234965	+	0.0724770i
$447$		0			0
$448$	−16.5221	−	15.3302i	−0.780594	−	0.724285i
$449$	35.4096	−	17.0523i	1.67108	−	0.804750i	0.673215	−	0.739447i	$-0.264913\pi$
$449$	35.4096	−	17.0523i	1.67108	−	0.804750i	0.997865	−	0.0653032i	$-0.0208014\pi$
$450$		0			0
$451$	1.13728	−	4.98275i	0.0535525	−	0.234629i
$452$	−2.87985	+	4.98805i	−0.135457	+	0.234618i
$453$		0			0
$454$	−2.94864	+	7.51302i	−0.138387	+	0.352603i
$455$	−50.0701	+	46.4583i	−2.34732	+	2.17800i
$456$		0			0
$457$	4.16018	+	10.6000i	0.194605	+	0.495845i	0.994554	−	0.104223i	$-0.0332354\pi$
$457$	4.16018	+	10.6000i	0.194605	+	0.495845i	−0.799949	+	0.600068i	$0.795140\pi$
$458$	2.51012	−	1.20881i	0.117290	−	0.0564840i
$459$		0			0
$460$	−29.8873	−	37.4774i	−1.39350	−	1.74739i
$461$	9.48629	+	24.1707i	0.441820	+	1.12574i	0.962330	+	0.271884i	$0.0876468\pi$
$461$	9.48629	+	24.1707i	0.441820	+	1.12574i	−0.520510	+	0.853856i	$0.674258\pi$
$462$		0			0
$463$	−0.164519	−	0.284956i	−0.00764587	−	0.0132430i	0.862177	−	0.506607i	$-0.169100\pi$
$463$	−0.164519	−	0.284956i	−0.00764587	−	0.0132430i	−0.869823	+	0.493364i	$0.835767\pi$
$464$	−20.5267	−	12.2733i	−0.952930	−	0.569773i
$465$		0			0
$466$	−21.2057	+	14.4578i	−0.982333	+	0.669743i
$467$	25.6715	−	32.1910i	1.18793	−	1.48962i	0.356235	−	0.934396i	$-0.384060\pi$
$467$	25.6715	−	32.1910i	1.18793	−	1.48962i	0.831699	−	0.555226i	$-0.187368\pi$
$468$		0			0
$469$	−5.06507	−	2.43921i	−0.233883	−	0.112632i
$470$	−3.05738	+	40.7979i	−0.141026	+	1.88187i
$471$		0			0
$472$	−3.97172	+	3.68522i	−0.182813	+	0.169626i
$473$	4.56436	−	4.23511i	0.209870	−	0.194731i
$474$		0			0
$475$	33.3041	+	30.9017i	1.52810	+	1.41787i
$476$	27.0754			1.24100
$477$		0			0
$478$	43.8569	−	21.1203i	2.00597	−	0.966022i
$479$	1.13812	−	15.1872i	0.0520021	−	0.693920i	−0.908897	−	0.417021i	$-0.863074\pi$
$479$	1.13812	−	15.1872i	0.0520021	−	0.693920i	0.960899	−	0.276899i	$-0.0893068\pi$
$480$		0			0
$481$	−0.119645	−	0.207231i	−0.00545534	−	0.00944892i
$482$	4.89238	−	1.50910i	0.222842	−	0.0687376i
$483$		0			0
$484$	−15.5223	−	4.78801i	−0.705561	−	0.217637i
$485$	12.2015	+	53.4582i	0.554041	+	2.42741i
$486$		0			0
$487$	26.8766	−	12.9431i	1.21789	−	0.586507i	0.289170	−	0.957278i	$-0.406621\pi$
$487$	26.8766	−	12.9431i	1.21789	−	0.586507i	0.928724	+	0.370771i	$0.120906\pi$
$488$	2.37445	−	1.61887i	0.107486	−	0.0732828i
$489$		0			0
$490$	−60.2468	−	9.08074i	−2.72167	−	0.410226i
$491$	−1.99076	−	26.5649i	−0.0898419	−	1.19886i	−0.841853	−	0.539707i	$-0.818535\pi$
$491$	−1.99076	−	26.5649i	−0.0898419	−	1.19886i	0.752011	−	0.659150i	$-0.229084\pi$
$492$		0			0
$493$	21.2535	−	4.51029i	0.957210	−	0.203133i
$494$	33.4556			1.50524
$495$		0			0
$496$	12.4974	−	15.6713i	0.561151	−	0.703661i
$497$	−38.3047	+	5.77351i	−1.71820	+	0.258977i
$498$		0			0
$499$	−6.14799	−	4.19163i	−0.275222	−	0.187643i	0.417841	−	0.908520i	$-0.362787\pi$
$499$	−6.14799	−	4.19163i	−0.275222	−	0.187643i	−0.693063	+	0.720877i	$0.743739\pi$
$500$	45.6985	+	6.88794i	2.04370	+	0.308038i
$501$		0			0
$502$	−7.53539	−	2.32436i	−0.336321	−	0.103741i
$503$	−6.41354	−	8.04232i	−0.285965	−	0.358589i	0.618013	−	0.786168i	$-0.287938\pi$
$503$	−6.41354	−	8.04232i	−0.285965	−	0.358589i	−0.903978	+	0.427579i	$0.859367\pi$
$504$		0			0
$505$	1.86442			0.0829656
$506$	12.5090	+	11.6067i	0.556093	+	0.515979i
$507$		0			0
$508$	−12.0678	−	8.22772i	−0.535424	−	0.365046i
$509$	10.1439	−	3.12899i	0.449622	−	0.138690i	−0.0616710	−	0.998097i	$-0.519643\pi$
$509$	10.1439	−	3.12899i	0.449622	−	0.138690i	0.511293	+	0.859407i	$0.329167\pi$
$510$		0			0
$511$	−11.8884	−	11.0309i	−0.525913	−	0.487976i
$512$	−18.3940	−	23.0654i	−0.812908	−	1.01935i
$513$		0			0
$514$	2.94747	+	12.9137i	0.130007	+	0.569600i
$515$	−11.0794	−	28.2298i	−0.488216	−	1.24395i
$516$		0			0
$517$	−0.507537	−	6.77261i	−0.0223214	−	0.297859i
$518$	0.148452	−	0.378249i	0.00652260	−	0.0166193i
$519$		0			0
$520$	−7.18119	+	4.89605i	−0.314916	+	0.214706i
$521$	15.5623			0.681795			0.340897	−	0.940101i	$-0.389269\pi$
$521$	15.5623			0.681795			0.340897	+	0.940101i	$0.389269\pi$
$522$		0			0
$523$	−1.40462			−0.0614198			−0.0307099	−	0.999528i	$-0.509777\pi$
