LMFDB - Embedded newform 729.2.e.r.82.1

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			82.1
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.r.649.1

$q$-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	$-0.905367\pi$
$2$	−0.223238	−	1.26604i	−0.157853	−	0.895229i	0.798278	−	0.602289i	$-0.205745\pi$
$3$		0			0
$3$		0			0
$4$	0.326352	−	0.118782i	0.163176	−	0.0593912i
$5$	−0.342020	−	0.286989i	−0.152956	−	0.128345i	0.563098	−	0.826390i	$-0.309609\pi$
$5$	−0.342020	−	0.286989i	−0.152956	−	0.128345i	−0.716054	+	0.698045i	$0.754054\pi$
$6$		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	−0.262553	−	0.964918i	$-0.584564\pi$
$11$	2.12965	−	1.78699i	0.642114	−	0.538797i	0.904667	+	0.426120i	$0.140120\pi$
$12$		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	$0.492282\pi$
$17$	−3.51968	+	6.09627i	−0.853648	+	1.47856i	−0.877894	+	0.478856i	$0.841052\pi$
$18$		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	0.490102	−	0.871665i	$-0.336960\pi$
$23$	6.83807	−	2.48886i	1.42584	−	0.518962i	0.935735	+	0.352703i	$0.114737\pi$
$24$		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	$-0.946471\pi$
$29$	−0.628461	−	3.56418i	−0.116702	−	0.661851i	0.869191	−	0.494476i	$-0.164640\pi$
$30$		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	$-0.820517\pi$
$41$	0.844075	−	4.78699i	0.131822	−	0.747602i	0.977020	−	0.213148i	$-0.0683716\pi$
$42$		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	0.540445	−	0.841380i	$-0.318256\pi$
$47$	2.83564	+	1.03209i	0.413621	+	0.150546i	−0.126824	+	0.991925i	$0.540478\pi$
$48$		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	$-0.705798\pi$
$53$	−8.77141			−1.20485			−0.602423	+	0.798177i	$0.705798\pi$
$54$		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	0.482923	−	0.875663i	$-0.339575\pi$
$59$	−2.27038	−	1.90508i	−0.295579	−	0.248020i	−0.778501	+	0.627643i	$0.784020\pi$
$60$		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	−0.664492	−	0.747296i	$-0.731352\pi$
$71$	2.65366	−	4.59627i	0.314931	−	0.545476i	0.979423	+	0.201819i	$0.0646853\pi$
$72$		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	$0.295306\pi$
$83$	2.82304	+	16.0103i	0.309869	+	1.75736i	−0.289781	+	0.957093i	$0.593583\pi$
$84$		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	$0.264288\pi$
$89$	9.21291	+	15.9572i	0.976567	+	1.69146i	0.301902	+	0.953339i	$0.402378\pi$
$90$		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	0.242903	−	0.970051i	$-0.421900\pi$
$101$	−1.95529	−	0.711667i	−0.194558	−	0.0708135i	−0.437462	+	0.899237i	$0.644122\pi$
$102$		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	$-0.465532\pi$
$107$	2.23583			0.216146			0.108073	+	0.994143i	$0.465532\pi$
$108$		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	0.579931	−	0.814666i	$-0.303079\pi$
$113$	−1.29320	−	1.08512i	−0.121654	−	0.102080i	−0.701585	+	0.712586i	$0.747524\pi$
$114$		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	−0.459089	−	0.888390i	$-0.651824\pi$
$131$	−2.74378	+	0.998656i	−0.239726	+	0.0872530i	0.219364	+	0.975643i	$0.429602\pi$
$132$		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	$0.00819647\pi$
$137$	0.808718	+	4.58647i	0.0690934	+	0.391848i	−0.930575	+	0.366101i	$0.880692\pi$
$138$		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	$0.366023\pi$
$149$	−3.50973	+	19.9047i	−0.287528	+	1.63065i	−0.696112	+	0.717933i	$0.745088\pi$
$150$		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	0.872061	−	0.489398i	$-0.162783\pi$
$167$	6.99811	+	5.87211i	0.541530	+	0.454398i	−0.330531	+	0.943795i	$0.607228\pi$
$168$		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	−0.448544	−	0.893761i	$-0.648057\pi$
$173$	4.65284	−	3.90420i	0.353749	−	0.296831i	0.802293	+	0.596930i	$0.203613\pi$
$174$		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	−0.991661	−	0.128872i	$-0.958864\pi$
$179$	−5.14057	+	8.90373i	−0.384224	+	0.665496i	0.607437	+	0.794368i	$0.292198\pi$
