LMFDB - Embedded newform 324.2.l.a.35.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.16
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37686 + 0.322907i) q^{2} +(1.79146 + 0.889191i) q^{4} +(1.27150 - 3.49343i) q^{5} +(-1.63150 - 0.287677i) q^{7} +(2.17946 + 1.80276i) q^{8} +O(q^{10})$	\(q+(1.37686 + 0.322907i) q^{2} +(1.79146 + 0.889191i) q^{4} +(1.27150 - 3.49343i) q^{5} +(-1.63150 - 0.287677i) q^{7} +(2.17946 + 1.80276i) q^{8} +(2.87873 - 4.39937i) q^{10} +(-0.526615 + 0.191672i) q^{11} +(1.99017 - 1.66995i) q^{13} +(-2.15344 - 0.922910i) q^{14} +(2.41868 + 3.18591i) q^{16} +(-4.50885 + 2.60318i) q^{17} +(0.925473 + 0.534322i) q^{19} +(5.38418 - 5.12774i) q^{20} +(-0.786966 + 0.0938576i) q^{22} +(1.54747 + 8.77613i) q^{23} +(-6.75711 - 5.66989i) q^{25} +(3.27942 - 1.65664i) q^{26} +(-2.66696 - 1.96607i) q^{28} +(0.702597 - 0.837323i) q^{29} +(-3.17422 + 0.559701i) q^{31} +(2.30142 + 5.16754i) q^{32} +(-7.04862 + 2.12827i) q^{34} +(-3.07943 + 5.33373i) q^{35} +(3.17849 + 5.50530i) q^{37} +(1.10171 + 1.03453i) q^{38} +(9.06902 - 5.32157i) q^{40} +(0.556211 + 0.662866i) q^{41} +(-0.690832 - 1.89805i) q^{43} +(-1.11385 - 0.124888i) q^{44} +(-0.703229 + 12.5832i) q^{46} +(1.22624 - 6.95438i) q^{47} +(-3.99883 - 1.45545i) q^{49} +(-7.47272 - 9.98853i) q^{50} +(5.05022 - 1.22201i) q^{52} +6.80497i q^{53} +2.08341i q^{55} +(-3.03717 - 3.56818i) q^{56} +(1.23775 - 0.925999i) q^{58} +(-8.57009 - 3.11926i) q^{59} +(0.832127 - 4.71923i) q^{61} +(-4.55118 - 0.254350i) q^{62} +(1.50009 + 7.85810i) q^{64} +(-3.30335 - 9.07588i) q^{65} +(-7.06749 - 8.42270i) q^{67} +(-10.3922 + 0.654280i) q^{68} +(-5.96223 + 6.34941i) q^{70} +(-3.98206 - 6.89713i) q^{71} +(1.92588 - 3.33572i) q^{73} +(2.59862 + 8.60636i) q^{74} +(1.18284 + 1.78014i) q^{76} +(0.914311 - 0.161218i) q^{77} +(-6.28979 + 7.49588i) q^{79} +(14.2051 - 4.39859i) q^{80} +(0.551778 + 1.09228i) q^{82} +(1.28797 + 1.08073i) q^{83} +(3.36102 + 19.0613i) q^{85} +(-0.338285 - 2.83641i) q^{86} +(-1.49328 - 0.531621i) q^{88} +(10.9229 + 6.30632i) q^{89} +(-3.72736 + 2.15199i) q^{91} +(-5.03143 + 17.0981i) q^{92} +(3.93398 - 9.17921i) q^{94} +(3.04336 - 2.55368i) q^{95} +(3.74927 - 1.36462i) q^{97} +(-5.03583 - 3.29520i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	1.37686	+	0.322907i	0.973584	+	0.228329i
$2$	1.37686	+	0.322907i	0.973584	+	0.228329i
$3$		0			0
$3$		0			0
$4$	1.79146	+	0.889191i	0.895731	+	0.444596i
$5$	1.27150	−	3.49343i	0.568634	−	1.56231i	−0.238004	−	0.971264i	$-0.576493\pi$
$5$	1.27150	−	3.49343i	0.568634	−	1.56231i	0.806638	−	0.591045i	$-0.201285\pi$
$6$		0			0
$7$	−1.63150	−	0.287677i	−0.616647	−	0.108732i	−0.143405	−	0.989664i	$-0.545805\pi$
$7$	−1.63150	−	0.287677i	−0.616647	−	0.108732i	−0.473242	+	0.880932i	$0.656916\pi$
$8$	2.17946	+	1.80276i	0.770555	+	0.637373i
$9$		0			0
$10$	2.87873	−	4.39937i	0.910334	−	1.39120i
$11$	−0.526615	+	0.191672i	−0.158781	+	0.0577914i	−0.420188	−	0.907437i	$-0.638036\pi$
$11$	−0.526615	+	0.191672i	−0.158781	+	0.0577914i	0.261407	+	0.965229i	$0.415814\pi$
$12$		0			0
$13$	1.99017	−	1.66995i	0.551974	−	0.463161i	−0.323635	−	0.946182i	$-0.604905\pi$
$13$	1.99017	−	1.66995i	0.551974	−	0.463161i	0.875609	+	0.483021i	$0.160460\pi$
$14$	−2.15344	−	0.922910i	−0.575531	−	0.246658i
$15$		0			0
$16$	2.41868	+	3.18591i	0.604669	+	0.796477i
$17$	−4.50885	+	2.60318i	−1.09356	+	0.631365i	−0.934521	−	0.355908i	$-0.884172\pi$
$17$	−4.50885	+	2.60318i	−1.09356	+	0.631365i	−0.159035	+	0.987273i	$0.550838\pi$
$18$		0			0
$19$	0.925473	+	0.534322i	0.212318	+	0.122582i	0.602388	−	0.798203i	$-0.294216\pi$
$19$	0.925473	+	0.534322i	0.212318	+	0.122582i	−0.390070	+	0.920785i	$0.627549\pi$
$20$	5.38418	−	5.12774i	1.20394	−	1.14660i
$21$		0			0
$22$	−0.786966	+	0.0938576i	−0.167782	+	0.0200105i
$23$	1.54747	+	8.77613i	0.322670	+	1.82995i	0.525570	+	0.850751i	$0.323852\pi$
$23$	1.54747	+	8.77613i	0.322670	+	1.82995i	−0.202900	+	0.979199i	$0.565037\pi$
$24$		0			0
$25$	−6.75711	−	5.66989i	−1.35142	−	1.13398i
$26$	3.27942	−	1.65664i	0.643147	−	0.324895i
$27$		0			0
$28$	−2.66696	−	1.96607i	−0.504009	−	0.371553i
$29$	0.702597	−	0.837323i	0.130469	−	0.155487i	−0.696855	−	0.717212i	$-0.745418\pi$
$29$	0.702597	−	0.837323i	0.130469	−	0.155487i	0.827324	+	0.561725i	$0.189862\pi$
$30$		0			0
$31$	−3.17422	+	0.559701i	−0.570107	+	0.100525i	−0.451269	−	0.892388i	$-0.649028\pi$
$31$	−3.17422	+	0.559701i	−0.570107	+	0.100525i	−0.118839	+	0.992914i	$0.537917\pi$
$32$	2.30142	+	5.16754i	0.406837	+	0.913501i
$33$		0			0
$34$	−7.04862	+	2.12827i	−1.20883	+	0.364996i
$35$	−3.07943	+	5.33373i	−0.520519	+	0.901566i
$36$		0			0
$37$	3.17849	+	5.50530i	0.522540	+	0.905066i	0.999656	+	0.0262257i	$0.00834884\pi$
$37$	3.17849	+	5.50530i	0.522540	+	0.905066i	−0.477116	+	0.878840i	$0.658318\pi$
$38$	1.10171	+	1.03453i	0.178720	+	0.167822i
$39$		0			0
$40$	9.06902	−	5.32157i	1.43394	−	0.841414i
$41$	0.556211	+	0.662866i	0.0868655	+	0.103522i	0.807726	−	0.589557i	$-0.200698\pi$
$41$	0.556211	+	0.662866i	0.0868655	+	0.103522i	−0.720861	+	0.693080i	$0.756253\pi$
$42$		0			0
$43$	−0.690832	−	1.89805i	−0.105351	−	0.289449i	0.875806	−	0.482664i	$-0.160331\pi$
$43$	−0.690832	−	1.89805i	−0.105351	−	0.289449i	−0.981156	+	0.193215i	$0.938109\pi$
$44$	−1.11385	−	0.124888i	−0.167919	−	0.0188276i
$45$		0			0
$46$	−0.703229	+	12.5832i	−0.103685	+	1.85528i
$47$	1.22624	−	6.95438i	0.178866	−	1.01440i	−0.754720	−	0.656047i	$-0.772227\pi$
$47$	1.22624	−	6.95438i	0.178866	−	1.01440i	0.933586	−	0.358353i	$-0.116662\pi$
$48$		0			0
$49$	−3.99883	−	1.45545i	−0.571261	−	0.207922i
$50$	−7.47272	−	9.98853i	−1.05680	−	1.41259i
$51$		0			0
$52$	5.05022	−	1.22201i	0.700340	−	0.169463i
$53$			6.80497i			0.934734i	0.884063	+	0.467367i	$0.154797\pi$
$53$			6.80497i			0.934734i	−0.884063	+	0.467367i	$0.845203\pi$
$54$		0			0
$55$			2.08341i			0.280926i
$56$	−3.03717	−	3.56818i	−0.405858	−	0.476818i
$57$		0			0
$58$	1.23775	−	0.925999i	0.162525	−	0.121590i
$59$	−8.57009	−	3.11926i	−1.11573	−	0.406093i	−0.282639	−	0.959226i	$-0.591210\pi$
$59$	−8.57009	−	3.11926i	−1.11573	−	0.406093i	−0.833093	+	0.553134i	$0.813432\pi$
$60$		0			0
$61$	0.832127	−	4.71923i	0.106543	−	0.604235i	−0.884050	−	0.467393i	$-0.845193\pi$
$61$	0.832127	−	4.71923i	0.106543	−	0.604235i	0.990593	−	0.136842i	$-0.0436954\pi$
$62$	−4.55118	−	0.254350i	−0.578000	−	0.0323024i
$63$		0			0
$64$	1.50009	+	7.85810i	0.187511	+	0.982262i
$65$	−3.30335	−	9.07588i	−0.409730	−	1.12572i
$66$		0			0
$67$	−7.06749	−	8.42270i	−0.863431	−	1.02900i	−0.999268	−	0.0382656i	$-0.987817\pi$
$67$	−7.06749	−	8.42270i	−0.863431	−	1.02900i	0.135837	−	0.990731i	$-0.456628\pi$
$68$	−10.3922	+	0.654280i	−1.26023	+	0.0793431i
$69$		0			0
$70$	−5.96223	+	6.34941i	−0.712623	+	0.758900i
$71$	−3.98206	−	6.89713i	−0.472583	−	0.818538i	0.526924	−	0.849912i	$-0.323345\pi$
$71$	−3.98206	−	6.89713i	−0.472583	−	0.818538i	−0.999508	+	0.0313737i	$0.990012\pi$
$72$		0			0
$73$	1.92588	−	3.33572i	0.225407	−	0.390416i	−0.731035	−	0.682340i	$-0.760962\pi$
$73$	1.92588	−	3.33572i	0.225407	−	0.390416i	0.956441	+	0.291924i	$0.0942955\pi$
$74$	2.59862	+	8.60636i	0.302083	+	1.00047i
$75$		0			0
$76$	1.18284	+	1.78014i	0.135681	+	0.204196i
$77$	0.914311	−	0.161218i	0.104195	−	0.0183725i
$78$		0			0
$79$	−6.28979	+	7.49588i	−0.707657	+	0.843353i	−0.993370	−	0.114963i	$-0.963325\pi$
$79$	−6.28979	+	7.49588i	−0.707657	+	0.843353i	0.285713	+	0.958315i	$0.407770\pi$
$80$	14.2051	−	4.39859i	1.58818	−	0.491777i
$81$		0			0
$82$	0.551778	+	1.09228i	0.0609337	+	0.120622i
$83$	1.28797	+	1.08073i	0.141373	+	0.118626i	0.710732	−	0.703463i	$-0.248364\pi$
$83$	1.28797	+	1.08073i	0.141373	+	0.118626i	−0.569359	+	0.822089i	$0.692809\pi$
