LMFDB - Embedded newform 216.2.v.b.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 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("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.505867 + 1.32064i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(-1.48820 + 1.33614i) q^{4} +(3.21396 + 1.16979i) q^{5} +(0.683248 - 2.35227i) q^{6} +(-0.199218 - 0.0351275i) q^{7} +(-2.51739 - 1.28947i) q^{8} +(0.811221 + 2.88824i) q^{9} +O(q^{10})$	\(q+(0.505867 + 1.32064i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(-1.48820 + 1.33614i) q^{4} +(3.21396 + 1.16979i) q^{5} +(0.683248 - 2.35227i) q^{6} +(-0.199218 - 0.0351275i) q^{7} +(-2.51739 - 1.28947i) q^{8} +(0.811221 + 2.88824i) q^{9} +(0.0809654 + 4.83625i) q^{10} +(1.37658 + 3.78212i) q^{11} +(3.45214 - 0.287608i) q^{12} +(1.09713 + 1.30751i) q^{13} +(-0.0543868 - 0.280866i) q^{14} +(-3.21293 - 4.97704i) q^{15} +(0.429466 - 3.97688i) q^{16} +(1.57350 - 0.908459i) q^{17} +(-3.40396 + 2.53240i) q^{18} +(-3.24004 + 5.61192i) q^{19} +(-6.34601 + 2.55343i) q^{20} +(0.238260 + 0.256900i) q^{21} +(-4.29847 + 3.73122i) q^{22} +(-1.37566 - 7.80173i) q^{23} +(2.12615 + 4.41356i) q^{24} +(5.13093 + 4.30536i) q^{25} +(-1.17176 + 2.11035i) q^{26} +(1.90163 - 4.83568i) q^{27} +(0.343411 - 0.213906i) q^{28} +(-3.08543 - 2.58898i) q^{29} +(4.94759 - 6.76085i) q^{30} +(7.51214 - 1.32459i) q^{31} +(5.46929 - 1.44460i) q^{32} +(2.05631 - 6.66106i) q^{33} +(1.99573 + 1.61847i) q^{34} +(-0.599188 - 0.345941i) q^{35} +(-5.06634 - 3.21437i) q^{36} +(1.53384 - 0.885560i) q^{37} +(-9.05037 - 1.44006i) q^{38} +(-0.146696 - 2.95269i) q^{39} +(-6.58240 - 7.08912i) q^{40} +(-6.61260 - 7.88059i) q^{41} +(-0.218745 + 0.444614i) q^{42} +(3.47909 - 1.26628i) q^{43} +(-7.10206 - 3.78924i) q^{44} +(-0.771390 + 10.2316i) q^{45} +(9.60741 - 5.76339i) q^{46} +(0.523875 - 2.97105i) q^{47} +(-4.75319 + 5.04056i) q^{48} +(-6.53939 - 2.38014i) q^{49} +(-3.09028 + 8.95407i) q^{50} +(-3.12248 - 0.392012i) q^{51} +(-3.37977 - 0.479915i) q^{52} +9.46508 q^{53} +(7.34818 + 0.0651731i) q^{54} +13.7659i q^{55} +(0.456214 + 0.345316i) q^{56} +(10.3435 - 4.35740i) q^{57} +(1.85830 - 5.38442i) q^{58} +(1.23077 - 3.38152i) q^{59} +(11.4315 + 3.11391i) q^{60} +(-8.13039 - 1.43361i) q^{61} +(5.54946 + 9.25079i) q^{62} +(-0.0601532 - 0.603885i) q^{63} +(4.67453 + 6.49221i) q^{64} +(1.99664 + 5.48571i) q^{65} +(9.83711 - 0.653959i) q^{66} +(-1.26475 + 1.06125i) q^{67} +(-1.12785 + 3.45438i) q^{68} +(-6.26262 + 12.2089i) q^{69} +(0.153756 - 0.966313i) q^{70} +(-2.24594 - 3.89008i) q^{71} +(1.68214 - 8.31688i) q^{72} +(-4.05026 + 7.01525i) q^{73} +(1.94543 + 1.57767i) q^{74} +(-2.57896 - 11.3109i) q^{75} +(-2.67648 - 12.6808i) q^{76} +(-0.141383 - 0.801822i) q^{77} +(3.82524 - 1.68740i) q^{78} +(-0.380899 + 0.453938i) q^{79} +(6.03238 - 12.2792i) q^{80} +(-7.68384 + 4.68600i) q^{81} +(7.06236 - 12.7194i) q^{82} +(-8.02454 + 9.56328i) q^{83} +(-0.697832 - 0.0639685i) q^{84} +(6.11986 - 1.07910i) q^{85} +(3.43227 + 3.95406i) q^{86} +(1.55083 + 6.80168i) q^{87} +(1.41154 - 11.2961i) q^{88} +(10.7122 + 6.18471i) q^{89} +(-13.9026 + 4.15712i) q^{90} +(-0.172639 - 0.299020i) q^{91} +(12.4714 + 9.77245i) q^{92} +(-11.7557 - 6.03016i) q^{93} +(4.18870 - 0.811100i) q^{94} +(-16.9781 + 14.2463i) q^{95} +(-9.06126 - 3.72741i) q^{96} +(-8.24324 + 3.00029i) q^{97} +(-0.164739 - 9.84024i) q^{98} +(-9.80695 + 7.04402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.505867	+	1.32064i	0.357702	+	0.933836i
$2$	0.505867	+	1.32064i	0.357702	+	0.933836i
$3$	−1.38044	−	1.04613i	−0.796997	−	0.603984i
$3$	−1.38044	−	1.04613i	−0.796997	−	0.603984i
$4$	−1.48820	+	1.33614i	−0.744099	+	0.668069i
$5$	3.21396	+	1.16979i	1.43733	+	0.523144i	0.939022	−	0.343857i	$-0.111734\pi$
$5$	3.21396	+	1.16979i	1.43733	+	0.523144i	0.498306	+	0.867001i	$0.333956\pi$
$6$	0.683248	−	2.35227i	0.278935	−	0.960310i
$7$	−0.199218	−	0.0351275i	−0.0752973	−	0.0132770i	0.135873	−	0.990726i	$-0.456616\pi$
$7$	−0.199218	−	0.0351275i	−0.0752973	−	0.0132770i	−0.211170	+	0.977449i	$0.567727\pi$
$8$	−2.51739	−	1.28947i	−0.890033	−	0.455897i
$9$	0.811221	+	2.88824i	0.270407	+	0.962746i
$10$	0.0809654	+	4.83625i	0.0256035	+	1.52936i
$11$	1.37658	+	3.78212i	0.415054	+	1.14035i	0.954469	+	0.298311i	$0.0964234\pi$
$11$	1.37658	+	3.78212i	0.415054	+	1.14035i	−0.539414	+	0.842040i	$0.681354\pi$
$12$	3.45214	−	0.287608i	0.996547	−	0.0830253i
$13$	1.09713	+	1.30751i	0.304290	+	0.362639i	0.896422	−	0.443202i	$-0.146158\pi$
$13$	1.09713	+	1.30751i	0.304290	+	0.362639i	−0.592131	+	0.805842i	$0.701713\pi$
$14$	−0.0543868	−	0.280866i	−0.0145355	−	0.0750646i
$15$	−3.21293	−	4.97704i	−0.829574	−	1.28507i
$16$	0.429466	−	3.97688i	0.107366	−	0.994220i
$17$	1.57350	−	0.908459i	0.381629	−	0.220334i	−0.296898	−	0.954909i	$-0.595952\pi$
$17$	1.57350	−	0.908459i	0.381629	−	0.220334i	0.678527	+	0.734576i	$0.262619\pi$
$18$	−3.40396	+	2.53240i	−0.802322	+	0.596892i
$19$	−3.24004	+	5.61192i	−0.743317	+	1.28746i	0.207661	+	0.978201i	$0.433415\pi$
$19$	−3.24004	+	5.61192i	−0.743317	+	1.28746i	−0.950977	+	0.309261i	$0.899918\pi$
$20$	−6.34601	+	2.55343i	−1.41901	+	0.570963i
$21$	0.238260	+	0.256900i	0.0519927	+	0.0560601i
$22$	−4.29847	+	3.73122i	−0.916436	+	0.795498i
$23$	−1.37566	−	7.80173i	−0.286844	−	1.62677i	−0.698623	−	0.715490i	$-0.746204\pi$
$23$	−1.37566	−	7.80173i	−0.286844	−	1.62677i	0.411779	−	0.911284i	$-0.364908\pi$
$24$	2.12615	+	4.41356i	0.433999	+	0.900913i
$25$	5.13093	+	4.30536i	1.02619	+	0.861072i
$26$	−1.17176	+	2.11035i	−0.229800	+	0.413874i
$27$	1.90163	−	4.83568i	0.365970	−	0.930627i
$28$	0.343411	−	0.213906i	0.0648986	−	0.0404245i
$29$	−3.08543	−	2.58898i	−0.572949	−	0.480761i	0.309674	−	0.950843i	$-0.399780\pi$
$29$	−3.08543	−	2.58898i	−0.572949	−	0.480761i	−0.882623	+	0.470081i	$0.844225\pi$
$30$	4.94759	−	6.76085i	0.903302	−	1.23436i
$31$	7.51214	−	1.32459i	1.34922	−	0.237904i	0.548103	−	0.836411i	$-0.315350\pi$
$31$	7.51214	−	1.32459i	1.34922	−	0.237904i	0.801117	+	0.598507i	$0.204239\pi$
$32$	5.46929	−	1.44460i	0.966843	−	0.255371i
$33$	2.05631	−	6.66106i	0.357957	−	1.15954i
$34$	1.99573	+	1.61847i	0.342265	+	0.277565i
$35$	−0.599188	−	0.345941i	−0.101281	−	0.0584747i
$36$	−5.06634	−	3.21437i	−0.844391	−	0.535728i
$37$	1.53384	−	0.885560i	0.252161	−	0.145585i	−0.368592	−	0.929591i	$-0.620160\pi$
$37$	1.53384	−	0.885560i	0.252161	−	0.145585i	0.620753	+	0.784006i	$0.286827\pi$
$38$	−9.05037	−	1.44006i	−1.46816	−	0.233608i
$39$	−0.146696	−	2.95269i	−0.0234902	−	0.472809i
$40$	−6.58240	−	7.08912i	−1.04077	−	1.12089i
$41$	−6.61260	−	7.88059i	−1.03271	−	1.23074i	−0.972584	−	0.232551i	$-0.925293\pi$
$41$	−6.61260	−	7.88059i	−1.03271	−	1.23074i	−0.0601305	−	0.998191i	$-0.519152\pi$
$42$	−0.218745	+	0.444614i	−0.0337530	+	0.0686054i
$43$	3.47909	−	1.26628i	0.530556	−	0.193107i	−0.0628305	−	0.998024i	$-0.520013\pi$
$43$	3.47909	−	1.26628i	0.530556	−	0.193107i	0.593387	+	0.804918i	$0.297791\pi$
$44$	−7.10206	−	3.78924i	−1.07068	−	0.571250i
$45$	−0.771390	+	10.2316i	−0.114992	+	1.52524i
$46$	9.60741	−	5.76339i	1.41654	−	0.849765i
$47$	0.523875	−	2.97105i	0.0764151	−	0.433371i	−0.922466	−	0.386078i	$-0.873829\pi$
$47$	0.523875	−	2.97105i	0.0764151	−	0.433371i	0.998881	−	0.0472931i	$-0.0150595\pi$
$48$	−4.75319	+	5.04056i	−0.686063	+	0.727542i
$49$	−6.53939	−	2.38014i	−0.934199	−	0.340021i
$50$	−3.09028	+	8.95407i	−0.437032	+	1.26630i
$51$	−3.12248	−	0.392012i	−0.437235	−	0.0548927i
$52$	−3.37977	−	0.479915i	−0.468690	−	0.0665523i
$53$	9.46508			1.30013			0.650064	−	0.759879i	$-0.274742\pi$
$53$	9.46508			1.30013			0.650064	+	0.759879i	$0.274742\pi$
$54$	7.34818	+	0.0651731i	0.999961	+	0.00886894i
$55$			13.7659i			1.85619i
$56$	0.456214	+	0.345316i	0.0609642	+	0.0461447i
$57$	10.3435	−	4.35740i	1.37003	−	0.577152i
$58$	1.85830	−	5.38442i	0.244007	−	0.707010i
$59$	1.23077	−	3.38152i	0.160233	−	0.440237i	−0.833432	−	0.552623i	$-0.813627\pi$
$59$	1.23077	−	3.38152i	0.160233	−	0.440237i	0.993665	+	0.112386i	$0.0358493\pi$
$60$	11.4315	+	3.11391i	1.47580	+	0.402004i
$61$	−8.13039	−	1.43361i	−1.04099	−	0.183555i	−0.373082	−	0.927798i	$-0.621699\pi$
$61$	−8.13039	−	1.43361i	−1.04099	−	0.183555i	−0.667908	+	0.744244i	$0.732810\pi$
$62$	5.54946	+	9.25079i	0.704782	+	1.17485i
$63$	−0.0601532	−	0.603885i	−0.00757859	−	0.0760824i
$64$	4.67453	+	6.49221i	0.584316	+	0.811526i
$65$	1.99664	+	5.48571i	0.247652	+	0.680419i
$66$	9.83711	−	0.653959i	1.21086	−	0.0804968i
$67$	−1.26475	+	1.06125i	−0.154514	+	0.129653i	−0.716767	−	0.697312i	$-0.754379\pi$
$67$	−1.26475	+	1.06125i	−0.154514	+	0.129653i	0.562253	+	0.826965i	$0.309935\pi$
$68$	−1.12785	+	3.45438i	−0.136772	+	0.418905i
$69$	−6.26262	+	12.2089i	−0.753931	+	1.46978i
$70$	0.153756	−	0.966313i	0.0183773	−	0.115497i
$71$	−2.24594	−	3.89008i	−0.266544	−	0.461668i	0.701423	−	0.712745i	$-0.252548\pi$
$71$	−2.24594	−	3.89008i	−0.266544	−	0.461668i	−0.967967	+	0.251078i	$0.919215\pi$
$72$	1.68214	−	8.31688i	0.198242	−	0.980153i
$73$	−4.05026	+	7.01525i	−0.474047	+	0.821073i	−0.999558	−	0.0297132i	$-0.990541\pi$
$73$	−4.05026	+	7.01525i	−0.474047	+	0.821073i	0.525512	+	0.850786i	$0.323874\pi$
$74$	1.94543	+	1.57767i	0.226151	+	0.183401i
$75$	−2.57896	−	11.3109i	−0.297793	−	1.30607i
$76$	−2.67648	−	12.6808i	−0.307013	−	1.45459i
$77$	−0.141383	−	0.801822i	−0.0161121	−	0.0913761i
