LMFDB - Embedded newform 729.2.k.a.4.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.13
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05837 - 0.0266128i) q^{2} +(0.611800 + 1.62040i) q^{3} +(2.23685 + 0.0578504i) q^{4} +(-2.65761 - 0.814392i) q^{5} +(-1.21619 - 3.35167i) q^{6} +(1.70918 - 4.26207i) q^{7} +(-0.488730 - 0.0189650i) q^{8} +(-2.25140 + 1.98272i) q^{9} +O(q^{10})$	\(q+(-2.05837 - 0.0266128i) q^{2} +(0.611800 + 1.62040i) q^{3} +(2.23685 + 0.0578504i) q^{4} +(-2.65761 - 0.814392i) q^{5} +(-1.21619 - 3.35167i) q^{6} +(1.70918 - 4.26207i) q^{7} +(-0.488730 - 0.0189650i) q^{8} +(-2.25140 + 1.98272i) q^{9} +(5.44867 + 1.74705i) q^{10} +(-0.0568156 - 0.0323146i) q^{11} +(1.27476 + 3.65998i) q^{12} +(-0.493390 - 1.10433i) q^{13} +(-3.63156 + 8.72744i) q^{14} +(-0.306283 - 4.80464i) q^{15} +(-3.46372 - 0.179281i) q^{16} +(-0.381134 - 0.173247i) q^{17} +(4.68698 - 4.02126i) q^{18} +(0.205864 + 0.300158i) q^{19} +(-5.89755 - 1.97541i) q^{20} +(7.95195 + 0.162028i) q^{21} +(0.116088 + 0.0680275i) q^{22} +(-2.62933 + 8.02163i) q^{23} +(-0.268274 - 0.803542i) q^{24} +(2.25808 + 1.52735i) q^{25} +(0.986190 + 2.28625i) q^{26} +(-4.59021 - 2.43515i) q^{27} +(4.06974 - 9.43473i) q^{28} +(-2.39919 + 1.53391i) q^{29} +(0.502580 + 9.89787i) q^{30} +(2.59194 + 9.54968i) q^{31} +(8.10101 + 0.524394i) q^{32} +(0.0176029 - 0.111834i) q^{33} +(0.779904 + 0.366749i) q^{34} +(-8.01334 + 9.93498i) q^{35} +(-5.15074 + 4.30480i) q^{36} +(0.472502 + 0.0927963i) q^{37} +(-0.415757 - 0.623314i) q^{38} +(1.48760 - 1.47512i) q^{39} +(1.28341 + 0.448419i) q^{40} +(-7.28978 + 2.76051i) q^{41} +(-16.3637 - 0.545137i) q^{42} +(-3.00135 + 1.31773i) q^{43} +(-0.125218 - 0.0755697i) q^{44} +(7.59806 - 3.43578i) q^{45} +(5.62562 - 16.4415i) q^{46} +(3.40924 - 12.5609i) q^{47} +(-1.82860 - 5.72231i) q^{48} +(-10.1835 - 9.73283i) q^{49} +(-4.60732 - 3.20394i) q^{50} +(0.0475514 - 0.723582i) q^{51} +(-1.03975 - 2.49876i) q^{52} +(-5.59164 + 5.92679i) q^{53} +(9.38355 + 5.13459i) q^{54} +(0.124677 + 0.132150i) q^{55} +(-0.916160 + 2.05059i) q^{56} +(-0.360428 + 0.517219i) q^{57} +(4.97924 - 3.09350i) q^{58} +(8.32036 - 1.41171i) q^{59} +(-0.407159 - 10.7650i) q^{60} +(-3.89003 + 7.15902i) q^{61} +(-5.08102 - 19.7257i) q^{62} +(4.60245 + 12.9845i) q^{63} +(-9.74505 - 0.757445i) q^{64} +(0.411883 + 3.33669i) q^{65} +(-0.0392095 + 0.229728i) q^{66} +(-0.604026 + 0.313197i) q^{67} +(-0.842516 - 0.409575i) q^{68} +(-14.6069 + 0.647051i) q^{69} +(16.7588 - 20.2366i) q^{70} +(-7.25979 - 5.62676i) q^{71} +(1.13793 - 0.926319i) q^{72} +(-11.1125 + 3.56307i) q^{73} +(-0.970113 - 0.203584i) q^{74} +(-1.09342 + 4.59343i) q^{75} +(0.443123 + 0.683316i) q^{76} +(-0.234836 + 0.186921i) q^{77} +(-3.10129 + 2.99675i) q^{78} +(-0.844570 + 4.45241i) q^{79} +(9.05922 + 3.29729i) q^{80} +(1.13762 - 8.92781i) q^{81} +(15.0785 - 5.48814i) q^{82} +(0.152532 + 0.935631i) q^{83} +(17.7779 + 0.822455i) q^{84} +(0.871814 + 0.770814i) q^{85} +(6.21295 - 2.63250i) q^{86} +(-3.95337 - 2.94920i) q^{87} +(0.0271547 + 0.0168706i) q^{88} +(-11.5515 - 4.71931i) q^{89} +(-15.7311 + 6.86990i) q^{90} +(-5.55002 + 0.215366i) q^{91} +(-6.34547 + 17.7910i) q^{92} +(-13.8886 + 10.0425i) q^{93} +(-7.35175 + 25.7643i) q^{94} +(-0.302661 - 0.965356i) q^{95} +(4.10646 + 13.4477i) q^{96} +(0.977177 - 4.24514i) q^{97} +(20.7024 + 20.3048i) q^{98} +(0.191986 - 0.0398964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.05837	−	0.0266128i	−1.45549	−	0.0188181i	−0.718878	−	0.695136i	$-0.755344\pi$
$2$	−2.05837	−	0.0266128i	−1.45549	−	0.0188181i	−0.736609	+	0.676318i	$0.763574\pi$
$3$	0.611800	+	1.62040i	0.353223	+	0.935539i
$3$	0.611800	+	1.62040i	0.353223	+	0.935539i
$4$	2.23685	+	0.0578504i	1.11842	+	0.0289252i
$5$	−2.65761	−	0.814392i	−1.18852	−	0.364207i	−0.364735	−	0.931111i	$-0.618841\pi$
$5$	−2.65761	−	0.814392i	−1.18852	−	0.364207i	−0.823784	+	0.566904i	$0.808141\pi$
$6$	−1.21619	−	3.35167i	−0.496506	−	1.36831i
$7$	1.70918	−	4.26207i	0.646011	−	1.61091i	−0.138190	−	0.990406i	$-0.544129\pi$
$7$	1.70918	−	4.26207i	0.646011	−	1.61091i	0.784201	−	0.620507i	$-0.213073\pi$
$8$	−0.488730	−	0.0189650i	−0.172792	−	0.00670512i
$9$	−2.25140	+	1.98272i	−0.750467	+	0.660908i
$10$	5.44867	+	1.74705i	1.72302	+	0.552464i
$11$	−0.0568156	−	0.0323146i	−0.0171306	−	0.00974323i	0.485802	−	0.874069i	$-0.338528\pi$
$11$	−0.0568156	−	0.0323146i	−0.0171306	−	0.00974323i	−0.502933	+	0.864326i	$0.667746\pi$
$12$	1.27476	+	3.65998i	0.367992	+	1.05655i
$13$	−0.493390	−	1.10433i	−0.136842	−	0.306285i	0.831663	−	0.555281i	$-0.187389\pi$
$13$	−0.493390	−	1.10433i	−0.136842	−	0.306285i	−0.968505	+	0.248995i	$0.919900\pi$
$14$	−3.63156	+	8.72744i	−0.970575	+	2.33251i
$15$	−0.306283	−	4.80464i	−0.0790820	−	1.24055i
$16$	−3.46372	−	0.179281i	−0.865931	−	0.0448202i
$17$	−0.381134	−	0.173247i	−0.0924386	−	0.0420185i	0.367058	−	0.930198i	$-0.380365\pi$
$17$	−0.381134	−	0.173247i	−0.0924386	−	0.0420185i	−0.459496	+	0.888180i	$0.651970\pi$
$18$	4.68698	−	4.02126i	1.10473	−	0.947820i
$19$	0.205864	+	0.300158i	0.0472285	+	0.0688609i	0.847570	−	0.530683i	$-0.178065\pi$
$19$	0.205864	+	0.300158i	0.0472285	+	0.0688609i	−0.800342	+	0.599544i	$0.795349\pi$
$20$	−5.89755	−	1.97541i	−1.31873	−	0.441716i
$21$	7.95195	+	0.162028i	1.73526	+	0.0353574i
$22$	0.116088	+	0.0680275i	0.0247500	+	0.0145035i
$23$	−2.62933	+	8.02163i	−0.548254	+	1.67262i	0.177055	+	0.984201i	$0.443343\pi$
$23$	−2.62933	+	8.02163i	−0.548254	+	1.67262i	−0.725309	+	0.688424i	$0.758303\pi$
$24$	−0.268274	−	0.803542i	−0.0547612	−	0.164022i
$25$	2.25808	+	1.52735i	0.451617	+	0.305469i
$26$	0.986190	+	2.28625i	0.193408	+	0.448370i
$27$	−4.59021	−	2.43515i	−0.883387	−	0.468644i
$28$	4.06974	−	9.43473i	0.769109	−	1.78300i
$29$	−2.39919	+	1.53391i	−0.445518	+	0.284840i	−0.742252	−	0.670121i	$-0.766242\pi$
$29$	−2.39919	+	1.53391i	−0.445518	+	0.284840i	0.296734	+	0.954960i	$0.404102\pi$
$30$	0.502580	+	9.89787i	0.0917580	+	1.80710i
$31$	2.59194	+	9.54968i	0.465526	+	1.71517i	0.675406	+	0.737446i	$0.263968\pi$
$31$	2.59194	+	9.54968i	0.465526	+	1.71517i	−0.209880	+	0.977727i	$0.567307\pi$
$32$	8.10101	+	0.524394i	1.43207	+	0.0927007i
$33$	0.0176029	−	0.111834i	0.00306427	−	0.0194678i
$34$	0.779904	+	0.366749i	0.133752	+	0.0628969i
$35$	−8.01334	+	9.93498i	−1.35450	+	1.67932i
$36$	−5.15074	+	4.30480i	−0.858457	+	0.717467i
$37$	0.472502	+	0.0927963i	0.0776788	+	0.0152556i	0.231401	−	0.972859i	$-0.425669\pi$
$37$	0.472502	+	0.0927963i	0.0776788	+	0.0152556i	−0.153722	+	0.988114i	$0.549126\pi$
$38$	−0.415757	−	0.623314i	−0.0674447	−	0.101115i
$39$	1.48760	−	1.47512i	0.238206	−	0.236208i
$40$	1.28341	+	0.448419i	0.202925	+	0.0709013i
$41$	−7.28978	+	2.76051i	−1.13847	+	0.431118i	−0.850216	−	0.526434i	$-0.823529\pi$
$41$	−7.28978	+	2.76051i	−1.13847	+	0.431118i	−0.288257	+	0.957553i	$0.593076\pi$
$42$	−16.3637	−	0.545137i	−2.52498	−	0.0841165i
$43$	−3.00135	+	1.31773i	−0.457701	+	0.200952i	−0.618099	−	0.786101i	$-0.712097\pi$
$43$	−3.00135	+	1.31773i	−0.457701	+	0.200952i	0.160398	+	0.987052i	$0.448722\pi$
$44$	−0.125218	−	0.0755697i	−0.0188774	−	0.0113926i
$45$	7.59806	−	3.43578i	1.13265	−	0.512176i
$46$	5.62562	−	16.4415i	0.829453	−	2.42417i
$47$	3.40924	−	12.5609i	0.497288	−	1.83220i	−0.0549184	−	0.998491i	$-0.517490\pi$
$47$	3.40924	−	12.5609i	0.497288	−	1.83220i	0.552207	−	0.833707i	$-0.313786\pi$
$48$	−1.82860	−	5.72231i	−0.263935	−	0.825944i
$49$	−10.1835	−	9.73283i	−1.45479	−	1.39040i
$50$	−4.60732	−	3.20394i	−0.651574	−	0.453106i