$180$		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	$0.122535\pi$
$191$	2.54747	+	14.4474i	0.184329	+	1.04538i	−0.742486	+	0.669861i	$0.766354\pi$
$192$		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	0.980818	−	0.194926i	$-0.0624468\pi$
$197$	4.51384	+	7.81820i	0.321598	+	0.557024i	−0.659220	+	0.751950i	$0.729113\pi$
$198$		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	−0.870495	−	0.492178i	$-0.836201\pi$
$227$	−8.09002	+	6.78833i	−0.536954	+	0.450557i	0.333541	+	0.942736i	$0.391756\pi$
$228$		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	−0.995535	−	0.0943883i	$-0.969910\pi$
$233$	−6.35035	+	10.9991i	−0.416025	+	0.720576i	0.579510	+	0.814965i	$0.303244\pi$
$234$		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	−0.158000	−	0.987439i	$-0.550505\pi$
$239$	5.49865	−	2.00134i	0.355678	−	0.129456i	0.513678	+	0.857983i	$0.328282\pi$
$240$		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	0.952738	−	0.303792i	$-0.0982529\pi$
$251$	3.37895	+	5.85251i	0.213277	+	0.369407i	−0.739461	+	0.673199i	$0.764920\pi$
$252$		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	−0.958342	−	0.285622i	$-0.907800\pi$
$257$	0.639540	−	3.62701i	0.0398934	−	0.226247i	0.998236	+	0.0593754i	$0.0189109\pi$
$258$		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	0.234466	−	0.972124i	$-0.424666\pi$
$263$	−3.41847	−	1.24422i	−0.210792	−	0.0767220i	−0.445258	+	0.895402i	$0.646888\pi$
$264$		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	$-0.569315\pi$
$269$	−7.08672			−0.432085			−0.216042	+	0.976384i	$0.569315\pi$
$270$		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	0.0226955	−	0.999742i	$-0.492775\pi$
$281$	16.9506	−	14.2233i	1.01119	−	0.848490i	0.988495	+	0.151253i	$0.0483307\pi$
$282$		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	−0.797810	−	0.602909i	$-0.794008\pi$
$293$	−17.4840	+	6.36366i	−1.02143	+	0.371769i	−0.223616	+	0.974677i	$0.571786\pi$
$294$		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	$-0.748287\pi$
$311$	3.53990	−	20.0758i	0.200729	−	1.13839i	0.904020	−	0.427491i	$-0.140602\pi$
$312$		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	0.225586	−	0.974223i	$-0.427570\pi$
$317$	−4.05629	−	1.47637i	−0.227824	−	0.0829210i	−0.453410	+	0.891302i	$0.649793\pi$
$318$		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	−0.305085	−	0.952325i	$-0.598685\pi$
$347$	1.36635	−	0.497312i	0.0733496	−	0.0266971i	0.378434	+	0.925628i	$0.376463\pi$
$348$		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	$0.0348731\pi$
$353$	1.82888	+	10.3721i	0.0973416	+	0.552052i	−0.896663	+	0.442714i	$0.854016\pi$
$354$		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	0.604127	−	0.796888i	$-0.293522\pi$
$359$	−7.35273	−	12.7353i	−0.388062	−	0.672143i	−0.992189	+	0.124745i	$0.960189\pi$
$360$		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	$-0.805579\pi$
$383$	−29.8693	−	25.0633i	−1.52625	−	1.28067i	−0.707054	−	0.707160i	$-0.749976\pi$
$384$		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	−0.422556	−	0.906337i	$-0.638867\pi$
$389$	7.82288	−	6.56418i	0.396636	−	0.332817i	0.819192	+	0.573520i	$0.194422\pi$
$390$		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	0.188714	−	0.982032i	$-0.439568\pi$
$401$	19.3144	−	7.02987i	0.964515	−	0.351055i	0.775801	+	0.630977i	$0.217346\pi$
$402$		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	$-0.605998\pi$
$419$	6.21286	−	35.2349i	0.303518	−	1.72134i	0.630399	−	0.776271i	$-0.282891\pi$
$420$		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	$-0.426645\pi$
$431$	9.48411			0.456833			0.228417	+	0.973563i	$0.426645\pi$
$432$		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	−0.847836	−	0.530258i	$-0.822095\pi$
$443$	−9.95253	+	8.35117i	−0.472859	+	0.396776i	0.374977	+	0.927034i	$0.377651\pi$
$444$		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	−0.806236	−	0.591594i	$-0.798499\pi$
$449$	2.31428	−	4.00846i	0.109218	−	0.189171i	0.915454	+	0.402424i	$0.131832\pi$
