LMFDB - Embedded newform 729.2.e.r.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.2
Root			$-0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.r.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.223238 + 1.26604i) q^{2} +(0.326352 - 0.118782i) q^{4} +(0.342020 + 0.286989i) q^{5} +(3.31908 + 1.20805i) q^{7} +(1.50881 + 2.61334i) q^{8} +O(q^{10})$	\(q+(0.223238 + 1.26604i) q^{2} +(0.326352 - 0.118782i) q^{4} +(0.342020 + 0.286989i) q^{5} +(3.31908 + 1.20805i) q^{7} +(1.50881 + 2.61334i) q^{8} +(-0.286989 + 0.497079i) q^{10} +(-2.12965 + 1.78699i) q^{11} +(0.571452 - 3.24086i) q^{13} +(-0.788496 + 4.47178i) q^{14} +(-2.43969 + 2.04715i) q^{16} +(3.51968 - 6.09627i) q^{17} +(2.59240 + 4.49016i) q^{19} +(0.145708 + 0.0530334i) q^{20} +(-2.73783 - 2.29731i) q^{22} +(-6.83807 + 2.48886i) q^{23} +(-0.833626 - 4.72773i) q^{25} +4.23065 q^{26} +1.22668 q^{28} +(0.628461 + 3.56418i) q^{29} +(1.81908 - 0.662090i) q^{31} +(1.48686 + 1.24763i) q^{32} +(8.50387 + 3.09516i) q^{34} +(0.788496 + 1.36571i) q^{35} +(1.61334 - 2.79439i) q^{37} +(-5.10602 + 4.28446i) q^{38} +(-0.233956 + 1.32683i) q^{40} +(-0.844075 + 4.78699i) q^{41} +(-4.41147 + 3.70167i) q^{43} +(-0.482753 + 0.836152i) q^{44} +(-4.67752 - 8.10170i) q^{46} +(-2.83564 - 1.03209i) q^{47} +(4.19459 + 3.51968i) q^{49} +(5.79942 - 2.11081i) q^{50} +(-0.198463 - 1.12554i) q^{52} +8.77141 q^{53} -1.24123 q^{55} +(1.85083 + 10.4966i) q^{56} +(-4.37211 + 1.59132i) q^{58} +(2.27038 + 1.90508i) q^{59} +(-7.41147 - 2.69756i) q^{61} +(1.24432 + 2.15523i) q^{62} +(-4.43242 + 7.67717i) q^{64} +(1.12554 - 0.944440i) q^{65} +(-1.63903 + 9.29542i) q^{67} +(0.424525 - 2.40760i) q^{68} +(-1.55303 + 1.30315i) q^{70} +(-2.65366 + 4.59627i) q^{71} +(0.777189 + 1.34613i) q^{73} +(3.89798 + 1.41875i) q^{74} +(1.37939 + 1.15744i) q^{76} +(-9.22724 + 3.35844i) q^{77} +(-2.06670 - 11.7209i) q^{79} -1.42193 q^{80} -6.24897 q^{82} +(-2.82304 - 16.0103i) q^{83} +(2.95336 - 1.07494i) q^{85} +(-5.67128 - 4.75877i) q^{86} +(-7.88326 - 2.86927i) q^{88} +(-9.21291 - 15.9572i) q^{89} +(5.81180 - 10.0663i) q^{91} +(-1.93599 + 1.62449i) q^{92} +(0.673648 - 3.82045i) q^{94} +(-0.401975 + 2.27972i) q^{95} +(7.74763 - 6.50103i) q^{97} +(-3.51968 + 6.09627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q + 6 * q^4 + 6 * q^7	$ 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 + 6 * q^7 + 12 * q^10 + 6 * q^13 - 18 * q^16 + 24 * q^19 + 6 * q^22 - 48 * q^25 - 12 * q^28 - 12 * q^31 + 54 * q^34 + 6 * q^37 - 12 * q^40 - 12 * q^43 - 6 * q^46 + 42 * q^49 + 54 * q^52 - 60 * q^55 + 6 * q^58 - 48 * q^61 - 6 * q^64 - 66 * q^67 + 6 * q^70 - 12 * q^73 - 6 * q^76 + 42 * q^79 - 24 * q^82 - 18 * q^85 - 24 * q^88 + 6 * q^94 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.223238	+	1.26604i	0.157853	+	0.895229i	0.956131	+	0.292939i	$0.0946334\pi$
$2$	0.223238	+	1.26604i	0.157853	+	0.895229i	−0.798278	+	0.602289i	$0.794255\pi$
$3$		0			0
$3$		0			0
$4$	0.326352	−	0.118782i	0.163176	−	0.0593912i
$5$	0.342020	+	0.286989i	0.152956	+	0.128345i	0.716054	−	0.698045i	$-0.245946\pi$
$5$	0.342020	+	0.286989i	0.152956	+	0.128345i	−0.563098	+	0.826390i	$0.690391\pi$
$6$		0			0
$7$	3.31908	+	1.20805i	1.25449	+	0.456598i	0.881918	−	0.471403i	$-0.156252\pi$
$7$	3.31908	+	1.20805i	1.25449	+	0.456598i	0.372576	+	0.928002i	$0.378475\pi$
$8$	1.50881	+	2.61334i	0.533446	+	0.923956i
$9$		0			0
$10$	−0.286989	+	0.497079i	−0.0907539	+	0.157190i
$11$	−2.12965	+	1.78699i	−0.642114	+	0.538797i	−0.904667	−	0.426120i	$-0.859880\pi$
$11$	−2.12965	+	1.78699i	−0.642114	+	0.538797i	0.262553	+	0.964918i	$0.415436\pi$
$12$		0			0
$13$	0.571452	−	3.24086i	0.158492	−	0.898854i	−0.797031	−	0.603938i	$-0.793597\pi$
$13$	0.571452	−	3.24086i	0.158492	−	0.898854i	0.955523	−	0.294916i	$-0.0952915\pi$
$14$	−0.788496	+	4.47178i	−0.210734	+	1.19513i
$15$		0			0
$16$	−2.43969	+	2.04715i	−0.609923	+	0.511786i
$17$	3.51968	−	6.09627i	0.853648	−	1.47856i	−0.0242455	−	0.999706i	$-0.507718\pi$
$17$	3.51968	−	6.09627i	0.853648	−	1.47856i	0.877894	−	0.478856i	$-0.158948\pi$
$18$		0			0
$19$	2.59240	+	4.49016i	0.594736	+	1.03011i	0.993584	+	0.113097i	$0.0360769\pi$
$19$	2.59240	+	4.49016i	0.594736	+	1.03011i	−0.398848	+	0.917017i	$0.630590\pi$
$20$	0.145708	+	0.0530334i	0.0325813	+	0.0118586i
$21$		0			0
$22$	−2.73783	−	2.29731i	−0.583706	−	0.489788i
$23$	−6.83807	+	2.48886i	−1.42584	+	0.518962i	−0.935735	−	0.352703i	$-0.885263\pi$
$23$	−6.83807	+	2.48886i	−1.42584	+	0.518962i	−0.490102	+	0.871665i	$0.663040\pi$
$24$		0			0
$25$	−0.833626	−	4.72773i	−0.166725	−	0.945545i
$26$	4.23065			0.829698
$27$		0			0
$28$	1.22668			0.231821
$29$	0.628461	+	3.56418i	0.116702	+	0.661851i	0.985893	+	0.167375i	$0.0535290\pi$
$29$	0.628461	+	3.56418i	0.116702	+	0.661851i	−0.869191	+	0.494476i	$0.835360\pi$
$30$		0			0
$31$	1.81908	−	0.662090i	0.326716	−	0.118915i	−0.173454	−	0.984842i	$-0.555493\pi$
$31$	1.81908	−	0.662090i	0.326716	−	0.118915i	0.500170	+	0.865927i	$0.333271\pi$
$32$	1.48686	+	1.24763i	0.262843	+	0.220551i
$33$		0			0
$34$	8.50387	+	3.09516i	1.45840	+	0.530815i
$35$	0.788496	+	1.36571i	0.133280	+	0.230848i
$36$		0			0
$37$	1.61334	−	2.79439i	0.265232	−	0.459395i	−0.702393	−	0.711790i	$-0.747885\pi$
$37$	1.61334	−	2.79439i	0.265232	−	0.459395i	0.967624	+	0.252395i	$0.0812183\pi$
$38$	−5.10602	+	4.28446i	−0.828306	+	0.695032i
$39$		0			0
$40$	−0.233956	+	1.32683i	−0.0369916	+	0.209790i
$41$	−0.844075	+	4.78699i	−0.131822	+	0.747602i	0.845198	+	0.534454i	$0.179483\pi$
$41$	−0.844075	+	4.78699i	−0.131822	+	0.747602i	−0.977020	+	0.213148i	$0.931628\pi$
$42$		0			0
$43$	−4.41147	+	3.70167i	−0.672743	+	0.564499i	−0.913876	−	0.405993i	$-0.866926\pi$
$43$	−4.41147	+	3.70167i	−0.672743	+	0.564499i	0.241133	+	0.970492i	$0.422481\pi$
$44$	−0.482753	+	0.836152i	−0.0727777	+	0.126055i
$45$		0			0
$46$	−4.67752	−	8.10170i	−0.689662	−	1.19453i
$47$	−2.83564	−	1.03209i	−0.413621	−	0.150546i	0.126824	−	0.991925i	$-0.459522\pi$
$47$	−2.83564	−	1.03209i	−0.413621	−	0.150546i	−0.540445	+	0.841380i	$0.681744\pi$
$48$		0			0
$49$	4.19459	+	3.51968i	0.599228	+	0.502812i
$50$	5.79942	−	2.11081i	0.820161	−	0.298514i
$51$		0			0
$52$	−0.198463	−	1.12554i	−0.0275219	−	0.156084i
$53$	8.77141			1.20485			0.602423	−	0.798177i	$-0.294202\pi$
$53$	8.77141			1.20485			0.602423	+	0.798177i	$0.294202\pi$
$54$		0			0
$55$	−1.24123			−0.167367
$56$	1.85083	+	10.4966i	0.247328	+	1.40267i
$57$		0			0
$58$	−4.37211	+	1.59132i	−0.574086	+	0.208950i
$59$	2.27038	+	1.90508i	0.295579	+	0.248020i	0.778501	−	0.627643i	$-0.215980\pi$
$59$	2.27038	+	1.90508i	0.295579	+	0.248020i	−0.482923	+	0.875663i	$0.660425\pi$
$60$		0			0
$61$	−7.41147	−	2.69756i	−0.948942	−	0.345387i	−0.179251	−	0.983803i	$-0.557367\pi$
$61$	−7.41147	−	2.69756i	−0.948942	−	0.345387i	−0.769691	+	0.638417i	$0.779590\pi$
$62$	1.24432	+	2.15523i	0.158029	+	0.273714i
$63$		0			0
$64$	−4.43242	+	7.67717i	−0.554052	+	0.959647i
$65$	1.12554	−	0.944440i	0.139606	−	0.117143i
$66$		0			0
$67$	−1.63903	+	9.29542i	−0.200240	+	1.13562i	0.704517	+	0.709687i	$0.251164\pi$
$67$	−1.63903	+	9.29542i	−0.200240	+	1.13562i	−0.904757	+	0.425929i	$0.859947\pi$
$68$	0.424525	−	2.40760i	0.0514813	−	0.291965i
$69$		0			0
$70$	−1.55303	+	1.30315i	−0.185623	+	0.155756i
$71$	−2.65366	+	4.59627i	−0.314931	+	0.545476i	−0.979423	−	0.201819i	$-0.935315\pi$
$71$	−2.65366	+	4.59627i	−0.314931	+	0.545476i	0.664492	+	0.747296i	$0.268648\pi$
$72$		0			0
$73$	0.777189	+	1.34613i	0.0909631	+	0.157553i	0.907917	−	0.419151i	$-0.137672\pi$
$73$	0.777189	+	1.34613i	0.0909631	+	0.157553i	−0.816954	+	0.576703i	$0.804339\pi$
$74$	3.89798	+	1.41875i	0.453131	+	0.164926i