$51$	0.0475514	−	0.723582i	0.00665853	−	0.101322i
$52$	−1.03975	−	2.49876i	−0.144188	−	0.346515i
$53$	−5.59164	+	5.92679i	−0.768070	+	0.814107i	−0.986845	−	0.161668i	$-0.948313\pi$
$53$	−5.59164	+	5.92679i	−0.768070	+	0.814107i	0.218775	+	0.975775i	$0.429794\pi$
$54$	9.38355	+	5.13459i	1.27694	+	0.698729i
$55$	0.124677	+	0.132150i	0.0168114	+	0.0178191i
$56$	−0.916160	+	2.05059i	−0.122427	+	0.274022i
$57$	−0.360428	+	0.517219i	−0.0477399	+	0.0685074i
$58$	4.97924	−	3.09350i	0.653806	−	0.406196i
$59$	8.32036	−	1.41171i	1.08322	−	0.183789i	0.401832	−	0.915713i	$-0.368374\pi$
$59$	8.32036	−	1.41171i	1.08322	−	0.183789i	0.681386	+	0.731924i	$0.261378\pi$
$60$	−0.407159	−	10.7650i	−0.0525640	−	1.38975i
$61$	−3.89003	+	7.15902i	−0.498067	+	0.916619i	0.500634	+	0.865659i	$0.333100\pi$
$61$	−3.89003	+	7.15902i	−0.498067	+	0.916619i	−0.998701	+	0.0509596i	$0.983772\pi$
$62$	−5.08102	−	19.7257i	−0.645291	−	2.50517i
$63$	4.60245	+	12.9845i	0.579854	+	1.63589i
$64$	−9.74505	−	0.757445i	−1.21813	−	0.0946806i
$65$	0.411883	+	3.33669i	0.0510878	+	0.413865i
$66$	−0.0392095	+	0.229728i	−0.00482636	+	0.0282775i
$67$	−0.604026	+	0.313197i	−0.0737936	+	0.0382631i	−0.496814	−	0.867857i	$-0.665497\pi$
$67$	−0.604026	+	0.313197i	−0.0737936	+	0.0382631i	0.423020	+	0.906120i	$0.360970\pi$
$68$	−0.842516	−	0.409575i	−0.102170	−	0.0496682i
$69$	−14.6069	+	0.647051i	−1.75846	+	0.0778958i
$70$	16.7588	−	20.2366i	2.00306	−	2.41874i
$71$	−7.25979	−	5.62676i	−0.861579	−	0.667774i	0.0828243	−	0.996564i	$-0.473606\pi$
$71$	−7.25979	−	5.62676i	−0.861579	−	0.667774i	−0.944403	+	0.328790i	$0.893359\pi$
$72$	1.13793	−	0.926319i	0.134106	−	0.109168i
$73$	−11.1125	+	3.56307i	−1.30061	+	0.417025i	−0.873346	−	0.487100i	$-0.838055\pi$
$73$	−11.1125	+	3.56307i	−1.30061	+	0.417025i	−0.427268	+	0.904125i	$0.640524\pi$
$74$	−0.970113	−	0.203584i	−0.112773	−	0.0236661i
$75$	−1.09342	+	4.59343i	−0.126257	+	0.530404i
$76$	0.443123	+	0.683316i	0.0508297	+	0.0783817i
$77$	−0.234836	+	0.186921i	−0.0267620	+	0.0213016i
$78$	−3.10129	+	2.99675i	−0.351151	+	0.339315i
$79$	−0.844570	+	4.45241i	−0.0950216	+	0.500935i	0.902507	+	0.430675i	$0.141724\pi$
$79$	−0.844570	+	4.45241i	−0.0950216	+	0.500935i	−0.997529	+	0.0702599i	$0.977617\pi$
$80$	9.05922	+	3.29729i	1.01285	+	0.368648i
$81$	1.13762	−	8.92781i	0.126402	−	0.991979i
$82$	15.0785	−	5.48814i	1.66515	−	0.606064i
$83$	0.152532	+	0.935631i	0.0167426	+	0.102699i	0.994005	−	0.109335i	$-0.0348720\pi$
$83$	0.152532	+	0.935631i	0.0167426	+	0.102699i	−0.977262	+	0.212034i	$0.931991\pi$
$84$	17.7779	+	0.822455i	1.93973	+	0.0897372i
$85$	0.871814	+	0.770814i	0.0945615	+	0.0836065i
$86$	6.21295	−	2.63250i	0.669959	−	0.283870i
$87$	−3.95337	−	2.94920i	−0.423846	−	0.316188i
$88$	0.0271547	+	0.0168706i	0.00289470	+	0.00179842i
$89$	−11.5515	−	4.71931i	−1.22446	−	0.500246i	−0.328550	−	0.944487i	$-0.606560\pi$
$89$	−11.5515	−	4.71931i	−1.22446	−	0.500246i	−0.895907	+	0.444241i	$0.853473\pi$
$90$	−15.7311	+	6.86990i	−1.65820	+	0.724151i
$91$	−5.55002	+	0.215366i	−0.581800	+	0.0225765i
$92$	−6.34547	+	17.7910i	−0.661561	+	1.85484i
$93$	−13.8886	+	10.0425i	−1.44018	+	1.04136i
$94$	−7.35175	+	25.7643i	−0.758276	+	2.65738i
$95$	−0.302661	−	0.965356i	−0.0310524	−	0.0990434i
$96$	4.10646	+	13.4477i	0.419114	+	1.37250i
$97$	0.977177	−	4.24514i	0.0992173	−	0.431028i	−0.900777	−	0.434281i	$-0.857002\pi$
$97$	0.977177	−	4.24514i	0.0992173	−	0.431028i	0.999995	+	0.00325280i	$0.00103540\pi$
$98$	20.7024	+	20.3048i	2.09126	+	2.05109i
$99$	0.191986	−	0.0398964i	0.0192953	−	0.00400974i
$100$	4.96263	+	3.54707i	0.496263	+	0.354707i
$101$	0.599201	−	4.00050i	0.0596227	−	0.398065i	−0.938922	−	0.344131i	$-0.888174\pi$
$101$	0.599201	−	4.00050i	0.0596227	−	0.398065i	0.998544	−	0.0539342i	$-0.0171761\pi$
$102$	−0.117135	+	1.48813i	−0.0115981	+	0.147347i
$103$	4.79087	+	13.4323i	0.472059	+	1.32353i	0.906263	+	0.422714i	$0.138923\pi$
$103$	4.79087	+	13.4323i	0.472059	+	1.32353i	−0.434204	+	0.900814i	$0.642970\pi$
$104$	0.220191	+	0.549076i	0.0215915	+	0.0538413i
$105$	−21.0012	−	6.90661i	−2.04951	−	0.674016i
$106$	11.6674	−	12.0507i	1.13324	−	1.17047i
$107$	0.504327	+	8.65895i	0.0487551	+	0.837093i	0.930710	+	0.365758i	$0.119190\pi$
$107$	0.504327	+	8.65895i	0.0487551	+	0.837093i	−0.881955	+	0.471334i	$0.843773\pi$
$108$	−10.1267	−	5.71259i	−0.974445	−	0.549695i
$109$	−0.429278	+	7.37041i	−0.0411173	+	0.705958i	0.913264	+	0.407368i	$0.133553\pi$
$109$	−0.429278	+	7.37041i	−0.0411173	+	0.705958i	−0.954382	+	0.298590i	$0.903484\pi$
$110$	−0.253114	−	0.275331i	−0.0241335	−	0.0262518i
$111$	0.138709	+	0.822415i	0.0131657	+	0.0780602i
$112$	−6.68425	+	14.4562i	−0.631602	+	1.36598i
$113$	−8.32809	+	6.11676i	−0.783441	+	0.575416i	−0.909061	−	0.416662i	$-0.863200\pi$
$113$	−8.32809	+	6.11676i	−0.783441	+	0.575416i	0.125621	+	0.992078i	$0.459908\pi$
$114$	0.755659	−	1.05504i	0.0707739	−	0.0988132i
$115$	13.5205	−	19.1770i	1.26079	−	1.78827i
$116$	−5.45535	+	3.29232i	−0.506517	+	0.305684i
$117$	3.30040	+	1.50803i	0.305122	+	0.139417i
$118$	−17.1639	+	2.68439i	−1.58007	+	0.247118i
$119$	−1.38982	+	1.32831i	−0.127404	+	0.121766i
$120$	0.0585702	+	2.35398i	0.00534670	+	0.214888i
$121$	−5.62051	−	9.45071i	−0.510956	−	0.859155i
$122$	8.19764	−	14.6324i	0.742179	−	1.32475i
$123$	−8.93302	−	10.1235i	−0.805463	−	0.912805i
$124$	5.24532	+	21.5111i	0.471043	+	1.93175i
$125$	3.96806	+	4.91962i	0.354914	+	0.440024i
$126$	−9.12799	−	26.8493i	−0.813186	−	2.39193i
$127$	0.211567	+	10.9084i	0.0187736	+	0.967960i	0.884251	+	0.467012i	$0.154670\pi$
$127$	0.211567	+	10.9084i	0.0187736	+	0.967960i	−0.865477	+	0.500948i	$0.832985\pi$
$128$	3.86927	+	0.351123i	0.341999	+	0.0310352i
$129$	−3.97147	−	4.05720i	−0.349669	−	0.357216i
$130$	−0.759009	−	6.87909i	−0.0665695	−	0.603336i
$131$	−4.42616	+	0.401658i	−0.386715	+	0.0350930i	−0.282013	−	0.959411i	$-0.591002\pi$
$131$	−4.42616	+	0.401658i	−0.386715	+	0.0350930i	−0.104702	+	0.994504i	$0.533389\pi$
$132$	0.0458447	−	0.249138i	0.00399027	−	0.0216847i
$133$	1.63115	−	0.364385i	0.141439	−	0.0315962i
$134$	1.25164	−	0.628600i	0.108126	−	0.0543027i
$135$	10.2158	+	10.2099i	0.879239	+	0.878728i
$136$	0.182986	+	0.0918990i	0.0156909	+	0.00788028i
$137$	−0.336884	−	0.0844574i	−0.0287820	−	0.00721568i	0.228758	−	0.973483i	$-0.426533\pi$
$137$	−0.336884	−	0.0844574i	−0.0287820	−	0.00721568i	−0.257540	+	0.966268i	$0.582912\pi$
$138$	30.0836	−	0.943140i	2.56088	−	0.0802854i
$139$	10.6675	+	1.52736i	0.904809	+	0.129549i	0.578470	−	0.815704i	$-0.303650\pi$
$139$	10.6675	+	1.52736i	0.904809	+	0.129549i	0.326339	+	0.945253i	$0.394185\pi$
$140$	−18.4994	+	21.7595i	−1.56348	+	1.83901i
$141$	22.4395	−	2.16043i	1.88975	−	0.181941i
$142$	14.7936	+	11.7752i	1.24145	+	0.988150i
$143$	−0.00765369	+	0.0786868i	−0.000640034	+	0.00658012i
$144$	8.15370	−	6.46397i	0.679475	−	0.538664i
$145$	7.62531	−	2.12265i	0.633247	−	0.176276i
$146$	22.9684	−	7.03837i	1.90088	−	0.582500i
$147$	9.54083	−	22.4559i	0.786914	−	1.85213i
$148$	1.05155	+	0.234905i	0.0864365	+	0.0193091i
$149$	−13.2847	+	3.33050i	−1.08833	+	0.272845i	−0.745468	−	0.666541i	$-0.767774\pi$
$149$	−13.2847	+	3.33050i	−1.08833	+	0.272845i	−0.342859	+	0.939387i	$0.611395\pi$
$150$	2.37291	−	9.42588i	0.193747	−	0.769620i
$151$	1.58933	+	1.86942i	0.129338	+	0.152131i	0.822736	−	0.568424i	$-0.192447\pi$
$151$	1.58933	+	1.86942i	0.129338	+	0.152131i	−0.693398	+	0.720555i	$0.743887\pi$
$152$	−0.0949196	−	0.150600i	−0.00769900	−	0.0122153i
$153$	1.20159	−	0.365635i	0.0971424	−	0.0295598i