$523$	−1.40462			−0.0614198			−0.0307099	+	0.999528i	$0.509777\pi$
$524$	18.6169	−	12.6928i	0.813284	−	0.554488i
$525$		0			0
$526$	8.53810	−	21.7547i	0.372279	−	0.948551i
$527$	1.36079	+	18.1585i	0.0592771	+	0.790998i
$528$		0			0
$529$	8.24753	+	21.0144i	0.358588	+	0.913668i
$530$	11.4782	+	50.2894i	0.498582	+	2.18443i
$531$		0			0
$532$	16.5176	+	20.7125i	0.716131	+	0.897999i
$533$	12.5613	+	11.6552i	0.544089	+	0.504841i
$534$		0			0
$535$	−7.99892	+	2.46734i	−0.345823	+	0.106672i
$536$	−0.591055	−	0.402975i	−0.0255297	−	0.0174059i
$537$		0			0
$538$	34.2062	+	31.7387i	1.47473	+	1.36835i
$539$	10.1142			0.435648
$540$		0			0
$541$	−25.0277	−	31.3837i	−1.07602	−	1.34929i	−0.933124	−	0.359555i	$-0.882928\pi$
$541$	−25.0277	−	31.3837i	−1.07602	−	1.34929i	−0.142901	−	0.989737i	$-0.545643\pi$
$542$	44.8750	+	13.8421i	1.92755	+	0.594569i
$543$		0			0
$544$	30.4006	+	4.58215i	1.30341	+	0.196458i
$545$	29.0990	+	19.8393i	1.24646	+	0.849824i
$546$		0			0
$547$	26.9712	−	4.06525i	1.15320	−	0.173818i	0.455522	−	0.890224i	$-0.349453\pi$
$547$	26.9712	−	4.06525i	1.15320	−	0.173818i	0.697683	+	0.716407i	$0.254215\pi$
$548$	−6.12673	+	7.68267i	−0.261721	+	0.328188i
$549$		0			0
$550$	−29.0902			−1.24041
$551$	16.4163	+	13.5072i	0.699358	+	0.575428i
$552$		0			0
$553$	0.507778	+	6.77583i	0.0215929	+	0.288137i
$554$	17.1714	+	2.58817i	0.729542	+	0.109961i
$555$		0			0
$556$	−19.0268	+	12.9723i	−0.806917	+	0.550147i
$557$	−31.1072	+	14.9804i	−1.31805	+	0.634742i	−0.954883	−	0.296981i	$-0.904020\pi$
$557$	−31.1072	+	14.9804i	−1.31805	+	0.634742i	−0.363171	+	0.931722i	$0.618306\pi$
$558$		0			0
$559$	4.64535	+	20.3526i	0.196477	+	0.860824i
$560$	−66.2138	−	20.4242i	−2.79804	−	0.863082i
$561$		0			0
$562$	−1.39797	+	0.431217i	−0.0589699	+	0.0181898i
$563$	0.422003	+	0.730931i	0.0177853	+	0.0308051i	0.874781	−	0.484518i	$-0.161005\pi$
$563$	0.422003	+	0.730931i	0.0177853	+	0.0308051i	−0.856996	+	0.515323i	$0.827672\pi$
$564$		0			0
$565$	−1.00072	+	13.3536i	−0.0421005	+	0.561792i
$566$	−40.4015	+	19.4563i	−1.69820	+	0.817810i
$567$		0			0
$568$	−4.92921			−0.206825
$569$	25.5179	+	23.6771i	1.06977	+	0.992598i	0.999988	−	0.00496494i	$-0.00158040\pi$
$569$	25.5179	+	23.6771i	1.06977	+	0.992598i	0.0697781	+	0.997563i	$0.477771\pi$
$570$		0			0
$571$	−5.55839	+	5.15743i	−0.232611	+	0.215832i	−0.787863	−	0.615851i	$-0.788812\pi$
$571$	−5.55839	+	5.15743i	−0.232611	+	0.215832i	0.555251	+	0.831682i	$0.312622\pi$
$572$	−7.32274	+	6.79451i	−0.306179	+	0.284093i
$573$		0			0
$574$	−2.17449	+	29.0166i	−0.0907615	+	1.21113i
$575$	−69.9994	−	33.7099i	−2.91918	−	1.40580i
$576$		0			0
$577$	27.8052	−	34.8666i	1.15755	−	1.45152i	0.288025	−	0.957623i	$-0.407001\pi$
$577$	27.8052	−	34.8666i	1.15755	−	1.45152i	0.869522	−	0.493895i	$-0.164427\pi$
$578$	1.15522	−	0.787617i	0.0480509	−	0.0327606i
$579$		0			0
$580$	38.0827	+	3.44009i	1.58130	+	0.142842i
$581$	−0.307404	−	0.532440i	−0.0127533	−	0.0220893i
$582$		0			0
$583$	−3.12839	−	7.97100i	−0.129564	−	0.330125i
$584$	−1.28667	−	1.61343i	−0.0532427	−	0.0667642i
$585$		0			0
$586$	28.0130	−	13.4904i	1.15721	−	0.557282i
$587$	−10.9098	−	27.7978i	−0.450297	−	1.14734i	−0.958245	−	0.285950i	$-0.907691\pi$
$587$	−10.9098	−	27.7978i	−0.450297	−	1.14734i	0.507948	−	0.861388i	$-0.330404\pi$
$588$		0			0
$589$	−13.0610	+	12.1188i	−0.538168	+	0.499347i
$590$	31.8631	−	81.1858i	1.31178	−	3.34237i
$591$		0			0
$592$	0.121376	−	0.210230i	0.00498854	−	0.00864041i
$593$	−7.15459	+	31.3463i	−0.293804	+	1.28724i	0.585382	+	0.810758i	$0.300945\pi$
$593$	−7.15459	+	31.3463i	−0.293804	+	1.28724i	−0.879185	+	0.476480i	$0.841912\pi$
$594$		0			0
$595$	56.7153	−	27.3126i	2.32510	−	1.11971i
$596$	−15.7599	−	14.6230i	−0.645549	−	0.598982i
$597$		0			0
$598$	−54.6706	+	16.8636i	−2.23565	+	0.689605i
$599$	−5.73528	+	14.6133i	−0.234337	+	0.597082i	−0.998871	−	0.0475018i	$-0.984874\pi$
$599$	−5.73528	+	14.6133i	−0.234337	+	0.597082i	0.764534	+	0.644584i	$0.222969\pi$
$600$		0			0
$601$	−8.99702	−	2.77521i	−0.366996	−	0.113203i	0.105771	−	0.994390i	$-0.466269\pi$
$601$	−8.99702	−	2.77521i	−0.366996	−	0.113203i	−0.472768	+	0.881187i	$0.656745\pi$