$75$		0			0
$76$	1.37939	+	1.15744i	0.158226	+	0.132768i
$77$	−9.22724	+	3.35844i	−1.05154	+	0.382730i
$78$		0			0
$79$	−2.06670	−	11.7209i	−0.232522	−	1.31870i	−0.847769	−	0.530365i	$-0.822055\pi$
$79$	−2.06670	−	11.7209i	−0.232522	−	1.31870i	0.615247	−	0.788335i	$-0.289056\pi$
$80$	−1.42193			−0.158977
$81$		0			0
$82$	−6.24897			−0.690083
$83$	−2.82304	−	16.0103i	−0.309869	−	1.75736i	−0.599650	−	0.800262i	$-0.704694\pi$
$83$	−2.82304	−	16.0103i	−0.309869	−	1.75736i	0.289781	−	0.957093i	$-0.406417\pi$
$84$		0			0
$85$	2.95336	−	1.07494i	0.320337	−	0.116593i
$86$	−5.67128	−	4.75877i	−0.611550	−	0.513151i
$87$		0			0
$88$	−7.88326	−	2.86927i	−0.840358	−	0.305865i
$89$	−9.21291	−	15.9572i	−0.976567	−	1.69146i	−0.674665	−	0.738125i	$-0.735712\pi$
$89$	−9.21291	−	15.9572i	−0.976567	−	1.69146i	−0.301902	−	0.953339i	$-0.597622\pi$
$90$		0			0
$91$	5.81180	−	10.0663i	0.609243	−	1.05524i
$92$	−1.93599	+	1.62449i	−0.201840	+	0.169364i
$93$		0			0
$94$	0.673648	−	3.82045i	0.0694815	−	0.394049i
$95$	−0.401975	+	2.27972i	−0.0412418	+	0.233894i
$96$		0			0
$97$	7.74763	−	6.50103i	0.786652	−	0.660080i	−0.158262	−	0.987397i	$-0.550589\pi$
$97$	7.74763	−	6.50103i	0.786652	−	0.660080i	0.944914	+	0.327318i	$0.106145\pi$
$98$	−3.51968	+	6.09627i	−0.355541	+	0.615816i
$99$		0			0
$100$	−0.833626	−	1.44388i	−0.0833626	−	0.144388i
$101$	1.95529	+	0.711667i	0.194558	+	0.0708135i	0.437462	−	0.899237i	$-0.355878\pi$
$101$	1.95529	+	0.711667i	0.194558	+	0.0708135i	−0.242903	+	0.970051i	$0.578100\pi$
$102$		0			0
$103$	−1.10947	−	0.930956i	−0.109319	−	0.0917298i	0.586490	−	0.809957i	$-0.300510\pi$
$103$	−1.10947	−	0.930956i	−0.109319	−	0.0917298i	−0.695809	+	0.718227i	$0.744954\pi$
$104$	9.33170	−	3.39646i	0.915048	−	0.333050i
$105$		0			0
$106$	1.95811	+	11.1050i	0.190189	+	1.07861i
$107$	−2.23583			−0.216146			−0.108073	−	0.994143i	$-0.534468\pi$
$107$	−2.23583			−0.216146			−0.108073	+	0.994143i	$0.534468\pi$
$108$		0			0
$109$	−11.5030			−1.10179			−0.550893	−	0.834576i	$-0.685713\pi$
$109$	−11.5030			−1.10179			−0.550893	+	0.834576i	$0.685713\pi$
$110$	−0.277089	−	1.57145i	−0.0264194	−	0.149832i
$111$		0			0
$112$	−10.5706	+	3.84737i	−0.998825	+	0.363543i
$113$	1.29320	+	1.08512i	0.121654	+	0.102080i	0.701585	−	0.712586i	$-0.252476\pi$
$113$	1.29320	+	1.08512i	0.121654	+	0.102080i	−0.579931	+	0.814666i	$0.696921\pi$
$114$		0			0
$115$	−3.05303	−	1.11121i	−0.284697	−	0.103621i
$116$	0.628461	+	1.08853i	0.0583511	+	0.101067i
$117$		0			0
$118$	−1.90508	+	3.29969i	−0.175377	+	0.303761i
$119$	19.0467	−	15.9820i	1.74600	−	1.46507i
$120$		0			0
$121$	−0.568048	+	3.22156i	−0.0516407	+	0.292869i
$122$	1.76070	−	9.98545i	0.159407	−	0.904040i
$123$		0			0
$124$	0.515015	−	0.432149i	0.0462497	−	0.0388081i
$125$	2.18788	−	3.78952i	0.195690	−	0.338945i
$126$		0			0
$127$	1.33615	+	2.31428i	0.118564	+	0.205359i	0.919199	−	0.393793i	$-0.128837\pi$
$127$	1.33615	+	2.31428i	0.118564	+	0.205359i	−0.800635	+	0.599153i	$0.795504\pi$
$128$	−7.06131	−	2.57011i	−0.624138	−	0.227168i
$129$		0			0
$130$	1.44697	+	1.21415i	0.126907	+	0.106488i
$131$	2.74378	−	0.998656i	0.239726	−	0.0872530i	−0.219364	−	0.975643i	$-0.570398\pi$
$131$	2.74378	−	0.998656i	0.239726	−	0.0872530i	0.459089	+	0.888390i	$0.348176\pi$
$132$		0			0
$133$	3.18004	+	18.0349i	0.275745	+	1.56383i
$134$	−12.1343			−1.04824
$135$		0			0
$136$	21.2422			1.82150
$137$	−0.808718	−	4.58647i	−0.0690934	−	0.391848i	−0.999668	−	0.0257471i	$-0.991804\pi$
$137$	−0.808718	−	4.58647i	−0.0690934	−	0.391848i	0.930575	−	0.366101i	$-0.119308\pi$
$138$		0			0
$139$	7.52007	−	2.73708i	0.637844	−	0.232156i	−0.00279796	−	0.999996i	$-0.500891\pi$
$139$	7.52007	−	2.73708i	0.637844	−	0.232156i	0.640642	+	0.767840i	$0.278668\pi$
$140$	0.419550	+	0.352044i	0.0354584	+	0.0297532i
$141$		0			0
$142$	−6.41147	−	2.33359i	−0.538039	−	0.195830i
$143$	4.57440	+	7.92309i	0.382530	+	0.662562i
$144$		0			0
$145$	−0.807934	+	1.39938i	−0.0670952	+	0.116212i
$146$	−1.53076	+	1.28446i	−0.126687	+	0.106303i
$147$		0			0
$148$	0.194593	−	1.10359i	0.0159954	−	0.0907145i
$149$	3.50973	−	19.9047i	0.287528	−	1.63065i	−0.408584	−	0.912721i	$-0.633977\pi$
$149$	3.50973	−	19.9047i	0.287528	−	1.63065i	0.696112	−	0.717933i	$-0.254912\pi$
$150$		0			0
$151$	5.13429	−	4.30818i	0.417822	−	0.350594i	−0.409512	−	0.912305i	$-0.634301\pi$
$151$	5.13429	−	4.30818i	0.417822	−	0.350594i	0.827334	+	0.561710i	$0.189856\pi$
$152$	−7.82288	+	13.5496i	−0.634520	+	1.09902i
$153$		0			0
$154$	−6.31180	−	10.9324i	−0.508620	−	0.880955i
$155$	0.812174	+	0.295607i	0.0652354	+	0.0237437i
$156$		0			0
$157$	4.07919	+	3.42285i	0.325555	+	0.273173i	0.790886	−	0.611964i	$-0.209620\pi$
$157$	4.07919	+	3.42285i	0.325555	+	0.273173i	−0.465331	+	0.885137i	$0.654065\pi$
$158$	14.3778	−	5.23308i	1.14383	−	0.416321i
$159$		0			0
$160$	0.150482	+	0.853427i	0.0118967	+	0.0674693i
$161$	−25.7028			−2.02566
$162$		0			0
$163$	3.81521			0.298830			0.149415	−	0.988775i	$-0.452261\pi$
$163$	3.81521			0.298830			0.149415	+	0.988775i	$0.452261\pi$
$164$	0.293144	+	1.66250i	0.0228907	+	0.129820i
$165$		0			0
$166$	19.6395	−	7.14819i	1.52432	−	0.554807i
$167$	−6.99811	−	5.87211i	−0.541530	−	0.454398i	0.330531	−	0.943795i	$-0.392772\pi$
$167$	−6.99811	−	5.87211i	−0.541530	−	0.454398i	−0.872061	+	0.489398i	$0.837217\pi$
$168$		0			0
$169$	2.03936	+	0.742267i	0.156874	+	0.0570975i
$170$	2.02022	+	3.49912i	0.154944	+	0.268370i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−4.65284	+	3.90420i	−0.353749	+	0.296831i	−0.802293	−	0.596930i	$-0.796387\pi$
$173$	−4.65284	+	3.90420i	−0.353749	+	0.296831i	0.448544	+	0.893761i	$0.351943\pi$
$174$		0			0
$175$	2.94444	−	16.6988i	0.222579	−	1.26231i
$176$	1.53747	−	8.71941i	0.115891	−	0.657250i
$177$		0			0
$178$	18.1459	−	15.2262i	1.36009	−	1.14125i
$179$	5.14057	−	8.90373i	0.384224	−	0.665496i	−0.607437	−	0.794368i	$-0.707802\pi$
$179$	5.14057	−	8.90373i	0.384224	−	0.665496i	0.991661	+	0.128872i	$0.0411355\pi$
$180$		0			0
$181$	11.5706	+	20.0408i	0.860034	+	1.48962i	0.871895	+	0.489693i	$0.162891\pi$
$181$	11.5706	+	20.0408i	0.860034	+	1.48962i	−0.0118609	+	0.999930i	$0.503776\pi$
$182$	14.0418	+	5.11081i	1.04085	+	0.378839i
$183$		0			0
$184$	−16.8216	−	14.1150i	−1.24011	−	1.04057i
$185$	1.35375	−	0.492726i	0.0995299	−	0.0362259i
$186$		0			0
$187$	3.39827	+	19.2725i	0.248506	+	1.40935i
$188$	−1.04801			−0.0764340
$189$		0			0
$190$	−2.97596			−0.215899
$191$	−2.54747	−	14.4474i	−0.184329	−	1.04538i	−0.926815	−	0.375518i	$-0.877465\pi$
$191$	−2.54747	−	14.4474i	−0.184329	−	1.04538i	0.742486	−	0.669861i	$-0.233646\pi$
$192$		0			0
$193$	−22.0278	+	8.01747i	−1.58560	+	0.577110i	−0.976411	−	0.215918i	$-0.930725\pi$
$193$	−22.0278	+	8.01747i	−1.58560	+	0.577110i	−0.609185	+	0.793028i	$0.708503\pi$
$194$	9.96016	+	8.35756i	0.715098	+	0.600038i
$195$		0			0
$196$	1.78699	+	0.650411i	0.127642	+	0.0464579i
$197$	−4.51384	−	7.81820i	−0.321598	−	0.557024i	0.659220	−	0.751950i	$-0.270887\pi$
$197$	−4.51384	−	7.81820i	−0.321598	−	0.557024i	−0.980818	+	0.194926i	$0.937553\pi$
$198$		0			0
$199$	−1.30200	+	2.25514i	−0.0922966	+	0.159862i	−0.908477	−	0.417935i	$-0.862754\pi$
$199$	−1.30200	+	2.25514i	−0.0922966	+	0.159862i	0.816181	+	0.577797i	$0.196087\pi$
$200$	11.0974	−	9.31180i	0.784703	−	0.658444i
$201$		0			0
$202$	−0.464508	+	2.63435i	−0.0326826	+	0.185352i
$203$	−2.21978	+	12.5890i	−0.155798	+	0.883574i
$204$		0			0
$205$	−1.66250	+	1.39501i	−0.116114	+	0.0974315i
$206$	0.930956	−	1.61246i	0.0648628	−	0.112346i
$207$		0			0
$208$	5.24035	+	9.07656i	0.363353	+	0.629346i
$209$	−13.5448	−	4.92989i	−0.936911	−	0.341008i