$84$		0			0
$85$	3.36102	+	19.0613i	0.364554	+	2.06749i
$86$	−0.338285	−	2.83641i	−0.0364782	−	0.305858i
$87$		0			0
$88$	−1.49328	−	0.531621i	−0.159184	−	0.0566710i
$89$	10.9229	+	6.30632i	1.15782	+	0.668469i	0.950781	−	0.309864i	$-0.100283\pi$
$89$	10.9229	+	6.30632i	1.15782	+	0.668469i	0.207041	+	0.978332i	$0.433617\pi$
$90$		0			0
$91$	−3.72736	+	2.15199i	−0.390734	+	0.225590i
$92$	−5.03143	+	17.0981i	−0.524563	+	1.78260i
$93$		0			0
$94$	3.93398	−	9.17921i	0.405759	−	0.946763i
$95$	3.04336	−	2.55368i	0.312242	−	0.262002i
$96$		0			0
$97$	3.74927	−	1.36462i	0.380681	−	0.138556i	−0.144590	−	0.989492i	$-0.546186\pi$
$97$	3.74927	−	1.36462i	0.380681	−	0.138556i	0.525271	+	0.850935i	$0.323964\pi$
$98$	−5.03583	−	3.29520i	−0.508696	−	0.332865i
$99$		0			0
$100$	−7.06349	−	16.1658i	−0.706349	−	1.61658i
$101$	−7.58285	−	1.33706i	−0.754522	−	0.133043i	−0.216860	−	0.976203i	$-0.569581\pi$
$101$	−7.58285	−	1.33706i	−0.754522	−	0.133043i	−0.537662	+	0.843160i	$0.680693\pi$
$102$		0			0
$103$	1.02587	−	2.81855i	0.101082	−	0.277720i	−0.878835	−	0.477125i	$-0.841679\pi$
$103$	1.02587	−	2.81855i	0.101082	−	0.277720i	0.979917	+	0.199405i	$0.0639011\pi$
$104$	7.34803	−	0.0517862i	0.720533	−	0.00507806i
$105$		0			0
$106$	−2.19737	+	9.36946i	−0.213427	+	0.910042i
$107$	11.8919			1.14963			0.574815	−	0.818283i	$-0.305074\pi$
$107$	11.8919			1.14963			0.574815	+	0.818283i	$0.305074\pi$
$108$		0			0
$109$	9.26570			0.887493			0.443747	−	0.896152i	$-0.353649\pi$
$109$	9.26570			0.887493			0.443747	+	0.896152i	$0.353649\pi$
$110$	−0.672746	+	2.86855i	−0.0641438	+	0.273506i
$111$		0			0
$112$	−3.02955	−	5.89359i	−0.286266	−	0.556892i
$113$	1.92797	−	5.29705i	0.181368	−	0.498304i	−0.815376	−	0.578931i	$-0.803470\pi$
$113$	1.92797	−	5.29705i	0.181368	−	0.498304i	0.996744	+	0.0806268i	$0.0256922\pi$
$114$		0			0
$115$	32.6264	+	5.75292i	3.04243	+	0.536462i
$116$	2.00322	−	0.875289i	0.185994	−	0.0812686i
$117$		0			0
$118$	−10.7926	−	7.06211i	−0.993535	−	0.650120i
$119$	8.10504	−	2.94999i	0.742988	−	0.270426i
$120$		0			0
$121$	−8.18590	+	6.86879i	−0.744173	+	0.624435i
$122$	2.66959	−	6.22899i	0.241693	−	0.563947i
$123$		0			0
$124$	−6.18419	−	1.81981i	−0.555356	−	0.163424i
$125$	−12.3012	+	7.10212i	−1.10026	+	0.635233i
$126$		0			0
$127$	7.01988	+	4.05293i	0.622914	+	0.359639i	0.778002	−	0.628261i	$-0.216233\pi$
$127$	7.01988	+	4.05293i	0.622914	+	0.359639i	−0.155089	+	0.987901i	$0.549566\pi$
$128$	−0.472023	+	11.3039i	−0.0417213	+	0.999129i
$129$		0			0
$130$	−1.61757	−	13.5628i	−0.141871	−	1.18954i
$131$	−1.61022	−	9.13203i	−0.140686	−	0.797869i	−0.970730	−	0.240172i	$-0.922796\pi$
$131$	−1.61022	−	9.13203i	−0.140686	−	0.797869i	0.830044	−	0.557697i	$-0.188315\pi$
$132$		0			0
$133$	−1.35619	−	1.13798i	−0.117597	−	0.0986755i
$134$	−7.01116	−	13.8790i	−0.605672	−	1.19896i
$135$		0			0
$136$	−14.5198	−	2.45485i	−1.24506	−	0.210501i
$137$	2.22025	−	2.64599i	0.189689	−	0.226062i	−0.662815	−	0.748783i	$-0.730638\pi$
$137$	2.22025	−	2.64599i	0.189689	−	0.226062i	0.852504	+	0.522721i	$0.175083\pi$
$138$		0			0
$139$	5.28870	−	0.932540i	0.448581	−	0.0790970i	0.0552061	−	0.998475i	$-0.482418\pi$
$139$	5.28870	−	0.932540i	0.448581	−	0.0790970i	0.393375	+	0.919378i	$0.371307\pi$
$140$	−10.2594	+	6.81698i	−0.867078	+	0.576140i
$141$		0			0
$142$	−3.25559	−	10.7822i	−0.273203	−	0.904821i
$143$	−0.727971	+	1.26088i	−0.0608760	+	0.105440i
$144$		0			0
$145$	−2.03177	−	3.51913i	−0.168730	−	0.292248i
$146$	3.72878	−	3.97092i	0.308596	−	0.328636i
$147$		0			0
$148$	0.798876	+	12.6888i	0.0656672	+	1.04302i
$149$	7.36478	+	8.77701i	0.603346	+	0.719040i	0.978112	−	0.208079i	$-0.0667212\pi$
$149$	7.36478	+	8.77701i	0.603346	+	0.719040i	−0.374766	+	0.927120i	$0.622277\pi$
$150$		0			0
$151$	−7.80528	−	21.4448i	−0.635185	−	1.74516i	−0.666348	−	0.745641i	$-0.732143\pi$
$151$	−7.80528	−	21.4448i	−0.635185	−	1.74516i	0.0311634	−	0.999514i	$-0.490079\pi$
$152$	1.05378	+	2.83294i	0.0854725	+	0.229782i
$153$		0			0
$154$	1.31093	+	0.0732635i	0.105638	+	0.00590374i
$155$	−2.08076	+	11.8006i	−0.167131	+	0.947846i
$156$		0			0
$157$	−7.79694	−	2.83786i	−0.622264	−	0.226485i	0.0115969	−	0.999933i	$-0.496309\pi$
$157$	−7.79694	−	2.83786i	−0.622264	−	0.226485i	−0.633861	+	0.773447i	$0.718531\pi$
$158$	−11.0806	+	8.28973i	−0.881525	+	0.659496i
$159$		0			0
$160$	20.9787	−	1.46930i	1.65851	−	0.116158i
$161$		−	14.7634i		−	1.16352i
$162$		0			0
$163$			8.81551i			0.690484i	0.938514	+	0.345242i	$0.112203\pi$
$163$			8.81551i			0.690484i	−0.938514	+	0.345242i	$0.887797\pi$
$164$	0.407016	+	1.68208i	0.0317826	+	0.131348i
$165$		0			0
$166$	1.42437	+	1.90390i	0.110552	+	0.147772i
$167$	21.1905	+	7.71271i	1.63977	+	0.596828i	0.986999	−	0.160727i	$-0.0513838\pi$
$167$	21.1905	+	7.71271i	1.63977	+	0.596828i	0.652772	+	0.757555i	$0.273606\pi$
$168$		0			0
$169$	−1.08538	+	6.15552i	−0.0834911	+	0.473502i
$170$	−1.52738	+	27.3300i	−0.117144	+	2.09611i
$171$		0			0
$172$	0.450126	−	4.01456i	0.0343218	−	0.306107i
$173$	3.50842	+	9.63931i	0.266740	+	0.732863i	0.998674	+	0.0514871i	$0.0163961\pi$
$173$	3.50842	+	9.63931i	0.266740	+	0.732863i	−0.731933	+	0.681376i	$0.761382\pi$
$174$		0			0
$175$	9.39310	+	11.1943i	0.710052	+	0.846207i
$176$	−1.88436	−	1.21415i	−0.142039	−	0.0915203i
$177$		0			0
$178$	13.0029	+	12.2100i	0.974606	+	0.915175i
$179$	−7.25044	−	12.5581i	−0.541923	−	0.938639i	−0.998794	−	0.0491053i	$-0.984363\pi$
$179$	−7.25044	−	12.5581i	−0.541923	−	0.938639i	0.456870	−	0.889533i	$-0.348970\pi$
$180$		0			0
$181$	−2.64382	+	4.57923i	−0.196513	+	0.340371i	−0.947396	−	0.320065i	$-0.896295\pi$
$181$	−2.64382	+	4.57923i	−0.196513	+	0.340371i	0.750882	+	0.660436i	$0.229629\pi$
$182$	−5.82693	+	1.75940i	−0.431921	+	0.130415i
$183$		0			0
$184$	−12.4486	+	21.9169i	−0.917726	+	1.61574i
$185$	23.2738	−	4.10381i	1.71113	−	0.301718i
$186$		0			0
$187$	1.87547	−	2.23510i	0.137148	−	0.163447i
$188$	8.38054	−	11.3681i	0.611214	−	0.829107i
$189$		0			0
$190$	5.01487	−	2.53333i	0.363817	−	0.183787i
$191$	−8.98845	−	7.54221i	−0.650381	−	0.545735i	0.256805	−	0.966463i	$-0.417330\pi$
$191$	−8.98845	−	7.54221i	−0.650381	−	0.545735i	−0.907187	+	0.420728i	$0.861775\pi$
$192$		0			0
$193$	−4.02043	−	22.8010i	−0.289397	−	1.64125i	−0.689144	−	0.724624i	$-0.742013\pi$
$193$	−4.02043	−	22.8010i	−0.289397	−	1.64125i	0.399748	−	0.916625i	$-0.369098\pi$
$194$	5.60285	−	0.668225i	0.402261	−	0.0479757i
$195$		0			0
$196$	−5.86957	−	6.16311i	−0.419255	−	0.440222i
$197$	0.386490	+	0.223140i	0.0275363	+	0.0158981i	0.513705	−	0.857967i	$-0.328273\pi$
$197$	0.386490	+	0.223140i	0.0275363	+	0.0158981i	−0.486169	+	0.873865i	$0.661606\pi$
$198$		0			0
$199$	9.88191	−	5.70532i	0.700510	−	0.404440i	−0.107027	−	0.994256i	$-0.534133\pi$
$199$	9.88191	−	5.70532i	0.700510	−	0.404440i	0.807537	+	0.589816i	$0.200800\pi$
$200$	−4.50538	−	24.5388i	−0.318579	−	1.73515i
$201$		0			0
$202$	−10.0087	−	4.28949i	−0.704213	−	0.301808i
$203$	−1.38716	+	1.16397i	−0.0973597	+	0.0816945i
$204$		0			0
$205$	3.02290	−	1.10025i	0.211129	−	0.0768445i
$206$	2.32260	−	3.54947i	0.161823	−	0.247304i
$207$		0			0
$208$	10.1339	+	2.30142i	0.702659	+	0.159575i
$209$	−0.589783	−	0.103995i	−0.0407962	−	0.00719346i
$210$		0			0
$211$	−1.98697	+	5.45916i	−0.136789	+	0.375824i	−0.989107	−	0.147200i	$-0.952974\pi$
$211$	−1.98697	+	5.45916i	−0.136789	+	0.375824i	0.852318	+	0.523024i	$0.175196\pi$
$212$	−6.05092	+	12.1908i	−0.415579	+	0.837271i
$213$		0			0
$214$	16.3734	+	3.83996i	1.11926	+	0.262494i
$215$	−7.50908			−0.512115
$216$		0			0
$217$	5.33975			0.362486
$218$	12.7575	+	2.99196i	0.864049	+	0.202641i
$219$		0			0