$602$	−22.1024	+	27.7156i	−0.900828	+	1.12960i
$603$		0			0
$604$	−22.4447	−	10.8088i	−0.913263	−	0.439804i
$605$	−37.3449	+	5.62883i	−1.51829	+	0.228845i
$606$		0			0
$607$	1.29069	+	17.2231i	0.0523875	+	0.699062i	0.960133	+	0.279542i	$0.0901827\pi$
$607$	1.29069	+	17.2231i	0.0523875	+	0.699062i	−0.907746	+	0.419520i	$0.862198\pi$
$608$	15.0409	+	26.0516i	0.609990	+	1.05653i
$609$		0			0
$610$	−23.1298	+	40.0621i	−0.936500	+	1.62207i
$611$	20.5156	+	9.87979i	0.829972	+	0.399693i
$612$		0			0
$613$	5.87230	+	7.36363i	0.237180	+	0.297414i	0.886149	−	0.463401i	$-0.153371\pi$
$613$	5.87230	+	7.36363i	0.237180	+	0.297414i	−0.648969	+	0.760815i	$0.724800\pi$
$614$	−40.7993	+	27.8165i	−1.64653	+	1.12258i
$615$		0			0
$616$	2.42267	+	0.365159i	0.0976121	+	0.0147127i
$617$	24.2780	−	22.5267i	0.977395	−	0.906890i	−0.0182765	−	0.999833i	$-0.505818\pi$
$617$	24.2780	−	22.5267i	0.977395	−	0.906890i	0.995671	+	0.0929430i	$0.0296274\pi$
$618$		0			0
$619$	−36.7001	+	5.53165i	−1.47510	+	0.222336i	−0.836825	−	0.547471i	$-0.815591\pi$
$619$	−36.7001	+	5.53165i	−1.47510	+	0.222336i	−0.638277	+	0.769807i	$0.720353\pi$
$620$	−7.13123	+	31.2440i	−0.286397	+	1.25479i
$621$		0			0
$622$	−1.18175	+	5.17758i	−0.0473839	+	0.207602i
$623$	1.21004	−	16.1469i	0.0484793	−	0.646911i
$624$		0			0
$625$	47.6873	−	14.7096i	1.90749	−	0.588383i
$626$	22.6677	+	39.2616i	0.905984	+	1.56921i
$627$		0			0
$628$	13.8815	−	2.09230i	0.553932	−	0.0834919i
$629$	0.0490728	+	0.215002i	0.00195666	+	0.00857270i
$630$		0			0
$631$	12.1390	−	15.2218i	0.483244	−	0.605969i	−0.479114	−	0.877752i	$-0.659042\pi$
$631$	12.1390	−	15.2218i	0.483244	−	0.605969i	0.962358	+	0.271784i	$0.0876135\pi$
$632$	−0.0646131	+	0.862202i	−0.00257017	+	0.0342966i
$633$		0			0
$634$	−18.3777	+	46.8255i	−0.729870	+	1.85968i
$635$	−33.5785	−	5.06115i	−1.33252	−	0.200846i
$636$		0			0
$637$	−16.9552	+	29.3672i	−0.671788	+	1.16357i
$638$	−13.5880	+	0.809604i	−0.537953	+	0.0320525i
$639$		0			0
$640$	−14.1960	−	6.83645i	−0.561147	−	0.270234i
$641$	−3.80900	−	9.70518i	−0.150447	−	0.383332i	0.835705	−	0.549179i	$-0.185059\pi$
$641$	−3.80900	−	9.70518i	−0.150447	−	0.383332i	−0.986151	+	0.165847i	$0.946964\pi$
$642$		0			0
$643$	2.38597	+	31.8386i	0.0940935	+	1.25559i	0.821829	+	0.569734i	$0.192954\pi$
$643$	2.38597	+	31.8386i	0.0940935	+	1.25559i	−0.727736	+	0.685857i	$0.759427\pi$
$644$	−37.4322	−	25.5209i	−1.47504	−	1.00566i
$645$		0			0
$646$	−29.4631	−	9.08816i	−1.15921	−	0.357569i
$647$	4.74981	+	20.8103i	0.186734	+	0.818136i	0.978324	+	0.207082i	$0.0663968\pi$
$647$	4.74981	+	20.8103i	0.186734	+	0.818136i	−0.791589	+	0.611053i	$0.790746\pi$
$648$		0			0
$649$	−3.22165	+	14.1150i	−0.126461	+	0.554061i
$650$	48.7662	−	84.4655i	1.91277	−	3.31301i
$651$		0			0
$652$	7.86964	+	5.36543i	0.308199	+	0.210127i
$653$	26.7585	+	18.2436i	1.04714	+	0.713927i	0.959352	−	0.282212i	$-0.0910681\pi$
$653$	26.7585	+	18.2436i	1.04714	+	0.713927i	0.0877871	+	0.996139i	$0.472020\pi$
$654$		0			0
$655$	26.1932	−	45.3679i	1.02345	−	1.77267i
$656$	−3.86821	+	16.9478i	−0.151028	+	0.661699i
$657$		0			0
$658$	8.60415	+	37.6972i	0.335425	+	1.46959i
$659$	4.31269	+	1.33029i	0.167998	+	0.0518206i	0.377613	−	0.925963i	$-0.376745\pi$
$659$	4.31269	+	1.33029i	0.167998	+	0.0518206i	−0.209615	+	0.977784i	$0.567221\pi$
$660$		0			0
$661$	31.6549	+	21.5819i	1.23123	+	0.839440i	0.991335	−	0.131358i	$-0.0419338\pi$
$661$	31.6549	+	21.5819i	1.23123	+	0.839440i	0.239898	+	0.970798i	$0.422886\pi$
$662$	−1.05649	−	14.0979i	−0.0410617	−	0.547931i
$663$		0			0
$664$	−0.0285815	−	0.0728245i	−0.00110918	−	0.00282614i
$665$	55.4938	+	26.7244i	2.15196	+	1.03633i
$666$		0			0
$667$	−33.6347	−	13.7977i	−1.30234	−	0.534249i
$668$	−4.88487	+	8.46085i	−0.189001	+	0.327360i
$669$		0			0
$670$	11.3865	+	1.71624i	0.439899	+	0.0663041i
$671$	2.80556	−	7.14845i	0.108307	−	0.275963i
$672$		0			0
$673$	1.25467	−	16.7424i	0.0483638	−	0.645371i	−0.919370	−	0.393395i	$-0.871301\pi$
$673$	1.25467	−	16.7424i	0.0483638	−	0.645371i	0.967734	−	0.251976i	$-0.0810804\pi$
$674$	23.5233	−	29.4972i	0.906082	−	1.13619i
$675$		0			0
$676$	−2.39730	−	10.5033i	−0.0922038	−	0.403971i