$78$	3.82524	−	1.68740i	0.433123	−	0.191060i
$79$	−0.380899	+	0.453938i	−0.0428545	+	0.0510720i	−0.787046	−	0.616894i	$-0.788391\pi$
$79$	−0.380899	+	0.453938i	−0.0428545	+	0.0510720i	0.744191	+	0.667966i	$0.232835\pi$
$80$	6.03238	−	12.2792i	0.674441	−	1.37285i
$81$	−7.68384	+	4.68600i	−0.853760	+	0.520666i
$82$	7.06236	−	12.7194i	0.779907	−	1.40462i
$83$	−8.02454	+	9.56328i	−0.880808	+	1.04971i	0.117586	+	0.993063i	$0.462484\pi$
$83$	−8.02454	+	9.56328i	−0.880808	+	1.04971i	−0.998394	+	0.0566436i	$0.981960\pi$
$84$	−0.697832	−	0.0639685i	−0.0761397	−	0.00697953i
$85$	6.11986	−	1.07910i	0.663792	−	0.117044i
$86$	3.43227	+	3.95406i	0.370111	+	0.426378i
$87$	1.55083	+	6.80168i	0.166266	+	0.729217i
$88$	1.41154	−	11.2961i	0.150471	−	1.20417i
$89$	10.7122	+	6.18471i	1.13549	+	0.655578i	0.945311	−	0.326171i	$-0.105759\pi$
$89$	10.7122	+	6.18471i	1.13549	+	0.655578i	0.190183	+	0.981749i	$0.439092\pi$
$90$	−13.9026	+	4.15712i	−1.46546	+	0.438199i
$91$	−0.172639	−	0.299020i	−0.0180975	−	0.0313458i
$92$	12.4714	+	9.77245i	1.30024	+	1.01885i
$93$	−11.7557	−	6.03016i	−1.21901	−	0.625299i
$94$	4.18870	−	0.811100i	0.432032	−	0.0836586i
$95$	−16.9781	+	14.2463i	−1.74192	+	1.46164i
$96$	−9.06126	−	3.72741i	−0.924811	−	0.380427i
$97$	−8.24324	+	3.00029i	−0.836974	+	0.304634i	−0.724718	−	0.689046i	$-0.758030\pi$
$97$	−8.24324	+	3.00029i	−0.836974	+	0.304634i	−0.112256	+	0.993679i	$0.535808\pi$
$98$	−0.164739	−	9.84024i	−0.0166412	−	0.994015i
$99$	−9.80695	+	7.04402i	−0.985636	+	0.707951i
$100$	−13.3884	+	0.448406i	−1.33884	+	0.0448406i
$101$	1.79803	−	10.1971i	0.178910	−	1.01465i	−0.754623	−	0.656159i	$-0.772180\pi$
$101$	1.79803	−	10.1971i	0.178910	−	1.01465i	0.933533	−	0.358491i	$-0.116709\pi$
$102$	−1.06185	−	4.32199i	−0.105139	−	0.427941i
$103$	2.22000	−	6.09941i	0.218744	−	0.600993i	−0.780979	−	0.624558i	$-0.785279\pi$
$103$	2.22000	−	6.09941i	0.218744	−	0.600993i	0.999722	+	0.0235646i	$0.00750153\pi$
$104$	−1.07592	−	4.70625i	−0.105502	−	0.461486i
$105$	0.465242	+	1.10438i	0.0454030	+	0.107776i
$106$	4.78807	+	12.5000i	0.465058	+	1.21411i
$107$		−	2.26037i		−	0.218518i	−0.994013	−	0.109259i	$-0.965152\pi$
$107$		−	2.26037i		−	0.218518i	0.994013	−	0.109259i	$-0.0348478\pi$
$108$	3.63113	+	9.73729i	0.349406	+	0.936972i
$109$			3.00655i			0.287975i	0.989580	+	0.143987i	$0.0459925\pi$
$109$			3.00655i			0.287975i	−0.989580	+	0.143987i	$0.954008\pi$
$110$	−18.1798	+	6.96371i	−1.73338	+	0.663963i
$111$	−3.04378	−	0.382131i	−0.288902	−	0.0362703i
$112$	−0.225255	+	0.777180i	−0.0212846	+	0.0734366i
$113$	1.92611	−	5.29194i	0.181193	−	0.497824i	−0.815530	−	0.578715i	$-0.803554\pi$
$113$	1.92611	−	5.29194i	0.181193	−	0.497824i	0.996723	+	0.0808910i	$0.0257766\pi$
$114$	10.9870	+	11.4558i	1.02903	+	1.07293i
$115$	4.70506	−	26.6837i	0.438749	−	2.48827i
$116$	8.05096	−	0.269644i	0.747513	−	0.0250358i
$117$	−2.88639	+	4.22947i	−0.266847	+	0.391014i
$118$	5.08839	−	0.0851866i	0.468424	−	0.00784206i
$119$	−0.345381	+	0.125708i	−0.0316610	+	0.0115237i
$120$	1.67045	+	16.6721i	0.152490	+	1.52195i
$121$	−3.98297	+	3.34211i	−0.362088	+	0.303828i
$122$	−2.21961	−	11.4626i	−0.200954	−	1.03777i
$123$	0.884160	+	17.7963i	0.0797220	+	1.60464i
$124$	−9.40971	+	12.0085i	−0.845017	+	1.07840i
$125$	2.90369	+	5.02934i	0.259714	+	0.449838i
$126$	0.767088	−	0.384926i	0.0683376	−	0.0342920i
$127$	9.60934	+	5.54795i	0.852691	+	0.492301i	0.861558	−	0.507660i	$-0.169489\pi$
$127$	9.60934	+	5.54795i	0.852691	+	0.492301i	−0.00886716	+	0.999961i	$0.502823\pi$
$128$	−6.20920	+	9.45758i	−0.548821	+	0.835940i
$129$	−6.12737	−	1.89155i	−0.539485	−	0.166542i
$130$	−6.23464	+	5.41188i	−0.546814	+	0.474654i
$131$	7.26270	−	1.28061i	0.634545	−	0.111887i	0.152883	−	0.988244i	$-0.451144\pi$
$131$	7.26270	−	1.28061i	0.634545	−	0.111887i	0.481662	+	0.876357i	$0.340033\pi$
$132$	5.83991	+	12.6605i	0.508299	+	1.10195i
$133$	0.842608	−	1.00418i	0.0730633	−	0.0870735i
$134$	−2.04134	−	1.13344i	−0.176345	−	0.0979139i
$135$	11.7685	−	13.3172i	1.01287	−	1.14616i
$136$	−5.13254	+	0.257970i	−0.440112	+	0.0221207i
$137$	7.46073	−	8.89135i	0.637413	−	0.759640i	−0.346546	−	0.938033i	$-0.612646\pi$
$137$	7.46073	−	8.89135i	0.637413	−	0.759640i	0.983959	+	0.178393i	$0.0570900\pi$
$138$	−19.2917	−	2.09460i	−1.64222	−	0.178305i
$139$	1.37040	+	7.77191i	0.116236	+	0.659205i	0.986131	+	0.165969i	$0.0530751\pi$
$139$	1.37040	+	7.77191i	0.116236	+	0.659205i	−0.869895	+	0.493236i	$0.835814\pi$
$140$	1.35393	−	0.285769i	0.114428	−	0.0241519i
$141$	−3.83128	+	3.55330i	−0.322652	+	0.299242i
$142$	4.00126	−	4.93395i	0.335779	−	0.414048i
$143$	−3.43488	+	5.94939i	−0.287239	+	0.497513i
$144$	11.8346	−	1.98573i	0.986214	−	0.165477i
$145$	−6.88789	−	11.9302i	−0.572008	−	0.990747i
$146$	−11.3135	−	1.80016i	−0.936315	−	0.148983i
$147$	6.53729	+	10.1267i	0.539186	+	0.835237i
$148$	−1.09942	+	3.36731i	−0.0903717	+	0.276791i
$149$	5.38903	−	4.52193i	0.441486	−	0.370451i	−0.394779	−	0.918776i	$-0.629179\pi$
$149$	5.38903	−	4.52193i	0.441486	−	0.370451i	0.836265	+	0.548325i	$0.184734\pi$
$150$	13.6331	−	9.12770i	1.11314	−	0.745274i
$151$	2.14375	+	5.88990i	0.174456	+	0.479313i	0.995846	−	0.0910533i	$-0.0290234\pi$
$151$	2.14375	+	5.88990i	0.174456	+	0.479313i	−0.821390	+	0.570367i	$0.806801\pi$
$152$	15.3929	−	9.94946i	1.24853	−	0.807008i
$153$	3.90030	+	3.80767i	0.315320	+	0.307832i
$154$	0.987400	−	0.592332i	0.0795670	−	0.0477314i
$155$	25.6932	+	4.53041i	2.06373	+	0.363891i
$156$	4.16351	+	4.19818i	0.333348	+	0.336123i
$157$	−1.70377	+	4.68108i	−0.135976	+	0.373591i	−0.988928	−	0.148399i	$-0.952588\pi$
$157$	−1.70377	+	4.68108i	−0.135976	+	0.373591i	0.852952	+	0.521990i	$0.174810\pi$
$158$	−0.792174	−	0.273400i	−0.0630220	−	0.0217505i
$159$	−13.0660	−	9.90171i	−1.03620	−	0.785257i
$160$	19.2680	+	1.75501i	1.52327	+	0.138746i
$161$			1.60257i			0.126300i
$162$	−10.0755	−	7.77713i	−0.791608	−	0.611029i
$163$	6.53033			0.511495			0.255747	−	0.966744i	$-0.417679\pi$
$163$	6.53033			0.511495			0.255747	+	0.966744i	$0.417679\pi$
$164$	20.3704	+	2.89252i	1.59066	+	0.225868i
$165$	14.4009	−	19.0030i	1.12111	−	1.47938i
$166$	−16.6890	−	5.75982i	−1.29532	−	0.447048i
$167$	−11.5164	−	4.19163i	−0.891167	−	0.324358i	−0.144460	−	0.989511i	$-0.546144\pi$
$167$	−11.5164	−	4.19163i	−0.891167	−	0.324358i	−0.746708	+	0.665152i	$0.768367\pi$
$168$	−0.268530	−	0.953947i	−0.0207176	−	0.0735986i
$169$	1.75154	−	9.93346i	0.134734	−	0.764113i
$170$	4.52094	+	7.53628i	0.346740	+	0.578006i
$171$	−18.8369	−	4.80551i	−1.44050	−	0.367487i
$172$	−3.48564	+	6.53303i	−0.265778	+	0.498139i
$173$	22.9308	−	8.34612i	1.74339	−	0.634543i	0.743961	−	0.668223i	$-0.232945\pi$
$173$	22.9308	−	8.34612i	1.74339	−	0.634543i	0.999433	+	0.0336797i	$0.0107226\pi$
$174$	−8.19809	+	5.48884i	−0.621495	+	0.416108i
$175$	−0.870937	−	1.03794i	−0.0658367	−	0.0784611i
$176$	15.6322	−	3.85020i	1.17832	−	0.290219i
$177$	−5.23652	+	3.38043i	−0.393601	+	0.254089i
$178$	−2.74883	+	17.2757i	−0.206034	+	1.29487i
$179$	−12.4964	+	7.21481i	−0.934026	+	0.539260i	−0.888083	−	0.459684i	$-0.847963\pi$
$179$	−12.4964	+	7.21481i	−0.934026	+	0.539260i	−0.0459437	+	0.998944i	$0.514629\pi$
$180$	−12.5229	−	16.2574i	−0.933403	−	1.21175i
$181$	−17.7079	−	10.2237i	−1.31622	−	0.759919i	−0.333100	−	0.942892i	$-0.608095\pi$
$181$	−17.7079	−	10.2237i	−1.31622	−	0.759919i	−0.983118	+	0.182973i	$0.941428\pi$
$182$	0.307566	−	0.379259i	0.0227983	−	0.0281126i
$183$	9.72376	+	10.4845i	0.718801	+	0.775034i
$184$	−6.59704	+	21.4139i	−0.486340	+	1.57865i
$185$	5.96560	−	1.05190i	0.438600	−	0.0773370i
$186$	2.01685	−	18.5756i	0.147883	−	1.36203i
$187$	5.60194	+	4.70059i	0.409655	+	0.343741i
$188$	3.19010	+	5.12147i	0.232662	+	0.373522i
$189$	−0.548705	+	0.896555i	−0.0399124	+	0.0652148i
$190$	−27.4030	−	15.2153i	−1.98802	−	1.10383i
$191$	15.9522	+	13.3855i	1.15426	+	0.968538i	0.999811	−	0.0194633i	$-0.00619574\pi$
$191$	15.9522	+	13.3855i	1.15426	+	0.968538i	0.154448	+	0.988001i	$0.450640\pi$
$192$	0.338794	−	13.8523i	0.0244504	−	0.999701i
$193$	0.989078	+	5.60934i	0.0711954	+	0.403769i	0.999490	+	0.0319244i	$0.0101636\pi$
$193$	0.989078	+	5.60934i	0.0711954	+	0.403769i	−0.928295	+	0.371845i	$0.878725\pi$
$194$	−8.13229	−	9.36863i	−0.583865	−	0.672628i
$195$	2.98254	−	9.66143i	0.213584	−	0.691869i
$196$	12.9121	−	5.19541i	0.922294	−	0.371101i
$197$	−13.4024	+	23.2137i	−0.954885	+	1.65391i	−0.220254	+	0.975443i	$0.570688\pi$
$197$	−13.4024	+	23.2137i	−0.954885	+	1.65391i	−0.734631	+	0.678467i	$0.762645\pi$
$198$	−14.2637	−	9.38815i	−1.01367	−	0.667187i
$199$	−22.2890	+	12.8685i	−1.58002	+	0.912226i	−0.585168	+	0.810912i	$0.698971\pi$
$199$	−22.2890	+	12.8685i	−1.58002	+	0.912226i	−0.994854	+	0.101314i	$0.967695\pi$
$200$	−7.36493	−	17.4545i	−0.520779	−	1.23422i
$201$	2.85613	−	0.141899i	0.201456	−	0.0100088i
$202$	14.3763	−	2.78383i	1.01151	−	0.195869i
$203$	0.523728	+	0.624155i	0.0367585	+	0.0438071i
$204$	5.17065	−	3.58868i	0.362018	−	0.251258i
$205$	−12.0340	−	33.0633i	−0.840494	−	2.30924i
$206$	9.17818	−	0.153655i	0.639474	−	0.0107057i
$207$	21.4173	−	10.3021i	1.48861	−	0.716049i
$208$	5.67100	−	3.80164i	0.393213	−	0.263596i
$209$	−25.6851	−	4.52898i	−1.77668	−	0.313276i
$210$	−1.22314	+	1.17309i	−0.0844047	+	0.0809507i
$211$	−2.22400	−	0.809471i	−0.153107	−	0.0557263i	0.264330	−	0.964432i	$-0.414849\pi$