$220$	−1.85255	+	3.73235i	−0.124899	+	0.251635i
$221$	−4.62619	+	12.7103i	−0.311191	+	0.854990i
$222$		0			0
$223$	−3.66426	−	0.646109i	−0.245377	−	0.0432666i	0.0496067	−	0.998769i	$-0.484203\pi$
$223$	−3.66426	−	0.646109i	−0.245377	−	0.0432666i	−0.294984	+	0.955502i	$0.595314\pi$
$224$	−2.26818	−	9.09288i	−0.151549	−	0.607544i
$225$		0			0
$226$	4.36498	−	6.67072i	0.290354	−	0.443729i
$227$	6.21679	−	2.26273i	0.412623	−	0.150183i	−0.127364	−	0.991856i	$-0.540652\pi$
$227$	6.21679	−	2.26273i	0.412623	−	0.150183i	0.539987	+	0.841674i	$0.318429\pi$
$228$		0			0
$229$	0.885467	−	0.742995i	0.0585133	−	0.0490985i	−0.613062	−	0.790035i	$-0.710062\pi$
$229$	0.885467	−	0.742995i	0.0585133	−	0.0490985i	0.671575	+	0.740936i	$0.265618\pi$
$230$	43.0642	+	18.4562i	2.83957	+	1.21697i
$231$		0			0
$232$	3.04078	−	0.558295i	0.199637	−	0.0366539i
$233$	14.7446	−	8.51281i	0.965953	−	0.557693i	0.0679527	−	0.997689i	$-0.478353\pi$
$233$	14.7446	−	8.51281i	0.965953	−	0.557693i	0.898000	+	0.439996i	$0.145020\pi$
$234$		0			0
$235$	−22.7355	−	13.1263i	−1.48310	−	0.856267i
$236$	−12.5794	−	13.2085i	−0.818848	−	0.859799i
$237$		0			0
$238$	12.1120	−	1.44455i	0.785107	−	0.0936360i
$239$	0.209499	+	1.18813i	0.0135514	+	0.0768536i	0.990833	−	0.135089i	$-0.0431321\pi$
$239$	0.209499	+	1.18813i	0.0135514	+	0.0768536i	−0.977282	+	0.211943i	$0.932021\pi$
$240$		0			0
$241$	−7.65607	−	6.42420i	−0.493171	−	0.413819i	0.361990	−	0.932182i	$-0.382097\pi$
$241$	−7.65607	−	6.42420i	−0.493171	−	0.413819i	−0.855161	+	0.518363i	$0.826542\pi$
$242$	−13.4888	+	6.81405i	−0.867092	+	0.438024i
$243$		0			0
$244$	5.68702	−	7.71440i	0.364074	−	0.493864i
$245$	−10.1691	+	12.1190i	−0.649677	+	0.774255i
$246$		0			0
$247$	2.73414	−	0.482103i	0.173969	−	0.0306755i
$248$	−7.92710	−	4.50253i	−0.503372	−	0.285911i
$249$		0			0
$250$	−19.2303	+	5.80645i	−1.21623	+	0.367232i
$251$	−6.65375	+	11.5246i	−0.419981	+	0.727429i	−0.995937	−	0.0900521i	$-0.971297\pi$
$251$	−6.65375	+	11.5246i	−0.419981	+	0.727429i	0.575956	+	0.817481i	$0.304630\pi$
$252$		0			0
$253$	−2.49706	−	4.32504i	−0.156989	−	0.271913i
$254$	8.35664	+	7.84706i	0.524342	+	0.492369i
$255$		0			0
$256$	−4.30000	+	15.4114i	−0.268750	+	0.963210i
$257$	−8.91483	−	10.6243i	−0.556092	−	0.662725i	0.412623	−	0.910902i	$-0.364613\pi$
$257$	−8.91483	−	10.6243i	−0.556092	−	0.662725i	−0.968715	+	0.248178i	$0.920168\pi$
$258$		0			0
$259$	−3.60194	−	9.89625i	−0.223814	−	0.614923i
$260$	2.15236	−	19.1964i	0.133484	−	1.19051i
$261$		0			0
$262$	0.731747	−	13.0934i	0.0452075	−	0.808916i
$263$	0.425181	−	2.41132i	0.0262178	−	0.148688i	−0.968889	−	0.247497i	$-0.920392\pi$
$263$	0.425181	−	2.41132i	0.0262178	−	0.148688i	0.995106	+	0.0988085i	$0.0315031\pi$
$264$		0			0
$265$	23.7727	+	8.65255i	1.46034	+	0.531522i
$266$	−1.49982	−	2.00476i	−0.0919599	−	0.122920i
$267$		0			0
$268$	−5.17175	−	21.3733i	−0.315915	−	1.30558i
$269$		−	4.12106i		−	0.251266i	−0.992077	−	0.125633i	$-0.959904\pi$
$269$		−	4.12106i		−	0.251266i	0.992077	−	0.125633i	$-0.0400961\pi$
$270$		0			0
$271$		−	11.9859i		−	0.728089i	−0.931382	−	0.364044i	$-0.881396\pi$
$271$		−	11.9859i		−	0.728089i	0.931382	−	0.364044i	$-0.118604\pi$
$272$	−19.1990	−	8.06850i	−1.16411	−	0.489225i
$273$		0			0
$274$	3.91137	−	2.92622i	0.236295	−	0.176779i
$275$	4.64516	+	1.69070i	0.280114	+	0.101953i
$276$		0			0
$277$	−5.21533	+	29.5776i	−0.313359	+	1.77715i	0.267921	+	0.963441i	$0.413664\pi$
$277$	−5.21533	+	29.5776i	−0.313359	+	1.77715i	−0.581279	+	0.813704i	$0.697448\pi$
$278$	7.58289	+	0.423782i	0.454792	+	0.0254167i
$279$		0			0
$280$	−16.3270	+	6.07317i	−0.975722	+	0.362941i
$281$	−2.37006	−	6.51169i	−0.141386	−	0.388455i	0.848708	−	0.528862i	$-0.177381\pi$
$281$	−2.37006	−	6.51169i	−0.141386	−	0.388455i	−0.990094	+	0.140407i	$0.955159\pi$
$282$		0			0
$283$	12.1288	+	14.4545i	0.720981	+	0.859232i	0.994726	−	0.102571i	$-0.0327068\pi$
$283$	12.1288	+	14.4545i	0.720981	+	0.859232i	−0.273745	+	0.961802i	$0.588262\pi$
$284$	−1.00084	−	15.8968i	−0.0593891	−	0.943299i
$285$		0			0
$286$	−1.40946	+	1.50099i	−0.0833430	+	0.0887553i
$287$	−0.716765	−	1.24147i	−0.0423093	−	0.0732818i
$288$		0			0
$289$	5.05314	−	8.75230i	0.297244	−	0.514841i
$290$	−1.66111	−	5.50141i	−0.0975436	−	0.323054i
$291$		0			0
$292$	6.41623	−	4.26334i	0.375481	−	0.249493i
$293$	−20.8109	+	3.66952i	−1.21578	+	0.214375i	−0.744510	−	0.667612i	$-0.767317\pi$
$293$	−20.8109	+	3.66952i	−1.21578	+	0.214375i	−0.471274	+	0.881987i	$0.656206\pi$
$294$		0			0
$295$	−21.7938	+	25.9729i	−1.26889	+	1.51220i
$296$	−2.99737	+	17.7286i	−0.174218	+	1.03046i
$297$		0			0
$298$	7.30609	+	14.4628i	0.423230	+	0.837808i
$299$	17.7354	+	14.8818i	1.02567	+	0.860637i
$300$		0			0
$301$	0.581066	+	3.29539i	0.0334921	+	0.189943i
$302$	−3.82207	−	32.0468i	−0.219935	−	1.84409i
$303$		0			0
$304$	0.536121	+	4.24082i	0.0307486	+	0.243228i
$305$	−15.4282	−	8.90750i	−0.883418	−	0.510042i
$306$		0			0
$307$	−17.4037	+	10.0480i	−0.993279	+	0.573470i	−0.906253	−	0.422736i	$-0.861070\pi$
$307$	−17.4037	+	10.0480i	−0.993279	+	0.573470i	−0.0870262	+	0.996206i	$0.527736\pi$
$308$	1.78131	+	0.524182i	0.101499	+	0.0298680i
$309$		0			0
$310$	−6.67540	+	15.5758i	−0.379137	+	0.884647i
$311$	−19.9629	+	16.7508i	−1.13199	+	0.949853i	−0.999147	−	0.0412837i	$-0.986855\pi$
$311$	−19.9629	+	16.7508i	−1.13199	+	0.949853i	−0.132844	+	0.991137i	$0.542411\pi$
$312$		0			0
$313$	22.8210	−	8.30617i	1.28992	−	0.469493i	0.396219	−	0.918156i	$-0.370322\pi$
$313$	22.8210	−	8.30617i	1.28992	−	0.469493i	0.893701	+	0.448663i	$0.148100\pi$
$314$	−9.81890	−	6.42500i	−0.554113	−	0.362584i
$315$		0			0
$316$	−17.9332	+	7.83576i	−1.00882	+	0.440796i
$317$	−6.07999	−	1.07207i	−0.341486	−	0.0602132i	0.000275215	−	1.00000i	$-0.499912\pi$
$317$	−6.07999	−	1.07207i	−0.341486	−	0.0602132i	−0.341762	+	0.939787i	$0.611024\pi$
$318$		0			0
$319$	−0.209507	+	0.575616i	−0.0117301	+	0.0322283i
$320$	29.3591	+	4.75115i	1.64122	+	0.265597i
$321$		0			0
$322$	4.76720	−	20.3271i	0.265665	−	1.13278i
$323$	−5.56376			−0.309576
$324$		0			0
$325$	−22.9162			−1.27116
$326$	−2.84659	+	12.1377i	−0.157658	+	0.672244i
$327$		0			0
$328$	0.0172484	+	2.44741i	0.000952386	+	0.135135i
$329$	−4.00123	+	10.9933i	−0.220595	+	0.606079i
$330$		0			0
$331$	−14.1356	−	2.49248i	−0.776962	−	0.136999i	−0.228914	−	0.973447i	$-0.573518\pi$
$331$	−14.1356	−	2.49248i	−0.776962	−	0.136999i	−0.548047	+	0.836447i	$0.684629\pi$
$332$	1.34637	+	3.08134i	0.0738914	+	0.169110i
$333$		0			0
$334$	26.6858	+	17.4618i	1.46018	+	0.955470i
$335$	−38.4105	+	13.9803i	−2.09859	+	0.763823i
$336$		0			0
$337$	−14.7441	+	12.3718i	−0.803163	+	0.673934i	−0.948966	−	0.315380i	$-0.897868\pi$
$337$	−14.7441	+	12.3718i	−0.803163	+	0.673934i	0.145802	+	0.989314i	$0.453424\pi$
$338$	−3.48207	+	8.12478i	−0.189400	+	0.441930i
$339$		0			0
$340$	−10.9280	+	37.1362i	−0.592654	+	2.01399i
$341$	1.56432	−	0.903158i	0.0847125	−	0.0489088i
$342$		0			0
$343$	16.1484	+	9.32326i	0.871930	+	0.503409i
$344$	1.91609	−	5.38212i	0.103308	−	0.290184i
$345$		0			0
$346$	1.71800	+	14.4048i	0.0923600	+	0.774409i
$347$	−5.51709	−	31.2889i	−0.296173	−	1.67968i	−0.662398	−	0.749152i	$-0.730461\pi$
$347$	−5.51709	−	31.2889i	−0.296173	−	1.67968i	0.366225	−	0.930526i	$-0.380650\pi$
$348$		0			0
$349$	13.2668	+	11.1322i	0.710158	+	0.595893i	0.924643	−	0.380834i	$-0.124363\pi$
$349$	13.2668	+	11.1322i	0.710158	+	0.595893i	−0.214485	+	0.976727i	$0.568807\pi$
$350$	9.31824	+	18.4460i	0.498081	+	0.985979i
$351$		0			0
$352$	−2.20244	−	2.28019i	−0.117390	−	0.121534i
$353$	2.57802	−	3.07236i	0.137214	−	0.163525i	−0.693061	−	0.720878i	$-0.743739\pi$
$353$	2.57802	−	3.07236i	0.137214	−	0.163525i	0.830276	+	0.557353i	$0.188183\pi$