$677$	−3.11639	+	0.469720i	−0.119773	+	0.0180528i	−0.208655	−	0.977989i	$-0.566909\pi$
$677$	−3.11639	+	0.469720i	−0.119773	+	0.0180528i	0.0888824	+	0.996042i	$0.471670\pi$
$678$		0			0
$679$	25.9116	+	44.8803i	0.994397	+	1.72235i
$680$	7.65422	−	2.36101i	0.293526	−	0.0905407i
$681$		0			0
$682$	0.852550	−	11.3765i	0.0326458	−	0.435629i
$683$	1.52220	−	6.66921i	0.0582455	−	0.255190i	−0.937419	−	0.348202i	$-0.886792\pi$
$683$	1.52220	−	6.66921i	0.0582455	−	0.255190i	0.995665	+	0.0930118i	$0.0296494\pi$
$684$		0			0
$685$	−5.08377	+	22.2734i	−0.194241	+	0.851024i
$686$	−5.48417	+	0.826606i	−0.209387	+	0.0315600i
$687$		0			0
$688$	−15.5247	+	14.4048i	−0.591873	+	0.549178i
$689$	28.3887	+	4.27891i	1.08152	+	0.163014i
$690$		0			0
$691$	−30.0566	+	20.4923i	−1.14341	+	0.779563i	−0.978398	−	0.206729i	$-0.933718\pi$
$691$	−30.0566	+	20.4923i	−1.14341	+	0.779563i	−0.165010	+	0.986292i	$0.552766\pi$
$692$	17.9136	+	22.4629i	0.680971	+	0.853911i
$693$		0			0
$694$	53.6438	+	25.8335i	2.03629	+	0.980626i
$695$	−26.7699	+	46.3668i	−1.01544	+	1.75879i
$696$		0			0
$697$	−7.89615	−	13.6765i	−0.299088	−	0.518035i
$698$	4.76155	+	63.5385i	0.180227	+	2.40497i
$699$		0			0
$700$	76.3696	−	11.5109i	2.88650	−	0.435070i
$701$	−31.3828	−	15.1131i	−1.18531	−	0.570816i	−0.265857	−	0.964013i	$-0.585655\pi$
$701$	−31.3828	−	15.1131i	−1.18531	−	0.570816i	−0.919454	+	0.393197i	$0.871369\pi$
$702$		0			0
$703$	−0.134538	+	0.168705i	−0.00507418	+	0.00636282i
$704$	−7.32325	−	2.25892i	−0.276005	−	0.0851364i
$705$		0			0
$706$	21.8197	−	55.5958i	0.821196	−	2.09237i
$707$	1.68380	−	0.519384i	0.0633259	−	0.0195334i
$708$		0			0
$709$	20.9312	+	19.4213i	0.786089	+	0.729384i	0.967183	−	0.254082i	$-0.0817733\pi$
$709$	20.9312	+	19.4213i	0.786089	+	0.729384i	−0.181094	+	0.983466i	$0.557964\pi$
$710$	71.4880	−	34.4268i	2.68290	−	1.29201i
$711$		0			0
$712$	0.458482	−	2.00874i	0.0171823	−	0.0752807i
$713$	15.2346	−	26.3872i	0.570542	−	0.988208i
$714$		0			0
$715$	−8.48503	+	21.6195i	−0.317322	+	0.808523i
$716$	13.8600	−	12.8602i	0.517974	−	0.480609i
$717$		0			0
$718$	3.20123	+	8.15659i	0.119469	+	0.304401i
$719$	3.82445	−	1.84176i	0.142628	−	0.0686859i	−0.361209	−	0.932485i	$-0.617636\pi$
$719$	3.82445	−	1.84176i	0.142628	−	0.0686859i	0.503836	+	0.863799i	$0.331921\pi$
$720$		0			0
$721$	−17.8702	−	22.4085i	−0.665521	−	0.834537i
$722$	2.41587	+	6.15554i	0.0899094	+	0.229085i
$723$		0			0
$724$	2.82177	+	4.88746i	0.104870	+	0.181641i
$725$	58.0308	−	21.7576i	2.15521	−	0.808058i
$726$		0			0
$727$	−8.42550	+	5.74441i	−0.312484	+	0.213048i	−0.709399	−	0.704807i	$-0.751033\pi$
$727$	−8.42550	+	5.74441i	−0.312484	+	0.213048i	0.396914	+	0.917856i	$0.370081\pi$
$728$	−5.12157	+	6.42225i	−0.189818	+	0.238024i
$729$		0			0
$730$	29.9290	+	14.4131i	1.10772	+	0.533451i
$731$	1.43777	−	19.1857i	0.0531779	−	0.709609i
$732$		0			0
$733$	24.8238	−	23.0331i	0.916888	−	0.850747i	−0.0723029	−	0.997383i	$-0.523035\pi$
$733$	24.8238	−	23.0331i	0.916888	−	0.850747i	0.989191	+	0.146635i	$0.0468444\pi$
$734$	−29.7541	+	27.6078i	−1.09825	+	1.01902i
$735$		0			0
$736$	−37.7103	−	34.9901i	−1.39002	−	1.28975i
$737$	−1.91155			−0.0704130
$738$		0			0
$739$	−25.2646	+	12.1668i	−0.929373	+	0.447562i	−0.836408	−	0.548107i	$-0.815349\pi$
$739$	−25.2646	+	12.1668i	−0.929373	+	0.447562i	−0.0929646	+	0.995669i	$0.529634\pi$
$740$	−0.0290043	+	0.387036i	−0.00106622	+	0.0142277i
$741$		0			0
$742$	24.3757	+	42.2199i	0.894860	+	1.54994i
$743$	12.4023	−	3.82560i	0.454996	−	0.140348i	−0.0587819	−	0.998271i	$-0.518722\pi$
$743$	12.4023	−	3.82560i	0.454996	−	0.140348i	0.513778	+	0.857923i	$0.328245\pi$
$744$		0			0
$745$	−47.7636	−	14.7331i	−1.74992	−	0.539780i
$746$	0.279118	+	1.22289i	0.0102192	+	0.0447733i
$747$		0			0
$748$	8.29460	−	3.99447i	0.303280	−	0.146052i
$749$	−6.53667	+	4.45662i	−0.238845	+	0.162841i
$750$		0			0
$751$	−2.00134	−	0.301653i	−0.0730299	−	0.0110075i	0.112426	−	0.993660i	$-0.464138\pi$
$751$	−2.00134	−	0.301653i	−0.0730299	−	0.0110075i	−0.185456	+	0.982653i	$0.559376\pi$
$752$	1.72628	+	23.0356i	0.0629508	+	0.840020i
$753$		0			0
$754$	20.4278	−	40.8108i	0.743938	−	1.48624i
$755$	−57.9189			−2.10788
$756$		0			0