$211$	−2.22400	−	0.809471i	−0.153107	−	0.0557263i	−0.417437	+	0.908706i	$0.637071\pi$
$212$	−14.0859	+	12.6467i	−0.967424	+	0.868576i
$213$	−0.969152	+	7.71956i	−0.0664052	+	0.528936i
$214$	2.98514	−	1.14344i	0.204060	−	0.0781643i
$215$	12.6629			0.863606
$216$	−11.0226	+	9.72120i	−0.749995	+	0.661444i
$217$	−1.54308			−0.104751
$218$	−3.97058	+	1.52091i	−0.268921	+	0.103009i
$219$	12.9300	−	5.44703i	0.873729	−	0.368076i
$220$	−18.3931	−	20.4864i	−1.24007	−	1.38119i
$221$	2.91416	+	1.06067i	0.196028	+	0.0713482i
$222$	−1.03509	−	4.21305i	−0.0694705	−	0.282761i
$223$	19.7258	+	3.47820i	1.32094	+	0.232917i	0.789277	−	0.614038i	$-0.210456\pi$
$223$	19.7258	+	3.47820i	1.32094	+	0.232917i	0.531664	+	0.846955i	$0.321567\pi$
$224$	−1.14033	+	0.0956676i	−0.0761913	+	0.00639206i
$225$	−8.27259	+	18.3119i	−0.551506	+	1.22080i
$226$	7.96312	−	0.133313i	0.529699	−	0.00886788i
$227$	−8.81116	−	24.2085i	−0.584817	−	1.60677i	−0.779843	−	0.625975i	$-0.784701\pi$
$227$	−8.81116	−	24.2085i	−0.584817	−	1.60677i	0.195026	−	0.980798i	$-0.437521\pi$
$228$	−9.57105	+	20.3050i	−0.633858	+	1.34473i
$229$	1.43440	+	1.70946i	0.0947880	+	0.112964i	0.811353	−	0.584556i	$-0.198731\pi$
$229$	1.43440	+	1.70946i	0.0947880	+	0.112964i	−0.716565	+	0.697520i	$0.754287\pi$
$230$	37.6198	−	7.28469i	2.48057	−	0.480338i
$231$	−0.643641	+	1.25477i	−0.0423484	+	0.0825579i
$232$	4.42881	+	10.4960i	0.290766	+	0.689099i
$233$	−7.43882	+	4.29480i	−0.487333	+	0.281362i	−0.723467	−	0.690358i	$-0.757453\pi$
$233$	−7.43882	+	4.29480i	−0.487333	+	0.281362i	0.236134	+	0.971720i	$0.424119\pi$
$234$	−7.04575	−	1.67235i	−0.460595	−	0.109325i
$235$	5.15920	−	8.93600i	0.336549	−	0.582921i
$236$	2.68655	+	6.67686i	0.174879	+	0.434626i
$237$	1.00069	−	0.228163i	0.0650016	−	0.0148208i
$238$	−0.340733	−	0.392533i	−0.0220864	−	0.0254442i
$239$	−0.254336	−	1.44241i	−0.0164516	−	0.0933018i	0.975476	−	0.220104i	$-0.0706397\pi$
$239$	−0.254336	−	1.44241i	−0.0164516	−	0.0933018i	−0.991928	+	0.126802i	$0.959529\pi$
$240$	−21.1729	+	10.6400i	−1.36671	+	0.686806i
$241$	1.54665	+	1.29779i	0.0996285	+	0.0835982i	0.691241	−	0.722624i	$-0.257064\pi$
$241$	1.54665	+	1.29779i	0.0996285	+	0.0835982i	−0.591613	+	0.806222i	$0.701509\pi$
$242$	−6.42858	−	3.56942i	−0.413245	−	0.229451i
$243$	15.5092	+	1.56957i	0.994918	+	0.100688i
$244$	14.0151	−	8.72984i	0.897227	−	0.558871i
$245$	−18.2331	−	15.2994i	−1.16487	−	0.977442i
$246$	−23.0553	+	10.1702i	−1.46995	+	0.648430i
$247$	−10.8924	+	1.92063i	−0.693068	+	0.122207i
$248$	−20.6190	−	6.35216i	−1.30931	−	0.403363i
$249$	21.0818	−	4.80680i	1.33601	−	0.304618i
$250$	−5.17309	+	6.37892i	−0.327175	+	0.403438i
$251$	−0.0195920	−	0.0113115i	−0.00123664	−	0.000713973i	0.499382	−	0.866382i	$-0.333561\pi$
$251$	−0.0195920	−	0.0113115i	−0.00123664	−	0.000713973i	−0.500618	+	0.865668i	$0.666894\pi$
$252$	0.896395	+	0.818328i	0.0564675	+	0.0515498i
$253$	27.6134	−	15.9426i	1.73604	−	1.00230i
$254$	−2.46582	+	15.4970i	−0.154720	+	0.972370i
$255$	−9.57697	−	4.91255i	−0.599733	−	0.307636i
$256$	−15.6311	−	3.41586i	−0.976945	−	0.213492i
$257$	−10.5865	−	12.6165i	−0.660369	−	0.786997i	0.327070	−	0.945000i	$-0.393939\pi$
$257$	−10.5865	−	12.6165i	−0.660369	−	0.786997i	−0.987439	+	0.158003i	$0.949494\pi$
$258$	−0.601563	−	9.04894i	−0.0374517	−	0.563363i
$259$	−0.336675	+	0.122540i	−0.0209200	+	0.00761425i
$260$	−10.3011	−	5.49604i	−0.638845	−	0.340850i
$261$	4.97463	−	11.0117i	0.307922	−	0.681606i
$262$	5.36519	+	8.94362i	0.331462	+	0.552538i
$263$	1.02766	−	5.82816i	0.0633684	−	0.359380i	−0.936592	−	0.350423i	$-0.886038\pi$
$263$	1.02766	−	5.82816i	0.0633684	−	0.359380i	0.999960	−	0.00895677i	$-0.00285107\pi$
$264$	−13.7658	+	14.1170i	−0.847225	+	0.868839i
$265$	30.4204	+	11.0721i	1.86871	+	0.680155i
$266$	1.75241	+	0.604803i	0.107447	+	0.0370828i
$267$	−8.31756	−	19.7440i	−0.509026	−	1.20831i
$268$	0.464221	−	3.26924i	0.0283568	−	0.199701i
$269$	−4.98736			−0.304085			−0.152042	−	0.988374i	$-0.548585\pi$
$269$	−4.98736			−0.304085			−0.152042	+	0.988374i	$0.548585\pi$
$270$	23.5405	+	8.80527i	1.43263	+	0.535871i
$271$		−	7.03519i		−	0.427358i	−0.976904	−	0.213679i	$-0.931455\pi$
$271$		−	7.03519i		−	0.427358i	0.976904	−	0.213679i	$-0.0685446\pi$
$272$	−2.93707	−	6.64776i	−0.178086	−	0.403079i
$273$	−0.0744961	+	0.593382i	−0.00450871	+	0.0359131i
$274$	15.5164	+	5.35513i	0.937382	+	0.323515i
$275$	−9.22026	+	25.3325i	−0.556003	+	1.52760i
$276$	−6.99280	−	26.5370i	−0.420917	−	1.59734i
$277$	−22.4822	−	3.96421i	−1.35082	−	0.238187i	−0.549037	−	0.835798i	$-0.685006\pi$
$277$	−22.4822	−	3.96421i	−1.35082	−	0.238187i	−0.801786	+	0.597611i	$0.796117\pi$
$278$	−9.57069	+	5.74136i	−0.574012	+	0.344344i
$279$	9.91974	+	20.6223i	0.593879	+	1.23463i
$280$	1.06231	+	1.64350i	0.0634851	+	0.0982182i
$281$	8.38379	+	23.0343i	0.500135	+	1.37411i	0.891143	+	0.453722i	$0.149904\pi$
$281$	8.38379	+	23.0343i	0.500135	+	1.37411i	−0.391008	+	0.920387i	$0.627874\pi$
$282$	−6.63076	−	3.26226i	−0.394856	−	0.194265i
$283$	−8.31451	+	6.97670i	−0.494246	+	0.414722i	−0.855545	−	0.517728i	$-0.826778\pi$
$283$	−8.31451	+	6.97670i	−0.494246	+	0.414722i	0.361299	+	0.932450i	$0.382333\pi$
$284$	8.54009	+	2.78832i	0.506761	+	0.165456i
$285$	38.3408	−	1.90485i	2.27111	−	0.112834i
$286$	−9.59461	−	1.52666i	−0.567341	−	0.0902730i
$287$	1.04052	+	1.80224i	0.0614202	+	0.106383i
$288$	8.60915	+	14.6247i	0.507299	+	0.861770i
$289$	−6.84941	+	11.8635i	−0.402906	+	0.697854i
$290$	12.2711	−	15.1315i	0.720587	−	0.888553i
$291$	14.5180	+	4.48178i	0.851059	+	0.262727i
$292$	−3.34577	−	15.8518i	−0.195796	−	0.927656i
$293$	−2.84714	−	16.1469i	−0.166332	−	0.943313i	−0.947681	−	0.319219i	$-0.896579\pi$
$293$	−2.84714	−	16.1469i	−0.166332	−	0.943313i	0.781349	−	0.624094i	$-0.214532\pi$
$294$	−10.0668	+	13.7562i	−0.587106	+	0.802277i
$295$	7.91132	−	9.42834i	0.460615	−	0.548939i
$296$	−5.00317	+	0.251467i	−0.290803	+	0.0146162i
$297$	20.9069	+	0.535518i	1.21314	+	0.0310739i
$298$	8.69799	+	4.82949i	0.503861	+	0.279765i
$299$	8.69159	−	10.3582i	0.502648	−	0.599032i
$300$	18.9510	+	13.3870i	1.09413	+	0.772900i
$301$	−0.737579	+	0.130055i	−0.0425133	+	0.00749625i
$302$	−6.69401	+	5.81063i	−0.385197	+	0.334364i
$303$	−13.1496	+	12.1955i	−0.755423	+	0.700614i
$304$	20.9264	+	15.2954i	1.20021	+	0.877250i
$305$	−24.4538	−	14.1184i	−1.40022	−	0.808416i
$306$	−3.05555	+	7.07708i	−0.174674	+	0.404570i
$307$	7.29100	+	12.6284i	0.416119	+	0.720740i	0.995545	−	0.0942851i	$-0.0300565\pi$
$307$	7.29100	+	12.6284i	0.416119	+	0.720740i	−0.579426	+	0.815025i	$0.696723\pi$
$308$	1.28175	+	1.00436i	0.0730346	+	0.0572289i
$309$	−9.44536	+	6.09745i	−0.537328	+	0.346872i
$310$	7.01429	+	36.2234i	0.398385	+	2.05735i
$311$	−18.0464	+	15.1428i	−1.02332	+	0.858667i	−0.990041	−	0.140779i	$-0.955039\pi$
$311$	−18.0464	+	15.1428i	−1.02332	+	0.858667i	−0.0332788	+	0.999446i	$0.510595\pi$
$312$	−3.43811	+	7.62224i	−0.194645	+	0.431524i
$313$	4.27277	−	1.55516i	0.241511	−	0.0879028i	−0.218429	−	0.975853i	$-0.570093\pi$
$313$	4.27277	−	1.55516i	0.241511	−	0.0879028i	0.459940	+	0.887950i	$0.347871\pi$
$314$	−7.04392	+	0.117925i	−0.397511	+	0.00665488i
$315$	0.513087	−	2.01123i	0.0289092	−	0.113320i
$316$	−0.0396708	−	1.18448i	−0.00223166	−	0.0666324i
$317$	−1.85951	+	10.5458i	−0.104440	+	0.592310i	0.887002	+	0.461765i	$0.152784\pi$
$317$	−1.85951	+	10.5458i	−0.104440	+	0.592310i	−0.991442	+	0.130545i	$0.958327\pi$
$318$	6.46700	−	22.2644i	0.362651	−	1.24853i
$319$	5.54450	−	15.2334i	0.310432	−	0.852906i
$320$	7.42927	+	26.3339i	0.415309	+	1.47211i
$321$	−2.36464	+	3.12030i	−0.131981	+	0.174158i
$322$	−2.11642	+	0.810686i	−0.117944	+	0.0451778i
$323$			11.7738i			0.655111i
$324$	5.17393	−	17.2404i	0.287441	−	0.957798i
$325$			11.4323i			0.634151i
$326$	3.30347	+	8.62423i	0.182963	+	0.477652i
$327$	3.14524	−	4.15035i	0.173932	−	0.229515i
$328$	6.48472	+	28.3653i	0.358059	+	1.56621i
$329$	−0.208731	+	0.573483i	−0.0115077	+	0.0316172i
$330$	32.3811	+	9.40552i	1.78252	+	0.517757i
$331$	−2.53127	+	14.3556i	−0.139131	+	0.789053i	0.832762	+	0.553631i	$0.186758\pi$
$331$	−2.53127	+	14.3556i	−0.139131	+	0.789053i	−0.971893	+	0.235422i	$0.924353\pi$
$332$	−0.835760	−	24.9540i	−0.0458683	−	1.36953i
$333$	3.80199	+	3.71170i	0.208348	+	0.203400i
$334$	−0.290119	−	17.3295i	−0.0158746	−	0.948228i
$335$	−5.30631	+	1.93134i	−0.289915	+	0.105520i
$336$	1.12398	−	0.837203i	0.0613183	−	0.0456731i
$337$	19.2969	−	16.1920i	1.05117	−	0.882035i	0.0579523	−	0.998319i	$-0.481543\pi$
$337$	19.2969	−	16.1920i	1.05117	−	0.882035i	0.993216	+	0.116285i	$0.0370984\pi$
$338$	14.0046	−	2.71185i	0.761750	−	0.147505i
$339$	−8.19494	+	5.29024i	−0.445088	+	0.287326i
$340$	−7.66574	+	9.78289i	−0.415733	+	0.530552i
$341$	15.3508	+	26.5884i	0.831293	+	1.43984i
$342$	−3.18262	−	27.3078i	−0.172096	−	1.47664i
$343$	2.44548	+	1.41190i	0.132044	+	0.0762354i
$344$	−10.3911	−	1.29845i	−0.560249	−	0.0700075i
$345$	−34.4097	+	31.9131i	−1.85255	+	1.71814i
$346$	22.6222	+	26.0613i	1.21617	+	1.40107i
$347$	−8.71967	+	1.53751i	−0.468097	+	0.0825380i	−0.402721	−	0.915323i	$-0.631936\pi$
$347$	−8.71967	+	1.53751i	−0.468097	+	0.0825380i	−0.0653753	+	0.997861i	$0.520824\pi$
$348$	−11.3959	−	8.05013i	−0.610886	−	0.431532i
$349$	−19.6221	+	23.3847i	−1.05035	+	1.25175i	−0.0834696	+	0.996510i	$0.526600\pi$