$154$	0.488353	−	0.378502i	0.0393526	−	0.0305006i
$155$	0.888817	−	27.4902i	0.0713915	−	2.20806i
$156$	3.41287	−	3.21355i	0.273248	−	0.257290i
$157$	0.634696	−	5.14171i	0.0506543	−	0.410353i	−0.945700	−	0.325041i	$-0.894622\pi$
$157$	0.634696	−	5.14171i	0.0506543	−	0.410353i	0.996354	−	0.0853121i	$-0.0271887\pi$
$158$	1.85693	−	9.14222i	0.147729	−	0.727316i
$159$	−13.0247	−	5.43469i	−1.03293	−	0.430999i
$160$	−21.1022	−	7.99103i	−1.66828	−	0.631746i
$161$	29.6948	+	24.9169i	2.34027	+	1.96372i
$162$	−2.57924	+	18.3465i	−0.202644	+	1.44143i
$163$	6.33937	−	5.31936i	0.496538	−	0.416645i	−0.359825	−	0.933020i	$-0.617163\pi$
$163$	6.33937	−	5.31936i	0.496538	−	0.416645i	0.856362	+	0.516375i	$0.172719\pi$
$164$	−16.4658	+	5.75311i	−1.28576	+	0.449242i
$165$	−0.137859	+	0.282876i	−0.0107323	+	0.0220219i
$166$	−0.289068	−	1.92993i	−0.0224361	−	0.149792i
$167$	−1.17267	+	2.29782i	−0.0907440	+	0.177811i	−0.931637	−	0.363391i	$-0.881619\pi$
$167$	−1.17267	+	2.29782i	−0.0907440	+	0.177811i	0.840893	+	0.541202i	$0.182030\pi$
$168$	−3.88328	−	0.229996i	−0.299602	−	0.0177446i
$169$	7.69758	−	8.59361i	0.592122	−	0.661047i
$170$	−1.77400	−	1.60982i	−0.136060	−	0.123468i
$171$	−1.05861	−	0.267603i	−0.0809541	−	0.0204641i
$172$	−6.78978	+	2.77393i	−0.517716	+	0.211510i
$173$	18.4326	+	3.12744i	1.40140	+	0.237775i	0.818379	−	0.574679i	$-0.194873\pi$
$173$	18.4326	+	3.12744i	1.40140	+	0.237775i	0.583024	+	0.812455i	$0.301869\pi$
$174$	8.05901	+	6.17576i	0.610952	+	0.468183i
$175$	10.3691	−	7.01360i	0.783834	−	0.530178i
$176$	0.191000	+	0.122115i	0.0143972	+	0.00920476i
$177$	7.37793	+	12.6186i	0.554559	+	0.948475i
$178$	23.6517	+	10.0215i	1.77277	+	0.751143i
$179$	−4.42069	−	9.24510i	−0.330418	−	0.691011i	0.668177	−	0.744003i	$-0.267075\pi$
$179$	−4.42069	−	9.24510i	−0.330418	−	0.691011i	−0.998595	+	0.0529914i	$0.983124\pi$
$180$	17.1945	−	7.24576i	1.28160	−	0.540067i
$181$	−19.6761	−	5.47722i	−1.46251	−	0.407118i	−0.556670	−	0.830733i	$-0.687921\pi$
$181$	−19.6761	−	5.47722i	−1.46251	−	0.407118i	−0.905842	+	0.423615i	$0.860761\pi$
$182$	11.4297	−	0.295601i	0.847228	−	0.0219114i
$183$	−13.9804	−	1.92352i	−1.03346	−	0.142191i
$184$	1.43716	−	3.87055i	0.105949	−	0.285340i
$185$	−1.18015	−	0.631418i	−0.0867665	−	0.0464227i
$186$	28.8551	−	20.3015i	2.11576	−	1.48858i
$187$	0.0160560	+	0.0221593i	0.00117413	+	0.00162045i
$188$	8.35260	−	27.8996i	0.609176	−	2.03479i
$189$	−18.2243	+	15.4017i	−1.32562	+	1.12031i
$190$	0.597298	+	1.99511i	0.0433325	+	0.144741i
$191$	10.3540	−	13.5389i	0.749190	−	0.979637i	−0.250743	−	0.968054i	$-0.580675\pi$
$191$	10.3540	−	13.5389i	0.749190	−	0.979637i	0.999933	−	0.0115834i	$-0.00368720\pi$
$192$	−4.73465	−	16.2543i	−0.341694	−	1.17305i
$193$	−1.54129	+	0.724788i	−0.110944	+	0.0521714i	−0.480217	−	0.877150i	$-0.659442\pi$
$193$	−1.54129	+	0.724788i	−0.110944	+	0.0521714i	0.369273	+	0.929321i	$0.379607\pi$
$194$	−2.12437	+	8.71205i	−0.152521	+	0.625489i
$195$	−5.15478	+	2.70880i	−0.369141	+	0.193981i
$196$	−22.2159	−	22.3600i	−1.58685	−	1.59714i
$197$	13.9837	−	2.74632i	0.996300	−	0.195667i	0.332118	−	0.943238i	$-0.392237\pi$
$197$	13.9837	−	2.74632i	0.996300	−	0.195667i	0.664182	+	0.747571i	$0.268780\pi$
$198$	−0.396240	+	0.0770122i	−0.0281595	+	0.00547302i
$199$	−0.310716	+	0.171446i	−0.0220261	+	0.0121535i	−0.494087	−	0.869412i	$-0.664498\pi$
$199$	−0.310716	+	0.171446i	−0.0220261	+	0.0121535i	0.472061	+	0.881566i	$0.343510\pi$
$200$	−1.07463	−	0.789285i	−0.0759876	−	0.0558109i
$201$	−0.877047	−	0.787152i	−0.0618622	−	0.0555214i
$202$	−1.33984	+	8.21857i	−0.0942710	+	0.578256i
$203$	2.43698	+	12.8472i	0.171042	+	0.901700i
$204$	0.148225	−	1.61579i	0.0103778	−	0.113128i
$205$	21.6215	−	1.39961i	1.51011	−	0.0977527i
$206$	−9.50391	−	27.7762i	−0.662169	−	1.93526i
$207$	−9.98497	−	23.2731i	−0.694003	−	1.61760i
$208$	1.51098	+	3.91354i	0.104768	+	0.271355i
$209$	−0.00199683	−	0.0237061i	−0.000138123	−	0.00163978i
$210$	43.0445	+	14.7753i	2.97035	+	1.01959i
$211$	−15.8426	+	23.7516i	−1.09065	+	1.63513i	−0.391456	+	0.920197i	$0.628028\pi$
$211$	−15.8426	+	23.7516i	−1.09065	+	1.63513i	−0.699193	+	0.714933i	$0.746457\pi$
$212$	−12.8505	+	12.9338i	−0.882576	+	0.888300i
$213$	4.67608	−	15.2062i	0.320399	−	1.04191i
$214$	−0.807651	−	17.8367i	−0.0552099	−	1.21930i
$215$	9.04955	−	1.05774i	0.617174	−	0.0721373i
$216$	2.19719	+	1.27718i	0.149500	+	0.0869013i
$217$	45.1315	+	5.27512i	3.06373	+	0.358098i
$218$	1.07976	−	15.1596i	0.0731306	−	1.02674i
$219$	−12.5722	−	15.8268i	−0.849550	−	1.06947i
$220$	0.271238	+	0.302812i	0.0182869	+	0.0204156i
$221$	−0.00327335	+	0.506375i	−0.000220189	+	0.0340625i
$222$	−0.263628	−	1.69653i	−0.0176935	−	0.113863i
$223$	−14.2799	+	12.6256i	−0.956255	+	0.845472i	−0.988067	−	0.154022i	$-0.950777\pi$
$223$	−14.2799	+	12.6256i	−0.956255	+	0.845472i	0.0318124	+	0.999494i	$0.489872\pi$
$224$	16.0811	−	33.6308i	1.07446	−	2.24705i
$225$	−8.11216	+	1.03848i	−0.540811	+	0.0692319i
$226$	17.3051	−	12.3689i	1.15112	−	0.822768i
$227$	3.21669	+	6.30303i	0.213499	+	0.418347i	0.972553	−	0.232681i	$-0.0747497\pi$
$227$	3.21669	+	6.30303i	0.213499	+	0.418347i	−0.759054	+	0.651028i	$0.774338\pi$
$228$	−0.836143	+	1.13609i	−0.0553750	+	0.0752393i
$229$	5.89614	+	7.70976i	0.389628	+	0.509475i	0.947196	−	0.320656i	$-0.103903\pi$
$229$	5.89614	+	7.70976i	0.389628	+	0.509475i	−0.557568	+	0.830131i	$0.688265\pi$
$230$	−28.3405	+	39.1136i	−1.86872	+	2.57908i
$231$	−0.446559	−	0.266170i	−0.0293814	−	0.0175127i
$232$	1.20165	−	0.704166i	0.0788919	−	0.0462308i
$233$	−0.850438	−	3.92606i	−0.0557141	−	0.257205i	0.940979	−	0.338465i	$-0.109908\pi$
$233$	−0.850438	−	3.92606i	−0.0557141	−	0.257205i	−0.996693	+	0.0812607i	$0.974105\pi$
$234$	−6.75330	−	3.19192i	−0.441477	−	0.208662i
$235$	−19.2899	+	30.6056i	−1.25834	+	1.99649i
$236$	18.6930	−	2.67644i	1.21681	−	0.174221i
$237$	−7.73139	+	1.35544i	−0.502208	+	0.0880452i
$238$	2.89611	−	2.69717i	0.187727	−	0.174831i
$239$	−11.0276	−	20.2946i	−0.713315	−	1.31275i	−0.940798	−	0.338968i	$-0.889922\pi$
$239$	−11.0276	−	20.2946i	−0.713315	−	1.31275i	0.227483	−	0.973782i	$-0.426950\pi$
$240$	0.199501	+	16.6968i	0.0128777	+	1.07778i
$241$	−12.7283	+	21.4022i	−0.819903	+	1.37864i	0.103429	+	0.994637i	$0.467018\pi$
$241$	−12.7283	+	21.4022i	−0.819903	+	1.37864i	−0.923332	+	0.384003i	$0.874545\pi$
$242$	11.3176	+	19.6026i	0.727522	+	1.26010i
$243$	15.1626	−	3.61863i	0.972684	−	0.232135i
$244$	−9.11555	+	15.7886i	−0.583563	+	1.01076i
$245$	19.1375	+	34.1594i	1.22265	+	2.18237i
$246$	18.1180	+	21.0756i	1.15516	+	1.34373i
$247$	0.229901	−	0.375437i	0.0146282	−	0.0238885i
$248$	−1.08565	−	4.71637i	−0.0689388	−	0.299490i
$249$	−1.42278	+	0.819583i	−0.0901650	+	0.0519390i
$250$	−8.03681	−	10.2320i	−0.508292	−	0.647128i
$251$	−7.94863	−	15.0901i	−0.501713	−	0.952479i	−0.996510	−	0.0834703i	$-0.973400\pi$
$251$	−7.94863	−	15.0901i	−0.501713	−	0.952479i	0.494797	−	0.869008i	$-0.335242\pi$
$252$	9.54382	+	29.3105i	0.601204	+	1.84639i
$253$	0.408603	−	0.370788i	0.0256887	−	0.0233112i
$254$	−0.145181	−	22.4591i	−0.00910950	−	1.40921i
$255$	−0.715652	+	1.88427i	−0.0448159	+	0.117998i
$256$	11.4894	+	1.19256i	0.718085	+	0.0745353i
$257$	21.6403	−	2.81343i	1.34988	−	0.175497i	0.580488	−	0.814269i	$-0.302862\pi$
$257$	21.6403	−	2.81343i	1.34988	−	0.175497i	0.769396	+	0.638772i	$0.220557\pi$
$258$	8.06679	+	8.45691i	0.502216	+	0.526504i
$259$	1.20310	−	1.85523i	0.0747568	−	0.115278i
$260$	0.728290	+	7.48748i	0.0451667	+	0.464354i
$261$	2.36022	−	8.21037i	0.146094	−	0.508209i