$354$		0			0
$355$	−29.1578	+	5.14131i	−1.54754	+	0.272873i
$356$	13.9604	+	21.0101i	0.739899	+	1.11353i
$357$		0			0
$358$	−5.92771	−	19.6319i	−0.313289	−	1.03758i
$359$	6.05065	−	10.4800i	0.319341	−	0.553115i	−0.661010	−	0.750377i	$-0.729872\pi$
$359$	6.05065	−	10.4800i	0.319341	−	0.553115i	0.980351	+	0.197262i	$0.0632051\pi$
$360$		0			0
$361$	−8.92900	−	15.4655i	−0.469947	−	0.813973i
$362$	−5.11882	+	5.45123i	−0.269039	+	0.286510i
$363$		0			0
$364$	−8.59097	+	0.540878i	−0.450289	+	0.0283497i
$365$	−9.20433	−	10.9693i	−0.481777	−	0.574159i
$366$		0			0
$367$	1.17616	+	3.23148i	0.0613952	+	0.168682i	0.966598	−	0.256299i	$-0.0825031\pi$
$367$	1.17616	+	3.23148i	0.0613952	+	0.168682i	−0.905202	+	0.424981i	$0.860281\pi$
$368$	−24.2171	+	26.1567i	−1.26240	+	1.36351i
$369$		0			0
$370$	33.3699	+	1.86493i	1.73482	+	0.0969529i
$371$	1.95763	−	11.1023i	0.101635	−	0.576402i
$372$		0			0
$373$	−5.38991	−	1.96177i	−0.279079	−	0.101576i	0.198689	−	0.980063i	$-0.436332\pi$
$373$	−5.38991	−	1.96177i	−0.279079	−	0.101576i	−0.477768	+	0.878486i	$0.658554\pi$
$374$	3.30398	−	2.47181i	0.170845	−	0.127814i
$375$		0			0
$376$	15.2096	−	12.9462i	0.784378	−	0.667647i
$377$		−	2.83972i		−	0.146253i
$378$		0			0
$379$		−	25.2439i		−	1.29669i	−0.761346	−	0.648346i	$-0.775461\pi$
$379$		−	25.2439i		−	1.29669i	0.761346	−	0.648346i	$-0.224539\pi$
$380$	7.72278	−	1.86870i	0.396170	−	0.0958622i
$381$		0			0
$382$	−9.94037	−	13.2870i	−0.508594	−	0.679820i
$383$	−9.14102	−	3.32706i	−0.467084	−	0.170005i	0.0977467	−	0.995211i	$-0.468836\pi$
$383$	−9.14102	−	3.32706i	−0.467084	−	0.170005i	−0.564831	+	0.825206i	$0.691059\pi$
$384$		0			0
$385$	0.599348	−	3.39907i	0.0305456	−	0.173233i
$386$	1.82703	−	32.6919i	0.0929936	−	1.66397i
$387$		0			0
$388$	7.93009	+	0.889148i	0.402589	+	0.0451396i
$389$	3.05382	+	8.39029i	0.154835	+	0.425405i	0.992721	−	0.120441i	$-0.0384308\pi$
$389$	3.05382	+	8.39029i	0.154835	+	0.425405i	−0.837886	+	0.545845i	$0.816209\pi$
$390$		0			0
$391$	−29.8232	−	35.5419i	−1.50822	−	1.79743i
$392$	−6.09145	−	10.3810i	−0.307664	−	0.524322i
$393$		0			0
$394$	0.460088	+	0.432032i	0.0231789	+	0.0217655i
$395$	18.1888	+	31.5040i	0.915180	+	1.58514i
$396$		0			0
$397$	−1.03466	+	1.79209i	−0.0519283	+	0.0899424i	−0.890821	−	0.454354i	$-0.849870\pi$
$397$	−1.03466	+	1.79209i	−0.0519283	+	0.0899424i	0.838893	+	0.544297i	$0.183203\pi$
$398$	15.4483	−	4.66447i	0.774351	−	0.233809i
$399$		0			0
$400$	1.72046	−	35.2411i	0.0860231	−	1.76206i
$401$	−30.0242	+	5.29408i	−1.49934	+	0.264374i	−0.862276	−	0.506439i	$-0.830961\pi$
$401$	−30.0242	+	5.29408i	−1.49934	+	0.264374i	−0.637062	+	0.770813i	$0.719850\pi$
$402$		0			0
$403$	−5.38257	+	6.41470i	−0.268125	+	0.319539i
$404$	−12.3955	−	9.13790i	−0.616699	−	0.454628i
$405$		0			0
$406$	−2.28578	+	1.15469i	−0.113441	+	0.0573064i
$407$	−2.72905	−	2.28995i	−0.135274	−	0.113509i
$408$		0			0
$409$	−6.17283	−	35.0079i	−0.305227	−	1.73103i	−0.622434	−	0.782672i	$-0.713856\pi$
$409$	−6.17283	−	35.0079i	−0.305227	−	1.73103i	0.317207	−	0.948356i	$-0.397255\pi$
$410$	4.51738	−	0.538766i	0.223097	−	0.0266077i
$411$		0			0
$412$	4.34403	−	4.13713i	0.214015	−	0.203822i
$413$	13.0847	+	7.55447i	0.643858	+	0.371731i
$414$		0			0
$415$	5.41311	−	3.12526i	0.265719	−	0.153413i
$416$	13.2098	+	6.44103i	0.647662	+	0.315797i
$417$		0			0
$418$	−0.778466	−	0.333630i	−0.0380760	−	0.0163184i
$419$	9.43828	−	7.91966i	0.461090	−	0.386901i	−0.382442	−	0.923980i	$-0.624917\pi$
$419$	9.43828	−	7.91966i	0.461090	−	0.386901i	0.843532	+	0.537079i	$0.180472\pi$
$420$		0			0
$421$	16.3519	−	5.95160i	0.796943	−	0.290063i	0.0887237	−	0.996056i	$-0.471721\pi$
$421$	16.3519	−	5.95160i	0.796943	−	0.290063i	0.708219	+	0.705993i	$0.249499\pi$
$422$	−4.49857	+	6.87487i	−0.218987	+	0.334663i
$423$		0			0
$424$	−12.2677	+	14.8312i	−0.595774	+	0.720265i
$425$	45.2265	+	7.97466i	2.19381	+	0.386828i
$426$		0			0
$427$	−2.71522	+	7.46001i	−0.131399	+	0.361015i
$428$	21.3038	+	10.5741i	1.02976	+	0.511121i
$429$		0			0
$430$	−10.3389	−	2.42473i	−0.498587	−	0.116931i
$431$	19.0526			0.917729			0.458865	−	0.888506i	$-0.348256\pi$
$431$	19.0526			0.917729			0.458865	+	0.888506i	$0.348256\pi$
$432$		0			0
$433$	−37.4918			−1.80174			−0.900870	−	0.434088i	$-0.857071\pi$
$433$	−37.4918			−1.80174			−0.900870	+	0.434088i	$0.857071\pi$
$434$	7.35206	+	1.72424i	0.352910	+	0.0827661i
$435$		0			0
$436$	16.5992	+	8.23898i	0.794956	+	0.394576i
$437$	−3.25714	+	8.94892i	−0.155810	+	0.428085i
$438$		0			0
$439$	22.1128	+	3.89909i	1.05539	+	0.186093i	0.674309	−	0.738449i	$-0.264442\pi$
$439$	22.1128	+	3.89909i	1.05539	+	0.186093i	0.381079	+	0.924543i	$0.375553\pi$
$440$	−3.75589	+	4.54070i	−0.179055	+	0.216469i
$441$		0			0
$442$	−10.4738	+	16.0065i	−0.498190	+	0.761351i
$443$	9.66840	−	3.51901i	0.459359	−	0.167193i	−0.101967	−	0.994788i	$-0.532514\pi$
$443$	9.66840	−	3.51901i	0.459359	−	0.167193i	0.561326	+	0.827595i	$0.310291\pi$
$444$		0			0
$445$	35.9192	−	30.1398i	1.70273	−	1.42876i
$446$	−4.83653	−	2.07281i	−0.229016	−	0.0981505i
$447$		0			0
$448$	−0.186800	−	13.2520i	−0.00882546	−	0.626098i
$449$	7.77889	−	4.49114i	0.367109	−	0.211950i	−0.305086	−	0.952325i	$-0.598685\pi$
$449$	7.77889	−	4.49114i	0.367109	−	0.211950i	0.672194	+	0.740375i	$0.265352\pi$
$450$		0			0
$451$	−0.419962	−	0.242465i	−0.0197753	−	0.0114172i
$452$	8.16397	−	7.77513i	0.384001	−	0.365711i
$453$		0			0
$454$	9.29028	−	1.10801i	0.436014	−	0.0520013i
$455$	2.77848	+	15.7576i	0.130257	+	0.738725i
$456$		0			0
$457$	−3.65475	−	3.06670i	−0.170962	−	0.143454i	0.553292	−	0.832987i	$-0.313371\pi$
$457$	−3.65475	−	3.06670i	−0.170962	−	0.143454i	−0.724254	+	0.689533i	$0.757816\pi$
$458$	1.45908	−	0.737074i	0.0681782	−	0.0344412i
$459$		0			0
$460$	53.3336	+	39.3173i	2.48669	+	1.83318i
$461$	18.3723	−	21.8953i	0.855684	−	1.01976i	−0.143861	−	0.989598i	$-0.545952\pi$
$461$	18.3723	−	21.8953i	0.855684	−	1.01976i	0.999545	−	0.0301663i	$-0.00960370\pi$
$462$		0			0
$463$	41.7768	−	7.36638i	1.94153	−	0.342345i	0.941548	−	0.336878i	$-0.109371\pi$
$463$	41.7768	−	7.36638i	1.94153	−	0.342345i	0.999985	−	0.00546674i	$-0.00174013\pi$
$464$	4.36699	+	0.213195i	0.202732	+	0.00989733i
$465$		0			0
$466$	23.0501	−	6.95978i	1.06777	−	0.322406i
$467$	−3.22767	+	5.59048i	−0.149359	+	0.258697i	−0.930991	−	0.365043i	$-0.881054\pi$
$467$	−3.22767	+	5.59048i	−0.149359	+	0.258697i	0.781632	+	0.623740i	$0.214388\pi$
$468$		0			0
$469$	9.10756	+	15.7748i	0.420548	+	0.728410i
$470$	−27.0649	−	25.4145i	−1.24841	−	1.17228i
$471$		0			0
$472$	−13.0549	−	22.2481i	−0.600900	−	1.02405i
$473$	0.727606	+	0.867127i	0.0334553	+	0.0398705i
$474$		0			0
$475$	−3.22398	−	8.85780i	−0.147926	−	0.406424i
$476$	17.1430	+	1.92213i	0.785748	+	0.0881006i
$477$		0			0
$478$	−0.0952044	+	1.70353i	−0.00435455	+	0.0779176i
$479$	−6.20075	+	35.1662i	−0.283319	+	1.60678i	0.427909	+	0.903822i	$0.359250\pi$
$479$	−6.20075	+	35.1662i	−0.283319	+	1.60678i	−0.711228	+	0.702961i	$0.751861\pi$
$480$		0			0
$481$	15.5193	+	5.64857i	0.707620	+	0.257553i
$482$	−8.46688	−	11.3174i	−0.385656	−	0.515493i
$483$		0			0
$484$	−20.7724	+	5.02634i	−0.944200	+	0.228470i
$485$		−	14.8329i		−	0.673529i
$486$		0			0
$487$			40.6600i			1.84248i	0.388993	+	0.921241i	$0.372823\pi$
$487$			40.6600i			1.84248i	−0.388993	+	0.921241i	$0.627177\pi$
$488$	10.3212	−	8.78524i	0.467220	−	0.397689i
$489$		0			0
$490$	−17.9146	+	13.4025i	−0.809300	+	0.605462i
$491$	−26.4253	−	9.61801i	−1.19256	−	0.434055i	−0.331935	−	0.943302i	$-0.607702\pi$
$491$	−26.4253	−	9.61801i	−1.19256	−	0.434055i	−0.860620	+	0.509247i	$0.829924\pi$
$492$		0			0
$493$	−0.988198	+	5.60435i	−0.0445062	+	0.252407i