$349$	−19.6221	+	23.3847i	−1.05035	+	1.25175i	−0.966877	+	0.255244i	$0.917844\pi$
$350$	0.930174	−	1.67526i	0.0497199	−	0.0895463i
$351$	8.40906	−	2.81897i	0.448843	−	0.150466i
$352$	12.9926	+	18.6969i	0.692506	+	0.996548i
$353$	−8.90806	+	10.6162i	−0.474128	+	0.565044i	−0.949107	−	0.314953i	$-0.898011\pi$
$353$	−8.90806	+	10.6162i	−0.474128	+	0.565044i	0.474979	+	0.879997i	$0.342456\pi$
$354$	−7.11333	−	5.20553i	−0.378069	−	0.276671i
$355$	−2.66780	−	15.1298i	−0.141592	−	0.803008i
$356$	−24.2055	+	5.10895i	−1.28289	+	0.270774i
$357$	0.608284	+	0.187781i	0.0321938	+	0.00993842i
$358$	−15.8497	−	12.8536i	−0.837684	−	0.679333i
$359$	9.49643	−	16.4483i	0.501202	−	0.868108i	−0.498797	−	0.866719i	$-0.666225\pi$
$359$	9.49643	−	16.4483i	0.501202	−	0.868108i	0.999999	−	0.00138897i	$-0.000442121\pi$
$360$	15.1353	−	24.7624i	0.797700	−	1.30509i
$361$	−11.4957	−	19.9112i	−0.605039	−	1.04796i
$362$	4.54397	−	28.5576i	0.238826	−	1.50096i
$363$	8.99452	−	0.446868i	0.472090	−	0.0234545i
$364$	0.656454	+	0.214331i	0.0344075	+	0.0112340i
$365$	−21.2237	+	17.8088i	−1.11090	+	0.932156i
$366$	−8.92730	+	18.1454i	−0.466638	+	0.948473i
$367$	−6.89218	−	18.9361i	−0.359769	−	0.988456i	−0.979109	−	0.203334i	$-0.934822\pi$
$367$	−6.89218	−	18.9361i	−0.359769	−	0.988456i	0.619341	−	0.785122i	$-0.287400\pi$
$368$	−31.6173	+	2.12024i	−1.64817	+	0.110525i
$369$	17.3967	−	25.4917i	0.905638	−	1.32704i
$370$	4.40698	+	7.34632i	0.229108	+	0.381917i
$371$	−1.88561	−	0.332485i	−0.0978962	−	0.0172617i
$372$	25.5520	−	6.73323i	1.32481	−	0.349102i
$373$	4.70270	−	12.9206i	0.243496	−	0.669001i	−0.756393	−	0.654118i	$-0.773040\pi$
$373$	4.70270	−	12.9206i	0.243496	−	0.669001i	0.999889	−	0.0148833i	$-0.00473766\pi$
$374$	−3.37396	+	9.77604i	−0.174464	+	0.505507i
$375$	1.25298	−	9.98034i	0.0647037	−	0.515383i
$376$	−5.14988	+	6.80377i	−0.265585	+	0.350877i
$377$		−	6.87469i		−	0.354065i
$378$	−1.46160	−	0.271107i	−0.0751766	−	0.0139442i
$379$	−23.0899			−1.18605			−0.593026	−	0.805184i	$-0.702067\pi$
$379$	−23.0899			−1.18605			−0.593026	+	0.805184i	$0.702067\pi$
$380$	6.23172	−	43.8865i	0.319680	−	2.25133i
$381$	−7.46121	−	17.7112i	−0.382249	−	0.907374i
$382$	−9.60775	+	27.8384i	−0.491575	+	1.42434i
$383$	−1.72830	−	0.629049i	−0.0883119	−	0.0321429i	0.297486	−	0.954726i	$-0.403852\pi$
$383$	−1.72830	−	0.629049i	−0.0883119	−	0.0321429i	−0.385798	+	0.922583i	$0.626074\pi$
$384$	18.4653	−	6.55997i	0.942303	−	0.334762i
$385$	0.483562	−	2.74241i	0.0246446	−	0.139766i
$386$	−6.90760	+	4.14380i	−0.351588	+	0.210914i
$387$	6.47964	+	9.02120i	0.329379	+	0.458573i
$388$	8.25876	−	15.4791i	0.419275	−	0.785834i
$389$	−27.9217	+	10.1627i	−1.41569	+	0.515268i	−0.932794	−	0.360411i	$-0.882636\pi$
$389$	−27.9217	+	10.1627i	−1.41569	+	0.515268i	−0.482894	+	0.875679i	$0.660414\pi$
$390$	14.2681	−	0.948525i	0.722492	−	0.0480304i
$391$	−9.25214	−	11.0263i	−0.467901	−	0.557623i
$392$	13.3931	+	14.4241i	0.676454	+	0.728528i
$393$	−11.3654	−	5.82993i	−0.573308	−	0.294081i
$394$	−37.4369	−	5.95681i	−1.88604	−	0.300100i
$395$	−1.75521	+	1.01337i	−0.0883140	+	0.0509881i
$396$	5.18290	−	23.5863i	0.260450	−	1.18526i
$397$	13.2935	+	7.67501i	0.667182	+	0.385198i	0.795008	−	0.606599i	$-0.207467\pi$
$397$	13.2935	+	7.67501i	0.667182	+	0.385198i	−0.127826	+	0.991797i	$0.540800\pi$
$398$	−28.2700	−	22.9260i	−1.41705	−	1.14918i
$399$	−2.21367	+	0.504732i	−0.110822	+	0.0252682i
$400$	19.3255	−	18.5561i	0.966273	−	0.927804i
$401$	16.6682	−	2.93905i	0.832368	−	0.146769i	0.258804	−	0.965930i	$-0.416672\pi$
$401$	16.6682	−	2.93905i	0.832368	−	0.146769i	0.573564	+	0.819161i	$0.305560\pi$
$402$	1.63222	+	3.70014i	0.0814076	+	0.184546i
$403$	9.97375	+	8.36897i	0.496828	+	0.416888i
$404$	10.9489	+	17.5777i	0.544730	+	0.874525i
$405$	−30.1772	+	6.07216i	−1.49952	+	0.301728i
$406$	−0.559349	+	1.00740i	−0.0277600	+	0.0499963i
$407$	5.46074	+	4.58210i	0.270679	+	0.227126i
$408$	7.35503	+	5.01320i	0.364128	+	0.248190i
$409$	0.249722	+	1.41624i	0.0123480	+	0.0700287i	0.990359	−	0.138524i	$-0.0442358\pi$
$409$	0.249722	+	1.41624i	0.0123480	+	0.0700287i	−0.978011	+	0.208553i	$0.933125\pi$
$410$	37.5771	−	32.6183i	1.85580	−	1.61090i
$411$	−19.6006	+	4.46906i	−0.966826	+	0.220443i
$412$	4.84586	+	12.0434i	0.238738	+	0.593334i
$413$	−0.363977	+	0.630426i	−0.0179101	+	0.0310212i
$414$	24.4398	+	23.0731i	1.20115	+	1.13398i
$415$	−36.9776	+	21.3490i	−1.81516	+	1.04798i
$416$	7.88938	+	5.56625i	0.386809	+	0.272908i
$417$	6.23869	−	12.1623i	0.305510	−	0.595589i
$418$	−7.01208	−	36.2119i	−0.342972	−	1.77118i
$419$	−17.2769	−	20.5898i	−0.844029	−	1.00588i	−0.999836	−	0.0180876i	$-0.994242\pi$
$419$	−17.2769	−	20.5898i	−0.844029	−	1.00588i	0.155807	−	0.987788i	$-0.450202\pi$
$420$	−2.16798	−	1.02191i	−0.105786	−	0.0498639i
$421$	13.1300	+	36.0744i	0.639917	+	1.75816i	0.651986	+	0.758231i	$0.273936\pi$
$421$	13.1300	+	36.0744i	0.639917	+	1.75816i	−0.0120688	+	0.999927i	$0.503842\pi$
$422$	−0.0560266	−	3.34660i	−0.00272733	−	0.162910i
$423$	9.00607	−	0.897096i	0.437890	−	0.0436183i
$424$	−23.8273	−	12.2049i	−1.15716	−	0.592724i
$425$	11.9847	+	2.11323i	0.581345	+	0.102507i
$426$	−10.6850	+	2.62516i	−0.517692	+	0.127190i
$427$	1.56936	+	0.571201i	0.0759467	+	0.0276424i
$428$	3.02016	+	3.36387i	0.145985	+	0.162599i
$429$	10.9655	−	4.61943i	0.529418	−	0.223028i
$430$	6.40576	+	16.7232i	0.308913	+	0.806466i
$431$	7.70543			0.371157			0.185579	−	0.982629i	$-0.440584\pi$
$431$	7.70543			0.371157			0.185579	+	0.982629i	$0.440584\pi$
$432$	−18.4142	−	9.63933i	−0.885954	−	0.463772i
$433$	−18.8564			−0.906183			−0.453091	−	0.891464i	$-0.649679\pi$
$433$	−18.8564			−0.906183			−0.453091	+	0.891464i	$0.649679\pi$
$434$	−0.780594	−	2.03786i	−0.0374697	−	0.0978205i
$435$	−2.97221	+	23.6745i	−0.142507	+	1.13511i
$436$	−4.01716	−	4.47434i	−0.192387	−	0.214282i
$437$	48.2399	+	17.5579i	2.30763	+	0.839907i
$438$	13.7344	+	14.3205i	0.656257	+	0.684258i
$439$	−16.3164	−	2.87702i	−0.778738	−	0.137313i	−0.229870	−	0.973221i	$-0.573830\pi$
$439$	−16.3164	−	2.87702i	−0.778738	−	0.137313i	−0.548868	+	0.835909i	$0.684941\pi$
$440$	17.7507	−	34.6542i	0.846232	−	1.65207i
$441$	1.56953	−	20.8182i	0.0747397	−	0.991341i
$442$	0.0734129	+	4.38512i	0.00349189	+	0.208579i
$443$	−2.23622	−	6.14396i	−0.106246	−	0.291908i	0.875166	−	0.483824i	$-0.160752\pi$
$443$	−2.23622	−	6.14396i	−0.106246	−	0.291908i	−0.981411	+	0.191915i	$0.938530\pi$
$444$	5.04032	−	3.49822i	0.239203	−	0.166018i
$445$	27.1939	+	32.4084i	1.28911	+	1.53631i
$446$	5.38519	+	27.8103i	0.254996	+	1.31686i
$447$	−12.1698	+	0.604620i	−0.575610	+	0.0285975i
$448$	−0.703196	−	1.45757i	−0.0332229	−	0.0688637i
$449$	9.04053	−	5.21955i	0.426649	−	0.246326i	−0.271269	−	0.962504i	$-0.587443\pi$
$449$	9.04053	−	5.21955i	0.426649	−	0.246326i	0.697918	+	0.716178i	$0.254110\pi$
$450$	−28.3684	−	1.66174i	−1.33730	−	0.0783353i
$451$	20.7026	−	35.8579i	0.974846	−	1.68848i
$452$	4.20434	+	10.4490i	0.197755	+	0.491480i
$453$	3.20229	−	10.3733i	0.150457	−	0.487380i
$454$	27.5135	−	23.8827i	1.29127	−	1.12087i
$455$	−0.205066	−	1.16299i	−0.00961366	−	0.0545218i
$456$	−31.6573	−	2.36833i	−1.48249	−	0.110907i
$457$	20.6728	+	17.3466i	0.967034	+	0.811438i	0.982083	−	0.188449i	$-0.0603460\pi$
$457$	20.6728	+	17.3466i	0.967034	+	0.811438i	−0.0150490	+	0.999887i	$0.504790\pi$
$458$	−1.53196	+	2.75909i	−0.0715840	+	0.128924i
$459$	−1.40080	−	9.33648i	−0.0653836	−	0.435790i
$460$	28.6511	+	45.9972i	1.33586	+	2.14463i
$461$	3.79701	+	3.18607i	0.176844	+	0.148390i	0.726913	−	0.686729i	$-0.240954\pi$
$461$	3.79701	+	3.18607i	0.176844	+	0.148390i	−0.550069	+	0.835119i	$0.685399\pi$
$462$	−1.98270	−	0.215273i	−0.0922436	−	0.0100154i
$463$	2.96473	−	0.522762i	0.137783	−	0.0242948i	−0.104331	−	0.994543i	$-0.533270\pi$
$463$	2.96473	−	0.522762i	0.137783	−	0.0242948i	0.242114	+	0.970248i	$0.422159\pi$
$464$	−11.6211	+	11.1585i	−0.539498	+	0.518020i
$465$	−30.7285	−	33.1324i	−1.42500	−	1.53648i
$466$	−9.43496	−	7.65143i	−0.437066	−	0.354446i
$467$	−29.0602	−	16.7779i	−1.34475	−	0.776390i	−0.357247	−	0.934010i	$-0.616284\pi$
$467$	−29.0602	−	16.7779i	−1.34475	−	0.776390i	−0.987500	+	0.157620i	$0.949618\pi$
$468$	−1.35563	−	10.1509i	−0.0626641	−	0.469226i
$469$	0.289241	−	0.166993i	0.0133559	−	0.00771104i
$470$	14.4111	+	2.29304i	0.664737	+	0.105770i
$471$	7.24898	−	4.67957i	0.334015	−	0.215623i
$472$	−7.45871	+	6.92557i	−0.343315	+	0.318775i
$473$	9.57848	+	11.4152i	0.440419	+	0.524871i
$474$	0.807536	+	1.20613i	0.0370913	+	0.0553994i
$475$	−40.7858	+	14.8448i	−1.87138	+	0.681126i
$476$	0.346031	−	0.648556i	0.0158603	−	0.0297265i
$477$	7.67827	+	27.3374i	0.351564	+	1.25169i
$478$	1.77625	−	1.06555i	0.0812438	−	0.0487373i
$479$	−2.69060	+	15.2592i	−0.122937	+	0.697208i	0.859575	+	0.511009i	$0.170728\pi$
$479$	−2.69060	+	15.2592i	−0.122937	+	0.697208i	−0.982512	+	0.186199i	$0.940383\pi$
$480$	−24.7623	−	22.5795i	−1.13024	−	1.03061i
$481$	2.84070	+	1.03393i	0.129525	+	0.0471432i
$482$	−0.931523	+	2.69908i	−0.0424297	+	0.122940i
$483$	1.67650	−	2.21225i	0.0762833	−	0.100661i
$484$	1.46193	−	10.2955i	0.0664512	−	0.467978i
$485$	−30.0031			−1.36237
$486$	5.77276	+	21.2762i	0.261858	+	0.965106i
$487$		−	42.9742i		−	1.94735i	−0.227945	−	0.973674i	$-0.573201\pi$
$487$		−	42.9742i		−	1.94735i	0.227945	−	0.973674i	$-0.426799\pi$
$488$	18.6188	+	14.0929i	0.842833	+	0.637953i
$489$	−9.01471	−	6.83157i	−0.407659	−	0.308934i