$262$	9.12136	−	0.708968i	0.563519	−	0.0438002i
$263$	3.34285	+	16.4579i	0.206129	+	1.01484i	0.941459	+	0.337126i	$0.109455\pi$
$263$	3.34285	+	16.4579i	0.206129	+	1.01484i	−0.735330	+	0.677709i	$0.762973\pi$
$264$	−0.0107240	+	0.0543229i	−0.000660017	+	0.00334334i
$265$	19.6871	−	11.1973i	1.20937	−	0.687845i
$266$	−3.36722	+	0.706629i	−0.206457	+	0.0433262i
$267$	0.579967	−	21.6054i	0.0354934	−	1.32223i
$268$	−1.36923	+	0.665630i	−0.0836392	+	0.0406598i
$269$	−11.9481	+	16.0491i	−0.728491	+	0.978533i	0.271380	+	0.962472i	$0.412520\pi$
$269$	−11.9481	+	16.0491i	−0.728491	+	0.978533i	−0.999871	+	0.0160609i	$0.994887\pi$
$270$	−20.7562	−	21.2876i	−1.26318	−	1.29552i
$271$	−19.3551	−	25.9985i	−1.17574	−	1.57929i	−0.728793	−	0.684734i	$-0.759918\pi$
$271$	−19.3551	−	25.9985i	−1.17574	−	1.57929i	−0.446948	−	0.894560i	$-0.647489\pi$
$272$	1.28908	+	0.668408i	0.0781621	+	0.0405282i
$273$	−3.74448	−	8.86150i	−0.226626	−	0.536323i
$274$	0.691184	+	0.182810i	0.0417560	+	0.0110440i
$275$	−0.0789387	−	0.159746i	−0.00476018	−	0.00963307i
$276$	−32.7108	+	0.602340i	−1.96896	+	0.0362566i
$277$	3.49851	−	2.43287i	0.210205	−	0.146177i	−0.461126	−	0.887335i	$-0.652554\pi$
$277$	3.49851	−	2.43287i	0.210205	−	0.146177i	0.671331	+	0.741158i	$0.265723\pi$
$278$	−21.9171	−	3.42777i	−1.31450	−	0.205584i
$279$	−24.7699	−	16.3611i	−1.48293	−	0.979512i
$280$	4.10478	−	4.70355i	0.245307	−	0.281091i
$281$	12.3179	−	24.9275i	0.734825	−	1.48705i	−0.133498	−	0.991049i	$-0.542621\pi$
$281$	12.3179	−	24.9275i	0.734825	−	1.48705i	0.868323	−	0.495999i	$-0.165198\pi$
$282$	−46.2463	+	3.84979i	−2.75393	+	0.229252i
$283$	15.1850	−	13.0800i	0.902656	−	0.777524i	−0.0728853	−	0.997340i	$-0.523221\pi$
$283$	15.1850	−	13.0800i	0.902656	−	0.777524i	0.975541	+	0.219816i	$0.0705458\pi$
$284$	−15.9135	−	13.0062i	−0.944294	−	0.771775i
$285$	1.37910	−	1.08104i	0.0816906	−	0.0640351i
$286$	0.0178482	−	0.161763i	0.00105539	−	0.00956524i
$287$	−0.694104	+	35.7878i	−0.0409717	+	2.11249i
$288$	−19.2783	+	14.8814i	−1.13599	+	0.876896i
$289$	−11.0626	−	12.6763i	−0.650742	−	0.745668i
$290$	−15.7522	+	4.16627i	−0.925000	+	0.244652i
$291$	7.47666	−	1.01375i	0.438290	−	0.0594273i
$292$	−25.0630	+	7.32717i	−1.46670	+	0.428790i
$293$	0.0759775	−	0.901995i	0.00443865	−	0.0526951i	−0.993903	−	0.110254i	$-0.964834\pi$
$293$	0.0759775	−	0.901995i	0.00443865	−	0.0526951i	0.998342	+	0.0575586i	$0.0183316\pi$
$294$	−20.2362	+	45.9687i	−1.18020	+	2.68095i
$295$	−23.2619	−	3.02426i	−1.35436	−	0.176079i
$296$	−0.229166	−	0.0543133i	−0.0133200	−	0.00315690i
$297$	0.182105	+	0.286686i	0.0105668	+	0.0166352i
$298$	27.4335	−	6.50186i	1.58918	−	0.376643i
$299$	10.1558	−	1.05414i	0.587325	−	0.0609627i
$300$	−2.71155	+	10.2115i	−0.156551	+	0.589564i
$301$	0.486412	+	15.0442i	0.0280363	+	0.867133i
$302$	−3.22169	−	3.89025i	−0.185387	−	0.223859i
$303$	6.84901	−	1.47656i	0.393465	−	0.0848262i
$304$	−0.659245	−	1.07657i	−0.0378103	−	0.0617455i
$305$	16.1684	−	15.8579i	0.925801	−	0.908019i
$306$	−2.48304	+	0.720634i	−0.141946	+	0.0411959i
$307$	−3.03941	+	4.43157i	−0.173469	+	0.252923i	−0.901655	−	0.432455i	$-0.857647\pi$
$307$	−3.03941	+	4.43157i	−0.173469	+	0.252923i	0.728187	+	0.685379i	$0.240363\pi$
$308$	−0.536105	+	0.404528i	−0.0305474	+	0.0230501i
$309$	−18.8347	+	15.9810i	−1.07147	+	0.909130i
$310$	−2.56110	+	56.5613i	−0.145461	+	3.21246i
$311$	0.868844	+	12.1984i	0.0492677	+	0.691708i	0.960229	+	0.279215i	$0.0900743\pi$
$311$	0.868844	+	12.1984i	0.0492677	+	0.691708i	−0.910961	+	0.412493i	$0.864658\pi$
$312$	−0.755010	+	0.692722i	−0.0427440	+	0.0392177i
$313$	−5.22007	−	14.0586i	−0.295056	−	0.794639i	−0.996629	−	0.0820416i	$-0.973856\pi$
$313$	−5.22007	−	14.0586i	−0.295056	−	0.794639i	0.701573	−	0.712598i	$-0.252481\pi$
$314$	−1.44328	+	10.5666i	−0.0814487	+	0.596310i
$315$	−1.65706	−	38.2559i	−0.0933650	−	2.15547i
$316$	−2.14675	+	9.91049i	−0.120764	+	0.557509i
$317$	10.6764	+	32.5719i	0.599649	+	1.82942i	0.557290	+	0.830318i	$0.311841\pi$
$317$	10.6764	+	32.5719i	0.599649	+	1.82942i	0.0423593	+	0.999102i	$0.486513\pi$
$318$	26.6651	+	11.5332i	1.49530	+	0.646751i
$319$	0.185879	−	0.00962103i	0.0104072	−	0.000538674i
$320$	25.2817	+	9.94928i	1.41329	+	0.556182i
$321$	−13.7224	+	6.11476i	−0.765912	+	0.341292i
$322$	−60.4597	−	52.0784i	−3.36929	−	2.90221i
$323$	−0.0264606	−	0.150066i	−0.00147231	−	0.00834987i
$324$	3.06116	−	19.9043i	0.170065	−	1.10580i
$325$	0.572576	−	3.24724i	0.0317608	−	0.180125i
$326$	−13.1903	+	10.7805i	−0.730545	+	0.597077i
$327$	−12.2057	+	3.81361i	−0.674975	+	0.210893i
$328$	3.61509	−	1.21089i	0.199610	−	0.0668603i
$329$	−47.7085	−	35.9993i	−2.63026	−	1.98471i
$330$	0.291292	−	0.578595i	0.0160351	−	0.0318506i
$331$	−8.80873	+	4.71294i	−0.484172	+	0.259047i	−0.695710	−	0.718323i	$-0.744910\pi$
$331$	−8.80873	+	4.71294i	−0.484172	+	0.259047i	0.211538	+	0.977370i	$0.432153\pi$
$332$	0.287065	+	2.10169i	0.0157547	+	0.115345i
$333$	−1.24778	+	0.727918i	−0.0683779	+	0.0398896i
$334$	2.47494	−	4.69856i	0.135423	−	0.257094i
$335$	1.86033	−	0.340440i	0.101641	−	0.0186002i
$336$	−27.5143	−	1.98685i	−1.50103	−	0.108392i
$337$	−18.2959	−	18.8970i	−0.996642	−	1.02939i	−0.999568	−	0.0293904i	$-0.990643\pi$
$337$	−18.2959	−	18.8970i	−0.996642	−	1.02939i	0.00292624	−	0.999996i	$-0.499069\pi$
$338$	−16.0732	+	17.4840i	−0.874265	+	0.951003i
$339$	−15.0067	−	9.75261i	−0.815054	−	0.529689i
$340$	1.90552	+	1.77463i	0.103341	+	0.0962427i
$341$	0.161332	−	0.626329i	0.00873661	−	0.0339176i
$342$	2.17189	+	0.579000i	0.117443	+	0.0313087i
$343$	−29.6248	+	13.4661i	−1.59959	+	0.727101i
$344$	1.49184	−	0.587094i	0.0804346	−	0.0316540i
$345$	39.3463	+	10.1761i	2.11834	+	0.547863i
$346$	−37.8578	−	6.92798i	−2.03525	−	0.372450i
$347$	−11.9010	+	15.1517i	−0.638879	+	0.813384i	−0.992531	−	0.121993i	$-0.961071\pi$
$347$	−11.9010	+	15.1517i	−0.638879	+	0.813384i	0.353652	+	0.935377i	$0.384940\pi$
$348$	−8.67247	−	6.82562i	−0.464893	−	0.365892i
$349$	1.99332	+	6.98561i	0.106700	+	0.373931i	0.996616	−	0.0821925i	$-0.0261922\pi$
$349$	1.99332	+	6.98561i	0.106700	+	0.373931i	−0.889916	+	0.456124i	$0.849238\pi$
$350$	−21.5302	+	14.1606i	−1.15084	+	0.756917i
$351$	−0.424433	+	6.27058i	−0.0226546	+	0.334699i
$352$	−0.443318	−	0.291575i	−0.0236289	−	0.0155410i
$353$	0.0985170	−	0.314226i	0.00524353	−	0.0167246i	−0.951543	−	0.307515i	$-0.900503\pi$
$353$	0.0985170	−	0.314226i	0.00524353	−	0.0167246i	0.956787	+	0.290790i	$0.0939182\pi$
$354$	−14.8507	−	26.1702i	−0.789305	−	1.39093i
$355$	14.7113	+	20.8660i	0.780795	+	1.10745i
$356$	−25.5659	−	11.2246i	−1.35499	−	0.594904i
$357$	−3.00269	−	1.43940i	−0.158919	−	0.0761813i
$358$	8.85339	+	19.1475i	0.467916	+	1.01198i
$359$	3.94480	+	2.17665i	0.208199	+	0.114879i	0.583785	−	0.811908i	$-0.301571\pi$
$359$	3.94480	+	2.17665i	0.208199	+	0.114879i	−0.375587	+	0.926787i	$0.622559\pi$
$360$	−3.77856	+	1.53507i	−0.199148	+	0.0809054i
$361$	6.79566	−	17.6012i	0.357666	−	0.926379i
$362$	40.3549	+	11.7978i	2.12101	+	0.620077i
$363$	11.8753	−	14.8894i	0.623292	−	0.781492i
$364$	−12.4270	+	0.160670i	−0.651352	+	0.00842139i
$365$	32.4343	−	0.419346i	1.69769	−	0.0219496i
$366$	28.7257	+	4.33137i	1.50151	+	0.226404i
$367$	−19.8391	−	5.79996i	−1.03559	−	0.302756i	−0.281525	−	0.959554i	$-0.590840\pi$
$367$	−19.8391	−	5.79996i	−1.03559	−	0.302756i	−0.754066	+	0.656798i	$0.771910\pi$
$368$	10.5454	−	27.3133i	0.549718	−	1.42380i
$369$	10.9389	−	20.6686i	0.569457	−	1.07597i
$370$	2.41239	+	1.33110i	0.125414	+	0.0692005i