$757$	−18.7005	+	23.4497i	−0.679681	+	0.852293i	−0.995325	−	0.0965848i	$-0.969208\pi$
$757$	−18.7005	+	23.4497i	−0.679681	+	0.852293i	0.315644	+	0.948878i	$0.397780\pi$
$758$	55.6774	−	8.39202i	2.02229	−	0.304812i
$759$		0			0
$760$	6.47570	+	4.41506i	0.234898	+	0.160151i
$761$	−14.2223	−	2.14366i	−0.515557	−	0.0777076i	−0.113890	−	0.993493i	$-0.536331\pi$
$761$	−14.2223	−	2.14366i	−0.515557	−	0.0777076i	−0.401667	+	0.915786i	$0.631569\pi$
$762$		0			0
$763$	31.8067	+	9.81108i	1.15148	+	0.355185i
$764$	−16.0338	−	20.1057i	−0.580081	−	0.727399i
$765$		0			0
$766$	−29.7064			−1.07333
$767$	−35.5831	−	33.0163i	−1.28483	−	1.19215i
$768$		0			0
$769$	−32.4720	−	22.1390i	−1.17097	−	0.798353i	−0.188008	−	0.982167i	$-0.560203\pi$
$769$	−32.4720	−	22.1390i	−1.17097	−	0.798353i	−0.982961	+	0.183814i	$0.941156\pi$
$770$	−37.6861	+	11.6246i	−1.35811	+	0.418923i
$771$		0			0
$772$	23.5001	+	21.8049i	0.845788	+	0.784776i
$773$	−8.51439	−	10.6767i	−0.306241	−	0.384014i	0.604767	−	0.796402i	$-0.293266\pi$
$773$	−8.51439	−	10.6767i	−0.306241	−	0.384014i	−0.911008	+	0.412388i	$0.864695\pi$
$774$		0			0
$775$	11.5582	+	50.6400i	0.415185	+	1.81904i
$776$	2.40919	+	6.13850i	0.0864847	+	0.220359i
$777$		0			0
$778$	−4.58820	−	61.2252i	−0.164495	−	2.19503i
$779$	5.64531	−	14.3840i	0.202264	−	0.515361i
$780$		0			0
$781$	−10.8830	+	7.41988i	−0.389423	+	0.265504i
$782$	52.7274			1.88553
$783$		0			0
$784$	−34.4011			−1.22861
$785$	26.9672	−	18.3859i	0.962500	−	0.656222i
$786$		0			0
$787$	2.87812	−	7.33334i	0.102594	−	0.261405i	−0.870355	−	0.492424i	$-0.836111\pi$
$787$	2.87812	−	7.33334i	0.102594	−	0.261405i	0.972949	+	0.231019i	$0.0742060\pi$
$788$	0.903722	+	12.0593i	0.0321938	+	0.429596i
$789$		0			0
$790$	−5.08475	−	12.9557i	−0.180907	−	0.460944i
$791$	2.81624	+	12.3388i	0.100134	+	0.438716i
$792$		0			0
$793$	16.0529	+	20.1296i	0.570054	+	0.714825i
$794$	−44.7993	−	41.5677i	−1.58987	−	1.47518i
$795$		0			0
$796$	−6.12571	+	1.88953i	−0.217120	+	0.0669726i
$797$	−30.2969	−	20.6561i	−1.07317	−	0.731676i	−0.108226	−	0.994126i	$-0.534517\pi$
$797$	−30.2969	−	20.6561i	−1.07317	−	0.731676i	−0.964945	+	0.262450i	$0.915469\pi$
$798$		0			0
$799$	−15.3835	−	14.2738i	−0.544229	−	0.504971i
$800$	87.6969			3.10055
$801$		0			0
$802$	−7.58961	−	9.51707i	−0.267998	−	0.336059i
$803$	−5.26944	−	1.62541i	−0.185955	−	0.0573594i
$804$		0			0
$805$	−104.154	−	15.6987i	−3.67096	−	0.553308i
$806$	31.6033	+	21.5468i	1.11318	+	0.758952i
$807$		0			0
$808$	0.221716	−	0.0334182i	0.00779992	−	0.00117565i
$809$	14.8021	−	18.5612i	0.520413	−	0.652577i	−0.450284	−	0.892886i	$-0.648677\pi$
$809$	14.8021	−	18.5612i	0.520413	−	0.652577i	0.970697	+	0.240308i	$0.0772485\pi$
$810$		0			0
$811$	−14.8118			−0.520113			−0.260056	−	0.965593i	$-0.583741\pi$
$811$	−14.8118			−0.520113			−0.260056	+	0.965593i	$0.583741\pi$
$812$	35.3517	−	7.50213i	1.24060	−	0.263273i
$813$		0			0
$814$	−0.0103251	−	0.137779i	−0.000361894	−	0.00482914i
$815$	21.8971	+	3.30046i	0.767023	+	0.115610i
$816$		0			0
$817$	15.5541	−	10.6046i	0.544168	−	0.371007i
$818$	−21.9804	+	10.5852i	−0.768527	+	0.370103i
$819$		0			0
$820$	−6.18462	−	27.0966i	−0.215976	−	0.946254i
$821$	−30.3370	−	9.35772i	−1.05877	−	0.326587i	−0.283995	−	0.958826i	$-0.591660\pi$
$821$	−30.3370	−	9.35772i	−1.05877	−	0.326587i	−0.774773	+	0.632239i	$0.782136\pi$
$822$		0			0
$823$	15.1951	−	4.68706i	0.529667	−	0.163381i	−0.0183756	−	0.999831i	$-0.505849\pi$
$823$	15.1951	−	4.68706i	0.529667	−	0.163381i	0.548042	+	0.836451i	$0.315373\pi$
$824$	−1.82355	−	3.15848i	−0.0635263	−	0.110031i
$825$		0			0
$826$	6.15982	−	82.1971i	0.214328	−	2.86000i
$827$	−12.4052	+	5.97404i	−0.431372	+	0.207738i	−0.636954	−	0.770902i	$-0.719806\pi$
$827$	−12.4052	+	5.97404i	−0.431372	+	0.207738i	0.205581	+	0.978640i	$0.434091\pi$
$828$		0			0
$829$	−0.0933682			−0.00324281			−0.00162140	−	0.999999i	$-0.500516\pi$
$829$	−0.0933682			−0.00324281			−0.00162140	+	0.999999i	$0.500516\pi$
$830$	0.923139	+	0.856548i	0.0320426	+	0.0297312i
$831$		0			0
$832$	18.8355	−	17.4768i	0.653003	−	0.605898i
$833$	22.9094	−	21.2568i	0.793762	−	0.736504i
$834$		0			0
$835$	−1.69744	+	22.6508i	−0.0587423	+	0.783862i