$490$	10.9815	−	31.8189i	0.496094	−	1.43743i
$491$	−4.27635	+	11.7492i	−0.192989	+	0.530233i	−0.998013	−	0.0630092i	$-0.979930\pi$
$491$	−4.27635	+	11.7492i	−0.192989	+	0.530233i	0.805024	+	0.593243i	$0.202152\pi$
$492$	−25.0942	−	25.3031i	−1.13133	−	1.14075i
$493$	−7.20689	−	1.27077i	−0.324582	−	0.0572325i
$494$	−8.04658	−	13.4134i	−0.362033	−	0.603498i
$495$	−39.7592	+	11.1672i	−1.78704	+	0.501927i
$496$	−2.04154	−	30.4437i	−0.0916678	−	1.36696i
$497$	0.310783	+	0.853868i	0.0139405	+	0.0383012i
$498$	17.0127	+	25.4100i	0.762355	+	1.13865i
$499$	0.451535	−	0.378883i	0.0202135	−	0.0169611i	−0.632625	−	0.774458i	$-0.718023\pi$
$499$	0.451535	−	0.378883i	0.0202135	−	0.0169611i	0.652838	+	0.757497i	$0.273578\pi$
$500$	−11.0412	−	3.60492i	−0.493776	−	0.161217i
$501$	11.5127	+	17.8340i	0.514350	+	0.796763i
$502$	0.00502745	−	0.0315962i	0.000224386	−	0.00141021i
$503$	−5.40120	−	9.35516i	−0.240828	−	0.417126i	0.720123	−	0.693847i	$-0.244086\pi$
$503$	−5.40120	−	9.35516i	−0.240828	−	0.417126i	−0.960950	+	0.276721i	$0.910752\pi$
$504$	−0.627263	+	1.59778i	−0.0279405	+	0.0711709i
$505$	17.7072	−	30.6698i	0.787961	−	1.36479i
$506$	35.0232	+	28.4026i	1.55697	+	1.26265i
$507$	−12.8096	+	11.8802i	−0.568894	+	0.527618i
$508$	−21.7134	+	4.58296i	−0.963378	+	0.203336i
$509$	−4.10539	−	23.2828i	−0.181968	−	1.03199i	−0.929789	−	0.368093i	$-0.880011\pi$
$509$	−4.10539	−	23.2828i	−0.181968	−	1.03199i	0.747821	−	0.663901i	$-0.231100\pi$
$510$	1.64306	−	15.1329i	0.0727558	−	0.670094i
$511$	1.05331	−	1.25529i	0.0465958	−	0.0555307i
$512$	−3.39612	−	22.3711i	−0.150089	−	0.988673i
$513$	20.9760	+	26.3396i	0.926115	+	1.16292i
$514$	11.3066	−	20.3633i	0.498711	−	0.898187i
$515$	14.2700	−	17.0064i	0.628812	−	0.749389i
$516$	11.6461	−	5.37201i	0.512692	−	0.236489i
$517$	11.9580	−	2.10852i	0.525912	−	0.0927325i
$518$	−0.332144	−	0.382639i	−0.0145936	−	0.0168122i
$519$	−40.3856	−	12.4673i	−1.77273	−	0.547253i
$520$	2.04735	−	16.3843i	0.0897821	−	0.718499i
$521$	29.7943	+	17.2017i	1.30531	+	0.753622i	0.981310	−	0.192434i	$-0.0616382\pi$
$521$	29.7943	+	17.2017i	1.30531	+	0.753622i	0.324002	+	0.946056i	$0.394972\pi$
$522$	17.0590	+	0.999270i	0.746652	+	0.0437368i
$523$	15.1865	+	26.3038i	0.664059	+	1.15018i	0.979539	+	0.201252i	$0.0645011\pi$
$523$	15.1865	+	26.3038i	0.664059	+	1.15018i	−0.315480	+	0.948932i	$0.602166\pi$
$524$	−9.09726	+	11.6098i	−0.397416	+	0.507175i
$525$	0.116452	+	2.34393i	0.00508236	+	0.102297i
$526$	8.21678	−	1.59110i	0.358269	−	0.0693751i
$527$	10.6170	−	8.90871i	0.462483	−	0.388070i
$528$	−25.6071	−	11.0384i	−1.11441	−	0.480384i
$529$	−37.3617	+	13.5985i	−1.62442	+	0.591241i
$530$	0.766345	+	45.7755i	0.0332879	+	1.98836i
$531$	10.7651	+	0.811606i	0.467164	+	0.0352207i
$532$	0.0877580	+	2.62026i	0.00380479	+	0.113603i
$533$	3.04907	−	17.2921i	0.132070	−	0.749005i
$534$	21.8672	−	20.9724i	0.946286	−	0.907563i
$535$	2.64415	−	7.26473i	0.114316	−	0.314082i
$536$	4.55234	−	1.04073i	0.196631	−	0.0449528i
$537$	24.7982	+	3.11329i	1.07012	+	0.134348i
$538$	−2.52294	−	6.58652i	−0.108772	−	0.283965i
$539$		−	28.0092i		−	1.20644i
$540$	0.279755	+	35.5429i	0.0120387	+	1.52952i
$541$			4.15389i			0.178590i	0.996005	+	0.0892948i	$0.0284613\pi$
$541$			4.15389i			0.178590i	−0.996005	+	0.0892948i	$0.971539\pi$
$542$	9.29098	−	3.55887i	0.399082	−	0.152867i
$543$	13.7494	+	32.6379i	0.590042	+	1.40063i
$544$	7.29355	−	7.24170i	0.312708	−	0.310485i
$545$	−3.51702	+	9.66293i	−0.150652	+	0.413914i
$546$	−0.821331	+	0.201789i	−0.0351497	+	0.00863578i
$547$	2.83365	−	16.0704i	0.121158	−	0.687122i	−0.862358	−	0.506300i	$-0.831013\pi$
$547$	2.83365	−	16.0704i	0.121158	−	0.687122i	0.983516	−	0.180823i	$-0.0578760\pi$
$548$	0.777039	+	23.2007i	0.0331935	+	0.991083i
$549$	−2.45494	−	24.6455i	−0.104774	−	1.05184i
$550$	−38.1194	+	0.638170i	−1.62542	+	0.0272117i
$551$	24.5260	−	8.92675i	1.04484	−	0.380292i
$552$	31.5085	−	22.6592i	1.34109	−	0.964439i
$553$	0.0918277	−	0.0770526i	0.00390491	−	0.00327661i
$554$	−6.13767	−	31.6963i	−0.260765	−	1.34665i
$555$	−9.33557	−	4.78872i	−0.396273	−	0.203270i
$556$	−12.4238	−	9.73510i	−0.526886	−	0.412860i
$557$	−14.8098	−	25.6513i	−0.627511	−	1.08688i	−0.988049	−	0.154137i	$-0.950740\pi$
$557$	−14.8098	−	25.6513i	−0.627511	−	1.08688i	0.360538	−	0.932745i	$-0.382593\pi$
$558$	−22.2167	+	23.5326i	−0.940506	+	0.996214i
$559$	5.47271	+	3.15967i	0.231471	+	0.133640i
$560$	−1.63310	+	2.23433i	−0.0690109	+	0.0944175i
$561$	−2.81571	−	12.3492i	−0.118879	−	0.521385i
$562$	−26.1790	+	22.7243i	−1.10429	+	0.958565i
$563$	22.0013	−	3.87943i	0.927246	−	0.163498i	0.310421	−	0.950599i	$-0.399530\pi$
$563$	22.0013	−	3.87943i	0.927246	−	0.163498i	0.616824	+	0.787101i	$0.288419\pi$
$564$	0.953996	−	10.4071i	0.0401705	−	0.438220i
$565$	12.3809	−	14.7550i	0.520868	−	0.620746i
$566$	−13.4198	−	7.45122i	−0.564075	−	0.313198i
$567$	1.69537	−	0.663621i	0.0711987	−	0.0278695i
$568$	0.637766	+	12.6889i	0.0267601	+	0.532416i
$569$	−1.10991	+	1.32274i	−0.0465299	+	0.0554522i	−0.788807	−	0.614640i	$-0.789301\pi$
$569$	−1.10991	+	1.32274i	−0.0465299	+	0.0554522i	0.742278	+	0.670093i	$0.233746\pi$
$570$	21.9110	+	49.6709i	0.917749	+	2.08048i
$571$	2.73361	+	15.5031i	0.114398	+	0.648783i	0.987047	+	0.160434i	$0.0512894\pi$
$571$	2.73361	+	15.5031i	0.114398	+	0.648783i	−0.872649	+	0.488349i	$0.837599\pi$
$572$	−2.83743	−	13.4433i	−0.118639	−	0.562095i
$573$	−8.01805	−	35.1659i	−0.334959	−	1.46907i
$574$	−1.85375	+	2.28585i	−0.0773740	+	0.0954097i
$575$	26.5309	−	45.9528i	1.10641	−	1.91637i
$576$	−14.9590	+	18.7678i	−0.623290	+	0.781991i
$577$	9.83883	+	17.0414i	0.409596	+	0.709441i	0.994844	−	0.101413i	$-0.0323364\pi$
$577$	9.83883	+	17.0414i	0.409596	+	0.709441i	−0.585248	+	0.810854i	$0.699003\pi$
$578$	−19.1324	−	3.04426i	−0.795801	−	0.126625i
$579$	4.50274	−	8.77806i	0.187128	−	0.364804i
$580$	26.1909	+	8.55128i	1.08752	+	0.355073i
$581$	1.93457	−	1.62330i	0.0802594	−	0.0673456i
$582$	1.42532	+	21.4403i	0.0590815	+	0.888727i
$583$	13.0294	+	35.7981i	0.539624	+	1.48260i
$584$	19.2421	−	12.4375i	0.796242	−	0.514666i
$585$	−14.2243	+	10.2169i	−0.588104	+	0.422416i
$586$	19.8841	−	11.9282i	0.821403	−	0.492751i
$587$	−1.96505	−	0.346492i	−0.0811063	−	0.0143012i	0.132948	−	0.991123i	$-0.457556\pi$
$587$	−1.96505	−	0.346492i	−0.0811063	−	0.0143012i	−0.214054	+	0.976822i	$0.568667\pi$
$588$	−23.2595	−	6.33582i	−0.959204	−	0.261285i
$589$	−16.9061	+	46.4492i	−0.696605	+	1.91391i
$590$	16.4536	+	5.67855i	0.677382	+	0.233782i
$591$	42.7858	−	18.0244i	1.75997	−	0.741425i
$592$	−2.86304	−	6.48019i	−0.117670	−	0.266334i
$593$			21.4365i			0.880291i	0.897927	+	0.440145i	$0.145073\pi$
$593$			21.4365i			0.880291i	−0.897927	+	0.440145i	$0.854927\pi$
$594$	9.86886	+	27.8814i	0.404924	+	1.14399i
$595$	−1.25709			−0.0515358
$596$	−1.97801	+	13.9300i	−0.0810225	+	0.570596i
$597$	44.2307	+	5.55294i	1.81024	+	0.227267i
$598$	18.0763	+	6.23861i	0.739196	+	0.255116i
$599$	39.6839	+	14.4438i	1.62144	+	0.590156i	0.983656	−	0.180059i	$-0.0576288\pi$
$599$	39.6839	+	14.4438i	1.62144	+	0.590156i	0.637785	+	0.770215i	$0.279851\pi$
$600$	−8.09282	+	31.7995i	−0.330388	+	1.29821i
$601$	−3.07096	+	17.4163i	−0.125267	+	0.710424i	0.855882	+	0.517171i	$0.173015\pi$
$601$	−3.07096	+	17.4163i	−0.125267	+	0.710424i	−0.981149	+	0.193253i	$0.938096\pi$
$602$	−0.544873	−	0.908288i	−0.0222074	−	0.0370191i
$603$	−4.09115	−	2.79200i	−0.166605	−	0.113699i
$604$	−11.0600	−	5.90099i	−0.450027	−	0.240108i
$605$	−16.7107	+	6.08218i	−0.679385	+	0.247276i
$606$	−22.7579	−	11.1966i	−0.924475	−	0.454831i
$607$	−25.0286	−	29.8279i	−1.01588	−	1.21068i	−0.977395	−	0.211420i	$-0.932191\pi$
$607$	−25.0286	−	29.8279i	−1.01588	−	1.21068i	−0.0384848	−	0.999259i	$-0.512253\pi$
$608$	−9.61376	+	35.3738i	−0.389889	+	1.43460i
$609$	−0.0700268	−	1.40950i	−0.00283763	−	0.0571156i
$610$	6.27501	−	39.4367i	0.254068	−	1.59675i
$611$	4.45944	−	2.57466i	0.180410	−	0.104160i
$612$	−10.8920	−	0.455230i	−0.440283	−	0.0184016i
$613$	2.98975	+	1.72613i	0.120755	+	0.0697178i	0.559161	−	0.829059i	$-0.311123\pi$
$613$	2.98975	+	1.72613i	0.120755	+	0.0697178i	−0.438406	+	0.898777i	$0.644457\pi$
$614$	−12.9893	+	16.0171i	−0.524206	+	0.646397i
$615$	−17.9762	+	58.2310i	−0.724872	+	2.34810i
$616$	−0.678010	+	2.20081i	−0.0273178	+	0.0886732i
$617$	3.45250	−	0.608769i	0.138992	−	0.0245081i	−0.103719	−	0.994607i	$-0.533074\pi$
$617$	3.45250	−	0.608769i	0.138992	−	0.0245081i	0.242711	+	0.970099i	$0.421963\pi$
$618$	−12.8307	−	9.38946i	−0.516124	−	0.377700i
$619$	−5.42408	−	4.55134i	−0.218012	−	0.182934i	0.527241	−	0.849716i	$-0.323227\pi$
$619$	−5.42408	−	4.55134i	−0.218012	−	0.182934i	−0.745253	+	0.666782i	$0.767671\pi$
$620$	−44.2898	+	27.5876i	−1.77872	+	1.10794i
$621$	−40.3427	−	8.18382i	−1.61890	−	0.328405i
$622$	−29.1273	−	16.1727i	−1.16790	−	0.648466i
$623$	−1.91682	−	1.60840i	−0.0767956	−	0.0644391i
$624$	−11.8055	−	0.684686i	−0.472598	−	0.0274094i
$625$	−2.36634	−	13.4202i	−0.0946535	−	0.536807i
$626$	4.21526	+	4.85610i	0.168476	+	0.194089i
$627$	30.7188	+	33.1220i	1.22679	+	1.32276i
$628$	−3.71902	−	9.24285i	−0.148405	−	0.368830i
$629$	1.60899	−	2.78685i	0.0641546	−	0.111119i
$630$	2.91567	−	0.339810i	0.116163	−	0.0135383i
$631$	6.49028	−	3.74717i	0.258374	−	0.149172i	−0.365219	−	0.930922i	$-0.619006\pi$