$210$		0			0
$211$	−12.5287	−	10.5128i	−0.862510	−	0.723732i	0.0999971	−	0.994988i	$-0.468117\pi$
$211$	−12.5287	−	10.5128i	−0.862510	−	0.723732i	−0.962507	+	0.271256i	$0.912561\pi$
$212$	2.86257	−	1.04189i	0.196602	−	0.0715572i
$213$		0			0
$214$	−0.499123	−	2.83067i	−0.0341193	−	0.193500i
$215$	−2.57115			−0.175351
$216$		0			0
$217$	6.83750			0.464159
$218$	−2.56790	−	14.5633i	−0.173920	−	0.986351i
$219$		0			0
$220$	−0.405078	+	0.147436i	−0.0273103	+	0.00994014i
$221$	−17.7458	−	14.8905i	−1.19371	−	1.00165i
$222$		0			0
$223$	−3.47906	−	1.26627i	−0.232975	−	0.0847959i	0.222895	−	0.974843i	$-0.428449\pi$
$223$	−3.47906	−	1.26627i	−0.232975	−	0.0847959i	−0.455869	+	0.890047i	$0.650672\pi$
$224$	3.42782	+	5.93717i	0.229031	+	0.396694i
$225$		0			0
$226$	−1.08512	+	1.87949i	−0.0721813	+	0.125022i
$227$	8.09002	−	6.78833i	0.536954	−	0.450557i	−0.333541	−	0.942736i	$-0.608244\pi$
$227$	8.09002	−	6.78833i	0.536954	−	0.450557i	0.870495	+	0.492178i	$0.163799\pi$
$228$		0			0
$229$	2.34864	−	13.3198i	0.155203	−	0.880197i	−0.803398	−	0.595443i	$-0.796977\pi$
$229$	2.34864	−	13.3198i	0.155203	−	0.880197i	0.958600	−	0.284755i	$-0.0919122\pi$
$230$	0.725293	−	4.11334i	0.0478244	−	0.271226i
$231$		0			0
$232$	−8.36618	+	7.02006i	−0.549267	+	0.460890i
$233$	6.35035	−	10.9991i	0.416025	−	0.720576i	−0.579510	−	0.814965i	$-0.696756\pi$
$233$	6.35035	−	10.9991i	0.416025	−	0.720576i	0.995535	+	0.0943883i	$0.0300895\pi$
$234$		0			0
$235$	−0.673648	−	1.16679i	−0.0439440	−	0.0761132i
$236$	0.967233	+	0.352044i	0.0629615	+	0.0229161i
$237$		0			0
$238$	24.4859	+	20.5461i	1.58719	+	1.33181i
$239$	−5.49865	+	2.00134i	−0.355678	+	0.129456i	−0.513678	−	0.857983i	$-0.671718\pi$
$239$	−5.49865	+	2.00134i	−0.355678	+	0.129456i	0.158000	+	0.987439i	$0.449495\pi$
$240$		0			0
$241$	−1.48293	−	8.41009i	−0.0955237	−	0.541742i	−0.994586	−	0.103920i	$-0.966861\pi$
$241$	−1.48293	−	8.41009i	−0.0955237	−	0.541742i	0.899062	−	0.437821i	$-0.144250\pi$
$242$	−4.20545			−0.270337
$243$		0			0
$244$	−2.73917			−0.175357
$245$	0.424525	+	2.40760i	0.0271219	+	0.153816i
$246$		0			0
$247$	16.0334	−	5.83569i	1.02018	−	0.371316i
$248$	4.47492	+	3.75490i	0.284157	+	0.238436i
$249$		0			0
$250$	5.28611	+	1.92399i	0.334323	+	0.121684i
$251$	−3.37895	−	5.85251i	−0.213277	−	0.369407i	0.739461	−	0.673199i	$-0.235080\pi$
$251$	−3.37895	−	5.85251i	−0.213277	−	0.369407i	−0.952738	+	0.303792i	$0.901747\pi$
$252$		0			0
$253$	10.1152	−	17.5200i	0.635934	−	1.10147i
$254$	−2.63171	+	2.20826i	−0.165128	+	0.138559i
$255$		0			0
$256$	−1.40121	+	7.94664i	−0.0875754	+	0.496665i
$257$	−0.639540	+	3.62701i	−0.0398934	+	0.226247i	−0.998236	−	0.0593754i	$-0.981089\pi$
$257$	−0.639540	+	3.62701i	−0.0398934	+	0.226247i	0.958342	+	0.285622i	$0.0922002\pi$
$258$		0			0
$259$	8.73055	−	7.32580i	0.542490	−	0.455203i
$260$	0.255139	−	0.441914i	0.0158231	−	0.0274064i
$261$		0			0
$262$	1.87686	+	3.25082i	0.115953	+	0.200836i
$263$	3.41847	+	1.24422i	0.210792	+	0.0767220i	0.445258	−	0.895402i	$-0.353112\pi$
$263$	3.41847	+	1.24422i	0.210792	+	0.0767220i	−0.234466	+	0.972124i	$0.575334\pi$
$264$		0			0
$265$	3.00000	+	2.51730i	0.184289	+	0.154636i
$266$	−22.1231	+	8.05216i	−1.35646	+	0.493709i
$267$		0			0
$268$	0.569230	+	3.22826i	0.0347713	+	0.197198i
$269$	7.08672			0.432085			0.216042	−	0.976384i	$-0.430685\pi$
$269$	7.08672			0.432085			0.216042	+	0.976384i	$0.430685\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	3.89300	+	22.0783i	0.236048	+	1.33869i
$273$		0			0
$274$	5.62613	−	2.04775i	0.339887	−	0.123709i
$275$	10.2237	+	8.57873i	0.616514	+	0.517317i
$276$		0			0
$277$	13.0544	+	4.75140i	0.784362	+	0.285484i	0.702990	−	0.711200i	$-0.251848\pi$
$277$	13.0544	+	4.75140i	0.784362	+	0.285484i	0.0813714	+	0.996684i	$0.474070\pi$
$278$	5.14403	+	8.90972i	0.308518	+	0.534369i
$279$		0			0
$280$	−2.37939	+	4.12122i	−0.142195	+	0.246290i
$281$	−16.9506	+	14.2233i	−1.01119	+	0.848490i	−0.988495	−	0.151253i	$-0.951669\pi$
$281$	−16.9506	+	14.2233i	−1.01119	+	0.848490i	−0.0226955	+	0.999742i	$0.507225\pi$
$282$		0			0
$283$	−4.12108	+	23.3718i	−0.244973	+	1.38931i	0.575583	+	0.817744i	$0.304775\pi$
$283$	−4.12108	+	23.3718i	−0.244973	+	1.38931i	−0.820556	+	0.571567i	$0.806336\pi$
$284$	−0.320070	+	1.81521i	−0.0189927	+	0.107713i
$285$		0			0
$286$	−9.00980	+	7.56012i	−0.532761	+	0.447039i
$287$	−8.58445	+	14.8687i	−0.506724	+	0.877672i
$288$		0			0
$289$	−16.2763	−	28.1914i	−0.957430	−	1.65832i
$290$	−1.95204	−	0.710485i	−0.114628	−	0.0417211i
$291$		0			0
$292$	0.413534	+	0.346996i	0.0242002	+	0.0203064i
$293$	17.4840	−	6.36366i	1.02143	−	0.371769i	0.223616	−	0.974677i	$-0.428214\pi$
$293$	17.4840	−	6.36366i	1.02143	−	0.371769i	0.797810	+	0.602909i	$0.205992\pi$
$294$		0			0
$295$	0.229780	+	1.30315i	0.0133783	+	0.0758723i
$296$	9.73692			0.565947
$297$		0			0
$298$	25.9837			1.50520
$299$	4.15841	+	23.5835i	0.240487	+	1.36387i
$300$		0			0
$301$	−19.1138	+	6.95686i	−1.10170	+	0.400987i
$302$	6.60051	+	5.53849i	0.379817	+	0.318704i
$303$		0			0
$304$	−15.5167	−	5.64760i	−0.889942	−	0.323912i
$305$	−1.76070	−	3.04963i	−0.100818	−	0.174621i
$306$		0			0
$307$	−10.3735	+	17.9674i	−0.592044	+	1.02545i	0.401912	+	0.915678i	$0.368346\pi$
$307$	−10.3735	+	17.9674i	−0.592044	+	1.02545i	−0.993957	+	0.109773i	$0.964988\pi$
$308$	−2.61240	+	2.19207i	−0.148855	+	0.124905i
$309$		0			0
$310$	−0.192944	+	1.09424i	−0.0109585	+	0.0621486i
$311$	−3.53990	+	20.0758i	−0.200729	+	1.13839i	0.703290	+	0.710903i	$0.251713\pi$
$311$	−3.53990	+	20.0758i	−0.200729	+	1.13839i	−0.904020	+	0.427491i	$0.859398\pi$
$312$		0			0
$313$	−22.8594	+	19.1813i	−1.29209	+	1.08419i	−0.300633	+	0.953740i	$0.597198\pi$
$313$	−22.8594	+	19.1813i	−1.29209	+	1.08419i	−0.991455	+	0.130451i	$0.958357\pi$
$314$	−3.42285	+	5.92855i	−0.193163	+	0.334567i
$315$		0			0
$316$	−2.06670	−	3.57964i	−0.116261	−	0.201370i
$317$	4.05629	+	1.47637i	0.227824	+	0.0829210i	0.453410	−	0.891302i	$-0.350207\pi$
$317$	4.05629	+	1.47637i	0.227824	+	0.0829210i	−0.225586	+	0.974223i	$0.572430\pi$
$318$		0			0
$319$	−7.70755	−	6.46740i	−0.431540	−	0.362105i
$320$	−3.71924	+	1.35369i	−0.207912	+	0.0756737i
$321$		0			0
$322$	−5.73783	−	32.5408i	−0.319757	−	1.81343i
$323$	36.4976			2.03078
$324$		0			0
$325$	−15.7983			−0.876332
$326$	0.851698	+	4.83022i	0.0471712	+	0.267521i
$327$		0			0
$328$	−13.7836	+	5.01681i	−0.761071	+	0.277007i
$329$	−8.16490	−	6.85117i	−0.450146	−	0.377717i
$330$		0			0
$331$	2.74288	+	0.998326i	0.150762	+	0.0548730i	0.416299	−	0.909228i	$-0.363327\pi$
$331$	2.74288	+	0.998326i	0.150762	+	0.0548730i	−0.265537	+	0.964101i	$0.585549\pi$
$332$	−2.82304	−	4.88965i	−0.154935	−	0.268355i
$333$		0			0
$334$	5.87211	−	10.1708i	0.321308	−	0.556521i
$335$	−3.22826	+	2.70884i	−0.176379	+	0.148000i
$336$		0			0
$337$	2.50774	−	14.2221i	0.136605	−	0.774727i	−0.837123	−	0.547015i	$-0.815764\pi$
$337$	2.50774	−	14.2221i	0.136605	−	0.774727i	0.973728	−	0.227713i	$-0.0731247\pi$
$338$	−0.484481	+	2.74763i	−0.0263523	+	0.149451i
$339$		0			0
$340$	0.836152	−	0.701615i	0.0453467	−	0.0380504i
$341$	−2.69085	+	4.66069i	−0.145718	+	0.252391i
$342$		0			0
$343$	−2.69207	−	4.66280i	−0.145358	−	0.251767i
$344$	−16.3298	−	5.94356i	−0.880444	−	0.320455i
$345$		0			0
$346$	−5.98158	−	5.01914i	−0.321572	−	0.269831i
$347$	−1.36635	+	0.497312i	−0.0733496	+	0.0266971i	−0.378434	−	0.925628i	$-0.623537\pi$
$347$	−1.36635	+	0.497312i	−0.0733496	+	0.0266971i	0.305085	+	0.952325i	$0.401315\pi$
$348$		0			0
$349$	−4.78952	−	27.1627i	−0.256377	−	1.45399i	−0.792514	−	0.609854i	$-0.791228\pi$