$494$	3.92019	+	0.219086i	0.176378	+	0.00985715i
$495$		0			0
$496$	−9.46058	−	8.75904i	−0.424793	−	0.393293i
$497$	4.51257	+	12.3982i	0.202416	+	0.556134i
$498$		0			0
$499$	21.2879	+	25.3699i	0.952977	+	1.13571i	0.990651	+	0.136423i	$0.0435607\pi$
$499$	21.2879	+	25.3699i	0.952977	+	1.13571i	−0.0376739	+	0.999290i	$0.511995\pi$
$500$	−28.3524	+	1.78504i	−1.26796	+	0.0798292i
$501$		0			0
$502$	−12.8826	+	13.7192i	−0.574980	+	0.612319i
$503$	13.4484	+	23.2932i	0.599633	+	1.03859i	0.992875	+	0.119159i	$0.0380200\pi$
$503$	13.4484	+	23.2932i	0.599633	+	1.03859i	−0.393242	+	0.919435i	$0.628647\pi$
$504$		0			0
$505$	−14.3126	+	24.7901i	−0.636901	+	1.10314i
$506$	−2.04151	−	6.76127i	−0.0907563	−	0.300575i
$507$		0			0
$508$	8.97202	+	13.5027i	0.398069	+	0.599085i
$509$	9.32093	−	1.64353i	0.413143	−	0.0728482i	0.0367864	−	0.999323i	$-0.488288\pi$
$509$	9.32093	−	1.64353i	0.413143	−	0.0728482i	0.376357	+	0.926475i	$0.377177\pi$
$510$		0			0
$511$	−4.10167	+	4.88818i	−0.181447	+	0.216240i
$512$	−10.8969	+	19.8307i	−0.481580	+	0.876402i
$513$		0			0
$514$	−8.84379	−	17.5068i	−0.390083	−	0.772190i
$515$	−8.54200	−	7.16759i	−0.376406	−	0.315842i
$516$		0			0
$517$	0.687203	+	3.89732i	0.0302231	+	0.171404i
$518$	−1.76379	−	14.7888i	−0.0774964	−	0.649783i
$519$		0			0
$520$	9.16214	−	25.7357i	0.401786	−	1.12858i
$521$	−15.6963	−	9.06226i	−0.687667	−	0.397025i	0.115070	−	0.993357i	$-0.463291\pi$
$521$	−15.6963	−	9.06226i	−0.687667	−	0.397025i	−0.802737	+	0.596333i	$0.796624\pi$
$522$		0			0
$523$	31.7246	−	18.3162i	1.38722	−	0.800912i	0.394219	−	0.919017i	$-0.371015\pi$
$523$	31.7246	−	18.3162i	1.38722	−	0.800912i	0.993001	+	0.118105i	$0.0376819\pi$
$524$	5.23547	−	17.7915i	0.228712	−	0.777225i
$525$		0			0
$526$	1.36404	−	3.18275i	0.0594751	−	0.138774i
$527$	12.8551	−	10.7867i	0.559976	−	0.469876i
$528$		0			0
$529$	−53.0129	+	19.2951i	−2.30491	+	0.838918i
$530$	29.9376	+	19.5897i	1.30041	+	0.850921i
$531$		0			0
$532$	−1.41769	−	3.24457i	−0.0614645	−	0.140670i
$533$	2.21391	+	0.390372i	0.0958951	+	0.0169089i
$534$		0			0
$535$	15.1206	−	41.5434i	0.653719	−	1.79608i
$536$	−0.219167	−	31.0979i	−0.00946657	−	1.34323i
$537$		0			0
$538$	1.33072	−	5.67411i	0.0573713	−	0.244628i
$539$	2.38481			0.102721
$540$		0			0
$541$	31.5175			1.35504			0.677521	−	0.735504i	$-0.263054\pi$
$541$	31.5175			1.35504			0.677521	+	0.735504i	$0.263054\pi$
$542$	3.87031	−	16.5028i	0.166244	−	0.708856i
$543$		0			0
$544$	−23.8288	−	17.3086i	−1.02165	−	0.742101i
$545$	11.7814	−	32.3691i	0.504659	−	1.38654i
$546$		0			0
$547$	31.0212	+	5.46987i	1.32637	+	0.233875i	0.791557	−	0.611095i	$-0.209271\pi$
$547$	31.0212	+	5.46987i	1.32637	+	0.233875i	0.534813	+	0.844970i	$0.320382\pi$
$548$	6.33029	−	2.76597i	0.270417	−	0.118156i
$549$		0			0
$550$	5.84977	+	3.82780i	0.249435	+	0.163218i
$551$	1.09763	−	0.399506i	0.0467608	−	0.0170195i
$552$		0			0
$553$	12.4182	−	10.4201i	0.528074	−	0.443107i
$554$	−16.7315	+	39.0400i	−0.710855	+	1.65865i
$555$		0			0
$556$	10.3037	+	3.03205i	0.436975	+	0.128588i
$557$	13.9805	−	8.07165i	0.592373	−	0.342007i	−0.173662	−	0.984805i	$-0.555560\pi$
$557$	13.9805	−	8.07165i	0.592373	−	0.342007i	0.766035	+	0.642799i	$0.222227\pi$
$558$		0			0
$559$	−4.54452	−	2.62378i	−0.192213	−	0.110974i
$560$	−24.4409	+	3.08980i	−1.03282	+	0.130568i
$561$		0			0
$562$	−1.16056	−	9.73096i	−0.0489555	−	0.410476i
$563$	5.14604	+	29.1846i	0.216880	+	1.22999i	0.877615	+	0.479366i	$0.159133\pi$
$563$	5.14604	+	29.1846i	0.216880	+	1.22999i	−0.660735	+	0.750619i	$0.729755\pi$
$564$		0			0
$565$	−16.0534	−	13.4704i	−0.675374	−	0.566706i
$566$	12.0321	+	23.8182i	0.505748	+	1.00116i
$567$		0			0
$568$	3.75515	−	22.2107i	0.157563	−	0.931941i
$569$	−23.6512	+	28.1864i	−0.991509	+	1.18163i	−0.00814907	+	0.999967i	$0.502594\pi$
$569$	−23.6512	+	28.1864i	−0.991509	+	1.18163i	−0.983360	+	0.181668i	$0.941850\pi$
$570$		0			0
$571$	−0.987914	+	0.174196i	−0.0413429	+	0.00728987i	−0.194281	−	0.980946i	$-0.562237\pi$
$571$	−0.987914	+	0.174196i	−0.0413429	+	0.00728987i	0.152938	+	0.988236i	$0.451126\pi$
$572$	−2.42530	+	1.61152i	−0.101407	+	0.0673810i
$573$		0			0
$574$	−0.586002	−	1.94078i	−0.0244592	−	0.0810064i
$575$	39.3033	−	68.0753i	1.63906	−	2.83893i
$576$		0			0
$577$	10.1847	+	17.6404i	0.423994	+	0.734379i	0.996326	−	0.0856433i	$-0.0272945\pi$
$577$	10.1847	+	17.6404i	0.423994	+	0.734379i	−0.572332	+	0.820022i	$0.693961\pi$
$578$	9.78362	−	10.4190i	0.406945	−	0.433372i
$579$		0			0
$580$	−0.510662	−	8.11103i	−0.0212041	−	0.336792i
$581$	−1.79041	−	2.13373i	−0.0742787	−	0.0885219i
$582$		0			0
$583$	−1.30432	−	3.58360i	−0.0540196	−	0.148418i
$584$	10.2109	−	3.79816i	0.422529	−	0.157169i
$585$		0			0
$586$	−29.8385	−	1.66757i	−1.23262	−	0.0688866i
$587$	4.50124	−	25.5278i	0.185786	−	1.05364i	−0.739155	−	0.673535i	$-0.764775\pi$
$587$	4.50124	−	25.5278i	0.185786	−	1.05364i	0.924941	−	0.380110i	$-0.124114\pi$
$588$		0			0
$589$	−3.23672	−	1.17807i	−0.133367	−	0.0485415i
$590$	−38.3938	+	28.7235i	−1.58065	+	1.18253i
$591$		0			0
$592$	−9.85164	+	23.4419i	−0.404900	+	0.963457i
$593$			41.3947i			1.69988i	0.526881	+	0.849939i	$0.323361\pi$
$593$			41.3947i			1.69988i	−0.526881	+	0.849939i	$0.676639\pi$
$594$		0			0
$595$		−	32.0653i		−	1.31455i
$596$	5.38930	+	22.2724i	0.220754	+	0.912312i
$597$		0			0
$598$	19.6137	+	26.2170i	0.802065	+	1.07209i
$599$	−20.6951	−	7.53238i	−0.845577	−	0.307765i	−0.117341	−	0.993092i	$-0.537437\pi$
$599$	−20.6951	−	7.53238i	−0.845577	−	0.307765i	−0.728236	+	0.685327i	$0.759659\pi$
$600$		0			0
$601$	1.14732	−	6.50676i	0.0468001	−	0.265416i	−0.952425	−	0.304773i	$-0.901420\pi$
$601$	1.14732	−	6.50676i	0.0468001	−	0.265416i	0.999225	+	0.0393561i	$0.0125307\pi$
$602$	−0.264059	+	4.72491i	−0.0107622	+	0.192573i
$603$		0			0
$604$	5.08569	−	45.3580i	0.206934	−	1.84559i
$605$	13.5872	+	37.3306i	0.552399	+	1.51770i
$606$		0			0
$607$	4.01395	+	4.78364i	0.162921	+	0.194162i	0.841329	−	0.540524i	$-0.181774\pi$
$607$	4.01395	+	4.78364i	0.162921	+	0.194162i	−0.678407	+	0.734686i	$0.737330\pi$
$608$	−0.631228	+	6.01212i	−0.0255997	+	0.243824i
$609$		0			0
$610$	−18.3662	−	17.2462i	−0.743624	−	0.698279i
$611$	−9.17304	−	15.8882i	−0.371101	−	0.642767i
$612$		0			0
$613$	−1.30807	+	2.26564i	−0.0528323	+	0.0915083i	−0.891232	−	0.453548i	$-0.850158\pi$
$613$	−1.30807	+	2.26564i	−0.0528323	+	0.0915083i	0.838400	+	0.545056i	$0.183492\pi$
$614$	−27.2069	+	8.21490i	−1.09798	+	0.331526i
$615$		0			0
$616$	2.28334	+	1.29692i	0.0919984	+	0.0522543i
$617$	−13.1781	+	2.32365i	−0.530528	+	0.0935465i	−0.432494	−	0.901637i	$-0.642366\pi$
$617$	−13.1781	+	2.32365i	−0.530528	+	0.0935465i	−0.0980339	+	0.995183i	$0.531255\pi$
$618$		0			0
$619$	−17.2591	+	20.5686i	−0.693703	+	0.826723i	−0.991798	−	0.127813i	$-0.959204\pi$
$619$	−17.2591	+	20.5686i	−0.693703	+	0.826723i	0.298095	+	0.954536i	$0.403649\pi$
$620$	−14.2206	+	19.2901i	−0.571113	+	0.774710i
$621$		0			0
$622$	−32.8950	+	16.6174i	−1.31897	+	0.666295i
$623$	−16.0064	−	13.4310i	−0.641284	−	0.538101i
$624$		0			0
$625$	1.51113	+	8.57003i	0.0604451	+	0.342801i
$626$	34.1034	−	4.06734i	1.36304	−	0.162564i
$627$		0			0
$628$	−11.4445	−	12.0169i	−0.456687	−	0.479526i
$629$	−28.6626	−	16.5484i	−1.14285	−	0.659827i
$630$		0			0
$631$	−24.9119	+	14.3829i	−0.991726	+	0.572573i	−0.905790	−	0.423727i	$-0.860722\pi$
$631$	−24.9119	+	14.3829i	−0.991726	+	0.572573i	−0.0859365	+	0.996301i	$0.527388\pi$
$632$	−27.2216	+	4.99797i	−1.08282	+	0.198809i
$633$		0			0
$634$	−8.02509	−	3.43935i	−0.318717	−	0.136594i
$635$	23.0844	−	19.3701i	0.916078	−	0.768681i
$636$		0			0
$637$	−10.3889	+	3.78125i	−0.411623	+	0.149818i