$836$	8.11595	+	3.90844i	0.280696	+	0.135176i
$837$		0			0
$838$	−17.8817	+	22.4230i	−0.617714	+	0.774589i
$839$	−29.3515	+	20.0115i	−1.01333	+	0.690875i	−0.951638	−	0.307220i	$-0.900601\pi$
$839$	−29.3515	+	20.0115i	−1.01333	+	0.690875i	−0.0616895	+	0.998095i	$0.519649\pi$
$840$		0			0
$841$	26.5005	−	11.7780i	0.913812	−	0.406138i
$842$	−14.6641	−	25.3990i	−0.505359	−	0.875308i
$843$		0			0
$844$	9.47101	+	24.1317i	0.326006	+	0.830649i
$845$	−15.6169	−	19.5830i	−0.537239	−	0.673677i
$846$		0			0
$847$	−32.1590	+	15.4869i	−1.10500	+	0.532138i
$848$	10.6405	+	27.1116i	0.365397	+	0.931017i
$849$		0			0
$850$	−65.8915	+	61.1384i	−2.26006	+	2.09703i
$851$	0.134814	−	0.343500i	0.00462136	−	0.0117750i
$852$		0			0
$853$	20.3518	−	35.2504i	0.696834	−	1.20695i	−0.272725	−	0.962092i	$-0.587925\pi$
$853$	20.3518	−	35.2504i	0.696834	−	1.20695i	0.969559	−	0.244859i	$-0.0787418\pi$
$854$	−9.72874	+	42.6244i	−0.332911	+	1.45858i
$855$		0			0
$856$	−0.907000	+	0.436788i	−0.0310006	+	0.0149291i
$857$	27.1258	+	25.1691i	0.926600	+	0.859759i	0.990404	−	0.138203i	$-0.0441328\pi$
$857$	27.1258	+	25.1691i	0.926600	+	0.859759i	−0.0638040	+	0.997962i	$0.520323\pi$
$858$		0			0
$859$	4.97416	−	1.53432i	0.169716	−	0.0523505i	−0.208733	−	0.977973i	$-0.566934\pi$
$859$	4.97416	−	1.53432i	0.169716	−	0.0523505i	0.378449	+	0.925622i	$0.376458\pi$
$860$	12.3706	−	31.5197i	0.421832	−	1.07481i
$861$		0			0
$862$	71.9671	+	22.1989i	2.45121	+	0.756098i
$863$	5.00214	−	6.27249i	0.170275	−	0.213518i	−0.689371	−	0.724409i	$-0.742113\pi$
$863$	5.00214	−	6.27249i	0.170275	−	0.213518i	0.859646	+	0.510891i	$0.170684\pi$
$864$		0			0
$865$	60.1835	+	28.9829i	2.04630	+	0.985447i
$866$	−49.5938	+	7.47507i	−1.68527	+	0.254013i
$867$		0			0
$868$	2.26346	+	30.2037i	0.0768268	+	1.02518i
$869$	1.15521	+	2.00087i	0.0391877	+	0.0678750i
$870$		0			0
$871$	3.20449	−	5.55033i	0.108580	−	0.188066i
$872$	3.81603	+	1.83770i	0.129227	+	0.0622325i
$873$		0			0
$874$	32.1669	+	40.3361i	1.08806	+	1.36439i
$875$	83.9043	−	57.2050i	2.83648	−	1.93388i
$876$		0			0
$877$	−14.6847	−	2.21337i	−0.495868	−	0.0747401i	−0.103653	−	0.994614i	$-0.533053\pi$
$877$	−14.6847	−	2.21337i	−0.495868	−	0.0747401i	−0.392215	+	0.919873i	$0.628291\pi$
$878$	−50.6167	+	46.9654i	−1.70823	+	1.58501i
$879$		0			0
$880$	−23.2979	+	3.51160i	−0.785373	+	0.118376i
$881$	2.95418	−	12.9431i	0.0995289	−	0.436064i	−0.900470	−	0.434917i	$-0.856778\pi$
$881$	2.95418	−	12.9431i	0.0995289	−	0.436064i	0.999999	−	0.00114731i	$-0.000365202\pi$
$882$		0			0
$883$	12.4995	−	54.7638i	0.420641	−	1.84295i	−0.108064	−	0.994144i	$-0.534465\pi$
$883$	12.4995	−	54.7638i	0.420641	−	1.84295i	0.528705	−	0.848806i	$-0.322678\pi$
$884$	−2.30666	+	30.7802i	−0.0775813	+	1.03525i
$885$		0			0
$886$	52.6605	−	16.2436i	1.76916	−	0.545715i
$887$	−6.08658	−	10.5423i	−0.204367	−	0.353975i	0.745564	−	0.666434i	$-0.232180\pi$
$887$	−6.08658	−	10.5423i	−0.204367	−	0.353975i	−0.949931	+	0.312460i	$0.898847\pi$
$888$		0			0
$889$	−31.7355	+	4.78335i	−1.06437	+	0.160429i
$890$	7.38020	+	32.3348i	0.247385	+	1.08386i
$891$		0			0
$892$	2.92280	−	3.66507i	0.0978626	−	0.122716i
$893$	1.53448	−	20.4762i	0.0513493	−	0.685209i
$894$		0			0
$895$	16.0599	−	40.9200i	0.536824	−	1.36781i
$896$	−14.7252	−	2.21947i	−0.491936	−	0.0741474i
$897$		0			0
$898$	−38.0414	+	65.8897i	−1.26946	+	2.19877i
$899$	6.80819	+	23.3322i	0.227066	+	0.778171i
$900$		0			0
$901$	−23.8386	−	11.4800i	−0.794177	−	0.382456i
$902$	3.61469	+	9.21009i	0.120356	+	0.306662i
$903$		0			0
$904$	0.120349	+	1.60594i	0.00400274	+	0.0534128i
$905$	10.8411	+	7.39134i	0.360370	+	0.245696i
$906$		0			0
$907$	−19.8044	−	6.10885i	−0.657594	−	0.202841i	−0.0520400	−	0.998645i	$-0.516572\pi$
$907$	−19.8044	−	6.10885i	−0.657594	−	0.202841i	−0.605554	+	0.795804i	$0.707049\pi$
$908$	−1.62128	−	7.10329i	−0.0538040	−	0.235731i
$909$		0			0
$910$	29.4233	−	128.912i	0.975371	−	4.27338i
$911$	19.2506	−	33.3430i	0.637801	−	1.10470i	−0.348113	−	0.937452i	$-0.613178\pi$
$911$	19.2506	−	33.3430i	0.637801	−	1.10470i	0.985914	−	0.167251i	$-0.0534890\pi$
$912$		0			0
$913$	−0.172725	−	0.117762i	−0.00571638	−	0.00389736i