$371$	15.7033	+	33.9619i	0.815274	+	1.76322i
$372$	−31.6475	+	21.6600i	−1.64085	+	1.12302i
$373$	20.8186	+	9.14031i	1.07794	+	0.473267i	0.863955	−	0.503569i	$-0.167980\pi$
$373$	20.8186	+	9.14031i	1.07794	+	0.473267i	0.213989	+	0.976836i	$0.431354\pi$
$374$	−0.0324594	−	0.0460394i	−0.00167843	−	0.00238064i
$375$	−5.54410	+	9.43967i	−0.286296	+	0.487462i
$376$	−1.90441	+	6.07424i	−0.0982127	+	0.313255i
$377$	2.87767	+	1.89268i	0.148208	+	0.0974777i
$378$	37.9222	−	31.2174i	1.95051	−	1.60565i
$379$	−5.30490	+	3.48909i	−0.272494	+	0.179222i	−0.678400	−	0.734692i	$-0.737326\pi$
$379$	−5.30490	+	3.48909i	−0.272494	+	0.179222i	0.405906	+	0.913915i	$0.366956\pi$
$380$	−0.621160	−	2.17686i	−0.0318649	−	0.111671i
$381$	−17.5465	+	7.01655i	−0.898933	+	0.359469i
$382$	−21.6727	+	27.5924i	−1.10887	+	1.41175i
$383$	0.838085	+	0.153369i	0.0428241	+	0.00783681i	0.201380	−	0.979513i	$-0.435457\pi$
$383$	0.838085	+	0.153369i	0.0428241	+	0.00783681i	−0.158556	+	0.987350i	$0.550684\pi$
$384$	1.79826	+	6.48460i	0.0917671	+	0.330916i
$385$	0.776328	−	0.305514i	0.0395654	−	0.0155704i
$386$	3.19183	−	1.45086i	0.162460	−	0.0738470i
$387$	4.14454	−	8.91758i	0.210679	−	0.453306i
$388$	2.43138	−	9.43919i	0.123434	−	0.479202i
$389$	23.0563	+	21.4725i	1.16900	+	1.08870i	0.994574	+	0.104029i	$0.0331734\pi$
$389$	23.0563	+	21.4725i	1.16900	+	1.08870i	0.174426	+	0.984670i	$0.444193\pi$
$390$	10.6825	−	5.43853i	0.540931	−	0.275391i
$391$	2.39185	−	2.60179i	0.120961	−	0.131578i
$392$	4.79241	+	4.94986i	0.242053	+	0.250006i
$393$	−3.35877	−	6.92642i	−0.169428	−	0.349392i
$394$	−28.8568	+	5.28079i	−1.45378	+	0.266042i
$395$	5.87054	−	11.1449i	0.295379	−	0.560763i
$396$	0.431751	−	0.0781356i	0.0216963	−	0.00392646i
$397$	3.17372	+	23.2357i	0.159284	+	1.16617i	0.880703	+	0.473669i	$0.157071\pi$
$397$	3.17372	+	23.2357i	0.159284	+	1.16617i	−0.721418	+	0.692500i	$0.756509\pi$
$398$	0.644131	−	0.344630i	0.0322874	−	0.0172747i
$399$	1.58839	+	2.42019i	0.0795189	+	0.121161i
$400$	−7.54755	−	5.69514i	−0.377378	−	0.284757i
$401$	7.65460	−	2.56394i	0.382252	−	0.128037i	−0.119966	−	0.992778i	$-0.538279\pi$
$401$	7.65460	−	2.56394i	0.382252	−	0.128037i	0.502219	+	0.864741i	$0.332517\pi$
$402$	1.78434	+	1.64359i	0.0889948	+	0.0819748i
$403$	9.26714	−	7.57407i	0.461629	−	0.377291i
$404$	1.57175	−	8.91385i	0.0781976	−	0.443480i
$405$	−10.2941	+	22.8002i	−0.511517	+	1.13295i
$406$	−4.67429	−	26.5092i	−0.231981	−	1.31563i
$407$	−0.0238468	−	0.0205410i	−0.00118204	−	0.00101818i
$408$	−0.0369625	+	0.352735i	−0.00182992	+	0.0174630i
$409$	33.2320	+	13.0780i	1.64322	+	0.646667i	0.993534	−	0.113538i	$-0.0362184\pi$
$409$	33.2320	+	13.0780i	1.64322	+	0.646667i	0.649683	+	0.760205i	$0.274902\pi$
$410$	−44.5424	+	2.30549i	−2.19979	+	0.113860i
$411$	−0.0692507	−	0.597559i	−0.00341589	−	0.0294754i
$412$	9.93938	+	30.3233i	0.489678	+	1.49392i
$413$	8.20421	−	37.8748i	0.403703	−	1.86370i
$414$	19.9334	+	48.1705i	0.979673	+	2.36745i
$415$	0.356599	−	2.61076i	0.0175047	−	0.128157i
$416$	−3.41785	−	9.20490i	−0.167574	−	0.451307i
$417$	4.05146	+	18.2201i	0.198401	+	0.892244i
$418$	0.00347932	+	0.0488490i	0.000170179	+	0.00238928i
$419$	1.38583	−	30.6056i	0.0677020	−	1.49518i	−0.628768	−	0.777593i	$-0.716440\pi$
$419$	1.38583	−	30.6056i	0.0677020	−	1.49518i	0.696470	−	0.717586i	$-0.254753\pi$
$420$	−46.5770	−	16.6640i	−2.27272	−	0.813118i
$421$	25.9532	−	19.5834i	1.26488	−	0.954439i	0.264929	−	0.964268i	$-0.414651\pi$
$421$	25.9532	−	19.5834i	1.26488	−	0.954439i	0.999952	+	0.00982933i	$0.00312882\pi$
$422$	33.2420	−	48.4680i	1.61820	−	2.35939i
$423$	17.2292	+	35.0392i	0.837715	+	1.70367i
$424$	2.84520	−	2.79056i	0.138175	−	0.135521i
$425$	−0.596024	−	0.973329i	−0.0289114	−	0.0472134i
$426$	−10.0298	+	31.1756i	−0.485944	+	1.51046i
$427$	23.8635	+	28.8157i	1.15484	+	1.39449i
$428$	0.627177	+	19.3979i	0.0303157	+	0.937634i
$429$	−0.132187	+	0.0357385i	−0.00638204	+	0.00172547i
$430$	−18.6555	+	1.93639i	−0.899647	+	0.0933809i
$431$	−27.3651	+	6.48565i	−1.31813	+	0.312403i	−0.828726	−	0.559654i	$-0.810934\pi$
$431$	−27.3651	+	6.48565i	−1.31813	+	0.312403i	−0.489404	+	0.872057i	$0.662786\pi$
$432$	15.4627	+	9.25761i	0.743947	+	0.445407i
$433$	15.8460	+	3.75558i	0.761512	+	0.180482i	0.592983	−	0.805215i	$-0.297950\pi$
$433$	15.8460	+	3.75558i	0.761512	+	0.180482i	0.168529	+	0.985697i	$0.446098\pi$
$434$	−92.7570	−	12.0592i	−4.45248	−	0.578861i
$435$	8.10470	+	11.0574i	0.388591	+	0.530163i
$436$	−1.38661	+	16.4616i	−0.0664066	+	0.788370i
$437$	−2.94904	+	0.862152i	−0.141072	+	0.0412423i
$438$	25.4570	+	32.9119i	1.21638	+	1.57259i
$439$	−19.4554	+	5.14571i	−0.928554	+	0.245591i	−0.688557	−	0.725182i	$-0.741755\pi$
$439$	−19.4554	+	5.14571i	−0.928554	+	0.245591i	−0.239997	+	0.970774i	$0.577146\pi$
$440$	−0.0584272	−	0.0669501i	−0.00278541	−	0.00319172i
$441$	42.2247	+	1.72145i	2.01070	+	0.0819736i
$442$	0.0202138	−	1.04222i	0.000961474	−	0.0495734i
$443$	3.43397	−	31.1229i	0.163153	−	1.47870i	−0.582756	−	0.812647i	$-0.698026\pi$
$443$	3.43397	−	31.1229i	0.163153	−	1.47870i	0.745909	−	0.666048i	$-0.232016\pi$
$444$	0.262694	+	1.84764i	0.0124669	+	0.0876851i
$445$	26.8560	+	21.9495i	1.27310	+	1.04051i
$446$	29.7294	−	25.6081i	1.40773	−	1.21258i
$447$	−13.5243	−	19.4890i	−0.639679	−	0.921797i
$448$	−19.8844	+	40.2395i	−0.939448	+	1.90114i
$449$	−7.37806	+	8.45432i	−0.348192	+	0.398984i	−0.900642	−	0.434562i	$-0.856903\pi$
$449$	−7.37806	+	8.45432i	−0.348192	+	0.398984i	0.552449	+	0.833546i	$0.313693\pi$
$450$	16.7255	−	1.92169i	0.788446	−	0.0905892i
$451$	0.503379	+	0.0787270i	0.0237032	+	0.00370711i
$452$	−18.9825	+	13.2005i	−0.892862	+	0.620898i
$453$	−2.05686	+	3.71907i	−0.0966395	+	0.174737i
$454$	−6.45339	−	13.0596i	−0.302873	−	0.612916i
$455$	14.9252	+	3.94753i	0.699703	+	0.185063i
$456$	0.185961	−	0.245945i	0.00870842	−	0.0115174i
$457$	−28.4651	−	14.7596i	−1.33154	−	0.690424i	−0.361275	−	0.932459i	$-0.617658\pi$
$457$	−28.4651	−	14.7596i	−1.33154	−	0.690424i	−0.970268	+	0.242035i	$0.922185\pi$
$458$	−11.9313	−	16.0265i	−0.557511	−	0.748867i
$459$	1.32761	+	1.72336i	0.0619673	+	0.0804394i
$460$	31.3527	−	42.1139i	1.46183	−	1.96357i
$461$	−10.9150	+	5.30617i	−0.508365	+	0.247133i	−0.673566	−	0.739127i	$-0.735238\pi$
$461$	−10.9150	+	5.30617i	−0.508365	+	0.247133i	0.165202	+	0.986260i	$0.447173\pi$
$462$	0.912100	+	0.559761i	0.0424348	+	0.0260424i
$463$	−4.65035	+	0.975902i	−0.216120	+	0.0453540i	−0.312186	−	0.950021i	$-0.601061\pi$
$463$	−4.65035	+	0.975902i	−0.216120	+	0.0453540i	0.0960660	+	0.995375i	$0.469374\pi$
$464$	8.58512	−	4.88290i	0.398554	−	0.226683i
$465$	45.0889	−	15.3782i	2.09095	−	0.713149i
$466$	1.64603	+	8.10392i	0.0762510	+	0.375407i
$467$	11.9917	−	0.932065i	0.554908	−	0.0431308i	0.203023	−	0.979174i	$-0.434924\pi$
$467$	11.9917	−	0.932065i	0.554908	−	0.0431308i	0.351885	+	0.936043i	$0.385541\pi$
$468$	7.29524	+	3.56416i	0.337223	+	0.164753i
$469$	0.302475	+	3.10972i	0.0139670	+	0.143593i
$470$	40.5203	−	62.4842i	1.86906	−	2.88218i
$471$	8.71994	−	2.11723i	0.401793	−	0.0975569i
$472$	−4.09318	+	0.532150i	−0.188404	+	0.0244942i
$473$	0.213105	+	0.0221198i	0.00979859	+	0.00101707i
$474$	15.9501	−	2.58424i	0.732614	−	0.118698i
$475$	0.00641390	+	0.992207i	0.000294290	+	0.0455256i
$476$	−3.18565	+	2.89083i	−0.146014	+	0.132501i
$477$	0.837845	−	24.4302i	0.0383623	−	1.11858i
$478$	22.1587	+	42.0673i	1.01352	+	1.92411i
$479$	−4.97967	−	6.33982i	−0.227527	−	0.289674i	0.659200	−	0.751967i	$-0.270895\pi$
$479$	−4.97967	−	6.33982i	−0.227527	−	0.289674i	−0.886727	+	0.462294i	$0.847027\pi$