$450$		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	$-0.769851\pi$
$461$	−5.82980	−	33.0624i	−0.271521	−	1.53987i	0.478280	−	0.878207i	$-0.341260\pi$
$462$		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	$-0.982532\pi$
$467$	−11.8154	−	20.4648i	−0.546750	−	0.946999i	0.451745	−	0.892147i	$-0.350802\pi$
$468$		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	0.465155	−	0.885229i	$-0.345999\pi$
$479$	5.52557	+	2.01114i	0.252470	+	0.0918915i	−0.212685	+	0.977121i	$0.568221\pi$
$480$		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	$-0.955538\pi$
$491$	−28.7912	−	24.1587i	−1.29933	−	1.09027i	−0.309068	−	0.951040i	$-0.600017\pi$
$492$		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	−0.578491	−	0.815689i	$-0.696358\pi$
$503$	9.35597	−	16.2050i	0.417162	−	0.722546i	0.995653	+	0.0931429i	$0.0296913\pi$
$504$		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	−0.752922	−	0.658109i	$-0.771356\pi$
$509$	−20.4554	+	7.44516i	−0.906670	+	0.330001i	−0.153747	+	0.988110i	$0.549134\pi$
$510$		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	0.928200	−	0.372081i	$-0.121356\pi$
$521$	3.23822	+	5.60876i	0.141869	+	0.245724i	−0.786332	+	0.617805i	$0.788022\pi$
$522$		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	−0.999983	−	0.00581674i	$-0.998148\pi$
$557$	−11.6813	+	20.2327i	−0.494954	+	0.857286i	0.505029	+	0.863102i	$0.331482\pi$
$558$		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	−0.907964	−	0.419048i	$-0.862364\pi$
$563$	−31.6561	+	11.5219i	−1.33415	+	0.485589i	−0.426182	+	0.904638i	$0.640142\pi$
$564$		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	$-0.832198\pi$
$569$	−5.34764	−	30.3280i	−0.224185	−	1.27142i	0.640052	−	0.768331i	$-0.278913\pi$
$570$		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	0.183469	−	0.983026i	$-0.441267\pi$
$587$	−7.45891	−	2.71482i	−0.307862	−	0.112053i	−0.491331	+	0.870973i	$0.663490\pi$
$588$		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	$-0.232533\pi$
$593$	36.2753			1.48965			0.744824	+	0.667261i	$0.232533\pi$
$594$		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	0.993414	−	0.114579i	$-0.0365521\pi$
$599$	25.7736	+	21.6266i	1.05308	+	0.883639i	0.0596658	+	0.998218i	$0.480996\pi$
$600$		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	−0.0827492	−	0.996570i	$-0.526370\pi$
$617$	12.2817	−	4.47019i	0.494444	−	0.179963i	0.577194	+	0.816607i	$0.304148\pi$
$618$		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	0.276133	−	0.961120i	$-0.410947\pi$
$641$	−3.29472	−	1.19918i	−0.130133	−	0.0473647i	−0.406266	+	0.913755i	$0.633169\pi$
$642$		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	$-0.519072\pi$
$647$	−3.04628			−0.119762			−0.0598808	+	0.998206i	$0.519072\pi$
$648$		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	0.0528264	−	0.998604i	$-0.483177\pi$
$653$	−23.5462	−	19.7576i	−0.921433	−	0.773174i	−0.974259	+	0.225430i	$0.927621\pi$
$654$		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	−0.985602	−	0.169082i	$-0.945920\pi$
$659$	−25.4204	+	21.3302i	−0.990237	+	0.830907i	−0.00463496	+	0.999989i	$0.501475\pi$
$660$		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	$-0.973990\pi$
$677$	−2.29029	−	12.9889i	−0.0880228	−	0.499202i	0.908640	−	0.417579i	$-0.137121\pi$
$678$		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	0.896530	−	0.442983i	$-0.146080\pi$
$683$	1.68907	+	2.92556i	0.0646305	+	0.111943i	−0.831900	+	0.554926i	$0.812746\pi$
$684$		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	$-0.170926\pi$
$701$	45.5001			1.71852			0.859258	+	0.511543i	$0.170926\pi$
$702$		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	$-0.461822\pi$
$719$	24.6591	−	42.7108i	0.919630	−	1.59285i	0.799978	−	0.600030i	$-0.204845\pi$
$720$		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	$0.391219\pi$
$743$	−8.23276	+	46.6903i	−0.302031	+	1.71290i	−0.637162	+	0.770730i	$0.719892\pi$
$744$		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	0.545175	−	0.838322i	$-0.316463\pi$