$914$	−18.2136	−	12.4178i	−0.602452	−	0.410744i
$915$		0			0
$916$	−1.25753	+	2.17811i	−0.0415500	+	0.0719666i
$917$	11.0172	−	48.2696i	0.363821	−	1.59400i
$918$		0			0
$919$	−2.44444	−	10.7098i	−0.0806345	−	0.353283i	0.918475	−	0.395479i	$-0.129422\pi$
$919$	−2.44444	−	10.7098i	−0.0806345	−	0.353283i	−0.999109	+	0.0421966i	$0.986564\pi$
$920$	−12.8076	−	3.95061i	−0.422253	−	0.130248i
$921$		0			0
$922$	−41.5317	−	28.3158i	−1.36777	−	0.932532i
$923$	−3.30019	−	44.0380i	−0.108627	−	1.44953i
$924$		0			0
$925$	0.229823	+	0.585579i	0.00755652	+	0.0192537i
$926$	0.573896	+	0.276374i	0.0188594	+	0.00908220i
$927$		0			0
$928$	40.9631	−	2.44068i	1.34468	−	0.0801192i
$929$	16.5839	−	28.7241i	0.544100	−	0.942409i	−0.454563	−	0.890715i	$-0.650205\pi$
$929$	16.5839	−	28.7241i	0.544100	−	0.942409i	0.998663	−	0.0516942i	$-0.0164621\pi$
$930$		0			0
$931$	30.2374	+	4.55756i	0.990991	+	0.149368i
$932$	8.46463	−	21.5675i	0.277268	−	0.706467i
$933$		0			0
$934$	−5.95653	+	79.4843i	−0.194903	+	2.60081i
$935$	13.3454	−	16.7346i	0.436440	−	0.547278i
$936$		0			0
$937$	11.3869	+	49.8894i	0.371995	+	1.62981i	0.721171	+	0.692758i	$0.243604\pi$
$937$	11.3869	+	49.8894i	0.371995	+	1.62981i	−0.349176	+	0.937057i	$0.613538\pi$
$938$	10.7615	−	1.62204i	0.351376	−	0.0529614i
$939$		0			0
$940$	−18.4666	−	31.9851i	−0.602314	−	1.04324i
$941$	−49.2005	+	15.1764i	−1.60389	+	0.494735i	−0.962227	−	0.272250i	$-0.912232\pi$
$941$	−49.2005	+	15.1764i	−1.60389	+	0.494735i	−0.641665	+	0.766985i	$0.721756\pi$
$942$		0			0
$943$	−1.97472	+	26.3509i	−0.0643058	+	0.858102i
$944$	10.9577	−	48.0090i	0.356644	−	1.56256i
$945$		0			0
$946$	−2.68221	+	11.7515i	−0.0872061	+	0.382075i
$947$	−13.4843	+	2.03244i	−0.438182	+	0.0660453i	−0.364429	−	0.931231i	$-0.618736\pi$
$947$	−13.4843	+	2.03244i	−0.438182	+	0.0660453i	−0.0737531	+	0.997277i	$0.523498\pi$
$948$		0			0
$949$	13.5531	−	12.5754i	0.439951	−	0.408215i
$950$	−86.9683	−	13.1084i	−2.82162	−	0.425291i
$951$		0			0
$952$	6.25498	−	4.26457i	0.202725	−	0.138216i
$953$	−32.2960	−	40.4979i	−1.04617	−	1.31186i	−0.948548	−	0.316633i	$-0.897448\pi$
$953$	−32.2960	−	40.4979i	−1.04617	−	1.31186i	−0.0976225	−	0.995224i	$-0.531124\pi$
$954$		0			0
$955$	−53.8681	−	25.9415i	−1.74313	−	0.839447i
$956$	−21.9716	+	38.0559i	−0.710611	+	1.23081i
$957$		0			0
$958$	14.7414	+	25.5329i	0.476274	+	0.824930i
$959$	1.61359	+	21.5319i	0.0521056	+	0.695301i
$960$		0			0
$961$	10.5109	−	1.58426i	0.339061	−	0.0511052i
$962$	0.417359	+	0.200989i	0.0134562	+	0.00648016i
$963$		0			0
$964$	−2.88170	+	3.61354i	−0.0928134	+	0.116384i
$965$	71.2221	+	21.9691i	2.29272	+	0.707210i
$966$		0			0
$967$	−14.0327	+	35.7547i	−0.451261	+	1.14979i	0.506503	+	0.862238i	$0.330938\pi$
$967$	−14.0327	+	35.7547i	−0.451261	+	1.14979i	−0.957764	+	0.287556i	$0.907157\pi$
$968$	−4.34013	+	1.33875i	−0.139497	+	0.0430292i
$969$		0			0
$970$	−77.8130	−	72.1999i	−2.49843	−	2.31820i
$971$	−37.2753	+	17.9508i	−1.19622	+	0.576070i	−0.922596	−	0.385766i	$-0.873937\pi$
$971$	−37.2753	+	17.9508i	−1.19622	+	0.576070i	−0.273625	+	0.961836i	$0.588223\pi$
$972$		0			0
$973$	−11.2598	+	49.3324i	−0.360972	+	1.58152i
$974$	−28.8742	+	50.0116i	−0.925190	+	1.60248i
$975$		0			0
$976$	−9.54250	+	24.3139i	−0.305448	+	0.778268i
$977$	−6.87849	+	6.38230i	−0.220062	+	0.204188i	−0.782498	−	0.622653i	$-0.786055\pi$
$977$	−6.87849	+	6.38230i	−0.220062	+	0.204188i	0.562436	+	0.826841i	$0.309864\pi$
$978$		0			0
$979$	−2.01147	−	5.12515i	−0.0642869	−	0.163800i
$980$	49.5547	−	23.8643i	1.58297	−	0.762316i
$981$		0			0
$982$	32.1536	+	40.3193i	1.02606	+	1.28664i
$983$	4.37429	+	11.1455i	0.139518	+	0.355487i	0.983506	−	0.180876i	$-0.0578933\pi$
$983$	4.37429	+	11.1455i	0.139518	+	0.355487i	−0.843988	+	0.536362i	$0.819798\pi$
$984$		0			0
$985$	14.0580	+	24.3492i	0.447927	+	0.775832i
$986$	−29.0763	+	30.3914i	−0.925977	+	0.967860i
$987$		0			0
$988$	−24.9538	+	17.0132i	−0.793887	+	0.541263i
$989$	−20.0719	+	25.1694i	−0.638250	+	0.800340i
$990$		0			0
$991$	−36.5422	−	17.5978i	−1.16080	−	0.559013i	−0.248541	−	0.968621i	$-0.579951\pi$
$991$	−36.5422	−	17.5978i	−1.16080	−	0.559013i	−0.912261	+	0.409608i	$0.865665\pi$