$480$	0.0383215	−	39.0830i	0.00174913	−	1.78389i
$481$	−0.130650	−	0.567582i	−0.00595713	−	0.0258795i
$482$	26.7691	−	43.7150i	1.21930	−	1.99116i
$483$	−22.2081	+	63.3615i	−1.01050	+	2.88305i
$484$	−12.0255	−	21.4649i	−0.546613	−	0.975679i
$485$	−6.05416	+	10.4861i	−0.274905	+	0.476150i
$486$	−31.3066	+	7.04495i	−1.42010	+	0.319566i
$487$	−12.0376	−	20.8498i	−0.545477	−	0.944793i	−0.998577	−	0.0533335i	$-0.983015\pi$
$487$	−12.0376	−	20.8498i	−0.545477	−	0.944793i	0.453100	−	0.891460i	$-0.350318\pi$
$488$	2.03694	−	3.42506i	0.0922082	−	0.155045i
$489$	12.4979	+	7.01794i	0.565176	+	0.317362i
$490$	−38.4829	−	70.8220i	−1.73848	−	3.19941i
$491$	11.3961	−	10.6133i	0.514301	−	0.478972i	−0.380912	−	0.924611i	$-0.624390\pi$
$491$	11.3961	−	10.6133i	0.514301	−	0.478972i	0.895213	+	0.445639i	$0.147024\pi$
$492$	−19.3961	−	23.1615i	−0.874445	−	1.04420i
$493$	1.18016	−	0.168973i	0.0531516	−	0.00761016i
$494$	−0.483213	+	0.766669i	−0.0217408	+	0.0344941i
$495$	−0.542715	−	0.0503226i	−0.0243932	−	0.00226183i
$496$	−7.26568	−	33.5421i	−0.326239	−	1.50609i
$497$	−36.3900	+	21.3246i	−1.63231	+	0.956539i
$498$	2.95042	−	1.64914i	0.132211	−	0.0738998i
$499$	−0.748350	+	1.03282i	−0.0335007	+	0.0462354i	−0.826197	−	0.563382i	$-0.809500\pi$
$499$	−0.748350	+	1.03282i	−0.0335007	+	0.0462354i	0.792696	+	0.609617i	$0.208677\pi$
$500$	8.59133	+	11.2340i	0.384216	+	0.502399i
$501$	−4.44084	−	0.494390i	−0.198402	−	0.0220877i
$502$	15.9596	+	31.2725i	0.712313	+	1.39576i
$503$	14.8780	−	10.6341i	0.663376	−	0.474153i	−0.199281	−	0.979942i	$-0.563861\pi$
$503$	14.8780	−	10.6341i	0.663376	−	0.474153i	0.862657	+	0.505790i	$0.168799\pi$
$504$	−2.00311	−	6.43319i	−0.0892254	−	0.286557i
$505$	−4.85042	+	10.1438i	−0.215841	+	0.451393i
$506$	−0.850925	+	0.752344i	−0.0378282	+	0.0334458i
$507$	18.6345	+	7.21560i	0.827586	+	0.320456i
$508$	−0.157809	+	24.4126i	−0.00700166	+	1.08313i
$509$	−20.3965	−	22.7707i	−0.904058	−	1.00929i	−0.999903	−	0.0138975i	$-0.995576\pi$
$509$	−20.3965	−	22.7707i	−0.904058	−	1.00929i	0.0958458	−	0.995396i	$-0.469444\pi$
$510$	1.52322	−	3.85949i	0.0674494	−	0.170901i
$511$	−3.80718	+	53.4520i	−0.168420	+	2.36458i
$512$	−31.3354	−	3.66259i	−1.38484	−	0.161865i
$513$	−0.214034	−	1.87910i	−0.00944983	−	0.0829642i
$514$	−44.6186	+	5.21517i	−1.96804	+	0.230031i
$515$	−1.79308	−	39.5996i	−0.0790124	−	1.74497i
$516$	−8.64887	−	9.30508i	−0.380745	−	0.409633i
$517$	−0.599600	+	0.603488i	−0.0263704	+	0.0265414i
$518$	−2.52579	+	3.78673i	−0.110977	+	0.166380i
$519$	6.20933	+	31.7815i	0.272560	+	1.39506i
$520$	−0.138020	−	1.63855i	−0.00605256	−	0.0718552i
$521$	−2.46339	−	6.38034i	−0.107923	−	0.279528i	0.868393	−	0.495876i	$-0.165153\pi$
$521$	−2.46339	−	6.38034i	−0.107923	−	0.279528i	−0.976316	+	0.216349i	$0.930585\pi$
$522$	−5.07671	+	16.8372i	−0.222202	+	0.736942i
$523$	0.429927	+	1.25651i	0.0187994	+	0.0549433i	0.955149	−	0.296126i	$-0.0956948\pi$
$523$	0.429927	+	1.25651i	0.0187994	+	0.0549433i	−0.936350	+	0.351069i	$0.885818\pi$
$524$	−9.92387	+	0.642392i	−0.433526	+	0.0280630i
$525$	17.7087	+	12.5113i	0.772871	+	0.546036i
$526$	−6.44283	−	33.9653i	−0.280921	−	1.48096i
$527$	0.666574	−	4.08875i	0.0290364	−	0.178109i
$528$	−0.0810214	+	0.384207i	−0.00352600	+	0.0167205i
$529$	−38.8959	−	28.5680i	−1.69112	−	1.24209i
$530$	−40.8213	+	22.5243i	−1.77317	+	0.978392i
$531$	−15.9334	+	19.6753i	−0.691452	+	0.853834i
$532$	3.66972	−	0.720710i	0.159103	−	0.0312467i
$533$	6.64521	+	6.68831i	0.287836	+	0.289703i
$534$	−1.76877	+	44.4564i	−0.0765420	+	1.92382i
$535$	5.71147	−	23.4228i	0.246929	−	1.01266i
$536$	0.301146	−	0.141613i	0.0130075	−	0.00611676i
$537$	12.2762	−	12.8195i	0.529757	−	0.553200i
$538$	25.0208	−	32.7171i	1.07872	−	1.41053i
$539$	0.264070	+	0.882054i	0.0113743	+	0.0379927i
$540$	22.2606	+	23.4290i	0.957944	+	1.00822i
$541$	8.23225	−	27.4976i	0.353932	−	1.18222i	−0.576914	−	0.816805i	$-0.695743\pi$
$541$	8.23225	−	27.4976i	0.353932	−	1.18222i	0.930846	−	0.365411i	$-0.119072\pi$
$542$	39.1481	+	54.0295i	1.68156	+	2.32077i
$543$	−3.16254	−	35.2341i	−0.135718	−	1.51204i
$544$	−2.99672	−	1.60334i	−0.128483	−	0.0687425i
$545$	7.14325	−	19.2381i	0.305983	−	0.824069i
$546$	7.47170	+	18.3399i	0.319759	+	0.784875i
$547$	−7.21516	+	0.186602i	−0.308498	+	0.00797853i	−0.179793	−	0.983704i	$-0.557543\pi$
$547$	−7.21516	+	0.186602i	−0.308498	+	0.00797853i	−0.128705	+	0.991683i	$0.541082\pi$
$548$	−0.748672	−	0.208407i	−0.0319817	−	0.00890271i
$549$	−5.43634	−	23.8307i	−0.232017	−	1.01707i
$550$	0.158234	+	0.330918i	0.00674711	+	0.0141104i
$551$	−0.954321	−	0.404358i	−0.0406555	−	0.0172262i
$552$	7.15109	−	0.0392146i	0.304371	−	0.00166908i
$553$	17.5330	+	11.2096i	0.745577	+	0.476681i
$554$	−7.26598	+	4.91464i	−0.308702	+	0.208803i
$555$	0.301133	−	2.29862i	0.0127824	−	0.0975710i
$556$	23.7733	+	4.03360i	1.00821	+	0.171063i
$557$	−36.5177	+	14.9191i	−1.54730	+	0.632143i	−0.981339	−	0.192287i	$-0.938410\pi$
$557$	−36.5177	+	14.9191i	−1.54730	+	0.632143i	−0.565964	+	0.824430i	$0.691496\pi$
$558$	50.5501	+	34.3363i	2.13996	+	1.45357i
$559$	2.93604	+	2.66432i	0.124181	+	0.112689i
$560$	29.5371	−	32.9754i	1.24817	−	1.39346i
$561$	−0.0260840	+	0.0395742i	−0.00110127	+	0.00167082i
$562$	−26.0182	+	50.9821i	−1.09751	+	2.15055i
$563$	1.52578	+	10.1867i	0.0643039	+	0.429318i	0.997543	+	0.0700615i	$0.0223196\pi$
$563$	1.52578	+	10.1867i	0.0643039	+	0.429318i	−0.933239	+	0.359257i	$0.883030\pi$
$564$	50.3187	−	3.53442i	2.11880	−	0.148826i
$565$	27.1142	−	9.47363i	1.14070	−	0.398559i
$566$	−31.6045	+	26.5193i	−1.32844	+	1.11469i
$567$	−36.1066	−	20.1079i	−1.51633	−	0.844453i
$568$	3.44137	+	2.88765i	0.144397	+	0.121163i
$569$	−11.0977	−	4.20248i	−0.465239	−	0.176177i	0.110390	−	0.993888i	$-0.464790\pi$
$569$	−11.0977	−	4.20248i	−0.465239	−	0.176177i	−0.575629	+	0.817711i	$0.695243\pi$
$570$	−2.86746	+	2.18847i	−0.120105	+	0.0916650i
$571$	3.44375	−	16.9546i	0.144116	−	0.709528i	−0.841463	−	0.540315i	$-0.818305\pi$
$571$	3.44375	−	16.9546i	0.144116	−	0.709528i	0.985579	−	0.169214i	$-0.0541227\pi$
$572$	−0.0216722	+	0.175568i	−0.000906160	+	0.00734085i
$573$	28.2730	+	8.49458i	1.18112	+	0.354866i
$574$	2.38114	−	73.6461i	0.0993868	−	3.07393i
$575$	−18.1891	+	14.0976i	−0.758536	+	0.587910i
$576$	23.4418	−	17.6164i	0.976743	−	0.734017i
$577$	1.53607	+	2.43714i	0.0639475	+	0.101460i	0.876438	−	0.481515i	$-0.159913\pi$
$577$	1.53607	+	2.43714i	0.0639475	+	0.101460i	−0.812490	+	0.582975i	$0.801889\pi$
$578$	22.4336	+	26.3870i	0.933115	+	1.09756i
$579$	−2.11741	−	2.05408i	−0.0879964	−	0.0853646i
$580$	17.1794	−	4.30691i	0.713337	−	0.178835i
$581$	4.24844	+	0.949061i	0.176255	+	0.0393737i
$582$	−15.4167	+	1.88771i	−0.639043	+	0.0782479i
$583$	0.509215	−	0.156043i	0.0210895	−	0.00646262i
$584$	5.49857	−	1.53063i	0.227532	−	0.0633379i
$585$	−7.54304	−	6.69557i	−0.311866	−	0.276828i
$586$	−0.180394	+	1.85462i	−0.00745203	+	0.0766135i
$587$	−29.9250	−	23.8192i	−1.23514	−	0.983124i	−0.999938	−	0.0111764i	$-0.996442\pi$
$587$	−29.9250	−	23.8192i	−1.23514	−	0.983124i	−0.235199	−	0.971947i	$-0.575574\pi$
$588$	22.6405	−	49.6785i	0.933677	−	2.04871i
$589$	−2.33282	+	2.74393i	−0.0961222	+	0.113062i
$590$	47.8012	+	6.84410i	1.96794	+	0.281767i
$591$	13.0054	+	20.9791i	0.534970	+	0.862964i
$592$	−1.61998	−	0.406131i	−0.0665807	−	0.0166919i
$593$	29.2162	+	14.6729i	1.19976	+	0.602544i	0.932532	−	0.361088i	$-0.117595\pi$
$593$	29.2162	+	14.6729i	1.19976	+	0.602544i	0.267233	+	0.963632i	$0.413891\pi$
