LMFDB - Embedded newform 324.2.p.a.83.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			83.29
Character	$\chi$	$=$	324.83
Dual form			324.2.p.a.203.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.162608 + 1.40483i) q^{2} +(-1.05551 - 1.37328i) q^{3} +(-1.94712 + 0.456876i) q^{4} +(0.550176 + 2.32138i) q^{5} +(1.75760 - 1.70612i) q^{6} +(3.79110 - 2.82237i) q^{7} +(-0.958452 - 2.66108i) q^{8} +(-0.771815 + 2.89902i) q^{9} +O(q^{10})$	\(q+(0.162608 + 1.40483i) q^{2} +(-1.05551 - 1.37328i) q^{3} +(-1.94712 + 0.456876i) q^{4} +(0.550176 + 2.32138i) q^{5} +(1.75760 - 1.70612i) q^{6} +(3.79110 - 2.82237i) q^{7} +(-0.958452 - 2.66108i) q^{8} +(-0.771815 + 2.89902i) q^{9} +(-3.17168 + 1.15038i) q^{10} +(-2.38854 + 2.53170i) q^{11} +(2.68261 + 2.19171i) q^{12} +(4.46063 + 2.24021i) q^{13} +(4.58142 + 4.86692i) q^{14} +(2.60719 - 3.20577i) q^{15} +(3.58253 - 1.77918i) q^{16} +(-0.831376 + 2.28419i) q^{17} +(-4.19814 - 0.612868i) q^{18} +(2.09262 + 5.74942i) q^{19} +(-2.13184 - 4.26863i) q^{20} +(-7.87744 - 2.22723i) q^{21} +(-3.94502 - 2.94382i) q^{22} +(0.667898 - 0.897143i) q^{23} +(-2.64277 + 4.12502i) q^{24} +(-0.617928 + 0.310335i) q^{25} +(-2.42179 + 6.63072i) q^{26} +(4.79583 - 2.00001i) q^{27} +(-6.09224 + 7.22754i) q^{28} +(-1.22730 + 1.86602i) q^{29} +(4.92753 + 3.14139i) q^{30} +(-4.14797 + 1.78926i) q^{31} +(3.08200 + 4.74355i) q^{32} +(5.99786 + 0.607914i) q^{33} +(-3.34409 - 0.796518i) q^{34} +(8.63755 + 7.24776i) q^{35} +(0.178324 - 5.99735i) q^{36} +(6.45572 - 5.41699i) q^{37} +(-7.73671 + 3.87469i) q^{38} +(-1.63177 - 8.49026i) q^{39} +(5.65006 - 3.68899i) q^{40} +(-2.53023 + 0.147369i) q^{41} +(1.84795 - 11.4287i) q^{42} +(-6.72342 + 2.01286i) q^{43} +(3.49409 - 6.02079i) q^{44} +(-7.15434 - 0.196703i) q^{45} +(1.36894 + 0.792403i) q^{46} +(3.79068 - 8.78778i) q^{47} +(-6.22470 - 3.04189i) q^{48} +(4.39904 - 14.6938i) q^{49} +(-0.536450 - 0.817624i) q^{50} +(4.01436 - 1.26926i) q^{51} +(-9.70886 - 2.32400i) q^{52} +(6.41965 - 3.70639i) q^{53} +(3.58952 + 6.41212i) q^{54} +(-7.19115 - 4.15181i) q^{55} +(-11.1441 - 7.38333i) q^{56} +(5.68682 - 8.94231i) q^{57} +(-2.82102 - 1.42073i) q^{58} +(3.29729 + 3.49492i) q^{59} +(-3.61187 + 7.43318i) q^{60} +(-5.83779 + 0.682339i) q^{61} +(-3.18811 - 5.53626i) q^{62} +(5.25607 + 13.1688i) q^{63} +(-6.16274 + 5.10104i) q^{64} +(-2.74624 + 11.5873i) q^{65} +(0.121285 + 8.52485i) q^{66} +(-4.36661 - 6.63910i) q^{67} +(0.575197 - 4.82742i) q^{68} +(-1.93700 + 0.0297259i) q^{69} +(-8.77737 + 13.3129i) q^{70} +(-0.225531 - 1.27905i) q^{71} +(8.45428 - 0.724703i) q^{72} +(0.400223 - 2.26978i) q^{73} +(8.65973 + 8.18837i) q^{74} +(1.07841 + 0.521030i) q^{75} +(-6.70135 - 10.2387i) q^{76} +(-1.90979 + 16.3393i) q^{77} +(11.6621 - 3.67296i) q^{78} +(-1.86572 - 0.108666i) q^{79} +(6.10117 + 7.33753i) q^{80} +(-7.80860 - 4.47501i) q^{81} +(-0.618466 - 3.53059i) q^{82} +(0.794679 - 13.6441i) q^{83} +(16.3559 + 0.737663i) q^{84} +(-5.75986 - 0.673231i) q^{85} +(-3.92102 - 9.11797i) q^{86} +(3.85801 - 0.284164i) q^{87} +(9.02638 + 3.92959i) q^{88} +(-2.15064 - 0.379215i) q^{89} +(-0.887021 - 10.0826i) q^{90} +(23.2334 - 4.09667i) q^{91} +(-0.890593 + 2.05199i) q^{92} +(6.83536 + 3.80776i) q^{93} +(12.9618 + 3.89631i) q^{94} +(-12.1953 + 8.02095i) q^{95} +(3.26117 - 9.23931i) q^{96} +(-7.20752 - 1.70821i) q^{97} +(21.3577 + 3.79058i) q^{98} +(-5.49594 - 8.87842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{54}\right)$

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 $

$2$	0.162608	+	1.40483i	0.114982	+	0.993368i
$2$	0.162608	+	1.40483i	0.114982	+	0.993368i
$3$	−1.05551	−	1.37328i	−0.609397	−	0.792866i
$3$	−1.05551	−	1.37328i	−0.609397	−	0.792866i
$4$	−1.94712	+	0.456876i	−0.973559	+	0.228438i
$5$	0.550176	+	2.32138i	0.246046	+	1.03815i	0.946052	+	0.324014i	$0.105032\pi$
$5$	0.550176	+	2.32138i	0.246046	+	1.03815i	−0.700006	+	0.714137i	$0.746819\pi$
$6$	1.75760	−	1.70612i	0.717538	−	0.696520i
$7$	3.79110	−	2.82237i	1.43290	−	1.06675i	0.447923	−	0.894072i	$-0.352164\pi$
$7$	3.79110	−	2.82237i	1.43290	−	1.06675i	0.984978	−	0.172683i	$-0.0552435\pi$
$8$	−0.958452	−	2.66108i	−0.338864	−	0.940835i
$9$	−0.771815	+	2.89902i	−0.257272	+	0.966339i
$10$	−3.17168	+	1.15038i	−1.00297	+	0.363783i
$11$	−2.38854	+	2.53170i	−0.720172	+	0.763337i	−0.979280	−	0.202511i	$-0.935090\pi$
$11$	−2.38854	+	2.53170i	−0.720172	+	0.763337i	0.259108	+	0.965848i	$0.416571\pi$
$12$	2.68261	+	2.19171i	0.774404	+	0.632692i
$13$	4.46063	+	2.24021i	1.23716	+	0.621323i	0.942476	−	0.334273i	$-0.108491\pi$
$13$	4.46063	+	2.24021i	1.23716	+	0.621323i	0.294680	+	0.955596i	$0.404787\pi$
$14$	4.58142	+	4.86692i	1.22444	+	1.30074i
$15$	2.60719	−	3.20577i	0.673174	−	0.827727i
$16$	3.58253	−	1.77918i	0.895632	−	0.444795i
$17$	−0.831376	+	2.28419i	−0.201638	+	0.553997i	−0.998758	−	0.0498245i	$-0.984134\pi$
$17$	−0.831376	+	2.28419i	−0.201638	+	0.553997i	0.797120	+	0.603821i	$0.206356\pi$
$18$	−4.19814	−	0.612868i	−0.989511	−	0.144454i
$19$	2.09262	+	5.74942i	0.480080	+	1.31901i	0.909425	+	0.415868i	$0.136522\pi$
$19$	2.09262	+	5.74942i	0.480080	+	1.31901i	−0.429345	+	0.903140i	$0.641256\pi$
$20$	−2.13184	−	4.26863i	−0.476693	−	0.954494i
$21$	−7.87744	−	2.22723i	−1.71900	−	0.486021i
$22$	−3.94502	−	2.94382i	−0.841081	−	0.627626i
$23$	0.667898	−	0.897143i	0.139266	−	0.187067i	−0.727018	−	0.686618i	$-0.759094\pi$
$23$	0.667898	−	0.897143i	0.139266	−	0.187067i	0.866284	+	0.499551i	$0.166502\pi$
$24$	−2.64277	+	4.12502i	−0.539454	+	0.842015i
$25$	−0.617928	+	0.310335i	−0.123586	+	0.0620671i
$26$	−2.42179	+	6.63072i	−0.474952	+	1.30039i
$27$	4.79583	−	2.00001i	0.922958	−	0.384902i
$28$	−6.09224	+	7.22754i	−1.15133	+	1.36588i
$29$	−1.22730	+	1.86602i	−0.227905	+	0.346512i	−0.931279	−	0.364308i	$-0.881306\pi$
$29$	−1.22730	+	1.86602i	−0.227905	+	0.346512i	0.703374	+	0.710820i	$0.251676\pi$
$30$	4.92753	+	3.14139i	0.899640	+	0.573536i
$31$	−4.14797	+	1.78926i	−0.744997	+	0.321360i	−0.734522	−	0.678585i	$-0.762594\pi$
$31$	−4.14797	+	1.78926i	−0.744997	+	0.321360i	−0.0104749	+	0.999945i	$0.503334\pi$
$32$	3.08200	+	4.74355i	0.544826	+	0.838549i
$33$	5.99786	+	0.607914i	1.04409	+	0.105824i
$34$	−3.34409	−	0.796518i	−0.573507	−	0.136602i
$35$	8.63755	+	7.24776i	1.46001	+	1.22510i
$36$	0.178324	−	5.99735i	0.0297207	−	0.999558i
$37$	6.45572	−	5.41699i	1.06131	−	0.890548i	0.0670762	−	0.997748i	$-0.478633\pi$
$37$	6.45572	−	5.41699i	1.06131	−	0.890548i	0.994237	+	0.107200i	$0.0341885\pi$
$38$	−7.73671	+	3.87469i	−1.25506	+	0.628557i
$39$	−1.63177	−	8.49026i	−0.261293	−	1.35953i
$40$	5.65006	−	3.68899i	0.893353	−	0.583281i
$41$	−2.53023	+	0.147369i	−0.395155	+	0.0230152i	−0.254572	−	0.967054i	$-0.581935\pi$
$41$	−2.53023	+	0.147369i	−0.395155	+	0.0230152i	−0.140583	+	0.990069i	$0.544898\pi$
$42$	1.84795	−	11.4287i	0.285144	−	1.76348i
$43$	−6.72342	+	2.01286i	−1.02531	+	0.306958i	−0.754937	−	0.655797i	$-0.772333\pi$
$43$	−6.72342	+	2.01286i	−1.02531	+	0.306958i	−0.270374	+	0.962755i	$0.587147\pi$
$44$	3.49409	−	6.02079i	0.526754	−	0.907668i
$45$	−7.15434	−	0.196703i	−1.06651	−	0.0293228i
$46$	1.36894	+	0.792403i	0.201840	+	0.116833i
$47$	3.79068	−	8.78778i	0.552927	−	1.28183i	−0.381069	−	0.924547i	$-0.624444\pi$
$47$	3.79068	−	8.78778i	0.552927	−	1.28183i	0.933996	−	0.357283i	$-0.116297\pi$
$48$	−6.22470	−	3.04189i	−0.898458	−	0.439059i
$49$	4.39904	−	14.6938i	0.628435	−	2.09912i
$50$	−0.536450	−	0.817624i	−0.0758655	−	0.115629i
$51$	4.01436	−	1.26926i	0.562123	−	0.177732i
$52$	−9.70886	−	2.32400i	−1.34638	−	0.322281i
$53$	6.41965	−	3.70639i	0.881806	−	0.509111i	0.0105528	−	0.999944i	$-0.496641\pi$
$53$	6.41965	−	3.70639i	0.881806	−	0.509111i	0.871254	+	0.490833i	$0.163308\pi$
$54$	3.58952	+	6.41212i	0.488472	+	0.872580i
$55$	−7.19115	−	4.15181i	−0.969655	−	0.559830i
$56$	−11.1441	−	7.38333i	−1.48920	−	0.986639i
$57$	5.68682	−	8.94231i	0.753237	−	1.18444i
$58$	−2.82102	−	1.42073i	−0.370419	−	0.186551i
$59$	3.29729	+	3.49492i	0.429270	+	0.455000i	0.905516	−	0.424312i	$-0.139484\pi$
$59$	3.29729	+	3.49492i	0.429270	+	0.455000i	−0.476246	+	0.879312i	$0.658003\pi$
$60$	−3.61187	+	7.43318i	−0.466290	+	0.959619i
$61$	−5.83779	+	0.682339i	−0.747452	+	0.0873646i	−0.481287	−	0.876563i	$-0.659831\pi$
$61$	−5.83779	+	0.682339i	−0.747452	+	0.0873646i	−0.266165	+	0.963928i	$0.585757\pi$
$62$	−3.18811	−	5.53626i	−0.404890	−	0.703105i
$63$	5.25607	+	13.1688i	0.662202	+	1.65911i
$64$	−6.16274	+	5.10104i	−0.770342	+	0.637630i
$65$	−2.74624	+	11.5873i	−0.340629	+	1.43723i
$66$	0.121285	+	8.52485i	0.0149292	+	1.04934i
$67$	−4.36661	−	6.63910i	−0.533466	−	0.811096i	0.463726	−	0.885978i	$-0.346512\pi$
$67$	−4.36661	−	6.63910i	−0.533466	−	0.811096i	−0.997192	+	0.0748828i	$0.976142\pi$
$68$	0.575197	−	4.82742i	0.0697529	−	0.585410i
$69$	−1.93700	+	0.0297259i	−0.233188	+	0.00357858i
$70$	−8.77737	+	13.3129i	−1.04910	+	1.59119i
$71$	−0.225531	−	1.27905i	−0.0267656	−	0.151795i	0.968496	−	0.249029i	$-0.0801116\pi$
$71$	−0.225531	−	1.27905i	−0.0267656	−	0.151795i	−0.995262	+	0.0972340i	$0.969000\pi$
$72$	8.45428	−	0.724703i	0.996346	−	0.0854071i
$73$	0.400223	−	2.26978i	0.0468426	−	0.265657i	−0.952388	−	0.304890i	$-0.901380\pi$
$73$	0.400223	−	2.26978i	0.0468426	−	0.265657i	0.999230	+	0.0392328i	$0.0124914\pi$
$74$	8.65973	+	8.18837i	1.00667	+	0.951878i
$75$	1.07841	+	0.521030i	0.124524	+	0.0601634i