$631$	6.49028	−	3.74717i	0.258374	−	0.149172i	0.623593	+	0.781749i	$0.285672\pi$
$632$	1.54421	−	0.651582i	0.0614255	−	0.0259185i
$633$	2.22329	+	3.44402i	0.0883677	+	0.136888i
$634$	−14.8679	+	2.87901i	−0.590479	+	0.114340i
$635$	24.3941	+	29.0718i	0.968051	+	1.15368i
$636$	32.6748	−	2.72223i	1.29564	−	0.107944i
$637$	−4.06252	−	11.1617i	−0.160963	−	0.442242i
$638$	22.9226	−	0.383756i	0.907516	−	0.0151930i
$639$	9.41353	−	9.64252i	0.372393	−	0.381452i
$640$	−31.0195	+	23.1329i	−1.22615	+	0.914407i
$641$	21.3252	+	3.76021i	0.842295	+	0.148519i	0.578116	−	0.815955i	$-0.303788\pi$
$641$	21.3252	+	3.76021i	0.842295	+	0.148519i	0.264178	+	0.964474i	$0.414899\pi$
$642$	−5.31699	−	1.54439i	−0.209845	−	0.0609523i
$643$	−22.2522	−	8.09915i	−0.877543	−	0.319399i	−0.136325	−	0.990664i	$-0.543529\pi$
$643$	−22.2522	−	8.09915i	−0.877543	−	0.319399i	−0.741218	+	0.671265i	$0.765751\pi$
$644$	−2.14126	−	2.38494i	−0.0843773	−	0.0939798i
$645$	−17.4804	−	13.2471i	−0.688291	−	0.521604i
$646$	−15.5490	+	5.95596i	−0.611766	+	0.234334i
$647$	−18.8024			−0.739198			−0.369599	−	0.929191i	$-0.620505\pi$
$647$	−18.8024			−0.739198			−0.369599	+	0.929191i	$0.620505\pi$
$648$	25.3857	−	1.88841i	0.997245	−	0.0741837i
$649$	14.4836			0.568530
$650$	−15.0980	+	5.78323i	−0.592193	+	0.226837i
$651$	2.13013	+	1.61427i	0.0834864	+	0.0632681i
$652$	−9.71842	+	8.72542i	−0.380603	+	0.341714i
$653$	10.1057	+	3.67818i	0.395467	+	0.143938i	0.532096	−	0.846684i	$-0.321405\pi$
$653$	10.1057	+	3.67818i	0.395467	+	0.143938i	−0.136629	+	0.990622i	$0.543627\pi$
$654$	7.07221	+	2.05422i	0.276545	+	0.0803262i
$655$	24.8401	+	4.37998i	0.970582	+	0.171140i
$656$	−34.1800	+	22.9131i	−1.33451	+	0.894605i
$657$	−23.5474	−	6.00719i	−0.918671	−	0.234363i
$658$	−0.862957	+	0.0144471i	−0.0336416	+	0.000563205i
$659$	8.25777	+	22.6880i	0.321677	+	0.883800i	0.990143	+	0.140058i	$0.0447289\pi$
$659$	8.25777	+	22.6880i	0.321677	+	0.883800i	−0.668466	+	0.743742i	$0.733049\pi$
$660$	3.95918	+	47.5218i	0.154111	+	1.84978i
$661$	−1.20921	−	1.44108i	−0.0470329	−	0.0560516i	0.742015	−	0.670383i	$-0.233870\pi$
$661$	−1.20921	−	1.44108i	−0.0470329	−	0.0560516i	−0.789048	+	0.614331i	$0.789426\pi$
$662$	−20.2391	+	3.91909i	−0.786614	+	0.152320i
$663$	−2.91322	−	4.51278i	−0.113140	−	0.175262i
$664$	32.5325	−	13.7271i	1.26251	−	0.532715i
$665$	3.88279	−	2.24173i	0.150568	−	0.0869305i
$666$	−2.97853	+	6.89869i	−0.115416	+	0.267319i
$667$	−15.9540	+	27.6332i	−0.617743	+	1.06996i
$668$	22.7393	−	9.14956i	0.879811	−	0.354007i
$669$	−23.5917	−	25.4373i	−0.912107	−	0.983461i
$670$	−5.23490	−	6.03075i	−0.202242	−	0.232988i
$671$	−5.77005	−	32.7236i	−0.222750	−	1.26328i
$672$	1.67423	+	1.06087i	0.0645849	+	0.0409238i
$673$	−20.7393	−	17.4023i	−0.799439	−	0.670809i	0.148623	−	0.988894i	$-0.452516\pi$
$673$	−20.7393	−	17.4023i	−0.799439	−	0.670809i	−0.948062	+	0.318085i	$0.896960\pi$
$674$	31.1455	+	17.2933i	1.19968	+	0.666113i
$675$	30.5765	−	16.6243i	1.17689	−	0.639870i
$676$	10.6659	+	17.1233i	0.410225	+	0.658587i
$677$	−18.1567	−	15.2353i	−0.697820	−	0.585540i	0.223333	−	0.974742i	$-0.428306\pi$
$677$	−18.1567	−	15.2353i	−0.697820	−	0.585540i	−0.921153	+	0.389202i	$0.872751\pi$
$678$	−11.1321	−	8.14644i	−0.427524	−	0.312862i
$679$	1.74759	−	0.308148i	0.0670665	−	0.0118256i
$680$	−16.7976	−	5.17487i	−0.644157	−	0.198447i
$681$	−13.1620	+	42.6359i	−0.504367	+	1.63381i
$682$	−27.3483	+	33.7231i	−1.04722	+	1.29133i
$683$	18.0209	+	10.4044i	0.689551	+	0.398113i	0.803444	−	0.595380i	$-0.202999\pi$
$683$	18.0209	+	10.4044i	0.689551	+	0.398113i	−0.113893	+	0.993493i	$0.536332\pi$
$684$	34.4539	−	18.0172i	1.31738	−	0.688906i
$685$	34.3795	−	19.8490i	1.31357	−	0.758392i
$686$	−0.627528	+	3.94384i	−0.0239591	+	0.150577i
$687$	−0.191792	−	3.86037i	−0.00731731	−	0.147282i
$688$	−3.54171	−	14.3797i	−0.135026	−	0.548222i
$689$	10.3845	+	12.3757i	0.395617	+	0.471478i
$690$	−59.5525	−	29.2991i	−2.26713	−	1.11540i
$691$	17.7551	−	6.46235i	0.675438	−	0.245839i	0.0185503	−	0.999828i	$-0.494095\pi$
$691$	17.7551	−	6.46235i	0.675438	−	0.245839i	0.656887	+	0.753989i	$0.271873\pi$
$692$	−22.9739	+	43.0594i	−0.873338	+	1.63687i
$693$	2.20116	−	1.05880i	0.0836152	−	0.0402206i
$694$	−6.44150	−	10.7378i	−0.244516	−	0.407601i
$695$	−4.68707	+	26.5817i	−0.177791	+	1.00830i
$696$	4.86653	−	19.1223i	0.184465	−	0.724827i
$697$	−17.5641	−	6.39281i	−0.665288	−	0.242145i
$698$	−40.8090	−	14.0842i	−1.54464	−	0.533097i
$699$	14.7618	+	1.85327i	0.558341	+	0.0700969i
$700$	2.68296	+	0.380971i	0.101406	+	0.0143993i
$701$	−7.59328			−0.286794			−0.143397	−	0.989665i	$-0.545803\pi$
$701$	−7.59328			−0.286794			−0.143397	+	0.989665i	$0.545803\pi$
$702$	7.97673	+	9.67935i	0.301062	+	0.365324i
$703$			11.4770i			0.432864i
$704$	−18.1194	+	26.6167i	−0.682902	+	1.00315i
$705$	−16.4702	+	6.93840i	−0.620303	+	0.261315i
$706$	−18.5265	−	6.39398i	−0.697255	−	0.240641i
$707$	−0.716398	+	1.96829i	−0.0269429	+	0.0740251i
$708$	3.27625	−	12.0275i	0.123129	−	0.452020i
$709$	47.1054	+	8.30595i	1.76908	+	0.311937i	0.960879	−	0.276969i	$-0.0893299\pi$
$709$	47.1054	+	8.30595i	1.76908	+	0.311937i	0.808202	+	0.588906i	$0.200441\pi$
$710$	18.6316	−	11.1769i	0.699230	−	0.419461i
$711$	−1.62007	−	0.731884i	−0.0607575	−	0.0274478i
$712$	−18.9919	−	29.3824i	−0.711751	−	1.10115i
$713$	−20.6682	−	56.7855i	−0.774032	−	2.12663i
$714$	0.0597192	+	0.898319i	0.00223493	+	0.0336187i
$715$	−17.9991	+	15.1030i	−0.673128	+	0.564821i
$716$	8.95716	−	27.4340i	0.334745	−	1.02526i
$717$	−1.15786	+	2.25723i	−0.0432409	+	0.0842978i
$718$	26.5263	+	4.22075i	0.989951	+	0.157517i
$719$	−3.52716	−	6.10922i	−0.131541	−	0.227835i	0.792730	−	0.609573i	$-0.208659\pi$
$719$	−3.52716	−	6.10922i	−0.131541	−	0.227835i	−0.924271	+	0.381738i	$0.875326\pi$
$720$	40.3587	+	7.46186i	1.50408	+	0.278087i
$721$	−0.656522	+	1.13713i	−0.0244502	+	0.0423489i
$722$	20.4803	−	25.2542i	0.762198	−	0.939864i
$723$	−0.777393	−	3.40952i	−0.0289116	−	0.126801i
$724$	40.0131	−	8.44538i	1.48707	−	0.313870i
$725$	−4.68461	−	26.5677i	−0.173982	−	0.986701i
$726$	5.14018	+	11.6525i	0.190770	+	0.432465i
$727$	18.2911	−	21.7985i	0.678380	−	0.808462i	−0.311518	−	0.950240i	$-0.600837\pi$
$727$	18.2911	−	21.7985i	0.678380	−	0.808462i	0.989898	+	0.141778i	$0.0452819\pi$
$728$	0.0490234	+	0.975364i	0.00181693	+	0.0361494i
$729$	−19.7676	−	18.3914i	−0.732132	−	0.681163i
$730$	−34.2555	−	19.0201i	−1.26785	−	0.703965i
$731$	4.32397	−	5.15310i	0.159928	−	0.190594i
$732$	−28.4796	−	2.61065i	−1.05264	−	0.0964924i
$733$	−14.2179	+	2.50701i	−0.525152	+	0.0925984i	−0.429938	−	0.902858i	$-0.641465\pi$
$733$	−14.2179	+	2.50701i	−0.525152	+	0.0925984i	−0.0952137	+	0.995457i	$0.530353\pi$
$734$	21.5213	−	18.6812i	0.794366	−	0.689537i
$735$	9.16451	+	40.1941i	0.338038	+	1.48258i
$736$	−18.7942	−	40.6827i	−0.692765	−	1.49958i
$737$	−5.75483	−	3.32255i	−0.211982	−	0.122388i
$738$	42.4658	+	10.0795i	1.56319	+	0.371032i
$739$	−7.63499	−	13.2242i	−0.280858	−	0.486460i	0.690738	−	0.723105i	$-0.257286\pi$
$739$	−7.63499	−	13.2242i	−0.280858	−	0.486460i	−0.971596	+	0.236645i	$0.923952\pi$
$740$	−7.47252	+	9.53631i	−0.274695	+	0.350562i
$741$	17.0455	+	8.74359i	0.626184	+	0.321204i
$742$	−0.514776	−	2.65842i	−0.0188980	−	0.0975936i
$743$	−9.41012	+	7.89602i	−0.345224	+	0.289677i	−0.798869	−	0.601505i	$-0.794568\pi$
$743$	−9.41012	+	7.89602i	−0.345224	+	0.289677i	0.453645	+	0.891182i	$0.350123\pi$
$744$	21.8181	+	30.3390i	0.799891	+	1.11228i
$745$	22.6098	−	8.22931i	0.828360	−	0.301498i
$746$	19.4424	−	0.325492i	0.711836	−	0.0119171i
$747$	−34.1307	−	15.4189i	−1.24878	−	0.564147i
$748$	−14.6174	+	0.489569i	−0.534466	+	0.0179004i
$749$	−0.0794011	+	0.450306i	−0.00290125	+	0.0164538i
$750$	13.8143	−	3.39398i	0.504427	−	0.123931i
$751$	−8.22636	+	22.6017i	−0.300184	+	0.824749i	0.694283	+	0.719702i	$0.255722\pi$
$751$	−8.22636	+	22.6017i	−0.300184	+	0.824749i	−0.994467	+	0.105047i	$0.966501\pi$
$752$	−11.5905	−	3.35935i	−0.422662	−	0.122503i
$753$	0.0152123	+	0.0361106i	0.000554367	+	0.00131594i
$754$	9.07902	−	3.47768i	0.330638	−	0.126650i
$755$			21.4376i			0.780196i
$756$	−0.381339	−	2.06740i	−0.0138692	−	0.0751905i
$757$			2.57077i			0.0934361i	0.998908	+	0.0467180i	$0.0148762\pi$
$757$			2.57077i			0.0934361i	−0.998908	+	0.0467180i	$0.985124\pi$
$758$	−11.6804	−	30.4936i	−0.424253	−	1.10758i
$759$	−54.7966	−	6.87944i	−1.98899	−	0.249708i
$760$	61.1108	−	13.9708i	2.21672	−	0.506775i
$761$	−8.41063	+	23.1080i	−0.304885	+	0.837665i	0.688748	+	0.725001i	$0.258161\pi$
$761$	−8.41063	+	23.1080i	−0.304885	+	0.837665i	−0.993633	+	0.112664i	$0.964062\pi$
$762$	19.6158	−	18.8131i	0.710607	−	0.681527i
$763$	0.105613	−	0.598958i	0.00382343	−	0.0216837i
$764$	−41.6248	+	1.39410i	−1.50593	+	0.0504369i
$765$	8.08125	+	16.8002i	0.292178	+	0.607414i
$766$	−0.0435389	−	2.60068i	−0.00157313	−	0.0939664i
$767$	5.77171	−	2.10073i	0.208404	−	0.0758530i
$768$	18.0044	+	21.0676i	0.649676	+	0.760211i
$769$	17.5940	−	14.7631i	0.634455	−	0.532371i	−0.267855	−	0.963459i	$-0.586315\pi$
$769$	17.5940	−	14.7631i	0.634455	−	0.532371i	0.902310	+	0.431088i	$0.141870\pi$
$770$	3.86637	−	0.748683i	0.139334	−	0.0269807i
$771$	1.41551	+	28.4912i	0.0509782	+	1.02609i
$772$	−8.96680	−	7.02626i	−0.322722	−	0.252881i
$773$	1.98617	+	3.44015i	0.0714375	+	0.123733i	0.899532	−	0.436856i	$-0.143908\pi$