$638$	−0.474331	+	0.724888i	−0.0187789	+	0.0286986i
$639$		0			0
$640$	38.8891	+	16.0219i	1.53722	+	0.633321i
$641$	−1.94287	−	0.342580i	−0.0767386	−	0.0135311i	0.135147	−	0.990826i	$-0.456849\pi$
$641$	−1.94287	−	0.342580i	−0.0767386	−	0.0135311i	−0.211886	+	0.977294i	$0.567960\pi$
$642$		0			0
$643$	−13.0375	+	35.8203i	−0.514150	+	1.41262i	0.362724	+	0.931897i	$0.381847\pi$
$643$	−13.0375	+	35.8203i	−0.514150	+	1.41262i	−0.876874	+	0.480720i	$0.840375\pi$
$644$	13.1275	−	26.4481i	0.517295	−	1.04220i
$645$		0			0
$646$	−7.66049	−	1.79657i	−0.301398	−	0.0706852i
$647$	−7.03763			−0.276678			−0.138339	−	0.990385i	$-0.544176\pi$
$647$	−7.03763			−0.276678			−0.138339	+	0.990385i	$0.544176\pi$
$648$		0			0
$649$	5.11102			0.200625
$650$	−31.5524	−	7.39980i	−1.23759	−	0.290244i
$651$		0			0
$652$	−7.83868	+	15.7927i	−0.306986	+	0.618488i
$653$	3.81006	−	10.4681i	0.149099	−	0.409647i	−0.842549	−	0.538620i	$-0.818946\pi$
$653$	3.81006	−	10.4681i	0.149099	−	0.409647i	0.991648	+	0.128973i	$0.0411681\pi$
$654$		0			0
$655$	−33.9495	−	5.98622i	−1.32652	−	0.233901i
$656$	−0.766535	+	3.37530i	−0.0299282	+	0.131783i
$657$		0			0
$658$	−9.05891	+	13.8441i	−0.353153	+	0.539700i
$659$	35.1305	−	12.7864i	1.36849	−	0.498089i	0.449821	−	0.893119i	$-0.351488\pi$
$659$	35.1305	−	12.7864i	1.36849	−	0.498089i	0.918668	+	0.395030i	$0.129266\pi$
$660$		0			0
$661$	4.29644	−	3.60514i	0.167112	−	0.140224i	−0.555396	−	0.831586i	$-0.687433\pi$
$661$	4.29644	−	3.60514i	0.167112	−	0.140224i	0.722509	+	0.691362i	$0.242989\pi$
$662$	−18.6578	−	7.99626i	−0.725157	−	0.310784i
$663$		0			0
$664$	0.858766	+	4.67731i	0.0333266	+	0.181515i
$665$	−5.69986	+	3.29082i	−0.221031	+	0.127612i
$666$		0			0
$667$	8.43570	+	4.87036i	0.326632	+	0.188581i
$668$	31.1039	+	32.6595i	1.20345	+	1.26363i
$669$		0			0
$670$	−57.4000	+	6.84582i	−2.21755	+	0.264477i
$671$	0.466334	+	2.64471i	0.0180026	+	0.102098i
$672$		0			0
$673$	29.0189	+	24.3497i	1.11860	+	0.938613i	0.998533	−	0.0541531i	$-0.0172459\pi$
$673$	29.0189	+	24.3497i	1.11860	+	0.938613i	0.120063	+	0.992766i	$0.461690\pi$
$674$	−24.2955	+	12.2732i	−0.935826	+	0.472746i
$675$		0			0
$676$	−7.41786	+	10.0623i	−0.285302	+	0.387010i
$677$	24.2754	−	28.9303i	0.932980	−	1.11188i	−0.0605328	−	0.998166i	$-0.519280\pi$
$677$	24.2754	−	28.9303i	0.932980	−	1.11188i	0.993513	−	0.113717i	$-0.0362756\pi$
$678$		0			0
$679$	−6.50949	+	1.14780i	−0.249811	+	0.0440485i
$680$	−27.0378	+	47.6025i	−1.03685	+	1.82547i
$681$		0			0
$682$	2.44547	−	0.738391i	0.0936420	−	0.0282744i
$683$	−13.9252	+	24.1192i	−0.532834	+	0.922895i	0.466431	+	0.884558i	$0.345540\pi$
$683$	−13.9252	+	24.1192i	−0.532834	+	0.922895i	−0.999265	+	0.0383376i	$0.987794\pi$
$684$		0			0
$685$	−6.42053	−	11.1207i	−0.245316	−	0.424900i
$686$	19.2234	+	18.0512i	0.733954	+	0.689198i
$687$		0			0
$688$	4.37609	−	6.79169i	0.166837	−	0.258931i
$689$	11.3640	+	13.5431i	0.432933	+	0.515949i
$690$		0			0
$691$	−1.46193	−	4.01662i	−0.0556145	−	0.152800i	0.908774	−	0.417288i	$-0.137019\pi$
$691$	−1.46193	−	4.01662i	−0.0556145	−	0.152800i	−0.964389	+	0.264488i	$0.914797\pi$
$692$	−2.28598	+	20.3881i	−0.0869001	+	0.775040i
$693$		0			0
$694$	2.50717	−	44.8619i	0.0951710	−	1.70293i
$695$	3.46684	−	19.6614i	0.131505	−	0.745800i
$696$		0			0
$697$	−4.23343	−	1.54084i	−0.160353	−	0.0583636i
$698$	14.6719	+	19.6114i	0.555339	+	0.742302i
$699$		0			0
$700$	6.87355	+	28.4064i	0.259796	+	1.07366i
$701$			20.9584i			0.791586i	0.918340	+	0.395793i	$0.129530\pi$
$701$			20.9584i			0.791586i	−0.918340	+	0.395793i	$0.870470\pi$
$702$		0			0
$703$			6.79334i			0.256216i
$704$	−2.29615	−	3.85067i	−0.0865395	−	0.145128i
$705$		0			0
$706$	4.54165	−	3.39774i	0.170927	−	0.127876i
$707$	11.9868	+	4.36282i	0.450808	+	0.164081i
$708$		0			0
$709$	−1.39089	+	7.88813i	−0.0522360	+	0.296245i	−0.999723	−	0.0235502i	$-0.992503\pi$
$709$	−1.39089	+	7.88813i	−0.0522360	+	0.296245i	0.947487	+	0.319795i	$0.103614\pi$
$710$	−41.8063	−	2.33641i	−1.56896	−	0.0876839i
$711$		0			0
$712$	12.4372	+	33.4357i	0.466102	+	1.25306i
$713$	−9.82403	−	26.9913i	−0.367913	−	1.01083i
$714$		0			0
$715$	3.47919	+	4.14634i	0.130114	+	0.155064i
$716$	−1.82231	−	28.9444i	−0.0681030	−	1.08170i
$717$		0			0
$718$	11.7149	−	12.4757i	0.437198	−	0.465589i
$719$	−4.27525	−	7.40496i	−0.159440	−	0.276158i	0.775227	−	0.631683i	$-0.217636\pi$
$719$	−4.27525	−	7.40496i	−0.159440	−	0.276158i	−0.934667	+	0.355525i	$0.884302\pi$
$720$		0			0
$721$	−2.48453	+	4.30333i	−0.0925287	+	0.160264i
$722$	−7.30004	−	24.1770i	−0.271679	−	0.899774i
$723$		0			0
$724$	−8.80811	+	5.85265i	−0.327351	+	0.217512i
$725$	−9.49505	+	1.67423i	−0.352637	+	0.0621795i
$726$		0			0
$727$	16.9742	−	20.2291i	0.629538	−	0.750255i	−0.353141	−	0.935570i	$-0.614886\pi$
$727$	16.9742	−	20.2291i	0.629538	−	0.750255i	0.982679	+	0.185316i	$0.0593307\pi$
$728$	−12.0032	−	2.02937i	−0.444867	−	0.0752134i
$729$		0			0
$730$	−9.13098	−	18.0753i	−0.337953	−	0.668996i
$731$	8.05582	+	6.75964i	0.297955	+	0.250014i
$732$		0			0
$733$	6.75770	+	38.3248i	0.249601	+	1.41556i	0.809559	+	0.587039i	$0.199706\pi$
$733$	6.75770	+	38.3248i	0.249601	+	1.41556i	−0.559957	+	0.828521i	$0.689182\pi$
$734$	0.575940	+	4.82907i	0.0212583	+	0.178244i
$735$		0			0
$736$	−41.7896	+	28.1942i	−1.54039	+	1.03925i
$737$	5.33625	+	3.08088i	0.196563	+	0.113486i
$738$		0			0
$739$	10.6334	−	6.13920i	0.391156	−	0.225834i	−0.291505	−	0.956569i	$-0.594156\pi$
$739$	10.6334	−	6.13920i	0.391156	−	0.225834i	0.682661	+	0.730735i	$0.260823\pi$
$740$	45.3433	+	13.3431i	1.66685	+	0.490502i
$741$		0			0
$742$	6.28037	−	14.6541i	0.230560	−	0.537969i
$743$	14.9811	−	12.5706i	0.549603	−	0.461172i	−0.325204	−	0.945644i	$-0.605433\pi$
$743$	14.9811	−	12.5706i	0.549603	−	0.461172i	0.874807	+	0.484472i	$0.160988\pi$
$744$		0			0
$745$	40.0262	−	14.5683i	1.46645	−	0.533743i
$746$	−6.78766	−	4.44151i	−0.248514	−	0.162615i
$747$		0			0
$748$	5.34727	−	2.33644i	0.195515	−	0.0854289i
$749$	−19.4015	−	3.42101i	−0.708917	−	0.125001i
$750$		0			0
$751$	0.401897	−	1.10420i	0.0146654	−	0.0402929i	−0.932144	−	0.362088i	$-0.882064\pi$
$751$	0.401897	−	1.10420i	0.0146654	−	0.0402929i	0.946809	+	0.321795i	$0.104286\pi$
$752$	25.1219	−	12.9137i	0.916101	−	0.470914i
$753$		0			0
$754$	0.916964	−	3.90988i	0.0333939	−	0.142390i
$755$	−84.8405			−3.08766
$756$		0			0
$757$	−15.1258			−0.549756			−0.274878	−	0.961479i	$-0.588638\pi$
$757$	−15.1258			−0.549756			−0.274878	+	0.961479i	$0.588638\pi$
$758$	8.15142	−	34.7572i	0.296073	−	1.26244i
$759$		0			0
$760$	11.2366	−	0.0791912i	0.407593	−	0.00287257i
$761$	−4.81963	+	13.2418i	−0.174711	+	0.480016i	−0.995881	−	0.0906683i	$-0.971100\pi$
$761$	−4.81963	+	13.2418i	−0.174711	+	0.480016i	0.821170	+	0.570684i	$0.193322\pi$
$762$		0			0
$763$	−15.1170	−	2.66553i	−0.547271	−	0.0964986i
$764$	−9.39601	−	21.5040i	−0.339936	−	0.777989i
$765$		0			0
$766$	−11.5115	−	7.53258i	−0.415929	−	0.272163i
$767$	−22.2650	+	8.10379i	−0.803941	+	0.292611i
$768$		0			0
$769$	−19.1139	+	16.0385i	−0.689265	+	0.578362i	−0.918697	−	0.394962i	$-0.870758\pi$
$769$	−19.1139	+	16.0385i	−0.689265	+	0.578362i	0.229432	+	0.973325i	$0.426313\pi$
$770$	1.92280	−	4.48649i	0.0692928	−	0.161682i
$771$		0			0
$772$	13.0720	−	44.4220i	0.470471	−	1.59878i
$773$	12.7170	−	7.34218i	0.457400	−	0.264080i	−0.253550	−	0.967322i	$-0.581598\pi$
$773$	12.7170	−	7.34218i	0.457400	−	0.264080i	0.710950	+	0.703242i	$0.248265\pi$
$774$		0			0
$775$	24.6220	+	14.2155i	0.884449	+	0.510637i
$776$	10.6315	+	3.78491i	0.381648	+	0.135870i
$777$		0			0
$778$	1.49538	+	12.5383i	0.0536121	+	0.449520i
$779$	0.160574	+	0.910661i	0.00575316	+	0.0326278i
$780$		0			0