$76$	−6.70135	−	10.2387i	−0.768697	−	1.17446i
$77$	−1.90979	+	16.3393i	−0.217640	+	1.86203i
$78$	11.6621	−	3.67296i	1.32047	−	0.415881i
$79$	−1.86572	−	0.108666i	−0.209910	−	0.0122259i	−0.0471325	−	0.998889i	$-0.515008\pi$
$79$	−1.86572	−	0.108666i	−0.209910	−	0.0122259i	−0.162778	+	0.986663i	$0.552045\pi$
$80$	6.10117	+	7.33753i	0.682131	+	0.820361i
$81$	−7.80860	−	4.47501i	−0.867622	−	0.497224i
$82$	−0.618466	−	3.53059i	−0.0682981	−	0.389888i
$83$	0.794679	−	13.6441i	0.0872274	−	1.49764i	−0.616606	−	0.787272i	$-0.711493\pi$
$83$	0.794679	−	13.6441i	0.0872274	−	1.49764i	0.703834	−	0.710365i	$-0.251470\pi$
$84$	16.3559	+	0.737663i	1.78457	+	0.0804856i
$85$	−5.75986	−	0.673231i	−0.624745	−	0.0730222i
$86$	−3.92102	−	9.11797i	−0.422814	−	0.983217i
$87$	3.85801	−	0.284164i	0.413622	−	0.0304655i
$88$	9.02638	+	3.92959i	0.962215	+	0.418895i
$89$	−2.15064	−	0.379215i	−0.227967	−	0.0401967i	0.0584976	−	0.998288i	$-0.481369\pi$
$89$	−2.15064	−	0.379215i	−0.227967	−	0.0401967i	−0.286465	+	0.958091i	$0.592480\pi$
$90$	−0.887021	−	10.0826i	−0.0935002	−	1.06280i
$91$	23.2334	−	4.09667i	2.43552	−	0.429448i
$92$	−0.890593	+	2.05199i	−0.0928507	+	0.213935i
$93$	6.83536	+	3.80776i	0.708794	+	0.394847i
$94$	12.9618	+	3.89631i	1.33690	+	0.401873i
$95$	−12.1953	+	8.02095i	−1.25121	+	0.822932i
$96$	3.26117	−	9.23931i	0.332841	−	0.942983i
$97$	−7.20752	−	1.70821i	−0.731813	−	0.173443i	−0.152217	−	0.988347i	$-0.548641\pi$
$97$	−7.20752	−	1.70821i	−0.731813	−	0.173443i	−0.579596	+	0.814904i	$0.696790\pi$
$98$	21.3577	+	3.79058i	2.15745	+	0.382907i
$99$	−5.49594	−	8.87842i	−0.552363	−	0.892315i
$100$	1.06139	−	0.886576i	0.106139	−	0.0886576i
$101$	−0.965798	−	8.26293i	−0.0961005	−	0.822192i	−0.952220	−	0.305414i	$-0.901205\pi$
$101$	−0.965798	−	8.26293i	−0.0961005	−	0.822192i	0.856119	−	0.516778i	$-0.172869\pi$
$102$	2.43587	+	5.43312i	0.241187	+	0.537959i
$103$	−6.12640	+	5.77996i	−0.603652	+	0.569517i	−0.926198	−	0.377037i	$-0.876943\pi$
$103$	−6.12640	+	5.77996i	−0.603652	+	0.569517i	0.322546	+	0.946554i	$0.395461\pi$
$104$	1.68609	−	14.0172i	0.165335	−	1.37450i
$105$	0.836253	−	19.5119i	0.0816099	−	1.90416i
$106$	6.25074	+	8.41585i	0.607126	+	0.817420i
$107$	−6.97597	+	12.0827i	−0.674393	+	1.16808i	0.302254	+	0.953228i	$0.402261\pi$
$107$	−6.97597	+	12.0827i	−0.674393	+	1.16808i	−0.976646	+	0.214855i	$0.931072\pi$
$108$	−8.42428	+	6.08535i	−0.810627	+	0.585563i
$109$	5.17765	+	8.96794i	0.495928	+	0.858973i	0.999989	−	0.00469502i	$-0.00149448\pi$
$109$	5.17765	+	8.96794i	0.495928	+	0.858973i	−0.504060	+	0.863668i	$0.668161\pi$
$110$	4.66327	−	10.7775i	0.444625	−	1.02759i
$111$	−14.2531	−	3.14787i	−1.35285	−	0.298782i
$112$	8.56022	−	16.8563i	0.808865	−	1.59277i
$113$	1.03666	+	0.310356i	0.0975208	+	0.0291958i	0.335192	−	0.942150i	$-0.391199\pi$
$113$	1.03666	+	0.310356i	0.0975208	+	0.0291958i	−0.237671	+	0.971346i	$0.576384\pi$
$114$	13.4872	+	6.53494i	1.26319	+	0.612053i
$115$	2.45007	+	1.05686i	0.228470	+	0.0985523i
$116$	1.53716	−	4.19409i	0.142722	−	0.389412i
$117$	−9.93719	+	11.2024i	−0.918694	+	1.03566i
$118$	−4.37362	+	5.20044i	−0.402624	+	0.478740i
$119$	3.29499	+	11.0060i	0.302051	+	1.00892i
$120$	−11.0297	−	3.86538i	−1.00687	−	0.352859i
$121$	−0.0648107	−	1.11276i	−0.00589188	−	0.101160i
$122$	−1.90785	−	8.09017i	−0.172728	−	0.732449i
$123$	2.87305	+	3.31917i	0.259054	+	0.299280i
$124$	7.25911	−	5.37900i	0.651887	−	0.483049i
$125$	6.60706	+	7.87399i	0.590953	+	0.704271i
$126$	−17.6453	+	9.52526i	−1.57197	+	0.848578i
$127$	−4.56776	+	5.44364i	−0.405323	+	0.483045i	−0.929635	−	0.368481i	$-0.879878\pi$
$127$	−4.56776	+	5.44364i	−0.405323	+	0.483045i	0.524312	+	0.851526i	$0.324322\pi$
$128$	−8.16823	−	7.82815i	−0.721977	−	0.691918i
$129$	9.86083	+	7.10857i	0.868198	+	0.625875i
$130$	−16.7248	−	1.97382i	−1.46686	−	0.173116i
$131$	−2.52252	−	5.84787i	−0.220394	−	0.510931i	0.771766	−	0.635907i	$-0.219374\pi$
$131$	−2.52252	−	5.84787i	−0.220394	−	0.510931i	−0.992160	+	0.124976i	$0.960115\pi$
$132$	−11.9563	+	1.55660i	−1.04066	+	0.135484i
$133$	24.1603	+	15.8905i	2.09497	+	1.37788i
$134$	8.61679	−	7.21393i	0.744377	−	0.623189i
$135$	7.28132	+	10.0326i	0.626676	+	0.863466i
$136$	6.87525	+	0.0230782i	0.589548	+	0.00197894i
$137$	−3.01669	−	6.00673i	−0.257733	−	0.513189i	0.727135	−	0.686495i	$-0.240852\pi$
$137$	−3.01669	−	6.00673i	−0.257733	−	0.513189i	−0.984868	+	0.173305i	$0.944555\pi$
$138$	−0.356733	−	2.71633i	−0.0303671	−	0.231230i
$139$	9.62564	+	7.16602i	0.816436	+	0.607814i	0.922260	−	0.386571i	$-0.126341\pi$
$139$	9.62564	+	7.16602i	0.816436	+	0.607814i	−0.105824	+	0.994385i	$0.533748\pi$
$140$	−20.1296	−	10.1660i	−1.70127	−	0.859180i
$141$	−16.0692	+	4.06988i	−1.35327	+	0.342745i
$142$	1.76018	−	0.524818i	0.147711	−	0.0440418i
$143$	−16.3259	+	5.94216i	−1.36524	+	0.496908i
$144$	2.39282	+	11.7590i	0.199402	+	0.979918i
$145$	−5.00698	−	1.82239i	−0.415807	−	0.151341i
$146$	3.25374	+	0.193162i	0.269281	+	0.0159862i
$147$	−24.8220	+	9.46828i	−2.04728	+	0.780931i
$148$	−10.0951	+	13.4970i	−0.829816	+	1.10944i
$149$	4.48791	−	8.93616i	0.367664	−	0.732079i	−0.631395	−	0.775462i	$-0.717517\pi$
$149$	4.48791	−	8.93616i	0.367664	−	0.732079i	0.999059	+	0.0433827i	$0.0138135\pi$
$150$	−0.556603	+	1.59970i	−0.0454465	+	0.130615i
$151$	−8.81281	−	8.31446i	−0.717176	−	0.676621i	0.238466	−	0.971151i	$-0.423355\pi$
$151$	−8.81281	−	8.31446i	−0.717176	−	0.676621i	−0.955642	+	0.294530i	$0.904837\pi$
$152$	13.2940	−	11.0792i	1.07829	−	0.898640i
$153$	−5.98023	−	4.17315i	−0.483473	−	0.337379i
$154$	−23.2645	−	0.0260306i	−1.87471	−	0.00209761i
$155$	−6.43565	−	8.64458i	−0.516924	−	0.694350i
$156$	7.05625	+	15.7860i	0.564952	+	1.26389i
$157$	−8.69018	+	2.05961i	−0.693552	+	0.164375i	−0.562250	−	0.826968i	$-0.690064\pi$
$157$	−8.69018	+	2.05961i	−0.693552	+	0.164375i	−0.131302	+	0.991342i	$0.541916\pi$
$158$	−0.150725	−	2.63870i	−0.0119910	−	0.209924i
$159$	−11.8659	−	4.90389i	−0.941027	−	0.388903i
$160$	−9.31592	+	9.76427i	−0.736488	+	0.771934i
$161$		−	5.28621i		−	0.416612i
$162$	5.01690	−	11.6975i	0.394165	−	0.919040i
$163$			11.4878i			0.899793i	0.893081	+	0.449896i	$0.148539\pi$
$163$			11.4878i			0.899793i	−0.893081	+	0.449896i	$0.851461\pi$
$164$	4.85932	−	1.44295i	0.379449	−	0.112675i
$165$	1.88869	+	14.2578i	0.147034	+	1.10996i
$166$	19.2969	−	1.10226i	1.49773	−	0.0855516i
$167$	20.7352	−	4.91433i	1.60454	−	0.380283i	0.671770	−	0.740760i	$-0.265534\pi$
$167$	20.7352	−	4.91433i	1.60454	−	0.380283i	0.932768	+	0.360477i	$0.117386\pi$
$168$	1.62331	+	23.0972i	0.125241	+	1.78199i
$169$	7.11560	+	9.55791i	0.547354	+	0.735223i
$170$	0.00917622	−	8.20112i	0.000703784	−	0.628997i
$171$	−18.2828	+	1.62905i	−1.39812	+	0.124576i
$172$	12.1717	−	6.99104i	0.928080	−	0.533061i
$173$	−7.21616	−	6.80810i	−0.548635	−	0.517610i	0.361251	−	0.932468i	$-0.382350\pi$
$173$	−7.21616	−	6.80810i	−0.548635	−	0.517610i	−0.909886	+	0.414858i	$0.863831\pi$
$174$	1.02655	+	5.37365i	0.0778223	+	0.407375i
$175$	−1.46675	+	2.92053i	−0.110876	+	0.220772i
$176$	−4.05265	+	13.3195i	−0.305480	+	1.00400i
$177$	1.31921	−	8.21702i	0.0991580	−	0.617629i
$178$	0.183023	−	3.08295i	0.0137181	−	0.231077i
$179$	−13.7475	−	5.00367i	−1.02754	−	0.373992i	−0.227393	−	0.973803i	$-0.573020\pi$
$179$	−13.7475	−	5.00367i	−1.02754	−	0.373992i	−0.800142	+	0.599811i	$0.795243\pi$
$180$	14.0202	−	2.88564i	1.04500	−	0.215083i
$181$	18.6287	−	6.78028i	1.38466	−	0.503975i	0.461071	−	0.887363i	$-0.347465\pi$
$181$	18.6287	−	6.78028i	1.38466	−	0.503975i	0.923587	+	0.383388i	$0.125243\pi$
$182$	9.53309	+	31.9729i	0.706640	+	2.36999i
$183$	7.09886	+	7.29672i	0.524763	+	0.539389i
$184$	−3.02752	−	0.917465i	−0.223192	−	0.0676364i
$185$	16.1267	+	12.0059i	1.18566	+	0.882688i
$186$	−4.23779	+	10.2217i	−0.310730	+	0.749493i
$187$	−3.79711	−	7.56067i	−0.277672	−	0.552891i
$188$	−3.36597	+	18.8427i	−0.245489	+	1.37425i
$189$	12.5367	−	21.1178i	0.911911	−	1.53610i
$190$	−13.2512	−	15.8280i	−0.961340	−	1.14829i
$191$	−6.40917	−	4.21538i	−0.463751	−	0.305014i	0.296047	−	0.955173i	$-0.404332\pi$
$191$	−6.40917	−	4.21538i	−0.463751	−	0.305014i	−0.759798	+	0.650160i	$0.774702\pi$
$192$	13.5100	+	3.07901i	0.974999	+	0.222208i
$193$	−9.22714	−	21.3909i	−0.664184	−	1.53975i	−0.832504	−	0.554019i	$-0.813093\pi$
$193$	−9.22714	−	21.3909i	−0.664184	−	1.53975i	0.168320	−	0.985732i	$-0.446166\pi$
$194$	1.22775	−	10.4031i	0.0881476	−	0.746902i
$195$	18.8113	−	8.45910i	1.34711	−	0.605769i
$196$	−1.85220	+	30.6204i	−0.132300	+	2.18717i
$197$	−7.33921	+	8.74653i	−0.522897	+	0.623164i	−0.961263	−	0.275632i	$-0.911113\pi$
$197$	−7.33921	+	8.74653i	−0.522897	+	0.623164i	0.438366	+	0.898796i	$0.355557\pi$
$198$	11.5790	−	9.16459i	0.822885	−	0.651299i
$199$	−2.05152	−	2.44491i	−0.145429	−	0.173315i	0.688413	−	0.725319i	$-0.258308\pi$
$199$	−2.05152	−	2.44491i	−0.145429	−	0.173315i	−0.833841	+	0.552004i	$0.813863\pi$
$200$	1.41808	+	1.34692i	0.100274	+	0.0952415i
$201$	−4.50839	+	13.0042i	−0.317998	+	0.917246i
$202$	11.4510	−	2.70041i	0.805689	−	0.190000i
$203$	0.613779	+	10.5382i	0.0430789	+	0.739635i
$204$	−7.23654	+	4.30546i	−0.506659	+	0.301442i
$205$	−1.73417	−	5.79253i	−0.121120	−	0.404568i
$206$	−9.11609	−	7.66671i	−0.635148	−	0.534165i
$207$	2.08534	+	2.62868i	0.144941	+	0.182706i
$208$	19.9661	+	0.0893606i	1.38440	+	0.00619604i
$209$	−19.5541	−	8.43483i	−1.35259	−	0.583450i
$210$	27.5469	−	1.99800i	1.90092	−	0.137875i