$761$	−5.12392	−	4.29948i	−0.185742	−	0.155856i	−0.730917	+	0.682466i	$0.760907\pi$
$762$		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	−0.759088	−	0.650988i	$-0.774355\pi$
$773$	5.12208	−	8.87170i	0.184228	−	0.319093i	0.943316	+	0.331895i	$0.107688\pi$
$774$		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	−0.955626	−	0.294584i	$-0.904819\pi$
$797$	1.21740	−	6.90420i	0.0431224	−	0.244559i	0.998748	+	0.0500247i	$0.0159300\pi$
$798$		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	$-0.791412\pi$
$809$	−45.1028			−1.58573			−0.792866	+	0.609396i	$0.791412\pi$
$810$		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	−0.555123	−	0.831768i	$-0.687329\pi$
$821$	4.80261	−	4.02987i	0.167612	−	0.140643i	0.722735	+	0.691125i	$0.242884\pi$
$822$		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	$-0.574354\pi$
$827$	20.9001	−	36.2001i	0.726769	−	1.25880i	0.958242	−	0.285960i	$-0.0923124\pi$
$828$		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	$0.113153\pi$
$839$	5.08559	+	28.8418i	0.175574	+	0.995731i	−0.761905	+	0.647689i	$0.775736\pi$
$840$		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	−0.168514	−	0.985699i	$-0.553897\pi$
$857$	−27.2604	−	9.92199i	−0.931199	−	0.338929i	−0.762685	+	0.646771i	$0.776119\pi$
$858$		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	$-0.756633\pi$
$863$	−42.4018			−1.44337			−0.721687	+	0.692219i	$0.756633\pi$
$864$		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	−0.963254	−	0.268591i	$-0.913442\pi$
$881$	−7.39133	+	12.8022i	−0.249020	+	0.431316i	0.714234	+	0.699907i	$0.246775\pi$
$882$		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	0.505132	−	0.863042i	$-0.331444\pi$
$887$	43.0905	−	15.6837i	1.44684	−	0.526606i	0.941706	+	0.336436i	$0.109222\pi$
$888$		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	0.747347	−	0.664434i	$-0.231327\pi$
$911$	26.9459	+	9.80752i	0.892759	+	0.324938i	0.145412	+	0.989371i	$0.453549\pi$
$912$		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	−0.466257	−	0.884649i	$-0.654398\pi$
$929$	9.87500	−	8.28611i	0.323988	−	0.271859i	0.790245	+	0.612791i	$0.209953\pi$
$930$		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	0.224820	−	0.974400i	$-0.427821\pi$
$941$	31.3927	−	11.4260i	1.02337	−	0.372478i	0.798554	+	0.601923i	$0.205598\pi$
$942$		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	$-0.974494\pi$
$947$	−2.69237	−	15.2692i	−0.0874903	−	0.496182i	0.909301	−	0.416139i	$-0.136617\pi$
$948$		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	0.624194	−	0.781269i	$-0.285427\pi$
$953$	−11.2524	−	19.4898i	−0.364502	−	0.631336i	−0.988696	+	0.149933i	$0.952094\pi$
$954$		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	$-0.304807\pi$
$971$	35.8662			1.15100			0.575501	+	0.817801i	$0.304807\pi$
$972$		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	0.798512	−	0.601979i	$-0.205621\pi$
$977$	10.7630	+	9.03121i	0.344338	+	0.288934i	−0.454174	+	0.890913i	$0.650065\pi$
$978$		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	−0.832781	−	0.553603i	$-0.813253\pi$
$983$	−13.5507	+	11.3704i	−0.432199	+	0.362658i	0.400582	+	0.916261i	$0.368808\pi$
$984$		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.82.1		12
3.2	odd	2	inner	729.2.e.r.82.2		12
9.2	odd	6		729.2.e.m.325.2		12
9.4	even	3		729.2.e.q.568.2		12
9.5	odd	6		729.2.e.q.568.1		12
9.7	even	3		729.2.e.m.325.1		12
27.2	odd	18	inner	729.2.e.r.649.2		12
27.4	even	9		729.2.c.c.487.5		12
27.5	odd	18		729.2.a.c.1.5	yes	6
27.7	even	9		729.2.e.m.406.1		12
27.11	odd	18		729.2.e.q.163.1		12
27.13	even	9		729.2.c.c.244.5		12
27.14	odd	18		729.2.c.c.244.2		12
27.16	even	9		729.2.e.q.163.2		12
27.20	odd	18		729.2.e.m.406.2		12
27.22	even	9		729.2.a.c.1.2	✓	6
27.23	odd	18		729.2.c.c.487.2		12
27.25	even	9	inner	729.2.e.r.649.1		12

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

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