$349$	−4.78952	−	27.1627i	−0.256377	−	1.45399i	0.536137	−	0.844131i	$-0.319883\pi$
$350$	21.7987			1.16519
$351$		0			0
$352$	−5.39599			−0.287607
$353$	−1.82888	−	10.3721i	−0.0973416	−	0.552052i	−0.994005	−	0.109338i	$-0.965127\pi$
$353$	−1.82888	−	10.3721i	−0.0973416	−	0.552052i	0.896663	−	0.442714i	$-0.145984\pi$
$354$		0			0
$355$	−2.22668	+	0.810446i	−0.118180	+	0.0430140i
$356$	−4.90209	−	4.11334i	−0.259810	−	0.218007i
$357$		0			0
$358$	12.4201	+	4.52054i	0.656422	+	0.238918i
$359$	7.35273	+	12.7353i	0.388062	+	0.672143i	0.992189	−	0.124745i	$-0.0398112\pi$
$359$	7.35273	+	12.7353i	0.388062	+	0.672143i	−0.604127	+	0.796888i	$0.706478\pi$
$360$		0			0
$361$	−3.94104	+	6.82608i	−0.207423	+	0.359267i
$362$	−22.7896	+	19.1227i	−1.19779	+	1.00507i
$363$		0			0
$364$	0.700989	−	3.97551i	0.0367418	−	0.208373i
$365$	−0.120510	+	0.683448i	−0.00630780	+	0.0357733i
$366$		0			0
$367$	−16.3648	+	13.7317i	−0.854238	+	0.716790i	−0.960719	−	0.277524i	$-0.910486\pi$
$367$	−16.3648	+	13.7317i	−0.854238	+	0.716790i	0.106481	+	0.994315i	$0.466042\pi$
$368$	11.5878	−	20.0706i	0.604053	−	1.04625i
$369$		0			0
$370$	0.926022	+	1.60392i	0.0481416	+	0.0833837i
$371$	29.1130	+	10.5963i	1.51147	+	0.550131i
$372$		0			0
$373$	17.3314	+	14.5428i	0.897386	+	0.752996i	0.969678	−	0.244387i	$-0.0785868\pi$
$373$	17.3314	+	14.5428i	0.897386	+	0.752996i	−0.0722916	+	0.997384i	$0.523031\pi$
$374$	−23.6413	+	8.60472i	−1.22246	+	0.444940i
$375$		0			0
$376$	−1.58125	−	8.96773i	−0.0815468	−	0.462475i
$377$	11.9101			0.613404
$378$		0			0
$379$	−17.0743			−0.877047			−0.438523	−	0.898720i	$-0.644498\pi$
$379$	−17.0743			−0.877047			−0.438523	+	0.898720i	$0.644498\pi$
$380$	0.139605	+	0.791737i	0.00716156	+	0.0406152i
$381$		0			0
$382$	17.7224	−	6.45043i	0.906757	−	0.330033i
$383$	29.8693	+	25.0633i	1.52625	+	1.28067i	0.819195	+	0.573515i	$0.194421\pi$
$383$	29.8693	+	25.0633i	1.52625	+	1.28067i	0.707054	+	0.707160i	$0.250024\pi$
$384$		0			0
$385$	−4.11974	−	1.49946i	−0.209961	−	0.0764196i
$386$	−15.0679	−	26.0984i	−0.766936	−	1.32837i
$387$		0			0
$388$	1.75624	−	3.04190i	0.0891598	−	0.154429i
$389$	−7.82288	+	6.56418i	−0.396636	+	0.332817i	−0.819192	−	0.573520i	$-0.805578\pi$
$389$	−7.82288	+	6.56418i	−0.396636	+	0.332817i	0.422556	+	0.906337i	$0.361133\pi$
$390$		0			0
$391$	−8.89512	+	50.4467i	−0.449845	+	2.55120i
$392$	−2.86927	+	16.2724i	−0.144920	+	0.821882i
$393$		0			0
$394$	8.89053	−	7.46004i	0.447898	−	0.375831i
$395$	2.65690	−	4.60189i	0.133683	−	0.231546i
$396$		0			0
$397$	0.571452	+	0.989783i	0.0286803	+	0.0496758i	0.880009	−	0.474956i	$-0.157536\pi$
$397$	0.571452	+	0.989783i	0.0286803	+	0.0496758i	−0.851329	+	0.524632i	$0.824203\pi$
$398$	−3.14576	−	1.14496i	−0.157683	−	0.0573918i
$399$		0			0
$400$	11.7121	+	9.82765i	0.585607	+	0.491382i
$401$	−19.3144	+	7.02987i	−0.964515	+	0.351055i	−0.775801	−	0.630977i	$-0.782654\pi$
$401$	−19.3144	+	7.02987i	−0.964515	+	0.351055i	−0.188714	+	0.982032i	$0.560432\pi$
$402$		0			0
$403$	−1.10623	−	6.27374i	−0.0551052	−	0.312517i
$404$	0.722645			0.0359530
$405$		0			0
$406$	−16.4338			−0.815594
$407$	1.55769	+	8.83409i	0.0772118	+	0.437890i
$408$		0			0
$409$	7.63816	−	2.78006i	0.377682	−	0.137465i	−0.146201	−	0.989255i	$-0.546705\pi$
$409$	7.63816	−	2.78006i	0.377682	−	0.137465i	0.523884	+	0.851790i	$0.324483\pi$
$410$	−2.13727	−	1.79339i	−0.105552	−	0.0885690i
$411$		0			0
$412$	−0.472659	−	0.172034i	−0.0232862	−	0.00847549i
$413$	5.23416	+	9.06583i	0.257556	+	0.446100i
$414$		0			0
$415$	3.62923	−	6.28602i	0.178152	−	0.308568i
$416$	4.89306	−	4.10576i	0.239902	−	0.201302i
$417$		0			0
$418$	3.21776	−	18.2488i	0.157386	−	0.892579i
$419$	−6.21286	+	35.2349i	−0.303518	+	1.72134i	0.326881	+	0.945066i	$0.394002\pi$
$419$	−6.21286	+	35.2349i	−0.303518	+	1.72134i	−0.630399	+	0.776271i	$0.717109\pi$
$420$		0			0
$421$	−10.0496	+	8.43264i	−0.489789	+	0.410982i	−0.853951	−	0.520354i	$-0.825800\pi$
$421$	−10.0496	+	8.43264i	−0.489789	+	0.410982i	0.364162	+	0.931336i	$0.381356\pi$
$422$	10.5128	−	18.2087i	0.511756	−	0.886387i
$423$		0			0
$424$	13.2344	+	22.9227i	0.642720	+	1.11322i
$425$	−31.7556	−	11.5581i	−1.54037	−	0.560650i
$426$		0			0
$427$	−21.3405	−	17.9068i	−1.03274	−	0.866571i
$428$	−0.729669	+	0.265578i	−0.0352699	+	0.0128372i
$429$		0			0
$430$	−0.573978	−	3.25519i	−0.0276797	−	0.156979i
$431$	−9.48411			−0.456833			−0.228417	−	0.973563i	$-0.573355\pi$
$431$	−9.48411			−0.456833			−0.228417	+	0.973563i	$0.573355\pi$
$432$		0			0
$433$	17.6628			0.848820			0.424410	−	0.905470i	$-0.360481\pi$
$433$	17.6628			0.848820			0.424410	+	0.905470i	$0.360481\pi$
$434$	1.52639	+	8.65657i	0.0732689	+	0.415529i
$435$		0			0
$436$	−3.75402	+	1.36635i	−0.179785	+	0.0654364i
$437$	−28.9024	−	24.2520i	−1.38259	−	1.16013i
$438$		0			0
$439$	16.6001	+	6.04196i	0.792281	+	0.288367i	0.706284	−	0.707929i	$-0.250370\pi$
$439$	16.6001	+	6.04196i	0.792281	+	0.288367i	0.0859973	+	0.996295i	$0.472592\pi$
$440$	−1.87278	−	3.24376i	−0.0892814	−	0.154640i
$441$		0			0
$442$	14.8905	−	25.7912i	0.708270	−	1.22676i
$443$	9.95253	−	8.35117i	0.472859	−	0.396776i	−0.374977	−	0.927034i	$-0.622349\pi$
$443$	9.95253	−	8.35117i	0.472859	−	0.396776i	0.847836	+	0.530258i	$0.177905\pi$
$444$		0			0
$445$	1.42855	−	8.10170i	0.0677197	−	0.384057i
$446$	0.826501	−	4.68732i	0.0391359	−	0.221951i
$447$		0			0
$448$	−23.9859	+	20.1266i	−1.13323	+	0.950891i
$449$	−2.31428	+	4.00846i	−0.109218	+	0.189171i	−0.915454	−	0.402424i	$-0.868168\pi$
$449$	−2.31428	+	4.00846i	−0.109218	+	0.189171i	0.806236	+	0.591594i	$0.201501\pi$
$450$		0			0
$451$	−6.75671	−	11.7030i	−0.318161	−	0.551071i
$452$	0.550931	+	0.200522i	0.0259136	+	0.00943178i
$453$		0			0
$454$	10.4003	+	8.72691i	0.488112	+	0.409574i
$455$	4.87668	−	1.77497i	0.228622	−	0.0832117i
$456$		0			0
$457$	3.57145	+	20.2547i	0.167065	+	0.947475i	0.946909	+	0.321501i	$0.104187\pi$
$457$	3.57145	+	20.2547i	0.167065	+	0.947475i	−0.779844	+	0.625974i	$0.784702\pi$
$458$	17.3878			0.812477
$459$		0			0
$460$	−1.12836			−0.0526098
$461$	5.82980	+	33.0624i	0.271521	+	1.53987i	0.749801	+	0.661663i	$0.230149\pi$
$461$	5.82980	+	33.0624i	0.271521	+	1.53987i	−0.478280	+	0.878207i	$0.658740\pi$
$462$		0			0
$463$	−12.3391	+	4.49108i	−0.573449	+	0.208718i	−0.612434	−	0.790522i	$-0.709810\pi$
$463$	−12.3391	+	4.49108i	−0.573449	+	0.208718i	0.0389856	+	0.999240i	$0.487587\pi$
$464$	−8.82964	−	7.40895i	−0.409906	−	0.343952i
$465$		0			0
$466$	15.3430	+	5.58440i	0.710751	+	0.258692i
$467$	11.8154	+	20.4648i	0.546750	+	0.946999i	0.998495	+	0.0548513i	$0.0174685\pi$
$467$	11.8154	+	20.4648i	0.546750	+	0.946999i	−0.451745	+	0.892147i	$0.649198\pi$
$468$		0			0
$469$	−16.6694	+	28.8722i	−0.769720	+	1.33319i
$470$	1.32683	−	1.11334i	0.0612020	−	0.0513546i
$471$		0			0
$472$	−1.55303	+	8.80769i	−0.0714842	+	0.405407i
$473$	2.78006	−	15.7665i	0.127827	−	0.724945i
$474$		0			0
$475$	19.0672	−	15.9993i	0.874862	−	0.734096i
$476$	4.31753	−	7.47818i	0.197894	−	0.342762i
$477$		0			0
$478$	−3.76130	−	6.51476i	−0.172038	−	0.297978i
$479$	−5.52557	−	2.01114i	−0.252470	−	0.0918915i	0.212685	−	0.977121i	$-0.431779\pi$
$479$	−5.52557	−	2.01114i	−0.252470	−	0.0918915i	−0.465155	+	0.885229i	$0.654001\pi$
$480$		0			0
$481$	−8.13429	−	6.82548i	−0.370891	−	0.311215i
$482$	10.3165	−	3.75490i	0.469904	−	0.171031i
$483$		0			0
$484$	0.197281	+	1.11884i	0.00896732	+	0.0508562i
$485$	4.51557			0.205041
$486$		0			0
$487$	38.7965			1.75804			0.879020	−	0.476786i	$-0.158198\pi$
$487$	38.7965			1.75804			0.879020	+	0.476786i	$0.158198\pi$
$488$	−4.13290	−	23.4388i	−0.187087	−	1.06103i
$489$		0			0
$490$	−2.95336	+	1.07494i	−0.133419	+	0.0485607i