$211$	1.62564	+	0.486686i	0.111914	+	0.0335048i	0.342271	−	0.939601i	$-0.388804\pi$
$211$	1.62564	+	0.486686i	0.111914	+	0.0335048i	−0.230357	+	0.973106i	$0.573989\pi$
$212$	−10.8064	+	10.1497i	−0.742190	+	0.697087i
$213$	−1.51845	+	1.65976i	−0.104042	+	0.113725i
$214$	−18.1086	−	7.83533i	−1.23788	−	0.535612i
$215$	−8.37166	−	14.5001i	−0.570943	−	0.988902i
$216$	−9.91876	−	10.8452i	−0.674886	−	0.737922i
$217$	−10.6754	+	18.4903i	−0.724694	+	1.25521i
$218$	−11.7565	+	8.73200i	−0.796254	+	0.591405i
$219$	−3.53949	+	1.84614i	−0.239176	+	0.124751i
$220$	15.8989	+	4.79860i	1.07190	+	0.323522i
$221$	−8.82553	+	8.32645i	−0.593669	+	0.560098i
$222$	2.10455	−	20.5351i	0.141248	−	1.37823i
$223$	−0.524712	−	4.48920i	−0.0351373	−	0.300619i	−0.999368	−	0.0355537i	$-0.988681\pi$
$223$	−0.524712	−	4.48920i	−0.0351373	−	0.300619i	0.964230	−	0.265065i	$-0.0853936\pi$
$224$	25.0722	+	9.28471i	1.67521	+	0.620361i
$225$	−0.422741	−	2.03091i	−0.0281827	−	0.135394i
$226$	−0.267429	+	1.50680i	−0.0177891	+	0.100231i
$227$	−6.86500	−	1.62703i	−0.455646	−	0.107990i	−0.00361715	−	0.999993i	$-0.501151\pi$
$227$	−6.86500	−	1.62703i	−0.455646	−	0.107990i	−0.452029	+	0.892003i	$0.649300\pi$
$228$	−6.98738	+	20.0099i	−0.462750	+	1.32519i
$229$	7.13822	−	4.69488i	0.471707	−	0.310247i	−0.291306	−	0.956630i	$-0.594090\pi$
$229$	7.13822	−	4.69488i	0.471707	−	0.310247i	0.763013	+	0.646383i	$0.223719\pi$
$230$	−1.08631	+	3.61379i	−0.0716289	+	0.238286i
$231$	24.4542	−	14.6235i	1.60897	−	0.962157i
$232$	6.14196	+	1.47746i	0.403239	+	0.0970002i
$233$	18.1339	−	3.19749i	1.18799	−	0.209475i	0.455490	−	0.890241i	$-0.349464\pi$
$233$	18.1339	−	3.19749i	1.18799	−	0.209475i	0.732501	+	0.680766i	$0.238353\pi$
$234$	−17.3534	−	12.1385i	−1.13443	−	0.793519i
$235$	22.4853	+	3.96476i	1.46678	+	0.258633i
$236$	−8.01695	−	5.29857i	−0.521859	−	0.344907i
$237$	1.82005	+	2.67686i	0.118225	+	0.173881i
$238$	−14.9259	+	6.41859i	−0.967499	+	0.416055i
$239$	16.0933	+	1.88104i	1.04099	+	0.121674i	0.619371	−	0.785099i	$-0.287388\pi$
$239$	16.0933	+	1.88104i	1.04099	+	0.121674i	0.421619	+	0.906773i	$0.361462\pi$
$240$	3.63670	−	16.1234i	0.234748	−	1.04076i
$241$	1.67934	−	28.8332i	0.108176	−	1.85731i	−0.312271	−	0.949993i	$-0.601090\pi$
$241$	1.67934	−	28.8332i	0.108176	−	1.85731i	0.420447	−	0.907317i	$-0.361873\pi$
$242$	1.55270	−	0.271992i	0.0998113	−	0.0174843i
$243$	2.09656	+	15.4468i	0.134495	+	0.990914i
$244$	11.0551	−	3.99574i	0.707731	−	0.255801i
$245$	36.5301	+	2.12764i	2.33382	+	0.135930i
$246$	−4.19571	+	4.57589i	−0.267508	+	0.291748i
$247$	−3.54553	+	30.3340i	−0.225597	+	1.93010i
$248$	8.73700	+	9.32317i	0.554800	+	0.592022i
$249$	−19.5760	+	13.3101i	−1.24058	+	0.843495i
$250$	−9.98728	+	10.5622i	−0.631651	+	0.668012i
$251$	3.76093	−	21.3293i	0.237388	−	1.34629i	−0.600139	−	0.799896i	$-0.704888\pi$
$251$	3.76093	−	21.3293i	0.237388	−	1.34629i	0.837526	−	0.546397i	$-0.184001\pi$
$252$	−16.2507	−	23.2398i	−1.02370	−	1.46397i
$253$	0.675999	+	3.83378i	0.0424997	+	0.241028i
$254$	−8.39017	−	5.53176i	−0.526446	−	0.347094i
$255$	5.15503	+	8.62052i	0.322820	+	0.539838i
$256$	9.66903	−	12.7479i	0.604315	−	0.796746i
$257$	6.07330	+	9.23400i	0.378842	+	0.576001i	0.973701	−	0.227829i	$-0.0731626\pi$
$257$	6.07330	+	9.23400i	0.378842	+	0.576001i	−0.594859	+	0.803830i	$0.702792\pi$
$258$	−8.38291	+	15.0087i	−0.521897	+	0.934403i
$259$	9.18552	−	38.7568i	0.570761	−	2.40823i
$260$	0.0532966	−	23.8165i	0.00330531	−	1.47704i
$261$	−4.46238	−	4.99820i	−0.276215	−	0.309381i
$262$	7.80510	−	4.49464i	0.482201	−	0.277680i
$263$	16.8176	−	1.96569i	1.03701	−	0.121210i	0.419489	−	0.907760i	$-0.362209\pi$
$263$	16.8176	−	1.96569i	1.03701	−	0.121210i	0.617526	+	0.786551i	$0.288135\pi$
$264$	−4.13095	−	16.5435i	−0.254243	−	1.01818i
$265$	12.1359	+	12.8632i	0.745499	+	0.790183i
$266$	−18.3948	+	36.5252i	−1.12786	+	2.23950i
$267$	1.74924	+	3.35370i	0.107052	+	0.205243i
$268$	11.5355	+	10.9321i	0.704645	+	0.667785i
$269$	−15.2690	−	8.81556i	−0.930967	−	0.537494i	−0.0438499	−	0.999038i	$-0.513962\pi$
$269$	−15.2690	−	8.81556i	−0.930967	−	0.537494i	−0.887117	+	0.461544i	$0.847296\pi$
$270$	−12.9101	+	11.8604i	−0.785682	+	0.721803i
$271$	0.531831	−	0.307052i	0.0323064	−	0.0186521i	−0.483760	−	0.875201i	$-0.660729\pi$
$271$	0.531831	−	0.307052i	0.0323064	−	0.0186521i	0.516066	+	0.856549i	$0.327396\pi$
$272$	1.08555	+	9.66234i	0.0658213	+	0.585865i
$273$	−30.1489	−	27.5820i	−1.82469	−	1.66934i
$274$	7.94791	−	5.21469i	0.480151	−	0.315031i
$275$	0.690269	−	2.30566i	0.0416248	−	0.139037i
$276$	3.75799	−	0.942849i	0.226204	−	0.0567528i
$277$	−0.571616	+	1.32515i	−0.0343451	+	0.0796208i	−0.934525	−	0.355897i	$-0.884175\pi$
$277$	−0.571616	+	1.32515i	−0.0343451	+	0.0796208i	0.900180	+	0.435518i	$0.143435\pi$
$278$	−8.50186	+	14.6877i	−0.509908	+	0.880908i
$279$	−1.98563	−	13.4060i	−0.118876	−	0.802597i
$280$	11.0082	−	29.9319i	0.657868	−	1.78877i
$281$	−1.03088	+	0.308625i	−0.0614970	+	0.0184110i	−0.317404	−	0.948290i	$-0.602811\pi$
$281$	−1.03088	+	0.308625i	−0.0614970	+	0.0184110i	0.255907	+	0.966701i	$0.417626\pi$
$282$	−8.33049	−	21.9128i	−0.496073	−	1.30489i
$283$	21.8439	−	1.27226i	1.29848	−	0.0756280i	0.605072	−	0.796171i	$-0.293144\pi$
$283$	21.8439	−	1.27226i	1.29848	−	0.0756280i	0.693410	+	0.720543i	$0.256107\pi$
$284$	1.02350	+	2.38742i	0.0607337	+	0.141667i
$285$	23.8872	+	8.28140i	1.41496	+	0.490548i
$286$	−11.0025	−	21.9690i	−0.650590	−	1.29905i
$287$	−9.17642	+	7.69993i	−0.541667	+	0.454512i
$288$	−16.1304	+	5.27364i	−0.950491	+	0.310752i
$289$	8.49643	+	7.12935i	0.499790	+	0.419374i
$290$	1.74598	−	7.33031i	0.102527	−	0.430450i
$291$	5.26172	+	11.7010i	0.308447	+	0.685925i
$292$	0.257725	+	4.60237i	0.0150822	+	0.269334i
$293$	−24.3754	+	10.5145i	−1.42402	+	0.614264i	−0.962110	−	0.272660i	$-0.912097\pi$
$293$	−24.3754	+	10.5145i	−1.42402	+	0.614264i	−0.461914	+	0.886925i	$0.652837\pi$
$294$	−17.3376	−	33.3312i	−1.01115	−	1.94391i
$295$	−6.29893	+	9.57706i	−0.366738	+	0.557598i
$296$	−20.6026	−	11.9873i	−1.19750	−	0.696747i
$297$	−6.39160	+	16.9187i	−0.370878	+	0.981723i
$298$	13.2836	+	4.85167i	0.769498	+	0.281050i
$299$	4.98903	−	2.50559i	0.288523	−	0.144902i
$300$	−2.33783	−	0.521810i	−0.134975	−	0.0301267i
$301$	−19.8081	+	26.6069i	−1.14172	+	1.53360i
$302$	10.2474	−	13.7325i	0.589671	−	0.790219i
$303$	−10.3279	+	10.0479i	−0.593325	+	0.577236i
$304$	17.7261	+	16.8743i	1.01666	+	0.967809i
$305$	−4.79578	−	13.1763i	−0.274605	−	0.754472i
$306$	4.89014	−	9.07982i	0.279551	−	0.519059i
$307$	−2.09272	+	5.74969i	−0.119438	+	0.328152i	−0.984976	−	0.172690i	$-0.944754\pi$
$307$	−2.09272	+	5.74969i	−0.119438	+	0.328152i	0.865539	+	0.500842i	$0.166976\pi$
$308$	−3.74644	−	32.6870i	−0.213473	−	1.86252i
$309$	14.4040	+	2.31250i	0.819414	+	0.131554i
$310$	11.0977	−	10.4467i	0.630308	−	0.593333i
$311$	14.1041	+	7.08336i	0.799772	+	0.401661i	0.801244	−	0.598338i	$-0.204172\pi$
$311$	14.1041	+	7.08336i	0.799772	+	0.401661i	−0.00147134	+	0.999999i	$0.500468\pi$
$312$	−21.0293	+	12.4798i	−1.19055	+	0.706529i
$313$	10.9485	−	11.6047i	0.618845	−	0.655937i	−0.339815	−	0.940492i	$-0.610364\pi$
$313$	10.9485	−	11.6047i	0.618845	−	0.655937i	0.958660	+	0.284555i	$0.0918459\pi$
$314$	−4.30651	−	11.8733i	−0.243030	−	0.670052i
$315$	−27.6780	+	19.4465i	−1.55948	+	1.09568i
$316$	3.68243	−	0.640818i	0.207153	−	0.0360488i
$317$	12.4938	−	9.30126i	0.701719	−	0.522411i	−0.186141	−	0.982523i	$-0.559598\pi$
$317$	12.4938	−	9.30126i	0.701719	−	0.522411i	0.887861	+	0.460112i	$0.152191\pi$
$318$	4.95965	−	17.4670i	0.278123	−	0.979502i
$319$	−1.79276	−	7.56424i	−0.100375	−	0.423516i
$320$	−15.2320	−	11.4996i	−0.851496	−	0.642845i
$321$	23.9562	−	3.17341i	1.33710	−	0.177123i
$322$	7.42625	−	0.859582i	0.413849	−	0.0479026i
$323$	−14.8725			−0.827529
$324$	17.2488	+	5.14581i	0.958266	+	0.285878i
$325$	−3.45157			−0.191458
$326$	−16.1384	+	1.86801i	−0.893825	+	0.103460i
$327$	6.85050	−	16.5761i	0.378833	−	0.916660i
$328$	2.81727	+	6.59191i	0.155557	+	0.363977i
$329$	−10.4315	−	44.0140i	−0.575108	−	2.42657i
$330$	−19.7227	+	4.97172i	−1.08570	+	0.273684i
$331$	−8.19473	+	6.10075i	−0.450423	+	0.335327i	−0.798350	−	0.602194i	$-0.794293\pi$
$331$	−8.19473	+	6.10075i	−0.450423	+	0.335327i	0.347927	+	0.937522i	$0.386886\pi$
$332$	4.68633	+	26.9298i	0.257196	+	1.47796i
$333$	10.7213	+	22.8962i	0.587525	+	1.25470i
$334$	10.2755	+	28.3304i	0.562253	+	1.55017i
$335$	13.0095	−	13.7892i	0.710782	−	0.753385i
$336$	−32.1838	+	6.03628i	−1.75577	+	0.329306i
$337$	−14.4015	−	7.23269i	−0.784498	−	0.393989i	0.0110052	−	0.999939i	$-0.496497\pi$
$337$	−14.4015	−	7.23269i	−0.784498	−	0.393989i	−0.795503	+	0.605950i	$0.792793\pi$
$338$	−12.2702	+	11.5504i	−0.667412	+	0.628260i
$339$	−0.667995	−	1.75121i	−0.0362805	−	0.0951127i
$340$	11.5227	−	1.32068i	0.624907	−	0.0716240i
$341$	5.37771	−	14.7751i	0.291219	−	0.800119i
$342$	−5.26148	−	25.4194i	−0.284508	−	1.37452i
$343$	−13.4787	−	37.0324i	−0.727780	−	1.99956i
$344$	11.8005	+	15.9623i	0.636238	+	0.860632i
$345$	−1.13470	−	4.48015i	−0.0610900	−	0.241203i
$346$	8.39084	−	11.2446i	0.451094	−	0.604511i
$347$	−16.5642	+	22.2496i	−0.889212	+	1.19442i	0.0908774	+	0.995862i	$0.471033\pi$
$347$	−16.5642	+	22.2496i	−0.889212	+	1.19442i	−0.980089	+	0.198557i	$0.936375\pi$
$348$	−7.38216	+	2.31593i	−0.395725	+	0.124147i