$781$	3.41900	+	2.86888i	0.122342	+	0.102657i
$782$	−29.5855	−	58.5662i	−1.05798	−	2.09432i
$783$		0			0
$784$	−5.03493	−	16.2602i	−0.179819	−	0.580720i
$785$	−19.8277	+	23.6297i	−0.707681	+	0.843381i
$786$		0			0
$787$	6.40180	−	1.12881i	0.228199	−	0.0402377i	−0.0583791	−	0.998294i	$-0.518593\pi$
$787$	6.40180	−	1.12881i	0.228199	−	0.0402377i	0.286578	+	0.958057i	$0.407482\pi$
$788$	0.493969	+	0.743411i	0.0175969	+	0.0264829i
$789$		0			0
$790$	14.8706	+	49.2497i	0.529071	+	1.75223i
$791$	−4.66931	+	8.08748i	−0.166021	+	0.287558i
$792$		0			0
$793$	−6.22481	−	10.7817i	−0.221049	−	0.382869i
$794$	−2.00326	+	2.13335i	−0.0710930	+	0.0757097i
$795$		0			0
$796$	22.7762	−	1.43397i	0.807281	−	0.0508256i
$797$	16.1321	+	19.2255i	0.571427	+	0.681001i	0.971923	−	0.235298i	$-0.0756066\pi$
$797$	16.1321	+	19.2255i	0.571427	+	0.681001i	−0.400496	+	0.916299i	$0.631162\pi$
$798$		0			0
$799$	12.5746	+	34.5484i	0.444857	+	1.22223i
$800$	13.7484	−	47.9664i	0.486080	−	1.69587i
$801$		0			0
$802$	−43.0485	−	2.40583i	−1.52010	−	0.0849529i
$803$	−0.374832	+	2.12578i	−0.0132275	+	0.0750170i
$804$		0			0
$805$	−51.5749	−	18.7717i	−1.81778	−	0.661616i
$806$	−9.48238	+	7.09405i	−0.334003	+	0.249877i
$807$		0			0
$808$	−14.1161	−	16.5842i	−0.496603	−	0.583429i
$809$		−	18.1165i		−	0.636944i	−0.947932	−	0.318472i	$-0.896830\pi$
$809$		−	18.1165i		−	0.636944i	0.947932	−	0.318472i	$-0.103170\pi$
$810$		0			0
$811$		−	6.98634i		−	0.245324i	−0.992449	−	0.122662i	$-0.960857\pi$
$811$		−	6.98634i		−	0.245324i	0.992449	−	0.122662i	$-0.0391430\pi$
$812$	−3.52004	+	0.851752i	−0.123529	+	0.0298906i
$813$		0			0
$814$	−3.01807	−	4.03416i	−0.105783	−	0.141397i
$815$	30.7964	+	11.2090i	1.07875	+	0.392633i
$816$		0			0
$817$	0.374821	−	2.12572i	0.0131133	−	0.0743694i
$818$	2.80517	−	50.1940i	0.0980805	−	1.75499i
$819$		0			0
$820$	6.39375	+	0.716888i	0.223279	+	0.0250348i
$821$	−12.3202	−	33.8494i	−0.429977	−	1.18135i	−0.945826	−	0.324673i	$-0.894746\pi$
$821$	−12.3202	−	33.8494i	−0.429977	−	1.18135i	0.515849	−	0.856679i	$-0.327477\pi$
$822$		0			0
$823$	−14.6929	−	17.5103i	−0.512161	−	0.610369i	0.446548	−	0.894760i	$-0.352653\pi$
$823$	−14.6929	−	17.5103i	−0.512161	−	0.610369i	−0.958709	+	0.284390i	$0.908209\pi$
$824$	7.31701	−	4.29352i	0.254900	−	0.149572i
$825$		0			0
$826$	15.5764	+	14.6266i	0.541972	+	0.508923i
$827$	17.2618	+	29.8984i	0.600253	+	1.03967i	0.992782	+	0.119929i	$0.0382667\pi$
$827$	17.2618	+	29.8984i	0.600253	+	1.03967i	−0.392530	+	0.919739i	$0.628400\pi$
$828$		0			0
$829$	11.3276	−	19.6199i	0.393423	−	0.681429i	−0.599475	−	0.800393i	$-0.704624\pi$
$829$	11.3276	−	19.6199i	0.393423	−	0.681429i	0.992899	+	0.118964i	$0.0379574\pi$
$830$	8.46224	−	2.55511i	0.293729	−	0.0886890i
$831$		0			0
$832$	16.1081	+	13.1339i	0.558447	+	0.455335i
$833$	21.8189	−	3.84726i	0.755981	−	0.133300i
$834$		0			0
$835$	53.8877	−	64.2208i	1.86486	−	2.22245i
$836$	−0.964103	−	0.710733i	−0.0333442	−	0.0245812i
$837$		0			0
$838$	15.5525	−	7.85655i	0.537251	−	0.271400i
$839$	−8.27145	−	6.94057i	−0.285562	−	0.239615i	0.488743	−	0.872428i	$-0.337456\pi$
$839$	−8.27145	−	6.94057i	−0.285562	−	0.239615i	−0.774305	+	0.632813i	$0.781900\pi$
$840$		0			0
$841$	4.82833	+	27.3828i	0.166494	+	0.944235i
$842$	24.4360	−	2.91436i	0.842121	−	0.100436i
$843$		0			0
$844$	−8.41382	+	8.01308i	−0.289616	+	0.275822i
$845$	20.1238	+	11.6185i	0.692280	+	0.399688i
$846$		0			0
$847$	15.3313	−	8.85151i	0.526788	−	0.304141i
$848$	−21.6800	+	16.4590i	−0.744494	+	0.565205i
$849$		0			0
$850$	59.6953	+	25.5839i	2.04753	+	0.877521i
$851$	−43.3966	+	36.4141i	−1.48762	+	1.24826i
$852$		0			0
$853$	16.8556	−	6.13495i	0.577126	−	0.210057i	−0.0369315	−	0.999318i	$-0.511758\pi$
$853$	16.8556	−	6.13495i	0.577126	−	0.210057i	0.614058	+	0.789261i	$0.289536\pi$
$854$	−6.14736	+	9.39460i	−0.210358	+	0.321477i
$855$		0			0
$856$	25.9179	+	21.4382i	0.885854	+	0.732743i
$857$	−5.62708	−	0.992207i	−0.192218	−	0.0338931i	0.0767105	−	0.997053i	$-0.475558\pi$
$857$	−5.62708	−	0.992207i	−0.192218	−	0.0338931i	−0.268928	+	0.963160i	$0.586669\pi$
$858$		0			0
$859$	−6.53894	+	17.9656i	−0.223106	+	0.612978i	−0.999858	−	0.0168277i	$-0.994643\pi$
$859$	−6.53894	+	17.9656i	−0.223106	+	0.612978i	0.776753	+	0.629806i	$0.216866\pi$
$860$	−13.4522	−	6.67701i	−0.458718	−	0.227684i
$861$		0			0
$862$	26.2326	+	6.15219i	0.893486	+	0.209545i
$863$	42.9009			1.46036			0.730181	−	0.683254i	$-0.239436\pi$
$863$	42.9009			1.46036			0.730181	+	0.683254i	$0.239436\pi$
$864$		0			0
$865$	38.1352			1.29664
$866$	−51.6208	−	12.1063i	−1.75415	−	0.411390i
$867$		0			0
$868$	9.56596	+	4.74806i	0.324690	+	0.161160i
$869$	1.87555	−	5.15303i	0.0636236	−	0.174804i
$870$		0			0
$871$	−28.1310	−	4.96026i	−0.953183	−	0.168072i
$872$	20.1942	+	16.7039i	0.683863	+	0.565664i
$873$		0			0
$874$	−7.37428	+	11.2696i	−0.249439	+	0.381201i
$875$	22.1125	−	8.04830i	0.747540	−	0.272082i
$876$		0			0
$877$	−20.7445	+	17.4067i	−0.700491	+	0.587781i	−0.921913	−	0.387397i	$-0.873374\pi$
$877$	−20.7445	+	17.4067i	−0.700491	+	0.587781i	0.221423	+	0.975178i	$0.428930\pi$
$878$	29.1871	+	12.5089i	0.985018	+	0.422154i
$879$		0			0
$880$	−6.63754	+	5.03909i	−0.223751	+	0.169868i
$881$	−6.75989	+	3.90282i	−0.227746	+	0.131489i	−0.609532	−	0.792761i	$-0.708643\pi$
$881$	−6.75989	+	3.90282i	−0.227746	+	0.131489i	0.381786	+	0.924251i	$0.375309\pi$
$882$		0			0
$883$	−43.9985	−	25.4025i	−1.48067	−	0.854864i	−0.480907	−	0.876772i	$-0.659693\pi$
$883$	−43.9985	−	25.4025i	−1.48067	−	0.854864i	−0.999760	+	0.0219080i	$0.993026\pi$
$884$	−19.5896	+	18.6565i	−0.658868	+	0.627487i
$885$		0			0
$886$	14.4483	−	1.72318i	0.485400	−	0.0578913i
$887$	0.849885	+	4.81994i	0.0285363	+	0.161838i	0.995746	−	0.0921422i	$-0.0293714\pi$
$887$	0.849885	+	4.81994i	0.0285363	+	0.161838i	−0.967210	+	0.253980i	$0.918260\pi$
$888$		0			0
$889$	−10.2870	−	8.63179i	−0.345014	−	0.289501i
$890$	59.1878	−	29.8996i	1.98398	−	1.00224i
$891$		0			0
$892$	−5.98988	−	4.41571i	−0.200556	−	0.147849i
$893$	4.85073	−	5.78088i	0.162324	−	0.193450i
$894$		0			0
$895$	−53.0899	+	9.36118i	−1.77460	+	0.312910i
$896$	4.02196	−	18.3064i	0.134364	−	0.611574i
$897$		0			0
$898$	12.1606	−	3.67180i	0.405805	−	0.122530i
$899$	−1.76155	+	3.05109i	−0.0587510	+	0.101760i
$900$		0			0
$901$	−17.7146	−	30.6826i	−0.590159	−	1.02218i
$902$	−0.499934	−	0.469448i	−0.0166460	−	0.0156309i
$903$		0			0
$904$	13.7512	−	8.06903i	0.457360	−	0.268372i
$905$	12.6356	+	15.0585i	0.420021	+	0.500561i
$906$		0			0
$907$	8.73803	+	24.0076i	0.290142	+	0.797158i	0.996045	+	0.0888495i	$0.0283190\pi$
$907$	8.73803	+	24.0076i	0.290142	+	0.797158i	−0.705903	+	0.708308i	$0.749459\pi$
$908$	13.1492	+	1.47433i	0.436370	+	0.0489272i
$909$		0			0
$910$	−1.26265	+	22.5931i	−0.0418564	+	0.748953i
$911$	−7.53014	+	42.7055i	−0.249485	+	1.41490i	0.560358	+	0.828250i	$0.310663\pi$
$911$	−7.53014	+	42.7055i	−0.249485	+	1.41490i	−0.809843	+	0.586647i	$0.800448\pi$
$912$		0			0
$913$	−0.885409	−	0.322262i	−0.0293028	−	0.0106653i
$914$	−4.04181	−	5.40255i	−0.133691	−	0.178700i
$915$		0			0
$916$	2.24695	−	0.543698i	0.0742412	−	0.0179643i
$917$			15.3621i			0.507301i
$918$		0			0
$919$			31.6571i			1.04427i	0.852862	+	0.522136i	$0.174865\pi$
$919$			31.6571i			1.04427i	−0.852862	+	0.522136i	$0.825135\pi$
$920$	60.7368	+	71.3560i	2.00243	+	2.35254i
$921$		0			0
$922$	32.3661	−	24.2141i	1.06592	−	0.797448i
$923$	−19.4429	−	7.07662i	−0.639969	−	0.232930i
$924$		0			0
$925$	9.73706	−	55.2216i	0.320152	−	1.81567i
$926$	59.8993	+	3.34756i	1.96841	+	0.110008i
$927$		0			0
$928$	5.94387	+	1.70367i	0.195117	+	0.0559256i
$929$	−16.4439	−	45.1792i	−0.539507	−	1.48228i	−0.847449	−	0.530877i	$-0.821863\pi$