$491$	28.7912	+	24.1587i	1.29933	+	1.09027i	0.990261	+	0.139227i	$0.0444616\pi$
$491$	28.7912	+	24.1587i	1.29933	+	1.09027i	0.309068	+	0.951040i	$0.399983\pi$
$492$		0			0
$493$	23.9402	+	8.71351i	1.07821	+	0.392437i
$494$	10.9675	+	18.9963i	0.493452	+	0.854684i
$495$		0			0
$496$	−3.08260	+	5.33921i	−0.138413	+	0.239738i
$497$	−14.3602	+	12.0496i	−0.644143	+	0.540500i
$498$		0			0
$499$	5.86097	−	33.2392i	0.262373	−	1.48799i	−0.514040	−	0.857766i	$-0.671852\pi$
$499$	5.86097	−	33.2392i	0.262373	−	1.48799i	0.776413	−	0.630225i	$-0.217037\pi$
$500$	0.263890	−	1.49660i	0.0118015	−	0.0669298i
$501$		0			0
$502$	6.65523	−	5.58440i	0.297037	−	0.249244i
$503$	−9.35597	+	16.2050i	−0.417162	+	0.722546i	−0.995653	−	0.0931429i	$-0.970309\pi$
$503$	−9.35597	+	16.2050i	−0.417162	+	0.722546i	0.578491	+	0.815689i	$0.303642\pi$
$504$		0			0
$505$	0.464508	+	0.804551i	0.0206703	+	0.0358020i
$506$	24.4391	+	8.89512i	1.08645	+	0.395436i
$507$		0			0
$508$	0.710952	+	0.596559i	0.0315434	+	0.0264680i
$509$	20.4554	−	7.44516i	0.906670	−	0.330001i	0.153747	−	0.988110i	$-0.450866\pi$
$509$	20.4554	−	7.44516i	0.906670	−	0.330001i	0.752922	+	0.658109i	$0.228644\pi$
$510$		0			0
$511$	0.953363	+	5.40679i	0.0421743	+	0.239182i
$512$	−25.4026			−1.12265
$513$		0			0
$514$	−4.73473			−0.208840
$515$	−0.112287	−	0.636812i	−0.00494796	−	0.0280613i
$516$		0			0
$517$	7.88326	−	2.86927i	0.346705	−	0.126190i
$518$	11.2238	+	9.41787i	0.493145	+	0.413797i
$519$		0			0
$520$	4.16637	+	1.51644i	0.182708	+	0.0665001i
$521$	−3.23822	−	5.60876i	−0.141869	−	0.245724i	0.786332	−	0.617805i	$-0.211978\pi$
$521$	−3.23822	−	5.60876i	−0.141869	−	0.245724i	−0.928200	+	0.372081i	$0.878644\pi$
$522$		0			0
$523$	5.43629	−	9.41593i	0.237712	−	0.411730i	−0.722345	−	0.691533i	$-0.756936\pi$
$523$	5.43629	−	9.41593i	0.237712	−	0.411730i	0.960057	+	0.279803i	$0.0902691\pi$
$524$	0.776816	−	0.651826i	0.0339354	−	0.0284752i
$525$		0			0
$526$	−0.812109	+	4.60570i	−0.0354096	+	0.200818i
$527$	2.36630	−	13.4199i	0.103077	−	0.584581i
$528$		0			0
$529$	22.9458	−	19.2538i	0.997645	−	0.837124i
$530$	−2.51730	+	4.36009i	−0.109344	+	0.189390i
$531$		0			0
$532$	3.18004	+	5.50800i	0.137872	+	0.238802i
$533$	15.0316	+	5.47107i	0.651092	+	0.236978i
$534$		0			0
$535$	−0.764700	−	0.641660i	−0.0330609	−	0.0277414i
$536$	−26.7651	+	9.74170i	−1.15608	+	0.420777i
$537$		0			0
$538$	1.58202	+	8.97210i	0.0682059	+	0.386815i
$539$	−15.2226			−0.655686
$540$		0			0
$541$	24.6459			1.05961			0.529805	−	0.848120i	$-0.322265\pi$
$541$	24.6459			1.05961			0.529805	+	0.848120i	$0.322265\pi$
$542$	−4.24152	−	24.0548i	−0.182189	−	1.03324i
$543$		0			0
$544$	12.8391	−	4.67307i	0.550474	−	0.200356i
$545$	−3.93426	−	3.30123i	−0.168525	−	0.141409i
$546$		0			0
$547$	−29.0621	−	10.5777i	−1.24261	−	0.452272i	−0.364709	−	0.931121i	$-0.618832\pi$
$547$	−29.0621	−	10.5777i	−1.24261	−	0.452272i	−0.877897	+	0.478850i	$0.841054\pi$
$548$	−0.808718	−	1.40074i	−0.0345467	−	0.0598367i
$549$		0			0
$550$	−8.57873	+	14.8588i	−0.365798	+	0.633581i
$551$	−14.3745	+	12.0617i	−0.612375	+	0.513844i
$552$		0			0
$553$	7.29978	−	41.3991i	0.310418	−	1.76047i
$554$	−3.10126	+	17.5881i	−0.131760	+	0.747247i
$555$		0			0
$556$	2.12907	−	1.78650i	0.0902927	−	0.0757646i
$557$	11.6813	−	20.2327i	0.494954	−	0.857286i	−0.505029	−	0.863102i	$-0.668518\pi$
$557$	11.6813	−	20.2327i	0.494954	−	0.857286i	0.999983	+	0.00581674i	$0.00185154\pi$
$558$		0			0
$559$	9.47565	+	16.4123i	0.400777	+	0.694167i
$560$	−4.71950	−	1.71776i	−0.199435	−	0.0725886i
$561$		0			0
$562$	−21.7913	−	18.2851i	−0.919212	−	0.771310i
$563$	31.6561	−	11.5219i	1.33415	−	0.485589i	0.426182	−	0.904638i	$-0.359858\pi$
$563$	31.6561	−	11.5219i	1.33415	−	0.485589i	0.907964	+	0.419048i	$0.137636\pi$
$564$		0			0
$565$	0.130882	+	0.742267i	0.00550624	+	0.0312274i
$566$	−30.5097			−1.28242
$567$		0			0
$568$	−16.0155			−0.671995
$569$	5.34764	+	30.3280i	0.224185	+	1.27142i	0.864237	+	0.503085i	$0.167802\pi$
$569$	5.34764	+	30.3280i	0.224185	+	1.27142i	−0.640052	+	0.768331i	$0.721087\pi$
$570$		0			0
$571$	28.0736	−	10.2179i	1.17484	−	0.427608i	0.320465	−	0.947260i	$-0.396161\pi$
$571$	28.0736	−	10.2179i	1.17484	−	0.427608i	0.854378	+	0.519653i	$0.173939\pi$
$572$	2.43398	+	2.04236i	0.101770	+	0.0853952i
$573$		0			0
$574$	−20.7408	−	7.54904i	−0.865705	−	0.315091i
$575$	17.4670	+	30.2538i	0.728425	+	1.26167i
$576$		0			0
$577$	−2.40373	+	4.16339i	−0.100069	+	0.173324i	−0.911713	−	0.410828i	$-0.865240\pi$
$577$	−2.40373	+	4.16339i	−0.100069	+	0.173324i	0.811644	+	0.584152i	$0.198573\pi$
$578$	32.0581	−	26.8999i	1.33344	−	1.11889i
$579$		0			0
$580$	−0.0974487	+	0.552659i	−0.00404634	+	0.0229479i
$581$	9.97124	−	56.5497i	0.413677	−	2.34608i
$582$		0			0
$583$	−18.6800	+	15.6744i	−0.773648	+	0.649168i
$584$	−2.34527	+	4.06212i	−0.0970478	+	0.168092i
$585$		0			0
$586$	11.9598	+	20.7149i	0.494053	+	0.855725i
$587$	7.45891	+	2.71482i	0.307862	+	0.112053i	0.491331	−	0.870973i	$-0.336510\pi$
$587$	7.45891	+	2.71482i	0.307862	+	0.112053i	−0.183469	+	0.983026i	$0.558733\pi$
$588$		0			0
$589$	7.68866	+	6.45155i	0.316806	+	0.265832i
$590$	−1.59855	+	0.581825i	−0.0658113	+	0.0239533i
$591$		0			0
$592$	1.78446	+	10.1202i	0.0733410	+	0.415937i
$593$	−36.2753			−1.48965			−0.744824	−	0.667261i	$-0.767467\pi$
$593$	−36.2753			−1.48965			−0.744824	+	0.667261i	$0.767467\pi$
$594$		0			0
$595$	11.1010			0.455097
$596$	−1.21892	−	6.91282i	−0.0499288	−	0.283160i
$597$		0			0
$598$	−28.9295	+	10.5295i	−1.18301	+	0.430582i
$599$	−25.7736	−	21.6266i	−1.05308	−	0.883639i	−0.0596658	−	0.998218i	$-0.519004\pi$
$599$	−25.7736	−	21.6266i	−1.05308	−	0.883639i	−0.993414	+	0.114579i	$0.963448\pi$
$600$		0			0
$601$	2.79813	+	1.01844i	0.114138	+	0.0415429i	0.398458	−	0.917187i	$-0.369545\pi$
$601$	2.79813	+	1.01844i	0.114138	+	0.0415429i	−0.284320	+	0.958730i	$0.591768\pi$
$602$	−13.0746	−	22.6459i	−0.532882	−	0.922978i
$603$		0			0
$604$	1.16385	−	2.01584i	0.0473563	−	0.0820235i
$605$	−1.11884	+	0.938815i	−0.0454872	+	0.0381683i
$606$		0			0
$607$	−2.71735	+	15.4108i	−0.110294	+	0.625507i	0.878679	+	0.477412i	$0.158425\pi$
$607$	−2.71735	+	15.4108i	−0.110294	+	0.625507i	−0.988973	+	0.148095i	$0.952686\pi$
$608$	−1.74751	+	9.91060i	−0.0708707	+	0.401928i
$609$		0			0
$610$	3.46791	−	2.90992i	0.140412	−	0.117819i
$611$	−4.96529	+	8.60014i	−0.200874	+	0.347924i
$612$		0			0
$613$	0.533433	+	0.923933i	0.0215452	+	0.0373173i	0.876597	−	0.481225i	$-0.159808\pi$
$613$	0.533433	+	0.923933i	0.0215452	+	0.0373173i	−0.855052	+	0.518543i	$0.826475\pi$
$614$	−25.0632	−	9.12226i	−1.01147	−	0.368145i
$615$		0			0
$616$	−22.6989	−	19.0467i	−0.914566	−	0.767412i
$617$	−12.2817	+	4.47019i	−0.494444	+	0.179963i	−0.577194	−	0.816607i	$-0.695852\pi$
$617$	−12.2817	+	4.47019i	−0.494444	+	0.179963i	0.0827492	+	0.996570i	$0.473630\pi$
$618$		0			0
$619$	3.56283	+	20.2058i	0.143202	+	0.812141i	0.968793	+	0.247871i	$0.0797310\pi$
$619$	3.56283	+	20.2058i	0.143202	+	0.812141i	−0.825591	+	0.564270i	$0.809158\pi$
$620$	0.300167			0.0120550
$621$		0			0
$622$	−26.2071			−1.05081
$623$	−11.3013	−	64.0929i	−0.452777	−	2.56783i
$624$		0			0
$625$	−20.7199	+	7.54142i	−0.828795	+	0.301657i
$626$	−29.3874	−	24.6590i	−1.17456	−	0.985572i
$627$		0			0
$628$	1.73783	+	0.632517i	0.0693468	+	0.0252402i
$629$	−11.3569	−	19.6707i	−0.452829	−	0.784323i
$630$		0			0
$631$	5.15611	−	8.93064i	0.205261	−	0.355523i	−0.744955	−	0.667115i	$-0.767529\pi$
$631$	5.15611	−	8.93064i	0.205261	−	0.355523i	0.950216	+	0.311592i	$0.100862\pi$
$632$	27.5123	−	23.0856i	1.09438	−	0.918295i
$633$		0			0
$634$	−0.963630	+	5.46502i	−0.0382706	+	0.217044i