$349$	−30.2948	+	15.2146i	−1.62164	+	0.814419i	−0.622138	+	0.782908i	$0.713736\pi$
$349$	−30.2948	+	15.2146i	−1.62164	+	0.814419i	−0.999503	+	0.0315107i	$0.989968\pi$
$350$	−4.34137	−	1.58563i	−0.232056	−	0.0847556i
$351$	25.8729	+	1.82238i	1.38099	+	0.0972714i
$352$	−19.3707	−	3.52744i	−1.03246	−	0.188013i
$353$	−4.29186	+	6.52545i	−0.228433	+	0.347315i	−0.931457	−	0.363850i	$-0.881462\pi$
$353$	−4.29186	+	6.52545i	−0.228433	+	0.347315i	0.703025	+	0.711165i	$0.251832\pi$
$354$	11.7581	+	0.517116i	0.624934	+	0.0274844i
$355$	2.84508	−	1.22725i	0.151001	−	0.0651355i
$356$	4.36080	−	0.244197i	0.231122	−	0.0129424i
$357$	11.6365	−	16.1419i	0.615870	−	0.854319i
$358$	4.79388	−	20.1266i	0.253364	−	1.06372i
$359$	16.7248	+	14.0338i	0.882703	+	0.740676i	0.966733	−	0.255787i	$-0.0823347\pi$
$359$	16.7248	+	14.0338i	0.882703	+	0.740676i	−0.0840300	+	0.996463i	$0.526779\pi$
$360$	6.33365	+	19.2268i	0.333813	+	1.01334i
$361$	−14.1220	+	11.8497i	−0.743262	+	0.623671i
$362$	12.5544	+	25.0677i	0.659842	+	1.31753i
$363$	−1.45972	+	1.26352i	−0.0766155	+	0.0663178i
$364$	−43.3664	+	18.5915i	−2.27302	+	0.974458i
$365$	5.48920	−	0.319709i	0.287318	−	0.0167344i
$366$	−9.09635	+	11.1592i	−0.475474	+	0.583302i
$367$	10.6665	−	3.19334i	0.556787	−	0.166691i	0.00396728	−	0.999992i	$-0.498737\pi$
$367$	10.6665	−	3.19334i	0.556787	−	0.166691i	0.552819	+	0.833301i	$0.313552\pi$
$368$	0.796585	−	4.40235i	0.0415249	−	0.229488i
$369$	1.52564	−	7.44892i	0.0794219	−	0.387775i
$370$	−14.2439	+	24.6075i	−0.740505	+	1.27928i
$371$	13.8767	−	32.1699i	0.720444	−	1.67018i
$372$	−15.0489	−	4.29125i	−0.780250	−	0.222491i
$373$	−5.44946	+	18.2025i	−0.282162	+	0.942488i	0.692989	+	0.720948i	$0.256293\pi$
$373$	−5.44946	+	18.2025i	−0.282162	+	0.942488i	−0.975151	+	0.221540i	$0.928892\pi$
$374$	10.0040	−	6.56374i	0.517297	−	0.339403i
$375$	3.83943	−	17.3844i	0.198267	−	0.897727i
$376$	−27.0182	−	1.66465i	−1.39336	−	0.0858477i
$377$	−9.65483	+	5.57422i	−0.497249	+	0.287087i
$378$	31.7056	+	14.1780i	1.63076	+	0.729240i
$379$	19.2080	+	11.0897i	0.986649	+	0.569642i	0.904271	−	0.426959i	$-0.140415\pi$
$379$	19.2080	+	11.0897i	0.986649	+	0.569642i	0.0823778	+	0.996601i	$0.473749\pi$
$380$	20.0810	−	21.1895i	1.03014	−	1.08700i
$381$	12.2970	+	0.527032i	0.629993	+	0.0270007i
$382$	4.87972	−	9.68927i	0.249668	−	0.495746i
$383$	−9.31787	−	9.87636i	−0.476121	−	0.504659i	0.444144	−	0.895956i	$-0.353508\pi$
$383$	−9.31787	−	9.87636i	−0.476121	−	0.504659i	−0.920264	+	0.391297i	$0.872027\pi$
$384$	−2.12866	+	19.4800i	−0.108628	+	0.994083i
$385$	−38.9803	+	4.55615i	−1.98662	+	0.232203i
$386$	28.5503	−	16.4409i	1.45317	−	0.836822i
$387$	−0.646076	−	21.0449i	−0.0328419	−	1.06977i
$388$	14.8143	+	0.0331515i	0.752084	+	0.00168301i
$389$	−6.40459	+	27.0231i	−0.324725	+	1.37012i	0.528655	+	0.848837i	$0.322696\pi$
$389$	−6.40459	+	27.0231i	−0.324725	+	1.37012i	−0.853381	+	0.521288i	$0.825452\pi$
$390$	14.9425	+	25.0513i	0.756643	+	1.26852i
$391$	1.49397	+	2.27147i	0.0755532	+	0.114873i
$392$	−43.3178	+	2.37710i	−2.18788	+	0.120062i
$393$	−5.36824	+	9.63660i	−0.270792	+	0.486102i
$394$	−13.4808	−	8.88811i	−0.679155	−	0.447776i
$395$	−0.774221	−	4.39083i	−0.0389553	−	0.220927i
$396$	14.7576	+	14.7764i	0.741596	+	0.742540i
$397$	4.29344	−	24.3493i	0.215482	−	1.22206i	−0.664587	−	0.747211i	$-0.731392\pi$
$397$	4.29344	−	24.3493i	0.215482	−	1.22206i	0.880069	−	0.474847i	$-0.157496\pi$
$398$	3.10110	−	3.27961i	0.155444	−	0.164392i
$399$	−3.67920	−	49.9515i	−0.184191	−	2.50070i
$400$	−1.66160	+	2.21119i	−0.0830802	+	0.110560i
$401$	0.640726	−	5.48176i	0.0319963	−	0.273746i	−0.967764	−	0.251858i	$-0.918958\pi$
$401$	0.640726	−	5.48176i	0.0319963	−	0.273746i	0.999760	−	0.0218878i	$-0.00696764\pi$
$402$	−19.0018	−	4.21895i	−0.947726	−	0.210422i
$403$	−22.5109	−	1.31111i	−1.12135	−	0.0653110i
$404$	5.65565	+	15.6476i	0.281379	+	0.778499i
$405$	6.09208	−	20.5887i	0.302718	−	1.02306i
$406$	−14.7046	+	2.57586i	−0.729777	+	0.127838i
$407$	−1.70552	+	29.2827i	−0.0845395	+	1.45149i
$408$	−7.22517	−	9.46603i	−0.357699	−	0.468638i
$409$	−0.969022	−	0.113262i	−0.0479150	−	0.00560047i	0.0921016	−	0.995750i	$-0.470642\pi$
$409$	−0.969022	−	0.113262i	−0.0479150	−	0.00560047i	−0.140017	+	0.990149i	$0.544716\pi$
$410$	7.85556	−	3.37814i	0.387958	−	0.166834i
$411$	−5.06480	+	10.4829i	−0.249828	+	0.517084i
$412$	9.28810	−	14.0533i	0.457592	−	0.692355i
$413$	22.3643	+	3.94343i	1.10047	+	0.194043i
$414$	−3.35376	+	3.35700i	−0.164828	+	0.164987i
$415$	32.1103	−	5.66192i	1.57623	−	0.277933i
$416$	3.12111	+	28.0636i	0.153025	+	1.37593i
$417$	−0.318936	−	20.7825i	−0.0156184	−	1.01772i
$418$	8.66987	−	28.8419i	0.424057	−	1.41070i
$419$	10.8816	−	7.15696i	0.531602	−	0.349640i	−0.255158	−	0.966899i	$-0.582127\pi$
$419$	10.8816	−	7.15696i	0.531602	−	0.349640i	0.786760	+	0.617259i	$0.211757\pi$
$420$	7.28621	+	38.3739i	0.355531	+	1.87246i
$421$	−13.0404	−	3.09063i	−0.635551	−	0.150628i	−0.0998041	−	0.995007i	$-0.531822\pi$
$421$	−13.0404	−	3.09063i	−0.635551	−	0.150628i	−0.535747	+	0.844379i	$0.679970\pi$
$422$	−0.419370	+	2.36290i	−0.0204146	+	0.115024i
$423$	22.5502	+	17.7718i	1.09643	+	0.864094i
$424$	−16.0159	−	13.5308i	−0.777802	−	0.657115i
$425$	−0.195133	−	1.66947i	−0.00946534	−	0.0809812i
$426$	−2.57861	−	1.86328i	−0.124934	−	0.0902762i
$427$	−20.2058	+	19.0632i	−0.977828	+	0.922533i
$428$	8.06272	−	26.7137i	0.389726	−	1.29125i
$429$	25.3924	+	16.1482i	1.22596	+	0.779641i
$430$	19.0090	−	14.1186i	0.916695	−	0.680861i
$431$	−5.34845	+	9.26378i	−0.257626	+	0.446221i	−0.965605	−	0.260012i	$-0.916273\pi$
$431$	−5.34845	+	9.26378i	−0.257626	+	0.446221i	0.707980	+	0.706233i	$0.249607\pi$
$432$	13.6228	−	15.6977i	0.655428	−	0.755257i
$433$	1.86478	+	3.22989i	0.0896155	+	0.155219i	0.907349	−	0.420379i	$-0.138103\pi$
$433$	1.86478	+	3.22989i	0.0896155	+	0.155219i	−0.817733	+	0.575598i	$0.804770\pi$
$434$	−27.7118	−	11.9905i	−1.33021	−	0.575562i
$435$	2.78223	+	8.79954i	0.133398	+	0.421906i
$436$	−14.1787	−	15.0961i	−0.679037	−	0.722972i
$437$	6.55571	+	1.96265i	0.313602	+	0.0938863i
$438$	−3.16907	−	4.67219i	−0.151424	−	0.223246i
$439$	−11.5750	−	4.99297i	−0.552445	−	0.238301i	0.101511	−	0.994834i	$-0.467632\pi$
$439$	−11.5750	−	4.99297i	−0.552445	−	0.238301i	−0.653955	+	0.756533i	$0.726892\pi$
$440$	−4.15595	+	23.1156i	−0.198127	+	1.10199i
$441$	39.2024	+	24.0938i	1.86678	+	1.14732i
$442$	−13.1324	−	11.0444i	−0.624644	−	0.525331i
$443$	−8.33099	−	27.8274i	−0.395817	−	1.32212i	−0.891265	−	0.453484i	$-0.850181\pi$
$443$	−8.33099	−	27.8274i	−0.395817	−	1.32212i	0.495447	−	0.868638i	$-0.335004\pi$
$444$	29.1907	−	0.382635i	1.38533	−	0.0181590i
$445$	−0.302928	−	5.20107i	−0.0143602	−	0.246554i
$446$	6.22126	−	1.46712i	0.294585	−	0.0694699i
$447$	−17.0089	+	3.26900i	−0.804493	+	0.154618i
$448$	−8.96653	+	36.7321i	−0.423629	+	1.73543i
$449$	−6.61791	−	7.88692i	−0.312319	−	0.372207i	0.586935	−	0.809634i	$-0.300334\pi$
$449$	−6.61791	−	7.88692i	−0.312319	−	0.372207i	−0.899254	+	0.437427i	$0.855890\pi$
$450$	2.78435	−	0.924123i	0.131255	−	0.0435636i
$451$	5.67046	−	6.75779i	0.267011	−	0.318212i
$452$	−2.16029	−	0.130674i	−0.101612	−	0.00614639i
$453$	−2.11614	+	20.8784i	−0.0994247	+	0.980955i
$454$	1.16941	−	9.90875i	0.0548830	−	0.465041i
$455$	22.2924	+	51.6795i	1.04508	+	2.42277i
$456$	−29.2468	−	6.56233i	−1.36961	−	0.307309i
$457$	17.9791	+	11.8250i	0.841026	+	0.553151i	0.895345	−	0.445372i	$-0.146929\pi$
$457$	17.9791	+	11.8250i	0.841026	+	0.553151i	−0.0543198	+	0.998524i	$0.517299\pi$
$458$	7.75627	+	9.26459i	0.362427	+	0.432906i
$459$	0.581256	+	12.6173i	0.0271307	+	0.588927i
$460$	−5.25342	−	0.938446i	−0.244942	−	0.0437553i
$461$	8.44175	+	16.8089i	0.393172	+	0.782869i	0.999928	−	0.0120191i	$-0.00382589\pi$
$461$	8.44175	+	16.8089i	0.393172	+	0.782869i	−0.606756	+	0.794888i	$0.707530\pi$
$462$	24.5201	+	31.9762i	1.14078	+	1.48767i
$463$	−1.16510	−	0.867384i	−0.0541467	−	0.0403107i	0.569745	−	0.821822i	$-0.307042\pi$
$463$	−1.16510	−	0.867384i	−0.0541467	−	0.0403107i	−0.623892	+	0.781511i	$0.714449\pi$
$464$	−1.07686	+	8.86868i	−0.0499918	+	0.411718i
$465$	−5.07859	+	17.9624i	−0.235514	+	0.832986i
$466$	7.44067	+	24.9552i	0.344682	+	1.15603i
$467$	−2.49317	+	0.907439i	−0.115370	+	0.0419913i	−0.399060	−	0.916925i	$-0.630664\pi$
$467$	−2.49317	+	0.907439i	−0.115370	+	0.0419913i	0.283690	+	0.958916i	$0.408441\pi$
$468$	14.2308	−	26.3525i	0.657818	−	1.21814i
$469$	−35.2922	−	12.8453i	−1.62964	−	0.593142i
$470$	−1.91354	+	32.2328i	−0.0882649	+	1.48679i
$471$	12.0010	+	9.76015i	0.552975	+	0.449724i
$472$	6.13999	−	12.1241i	0.282616	−	0.558056i
$473$	10.9632	−	21.8295i	0.504088	−	1.00372i
$474$	−3.46459	+	2.99215i	−0.159134	+	0.137434i
$475$	−3.07734	−	2.90332i	−0.141198	−	0.133213i
$476$	−11.4441	−	19.9246i	−0.524540	−	0.913244i
$477$	5.79009	+	21.4713i	0.265110	+	0.983104i
$478$	−0.0256388	+	22.9143i	−0.00117269	+	1.04808i
$479$	22.5204	+	30.2502i	1.02899	+	1.38217i	0.921685	+	0.387940i	$0.126813\pi$
$479$	22.5204	+	30.2502i	1.02899	+	1.38217i	0.107301	+	0.994227i	$0.465779\pi$
$480$	23.2421	+	2.48715i	1.06085	+	0.113522i
$481$	40.9318	−	9.70101i	1.86633	−	0.442328i
$482$	40.7789	−	2.32932i	1.85743	−	0.106098i
$483$	−7.25947	+	5.57963i	−0.330317	+	0.253882i
$484$	0.634585	+	2.13706i	0.0288448	+	0.0971389i
$485$		−	17.6712i		−	0.802407i
$486$	−21.3593	+	5.45711i	−0.968878	+	0.247539i
$487$			0.568421i			0.0257576i	0.999917	+	0.0128788i	$0.00409956\pi$