$773$	1.98617	+	3.44015i	0.0714375	+	0.123733i	−0.828094	+	0.560589i	$0.810575\pi$
$774$	−8.63596	+	13.1208i	−0.310413	+	0.471618i
$775$	44.2471	+	25.5461i	1.58940	+	0.917642i
$776$	24.6202	+	3.07649i	0.883815	+	0.110440i
$777$	0.592952	+	0.183048i	0.0212720	+	0.00656680i
$778$	−27.5459	−	31.7337i	−0.987570	−	1.13771i
$779$	65.6503	−	11.5759i	2.35217	−	0.414751i
$780$	8.47040	+	18.3632i	0.303289	+	0.657508i
$781$	11.6210	−	13.8494i	0.415833	−	0.495571i
$782$	9.88143	−	17.7966i	0.353359	−	0.636405i
$783$	−18.3868	+	9.99683i	−0.657091	+	0.357258i
$784$	−12.2740	+	24.9842i	−0.438357	+	0.892292i
$785$	−10.9517	+	13.0518i	−0.390884	+	0.465837i
$786$	1.94988	−	17.9588i	0.0695501	−	0.640569i
$787$	2.43923	+	13.8335i	0.0869490	+	0.493112i	0.996919	+	0.0784382i	$0.0249933\pi$
$787$	2.43923	+	13.8335i	0.0869490	+	0.493112i	−0.909970	+	0.414674i	$0.863896\pi$
$788$	−11.0713	−	52.4541i	−0.394397	−	1.86860i
$789$	−7.51564	+	6.97035i	−0.267564	+	0.248151i
$790$	−2.22620	−	1.80537i	−0.0792046	−	0.0642322i
$791$	−0.569609	+	0.986591i	−0.0202529	+	0.0350791i
$792$	33.7710	−	5.08679i	1.20000	−	0.180751i
$793$	−7.04567	−	12.2035i	−0.250199	−	0.433358i
$794$	−3.41121	+	21.4385i	−0.121059	+	0.760825i
$795$	−30.4106	−	47.1081i	−1.07855	−	1.67075i
$796$	15.9762	−	48.9321i	0.566262	−	1.73435i
$797$	−18.0786	+	15.1698i	−0.640378	+	0.537341i	−0.904134	−	0.427248i	$-0.859483\pi$
$797$	−18.0786	+	15.1698i	−0.640378	+	0.537341i	0.263756	+	0.964589i	$0.415039\pi$
$798$	−1.78639	−	2.66814i	−0.0632376	−	0.0944513i
$799$	−1.87476	−	5.15085i	−0.0663241	−	0.182224i
$800$	34.2821	+	16.1351i	1.21205	+	0.570463i
$801$	−9.17293	+	35.9566i	−0.324109	+	1.27046i
$802$	12.3133	+	20.5259i	0.434798	+	0.724796i
$803$	−32.1080	−	5.66151i	−1.13307	−	0.199790i
$804$	−4.06089	+	4.02735i	−0.143216	+	0.142034i
$805$	−1.87466	+	5.15060i	−0.0660732	+	0.181535i
$806$	−6.00704	+	17.4053i	−0.211589	+	0.613077i
$807$	6.88474	+	5.21743i	0.242354	+	0.183662i
$808$	−17.6752	+	23.3516i	−0.621812	+	0.821507i
$809$			30.1592i			1.06034i	0.847891	+	0.530170i	$0.177872\pi$
$809$			30.1592i			1.06034i	−0.847891	+	0.530170i	$0.822128\pi$
$810$	−23.2848	−	36.7816i	−0.818144	−	1.29237i
$811$	−19.2303			−0.675266			−0.337633	−	0.941278i	$-0.609626\pi$
$811$	−19.2303			−0.675266			−0.337633	+	0.941278i	$0.609626\pi$
$812$	−1.61337	−	0.229092i	−0.0566181	−	0.00803956i
$813$	−7.35973	+	9.71165i	−0.258117	+	0.340602i
$814$	−3.28892	+	9.52962i	−0.115277	+	0.334013i
$815$	20.9882	+	7.63909i	0.735185	+	0.267586i
$816$	−2.89998	+	12.2494i	−0.101520	+	0.428814i
$817$	−4.16611	+	23.6272i	−0.145754	+	0.826610i
$818$	−1.74403	+	1.04622i	−0.0609785	+	0.0365804i
$819$	0.723592	−	0.741194i	0.0252844	−	0.0258994i
$820$	62.0861	+	33.1255i	2.16814	+	1.15679i
$821$	−4.28889	+	1.56103i	−0.149683	+	0.0544802i	−0.415775	−	0.909467i	$-0.636490\pi$
$821$	−4.28889	+	1.56103i	−0.149683	+	0.0544802i	0.266092	+	0.963948i	$0.414267\pi$
$822$	−15.8173	−	23.6246i	−0.551693	−	0.824004i
$823$	9.86833	+	11.7606i	0.343988	+	0.409949i	0.910106	−	0.414375i	$-0.136000\pi$
$823$	9.86833	+	11.7606i	0.343988	+	0.409949i	−0.566118	+	0.824324i	$0.691555\pi$
$824$	−13.4536	+	12.4920i	−0.468680	+	0.435179i
$825$	39.2291	−	25.3243i	1.36578	−	0.881679i
$826$	−1.01669	−	0.161772i	−0.0353752	−	0.00562876i
$827$	30.5131	−	17.6168i	1.06104	−	0.612594i	0.135324	−	0.990801i	$-0.456793\pi$
$827$	30.5131	−	17.6168i	1.06104	−	0.612594i	0.925721	+	0.378207i	$0.123459\pi$
$828$	−18.1081	+	43.9481i	−0.629299	+	1.52730i
$829$	−32.1764	−	18.5771i	−1.11753	−	0.645208i	−0.176763	−	0.984253i	$-0.556563\pi$
$829$	−32.1764	−	18.5771i	−1.11753	−	0.645208i	−0.940770	+	0.339045i	$0.889896\pi$
$830$	−46.9002	−	38.0344i	−1.62793	−	1.32019i
$831$	26.8882	+	28.9917i	0.932741	+	1.00571i
$832$	−3.36006	+	13.2348i	−0.116489	+	0.458835i
$833$	−12.4520	+	2.19562i	−0.431435	+	0.0760737i
$834$	19.2180	+	2.08660i	0.665463	+	0.0722530i
$835$	−32.1100	−	26.9435i	−1.11121	−	0.932418i
$836$	44.2759	−	27.5789i	1.53131	−	0.953835i
$837$	7.88004	−	38.8452i	0.272374	−	1.34269i
$838$	18.4519	−	33.2322i	0.637411	−	1.14799i
$839$	12.7067	+	10.6622i	0.438683	+	0.368099i	0.835216	−	0.549921i	$-0.185342\pi$
$839$	12.7067	+	10.6622i	0.438683	+	0.368099i	−0.396533	+	0.918020i	$0.629787\pi$
$840$	0.252867	−	3.38007i	0.00872476	−	0.116624i
$841$	−2.21876	−	12.5832i	−0.0765090	−	0.433904i
$842$	−40.9994	+	35.5889i	−1.41293	+	1.22647i
$843$	12.5236	−	40.5679i	0.431334	−	1.39723i
$844$	4.39132	−	1.76692i	0.151155	−	0.0608200i
$845$	17.2494	−	29.8769i	0.593398	−	1.02779i
$846$	5.74061	+	11.4400i	0.197366	+	0.393315i
$847$	0.910879	−	0.525896i	0.0312982	−	0.0180700i
$848$	4.06493	−	37.6415i	0.139590	−	1.29261i
$849$	18.7762	−	0.932843i	0.644398	−	0.0320151i
$850$	3.27185	+	16.8966i	0.112224	+	0.579548i
$851$	−9.01893	−	10.7483i	−0.309165	−	0.368449i
$852$	−8.87212	−	12.7832i	−0.303954	−	0.437944i
$853$	6.77920	+	18.6257i	0.232115	+	0.637732i	0.999996	−	0.00286126i	$-0.000910768\pi$
$853$	6.77920	+	18.6257i	0.232115	+	0.637732i	−0.767880	+	0.640593i	$0.778689\pi$
$854$	0.0395350	+	2.36152i	0.00135286	+	0.0808095i
$855$	−54.9198	−	37.4799i	−1.87822	−	1.28179i
$856$	−2.91468	+	5.69023i	−0.0996216	+	0.194488i
$857$	−17.6147	−	3.10595i	−0.601708	−	0.106097i	−0.135507	−	0.990776i	$-0.543266\pi$
$857$	−17.6147	−	3.10595i	−0.601708	−	0.106097i	−0.466201	+	0.884679i	$0.654377\pi$
$858$	11.6477	+	12.1447i	0.397646	+	0.414612i
$859$	7.25730	+	2.64144i	0.247616	+	0.0901249i	0.462847	−	0.886438i	$-0.346828\pi$
$859$	7.25730	+	2.64144i	0.247616	+	0.0901249i	−0.215231	+	0.976563i	$0.569050\pi$
$860$	−18.8450	+	16.9195i	−0.642608	+	0.576949i
$861$	0.449000	−	3.57641i	0.0153019	−	0.121884i
$862$	3.89792	+	10.1761i	0.132764	+	0.346600i
$863$	−8.69446			−0.295963			−0.147981	−	0.988990i	$-0.547278\pi$
$863$	−8.69446			−0.295963			−0.147981	+	0.988990i	$0.547278\pi$
$864$	3.41498	−	29.1948i	0.116180	−	0.993228i
$865$	83.4618			2.83779
$866$	−9.53884	−	24.9026i	−0.324143	−	0.846226i
$867$	21.8660	−	9.21148i	0.742607	−	0.312838i
$868$	2.29641	−	2.06177i	0.0779453	−	0.0699812i
$869$	−2.24118	−	0.815725i	−0.0760270	−	0.0276716i
$870$	−32.7691	+	8.05090i	−1.11098	+	0.272951i
$871$	−2.77521	−	0.489344i	−0.0940344	−	0.0165808i
$872$	3.87685	−	7.56866i	0.131287	−	0.256307i
$873$	−15.3526	−	21.3745i	−0.519608	−	0.723418i
$874$	1.21525	+	72.5896i	0.0411064	+	2.45538i
$875$	−0.401800	−	1.10394i	−0.0135833	−	0.0373198i
$876$	−11.9644	+	25.3825i	−0.404240	+	0.857596i
$877$	−27.2022	−	32.4183i	−0.918553	−	1.09469i	−0.995223	−	0.0976318i	$-0.968873\pi$
$877$	−27.2022	−	32.4183i	−0.918553	−	1.09469i	0.0766700	−	0.997057i	$-0.475571\pi$
$878$	−4.45440	−	23.0035i	−0.150329	−	0.776331i
$879$	−12.9615	+	25.2683i	−0.437180	+	0.852279i
$880$	54.7453	+	5.91198i	1.84546	+	0.199293i
$881$	23.5185	−	13.5784i	0.792359	−	0.457468i	−0.0484336	−	0.998826i	$-0.515423\pi$
$881$	23.5185	−	13.5784i	0.792359	−	0.457468i	0.840792	+	0.541358i	$0.182090\pi$
$882$	28.2873	−	8.45841i	0.952484	−	0.284810i
$883$	4.48989	−	7.77672i	0.151097	−	0.261707i	−0.780534	−	0.625113i	$-0.785053\pi$
$883$	4.48989	−	7.77672i	0.151097	−	0.261707i	0.931631	+	0.363406i	$0.118386\pi$
$884$	−5.75404	+	2.31524i	−0.193529	+	0.0778699i
$885$	−20.7844	+	4.73897i	−0.698659	+	0.159299i
$886$	6.98275	−	6.06127i	0.234590	−	0.203632i
$887$	−1.66173	−	9.42413i	−0.0557954	−	0.316431i	0.944118	−	0.329608i	$-0.106917\pi$
$887$	−1.66173	−	9.42413i	−0.0557954	−	0.316431i	−0.999913	+	0.0131769i	$0.995806\pi$
$888$	7.16963	+	4.88683i	0.240597	+	0.163991i
$889$	−1.71947	−	1.44280i	−0.0576691	−	0.0483901i
$890$	−29.0435	+	52.3078i	−0.973540	+	1.75336i
$891$	−28.3004	−	22.6106i	−0.948100	−	0.757482i
$892$	−34.0033	+	21.1802i	−1.13852	+	0.709166i
$893$	14.9759	+	12.5663i	0.501149	+	0.420514i
$894$	−6.95476	−	15.7661i	−0.232602	−	0.527296i
$895$	−48.6028	+	8.56999i	−1.62461	+	0.286463i
$896$	1.56921	−	1.66601i	0.0524235	−	0.0556574i
$897$	−22.8343	+	5.20637i	−0.762414	+	0.173836i
$898$	11.4665	+	9.29892i	0.382641	+	0.310309i
$899$	−26.6075	−	15.3618i	−0.887409	−	0.512346i
$900$	−12.1560	−	38.3051i	−0.405202	−	1.27684i
$901$	14.8933	−	8.59864i	0.496167	−	0.286462i
$902$	57.8282	+	9.20139i	1.92547	+	0.306373i
$903$	1.15424	+	0.592071i	0.0384106	+	0.0197029i
$904$	−11.6726	+	10.8382i	−0.388224	+	0.360474i
$905$	−44.9530	−	53.5729i	−1.49429	−	1.78082i
$906$	15.3193	−	1.01841i	0.508951	−	0.0338345i
$907$	22.4084	−	8.15601i	0.744060	−	0.270816i	0.0579560	−	0.998319i	$-0.481542\pi$
$907$	22.4084	−	8.15601i	0.744060	−	0.270816i	0.686104	+	0.727503i	$0.259319\pi$
$908$	45.4586	+	24.2541i	1.50860	+	0.804899i
$909$	30.9103	−	3.07898i	1.02523	−	0.102123i
$910$	1.43216	−	0.859137i	0.0474756	−	0.0284801i
$911$	4.55164	−	25.8136i	0.150802	−	0.855243i	−0.811721	−	0.584045i	$-0.801469\pi$
$911$	4.55164	−	25.8136i	0.150802	−	0.855243i	0.962524	−	0.271198i	$-0.0874198\pi$
$912$	−12.8867	−	43.0061i	−0.426720	−	1.42407i
$913$	−47.2159	−	17.1852i	−1.56262	−	0.568746i
$914$	−12.4509	+	36.0765i	−0.411840	+	1.19330i
$915$	18.9872	+	45.0714i	0.627698	+	1.49001i
$916$	−4.41875	−	0.627446i	−0.145999	−	0.0207314i
$917$	−1.49185			−0.0492651
$918$	11.6215	−	6.57297i	0.383568	−	0.216940i
$919$		−	28.4248i		−	0.937649i	−0.883291	−	0.468824i	$-0.844678\pi$
$919$		−	28.4248i		−	0.937649i	0.883291	−	0.468824i	$-0.155322\pi$
$920$	−46.2523	+	61.1063i	−1.52489	+	2.01462i