$635$	−0.207183	+	1.17499i	−0.00822180	+	0.0466281i
$636$		0			0
$637$	13.8038	−	11.5828i	0.546927	−	0.458926i
$638$	6.46740	−	11.2019i	0.256047	−	0.443486i
$639$		0			0
$640$	−1.67752	−	2.90555i	−0.0663097	−	0.114852i
$641$	3.29472	+	1.19918i	0.130133	+	0.0473647i	0.406266	−	0.913755i	$-0.366831\pi$
$641$	3.29472	+	1.19918i	0.130133	+	0.0473647i	−0.276133	+	0.961120i	$0.589053\pi$
$642$		0			0
$643$	24.1700	+	20.2810i	0.953172	+	0.799806i	0.979829	−	0.199839i	$-0.0640418\pi$
$643$	24.1700	+	20.2810i	0.953172	+	0.799806i	−0.0266572	+	0.999645i	$0.508486\pi$
$644$	−8.38814	+	3.05303i	−0.330539	+	0.120306i
$645$		0			0
$646$	8.14765	+	46.2076i	0.320565	+	1.81801i
$647$	3.04628			0.119762			0.0598808	−	0.998206i	$-0.480928\pi$
$647$	3.04628			0.119762			0.0598808	+	0.998206i	$0.480928\pi$
$648$		0			0
$649$	−8.23947			−0.323428
$650$	−3.52678	−	20.0013i	−0.138332	−	0.784517i
$651$		0			0
$652$	1.24510	−	0.453179i	0.0487619	−	0.0177479i
$653$	23.5462	+	19.7576i	0.921433	+	0.773174i	0.974259	−	0.225430i	$-0.0723785\pi$
$653$	23.5462	+	19.7576i	0.921433	+	0.773174i	−0.0528264	+	0.998604i	$0.516823\pi$
$654$		0			0
$655$	1.22503	+	0.445875i	0.0478660	+	0.0174218i
$656$	−7.74038	−	13.4067i	−0.302211	−	0.523445i
$657$		0			0
$658$	6.85117	−	11.8666i	0.267086	−	0.462607i
$659$	25.4204	−	21.3302i	0.990237	−	0.830907i	0.00463496	−	0.999989i	$-0.498525\pi$
$659$	25.4204	−	21.3302i	0.990237	−	0.830907i	0.985602	+	0.169082i	$0.0540802\pi$
$660$		0			0
$661$	−2.58869	+	14.6812i	−0.100688	+	0.571032i	0.892167	+	0.451706i	$0.149184\pi$
$661$	−2.58869	+	14.6812i	−0.100688	+	0.571032i	−0.992855	+	0.119326i	$0.961927\pi$
$662$	−0.651611	+	3.69547i	−0.0253256	+	0.143629i
$663$		0			0
$664$	37.5808	−	31.5341i	1.45842	−	1.22376i
$665$	−4.08819	+	7.08095i	−0.158533	+	0.274587i
$666$		0			0
$667$	−13.1682	−	22.8080i	−0.509874	−	0.883128i
$668$	−2.98135	−	1.08512i	−0.115352	−	0.0419846i
$669$		0			0
$670$	−4.15018	−	3.48241i	−0.160335	−	0.134537i
$671$	20.6044	−	7.49937i	0.795422	−	0.289510i
$672$		0			0
$673$	1.19624	+	6.78422i	0.0461117	+	0.261513i	0.999145	−	0.0413545i	$-0.0131673\pi$
$673$	1.19624	+	6.78422i	0.0461117	+	0.261513i	−0.953033	+	0.302867i	$0.902056\pi$
$674$	18.5656			0.715122
$675$		0			0
$676$	0.753718			0.0289892
$677$	2.29029	+	12.9889i	0.0880228	+	0.499202i	0.996663	+	0.0816229i	$0.0260103\pi$
$677$	2.29029	+	12.9889i	0.0880228	+	0.499202i	−0.908640	+	0.417579i	$0.862879\pi$
$678$		0			0
$679$	33.5685	−	12.2179i	1.28824	−	0.468882i
$680$	7.26525	+	6.09627i	0.278610	+	0.233781i
$681$		0			0
$682$	−6.50134	−	2.36630i	−0.248949	−	0.0906101i
$683$	−1.68907	−	2.92556i	−0.0646305	−	0.111943i	0.831900	−	0.554926i	$-0.187254\pi$
$683$	−1.68907	−	2.92556i	−0.0646305	−	0.111943i	−0.896530	+	0.442983i	$0.853920\pi$
$684$		0			0
$685$	1.03967	−	1.80076i	0.0397237	−	0.0688034i
$686$	5.30234	−	4.44919i	0.202444	−	0.169871i
$687$		0			0
$688$	3.18479	−	18.0619i	0.121419	−	0.688602i
$689$	5.01244	−	28.4270i	0.190959	−	1.08298i
$690$		0			0
$691$	17.9370	−	15.0509i	0.682356	−	0.572565i	−0.234338	−	0.972155i	$-0.575292\pi$
$691$	17.9370	−	15.0509i	0.682356	−	0.572565i	0.916694	+	0.399591i	$0.130848\pi$
$692$	−1.05471	+	1.82682i	−0.0400942	+	0.0694452i
$693$		0			0
$694$	−0.934640	−	1.61884i	−0.0354785	−	0.0614505i
$695$	3.35753	+	1.22204i	0.127358	+	0.0463546i
$696$		0			0
$697$	26.2119	+	21.9944i	0.992846	+	0.833097i
$698$	33.3200	−	12.1275i	1.26118	−	0.459032i
$699$		0			0
$700$	−1.02259	−	5.79942i	−0.0386504	−	0.219197i
$701$	−45.5001			−1.71852			−0.859258	−	0.511543i	$-0.829074\pi$
$701$	−45.5001			−1.71852			−0.859258	+	0.511543i	$0.829074\pi$
$702$		0			0
$703$	16.7297			0.630972
$704$	−4.27952	−	24.2704i	−0.161291	−	0.914724i
$705$		0			0
$706$	12.7233	−	4.63089i	0.478847	−	0.174286i
$707$	5.63003	+	4.72416i	0.211739	+	0.177670i
$708$		0			0
$709$	−36.2879	−	13.2077i	−1.36282	−	0.496026i	−0.445896	−	0.895085i	$-0.647115\pi$
$709$	−36.2879	−	13.2077i	−1.36282	−	0.496026i	−0.916926	+	0.399058i	$0.869337\pi$
$710$	−1.52314	−	2.63816i	−0.0571624	−	0.0990082i
$711$		0			0
$712$	27.8011	−	48.1530i	1.04189	−	1.80461i
$713$	−10.7911	+	9.05484i	−0.404131	+	0.339107i
$714$		0			0
$715$	−0.709303	+	4.02266i	−0.0265264	+	0.150439i
$716$	0.620029	−	3.51636i	0.0231716	−	0.131413i
$717$		0			0
$718$	−14.4820	+	12.1519i	−0.540465	+	0.453504i
$719$	−24.6591	+	42.7108i	−0.919630	+	1.59285i	−0.119652	+	0.992816i	$0.538178\pi$
$719$	−24.6591	+	42.7108i	−0.919630	+	1.59285i	−0.799978	+	0.600030i	$0.795155\pi$
$720$		0			0
$721$	−2.55778	−	4.43021i	−0.0952567	−	0.164990i
$722$	−9.52190	−	3.46569i	−0.354369	−	0.128980i
$723$		0			0
$724$	6.15657	+	5.16598i	0.228807	+	0.191992i
$725$	16.3266	−	5.94238i	0.606353	−	0.220694i
$726$		0			0
$727$	−5.60788	−	31.8039i	−0.207985	−	1.17954i	−0.892673	−	0.450704i	$-0.851173\pi$
$727$	−5.60788	−	31.8039i	−0.207985	−	1.17954i	0.684689	−	0.728836i	$-0.259938\pi$
$728$	35.0757			1.29999
$729$		0			0
$730$	−0.892178			−0.0330210
$731$	7.03936	+	39.9222i	0.260360	+	1.47658i
$732$		0			0
$733$	−37.0861	+	13.4982i	−1.36980	+	0.498568i	−0.919072	−	0.394091i	$-0.871060\pi$
$733$	−37.0861	+	13.4982i	−1.36980	+	0.498568i	−0.450733	+	0.892659i	$0.648837\pi$
$734$	−21.0382	−	17.6532i	−0.776535	−	0.651590i
$735$		0			0
$736$	−13.2724	−	4.83077i	−0.489229	−	0.178065i
$737$	−13.1202	−	22.7249i	−0.483290	−	0.837083i
$738$		0			0
$739$	−17.6545	+	30.5785i	−0.649432	+	1.12485i	0.333827	+	0.942634i	$0.391660\pi$
$739$	−17.6545	+	30.5785i	−0.649432	+	1.12485i	−0.983259	+	0.182215i	$0.941673\pi$
$740$	0.383273	−	0.321604i	0.0140894	−	0.0118224i
$741$		0			0
$742$	−6.91622	+	39.2238i	−0.253902	+	1.43995i
$743$	8.23276	−	46.6903i	0.302031	−	1.71290i	−0.335131	−	0.942171i	$-0.608781\pi$
$743$	8.23276	−	46.6903i	0.302031	−	1.71290i	0.637162	−	0.770730i	$-0.280108\pi$
$744$		0			0
$745$	6.91282	−	5.80054i	0.253266	−	0.212515i
$746$	−14.5428	+	25.1888i	−0.532449	+	0.922228i
$747$		0			0
$748$	3.39827	+	5.88598i	0.124253	+	0.215213i
$749$	−7.42091	−	2.70099i	−0.271154	−	0.0986920i
$750$		0			0
$751$	−6.83931	−	5.73886i	−0.249570	−	0.209414i	0.509417	−	0.860520i	$-0.329861\pi$
$751$	−6.83931	−	5.73886i	−0.249570	−	0.209414i	−0.758987	+	0.651106i	$0.774305\pi$
$752$	9.03093	−	3.28699i	0.329324	−	0.119864i
$753$		0			0
$754$	2.65880	+	15.0788i	0.0968276	+	0.549137i
$755$	2.99243			0.108906
$756$		0			0
$757$	−3.63816			−0.132231			−0.0661155	−	0.997812i	$-0.521061\pi$
$757$	−3.63816			−0.132231			−0.0661155	+	0.997812i	$0.521061\pi$
$758$	−3.81163	−	21.6168i	−0.138444	−	0.785158i
$759$		0			0
$760$	−6.56418	+	2.38917i	−0.238108	+	0.0866641i
$761$	5.12392	+	4.29948i	0.185742	+	0.155856i	0.730917	−	0.682466i	$-0.239093\pi$
$761$	5.12392	+	4.29948i	0.185742	+	0.155856i	−0.545175	+	0.838322i	$0.683537\pi$
$762$		0			0
$763$	−38.1793	−	13.8961i	−1.38218	−	0.503074i
$764$	−2.54747	−	4.41235i	−0.0921643	−	0.159633i
$765$		0			0
$766$	−25.0633	+	43.4109i	−0.905574	+	1.56850i
$767$	7.47151	−	6.26934i	0.269781	−	0.226373i
$768$		0			0
$769$	−3.72844	+	21.1450i	−0.134451	+	0.762509i	0.840790	+	0.541362i	$0.182091\pi$
$769$	−3.72844	+	21.1450i	−0.134451	+	0.762509i	−0.975241	+	0.221147i	$0.929020\pi$
$770$	0.978704	−	5.55051i	0.0352701	−	0.200026i
$771$		0			0
$772$	−6.23648	+	5.23303i	−0.224456	+	0.188341i
$773$	−5.12208	+	8.87170i	−0.184228	+	0.319093i	−0.943316	−	0.331895i	$-0.892312\pi$
$773$	−5.12208	+	8.87170i	−0.184228	+	0.319093i	0.759088	+	0.650988i	$0.225645\pi$
$774$		0			0
$775$	−4.64661	−	8.04817i	−0.166911	−	0.289099i
$776$	28.6791	+	10.4383i	1.02952	+	0.374715i
$777$		0			0
$778$	−10.0569	−	8.43874i	−0.360557	−	0.302544i