$594$	−0.367210	−	0.594951i	−0.0150668	−	0.0244111i
$595$	4.77536	−	2.39827i	0.195771	−	0.0983197i
$596$	−29.9086	+	6.68129i	−1.22510	+	0.273677i
$597$	−0.467907	−	0.398594i	−0.0191501	−	0.0163134i
$598$	−20.9324	+	1.89954i	−0.855991	+	0.0776781i
$599$	−2.60778	−	23.6350i	−0.106551	−	0.965700i	−0.922084	−	0.386989i	$-0.873515\pi$
$599$	−2.60778	−	23.6350i	−0.106551	−	0.965700i	0.815533	−	0.578711i	$-0.196444\pi$
$600$	0.621502	−	2.22421i	0.0253727	−	0.0908031i
$601$	−28.4126	−	2.57834i	−1.15898	−	0.105173i	−0.505987	−	0.862541i	$-0.668872\pi$
$601$	−28.4126	−	2.57834i	−1.15898	−	0.105173i	−0.652988	+	0.757368i	$0.726485\pi$
$602$	−0.600846	−	30.9795i	−0.0244887	−	1.26263i
$603$	0.738924	−	1.90275i	0.0300913	−	0.0774859i
$604$	3.44695	+	4.27355i	0.140254	+	0.173888i
$605$	7.24055	+	29.6936i	0.294370	+	1.20722i
$606$	−14.1371	+	2.85704i	−0.574280	+	0.116059i
$607$	21.1834	−	37.8113i	0.859807	−	1.53471i	0.0148430	−	0.999890i	$-0.495275\pi$
$607$	21.1834	−	37.8113i	0.859807	−	1.53471i	0.844964	−	0.534824i	$-0.179622\pi$
$608$	1.51031	+	2.53953i	0.0612510	+	0.102992i
$609$	−19.3268	+	11.8088i	−0.783160	+	0.478518i
$610$	−33.7026	+	32.2111i	−1.36458	+	1.30419i
$611$	−15.5535	+	2.43252i	−0.629226	+	0.0984091i
$612$	2.70891	−	0.748357i	0.109501	−	0.0302505i
$613$	−8.46056	+	5.10597i	−0.341719	+	0.206228i	−0.677165	−	0.735831i	$-0.736792\pi$
$613$	−8.46056	+	5.10597i	−0.341719	+	0.206228i	0.335447	+	0.942059i	$0.391113\pi$
$614$	6.37417	−	9.04093i	0.257241	−	0.364862i
$615$	15.4960	+	34.1793i	0.624858	+	1.37824i
$616$	0.118316	−	0.0869002i	0.00476710	−	0.00350131i
$617$	3.44154	−	7.44313i	0.138551	−	0.299649i	−0.825943	−	0.563754i	$-0.809356\pi$
$617$	3.44154	−	7.44313i	0.138551	−	0.299649i	0.964494	+	0.264105i	$0.0850767\pi$
$618$	39.1942	−	32.3937i	1.57662	−	1.30306i
$619$	6.12201	+	6.65936i	0.246064	+	0.267662i	0.846950	−	0.531673i	$-0.178436\pi$
$619$	6.12201	+	6.65936i	0.246064	+	0.267662i	−0.600886	+	0.799335i	$0.705185\pi$
$620$	3.57846	−	61.4399i	0.143715	−	2.46748i
$621$	31.6030	−	30.4182i	1.26819	−	1.22064i
$622$	−1.46377	−	25.1319i	−0.0586918	−	1.00770i
$623$	−39.8577	+	41.1672i	−1.59686	+	1.64933i
$624$	−5.41709	+	4.84270i	−0.216857	+	0.193863i
$625$	−11.6125	−	28.9572i	−0.464499	−	1.15829i
$626$	10.3707	+	29.0767i	0.414497	+	1.16214i
$627$	0.0371917	−	0.0177390i	0.00148529	−	0.000708429i
$628$	1.71717	−	11.4645i	0.0685225	−	0.457483i
$629$	−0.164010	−	0.117227i	−0.00653950	−	0.00467415i
$630$	2.39275	+	78.7888i	0.0953296	+	3.13902i
$631$	1.64570	+	1.61409i	0.0655141	+	0.0642558i	0.732237	−	0.681050i	$-0.238476\pi$
$631$	1.64570	+	1.61409i	0.0655141	+	0.0642558i	−0.666723	+	0.745306i	$0.732304\pi$
$632$	0.497207	−	2.16001i	0.0197778	−	0.0859205i
$633$	−48.1797	−	11.1401i	−1.91497	−	0.442780i
$634$	−21.1092	−	67.3292i	−0.838355	−	2.67398i
$635$	8.32141	−	29.1624i	0.330225	−	1.15728i
$636$	−28.8199	−	12.9101i	−1.14279	−	0.511917i
$637$	−5.72380	+	16.0480i	−0.226785	+	0.635846i
$638$	−0.382864	+	0.0148569i	−0.0151577	+	0.000588189i
$639$	27.5010	−	1.72605i	1.08792	−	0.0682813i
$640$	−9.99707	−	4.08425i	−0.395169	−	0.161444i
$641$	−10.2782	−	6.38563i	−0.405964	−	0.252217i	0.309453	−	0.950915i	$-0.399854\pi$
$641$	−10.2782	−	6.38563i	−0.405964	−	0.252217i	−0.715417	+	0.698697i	$0.753763\pi$
$642$	28.4086	−	12.2212i	1.12120	−	0.482334i
$643$	−17.2994	+	7.32997i	−0.682223	+	0.289066i	−0.703487	−	0.710708i	$-0.748375\pi$
$643$	−17.2994	+	7.32997i	−0.682223	+	0.289066i	0.0212647	+	0.999774i	$0.493231\pi$
$644$	64.9811	+	57.4530i	2.56062	+	2.26397i
$645$	7.25048	+	14.0168i	0.285487	+	0.551910i
$646$	0.0504720	+	0.309595i	0.00198580	+	0.0121808i
$647$	29.5257	−	10.7465i	1.16078	−	0.422488i	0.311402	−	0.950278i	$-0.399201\pi$
$647$	29.5257	−	10.7465i	1.16078	−	0.422488i	0.849375	+	0.527790i	$0.176979\pi$
$648$	−0.725306	+	4.34172i	−0.0284927	+	0.170559i
$649$	−0.518345	−	0.188662i	−0.0203468	−	0.00740564i
$650$	−1.26499	+	6.66879i	−0.0496171	+	0.261571i
$651$	19.0637	+	76.3585i	0.747163	+	2.99273i
$652$	14.4879	−	11.5319i	0.567391	−	0.451623i
$653$	3.63889	+	5.61134i	0.142401	+	0.219589i	0.903008	−	0.429624i	$-0.141354\pi$
$653$	3.63889	+	5.61134i	0.142401	+	0.219589i	−0.760607	+	0.649212i	$0.775099\pi$
$654$	25.2253	−	7.52500i	0.986385	−	0.294251i
$655$	12.0901	+	2.53718i	0.472399	+	0.0991356i
$656$	25.7447	−	8.25471i	1.00516	−	0.322292i
$657$	17.9540	−	30.0548i	0.700454	−	1.17255i
$658$	97.2438	+	75.3696i	3.79096	+	2.93821i
$659$	−23.9937	+	28.9728i	−0.934661	+	1.12862i	0.0568223	+	0.998384i	$0.481903\pi$
$659$	−23.9937	+	28.9728i	−0.934661	+	1.12862i	−0.991483	+	0.130237i	$0.958426\pi$
$660$	−0.324733	+	0.624775i	−0.0126402	+	0.0243193i
$661$	18.4337	+	8.96124i	0.716989	+	0.348552i	0.759467	−	0.650545i	$-0.225460\pi$
$661$	18.4337	+	8.96124i	0.716989	+	0.348552i	−0.0424788	+	0.999097i	$0.513526\pi$
$662$	18.2571	−	9.46655i	0.709581	−	0.367928i
$663$	−0.822534	+	0.304496i	−0.0319446	+	0.0118256i
$664$	−0.0568030	−	0.460164i	−0.00220438	−	0.0178578i
$665$	−4.63172	−	0.360006i	−0.179610	−	0.0139604i
$666$	2.58777	−	1.46512i	0.100274	−	0.0567721i
$667$	−5.99617	−	23.2785i	−0.232172	−	0.901349i
$668$	−2.75601	+	5.07204i	−0.106633	+	0.196243i
$669$	−29.1950	−	15.4149i	−1.12874	−	0.595974i
$670$	−3.83831	+	0.651243i	−0.148287	+	0.0251597i
$671$	0.452356	−	0.281040i	0.0174630	−	0.0108494i
$672$	64.3338	+	5.48255i	2.48173	+	0.211494i
$673$	15.8379	−	35.4492i	0.610508	−	1.36647i	−0.300383	−	0.953819i	$-0.597114\pi$
$673$	15.8379	−	35.4492i	0.610508	−	1.36647i	0.910891	−	0.412648i	$-0.135396\pi$
$674$	37.1568	+	39.3840i	1.43123	+	1.51701i
$675$	−6.64577	−	12.5096i	−0.255796	−	0.481495i
$676$	17.7155	−	18.7773i	0.681364	−	0.722203i
$677$	9.22867	+	22.1785i	0.354687	+	0.852391i	0.996347	+	0.0854014i	$0.0272173\pi$
$677$	9.22867	+	22.1785i	0.354687	+	0.852391i	−0.641660	+	0.766989i	$0.721754\pi$
$678$	30.6298	+	20.4739i	1.17633	+	0.786294i
$679$	−16.4229	−	11.4205i	−0.630253	−	0.438279i
$680$	−0.411463	−	0.393254i	−0.0157789	−	0.0150806i
$681$	−8.24547	+	9.06852i	−0.315967	+	0.347506i
$682$	−0.348749	+	1.28492i	−0.0133543	+	0.0492022i
$683$	−9.72359	+	28.4183i	−0.372063	+	1.08740i	0.588300	+	0.808643i	$0.299797\pi$
$683$	−9.72359	+	28.4183i	−0.372063	+	1.08740i	−0.960363	+	0.278752i	$0.910079\pi$
$684$	−2.35247	−	0.659829i	−0.0899490	−	0.0252292i
$685$	0.826525	+	0.498810i	0.0315799	+	0.0190586i
$686$	61.3371	−	26.9298i	2.34186	−	1.02819i
$687$	−8.88565	+	14.2709i	−0.339009	+	0.544470i
$688$	10.6321	−	4.02617i	0.405344	−	0.153496i
$689$	9.30398	+	3.25078i	0.354453	+	0.123845i
$690$	−80.7185	−	21.9933i	−3.07290	−	0.837271i
$691$	18.4011	+	27.5875i	0.700012	+	1.04948i	0.995558	+	0.0941488i	$0.0300130\pi$
$691$	18.4011	+	27.5875i	0.700012	+	1.04948i	−0.295546	+	0.955329i	$0.595501\pi$
$692$	41.0499	+	8.06194i	1.56048	+	0.306469i
$693$	0.158098	−	0.886448i	0.00600564	−	0.0336734i
$694$	24.8999	−	30.8710i	0.945187	−	1.17185i
$695$	−27.1063	−	12.7467i	−1.02820	−	0.483510i
$696$	1.87620	+	1.51634i	0.0711171	+	0.0574767i
$697$	3.25663	+	0.210808i	0.123354	+	0.00798494i
$698$	−3.91708	−	14.4320i	−0.148264	−	0.546260i
$699$	5.84150	−	3.78001i	0.220946	−	0.142973i
$700$	23.5999	−	15.0885i	0.891993	−	0.570291i
$701$	9.00814	−	20.8832i	0.340233	−	0.788748i	−0.659094	−	0.752061i	$-0.729060\pi$
$701$	9.00814	−	20.8832i	0.340233	−	0.788748i	0.999327	−	0.0366878i	$-0.0116807\pi$
$702$	1.04052	−	12.8959i	0.0392718	−	0.486723i
$703$	0.0694177	+	0.160928i	0.00261814	+	0.00606953i
$704$	0.529195	+	0.357943i	0.0199448	+	0.0134905i