$921$	3.14616	−	25.0600i	0.103670	−	0.825756i
$922$	−2.28688	+	6.62623i	−0.0753145	+	0.218223i
$923$	2.62224	−	7.20454i	0.0863120	−	0.237140i
$924$	−0.718684	−	2.72734i	−0.0236430	−	0.0897229i
$925$	11.6827	+	2.05997i	0.384123	+	0.0677313i
$926$	2.19014	+	3.65090i	0.0719725	+	0.119976i
$927$	19.4175	+	1.46393i	0.637753	+	0.0480819i
$928$	−20.6151	−	9.70267i	−0.676725	−	0.318506i
$929$	0.817461	+	2.24596i	0.0268200	+	0.0736874i	0.952380	−	0.304913i	$-0.0986275\pi$
$929$	0.817461	+	2.24596i	0.0268200	+	0.0736874i	−0.925560	+	0.378601i	$0.876405\pi$
$930$	28.2116	−	57.3420i	0.925094	−	1.88032i
$931$	34.5451	−	28.9868i	1.13217	−	0.950003i
$932$	5.33198	−	16.3308i	0.174655	−	0.534934i
$933$	40.7533	−	2.02471i	1.33420	−	0.0662861i
$934$	7.45706	−	46.8656i	0.244002	−	1.53349i
$935$	12.5057	+	21.6606i	0.408982	+	0.708377i
$936$	12.7200	−	6.92531i	0.415765	−	0.226361i
$937$	−25.1607	+	43.5796i	−0.821965	+	1.42368i	0.0822523	+	0.996612i	$0.473789\pi$
$937$	−25.1607	+	43.5796i	−0.821965	+	1.42368i	−0.904217	+	0.427073i	$0.859545\pi$
$938$	0.366856	+	0.297508i	0.0119783	+	0.00971398i
$939$	−7.52519	−	2.32307i	−0.245575	−	0.0758105i
$940$	4.26183	+	20.1920i	0.139005	+	0.658589i
$941$	7.57703	+	42.9715i	0.247004	+	1.40083i	0.815792	+	0.578346i	$0.196302\pi$
$941$	7.57703	+	42.9715i	0.247004	+	1.40083i	−0.568787	+	0.822485i	$0.692587\pi$
$942$	9.84706	+	7.20607i	0.320835	+	0.234787i
$943$	−52.3856	+	62.4307i	−1.70591	+	2.03302i
$944$	−12.9193	−	6.34688i	−0.420488	−	0.206573i
$945$	−2.81230	+	2.23962i	−0.0914840	+	0.0728550i
$946$	−10.2300	+	18.4243i	−0.332605	+	0.599026i
$947$	−19.4528	+	23.1830i	−0.632132	+	0.753345i	−0.983105	−	0.183040i	$-0.941406\pi$
$947$	−19.4528	+	23.1830i	−0.632132	+	0.753345i	0.350974	+	0.936385i	$0.385851\pi$
$948$	−1.18436	+	1.67661i	−0.0384663	+	0.0544537i
$949$	−13.6162	+	2.40091i	−0.442001	+	0.0779367i
$950$	−40.2368	−	46.3539i	−1.30546	−	1.50392i
$951$	13.5992	−	12.6125i	0.440984	−	0.408989i
$952$	1.03156	+	0.128901i	0.0334329	+	0.00417771i
$953$	27.2578	+	15.7373i	0.882965	+	0.509780i	0.871635	−	0.490156i	$-0.163060\pi$
$953$	27.2578	+	15.7373i	0.882965	+	0.509780i	0.0113304	+	0.999936i	$0.496393\pi$
$954$	−32.2188	+	23.9693i	−1.04312	+	0.776036i
$955$	35.6115	+	61.6810i	1.15236	+	1.99595i
$956$	2.30576	+	1.80677i	0.0745737	+	0.0584350i
$957$	−23.5899	+	15.2285i	−0.762555	+	0.492267i
$958$	−21.5130	+	4.16577i	−0.695053	+	0.134590i
$959$	−1.79864	+	1.50924i	−0.0580812	+	0.0487359i
$960$	17.2931	−	44.1243i	0.558131	−	1.42411i
$961$	25.5472	−	9.29843i	0.824104	−	0.299949i
$962$	0.0715624	+	4.27459i	0.00230727	+	0.137818i
$963$	6.52848	−	1.83366i	0.210377	−	0.0590888i
$964$	−4.03575	+	0.135166i	−0.129983	+	0.00435340i
$965$	−3.38287	+	19.1852i	−0.108899	+	0.617594i
$966$	3.76968	+	1.09495i	0.121287	+	0.0352295i
$967$	−2.57740	+	7.08136i	−0.0828837	+	0.227721i	−0.974211	−	0.225640i	$-0.927553\pi$
$967$	−2.57740	+	7.08136i	−0.0828837	+	0.227721i	0.891327	+	0.453361i	$0.149775\pi$
$968$	14.3362	−	3.27748i	0.460784	−	0.105342i
$969$	12.3169	−	16.2530i	0.395676	−	0.522121i
$970$	−15.1776	−	39.6235i	−0.487323	−	1.27223i
$971$		−	15.5087i		−	0.497696i	−0.968543	−	0.248848i	$-0.919948\pi$
$971$		−	15.5087i		−	0.497696i	0.968543	−	0.248848i	$-0.0800520\pi$
$972$	−25.1780	+	18.3867i	−0.807584	+	0.589752i
$973$		−	1.59644i		−	0.0511796i
$974$	56.7536	−	21.7392i	1.81850	−	0.696570i
$975$	11.9597	−	15.7816i	0.383017	−	0.505416i
$976$	−9.19301	+	31.7179i	−0.294261	+	1.01526i
$977$	−7.54941	+	20.7418i	−0.241527	+	0.663590i	0.758403	+	0.651786i	$0.225980\pi$
$977$	−7.54941	+	20.7418i	−0.241527	+	0.663590i	−0.999930	+	0.0118046i	$0.996242\pi$
$978$	4.46183	−	15.3611i	0.142674	−	0.491193i
$979$	−8.64507	+	49.0287i	−0.276298	+	1.56696i
$980$	47.5766	−	1.59344i	1.51978	−	0.0509006i
$981$	−8.68362	+	2.43897i	−0.277247	+	0.0778704i
$982$	−17.6798	+	0.295983i	−0.564184	+	0.00944520i
$983$	−13.7881	+	5.01845i	−0.439771	+	0.160064i	−0.552410	−	0.833572i	$-0.686292\pi$
$983$	−13.7881	+	5.01845i	−0.439771	+	0.160064i	0.112639	+	0.993636i	$0.464070\pi$
$984$	20.7220	−	45.9404i	0.660595	−	1.46453i
$985$	−70.2301	+	58.9300i	−2.23772	+	1.87767i
$986$	−1.96749	−	10.1606i	−0.0626577	−	0.323578i
$987$	0.888079	−	0.573299i	0.0282679	−	0.0182483i
$988$	13.6439	−	17.4121i	0.434069	−	0.553951i
$989$	−14.6652	−	25.4010i	−0.466328	−	0.807703i
$990$	−34.8607	−	46.8586i	−1.10795	−	1.48926i
$991$	−10.0032	−	5.77533i	−0.317761	−	0.183460i	0.332633	−	0.943056i	$-0.392063\pi$
$991$	−10.0032	−	5.77533i	−0.317761	−	0.183460i	−0.650394	+	0.759597i	$0.725396\pi$
$992$	39.1726	−	18.0966i	1.24373	−	0.574568i
$993$	18.5121	−	17.1689i	0.587463	−	0.544840i
$994$	−0.970441	+	0.842377i	−0.0307805	+	0.0267186i
$995$	−86.6893	+	15.2857i	−2.74824	+	0.484588i
$996$	−24.9514	+	35.3217i	−0.790615	+	1.11921i
$997$	−27.6917	+	33.0016i	−0.877004	+	1.04517i	0.121612	+	0.992578i	$0.461194\pi$
$997$	−27.6917	+	33.0016i	−0.877004	+	1.04517i	−0.998616	+	0.0525950i	$0.983251\pi$
$998$	0.728786	+	0.404653i	0.0230693	+	0.0128091i
$999$	−1.36549	−	9.10114i	−0.0432022	−	0.287947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.20	yes	192
3.2	odd	2		648.2.v.b.35.13		192
4.3	odd	2		864.2.bh.b.335.26		192
8.3	odd	2	inner	216.2.v.b.11.3	✓	192
8.5	even	2		864.2.bh.b.335.25		192
24.11	even	2		648.2.v.b.35.30		192
27.5	odd	18	inner	216.2.v.b.59.3	yes	192
27.22	even	9		648.2.v.b.611.30		192
108.59	even	18		864.2.bh.b.815.25		192
216.5	odd	18		864.2.bh.b.815.26		192
216.59	even	18	inner	216.2.v.b.59.20	yes	192
216.211	odd	18		648.2.v.b.611.13		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.3	✓	192	8.3	odd	2	inner
216.2.v.b.11.20	yes	192	1.1	even	1	trivial
216.2.v.b.59.3	yes	192	27.5	odd	18	inner
216.2.v.b.59.20	yes	192	216.59	even	18	inner
648.2.v.b.35.13		192	3.2	odd	2
648.2.v.b.35.30		192	24.11	even	2
648.2.v.b.611.13		192	216.211	odd	18
648.2.v.b.611.30		192	27.22	even	9
864.2.bh.b.335.25		192	8.5	even	2
864.2.bh.b.335.26		192	4.3	odd	2
864.2.bh.b.815.25		192	108.59	even	18
864.2.bh.b.815.26		192	216.5	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.505867 + 1.32064i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(-1.48820 + 1.33614i) q^{4} +(3.21396 + 1.16979i) q^{5} +(0.683248 - 2.35227i) q^{6} +(-0.199218 - 0.0351275i) q^{7} +(-2.51739 - 1.28947i) q^{8} +(0.811221 + 2.88824i) q^{9} +O(q^{10})\)	\(q+(0.505867 + 1.32064i) q^{2} +(-1.38044 - 1.04613i) q^{3} +(-1.48820 + 1.33614i) q^{4} +(3.21396 + 1.16979i) q^{5} +(0.683248 - 2.35227i) q^{6} +(-0.199218 - 0.0351275i) q^{7} +(-2.51739 - 1.28947i) q^{8} +(0.811221 + 2.88824i) q^{9} +(0.0809654 + 4.83625i) q^{10} +(1.37658 + 3.78212i) q^{11} +(3.45214 - 0.287608i) q^{12} +(1.09713 + 1.30751i) q^{13} +(-0.0543868 - 0.280866i) q^{14} +(-3.21293 - 4.97704i) q^{15} +(0.429466 - 3.97688i) q^{16} +(1.57350 - 0.908459i) q^{17} +(-3.40396 + 2.53240i) q^{18} +(-3.24004 + 5.61192i) q^{19} +(-6.34601 + 2.55343i) q^{20} +(0.238260 + 0.256900i) q^{21} +(-4.29847 + 3.73122i) q^{22} +(-1.37566 - 7.80173i) q^{23} +(2.12615 + 4.41356i) q^{24} +(5.13093 + 4.30536i) q^{25} +(-1.17176 + 2.11035i) q^{26} +(1.90163 - 4.83568i) q^{27} +(0.343411 - 0.213906i) q^{28} +(-3.08543 - 2.58898i) q^{29} +(4.94759 - 6.76085i) q^{30} +(7.51214 - 1.32459i) q^{31} +(5.46929 - 1.44460i) q^{32} +(2.05631 - 6.66106i) q^{33} +(1.99573 + 1.61847i) q^{34} +(-0.599188 - 0.345941i) q^{35} +(-5.06634 - 3.21437i) q^{36} +(1.53384 - 0.885560i) q^{37} +(-9.05037 - 1.44006i) q^{38} +(-0.146696 - 2.95269i) q^{39} +(-6.58240 - 7.08912i) q^{40} +(-6.61260 - 7.88059i) q^{41} +(-0.218745 + 0.444614i) q^{42} +(3.47909 - 1.26628i) q^{43} +(-7.10206 - 3.78924i) q^{44} +(-0.771390 + 10.2316i) q^{45} +(9.60741 - 5.76339i) q^{46} +(0.523875 - 2.97105i) q^{47} +(-4.75319 + 5.04056i) q^{48} +(-6.53939 - 2.38014i) q^{49} +(-3.09028 + 8.95407i) q^{50} +(-3.12248 - 0.392012i) q^{51} +(-3.37977 - 0.479915i) q^{52} +9.46508 q^{53} +(7.34818 + 0.0651731i) q^{54} +13.7659i q^{55} +(0.456214 + 0.345316i) q^{56} +(10.3435 - 4.35740i) q^{57} +(1.85830 - 5.38442i) q^{58} +(1.23077 - 3.38152i) q^{59} +(11.4315 + 3.11391i) q^{60} +(-8.13039 - 1.43361i) q^{61} +(5.54946 + 9.25079i) q^{62} +(-0.0601532 - 0.603885i) q^{63} +(4.67453 + 6.49221i) q^{64} +(1.99664 + 5.48571i) q^{65} +(9.83711 - 0.653959i) q^{66} +(-1.26475 + 1.06125i) q^{67} +(-1.12785 + 3.45438i) q^{68} +(-6.26262 + 12.2089i) q^{69} +(0.153756 - 0.966313i) q^{70} +(-2.24594 - 3.89008i) q^{71} +(1.68214 - 8.31688i) q^{72} +(-4.05026 + 7.01525i) q^{73} +(1.94543 + 1.57767i) q^{74} +(-2.57896 - 11.3109i) q^{75} +(-2.67648 - 12.6808i) q^{76} +(-0.141383 - 0.801822i) q^{77} +(3.82524 - 1.68740i) q^{78} +(-0.380899 + 0.453938i) q^{79} +(6.03238 - 12.2792i) q^{80} +(-7.68384 + 4.68600i) q^{81} +(7.06236 - 12.7194i) q^{82} +(-8.02454 + 9.56328i) q^{83} +(-0.697832 - 0.0639685i) q^{84} +(6.11986 - 1.07910i) q^{85} +(3.43227 + 3.95406i) q^{86} +(1.55083 + 6.80168i) q^{87} +(1.41154 - 11.2961i) q^{88} +(10.7122 + 6.18471i) q^{89} +(-13.9026 + 4.15712i) q^{90} +(-0.172639 - 0.299020i) q^{91} +(12.4714 + 9.77245i) q^{92} +(-11.7557 - 6.03016i) q^{93} +(4.18870 - 0.811100i) q^{94} +(-16.9781 + 14.2463i) q^{95} +(-9.06126 - 3.72741i) q^{96} +(-8.24324 + 3.00029i) q^{97} +(-0.164739 - 9.84024i) q^{98} +(-9.80695 + 7.04402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more