$779$	−23.6825	+	8.61974i	−0.848515	+	0.308834i
$780$		0			0
$781$	−2.56212	−	14.5305i	−0.0916798	−	0.519942i
$782$	−65.8535			−2.35492
$783$		0			0
$784$	−17.4388			−0.622815
$785$	0.412846	+	2.34137i	0.0147351	+	0.0835670i
$786$		0			0
$787$	−0.890530	+	0.324126i	−0.0317440	+	0.0115539i	−0.357843	−	0.933782i	$-0.616488\pi$
$787$	−0.890530	+	0.324126i	−0.0317440	+	0.0115539i	0.326099	+	0.945335i	$0.394266\pi$
$788$	−2.40176	−	2.01532i	−0.0855593	−	0.0717928i
$789$		0			0
$790$	6.41932	+	2.33644i	0.228389	+	0.0831269i
$791$	2.98135	+	5.16385i	0.106005	+	0.183605i
$792$		0			0
$793$	−12.9777	+	22.4781i	−0.460852	+	0.798219i
$794$	−1.12554	+	0.944440i	−0.0399439	+	0.0335169i
$795$		0			0
$796$	−0.157041	+	0.890623i	−0.00556617	+	0.0315673i
$797$	−1.21740	+	6.90420i	−0.0431224	+	0.244559i	−0.998748	−	0.0500247i	$-0.984070\pi$
$797$	−1.21740	+	6.90420i	−0.0431224	+	0.244559i	0.955626	+	0.294584i	$0.0951811\pi$
$798$		0			0
$799$	−16.2724	+	13.6542i	−0.575678	+	0.483051i
$800$	4.65895	−	8.06953i	0.164719	−	0.285301i
$801$		0			0
$802$	−13.2118	−	22.8836i	−0.466526	−	0.808047i
$803$	−4.06066	−	1.47796i	−0.143298	−	0.0521561i
$804$		0			0
$805$	−8.79086	−	7.37641i	−0.309837	−	0.259984i
$806$	7.69588	−	2.80107i	0.271076	−	0.0986635i
$807$		0			0
$808$	1.09034	+	6.18361i	0.0383579	+	0.217539i
$809$	45.1028			1.58573			0.792866	−	0.609396i	$-0.208588\pi$
$809$	45.1028			1.58573			0.792866	+	0.609396i	$0.208588\pi$
$810$		0			0
$811$	8.07285			0.283476			0.141738	−	0.989904i	$-0.454731\pi$
$811$	8.07285			0.283476			0.141738	+	0.989904i	$0.454731\pi$
$812$	0.770921	+	4.37211i	0.0270540	+	0.153431i
$813$		0			0
$814$	−10.8366	+	3.94421i	−0.379823	+	0.138244i
$815$	1.30488	+	1.09492i	0.0457079	+	0.0383535i
$816$		0			0
$817$	−28.0574	−	10.2120i	−0.981603	−	0.357274i
$818$	5.22481	+	9.04963i	0.182681	+	0.316413i
$819$		0			0
$820$	−0.376859	+	0.652739i	−0.0131605	+	0.0227946i
$821$	−4.80261	+	4.02987i	−0.167612	+	0.140643i	−0.722735	−	0.691125i	$-0.757116\pi$
$821$	−4.80261	+	4.02987i	−0.167612	+	0.140643i	0.555123	+	0.831768i	$0.312671\pi$
$822$		0			0
$823$	−3.43700	+	19.4922i	−0.119806	+	0.679456i	0.864451	+	0.502717i	$0.167666\pi$
$823$	−3.43700	+	19.4922i	−0.119806	+	0.679456i	−0.984258	+	0.176739i	$0.943445\pi$
$824$	0.758922	−	4.30406i	0.0264383	−	0.149939i
$825$		0			0
$826$	−10.3093	+	8.65051i	−0.358706	+	0.300990i
$827$	−20.9001	+	36.2001i	−0.726769	+	1.25880i	0.231472	+	0.972841i	$0.425646\pi$
$827$	−20.9001	+	36.2001i	−0.726769	+	1.25880i	−0.958242	+	0.285960i	$0.907688\pi$
$828$		0			0
$829$	−16.8640	−	29.2092i	−0.585710	−	1.01448i	−0.994787	−	0.101979i	$-0.967483\pi$
$829$	−16.8640	−	29.2092i	−0.585710	−	1.01448i	0.409077	−	0.912500i	$-0.365851\pi$
$830$	8.76856	+	3.19149i	0.304361	+	0.110778i
$831$		0			0
$832$	22.3478	+	18.7520i	0.774769	+	0.650109i
$833$	36.2205	−	13.1832i	1.25497	−	0.456771i
$834$		0			0
$835$	−0.708263	−	4.01676i	−0.0245105	−	0.139006i
$836$	−5.00594			−0.173134
$837$		0			0
$838$	−45.9959			−1.58890
$839$	−5.08559	−	28.8418i	−0.175574	−	0.995731i	−0.937479	−	0.348042i	$-0.886847\pi$
$839$	−5.08559	−	28.8418i	−0.175574	−	0.995731i	0.761905	−	0.647689i	$-0.224264\pi$
$840$		0			0
$841$	14.9427	−	5.43869i	0.515265	−	0.187541i
$842$	−12.9196	−	10.8408i	−0.445237	−	0.373598i
$843$		0			0
$844$	−5.33750	−	1.94269i	−0.183724	−	0.0668701i
$845$	0.484481	+	0.839145i	0.0166666	+	0.0288675i
$846$		0			0
$847$	−5.77719	+	10.0064i	−0.198507	+	0.343823i
$848$	−21.3996	+	17.9564i	−0.734864	+	0.616624i
$849$		0			0
$850$	7.54400	−	42.7842i	0.258757	−	1.46749i
$851$	−4.07732	+	23.1236i	−0.139769	+	0.792667i
$852$		0			0
$853$	28.8018	−	24.1676i	0.986156	−	0.827483i	0.00114955	−	0.999999i	$-0.499634\pi$
$853$	28.8018	−	24.1676i	0.986156	−	0.827483i	0.985007	+	0.172516i	$0.0551896\pi$
$854$	17.9068	−	31.0155i	0.612758	−	1.06133i
$855$		0			0
$856$	−3.37346	−	5.84300i	−0.115302	−	0.199710i
$857$	27.2604	+	9.92199i	0.931199	+	0.338929i	0.762685	−	0.646771i	$-0.223881\pi$
$857$	27.2604	+	9.92199i	0.931199	+	0.338929i	0.168514	+	0.985699i	$0.446103\pi$
$858$		0			0
$859$	−19.0496	−	15.9845i	−0.649965	−	0.545385i	0.257095	−	0.966386i	$-0.417235\pi$
$859$	−19.0496	−	15.9845i	−0.649965	−	0.545385i	−0.907060	+	0.421001i	$0.861679\pi$
$860$	−0.839100	+	0.305407i	−0.0286131	+	0.0104143i
$861$		0			0
$862$	−2.11721	−	12.0073i	−0.0721125	−	0.408970i
$863$	42.4018			1.44337			0.721687	−	0.692219i	$-0.243367\pi$
$863$	42.4018			1.44337			0.721687	+	0.692219i	$0.243367\pi$
$864$		0			0
$865$	−2.71183			−0.0922050
$866$	3.94301	+	22.3619i	0.133989	+	0.759888i
$867$		0			0
$868$	2.23143	−	0.812174i	0.0757396	−	0.0275670i
$869$	25.3464	+	21.2682i	0.859818	+	0.721473i
$870$		0			0
$871$	29.1886	+	10.6238i	0.989017	+	0.359973i
$872$	−17.3559	−	30.0612i	−0.587744	−	1.01800i
$873$		0			0
$874$	24.2520	−	42.0056i	0.820335	−	1.42086i
$875$	11.8396	−	9.93464i	0.400253	−	0.335852i
$876$		0			0
$877$	2.09327	−	11.8715i	0.0706848	−	0.400874i	−0.928852	−	0.370450i	$-0.879203\pi$
$877$	2.09327	−	11.8715i	0.0706848	−	0.400874i	0.999537	−	0.0304232i	$-0.00968552\pi$
$878$	−3.94361	+	22.3653i	−0.133090	+	0.754792i
$879$		0			0
$880$	3.02822	−	2.54098i	0.102081	−	0.0856563i
$881$	7.39133	−	12.8022i	0.249020	−	0.431316i	−0.714234	−	0.699907i	$-0.753225\pi$
$881$	7.39133	−	12.8022i	0.249020	−	0.431316i	0.963254	+	0.268591i	$0.0865581\pi$
$882$		0			0
$883$	12.9231	+	22.3834i	0.434896	+	0.753263i	0.997287	−	0.0736089i	$-0.0234516\pi$
$883$	12.9231	+	22.3834i	0.434896	+	0.753263i	−0.562391	+	0.826872i	$0.690118\pi$
$884$	−7.56012	−	2.75166i	−0.254274	−	0.0925483i
$885$		0			0
$886$	12.7947	+	10.7361i	0.429847	+	0.360685i
$887$	−43.0905	+	15.6837i	−1.44684	+	0.526606i	−0.941706	−	0.336436i	$-0.890778\pi$
$887$	−43.0905	+	15.6837i	−1.44684	+	0.526606i	−0.505132	+	0.863042i	$0.668556\pi$
$888$		0			0
$889$	1.63903	+	9.29542i	0.0549714	+	0.311758i
$890$	10.5760			0.354509
$891$		0			0
$892$	−1.28581			−0.0430520
$893$	−2.71686	−	15.4081i	−0.0909162	−	0.515611i
$894$		0			0
$895$	4.31345	−	1.56997i	0.144183	−	0.0524783i
$896$	−20.3322	−	17.0608i	−0.679252	−	0.569960i
$897$		0			0
$898$	−5.59152	−	2.03515i	−0.186591	−	0.0679137i
$899$	3.50303	+	6.06742i	0.116832	+	0.202360i
$900$		0			0
$901$	30.8726	−	53.4729i	1.02851	−	1.78144i
$902$	13.3081	−	11.1668i	0.443112	−	0.371815i
$903$		0			0
$904$	−0.884600	+	5.01681i	−0.0294214	+	0.166857i
$905$	−1.79413	+	10.1750i	−0.0596388	+	0.338228i
$906$		0			0
$907$	−8.96270	+	7.52060i	−0.297601	+	0.249717i	−0.779345	−	0.626595i	$-0.784448\pi$
$907$	−8.96270	+	7.52060i	−0.297601	+	0.249717i	0.481744	+	0.876312i	$0.340004\pi$
$908$	1.83386	−	3.17634i	0.0608587	−	0.105410i
$909$		0			0
$910$	3.33585	+	5.77786i	0.110582	+	0.191534i
$911$	−26.9459	−	9.80752i	−0.892759	−	0.324938i	−0.145412	−	0.989371i	$-0.546451\pi$
$911$	−26.9459	−	9.80752i	−0.892759	−	0.324938i	−0.747347	+	0.664434i	$0.768673\pi$
$912$		0			0
$913$	34.6223	+	29.0515i	1.14583	+	0.961465i
$914$	−24.8461	+	9.04323i	−0.821835	+	0.299124i
$915$		0			0
$916$	−0.815674	−	4.62592i	−0.0269506	−	0.152845i
$917$	10.3133			0.340574
$918$		0			0
$919$	4.33511			0.143002			0.0715011	−	0.997441i	$-0.477221\pi$
$919$	4.33511			0.143002			0.0715011	+	0.997441i	$0.477221\pi$
$920$	−1.70248	−	9.65523i	−0.0561290	−	0.318324i
$921$		0			0
$922$	−40.5571	+	14.7616i	−1.33568	+	0.486146i
$923$	13.3794	+	11.2267i	0.440390	+	0.369531i
$924$		0			0
$925$	−14.5560	−	5.29796i	−0.478599	−	0.174196i
$926$	−8.44047	−	14.6193i	−0.277371	−	0.480421i
$927$		0			0
$928$	−3.51233	+	6.08353i	−0.115298	+	0.199702i