$487$			0.568421i			0.0257576i	−0.999917	+	0.0128788i	$0.995900\pi$
$488$	7.41100	+	14.8809i	0.335480	+	0.673624i
$489$	15.7760	−	12.1254i	0.713415	−	0.548331i
$490$	2.95113	+	51.6647i	0.133318	+	2.33398i
$491$	7.71699	−	1.82896i	0.348263	−	0.0825398i	−0.0527617	−	0.998607i	$-0.516802\pi$
$491$	7.71699	−	1.82896i	0.348263	−	0.0825398i	0.401024	+	0.916067i	$0.368654\pi$
$492$	−7.11062	−	5.15019i	−0.320571	−	0.232189i
$493$	−3.24200	−	4.35476i	−0.146012	−	0.196129i
$494$	−43.1907	−	0.0483260i	−1.94324	−	0.00217429i
$495$	17.5864	−	17.6428i	0.790451	−	0.792987i
$496$	−11.6768	+	13.7901i	−0.524304	+	0.619192i
$497$	−4.46496	−	4.21248i	−0.200281	−	0.188955i
$498$	−21.8817	−	25.3367i	−0.980544	−	1.13537i
$499$	−16.7053	+	33.2630i	−0.747833	+	1.48906i	0.120306	+	0.992737i	$0.461612\pi$
$499$	−16.7053	+	33.2630i	−0.747833	+	1.48906i	−0.868139	+	0.496321i	$0.834684\pi$
$500$	−16.4622	−	12.3130i	−0.736210	−	0.550653i
$501$	−28.6349	−	23.2882i	−1.27931	−	1.04044i
$502$	30.5757	+	1.81516i	1.36466	+	0.0810145i
$503$	−17.7141	−	6.44741i	−0.789834	−	0.287476i	−0.0845668	−	0.996418i	$-0.526951\pi$
$503$	−17.7141	−	6.44741i	−0.789834	−	0.287476i	−0.705267	+	0.708942i	$0.749173\pi$
$504$	30.0056	−	26.6085i	1.33656	−	1.18524i
$505$	18.6500	−	6.78805i	0.829914	−	0.302064i
$506$	−5.27590	+	1.57307i	−0.234542	+	0.0699315i
$507$	5.61516	−	19.8602i	0.249378	−	0.882020i
$508$	6.40689	−	12.6863i	0.284260	−	0.562864i
$509$	−11.4349	−	8.51296i	−0.506842	−	0.377330i	0.313151	−	0.949703i	$-0.398615\pi$
$509$	−11.4349	−	8.51296i	−0.506842	−	0.377330i	−0.819993	+	0.572373i	$0.806023\pi$
$510$	−11.2722	+	8.64373i	−0.499139	+	0.382751i
$511$	−4.88886	−	9.73452i	−0.216271	−	0.430630i
$512$	19.4810	+	11.5105i	0.860947	+	0.508695i
$513$	21.5347	+	23.3880i	0.950782	+	1.03261i
$514$	−11.9847	+	10.0335i	−0.528621	+	0.442559i
$515$	−16.7881	−	11.0417i	−0.739771	−	0.486555i
$516$	−22.4479	−	9.33605i	−0.988215	−	0.410997i
$517$	13.1939	+	30.5868i	0.580266	+	1.34521i
$518$	55.9405	+	6.60196i	2.45788	+	0.290073i
$519$	−1.73275	+	17.0958i	−0.0760592	+	0.750423i
$520$	33.4669	−	3.79790i	1.46762	−	0.166549i
$521$	28.0640	−	33.4453i	1.22950	−	1.46527i	0.390983	−	0.920398i	$-0.372135\pi$
$521$	28.0640	−	33.4453i	1.22950	−	1.46527i	0.838522	−	0.544868i	$-0.183420\pi$
$522$	6.29602	−	7.08166i	0.275569	−	0.309956i
$523$	−10.1770	−	12.1285i	−0.445009	−	0.530342i	0.496181	−	0.868219i	$-0.334735\pi$
$523$	−10.1770	−	12.1285i	−0.445009	−	0.530342i	−0.941190	+	0.337878i	$0.890291\pi$
$524$	7.58340	+	10.2340i	0.331282	+	0.447075i
$525$	5.55888	−	1.06838i	0.242609	−	0.0466279i
$526$	5.49614	+	23.3062i	0.239643	+	1.01620i
$527$	−0.638480	−	10.9623i	−0.0278126	−	0.477525i
$528$	22.5691	−	8.49341i	0.982194	−	0.369628i
$529$	6.23770	+	20.8354i	0.271204	+	0.905885i
$530$	−16.0973	+	19.1405i	−0.699224	+	0.831411i
$531$	−12.6767	+	6.86146i	−0.550123	+	0.297762i
$532$	−54.3029	−	19.9024i	−2.35433	−	0.862878i
$533$	−11.6166	−	5.01089i	−0.503169	−	0.217046i
$534$	−4.42695	+	3.00273i	−0.191573	+	0.129941i
$535$	−31.8866	−	9.54622i	−1.37858	−	0.412719i
$536$	−13.4820	+	17.9832i	−0.582335	+	0.776755i
$537$	7.63908	+	24.1606i	0.329651	+	1.04261i
$538$	9.90153	−	22.8839i	0.426885	−	0.986595i
$539$	26.6931	+	46.2338i	1.14975	+	1.99143i
$540$	−18.7612	−	16.2079i	−0.807354	−	0.697478i
$541$	−14.9805	+	25.9470i	−0.644063	+	1.11555i	0.340455	+	0.940261i	$0.389419\pi$
$541$	−14.9805	+	25.9470i	−0.644063	+	1.11555i	−0.984517	+	0.175288i	$0.943914\pi$
$542$	0.517838	+	0.697204i	0.0222430	+	0.0299475i
$543$	−28.9739	−	18.4258i	−1.24339	−	0.790728i
$544$	−13.3975	+	3.09620i	−0.574411	+	0.132748i
$545$	−17.9694	+	16.9532i	−0.769723	+	0.726196i
$546$	33.8456	−	46.8392i	1.44846	−	2.00453i
$547$	0.955665	+	8.17624i	0.0408613	+	0.349591i	0.998167	+	0.0605143i	$0.0192741\pi$
$547$	0.955665	+	8.17624i	0.0408613	+	0.349591i	−0.957306	+	0.289076i	$0.906652\pi$
$548$	8.61818	+	10.3175i	0.368150	+	0.440744i
$549$	2.52758	−	17.4505i	0.107874	−	0.744768i
$550$	3.35131	+	0.594794i	0.142900	+	0.0253621i
$551$	−13.2968	−	3.15141i	−0.566465	−	0.134255i
$552$	1.93563	+	5.12603i	0.0823857	+	0.218178i
$553$	−7.37983	+	4.85379i	−0.313822	+	0.206404i
$554$	−1.95457	−	0.587544i	−0.0830418	−	0.0249624i
$555$	−0.534341	−	34.8187i	−0.0226815	−	1.47797i
$556$	−22.0162	−	9.55536i	−0.933696	−	0.405238i
$557$	−43.9720	+	7.75345i	−1.86315	+	0.328524i	−0.987894	−	0.155129i	$-0.950421\pi$
$557$	−43.9720	+	7.75345i	−1.86315	+	0.328524i	−0.875260	+	0.483653i	$0.839310\pi$
$558$	18.5103	−	4.96940i	0.783605	−	0.210372i
$559$	−34.4999	−	6.08326i	−1.45919	−	0.257295i
$560$	43.8394	+	10.5976i	1.85255	+	0.447829i
$561$	−6.37507	+	13.1948i	−0.269156	+	0.557087i
$562$	−0.601196	−	1.39803i	−0.0253599	−	0.0589722i
$563$	3.18210	+	0.371935i	0.134110	+	0.0156752i	0.182883	−	0.983135i	$-0.441457\pi$
$563$	3.18210	+	0.371935i	0.134110	+	0.0156752i	−0.0487732	+	0.998810i	$0.515531\pi$
$564$	29.4292	−	15.2662i	1.23919	−	0.642821i
$565$	−0.150106	+	2.57723i	−0.00631503	+	0.108425i
$566$	5.33931	+	30.4801i	0.224428	+	1.28117i
$567$	−42.2333	+	5.07354i	−1.77363	+	0.213069i
$568$	−3.18750	+	1.82607i	−0.133745	+	0.0766200i
$569$	−2.06686	−	0.120381i	−0.0866473	−	0.00504663i	0.0147664	−	0.999891i	$-0.495300\pi$
$569$	−2.06686	−	0.120381i	−0.0866473	−	0.00504663i	−0.101414	+	0.994844i	$0.532337\pi$
$570$	−7.74972	+	34.9042i	−0.324600	+	1.46198i
$571$	5.08001	−	43.4622i	0.212592	−	1.81884i	−0.293054	−	0.956096i	$-0.594671\pi$
$571$	5.08001	−	43.4622i	0.212592	−	1.81884i	0.505645	−	0.862741i	$-0.331254\pi$
$572$	29.0737	−	19.0290i	1.21563	−	0.795642i
$573$	0.976007	+	13.2510i	0.0407733	+	0.553567i
$574$	−12.3093	−	11.6393i	−0.513780	−	0.485814i
$575$	−0.134298	+	0.761642i	−0.00560062	+	0.0317627i
$576$	−10.0315	−	21.8030i	−0.417980	−	0.908456i
$577$	−1.24263	−	7.04730i	−0.0517314	−	0.293383i	0.947956	−	0.318403i	$-0.103146\pi$
$577$	−1.24263	−	7.04730i	−0.0517314	−	0.293383i	−0.999687	+	0.0250194i	$0.992035\pi$
$578$	−8.63396	+	13.0954i	−0.359125	+	0.544695i
$579$	−19.6365	+	35.2497i	−0.816065	+	1.46493i
$580$	10.5818	+	1.26084i	0.439384	+	0.0523536i
$581$	−35.4960	−	53.9691i	−1.47262	−	2.23901i
$582$	−15.5824	+	9.29452i	−0.645910	+	0.385270i
$583$	−5.95011	+	25.1055i	−0.246428	+	1.03976i
$584$	−6.42366	+	1.11045i	−0.265813	+	0.0459506i
$585$	−31.4722	−	16.9047i	−1.30122	−	0.698922i
$586$	−18.7348	−	32.5336i	−0.773927	−	1.34395i
$587$	3.72813	−	0.435756i	0.153877	−	0.0179856i	−0.0388058	−	0.999247i	$-0.512355\pi$
$587$	3.72813	−	0.435756i	0.153877	−	0.0179856i	0.192682	+	0.981261i	$0.438281\pi$
$588$	44.0055	−	29.7764i	1.81476	−	1.22796i
$589$	−18.9673	−	20.1042i	−0.781535	−	0.828379i
$590$	−14.4784	−	7.29165i	−0.596068	−	0.300192i
$591$	19.7580	+	0.846804i	0.812737	+	0.0348328i
$592$	13.4900	−	30.8924i	0.554435	−	1.26967i
$593$	−12.3317	−	7.11973i	−0.506404	−	0.292372i	0.224950	−	0.974370i	$-0.427778\pi$
$593$	−12.3317	−	7.11973i	−0.506404	−	0.292372i	−0.731354	+	0.681998i	$0.761111\pi$
$594$	−24.8073	−	6.22801i	−1.01786	−	0.255538i
$595$	−23.7363	+	13.7042i	−0.973094	+	0.561816i
$596$	−4.65577	+	19.4502i	−0.190708	+	0.796710i
$597$	−1.19216	+	5.39794i	−0.0487918	+	0.220923i
$598$	4.33119	+	6.60134i	0.177116	+	0.269949i
$599$	3.06292	−	10.2309i	0.125148	−	0.418022i	−0.872337	−	0.488905i	$-0.837396\pi$
$599$	3.06292	−	10.2309i	0.125148	−	0.418022i	0.997485	+	0.0708828i	$0.0225816\pi$
$600$	0.352906	−	3.36911i	0.0144073	−	0.137543i
$601$	−6.69323	+	15.5167i	−0.273023	+	0.632938i	−0.998467	−	0.0553427i	$-0.982375\pi$
$601$	−6.69323	+	15.5167i	−0.273023	+	0.632938i	0.725445	+	0.688280i	$0.241634\pi$
$602$	−40.5992	−	23.5006i	−1.65470	−	0.957812i
$603$	22.6171	−	7.53471i	0.921039	−	0.306837i
$604$	20.9582	+	12.1629i	0.852779	+	0.494900i
$605$	2.54747	−	0.762662i	0.103569	−	0.0310066i
$606$	−15.7950	−	12.8752i	−0.641629	−	0.523018i
$607$	0.923673	−	0.0537978i	0.0374907	−	0.00218359i	−0.0393892	−	0.999224i	$-0.512541\pi$
$607$	0.923673	−	0.0537978i	0.0374907	−	0.00218359i	0.0768799	+	0.997040i	$0.475504\pi$
$608$	−20.8232	+	27.6462i	−0.844493	+	1.12120i
$609$	13.8241	−	11.9660i	0.560179	−	0.484887i
$610$	17.7307	−	8.87985i	0.717894	−	0.359534i
$611$	36.5953	−	30.7071i	1.48049	−	1.24228i
$612$	13.5508	+	5.39338i	0.547759	+	0.218015i
$613$	−23.0886	−	19.3736i	−0.932539	−	0.782493i	0.0437326	−	0.999043i	$-0.486075\pi$
$613$	−23.0886	−	19.3736i	−0.932539	−	0.782493i	−0.976271	+	0.216550i	$0.930519\pi$
$614$	−8.41766	−	2.00497i	−0.339709	−	0.0809140i
$615$	−6.12436	+	8.49556i	−0.246958	+	0.342574i
$616$	45.3106	−	10.5783i	1.82562	−	0.426212i
$617$	16.4174	−	7.08176i	0.660938	−	0.285101i	−0.0390690	−	0.999237i	$-0.512439\pi$
$617$	16.4174	−	7.08176i	0.660938	−	0.285101i	0.700008	+	0.714135i	$0.253180\pi$
$618$	−0.906476	+	20.6112i	−0.0364638	+	0.829105i
$619$	−17.9118	+	27.2336i	−0.719937	+	1.09461i	0.271297	+	0.962496i	$0.412547\pi$
$619$	−17.9118	+	27.2336i	−0.719937	+	1.09461i	−0.991234	+	0.132116i	$0.957823\pi$
$620$	16.4805	+	13.8917i	0.661872	+	0.557905i
$621$	1.40883	−	5.63834i	0.0565345	−	0.226259i
$622$	−7.65750	+	20.9658i	−0.307038	+	0.840652i
$623$	−9.22356	+	4.63225i	−0.369534	+	0.185587i
$624$	−20.9516	−	27.5134i	−0.838735	−	1.10142i
$625$	−16.7081	+	22.4428i	−0.668322	+	0.897712i
$626$	18.0830	+	13.4938i	0.722742	+	0.539320i
$627$	9.05609	+	35.7564i	0.361665	+	1.42797i
$628$	15.9798	−	7.98063i	0.637664	−	0.318462i