$992$	−2.57015	+	34.2962i	−0.0816023	+	1.08891i
$993$		0			0
$994$	54.9720	−	51.0065i	1.74360	−	1.61783i
$995$	−10.9255	+	10.1374i	−0.346363	+	0.321378i
$996$		0			0
$997$	−23.4381	−	21.7474i	−0.742292	−	0.688746i	0.215405	−	0.976525i	$-0.430893\pi$
$997$	−23.4381	−	21.7474i	−0.742292	−	0.688746i	−0.957697	+	0.287778i	$0.907083\pi$
$998$	14.4047			0.455972
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.u.a.451.5		336
3.2	odd	2		261.2.q.a.16.24	✓	336
9.4	even	3	inner	783.2.u.a.712.5		336
9.5	odd	6		261.2.q.a.103.24	yes	336
29.20	even	7	inner	783.2.u.a.397.5		336
87.20	odd	14		261.2.q.a.223.24	yes	336
261.49	even	21	inner	783.2.u.a.658.5		336
261.194	odd	42		261.2.q.a.49.24	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.q.a.16.24	✓	336	3.2	odd	2
261.2.q.a.49.24	yes	336	261.194	odd	42
261.2.q.a.103.24	yes	336	9.5	odd	6
261.2.q.a.223.24	yes	336	87.20	odd	14
783.2.u.a.397.5		336	29.20	even	7	inner
783.2.u.a.451.5		336	1.1	even	1	trivial
783.2.u.a.658.5		336	261.49	even	21	inner
783.2.u.a.712.5		336	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.u (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59949 + 1.09051i) q^{2} +(0.638466 - 1.62678i) q^{4} +(-0.303634 - 4.05171i) q^{5} +(-1.40293 - 3.57461i) q^{7} +(-0.108732 - 0.476384i) q^{8} +(4.90411 + 6.14956i) q^{10} +(-0.957158 - 0.888113i) q^{11} +(4.18326 - 1.29036i) q^{13} +(6.14214 + 4.18764i) q^{14} +(3.25556 + 3.02072i) q^{16} -4.03457 q^{17} +(-2.46134 - 3.08642i) q^{19} +(-6.78512 - 2.09293i) q^{20} +(2.49946 + 0.376734i) q^{22} +(5.57787 + 3.80293i) q^{23} +(-11.3800 + 1.71526i) q^{25} +(-5.28392 + 6.62583i) q^{26} -6.71085 q^{28} +(-5.26785 + 1.11791i) q^{29} +(-0.337284 - 4.50074i) q^{31} +(-7.53503 - 1.13572i) q^{32} +(6.45325 - 4.39975i) q^{34} +(-14.0573 + 6.76965i) q^{35} +(-0.0121631 - 0.0532900i) q^{37} +(7.30266 + 2.25257i) q^{38} +(-1.89716 + 0.585196i) q^{40} +(1.95712 + 3.38984i) q^{41} +(-0.356363 + 4.75533i) q^{43} +(-2.05588 + 0.990060i) q^{44} -13.0689 q^{46} +(3.81292 + 3.53787i) q^{47} +(-5.67827 + 5.26866i) q^{49} +(16.3317 - 15.1536i) q^{50} +(0.571723 - 7.62911i) q^{52} +(5.90857 + 2.84542i) q^{53} +(-3.30775 + 4.14779i) q^{55} +(-1.55035 + 1.05701i) q^{56} +(7.20678 - 7.53276i) q^{58} +(-5.54407 - 9.60261i) q^{59} +(2.14867 + 5.47473i) q^{61} +(5.44760 + 6.83107i) q^{62} +(5.28812 - 2.54662i) q^{64} +(-6.49837 - 16.5576i) q^{65} +(1.07318 - 0.995765i) q^{67} +(-2.57593 + 6.56338i) q^{68} +(15.1022 - 26.1577i) q^{70} +(2.24473 - 9.83479i) q^{71} +(3.80506 - 1.83242i) q^{73} +(0.0775682 + 0.0719728i) q^{74} +(-6.59241 + 2.03349i) q^{76} +(-1.83183 + 4.66743i) q^{77} +(-1.69085 - 0.521557i) q^{79} +(11.2506 - 14.1078i) q^{80} +(-6.82706 - 3.28774i) q^{82} +(0.158316 - 0.0238622i) q^{83} +(1.22503 + 16.3469i) q^{85} +(-4.61575 - 7.99472i) q^{86} +(-0.319010 + 0.552541i) q^{88} +(3.79906 + 1.82953i) q^{89} +(-10.4814 - 13.1432i) q^{91} +(9.74782 - 6.64595i) q^{92} +(-9.95683 - 1.50075i) q^{94} +(-11.7579 + 10.9098i) q^{95} +(-13.3447 + 2.01139i) q^{97} +(3.33678 - 14.6194i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 5 q^{2} + 21 q^{4} + 9 q^{5} - 5 q^{7} - 2 q^{8} - 28 q^{10} + q^{11} - 5 q^{13} + 9 q^{14} + 21 q^{16} + 60 q^{17} - 20 q^{19} + 15 q^{20} - 13 q^{22} + 32 q^{23} + 15 q^{25} + 4 q^{26} - 72 q^{28}+ \cdots + 88 q^{98}+O(q^{100}) \) 336 * q + 5 * q^2 + 21 * q^4 + 9 * q^5 - 5 * q^7 - 2 * q^8 - 28 * q^10 + q^11 - 5 * q^13 + 9 * q^14 + 21 * q^16 + 60 * q^17 - 20 * q^19 + 15 * q^20 - 13 * q^22 + 32 * q^23 + 15 * q^25 + 4 * q^26 - 72 * q^28 + q^29 - 5 * q^31 - 7 * q^32 - 15 * q^34 - 16 * q^35 - 20 * q^37 - 63 * q^38 + 5 * q^40 + 20 * q^41 - 5 * q^43 + 8 * q^44 - 80 * q^46 - 5 * q^47 - 19 * q^49 + 3 * q^50 + q^52 + 4 * q^53 - 100 * q^55 + 5 * q^56 - 7 * q^58 - 154 * q^59 + 7 * q^61 + 4 * q^62 + 18 * q^64 + 65 * q^65 - 5 * q^67 + 9 * q^68 - 14 * q^70 - 18 * q^71 - 20 * q^73 + 77 * q^74 - 5 * q^76 - 39 * q^77 - 5 * q^79 + 104 * q^80 + 12 * q^82 + 23 * q^83 - 42 * q^85 - 128 * q^86 - 8 * q^88 - 34 * q^89 + 12 * q^91 + 115 * q^92 - 25 * q^94 - 89 * q^95 + 55 * q^97 + 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more