$705$	−61.3949	−	12.5330i	−2.31226	−	0.472018i
$706$	−0.211147	+	0.644171i	−0.00794662	+	0.0242437i
$707$	−16.0263	−	9.39144i	−0.602731	−	0.353201i
$708$	15.7733	+	28.6528i	0.592797	+	1.07684i
$709$	23.1572	+	7.75661i	0.869687	+	0.291306i	0.717088	−	0.696983i	$-0.245475\pi$
$709$	23.1572	+	7.75661i	0.869687	+	0.291306i	0.152599	+	0.988288i	$0.451236\pi$
$710$	−29.7260	−	43.3415i	−1.11560	−	1.62658i
$711$	−6.92642	−	11.6987i	−0.259761	−	0.438736i
$712$	5.55607	+	2.52554i	0.208222	+	0.0946487i
$713$	−83.4190	−	4.31774i	−3.12407	−	0.161700i
$714$	6.14233	+	3.04273i	0.229871	+	0.113871i
$715$	0.0844224	−	0.202886i	0.00315722	−	0.00758750i
$716$	−9.35358	−	20.9356i	−0.349560	−	0.782400i
$717$	26.1388	−	30.2854i	0.976170	−	1.13103i
$718$	−8.06193	−	4.58533i	−0.300869	−	0.171123i
$719$	5.72844	+	1.83675i	0.213635	+	0.0684993i	0.410216	−	0.911988i	$-0.365453\pi$
$719$	5.72844	+	1.83675i	0.213635	+	0.0684993i	−0.196581	+	0.980487i	$0.562984\pi$
$720$	−26.9335	+	10.5384i	−1.00375	+	0.392743i
$721$	65.4381	+	2.53930i	2.43704	+	0.0945684i
$722$	−14.4564	+	36.0489i	−0.538012	+	1.34160i
$723$	−42.4674	−	7.53109i	−1.57938	−	0.280084i
$724$	−43.6955	−	13.3900i	−1.62393	−	0.497634i
$725$	−7.76038	−	0.200703i	−0.288213	−	0.00745391i
$726$	−24.8400	+	30.3319i	−0.921900	+	1.12572i
$727$	−6.44472	−	0.0833243i	−0.239021	−	0.00309033i	−0.106675	−	0.994294i	$-0.534021\pi$
$727$	−6.44472	−	0.0833243i	−0.239021	−	0.00309033i	−0.132346	+	0.991204i	$0.542251\pi$
$728$	2.71655			0.100682
$729$	15.1401	+	22.3557i	0.560745	+	0.827988i
$730$	−66.7729			−2.47138
$731$	1.37221	+	0.0177414i	0.0507529	+	0.000656189i
$732$	−31.1608	−	5.11139i	−1.15173	−	0.188922i
$733$	26.3697	+	0.681985i	0.973985	+	0.0251897i	0.509571	−	0.860428i	$-0.329804\pi$
$733$	26.3697	+	0.681985i	0.973985	+	0.0251897i	0.464414	+	0.885618i	$0.346265\pi$
$734$	40.6818	+	12.4664i	1.50159	+	0.460145i
$735$	−43.6437	+	51.9091i	−1.60982	+	1.91470i
$736$	−25.5068	+	63.6044i	−0.940191	+	2.34449i
$737$	0.0444390	+	0.00172443i	0.00163693	+	6.35204e-5i
$738$	−23.0664	+	42.2526i	−0.849086	+	1.55534i
$739$	19.7916	+	6.34592i	0.728046	+	0.233439i	0.646159	−	0.763203i	$-0.276374\pi$
$739$	19.7916	+	6.34592i	0.728046	+	0.233439i	0.0818872	+	0.996642i	$0.473905\pi$
$740$	−2.60329	−	1.48066i	−0.0956989	−	0.0544300i
$741$	0.749011	+	0.142840i	0.0275156	+	0.00524735i
$742$	−31.4193	−	70.3241i	−1.15344	−	2.58168i
$743$	−10.2573	+	24.6507i	−0.376306	+	0.904346i	0.616800	+	0.787120i	$0.288429\pi$
$743$	−10.2573	+	24.6507i	−0.376306	+	0.904346i	−0.993105	+	0.117226i	$0.962600\pi$
$744$	6.97822	−	4.64466i	0.255834	−	0.170282i
$745$	38.0179	+	1.96779i	1.39287	+	0.0720944i
$746$	−42.6090	−	19.3682i	−1.56003	−	0.709119i
$747$	−2.19851	−	1.80405i	−0.0804392	−	0.0660068i
$748$	0.0346328	+	0.0504959i	0.00126630	+	0.00184631i
$749$	37.7671	+	12.6503i	1.37998	+	0.462231i
$750$	11.6630	−	19.2828i	0.425874	−	0.704108i
$751$	−31.1063	−	18.2283i	−1.13508	−	0.665162i	−0.186742	−	0.982409i	$-0.559793\pi$
$751$	−31.1063	−	18.2283i	−1.13508	−	0.665162i	−0.948343	+	0.317247i	$0.897241\pi$
$752$	−14.0606	+	42.8963i	−0.512737	+	1.56427i
$753$	19.5891	−	22.1121i	0.713865	−	0.805809i
$754$	−5.87295	−	3.97241i	−0.213880	−	0.144667i
$755$	−2.70139	−	6.26253i	−0.0983136	−	0.227917i
$756$	−41.6559	+	33.3970i	−1.51501	+	1.21464i
$757$	−5.01090	+	11.6166i	−0.182124	+	0.422212i	−0.984681	−	0.174364i	$-0.944213\pi$
$757$	−5.01090	+	11.6166i	−0.182124	+	0.422212i	0.802557	+	0.596575i	$0.203472\pi$
$758$	11.0123	−	7.04066i	0.399985	−	0.255728i
$759$	0.850809	+	0.435254i	0.0308824	+	0.0157987i
$760$	0.129612	+	0.477538i	0.00470151	+	0.0173221i
$761$	−21.8075	−	1.41164i	−0.790520	−	0.0511719i	−0.335946	−	0.941881i	$-0.609056\pi$
$761$	−21.8075	−	1.41164i	−0.790520	−	0.0511719i	−0.454573	+	0.890709i	$0.650208\pi$
$762$	36.3039	−	13.9757i	1.31515	−	0.506286i
$763$	30.6795	+	14.4270i	1.11067	+	0.522293i
$764$	23.9436	−	29.6854i	0.866248	−	1.07398i
$765$	−3.49111	−	0.00684620i	−0.126222	−	0.000247525i
$766$	−1.72101	−	0.337995i	−0.0621825	−	0.0122122i
$767$	−5.66417	−	8.49188i	−0.204521	−	0.306624i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05837 - 0.0266128i) q^{2} +(0.611800 + 1.62040i) q^{3} +(2.23685 + 0.0578504i) q^{4} +(-2.65761 - 0.814392i) q^{5} +(-1.21619 - 3.35167i) q^{6} +(1.70918 - 4.26207i) q^{7} +(-0.488730 - 0.0189650i) q^{8} +(-2.25140 + 1.98272i) q^{9} +O(q^{10})\)	\(q+(-2.05837 - 0.0266128i) q^{2} +(0.611800 + 1.62040i) q^{3} +(2.23685 + 0.0578504i) q^{4} +(-2.65761 - 0.814392i) q^{5} +(-1.21619 - 3.35167i) q^{6} +(1.70918 - 4.26207i) q^{7} +(-0.488730 - 0.0189650i) q^{8} +(-2.25140 + 1.98272i) q^{9} +(5.44867 + 1.74705i) q^{10} +(-0.0568156 - 0.0323146i) q^{11} +(1.27476 + 3.65998i) q^{12} +(-0.493390 - 1.10433i) q^{13} +(-3.63156 + 8.72744i) q^{14} +(-0.306283 - 4.80464i) q^{15} +(-3.46372 - 0.179281i) q^{16} +(-0.381134 - 0.173247i) q^{17} +(4.68698 - 4.02126i) q^{18} +(0.205864 + 0.300158i) q^{19} +(-5.89755 - 1.97541i) q^{20} +(7.95195 + 0.162028i) q^{21} +(0.116088 + 0.0680275i) q^{22} +(-2.62933 + 8.02163i) q^{23} +(-0.268274 - 0.803542i) q^{24} +(2.25808 + 1.52735i) q^{25} +(0.986190 + 2.28625i) q^{26} +(-4.59021 - 2.43515i) q^{27} +(4.06974 - 9.43473i) q^{28} +(-2.39919 + 1.53391i) q^{29} +(0.502580 + 9.89787i) q^{30} +(2.59194 + 9.54968i) q^{31} +(8.10101 + 0.524394i) q^{32} +(0.0176029 - 0.111834i) q^{33} +(0.779904 + 0.366749i) q^{34} +(-8.01334 + 9.93498i) q^{35} +(-5.15074 + 4.30480i) q^{36} +(0.472502 + 0.0927963i) q^{37} +(-0.415757 - 0.623314i) q^{38} +(1.48760 - 1.47512i) q^{39} +(1.28341 + 0.448419i) q^{40} +(-7.28978 + 2.76051i) q^{41} +(-16.3637 - 0.545137i) q^{42} +(-3.00135 + 1.31773i) q^{43} +(-0.125218 - 0.0755697i) q^{44} +(7.59806 - 3.43578i) q^{45} +(5.62562 - 16.4415i) q^{46} +(3.40924 - 12.5609i) q^{47} +(-1.82860 - 5.72231i) q^{48} +(-10.1835 - 9.73283i) q^{49} +(-4.60732 - 3.20394i) q^{50} +(0.0475514 - 0.723582i) q^{51} +(-1.03975 - 2.49876i) q^{52} +(-5.59164 + 5.92679i) q^{53} +(9.38355 + 5.13459i) q^{54} +(0.124677 + 0.132150i) q^{55} +(-0.916160 + 2.05059i) q^{56} +(-0.360428 + 0.517219i) q^{57} +(4.97924 - 3.09350i) q^{58} +(8.32036 - 1.41171i) q^{59} +(-0.407159 - 10.7650i) q^{60} +(-3.89003 + 7.15902i) q^{61} +(-5.08102 - 19.7257i) q^{62} +(4.60245 + 12.9845i) q^{63} +(-9.74505 - 0.757445i) q^{64} +(0.411883 + 3.33669i) q^{65} +(-0.0392095 + 0.229728i) q^{66} +(-0.604026 + 0.313197i) q^{67} +(-0.842516 - 0.409575i) q^{68} +(-14.6069 + 0.647051i) q^{69} +(16.7588 - 20.2366i) q^{70} +(-7.25979 - 5.62676i) q^{71} +(1.13793 - 0.926319i) q^{72} +(-11.1125 + 3.56307i) q^{73} +(-0.970113 - 0.203584i) q^{74} +(-1.09342 + 4.59343i) q^{75} +(0.443123 + 0.683316i) q^{76} +(-0.234836 + 0.186921i) q^{77} +(-3.10129 + 2.99675i) q^{78} +(-0.844570 + 4.45241i) q^{79} +(9.05922 + 3.29729i) q^{80} +(1.13762 - 8.92781i) q^{81} +(15.0785 - 5.48814i) q^{82} +(0.152532 + 0.935631i) q^{83} +(17.7779 + 0.822455i) q^{84} +(0.871814 + 0.770814i) q^{85} +(6.21295 - 2.63250i) q^{86} +(-3.95337 - 2.94920i) q^{87} +(0.0271547 + 0.0168706i) q^{88} +(-11.5515 - 4.71931i) q^{89} +(-15.7311 + 6.86990i) q^{90} +(-5.55002 + 0.215366i) q^{91} +(-6.34547 + 17.7910i) q^{92} +(-13.8886 + 10.0425i) q^{93} +(-7.35175 + 25.7643i) q^{94} +(-0.302661 - 0.965356i) q^{95} +(4.10646 + 13.4477i) q^{96} +(0.977177 - 4.24514i) q^{97} +(20.7024 + 20.3048i) q^{98} +(0.191986 - 0.0398964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

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