$629$	7.00629	+	19.2496i	0.279359	+	0.767533i
$630$	−31.8197	−	35.7208i	−1.26773	−	1.42315i
$631$	−3.65498	+	10.0420i	−0.145502	+	0.399764i	−0.990939	−	0.134311i	$-0.957118\pi$
$631$	−3.65498	+	10.0420i	−0.145502	+	0.399764i	0.845437	+	0.534075i	$0.179340\pi$
$632$	1.49904	+	5.06899i	0.0596284	+	0.201634i
$633$	−1.04752	−	2.74617i	−0.0416351	−	0.109150i
$634$	15.0983	+	16.0392i	0.599631	+	0.636998i
$635$	−15.1498	−	7.60852i	−0.601202	−	0.301935i
$636$	25.3447	+	4.12720i	1.00498	+	0.163654i
$637$	52.5398	−	55.6889i	2.08170	−	2.20647i
$638$	10.3350	−	3.74854i	0.409166	−	0.148406i
$639$	3.88206	+	0.333372i	0.153572	+	0.0131880i
$640$	13.6781	−	23.2684i	0.540675	−	0.919764i
$641$	35.4390	−	26.3834i	1.39976	−	1.04208i	0.408134	−	0.912922i	$-0.366180\pi$
$641$	35.4390	−	26.3834i	1.39976	−	1.04208i	0.991624	−	0.129159i	$-0.0412278\pi$
$642$	8.35359	+	33.1385i	0.329690	+	1.30787i
$643$	−0.952013	−	4.01686i	−0.0375437	−	0.158409i	0.951044	−	0.309055i	$-0.100013\pi$
$643$	−0.952013	−	4.01686i	−0.0375437	−	0.158409i	−0.988588	+	0.150646i	$0.951865\pi$
$644$	2.41514	+	10.2929i	0.0951699	+	0.405596i
$645$	−11.0765	+	26.8017i	−0.436136	+	1.05531i
$646$	−2.41840	−	20.8934i	−0.0951505	−	0.822041i
$647$	−23.5894			−0.927393			−0.463697	−	0.885994i	$-0.653477\pi$
$647$	−23.5894			−0.927393			−0.463697	+	0.885994i	$0.653477\pi$
$648$	−4.42421	+	25.0684i	−0.173800	+	0.984781i
$649$	−16.7238			−0.656467
$650$	−0.561254	−	4.84888i	−0.0220142	−	0.190189i
$651$	36.6604	−	4.85631i	1.43684	−	0.190334i
$652$	−5.24849	−	22.3681i	−0.205547	−	0.876001i
$653$	10.8337	+	45.7111i	0.423956	+	1.78881i	0.595193	+	0.803583i	$0.297076\pi$
$653$	10.8337	+	45.7111i	0.423956	+	1.78881i	−0.171236	+	0.985230i	$0.554776\pi$
$654$	24.4006	+	6.92840i	0.954139	+	0.270922i
$655$	12.1873	−	9.07309i	0.476196	−	0.354515i
$656$	−8.80242	+	5.02969i	−0.343677	+	0.196376i
$657$	6.27122	+	2.91210i	0.244664	+	0.113612i
$658$	60.1362	−	21.8116i	2.34435	−	0.850305i
$659$	−22.1996	+	23.5302i	−0.864773	+	0.916606i	−0.997215	−	0.0745850i	$-0.976237\pi$
$659$	−22.1996	+	23.5302i	−0.864773	+	0.916606i	0.132442	+	0.991191i	$0.457718\pi$
$660$	−10.1915	−	26.8986i	−0.396704	−	1.04703i
$661$	−9.96605	−	5.00514i	−0.387634	−	0.194677i	0.244299	−	0.969700i	$-0.421442\pi$
$661$	−9.96605	−	5.00514i	−0.387634	−	0.194677i	−0.631933	+	0.775023i	$0.717738\pi$
$662$	−9.90307	−	10.5202i	−0.384894	−	0.408879i
$663$	20.7500	+	3.33133i	0.805862	+	0.129378i
$664$	−37.0698	+	10.9625i	−1.43859	+	0.425428i
$665$	−23.5954	+	64.8277i	−0.914989	+	2.51391i
$666$	−30.4219	+	18.7848i	−1.17883	+	0.727896i
$667$	0.854377	+	2.34738i	0.0330816	+	0.0908909i
$668$	−38.1286	+	19.0422i	−1.47524	+	0.736764i
$669$	−5.61111	+	5.45896i	−0.216938	+	0.211055i
$670$	21.4870	+	16.0339i	0.830115	+	0.619443i
$671$	12.2163	−	16.4093i	0.471605	−	0.633475i
$672$	−13.7133	−	44.2313i	−0.529003	−	1.70626i
$673$	27.8240	−	13.9737i	1.07254	−	0.538648i	0.177262	−	0.984164i	$-0.443276\pi$
$673$	27.8240	−	13.9737i	1.07254	−	0.538648i	0.895274	+	0.445516i	$0.146980\pi$
$674$	7.81892	−	21.4078i	0.301174	−	0.824596i
$675$	−2.34281	+	2.72418i	−0.0901746	+	0.104854i
$676$	−18.2217	−	15.3594i	−0.700834	−	0.590747i
$677$	24.6106	−	37.4186i	0.945861	−	1.43811i	0.0474913	−	0.998872i	$-0.484877\pi$
$677$	24.6106	−	37.4186i	0.945861	−	1.43811i	0.898370	−	0.439240i	$-0.144752\pi$
$678$	2.35154	−	1.22318i	0.0903103	−	0.0469761i
$679$	−32.1456	+	13.8663i	−1.23364	+	0.532139i
$680$	3.72903	+	15.9727i	0.143002	+	0.612527i
$681$	5.01166	+	11.1449i	0.192047	+	0.427075i
$682$	21.6311	+	5.15223i	0.828297	+	0.197289i
$683$	−4.21789	−	3.53923i	−0.161393	−	0.135425i	0.558515	−	0.829495i	$-0.311371\pi$
$683$	−4.21789	−	3.53923i	−0.161393	−	0.135425i	−0.719908	+	0.694070i	$0.755816\pi$
$684$	34.8545	−	11.5249i	1.33269	−	0.440666i
$685$	12.2842	−	10.3076i	0.469354	−	0.393834i
$686$	49.8326	−	24.9571i	1.90262	−	0.952866i
$687$	−13.9818	−	4.84733i	−0.533440	−	0.184937i
$688$	−20.5056	+	19.1733i	−0.781768	+	0.730975i
$689$	36.9388	−	2.15144i	1.40725	−	0.0819632i
$690$	6.10936	−	2.32257i	0.232579	−	0.0884188i
$691$	32.4682	−	9.72034i	1.23515	−	0.369779i	0.398321	−	0.917246i	$-0.369593\pi$
$691$	32.4682	−	9.72034i	1.23515	−	0.369779i	0.836827	+	0.547467i	$0.184408\pi$
$692$	17.1612	+	9.95927i	0.652370	+	0.378595i
$693$	−45.8938	−	18.1474i	−1.74336	−	0.689363i
$694$	−33.9504	−	19.6520i	−1.28874	−	0.745978i
$695$	−11.3392	+	26.2873i	−0.430122	+	0.997134i
$696$	−4.45390	−	9.99412i	−0.168825	−	0.378826i
$697$	1.76695	−	5.90204i	0.0669282	−	0.223556i
$698$	−26.3002	−	40.0851i	−0.995476	−	1.51724i
$699$	−23.5315	−	21.5280i	−0.890043	−	0.814264i
$700$	1.52161	−	6.35674i	0.0575114	−	0.240262i
$701$	−37.6869	+	21.7585i	−1.42341	+	0.821809i	−0.996589	−	0.0825250i	$-0.973702\pi$
$701$	−37.6869	+	21.7585i	−1.42341	+	0.821809i	−0.426826	+	0.904334i	$0.640368\pi$
$702$	1.64700	+	36.6434i	0.0621622	+	1.38302i
$703$	44.6539	+	25.7810i	1.68416	+	0.972348i
$704$	1.80561	−	27.7863i	0.0680517	−	1.04723i
$705$	−18.2886	−	35.0635i	−0.688789	−	1.32057i
$706$	−9.86507	−	4.96825i	−0.371277	−	0.186983i
$707$	−26.9825	−	28.5997i	−1.01478	−	1.07560i
$708$	1.18550	+	16.6022i	0.0445537	+	0.623949i
$709$	8.30864	−	0.971141i	0.312037	−	0.0364719i	0.0413670	−	0.999144i	$-0.486829\pi$
$709$	8.30864	−	0.971141i	0.312037	−	0.0364719i	0.270670	+	0.962672i	$0.412755\pi$
$710$	2.18671	+	3.79730i	0.0820658	+	0.142510i
$711$	1.75502	−	5.32489i	0.0658183	−	0.199699i
$712$	1.05216	+	6.08649i	0.0394313	+	0.228101i
$713$	−1.16520	+	4.91636i	−0.0436370	+	0.184119i
$714$	24.5689	+	13.7226i	0.919467	+	0.513554i
$715$	−22.7761	−	34.6294i	−0.851779	−	1.29507i
$716$	29.0540	+	3.46185i	1.08580	+	0.129375i
$717$	−14.4034	−	24.0861i	−0.537904	−	0.899513i
$718$	−16.9956	+	25.7776i	−0.634269	+	0.962013i
$719$	3.94453	+	22.3706i	0.147106	+	0.834281i	0.965652	+	0.259839i	$0.0836696\pi$
$719$	3.94453	+	22.3706i	0.147106	+	0.834281i	−0.818546	+	0.574442i	$0.805219\pi$
$720$	−25.9806	+	12.0242i	−0.968240	+	0.448114i
$721$	−6.91261	+	39.2034i	−0.257439	+	1.46001i
$722$	−18.9433	−	17.9122i	−0.704996	−	0.666622i
$723$	−41.3687	+	28.1274i	−1.53852	+	1.04607i
$724$	−33.1745	+	21.7130i	−1.23292	+	0.806957i
$725$	0.179292	−	1.53395i	0.00665875	−	0.0569693i
$726$	−2.01240	−	1.84521i	−0.0746873	−	0.0684821i
$727$	16.6930	+	0.972259i	0.619111	+	0.0360591i	0.364834	−	0.931072i	$-0.381126\pi$
$727$	16.6930	+	0.972259i	0.619111	+	0.0360591i	0.254277	+	0.967132i	$0.418163\pi$
$728$	−33.1697	−	57.8995i	−1.22935	−	2.14590i
$729$	18.9999	−	19.1834i	0.703701	−	0.710496i
$730$	1.34173	+	7.65943i	0.0496596	+	0.283488i
$731$	0.991942	−	17.0310i	0.0366883	−	0.629914i
$732$	−17.1560	−	10.9643i	−0.634104	−	0.405251i
$733$	29.6629	+	3.46710i	1.09562	+	0.128060i	0.644651	−	0.764477i	$-0.277003\pi$
$733$	29.6629	+	3.46710i	1.09562	+	0.128060i	0.450974	+	0.892537i	$0.351077\pi$
$734$	6.22057	+	14.4654i	0.229606	+	0.533927i
$735$	−35.6359	−	52.4120i	−1.31445	−	1.93324i
$736$	6.31410	+	0.403211i	0.232741	+	0.0148625i
$737$	27.2381	+	4.80280i	1.00333	+	0.176914i
$738$	10.7126	+	0.932020i	0.394335	+	0.0343081i
$739$	−9.39326	+	1.65628i	−0.345537	+	0.0609274i	−0.343723	−	0.939071i	$-0.611688\pi$
$739$	−9.39326	+	1.65628i	−0.345537	+	0.0609274i	−0.00181317	+	0.999998i	$0.500577\pi$
$740$	−36.8857	−	16.0089i	−1.35594	−	0.588500i
$741$	45.3995	−	27.1486i	1.66779	−	0.997330i
$742$	47.4498	+	14.2634i	1.74194	+	0.523626i
$743$	−8.60350	+	5.65861i	−0.315632	+	0.207594i	−0.697433	−	0.716650i	$-0.745674\pi$
$743$	−8.60350	+	5.65861i	−0.315632	+	0.207594i	0.381801	+	0.924245i	$0.375304\pi$
$744$	3.58141	−	21.8390i	0.131301	−	0.800658i
$745$	23.2133	+	5.50166i	0.850471	+	0.201565i
$746$	−26.4576	−	4.69571i	−0.968680	−	0.171922i
$747$	38.9412	+	12.8345i	1.42478	+	0.469591i
$748$	10.8477	+	12.9867i	0.396631	+	0.474841i
$749$	7.65534	+	65.4956i	0.279720	+	2.39316i
$750$	25.0465	+	2.56691i	0.914570	+	0.0937302i
$751$	−5.07469	+	4.78773i	−0.185178	+	0.174707i	−0.773248	−	0.634103i	$-0.781369\pi$
$751$	−5.07469	+	4.78773i	−0.185178	+	0.174707i	0.588070	+	0.808810i	$0.299888\pi$
$752$	−2.05483	−	38.2268i	−0.0749320	−	1.39399i
$753$	−33.2608	+	17.3484i	−1.21209	+	0.632210i
$754$	−9.40081	−	12.6570i	−0.342357	−	0.460942i
$755$	14.4524	−	25.0323i	0.525976	−	0.911017i
$756$	−14.7622	+	46.8466i	−0.536896	+	1.70379i
$757$	−4.28565	−	7.42297i	−0.155765	−	0.269792i	0.777573	−	0.628793i	$-0.216451\pi$
$757$	−4.28565	−	7.42297i	−0.155765	−	0.269792i	−0.933337	+	0.359001i	$0.883117\pi$
$758$	−12.4559	+	28.7873i	−0.452417	+	1.04560i
$759$	4.55135	−	4.97492i	0.165203	−	0.180578i
$760$	33.0330	+	24.7649i	1.19823	+	0.898318i
$761$	−40.0772	−	11.9983i	−1.45280	−	0.434939i	−0.539413	−	0.842041i	$-0.681354\pi$
$761$	−40.0772	−	11.9983i	−1.45280	−	0.434939i	−0.913382	+	0.407102i	$0.866539\pi$
$762$	1.25920	+	17.3609i	0.0456159	+	0.628919i
$763$	44.9398	+	19.3851i	1.62693	+	0.701789i
$764$	14.4053	+	5.27964i	0.521165	+	0.191011i
$765$	6.39726	−	16.1783i	0.231293	−	0.584929i
$766$	12.3595	−	14.6960i	0.446566	−	0.530989i
$767$	6.87861	+	22.9762i	0.248372	+	0.829621i
$768$	−27.7122	+	0.177194i	−0.999980	+	0.00639394i
$769$	−1.83419	−	31.4918i	−0.0661425	−	1.13562i	−0.854174	−	0.519988i	$-0.825937\pi$
$769$	−1.83419	−	31.4918i	−0.0661425	−	1.13562i	0.788031	−	0.615635i	$-0.211100\pi$
$770$	−12.7392	−	54.0200i	−0.459087	−	1.94675i