$929$	−16.4439	−	45.1792i	−0.539507	−	1.48228i	0.307942	−	0.951405i	$-0.400360\pi$
$930$		0			0
$931$	−2.92313	−	3.48365i	−0.0958016	−	0.114172i
$932$	33.9840	−	2.13960i	1.11318	−	0.0700848i
$933$		0			0
$934$	−6.24924	+	6.65505i	−0.204481	+	0.217760i
$935$	−5.42349	−	9.39376i	−0.177367	−	0.307209i
$936$		0			0
$937$	28.1506	−	48.7583i	0.919641	−	1.59287i	0.119681	−	0.992812i	$-0.461813\pi$
$937$	28.1506	−	48.7583i	0.919641	−	1.59287i	0.799961	−	0.600053i	$-0.204854\pi$
$938$	7.44602	+	24.6604i	0.243121	+	0.805192i
$939$		0			0
$940$	−29.0579	−	43.7315i	−0.947765	−	1.42636i
$941$	54.1362	−	9.54567i	1.76479	−	0.311180i	0.805288	−	0.592884i	$-0.202011\pi$
$941$	54.1362	−	9.54567i	1.76479	−	0.311180i	0.959501	+	0.281704i	$0.0908997\pi$
$942$		0			0
$943$	−4.95668	+	5.90715i	−0.161412	+	0.192363i
$944$	−10.7906	−	34.8480i	−0.351205	−	1.13421i
$945$		0			0
$946$	0.721807	+	1.42886i	0.0234680	+	0.0464561i
$947$	36.2498	+	30.4172i	1.17796	+	0.988427i	0.999990	+	0.00439122i	$0.00139777\pi$
$947$	36.2498	+	30.4172i	1.17796	+	0.988427i	0.177971	+	0.984036i	$0.443047\pi$
$948$		0			0
$949$	−1.73766	−	9.85477i	−0.0564069	−	0.319899i
$950$	−1.57871	−	13.2370i	−0.0512200	−	0.429463i
$951$		0			0
$952$	22.9828	+	8.18208i	0.744875	+	0.265183i
$953$	29.6972	+	17.1457i	0.961985	+	0.555402i	0.896783	−	0.442470i	$-0.145898\pi$
$953$	29.6972	+	17.1457i	0.961985	+	0.555402i	0.0652018	+	0.997872i	$0.479231\pi$
$954$		0			0
$955$	−37.7770	+	21.8106i	−1.22244	+	0.705774i
$956$	−0.681164	+	2.31477i	−0.0220304	+	0.0748651i
$957$		0			0
$958$	−19.8929	+	46.4165i	−0.642711	+	1.49965i
$959$	−4.38352	+	3.67821i	−0.141551	+	0.118776i
$960$		0			0
$961$	−19.3680	+	7.04939i	−0.624775	+	0.227400i
$962$	19.5439	+	12.7886i	0.630121	+	0.412320i
$963$		0			0
$964$	−8.00321	−	18.3164i	−0.257766	−	0.589932i
$965$	−84.7656	−	14.9465i	−2.72870	−	0.481143i
$966$		0			0
$967$	8.31365	−	22.8416i	0.267349	−	0.734535i	−0.731275	−	0.682083i	$-0.761074\pi$
$967$	8.31365	−	22.8416i	0.267349	−	0.734535i	0.998623	−	0.0524519i	$-0.0167036\pi$
$968$	−30.2236	+	0.213005i	−0.971425	+	0.00684625i
$969$		0			0
$970$	4.78965	−	20.4228i	0.153786	−	0.655737i
$971$	−39.8444			−1.27867			−0.639334	−	0.768929i	$-0.720790\pi$
$971$	−39.8444			−1.27867			−0.639334	+	0.768929i	$0.720790\pi$
$972$		0			0
$973$	−8.89676			−0.285217
$974$	−13.1294	+	55.9830i	−0.420693	+	1.79381i
$975$		0			0
$976$	17.0477	−	8.76321i	0.545682	−	0.280503i
$977$	−15.9360	+	43.7837i	−0.509836	+	1.40076i	0.371570	+	0.928405i	$0.378820\pi$
$977$	−15.9360	+	43.7837i	−0.509836	+	1.40076i	−0.881406	+	0.472359i	$0.843403\pi$
$978$		0			0
$979$	−6.96090	−	1.22739i	−0.222471	−	0.0392277i
$980$	−28.9936	+	12.6685i	−0.926167	+	0.404681i
$981$		0			0
$982$	−33.2781	−	21.7755i	−1.06195	−	0.694884i
$983$	−9.94420	+	3.61939i	−0.317171	+	0.115441i	−0.495700	−	0.868494i	$-0.665088\pi$
$983$	−9.94420	+	3.61939i	−0.317171	+	0.115441i	0.178529	+	0.983935i	$0.442866\pi$
$984$		0			0
$985$	1.27095	−	1.06645i	0.0404958	−	0.0339800i
$986$	−3.17029	+	7.39729i	−0.100963	+	0.235578i
$987$		0			0
$988$	5.32680	+	1.56751i	0.169468	+	0.0498690i
$989$	15.5885	−	9.00000i	0.495684	−	0.286183i
$990$		0			0
$991$	−20.1628	−	11.6410i	−0.640492	−	0.369788i	0.144312	−	0.989532i	$-0.453903\pi$
$991$	−20.1628	−	11.6410i	−0.640492	−	0.369788i	−0.784804	+	0.619744i	$0.787236\pi$
$992$	−10.1975	−	15.1148i	−0.323771	−	0.479896i
$993$		0			0
$994$	2.20970	+	18.5276i	0.0700875	+	0.587661i
$995$	−7.36626	−	41.7761i	−0.233526	−	1.32439i
$996$		0			0
$997$	−43.9556	−	36.8831i	−1.39209	−	1.16810i	−0.964486	−	0.264134i	$-0.914914\pi$
$997$	−43.9556	−	36.8831i	−1.39209	−	1.16810i	−0.427602	−	0.903967i	$-0.640642\pi$
$998$	21.1182	+	41.8047i	0.668486	+	1.32330i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.35.16		96
3.2	odd	2		108.2.l.a.11.1	✓	96
4.3	odd	2	inner	324.2.l.a.35.6		96
9.2	odd	6		972.2.l.d.755.10		96
9.4	even	3		972.2.l.b.431.5		96
9.5	odd	6		972.2.l.c.431.12		96
9.7	even	3		972.2.l.a.755.7		96
12.11	even	2		108.2.l.a.11.11	yes	96
27.4	even	9		972.2.l.d.215.12		96
27.5	odd	18	inner	324.2.l.a.287.6		96
27.13	even	9		972.2.l.c.539.2		96
27.14	odd	18		972.2.l.b.539.15		96
27.22	even	9		108.2.l.a.59.11	yes	96
27.23	odd	18		972.2.l.a.215.5		96
36.7	odd	6		972.2.l.a.755.5		96
36.11	even	6		972.2.l.d.755.12		96
36.23	even	6		972.2.l.c.431.2		96
36.31	odd	6		972.2.l.b.431.15		96
108.23	even	18		972.2.l.a.215.7		96
108.31	odd	18		972.2.l.d.215.10		96
108.59	even	18	inner	324.2.l.a.287.16		96
108.67	odd	18		972.2.l.c.539.12		96
108.95	even	18		972.2.l.b.539.5		96
108.103	odd	18		108.2.l.a.59.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.1	✓	96	3.2	odd	2
108.2.l.a.11.11	yes	96	12.11	even	2
108.2.l.a.59.1	yes	96	108.103	odd	18
108.2.l.a.59.11	yes	96	27.22	even	9
324.2.l.a.35.6		96	4.3	odd	2	inner
324.2.l.a.35.16		96	1.1	even	1	trivial
324.2.l.a.287.6		96	27.5	odd	18	inner
324.2.l.a.287.16		96	108.59	even	18	inner
972.2.l.a.215.5		96	27.23	odd	18
972.2.l.a.215.7		96	108.23	even	18
972.2.l.a.755.5		96	36.7	odd	6
972.2.l.a.755.7		96	9.7	even	3
972.2.l.b.431.5		96	9.4	even	3
972.2.l.b.431.15		96	36.31	odd	6
972.2.l.b.539.5		96	108.95	even	18
972.2.l.b.539.15		96	27.14	odd	18
972.2.l.c.431.2		96	36.23	even	6
972.2.l.c.431.12		96	9.5	odd	6
972.2.l.c.539.2		96	27.13	even	9
972.2.l.c.539.12		96	108.67	odd	18
972.2.l.d.215.10		96	108.31	odd	18
972.2.l.d.215.12		96	27.4	even	9
972.2.l.d.755.10		96	9.2	odd	6
972.2.l.d.755.12		96	36.11	even	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37686 + 0.322907i) q^{2} +(1.79146 + 0.889191i) q^{4} +(1.27150 - 3.49343i) q^{5} +(-1.63150 - 0.287677i) q^{7} +(2.17946 + 1.80276i) q^{8} +O(q^{10})\)	\(q+(1.37686 + 0.322907i) q^{2} +(1.79146 + 0.889191i) q^{4} +(1.27150 - 3.49343i) q^{5} +(-1.63150 - 0.287677i) q^{7} +(2.17946 + 1.80276i) q^{8} +(2.87873 - 4.39937i) q^{10} +(-0.526615 + 0.191672i) q^{11} +(1.99017 - 1.66995i) q^{13} +(-2.15344 - 0.922910i) q^{14} +(2.41868 + 3.18591i) q^{16} +(-4.50885 + 2.60318i) q^{17} +(0.925473 + 0.534322i) q^{19} +(5.38418 - 5.12774i) q^{20} +(-0.786966 + 0.0938576i) q^{22} +(1.54747 + 8.77613i) q^{23} +(-6.75711 - 5.66989i) q^{25} +(3.27942 - 1.65664i) q^{26} +(-2.66696 - 1.96607i) q^{28} +(0.702597 - 0.837323i) q^{29} +(-3.17422 + 0.559701i) q^{31} +(2.30142 + 5.16754i) q^{32} +(-7.04862 + 2.12827i) q^{34} +(-3.07943 + 5.33373i) q^{35} +(3.17849 + 5.50530i) q^{37} +(1.10171 + 1.03453i) q^{38} +(9.06902 - 5.32157i) q^{40} +(0.556211 + 0.662866i) q^{41} +(-0.690832 - 1.89805i) q^{43} +(-1.11385 - 0.124888i) q^{44} +(-0.703229 + 12.5832i) q^{46} +(1.22624 - 6.95438i) q^{47} +(-3.99883 - 1.45545i) q^{49} +(-7.47272 - 9.98853i) q^{50} +(5.05022 - 1.22201i) q^{52} +6.80497i q^{53} +2.08341i q^{55} +(-3.03717 - 3.56818i) q^{56} +(1.23775 - 0.925999i) q^{58} +(-8.57009 - 3.11926i) q^{59} +(0.832127 - 4.71923i) q^{61} +(-4.55118 - 0.254350i) q^{62} +(1.50009 + 7.85810i) q^{64} +(-3.30335 - 9.07588i) q^{65} +(-7.06749 - 8.42270i) q^{67} +(-10.3922 + 0.654280i) q^{68} +(-5.96223 + 6.34941i) q^{70} +(-3.98206 - 6.89713i) q^{71} +(1.92588 - 3.33572i) q^{73} +(2.59862 + 8.60636i) q^{74} +(1.18284 + 1.78014i) q^{76} +(0.914311 - 0.161218i) q^{77} +(-6.28979 + 7.49588i) q^{79} +(14.2051 - 4.39859i) q^{80} +(0.551778 + 1.09228i) q^{82} +(1.28797 + 1.08073i) q^{83} +(3.36102 + 19.0613i) q^{85} +(-0.338285 - 2.83641i) q^{86} +(-1.49328 - 0.531621i) q^{88} +(10.9229 + 6.30632i) q^{89} +(-3.72736 + 2.15199i) q^{91} +(-5.03143 + 17.0981i) q^{92} +(3.93398 - 9.17921i) q^{94} +(3.04336 - 2.55368i) q^{95} +(3.74927 - 1.36462i) q^{97} +(-5.03583 - 3.29520i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more