$929$	−9.87500	+	8.28611i	−0.323988	+	0.271859i	−0.790245	−	0.612791i	$-0.790047\pi$
$929$	−9.87500	+	8.28611i	−0.323988	+	0.271859i	0.466257	+	0.884649i	$0.345602\pi$
$930$		0			0
$931$	−4.92989	+	27.9588i	−0.161571	+	0.916313i
$932$	0.765945	−	4.34389i	0.0250894	−	0.142289i
$933$		0			0
$934$	−23.2717	+	19.5273i	−0.761474	+	0.638953i
$935$	−4.36873	+	7.56687i	−0.142873	+	0.247463i
$936$		0			0
$937$	26.6040	+	46.0795i	0.869115	+	1.50535i	0.862902	+	0.505371i	$0.168644\pi$
$937$	26.6040	+	46.0795i	0.869115	+	1.50535i	0.00621270	+	0.999981i	$0.498022\pi$
$938$	−40.2747	−	14.6588i	−1.31502	−	0.478627i
$939$		0			0
$940$	−0.358441	−	0.300767i	−0.0116910	−	0.00980995i
$941$	−31.3927	+	11.4260i	−1.02337	+	0.372478i	−0.798554	−	0.601923i	$-0.794402\pi$
$941$	−31.3927	+	11.4260i	−1.02337	+	0.372478i	−0.224820	+	0.974400i	$0.572179\pi$
$942$		0			0
$943$	−6.14227	−	34.8346i	−0.200020	−	1.13437i
$944$	−9.43901			−0.307214
$945$		0			0
$946$	20.5817			0.669169
$947$	2.69237	+	15.2692i	0.0874903	+	0.496182i	0.996791	+	0.0800434i	$0.0255059\pi$
$947$	2.69237	+	15.2692i	0.0874903	+	0.496182i	−0.909301	+	0.416139i	$0.863383\pi$
$948$		0			0
$949$	4.80675	−	1.74951i	0.156034	−	0.0567916i
$950$	24.5123	+	20.5682i	0.795283	+	0.667322i
$951$		0			0
$952$	70.5044	+	25.6615i	2.28506	+	0.831694i
$953$	11.2524	+	19.4898i	0.364502	+	0.631336i	0.988696	−	0.149933i	$-0.0479059\pi$
$953$	11.2524	+	19.4898i	0.364502	+	0.631336i	−0.624194	+	0.781269i	$0.714573\pi$
$954$		0			0
$955$	3.27497	−	5.67241i	0.105975	−	0.183555i
$956$	−1.55677	+	1.30628i	−0.0503495	+	0.0422483i
$957$		0			0
$958$	1.31268	−	7.44459i	0.0424108	−	0.240524i
$959$	2.85646	−	16.1998i	0.0922400	−	0.523119i
$960$		0			0
$961$	−20.8767	+	17.5176i	−0.673442	+	0.565085i
$962$	6.82548	−	11.8221i	0.220062	−	0.381159i
$963$		0			0
$964$	−1.48293	−	2.56850i	−0.0477618	−	0.0827259i
$965$	−9.83488	−	3.57960i	−0.316596	−	0.115231i
$966$		0			0
$967$	−32.0271	−	26.8739i	−1.02992	−	0.864207i	−0.0390802	−	0.999236i	$-0.512443\pi$
$967$	−32.0271	−	26.8739i	−1.02992	−	0.864207i	−0.990842	+	0.135029i	$0.956887\pi$
$968$	−9.27612	+	3.37623i	−0.298146	+	0.108516i
$969$		0			0
$970$	1.00805	+	5.71691i	0.0323664	+	0.183559i
$971$	−35.8662			−1.15100			−0.575501	−	0.817801i	$-0.695193\pi$
$971$	−35.8662			−1.15100			−0.575501	+	0.817801i	$0.695193\pi$
$972$		0			0
$973$	28.2662			0.906173
$974$	8.66085	+	49.1181i	0.277512	+	1.57385i
$975$		0			0
$976$	23.6040	−	8.59116i	0.755546	−	0.274996i
$977$	−10.7630	−	9.03121i	−0.344338	−	0.288934i	0.454174	−	0.890913i	$-0.349935\pi$
$977$	−10.7630	−	9.03121i	−0.344338	−	0.288934i	−0.798512	+	0.601979i	$0.794379\pi$
$978$		0			0
$979$	48.1357	+	17.5200i	1.53842	+	0.559940i
$980$	0.424525	+	0.735300i	0.0135610	+	0.0234883i
$981$		0			0
$982$	−24.1587	+	41.8441i	−0.770935	+	1.33530i
$983$	13.5507	−	11.3704i	0.432199	−	0.362658i	−0.400582	−	0.916261i	$-0.631192\pi$
$983$	13.5507	−	11.3704i	0.432199	−	0.362658i	0.832781	+	0.553603i	$0.186747\pi$
$984$		0			0
$985$	0.699913	−	3.96940i	0.0223011	−	0.126476i
$986$	−5.68734	+	32.2545i	−0.181122	+	1.02719i
$987$		0			0
$988$	4.53936	−	3.80898i	0.144416	−	0.121180i
$989$	20.9531	−	36.2918i	0.666269	−	1.15401i
$990$		0			0
$991$	−16.4479	−	28.4886i	−0.522485	−	0.904970i	−0.999658	−	0.0261608i	$-0.991672\pi$
$991$	−16.4479	−	28.4886i	−0.522485	−	0.904970i	0.477173	−	0.878809i	$-0.341662\pi$
$992$	3.53076	+	1.28509i	0.112102	+	0.0408017i
$993$		0			0
$994$	−18.4611	−	15.4907i	−0.585551	−	0.491335i
$995$	−1.09251	+	0.397641i	−0.0346349	+	0.0126061i
$996$		0			0
$997$	3.47415	+	19.7029i	0.110027	+	0.623996i	0.989093	+	0.147295i	$0.0470565\pi$
$997$	3.47415	+	19.7029i	0.110027	+	0.623996i	−0.879065	+	0.476701i	$0.841832\pi$
$998$	43.3907			1.37351
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.r.82.2		12
3.2	odd	2	inner	729.2.e.r.82.1		12
9.2	odd	6		729.2.e.m.325.1		12
9.4	even	3		729.2.e.q.568.1		12
9.5	odd	6		729.2.e.q.568.2		12
9.7	even	3		729.2.e.m.325.2		12
27.2	odd	18	inner	729.2.e.r.649.1		12
27.4	even	9		729.2.c.c.487.2		12
27.5	odd	18		729.2.a.c.1.2	✓	6
27.7	even	9		729.2.e.m.406.2		12
27.11	odd	18		729.2.e.q.163.2		12
27.13	even	9		729.2.c.c.244.2		12
27.14	odd	18		729.2.c.c.244.5		12
27.16	even	9		729.2.e.q.163.1		12
27.20	odd	18		729.2.e.m.406.1		12
27.22	even	9		729.2.a.c.1.5	yes	6
27.23	odd	18		729.2.c.c.487.5		12
27.25	even	9	inner	729.2.e.r.649.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.2	✓	6	27.5	odd	18
729.2.a.c.1.5	yes	6	27.22	even	9
729.2.c.c.244.2		12	27.13	even	9
729.2.c.c.244.5		12	27.14	odd	18
729.2.c.c.487.2		12	27.4	even	9
729.2.c.c.487.5		12	27.23	odd	18
729.2.e.m.325.1		12	9.2	odd	6
729.2.e.m.325.2		12	9.7	even	3
729.2.e.m.406.1		12	27.20	odd	18
729.2.e.m.406.2		12	27.7	even	9
729.2.e.q.163.1		12	27.16	even	9
729.2.e.q.163.2		12	27.11	odd	18
729.2.e.q.568.1		12	9.4	even	3
729.2.e.q.568.2		12	9.5	odd	6
729.2.e.r.82.1		12	3.2	odd	2	inner
729.2.e.r.82.2		12	1.1	even	1	trivial
729.2.e.r.649.1		12	27.2	odd	18	inner
729.2.e.r.649.2		12	27.25	even	9	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.223238 + 1.26604i) q^{2} +(0.326352 - 0.118782i) q^{4} +(0.342020 + 0.286989i) q^{5} +(3.31908 + 1.20805i) q^{7} +(1.50881 + 2.61334i) q^{8} +O(q^{10})\)	\(q+(0.223238 + 1.26604i) q^{2} +(0.326352 - 0.118782i) q^{4} +(0.342020 + 0.286989i) q^{5} +(3.31908 + 1.20805i) q^{7} +(1.50881 + 2.61334i) q^{8} +(-0.286989 + 0.497079i) q^{10} +(-2.12965 + 1.78699i) q^{11} +(0.571452 - 3.24086i) q^{13} +(-0.788496 + 4.47178i) q^{14} +(-2.43969 + 2.04715i) q^{16} +(3.51968 - 6.09627i) q^{17} +(2.59240 + 4.49016i) q^{19} +(0.145708 + 0.0530334i) q^{20} +(-2.73783 - 2.29731i) q^{22} +(-6.83807 + 2.48886i) q^{23} +(-0.833626 - 4.72773i) q^{25} +4.23065 q^{26} +1.22668 q^{28} +(0.628461 + 3.56418i) q^{29} +(1.81908 - 0.662090i) q^{31} +(1.48686 + 1.24763i) q^{32} +(8.50387 + 3.09516i) q^{34} +(0.788496 + 1.36571i) q^{35} +(1.61334 - 2.79439i) q^{37} +(-5.10602 + 4.28446i) q^{38} +(-0.233956 + 1.32683i) q^{40} +(-0.844075 + 4.78699i) q^{41} +(-4.41147 + 3.70167i) q^{43} +(-0.482753 + 0.836152i) q^{44} +(-4.67752 - 8.10170i) q^{46} +(-2.83564 - 1.03209i) q^{47} +(4.19459 + 3.51968i) q^{49} +(5.79942 - 2.11081i) q^{50} +(-0.198463 - 1.12554i) q^{52} +8.77141 q^{53} -1.24123 q^{55} +(1.85083 + 10.4966i) q^{56} +(-4.37211 + 1.59132i) q^{58} +(2.27038 + 1.90508i) q^{59} +(-7.41147 - 2.69756i) q^{61} +(1.24432 + 2.15523i) q^{62} +(-4.43242 + 7.67717i) q^{64} +(1.12554 - 0.944440i) q^{65} +(-1.63903 + 9.29542i) q^{67} +(0.424525 - 2.40760i) q^{68} +(-1.55303 + 1.30315i) q^{70} +(-2.65366 + 4.59627i) q^{71} +(0.777189 + 1.34613i) q^{73} +(3.89798 + 1.41875i) q^{74} +(1.37939 + 1.15744i) q^{76} +(-9.22724 + 3.35844i) q^{77} +(-2.06670 - 11.7209i) q^{79} -1.42193 q^{80} -6.24897 q^{82} +(-2.82304 - 16.0103i) q^{83} +(2.95336 - 1.07494i) q^{85} +(-5.67128 - 4.75877i) q^{86} +(-7.88326 - 2.86927i) q^{88} +(-9.21291 - 15.9572i) q^{89} +(5.81180 - 10.0663i) q^{91} +(-1.93599 + 1.62449i) q^{92} +(0.673648 - 3.82045i) q^{94} +(-0.401975 + 2.27972i) q^{95} +(7.74763 - 6.50103i) q^{97} +(-3.51968 + 6.09627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q + 6 * q^4 + 6 * q^7	\( 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 + 6 * q^7 + 12 * q^10 + 6 * q^13 - 18 * q^16 + 24 * q^19 + 6 * q^22 - 48 * q^25 - 12 * q^28 - 12 * q^31 + 54 * q^34 + 6 * q^37 - 12 * q^40 - 12 * q^43 - 6 * q^46 + 42 * q^49 + 54 * q^52 - 60 * q^55 + 6 * q^58 - 48 * q^61 - 6 * q^64 - 66 * q^67 + 6 * q^70 - 12 * q^73 - 6 * q^76 + 42 * q^79 - 24 * q^82 - 18 * q^85 - 24 * q^88 + 6 * q^94 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more