$771$	6.27050	−	18.0869i	0.225827	−	0.651384i
$772$	27.7393	+	37.4350i	0.998359	+	1.34731i
$773$	22.3808	+	26.6723i	0.804980	+	0.959337i	0.999769	−	0.0215078i	$-0.00684666\pi$
$773$	22.3808	+	26.6723i	0.804980	+	0.959337i	−0.194789	+	0.980845i	$0.562402\pi$
$774$	29.4595	−	4.32970i	1.05890	−	0.155628i
$775$	2.00788	−	2.39289i	0.0721251	−	0.0859553i
$776$	2.36236	+	20.8171i	0.0848039	+	0.747289i
$777$	−62.9194	+	28.2937i	−2.25722	+	1.01503i
$778$	−39.0044	−	4.60320i	−1.39837	−	0.165033i
$779$	−6.14209	−	14.2390i	−0.220063	−	0.510164i
$780$	−32.7631	+	25.0653i	−1.17311	+	0.897482i
$781$	3.77687	+	2.48409i	0.135147	+	0.0888876i
$782$	−2.94810	+	2.46814i	−0.105424	+	0.0882604i
$783$	−2.15387	+	11.4037i	−0.0769731	+	0.407537i
$784$	−10.3833	−	60.4677i	−0.370831	−	2.15956i
$785$	−9.56226	−	19.0400i	−0.341292	−	0.679568i
$786$	−14.4107	−	5.97450i	−0.514014	−	0.213103i
$787$	21.0061	+	15.6385i	0.748787	+	0.557451i	0.902513	−	0.430662i	$-0.141720\pi$
$787$	21.0061	+	15.6385i	0.748787	+	0.557451i	−0.153726	+	0.988114i	$0.549127\pi$
$788$	10.2942	−	20.3836i	0.366716	−	0.726136i
$789$	−20.4505	−	21.0205i	−0.728056	−	0.748349i
$790$	6.04249	−	1.80164i	0.214982	−	0.0640994i
$791$	4.80602	−	1.74925i	0.170882	−	0.0621961i
$792$	−18.3586	+	23.1347i	−0.652346	+	0.822056i
$793$	−27.5688	−	10.0342i	−0.978996	−	0.356325i
$794$	34.9049	+	2.07217i	1.23873	+	0.0735386i
$795$	4.85543	−	30.2432i	0.172204	−	1.07262i
$796$	5.11157	+	3.82323i	0.181175	+	0.135511i
$797$	17.1416	−	34.1317i	0.607186	−	1.20901i	−0.354552	−	0.935036i	$-0.615367\pi$
$797$	17.1416	−	34.1317i	0.607186	−	1.20901i	0.961738	−	0.273970i	$-0.0883370\pi$
$798$	69.5753	−	13.2912i	2.46294	−	0.470503i
$799$	16.9215	+	15.9646i	0.598638	+	0.564786i
$800$	−3.37655	−	1.97472i	−0.119379	−	0.0698169i
$801$	2.75925	−	5.94205i	0.0974932	−	0.209952i
$802$	7.80515	+	0.00873317i	0.275610	+	0.000308379i
$803$	4.79045	+	6.43470i	0.169051	+	0.227076i
$804$	2.83707	−	27.3805i	0.100056	−	0.965635i
$805$	12.2713	−	2.90835i	0.432506	−	0.102506i
$806$	−1.81857	−	31.8372i	−0.0640562	−	1.12142i
$807$	4.01025	+	30.2735i	0.141168	+	1.06568i
$808$	−21.0627	+	10.4897i	−0.740982	+	0.369026i
$809$		−	6.14425i		−	0.216020i	−0.994150	−	0.108010i	$-0.965552\pi$
$809$		−	6.14425i		−	0.216020i	0.994150	−	0.108010i	$-0.0344479\pi$
$810$	29.9144	+	5.21045i	1.05108	+	0.183077i
$811$		−	36.9184i		−	1.29638i	−0.761478	−	0.648190i	$-0.775526\pi$
$811$		−	36.9184i		−	1.29638i	0.761478	−	0.648190i	$-0.224474\pi$
$812$	−6.00974	−	20.2387i	−0.210901	−	0.710238i
$813$	−0.983020	−	0.406258i	−0.0344760	−	0.0142481i
$814$	−41.4146	+	2.36563i	−1.45158	+	0.0829154i
$815$	−26.6675	+	6.32030i	−0.934121	+	0.221391i
$816$	12.1233	−	11.6894i	0.424401	−	0.409212i
$817$	−25.6423	−	34.4436i	−0.897111	−	1.20503i
$818$	0.00154378	−	1.37973i	5.39770e−5	−	0.0482412i
$819$	−6.05556	+	70.5159i	−0.211598	+	2.46402i
$820$	6.02310	+	10.4864i	0.210336	+	0.366202i
$821$	−18.5930	−	17.5416i	−0.648900	−	0.612205i	0.289740	−	0.957105i	$-0.406431\pi$
$821$	−18.5930	−	17.5416i	−0.648900	−	0.612205i	−0.938639	+	0.344900i	$0.887913\pi$
$822$	−15.5503	−	5.41060i	−0.542380	−	0.188716i
$823$	12.6702	−	25.2283i	0.441654	−	0.879405i	−0.557146	−	0.830415i	$-0.688103\pi$
$823$	12.6702	−	25.2283i	0.441654	−	0.879405i	0.998799	−	0.0489900i	$-0.0156003\pi$
$824$	21.2528	+	10.7631i	0.740377	+	0.374949i
$825$	−3.89491	+	1.48570i	−0.135603	+	0.0517255i
$826$	−1.90324	+	32.0593i	−0.0662222	+	1.11549i
$827$	−17.5781	−	6.39790i	−0.611250	−	0.222477i	0.0178001	−	0.999842i	$-0.494334\pi$
$827$	−17.5781	−	6.39790i	−0.611250	−	0.222477i	−0.629050	+	0.777365i	$0.716556\pi$
$828$	−5.26138	−	4.16560i	−0.182845	−	0.144765i
$829$	−4.16533	+	1.51606i	−0.144668	+	0.0526548i	−0.413339	−	0.910577i	$-0.635638\pi$
$829$	−4.16533	+	1.51606i	−0.144668	+	0.0526548i	0.268671	+	0.963232i	$0.413415\pi$
$830$	13.1755	+	44.1890i	0.457327	+	1.53382i
$831$	2.42316	−	0.613718i	0.0840584	−	0.0212896i
$832$	−38.9171	+	8.94802i	−1.34921	+	0.310217i
$833$	29.9062	+	22.2643i	1.03619	+	0.771413i
$834$	29.1441	−	3.82746i	1.00918	−	0.132534i
$835$	22.8160	+	45.4304i	0.789581	+	1.57219i
$836$	41.9279	+	7.48980i	1.45011	+	0.259040i
$837$	−16.3144	+	16.8769i	−0.563908	+	0.583353i
$838$	11.8238	+	14.1231i	0.408446	+	0.487874i
$839$	−30.7931	−	20.2530i	−1.06310	−	0.699210i	−0.107595	−	0.994195i	$-0.534315\pi$
$839$	−30.7931	−	20.2530i	−1.06310	−	0.699210i	−0.955502	+	0.294985i	$0.904685\pi$
$840$	−52.7242	+	16.4758i	−1.81916	+	0.568471i
$841$	9.51054	+	22.0479i	0.327950	+	0.760273i
$842$	2.22135	−	18.8222i	0.0765527	−	0.648655i
$843$	1.51193	+	1.08993i	0.0520735	+	0.0375393i
$844$	−3.38767	−	0.204917i	−0.116609	−	0.00705354i
$845$	−18.2727	+	21.7765i	−0.628599	+	0.749135i
$846$	−21.2996	+	34.5692i	−0.732294	+	1.18851i
$847$	−3.38631	−	4.03565i	−0.116355	−	0.138667i
$848$	16.4042	−	24.6999i	0.563324	−	0.848200i
$849$	−24.8035	−	28.6549i	−0.851253	−	0.983435i
$850$	2.31360	−	0.545599i	0.0793558	−	0.0187139i
$851$	−0.548053	−	9.40970i	−0.0187870	−	0.322560i
$852$	2.19829	−	3.92550i	0.0753123	−	0.134485i
$853$	−9.30994	−	31.0974i	−0.318766	−	1.06475i	−0.955825	−	0.293938i	$-0.905034\pi$
$853$	−9.30994	−	31.0974i	−0.318766	−	1.06475i	0.637058	−	0.770816i	$-0.280151\pi$
$854$	−30.0663	−	25.2860i	−1.02885	−	0.865268i
$855$	−13.8404	−	41.5450i	−0.473331	−	1.42081i
$856$	38.8393	+	6.98292i	1.32750	+	0.238671i
$857$	−24.9927	−	10.7808i	−0.853733	−	0.368265i	−0.0761894	−	0.997093i	$-0.524275\pi$
$857$	−24.9927	−	10.7808i	−0.853733	−	0.368265i	−0.777544	+	0.628829i	$0.783535\pi$
$858$	−18.5565	+	38.2979i	−0.633508	+	1.30747i
$859$	24.4310	+	7.31415i	0.833574	+	0.249556i	0.675024	−	0.737795i	$-0.264133\pi$
$859$	24.4310	+	7.31415i	0.833574	+	0.249556i	0.158549	+	0.987351i	$0.449318\pi$
$860$	22.9254	+	24.4087i	0.781749	+	0.832329i
$861$	20.2599	+	4.47450i	0.690457	+	0.152491i
$862$	−13.8838	−	6.00731i	−0.472884	−	0.204610i
$863$	10.7532	+	18.6250i	0.366042	+	0.634003i	0.988943	−	0.148298i	$-0.0473793\pi$
$863$	10.7532	+	18.6250i	0.366042	+	0.634003i	−0.622901	+	0.782301i	$0.714046\pi$
$864$	24.2679	+	16.5852i	0.825610	+	0.564241i
$865$	11.8340	−	20.4971i	0.402368	−	0.696921i
$866$	−4.23423	+	3.14491i	−0.143885	+	0.106868i
$867$	0.822590	−	19.1931i	0.0279366	−	0.651831i
$868$	12.3385	−	40.8802i	0.418795	−	1.38756i
$869$	4.73146	−	4.46390i	0.160504	−	0.151428i
$870$	−11.9095	+	5.33946i	−0.403769	+	0.181025i
$871$	−4.60481	−	39.3967i	−0.156028	−	1.33491i
$872$	18.9019	−	22.3735i	0.640100	−	0.757662i
$873$	10.5150	−	19.5763i	0.355880	−	0.662558i
$874$	−1.69118	+	9.52883i	−0.0572052	+	0.322317i
$875$	47.2713	+	11.2035i	1.59806	+	0.378748i
$876$	6.04833	−	5.21176i	0.204354	−	0.176089i
$877$	−0.0743305	+	0.0488879i	−0.00250996	+	0.00165083i	−0.550763	−	0.834661i	$-0.685663\pi$
$877$	−0.0743305	+	0.0488879i	−0.00250996	+	0.00165083i	0.548253	+	0.836312i	$0.315293\pi$
$878$	5.13210	−	17.0729i	0.173200	−	0.576181i
$879$	40.1678	+	22.3762i	1.35482	+	0.754730i
$880$	−33.1493	−	2.07964i	−1.11746	−	0.0701045i
$881$	−27.0573	+	4.77094i	−0.911585	+	0.160737i	−0.609723	−	0.792615i	$-0.708719\pi$
$881$	−27.0573	+	4.77094i	−0.911585	+	0.160737i	−0.301862	+	0.953352i	$0.597608\pi$
$882$	−27.4732	+	58.9907i	−0.925070	+	1.98632i
$883$	12.1126	+	2.13577i	0.407620	+	0.0718744i	0.373699	−	0.927550i	$-0.378089\pi$
$883$	12.1126	+	2.13577i	0.407620	+	0.0718744i	0.0339212	+	0.999425i	$0.489200\pi$
$884$	13.3802	−	20.2447i	0.450024	−	0.680905i
$885$	19.8006	−	1.45842i	0.665589	−	0.0490244i
$886$	37.7382	−	16.2286i	1.26784	−	0.545212i
$887$	−1.35506	−	0.158384i	−0.0454984	−	0.00531800i	0.0933133	−	0.995637i	$-0.470254\pi$
$887$	−1.35506	−	0.158384i	−0.0454984	−	0.00531800i	−0.138812	+	0.990319i	$0.544328\pi$
$888$	5.28419	+	40.9458i	0.177326	+	1.37405i
$889$	−1.95286	+	33.5293i	−0.0654968	+	1.12454i
$890$	7.25738	−	1.27130i	0.243268	−	0.0426141i
$891$	29.9806	−	9.08032i	1.00439	−	0.304202i
$892$	3.07268	+	8.50127i	0.102881	+	0.284644i
$893$	58.4571	+	3.40474i	1.95619	+	0.113935i
$894$	−7.35819	−	23.3631i	−0.246095	−	0.781379i
$895$	4.05187	−	34.6660i	0.135439	−	1.15876i
$896$	−53.0605	−	6.62354i	−1.77263	−	0.221277i
$897$	−8.70684	−	4.20670i	−0.290713	−	0.140458i
$898$	10.0037	−	10.5795i	0.333827	−	0.353044i
$899$	1.75202	−	9.93617i	0.0584330	−	0.331390i
$900$	1.75100	+	3.76127i	0.0583666	+	0.125376i
$901$	3.12894	+	17.7451i	0.104240	+	0.591174i
$902$	10.4156	+	6.86718i	0.346803	+	0.228652i
$903$	57.4464	−	0.881593i	1.91170	−	0.0293376i
$904$	−0.167706	−	3.05610i	−0.00557783	−	0.101644i
$905$	25.9886	+	39.5138i	0.863892	+	1.31348i
$906$	−29.6748	+	0.422191i	−0.985881	+	0.0140263i
$907$	−0.222209	+	0.937574i	−0.00737833	+	0.0311316i	−0.976610	−	0.215021i	$-0.931018\pi$
$907$	−0.222209	+	0.937574i	−0.00737833	+	0.0311316i	0.969231	+	0.246152i	$0.0791663\pi$
$908$	14.1103	+	0.0315760i	0.468267	+	0.00104789i
$909$	24.6998	+	3.57759i	0.819240	+	0.118661i
$910$	−68.9762	+	39.7206i	−2.28654	+	1.31673i
$911$	−21.1467	+	2.47170i	−0.700622	+	0.0818910i	−0.458944	−	0.888465i	$-0.651772\pi$
$911$	−21.1467	+	2.47170i	−0.700622	+	0.0818910i	−0.241678	+	0.970356i	$0.577698\pi$
$912$	4.46321	−	42.1540i	0.147792	−	1.39586i
$913$	32.6447	+	34.6014i	1.08038	+	1.14514i
$914$	−13.6886	+	27.1805i	−0.452780	+	0.899050i
$915$	−13.0328	+	20.4936i	−0.430851	+	0.677498i
$916$	−11.7540	+	12.4028i	−0.388362	+	0.409799i
$917$	−26.0680	−	15.0504i	−0.860841	−	0.497007i
$918$	−17.6307	+	2.86825i	−0.581901	+	0.0946664i
$919$	−36.0445	+	20.8103i	−1.18900	+	0.686468i	−0.958079	−	0.286505i	$-0.907506\pi$
$919$	−36.0445	+	20.8103i	−1.18900	+	0.686468i	−0.230919	+	0.972973i	$0.574173\pi$
$920$	0.464111	−	7.53278i	0.0153013	−	0.248348i
$921$	10.1048	−	3.19494i	0.332965	−	0.105277i
$922$	−22.2410	+	14.5925i	−0.732469	+	0.480579i
$923$	1.85933	−	6.21061i	0.0612007	−	0.204425i
$924$	−40.9342	+	39.6462i	−1.34663	+	1.30427i
$925$	−2.30809	+	5.35075i	−0.0758895	+	0.175932i
$926$	1.02908	−	1.77781i	0.0338175	−	0.0584226i
$927$	−12.0278	−	22.2216i	−0.395043	−	0.729853i
$928$	−12.6341	−	0.0706822i	−0.414736	−	0.00232026i
$929$	−42.6889	+	12.7802i	−1.40058	+	0.419306i	−0.895998	−	0.444059i	$-0.853538\pi$
$929$	−42.6889	+	12.7802i	−1.40058	+	0.419306i	−0.504581	+	0.863364i	$0.668353\pi$
$930$	−26.0600	−	4.21375i	−0.854541	−	0.138174i
$931$	93.6865	−	5.45662i	3.07045	−	0.178833i
$932$	−33.8479	+	14.5108i	−1.10873	+	0.475318i
$933$	−5.15953	−	26.8455i	−0.168915	−	0.878883i
$934$	−1.68021	−	3.35493i	−0.0549782	−	0.109777i
$935$	15.4621	−	12.9742i	0.505664	−	0.424302i
$936$	39.3349	+	15.7067i	1.28570	+	0.513391i
$937$	36.8555	+	30.9254i	1.20402	+	1.01029i	0.999506	+	0.0314261i	$0.0100049\pi$
$937$	36.8555	+	30.9254i	1.20402	+	1.01029i	0.204511	+	0.978864i	$0.434440\pi$
$938$	12.3067	−	51.6685i	0.401829	−	1.68704i
$939$	−27.4927	−	2.78653i	−0.897192	−	0.0909349i
$940$	−45.5929	+	2.55312i	−1.48708	+	0.0832737i
$941$	48.0909	−	20.7444i	1.56772	−	0.676248i	0.577581	−	0.816334i	$-0.303997\pi$
$941$	48.0909	−	20.7444i	1.56772	−	0.676248i	0.990139	+	0.140085i	$0.0447376\pi$
$942$	−11.7599	+	18.4464i	−0.383159	+	0.601018i
$943$	−1.55772	+	2.36840i	−0.0507265	+	0.0771259i
$944$	18.0307	+	6.65418i	0.586850	+	0.216575i
$945$	55.9198	+	17.4839i	1.81907	+	0.568750i
$946$	32.4495	+	11.8518i	1.05502	+	0.385335i
$947$	−9.08075	+	4.56052i	−0.295085	+	0.148197i	−0.590182	−	0.807270i	$-0.700944\pi$
$947$	−9.08075	+	4.56052i	−0.295085	+	0.148197i	0.295098	+	0.955467i	$0.404648\pi$
$948$	−4.76685	−	4.38063i	−0.154820	−	0.142276i
$949$	6.87003	−	9.22805i	0.223011	−	0.299555i
$950$	3.57828	−	4.79525i	0.116095	−	0.155579i
$951$	−25.9605	−	7.33994i	−0.841827	−	0.238014i
$952$	26.1299	−	19.3170i	0.846874	−	0.626067i
$953$	8.27954	+	22.7479i	0.268201	+	0.736876i	0.998552	+	0.0538033i	$0.0171344\pi$
$953$	8.27954	+	22.7479i	0.268201	+	0.736876i	−0.730351	+	0.683072i	$0.760643\pi$
$954$	−29.2221	+	11.6255i	−0.946101	+	0.376391i
$955$	6.25930	−	17.1973i	0.202546	−	0.556491i
$956$	−32.1950	+	3.69004i	−1.04126	+	0.119344i
$957$	−8.49558	+	10.4461i	−0.274623	+	0.337673i
$958$	−38.8345	+	36.5564i	−1.25469	+	1.18108i
$959$	−28.3898	−	14.2579i	−0.916753	−	0.460411i
$960$	0.285337	+	33.0557i	0.00920921	+	1.06687i
$961$	−7.26930	+	7.70501i	−0.234494	+	0.248549i
$962$	20.2842	+	55.9249i	0.653987	+	1.80309i
$963$	−29.6439	−	29.5491i	−0.955261	−	0.952206i
$964$	9.90331	+	56.9089i	0.318964	+	1.83291i
$965$	44.5798	−	33.1884i	1.43507	−	1.06837i
$966$	−9.01890	−	9.29105i	−0.290178	−	0.298935i
$967$	2.98964	+	12.6143i	0.0961405	+	0.405649i	0.999742	−	0.0227260i	$-0.00723454\pi$
$967$	2.98964	+	12.6143i	0.0961405	+	0.405649i	−0.903601	+	0.428375i	$0.859086\pi$
$968$	−2.89902	+	1.23899i	−0.0931780	+	0.0398226i
$969$	15.6980	+	20.4242i	0.504293	+	0.656119i
$970$	24.8251	−	2.87348i	0.797086	−	0.0922620i
$971$	−36.5999			−1.17455			−0.587273	−	0.809389i	$-0.699798\pi$
$971$	−36.5999			−1.17455			−0.587273	+	0.809389i	$0.699798\pi$
$972$	−11.1395	−	29.1189i	−0.357301	−	0.933989i
$973$	56.7169			1.81826
$974$	−0.798537	+	0.0924300i	−0.0255868	+	0.00296165i
$975$	3.64315	+	4.73998i	0.116674	+	0.151801i
$976$	−19.7000	+	12.8310i	−0.630583	+	0.410710i
$977$	8.12221	+	34.2703i	0.259853	+	1.09640i	0.933848	+	0.357669i	$0.116428\pi$
$977$	8.12221	+	34.2703i	0.259853	+	1.09640i	−0.673996	+	0.738735i	$0.735423\pi$
$978$	19.5995	+	20.1909i	0.626723	+	0.645635i
$979$	6.09694	−	4.53900i	0.194859	−	0.145067i
$980$	−72.1005	+	12.5470i	−2.30317	+	0.400798i
$981$	−29.9944	+	8.08849i	−0.957648	+	0.258245i
$982$	3.82423	+	10.5437i	0.122036	+	0.336462i
$983$	10.8519	−	11.5023i	0.346122	−	0.366868i	−0.530803	−	0.847495i	$-0.678110\pi$
$983$	10.8519	−	11.5023i	0.346122	−	0.366868i	0.876925	+	0.480627i	$0.159591\pi$
$984$	6.07892	−	10.8267i	0.193789	−	0.345143i
$985$	−24.3418	−	12.2249i	−0.775595	−	0.389519i
$986$	5.59054	−	5.26259i	0.178039	−	0.167595i
$987$	−49.4332	+	60.7825i	−1.57348	+	1.93473i
$988$	−6.95528	−	60.6836i	−0.221277	−	1.93060i
$989$	−2.68473	+	7.37625i	−0.0853696	+	0.234551i
$990$	27.6450	+	21.8371i	0.878615	+	0.694030i
$991$	6.22513	+	17.1034i	0.197748	+	0.543307i	0.998444	−	0.0557631i	$-0.0177591\pi$
$991$	6.22513	+	17.1034i	0.197748	+	0.543307i	−0.800696	+	0.599070i	$0.795537\pi$
$992$	−21.2715	−	14.1616i	−0.675370	−	0.449631i
$993$	17.0276	+	4.81431i	0.540356	+	0.152777i
$994$	5.19179	−	6.95752i	0.164674	−	0.220679i
$995$	4.54685	−	6.10748i	0.144145	−	0.193620i
$996$	32.0358	−	34.8602i	1.01509	−	1.10459i
$997$	0.823976	−	0.413816i	0.0260956	−	0.0131057i	−0.435704	−	0.900090i	$-0.643500\pi$
$997$	0.823976	−	0.413816i	0.0260956	−	0.0131057i	0.461799	+	0.886985i	$0.347204\pi$
$998$	−49.4455	−	18.0594i	−1.56517	−	0.571659i
$999$	20.1265	−	38.8905i	0.636774	−	1.23044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.83.29	✓	936
3.2	odd	2		972.2.p.a.251.24		936
4.3	odd	2	inner	324.2.p.a.83.32	yes	936
12.11	even	2		972.2.p.a.251.21		936
81.40	even	27		972.2.p.a.395.21		936
81.41	odd	54	inner	324.2.p.a.203.32	yes	936
324.203	even	54	inner	324.2.p.a.203.29	yes	936
324.283	odd	54		972.2.p.a.395.24		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.83.29	✓	936	1.1	even	1	trivial
324.2.p.a.83.32	yes	936	4.3	odd	2	inner
324.2.p.a.203.29	yes	936	324.203	even	54	inner
324.2.p.a.203.32	yes	936	81.41	odd	54	inner
972.2.p.a.251.21		936	12.11	even	2
972.2.p.a.251.24		936	3.2	odd	2
972.2.p.a.395.21		936	81.40	even	27
972.2.p.a.395.24		936	324.283	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.162608 + 1.40483i) q^{2} +(-1.05551 - 1.37328i) q^{3} +(-1.94712 + 0.456876i) q^{4} +(0.550176 + 2.32138i) q^{5} +(1.75760 - 1.70612i) q^{6} +(3.79110 - 2.82237i) q^{7} +(-0.958452 - 2.66108i) q^{8} +(-0.771815 + 2.89902i) q^{9} +O(q^{10})\)	\(q+(0.162608 + 1.40483i) q^{2} +(-1.05551 - 1.37328i) q^{3} +(-1.94712 + 0.456876i) q^{4} +(0.550176 + 2.32138i) q^{5} +(1.75760 - 1.70612i) q^{6} +(3.79110 - 2.82237i) q^{7} +(-0.958452 - 2.66108i) q^{8} +(-0.771815 + 2.89902i) q^{9} +(-3.17168 + 1.15038i) q^{10} +(-2.38854 + 2.53170i) q^{11} +(2.68261 + 2.19171i) q^{12} +(4.46063 + 2.24021i) q^{13} +(4.58142 + 4.86692i) q^{14} +(2.60719 - 3.20577i) q^{15} +(3.58253 - 1.77918i) q^{16} +(-0.831376 + 2.28419i) q^{17} +(-4.19814 - 0.612868i) q^{18} +(2.09262 + 5.74942i) q^{19} +(-2.13184 - 4.26863i) q^{20} +(-7.87744 - 2.22723i) q^{21} +(-3.94502 - 2.94382i) q^{22} +(0.667898 - 0.897143i) q^{23} +(-2.64277 + 4.12502i) q^{24} +(-0.617928 + 0.310335i) q^{25} +(-2.42179 + 6.63072i) q^{26} +(4.79583 - 2.00001i) q^{27} +(-6.09224 + 7.22754i) q^{28} +(-1.22730 + 1.86602i) q^{29} +(4.92753 + 3.14139i) q^{30} +(-4.14797 + 1.78926i) q^{31} +(3.08200 + 4.74355i) q^{32} +(5.99786 + 0.607914i) q^{33} +(-3.34409 - 0.796518i) q^{34} +(8.63755 + 7.24776i) q^{35} +(0.178324 - 5.99735i) q^{36} +(6.45572 - 5.41699i) q^{37} +(-7.73671 + 3.87469i) q^{38} +(-1.63177 - 8.49026i) q^{39} +(5.65006 - 3.68899i) q^{40} +(-2.53023 + 0.147369i) q^{41} +(1.84795 - 11.4287i) q^{42} +(-6.72342 + 2.01286i) q^{43} +(3.49409 - 6.02079i) q^{44} +(-7.15434 - 0.196703i) q^{45} +(1.36894 + 0.792403i) q^{46} +(3.79068 - 8.78778i) q^{47} +(-6.22470 - 3.04189i) q^{48} +(4.39904 - 14.6938i) q^{49} +(-0.536450 - 0.817624i) q^{50} +(4.01436 - 1.26926i) q^{51} +(-9.70886 - 2.32400i) q^{52} +(6.41965 - 3.70639i) q^{53} +(3.58952 + 6.41212i) q^{54} +(-7.19115 - 4.15181i) q^{55} +(-11.1441 - 7.38333i) q^{56} +(5.68682 - 8.94231i) q^{57} +(-2.82102 - 1.42073i) q^{58} +(3.29729 + 3.49492i) q^{59} +(-3.61187 + 7.43318i) q^{60} +(-5.83779 + 0.682339i) q^{61} +(-3.18811 - 5.53626i) q^{62} +(5.25607 + 13.1688i) q^{63} +(-6.16274 + 5.10104i) q^{64} +(-2.74624 + 11.5873i) q^{65} +(0.121285 + 8.52485i) q^{66} +(-4.36661 - 6.63910i) q^{67} +(0.575197 - 4.82742i) q^{68} +(-1.93700 + 0.0297259i) q^{69} +(-8.77737 + 13.3129i) q^{70} +(-0.225531 - 1.27905i) q^{71} +(8.45428 - 0.724703i) q^{72} +(0.400223 - 2.26978i) q^{73} +(8.65973 + 8.18837i) q^{74} +(1.07841 + 0.521030i) q^{75} +(-6.70135 - 10.2387i) q^{76} +(-1.90979 + 16.3393i) q^{77} +(11.6621 - 3.67296i) q^{78} +(-1.86572 - 0.108666i) q^{79} +(6.10117 + 7.33753i) q^{80} +(-7.80860 - 4.47501i) q^{81} +(-0.618466 - 3.53059i) q^{82} +(0.794679 - 13.6441i) q^{83} +(16.3559 + 0.737663i) q^{84} +(-5.75986 - 0.673231i) q^{85} +(-3.92102 - 9.11797i) q^{86} +(3.85801 - 0.284164i) q^{87} +(9.02638 + 3.92959i) q^{88} +(-2.15064 - 0.379215i) q^{89} +(-0.887021 - 10.0826i) q^{90} +(23.2334 - 4.09667i) q^{91} +(-0.890593 + 2.05199i) q^{92} +(6.83536 + 3.80776i) q^{93} +(12.9618 + 3.89631i) q^{94} +(-12.1953 + 8.02095i) q^{95} +(3.26117 - 9.23931i) q^{96} +(-7.20752 - 1.70821i) q^{97} +(21.3577 + 3.79058i) q^{98} +(-5.49594 - 8.87842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

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